LMFDB - Embedded newform 975.2.bn.d.407.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(218,975)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("975.218"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bn (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,2,0,0,-12,12,0,0,0,0,12,24,0,0,16,0,0,0,0,0,-20,0,0,0,0, 32,36,0,0,0,0,-30,0,0,-4,84,0,0,0,0,48,-8,0,0,0,0,28,0,0,-16,-28,0,0,0, 0,0,-84,0,0,-32,0,-90,0,0,0,-36,0,0,0,0,-90,0,0,0,72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(76)] == traces)

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			407.17
Character	$\chi$	$=$	975.407
Dual form			975.2.bn.d.218.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.05989 - 0.283997i) q^{2} +(1.73203 + 0.00769600i) q^{3} +(-0.689337 + 0.397989i) q^{4} +(1.83795 - 0.483735i) q^{6} +(0.160495 + 0.0430045i) q^{7} +(-2.16938 + 2.16938i) q^{8} +(2.99988 + 0.0266595i) q^{9} +(2.43760 - 4.22205i) q^{11} +(-1.19702 + 0.684025i) q^{12} +(2.24451 + 2.82173i) q^{13} +0.182320 q^{14} +(-0.887232 + 1.53673i) q^{16} +(4.65999 + 1.24864i) q^{17} +(3.18712 - 0.823701i) q^{18} +(1.37389 + 2.37966i) q^{19} +(0.277652 + 0.0757204i) q^{21} +(1.38454 - 5.16719i) q^{22} +(-5.64603 + 1.51285i) q^{23} +(-3.77414 + 3.74075i) q^{24} +(3.18030 + 2.35330i) q^{26} +(5.19569 + 0.0692622i) q^{27} +(-0.127750 + 0.0342306i) q^{28} +(2.47205 - 4.28172i) q^{29} +2.41720i q^{31} +(1.08416 - 4.04612i) q^{32} +(4.25451 - 7.29398i) q^{33} +5.29369 q^{34} +(-2.07854 + 1.17554i) q^{36} +(1.20299 + 4.48963i) q^{37} +(2.13199 + 2.13199i) q^{38} +(3.86585 + 4.90461i) q^{39} +(2.16059 - 3.74226i) q^{41} +(0.315785 + 0.00140314i) q^{42} +(-1.27129 - 0.340642i) q^{43} +3.88056i q^{44} +(-5.55453 + 3.20691i) q^{46} +(3.58251 + 3.58251i) q^{47} +(-1.54854 + 2.65484i) q^{48} +(-6.03827 - 3.48620i) q^{49} +(8.06165 + 2.19855i) q^{51} +(-2.67024 - 1.05184i) q^{52} +(3.34661 + 3.34661i) q^{53} +(5.52653 - 1.40215i) q^{54} +(-0.441468 + 0.254882i) q^{56} +(2.36132 + 4.13222i) q^{57} +(1.40411 - 5.24021i) q^{58} +(-8.49452 + 4.90431i) q^{59} +(-7.20685 - 12.4826i) q^{61} +(0.686477 + 2.56197i) q^{62} +(0.480319 + 0.133287i) q^{63} -8.14527i q^{64} +(2.43784 - 8.93909i) q^{66} +(0.188179 + 0.702294i) q^{67} +(-3.70925 + 0.993890i) q^{68} +(-9.79075 + 2.57685i) q^{69} +(1.37489 + 2.38137i) q^{71} +(-6.56572 + 6.45005i) q^{72} +(-5.45193 - 5.45193i) q^{73} +(2.55008 + 4.41687i) q^{74} +(-1.89415 - 1.09359i) q^{76} +(0.572790 - 0.572790i) q^{77} +(5.49027 + 4.10047i) q^{78} -7.39276i q^{79} +(8.99858 + 0.159950i) q^{81} +(1.22720 - 4.57999i) q^{82} +(-1.60997 + 1.60997i) q^{83} +(-0.221531 + 0.0583054i) q^{84} -1.44417 q^{86} +(4.31463 - 7.39706i) q^{87} +(3.87115 + 14.4473i) q^{88} +(5.98500 + 3.45544i) q^{89} +(0.238885 + 0.549398i) q^{91} +(3.28992 - 3.28992i) q^{92} +(-0.0186028 + 4.18667i) q^{93} +(4.81449 + 2.77964i) q^{94} +(1.90893 - 6.99968i) q^{96} +(-16.2824 - 4.36286i) q^{97} +(-7.38997 - 1.98014i) q^{98} +(7.42508 - 12.6007i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) $ 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.05989	−	0.283997i	0.749456	−	0.200816i	0.136179	−	0.990684i	$-0.456518\pi$
$2$	1.05989	−	0.283997i	0.749456	−	0.200816i	0.613277	+	0.789868i	$0.289851\pi$
$3$	1.73203	+	0.00769600i	0.999990	+	0.00444329i
$3$	1.73203	+	0.00769600i	0.999990	+	0.00444329i
$4$	−0.689337	+	0.397989i	−0.344668	+	0.198994i
$5$		0			0
$5$		0			0
$6$	1.83795	−	0.483735i	0.750341	−	0.197484i
$7$	0.160495	+	0.0430045i	0.0606614	+	0.0162542i	0.289022	−	0.957322i	$-0.406670\pi$
$7$	0.160495	+	0.0430045i	0.0606614	+	0.0162542i	−0.228361	+	0.973577i	$0.573337\pi$
$8$	−2.16938	+	2.16938i	−0.766992	+	0.766992i
$9$	2.99988	+	0.0266595i	0.999961	+	0.00888649i
$10$		0			0
$11$	2.43760	−	4.22205i	0.734965	−	1.27300i	−0.219773	−	0.975551i	$-0.570532\pi$
$11$	2.43760	−	4.22205i	0.734965	−	1.27300i	0.954739	−	0.297446i	$-0.0961350\pi$
$12$	−1.19702	+	0.684025i	−0.345549	+	0.197461i
$13$	2.24451	+	2.82173i	0.622514	+	0.782608i
$13$	2.24451	+	2.82173i	0.622514	+	0.782608i
$14$	0.182320			0.0487271
$15$		0			0
$16$	−0.887232	+	1.53673i	−0.221808	+	0.384183i
$17$	4.65999	+	1.24864i	1.13021	+	0.302840i	0.775010	−	0.631949i	$-0.217745\pi$
$17$	4.65999	+	1.24864i	1.13021	+	0.302840i	0.355204	+	0.934789i	$0.384412\pi$
$18$	3.18712	−	0.823701i	0.751211	−	0.194148i
$19$	1.37389	+	2.37966i	0.315193	+	0.545930i	0.979479	−	0.201549i	$-0.0645974\pi$
$19$	1.37389	+	2.37966i	0.315193	+	0.545930i	−0.664285	+	0.747479i	$0.731264\pi$
$20$		0			0
$21$	0.277652	+	0.0757204i	0.0605886	+	0.0165235i
$22$	1.38454	−	5.16719i	0.295186	−	1.10165i
$23$	−5.64603	+	1.51285i	−1.17728	+	0.315451i	−0.793846	−	0.608118i	$-0.791925\pi$
$23$	−5.64603	+	1.51285i	−1.17728	+	0.315451i	−0.383432	+	0.923569i	$0.625258\pi$
$24$	−3.77414	+	3.74075i	−0.770393	+	0.763577i
$25$		0			0
$26$	3.18030	+	2.35330i	0.623707	+	0.461520i
$27$	5.19569	+	0.0692622i	0.999911	+	0.0133295i
$28$	−0.127750	+	0.0342306i	−0.0241426	+	0.00646898i
$29$	2.47205	−	4.28172i	0.459049	−	0.795096i	−0.539862	−	0.841754i	$-0.681524\pi$
$29$	2.47205	−	4.28172i	0.459049	−	0.795096i	0.998911	+	0.0466574i	$0.0148569\pi$
$30$		0			0
$31$			2.41720i			0.434142i	0.976156	+	0.217071i	$0.0696502\pi$
$31$			2.41720i			0.434142i	−0.976156	+	0.217071i	$0.930350\pi$
$32$	1.08416	−	4.04612i	0.191653	−	0.715260i
$33$	4.25451	−	7.29398i	0.740614	−	1.26972i
$34$	5.29369			0.907860
$35$		0			0
$36$	−2.07854	+	1.17554i	−0.346423	+	0.195924i
$37$	1.20299	+	4.48963i	0.197771	+	0.738090i	0.991532	+	0.129861i	$0.0414531\pi$
$37$	1.20299	+	4.48963i	0.197771	+	0.738090i	−0.793762	+	0.608229i	$0.791880\pi$
$38$	2.13199	+	2.13199i	0.345855	+	0.345855i
$39$	3.86585	+	4.90461i	0.619031	+	0.785367i
$40$		0			0
$41$	2.16059	−	3.74226i	0.337428	−	0.584443i	−0.646520	−	0.762897i	$-0.723776\pi$
$41$	2.16059	−	3.74226i	0.337428	−	0.584443i	0.983948	+	0.178454i	$0.0571097\pi$
$42$	0.315785	+	0.00140314i	0.0487266	+	0.000216509i
$43$	−1.27129	−	0.340642i	−0.193871	−	0.0519475i	0.160577	−	0.987023i	$-0.448664\pi$
$43$	−1.27129	−	0.340642i	−0.193871	−	0.0519475i	−0.354448	+	0.935076i	$0.615331\pi$
$44$			3.88056i			0.585016i
$45$		0			0
$46$	−5.55453	+	3.20691i	−0.818970	+	0.472833i
$47$	3.58251	+	3.58251i	0.522562	+	0.522562i	0.918344	−	0.395782i	$-0.129526\pi$
$47$	3.58251	+	3.58251i	0.522562	+	0.522562i	−0.395782	+	0.918344i	$0.629526\pi$
$48$	−1.54854	+	2.65484i	−0.223513	+	0.383193i
$49$	−6.03827	−	3.48620i	−0.862610	−	0.498028i
$50$		0			0
$51$	8.06165	+	2.19855i	1.12886	+	0.307859i
$52$	−2.67024	−	1.05184i	−0.370296	−	0.145864i
$53$	3.34661	+	3.34661i	0.459692	+	0.459692i	0.898554	−	0.438862i	$-0.144618\pi$
$53$	3.34661	+	3.34661i	0.459692	+	0.459692i	−0.438862	+	0.898554i	$0.644618\pi$
$54$	5.52653	−	1.40215i	0.752066	−	0.190808i
$55$		0			0
$56$	−0.441468	+	0.254882i	−0.0589936	+	0.0340600i
$57$	2.36132	+	4.13222i	0.312764	+	0.547326i
$58$	1.40411	−	5.24021i	0.184369	−	0.688074i
$59$	−8.49452	+	4.90431i	−1.10589	+	0.638487i	−0.937762	−	0.347278i	$-0.887106\pi$
$59$	−8.49452	+	4.90431i	−1.10589	+	0.638487i	−0.168130	+	0.985765i	$0.553773\pi$
$60$		0			0
$61$	−7.20685	−	12.4826i	−0.922742	−	1.59824i	−0.795153	−	0.606409i	$-0.792609\pi$
$61$	−7.20685	−	12.4826i	−0.922742	−	1.59824i	−0.127590	−	0.991827i	$-0.540724\pi$
$62$	0.686477	+	2.56197i	0.0871826	+	0.325370i
$63$	0.480319	+	0.133287i	0.0605145	+	0.0167926i
$64$		−	8.14527i		−	1.01816i
$65$		0			0
$66$	2.43784	−	8.93909i	0.300078	−	1.10033i
$67$	0.188179	+	0.702294i	0.0229897	+	0.0857989i	0.976468	−	0.215664i	$-0.0691917\pi$
$67$	0.188179	+	0.702294i	0.0229897	+	0.0857989i	−0.953478	+	0.301463i	$0.902525\pi$
$68$	−3.70925	+	0.993890i	−0.449812	+	0.120527i
$69$	−9.79075	+	2.57685i	−1.17867	+	0.310217i
$70$		0			0
$71$	1.37489	+	2.38137i	0.163169	+	0.282617i	0.936004	−	0.351990i	$-0.114495\pi$
$71$	1.37489	+	2.38137i	0.163169	+	0.282617i	−0.772834	+	0.634608i	$0.781162\pi$
$72$	−6.56572	+	6.45005i	−0.773778	+	0.760146i
$73$	−5.45193	−	5.45193i	−0.638101	−	0.638101i	0.311986	−	0.950087i	$-0.399006\pi$
$73$	−5.45193	−	5.45193i	−0.638101	−	0.638101i	−0.950087	+	0.311986i	$0.899006\pi$
$74$	2.55008	+	4.41687i	0.296441	+	0.513450i
$75$		0			0
$76$	−1.89415	−	1.09359i	−0.217274	−	0.125443i
