LMFDB - Embedded newform 32.9.h.a.11.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [32,9,Mod(3,32)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(32, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("32.3");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 32 = 2^{5} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	32.h (of order $8$, degree $4$, 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:	$13.0361155220$
Analytic rank:	$0$
Dimension:	$124$
Relative dimension:	$31$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			11.8
Character	$\chi$	$=$	32.11
Dual form			32.9.h.a.3.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.4539 - 11.1717i) q^{2} +(34.8964 + 84.2473i) q^{3} +(6.38569 + 255.920i) q^{4} +(-296.689 + 716.270i) q^{5} +(541.485 - 1354.82i) q^{6} +(-3146.79 + 3146.79i) q^{7} +(2785.93 - 3002.64i) q^{8} +(-1240.52 + 1240.52i) q^{9} +O(q^{10})$	\(q+(-11.4539 - 11.1717i) q^{2} +(34.8964 + 84.2473i) q^{3} +(6.38569 + 255.920i) q^{4} +(-296.689 + 716.270i) q^{5} +(541.485 - 1354.82i) q^{6} +(-3146.79 + 3146.79i) q^{7} +(2785.93 - 3002.64i) q^{8} +(-1240.52 + 1240.52i) q^{9} +(11400.2 - 4889.60i) q^{10} +(8217.21 - 19838.1i) q^{11} +(-21337.8 + 9468.67i) q^{12} +(-10905.6 - 26328.4i) q^{13} +(71198.1 - 888.125i) q^{14} -70697.2 q^{15} +(-65454.4 + 3268.46i) q^{16} +78434.5i q^{17} +(28067.6 - 350.116i) q^{18} +(-78.8755 + 32.6713i) q^{19} +(-185203. - 71354.8i) q^{20} +(-374920. - 155297. i) q^{21} +(-315745. + 135424. i) q^{22} +(-40229.1 - 40229.1i) q^{23} +(350183. + 129926. i) q^{24} +(-148805. - 148805. i) q^{25} +(-169221. + 423398. i) q^{26} +(404946. + 167734. i) q^{27} +(-825421. - 785232. i) q^{28} +(-324418. + 134378. i) q^{29} +(809762. + 789809. i) q^{30} -1.14104e6i q^{31} +(786226. + 693802. i) q^{32} +1.95806e6 q^{33} +(876248. - 898385. i) q^{34} +(-1.32033e6 - 3.18757e6i) q^{35} +(-325397. - 309553. i) q^{36} +(-971788. + 2.34610e6i) q^{37} +(1268.43 + 506.959i) q^{38} +(1.83753e6 - 1.83753e6i) q^{39} +(1.32415e6 + 2.88633e6i) q^{40} +(-160516. + 160516. i) q^{41} +(2.55938e6 + 5.96726e6i) q^{42} +(-1.39352e6 + 3.36426e6i) q^{43} +(5.12944e6 + 1.97627e6i) q^{44} +(-520500. - 1.25660e6i) q^{45} +(11353.9 + 910209. i) q^{46} -7.12098e6 q^{47} +(-2.55948e6 - 5.40030e6i) q^{48} -1.40397e7i q^{49} +(41997.6 + 3.36682e6i) q^{50} +(-6.60790e6 + 2.73708e6i) q^{51} +(6.66834e6 - 2.95909e6i) q^{52} +(3.61684e6 + 1.49814e6i) q^{53} +(-2.76435e6 - 6.44516e6i) q^{54} +(1.17715e7 + 1.17715e7i) q^{55} +(681938. + 1.82154e7i) q^{56} +(-5504.93 - 5504.93i) q^{57} +(5.21710e6 + 2.08514e6i) q^{58} +(-1.12276e7 - 4.65062e6i) q^{59} +(-451450. - 1.80929e7i) q^{60} +(6.31482e6 - 2.61568e6i) q^{61} +(-1.27474e7 + 1.30694e7i) q^{62} -7.80732e6i q^{63} +(-1.25444e6 - 1.67303e7i) q^{64} +2.20938e7 q^{65} +(-2.24275e7 - 2.18748e7i) q^{66} +(-1.11553e7 - 2.69312e7i) q^{67} +(-2.00730e7 + 500859. i) q^{68} +(1.98534e6 - 4.79304e6i) q^{69} +(-2.04876e7 + 5.12606e7i) q^{70} +(-2.54656e7 + 2.54656e7i) q^{71} +(268833. + 7.18085e6i) q^{72} +(4.40649e6 - 4.40649e6i) q^{73} +(3.73408e7 - 1.60156e7i) q^{74} +(7.34367e6 - 1.77292e7i) q^{75} +(-8864.92 - 19977.2i) q^{76} +(3.65685e7 + 8.82841e7i) q^{77} +(-4.15754e7 + 518611. i) q^{78} -3.78380e7 q^{79} +(1.70785e7 - 4.78528e7i) q^{80} +5.14793e7i q^{81} +(3.63177e6 - 45302.7i) q^{82} +(-2.61410e7 + 1.08280e7i) q^{83} +(3.73495e7 - 9.69413e7i) q^{84} +(-5.61803e7 - 2.32706e7i) q^{85} +(5.35459e7 - 2.29661e7i) q^{86} +(-2.26420e7 - 2.26420e7i) q^{87} +(-3.66740e7 - 7.99408e7i) q^{88} +(4.51667e7 + 4.51667e7i) q^{89} +(-8.07658e6 + 2.02079e7i) q^{90} +(1.17167e8 + 4.85323e7i) q^{91} +(1.00385e7 - 1.05523e7i) q^{92} +(9.61296e7 - 3.98182e7i) q^{93} +(8.15633e7 + 7.95535e7i) q^{94} -66189.3i q^{95} +(-3.10145e7 + 9.04486e7i) q^{96} -4.13701e7 q^{97} +(-1.56848e8 + 1.60810e8i) q^{98} +(1.44160e7 + 3.48032e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 124 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 124 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 124 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 34996 q^{10} - 4 q^{11} - 45364 q^{12} - 4 q^{13} + 145580 q^{14} - 8 q^{15} - 278384 q^{16} - 131224 q^{18} - 4 q^{19} + 689996 q^{20} - 4 q^{21} + 6048 q^{22} + 845564 q^{23} - 310832 q^{24} - 4 q^{25} + 1682096 q^{26} - 51076 q^{27} - 1807624 q^{28} - 4 q^{29} - 3968188 q^{30} + 2420456 q^{32} - 8 q^{33} + 4139280 q^{34} - 2415748 q^{35} - 2364816 q^{36} - 4 q^{37} - 4553644 q^{38} + 7650044 q^{39} - 14971800 q^{40} - 4 q^{41} + 17019656 q^{42} - 1859716 q^{43} + 13377860 q^{44} - 26248 q^{45} + 11790684 q^{46} - 8 q^{47} - 21819984 q^{48} - 49149676 q^{50} - 27697792 q^{51} - 33503196 q^{52} - 5358724 q^{53} + 82403296 q^{54} + 46326780 q^{55} + 87708200 q^{56} - 4 q^{57} - 37235424 q^{58} - 44938756 q^{59} - 167711176 q^{60} + 48952060 q^{61} + 23721528 q^{62} + 27135128 q^{64} - 8 q^{65} + 226680332 q^{66} + 93380476 q^{67} - 491760 q^{68} - 17273092 q^{69} - 167238952 q^{70} - 79832068 q^{71} - 184202092 q^{72} - 4 q^{73} + 28015148 q^{74} - 27399560 q^{75} + 201789948 q^{76} - 94964356 q^{77} + 473461108 q^{78} + 144406520 q^{79} - 447998920 q^{80} - 231632004 q^{82} - 140384644 q^{83} + 263072 q^{84} + 1562496 q^{85} + 268005440 q^{86} - 149712644 q^{87} + 220344096 q^{88} - 4 q^{89} + 51924392 q^{90} + 350400764 q^{91} - 622977496 q^{92} + 26240 q^{93} - 100742552 q^{94} + 101686144 q^{96} - 8 q^{97} + 721239576 q^{98} - 630043272 q^{99}+O(q^{100}) \) 124 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 34996 * q^10 - 4 * q^11 - 45364 * q^12 - 4 * q^13 + 145580 * q^14 - 8 * q^15 - 278384 * q^16 - 131224 * q^18 - 4 * q^19 + 689996 * q^20 - 4 * q^21 + 6048 * q^22 + 845564 * q^23 - 310832 * q^24 - 4 * q^25 + 1682096 * q^26 - 51076 * q^27 - 1807624 * q^28 - 4 * q^29 - 3968188 * q^30 + 2420456 * q^32 - 8 * q^33 + 4139280 * q^34 - 2415748 * q^35 - 2364816 * q^36 - 4 * q^37 - 4553644 * q^38 + 7650044 * q^39 - 14971800 * q^40 - 4 * q^41 + 17019656 * q^42 - 1859716 * q^43 + 13377860 * q^44 - 26248 * q^45 + 11790684 * q^46 - 8 * q^47 - 21819984 * q^48 - 49149676 * q^50 - 27697792 * q^51 - 33503196 * q^52 - 5358724 * q^53 + 82403296 * q^54 + 46326780 * q^55 + 87708200 * q^56 - 4 * q^57 - 37235424 * q^58 - 44938756 * q^59 - 167711176 * q^60 + 48952060 * q^61 + 23721528 * q^62 + 27135128 * q^64 - 8 * q^65 + 226680332 * q^66 + 93380476 * q^67 - 491760 * q^68 - 17273092 * q^69 - 167238952 * q^70 - 79832068 * q^71 - 184202092 * q^72 - 4 * q^73 + 28015148 * q^74 - 27399560 * q^75 + 201789948 * q^76 - 94964356 * q^77 + 473461108 * q^78 + 144406520 * q^79 - 447998920 * q^80 - 231632004 * q^82 - 140384644 * q^83 + 263072 * q^84 + 1562496 * q^85 + 268005440 * q^86 - 149712644 * q^87 + 220344096 * q^88 - 4 * q^89 + 51924392 * q^90 + 350400764 * q^91 - 622977496 * q^92 + 26240 * q^93 - 100742552 * q^94 + 101686144 * q^96 - 8 * q^97 + 721239576 * q^98 - 630043272 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

$n$	$5$	$31$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$

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 $

$2$	−11.4539	−	11.1717i	−0.715872	−	0.698232i
$2$	−11.4539	−	11.1717i	−0.715872	−	0.698232i
$3$	34.8964	+	84.2473i	0.430819	+	1.04009i	0.979024	+	0.203746i	$0.0653116\pi$
$3$	34.8964	+	84.2473i	0.430819	+	1.04009i	−0.548204	+	0.836344i	$0.684688\pi$
$4$	6.38569	+	255.920i	0.0249441	+	0.999689i
$5$	−296.689	+	716.270i	−0.474702	+	1.14603i	0.487360	+	0.873201i	$0.337960\pi$
$5$	−296.689	+	716.270i	−0.474702	+	1.14603i	−0.962062	+	0.272831i	$0.912040\pi$
$6$	541.485	−	1354.82i	0.417813	−	1.04538i
$7$	−3146.79	+	3146.79i	−1.31062	+	1.31062i	−0.389654	+	0.920961i	$0.627405\pi$
$7$	−3146.79	+	3146.79i	−1.31062	+	1.31062i	−0.920961	+	0.389654i	$0.872595\pi$
$8$	2785.93	−	3002.64i	0.680158	−	0.733066i
$9$	−1240.52	+	1240.52i	−0.189075	+	0.189075i
$10$	11400.2	−	4889.60i	1.14002	−	0.488960i
$11$	8217.21	−	19838.1i	0.561246	−	1.35497i	−0.347524	−	0.937671i	$-0.612977\pi$
$11$	8217.21	−	19838.1i	0.561246	−	1.35497i	0.908770	−	0.417297i	$-0.137023\pi$
$12$	−21337.8	+	9468.67i	−1.02902	+	0.456629i
$13$	−10905.6	−	26328.4i	−0.381835	−	0.921831i	−0.991611	−	0.129257i	$-0.958741\pi$
$13$	−10905.6	−	26328.4i	−0.381835	−	0.921831i	0.609776	−	0.792574i	$-0.291259\pi$
$14$	71198.1	−	888.125i	1.85335	−	0.0231186i
$15$	−70697.2			−1.39649
$16$	−65454.4	+	3268.46i	−0.998756	+	0.0498727i
$17$			78434.5i			0.939099i	0.882906	+	0.469550i	$0.155584\pi$
$17$			78434.5i			0.939099i	−0.882906	+	0.469550i	$0.844416\pi$
$18$	28067.6	−	350.116i	0.267372	−	0.00333520i
$19$	−78.8755	+	32.6713i	−0.000605240	+	0.000250699i	−0.382986	−	0.923754i	$-0.625104\pi$
$19$	−78.8755	+	32.6713i	−0.000605240	+	0.000250699i	0.382381	+	0.924005i	$0.375104\pi$
$20$	−185203.	−	71354.8i	−1.15752	−	0.445968i
$21$	−374920.	−	155297.i	−1.92780	−	0.798519i
$22$	−315745.	+	135424.i	−1.34786	+	0.578103i
$23$	−40229.1	−	40229.1i	−0.143757	−	0.143757i	0.631566	−	0.775322i	$-0.282413\pi$
$23$	−40229.1	−	40229.1i	−0.143757	−	0.143757i	−0.775322	+	0.631566i	$0.782413\pi$
$24$	350183.	+	129926.i	1.05548	+	0.391607i
$25$	−148805.	−	148805.i	−0.380941	−	0.380941i
$26$	−169221.	+	423398.i	−0.370307	+	0.926522i
$27$	404946.	+	167734.i	0.761977	+	0.315621i
$28$	−825421.	−	785232.i	−1.34290	−	1.27752i
$29$	−324418.	+	134378.i	−0.458683	+	0.189993i	−0.600047	−	0.799965i	$-0.704851\pi$
$29$	−324418.	+	134378.i	−0.458683	+	0.189993i	0.141364	+	0.989958i	$0.454851\pi$
$30$	809762.	+	789809.i	0.999706	+	0.975073i
$31$		−	1.14104e6i		−	1.23553i	−0.786362	−	0.617766i	$-0.788038\pi$
$31$		−	1.14104e6i		−	1.23553i	0.786362	−	0.617766i	$-0.211962\pi$
$32$	786226.	+	693802.i	0.749803	+	0.661661i
$33$	1.95806e6			1.65108
$34$	876248.	−	898385.i	0.655709	−	0.672275i
$35$	−1.32033e6	−	3.18757e6i	−0.879856	−	2.12416i
$36$	−325397.	−	309553.i	−0.193733	−	0.184300i
$37$	−971788.	+	2.34610e6i	−0.518519	+	1.25182i	0.420294	+	0.907388i	$0.361927\pi$
$37$	−971788.	+	2.34610e6i	−0.518519	+	1.25182i	−0.938813	+	0.344428i	$0.888073\pi$
$38$	1268.43	+	506.959i	0.000608320	+	0.000243130i
$39$	1.83753e6	−	1.83753e6i	0.794285	−	0.794285i
$40$	1.32415e6	+	2.88633e6i	0.517244	+	1.12747i
$41$	−160516.	+	160516.i	−0.0568044	+	0.0568044i	−0.734938	−	0.678134i	$-0.762789\pi$
$41$	−160516.	+	160516.i	−0.0568044	+	0.0568044i	0.678134	+	0.734938i	$0.262789\pi$
$42$	2.55938e6	+	5.96726e6i	0.822503	+	1.91769i
