LMFDB - Embedded newform 975.2.bn.d.257.17

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			257.17
Character	$\chi$	$=$	975.257
Dual form			975.2.bn.d.368.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.283997 - 1.05989i) q^{2} +(-0.872682 + 1.49614i) q^{3} +(0.689337 + 0.397989i) q^{4} +(1.33790 + 1.34985i) q^{6} +(0.0430045 + 0.160495i) q^{7} +(2.16938 - 2.16938i) q^{8} +(-1.47685 - 2.61130i) q^{9} +(-2.43760 - 4.22205i) q^{11} +(-1.19702 + 0.684025i) q^{12} +(-2.82173 - 2.24451i) q^{13} +0.182320 q^{14} +(-0.887232 - 1.53673i) q^{16} +(-1.24864 - 4.65999i) q^{17} +(-3.18712 + 0.823701i) q^{18} +(-1.37389 + 2.37966i) q^{19} +(-0.277652 - 0.0757204i) q^{21} +(-5.16719 + 1.38454i) q^{22} +(1.51285 - 5.64603i) q^{23} +(1.35251 + 5.13887i) q^{24} +(-3.18030 + 2.35330i) q^{26} +(5.19569 + 0.0692622i) q^{27} +(-0.0342306 + 0.127750i) q^{28} +(2.47205 + 4.28172i) q^{29} -2.41720i q^{31} +(4.04612 - 1.08416i) q^{32} +(8.44403 + 0.0375196i) q^{33} -5.29369 q^{34} +(0.0212203 - 2.38784i) q^{36} +(4.48963 + 1.20299i) q^{37} +(2.13199 + 2.13199i) q^{38} +(5.82057 - 2.26296i) q^{39} +(-2.16059 - 3.74226i) q^{41} +(-0.159108 + 0.272776i) q^{42} +(0.340642 + 1.27129i) q^{43} -3.88056i q^{44} +(-5.55453 - 3.20691i) q^{46} +(-3.58251 - 3.58251i) q^{47} +(3.07343 + 0.0136563i) q^{48} +(6.03827 - 3.48620i) q^{49} +(8.06165 + 2.19855i) q^{51} +(-1.05184 - 2.67024i) q^{52} +(3.34661 + 3.34661i) q^{53} +(1.54897 - 5.48719i) q^{54} +(0.441468 + 0.254882i) q^{56} +(-2.36132 - 4.13222i) q^{57} +(5.24021 - 1.40411i) q^{58} +(-8.49452 - 4.90431i) q^{59} +(-7.20685 + 12.4826i) q^{61} +(-2.56197 - 0.686477i) q^{62} +(0.355590 - 0.349325i) q^{63} -8.14527i q^{64} +(2.43784 - 8.93909i) q^{66} +(0.702294 + 0.188179i) q^{67} +(0.993890 - 3.70925i) q^{68} +(7.12700 + 7.19061i) q^{69} +(-1.37489 + 2.38137i) q^{71} +(-8.86877 - 2.46106i) 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} +(-0.745469 - 6.81184i) q^{78} -7.39276i q^{79} +(-4.63781 + 7.71302i) q^{81} +(-4.57999 + 1.22720i) q^{82} +(1.60997 - 1.60997i) q^{83} +(-0.161260 - 0.162699i) q^{84} +1.44417 q^{86} +(-8.56336 - 0.0380499i) q^{87} +(-14.4473 - 3.87115i) q^{88} +(5.98500 - 3.45544i) q^{89} +(0.238885 - 0.549398i) q^{91} +(3.28992 - 3.28992i) q^{92} +(3.61646 + 2.10944i) q^{93} +(-4.81449 + 2.77964i) q^{94} +(-1.90893 + 6.99968i) q^{96} +(-4.36286 - 16.2824i) q^{97} +(-1.98014 - 7.38997i) 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 $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.283997	−	1.05989i	0.200816	−	0.749456i	−0.789868	−	0.613277i	$-0.789851\pi$
$2$	0.283997	−	1.05989i	0.200816	−	0.749456i	0.990684	−	0.136179i	$-0.0434823\pi$
$3$	−0.872682	+	1.49614i	−0.503843	+	0.863795i
$3$	−0.872682	+	1.49614i	−0.503843	+	0.863795i
$4$	0.689337	+	0.397989i	0.344668	+	0.198994i
$5$		0			0
$5$		0			0
$6$	1.33790	+	1.34985i	0.546197	+	0.551072i
$7$	0.0430045	+	0.160495i	0.0162542	+	0.0606614i	0.973577	−	0.228361i	$-0.0733366\pi$
$7$	0.0430045	+	0.160495i	0.0162542	+	0.0606614i	−0.957322	+	0.289022i	$0.906670\pi$
$8$	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	$-0.429468\pi$
$12$	−1.19702	+	0.684025i	−0.345549	+	0.197461i
$13$	−2.82173	−	2.24451i	−0.782608	−	0.622514i
$13$	−2.82173	−	2.24451i	−0.782608	−	0.622514i
$14$	0.182320			0.0487271
$15$		0			0
$16$	−0.887232	−	1.53673i	−0.221808	−	0.384183i
$17$	−1.24864	−	4.65999i	−0.302840	−	1.13021i	−0.934789	−	0.355204i	$-0.884412\pi$
$17$	−1.24864	−	4.65999i	−0.302840	−	1.13021i	0.631949	−	0.775010i	$-0.282255\pi$
$18$	−3.18712	+	0.823701i	−0.751211	+	0.194148i
$19$	−1.37389	+	2.37966i	−0.315193	+	0.545930i	−0.979479	−	0.201549i	$-0.935403\pi$
$19$	−1.37389	+	2.37966i	−0.315193	+	0.545930i	0.664285	+	0.747479i	$0.268736\pi$
$20$		0			0
$21$	−0.277652	−	0.0757204i	−0.0605886	−	0.0165235i
$22$	−5.16719	+	1.38454i	−1.10165	+	0.295186i
$23$	1.51285	−	5.64603i	0.315451	−	1.17728i	−0.608118	−	0.793846i	$-0.708075\pi$
$23$	1.51285	−	5.64603i	0.315451	−	1.17728i	0.923569	−	0.383432i	$-0.125258\pi$
$24$	1.35251	+	5.13887i	0.276081	+	1.04897i
$25$		0			0
$26$	−3.18030	+	2.35330i	−0.623707	+	0.461520i
$27$	5.19569	+	0.0692622i	0.999911	+	0.0133295i
$28$	−0.0342306	+	0.127750i	−0.00646898	+	0.0241426i
$29$	2.47205	+	4.28172i	0.459049	+	0.795096i	0.998911	−	0.0466574i	$-0.0148569\pi$
$29$	2.47205	+	4.28172i	0.459049	+	0.795096i	−0.539862	+	0.841754i	$0.681524\pi$
$30$		0			0
$31$		−	2.41720i		−	0.434142i	−0.976156	−	0.217071i	$-0.930350\pi$
$31$		−	2.41720i		−	0.434142i	0.976156	−	0.217071i	$-0.0696502\pi$
$32$	4.04612	−	1.08416i	0.715260	−	0.191653i
$33$	8.44403	+	0.0375196i	1.46992	+	0.00653133i
$34$	−5.29369			−0.907860
$35$		0			0
$36$	0.0212203	−	2.38784i	0.00353672	−	0.397973i
$37$	4.48963	+	1.20299i	0.738090	+	0.197771i	0.608229	−	0.793762i	$-0.291880\pi$
$37$	4.48963	+	1.20299i	0.738090	+	0.197771i	0.129861	+	0.991532i	$0.458547\pi$
$38$	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	$0.942890\pi$
$42$	−0.159108	+	0.272776i	−0.0245508	+	0.0420903i
$43$	0.340642	+	1.27129i	0.0519475	+	0.193871i	0.987023	−	0.160577i	$-0.0513355\pi$
$43$	0.340642	+	1.27129i	0.0519475	+	0.193871i	−0.935076	+	0.354448i	$0.884669\pi$
$44$		−	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	0.395782	−	0.918344i	$-0.370474\pi$
$47$	−3.58251	−	3.58251i	−0.522562	−	0.522562i	−0.918344	+	0.395782i	$0.870474\pi$
$48$	3.07343	+	0.0136563i	0.443612	+	0.00197111i
$49$	6.03827	−	3.48620i	0.862610	−	0.498028i
$50$		0			0
$51$	8.06165	+	2.19855i	1.12886	+	0.307859i
$52$	−1.05184	−	2.67024i	−0.145864	−	0.370296i
$53$	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	$0.644618\pi$
$54$	1.54897	−	5.48719i	0.210788	−	0.746712i
$55$		0			0
$56$	0.441468	+	0.254882i	0.0589936	+	0.0340600i
$57$	−2.36132	−	4.13222i	−0.312764	−	0.547326i
$58$	5.24021	−	1.40411i	0.688074	−	0.184369i
$59$	−8.49452	−	4.90431i	−1.10589	−	0.638487i	−0.168130	−	0.985765i	$-0.553773\pi$
$59$	−8.49452	−	4.90431i	−1.10589	−	0.638487i	−0.937762	+	0.347278i	$0.887106\pi$
$60$		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	$0.792609\pi$
$62$	−2.56197	−	0.686477i	−0.325370	−	0.0871826i
$63$	0.355590	−	0.349325i	0.0448001	−	0.0440108i
$64$		−	8.14527i		−	1.01816i
$65$		0			0
$66$	2.43784	−	8.93909i	0.300078	−	1.10033i
$67$	0.702294	+	0.188179i	0.0857989	+	0.0229897i	0.301463	−	0.953478i	$-0.402525\pi$
$67$	0.702294	+	0.188179i	0.0857989	+	0.0229897i	−0.215664	+	0.976468i	$0.569192\pi$
$68$	0.993890	−	3.70925i	0.120527	−	0.449812i
$69$	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	$0.218838\pi$
$72$	−8.86877	−	2.46106i	−1.04519	−	0.290038i
$73$	5.45193	+	5.45193i	0.638101	+	0.638101i	0.950087	−	0.311986i	$-0.100994\pi$
$73$	5.45193	+	5.45193i	0.638101	+	0.638101i	−0.311986	+	0.950087i	$0.600994\pi$
$74$	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
