LMFDB - Embedded newform 975.2.bn.d.368.7

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)

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")

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);

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			368.7
Character	$\chi$	$=$	975.368
Dual form			975.2.bn.d.257.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.381405 - 1.42342i) q^{2} +(1.70154 + 0.323695i) q^{3} +(-0.148609 + 0.0857994i) q^{4} +(-0.188219 - 2.54546i) q^{6} +(-1.06453 + 3.97287i) q^{7} +(-1.90523 - 1.90523i) q^{8} +(2.79044 + 1.10156i) q^{9} +(-2.13830 + 3.70364i) q^{11} +(-0.280636 + 0.0978867i) q^{12} +(-0.217053 + 3.59901i) q^{13} +6.06108 q^{14} +(-2.15688 + 3.73582i) q^{16} +(-0.606673 + 2.26413i) q^{17} +(0.503692 - 4.39212i) q^{18} +(2.42558 + 4.20123i) q^{19} +(-3.09733 + 6.41539i) q^{21} +(6.08741 + 1.63112i) q^{22} +(-0.730756 - 2.72722i) q^{23} +(-2.62510 - 3.85852i) q^{24} +(5.20570 - 1.06372i) q^{26} +(4.39147 + 2.77759i) q^{27} +(-0.182671 - 0.681739i) q^{28} +(0.553990 - 0.959539i) q^{29} -2.59652i q^{31} +(0.935116 + 0.250564i) q^{32} +(-4.83724 + 5.60972i) q^{33} +3.45421 q^{34} +(-0.509198 + 0.0757171i) q^{36} +(0.955101 - 0.255918i) q^{37} +(5.05499 - 5.05499i) q^{38} +(-1.53431 + 6.05359i) q^{39} +(-0.575209 + 0.996292i) q^{41} +(10.3131 + 1.96194i) q^{42} +(2.63809 - 9.84550i) q^{43} -0.733860i q^{44} +(-3.60327 + 2.08035i) q^{46} +(3.07931 - 3.07931i) q^{47} +(-4.87927 + 5.65846i) q^{48} +(-8.58827 - 4.95844i) q^{49} +(-1.76516 + 3.65613i) q^{51} +(-0.276537 - 0.553469i) q^{52} +(2.89463 - 2.89463i) q^{53} +(2.27876 - 7.31030i) q^{54} +(9.59737 - 5.54104i) q^{56} +(2.76729 + 7.93368i) q^{57} +(-1.57712 - 0.422589i) q^{58} +(-7.54722 + 4.35739i) q^{59} +(1.64416 + 2.84776i) q^{61} +(-3.69594 + 0.990323i) q^{62} +(-7.34684 + 9.91342i) q^{63} +7.20087i q^{64} +(9.82995 + 4.74586i) q^{66} +(-5.95621 + 1.59596i) q^{67} +(-0.104104 - 0.388523i) q^{68} +(-0.360619 - 4.87700i) q^{69} +(-4.38783 - 7.59994i) q^{71} +(-3.21771 - 7.41514i) q^{72} +(8.00201 - 8.00201i) q^{73} +(-0.728560 - 1.26190i) q^{74} +(-0.720926 - 0.416227i) q^{76} +(-12.4378 - 12.4378i) q^{77} +(9.20200 - 0.124901i) q^{78} -2.06111i q^{79} +(6.57314 + 6.14767i) q^{81} +(1.63753 + 0.438775i) q^{82} +(6.21215 + 6.21215i) q^{83} +(-0.0901463 - 1.21913i) q^{84} -15.0205 q^{86} +(1.25323 - 1.45336i) q^{87} +(11.1302 - 2.98233i) q^{88} +(3.27478 + 1.89069i) q^{89} +(-14.0673 - 4.69357i) q^{91} +(0.342591 + 0.342591i) q^{92} +(0.840480 - 4.41806i) q^{93} +(-5.55763 - 3.20870i) q^{94} +(1.51003 + 0.729035i) q^{96} +(-1.31670 + 4.91400i) q^{97} +(-3.78234 + 14.1159i) q^{98} +(-10.0466 + 7.97935i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) $ 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Character values

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

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

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 $

$2$	−0.381405	−	1.42342i	−0.269694	−	1.00651i	−0.959314	−	0.282340i	$-0.908889\pi$
$2$	−0.381405	−	1.42342i	−0.269694	−	1.00651i	0.689621	−	0.724171i	$-0.257777\pi$
$3$	1.70154	+	0.323695i	0.982382	+	0.186885i
$3$	1.70154	+	0.323695i	0.982382	+	0.186885i
$4$	−0.148609	+	0.0857994i	−0.0743045	+	0.0428997i
$5$		0			0
$5$		0			0
$6$	−0.188219	−	2.54546i	−0.0768400	−	1.03918i
$7$	−1.06453	+	3.97287i	−0.402353	+	1.50160i	0.406533	+	0.913636i	$0.366738\pi$
$7$	−1.06453	+	3.97287i	−0.402353	+	1.50160i	−0.808886	+	0.587966i	$0.799929\pi$
$8$	−1.90523	−	1.90523i	−0.673599	−	0.673599i
$9$	2.79044	+	1.10156i	0.930148	+	0.367186i
$10$		0			0
$11$	−2.13830	+	3.70364i	−0.644722	+	1.11669i	0.339644	+	0.940554i	$0.389693\pi$
$11$	−2.13830	+	3.70364i	−0.644722	+	1.11669i	−0.984366	+	0.176137i	$0.943640\pi$
$12$	−0.280636	+	0.0978867i	−0.0810127	+	0.0282575i
$13$	−0.217053	+	3.59901i	−0.0601997	+	0.998186i
$13$	−0.217053	+	3.59901i	−0.0601997	+	0.998186i
$14$	6.06108			1.61989
$15$		0			0
$16$	−2.15688	+	3.73582i	−0.539219	+	0.933955i
$17$	−0.606673	+	2.26413i	−0.147140	+	0.549133i	0.852511	+	0.522709i	$0.175079\pi$
$17$	−0.606673	+	2.26413i	−0.147140	+	0.549133i	−0.999651	+	0.0264240i	$0.991588\pi$
$18$	0.503692	−	4.39212i	0.118721	−	1.03523i
$19$	2.42558	+	4.20123i	0.556466	+	0.963827i	0.997788	+	0.0664784i	$0.0211764\pi$
$19$	2.42558	+	4.20123i	0.556466	+	0.963827i	−0.441322	+	0.897349i	$0.645490\pi$
$20$		0			0
$21$	−3.09733	+	6.41539i	−0.675892	+	1.39995i
$22$	6.08741	+	1.63112i	1.29784	+	0.347755i
$23$	−0.730756	−	2.72722i	−0.152373	−	0.568664i	−0.999316	−	0.0369803i	$-0.988226\pi$
$23$	−0.730756	−	2.72722i	−0.152373	−	0.568664i	0.846943	−	0.531684i	$-0.178441\pi$
$24$	−2.62510	−	3.85852i	−0.535845	−	0.787617i
$25$		0			0
$26$	5.20570	−	1.06372i	1.02092	−	0.208613i
$27$	4.39147	+	2.77759i	0.845138	+	0.534548i
$28$	−0.182671	−	0.681739i	−0.0345217	−	0.128837i
$29$	0.553990	−	0.959539i	0.102873	−	0.178182i	−0.809994	−	0.586438i	$-0.800530\pi$
$29$	0.553990	−	0.959539i	0.102873	−	0.178182i	0.912867	+	0.408256i	$0.133863\pi$
$30$		0			0
$31$		−	2.59652i		−	0.466348i	−0.972435	−	0.233174i	$-0.925089\pi$
$31$		−	2.59652i		−	0.466348i	0.972435	−	0.233174i	$-0.0749112\pi$
$32$	0.935116	+	0.250564i	0.165307	+	0.0442938i
$33$	−4.83724	+	5.60972i	−0.842056	+	0.976528i
$34$	3.45421			0.592391
$35$		0			0
$36$	−0.509198	+	0.0757171i	−0.0848663	+	0.0126195i
$37$	0.955101	−	0.255918i	0.157018	−	0.0420727i	−0.179454	−	0.983766i	$-0.557433\pi$
$37$	0.955101	−	0.255918i	0.157018	−	0.0420727i	0.336472	+	0.941694i	$0.390766\pi$
$38$	5.05499	−	5.05499i	0.820027	−	0.820027i
$39$	−1.53431	+	6.05359i	−0.245686	+	0.969350i
$40$		0			0
$41$	−0.575209	+	0.996292i	−0.0898326	+	0.155595i	−0.907440	−	0.420181i	$-0.861967\pi$
$41$	−0.575209	+	0.996292i	−0.0898326	+	0.155595i	0.817608	+	0.575776i	$0.195300\pi$
$42$	10.3131	+	1.96194i	1.59135	+	0.302734i
$43$	2.63809	−	9.84550i	0.402305	−	1.50142i	−0.406666	−	0.913577i	$-0.633309\pi$
$43$	2.63809	−	9.84550i	0.402305	−	1.50142i	0.808972	−	0.587847i	$-0.200024\pi$
$44$		−	0.733860i		−	0.110634i
$45$		0			0
$46$	−3.60327	+	2.08035i	−0.531273	+	0.306730i
$47$	3.07931	−	3.07931i	0.449164	−	0.449164i	−0.445913	−	0.895077i	$-0.647121\pi$
$47$	3.07931	−	3.07931i	0.449164	−	0.449164i	0.895077	+	0.445913i	$0.147121\pi$
$48$	−4.87927	+	5.65846i	−0.704261	+	0.816728i
$49$	−8.58827	−	4.95844i	−1.22690	−	0.708349i
$50$		0			0
$51$	−1.76516	+	3.65613i	−0.247172	+	0.511960i
$52$	−0.276537	−	0.553469i	−0.0383488	−	0.0767523i
$53$	2.89463	−	2.89463i	0.397608	−	0.397608i	−0.479780	−	0.877389i	$-0.659284\pi$
$53$	2.89463	−	2.89463i	0.397608	−	0.397608i	0.877389	+	0.479780i	$0.159284\pi$
$54$	2.27876	−	7.31030i	0.310100	−	0.994805i
$55$		0			0
$56$	9.59737	−	5.54104i	1.28250	−	0.740453i
$57$	2.76729	+	7.93368i	0.366537	+	1.05084i
$58$	−1.57712	−	0.422589i	−0.207086	−	0.0554886i
$59$	−7.54722	+	4.35739i	−0.982564	+	0.567284i	−0.903043	−	0.429550i	$-0.858672\pi$
$59$	−7.54722	+	4.35739i	−0.982564	+	0.567284i	−0.0795208	+	0.996833i	$0.525339\pi$
$60$		0			0
$61$	1.64416	+	2.84776i	0.210513	+	0.364619i	0.951875	−	0.306486i	$-0.0991534\pi$
$61$	1.64416	+	2.84776i	0.210513	+	0.364619i	−0.741362	+	0.671105i	$0.765820\pi$
$62$	−3.69594	+	0.990323i	−0.469385	+	0.125771i
$63$	−7.34684	+	9.91342i	−0.925615	+	1.24897i
$64$			7.20087i			0.900109i
$65$		0			0
$66$	9.82995	+	4.74586i	1.20998	+	0.584175i
$67$	−5.95621	+	1.59596i	−0.727667	+	0.194978i	−0.603590	−	0.797295i	$-0.706264\pi$
$67$	−5.95621	+	1.59596i	−0.727667	+	0.194978i	−0.124077	+	0.992273i	$0.539597\pi$
