LMFDB - Embedded newform 37.10.h.a.3.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,10,Mod(3,37)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([13]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("37.3");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	37.h (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.0563259381$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$28$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.8
Character	$\chi$	$=$	37.3
Dual form			37.10.h.a.25.8

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15.3360 + 18.2767i) q^{2} +(-37.8456 + 31.7562i) q^{3} +(-9.93794 - 56.3609i) q^{4} +(-278.257 + 764.505i) q^{5} -1178.71i q^{6} +(-396.292 - 144.238i) q^{7} +(-9396.50 - 5425.07i) q^{8} +(-2994.09 + 16980.3i) q^{9} +O(q^{10})$	\(q+(-15.3360 + 18.2767i) q^{2} +(-37.8456 + 31.7562i) q^{3} +(-9.93794 - 56.3609i) q^{4} +(-278.257 + 764.505i) q^{5} -1178.71i q^{6} +(-396.292 - 144.238i) q^{7} +(-9396.50 - 5425.07i) q^{8} +(-2994.09 + 16980.3i) q^{9} +(-9705.29 - 16810.1i) q^{10} +(-5987.20 + 10370.1i) q^{11} +(2165.92 + 1817.42i) q^{12} +(-116710. + 20579.1i) q^{13} +(8713.72 - 5030.87i) q^{14} +(-13747.0 - 37769.6i) q^{15} +(270792. - 98560.2i) q^{16} +(-446767. - 78777.1i) q^{17} +(-264427. - 315132. i) q^{18} +(199704. + 237998. i) q^{19} +(45853.5 + 8085.21i) q^{20} +(19578.4 - 7125.94i) q^{21} +(-97712.4 - 268463. i) q^{22} +(2.14085e6 - 1.23602e6i) q^{23} +(527896. - 93082.3i) q^{24} +(989139. + 829986. i) q^{25} +(1.41374e6 - 2.44867e6i) q^{26} +(-912126. - 1.57985e6i) q^{27} +(-4191.08 + 23768.8i) q^{28} +(3.50604e6 + 2.02421e6i) q^{29} +(901127. + 327983. i) q^{30} -8.37204e6i q^{31} +(-451487. + 1.24045e6i) q^{32} +(-102727. - 582595. i) q^{33} +(8.29140e6 - 6.95731e6i) q^{34} +(220542. - 262832. i) q^{35} +986779. q^{36} +(-2.61183e6 + 1.10968e7i) q^{37} -7.41248e6 q^{38} +(3.76344e6 - 4.48509e6i) q^{39} +(6.76214e6 - 5.67411e6i) q^{40} +(-4.82767e6 - 2.73791e7i) q^{41} +(-170015. + 467112. i) q^{42} +2.19112e7i q^{43} +(643971. + 234386. i) q^{44} +(-1.21484e7 - 7.01389e6i) q^{45} +(-1.02416e7 + 5.80833e7i) q^{46} +(-2.57430e6 - 4.45881e6i) q^{47} +(-7.11838e6 + 1.23294e7i) q^{48} +(-3.07764e7 - 2.58245e7i) q^{49} +(-3.03388e7 + 5.34956e6i) q^{50} +(1.94098e7 - 1.12063e7i) q^{51} +(2.31971e6 + 6.37335e6i) q^{52} +(-5.22413e7 + 1.90143e7i) q^{53} +(4.28628e7 + 7.55787e6i) q^{54} +(-6.26205e6 - 7.46282e6i) q^{55} +(2.94125e6 + 3.50525e6i) q^{56} +(-1.51158e7 - 2.66533e6i) q^{57} +(-9.07645e7 + 3.30356e7i) q^{58} +(2.92315e7 + 8.03129e7i) q^{59} +(-1.99211e6 + 1.15014e6i) q^{60} +(9.98218e7 - 1.76013e7i) q^{61} +(1.53013e8 + 1.28393e8i) q^{62} +(3.63574e6 - 6.29729e6i) q^{63} +(5.80243e7 + 1.00501e8i) q^{64} +(1.67425e7 - 9.49515e7i) q^{65} +(1.22234e7 + 7.05715e6i) q^{66} +(-2.12111e8 - 7.72020e7i) q^{67} +2.59631e7i q^{68} +(-4.17704e7 + 1.14763e8i) q^{69} +(1.42147e6 + 8.06157e6i) q^{70} +(1.73438e8 - 1.45532e8i) q^{71} +(1.20253e8 - 1.43312e8i) q^{72} -2.96839e8 q^{73} +(-1.62759e8 - 2.17917e8i) q^{74} -6.37918e7 q^{75} +(1.14291e7 - 1.36207e7i) q^{76} +(3.86845e6 - 3.24602e6i) q^{77} +(2.42567e7 + 1.37566e8i) q^{78} +(-6.18158e7 + 1.69837e8i) q^{79} +2.34447e8i q^{80} +(-2.34222e8 - 8.52499e7i) q^{81} +(5.74436e8 + 3.31651e8i) q^{82} +(8.61409e7 - 4.88530e8i) q^{83} +(-596193. - 1.03264e6i) q^{84} +(1.84542e8 - 3.19636e8i) q^{85} +(-4.00465e8 - 3.36030e8i) q^{86} +(-1.96970e8 + 3.47310e7i) q^{87} +(1.12518e8 - 6.49620e7i) q^{88} +(-2.05828e8 - 5.65508e8i) q^{89} +(3.14498e8 - 1.14468e8i) q^{90} +(4.92194e7 + 8.67871e6i) q^{91} +(-9.09388e7 - 1.08377e8i) q^{92} +(2.65865e8 + 3.16845e8i) q^{93} +(1.20972e8 + 2.13306e7i) q^{94} +(-2.37520e8 + 8.64501e7i) q^{95} +(-2.23052e7 - 6.12831e7i) q^{96} +(5.56906e8 - 3.21530e8i) q^{97} +(9.43973e8 - 1.66448e8i) q^{98} +(-1.58162e8 - 1.32714e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 45 q^{2} + 216 q^{3} + 249 q^{4} + 177 q^{5} - 5820 q^{7} - 74520 q^{8} - 30198 q^{9}+O(q^{10}) $ 168 * q + 45 * q^2 + 216 * q^3 + 249 * q^4 + 177 * q^5 - 5820 * q^7 - 74520 * q^8 - 30198 * q^9	\( 168 q + 45 q^{2} + 216 q^{3} + 249 q^{4} + 177 q^{5} - 5820 q^{7} - 74520 q^{8} - 30198 q^{9} - 60003 q^{10} + 175689 q^{11} - 307257 q^{12} - 713598 q^{13} + 290583 q^{14} - 385260 q^{15} + 292473 q^{16} + 951645 q^{17} - 2634174 q^{18} + 87108 q^{19} - 6701172 q^{20} + 1892136 q^{21} - 1410435 q^{22} - 9 q^{23} + 6919605 q^{24} - 1830519 q^{25} - 12361155 q^{26} + 12227553 q^{27} - 14971305 q^{28} - 8346069 q^{29} + 32076480 q^{30} + 25901316 q^{32} + 29661003 q^{33} + 17761257 q^{34} - 25104648 q^{35} - 302330892 q^{36} - 89711496 q^{37} + 137852370 q^{38} + 3073230 q^{39} + 72127485 q^{40} + 40690731 q^{41} + 229015377 q^{42} + 187195086 q^{44} - 293199021 q^{45} - 286926930 q^{46} - 134086527 q^{47} + 86156133 q^{48} + 67568640 q^{49} + 134153859 q^{50} - 528106959 q^{51} + 402280539 q^{52} + 147470676 q^{53} + 422122437 q^{54} - 55011861 q^{55} - 616228263 q^{56} - 449072832 q^{57} + 529606191 q^{58} + 773443290 q^{59} + 1433547972 q^{60} + 469275144 q^{61} - 914552304 q^{62} - 673379979 q^{63} + 1146585192 q^{64} - 243884745 q^{65} + 1805055381 q^{66} + 214516206 q^{67} + 722409993 q^{69} - 2605801512 q^{70} - 1455384636 q^{71} - 4689293691 q^{72} + 930909090 q^{73} - 1261741251 q^{74} + 3013150476 q^{75} + 195486513 q^{76} + 1827454371 q^{77} + 1710012453 q^{78} + 1230271476 q^{79} + 2262925611 q^{81} - 3346032141 q^{82} - 2122951164 q^{83} - 6124511730 q^{84} - 39169146 q^{85} - 2603533938 q^{86} + 1185003879 q^{87} - 261497646 q^{88} + 1603969074 q^{89} + 7288796094 q^{90} - 4883515182 q^{91} - 7533267018 q^{92} + 1209552852 q^{93} + 1712695200 q^{94} + 2036912394 q^{95} + 7661250639 q^{96} - 7583351877 q^{97} - 10074558573 q^{98} - 7520510685 q^{99}+O(q^{100}) \) 168 * q + 45 * q^2 + 216 * q^3 + 249 * q^4 + 177 * q^5 - 5820 * q^7 - 74520 * q^8 - 30198 * q^9 - 60003 * q^10 + 175689 * q^11 - 307257 * q^12 - 713598 * q^13 + 290583 * q^14 - 385260 * q^15 + 292473 * q^16 + 951645 * q^17 - 2634174 * q^18 + 87108 * q^19 - 6701172 * q^20 + 1892136 * q^21 - 1410435 * q^22 - 9 * q^23 + 6919605 * q^24 - 1830519 * q^25 - 12361155 * q^26 + 12227553 * q^27 - 14971305 * q^28 - 8346069 * q^29 + 32076480 * q^30 + 25901316 * q^32 + 29661003 * q^33 + 17761257 * q^34 - 25104648 * q^35 - 302330892 * q^36 - 89711496 * q^37 + 137852370 * q^38 + 3073230 * q^39 + 72127485 * q^40 + 40690731 * q^41 + 229015377 * q^42 + 187195086 * q^44 - 293199021 * q^45 - 286926930 * q^46 - 134086527 * q^47 + 86156133 * q^48 + 67568640 * q^49 + 134153859 * q^50 - 528106959 * q^51 + 402280539 * q^52 + 147470676 * q^53 + 422122437 * q^54 - 55011861 * q^55 - 616228263 * q^56 - 449072832 * q^57 + 529606191 * q^58 + 773443290 * q^59 + 1433547972 * q^60 + 469275144 * q^61 - 914552304 * q^62 - 673379979 * q^63 + 1146585192 * q^64 - 243884745 * q^65 + 1805055381 * q^66 + 214516206 * q^67 + 722409993 * q^69 - 2605801512 * q^70 - 1455384636 * q^71 - 4689293691 * q^72 + 930909090 * q^73 - 1261741251 * q^74 + 3013150476 * q^75 + 195486513 * q^76 + 1827454371 * q^77 + 1710012453 * q^78 + 1230271476 * q^79 + 2262925611 * q^81 - 3346032141 * q^82 - 2122951164 * q^83 - 6124511730 * q^84 - 39169146 * q^85 - 2603533938 * q^86 + 1185003879 * q^87 - 261497646 * q^88 + 1603969074 * q^89 + 7288796094 * q^90 - 4883515182 * q^91 - 7533267018 * q^92 + 1209552852 * q^93 + 1712695200 * q^94 + 2036912394 * q^95 + 7661250639 * q^96 - 7583351877 * q^97 - 10074558573 * q^98 - 7520510685 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−15.3360	+	18.2767i	−0.677761	+	0.807724i	−0.989818	−	0.142339i	$-0.954538\pi$
$2$	−15.3360	+	18.2767i	−0.677761	+	0.807724i	0.312057	+	0.950063i	$0.398982\pi$
$3$	−37.8456	+	31.7562i	−0.269755	+	0.226352i	−0.767623	−	0.640901i	$-0.778561\pi$
$3$	−37.8456	+	31.7562i	−0.269755	+	0.226352i	0.497868	+	0.867253i	$0.334116\pi$
$4$	−9.93794	−	56.3609i	−0.0194100	−	0.110080i
$5$	−278.257	+	764.505i	−0.199105	+	0.547036i	−0.998557	−	0.0536934i	$-0.982901\pi$
$5$	−278.257	+	764.505i	−0.199105	+	0.547036i	0.799453	+	0.600729i	$0.205123\pi$
$6$		−	1178.71i		−	0.371300i
$7$	−396.292	−	144.238i	−0.0623841	−	0.0227060i	0.310640	−	0.950528i	$-0.399457\pi$
$7$	−396.292	−	144.238i	−0.0623841	−	0.0227060i	−0.373024	+	0.927822i	$0.621679\pi$
$8$	−9396.50	−	5425.07i	−0.811075	−	0.468275i
$9$	−2994.09	+	16980.3i	−0.152115	+	0.862689i
$10$	−9705.29	−	16810.1i	−0.306908	−	0.531581i
$11$	−5987.20	+	10370.1i	−0.123298	+	0.213559i	−0.921066	−	0.389405i	$-0.872681\pi$
$11$	−5987.20	+	10370.1i	−0.123298	+	0.213559i	0.797768	+	0.602964i	$0.206014\pi$
$12$	2165.92	+	1817.42i	0.0301527	+	0.0253011i
$13$	−116710.	+	20579.1i	−1.13334	+	0.199839i	−0.708693	−	0.705517i	$-0.750715\pi$
$13$	−116710.	+	20579.1i	−1.13334	+	0.199839i	−0.424652	+	0.905357i	$0.639604\pi$
$14$	8713.72	−	5030.87i	0.0606216	−	0.0349999i
$15$	−13747.0	−	37769.6i	−0.0701128	−	0.192633i
$16$	270792.	−	98560.2i	1.03299	−	0.375977i
$17$	−446767.	−	78777.1i	−1.29736	−	0.228760i	−0.518025	−	0.855365i	$-0.673333\pi$
$17$	−446767.	−	78777.1i	−1.29736	−	0.228760i	−0.779337	+	0.626606i	$0.784444\pi$
$18$	−264427.	−	315132.i	−0.593717	−	0.707564i
$19$	199704.	+	237998.i	0.351557	+	0.418969i	0.912623	−	0.408802i	$-0.134053\pi$
$19$	199704.	+	237998.i	0.351557	+	0.418969i	−0.561066	+	0.827771i	$0.689609\pi$
$20$	45853.5	+	8085.21i	0.0640822	+	0.0112994i
$21$	19578.4	−	7125.94i	0.0219680	−	0.00799568i
$22$	−97712.4	−	268463.i	−0.0889299	−	0.244333i
$23$	2.14085e6	−	1.23602e6i	1.59518	−	0.920980i	0.602788	−	0.797902i	$-0.294057\pi$
$23$	2.14085e6	−	1.23602e6i	1.59518	−	0.920980i	0.992397	−	0.123078i	$-0.0392767\pi$
$24$	527896.	−	93082.3i	0.324786	−	0.0572686i
$25$	989139.	+	829986.i	0.506439	+	0.424953i
$26$	1.41374e6	−	2.44867e6i	0.606722	−	1.05087i
$27$	−912126.	−	1.57985e6i	−0.330307	−	0.572109i
$28$	−4191.08	+	23768.8i	−0.00128859	+	0.00730795i
$29$	3.50604e6	+	2.02421e6i	0.920504	+	0.531453i	0.883796	−	0.467873i	$-0.154979\pi$
$29$	3.50604e6	+	2.02421e6i	0.920504	+	0.531453i	0.0367083	+	0.999326i	$0.488313\pi$
$30$	901127.	+	327983.i	0.203114	+	0.0739275i
$31$		−	8.37204e6i		−	1.62819i	−0.580735	−	0.814093i	$-0.697235\pi$
$31$		−	8.37204e6i		−	1.62819i	0.580735	−	0.814093i	$-0.302765\pi$
$32$	−451487.	+	1.24045e6i	−0.0761149	+	0.209124i
$33$	−102727.	−	582595.i	−0.0150790	−	0.0855174i
$34$	8.29140e6	−	6.95731e6i	1.06408	−	0.892866i
$35$	220542.	−	262832.i	0.0248419	−	0.0296055i
$36$	986779.			0.0979172
$37$	−2.61183e6	+	1.10968e7i	−0.229106	+	0.973401i
$37$	−2.61183e6	+	1.10968e7i	−0.229106	+	0.973401i
$38$	−7.41248e6			−0.576683
$39$	3.76344e6	−	4.48509e6i	0.260492	−	0.310442i
$40$	6.76214e6	−	5.67411e6i	0.417652	−	0.350451i
$41$	−4.82767e6	−	2.73791e7i	−0.266815	−	1.51318i	−0.763817	−	0.645433i	$-0.776677\pi$
