LMFDB - Embedded newform 975.2.bn.d.218.8

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			218.8
Character	$\chi$	$=$	975.218
Dual form			975.2.bn.d.407.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.05989 - 0.283997i) q^{2} +(-1.49614 - 0.872682i) q^{3} +(-0.689337 - 0.397989i) q^{4} +(1.33790 + 1.34985i) q^{6} +(0.160495 - 0.0430045i) q^{7} +(2.16938 + 2.16938i) q^{8} +(1.47685 + 2.61130i) q^{9} +(-2.43760 - 4.22205i) q^{11} +(0.684025 + 1.19702i) q^{12} +(2.24451 - 2.82173i) q^{13} -0.182320 q^{14} +(-0.887232 - 1.53673i) q^{16} +(-4.65999 + 1.24864i) q^{17} +(-0.823701 - 3.18712i) 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} +(-1.35251 - 5.13887i) q^{24} +(-3.18030 + 2.35330i) q^{26} +(0.0692622 - 5.19569i) q^{27} +(-0.127750 - 0.0342306i) q^{28} +(-2.47205 - 4.28172i) q^{29} -2.41720i q^{31} +(-1.08416 - 4.04612i) q^{32} +(-0.0375196 + 8.44403i) q^{33} +5.29369 q^{34} +(0.0212203 - 2.38784i) q^{36} +(1.20299 - 4.48963i) q^{37} +(-2.13199 + 2.13199i) q^{38} +(-5.82057 + 2.26296i) q^{39} +(-2.16059 - 3.74226i) q^{41} +(0.272776 + 0.159108i) q^{42} +(-1.27129 + 0.340642i) q^{43} +3.88056i q^{44} +(-5.55453 - 3.20691i) q^{46} +(-3.58251 + 3.58251i) q^{47} +(-0.0136563 + 3.07343i) 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} +(-1.54897 + 5.48719i) q^{54} +(0.441468 + 0.254882i) q^{56} +(-4.13222 + 2.36132i) 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} +(0.349325 + 0.355590i) q^{63} +8.14527i q^{64} +(2.43784 - 8.93909i) q^{66} +(0.188179 - 0.702294i) q^{67} +(3.70925 + 0.993890i) q^{68} +(-7.12700 - 7.19061i) q^{69} +(-1.37489 + 2.38137i) q^{71} +(-2.46106 + 8.86877i) 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} +(6.81184 - 0.745469i) q^{78} +7.39276i q^{79} +(-4.63781 + 7.71302i) q^{81} +(1.22720 + 4.57999i) q^{82} +(1.60997 + 1.60997i) q^{83} +(0.161260 + 0.162699i) q^{84} +1.44417 q^{86} +(-0.0380499 + 8.56336i) 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} +(-2.10944 + 3.61646i) 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 $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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	$-0.543482\pi$
$2$	−1.05989	−	0.283997i	−0.749456	−	0.200816i	−0.613277	+	0.789868i	$0.710149\pi$
$3$	−1.49614	−	0.872682i	−0.863795	−	0.503843i
$3$	−1.49614	−	0.872682i	−0.863795	−	0.503843i
$4$	−0.689337	−	0.397989i	−0.344668	−	0.198994i
$5$		0			0
$5$		0			0
$6$	1.33790	+	1.34985i	0.546197	+	0.551072i
$7$	0.160495	−	0.0430045i	0.0606614	−	0.0162542i	−0.228361	−	0.973577i	$-0.573337\pi$
$7$	0.160495	−	0.0430045i	0.0606614	−	0.0162542i	0.289022	+	0.957322i	$0.406670\pi$
$8$	2.16938	+	2.16938i	0.766992	+	0.766992i
$9$	1.47685	+	2.61130i	0.492284	+	0.870434i
$10$		0			0
$11$	−2.43760	−	4.22205i	−0.734965	−	1.27300i	−0.954739	−	0.297446i	$-0.903865\pi$
$11$	−2.43760	−	4.22205i	−0.734965	−	1.27300i	0.219773	−	0.975551i	$-0.429468\pi$
$12$	0.684025	+	1.19702i	0.197461	+	0.345549i
$13$	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	$-0.782255\pi$
$17$	−4.65999	+	1.24864i	−1.13021	+	0.302840i	−0.355204	+	0.934789i	$0.615588\pi$
$18$	−0.823701	−	3.18712i	−0.194148	−	0.751211i
$19$	1.37389	−	2.37966i	0.315193	−	0.545930i	−0.664285	−	0.747479i	$-0.731264\pi$
$19$	1.37389	−	2.37966i	0.315193	−	0.545930i	0.979479	+	0.201549i	$0.0645974\pi$
$20$		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	$-0.208075\pi$
$23$	5.64603	+	1.51285i	1.17728	+	0.315451i	0.383432	+	0.923569i	$0.374742\pi$
$24$	−1.35251	−	5.13887i	−0.276081	−	1.04897i
$25$		0			0
$26$	−3.18030	+	2.35330i	−0.623707	+	0.461520i
$27$	0.0692622	−	5.19569i	0.0133295	−	0.999911i
$28$	−0.127750	−	0.0342306i	−0.0241426	−	0.00646898i
$29$	−2.47205	−	4.28172i	−0.459049	−	0.795096i	0.539862	−	0.841754i	$-0.318476\pi$
$29$	−2.47205	−	4.28172i	−0.459049	−	0.795096i	−0.998911	+	0.0466574i	$0.985143\pi$
$30$		0			0
$31$		−	2.41720i		−	0.434142i	−0.976156	−	0.217071i	$-0.930350\pi$
$31$		−	2.41720i		−	0.434142i	0.976156	−	0.217071i	$-0.0696502\pi$
$32$	−1.08416	−	4.04612i	−0.191653	−	0.715260i
$33$	−0.0375196	+	8.44403i	−0.00653133	+	1.46992i
$34$	5.29369			0.907860
$35$		0			0
$36$	0.0212203	−	2.38784i	0.00353672	−	0.397973i
$37$	1.20299	−	4.48963i	0.197771	−	0.738090i	−0.793762	−	0.608229i	$-0.791880\pi$
$37$	1.20299	−	4.48963i	0.197771	−	0.738090i	0.991532	−	0.129861i	$-0.0414531\pi$
$38$	−2.13199	+	2.13199i	−0.345855	+	0.345855i
$39$	−5.82057	+	2.26296i	−0.932037	+	0.362364i
$40$		0			0
$41$	−2.16059	−	3.74226i	−0.337428	−	0.584443i	0.646520	−	0.762897i	$-0.276224\pi$
$41$	−2.16059	−	3.74226i	−0.337428	−	0.584443i	−0.983948	+	0.178454i	$0.942890\pi$
$42$	0.272776	+	0.159108i	0.0420903	+	0.0245508i
$43$	−1.27129	+	0.340642i	−0.193871	+	0.0519475i	−0.354448	−	0.935076i	$-0.615331\pi$
$43$	−1.27129	+	0.340642i	−0.193871	+	0.0519475i	0.160577	+	0.987023i	$0.448664\pi$
$44$			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	$-0.870474\pi$
$47$	−3.58251	+	3.58251i	−0.522562	+	0.522562i	0.395782	+	0.918344i	$0.370474\pi$
$48$	−0.0136563	+	3.07343i	−0.00197111	+	0.443612i
$49$	−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	$-0.855382\pi$
$53$	−3.34661	+	3.34661i	−0.459692	+	0.459692i	0.438862	+	0.898554i	$0.355382\pi$
$54$	−1.54897	+	5.48719i	−0.210788	+	0.746712i
$55$		0			0
$56$	0.441468	+	0.254882i	0.0589936	+	0.0340600i
$57$	−4.13222	+	2.36132i	−0.547326	+	0.312764i
$58$	1.40411	+	5.24021i	0.184369	+	0.688074i
$59$	8.49452	+	4.90431i	1.10589	+	0.638487i	0.937762	−	0.347278i	$-0.112894\pi$
$59$	8.49452	+	4.90431i	1.10589	+	0.638487i	0.168130	+	0.985765i	$0.446227\pi$
$60$		0			0
$61$	−7.20685	+	12.4826i	−0.922742	+	1.59824i	−0.127590	+	0.991827i	$0.540724\pi$
$61$	−7.20685	+	12.4826i	−0.922742	+	1.59824i	−0.795153	+	0.606409i	$0.792609\pi$
$62$	−0.686477	+	2.56197i	−0.0871826	+	0.325370i
$63$	0.349325	+	0.355590i	0.0440108	+	0.0448001i
$64$			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	−0.953478	−	0.301463i	$-0.902525\pi$
$67$	0.188179	−	0.702294i	0.0229897	−	0.0857989i	0.976468	+	0.215664i	$0.0691917\pi$
$68$	3.70925	+	0.993890i	0.449812	+	0.120527i
$69$	−7.12700	−	7.19061i	−0.857990	−	0.865648i
$70$		0			0
$71$	−1.37489	+	2.38137i	−0.163169	+	0.282617i	−0.936004	−	0.351990i	$-0.885505\pi$
$71$	−1.37489	+	2.38137i	−0.163169	+	0.282617i	0.772834	+	0.634608i	$0.218838\pi$
$72$	−2.46106	+	8.86877i	−0.290038	+	1.04519i
$73$	−5.45193	+	5.45193i	−0.638101	+	0.638101i	−0.950087	−	0.311986i	$-0.899006\pi$
$73$	−5.45193	+	5.45193i	−0.638101	+	0.638101i	0.311986	+	0.950087i	$0.399006\pi$
$74$	−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
$78$	6.81184	−	0.745469i	0.771289	−	0.0844077i
$79$			7.39276i			0.831750i	0.909422	+	0.415875i	$0.136525\pi$