$43$	−1.39352e6	+	3.36426e6i	−0.407606	+	0.984048i	0.578160	+	0.815924i	$0.303771\pi$
$43$	−1.39352e6	+	3.36426e6i	−0.407606	+	0.984048i	−0.985766	+	0.168124i	$0.946229\pi$
$44$	5.12944e6	+	1.97627e6i	1.36855	+	0.527273i
$45$	−520500.	−	1.25660e6i	−0.126932	−	0.306441i
$46$	11353.9	+	910209.i	0.00253580	+	0.203287i
$47$	−7.12098e6			−1.45931			−0.729656	−	0.683814i	$-0.760320\pi$
$47$	−7.12098e6			−1.45931			−0.729656	+	0.683814i	$0.760320\pi$
$48$	−2.55948e6	−	5.40030e6i	−0.482155	−	1.01731i
$49$		−	1.40397e7i		−	2.43542i
$50$	41997.6	+	3.36682e6i	0.00671962	+	0.538690i
$51$	−6.60790e6	+	2.73708e6i	−0.976748	+	0.404582i
$52$	6.66834e6	−	2.95909e6i	0.912019	−	0.404710i
$53$	3.61684e6	+	1.49814e6i	0.458380	+	0.189867i	0.599911	−	0.800067i	$-0.295203\pi$
$53$	3.61684e6	+	1.49814e6i	0.458380	+	0.189867i	−0.141531	+	0.989934i	$0.545203\pi$
$54$	−2.76435e6	−	6.44516e6i	−0.325101	−	0.757981i
$55$	1.17715e7	+	1.17715e7i	1.28641	+	1.28641i
$56$	681938.	+	1.82154e7i	0.0693415	+	1.85219i
$57$	−5504.93	−	5504.93i	−0.000521498	−	0.000521498i
$58$	5.21710e6	+	2.08514e6i	0.461017	+	0.184257i
$59$	−1.12276e7	−	4.65062e6i	−0.926571	−	0.383798i	−0.132194	−	0.991224i	$-0.542202\pi$
$59$	−1.12276e7	−	4.65062e6i	−0.926571	−	0.383798i	−0.794376	+	0.607426i	$0.792202\pi$
$60$	−451450.	−	1.80929e7i	−0.0348341	−	1.39605i
$61$	6.31482e6	−	2.61568e6i	0.456080	−	0.188915i	−0.142803	−	0.989751i	$-0.545611\pi$
$61$	6.31482e6	−	2.61568e6i	0.456080	−	0.188915i	0.598883	+	0.800836i	$0.295611\pi$
$62$	−1.27474e7	+	1.30694e7i	−0.862689	+	0.884483i
$63$		−	7.80732e6i		−	0.495610i
$64$	−1.25444e6	−	1.67303e7i	−0.0747702	−	0.997201i
$65$	2.20938e7			1.23771
$66$	−2.24275e7	−	2.18748e7i	−1.18196	−	1.15284i
$67$	−1.11553e7	−	2.69312e7i	−0.553580	−	1.33646i	−0.914772	−	0.403970i	$-0.867630\pi$
$67$	−1.11553e7	−	2.69312e7i	−0.553580	−	1.33646i	0.361192	−	0.932492i	$-0.382370\pi$
$68$	−2.00730e7	+	500859.i	−0.938807	+	0.0234250i
$69$	1.98534e6	−	4.79304e6i	0.0875868	−	0.211453i
$70$	−2.04876e7	+	5.12606e7i	−0.853293	+	2.13497i
$71$	−2.54656e7	+	2.54656e7i	−1.00212	+	1.00212i	−0.00212336	+	0.999998i	$0.500676\pi$
$71$	−2.54656e7	+	2.54656e7i	−1.00212	+	1.00212i	−0.999998	+	0.00212336i	$0.999324\pi$
$72$	268833.	+	7.18085e6i	0.0100035	+	0.267206i
$73$	4.40649e6	−	4.40649e6i	0.155168	−	0.155168i	−0.625254	−	0.780421i	$-0.715005\pi$
$73$	4.40649e6	−	4.40649e6i	0.155168	−	0.155168i	0.780421	+	0.625254i	$0.215005\pi$
$74$	3.73408e7	−	1.60156e7i	1.24525	−	0.534093i
$75$	7.34367e6	−	1.77292e7i	0.232096	−	0.560330i
$76$	−8864.92	−	19977.2i	−0.000265718	−	0.000598798i
$77$	3.65685e7	+	8.82841e7i	1.04026	+	2.51142i
$78$	−4.15754e7	+	518611.i	−1.12320	+	0.0140108i
$79$	−3.78380e7			−0.971448			−0.485724	−	0.874112i	$-0.661444\pi$
$79$	−3.78380e7			−0.971448			−0.485724	+	0.874112i	$0.661444\pi$
$80$	1.70785e7	−	4.78528e7i	0.416956	−	1.16828i
$81$			5.14793e7i			1.19589i
$82$	3.63177e6	−	45302.7i	0.0803273	−	0.00100200i
$83$	−2.61410e7	+	1.08280e7i	−0.550820	+	0.228157i	−0.640695	−	0.767796i	$-0.721353\pi$
$83$	−2.61410e7	+	1.08280e7i	−0.550820	+	0.228157i	0.0898743	+	0.995953i	$0.471353\pi$
$84$	3.73495e7	−	9.69413e7i	0.750184	−	1.94712i
$85$	−5.61803e7	−	2.32706e7i	−1.07624	−	0.445793i
$86$	5.35459e7	−	2.29661e7i	0.978888	−	0.419848i
$87$	−2.26420e7	−	2.26420e7i	−0.395219	−	0.395219i
$88$	−3.66740e7	−	7.99408e7i	−0.611545	−	1.33302i
$89$	4.51667e7	+	4.51667e7i	0.719877	+	0.719877i	0.968580	−	0.248703i	$-0.0800042\pi$
$89$	4.51667e7	+	4.51667e7i	0.719877	+	0.719877i	−0.248703	+	0.968580i	$0.580004\pi$
$90$	−8.07658e6	+	2.02079e7i	−0.123100	+	0.308000i
$91$	1.17167e8	+	4.85323e7i	1.70860	+	0.707727i
$92$	1.00385e7	−	1.05523e7i	0.140126	−	0.147298i
$93$	9.61296e7	−	3.98182e7i	1.28507	−	0.532292i
$94$	8.15633e7	+	7.95535e7i	1.04468	+	1.01894i
$95$		−	66189.3i		−	0.000812632i
$96$	−3.10145e7	+	9.04486e7i	−0.365157	+	1.06492i
$97$	−4.13701e7			−0.467304			−0.233652	−	0.972320i	$-0.575068\pi$
$97$	−4.13701e7			−0.467304			−0.233652	+	0.972320i	$0.575068\pi$
$98$	−1.56848e8	+	1.60810e8i	−1.70049	+	1.74345i
$99$	1.44160e7	+	3.48032e7i	0.150073	+	0.362309i
$100$	3.71321e7	−	3.90325e7i	0.371321	−	0.390325i
$101$	−8.80601e6	+	2.12596e7i	−0.0846241	+	0.204301i	−0.960527	−	0.278187i	$-0.910267\pi$
$101$	−8.80601e6	+	2.12596e7i	−0.0846241	+	0.204301i	0.875903	+	0.482487i	$0.160267\pi$
$102$	1.06264e8	+	4.24712e7i	0.981718	+	0.392368i
$103$	9.20578e7	−	9.20578e7i	0.817922	−	0.817922i	−0.167885	−	0.985807i	$-0.553694\pi$
$103$	9.20578e7	−	9.20578e7i	0.817922	−	0.817922i	0.985807	+	0.167885i	$0.0536937\pi$
$104$	−1.09437e8	−	4.06035e7i	−0.935470	−	0.347081i
$105$	2.22469e8	−	2.22469e8i	1.83026	−	1.83026i
$106$	−2.46902e7	−	5.75659e7i	−0.195570	−	0.455976i
$107$	−5.78660e7	+	1.39701e8i	−0.441457	+	1.06577i	0.533981	+	0.845496i	$0.320695\pi$
$107$	−5.78660e7	+	1.39701e8i	−0.441457	+	1.06577i	−0.975438	+	0.220274i	$0.929305\pi$
$108$	−4.03407e7	+	1.04705e8i	−0.296516	+	0.769613i
$109$	5.96115e7	+	1.43915e8i	0.422303	+	1.01953i	0.981666	+	0.190607i	$0.0610457\pi$
$109$	5.96115e7	+	1.43915e8i	0.422303	+	1.01953i	−0.559363	+	0.828923i	$0.688954\pi$
$110$	−3.32229e6	−	2.66337e8i	−0.0226917	−	1.81912i
$111$	−2.31565e8			−1.52539
$112$	1.95686e8	−	2.16256e8i	1.24362	−	1.37435i
$113$			1.09344e8i			0.670628i	0.942106	+	0.335314i	$0.108842\pi$
$113$			1.09344e8i			0.670628i	−0.942106	+	0.335314i	$0.891158\pi$
$114$	1553.67	+	124553.i	9.19897e−6	+	0.000737452i
$115$	4.07504e7	−	1.68794e7i	0.232992	−	0.0965083i
$116$	−3.64617e7	−	8.21670e7i	−0.201375	−	0.453801i
$117$	4.61896e7	+	1.91324e7i	0.246491	+	0.102100i
$118$	7.66448e7	+	1.78699e8i	0.395325	+	0.921711i
$119$	−2.46817e8	−	2.46817e8i	−1.23080	−	1.23080i
$120$	−1.96957e8	+	2.12278e8i	−0.949832	+	1.02372i
$121$	−1.74453e8	−	1.74453e8i	−0.813835	−	0.813835i
$122$	−1.01551e8	−	4.05874e7i	−0.458401	−	0.183211i
$123$	−1.91244e7	−	7.92159e6i	−0.0835541	−	0.0346092i
$124$	2.92015e8	−	7.28633e6i	1.23515	−	0.0308193i
$125$	−1.29059e8	+	5.34582e7i	−0.528628	+	0.218965i
$126$	−8.72212e7	+	8.94246e7i	−0.346051	+	0.354793i
$127$		−	1.13628e8i		−	0.436786i	−0.975861	−	0.218393i	$-0.929919\pi$
$127$		−	1.13628e8i		−	0.436786i	0.975861	−	0.218393i	$-0.0700815\pi$
$128$	−1.72537e8	+	2.05642e8i	−0.642752	+	0.766075i
$129$	−3.32059e8			−1.19910
$130$	−2.53061e8	−	2.46826e8i	−0.886038	−	0.864206i
$131$	−2.40287e7	−	5.80104e7i	−0.0815916	−	0.196979i	0.877819	−	0.478992i	$-0.158998\pi$
$131$	−2.40287e7	−	5.80104e7i	−0.0815916	−	0.196979i	−0.959411	+	0.282013i	$0.908998\pi$
$132$	1.25035e7	+	5.01106e8i	0.0411848	+	1.65057i
$133$	145395.	−	351014.i	0.000464667	−	0.00112181i
$134$	−1.73096e8	+	4.33092e8i	−0.536868	+	1.34326i
$135$	−2.40286e8	+	2.40286e8i	−0.723425	+	0.723425i
$136$	2.35510e8	+	2.18513e8i	0.688421	+	0.638736i
$137$	1.68844e8	−	1.68844e8i	0.479295	−	0.479295i	−0.425611	−	0.904906i	$-0.639941\pi$
$137$	1.68844e8	−	1.68844e8i	0.479295	−	0.479295i	0.904906	+	0.425611i	$0.139941\pi$
$138$	−7.62864e7	+	3.27195e7i	−0.210344	+	0.0902175i
$139$	−3.31165e7	+	7.99503e7i	−0.0887126	+	0.214171i	−0.962009	−	0.273019i	$-0.911978\pi$
$139$	−3.31165e7	+	7.99503e7i	−0.0887126	+	0.214171i	0.873296	+	0.487190i	$0.161978\pi$
$140$	8.07332e8	−	3.58255e8i	2.10155	−	0.932567i
$141$	−2.48496e8	−	5.99923e8i	−0.628700	−	1.51782i
$142$	5.76176e8	−	7.18721e6i	1.41710	−	0.0176769i
$143$	−6.11919e8			−1.46335
$144$	7.71431e7	−	8.52523e7i	0.179410	−	0.198270i
$145$		−	2.72239e8i		−	0.615855i
$146$	−9.96997e7	+	1.24365e6i	−0.219423	+	0.00273708i
$147$	1.18281e9	−	4.89936e8i	2.53306	−	1.04923i
$148$	−6.06621e8	−	2.33719e8i	−1.26436	−	0.487132i
$149$	6.34090e7	+	2.62649e7i	0.128649	+	0.0532881i	0.446079	−	0.894993i	$-0.352820\pi$
$149$	6.34090e7	+	2.62649e7i	0.128649	+	0.0532881i	−0.317430	+	0.948282i	$0.602820\pi$
$150$	−2.82180e8	+	1.21028e8i	−0.557392	+	0.239067i
$151$	4.04326e8	+	4.04326e8i	0.777721	+	0.777721i	0.979443	−	0.201722i	$-0.0646537\pi$
$151$	4.04326e8	+	4.04326e8i	0.777721	+	0.777721i	−0.201722	+	0.979443i	$0.564654\pi$
$152$	−121641.	+	327854.i	−0.000227880	+	0.000614195i
$153$	−9.72998e7	−	9.72998e7i	−0.177560	−	0.177560i
$154$	5.67431e8	−	1.41973e9i	1.00886	−	2.52420i
$155$	8.17293e8	+	3.38534e8i	1.41596	+	0.586510i
$156$	4.81996e8	+	4.58528e8i	0.813851	+	0.774225i
$157$	−4.81904e8	+	1.99611e8i	−0.793163	+	0.328539i	−0.742214	−	0.670163i	$-0.766224\pi$
$157$	−4.81904e8	+	1.99611e8i	−0.793163	+	0.328539i	−0.0509483	+	0.998701i	$0.516224\pi$
$158$	4.33394e8	+	4.22715e8i	0.695432	+	0.678296i
$159$			3.56989e8i			0.558555i
$160$	−7.30214e8	+	3.57307e8i	−1.11422	+	0.545207i
$161$	2.53185e8			0.376820
$162$	5.75112e8	−	5.89641e8i	0.835011	−	0.856106i
$163$	−2.13875e8	−	5.16340e8i	−0.302977	−	0.731451i	−0.999898	−	0.0143029i	$-0.995447\pi$
$163$	−2.13875e8	−	5.16340e8i	−0.302977	−	0.731451i	0.696921	−	0.717148i	$-0.254553\pi$
$164$	−4.21042e7	−	4.00542e7i	−0.0582036	−	0.0553698i
$165$	−5.80933e8	+	1.40250e9i	−0.783774	+	1.89220i
$166$	4.20384e8	+	1.68017e8i	0.553623	+	0.221269i
$167$	6.11533e8	−	6.11533e8i	0.786238	−	0.786238i	−0.194638	−	0.980875i	$-0.562353\pi$
$167$	6.11533e8	−	6.11533e8i	0.786238	−	0.786238i	0.980875	+	0.194638i	$0.0623531\pi$
$168$	−1.51080e9	+	6.93102e8i	−1.89657	+	0.870082i
$169$	2.55539e6	−	2.55539e6i	0.00313264	−	0.00313264i
$170$	3.83513e8	+	8.94171e8i	0.459182	+	1.07059i
$171$	57317.3	−	138376.i	6.70350e−5	−	0.000161837i
$172$	−8.69882e8	−	3.35148e8i	−0.993909	−	0.382933i
$173$	4.52488e8	+	1.09240e9i	0.505153	+	1.21955i	0.946644	+	0.322281i	$0.104450\pi$
$173$	4.52488e8	+	1.09240e9i	0.505153	+	1.21955i	−0.441491	+	0.897266i	$0.645550\pi$
$174$	6.39030e6	+	5.12290e8i	0.00697147	+	0.558881i
$175$	9.36517e8			0.998535
$176$	−4.73013e8	+	1.32535e9i	−0.492972	+	1.38127i
$177$		−	1.10818e9i		−	1.12906i
$178$	−1.27475e7	−	1.02193e9i	−0.0126983	−	1.01798i
$179$	−1.05712e9	+	4.37874e8i	−1.02970	+	0.426517i	−0.832606	−	0.553866i	$-0.813152\pi$
$179$	−1.05712e9	+	4.37874e8i	−1.02970	+	0.426517i	−0.197098	+	0.980384i	$0.563152\pi$
$180$	3.18265e8	−	1.41231e8i	0.303179	−	0.134536i
$181$	9.64363e8	+	3.99452e8i	0.898517	+	0.372178i	0.783650	−	0.621203i	$-0.213356\pi$
$181$	9.64363e8	+	3.99452e8i	0.898517	+	0.372178i	0.114867	+	0.993381i	$0.463356\pi$
$182$	−7.99840e8	−	1.86485e9i	−0.728983	−	1.69964i
$183$	4.40728e8	+	4.40728e8i	0.392977	+	0.392977i
$184$	−2.32868e8	+	8.71802e6i	−0.203161	+	0.00760583i
$185$	−1.39213e9	−	1.39213e9i	−1.18848	−	1.18848i
$186$	−1.54590e9	−	6.17857e8i	−1.29160	−	0.516221i
$187$	1.55599e9	+	6.44513e8i	1.27245	+	0.527066i