$41$	−4.82767e6	−	2.73791e7i	−0.266815	−	1.51318i	0.497002	−	0.867750i	$-0.334434\pi$
$42$	−170015.	+	467112.i	−0.00843072	+	0.0231632i
$43$			2.19112e7i			0.977369i	0.872461	+	0.488685i	$0.162523\pi$
$43$			2.19112e7i			0.977369i	−0.872461	+	0.488685i	$0.837477\pi$
$44$	643971.	+	234386.i	0.0259017	+	0.00942746i
$45$	−1.21484e7	−	7.01389e6i	−0.441635	−	0.254978i
$46$	−1.02416e7	+	5.80833e7i	−0.337256	+	1.91267i
$47$	−2.57430e6	−	4.45881e6i	−0.0769517	−	0.133284i	0.824982	−	0.565160i	$-0.191185\pi$
$47$	−2.57430e6	−	4.45881e6i	−0.0769517	−	0.133284i	−0.901933	+	0.431875i	$0.857852\pi$
$48$	−7.11838e6	+	1.23294e7i	−0.193551	+	0.335240i
$49$	−3.07764e7	−	2.58245e7i	−0.762668	−	0.639955i
$50$	−3.03388e7	+	5.34956e6i	−0.686489	+	0.121047i
$51$	1.94098e7	−	1.12063e7i	0.401750	−	0.231951i
$52$	2.31971e6	+	6.37335e6i	0.0439965	+	0.120879i
$53$	−5.22413e7	+	1.90143e7i	−0.909436	+	0.331008i	−0.754028	−	0.656842i	$-0.771892\pi$
$53$	−5.22413e7	+	1.90143e7i	−0.909436	+	0.331008i	−0.155409	+	0.987850i	$0.549669\pi$
$54$	4.28628e7	+	7.55787e6i	0.685975	+	0.120956i
$55$	−6.26205e6	−	7.46282e6i	−0.0922750	−	0.109969i
$56$	2.94125e6	+	3.50525e6i	0.0399656	+	0.0476291i
$57$	−1.51158e7	−	2.66533e6i	−0.189669	−	0.0334437i
$58$	−9.07645e7	+	3.30356e7i	−1.05315	+	0.383315i
$59$	2.92315e7	+	8.03129e7i	0.314063	+	0.862881i	0.991826	+	0.127600i	$0.0407275\pi$
$59$	2.92315e7	+	8.03129e7i	0.314063	+	0.862881i	−0.677763	+	0.735281i	$0.737050\pi$
$60$	−1.99211e6	+	1.15014e6i	−0.0198441	+	0.0114570i
$61$	9.98218e7	−	1.76013e7i	0.923084	−	0.162765i	0.308145	−	0.951339i	$-0.400292\pi$
$61$	9.98218e7	−	1.76013e7i	0.923084	−	0.162765i	0.614939	+	0.788575i	$0.289181\pi$
$62$	1.53013e8	+	1.28393e8i	1.31512	+	1.10352i
$63$	3.63574e6	−	6.29729e6i	0.0290777	−	0.0503641i
$64$	5.80243e7	+	1.00501e8i	0.432315	+	0.748792i
$65$	1.67425e7	−	9.49515e7i	0.116335	−	0.659769i
$66$	1.22234e7	+	7.05715e6i	0.0792944	+	0.0457806i
$67$	−2.12111e8	−	7.72020e7i	−1.28596	−	0.468050i	−0.393558	−	0.919300i	$-0.628756\pi$
$67$	−2.12111e8	−	7.72020e7i	−1.28596	−	0.468050i	−0.892398	+	0.451250i	$0.850978\pi$
$68$			2.59631e7i			0.147254i
$69$	−4.17704e7	+	1.14763e8i	−0.221844	+	0.609512i
$70$	1.42147e6	+	8.06157e6i	0.00707615	+	0.0401308i
$71$	1.73438e8	−	1.45532e8i	0.809992	−	0.679664i	−0.140614	−	0.990065i	$-0.544908\pi$
$71$	1.73438e8	−	1.45532e8i	0.809992	−	0.679664i	0.950606	+	0.310400i	$0.100463\pi$
$72$	1.20253e8	−	1.43312e8i	0.527352	−	0.628474i
$73$	−2.96839e8			−1.22340			−0.611699	−	0.791091i	$-0.709513\pi$
$73$	−2.96839e8			−1.22340			−0.611699	+	0.791091i	$0.709513\pi$
$74$	−1.62759e8	−	2.17917e8i	−0.630960	−	0.844788i
$75$	−6.37918e7			−0.232803
$76$	1.14291e7	−	1.36207e7i	0.0392963	−	0.0468315i
$77$	3.86845e6	−	3.24602e6i	0.0125409	−	0.0105231i
$78$	2.42567e7	+	1.37566e8i	0.0742003	+	0.420811i
$79$	−6.18158e7	+	1.69837e8i	−0.178557	+	0.490582i	−0.996392	−	0.0848713i	$-0.972952\pi$
$79$	−6.18158e7	+	1.69837e8i	−0.178557	+	0.490582i	0.817835	+	0.575453i	$0.195174\pi$
$80$			2.34447e8i			0.639940i
$81$	−2.34222e8	−	8.52499e7i	−0.604568	−	0.220045i
$82$	5.74436e8	+	3.31651e8i	1.40307	+	0.810063i
$83$	8.61409e7	−	4.88530e8i	0.199232	−	1.12990i	−0.707031	−	0.707183i	$-0.749966\pi$
$83$	8.61409e7	−	4.88530e8i	0.199232	−	1.12990i	0.906262	−	0.422716i	$-0.138923\pi$
$84$	−596193.	−	1.03264e6i	−0.00130656	−	0.00226303i
$85$	1.84542e8	−	3.19636e8i	0.383450	−	0.664156i
$86$	−4.00465e8	−	3.36030e8i	−0.789445	−	0.662423i
$87$	−1.96970e8	+	3.47310e7i	−0.368606	+	0.0649952i
$88$	1.12518e8	−	6.49620e7i	0.200008	−	0.115475i
$89$	−2.05828e8	−	5.65508e8i	−0.347736	−	0.955396i	−0.983082	−	0.183168i	$-0.941365\pi$
$89$	−2.05828e8	−	5.65508e8i	−0.347736	−	0.955396i	0.635346	−	0.772228i	$-0.280858\pi$
$90$	3.14498e8	−	1.14468e8i	0.505274	−	0.183905i
$91$	4.92194e7	+	8.67871e6i	0.0752402	+	0.0132669i
$92$	−9.09388e7	−	1.08377e8i	−0.132344	−	0.157721i
$93$	2.65865e8	+	3.16845e8i	0.368542	+	0.439212i
$94$	1.20972e8	+	2.13306e7i	0.159812	+	0.0281791i
$95$	−2.37520e8	+	8.64501e7i	−0.299188	+	0.108895i
$96$	−2.23052e7	−	6.12831e7i	−0.0268031	−	0.0736410i
$97$	5.56906e8	−	3.21530e8i	0.638718	−	0.368764i	−0.145402	−	0.989373i	$-0.546448\pi$
$97$	5.56906e8	−	3.21530e8i	0.638718	−	0.368764i	0.784121	+	0.620608i	$0.213114\pi$
$98$	9.43973e8	−	1.66448e8i	1.03381	−	0.182289i
$99$	−1.58162e8	−	1.32714e8i	−0.165479	−	0.138854i
$100$	3.69487e7	−	6.39971e7i	0.0369487	−	0.0639971i
$101$	−5.76051e7	−	9.97750e7i	−0.0550826	−	0.0954059i	0.837169	−	0.546944i	$-0.184209\pi$
$101$	−5.76051e7	−	9.97750e7i	−0.0550826	−	0.0954059i	−0.892252	+	0.451538i	$0.850876\pi$
$102$	−9.28550e7	+	5.26607e8i	−0.0849385	+	0.481710i
$103$	6.43185e8	+	3.71343e8i	0.563078	+	0.325093i	0.754380	−	0.656438i	$-0.227938\pi$
$103$	6.43185e8	+	3.71343e8i	0.563078	+	0.325093i	−0.191302	+	0.981531i	$0.561271\pi$
$104$	1.20831e9	+	4.39787e8i	1.01281	+	0.368632i
$105$			1.69506e7i			0.0136092i
$106$	4.53653e8	−	1.24640e9i	0.349018	−	0.958918i
$107$	−1.44387e8	−	8.18858e8i	−0.106488	−	0.603923i	−0.990616	−	0.136678i	$-0.956358\pi$
$107$	−1.44387e8	−	8.18858e8i	−0.106488	−	0.603923i	0.884128	−	0.467245i	$-0.154754\pi$
$108$	−7.99770e7	+	6.71087e7i	−0.0565664	+	0.0474648i
$109$	−1.36864e9	+	1.63108e9i	−0.928686	+	1.10676i	0.0653663	+	0.997861i	$0.479178\pi$
$109$	−1.36864e9	+	1.63108e9i	−0.928686	+	1.10676i	−0.994052	+	0.108904i	$0.965266\pi$
$110$	2.32430e8			0.151365
$111$	−2.53548e8	−	5.02909e8i	−0.158528	−	0.314439i
$112$	−1.21529e8			−0.0729790
$113$	−1.28357e9	+	1.52970e9i	−0.740572	+	0.882579i	−0.996455	−	0.0841285i	$-0.973189\pi$
$113$	−1.28357e9	+	1.52970e9i	−0.740572	+	0.882579i	0.255883	+	0.966708i	$0.417634\pi$
$114$	2.80530e8	−	2.35392e8i	0.155563	−	0.130533i
$115$	3.49237e8	+	1.98062e9i	0.186200	+	1.05599i
$116$	7.92435e7	−	2.17720e8i	0.0406353	−	0.111644i
$117$		−	2.04338e9i		−	1.00812i
$118$	−1.91615e9	−	6.97421e8i	−0.909830	−	0.331151i
$119$	1.65687e8	+	9.56597e7i	0.0757405	+	0.0437288i
$120$	−7.57290e7	+	4.29480e8i	−0.0333385	+	0.189072i
$121$	1.10728e9	+	1.91787e9i	0.469595	+	0.813363i
$122$	−1.20917e9	+	2.09435e9i	−0.494161	+	0.855912i
$123$	1.05216e9	+	8.82869e8i	0.414486	+	0.347795i
$124$	−4.71856e8	+	8.32009e7i	−0.179230	+	0.0316031i
$125$	−2.28588e9	+	1.31975e9i	−0.837449	+	0.483502i
$126$	5.93361e7	+	1.63025e8i	0.0209726	+	0.0576216i
$127$	−5.18397e9	+	1.88681e9i	−1.76826	+	0.643594i	−0.768265	+	0.640132i	$0.778880\pi$
$127$	−5.18397e9	+	1.88681e9i	−1.76826	+	0.643594i	−0.999994	+	0.00346130i	$0.998898\pi$
$128$	−3.39229e9	−	5.98152e8i	−1.11699	−	0.196955i
$129$	−6.95818e8	−	8.29244e8i	−0.221229	−	0.263650i
$130$	1.47864e9	+	1.76217e9i	0.454064	+	0.541132i
$131$	−5.90712e9	−	1.04158e9i	−1.75249	−	0.309011i	−0.796985	−	0.603999i	$-0.793573\pi$
$131$	−5.90712e9	−	1.04158e9i	−1.75249	−	0.309011i	−0.955501	+	0.294988i	$0.904684\pi$
$132$	−3.18147e7	+	1.15796e7i	−0.00912105	+	0.00331979i
$133$	−4.48126e7	−	1.23122e8i	−0.0124185	−	0.0341194i
$134$	4.66393e9	−	2.69272e9i	1.24963	−	0.721472i
$135$	1.46161e9	−	2.57721e8i	0.378730	−	0.0667802i
$136$	3.77068e9	+	3.16397e9i	0.945136	+	0.793063i
$137$	2.56668e9	−	4.44562e9i	0.622485	−	1.07818i	−0.366536	−	0.930404i	$-0.619456\pi$
$137$	2.56668e9	−	4.44562e9i	0.622485	−	1.07818i	0.989021	−	0.147772i	$-0.0472103\pi$
$138$	−1.45690e9	−	2.52343e9i	−0.341960	−	0.592292i
$139$	−7.34092e7	+	4.16324e8i	−0.0166795	+	0.0945943i	−0.992011	−	0.126151i	$-0.959738\pi$
$139$	−7.34092e7	+	4.16324e8i	−0.0166795	+	0.0945943i	0.975332	+	0.220745i	$0.0708488\pi$
$140$	−1.70052e7	−	9.81793e6i	−0.00374114	−	0.00215995i
$141$	2.39021e8	+	8.69965e7i	0.0509272	+	0.0185360i
$142$			5.40174e9i			1.11490i
$143$	4.85357e8	−	1.33351e9i	0.0970620	−	0.266676i
$144$	8.62807e8	+	4.89322e9i	0.167218	+	0.948340i
$145$	−2.52310e9	+	2.11713e9i	−0.474000	+	0.397734i
$146$	4.55231e9	−	5.42523e9i	0.829171	−	0.988167i
$147$	1.98484e9			0.350588
$148$	6.51384e8	+	3.69252e7i	0.111599	+	0.00632624i
$149$	3.05407e9			0.507623			0.253811	−	0.967254i	$-0.418316\pi$
$149$	3.05407e9			0.507623			0.253811	+	0.967254i	$0.418316\pi$
$150$	9.78310e8	−	1.16590e9i	0.157785	−	0.188041i
$151$	−2.07557e8	+	1.74161e8i	−0.0324893	+	0.0272618i	−0.658888	−	0.752241i	$-0.728973\pi$
$151$	−2.07557e8	+	1.74161e8i	−0.0324893	+	0.0272618i	0.626398	+	0.779503i	$0.284528\pi$
$152$	−5.85363e8	−	3.31976e9i	−0.0889465	−	0.504441i
$153$	2.67532e9	−	7.35038e9i	0.394697	−	1.08442i
$154$			1.20483e8i			0.0172617i
$155$	6.40047e9	+	2.32958e9i	0.890675	+	0.324179i
$156$	−2.90184e8	−	1.67538e8i	−0.0392295	−	0.0226492i
$157$	8.60109e8	−	4.87792e9i	0.112981	−	0.640746i	−0.874749	−	0.484576i	$-0.838974\pi$
$157$	8.60109e8	−	4.87792e9i	0.112981	−	0.640746i	0.987730	−	0.156170i	$-0.0499149\pi$
$158$	−2.15606e9	−	3.73441e9i	−0.275236	−	0.476722i
$159$	1.37328e9	−	2.37859e9i	0.170401	−	0.295143i
$160$	−8.22701e8	−	6.90328e8i	−0.0992435	−	0.0832752i
$161$	−1.02668e9	+	1.81032e8i	−0.120426	+	0.0212343i
$162$	5.15011e9	−	2.97342e9i	0.587488	−	0.339186i
$163$	−5.17180e8	−	1.42094e9i	−0.0573849	−	0.157664i	0.907688	−	0.419646i	$-0.137846\pi$
$163$	−5.17180e8	−	1.42094e9i	−0.0573849	−	0.157664i	−0.965073	+	0.261983i	$0.915624\pi$
$164$	−1.49513e9	+	5.44183e8i	−0.161392	+	0.0587419i
$165$	4.73982e8	+	8.35758e7i	0.0497833	+	0.00877815i
$166$	7.60766e9	+	9.06645e9i	0.777615	+	0.926725i
$167$	−6.80615e9	−	8.11125e9i	−0.677138	−	0.806982i	0.312598	−	0.949885i	$-0.398801\pi$
$167$	−6.80615e9	−	8.11125e9i	−0.677138	−	0.806982i	−0.989737	+	0.142903i	$0.954356\pi$
$168$	−2.22627e8	−	3.92551e7i	−0.0215618	−	0.00380194i
$169$	3.23269e9	−	1.17660e9i	0.304842	−	0.110953i
$170$	3.01176e9	+	8.27474e9i	0.276567	+	0.759861i
$171$	−4.63921e9	+	2.67845e9i	−0.414917	+	0.239553i
$172$	1.23494e9	−	2.17752e8i	0.107589	−	0.0189708i
$173$	−9.75671e9	−	8.18685e9i	−0.828125	−	0.694880i	0.126734	−	0.991937i	$-0.459550\pi$
$173$	−9.75671e9	−	8.18685e9i	−0.828125	−	0.694880i	−0.954860	+	0.297057i	$0.903995\pi$
$174$	2.38595e9	−	4.13259e9i	0.197329	−	0.341783i
$175$	−2.72272e8	−	4.71589e8i	−0.0219448	−	0.0380095i
$176$	−5.99203e8	+	3.39825e9i	−0.0470725	+	0.266961i
$177$	−3.65672e9	−	2.11121e9i	−0.280035	−	0.161678i
$178$	1.34922e10	+	4.91076e9i	1.00738	+	0.366656i
$179$		−	1.17612e10i		−	0.856272i	−0.903714	−	0.428136i	$-0.859170\pi$
$179$		−	1.17612e10i		−	0.856272i	0.903714	−	0.428136i	$-0.140830\pi$
$180$	−2.74578e8	+	7.54398e8i	−0.0194958	+	0.0535642i
$181$	1.18524e9	+	6.72183e9i	0.0820829	+	0.465515i	0.997948	+	0.0640291i	$0.0203950\pi$
$181$	1.18524e9	+	6.72183e9i	0.0820829	+	0.465515i	−0.915865	+	0.401486i	$0.868494\pi$
$182$	−9.13446e8	+	7.66472e8i	−0.0617109	+	0.0517816i
$183$	−3.21887e9	+	3.83610e9i	−0.212165	+	0.252848i
$184$	−2.68220e10			−1.72509
$185$	−7.75684e9	−	5.08454e9i	−0.486869	−	0.319138i
$186$	−9.86818e9			−0.604545
$187$	3.49182e9	−	4.16138e9i	0.208816	−	0.248857i