$79$			7.39276i			0.831750i	−0.909422	+	0.415875i	$0.863475\pi$
$80$		0			0
$81$	−4.63781	+	7.71302i	−0.515312	+	0.857002i
$82$	1.22720	+	4.57999i	0.135522	+	0.505775i
$83$	1.60997	+	1.60997i	0.176717	+	0.176717i	0.789923	−	0.613206i	$-0.210120\pi$
$83$	1.60997	+	1.60997i	0.176717	+	0.176717i	−0.613206	+	0.789923i	$0.710120\pi$
$84$	0.161260	+	0.162699i	0.0175949	+	0.0177519i
$85$		0			0
$86$	1.44417			0.155729
$87$	−0.0380499	+	8.56336i	−0.00407937	+	0.918089i
$88$	3.87115	−	14.4473i	0.412666	−	1.54009i
$89$	−5.98500	+	3.45544i	−0.634408	+	0.366276i	−0.782457	−	0.622704i	$-0.786034\pi$
$89$	−5.98500	+	3.45544i	−0.634408	+	0.366276i	0.148049	+	0.988980i	$0.452701\pi$
$90$		0			0
$91$	0.238885	−	0.549398i	0.0250419	−	0.0575926i
$92$	−3.28992	−	3.28992i	−0.342998	−	0.342998i
$93$	−2.10944	+	3.61646i	−0.218739	+	0.375009i
$94$	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	−0.960514	−	0.278231i	$-0.910252\pi$
$97$	−16.2824	+	4.36286i	−1.65323	+	0.442981i	−0.692714	+	0.721212i	$0.743585\pi$
$98$	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	$-0.393794\pi$
$101$	13.1605	−	7.59820i	1.30952	−	0.756049i	0.982015	+	0.188802i	$0.0604604\pi$
$102$	−7.92008	−	4.61971i	−0.784205	−	0.457419i
$103$	−12.4089	−	12.4089i	−1.22268	−	1.22268i	−0.966674	−	0.256009i	$-0.917592\pi$
$103$	−12.4089	−	12.4089i	−1.22268	−	1.22268i	−0.256009	−	0.966674i	$-0.582408\pi$
$104$	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	$-0.883022\pi$
$107$	0.564899	−	2.10823i	0.0546109	−	0.203811i	0.987841	+	0.155469i	$0.0496890\pi$
$108$	−2.11557	+	3.55402i	−0.203571	+	0.341985i
$109$	−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
$111$	−5.71785	+	5.66727i	−0.542715	+	0.537913i
$112$	−0.208483	−	0.208483i	−0.0196997	−	0.0196997i
$113$	−3.86420	−	14.4214i	−0.363513	−	1.35665i	−0.869425	−	0.494065i	$-0.835511\pi$
$113$	−3.86420	−	14.4214i	−0.363513	−	1.35665i	0.505912	−	0.862585i	$-0.331156\pi$
$114$	5.05031	−	1.32920i	0.473004	−	0.124491i
$115$		0			0
$116$			3.93540i			0.365393i
$117$	10.6832	+	1.69380i	0.987663	+	0.156592i
$118$	−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
$123$	−0.0332559	+	7.48444i	−0.00299858	+	0.674850i
$124$	−0.962018	+	1.66626i	−0.0863918	+	0.149635i
$125$		0			0
$126$	−0.269260	−	0.476093i	−0.0239876	−	0.0424138i
$127$	−1.36576	−	0.365954i	−0.121192	−	0.0324732i	0.197713	−	0.980260i	$-0.436648\pi$
$127$	−1.36576	−	0.365954i	−0.121192	−	0.0324732i	−0.318905	+	0.947787i	$0.603315\pi$
$128$	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	$0.982768\pi$
$132$	3.38649	−	5.80585i	0.294756	−	0.505334i
$133$	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	$-0.0278628\pi$
$137$	1.05050	+	3.92054i	0.0897507	+	0.334954i	−0.906421	+	0.422376i	$0.861196\pi$
$138$	5.51172	+	9.64531i	0.469189	+	0.821063i
$139$	6.39677	+	3.69318i	0.542567	+	0.313251i	0.746119	−	0.665813i	$-0.231915\pi$
$139$	6.39677	+	3.69318i	0.542567	+	0.313251i	−0.203552	+	0.979064i	$0.565248\pi$
$140$		0			0
$141$	8.48631	−	2.23353i	0.714676	−	0.188097i
$142$	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
$147$	12.0764	+	0.0536595i	0.996046	+	0.00442576i
$148$	−2.61609	+	2.61609i	−0.215041	+	0.215041i
$149$	−5.05279	−	2.91723i	−0.413941	−	0.238989i	0.278541	−	0.960424i	$-0.410149\pi$
$149$	−5.05279	−	2.91723i	−0.413941	−	0.238989i	−0.692482	+	0.721435i	$0.743483\pi$
$150$		0			0
$151$		−	16.4599i		−	1.33949i	−0.742591	−	0.669745i	$-0.766403\pi$
$151$		−	16.4599i		−	1.33949i	0.742591	−	0.669745i	$-0.233597\pi$
$152$	8.14288	−	2.18188i	0.660475	−	0.176974i
$153$	−10.1427	−	10.3246i	−0.819988	−	0.834693i
$154$	0.444425	+	0.769766i	0.0358127	+	0.0620295i
$155$		0			0
$156$	4.91297	+	0.756578i	0.393352	+	0.0605747i
$157$	5.15467	−	5.15467i	0.411387	−	0.411387i	−0.470834	−	0.882222i	$-0.656047\pi$
$157$	5.15467	−	5.15467i	0.411387	−	0.411387i	0.882222	+	0.470834i	$0.156047\pi$
$158$	2.09952	−	7.83551i	0.167029	−	0.623360i
$159$	7.92751	−	2.08646i	0.628692	−	0.165467i
$160$		0			0
$161$	0.971218			0.0765427
$162$	7.10605	−	6.85784i	0.558304	−	0.538803i
$163$	5.68770	+	21.2268i	0.445495	+	1.66261i	0.714626	+	0.699506i	$0.246597\pi$
$163$	5.68770	+	21.2268i	0.445495	+	1.66261i	−0.269131	+	0.963103i	$0.586737\pi$
$164$			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	$-0.232014\pi$
$167$	13.6836	+	3.66650i	1.05887	+	0.283723i	0.312956	+	0.949768i	$0.398681\pi$
$168$	−0.438066	−	0.766599i	−0.0337975	−	0.0591444i
$169$	−2.92437	−	12.6668i	−0.224952	−	0.974370i
$170$		0			0
$171$	8.24304	+	0.0732546i	0.630361	+	0.00560192i
$172$	1.01192	+	0.271144i	0.0771583	+	0.0206745i
$173$	−0.246123	−	0.918542i	−0.0187123	−	0.0698354i	0.955938	−	0.293568i	$-0.0948426\pi$
$173$	−0.246123	−	0.918542i	−0.0187123	−	0.0698354i	−0.974651	+	0.223732i	$0.928176\pi$
$174$	2.47230	−	9.06542i	0.187424	−	0.687248i
$175$		0			0
$176$	−4.32544	+	7.49188i	−0.326042	+	0.564722i
$177$	−8.42906	−	14.7505i	−0.633567	−	1.10872i
$178$	7.32477	−	1.96267i	0.549015	−	0.147108i
$179$	−8.16594	−	14.1438i	−0.610351	−	1.05716i	−0.991181	−	0.132514i	$-0.957695\pi$
$179$	−8.16594	−	14.1438i	−0.610351	−	1.05716i	0.380830	−	0.924645i	$-0.375638\pi$
$180$		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
$183$	21.6758	−	12.3864i	1.60232	−	0.915632i
$184$	8.96644	+	15.5303i	0.661015	+	1.14491i
$185$		0			0
$186$	3.26284	−	3.23398i	0.239243	−	0.237127i
$187$	16.6310	+	16.6310i	1.21618	+	1.21618i
$188$	3.89535	−	1.04376i	0.284098	−	0.0761238i
$189$	−0.212322	−	0.836861i	−0.0154441	−	0.0608726i
$190$		0			0
$191$	−2.49022	−	1.43773i	−0.180186	−	0.104030i	0.407194	−	0.913342i	$-0.366507\pi$
$191$	−2.49022	−	1.43773i	−0.180186	−	0.104030i	−0.587380	+	0.809311i	$0.699841\pi$
$192$	7.10823	−	12.1864i	0.512992	−	0.879481i
$193$	10.1951	+	2.73177i	0.733861	+	0.196637i	0.606348	−	0.795199i	$-0.292634\pi$
$193$	10.1951	+	2.73177i	0.733861	+	0.196637i	0.127513	+	0.991837i	$0.459301\pi$
$194$	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	$-0.663990\pi$
$197$	−19.0112	−	5.09403i	−1.35449	−	0.362934i	−0.861790	+	0.507265i	$0.830656\pi$
$198$	−11.4483	+	11.2466i	−0.813597	+	0.799264i
$199$	−10.9231	−	6.30646i	−0.774318	−	0.447053i	0.0600946	−	0.998193i	$-0.480860\pi$
$199$	−10.9231	−	6.30646i	−0.774318	−	0.447053i	−0.834413	+	0.551140i	$0.814193\pi$
$200$		0			0
$201$	−0.894421	+	0.886508i	−0.0630876	+	0.0625295i
$202$	−16.1065	+	4.31573i	−1.13325	+	0.303654i
$203$	−0.580885	−	0.580885i	−0.0407702	−	0.0407702i
$204$	−4.68219	−	4.72399i	−0.327819	−	0.330745i
$205$		0			0
$206$	9.62798	+	16.6761i	0.670813	+	1.16188i
$207$	4.38785	+	16.9777i	0.304976	+	1.18003i
$208$	−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	0.771351	−	0.636409i	$-0.219581\pi$