$77$	0.572790	−	0.572790i	0.0652755	−	0.0652755i
$78$	5.49027	+	4.10047i	0.621651	+	0.464286i
$79$		−	7.39276i		−	0.831750i	−0.909422	−	0.415875i	$-0.863475\pi$
$79$		−	7.39276i		−	0.831750i	0.909422	−	0.415875i	$-0.136525\pi$
$80$		0			0
$81$	8.99858	+	0.159950i	0.999842	+	0.0177723i
$82$	1.22720	−	4.57999i	0.135522	−	0.505775i
$83$	−1.60997	+	1.60997i	−0.176717	+	0.176717i	−0.789923	−	0.613206i	$-0.789880\pi$
$83$	−1.60997	+	1.60997i	−0.176717	+	0.176717i	0.613206	+	0.789923i	$0.289880\pi$
$84$	−0.221531	+	0.0583054i	−0.0241711	+	0.00636164i
$85$		0			0
$86$	−1.44417			−0.155729
$87$	4.31463	−	7.39706i	0.462577	−	0.793049i
$88$	3.87115	+	14.4473i	0.412666	+	1.54009i
$89$	5.98500	+	3.45544i	0.634408	+	0.366276i	0.782457	−	0.622704i	$-0.213966\pi$
$89$	5.98500	+	3.45544i	0.634408	+	0.366276i	−0.148049	+	0.988980i	$0.547299\pi$
$90$		0			0
$91$	0.238885	+	0.549398i	0.0250419	+	0.0575926i
$92$	3.28992	−	3.28992i	0.342998	−	0.342998i
$93$	−0.0186028	+	4.18667i	−0.00192902	+	0.434137i
$94$	4.81449	+	2.77964i	0.496576	+	0.286698i
$95$		0			0
$96$	1.90893	−	6.99968i	0.194830	−	0.714402i
$97$	−16.2824	−	4.36286i	−1.65323	−	0.442981i	−0.692714	−	0.721212i	$-0.743585\pi$
$97$	−16.2824	−	4.36286i	−1.65323	−	0.442981i	−0.960514	+	0.278231i	$0.910252\pi$
$98$	−7.38997	−	1.98014i	−0.746500	−	0.200024i
$99$	7.42508	−	12.6007i	0.746249	−	1.26642i
$100$		0			0
$101$	−13.1605	−	7.59820i	−1.30952	−	0.756049i	−0.327500	−	0.944851i	$-0.606206\pi$
$101$	−13.1605	−	7.59820i	−1.30952	−	0.756049i	−0.982015	+	0.188802i	$0.939540\pi$
$102$	9.16885	+	0.0407402i	0.907851	+	0.00403388i
$103$	−12.4089	+	12.4089i	−1.22268	+	1.22268i	−0.256009	+	0.966674i	$0.582408\pi$
$103$	−12.4089	+	12.4089i	−1.22268	+	1.22268i	−0.966674	+	0.256009i	$0.917592\pi$
$104$	−10.9906	−	1.25223i	−1.07772	−	0.122791i
$105$		0			0
$106$	4.49746	+	2.59661i	0.436832	+	0.252205i
$107$	−0.564899	−	2.10823i	−0.0546109	−	0.203811i	0.933230	−	0.359280i	$-0.116978\pi$
$107$	−0.564899	−	2.10823i	−0.0546109	−	0.203811i	−0.987841	+	0.155469i	$0.950311\pi$
$108$	−3.60915	+	2.02008i	−0.347290	+	0.194382i
$109$	−10.3074			−0.987274			−0.493637	−	0.869668i	$-0.664333\pi$
$109$	−10.3074			−0.987274			−0.493637	+	0.869668i	$0.664333\pi$
$110$		0			0
$111$	2.04907	+	7.78544i	0.194489	+	0.738961i
$112$	−0.208483	+	0.208483i	−0.0196997	+	0.0196997i
$113$	3.86420	−	14.4214i	0.363513	−	1.35665i	−0.505912	−	0.862585i	$-0.668844\pi$
$113$	3.86420	−	14.4214i	0.363513	−	1.35665i	0.869425	−	0.494065i	$-0.164489\pi$
$114$	3.67628	+	3.70909i	0.344315	+	0.347388i
$115$		0			0
$116$			3.93540i			0.365393i
$117$	6.65803	+	8.52471i	0.615535	+	0.788109i
$118$	−7.61045	+	7.61045i	−0.700599	+	0.700599i
$119$	0.694207	+	0.400801i	0.0636379	+	0.0367414i
$120$		0			0
$121$	−6.38383	−	11.0571i	−0.580348	−	1.00519i
$122$	−11.1835	−	11.1835i	−1.01251	−	1.01251i
$123$	3.77102	−	6.46509i	0.340022	−	0.582938i
$124$	−0.962018	−	1.66626i	−0.0863918	−	0.149635i
$125$		0			0
$126$	0.546939	+	0.00486056i	0.0487252	+	0.000433013i
$127$	−1.36576	+	0.365954i	−0.121192	+	0.0324732i	−0.318905	−	0.947787i	$-0.603315\pi$
$127$	−1.36576	+	0.365954i	−0.121192	+	0.0324732i	0.197713	+	0.980260i	$0.436648\pi$
$128$	−0.144921	−	0.540851i	−0.0128093	−	0.0478049i
$129$	−2.19930	−	0.599788i	−0.193638	−	0.0528084i
$130$		0			0
$131$			1.23865i			0.108221i	0.998535	+	0.0541107i	$0.0172324\pi$
$131$			1.23865i			0.108221i	−0.998535	+	0.0541107i	$0.982768\pi$
$132$	−0.0298648	+	6.72126i	−0.00259939	+	0.585010i
$133$	0.118167	+	0.441006i	0.0102464	+	0.0382401i
$134$	0.398899	+	0.690913i	0.0344596	+	0.0596858i
$135$		0			0
$136$	−12.8181	+	7.40052i	−1.09914	+	0.634589i
$137$	−1.05050	+	3.92054i	−0.0897507	+	0.334954i	−0.996171	−	0.0874219i	$-0.972137\pi$
$137$	−1.05050	+	3.92054i	−0.0897507	+	0.334954i	0.906421	+	0.422376i	$0.138804\pi$
$138$	−9.64531	+	5.51172i	−0.821063	+	0.469189i
$139$	6.39677	−	3.69318i	0.542567	−	0.313251i	−0.203552	−	0.979064i	$-0.565248\pi$
$139$	6.39677	−	3.69318i	0.542567	−	0.313251i	0.746119	+	0.665813i	$0.231915\pi$
$140$		0			0
$141$	6.17745	+	6.23259i	0.520235	+	0.524879i
$142$	2.13353	+	2.13353i	0.179042	+	0.179042i
$143$	17.3847	−	2.59816i	1.45378	−	0.217269i
$144$	−2.70256	+	4.58636i	−0.225213	+	0.382196i
$145$		0			0
$146$	−7.32679	−	4.23012i	−0.606369	−	0.350087i
$147$	−10.4317	−	6.08468i	−0.860388	−	0.501856i
$148$	−2.61609	−	2.61609i	−0.215041	−	0.215041i
$149$	5.05279	−	2.91723i	0.413941	−	0.238989i	−0.278541	−	0.960424i	$-0.589851\pi$
$149$	5.05279	−	2.91723i	0.413941	−	0.238989i	0.692482	+	0.721435i	$0.256517\pi$
$150$		0			0
$151$			16.4599i			1.33949i	0.742591	+	0.669745i	$0.233597\pi$
$151$			16.4599i			1.33949i	−0.742591	+	0.669745i	$0.766403\pi$
$152$	−8.14288	−	2.18188i	−0.660475	−	0.176974i
$153$	13.9461	+	3.87001i	1.12748	+	0.312871i
$154$	0.444425	−	0.769766i	0.0358127	−	0.0620295i
$155$		0			0
$156$	−4.61685	−	1.84237i	−0.369644	−	0.147507i
$157$	5.15467	+	5.15467i	0.411387	+	0.411387i	0.882222	−	0.470834i	$-0.156047\pi$
$157$	5.15467	+	5.15467i	0.411387	+	0.411387i	−0.470834	+	0.882222i	$0.656047\pi$
$158$	−2.09952	−	7.83551i	−0.167029	−	0.623360i
$159$	5.77068	+	5.82219i	0.457645	+	0.461730i
$160$		0			0
$161$	−0.971218			−0.0765427
$162$	9.58293	−	2.38604i	0.752906	−	0.187465i
$163$	5.68770	−	21.2268i	0.445495	−	1.66261i	−0.269131	−	0.963103i	$-0.586737\pi$
$163$	5.68770	−	21.2268i	0.445495	−	1.66261i	0.714626	−	0.699506i	$-0.246597\pi$
$164$			3.43957i			0.268585i
$165$		0			0
$166$	−1.24917	+	2.16362i	−0.0969541	+	0.167929i
$167$	−13.6836	+	3.66650i	−1.05887	+	0.283723i	−0.745911	−	0.666045i	$-0.767986\pi$
$167$	−13.6836	+	3.66650i	−1.05887	+	0.283723i	−0.312956	+	0.949768i	$0.601319\pi$
$168$	−0.766599	+	0.438066i	−0.0591444	+	0.0337975i
$169$	−2.92437	+	12.6668i	−0.224952	+	0.974370i
$170$		0			0
$171$	4.05808	+	7.17531i	0.310329	+	0.548710i
$172$	1.01192	−	0.271144i	0.0771583	−	0.0206745i
$173$	0.246123	−	0.918542i	0.0187123	−	0.0698354i	−0.955938	−	0.293568i	$-0.905157\pi$
$173$	0.246123	−	0.918542i	0.0187123	−	0.0698354i	0.974651	+	0.223732i	$0.0718241\pi$
$174$	2.47230	−	9.06542i	0.187424	−	0.687248i
$175$		0			0
$176$	4.32544	+	7.49188i	0.326042	+	0.564722i
$177$	−14.7505	+	8.42906i	−1.10872	+	0.633567i
$178$	7.32477	+	1.96267i	0.549015	+	0.147108i
$179$	8.16594	−	14.1438i	0.610351	−	1.05716i	−0.380830	−	0.924645i	$-0.624362\pi$
$179$	8.16594	−	14.1438i	0.610351	−	1.05716i	0.991181	−	0.132514i	$-0.0423048\pi$
$180$		0			0
$181$	−12.4459			−0.925096			−0.462548	−	0.886594i	$-0.653065\pi$
$181$	−12.4459			−0.925096			−0.462548	+	0.886594i	$0.653065\pi$
$182$	0.409219	+	0.514459i	0.0303333	+	0.0381343i
$183$	−12.3864	−	21.6758i	−0.915632	−	1.60232i
$184$	8.96644	−	15.5303i	0.661015	−	1.14491i
$185$		0			0
$186$	1.16928	+	4.44269i	0.0857360	+	0.325754i
$187$	16.6310	−	16.6310i	1.21618	−	1.21618i
$188$	−3.89535	−	1.04376i	−0.284098	−	0.0761238i
$189$	0.830903	+	0.234554i	0.0604393	+	0.0170613i
$190$		0			0
$191$	2.49022	−	1.43773i	0.180186	−	0.104030i	−0.407194	−	0.913342i	$-0.633493\pi$
$191$	2.49022	−	1.43773i	0.180186	−	0.104030i	0.587380	+	0.809311i	$0.300159\pi$
$192$	0.0626860	−	14.1079i	0.00452397	−	1.01815i
$193$	10.1951	−	2.73177i	0.733861	−	0.196637i	0.127513	−	0.991837i	$-0.459301\pi$
$193$	10.1951	−	2.73177i	0.733861	−	0.196637i	0.606348	+	0.795199i	$0.292634\pi$
$194$	−18.4966			−1.32798
$195$		0			0
$196$	5.54987			0.396419
$197$	19.0112	−	5.09403i	1.35449	−	0.362934i	0.492700	−	0.870199i	$-0.336010\pi$
$197$	19.0112	−	5.09403i	1.35449	−	0.362934i	0.861790	+	0.507265i	$0.169344\pi$
$198$	4.29122	−	15.4640i	0.304964	−	1.09898i
$199$	−10.9231	+	6.30646i	−0.774318	+	0.447053i	−0.834413	−	0.551140i	$-0.814193\pi$
$199$	−10.9231	+	6.30646i	−0.774318	+	0.447053i	0.0600946	+	0.998193i	$0.480860\pi$
$200$		0			0
$201$	0.320528	+	1.21785i	0.0226083	+	0.0859002i
$202$	−16.1065	−	4.31573i	−1.13325	−	0.303654i
$203$	0.580885	−	0.580885i	0.0407702	−	0.0407702i
$204$	−6.43219	+	1.69290i	−0.450343	+	0.118527i
$205$		0			0
$206$	−9.62798	+	16.6761i	−0.670813	+	1.16188i
$207$	−16.9777	+	4.38785i	−1.18003	+	0.304976i
$208$	−6.32765	+	0.945670i	−0.438743	+	0.0655704i
$209$	13.3960			0.926624
$210$		0			0
$211$	−2.40360	+	4.16317i	−0.165471	+	0.286604i	−0.936822	−	0.349805i	$-0.886248\pi$