$188$	−2.25719e8	+	1.89401e8i	−0.0131783	+	0.0110579i
$189$	1.33593e8	+	7.57645e8i	0.00761564	+	0.0431904i
$190$	2.06257e9	−	5.66688e9i	0.114820	−	0.315466i
$191$			1.39931e10i			0.760791i	0.924824	+	0.380395i	$0.124212\pi$
$191$			1.39931e10i			0.760791i	−0.924824	+	0.380395i	$0.875788\pi$
$192$	−5.38750e9	−	1.96089e9i	−0.286109	−	0.104135i
$193$	2.84279e10	+	1.64129e10i	1.47481	+	0.851484i	0.999597	−	0.0283858i	$-0.00903669\pi$
$193$	2.84279e10	+	1.64129e10i	1.47481	+	0.851484i	0.475216	+	0.879869i	$0.342370\pi$
$194$	−2.66419e9	+	1.51094e10i	−0.135039	+	0.765842i
$195$	2.38167e9	+	4.12518e9i	0.117958	+	0.204309i
$196$	−1.14964e9	+	1.99123e9i	−0.0556427	+	0.0963759i
$197$	−1.49530e10	−	1.25471e10i	−0.707345	−	0.593533i	0.216508	−	0.976281i	$-0.430533\pi$
$197$	−1.49530e10	−	1.25471e10i	−0.707345	−	0.593533i	−0.923853	+	0.382748i	$0.874978\pi$
$198$	4.85114e9	−	8.55386e8i	0.224311	−	0.0395520i
$199$	−1.76584e10	+	1.01951e10i	−0.798200	+	0.460841i	−0.842841	−	0.538162i	$-0.819119\pi$
$199$	−1.76584e10	+	1.01951e10i	−0.798200	+	0.460841i	0.0446414	+	0.999003i	$0.485785\pi$
$200$	−4.79171e9	−	1.31651e10i	−0.211766	−	0.581822i
$201$	1.04791e10	−	3.81408e9i	0.452837	−	0.164819i
$202$	2.70699e9	+	4.77315e8i	0.114395	+	0.0201708i
$203$	−1.09745e9	−	1.30788e9i	−0.0453577	−	0.0540552i
$204$	−8.24489e8	−	9.82588e8i	−0.0333311	−	0.0397224i
$205$	2.22748e10	+	3.92765e9i	0.880889	+	0.155324i
$206$	−1.66508e10	+	6.06040e9i	−0.644218	+	0.234476i
$207$	1.45781e10	+	4.00530e10i	0.551867	+	1.51624i
$208$	−2.95758e10	+	1.70756e10i	−1.09560	+	0.632543i
$209$	−3.66374e9	+	6.46016e8i	−0.132821	+	0.0234199i
$210$	−3.09801e8	−	2.59954e8i	−0.0109925	−	0.00922381i
$211$	6.91182e9	−	1.19716e10i	0.240061	−	0.415797i	−0.720671	−	0.693278i	$-0.756166\pi$
$211$	6.91182e9	−	1.19716e10i	0.240061	−	0.415797i	0.960731	+	0.277480i	$0.0894993\pi$
$212$	1.59083e9	+	2.75540e9i	0.0540895	+	0.0936857i
$213$	−1.94232e9	+	1.10155e10i	−0.0646566	+	0.366686i
$214$	1.71803e10	+	9.91907e9i	0.559976	+	0.323302i
$215$	−1.67512e10	−	6.09696e9i	−0.534656	−	0.194599i
$216$			1.97934e10i			0.618698i
$217$	−1.20757e9	+	3.31777e9i	−0.0369695	+	0.101573i
$218$	−8.82135e9	−	5.00283e10i	−0.264533	−	1.50024i
$219$	1.12340e10	−	9.42648e9i	0.330018	−	0.276918i
$220$	−3.58379e8	+	4.27099e8i	−0.0103143	+	0.0122921i
$221$	5.37632e10			1.51607
$222$	1.30799e10	+	3.07858e9i	0.361424	+	0.0850672i
$223$	−6.13356e9			−0.166089			−0.0830445	−	0.996546i	$-0.526464\pi$
$223$	−6.13356e9			−0.166089			−0.0830445	+	0.996546i	$0.526464\pi$
$224$	3.57841e8	−	4.26458e8i	0.00949672	−	0.0113178i
$225$	−1.70550e10	+	1.43108e10i	−0.443639	+	0.372258i
$226$	−8.27308e9	−	4.69189e10i	−0.210950	−	1.19636i
$227$	−1.85109e10	+	5.08582e10i	−0.462712	+	1.27129i	0.460726	+	0.887542i	$0.347589\pi$
$227$	−1.85109e10	+	5.08582e10i	−0.462712	+	1.27129i	−0.923438	+	0.383748i	$0.874633\pi$
$228$			8.78430e8i			0.0215278i
$229$	4.70700e10	+	1.71321e10i	1.13106	+	0.411671i	0.838676	−	0.544630i	$-0.183330\pi$
$229$	4.70700e10	+	1.71321e10i	1.13106	+	0.411671i	0.292382	+	0.956302i	$0.405552\pi$
$230$	−4.15552e10	−	2.39919e10i	−0.979151	−	0.565313i
$231$	−4.33227e7	+	2.45695e8i	−0.00100106	+	0.00567731i
$232$	−2.19630e10	−	3.80410e10i	−0.497732	−	0.862097i
$233$	−5.16070e9	+	8.93860e9i	−0.114712	+	0.198686i	−0.917664	−	0.397356i	$-0.869928\pi$
$233$	−5.16070e9	+	8.93860e9i	−0.114712	+	0.198686i	0.802953	+	0.596043i	$0.203261\pi$
$234$	3.73463e10	+	3.13373e10i	0.814285	+	0.683266i
$235$	4.12510e9	−	7.27367e8i	0.0882327	−	0.0155578i
$236$	4.23600e9	−	2.44566e9i	0.0888898	−	0.0513206i
$237$	−3.05394e9	−	8.39064e9i	−0.0628772	−	0.172754i
$238$	−4.28932e9	+	1.56119e9i	−0.0866548	+	0.0315398i
$239$	2.10939e10	+	3.71943e9i	0.418183	+	0.0737370i	0.378781	−	0.925486i	$-0.376343\pi$
$239$	2.10939e10	+	3.71943e9i	0.418183	+	0.0737370i	0.0394024	+	0.999223i	$0.487455\pi$
$240$	−7.44515e9	−	8.87278e9i	−0.144851	−	0.172627i
$241$	−3.00344e10	−	3.57936e10i	−0.573512	−	0.683485i	0.398836	−	0.917022i	$-0.369414\pi$
$241$	−3.00344e10	−	3.57936e10i	−0.573512	−	0.683485i	−0.972348	+	0.233538i	$0.924970\pi$
$242$	−5.20335e10	−	9.17491e9i	−0.975246	−	0.171962i
$243$	4.53128e10	−	1.64925e10i	0.833667	−	0.303430i
$244$	−1.98405e9	−	5.45112e9i	−0.0358342	−	0.0984536i
$245$	2.83067e10	−	1.63429e10i	0.501929	−	0.289789i
$246$	−3.22719e10	+	5.69040e9i	−0.561845	+	0.0990684i
$247$	−2.82052e10	−	2.36670e10i	−0.482162	−	0.404582i
$248$	−4.54189e10	+	7.86679e10i	−0.762438	+	1.32058i
$249$	1.22538e10	+	2.12242e10i	0.202010	+	0.349892i
$250$	1.09355e10	−	6.20181e10i	0.177055	−	1.00413i
$251$	3.24278e9	+	1.87222e9i	0.0515687	+	0.0297732i	0.525563	−	0.850755i	$-0.323855\pi$
$251$	3.24278e9	+	1.87222e9i	0.0515687	+	0.0297732i	−0.473994	+	0.880528i	$0.657188\pi$
$252$	−3.91053e8	−	1.42331e8i	−0.00610847	−	0.00222330i
$253$			2.96012e10i			0.454221i
$254$	4.50166e10	−	1.23682e11i	0.678611	−	1.86447i
$255$	3.16633e9	+	1.79572e10i	0.0468949	+	0.265954i
$256$	1.74404e10	−	1.46342e10i	0.253791	−	0.212956i
$257$	7.88846e9	−	9.40110e9i	0.112796	−	0.134425i	−0.706692	−	0.707521i	$-0.749813\pi$
$257$	7.88846e9	−	9.40110e9i	0.112796	−	0.134425i	0.819488	+	0.573096i	$0.194258\pi$
$258$	2.58269e10			0.362897
$259$	2.63564e9	−	4.02086e9i	0.0363946	−	0.0555227i
$260$	−5.51793e9			−0.0748853
$261$	−4.48691e10	+	5.34729e10i	−0.598502	+	0.713266i
$262$	1.09628e11	−	9.19889e10i	1.43736	−	1.20609i
$263$	−2.56480e9	−	1.45457e10i	−0.0330562	−	0.187471i	0.963809	−	0.266595i	$-0.0858987\pi$
$263$	−2.56480e9	−	1.45457e10i	−0.0330562	−	0.187471i	−0.996865	+	0.0791243i	$0.974788\pi$
$264$	−2.19535e9	+	6.03166e9i	−0.0278154	+	0.0764222i
$265$		−	4.52296e10i		−	0.563399i
$266$	2.93750e9	+	1.06916e9i	0.0359758	+	0.0130941i
$267$	2.57481e10	+	1.48657e10i	0.310059	+	0.179013i
$268$	−2.24323e9	+	1.27220e10i	−0.0265624	+	0.150643i
$269$	−4.99614e10	−	8.65357e10i	−0.581767	−	1.00765i	−0.995270	−	0.0971477i	$-0.969028\pi$
$269$	−4.99614e10	−	8.65357e10i	−0.581767	−	1.00765i	0.413503	−	0.910503i	$-0.364305\pi$
$270$	−1.77049e10	+	3.06658e10i	−0.202748	+	0.351170i
$271$	9.10160e10	+	7.63715e10i	1.02508	+	0.860141i	0.990257	−	0.139253i	$-0.0444701\pi$
$271$	9.10160e10	+	7.63715e10i	1.02508	+	0.860141i	0.0348189	+	0.999394i	$0.488915\pi$
$272$	−1.28745e11	+	2.27012e10i	−1.42617	+	0.251472i
$273$	−2.13834e9	+	1.23457e9i	−0.0232994	+	0.0134519i
$274$	4.18887e10	+	1.15088e11i	0.448973	+	1.23354i
$275$	−1.45293e10	+	5.28822e9i	−0.153196	+	0.0557586i
$276$	6.88327e9	+	1.21371e9i	0.0714009	+	0.0125899i
$277$	−1.95981e10	−	2.33561e10i	−0.200012	−	0.238365i	0.656710	−	0.754143i	$-0.271947\pi$
$277$	−1.95981e10	−	2.33561e10i	−0.200012	−	0.238365i	−0.856722	+	0.515778i	$0.827503\pi$
$278$	−6.48323e9	−	7.72642e9i	−0.0651013	−	0.0775848i
$279$	1.42160e11	+	2.50666e10i	1.40462	+	0.247672i
$280$	−3.49821e9	+	1.27324e9i	−0.0340122	+	0.0123794i
$281$	−3.27830e10	−	9.00706e10i	−0.313668	−	0.861796i	−0.991908	−	0.126956i	$-0.959479\pi$
$281$	−3.27830e10	−	9.00706e10i	−0.313668	−	0.861796i	0.678240	−	0.734840i	$-0.262743\pi$
$282$	−5.25563e9	+	3.03434e9i	−0.0494884	+	0.0285722i
$283$	5.32125e10	−	9.38280e9i	0.493145	−	0.0869548i	0.0784554	−	0.996918i	$-0.475001\pi$
$283$	5.32125e10	−	9.38280e9i	0.493145	−	0.0869548i	0.414690	+	0.909963i	$0.363890\pi$
$284$	−9.92589e9	−	8.32881e9i	−0.0905393	−	0.0759715i
$285$	6.24375e9	−	1.08145e10i	0.0560588	−	0.0970967i
$286$	1.69287e10	+	2.93214e10i	0.149615	+	0.259142i
$287$	−2.03595e9	+	1.15464e10i	−0.0177132	+	0.100457i
$288$	−1.97114e10	−	1.13804e10i	−0.168831	−	0.0974745i
$289$	8.19589e10	+	2.98306e10i	0.691123	+	0.251548i
$290$		−	7.85823e10i		−	0.652430i
$291$	−1.08659e10	+	2.98537e10i	−0.0888273	+	0.244051i
$292$	2.94996e9	+	1.67301e10i	0.0237462	+	0.134671i
$293$	5.56752e9	−	4.67170e9i	0.0441324	−	0.0370315i	−0.620455	−	0.784242i	$-0.713052\pi$
$293$	5.56752e9	−	4.67170e9i	0.0441324	−	0.0370315i	0.664587	+	0.747211i	$0.268607\pi$
$294$	−3.04395e10	+	3.62763e10i	−0.237615	+	0.283179i
$295$	−6.95335e10			−0.534558
$296$	8.47433e10	−	9.01022e10i	0.641642	−	0.682217i
$297$	2.18443e10			0.162905
$298$	−4.68372e10	+	5.58184e10i	−0.344047	+	0.410019i
$299$	−2.24422e11	+	1.88312e11i	−1.62385	+	1.36257i
$300$	6.33959e8	+	3.59536e9i	0.00451872	+	0.0256269i
$301$	3.16044e9	−	8.68324e9i	0.0221921	−	0.0609723i
$302$		−	6.46438e9i		−	0.0447194i
$303$	5.34858e9	+	1.94672e9i	0.0364541	+	0.0132682i
$304$	7.75353e10	+	4.47650e10i	0.520677	+	0.300613i
$305$	−1.43199e10	+	8.12120e10i	−0.0947523	+	0.537367i
$306$	9.33120e10	+	1.61621e11i	0.608403	+	1.05378i
$307$	4.61729e10	−	7.99738e10i	0.296664	−	0.513837i	−0.678707	−	0.734409i	$-0.737459\pi$
$307$	4.61729e10	−	7.99738e10i	0.296664	−	0.513837i	0.975371	+	0.220573i	$0.0707926\pi$
$308$	−2.21393e8	−	1.85771e8i	−0.00140180	−	0.00117625i
$309$	−3.61342e10	+	6.37143e9i	−0.225478	+	0.0397579i
$310$	−1.40735e11	+	8.12532e10i	−0.865512	+	0.499704i
$311$	−4.12584e10	−	1.13356e11i	−0.250087	−	0.687107i	−0.999682	−	0.0252112i	$-0.991974\pi$
$311$	−4.12584e10	−	1.13356e11i	−0.250087	−	0.687107i	0.749596	−	0.661896i	$-0.230248\pi$
$312$	−5.96951e10	+	2.17272e10i	−0.356650	+	0.129810i
$313$	−1.59002e11	−	2.80364e10i	−0.936384	−	0.165110i	−0.315423	−	0.948951i	$-0.602146\pi$
$313$	−1.59002e11	−	2.80364e10i	−0.936384	−	0.165110i	−0.620961	+	0.783842i	$0.713257\pi$
$314$	7.59617e10	+	9.05276e10i	0.440972	+	0.525530i
$315$	3.80264e9	+	4.53181e9i	0.0217615	+	0.0259343i
$316$	1.01865e10	+	1.79616e9i	0.0574690	+	0.0101333i
$317$	−1.38956e11	+	5.05758e10i	−0.772877	+	0.281304i	−0.698199	−	0.715903i	$-0.746015\pi$
$317$	−1.38956e11	+	5.05758e10i	−0.772877	+	0.281304i	−0.0746779	+	0.997208i	$0.523793\pi$
$318$	2.24122e10	+	6.15771e10i	0.122903	+	0.337674i
$319$	−4.19827e10	+	2.42388e10i	−0.226993	+	0.131055i
$320$	−9.29793e10	+	1.63948e10i	−0.495691	+	0.0874038i
$321$	3.14682e10	+	2.64050e10i	0.165425	+	0.138808i
$322$	1.24365e10	−	2.15407e10i	0.0644685	−	0.111663i
$323$	−7.04724e10	−	1.22062e11i	−0.360253	−	0.623977i
$324$	−2.47707e9	+	1.40482e10i	−0.0124878	+	0.0708218i
$325$	−1.32523e11	−	7.65119e10i	−0.658892	−	0.380412i
$326$	3.39016e10	+	1.23392e10i	0.166242	+	0.0605071i
$327$		−	1.05192e11i		−	0.508765i
$328$	−1.03170e11	+	2.83458e11i	−0.492178	+	1.35225i
$329$	3.77041e8	+	2.13830e9i	0.00177422	+	0.0100621i
$330$	−8.79647e9	+	7.38111e9i	−0.0408315	+	0.0342617i
$331$	−1.13080e11	+	1.34763e11i	−0.517797	+	0.617086i	−0.960058	−	0.279800i	$-0.909732\pi$
$331$	−1.13080e11	+	1.34763e11i	−0.517797	+	0.617086i	0.442262	+	0.896886i	$0.354176\pi$
$332$	−2.83900e10			−0.128246
$333$	−1.80608e11	−	7.75746e10i	−0.804892	−	0.345717i
$334$	2.52626e11			1.11076
$335$	1.18043e11	−	1.40678e11i	0.512080	−	0.610273i
$336$	4.59933e9	−	3.85929e9i	0.0196865	−	0.0165189i
$337$	−4.34581e10	−	2.46463e11i	−0.183542	−	1.04092i	−0.927814	−	0.373044i	$-0.878314\pi$
