LMFDB - Embedded newform 32.9.h.a.11.1

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			11.1
Character	$\chi$	$=$	32.11
Dual form			32.9.h.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15.8385 + 2.26783i) q^{2} +(4.27937 + 10.3313i) q^{3} +(245.714 - 71.8380i) q^{4} +(-201.753 + 487.075i) q^{5} +(-91.2084 - 153.927i) q^{6} +(901.611 - 901.611i) q^{7} +(-3728.81 + 1695.04i) q^{8} +(4550.90 - 4550.90i) q^{9} +O(q^{10})$	\(q+(-15.8385 + 2.26783i) q^{2} +(4.27937 + 10.3313i) q^{3} +(245.714 - 71.8380i) q^{4} +(-201.753 + 487.075i) q^{5} +(-91.2084 - 153.927i) q^{6} +(901.611 - 901.611i) q^{7} +(-3728.81 + 1695.04i) q^{8} +(4550.90 - 4550.90i) q^{9} +(2090.85 - 8172.06i) q^{10} +(1314.04 - 3172.37i) q^{11} +(1793.68 + 2231.13i) q^{12} +(1717.89 + 4147.36i) q^{13} +(-12235.4 + 16324.8i) q^{14} -5895.50 q^{15} +(55214.6 - 35303.2i) q^{16} +163335. i q^{17} +(-61758.6 + 82400.0i) q^{18} +(-169580. + 70242.4i) q^{19} +(-14583.0 + 134175. i) q^{20} +(13173.2 + 5456.50i) q^{21} +(-13617.9 + 53225.4i) q^{22} +(260249. + 260249. i) q^{23} +(-33469.0 - 31269.8i) q^{24} +(79675.7 + 79675.7i) q^{25} +(-36614.3 - 61791.9i) q^{26} +(134276. + 55618.8i) q^{27} +(156768. - 286308. i) q^{28} +(-585227. + 242409. i) q^{29} +(93375.7 - 13370.0i) q^{30} +480883. i q^{31} +(-794453. + 684366. i) q^{32} +38398.0 q^{33} +(-370416. - 2.58697e6i) q^{34} +(257249. + 621055. i) q^{35} +(791292. - 1.44515e6i) q^{36} +(502664. - 1.21354e6i) q^{37} +(2.52659e6 - 1.49711e6i) q^{38} +(-35496.2 + 35496.2i) q^{39} +(-73312.9 - 2.15819e6i) q^{40} +(-1.62510e6 + 1.62510e6i) q^{41} +(-221017. - 56548.1i) q^{42} +(70859.8 - 171071. i) q^{43} +(94980.7 - 873892. i) q^{44} +(1.29847e6 + 3.13479e6i) q^{45} +(-4.71215e6 - 3.53175e6i) q^{46} +3.09684e6 q^{47} +(601012. + 419364. i) q^{48} +4.13900e6i q^{49} +(-1.44263e6 - 1.08125e6i) q^{50} +(-1.68746e6 + 698971. i) q^{51} +(720048. + 895654. i) q^{52} +(-3.86788e6 - 1.60213e6i) q^{53} +(-2.25285e6 - 576401. i) q^{54} +(1.28007e6 + 1.28007e6i) q^{55} +(-1.83367e6 + 4.89021e6i) q^{56} +(-1.45139e6 - 1.45139e6i) q^{57} +(8.71936e6 - 5.16658e6i) q^{58} +(1.68932e7 + 6.99740e6i) q^{59} +(-1.44861e6 + 423521. i) q^{60} +(-1.47937e7 + 6.12773e6i) q^{61} +(-1.09056e6 - 7.61645e6i) q^{62} -8.20629e6i q^{63} +(1.10309e7 - 1.26410e7i) q^{64} -2.36667e6 q^{65} +(-608165. + 87080.2i) q^{66} +(-3.17251e6 - 7.65912e6i) q^{67} +(1.17336e7 + 4.01336e7i) q^{68} +(-1.57501e6 + 3.80242e6i) q^{69} +(-5.48289e6 - 9.25316e6i) q^{70} +(-3.40968e6 + 3.40968e6i) q^{71} +(-9.25550e6 + 2.46834e7i) q^{72} +(-1.11596e7 + 1.11596e7i) q^{73} +(-5.20932e6 + 2.03605e7i) q^{74} +(-482193. + 1.16412e6i) q^{75} +(-3.66221e7 + 2.94418e7i) q^{76} +(-1.67549e6 - 4.04499e6i) q^{77} +(481706. - 642704. i) q^{78} +4.91184e7 q^{79} +(6.05559e6 + 3.40162e7i) q^{80} -4.06010e7i q^{81} +(2.20537e7 - 2.94246e7i) q^{82} +(5.61076e7 - 2.32405e7i) q^{83} +(3.62881e6 + 394405. i) q^{84} +(-7.95563e7 - 3.29533e7i) q^{85} +(-734350. + 2.87019e6i) q^{86} +(-5.00881e6 - 5.00881e6i) q^{87} +(477494. + 1.40565e7i) q^{88} +(-1.78414e7 - 1.78414e7i) q^{89} +(-2.76750e7 - 4.67056e7i) q^{90} +(5.28817e6 + 2.19043e6i) q^{91} +(8.26426e7 + 4.52511e7i) q^{92} +(-4.96815e6 + 2.05788e6i) q^{93} +(-4.90492e7 + 7.02312e6i) q^{94} -9.67699e7i q^{95} +(-1.04702e7 - 5.27909e6i) q^{96} -7.01094e6 q^{97} +(-9.38655e6 - 6.55553e7i) q^{98} +(-8.45708e6 - 2.04172e7i) 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 $

$2$	−15.8385	+	2.26783i	−0.989904	+	0.141740i
$2$	−15.8385	+	2.26783i	−0.989904	+	0.141740i
$3$	4.27937	+	10.3313i	0.0528318	+	0.127547i	0.948092	−	0.317997i	$-0.103010\pi$
$3$	4.27937	+	10.3313i	0.0528318	+	0.127547i	−0.895260	+	0.445544i	$0.853010\pi$
$4$	245.714	−	71.8380i	0.959820	−	0.280617i
$5$	−201.753	+	487.075i	−0.322805	+	0.779320i	0.676284	+	0.736641i	$0.263589\pi$
$5$	−201.753	+	487.075i	−0.322805	+	0.779320i	−0.999089	+	0.0426791i	$0.986411\pi$
$6$	−91.2084	−	153.927i	−0.0703768	−	0.118771i
$7$	901.611	−	901.611i	0.375515	−	0.375515i	−0.493966	−	0.869481i	$-0.664453\pi$
$7$	901.611	−	901.611i	0.375515	−	0.375515i	0.869481	+	0.493966i	$0.164453\pi$
$8$	−3728.81	+	1695.04i	−0.910355	+	0.413829i
$9$	4550.90	−	4550.90i	0.693630	−	0.693630i
$10$	2090.85	−	8172.06i	0.209085	−	0.817206i
$11$	1314.04	−	3172.37i	0.0897505	−	0.216677i	−0.872630	−	0.488382i	$-0.837587\pi$
$11$	1314.04	−	3172.37i	0.0897505	−	0.216677i	0.962381	+	0.271705i	$0.0875874\pi$
$12$	1793.68	+	2231.13i	0.0865009	+	0.107597i
$13$	1717.89	+	4147.36i	0.0601482	+	0.145211i	0.951096	−	0.308895i	$-0.0999590\pi$
$13$	1717.89	+	4147.36i	0.0601482	+	0.145211i	−0.890948	+	0.454105i	$0.849959\pi$
$14$	−12235.4	+	16324.8i	−0.318498	+	0.424949i
$15$	−5895.50			−0.116454
$16$	55214.6	−	35303.2i	0.842508	−	0.538684i
$17$			163335.i			1.95561i	0.209508	+	0.977807i	$0.432814\pi$
$17$			163335.i			1.95561i	−0.209508	+	0.977807i	$0.567186\pi$
$18$	−61758.6	+	82400.0i	−0.588312	+	0.784942i
$19$	−169580.	+	70242.4i	−1.30125	+	0.538995i	−0.922319	−	0.386430i	$-0.873708\pi$
$19$	−169580.	+	70242.4i	−1.30125	+	0.538995i	−0.378931	+	0.925425i	$0.623708\pi$
$20$	−14583.0	+	134175.i	−0.0911440	+	0.838592i
$21$	13173.2	+	5456.50i	0.0677349	+	0.0280567i
$22$	−13617.9	+	53225.4i	−0.0581327	+	0.227211i
$23$	260249.	+	260249.i	0.929990	+	0.929990i	0.997705	−	0.0677150i	$-0.0215709\pi$
$23$	260249.	+	260249.i	0.929990	+	0.929990i	−0.0677150	+	0.997705i	$0.521571\pi$
$24$	−33469.0	−	31269.8i	−0.100878	−	0.0942499i
$25$	79675.7	+	79675.7i	0.203970	+	0.203970i
$26$	−36614.3	−	61791.9i	−0.0801230	−	0.135219i
$27$	134276.	+	55618.8i	0.252663	+	0.104657i
$28$	156768.	−	286308.i	0.255051	−	0.465802i
$29$	−585227.	+	242409.i	−0.827432	+	0.342734i	−0.755886	−	0.654704i	$-0.772793\pi$
$29$	−585227.	+	242409.i	−0.827432	+	0.342734i	−0.0715466	+	0.997437i	$0.522793\pi$
$30$	93375.7	−	13370.0i	0.115279	−	0.0165062i
$31$			480883.i			0.520706i	0.965514	+	0.260353i	$0.0838389\pi$
$31$			480883.i			0.520706i	−0.965514	+	0.260353i	$0.916161\pi$
$32$	−794453.	+	684366.i	−0.757649	+	0.652662i
$33$	38398.0			0.0323782
$34$	−370416.	−	2.58697e6i	−0.277188	−	1.93587i
$35$	257249.	+	621055.i	0.171428	+	0.413864i
$36$	791292.	−	1.44515e6i	0.471115	−	0.860404i
$37$	502664.	−	1.21354e6i	0.268207	−	0.647510i	−0.731192	−	0.682172i	$-0.761036\pi$
$37$	502664.	−	1.21354e6i	0.268207	−	0.647510i	0.999399	+	0.0346621i	$0.0110355\pi$
$38$	2.52659e6	−	1.49711e6i	1.21171	−	0.717992i
$39$	−35496.2	+	35496.2i	−0.0153435	+	0.0153435i
$40$	−73312.9	−	2.15819e6i	−0.0286379	−	0.843044i
$41$	−1.62510e6	+	1.62510e6i	−0.575103	+	0.575103i	−0.933550	−	0.358447i	$-0.883306\pi$
$41$	−1.62510e6	+	1.62510e6i	−0.575103	+	0.575103i	0.358447	+	0.933550i	$0.383306\pi$
$42$	−221017.	−	56548.1i	−0.0710278	−	0.0181727i
$43$	70859.8	−	171071.i	0.0207265	−	0.0500382i	−0.913177	−	0.407562i	$-0.866379\pi$
$43$	70859.8	−	171071.i	0.0207265	−	0.0500382i	0.933904	+	0.357524i	$0.116379\pi$
$44$	94980.7	−	873892.i	0.0253410	−	0.233156i
$45$	1.29847e6	+	3.13479e6i	0.316653	+	0.764467i
$46$	−4.71215e6	−	3.53175e6i	−1.05242	−	0.788784i
$47$	3.09684e6			0.634640			0.317320	−	0.948319i	$-0.397217\pi$
$47$	3.09684e6			0.634640			0.317320	+	0.948319i	$0.397217\pi$
$48$	601012.	+	419364.i	0.113219	+	0.0789999i
$49$			4.13900e6i			0.717977i
$50$	−1.44263e6	−	1.08125e6i	−0.230821	−	0.173000i
$51$	−1.68746e6	+	698971.i	−0.249433	+	0.103319i
$52$	720048.	+	895654.i	0.0984800	+	0.122497i
$53$	−3.86788e6	−	1.60213e6i	−0.490195	−	0.203046i	0.123874	−	0.992298i	$-0.460468\pi$
$53$	−3.86788e6	−	1.60213e6i	−0.490195	−	0.203046i	−0.614069	+	0.789252i	$0.710468\pi$
$54$	−2.25285e6	−	576401.i	−0.264946	−	0.0677875i
$55$	1.28007e6	+	1.28007e6i	0.139889	+	0.139889i
$56$	−1.83367e6	+	4.89021e6i	−0.186453	+	0.497250i
$57$	−1.45139e6	−	1.45139e6i	−0.137495	−	0.137495i
$58$	8.71936e6	−	5.16658e6i	0.770500	−	0.456553i
$59$	1.68932e7	+	6.99740e6i	1.39413	+	0.577469i	0.948222	−	0.317609i	$-0.102880\pi$
$59$	1.68932e7	+	6.99740e6i	1.39413	+	0.577469i	0.445911	+	0.895077i	$0.352880\pi$
$60$	−1.44861e6	+	423521.i	−0.111775	+	0.0326791i
$61$	−1.47937e7	+	6.12773e6i	−1.06845	+	0.442568i	−0.846445	−	0.532476i	$-0.821262\pi$
$61$	−1.47937e7	+	6.12773e6i	−1.06845	+	0.442568i	−0.222010	+	0.975044i	$0.571262\pi$
$62$	−1.09056e6	−	7.61645e6i	−0.0738046	−	0.515449i
$63$		−	8.20629e6i		−	0.520936i
$64$	1.10309e7	−	1.26410e7i	0.657492	−	0.753462i
$65$	−2.36667e6			−0.132582
$66$	−608165.	+	87080.2i	−0.0320513	+	0.00458927i
$67$	−3.17251e6	−	7.65912e6i	−0.157436	−	0.380084i	0.825404	−	0.564542i	$-0.190947\pi$
$67$	−3.17251e6	−	7.65912e6i	−0.157436	−	0.380084i	−0.982840	+	0.184458i	$0.940947\pi$
$68$	1.17336e7	+	4.01336e7i	0.548779	+	1.87704i
$69$	−1.57501e6	+	3.80242e6i	−0.0694845	+	0.167750i
$70$	−5.48289e6	−	9.25316e6i	−0.228358	−	0.385388i
$71$	−3.40968e6	+	3.40968e6i	−0.134178	+	0.134178i	−0.771006	−	0.636828i	$-0.780246\pi$
$71$	−3.40968e6	+	3.40968e6i	−0.134178	+	0.134178i	0.636828	+	0.771006i	$0.280246\pi$
$72$	−9.25550e6	+	2.46834e7i	−0.344405	+	0.918493i
$73$	−1.11596e7	+	1.11596e7i	−0.392966	+	0.392966i	−0.875743	−	0.482777i	$-0.839628\pi$
$73$	−1.11596e7	+	1.11596e7i	−0.392966	+	0.392966i	0.482777	+	0.875743i	$0.339628\pi$
$74$	−5.20932e6	+	2.03605e7i	−0.173722	+	0.678988i
$75$	−482193.	+	1.16412e6i	−0.0152397	+	0.0367918i
$76$	−3.66221e7	+	2.94418e7i	−1.09771	+	0.882491i
$77$	−1.67549e6	−	4.04499e6i	−0.0476627	−	0.115068i
$78$	481706.	−	642704.i	0.0130138	−	0.0173633i
$79$	4.91184e7			1.26106			0.630530	−	0.776165i	$-0.282838\pi$
$79$	4.91184e7			1.26106			0.630530	+	0.776165i	$0.282838\pi$
$80$	6.05559e6	+	3.40162e7i	0.147841	+	0.830473i
