LMFDB - Embedded newform 37.10.h.a.25.20

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			25.20
Character	$\chi$	$=$	37.25
Dual form			37.10.h.a.3.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(12.3034 + 14.6627i) q^{2} +(154.895 + 129.973i) q^{3} +(25.2886 - 143.419i) q^{4} +(-383.475 - 1053.59i) q^{5} +3870.29i q^{6} +(1863.39 - 678.219i) q^{7} +(10901.1 - 6293.78i) q^{8} +(3681.76 + 20880.3i) q^{9} +O(q^{10})$	\(q+(12.3034 + 14.6627i) q^{2} +(154.895 + 129.973i) q^{3} +(25.2886 - 143.419i) q^{4} +(-383.475 - 1053.59i) q^{5} +3870.29i q^{6} +(1863.39 - 678.219i) q^{7} +(10901.1 - 6293.78i) q^{8} +(3681.76 + 20880.3i) q^{9} +(10730.4 - 18585.5i) q^{10} +(43401.1 + 75172.9i) q^{11} +(22557.6 - 18928.1i) q^{12} +(135626. + 23914.5i) q^{13} +(32870.6 + 18977.9i) q^{14} +(77539.1 - 213037. i) q^{15} +(156339. + 56902.7i) q^{16} +(-272495. + 48048.2i) q^{17} +(-260862. + 310884. i) q^{18} +(-30926.5 + 36856.7i) q^{19} +(-160802. + 28353.7i) q^{20} +(376780. + 137137. i) q^{21} +(-568253. + 1.56126e6i) q^{22} +(-1.34904e6 - 778868. i) q^{23} +(2.50655e6 + 441973. i) q^{24} +(533186. - 447396. i) q^{25} +(1.31801e6 + 2.28286e6i) q^{26} +(-153612. + 266063. i) q^{27} +(-50146.8 - 284396. i) q^{28} +(2.24298e6 - 1.29499e6i) q^{29} +(4.07769e6 - 1.48416e6i) q^{30} +9.12850e6i q^{31} +(-1.11510e6 - 3.06372e6i) q^{32} +(-3.04779e6 + 1.72849e7i) q^{33} +(-4.05714e6 - 3.40435e6i) q^{34} +(-1.42913e6 - 1.70317e6i) q^{35} +3.08773e6 q^{36} +(-3.42866e6 - 1.08723e7i) q^{37} -920921. q^{38} +(1.78995e7 + 2.13318e7i) q^{39} +(-1.08114e7 - 9.07181e6i) q^{40} +(866208. - 4.91251e6i) q^{41} +(2.62490e6 + 7.21186e6i) q^{42} -1.56517e7i q^{43} +(1.18788e7 - 4.32352e6i) q^{44} +(2.05874e7 - 1.18861e7i) q^{45} +(-5.17754e6 - 2.93633e7i) q^{46} +(-1.75562e7 + 3.04083e7i) q^{47} +(1.68204e7 + 2.91337e7i) q^{48} +(-2.79004e7 + 2.34112e7i) q^{49} +(1.31200e7 + 2.31342e6i) q^{50} +(-4.84531e7 - 2.79744e7i) q^{51} +(6.85956e6 - 1.88465e7i) q^{52} +(-3.21074e7 - 1.16861e7i) q^{53} +(-5.79115e6 + 1.02114e6i) q^{54} +(6.25581e7 - 7.45538e7i) q^{55} +(1.60445e7 - 1.91211e7i) q^{56} +(-9.58073e6 + 1.68934e6i) q^{57} +(4.65844e7 + 1.69553e7i) q^{58} +(3.82396e7 - 1.05063e8i) q^{59} +(-2.85926e7 - 1.65080e7i) q^{60} +(-6.70059e7 - 1.18149e7i) q^{61} +(-1.33848e8 + 1.12312e8i) q^{62} +(2.10219e7 + 3.64111e7i) q^{63} +(7.37940e7 - 1.27815e8i) q^{64} +(-2.68130e7 - 1.52064e8i) q^{65} +(-2.90941e8 + 1.67975e8i) q^{66} +(-1.63987e8 + 5.96862e7i) q^{67} +4.02960e7i q^{68} +(-1.07728e8 - 2.95981e8i) q^{69} +(7.38980e6 - 4.19096e7i) q^{70} +(-8.67460e7 - 7.27885e7i) q^{71} +(1.71551e8 + 2.04447e8i) q^{72} +7.25095e7 q^{73} +(1.17232e8 - 1.84040e8i) q^{74} +1.40737e8 q^{75} +(4.50386e6 + 5.36749e6i) q^{76} +(1.31857e8 + 1.10641e8i) q^{77} +(-9.25558e7 + 5.24910e8i) q^{78} +(1.69402e8 + 4.65428e8i) q^{79} -1.86537e8i q^{80} +(3.33784e8 - 1.21488e8i) q^{81} +(8.26879e7 - 4.77399e7i) q^{82} +(1.79757e7 + 1.01945e8i) q^{83} +(2.91962e7 - 5.05693e7i) q^{84} +(1.55118e8 + 2.68672e8i) q^{85} +(2.29495e8 - 1.92570e8i) q^{86} +(5.15740e8 + 9.09389e7i) q^{87} +(9.46244e8 + 5.46314e8i) q^{88} +(2.13360e8 - 5.86202e8i) q^{89} +(4.27578e8 + 1.55626e8i) q^{90} +(2.68943e8 - 4.74218e7i) q^{91} +(-1.45820e8 + 1.73781e8i) q^{92} +(-1.18645e9 + 1.41396e9i) q^{93} +(-6.61869e8 + 1.16705e8i) q^{94} +(5.06914e7 + 1.84501e7i) q^{95} +(2.25475e8 - 6.19488e8i) q^{96} +(-1.26259e9 - 7.28959e8i) q^{97} +(-6.86542e8 - 1.21056e8i) q^{98} +(-1.40984e9 + 1.18300e9i) 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 $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	12.3034	+	14.6627i	0.543741	+	0.648005i	0.966022	−	0.258460i	$-0.0832150\pi$
$2$	12.3034	+	14.6627i	0.543741	+	0.648005i	−0.422281	+	0.906465i	$0.638771\pi$
$3$	154.895	+	129.973i	1.10406	+	0.926416i	0.997691	−	0.0679111i	$-0.0216334\pi$
$3$	154.895	+	129.973i	1.10406	+	0.926416i	0.106368	+	0.994327i	$0.466078\pi$
$4$	25.2886	−	143.419i	0.0493918	−	0.280115i
$5$	−383.475	−	1053.59i	−0.274392	−	0.753886i	−0.997973	−	0.0636461i	$-0.979727\pi$
$5$	−383.475	−	1053.59i	−0.274392	−	0.753886i	0.723580	−	0.690240i	$-0.242495\pi$
$6$			3870.29i			1.21917i
$7$	1863.39	−	678.219i	0.293334	−	0.106765i	−0.191161	−	0.981559i	$-0.561225\pi$
$7$	1863.39	−	678.219i	0.293334	−	0.106765i	0.484496	+	0.874794i	$0.339003\pi$
$8$	10901.1	−	6293.78i	0.940952	−	0.543259i
$9$	3681.76	+	20880.3i	0.187053	+	1.06083i
$10$	10730.4	−	18585.5i	0.339324	−	0.587726i
$11$	43401.1	+	75172.9i	0.893787	+	1.54808i	0.835299	+	0.549796i	$0.185294\pi$
$11$	43401.1	+	75172.9i	0.893787	+	1.54808i	0.0584876	+	0.998288i	$0.481372\pi$
$12$	22557.6	−	18928.1i	0.314034	−	0.263506i
$13$	135626.	+	23914.5i	1.31703	+	0.232228i	0.787633	−	0.616144i	$-0.211306\pi$
$13$	135626.	+	23914.5i	1.31703	+	0.232228i	0.529399	+	0.848373i	$0.322417\pi$
$14$	32870.6	+	18977.9i	0.228682	+	0.132030i
$15$	77539.1	−	213037.i	0.395467	−	1.08654i
$16$	156339.	+	56902.7i	0.596385	+	0.217067i
$17$	−272495.	+	48048.2i	−0.791295	+	0.139527i	−0.554666	−	0.832073i	$-0.687154\pi$
$17$	−272495.	+	48048.2i	−0.791295	+	0.139527i	−0.236629	+	0.971600i	$0.576043\pi$
$18$	−260862.	+	310884.i	−0.585714	+	0.698026i
$19$	−30926.5	+	36856.7i	−0.0544427	+	0.0648822i	−0.792579	−	0.609770i	$-0.791262\pi$
$19$	−30926.5	+	36856.7i	−0.0544427	+	0.0648822i	0.738136	+	0.674652i	$0.235706\pi$
$20$	−160802.	+	28353.7i	−0.224727	+	0.0396255i
$21$	376780.	+	137137.i	0.422767	+	0.153875i
$22$	−568253.	+	1.56126e6i	−0.517178	+	1.42093i
$23$	−1.34904e6	−	778868.i	−1.00519	−	0.580348i	−0.0954120	−	0.995438i	$-0.530417\pi$
$23$	−1.34904e6	−	778868.i	−1.00519	−	0.580348i	−0.909780	+	0.415090i	$0.863750\pi$
$24$	2.50655e6	+	441973.i	1.54215	+	0.271923i
$25$	533186.	−	447396.i	0.272991	−	0.229067i
$26$	1.31801e6	+	2.28286e6i	0.565639	+	0.979716i
$27$	−153612.	+	266063.i	−0.0556272	+	0.0963491i
$28$	−50146.8	−	284396.i	−0.0154181	−	0.0874406i
$29$	2.24298e6	−	1.29499e6i	0.588891	−	0.339997i	−0.175768	−	0.984432i	$-0.556241\pi$
$29$	2.24298e6	−	1.29499e6i	0.588891	−	0.339997i	0.764659	+	0.644435i	$0.222907\pi$
$30$	4.07769e6	−	1.48416e6i	0.919112	−	0.334529i
$31$			9.12850e6i			1.77530i	0.460519	+	0.887650i	$0.347663\pi$
$31$			9.12850e6i			1.77530i	−0.460519	+	0.887650i	$0.652337\pi$
$32$	−1.11510e6	−	3.06372e6i	−0.187992	−	0.516504i
$33$	−3.04779e6	+	1.72849e7i	−0.447376	+	2.53719i
$34$	−4.05714e6	−	3.40435e6i	−0.520673	−	0.436897i
$35$	−1.42913e6	−	1.70317e6i	−0.160977	−	0.191845i
$36$	3.08773e6			0.306393
$37$	−3.42866e6	−	1.08723e7i	−0.300757	−	0.953701i
$37$	−3.42866e6	−	1.08723e7i	−0.300757	−	0.953701i
$38$	−920921.			−0.0716467
$39$	1.78995e7	+	2.13318e7i	1.23894	+	1.47651i
$40$	−1.08114e7	−	9.07181e6i	−0.667745	−	0.560305i
$41$	866208.	−	4.91251e6i	0.0478735	−	0.271504i	−0.951470	−	0.307742i	$-0.900426\pi$
$41$	866208.	−	4.91251e6i	0.0478735	−	0.271504i	0.999343	+	0.0362385i	$0.0115376\pi$
$42$	2.62490e6	+	7.21186e6i	0.130164	+	0.357623i
$43$		−	1.56517e7i		−	0.698157i	−0.937094	−	0.349078i	$-0.886495\pi$
$43$		−	1.56517e7i		−	0.698157i	0.937094	−	0.349078i	$-0.113505\pi$
$44$	1.18788e7	−	4.32352e6i	0.477787	−	0.173900i
$45$	2.05874e7	−	1.18861e7i	0.748418	−	0.432099i
$46$	−5.17754e6	−	2.93633e7i	−0.170496	−	0.966928i
$47$	−1.75562e7	+	3.04083e7i	−0.524797	+	0.908975i	0.474786	+	0.880101i	$0.342525\pi$
$47$	−1.75562e7	+	3.04083e7i	−0.524797	+	0.908975i	−0.999583	+	0.0288737i	$0.990808\pi$
$48$	1.68204e7	+	2.91337e7i	0.457351	+	0.792155i
$49$	−2.79004e7	+	2.34112e7i	−0.691398	+	0.580152i
$50$	1.31200e7	+	2.31342e6i	0.296873	+	0.0523466i
$51$	−4.84531e7	−	2.79744e7i	−1.00290	−	0.579022i
$52$	6.85956e6	−	1.88465e7i	0.130101	−	0.357450i
$53$	−3.21074e7	−	1.16861e7i	−0.558938	−	0.203437i	0.0470754	−	0.998891i	$-0.485010\pi$
$53$	−3.21074e7	−	1.16861e7i	−0.558938	−	0.203437i	−0.606013	+	0.795455i	$0.707232\pi$
$54$	−5.79115e6	+	1.02114e6i	−0.0926815	+	0.0163422i
$55$	6.25581e7	−	7.45538e7i	0.921831	−	1.09860i
$56$	1.60445e7	−	1.91211e7i	0.218012	−	0.259817i
$57$	−9.58073e6	+	1.68934e6i	−0.120216	+	0.0211973i
$58$	4.65844e7	+	1.69553e7i	0.540523	+	0.196734i
$59$	3.82396e7	−	1.05063e8i	0.410847	−	1.12879i	−0.545895	−	0.837853i	$-0.683810\pi$
$59$	3.82396e7	−	1.05063e8i	0.410847	−	1.12879i	0.956742	−	0.290938i	$-0.0939674\pi$
$60$	−2.85926e7	−	1.65080e7i	−0.284822	−	0.164442i
$61$	−6.70059e7	−	1.18149e7i	−0.619625	−	0.109257i	−0.144981	−	0.989434i	$-0.546312\pi$
$61$	−6.70059e7	−	1.18149e7i	−0.619625	−	0.109257i	−0.474644	+	0.880178i	$0.657423\pi$
$62$	−1.33848e8	+	1.12312e8i	−1.15040	+	0.965303i
$63$	2.10219e7	+	3.64111e7i	0.168128	+	0.291206i
$64$	7.37940e7	−	1.27815e8i	0.549808	−	0.952296i
$65$	−2.68130e7	−	1.52064e8i	−0.186310	−	1.05661i
$66$	−2.90941e8	+	1.67975e8i	−1.88737	+	1.08967i
$67$	−1.63987e8	+	5.96862e7i	−0.994195	+	0.361857i	−0.787343	−	0.616515i	$-0.788544\pi$
$67$	−1.63987e8	+	5.96862e7i	−0.994195	+	0.361857i	−0.206852	+	0.978372i	$0.566322\pi$
$68$			4.02960e7i			0.228545i
$69$	−1.07728e8	−	2.95981e8i	−0.572148	−	1.57196i
$70$	7.38980e6	−	4.19096e7i	0.0367867	−	0.208628i
$71$	−8.67460e7	−	7.27885e7i	−0.405123	−	0.339938i	0.417347	−	0.908747i	$-0.362960\pi$
$71$	−8.67460e7	−	7.27885e7i	−0.405123	−	0.339938i	−0.822470	+	0.568809i	$0.807404\pi$
$72$	1.71551e8	+	2.04447e8i	0.752312	+	0.896570i
$73$	7.25095e7			0.298842			0.149421	−	0.988774i	$-0.452259\pi$
$73$	7.25095e7			0.298842			0.149421	+	0.988774i	$0.452259\pi$
$74$	1.17232e8	−	1.84040e8i	0.454469	−	0.713458i
$75$	1.40737e8			0.513609
$76$	4.50386e6	+	5.36749e6i	0.0154855	+	0.0184548i
$77$	1.31857e8	+	1.10641e8i	0.427459	+	0.358681i
$78$	−9.25558e7	+	5.24910e8i	−0.283125	+	1.60568i
$79$	1.69402e8	+	4.65428e8i	0.489324	+	1.34441i	0.901294	+	0.433208i	$0.142619\pi$
$79$	1.69402e8	+	4.65428e8i	0.489324	+	1.34441i	−0.411970	+	0.911197i	$0.635159\pi$