$78$	−0.745469	−	6.81184i	−0.0844077	−	0.771289i
$79$		−	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
$81$	−4.63781	+	7.71302i	−0.515312	+	0.857002i
$82$	−4.57999	+	1.22720i	−0.505775	+	0.135522i
$83$	1.60997	−	1.60997i	0.176717	−	0.176717i	−0.613206	−	0.789923i	$-0.710120\pi$
$83$	1.60997	−	1.60997i	0.176717	−	0.176717i	0.789923	+	0.613206i	$0.210120\pi$
$84$	−0.161260	−	0.162699i	−0.0175949	−	0.0177519i
$85$		0			0
$86$	1.44417			0.155729
$87$	−8.56336	−	0.0380499i	−0.918089	−	0.00407937i
$88$	−14.4473	−	3.87115i	−1.54009	−	0.412666i
$89$	5.98500	−	3.45544i	0.634408	−	0.366276i	−0.148049	−	0.988980i	$-0.547299\pi$
$89$	5.98500	−	3.45544i	0.634408	−	0.366276i	0.782457	+	0.622704i	$0.213966\pi$
$90$		0			0
$91$	0.238885	−	0.549398i	0.0250419	−	0.0575926i
$92$	3.28992	−	3.28992i	0.342998	−	0.342998i
$93$	3.61646	+	2.10944i	0.375009	+	0.218739i
$94$	−4.81449	+	2.77964i	−0.496576	+	0.286698i
$95$		0			0
$96$	−1.90893	+	6.99968i	−0.194830	+	0.714402i
$97$	−4.36286	−	16.2824i	−0.442981	−	1.65323i	−0.721212	−	0.692714i	$-0.756415\pi$
$97$	−4.36286	−	16.2824i	−0.442981	−	1.65323i	0.278231	−	0.960514i	$-0.410252\pi$
$98$	−1.98014	−	7.38997i	−0.200024	−	0.746500i
$99$	−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	$0.0604604\pi$
$102$	4.61971	−	7.92008i	0.457419	−	0.784205i
$103$	−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
$107$	2.10823	+	0.564899i	0.203811	+	0.0546109i	0.359280	−	0.933230i	$-0.383022\pi$
$107$	2.10823	+	0.564899i	0.203811	+	0.0546109i	−0.155469	+	0.987841i	$0.549689\pi$
$108$	3.55402	+	2.11557i	0.341985	+	0.203571i
$109$	10.3074			0.987274			0.493637	−	0.869668i	$-0.335667\pi$
$109$	10.3074			0.987274			0.493637	+	0.869668i	$0.335667\pi$
$110$		0			0
$111$	−5.71785	+	5.66727i	−0.542715	+	0.537913i
$112$	0.208483	−	0.208483i	0.0196997	−	0.0196997i
$113$	−14.4214	+	3.86420i	−1.35665	+	0.363513i	−0.862585	−	0.505912i	$-0.831156\pi$
$113$	−14.4214	+	3.86420i	−1.35665	+	0.363513i	−0.494065	+	0.869425i	$0.664489\pi$
$114$	−5.05031	+	1.32920i	−0.473004	+	0.124491i
$115$		0			0
$116$			3.93540i			0.365393i
$117$	−1.69380	+	10.6832i	−0.156592	+	0.987663i
$118$	−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
$123$	7.48444	+	0.0332559i	0.674850	+	0.00299858i
$124$	0.962018	−	1.66626i	0.0863918	−	0.149635i
$125$		0			0
$126$	−0.269260	−	0.476093i	−0.0239876	−	0.0424138i
$127$	0.365954	−	1.36576i	0.0324732	−	0.121192i	−0.947787	−	0.318905i	$-0.896685\pi$
$127$	0.365954	−	1.36576i	0.0324732	−	0.121192i	0.980260	+	0.197713i	$0.0633516\pi$
$128$	−0.540851	−	0.144921i	−0.0478049	−	0.0128093i
$129$	−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	$0.982768\pi$
$132$	5.80585	+	3.38649i	0.505334	+	0.294756i
$133$	−0.441006	−	0.118167i	−0.0382401	−	0.0102464i
$134$	0.398899	−	0.690913i	0.0344596	−	0.0596858i
$135$		0			0
$136$	−12.8181	−	7.40052i	−1.09914	−	0.634589i
$137$	−3.92054	+	1.05050i	−0.334954	+	0.0897507i	−0.422376	−	0.906421i	$-0.638804\pi$
$137$	−3.92054	+	1.05050i	−0.334954	+	0.0897507i	0.0874219	+	0.996171i	$0.472137\pi$
$138$	9.64531	−	5.51172i	0.821063	−	0.469189i
$139$	−6.39677	−	3.69318i	−0.542567	−	0.313251i	0.203552	−	0.979064i	$-0.434752\pi$
$139$	−6.39677	−	3.69318i	−0.542567	−	0.313251i	−0.746119	+	0.665813i	$0.768085\pi$
$140$		0			0
$141$	8.48631	−	2.23353i	0.714676	−	0.188097i
$142$	2.13353	+	2.13353i	0.179042	+	0.179042i
$143$	−2.59816	+	17.3847i	−0.217269	+	1.45378i
$144$	−2.70256	+	4.58636i	−0.225213	+	0.382196i
$145$		0			0
$146$	7.32679	−	4.23012i	0.606369	−	0.350087i
$147$	−0.0536595	+	12.0764i	−0.00442576	+	0.996046i
$148$	2.61609	+	2.61609i	0.215041	+	0.215041i
$149$	5.05279	+	2.91723i	0.413941	+	0.238989i	0.692482	−	0.721435i	$-0.256517\pi$
$149$	5.05279	+	2.91723i	0.413941	+	0.238989i	−0.278541	+	0.960424i	$0.589851\pi$
$150$		0			0
$151$		−	16.4599i		−	1.33949i	−0.742591	−	0.669745i	$-0.766403\pi$
$151$		−	16.4599i		−	1.33949i	0.742591	−	0.669745i	$-0.233597\pi$
$152$	2.18188	+	8.14288i	0.176974	+	0.660475i
$153$	−10.3246	+	10.1427i	−0.834693	+	0.819988i
$154$	−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	0.882222	−	0.470834i	$-0.156047\pi$
$157$	5.15467	+	5.15467i	0.411387	+	0.411387i	−0.470834	+	0.882222i	$0.656047\pi$
$158$	−7.83551	−	2.09952i	−0.623360	−	0.167029i
$159$	−7.92751	+	2.08646i	−0.628692	+	0.165467i
$160$		0			0
$161$	0.971218			0.0765427
$162$	6.85784	+	7.10605i	0.538803	+	0.558304i
$163$	21.2268	−	5.68770i	1.66261	−	0.445495i	0.699506	−	0.714626i	$-0.253403\pi$
$163$	21.2268	−	5.68770i	1.66261	−	0.445495i	0.963103	+	0.269131i	$0.0867366\pi$
$164$		−	3.43957i		−	0.268585i
$165$		0			0
$166$	−1.24917	−	2.16362i	−0.0969541	−	0.167929i
$167$	−3.66650	+	13.6836i	−0.283723	+	1.05887i	0.666045	+	0.745911i	$0.267986\pi$
$167$	−3.66650	+	13.6836i	−0.283723	+	1.05887i	−0.949768	+	0.312956i	$0.898681\pi$
$168$	−0.766599	+	0.438066i	−0.0591444	+	0.0337975i
$169$	2.92437	+	12.6668i	0.224952	+	0.974370i
$170$		0			0
$171$	8.24304	+	0.0732546i	0.630361	+	0.00560192i
$172$	−0.271144	+	1.01192i	−0.0206745	+	0.0771583i
$173$	−0.918542	+	0.246123i	−0.0698354	+	0.0187123i	−0.293568	−	0.955938i	$-0.594843\pi$
$173$	−0.918542	+	0.246123i	−0.0698354	+	0.0187123i	0.223732	+	0.974651i	$0.428176\pi$
$174$	−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
$178$	−1.96267	−	7.32477i	−0.147108	−	0.549015i
$179$	8.16594	+	14.1438i	0.610351	+	1.05716i	0.991181	+	0.132514i	$0.0423048\pi$
$179$	8.16594	+	14.1438i	0.610351	+	1.05716i	−0.380830	+	0.924645i	$0.624362\pi$
$180$		0			0
$181$	−12.4459			−0.925096			−0.462548	−	0.886594i	$-0.653065\pi$
$181$	−12.4459			−0.925096			−0.462548	+	0.886594i	$0.653065\pi$
$182$	−0.514459	−	0.409219i	−0.0381343	−	0.0303333i
$183$	−12.3864	−	21.6758i	−0.915632	−	1.60232i
$184$	−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
$188$	−1.04376	−	3.89535i	−0.0761238	−	0.284098i
$189$	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	$0.699841\pi$
$192$	12.1864	+	7.10823i	0.879481	+	0.512992i
$193$	2.73177	−	10.1951i	0.196637	−	0.733861i	−0.795199	−	0.606348i	$-0.792634\pi$
$193$	2.73177	−	10.1951i	0.196637	−	0.733861i	0.991837	−	0.127513i	$-0.0406994\pi$
$194$	−18.4966			−1.32798
$195$		0			0
$196$	5.54987			0.396419
$197$	5.09403	−	19.0112i	0.362934	−	1.35449i	−0.507265	−	0.861790i	$-0.669344\pi$
$197$	5.09403	−	19.0112i	0.362934	−	1.35449i	0.870199	−	0.492700i	$-0.163990\pi$
$198$	11.2466	+	11.4483i	0.799264	+	0.813597i
$199$	10.9231	+	6.30646i	0.774318	+	0.447053i	0.834413	−	0.551140i	$-0.185807\pi$
$199$	10.9231	+	6.30646i	0.774318	+	0.447053i	−0.0600946	+	0.998193i	$0.519140\pi$
$200$		0			0
$201$	−0.894421	+	0.886508i	−0.0630876	+	0.0625295i
$202$	−4.31573	−	16.1065i	−0.303654	−	1.13325i
$203$	−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