$188$	−4.54724e7	−	1.82240e9i	−0.0364012	−	1.45886i
$189$	−1.80210e9	+	7.46455e8i	−1.41232	+	0.585001i
$190$	−739448.	+	758129.i	−0.000567405	+	0.000581740i
$191$		−	1.15509e9i		−	0.867922i	−0.900932	−	0.433961i	$-0.857116\pi$
$191$		−	1.15509e9i		−	0.867922i	0.900932	−	0.433961i	$-0.142884\pi$
$192$	1.36570e9	−	6.89508e8i	1.00497	−	0.507381i
$193$	−4.33562e8			−0.312480			−0.156240	−	0.987719i	$-0.549937\pi$
$193$	−4.33562e8			−0.312480			−0.156240	+	0.987719i	$0.549937\pi$
$194$	4.73850e8	+	4.62174e8i	0.334529	+	0.326286i
$195$	7.70994e8	+	1.86134e9i	0.533228	+	1.28733i
$196$	3.59306e9	−	8.96534e7i	2.43467	−	0.0607495i
$197$	−7.37648e8	+	1.78084e9i	−0.489761	+	1.18239i	0.465080	+	0.885269i	$0.346026\pi$
$197$	−7.37648e8	+	1.78084e9i	−0.489761	+	1.18239i	−0.954841	+	0.297119i	$0.903974\pi$
$198$	2.23692e8	−	5.59685e8i	0.145542	−	0.364152i
$199$	−1.63143e9	+	1.63143e9i	−1.04029	+	1.04029i	−0.0411383	+	0.999153i	$0.513098\pi$
$199$	−1.63143e9	+	1.63143e9i	−1.04029	+	1.04029i	−0.999153	+	0.0411383i	$0.986902\pi$
$200$	−8.61368e8	+	3.22475e7i	−0.538355	+	0.0201547i
$201$	1.87960e9	−	1.87960e9i	1.15155	−	1.15155i
$202$	3.38370e8	−	1.45128e8i	0.203229	−	0.0871657i
$203$	5.98014e8	−	1.44373e9i	0.352149	−	0.850164i
$204$	−7.42671e8	−	1.67362e9i	−0.428821	−	0.966352i
$205$	−6.73493e7	−	1.62596e8i	−0.0381345	−	0.0920648i
$206$	−2.08287e9	+	2.59817e7i	−1.15663	+	0.0144277i
$207$	9.98101e7			0.0543617
$208$	7.99872e8	+	1.68767e9i	0.427334	+	0.901640i
$209$			1.83321e6i			0.000960784i
$210$	−5.03351e9	+	6.27879e7i	−2.58817	+	0.0322849i
$211$	−1.32918e9	+	5.50564e8i	−0.670585	+	0.277765i	−0.691885	−	0.722008i	$-0.743219\pi$
$211$	−1.32918e9	+	5.50564e8i	−0.670585	+	0.277765i	0.0213002	+	0.999773i	$0.493219\pi$
$212$	−3.60309e8	+	9.35189e8i	−0.178374	+	0.462973i
$213$	−3.03406e9	−	1.25675e9i	−1.47403	−	0.610563i
$214$	2.22349e9	−	9.53663e8i	1.06018	−	0.454716i
$215$	−1.99628e9	−	1.99628e9i	−0.934260	−	0.934260i
$216$	1.63179e9	−	7.48611e8i	0.749636	−	0.343907i
$217$	3.59061e9	+	3.59061e9i	1.61931	+	1.61931i
$218$	9.24990e8	−	2.31436e9i	0.409554	−	1.02472i
$219$	5.25005e8	+	2.17464e8i	0.228238	+	0.0945391i
$220$	−2.93739e9	+	3.08773e9i	−1.25392	+	1.31810i
$221$	2.06506e9	−	8.55374e8i	0.865691	−	0.358581i
$222$	2.65233e9	+	2.58698e9i	1.09198	+	1.06508i
$223$		−	2.91654e9i		−	1.17936i	−0.807636	−	0.589682i	$-0.799253\pi$
$223$		−	2.91654e9i		−	1.17936i	0.807636	−	0.589682i	$-0.200747\pi$
$224$	−4.65733e9	+	2.90840e8i	−1.84989	+	0.115521i
$225$	3.69192e8			0.144053
$226$	1.22156e9	−	1.25242e9i	0.468254	−	0.480084i
$227$	1.56401e9	+	3.77585e9i	0.589028	+	1.42204i	0.884433	+	0.466667i	$0.154546\pi$
$227$	1.56401e9	+	3.77585e9i	0.589028	+	1.42204i	−0.295405	+	0.955372i	$0.595454\pi$
$228$	1.37367e6	−	1.44398e6i	0.000508328	−	0.000534344i
$229$	9.65189e8	−	2.33017e9i	0.350970	−	0.847317i	−0.645530	−	0.763735i	$-0.723364\pi$
$229$	9.65189e8	−	2.33017e9i	0.350970	−	0.847317i	0.996501	−	0.0835829i	$-0.0266363\pi$
$230$	−6.55324e8	−	2.61916e8i	−0.234177	−	0.0935947i
$231$	−6.16159e9	+	6.16159e9i	−2.16394	+	2.16394i
$232$	−5.00315e8	+	1.34848e9i	−0.172700	+	0.465470i
$233$	−1.10979e9	+	1.10979e9i	−0.376545	+	0.376545i	−0.869854	−	0.493309i	$-0.835787\pi$
$233$	−1.10979e9	+	1.10979e9i	−0.376545	+	0.376545i	0.493309	+	0.869854i	$0.335787\pi$
$234$	−3.15312e8	−	7.35158e8i	−0.105166	−	0.245198i
$235$	2.11272e9	−	5.10055e9i	0.692739	−	1.67242i
$236$	1.11849e9	−	2.90307e9i	0.360566	−	0.935856i
$237$	−1.32041e9	−	3.18775e9i	−0.418519	−	1.01039i
$238$	6.96597e7	+	5.58439e9i	0.0217107	+	1.74048i
$239$	2.67338e9			0.819350			0.409675	−	0.912232i	$-0.365642\pi$
$239$	2.67338e9			0.819350			0.409675	+	0.912232i	$0.365642\pi$
$240$	4.62745e9	−	2.31071e8i	1.39475	−	0.0696466i
$241$		−	3.83117e9i		−	1.13570i	−0.823132	−	0.567850i	$-0.807775\pi$
$241$		−	3.83117e9i		−	1.13570i	0.823132	−	0.567850i	$-0.192225\pi$
$242$	4.92362e7	+	3.94711e9i	0.0143557	+	1.15085i
$243$	−1.68014e9	+	6.95937e8i	−0.481860	+	0.199593i
$244$	7.09731e8	+	1.59939e9i	0.200232	+	0.451226i
$245$	1.00562e10	+	4.16543e9i	2.79108	+	1.15610i
$246$	1.30552e8	+	3.04386e8i	0.0356487	+	0.0831159i
$247$	1.72037e6	+	1.72037e6i	0.000462203	+	0.000462203i
$248$	−3.42613e9	−	3.17886e9i	−0.905727	−	0.840357i
$249$	−1.82445e9	−	1.82445e9i	−0.474608	−	0.474608i
$250$	2.07546e9	+	8.29508e8i	0.531318	+	0.212354i
$251$	2.92211e9	+	1.21038e9i	0.736209	+	0.304948i	0.719101	−	0.694906i	$-0.244554\pi$
$251$	2.92211e9	+	1.21038e9i	0.736209	+	0.304948i	0.0171085	+	0.999854i	$0.494554\pi$
$252$	1.99805e9	−	4.98551e7i	0.495456	−	0.0123625i
$253$	−1.12864e9	+	4.67497e8i	−0.275469	+	0.114103i
$254$	−1.26941e9	+	1.30148e9i	−0.304978	+	0.312683i
$255$		−	5.54510e9i		−	1.31144i
$256$	4.27360e9	−	4.27870e8i	0.995025	−	0.0996212i
$257$	−3.54713e9			−0.813100			−0.406550	−	0.913628i	$-0.633268\pi$
$257$	−3.54713e9			−0.813100			−0.406550	+	0.913628i	$0.633268\pi$
$258$	3.80339e9	+	3.70967e9i	0.858404	+	0.837252i
$259$	−4.32468e9	−	1.04407e10i	−0.961070	−	2.32023i
$260$	1.41084e8	+	5.65426e9i	0.0308735	+	1.23732i
$261$	2.35748e8	−	5.69147e8i	0.0508027	−	0.122648i
$262$	−3.72852e8	+	9.32890e8i	−0.0791283	+	0.197982i
$263$	1.62297e9	−	1.62297e9i	0.339226	−	0.339226i	−0.516850	−	0.856076i	$-0.672896\pi$
$263$	1.62297e9	−	1.62297e9i	0.339226	−	0.339226i	0.856076	+	0.516850i	$0.172896\pi$
$264$	5.45500e9	−	5.87933e9i	1.12300	−	1.21035i
$265$	−2.14615e9	+	2.14615e9i	−0.435188	+	0.435188i
$266$	−5.58677e6	+	2.39619e6i	−0.00111592	+	0.000478623i
$267$	−2.22902e9	+	5.38133e9i	−0.438600	+	1.05887i
$268$	6.82101e9	−	3.02683e9i	1.32224	−	0.586745i
$269$	−1.80552e9	−	4.35890e9i	−0.344820	−	0.832469i	−0.997214	−	0.0745895i	$-0.976235\pi$
$269$	−1.80552e9	−	4.35890e9i	−0.344820	−	0.832469i	0.652394	−	0.757880i	$-0.273765\pi$
$270$	5.43663e9	−	6.78165e7i	1.02300	−	0.0127609i
$271$	−5.46685e9			−1.01359			−0.506793	−	0.862068i	$-0.669169\pi$
$271$	−5.46685e9			−1.01359			−0.506793	+	0.862068i	$0.669169\pi$
$272$	−2.56360e8	−	5.13389e9i	−0.0468354	−	0.937931i
$273$			1.15646e10i			2.08200i
$274$	−3.82020e9	+	4.76532e7i	−0.677772	+	0.00845453i
$275$	−4.17477e9	+	1.72925e9i	−0.729965	+	0.302362i
$276$	1.23931e9	+	4.77482e8i	0.213572	+	0.0822851i
$277$	4.42226e9	+	1.83176e9i	0.751147	+	0.311135i	0.725209	−	0.688528i	$-0.241743\pi$
$277$	4.42226e9	+	1.83176e9i	0.751147	+	0.311135i	0.0259373	+	0.999664i	$0.491743\pi$
$278$	1.27250e9	−	5.45778e8i	0.213048	−	0.0913770i
$279$	1.41549e9	+	1.41549e9i	0.233609	+	0.233609i
$280$	−1.32495e10	−	4.91585e9i	−2.15559	−	0.799772i
$281$	4.89695e8	+	4.89695e8i	0.0785417	+	0.0785417i	0.745286	−	0.666745i	$-0.232313\pi$
$281$	4.89695e8	+	4.89695e8i	0.0785417	+	0.0785417i	−0.666745	+	0.745286i	$0.732313\pi$
$282$	−3.85591e9	+	9.64762e9i	−0.609720	+	1.52554i
$283$	−5.88100e9	−	2.43599e9i	−0.916865	−	0.379778i	−0.126185	−	0.992007i	$-0.540273\pi$
$283$	−5.88100e9	−	2.43599e9i	−0.916865	−	0.379778i	−0.790681	+	0.612229i	$0.790273\pi$
$284$	−6.67978e9	−	6.35455e9i	−1.02681	−	0.976812i
$285$	5.57627e6	−	2.30977e6i	0.000845210	−	0.000350097i
$286$	7.00888e9	+	6.83618e9i	1.04757	+	1.02176i
$287$		−	1.01022e9i		−	0.148897i
$288$	−1.83601e9	+	1.14654e8i	−0.266873	+	0.0166656i
$289$	8.23783e8			0.118092
$290$	−3.04138e9	+	3.11821e9i	−0.430010	+	0.440873i
$291$	−1.44366e9	−	3.48532e9i	−0.201323	−	0.486038i
$292$	1.15585e9	+	1.09957e9i	0.158990	+	0.151249i
$293$	−3.49154e9	+	8.42932e9i	−0.473747	+	1.14373i	0.488747	+	0.872425i	$0.337454\pi$
$293$	−3.49154e9	+	8.42932e9i	−0.473747	+	1.14373i	−0.962494	+	0.271301i	$0.912546\pi$
$294$	−1.90213e10	−	7.60231e9i	−2.54595	−	1.01755i
$295$	6.66220e9	−	6.66220e9i	0.879690	−	0.879690i
$296$	4.33717e9	+	9.45400e9i	0.564988	+	1.23154i
$297$	6.65505e9	−	6.65505e9i	0.855314	−	0.855314i
$298$	−4.32860e8	−	1.00922e9i	−0.0548886	−	0.127974i
$299$	−6.20446e8	+	1.49789e9i	−0.0776281	+	0.187411i
$300$	4.58416e9	+	1.76618e9i	0.565945	+	0.218047i
$301$	−6.20150e9	−	1.49717e10i	−0.755494	−	1.82392i
$302$	−1.14114e8	−	9.14814e9i	−0.0137186	−	1.09978i
$303$	−2.09836e9			−0.248949
$304$	5.05596e6	−	2.39628e6i	0.000591984	−	0.000280571i
$305$			5.29916e9i			0.612361i
$306$	2.74611e7	+	2.20147e9i	0.00313208	+	0.251089i
$307$	−3.90152e9	+	1.61606e9i	−0.439219	+	0.181930i	−0.591324	−	0.806434i	$-0.701395\pi$
$307$	−3.90152e9	+	1.61606e9i	−0.439219	+	0.181930i	0.152106	+	0.988364i	$0.451395\pi$
$308$	−2.23602e10	+	9.92237e9i	−2.48469	+	1.10259i
$309$	1.09681e10	+	4.54314e9i	1.20309	+	0.498336i
$310$	−5.57923e9	−	1.30081e10i	−0.604126	−	1.40853i
$311$	4.55832e9	+	4.55832e9i	0.487263	+	0.487263i	0.907442	−	0.420178i	$-0.138032\pi$
$311$	4.55832e9	+	4.55832e9i	0.487263	+	0.487263i	−0.420178	+	0.907442i	$0.638032\pi$
$312$	−3.98210e8	−	1.06367e10i	−0.0420237	−	1.12250i
$313$	6.04232e9	+	6.04232e9i	0.629544	+	0.629544i	0.947953	−	0.318409i	$-0.103149\pi$
$313$	6.04232e9	+	6.04232e9i	0.629544	+	0.629544i	−0.318409	+	0.947953i	$0.603149\pi$
$314$	7.74971e9	+	3.09736e9i	0.797199	+	0.318620i
$315$	5.59215e9	+	2.31635e9i	0.567985	+	0.235267i
$316$	−2.41622e8	−	9.68351e9i	−0.0242319	−	0.971146i
$317$	9.53853e9	−	3.95099e9i	0.944592	−	0.391263i	0.143396	−	0.989665i	$-0.454198\pi$
$317$	9.53853e9	−	3.95099e9i	0.944592	−	0.391263i	0.801196	+	0.598403i	$0.204198\pi$
$318$	3.98817e9	−	4.08893e9i	0.390001	−	0.399854i
$319$			7.54004e9i			0.728133i
$320$	1.23556e10	+	4.06516e9i	1.17832	+	0.387684i
$321$	−1.37887e10			−1.29869
$322$	−2.89996e9	−	2.82851e9i	−0.269755	−	0.263108i
$323$	−2.56256e6	−	6.18656e6i	−0.000235431	−	0.000568380i
$324$	−1.31746e10	+	3.28731e8i	−1.19552	+	0.0298305i
$325$	−2.29500e9	+	5.54061e9i	−0.205707	+	0.496620i
$326$	−3.31869e9	+	8.30348e9i	−0.293830	+	0.735173i
$327$	−1.00442e10	+	1.00442e10i	−0.878467	+	0.878467i
$328$	3.47852e7	+	9.29155e8i	0.00300538	+	0.0802773i
$329$	2.24082e10	−	2.24082e10i	1.91260	−	1.91260i
$330$	2.23223e10	−	9.57411e9i	1.88227	−	0.807314i
$331$	−6.96853e9	+	1.68235e10i	−0.580536	+	1.40154i	0.311792	+	0.950150i	$0.399071\pi$
$331$	−6.96853e9	+	1.68235e10i	−0.580536	+	1.40154i	−0.892328	+	0.451387i	$0.850929\pi$
$332$	−2.93802e9	−	6.62087e9i	−0.241826	−	0.544958i
$333$	−1.70487e9	−	4.11592e9i	−0.138648	−	0.334727i
$334$	−1.38363e10	+	1.72594e8i	−1.11182	+	0.0138689i
$335$	2.25997e10			1.79441
$336$	2.50477e10	+	8.93946e9i	1.96522	+	0.701381i
$337$			2.21918e10i			1.72058i	0.509809	+	0.860288i	$0.329716\pi$
$337$			2.21918e10i			1.72058i	−0.509809	+	0.860288i	$0.670284\pi$
$338$	−5.78174e7	+	721214.i	−0.00442988	+	5.52583e-5i