$80$		−	1.86537e8i		−	0.509168i
$81$	3.33784e8	−	1.21488e8i	0.861555	−	0.313581i
$82$	8.26879e7	−	4.77399e7i	0.201967	−	0.116605i
$83$	1.79757e7	+	1.01945e8i	0.0415751	+	0.235784i	0.998513	−	0.0545074i	$-0.0173588\pi$
$83$	1.79757e7	+	1.01945e8i	0.0415751	+	0.235784i	−0.956938	+	0.290292i	$0.906248\pi$
$84$	2.91962e7	−	5.05693e7i	0.0639838	−	0.110823i
$85$	1.55118e8	+	2.68672e8i	0.322312	+	0.558261i
$86$	2.29495e8	−	1.92570e8i	0.452409	−	0.379616i
$87$	5.15740e8	+	9.09389e7i	0.965149	+	0.170182i
$88$	9.46244e8	+	5.46314e8i	1.68202	+	0.971115i
$89$	2.13360e8	−	5.86202e8i	0.360461	−	0.990359i	−0.618406	−	0.785859i	$-0.712221\pi$
$89$	2.13360e8	−	5.86202e8i	0.360461	−	0.990359i	0.978867	−	0.204499i	$-0.0655567\pi$
$90$	4.27578e8	+	1.55626e8i	0.686948	+	0.250028i
$91$	2.68943e8	−	4.74218e7i	0.411125	−	0.0724924i
$92$	−1.45820e8	+	1.73781e8i	−0.212212	+	0.252905i
$93$	−1.18645e9	+	1.41396e9i	−1.64467	+	1.96004i
$94$	−6.61869e8	+	1.16705e8i	−0.874373	+	0.154176i
$95$	5.06914e7	+	1.84501e7i	0.0638525	+	0.0232404i
$96$	2.25475e8	−	6.19488e8i	0.270943	−	0.744410i
$97$	−1.26259e9	−	7.28959e8i	−1.44808	−	0.836047i	−0.449709	−	0.893175i	$-0.648472\pi$
$97$	−1.26259e9	−	7.28959e8i	−1.44808	−	0.836047i	−0.998367	+	0.0571285i	$0.981806\pi$
$98$	−6.86542e8	−	1.21056e8i	−0.751883	−	0.132577i
$99$	−1.40984e9	+	1.18300e9i	−1.47507	+	1.23773i
$100$	−5.06815e7	−	8.77828e7i	−0.0506815	−	0.0877828i
$101$	−6.23753e8	+	1.08037e9i	−0.596439	+	1.03306i	0.396903	+	0.917861i	$0.370085\pi$
$101$	−6.23753e8	+	1.08037e9i	−0.596439	+	1.03306i	−0.993342	+	0.115203i	$0.963248\pi$
$102$	−1.85960e8	−	1.05463e9i	−0.170106	−	0.964720i
$103$	8.77288e7	−	5.06503e7i	0.0768024	−	0.0443419i	−0.461107	−	0.887345i	$-0.652548\pi$
$103$	8.77288e7	−	5.06503e7i	0.0768024	−	0.0443419i	0.537909	+	0.843003i	$0.319214\pi$
$104$	1.62899e9	−	5.92903e8i	1.36542	−	0.496974i
$105$		−	4.49559e8i		−	0.360940i
$106$	−2.23681e8	−	6.14560e8i	−0.172089	−	0.472811i
$107$	−9.08878e7	+	5.15450e8i	−0.0670314	+	0.380154i	0.932775	+	0.360460i	$0.117380\pi$
$107$	−9.08878e7	+	5.15450e8i	−0.0670314	+	0.380154i	−0.999806	+	0.0196940i	$0.993731\pi$
$108$	3.42738e7	+	2.87592e7i	0.0242413	+	0.0203409i
$109$	−7.07767e8	−	8.43484e8i	−0.480254	−	0.572344i	0.470457	−	0.882423i	$-0.344089\pi$
$109$	−7.07767e8	−	8.43484e8i	−0.480254	−	0.572344i	−0.950711	+	0.310079i	$0.899645\pi$
$110$	1.86284e9			1.21313
$111$	8.82013e8	−	2.12969e9i	0.551470	−	1.33157i
$112$	3.29913e8			0.198115
$113$	−1.55569e9	−	1.85400e9i	−0.897574	−	1.06969i	−0.997209	−	0.0746635i	$-0.976212\pi$
$113$	−1.55569e9	−	1.85400e9i	−0.897574	−	1.06969i	0.0996343	−	0.995024i	$-0.468233\pi$
$114$	−1.42646e8	−	1.19694e8i	−0.0791022	−	0.0663746i
$115$	−3.03284e8	+	1.72001e9i	−0.161700	+	0.917044i
$116$	−1.29004e8	−	3.54434e8i	−0.0661517	−	0.181750i
$117$			2.91995e9i			1.44058i
$118$	2.01098e9	−	7.31936e8i	0.954856	−	0.347539i
$119$	−4.75177e8	+	2.74344e8i	−0.217217	+	0.125410i
$120$	−4.95543e8	−	2.81036e9i	−0.218155	−	1.23722i
$121$	−2.58834e9	+	4.48314e9i	−1.09771	+	1.90129i
$122$	−6.51165e8	−	1.12785e9i	−0.266116	−	0.460927i
$123$	7.72663e8	−	6.48341e8i	0.304381	−	0.255406i
$124$	1.30920e9	+	2.30847e8i	0.497288	+	0.0876853i
$125$	−2.57230e9	−	1.48512e9i	−0.942382	−	0.544085i
$126$	−2.75241e8	+	7.56220e8i	−0.0972851	+	0.267289i
$127$	3.39757e9	+	1.23662e9i	1.15892	+	0.421811i	0.848710	−	0.528858i	$-0.177380\pi$
$127$	3.39757e9	+	1.23662e9i	1.15892	+	0.421811i	0.310206	+	0.950669i	$0.399602\pi$
$128$	1.13810e9	−	2.00677e8i	0.374744	−	0.0660774i
$129$	2.03429e9	−	2.42437e9i	0.646783	−	0.770806i
$130$	1.89977e9	−	2.26406e9i	0.583387	−	0.695254i
$131$	−3.47830e8	+	6.13318e7i	−0.103192	+	0.0181955i	−0.225006	−	0.974357i	$-0.572240\pi$
$131$	−3.47830e8	+	6.13318e7i	−0.103192	+	0.0181955i	0.121814	+	0.992553i	$0.461129\pi$
$132$	2.40190e9	+	8.74221e8i	0.688609	+	0.250633i
$133$	−3.26312e7	+	8.96534e7i	−0.00904275	+	0.0248447i
$134$	−2.89276e9	−	1.67014e9i	−0.775069	−	0.447487i
$135$	3.39227e8	+	5.98149e7i	0.0879000	+	0.0154991i
$136$	−2.66810e9	+	2.23880e9i	−0.668771	+	0.561166i
$137$	−3.36703e9	−	5.83186e9i	−0.816590	−	1.41438i	−0.908180	−	0.418579i	$-0.862528\pi$
$137$	−3.36703e9	−	5.83186e9i	−0.816590	−	1.41438i	0.0915903	−	0.995797i	$-0.470805\pi$
$138$	3.01444e9	−	5.22117e9i	0.707540	−	1.22550i
$139$	−4.27558e8	−	2.42480e9i	−0.0971468	−	0.550947i	−0.994068	−	0.108757i	$-0.965313\pi$
$139$	−4.27558e8	−	2.42480e9i	−0.0971468	−	0.550947i	0.896921	−	0.442190i	$-0.145798\pi$
$140$	−2.80407e8	+	1.61893e8i	−0.0616896	+	0.0356165i
$141$	−6.67162e9	+	2.42827e9i	−1.42150	+	0.517382i
$142$		−	2.16748e9i		−	0.447360i
$143$	4.08858e9	+	1.12333e10i	0.817637	+	2.24644i
$144$	−6.12542e8	+	3.47390e9i	−0.118715	+	0.673265i
$145$	−2.22451e9	−	1.86659e9i	−0.417906	−	0.350665i
$146$	8.92117e8	+	1.06318e9i	0.162493	+	0.193651i
$147$	−7.36446e9			−1.30081
$148$	−1.64599e9	+	2.16789e8i	−0.282001	+	0.0371416i
$149$	−1.65178e9			−0.274545			−0.137273	−	0.990533i	$-0.543834\pi$
$149$	−1.65178e9			−0.274545			−0.137273	+	0.990533i	$0.543834\pi$
$150$	1.73155e9	+	2.06358e9i	0.279270	+	0.332821i
$151$	5.43124e9	+	4.55735e9i	0.850164	+	0.713372i	0.959826	−	0.280597i	$-0.0905324\pi$
$151$	5.43124e9	+	4.55735e9i	0.850164	+	0.713372i	−0.109662	+	0.993969i	$0.534977\pi$
$152$	−1.05166e8	+	5.96425e8i	−0.0159801	+	0.0906275i
$153$	−2.00652e9	−	5.51287e9i	−0.296028	−	0.813329i
$154$			3.29464e9i			0.472025i
$155$	9.61768e9	−	3.50055e9i	1.33837	−	0.487128i
$156$	3.51204e9	−	2.02768e9i	0.474787	−	0.274118i
$157$	2.50681e8	+	1.42169e9i	0.0329286	+	0.186748i	0.996835	−	0.0794921i	$-0.0253298\pi$
$157$	2.50681e8	+	1.42169e9i	0.0329286	+	0.186748i	−0.963907	+	0.266240i	$0.914219\pi$
$158$	−4.74019e9	+	8.21025e9i	−0.605116	+	1.04809i
$159$	−3.45440e9	−	5.98320e9i	−0.428633	−	0.742415i
$160$	−2.80028e9	+	2.34972e9i	−0.337802	+	0.283449i
$161$	−3.04203e9	−	5.36392e8i	−0.356818	−	0.0629167i
$162$	5.88803e9	+	3.39945e9i	0.671664	+	0.387786i
$163$	−2.22516e9	+	6.11359e9i	−0.246898	+	0.678347i	0.752898	+	0.658138i	$0.228656\pi$
$163$	−2.22516e9	+	6.11359e9i	−0.246898	+	0.678347i	−0.999796	+	0.0202095i	$0.993567\pi$
$164$	−6.82641e8	−	2.48461e8i	−0.0736877	−	0.0268201i
$165$	1.93799e10	−	3.41720e9i	2.03551	−	0.358916i
$166$	−1.27362e9	+	1.51785e9i	−0.130183	+	0.155146i
$167$	−8.63305e9	+	1.02885e10i	−0.858895	+	1.02359i	0.140543	+	0.990075i	$0.455115\pi$
$167$	−8.63305e9	+	1.02885e10i	−0.858895	+	1.02359i	−0.999438	+	0.0335168i	$0.989329\pi$
$168$	4.97044e9	−	8.76423e8i	0.481397	−	0.0848833i
$169$	7.85743e9	+	2.85987e9i	0.740953	+	0.269685i
$170$	−2.03097e9	+	5.58004e9i	−0.186502	+	0.512409i
$171$	−8.83443e8	−	5.10056e8i	−0.0790125	−	0.0456179i
$172$	−2.24474e9	−	3.95809e8i	−0.195564	−	0.0344832i
$173$	7.04901e9	−	5.91482e9i	0.598302	−	0.502035i	−0.292597	−	0.956236i	$-0.594519\pi$
$173$	7.04901e9	−	5.91482e9i	0.598302	−	0.502035i	0.890899	+	0.454201i	$0.150075\pi$
$174$	5.01197e9	+	8.68099e9i	0.414512	+	0.717956i
$175$	6.90101e8	−	1.19529e9i	0.0556213	−	0.0963389i
$176$	2.50774e9	+	1.42221e10i	0.197004	+	1.11727i
$177$	1.95784e10	−	1.13036e10i	1.49933	−	0.865638i
$178$	1.12204e10	−	4.08388e9i	0.837754	−	0.304918i
$179$		−	6.30910e9i		−	0.459335i	−0.973269	−	0.229667i	$-0.926236\pi$
$179$		−	6.30910e9i		−	0.459335i	0.973269	−	0.229667i	$-0.0737638\pi$
$180$	−1.18407e9	−	3.25320e9i	−0.0840717	−	0.230985i
$181$	−1.04344e9	+	5.91765e9i	−0.0722628	+	0.409823i	0.927122	+	0.374759i	$0.122275\pi$
$181$	−1.04344e9	+	5.91765e9i	−0.0722628	+	0.409823i	−0.999385	+	0.0350637i	$0.988837\pi$
$182$	4.00425e9	+	3.35997e9i	0.270520	+	0.226994i
$183$	−8.84328e9	−	1.05390e10i	−0.582886	−	0.694656i
$184$	−1.96081e10			−1.26112
$185$	−1.01401e10	+	7.78163e9i	−0.636456	+	0.488425i
$186$	−3.53299e10			−2.16438
$187$	−1.54385e10	−	1.83989e10i	−0.923248	−	1.10028i
$188$	3.91715e9	+	3.28688e9i	0.228697	+	0.191899i
$189$	−1.05789e8	+	5.99962e8i	−0.00603065	+	0.0342015i
$190$	3.53150e8	+	9.70271e8i	0.0196593	+	0.0540134i
$191$			2.16122e10i			1.17503i	0.809214	+	0.587514i	$0.199893\pi$
$191$			2.16122e10i			1.17503i	−0.809214	+	0.587514i	$0.800107\pi$
$192$	2.80428e10	−	1.02067e10i	1.48924	−	0.542040i
$193$	2.66173e10	−	1.53675e10i	1.38088	−	0.797252i	0.388617	−	0.921399i	$-0.372953\pi$
$193$	2.66173e10	−	1.53675e10i	1.38088	−	0.797252i	0.992264	+	0.124147i	$0.0396194\pi$
$194$	−4.84577e9	−	2.74817e10i	−0.245615	−	1.39295i
$195$	1.56110e10	−	2.70390e10i	0.773167	−	1.33917i
$196$	2.65205e9	+	4.59348e9i	0.128360	+	0.222326i
$197$	−2.85378e10	+	2.39460e10i	−1.34996	+	1.13275i	−0.371020	+	0.928625i	$0.620992\pi$
$197$	−2.85378e10	+	2.39460e10i	−1.34996	+	1.13275i	−0.978944	+	0.204129i	$0.934564\pi$
$198$	−3.46918e10	−	6.11710e9i	−1.60411	−	0.282847i
$199$	2.67168e10	+	1.54250e10i	1.20766	+	0.697244i	0.962248	−	0.272174i	$-0.0877426\pi$
$199$	2.67168e10	+	1.54250e10i	1.20766	+	0.697244i	0.245414	+	0.969418i	$0.421076\pi$
$200$	2.99652e9	−	8.23288e9i	0.132429	−	0.363845i
$201$	−3.31583e10	−	1.20686e10i	−1.43288	−	0.521526i
$202$	−2.35154e10	+	4.14641e9i	−0.993738	+	0.175223i
$203$	3.30127e9	−	3.93430e9i	0.136442	−	0.162606i
$204$	−5.23737e9	+	6.24165e9i	−0.211728	+	0.252327i
$205$	−5.50793e9	+	9.71197e8i	−0.217819	+	0.0384074i
$206$	1.82204e9	+	6.63167e8i	0.0704943	+	0.0256578i
$207$	1.12961e10	−	3.10359e10i	0.427626	−	1.17489i
$208$	1.98428e10	+	1.14562e10i	0.735050	+	0.424381i
$209$	−4.11287e9	−	7.25211e8i	−0.149103	−	0.0262909i
$210$	6.59174e9	−	5.53113e9i	0.233891	−	0.196258i
$211$	9.45383e9	+	1.63745e10i	0.328350	+	0.568719i	0.982185	−	0.187919i	$-0.0601741\pi$
$211$	9.45383e9	+	1.63745e10i	0.328350	+	0.568719i	−0.653835	+	0.756637i	$0.726841\pi$
$212$	−2.48796e9	+	4.30928e9i	−0.0845926	+	0.146519i
$213$	−3.97603e9	−	2.25492e10i	−0.132355	−	0.750624i
$214$	−8.67611e9	+	5.00915e9i	−0.282789	+	0.163268i
$215$	−1.64904e10	+	6.00202e9i	−0.526331	+	0.191569i
