LMFDB - Embedded newform 429.2.bm.a.413.40

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(17,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 27, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("429.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bm (of order $30$, degree $8$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			413.40
Character	$\chi$	$=$	429.413
Dual form			429.2.bm.a.134.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.27986 + 1.15239i) q^{2} +(-1.73168 - 0.0360263i) q^{3} +(0.100980 + 0.960764i) q^{4} +(0.368818 - 1.13510i) q^{5} +(-2.17479 - 2.04168i) q^{6} +(0.130072 + 1.23755i) q^{7} +(1.04666 - 1.44060i) q^{8} +(2.99740 + 0.124772i) q^{9} +O(q^{10})$	\(q+(1.27986 + 1.15239i) q^{2} +(-1.73168 - 0.0360263i) q^{3} +(0.100980 + 0.960764i) q^{4} +(0.368818 - 1.13510i) q^{5} +(-2.17479 - 2.04168i) q^{6} +(0.130072 + 1.23755i) q^{7} +(1.04666 - 1.44060i) q^{8} +(2.99740 + 0.124772i) q^{9} +(1.78012 - 1.02775i) q^{10} +(2.50916 - 2.16889i) q^{11} +(-0.140253 - 1.66737i) q^{12} +(1.95174 + 3.03162i) q^{13} +(-1.25967 + 1.73379i) q^{14} +(-0.679567 + 1.95235i) q^{15} +(4.88961 - 1.03932i) q^{16} +(-0.467929 - 0.519688i) q^{17} +(3.69248 + 3.61388i) q^{18} +(-0.638873 + 0.284445i) q^{19} +(1.12781 + 0.239724i) q^{20} +(-0.180658 - 2.14772i) q^{21} +(5.71080 + 0.115658i) q^{22} +(2.00409 - 1.15706i) q^{23} +(-1.86437 + 2.45695i) q^{24} +(2.89265 + 2.10163i) q^{25} +(-0.995668 + 6.12922i) q^{26} +(-5.18604 - 0.324050i) q^{27} +(-1.17586 + 0.249937i) q^{28} +(2.81676 + 1.25410i) q^{29} +(-3.11962 + 1.71561i) q^{30} +(0.786706 - 0.255616i) q^{31} +(4.37150 + 2.52389i) q^{32} +(-4.42320 + 3.66543i) q^{33} -1.20437i q^{34} +(1.45272 + 0.308786i) q^{35} +(0.182803 + 2.89240i) q^{36} +(0.203215 - 0.456429i) q^{37} +(-1.14546 - 0.372183i) q^{38} +(-3.27055 - 5.32010i) q^{39} +(-1.24921 - 1.71939i) q^{40} +(-4.32445 - 0.454518i) q^{41} +(2.24381 - 2.95698i) q^{42} +(-9.76151 - 5.63581i) q^{43} +(2.33717 + 2.19170i) q^{44} +(1.24713 - 3.35635i) q^{45} +(3.89834 + 0.828618i) q^{46} +(-4.69563 - 3.41158i) q^{47} +(-8.50467 + 1.62361i) q^{48} +(5.33242 - 1.13344i) q^{49} +(1.28029 + 6.02327i) q^{50} +(0.791579 + 0.916788i) q^{51} +(-2.71559 + 2.18129i) q^{52} +(-8.86976 + 2.88196i) q^{53} +(-6.26398 - 6.39109i) q^{54} +(-1.53650 - 3.64809i) q^{55} +(1.91896 + 1.10791i) q^{56} +(1.11657 - 0.469550i) q^{57} +(2.15985 + 4.85110i) q^{58} +(0.558197 + 5.31089i) q^{59} +(-1.94437 - 0.455755i) q^{60} +(4.64648 - 4.18371i) q^{61} +(1.30144 + 0.579441i) q^{62} +(0.235466 + 3.72567i) q^{63} +(-0.403051 - 1.24046i) q^{64} +(4.16104 - 1.09731i) q^{65} +(-9.88509 - 0.406021i) q^{66} +(6.76153 - 3.90377i) q^{67} +(0.452046 - 0.502048i) q^{68} +(-3.51211 + 1.93145i) q^{69} +(1.50344 + 2.06931i) q^{70} +(-0.725281 - 0.805506i) q^{71} +(3.31701 - 4.18747i) q^{72} +(-7.27022 + 5.28212i) q^{73} +(0.786073 - 0.349982i) q^{74} +(-4.93342 - 3.74356i) q^{75} +(-0.337798 - 0.585083i) q^{76} +(3.01049 + 2.82311i) q^{77} +(1.94499 - 10.5780i) q^{78} +(-6.44207 + 2.09316i) q^{79} +(0.623640 - 5.93354i) q^{80} +(8.96886 + 0.747984i) q^{81} +(-5.01092 - 5.56519i) q^{82} +(-7.61540 - 2.47439i) q^{83} +(2.04521 - 0.390448i) q^{84} +(-0.762480 + 0.339478i) q^{85} +(-5.99872 - 18.4622i) q^{86} +(-4.83254 - 2.27318i) q^{87} +(-0.498275 - 5.88480i) q^{88} +(7.39533 + 12.8091i) q^{89} +(5.46398 - 2.85849i) q^{90} +(-3.49792 + 2.80970i) q^{91} +(1.31404 + 1.80861i) q^{92} +(-1.37153 + 0.414302i) q^{93} +(-2.07829 - 9.77757i) q^{94} +(0.0872467 + 0.830097i) q^{95} +(-7.47909 - 4.52804i) q^{96} +(-1.65673 + 7.79430i) q^{97} +(8.13093 + 4.69439i) q^{98} +(7.79159 - 6.18798i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 3 q^{3} - 54 q^{4} - 15 q^{6} - 30 q^{7} - 9 q^{9}+O(q^{10}) $ 416 * q - 3 * q^3 - 54 * q^4 - 15 * q^6 - 30 * q^7 - 9 * q^9	$ 416 q - 3 q^{3} - 54 q^{4} - 15 q^{6} - 30 q^{7} - 9 q^{9} - 36 q^{12} - 20 q^{13} - 9 q^{15} + 14 q^{16} - 30 q^{19} - 28 q^{22} + 15 q^{24} - 84 q^{25} - 24 q^{27} - 30 q^{28} - 5 q^{30} - 27 q^{33} - 73 q^{36} - 18 q^{37} - 65 q^{39} - 120 q^{40} - 25 q^{42} + 36 q^{45} + 30 q^{46} - 41 q^{48} + 14 q^{49} + 60 q^{51} + 20 q^{52} + 18 q^{55} - 126 q^{58} - 30 q^{61} + 105 q^{63} - 56 q^{64} + 170 q^{66} - 33 q^{69} - 195 q^{72} + 77 q^{75} + 4 q^{78} - 13 q^{81} + 36 q^{82} - 60 q^{84} - 30 q^{85} + 38 q^{88} - 190 q^{90} - 56 q^{91} + 24 q^{93} - 90 q^{94} + 54 q^{97}+O(q^{100}) $ 416 * q - 3 * q^3 - 54 * q^4 - 15 * q^6 - 30 * q^7 - 9 * q^9 - 36 * q^12 - 20 * q^13 - 9 * q^15 + 14 * q^16 - 30 * q^19 - 28 * q^22 + 15 * q^24 - 84 * q^25 - 24 * q^27 - 30 * q^28 - 5 * q^30 - 27 * q^33 - 73 * q^36 - 18 * q^37 - 65 * q^39 - 120 * q^40 - 25 * q^42 + 36 * q^45 + 30 * q^46 - 41 * q^48 + 14 * q^49 + 60 * q^51 + 20 * q^52 + 18 * q^55 - 126 * q^58 - 30 * q^61 + 105 * q^63 - 56 * q^64 + 170 * q^66 - 33 * q^69 - 195 * q^72 + 77 * q^75 + 4 * q^78 - 13 * q^81 + 36 * q^82 - 60 * q^84 - 30 * q^85 + 38 * q^88 - 190 * q^90 - 56 * q^91 + 24 * q^93 - 90 * q^94 + 54 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{10}\right)$	$-1$

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 $

$2$	1.27986	+	1.15239i	0.904999	+	0.814865i	0.983286	−	0.182066i	$-0.0582784\pi$
$2$	1.27986	+	1.15239i	0.904999	+	0.814865i	−0.0782872	+	0.996931i	$0.524945\pi$
$3$	−1.73168	−	0.0360263i	−0.999784	−	0.0207998i
$3$	−1.73168	−	0.0360263i	−0.999784	−	0.0207998i
$4$	0.100980	+	0.960764i	0.0504902	+	0.480382i
$5$	0.368818	−	1.13510i	0.164940	−	0.507634i	−0.834092	−	0.551626i	$-0.814008\pi$
$5$	0.368818	−	1.13510i	0.164940	−	0.507634i	0.999032	+	0.0439918i	$0.0140076\pi$
$6$	−2.17479	−	2.04168i	−0.887854	−	0.833512i
$7$	0.130072	+	1.23755i	0.0491626	+	0.467751i	0.991213	+	0.132278i	$0.0422292\pi$
$7$	0.130072	+	1.23755i	0.0491626	+	0.467751i	−0.942050	+	0.335472i	$0.891104\pi$
$8$	1.04666	−	1.44060i	0.370050	−	0.509330i
$9$	2.99740	+	0.124772i	0.999135	+	0.0415906i
$10$	1.78012	−	1.02775i	0.562924	−	0.325004i
$11$	2.50916	−	2.16889i	0.756541	−	0.653946i
$11$	2.50916	−	2.16889i	0.756541	−	0.653946i
$12$	−0.140253	−	1.66737i	−0.0404874	−	0.481328i
$13$	1.95174	+	3.03162i	0.541314	+	0.840821i
$13$	1.95174	+	3.03162i	0.541314	+	0.840821i
$14$	−1.25967	+	1.73379i	−0.336661	+	0.463375i
$15$	−0.679567	+	1.95235i	−0.175463	+	0.504094i
$16$	4.88961	−	1.03932i	1.22240	−	0.259830i
$17$	−0.467929	−	0.519688i	−0.113489	−	0.126043i	0.683723	−	0.729742i	$-0.260360\pi$
$17$	−0.467929	−	0.519688i	−0.113489	−	0.126043i	−0.797212	+	0.603699i	$0.793693\pi$
$18$	3.69248	+	3.61388i	0.870325	+	0.851799i
$19$	−0.638873	+	0.284445i	−0.146568	+	0.0652561i	−0.478710	−	0.877973i	$-0.658895\pi$
$19$	−0.638873	+	0.284445i	−0.146568	+	0.0652561i	0.332142	+	0.943229i	$0.392229\pi$
$20$	1.12781	+	0.239724i	0.252186	+	0.0536039i
$21$	−0.180658	−	2.14772i	−0.0394228	−	0.468672i
$22$	5.71080	+	0.115658i	1.21755	+	0.0246583i
$23$	2.00409	−	1.15706i	0.417881	−	0.241264i	−0.276289	−	0.961075i	$-0.589105\pi$
$23$	2.00409	−	1.15706i	0.417881	−	0.241264i	0.694170	+	0.719811i	$0.255771\pi$
$24$	−1.86437	+	2.45695i	−0.380564	+	0.501523i
$25$	2.89265	+	2.10163i	0.578530	+	0.420326i
$26$	−0.995668	+	6.12922i	−0.195267	+	1.20204i
$27$	−5.18604	−	0.324050i	−0.998054	−	0.0623634i
$28$	−1.17586	+	0.249937i	−0.222217	+	0.0472336i
$29$	2.81676	+	1.25410i	0.523060	+	0.232881i	0.651243	−	0.758869i	$-0.274248\pi$
$29$	2.81676	+	1.25410i	0.523060	+	0.232881i	−0.128183	+	0.991751i	$0.540914\pi$
$30$	−3.11962	+	1.71561i	−0.569562	+	0.313225i
$31$	0.786706	−	0.255616i	0.141297	−	0.0459100i	−0.237515	−	0.971384i	$-0.576333\pi$
$31$	0.786706	−	0.255616i	0.141297	−	0.0459100i	0.378811	+	0.925474i	$0.376333\pi$
$32$	4.37150	+	2.52389i	0.772779	+	0.446164i
$33$	−4.42320	+	3.66543i	−0.769980	+	0.638069i
$34$		−	1.20437i		−	0.206547i
$35$	1.45272	+	0.308786i	0.245555	+	0.0521943i
$36$	0.182803	+	2.89240i	0.0304671	+	0.482066i
$37$	0.203215	−	0.456429i	0.0334084	−	0.0750364i	−0.896071	−	0.443912i	$-0.853590\pi$
$37$	0.203215	−	0.456429i	0.0334084	−	0.0750364i	0.929479	+	0.368875i	$0.120257\pi$
$38$	−1.14546	−	0.372183i	−0.185818	−	0.0603761i
$39$	−3.27055	−	5.32010i	−0.523708	−	0.851898i
$40$	−1.24921	−	1.71939i	−0.197517	−	0.271859i
$41$	−4.32445	−	0.454518i	−0.675366	−	0.0709838i	−0.239364	−	0.970930i	$-0.576939\pi$
$41$	−4.32445	−	0.454518i	−0.675366	−	0.0709838i	−0.436001	+	0.899946i	$0.643606\pi$
$42$	2.24381	−	2.95698i	0.346227	−	0.456272i
$43$	−9.76151	−	5.63581i	−1.48862	−	0.859453i	−0.488701	−	0.872451i	$-0.662529\pi$
$43$	−9.76151	−	5.63581i	−1.48862	−	0.859453i	−0.999916	+	0.0129978i	$0.995863\pi$
$44$	2.33717	+	2.19170i	0.352342	+	0.330411i
$45$	1.24713	−	3.35635i	0.185910	−	0.500335i
$46$	3.89834	+	0.828618i	0.574779	+	0.122173i
$47$	−4.69563	−	3.41158i	−0.684929	−	0.497630i	0.190060	−	0.981772i	$-0.439132\pi$
$47$	−4.69563	−	3.41158i	−0.684929	−	0.497630i	−0.874989	+	0.484143i	$0.839132\pi$
$48$	−8.50467	+	1.62361i	−1.22754	+	0.234348i
$49$	5.33242	−	1.13344i	0.761774	−	0.161920i
$50$	1.28029	+	6.02327i	0.181060	+	0.851819i
$51$	0.791579	+	0.916788i	0.110843	+	0.128376i
$52$	−2.71559	+	2.18129i	−0.376584	+	0.302491i
$53$	−8.86976	+	2.88196i	−1.21836	+	0.395868i	−0.846483	−	0.532416i	$-0.821284\pi$
$53$	−8.86976	+	2.88196i	−1.21836	+	0.395868i	−0.371872	+	0.928284i	$0.621284\pi$
$54$	−6.26398	−	6.39109i	−0.852420	−	0.869718i
$55$	−1.53650	−	3.64809i	−0.207181	−	0.491908i
$56$	1.91896	+	1.10791i	0.256432	+	0.148051i
$57$	1.11657	−	0.469550i	0.147893	−	0.0621934i
$58$	2.15985	+	4.85110i	0.283602	+	0.636981i
$59$	0.558197	+	5.31089i	0.0726710	+	0.691418i	0.968837	+	0.247699i	$0.0796745\pi$
$59$	0.558197	+	5.31089i	0.0726710	+	0.691418i	−0.896166	+	0.443719i	$0.853659\pi$
$60$	−1.94437	−	0.455755i	−0.251017	−	0.0588377i