$68$	−0.104104	−	0.388523i	−0.0126245	−	0.0471153i
$69$	−0.360619	−	4.87700i	−0.0434135	−	0.587122i
$70$		0			0
$71$	−4.38783	−	7.59994i	−0.520739	−	0.901947i	−0.999709	−	0.0241156i	$-0.992323\pi$
$71$	−4.38783	−	7.59994i	−0.520739	−	0.901947i	0.478970	−	0.877831i	$-0.341010\pi$
$72$	−3.21771	−	7.41514i	−0.379210	−	0.873882i
$73$	8.00201	−	8.00201i	0.936565	−	0.936565i	−0.0615398	−	0.998105i	$-0.519601\pi$
$73$	8.00201	−	8.00201i	0.936565	−	0.936565i	0.998105	+	0.0615398i	$0.0196011\pi$
$74$	−0.728560	−	1.26190i	−0.0846934	−	0.146693i
$75$		0			0
$76$	−0.720926	−	0.416227i	−0.0826958	−	0.0477445i
$77$	−12.4378	−	12.4378i	−1.41742	−	1.41742i
$78$	9.20200	−	0.124901i	1.04192	−	0.0141423i
$79$		−	2.06111i		−	0.231893i	−0.993255	−	0.115946i	$-0.963010\pi$
$79$		−	2.06111i		−	0.231893i	0.993255	−	0.115946i	$-0.0369901\pi$
$80$		0			0
$81$	6.57314	+	6.14767i	0.730349	+	0.683074i
$82$	1.63753	+	0.438775i	0.180835	+	0.0484546i
$83$	6.21215	+	6.21215i	0.681872	+	0.681872i	0.960422	−	0.278550i	$-0.0898538\pi$
$83$	6.21215	+	6.21215i	0.681872	+	0.681872i	−0.278550	+	0.960422i	$0.589854\pi$
$84$	−0.0901463	−	1.21913i	−0.00983576	−	0.133018i
$85$		0			0
$86$	−15.0205			−1.61970
$87$	1.25323	−	1.45336i	0.134360	−	0.155817i
$88$	11.1302	−	2.98233i	1.18649	−	0.317918i
$89$	3.27478	+	1.89069i	0.347126	+	0.200413i	0.663419	−	0.748248i	$-0.269105\pi$
$89$	3.27478	+	1.89069i	0.347126	+	0.200413i	−0.316293	+	0.948662i	$0.602438\pi$
$90$		0			0
$91$	−14.0673	−	4.69357i	−1.47466	−	0.492019i
$92$	0.342591	+	0.342591i	0.0357175	+	0.0357175i
$93$	0.840480	−	4.41806i	0.0871537	−	0.458132i
$94$	−5.55763	−	3.20870i	−0.573225	−	0.330952i
$95$		0			0
$96$	1.51003	+	0.729035i	0.154116	+	0.0744068i
$97$	−1.31670	+	4.91400i	−0.133691	+	0.498941i	−1.00000		0.000567486i	$-0.999819\pi$
$97$	−1.31670	+	4.91400i	−0.133691	+	0.498941i	0.866309	+	0.499508i	$0.166486\pi$
$98$	−3.78234	+	14.1159i	−0.382075	+	1.42592i
$99$	−10.0466	+	7.97935i	−1.00972	+	0.801955i
$100$		0			0
$101$	16.9579	+	9.79064i	1.68737	+	0.974205i	0.956518	+	0.291673i	$0.0942119\pi$
$101$	16.9579	+	9.79064i	1.68737	+	0.974205i	0.730855	+	0.682533i	$0.239121\pi$
$102$	5.87745	+	1.11811i	0.581954	+	0.110709i
$103$	−11.6815	−	11.6815i	−1.15101	−	1.15101i	−0.986350	−	0.164663i	$-0.947346\pi$
$103$	−11.6815	−	11.6815i	−1.15101	−	1.15101i	−0.164663	−	0.986350i	$-0.552654\pi$
$104$	7.27046	−	6.44339i	0.712928	−	0.631827i
$105$		0			0
$106$	−5.22431	−	3.01626i	−0.507430	−	0.292965i
$107$	8.94599	−	2.39707i	0.864841	−	0.231734i	0.200986	−	0.979594i	$-0.435586\pi$
$107$	8.94599	−	2.39707i	0.864841	−	0.231734i	0.663856	+	0.747861i	$0.268919\pi$
$108$	−0.890927	−	0.0359895i	−0.0857295	−	0.00346309i
$109$	13.8177			1.32349			0.661746	−	0.749728i	$-0.269816\pi$
$109$	13.8177			1.32349			0.661746	+	0.749728i	$0.269816\pi$
$110$		0			0
$111$	1.70798	−	0.126293i	0.162114	−	0.0119872i
$112$	−12.5459	−	12.5459i	−1.18547	−	1.18547i
$113$	−1.38839	−	0.372017i	−0.130608	−	0.0349964i	0.192923	−	0.981214i	$-0.438203\pi$
$113$	−1.38839	−	0.372017i	−0.130608	−	0.0349964i	−0.323531	+	0.946218i	$0.604870\pi$
$114$	10.2375	−	6.96497i	0.958831	−	0.652329i
$115$		0			0
$116$			0.190128i			0.0176529i
$117$	−4.57019	+	9.80374i	−0.422514	+	0.906356i
$118$	9.08095	+	9.08095i	0.835969	+	0.835969i
$119$	−8.34928	−	4.82046i	−0.765377	−	0.441891i
$120$		0			0
$121$	−3.64466	−	6.31273i	−0.331332	−	0.573884i
$122$	3.42648	−	3.42648i	0.310219	−	0.310219i
$123$	−1.30123	+	1.50903i	−0.117328	+	0.136065i
$124$	0.222780	+	0.385866i	0.0200062	+	0.0346518i
$125$		0			0
$126$	16.9131	+	6.67663i	1.50674	+	0.594801i
$127$	0.770609	+	2.87595i	0.0683805	+	0.255199i	0.991651	−	0.128951i	$-0.0411610\pi$
$127$	0.770609	+	2.87595i	0.0683805	+	0.255199i	−0.923270	+	0.384150i	$0.874494\pi$
$128$	12.1201	−	3.24757i	1.07128	−	0.287048i
$129$	7.67575	−	15.8985i	0.675812	−	1.39979i
$130$		0			0
$131$		−	2.62072i		−	0.228973i	−0.993425	−	0.114487i	$-0.963478\pi$
$131$		−	2.62072i		−	0.228973i	0.993425	−	0.114487i	$-0.0365223\pi$
$132$	0.237547	−	1.24869i	0.0206758	−	0.108684i
$133$	−19.2730	+	5.16418i	−1.67118	+	0.447792i
$134$	4.54345	+	7.86949i	0.392494	+	0.679820i
$135$		0			0
$136$	5.46953	−	3.15784i	0.469009	−	0.270782i
$137$	10.0236	+	2.68583i	0.856377	+	0.229466i	0.660188	−	0.751100i	$-0.270477\pi$
$137$	10.0236	+	2.68583i	0.856377	+	0.229466i	0.196189	+	0.980566i	$0.437143\pi$
$138$	−6.80448	+	2.37342i	−0.579236	+	0.202039i
$139$	1.68558	−	0.973168i	0.142969	−	0.0825431i	−0.426809	−	0.904342i	$-0.640362\pi$
$139$	1.68558	−	0.973168i	0.142969	−	0.0825431i	0.569778	+	0.821799i	$0.307029\pi$
$140$		0			0
$141$	6.23632	−	4.24280i	0.525193	−	0.357308i
$142$	−9.14438	+	9.14438i	−0.767379	+	0.767379i
$143$	−12.8653	−	8.49966i	−1.07585	−	0.710777i
$144$	−10.1339	+	8.04867i	−0.844488	+	0.670722i
$145$		0			0
$146$	−14.4422	−	8.33823i	−1.19525	−	0.690077i
$147$	−13.0082	−	11.2169i	−1.07290	−	0.925158i
$148$	−0.119979	+	0.119979i	−0.00986220	+	0.00986220i
$149$	8.56121	−	4.94282i	0.701362	−	0.404931i	−0.106493	−	0.994313i	$-0.533962\pi$
$149$	8.56121	−	4.94282i	0.701362	−	0.404931i	0.807854	+	0.589382i	$0.200629\pi$
$150$		0			0
$151$		−	20.0349i		−	1.63042i	−0.579165	−	0.815210i	$-0.696621\pi$
$151$		−	20.0349i		−	1.63042i	0.579165	−	0.815210i	$-0.303379\pi$
$152$	3.38301	−	12.6256i	0.274398	−	1.02407i
$153$	−4.18696	+	5.64965i	−0.338496	+	0.456747i
$154$	−12.9604	+	22.4481i	−1.04438	+	1.80892i
$155$		0			0
$156$	−0.291383	−	1.03126i	−0.0233293	−	0.0825669i
$157$	5.41204	−	5.41204i	0.431928	−	0.431928i	−0.457356	−	0.889284i	$-0.651203\pi$
$157$	5.41204	−	5.41204i	0.431928	−	0.431928i	0.889284	+	0.457356i	$0.151203\pi$
$158$	−2.93383	+	0.786117i	−0.233403	+	0.0625401i
$159$	5.86230	−	3.98834i	0.464910	−	0.316296i
$160$		0			0
$161$	11.6128			0.915215
$162$	6.24369	−	11.7011i	0.490551	−	0.919325i
$163$	−6.76947	−	1.81388i	−0.530226	−	0.142074i	−0.0162335	−	0.999868i	$-0.505167\pi$
$163$	−6.76947	−	1.81388i	−0.530226	−	0.142074i	−0.513993	+	0.857795i	$0.671834\pi$
$164$		−	0.197410i		−	0.0154152i
$165$		0			0
$166$	6.47316	−	11.2118i	0.502415	−	0.870208i
$167$	6.59002	+	24.5943i	0.509951	+	1.90316i	0.420822	+	0.907143i	$0.361742\pi$
$167$	6.59002	+	24.5943i	0.509951	+	1.90316i	0.0891292	+	0.996020i	$0.471592\pi$
$168$	18.1239	−	6.32166i	1.39829	−	0.487726i
$169$	−12.9058	−	1.56235i	−0.992752	−	0.120181i
$170$		0			0
$171$	2.14055	+	14.3952i	0.163692	+	1.10083i
$172$	0.452694	+	1.68948i	0.0345176	+	0.128821i
$173$	18.5004	+	4.95717i	1.40656	+	0.376887i	0.880696	−	0.473681i	$-0.157075\pi$
$173$	18.5004	+	4.95717i	1.40656	+	0.376887i	0.525865	+	0.850568i	$0.323742\pi$
$174$	−2.54674	−	1.22956i	−0.193068	−	0.0932124i
$175$		0			0
$176$	−9.22410	−	15.9766i	−0.695292	−	1.20428i
$177$	−14.2523	+	4.97125i	−1.07127	+	0.373662i
$178$	1.44224	−	5.38251i	0.108100	−	0.403436i
$179$	−3.01935	+	5.22967i	−0.225677	+	0.390884i	−0.956522	−	0.291659i	$-0.905793\pi$
$179$	−3.01935	+	5.22967i	−0.225677	+	0.390884i	0.730845	+	0.682543i	$0.239126\pi$
$180$		0			0
$181$	5.56311			0.413503			0.206751	−	0.978394i	$-0.433711\pi$
$181$	5.56311			0.413503			0.206751	+	0.978394i	$0.433711\pi$
$182$	−1.31558	+	21.8139i	−0.0975170	+	1.61695i
$183$	1.87578	+	5.37777i	0.138662	+	0.397536i
$184$	−3.80371	+	6.58822i	−0.280413	+	0.485690i
$185$		0			0
$186$	−6.60933	+	0.488713i	−0.484620	+	0.0358342i
$187$	−7.08830	−	7.08830i	−0.518348	−	0.518348i
$188$	−0.193410	+	0.721817i	−0.0141059	+	0.0526439i
$189$	−15.7098	+	14.4899i	−1.14272	+	1.05398i
$190$		0			0
$191$	2.61637	−	1.51056i	0.189314	−	0.109300i	−0.402348	−	0.915487i	$-0.631806\pi$