$211$	−2.40360	+	4.16317i	−0.165471	+	0.286604i	0.771351	+	0.636409i	$0.219581\pi$
$212$	−3.63885	−	0.975028i	−0.249917	−	0.0669652i
$213$	2.36302	+	4.13520i	0.161912	+	0.283339i
$214$	−1.19746	−	2.07407i	−0.0818569	−	0.141780i
$215$		0			0
$216$	−11.4217	+	11.1212i	−0.777148	+	0.756700i
$217$	−0.103950	+	0.387948i	−0.00705661	+	0.0263356i
$218$	−10.9248	+	2.92728i	−0.739918	+	0.198260i
$219$	−9.40098	−	9.48489i	−0.635259	−	0.640930i
$220$		0			0
$221$	6.93605	+	15.9518i	0.466569	+	1.07304i
$222$	4.38283	+	7.66979i	0.294156	+	0.514762i
$223$	−11.0162	+	2.95177i	−0.737697	+	0.197665i	−0.608054	−	0.793896i	$-0.708050\pi$
$223$	−11.0162	+	2.95177i	−0.737697	+	0.197665i	−0.129643	+	0.991561i	$0.541383\pi$
$224$	0.348003	−	0.602759i	0.0232519	−	0.0402735i
$225$		0			0
$226$		−	16.3825i		−	1.08975i
$227$	−6.87249	+	25.6485i	−0.456143	+	1.70235i	0.228561	+	0.973530i	$0.426598\pi$
$227$	−6.87249	+	25.6485i	−0.456143	+	1.70235i	−0.684705	+	0.728821i	$0.740069\pi$
$228$	−3.27232	−	1.90871i	−0.216715	−	0.126408i
$229$	−6.38857			−0.422169			−0.211084	−	0.977468i	$-0.567699\pi$
$229$	−6.38857			−0.422169			−0.211084	+	0.977468i	$0.567699\pi$
$230$		0			0
$231$	0.996501	−	0.987684i	0.0655649	−	0.0649848i
$232$	3.92586	+	14.6515i	0.257746	+	0.961920i
$233$	12.9039	+	12.9039i	0.845365	+	0.845365i	0.989551	−	0.144186i	$-0.0460562\pi$
$233$	12.9039	+	12.9039i	0.845365	+	0.845365i	−0.144186	+	0.989551i	$0.546056\pi$
$234$	9.47777	+	7.14440i	0.619581	+	0.467044i
$235$		0			0
$236$	3.90372	−	6.76145i	0.254111	−	0.440133i
$237$	0.0568947	−	12.8045i	0.00369571	−	0.831742i
$238$	0.849610	+	0.227652i	0.0550720	+	0.0147565i
$239$		−	3.20751i		−	0.207477i	−0.994605	−	0.103738i	$-0.966920\pi$
$239$		−	3.20751i		−	0.207477i	0.994605	−	0.103738i	$-0.0330805\pi$
$240$		0			0
$241$	5.19991	−	3.00217i	0.334956	−	0.193387i	−0.323083	−	0.946370i	$-0.604719\pi$
$241$	5.19991	−	3.00217i	0.334956	−	0.193387i	0.658039	+	0.752984i	$0.271386\pi$
$242$	−9.90635	−	9.90635i	−0.636804	−	0.636804i
$243$	15.5846	+	0.346293i	0.999753	+	0.0222147i
$244$	9.93589	+	5.73649i	0.636080	+	0.367241i
$245$		0			0
$246$	2.16081	−	7.92325i	0.137768	−	0.505168i
$247$	−3.63104	+	9.21792i	−0.231038	+	0.586522i
$248$	−5.24382	−	5.24382i	−0.332983	−	0.332983i
$249$	−2.80091	+	2.77613i	−0.177501	+	0.175930i
$250$		0			0
$251$	21.2638	−	12.2767i	1.34216	−	0.774897i	0.355036	−	0.934852i	$-0.384468\pi$
$251$	21.2638	−	12.2767i	1.34216	−	0.774897i	0.987124	+	0.159956i	$0.0511351\pi$
$252$	−0.384149	+	0.0992820i	−0.0241991	+	0.00625418i
$253$	−7.37545	+	27.5256i	−0.463691	+	1.73052i
$254$	−1.34363	+	0.775742i	−0.0843066	+	0.0486744i
$255$		0			0
$256$	7.83807	+	13.5759i	0.489880	+	0.848496i
$257$	−1.24454	−	4.64467i	−0.0776320	−	0.289727i	0.916185	−	0.400755i	$-0.131252\pi$
$257$	−1.24454	−	4.64467i	−0.0776320	−	0.289727i	−0.993817	+	0.111028i	$0.964586\pi$
$258$	−2.50136	−	0.0111144i	−0.155728	−	0.000691950i
$259$			0.772296i			0.0479881i
$260$		0			0
$261$	7.53002	−	12.7788i	0.466096	−	0.790985i
$262$	0.351773	+	1.31283i	0.0217326	+	0.0811072i
$263$	11.3760	−	3.04819i	0.701474	−	0.187959i	0.109583	−	0.993978i	$-0.465048\pi$
$263$	11.3760	−	3.04819i	0.701474	−	0.187959i	0.591891	+	0.806018i	$0.298382\pi$
$264$	6.59378	+	25.0531i	0.405819	+	1.54191i
$265$		0			0
$266$	0.250489	+	0.433859i	0.0153585	+	0.0266016i
$267$	10.3396	+	6.03100i	0.632775	+	0.369091i
$268$	−0.409224	−	0.409224i	−0.0249973	−	0.0249973i
$269$	−0.648587	−	1.12339i	−0.0395451	−	0.0684941i	0.845575	−	0.533856i	$-0.179258\pi$
$269$	−0.648587	−	1.12339i	−0.0395451	−	0.0684941i	−0.885121	+	0.465362i	$0.845924\pi$
$270$		0			0
$271$	5.30394	+	3.06223i	0.322191	+	0.186017i	0.652369	−	0.757902i	$-0.273775\pi$
$271$	5.30394	+	3.06223i	0.322191	+	0.186017i	−0.330178	+	0.943919i	$0.607109\pi$
$272$	−6.05331	+	6.05331i	−0.367036	+	0.367036i
$273$	0.409528	+	0.953414i	0.0247858	+	0.0577033i
$274$			4.45368i			0.269057i
$275$		0			0
$276$	5.72357	−	5.67293i	0.344518	−	0.341470i
$277$	−2.69179	+	10.0459i	−0.161734	+	0.603600i	0.836700	+	0.547661i	$0.184482\pi$
$277$	−2.69179	+	10.0459i	−0.161734	+	0.603600i	−0.998434	+	0.0559386i	$0.982185\pi$
$278$	5.73103	−	5.73103i	0.343724	−	0.343724i
$279$	−0.0644412	+	7.25131i	−0.00385799	+	0.434124i
$280$		0			0
$281$	−21.9271			−1.30806			−0.654031	−	0.756468i	$-0.726923\pi$
$281$	−21.9271			−1.30806			−0.654031	+	0.756468i	$0.726923\pi$
$282$	8.31746	+	4.85149i	0.495297	+	0.288902i
$283$	−1.43469	−	5.35432i	−0.0852833	−	0.318281i	0.910084	−	0.414423i	$-0.136017\pi$
$283$	−1.43469	−	5.35432i	−0.0852833	−	0.318281i	−0.995368	+	0.0961414i	$0.969350\pi$
$284$	−1.89552	−	1.09438i	−0.112479	−	0.0649395i
$285$		0			0
$286$	17.6881	−	7.69098i	1.04592	−	0.454777i
$287$	0.507698	−	0.507698i	0.0299685	−	0.0299685i
$288$	3.36021	−	12.1090i	0.198002	−	0.713529i
$289$	5.43396	+	3.13730i	0.319645	+	0.184547i
$290$		0			0
$291$	−28.1681	−	7.68193i	−1.65124	−	0.450323i
$292$	5.92803	+	1.58841i	0.346912	+	0.0929547i
$293$	−4.73086	−	1.26763i	−0.276380	−	0.0740557i	0.117967	−	0.993018i	$-0.462362\pi$
$293$	−4.73086	−	1.26763i	−0.276380	−	0.0740557i	−0.394347	+	0.918962i	$0.629029\pi$
$294$	−12.7844	−	3.48654i	−0.745604	−	0.203339i
$295$		0			0
$296$	−12.3495	−	7.12996i	−0.717798	−	0.414421i
$297$	12.9575	−	21.7677i	0.751869	−	1.26309i
$298$	4.52692	−	4.52692i	0.262238	−	0.262238i
$299$	−16.9414	−	12.5360i	−0.979747	−	0.724975i
$300$		0			0
$301$	−0.189387	−	0.109343i	−0.0109161	−	0.00630241i
$302$	4.67457	+	17.4457i	0.268991	+	1.00389i
$303$	−22.7359	−	13.2616i	−1.30614	−	0.761860i
$304$	−4.87585			−0.279649
$305$		0			0
$306$	15.8804	+	0.141127i	0.907824	+	0.00806769i
$307$	−15.7142	+	15.7142i	−0.896858	+	0.896858i	−0.995157	−	0.0982987i	$-0.968660\pi$
$307$	−15.7142	+	15.7142i	−0.896858	+	0.896858i	0.0982987	+	0.995157i	$0.468660\pi$
$308$	−0.166881	+	0.622810i	−0.00950895	+	0.0354879i
$309$	−21.5881	+	21.3971i	−1.22810	+	1.21724i
$310$		0			0
$311$			27.3000i			1.54804i	0.633161	+	0.774020i	$0.281757\pi$
$311$			27.3000i			1.54804i	−0.633161	+	0.774020i	$0.718243\pi$
$312$	−19.0265	−	2.25348i	−1.07716	−	0.127578i
$313$	13.0107	−	13.0107i	0.735406	−	0.735406i	−0.236280	−	0.971685i	$-0.575928\pi$
$313$	13.0107	−	13.0107i	0.735406	−	0.735406i	0.971685	+	0.236280i	$0.0759281\pi$
$314$	6.92729	+	3.99948i	0.390930	+	0.225703i
$315$		0			0
$316$	2.94224	+	5.09610i	0.165514	+	0.286678i
$317$	−6.64936	−	6.64936i	−0.373465	−	0.373465i	0.495272	−	0.868738i	$-0.335068\pi$
$317$	−6.64936	−	6.64936i	−0.373465	−	0.373465i	−0.868738	+	0.495272i	$0.835068\pi$
$318$	7.76978	+	4.53203i	0.435707	+	0.254144i
$319$	−12.0518	−	20.8743i	−0.674770	−	1.16874i
$320$		0			0
$321$	−0.962200	−	3.65588i	−0.0537048	−	0.204051i
$322$	−1.02938	+	0.275823i	−0.0573654	+	0.0153710i
$323$	3.43100	+	12.8047i	0.190906	+	0.712471i
$324$	−6.26671	+	3.47107i	−0.348151	+	0.192837i
$325$		0			0
$326$		−	24.1134i		−	1.33552i
$327$	−17.8528	−	0.0793261i	−0.987264	−	0.00438674i
$328$	3.43123	+	12.8055i	0.189458	+	0.707068i
$329$	0.420910	+	0.729038i	0.0232055	+	0.0401932i
$330$		0			0
$331$	5.50158	−	3.17634i	0.302394	−	0.174587i	−0.341124	−	0.940018i	$-0.610807\pi$
$331$	5.50158	−	3.17634i	0.302394	−	0.174587i	0.643518	+	0.765431i	$0.277474\pi$
$332$	0.469062	−	1.75056i	0.0257431	−	0.0960746i
$333$	3.48914	+	13.5004i	0.191204	+	0.739818i
$334$	−13.4618	+	7.77219i	−0.736598	+	0.425275i
$335$		0			0
$336$	−0.362703	+	0.359494i	−0.0197871	+	0.0196120i
$337$	−12.5904	−	12.5904i	−0.685841	−	0.685841i	0.275469	−	0.961310i	$-0.411167\pi$
$337$	−12.5904	−	12.5904i	−0.685841	−	0.685841i	−0.961310	+	0.275469i	$0.911167\pi$
$338$	0.497817	+	14.2559i	0.0270777	+	0.775421i
$339$	6.80391	−	24.9486i	0.369538	−	1.35502i
$340$		0			0
$341$	10.2055	+	5.89217i	0.552661	+	0.319079i
$342$	6.33889	+	6.45256i	0.342768	+	0.348915i
$343$	−1.64162	−	1.64162i	−0.0886393	−	0.0886393i
$344$	3.49691	−	2.01894i	0.188541	−	0.108854i
$345$		0			0
$346$		−	1.04345i		−	0.0560963i
$347$	−7.74058	−	2.07408i	−0.415536	−	0.111343i	0.0449927	−	0.998987i	$-0.485674\pi$
$347$	−7.74058	−	2.07408i	−0.415536	−	0.111343i	−0.460529	+	0.887645i	$0.652340\pi$
$348$	−0.0302868	+	6.81625i	−0.00162355	+	0.365389i
$349$	9.47261	−	16.4070i	0.507057	−	0.878249i	−0.492909	−	0.870081i	$-0.664067\pi$