$61$	4.64648	−	4.18371i	0.594920	−	0.535669i	−0.315729	−	0.948849i	$-0.602249\pi$
$61$	4.64648	−	4.18371i	0.594920	−	0.535669i	0.910649	+	0.413181i	$0.135582\pi$
$62$	1.30144	+	0.579441i	0.165284	+	0.0735890i
$63$	0.235466	+	3.72567i	0.0296660	+	0.469390i
$64$	−0.403051	−	1.24046i	−0.0503814	−	0.155058i
$65$	4.16104	−	1.09731i	0.516114	−	0.136104i
$66$	−9.88509	−	0.406021i	−1.21677	−	0.0499777i
$67$	6.76153	−	3.90377i	0.826052	−	0.476921i	−0.0264469	−	0.999650i	$-0.508419\pi$
$67$	6.76153	−	3.90377i	0.826052	−	0.476921i	0.852499	+	0.522729i	$0.175086\pi$
$68$	0.452046	−	0.502048i	0.0548186	−	0.0608822i
$69$	−3.51211	+	1.93145i	−0.422809	+	0.232520i
$70$	1.50344	+	2.06931i	0.179696	+	0.247330i
$71$	−0.725281	−	0.805506i	−0.0860750	−	0.0955960i	0.698569	−	0.715543i	$-0.253821\pi$
$71$	−0.725281	−	0.805506i	−0.0860750	−	0.0955960i	−0.784644	+	0.619947i	$0.787154\pi$
$72$	3.31701	−	4.18747i	0.390913	−	0.493499i
$73$	−7.27022	+	5.28212i	−0.850915	+	0.618226i	−0.925398	−	0.378997i	$-0.876269\pi$
$73$	−7.27022	+	5.28212i	−0.850915	+	0.618226i	0.0744834	+	0.997222i	$0.476269\pi$
$74$	0.786073	−	0.349982i	0.0913791	−	0.0406846i
$75$	−4.93342	−	3.74356i	−0.569662	−	0.432269i
$76$	−0.337798	−	0.585083i	−0.0387481	−	0.0671137i
$77$	3.01049	+	2.82311i	0.343077	+	0.321723i
$78$	1.94499	−	10.5780i	0.220227	−	1.19772i
$79$	−6.44207	+	2.09316i	−0.724790	+	0.235498i	−0.648099	−	0.761556i	$-0.724436\pi$
$79$	−6.44207	+	2.09316i	−0.724790	+	0.235498i	−0.0766912	+	0.997055i	$0.524436\pi$
$80$	0.623640	−	5.93354i	0.0697251	−	0.663390i
$81$	8.96886	+	0.747984i	0.996540	+	0.0831093i
$82$	−5.01092	−	5.56519i	−0.553363	−	0.614572i
$83$	−7.61540	−	2.47439i	−0.835899	−	0.271600i	−0.140371	−	0.990099i	$-0.544829\pi$
$83$	−7.61540	−	2.47439i	−0.835899	−	0.271600i	−0.695528	+	0.718499i	$0.744829\pi$
$84$	2.04521	−	0.390448i	0.223151	−	0.0426013i
$85$	−0.762480	+	0.339478i	−0.0827026	+	0.0368216i
$86$	−5.99872	−	18.4622i	−0.646859	−	1.99083i
$87$	−4.83254	−	2.27318i	−0.518103	−	0.243711i
$88$	−0.498275	−	5.88480i	−0.0531163	−	0.627322i
$89$	7.39533	+	12.8091i	0.783903	+	1.35776i	0.929652	+	0.368438i	$0.120107\pi$
$89$	7.39533	+	12.8091i	0.783903	+	1.35776i	−0.145749	+	0.989322i	$0.546559\pi$
$90$	5.46398	−	2.85849i	0.575954	−	0.301311i
$91$	−3.49792	+	2.80970i	−0.366682	+	0.294537i
$92$	1.31404	+	1.80861i	0.136998	+	0.188561i
$93$	−1.37153	+	0.414302i	−0.142221	+	0.0429611i
$94$	−2.07829	−	9.77757i	−0.214359	−	1.00848i
$95$	0.0872467	+	0.830097i	0.00895132	+	0.0851661i
$96$	−7.47909	−	4.52804i	−0.763332	−	0.462141i
$97$	−1.65673	+	7.79430i	−0.168215	+	0.791391i	0.810430	+	0.585836i	$0.199234\pi$
$97$	−1.65673	+	7.79430i	−0.168215	+	0.791391i	−0.978645	+	0.205556i	$0.934100\pi$
$98$	8.13093	+	4.69439i	0.821348	+	0.474205i
$99$	7.79159	−	6.18798i	0.783085	−	0.621915i
$100$	−1.72707	+	2.99138i	−0.172707	+	0.299138i
$101$	5.46997	−	6.07502i	0.544282	−	0.604487i	−0.406765	−	0.913533i	$-0.633343\pi$
$101$	5.46997	−	6.07502i	0.544282	−	0.604487i	0.951047	+	0.309046i	$0.100010\pi$
$102$	−0.0433889	+	2.08557i	−0.00429614	+	0.206502i
$103$	−10.4759	+	7.61119i	−1.03222	+	0.749952i	−0.968752	−	0.248031i	$-0.920216\pi$
$103$	−10.4759	+	7.61119i	−1.03222	+	0.749952i	−0.0634690	+	0.997984i	$0.520216\pi$
$104$	6.41016	+	0.361400i	0.628568	+	0.0354382i
$105$	−2.50452	−	0.587053i	−0.244416	−	0.0572906i
$106$	−14.6732	−	6.53294i	−1.42519	−	0.634535i
$107$	−1.10768	+	10.5389i	−0.107084	+	1.01883i	0.800606	+	0.599191i	$0.204511\pi$
$107$	−1.10768	+	10.5389i	−0.107084	+	1.01883i	−0.907690	+	0.419642i	$0.862156\pi$
$108$	−0.212353	−	5.01528i	−0.0204336	−	0.482596i
$109$	−16.8727			−1.61611			−0.808055	−	0.589107i	$-0.799480\pi$
$109$	−16.8727			−1.61611			−0.808055	+	0.589107i	$0.799480\pi$
$110$	2.23753	−	6.43970i	0.213340	−	0.614001i
$111$	−0.368346	+	0.783066i	−0.0349619	+	0.0743253i
$112$	1.92221	+	5.91596i	0.181632	+	0.559006i
$113$	−0.696090	−	1.56344i	−0.0654826	−	0.147076i	0.877840	−	0.478955i	$-0.158984\pi$
$113$	−0.696090	−	1.56344i	−0.0654826	−	0.147076i	−0.943322	+	0.331879i	$0.892318\pi$
$114$	1.97016	+	0.685768i	0.184522	+	0.0642280i
$115$	−0.574241	−	2.70159i	−0.0535483	−	0.251925i
$116$	−0.920461	+	2.83289i	−0.0854626	+	0.263027i
$117$	5.47188	+	9.33052i	0.505875	+	0.862607i
$118$	−5.40581	+	7.44046i	−0.497645	+	0.684950i
$119$	0.582276	−	0.646683i	0.0533771	−	0.0592813i
$120$	2.10128	+	3.02243i	0.191820	+	0.275909i
$121$	1.59180	−	10.8842i	0.144709	−	0.989474i
$122$	10.7681			0.974900
$123$	7.47217	+	0.942872i	0.673743	+	0.0850159i
$124$	0.325029	+	0.730027i	0.0291884	+	0.0655583i
$125$	8.28032	−	6.01601i	0.740615	−	0.538088i
$126$	−3.99207	+	5.03970i	−0.355642	+	0.448972i
$127$	0.983435	+	4.62670i	0.0872657	+	0.410553i	0.999998	+	0.00199476i	$0.000634951\pi$
$127$	0.983435	+	4.62670i	0.0872657	+	0.410553i	−0.912732	+	0.408558i	$0.866032\pi$
$128$	5.01988	−	11.2748i	0.443699	−	0.996564i
$129$	16.7007	+	10.1111i	1.47042	+	0.890230i
$130$	6.59009	+	3.39075i	0.577989	+	0.297389i
$131$	−16.6274			−1.45274			−0.726371	−	0.687303i	$-0.758794\pi$
$131$	−16.6274			−1.45274			−0.726371	+	0.687303i	$0.758794\pi$
$132$	−3.96827	−	3.87951i	−0.345393	−	0.337668i
$133$	−0.435115	−	0.753640i	−0.0377292	−	0.0653489i
$134$	13.1525	+	2.79565i	1.13620	+	0.241507i
$135$	−2.28053	+	5.76718i	−0.196277	+	0.496360i
$136$	−1.23843	+	0.130164i	−0.106194	+	0.0111614i
$137$	10.2536	+	11.3878i	0.876026	+	0.972926i	0.999812	−	0.0193831i	$-0.00617022\pi$
$137$	10.2536	+	11.3878i	0.876026	+	0.972926i	−0.123786	+	0.992309i	$0.539504\pi$
$138$	−6.72081	−	1.57534i	−0.572114	−	0.134102i
$139$	1.63872	−	0.172236i	0.138994	−	0.0146089i	−0.0347757	−	0.999395i	$-0.511072\pi$
$139$	1.63872	−	0.172236i	0.138994	−	0.0146089i	0.173770	+	0.984786i	$0.444405\pi$
$140$	−0.149974	+	1.42691i	−0.0126751	+	0.120596i
$141$	8.00841	+	6.07691i	0.674430	+	0.511769i
$142$		−	1.86675i		−	0.156654i
$143$	11.4725	+	3.37373i	0.959378	+	0.282125i
$144$	14.7858	−	2.50517i	1.23215	−	0.208764i
$145$	2.46241	−	2.73479i	0.204492	−	0.227112i
$146$	−15.3920	−	1.61776i	−1.27385	−	0.133887i
$147$	−9.27485	+	1.77064i	−0.764977	+	0.146040i
$148$	0.459041	+	0.149152i	0.0377330	+	0.0122602i
$149$	−1.40248	+	1.26280i	−0.114896	+	0.103453i	−0.724576	−	0.689195i	$-0.757964\pi$
$149$	−1.40248	+	1.26280i	−0.114896	+	0.103453i	0.609680	+	0.792647i	$0.291298\pi$
$150$	−2.00004	−	10.4765i	−0.163303	−	0.855400i
$151$	−0.262337	−	0.190599i	−0.0213487	−	0.0155107i	0.577060	−	0.816702i	$-0.304200\pi$
$151$	−0.262337	−	0.190599i	−0.0213487	−	0.0155107i	−0.598408	+	0.801191i	$0.704200\pi$
$152$	−0.258911	+	1.21808i	−0.0210004	+	0.0987993i
$153$	−1.33773	−	1.61610i	−0.108149	−	0.130654i
$154$	0.599682	+	7.08245i	0.0483238	+	0.570720i
$155$		−	0.987269i		−	0.0792994i
$156$	4.78110	−	3.67946i	0.382794	−	0.294592i
$157$	6.95020	+	5.04962i	0.554686	+	0.403003i	0.829510	−	0.558491i	$-0.188620\pi$
$157$	6.95020	+	5.04962i	0.554686	+	0.403003i	−0.274824	+	0.961495i	$0.588620\pi$
$158$	−10.6571	−	4.74485i	−0.847834	−	0.377480i
$159$	15.4634	−	4.67108i	1.22633	−	0.370440i
$160$	4.47716	−	4.03125i	0.353951	−	0.318699i
$161$	1.69260	+	2.32966i	0.133395	+	0.183603i
$162$	10.6169	+	11.2930i	0.834145	+	0.887260i
$163$	4.77087	−	22.4452i	0.373684	−	1.75804i	−0.242219	−	0.970222i	$-0.577875\pi$
$163$	4.77087	−	22.4452i	0.373684	−	1.75804i	0.615903	−	0.787822i	$-0.288791\pi$
$164$		−	4.20068i		−	0.328018i
$165$	2.52929	+	6.37266i	0.196905	+	0.496111i
$166$	−6.89519	−	11.9428i	−0.535170	−	0.926942i
$167$	−4.80769	−	4.32886i	−0.372030	−	0.334978i	0.461815	−	0.886977i	$-0.347199\pi$
$167$	−4.80769	−	4.32886i	−0.372030	−	0.334978i	−0.833845	+	0.551999i	$0.813865\pi$
$168$	−3.28310	−	1.98768i	−0.253297	−	0.153353i
$169$	−5.38146	+	11.8338i	−0.413958	+	0.910296i
$170$	−1.36708	−	0.444192i	−0.104850	−	0.0340680i
$171$	−1.95045	+	0.772883i	−0.149155	+	0.0591038i
$172$	4.42897	−	9.94762i	0.337706	−	0.758499i
$173$	−19.1166	+	8.51124i	−1.45340	+	0.647097i	−0.973179	−	0.230048i	$-0.926112\pi$
$173$	−19.1166	+	8.51124i	−1.45340	+	0.647097i	−0.480225	+	0.877145i	$0.659445\pi$
$174$	−3.56539	−	8.47835i	−0.270292	−	0.642742i
$175$	−2.22463	+	3.85317i	−0.168166	+	0.291272i
$176$	10.0147	−	13.2129i	0.754883	−	0.995957i
$177$	−0.775284	−	9.21684i	−0.0582739	−	0.692780i
$178$	−5.29610	+	24.9162i	−0.396959	+	1.86755i
$179$	15.8540	+	1.66632i	1.18498	+	0.124547i	0.676445	−	0.736493i	$-0.263520\pi$
$179$	15.8540	+	1.66632i	1.18498	+	0.124547i	0.508537	+	0.861040i	$0.330186\pi$
$180$	3.35060	+	0.859268i	0.249739	+	0.0640461i
$181$	−0.370770	+	1.14111i	−0.0275591	+	0.0848183i	−0.963890	−	0.266300i	$-0.914199\pi$
$181$	−0.370770	+	1.14111i	−0.0275591	+	0.0848183i	0.936331	+	0.351119i	$0.114199\pi$
$182$	−7.71474	−	0.434951i	−0.571854	−	0.0322407i
$183$	−8.19691	+	7.07743i	−0.605933	+	0.523178i
$184$	0.430732	−	4.09814i	0.0317540	−	0.302119i
$185$	−0.443145	−	0.399010i	−0.0325807	−	0.0293358i
$186$	−2.23281	−	1.05029i	−0.163717	−	0.0770110i
$187$	−2.30126	−	0.289093i	−0.168285	−	0.0211406i
$188$	2.80356	−	4.85590i	0.204470	−	0.354153i
$189$	−0.273529	−	6.46014i	−0.0198963	−	0.469906i
$190$	−0.844934	+	1.16295i	−0.0612979	+	0.0843694i
$191$	−9.13673	+	0.960309i	−0.661110	+	0.0694855i	−0.429141	−	0.903238i	$-0.641184\pi$
$191$	−9.13673	+	0.960309i	−0.661110	+	0.0694855i	−0.231970	+	0.972723i	$0.574517\pi$
$192$	0.653264	+	2.16260i	0.0471453	+	0.156072i
$193$	22.0600	−	4.68900i	1.58791	−	0.337522i	0.672520	−	0.740079i	$-0.265212\pi$
$193$	22.0600	−	4.68900i	1.58791	−	0.337522i	0.915395	+	0.402558i	$0.131879\pi$
$194$	−11.1025	+	8.06643i	−0.797112	+	0.579136i
$195$	−7.24511	+	1.75027i	−0.518833	+	0.125340i
$196$	1.62744	+	5.00874i	0.116246	+	0.357767i