$339$	−9.21195e9	+	3.81571e9i	−0.697514	+	0.288920i
$340$	5.59668e9	−	1.45263e10i	0.418808	−	1.08702i
$341$	−2.26361e10	−	9.37617e9i	−1.67411	−	0.693438i
$342$	−2.20241e6	+	944622.i	−0.000160988	+	6.90484e-5i
$343$	2.60395e10	+	2.60395e10i	1.88129	+	1.88129i
$344$	6.21941e9	+	1.35568e10i	0.444135	+	0.968110i
$345$	2.84408e9	+	2.84408e9i	0.200755	+	0.200755i
$346$	7.02124e9	−	1.75674e10i	0.489902	−	1.22575i
$347$	9.92275e9	+	4.11014e9i	0.684407	+	0.283491i	0.697668	−	0.716422i	$-0.254221\pi$
$347$	9.92275e9	+	4.11014e9i	0.684407	+	0.283491i	−0.0132610	+	0.999912i	$0.504221\pi$
$348$	5.64996e9	−	5.93913e9i	0.385238	−	0.404954i
$349$	−2.18999e10	+	9.07122e9i	−1.47618	+	0.611454i	−0.968259	−	0.249948i	$-0.919586\pi$
$349$	−2.18999e10	+	9.07122e9i	−1.47618	+	0.611454i	−0.507922	+	0.861403i	$0.669586\pi$
$350$	−1.07268e10	−	1.04625e10i	−0.714823	−	0.697209i
$351$		−	1.24908e10i		−	0.822930i
$352$	2.02243e10	−	9.89611e9i	1.31735	−	0.644605i
$353$	2.42955e9			0.156469			0.0782344	−	0.996935i	$-0.475072\pi$
$353$	2.42955e9			0.156469			0.0782344	+	0.996935i	$0.475072\pi$
$354$	−1.23803e10	+	1.26931e10i	−0.788349	+	0.808265i
$355$	−1.06849e10	−	2.57956e10i	−0.672754	−	1.62417i
$356$	−1.12707e10	+	1.18475e10i	−0.701696	+	0.737610i
$357$	1.21806e10	−	2.94067e10i	0.749889	−	1.81039i
$358$	1.70000e10	+	6.79447e9i	1.03494	+	0.413641i
$359$	−1.14282e9	+	1.14282e9i	−0.0688021	+	0.0688021i	−0.740671	−	0.671868i	$-0.765492\pi$
$359$	−1.14282e9	+	1.14282e9i	−0.0688021	+	0.0688021i	0.671868	+	0.740671i	$0.265492\pi$
$360$	−5.22319e9	−	1.93792e9i	−0.310975	−	0.115379i
$361$	−1.20092e10	+	1.20092e10i	−0.707106	+	0.707106i
$362$	−6.58320e9	−	1.53489e10i	−0.383356	−	0.893805i
$363$	8.60941e9	−	2.07849e10i	0.495846	−	1.19708i
$364$	−1.16722e10	+	3.02954e10i	−0.664887	+	1.72573i
$365$	1.84888e9	+	4.46359e9i	0.104169	+	0.251486i
$366$	−1.24388e8	−	9.97177e9i	−0.00693192	−	0.555710i
$367$	1.68318e10			0.927827			0.463914	−	0.885880i	$-0.346445\pi$
$367$	1.68318e10			0.927827			0.463914	+	0.885880i	$0.346445\pi$
$368$	2.76466e9	+	2.50168e9i	0.150748	+	0.136408i
$369$		−	3.98246e8i		−	0.0214806i
$370$	3.92903e8	+	3.14978e10i	0.0209642	+	1.68063i
$371$	−1.60958e10	+	6.66708e9i	−0.849603	+	0.351917i
$372$	1.08041e10	+	2.43472e10i	0.564181	+	1.27139i
$373$	1.43991e10	+	5.96430e9i	0.743875	+	0.308123i	0.722240	−	0.691643i	$-0.243113\pi$
$373$	1.43991e10	+	5.96430e9i	0.743875	+	0.308123i	0.0216352	+	0.999766i	$0.493113\pi$
$374$	−1.06219e10	−	2.47653e10i	−0.542896	−	1.26578i
$375$	−9.00742e9	−	9.00742e9i	−0.455486	−	0.455486i
$376$	−1.98385e10	+	2.13817e10i	−0.992563	+	1.06977i
$377$	7.07593e9	+	7.07593e9i	0.350282	+	0.350282i
$378$	2.89804e10	+	1.15827e10i	1.41950	+	0.567340i
$379$	1.04238e10	+	4.31770e9i	0.505209	+	0.209264i	0.620706	−	0.784043i	$-0.286846\pi$
$379$	1.04238e10	+	4.31770e9i	0.505209	+	0.209264i	−0.115497	+	0.993308i	$0.536846\pi$
$380$	1.69392e7	−	422665.i	0.000812379	−	2.02704e-5i
$381$	9.57281e9	−	3.96519e9i	0.454297	−	0.188176i
$382$	−1.29043e10	+	1.32303e10i	−0.606011	+	0.621320i
$383$		−	2.27066e10i		−	1.05525i	−0.849476	−	0.527627i	$-0.823082\pi$
$383$		−	2.27066e10i		−	1.05525i	0.849476	−	0.527627i	$-0.176918\pi$
$384$	−2.33457e10	−	7.35966e9i	−1.07370	−	0.338480i
$385$	−7.40847e10			−3.37198
$386$	4.96599e9	+	4.84363e9i	0.223695	+	0.218183i
$387$	−2.44475e9	−	5.90215e9i	−0.108991	−	0.263127i
$388$	−2.64176e8	−	1.05874e10i	−0.0116565	−	0.467158i
$389$	−1.13740e10	+	2.74593e10i	−0.496724	+	1.19920i	0.454514	+	0.890740i	$0.349813\pi$
$389$	−1.13740e10	+	2.74593e10i	−0.496724	+	1.19920i	−0.951238	+	0.308458i	$0.900187\pi$
$390$	1.19635e10	−	2.99331e10i	0.517129	−	1.29388i
$391$	3.15535e9	−	3.15535e9i	0.135002	−	0.135002i
$392$	−4.21562e10	−	3.91137e10i	−1.78533	−	1.65647i
$393$	4.04871e9	−	4.04871e9i	0.169725	−	0.169725i
$394$	2.83440e10	−	1.21568e10i	1.17619	−	0.504471i
$395$	1.12261e10	−	2.71022e10i	0.461148	−	1.11331i
$396$	−8.81480e9	+	3.91158e9i	−0.358453	+	0.159064i
$397$	−3.65318e8	−	8.81956e8i	−0.0147065	−	0.0355046i	0.916356	−	0.400365i	$-0.131117\pi$
$397$	−3.65318e8	−	8.81956e8i	−0.0147065	−	0.0355046i	−0.931062	+	0.364860i	$0.881117\pi$
$398$	3.69121e10	−	4.60441e8i	1.47108	−	0.0183502i
$399$	3.46457e7			0.00136697
$400$	1.02263e10	+	9.25360e9i	0.399466	+	0.361469i
$401$			2.81629e10i			1.08918i	0.838702	+	0.544591i	$0.183315\pi$
$401$			2.81629e10i			1.08918i	−0.838702	+	0.544591i	$0.816685\pi$
$402$	−4.25272e10	+	5.30484e8i	−1.62841	+	0.0203127i
$403$	−3.00418e10	+	1.24437e10i	−1.13895	+	0.471769i
$404$	−5.49700e9	−	2.11788e9i	−0.206348	−	0.0795016i
$405$	−3.68731e10	−	1.52733e10i	−1.37053	−	0.567693i
$406$	−2.29786e10	+	9.85560e9i	−0.845705	+	0.362726i
$407$	3.85569e10	+	3.85569e10i	1.40515	+	1.40515i
$408$	−1.01907e10	+	2.74664e10i	−0.367758	+	0.991200i
$409$	−3.69709e10	−	3.69709e10i	−1.32120	−	1.32120i	−0.912809	−	0.408386i	$-0.866092\pi$
$409$	−3.69709e10	−	3.69709e10i	−1.32120	−	1.32120i	−0.408386	−	0.912809i	$-0.633908\pi$
$410$	−1.04506e9	+	2.61477e9i	−0.0369832	+	0.0925333i
$411$	2.01167e10	+	8.33259e9i	0.704999	+	0.292020i
$412$	2.41473e10	+	2.29716e10i	0.838069	+	0.797265i
$413$	4.99654e10	−	2.06963e10i	1.71739	−	0.711366i
$414$	−1.14322e9	−	1.11505e9i	−0.0389160	−	0.0379571i
$415$		−	2.19366e10i		−	0.739565i
$416$	9.69244e9	−	2.82664e10i	0.323638	−	0.943837i
$417$	−7.89124e9			−0.260976
$418$	2.04800e7	−	2.09974e7i	0.000670850	−	0.000687798i
$419$	−1.22845e9	−	2.96575e9i	−0.0398568	−	0.0962229i	0.902698	−	0.430276i	$-0.141584\pi$
$419$	−1.22845e9	−	2.96575e9i	−0.0398568	−	0.0962229i	−0.942554	+	0.334053i	$0.891584\pi$
$420$	5.83550e10	+	5.55137e10i	1.87534	+	1.78403i
$421$	1.12399e10	−	2.71355e10i	0.357794	−	0.863792i	−0.637815	−	0.770189i	$-0.720162\pi$
$421$	1.12399e10	−	2.71355e10i	0.357794	−	0.863792i	0.995610	−	0.0936027i	$-0.0298384\pi$
$422$	2.13751e10	+	8.54307e9i	0.673997	+	0.269379i
$423$	8.83374e9	−	8.83374e9i	0.275920	−	0.275920i
$424$	1.45746e10	−	6.68633e9i	0.450956	−	0.206883i
$425$	1.16715e10	−	1.16715e10i	0.357742	−	0.357742i
$426$	2.07119e10	+	4.82904e10i	0.628901	+	1.46630i
$427$	−1.16404e10	+	2.81024e10i	−0.350152	+	0.845341i
$428$	−3.61218e10	−	1.39170e10i	−1.07645	−	0.414735i
$429$	−2.13537e10	−	5.15525e10i	−0.630442	−	1.52202i
$430$	5.63415e8	+	4.51671e10i	0.0164799	+	1.32114i
$431$	−2.84009e10			−0.823045			−0.411522	−	0.911400i	$-0.635003\pi$
$431$	−2.84009e10			−0.823045			−0.411522	+	0.911400i	$0.635003\pi$
$432$	−2.70538e10	−	9.65540e9i	−0.776770	−	0.277227i
$433$		−	4.67074e10i		−	1.32872i	−0.747411	−	0.664362i	$-0.768703\pi$
$433$		−	4.67074e10i		−	1.32872i	0.747411	−	0.664362i	$-0.231297\pi$
$434$	−1.01339e9	−	8.12399e10i	−0.0285638	−	2.28987i
$435$	2.29354e10	−	9.50016e9i	0.640545	−	0.265322i
$436$	−3.64501e10	+	1.61748e10i	−1.00868	+	0.447603i
$437$	4.48742e6	+	1.85875e6i	0.000123047	+	5.09677e-5i
$438$	−3.58393e9	−	8.35603e9i	−0.0973786	−	0.227041i
$439$	−2.91789e10	−	2.91789e10i	−0.785617	−	0.785617i	0.195155	−	0.980772i	$-0.437479\pi$
$439$	−2.91789e10	−	2.91789e10i	−0.785617	−	0.785617i	−0.980772	+	0.195155i	$0.937479\pi$
$440$	6.81400e10	−	2.55099e9i	1.81799	−	0.0680610i
$441$	1.74166e10	+	1.74166e10i	0.460479	+	0.460479i
$442$	−3.32090e10	−	1.32728e10i	−0.870096	−	0.347755i
$443$	3.60733e10	+	1.49421e10i	0.936637	+	0.387968i	0.798193	−	0.602402i	$-0.205790\pi$
$443$	3.60733e10	+	1.49421e10i	0.936637	+	0.387968i	0.138445	+	0.990370i	$0.455790\pi$
$444$	−1.47870e9	−	5.92622e10i	−0.0380495	−	1.52491i
$445$	−4.57520e10	+	1.89511e10i	−1.16673	+	0.483275i
$446$	−3.25827e10	+	3.34058e10i	−0.823470	+	0.844273i
$447$			6.25859e9i			0.156764i
$448$	5.65940e10	+	4.86991e10i	1.40494	+	1.20895i
$449$	7.30332e10			1.79695			0.898473	−	0.439028i	$-0.144677\pi$
$449$	7.30332e10			1.79695			0.898473	+	0.439028i	$0.144677\pi$
$450$	−4.22871e9	−	4.12451e9i	−0.103124	−	0.100583i
$451$	1.86533e9	+	4.50331e9i	0.0450869	+	0.108849i
$452$	−2.79834e10	+	6.98238e8i	−0.670419	+	0.0167282i
$453$	−1.99539e10	+	4.81729e10i	−0.473843	+	1.14396i
$454$	2.42687e10	−	6.07211e10i	0.571245	−	1.42928i
$455$	−6.95246e10	+	6.95246e10i	−1.62216	+	1.62216i
$456$	−3.18657e7	+	1.19297e6i	−0.000736993	+	2.75912e-5i
$457$	−3.87463e10	+	3.87463e10i	−0.888313	+	0.888313i	−0.994361	−	0.106048i	$-0.966180\pi$
$457$	−3.87463e10	+	3.87463e10i	−0.888313	+	0.888313i	0.106048	+	0.994361i	$0.466180\pi$
$458$	−3.70872e10	+	1.59069e10i	−0.842874	+	0.361512i
$459$	−1.31561e10	+	3.17618e10i	−0.296400	+	0.715573i
$460$	4.57999e9	+	1.03211e10i	0.102290	+	0.230512i
$461$	−4.61368e8	−	1.11384e9i	−0.0102151	−	0.0246615i	0.918690	−	0.394980i	$-0.129249\pi$
$461$	−4.61368e8	−	1.11384e9i	−0.0102151	−	0.0246615i	−0.928905	+	0.370319i	$0.879249\pi$
$462$	1.39410e11	−	1.73900e9i	3.06003	−	0.0381708i
$463$	−3.30829e10			−0.719911			−0.359956	−	0.932969i	$-0.617208\pi$
$463$	−3.30829e10			−0.719911			−0.359956	+	0.932969i	$0.617208\pi$
$464$	2.07954e10	−	9.85599e9i	0.448637	−	0.212632i
$465$			8.06684e10i			1.72541i
$466$	2.51097e10	−	3.13218e8i	0.532474	−	0.00664207i
$467$	1.08141e10	−	4.47933e9i	0.227364	−	0.0941772i	−0.266093	−	0.963947i	$-0.585733\pi$
$467$	1.08141e10	−	4.47933e9i	0.227364	−	0.0941772i	0.493457	+	0.869770i	$0.335733\pi$
$468$	−4.60141e9	+	1.19430e10i	−0.0959196	+	0.248961i
$469$	1.19850e11	+	4.96435e10i	2.47712	+	1.02606i
$470$	−8.11808e10	+	3.48187e10i	−1.66365	+	0.713545i
$471$	−3.36334e10	−	3.36334e10i	−0.683420	−	0.683420i
$472$	−4.52434e10	+	2.07561e10i	−0.911564	+	0.418194i
$473$	5.52897e10	+	5.52897e10i	1.10459	+	1.10459i
$474$	−2.04887e10	+	5.12635e10i	−0.405883	+	1.01554i
$475$	1.65987e7	+	6.87542e6i	0.000326062	+	0.000135059i
$476$	6.15893e10	−	6.47415e10i	1.19971	−	1.26112i
$477$	−6.34525e9	+	2.62829e9i	−0.122567	+	0.0507691i
$478$	−3.06208e10	−	2.98663e10i	−0.586549	−	0.572096i
$479$		−	4.25796e10i		−	0.808833i	−0.914575	−	0.404417i	$-0.867475\pi$
$479$		−	4.25796e10i		−	0.808833i	0.914575	−	0.404417i	$-0.132525\pi$
$480$	−5.55840e10	−	4.90498e10i	−1.04709	−	0.924001i
$481$	7.23671e10			1.35195
$482$	−4.28008e10	+	4.38821e10i	−0.792982	+	0.813015i
$483$	8.83522e9	+	2.13301e10i	0.162341	+	0.391927i
$484$	4.35320e10	−	4.57600e10i	0.793281	−	0.833882i
$485$	1.22740e10	−	2.96321e10i	0.221830	−	0.535545i
$486$	2.70191e10	+	1.07988e10i	0.484312	+	0.193567i
$487$	4.87754e10	−	4.87754e10i	0.867132	−	0.867132i	−0.125022	−	0.992154i	$-0.539900\pi$
$487$	4.87754e10	−	4.87754e10i	0.867132	−	0.867132i	0.992154	+	0.125022i	$0.0399003\pi$