$337$	−4.34581e10	−	2.46463e11i	−0.183542	−	1.04092i	0.744271	−	0.667877i	$-0.232797\pi$
$338$	−2.80721e10	+	7.71274e10i	−0.116990	+	0.321428i
$339$		−	9.86539e10i		−	0.405710i
$340$	−1.98489e10	−	7.22441e9i	−0.0805529	−	0.0293189i
$341$	8.68193e10	+	5.01251e10i	0.347713	+	0.200752i
$342$	2.21936e10	−	1.25866e11i	0.0877223	−	0.497498i
$343$	1.69806e10	+	2.94113e10i	0.0662415	+	0.114734i
$344$	1.18870e11	−	2.05889e11i	0.457677	−	0.792720i
$345$	−7.61142e10	−	6.38674e10i	−0.289254	−	0.242713i
$346$	2.99258e11	−	5.27672e10i	1.12254	−	0.197934i
$347$	−1.67121e11	+	9.64874e10i	−0.618797	+	0.357263i	−0.776401	−	0.630240i	$-0.782957\pi$
$347$	−1.67121e11	+	9.64874e10i	−0.618797	+	0.357263i	0.157603	+	0.987503i	$0.449623\pi$
$348$	3.91494e9	+	1.07562e10i	0.0143093	+	0.0393145i
$349$	2.25558e10	−	8.20963e9i	0.0813848	−	0.0296216i	−0.301007	−	0.953622i	$-0.597323\pi$
$349$	2.25558e10	−	8.20963e9i	0.0813848	−	0.0296216i	0.382392	+	0.924000i	$0.375101\pi$
$350$	1.27946e10	+	2.25604e9i	0.0455745	+	0.00803601i
$351$	1.38966e11	+	1.65613e11i	0.488682	+	0.582388i
$352$	−1.01605e10	−	1.21088e10i	−0.0352755	−	0.0420397i
$353$	3.32521e11	+	5.86324e10i	1.13981	+	0.200979i	0.711523	−	0.702663i	$-0.248006\pi$
$353$	3.32521e11	+	5.86324e10i	1.13981	+	0.200979i	0.428288	+	0.903642i	$0.359117\pi$
$354$	9.46653e10	−	3.44553e10i	0.320388	−	0.116612i
$355$	6.29993e10	+	1.73089e11i	0.210527	+	0.578419i
$356$	−2.98270e10	+	1.72206e10i	−0.0984202	+	0.0568229i
$357$	−9.30833e9	+	1.64131e9i	−0.0303295	+	0.00534791i
$358$	2.14955e11	+	1.80369e11i	0.691631	+	0.580348i
$359$	1.56034e11	−	2.70258e11i	0.495785	−	0.858725i	−0.504203	−	0.863585i	$-0.668214\pi$
$359$	1.56034e11	−	2.70258e11i	0.495785	−	0.858725i	0.999988	+	0.00485992i	$0.00154697\pi$
$360$	7.61017e10	+	1.31812e11i	0.238799	+	0.413612i
$361$	3.92728e10	−	2.22727e11i	0.121705	−	0.690225i
$362$	−1.41030e11	−	8.14235e10i	−0.431640	−	0.249208i
$363$	−1.02810e11	−	3.74198e10i	−0.310782	−	0.113115i
$364$		−	2.86030e9i		−	0.00853994i
$365$	8.25975e10	−	2.26935e11i	0.243584	−	0.669242i
$366$	−2.07467e10	−	1.17661e11i	−0.0604345	−	0.342741i
$367$	−5.53090e10	+	4.64098e10i	−0.159147	+	0.133540i	−0.718884	−	0.695130i	$-0.755347\pi$
$367$	−5.53090e10	+	4.64098e10i	−0.159147	+	0.133540i	0.559737	+	0.828670i	$0.310902\pi$
$368$	4.57902e11	−	5.45707e11i	1.30154	−	1.55112i
$369$	4.79359e11			1.34599
$370$	2.11887e11	−	6.37931e10i	0.587756	−	0.176956i
$371$	2.34454e10			0.0642502
$372$	1.52155e10	−	1.81331e10i	0.0411949	−	0.0490942i
$373$	3.53868e11	−	2.96931e11i	0.946568	−	0.794265i	−0.0321484	−	0.999483i	$-0.510235\pi$
$373$	3.53868e11	−	2.96931e11i	0.946568	−	0.794265i	0.978716	+	0.205218i	$0.0657905\pi$
$374$	2.25060e10	+	1.27638e11i	0.0594807	+	0.337332i
$375$	4.46001e10	−	1.22538e11i	0.116465	−	0.319985i
$376$			5.58630e10i			0.144138i
$377$	−4.50845e11	−	1.64094e11i	−1.14945	−	0.418367i
$378$	−1.58960e10	−	9.17758e9i	−0.0400475	−	0.0231215i
$379$	−1.08313e11	+	6.14274e11i	−0.269653	+	1.52928i	0.485798	+	0.874071i	$0.338529\pi$
$379$	−1.08313e11	+	6.14274e11i	−0.269653	+	1.52928i	−0.755451	+	0.655205i	$0.772582\pi$
$380$	7.23286e9	+	1.25277e10i	0.0177944	+	0.0308208i
$381$	1.36273e11	−	2.36031e11i	0.331319	−	0.573861i
$382$	−2.55749e11	−	2.14599e11i	−0.614509	−	0.515634i
$383$	−4.12879e11	+	7.28017e10i	−0.980456	+	0.172881i	−0.640832	−	0.767681i	$-0.721411\pi$
$383$	−4.12879e11	+	7.28017e10i	−0.980456	+	0.172881i	−0.339623	+	0.940562i	$0.610300\pi$
$384$	1.47378e11	−	8.50890e10i	0.345894	−	0.199702i
$385$	1.40517e9	+	3.86068e9i	0.00325954	+	0.00895551i
$386$	−7.35943e11	+	2.67861e11i	−1.68733	+	0.614139i
$387$	−3.72059e11	−	6.56041e10i	−0.843165	−	0.148673i
$388$	−2.36562e10	−	2.81924e10i	−0.0529910	−	0.0631522i
$389$	3.87052e11	+	4.61270e11i	0.857029	+	1.02137i	0.999502	+	0.0315691i	$0.0100504\pi$
$389$	3.87052e11	+	4.61270e11i	0.857029	+	1.02137i	−0.142472	+	0.989799i	$0.545505\pi$
$390$	−1.11920e11	−	1.97345e10i	−0.244972	−	0.0431952i
$391$	−1.05383e12	+	3.83563e11i	−2.28021	+	0.829930i
$392$	1.49091e11	+	4.09624e11i	0.318907	+	0.876190i
$393$	2.56635e11	−	1.48168e11i	0.542687	−	0.313321i
$394$	4.58639e11	−	8.08704e10i	0.958821	−	0.169066i
$395$	−1.12641e11	−	9.45170e10i	−0.232814	−	0.195354i
$396$	−5.90805e9	+	1.02330e10i	−0.0120730	+	0.0209111i
$397$	−4.16910e11	−	7.22110e11i	−0.842336	−	1.45897i	−0.887915	−	0.460008i	$-0.847847\pi$
$397$	−4.16910e11	−	7.22110e11i	−0.842336	−	1.45897i	0.0455787	−	0.998961i	$-0.485487\pi$
$398$	8.44762e10	−	4.79088e11i	0.168756	−	0.957065i
$399$	5.60584e9	+	3.23653e9i	0.0110729	+	0.00639296i
$400$	3.49654e11	+	1.27264e11i	0.682919	+	0.248562i
$401$		−	2.57608e11i		−	0.497519i	−0.968565	−	0.248759i	$-0.919977\pi$
$401$		−	2.57608e11i		−	0.497519i	0.968565	−	0.248759i	$-0.0800228\pi$
$402$	−9.09985e10	+	2.50016e11i	−0.173787	+	0.477475i
$403$	1.72289e11	+	9.77099e11i	0.325375	+	1.84530i
$404$	−5.05093e9	+	4.23823e9i	−0.00943311	+	0.00791532i
$405$	1.30348e11	−	1.55343e11i	0.240745	−	0.286908i
$406$	4.07342e10			0.0744033
$407$	−9.94383e10	−	9.35242e10i	−0.179630	−	0.168946i
$408$	−2.43179e11			−0.434466
$409$	−3.09557e11	+	3.68916e11i	−0.546999	+	0.651888i	−0.966742	−	0.255755i	$-0.917676\pi$
$409$	−3.09557e11	+	3.68916e11i	−0.546999	+	0.651888i	0.419743	+	0.907643i	$0.362120\pi$
$410$	−4.13390e11	+	3.46875e11i	−0.722491	+	0.606242i
$411$	4.40386e10	+	2.49755e11i	0.0761281	+	0.431744i
$412$	1.45373e10	−	3.99408e10i	0.0248568	−	0.0682936i
$413$		−	3.60436e10i		−	0.0609612i
$414$	−9.55607e11	−	3.47813e11i	−1.59874	−	0.581894i
$415$	3.49514e11	+	2.01792e11i	0.578427	+	0.333955i
$416$	2.71656e10	−	1.54064e11i	0.0444733	−	0.252220i
$417$	−1.04427e10	−	1.80872e10i	−0.0169122	−	0.0292927i
$418$	4.43800e10	−	7.68684e10i	0.0711040	−	0.123156i
$419$	8.39091e11	+	7.04081e11i	1.32998	+	1.11599i	0.984082	+	0.177717i	$0.0568712\pi$
$419$	8.39091e11	+	7.04081e11i	1.32998	+	1.11599i	0.345901	+	0.938271i	$0.387573\pi$
$420$	9.55351e8	−	1.68454e8i	0.00149810	−	0.000264156i
$421$	−5.74129e11	+	3.31473e11i	−0.890717	+	0.514256i	−0.874177	−	0.485607i	$-0.838599\pi$
$421$	−5.74129e11	+	3.31473e11i	−0.890717	+	0.514256i	−0.0165403	+	0.999863i	$0.505265\pi$
$422$	1.12802e11	+	3.09922e11i	0.173146	+	0.475714i
$423$	8.34197e10	−	3.03623e10i	0.126688	−	0.0461108i
$424$	5.94039e11	+	1.04745e11i	0.892624	+	0.157394i
$425$	−3.76531e11	−	4.48732e11i	−0.559823	−	0.667171i
$426$	−1.71539e11	−	2.04432e11i	−0.252359	−	0.300750i
$427$	−4.20973e10	−	7.42290e9i	−0.0612815	−	0.0108056i
$428$	−4.47166e10	+	1.62755e10i	−0.0644128	+	0.0234443i
$429$	2.39786e10	+	6.58805e10i	0.0341795	+	0.0939073i
$430$	3.68329e11	−	2.12655e11i	0.519551	−	0.299963i
$431$	−9.36436e11	+	1.65119e11i	−1.30716	+	0.230488i	−0.783476	−	0.621422i	$-0.786555\pi$
$431$	−9.36436e11	+	1.65119e11i	−1.30716	+	0.230488i	−0.523688	+	0.851910i	$0.675444\pi$
$432$	−4.02707e11	−	3.37911e11i	−0.556303	−	0.466794i
$433$	−6.11025e11	+	1.05833e12i	−0.835341	+	1.44685i	0.0584118	+	0.998293i	$0.481396\pi$
$433$	−6.11025e11	+	1.05833e12i	−0.835341	+	1.44685i	−0.893753	+	0.448560i	$0.851937\pi$
$434$	−4.21187e10	−	7.29517e10i	−0.0569864	−	0.0987033i
$435$	2.82561e10	−	1.60248e11i	0.0378365	−	0.214581i
$436$	1.05530e11	+	6.09280e10i	0.139858	+	0.0807472i
$437$	7.21706e11	+	2.62680e11i	0.946660	+	0.344556i
$438$			3.49886e11i			0.454247i
$439$	1.26505e11	−	3.47570e11i	0.162561	−	0.446634i	−0.831491	−	0.555539i	$-0.812512\pi$
$439$	1.26505e11	−	3.47570e11i	0.162561	−	0.446634i	0.994052	+	0.108905i	$0.0347343\pi$
$440$	1.83550e10	+	1.04096e11i	0.0233463	+	0.132403i
$441$	5.30655e11	−	4.45272e11i	0.668095	−	0.560598i
$442$	−8.24512e11	+	9.82615e11i	−1.02753	+	1.22457i
$443$	1.26022e12			1.55464			0.777321	−	0.629104i	$-0.216578\pi$
$443$	1.26022e12			1.55464			0.777321	+	0.629104i	$0.216578\pi$
$444$	−2.58246e10	+	1.92881e10i	−0.0315363	+	0.0235540i
$445$	4.89607e11			0.591871
$446$	9.40641e10	−	1.12101e11i	0.112569	−	0.134154i
$447$	−1.15583e11	+	9.69858e10i	−0.136934	+	0.114901i
$448$	−8.49845e9	−	4.81971e10i	−0.00996755	−	0.0565288i
$449$	2.55225e11	−	7.01224e11i	0.296356	−	0.814232i	−0.698745	−	0.715371i	$-0.746258\pi$
$449$	2.55225e11	−	7.01224e11i	0.296356	−	0.814232i	0.995101	−	0.0988614i	$-0.0315200\pi$
$450$		−	5.31180e11i		−	0.610640i
$451$	3.12829e11	+	1.13861e11i	0.356051	+	0.129592i
$452$	9.89713e10	+	5.71411e10i	0.111529	+	0.0643911i
$453$	2.32442e9	−	1.31824e10i	0.00259342	−	0.0147080i
$454$	−6.45638e11	−	1.11828e12i	−0.713244	−	1.23537i
$455$	−2.03306e10	+	3.52136e10i	−0.0222381	+	0.0385176i
$456$	1.27576e11	+	1.07049e11i	0.138175	+	0.115942i
$457$	−1.55944e11	+	2.74971e10i	−0.167242	+	0.0294893i	−0.256642	−	0.966507i	$-0.582616\pi$
$457$	−1.55944e11	+	2.74971e10i	−0.167242	+	0.0294893i	0.0894001	+	0.995996i	$0.471505\pi$
$458$	−1.03498e12	+	5.97548e11i	−1.09910	+	0.634568i
$459$	2.83052e11	+	7.77679e11i	0.297652	+	0.817793i
$460$	1.08159e11	−	3.93666e10i	0.112629	−	0.0409938i
$461$	1.64185e12	+	2.89502e11i	1.69308	+	0.298536i	0.935270	−	0.353935i	$-0.115156\pi$
$461$	1.64185e12	+	2.89502e11i	1.69308	+	0.298536i	0.757814	+	0.652471i	$0.226268\pi$
$462$	−3.82610e9	−	4.55977e9i	−0.00390722	−	0.00465644i
$463$	−6.62709e11	−	7.89786e11i	−0.670206	−	0.798721i	0.318606	−	0.947887i	$-0.396785\pi$
$463$	−6.62709e11	−	7.89786e11i	−0.670206	−	0.798721i	−0.988812	+	0.149167i	$0.952341\pi$
$464$	1.14891e12	+	2.02584e11i	1.15068	+	0.202897i
$465$	−3.16209e11	+	1.15090e11i	−0.313643	+	0.114157i
$466$	−8.42237e10	−	2.31403e11i	−0.0827366	−	0.227317i
$467$	1.92468e11	−	1.11121e11i	0.187254	−	0.108111i	−0.403442	−	0.915005i	$-0.632186\pi$
$467$	1.92468e11	−	1.11121e11i	0.187254	−	0.108111i	0.590697	+	0.806894i	$0.298853\pi$
$468$	−1.15167e11	+	2.03070e10i	−0.110974	+	0.0195677i
$469$	7.29223e10	+	6.11890e10i	0.0695957	+	0.0583977i
$470$	−4.99686e10	+	8.65482e10i	−0.0472343	+	0.0818121i
$471$	1.22353e11	+	2.11922e11i	0.114557	+	0.198418i
$472$	1.61029e11	−	9.13243e11i	0.149337	−	0.846930i
$473$	−2.27223e11	−	1.31187e11i	−0.208726	−	0.120508i
$474$	2.00188e11	+	7.28626e10i	0.182153	+	0.0662983i
$475$			4.01165e11i			0.361578i
$476$	3.74487e9	−	1.02889e10i	0.00334353	−	0.00918628i
$477$	−1.66453e11	−	9.44003e11i	−0.147217	−	0.834912i
$478$	−3.91475e11	+	3.28486e11i	−0.342987	+	0.287801i
$479$	−7.07991e11	+	8.43751e11i	−0.614495	+	0.732326i	−0.980113	−	0.198438i	$-0.936413\pi$
$479$	−7.07991e11	+	8.43751e11i	−0.614495	+	0.732326i	0.365619	+	0.930765i	$0.380857\pi$
$480$	5.30578e10			0.0456209
$481$	7.64633e10	−	1.34886e12i	0.0651328	−	1.14898i
$482$	1.11480e12			0.940771
$483$	3.31065e10	−	3.94548e10i	0.0276791	−	0.0329866i
$484$	9.70885e10	−	8.14669e10i	0.0804199	−	0.0674803i
$485$	9.08482e10	+	5.15226e11i	0.0745553	+	0.422824i
$486$	−3.93487e11	+	1.08110e12i	−0.319939	+	0.879026i
$487$		−	1.47628e12i		−	1.18929i	−0.803988	−	0.594646i	$-0.797292\pi$