$197$	−21.5309	+	12.4309i	−1.53401	+	0.885664i	−0.534844	+	0.844951i	$0.679630\pi$
$197$	−21.5309	+	12.4309i	−1.53401	+	0.885664i	−0.999171	+	0.0407127i	$0.987037\pi$
$198$	17.1031	+	1.05922i	1.21547	+	0.0752755i
$199$	−9.23559	+	15.9965i	−0.654694	+	1.13396i	0.327277	+	0.944929i	$0.393869\pi$
$199$	−9.23559	+	15.9965i	−0.654694	+	1.13396i	−0.981971	+	0.189034i	$0.939464\pi$
$200$	6.05523	−	1.96746i	0.428170	−	0.139121i
$201$	−11.8494	+	6.51647i	−0.835793	+	0.459637i
$202$	14.0016	−	1.47163i	0.985150	−	0.103543i
$203$	−1.18564	+	3.64902i	−0.0832154	+	0.256111i
$204$	−0.800884	+	0.853098i	−0.0560731	+	0.0597288i
$205$	−2.11086	+	4.74107i	−0.147429	+	0.331131i
$206$	−22.1788	−	2.33108i	−1.54527	−	0.162414i
$207$	6.15143	−	3.21812i	0.427554	−	0.223675i
$208$	12.6940	+	12.7950i	0.880174	+	0.887172i
$209$	−0.986107	+	2.09937i	−0.0682105	+	0.145216i
$210$	−2.52893	−	3.63754i	−0.174513	−	0.251014i
$211$	−6.25355	−	5.63072i	−0.430512	−	0.387635i	0.425190	−	0.905104i	$-0.360207\pi$
$211$	−6.25355	−	5.63072i	−0.430512	−	0.387635i	−0.855702	+	0.517470i	$0.826874\pi$
$212$	−3.66456	−	8.23073i	−0.251683	−	0.565289i
$213$	1.22693	+	1.42101i	0.0840680	+	0.0973657i
$214$	−13.5626	+	12.2118i	−0.927122	+	0.834785i
$215$	−9.99746	+	9.00175i	−0.681821	+	0.613914i
$216$	−5.89484	+	7.13185i	−0.401093	+	0.485261i
$217$	0.418666	+	0.940340i	0.0284209	+	0.0638345i
$218$	−21.5947	−	19.4440i	−1.46258	−	1.31691i
$219$	12.7800	−	8.88501i	0.863590	−	0.600393i
$220$	3.34980	−	1.84460i	0.225843	−	0.124363i
$221$	0.662223	−	2.43288i	0.0445459	−	0.163653i
$222$	−1.37383	+	0.577736i	−0.0922055	+	0.0387751i
$223$	−10.3084	−	1.08345i	−0.690300	−	0.0725535i	−0.247118	−	0.968985i	$-0.579484\pi$
$223$	−10.3084	−	1.08345i	−0.690300	−	0.0725535i	−0.443182	+	0.896432i	$0.646150\pi$
$224$	−2.55483	+	5.73824i	−0.170702	+	0.383402i
$225$	8.40821	+	6.66036i	0.560548	+	0.444024i
$226$	0.910802	−	2.80316i	0.0605857	−	0.186463i
$227$	−2.26569	+	0.238133i	−0.150379	+	0.0158055i	−0.179419	−	0.983773i	$-0.557422\pi$
$227$	−2.26569	+	0.238133i	−0.150379	+	0.0158055i	0.0290398	+	0.999578i	$0.490755\pi$
$228$	0.563878	+	1.02534i	0.0373438	+	0.0679051i
$229$	17.6428	−	5.73248i	1.16587	−	0.378813i	0.338768	−	0.940870i	$-0.389990\pi$
$229$	17.6428	−	5.73248i	1.16587	−	0.378813i	0.827098	+	0.562057i	$0.189990\pi$
$230$	2.37835	−	4.11942i	0.156824	−	0.271626i
$231$	−5.11149	−	4.99716i	−0.336311	−	0.328789i
$232$	4.75486	−	2.74522i	0.312172	−	0.180232i
$233$	−7.92740	−	24.3980i	−0.519342	−	1.59837i	−0.775241	−	0.631665i	$-0.782372\pi$
$233$	−7.92740	−	24.3980i	−0.519342	−	1.59837i	0.255900	−	0.966703i	$-0.417628\pi$
$234$	−3.74917	+	18.2475i	−0.245091	+	1.19288i
$235$	−5.60433	+	4.07179i	−0.365586	+	0.265614i
$236$	−5.04614	+	1.07259i	−0.328476	+	0.0698197i
$237$	11.2310	−	3.39258i	0.729531	−	0.220372i
$238$	1.49047	−	0.156654i	0.0966125	−	0.0101544i
$239$	−4.87376	+	6.70815i	−0.315257	+	0.433914i	−0.937012	−	0.349298i	$-0.886420\pi$
$239$	−4.87376	+	6.70815i	−0.315257	+	0.433914i	0.621754	+	0.783212i	$0.286420\pi$
$240$	−1.29371	+	10.2525i	−0.0835084	+	0.661796i
$241$	6.95746	−	12.0507i	0.448169	−	0.776252i	−0.550098	−	0.835100i	$-0.685410\pi$
$241$	6.95746	−	12.0507i	0.448169	−	0.776252i	0.998267	+	0.0588484i	$0.0187429\pi$
$242$	14.5802	−	12.0959i	0.937250	−	0.777555i
$243$	−15.5042	−	1.61838i	−0.994596	−	0.103819i
$244$	4.48876	+	4.04170i	0.287363	+	0.258743i
$245$	0.680118	−	6.47089i	0.0434511	−	0.413410i
$246$	8.47679	+	9.81763i	0.540460	+	0.625949i
$247$	−2.10924	−	1.38166i	−0.134208	−	0.0879130i
$248$	0.455171	−	1.40087i	0.0289034	−	0.0889555i
$249$	13.0983	+	4.55920i	0.830069	+	0.288928i
$250$	17.5305	+	1.84253i	1.10872	+	0.116532i
$251$	−1.90721	+	8.97273i	−0.120382	+	0.566354i	0.876069	+	0.482185i	$0.160157\pi$
$251$	−1.90721	+	8.97273i	−0.120382	+	0.566354i	−0.996452	+	0.0841685i	$0.973177\pi$
$252$	−3.55571	+	0.602448i	−0.223989	+	0.0379506i
$253$	2.51904	−	7.24990i	0.158371	−	0.455797i
$254$	−4.07311	+	7.05484i	−0.255570	+	0.442660i
$255$	1.33260	−	0.560397i	0.0834506	−	0.0350934i
$256$	17.0347	−	7.58434i	1.06467	−	0.474022i
$257$	−8.59680	+	19.3087i	−0.536254	+	1.20445i	0.418818	+	0.908070i	$0.362445\pi$
$257$	−8.59680	+	19.3087i	−0.536254	+	1.20445i	−0.955071	+	0.296376i	$0.904222\pi$
$258$	9.72272	+	32.1866i	0.605310	+	2.00385i
$259$	0.591287	+	0.192121i	0.0367408	+	0.0119378i
$260$	1.47444	+	3.88698i	0.0914407	+	0.241060i
$261$	8.28651	+	4.11051i	0.512922	+	0.254434i
$262$	−21.2808	−	19.1613i	−1.31473	−	1.18379i
$263$	13.2141	+	22.8874i	0.814814	+	1.41130i	0.909461	+	0.415789i	$0.136494\pi$
$263$	13.2141	+	22.8874i	0.814814	+	1.41130i	−0.0946470	+	0.995511i	$0.530172\pi$
$264$	0.650843	+	10.2085i	0.0400566	+	0.628291i
$265$			11.1310i			0.683773i
$266$	0.311603	−	1.46598i	0.0191056	−	0.0898849i
$267$	−12.3448	−	22.4476i	−0.755492	−	1.37377i
$268$	4.43338	+	6.10203i	0.270812	+	0.372741i
$269$	15.6869	−	14.1245i	0.956446	−	0.861188i	−0.0339536	−	0.999423i	$-0.510810\pi$
$269$	15.6869	−	14.1245i	0.956446	−	0.861188i	0.990399	+	0.138236i	$0.0441432\pi$
$270$	−9.56483	+	4.75312i	−0.582097	+	0.289266i
$271$	−8.85558	−	3.94276i	−0.537938	−	0.239506i	0.119739	−	0.992805i	$-0.461794\pi$
$271$	−8.85558	−	3.94276i	−0.537938	−	0.239506i	−0.657677	+	0.753300i	$0.728461\pi$
$272$	−2.82811	−	2.05474i	−0.171479	−	0.124587i
$273$	6.15849	−	4.73948i	0.372729	−	0.286846i
$274$			26.3910i			1.59434i
$275$	11.8163	−	1.00051i	0.712552	−	0.0603329i
$276$	−2.21033	−	3.17927i	−0.133046	−	0.191370i
$277$	2.64038	−	12.4220i	0.158645	−	0.746366i	−0.824839	−	0.565368i	$-0.808734\pi$
$277$	2.64038	−	12.4220i	0.158645	−	0.746366i	0.983484	−	0.180998i	$-0.0579327\pi$
$278$	2.29582	+	1.66801i	0.137694	+	0.100041i
$279$	2.38997	−	0.668026i	0.143084	−	0.0399937i
$280$	1.96534	−	1.76960i	0.117452	−	0.105754i
$281$	5.63146	+	1.82977i	0.335945	+	0.109155i	0.472132	−	0.881528i	$-0.343485\pi$
$281$	5.63146	+	1.82977i	0.335945	+	0.109155i	−0.136187	+	0.990683i	$0.543485\pi$
$282$	3.24667	+	17.0065i	0.193336	+	1.01272i
$283$	25.9656	+	2.72910i	1.54350	+	0.162228i	0.837678	−	0.546165i	$-0.183913\pi$
$283$	25.9656	+	2.72910i	1.54350	+	0.162228i	0.705818	+	0.708393i	$0.250580\pi$
$284$	0.700662	−	0.778165i	0.0415767	−	0.0461756i
$285$	−0.121178	−	1.44060i	−0.00717794	−	0.0853339i
$286$	10.7953	+	17.5387i	0.638342	+	1.03709i
$287$		−	5.41085i		−	0.319392i
$288$	12.7882	+	8.11055i	0.753554	+	0.477919i
$289$	1.72587	−	16.4205i	0.101522	−	0.965913i
$290$	6.30310	−	0.662482i	0.370131	−	0.0389023i
$291$	3.14972	−	13.4375i	0.184640	−	0.787721i
$292$	−5.80903	−	6.45158i	−0.339947	−	0.377550i
$293$	−7.96717	+	0.837383i	−0.465447	+	0.0489204i	−0.334350	−	0.942449i	$-0.608517\pi$
$293$	−7.96717	+	0.837383i	−0.465447	+	0.0489204i	−0.131097	+	0.991370i	$0.541850\pi$
$294$	−13.9110	−	8.42210i	−0.811307	−	0.491187i
$295$	6.23428	+	1.32514i	0.362974	+	0.0771525i
$296$	−0.444835	−	0.770477i	−0.0258555	−	0.0447831i
$297$	−13.7154	+	10.4349i	−0.795851	+	0.605493i
$298$	−3.25022			−0.188280
$299$	7.41921	+	3.81736i	0.429064	+	0.220764i
$300$	3.09850	−	5.11788i	0.178892	−	0.295481i
$301$	5.70491	−	12.8134i	0.328826	−	0.738554i
$302$	−0.116110	−	0.546255i	−0.00668138	−	0.0314334i
$303$	−9.69108	+	10.3229i	−0.556738	+	0.593035i
$304$	−2.82821	+	2.05482i	−0.162209	+	0.117852i
$305$	−3.03524	−	6.81726i	−0.173797	−	0.390355i
$306$	0.150271	−	3.60997i	0.00859042	−	0.206368i
$307$	−1.60054			−0.0913475			−0.0456738	−	0.998956i	$-0.514543\pi$
$307$	−1.60054			−0.0913475			−0.0456738	+	0.998956i	$0.514543\pi$
$308$	−2.40834	+	3.17745i	−0.137228	+	0.181052i
$309$	18.4151	−	12.8027i	1.04760	−	0.728320i
$310$	1.13772	−	1.26357i	0.0646183	−	0.0717659i
$311$	19.3328	−	26.6093i	1.09626	−	1.50887i	0.256009	−	0.966674i	$-0.417592\pi$
$311$	19.3328	−	26.6093i	1.09626	−	1.50887i	0.840251	−	0.542198i	$-0.182408\pi$
$312$	−11.0873	−	0.856762i	−0.627695	−	0.0485046i
$313$	2.88056	−	8.86546i	0.162819	−	0.501105i	−0.836050	−	0.548653i	$-0.815141\pi$
$313$	2.88056	−	8.86546i	0.162819	−	0.501105i	0.998869	+	0.0475480i	$0.0151407\pi$
$314$	3.07616	+	14.4722i	0.173598	+	0.816712i
$315$	4.31587	+	1.10682i	0.243172	+	0.0623620i
$316$	−2.66155	−	5.97795i	−0.149724	−	0.336286i
$317$	−8.49172	−	26.1348i	−0.476942	−	1.46788i	−0.843320	−	0.537412i	$-0.819402\pi$
$317$	−8.49172	−	26.1348i	−0.476942	−	1.46788i	0.366378	−	0.930466i	$-0.380598\pi$
$318$	25.1739	+	11.8416i	1.41168	+	0.664041i
$319$	9.78774	−	2.96251i	0.548008	−	0.165869i
$320$	−1.55671			−0.0870226
$321$	2.29782	−	18.2100i	0.128252	−	1.01639i
$322$	−0.518393	+	4.93218i	−0.0288889	+	0.274860i
$323$	0.446770	+	0.198915i	0.0248589	+	0.0110679i
$324$	0.187044	+	8.69250i	0.0103913	+	0.482916i
$325$	−0.725670	+	12.8712i	−0.0402529	+	0.713968i
$326$	31.9718	−	23.2288i	1.77075	−	1.28653i
$327$	29.2180	+	0.607861i	1.61576	+	0.0336148i
$328$	−5.18100	+	5.75409i	−0.286073	+	0.317716i
$329$	3.61123	−	6.25484i	0.199094	−	0.344841i
$330$	−4.10667	+	11.0709i	−0.226065	+	0.609431i
$331$	−12.7943	−	7.38678i	−0.703238	−	0.406014i	0.105315	−	0.994439i	$-0.466415\pi$
$331$	−12.7943	−	7.38678i	−0.703238	−	0.406014i	−0.808552	+	0.588425i	$0.799748\pi$
$332$	1.60830	−	7.56647i	0.0882671	−	0.415264i
$333$	0.666067	−	1.34275i	0.0365003	−	0.0735820i
$334$	−1.16463	−	11.0807i	−0.0637256	−	0.606309i
$335$	−1.93742	−	9.11482i	−0.105852	−	0.497996i
$336$	−3.11552	−	10.3138i	−0.169965	−	0.562663i
$337$	14.6333	+	20.1410i	0.797127	+	1.09715i	0.993184	+	0.116558i	$0.0371861\pi$
$337$	14.6333	+	20.1410i	0.797127	+	1.09715i	−0.196057	+	0.980592i	$0.562814\pi$
$338$	−20.5248	+	8.94413i	−1.11640	+	0.486497i
$339$	1.14908	+	2.73245i	0.0624093	+	0.148407i
$340$	−0.403154	−	0.698283i	−0.0218641	−	0.0378697i
$341$	1.41957	−	2.34766i	0.0768740	−	0.127133i
$342$	−3.38697	−	1.25850i	−0.183147	−	0.0680521i