$211$	−2.40360	−	4.16317i	−0.165471	−	0.286604i	−0.936822	+	0.349805i	$0.886248\pi$
$212$	3.63885	−	0.975028i	0.249917	−	0.0669652i
$213$	4.13520	−	2.36302i	0.283339	−	0.161912i
$214$	−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
$219$	12.9146	−	3.39904i	0.872691	−	0.229686i
$220$		0			0
$221$	−6.93605	+	15.9518i	−0.466569	+	1.07304i
$222$	7.66979	−	4.38283i	0.514762	−	0.294156i
$223$	−11.0162	−	2.95177i	−0.737697	−	0.197665i	−0.129643	−	0.991561i	$-0.541383\pi$
$223$	−11.0162	−	2.95177i	−0.737697	−	0.197665i	−0.608054	+	0.793896i	$0.708050\pi$
$224$	−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	0.684705	+	0.728821i	$0.259931\pi$
$227$	6.87249	+	25.6485i	0.456143	+	1.70235i	−0.228561	+	0.973530i	$0.573402\pi$
$228$	3.78827	+	0.0168325i	0.250884	+	0.00111476i
$229$	−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
$231$	0.357109	+	1.35684i	0.0234961	+	0.0892733i
$232$	3.92586	−	14.6515i	0.257746	−	0.961920i
$233$	−12.9039	+	12.9039i	−0.845365	+	0.845365i	−0.989551	−	0.144186i	$-0.953944\pi$
$233$	−12.9039	+	12.9039i	−0.845365	+	0.845365i	0.144186	+	0.989551i	$0.453944\pi$
$234$	−10.8420	−	4.82924i	−0.708764	−	0.315698i
$235$		0			0
$236$	−3.90372	−	6.76145i	−0.254111	−	0.440133i
$237$	6.45152	−	11.0606i	0.419072	−	0.718462i
$238$	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	0.658039	−	0.752984i	$-0.271386\pi$
$241$	5.19991	+	3.00217i	0.334956	+	0.193387i	−0.323083	+	0.946370i	$0.604719\pi$
$242$	9.90635	−	9.90635i	0.636804	−	0.636804i
$243$	13.6698	−	7.49241i	0.876919	−	0.480638i
$244$	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
$249$	−1.00374	−	3.81373i	−0.0636097	−	0.241685i
$250$		0			0
$251$	−21.2638	−	12.2767i	−1.34216	−	0.774897i	−0.355036	−	0.934852i	$-0.615532\pi$
$251$	−21.2638	−	12.2767i	−1.34216	−	0.774897i	−0.987124	+	0.159956i	$0.948865\pi$
$252$	−0.0992820	−	0.384149i	−0.00625418	−	0.0241991i
$253$	−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	$-0.868748\pi$
$257$	1.24454	−	4.64467i	0.0776320	−	0.289727i	0.993817	+	0.111028i	$0.0354145\pi$
$258$	−2.16068	−	1.26030i	−0.134518	−	0.0784631i
$259$		−	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	$-0.534952\pi$
$263$	−11.3760	−	3.04819i	−0.701474	−	0.187959i	−0.591891	+	0.806018i	$0.701618\pi$
$264$	−18.3997	+	18.2369i	−1.13242	+	1.12240i
$265$		0			0
$266$	−0.250489	+	0.433859i	−0.0153585	+	0.0266016i
$267$	11.9699	+	0.0531861i	0.732544	+	0.00325494i
$268$	−0.409224	+	0.409224i	−0.0249973	+	0.0249973i
$269$	0.648587	−	1.12339i	0.0395451	−	0.0684941i	−0.845575	−	0.533856i	$-0.820742\pi$
$269$	0.648587	−	1.12339i	0.0395451	−	0.0684941i	0.885121	+	0.465362i	$0.154076\pi$
$270$		0			0
$271$	5.30394	−	3.06223i	0.322191	−	0.186017i	−0.330178	−	0.943919i	$-0.607109\pi$
$271$	5.30394	−	3.06223i	0.322191	−	0.186017i	0.652369	+	0.757902i	$0.273775\pi$
$272$	6.05331	+	6.05331i	0.367036	+	0.367036i
$273$	−0.836854	+	0.613504i	−0.0506487	+	0.0371310i
$274$		−	4.45368i		−	0.269057i
$275$		0			0
$276$	2.05112	+	7.79322i	0.123463	+	0.469097i
$277$	−2.69179	−	10.0459i	−0.161734	−	0.603600i	−0.998434	−	0.0559386i	$-0.982185\pi$
$277$	−2.69179	−	10.0459i	−0.161734	−	0.603600i	0.836700	−	0.547661i	$-0.184482\pi$
$278$	−5.73103	−	5.73103i	−0.343724	−	0.343724i
$279$	6.31204	−	3.56985i	0.377892	−	0.213721i
$280$		0			0
$281$	21.9271			1.30806			0.654031	−	0.756468i	$-0.273077\pi$
$281$	21.9271			1.30806			0.654031	+	0.756468i	$0.273077\pi$
$282$	−9.62888	−	0.0427843i	−0.573391	−	0.00254777i
$283$	−1.43469	+	5.35432i	−0.0852833	+	0.318281i	−0.995368	−	0.0961414i	$-0.969350\pi$
$283$	−1.43469	+	5.35432i	−0.0852833	+	0.318281i	0.910084	+	0.414423i	$0.136017\pi$
$284$	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
$288$	8.96452	−	8.80659i	0.528239	−	0.518933i
$289$	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	$-0.537638\pi$
$293$	4.73086	−	1.26763i	0.276380	−	0.0740557i	0.394347	+	0.918962i	$0.370971\pi$
$294$	−12.7844	−	3.48654i	−0.745604	−	0.203339i
$295$		0			0
$296$	12.3495	−	7.12996i	0.717798	−	0.414421i
$297$	−22.1053	+	12.3726i	−1.28268	+	0.717932i
$298$	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
$303$	−26.3207	−	0.116952i	−1.51208	−	0.00671869i
$304$	−4.87585			−0.279649
$305$		0			0
$306$	7.81800	+	13.8234i	0.446925	+	0.790233i
$307$	−15.7142	−	15.7142i	−0.896858	−	0.896858i	0.0982987	−	0.995157i	$-0.468660\pi$
$307$	−15.7142	−	15.7142i	−0.896858	−	0.896858i	−0.995157	+	0.0982987i	$0.968660\pi$
$308$	0.166881	+	0.622810i	0.00950895	+	0.0354879i
$309$	7.73639	+	29.3944i	0.440108	+	1.67219i
$310$		0			0
$311$			27.3000i			1.54804i	0.633161	+	0.774020i	$0.281757\pi$
$311$			27.3000i			1.54804i	−0.633161	+	0.774020i	$0.718243\pi$
$312$	−17.5363	−	7.71780i	−0.992795	−	0.436935i
$313$	13.0107	+	13.0107i	0.735406	+	0.735406i	0.971685	−	0.236280i	$-0.0759281\pi$
$313$	13.0107	+	13.0107i	0.735406	+	0.735406i	−0.236280	+	0.971685i	$0.575928\pi$
$314$	−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	$-0.664932\pi$
$317$	6.64936	−	6.64936i	0.373465	−	0.373465i	0.868738	+	0.495272i	$0.164932\pi$
$318$	−8.99484	−	0.0399671i	−0.504406	−	0.00224124i
$319$	−12.0518	+	20.8743i	−0.674770	+	1.16874i
$320$		0			0
$321$	−2.68498	+	2.66123i	−0.149861	+	0.148535i
$322$	−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
$327$	15.4213	+	8.99512i	0.852802	+	0.497431i
$328$	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	0.643518	−	0.765431i	$-0.277474\pi$
$331$	5.50158	+	3.17634i	0.302394	+	0.174587i	−0.341124	+	0.940018i	$0.610807\pi$
$332$	−0.469062	−	1.75056i	−0.0257431	−	0.0960746i
$333$	13.5004	−	3.48914i	0.739818	−	0.191204i
$334$	−13.4618	−	7.77219i	−0.736598	−	0.425275i
$335$		0			0
$336$	0.129980	+	0.493857i	0.00709097	+	0.0269421i
$337$	−12.5904	+	12.5904i	−0.685841	+	0.685841i	−0.961310	−	0.275469i	$-0.911167\pi$
$337$	−12.5904	+	12.5904i	−0.685841	+	0.685841i	0.275469	+	0.961310i	$0.411167\pi$
$338$	−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
$342$	−8.71592	−	2.41864i	−0.471303	−	0.130785i
$343$	−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	$-0.514326\pi$
$347$	7.74058	−	2.07408i	0.415536	−	0.111343i	0.460529	+	0.887645i	$0.347660\pi$
$348$	3.43435	−	5.88790i	0.184101	−	0.315625i
$349$	9.47261	+	16.4070i	0.507057	+	0.878249i	0.999967	+	0.00816849i	$0.00260014\pi$
$349$	9.47261	+	16.4070i	0.507057	+	0.878249i	−0.492909	+	0.870081i	$0.664067\pi$
$350$		0			0
$351$	−14.5054	−	11.8572i	−0.774241	−	0.632891i
$352$	−14.4402	+	14.4402i	−0.769666	+	0.769666i
$353$	0.589602	−	2.20043i	0.0313814	−	0.117117i	−0.948458	−	0.316901i	$-0.897358\pi$
$353$	0.589602	−	2.20043i	0.0313814	−	0.117117i	0.979840	+	0.199785i	$0.0640242\pi$
$354$	4.74478	+	18.0278i	0.252182	+	0.958166i