$216$			3.86719e9i			0.120880i
$217$	6.19112e9	+	1.70100e10i	0.189540	+	0.520756i
$218$	3.65976e9	−	2.07555e10i	0.109748	−	0.622414i
$219$	1.12314e10	+	9.42425e9i	0.329940	+	0.276852i
$220$	−9.11041e9	−	1.08574e10i	−0.262202	−	0.312480i
$221$	−3.81063e10			−1.07456
$222$	4.20788e10	−	1.32699e10i	1.16272	−	0.366673i
$223$	−4.05477e9			−0.109798			−0.0548989	−	0.998492i	$-0.517484\pi$
$223$	−4.05477e9			−0.109798			−0.0548989	+	0.998492i	$0.517484\pi$
$224$	−4.15574e9	−	4.95262e9i	−0.110289	−	0.131437i
$225$	1.13048e10	+	9.48586e9i	0.294064	+	0.246749i
$226$	8.04425e9	−	4.56212e10i	0.205115	−	1.16327i
$227$	−6.09353e9	−	1.67418e10i	−0.152319	−	0.418492i	0.839940	−	0.542679i	$-0.182590\pi$
$227$	−6.09353e9	−	1.67418e10i	−0.152319	−	0.418492i	−0.992259	+	0.124187i	$0.960368\pi$
$228$			1.41678e9i			0.0347212i
$229$	1.97193e10	−	7.17723e9i	0.473839	−	0.172463i	−0.0940514	−	0.995567i	$-0.529982\pi$
$229$	1.97193e10	−	7.17723e9i	0.473839	−	0.172463i	0.567891	+	0.823104i	$0.307760\pi$
$230$	−2.89513e10	+	1.67151e10i	−0.682171	+	0.393852i
$231$	6.04371e9	+	3.42756e10i	0.139653	+	0.792010i
$232$	1.63007e10	−	2.82337e10i	0.369412	−	0.639841i
$233$	−5.64644e9	−	9.77993e9i	−0.125509	−	0.217387i	0.796423	−	0.604740i	$-0.206723\pi$
$233$	−5.64644e9	−	9.77993e9i	−0.125509	−	0.217387i	−0.921932	+	0.387353i	$0.873390\pi$
$234$	−4.28142e10	+	3.59254e10i	−0.933506	+	0.783304i
$235$	3.87702e10	+	6.83623e9i	0.829264	+	0.146222i
$236$	−1.41009e10	−	8.14117e9i	−0.295899	−	0.170837i
$237$	−3.42533e10	+	9.41101e10i	−0.705236	+	1.93762i
$238$	−9.86893e9	−	3.59200e9i	−0.199376	−	0.0725671i
$239$	−1.10827e10	+	1.95418e9i	−0.219713	+	0.0387414i	−0.282421	−	0.959291i	$-0.591137\pi$
$239$	−1.10827e10	+	1.95418e9i	−0.219713	+	0.0387414i	0.0627078	+	0.998032i	$0.480026\pi$
$240$	2.42448e10	−	2.88938e10i	0.471701	−	0.562152i
$241$	4.77907e10	−	5.69547e10i	0.912571	−	1.08756i	−0.0832772	−	0.996526i	$-0.526539\pi$
$241$	4.77907e10	−	5.69547e10i	0.912571	−	1.08756i	0.995848	−	0.0910330i	$-0.0290169\pi$
$242$	−9.75803e10	+	1.72060e10i	−1.82891	+	0.322487i
$243$	7.31740e10	+	2.66332e10i	1.34626	+	0.489998i
$244$	−3.38897e9	+	9.31112e9i	−0.0612088	+	0.168170i
$245$	3.53649e10	+	2.04179e10i	0.627083	+	0.362046i
$246$	1.90128e10	+	3.35248e9i	0.331008	+	0.0583657i
$247$	−5.07583e9	+	4.25913e9i	−0.0867703	+	0.0728089i
$248$	5.74528e10	+	9.95111e10i	0.964447	+	1.67047i
$249$	−1.04657e10	+	1.81271e10i	−0.172533	+	0.298836i
$250$	−9.87236e9	−	5.59889e10i	−0.159842	−	0.906509i
$251$	−3.31674e10	+	1.91492e10i	−0.527448	+	0.304522i	−0.739977	−	0.672632i	$-0.765164\pi$
$251$	−3.31674e10	+	1.91492e10i	−0.527448	+	0.304522i	0.212528	+	0.977155i	$0.431830\pi$
$252$	5.75365e9	−	2.09416e9i	0.0898754	−	0.0327120i
$253$		−	1.35215e11i		−	2.07483i
$254$	2.36698e10	+	6.50321e10i	0.356814	+	0.980339i
$255$	−1.08930e10	+	6.17771e10i	−0.161330	+	0.914949i
$256$	−4.09412e10	−	3.43538e10i	−0.595773	−	0.499913i
$257$	3.27886e10	+	3.90759e10i	0.468839	+	0.558740i	0.947705	−	0.319148i	$-0.103397\pi$
$257$	3.27886e10	+	3.90759e10i	0.468839	+	0.558740i	−0.478866	+	0.877888i	$0.658952\pi$
$258$	6.05765e10			0.851168
$259$	−1.37627e10	−	1.79339e10i	−0.190044	−	0.247643i
$260$	−2.24869e10			−0.305176
$261$	3.52978e10	+	4.20663e10i	0.470832	+	0.561115i
$262$	−5.17880e9	−	4.34553e9i	−0.0679005	−	0.0569753i
$263$	2.11737e10	−	1.20082e11i	0.272895	−	1.54767i	−0.472673	−	0.881238i	$-0.656711\pi$
$263$	2.11737e10	−	1.20082e11i	0.272895	−	1.54767i	0.745568	−	0.666429i	$-0.232178\pi$
$264$	7.55629e10	+	2.07607e11i	0.957394	+	2.63042i
$265$			3.83093e10i			0.477197i
$266$	−1.71603e9	+	6.24586e8i	−0.0210164	+	0.00764935i
$267$	1.09239e11	−	6.30690e10i	1.31545	−	0.759478i
$268$	4.41313e9	+	2.50281e10i	0.0522565	+	0.296362i
$269$	−6.79362e10	+	1.17669e11i	−0.791072	+	1.37018i	0.134231	+	0.990950i	$0.457143\pi$
$269$	−6.79362e10	+	1.17669e11i	−0.791072	+	1.37018i	−0.925304	+	0.379227i	$0.876190\pi$
$270$	3.29662e9	+	5.70991e9i	0.0377513	+	0.0653871i
$271$	3.49777e10	−	2.93498e10i	0.393939	−	0.330554i	−0.424206	−	0.905566i	$-0.639447\pi$
$271$	3.49777e10	−	2.93498e10i	0.393939	−	0.330554i	0.818145	+	0.575011i	$0.195002\pi$
$272$	−4.53356e10	−	7.99389e9i	−0.502203	−	0.0885520i
$273$	4.78215e10	+	2.76097e10i	0.521064	+	0.300836i
$274$	4.40847e10	−	1.21122e11i	0.472509	−	1.29821i
$275$	5.67729e10	+	2.06637e10i	0.598610	+	0.217876i
$276$	−4.51735e10	+	7.96531e9i	−0.468590	+	0.0826251i
$277$	1.16153e11	−	1.38426e11i	1.18542	−	1.41272i	0.296268	−	0.955105i	$-0.404258\pi$
$277$	1.16153e11	−	1.38426e11i	1.18542	−	1.41272i	0.889148	−	0.457619i	$-0.151298\pi$
$278$	3.02937e10	−	3.61026e10i	0.304194	−	0.362524i
$279$	−1.90606e11	+	3.36089e10i	−1.88329	+	0.332075i
$280$	−2.62985e10	−	9.57186e9i	−0.255693	−	0.0930648i
$281$	−2.56478e10	+	7.04667e10i	−0.245398	+	0.674226i	0.754442	+	0.656366i	$0.227907\pi$
$281$	−2.56478e10	+	7.04667e10i	−0.245398	+	0.674226i	−0.999841	+	0.0178597i	$0.994315\pi$
$282$	−1.17689e11	−	6.79477e10i	−1.10819	−	0.639814i
$283$	−1.47067e10	−	2.59319e9i	−0.136294	−	0.0240323i	0.105085	−	0.994463i	$-0.466489\pi$
$283$	−1.47067e10	−	2.59319e9i	−0.136294	−	0.0240323i	−0.241379	+	0.970431i	$0.577600\pi$
$284$	−1.26329e10	+	1.06003e10i	−0.115232	+	0.0966907i
$285$	5.45384e9	+	9.44632e9i	0.0489666	+	0.0848127i
$286$	−1.14406e11	+	1.98158e11i	−1.01112	+	1.75131i
$287$	−1.71767e9	−	9.74141e9i	−0.0149442	−	0.0847526i
$288$	5.98657e10	−	3.45635e10i	0.512758	−	0.296041i
$289$	−3.94913e10	+	1.43736e10i	−0.333013	+	0.121207i
$290$		−	5.55827e10i		−	0.461476i
$291$	−1.00825e11	−	2.77015e11i	−0.824234	−	2.26457i
$292$	1.83366e9	−	1.03992e10i	0.0147604	−	0.0837102i
$293$	1.72309e11	+	1.44585e11i	1.36585	+	1.14609i	0.974126	+	0.226008i	$0.0725674\pi$
$293$	1.72309e11	+	1.44585e11i	1.36585	+	1.14609i	0.391729	+	0.920081i	$0.371877\pi$
$294$	−9.06082e10	−	1.07983e11i	−0.707301	−	0.842929i
$295$	−1.25357e11			−0.963714
$296$	−1.05804e11	−	9.69409e10i	−0.801104	−	0.733997i
$297$	−2.66677e10			−0.198875
$298$	−2.03226e10	−	2.42195e10i	−0.149281	−	0.177907i
$299$	−1.64338e11	−	1.37896e11i	−1.18910	−	0.997772i
$300$	3.55904e9	−	2.01843e10i	0.0253681	−	0.143870i
$301$	−1.06153e10	−	2.91652e10i	−0.0745386	−	0.204793i
$302$			1.35708e11i			0.938799i
$303$	−2.37035e11	+	8.62737e10i	−1.61555	+	0.588012i
$304$	−6.93226e9	+	4.00234e9i	−0.0465526	+	0.0268771i
$305$	1.32470e10	+	7.51274e10i	0.0876532	+	0.497106i
$306$	5.61463e10	−	9.72483e10i	0.366079	−	0.634067i
$307$	−1.07256e11	−	1.85774e11i	−0.689129	−	1.19361i	−0.972120	−	0.234484i	$-0.924660\pi$
$307$	−1.07256e11	−	1.85774e11i	−0.689129	−	1.19361i	0.282991	−	0.959123i	$-0.408673\pi$
$308$	1.92025e10	−	1.61128e10i	0.121585	−	0.102022i
$309$	2.01719e10	+	3.55685e9i	0.125873	+	0.0221949i
$310$	1.69658e11	+	9.79521e10i	1.04339	+	0.602401i
$311$	3.49644e10	−	9.60640e10i	0.211936	−	0.582289i	−0.787484	−	0.616335i	$-0.788617\pi$
$311$	3.49644e10	−	9.60640e10i	0.211936	−	0.582289i	0.999420	+	0.0340455i	$0.0108391\pi$
$312$	3.29383e11	+	1.19886e11i	1.96791	+	0.716262i
$313$	1.99586e11	−	3.51923e10i	1.17538	−	0.207252i	0.448353	−	0.893857i	$-0.352011\pi$
$313$	1.99586e11	−	3.51923e10i	1.17538	−	0.207252i	0.727031	+	0.686605i	$0.240900\pi$
$314$	−1.77615e10	+	2.11673e10i	−0.103109	+	0.122880i
$315$	3.03009e10	−	3.61112e10i	0.173404	−	0.206654i
$316$	7.10350e10	−	1.25254e10i	0.400757	−	0.0706642i
$317$	1.90228e10	+	6.92375e9i	0.105806	+	0.0385101i	0.394381	−	0.918947i	$-0.370959\pi$
$317$	1.90228e10	+	6.92375e9i	0.105806	+	0.0385101i	−0.288575	+	0.957457i	$0.593181\pi$
$318$	4.52287e10	−	1.24265e11i	0.248023	−	0.681438i
$319$	1.94696e11	+	1.12408e11i	1.05269	+	0.607769i
$320$	−1.62962e11	−	2.87347e10i	−0.868786	−	0.153190i
$321$	−8.10724e10	+	6.80278e10i	−0.426187	+	0.357614i
$322$	−2.95625e10	−	5.12037e10i	−0.153246	−	0.265430i
$323$	6.65641e9	−	1.15292e10i	0.0340274	−	0.0589372i
$324$	−8.98266e9	−	5.09432e10i	−0.0452848	−	0.256823i
$325$	8.30128e10	−	4.79275e10i	0.412734	−	0.238292i
$326$	−1.17019e11	+	4.25913e10i	−0.573821	+	0.208854i
$327$		−	2.22642e11i		−	1.07682i
$328$	−2.14756e10	−	5.90038e10i	−0.102450	−	0.281480i
$329$	−1.20907e10	+	6.85695e10i	−0.0568942	+	0.322663i
$330$	2.88545e11	+	2.42118e11i	1.33937	+	1.12386i
$331$	−3.94786e10	−	4.70488e10i	−0.180774	−	0.215438i	0.668046	−	0.744120i	$-0.267131\pi$
$331$	−3.94786e10	−	4.70488e10i	−0.180774	−	0.215438i	−0.848820	+	0.528682i	$0.822686\pi$
$332$	1.50754e10			0.0681001
$333$	2.14392e11	−	1.11620e11i	0.955455	−	0.497444i
$334$	−2.57073e11			−1.13031
$335$	1.25769e11	+	1.49886e11i	0.545599	+	0.650219i
$336$	5.11019e10	+	4.28796e10i	0.218731	+	0.183537i
$337$	−1.93995e10	+	1.10020e11i	−0.0819325	+	0.464662i	0.916044	+	0.401078i	$0.131364\pi$
$337$	−1.93995e10	+	1.10020e11i	−0.0819325	+	0.464662i	−0.997976	+	0.0635845i	$0.979747\pi$
$338$	5.47401e10	+	1.50397e11i	0.228129	+	0.626779i
$339$		−	4.89373e11i		−	2.01253i
$340$	4.24554e10	−	1.54525e10i	0.172297	−	0.0627109i
$341$	−6.86216e11	+	3.96187e11i	−2.74831	+	1.58674i
$342$	−3.39061e9	−	1.92291e10i	−0.0134017	−	0.0760048i
$343$	−7.61216e10	+	1.31846e11i	−0.296951	+	0.514334i
$344$	−9.85082e10	−	1.70621e11i	−0.379280	−	0.656932i
$345$	−2.70531e11	+	2.27002e11i	−1.02809	+	0.862670i
$346$	1.73454e11	+	3.05847e10i	0.650643	+	0.114726i
$347$	3.84172e11	+	2.21802e11i	1.42247	+	0.821263i	0.996510	−	0.0834790i	$-0.0266031\pi$
$347$	3.84172e11	+	2.21802e11i	1.42247	+	0.821263i	0.425960	+	0.904742i	$0.359936\pi$
$348$	2.60847e10	−	7.16671e10i	0.0953409	−	0.261947i
$349$	3.14113e11	+	1.14328e11i	1.13337	+	0.412513i	0.839515	−	0.543336i	$-0.182839\pi$
$349$	3.14113e11	+	1.14328e11i	1.13337	+	0.412513i	0.293856	+	0.955850i	$0.405061\pi$
$350$	2.60168e10	−	4.58746e9i	0.0926717	−	0.0163405i
$351$	−2.71964e10	+	3.24114e10i	−0.0956379	+	0.113977i
$352$	1.81912e11	−	2.16794e11i	0.631567	−	0.752672i