$343$	4.78801	+	14.7360i	0.258528	+	0.795667i
$344$	−18.3359	+	8.16369i	−0.988608	+	0.440156i
$345$	0.897071	+	4.69897i	0.0482967	+	0.252984i
$346$	−34.2748	−	11.1366i	−1.84263	−	0.598706i
$347$	4.41265	+	4.90074i	0.236883	+	0.263086i	0.849852	−	0.527022i	$-0.176691\pi$
$347$	4.41265	+	4.90074i	0.236883	+	0.263086i	−0.612968	+	0.790107i	$0.710025\pi$
$348$	1.69600	−	4.87248i	0.0909151	−	0.261192i
$349$	2.10393	−	20.0175i	0.112621	−	1.07151i	−0.781567	−	0.623822i	$-0.785579\pi$
$349$	2.10393	−	20.0175i	0.112621	−	1.07151i	0.894187	−	0.447693i	$-0.147754\pi$
$350$	−7.28758	+	2.36788i	−0.389537	+	0.126568i
$351$	−9.13938	−	16.3546i	−0.487824	−	0.872942i
$352$	16.4428	−	3.14847i	0.876407	−	0.167814i
$353$	−7.84030	−	13.5798i	−0.417297	−	0.722779i	0.578370	−	0.815775i	$-0.303689\pi$
$353$	−7.84030	−	13.5798i	−0.417297	−	0.722779i	−0.995667	+	0.0929954i	$0.970356\pi$
$354$	9.62917	−	12.6897i	0.511785	−	0.674451i
$355$	−1.18183	+	0.526185i	−0.0627250	+	0.0279270i
$356$	−11.5597	+	8.39863i	−0.612664	+	0.445127i
$357$	−1.03161	+	1.09887i	−0.0545986	+	0.0581583i
$358$	18.3706	+	20.4027i	0.970919	+	1.07831i
$359$	14.1056	+	19.4146i	0.744463	+	1.02467i	0.998349	+	0.0574317i	$0.0182911\pi$
$359$	14.1056	+	19.4146i	0.744463	+	1.02467i	−0.253886	+	0.967234i	$0.581709\pi$
$360$	−3.52985	−	5.30957i	−0.186039	−	0.279839i
$361$	−12.3862	+	13.7563i	−0.651907	+	0.724016i
$362$	−1.78955	+	1.03319i	−0.0940564	+	0.0543035i
$363$	−3.14860	+	18.7906i	−0.165259	+	0.986250i
$364$	−3.05268	−	3.07695i	−0.160004	−	0.161276i
$365$	3.31438	+	10.2006i	0.173482	+	0.533924i
$366$	−18.6469	−	0.387936i	−0.974689	−	0.0202777i
$367$	−16.9289	−	7.53722i	−0.883680	−	0.393440i	−0.0858399	−	0.996309i	$-0.527357\pi$
$367$	−16.9289	−	7.53722i	−0.883680	−	0.393440i	−0.797840	+	0.602869i	$0.794024\pi$
$368$	8.59665	−	7.74046i	0.448131	−	0.403499i
$369$	−12.9054	−	1.90194i	−0.671829	−	0.0990113i
$370$	−0.107349	−	1.02135i	−0.00558079	−	0.0530977i
$371$	−4.72028	−	10.6019i	−0.245065	−	0.550424i
$372$	−0.536544	−	1.27588i	−0.0278185	−	0.0661512i
$373$	27.2944	+	15.7584i	1.41325	+	0.815940i	0.995693	−	0.0927115i	$-0.0295534\pi$
$373$	27.2944	+	15.7584i	1.41325	+	0.815940i	0.417556	+	0.908651i	$0.362887\pi$
$374$	−2.61214	−	3.02195i	−0.135071	−	0.156261i
$375$	−14.5556	+	10.1195i	−0.751646	+	0.522567i
$376$	−9.82946	+	3.19378i	−0.506915	+	0.164707i
$377$	1.69561	+	10.9870i	0.0873283	+	0.565862i
$378$	7.09454	−	8.58330i	0.364904	−	0.441477i
$379$	−5.03410	−	23.6836i	−0.258584	−	1.21654i	−0.895307	−	0.445450i	$-0.853044\pi$
$379$	−5.03410	−	23.6836i	−0.258584	−	1.21654i	0.636722	−	0.771093i	$-0.280290\pi$
$380$	−0.788717	+	0.167647i	−0.0404603	+	0.00860011i
$381$	−1.53631	−	8.04737i	−0.0787074	−	0.412279i
$382$	−12.8004	−	9.30004i	−0.654926	−	0.475831i
$383$	−18.9569	−	4.02941i	−0.968651	−	0.205893i	−0.303690	−	0.952771i	$-0.598219\pi$
$383$	−18.9569	−	4.02941i	−0.968651	−	0.205893i	−0.664961	+	0.746878i	$0.731552\pi$
$384$	−9.09900	+	19.3435i	−0.464331	+	0.987119i
$385$	4.31484	−	2.37601i	0.219905	−	0.121093i
$386$	33.6373	+	19.4205i	1.71210	+	0.988479i
$387$	−28.5560	−	18.1108i	−1.45158	−	0.920622i
$388$	−7.65578	−	0.804655i	−0.388664	−	0.0408502i
$389$	2.44660	+	3.36745i	0.124047	+	0.170737i	0.866524	−	0.499135i	$-0.166349\pi$
$389$	2.44660	+	3.36745i	0.124047	+	0.170737i	−0.742477	+	0.669872i	$0.766349\pi$
$390$	−11.2897	−	6.10911i	−0.571678	−	0.309347i
$391$	−1.53908	−	0.500077i	−0.0778346	−	0.0252900i
$392$	3.94839	−	8.86822i	0.199424	−	0.447913i
$393$	28.7932	+	0.599024i	1.45243	+	0.0302167i
$394$	−41.8819	−	8.90227i	−2.10998	−	0.448490i
$395$			8.08442i			0.406771i
$396$	6.73199	+	6.86102i	0.338295	+	0.344779i
$397$	10.0502	+	5.80247i	0.504403	+	0.291217i	0.730530	−	0.682880i	$-0.239273\pi$
$397$	10.0502	+	5.80247i	0.504403	+	0.291217i	−0.226127	+	0.974098i	$0.572606\pi$
$398$	−30.2546	+	9.83030i	−1.51652	+	0.492748i
$399$	0.726327	+	1.32074i	0.0363618	+	0.0661195i
$400$	16.3282	+	7.26978i	0.816410	+	0.363489i
$401$	−11.6553	+	2.47741i	−0.582038	+	0.123716i	−0.489516	−	0.871995i	$-0.662826\pi$
$401$	−11.6553	+	2.47741i	−0.582038	+	0.123716i	−0.0925226	+	0.995711i	$0.529493\pi$
$402$	−22.6752	−	5.31500i	−1.13093	−	0.265088i
$403$	2.31037	+	1.88610i	0.115088	+	0.0939533i
$404$	6.38902	+	4.64189i	0.317866	+	0.230943i
$405$	4.15692	−	9.90473i	0.206559	−	0.492170i
$406$	−5.72255	+	3.30392i	−0.284005	+	0.163971i
$407$	−0.480045	−	1.58601i	−0.0237950	−	0.0786154i
$408$	2.14924	−	0.180785i	0.106403	−	0.00895022i
$409$	−23.5940	−	5.01506i	−1.16665	−	0.247979i	−0.416429	−	0.909168i	$-0.636718\pi$
$409$	−23.5940	−	5.01506i	−1.16665	−	0.247979i	−0.750219	+	0.661190i	$0.770052\pi$
$410$	−8.16519	+	3.63537i	−0.403250	+	0.179538i
$411$	−17.3457	−	20.0894i	−0.855600	−	0.990937i
$412$	−8.37042	−	9.29629i	−0.412381	−	0.457995i
$413$	−6.49989	+	1.38159i	−0.319839	+	0.0679838i
$414$	11.5815	+	2.97011i	0.569201	+	0.145973i
$415$	−5.61739	+	7.73167i	−0.275747	+	0.379533i
$416$	0.880540	+	18.1787i	0.0431720	+	0.891283i
$417$	−2.84394	+	0.239221i	−0.139268	+	0.0117147i
$418$	−3.68138	+	1.55052i	−0.180062	+	0.0758383i
$419$	−6.66176	+	3.84617i	−0.325448	+	0.187898i	−0.653818	−	0.756651i	$-0.726834\pi$
$419$	−6.66176	+	3.84617i	−0.325448	+	0.187898i	0.328370	+	0.944549i	$0.393501\pi$
$420$	0.311112	−	2.46554i	0.0151807	−	0.120306i
$421$	13.5147	−	18.6014i	0.658668	−	0.906579i	−0.340769	−	0.940147i	$-0.610687\pi$
$421$	13.5147	−	18.6014i	0.658668	−	0.906579i	0.999436	+	0.0335687i	$0.0106873\pi$
$422$	−1.51488	−	14.4131i	−0.0737430	−	0.701618i
$423$	−13.6490	−	10.8118i	−0.663639	−	0.525686i
$424$	−5.13185	+	15.7942i	−0.249225	+	0.767035i
$425$	−0.261361	−	2.48669i	−0.0126779	−	0.120622i
$426$	−0.0672520	+	3.23260i	−0.00325837	+	0.156620i
$427$	5.78193	+	5.20607i	0.279807	+	0.251939i
$428$	−10.2372			−0.494836
$429$	−19.7451	−	6.25552i	−0.953302	−	0.302019i
$430$	−23.1689			−1.11730
$431$	4.18144	+	3.76499i	0.201413	+	0.181353i	0.763665	−	0.645613i	$-0.223398\pi$
$431$	4.18144	+	3.76499i	0.201413	+	0.181353i	−0.562252	+	0.826966i	$0.690065\pi$
$432$	−25.6945	+	3.80547i	−1.23623	+	0.183091i
$433$	−0.570205	−	5.42514i	−0.0274023	−	0.260715i	−0.999643	−	0.0267311i	$-0.991490\pi$
$433$	−0.570205	−	5.42514i	−0.0274023	−	0.260715i	0.972240	−	0.233984i	$-0.0751764\pi$
$434$	−0.547806	+	1.68597i	−0.0262955	+	0.0809293i
$435$	−4.36263	+	4.64705i	−0.209172	+	0.222809i
$436$	−1.70381	−	16.2107i	−0.0815978	−	0.776351i
$437$	−0.951238	+	1.30927i	−0.0455039	+	0.0626307i
$438$	26.5956	+	3.35595i	1.27079	+	0.160354i
$439$	22.3055	−	12.8781i	1.06458	−	0.614636i	0.137886	−	0.990448i	$-0.455969\pi$
$439$	22.3055	−	12.8781i	1.06458	−	0.614636i	0.926696	+	0.375812i	$0.122636\pi$
$440$	−6.86364	−	1.60482i	−0.327211	−	0.0765070i
$441$	16.1248	−	2.73204i	0.767849	−	0.130097i
$442$	3.65118	−	2.35060i	0.173669	−	0.111807i
$443$	10.2486	−	14.1060i	0.486925	−	0.670194i	−0.492892	−	0.870090i	$-0.664060\pi$
$443$	10.2486	−	14.1060i	0.486925	−	0.670194i	0.979817	+	0.199896i	$0.0640604\pi$
$444$	−0.789537	−	0.274820i	−0.0374698	−	0.0130424i
$445$	17.2672	−	3.67025i	0.818543	−	0.173987i
$446$	−11.9447	−	13.2660i	−0.565600	−	0.628162i
$447$	2.47414	−	2.13623i	0.117023	−	0.101040i
$448$	1.48271	−	0.660146i	0.0700515	−	0.0311889i
$449$	−6.17186	−	1.31187i	−0.291268	−	0.0619110i	0.0599602	−	0.998201i	$-0.480903\pi$
$449$	−6.17186	−	1.31187i	−0.291268	−	0.0619110i	−0.351228	+	0.936290i	$0.614236\pi$
$450$	3.08600	+	18.2139i	0.145475	+	0.858612i
$451$	−11.8366	+	8.23881i	−0.557362	+	0.387951i
$452$	1.43181	−	0.826655i	0.0673466	−	0.0388826i
$453$	0.447416	+	0.339506i	0.0210214	+	0.0159514i
$454$	−3.17419	−	2.30618i	−0.148972	−	0.108235i
$455$	1.89921	+	5.00678i	0.0890363	+	0.234721i
$456$	0.492232	−	2.09999i	0.0230509	−	0.0983411i
$457$	−2.98041	+	0.633506i	−0.139418	+	0.0296342i	−0.277092	−	0.960843i	$-0.589371\pi$
$457$	−2.98041	+	0.633506i	−0.139418	+	0.0296342i	0.137674	+	0.990478i	$0.456037\pi$
$458$	29.1864	+	12.9946i	1.36379	+	0.607198i
$459$	2.25829	+	2.84675i	0.105408	+	0.132875i
$460$	2.53761	−	0.824518i	0.118317	−	0.0384434i
$461$	−35.7971	−	20.6675i	−1.66724	−	0.962580i	−0.969118	−	0.246597i	$-0.920687\pi$
$461$	−35.7971	−	20.6675i	−1.66724	−	0.962580i	−0.698119	−	0.715982i	$-0.745979\pi$
$462$	−0.783301	−	12.2861i	−0.0364424	−	0.571602i
$463$			29.4550i			1.36889i	0.729065	+	0.684445i	$0.239955\pi$
$463$			29.4550i			1.36889i	−0.729065	+	0.684445i	$0.760045\pi$
$464$	15.0763	+	3.20457i	0.699900	+	0.148768i
$465$	−0.0355677	+	1.70963i	−0.00164941	+	0.0792822i
$466$	17.9701	−	40.3616i	0.832451	−	1.86972i
$467$	−31.0813	−	10.0989i	−1.43827	−	0.467322i	−0.516912	−	0.856039i	$-0.672919\pi$
$467$	−31.0813	−	10.0989i	−1.43827	−	0.467322i	−0.921357	+	0.388717i	$0.872919\pi$
$468$	−8.41188	+	6.19938i	−0.388839	+	0.286567i
$469$	5.71060	+	7.85997i	0.263691	+	0.362940i
$470$	−11.8651	−	1.24707i	−0.547295	−	0.0575230i
$471$	−11.8536	−	8.99469i	−0.546184	−	0.414453i
$472$	8.23512	+	4.75455i	0.379052	+	0.218846i
$473$	−36.7167	+	7.03051i	−1.68824	+	0.323263i
$474$	18.2837	+	8.60048i	0.839799	+	0.395033i
$475$	−2.44583	−	0.519878i	−0.112223	−	0.0238536i
$476$	0.680108	+	0.494128i	0.0311727	+	0.0226483i
$477$	−26.9458	+	7.53170i	−1.23377	+	0.344853i
$478$	−13.9682	+	2.96903i	−0.638889	+	0.135800i
$479$	0.788501	+	3.70960i	0.0360275	+	0.169496i	0.992483	−	0.122382i	$-0.0390532\pi$
$479$	0.788501	+	3.70960i	0.0360275	+	0.169496i	−0.956456	+	0.291878i	$0.905720\pi$
$480$	−7.89823	+	6.81953i	−0.360503	+	0.311268i
$481$	1.78034	−	0.274756i	0.0811766	−	0.0125278i
$482$	22.7917	−	7.40547i	1.03813	−	0.337310i
$483$	−2.84710	−	4.09519i	−0.129548	−	0.186338i
$484$	10.6179	+	0.430254i	0.482632	+	0.0195570i
$485$	8.23632	+	4.75524i	0.373992	+	0.215924i