$488$	9.73868e9	−	2.62482e10i	0.171720	−	0.462829i
$489$	3.60368e10	−	3.60368e10i	0.630247	−	0.630247i
$490$	−6.86487e10	−	1.60056e11i	−1.19082	−	2.77644i
$491$	2.20134e10	−	5.31451e10i	0.378758	−	0.914402i	−0.613441	−	0.789740i	$-0.710215\pi$
$491$	2.20134e10	−	5.31451e10i	0.378758	−	0.914402i	0.992199	−	0.124662i	$-0.0397847\pi$
$492$	1.90517e9	−	4.94491e9i	0.0325143	−	0.0843914i
$493$	−1.05399e10	−	2.54455e10i	−0.178422	−	0.430749i
$494$	−485543.	−	3.89244e7i	−8.15304e−6	−	0.000653603i
$495$	−2.92056e10			−0.486458
$496$	3.72944e9	+	7.46862e10i	0.0616193	+	1.23400i
$497$		−	1.60270e11i		−	2.62679i
$498$	5.14919e8	+	4.12794e10i	0.00837186	+	0.671145i
$499$	1.64462e10	−	6.81225e9i	0.265255	−	0.109872i	−0.246092	−	0.969246i	$-0.579147\pi$
$499$	1.64462e10	−	6.81225e9i	0.265255	−	0.109872i	0.511347	+	0.859374i	$0.329147\pi$
$500$	−1.45052e10	−	3.26876e10i	−0.232083	−	0.523001i
$501$	7.28603e10	+	3.01797e10i	1.15648	+	0.479032i
$502$	−1.99477e10	−	4.65085e10i	−0.314107	−	0.732348i
$503$	2.39901e10	+	2.39901e10i	0.374766	+	0.374766i	0.869210	−	0.494443i	$-0.164628\pi$
$503$	2.39901e10	+	2.39901e10i	0.374766	+	0.374766i	−0.494443	+	0.869210i	$0.664628\pi$
$504$	−2.34426e10	−	2.17506e10i	−0.363315	−	0.337093i
$505$	−1.26150e10	−	1.26150e10i	−0.193964	−	0.193964i
$506$	1.81501e10	+	7.25413e9i	0.276871	+	0.110658i
$507$	3.04459e8	+	1.26111e8i	0.00460783	+	0.00190863i
$508$	2.90796e10	−	7.25590e8i	0.436650	−	0.0108952i
$509$	−6.90562e10	+	2.86040e10i	−1.02880	+	0.426143i	−0.832280	−	0.554356i	$-0.812965\pi$
$509$	−6.90562e10	+	2.86040e10i	−1.02880	+	0.426143i	−0.196521	+	0.980500i	$0.562965\pi$
$510$	−6.19483e10	+	6.35133e10i	−0.915690	+	0.938823i
$511$			2.77326e10i			0.406730i
$512$	−5.37296e10	−	4.28426e10i	−0.781869	−	0.623443i
$513$	−3.74204e7			−0.000540305
$514$	4.06286e10	+	3.96275e10i	0.582075	+	0.567733i
$515$	3.86257e10	+	9.32508e10i	0.549096	+	1.32563i
$516$	−2.12043e9	−	8.49807e10i	−0.0299106	−	1.19873i
$517$	−5.85146e10	+	1.41267e11i	−0.819034	+	1.97732i
$518$	−6.71059e10	+	1.67901e11i	−0.932055	+	2.33204i
$519$	−7.62418e10	+	7.62418e10i	−1.05081	+	1.05081i
$520$	6.15518e10	−	6.63397e10i	0.841835	−	0.907319i
$521$	−4.42642e9	+	4.42642e9i	−0.0600761	+	0.0600761i	−0.736507	−	0.676430i	$-0.763526\pi$
$521$	−4.42642e9	+	4.42642e9i	−0.0600761	+	0.0600761i	0.676430	+	0.736507i	$0.263526\pi$
$522$	−9.05859e9	+	3.88526e9i	−0.122005	+	0.0523285i
$523$	−2.28384e10	+	5.51369e10i	−0.305253	+	0.736945i	0.694593	+	0.719403i	$0.255584\pi$
$523$	−2.28384e10	+	5.51369e10i	−0.305253	+	0.736945i	−0.999846	+	0.0175427i	$0.994416\pi$
$524$	1.46926e10	−	6.51987e9i	0.194883	−	0.0864797i
$525$	3.26810e10	+	7.88990e10i	0.430188	+	1.03857i
$526$	−3.67209e10	+	4.58056e8i	−0.479700	+	0.00598378i
$527$	8.94970e10			1.16029
$528$	−1.28163e11	+	6.39982e9i	−1.64903	+	0.0823440i
$529$		−	7.50742e10i		−	0.958668i
$530$	4.85581e10	−	6.05713e8i	0.615401	−	0.00767650i
$531$	1.96973e10	−	8.15888e9i	0.247758	−	0.102625i
$532$	9.07600e7	+	3.49680e7i	0.00113305	+	0.000436540i
$533$	5.97664e9	+	2.47560e9i	0.0740539	+	0.0306741i
$534$	8.56497e10	−	3.67355e10i	1.05332	−	0.451773i
$535$	−8.28953e10	−	8.28953e10i	−1.01185	−	1.01185i
$536$	−1.11942e11	−	4.15331e10i	−1.35624	−	0.503194i
$537$	−7.37794e10	−	7.37794e10i	−0.887233	−	0.887233i
$538$	−2.80161e10	+	7.00974e10i	−0.334410	+	0.836705i
$539$	−2.78522e11	−	1.15367e11i	−3.29992	−	1.36687i
$540$	−6.30285e10	−	5.99597e10i	−0.741245	−	0.705154i
$541$	−5.90788e10	+	2.44713e10i	−0.689673	+	0.285672i	−0.699864	−	0.714276i	$-0.746756\pi$
$541$	−5.90788e10	+	2.44713e10i	−0.689673	+	0.285672i	0.0101912	+	0.999948i	$0.496756\pi$
$542$	6.26170e10	+	6.10741e10i	0.725597	+	0.707718i
$543$			9.51844e10i			1.09488i
$544$	−5.44180e10	+	6.16673e10i	−0.621365	+	0.704140i
$545$	−1.20768e11			−1.36888
$546$	1.29197e11	−	1.32461e11i	1.45372	−	1.49045i
$547$	−1.22215e10	−	2.95053e10i	−0.136513	−	0.329572i	0.840808	−	0.541333i	$-0.182080\pi$
$547$	−1.22215e10	−	2.95053e10i	−0.136513	−	0.329572i	−0.977321	+	0.211761i	$0.932080\pi$
$548$	4.42887e10	+	4.21324e10i	0.491101	+	0.467190i
$549$	−4.58886e9	+	1.10785e10i	−0.0505144	+	0.121953i
$550$	6.71363e10	+	2.68327e10i	0.733680	+	0.293233i
$551$	2.11983e7	−	2.11983e7i	0.000229982	−	0.000229982i
$552$	−8.86074e9	−	1.93143e10i	−0.0954363	−	0.208029i
$553$	1.19068e11	−	1.19068e11i	1.27319	−	1.27319i
$554$	−3.01884e10	−	7.03850e10i	−0.320480	−	0.747207i
$555$	6.87027e10	−	1.65863e11i	0.724106	−	1.74815i
$556$	−2.06724e10	−	7.96465e9i	−0.216317	−	0.0833427i
$557$	5.83338e10	+	1.40830e11i	0.606037	+	1.46310i	0.867275	+	0.497829i	$0.165869\pi$
$557$	5.83338e10	+	1.40830e11i	0.606037	+	1.46310i	−0.261238	+	0.965275i	$0.584131\pi$
$558$	−3.99496e8	−	3.20263e10i	−0.00412074	−	0.330347i
$559$	1.03773e11			1.06276
$560$	9.68401e10	+	2.04325e11i	0.984698	+	2.07764i
$561$			1.53579e11i			1.55053i
$562$	−1.38208e8	−	1.10797e10i	−0.00138544	−	0.111066i
$563$	−5.16076e10	+	2.13766e10i	−0.513665	+	0.212767i	−0.624432	−	0.781079i	$-0.714669\pi$
$563$	−5.16076e10	+	2.13766e10i	−0.513665	+	0.212767i	0.110767	+	0.993846i	$0.464669\pi$
$564$	1.51946e11	−	6.74262e10i	1.50166	−	0.666365i
$565$	−7.83200e10	−	3.24412e10i	−0.768562	−	0.318349i
$566$	4.01465e10	+	9.36025e10i	0.391185	+	0.912057i
$567$	−1.61994e11	−	1.61994e11i	−1.56736	−	1.56736i
$568$	5.51863e9	+	1.47409e11i	0.0530198	+	1.41622i
$569$	−8.05937e7	−	8.05937e7i	−0.000768869	−	0.000768869i	0.706722	−	0.707491i	$-0.250173\pi$
$569$	−8.05937e7	−	8.05937e7i	−0.000768869	−	0.000768869i	−0.707491	+	0.706722i	$0.750173\pi$
$570$	−8.96744e7	−	3.58406e7i	−0.000849511	−	0.000339528i
$571$	1.73576e11	+	7.18974e10i	1.63284	+	0.676346i	0.995546	−	0.0942721i	$-0.0300524\pi$
$571$	1.73576e11	+	7.18974e10i	1.63284	+	0.676346i	0.637297	+	0.770618i	$0.280052\pi$
$572$	−3.90752e9	−	1.56602e11i	−0.0365021	−	1.46290i
$573$	9.73128e10	−	4.03083e10i	0.902717	−	0.373918i
$574$	−1.12858e10	+	1.15710e10i	−0.103965	+	0.106591i
$575$			1.19726e10i			0.109526i
$576$	2.23104e10	+	1.91981e10i	0.202683	+	0.174409i
$577$	8.18838e10			0.738745			0.369373	−	0.929281i	$-0.379573\pi$
$577$	8.18838e10			0.738745			0.369373	+	0.929281i	$0.379573\pi$
$578$	−9.43556e9	−	9.20306e9i	−0.0845388	−	0.0824558i
$579$	−1.51297e10	−	3.65264e10i	−0.134622	−	0.325007i
$580$	6.96716e10	−	1.73844e9i	0.615664	−	0.0153620i
$581$	4.81869e10	−	1.16333e11i	0.422887	−	1.02094i
$582$	−2.24013e10	+	5.60488e10i	−0.195245	+	0.488511i
$583$	5.94406e10	−	5.94406e10i	0.514528	−	0.514528i
$584$	−9.54928e8	−	2.55072e10i	−0.00820954	−	0.219287i
$585$	−2.74079e10	+	2.74079e10i	−0.234020	+	0.234020i
$586$	1.34162e11	−	5.75425e10i	1.13773	−	0.487976i
$587$	−7.02079e9	+	1.69497e10i	−0.0591335	+	0.142761i	−0.950685	−	0.310159i	$-0.899618\pi$
$587$	−7.02079e9	+	1.69497e10i	−0.0591335	+	0.142761i	0.891551	+	0.452920i	$0.149618\pi$
$588$	1.32938e11	+	2.99577e11i	1.11209	+	2.50610i
$589$	3.72793e7	+	9.00001e7i	0.000309746	+	0.000747794i
$590$	−1.50737e11	+	1.88029e9i	−1.24397	+	0.0155173i
$591$	−1.75772e11			−1.44079
$592$	5.59397e10	−	1.56739e11i	0.455442	−	1.27612i
$593$		−	9.62253e10i		−	0.778163i	−0.921203	−	0.389081i	$-0.872792\pi$
$593$		−	9.62253e10i		−	0.778163i	0.921203	−	0.389081i	$-0.127208\pi$
$594$	−1.50575e11	+	1.87827e9i	−1.20950	+	0.0150873i
$595$	2.50015e11	−	1.03560e11i	1.99480	−	0.826272i
$596$	−6.31681e9	+	1.63954e10i	−0.0500625	+	0.129938i
$597$	−1.94374e11	−	8.05124e10i	−1.53018	−	0.633819i
$598$	2.38405e10	−	1.02253e10i	0.186428	−	0.0799597i
$599$	1.11986e11	+	1.11986e11i	0.869872	+	0.869872i	0.992458	−	0.122586i	$-0.0391187\pi$
$599$	1.11986e11	+	1.11986e11i	0.869872	+	0.869872i	−0.122586	+	0.992458i	$0.539119\pi$
$600$	−3.27754e10	−	7.14426e10i	−0.252897	−	0.551255i
$601$	1.20875e10	+	1.20875e10i	0.0926484	+	0.0926484i	0.751912	−	0.659264i	$-0.229132\pi$
$601$	1.20875e10	+	1.20875e10i	0.0926484	+	0.0926484i	−0.659264	+	0.751912i	$0.729132\pi$
$602$	−9.62284e10	+	2.40767e11i	−0.732685	+	1.83320i
$603$	4.72471e10	+	1.95704e10i	0.357360	+	0.148023i
$604$	−1.00893e11	+	1.06057e11i	−0.758079	+	0.796879i
$605$	1.76714e11	−	7.31971e10i	1.31901	−	0.546352i
$606$	2.40345e10	+	2.34423e10i	0.178215	+	0.173824i
$607$			1.21640e11i			0.896031i	0.894026	+	0.448016i	$0.147869\pi$
$607$			1.21640e11i			0.896031i	−0.894026	+	0.448016i	$0.852131\pi$
$608$	−8.46813e7	−	2.90369e7i	−0.000619688	−	0.000212489i
$609$	1.42499e11			1.03596
$610$	5.92007e10	−	6.06963e10i	0.427570	−	0.438372i
$611$	7.76584e10	+	1.87484e11i	0.557216	+	1.34524i
$612$	2.42797e10	−	2.55223e10i	0.173076	−	0.181934i
$613$	2.87503e9	−	6.94093e9i	0.0203611	−	0.0491559i	−0.913372	−	0.407126i	$-0.866531\pi$
$613$	2.87503e9	−	6.94093e9i	0.0203611	−	0.0491559i	0.933733	+	0.357970i	$0.116531\pi$
$614$	6.27420e10	+	2.50764e10i	0.441454	+	0.176438i
$615$	1.13480e10	−	1.13480e10i	0.0793266	−	0.0793266i
$616$	3.66962e11	+	1.36151e11i	2.54858	+	0.945581i
$617$	−1.11404e11	+	1.11404e11i	−0.768705	+	0.768705i	−0.977879	−	0.209173i	$-0.932923\pi$
$617$	−1.11404e11	+	1.11404e11i	−0.768705	+	0.768705i	0.209173	+	0.977879i	$0.432923\pi$
$618$	−7.48734e10	−	1.74569e11i	−0.513303	−	1.19678i
$619$	3.55819e10	−	8.59022e10i	0.242363	−	0.585116i	−0.755154	−	0.655548i	$-0.772438\pi$
$619$	3.55819e10	−	8.59022e10i	0.242363	−	0.585116i	0.997517	+	0.0704321i	$0.0224378\pi$
$620$	−8.14188e10	+	2.11324e11i	−0.551008	+	1.43015i
$621$	−9.54281e9	−	2.30384e10i	−0.0641667	−	0.154912i
$622$	−1.28651e9	−	1.03135e11i	−0.00859509	−	0.689041i
$623$	−2.84260e11			−1.88696
$624$	−1.14269e11	+	1.26281e11i	−0.753684	+	0.832910i
$625$		−	1.90506e11i		−	1.24850i
$626$	−1.70534e9	−	1.36711e11i	−0.0111049	−	0.890241i
$627$	−1.54443e8	+	6.39722e7i	−0.000999302	+	0.000413925i
$628$	−5.41619e10	−	1.22054e11i	−0.348221	−	0.784721i
$629$	−1.84016e11	−	7.62218e10i	−1.17558	−	0.486941i
$630$	−3.81747e10	−	8.90052e10i	−0.242333	−	0.565006i
$631$	2.99448e10	+	2.99448e10i	0.188888	+	0.188888i	0.795215	−	0.606327i	$-0.207358\pi$
$631$	2.99448e10	+	2.99448e10i	0.188888	+	0.188888i	−0.606327	+	0.795215i	$0.707358\pi$
$632$	−1.05414e11	+	1.13614e11i	−0.660738	+	0.712135i
$633$	−9.27670e10	−	9.27670e10i	−0.577802	−	0.577802i
$634$	−1.53393e11	−	6.13073e10i	−0.949399	−	0.379450i
$635$	8.13880e10	+	3.37120e10i	0.500571	+	0.207343i
$636$	−9.13606e10	+	2.27962e9i	−0.558381	+	0.0139327i
$637$	−3.69644e11	+	1.53112e11i	−2.24505	+	0.929930i
$638$	8.42352e10	−	8.63632e10i	0.508406	−	0.521250i
$639$		−	6.31813e10i		−	0.378953i
$640$	−9.61050e10	−	1.84595e11i	−0.572831	−	1.10027i