$355$		0			0
$356$	5.50091			0.291547
$357$	1.38840	+	0.00616913i	0.0734820	+	0.000326505i
$358$	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
$363$	19.2004	−	10.9719i	1.00776	−	0.575876i
$364$	−0.383326	+	0.283647i	−0.0200918	+	0.0148671i
$365$		0			0
$366$	−26.4917	+	6.97241i	−1.38474	+	0.364454i
$367$	11.4217	+	3.06044i	0.596209	+	0.159754i	0.544289	−	0.838897i	$-0.316799\pi$
$367$	11.4217	+	3.06044i	0.596209	+	0.159754i	0.0519198	+	0.998651i	$0.483466\pi$
$368$	−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
$372$	2.89343	−	1.65342i	0.150017	−	0.0857260i
$373$	−23.7612	+	6.36680i	−1.23031	+	0.329661i	−0.814700	−	0.579882i	$-0.803099\pi$
$373$	−23.7612	+	6.36680i	−1.23031	+	0.329661i	−0.415610	+	0.909543i	$0.636432\pi$
$374$	−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
$378$	−0.0126279	+	0.947279i	−0.000649509	+	0.0487228i
$379$	−7.85016	−	13.5969i	−0.403236	−	0.698425i	0.590879	−	0.806760i	$-0.298781\pi$
$379$	−7.85016	−	13.5969i	−0.403236	−	0.698425i	−0.994114	+	0.108336i	$0.965448\pi$
$380$		0			0
$381$	1.72400	+	1.73939i	0.0883233	+	0.0891117i
$382$	2.23105	+	2.23105i	0.114150	+	0.114150i
$383$	2.30709	−	0.618182i	0.117887	−	0.0315876i	−0.199393	−	0.979920i	$-0.563897\pi$
$383$	2.30709	−	0.618182i	0.117887	−	0.0315876i	0.317280	+	0.948332i	$0.397231\pi$
$384$	−0.688812	+	0.682718i	−0.0351508	+	0.0348398i
$385$		0			0
$386$	−10.0299	−	5.79076i	−0.510508	−	0.294742i
$387$	−2.76704	−	2.81666i	−0.140656	−	0.143179i
$388$	12.9604	+	3.47274i	0.657966	+	0.176302i
$389$	−14.0757			−0.713666			−0.356833	−	0.934168i	$-0.616143\pi$
$389$	−14.0757			−0.713666			−0.356833	+	0.934168i	$0.616143\pi$
$390$		0			0
$391$	−28.1994			−1.42611
$392$	−20.6622	−	5.53642i	−1.04360	−	0.279631i
$393$	1.08095	−	1.85319i	0.0545266	−	0.0934812i
$394$	18.7031	+	10.7982i	0.942247	+	0.544007i
$395$		0			0
$396$	−10.1333	+	5.73101i	−0.509218	+	0.287994i
$397$	31.0598	−	8.32246i	1.55885	−	0.417692i	0.626549	−	0.779382i	$-0.284467\pi$
$397$	31.0598	−	8.32246i	1.55885	−	0.417692i	0.932299	+	0.361690i	$0.117800\pi$
$398$	9.78628	+	9.78628i	0.490542	+	0.490542i
$399$	−0.561653	+	0.556683i	−0.0281178	+	0.0278690i
$400$		0			0
$401$	0.597410	+	1.03474i	0.0298332	+	0.0516726i	0.880557	−	0.473941i	$-0.157169\pi$
$401$	0.597410	+	1.03474i	0.0298332	+	0.0516726i	−0.850723	+	0.525614i	$0.823836\pi$
$402$	1.19975	−	0.685589i	0.0598383	−	0.0341941i
$403$	−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
$408$	12.7193	+	22.2583i	0.629699	+	1.10195i
$409$	8.93012	−	15.4674i	0.441566	−	0.764815i	−0.556240	−	0.831022i	$-0.687756\pi$
$409$	8.93012	−	15.4674i	0.441566	−	0.764815i	0.997806	+	0.0662068i	$0.0210897\pi$
$410$		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
$414$	0.170989	−	19.2407i	0.00840364	−	0.945628i
$415$		0			0
$416$	−13.8505	−	6.02235i	−0.679076	−	0.295270i
$417$	−6.34748	−	11.1078i	−0.310837	−	0.543954i
$418$	14.1983	+	3.80444i	0.694464	+	0.186081i
$419$	5.31145	+	9.19969i	0.259481	+	0.449435i	0.966103	−	0.258157i	$-0.0831151\pi$
$419$	5.31145	+	9.19969i	0.259481	+	0.449435i	−0.706622	+	0.707591i	$0.749782\pi$
$420$		0			0
$421$		−	23.8749i		−	1.16359i	−0.813335	−	0.581796i	$-0.802350\pi$
$421$		−	23.8749i		−	1.16359i	0.813335	−	0.581796i	$-0.197650\pi$
$422$	1.36523	+	5.09512i	0.0664585	+	0.248026i
$423$	−14.6458	−	4.06418i	−0.712105	−	0.197607i
$424$	−14.5201			−0.705160
$425$		0			0
$426$	−5.05395	+	1.33016i	−0.244865	+	0.0644466i
$427$	−0.619853	+	2.31332i	−0.0299968	+	0.111950i
$428$	−1.22846	+	1.22846i	−0.0593798	+	0.0593798i
$429$	23.7426	+	19.0585i	1.14630	+	0.920155i
$430$		0			0
$431$	−8.35107	−	14.4645i	−0.402257	−	0.696729i	0.591741	−	0.806128i	$-0.298441\pi$
$431$	−8.35107	−	14.4645i	−0.402257	−	0.696729i	−0.993998	+	0.109399i	$0.965107\pi$
$432$	−8.04583	+	4.50335i	−0.387105	+	0.216667i
$433$	−26.5522	+	7.11463i	−1.27602	+	0.341907i	−0.832333	−	0.554277i	$-0.812995\pi$
$433$	−26.5522	+	7.11463i	−1.27602	+	0.341907i	−0.443683	+	0.896184i	$0.646328\pi$
$434$			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
$438$	−14.6534	−	0.0651100i	−0.700168	−	0.00311108i
$439$	16.5480	−	9.55397i	0.789791	−	0.455986i	−0.0500980	−	0.998744i	$-0.515953\pi$
$439$	16.5480	−	9.55397i	0.789791	−	0.455986i	0.839889	+	0.542758i	$0.182620\pi$
$440$		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	$-0.655060\pi$
$443$	8.74698	−	8.74698i	0.415581	−	0.415581i	0.883678	+	0.468096i	$0.155060\pi$
$444$	6.19704	−	1.63101i	0.294098	−	0.0774045i
$445$		0			0
$446$	10.8376	+	6.25711i	0.513177	+	0.296283i
$447$	5.01386	+	8.77406i	0.237147	+	0.414999i
$448$	0.350283	+	1.30727i	0.0165493	+	0.0617629i
$449$	25.7950	+	14.8928i	1.21734	+	0.702834i	0.964349	−	0.264634i	$-0.0852512\pi$
$449$	25.7950	+	14.8928i	1.21734	+	0.702834i	0.252994	+	0.967468i	$0.418585\pi$
$450$		0			0
$451$	−10.5333	+	18.2443i	−0.495996	+	0.859090i
$452$	−3.07582	+	11.4791i	−0.144674	+	0.539932i
$453$	−14.3643	+	24.6263i	−0.674893	+	1.15705i
$454$		−	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	−0.941544	−	0.336891i	$-0.890624\pi$
$457$	0.904330	−	3.37500i	0.0423028	−	0.157876i	0.983846	+	0.179015i	$0.0572912\pi$
$458$	6.77119	+	1.81433i	0.316397	+	0.0847783i
$459$	6.16479	+	24.2983i	0.287748	+	1.13415i
$460$		0			0
$461$	1.56492	−	2.71052i	0.0728856	−	0.126242i	−0.827279	−	0.561791i	$-0.810113\pi$
$461$	1.56492	−	2.71052i	0.0728856	−	0.126242i	0.900165	+	0.435549i	$0.143446\pi$
$462$	0.00684058	−	1.53952i	0.000318253	−	0.0716248i
$463$	27.4762	−	27.4762i	1.27693	−	1.27693i	0.334548	−	0.942379i	$-0.391416\pi$
$463$	27.4762	−	27.4762i	1.27693	−	1.27693i	0.942379	−	0.334548i	$-0.108584\pi$
$464$	−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	$-0.482677\pi$
$467$	−20.4027	−	20.4027i	−0.944124	−	0.944124i	−0.998519	+	0.0543954i	$0.982677\pi$
$468$	−6.69022	−	5.41940i	−0.309255	−	0.250512i
$469$		−	0.120807i		−	0.00557836i
$470$		0			0
$471$	−12.2105	+	3.21371i	−0.562629	+	0.148080i
$472$	7.78853	+	29.0672i	0.358496	+	1.33793i
$473$	4.53712	+	4.53712i	0.208617	+	0.208617i
$474$	−9.97908	+	9.89079i	−0.458354	+	0.454299i
$475$		0			0
$476$	0.638057			0.0292453
$477$	−13.6815	−	3.79656i	−0.626431	−	0.173833i
$478$	−0.910923	+	3.39961i	−0.0416647	+	0.155495i
$479$	−0.117001	+	0.0675507i	−0.00534593	+	0.00308647i	−0.502671	−	0.864478i	$-0.667649\pi$
$479$	−0.117001	+	0.0675507i	−0.00534593	+	0.00308647i	0.497325	+	0.867565i	$0.334316\pi$
$480$		0			0
$481$	−9.96841	−	13.4715i	−0.454520	−	0.614248i
$482$	−4.65873	−	4.65873i	−0.212199	−	0.212199i
$483$	−1.45308	−	0.847564i	−0.0661172	−	0.0385655i
$484$	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	−0.465927	−	0.884823i	$-0.654279\pi$