$81$		−	4.06010e7i		−	0.943185i
$82$	2.20537e7	−	2.94246e7i	0.487782	−	0.650811i
$83$	5.61076e7	−	2.32405e7i	1.18225	−	0.489704i	0.297027	−	0.954869i	$-0.404005\pi$
$83$	5.61076e7	−	2.32405e7i	1.18225	−	0.489704i	0.885224	+	0.465165i	$0.154005\pi$
$84$	3.62881e6	+	394405.i	0.0728865	+	0.00792182i
$85$	−7.95563e7	−	3.29533e7i	−1.52405	−	0.631282i
$86$	−734350.	+	2.87019e6i	−0.0134248	+	0.0524708i
$87$	−5.00881e6	−	5.00881e6i	−0.0874294	−	0.0874294i
$88$	477494.	+	1.40565e7i	0.00796228	+	0.234394i
$89$	−1.78414e7	−	1.78414e7i	−0.284361	−	0.284361i	0.550485	−	0.834845i	$-0.314443\pi$
$89$	−1.78414e7	−	1.78414e7i	−0.284361	−	0.284361i	−0.834845	+	0.550485i	$0.814443\pi$
$90$	−2.76750e7	−	4.67056e7i	−0.421811	−	0.711867i
$91$	5.28817e6	+	2.19043e6i	0.0771152	+	0.0319422i
$92$	8.26426e7	+	4.52511e7i	1.15359	+	0.631651i
$93$	−4.96815e6	+	2.05788e6i	−0.0664145	+	0.0275098i
$94$	−4.90492e7	+	7.02312e6i	−0.628232	+	0.0899536i
$95$		−	9.67699e7i		−	1.18808i
$96$	−1.04702e7	−	5.27909e6i	−0.123273	−	0.0621547i
$97$	−7.01094e6			−0.0791934			−0.0395967	−	0.999216i	$-0.512607\pi$
$97$	−7.01094e6			−0.0791934			−0.0395967	+	0.999216i	$0.512607\pi$
$98$	−9.38655e6	−	6.55553e7i	−0.101766	−	0.710729i
$99$	−8.45708e6	−	2.04172e7i	−0.0880399	−	0.212547i
$100$	2.53012e7	+	1.38537e7i	0.253012	+	0.138537i
$101$	6.61814e6	−	1.59776e7i	0.0635990	−	0.153542i	−0.888885	−	0.458131i	$-0.848519\pi$
$101$	6.61814e6	−	1.59776e7i	0.0635990	−	0.153542i	0.952484	+	0.304589i	$0.0985192\pi$
$102$	2.51417e7	−	1.48975e7i	0.232270	−	0.137630i
$103$	1.27876e8	−	1.27876e8i	1.13616	−	1.13616i	0.147033	−	0.989132i	$-0.453028\pi$
$103$	1.27876e8	−	1.27876e8i	1.13616	−	1.13616i	0.989132	−	0.147033i	$-0.0469722\pi$
$104$	−1.34356e7	−	1.25528e7i	−0.114848	−	0.107302i
$105$	−5.31545e6	+	5.31545e6i	−0.0437304	+	0.0437304i
$106$	6.48946e7	+	1.66035e7i	0.514026	+	0.131515i
$107$	−3.11288e7	+	7.51515e7i	−0.237480	+	0.573327i	−0.997021	−	0.0771323i	$-0.975424\pi$
$107$	−3.11288e7	+	7.51515e7i	−0.237480	+	0.573327i	0.759541	+	0.650459i	$0.225424\pi$
$108$	3.69889e7	+	4.02021e6i	0.271880	+	0.0295498i
$109$	−5.96749e7	−	1.44068e8i	−0.422752	−	1.02061i	−0.981532	−	0.191298i	$-0.938730\pi$
$109$	−5.96749e7	−	1.44068e8i	−0.422752	−	1.02061i	0.558780	−	0.829316i	$-0.311270\pi$
$110$	−2.31773e7	−	1.73714e7i	−0.158304	−	0.118649i
$111$	1.46885e7			0.0967579
$112$	1.79524e7	−	8.16118e7i	0.114090	−	0.518658i
$113$			2.70973e8i			1.66193i	0.556324	+	0.830965i	$0.312211\pi$
$113$			2.70973e8i			1.66193i	−0.556324	+	0.830965i	$0.687789\pi$
$114$	2.62793e7	+	1.96963e7i	0.155595	+	0.116618i
$115$	−1.79267e8	+	7.42548e7i	−1.02497	+	0.424554i
$116$	−1.26384e8	+	1.01605e8i	−0.698009	+	0.561154i
$117$	2.66922e7	+	1.10563e7i	0.142443	+	0.0590018i
$118$	−2.83431e8	−	7.25170e7i	−1.46191	−	0.374035i
$119$	1.47264e8	+	1.47264e8i	0.734362	+	0.734362i
$120$	2.19832e7	−	9.99313e6i	0.106015	−	0.0481922i
$121$	1.43237e8	+	1.43237e8i	0.668213	+	0.668213i
$122$	2.20412e8	−	1.30603e8i	0.994938	−	0.589543i
$123$	−2.37439e7	−	9.83503e6i	−0.103736	−	0.0429690i
$124$	3.45457e7	+	1.18160e8i	0.146119	+	0.499784i
$125$	−2.45147e8	+	1.01543e8i	−1.00412	+	0.415920i
$126$	1.86105e7	+	1.29975e8i	0.0738373	+	0.515677i
$127$		−	6.13521e6i		−	0.0235839i	−0.999930	−	0.0117919i	$-0.996246\pi$
$127$		−	6.13521e6i		−	0.0235839i	0.999930	−	0.0117919i	$-0.00375357\pi$
$128$	−1.46045e8	+	2.25230e8i	−0.544058	+	0.839047i
$129$	2.07062e6			0.00747725
$130$	3.74843e7	−	5.36720e6i	0.131243	−	0.0187921i
$131$	1.98612e8	+	4.79493e8i	0.674405	+	1.62816i	0.774041	+	0.633135i	$0.218232\pi$
$131$	1.98612e8	+	4.79493e8i	0.674405	+	1.62816i	−0.0996360	+	0.995024i	$0.531768\pi$
$132$	9.43492e6	−	2.75843e6i	0.0310772	−	0.00908588i
$133$	−8.95640e7	+	2.16227e8i	−0.286238	+	0.691039i
$134$	6.76173e7	+	1.14114e8i	0.209720	+	0.353932i
$135$	−5.41811e7	+	5.41811e7i	−0.163122	+	0.163122i
$136$	−2.76859e8	−	6.09045e8i	−0.809289	−	1.78030i
$137$	2.00035e8	−	2.00035e8i	0.567838	−	0.567838i	−0.363684	−	0.931522i	$-0.618481\pi$
$137$	2.00035e8	−	2.00035e8i	0.567838	−	0.567838i	0.931522	+	0.363684i	$0.118481\pi$
$138$	1.63225e7	−	6.37964e7i	0.0450061	−	0.175906i
$139$	−1.09539e8	+	2.64451e8i	−0.293434	+	0.708411i	0.706566	+	0.707647i	$0.250243\pi$
$139$	−1.09539e8	+	2.64451e8i	−0.293434	+	0.708411i	−1.00000		0.000764310i	$0.999757\pi$
$140$	1.07825e8	+	1.34122e8i	0.280678	+	0.349129i
$141$	1.32525e7	+	3.19944e7i	0.0335291	+	0.0809465i
$142$	4.62715e7	−	6.17367e7i	0.113805	−	0.151841i
$143$	1.54143e7			0.0368621
$144$	9.06150e7	−	4.11938e8i	0.210741	−	0.958036i
$145$		−	3.33956e8i		−	0.755471i
$146$	1.51442e8	−	2.02058e8i	0.333300	−	0.444698i
$147$	−4.27613e7	+	1.77123e7i	−0.0915759	+	0.0379320i
$148$	3.63333e7	−	3.34293e8i	0.0757283	−	0.696756i
$149$	−2.35725e8	−	9.76406e7i	−0.478257	−	0.198100i	0.130514	−	0.991446i	$-0.458337\pi$
$149$	−2.35725e8	−	9.76406e7i	−0.478257	−	0.198100i	−0.608771	+	0.793346i	$0.708337\pi$
$150$	4.99717e6	−	1.95314e7i	0.00987096	−	0.0385805i
$151$	−6.59287e8	−	6.59287e8i	−1.26814	−	1.26814i	−0.947049	−	0.321089i	$-0.895951\pi$
$151$	−6.59287e8	−	6.59287e8i	−1.26814	−	1.26814i	−0.321089	−	0.947049i	$-0.604049\pi$
$152$	5.13269e8	−	5.49366e8i	0.961547	−	1.02917i
$153$	7.43321e8	+	7.43321e8i	1.35647	+	1.35647i
$154$	3.57106e7	+	6.02667e7i	0.0634912	+	0.107151i
$155$	−2.34226e8	−	9.70196e7i	−0.405797	−	0.168086i
$156$	−6.17193e6	+	1.12719e7i	−0.0104213	+	0.0190326i
$157$	4.88222e8	−	2.02228e8i	0.803560	−	0.332846i	0.0571789	−	0.998364i	$-0.481789\pi$
$157$	4.88222e8	−	2.02228e8i	0.803560	−	0.332846i	0.746381	+	0.665518i	$0.231789\pi$
$158$	−7.77960e8	+	1.11392e8i	−1.24833	+	0.178742i
$159$		−	4.68164e7i		−	0.0732502i
$160$	−1.73054e8	−	5.25031e8i	−0.264060	−	0.801134i
$161$	4.69287e8			0.698450
$162$	9.20764e7	+	6.43058e8i	0.133687	+	0.933662i
$163$	−2.80480e8	−	6.77139e8i	−0.397330	−	0.959240i	−0.988297	−	0.152544i	$-0.951253\pi$
$163$	−2.80480e8	−	6.77139e8i	−0.397330	−	0.959240i	0.590966	−	0.806696i	$-0.298747\pi$
$164$	−2.82566e8	+	5.16054e8i	−0.390611	+	0.713379i
$165$	−7.74691e6	+	1.87027e7i	−0.0104518	+	0.0252330i
$166$	−8.35953e8	+	4.95337e8i	−1.10090	+	0.652332i
$167$	3.77784e8	−	3.77784e8i	0.485711	−	0.485711i	−0.421239	−	0.906950i	$-0.638405\pi$
$167$	3.77784e8	−	3.77784e8i	0.485711	−	0.485711i	0.906950	+	0.421239i	$0.138405\pi$
$168$	−5.83692e7	+	1.98278e6i	−0.0732735	+	0.00248907i
$169$	5.62559e8	−	5.62559e8i	0.689638	−	0.689638i
$170$	1.33478e9	+	3.41509e8i	1.59814	+	0.408890i
$171$	−4.52077e8	+	1.09141e9i	−0.528722	+	1.27645i
$172$	5.12186e6	−	4.71248e7i	0.00585213	−	0.0538439i
$173$	−4.51044e8	−	1.08892e9i	−0.503540	−	1.21565i	−0.947543	−	0.319628i	$-0.896442\pi$
$173$	−4.51044e8	−	1.08892e9i	−0.503540	−	1.21565i	0.444003	−	0.896025i	$-0.353558\pi$
$174$	9.06910e7	+	6.79727e7i	0.0989389	+	0.0741545i
$175$	1.43673e8			0.153187
$176$	−3.94406e7	−	2.21551e8i	−0.0411048	−	0.230899i
$177$			2.04474e8i			0.208326i
$178$	3.23042e8	+	2.42119e8i	0.321795	+	0.241184i
$179$	−1.33803e9	+	5.54232e8i	−1.30333	+	0.539858i	−0.922931	−	0.384964i	$-0.874214\pi$
$179$	−1.33803e9	+	5.54232e8i	−1.30333	+	0.539858i	−0.380400	+	0.924822i	$0.624214\pi$
$180$	5.44250e8	+	6.76982e8i	0.518452	+	0.644892i
$181$	−6.16378e8	−	2.55312e8i	−0.574292	−	0.237880i	0.0765846	−	0.997063i	$-0.475598\pi$
$181$	−6.16378e8	−	2.55312e8i	−0.574292	−	0.237880i	−0.650877	+	0.759184i	$0.725598\pi$
$182$	−8.87241e7	−	2.27004e7i	−0.0808642	−	0.0206894i
$183$	−1.26615e8	−	1.26615e8i	−0.112897	−	0.112897i
$184$	−1.41155e9	−	5.29288e8i	−1.23148	−	0.461764i
$185$	4.89670e8	+	4.89670e8i	0.418039	+	0.418039i
$186$	7.40210e7	−	4.38605e7i	0.0618448	−	0.0366456i
$187$	5.18158e8	+	2.14628e8i	0.423736	+	0.175517i
$188$	7.60936e8	−	2.22471e8i	0.609140	−	0.178091i
$189$	1.71211e8	−	7.09179e7i	0.134179	−	0.0555787i
$190$	2.19458e8	+	1.53269e9i	0.168398	+	1.17609i
$191$		−	2.41237e9i		−	1.81263i	−0.422599	−	0.906317i	$-0.638882\pi$
$191$		−	2.41237e9i		−	1.81263i	0.422599	−	0.906317i	$-0.361118\pi$
$192$	1.77803e8	+	5.98681e7i	0.130838	+	0.0440545i
$193$	6.88285e8			0.496066			0.248033	−	0.968752i	$-0.420216\pi$
$193$	6.88285e8			0.496066			0.248033	+	0.968752i	$0.420216\pi$
$194$	1.11042e8	−	1.58996e7i	0.0783939	−	0.0112248i
$195$	−1.01278e7	−	2.44508e7i	−0.00700452	−	0.0169104i
$196$	2.97337e8	+	1.01701e9i	0.201477	+	0.689129i
$197$	3.98567e8	−	9.62226e8i	0.264629	−	0.638870i	−0.734585	−	0.678516i	$-0.762623\pi$
$197$	3.98567e8	−	9.62226e8i	0.264629	−	0.638870i	0.999214	+	0.0396466i	$0.0126232\pi$
$198$	1.80250e8	+	3.04198e8i	0.117277	+	0.197923i
$199$	−1.05065e9	+	1.05065e9i	−0.669958	+	0.669958i	−0.957706	−	0.287748i	$-0.907093\pi$
$199$	−1.05065e9	+	1.05065e9i	−0.669958	+	0.669958i	0.287748	+	0.957706i	$0.407093\pi$
$200$	−4.32149e8	−	1.62042e8i	−0.270093	−	0.101276i
$201$	6.55525e7	−	6.55525e7i	0.0401610	−	0.0401610i
$202$	−6.85866e7	+	2.68069e8i	−0.0411940	+	0.161006i
$203$	−3.09089e8	+	7.46206e8i	−0.182011	+	0.439415i
$204$	−3.64421e8	+	2.92971e8i	−0.210418	+	0.169162i
$205$	−4.63678e8	−	1.11942e9i	−0.262543	−	0.633835i
$206$	−1.73536e9	+	2.31537e9i	−0.963654	+	1.28573i
$207$	2.36874e9			1.29014
$208$	2.41268e8	+	1.68348e8i	0.128898	+	0.0899402i
$209$			6.30271e8i			0.330326i
$210$	7.21340e7	−	9.62432e7i	0.0370905	−	0.0494872i
$211$	−4.99360e8	+	2.06842e8i	−0.251932	+	0.104354i	−0.505076	−	0.863075i	$-0.668536\pi$
$211$	−4.99360e8	+	2.06842e8i	−0.251932	+	0.104354i	0.253144	+	0.967429i	$0.418536\pi$
$212$	−1.06548e9	−	1.15804e8i	−0.527477	−	0.0573299i
$213$	−4.98178e7	−	2.06352e7i	−0.0242028	−	0.0100251i
$214$	3.22601e8	−	1.26088e9i	0.153819	−	0.601199i
$215$	6.90281e7	+	6.90281e7i	0.0323052	+	0.0323052i