$349$	9.47261	−	16.4070i	0.507057	−	0.878249i	0.999967	−	0.00816849i	$-0.00260014\pi$
$350$		0			0
$351$	11.4663	+	14.8163i	0.612027	+	0.790837i
$352$	−14.4402	−	14.4402i	−0.769666	−	0.769666i
$353$	−0.589602	−	2.20043i	−0.0313814	−	0.117117i	0.948458	−	0.316901i	$-0.102642\pi$
$353$	−0.589602	−	2.20043i	−0.0313814	−	0.117117i	−0.979840	+	0.199785i	$0.935976\pi$
$354$	−13.2401	+	13.1230i	−0.703705	+	0.697479i
$355$		0			0
$356$	−5.50091			−0.291547
$357$	1.19931	+	0.699543i	0.0634740	+	0.0370237i
$358$	4.63820	−	17.3100i	0.245136	−	0.914862i
$359$		−	9.83095i		−	0.518858i	−0.965762	−	0.259429i	$-0.916466\pi$
$359$		−	9.83095i		−	0.518858i	0.965762	−	0.259429i	$-0.0835343\pi$
$360$		0			0
$361$	5.72483	−	9.91569i	0.301307	−	0.521878i
$362$	−13.1913	+	3.53460i	−0.693319	+	0.185774i
$363$	−10.9719	−	19.2004i	−0.575876	−	1.00776i
$364$	−0.383326	−	0.283647i	−0.0200918	−	0.0148671i
$365$		0			0
$366$	−19.2841	−	19.4563i	−1.00800	−	1.01699i
$367$	11.4217	−	3.06044i	0.596209	−	0.159754i	0.0519198	−	0.998651i	$-0.483466\pi$
$367$	11.4217	−	3.06044i	0.596209	−	0.159754i	0.544289	+	0.838897i	$0.316799\pi$
$368$	2.68449	−	10.0187i	0.139939	−	0.522259i
$369$	6.58129	−	11.1687i	0.342608	−	0.581421i
$370$		0			0
$371$	0.393194	+	0.681033i	0.0204136	+	0.0353575i
$372$	−1.65342	−	2.89343i	−0.0857260	−	0.150017i
$373$	−23.7612	−	6.36680i	−1.23031	−	0.329661i	−0.415610	−	0.909543i	$-0.636432\pi$
$373$	−23.7612	−	6.36680i	−1.23031	−	0.329661i	−0.814700	+	0.579882i	$0.803099\pi$
$374$	12.9039	−	22.3502i	0.667246	−	1.15570i
$375$		0			0
$376$	−15.5436			−0.801602
$377$	17.6304	−	2.63488i	0.908013	−	0.135703i
$378$	0.947279	+	0.0126279i	0.0487228	+	0.000649509i
$379$	−7.85016	+	13.5969i	−0.403236	+	0.698425i	−0.994114	−	0.108336i	$-0.965448\pi$
$379$	−7.85016	+	13.5969i	−0.403236	+	0.698425i	0.590879	+	0.806760i	$0.298781\pi$
$380$		0			0
$381$	−2.36836	+	0.623334i	−0.121335	+	0.0319344i
$382$	2.23105	−	2.23105i	0.114150	−	0.114150i
$383$	−2.30709	−	0.618182i	−0.117887	−	0.0315876i	0.199393	−	0.979920i	$-0.436103\pi$
$383$	−2.30709	−	0.618182i	−0.117887	−	0.0315876i	−0.317280	+	0.948332i	$0.602769\pi$
$384$	−0.246845	−	0.937887i	−0.0125968	−	0.0478614i
$385$		0			0
$386$	10.0299	−	5.79076i	0.510508	−	0.294742i
$387$	−3.80465	−	1.05578i	−0.193401	−	0.0536682i
$388$	12.9604	−	3.47274i	0.657966	−	0.176302i
$389$	14.0757			0.713666			0.356833	−	0.934168i	$-0.383857\pi$
$389$	14.0757			0.713666			0.356833	+	0.934168i	$0.383857\pi$
$390$		0			0
$391$	−28.1994			−1.42611
$392$	20.6622	−	5.53642i	1.04360	−	0.279631i
$393$	−0.00953266	+	2.14539i	−0.000480859	+	0.108220i
$394$	18.7031	−	10.7982i	0.942247	−	0.544007i
$395$		0			0
$396$	−0.103454	+	11.6412i	−0.00519874	+	0.584993i
$397$	31.0598	+	8.32246i	1.55885	+	0.417692i	0.932299	−	0.361690i	$-0.117800\pi$
$397$	31.0598	+	8.32246i	1.55885	+	0.417692i	0.626549	+	0.779382i	$0.284467\pi$
$398$	−9.78628	+	9.78628i	−0.490542	+	0.490542i
$399$	0.201276	+	0.764747i	0.0100764	+	0.0382852i
$400$		0			0
$401$	−0.597410	+	1.03474i	−0.0298332	+	0.0516726i	−0.880557	−	0.473941i	$-0.842831\pi$
$401$	−0.597410	+	1.03474i	−0.0298332	+	0.0516726i	0.850723	+	0.525614i	$0.176164\pi$
$402$	0.685589	+	1.19975i	0.0341941	+	0.0598383i
$403$	−6.82069	+	5.42542i	−0.339763	+	0.270259i
$404$	12.0960			0.601798
$405$		0			0
$406$	0.450705	−	0.780645i	0.0223681	−	0.0387427i
$407$	21.8879	+	5.86484i	1.08494	+	0.290709i
$408$	−22.2583	+	12.7193i	−1.10195	+	0.629699i
$409$	8.93012	+	15.4674i	0.441566	+	0.764815i	0.997806	−	0.0662068i	$-0.0210897\pi$
$409$	8.93012	+	15.4674i	0.441566	+	0.764815i	−0.556240	+	0.831022i	$0.687756\pi$
$410$		0			0
$411$	−1.84968	+	6.78242i	−0.0912381	+	0.334552i
$412$	3.61530	−	13.4925i	0.178113	−	0.664728i
$413$	−1.57423	+	0.421815i	−0.0774630	+	0.0207562i
$414$	−16.7484	+	9.47226i	−0.823140	+	0.465536i
$415$		0			0
$416$	13.8505	−	6.02235i	0.679076	−	0.295270i
$417$	11.1078	−	6.34748i	0.543954	−	0.310837i
$418$	14.1983	−	3.80444i	0.694464	−	0.186081i
$419$	−5.31145	+	9.19969i	−0.259481	+	0.449435i	−0.966103	−	0.258157i	$-0.916885\pi$
$419$	−5.31145	+	9.19969i	−0.259481	+	0.449435i	0.706622	+	0.707591i	$0.250218\pi$
$420$		0			0
$421$			23.8749i			1.16359i	0.813335	+	0.581796i	$0.197650\pi$
$421$			23.8749i			1.16359i	−0.813335	+	0.581796i	$0.802350\pi$
$422$	−1.36523	+	5.09512i	−0.0664585	+	0.248026i
$423$	10.6516	+	10.8426i	0.517898	+	0.527185i
$424$	−14.5201			−0.705160
$425$		0			0
$426$	3.67893	+	3.71177i	0.178245	+	0.179836i
$427$	−0.619853	−	2.31332i	−0.0299968	−	0.111950i
$428$	1.22846	+	1.22846i	0.0593798	+	0.0593798i
$429$	30.1310	−	4.36631i	1.45474	−	0.210807i
$430$		0			0
$431$	8.35107	−	14.4645i	0.402257	−	0.696729i	−0.591741	−	0.806128i	$-0.701559\pi$
$431$	8.35107	−	14.4645i	0.402257	−	0.696729i	0.993998	+	0.109399i	$0.0348926\pi$
$432$	−4.71622	+	7.92293i	−0.226909	+	0.381192i
$433$	−26.5522	−	7.11463i	−1.27602	−	0.341907i	−0.443683	−	0.896184i	$-0.646328\pi$
$433$	−26.5522	−	7.11463i	−1.27602	−	0.341907i	−0.832333	+	0.554277i	$0.812995\pi$
$434$			0.440704i			0.0211545i
$435$		0			0
$436$	7.10530	−	4.10225i	0.340282	−	0.196462i
$437$	−11.3571	−	11.3571i	−0.543284	−	0.543284i
$438$	−12.6577	−	7.38310i	−0.604808	−	0.352778i
$439$	16.5480	+	9.55397i	0.789791	+	0.455986i	0.839889	−	0.542758i	$-0.182620\pi$
$439$	16.5480	+	9.55397i	0.789791	+	0.455986i	−0.0500980	+	0.998744i	$0.515953\pi$
$440$		0			0
$441$	−18.0212	−	10.6192i	−0.858150	−	0.505674i
$442$	11.8817	+	14.9374i	0.565156	+	0.710499i
$443$	−8.74698	−	8.74698i	−0.415581	−	0.415581i	0.468096	−	0.883678i	$-0.344940\pi$
$443$	−8.74698	−	8.74698i	−0.415581	−	0.415581i	−0.883678	+	0.468096i	$0.844940\pi$
$444$	−4.51102	−	4.55129i	−0.214083	−	0.215994i
$445$		0			0
$446$	−10.8376	+	6.25711i	−0.513177	+	0.296283i
$447$	8.77406	−	5.01386i	0.414999	−	0.237147i
$448$	0.350283	−	1.30727i	0.0165493	−	0.0617629i
$449$	−25.7950	+	14.8928i	−1.21734	+	0.702834i	−0.964349	−	0.264634i	$-0.914749\pi$
$449$	−25.7950	+	14.8928i	−1.21734	+	0.702834i	−0.252994	+	0.967468i	$0.581415\pi$
$450$		0			0
$451$	−10.5333	−	18.2443i	−0.495996	−	0.859090i
$452$	3.07582	+	11.4791i	0.144674	+	0.539932i
$453$	−0.126676	+	28.5092i	−0.00595174	+	1.33948i
$454$			29.1364i			1.36744i
$455$		0			0
$456$	−14.0870	−	3.84176i	−0.659682	−	0.179907i
$457$	0.904330	+	3.37500i	0.0423028	+	0.157876i	0.983846	−	0.179015i	$-0.0572912\pi$
$457$	0.904330	+	3.37500i	0.0423028	+	0.157876i	−0.941544	+	0.336891i	$0.890624\pi$
$458$	−6.77119	+	1.81433i	−0.316397	+	0.0847783i
$459$	24.1254	+	6.81031i	1.12608	+	0.317878i
$460$		0			0
$461$	−1.56492	−	2.71052i	−0.0728856	−	0.126242i	0.827279	−	0.561791i	$-0.189887\pi$
$461$	−1.56492	−	2.71052i	−0.0728856	−	0.126242i	−0.900165	+	0.435549i	$0.856554\pi$
$462$	0.775682	−	1.32984i	0.0360880	−	0.0618698i
$463$	27.4762	+	27.4762i	1.27693	+	1.27693i	0.942379	+	0.334548i	$0.108584\pi$
$463$	27.4762	+	27.4762i	1.27693	+	1.27693i	0.334548	+	0.942379i	$0.391416\pi$
$464$	4.38657	+	7.59776i	0.203641	+	0.352717i
$465$		0			0
$466$	17.3414	+	10.0121i	0.803327	+	0.463801i
$467$	20.4027	−	20.4027i	0.944124	−	0.944124i	−0.0543954	−	0.998519i	$-0.517323\pi$
$467$	20.4027	−	20.4027i	0.944124	−	0.944124i	0.998519	+	0.0543954i	$0.0173232\pi$
$468$	−7.98236	−	3.22657i	−0.368985	−	0.149148i
$469$			0.120807i			0.00557836i
$470$		0			0
$471$	8.88839	+	8.96773i	0.409555	+	0.413211i
$472$	7.78853	−	29.0672i	0.358496	−	1.33793i
$473$	−4.53712	+	4.53712i	−0.208617	+	0.208617i
$474$	−3.57614	−	13.5875i	−0.164257	−	0.624096i
$475$		0			0
$476$	−0.638057			−0.0292453
$477$	9.95021	+	10.1286i	0.455589	+	0.463759i
$478$	−0.910923	−	3.39961i	−0.0416647	−	0.155495i
$479$	0.117001	+	0.0675507i	0.00534593	+	0.00308647i	0.502671	−	0.864478i	$-0.332351\pi$
$479$	0.117001	+	0.0675507i	0.00534593	+	0.00308647i	−0.497325	+	0.867565i	$0.665684\pi$
$480$		0			0
$481$	−9.96841	+	13.4715i	−0.454520	+	0.614248i
$482$	4.65873	−	4.65873i	0.212199	−	0.212199i
$483$	−1.68218	−	0.00747449i	−0.0765419	−	0.000340101i
$484$	8.80122	+	5.08139i	0.400056	+	0.230972i
$485$		0			0
$486$	16.6163	−	4.05895i	0.753732	−	0.184118i
$487$	−9.42349	−	2.52502i	−0.427019	−	0.114419i	0.0389075	−	0.999243i	$-0.487612\pi$
$487$	−9.42349	−	2.52502i	−0.427019	−	0.114419i	−0.465927	+	0.884823i	$0.654279\pi$