$487$	−9.42349	+	2.52502i	−0.427019	+	0.114419i	0.0389075	+	0.999243i	$0.487612\pi$
$488$	−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	$-0.830310\pi$
$491$	−18.8733	+	10.8965i	−0.851741	+	0.491753i	0.00949666	+	0.999955i	$0.496977\pi$
$492$	3.00165	−	5.14607i	0.135325	−	0.232003i
$493$	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
$498$	−0.0192272	+	4.32719i	−0.000861589	+	0.193906i
$499$	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
$501$	−17.2728	−	17.4270i	−0.771693	−	0.778581i
$502$	19.0508	+	19.0508i	0.850278	+	0.850278i
$503$	1.95641	+	7.30144i	0.0872322	+	0.325555i	0.995728	−	0.0923400i	$-0.0294347\pi$
$503$	1.95641	+	7.30144i	0.0872322	+	0.325555i	−0.908495	+	0.417895i	$0.862768\pi$
$504$	−0.0135900	+	1.52923i	−0.000605347	+	0.0681173i
$505$		0			0
$506$			31.2687i			1.39006i
$507$	−6.67883	+	21.5033i	−0.296617	+	0.954996i
$508$	0.795823	+	0.795823i	0.0353089	+	0.0353089i
$509$	−38.2650	+	22.0923i	−1.69607	+	0.979224i	−0.746643	+	0.665225i	$0.768336\pi$
$509$	−38.2650	+	22.0923i	−1.69607	+	0.979224i	−0.949423	+	0.313999i	$0.898331\pi$
$510$		0			0
$511$	−0.640550	+	1.10947i	−0.0283363	+	0.0490799i
$512$	−12.9549	+	12.9549i	−0.572530	+	0.572530i
$513$	−12.2688	−	7.30315i	−0.541681	−	0.322442i
$514$	−2.63814	+	4.56940i	−0.116364	+	0.201548i
$515$		0			0
$516$	−1.27735	−	1.28875i	−0.0562323	−	0.0567342i
$517$	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	$-0.263738\pi$
$522$	−11.6101	+	11.4056i	−0.508161	+	0.499209i
$523$	8.15764	−	30.4447i	0.356709	−	1.33125i	−0.521612	−	0.853183i	$-0.674669\pi$
$523$	8.15764	−	30.4447i	0.356709	−	1.33125i	0.878321	−	0.478072i	$-0.158664\pi$
$524$	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
$528$	13.0095	−	7.43415i	0.566165	−	0.323530i
$529$	9.67033	+	5.58317i	0.420449	+	0.242746i
$530$		0			0
$531$	−0.261493	+	29.4247i	−0.0113478	+	1.27692i
$532$	−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
$537$	−0.125690	+	28.2874i	−0.00542393	+	1.22069i
$538$	−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	$0.239745\pi$
$541$			31.8172i			1.36793i	−0.729516	+	0.683964i	$0.760255\pi$
$542$	−6.49126	+	1.73933i	−0.278823	+	0.0747105i
$543$	18.6208	+	10.8613i	0.799094	+	0.466103i
$544$	10.1043	+	17.5012i	0.433218	+	0.750356i
$545$		0			0
$546$	1.06121	−	0.412584i	0.0454155	−	0.0176569i
$547$	−3.86162	+	3.86162i	−0.165111	+	0.165111i	−0.784826	−	0.619716i	$-0.787248\pi$
$547$	−3.86162	+	3.86162i	−0.165111	+	0.165111i	0.619716	+	0.784826i	$0.287248\pi$
$548$	0.836179	−	3.12066i	0.0357198	−	0.133308i
$549$	−43.2394	−	0.384261i	−1.84541	−	0.0163999i
$550$		0			0
$551$	−13.5854			−0.578756
$552$	0.138011	−	31.0604i	0.00587416	−	1.32202i
$553$	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	$-0.367652\pi$
$557$	6.99288	+	1.87374i	0.296298	+	0.0793928i	−0.107608	+	0.994193i	$0.534319\pi$
$558$	−7.70389	+	1.99105i	−0.326132	+	0.0842878i
$559$	−1.89223	+	4.35183i	−0.0800327	+	0.184063i
$560$		0			0
$561$	−10.3687	−	39.3959i	−0.437767	−	1.66330i
$562$	−23.2403	−	6.22723i	−0.980334	−	0.262680i
$563$	0.945024	+	3.52688i	0.0398280	+	0.148640i	0.982976	−	0.183732i	$-0.0588178\pi$
$563$	0.945024	+	3.52688i	0.0398280	+	0.148640i	−0.943148	+	0.332372i	$0.892151\pi$
$564$	−6.73885	−	1.83780i	−0.283757	−	0.0773853i
$565$		0			0
$566$	3.04122	−	5.26755i	0.127832	−	0.221412i
$567$	−0.412650	+	1.43735i	−0.0173297	+	0.0603629i
$568$	−8.14877	+	2.18346i	−0.341915	+	0.0916158i
$569$	−19.6847	−	34.0948i	−0.825224	−	1.42933i	−0.901748	−	0.432262i	$-0.857715\pi$
$569$	−19.6847	−	34.0948i	−0.825224	−	1.42933i	0.0765237	−	0.997068i	$-0.475618\pi$
$570$		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
$573$	2.47103	+	4.32420i	0.103229	+	0.180646i
$574$	0.393920	+	0.682289i	0.0164419	+	0.0284782i
$575$		0			0
$576$	−21.2698	+	12.0294i	−0.886241	+	0.501224i
$577$	−24.8261	−	24.8261i	−1.03352	−	1.03352i	−0.999418	−	0.0341041i	$-0.989142\pi$
$577$	−24.8261	−	24.8261i	−1.03352	−	1.03352i	−0.0341041	−	0.999418i	$-0.510858\pi$
$578$	−6.65039	+	1.78197i	−0.276620	+	0.0741200i
$579$	−12.8693	−	12.9842i	−0.534831	−	0.539605i
$580$		0			0
$581$	0.327628	+	0.189156i	0.0135923	+	0.00784752i
$582$	−27.6735	−	16.1417i	−1.14710	−	0.669093i
$583$	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	$-0.416758\pi$
$587$	−0.0134708	−	0.00360950i	−0.000556001	−	0.000148980i	−0.259097	+	0.965851i	$0.583425\pi$
$588$	−8.30337	−	4.84327i	−0.342425	−	0.199733i
$589$	−5.75210	−	3.32098i	−0.237011	−	0.136838i
$590$		0			0
$591$	23.9979	+	24.2121i	0.987140	+	0.995951i
$592$	−7.96668	+	2.13466i	−0.327428	+	0.0877342i
$593$	25.7961	+	25.7961i	1.05932	+	1.05932i	0.998126	+	0.0611927i	$0.0194904\pi$
$593$	25.7961	+	25.7961i	1.05932	+	1.05932i	0.0611927	+	0.998126i	$0.480510\pi$
$594$	26.9430	−	6.83577i	1.10549	−	0.280475i
$595$		0			0
$596$	2.32205	+	4.02191i	0.0951150	+	0.164744i
$597$	10.8389	+	18.9677i	0.443608	+	0.776297i
$598$	−21.5162	+	8.47547i	−0.879864	+	0.346588i
$599$	28.2847			1.15568			0.577841	−	0.816149i	$-0.303895\pi$
$599$	28.2847			1.15568			0.577841	+	0.816149i	$0.303895\pi$
$600$		0			0
$601$	8.59509	+	14.8871i	0.350601	+	0.607259i	0.986355	−	0.164633i	$-0.0526440\pi$
$601$	8.59509	+	14.8871i	0.350601	+	0.607259i	−0.635754	+	0.771892i	$0.719311\pi$
$602$	0.231783	−	0.0621060i	0.00944675	−	0.00253125i
$603$	2.11182	−	0.545792i	0.0859998	−	0.0222264i
$604$	−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	0.871091	−	0.491121i	$-0.163413\pi$
$607$	−3.17469	−	11.8481i	−0.128857	−	0.480900i	−0.999948	+	0.0102219i	$0.996746\pi$
$608$	−11.1179	−	2.97903i	−0.450890	−	0.120816i
$609$	0.362156	+	1.37601i	0.0146753	+	0.0557588i
$610$		0			0
$611$	2.06792	+	18.1498i	0.0836591	+	0.734264i
$612$	2.88267	+	11.1538i	0.116525	+	0.450866i
$613$	10.3165	+	2.76430i	0.416680	+	0.111649i	0.461067	−	0.887365i	$-0.347467\pi$
$613$	10.3165	+	2.76430i	0.416680	+	0.111649i	−0.0443871	+	0.999014i	$0.514134\pi$
$614$	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	$-0.112478\pi$
$617$	−1.17565	−	4.38758i	−0.0473299	−	0.176637i	−0.985545	+	0.169416i	$0.945812\pi$
$618$	0.148194	−	33.3520i	0.00596123	−	1.34161i
$619$	−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
$621$	8.25135	−	29.2302i	0.331115	−	1.17297i
$622$	7.75311	−	28.9350i	0.310871	−	1.16019i
$623$	−0.811962	+	0.811962i	−0.0325306	+	0.0325306i
$624$	8.64176	+	6.93687i	0.345947	+	0.277697i
$625$		0			0
$626$	−10.0949	−	17.4849i	−0.403473	−	0.698835i
$627$	20.0423	+	11.6905i	0.800413	+	0.466873i
$628$	−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	0.970271	−	0.242020i	$-0.0778099\pi$
$631$	31.2944	+	18.0678i	1.24581	+	0.719270i	0.275540	+	0.961289i	$0.411143\pi$
$632$	−16.0377	+	16.0377i	−0.637946	+	0.637946i