$216$	−5.94965e8	+	2.02107e7i	−0.273323	+	0.00928468i
$217$	4.33569e8	+	4.33569e8i	0.195533	+	0.195533i
$218$	1.27188e9	+	2.14648e9i	0.563145	+	0.950389i
$219$	−1.63049e8	−	6.75370e7i	−0.0708829	−	0.0293606i
$220$	4.06489e8	+	2.22573e8i	0.173523	+	0.0950128i
$221$	−6.77408e8	+	2.80592e8i	−0.283976	+	0.117627i
$222$	−2.32644e8	+	3.33111e7i	−0.0957810	+	0.0137144i
$223$		−	2.08411e8i		−	0.0842753i	−0.999112	−	0.0421377i	$-0.986583\pi$
$223$		−	2.08411e8i		−	0.0842753i	0.999112	−	0.0421377i	$-0.0134168\pi$
$224$	−9.92556e7	+	1.33332e9i	−0.0394242	+	0.529593i
$225$	7.25193e8			0.282959
$226$	−6.14523e8	−	4.29180e9i	−0.235561	−	1.64515i
$227$	−7.00472e8	−	1.69109e9i	−0.263808	−	0.636888i	0.735360	−	0.677677i	$-0.237013\pi$
$227$	−7.00472e8	−	1.69109e9i	−0.263808	−	0.636888i	−0.999168	+	0.0407885i	$0.987013\pi$
$228$	−4.60892e8	−	2.52362e8i	−0.170553	−	0.0933867i
$229$	−1.45908e9	+	3.52254e9i	−0.530565	+	1.28090i	0.400585	+	0.916260i	$0.368807\pi$
$229$	−1.45908e9	+	3.52254e9i	−0.530565	+	1.28090i	−0.931150	+	0.364637i	$0.881193\pi$
$230$	2.67092e9	−	1.58263e9i	0.954441	−	0.565546i
$231$	3.46200e7	−	3.46200e7i	0.0121585	−	0.0121585i
$232$	1.77131e9	−	1.89588e9i	0.611424	−	0.654424i
$233$	−1.03815e9	+	1.03815e9i	−0.352239	+	0.352239i	−0.860942	−	0.508703i	$-0.830125\pi$
$233$	−1.03815e9	+	1.03815e9i	−0.352239	+	0.352239i	0.508703	+	0.860942i	$0.330125\pi$
$234$	−4.47837e8	−	1.14581e8i	−0.149368	−	0.0382163i
$235$	−6.24797e8	+	1.50839e9i	−0.204865	+	0.494588i
$236$	4.65357e9	+	5.05783e8i	1.50016	+	0.163048i
$237$	2.10196e8	+	5.07458e8i	0.0666240	+	0.160845i
$238$	−2.66641e9	−	1.99847e9i	−0.831036	−	0.622860i
$239$	6.54971e8			0.200738			0.100369	−	0.994950i	$-0.467998\pi$
$239$	6.54971e8			0.200738			0.100369	+	0.994950i	$0.467998\pi$
$240$	−3.25518e8	+	2.08130e8i	−0.0981138	+	0.0627321i
$241$		−	1.22647e9i		−	0.363569i	−0.983338	−	0.181785i	$-0.941813\pi$
$241$		−	1.22647e9i		−	0.363569i	0.983338	−	0.181785i	$-0.0581874\pi$
$242$	−2.59350e9	−	1.94382e9i	−0.756179	−	0.566755i
$243$	1.30044e9	−	5.38662e8i	0.372964	−	0.154487i
$244$	−3.19480e9	+	2.56842e9i	−0.901332	+	0.724613i
$245$	−2.01600e9	−	8.35055e8i	−0.559534	−	0.231767i
$246$	3.98371e8	+	1.01925e8i	0.108779	+	0.0278316i
$247$	−5.82641e8	−	5.82641e8i	−0.156536	−	0.156536i
$248$	−8.15116e8	−	1.79312e9i	−0.215483	−	0.474027i
$249$	4.80211e8	+	4.80211e8i	0.124921	+	0.124921i
$250$	3.65246e9	−	2.16424e9i	0.935031	−	0.554045i
$251$	6.73754e9	+	2.79078e9i	1.69749	+	0.703122i	0.999910	−	0.0133885i	$-0.00426181\pi$
$251$	6.73754e9	+	2.79078e9i	1.69749	+	0.703122i	0.697576	+	0.716510i	$0.254262\pi$
$252$	−5.89524e8	−	2.01640e9i	−0.146184	−	0.500005i
$253$	1.16758e9	−	4.83629e8i	0.284974	−	0.118040i
$254$	1.39136e7	+	9.71724e7i	0.00334277	+	0.0233458i
$255$		−	9.62941e8i		−	0.227740i
$256$	1.80234e9	−	3.89850e9i	0.419639	−	0.907691i
$257$	−5.33167e9			−1.22217			−0.611084	−	0.791566i	$-0.709266\pi$
$257$	−5.33167e9			−1.22217			−0.611084	+	0.791566i	$0.709266\pi$
$258$	−3.27954e7	+	4.69582e6i	−0.00740175	+	0.00105982i
$259$	−6.40932e8	−	1.54735e9i	−0.142434	−	0.343865i
$260$	−5.81523e8	+	1.70017e8i	−0.127255	+	0.0372047i
$261$	−1.56013e9	+	3.76649e9i	−0.336201	+	0.811662i
$262$	−4.23312e9	−	7.14401e9i	−0.898371	−	1.51613i
$263$	−1.84292e9	+	1.84292e9i	−0.385197	+	0.385197i	−0.872970	−	0.487774i	$-0.837809\pi$
$263$	−1.84292e9	+	1.84292e9i	−0.385197	+	0.385197i	0.487774	+	0.872970i	$0.337809\pi$
$264$	−1.43179e8	+	6.50862e7i	−0.0294756	+	0.0133990i
$265$	1.56071e9	−	1.56071e9i	0.316475	−	0.316475i
$266$	9.28190e8	−	3.62781e9i	0.185400	−	0.724634i
$267$	1.07975e8	−	2.60675e8i	0.0212461	−	0.0512926i
$268$	−1.32975e9	−	1.65405e9i	−0.257768	−	0.320633i
$269$	−1.79288e9	−	4.32838e9i	−0.342406	−	0.826641i	−0.997471	−	0.0710686i	$-0.977359\pi$
$269$	−1.79288e9	−	4.32838e9i	−0.342406	−	0.826641i	0.655066	−	0.755572i	$-0.272641\pi$
$270$	7.35271e8	−	9.81018e8i	0.138354	−	0.184596i
$271$	8.24996e9			1.52959			0.764794	−	0.644275i	$-0.222841\pi$
$271$	8.24996e9			1.52959			0.764794	+	0.644275i	$0.222841\pi$
$272$	5.76624e9	+	9.01847e9i	1.05346	+	1.64762i
$273$			6.40075e7i			0.0115234i
$274$	−2.71461e9	+	3.62190e9i	−0.481620	+	0.642591i
$275$	3.57457e8	−	1.48064e8i	0.0625019	−	0.0258891i
$276$	−1.13845e8	+	1.04745e9i	−0.0196190	+	0.180509i
$277$	3.85632e9	+	1.59734e9i	0.655020	+	0.271318i	0.685341	−	0.728222i	$-0.259653\pi$
$277$	3.85632e9	+	1.59734e9i	0.655020	+	0.271318i	−0.0303213	+	0.999540i	$0.509653\pi$
$278$	1.13520e9	−	4.43691e9i	0.190061	−	0.742850i
$279$	2.18845e9	+	2.18845e9i	0.361177	+	0.361177i
$280$	−2.01195e9	−	1.87975e9i	−0.327329	−	0.305822i
$281$	2.82842e9	+	2.82842e9i	0.453648	+	0.453648i	0.896564	−	0.442915i	$-0.146056\pi$
$281$	2.82842e9	+	2.82842e9i	0.453648	+	0.453648i	−0.442915	+	0.896564i	$0.646056\pi$
$282$	−2.82458e8	−	4.76688e8i	−0.0446639	−	0.0753768i
$283$	1.58423e9	+	6.56211e8i	0.246987	+	0.102305i	0.502743	−	0.864436i	$-0.332324\pi$
$283$	1.58423e9	+	6.56211e8i	0.246987	+	0.102305i	−0.255756	+	0.966741i	$0.582324\pi$
$284$	−5.92861e8	+	1.08275e9i	−0.0911339	+	0.166439i
$285$	9.99760e8	−	4.14114e8i	0.151536	−	0.0627684i
$286$	−2.44139e8	+	3.49571e7i	−0.0364899	+	0.00522482i
$287$			2.93042e9i			0.431919i
$288$	−5.00995e8	+	6.72996e9i	−0.0728222	+	0.978234i
$289$	−1.97025e10			−2.82443
$290$	7.57358e8	+	5.28936e9i	0.107080	+	0.747844i
$291$	−3.00024e7	−	7.24322e7i	−0.00418393	−	0.0101009i
$292$	−1.94038e9	+	3.54374e9i	−0.266904	+	0.487450i
$293$	−3.97359e9	+	9.59311e9i	−0.539154	+	1.30163i	0.386160	+	0.922432i	$0.373801\pi$
$293$	−3.97359e9	+	9.59311e9i	−0.539154	+	1.30163i	−0.925314	+	0.379202i	$0.876199\pi$
$294$	6.37104e8	−	3.77511e8i	0.0852749	−	0.0505290i
$295$	−6.81652e9	+	6.81652e9i	−0.900066	+	0.900066i
$296$	1.82658e8	+	5.37709e9i	0.0237942	+	0.700456i
$297$	3.52886e8	−	3.52886e8i	0.0453533	−	0.0453533i
$298$	3.95496e9	+	1.01189e9i	0.501507	+	0.128313i
$299$	−6.32267e8	+	1.52643e9i	−0.0791071	+	0.190982i
$300$	−3.48537e7	+	3.20679e8i	−0.00430292	+	0.0395901i
$301$	−9.03512e7	−	2.18127e8i	−0.0110070	−	0.0265732i
$302$	1.19372e10	+	8.94694e9i	1.43508	+	1.07559i
$303$	1.93391e8			0.0229438
$304$	−6.88352e9	+	9.86512e9i	−0.805965	+	1.15507i
$305$		−	8.44191e9i		−	0.975532i
$306$	−1.34588e10	−	1.00873e10i	−1.53504	−	1.15051i
$307$	1.04143e10	−	4.31374e9i	1.17240	−	0.485624i	0.290414	−	0.956901i	$-0.406207\pi$
$307$	1.04143e10	−	4.31374e9i	1.17240	−	0.485624i	0.881985	+	0.471277i	$0.156207\pi$
$308$	−7.02275e8	−	8.73546e8i	−0.0780377	−	0.0970696i
$309$	1.86836e9	+	7.73900e8i	0.204940	+	0.0848889i
$310$	3.92981e9	+	1.00546e9i	0.425524	+	0.108872i
$311$	−9.39202e9	−	9.39202e9i	−1.00396	−	1.00396i	−0.999992	−	0.00397010i	$-0.998736\pi$
$311$	−9.39202e9	−	9.39202e9i	−1.00396	−	1.00396i	−0.00397010	−	0.999992i	$-0.501264\pi$
$312$	7.21911e7	−	1.92526e8i	0.00761843	−	0.0203175i
$313$	4.45550e9	+	4.45550e9i	0.464215	+	0.464215i	0.900034	−	0.435819i	$-0.143541\pi$
$313$	4.45550e9	+	4.45550e9i	0.464215	+	0.464215i	−0.435819	+	0.900034i	$0.643541\pi$
$314$	−7.27406e9	+	4.31019e9i	−0.748270	+	0.443382i
$315$	3.99708e9	+	1.65565e9i	0.405976	+	0.168161i
$316$	1.20691e10	−	3.52857e9i	1.21039	−	0.353875i
$317$	1.46531e10	−	6.06953e9i	1.45109	−	0.601060i	0.488629	−	0.872492i	$-0.337497\pi$
$317$	1.46531e10	−	6.06953e9i	1.45109	−	0.601060i	0.962458	+	0.271432i	$0.0874971\pi$
$318$	1.06172e8	+	7.41499e8i	0.0103825	+	0.0725107i
$319$			2.17509e9i			0.210046i
$320$	3.93160e9	+	7.92323e9i	0.374946	+	0.755618i
$321$	−9.09626e8			−0.0856727
$322$	−7.43279e9	+	1.06427e9i	−0.691398	+	0.0989980i
$323$	−1.14730e10	−	2.76983e10i	−1.05407	−	2.54474i
$324$	−2.91670e9	−	9.97623e9i	−0.264674	−	0.905287i
$325$	−1.93569e8	+	4.67318e8i	−0.0173502	+	0.0418870i
$326$	5.97801e9	+	1.00888e10i	0.529281	+	0.893238i
$327$	1.23304e9	−	1.23304e9i	0.107842	−	0.107842i
$328$	3.30509e9	−	8.81432e9i	0.285554	−	0.761541i
$329$	2.79214e9	−	2.79214e9i	0.238317	−	0.238317i
$330$	8.02846e7	−	3.13791e8i	0.00676981	−	0.0264597i
$331$	2.71627e9	−	6.55766e9i	0.226288	−	0.546307i	−0.769432	−	0.638728i	$-0.779461\pi$
$331$	2.71627e9	−	6.55766e9i	0.226288	−	0.546307i	0.995720	+	0.0924216i	$0.0294607\pi$
$332$	1.21169e10	−	9.74118e9i	0.997328	−	0.801788i
$333$	−3.23512e9	−	7.81027e9i	−0.263095	−	0.635169i
$334$	−5.12677e9	+	6.84027e9i	−0.411962	+	0.549651i
$335$	4.37063e9			0.347028
$336$	9.19983e8	−	1.63776e8i	0.0721809	−	0.0128497i
$337$		−	8.92432e9i		−	0.691919i	−0.938249	−	0.345960i	$-0.887553\pi$
$337$		−	8.92432e9i		−	0.691919i	0.938249	−	0.345960i	$-0.112447\pi$
$338$	−7.63428e9	+	1.01859e10i	−0.584927	+	0.780425i
$339$	−2.79951e9	+	1.15960e9i	−0.211974	+	0.0878027i
$340$	−2.19154e10	−	2.38192e9i	−1.63996	−	0.178242i
$341$	1.52554e9	+	6.31898e8i	0.112825	+	0.0467336i
$342$	4.68506e9	−	1.83115e10i	0.342461	−	1.33850i
$343$	8.92937e9	+	8.92937e9i	0.645126	+	0.645126i
$344$	2.57490e7	+	7.58001e8i	0.00183877	+	0.0541297i
$345$	−1.53430e9	−	1.53430e9i	−0.108301	−	0.108301i
$346$	9.61332e9	+	1.62239e10i	0.670763	+	1.13201i
$347$	−1.04419e10	−	4.32520e9i	−0.720217	−	0.298324i	−0.00769226	−	0.999970i	$-0.502449\pi$
$347$	−1.04419e10	−	4.32520e9i	−0.720217	−	0.298324i	−0.712525	+	0.701647i	$0.752449\pi$
$348$	−1.59056e9	−	8.70911e8i	−0.108451	−	0.0593823i
$349$	1.34125e10	−	5.55563e9i	0.904080	−	0.374482i	0.118293	−	0.992979i	$-0.462258\pi$
$349$	1.34125e10	−	5.55563e9i	0.904080	−	0.374482i	0.785788	+	0.618496i	$0.212258\pi$
$350$	−2.27556e9	+	3.25826e8i	−0.151641	+	0.0217127i
$351$			6.52436e8i			0.0429843i
$352$	1.12712e9	+	3.41958e9i	0.0734174	+	0.222742i
$353$	−1.46787e10			−0.945344			−0.472672	−	0.881238i	$-0.656711\pi$
$353$	−1.46787e10			−0.945344			−0.472672	+	0.881238i	$0.656711\pi$