$191$	2.61637	−	1.51056i	0.189314	−	0.109300i	0.591661	+	0.806187i	$0.298472\pi$
$192$	−2.33089	+	12.2525i	−0.168217	+	0.884251i
$193$	0.906445	+	3.38290i	0.0652473	+	0.243506i	0.990845	−	0.135002i	$-0.0431040\pi$
$193$	0.906445	+	3.38290i	0.0652473	+	0.243506i	−0.925598	+	0.378508i	$0.876437\pi$
$194$	7.49689			0.538245
$195$		0			0
$196$	1.70173			0.121552
$197$	−1.20138	−	4.48363i	−0.0855951	−	0.319445i	0.909831	−	0.414979i	$-0.136211\pi$
$197$	−1.20138	−	4.48363i	−0.0855951	−	0.319445i	−0.995426	+	0.0955335i	$0.969544\pi$
$198$	15.1898	+	11.2572i	1.07949	+	0.800012i
$199$	3.93217	−	2.27024i	0.278744	−	0.160933i	−0.354111	−	0.935204i	$-0.615216\pi$
$199$	3.93217	−	2.27024i	0.278744	−	0.160933i	0.632855	+	0.774271i	$0.281883\pi$
$200$		0			0
$201$	−10.6513	+	0.787588i	−0.751285	+	0.0555522i
$202$	7.46839	−	27.8724i	0.525474	−	1.96110i
$203$	3.22238	+	3.22238i	0.226167	+	0.226167i
$204$	−0.0513743	−	0.694783i	−0.00359692	−	0.0486446i
$205$		0			0
$206$	−12.1723	+	21.0831i	−0.848086	+	1.46893i
$207$	0.965054	−	8.41511i	0.0670759	−	0.584891i
$208$	−12.9771	−	8.57349i	−0.899800	−	0.594465i
$209$	−20.7465			−1.43506
$210$		0			0
$211$	−6.07034	+	10.5141i	−0.417899	+	0.723823i	−0.995728	−	0.0923352i	$-0.970567\pi$
$211$	−6.07034	+	10.5141i	−0.417899	+	0.723823i	0.577829	+	0.816158i	$0.303900\pi$
$212$	−0.181811	+	0.678526i	−0.0124868	+	0.0466014i
$213$	−5.00598	−	14.3519i	−0.343004	−	0.983375i
$214$	−6.82408	−	11.8197i	−0.466485	−	0.807975i
$215$		0			0
$216$	−3.07480	−	13.6587i	−0.209214	−	0.929355i
$217$	10.3156	+	2.76406i	0.700269	+	0.187637i
$218$	−5.27012	−	19.6684i	−0.356938	−	1.33211i
$219$	16.2059	−	11.0255i	1.09509	−	0.745034i
$220$		0			0
$221$	−8.01697	−	2.67486i	−0.539279	−	0.179931i
$222$	−0.831198	−	2.38300i	−0.0557864	−	0.159937i
$223$	4.52055	+	16.8709i	0.302718	+	1.12976i	0.934892	+	0.354933i	$0.115496\pi$
$223$	4.52055	+	16.8709i	0.302718	+	1.12976i	−0.632174	+	0.774827i	$0.717837\pi$
$224$	−1.99091	+	3.44836i	−0.133023	+	0.230403i
$225$		0			0
$226$			2.11815i			0.140897i
$227$	−9.26536	−	2.48265i	−0.614964	−	0.164779i	−0.0621264	−	0.998068i	$-0.519788\pi$
$227$	−9.26536	−	2.48265i	−0.614964	−	0.164779i	−0.552837	+	0.833289i	$0.686455\pi$
$228$	−1.09195	−	0.941584i	−0.0723161	−	0.0623579i
$229$	−5.60158			−0.370163			−0.185081	−	0.982723i	$-0.559255\pi$
$229$	−5.60158			−0.370163			−0.185081	+	0.982723i	$0.559255\pi$
$230$		0			0
$231$	−17.1373	−	25.1894i	−1.12755	−	1.65734i
$232$	−2.88361	+	0.772662i	−0.189318	+	0.0507277i
$233$	−19.2843	+	19.2843i	−1.26336	+	1.26336i	−0.313900	+	0.949456i	$0.601636\pi$
$233$	−19.2843	+	19.2843i	−1.26336	+	1.26336i	−0.949456	+	0.313900i	$0.898364\pi$
$234$	15.6980	+	2.76612i	1.02621	+	0.180827i
$235$		0			0
$236$	0.747723	−	1.29509i	0.0486726	−	0.0843034i
$237$	0.667171	−	3.50705i	0.0433374	−	0.227807i
$238$	−3.67709	+	13.7231i	−0.238351	+	0.889536i
$239$			17.3432i			1.12184i	0.827870	+	0.560921i	$0.189553\pi$
$239$			17.3432i			1.12184i	−0.827870	+	0.560921i	$0.810447\pi$
$240$		0			0
$241$	−1.44789	+	0.835937i	−0.0932665	+	0.0538475i	−0.545908	−	0.837845i	$-0.683815\pi$
$241$	−1.44789	+	0.835937i	−0.0932665	+	0.0538475i	0.452641	+	0.891693i	$0.350482\pi$
$242$	−7.59559	+	7.59559i	−0.488263	+	0.488263i
$243$	9.19446	+	12.5882i	0.589825	+	0.807531i
$244$	−0.488673	−	0.282135i	−0.0312841	−	0.0180619i
$245$		0			0
$246$	2.64429	+	1.27665i	0.168594	+	0.0813963i
$247$	−15.6467	+	7.81780i	−0.995578	+	0.497435i
$248$	−4.94695	+	4.94695i	−0.314131	+	0.314131i
$249$	8.55934	+	12.5810i	0.542426	+	0.797290i
$250$		0			0
$251$	6.81314	−	3.93357i	0.430042	−	0.248285i	−0.269323	−	0.963050i	$-0.586800\pi$
$251$	6.81314	−	3.93357i	0.430042	−	0.248285i	0.699364	+	0.714765i	$0.253466\pi$
$252$	0.241240	−	2.10358i	0.0151967	−	0.132513i
$253$	11.6632	+	3.12515i	0.733260	+	0.196477i
$254$	3.79978	−	2.19380i	0.238419	−	0.137651i
$255$		0			0
$256$	−2.04446	−	3.54111i	−0.127779	−	0.221319i
$257$	−9.19920	+	2.46492i	−0.573830	+	0.153757i	−0.534053	−	0.845451i	$-0.679332\pi$
$257$	−9.19920	+	2.46492i	−0.573830	+	0.153757i	−0.0397776	+	0.999209i	$0.512665\pi$
$258$	−25.5579	−	4.86205i	−1.59116	−	0.302698i
$259$			4.06692i			0.252706i
$260$		0			0
$261$	2.60286	−	2.06729i	0.161113	−	0.127962i
$262$	−3.73039	+	0.999554i	−0.230464	+	0.0617526i
$263$	−6.09110	−	22.7323i	−0.375593	−	1.40173i	−0.852476	−	0.522766i	$-0.824900\pi$
$263$	−6.09110	−	22.7323i	−0.375593	−	1.40173i	0.476883	−	0.878967i	$-0.341767\pi$
$264$	19.9038	−	1.47175i	1.22500	−	0.0905798i
$265$		0			0
$266$	14.7016	+	25.4640i	0.901414	+	1.56130i
$267$	4.96014	+	4.27711i	0.303556	+	0.261755i
$268$	0.748213	−	0.748213i	0.0457044	−	0.0457044i
$269$	−5.95253	−	10.3101i	−0.362932	−	0.628617i	0.625510	−	0.780216i	$-0.284891\pi$
$269$	−5.95253	−	10.3101i	−0.362932	−	0.628617i	−0.988442	+	0.151599i	$0.951558\pi$
$270$		0			0
$271$	−17.4412	−	10.0697i	−1.05947	−	0.611688i	−0.134188	−	0.990956i	$-0.542843\pi$
$271$	−17.4412	−	10.0697i	−1.05947	−	0.611688i	−0.925287	+	0.379268i	$0.876176\pi$
$272$	−7.14988	−	7.14988i	−0.433525	−	0.433525i
$273$	−22.4168	−	12.5398i	−1.35673	−	0.758943i
$274$		−	15.2923i		−	0.923839i
$275$		0			0
$276$	0.472035	+	0.693825i	0.0284132	+	0.0417633i
$277$	−4.24989	−	1.13875i	−0.255351	−	0.0684211i	0.128873	−	0.991661i	$-0.458864\pi$
$277$	−4.24989	−	1.13875i	−0.255351	−	0.0684211i	−0.384224	+	0.923240i	$0.625531\pi$
$278$	−2.02812	−	2.02812i	−0.121638	−	0.121638i
$279$	2.86021	−	7.24543i	0.171236	−	0.433773i
$280$		0			0
$281$	−23.0139			−1.37290			−0.686448	−	0.727179i	$-0.740831\pi$
$281$	−23.0139			−1.37290			−0.686448	+	0.727179i	$0.740831\pi$
$282$	−8.41785	−	7.25869i	−0.501276	−	0.432248i
$283$	−13.1933	+	3.53515i	−0.784263	+	0.210143i	−0.628663	−	0.777678i	$-0.716398\pi$
$283$	−13.1933	+	3.53515i	−0.784263	+	0.210143i	−0.155600	+	0.987820i	$0.549731\pi$
$284$	1.30414	+	0.752946i	0.0773865	+	0.0446791i
$285$		0			0
$286$	−7.19170	+	21.5546i	−0.425254	+	1.27455i
$287$	−3.34581	−	3.34581i	−0.197497	−	0.197497i
$288$	2.33338	+	1.72927i	0.137496	+	0.101898i
$289$	9.96418	+	5.75282i	0.586128	+	0.338401i
$290$		0			0
$291$	−3.83105	+	7.93513i	−0.224580	+	0.465166i
$292$	−0.502603	+	1.87574i	−0.0294126	+	0.109769i
$293$	−6.27918	+	23.4342i	−0.366834	+	1.36904i	0.498084	+	0.867129i	$0.334037\pi$
$293$	−6.27918	+	23.4342i	−0.366834	+	1.36904i	−0.864918	+	0.501914i	$0.832630\pi$
$294$	−11.0050	+	22.7944i	−0.641827	+	1.32940i
$295$		0			0
$296$	−2.30726	−	1.33210i	−0.134107	−	0.0774267i
$297$	−19.6775	+	10.3251i	−1.14180	+	0.599124i
$298$	−10.3010	−	10.3010i	−0.596721	−	0.596721i
$299$	9.97390	−	2.03805i	0.576806	−	0.117863i
$300$		0			0
$301$	36.3065	+	20.9616i	2.09267	+	1.20821i
$302$	−28.5182	+	7.64142i	−1.64104	+	0.439714i
$303$	25.6853	+	22.1483i	1.47558	+	1.27239i
$304$	−20.9267			−1.20023
$305$		0			0
$306$	9.63876	+	3.80501i	0.551011	+	0.217518i
$307$	12.8951	+	12.8951i	0.735962	+	0.735962i	0.971794	−	0.235832i	$-0.0757814\pi$
$307$	12.8951	+	12.8951i	0.735962	+	0.735962i	−0.235832	+	0.971794i	$0.575781\pi$
$308$	2.91553	+	0.781213i	0.166128	+	0.0445137i
$309$	−16.0952	−	23.6577i	−0.915626	−	1.34584i
$310$		0			0
$311$			8.39481i			0.476026i	0.971262	+	0.238013i	$0.0764960\pi$
$311$			8.39481i			0.476026i	−0.971262	+	0.238013i	$0.923504\pi$
$312$	14.4566	−	8.61024i	0.818446	−	0.487459i
$313$	0.445796	+	0.445796i	0.0251979	+	0.0251979i	0.719593	−	0.694396i	$-0.244328\pi$
$313$	0.445796	+	0.445796i	0.0251979	+	0.0251979i	−0.694396	+	0.719593i	$0.744328\pi$
$314$	−9.76780	−	5.63944i	−0.551229	−	0.318252i