$486$	−17.9783	−	19.9383i	−0.815510	−	0.904418i
$487$	−0.456092	−	1.02440i	−0.0206675	−	0.0464200i	0.902917	−	0.429815i	$-0.141421\pi$
$487$	−0.456092	−	1.02440i	−0.0206675	−	0.0464200i	−0.923584	+	0.383395i	$0.874755\pi$
$488$	−1.16378	−	11.0726i	−0.0526819	−	0.501235i
$489$	−9.07023	+	38.6959i	−0.410170	+	1.74989i
$490$	8.32746	−	7.49808i	0.376196	−	0.338729i
$491$	6.09858	+	2.71526i	0.275225	+	0.122538i	0.539708	−	0.841852i	$-0.318535\pi$
$491$	6.09858	+	2.71526i	0.275225	+	0.122538i	−0.264483	+	0.964390i	$0.585201\pi$
$492$	−0.151335	+	7.27421i	−0.00682271	+	0.327947i
$493$	−0.666303	−	2.05067i	−0.0300088	−	0.0923575i
$494$	−1.10732	−	4.19901i	−0.0498207	−	0.188922i
$495$	−4.15032	−	11.1265i	−0.186543	−	0.500100i
$496$	3.58102	−	2.06750i	0.160792	−	0.0928336i
$497$	0.902517	−	1.00235i	0.0404834	−	0.0449614i
$498$	11.5100	+	20.9295i	0.515774	+	0.937873i
$499$	−16.2082	−	22.3086i	−0.725577	−	0.998672i	−0.999320	−	0.0368687i	$-0.988262\pi$
$499$	−16.2082	−	22.3086i	−0.725577	−	0.998672i	0.273743	−	0.961803i	$-0.411738\pi$
$500$	6.61611	+	7.34794i	0.295882	+	0.328610i
$501$	8.16941	+	7.66939i	0.364982	+	0.342643i
$502$	−12.7811	+	9.28600i	−0.570447	+	0.414454i
$503$	15.0391	−	6.69583i	0.670559	−	0.298552i	−0.0430739	−	0.999072i	$-0.513715\pi$
$503$	15.0391	−	6.69583i	0.670559	−	0.298552i	0.713633	+	0.700520i	$0.247048\pi$
$504$	5.61366	+	3.56029i	0.250052	+	0.158588i
$505$	−4.87836	−	8.44956i	−0.217084	−	0.376001i
$506$	11.5788	−	6.37595i	0.514739	−	0.283446i
$507$	9.74528	−	20.2985i	0.432803	−	0.901489i
$508$	−4.34586	+	1.41205i	−0.192816	+	0.0626498i
$509$	1.79340	−	17.0631i	0.0794911	−	0.756307i	−0.880077	−	0.474831i	$-0.842509\pi$
$509$	1.79340	−	17.0631i	0.0794911	−	0.756307i	0.959568	−	0.281476i	$-0.0908241\pi$
$510$	2.35134	+	0.818447i	0.104119	+	0.0362415i
$511$	−7.48255	−	8.31021i	−0.331009	−	0.367622i
$512$	7.06666	+	2.29610i	0.312305	+	0.101474i
$513$	3.40540	−	1.26811i	0.150352	−	0.0559886i
$514$	−33.2540	+	14.8056i	−1.46677	+	0.653048i
$515$	4.77579	+	14.6984i	0.210447	+	0.647688i
$516$	−8.02791	+	17.0665i	−0.353409	+	0.751311i
$517$	−19.1815	+	1.62412i	−0.843600	+	0.0714289i
$518$	0.535367	+	0.927282i	0.0235227	+	0.0407425i
$519$	33.4103	−	14.0500i	1.46655	−	0.616727i
$520$	2.77441	−	7.14292i	0.121666	−	0.313238i
$521$	17.7339	+	24.4087i	0.776938	+	1.06936i	0.995613	+	0.0935653i	$0.0298264\pi$
$521$	17.7339	+	24.4087i	0.776938	+	1.06936i	−0.218676	+	0.975798i	$0.570174\pi$
$522$	5.86866	+	14.8102i	0.256864	+	0.648225i
$523$	−4.69523	−	22.0893i	−0.205308	−	0.965899i	−0.953261	−	0.302147i	$-0.902297\pi$
$523$	−4.69523	−	22.0893i	−0.205308	−	0.965899i	0.747953	−	0.663752i	$-0.231037\pi$
$524$	−1.67904	−	15.9750i	−0.0733492	−	0.697871i
$525$	3.99115	−	6.59229i	0.174188	−	0.287711i
$526$	−9.46314	+	44.5206i	−0.412612	+	1.94119i
$527$	−0.500963	−	0.289231i	−0.0218223	−	0.0125991i
$528$	−17.8182	+	22.5196i	−0.775436	+	0.980040i
$529$	−8.82242	+	15.2809i	−0.383584	+	0.664386i
$530$	−12.8273	+	14.2462i	−0.557183	+	0.618814i
$531$	1.01049	+	15.9885i	0.0438516	+	0.693843i
$532$	0.680133	−	0.494145i	0.0294875	−	0.0214239i
$533$	−7.06225	−	13.9972i	−0.305900	−	0.606286i
$534$	10.0688	−	42.9560i	0.435718	−	1.85889i
$535$	11.5542	+	5.14427i	0.499532	+	0.222406i
$536$	1.45323	−	13.8266i	0.0627701	−	0.597218i
$537$	−27.3939	−	3.45669i	−1.18213	−	0.149167i
$538$	36.3540			1.56733
$539$	10.9216	−	14.4094i	0.470426	−	0.620658i
$540$	−5.77119	−	1.60868i	−0.248353	−	0.0692267i
$541$	3.16030	+	9.72640i	0.135872	+	0.418171i	0.995725	−	0.0923714i	$-0.0294447\pi$
$541$	3.16030	+	9.72640i	0.135872	+	0.418171i	−0.859853	+	0.510542i	$0.829445\pi$
$542$	−6.79032	−	15.2513i	−0.291669	−	0.655099i
$543$	0.683164	−	1.96268i	0.0293174	−	0.0842267i
$544$	−0.733918	−	3.45281i	−0.0314665	−	0.148038i
$545$	−6.22295	+	19.1523i	−0.266562	+	0.820393i
$546$	13.3438	+	1.03113i	0.571060	+	0.0441282i
$547$	−9.84070	+	13.5446i	−0.420758	+	0.579124i	−0.965801	−	0.259284i	$-0.916513\pi$
$547$	−9.84070	+	13.5446i	−0.420758	+	0.579124i	0.545043	+	0.838408i	$0.316513\pi$
$548$	−9.90558	+	11.0013i	−0.423146	+	0.469951i
$549$	14.4494	−	11.9605i	0.616684	−	0.510462i
$550$	16.2763	+	12.3366i	0.694023	+	0.526033i
$551$	−2.15628			−0.0918606
$552$	−0.893529	+	7.08113i	−0.0380311	+	0.301393i
$553$	−3.42832	−	7.70014i	−0.145787	−	0.327443i
$554$	17.6944	−	12.8557i	0.751761	−	0.546186i
$555$	0.753009	+	0.706920i	0.0319634	+	0.0300071i
$556$	0.330957	+	1.55703i	0.0140357	+	0.0660328i
$557$	4.68006	−	10.5116i	0.198301	−	0.445390i	−0.786836	−	0.617162i	$-0.788282\pi$
$557$	4.68006	−	10.5116i	0.198301	−	0.445390i	0.985137	+	0.171772i	$0.0549491\pi$
$558$	3.82866	+	1.89920i	0.162080	+	0.0803996i
$559$	−1.96624	−	40.5928i	−0.0831630	−	1.71689i
$560$	7.42418			0.313729
$561$	3.97462	+	0.583522i	0.167808	+	0.0246363i
$562$	5.09888	+	8.83152i	0.215083	+	0.372535i
$563$	23.2386	+	4.93952i	0.979391	+	0.208176i	0.669676	−	0.742653i	$-0.266433\pi$
$563$	23.2386	+	4.93952i	0.979391	+	0.208176i	0.309715	+	0.950829i	$0.399766\pi$
$564$	−5.02979	+	8.30785i	−0.211792	+	0.349823i
$565$	−2.03140	+	0.213509i	−0.0854617	+	0.00898239i
$566$	30.0874	+	33.4155i	1.26467	+	1.40456i
$567$	0.240929	+	11.1967i	0.0101181	+	0.470218i
$568$	−1.91954	+	0.201751i	−0.0805419	+	0.00846530i
$569$	−2.10701	+	20.0469i	−0.0883305	+	0.840408i	0.857224	+	0.514944i	$0.172187\pi$
$569$	−2.10701	+	20.0469i	−0.0883305	+	0.840408i	−0.945554	+	0.325464i	$0.894479\pi$
$570$	1.50505	−	1.98342i	0.0630395	−	0.0830761i
$571$			25.1474i			1.05238i	0.850366	+	0.526192i	$0.176381\pi$
$571$			25.1474i			1.05238i	−0.850366	+	0.526192i	$0.823619\pi$
$572$	−2.08286	+	11.3630i	−0.0870888	+	0.475112i
$573$	15.8565	−	1.33378i	0.662413	−	0.0557195i
$574$	6.23543	−	6.92514i	0.260262	−	0.289050i
$575$	8.22883	+	0.864885i	0.343166	+	0.0360682i
$576$	−1.05333	−	3.76846i	−0.0438888	−	0.157019i
$577$	−7.23072	−	2.34940i	−0.301019	−	0.0978069i	0.154614	−	0.987975i	$-0.450587\pi$
$577$	−7.23072	−	2.34940i	−0.301019	−	0.0978069i	−0.455632	+	0.890168i	$0.650587\pi$
$578$	21.1318	−	19.0271i	0.878965	−	0.791424i
$579$	−38.3697	+	7.32509i	−1.59459	+	0.304420i
$580$	2.87614	+	2.08964i	0.119425	+	0.0867675i
$581$	2.07164	−	9.74630i	0.0859461	−	0.404345i
$582$	19.5165	−	13.5685i	0.808985	−	0.562431i
$583$	−16.0050	+	26.4689i	−0.662860	+	1.09623i
$584$			16.0021i			0.662171i
$585$	12.6092	−	2.76989i	0.521328	−	0.114521i
$586$	−11.1619	−	8.10957i	−0.461093	−	0.335003i
$587$	35.3259	+	15.7281i	1.45806	+	0.649168i	0.974140	−	0.225946i	$-0.0725473\pi$
$587$	35.3259	+	15.7281i	1.45806	+	0.649168i	0.483916	+	0.875114i	$0.339214\pi$
$588$	−2.63775	−	8.73215i	−0.108779	−	0.360108i
$589$	−0.429897	+	0.387081i	−0.0177136	+	0.0159494i
$590$	6.45194	+	8.88034i	0.265622	+	0.365598i
$591$	37.7324	−	20.7506i	1.55210	−	0.853565i
$592$	0.519268	−	2.44296i	0.0213418	−	0.100405i
$593$			35.8539i			1.47234i	0.676795	+	0.736171i	$0.263368\pi$
$593$			35.8539i			1.47234i	−0.676795	+	0.736171i	$0.736632\pi$
$594$	−29.5790	−	2.45039i	−1.21364	−	0.100541i
$595$	−0.519299	−	0.899452i	−0.0212892	−	0.0368739i
$596$	−1.35488	−	1.21993i	−0.0554978	−	0.0499705i
$597$	16.5693	−	27.3681i	0.678138	−	1.12010i
$598$	5.09647	+	13.4355i	0.208410	+	0.549420i
$599$	22.7233	+	7.38326i	0.928450	+	0.301672i	0.733929	−	0.679226i	$-0.237685\pi$
$599$	22.7233	+	7.38326i	0.928450	+	0.301672i	0.194522	+	0.980898i	$0.437685\pi$
$600$	−10.5566	+	3.18886i	−0.430971	+	0.130185i
$601$	2.90617	−	6.52737i	0.118545	−	0.266257i	−0.844521	−	0.535523i	$-0.820114\pi$
$601$	2.90617	−	6.52737i	0.118545	−	0.266257i	0.963066	+	0.269266i	$0.0867812\pi$
$602$	22.0676	−	9.82513i	0.899409	−	0.400443i
$603$	20.7541	−	10.8575i	0.845173	−	0.442153i
$604$	0.156630	−	0.271290i	0.00637317	−	0.0110387i
$605$	−11.7676	−	5.82116i	−0.478423	−	0.236664i
$606$	−24.2993	+	2.04396i	−0.987091	+	0.0830301i
$607$	−8.58568	+	40.3924i	−0.348482	+	1.63948i	0.359426	+	0.933174i	$0.382972\pi$
$607$	−8.58568	+	40.3924i	−0.348482	+	1.63948i	−0.707908	+	0.706305i	$0.750361\pi$
$608$	−3.51074	−	0.368994i	−0.142379	−	0.0149647i
$609$	2.18460	−	6.27620i	0.0885245	−	0.254324i
$610$	3.97148	−	12.2229i	0.160800	−	0.494893i
$611$	1.17798	−	20.8939i	0.0476560	−	0.845276i
$612$	1.41761	−	1.44844i	0.0573033	−	0.0585496i
$613$	−4.38863	+	41.7550i	−0.177255	+	1.68647i	0.438658	+	0.898654i	$0.355454\pi$
$613$	−4.38863	+	41.7550i	−0.177255	+	1.68647i	−0.615913	+	0.787814i	$0.711213\pi$
$614$	−2.04847	−	1.84445i	−0.0826694	−	0.0744359i
$615$	3.82613	−	8.13395i	0.154284	−	0.327993i
$616$	7.21793	−	1.38209i	0.290819	−	0.0556859i
$617$	−11.3559	+	19.6690i	−0.457171	+	0.791844i	−0.998810	−	0.0487672i	$-0.984471\pi$
$617$	−11.3559	+	19.6690i	−0.457171	+	0.791844i	0.541639	+	0.840611i	$0.317804\pi$
$618$	38.3225	+	4.83570i	1.54156	+	0.194521i
$619$	17.8272	−	24.5371i	0.716537	−	0.986228i	−0.283095	−	0.959092i	$-0.591361\pi$
$619$	17.8272	−	24.5371i	0.716537	−	0.986228i	0.999632	−	0.0271363i	$-0.00863882\pi$
$620$	0.948533	−	0.0996948i	0.0380940	−	0.00400384i
$621$	−10.7682	+	5.35113i	−0.432114	+	0.214734i
$622$	55.4076	−	11.7772i	2.22164	−	0.472224i
$623$	−14.8900	+	10.8182i	−0.596554	+	0.433422i
$624$	−21.5210	−	22.6141i	−0.861530	−	0.905287i
$625$	1.74960	+	5.38472i	0.0699841	+	0.215389i
$626$	13.9032	−	8.02702i	0.555684	−	0.320824i
$627$	1.78325	−	3.59990i	0.0712162	−	0.143766i
$628$	−4.14966	+	7.18742i	−0.165589	+	0.286809i
$629$	−0.332291	+	0.107968i	−0.0132493	+	0.00430496i
$630$	4.24823	+	6.39015i	0.169254	+	0.254590i
$631$	−10.9165	+	1.14737i	−0.434577	+	0.0456759i	−0.319292	−	0.947656i	$-0.603445\pi$
$631$	−10.9165	+	1.14737i	−0.434577	+	0.0456759i	−0.115286	+	0.993332i	$0.536778\pi$
$632$	−3.72725	+	11.4713i	−0.148262	+	0.456303i
$633$	10.6263	+	9.97587i	0.422356	+	0.396505i