$354$	−4.63712e8	−	3.23855e9i	−0.0295281	−	0.206223i
$355$	−9.72857e8	−	2.34869e9i	−0.0612542	−	0.147881i
$356$	−5.66558e9	−	3.10219e9i	−0.352731	−	0.193138i
$357$	−8.91237e8	+	2.15164e9i	−0.0548681	+	0.132463i
$358$	1.99355e10	−	1.18126e10i	1.21365	−	0.719141i
$359$	−2.02170e10	+	2.02170e10i	−1.21713	+	1.21713i	−0.248501	+	0.968632i	$0.579938\pi$
$359$	−2.02170e10	+	2.02170e10i	−1.21713	+	1.21713i	−0.968632	+	0.248501i	$0.920062\pi$
$360$	−1.01554e10	−	9.48809e9i	−0.604624	−	0.564896i
$361$	1.18142e10	−	1.18142e10i	0.695627	−	0.695627i
$362$	1.03415e10	+	2.64591e9i	0.602211	+	0.154078i
$363$	−8.66865e8	+	2.09280e9i	−0.0499258	+	0.120532i
$364$	1.45673e9	+	1.58328e8i	0.0829803	+	0.00901887i
$365$	−3.18407e9	−	7.68702e9i	−0.179395	−	0.433098i
$366$	2.29253e9	+	1.71825e9i	0.127759	+	0.0957549i
$367$	−7.10171e9			−0.391470			−0.195735	−	0.980657i	$-0.562709\pi$
$367$	−7.10171e9			−0.391470			−0.195735	+	0.980657i	$0.562709\pi$
$368$	2.35572e10	+	5.18193e9i	1.28449	+	0.282553i
$369$			1.47914e10i			0.797817i
$370$	−8.86611e9	−	6.64513e9i	−0.473071	−	0.354566i
$371$	−4.93181e9	+	2.04282e9i	−0.260322	+	0.107829i
$372$	−1.07291e9	+	8.62551e8i	−0.0560263	+	0.0450415i
$373$	2.72271e10	+	1.12778e10i	1.40659	+	0.582627i	0.951452	−	0.307796i	$-0.0995915\pi$
$373$	2.72271e10	+	1.12778e10i	1.40659	+	0.582627i	0.455134	+	0.890423i	$0.349592\pi$
$374$	−8.69357e9	−	2.22428e9i	−0.444336	−	0.113685i
$375$	−2.09815e9	−	2.09815e9i	−0.106099	−	0.106099i
$376$	−1.15475e10	+	5.24927e9i	−0.577747	+	0.262632i
$377$	−2.01071e9	−	2.01071e9i	−0.0995371	−	0.0995371i
$378$	−2.55089e9	+	1.51151e9i	−0.124947	+	0.0740361i
$379$	3.00499e10	+	1.24471e10i	1.45642	+	0.603269i	0.963716	−	0.266928i	$-0.0860086\pi$
$379$	3.00499e10	+	1.24471e10i	1.45642	+	0.603269i	0.492704	+	0.870197i	$0.336009\pi$
$380$	−6.95176e9	−	2.37777e10i	−0.333396	−	1.14034i
$381$	6.33849e7	−	2.62549e7i	0.00300805	−	0.00124598i
$382$	5.47085e9	+	3.82082e10i	0.256922	+	1.79433i
$383$		−	2.39552e10i		−	1.11328i	−0.830754	−	0.556639i	$-0.812091\pi$
$383$		−	2.39552e10i		−	1.11328i	0.830754	−	0.556639i	$-0.187909\pi$
$384$	−2.95190e9	−	5.44990e8i	−0.135762	−	0.0250648i
$385$	2.30825e9			0.105061
$386$	−1.09014e10	+	1.56092e9i	−0.491057	+	0.0703122i
$387$	−4.56050e8	−	1.10100e9i	−0.0203315	−	0.0490845i
$388$	−1.72268e9	+	5.03652e8i	−0.0760114	+	0.0222230i
$389$	−7.70249e9	+	1.85954e10i	−0.336382	+	0.812098i	0.661675	+	0.749791i	$0.269846\pi$
$389$	−7.70249e9	+	1.85954e10i	−0.336382	+	0.812098i	−0.998057	+	0.0623070i	$0.980154\pi$
$390$	2.15860e8	+	3.64294e8i	0.00933068	+	0.0157469i
$391$	−4.25078e10	+	4.25078e10i	−1.81870	+	1.81870i
$392$	−7.01577e9	−	1.54335e10i	−0.297120	−	0.653614i
$393$	−4.10385e9	+	4.10385e9i	−0.172037	+	0.172037i
$394$	−4.13052e9	+	1.61441e10i	−0.171404	+	0.669928i
$395$	−9.90979e9	+	2.39243e10i	−0.407076	+	0.982769i
$396$	−3.54475e9	−	4.40925e9i	−0.144147	−	0.179301i
$397$	1.28092e10	+	3.09242e10i	0.515657	+	1.24491i	0.940548	+	0.339661i	$0.110312\pi$
$397$	1.28092e10	+	3.09242e10i	0.515657	+	1.24491i	−0.424891	+	0.905244i	$0.639688\pi$
$398$	1.42580e10	−	1.90235e10i	0.568235	−	0.758154i
$399$	−2.61718e9			−0.103262
$400$	7.21207e9	+	1.58646e9i	0.281721	+	0.0619709i
$401$		−	3.40792e10i		−	1.31799i	−0.752147	−	0.658995i	$-0.770982\pi$
$401$		−	3.40792e10i		−	1.31799i	0.752147	−	0.658995i	$-0.229018\pi$
$402$	−8.89588e8	+	1.18691e9i	−0.0340631	+	0.0454480i
$403$	−1.99439e9	+	8.26105e8i	−0.0756120	+	0.0313195i
$404$	4.78369e8	−	4.40135e9i	0.0179572	−	0.165219i
$405$	1.97757e10	+	8.19138e9i	0.735043	+	0.304465i
$406$	3.20322e9	−	1.25197e10i	0.117891	−	0.460777i
$407$	−3.18927e9	−	3.18927e9i	−0.116229	−	0.116229i
$408$	5.10745e9	−	5.46665e9i	0.184316	−	0.197279i
$409$	1.53524e10	+	1.53524e10i	0.548635	+	0.548635i	0.926046	−	0.377411i	$-0.123186\pi$
$409$	1.53524e10	+	1.53524e10i	0.548635	+	0.548635i	−0.377411	+	0.926046i	$0.623186\pi$
$410$	9.88259e9	+	1.66783e10i	0.349732	+	0.590223i
$411$	2.92266e9	+	1.21060e9i	0.102426	+	0.0424263i
$412$	2.22346e10	−	4.06074e10i	0.771686	−	1.40934i
$413$	2.15400e10	−	8.92217e9i	0.740365	−	0.306669i
$414$	−3.75172e10	+	5.37191e9i	−1.27711	+	0.182863i
$415$			3.20175e10i			1.07943i
$416$	−4.20309e9	−	2.11921e9i	−0.140345	−	0.0707622i
$417$	−3.20088e9			−0.105858
$418$	−1.42935e9	−	9.98253e9i	−0.0468202	−	0.326991i
$419$	−1.90378e10	−	4.59614e10i	−0.617677	−	1.49120i	−0.854394	−	0.519625i	$-0.826072\pi$
$419$	−1.90378e10	−	4.59614e10i	−0.617677	−	1.49120i	0.236717	−	0.971579i	$-0.423928\pi$
$420$	−9.24229e8	+	1.68793e9i	−0.0297018	+	0.0542448i
$421$	−6.07180e9	+	1.46586e10i	−0.193281	+	0.466621i	−0.990575	−	0.136969i	$-0.956264\pi$
$421$	−6.07180e9	+	1.46586e10i	−0.193281	+	0.466621i	0.797294	+	0.603591i	$0.206264\pi$
$422$	7.44001e9	−	4.40852e9i	0.234598	−	0.139009i
$423$	1.40934e10	−	1.40934e10i	0.440205	−	0.440205i
$424$	1.71383e10	−	5.82180e8i	0.530278	−	0.0180133i
$425$	−1.30138e10	+	1.30138e10i	−0.398886	+	0.398886i
$426$	8.35835e8	+	2.13851e8i	0.0253794	+	0.00649343i
$427$	−7.81329e9	+	1.88630e10i	−0.235030	+	0.567412i
$428$	−2.25004e9	+	2.07020e10i	−0.0670524	+	0.616932i
$429$	6.59636e7	+	1.59250e8i	0.00194749	+	0.00470166i
$430$	−1.24984e9	−	9.36754e8i	−0.0365579	−	0.0274001i
$431$	3.61014e10			1.04620			0.523100	−	0.852271i	$-0.324775\pi$
$431$	3.61014e10			1.04620			0.523100	+	0.852271i	$0.324775\pi$
$432$	9.37750e9	−	1.66939e9i	0.269248	−	0.0479316i
$433$			1.33063e10i			0.378535i	0.981926	+	0.189267i	$0.0606113\pi$
$433$			1.33063e10i			0.378535i	−0.981926	+	0.189267i	$0.939389\pi$
$434$	−7.85033e9	−	5.88381e9i	−0.221273	−	0.165844i
$435$	3.45021e9	−	1.42912e9i	0.0963581	−	0.0399129i
$436$	−2.50125e10	−	3.11126e10i	−0.692168	−	0.860974i
$437$	−6.24136e10	−	2.58526e10i	−1.71141	−	0.708889i
$438$	2.73561e9	+	6.99915e8i	0.0743288	+	0.0190173i
$439$	−2.34264e10	−	2.34264e10i	−0.630735	−	0.630735i	0.317517	−	0.948253i	$-0.397151\pi$
$439$	−2.34264e10	−	2.34264e10i	−0.630735	−	0.630735i	−0.948253	+	0.317517i	$0.897151\pi$
$440$	−6.94291e9	−	2.60337e9i	−0.185238	−	0.0694585i
$441$	1.88362e10	+	1.88362e10i	0.498010	+	0.498010i
$442$	1.00928e10	−	5.98039e9i	0.264436	−	0.156690i
$443$	1.51867e10	+	6.29052e9i	0.394319	+	0.163332i	0.571027	−	0.820931i	$-0.306545\pi$
$443$	1.51867e10	+	6.29052e9i	0.394319	+	0.163332i	−0.176709	+	0.984263i	$0.556545\pi$
$444$	3.60918e9	−	1.05519e9i	0.0928701	−	0.0271519i
$445$	1.22897e10	−	5.09055e9i	0.313401	−	0.129815i
$446$	4.72641e8	+	3.30090e9i	0.0119451	+	0.0834245i
$447$		−	2.85319e9i		−	0.0714663i
$448$	−1.45169e9	−	2.13428e10i	−0.0360381	−	0.529834i
$449$	−2.30043e10			−0.566010			−0.283005	−	0.959118i	$-0.591331\pi$
$449$	−2.30043e10			−0.566010			−0.283005	+	0.959118i	$0.591331\pi$
$450$	−1.14859e10	+	1.64462e9i	−0.280102	+	0.0401065i
$451$	3.01998e9	+	7.29087e9i	0.0729957	+	0.176227i
$452$	1.94662e10	+	6.65819e10i	0.466366	+	1.59515i
$453$	3.98997e9	−	9.63263e9i	0.0947494	−	0.228745i
$454$	1.49295e10	+	2.51957e10i	0.351417	+	0.593066i
$455$	−2.13381e9	+	2.13381e9i	−0.0497864	+	0.0497864i
$456$	7.87214e9	+	2.95180e9i	0.182068	+	0.0682697i
$457$	2.42057e10	−	2.42057e10i	0.554950	−	0.554950i	−0.372916	−	0.927865i	$-0.621642\pi$
$457$	2.42057e10	−	2.42057e10i	0.554950	−	0.554950i	0.927865	+	0.372916i	$0.121642\pi$
$458$	1.51211e10	−	5.91006e10i	0.343654	−	1.34317i
$459$	−9.08449e9	+	2.19319e10i	−0.204668	+	0.494112i
$460$	−3.87141e10	+	3.11236e10i	−0.864645	+	0.695119i
$461$	−1.57500e10	−	3.80240e10i	−0.348721	−	0.841887i	−0.996772	−	0.0802896i	$-0.974415\pi$
$461$	−1.57500e10	−	3.80240e10i	−0.348721	−	0.841887i	0.648051	−	0.761597i	$-0.275585\pi$
$462$	−4.69816e8	+	6.26841e8i	−0.0103124	+	0.0137591i
$463$	5.06544e10			1.10228			0.551142	−	0.834412i	$-0.314192\pi$
$463$	5.06544e10			1.10228			0.551142	+	0.834412i	$0.314192\pi$
$464$	−2.37553e10	+	3.40449e10i	−0.512493	+	0.734480i
$465$		−	2.83505e9i		−	0.0606385i
$466$	1.40884e10	−	1.87971e10i	0.298756	−	0.398609i
$467$	−3.11067e9	+	1.28848e9i	−0.0654014	+	0.0270901i	−0.415144	−	0.909756i	$-0.636269\pi$
$467$	−3.11067e9	+	1.28848e9i	−0.0654014	+	0.0270901i	0.349743	+	0.936846i	$0.386269\pi$
$468$	7.35290e9	+	7.99165e8i	0.153276	+	0.0166592i
$469$	−9.76592e9	−	4.04518e9i	−0.201847	−	0.0836077i
$470$	6.47504e9	−	2.53076e10i	0.132694	−	0.518632i
$471$	4.17856e9	+	4.17856e9i	0.0849070	+	0.0849070i
$472$	−7.48525e10	+	2.54271e9i	−1.50813	+	0.0512305i
$473$	−4.49586e8	−	4.49586e8i	−0.00898191	−	0.00898191i
$474$	−4.48001e9	−	7.56066e9i	−0.0887494	−	0.149777i
$475$	−1.91080e10	−	7.91480e9i	−0.375354	−	0.155477i
$476$	4.67641e10	+	2.56057e10i	0.910930	+	0.498781i
$477$	−2.48935e10	+	1.03112e10i	−0.480852	+	0.199176i
$478$	−1.03737e10	+	1.48537e9i	−0.198712	+	0.0284526i
$479$		−	8.23816e10i		−	1.56490i	−0.622710	−	0.782452i	$-0.713969\pi$
$479$		−	8.23816e10i		−	1.56490i	0.622710	−	0.782452i	$-0.286031\pi$
$480$	4.68370e9	−	4.03468e9i	0.0882316	−	0.0760054i
$481$	5.89650e9			0.110157
$482$	2.78142e9	+	1.94253e10i	0.0515322	+	0.359899i
$483$	2.00825e9	+	4.84835e9i	0.0369003	+	0.0890853i
$484$	4.54853e10	+	2.49055e10i	0.828876	+	0.453852i
$485$	1.41448e9	−	3.41485e9i	0.0255640	−	0.0617170i
$486$	−1.93754e10	+	1.14808e10i	−0.347301	+	0.205791i
$487$	7.29548e10	−	7.29548e10i	1.29699	−	1.29699i	0.366625	−	0.930369i	$-0.380513\pi$
$487$	7.29548e10	−	7.29548e10i	1.29699	−	1.29699i	0.930369	−	0.366625i	$-0.119487\pi$
$488$	4.47760e10	−	4.79250e10i	0.789526	−	0.845051i
$489$	5.79546e9	−	5.79546e9i	0.101357	−	0.101357i
$490$	3.38241e10	+	8.65404e9i	0.586736	+	0.150119i
$491$	4.17092e10	−	1.00695e11i	0.717639	−	1.73253i	0.0376747	−	0.999290i	$-0.488005\pi$
$491$	4.17092e10	−	1.00695e11i	0.717639	−	1.73253i	0.679965	−	0.733245i	$-0.261995\pi$