$641$	8.12255e10			0.481128			0.240564	−	0.970633i	$-0.422668\pi$
$641$	8.12255e10			0.481128			0.240564	+	0.970633i	$0.422668\pi$
$642$	1.57935e11	+	1.54044e11i	0.929692	+	0.906784i
$643$	−3.68661e9	−	8.90025e9i	−0.0215667	−	0.0520665i	0.912729	−	0.408565i	$-0.133971\pi$
$643$	−3.68661e9	−	8.90025e9i	−0.0215667	−	0.0520665i	−0.934296	+	0.356498i	$0.883971\pi$
$644$	1.61676e9	+	6.47951e10i	0.00939943	+	0.376703i
$645$	9.85182e10	−	2.37844e11i	0.569217	−	1.37421i
$646$	−3.97631e7	+	9.94887e7i	−0.000228323	+	0.000571273i
$647$	1.84732e11	−	1.84732e11i	1.05420	−	1.05420i	0.0557587	−	0.998444i	$-0.482242\pi$
$647$	1.84732e11	−	1.84732e11i	1.05420	−	1.05420i	0.998444	−	0.0557587i	$-0.0177578\pi$
$648$	1.54574e11	+	1.43418e11i	0.876669	+	0.813397i
$649$	−1.84519e11	+	1.84519e11i	−1.04007	+	1.04007i
$650$	8.81849e10	−	3.78228e10i	0.494016	−	0.211885i
$651$	−1.77200e11	+	4.27799e11i	−0.986597	+	2.38186i
$652$	1.30776e11	−	5.80321e10i	0.723666	−	0.321128i
$653$	5.86224e10	+	1.41527e11i	0.322412	+	0.778370i	0.999113	+	0.0421126i	$0.0134088\pi$
$653$	5.86224e10	+	1.41527e11i	0.322412	+	0.778370i	−0.676701	+	0.736258i	$0.736591\pi$
$654$	2.27257e11	−	2.83480e9i	1.24224	−	0.0154957i
$655$	4.86802e10			0.264477
$656$	9.98182e9	−	1.10311e10i	0.0539007	−	0.0595667i
$657$			1.09327e10i			0.0586767i
$658$	−5.07000e11	+	6.32432e9i	−2.70461	+	0.0337373i
$659$	−1.77144e11	+	7.33753e10i	−0.939256	+	0.389053i	−0.799182	−	0.601088i	$-0.794734\pi$
$659$	−1.77144e11	+	7.33753e10i	−0.939256	+	0.389053i	−0.140074	+	0.990141i	$0.544734\pi$
$660$	−3.62637e11	−	1.39717e11i	−1.91116	−	0.736331i
$661$	−3.96654e10	−	1.64299e10i	−0.207781	−	0.0860657i	0.276366	−	0.961053i	$-0.410870\pi$
$661$	−3.96654e10	−	1.64299e10i	−0.207781	−	0.0860657i	−0.484147	+	0.874987i	$0.660870\pi$
$662$	2.67765e11	−	1.14845e11i	1.39419	−	0.597972i
$663$	1.44126e11	+	1.44126e11i	0.745913	+	0.745913i
$664$	−4.03145e10	+	1.08658e11i	−0.207391	+	0.558970i
$665$	2.08284e8	+	2.08284e8i	0.00106505	+	0.00106505i
$666$	−2.64544e10	+	6.61899e10i	−0.134462	+	0.336430i
$667$	1.84569e10	+	7.64511e9i	0.0932515	+	0.0386261i
$668$	1.60409e11	+	1.52599e11i	0.805605	+	0.766381i
$669$	2.45710e11	−	1.01777e11i	1.22664	−	0.508093i
$670$	−2.58855e11	−	2.52477e11i	−1.28457	−	1.25292i
$671$		−	1.46768e11i		−	0.724002i
$672$	−1.87026e11	−	3.82218e11i	−0.917119	−	1.87428i
$673$	−2.36857e11			−1.15459			−0.577294	−	0.816537i	$-0.695891\pi$
$673$	−2.36857e11			−1.15459			−0.577294	+	0.816537i	$0.695891\pi$
$674$	2.47921e11	−	2.54184e11i	1.20136	−	1.23171i
$675$	−3.52984e10	−	8.52178e10i	−0.170035	−	0.410502i
$676$	6.70295e8	+	6.37659e8i	0.00320981	+	0.00305353i
$677$	−5.56024e10	+	1.34236e11i	−0.264691	+	0.639020i	−0.999217	−	0.0395600i	$-0.987404\pi$
$677$	−5.56024e10	+	1.34236e11i	−0.264691	+	0.639020i	0.734526	+	0.678580i	$0.237404\pi$
$678$	1.48141e11	+	5.92083e10i	0.701063	+	0.280197i
$679$	1.30183e11	−	1.30183e11i	0.612455	−	0.612455i
$680$	−2.26388e11	+	1.03859e11i	−1.05881	+	0.485744i
$681$	−2.63527e11	+	2.63527e11i	−1.22528	+	1.22528i
$682$	1.54524e11	+	3.60278e11i	0.714265	+	1.66533i
$683$	−1.33229e11	+	3.21643e11i	−0.612231	+	1.47806i	0.248313	+	0.968680i	$0.420124\pi$
$683$	−1.33229e11	+	3.21643e11i	−0.612231	+	1.47806i	−0.860544	+	0.509377i	$0.829876\pi$
$684$	3.57793e7	+	1.37850e7i	0.000163459	+	6.29773e-5i
$685$	7.08437e10	+	1.71032e11i	0.321765	+	0.776810i
$686$	−7.34918e9	−	5.89160e11i	−0.0331850	−	2.66034i
$687$	2.29992e11			1.03249
$688$	8.02164e10	−	2.24761e11i	0.358022	−	1.00315i
$689$		−	1.11564e11i		−	0.495047i
$690$	−8.02692e8	−	6.43492e10i	−0.00354122	−	0.283888i
$691$	4.05223e11	−	1.67849e11i	1.77738	−	0.736217i	0.784084	−	0.620654i	$-0.213133\pi$
$691$	4.05223e11	−	1.67849e11i	1.77738	−	0.736217i	0.993300	−	0.115563i	$-0.0368671\pi$
$692$	−2.76679e11	+	1.22777e11i	−1.20657	+	0.535416i
$693$	−1.54882e11	−	6.41544e10i	−0.671536	−	0.278159i
$694$	−6.77374e10	−	1.57931e11i	−0.292005	−	0.680817i
$695$	−4.74407e10	−	4.74407e10i	−0.203335	−	0.203335i
$696$	−1.31065e11	+	4.90673e9i	−0.558533	+	0.0209101i
$697$	−1.25900e10	−	1.25900e10i	−0.0533449	−	0.0533449i
$698$	3.52181e11	+	1.40758e11i	1.48369	+	0.592994i
$699$	−1.32224e11	−	5.47691e10i	−0.553864	−	0.229418i
$700$	5.98030e9	+	2.39674e11i	0.0249076	+	0.998224i
$701$	1.31032e11	−	5.42751e10i	0.542631	−	0.224765i	−0.0944943	−	0.995525i	$-0.530123\pi$
$701$	1.31032e11	−	5.42751e10i	0.542631	−	0.224765i	0.637125	+	0.770760i	$0.280123\pi$
$702$	−1.39544e11	+	1.43069e11i	−0.574596	+	0.589112i
$703$		−	2.16800e8i		−	0.000887641i
$704$	−3.42204e11	−	1.12590e11i	−1.39314	−	0.458364i
$705$	5.03433e11			2.03791
$706$	−2.78280e10	−	2.71423e10i	−0.112012	−	0.109251i
$707$	−3.91888e10	−	9.46101e10i	−0.156850	−	0.378669i
$708$	2.83607e11	−	7.07652e9i	1.12871	−	0.0281635i
$709$	6.89957e10	−	1.66570e11i	0.273047	−	0.659193i	−0.726564	−	0.687099i	$-0.758884\pi$
$709$	6.89957e10	−	1.66570e11i	0.273047	−	0.659193i	0.999611	+	0.0279058i	$0.00888384\pi$
$710$	−1.65797e11	+	4.14830e11i	−0.652444	+	1.63244i
$711$	4.69389e10	−	4.69389e10i	0.183677	−	0.183677i
$712$	2.61450e11	−	9.78805e9i	1.01735	−	0.0380870i
$713$	−4.59030e10	+	4.59030e10i	−0.177616	+	0.177616i
$714$	−4.68039e11	+	2.00744e11i	−1.80090	+	0.772412i
$715$	1.81549e11	−	4.38299e11i	0.694658	−	1.67705i
$716$	−1.18811e11	−	2.67743e11i	−0.452070	−	1.01874i
$717$	9.32914e10	+	2.25225e11i	0.352992	+	0.852198i
$718$	2.58572e10	−	3.22542e8i	0.0972933	−	0.00121364i
$719$	−7.98468e10			−0.298773			−0.149387	−	0.988779i	$-0.547730\pi$
$719$	−7.98468e10			−0.298773			−0.149387	+	0.988779i	$0.547730\pi$
$720$	3.81762e10	+	8.05488e10i	0.142057	+	0.299729i
$721$			5.79373e11i			2.14396i
$722$	2.71716e11	−	3.38938e9i	0.999922	−	0.0124730i
$723$	3.22766e11	−	1.33694e11i	1.18123	−	0.489282i
$724$	−9.60698e10	+	2.49351e11i	−0.349649	+	0.907521i
$725$	6.82712e10	+	2.82789e10i	0.247107	+	0.102355i
$726$	−3.30815e11	+	1.41888e11i	−1.19080	+	0.510738i
$727$	1.99932e11	+	1.99932e11i	0.715721	+	0.715721i	0.967726	−	0.252005i	$-0.0810899\pi$
$727$	1.99932e11	+	1.99932e11i	0.715721	+	0.715721i	−0.252005	+	0.967726i	$0.581090\pi$
$728$	4.72145e11	−	2.16604e11i	1.68093	−	0.771153i
$729$	1.21568e11	+	1.21568e11i	0.430435	+	0.430435i
$730$	2.86890e10	−	7.17809e10i	0.101024	−	0.252765i
$731$	−2.63875e11	−	1.09300e11i	−0.924119	−	0.382783i
$732$	−1.09977e11	+	1.15606e11i	−0.383052	+	0.402657i
$733$	2.71902e11	−	1.12625e11i	0.941882	−	0.390140i	0.141708	−	0.989908i	$-0.454741\pi$
$733$	2.71902e11	−	1.12625e11i	0.941882	−	0.390140i	0.800174	+	0.599768i	$0.204741\pi$
$734$	−1.92791e11	−	1.88040e11i	−0.664205	−	0.647839i
$735$			9.92570e11i			3.40104i
$736$	−3.71814e9	−	5.95401e10i	−0.0126711	−	0.202908i
$737$	−6.25929e11			−2.12156
$738$	−4.44909e9	+	4.56149e9i	−0.0149984	+	0.0153774i
$739$	5.36777e10	+	1.29589e11i	0.179977	+	0.434502i	0.987961	−	0.154702i	$-0.0494416\pi$
$739$	5.36777e10	+	1.29589e11i	0.179977	+	0.434502i	−0.807985	+	0.589203i	$0.799442\pi$
$740$	3.47384e11	−	3.65163e11i	1.15846	−	1.21776i
$741$	−8.49016e7	+	2.04971e8i	−0.000281607	+	0.000679859i
$742$	2.58843e11	+	1.03453e11i	0.853926	+	0.341292i
$743$	2.76604e11	−	2.76604e11i	0.907619	−	0.907619i	−0.0884602	−	0.996080i	$-0.528195\pi$
$743$	2.76604e11	−	2.76604e11i	0.907619	−	0.907619i	0.996080	+	0.0884602i	$0.0281946\pi$
$744$	1.48250e11	−	3.99573e11i	0.483843	−	1.30408i
$745$	−3.76255e10	+	3.76255e10i	−0.122140	+	0.122140i
$746$	−9.82950e10	−	2.29177e11i	−0.317377	−	0.739974i
$747$	1.89962e10	−	4.58608e10i	0.0610076	−	0.147285i
$748$	−1.55008e11	+	4.02325e11i	−0.495162	+	1.28520i
$749$	−2.57517e11	−	6.21700e11i	−0.818235	−	1.97539i
$750$	2.54218e9	+	2.03799e11i	0.00803456	+	0.644105i
$751$	1.08985e11			0.342614			0.171307	−	0.985218i	$-0.445201\pi$
$751$	1.08985e11			0.342614			0.171307	+	0.985218i	$0.445201\pi$
$752$	4.66100e11	−	2.32746e10i	1.45750	−	0.0727798i
$753$			2.88417e11i			0.897102i
$754$	−1.99706e9	−	1.60098e11i	−0.00617881	−	0.495335i
$755$	−4.09566e11	+	1.69648e11i	−1.26048	+	0.522108i
$756$	−2.02541e11	−	4.56428e11i	−0.620048	−	1.39729i
$757$	−3.06581e11	−	1.26990e11i	−0.933602	−	0.386710i	−0.136558	−	0.990632i	$-0.543604\pi$
$757$	−3.06581e11	−	1.26990e11i	−0.933602	−	0.386710i	−0.797044	+	0.603922i	$0.793604\pi$
$758$	−7.11581e10	−	1.65907e11i	−0.215550	−	0.502560i
$759$	−7.87708e10	−	7.87708e10i	−0.237355	−	0.237355i
$760$	−1.98743e8	−	1.84399e8i	−0.000595712	−	0.000552718i
$761$	1.39692e11	+	1.39692e11i	0.416517	+	0.416517i	0.884001	−	0.467484i	$-0.154840\pi$
$761$	1.39692e11	+	1.39692e11i	0.416517	+	0.416517i	−0.467484	+	0.884001i	$0.654840\pi$
$762$	−1.53944e11	−	6.15277e10i	−0.456609	−	0.182495i
$763$	−6.40455e11	−	2.65285e11i	−1.88969	−	0.782735i
$764$	2.95610e11	−	7.37602e9i	0.867652	−	0.0216495i
$765$	9.85607e10	−	4.08252e10i	0.287778	−	0.119202i
$766$	−2.53672e11	+	2.60080e11i	−0.736812	+	0.755426i
$767$			3.46322e11i			1.00069i
$768$	1.85180e11	+	3.45108e11i	0.532291	+	0.991997i
$769$	4.45367e11			1.27354			0.636769	−	0.771054i	$-0.280270\pi$
$769$	4.45367e11			1.27354			0.636769	+	0.771054i	$0.280270\pi$
$770$	8.48562e11	+	8.27653e11i	2.41391	+	2.35443i
$771$	−1.23782e11	−	2.98836e11i	−0.350299	−	0.845698i
$772$	−2.76859e9	−	1.10957e11i	−0.00779453	−	0.312383i
$773$	2.48415e11	−	5.99726e11i	0.695759	−	1.67971i	−0.0370820	−	0.999312i	$-0.511806\pi$
$773$	2.48415e11	−	5.99726e11i	0.695759	−	1.67971i	0.732841	−	0.680400i	$-0.238194\pi$
$774$	−3.79351e10	+	9.49149e10i	−0.105700	+	0.264466i
$775$	−1.69793e11	+	1.69793e11i	−0.470665	+	0.470665i
$776$	−1.15254e11	+	1.24219e11i	−0.317840	+	0.342564i
$777$	7.28685e11	−	7.28685e11i	1.99920	−	1.99920i
$778$	4.37045e11	−	1.87450e11i	1.19291	−	0.511643i
$779$	7.41649e6	−	1.79050e7i	2.01395e−5	−	4.86210e-5i
$780$	−4.71433e11	+	2.09199e11i	−1.27362	+	0.565173i
$781$	2.95933e11	+	7.14444e11i	0.795406	+	1.92028i
$782$	−7.13918e10	+	8.90541e8i	−0.190907	+	0.00238137i
$783$	−1.53911e11			−0.409472
$784$	4.58883e10	+	9.18963e11i	0.121461	+	2.43239i
$785$		−	4.04396e11i		−	1.06495i
$786$	−9.16047e10	+	1.14268e9i	−0.240009	+	0.00299387i
$787$	−4.75702e11	+	1.97042e11i	−1.24004	+	0.513642i	−0.903728	−	0.428108i	$-0.859180\pi$
$787$	−4.75702e11	+	1.97042e11i	−1.24004	+	0.513642i	−0.336314	+	0.941750i	$0.609180\pi$
$788$	−4.60463e11	−	1.77407e11i	−1.19424	−	0.460115i
$789$	1.93367e11	+	8.00953e10i	0.498970	+	0.206680i
$790$	−4.31361e11	+	1.85012e11i	−1.10747	+	0.474999i
$791$	−3.44083e11	−	3.44083e11i	−0.878935	−	0.878935i