$634$	19.2494	−	43.2348i	0.764490	−	1.71707i
$635$	5.61449	+	0.590107i	0.222804	+	0.0234177i
$636$	6.04930	+	14.3850i	0.239870	+	0.570401i
$637$	13.8436	+	13.9537i	0.548505	+	0.552866i
$638$	15.9409	+	7.48772i	0.631108	+	0.296442i
$639$	−2.07346	−	2.50492i	−0.0820246	−	0.0990932i
$640$	−10.9467	−	9.85645i	−0.432706	−	0.389610i
$641$	2.14806	+	4.82463i	0.0848433	+	0.190561i	0.950985	−	0.309238i	$-0.100074\pi$
$641$	2.14806	+	4.82463i	0.0848433	+	0.190561i	−0.866141	+	0.499799i	$0.833407\pi$
$642$	23.9260	−	20.6584i	0.944285	−	0.815320i
$643$	17.4863	−	15.7447i	0.689593	−	0.620912i	−0.247954	−	0.968772i	$-0.579758\pi$
$643$	17.4863	−	15.7447i	0.689593	−	0.620912i	0.937547	+	0.347860i	$0.113092\pi$
$644$	−2.06733	+	1.86144i	−0.0814644	+	0.0733509i
$645$	17.6367	−	15.2279i	0.694443	−	0.599600i
$646$	0.342576	+	0.769438i	0.0134785	+	0.0302731i
$647$	24.6739	+	22.2165i	0.970031	+	0.873420i	0.991987	−	0.126339i	$-0.0403228\pi$
$647$	24.6739	+	22.2165i	0.970031	+	0.873420i	−0.0219562	+	0.999759i	$0.506989\pi$
$648$	10.4649	−	12.1377i	0.411100	−	0.476813i
$649$	12.9194	+	12.1152i	0.507129	+	0.475564i
$650$	−15.7615	+	15.6372i	−0.618217	+	0.613340i
$651$	−0.691118	−	1.64345i	−0.0270870	−	0.0644118i
$652$	22.0463	+	2.31716i	0.863400	+	0.0907470i
$653$	10.7033	−	24.0400i	0.418852	−	0.940757i	−0.573715	−	0.819055i	$-0.694498\pi$
$653$	10.7033	−	24.0400i	0.418852	−	0.940757i	0.992567	−	0.121702i	$-0.0388351\pi$
$654$	36.6946	+	34.4486i	1.43487	+	1.34705i
$655$	−6.13248	+	18.8738i	−0.239616	+	0.737461i
$656$	−21.6173	+	2.27207i	−0.844013	+	0.0887093i
$657$	−22.4508	+	14.9255i	−0.875891	+	0.582301i
$658$	11.8299	−	3.84377i	0.461178	−	0.149846i
$659$	18.1801	−	31.4889i	0.708196	−	1.22663i	−0.257329	−	0.966324i	$-0.582842\pi$
$659$	18.1801	−	31.4889i	0.708196	−	1.22663i	0.965526	−	0.260308i	$-0.0838242\pi$
$660$	−5.86722	+	3.07356i	−0.228381	+	0.119638i
$661$	−35.9767	+	20.7712i	−1.39933	+	0.807904i	−0.994322	−	0.106409i	$-0.966065\pi$
$661$	−35.9767	+	20.7712i	−1.39933	+	0.807904i	−0.405009	+	0.914313i	$0.632732\pi$
$662$	−7.86244	−	24.1981i	−0.305583	−	0.940486i
$663$	−1.23440	+	4.18910i	−0.0479403	+	0.162691i
$664$	−11.5353	+	8.38092i	−0.447658	+	0.325243i
$665$	−1.01594	+	0.215944i	−0.0393964	+	0.00837397i
$666$	2.39985	−	0.950958i	0.0929921	−	0.0368489i
$667$	7.09611	−	0.745832i	0.274763	−	0.0288787i
$668$	3.67354	−	5.05619i	0.142133	−	0.195630i
$669$	17.8117	+	2.24756i	0.688642	+	0.0868959i
$670$	8.02423	−	13.8984i	0.310003	−	0.536941i
$671$	2.58476	−	20.5753i	0.0997834	−	0.794301i
$672$	4.63087	−	9.84473i	0.178640	−	0.379769i
$673$	−21.1145	−	19.0116i	−0.813904	−	0.732843i	0.152933	−	0.988237i	$-0.451128\pi$
$673$	−21.1145	−	19.0116i	−0.813904	−	0.732843i	−0.966837	+	0.255394i	$0.917795\pi$
$674$	−4.48175	+	42.6410i	−0.172631	+	1.64247i
$675$	−14.3204	−	11.8365i	−0.551191	−	0.455587i
$676$	−11.9130	−	3.97533i	−0.458191	−	0.152897i
$677$	−7.17343	+	22.0775i	−0.275697	+	0.848509i	0.713337	+	0.700821i	$0.247183\pi$
$677$	−7.17343	+	22.0775i	−0.275697	+	0.848509i	−0.989034	+	0.147687i	$0.952817\pi$
$678$	−1.67820	+	4.82135i	−0.0644510	+	0.185163i
$679$	−9.86134	−	1.03647i	−0.378444	−	0.0397760i
$680$	−0.309004	+	1.45375i	−0.0118498	+	0.0557487i
$681$	3.93201	−	0.330745i	0.150675	−	0.0126742i
$682$	4.52228	−	1.36878i	0.173167	−	0.0524135i
$683$	−3.07617	+	5.32808i	−0.117706	+	0.203873i	−0.918858	−	0.394588i	$-0.870887\pi$
$683$	−3.07617	+	5.32808i	−0.117706	+	0.203873i	0.801152	+	0.598461i	$0.204221\pi$
$684$	−0.939515	−	1.79588i	−0.0359233	−	0.0686672i
$685$	16.7081	−	7.43891i	0.638383	−	0.284226i
$686$	−10.8536	+	24.3777i	−0.414394	+	0.930744i
$687$	−30.7581	+	9.29119i	−1.17349	+	0.354481i
$688$	−53.5874	−	17.4116i	−2.04300	−	0.663811i
$689$	−26.0484	−	21.2649i	−0.992366	−	0.810129i
$690$	−4.26693	+	7.04781i	−0.162439	+	0.268306i
$691$	2.31746	+	2.08665i	0.0881604	+	0.0793799i	0.712033	−	0.702146i	$-0.247775\pi$
$691$	2.31746	+	2.08665i	0.0881604	+	0.0793799i	−0.623872	+	0.781526i	$0.714441\pi$
$692$	−10.1077	−	17.5070i	−0.384237	−	0.665518i
$693$	8.67141	+	8.83762i	0.329400	+	0.335713i
$694$			11.3574i			0.431120i
$695$	0.408883	−	1.92364i	0.0155098	−	0.0729679i
$696$	−8.33277	+	4.58253i	−0.315853	+	0.173700i
$697$	1.78733	+	2.46005i	0.0676999	+	0.0931809i
$698$	25.7608	−	23.1951i	0.975061	−	0.877949i
$699$	12.8487	+	42.5351i	0.485983	+	1.60883i
$700$	−3.92663	−	1.74825i	−0.148413	−	0.0660775i
$701$	18.2265	+	13.2423i	0.688404	+	0.500155i	0.876135	−	0.482066i	$-0.160113\pi$
$701$	18.2265	+	13.2423i	0.688404	+	0.500155i	−0.187731	+	0.982220i	$0.560113\pi$
$702$	7.14975	−	31.4637i	0.269850	−	1.18752i
$703$			0.349404i			0.0131780i
$704$	−3.70175	−	2.23835i	−0.139515	−	0.0843610i
$705$	9.85158	−	6.84911i	0.371032	−	0.257952i
$706$	5.61476	−	26.4154i	0.211314	−	0.994155i
$707$	8.22964	+	5.97918i	0.309507	+	0.224870i
$708$	8.77693	−	1.67559i	0.329857	−	0.0629724i
$709$	6.62827	−	5.96812i	0.248930	−	0.224137i	−0.535214	−	0.844716i	$-0.679769\pi$
$709$	6.62827	−	5.96812i	0.248930	−	0.224137i	0.784144	+	0.620579i	$0.213102\pi$
$710$	−2.11895	−	0.688489i	−0.0795228	−	0.0258385i
$711$	−19.5707	+	5.47025i	−0.733957	+	0.205150i
$712$	26.1932	+	2.75301i	0.981631	+	0.103174i
$713$	1.28086	−	1.42254i	0.0479687	−	0.0532746i
$714$	−2.58665	+	0.217578i	−0.0968028	+	0.00814267i
$715$	8.06079	−	11.7782i	0.301457	−	0.440479i
$716$			15.4002i			0.575533i
$717$	8.68144	−	11.4408i	0.324214	−	0.427263i
$718$	−4.32012	+	41.1032i	−0.161226	+	1.53396i
$719$	−2.08773	+	0.219429i	−0.0778591	+	0.00818332i	−0.143378	−	0.989668i	$-0.545796\pi$
$719$	−2.08773	+	0.219429i	−0.0778591	+	0.00818332i	0.0655188	+	0.997851i	$0.479130\pi$
$720$	2.60964	−	17.7074i	0.0972556	−	0.659916i
$721$	−10.7819	−	11.9745i	−0.401537	−	0.445952i
$722$	−31.7053	+	3.33236i	−1.17995	+	0.124018i
$723$	−12.4822	+	20.6172i	−0.464218	+	0.766762i
$724$	−1.13378	−	0.240993i	−0.0421367	−	0.00895642i
$725$	5.51224	+	9.54749i	0.204720	+	0.354585i
$726$	−25.6839	+	20.4209i	−0.953220	+	0.757892i
$727$	27.7235			1.02821			0.514103	−	0.857728i	$-0.328125\pi$
$727$	27.7235			1.02821			0.514103	+	0.857728i	$0.328125\pi$
$728$	0.386531	+	7.97991i	0.0143258	+	0.295755i
$729$	26.7900	+	3.36107i	0.992222	+	0.124484i
$730$	−7.51316	+	16.8748i	−0.278074	+	0.624565i
$731$	1.63883	+	7.71010i	0.0606144	+	0.285168i
$732$	−7.62747	−	7.16062i	−0.281919	−	0.264664i
$733$	−24.6217	+	17.8887i	−0.909423	+	0.660734i	−0.940869	−	0.338771i	$-0.889989\pi$
$733$	−24.6217	+	17.8887i	−0.909423	+	0.660734i	0.0314461	+	0.999505i	$0.489989\pi$
$734$	−12.9808	−	29.1553i	−0.479129	−	1.07614i
$735$	−1.41087	+	11.1810i	−0.0520406	+	0.412417i
$736$	11.6811			0.430573
$737$	8.49892	−	24.4602i	0.313062	−	0.901004i
$738$	−14.3254	−	17.3063i	−0.527324	−	0.637055i
$739$	−3.31905	+	3.68618i	−0.122093	+	0.135598i	−0.801092	−	0.598541i	$-0.795747\pi$
$739$	−3.31905	+	3.68618i	−0.122093	+	0.135598i	0.678999	+	0.734139i	$0.262414\pi$
$740$	0.338605	−	0.466050i	0.0124474	−	0.0171323i
$741$	3.60275	+	2.46858i	0.132350	+	0.0906855i
$742$	6.17627	−	19.0086i	0.226738	−	0.697828i
$743$	−0.758930	−	3.57048i	−0.0278424	−	0.130988i	0.962031	−	0.272939i	$-0.0879958\pi$
$743$	−0.758930	−	3.57048i	−0.0278424	−	0.130988i	−0.989874	+	0.141951i	$0.954662\pi$
$744$	−0.838677	+	2.40946i	−0.0307474	+	0.0883351i
$745$	0.916149	+	2.05770i	0.0335651	+	0.0753885i
$746$	16.7731	+	51.6224i	0.614109	+	1.89003i
$747$	−22.5177	−	8.36694i	−0.823879	−	0.306130i
$748$	0.0453687	−	2.24016i	0.00165884	−	0.0819083i
$749$	−13.1865			−0.481824
$750$	−30.2907	−	3.82222i	−1.10606	−	0.139568i
$751$	−4.47266	+	42.5546i	−0.163210	+	1.55284i	0.539883	+	0.841740i	$0.318468\pi$
$751$	−4.47266	+	42.5546i	−0.163210	+	1.55284i	−0.703093	+	0.711098i	$0.748198\pi$
$752$	−26.5055	−	11.8010i	−0.966558	−	0.430339i
$753$	3.62593	−	15.4692i	0.132136	−	0.563727i
$754$	−10.4912	+	16.0159i	−0.382069	+	0.583265i
$755$	−0.313104	+	0.227483i	−0.0113950	+	0.00827897i
$756$	6.17905	−	0.915145i	0.224730	−	0.0332835i
$757$	−23.2061	+	25.7730i	−0.843440	+	0.936735i	−0.998691	−	0.0511403i	$-0.983714\pi$
$757$	−23.2061	+	25.7730i	−0.843440	+	0.936735i	0.155252	+	0.987875i	$0.450381\pi$
$758$	20.8498	−	36.1130i	0.757300	−	1.31168i
$759$	−4.62335	+	12.4637i	−0.167817	+	0.452405i
$760$	1.28716	+	0.743140i	0.0466901	+	0.0269565i
$761$	2.80508	−	13.1969i	0.101684	−	0.478386i	−0.897609	−	0.440792i	$-0.854697\pi$
$761$	2.80508	−	13.1969i	0.101684	−	0.478386i	0.999293	−	0.0375935i	$-0.0119692\pi$
$762$	7.30747	−	12.0700i	0.264722	−	0.437248i
$763$	−2.19466	−	20.8808i	−0.0794521	−	0.755937i
$764$	−1.84526	−	8.68127i	−0.0667592	−	0.314077i
$765$	−2.32782	+	0.922417i	−0.0841625	+	0.0333501i
$766$	−19.6187	−	27.0028i	−0.708853	−	0.975653i
$767$	−15.0111	+	12.0577i	−0.542021	+	0.435378i
$768$	−29.7718	+	12.5199i	−1.07430	+	0.451774i
$769$	4.31818	+	7.47931i	0.155718	+	0.269711i	0.933320	−	0.359045i	$-0.116898\pi$
$769$	4.31818	+	7.47931i	0.155718	+	0.269711i	−0.777602	+	0.628756i	$0.783564\pi$
$770$	8.26050	+	1.93143i	0.297688	+	0.0696040i
$771$	15.5825	−	33.1268i	0.561190	−	1.19303i
$772$	6.73265	+	20.7210i	0.242313	+	0.745764i
$773$	24.5225	−	10.9181i	0.882014	−	0.392698i	0.0848024	−	0.996398i	$-0.472974\pi$
$773$	24.5225	−	10.9181i	0.882014	−	0.392698i	0.797212	+	0.603700i	$0.206307\pi$
$774$	−15.6770	−	56.0870i	−0.563499	−	2.01601i
$775$	2.81287	+	0.913958i	0.101041	+	0.0328304i
$776$	9.49446	+	10.5447i	0.340831	+	0.378531i
$777$	−1.01700	−	0.353993i	−0.0364845	−	0.0126994i
$778$	−0.749321	+	7.12931i	−0.0268645	+	0.255598i
$779$	2.89206	−	0.939688i	0.103619	−	0.0336678i
$780$	−2.41321	−	6.78410i	−0.0864070	−	0.242910i
$781$	−3.56691	−	0.448089i	−0.127634	−	0.0160339i
$782$	−1.39352	−	2.41365i	−0.0498323	−	0.0863121i
$783$	−14.2015	−	7.41661i	−0.507519	−	0.265048i