$315$		0			0
$316$	0.176842	+	0.306299i	0.00994814	+	0.0172307i
$317$	12.5839	−	12.5839i	0.706781	−	0.706781i	−0.259076	−	0.965857i	$-0.583418\pi$
$317$	12.5839	−	12.5839i	0.706781	−	0.706781i	0.965857	+	0.259076i	$0.0834179\pi$
$318$	−7.91300	−	6.82335i	−0.443739	−	0.382634i
$319$	2.36919	+	4.10356i	0.132649	+	0.229755i
$320$		0			0
$321$	15.9978	−	1.18293i	0.892912	−	0.0660245i
$322$	−4.42917	−	16.5299i	−0.246828	−	0.921174i
$323$	−10.9837	+	2.94307i	−0.611148	+	0.163757i
$324$	−1.50429	−	0.349626i	−0.0835719	−	0.0194237i
$325$		0			0
$326$			10.3276i			0.571995i
$327$	23.5112	+	4.47271i	1.30017	+	0.247341i
$328$	2.99406	−	0.802257i	0.165319	−	0.0442972i
$329$	8.95569	+	15.5117i	0.493743	+	0.855188i
$330$		0			0
$331$	−12.2822	+	7.09113i	−0.675091	+	0.389764i	−0.798003	−	0.602654i	$-0.794110\pi$
$331$	−12.2822	+	7.09113i	−0.675091	+	0.389764i	0.122912	+	0.992418i	$0.460777\pi$
$332$	−1.45618	−	0.390182i	−0.0799182	−	0.0214140i
$333$	2.94706	+	0.337972i	0.161498	+	0.0185208i
$334$	32.4946	−	18.7608i	1.77802	−	1.02654i
$335$		0			0
$336$	−17.2862	−	25.4082i	−0.943038	−	1.38613i
$337$	5.88105	−	5.88105i	0.320361	−	0.320361i	−0.528544	−	0.848906i	$-0.677262\pi$
$337$	5.88105	−	5.88105i	0.320361	−	0.320361i	0.848906	+	0.528544i	$0.177262\pi$
$338$	2.69843	+	18.9663i	0.146775	+	1.03163i
$339$	−2.24197	−	1.08241i	−0.121767	−	0.0587886i
$340$		0			0
$341$	9.61657	+	5.55213i	0.520767	+	0.300665i
$342$	19.6740	−	8.53730i	1.06385	−	0.461644i
$343$	8.48328	−	8.48328i	0.458054	−	0.458054i
$344$	−23.7840	+	13.7317i	−1.28235	+	0.740365i
$345$		0			0
$346$		−	28.2246i		−	1.51736i
$347$	1.26288	−	4.71314i	0.0677950	−	0.253014i	−0.923708	−	0.383097i	$-0.874858\pi$
$347$	1.26288	−	4.71314i	0.0677950	−	0.253014i	0.991503	+	0.130082i	$0.0415242\pi$
$348$	−0.0615435	+	0.323510i	−0.00329908	+	0.0173419i
$349$	−6.13414	+	10.6246i	−0.328353	+	0.568724i	−0.982185	−	0.187916i	$-0.939827\pi$
$349$	−6.13414	+	10.6246i	−0.328353	+	0.568724i	0.653832	+	0.756640i	$0.273160\pi$
$350$		0			0
$351$	−10.9498	+	15.2021i	−0.584455	+	0.811426i
$352$	−2.92756	+	2.92756i	−0.156039	+	0.156039i
$353$	−10.4429	+	2.79817i	−0.555820	+	0.148932i	−0.525785	−	0.850617i	$-0.676229\pi$
$353$	−10.4429	+	2.79817i	−0.555820	+	0.148932i	−0.0300349	+	0.999549i	$0.509562\pi$
$354$	12.5121	+	18.3910i	0.665010	+	0.977471i
$355$		0			0
$356$	−0.648882			−0.0343907
$357$	−12.6462	−	10.9048i	−0.669310	−	0.577143i
$358$	8.59563	+	2.30319i	0.454293	+	0.121727i
$359$		−	37.2979i		−	1.96851i	−0.176755	−	0.984255i	$-0.556560\pi$
$359$		−	37.2979i		−	1.96851i	0.176755	−	0.984255i	$-0.443440\pi$
$360$		0			0
$361$	−2.26687	+	3.92633i	−0.119309	+	0.206649i
$362$	−2.12180	−	7.91865i	−0.111519	−	0.416195i
$363$	−4.15811	−	11.9211i	−0.218244	−	0.625695i
$364$	2.49324	−	0.509463i	0.130681	−	0.0267031i
$365$		0			0
$366$	6.93940	−	4.72114i	0.362728	−	0.246778i
$367$	0.169976	+	0.634359i	0.00887268	+	0.0331133i	0.970220	−	0.242224i	$-0.0778770\pi$
$367$	0.169976	+	0.634359i	0.00887268	+	0.0331133i	−0.961348	+	0.275338i	$0.911210\pi$
$368$	11.7645	+	3.15230i	0.613269	+	0.164325i
$369$	−2.70256	+	2.14647i	−0.140690	+	0.111741i
$370$		0			0
$371$	8.41857	+	14.5814i	0.437071	+	0.757028i
$372$	0.254165	+	0.728677i	0.0131778	+	0.0377801i
$373$	8.68391	−	32.4088i	0.449636	−	1.67806i	−0.253762	−	0.967267i	$-0.581668\pi$
$373$	8.68391	−	32.4088i	0.449636	−	1.67806i	0.703398	−	0.710796i	$-0.251665\pi$
$374$	−7.38613	+	12.7932i	−0.381928	+	0.661518i
$375$		0			0
$376$	−11.7336			−0.605113
$377$	3.33315	+	2.20209i	0.171666	+	0.113413i
$378$	26.6170	+	16.8352i	1.36903	+	0.865909i
$379$	8.79891	−	15.2402i	0.451969	−	0.782834i	−0.546539	−	0.837434i	$-0.684055\pi$
$379$	8.79891	−	15.2402i	0.451969	−	0.782834i	0.998508	+	0.0545997i	$0.0173883\pi$
$380$		0			0
$381$	0.380286	+	5.14297i	0.0194827	+	0.263482i
$382$	−3.14806	−	3.14806i	−0.161069	−	0.161069i
$383$	5.41553	−	20.2110i	0.276721	−	1.03274i	−0.677959	−	0.735100i	$-0.737135\pi$
$383$	5.41553	−	20.2110i	0.276721	−	1.03274i	0.954680	−	0.297635i	$-0.0961980\pi$
$384$	21.6740	−	1.60264i	1.10605	−	0.0817844i
$385$		0			0
$386$	4.46957	−	2.58051i	0.227495	−	0.131344i
$387$	18.2068	−	24.5673i	0.925505	−	1.24883i
$388$	−0.225945	−	0.843237i	−0.0114706	−	0.0428089i
$389$	−9.74450			−0.494066			−0.247033	−	0.969007i	$-0.579456\pi$
$389$	−9.74450			−0.494066			−0.247033	+	0.969007i	$0.579456\pi$
$390$		0			0
$391$	6.61812			0.334693
$392$	6.91564	+	25.8095i	0.349293	+	1.30358i
$393$	0.848313	−	4.45924i	0.0427918	−	0.224939i
$394$	−5.92388	+	3.42015i	−0.298441	+	0.172305i
$395$		0			0
$396$	0.808389	−	2.04779i	0.0406231	−	0.102906i
$397$	−0.748237	+	2.79246i	−0.0375530	+	0.140150i	−0.982157	−	0.188062i	$-0.939779\pi$
$397$	−0.748237	+	2.79246i	−0.0375530	+	0.140150i	0.944604	+	0.328212i	$0.106446\pi$
$398$	−4.73125	−	4.73125i	−0.237156	−	0.237156i
$399$	−34.4653	+	2.54847i	−1.72542	+	0.127583i
$400$		0			0
$401$	0.557130	−	0.964978i	0.0278218	−	0.0481887i	−0.851779	−	0.523901i	$-0.824476\pi$
$401$	0.557130	−	0.964978i	0.0278218	−	0.0481887i	0.879601	+	0.475712i	$0.157810\pi$
$402$	5.18353	+	14.8609i	0.258531	+	0.741194i
$403$	9.34489	+	0.563582i	0.465502	+	0.0280740i
$404$	−3.36013			−0.167173
$405$		0			0
$406$	3.35778	−	5.81584i	0.166644	−	0.288635i
$407$	−1.09446	+	4.08458i	−0.0542504	+	0.202465i
$408$	10.3288	−	3.60271i	0.511351	−	0.178361i
$409$	6.17475	+	10.6950i	0.305322	+	0.528833i	0.977333	−	0.211708i	$-0.0679027\pi$
$409$	6.17475	+	10.6950i	0.305322	+	0.528833i	−0.672011	+	0.740541i	$0.734569\pi$
$410$		0			0
$411$	16.1862	+	7.81463i	0.798406	+	0.385467i
$412$	2.73824	+	0.733710i	0.134904	+	0.0361473i
$413$	−9.27711	−	34.6226i	−0.456497	−	1.70367i
$414$	−12.3463	+	1.83589i	−0.606789	+	0.0902288i
$415$		0			0
$416$	−1.10475	+	3.31111i	−0.0541649	+	0.162340i
$417$	3.18308	−	1.11027i	0.155876	−	0.0543700i
$418$	7.91280	+	29.5310i	0.387028	+	1.44441i
$419$	9.48656	−	16.4312i	0.463449	−	0.802717i	−0.535681	−	0.844420i	$-0.679945\pi$
$419$	9.48656	−	16.4312i	0.463449	−	0.802717i	0.999130	+	0.0417034i	$0.0132785\pi$
$420$		0			0
$421$		−	30.3717i		−	1.48022i	−0.672484	−	0.740112i	$-0.734772\pi$
$421$		−	30.3717i		−	1.48022i	0.672484	−	0.740112i	$-0.265228\pi$
$422$	17.2813	+	4.63051i	0.841241	+	0.225410i
$423$	11.9847	−	5.20061i	0.582715	−	0.252862i
$424$	−11.0299			−0.535657
$425$		0			0
$426$	−18.5195	+	12.5995i	−0.897272	+	0.610447i
$427$	−13.0640	+	3.50049i	−0.632212	+	0.169401i
$428$	−1.12379	+	1.12379i	−0.0543203	+	0.0543203i
$429$	−19.1395	−	18.6269i	−0.924065	−	0.899316i
$430$		0			0
$431$	13.0681	−	22.6347i	0.629469	−	1.09027i	−0.358189	−	0.933649i	$-0.616606\pi$
$431$	13.0681	−	22.6347i	0.629469	−	1.09027i	0.987658	−	0.156624i	$-0.0500611\pi$
$432$	−19.8484	+	10.4148i	−0.954958	+	0.501083i
$433$	−2.31995	+	8.65818i	−0.111490	+	0.416086i	−0.999000	−	0.0447016i	$-0.985766\pi$
$433$	−2.31995	+	8.65818i	−0.111490	+	0.416086i	0.887511	+	0.460787i	$0.152433\pi$
$434$		−	15.7377i		−	0.755433i
$435$		0			0
$436$	−2.05343	+	1.18555i	−0.0983414	+	0.0567774i
$437$	9.68515	−	9.68515i	0.463304	−	0.463304i
$438$	−21.8749	−	18.8627i	−1.04523	−	0.901294i
$439$	14.8493	+	8.57324i	0.708718	+	0.409179i	0.810586	−	0.585619i	$-0.199149\pi$
$439$	14.8493	+	8.57324i	0.708718	+	0.409179i	−0.101868	+	0.994798i	$0.532482\pi$
$440$		0			0
$441$	−18.5031	−	23.2967i	−0.881099	−	1.10937i
$442$	−0.749747	+	12.4317i	−0.0356618	+	0.591317i
$443$	−16.8516	+	16.8516i	−0.800642	+	0.800642i	−0.983196	−	0.182554i	$-0.941564\pi$
$443$	−16.8516	+	16.8516i	−0.800642	+	0.800642i	0.182554	+	0.983196i	$0.441564\pi$