$633$	−0.0369963	+	8.32625i	−0.00147047	+	0.330939i
$634$	−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
$639$	−8.24900	−	0.0733075i	−0.326325	−	0.00290000i
$640$		0			0
$641$	−30.0234	−	17.3340i	−1.18585	−	0.684653i	−0.228492	−	0.973546i	$-0.573380\pi$
$641$	−30.0234	−	17.3340i	−1.18585	−	0.684653i	−0.957361	+	0.288893i	$0.906713\pi$
$642$	3.60157	−	2.05808i	0.142143	−	0.0812261i
$643$	7.35878	+	27.4633i	0.290202	+	1.08305i	0.944954	+	0.327204i	$0.106107\pi$
$643$	7.35878	+	27.4633i	0.290202	+	1.08305i	−0.654752	+	0.755844i	$0.727227\pi$
$644$	−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	$-0.897829\pi$
$647$	0.778760	−	2.90637i	0.0306162	−	0.114261i	0.979543	+	0.201235i	$0.0644956\pi$
$648$	−26.7937	+	6.67131i	−1.05255	+	0.262074i
$649$		−	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	$-0.462372\pi$
$653$	−7.06400	−	1.89279i	−0.276436	−	0.0740707i	−0.394373	+	0.918950i	$0.629038\pi$
$654$	−13.7904	−	13.9135i	−0.539246	−	0.544059i
$655$		0			0
$656$	−3.83390	+	6.64050i	−0.149689	+	0.259268i
$657$	−22.2884	−	6.18495i	−0.869552	−	0.241298i
$658$	0.653163	−	0.653163i	0.0254630	−	0.0254630i
$659$	−17.7103	+	30.6751i	−0.689894	+	1.19493i	0.281978	+	0.959421i	$0.409010\pi$
$659$	−17.7103	+	30.6751i	−0.689894	+	1.19493i	−0.971872	+	0.235511i	$0.924324\pi$
$660$		0			0
$661$	29.1120	−	16.8078i	1.13233	−	0.653748i	0.187807	−	0.982206i	$-0.439862\pi$
$661$	29.1120	−	16.8078i	1.13233	−	0.653748i	0.944519	+	0.328458i	$0.106529\pi$
$662$	−4.92901	−	4.92901i	−0.191571	−	0.191571i
$663$	24.2982	−	17.8132i	0.943662	−	0.691806i
$664$			6.98528i			0.271081i
$665$		0			0
$666$	−15.2999	−	0.135967i	−0.592858	−	0.00526863i
$667$	−7.47969	−	27.9146i	−0.289615	−	1.08086i
$668$	−7.97337	−	7.97337i	−0.308499	−	0.308499i
$669$	13.9057	+	14.0299i	0.537627	+	0.542426i
$670$		0			0
$671$	70.2698			2.71273
$672$	−0.00535646	+	1.20551i	−0.000206630	+	0.0465034i
$673$	−4.75245	+	17.7364i	−0.183194	+	0.683688i	0.811816	+	0.583913i	$0.198479\pi$
$673$	−4.75245	+	17.7364i	−0.183194	+	0.683688i	−0.995010	+	0.0997751i	$0.968188\pi$
$674$	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	−0.981336	−	0.192303i	$-0.938404\pi$
$677$	−30.5372	−	30.5372i	−1.17364	−	1.17364i	−0.192303	−	0.981336i	$-0.561596\pi$
$678$	14.2967	−	24.5105i	0.549062	−	0.941319i
$679$	−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	$-0.429039\pi$
$683$	23.5257	−	6.30369i	0.900186	−	0.241204i	0.679096	+	0.734049i	$0.262372\pi$
$684$	−5.65308	−	3.33114i	−0.216151	−	0.127369i
$685$		0			0
$686$	2.20616	−	1.27372i	0.0842314	−	0.0486310i
$687$	9.55818	+	5.57519i	0.364667	+	0.212707i
$688$	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	−0.490006	−	0.871719i	$-0.663005\pi$
$691$	0.523687	−	0.302351i	0.0199220	−	0.0115020i	0.509928	+	0.860217i	$0.329672\pi$
$692$	−0.195908	+	0.731139i	−0.00744731	+	0.0277937i
$693$	0.649802	−	2.34166i	0.0246839	−	0.0889522i
$694$	−8.79320			−0.333785
$695$		0			0
$696$	−18.6597	+	18.4947i	−0.707296	+	0.701038i
$697$	14.7411	+	14.7411i	0.558358	+	0.558358i
$698$	−5.38038	−	20.0799i	−0.203651	−	0.760034i
$699$	30.5671	−	8.04503i	1.15615	−	0.304291i
$700$		0			0
$701$		−	35.7248i		−	1.34931i	−0.738134	−	0.674654i	$-0.764293\pi$
$701$		−	35.7248i		−	1.34931i	0.738134	−	0.674654i	$-0.235707\pi$
$702$	12.0067	+	16.6868i	0.453165	+	0.629804i
$703$	−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
$708$	−0.0600861	+	13.5228i	−0.00225817	+	0.508217i
$709$	−2.01558	+	3.49108i	−0.0756966	+	0.131110i	−0.901389	−	0.433010i	$-0.857451\pi$
$709$	−2.01558	+	3.49108i	−0.0756966	+	0.131110i	0.825692	+	0.564121i	$0.190785\pi$
$710$		0			0
$711$	−19.3047	+	10.9180i	−0.723984	+	0.409458i
$712$	−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
$717$	−2.79914	+	4.79888i	−0.104536	+	0.179217i
$718$	−2.79196	+	10.4197i	−0.104195	+	0.388861i
$719$	18.2661	−	31.6378i	0.681211	−	1.17989i	−0.293400	−	0.955990i	$-0.594787\pi$
$719$	18.2661	−	31.6378i	0.681211	−	1.17989i	0.974612	−	0.223903i	$-0.0718797\pi$
$720$		0			0
$721$	−2.52520	−	1.45793i	−0.0940434	−	0.0542960i
$722$	−3.25166	−	12.1354i	−0.121014	−	0.451632i
$723$	−5.15984	−	9.02953i	−0.191897	−	0.335812i
$724$	8.57942	+	4.95333i	0.318852	+	0.184089i
$725$		0			0
$726$	−23.4663	+	6.17617i	−0.870918	+	0.229219i
$727$	6.38702	−	6.38702i	0.236881	−	0.236881i	−0.578676	−	0.815557i	$-0.696430\pi$
$727$	6.38702	−	6.38702i	0.236881	−	0.236881i	0.815557	+	0.578676i	$0.196430\pi$
$728$	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
$732$	−19.8716	−	0.0882961i	−0.734475	−	0.00326352i
$733$	−15.5660	+	15.5660i	−0.574943	+	0.574943i	−0.933506	−	0.358562i	$-0.883267\pi$
$733$	−15.5660	+	15.5660i	−0.574943	+	0.574943i	0.358562	+	0.933506i	$0.383267\pi$
$734$	−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
$738$	−10.1473	+	9.96857i	−0.373529	+	0.366948i
$739$	−24.9818	−	43.2698i	−0.918972	−	1.59171i	−0.800980	−	0.598691i	$-0.795688\pi$
$739$	−24.9818	−	43.2698i	−0.918972	−	1.59171i	−0.117992	−	0.993015i	$-0.537646\pi$
$740$		0			0
$741$	−2.61178	+	16.9600i	−0.0959461	+	0.623042i
$742$	0.610154	−	0.610154i	0.0223995	−	0.0223995i
$743$	7.11227	−	26.5434i	0.260924	−	0.973781i	−0.703774	−	0.710424i	$-0.748503\pi$
$743$	7.11227	−	26.5434i	0.260924	−	0.973781i	0.964698	−	0.263358i	$-0.0848299\pi$
$744$	−12.4217	+	3.26929i	−0.455401	+	0.119858i
$745$		0			0
$746$	26.9925			0.988264
$747$	−1.82643	+	6.58181i	−0.0668256	+	0.240816i
$748$	−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	0.680112	−	0.733108i	$-0.261931\pi$
$751$	−8.07976	−	13.9946i	−0.294835	−	0.510669i	−0.974946	+	0.222440i	$0.928598\pi$
$752$	8.68386	+	2.32683i	0.316668	+	0.0848509i
$753$	21.1000	+	36.9241i	0.768926	+	1.34559i
$754$	17.9380	+	7.79967i	0.653265	+	0.284047i
$755$		0			0
$756$	−0.186700	+	0.661381i	−0.00679021	+	0.0240542i
$757$	−12.4869	−	3.34586i	−0.453845	−	0.121607i	0.0246532	−	0.999696i	$-0.492152\pi$
$757$	−12.4869	−	3.34586i	−0.453845	−	0.121607i	−0.478498	+	0.878089i	$0.658819\pi$
$758$	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	$-0.999534\pi$
$761$	−13.7581	+	23.8298i	−0.498732	+	0.863828i	0.501267	+	0.865292i	$0.332867\pi$
$762$	−1.33327	−	2.33317i	−0.0482993	−	0.0845220i
$763$	−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
$768$	−23.5743	+	13.4713i	−0.850665	+	0.486105i
$769$	−5.76778	−	9.99009i	−0.207992	−	0.360252i	0.743090	−	0.669191i	$-0.233359\pi$
$769$	−5.76778	−	9.99009i	−0.207992	−	0.360252i	−0.951082	+	0.308939i	$0.900026\pi$
$770$		0			0
$771$	−5.91532	+	5.86298i	−0.213035	+	0.211150i
$772$	−5.94066	−	5.94066i	−0.213809	−	0.213809i
$773$	5.03736	−	1.34976i	0.181181	−	0.0485474i	−0.167088	−	0.985942i	$-0.553436\pi$
$773$	5.03736	−	1.34976i	0.181181	−	0.0485474i	0.348269	+	0.937395i	$0.386770\pi$