$492$	−6.54073e9	−	7.10892e8i	−0.111626	−	0.0121323i
$493$	−3.95938e10	−	9.55880e10i	−0.670255	−	1.61814i
$494$	1.05495e10	+	7.90680e9i	0.177142	+	0.132768i
$495$	1.16509e10			0.194062
$496$	1.69767e10	+	2.65518e10i	0.280496	+	0.438699i
$497$			6.14841e9i			0.100771i
$498$	−8.69484e9	−	6.51676e9i	−0.141366	−	0.105953i
$499$	−6.45251e10	+	2.67272e10i	−1.04070	+	0.431073i	−0.836564	−	0.547869i	$-0.815439\pi$
$499$	−6.45251e10	+	2.67272e10i	−1.04070	+	0.431073i	−0.204138	+	0.978942i	$0.565439\pi$
$500$	−5.29413e10	+	4.25614e10i	−0.847060	+	0.680982i
$501$	5.51968e9	+	2.28633e9i	0.0876119	+	0.0362901i
$502$	−1.13041e11	−	2.89220e10i	−1.78001	−	0.455422i
$503$	3.65609e10	+	3.65609e10i	0.571143	+	0.571143i	0.932448	−	0.361305i	$-0.117669\pi$
$503$	3.65609e10	+	3.65609e10i	0.571143	+	0.571143i	−0.361305	+	0.932448i	$0.617669\pi$
$504$	1.39100e10	+	3.05997e10i	0.215578	+	0.474237i
$505$	6.44706e9	+	6.44706e9i	0.0991280	+	0.0991280i
$506$	−1.73959e10	+	1.03078e10i	−0.265366	+	0.157241i
$507$	8.21938e9	+	3.40458e9i	0.124396	+	0.0515266i
$508$	−4.40742e8	−	1.50751e9i	−0.00661804	−	0.0226363i
$509$	−1.01437e11	+	4.20167e10i	−1.51121	+	0.625965i	−0.975808	−	0.218629i	$-0.929841\pi$
$509$	−1.01437e11	+	4.20167e10i	−1.51121	+	0.625965i	−0.535406	+	0.844595i	$0.679841\pi$
$510$	2.18379e9	+	1.52515e10i	0.0322798	+	0.225441i
$511$			2.01232e10i			0.295129i
$512$	−1.97051e10	+	6.58337e10i	−0.286747	+	0.958006i
$513$	−2.66773e10			−0.385187
$514$	8.44455e10	−	1.20914e10i	1.20983	−	0.173230i
$515$	3.64859e10	+	8.80848e10i	0.518676	+	1.25220i
$516$	5.08780e8	−	1.48749e8i	0.00717681	−	0.00209824i
$517$	4.06936e9	−	9.82431e9i	0.0569592	−	0.137512i
$518$	1.36605e10	+	2.30541e10i	0.189735	+	0.320205i
$519$	9.31975e9	−	9.31975e9i	0.128450	−	0.128450i
$520$	8.82485e9	−	4.01160e9i	0.120696	−	0.0548661i
$521$	−4.05814e10	+	4.05814e10i	−0.550778	+	0.550778i	−0.926665	−	0.375887i	$-0.877338\pi$
$521$	−4.05814e10	+	4.05814e10i	−0.550778	+	0.550778i	0.375887	+	0.926665i	$0.377338\pi$
$522$	1.61683e10	−	6.31936e10i	0.217762	−	0.851120i
$523$	−3.16546e10	+	7.64211e10i	−0.423088	+	1.02142i	0.558343	+	0.829610i	$0.311437\pi$
$523$	−3.16546e10	+	7.64211e10i	−0.423088	+	1.02142i	−0.981431	+	0.191815i	$0.938563\pi$
$524$	8.32476e10	+	1.03550e11i	1.10420	+	1.37349i
$525$	6.14830e8	+	1.48433e9i	0.00809316	+	0.0195386i
$526$	2.50095e10	−	3.33684e10i	0.326710	−	0.435905i
$527$	−7.85449e10			−1.01830
$528$	2.12013e9	−	1.35557e9i	0.0272789	−	0.0174416i
$529$			5.71483e10i			0.729762i
$530$	−2.11798e10	+	2.82587e10i	−0.268423	+	0.358137i
$531$	1.08724e11	−	4.50349e10i	1.36756	−	0.566462i
$532$	−6.47383e9	+	5.95640e10i	−0.0808192	+	0.743596i
$533$	−9.53163e9	−	3.94813e9i	−0.118102	−	0.0489196i
$534$	−1.11899e9	+	4.37357e9i	−0.0137614	+	0.0537862i
$535$	−3.03241e10	−	3.03241e10i	−0.370146	−	0.370146i
$536$	2.48122e10	+	2.31819e10i	0.300612	+	0.280860i
$537$	−1.14519e10	−	1.14519e10i	−0.137715	−	0.137715i
$538$	3.82125e10	+	6.44890e10i	0.456117	+	0.769762i
$539$	1.31304e10	+	5.43879e9i	0.155569	+	0.0644388i
$540$	−9.42078e9	+	1.72053e10i	−0.110793	+	0.202343i
$541$	5.61380e9	−	2.32531e9i	0.0655342	−	0.0271451i	−0.349676	−	0.936871i	$-0.613708\pi$
$541$	5.61380e9	−	2.32531e9i	0.0655342	−	0.0271451i	0.415210	+	0.909726i	$0.363708\pi$
$542$	−1.30667e11	+	1.87095e10i	−1.51415	+	0.216803i
$543$		−	7.46057e9i		−	0.0858169i
$544$	−1.11781e11	−	1.29762e11i	−1.27636	−	1.48167i
$545$	8.22115e10			0.931852
$546$	−1.45158e8	−	1.01378e9i	−0.00163332	−	0.0114070i
$547$	3.52496e10	+	8.51001e10i	0.393736	+	0.950563i	0.989119	+	0.147121i	$0.0470006\pi$
$547$	3.52496e10	+	8.51001e10i	0.393736	+	0.950563i	−0.595382	+	0.803442i	$0.702999\pi$
$548$	3.47813e10	−	6.35216e10i	0.385677	−	0.704368i
$549$	−3.94378e10	+	9.52112e10i	−0.434133	+	1.04809i
$550$	−5.32579e9	+	3.15575e9i	−0.0582014	+	0.0344868i
$551$	8.22155e10	−	8.22155e10i	0.891964	−	0.891964i
$552$	−5.72328e8	−	1.68482e10i	−0.00616437	−	0.181467i
$553$	4.42857e10	−	4.42857e10i	0.473547	−	0.473547i
$554$	−6.47008e10	−	1.65539e10i	−0.686863	−	0.175737i
$555$	−2.96346e9	+	7.15442e9i	−0.0312339	+	0.0754054i
$556$	−7.91766e9	+	7.28483e10i	−0.0828509	+	0.762290i
$557$	4.46397e10	+	1.07770e11i	0.463768	+	1.11964i	0.966838	+	0.255390i	$0.0822038\pi$
$557$	4.46397e10	+	1.07770e11i	0.463768	+	1.11964i	−0.503070	+	0.864246i	$0.667796\pi$
$558$	−3.96248e10	−	2.96987e10i	−0.408724	−	0.306338i
$559$	8.31221e8			0.00851273
$560$	3.61292e10	+	2.52096e10i	0.367372	+	0.256338i
$561$			6.27173e9i			0.0633192i
$562$	−5.12123e10	−	3.83835e10i	−0.513368	−	0.384768i
$563$	−2.51898e10	+	1.04339e10i	−0.250721	+	0.103852i	−0.504505	−	0.863409i	$-0.668325\pi$
$563$	−2.51898e10	+	1.04339e10i	−0.250721	+	0.103852i	0.253784	+	0.967261i	$0.418325\pi$
$564$	5.55475e9	+	6.90944e9i	0.0548969	+	0.0682852i
$565$	−1.31984e11	−	5.46697e10i	−1.29518	−	0.536480i
$566$	−2.65800e10	−	6.80060e9i	−0.258994	−	0.0662646i
$567$	−3.66063e10	−	3.66063e10i	−0.354180	−	0.354180i
$568$	6.93451e9	−	1.84936e10i	0.0666228	−	0.177676i
$569$	−2.97766e9	−	2.97766e9i	−0.0284070	−	0.0284070i	0.692761	−	0.721168i	$-0.256394\pi$
$569$	−2.97766e9	−	2.97766e9i	−0.0284070	−	0.0284070i	−0.721168	+	0.692761i	$0.756394\pi$
$570$	−1.48955e10	+	8.82623e9i	−0.141110	+	0.0836133i
$571$	−7.70505e10	−	3.19154e10i	−0.724821	−	0.300231i	−0.0103993	−	0.999946i	$-0.503310\pi$
$571$	−7.70505e10	−	3.19154e10i	−0.724821	−	0.300231i	−0.714422	+	0.699715i	$0.753310\pi$
$572$	3.78751e9	−	1.10733e9i	0.0353810	−	0.0103441i
$573$	2.49229e10	−	1.03234e10i	0.231196	−	0.0957646i
$574$	−6.64571e9	−	4.64134e10i	−0.0612200	−	0.427558i
$575$			4.14711e10i			0.379380i
$576$	−7.32744e9	−	1.07728e11i	−0.0665675	−	0.978679i
$577$	1.46895e11			1.32526			0.662632	−	0.748945i	$-0.269439\pi$
$577$	1.46895e11			1.32526			0.662632	+	0.748945i	$0.269439\pi$
$578$	3.12058e11	−	4.46820e10i	2.79591	−	0.400333i
$579$	2.94543e9	+	7.11089e9i	0.0262080	+	0.0632718i
$580$	−2.39908e10	−	8.20577e10i	−0.211998	−	0.725116i
$581$	2.96333e10	−	7.15412e10i	0.260061	−	0.627844i
$582$	6.39456e8	+	1.07917e9i	0.00557338	+	0.00940588i
$583$	−1.01651e10	+	1.01651e10i	−0.0879905	+	0.0879905i
$584$	2.26960e10	−	6.05278e10i	0.195118	−	0.520360i
$585$	−1.07705e10	+	1.07705e10i	−0.0919626	+	0.0919626i
$586$	4.11801e10	−	1.60952e11i	0.349218	−	1.36491i
$587$	−1.98206e10	+	4.78512e10i	−0.166942	+	0.403033i	−0.985105	−	0.171953i	$-0.944992\pi$
$587$	−1.98206e10	+	4.78512e10i	−0.166942	+	0.403033i	0.818164	+	0.574986i	$0.194992\pi$
$588$	−9.23462e9	+	7.42404e9i	−0.0772520	+	0.0621057i
$589$	−3.37784e10	−	8.15482e10i	−0.280658	−	0.677568i
$590$	9.25044e10	−	1.23422e11i	0.763404	−	1.01855i
$591$	1.16467e10			0.0954668
$592$	−1.50874e10	−	8.47506e10i	−0.122836	−	0.690011i
$593$			8.58923e10i			0.694601i	0.937754	+	0.347301i	$0.112902\pi$
$593$			8.58923e10i			0.694601i	−0.937754	+	0.347301i	$0.887098\pi$
$594$	−4.78889e9	+	6.38946e9i	−0.0384671	+	0.0513238i
$595$	−1.01440e11	+	4.20178e10i	−0.809359	+	0.335247i
$596$	−6.49353e10	−	7.05762e9i	−0.514631	−	0.0559337i
$597$	−1.53508e10	−	6.35850e9i	−0.120846	−	0.0500562i
$598$	6.55245e9	−	2.56101e10i	0.0512388	−	0.200266i
$599$	1.28024e11	+	1.28024e11i	0.994454	+	0.994454i	0.999985	−	0.00553098i	$-0.00176058\pi$
$599$	1.28024e11	+	1.28024e11i	0.994454	+	0.994454i	−0.00553098	+	0.999985i	$0.501761\pi$
$600$	−1.75219e8	−	5.15811e9i	−0.00135200	−	0.0398002i
$601$	1.33870e10	+	1.33870e10i	0.102609	+	0.102609i	0.756547	−	0.653939i	$-0.226885\pi$
$601$	1.33870e10	+	1.33870e10i	0.102609	+	0.102609i	−0.653939	+	0.756547i	$0.726885\pi$
$602$	1.92570e9	+	3.24990e9i	0.0146623	+	0.0247448i
$603$	−4.92937e10	−	2.04181e10i	−0.372840	−	0.154435i
$604$	−2.09358e11	−	1.14634e11i	−1.57305	−	0.861323i
$605$	−9.86660e10	+	4.08688e10i	−0.736455	+	0.305049i
$606$	−3.06302e9	+	4.38579e8i	−0.0227122	+	0.00325205i
$607$		−	4.62776e10i		−	0.340891i	−0.985367	−	0.170446i	$-0.945479\pi$
$607$		−	4.62776e10i		−	0.340891i	0.985367	−	0.170446i	$-0.0545207\pi$
$608$	8.66519e10	−	1.71859e11i	0.634109	−	1.25765i
$609$	−9.03199e9			−0.0656621
$610$	1.91449e10	+	1.33707e11i	0.138271	+	0.965683i
$611$	5.32004e9	+	1.28437e10i	0.0381724	+	0.0921564i
$612$	2.36043e11	+	1.29246e11i	1.68262	+	0.921319i
$613$	8.92577e10	−	2.15487e11i	0.632126	−	1.52609i	−0.204819	−	0.978800i	$-0.565660\pi$
$613$	8.92577e10	−	2.15487e11i	0.632126	−	1.52609i	0.836945	−	0.547287i	$-0.184340\pi$
$614$	−1.55163e11	+	9.19408e10i	−1.09173	+	0.646896i
$615$	9.58080e9	−	9.58080e9i	0.0669732	−	0.0669732i
$616$	1.31040e10	+	1.22430e10i	0.0910084	+	0.0850285i
$617$	−9.72505e10	+	9.72505e10i	−0.671044	+	0.671044i	−0.957957	−	0.286912i	$-0.907371\pi$
$617$	−9.72505e10	+	9.72505e10i	−0.671044	+	0.671044i	0.286912	+	0.957957i	$0.407371\pi$
$618$	−3.13470e10	−	8.02026e9i	−0.214903	−	0.0549838i
$619$	2.88425e9	−	6.96320e9i	0.0196459	−	0.0474293i	−0.913752	−	0.406272i	$-0.866829\pi$
$619$	2.88425e9	−	6.96320e9i	0.0196459	−	0.0474293i	0.933398	+	0.358843i	$0.116829\pi$
$620$	−6.45223e10	−	7.01273e9i	−0.436660	−	0.0474592i
$621$	2.04704e10	+	4.94199e10i	0.137645	+	0.332304i
$622$	1.70055e11	+	1.27456e11i	1.13613	+	0.851525i
$623$	−3.21720e10			−0.213563
$624$	−7.06779e8	+	3.21304e9i	−0.00466171	+	0.0211923i
$625$		−	9.58764e10i		−	0.628336i
$626$	−8.06726e10	−	6.04640e10i	−0.525326	−	0.393731i
$627$	−6.51153e9	+	2.69717e9i	−0.0421321	+	0.0174517i
$628$	1.05435e11	−	8.47631e10i	0.677871	−	0.544965i
$629$	1.98213e11	+	8.21025e10i	1.26628	+	0.524510i
$630$	−6.70623e10	−	1.71582e10i	−0.425713	−	0.108920i
$631$	−6.27260e10	−	6.27260e10i	−0.395667	−	0.395667i	0.481034	−	0.876702i	$-0.340261\pi$