$207$	−16.9777	+	4.38785i	−1.18003	+	0.304976i
$208$	−0.945670	+	6.32765i	−0.0655704	+	0.438743i
$209$	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	$0.886248\pi$
$212$	0.975028	+	3.63885i	0.0669652	+	0.249917i
$213$	−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
$217$	0.387948	−	0.103950i	0.0263356	−	0.00705661i
$218$	2.92728	−	10.9248i	0.198260	−	0.739918i
$219$	−12.9146	+	3.39904i	−0.872691	+	0.229686i
$220$		0			0
$221$	−6.93605	+	15.9518i	−0.466569	+	1.07304i
$222$	4.38283	+	7.66979i	0.294156	+	0.514762i
$223$	−2.95177	+	11.0162i	−0.197665	+	0.737697i	0.793896	+	0.608054i	$0.208050\pi$
$223$	−2.95177	+	11.0162i	−0.197665	+	0.737697i	−0.991561	+	0.129643i	$0.958617\pi$
$224$	0.348003	+	0.602759i	0.0232519	+	0.0402735i
$225$		0			0
$226$			16.3825i			1.08975i
$227$	−25.6485	+	6.87249i	−1.70235	+	0.456143i	−0.973530	−	0.228561i	$-0.926598\pi$
$227$	−25.6485	+	6.87249i	−1.70235	+	0.456143i	−0.728821	+	0.684705i	$0.759931\pi$
$228$	0.0168325	−	3.78827i	0.00111476	−	0.250884i
$229$	6.38857			0.422169			0.211084	−	0.977468i	$-0.432301\pi$
$229$	6.38857			0.422169			0.211084	+	0.977468i	$0.432301\pi$
$230$		0			0
$231$	0.357109	+	1.35684i	0.0234961	+	0.0892733i
$232$	14.6515	+	3.92586i	0.961920	+	0.257746i
$233$	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	$0.546056\pi$
$234$	10.8420	+	4.82924i	0.708764	+	0.315698i
$235$		0			0
$236$	−3.90372	−	6.76145i	−0.254111	−	0.440133i
$237$	11.0606	+	6.45152i	0.718462	+	0.419072i
$238$	−0.227652	−	0.849610i	−0.0147565	−	0.0550720i
$239$			3.20751i			0.207477i	0.994605	+	0.103738i	$0.0330805\pi$
$239$			3.20751i			0.207477i	−0.994605	+	0.103738i	$0.966920\pi$
$240$		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
$243$	−7.49241	−	13.6698i	−0.480638	−	0.876919i
$244$	−9.93589	+	5.73649i	−0.636080	+	0.367241i
$245$		0			0
$246$	2.16081	−	7.92325i	0.137768	−	0.505168i
$247$	9.21792	−	3.63104i	0.586522	−	0.231038i
$248$	−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	$0.948865\pi$
$252$	0.384149	−	0.0992820i	0.0241991	−	0.00625418i
$253$	−27.5256	+	7.37545i	−1.73052	+	0.463691i
$254$	−1.34363	−	0.775742i	−0.0843066	−	0.0486744i
$255$		0			0
$256$	7.83807	−	13.5759i	0.489880	−	0.848496i
$257$	4.64467	+	1.24454i	0.289727	+	0.0776320i	0.400755	−	0.916185i	$-0.368748\pi$
$257$	4.64467	+	1.24454i	0.289727	+	0.0776320i	−0.111028	+	0.993817i	$0.535414\pi$
$258$	−1.26030	+	2.16068i	−0.0784631	+	0.134518i
$259$			0.772296i			0.0479881i
$260$		0			0
$261$	7.53002	−	12.7788i	0.466096	−	0.790985i
$262$	1.31283	+	0.351773i	0.0811072	+	0.0217326i
$263$	−3.04819	+	11.3760i	−0.187959	+	0.701474i	0.806018	+	0.591891i	$0.201618\pi$
$263$	−3.04819	+	11.3760i	−0.187959	+	0.701474i	−0.993978	+	0.109583i	$0.965048\pi$
$264$	18.3997	−	18.2369i	1.13242	−	1.12240i
$265$		0			0
$266$	−0.250489	+	0.433859i	−0.0153585	+	0.0266016i
$267$	−0.0531861	+	11.9699i	−0.00325494	+	0.732544i
$268$	0.409224	+	0.409224i	0.0249973	+	0.0249973i
$269$	−0.648587	+	1.12339i	−0.0395451	+	0.0684941i	−0.885121	−	0.465362i	$-0.845924\pi$
$269$	−0.648587	+	1.12339i	−0.0395451	+	0.0684941i	0.845575	+	0.533856i	$0.179258\pi$
$270$		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
$273$	0.613504	+	0.836854i	0.0371310	+	0.0506487i
$274$			4.45368i			0.269057i
$275$		0			0
$276$	2.05112	+	7.79322i	0.123463	+	0.469097i
$277$	10.0459	−	2.69179i	0.603600	−	0.161734i	0.0559386	−	0.998434i	$-0.482185\pi$
$277$	10.0459	−	2.69179i	0.603600	−	0.161734i	0.547661	+	0.836700i	$0.315518\pi$
$278$	−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	$0.273077\pi$
$282$	0.0427843	−	9.62888i	0.00254777	−	0.573391i
$283$	5.35432	+	1.43469i	0.318281	+	0.0852833i	0.414423	−	0.910084i	$-0.363983\pi$
$283$	5.35432	+	1.43469i	0.318281	+	0.0852833i	−0.0961414	+	0.995368i	$0.530650\pi$
$284$	−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
$288$	−8.80659	−	8.96452i	−0.518933	−	0.528239i
$289$	−5.43396	+	3.13730i	−0.319645	+	0.184547i
$290$		0			0
$291$	28.1681	+	7.68193i	1.65124	+	0.450323i
$292$	1.58841	+	5.92803i	0.0929547	+	0.346912i
$293$	−1.26763	−	4.73086i	−0.0740557	−	0.276380i	0.918962	−	0.394347i	$-0.129029\pi$
$293$	−1.26763	−	4.73086i	−0.0740557	−	0.276380i	−0.993018	+	0.117967i	$0.962362\pi$
$294$	12.7844	+	3.48654i	0.745604	+	0.203339i
$295$		0			0
$296$	12.3495	−	7.12996i	0.717798	−	0.414421i
$297$	−12.3726	−	22.1053i	−0.717932	−	1.28268i
$298$	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
$302$	−17.4457	−	4.67457i	−1.00389	−	0.268991i
$303$	−0.116952	+	26.3207i	−0.00671869	+	1.51208i
$304$	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	$-0.531340\pi$
$307$	15.7142	−	15.7142i	0.896858	−	0.896858i	0.995157	+	0.0982987i	$0.0313401\pi$
$308$	0.622810	−	0.166881i	0.0354879	−	0.00950895i
$309$	−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	$0.718243\pi$
$312$	7.71780	−	17.5363i	0.436935	−	0.992795i
$313$	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	0.868738	−	0.495272i	$-0.164932\pi$
$317$	6.64936	+	6.64936i	0.373465	+	0.373465i	−0.495272	+	0.868738i	$0.664932\pi$
$318$	−0.0399671	+	8.99484i	−0.00224124	+	0.504406i
$319$	12.0518	−	20.8743i	0.674770	−	1.16874i
$320$		0			0
$321$	−2.68498	+	2.66123i	−0.149861	+	0.148535i
$322$	0.275823	−	1.02938i	0.0153710	−	0.0573654i
$323$	12.8047	+	3.43100i	0.712471	+	0.190906i
$324$	−6.26671	+	3.47107i	−0.348151	+	0.192837i
$325$		0			0
$326$		−	24.1134i		−	1.33552i
$327$	−8.99512	+	15.4213i	−0.497431	+	0.852802i
$328$	−12.8055	−	3.43123i	−0.707068	−	0.189458i
$329$	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	$0.610807\pi$
$332$	1.75056	−	0.469062i	0.0960746	−	0.0257431i
$333$	−3.48914	−	13.5004i	−0.191204	−	0.739818i
$334$	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	0.275469	−	0.961310i	$-0.411167\pi$
$337$	−12.5904	−	12.5904i	−0.685841	−	0.685841i	−0.961310	+	0.275469i	$0.911167\pi$
$338$	14.2559	+	0.497817i	0.775421	+	0.0270777i
$339$	6.80391	−	24.9486i	0.369538	−	1.35502i
$340$		0			0
$341$	−10.2055	+	5.89217i	−0.552661	+	0.319079i
$342$	2.41864	−	8.71592i	0.130785	−	0.471303i
$343$	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
$347$	2.07408	+	7.74058i	0.111343	+	0.415536i	0.998987	−	0.0449927i	$-0.0143265\pi$
$347$	2.07408	+	7.74058i	0.111343	+	0.415536i	−0.887645	+	0.460529i	$0.847660\pi$
$348$	−5.88790	−	3.43435i	−0.315625	−	0.184101i
$349$	−9.47261	−	16.4070i	−0.507057	−	0.878249i	−0.999967	−	0.00816849i	$-0.997400\pi$
$349$	−9.47261	−	16.4070i	−0.507057	−	0.878249i	0.492909	−	0.870081i	$-0.335933\pi$
$350$		0			0
$351$	−14.5054	−	11.8572i	−0.774241	−	0.632891i
$352$	−14.4402	−	14.4402i	−0.769666	−	0.769666i
$353$	−2.20043	−	0.589602i	−0.117117	−	0.0313814i	0.199785	−	0.979840i	$-0.435976\pi$
$353$	−2.20043	−	0.589602i	−0.117117	−	0.0313814i	−0.316901	+	0.948458i	$0.602642\pi$