$353$	−2.91003e11	+	5.13117e10i	−0.997497	+	0.175886i	−0.648481	−	0.761231i	$-0.724595\pi$
$353$	−2.91003e11	+	5.13117e10i	−0.997497	+	0.175886i	−0.349016	+	0.937117i	$0.613484\pi$
$354$	4.06622e11	+	1.47998e11i	1.37618	+	0.500890i
$355$	−4.34242e10	+	1.19307e11i	−0.145112	+	0.398693i
$356$	−7.86768e10	−	4.54241e10i	−0.259610	−	0.149886i
$357$	−1.09260e11	−	1.92655e10i	−0.356003	−	0.0627729i
$358$	9.25083e10	−	7.76237e10i	0.297651	−	0.249759i
$359$	2.22476e10	+	3.85340e10i	0.0706900	+	0.122439i	0.899204	−	0.437530i	$-0.144147\pi$
$359$	2.22476e10	+	3.85340e10i	0.0706900	+	0.122439i	−0.828514	+	0.559969i	$0.810813\pi$
$360$	1.49617e11	−	2.59145e11i	0.469483	−	0.813169i
$361$	5.56322e10	+	3.15506e11i	0.172402	+	0.977743i
$362$	−9.96065e10	+	5.75079e10i	−0.304859	+	0.176011i
$363$	−9.83607e11	+	3.58003e11i	−2.97332	+	1.08220i
$364$		−	3.97707e10i		−	0.118743i
$365$	−2.78056e10	−	7.63952e10i	−0.0820000	−	0.225293i
$366$	4.57273e10	−	2.59332e11i	0.133202	−	0.755425i
$367$	7.47481e10	+	6.27211e10i	0.215081	+	0.180475i	0.743963	−	0.668221i	$-0.232944\pi$
$367$	7.47481e10	+	6.27211e10i	0.215081	+	0.180475i	−0.528881	+	0.848696i	$0.677388\pi$
$368$	−1.66588e11	−	1.98531e11i	−0.473508	−	0.564305i
$369$	1.05764e11			0.296974
$370$	−2.38857e11	−	5.29399e10i	−0.662569	−	0.146850i
$371$	−6.77543e10			−0.185675
$372$	1.72785e11	+	2.05917e11i	0.467802	+	0.557505i
$373$	−2.00802e11	−	1.68493e11i	−0.537128	−	0.450704i	0.333427	−	0.942776i	$-0.391795\pi$
$373$	−2.00802e11	−	1.68493e11i	−0.537128	−	0.450704i	−0.870554	+	0.492072i	$0.836240\pi$
$374$	7.98302e10	−	4.52740e11i	0.210982	−	1.19654i
$375$	−2.05413e11	−	5.64367e11i	−0.536397	−	1.47374i
$376$			4.41981e11i			1.14040i
$377$	3.35175e11	−	1.21994e11i	0.854546	−	0.311029i
$378$	−1.00986e10	+	5.83044e9i	−0.0254419	+	0.0146889i
$379$	7.39935e10	+	4.19638e11i	0.184212	+	1.04472i	0.926964	+	0.375150i	$0.122409\pi$
$379$	7.39935e10	+	4.19638e11i	0.184212	+	1.04472i	−0.742752	+	0.669566i	$0.766480\pi$
$380$	3.92801e9	−	6.80351e9i	0.00966377	−	0.0167381i
$381$	3.65542e11	+	6.33137e11i	0.888740	+	1.53934i
$382$	−3.16892e11	+	2.65904e11i	−0.761424	+	0.638911i
$383$	−4.32703e11	−	7.62972e10i	−1.02753	−	0.181182i	−0.365621	−	0.930764i	$-0.619143\pi$
$383$	−4.32703e11	−	7.62972e10i	−1.02753	−	0.181182i	−0.661911	+	0.749582i	$0.730254\pi$
$384$	2.02368e11	+	1.16837e11i	0.474954	+	0.274215i
$385$	6.60063e10	−	1.81351e11i	0.153113	−	0.420675i
$386$	5.52813e11	+	2.01208e11i	1.26746	+	0.461319i
$387$	3.26811e11	−	5.76257e10i	0.740624	−	0.130592i
$388$	−1.36476e11	+	1.62645e11i	−0.305712	+	0.364334i
$389$	1.82652e11	−	2.17677e11i	0.404438	−	0.481990i	−0.524930	−	0.851146i	$-0.675908\pi$
$389$	1.82652e11	−	2.17677e11i	0.404438	−	0.481990i	0.929368	+	0.369155i	$0.120353\pi$
$390$	5.88532e11	−	1.03774e11i	1.28819	−	0.227142i
$391$	4.05030e11	+	1.47419e11i	0.876378	+	0.318975i
$392$	−1.56801e11	+	4.30808e11i	−0.335400	+	0.921503i
$393$	−6.18487e10	−	3.57084e10i	−0.130787	−	0.0755098i
$394$	−7.02226e11	−	1.23821e11i	−1.46806	−	0.258859i
$395$	4.25408e11	−	3.56959e11i	0.879262	−	0.737789i
$396$	1.34011e11	+	2.32114e11i	0.273850	+	0.474321i
$397$	−3.02246e10	+	5.23506e10i	−0.0610666	+	0.105770i	−0.894942	−	0.446182i	$-0.852784\pi$
$397$	−3.02246e10	+	5.23506e10i	−0.0610666	+	0.105770i	0.833876	+	0.551952i	$0.186117\pi$
$398$	1.02538e11	+	5.81520e11i	0.204837	+	1.16169i
$399$	−1.67069e10	+	9.64573e9i	−0.0330003	+	0.0190527i
$400$	1.08816e11	−	3.96057e10i	0.212531	−	0.0773548i
$401$		−	3.07478e11i		−	0.593834i	−0.954903	−	0.296917i	$-0.904042\pi$
$401$		−	3.07478e11i		−	0.593834i	0.954903	−	0.296917i	$-0.0959584\pi$
$402$	−2.31003e11	−	6.34675e11i	−0.441164	−	1.21209i
$403$	−2.18303e11	+	1.23806e12i	−0.412275	+	2.33813i
$404$	1.39172e11	+	1.16779e11i	0.259917	+	0.218096i
$405$	−2.55996e11	−	3.05084e11i	−0.472808	−	0.563471i
$406$	9.83044e10			0.179558
$407$	6.68492e11	−	7.29610e11i	1.20760	−	1.31800i
$408$	−7.04260e11			−1.25824
$409$	3.04305e11	+	3.62656e11i	0.537717	+	0.640827i	0.964674	−	0.263445i	$-0.0848589\pi$
$409$	3.04305e11	+	3.62656e11i	0.537717	+	0.640827i	−0.426957	+	0.904272i	$0.640414\pi$
$410$	−8.20069e10	−	6.88120e10i	−0.143325	−	0.120264i
$411$	2.36445e11	−	1.34095e12i	0.408736	−	2.31806i
$412$	−5.04566e9	−	1.38628e10i	−0.00862741	−	0.0237036i
$413$		−	2.21707e11i		−	0.374977i
$414$	5.94051e11	−	2.16217e11i	0.993853	−	0.361733i
$415$	1.00515e11	−	5.80323e10i	0.166347	−	0.0960402i
$416$	−7.79692e10	−	4.42185e11i	−0.127645	−	0.723910i
$417$	2.48931e11	−	4.31161e11i	0.403150	−	0.698277i
$418$	−3.99690e10	−	6.92283e10i	−0.0640368	−	0.110915i
$419$	2.99350e11	−	2.51184e11i	0.474478	−	0.398134i	−0.373947	−	0.927450i	$-0.621996\pi$
$419$	2.99350e11	−	2.51184e11i	0.474478	−	0.398134i	0.848425	+	0.529316i	$0.177551\pi$
$420$	−6.44753e10	−	1.13687e10i	−0.101105	−	0.0178275i
$421$	2.26722e11	+	1.30898e11i	0.351741	+	0.203078i	0.665452	−	0.746441i	$-0.268239\pi$
$421$	2.26722e11	+	1.30898e11i	0.351741	+	0.203078i	−0.313711	+	0.949519i	$0.601572\pi$
$422$	−1.23780e11	+	3.40081e11i	−0.189995	+	0.522008i
$423$	−6.99572e11	−	2.54623e11i	−1.06243	−	0.386693i
$424$	−4.23557e11	+	7.46846e10i	−0.636452	+	0.112224i
$425$	−1.23794e11	+	1.47532e11i	−0.184056	+	0.219349i
$426$	2.81712e11	−	3.35732e11i	0.414441	−	0.493912i
$427$	−1.32871e11	+	2.34288e10i	−0.193422	+	0.0341055i
$428$	7.16268e10	+	2.60700e10i	0.103176	+	0.0375530i
$429$	−8.26717e11	+	2.27139e12i	−1.17842	+	3.23768i
$430$	−2.90895e11	−	1.67948e11i	−0.410325	−	0.236901i
$431$	−7.74394e11	−	1.36547e11i	−1.08097	−	0.190604i	−0.395327	−	0.918541i	$-0.629369\pi$
$431$	−7.74394e11	−	1.36547e11i	−1.08097	−	0.190604i	−0.685645	+	0.727936i	$0.740480\pi$
$432$	−3.91552e10	+	3.28551e10i	−0.0540894	+	0.0453864i
$433$	−4.52786e11	−	7.84248e11i	−0.619009	−	1.07216i	−0.989667	−	0.143386i	$-0.954201\pi$
$433$	−4.52786e11	−	7.84248e11i	−0.619009	−	1.07216i	0.370657	−	0.928770i	$-0.379132\pi$
$434$	−1.73239e11	+	3.00059e11i	−0.234392	+	0.405979i
$435$	−1.01961e11	−	5.78251e11i	−0.136532	−	0.774309i
$436$	−1.38870e11	+	8.01765e10i	−0.184043	+	0.106257i
$437$	7.04276e10	−	2.56335e10i	0.0923796	−	0.0336234i
$438$			2.80633e11i			0.364338i
$439$	−9.52475e10	−	2.61690e11i	−0.122395	−	0.336277i	0.863330	−	0.504639i	$-0.168374\pi$
$439$	−9.52475e10	−	2.61690e11i	−0.122395	−	0.336277i	−0.985725	+	0.168362i	$0.946152\pi$
$440$	2.12730e11	−	1.20645e12i	0.270577	−	1.53452i
$441$	−5.91556e11	−	4.96374e11i	−0.744769	−	0.624936i
$442$	−4.68839e11	−	5.58741e11i	−0.584284	−	0.696322i
$443$	−1.55288e12			−1.91567			−0.957835	−	0.287318i	$-0.907236\pi$
$443$	−1.55288e12			−1.91567			−0.957835	+	0.287318i	$0.907236\pi$
$444$	−2.83133e11	−	1.80354e11i	−0.345754	−	0.220243i
$445$	−6.99434e11			−0.845525
$446$	−4.98876e10	−	5.94537e10i	−0.0597015	−	0.0711495i
$447$	−2.55853e11	−	2.14686e11i	−0.303114	−	0.254343i
$448$	5.08205e10	−	2.88218e11i	0.0596058	−	0.338041i
$449$	1.22220e11	+	3.35796e11i	0.141916	+	0.389912i	0.990205	−	0.139622i	$-0.0445888\pi$
$449$	1.22220e11	+	3.35796e11i	0.141916	+	0.389912i	−0.848288	+	0.529535i	$0.822367\pi$
$450$			2.82468e11i			0.324722i
$451$	4.06882e11	−	1.48093e11i	0.463100	−	0.168555i
$452$	−3.05240e11	+	1.76230e11i	−0.343968	+	0.198590i
$453$	2.48943e11	+	1.41182e12i	0.277752	+	1.57521i
$454$	1.70509e11	−	2.95330e11i	0.188363	−	0.326254i
$455$	−1.53096e11	−	2.65170e11i	−0.167460	−	0.290050i
$456$	−9.38086e10	+	7.87148e10i	−0.101602	+	0.0852539i
$457$	1.54710e12	+	2.72795e11i	1.65918	+	0.292559i	0.923165	−	0.384403i	$-0.125593\pi$
$457$	1.54710e12	+	2.72795e11i	1.65918	+	0.292559i	0.736018	+	0.676962i	$0.236704\pi$
$458$	3.47852e11	+	2.00833e11i	0.369403	+	0.213275i
$459$	2.90745e10	−	7.98817e10i	0.0305743	−	0.0840021i
$460$	2.39012e11	+	8.69932e10i	0.248891	+	0.0905889i
$461$	5.64980e11	−	9.96213e10i	0.582612	−	0.102730i	0.125428	−	0.992103i	$-0.459969\pi$
$461$	5.64980e11	−	9.96213e10i	0.582612	−	0.102730i	0.457183	+	0.889372i	$0.348858\pi$
$462$	−4.28213e11	+	5.10324e11i	−0.437291	+	0.521144i
$463$	6.20574e11	−	7.39571e11i	0.627594	−	0.747938i	−0.354762	−	0.934957i	$-0.615438\pi$
$463$	6.20574e11	−	7.39571e11i	0.627594	−	0.747938i	0.982356	+	0.187019i	$0.0598826\pi$
$464$	4.24354e11	−	7.48250e10i	0.425008	−	0.0749404i
$465$	1.94471e12	+	7.07816e11i	1.92893	+	0.702072i
$466$	7.39292e10	−	2.03119e11i	0.0726239	−	0.199532i
$467$	1.05859e12	+	6.11176e11i	1.02991	+	0.594621i	0.916960	−	0.398979i	$-0.130636\pi$
$467$	1.05859e12	+	6.11176e11i	1.02991	+	0.594621i	0.112954	+	0.993600i	$0.463969\pi$
$468$	4.18775e11	+	7.38414e10i	0.403529	+	0.0711531i
$469$	−2.65091e11	+	2.22437e11i	−0.252998	+	0.212290i
$470$	3.76770e11	+	6.52584e11i	0.356152	+	0.616873i
$471$	−1.45951e11	+	2.52794e11i	−0.136651	+	0.236686i
$472$	−2.44385e11	−	1.38597e12i	−0.226639	−	1.28533i
$473$	1.17658e12	−	6.79300e11i	1.08081	−	0.624003i
$474$	−1.80134e12	+	6.55634e11i	−1.63905	+	0.596566i
$475$			3.34879e10i			0.0301833i
$476$	2.73295e10	+	7.50871e10i	0.0244006	+	0.0670400i
$477$	1.25798e11	−	7.13437e11i	0.111261	−	0.630990i
$478$	−1.65009e11	−	1.38459e11i	−0.144572	−	0.121310i
$479$	9.74075e11	+	1.16086e12i	0.845439	+	1.00756i	0.999809	+	0.0195423i	$0.00622091\pi$
$479$	9.74075e11	+	1.16086e12i	0.845439	+	1.00756i	−0.154370	+	0.988013i	$0.549335\pi$
$480$	−7.39149e11			−0.635545
$481$	−2.05009e11	−	1.55655e12i	−0.174631	−	1.32590i
$482$	1.42310e12			1.20095
$483$	−4.01480e11	−	4.78465e11i	−0.335661	−	0.400026i
$484$	5.77511e11	+	4.84589e11i	0.478361	+	0.401393i
$485$	−2.83850e11	+	1.60979e12i	−0.232944	+	1.32109i
$486$	5.09779e11	+	1.40061e12i	0.414494	+	1.13881i
$487$			2.37905e12i			1.91656i	0.285831	+	0.958280i	$0.407730\pi$
$487$			2.37905e12i			1.91656i	−0.285831	+	0.958280i	$0.592270\pi$
$488$	−8.04802e11	+	2.92924e11i	−0.642392	+	0.233811i
$489$	−1.13927e12	+	6.57756e11i	−0.901022	+	0.520205i