$444$	−0.242985	+	0.165312i	−0.0115315	+	0.00784535i
$445$		0			0
$446$	22.2903	−	12.8693i	1.05547	−	0.609378i
$447$	16.1672	−	5.63915i	0.764681	−	0.266723i
$448$	−28.6081	−	7.66552i	−1.35161	−	0.362162i
$449$	5.80271	−	3.35020i	0.273847	−	0.158105i	−0.356788	−	0.934185i	$-0.616128\pi$
$449$	5.80271	−	3.35020i	0.273847	−	0.158105i	0.630634	+	0.776080i	$0.282795\pi$
$450$		0			0
$451$	−2.45994	−	4.26074i	−0.115834	−	0.200630i
$452$	0.238245	−	0.0638377i	0.0112061	−	0.00300267i
$453$	6.48521	−	34.0901i	0.304702	−	1.60169i
$454$			14.1354i			0.663407i
$455$		0			0
$456$	9.84314	−	20.3878i	0.460947	−	0.954744i
$457$	35.9291	−	9.62717i	1.68069	−	0.450340i	0.712731	−	0.701438i	$-0.247458\pi$
$457$	35.9291	−	9.62717i	1.68069	−	0.450340i	0.967962	+	0.251097i	$0.0807915\pi$
$458$	2.13647	+	7.97341i	0.0998306	+	0.372573i
$459$	−8.95302	+	8.25778i	−0.417891	+	0.385440i
$460$		0			0
$461$	−4.19385	−	7.26397i	−0.195327	−	0.338317i	0.751681	−	0.659527i	$-0.229244\pi$
$461$	−4.19385	−	7.26397i	−0.195327	−	0.338317i	−0.947008	+	0.321211i	$0.895910\pi$
$462$	−29.3189	+	34.0010i	−1.36404	+	1.58187i
$463$	7.19262	−	7.19262i	0.334269	−	0.334269i	−0.519936	−	0.854205i	$-0.674044\pi$
$463$	7.19262	−	7.19262i	0.334269	−	0.334269i	0.854205	+	0.519936i	$0.174044\pi$
$464$	2.38977	+	4.13921i	0.110942	+	0.192158i
$465$		0			0
$466$	34.8048	+	20.0946i	1.61230	+	0.930863i
$467$	20.1687	+	20.1687i	0.933297	+	0.933297i	0.997910	−	0.0646132i	$-0.0205814\pi$
$467$	20.1687	+	20.1687i	0.933297	+	0.933297i	−0.0646132	+	0.997910i	$0.520581\pi$
$468$	−0.161984	−	1.84904i	−0.00748770	−	0.0854721i
$469$		−	25.3622i		−	1.17112i
$470$		0			0
$471$	10.9606	−	7.45693i	0.505039	−	0.343597i
$472$	22.6810	+	6.07734i	1.04398	+	0.279732i
$473$	30.8232	+	30.8232i	1.41725	+	1.41725i
$474$	−5.24647	+	0.387939i	−0.240978	+	0.0178186i
$475$		0			0
$476$	1.65437			0.0758280
$477$	11.2659	−	4.88870i	0.515831	−	0.223838i
$478$	24.6868	−	6.61480i	1.12915	−	0.302554i
$479$	−10.4307	−	6.02217i	−0.476591	−	0.275160i	0.242404	−	0.970175i	$-0.422064\pi$
$479$	−10.4307	−	6.02217i	−0.476591	−	0.275160i	−0.718995	+	0.695016i	$0.755397\pi$
$480$		0			0
$481$	0.713746	+	3.49297i	0.0325440	+	0.159266i
$482$	1.74212	+	1.74212i	0.0793515	+	0.0793515i
$483$	19.7596	+	3.75900i	0.899091	+	0.171040i
$484$	1.08326	+	0.625419i	0.0492390	+	0.0284281i
$485$		0			0
$486$	14.4115	−	17.8888i	0.653717	−	0.811452i
$487$	−10.3784	+	38.7327i	−0.470290	+	1.75515i	0.168435	+	0.985713i	$0.446129\pi$
$487$	−10.3784	+	38.7327i	−0.470290	+	1.75515i	−0.638726	+	0.769434i	$0.720538\pi$
$488$	2.29314	−	8.55811i	0.103806	−	0.387408i
$489$	−10.9314	−	5.27762i	−0.494333	−	0.238662i
$490$		0			0
$491$	−16.8964	−	9.75516i	−0.762525	−	0.440244i	0.0676765	−	0.997707i	$-0.478441\pi$
$491$	−16.8964	−	9.75516i	−0.762525	−	0.440244i	−0.830202	+	0.557463i	$0.811775\pi$
$492$	0.0639008	−	0.335901i	0.00288087	−	0.0151436i
$493$	1.83643	+	1.83643i	0.0827088	+	0.0827088i
$494$	17.0958	+	19.2902i	0.769175	+	0.867906i
$495$		0			0
$496$	9.70011	+	5.60036i	0.435548	+	0.251464i
$497$	34.8645	−	9.34191i	1.56389	−	0.419042i
$498$	14.6435	−	16.9820i	0.656192	−	0.760982i
$499$	7.54758			0.337876			0.168938	−	0.985627i	$-0.445966\pi$
$499$	7.54758			0.337876			0.168938	+	0.985627i	$0.445966\pi$
$500$		0			0
$501$	3.25210	+	43.9812i	0.145293	+	1.96494i
$502$	−8.19769	−	8.19769i	−0.365881	−	0.365881i
$503$	30.7880	+	8.24963i	1.37277	+	0.367833i	0.868490	−	0.495707i	$-0.165091\pi$
$503$	30.7880	+	8.24963i	1.37277	+	0.367833i	0.504281	+	0.863540i	$0.331758\pi$
$504$	32.8847	−	4.88991i	1.46480	−	0.217814i
$505$		0			0
$506$		−	17.7936i		−	0.791023i
$507$	−21.4539	−	6.83594i	−0.952801	−	0.303595i
$508$	−0.361274	−	0.361274i	−0.0160290	−	0.0160290i
$509$	8.77183	+	5.06442i	0.388804	+	0.224476i	0.681642	−	0.731686i	$-0.261266\pi$
$509$	8.77183	+	5.06442i	0.388804	+	0.224476i	−0.292838	+	0.956162i	$0.594600\pi$
$510$		0			0
$511$	23.2726	+	40.3093i	1.02952	+	1.78318i
$512$	13.4843	−	13.4843i	0.595930	−	0.595930i
$513$	−1.01744	+	25.1868i	−0.0449209	+	1.11202i
$514$	7.01724	+	12.1542i	0.309517	+	0.536099i
$515$		0			0
$516$	0.223399	+	3.02124i	0.00983460	+	0.133003i
$517$	4.82019	+	17.9892i	0.211992	+	0.791163i
$518$	5.78894	−	1.55114i	0.254351	−	0.0681533i
$519$	29.8745	+	14.4233i	1.31135	+	0.633113i
$520$		0			0
$521$		−	27.9873i		−	1.22615i	−0.790026	−	0.613074i	$-0.789933\pi$
$521$		−	27.9873i		−	1.22615i	0.790026	−	0.613074i	$-0.210067\pi$
$522$	−3.93536	−	2.91650i	−0.172246	−	0.127652i
$523$	15.7570	−	4.22208i	0.689007	−	0.184619i	0.102705	−	0.994712i	$-0.467250\pi$
$523$	15.7570	−	4.22208i	0.689007	−	0.184619i	0.586301	+	0.810093i	$0.300583\pi$
$524$	0.224856	+	0.389462i	0.00982288	+	0.0170137i
$525$		0			0
$526$	−30.0345	+	17.3404i	−1.30956	+	0.756078i
$527$	5.87886	+	1.57524i	0.256087	+	0.0686184i
$528$	−10.5236	−	30.1705i	−0.457980	−	1.31300i
$529$	13.0149	−	7.51414i	0.565864	−	0.326702i
$530$		0			0
$531$	−25.8600	+	3.84535i	−1.12223	+	0.166874i
$532$	2.42106	−	2.42106i	0.104966	−	0.104966i
$533$	−3.46081	−	2.28643i	−0.149905	−	0.0990364i
$534$	4.19631	−	8.69168i	0.181592	−	0.376126i
$535$		0			0
$536$	14.3886	+	8.30725i	0.621492	+	0.358819i
$537$	−6.83036	+	7.92112i	−0.294752	+	0.341822i
$538$	−12.4053	+	12.4053i	−0.534829	+	0.534829i
$539$	36.7286	−	21.2053i	1.58201	−	0.913376i
$540$		0			0
$541$			1.73534i			0.0746081i	0.999304	+	0.0373041i	$0.0118770\pi$
$541$			1.73534i			0.0746081i	−0.999304	+	0.0373041i	$0.988123\pi$
$542$	−7.68123	+	28.6667i	−0.329937	+	1.23134i
$543$	9.46582	+	1.80075i	0.406217	+	0.0772776i
$544$	−1.13462	+	1.96522i	−0.0486464	+	0.0842580i
$545$		0			0
$546$	−9.29955	+	36.6913i	−0.397984	+	1.57024i
$547$	11.2029	−	11.2029i	0.479001	−	0.479001i	−0.425811	−	0.904812i	$-0.640011\pi$
$547$	11.2029	−	11.2029i	0.479001	−	0.479001i	0.904812	+	0.425811i	$0.140011\pi$
$548$	−1.72005	+	0.460885i	−0.0734767	+	0.0196880i
$549$	1.45095	+	9.75765i	0.0619251	+	0.416446i
$550$		0			0
$551$	5.37498			0.228982
$552$	−8.60472	+	9.97884i	−0.366241	+	0.424728i
$553$	8.18851	+	2.19410i	0.348211	+	0.0933028i
$554$			6.48371i			0.275466i
$555$		0			0
$556$	−0.166995	+	0.289243i	−0.00708215	+	0.0122666i
$557$	−10.8998	−	40.6785i	−0.461838	−	1.72360i	−0.667166	−	0.744909i	$-0.732493\pi$
$557$	−10.8998	−	40.6785i	−0.461838	−	1.72360i	0.205328	−	0.978693i	$-0.434174\pi$
$558$	−11.4042	−	1.30785i	−0.482778	−	0.0553655i
$559$	34.8615	+	11.6315i	1.47448	+	0.491961i
$560$		0			0
$561$	−9.76654	−	14.3554i	−0.412344	−	0.606087i
$562$	8.77762	+	32.7585i	0.370262	+	1.38184i
$563$	−2.59466	−	0.695238i	−0.109352	−	0.0293008i	0.203728	−	0.979028i	$-0.434694\pi$
$563$	−2.59466	−	0.695238i	−0.109352	−	0.0293008i	−0.313080	+	0.949727i	$0.601361\pi$
$564$	−0.562743	+	1.16559i	−0.0236958	+	0.0490802i
$565$		0			0
$566$	10.0640	+	17.4314i	0.423022	+	0.732695i
$567$	−31.4211	+	19.5699i	−1.31956	+	0.821857i
$568$	−6.11980	+	22.8394i	−0.256781	+	0.958320i
$569$	−5.33657	+	9.24321i	−0.223721	+	0.387496i	−0.955935	−	0.293579i	$-0.905154\pi$
$569$	−5.33657	+	9.24321i	−0.223721	+	0.387496i	0.732214	+	0.681074i	$0.238487\pi$
$570$		0			0
$571$	−22.6560			−0.948123			−0.474061	−	0.880492i	$-0.657213\pi$
$571$	−22.6560			−0.948123			−0.474061	+	0.880492i	$0.657213\pi$
$572$	2.64117	+	0.159287i	0.110433	+	0.00666011i
$573$	4.94080	−	1.72337i	0.206405	−	0.0719946i
$574$	−3.48639	+	6.03860i	−0.145519	+	0.252046i
$575$		0			0
$576$	−7.93217	+	20.0936i	−0.330507	+	0.837234i
$577$	6.87604	+	6.87604i	0.286253	+	0.286253i	0.835597	−	0.549343i	$-0.185122\pi$