$488$	42.7140	+	11.4452i	1.93357	+	0.518099i
$489$	10.0146	−	36.7217i	0.452878	−	1.66061i
$490$		0			0
$491$	18.8733	+	10.8965i	0.851741	+	0.491753i	0.861238	−	0.508202i	$-0.169690\pi$
$491$	18.8733	+	10.8965i	0.851741	+	0.491753i	−0.00949666	+	0.999955i	$0.503023\pi$
$492$	−0.0264709	+	5.95745i	−0.00119340	+	0.268583i
$493$	16.8661	−	16.8661i	0.759610	−	0.759610i
$494$	−1.23064	+	10.8012i	−0.0553693	+	0.485969i
$495$		0			0
$496$	−3.71458	−	2.14462i	−0.166790	−	0.0962961i
$497$	0.118253	+	0.441325i	0.00530436	+	0.0197961i
$498$	−2.18025	+	3.73785i	−0.0976993	+	0.167497i
$499$	18.1795			0.813827			0.406913	−	0.913467i	$-0.366605\pi$
$499$	18.1795			0.813827			0.406913	+	0.913467i	$0.366605\pi$
$500$		0			0
$501$	−23.7286	+	6.24520i	−1.06012	+	0.279015i
$502$	19.0508	−	19.0508i	0.850278	−	0.850278i
$503$	−1.95641	+	7.30144i	−0.0872322	+	0.325555i	−0.995728	−	0.0923400i	$-0.970565\pi$
$503$	−1.95641	+	7.30144i	−0.0872322	+	0.325555i	0.908495	+	0.417895i	$0.137232\pi$
$504$	−1.33115	+	0.752845i	−0.0592940	+	0.0335344i
$505$		0			0
$506$			31.2687i			1.39006i
$507$	−5.16260	+	21.9168i	−0.229279	+	0.973361i
$508$	0.795823	−	0.795823i	0.0353089	−	0.0353089i
$509$	38.2650	+	22.0923i	1.69607	+	0.979224i	0.949423	+	0.313999i	$0.101669\pi$
$509$	38.2650	+	22.0923i	1.69607	+	0.979224i	0.746643	+	0.665225i	$0.231664\pi$
$510$		0			0
$511$	−0.640550	−	1.10947i	−0.0283363	−	0.0490799i
$512$	12.9549	+	12.9549i	0.572530	+	0.572530i
$513$	6.97351	+	12.4591i	0.307888	+	0.550083i
$514$	−2.63814	−	4.56940i	−0.116364	−	0.201548i
$515$		0			0
$516$	1.75477	−	0.461842i	0.0772494	−	0.0203315i
$517$	23.8583	−	6.39281i	1.04929	−	0.281155i
$518$	0.219330	+	0.818549i	0.00963679	+	0.0359650i
$519$	0.433362	−	1.58905i	0.0190225	−	0.0697516i
$520$		0			0
$521$		−	33.6427i		−	1.47391i	−0.675940	−	0.736956i	$-0.736262\pi$
$521$		−	33.6427i		−	1.47391i	0.675940	−	0.736956i	$-0.263738\pi$
$522$	4.35187	−	15.6826i	0.190476	−	0.686408i
$523$	8.15764	+	30.4447i	0.356709	+	1.33125i	0.878321	+	0.478072i	$0.158664\pi$
$523$	8.15764	+	30.4447i	0.356709	+	1.33125i	−0.521612	+	0.853183i	$0.674669\pi$
$524$	−0.492969	−	0.853848i	−0.0215355	−	0.0373005i
$525$		0			0
$526$	11.1916	−	6.46150i	0.487979	−	0.281735i
$527$	−3.01821	+	11.2641i	−0.131475	+	0.490673i
$528$	7.43415	+	13.0095i	0.323530	+	0.566165i
$529$	9.67033	−	5.58317i	0.420449	−	0.242746i
$530$		0			0
$531$	−25.6133	+	14.4859i	−1.11152	+	0.628635i
$532$	−0.256973	−	0.256973i	−0.0111412	−	0.0111412i
$533$	15.4091	−	2.30290i	0.667444	−	0.0997498i
$534$	12.6717	+	3.45578i	0.548356	+	0.149546i
$535$		0			0
$536$	−1.93178	−	1.11531i	−0.0834400	−	0.0481741i
$537$	14.2525	−	24.4347i	0.615042	−	1.05444i
$538$	−1.00647	−	1.00647i	−0.0433920	−	0.0433920i
$539$	−29.4378	+	16.9959i	−1.26798	+	0.732067i
$540$		0			0
$541$		−	31.8172i		−	1.36793i	−0.729516	−	0.683964i	$-0.760255\pi$
$541$		−	31.8172i		−	1.36793i	0.729516	−	0.683964i	$-0.239745\pi$
$542$	6.49126	+	1.73933i	0.278823	+	0.0747105i
$543$	−21.5567	−	0.0957836i	−0.925087	−	0.00411047i
$544$	10.1043	−	17.5012i	0.433218	−	0.750356i
$545$		0			0
$546$	0.704822	+	0.894210i	0.0301636	+	0.0382687i
$547$	−3.86162	−	3.86162i	−0.165111	−	0.165111i	0.619716	−	0.784826i	$-0.287248\pi$
$547$	−3.86162	−	3.86162i	−0.165111	−	0.165111i	−0.784826	+	0.619716i	$0.787248\pi$
$548$	−0.836179	−	3.12066i	−0.0357198	−	0.133308i
$549$	−21.2869	−	37.6385i	−0.908503	−	1.60637i
$550$		0			0
$551$	13.5854			0.578756
$552$	15.6497	−	26.8301i	0.666096	−	1.14196i
$553$	0.317922	−	1.18650i	0.0135194	−	0.0504551i
$554$			11.4120i			0.484850i
$555$		0			0
$556$	−2.93969	+	5.09169i	−0.124671	+	0.215936i
$557$	−6.99288	+	1.87374i	−0.296298	+	0.0793928i	−0.403906	−	0.914801i	$-0.632348\pi$
$557$	−6.99288	+	1.87374i	−0.296298	+	0.0793928i	0.107608	+	0.994193i	$0.465681\pi$
$558$	1.99105	+	7.70389i	0.0842878	+	0.326132i
$559$	−1.89223	−	4.35183i	−0.0800327	−	0.184063i
$560$		0			0
$561$	28.9335	−	28.6775i	1.22157	−	1.21077i
$562$	−23.2403	+	6.22723i	−0.980334	+	0.262680i
$563$	−0.945024	+	3.52688i	−0.0398280	+	0.148640i	−0.982976	−	0.183732i	$-0.941182\pi$
$563$	−0.945024	+	3.52688i	−0.0398280	+	0.148640i	0.943148	+	0.332372i	$0.107849\pi$
$564$	−6.73885	−	1.83780i	−0.283757	−	0.0773853i
$565$		0			0
$566$	−3.04122	−	5.26755i	−0.127832	−	0.221412i
$567$	1.43735	+	0.412650i	0.0603629	+	0.0173297i
$568$	−8.14877	−	2.18346i	−0.341915	−	0.0916158i
$569$	19.6847	−	34.0948i	0.825224	−	1.42933i	−0.0765237	−	0.997068i	$-0.524382\pi$
$569$	19.6847	−	34.0948i	0.825224	−	1.42933i	0.901748	−	0.432262i	$-0.142285\pi$
$570$		0			0
$571$	40.5072			1.69517			0.847586	−	0.530658i	$-0.178055\pi$
$571$	40.5072			1.69517			0.847586	+	0.530658i	$0.178055\pi$
$572$	−10.9499	+	8.70994i	−0.457839	+	0.364181i
$573$	4.32420	−	2.47103i	0.180646	−	0.103229i
$574$	0.393920	−	0.682289i	0.0164419	−	0.0284782i
$575$		0			0
$576$	0.217149	−	24.4349i	0.00904786	−	1.01812i
$577$	−24.8261	+	24.8261i	−1.03352	+	1.03352i	−0.0341041	+	0.999418i	$0.510858\pi$
$577$	−24.8261	+	24.8261i	−1.03352	+	1.03352i	−0.999418	+	0.0341041i	$0.989142\pi$
$578$	6.65039	+	1.78197i	0.276620	+	0.0741200i
$579$	17.6793	−	4.65306i	0.734727	−	0.193375i
$580$		0			0
$581$	−0.327628	+	0.189156i	−0.0135923	+	0.00784752i
$582$	−32.0367	−	0.142350i	−1.32797	−	0.00590059i
$583$	22.2873	−	5.97186i	0.923044	−	0.247329i
$584$	23.6547			0.978836
$585$		0			0
$586$	−5.37420			−0.222006
$587$	0.0134708	−	0.00360950i	0.000556001	−	0.000148980i	−0.258541	−	0.966000i	$-0.583242\pi$
$587$	0.0134708	−	0.00360950i	0.000556001	−	0.000148980i	0.259097	+	0.965851i	$0.416575\pi$
$588$	9.61256	+	0.0427118i	0.396415	+	0.00176140i
$589$	−5.75210	+	3.32098i	−0.237011	+	0.136838i
$590$		0			0
$591$	32.9672	−	8.67672i	1.35609	−	0.356912i
$592$	−7.96668	−	2.13466i	−0.327428	−	0.0877342i
$593$	−25.7961	+	25.7961i	−1.05932	+	1.05932i	−0.0611927	+	0.998126i	$0.519490\pi$
$593$	−25.7961	+	25.7961i	−1.05932	+	1.05932i	−0.998126	+	0.0611927i	$0.980510\pi$
$594$	7.55155	−	26.7512i	0.309844	−	1.09762i
$595$		0			0
$596$	−2.32205	+	4.02191i	−0.0951150	+	0.164744i
$597$	−18.9677	+	10.8389i	−0.776297	+	0.443608i
$598$	−21.5162	−	8.47547i	−0.879864	−	0.346588i
$599$	−28.2847			−1.15568			−0.577841	−	0.816149i	$-0.696105\pi$
$599$	−28.2847			−1.15568			−0.577841	+	0.816149i	$0.696105\pi$
$600$		0			0
$601$	8.59509	−	14.8871i	0.350601	−	0.607259i	−0.635754	−	0.771892i	$-0.719311\pi$
$601$	8.59509	−	14.8871i	0.350601	−	0.607259i	0.986355	+	0.164633i	$0.0526440\pi$
$602$	−0.231783	−	0.0621060i	−0.00944675	−	0.00253125i
$603$	0.545792	+	2.11182i	0.0222264	+	0.0859998i
$604$	−6.55087	−	11.3464i	−0.266551	−	0.461680i
$605$		0			0
$606$	−27.8638	−	7.59895i	−1.13189	−	0.308686i
$607$	−3.17469	+	11.8481i	−0.128857	+	0.480900i	−0.999948	−	0.0102219i	$-0.996746\pi$
$607$	−3.17469	+	11.8481i	−0.128857	+	0.480900i	0.871091	+	0.491121i	$0.163413\pi$
$608$	11.1179	−	2.97903i	0.450890	−	0.120816i
$609$	1.01058	−	1.00164i	0.0409509	−	0.0405886i
$610$		0			0
$611$	−2.06792	+	18.1498i	−0.0836591	+	0.734264i
$612$	−11.1538	+	2.88267i	−0.450866	+	0.116525i
$613$	10.3165	−	2.76430i	0.416680	−	0.111649i	−0.0443871	−	0.999014i	$-0.514134\pi$
$613$	10.3165	−	2.76430i	0.416680	−	0.111649i	0.461067	+	0.887365i	$0.347467\pi$
$614$	−12.1926	+	21.1181i	−0.492052	+	0.852259i
$615$		0			0
$616$			2.48520i			0.100132i
$617$	1.17565	−	4.38758i	0.0473299	−	0.176637i	−0.938215	−	0.346054i	$-0.887522\pi$
$617$	1.17565	−	4.38758i	0.0473299	−	0.176637i	0.985545	+	0.169416i	$0.0541882\pi$
$618$	−16.8043	+	28.8095i	−0.675969	+	1.15889i
$619$	−31.2573			−1.25634			−0.628168	−	0.778078i	$-0.716195\pi$
$619$	−31.2573			−1.25634			−0.628168	+	0.778078i	$0.716195\pi$
$620$		0			0
$621$	−29.4398	+	7.46924i	−1.18138	+	0.299730i
$622$	7.75311	+	28.9350i	0.310871	+	1.16019i
$623$	0.811962	+	0.811962i	0.0325306	+	0.0325306i
$624$	−10.9670	+	1.58924i	−0.439030	+	0.0636203i
$625$		0			0
$626$	10.0949	−	17.4849i	0.403473	−	0.698835i
$627$	23.2024	+	0.103096i	0.926615	+	0.00411726i
$628$	−5.60480	−	1.50180i	−0.223656	−	0.0599285i
$629$			22.4237i			0.894092i
$630$		0			0
$631$	31.2944	−	18.0678i	1.24581	−	0.719270i	0.275540	−	0.961289i	$-0.411143\pi$
$631$	31.2944	−	18.0678i	1.24581	−	0.719270i	0.970271	+	0.242020i	$0.0778099\pi$