$792$	1.44663e11	+	5.36734e10i	0.367670	+	0.136414i
$793$	−1.37734e11	−	1.37734e11i	−0.348295	−	0.348295i
$794$	−5.66863e9	+	1.41831e10i	−0.0142625	+	0.0356853i
$795$	−2.55700e11	−	1.05915e11i	−0.640122	−	0.265147i
$796$	−4.27933e11	−	4.07097e11i	−1.06592	−	1.01402i
$797$	−2.73779e11	+	1.13403e11i	−0.678526	+	0.281055i	−0.695211	−	0.718806i	$-0.744689\pi$
$797$	−2.73779e11	+	1.13403e11i	−0.678526	+	0.281055i	0.0166846	+	0.999861i	$0.494689\pi$
$798$	−3.96830e8	−	3.87052e8i	−0.000978573	−	0.000954460i
$799$		−	5.58531e11i		−	1.37044i
$800$	−1.37532e10	−	2.20236e11i	−0.0335772	−	0.537685i
$801$	−1.12061e11			−0.272222
$802$	3.14628e11	−	3.22577e11i	0.760502	−	0.779715i
$803$	−5.12073e10	−	1.23625e11i	−0.123160	−	0.297335i
$804$	4.93031e11	+	4.69026e11i	1.17991	+	1.12246i
$805$	−7.51170e10	+	1.81349e11i	−0.178877	+	0.431848i
$806$	4.83114e11	+	1.93089e11i	1.14475	+	0.457527i
$807$	3.04220e11	−	3.04220e11i	0.717288	−	0.717288i
$808$	3.93019e10	+	8.56689e10i	0.0922080	+	0.200992i
$809$	−4.26272e11	+	4.26272e11i	−0.995160	+	0.995160i	−0.999988	−	0.00482806i	$-0.998463\pi$
$809$	−4.26272e11	+	4.26272e11i	−0.995160	+	0.995160i	0.00482806	+	0.999988i	$0.498463\pi$
$810$	2.51713e11	+	5.86876e11i	0.584744	+	1.36335i
$811$	−8.22656e10	+	1.98607e11i	−0.190167	+	0.459103i	−0.989991	−	0.141131i	$-0.954926\pi$
$811$	−8.22656e10	+	1.98607e11i	−0.190167	+	0.459103i	0.799824	+	0.600235i	$0.204926\pi$
$812$	3.73299e11	+	1.43825e11i	0.858684	+	0.330833i
$813$	−1.90773e11	−	4.60568e11i	−0.436672	−	1.05422i
$814$	−1.08820e10	−	8.72374e11i	−0.0247862	−	1.98703i
$815$	4.33293e11			0.982090
$816$	4.23570e11	−	2.00752e11i	0.955355	−	0.452792i
$817$		−	3.10886e8i		−	0.000697771i
$818$	1.04344e10	+	8.36491e11i	0.0233052	+	1.86831i
$819$	−2.05554e11	+	8.51434e10i	−0.456868	+	0.189241i
$820$	4.11815e10	−	1.82744e10i	0.0910849	−	0.0404191i
$821$	−6.42682e8	−	2.66207e8i	−0.00141457	−	0.000585932i	0.381976	−	0.924172i	$-0.375244\pi$
$821$	−6.42682e8	−	2.66207e8i	−0.00141457	−	0.000585932i	−0.383391	+	0.923586i	$0.625244\pi$
$822$	−1.37326e11	−	3.20179e11i	−0.300791	−	0.701302i
$823$	−4.36204e11	−	4.36204e11i	−0.950802	−	0.950802i	0.0480432	−	0.998845i	$-0.484701\pi$
$823$	−4.36204e11	−	4.36204e11i	−0.950802	−	0.950802i	−0.998845	+	0.0480432i	$0.984701\pi$
$824$	−1.99498e10	−	5.32882e11i	−0.0432742	−	1.15591i
$825$	−2.91369e11	−	2.91369e11i	−0.628966	−	0.628966i
$826$	−8.03514e11	−	3.21144e11i	−1.72613	−	0.689890i
$827$	−5.81813e11	−	2.40995e11i	−1.24383	−	0.515211i	−0.338921	−	0.940815i	$-0.610062\pi$
$827$	−5.81813e11	−	2.40995e11i	−1.24383	−	0.515211i	−0.904910	+	0.425603i	$0.860062\pi$
$828$	6.37357e8	+	2.55434e10i	0.00135600	+	0.0543448i
$829$	−3.07875e11	+	1.27526e11i	−0.651862	+	0.270010i	−0.684010	−	0.729473i	$-0.739765\pi$
$829$	−3.07875e11	+	1.27526e11i	−0.651862	+	0.270010i	0.0321475	+	0.999483i	$0.489765\pi$
$830$	−2.45069e11	+	2.51260e11i	−0.516388	+	0.529433i
$831$			4.36485e11i			0.915303i
$832$	−4.26801e11	+	2.15480e11i	−0.890700	+	0.449691i
$833$	1.10120e12			2.28711
$834$	9.03859e10	+	8.81587e10i	0.186826	+	0.182222i
$835$	2.56588e11	+	6.19458e11i	0.527825	+	1.27428i
$836$	−4.69155e8	+	1.17063e7i	−0.000960485	+	2.39659e-5i
$837$	1.91391e11	−	4.62060e11i	0.389961	−	0.941448i
$838$	−1.90619e10	+	4.76934e10i	−0.0386535	+	0.0967125i
$839$	−4.74939e11	+	4.74939e11i	−0.958496	+	0.958496i	−0.999172	−	0.0406763i	$-0.987049\pi$
$839$	−4.74939e11	+	4.74939e11i	−0.958496	+	0.958496i	0.0406763	+	0.999172i	$0.487049\pi$
$840$	−4.82111e10	−	1.28778e12i	−0.0968345	−	2.58656i
$841$	−2.66538e11	+	2.66538e11i	−0.532814	+	0.532814i
$842$	−4.31891e11	+	1.85240e11i	−0.859262	+	0.368541i
$843$	−2.41669e10	+	5.83440e10i	−0.0478531	+	0.115528i
$844$	−1.49388e11	−	3.36648e11i	−0.294406	−	0.663447i
$845$	1.07219e9	+	2.58851e9i	0.00210304	+	0.00507718i
$846$	−1.99869e11	+	2.49317e9i	−0.390179	+	0.00486709i
$847$	1.09793e12			2.13325
$848$	−2.41635e11	−	8.62387e10i	−0.467279	−	0.166770i
$849$		−	5.80466e11i		−	1.11724i
$850$	−2.64075e11	+	3.29406e9i	−0.505884	+	0.00631039i
$851$	1.33476e11	−	5.52875e10i	0.254498	−	0.105416i
$852$	3.02253e11	−	7.84504e11i	0.573605	−	1.48880i
$853$	2.82169e11	+	1.16878e11i	0.532983	+	0.220769i	0.632909	−	0.774226i	$-0.281861\pi$
$853$	2.82169e11	+	1.16878e11i	0.532983	+	0.220769i	−0.0999262	+	0.994995i	$0.531861\pi$
$854$	4.47280e11	−	1.91840e11i	0.840907	−	0.360668i
$855$	8.21094e7	+	8.21094e7i	0.000153649	+	0.000153649i
$856$	2.58260e11	+	5.62947e11i	0.481019	+	1.04851i
$857$	6.13812e11	+	6.13812e11i	1.13792	+	1.13792i	0.988822	+	0.149099i	$0.0476374\pi$
$857$	6.13812e11	+	6.13812e11i	1.13792	+	1.13792i	0.149099	+	0.988822i	$0.452363\pi$
$858$	−3.31345e11	+	8.29037e11i	−0.611408	+	1.52977i
$859$	−3.14918e11	−	1.30443e11i	−0.578395	−	0.239579i	0.0742544	−	0.997239i	$-0.476342\pi$
$859$	−3.14918e11	−	1.30443e11i	−0.578395	−	0.239579i	−0.652649	+	0.757660i	$0.726342\pi$
$860$	4.98141e11	−	5.23636e11i	0.910665	−	0.957273i
$861$	8.51080e10	−	3.52529e10i	0.154867	−	0.0641479i
$862$	3.25303e11	+	3.17287e11i	0.589194	+	0.574676i
$863$		−	8.75685e11i		−	1.57872i	−0.613932	−	0.789359i	$-0.710413\pi$
$863$		−	8.75685e11i		−	1.57872i	0.613932	−	0.789359i	$-0.289587\pi$
$864$	2.02005e11	+	4.12829e11i	0.362499	+	0.740825i
$865$	−9.16704e11			−1.63744
$866$	−5.21802e11	+	5.34985e11i	−0.927757	+	0.951195i
$867$	2.87470e10	+	6.94015e10i	0.0508764	+	0.122827i
$868$	−8.95982e11	+	9.41839e11i	−1.57841	+	1.65920i
$869$	−3.10922e11	+	7.50633e11i	−0.545222	+	1.31628i
$870$	−3.68834e11	−	1.47414e11i	−0.643805	−	0.257312i
$871$	−5.87401e11	+	5.87401e11i	−1.02062	+	1.02062i
$872$	5.98198e11	+	2.21945e11i	1.03462	+	0.383866i
$873$	5.13205e10	−	5.13205e10i	0.0883556	−	0.0883556i
$874$	−3.06332e7	−	7.14222e7i	−5.24985e−5	−	0.000122402i
$875$	2.37901e11	−	5.74344e11i	0.405849	−	0.979806i
$876$	−5.23010e10	+	1.35748e11i	−0.0888165	+	0.230525i
$877$	−7.85502e10	−	1.89637e11i	−0.132785	−	0.320571i	0.843477	−	0.537166i	$-0.180505\pi$
$877$	−7.85502e10	−	1.89637e11i	−0.132785	−	0.320571i	−0.976262	+	0.216595i	$0.930505\pi$
$878$	8.23523e9	+	6.60192e11i	0.0138579	+	1.11094i
$879$	−8.31990e11			−1.39368
$880$	−8.08970e11	−	7.32021e11i	−1.34897	−	1.22066i
$881$			2.75725e11i			0.457690i	0.973463	+	0.228845i	$0.0734950\pi$
$881$			2.75725e11i			0.457690i	−0.973463	+	0.228845i	$0.926505\pi$
$882$	−4.91553e9	−	3.94062e11i	−0.00812262	−	0.651164i
$883$	7.71266e11	−	3.19469e11i	1.26871	−	0.525516i	0.356137	−	0.934434i	$-0.384094\pi$
$883$	7.71266e11	−	3.19469e11i	1.26871	−	0.525516i	0.912571	+	0.408918i	$0.134094\pi$
$884$	2.32094e11	+	5.23028e11i	0.380063	+	0.856477i
$885$	7.93759e11	+	3.28786e11i	1.29394	+	0.535969i
$886$	−2.46254e11	−	5.74146e11i	−0.399620	−	0.931725i
$887$	3.60640e11	+	3.60640e11i	0.582612	+	0.582612i	0.935620	−	0.353008i	$-0.114841\pi$
$887$	3.60640e11	+	3.60640e11i	0.582612	+	0.582612i	−0.353008	+	0.935620i	$0.614841\pi$
$888$	−6.45123e11	+	6.95305e11i	−1.03751	+	1.11821i
$889$	3.57562e11	+	3.57562e11i	0.572458	+	0.572458i
$890$	7.35758e11	+	2.94064e11i	1.17267	+	0.468685i
$891$	1.02125e12	+	4.23016e11i	1.62040	+	0.671191i
$892$	7.46401e11	−	1.86241e10i	1.17900	−	0.0294182i
$893$	5.61671e8	−	2.32652e8i	0.000883234	−	0.000365848i
$894$	6.99191e10	−	7.16855e10i	0.109458	−	0.112223i
$895$		−	8.87096e11i		−	1.38254i
$896$	−1.04172e11	−	1.19005e12i	−0.161629	−	1.84643i
$897$	−1.47844e11			−0.228368
$898$	−8.36519e11	−	8.15906e11i	−1.28638	−	1.25469i
$899$	1.53331e11	+	3.70174e11i	0.234742	+	0.566718i
$900$	2.35755e9	+	9.44839e10i	0.00359328	+	0.144008i
$901$	−1.17506e11	+	2.83685e11i	−0.178304	+	0.430464i
$902$	2.89443e10	−	7.24196e10i	0.0437257	−	0.109403i
$903$	1.04492e12	−	1.04492e12i	1.57156	−	1.57156i
$904$	3.28321e11	+	3.04625e11i	0.491614	+	0.456133i
$905$	−5.72232e11	+	5.72232e11i	−0.853056	+	0.853056i
$906$	7.66724e11	−	3.28851e11i	1.13796	−	0.488074i
$907$	1.62290e11	−	3.91803e11i	0.239807	−	0.578946i	−0.757455	−	0.652887i	$-0.773558\pi$
$907$	1.62290e11	−	3.91803e11i	0.239807	−	0.578946i	0.997263	+	0.0739409i	$0.0235576\pi$
$908$	−9.56330e11	+	4.24373e11i	−1.40690	+	0.624316i
$909$	−1.54490e10	−	3.72971e10i	−0.0226279	−	0.0546285i
$910$	1.57304e12	−	1.96221e10i	2.29390	−	0.0286140i
$911$	−6.97828e11			−1.01315			−0.506577	−	0.862195i	$-0.669089\pi$
$911$	−6.97828e11			−1.01315			−0.506577	+	0.862195i	$0.669089\pi$
$912$	3.78315e8	+	3.42330e8i	0.000546858	+	0.000494841i
$913$			6.07563e11i			0.874396i
$914$	8.76661e11	−	1.09355e10i	1.25617	−	0.0156694i
$915$	−4.46440e11	+	1.84921e11i	−0.636911	+	0.263817i
$916$	6.02502e11	+	2.32132e11i	0.855808	+	0.329726i
$917$	2.58160e11	+	1.06933e11i	0.365100	+	0.151229i
$918$	5.05523e11	−	2.16821e11i	0.711820	−	0.305302i
$919$	3.72437e11	+	3.72437e11i	0.522145	+	0.522145i	0.918219	−	0.396074i	$-0.129627\pi$
$919$	3.72437e11	+	3.72437e11i	0.522145	+	0.522145i	−0.396074	+	0.918219i	$0.629627\pi$
$920$	6.28450e10	−	1.69383e11i	0.0877242	−	0.236439i
$921$	−2.72298e11	−	2.72298e11i	−0.378448	−	0.378448i
$922$	−7.15903e9	+	1.79122e10i	−0.00990673	+	0.0247870i
$923$	9.48185e11	+	3.92751e11i	1.30643	+	0.541141i
$924$	−1.61622e12	−	1.53753e12i	−2.21724	−	2.10929i
$925$	4.93720e11	−	2.04505e11i	0.674394	−	0.279343i
$926$	3.78929e11	+	3.69592e11i	0.515364	+	0.502665i
$927$			2.28400e11i			0.309298i
$928$	−3.48297e11	−	1.19430e11i	−0.469633	−	0.161035i
$929$	1.05605e12			1.41782			0.708910	−	0.705298i	$-0.249187\pi$
$929$	1.05605e12			1.41782			0.708910	+	0.705298i	$0.249187\pi$
$930$	9.01204e11	−	9.23971e11i	1.20473	−	1.23517i
$931$	4.58696e8	+	1.10739e9i	0.000610557	+	0.00147402i
$932$	−2.91104e11	−	2.76931e11i	−0.385820	−	0.367035i
$933$	−2.24957e11	+	5.43095e11i	−0.296875	+	0.716720i
$934$	−1.73906e11	−	6.95056e10i	−0.228521	−	0.0913340i
$935$	−9.23291e11	+	9.23291e11i	−1.20807	+	1.20807i
$936$	1.86128e11	−	8.53893e10i	0.242499	−	0.111250i
$937$	−5.45101e11	+	5.45101e11i	−0.707162	+	0.707162i	−0.965937	−	0.258776i	$-0.916681\pi$
$937$	−5.45101e11	+	5.45101e11i	−0.707162	+	0.707162i	0.258776	+	0.965937i	$0.416681\pi$
$938$	−8.18152e11	−	1.90754e12i	−1.05687	−	2.46413i
$939$	−2.98194e11	+	7.19904e11i	−0.383563	+	0.926003i
$940$	1.31882e12	+	5.08116e11i	1.68918	+	0.650806i
$941$	−4.74830e11	−	1.14634e12i	−0.605591	−	1.46203i	−0.867750	−	0.497002i	$-0.834434\pi$
$941$	−4.74830e11	−	1.14634e12i	−0.605591	−	1.46203i	0.262158	−	0.965025i	$-0.415566\pi$
$942$	9.49244e9	+	7.60978e11i	0.0120552	+	0.966426i
$943$	1.29148e10			0.0163320
$944$	7.50096e11	+	2.67707e11i	0.944559	+	0.337110i