$577$	6.87604	+	6.87604i	0.286253	+	0.286253i	−0.549343	+	0.835597i	$0.685122\pi$
$578$	4.38831	−	16.3774i	0.182529	−	0.681209i
$579$	0.447320	+	6.04953i	0.0185900	+	0.251410i
$580$		0			0
$581$	−31.2930	+	18.0670i	−1.29825	+	0.749547i
$582$	12.7562	+	2.42671i	0.528762	+	0.100590i
$583$	4.53110	+	16.9103i	0.187659	+	0.700352i
$584$	−30.4913			−1.26174
$585$		0			0
$586$	35.7517			1.47689
$587$	−9.46089	−	35.3085i	−0.390493	−	1.45734i	−0.829323	−	0.558769i	$-0.811274\pi$
$587$	−9.46089	−	35.3085i	−0.390493	−	1.45734i	0.438830	−	0.898570i	$-0.355393\pi$
$588$	2.89555	+	0.550840i	0.119410	+	0.0227163i
$589$	10.9086	−	6.29805i	0.449479	−	0.259507i
$590$		0			0
$591$	−0.592869	−	8.01793i	−0.0243874	−	0.329814i
$592$	−1.10397	+	4.12007i	−0.0453728	+	0.169334i
$593$	−28.7633	−	28.7633i	−1.18117	−	1.18117i	−0.979442	−	0.201727i	$-0.935345\pi$
$593$	−28.7633	−	28.7633i	−1.18117	−	1.18117i	−0.201727	−	0.979442i	$-0.564655\pi$
$594$	22.2021	+	24.0713i	0.910962	+	0.987658i
$595$		0			0
$596$	−0.848182	+	1.46909i	−0.0347429	+	0.0601764i
$597$	7.42559	−	2.59007i	0.303909	−	0.106004i
$598$	−6.70509	−	13.4197i	−0.274192	−	0.548774i
$599$	−10.0471			−0.410513			−0.205256	−	0.978708i	$-0.565803\pi$
$599$	−10.0471			−0.410513			−0.205256	+	0.978708i	$0.565803\pi$
$600$		0			0
$601$	−17.9309	+	31.0572i	−0.731415	+	1.26685i	0.224864	+	0.974390i	$0.427806\pi$
$601$	−17.9309	+	31.0572i	−0.731415	+	1.26685i	−0.956279	+	0.292458i	$0.905527\pi$
$602$	15.9897	−	59.6743i	0.651691	−	2.43214i
$603$	−18.3785	−	2.10767i	−0.748430	−	0.0858308i
$604$	1.71899	+	2.97737i	0.0699446	+	0.121148i
$605$		0			0
$606$	21.7299	−	45.0084i	0.882717	−	1.82834i
$607$	−10.9405	−	2.93149i	−0.444060	−	0.118985i	0.0298588	−	0.999554i	$-0.490494\pi$
$607$	−10.9405	−	2.93149i	−0.444060	−	0.118985i	−0.473919	+	0.880569i	$0.657161\pi$
$608$	1.21552	+	4.53639i	0.0492960	+	0.183975i
$609$	4.43993	+	6.52606i	0.179915	+	0.264449i
$610$		0			0
$611$	10.4141	+	11.7509i	0.421310	+	0.475389i
$612$	0.137483	−	1.19883i	0.00555741	−	0.0484597i
$613$	5.16141	+	19.2626i	0.208467	+	0.778011i	0.988365	+	0.152103i	$0.0486046\pi$
$613$	5.16141	+	19.2626i	0.208467	+	0.778011i	−0.779897	+	0.625908i	$0.784729\pi$
$614$	13.4369	−	23.2734i	0.542270	−	0.939239i
$615$		0			0
$616$			47.3936i			1.90954i
$617$	−17.9740	−	4.81611i	−0.723605	−	0.193889i	−0.121825	−	0.992552i	$-0.538875\pi$
$617$	−17.9740	−	4.81611i	−0.723605	−	0.193889i	−0.601780	+	0.798662i	$0.705541\pi$
$618$	−27.5361	+	31.9335i	−1.10767	+	1.28455i
$619$	−36.0310			−1.44821			−0.724104	−	0.689691i	$-0.757746\pi$
$619$	−36.0310			−1.44821			−0.724104	+	0.689691i	$0.757746\pi$
$620$		0			0
$621$	4.36600	−	14.0062i	0.175202	−	0.562051i
$622$	11.9493	−	3.20182i	0.479125	−	0.128381i
$623$	−10.9976	+	10.9976i	−0.440608	+	0.440608i
$624$	−19.3058	−	18.7887i	−0.772850	−	0.752151i
$625$		0			0
$626$	0.464527	−	0.804584i	0.0185662	−	0.0321576i
$627$	−35.3008	−	6.71553i	−1.40978	−	0.268192i
$628$	−0.339928	+	1.26863i	−0.0135646	+	0.0506238i
$629$			2.31773i			0.0924141i
$630$		0			0
$631$	28.1867	−	16.2736i	1.12209	−	0.647841i	0.180159	−	0.983637i	$-0.442339\pi$
$631$	28.1867	−	16.2736i	1.12209	−	0.647841i	0.941935	+	0.335796i	$0.109005\pi$
$632$	−3.92688	+	3.92688i	−0.156203	+	0.156203i
$633$	−13.7323	+	15.9252i	−0.545809	+	0.632971i
$634$	−22.7117	−	13.1126i	−0.901998	−	0.520769i
$635$		0			0
$636$	−0.528993	+	1.09568i	−0.0209759	+	0.0434467i
$637$	19.7096	−	29.8330i	0.780923	−	1.18203i
$638$	4.93748	−	4.93748i	0.195477	−	0.195477i
$639$	−3.87221	−	26.0406i	−0.153182	−	1.03015i
$640$		0			0
$641$	−5.53230	+	3.19407i	−0.218513	+	0.126158i	−0.605261	−	0.796027i	$-0.706931\pi$
$641$	−5.53230	+	3.19407i	−0.218513	+	0.126158i	0.386749	+	0.922185i	$0.373598\pi$
$642$	−7.78545	−	22.3205i	−0.307267	−	0.880919i
$643$	−31.0990	−	8.33296i	−1.22643	−	0.328620i	−0.413239	−	0.910623i	$-0.635602\pi$
$643$	−31.0990	−	8.33296i	−1.22643	−	0.328620i	−0.813187	+	0.582003i	$0.802269\pi$
$644$	−1.72576	+	0.996370i	−0.0680046	+	0.0392625i
$645$		0			0
$646$	8.37845	+	14.5119i	0.329646	+	0.570963i
$647$	−16.6403	+	4.45875i	−0.654196	+	0.175291i	−0.570625	−	0.821210i	$-0.693299\pi$
$647$	−16.6403	+	4.45875i	−0.654196	+	0.175291i	−0.0835709	+	0.996502i	$0.526633\pi$
$648$	−0.810632	−	24.2360i	−0.0318446	−	0.952080i
$649$		−	37.2696i		−	1.46296i
$650$		0			0
$651$	16.6577	+	8.04226i	0.652865	+	0.315201i
$652$	1.16163	−	0.311259i	0.0454931	−	0.0121898i
$653$	−6.06514	−	22.6354i	−0.237347	−	0.885791i	−0.977077	−	0.212887i	$-0.931713\pi$
$653$	−6.06514	−	22.6354i	−0.237347	−	0.885791i	0.739730	−	0.672904i	$-0.234953\pi$
$654$	−2.60074	−	35.1723i	−0.101697	−	1.37535i
$655$		0			0
$656$	−2.48131	−	4.29775i	−0.0968789	−	0.167799i
$657$	31.1438	−	13.5145i	1.21504	−	0.527250i
$658$	18.6640	−	18.6640i	0.727597	−	0.727597i
$659$	6.20035	+	10.7393i	0.241532	+	0.418345i	0.961151	−	0.276024i	$-0.0890169\pi$
$659$	6.20035	+	10.7393i	0.241532	+	0.418345i	−0.719619	+	0.694369i	$0.755684\pi$
$660$		0			0
$661$	−19.8030	−	11.4332i	−0.770246	−	0.444702i	0.0627164	−	0.998031i	$-0.480024\pi$
$661$	−19.8030	−	11.4332i	−0.770246	−	0.444702i	−0.832962	+	0.553330i	$0.813357\pi$
$662$	14.7782	+	14.7782i	0.574370	+	0.574370i
$663$	−12.7753	−	7.14642i	−0.496152	−	0.277544i
$664$		−	23.6711i		−	0.918616i
$665$		0			0
$666$	−0.642947	−	4.32382i	−0.0249137	−	0.167545i
$667$	−3.02170	−	0.809663i	−0.117001	−	0.0313503i
$668$	−3.08951	−	3.08951i	−0.119537	−	0.119537i
$669$	2.23084	+	30.1697i	0.0862491	+	1.16643i
$670$		0			0
$671$	−14.0628			−0.542888
$672$	−4.50382	+	5.22305i	−0.173739	+	0.201484i
$673$	6.79109	−	1.81967i	0.261777	−	0.0701431i	−0.125543	−	0.992088i	$-0.540067\pi$
$673$	6.79109	−	1.81967i	0.261777	−	0.0701431i	0.387321	+	0.921945i	$0.373401\pi$
$674$	−10.6143	−	6.12816i	−0.408847	−	0.236048i
$675$		0			0
$676$	2.05196	−	0.875128i	0.0789217	−	0.0336588i
$677$	26.7622	+	26.7622i	1.02856	+	1.02856i	0.999580	+	0.0289760i	$0.00922463\pi$
$677$	26.7622	+	26.7622i	1.02856	+	1.02856i	0.0289760	+	0.999580i	$0.490775\pi$
$678$	−0.685634	+	3.60410i	−0.0263316	+	0.138415i
$679$	−18.1210	−	10.4622i	−0.695420	−	0.401501i
$680$		0			0
$681$	−14.9617	−	7.22346i	−0.573334	−	0.276804i
$682$	4.23522	−	15.8060i	0.162175	−	0.605245i
$683$	2.67180	−	9.97129i	0.102234	−	0.381541i	−0.895783	−	0.444491i	$-0.853384\pi$
$683$	2.67180	−	9.97129i	0.102234	−	0.381541i	0.998017	+	0.0629506i	$0.0200511\pi$
$684$	−1.55320	−	1.95560i	−0.0593883	−	0.0747741i
$685$		0			0
$686$	−15.3108	−	8.83972i	−0.584571	−	0.337502i
$687$	−9.53128	−	1.81320i	−0.363641	−	0.0691780i
$688$	31.0909	+	31.0909i	1.18533	+	1.18533i
$689$	9.78953	+	11.0461i	0.372951	+	0.420823i
$690$		0			0
$691$	−21.8645	−	12.6235i	−0.831765	−	0.480220i	0.0226915	−	0.999743i	$-0.492776\pi$
$691$	−21.8645	−	12.6235i	−0.831765	−	0.480220i	−0.854457	+	0.519523i	$0.826110\pi$
$692$	−3.17465	+	0.850645i	−0.120682	+	0.0323367i
$693$	−21.0060	−	48.4079i	−0.797953	−	1.83887i
$694$	−7.19045			−0.272946
$695$		0			0
$696$	−5.15667	+	0.381299i	−0.195463	+	0.0144531i
$697$	−1.90677	−	1.90677i	−0.0722242	−	0.0722242i
$698$	17.4629	+	4.67918i	0.660982	+	0.177110i
$699$	−39.0551	+	26.5707i	−1.47720	+	1.00499i
$700$		0			0
$701$		−	5.83428i		−	0.220358i	−0.993912	−	0.110179i	$-0.964858\pi$
$701$		−	5.83428i		−	0.220358i	0.993912	−	0.110179i	$-0.0351424\pi$
$702$	25.8152	+	9.78800i	0.974333	+	0.369424i
$703$	3.39184	+	3.39184i	0.127926	+	0.127926i
$704$	−26.6695	−	15.3976i	−1.00514	−	0.580320i
$705$		0			0
$706$	7.96595	+	13.7974i	0.299803	+	0.519273i
$707$	−56.9490	+	56.9490i	−2.14179	+	2.14179i