$487$		−	1.47628e12i		−	1.18929i	0.803988	−	0.594646i	$-0.202708\pi$
$488$	−1.03346e12	−	3.76150e11i	−0.824909	−	0.300242i
$489$	6.46967e10	+	3.73526e10i	0.0511673	+	0.0295414i
$490$	−1.35417e11	+	7.67988e11i	−0.106118	+	0.601827i
$491$	−4.34540e11	−	7.52646e11i	−0.337414	−	0.584419i	0.646531	−	0.762887i	$-0.276219\pi$
$491$	−4.34540e11	−	7.52646e11i	−0.337414	−	0.584419i	−0.983946	+	0.178469i	$0.942886\pi$
$492$	3.93029e10	−	6.80747e10i	0.0302400	−	0.0523772i
$493$	−1.40692e12	−	1.18055e12i	−1.07265	−	0.900062i
$494$	8.65108e11	−	1.52542e11i	0.653580	−	0.115244i
$495$	1.45470e11	−	8.39871e10i	0.108906	−	0.0628767i
$496$	−8.25150e11	−	2.26708e12i	−0.612161	−	1.68190i
$497$	−8.97232e10	+	3.26566e10i	−0.0659631	+	0.0240086i
$498$	−5.75833e11	−	1.01535e11i	−0.419531	−	0.0739747i
$499$	1.16593e12	+	1.38950e12i	0.841824	+	1.00325i	0.999875	+	0.0158153i	$0.00503438\pi$
$499$	1.16593e12	+	1.38950e12i	0.841824	+	1.00325i	−0.158051	+	0.987431i	$0.550521\pi$
$500$	9.70994e10	+	1.15719e11i	0.0694787	+	0.0828015i
$501$	5.15166e11	+	9.08376e10i	0.365323	+	0.0644163i
$502$	−8.39493e10	+	3.05550e10i	−0.0589998	+	0.0214742i
$503$	7.85116e11	+	2.15709e12i	0.546862	+	1.50249i	0.837924	+	0.545787i	$0.183769\pi$
$503$	7.85116e11	+	2.15709e12i	0.546862	+	1.50249i	−0.291061	+	0.956704i	$0.594008\pi$
$504$	−6.83265e10	+	3.94483e10i	−0.0471685	+	0.0272327i
$505$	9.23075e10	−	1.62763e10i	0.0631577	−	0.0111364i
$506$	−5.41013e11	−	4.53964e11i	−0.366885	−	0.307853i
$507$	−8.49787e10	+	1.47187e11i	−0.0571182	+	0.0989316i
$508$	1.57860e11	+	2.73422e11i	0.105169	+	0.182157i
$509$	4.45408e11	−	2.52604e12i	0.294122	−	1.66805i	−0.376625	−	0.926366i	$-0.622916\pi$
$509$	4.45408e11	−	2.52604e12i	0.294122	−	1.66805i	0.670748	−	0.741686i	$-0.265973\pi$
$510$	−3.76756e11	−	2.17520e11i	−0.246601	−	0.142375i
$511$	1.17635e11	+	4.28155e10i	0.0763205	+	0.0277784i
$512$		−	1.22046e12i		−	0.784893i
$513$	1.93846e11	−	5.32586e11i	0.123574	−	0.339517i
$514$	5.08439e10	+	2.88350e11i	0.0321296	+	0.182216i
$515$	−4.62865e11	+	3.88389e11i	−0.289949	+	0.243296i
$516$	−3.98219e10	+	4.74579e10i	−0.0247285	+	0.0294703i
$517$	6.16514e10			0.0379521
$518$	3.30680e10	+	1.09835e11i	0.0201802	+	0.0670279i
$519$	6.29232e11			0.380678
$520$	−6.72440e11	+	8.01382e11i	−0.403309	+	0.480645i
$521$	1.14105e12	−	9.57455e11i	0.678477	−	0.569310i	−0.237084	−	0.971489i	$-0.576192\pi$
$521$	1.14105e12	−	9.57455e11i	0.678477	−	0.569310i	0.915561	+	0.402180i	$0.131747\pi$
$522$	−2.89197e11	−	1.64012e12i	−0.170481	−	0.966848i
$523$	−4.52834e10	+	1.24415e11i	−0.0264656	+	0.0727135i	−0.952222	−	0.305407i	$-0.901207\pi$
$523$	−4.52834e10	+	1.24415e11i	−0.0264656	+	0.0727135i	0.925756	+	0.378121i	$0.123430\pi$
$524$			3.43281e11i			0.198911i
$525$	2.52802e10	+	9.20123e9i	0.0145232	+	0.00528602i
$526$	3.05182e11	+	1.76197e11i	0.173829	+	0.100360i
$527$	−6.59525e11	+	3.74035e12i	−0.372463	+	2.11235i
$528$	−8.52384e10	−	1.47637e11i	−0.0477290	−	0.0826691i
$529$	2.15492e12	−	3.73242e12i	1.19641	−	2.07224i
$530$	8.26648e11	+	6.93640e11i	0.455071	+	0.381850i
$531$	−1.45126e12	+	2.55896e11i	−0.792172	+	0.139681i
$532$	−6.49389e9	+	3.74925e9i	−0.00351482	+	0.00202928i
$533$	1.12687e12	+	3.09606e12i	0.604787	+	1.66164i
$534$	−6.66567e11	+	2.42611e11i	−0.354739	+	0.129114i
$535$	6.66198e11	+	1.17469e11i	0.351569	+	0.0619912i
$536$	1.57427e12	+	1.87615e12i	0.823832	+	0.981804i
$537$	3.73490e11	+	4.45108e11i	0.193818	+	0.230984i
$538$	2.34779e12	+	4.13980e11i	1.20820	+	0.213039i
$539$	4.52068e11	−	1.64539e11i	0.230704	−	0.0839693i
$540$	−2.90508e10	−	7.98163e10i	−0.0147023	−	0.0403943i
$541$	−7.59786e11	+	4.38663e11i	−0.381332	+	0.220162i	−0.678398	−	0.734695i	$-0.737325\pi$
$541$	−7.59786e11	+	4.38663e11i	−0.381332	+	0.220162i	0.297065	+	0.954857i	$0.403992\pi$
$542$	−2.79164e12	+	4.92241e11i	−1.38951	+	0.245009i
$543$	−2.58316e11	−	2.16753e11i	−0.127512	−	0.106996i
$544$	2.99428e11	−	5.18625e11i	0.146588	−	0.253898i
$545$	−8.66135e11	−	1.50019e12i	−0.420534	−	0.728386i
$546$	1.02296e10	−	5.80152e10i	0.00492599	−	0.0279367i
$547$	−2.73023e12	−	1.57630e12i	−1.30394	−	0.752829i	−0.322860	−	0.946447i	$-0.604644\pi$
$547$	−2.73023e12	−	1.57630e12i	−1.30394	−	0.752829i	−0.981077	+	0.193618i	$0.937978\pi$
$548$	−2.76066e11	−	1.00480e11i	−0.130768	−	0.0475956i
$549$			1.74770e12i			0.821093i
$550$	1.26169e11	−	3.46647e11i	0.0587924	−	0.161531i
$551$	2.18412e11	+	1.23867e12i	0.100947	+	0.572499i
$552$	1.01509e12	−	8.51766e11i	0.465351	−	0.390476i
$553$	4.89942e10	−	5.83890e10i	0.0222783	−	0.0265502i
$554$	7.27430e11			0.328093
$555$	4.55028e11	−	5.39006e10i	0.203573	−	0.0241143i
$556$	2.41939e10			0.0107367
$557$	−1.52331e11	+	1.81541e11i	−0.0670563	+	0.0799146i	−0.798530	−	0.601955i	$-0.794389\pi$
$557$	−1.52331e11	+	1.81541e11i	−0.0670563	+	0.0799146i	0.731473	+	0.681870i	$0.238833\pi$
$558$	−2.63830e12	+	2.21379e12i	−1.15205	+	0.966681i
$559$	−4.50913e11	−	2.55725e12i	−0.195317	−	1.10770i
$560$	3.38162e10	−	9.29094e10i	0.0145305	−	0.0399221i
$561$			2.68377e11i			0.114396i
$562$	2.14895e12	+	7.82155e11i	0.908685	+	0.330734i
$563$	1.92932e12	+	1.11389e12i	0.809312	+	0.467257i	0.846717	−	0.532043i	$-0.178576\pi$
$563$	1.92932e12	+	1.11389e12i	0.809312	+	0.467257i	−0.0374046	+	0.999300i	$0.511909\pi$
$564$	2.52782e9	−	1.43360e10i	0.00105194	−	0.00596584i
$565$	−8.12302e11	−	1.40695e12i	−0.335351	−	0.580845i
$566$	−6.44579e11	+	1.11644e12i	−0.263999	+	0.457260i
$567$	8.05240e10	+	6.75676e10i	0.0327191	+	0.0274546i
$568$	−2.41923e12	+	4.26575e11i	−0.975234	+	0.171960i
$569$	−2.57281e11	+	1.48541e11i	−0.102897	+	0.0594075i	−0.550565	−	0.834792i	$-0.685588\pi$
$569$	−2.57281e11	+	1.48541e11i	−0.102897	+	0.0594075i	0.447669	+	0.894200i	$0.352254\pi$
$570$	1.01899e11	+	2.79966e11i	0.0404328	+	0.111088i
$571$	−4.50147e12	+	1.63840e12i	−1.77212	+	0.644998i	−0.772163	+	0.635425i	$0.780825\pi$
$571$	−4.50147e12	+	1.63840e12i	−1.77212	+	0.644998i	−0.999954	+	0.00957267i	$0.996953\pi$
$572$	−7.99811e10	−	1.41028e10i	−0.0312396	−	0.00550838i
$573$	−4.44370e11	−	5.29579e11i	−0.172206	−	0.205227i
$574$	−1.79808e11	−	2.14286e11i	−0.0691360	−	0.0823931i
$575$	3.14348e12	+	5.54280e11i	1.19924	+	0.211458i
$576$	−1.88027e12	+	6.84362e11i	−0.711736	+	0.259051i
$577$	3.69156e11	+	1.01425e12i	0.138650	+	0.380937i	0.989512	−	0.144452i	$-0.0461421\pi$
$577$	3.69156e11	+	1.01425e12i	0.138650	+	0.380937i	−0.850862	+	0.525389i	$0.823920\pi$
$578$	−1.80212e12	+	1.04046e12i	−0.671598	+	0.387747i
$579$	−1.59708e12	+	2.81609e11i	−0.590573	+	0.104134i
$580$	1.44398e11	+	1.21164e11i	0.0529828	+	0.0444579i
$581$	−1.04602e11	+	1.81175e11i	−0.0380843	+	0.0659639i
$582$	−3.78989e11	−	6.56429e11i	−0.136922	−	0.237156i
$583$	1.15599e11	−	6.55592e11i	0.0414423	−	0.235031i
$584$	2.78924e12	+	1.61037e12i	0.992267	+	0.572886i
$585$	1.56218e12	+	5.68586e11i	0.551479	+	0.200722i
$586$			1.73401e11i			0.0607453i
$587$	−6.69301e11	+	1.83889e12i	−0.232675	+	0.639270i	−0.999998	−	0.00199101i	$-0.999366\pi$
$587$	−6.69301e11	+	1.83889e12i	−0.232675	+	0.639270i	0.767323	+	0.641261i	$0.221588\pi$
$588$	−1.97252e10	−	1.11867e11i	−0.00680493	−	0.0385927i
$589$	1.99253e12	−	1.67193e12i	0.682159	−	0.572400i
$590$	1.06636e12	−	1.27084e12i	0.362303	−	0.431775i
$591$	9.64355e11			0.325157
$592$	3.86445e11	+	3.26236e12i	0.129312	+	1.09165i
$593$	−5.60597e12			−1.86168			−0.930839	−	0.365430i	$-0.880922\pi$
$593$	−5.60597e12			−1.86168			−0.930839	+	0.365430i	$0.880922\pi$
$594$	−3.35004e11	+	3.99243e11i	−0.110411	+	0.131582i
$595$	−1.19236e11	+	1.00051e11i	−0.0390015	+	0.0327261i
$596$	−3.03512e10	−	1.72130e11i	−0.00985297	−	0.0558790i
$597$	3.44535e11	−	9.46602e11i	0.111007	−	0.304988i
$598$		−	6.98965e12i		−	2.23511i
$599$	5.92798e11	+	2.15761e11i	0.188142	+	0.0684781i	0.434373	−	0.900733i	$-0.356970\pi$
$599$	5.92798e11	+	2.15761e11i	0.188142	+	0.0684781i	−0.246231	+	0.969211i	$0.579192\pi$
$600$	5.99420e11	+	3.46075e11i	0.188821	+	0.109016i
$601$	−7.47815e11	+	4.24107e12i	−0.233808	+	1.32599i	0.611302	+	0.791397i	$0.290646\pi$
$601$	−7.47815e11	+	4.24107e12i	−0.233808	+	1.32599i	−0.845110	+	0.534592i	$0.820465\pi$
$602$	1.10233e11	+	1.90928e11i	0.0342078	+	0.0592497i
$603$	1.94599e12	−	3.37056e12i	0.599395	−	1.03818i
$604$	1.18785e10	+	9.96728e9i	0.00363159	+	0.00304727i
$605$	−1.77433e12	+	3.12862e11i	−0.538437	+	0.0949409i
$606$	−1.17605e11	+	6.78995e10i	−0.0354242	+	0.0204522i
$607$	−7.95038e11	−	2.18435e12i	−0.237705	−	0.653090i	−0.999983	−	0.00583981i	$-0.998141\pi$
$607$	−7.95038e11	−	2.18435e12i	−0.237705	−	0.653090i	0.762278	−	0.647250i	$-0.224081\pi$
$608$	−3.85388e11	+	1.40270e11i	−0.114375	+	0.0416292i
$609$	8.30670e10	+	1.46469e10i	0.0244709	+	0.00431489i
$610$	−1.26468e12	−	1.50719e12i	−0.369825	−	0.440740i
$611$	3.92204e11	+	4.67410e11i	0.113848	+	0.135679i
$612$	−4.40861e11	−	7.77356e10i	−0.127034	−	0.0223995i
$613$	−8.05652e11	+	2.93233e11i	−0.230449	+	0.0838767i	−0.454664	−	0.890663i	$-0.650241\pi$
$613$	−8.05652e11	+	2.93233e11i	−0.230449	+	0.0838767i	0.224215	+	0.974540i	$0.428018\pi$
$614$	7.53551e11	+	2.07036e12i	0.213971	+	0.587881i
$615$	−9.67730e11	+	5.58719e11i	−0.272782	+	0.157491i
$616$	−5.39598e10	+	9.51457e9i	−0.0150993	+	0.00266242i
$617$	−4.91145e11	−	4.12119e11i	−0.136435	−	0.114483i	0.572016	−	0.820242i	$-0.306161\pi$
$617$	−4.91145e11	−	4.12119e11i	−0.136435	−	0.114483i	−0.708451	+	0.705760i	$0.750606\pi$
$618$	4.37704e11	−	7.58126e11i	0.120707	−	0.209071i
$619$	3.42420e10	+	5.93089e10i	0.00937456	+	0.0162372i	0.870675	−	0.491859i	$-0.163683\pi$
$619$	3.42420e10	+	5.93089e10i	0.00937456	+	0.0162372i	−0.861300	+	0.508097i	$0.830349\pi$
$620$	6.76897e10	−	3.83887e11i	0.0183975	−	0.104338i
$621$	−3.90545e12	−	2.25481e12i	−1.05380	−	0.608413i
$622$	2.70452e12	+	9.84365e11i	0.724492	+	0.263694i
$623$			2.53794e11i			0.0674972i
$624$	5.77057e11	−	1.58545e12i	0.152366	−	0.418622i
$625$	6.50328e10	+	3.68819e11i	0.0170480	+	0.0966837i
$626$	2.95087e12	−	2.47607e12i	0.768007	−	0.644435i
$627$	1.18141e11	−	1.40796e11i	0.0305280	−	0.0363819i
$628$	−2.83471e11			−0.0727262
$629$	2.04106e12	−	4.75195e12i	0.519909	−	1.21044i
$630$	−1.41144e11			−0.0356968
$631$	−3.44629e12	+	4.10712e12i	−0.865404	+	1.03135i	0.133782	+	0.991011i	$0.457288\pi$
$631$	−3.44629e12	+	4.10712e12i	−0.865404	+	1.03135i	−0.999186	+	0.0403380i	$0.987157\pi$
$632$	1.50223e12	−	1.26052e12i	0.374550	−	0.314285i
$633$	1.18592e11	+	6.72567e11i	0.0293587	+	0.166502i
$634$	1.20667e12	−	3.31529e12i	0.296610	−	0.814929i
$635$		−	4.48819e12i		−	1.09544i
$636$	−1.47707e11	−	5.37610e10i	−0.0357968	−	0.0130290i
$637$	4.12335e12	+	2.38062e12i	0.992254	+	0.572878i
$638$	2.00842e11	−	1.13903e12i	0.0479912	−	0.272171i
$639$	1.95188e12	+	3.38076e12i	0.463126	+	0.802159i
$640$	1.40122e12	−	2.42698e12i	0.330139	−	0.571817i
$641$	3.56727e12	+	2.99329e12i	0.834593	+	0.700306i	0.956341	−	0.292255i	$-0.0944055\pi$