$354$	−4.74478	−	18.0278i	−0.252182	−	0.958166i
$355$		0			0
$356$	5.50091			0.291547
$357$	−0.00616913	+	1.38840i	−0.000326505	+	0.0734820i
$358$	17.3100	−	4.63820i	0.914862	−	0.245136i
$359$			9.83095i			0.518858i	0.965762	+	0.259429i	$0.0835343\pi$
$359$			9.83095i			0.518858i	−0.965762	+	0.259429i	$0.916466\pi$
$360$		0			0
$361$	5.72483	+	9.91569i	0.301307	+	0.521878i
$362$	−3.53460	+	13.1913i	−0.185774	+	0.693319i
$363$	−10.9719	−	19.2004i	−0.575876	−	1.00776i
$364$	0.383326	−	0.283647i	0.0200918	−	0.0148671i
$365$		0			0
$366$	−26.4917	+	6.97241i	−1.38474	+	0.364454i
$367$	−3.06044	+	11.4217i	−0.159754	+	0.596209i	0.838897	+	0.544289i	$0.183201\pi$
$367$	−3.06044	+	11.4217i	−0.159754	+	0.596209i	−0.998651	+	0.0519198i	$0.983466\pi$
$368$	−10.0187	+	2.68449i	−0.522259	+	0.139939i
$369$	−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
$373$	6.36680	+	23.7612i	0.329661	+	1.23031i	0.909543	+	0.415610i	$0.136432\pi$
$373$	6.36680	+	23.7612i	0.329661	+	1.23031i	−0.579882	+	0.814700i	$0.696901\pi$
$374$	12.9039	+	22.3502i	0.667246	+	1.15570i
$375$		0			0
$376$	−15.5436			−0.801602
$377$	2.63488	−	17.6304i	0.135703	−	0.908013i
$378$	0.947279	+	0.0126279i	0.0487228	+	0.000649509i
$379$	7.85016	+	13.5969i	0.403236	+	0.698425i	0.994114	−	0.108336i	$-0.0345522\pi$
$379$	7.85016	+	13.5969i	0.403236	+	0.698425i	−0.590879	+	0.806760i	$0.701219\pi$
$380$		0			0
$381$	1.72400	+	1.73939i	0.0883233	+	0.0891117i
$382$	−2.23105	+	2.23105i	−0.114150	+	0.114150i
$383$	−0.618182	−	2.30709i	−0.0315876	−	0.117887i	0.948332	−	0.317280i	$-0.102769\pi$
$383$	−0.618182	−	2.30709i	−0.0315876	−	0.117887i	−0.979920	+	0.199393i	$0.936103\pi$
$384$	0.688812	−	0.682718i	0.0351508	−	0.0348398i
$385$		0			0
$386$	−10.0299	−	5.79076i	−0.510508	−	0.294742i
$387$	2.81666	−	2.76704i	0.143179	−	0.140656i
$388$	3.47274	−	12.9604i	0.176302	−	0.657966i
$389$	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
$392$	5.53642	−	20.6622i	0.279631	−	1.04360i
$393$	−1.85319	−	1.08095i	−0.0934812	−	0.0545266i
$394$	−18.7031	−	10.7982i	−0.942247	−	0.544007i
$395$		0			0
$396$	−10.1333	+	5.73101i	−0.509218	+	0.287994i
$397$	8.32246	+	31.0598i	0.417692	+	1.55885i	0.779382	+	0.626549i	$0.215533\pi$
$397$	8.32246	+	31.0598i	0.417692	+	1.55885i	−0.361690	+	0.932299i	$0.617800\pi$
$398$	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	$0.823836\pi$
$402$	0.685589	+	1.19975i	0.0341941	+	0.0598383i
$403$	−5.42542	+	6.82069i	−0.270259	+	0.339763i
$404$	12.0960			0.601798
$405$		0			0
$406$	0.450705	+	0.780645i	0.0223681	+	0.0387427i
$407$	−5.86484	−	21.8879i	−0.290709	−	1.08494i
$408$	22.2583	−	12.7193i	1.10195	−	0.629699i
$409$	−8.93012	+	15.4674i	−0.441566	+	0.764815i	−0.997806	−	0.0662068i	$-0.978910\pi$
$409$	−8.93012	+	15.4674i	−0.441566	+	0.764815i	0.556240	+	0.831022i	$0.312244\pi$
$410$		0			0
$411$	1.84968	−	6.78242i	0.0912381	−	0.334552i
$412$	−13.4925	+	3.61530i	−0.664728	+	0.178113i
$413$	0.421815	−	1.57423i	0.0207562	−	0.0774630i
$414$	−0.170989	+	19.2407i	−0.00840364	+	0.945628i
$415$		0			0
$416$	−13.8505	−	6.02235i	−0.679076	−	0.295270i
$417$	11.1078	−	6.34748i	0.543954	−	0.310837i
$418$	3.80444	−	14.1983i	0.186081	−	0.694464i
$419$	−5.31145	−	9.19969i	−0.259481	−	0.449435i	0.706622	−	0.707591i	$-0.250218\pi$
$419$	−5.31145	−	9.19969i	−0.259481	−	0.449435i	−0.966103	+	0.258157i	$0.916885\pi$
$420$		0			0
$421$		−	23.8749i		−	1.16359i	−0.813335	−	0.581796i	$-0.802350\pi$
$421$		−	23.8749i		−	1.16359i	0.813335	−	0.581796i	$-0.197650\pi$
$422$	−5.09512	+	1.36523i	−0.248026	+	0.0664585i
$423$	−4.06418	+	14.6458i	−0.197607	+	0.712105i
$424$	14.5201			0.705160
$425$		0			0
$426$	−5.05395	+	1.33016i	−0.244865	+	0.0644466i
$427$	−2.31332	−	0.619853i	−0.111950	−	0.0299968i
$428$	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	$0.965107\pi$
$432$	−4.50335	−	8.04583i	−0.216667	−	0.387105i
$433$	7.11463	+	26.5522i	0.341907	+	1.27602i	0.896184	+	0.443683i	$0.146328\pi$
$433$	7.11463	+	26.5522i	0.341907	+	1.27602i	−0.554277	+	0.832333i	$0.687005\pi$
$434$		−	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
$438$	−0.0651100	+	14.6534i	−0.00311108	+	0.700168i
$439$	−16.5480	+	9.55397i	−0.789791	+	0.455986i	−0.839889	−	0.542758i	$-0.817380\pi$
$439$	−16.5480	+	9.55397i	−0.789791	+	0.455986i	0.0500980	+	0.998744i	$0.484047\pi$
$440$		0			0
$441$	−18.0212	−	10.6192i	−0.858150	−	0.505674i
$442$	14.9374	+	11.8817i	0.710499	+	0.565156i
$443$	−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	$0.844940\pi$
$444$	−6.19704	+	1.63101i	−0.294098	+	0.0774045i
$445$		0			0
$446$	10.8376	+	6.25711i	0.513177	+	0.296283i
$447$	−8.77406	+	5.01386i	−0.414999	+	0.237147i
$448$	1.30727	−	0.350283i	0.0617629	−	0.0165493i
$449$	−25.7950	−	14.8928i	−1.21734	−	0.702834i	−0.252994	−	0.967468i	$-0.581415\pi$
$449$	−25.7950	−	14.8928i	−1.21734	−	0.702834i	−0.964349	+	0.264634i	$0.914749\pi$
$450$		0			0
$451$	−10.5333	+	18.2443i	−0.495996	+	0.859090i
$452$	−11.4791	−	3.07582i	−0.539932	−	0.144674i
$453$	24.6263	+	14.3643i	1.15705	+	0.674893i
$454$			29.1364i			1.36744i
$455$		0			0
$456$	−14.0870	−	3.84176i	−0.659682	−	0.179907i
$457$	3.37500	+	0.904330i	0.157876	+	0.0423028i	0.336891	−	0.941544i	$-0.390624\pi$
$457$	3.37500	+	0.904330i	0.157876	+	0.0423028i	−0.179015	+	0.983846i	$0.557291\pi$
$458$	1.81433	−	6.77119i	0.0847783	−	0.316397i
$459$	−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	$0.143446\pi$
$462$	1.53952	+	0.00684058i	0.0716248	+	0.000318253i
$463$	−27.4762	−	27.4762i	−1.27693	−	1.27693i	−0.942379	−	0.334548i	$-0.891416\pi$
$463$	−27.4762	−	27.4762i	−1.27693	−	1.27693i	−0.334548	−	0.942379i	$-0.608584\pi$
$464$	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	$0.0173232\pi$
$468$	−5.41940	+	6.69022i	−0.250512	+	0.309255i
$469$			0.120807i			0.00557836i
$470$		0			0
$471$	−12.2105	+	3.21371i	−0.562629	+	0.148080i
$472$	−29.0672	+	7.78853i	−1.33793	+	0.358496i
$473$	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
$477$	3.79656	−	13.6815i	0.173833	−	0.626431i
$478$	3.39961	+	0.910923i	0.155495	+	0.0416647i
$479$	0.117001	−	0.0675507i	0.00534593	−	0.00308647i	−0.497325	−	0.867565i	$-0.665684\pi$
$479$	0.117001	−	0.0675507i	0.00534593	−	0.00308647i	0.502671	+	0.864478i	$0.332351\pi$
$480$		0			0
$481$	−9.96841	−	13.4715i	−0.454520	−	0.614248i
$482$	4.65873	−	4.65873i	0.212199	−	0.212199i
$483$	−0.847564	+	1.45308i	−0.0385655	+	0.0661172i
$484$	−8.80122	+	5.08139i	−0.400056	+	0.230972i
$485$		0			0
$486$	−16.6163	+	4.05895i	−0.753732	+	0.184118i
$487$	−2.52502	−	9.42349i	−0.114419	−	0.427019i	0.884823	−	0.465927i	$-0.154279\pi$
$487$	−2.52502	−	9.42349i	−0.114419	−	0.427019i	−0.999243	+	0.0389075i	$0.987612\pi$
$488$	11.4452	+	42.7140i	0.518099	+	1.93357i
$489$	−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	$0.496977\pi$