$490$	1.35729e11	+	7.69755e11i	0.106363	+	0.603212i
$491$	1.12121e12	−	1.94200e12i	0.870605	−	1.50793i	0.00923206	−	0.999957i	$-0.497061\pi$
$491$	1.12121e12	−	1.94200e12i	0.870605	−	1.50793i	0.861372	−	0.507974i	$-0.169605\pi$
$492$	−7.34448e10	−	1.27210e11i	−0.0565090	−	0.0978765i
$493$	−5.48980e11	+	4.60649e11i	−0.418548	+	0.351204i
$494$	−1.24900e11	−	2.20233e10i	−0.0943610	−	0.0166384i
$495$	1.78703e12	+	1.03174e12i	1.33785	+	0.772409i
$496$	−5.19436e11	+	1.42714e12i	−0.385358	+	1.05876i
$497$	−2.11008e11	−	7.68007e10i	−0.155130	−	0.0564626i
$498$	−3.94557e11	+	6.95710e10i	−0.287460	+	0.0506869i
$499$	3.26984e11	−	3.89684e11i	0.236088	−	0.281359i	−0.634972	−	0.772535i	$-0.718988\pi$
$499$	3.26984e11	−	3.89684e11i	0.236088	−	0.281359i	0.871060	+	0.491176i	$0.163433\pi$
$500$	−2.78044e11	+	3.31360e11i	−0.198952	+	0.237102i
$501$	−2.67444e12	+	4.71575e11i	−1.89654	+	0.334412i
$502$	−6.88852e11	−	2.50722e11i	−0.484127	−	0.176208i
$503$	5.78235e11	−	1.58869e12i	0.402762	−	1.10658i	−0.558153	−	0.829738i	$-0.688490\pi$
$503$	5.78235e11	−	1.58869e12i	0.402762	−	1.10658i	0.960915	−	0.276842i	$-0.0892878\pi$
$504$	4.58327e11	+	2.64615e11i	0.316401	+	0.182674i
$505$	1.37746e12	+	2.42883e11i	0.942470	+	0.166183i
$506$	1.98261e12	−	1.66361e12i	1.34450	−	1.12817i
$507$	8.45374e11	+	1.46423e12i	0.568216	+	0.984178i
$508$	2.63274e11	−	4.56004e11i	0.175397	−	0.303796i
$509$	−2.68732e11	−	1.52406e12i	−0.177456	−	1.00640i	−0.935271	−	0.353932i	$-0.884844\pi$
$509$	−2.68732e11	−	1.52406e12i	−0.177456	−	1.00640i	0.757816	−	0.652469i	$-0.226267\pi$
$510$	−1.03984e12	+	6.00351e11i	−0.680613	+	0.392952i
$511$	1.35114e11	−	4.91773e10i	0.0876607	−	0.0319059i
$512$		−	1.61467e12i		−	1.03841i
$513$	−5.05556e9	−	1.38900e10i	−0.00322286	−	0.00885472i
$514$	−1.69545e11	+	9.61536e11i	−0.107140	+	0.607619i
$515$	−8.70063e10	−	7.30070e10i	−0.0545027	−	0.0457332i
$516$	−2.96256e11	−	3.53064e11i	−0.183968	−	0.219245i
$517$	−3.04784e12			−1.87623
$518$	9.36302e10	−	4.22446e11i	0.0571389	−	0.257803i
$519$	1.86062e12			1.12565
$520$	−1.24935e12	−	1.48892e12i	−0.749324	−	0.893009i
$521$	6.15071e11	+	5.16106e11i	0.365726	+	0.306880i	0.807068	−	0.590459i	$-0.201053\pi$
$521$	6.15071e11	+	5.16106e11i	0.365726	+	0.306880i	−0.441342	+	0.897339i	$0.645498\pi$
$522$	−1.82520e11	+	1.03512e12i	−0.107595	+	0.610202i
$523$	−1.46444e11	−	4.02352e11i	−0.0855884	−	0.235152i	0.889514	−	0.456908i	$-0.151043\pi$
$523$	−1.46444e11	−	4.02352e11i	−0.0855884	−	0.235152i	−0.975102	+	0.221756i	$0.928821\pi$
$524$			5.14364e10i			0.0298043i
$525$	2.62248e11	−	9.54505e10i	0.150659	−	0.0548354i
$526$	2.02123e12	−	1.16696e12i	1.15128	−	0.664692i
$527$	−4.38608e11	−	2.48747e12i	−0.247702	−	1.40479i
$528$	−1.46004e12	+	2.52887e12i	−0.817548	+	1.41604i
$529$	3.12694e11	+	5.41603e11i	0.173608	+	0.300698i
$530$	−5.61717e11	+	4.71336e11i	−0.309226	+	0.259471i
$531$	2.33452e12	+	4.11640e11i	1.27430	+	0.224694i
$532$	1.20328e10	+	6.94713e9i	0.00651274	+	0.00376013i
$533$	2.34960e11	−	6.45547e11i	0.126102	−	0.346462i
$534$	2.26877e12	+	8.25765e11i	1.20741	+	0.439462i
$535$	5.77925e11	−	1.01904e11i	0.304986	−	0.0537772i
$536$	−1.41199e12	+	1.68274e12i	−0.738907	+	0.880595i
$537$	8.20010e11	−	9.77250e11i	0.425535	−	0.507133i
$538$	−2.56119e12	+	4.51607e11i	−1.31802	+	0.232402i
$539$	−2.97080e12	−	1.08128e12i	−1.51609	−	0.551810i
$540$	1.71572e10	−	4.71389e10i	0.00868308	−	0.0238566i
$541$	−1.82236e12	−	1.05214e12i	−0.914634	−	0.528064i	−0.0327149	−	0.999465i	$-0.510415\pi$
$541$	−1.82236e12	−	1.05214e12i	−0.914634	−	0.528064i	−0.881919	+	0.471400i	$0.843749\pi$
$542$	8.60692e11	+	1.51763e11i	0.428402	+	0.0755388i
$543$	−9.30757e11	+	7.80997e11i	−0.459449	+	0.385523i
$544$	4.51066e11	+	7.81269e11i	0.220823	+	0.382477i
$545$	−6.17274e11	+	1.06915e12i	−0.299705	+	0.519104i
$546$	1.83536e11	+	1.04089e12i	0.0883802	+	0.501229i
$547$	2.43442e12	−	1.40551e12i	1.16266	−	0.671262i	0.210719	−	0.977547i	$-0.432419\pi$
$547$	2.43442e12	−	1.40551e12i	1.16266	−	0.671262i	0.951940	+	0.306285i	$0.0990861\pi$
$548$	−9.21546e11	+	3.35415e11i	−0.436520	+	0.158880i
$549$		−	1.44260e12i		−	0.677752i
$550$	3.95518e11	+	1.08668e12i	0.184304	+	0.506370i
$551$	−2.16386e10	+	1.22718e11i	−0.0100011	+	0.0567189i
$552$	−3.03720e12	−	2.54851e12i	−1.39235	−	1.16832i
$553$	6.31323e11	+	7.52382e11i	0.287071	+	0.342118i
$554$	3.45877e12			1.56001
$555$	−2.58205e12	−	1.12595e11i	−1.15517	−	0.0503734i
$556$	−3.58575e11			−0.159127
$557$	8.86571e11	+	1.05657e12i	0.390270	+	0.465106i	0.925028	−	0.379900i	$-0.124042\pi$
$557$	8.86571e11	+	1.05657e12i	0.390270	+	0.465106i	−0.534758	+	0.845006i	$0.679597\pi$
$558$	−2.83790e12	−	2.38128e12i	−1.23921	−	1.03982i
$559$	3.74301e11	−	2.12277e12i	0.162132	−	0.919495i
$560$	−1.26513e11	−	3.47592e11i	−0.0543613	−	0.149356i
$561$		−	4.85649e12i		−	2.07009i
$562$	−1.34879e12	+	4.90918e11i	−0.570335	+	0.207585i
$563$	5.47301e11	−	3.15984e11i	0.229582	−	0.132549i	−0.380797	−	0.924659i	$-0.624350\pi$
$563$	5.47301e11	−	3.15984e11i	0.229582	−	0.132549i	0.610379	+	0.792109i	$0.291017\pi$
$564$	1.79544e11	+	1.01824e12i	0.0747162	+	0.423736i
$565$	−1.35678e12	+	2.35002e12i	−0.560135	+	0.970183i
$566$	−1.42920e11	−	2.47545e11i	−0.0585355	−	0.101386i
$567$	5.39575e11	−	4.52757e11i	0.219244	−	0.183968i
$568$	−1.40375e12	−	2.47518e11i	−0.565875	−	0.0997791i
$569$	1.53603e12	+	8.86828e11i	0.614320	+	0.354678i	0.774654	−	0.632385i	$-0.217924\pi$
$569$	1.53603e12	+	8.86828e11i	0.614320	+	0.354678i	−0.160334	+	0.987063i	$0.551257\pi$
$570$	−7.14074e10	+	1.96190e11i	−0.0283339	+	0.0778467i
$571$	−2.57795e12	−	9.38296e11i	−1.01487	−	0.369383i	−0.219571	−	0.975597i	$-0.570466\pi$
$571$	−2.57795e12	−	9.38296e11i	−1.01487	−	0.369383i	−0.795302	+	0.606213i	$0.792688\pi$
$572$	1.71446e12	−	3.02305e11i	0.669646	−	0.118077i
$573$	−2.80899e12	+	3.34762e12i	−1.08857	+	1.29730i
$574$	1.21702e11	−	1.45039e11i	0.0467943	−	0.0557673i
$575$	−1.06775e12	+	1.88273e11i	−0.407347	+	0.0718263i
$576$	2.94050e12	+	1.07026e12i	1.11307	+	0.405123i
$577$	9.95027e11	−	2.73381e12i	0.373718	−	1.02678i	−0.600194	−	0.799854i	$-0.704910\pi$
$577$	9.95027e11	−	2.73381e12i	0.373718	−	1.02678i	0.973912	−	0.226927i	$-0.0728678\pi$
$578$	−6.96634e11	−	4.02202e11i	−0.259615	−	0.149889i
$579$	6.12025e12	+	1.07917e12i	2.26316	+	0.399056i
$580$	−3.23958e11	+	2.71833e11i	−0.118868	+	0.0997417i
$581$	1.02637e11	+	1.77772e11i	0.0373689	+	0.0647248i
$582$	2.82128e12	−	4.88661e12i	1.01928	−	1.76544i
$583$	−5.15015e11	−	2.92080e12i	−0.184634	−	1.04711i
$584$	7.90437e11	−	4.56359e11i	0.281196	−	0.162349i
$585$	3.07642e12	−	1.11973e12i	1.08604	−	0.395285i
$586$			4.30541e12i			1.50825i
$587$	−1.48083e11	−	4.06855e11i	−0.0514794	−	0.141439i	0.911288	−	0.411770i	$-0.135089\pi$
$587$	−1.48083e11	−	4.06855e11i	−0.0514794	−	0.141439i	−0.962767	+	0.270331i	$0.912867\pi$
$588$	−1.86237e11	+	1.05620e12i	−0.0642492	+	0.364375i
$589$	−3.36447e11	−	2.82312e11i	−0.115185	−	0.0966521i
$590$	−1.54232e12	−	1.83806e12i	−0.524010	−	0.624491i
$591$	−7.53269e12			−2.53984
$592$	8.26288e10	−	1.89486e12i	0.0276493	−	0.634058i
$593$	−3.15285e12			−1.04703			−0.523513	−	0.852017i	$-0.675379\pi$
$593$	−3.15285e12			−1.04703			−0.523513	+	0.852017i	$0.675379\pi$
$594$	−3.28104e11	−	3.91019e11i	−0.108137	−	0.128872i
$595$	4.71264e11	+	3.95437e11i	0.154148	+	0.129345i
$596$	−4.17712e10	+	2.36896e11i	−0.0135603	+	0.0769042i
$597$	2.13348e12	+	5.86170e12i	0.687393	+	1.88860i
$598$		−	4.10623e12i		−	1.31307i
$599$	5.80754e11	−	2.11377e11i	0.184320	−	0.0670868i	−0.248212	−	0.968706i	$-0.579843\pi$
$599$	5.80754e11	−	2.11377e11i	0.184320	−	0.0670868i	0.432531	+	0.901619i	$0.357621\pi$
$600$	1.53420e12	−	8.85768e11i	0.483282	−	0.279023i
$601$	5.95743e11	+	3.37863e12i	0.186262	+	1.05634i	0.924323	+	0.381610i	$0.124630\pi$
$601$	5.95743e11	+	3.37863e12i	0.186262	+	1.05634i	−0.738062	+	0.674733i	$0.764259\pi$
$602$	2.97035e11	−	5.14480e11i	0.0921773	−	0.159656i
$603$	−1.85002e12	−	3.20433e12i	−0.569835	−	0.986984i
$604$	7.90958e11	−	6.63692e11i	0.241817	−	0.202909i
$605$	5.71594e12	+	1.00788e12i	1.73456	+	0.305849i
$606$	−4.18135e12	−	2.41410e12i	−1.25948	−	0.727158i
$607$	−2.13111e12	+	5.85518e12i	−0.637172	+	1.75062i	0.0232587	+	0.999729i	$0.492596\pi$
$607$	−2.13111e12	+	5.85518e12i	−0.637172	+	1.75062i	−0.660431	+	0.750887i	$0.729626\pi$
$608$	1.47405e11	+	5.36510e10i	0.0437467	+	0.0159225i
$609$	1.02270e12	−	1.80330e11i	0.301281	−	0.0531239i
$610$	−9.38584e11	+	1.11856e12i	−0.274466	+	0.327096i
$611$	−3.10827e12	+	3.70430e12i	−0.902265	+	1.07528i
$612$	−8.41391e11	+	1.48360e11i	−0.242447	+	0.0427499i
$613$	3.44623e12	+	1.25433e12i	0.985763	+	0.358788i	0.784078	−	0.620662i	$-0.213136\pi$
$613$	3.44623e12	+	1.25433e12i	0.985763	+	0.358788i	0.201685	+	0.979450i	$0.435358\pi$
$614$	1.40431e12	−	3.85832e12i	0.398755	−	1.09557i
$615$	−9.79382e11	−	5.65446e11i	−0.276067	−	0.159387i
$616$	2.13374e12	+	3.76236e11i	0.597075	+	0.105280i
$617$	−5.01495e12	+	4.20804e12i	−1.39310	+	1.16895i	−0.429039	+	0.903286i	$0.641148\pi$
$617$	−5.01495e12	+	4.20804e12i	−1.39310	+	1.16895i	−0.964065	+	0.265667i	$0.914408\pi$
$618$	1.96031e11	+	3.39536e11i	0.0540601	+	0.0936349i
$619$	2.00085e12	−	3.46558e12i	0.547781	−	0.948785i	−0.450645	−	0.892703i	$-0.648806\pi$
$619$	2.00085e12	−	3.46558e12i	0.547781	−	0.948785i	0.998426	−	0.0560819i	$-0.0178608\pi$
$620$	−2.58827e11	−	1.46788e12i	−0.0703472	−	0.398959i
$621$	4.14456e11	−	2.39286e11i	0.111832	−	0.0645663i
$622$	1.83874e12	−	6.69246e11i	0.492564	−	0.179279i
$623$		−	1.23703e12i		−	0.328991i
$624$	1.58455e12	+	4.35353e12i	0.418385	+	1.14950i
$625$	−3.42230e11	+	1.94088e12i	−0.0897136	+	0.508791i
$626$	2.97160e12	+	2.49347e12i	0.773404	+	0.648963i
$627$	−5.42807e11	−	6.46892e11i	−0.140263	−	0.167158i
$628$	2.10236e11			0.0539372
$629$	1.45668e12	+	2.79790e12i	0.371054	+	0.712695i