$632$	16.0377	+	16.0377i	0.637946	+	0.637946i
$633$	−4.19516	+	7.19224i	−0.166743	+	0.285866i
$634$	−8.93599	−	5.15920i	−0.354893	−	0.204898i
$635$		0			0
$636$	−6.29511	−	1.71679i	−0.249617	−	0.0680750i
$637$	−3.71582	−	24.8632i	−0.147226	−	0.985115i
$638$	−18.7018	−	18.7018i	−0.740411	−	0.740411i
$639$	4.06101	+	7.18050i	0.160651	+	0.284056i
$640$		0			0
$641$	30.0234	−	17.3340i	1.18585	−	0.684653i	0.228492	−	0.973546i	$-0.426620\pi$
$641$	30.0234	−	17.3340i	1.18585	−	0.684653i	0.957361	+	0.288893i	$0.0932871\pi$
$642$	−2.05808	−	3.60157i	−0.0812261	−	0.142143i
$643$	7.35878	−	27.4633i	0.290202	−	1.08305i	−0.654752	−	0.755844i	$-0.727227\pi$
$643$	7.35878	−	27.4633i	0.290202	−	1.08305i	0.944954	−	0.327204i	$-0.106107\pi$
$644$	0.669496	−	0.386534i	0.0263819	−	0.0152316i
$645$		0			0
$646$	7.27297	+	12.5972i	0.286151	+	0.495628i
$647$	−0.778760	−	2.90637i	−0.0306162	−	0.114261i	0.948927	−	0.315497i	$-0.102171\pi$
$647$	−0.778760	−	2.90637i	−0.0306162	−	0.114261i	−0.979543	+	0.201235i	$0.935504\pi$
$648$	−19.8683	+	19.1744i	−0.780502	+	0.753240i
$649$			47.8191i			1.87706i
$650$		0			0
$651$	−0.183031	+	0.671139i	−0.00717356	+	0.0263040i
$652$	4.52728	+	16.8960i	0.177302	+	0.661700i
$653$	7.06400	−	1.89279i	0.276436	−	0.0740707i	−0.117938	−	0.993021i	$-0.537628\pi$
$653$	7.06400	−	1.89279i	0.276436	−	0.0740707i	0.394373	+	0.918950i	$0.370962\pi$
$654$	−18.9446	+	4.98607i	−0.740792	+	0.194971i
$655$		0			0
$656$	3.83390	+	6.64050i	0.149689	+	0.259268i
$657$	−16.2098	−	16.5005i	−0.632405	−	0.643746i
$658$	0.653163	+	0.653163i	0.0254630	+	0.0254630i
$659$	17.7103	+	30.6751i	0.689894	+	1.19493i	0.971872	+	0.235511i	$0.0756762\pi$
$659$	17.7103	+	30.6751i	0.689894	+	1.19493i	−0.281978	+	0.959421i	$0.590990\pi$
$660$		0			0
$661$	29.1120	+	16.8078i	1.13233	+	0.653748i	0.944519	−	0.328458i	$-0.106529\pi$
$661$	29.1120	+	16.8078i	1.13233	+	0.653748i	0.187807	+	0.982206i	$0.439862\pi$
$662$	4.92901	−	4.92901i	0.191571	−	0.191571i
$663$	11.8907	+	27.6825i	0.461797	+	1.07510i
$664$		−	6.98528i		−	0.271081i
$665$		0			0
$666$	7.53218	+	13.3181i	0.291866	+	0.516064i
$667$	−7.47969	+	27.9146i	−0.289615	+	1.08086i
$668$	7.97337	−	7.97337i	0.308499	−	0.308499i
$669$	−19.1031	+	5.02779i	−0.738568	+	0.194386i
$670$		0			0
$671$	−70.2698			−2.71273
$672$	0.607392	−	1.04132i	0.0234306	−	0.0401698i
$673$	−4.75245	−	17.7364i	−0.183194	−	0.683688i	−0.995010	−	0.0997751i	$-0.968188\pi$
$673$	−4.75245	−	17.7364i	−0.183194	−	0.683688i	0.811816	−	0.583913i	$-0.198479\pi$
$674$	−16.9200	−	9.76878i	−0.651735	−	0.376279i
$675$		0			0
$676$	−3.02537	−	9.89557i	−0.116360	−	0.380599i
$677$	30.5372	−	30.5372i	1.17364	−	1.17364i	0.192303	−	0.981336i	$-0.438404\pi$
$677$	30.5372	−	30.5372i	1.17364	−	1.17364i	0.981336	−	0.192303i	$-0.0615955\pi$
$678$	0.126080	−	28.3751i	0.00484207	−	1.08974i
$679$	−2.42562	−	1.40043i	−0.0930868	−	0.0537437i
$680$		0			0
$681$	−12.1008	+	44.3712i	−0.463703	+	1.70031i
$682$	12.4901	+	3.34672i	0.478271	+	0.128152i
$683$	−23.5257	−	6.30369i	−0.900186	−	0.241204i	−0.221090	−	0.975253i	$-0.570961\pi$
$683$	−23.5257	−	6.30369i	−0.900186	−	0.241204i	−0.679096	+	0.734049i	$0.737628\pi$
$684$	−5.65308	−	3.33114i	−0.216151	−	0.127369i
$685$		0			0
$686$	−2.20616	−	1.27372i	−0.0842314	−	0.0486310i
$687$	−11.0652	−	0.0491665i	−0.422165	−	0.00187582i
$688$	1.65141	−	1.65141i	0.0629594	−	0.0629594i
$689$	−1.93175	+	16.9547i	−0.0735940	+	0.645924i
$690$		0			0
$691$	0.523687	+	0.302351i	0.0199220	+	0.0115020i	0.509928	−	0.860217i	$-0.329672\pi$
$691$	0.523687	+	0.302351i	0.0199220	+	0.0115020i	−0.490006	+	0.871719i	$0.663005\pi$
$692$	0.195908	+	0.731139i	0.00744731	+	0.0277937i
$693$	1.73357	−	1.70303i	0.0658530	−	0.0646929i
$694$	−8.79320			−0.333785
$695$		0			0
$696$	6.68697	+	25.4071i	0.253469	+	0.963055i
$697$	14.7411	−	14.7411i	0.558358	−	0.558358i
$698$	5.38038	−	20.0799i	0.203651	−	0.760034i
$699$	22.2507	+	22.4494i	0.841601	+	0.849113i
$700$		0			0
$701$		−	35.7248i		−	1.34931i	−0.738134	−	0.674654i	$-0.764293\pi$
$701$		−	35.7248i		−	1.34931i	0.738134	−	0.674654i	$-0.235707\pi$
$702$	16.3608	+	12.4473i	0.617500	+	0.469792i
$703$	−9.03098	+	9.03098i	−0.340610	+	0.340610i
$704$	−34.3898	−	19.8550i	−1.29611	−	0.748312i
$705$		0			0
$706$	−1.24983	−	2.16477i	−0.0470379	−	0.0814720i
$707$	−1.78543	−	1.78543i	−0.0671481	−	0.0671481i
$708$	6.81342	−	11.6810i	0.256064	−	0.438999i
$709$	−2.01558	−	3.49108i	−0.0756966	−	0.131110i	0.825692	−	0.564121i	$-0.190785\pi$
$709$	−2.01558	−	3.49108i	−0.0756966	−	0.131110i	−0.901389	+	0.433010i	$0.857451\pi$
$710$		0			0
$711$	0.197087	−	22.1774i	0.00739134	−	0.831717i
$712$	−20.4799	+	5.48757i	−0.767517	+	0.205656i
$713$	−3.65685	−	13.6476i	−0.136950	−	0.511105i
$714$	1.46980	+	0.400840i	0.0550059	+	0.0150011i
$715$		0			0
$716$			12.9998i			0.485826i
$717$	0.0246850	−	5.55552i	0.000921879	−	0.207475i
$718$	−2.79196	−	10.4197i	−0.104195	−	0.388861i
$719$	−18.2661	−	31.6378i	−0.681211	−	1.17989i	−0.974612	−	0.223903i	$-0.928120\pi$
$719$	−18.2661	−	31.6378i	−0.681211	−	1.17989i	0.293400	−	0.955990i	$-0.405213\pi$
$720$		0			0
$721$	−2.52520	+	1.45793i	−0.0940434	+	0.0542960i
$722$	3.25166	−	12.1354i	0.121014	−	0.451632i
$723$	9.02953	−	5.15984i	0.335812	−	0.191897i
$724$	8.57942	−	4.95333i	0.318852	−	0.184089i
$725$		0			0
$726$	−17.0819	−	17.2344i	−0.633969	−	0.639628i
$727$	6.38702	+	6.38702i	0.236881	+	0.236881i	0.815557	−	0.578676i	$-0.196430\pi$
$727$	6.38702	+	6.38702i	0.236881	+	0.236881i	−0.578676	+	0.815557i	$0.696430\pi$
$728$	−1.71009	−	0.673622i	−0.0633800	−	0.0249661i
$729$	26.9904	+	0.719730i	0.999645	+	0.0266567i
$730$		0			0
$731$	−5.49888	−	3.17478i	−0.203383	−	0.117423i
$732$	17.1652	+	10.0123i	0.634442	+	0.370064i
$733$	−15.5660	−	15.5660i	−0.574943	−	0.574943i	0.358562	−	0.933506i	$-0.383267\pi$
$733$	−15.5660	−	15.5660i	−0.574943	−	0.574943i	−0.933506	+	0.358562i	$0.883267\pi$
$734$	11.2366	−	6.48747i	0.414751	−	0.239457i
$735$		0			0
$736$			24.4847i			0.902518i
$737$	3.42383	+	0.917413i	0.126118	+	0.0337933i
$738$	3.80357	−	13.7067i	0.140011	−	0.504551i
$739$	−24.9818	+	43.2698i	−0.918972	+	1.59171i	−0.117992	+	0.993015i	$0.537646\pi$
$739$	−24.9818	+	43.2698i	−0.918972	+	1.59171i	−0.800980	+	0.598691i	$0.795688\pi$
$740$		0			0
$741$	−6.36003	+	15.9378i	−0.233641	+	0.585490i
$742$	0.610154	+	0.610154i	0.0223995	+	0.0223995i
$743$	−7.11227	−	26.5434i	−0.260924	−	0.973781i	−0.964698	−	0.263358i	$-0.915170\pi$
$743$	−7.11227	−	26.5434i	−0.260924	−	0.973781i	0.703774	−	0.710424i	$-0.251497\pi$
$744$	−9.04212	−	9.12284i	−0.331500	−	0.334459i
$745$		0			0
$746$	−26.9925			−0.988264
$747$	−4.87264	+	4.78680i	−0.178281	+	0.175140i
$748$	−4.84542	+	18.0834i	−0.177166	+	0.661193i
$749$		−	0.362654i		−	0.0132511i
$750$		0			0
$751$	−8.07976	+	13.9946i	−0.294835	+	0.510669i	−0.974946	−	0.222440i	$-0.928598\pi$
$751$	−8.07976	+	13.9946i	−0.294835	+	0.510669i	0.680112	+	0.733108i	$0.261931\pi$
$752$	−8.68386	+	2.32683i	−0.316668	+	0.0848509i
$753$	36.9241	−	21.1000i	1.34559	−	0.768926i
$754$	17.9380	−	7.79967i	0.653265	−	0.284047i
$755$		0			0
$756$	−0.666122	+	0.169003i	−0.0242266	+	0.00614659i
$757$	−12.4869	+	3.34586i	−0.453845	+	0.121607i	−0.478498	−	0.878089i	$-0.658819\pi$
$757$	−12.4869	+	3.34586i	−0.453845	+	0.121607i	0.0246532	+	0.999696i	$0.492152\pi$
$758$	−4.45884	+	16.6406i	−0.161952	+	0.604415i
$759$	−12.9864	+	47.6184i	−0.471375	+	1.72844i
$760$		0			0
$761$	13.7581	+	23.8298i	0.498732	+	0.863828i	0.999999	−	0.00146412i	$-0.000466042\pi$
$761$	13.7581	+	23.8298i	0.498732	+	0.863828i	−0.501267	+	0.865292i	$0.667133\pi$
$762$	−2.33317	+	1.33327i	−0.0845220	+	0.0482993i
$763$	−1.65429	−	0.443266i	−0.0598894	−	0.0160473i
$764$	−1.14440	+	1.98216i	−0.0414029	+	0.0717119i
$765$		0			0
$766$	−2.62082			−0.0946941
$767$	−32.9047	−	12.9615i	−1.18812	−	0.468013i
$768$	13.4713	+	23.5743i	0.486105	+	0.850665i
$769$	−5.76778	+	9.99009i	−0.207992	+	0.360252i	−0.951082	−	0.308939i	$-0.900026\pi$
$769$	−5.76778	+	9.99009i	−0.207992	+	0.360252i	0.743090	+	0.669191i	$0.233359\pi$
$770$		0			0
$771$	−2.11983	−	8.05431i	−0.0763439	−	0.290069i
$772$	−5.94066	+	5.94066i	−0.213809	+	0.213809i
$773$	−5.03736	−	1.34976i	−0.181181	−	0.0485474i	0.167088	−	0.985942i	$-0.446564\pi$