$631$	−6.27260e10	−	6.27260e10i	−0.395667	−	0.395667i	−0.876702	+	0.481034i	$0.840261\pi$
$632$	−1.83153e11	+	8.32577e10i	−1.14801	+	0.521863i
$633$	−4.27389e9	−	4.27389e9i	−0.0266201	−	0.0266201i
$634$	−2.18318e11	+	1.29363e11i	−1.35124	+	0.800668i
$635$	2.98831e9	+	1.23780e9i	0.0183794	+	0.00761299i
$636$	−3.36319e9	−	1.15034e10i	−0.0205553	−	0.0703070i
$637$	−1.71659e10	+	7.11035e9i	−0.104258	+	0.0431850i
$638$	−4.93274e9	−	3.44501e10i	−0.0297718	−	0.207925i
$639$			3.10343e10i			0.186139i
$640$	−8.02390e10	−	1.16576e11i	−0.478262	−	0.694844i
$641$	2.32024e11			1.37436			0.687181	−	0.726486i	$-0.258848\pi$
$641$	2.32024e11			1.37436			0.687181	+	0.726486i	$0.258848\pi$
$642$	1.44071e10	−	2.06288e9i	0.0848078	−	0.0121432i
$643$	1.70521e10	+	4.11673e10i	0.0997547	+	0.240829i	0.965876	−	0.259005i	$-0.0833945\pi$
$643$	1.70521e10	+	4.11673e10i	0.0997547	+	0.240829i	−0.866121	+	0.499834i	$0.833394\pi$
$644$	1.15310e11	−	3.37127e10i	0.670386	−	0.195997i
$645$	−4.17754e8	+	1.00855e9i	−0.00241369	+	0.00582717i
$646$	2.44530e11	+	4.12680e11i	1.40412	+	2.36965i
$647$	−2.11058e10	+	2.11058e10i	−0.120444	+	0.120444i	−0.764760	−	0.644316i	$-0.777142\pi$
$647$	−2.11058e10	+	2.11058e10i	−0.120444	+	0.120444i	0.644316	+	0.764760i	$0.277142\pi$
$648$	6.88204e10	+	1.51394e11i	0.390317	+	0.858633i
$649$	4.43966e10	−	4.43966e10i	0.250248	−	0.250248i
$650$	2.00604e9	−	7.84058e9i	0.0112379	−	0.0439233i
$651$	−2.62394e9	+	6.33475e9i	−0.0146093	+	0.0352700i
$652$	−1.17562e11	−	1.46233e11i	−0.650545	−	0.809200i
$653$	1.22467e11	+	2.95662e11i	0.673546	+	1.62608i	0.775540	+	0.631298i	$0.217478\pi$
$653$	1.22467e11	+	2.95662e11i	0.673546	+	1.62608i	−0.101994	+	0.994785i	$0.532522\pi$
$654$	−1.67331e10	+	2.23258e10i	−0.0914674	+	0.122038i
$655$	−2.73620e11			−1.48656
$656$	−3.23581e10	+	1.47101e11i	−0.174730	+	0.794327i
$657$			1.01572e11i			0.545146i
$658$	−3.78912e10	+	5.05554e10i	−0.202132	+	0.269689i
$659$	−1.41147e11	+	5.84652e10i	−0.748395	+	0.309996i	−0.724087	−	0.689709i	$-0.757738\pi$
$659$	−1.41147e11	+	5.84652e10i	−0.748395	+	0.309996i	−0.0243088	+	0.999704i	$0.507738\pi$
$660$	−5.59959e8	+	5.15204e9i	−0.00295108	+	0.0271521i
$661$	−1.31485e10	−	5.44628e9i	−0.0688763	−	0.0285295i	0.347979	−	0.937502i	$-0.386868\pi$
$661$	−1.31485e10	−	5.44628e9i	−0.0688763	−	0.0285295i	−0.416856	+	0.908973i	$0.636868\pi$
$662$	−2.81499e10	+	1.10023e11i	−0.146570	+	0.572865i
$663$	−5.79776e9	−	5.79776e9i	−0.0300059	−	0.0300059i
$664$	−1.69821e11	+	1.81764e11i	−0.873614	+	0.935054i
$665$	−8.72488e10	−	8.72488e10i	−0.446142	−	0.446142i
$666$	6.89517e10	+	1.16366e11i	0.350468	+	0.591465i
$667$	−2.15392e11	−	8.92182e10i	−1.08824	−	0.450765i
$668$	6.56875e10	−	1.19966e11i	0.329896	−	0.602493i
$669$	2.15316e9	−	8.91866e8i	0.0107491	−	0.00445241i
$670$	−6.92241e10	+	9.91187e9i	−0.343525	+	0.0491877i
$671$			5.49830e10i			0.271230i
$672$	−1.41997e10	+	4.68033e9i	−0.0696309	+	0.0229509i
$673$	6.52817e10			0.318223			0.159111	−	0.987261i	$-0.449137\pi$
$673$	6.52817e10			0.318223			0.159111	+	0.987261i	$0.449137\pi$
$674$	2.02389e10	+	1.41347e11i	0.0980724	+	0.684934i
$675$	6.26704e9	+	1.51300e10i	0.0301889	+	0.0728825i
$676$	9.78155e10	−	1.78642e11i	0.468404	−	0.855453i
$677$	1.14038e11	−	2.75313e11i	0.542870	−	1.31060i	−0.379820	−	0.925061i	$-0.624014\pi$
$677$	1.14038e11	−	2.75313e11i	0.542870	−	1.31060i	0.922690	−	0.385544i	$-0.125986\pi$
$678$	4.17102e10	−	2.47150e10i	0.197389	−	0.116961i
$679$	−6.32114e9	+	6.32114e9i	−0.0297383	+	0.0297383i
$680$	3.52508e11	−	1.19746e10i	1.64867	−	0.0560046i
$681$	1.44736e10	−	1.44736e10i	0.0672958	−	0.0672958i
$682$	−2.55952e10	−	6.54863e9i	−0.118310	−	0.0302700i
$683$	1.40999e11	−	3.40401e11i	0.647937	−	1.56426i	−0.167791	−	0.985823i	$-0.553663\pi$
$683$	1.40999e11	−	3.40401e11i	0.647937	−	1.56426i	0.815728	−	0.578436i	$-0.196337\pi$
$684$	−3.26768e10	+	3.00651e11i	−0.149285	+	1.37353i
$685$	5.70745e10	+	1.37790e11i	0.259227	+	0.625829i
$686$	−1.61678e11	−	1.21177e11i	−0.730053	−	0.547173i
$687$	−4.26364e10			−0.191405
$688$	−2.12684e9	−	1.19472e10i	−0.00949253	−	0.0533226i
$689$		−	1.87938e10i		−	0.0833943i
$690$	2.77805e10	+	2.08214e10i	0.122559	+	0.0918574i
$691$	1.38747e11	−	5.74708e10i	0.608570	−	0.252078i	−0.0570468	−	0.998372i	$-0.518168\pi$
$691$	1.38747e11	−	5.74708e10i	0.608570	−	0.252078i	0.665617	+	0.746293i	$0.268168\pi$
$692$	−1.89053e11	−	2.35160e11i	−0.824441	−	1.02551i
$693$	−2.60334e10	−	1.07834e10i	−0.112875	−	0.0467543i
$694$	1.75193e11	+	4.48239e10i	0.755230	+	0.193229i
$695$	−1.06708e11	−	1.06708e11i	−0.457357	−	0.457357i
$696$	2.71671e10	+	1.01868e10i	0.115773	+	0.0434110i
$697$	−2.65436e11	−	2.65436e11i	−1.12468	−	1.12468i
$698$	−1.99834e11	+	1.18410e11i	−0.841874	+	0.498846i
$699$	−1.51681e10	−	6.28284e9i	−0.0635364	−	0.0263176i
$700$	3.53024e10	−	1.03212e10i	0.147032	−	0.0429870i
$701$	2.18495e11	−	9.05037e10i	0.904836	−	0.374795i	0.118758	−	0.992923i	$-0.462109\pi$
$701$	2.18495e11	−	9.05037e10i	0.904836	−	0.374795i	0.786077	+	0.618128i	$0.212109\pi$
$702$	−1.47962e9	−	1.03336e10i	−0.00609257	−	0.0425503i
$703$			2.41100e11i			0.987134i
$704$	−2.56069e10	−	5.16047e10i	−0.104247	−	0.210087i
$705$	−1.82574e10			−0.0739066
$706$	2.32489e11	−	3.32889e10i	0.935800	−	0.133993i
$707$	−8.43859e9	−	2.03726e10i	−0.0337748	−	0.0815395i
$708$	1.46890e10	+	5.02420e10i	0.0584599	+	0.199956i
$709$	1.11354e11	−	2.68832e11i	0.440677	−	1.06389i	−0.535034	−	0.844830i	$-0.679701\pi$
$709$	1.11354e11	−	2.68832e11i	0.440677	−	1.06389i	0.975712	−	0.219059i	$-0.0702986\pi$
$710$	2.07350e10	+	3.49933e10i	0.0815963	+	0.137706i
$711$	2.23533e11	−	2.23533e11i	0.874708	−	0.874708i
$712$	9.67693e10	+	3.62854e10i	0.376546	+	0.141192i
$713$	−1.25149e11	+	1.25149e11i	−0.484251	+	0.484251i
$714$	9.23627e9	−	3.60998e10i	0.0355389	−	0.138903i
$715$	−3.10989e9	+	7.50793e9i	−0.0118993	+	0.0287274i
$716$	−2.88959e11	+	2.32304e11i	−1.09947	+	0.883903i
$717$	2.80286e9	+	6.76671e9i	0.0106054	+	0.0256036i
$718$	2.74357e11	−	3.66054e11i	1.03233	−	1.37736i
$719$	−1.47731e11			−0.552786			−0.276393	−	0.961045i	$-0.589139\pi$
$719$	−1.47731e11			−0.552786			−0.276393	+	0.961045i	$0.589139\pi$
$720$	1.82363e11	+	1.27246e11i	0.678588	+	0.473494i
$721$		−	2.30589e11i		−	0.853293i
$722$	−1.60327e11	+	2.13912e11i	−0.590006	+	0.787202i
$723$	1.26710e10	−	5.24850e9i	0.0463722	−	0.0192080i
$724$	−1.69794e11	−	1.84544e10i	−0.617970	−	0.0671653i
$725$	−6.59425e10	−	2.73143e10i	−0.238679	−	0.0988639i
$726$	8.98369e9	−	3.51126e10i	0.0323376	−	0.126391i
$727$	2.72831e11	+	2.72831e11i	0.976688	+	0.976688i	0.999734	−	0.0230462i	$-0.00733647\pi$
$727$	2.72831e11	+	2.72831e11i	0.976688	+	0.976688i	−0.0230462	+	0.999734i	$0.507336\pi$
$728$	−2.34315e10	+	7.95958e8i	−0.0834208	+	0.00283377i
$729$	−1.77231e11	−	1.77231e11i	−0.627524	−	0.627524i
$730$	6.78636e10	+	1.14530e11i	0.238971	+	0.403298i
$731$	2.79418e10	+	1.15739e10i	0.0978554	+	0.0405330i
$732$	−4.02069e10	−	2.20153e10i	−0.140041	−	0.0766797i
$733$	−2.55474e11	+	1.05821e11i	−0.884976	+	0.366569i	−0.778425	−	0.627738i	$-0.783981\pi$
$733$	−2.55474e11	+	1.05821e11i	−0.884976	+	0.366569i	−0.106551	+	0.994307i	$0.533981\pi$
$734$	1.12480e11	−	1.61055e10i	0.387518	−	0.0554869i
$735$		−	2.44015e10i		−	0.0836116i
$736$	−3.84861e11	−	2.86500e10i	−1.31157	−	0.0976369i
$737$	−2.84663e10			−0.0964854
$738$	−3.35444e10	−	2.34273e11i	−0.113082	−	0.789762i
$739$	1.21004e11	+	2.92129e11i	0.405716	+	0.979484i	0.986252	+	0.165250i	$0.0528430\pi$
$739$	1.21004e11	+	2.92129e11i	0.405716	+	0.979484i	−0.580536	+	0.814234i	$0.697157\pi$
$740$	1.55496e11	+	8.51418e10i	0.518551	+	0.283933i
$741$	3.52611e9	−	8.51278e9i	0.0116956	−	0.0282357i
$742$	7.34796e10	−	4.35397e10i	0.242410	−	0.143638i
$743$	−8.82596e10	+	8.82596e10i	−0.289605	+	0.289605i	−0.836924	−	0.547319i	$-0.815649\pi$
$743$	−8.82596e10	+	8.82596e10i	−0.289605	+	0.289605i	0.547319	+	0.836924i	$0.315649\pi$
$744$	1.50371e10	−	1.60947e10i	0.0490765	−	0.0525279i
$745$	9.51167e10	−	9.51167e10i	0.308767	−	0.308767i
$746$	−4.56812e11	−	1.16877e11i	−1.47497	−	0.377376i
$747$	1.49575e11	−	3.61106e11i	0.480371	−	1.15972i
$748$	1.42737e11	+	1.55137e10i	0.455964	+	0.0495573i
$749$	3.96914e10	+	9.58235e10i	0.126116	+	0.304470i
$750$	3.79897e10	+	2.84732e10i	0.120066	+	0.0899893i
$751$	−3.92421e11			−1.23365			−0.616825	−	0.787100i	$-0.711581\pi$
$751$	−3.92421e11			−1.23365			−0.616825	+	0.787100i	$0.711581\pi$
$752$	1.70991e11	−	1.09328e11i	0.534689	−	0.341870i
$753$			8.15504e10i			0.253657i
$754$	3.64066e10	+	2.72867e10i	0.112641	+	0.0844238i
$755$	4.54135e11	−	1.88109e11i	1.39765	−	0.578924i
$756$	3.69743e10	−	2.97250e10i	0.113191	−	0.0909985i
$757$	5.76269e11	+	2.38699e11i	1.75486	+	0.726886i	0.997245	+	0.0741816i	$0.0236345\pi$
$757$	5.76269e11	+	2.38699e11i	1.75486	+	0.726886i	0.757613	+	0.652704i	$0.226366\pi$
$758$	−5.04173e11	−	1.28995e11i	−1.52722	−	0.390746i
$759$	9.99304e9	+	9.99304e9i	0.0301114	+	0.0301114i
$760$	1.64029e11	+	3.60837e11i	0.491662	+	1.08157i
$761$	−6.36634e10	−	6.36634e10i	−0.189824	−	0.189824i	0.605796	−	0.795620i	$-0.292855\pi$
$761$	−6.36634e10	−	6.36634e10i	−0.189824	−	0.189824i	−0.795620	+	0.605796i	$0.792855\pi$
$762$	−9.44377e8	+	5.59583e8i	−0.00280108	+	0.00165976i
$763$	−1.83697e11	−	7.60897e10i	−0.542005	−	0.224506i
$764$	−1.73300e11	−	5.92752e11i	−0.508656	−	1.73980i
$765$	−5.12021e11	+	2.12086e11i	−1.49500	+	0.619250i
$766$	5.43263e10	+	3.79413e11i	0.157796	+	1.10204i
$767$			8.20830e10i			0.237176i
$768$	4.79895e10	+	1.93738e9i	0.137944	+	0.00556890i
$769$	−1.23126e11			−0.352083			−0.176042	−	0.984383i	$-0.556329\pi$
$769$	−1.23126e11			−0.352083			−0.176042	+	0.984383i	$0.556329\pi$