$630$	9.02292e11			0.228199
$631$	1.29198e10	+	1.53972e10i	0.00324433	+	0.00386644i	0.767664	−	0.640852i	$-0.221419\pi$
$631$	1.29198e10	+	1.53972e10i	0.00324433	+	0.00386644i	−0.764420	+	0.644719i	$0.776974\pi$
$632$	4.77597e12	+	4.00752e12i	1.19079	+	0.999191i
$633$	−6.63884e11	+	3.76507e12i	−0.164352	+	0.932088i
$634$	1.32526e11	+	3.64112e11i	0.0325761	+	0.0895021i
$635$		−	4.05385e12i		−	0.989433i
$636$	−9.45461e11	+	3.44120e11i	−0.229132	+	0.0833974i
$637$	−4.34388e12	+	2.50794e12i	−1.04532	+	0.603517i
$638$	7.47233e11	+	4.23777e12i	0.178551	+	1.01261i
$639$	1.20047e12	−	2.07927e12i	0.284837	−	0.493352i
$640$	−6.47862e11	−	1.12213e12i	−0.152642	−	0.264383i
$641$	4.72456e12	−	3.96438e12i	1.10535	−	0.927500i	0.107578	−	0.994197i	$-0.465690\pi$
$641$	4.72456e12	−	3.96438e12i	1.10535	−	0.927500i	0.997773	+	0.0666965i	$0.0212459\pi$
$642$	−1.99494e12	−	3.51762e11i	−0.463471	−	0.0817224i
$643$	−3.94203e11	−	2.27593e11i	−0.0909434	−	0.0525062i	0.453839	−	0.891084i	$-0.350054\pi$
$643$	−3.94203e11	−	2.27593e11i	−0.0909434	−	0.0525062i	−0.544782	+	0.838578i	$0.683388\pi$
$644$	−1.53857e11	+	4.22720e11i	−0.0352478	+	0.0968425i
$645$	−3.33439e12	−	1.21362e12i	−0.758573	−	0.276098i
$646$	2.50946e11	−	4.42486e10i	0.0566937	−	0.00999662i
$647$	−4.46887e12	+	5.32579e12i	−1.00260	+	1.19485i	−0.0218171	+	0.999762i	$0.506945\pi$
$647$	−4.46887e12	+	5.32579e12i	−1.00260	+	1.19485i	−0.980785	+	0.195093i	$0.937499\pi$
$648$	2.87402e12	−	3.42512e12i	0.640327	−	0.763112i
$649$	9.55750e12	−	1.68525e12i	2.11467	−	0.372874i
$650$	1.72409e12	+	6.27517e11i	0.378835	+	0.137884i
$651$	−1.25185e12	+	3.43944e12i	−0.273174	+	0.750538i
$652$	8.20532e11	+	4.73735e11i	0.177820	+	0.102665i
$653$	−1.48237e12	−	2.61381e11i	−0.319041	−	0.0562555i	0.0118344	−	0.999930i	$-0.496233\pi$
$653$	−1.48237e12	−	2.61381e11i	−0.319041	−	0.0562555i	−0.330875	+	0.943674i	$0.607344\pi$
$654$	3.26452e12	−	2.73926e12i	0.697783	−	0.585509i
$655$	1.98003e11	+	3.42950e11i	0.0420325	+	0.0728024i
$656$	4.14957e11	−	7.18727e11i	0.0874855	−	0.151529i
$657$	2.66962e11	+	1.51402e12i	0.0558993	+	0.317020i
$658$	−1.15417e12	+	6.66360e11i	−0.240023	+	0.138577i
$659$	−6.77919e12	+	2.46742e12i	−1.40021	+	0.509635i	−0.928241	−	0.371980i	$-0.878679\pi$
$659$	−6.77919e12	+	2.46742e12i	−1.40021	+	0.509635i	−0.471969	+	0.881615i	$0.656457\pi$
$660$		−	2.86586e12i		−	0.587905i
$661$	2.17079e12	+	5.96420e12i	0.442295	+	1.21519i	0.937979	+	0.346692i	$0.112695\pi$
$661$	2.17079e12	+	5.96420e12i	0.442295	+	1.21519i	−0.495684	+	0.868503i	$0.665083\pi$
$662$	2.04138e11	−	1.15772e12i	0.0413108	−	0.234285i
$663$	−5.90249e12	−	4.95278e12i	−1.18638	−	0.995493i
$664$	8.37575e11	+	9.98183e11i	0.167212	+	0.199275i
$665$	1.06971e11			0.0212114
$666$	4.27442e12	+	1.77025e12i	0.841866	+	0.348659i
$667$	−4.03450e12			−0.789266
$668$	1.25724e12	+	1.49832e12i	0.244301	+	0.291146i
$669$	−6.28064e11	−	5.27008e11i	−0.121223	−	0.101718i
$670$	−6.50335e11	+	3.68823e12i	−0.124681	+	0.707101i
$671$	−2.01997e12	−	5.54981e12i	−0.384674	−	1.05688i
$672$		−	1.30727e12i		−	0.247288i
$673$	4.41617e12	−	1.60735e12i	0.829809	−	0.302026i	0.108028	−	0.994148i	$-0.465546\pi$
$673$	4.41617e12	−	1.60735e12i	0.829809	−	0.302026i	0.721780	+	0.692122i	$0.243324\pi$
$674$	−1.85187e12	+	1.06918e12i	−0.345653	+	0.199563i
$675$	3.71320e10	+	2.10586e11i	0.00688465	+	0.0390448i
$676$	6.08863e11	−	1.05458e12i	0.112140	−	0.194232i
$677$	6.04703e11	+	1.04738e12i	0.110635	+	0.191626i	0.916027	−	0.401118i	$-0.131378\pi$
$677$	6.04703e11	+	1.04738e12i	0.110635	+	0.191626i	−0.805391	+	0.592743i	$0.798045\pi$
$678$	7.17552e12	−	6.02097e12i	1.30413	−	1.09429i
$679$	−2.84710e12	−	5.02021e11i	−0.514031	−	0.0906374i
$680$	3.38193e12	+	1.95256e12i	0.606561	+	0.350198i
$681$	1.23212e12	−	3.38522e12i	0.219529	−	0.603150i
$682$	−1.42520e13	−	5.18730e12i	−2.52258	−	0.918146i
$683$	−6.44335e12	+	1.13614e12i	−1.13297	+	0.199773i	−0.708529	−	0.705682i	$-0.750641\pi$
$683$	−6.44335e12	+	1.13614e12i	−1.13297	+	0.199773i	−0.424442	+	0.905455i	$0.639530\pi$
$684$	−9.54927e10	+	1.13804e11i	−0.0166808	+	0.0198794i
$685$	−4.85321e12	+	5.78383e12i	−0.842212	+	1.00371i
$686$	−2.86978e12	+	5.06020e11i	−0.494755	+	0.0872386i
$687$	3.98726e12	+	1.45125e12i	0.682920	+	0.248562i
$688$	8.90623e11	−	2.44697e12i	0.151546	−	0.416370i
$689$	−4.07511e12	−	2.35277e12i	−0.688896	−	0.397734i
$690$	−6.65692e12	−	1.17380e12i	−1.11803	−	0.197139i
$691$	7.59879e11	−	6.37614e11i	0.126792	−	0.106391i	−0.577186	−	0.816612i	$-0.695849\pi$
$691$	7.59879e11	−	6.37614e11i	0.126792	−	0.106391i	0.703979	+	0.710221i	$0.251405\pi$
$692$	−6.70037e11	−	1.16054e12i	−0.111076	−	0.192390i
$693$	−1.82475e12	+	3.16056e12i	−0.300541	+	0.520553i
$694$	1.47443e12	+	8.36191e12i	0.241272	+	1.36832i
$695$	−2.39079e12	+	1.38032e12i	−0.388695	+	0.224413i
$696$	6.19451e12	−	2.25462e12i	1.00061	−	0.364193i
$697$			1.38025e12i			0.221519i
$698$	2.18832e12	+	6.01237e12i	0.348949	+	0.958730i
$699$	3.96515e11	−	2.24875e12i	0.0628221	−	0.356282i
$700$	−1.53975e11	−	1.29201e11i	−0.0242387	−	0.0203387i
$701$	−4.78532e12	−	5.70293e12i	−0.748480	−	0.892004i	0.248581	−	0.968611i	$-0.420036\pi$
$701$	−4.78532e12	−	5.70293e12i	−0.748480	−	0.892004i	−0.997061	+	0.0766071i	$0.975591\pi$
$702$	−8.09848e11			−0.125860
$703$	5.06752e11	+	2.09872e11i	0.0782523	+	0.0324082i
$704$	1.28110e13			1.96564
$705$	5.11680e12	+	6.09796e12i	0.780094	+	0.929680i
$706$	−4.33271e12	−	3.63557e12i	−0.656354	−	0.550746i
$707$	−4.29567e11	+	2.43619e12i	−0.0646611	+	0.366712i
$708$	−1.12604e12	−	3.09376e12i	−0.168424	−	0.462740i
$709$		−	8.24527e12i		−	1.22545i	−0.790295	−	0.612726i	$-0.790073\pi$
$709$		−	8.24527e12i		−	1.22545i	0.790295	−	0.612726i	$-0.209927\pi$
$710$	−2.28363e12	+	8.31173e11i	−0.337258	+	0.122752i
$711$	−9.09456e12	+	5.25075e12i	−1.33465	+	0.770563i
$712$	−1.36356e12	−	7.73312e12i	−0.198845	−	1.12770i
$713$	7.10990e12	−	1.23147e13i	1.03029	−	1.78452i
$714$	−1.06179e12	−	1.83907e12i	−0.152896	−	0.264824i
$715$	1.02674e13	−	8.61537e12i	1.46921	−	1.23281i
$716$	−9.04844e11	−	1.59548e11i	−0.128666	−	0.0226874i
$717$	−1.97065e12	−	1.13776e12i	−0.278467	−	0.160773i
$718$	−2.91289e11	+	8.00310e11i	−0.0409038	+	0.112382i
$719$	9.72025e12	+	3.53788e12i	1.35643	+	0.493700i	0.914949	−	0.403570i	$-0.132231\pi$
$719$	9.72025e12	+	3.53788e12i	1.35643	+	0.493700i	0.441481	+	0.897271i	$0.354453\pi$
$720$	3.89496e12	−	6.86786e11i	0.540140	−	0.0952412i
$721$	1.29121e11	−	1.53881e11i	0.0177946	−	0.0212068i
$722$	−3.94169e12	+	4.69752e12i	−0.539840	+	0.643356i
$723$	1.48051e13	−	2.61054e12i	2.01506	−	0.355310i
$724$	8.22315e11	+	2.99298e11i	0.111228	+	0.0404838i
$725$	6.16555e11	−	1.69397e12i	0.0828802	−	0.227711i
$726$	−1.73510e13	−	1.00176e13i	−2.31798	−	1.33829i
$727$	1.22988e13	+	2.16861e12i	1.63289	+	0.287923i	0.913548	−	0.406731i	$-0.133331\pi$
$727$	1.22988e13	+	2.16861e12i	1.63289	+	0.287923i	0.719344	+	0.694654i	$0.244442\pi$
$728$	2.63332e12	−	2.20962e12i	0.347466	−	0.291559i
$729$	4.37697e12	+	7.58113e12i	0.573984	+	0.994169i
$730$	7.78053e11	−	1.34763e12i	0.101404	−	0.175637i
$731$	7.52035e11	+	4.26500e12i	0.0974115	+	0.552448i
$732$	−1.73513e12	+	1.00178e12i	−0.223373	+	0.128965i
$733$	7.50789e12	−	2.73265e12i	0.960616	−	0.349636i	0.186341	−	0.982485i	$-0.440337\pi$
$733$	7.50789e12	−	2.73265e12i	0.960616	−	0.349636i	0.774275	+	0.632849i	$0.218115\pi$
$734$			1.86769e12i			0.237505i
$735$	2.82408e12	+	7.75910e12i	0.356931	+	0.980660i
$736$	−8.81915e11	+	5.00159e12i	−0.110784	+	0.628287i
$737$	−1.16040e13	−	9.73690e12i	−1.44878	−	1.21567i
$738$	1.30126e12	+	1.55078e12i	0.161477	+	0.192441i
$739$	−7.96980e12			−0.982986			−0.491493	−	0.870881i	$-0.663549\pi$
$739$	−7.96980e12			−0.982986			−0.491493	+	0.870881i	$0.663549\pi$
$740$	8.59603e11	+	1.65106e12i	0.105379	+	0.202405i
$741$	−1.33979e12			−0.163251
$742$	−8.33612e11	−	9.93460e11i	−0.100959	−	0.120319i
$743$	−1.02501e13	−	8.60087e12i	−1.23390	−	1.03536i	−0.997976	−	0.0635914i	$-0.979745\pi$
$743$	−1.02501e13	−	8.60087e12i	−1.23390	−	1.03536i	−0.235922	−	0.971772i	$-0.575811\pi$
$744$	−4.03455e12	+	2.28811e13i	−0.482744	+	2.73778i
$745$	6.33416e11	+	1.74030e12i	0.0753331	+	0.206976i
$746$		−	5.01733e12i		−	0.593127i
$747$	−2.06246e12	+	7.50674e11i	−0.242350	+	0.0882081i
$748$	−3.02917e12	+	1.74889e12i	−0.353807	+	0.204270i
$749$	1.80228e11	+	1.02213e12i	0.0209245	+	0.118669i
$750$	5.74784e12	−	9.95555e12i	0.663329	−	1.14892i
$751$	2.55183e12	+	4.41990e12i	0.292734	+	0.507029i	0.974455	−	0.224582i	$-0.0721018\pi$
$751$	2.55183e12	+	4.41990e12i	0.292734	+	0.507029i	−0.681722	+	0.731612i	$0.738768\pi$
$752$	−4.47504e12	+	3.75500e12i	−0.510289	+	0.428183i
$753$	−7.62635e12	−	1.34473e12i	−0.864449	−	0.152426i
$754$	5.91256e12	+	3.41362e12i	0.666200	+	0.384631i
$755$	2.71883e12	−	7.46991e12i	0.304523	−	0.836670i
$756$	8.33705e10	+	3.03444e10i	0.00928249	+	0.00337855i
$757$	−1.60992e13	+	2.83872e12i	−1.78186	+	0.314189i	−0.964921	−	0.262540i	$-0.915440\pi$
$757$	−1.60992e13	+	2.83872e12i	−1.78186	+	0.314189i	−0.816935	+	0.576730i	$0.804329\pi$
$758$	−5.24264e12	+	6.24794e12i	−0.576818	+	0.687425i
$759$	1.75742e13	−	2.09442e13i	1.92216	−	2.29074i
$760$	6.68715e11	−	1.17913e11i	0.0727076	−	0.0128203i
$761$	−1.40024e13	−	5.09644e12i	−1.51346	−	0.550853i	−0.553953	−	0.832548i	$-0.686881\pi$
$761$	−1.40024e13	−	5.09644e12i	−1.51346	−	0.550853i	−0.959504	+	0.281695i	$0.909103\pi$
$762$	−4.78606e12	+	1.31496e13i	−0.514258	+	1.41291i
$763$	−1.89091e12	−	1.09172e12i	−0.201981	−	0.116614i
$764$	3.09959e12	+	5.46542e11i	0.329143	+	0.0580368i
$765$	−5.03884e12	+	4.22809e12i	−0.531930	+	0.446342i
$766$	−4.20502e12	−	7.28330e12i	−0.441304	−	0.764362i
$767$	7.69879e12	−	1.33347e13i	0.803236	−	1.39125i
$768$	−1.87655e12	−	1.06425e13i	−0.194642	−	1.10387i