$784$	24.8954	−	11.0842i	0.889123	−	0.395863i
$785$	8.29520	−	6.02682i	0.296068	−	0.215106i
$786$	36.1611	+	33.9478i	1.28982	+	1.21088i
$787$	−7.76892	−	8.62825i	−0.276932	−	0.307564i	0.588593	−	0.808429i	$-0.299682\pi$
$787$	−7.76892	−	8.62825i	−0.276932	−	0.307564i	−0.865525	+	0.500865i	$0.833015\pi$
$788$	−14.1174	−	19.4309i	−0.502910	−	0.692196i
$789$	−22.0579	−	40.1097i	−0.785283	−	1.42794i
$790$	−9.31643	+	10.3469i	−0.331464	+	0.368128i
$791$	1.84430	−	1.06481i	0.0655757	−	0.0378602i
$792$	−0.759274	−	17.7013i	−0.0269796	−	0.628988i
$793$	21.7521	+	5.92087i	0.772440	+	0.210256i
$794$	6.17610	+	19.0081i	0.219182	+	0.674572i
$795$	0.401010	−	19.2753i	0.0142224	−	0.683625i
$796$	−16.3015	−	7.25789i	−0.577791	−	0.257249i
$797$	−30.0892	+	27.0924i	−1.06581	+	0.959662i	−0.999273	−	0.0381216i	$-0.987863\pi$
$797$	−30.0892	+	27.0924i	−1.06581	+	0.959662i	−0.0665397	+	0.997784i	$0.521196\pi$
$798$	−0.592410	+	2.52737i	−0.0209711	+	0.0894681i
$799$	0.424268	+	4.03664i	0.0150095	+	0.142806i
$800$	7.34093	+	16.4880i	0.259541	+	0.582939i
$801$	20.5686	+	39.3167i	0.726755	+	1.38919i
$802$	−17.7721	−	10.2607i	−0.627556	−	0.362320i
$803$	−6.78580	+	29.0220i	−0.239466	+	1.02417i
$804$	−7.45735	−	10.7265i	−0.263001	−	0.378293i
$805$	3.26867	−	1.06205i	0.115205	−	0.0374325i
$806$	0.783431	+	5.07640i	0.0275952	+	0.178809i
$807$	−27.6734	+	23.8940i	−0.974151	+	0.841107i
$808$	−3.02649	−	14.2385i	−0.106472	−	0.500909i
$809$	−9.60663	+	2.04195i	−0.337751	+	0.0717912i	−0.373665	−	0.927564i	$-0.621899\pi$
$809$	−9.60663	+	2.04195i	−0.337751	+	0.0717912i	0.0359140	+	0.999355i	$0.488566\pi$
$810$	16.7344	−	7.88629i	0.587988	−	0.277096i
$811$	−4.15964	−	3.02216i	−0.146065	−	0.106122i	0.512353	−	0.858775i	$-0.328774\pi$
$811$	−4.15964	−	3.02216i	−0.146065	−	0.106122i	−0.658418	+	0.752653i	$0.728774\pi$
$812$	−3.62557	−	0.770639i	−0.127233	−	0.0270441i
$813$	15.1930	+	7.14662i	0.532840	+	0.250643i
$814$	1.21331	−	2.58307i	0.0425265	−	0.0905365i
$815$	−23.7181	−	13.6936i	−0.830808	−	0.479667i
$816$	4.82335	+	3.66004i	0.168851	+	0.128127i
$817$	7.83945	+	0.823959i	0.274268	+	0.0288267i
$818$	−24.4177	−	33.6081i	−0.853746	−	1.17508i
$819$	−10.8353	+	7.98537i	−0.378615	+	0.279031i
$820$	−4.76821	−	1.54928i	−0.166513	−	0.0541034i
$821$	−3.07992	+	6.91762i	−0.107490	+	0.241427i	−0.959280	−	0.282457i	$-0.908851\pi$
$821$	−3.07992	+	6.91762i	−0.107490	+	0.241427i	0.851790	+	0.523884i	$0.175517\pi$
$822$	0.950772	−	45.7007i	0.0331620	−	1.59400i
$823$	−27.8305	−	5.91556i	−0.970110	−	0.206203i	−0.304508	−	0.952510i	$-0.598492\pi$
$823$	−27.8305	−	5.91556i	−0.970110	−	0.206203i	−0.665602	+	0.746307i	$0.731825\pi$
$824$			23.0579i			0.803261i
$825$	−20.4981	+	1.30686i	−0.713653	+	0.0454989i
$826$	−9.91110	−	5.72218i	−0.344851	−	0.199100i
$827$	15.5834	−	5.06335i	0.541888	−	0.176070i	−0.0252677	−	0.999681i	$-0.508044\pi$
$827$	15.5834	−	5.06335i	0.541888	−	0.176070i	0.567156	+	0.823611i	$0.308044\pi$
$828$	3.71303	+	5.58510i	0.129037	+	0.194096i
$829$	46.4295	+	20.6717i	1.61256	+	0.717959i	0.997510	−	0.0705263i	$-0.0224679\pi$
$829$	46.4295	+	20.6717i	1.61256	+	0.717959i	0.615053	+	0.788486i	$0.289135\pi$
$830$	−16.0994	+	3.42204i	−0.558819	+	0.118781i
$831$	−5.01980	+	21.4158i	−0.174135	+	0.742905i
$832$	2.97397	−	3.64295i	0.103104	−	0.126297i
$833$	−3.08423	−	2.24082i	−0.106862	−	0.0776399i
$834$	−3.91552	−	2.97116i	−0.135583	−	0.102883i
$835$	−6.68688	+	3.86067i	−0.231409	+	0.133604i
$836$	−2.11657	−	0.735422i	−0.0732033	−	0.0254351i
$837$	−4.16272	+	1.07070i	−0.143885	+	0.0370089i
$838$	−12.9584	−	2.75440i	−0.447642	−	0.0951492i
$839$	16.7919	−	7.47621i	0.579719	−	0.258108i	−0.0958603	−	0.995395i	$-0.530560\pi$
$839$	16.7919	−	7.47621i	0.579719	−	0.258108i	0.675579	+	0.737287i	$0.263894\pi$
$840$	−3.46709	+	2.99358i	−0.119626	+	0.103288i
$841$	−13.0434	−	14.4862i	−0.449772	−	0.499523i
$842$	38.7332	−	8.23299i	1.33483	−	0.283727i
$843$	−9.68595	−	3.37146i	−0.333602	−	0.116119i
$844$	4.77831	−	6.57678i	0.164476	−	0.226382i
$845$	11.4479	+	10.4731i	0.393819	+	0.360284i
$846$	−5.00950	−	29.5666i	−0.172230	−	1.01652i
$847$	13.6768	+	0.554206i	0.469941	+	0.0190428i
$848$	−40.3744	+	23.3102i	−1.38646	+	0.800474i
$849$	−44.8657	−	5.66136i	−1.53979	−	0.194297i
$850$	2.53114	−	3.48381i	0.0868172	−	0.119494i
$851$	−0.120855	−	1.14985i	−0.00414284	−	0.0394165i
$852$	−1.24135	+	1.32229i	−0.0425281	+	0.0453008i
$853$	17.1391	−	52.7487i	0.586831	−	1.80608i	−0.00495678	−	0.999988i	$-0.501578\pi$
$853$	17.1391	−	52.7487i	0.586831	−	1.80608i	0.591788	−	0.806094i	$-0.298422\pi$
$854$	1.40063	+	13.3261i	0.0479286	+	0.456010i
$855$	0.157941	+	2.49902i	0.00540146	+	0.0854647i
$856$	14.0230	+	12.6264i	0.479296	+	0.431560i
$857$	−17.9504			−0.613173			−0.306587	−	0.951843i	$-0.599187\pi$
$857$	−17.9504			−0.613173			−0.306587	+	0.951843i	$0.599187\pi$
$858$	−18.0622	−	30.7603i	−0.616633	−	1.05014i
$859$	9.39050			0.320400			0.160200	−	0.987085i	$-0.448786\pi$
$859$	9.39050			0.320400			0.160200	+	0.987085i	$0.448786\pi$
$860$	−9.65811	−	8.69620i	−0.329339	−	0.296538i
$861$	−0.194933	+	9.36984i	−0.00664330	+	0.319323i
$862$	1.01292	+	9.63733i	0.0345003	+	0.328249i
$863$	4.90783	−	15.1047i	0.167064	−	0.514171i	−0.832118	−	0.554598i	$-0.812872\pi$
$863$	4.90783	−	15.1047i	0.167064	−	0.514171i	0.999182	+	0.0404272i	$0.0128719\pi$
$864$	−21.8529	−	14.5056i	−0.743451	−	0.493489i
$865$	2.61062	+	24.8384i	0.0887637	+	0.844530i
$866$	5.52211	−	7.60053i	0.187649	−	0.258276i
$867$	−3.58021	+	28.3728i	−0.121590	+	0.963592i
$868$	−0.861168	+	0.497196i	−0.0292300	+	0.0168759i
$869$	−11.6244	+	19.2242i	−0.394330	+	0.652138i
$870$	−10.9388	+	0.920127i	−0.370860	+	0.0311952i
$871$	25.0315	+	12.8793i	0.848159	+	0.436397i
$872$	−17.6600	+	24.3068i	−0.598041	+	0.823133i
$873$	−5.93840	+	23.1560i	−0.200984	+	0.783710i
$874$	−2.72624	+	0.579481i	−0.0922166	+	0.0196012i
$875$	8.52216	+	9.46481i	0.288101	+	0.319969i
$876$	9.82692	+	11.3813i	0.332021	+	0.384539i
$877$	25.5467	−	11.3741i	0.862650	−	0.384077i	0.0727781	−	0.997348i	$-0.476814\pi$
$877$	25.5467	−	11.3741i	0.862650	−	0.384077i	0.789872	+	0.613272i	$0.210147\pi$
$878$	43.3885	+	9.22251i	1.46429	+	0.311245i
$879$	13.8267	−	1.16305i	0.466364	−	0.0392287i
$880$	−11.3044	−	16.2408i	−0.381071	−	0.547478i
$881$	30.9363	−	17.8611i	1.04227	−	0.601754i	0.121794	−	0.992555i	$-0.461135\pi$
$881$	30.9363	−	17.8611i	1.04227	−	0.601754i	0.920475	+	0.390801i	$0.127802\pi$
$882$	23.7860	+	15.0855i	0.800915	+	0.507955i
$883$	30.6129	+	22.2415i	1.03020	+	0.748488i	0.968350	−	0.249598i	$-0.0802983\pi$
$883$	30.6129	+	22.2415i	1.03020	+	0.748488i	0.0618551	+	0.998085i	$0.480298\pi$
$884$	2.40429	+	0.390568i	0.0808651	+	0.0131362i
$885$	−10.7480	−	2.51931i	−0.361291	−	0.0846856i
$886$	29.3724	−	6.24329i	0.986784	−	0.209747i
$887$	8.66202	+	3.85658i	0.290842	+	0.129491i	0.546971	−	0.837151i	$-0.315781\pi$
$887$	8.66202	+	3.85658i	0.290842	+	0.129491i	−0.256129	+	0.966643i	$0.582447\pi$
$888$	0.742553	+	1.35024i	0.0249185	+	0.0453112i
$889$	−5.59786	+	1.81885i	−0.187746	+	0.0610024i
$890$	26.3292	+	15.2012i	0.882556	+	0.509544i
$891$	24.1266	−	17.5757i	0.808273	−	0.588808i
$892$		−	10.0133i		−	0.335271i
$893$	3.97032	+	0.843918i	0.132862	+	0.0282406i
$894$	5.62833	+	0.117094i	0.188240	+	0.00391619i
$895$	7.73868	−	17.3814i	0.258675	−	0.580995i
$896$	14.6061	+	4.74582i	0.487957	+	0.158547i
$897$	−12.7101	−	6.87771i	−0.424380	−	0.229640i
$898$	−6.38735	−	8.79143i	−0.213148	−	0.293374i
$899$	2.53653	+	0.266600i	0.0845982	+	0.00889162i
$900$	−5.54997	+	8.75088i	−0.184999	+	0.291696i
$901$	5.64813	+	3.26095i	0.188167	+	0.108638i
$902$	−24.6435	−	3.09582i	−0.820539	−	0.103079i
$903$	−10.3407	+	21.9832i	−0.344116	+	0.731555i
$904$	−2.98087	−	0.633603i	−0.0991422	−	0.0210733i
$905$	1.15854	+	0.841726i	0.0385110	+	0.0279799i
$906$	0.181385	+	0.950120i	0.00602613	+	0.0315656i
$907$	−23.2496	+	4.94186i	−0.771990	+	0.164092i	−0.577034	−	0.816720i	$-0.695790\pi$
$907$	−23.2496	+	4.94186i	−0.771990	+	0.164092i	−0.194957	+	0.980812i	$0.562457\pi$
$908$	−0.457580	−	2.15274i	−0.0151853	−	0.0714413i
$909$	17.1537	−	17.5268i	0.568952	−	0.581327i
$910$	−3.33905	+	8.59662i	−0.110688	+	0.284975i
$911$	9.95029	−	3.23304i	0.329668	−	0.107116i	−0.139507	−	0.990221i	$-0.544552\pi$
$911$	9.95029	−	3.23304i	0.329668	−	0.107116i	0.469174	+	0.883106i	$0.344552\pi$
$912$	4.97158	−	3.45639i	0.164625	−	0.114452i
$913$	−24.4750	+	10.3083i	−0.810003	+	0.341156i
$914$	−4.54456	−	2.62381i	−0.150321	−	0.0867878i
$915$	5.01045	+	11.9146i	0.165640	+	0.393886i
$916$	7.28913	+	16.3717i	0.240840	+	0.540935i
$917$	−2.16276	−	20.5772i	−0.0714205	−	0.679520i
$918$	−0.390275	+	6.24589i	−0.0128810	+	0.206145i
$919$	−14.8940	+	13.4106i	−0.491308	+	0.442375i	−0.877169	−	0.480181i	$-0.840571\pi$
$919$	−14.8940	+	13.4106i	−0.491308	+	0.442375i	0.385862	+	0.922557i	$0.373904\pi$
$920$	−4.49296	−	2.00039i	−0.148128	−	0.0659510i
$921$	2.77161	+	0.0576615i	0.0913278	+	0.00190001i
$922$	−21.9983	−	67.7038i	−0.724475	−	2.22971i
$923$	1.02643	−	3.77091i	0.0337855	−	0.124121i
$924$	4.28494	−	5.41555i	0.140964	−	0.178158i
$925$	1.54708	−	0.893204i	0.0508675	−	0.0293684i
$926$	−33.9437	+	37.6983i	−1.11546	+	1.23884i
$927$	−32.3502	+	21.5067i	−1.06252	+	0.706373i
$928$	9.14827	+	12.5915i	0.300307	+	0.413337i
$929$	−9.97978	−	11.0837i	−0.327426	−	0.363643i	0.556846	−	0.830616i	$-0.312011\pi$
$929$	−9.97978	−	11.0837i	−0.327426	−	0.363643i	−0.884272	+	0.466973i	$0.845345\pi$
$930$	−2.01569	+	2.14710i	−0.0660970	+	0.0704063i
$931$	−3.08434	+	2.24090i	−0.101085	+	0.0734426i
$932$	22.6403	−	10.0801i	0.741606	−	0.330184i
$933$	−34.4367	+	45.3821i	−1.12741	+	1.48574i
$934$	−28.1418	−	48.7430i	−0.920828	−	1.59492i