$708$	1.69149	−	1.96161i	0.0635702	−	0.0737220i
$709$	9.66759	+	16.7448i	0.363074	+	0.628863i	0.988465	−	0.151449i	$-0.0483939\pi$
$709$	9.66759	+	16.7448i	0.363074	+	0.628863i	−0.625391	+	0.780311i	$0.715061\pi$
$710$		0			0
$711$	2.27043	−	5.75141i	0.0851478	−	0.215695i
$712$	−2.63699	−	9.84138i	−0.0988254	−	0.368821i
$713$	−7.08126	+	1.89742i	−0.265195	+	0.0710589i
$714$	−10.6988	+	22.1601i	−0.400393	+	0.829320i
$715$		0			0
$716$		−	1.03624i		−	0.0387259i
$717$	−5.61392	+	29.5101i	−0.209656	+	1.10208i
$718$	−53.0907	+	14.2256i	−1.98133	+	0.530895i
$719$	19.2268	+	33.3018i	0.717038	+	1.24195i	0.962168	+	0.272456i	$0.0878359\pi$
$719$	19.2268	+	33.3018i	0.717038	+	1.24195i	−0.245130	+	0.969490i	$0.578831\pi$
$720$		0			0
$721$	58.8443	−	33.9738i	2.19148	−	1.26525i
$722$	6.45341	+	1.72919i	0.240171	+	0.0643537i
$723$	−2.73422	+	0.953703i	−0.101687	+	0.0354686i
$724$	−0.826728	+	0.477312i	−0.0307251	+	0.0177391i
$725$		0			0
$726$	−15.3828	+	10.4655i	−0.570910	+	0.388411i
$727$	−24.8141	+	24.8141i	−0.920304	+	0.920304i	−0.997051	−	0.0767466i	$-0.975547\pi$
$727$	−24.8141	+	24.8141i	−0.920304	+	0.920304i	0.0767466	+	0.997051i	$0.475547\pi$
$728$	17.8591	+	35.7437i	0.661904	+	1.32475i
$729$	11.5700	+	24.3954i	0.428518	+	0.903533i
$730$		0			0
$731$	20.6911	+	11.9460i	0.765287	+	0.441838i
$732$	−0.740168	−	0.638244i	−0.0273574	−	0.0235902i
$733$	28.6087	−	28.6087i	1.05668	−	1.05668i	0.0583912	−	0.998294i	$-0.481403\pi$
$733$	28.6087	−	28.6087i	1.05668	−	1.05668i	0.998294	−	0.0583912i	$-0.0185971\pi$
$734$	0.838131	−	0.483895i	0.0309360	−	0.0178609i
$735$		0			0
$736$		−	2.73337i		−	0.100753i
$737$	6.82529	−	25.4723i	0.251413	−	0.938285i
$738$	4.08610	+	3.02821i	0.150411	+	0.111470i
$739$	−7.80807	+	13.5240i	−0.287225	+	0.497488i	−0.973146	−	0.230188i	$-0.926066\pi$
$739$	−7.80807	+	13.5240i	−0.287225	+	0.497488i	0.685922	+	0.727675i	$0.259399\pi$
$740$		0			0
$741$	−29.1541	+	8.23748i	−1.07100	+	0.302611i
$742$	17.5446	−	17.5446i	0.644082	−	0.644082i
$743$	7.86421	−	2.10721i	0.288510	−	0.0773060i	−0.111661	−	0.993746i	$-0.535617\pi$
$743$	7.86421	−	2.10721i	0.288510	−	0.0773060i	0.400171	+	0.916440i	$0.368951\pi$
$744$	−10.0187	+	6.81610i	−0.367304	+	0.249890i
$745$		0			0
$746$	−49.4434			−1.81025
$747$	10.4916	+	24.1777i	0.383868	+	0.884615i
$748$	1.66156	+	0.445213i	0.0607525	+	0.0162786i
$749$			38.0930i			1.39189i
$750$		0			0
$751$	−5.93245	+	10.2753i	−0.216478	+	0.374951i	−0.953729	−	0.300668i	$-0.902790\pi$
$751$	−5.93245	+	10.2753i	−0.216478	+	0.374951i	0.737251	+	0.675619i	$0.236124\pi$
$752$	4.86206	+	18.1454i	0.177301	+	0.661696i
$753$	12.8661	−	4.48772i	0.468866	−	0.163542i
$754$	1.86322	−	5.58436i	0.0678545	−	0.203370i
$755$		0			0
$756$	1.09140	−	3.50122i	0.0396937	−	0.127338i
$757$	−2.28233	−	8.51775i	−0.0829525	−	0.309583i	0.911966	−	0.410266i	$-0.134564\pi$
$757$	−2.28233	−	8.51775i	−0.0829525	−	0.309583i	−0.994919	+	0.100683i	$0.967897\pi$
$758$	−25.0491	−	6.71189i	−0.909825	−	0.243787i
$759$	18.8338	+	9.09288i	0.683623	+	0.330051i
$760$		0			0
$761$	−6.00928	−	10.4084i	−0.217836	−	0.377304i	0.736310	−	0.676645i	$-0.236567\pi$
$761$	−6.00928	−	10.4084i	−0.217836	−	0.377304i	−0.954146	+	0.299341i	$0.903233\pi$
$762$	7.17558	−	2.50286i	0.259944	−	0.0906691i
$763$	−14.7093	+	54.8957i	−0.532511	+	1.98736i
$764$	−0.259210	+	0.448965i	−0.00937790	+	0.0162430i
$765$		0			0
$766$	−30.8343			−1.11409
$767$	−14.0441	−	28.1083i	−0.507105	−	1.01493i
$768$	−2.33248	−	6.68711i	−0.0841662	−	0.241300i
$769$	6.86300	−	11.8871i	0.247486	−	0.428658i	−0.715342	−	0.698775i	$-0.753729\pi$
$769$	6.86300	−	11.8871i	0.247486	−	0.428658i	0.962828	+	0.270117i	$0.0870622\pi$
$770$		0			0
$771$	−16.4506	+	1.21641i	−0.592455	+	0.0438079i
$772$	−0.424956	−	0.424956i	−0.0152945	−	0.0152945i
$773$	5.58461	−	20.8420i	0.200864	−	0.749636i	−0.789806	−	0.613357i	$-0.789819\pi$
$773$	5.58461	−	20.8420i	0.200864	−	0.749636i	0.990670	−	0.136279i	$-0.0435144\pi$
$774$	−41.9138	−	16.5459i	−1.50656	−	0.594730i
$775$		0			0
$776$	11.8709	−	6.85366i	0.426140	−	0.246032i
$777$	−1.31644	+	6.92000i	−0.0472271	+	0.248254i
$778$	3.71660	+	13.8705i	0.133247	+	0.497283i
$779$	−5.58086			−0.199955
$780$		0			0
$781$	37.5300			1.34293
$782$	−2.52418	−	9.42037i	−0.0902645	−	0.336872i
$783$	5.09803	−	2.67503i	0.182189	−	0.0955976i
$784$	37.0477	−	21.3895i	1.32313	−	0.763910i
$785$		0			0
$786$	−6.67093	+	0.493268i	−0.237944	+	0.0175943i
$787$	−4.45618	+	16.6307i	−0.158846	+	0.592820i	0.839900	+	0.542742i	$0.182614\pi$
$787$	−4.45618	+	16.6307i	−0.158846	+	0.592820i	−0.998745	+	0.0500781i	$0.984053\pi$
$788$	0.563229	+	0.563229i	0.0200642	+	0.0200642i
$789$	−3.00589	−	40.6515i	−0.107012	−	1.44723i
$790$		0			0
$791$	2.95595	−	5.11985i	0.105101	−	0.182041i
$792$	34.3435	+	3.93854i	1.22034	+	0.139950i
$793$	−10.6060	+	5.29922i	−0.376630	+	0.188181i
$794$	4.26023			0.151190
$795$		0			0
$796$	−0.389570	+	0.674755i	−0.0138080	+	0.0239161i
$797$	−11.9555	+	44.6186i	−0.423486	+	1.58047i	0.343721	+	0.939072i	$0.388313\pi$
$797$	−11.9555	+	44.6186i	−0.423486	+	1.58047i	−0.767207	+	0.641400i	$0.778354\pi$
$798$	16.7728	+	48.0867i	0.593750	+	1.70225i
$799$	5.10384	+	8.84011i	0.180561	+	0.312741i
$800$		0			0
$801$	7.05537	+	8.88323i	0.249289	+	0.313873i
$802$	−1.58606	−	0.424984i	−0.0560058	−	0.0150067i
$803$	12.5259	+	46.7473i	0.442030	+	1.64968i
$804$	1.51530	−	1.03092i	0.0534407	−	0.0363577i
$805$		0			0
$806$	−2.76197	−	13.5167i	−0.0972863	−	0.476105i
$807$	−6.79111	−	19.4698i	−0.239058	−	0.685368i
$808$	−13.6552	−	50.9620i	−0.480389	−	1.79284i
$809$	6.99405	−	12.1140i	0.245898	−	0.425907i	−0.716486	−	0.697602i	$-0.754251\pi$
$809$	6.99405	−	12.1140i	0.245898	−	0.425907i	0.962384	+	0.271694i	$0.0875840\pi$
$810$		0			0
$811$		−	19.5998i		−	0.688243i	−0.938925	−	0.344122i	$-0.888177\pi$
$811$		−	19.5998i		−	0.688243i	0.938925	−	0.344122i	$-0.111823\pi$
$812$	−0.755353	−	0.202396i	−0.0265077	−	0.00710272i
$813$	−26.4172	−	22.7795i	−0.926493	−	0.798912i
$814$	6.23152			0.218415
$815$		0			0
$816$	−9.85138	−	14.4801i	−0.344867	−	0.506906i
$817$	47.7621	−	12.7978i	1.67098	−	0.447738i
$818$	12.8684	−	12.8684i	0.449933	−	0.449933i
$819$	−34.0839	−	28.5931i	−1.19099	−	0.999124i
$820$		0			0
$821$	−4.61577	+	7.99475i	−0.161091	+	0.279019i	−0.935260	−	0.353960i	$-0.884835\pi$
$821$	−4.61577	+	7.99475i	−0.161091	+	0.279019i	0.774169	+	0.632979i	$0.218168\pi$
$822$	4.95003	−	26.0203i	0.172652	−	0.907562i
$823$	−11.9403	+	44.5620i	−0.416214	+	1.55333i	0.366177	+	0.930545i	$0.380667\pi$
$823$	−11.9403	+	44.5620i	−0.416214	+	1.55333i	−0.782391	+	0.622788i	$0.786000\pi$
$824$			44.5118i			1.55064i
$825$		0			0
$826$	−45.7443	+	26.4105i	−1.59165	+	0.918938i
$827$	−31.7914	+	31.7914i	−1.10549	+	1.10549i	−0.111759	+	0.993735i	$0.535649\pi$
$827$	−31.7914	+	31.7914i	−1.10549	+	1.10549i	−0.993735	+	0.111759i	$0.964351\pi$
$828$	0.578596	+	1.33336i	0.0201076	+	0.0463376i
$829$	21.8064	+	12.5900i	0.757369	+	0.437267i	0.828350	−	0.560210i	$-0.189280\pi$
$829$	21.8064	+	12.5900i	0.757369	+	0.437267i	−0.0709813	+	0.997478i	$0.522613\pi$
$830$		0			0
$831$	−6.86273	−	3.31330i	−0.238065	−	0.114937i
$832$	−25.9160	−	1.56297i	−0.898477	−	0.0541863i
$833$	16.4368	−	16.4368i	0.569503	−	0.569503i
$834$	−2.79442	−	4.10740i	−0.0967628	−	0.142228i
$835$		0			0
$836$	3.08311	−	1.78003i	0.106632	−	0.0615638i
$837$	7.21206	−	11.4025i	0.249285	−	0.394129i
$838$	−27.0068	−	7.23644i	−0.932933	−	0.249979i
$839$	39.9358	−	23.0569i	1.37874	−	0.796014i	0.386730	−	0.922193i	$-0.373605\pi$
$839$	39.9358	−	23.0569i	1.37874	−	0.796014i	0.992008	+	0.126179i	$0.0402713\pi$