$641$	3.56727e12	+	2.99329e12i	0.834593	+	0.700306i	−0.121748	+	0.992561i	$0.538850\pi$
$642$	−9.65193e11	+	1.70190e11i	−0.224237	+	0.0395390i
$643$	−2.22067e12	+	1.28210e12i	−0.512311	+	0.295783i	−0.733783	−	0.679384i	$-0.762247\pi$
$643$	−2.22067e12	+	1.28210e12i	−0.512311	+	0.295783i	0.221472	+	0.975167i	$0.428914\pi$
$644$	2.04062e10	+	5.60656e10i	0.00467494	+	0.0128443i
$645$	8.27578e11	−	3.01214e11i	0.188274	−	0.0685261i
$646$	3.31165e12	+	5.83933e11i	0.748166	+	0.131922i
$647$	4.50336e12	+	5.36690e12i	1.01034	+	1.20408i	0.978851	+	0.204573i	$0.0655806\pi$
$647$	4.50336e12	+	5.36690e12i	1.01034	+	1.20408i	0.0314894	+	0.999504i	$0.489975\pi$
$648$	1.73838e12	+	2.07172e12i	0.387309	+	0.461577i
$649$	−1.00787e12	−	1.77715e11i	−0.222999	−	0.0393208i
$650$	3.43075e12	−	1.24869e12i	0.753839	−	0.274375i
$651$	−5.96587e10	−	1.63911e11i	−0.0130185	−	0.0357679i
$652$	−7.49457e10	+	4.32699e10i	−0.0162417	+	0.00937717i
$653$	−4.63637e10	+	8.17517e9i	−0.00997859	+	0.00175949i	−0.178635	−	0.983915i	$-0.557168\pi$
$653$	−4.63637e10	+	8.17517e9i	−0.00997859	+	0.00175949i	0.168657	+	0.985675i	$0.446057\pi$
$654$	1.92256e12	+	1.61322e12i	0.410942	+	0.344821i
$655$	2.43999e12	−	4.22619e12i	0.517968	−	0.897147i
$656$	−4.00578e12	−	6.93821e12i	−0.844539	−	1.46278i
$657$	8.88760e11	−	5.04041e12i	0.186097	−	1.05541i
$658$	−4.48634e10	−	2.59019e10i	−0.00932988	−	0.00538661i
$659$	−6.09757e12	−	2.21933e12i	−1.25942	−	0.458393i	−0.375849	−	0.926681i	$-0.622649\pi$
$659$	−6.09757e12	−	2.21933e12i	−1.25942	−	0.458393i	−0.883576	+	0.468288i	$0.844871\pi$
$660$		−	2.75446e10i		−	0.00565052i
$661$	1.50056e12	−	4.12275e12i	0.305736	−	0.840002i	−0.687740	−	0.725957i	$-0.741397\pi$
$661$	1.50056e12	−	4.12275e12i	0.305736	−	0.840002i	0.993476	−	0.114045i	$-0.0363808\pi$
$662$	−7.28840e11	−	4.13345e12i	−0.147493	−	0.836474i
$663$	−2.03470e12	+	1.70732e12i	−0.408969	+	0.343165i
$664$	−3.45973e12	+	4.12315e12i	−0.690695	+	0.823138i
$665$	1.06597e11			0.0211371
$666$	4.18761e12	−	2.11123e12i	0.824768	−	0.415817i
$667$	1.00079e13			1.95783
$668$	−3.89518e11	+	4.64210e11i	−0.0756891	+	0.0902028i
$669$	2.32128e11	−	1.94779e11i	0.0448033	−	0.0375945i
$670$	7.60827e11	+	4.31486e12i	0.145864	+	0.827238i
$671$	−4.15126e11	+	1.14055e12i	−0.0790548	+	0.217201i
$672$			2.75032e10i			0.00520262i
$673$	−9.27851e12	−	3.37710e12i	−1.74345	−	0.634566i	−0.744019	−	0.668158i	$-0.767083\pi$
$673$	−9.27851e12	−	3.37710e12i	−1.74345	−	0.634566i	−0.999436	+	0.0335927i	$0.989305\pi$
$674$	5.17101e12	+	2.98548e12i	0.965175	+	0.557244i
$675$	4.09033e11	−	2.31974e12i	0.0758388	−	0.430103i
$676$	−9.84407e10	−	1.70504e11i	−0.0181307	−	0.0314033i
$677$	−1.54302e12	+	2.67258e12i	−0.282307	+	0.488970i	−0.971953	−	0.235177i	$-0.924433\pi$
$677$	−1.54302e12	+	2.67258e12i	−0.282307	+	0.488970i	0.689645	+	0.724147i	$0.257766\pi$
$678$	1.80307e12	+	1.51295e12i	0.327702	+	0.274974i
$679$	−2.67074e11	+	4.70924e10i	−0.0482190	+	0.00850231i
$680$	−3.46809e12	+	2.00230e12i	−0.622014	+	0.359120i
$681$	−9.14510e11	−	2.51260e12i	−0.162940	−	0.447673i
$682$	−2.24758e12	+	8.18053e11i	−0.397819	+	0.144794i
$683$	−4.77503e12	−	8.41967e11i	−0.839620	−	0.148048i	−0.262730	−	0.964869i	$-0.584623\pi$
$683$	−4.77503e12	−	8.41967e11i	−0.839620	−	0.148048i	−0.576890	+	0.816822i	$0.695734\pi$
$684$	1.97064e11	+	2.34851e11i	0.0344234	+	0.0410243i
$685$	2.68450e12	+	3.19927e12i	0.465861	+	0.555191i
$686$	−7.97956e11	−	1.40701e11i	−0.137569	−	0.0242571i
$687$	−2.32544e12	+	8.46393e11i	−0.398291	+	0.144966i
$688$	2.15957e12	+	5.93338e12i	0.367468	+	1.00961i
$689$	5.70577e12	−	3.29423e12i	0.964557	−	0.556887i
$690$	2.33457e12	−	4.11648e11i	0.392091	−	0.0691361i
$691$	−3.90128e12	−	3.27356e12i	−0.650962	−	0.546222i	0.256401	−	0.966571i	$-0.417463\pi$
$691$	−3.90128e12	−	3.27356e12i	−0.650962	−	0.546222i	−0.907363	+	0.420349i	$0.861908\pi$
$692$	−3.64457e11	+	6.31257e11i	−0.0604183	+	0.104648i
$693$	4.35359e10	+	7.54063e10i	0.00717047	+	0.0124196i
$694$	7.99493e11	−	4.53415e12i	0.130827	−	0.741956i
$695$	−2.97855e11	−	1.71967e11i	−0.0484255	−	0.0279585i
$696$	2.03924e12	+	7.42224e11i	0.329403	+	0.119893i
$697$			1.26124e13i			2.02418i
$698$	−1.95870e11	+	5.38148e11i	−0.0312333	+	0.0858129i
$699$	−8.85463e10	−	5.02171e11i	−0.0140289	−	0.0795618i
$700$	−2.38733e10	+	2.00321e10i	−0.00375813	+	0.00315344i
$701$	−6.04139e12	+	7.19984e12i	−0.944943	+	1.12614i	0.0469292	+	0.998898i	$0.485056\pi$
$701$	−6.04139e12	+	7.19984e12i	−0.944943	+	1.12614i	−0.991872	+	0.127241i	$0.959388\pi$
$702$	−5.15804e12			−0.801618
$703$	−3.16262e12	+	1.59447e12i	−0.488369	+	0.246217i
$704$	−1.38961e12			−0.213215
$705$	−1.33019e11	+	1.58525e11i	−0.0202797	+	0.0241684i
$706$	−6.17114e12	+	5.17820e12i	−0.934855	+	0.784437i
$707$	8.43705e9	+	4.78489e10i	0.00127000	+	0.00720252i
$708$	−8.26492e10	+	2.27077e11i	−0.0123620	+	0.0339643i
$709$		−	7.19269e11i		−	0.106901i	−0.998570	−	0.0534507i	$-0.982978\pi$
$709$		−	7.19269e11i		−	0.106901i	0.998570	−	0.0534507i	$-0.0170220\pi$
$710$	−4.12966e12	−	1.50307e12i	−0.609890	−	0.221982i
$711$	−2.69881e12	−	1.55816e12i	−0.396058	−	0.228664i
$712$	−1.13386e12	+	6.43042e12i	−0.165348	+	0.937734i
$713$	−1.03480e13	−	1.79233e13i	−1.49953	−	2.59726i
$714$	1.12755e11	−	1.95297e11i	0.0162365	−	0.0281224i
$715$	8.84420e11	+	7.42116e11i	0.126556	+	0.106193i
$716$	−6.62869e11	+	1.16882e11i	−0.0942582	+	0.0166203i
$717$	−9.16427e11	+	5.29099e11i	−0.129498	+	0.0747654i
$718$	2.54650e12	+	6.99646e12i	0.357589	+	0.982468i
$719$	1.52775e12	−	5.56056e11i	0.213193	−	0.0775958i	−0.233216	−	0.972425i	$-0.574925\pi$
$719$	1.52775e12	−	5.56056e11i	0.213193	−	0.0775958i	0.446409	+	0.894829i	$0.352703\pi$
$720$	−3.98098e12	−	7.01954e11i	−0.552069	−	0.0973447i
$721$	−2.01327e11	−	2.39932e11i	−0.0277455	−	0.0330659i
$722$	3.46843e12	+	4.13351e12i	0.475024	+	0.566112i
$723$	2.27334e12	+	4.00851e11i	0.309416	+	0.0545583i
$724$	3.67069e11	−	1.33602e11i	0.0496506	−	0.0180713i
$725$	1.78789e12	+	4.91219e12i	0.240337	+	0.660320i
$726$	2.26060e12	−	1.30516e12i	0.302001	−	0.174361i
$727$	−4.58681e12	+	8.08779e11i	−0.608984	+	0.107380i	−0.469632	−	0.882862i	$-0.655613\pi$
$727$	−4.58681e12	+	8.08779e11i	−0.608984	+	0.107380i	−0.139353	+	0.990243i	$0.544502\pi$
$728$	−4.15407e11	−	3.48568e11i	−0.0548129	−	0.0459935i
$729$	1.26188e12	−	2.18564e12i	0.165480	−	0.286619i
$730$	2.88091e12	+	4.98988e12i	0.375471	+	0.650335i
$731$	1.72610e12	−	9.78921e12i	0.223583	−	1.26800i
$732$	2.48195e11	+	1.43295e11i	0.0319516	+	0.0184473i
$733$	−3.12650e12	−	1.13795e12i	−0.400028	−	0.145598i	0.134169	−	0.990958i	$-0.457164\pi$
$733$	−3.12650e12	−	1.13795e12i	−0.400028	−	0.145598i	−0.534197	+	0.845360i	$0.679386\pi$
$734$		−	1.72261e12i		−	0.219055i
$735$	−5.52296e11	+	1.51742e12i	−0.0698038	+	0.191784i
$736$	5.66655e11	+	3.21366e12i	0.0711818	+	0.403692i
$737$	2.07055e12	−	1.73739e12i	0.258512	−	0.216918i
$738$	−7.35145e12	+	8.76111e12i	−0.912261	+	1.08719i
$739$	9.19891e11			0.113458			0.0567292	−	0.998390i	$-0.481933\pi$
$739$	9.19891e11			0.113458			0.0567292	+	0.998390i	$0.481933\pi$
$740$	−2.09482e11	+	4.87712e11i	−0.0256805	+	0.0597889i
$741$	1.81902e12			0.221643
$742$	−3.59558e11	+	4.28504e11i	−0.0435463	+	0.0518964i
$743$	−8.69772e12	+	7.29825e12i	−1.04702	+	0.878556i	−0.992777	−	0.119972i	$-0.961719\pi$
$743$	−8.69772e12	+	7.29825e12i	−1.04702	+	0.878556i	−0.0542445	+	0.998528i	$0.517275\pi$
$744$	−7.79289e11	−	4.41957e12i	−0.0932439	−	0.528813i
$745$	−8.49817e11	+	2.33485e12i	−0.101070	+	0.277688i
$746$			1.10213e13i			1.30289i
$747$	8.03747e12	+	2.92540e12i	0.944445	+	0.343750i
$748$	−2.69241e11	−	1.55446e11i	−0.0314473	−	0.0181561i
$749$	−6.08915e10	+	3.45333e11i	−0.00706949	+	0.0400931i
$750$	1.55560e12	+	2.69438e12i	0.179524	+	0.310945i
$751$	2.13392e12	−	3.69606e12i	0.244793	−	0.423993i	−0.717281	−	0.696784i	$-0.754613\pi$
$751$	2.13392e12	−	3.69606e12i	0.244793	−	0.423993i	0.962073	+	0.272791i	$0.0879468\pi$
$752$	−1.13656e12	−	9.53687e11i	−0.129602	−	0.108749i
$753$	−1.82180e11	+	3.21232e10i	−0.0206501	+	0.00364118i
$754$	9.91326e12	−	5.72342e12i	1.11698	−	0.644889i
$755$	−7.53927e10	−	2.07140e11i	−0.00844439	−	0.0232008i
$756$	4.13739e10	−	1.50589e10i	0.00460657	−	0.00167666i
$757$	1.19641e13	+	2.10960e12i	1.32419	+	0.233490i	0.790642	−	0.612279i	$-0.209747\pi$
$757$	1.19641e13	+	2.10960e12i	1.32419	+	0.233490i	0.533548	+	0.845770i	$0.320858\pi$
$758$	−9.56582e12	−	1.14001e13i	−1.05247	−	1.25429i
$759$	−9.40023e11	−	1.12028e12i	−0.102814	−	0.122529i
$760$	2.70085e12	+	4.76233e11i	0.293657	+	0.0517796i
$761$	−2.58761e12	+	9.41813e11i	−0.279684	+	0.101797i	−0.478054	−	0.878331i	$-0.658658\pi$
$761$	−2.58761e12	+	9.41813e11i	−0.279684	+	0.101797i	0.198370	+	0.980127i	$0.436435\pi$
$762$	2.22400e12	+	6.11038e12i	0.238966	+	0.656554i
$763$	7.77643e11	−	4.48973e11i	0.0830654	−	0.0479578i
$764$	7.88666e11	−	1.39063e11i	0.0837477	−	0.0147670i
$765$	4.87497e12	+	4.09059e12i	0.514631	+	0.431827i
$766$	5.00132e12	−	8.66255e12i	0.524875	−	0.909109i
$767$	−5.06436e12	−	8.77174e12i	−0.528379	−	0.915180i
$768$	−1.95314e11	+	1.10768e12i	−0.0202585	+	0.114892i
$769$	9.04807e12	+	5.22391e12i	0.933013	+	0.538675i	0.887763	−	0.460301i	$-0.152258\pi$
$769$	9.04807e12	+	5.22391e12i	0.933013	+	0.538675i	0.0452496	+	0.998976i	$0.485592\pi$
$770$	−9.21102e10	−	3.35254e10i	−0.00944277	−	0.00343689i
$771$			6.06298e11i			0.0617933i
$772$	6.42528e11	−	1.76533e12i	0.0651050	−	0.178874i
$773$	2.79081e11	+	1.58275e12i	0.0281140	+	0.159443i	0.995633	−	0.0933570i	$-0.0297598\pi$
$773$	2.79081e11	+	1.58275e12i	0.0281140	+	0.159443i	−0.967519	+	0.252800i	$0.918649\pi$
$774$	6.90492e12	−	5.79392e12i	0.691551	−	0.580280i
$775$	6.94868e12	−	8.28112e12i	0.691902	−	0.824577i
$776$	−6.97729e12			−0.690731
$777$	2.79401e10	+	2.35870e11i	0.00275001	+	0.0232155i
$778$	−1.43663e13			−1.40584
$779$	5.55206e12	−	6.61669e12i	0.540176	−	0.643757i
$780$	2.08830e11	−	1.75229e11i	0.0202007	−	0.0169504i
$781$	4.70775e11	+	2.66990e12i	0.0452777	+	0.256782i
$782$	9.15126e12	−	2.51429e13i	0.875086	−	2.40428i
$783$		−	7.38535e12i		−	0.702171i
$784$	−1.08793e13	−	3.95973e12i	−1.02844	−	0.374320i
$785$	3.48986e12	+	2.01487e12i	0.328016	+	0.189380i
$786$	−1.22772e12	+	6.96275e12i	−0.114736	+	0.650698i
$787$	6.72926e12	+	1.16554e13i	0.625289	+	1.08303i	0.988485	+	0.151319i	$0.0483522\pi$
$787$	6.72926e12	+	1.16554e13i	0.625289	+	1.08303i	−0.363196	+	0.931713i	$0.618314\pi$
$788$	−5.58562e11	+	9.67458e11i	−0.0516064	+	0.0893849i
$789$	5.58984e11	+	4.69043e11i	0.0513514	+	0.0430890i
$790$	3.45492e12	−	6.09195e11i	0.315585	−	0.0556461i
$791$	7.29311e11	−	4.21068e11i	0.0662397	−	0.0382435i
$792$	7.66188e11	+	2.10508e12i	0.0691946	+	0.190110i
$793$	−1.12880e13	+	4.10848e12i	−1.01365	+	0.368937i
$794$	1.95915e13	+	3.45451e12i	1.74935	+	0.308457i
$795$	1.43632e12	+	1.71174e12i	0.127526	+	0.151980i