$774$	2.13283	+	3.77118i	0.0766631	+	0.135552i
$775$		0			0
$776$	−44.7875	−	25.8581i	−1.60778	−	0.928250i
$777$	−0.673969	+	1.15546i	−0.0241785	+	0.0414519i
$778$	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
$783$	−22.4177	+	12.5475i	−0.801144	+	0.448410i
$784$	10.7147	+	6.18613i	0.382667	+	0.220933i
$785$		0			0
$786$	−1.67199	+	1.65720i	−0.0596378	+	0.0591102i
$787$	38.7052	−	10.3710i	1.37969	−	0.369687i	0.508683	−	0.860954i	$-0.330133\pi$
$787$	38.7052	−	10.3710i	1.37969	−	0.369687i	0.871009	+	0.491267i	$0.163466\pi$
$788$	11.0777	+	11.0777i	0.394628	+	0.394628i
$789$	14.3600	+	14.4881i	0.511228	+	0.515791i
$790$		0			0
$791$	−1.24037	−	2.14838i	−0.0441024	−	0.0763876i
$792$	43.4435	−	11.2278i	1.54370	−	0.398964i
$793$	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	$-0.373338\pi$
$797$	33.4264	−	8.95658i	1.18402	−	0.317259i	0.796522	+	0.604610i	$0.206671\pi$
$798$	0.753387	−	0.430516i	0.0266696	−	0.0152401i
$799$	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
$804$	0.969378	−	0.255133i	0.0341873	−	0.00899785i
$805$		0			0
$806$	5.68838	+	7.68740i	0.200365	+	0.270777i
$807$	−1.95073	+	1.11473i	−0.0686691	+	0.0392403i
$808$	45.0335	+	12.0667i	1.58427	+	0.424504i
$809$	0.776492	+	1.34492i	0.0273000	+	0.0472850i	0.879353	−	0.476171i	$-0.157976\pi$
$809$	0.776492	+	1.34492i	0.0273000	+	0.0472850i	−0.852053	+	0.523456i	$0.824642\pi$
$810$		0			0
$811$			15.7167i			0.551889i	0.961174	+	0.275945i	$0.0889906\pi$
$811$			15.7167i			0.551889i	−0.961174	+	0.275945i	$0.911009\pi$
$812$	0.169240	+	0.631612i	0.00593915	+	0.0221652i
$813$	−10.6078	−	0.0471338i	−0.372031	−	0.00165306i
$814$	24.8643			0.871494
$815$		0			0
$816$	−3.77397	−	14.3392i	−0.132115	−	0.501973i
$817$	−0.936013	+	3.49325i	−0.0327470	+	0.122213i
$818$	−13.8577	+	13.8577i	−0.484522	+	0.484522i
$819$	1.78744	−	0.187579i	0.0624583	−	0.00655456i
$820$		0			0
$821$	23.5322	+	40.7590i	0.821280	+	1.42250i	0.904729	+	0.425987i	$0.140073\pi$
$821$	23.5322	+	40.7590i	0.821280	+	1.42250i	−0.0834487	+	0.996512i	$0.526593\pi$
$822$	−3.88665	+	6.66332i	−0.135562	+	0.232410i
$823$	44.5459	−	11.9360i	1.55277	−	0.416064i	0.622405	−	0.782695i	$-0.286156\pi$
$823$	44.5459	−	11.9360i	1.55277	−	0.416064i	0.930366	+	0.366631i	$0.119489\pi$
$824$		−	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	$-0.531362\pi$
$827$	25.7893	−	25.7893i	0.896781	−	0.896781i	0.995150	+	0.0983687i	$0.0313625\pi$
$828$	3.73225	−	13.4497i	0.129705	−	0.467409i
$829$	−35.8684	+	20.7086i	−1.24576	+	0.719241i	−0.970261	−	0.242060i	$-0.922177\pi$
$829$	−35.8684	+	20.7086i	−1.24576	+	0.719241i	−0.275500	+	0.961301i	$0.588843\pi$
$830$		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
$834$	3.57304	+	13.5758i	0.123724	+	0.470090i
$835$		0			0
$836$	9.23439	+	5.33148i	0.319378	+	0.184393i
$837$	−12.5590	−	0.167420i	−0.434103	−	0.00578689i
$838$	−3.01687	−	11.2591i	−0.104216	−	0.388939i
$839$	12.9769	+	7.49223i	0.448013	+	0.258660i	0.706991	−	0.707223i	$-0.250052\pi$
$839$	12.9769	+	7.49223i	0.448013	+	0.258660i	−0.258978	+	0.965883i	$0.583386\pi$
$840$		0			0
$841$	2.27790	−	3.94543i	0.0785481	−	0.136049i
$842$	−6.78040	+	25.3048i	−0.233668	+	0.872061i
$843$	−32.8060	−	19.1354i	−1.12990	−	0.659058i
$844$			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
$849$	6.81911	−	6.75878i	0.234031	−	0.231961i
$850$		0			0
$851$	13.5842	−	23.5286i	0.465662	−	0.806550i
$852$	−3.79101	−	0.0168447i	−0.129878	−	0.000577090i
$853$	−9.05692	+	9.05692i	−0.310103	+	0.310103i	−0.844949	−	0.534846i	$-0.820369\pi$
$853$	−9.05692	+	9.05692i	−0.310103	+	0.310103i	0.534846	+	0.844949i	$0.320369\pi$
$854$	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	$-0.350707\pi$
$857$	−12.8809	−	12.8809i	−0.440004	−	0.440004i	−0.892013	+	0.452009i	$0.850707\pi$
$858$	−19.7520	−	26.9428i	−0.674321	−	0.919812i
$859$		−	10.9311i		−	0.372966i	−0.982458	−	0.186483i	$-0.940291\pi$
$859$		−	10.9311i		−	0.372966i	0.982458	−	0.186483i	$-0.0597089\pi$
$860$		0			0
$861$	0.316527	+	1.20265i	0.0107872	+	0.0409860i
$862$	4.74335	+	17.7024i	0.161559	+	0.602947i
$863$	21.3829	+	21.3829i	0.727881	+	0.727881i	0.970197	−	0.242316i	$-0.0779072\pi$
$863$	21.3829	+	21.3829i	0.727881	+	0.727881i	−0.242316	+	0.970197i	$0.577907\pi$
$864$	−21.0975	+	5.35269i	−0.717751	+	0.182102i
$865$		0			0
$866$	30.1629			1.02498
$867$	−10.8678	−	0.0482893i	−0.369090	−	0.00163999i
$868$	−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
$873$	−35.4395	−	36.0750i	−1.19944	−	1.22095i
$874$	−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	−0.498996	−	0.866604i	$-0.666298\pi$
$877$	−14.7430	+	3.95038i	−0.497836	+	0.133395i	0.00115930	+	0.999999i	$0.499631\pi$
$878$	−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	$-0.568176\pi$
$881$	15.6546	−	9.03820i	0.527417	−	0.304505i	0.739964	+	0.672646i	$0.234842\pi$
$882$	16.0846	+	16.3731i	0.541598	+	0.551311i
$883$	−21.5666	−	21.5666i	−0.725775	−	0.725775i	0.244000	−	0.969775i	$-0.421540\pi$
$883$	−21.5666	−	21.5666i	−0.725775	−	0.725775i	−0.969775	+	0.244000i	$0.921540\pi$
$884$	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	0.673142	+	0.739514i	$0.264944\pi$
$887$	−8.32639	+	31.0745i	−0.279573	+	1.04338i	−0.952715	+	0.303867i	$0.901722\pi$
$888$	−24.6987	−	0.109744i	−0.828833	−	0.00368278i
$889$	−0.234935			−0.00787947
$890$		0			0
$891$	43.8700	+	0.779792i	1.46970	+	0.0261240i
$892$	6.41908	+	6.41908i	0.214927	+	0.214927i
$893$	3.60314	+	13.4471i	0.120575	+	0.449991i
$894$	−2.82234	−	10.7235i	−0.0943930	−	0.358646i
$895$		0			0
$896$		−	0.0930361i		−	0.00310812i
$897$	−36.2866	+	3.97111i	−1.21157	+	0.132591i
$898$	−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
$903$	0.378771	+	0.00168300i	0.0126047	+	5.60068e-5i
$904$	22.9026	−	39.6684i	0.761728	−	1.31935i
$905$		0			0
$906$	22.2184	−	22.0218i	0.738156	−	0.731625i
$907$	−12.8475	−	3.44249i	−0.426596	−	0.114306i	0.0391321	−	0.999234i	$-0.487541\pi$
$907$	−12.8475	−	3.44249i	−0.426596	−	0.114306i	−0.465728	+	0.884928i	$0.654207\pi$
$908$	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	$-0.0328831\pi$
$912$	7.29495	+	4.25507i	0.241560	+	0.140899i
$913$	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
$918$	0.366652	−	27.5044i	0.0121013	−	0.907779i
$919$	−51.3893	−	29.6696i	−1.69518	−	0.978711i	−0.950210	−	0.311611i	$-0.899132\pi$
$919$	−51.3893	−	29.6696i	−1.69518	−	0.978711i	−0.744968	−	0.667101i	$-0.767535\pi$
$920$		0			0
$921$	9.79712	+	37.2242i	0.322826	+	1.22658i
$922$	−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
$927$	14.0773	−	50.7295i	0.462358	−	1.66617i
$928$	−14.6443	+	14.6443i	−0.480722	+	0.480722i