$773$	−5.03736	−	1.34976i	−0.181181	−	0.0485474i	−0.348269	+	0.937395i	$0.613230\pi$
$774$	−4.33235	−	0.0385009i	−0.155723	−	0.00138389i
$775$		0			0
$776$	44.7875	−	25.8581i	1.60778	−	0.928250i
$777$	−0.00594359	+	1.33764i	−0.000213225	+	0.0479877i
$778$	14.9187	−	3.99745i	0.534861	−	0.143316i
$779$	11.8737			0.425420
$780$		0			0
$781$	13.4057			0.479695
$782$	−29.8883	+	8.00855i	−1.06880	+	0.286385i
$783$	13.1406	−	22.0753i	0.469606	−	0.788907i
$784$	10.7147	−	6.18613i	0.382667	−	0.220933i
$785$		0			0
$786$	0.599179	+	2.27658i	0.0213720	+	0.0812030i
$787$	38.7052	+	10.3710i	1.37969	+	0.369687i	0.871009	−	0.491267i	$-0.163466\pi$
$787$	38.7052	+	10.3710i	1.37969	+	0.369687i	0.508683	+	0.860954i	$0.330133\pi$
$788$	−11.0777	+	11.0777i	−0.394628	+	0.394628i
$789$	19.7271	−	5.19202i	0.702303	−	0.184841i
$790$		0			0
$791$	1.24037	−	2.14838i	0.0441024	−	0.0763876i
$792$	11.2278	+	43.4435i	0.398964	+	1.54370i
$793$	19.0468	−	48.3532i	0.676373	−	1.71707i
$794$	35.2836			1.25217
$795$		0			0
$796$	5.01980	−	8.69455i	0.177922	−	0.308170i
$797$	−33.4264	−	8.95658i	−1.18402	−	0.317259i	−0.387503	−	0.921868i	$-0.626662\pi$
$797$	−33.4264	−	8.95658i	−1.18402	−	0.317259i	−0.796522	+	0.604610i	$0.793329\pi$
$798$	0.430516	+	0.753387i	0.0152401	+	0.0266696i
$799$	12.2212	+	21.1677i	0.432354	+	0.748859i
$800$		0			0
$801$	17.8622	+	10.5255i	0.631128	+	0.371899i
$802$	−0.339325	+	1.26638i	−0.0119820	+	0.0447174i
$803$	−36.3080	+	9.72871i	−1.28128	+	0.343319i
$804$	−0.705641	−	0.711939i	−0.0248860	−	0.0251082i
$805$		0			0
$806$	−5.68838	+	7.68740i	−0.200365	+	0.270777i
$807$	−1.11473	−	1.95073i	−0.0392403	−	0.0686691i
$808$	45.0335	−	12.0667i	1.58427	−	0.424504i
$809$	−0.776492	+	1.34492i	−0.0273000	+	0.0472850i	−0.879353	−	0.476171i	$-0.842024\pi$
$809$	−0.776492	+	1.34492i	−0.0273000	+	0.0472850i	0.852053	+	0.523456i	$0.175358\pi$
$810$		0			0
$811$		−	15.7167i		−	0.551889i	−0.961174	−	0.275945i	$-0.911009\pi$
$811$		−	15.7167i		−	0.551889i	0.961174	−	0.275945i	$-0.0889906\pi$
$812$	−0.169240	+	0.631612i	−0.00593915	+	0.0221652i
$813$	9.16303	+	5.34470i	0.321361	+	0.187447i
$814$	24.8643			0.871494
$815$		0			0
$816$	−10.5311	+	10.4380i	−0.368663	+	0.365402i
$817$	−0.936013	−	3.49325i	−0.0327470	−	0.122213i
$818$	13.8577	+	13.8577i	0.484522	+	0.484522i
$819$	0.701979	+	1.65450i	0.0245291	+	0.0578128i
$820$		0			0
$821$	−23.5322	+	40.7590i	−0.821280	+	1.42250i	0.0834487	+	0.996512i	$0.473407\pi$
$821$	−23.5322	+	40.7590i	−0.821280	+	1.42250i	−0.904729	+	0.425987i	$0.859927\pi$
$822$	−0.0342755	+	7.71393i	−0.00119550	+	0.269054i
$823$	44.5459	+	11.9360i	1.55277	+	0.416064i	0.930366	−	0.366631i	$-0.119489\pi$
$823$	44.5459	+	11.9360i	1.55277	+	0.416064i	0.622405	+	0.782695i	$0.286156\pi$
$824$		−	53.8392i		−	1.87558i
$825$		0			0
$826$	−1.54872	+	0.894155i	−0.0538870	+	0.0311116i
$827$	−25.7893	−	25.7893i	−0.896781	−	0.896781i	0.0983687	−	0.995150i	$-0.468638\pi$
$827$	−25.7893	−	25.7893i	−0.896781	−	0.896781i	−0.995150	+	0.0983687i	$0.968638\pi$
$828$	9.95707	−	9.78166i	0.346032	−	0.339936i
$829$	−35.8684	−	20.7086i	−1.24576	−	0.719241i	−0.275500	−	0.961301i	$-0.588843\pi$
$829$	−35.8684	−	20.7086i	−1.24576	−	0.719241i	−0.970261	+	0.242060i	$0.922177\pi$
$830$		0			0
$831$	−4.73959	+	17.3791i	−0.164414	+	0.602875i
$832$	22.9838	−	18.2821i	0.796820	−	0.633819i
$833$	−23.7853	−	23.7853i	−0.824110	−	0.824110i
$834$	9.97044	−	9.88223i	0.345248	−	0.342193i
$835$		0			0
$836$	−9.23439	+	5.33148i	−0.319378	+	0.184393i
$837$	−0.167420	+	12.5590i	−0.00578689	+	0.434103i
$838$	−3.01687	+	11.2591i	−0.104216	+	0.388939i
$839$	−12.9769	+	7.49223i	−0.448013	+	0.258660i	−0.706991	−	0.707223i	$-0.749948\pi$
$839$	−12.9769	+	7.49223i	−0.448013	+	0.258660i	0.258978	+	0.965883i	$0.416614\pi$
$840$		0			0
$841$	2.27790	+	3.94543i	0.0785481	+	0.136049i
$842$	6.78040	+	25.3048i	0.233668	+	0.872061i
$843$	−37.9785	−	0.168751i	−1.30805	−	0.00581209i
$844$		−	3.82643i		−	0.131711i
$845$		0			0
$846$	14.3688	+	8.46696i	0.494009	+	0.291100i
$847$	−0.549067	−	2.04915i	−0.0188662	−	0.0704095i
$848$	−8.11205	+	2.17362i	−0.278569	+	0.0746424i
$849$	−2.44372	−	9.28491i	−0.0838682	−	0.318657i
$850$		0			0
$851$	−13.5842	−	23.5286i	−0.465662	−	0.806550i
$852$	−3.27468	−	1.91009i	−0.112189	−	0.0654386i
$853$	−9.05692	−	9.05692i	−0.310103	−	0.310103i	0.534846	−	0.844949i	$-0.320369\pi$
$853$	−9.05692	−	9.05692i	−0.310103	−	0.310103i	−0.844949	+	0.534846i	$0.820369\pi$
$854$	−1.31395	−	2.27583i	−0.0449626	−	0.0778775i
$855$		0			0
$856$	5.79905	+	3.34808i	0.198207	+	0.114435i
$857$	12.8809	−	12.8809i	0.440004	−	0.440004i	−0.452009	−	0.892013i	$-0.649293\pi$
$857$	12.8809	−	12.8809i	0.440004	−	0.440004i	0.892013	+	0.452009i	$0.149293\pi$
$858$	30.6955	−	13.1849i	1.04793	−	0.450125i
$859$			10.9311i			0.372966i	0.982458	+	0.186483i	$0.0597089\pi$
$859$			10.9311i			0.372966i	−0.982458	+	0.186483i	$0.940291\pi$
$860$		0			0
$861$	0.883258	−	0.875443i	0.0301013	−	0.0298350i
$862$	4.74335	−	17.7024i	0.161559	−	0.602947i
$863$	−21.3829	+	21.3829i	−0.727881	+	0.727881i	−0.970197	−	0.242316i	$-0.922093\pi$
$863$	−21.3829	+	21.3829i	−0.727881	+	0.727881i	0.242316	+	0.970197i	$0.422093\pi$
$864$	5.91318	−	20.9473i	0.201170	−	0.712642i
$865$		0			0
$866$	−30.1629			−1.02498
$867$	9.38766	+	5.47573i	0.318822	+	0.185965i
$868$	−0.0827422	−	0.308798i	−0.00280845	−	0.0104813i
$869$	−31.2126	−	18.0206i	−1.05882	−	0.611308i
$870$		0			0
$871$	−1.55932	+	2.10730i	−0.0528355	+	0.0714030i
$872$	22.3608	−	22.3608i	0.757231	−	0.757231i
$873$	−48.7290	−	13.5221i	−1.64923	−	0.457655i
$874$	−15.2627	−	8.81191i	−0.516268	−	0.298067i
$875$		0			0
$876$	10.2553	+	2.79680i	0.346495	+	0.0944952i
$877$	−14.7430	−	3.95038i	−0.497836	−	0.133395i	0.00115930	−	0.999999i	$-0.499631\pi$
$877$	−14.7430	−	3.95038i	−0.497836	−	0.133395i	−0.498996	+	0.866604i	$0.666298\pi$
$878$	20.2523	+	5.42659i	0.683483	+	0.183139i
$879$	−8.18425	−	2.23199i	−0.276048	−	0.0752830i
$880$		0			0
$881$	−15.6546	−	9.03820i	−0.527417	−	0.304505i	0.212547	−	0.977151i	$-0.431824\pi$
$881$	−15.6546	−	9.03820i	−0.527417	−	0.304505i	−0.739964	+	0.672646i	$0.765158\pi$
$882$	−22.1163	−	6.13719i	−0.744693	−	0.206650i
$883$	−21.5666	+	21.5666i	−0.725775	+	0.725775i	−0.969775	−	0.244000i	$-0.921540\pi$
$883$	−21.5666	+	21.5666i	−0.725775	+	0.725775i	0.244000	+	0.969775i	$0.421540\pi$
$884$	−11.1299	−	8.23572i	−0.374340	−	0.276997i
$885$		0			0
$886$	−11.7550	−	6.78673i	−0.394915	−	0.228005i
$887$	8.32639	+	31.0745i	0.279573	+	1.04338i	0.952715	+	0.303867i	$0.0982777\pi$
$887$	8.32639	+	31.0745i	0.279573	+	1.04338i	−0.673142	+	0.739514i	$0.735056\pi$
$888$	−21.3348	−	12.4444i	−0.715949	−	0.417606i
$889$	−0.234935			−0.00787947
$890$		0			0
$891$	22.6103	−	37.6026i	0.757473	−	1.25973i
$892$	6.41908	−	6.41908i	0.214927	−	0.214927i
$893$	−3.60314	+	13.4471i	−0.120575	+	0.449991i
$894$	7.87562	−	7.80595i	0.263400	−	0.261070i
$895$		0			0
$896$		−	0.0930361i		−	0.00310812i
$897$	−29.2466	−	21.8431i	−0.976516	−	0.729321i
$898$	−23.1104	+	23.1104i	−0.771205	+	0.771205i
$899$	10.3498	+	5.97544i	0.345184	+	0.199292i
$900$		0			0
$901$	11.4164	+	19.7739i	0.380337	+	0.658763i
$902$	−16.3455	−	16.3455i	−0.544246	−	0.544246i
$903$	−0.327183	−	0.190843i	−0.0108880	−	0.00635085i
$904$	22.9026	+	39.6684i	0.761728	+	1.31935i
$905$		0			0
$906$	7.96225	+	30.2526i	0.264528	+	1.00507i
$907$	−12.8475	+	3.44249i	−0.426596	+	0.114306i	−0.465728	−	0.884928i	$-0.654207\pi$
$907$	−12.8475	+	3.44249i	−0.426596	+	0.114306i	0.0391321	+	0.999234i	$0.487541\pi$
$908$	−5.47035	−	20.4156i	−0.181540	−	0.677517i
$909$	−39.2773	−	23.1446i	−1.30275	−	0.767656i
$910$		0			0
$911$		−	6.22499i		−	0.206243i	−0.994669	−	0.103122i	$-0.967117\pi$
$911$		−	6.22499i		−	0.206243i	0.994669	−	0.103122i	$-0.0328831\pi$
$912$	−8.44514	−	0.0375246i	−0.279647	−	0.00124256i
$913$	2.87291	+	10.7219i	0.0950795	+	0.354841i
$914$	1.91698	+	3.32031i	0.0634081	+	0.109826i
$915$		0			0
$916$	4.40388	−	2.54258i	0.145508	−	0.0840092i
$917$	−0.0532676	+	0.198797i	−0.00175905	+	0.00656486i
$918$	27.5044	+	0.366652i	0.907779	+	0.0121013i
$919$	−51.3893	+	29.6696i	−1.69518	+	0.978711i	−0.744968	+	0.667101i	$0.767535\pi$
$919$	−51.3893	+	29.6696i	−1.69518	+	0.978711i	−0.950210	+	0.311611i	$0.899132\pi$
$920$		0			0