$796$	7.50090e11	+	8.93923e11i	0.0662224	+	0.0789207i
$797$	−9.31908e10	−	1.64320e10i	−0.00818108	−	0.00144254i	0.169556	−	0.985521i	$-0.445767\pi$
$797$	−9.31908e10	−	1.64320e10i	−0.00818108	−	0.00144254i	−0.177737	+	0.984078i	$0.556878\pi$
$798$	−1.45124e11	+	5.28209e10i	−0.0126685	+	0.00461097i
$799$	7.98859e11	+	2.19485e12i	0.0693441	+	0.190521i
$800$	−1.47614e12	+	8.52249e11i	−0.127416	+	0.0735634i
$801$	1.02188e13	−	1.80184e12i	0.877105	−	0.154657i
$802$	4.70822e12	+	3.95067e12i	0.401858	+	0.337199i
$803$	1.77723e12	−	3.07826e12i	0.150843	−	0.261267i
$804$	−3.19106e11	−	5.52707e11i	−0.0269329	−	0.0466491i
$805$	1.47282e11	−	8.35278e11i	0.0123614	−	0.0701051i
$806$	−2.05004e13	−	1.18359e13i	−1.71102	−	0.987856i
$807$	4.63887e12	+	1.68841e12i	0.385018	+	0.140135i
$808$			1.25005e12i			0.103175i
$809$	−7.75777e11	+	2.13143e12i	−0.0636750	+	0.174946i	−0.967450	−	0.253062i	$-0.918562\pi$
$809$	−7.75777e11	+	2.13143e12i	−0.0636750	+	0.174946i	0.903775	+	0.428008i	$0.140784\pi$
$810$	8.40139e11	+	4.76466e12i	0.0685754	+	0.388911i
$811$	4.33947e11	−	3.64125e11i	0.0352243	−	0.0295567i	−0.625006	−	0.780620i	$-0.714903\pi$
$811$	4.33947e11	−	3.64125e11i	0.0352243	−	0.0295567i	0.660230	+	0.751064i	$0.270459\pi$
$812$	−6.28071e10	+	7.48506e10i	−0.00506999	+	0.00604217i
$813$	−5.86983e12			−0.471214
$814$	3.23430e12	−	3.83121e11i	0.258208	−	0.0305862i
$815$	1.23022e12			0.0976732
$816$	4.15153e12	−	4.94760e12i	0.327795	−	0.390651i
$817$	−5.21483e12	+	4.37576e12i	−0.409487	+	0.343601i
$818$	−1.99521e12	−	1.13154e13i	−0.155811	−	0.883648i
$819$	−2.94734e11	+	8.09775e11i	−0.0228904	+	0.0628908i
$820$		−	1.29446e12i		−	0.0999829i
$821$	−1.02717e13	−	3.73859e12i	−0.789038	−	0.287186i	−0.0841021	−	0.996457i	$-0.526802\pi$
$821$	−1.02717e13	−	3.73859e12i	−0.789038	−	0.287186i	−0.704936	+	0.709271i	$0.749024\pi$
$822$	−5.24008e12	−	3.02536e12i	−0.400327	−	0.231129i
$823$	2.46755e12	−	1.39942e13i	0.187485	−	1.06328i	−0.735236	−	0.677811i	$-0.762929\pi$
$823$	2.46755e12	−	1.39942e13i	0.187485	−	1.06328i	0.922721	−	0.385469i	$-0.125960\pi$
$824$	−4.02913e12	−	6.97865e12i	−0.304466	−	0.527350i
$825$	3.81935e11	−	6.61530e11i	0.0287043	−	0.0497172i
$826$	6.58759e11	+	5.52764e11i	0.0492398	+	0.0413171i
$827$	3.60006e12	−	6.34788e11i	0.267630	−	0.0471904i	−0.0382225	−	0.999269i	$-0.512170\pi$
$827$	3.60006e12	−	6.34788e11i	0.267630	−	0.0471904i	0.305853	+	0.952079i	$0.401058\pi$
$828$	2.11255e12	−	1.21968e12i	0.156196	−	0.0901798i
$829$	−3.83303e11	−	1.05312e12i	−0.0281869	−	0.0774428i	0.924801	−	0.380451i	$-0.124231\pi$
$829$	−3.83303e11	−	1.05312e12i	−0.0281869	−	0.0774428i	−0.952988	+	0.303008i	$0.902009\pi$
$830$	−9.04824e12	+	3.29329e12i	−0.661778	+	0.240868i
$831$	1.48341e12	+	2.61565e11i	0.107908	+	0.0190272i
$832$	−8.84022e12	−	1.05354e13i	−0.639600	−	0.762245i
$833$	1.17155e13	+	1.39620e13i	0.843061	+	1.00472i
$834$	4.90724e11	+	8.65278e10i	0.0351229	+	0.00619311i
$835$	8.09496e12	−	2.94632e12i	0.576269	−	0.209745i
$836$	7.28201e10	+	2.00072e11i	0.00515612	+	0.0141663i
$837$	−1.32266e13	+	7.63636e12i	−0.931499	+	0.537801i
$838$	−2.57366e13	+	4.53805e12i	−1.80282	+	0.317886i
$839$	−1.06709e13	−	8.95397e12i	−0.743487	−	0.623860i	0.190285	−	0.981729i	$-0.439059\pi$
$839$	−1.06709e13	−	8.95397e12i	−0.743487	−	0.623860i	−0.933772	+	0.357869i	$0.883503\pi$
$840$	9.19583e10	−	1.59276e11i	0.00637286	−	0.0110381i
$841$	9.41300e11	+	1.63038e12i	0.0648853	+	0.112385i
$842$	2.74658e12	−	1.55767e13i	0.188317	−	1.06800i
$843$	4.10100e12	+	2.36771e12i	0.279682	+	0.161475i
$844$	−7.43420e11	−	2.70583e11i	−0.0504305	−	0.0183552i
$845$			2.79881e12i			0.188851i
$846$	−7.24400e11	+	1.99027e12i	−0.0486196	+	0.133581i
$847$	−1.62176e11	−	9.19747e11i	−0.0108271	−	0.0614035i
$848$	−1.22725e13	+	1.02978e13i	−0.814986	+	0.683855i
$849$	−1.71590e12	+	2.04493e12i	−0.113346	+	0.135081i
$850$	1.39758e13			0.918316
$851$	8.12439e12	+	2.69850e13i	0.531016	+	1.76376i
$852$	6.40143e11			0.0416197
$853$	2.77056e12	−	3.30182e12i	0.179183	−	0.213542i	−0.668976	−	0.743284i	$-0.733267\pi$
$853$	2.77056e12	−	3.30182e12i	0.179183	−	0.213542i	0.848159	+	0.529743i	$0.177711\pi$
$854$	7.81270e11	−	6.55563e11i	0.0502621	−	0.0421749i
$855$	−7.56795e11	−	4.29200e12i	−0.0484318	−	0.274670i
$856$	−3.08563e12	+	8.47771e12i	−0.196432	+	0.539693i
$857$			2.22118e13i			1.40660i	0.710894	+	0.703299i	$0.248291\pi$
$857$			2.22118e13i			1.40660i	−0.710894	+	0.703299i	$0.751709\pi$
$858$	−1.57181e12	−	5.72093e11i	−0.0990167	−	0.0360391i
$859$	−1.56611e13	−	9.04192e12i	−0.981413	−	0.566619i	−0.0787166	−	0.996897i	$-0.525082\pi$
$859$	−1.56611e13	−	9.04192e12i	−0.981413	−	0.566619i	−0.902696	+	0.430278i	$0.858416\pi$
$860$	−1.77157e11	+	1.00471e12i	−0.0110437	+	0.0626320i
$861$	−2.89620e11	−	5.01636e11i	−0.0179603	−	0.0311082i
$862$	1.13433e13	−	1.96472e13i	0.699774	−	1.21204i
$863$	2.32308e13	+	1.94930e13i	1.42566	+	1.19627i	0.948223	+	0.317606i	$0.102879\pi$
$863$	2.32308e13	+	1.94930e13i	1.42566	+	1.19627i	0.477438	+	0.878665i	$0.341565\pi$
$864$	2.37154e12	−	4.18166e11i	0.144783	−	0.0255292i
$865$	8.97377e12	−	5.18101e12i	0.545007	−	0.314660i
$866$	−9.97206e12	−	2.73980e13i	−0.602496	−	1.65535i
$867$	−4.04909e12	+	1.47375e12i	−0.243373	+	0.0885803i
$868$	1.98993e11	+	3.50879e10i	0.0118987	+	0.00209806i
$869$	−1.39114e12	−	1.65789e12i	−0.0827523	−	0.0986204i
$870$	2.49548e12	+	2.97400e12i	0.147678	+	0.175996i
$871$	2.63441e13	+	4.64518e12i	1.55097	+	0.273477i
$872$	2.17091e13	−	7.90147e12i	1.27150	−	0.462790i
$873$	3.79225e12	+	1.04191e13i	0.220970	+	0.607110i
$874$	−1.58690e13	+	9.16197e12i	−0.919916	+	0.531114i
$875$	1.09624e12	−	1.93296e11i	0.0632219	−	0.0111477i
$876$	−6.42928e11	−	5.39480e11i	−0.0368887	−	0.0309533i
$877$	−4.24632e12	+	7.35485e12i	−0.242390	+	0.419832i	−0.961395	−	0.275174i	$-0.911265\pi$
$877$	−4.24632e12	+	7.35485e12i	−0.242390	+	0.419832i	0.719005	+	0.695005i	$0.244598\pi$
$878$	4.41235e12	+	7.64242e12i	0.250579	+	0.434016i
$879$	−6.23505e10	+	3.53607e11i	−0.00352281	+	0.0199789i
$880$	−2.43125e12	−	1.40368e12i	−0.136665	−	0.0789035i
$881$	−1.29694e13	−	4.72048e12i	−0.725318	−	0.263994i	−0.0471362	−	0.998888i	$-0.515009\pi$
$881$	−1.29694e13	−	4.72048e12i	−0.725318	−	0.263994i	−0.678182	+	0.734894i	$0.737232\pi$
$882$			1.65273e13i			0.919588i
$883$	1.60807e12	−	4.41813e12i	0.0890187	−	0.244577i	−0.887192	−	0.461400i	$-0.847347\pi$
$883$	1.60807e12	−	4.41813e12i	0.0890187	−	0.244577i	0.976211	+	0.216823i	$0.0695695\pi$
$884$	−5.34296e11	−	3.03014e12i	−0.0294270	−	0.166889i
$885$	2.63154e12	−	2.20812e12i	0.144200	−	0.120998i
$886$	−1.93267e13	+	2.30327e13i	−1.05368	+	1.25572i
$887$	−3.41680e13			−1.85338			−0.926688	−	0.375831i	$-0.877357\pi$
$887$	−3.41680e13			−1.85338			−0.926688	+	0.375831i	$0.877357\pi$
$888$	−3.45855e11	+	6.10110e12i	−0.0186653	+	0.329268i
$889$	2.32652e12			0.124925
$890$	−7.50860e12	+	8.94840e12i	−0.401147	+	0.478069i
$891$	2.28639e12	−	1.91851e12i	0.121535	−	0.101980i
$892$	6.09549e10	+	3.45693e11i	0.00322379	+	0.0182830i
$893$	5.47091e11	−	1.50312e12i	0.0287891	−	0.0790974i
$894$		−	3.59985e12i		−	0.188480i
$895$	8.99147e12	+	3.27263e12i	0.468411	+	0.170488i
$896$	1.25806e12	+	7.26342e11i	0.0652102	+	0.0376491i
$897$	2.51329e12	−	1.42536e13i	0.129621	−	0.735120i
$898$	8.90195e12	+	1.54186e13i	0.456816	+	0.791229i
$899$	1.69468e13	−	2.93527e13i	0.865305	−	1.49875i
$900$	9.76062e11	+	8.19013e11i	0.0495891	+	0.0416102i
$901$	2.48376e13	−	4.37953e12i	1.25559	−	0.221394i
$902$	−6.87854e12	+	3.97133e12i	−0.345992	+	0.199759i
$903$	1.56138e11	+	4.28986e11i	0.00781473	+	0.0214708i
$904$	2.03598e13	−	7.41037e12i	1.01395	−	0.369047i
$905$	−5.46867e12	−	9.64275e11i	−0.270996	−	0.0477840i
$906$	2.05284e11	+	2.44648e11i	0.0101223	+	0.0120633i
$907$	1.27515e13	+	1.51967e13i	0.625648	+	0.745618i	0.982031	−	0.188722i	$-0.0604345\pi$
$907$	1.27515e13	+	1.51967e13i	0.625648	+	0.745618i	−0.356383	+	0.934340i	$0.615990\pi$
$908$	3.05037e12	+	5.37863e11i	0.148925	+	0.0262594i
$909$	1.86668e12	−	6.79417e11i	0.0906845	−	0.0330065i
$910$	−3.31799e11	−	9.11611e11i	−0.0160394	−	0.0440680i
$911$	−2.36635e13	+	1.36621e13i	−1.13827	+	0.657182i	−0.946002	−	0.324160i	$-0.894918\pi$
$911$	−2.36635e13	+	1.36621e13i	−1.13827	+	0.657182i	−0.192271	+	0.981342i	$0.561585\pi$
$912$	−4.35594e12	+	7.68070e11i	−0.208500	+	0.0367641i
$913$	4.55038e12	+	3.81822e12i	0.216735	+	0.181862i
$914$	1.88899e12	−	3.27183e12i	0.0895308	−	0.155072i
$915$	−2.03704e12	−	3.52826e12i	−0.0960739	−	0.166405i
$916$	4.97800e11	−	2.82317e12i	0.0233628	−	0.132497i
$917$	2.19070e12	+	1.26480e12i	0.102311	+	0.0590692i
$918$	−1.85543e13	−	6.75321e12i	−0.862288	−	0.313847i
$919$			3.37556e12i			0.156108i	0.996949	+	0.0780541i	$0.0248707\pi$
$919$			3.37556e12i			0.156108i	−0.996949	+	0.0780541i	$0.975129\pi$
$920$	7.46341e12	−	2.05056e13i	0.343473	−	0.943684i
$921$	7.92226e11	+	4.49293e12i	0.0362811	+	0.205760i
$922$	−3.04705e13	+	2.55678e13i	−1.38864	+	1.16521i
$923$	−1.72470e13	+	2.05541e13i	−0.782177	+	0.932162i
$924$	1.42781e10			0.000644387
$925$	−1.17937e13	+	8.80854e12i	−0.529678	+	0.395609i
$926$	2.45980e13			1.09939
$927$	−8.23127e12	+	9.80964e12i	−0.366107	+	0.436309i
$928$	−4.09386e12	+	3.43516e12i	−0.181204	+	0.152048i
$929$	1.89057e12	+	1.07219e13i	0.0832763	+	0.472283i	0.997715	+	0.0675594i	$0.0215212\pi$
$929$	1.89057e12	+	1.07219e13i	0.0832763	+	0.472283i	−0.914439	+	0.404724i	$0.867368\pi$
$930$	2.74589e12	−	7.54428e12i	0.120368	−	0.330708i
$931$		−	1.24820e13i		−	0.544515i
$932$	5.55074e11	+	2.02030e11i	0.0240979	+	0.00877092i
$933$	5.16122e12	+	2.97983e12i	0.222990	+	0.128743i
$934$	−9.20750e11	+	5.22183e12i	−0.0395896	+	0.224524i
$935$	2.20978e12	+	3.82745e12i	0.0945576	+	0.163779i
$936$	−1.10855e13	+	1.92006e13i	−0.472078	+	0.817663i
$937$	−3.10361e12	−	2.60424e12i	−0.131534	−	0.110371i	0.574647	−	0.818401i	$-0.305139\pi$
$937$	−3.10361e12	−	2.60424e12i	−0.131534	−	0.110371i	−0.706182	+	0.708031i	$0.749584\pi$
$938$	−2.23667e12	+	3.94385e11i	−0.0943385	+	0.0166344i
$939$	6.90787e12	−	3.98826e12i	0.289967	−	0.167413i
$940$	−8.19901e10	−	2.25266e11i	−0.00342520	−	0.00941066i
$941$	−3.54393e13	+	1.28988e13i	−1.47344	+	0.536287i	−0.949031	−	0.315182i	$-0.897934\pi$
$941$	−3.54393e13	+	1.28988e13i	−1.47344	+	0.536287i	−0.524405	+	0.851469i	$0.675712\pi$
$942$	−5.74963e12	−	1.01382e12i	−0.237909	−	0.0419498i
$943$	−4.41764e13	−	5.26474e13i	−1.81923	−	2.16807i
$944$	1.58313e13	+	1.88670e13i	0.648847	+	0.773266i
$945$	−6.16397e11	−	1.08687e11i	−0.0251430	−	0.00443339i
$946$	5.88235e12	−	2.14100e12i	0.238803	−	0.0869173i
$947$	−1.51741e13	−	4.16904e13i	−0.613094	−	1.68446i	−0.723284	−	0.690550i	$-0.757368\pi$
$947$	−1.51741e13	−	4.16904e13i	−0.613094	−	1.68446i	0.110191	−	0.993910i	$-0.464854\pi$
$948$	−4.42554e11	+	2.55508e11i	−0.0177962	+	0.0102747i
$949$	3.46440e13	−	6.10866e12i	1.38653	−	0.244483i