$770$	−3.65591e10	+	5.23473e9i	−0.104000	+	0.0148912i
$771$	−2.28162e10	−	5.50832e10i	−0.0645693	−	0.155884i
$772$	1.69121e11	−	4.94450e10i	0.476134	−	0.139205i
$773$	−1.88098e11	+	4.54109e11i	−0.526825	+	1.27187i	0.406768	+	0.913532i	$0.366656\pi$
$773$	−1.88098e11	+	4.54109e11i	−0.526825	+	1.27187i	−0.933593	+	0.358336i	$0.883344\pi$
$774$	9.72002e9	+	1.64039e10i	0.0270834	+	0.0457072i
$775$	−3.83147e10	+	3.83147e10i	−0.106208	+	0.106208i
$776$	2.61425e10	−	1.18838e10i	0.0720941	−	0.0327725i
$777$	1.32433e10	−	1.32433e10i	0.0363340	−	0.0363340i
$778$	7.98242e10	−	3.11991e11i	0.217879	−	0.851577i
$779$	1.61434e11	−	3.89736e11i	0.438374	−	1.05833i
$780$	−4.24505e9	−	5.28033e9i	−0.0114684	−	0.0142654i
$781$	6.33631e9	+	1.52972e10i	0.0170307	+	0.0411157i
$782$	5.76857e11	−	7.69658e11i	1.54256	−	2.05812i
$783$	−9.20642e10			−0.244931
$784$	1.46120e11	+	2.28533e11i	0.386763	+	0.604902i
$785$			2.78601e11i			0.733675i
$786$	5.56919e10	−	7.43056e10i	0.145916	−	0.194685i
$787$	1.16266e11	−	4.81589e10i	0.303077	−	0.125539i	−0.225962	−	0.974136i	$-0.572553\pi$
$787$	1.16266e11	−	4.81589e10i	0.303077	−	0.125539i	0.529039	+	0.848598i	$0.322553\pi$
$788$	2.88091e10	−	2.65065e11i	0.0747178	−	0.687459i
$789$	−2.69263e10	−	1.11532e10i	−0.0694813	−	0.0287801i
$790$	1.02699e11	−	4.01399e11i	0.263669	−	1.03055i
$791$	2.44313e11	+	2.44313e11i	0.624080	+	0.624080i
$792$	6.61429e10	+	6.17968e10i	0.168106	+	0.157060i
$793$	−5.08278e10	−	5.08278e10i	−0.128531	−	0.128531i
$794$	−2.73009e11	−	4.60742e11i	−0.686903	−	1.15925i
$795$	2.28031e10	+	9.44535e9i	0.0570854	+	0.0236455i
$796$	−1.82683e11	+	3.33637e11i	−0.455037	+	0.831041i
$797$	5.53731e11	−	2.29363e11i	1.37235	−	0.568447i	0.429928	−	0.902863i	$-0.358539\pi$
$797$	5.53731e11	−	2.29363e11i	1.37235	−	0.568447i	0.942426	+	0.334416i	$0.108539\pi$
$798$	4.14522e10	−	5.93534e9i	0.102220	−	0.0146364i
$799$			5.05822e11i			1.24111i
$800$	−1.17826e11	−	8.77126e9i	−0.287661	−	0.0214142i
$801$	−1.62389e11			−0.394482
$802$	7.72860e10	+	5.39763e11i	0.186811	+	1.30468i
$803$	2.07381e10	+	5.00663e10i	0.0498778	+	0.120416i
$804$	1.13980e10	−	2.08163e10i	0.0272775	−	0.0498172i
$805$	−9.46802e10	+	2.28578e11i	−0.225463	+	0.544316i
$806$	2.97147e10	−	1.76072e10i	0.0704094	−	0.0417205i
$807$	3.70455e10	−	3.70455e10i	0.0873457	−	0.0873457i
$808$	2.40490e9	+	7.07955e10i	0.00564223	+	0.166096i
$809$	−4.96119e11	+	4.96119e11i	−1.15822	+	1.15822i	−0.173363	+	0.984858i	$0.555463\pi$
$809$	−4.96119e11	+	4.96119e11i	−1.15822	+	1.15822i	−0.984858	+	0.173363i	$0.944537\pi$
$810$	−3.31794e11	−	8.48908e10i	−0.770777	−	0.197206i
$811$	−1.33951e11	+	3.23385e11i	−0.309643	+	0.747544i	0.690074	+	0.723739i	$0.257578\pi$
$811$	−1.33951e11	+	3.23385e11i	−0.309643	+	0.747544i	−0.999717	+	0.0238051i	$0.992422\pi$
$812$	−2.23414e10	+	2.05557e11i	−0.0513909	+	0.472834i
$813$	3.53046e10	+	8.52329e10i	0.0808108	+	0.195095i
$814$	5.77458e10	+	4.32804e10i	0.131529	+	0.0985810i
$815$	3.86405e11			0.875815
$816$	−6.84968e10	+	9.81662e10i	−0.154493	+	0.221412i
$817$			3.39875e10i			0.0762836i
$818$	−2.77976e11	−	2.08342e11i	−0.620860	−	0.465333i
$819$	3.40344e10	−	1.40975e10i	0.0756455	−	0.0313334i
$820$	−1.94349e11	−	2.41747e11i	−0.429859	−	0.534693i
$821$	−4.24475e11	−	1.75823e11i	−0.934285	−	0.386993i	−0.136982	−	0.990574i	$-0.543740\pi$
$821$	−4.24475e11	−	1.75823e11i	−0.934285	−	0.386993i	−0.797302	+	0.603580i	$0.793740\pi$
$822$	−4.90358e10	−	1.25460e10i	−0.107405	−	0.0274801i
$823$	8.17021e10	+	8.17021e10i	0.178088	+	0.178088i	0.790522	−	0.612434i	$-0.209809\pi$
$823$	8.17021e10	+	8.17021e10i	0.178088	+	0.178088i	−0.612434	+	0.790522i	$0.709809\pi$
$824$	−2.60071e11	+	6.93582e11i	−0.564135	+	1.50449i
$825$	3.05939e9	+	3.05939e9i	0.00660417	+	0.00660417i
$826$	−3.20927e11	+	1.90163e11i	−0.689424	+	0.408512i
$827$	1.66103e11	+	6.88021e10i	0.355104	+	0.147089i	0.553102	−	0.833114i	$-0.313444\pi$
$827$	1.66103e11	+	6.88021e10i	0.355104	+	0.147089i	−0.197998	+	0.980202i	$0.563444\pi$
$828$	5.82032e11	−	1.70165e11i	1.23830	−	0.362035i
$829$	2.04254e11	−	8.46048e10i	0.432467	−	0.179134i	−0.155821	−	0.987785i	$-0.549802\pi$
$829$	2.04254e11	−	8.46048e10i	0.432467	−	0.179134i	0.588288	+	0.808652i	$0.299802\pi$
$830$	−7.26103e10	−	5.07108e11i	−0.152998	−	1.06853i
$831$			4.66765e10i			0.0978801i
$832$	7.13766e10	+	2.40332e10i	0.148958	+	0.0501554i
$833$	−6.76042e11			−1.40409
$834$	5.06971e10	−	7.25907e9i	0.104790	−	0.0150043i
$835$	1.07790e11	+	2.60228e11i	0.221734	+	0.535314i
$836$	4.52774e10	+	1.54866e11i	0.0926951	+	0.317053i
$837$	−2.67461e10	+	6.45708e10i	−0.0544953	+	0.131563i
$838$	4.05763e11	+	6.84783e11i	0.822804	+	1.38860i
$839$	1.27994e11	−	1.27994e11i	0.258311	−	0.258311i	−0.566056	−	0.824367i	$-0.691531\pi$
$839$	1.27994e11	−	1.27994e11i	0.258311	−	0.258311i	0.824367	+	0.566056i	$0.191531\pi$
$840$	1.08104e10	−	2.88302e10i	0.0217133	−	0.0579070i
$841$	−6.99990e10	+	6.99990e10i	−0.139929	+	0.139929i
$842$	6.29247e10	−	2.45940e11i	0.125191	−	0.489306i
$843$	−1.71175e10	+	4.13252e10i	−0.0338945	+	0.0818286i
$844$	−1.07841e11	+	8.66969e10i	−0.212526	+	0.170857i
$845$	1.60511e11	+	3.87507e11i	0.314830	+	0.760068i
$846$	−1.91257e11	+	2.55180e11i	−0.373366	+	0.498155i
$847$	2.58289e11			0.501848
$848$	−2.70123e11	+	4.80876e10i	−0.522371	+	0.0929928i
$849$			1.91754e10i			0.0369074i
$850$	1.76606e11	−	2.35632e11i	0.338321	−	0.451397i
$851$	4.46640e11	−	1.85004e11i	0.851608	−	0.352747i
$852$	−1.37233e10	−	1.49155e9i	−0.0260436	−	0.00283060i
$853$	−7.95834e10	−	3.29645e10i	−0.150323	−	0.0622659i	0.306253	−	0.951950i	$-0.400925\pi$
$853$	−7.95834e10	−	3.29645e10i	−0.150323	−	0.0622659i	−0.456577	+	0.889684i	$0.650925\pi$
$854$	8.09725e10	−	3.16479e11i	0.152232	−	0.594996i
$855$	−4.40391e11	−	4.40391e11i	−0.824088	−	0.824088i
$856$	−1.13116e10	−	3.32990e11i	−0.0210682	−	0.620207i
$857$	3.03128e10	+	3.03128e10i	0.0561956	+	0.0561956i	0.734646	−	0.678451i	$-0.237348\pi$
$857$	3.03128e10	+	3.03128e10i	0.0561956	+	0.0561956i	−0.678451	+	0.734646i	$0.737348\pi$
$858$	−1.40591e9	−	2.37268e9i	−0.00259424	−	0.00437815i
$859$	5.61370e10	+	2.32527e10i	0.103104	+	0.0427072i	0.433639	−	0.901087i	$-0.357229\pi$
$859$	5.61370e10	+	2.32527e10i	0.103104	+	0.0427072i	−0.330535	+	0.943794i	$0.607229\pi$
$860$	2.19200e10	+	1.20023e10i	0.0400725	+	0.0219417i
$861$	−3.02751e10	+	1.25404e10i	−0.0550900	+	0.0228190i
$862$	−5.71790e11	+	8.18719e10i	−1.03564	+	0.148288i
$863$			3.60402e11i			0.649746i	0.945758	+	0.324873i	$0.105322\pi$
$863$			3.60402e11i			0.649746i	−0.945758	+	0.324873i	$0.894678\pi$
$864$	−1.44739e11	+	4.77071e10i	−0.259735	+	0.0856108i
$865$	6.21383e11			1.10993
$866$	−3.01765e10	−	2.10751e11i	−0.0536534	−	0.374713i
$867$	−8.43144e10	−	2.03553e11i	−0.149219	−	0.360247i
$868$	1.37681e11	+	7.53872e10i	0.242546	+	0.132806i
$869$	6.45434e10	−	1.55821e11i	0.113181	−	0.273242i
$870$	−5.14050e10	+	3.04596e10i	−0.0897281	+	0.0531677i
$871$	2.63151e10	−	2.63151e10i	0.0457227	−	0.0457227i
$872$	4.66718e11	+	4.36051e11i	0.807214	+	0.754174i
$873$	−3.19061e10	+	3.19061e10i	−0.0549309	+	0.0549309i
$874$	1.04717e12	+	2.67921e11i	1.79461	+	0.459157i
$875$	−1.29475e11	+	3.12579e11i	−0.220878	+	0.533246i
$876$	−4.49151e10	−	4.88168e9i	−0.0762739	−	0.00828997i
$877$	−3.66067e11	−	8.83763e11i	−0.618817	−	1.49396i	−0.853079	−	0.521782i	$-0.825267\pi$
$877$	−3.66067e11	−	8.83763e11i	−0.618817	−	1.49396i	0.234262	−	0.972173i	$-0.424733\pi$
$878$	4.24165e11	+	3.17911e11i	0.713768	+	0.534967i
$879$	−1.16114e11			−0.194504
$880$	1.15869e11	+	2.54880e10i	0.193213	+	0.0425016i
$881$		−	4.51176e11i		−	0.748932i	−0.927241	−	0.374466i	$-0.877826\pi$
$881$		−	4.51176e11i		−	0.748932i	0.927241	−	0.374466i	$-0.122174\pi$
$882$	−3.41053e11	−	2.55619e11i	−0.563570	−	0.422395i
$883$	−7.88917e11	+	3.26780e11i	−1.29774	+	0.537543i	−0.921284	−	0.388890i	$-0.872858\pi$
$883$	−7.88917e11	+	3.26780e11i	−1.29774	+	0.537543i	−0.376459	+	0.926433i	$0.622858\pi$
$884$	−1.46291e11	+	1.17609e11i	−0.239558	+	0.192589i
$885$	−9.95940e10	−	4.12532e10i	−0.162353	−	0.0672488i
$886$	−2.54799e11	−	6.51914e10i	−0.413488	−	0.105793i
$887$	3.02343e11	+	3.02343e11i	0.488434	+	0.488434i	0.907812	−	0.419378i	$-0.137752\pi$
$887$	3.02343e11	+	3.02343e11i	0.488434	+	0.488434i	−0.419378	+	0.907812i	$0.637752\pi$
$888$	−5.47708e10	+	2.48977e10i	−0.0880840	+	0.0400412i
$889$	−5.53158e9	−	5.53158e9i	−0.00885609	−	0.00885609i
$890$	−1.83105e11	+	1.08497e11i	−0.291837	+	0.172926i
$891$	−1.28801e11	−	5.33512e10i	−0.204366	−	0.0846513i
$892$	−1.49718e10	−	5.12094e10i	−0.0236491	−	0.0808891i
$893$	−5.25162e11	+	2.17529e11i	−0.825825	+	0.342068i
$894$	6.47057e9	+	4.51902e10i	0.0101296	+	0.0707448i
$895$		−	7.63541e11i		−	1.18998i
$896$	7.13945e10	+	3.34745e11i	0.110773	+	0.519377i
$897$	−1.84757e10			−0.0285385
$898$	3.64353e11	−	5.21700e10i	0.560296	−	0.0802261i
$899$	−1.16570e11	−	2.81426e11i	−0.178463	−	0.430849i
$900$	1.78190e11	−	5.20964e10i	0.271590	−	0.0794032i
$901$	2.61683e11	−	6.31759e11i	0.397079	−	0.958633i
$902$	−6.43662e10	−	1.08627e11i	−0.0972371	−	0.164102i
$903$	1.86689e9	−	1.86689e9i	0.00280782	−	0.00280782i
$904$	−4.59311e11	−	1.01041e12i	−0.687754	−	1.51295i
$905$	2.48712e11	−	2.48712e11i	0.370769	−	0.370769i
$906$	−4.13497e10	+	1.61615e11i	−0.0613706	+	0.239866i
$907$	2.58931e11	−	6.25114e11i	0.382608	−	0.923698i	−0.608852	−	0.793284i	$-0.708369\pi$
$907$	2.58931e11	−	6.25114e11i	0.382608	−	0.923698i	0.991460	−	0.130414i	$-0.0416305\pi$
$908$	−2.93600e11	−	3.65204e11i	−0.431930	−	0.537269i
$909$	−4.25940e10	−	1.02831e11i	−0.0623868	−	0.150615i
$910$	2.89572e10	−	3.86354e10i	0.0422270	−	0.0563404i
$911$	8.74775e11			1.27006			0.635028	−	0.772489i	$-0.280989\pi$