$921$	−27.3385	+	27.0966i	−0.900834	+	0.892864i
$922$	−2.42842	−	2.42842i	−0.0799759	−	0.0799759i
$923$	−3.63366	+	9.22458i	−0.119603	+	0.303631i
$924$	−0.293837	+	1.07744i	−0.00966654	+	0.0354453i
$925$		0			0
$926$	36.9249	+	21.3186i	1.21343	+	0.700573i
$927$	−37.5560	+	36.8944i	−1.23350	+	1.21177i
$928$	−14.6443	−	14.6443i	−0.480722	−	0.480722i
$929$	−9.30395	+	5.37164i	−0.305253	+	0.176238i	−0.644800	−	0.764351i	$-0.723059\pi$
$929$	−9.30395	+	5.37164i	−0.305253	+	0.176238i	0.339548	+	0.940589i	$0.389726\pi$
$930$		0			0
$931$		−	19.1587i		−	0.627900i
$932$	−14.0308	−	3.75954i	−0.459594	−	0.123148i
$933$	−0.210101	+	47.2845i	−0.00687839	+	1.54803i
$934$	15.8303	−	27.4189i	0.517984	−	0.897175i
$935$		0			0
$936$	−32.9372	−	4.04954i	−1.07658	−	0.132363i
$937$	7.07205	+	7.07205i	0.231034	+	0.231034i	0.813124	−	0.582090i	$-0.197765\pi$
$937$	7.07205	+	7.07205i	0.231034	+	0.231034i	−0.582090	+	0.813124i	$0.697765\pi$
$938$	0.0343089	+	0.128042i	0.00112022	+	0.00418073i
$939$	22.6350	−	22.4348i	0.738666	−	0.732131i
$940$		0			0
$941$	28.4220			0.926529			0.463265	−	0.886220i	$-0.346678\pi$
$941$	28.4220			0.926529			0.463265	+	0.886220i	$0.346678\pi$
$942$	11.9675	+	6.98054i	0.389923	+	0.227438i
$943$	−6.53730	+	24.3975i	−0.212884	+	0.794494i
$944$		−	17.4051i		−	0.566486i
$945$		0			0
$946$	−3.52033	+	6.09738i	−0.114456	+	0.198243i
$947$	−15.0316	+	4.02771i	−0.488461	+	0.130883i	−0.494640	−	0.869098i	$-0.664700\pi$
$947$	−15.0316	+	4.02771i	−0.488461	+	0.130883i	0.00617839	+	0.999981i	$0.498033\pi$
$948$	5.05683	+	8.84926i	0.164238	+	0.287411i
$949$	3.14701	−	27.6208i	0.102156	−	0.896610i
$950$		0			0
$951$	−11.4657	−	11.5681i	−0.371802	−	0.375121i
$952$	−2.37549	+	0.636511i	−0.0769901	+	0.0206294i
$953$	10.2413	−	38.2209i	0.331747	−	1.23810i	−0.575607	−	0.817727i	$-0.695234\pi$
$953$	10.2413	−	38.2209i	0.331747	−	1.23810i	0.907353	−	0.420369i	$-0.138099\pi$
$954$	13.4226	+	7.90943i	0.434574	+	0.256077i
$955$		0			0
$956$	1.27655	+	2.21106i	0.0412867	+	0.0715107i
$957$	−20.7134	−	36.2477i	−0.669571	−	1.17172i
$958$	0.143193	+	0.0383684i	0.00462635	+	0.00123963i
$959$	−0.337201	+	0.584050i	−0.0108888	+	0.0188600i
$960$		0			0
$961$	25.1572			0.811521
$962$	−6.73955	+	17.1093i	−0.217292	+	0.551627i
$963$	−1.63843	−	6.33951i	−0.0527976	−	0.204288i
$964$	−2.38966	+	4.13901i	−0.0769658	+	0.133309i
$965$		0			0
$966$	−1.78505	+	0.469812i	−0.0574331	+	0.0151160i
$967$	−32.4327	+	32.4327i	−1.04296	+	1.04296i	−0.0439297	+	0.999035i	$0.513988\pi$
$967$	−32.4327	+	32.4327i	−1.04296	+	1.04296i	−0.999035	+	0.0439297i	$0.986012\pi$
$968$	37.8361	+	10.1381i	1.21610	+	0.325852i
$969$	5.84406	+	22.2045i	0.187738	+	0.713312i
$970$		0			0
$971$	−29.2025	+	16.8601i	−0.937154	+	0.541066i	−0.889067	−	0.457777i	$-0.848646\pi$
$971$	−29.2025	+	16.8601i	−0.937154	+	0.541066i	−0.0480872	+	0.998843i	$0.515313\pi$
$972$	−10.8809	+	5.96379i	−0.349004	+	0.191289i
$973$	1.18547	−	0.317646i	0.0380045	−	0.0101833i
$974$	−10.7050			−0.343009
$975$		0			0
$976$	25.5766			0.818686
$977$	−2.30444	+	0.617472i	−0.0737254	+	0.0197547i	−0.295493	−	0.955345i	$-0.595484\pi$
$977$	−2.30444	+	0.617472i	−0.0737254	+	0.0197547i	0.221768	+	0.975100i	$0.428817\pi$
$978$	0.185576	−	41.7651i	0.00593408	−	1.33550i
$979$	29.1781	−	16.8460i	0.932536	−	0.538400i
$980$		0			0
$981$	−30.9211	−	0.274791i	−0.987235	−	0.00877340i
$982$	23.0982	+	6.18915i	0.737094	+	0.197504i
$983$	2.74521	−	2.74521i	0.0875586	−	0.0875586i	−0.661971	−	0.749530i	$-0.730280\pi$
$983$	2.74521	−	2.74521i	0.0875586	−	0.0875586i	0.749530	+	0.661971i	$0.230280\pi$
$984$	5.84446	+	22.2060i	0.186315	+	0.707903i
$985$		0			0
$986$	13.0863	−	22.6661i	0.416752	−	0.721836i
$987$	0.723420	+	1.26596i	0.0230267	+	0.0402959i
$988$	−1.16562	−	7.79937i	−0.0370833	−	0.248131i
$989$	7.69310			0.244626
$990$		0			0
$991$	−8.53170	+	14.7773i	−0.271019	+	0.469418i	−0.969123	−	0.246578i	$-0.920694\pi$
$991$	−8.53170	+	14.7773i	−0.271019	+	0.469418i	0.698104	+	0.715996i	$0.254027\pi$
$992$	9.78028	+	2.62062i	0.310524	+	0.0832047i
$993$	9.55337	−	5.45919i	0.303167	−	0.173242i
$994$	0.250670	+	0.434173i	0.00795076	+	0.0137711i
$995$		0			0
$996$	0.825903	−	3.02842i	0.0261697	−	0.0959592i
$997$	−1.53450	+	5.72683i	−0.0485981	+	0.181371i	−0.985958	−	0.166991i	$-0.946595\pi$
$997$	−1.53450	+	5.72683i	−0.0485981	+	0.181371i	0.937360	+	0.348361i	$0.113262\pi$
$998$	19.2683	−	5.16292i	0.609927	−	0.163429i
$999$	5.93941	+	23.4100i	0.187915	+	0.740660i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bn.d.407.17		96
3.2	odd	2	inner	975.2.bn.d.407.8		96
5.2	odd	4		195.2.bf.a.173.17	yes	96
5.3	odd	4	inner	975.2.bn.d.368.8		96
5.4	even	2		195.2.bf.a.17.8	✓	96
13.10	even	6	inner	975.2.bn.d.257.17		96
15.2	even	4		195.2.bf.a.173.8	yes	96
15.8	even	4	inner	975.2.bn.d.368.17		96
15.14	odd	2		195.2.bf.a.17.17	yes	96
39.23	odd	6	inner	975.2.bn.d.257.8		96
65.23	odd	12	inner	975.2.bn.d.218.8		96
65.49	even	6		195.2.bf.a.62.8	yes	96
65.62	odd	12		195.2.bf.a.23.17	yes	96
195.23	even	12	inner	975.2.bn.d.218.17		96
195.62	even	12		195.2.bf.a.23.8	yes	96
195.179	odd	6		195.2.bf.a.62.17	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.8	✓	96	5.4	even	2
195.2.bf.a.17.17	yes	96	15.14	odd	2
195.2.bf.a.23.8	yes	96	195.62	even	12
195.2.bf.a.23.17	yes	96	65.62	odd	12
195.2.bf.a.62.8	yes	96	65.49	even	6
195.2.bf.a.62.17	yes	96	195.179	odd	6
195.2.bf.a.173.8	yes	96	15.2	even	4
195.2.bf.a.173.17	yes	96	5.2	odd	4
975.2.bn.d.218.8		96	65.23	odd	12	inner
975.2.bn.d.218.17		96	195.23	even	12	inner
975.2.bn.d.257.8		96	39.23	odd	6	inner
975.2.bn.d.257.17		96	13.10	even	6	inner
975.2.bn.d.368.8		96	5.3	odd	4	inner
975.2.bn.d.368.17		96	15.8	even	4	inner
975.2.bn.d.407.8		96	3.2	odd	2	inner
975.2.bn.d.407.17		96	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.05989 - 0.283997i) q^{2} +(1.73203 + 0.00769600i) q^{3} +(-0.689337 + 0.397989i) q^{4} +(1.83795 - 0.483735i) q^{6} +(0.160495 + 0.0430045i) q^{7} +(-2.16938 + 2.16938i) q^{8} +(2.99988 + 0.0266595i) q^{9} +(2.43760 - 4.22205i) q^{11} +(-1.19702 + 0.684025i) q^{12} +(2.24451 + 2.82173i) q^{13} +0.182320 q^{14} +(-0.887232 + 1.53673i) q^{16} +(4.65999 + 1.24864i) q^{17} +(3.18712 - 0.823701i) q^{18} +(1.37389 + 2.37966i) q^{19} +(0.277652 + 0.0757204i) q^{21} +(1.38454 - 5.16719i) q^{22} +(-5.64603 + 1.51285i) q^{23} +(-3.77414 + 3.74075i) q^{24} +(3.18030 + 2.35330i) q^{26} +(5.19569 + 0.0692622i) q^{27} +(-0.127750 + 0.0342306i) q^{28} +(2.47205 - 4.28172i) q^{29} +2.41720i q^{31} +(1.08416 - 4.04612i) q^{32} +(4.25451 - 7.29398i) q^{33} +5.29369 q^{34} +(-2.07854 + 1.17554i) q^{36} +(1.20299 + 4.48963i) q^{37} +(2.13199 + 2.13199i) q^{38} +(3.86585 + 4.90461i) q^{39} +(2.16059 - 3.74226i) q^{41} +(0.315785 + 0.00140314i) q^{42} +(-1.27129 - 0.340642i) q^{43} +3.88056i q^{44} +(-5.55453 + 3.20691i) q^{46} +(3.58251 + 3.58251i) q^{47} +(-1.54854 + 2.65484i) q^{48} +(-6.03827 - 3.48620i) q^{49} +(8.06165 + 2.19855i) q^{51} +(-2.67024 - 1.05184i) q^{52} +(3.34661 + 3.34661i) q^{53} +(5.52653 - 1.40215i) q^{54} +(-0.441468 + 0.254882i) q^{56} +(2.36132 + 4.13222i) q^{57} +(1.40411 - 5.24021i) q^{58} +(-8.49452 + 4.90431i) q^{59} +(-7.20685 - 12.4826i) q^{61} +(0.686477 + 2.56197i) q^{62} +(0.480319 + 0.133287i) q^{63} -8.14527i q^{64} +(2.43784 - 8.93909i) q^{66} +(0.188179 + 0.702294i) q^{67} +(-3.70925 + 0.993890i) q^{68} +(-9.79075 + 2.57685i) q^{69} +(1.37489 + 2.38137i) q^{71} +(-6.56572 + 6.45005i) q^{72} +(-5.45193 - 5.45193i) q^{73} +(2.55008 + 4.41687i) q^{74} +(-1.89415 - 1.09359i) q^{76} +(0.572790 - 0.572790i) q^{77} +(5.49027 + 4.10047i) q^{78} -7.39276i q^{79} +(8.99858 + 0.159950i) q^{81} +(1.22720 - 4.57999i) q^{82} +(-1.60997 + 1.60997i) q^{83} +(-0.221531 + 0.0583054i) q^{84} -1.44417 q^{86} +(4.31463 - 7.39706i) q^{87} +(3.87115 + 14.4473i) q^{88} +(5.98500 + 3.45544i) q^{89} +(0.238885 + 0.549398i) q^{91} +(3.28992 - 3.28992i) q^{92} +(-0.0186028 + 4.18667i) q^{93} +(4.81449 + 2.77964i) q^{94} +(1.90893 - 6.99968i) q^{96} +(-16.2824 - 4.36286i) q^{97} +(-7.38997 - 1.98014i) q^{98} +(7.42508 - 12.6007i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) \) 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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