$950$	−7.33197e12	−	6.15225e12i	−0.292055	−	0.245063i
$951$	3.65278e12	−	6.32679e12i	0.144814	−	0.250825i
$952$	−1.03792e12	−	1.79773e12i	−0.0409542	−	0.0709347i
$953$	−2.52162e12	+	1.43008e13i	−0.0990289	+	0.561621i	0.894409	+	0.447250i	$0.147596\pi$
$953$	−2.52162e12	+	1.43008e13i	−0.0990289	+	0.561621i	−0.993438	+	0.114371i	$0.963515\pi$
$954$	1.98060e13	+	1.14350e13i	0.774157	+	0.446960i
$955$	−1.06978e13	−	3.89369e12i	−0.416180	−	0.151477i
$956$		−	1.22583e12i		−	0.0474648i
$957$	8.19131e11	−	2.25054e12i	0.0315682	−	0.0867329i
$958$	−4.56325e12	−	2.58795e13i	−0.175037	−	0.992684i
$959$	−1.65838e12	+	1.39155e12i	−0.0633142	+	0.0531269i
$960$	2.99822e12	−	3.57314e12i	0.113931	−	0.135778i
$961$	−4.36515e13			−1.65099
$962$	2.34801e13	+	2.20836e13i	0.883917	+	0.831346i
$963$	1.43368e13			0.537196
$964$	−1.71888e12	+	2.04848e12i	−0.0641060	+	0.0763985i
$965$	−2.04580e13	+	1.71663e13i	−0.759434	+	0.637241i
$966$	2.13383e11	+	1.21016e12i	0.00788431	+	0.0447141i
$967$	1.83336e13	−	5.03711e13i	0.674261	−	1.85252i	0.178801	−	0.983885i	$-0.442778\pi$
$967$	1.83336e13	−	5.03711e13i	0.674261	−	1.85252i	0.495460	−	0.868631i	$-0.335000\pi$
$968$		−	2.40283e13i		−	0.879598i
$969$	6.54329e12	+	2.38156e12i	0.238418	+	0.0867771i
$970$	−1.08099e13	−	6.24109e12i	−0.392056	−	0.226354i
$971$	−5.07942e12	+	2.88068e13i	−0.183370	+	1.03994i	0.744663	+	0.667441i	$0.232610\pi$
$971$	−5.07942e12	+	2.88068e13i	−0.183370	+	1.03994i	−0.928032	+	0.372500i	$0.878501\pi$
$972$	−1.37985e12	−	2.38997e12i	−0.0495830	−	0.0858804i
$973$	8.91414e10	−	1.54397e11i	0.00318839	−	0.00552245i
$974$	2.69815e13	+	2.26402e13i	0.960620	+	0.806056i
$975$	7.44513e12	−	1.31278e12i	0.263846	−	0.0465232i
$976$	2.52961e13	−	1.46047e13i	0.892339	−	0.515192i
$977$	2.50051e12	+	6.87010e12i	0.0878018	+	0.241233i	0.975820	−	0.218574i	$-0.0701406\pi$
$977$	2.50051e12	+	6.87010e12i	0.0878018	+	0.241233i	−0.888019	+	0.459808i	$0.847918\pi$
$978$	−1.67487e12	+	6.09603e11i	−0.0585405	+	0.0213070i
$979$	7.09673e12	+	1.25134e12i	0.246909	+	0.0435366i
$980$	−1.20241e12	−	1.43298e12i	−0.0416423	−	0.0496274i
$981$	−2.35984e13	−	2.81234e13i	−0.813526	−	0.969523i
$982$	2.04200e13	+	3.60060e12i	0.700735	+	0.123559i
$983$	2.39653e13	−	8.72266e12i	0.818639	−	0.297960i	0.101451	−	0.994841i	$-0.467651\pi$
$983$	2.39653e13	−	8.72266e12i	0.818639	−	0.297960i	0.717187	+	0.696880i	$0.245429\pi$
$984$	−5.09702e12	−	1.40039e13i	−0.173316	−	0.476181i
$985$	1.37531e13	−	7.94036e12i	0.465519	−	0.268768i
$986$	4.31530e13	−	7.60904e12i	1.45400	−	0.256380i
$987$	−8.21738e10	−	6.89520e10i	−0.00275617	−	0.00231270i
$988$	−1.05359e12	+	1.82487e12i	−0.0351775	+	0.0609292i
$989$	2.70827e13	+	4.69086e13i	0.900138	+	1.55908i
$990$	−6.95916e11	+	3.94674e12i	−0.0230249	+	0.130581i
$991$	−1.88309e13	−	1.08720e13i	−0.620211	−	0.358079i	0.156740	−	0.987640i	$-0.449901\pi$
$991$	−1.88309e13	−	1.08720e13i	−0.620211	−	0.358079i	−0.776951	+	0.629561i	$0.783235\pi$
$992$	1.03851e13	+	3.77987e12i	0.340493	+	0.123929i
$993$		−	8.69119e12i		−	0.283666i
$994$	7.79138e11	−	2.14066e12i	0.0253149	−	0.0695520i
$995$	−2.88061e12	−	1.63368e13i	−0.0931710	−	0.528399i
$996$	1.07444e12	−	9.01560e11i	0.0345951	−	0.0290287i
$997$	−1.06910e13	+	1.27410e13i	−0.342680	+	0.408391i	−0.909668	−	0.415336i	$-0.863664\pi$
$997$	−1.06910e13	+	1.27410e13i	−0.342680	+	0.408391i	0.566988	+	0.823726i	$0.308109\pi$
$998$	−4.32763e13			−1.38090
$999$	1.99137e13	−	5.99543e12i	0.632567	−	0.190448i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.10.h.a.3.8	✓	168
37.25	even	18	inner	37.10.h.a.25.8	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.h.a.3.8	✓	168	1.1	even	1	trivial
37.10.h.a.25.8	yes	168	37.25	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	37.h (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-15.3360 + 18.2767i) q^{2} +(-37.8456 + 31.7562i) q^{3} +(-9.93794 - 56.3609i) q^{4} +(-278.257 + 764.505i) q^{5} -1178.71i q^{6} +(-396.292 - 144.238i) q^{7} +(-9396.50 - 5425.07i) q^{8} +(-2994.09 + 16980.3i) q^{9} +O(q^{10})\)	\(q+(-15.3360 + 18.2767i) q^{2} +(-37.8456 + 31.7562i) q^{3} +(-9.93794 - 56.3609i) q^{4} +(-278.257 + 764.505i) q^{5} -1178.71i q^{6} +(-396.292 - 144.238i) q^{7} +(-9396.50 - 5425.07i) q^{8} +(-2994.09 + 16980.3i) q^{9} +(-9705.29 - 16810.1i) q^{10} +(-5987.20 + 10370.1i) q^{11} +(2165.92 + 1817.42i) q^{12} +(-116710. + 20579.1i) q^{13} +(8713.72 - 5030.87i) q^{14} +(-13747.0 - 37769.6i) q^{15} +(270792. - 98560.2i) q^{16} +(-446767. - 78777.1i) q^{17} +(-264427. - 315132. i) q^{18} +(199704. + 237998. i) q^{19} +(45853.5 + 8085.21i) q^{20} +(19578.4 - 7125.94i) q^{21} +(-97712.4 - 268463. i) q^{22} +(2.14085e6 - 1.23602e6i) q^{23} +(527896. - 93082.3i) q^{24} +(989139. + 829986. i) q^{25} +(1.41374e6 - 2.44867e6i) q^{26} +(-912126. - 1.57985e6i) q^{27} +(-4191.08 + 23768.8i) q^{28} +(3.50604e6 + 2.02421e6i) q^{29} +(901127. + 327983. i) q^{30} -8.37204e6i q^{31} +(-451487. + 1.24045e6i) q^{32} +(-102727. - 582595. i) q^{33} +(8.29140e6 - 6.95731e6i) q^{34} +(220542. - 262832. i) q^{35} +986779. q^{36} +(-2.61183e6 + 1.10968e7i) q^{37} -7.41248e6 q^{38} +(3.76344e6 - 4.48509e6i) q^{39} +(6.76214e6 - 5.67411e6i) q^{40} +(-4.82767e6 - 2.73791e7i) q^{41} +(-170015. + 467112. i) q^{42} +2.19112e7i q^{43} +(643971. + 234386. i) q^{44} +(-1.21484e7 - 7.01389e6i) q^{45} +(-1.02416e7 + 5.80833e7i) q^{46} +(-2.57430e6 - 4.45881e6i) q^{47} +(-7.11838e6 + 1.23294e7i) q^{48} +(-3.07764e7 - 2.58245e7i) q^{49} +(-3.03388e7 + 5.34956e6i) q^{50} +(1.94098e7 - 1.12063e7i) q^{51} +(2.31971e6 + 6.37335e6i) q^{52} +(-5.22413e7 + 1.90143e7i) q^{53} +(4.28628e7 + 7.55787e6i) q^{54} +(-6.26205e6 - 7.46282e6i) q^{55} +(2.94125e6 + 3.50525e6i) q^{56} +(-1.51158e7 - 2.66533e6i) q^{57} +(-9.07645e7 + 3.30356e7i) q^{58} +(2.92315e7 + 8.03129e7i) q^{59} +(-1.99211e6 + 1.15014e6i) q^{60} +(9.98218e7 - 1.76013e7i) q^{61} +(1.53013e8 + 1.28393e8i) q^{62} +(3.63574e6 - 6.29729e6i) q^{63} +(5.80243e7 + 1.00501e8i) q^{64} +(1.67425e7 - 9.49515e7i) q^{65} +(1.22234e7 + 7.05715e6i) q^{66} +(-2.12111e8 - 7.72020e7i) q^{67} +2.59631e7i q^{68} +(-4.17704e7 + 1.14763e8i) q^{69} +(1.42147e6 + 8.06157e6i) q^{70} +(1.73438e8 - 1.45532e8i) q^{71} +(1.20253e8 - 1.43312e8i) q^{72} -2.96839e8 q^{73} +(-1.62759e8 - 2.17917e8i) q^{74} -6.37918e7 q^{75} +(1.14291e7 - 1.36207e7i) q^{76} +(3.86845e6 - 3.24602e6i) q^{77} +(2.42567e7 + 1.37566e8i) q^{78} +(-6.18158e7 + 1.69837e8i) q^{79} +2.34447e8i q^{80} +(-2.34222e8 - 8.52499e7i) q^{81} +(5.74436e8 + 3.31651e8i) q^{82} +(8.61409e7 - 4.88530e8i) q^{83} +(-596193. - 1.03264e6i) q^{84} +(1.84542e8 - 3.19636e8i) q^{85} +(-4.00465e8 - 3.36030e8i) q^{86} +(-1.96970e8 + 3.47310e7i) q^{87} +(1.12518e8 - 6.49620e7i) q^{88} +(-2.05828e8 - 5.65508e8i) q^{89} +(3.14498e8 - 1.14468e8i) q^{90} +(4.92194e7 + 8.67871e6i) q^{91} +(-9.09388e7 - 1.08377e8i) q^{92} +(2.65865e8 + 3.16845e8i) q^{93} +(1.20972e8 + 2.13306e7i) q^{94} +(-2.37520e8 + 8.64501e7i) q^{95} +(-2.23052e7 - 6.12831e7i) q^{96} +(5.56906e8 - 3.21530e8i) q^{97} +(9.43973e8 - 1.66448e8i) q^{98} +(-1.58162e8 - 1.32714e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 45 q^{2} + 216 q^{3} + 249 q^{4} + 177 q^{5} - 5820 q^{7} - 74520 q^{8} - 30198 q^{9}+O(q^{10}) \) 168 * q + 45 * q^2 + 216 * q^3 + 249 * q^4 + 177 * q^5 - 5820 * q^7 - 74520 * q^8 - 30198 * q^9	\( 168 q + 45 q^{2} + 216 q^{3} + 249 q^{4} + 177 q^{5} - 5820 q^{7} - 74520 q^{8} - 30198 q^{9} - 60003 q^{10} + 175689 q^{11} - 307257 q^{12} - 713598 q^{13} + 290583 q^{14} - 385260 q^{15} + 292473 q^{16} + 951645 q^{17} - 2634174 q^{18} + 87108 q^{19} - 6701172 q^{20} + 1892136 q^{21} - 1410435 q^{22} - 9 q^{23} + 6919605 q^{24} - 1830519 q^{25} - 12361155 q^{26} + 12227553 q^{27} - 14971305 q^{28} - 8346069 q^{29} + 32076480 q^{30} + 25901316 q^{32} + 29661003 q^{33} + 17761257 q^{34} - 25104648 q^{35} - 302330892 q^{36} - 89711496 q^{37} + 137852370 q^{38} + 3073230 q^{39} + 72127485 q^{40} + 40690731 q^{41} + 229015377 q^{42} + 187195086 q^{44} - 293199021 q^{45} - 286926930 q^{46} - 134086527 q^{47} + 86156133 q^{48} + 67568640 q^{49} + 134153859 q^{50} - 528106959 q^{51} + 402280539 q^{52} + 147470676 q^{53} + 422122437 q^{54} - 55011861 q^{55} - 616228263 q^{56} - 449072832 q^{57} + 529606191 q^{58} + 773443290 q^{59} + 1433547972 q^{60} + 469275144 q^{61} - 914552304 q^{62} - 673379979 q^{63} + 1146585192 q^{64} - 243884745 q^{65} + 1805055381 q^{66} + 214516206 q^{67} + 722409993 q^{69} - 2605801512 q^{70} - 1455384636 q^{71} - 4689293691 q^{72} + 930909090 q^{73} - 1261741251 q^{74} + 3013150476 q^{75} + 195486513 q^{76} + 1827454371 q^{77} + 1710012453 q^{78} + 1230271476 q^{79} + 2262925611 q^{81} - 3346032141 q^{82} - 2122951164 q^{83} - 6124511730 q^{84} - 39169146 q^{85} - 2603533938 q^{86} + 1185003879 q^{87} - 261497646 q^{88} + 1603969074 q^{89} + 7288796094 q^{90} - 4883515182 q^{91} - 7533267018 q^{92} + 1209552852 q^{93} + 1712695200 q^{94} + 2036912394 q^{95} + 7661250639 q^{96} - 7583351877 q^{97} - 10074558573 q^{98} - 7520510685 q^{99}+O(q^{100}) \) 168 * q + 45 * q^2 + 216 * q^3 + 249 * q^4 + 177 * q^5 - 5820 * q^7 - 74520 * q^8 - 30198 * q^9 - 60003 * q^10 + 175689 * q^11 - 307257 * q^12 - 713598 * q^13 + 290583 * q^14 - 385260 * q^15 + 292473 * q^16 + 951645 * q^17 - 2634174 * q^18 + 87108 * q^19 - 6701172 * q^20 + 1892136 * q^21 - 1410435 * q^22 - 9 * q^23 + 6919605 * q^24 - 1830519 * q^25 - 12361155 * q^26 + 12227553 * q^27 - 14971305 * q^28 - 8346069 * q^29 + 32076480 * q^30 + 25901316 * q^32 + 29661003 * q^33 + 17761257 * q^34 - 25104648 * q^35 - 302330892 * q^36 - 89711496 * q^37 + 137852370 * q^38 + 3073230 * q^39 + 72127485 * q^40 + 40690731 * q^41 + 229015377 * q^42 + 187195086 * q^44 - 293199021 * q^45 - 286926930 * q^46 - 134086527 * q^47 + 86156133 * q^48 + 67568640 * q^49 + 134153859 * q^50 - 528106959 * q^51 + 402280539 * q^52 + 147470676 * q^53 + 422122437 * q^54 - 55011861 * q^55 - 616228263 * q^56 - 449072832 * q^57 + 529606191 * q^58 + 773443290 * q^59 + 1433547972 * q^60 + 469275144 * q^61 - 914552304 * q^62 - 673379979 * q^63 + 1146585192 * q^64 - 243884745 * q^65 + 1805055381 * q^66 + 214516206 * q^67 + 722409993 * q^69 - 2605801512 * q^70 - 1455384636 * q^71 - 4689293691 * q^72 + 930909090 * q^73 - 1261741251 * q^74 + 3013150476 * q^75 + 195486513 * q^76 + 1827454371 * q^77 + 1710012453 * q^78 + 1230271476 * q^79 + 2262925611 * q^81 - 3346032141 * q^82 - 2122951164 * q^83 - 6124511730 * q^84 - 39169146 * q^85 - 2603533938 * q^86 + 1185003879 * q^87 - 261497646 * q^88 + 1603969074 * q^89 + 7288796094 * q^90 - 4883515182 * q^91 - 7533267018 * q^92 + 1209552852 * q^93 + 1712695200 * q^94 + 2036912394 * q^95 + 7661250639 * q^96 - 7583351877 * q^97 - 10074558573 * q^98 - 7520510685 * q^99

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