$945$		−	1.51226e12i		−	1.89626i
$946$	−1.56045e10	−	1.25097e12i	−0.0194844	−	1.56200i
$947$	−3.08218e11	+	1.27668e11i	−0.383229	+	0.158739i	−0.565977	−	0.824421i	$-0.691501\pi$
$947$	−3.08218e11	+	1.27668e11i	−0.383229	+	0.158739i	0.182748	+	0.983160i	$0.441501\pi$
$948$	8.07378e11	−	3.58275e11i	0.999640	−	0.443592i
$949$	−1.64071e11	−	6.79605e10i	−0.202287	−	0.0837899i
$950$	−1.13311e8	−	2.64187e8i	−0.000139116	−	0.000324352i
$951$	6.65720e11	+	6.65720e11i	0.813897	+	0.813897i
$952$	−1.42871e12	+	5.34875e10i	−1.73939	+	0.0651185i
$953$	−2.00302e11	−	2.00302e11i	−0.242836	−	0.242836i	0.575186	−	0.818023i	$-0.304930\pi$
$953$	−2.00302e11	−	2.00302e11i	−0.242836	−	0.242836i	−0.818023	+	0.575186i	$0.804930\pi$
$954$	1.02041e11	+	4.07830e10i	0.123191	+	0.0492364i
$955$	8.27353e11	+	3.42701e11i	0.994666	+	0.412004i
$956$	1.70714e10	+	6.84173e11i	0.0204380	+	0.819095i
$957$	−6.35228e11	+	2.63120e11i	−0.757324	+	0.313694i
$958$	−4.75687e11	+	4.87704e11i	−0.564753	+	0.579021i
$959$			1.06263e12i			1.25634i
$960$	8.86851e10	+	1.18278e12i	0.104416	+	1.39258i
$961$	−4.49082e11			−0.526541
$962$	−8.28889e11	−	8.08465e11i	−0.967823	−	0.943975i
$963$	−1.01518e11	−	2.45086e11i	−0.118042	−	0.284979i
$964$	9.80475e11	−	2.44647e10i	1.13535	−	0.0283290i
$965$	1.28633e11	−	3.10548e11i	0.148335	−	0.358112i
$966$	1.37096e11	−	3.43019e11i	0.157440	−	0.393921i
$967$	−5.87775e11	+	5.87775e11i	−0.672210	+	0.672210i	−0.958225	−	0.286015i	$-0.907669\pi$
$967$	−5.87775e11	+	5.87775e11i	−0.672210	+	0.672210i	0.286015	+	0.958225i	$0.407669\pi$
$968$	−1.00983e12	+	3.78056e10i	−1.15013	+	0.0430580i
$969$	4.31777e8	−	4.31777e8i	0.000489739	−	0.000489739i
$970$	−4.71628e11	+	2.02283e11i	−0.532737	+	0.228493i
$971$	−4.70046e10	+	1.13479e11i	−0.0528766	+	0.127655i	−0.948110	−	0.317941i	$-0.897008\pi$
$971$	−4.70046e10	+	1.13479e11i	−0.0528766	+	0.127655i	0.895234	+	0.445597i	$0.147008\pi$
$972$	−1.88833e11	−	4.25538e11i	−0.211550	−	0.476731i
$973$	−1.47376e11	−	3.55797e11i	−0.164428	−	0.396964i
$974$	−1.10358e12	+	1.37660e10i	−1.22621	+	0.0152958i
$975$	−5.46869e11			−0.605152
$976$	−4.04784e11	+	1.91848e11i	−0.446091	+	0.211426i
$977$			5.95537e11i			0.653628i	0.945089	+	0.326814i	$0.105975\pi$
$977$			5.95537e11i			0.653628i	−0.945089	+	0.326814i	$0.894025\pi$
$978$	−8.15356e11	+	1.01707e10i	−0.891234	+	0.0111172i
$979$	1.26717e12	−	5.24877e11i	1.37944	−	0.571382i
$980$	−1.00180e12	+	2.60020e12i	−1.08612	+	2.81905i
$981$	−2.52479e11	−	1.04580e11i	−0.272615	−	0.112921i
$982$	−8.45862e11	+	3.62793e11i	−0.909607	+	0.390134i
$983$	−7.48127e11	−	7.48127e11i	−0.801237	−	0.801237i	0.182052	−	0.983289i	$-0.441726\pi$
$983$	−7.48127e11	−	7.48127e11i	−0.801237	−	0.801237i	−0.983289	+	0.182052i	$0.941726\pi$
$984$	−7.70649e10	+	3.53547e10i	−0.0822008	+	0.0377109i
$985$	−1.05671e12	−	1.05671e12i	−1.12256	−	1.12256i
$986$	−1.63547e11	+	4.09200e11i	−0.173035	+	0.432941i
$987$	2.66980e12	+	1.10587e12i	2.81326	+	1.16529i
$988$	−4.29291e8	+	4.51262e8i	−0.000450530	+	0.000473589i
$989$	1.91401e11	−	7.92810e10i	0.200060	−	0.0828675i
$990$	3.34519e11	+	3.26276e11i	0.348241	+	0.339660i
$991$		−	6.53043e11i		−	0.677091i	−0.940950	−	0.338546i	$-0.890065\pi$
$991$		−	6.53043e11i		−	0.677091i	0.940950	−	0.338546i	$-0.109935\pi$
$992$	7.91656e11	−	8.97116e11i	0.817503	−	0.926407i
$993$	−1.66051e12			−1.70783
$994$	−1.79049e12	+	1.83572e12i	−1.83411	+	1.88044i
$995$	−6.84516e11	−	1.65257e12i	−0.698379	−	1.68604i
$996$	4.55264e11	−	4.78565e11i	0.462622	−	0.486299i
$997$	3.49426e11	−	8.43590e11i	0.353651	−	0.853789i	−0.642512	−	0.766276i	$-0.722108\pi$
$997$	3.49426e11	−	8.43590e11i	0.353651	−	0.853789i	0.996163	−	0.0875140i	$-0.0278922\pi$
$998$	−2.64479e11	−	1.05705e11i	−0.266605	−	0.106555i
$999$	−7.87044e11	+	7.87044e11i	−0.790200	+	0.790200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.9.h.a.11.8	yes	124
32.3	odd	8	inner	32.9.h.a.3.8	✓	124

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.9.h.a.3.8	✓	124	32.3	odd	8	inner
32.9.h.a.11.8	yes	124	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	32.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-11.4539 - 11.1717i) q^{2} +(34.8964 + 84.2473i) q^{3} +(6.38569 + 255.920i) q^{4} +(-296.689 + 716.270i) q^{5} +(541.485 - 1354.82i) q^{6} +(-3146.79 + 3146.79i) q^{7} +(2785.93 - 3002.64i) q^{8} +(-1240.52 + 1240.52i) q^{9} +O(q^{10})\)	\(q+(-11.4539 - 11.1717i) q^{2} +(34.8964 + 84.2473i) q^{3} +(6.38569 + 255.920i) q^{4} +(-296.689 + 716.270i) q^{5} +(541.485 - 1354.82i) q^{6} +(-3146.79 + 3146.79i) q^{7} +(2785.93 - 3002.64i) q^{8} +(-1240.52 + 1240.52i) q^{9} +(11400.2 - 4889.60i) q^{10} +(8217.21 - 19838.1i) q^{11} +(-21337.8 + 9468.67i) q^{12} +(-10905.6 - 26328.4i) q^{13} +(71198.1 - 888.125i) q^{14} -70697.2 q^{15} +(-65454.4 + 3268.46i) q^{16} +78434.5i q^{17} +(28067.6 - 350.116i) q^{18} +(-78.8755 + 32.6713i) q^{19} +(-185203. - 71354.8i) q^{20} +(-374920. - 155297. i) q^{21} +(-315745. + 135424. i) q^{22} +(-40229.1 - 40229.1i) q^{23} +(350183. + 129926. i) q^{24} +(-148805. - 148805. i) q^{25} +(-169221. + 423398. i) q^{26} +(404946. + 167734. i) q^{27} +(-825421. - 785232. i) q^{28} +(-324418. + 134378. i) q^{29} +(809762. + 789809. i) q^{30} -1.14104e6i q^{31} +(786226. + 693802. i) q^{32} +1.95806e6 q^{33} +(876248. - 898385. i) q^{34} +(-1.32033e6 - 3.18757e6i) q^{35} +(-325397. - 309553. i) q^{36} +(-971788. + 2.34610e6i) q^{37} +(1268.43 + 506.959i) q^{38} +(1.83753e6 - 1.83753e6i) q^{39} +(1.32415e6 + 2.88633e6i) q^{40} +(-160516. + 160516. i) q^{41} +(2.55938e6 + 5.96726e6i) q^{42} +(-1.39352e6 + 3.36426e6i) q^{43} +(5.12944e6 + 1.97627e6i) q^{44} +(-520500. - 1.25660e6i) q^{45} +(11353.9 + 910209. i) q^{46} -7.12098e6 q^{47} +(-2.55948e6 - 5.40030e6i) q^{48} -1.40397e7i q^{49} +(41997.6 + 3.36682e6i) q^{50} +(-6.60790e6 + 2.73708e6i) q^{51} +(6.66834e6 - 2.95909e6i) q^{52} +(3.61684e6 + 1.49814e6i) q^{53} +(-2.76435e6 - 6.44516e6i) q^{54} +(1.17715e7 + 1.17715e7i) q^{55} +(681938. + 1.82154e7i) q^{56} +(-5504.93 - 5504.93i) q^{57} +(5.21710e6 + 2.08514e6i) q^{58} +(-1.12276e7 - 4.65062e6i) q^{59} +(-451450. - 1.80929e7i) q^{60} +(6.31482e6 - 2.61568e6i) q^{61} +(-1.27474e7 + 1.30694e7i) q^{62} -7.80732e6i q^{63} +(-1.25444e6 - 1.67303e7i) q^{64} +2.20938e7 q^{65} +(-2.24275e7 - 2.18748e7i) q^{66} +(-1.11553e7 - 2.69312e7i) q^{67} +(-2.00730e7 + 500859. i) q^{68} +(1.98534e6 - 4.79304e6i) q^{69} +(-2.04876e7 + 5.12606e7i) q^{70} +(-2.54656e7 + 2.54656e7i) q^{71} +(268833. + 7.18085e6i) q^{72} +(4.40649e6 - 4.40649e6i) q^{73} +(3.73408e7 - 1.60156e7i) q^{74} +(7.34367e6 - 1.77292e7i) q^{75} +(-8864.92 - 19977.2i) q^{76} +(3.65685e7 + 8.82841e7i) q^{77} +(-4.15754e7 + 518611. i) q^{78} -3.78380e7 q^{79} +(1.70785e7 - 4.78528e7i) q^{80} +5.14793e7i q^{81} +(3.63177e6 - 45302.7i) q^{82} +(-2.61410e7 + 1.08280e7i) q^{83} +(3.73495e7 - 9.69413e7i) q^{84} +(-5.61803e7 - 2.32706e7i) q^{85} +(5.35459e7 - 2.29661e7i) q^{86} +(-2.26420e7 - 2.26420e7i) q^{87} +(-3.66740e7 - 7.99408e7i) q^{88} +(4.51667e7 + 4.51667e7i) q^{89} +(-8.07658e6 + 2.02079e7i) q^{90} +(1.17167e8 + 4.85323e7i) q^{91} +(1.00385e7 - 1.05523e7i) q^{92} +(9.61296e7 - 3.98182e7i) q^{93} +(8.15633e7 + 7.95535e7i) q^{94} -66189.3i q^{95} +(-3.10145e7 + 9.04486e7i) q^{96} -4.13701e7 q^{97} +(-1.56848e8 + 1.60810e8i) q^{98} +(1.44160e7 + 3.48032e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 124 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 124 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 124 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 34996 q^{10} - 4 q^{11} - 45364 q^{12} - 4 q^{13} + 145580 q^{14} - 8 q^{15} - 278384 q^{16} - 131224 q^{18} - 4 q^{19} + 689996 q^{20} - 4 q^{21} + 6048 q^{22} + 845564 q^{23} - 310832 q^{24} - 4 q^{25} + 1682096 q^{26} - 51076 q^{27} - 1807624 q^{28} - 4 q^{29} - 3968188 q^{30} + 2420456 q^{32} - 8 q^{33} + 4139280 q^{34} - 2415748 q^{35} - 2364816 q^{36} - 4 q^{37} - 4553644 q^{38} + 7650044 q^{39} - 14971800 q^{40} - 4 q^{41} + 17019656 q^{42} - 1859716 q^{43} + 13377860 q^{44} - 26248 q^{45} + 11790684 q^{46} - 8 q^{47} - 21819984 q^{48} - 49149676 q^{50} - 27697792 q^{51} - 33503196 q^{52} - 5358724 q^{53} + 82403296 q^{54} + 46326780 q^{55} + 87708200 q^{56} - 4 q^{57} - 37235424 q^{58} - 44938756 q^{59} - 167711176 q^{60} + 48952060 q^{61} + 23721528 q^{62} + 27135128 q^{64} - 8 q^{65} + 226680332 q^{66} + 93380476 q^{67} - 491760 q^{68} - 17273092 q^{69} - 167238952 q^{70} - 79832068 q^{71} - 184202092 q^{72} - 4 q^{73} + 28015148 q^{74} - 27399560 q^{75} + 201789948 q^{76} - 94964356 q^{77} + 473461108 q^{78} + 144406520 q^{79} - 447998920 q^{80} - 231632004 q^{82} - 140384644 q^{83} + 263072 q^{84} + 1562496 q^{85} + 268005440 q^{86} - 149712644 q^{87} + 220344096 q^{88} - 4 q^{89} + 51924392 q^{90} + 350400764 q^{91} - 622977496 q^{92} + 26240 q^{93} - 100742552 q^{94} + 101686144 q^{96} - 8 q^{97} + 721239576 q^{98} - 630043272 q^{99}+O(q^{100}) \) 124 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 34996 * q^10 - 4 * q^11 - 45364 * q^12 - 4 * q^13 + 145580 * q^14 - 8 * q^15 - 278384 * q^16 - 131224 * q^18 - 4 * q^19 + 689996 * q^20 - 4 * q^21 + 6048 * q^22 + 845564 * q^23 - 310832 * q^24 - 4 * q^25 + 1682096 * q^26 - 51076 * q^27 - 1807624 * q^28 - 4 * q^29 - 3968188 * q^30 + 2420456 * q^32 - 8 * q^33 + 4139280 * q^34 - 2415748 * q^35 - 2364816 * q^36 - 4 * q^37 - 4553644 * q^38 + 7650044 * q^39 - 14971800 * q^40 - 4 * q^41 + 17019656 * q^42 - 1859716 * q^43 + 13377860 * q^44 - 26248 * q^45 + 11790684 * q^46 - 8 * q^47 - 21819984 * q^48 - 49149676 * q^50 - 27697792 * q^51 - 33503196 * q^52 - 5358724 * q^53 + 82403296 * q^54 + 46326780 * q^55 + 87708200 * q^56 - 4 * q^57 - 37235424 * q^58 - 44938756 * q^59 - 167711176 * q^60 + 48952060 * q^61 + 23721528 * q^62 + 27135128 * q^64 - 8 * q^65 + 226680332 * q^66 + 93380476 * q^67 - 491760 * q^68 - 17273092 * q^69 - 167238952 * q^70 - 79832068 * q^71 - 184202092 * q^72 - 4 * q^73 + 28015148 * q^74 - 27399560 * q^75 + 201789948 * q^76 - 94964356 * q^77 + 473461108 * q^78 + 144406520 * q^79 - 447998920 * q^80 - 231632004 * q^82 - 140384644 * q^83 + 263072 * q^84 + 1562496 * q^85 + 268005440 * q^86 - 149712644 * q^87 + 220344096 * q^88 - 4 * q^89 + 51924392 * q^90 + 350400764 * q^91 - 622977496 * q^92 + 26240 * q^93 - 100742552 * q^94 + 101686144 * q^96 - 8 * q^97 + 721239576 * q^98 - 630043272 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more