$929$	9.30395	+	5.37164i	0.305253	+	0.176238i	0.644800	−	0.764351i	$-0.276941\pi$
$929$	9.30395	+	5.37164i	0.305253	+	0.176238i	−0.339548	+	0.940589i	$0.610274\pi$
$930$		0			0
$931$			19.1587i			0.627900i
$932$	14.0308	−	3.75954i	0.459594	−	0.123148i
$933$	23.8242	−	40.8445i	0.779969	−	1.33719i
$934$	15.8303	+	27.4189i	0.517984	+	0.897175i
$935$		0			0
$936$	19.5015	+	26.8505i	0.637425	+	0.877635i
$937$	7.07205	−	7.07205i	0.231034	−	0.231034i	−0.582090	−	0.813124i	$-0.697765\pi$
$937$	7.07205	−	7.07205i	0.231034	−	0.231034i	0.813124	+	0.582090i	$0.197765\pi$
$938$	−0.0343089	+	0.128042i	−0.00112022	+	0.00418073i
$939$	−8.11156	−	30.8199i	−0.264711	−	1.00577i
$940$		0			0
$941$	−28.4220			−0.926529			−0.463265	−	0.886220i	$-0.653322\pi$
$941$	−28.4220			−0.926529			−0.463265	+	0.886220i	$0.653322\pi$
$942$	13.8545	+	0.0615599i	0.451402	+	0.00200573i
$943$	−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	$-0.335300\pi$
$947$	15.0316	+	4.02771i	0.488461	+	0.130883i	−0.00617839	+	0.999981i	$0.501967\pi$
$948$	−8.84926	+	5.05683i	−0.287411	+	0.164238i
$949$	3.14701	+	27.6208i	0.102156	+	0.896610i
$950$		0			0
$951$	−15.7511	+	4.14558i	−0.510765	+	0.134430i
$952$	−2.37549	−	0.636511i	−0.0769901	−	0.0206294i
$953$	−10.2413	−	38.2209i	−0.331747	−	1.23810i	−0.907353	−	0.420369i	$-0.861901\pi$
$953$	−10.2413	−	38.2209i	−0.331747	−	1.23810i	0.575607	−	0.817727i	$-0.304766\pi$
$954$	13.4226	+	7.90943i	0.434574	+	0.256077i
$955$		0			0
$956$	−1.27655	+	2.21106i	−0.0412867	+	0.0715107i
$957$	36.2477	−	20.7134i	1.17172	−	0.669571i
$958$	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
$963$	6.33951	−	1.63843i	0.204288	−	0.0527976i
$964$	−2.38966	−	4.13901i	−0.0769658	−	0.133309i
$965$		0			0
$966$	1.29940	+	1.31099i	0.0418074	+	0.0421805i
$967$	−32.4327	−	32.4327i	−1.04296	−	1.04296i	−0.999035	−	0.0439297i	$-0.986012\pi$
$967$	−32.4327	−	32.4327i	−1.04296	−	1.04296i	−0.0439297	−	0.999035i	$-0.513988\pi$
$968$	−37.8361	+	10.1381i	−1.21610	+	0.325852i
$969$	16.3076	−	16.1634i	0.523877	−	0.519242i
$970$		0			0
$971$	29.2025	+	16.8601i	0.937154	+	0.541066i	0.889067	−	0.457777i	$-0.151354\pi$
$971$	29.2025	+	16.8601i	0.937154	+	0.541066i	0.0480872	+	0.998843i	$0.484687\pi$
$972$	−12.4050	−	0.275641i	−0.397891	−	0.00884120i
$973$	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	$-0.404516\pi$
$977$	2.30444	+	0.617472i	0.0737254	+	0.0197547i	−0.221768	+	0.975100i	$0.571183\pi$
$978$	−21.0433	+	36.0769i	−0.672890	+	1.15361i
$979$	29.1781	+	16.8460i	0.932536	+	0.538400i
$980$		0			0
$981$	−15.2226	−	26.9159i	−0.486019	−	0.859357i
$982$	23.0982	−	6.18915i	0.737094	−	0.197504i
$983$	−2.74521	−	2.74521i	−0.0875586	−	0.0875586i	0.661971	−	0.749530i	$-0.269720\pi$
$983$	−2.74521	−	2.74521i	−0.0875586	−	0.0875586i	−0.749530	+	0.661971i	$0.769720\pi$
$984$	−16.3088	+	16.1645i	−0.519904	+	0.515305i
$985$		0			0
$986$	−13.0863	−	22.6661i	−0.416752	−	0.721836i
$987$	1.26596	−	0.723420i	0.0402959	−	0.0230267i
$988$	−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	0.698104	−	0.715996i	$-0.254027\pi$
$991$	−8.53170	−	14.7773i	−0.271019	−	0.469418i	−0.969123	+	0.246578i	$0.920694\pi$
$992$	−9.78028	+	2.62062i	−0.310524	+	0.0832047i
$993$	−5.45919	−	9.55337i	−0.173242	−	0.303167i
$994$	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	0.937360	−	0.348361i	$-0.113262\pi$
$997$	−1.53450	−	5.72683i	−0.0485981	−	0.181371i	−0.985958	+	0.166991i	$0.946595\pi$
$998$	−19.2683	−	5.16292i	−0.609927	−	0.163429i
$999$	−23.2434	−	6.56133i	−0.735388	−	0.207591i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bn.d.218.8		96
3.2	odd	2	inner	975.2.bn.d.218.17		96
5.2	odd	4	inner	975.2.bn.d.257.17		96
5.3	odd	4		195.2.bf.a.62.8	yes	96
5.4	even	2		195.2.bf.a.23.17	yes	96
13.4	even	6	inner	975.2.bn.d.368.8		96
15.2	even	4	inner	975.2.bn.d.257.8		96
15.8	even	4		195.2.bf.a.62.17	yes	96
15.14	odd	2		195.2.bf.a.23.8	yes	96
39.17	odd	6	inner	975.2.bn.d.368.17		96
65.4	even	6		195.2.bf.a.173.17	yes	96
65.17	odd	12	inner	975.2.bn.d.407.17		96
65.43	odd	12		195.2.bf.a.17.8	✓	96
195.17	even	12	inner	975.2.bn.d.407.8		96
195.134	odd	6		195.2.bf.a.173.8	yes	96
195.173	even	12		195.2.bf.a.17.17	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.8	✓	96	65.43	odd	12
195.2.bf.a.17.17	yes	96	195.173	even	12
195.2.bf.a.23.8	yes	96	15.14	odd	2
195.2.bf.a.23.17	yes	96	5.4	even	2
195.2.bf.a.62.8	yes	96	5.3	odd	4
195.2.bf.a.62.17	yes	96	15.8	even	4
195.2.bf.a.173.8	yes	96	195.134	odd	6
195.2.bf.a.173.17	yes	96	65.4	even	6
975.2.bn.d.218.8		96	1.1	even	1	trivial
975.2.bn.d.218.17		96	3.2	odd	2	inner
975.2.bn.d.257.8		96	15.2	even	4	inner
975.2.bn.d.257.17		96	5.2	odd	4	inner
975.2.bn.d.368.8		96	13.4	even	6	inner
975.2.bn.d.368.17		96	39.17	odd	6	inner
975.2.bn.d.407.8		96	195.17	even	12	inner
975.2.bn.d.407.17		96	65.17	odd	12	inner

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} +(-1.49614 - 0.872682i) q^{3} +(-0.689337 - 0.397989i) q^{4} +(1.33790 + 1.34985i) q^{6} +(0.160495 - 0.0430045i) q^{7} +(2.16938 + 2.16938i) q^{8} +(1.47685 + 2.61130i) q^{9} +(-2.43760 - 4.22205i) q^{11} +(0.684025 + 1.19702i) q^{12} +(2.24451 - 2.82173i) q^{13} -0.182320 q^{14} +(-0.887232 - 1.53673i) q^{16} +(-4.65999 + 1.24864i) q^{17} +(-0.823701 - 3.18712i) 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} +(-1.35251 - 5.13887i) q^{24} +(-3.18030 + 2.35330i) q^{26} +(0.0692622 - 5.19569i) q^{27} +(-0.127750 - 0.0342306i) q^{28} +(-2.47205 - 4.28172i) q^{29} -2.41720i q^{31} +(-1.08416 - 4.04612i) q^{32} +(-0.0375196 + 8.44403i) q^{33} +5.29369 q^{34} +(0.0212203 - 2.38784i) q^{36} +(1.20299 - 4.48963i) q^{37} +(-2.13199 + 2.13199i) q^{38} +(-5.82057 + 2.26296i) q^{39} +(-2.16059 - 3.74226i) q^{41} +(0.272776 + 0.159108i) q^{42} +(-1.27129 + 0.340642i) q^{43} +3.88056i q^{44} +(-5.55453 - 3.20691i) q^{46} +(-3.58251 + 3.58251i) q^{47} +(-0.0136563 + 3.07343i) 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} +(-1.54897 + 5.48719i) q^{54} +(0.441468 + 0.254882i) q^{56} +(-4.13222 + 2.36132i) 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} +(0.349325 + 0.355590i) q^{63} +8.14527i q^{64} +(2.43784 - 8.93909i) q^{66} +(0.188179 - 0.702294i) q^{67} +(3.70925 + 0.993890i) q^{68} +(-7.12700 - 7.19061i) q^{69} +(-1.37489 + 2.38137i) q^{71} +(-2.46106 + 8.86877i) 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} +(6.81184 - 0.745469i) q^{78} +7.39276i q^{79} +(-4.63781 + 7.71302i) q^{81} +(1.22720 + 4.57999i) q^{82} +(1.60997 + 1.60997i) q^{83} +(0.161260 + 0.162699i) q^{84} +1.44417 q^{86} +(-0.0380499 + 8.56336i) 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} +(-2.10944 + 3.61646i) 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

Related objects

Downloads

Learn more