$492$	5.14607	+	3.00165i	0.232003	+	0.135325i
$493$	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
$497$	−0.441325	−	0.118253i	−0.0197961	−	0.00530436i
$498$	4.32719	+	0.0192272i	0.193906	+	0.000861589i
$499$	−18.1795			−0.813827			−0.406913	−	0.913467i	$-0.633395\pi$
$499$	−18.1795			−0.813827			−0.406913	+	0.913467i	$0.633395\pi$
$500$		0			0
$501$	−17.2728	−	17.4270i	−0.771693	−	0.778581i
$502$	−19.0508	+	19.0508i	−0.850278	+	0.850278i
$503$	7.30144	−	1.95641i	0.325555	−	0.0872322i	−0.0923400	−	0.995728i	$-0.529435\pi$
$503$	7.30144	−	1.95641i	0.325555	−	0.0872322i	0.417895	+	0.908495i	$0.362768\pi$
$504$	0.0135900	−	1.52923i	0.000605347	−	0.0681173i
$505$		0			0
$506$			31.2687i			1.39006i
$507$	−21.5033	−	6.67883i	−0.954996	−	0.296617i
$508$	0.795823	−	0.795823i	0.0353089	−	0.0353089i
$509$	38.2650	−	22.0923i	1.69607	−	0.979224i	0.746643	−	0.665225i	$-0.231664\pi$
$509$	38.2650	−	22.0923i	1.69607	−	0.979224i	0.949423	−	0.313999i	$-0.101669\pi$
$510$		0			0
$511$	−0.640550	+	1.10947i	−0.0283363	+	0.0490799i
$512$	−12.9549	−	12.9549i	−0.572530	−	0.572530i
$513$	−7.30315	+	12.2688i	−0.322442	+	0.541681i
$514$	2.63814	−	4.56940i	0.116364	−	0.201548i
$515$		0			0
$516$	−1.27735	−	1.28875i	−0.0562323	−	0.0567342i
$517$	−6.39281	+	23.8583i	−0.281155	+	1.04929i
$518$	0.818549	+	0.219330i	0.0359650	+	0.00963679i
$519$	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	$-0.263738\pi$
$522$	−11.4056	−	11.6101i	−0.499209	−	0.508161i
$523$	−30.4447	−	8.15764i	−1.33125	−	0.356709i	−0.478072	−	0.878321i	$-0.658664\pi$
$523$	−30.4447	−	8.15764i	−1.33125	−	0.356709i	−0.853183	+	0.521612i	$0.825331\pi$
$524$	−0.492969	+	0.853848i	−0.0215355	+	0.0373005i
$525$		0			0
$526$	11.1916	+	6.46150i	0.487979	+	0.281735i
$527$	−11.2641	+	3.01821i	−0.490673	+	0.131475i
$528$	−7.43415	−	13.0095i	−0.323530	−	0.566165i
$529$	−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
$533$	−2.30290	+	15.4091i	−0.0997498	+	0.667444i
$534$	12.6717	+	3.45578i	0.548356	+	0.149546i
$535$		0			0
$536$	1.93178	−	1.11531i	0.0834400	−	0.0481741i
$537$	−28.2874	−	0.125690i	−1.22069	−	0.00542393i
$538$	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	$0.760255\pi$
$542$	−1.73933	−	6.49126i	−0.0747105	−	0.278823i
$543$	10.8613	−	18.6208i	0.466103	−	0.799094i
$544$	−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	0.619716	−	0.784826i	$-0.287248\pi$
$547$	−3.86162	−	3.86162i	−0.165111	−	0.165111i	−0.784826	+	0.619716i	$0.787248\pi$
$548$	−3.12066	−	0.836179i	−0.133308	−	0.0357198i
$549$	43.2394	+	0.384261i	1.84541	+	0.0163999i
$550$		0			0
$551$	−13.5854			−0.578756
$552$	31.0604	+	0.138011i	1.32202	+	0.00587416i
$553$	1.18650	−	0.317922i	0.0504551	−	0.0135194i
$554$		−	11.4120i		−	0.484850i
$555$		0			0
$556$	−2.93969	−	5.09169i	−0.124671	−	0.215936i
$557$	−1.87374	+	6.99288i	−0.0793928	+	0.296298i	−0.994193	−	0.107608i	$-0.965681\pi$
$557$	−1.87374	+	6.99288i	−0.0793928	+	0.296298i	0.914801	+	0.403906i	$0.132348\pi$
$558$	1.99105	+	7.70389i	0.0842878	+	0.326132i
$559$	1.89223	−	4.35183i	0.0800327	−	0.184063i
$560$		0			0
$561$	−10.3687	−	39.3959i	−0.437767	−	1.66330i
$562$	6.22723	−	23.2403i	0.262680	−	0.980334i
$563$	3.52688	−	0.945024i	0.148640	−	0.0398280i	−0.183732	−	0.982976i	$-0.558818\pi$
$563$	3.52688	−	0.945024i	0.148640	−	0.0398280i	0.332372	+	0.943148i	$0.392151\pi$
$564$	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
$568$	2.18346	+	8.14877i	0.0916158	+	0.341915i
$569$	19.6847	+	34.0948i	0.825224	+	1.42933i	0.901748	+	0.432262i	$0.142285\pi$
$569$	19.6847	+	34.0948i	0.825224	+	1.42933i	−0.0765237	+	0.997068i	$0.524382\pi$
$570$		0			0
$571$	40.5072			1.69517			0.847586	−	0.530658i	$-0.178055\pi$
$571$	40.5072			1.69517			0.847586	+	0.530658i	$0.178055\pi$
$572$	−8.70994	+	10.9499i	−0.364181	+	0.457839i
$573$	4.32420	−	2.47103i	0.180646	−	0.103229i
$574$	−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	0.0341041	−	0.999418i	$-0.489142\pi$
$577$	24.8261	−	24.8261i	1.03352	−	1.03352i	0.999418	−	0.0341041i	$-0.0108578\pi$
$578$	1.78197	+	6.65039i	0.0741200	+	0.276620i
$579$	12.8693	+	12.9842i	0.534831	+	0.539605i
$580$		0			0
$581$	0.327628	+	0.189156i	0.0135923	+	0.00784752i
$582$	16.1417	−	27.6735i	0.669093	−	1.14710i
$583$	5.97186	−	22.2873i	0.247329	−	0.923044i
$584$	23.6547			0.978836
$585$		0			0
$586$	−5.37420			−0.222006
$587$	0.00360950	−	0.0134708i	0.000148980	−	0.000556001i	−0.965851	−	0.259097i	$-0.916575\pi$
$587$	0.00360950	−	0.0134708i	0.000148980	−	0.000556001i	0.966000	+	0.258541i	$0.0832417\pi$
$588$	−4.84327	+	8.30337i	−0.199733	+	0.342425i
$589$	5.75210	+	3.32098i	0.237011	+	0.136838i
$590$		0			0
$591$	23.9979	+	24.2121i	0.987140	+	0.995951i
$592$	−2.13466	−	7.96668i	−0.0877342	−	0.327428i
$593$	25.7961	−	25.7961i	1.05932	−	1.05932i	0.0611927	−	0.998126i	$-0.480510\pi$
$593$	25.7961	−	25.7961i	1.05932	−	1.05932i	0.998126	−	0.0611927i	$-0.0194904\pi$
$594$	−26.9430	+	6.83577i	−1.10549	+	0.280475i
$595$		0			0
$596$	2.32205	+	4.02191i	0.0951150	+	0.164744i
$597$	−18.9677	+	10.8389i	−0.776297	+	0.443608i
$598$	8.47547	+	21.5162i	0.346588	+	0.879864i
$599$	−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	0.986355	−	0.164633i	$-0.0526440\pi$
$601$	8.59509	+	14.8871i	0.350601	+	0.607259i	−0.635754	+	0.771892i	$0.719311\pi$
$602$	0.0621060	+	0.231783i	0.00253125	+	0.00944675i
$603$	−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
$607$	11.8481	−	3.17469i	0.480900	−	0.128857i	−0.0102219	−	0.999948i	$-0.503254\pi$
$607$	11.8481	−	3.17469i	0.480900	−	0.128857i	0.491121	+	0.871091i	$0.336587\pi$
$608$	−2.97903	+	11.1179i	−0.120816	+	0.450890i
$609$	−0.362156	−	1.37601i	−0.0146753	−	0.0557588i
$610$		0			0
$611$	2.06792	+	18.1498i	0.0836591	+	0.734264i
$612$	−11.1538	+	2.88267i	−0.450866	+	0.116525i
$613$	2.76430	−	10.3165i	0.111649	−	0.416680i	−0.887365	−	0.461067i	$-0.847467\pi$
$613$	2.76430	−	10.3165i	0.111649	−	0.416680i	0.999014	+	0.0443871i	$0.0141335\pi$
$614$	−12.1926	−	21.1181i	−0.492052	−	0.852259i
$615$		0			0
$616$		−	2.48520i		−	0.100132i
$617$	4.38758	−	1.17565i	0.176637	−	0.0473299i	−0.169416	−	0.985545i	$-0.554188\pi$
$617$	4.38758	−	1.17565i	0.176637	−	0.0473299i	0.346054	+	0.938215i	$0.387522\pi$
$618$	−33.3520	−	0.148194i	−1.34161	−	0.00596123i
$619$	31.2573			1.25634			0.628168	−	0.778078i	$-0.283805\pi$
$619$	31.2573			1.25634			0.628168	+	0.778078i	$0.283805\pi$
$620$		0			0
$621$	8.25135	−	29.2302i	0.331115	−	1.17297i
$622$	28.9350	+	7.75311i	1.16019	+	0.310871i
$623$	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
$627$	−11.6905	+	20.0423i	−0.466873	+	0.800413i
$628$	1.50180	+	5.60480i	0.0599285	+	0.223656i
$629$		−	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
$633$	8.32625	+	0.0369963i	0.330939	+	0.00147047i
$634$	8.93599	−	5.15920i	0.354893	−	0.204898i