$769$	2.95018e12	−	1.70329e12i	0.304215	−	0.175638i	−0.340120	−	0.940382i	$-0.610468\pi$
$769$	2.95018e12	−	1.70329e12i	0.304215	−	0.175638i	0.644335	+	0.764744i	$0.277134\pi$
$770$	3.47120e12	−	1.26341e12i	0.355853	−	0.129520i
$771$			1.03143e13i			1.05122i
$772$	−1.53088e12	−	4.20605e12i	−0.155118	−	0.426183i
$773$	−1.57432e12	+	8.92843e12i	−0.158594	+	0.899430i	0.796833	+	0.604200i	$0.206507\pi$
$773$	−1.57432e12	+	8.92843e12i	−0.158594	+	0.899430i	−0.955426	+	0.295230i	$0.904604\pi$
$774$	4.86585e12	+	4.08294e12i	0.487332	+	0.408920i
$775$	4.08405e12	+	4.86718e12i	0.406662	+	0.484641i
$776$	−1.83516e13			−1.81676
$777$	1.99137e11	−	4.56665e12i	0.0196001	−	0.449472i
$778$	5.43897e12			0.532241
$779$	1.54270e11	+	1.83852e11i	0.0150094	+	0.0178875i
$780$	−3.48312e12	−	2.92268e12i	−0.336932	−	0.282719i
$781$	1.70685e12	−	9.68005e12i	0.164160	−	0.930996i
$782$	2.82171e12	+	7.75258e12i	0.269825	+	0.741337i
$783$			7.95701e11i			0.0756522i
$784$	−5.69408e12	+	2.07248e12i	−0.538271	+	0.195915i
$785$	1.40174e12	−	8.09295e11i	0.131751	−	0.0760665i
$786$	−2.37372e11	−	1.34620e12i	−0.0221834	−	0.125808i
$787$	−1.03131e13	+	1.78629e13i	−0.958306	+	1.65983i	−0.231691	+	0.972789i	$0.574426\pi$
$787$	−1.03131e13	+	1.78629e13i	−0.958306	+	1.65983i	−0.726615	+	0.687045i	$0.758908\pi$
$788$	2.71263e12	+	4.69842e12i	0.250624	+	0.434094i
$789$	1.88871e13	−	1.58481e13i	1.73508	−	1.45590i
$790$	1.04680e13	+	1.84578e12i	0.956181	+	0.168601i
$791$	−4.15628e12	−	2.39963e12i	−0.377494	−	0.217946i
$792$	−7.92336e12	+	2.17692e13i	−0.715560	+	1.96598i
$793$	−8.80517e12	−	3.20482e12i	−0.790694	−	0.287789i
$794$	−1.13947e12	+	2.00919e11i	−0.101744	+	0.0179402i
$795$	−4.97915e12	+	5.93393e12i	−0.442083	+	0.526854i
$796$	2.88786e12	−	3.44162e12i	0.254957	−	0.303846i
$797$	1.25898e13	−	2.21993e12i	1.10524	−	0.194884i	0.408889	−	0.912584i	$-0.365916\pi$
$797$	1.25898e13	−	2.21993e12i	1.10524	−	0.194884i	0.696352	+	0.717700i	$0.254805\pi$
$798$	−3.46985e11	−	1.26292e11i	−0.0302899	−	0.0110246i
$799$	3.32292e12	−	9.12966e12i	0.288443	−	0.792490i
$800$	−1.96525e12	−	1.13464e12i	−0.169634	−	0.0979382i
$801$	1.30256e13	+	2.29677e12i	1.11803	+	0.197138i
$802$	4.50845e12	−	3.78304e12i	0.384807	−	0.322891i
$803$	3.14700e12	+	5.45076e12i	0.267101	+	0.462633i
$804$	−2.56940e12	+	4.45032e12i	−0.216860	+	0.375612i
$805$	6.01405e11	+	3.41074e12i	0.0504761	+	0.286264i
$806$	−2.08391e13	+	1.20315e13i	−1.73929	+	1.00418i
$807$	−2.58167e13	+	9.39652e12i	−2.14274	+	0.779895i
$808$			1.57031e13i			1.29608i
$809$	1.67255e12	+	4.59531e12i	0.137281	+	0.377178i	0.989215	−	0.146473i	$-0.0467920\pi$
$809$	1.67255e12	+	4.59531e12i	0.137281	+	0.377178i	−0.851933	+	0.523650i	$0.824570\pi$
$810$	1.32371e12	−	7.50716e12i	0.108047	−	0.612764i
$811$	1.68171e13	+	1.41112e13i	1.36508	+	1.14543i	0.974378	+	0.224916i	$0.0722108\pi$
$811$	1.68171e13	+	1.41112e13i	1.36508	+	1.14543i	0.390698	+	0.920519i	$0.372234\pi$
$812$	−4.80768e11	−	5.72957e11i	−0.0388091	−	0.0462509i
$813$	9.23254e12			0.741163
$814$	1.89228e13	+	8.25165e11i	1.51069	+	0.0658765i
$815$	7.29450e12			0.579144
$816$	−5.98329e12	−	7.13060e12i	−0.472426	−	0.563016i
$817$	5.76870e11	+	4.84051e11i	0.0452980	+	0.0380095i
$818$	−1.57351e12	+	8.92385e12i	−0.122880	+	0.696887i
$819$	1.98036e12	+	5.44100e12i	0.153804	+	0.422573i
$820$			8.14501e11i			0.0629114i
$821$	−1.37300e13	+	4.99731e12i	−1.05469	+	0.383877i	−0.810432	−	0.585833i	$-0.800768\pi$
$821$	−1.37300e13	+	4.99731e12i	−1.05469	+	0.383877i	−0.244261	+	0.969710i	$0.578545\pi$
$822$	2.25710e13	−	1.30314e13i	1.72436	−	0.995559i
$823$	−3.49768e11	−	1.98363e12i	−0.0265755	−	0.150717i	0.968633	−	0.248498i	$-0.0799368\pi$
$823$	−3.49768e11	−	1.98363e12i	−0.0265755	−	0.150717i	−0.995208	+	0.0977805i	$0.968826\pi$
$824$	6.37563e11	−	1.10429e12i	0.0481782	−	0.0834472i
$825$	6.10815e12	+	1.05796e13i	0.459057	+	0.795110i
$826$	3.25082e12	−	2.72776e12i	0.242987	−	0.203890i
$827$	9.03109e12	+	1.59243e12i	0.671376	+	0.118382i	0.498936	−	0.866639i	$-0.333724\pi$
$827$	9.03109e12	+	1.59243e12i	0.671376	+	0.118382i	0.172439	+	0.985020i	$0.444835\pi$
$828$	−4.16547e12	−	2.40494e12i	−0.307984	−	0.177814i
$829$	4.57861e12	−	1.25796e13i	0.336696	−	0.925066i	−0.649628	−	0.760252i	$-0.725076\pi$
$829$	4.57861e12	−	1.25796e13i	0.336696	−	0.925066i	0.986325	−	0.164814i	$-0.0527023\pi$
$830$	2.08759e12	+	7.59820e11i	0.152684	+	0.0555724i
$831$	3.59830e13	−	6.34478e12i	2.61754	−	0.461543i
$832$	1.30650e13	−	1.55702e13i	0.945266	−	1.12652i
$833$	6.47786e12	−	7.72001e12i	0.466153	−	0.555540i
$834$	9.38469e12	−	1.65477e12i	0.671696	−	0.118438i
$835$	1.41504e13	+	5.15031e12i	1.00735	+	0.366644i
$836$	−2.08018e11	+	5.71524e11i	−0.0147290	+	0.0404675i
$837$	−2.42876e12	−	1.40224e12i	−0.171049	−	0.0987550i
$838$	7.36607e12	+	1.29884e12i	0.515986	+	0.0909822i
$839$	−5.08058e12	+	4.26311e12i	−0.353984	+	0.297028i	−0.802388	−	0.596803i	$-0.796437\pi$
$839$	−5.08058e12	+	4.26311e12i	−0.353984	+	0.297028i	0.448403	+	0.893831i	$0.351993\pi$
$840$	−2.82943e12	−	4.90071e12i	−0.196084	−	0.339627i
$841$	−3.89959e12	+	6.75429e12i	−0.268805	+	0.465583i
$842$	8.70145e11	+	4.93484e12i	0.0596606	+	0.338352i
$843$	−1.31315e13	+	7.58145e12i	−0.895548	+	0.517045i
$844$	2.58749e12	−	9.41769e11i	0.175524	−	0.0638856i
$845$		−	9.37519e12i		−	0.632594i
$846$	−4.87368e12	−	1.33903e13i	−0.327108	−	0.898721i
$847$	−1.78254e12	+	1.01093e13i	−0.119005	+	0.674910i
$848$	−4.35466e12	−	3.65399e12i	−0.289183	−	0.242653i
$849$	−1.94095e12	−	2.31314e12i	−0.128213	−	0.152798i
$850$	−3.68630e12			−0.242218
$851$	−3.84267e12	+	1.73376e13i	−0.251160	+	1.13320i
$852$	−3.33452e12			−0.216798
$853$	−8.93050e12	−	1.06430e13i	−0.577570	−	0.688322i	0.395596	−	0.918425i	$-0.370538\pi$
$853$	−8.93050e12	−	1.06430e13i	−0.577570	−	0.688322i	−0.973166	+	0.230103i	$0.926094\pi$
$854$	−1.97830e12	−	1.65999e12i	−0.127272	−	0.106794i
$855$	−1.98611e11	+	1.12638e12i	−0.0127103	+	0.0720837i
$856$	2.25335e12	+	6.19103e12i	0.143449	+	0.394122i
$857$			1.31509e13i			0.832805i	0.909180	+	0.416403i	$0.136709\pi$
$857$			1.31509e13i			0.832805i	−0.909180	+	0.416403i	$0.863291\pi$
$858$	−4.34761e13	+	1.58240e13i	−2.73878	+	0.996835i
$859$	7.62907e11	−	4.40464e11i	0.0478082	−	0.0276021i	−0.475905	−	0.879496i	$-0.657880\pi$
$859$	7.62907e11	−	4.40464e11i	0.0478082	−	0.0276021i	0.523714	+	0.851894i	$0.324546\pi$
$860$	4.43783e11	+	2.51682e12i	0.0276648	+	0.156895i
$861$	1.00006e12	−	1.73215e12i	0.0620169	−	0.107416i
$862$	−7.52558e12	−	1.30347e13i	−0.464256	−	0.804114i
$863$	2.80533e12	−	2.35395e12i	0.172161	−	0.144460i	−0.552636	−	0.833423i	$-0.686378\pi$
$863$	2.80533e12	−	2.35395e12i	0.172161	−	0.144460i	0.724797	+	0.688963i	$0.241934\pi$
$864$	9.86435e11	+	1.73935e11i	0.0602222	+	0.0106188i
$865$	−8.93490e12	−	5.15857e12i	−0.542647	−	0.313297i
$866$	5.92835e12	−	1.62880e13i	0.358182	−	0.984096i
$867$	−7.98519e12	−	2.90637e12i	−0.479953	−	0.174689i
$868$	2.59611e12	−	4.57765e11i	0.155233	−	0.0273718i
$869$	−2.76353e13	+	3.29345e13i	−1.64390	+	1.95913i
$870$	7.22423e12	−	8.60950e12i	0.427518	−	0.509496i
$871$	−2.36681e13	+	4.17333e12i	−1.39342	+	0.245698i
$872$	−1.30242e13	−	4.74041e12i	−0.762827	−	0.277646i
$873$	1.05723e13	−	2.90472e13i	0.616036	−	1.69254i
$874$	1.24236e12	+	7.17276e11i	0.0720187	+	0.0415800i
$875$	−5.80044e12	−	1.02277e12i	−0.334522	−	0.0589853i
$876$	1.63564e12	−	1.37247e12i	0.0938468	−	0.0787468i
$877$	−1.74997e10	−	3.03104e10i	−0.000998925	−	0.00173019i	0.865526	−	0.500865i	$-0.166985\pi$
$877$	−1.74997e10	−	3.03104e10i	−0.000998925	−	0.00173019i	−0.866524	+	0.499135i	$0.833651\pi$
$878$	2.66521e12	−	4.61628e12i	0.151358	−	0.262160i
$879$	7.89785e12	+	4.47910e13i	0.446230	+	2.53070i
$880$	1.40226e13	−	8.09594e12i	0.788235	−	0.455088i
$881$	−1.05981e13	+	3.85738e12i	−0.592700	+	0.215725i	−0.620917	−	0.783877i	$-0.713239\pi$
$881$	−1.05981e13	+	3.85738e12i	−0.592700	+	0.215725i	0.0282165	+	0.999602i	$0.491017\pi$
$882$		−	1.47809e13i		−	0.822417i
$883$	−9.84171e12	−	2.70399e13i	−0.544813	−	1.49686i	−0.840626	−	0.541616i	$-0.817813\pi$
$883$	−9.84171e12	−	2.70399e13i	−0.544813	−	1.49686i	0.295813	−	0.955246i	$-0.404410\pi$
$884$	−9.63656e11	+	5.46517e12i	−0.0530746	+	0.301001i
$885$	−1.94171e13	−	1.62929e13i	−1.06400	−	0.892799i
$886$	−1.91058e13	−	2.27694e13i	−1.04163	−	1.24136i
$887$	1.84524e13			1.00091			0.500457	−	0.865762i	$-0.333166\pi$
$887$	1.84524e13			1.00091			0.500457	+	0.865762i	$0.333166\pi$
$888$	−3.78886e12	−	2.87673e13i	−0.204480	−	1.55253i
$889$	7.16970e12			0.384984
$890$	−8.60545e12	−	1.02556e13i	−0.459746	−	0.547904i
$891$	2.36192e13	+	1.98188e13i	1.25550	+	1.05349i
$892$	−1.02539e11	+	5.81530e11i	−0.00542311	+	0.0307560i
$893$	−5.77798e11	−	1.58749e12i	−0.0304050	−	0.0835370i
$894$		−	6.39286e12i		−	0.334716i
$895$	−6.64720e12	+	2.41938e12i	−0.346286	+	0.126038i
$896$	1.98461e12	−	1.14582e12i	0.102870	−	0.0593922i
$897$	−7.53249e12	−	4.27189e13i	−0.388483	−	2.20320i
$898$	−3.41994e12	+	5.92351e12i	−0.175499	+	0.303974i
$899$	1.18213e13	+	2.04751e13i	0.603596	+	1.04546i
$900$	1.64633e12	−	1.38144e12i	0.0836424	−	0.0701843i
$901$	9.31060e12	+	1.64171e12i	0.470669	+	0.0829917i
$902$	7.17750e12	+	4.14393e12i	0.361030	+	0.208441i
$903$	2.14642e12	−	5.89724e12i	0.107429	−	0.295158i
$904$	−2.86275e13	−	1.04196e13i	−1.42569	−	0.518909i
$905$	6.63490e12	−	1.16991e12i	0.328788	−	0.0579742i
$906$	−1.76383e13	+	2.10205e13i	−0.869718	+	1.03649i
$907$	−7.99843e12	+	9.53216e12i	−0.392439	+	0.467690i	−0.925699	−	0.378261i	$-0.876522\pi$
$907$	−7.99843e12	+	9.53216e12i	−0.392439	+	0.467690i	0.533260	+	0.845951i	$0.320967\pi$
$908$	−2.55519e12	+	4.50549e11i	−0.124749	+	0.0219966i
$909$	−2.48550e13	−	9.04647e12i	−1.20747	−	0.439482i
$910$	2.00449e12	−	5.50729e12i	0.0968987	−	0.266227i
$911$	−2.29850e11	−	1.32704e11i	−0.0110564	−	0.00638339i	0.494462	−	0.869199i	$-0.335365\pi$