$935$	−1.17690	+	2.50554i	−0.0384886	+	0.0819401i
$936$	19.1688	+	1.88307i	0.626550	+	0.0615500i
$937$	27.0101	−	8.77611i	0.882381	−	0.286703i	0.167435	−	0.985883i	$-0.446451\pi$
$937$	27.0101	−	8.77611i	0.882381	−	0.286703i	0.714946	+	0.699180i	$0.246451\pi$
$938$	−1.74899	+	16.6405i	−0.0571066	+	0.543333i
$939$	−5.30759	+	15.2483i	−0.173207	+	0.497610i
$940$	−4.47795	−	4.97327i	−0.146055	−	0.162210i
$941$	−1.39876	−	0.454485i	−0.0455983	−	0.0148158i	0.286129	−	0.958191i	$-0.407631\pi$
$941$	−1.39876	−	0.454485i	−0.0455983	−	0.0148158i	−0.331727	+	0.943375i	$0.607631\pi$
$942$	−4.80553	−	25.1719i	−0.156572	−	0.820146i
$943$	−9.19248	+	4.09275i	−0.299348	+	0.133278i
$944$	8.24907	+	25.3880i	0.268484	+	0.826310i
$945$	−7.43382	−	2.07213i	−0.241822	−	0.0674064i
$946$	−55.0942	−	33.3140i	−1.79127	−	1.08313i
$947$	−25.7583	−	44.6147i	−0.837033	−	1.44978i	−0.892365	−	0.451315i	$-0.850955\pi$
$947$	−25.7583	−	44.6147i	−0.837033	−	1.44978i	0.0553317	−	0.998468i	$-0.482378\pi$
$948$	4.39358	+	10.4478i	0.142697	+	0.339327i
$949$	−30.2029	−	11.7312i	−0.980429	−	0.380812i
$950$	−2.53123	−	3.48394i	−0.0821239	−	0.113034i
$951$	13.7634	+	45.5630i	0.446308	+	1.47748i
$952$	−0.322169	−	1.51568i	−0.0104415	−	0.0491236i
$953$	−2.91249	−	27.7104i	−0.0943447	−	0.897630i	−0.934663	−	0.355536i	$-0.884298\pi$
$953$	−2.91249	−	27.7104i	−0.0943447	−	0.897630i	0.840318	−	0.542094i	$-0.182368\pi$
$954$	−43.1664	−	21.4127i	−1.39757	−	0.693260i
$955$	−2.27974	+	10.7253i	−0.0737706	+	0.347063i
$956$	−6.93711	−	4.00514i	−0.224362	−	0.129536i
$957$	−17.0559	+	4.77749i	−0.551340	+	0.154434i
$958$	−3.26575	+	5.65644i	−0.105512	+	0.182751i
$959$	−12.7593	+	14.1706i	−0.412019	+	0.457593i
$960$	2.69571	+	0.0560825i	0.0870038	+	0.00181005i
$961$	−24.5260	+	17.8192i	−0.791160	+	0.574811i
$962$	2.59522	+	1.70000i	0.0836732	+	0.0548103i
$963$	−4.63513	+	31.4511i	−0.149365	+	1.01350i
$964$	12.2804	+	5.46760i	0.395526	+	0.176099i
$965$	2.81362	−	26.7698i	0.0905737	−	0.861751i
$966$	1.07538	−	8.52226i	0.0345997	−	0.274199i
$967$	−42.0622			−1.35263			−0.676315	−	0.736613i	$-0.736424\pi$
$967$	−42.0622			−1.35263			−0.676315	+	0.736613i	$0.736424\pi$
$968$	−14.0138	−	13.6852i	−0.450419	−	0.439860i
$969$	−0.766494	−	0.360551i	−0.0246233	−	0.0115826i
$970$	5.06144	+	15.5775i	0.162513	+	0.500164i
$971$	−8.50135	−	19.0943i	−0.272821	−	0.612767i	0.724225	−	0.689563i	$-0.242197\pi$
$971$	−8.50135	−	19.0943i	−0.272821	−	0.612767i	−0.997047	+	0.0767965i	$0.975531\pi$
$972$	−0.0107401	−	15.0593i	−0.000344489	−	0.483028i
$973$	0.426303	+	2.00560i	0.0136666	+	0.0642965i
$974$	0.596776	−	1.83669i	0.0191219	−	0.0588512i
$975$	1.72033	−	22.2627i	0.0550946	−	0.712977i
$976$	18.3713	−	25.2859i	0.588050	−	0.809381i
$977$	20.3623	−	22.6146i	0.651446	−	0.723505i	−0.323430	−	0.946252i	$-0.604836\pi$
$977$	20.3623	−	22.6146i	0.651446	−	0.723505i	0.974876	+	0.222748i	$0.0715026\pi$
$978$	−56.2016	+	39.0730i	−1.79713	+	1.24942i
$979$	46.3376	+	16.1004i	1.48096	+	0.514571i
$980$	6.28568			0.200789
$981$	−50.5743	−	2.10524i	−1.61471	−	0.0672151i
$982$	4.67629	+	10.5031i	0.149226	+	0.335168i
$983$	29.6666	−	21.5540i	0.946216	−	0.687466i	−0.00369283	−	0.999993i	$-0.501175\pi$
$983$	29.6666	−	21.5540i	0.946216	−	0.687466i	0.949909	+	0.312527i	$0.101175\pi$
$984$	9.17912	−	9.77757i	0.292620	−	0.311697i
$985$	6.16937	+	29.0246i	0.196572	+	0.924800i
$986$	1.51040	−	3.39242i	0.0481010	−	0.108037i
$987$	−6.47883	+	10.7013i	−0.206223	+	0.340625i
$988$	1.11446	−	2.16600i	0.0354557	−	0.0689098i
$989$	−26.0839			−0.829419
$990$	7.51027	−	19.0232i	0.238692	−	0.604597i
$991$	7.25232	+	12.5614i	0.230378	+	0.399026i	0.957919	−	0.287038i	$-0.0926705\pi$
$991$	7.25232	+	12.5614i	0.230378	+	0.399026i	−0.727542	+	0.686064i	$0.759337\pi$
$992$	4.08423	+	0.868130i	0.129674	+	0.0275631i
$993$	21.8894	+	13.2525i	0.694640	+	0.420554i
$994$	2.31019	−	0.242811i	0.0732749	−	0.00770150i
$995$	14.7515	+	16.3832i	0.467653	+	0.519381i
$996$	−3.05765	+	13.0447i	−0.0968854	+	0.413338i
$997$	−48.6579	+	5.11415i	−1.54101	+	0.161967i	−0.836596	−	0.547821i	$-0.815458\pi$
$997$	−48.6579	+	5.11415i	−1.54101	+	0.161967i	−0.704416	+	0.709788i	$0.748791\pi$
$998$	4.96409	−	47.2302i	0.157136	−	1.49504i
$999$	−1.20179	+	2.30120i	−0.0380229	+	0.0728069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bm.a.413.40	yes	416
3.2	odd	2	inner	429.2.bm.a.413.13	yes	416
11.2	odd	10	inner	429.2.bm.a.101.40	yes	416
13.4	even	6	inner	429.2.bm.a.17.13	✓	416
33.2	even	10	inner	429.2.bm.a.101.13	yes	416
39.17	odd	6	inner	429.2.bm.a.17.40	yes	416
143.134	odd	30	inner	429.2.bm.a.134.13	yes	416
429.134	even	30	inner	429.2.bm.a.134.40	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bm.a.17.13	✓	416	13.4	even	6	inner
429.2.bm.a.17.40	yes	416	39.17	odd	6	inner
429.2.bm.a.101.13	yes	416	33.2	even	10	inner
429.2.bm.a.101.40	yes	416	11.2	odd	10	inner
429.2.bm.a.134.13	yes	416	143.134	odd	30	inner
429.2.bm.a.134.40	yes	416	429.134	even	30	inner
429.2.bm.a.413.13	yes	416	3.2	odd	2	inner
429.2.bm.a.413.40	yes	416	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bm (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.27986 + 1.15239i) q^{2} +(-1.73168 - 0.0360263i) q^{3} +(0.100980 + 0.960764i) q^{4} +(0.368818 - 1.13510i) q^{5} +(-2.17479 - 2.04168i) q^{6} +(0.130072 + 1.23755i) q^{7} +(1.04666 - 1.44060i) q^{8} +(2.99740 + 0.124772i) q^{9} +O(q^{10})\)	\(q+(1.27986 + 1.15239i) q^{2} +(-1.73168 - 0.0360263i) q^{3} +(0.100980 + 0.960764i) q^{4} +(0.368818 - 1.13510i) q^{5} +(-2.17479 - 2.04168i) q^{6} +(0.130072 + 1.23755i) q^{7} +(1.04666 - 1.44060i) q^{8} +(2.99740 + 0.124772i) q^{9} +(1.78012 - 1.02775i) q^{10} +(2.50916 - 2.16889i) q^{11} +(-0.140253 - 1.66737i) q^{12} +(1.95174 + 3.03162i) q^{13} +(-1.25967 + 1.73379i) q^{14} +(-0.679567 + 1.95235i) q^{15} +(4.88961 - 1.03932i) q^{16} +(-0.467929 - 0.519688i) q^{17} +(3.69248 + 3.61388i) q^{18} +(-0.638873 + 0.284445i) q^{19} +(1.12781 + 0.239724i) q^{20} +(-0.180658 - 2.14772i) q^{21} +(5.71080 + 0.115658i) q^{22} +(2.00409 - 1.15706i) q^{23} +(-1.86437 + 2.45695i) q^{24} +(2.89265 + 2.10163i) q^{25} +(-0.995668 + 6.12922i) q^{26} +(-5.18604 - 0.324050i) q^{27} +(-1.17586 + 0.249937i) q^{28} +(2.81676 + 1.25410i) q^{29} +(-3.11962 + 1.71561i) q^{30} +(0.786706 - 0.255616i) q^{31} +(4.37150 + 2.52389i) q^{32} +(-4.42320 + 3.66543i) q^{33} -1.20437i q^{34} +(1.45272 + 0.308786i) q^{35} +(0.182803 + 2.89240i) q^{36} +(0.203215 - 0.456429i) q^{37} +(-1.14546 - 0.372183i) q^{38} +(-3.27055 - 5.32010i) q^{39} +(-1.24921 - 1.71939i) q^{40} +(-4.32445 - 0.454518i) q^{41} +(2.24381 - 2.95698i) q^{42} +(-9.76151 - 5.63581i) q^{43} +(2.33717 + 2.19170i) q^{44} +(1.24713 - 3.35635i) q^{45} +(3.89834 + 0.828618i) q^{46} +(-4.69563 - 3.41158i) q^{47} +(-8.50467 + 1.62361i) q^{48} +(5.33242 - 1.13344i) q^{49} +(1.28029 + 6.02327i) q^{50} +(0.791579 + 0.916788i) q^{51} +(-2.71559 + 2.18129i) q^{52} +(-8.86976 + 2.88196i) q^{53} +(-6.26398 - 6.39109i) q^{54} +(-1.53650 - 3.64809i) q^{55} +(1.91896 + 1.10791i) q^{56} +(1.11657 - 0.469550i) q^{57} +(2.15985 + 4.85110i) q^{58} +(0.558197 + 5.31089i) q^{59} +(-1.94437 - 0.455755i) q^{60} +(4.64648 - 4.18371i) q^{61} +(1.30144 + 0.579441i) q^{62} +(0.235466 + 3.72567i) q^{63} +(-0.403051 - 1.24046i) q^{64} +(4.16104 - 1.09731i) q^{65} +(-9.88509 - 0.406021i) q^{66} +(6.76153 - 3.90377i) q^{67} +(0.452046 - 0.502048i) q^{68} +(-3.51211 + 1.93145i) q^{69} +(1.50344 + 2.06931i) q^{70} +(-0.725281 - 0.805506i) q^{71} +(3.31701 - 4.18747i) q^{72} +(-7.27022 + 5.28212i) q^{73} +(0.786073 - 0.349982i) q^{74} +(-4.93342 - 3.74356i) q^{75} +(-0.337798 - 0.585083i) q^{76} +(3.01049 + 2.82311i) q^{77} +(1.94499 - 10.5780i) q^{78} +(-6.44207 + 2.09316i) q^{79} +(0.623640 - 5.93354i) q^{80} +(8.96886 + 0.747984i) q^{81} +(-5.01092 - 5.56519i) q^{82} +(-7.61540 - 2.47439i) q^{83} +(2.04521 - 0.390448i) q^{84} +(-0.762480 + 0.339478i) q^{85} +(-5.99872 - 18.4622i) q^{86} +(-4.83254 - 2.27318i) q^{87} +(-0.498275 - 5.88480i) q^{88} +(7.39533 + 12.8091i) q^{89} +(5.46398 - 2.85849i) q^{90} +(-3.49792 + 2.80970i) q^{91} +(1.31404 + 1.80861i) q^{92} +(-1.37153 + 0.414302i) q^{93} +(-2.07829 - 9.77757i) q^{94} +(0.0872467 + 0.830097i) q^{95} +(-7.47909 - 4.52804i) q^{96} +(-1.65673 + 7.79430i) q^{97} +(8.13093 + 4.69439i) q^{98} +(7.79159 - 6.18798i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 3 q^{3} - 54 q^{4} - 15 q^{6} - 30 q^{7} - 9 q^{9}+O(q^{10}) \) 416 * q - 3 * q^3 - 54 * q^4 - 15 * q^6 - 30 * q^7 - 9 * q^9	\( 416 q - 3 q^{3} - 54 q^{4} - 15 q^{6} - 30 q^{7} - 9 q^{9} - 36 q^{12} - 20 q^{13} - 9 q^{15} + 14 q^{16} - 30 q^{19} - 28 q^{22} + 15 q^{24} - 84 q^{25} - 24 q^{27} - 30 q^{28} - 5 q^{30} - 27 q^{33} - 73 q^{36} - 18 q^{37} - 65 q^{39} - 120 q^{40} - 25 q^{42} + 36 q^{45} + 30 q^{46} - 41 q^{48} + 14 q^{49} + 60 q^{51} + 20 q^{52} + 18 q^{55} - 126 q^{58} - 30 q^{61} + 105 q^{63} - 56 q^{64} + 170 q^{66} - 33 q^{69} - 195 q^{72} + 77 q^{75} + 4 q^{78} - 13 q^{81} + 36 q^{82} - 60 q^{84} - 30 q^{85} + 38 q^{88} - 190 q^{90} - 56 q^{91} + 24 q^{93} - 90 q^{94} + 54 q^{97}+O(q^{100}) \) 416 * q - 3 * q^3 - 54 * q^4 - 15 * q^6 - 30 * q^7 - 9 * q^9 - 36 * q^12 - 20 * q^13 - 9 * q^15 + 14 * q^16 - 30 * q^19 - 28 * q^22 + 15 * q^24 - 84 * q^25 - 24 * q^27 - 30 * q^28 - 5 * q^30 - 27 * q^33 - 73 * q^36 - 18 * q^37 - 65 * q^39 - 120 * q^40 - 25 * q^42 + 36 * q^45 + 30 * q^46 - 41 * q^48 + 14 * q^49 + 60 * q^51 + 20 * q^52 + 18 * q^55 - 126 * q^58 - 30 * q^61 + 105 * q^63 - 56 * q^64 + 170 * q^66 - 33 * q^69 - 195 * q^72 + 77 * q^75 + 4 * q^78 - 13 * q^81 + 36 * q^82 - 60 * q^84 - 30 * q^85 + 38 * q^88 - 190 * q^90 - 56 * q^91 + 24 * q^93 - 90 * q^94 + 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more