$635$		0			0
$636$	−6.29511	−	1.71679i	−0.249617	−	0.0680750i
$637$	−24.8632	−	3.71582i	−0.985115	−	0.147226i
$638$	−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	$0.906713\pi$
$642$	2.05808	+	3.60157i	0.0812261	+	0.142143i
$643$	27.4633	−	7.35878i	1.08305	−	0.290202i	0.327204	−	0.944954i	$-0.393893\pi$
$643$	27.4633	−	7.35878i	1.08305	−	0.290202i	0.755844	+	0.654752i	$0.227227\pi$
$644$	0.669496	+	0.386534i	0.0263819	+	0.0152316i
$645$		0			0
$646$	7.27297	−	12.5972i	0.286151	−	0.495628i
$647$	2.90637	+	0.778760i	0.114261	+	0.0306162i	0.315497	−	0.948927i	$-0.397829\pi$
$647$	2.90637	+	0.778760i	0.114261	+	0.0306162i	−0.201235	+	0.979543i	$0.564496\pi$
$648$	6.67131	+	26.7937i	0.262074	+	1.05255i
$649$			47.8191i			1.87706i
$650$		0			0
$651$	−0.183031	+	0.671139i	−0.00717356	+	0.0263040i
$652$	16.8960	+	4.52728i	0.661700	+	0.177302i
$653$	−1.89279	+	7.06400i	−0.0740707	+	0.276436i	−0.993021	−	0.117938i	$-0.962372\pi$
$653$	−1.89279	+	7.06400i	−0.0740707	+	0.276436i	0.918950	+	0.394373i	$0.129038\pi$
$654$	13.7904	+	13.9135i	0.539246	+	0.544059i
$655$		0			0
$656$	−3.83390	+	6.64050i	−0.149689	+	0.259268i
$657$	6.18495	−	22.2884i	0.241298	−	0.869552i
$658$	−0.653163	−	0.653163i	−0.0254630	−	0.0254630i
$659$	17.7103	−	30.6751i	0.689894	−	1.19493i	−0.281978	−	0.959421i	$-0.590990\pi$
$659$	17.7103	−	30.6751i	0.689894	−	1.19493i	0.971872	−	0.235511i	$-0.0756762\pi$
$660$		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
$663$	−17.8132	−	24.2982i	−0.691806	−	0.943662i
$664$		−	6.98528i		−	0.271081i
$665$		0			0
$666$	−15.2999	−	0.135967i	−0.592858	−	0.00526863i
$667$	27.9146	−	7.47969i	1.08086	−	0.289615i
$668$	−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
$672$	−1.20551	−	0.00535646i	−0.0465034	−	0.000206630i
$673$	17.7364	+	4.75245i	0.683688	+	0.183194i	0.583913	−	0.811816i	$-0.301521\pi$
$673$	17.7364	+	4.75245i	0.683688	+	0.183194i	0.0997751	+	0.995010i	$0.468188\pi$
$674$	−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	$-0.0615955\pi$
$678$	−24.5105	−	14.2967i	−0.941319	−	0.549062i
$679$	2.42562	−	1.40043i	0.0930868	−	0.0537437i
$680$		0			0
$681$	12.1008	−	44.3712i	0.463703	−	1.70031i
$682$	3.34672	+	12.4901i	0.128152	+	0.478271i
$683$	−6.30369	−	23.5257i	−0.241204	−	0.900186i	−0.975253	−	0.221090i	$-0.929039\pi$
$683$	−6.30369	−	23.5257i	−0.241204	−	0.900186i	0.734049	−	0.679096i	$-0.237628\pi$
$684$	5.65308	+	3.33114i	0.216151	+	0.127369i
$685$		0			0
$686$	2.20616	−	1.27372i	0.0842314	−	0.0486310i
$687$	−5.57519	+	9.55818i	−0.212707	+	0.364667i
$688$	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	$0.329672\pi$
$692$	−0.731139	−	0.195908i	−0.0277937	−	0.00744731i
$693$	−2.34166	−	0.649802i	−0.0889522	−	0.0246839i
$694$	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
$698$	−20.0799	+	5.38038i	−0.760034	+	0.203651i
$699$	−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	$-0.235707\pi$
$702$	−16.6868	+	12.0067i	−0.629804	+	0.453165i
$703$	−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
$708$	13.5228	+	0.0600861i	0.508217	+	0.00225817i
$709$	2.01558	−	3.49108i	0.0756966	−	0.131110i	−0.825692	−	0.564121i	$-0.809215\pi$
$709$	2.01558	−	3.49108i	0.0756966	−	0.131110i	0.901389	+	0.433010i	$0.142549\pi$
$710$		0			0
$711$	−19.3047	+	10.9180i	−0.723984	+	0.409458i
$712$	5.48757	−	20.4799i	0.205656	−	0.767517i
$713$	−13.6476	−	3.65685i	−0.511105	−	0.136950i
$714$	1.46980	+	0.400840i	0.0550059	+	0.0150011i
$715$		0			0
$716$			12.9998i			0.485826i
$717$	−4.79888	−	2.79914i	−0.179217	−	0.104536i
$718$	10.4197	+	2.79196i	0.388861	+	0.104195i
$719$	−18.2661	+	31.6378i	−0.681211	+	1.17989i	0.293400	+	0.955990i	$0.405213\pi$
$719$	−18.2661	+	31.6378i	−0.681211	+	1.17989i	−0.974612	+	0.223903i	$0.928120\pi$
$720$		0			0
$721$	−2.52520	−	1.45793i	−0.0940434	−	0.0542960i
$722$	12.1354	−	3.25166i	0.451632	−	0.121014i
$723$	−9.02953	+	5.15984i	−0.335812	+	0.191897i
$724$	−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	0.815557	−	0.578676i	$-0.196430\pi$
$727$	6.38702	+	6.38702i	0.236881	+	0.236881i	−0.578676	+	0.815557i	$0.696430\pi$
$728$	−0.673622	−	1.71009i	−0.0249661	−	0.0633800i
$729$	26.9904	+	0.719730i	0.999645	+	0.0266567i
$730$		0			0
$731$	5.49888	−	3.17478i	0.203383	−	0.117423i
$732$	0.0882961	−	19.8716i	0.00326352	−	0.734475i
$733$	15.5660	+	15.5660i	0.574943	+	0.574943i	0.933506	−	0.358562i	$-0.116733\pi$
$733$	15.5660	+	15.5660i	0.574943	+	0.574943i	−0.358562	+	0.933506i	$0.616733\pi$
$734$	11.2366	+	6.48747i	0.414751	+	0.239457i
$735$		0			0
$736$		−	24.4847i		−	0.902518i
$737$	−0.917413	−	3.42383i	−0.0337933	−	0.126118i
$738$	9.96857	+	10.1473i	0.366948	+	0.373529i
$739$	24.9818	+	43.2698i	0.918972	+	1.59171i	0.800980	+	0.598691i	$0.204312\pi$
$739$	24.9818	+	43.2698i	0.918972	+	1.59171i	0.117992	+	0.993015i	$0.462354\pi$
$740$		0			0
$741$	−2.61178	+	16.9600i	−0.0959461	+	0.623042i
$742$	0.610154	+	0.610154i	0.0223995	+	0.0223995i
$743$	−26.5434	−	7.11227i	−0.973781	−	0.260924i	−0.263358	−	0.964698i	$-0.584830\pi$
$743$	−26.5434	−	7.11227i	−0.973781	−	0.260924i	−0.710424	+	0.703774i	$0.751497\pi$
$744$	12.4217	−	3.26929i	0.455401	−	0.119858i
$745$		0			0
$746$	26.9925			0.988264
$747$	−6.58181	−	1.82643i	−0.240816	−	0.0668256i
$748$	−18.0834	+	4.84542i	−0.661193	+	0.177166i
$749$			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	$0.928598\pi$
$752$	−2.32683	+	8.68386i	−0.0848509	+	0.316668i
$753$	36.9241	−	21.1000i	1.34559	−	0.768926i
$754$	−17.9380	−	7.79967i	−0.653265	−	0.284047i
$755$		0			0
$756$	−0.186700	+	0.661381i	−0.00679021	+	0.0240542i
$757$	3.34586	−	12.4869i	0.121607	−	0.453845i	−0.878089	−	0.478498i	$-0.841181\pi$
$757$	3.34586	−	12.4869i	0.121607	−	0.453845i	0.999696	+	0.0246532i	$0.00784815\pi$
$758$	16.6406	−	4.45884i	0.604415	−	0.161952i
$759$	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	$0.332867\pi$
$762$	2.33317	−	1.33327i	0.0845220	−	0.0482993i
$763$	0.443266	+	1.65429i	0.0160473	+	0.0598894i
$764$	−1.14440	−	1.98216i	−0.0414029	−	0.0717119i
$765$		0			0
$766$	−2.62082			−0.0946941
$767$	12.9615	+	32.9047i	0.468013	+	1.18812i
$768$	13.4713	+	23.5743i	0.486105	+	0.850665i
$769$	5.76778	+	9.99009i	0.207992	+	0.360252i	0.951082	−	0.308939i	$-0.0999740\pi$
$769$	5.76778	+	9.99009i	0.207992	+	0.360252i	−0.743090	+	0.669191i	$0.766641\pi$
$770$		0			0
$771$	−5.91532	+	5.86298i	−0.213035	+	0.211150i
$772$	5.94066	−	5.94066i	0.213809	−	0.213809i
$773$	−1.34976	−	5.03736i	−0.0485474	−	0.181181i	0.937395	−	0.348269i	$-0.113230\pi$
$773$	−1.34976	−	5.03736i	−0.0485474	−	0.181181i	−0.985942	+	0.167088i	$0.946564\pi$
$774$	−2.13283	−	3.77118i	−0.0766631	−	0.135552i
$775$		0			0
$776$	−44.7875	−	25.8581i	−1.60778	−	0.928250i
$777$	−1.15546	−	0.673969i	−0.0414519	−	0.0241785i
$778$	3.99745	−	14.9187i	0.143316	−	0.534861i