$911$	−2.29850e11	−	1.32704e11i	−0.0110564	−	0.00638339i	−0.505518	+	0.862816i	$0.668699\pi$
$912$	−1.59397e12	−	2.81060e11i	−0.0762962	−	0.0134531i
$913$	−6.88334e12	+	5.77581e12i	−0.327854	+	0.275102i
$914$	1.50347e13	+	2.60409e13i	0.712586	+	1.23424i
$915$	−7.71260e12	+	1.33586e13i	−0.363752	+	0.630038i
$916$	−5.30676e11	−	3.00962e12i	−0.0249058	−	0.141248i
$917$	−6.06547e11	+	3.50190e11i	−0.0283271	+	0.0163547i
$918$	1.52900e12	−	5.56509e11i	0.0710582	−	0.0258631i
$919$		−	3.03096e13i		−	1.40172i	−0.713299	−	0.700859i	$-0.752800\pi$
$919$		−	3.03096e13i		−	1.40172i	0.713299	−	0.700859i	$-0.247200\pi$
$920$	7.51921e12	+	2.06589e13i	0.346041	+	0.950739i
$921$	7.53195e12	−	4.27158e13i	0.344937	−	1.95623i
$922$	8.41192e12	+	7.05844e12i	0.383359	+	0.321677i
$923$	−1.00243e13	−	1.19465e13i	−0.454617	−	0.541791i
$924$	5.06860e12			0.228751
$925$	−6.69231e12	−	4.26297e12i	−0.300565	−	0.191458i
$926$	1.84793e13			0.825916
$927$	1.38059e12	+	1.64532e12i	0.0614052	+	0.0731799i
$928$	−6.46863e12	−	5.42782e12i	−0.286316	−	0.240248i
$929$	7.01770e12	−	3.97994e13i	0.309118	−	1.75309i	−0.294341	−	0.955701i	$-0.595100\pi$
$929$	7.01770e12	−	3.97994e13i	0.309118	−	1.75309i	0.603459	−	0.797394i	$-0.293789\pi$
$930$	1.35481e13	+	3.72232e13i	0.593890	+	1.63170i
$931$		−	1.75235e12i		−	0.0764445i
$932$	−1.54542e12	+	5.62486e11i	−0.0670925	+	0.0244197i
$933$	1.79015e13	−	1.03354e13i	0.773432	−	0.446541i
$934$	4.06280e12	+	2.30413e13i	0.174689	+	0.990708i
$935$	−1.34646e13	+	2.33214e13i	−0.576157	+	0.997933i
$936$	1.83775e13	+	3.18308e13i	0.782610	+	1.35552i
$937$	5.56105e12	−	4.66628e12i	0.235683	−	0.197762i	−0.517295	−	0.855807i	$-0.673061\pi$
$937$	5.56105e12	−	4.66628e12i	0.235683	−	0.197762i	0.752978	+	0.658045i	$0.228617\pi$
$938$	−6.52306e12	−	1.15019e12i	−0.275130	−	0.0485129i
$939$	3.54889e13	+	2.04895e13i	1.48969	+	0.860076i
$940$	1.96089e12	−	5.38750e12i	0.0819177	−	0.225067i
$941$	8.09568e12	+	2.94659e12i	0.336589	+	0.122508i	0.504785	−	0.863245i	$-0.331572\pi$
$941$	8.09568e12	+	2.94659e12i	0.336589	+	0.122508i	−0.168196	+	0.985754i	$0.553794\pi$
$942$	−5.50233e12	+	9.70209e11i	−0.227676	+	0.0401455i
$943$	−4.99475e12	+	5.95251e12i	−0.205689	+	0.245131i
$944$	1.19567e13	−	1.42494e13i	0.490046	−	0.584014i
$945$	6.72680e11	−	1.18612e11i	0.0274388	−	0.00483821i
$946$	2.44364e13	+	8.89412e12i	0.992034	+	0.361071i
$947$	5.98488e12	−	1.64433e13i	0.241813	−	0.664377i	−0.758111	−	0.652125i	$-0.773878\pi$
$947$	5.98488e12	−	1.64433e13i	0.241813	−	0.664377i	0.999925	−	0.0122521i	$-0.00390005\pi$
$948$	1.26309e13	+	7.29248e12i	0.507923	+	0.293250i
$949$	9.83415e12	+	1.73403e12i	0.393585	+	0.0693997i
$950$	−4.91022e11	+	4.12016e11i	−0.0195589	+	0.0164119i
$951$	2.04665e12	+	3.54490e12i	0.0811393	+	0.140537i
$952$	−3.45332e12	+	5.98133e12i	−0.136261	+	0.236010i
$953$	9.94219e11	+	5.63850e12i	0.0390449	+	0.221435i	0.998087	−	0.0618300i	$-0.0196937\pi$
$953$	9.94219e11	+	5.63850e12i	0.0390449	+	0.221435i	−0.959042	+	0.283265i	$0.908583\pi$
$954$	1.20086e13	−	6.93319e12i	0.469382	−	0.270998i
$955$	2.27703e13	−	8.28772e12i	0.885838	−	0.322419i
$956$			1.63889e12i			0.0634584i
$957$	1.55476e13	+	4.27166e13i	0.599182	+	1.64624i
$958$	−5.03679e12	+	2.85651e13i	−0.193201	+	1.09570i
$959$	−1.02294e13	−	8.58346e12i	−0.390539	−	0.327702i
$960$	−2.15074e13	−	2.56315e13i	−0.817273	−	0.973988i
$961$	−5.68899e13			−2.15169
$962$	2.03009e13	−	2.21569e13i	0.764235	−	0.834107i
$963$	−1.10974e13			−0.415817
$964$	−6.95982e12	−	8.29439e12i	−0.259568	−	0.309341i
$965$	−2.63981e13	−	2.21506e13i	−0.979940	−	0.822268i
$966$	2.07599e12	−	1.17735e13i	0.0767058	−	0.435020i
$967$	1.85563e12	+	5.09831e12i	0.0682453	+	0.187502i	0.969127	−	0.246563i	$-0.0793011\pi$
$967$	1.85563e12	+	5.09831e12i	0.0682453	+	0.187502i	−0.900882	+	0.434065i	$0.857079\pi$
$968$			6.51618e13i			2.38536i
$969$	2.52953e12	−	9.20674e11i	0.0921686	−	0.0335466i
$970$	−2.70962e13	+	1.56440e13i	−0.982733	+	0.567381i
$971$	−7.03407e12	−	3.98922e13i	−0.253934	−	1.44013i	−0.798795	−	0.601603i	$-0.794529\pi$
$971$	−7.03407e12	−	3.98922e13i	−0.253934	−	1.44013i	0.544861	−	0.838526i	$-0.316582\pi$
$972$	5.67016e12	−	9.82101e12i	0.203750	−	0.352905i
$973$	−2.44125e12	−	4.22838e12i	−0.0873183	−	0.151240i
$974$	−3.48832e13	+	2.92705e13i	−1.24194	+	1.04211i
$975$	1.90876e13	+	3.36565e12i	0.676440	+	0.119275i
$976$	−9.80332e12	−	5.65995e12i	−0.345819	−	0.199659i
$977$	−1.28331e13	+	3.52588e13i	−0.450617	+	1.23806i	0.481674	+	0.876350i	$0.340029\pi$
$977$	−1.28331e13	+	3.52588e13i	−0.450617	+	1.23806i	−0.932291	+	0.361709i	$0.882193\pi$
$978$	−2.36614e13	−	8.61203e12i	−0.827017	−	0.301010i
$979$	5.33266e13	−	9.40292e12i	1.85533	−	0.327145i
$980$	3.82264e12	−	4.55565e12i	0.132387	−	0.157773i
$981$	1.50064e13	−	1.78839e13i	0.517326	−	0.616526i
$982$	4.22696e13	−	7.45327e12i	1.45053	−	0.255768i
$983$	7.96643e12	+	2.89954e12i	0.272128	+	0.0990464i	0.474480	−	0.880266i	$-0.342636\pi$
$983$	7.96643e12	+	2.89954e12i	0.272128	+	0.0990464i	−0.202352	+	0.979313i	$0.564858\pi$
$984$	4.34240e12	−	1.19306e13i	0.147656	−	0.405682i
$985$	3.61728e13	+	2.08844e13i	1.22439	+	0.706900i
$986$	−1.35087e13	−	2.38195e12i	−0.455163	−	0.0802576i
$987$	−1.07849e13	+	9.04964e12i	−0.361735	+	0.303532i
$988$	4.82478e11	+	8.35677e11i	0.0161091	+	0.0279018i
$989$	−1.21906e13	+	2.11147e13i	−0.405174	+	0.701782i
$990$	6.85852e12	+	3.88966e13i	0.226920	+	1.28692i
$991$	−1.09187e13	+	6.30394e12i	−0.359618	+	0.207626i	−0.668913	−	0.743341i	$-0.733240\pi$
$991$	−1.09187e13	+	6.30394e12i	−0.359618	+	0.207626i	0.309295	+	0.950966i	$0.399907\pi$
$992$	2.79671e13	−	1.01792e13i	0.916950	−	0.333742i
$993$		−	1.24188e13i		−	0.405328i
$994$	−1.47002e12	−	4.03886e12i	−0.0477623	−	0.131226i
$995$	6.00633e12	−	3.40636e13i	0.194270	−	1.10176i
$996$	2.33511e12	+	1.95939e12i	0.0751866	+	0.0630890i
$997$	−5.65170e12	−	6.73544e12i	−0.181155	−	0.215893i	0.667823	−	0.744320i	$-0.267226\pi$
$997$	−5.65170e12	−	6.73544e12i	−0.181155	−	0.215893i	−0.848978	+	0.528428i	$0.822782\pi$
$998$	9.73684e12			0.310692
$999$	3.41939e12	+	7.57867e11i	0.108619	+	0.0240740i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.10.h.a.25.20	yes	168
37.3	even	18	inner	37.10.h.a.3.20	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.h.a.3.20	✓	168	37.3	even	18	inner
37.10.h.a.25.20	yes	168	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	37.h (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(12.3034 + 14.6627i) q^{2} +(154.895 + 129.973i) q^{3} +(25.2886 - 143.419i) q^{4} +(-383.475 - 1053.59i) q^{5} +3870.29i q^{6} +(1863.39 - 678.219i) q^{7} +(10901.1 - 6293.78i) q^{8} +(3681.76 + 20880.3i) q^{9} +O(q^{10})\)	\(q+(12.3034 + 14.6627i) q^{2} +(154.895 + 129.973i) q^{3} +(25.2886 - 143.419i) q^{4} +(-383.475 - 1053.59i) q^{5} +3870.29i q^{6} +(1863.39 - 678.219i) q^{7} +(10901.1 - 6293.78i) q^{8} +(3681.76 + 20880.3i) q^{9} +(10730.4 - 18585.5i) q^{10} +(43401.1 + 75172.9i) q^{11} +(22557.6 - 18928.1i) q^{12} +(135626. + 23914.5i) q^{13} +(32870.6 + 18977.9i) q^{14} +(77539.1 - 213037. i) q^{15} +(156339. + 56902.7i) q^{16} +(-272495. + 48048.2i) q^{17} +(-260862. + 310884. i) q^{18} +(-30926.5 + 36856.7i) q^{19} +(-160802. + 28353.7i) q^{20} +(376780. + 137137. i) q^{21} +(-568253. + 1.56126e6i) q^{22} +(-1.34904e6 - 778868. i) q^{23} +(2.50655e6 + 441973. i) q^{24} +(533186. - 447396. i) q^{25} +(1.31801e6 + 2.28286e6i) q^{26} +(-153612. + 266063. i) q^{27} +(-50146.8 - 284396. i) q^{28} +(2.24298e6 - 1.29499e6i) q^{29} +(4.07769e6 - 1.48416e6i) q^{30} +9.12850e6i q^{31} +(-1.11510e6 - 3.06372e6i) q^{32} +(-3.04779e6 + 1.72849e7i) q^{33} +(-4.05714e6 - 3.40435e6i) q^{34} +(-1.42913e6 - 1.70317e6i) q^{35} +3.08773e6 q^{36} +(-3.42866e6 - 1.08723e7i) q^{37} -920921. q^{38} +(1.78995e7 + 2.13318e7i) q^{39} +(-1.08114e7 - 9.07181e6i) q^{40} +(866208. - 4.91251e6i) q^{41} +(2.62490e6 + 7.21186e6i) q^{42} -1.56517e7i q^{43} +(1.18788e7 - 4.32352e6i) q^{44} +(2.05874e7 - 1.18861e7i) q^{45} +(-5.17754e6 - 2.93633e7i) q^{46} +(-1.75562e7 + 3.04083e7i) q^{47} +(1.68204e7 + 2.91337e7i) q^{48} +(-2.79004e7 + 2.34112e7i) q^{49} +(1.31200e7 + 2.31342e6i) q^{50} +(-4.84531e7 - 2.79744e7i) q^{51} +(6.85956e6 - 1.88465e7i) q^{52} +(-3.21074e7 - 1.16861e7i) q^{53} +(-5.79115e6 + 1.02114e6i) q^{54} +(6.25581e7 - 7.45538e7i) q^{55} +(1.60445e7 - 1.91211e7i) q^{56} +(-9.58073e6 + 1.68934e6i) q^{57} +(4.65844e7 + 1.69553e7i) q^{58} +(3.82396e7 - 1.05063e8i) q^{59} +(-2.85926e7 - 1.65080e7i) q^{60} +(-6.70059e7 - 1.18149e7i) q^{61} +(-1.33848e8 + 1.12312e8i) q^{62} +(2.10219e7 + 3.64111e7i) q^{63} +(7.37940e7 - 1.27815e8i) q^{64} +(-2.68130e7 - 1.52064e8i) q^{65} +(-2.90941e8 + 1.67975e8i) q^{66} +(-1.63987e8 + 5.96862e7i) q^{67} +4.02960e7i q^{68} +(-1.07728e8 - 2.95981e8i) q^{69} +(7.38980e6 - 4.19096e7i) q^{70} +(-8.67460e7 - 7.27885e7i) q^{71} +(1.71551e8 + 2.04447e8i) q^{72} +7.25095e7 q^{73} +(1.17232e8 - 1.84040e8i) q^{74} +1.40737e8 q^{75} +(4.50386e6 + 5.36749e6i) q^{76} +(1.31857e8 + 1.10641e8i) q^{77} +(-9.25558e7 + 5.24910e8i) q^{78} +(1.69402e8 + 4.65428e8i) q^{79} -1.86537e8i q^{80} +(3.33784e8 - 1.21488e8i) q^{81} +(8.26879e7 - 4.77399e7i) q^{82} +(1.79757e7 + 1.01945e8i) q^{83} +(2.91962e7 - 5.05693e7i) q^{84} +(1.55118e8 + 2.68672e8i) q^{85} +(2.29495e8 - 1.92570e8i) q^{86} +(5.15740e8 + 9.09389e7i) q^{87} +(9.46244e8 + 5.46314e8i) q^{88} +(2.13360e8 - 5.86202e8i) q^{89} +(4.27578e8 + 1.55626e8i) q^{90} +(2.68943e8 - 4.74218e7i) q^{91} +(-1.45820e8 + 1.73781e8i) q^{92} +(-1.18645e9 + 1.41396e9i) q^{93} +(-6.61869e8 + 1.16705e8i) q^{94} +(5.06914e7 + 1.84501e7i) q^{95} +(2.25475e8 - 6.19488e8i) q^{96} +(-1.26259e9 - 7.28959e8i) q^{97} +(-6.86542e8 - 1.21056e8i) q^{98} +(-1.40984e9 + 1.18300e9i) 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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