$911$	8.74775e11			1.27006			0.635028	+	0.772489i	$0.280989\pi$
$912$	−1.31377e11	−	2.88993e10i	−0.189906	−	0.0417742i
$913$		−	2.08533e11i		−	0.300118i
$914$	−3.28487e11	+	4.38276e11i	−0.470688	+	0.628005i
$915$	8.72161e10	−	3.61261e10i	0.124426	−	0.0515391i
$916$	−1.05465e11	+	9.70355e11i	−0.149805	+	1.37832i
$917$	6.11387e11	+	2.53245e11i	0.864647	+	0.358148i
$918$	9.41464e10	−	3.67970e11i	0.132566	−	0.518133i
$919$	−5.06922e11	−	5.06922e11i	−0.710688	−	0.710688i	0.255991	−	0.966679i	$-0.417598\pi$
$919$	−5.06922e11	−	5.06922e11i	−0.710688	−	0.710688i	−0.966679	+	0.255991i	$0.917598\pi$
$920$	5.42588e11	−	5.80748e11i	0.757389	−	0.810655i
$921$	8.91331e10	+	8.91331e10i	0.123880	+	0.123880i
$922$	3.35689e11	+	5.66523e11i	0.464529	+	0.783960i
$923$	−1.99986e10	−	8.28371e9i	−0.0275546	−	0.0114135i
$924$	6.01959e9	−	1.09937e10i	0.00825808	−	0.0150818i
$925$	1.36740e11	−	5.66394e10i	0.186779	−	0.0773663i
$926$	−8.02288e11	+	1.14876e11i	−1.09116	+	0.156237i
$927$		−	1.16391e12i		−	1.57615i
$928$	2.99039e11	−	5.93092e11i	0.403214	−	0.799706i
$929$	1.59343e11			0.213929			0.106965	−	0.994263i	$-0.465887\pi$
$929$	1.59343e11			0.213929			0.106965	+	0.994263i	$0.465887\pi$
$930$	6.42942e9	+	4.49028e10i	0.00859488	+	0.0600263i
$931$	−2.90733e11	−	7.01891e11i	−0.386986	−	0.934268i
$932$	−1.80509e11	+	3.29667e11i	−0.239241	+	0.436930i
$933$	5.68400e10	−	1.37224e11i	0.0750114	−	0.181094i
$934$	4.63462e10	−	2.74621e10i	0.0609013	−	0.0360866i
$935$	−2.09080e11	+	2.09080e11i	−0.273568	+	0.273568i
$936$	−1.18271e11	+	4.01762e9i	−0.154090	+	0.00523438i
$937$	8.28396e11	−	8.28396e11i	1.07468	−	1.07468i	0.0777053	−	0.996976i	$-0.475241\pi$
$937$	8.28396e11	−	8.28396e11i	1.07468	−	1.07468i	0.996976	−	0.0777053i	$-0.0247593\pi$
$938$	1.63851e11	+	4.19219e10i	0.211659	+	0.0541539i
$939$	−2.69644e10	+	6.50979e10i	−0.0346840	+	0.0837346i
$940$	−4.51613e10	+	4.15517e11i	−0.0578436	+	0.532204i
$941$	2.70475e10	+	6.52985e10i	0.0344960	+	0.0832808i	0.940189	−	0.340654i	$-0.110649\pi$
$941$	2.70475e10	+	6.52985e10i	0.0344960	+	0.0832808i	−0.905693	+	0.423935i	$0.860649\pi$
$942$	−7.56583e10	−	5.67058e10i	−0.0960845	−	0.0720151i
$943$	−8.45863e11			−1.06968
$944$	1.17978e12	−	2.10026e11i	1.48564	−	0.264475i
$945$			9.77005e10i			0.122509i
$946$	8.14034e9	+	6.10117e9i	0.0101643	+	0.00761813i
$947$	−1.15933e12	+	4.80212e11i	−1.44148	+	0.597081i	−0.960157	−	0.279463i	$-0.909844\pi$
$947$	−1.15933e12	+	4.80212e11i	−1.44148	+	0.597081i	−0.481323	+	0.876543i	$0.659844\pi$
$948$	8.81028e10	+	1.09589e11i	0.109083	+	0.135686i
$949$	−6.54536e10	−	2.71118e10i	−0.0806991	−	0.0334267i
$950$	3.20591e11	+	8.20245e10i	0.393602	+	0.100705i
$951$	1.25412e11	+	1.25412e11i	0.153327	+	0.153327i
$952$	−7.98741e11	−	2.99502e11i	−0.972430	−	0.364630i
$953$	1.96515e11	+	1.96515e11i	0.238245	+	0.238245i	0.816123	−	0.577878i	$-0.196119\pi$
$953$	1.96515e11	+	1.96515e11i	0.238245	+	0.238245i	−0.577878	+	0.816123i	$0.696119\pi$
$954$	3.70890e11	−	2.19768e11i	0.447767	−	0.265321i
$955$	1.17500e12	+	4.86703e11i	1.41262	+	0.585127i
$956$	1.60935e11	−	4.70518e10i	0.192673	−	0.0563306i
$957$	−2.24715e10	+	9.30802e9i	−0.0267908	+	0.0110971i
$958$	1.86828e11	+	1.30480e12i	0.221809	+	1.54911i
$959$		−	3.60708e11i		−	0.426463i
$960$	−6.50326e10	+	7.45250e10i	−0.0765678	+	0.0877439i
$961$	6.21643e11			0.728865
$962$	−9.33915e10	+	1.33723e10i	−0.109045	+	0.0156137i
$963$	2.00343e11	+	4.83671e11i	0.232954	+	0.562400i
$964$	−8.81068e10	−	3.01360e11i	−0.102024	−	0.348961i
$965$	−1.38864e11	+	3.35247e11i	−0.160133	+	0.386594i
$966$	−4.28029e10	−	7.22361e10i	−0.0491547	−	0.0829556i
$967$	−8.95823e11	+	8.95823e11i	−1.02451	+	1.02451i	−0.0248182	+	0.999692i	$0.507901\pi$
$967$	−8.95823e11	+	8.95823e11i	−1.02451	+	1.02451i	−0.999692	+	0.0248182i	$0.992099\pi$
$968$	−7.76899e11	−	2.91312e11i	−0.884837	−	0.331785i
$969$	2.37063e11	−	2.37063e11i	0.268886	−	0.268886i
$970$	−1.46588e10	+	5.72938e10i	−0.0165582	+	0.0647174i
$971$	−1.36195e11	+	3.28803e11i	−0.153209	+	0.369878i	−0.981784	−	0.189999i	$-0.939152\pi$
$971$	−1.36195e11	+	3.28803e11i	−0.153209	+	0.369878i	0.828576	+	0.559877i	$0.189152\pi$
$972$	2.80841e11	−	2.25778e11i	0.314626	−	0.252939i
$973$	1.39670e11	+	3.37193e11i	0.155830	+	0.376208i
$974$	−9.90042e11	+	1.32094e12i	−1.10006	+	1.46773i
$975$	−5.65637e9			−0.00625920
$976$	−6.00497e11	+	8.60603e11i	−0.661777	+	0.948427i
$977$			7.16818e11i			0.786739i	0.919381	+	0.393369i	$0.128691\pi$
$977$			7.16818e11i			0.786739i	−0.919381	+	0.393369i	$0.871309\pi$
$978$	−7.86480e10	+	1.04934e11i	−0.0859671	+	0.114700i
$979$	−8.00438e10	+	3.31552e10i	−0.0871359	+	0.0360929i
$980$	−5.55348e11	−	6.03591e10i	−0.602090	−	0.0654393i
$981$	−9.27214e11	−	3.84065e11i	−1.00116	−	0.414695i
$982$	−4.32251e11	+	1.68944e12i	−0.464825	+	1.81676i
$983$	−5.13349e11	−	5.13349e11i	−0.549793	−	0.549793i	0.376588	−	0.926381i	$-0.377097\pi$
$983$	−5.13349e11	−	5.13349e11i	−0.549793	−	0.549793i	−0.926381	+	0.376588i	$0.877097\pi$
$984$	1.05207e11	−	3.57385e9i	0.112219	−	0.00381202i
$985$	3.88264e11	+	3.88264e11i	0.412461	+	0.412461i
$986$	8.43883e11	+	1.42417e12i	0.892842	+	1.50680i
$987$	4.07952e10	+	1.68979e10i	0.0429873	+	0.0178059i
$988$	−1.85019e11	−	1.01307e11i	−0.194173	−	0.106319i
$989$	6.29622e10	−	2.60798e10i	0.0658104	−	0.0272596i
$990$	−1.84533e11	+	2.64224e10i	−0.192103	+	0.0275063i
$991$			4.86131e11i			0.504033i	0.967723	+	0.252016i	$0.0810937\pi$
$991$			4.86131e11i			0.504033i	−0.967723	+	0.252016i	$0.918906\pi$
$992$	−3.29100e11	−	3.82039e11i	−0.339845	−	0.394512i
$993$	7.93732e10			0.0816351
$994$	−1.39436e10	−	9.73814e10i	−0.0142833	−	0.0997540i
$995$	−2.99775e11	−	7.23721e11i	−0.305846	−	0.738378i
$996$	1.52492e11	+	8.34971e10i	0.154956	+	0.0848465i
$997$	−5.88816e11	+	1.42153e12i	−0.595935	+	1.43872i	0.281755	+	0.959486i	$0.409084\pi$
$997$	−5.88816e11	+	1.42153e12i	−0.595935	+	1.43872i	−0.877690	+	0.479229i	$0.840916\pi$
$998$	9.61366e11	−	5.69650e11i	0.969095	−	0.574230i
$999$	1.34991e11	−	1.34991e11i	0.135532	−	0.135532i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.9.h.a.11.1	yes	124
32.3	odd	8	inner	32.9.h.a.3.1	✓	124

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.9.h.a.3.1	✓	124	32.3	odd	8	inner
32.9.h.a.11.1	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)

\(f(q)\)	\(=\)	\(q+(-15.8385 + 2.26783i) q^{2} +(4.27937 + 10.3313i) q^{3} +(245.714 - 71.8380i) q^{4} +(-201.753 + 487.075i) q^{5} +(-91.2084 - 153.927i) q^{6} +(901.611 - 901.611i) q^{7} +(-3728.81 + 1695.04i) q^{8} +(4550.90 - 4550.90i) q^{9} +O(q^{10})\)	\(q+(-15.8385 + 2.26783i) q^{2} +(4.27937 + 10.3313i) q^{3} +(245.714 - 71.8380i) q^{4} +(-201.753 + 487.075i) q^{5} +(-91.2084 - 153.927i) q^{6} +(901.611 - 901.611i) q^{7} +(-3728.81 + 1695.04i) q^{8} +(4550.90 - 4550.90i) q^{9} +(2090.85 - 8172.06i) q^{10} +(1314.04 - 3172.37i) q^{11} +(1793.68 + 2231.13i) q^{12} +(1717.89 + 4147.36i) q^{13} +(-12235.4 + 16324.8i) q^{14} -5895.50 q^{15} +(55214.6 - 35303.2i) q^{16} +163335. i q^{17} +(-61758.6 + 82400.0i) q^{18} +(-169580. + 70242.4i) q^{19} +(-14583.0 + 134175. i) q^{20} +(13173.2 + 5456.50i) q^{21} +(-13617.9 + 53225.4i) q^{22} +(260249. + 260249. i) q^{23} +(-33469.0 - 31269.8i) q^{24} +(79675.7 + 79675.7i) q^{25} +(-36614.3 - 61791.9i) q^{26} +(134276. + 55618.8i) q^{27} +(156768. - 286308. i) q^{28} +(-585227. + 242409. i) q^{29} +(93375.7 - 13370.0i) q^{30} +480883. i q^{31} +(-794453. + 684366. i) q^{32} +38398.0 q^{33} +(-370416. - 2.58697e6i) q^{34} +(257249. + 621055. i) q^{35} +(791292. - 1.44515e6i) q^{36} +(502664. - 1.21354e6i) q^{37} +(2.52659e6 - 1.49711e6i) q^{38} +(-35496.2 + 35496.2i) q^{39} +(-73312.9 - 2.15819e6i) q^{40} +(-1.62510e6 + 1.62510e6i) q^{41} +(-221017. - 56548.1i) q^{42} +(70859.8 - 171071. i) q^{43} +(94980.7 - 873892. i) q^{44} +(1.29847e6 + 3.13479e6i) q^{45} +(-4.71215e6 - 3.53175e6i) q^{46} +3.09684e6 q^{47} +(601012. + 419364. i) q^{48} +4.13900e6i q^{49} +(-1.44263e6 - 1.08125e6i) q^{50} +(-1.68746e6 + 698971. i) q^{51} +(720048. + 895654. i) q^{52} +(-3.86788e6 - 1.60213e6i) q^{53} +(-2.25285e6 - 576401. i) q^{54} +(1.28007e6 + 1.28007e6i) q^{55} +(-1.83367e6 + 4.89021e6i) q^{56} +(-1.45139e6 - 1.45139e6i) q^{57} +(8.71936e6 - 5.16658e6i) q^{58} +(1.68932e7 + 6.99740e6i) q^{59} +(-1.44861e6 + 423521. i) q^{60} +(-1.47937e7 + 6.12773e6i) q^{61} +(-1.09056e6 - 7.61645e6i) q^{62} -8.20629e6i q^{63} +(1.10309e7 - 1.26410e7i) q^{64} -2.36667e6 q^{65} +(-608165. + 87080.2i) q^{66} +(-3.17251e6 - 7.65912e6i) q^{67} +(1.17336e7 + 4.01336e7i) q^{68} +(-1.57501e6 + 3.80242e6i) q^{69} +(-5.48289e6 - 9.25316e6i) q^{70} +(-3.40968e6 + 3.40968e6i) q^{71} +(-9.25550e6 + 2.46834e7i) q^{72} +(-1.11596e7 + 1.11596e7i) q^{73} +(-5.20932e6 + 2.03605e7i) q^{74} +(-482193. + 1.16412e6i) q^{75} +(-3.66221e7 + 2.94418e7i) q^{76} +(-1.67549e6 - 4.04499e6i) q^{77} +(481706. - 642704. i) q^{78} +4.91184e7 q^{79} +(6.05559e6 + 3.40162e7i) q^{80} -4.06010e7i q^{81} +(2.20537e7 - 2.94246e7i) q^{82} +(5.61076e7 - 2.32405e7i) q^{83} +(3.62881e6 + 394405. i) q^{84} +(-7.95563e7 - 3.29533e7i) q^{85} +(-734350. + 2.87019e6i) q^{86} +(-5.00881e6 - 5.00881e6i) q^{87} +(477494. + 1.40565e7i) q^{88} +(-1.78414e7 - 1.78414e7i) q^{89} +(-2.76750e7 - 4.67056e7i) q^{90} +(5.28817e6 + 2.19043e6i) q^{91} +(8.26426e7 + 4.52511e7i) q^{92} +(-4.96815e6 + 2.05788e6i) q^{93} +(-4.90492e7 + 7.02312e6i) q^{94} -9.67699e7i q^{95} +(-1.04702e7 - 5.27909e6i) q^{96} -7.01094e6 q^{97} +(-9.38655e6 - 6.55553e7i) q^{98} +(-8.45708e6 - 2.04172e7i) 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

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