$779$	11.8737			0.425420
$780$		0			0
$781$	13.4057			0.479695
$782$	−8.00855	+	29.8883i	−0.286385	+	1.06880i
$783$	12.5475	+	22.4177i	0.448410	+	0.801144i
$784$	−10.7147	−	6.18613i	−0.382667	−	0.220933i
$785$		0			0
$786$	−1.67199	+	1.65720i	−0.0596378	+	0.0591102i
$787$	10.3710	+	38.7052i	0.369687	+	1.37969i	0.860954	+	0.508683i	$0.169867\pi$
$787$	10.3710	+	38.7052i	0.369687	+	1.37969i	−0.491267	+	0.871009i	$0.663466\pi$
$788$	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
$792$	11.2278	+	43.4435i	0.398964	+	1.54370i
$793$	48.3532	−	19.0468i	1.71707	−	0.676373i
$794$	35.2836			1.25217
$795$		0			0
$796$	5.01980	+	8.69455i	0.177922	+	0.308170i
$797$	8.95658	+	33.4264i	0.317259	+	1.18402i	0.921868	+	0.387503i	$0.126662\pi$
$797$	8.95658	+	33.4264i	0.317259	+	1.18402i	−0.604610	+	0.796522i	$0.706671\pi$
$798$	−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
$802$	1.26638	−	0.339325i	0.0447174	−	0.0119820i
$803$	9.72871	−	36.3080i	0.343319	−	1.28128i
$804$	−0.969378	+	0.255133i	−0.0341873	+	0.00899785i
$805$		0			0
$806$	5.68838	+	7.68740i	0.200365	+	0.270777i
$807$	−1.11473	−	1.95073i	−0.0392403	−	0.0686691i
$808$	12.0667	−	45.0335i	0.424504	−	1.58427i
$809$	−0.776492	−	1.34492i	−0.0273000	−	0.0472850i	0.852053	−	0.523456i	$-0.175358\pi$
$809$	−0.776492	−	1.34492i	−0.0273000	−	0.0472850i	−0.879353	+	0.476171i	$0.842024\pi$
$810$		0			0
$811$			15.7167i			0.551889i	0.961174	+	0.275945i	$0.0889906\pi$
$811$			15.7167i			0.551889i	−0.961174	+	0.275945i	$0.911009\pi$
$812$	−0.631612	+	0.169240i	−0.0221652	+	0.00593915i
$813$	−0.0471338	+	10.6078i	−0.00165306	+	0.372031i
$814$	−24.8643			−0.871494
$815$		0			0
$816$	−3.77397	−	14.3392i	−0.132115	−	0.501973i
$817$	−3.49325	−	0.936013i	−0.122213	−	0.0327470i
$818$	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	$0.526593\pi$
$822$	−6.66332	−	3.88665i	−0.232410	−	0.135562i
$823$	−11.9360	−	44.5459i	−0.416064	−	1.55277i	−0.782695	−	0.622405i	$-0.786156\pi$
$823$	−11.9360	−	44.5459i	−0.416064	−	1.55277i	0.366631	−	0.930366i	$-0.380511\pi$
$824$			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	0.995150	−	0.0983687i	$-0.0313625\pi$
$827$	25.7893	+	25.7893i	0.896781	+	0.896781i	−0.0983687	+	0.995150i	$0.531362\pi$
$828$	−13.4497	−	3.73225i	−0.467409	−	0.129705i
$829$	35.8684	−	20.7086i	1.24576	−	0.719241i	0.275500	−	0.961301i	$-0.411157\pi$
$829$	35.8684	−	20.7086i	1.24576	−	0.719241i	0.970261	+	0.242060i	$0.0778232\pi$
$830$		0			0
$831$	−4.73959	+	17.3791i	−0.164414	+	0.602875i
$832$	−18.2821	+	22.9838i	−0.633819	+	0.796820i
$833$	−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
$837$	0.167420	−	12.5590i	0.00578689	−	0.434103i
$838$	−11.2591	+	3.01687i	−0.388939	+	0.104216i
$839$	−12.9769	−	7.49223i	−0.448013	−	0.258660i	0.258978	−	0.965883i	$-0.416614\pi$
$839$	−12.9769	−	7.49223i	−0.448013	−	0.258660i	−0.706991	+	0.707223i	$0.749948\pi$
$840$		0			0
$841$	2.27790	−	3.94543i	0.0785481	−	0.136049i
$842$	−25.3048	−	6.78040i	−0.872061	−	0.233668i
$843$	−19.1354	+	32.8060i	−0.659058	+	1.12990i
$844$		−	3.82643i		−	0.131711i
$845$		0			0
$846$	14.3688	+	8.46696i	0.494009	+	0.291100i
$847$	−2.04915	−	0.549067i	−0.0704095	−	0.0188662i
$848$	2.17362	−	8.11205i	0.0746424	−	0.278569i
$849$	−6.81911	+	6.75878i	−0.234031	+	0.231961i
$850$		0			0
$851$	13.5842	−	23.5286i	0.465662	−	0.806550i
$852$	0.0168447	−	3.79101i	0.000577090	−	0.129878i
$853$	9.05692	+	9.05692i	0.310103	+	0.310103i	0.844949	−	0.534846i	$-0.179631\pi$
$853$	9.05692	+	9.05692i	0.310103	+	0.310103i	−0.534846	+	0.844949i	$0.679631\pi$
$854$	−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	$0.149293\pi$
$858$	−26.9428	+	19.7520i	−0.919812	+	0.674321i
$859$			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
$861$	0.316527	+	1.20265i	0.0107872	+	0.0409860i
$862$	−17.7024	+	4.74335i	−0.602947	+	0.161559i
$863$	21.3829	−	21.3829i	0.727881	−	0.727881i	−0.242316	−	0.970197i	$-0.577907\pi$
$863$	21.3829	−	21.3829i	0.727881	−	0.727881i	0.970197	+	0.242316i	$0.0779072\pi$
$864$	21.0975	−	5.35269i	0.717751	−	0.182102i
$865$		0			0
$866$	30.1629			1.02498
$867$	0.0482893	−	10.8678i	0.00163999	−	0.369090i
$868$	0.308798	+	0.0827422i	0.0104813	+	0.00280845i
$869$	−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
$873$	−36.0750	+	35.4395i	−1.22095	+	1.19944i
$874$	15.2627	−	8.81191i	0.516268	−	0.298067i
$875$		0			0
$876$	−10.2553	−	2.79680i	−0.346495	−	0.0944952i
$877$	−3.95038	−	14.7430i	−0.133395	−	0.497836i	0.866604	−	0.498996i	$-0.166298\pi$
$877$	−3.95038	−	14.7430i	−0.133395	−	0.497836i	−0.999999	+	0.00115930i	$0.999631\pi$
$878$	5.42659	+	20.2523i	0.183139	+	0.683483i
$879$	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	$0.234842\pi$
$882$	−16.3731	+	16.0846i	−0.551311	+	0.541598i
$883$	−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
$887$	−31.0745	−	8.32639i	−1.04338	−	0.279573i	−0.303867	−	0.952715i	$-0.598278\pi$
$887$	−31.0745	−	8.32639i	−1.04338	−	0.279573i	−0.739514	+	0.673142i	$0.764944\pi$
$888$	−0.109744	+	24.6987i	−0.00368278	+	0.828833i
$889$	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
$893$	13.4471	−	3.60314i	0.449991	−	0.120575i
$894$	2.82234	+	10.7235i	0.0943930	+	0.358646i
$895$		0			0
$896$		−	0.0930361i		−	0.00310812i
$897$	−3.97111	−	36.2866i	−0.132591	−	1.21157i
$898$	−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
$903$	0.00168300	−	0.378771i	5.60068e−5	−	0.0126047i
$904$	−22.9026	+	39.6684i	−0.761728	+	1.31935i
$905$		0			0
$906$	22.2184	−	22.0218i	0.738156	−	0.731625i
$907$	3.44249	−	12.8475i	0.114306	−	0.426596i	−0.884928	−	0.465728i	$-0.845793\pi$
$907$	3.44249	−	12.8475i	0.114306	−	0.426596i	0.999234	+	0.0391321i	$0.0124593\pi$
$908$	−20.4156	−	5.47035i	−0.677517	−	0.181540i
$909$	−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	$-0.0328831\pi$
$912$	−4.25507	+	7.29495i	−0.140899	+	0.241560i
$913$	−10.7219	−	2.87291i	−0.354841	−	0.0950795i
$914$	1.91698	−	3.32031i	0.0634081	−	0.109826i
$915$		0			0
$916$	4.40388	+	2.54258i	0.145508	+	0.0840092i
$917$	−0.198797	+	0.0532676i	−0.00656486	+	0.00175905i
$918$	−27.5044	−	0.366652i	−0.907779	−	0.0121013i
$919$	51.3893	+	29.6696i	1.69518	+	0.978711i	0.950210	+	0.311611i	$0.100868\pi$
$919$	51.3893	+	29.6696i	1.69518	+	0.978711i	0.744968	+	0.667101i	$0.232465\pi$
$920$		0			0
$921$	9.79712	+	37.2242i	0.322826	+	1.22658i
$922$	−2.42842	−	2.42842i	−0.0799759	−	0.0799759i
$923$	9.22458	−	3.63366i	0.303631	−	0.119603i
$924$	−0.293837	+	1.07744i	−0.00966654	+	0.0354453i
$925$		0			0
$926$	−36.9249	+	21.3186i	−1.21343	+	0.700573i
$927$	50.7295	+	14.0773i	1.66617	+	0.462358i
$928$	14.6443	+	14.6443i	0.480722	+	0.480722i
$929$	−9.30395	−	5.37164i	−0.305253	−	0.176238i	0.339548	−	0.940589i	$-0.389726\pi$
$929$	−9.30395	−	5.37164i	−0.305253	−	0.176238i	−0.644800	+	0.764351i	$0.723059\pi$
$930$		0			0
$931$			19.1587i			0.627900i
$932$	3.75954	+	14.0308i	0.123148	+	0.459594i
$933$	−40.8445	−	23.8242i	−1.33719	−	0.779969i
$934$	−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	0.813124	−	0.582090i	$-0.197765\pi$
$937$	7.07205	+	7.07205i	0.231034	+	0.231034i	−0.582090	+	0.813124i	$0.697765\pi$
$938$	0.128042	+	0.0343089i	0.00418073	+	0.00112022i
$939$	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	$0.653322\pi$
$942$	−0.0615599	+	13.8545i	−0.00200573	+	0.451402i
$943$	−24.3975	+	6.53730i	−0.794494	+	0.212884i
$944$			17.4051i			0.566486i
$945$		0			0
$946$	−3.52033	−	6.09738i	−0.114456	−	0.198243i
$947$	−4.02771	+	15.0316i	−0.130883	+	0.488461i	−0.999981	−	0.00617839i	$-0.998033\pi$
$947$	−4.02771	+	15.0316i	−0.130883	+	0.488461i	0.869098	+	0.494640i	$0.164700\pi$
$948$	5.05683	+	8.84926i	0.164238	+	0.287411i
$949$	−3.14701	−	27.6208i	−0.102156	−	0.896610i
$950$		0			0
$951$	−15.7511	+	4.14558i	−0.510765	+	0.134430i
$952$	0.636511	−	2.37549i	0.0206294	−	0.0769901i
$953$	−38.2209	+	10.2413i	−1.23810	+	0.331747i	−0.817727	−	0.575607i	$-0.804766\pi$
$953$	−38.2209	+	10.2413i	−1.23810	+	0.331747i	−0.420369	+	0.907353i	$0.638099\pi$
$954$	−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
$958$	−0.0383684	−	0.143193i	−0.00123963	−	0.00462635i
$959$	−0.337201	−	0.584050i	−0.0108888	−	0.0188600i
$960$		0			0
$961$	25.1572			0.811521
$962$	−17.1093	+	6.73955i	−0.551627	+	0.217292i
$963$	−1.63843	−	6.33951i	−0.0527976	−	0.204288i
$964$	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	0.0439297	−	0.999035i	$-0.486012\pi$
$967$	32.4327	−	32.4327i	1.04296	−	1.04296i	0.999035	−	0.0439297i	$-0.0139877\pi$
$968$	10.1381	+	37.8361i	0.325852	+	1.21610i
$969$	−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	$0.484687\pi$
$972$	0.275641	−	12.4050i	0.00884120	−	0.397891i
$973$	0.317646	−	1.18547i	0.0101833	−	0.0380045i
$974$	−10.7050			−0.343009
$975$		0			0
$976$	25.5766			0.818686
$977$	−0.617472	+	2.30444i	−0.0197547	+	0.0737254i	−0.975100	−	0.221768i	$-0.928817\pi$
$977$	−0.617472	+	2.30444i	−0.0197547	+	0.0737254i	0.955345	+	0.295493i	$0.0954840\pi$
$978$	36.0769	+	21.0433i	1.15361	+	0.672890i
$979$	−29.1781	−	16.8460i	−0.932536	−	0.538400i
$980$		0			0
$981$	−15.2226	−	26.9159i	−0.486019	−	0.859357i
$982$	6.18915	+	23.0982i	0.197504	+	0.737094i
$983$	−2.74521	+	2.74521i	−0.0875586	+	0.0875586i	−0.749530	−	0.661971i	$-0.769720\pi$
$983$	−2.74521	+	2.74521i	−0.0875586	+	0.0875586i	0.661971	+	0.749530i	$0.269720\pi$
$984$	16.3088	−	16.1645i	0.519904	−	0.515305i
$985$		0			0
$986$	−13.0863	−	22.6661i	−0.416752	−	0.721836i
$987$	0.723420	+	1.26596i	0.0230267	+	0.0402959i
$988$	7.79937	+	1.16562i	0.248131	+	0.0370833i
$989$	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	$0.920694\pi$
$992$	−2.62062	−	9.78028i	−0.0832047	−	0.310524i
$993$	−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
$997$	5.72683	−	1.53450i	0.181371	−	0.0485981i	−0.166991	−	0.985958i	$-0.553405\pi$
$997$	5.72683	−	1.53450i	0.181371	−	0.0485981i	0.348361	+	0.937360i	$0.386738\pi$
$998$	−5.16292	+	19.2683i	−0.163429	+	0.609927i
$999$	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.257.17		96
3.2	odd	2	inner	975.2.bn.d.257.8		96
5.2	odd	4		195.2.bf.a.23.17	yes	96
5.3	odd	4	inner	975.2.bn.d.218.8		96
5.4	even	2		195.2.bf.a.62.8	yes	96
13.4	even	6	inner	975.2.bn.d.407.17		96
15.2	even	4		195.2.bf.a.23.8	yes	96
15.8	even	4	inner	975.2.bn.d.218.17		96
15.14	odd	2		195.2.bf.a.62.17	yes	96
39.17	odd	6	inner	975.2.bn.d.407.8		96
65.4	even	6		195.2.bf.a.17.8	✓	96
65.17	odd	12		195.2.bf.a.173.17	yes	96
65.43	odd	12	inner	975.2.bn.d.368.8		96
195.17	even	12		195.2.bf.a.173.8	yes	96
195.134	odd	6		195.2.bf.a.17.17	yes	96
195.173	even	12	inner	975.2.bn.d.368.17		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.8	✓	96	65.4	even	6
195.2.bf.a.17.17	yes	96	195.134	odd	6
195.2.bf.a.23.8	yes	96	15.2	even	4
195.2.bf.a.23.17	yes	96	5.2	odd	4
195.2.bf.a.62.8	yes	96	5.4	even	2
195.2.bf.a.62.17	yes	96	15.14	odd	2
195.2.bf.a.173.8	yes	96	195.17	even	12
195.2.bf.a.173.17	yes	96	65.17	odd	12
975.2.bn.d.218.8		96	5.3	odd	4	inner
975.2.bn.d.218.17		96	15.8	even	4	inner
975.2.bn.d.257.8		96	3.2	odd	2	inner
975.2.bn.d.257.17		96	1.1	even	1	trivial
975.2.bn.d.368.8		96	65.43	odd	12	inner
975.2.bn.d.368.17		96	195.173	even	12	inner
975.2.bn.d.407.8		96	39.17	odd	6	inner
975.2.bn.d.407.17		96	13.4	even	6	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+(0.283997 - 1.05989i) q^{2} +(-0.872682 + 1.49614i) q^{3} +(0.689337 + 0.397989i) q^{4} +(1.33790 + 1.34985i) q^{6} +(0.0430045 + 0.160495i) q^{7} +(2.16938 - 2.16938i) q^{8} +(-1.47685 - 2.61130i) q^{9} +(-2.43760 - 4.22205i) q^{11} +(-1.19702 + 0.684025i) q^{12} +(-2.82173 - 2.24451i) q^{13} +0.182320 q^{14} +(-0.887232 - 1.53673i) q^{16} +(-1.24864 - 4.65999i) q^{17} +(-3.18712 + 0.823701i) q^{18} +(-1.37389 + 2.37966i) q^{19} +(-0.277652 - 0.0757204i) q^{21} +(-5.16719 + 1.38454i) q^{22} +(1.51285 - 5.64603i) q^{23} +(1.35251 + 5.13887i) q^{24} +(-3.18030 + 2.35330i) q^{26} +(5.19569 + 0.0692622i) q^{27} +(-0.0342306 + 0.127750i) q^{28} +(2.47205 + 4.28172i) q^{29} -2.41720i q^{31} +(4.04612 - 1.08416i) q^{32} +(8.44403 + 0.0375196i) q^{33} -5.29369 q^{34} +(0.0212203 - 2.38784i) q^{36} +(4.48963 + 1.20299i) q^{37} +(2.13199 + 2.13199i) q^{38} +(5.82057 - 2.26296i) q^{39} +(-2.16059 - 3.74226i) q^{41} +(-0.159108 + 0.272776i) q^{42} +(0.340642 + 1.27129i) q^{43} -3.88056i q^{44} +(-5.55453 - 3.20691i) q^{46} +(-3.58251 - 3.58251i) q^{47} +(3.07343 + 0.0136563i) q^{48} +(6.03827 - 3.48620i) q^{49} +(8.06165 + 2.19855i) q^{51} +(-1.05184 - 2.67024i) q^{52} +(3.34661 + 3.34661i) q^{53} +(1.54897 - 5.48719i) q^{54} +(0.441468 + 0.254882i) q^{56} +(-2.36132 - 4.13222i) q^{57} +(5.24021 - 1.40411i) q^{58} +(-8.49452 - 4.90431i) q^{59} +(-7.20685 + 12.4826i) q^{61} +(-2.56197 - 0.686477i) q^{62} +(0.355590 - 0.349325i) q^{63} -8.14527i q^{64} +(2.43784 - 8.93909i) q^{66} +(0.702294 + 0.188179i) q^{67} +(0.993890 - 3.70925i) q^{68} +(7.12700 + 7.19061i) q^{69} +(-1.37489 + 2.38137i) q^{71} +(-8.86877 - 2.46106i) 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} +(-0.745469 - 6.81184i) q^{78} -7.39276i q^{79} +(-4.63781 + 7.71302i) q^{81} +(-4.57999 + 1.22720i) q^{82} +(1.60997 - 1.60997i) q^{83} +(-0.161260 - 0.162699i) q^{84} +1.44417 q^{86} +(-8.56336 - 0.0380499i) q^{87} +(-14.4473 - 3.87115i) q^{88} +(5.98500 - 3.45544i) q^{89} +(0.238885 - 0.549398i) q^{91} +(3.28992 - 3.28992i) q^{92} +(3.61646 + 2.10944i) q^{93} +(-4.81449 + 2.77964i) q^{94} +(-1.90893 + 6.99968i) q^{96} +(-4.36286 - 16.2824i) q^{97} +(-1.98014 - 7.38997i) 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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