$840$		0			0
$841$	13.8862	+	24.0516i	0.478834	+	0.829365i
$842$	−43.2317	+	11.5839i	−1.48986	+	0.399207i
$843$	−39.1590	−	7.44950i	−1.34871	−	0.256574i
$844$		−	2.08333i		−	0.0717110i
$845$		0			0
$846$	−11.9737	−	15.0757i	−0.411663	−	0.518314i
$847$	28.9595	−	7.75966i	0.995059	−	0.266625i
$848$	4.57046	+	17.0572i	0.156950	+	0.585746i
$849$	−23.5932	+	1.74455i	−0.809718	+	0.0598729i
$850$		0			0
$851$	−1.39589	−	2.41775i	−0.0478505	−	0.0828795i
$852$	1.97532	+	1.70331i	0.0676732	+	0.0583544i
$853$	29.1777	−	29.1777i	0.999026	−	0.999026i	−0.000973237	−	1.00000i	$-0.500310\pi$
$853$	29.1777	−	29.1777i	0.999026	−	0.999026i	1.00000		0.000973237i	$0.000309791\pi$
$854$	9.96536	+	17.2605i	0.341008	+	0.590642i
$855$		0			0
$856$	−21.6111	−	12.4772i	−0.738652	−	0.426461i
$857$	−27.5270	−	27.5270i	−0.940305	−	0.940305i	0.0580111	−	0.998316i	$-0.481524\pi$
$857$	−27.5270	−	27.5270i	−0.940305	−	0.940305i	−0.998316	+	0.0580111i	$0.981524\pi$
$858$	−19.2140	+	34.3480i	−0.655957	+	1.17262i
$859$			40.5927i			1.38500i	0.721416	+	0.692502i	$0.243492\pi$
$859$			40.5927i			1.38500i	−0.721416	+	0.692502i	$0.756508\pi$
$860$		0			0
$861$	−4.60999	−	6.77603i	−0.157108	−	0.230926i
$862$	−37.2029	−	9.96849i	−1.26714	−	0.339528i
$863$	−28.4894	−	28.4894i	−0.969792	−	0.969792i	0.0297651	−	0.999557i	$-0.490524\pi$
$863$	−28.4894	−	28.4894i	−0.969792	−	0.969792i	−0.999557	+	0.0297651i	$0.990524\pi$
$864$	3.41057	+	3.69771i	0.116030	+	0.125799i
$865$		0			0
$866$	13.2091			0.448863
$867$	15.0922	+	13.0140i	0.512559	+	0.441978i
$868$	−1.77015	+	0.474310i	−0.0600827	+	0.0160991i
$869$	7.63362	+	4.40727i	0.258953	+	0.149506i
$870$		0			0
$871$	−4.45107	−	21.7829i	−0.150819	−	0.738084i
$872$	−26.3258	−	26.3258i	−0.891503	−	0.891503i
$873$	−9.08723	+	12.2618i	−0.307556	+	0.414999i
$874$	−17.4800	−	10.0921i	−0.591270	−	0.341370i
$875$		0			0
$876$	−1.46236	+	3.02895i	−0.0494087	+	0.102339i
$877$	4.55671	−	17.0059i	0.153869	−	0.574248i	−0.845330	−	0.534244i	$-0.820596\pi$
$877$	4.55671	−	17.0059i	0.153869	−	0.574248i	0.999200	−	0.0400039i	$-0.0127370\pi$
$878$	6.53975	−	24.4067i	0.220706	−	0.823686i
$879$	−18.2698	+	37.8416i	−0.616225	+	1.27637i
$880$		0			0
$881$	34.8199	+	20.1033i	1.17311	+	0.677297i	0.954411	−	0.298495i	$-0.0964847\pi$
$881$	34.8199	+	20.1033i	1.17311	+	0.677297i	0.218701	+	0.975792i	$0.429818\pi$
$882$	−26.1039	+	35.2232i	−0.878964	+	1.18603i
$883$	1.83119	+	1.83119i	0.0616243	+	0.0616243i	0.737247	−	0.675623i	$-0.236125\pi$
$883$	1.83119	+	1.83119i	0.0616243	+	0.0616243i	−0.675623	+	0.737247i	$0.736125\pi$
$884$	1.42089	−	0.290343i	0.0477899	−	0.00976528i
$885$		0			0
$886$	30.4142	+	17.5596i	1.02178	+	0.589927i
$887$	37.9885	−	10.1790i	1.27553	−	0.341777i	0.443381	−	0.896333i	$-0.353779\pi$
$887$	37.9885	−	10.1790i	1.27553	−	0.341777i	0.832146	+	0.554557i	$0.187112\pi$
$888$	−3.49470	−	3.01346i	−0.117274	−	0.101125i
$889$	−12.2461			−0.410721
$890$		0			0
$891$	−36.8241	+	11.1990i	−1.23365	+	0.375182i
$892$	−2.11931	−	2.11931i	−0.0709597	−	0.0709597i
$893$	20.4060	+	5.46777i	0.682861	+	0.182972i
$894$	−14.1931	−	20.8619i	−0.474689	−	0.697726i
$895$		0			0
$896$			51.6087i			1.72413i
$897$	17.6306	−	0.239305i	0.588670	−	0.00799018i
$898$	−6.98192	−	6.98192i	−0.232990	−	0.232990i
$899$	−2.49146	−	1.43844i	−0.0830948	−	0.0479748i
$900$		0			0
$901$	4.79774	+	8.30993i	0.159836	+	0.276844i
$902$	−5.12660	+	5.12660i	−0.170697	+	0.170697i
$903$	54.9917	+	47.4191i	1.83001	+	1.57801i
$904$	1.93641	+	3.35396i	0.0644041	+	0.111551i
$905$		0			0
$906$	−50.9981	+	3.77095i	−1.69430	+	0.125281i
$907$	−12.0894	−	45.1184i	−0.401423	−	1.49813i	−0.810559	−	0.585658i	$-0.800836\pi$
$907$	−12.0894	−	45.1184i	−0.401423	−	1.49813i	0.409135	−	0.912474i	$-0.365830\pi$
$908$	1.58993	−	0.426019i	0.0527635	−	0.0141379i
$909$	36.5351	+	46.0003i	1.21179	+	1.52573i
$910$		0			0
$911$			17.5547i			0.581613i	0.956782	+	0.290807i	$0.0939236\pi$
$911$			17.5547i			0.581613i	−0.956782	+	0.290807i	$0.906076\pi$
$912$	−35.6075	−	6.77387i	−1.17908	−	0.224305i
$913$	−36.2910	+	9.72415i	−1.20106	+	0.321822i
$914$	−27.4071	−	47.4704i	−0.906545	−	1.57018i
$915$		0			0
$916$	0.832445	−	0.480612i	0.0275048	−	0.0158799i
$917$	10.4118	+	2.78982i	0.343827	+	0.0921281i
$918$	15.1690	+	9.59437i	0.500653	+	0.316661i
$919$	−28.1500	+	16.2524i	−0.928583	+	0.536118i	−0.886363	−	0.462991i	$-0.846776\pi$
$919$	−28.1500	+	16.2524i	−0.928583	+	0.536118i	−0.0422199	+	0.999108i	$0.513443\pi$
$920$		0			0
$921$	17.7674	+	26.1155i	0.585455	+	0.860536i
$922$	−8.74013	+	8.74013i	−0.287841	+	0.287841i
$923$	28.3047	−	14.1423i	0.931659	−	0.465498i
$924$	4.70800	+	2.27300i	0.154882	+	0.0747763i
$925$		0			0
$926$	−12.9814	−	7.49483i	−0.426596	−	0.246295i
$927$	−19.7287	−	45.4644i	−0.647976	−	1.49325i
$928$	0.758470	−	0.758470i	0.0248980	−	0.0248980i
$929$	22.2780	−	12.8622i	0.730916	−	0.421995i	−0.0878410	−	0.996135i	$-0.527997\pi$
$929$	22.2780	−	12.8622i	0.730916	−	0.421995i	0.818757	+	0.574140i	$0.194663\pi$
$930$		0			0
$931$		−	48.1084i		−	1.57669i
$932$	1.21124	−	4.52040i	0.0396754	−	0.148071i
$933$	−2.71736	+	14.2841i	−0.0889623	+	0.467639i
$934$	21.0162	−	36.4010i	0.687670	−	1.19108i
$935$		0			0
$936$	27.3856	−	9.97109i	0.895126	−	0.325915i
$937$	−19.2546	+	19.2546i	−0.629022	+	0.629022i	−0.947822	−	0.318800i	$-0.896720\pi$
$937$	−19.2546	+	19.2546i	−0.629022	+	0.629022i	0.318800	+	0.947822i	$0.396720\pi$
$938$	−36.1010	+	9.67325i	−1.17874	+	0.315843i
$939$	0.614235	+	0.902839i	0.0200448	+	0.0294630i
$940$		0			0
$941$	−27.3108			−0.890306			−0.445153	−	0.895455i	$-0.646851\pi$
$941$	−27.3108			−0.890306			−0.445153	+	0.895455i	$0.646851\pi$
$942$	−14.7948	−	12.7575i	−0.482040	−	0.415662i
$943$	3.13744	+	0.840675i	0.102169	+	0.0273761i
$944$		−	37.5934i		−	1.22356i
$945$		0			0
$946$	32.1183	−	55.6305i	1.04426	−	1.80870i
$947$	−0.725183	−	2.70642i	−0.0235653	−	0.0879469i	0.953142	−	0.302524i	$-0.0978293\pi$
$947$	−0.725183	−	2.70642i	−0.0235653	−	0.0879469i	−0.976707	+	0.214577i	$0.931163\pi$
$948$	0.201755	+	0.578422i	0.00655271	+	0.0187863i
$949$	27.0625	+	30.5362i	0.878485	+	0.991247i
$950$		0			0
$951$	25.4853	−	17.3386i	0.826416	−	0.562242i
$952$	6.72320	+	25.0913i	0.217900	+	0.813215i
$953$	−2.77028	−	0.742295i	−0.0897382	−	0.0240453i	0.213671	−	0.976906i	$-0.431458\pi$
$953$	−2.77028	−	0.742295i	−0.0897382	−	0.0240453i	−0.303409	+	0.952860i	$0.598125\pi$
$954$	−11.2556	−	14.1716i	−0.364412	−	0.458821i
$955$		0			0
$956$	−1.48804	−	2.57736i	−0.0481267	−	0.0833579i
$957$	2.70296	+	7.74925i	0.0873743	+	0.250498i
$958$	−4.59377	+	17.1442i	−0.148418	+	0.553903i
$959$	−21.3409	+	36.9634i	−0.689132	+	1.19361i
$960$		0			0
$961$	24.2581			0.782519
$962$	4.69974	−	2.34820i	0.151526	−	0.0757089i
$963$	27.6038	+	3.16563i	0.889519	+	0.102011i
$964$	0.143446	−	0.248456i	0.00462008	−	0.00800222i
$965$		0			0
$966$	−2.18574	−	29.5599i	−0.0703251	−	0.951073i
$967$	−34.7663	−	34.7663i	−1.11801	−	1.11801i	−0.992033	−	0.125975i	$-0.959794\pi$
$967$	−34.7663	−	34.7663i	−1.11801	−	1.11801i	−0.125975	−	0.992033i	$-0.540206\pi$
$968$	−5.08328	+	18.9711i	−0.163383	+	0.609753i
$969$	−19.6418	+	1.45237i	−0.630984	+	0.0466568i
$970$		0			0
$971$	43.8854	−	25.3373i	1.40835	−	0.813112i	0.413121	−	0.910676i	$-0.364439\pi$
$971$	43.8854	−	25.3373i	1.40835	−	0.813112i	0.995229	+	0.0975644i	$0.0311052\pi$
$972$	−2.44644	−	1.08183i	−0.0784695	−	0.0346998i
$973$	2.07193	+	7.73254i	0.0664229	+	0.247894i
$974$	59.0914			1.89341
$975$		0			0
$976$	−14.1850			−0.454050
$977$	−2.70297	−	10.0876i	−0.0864755	−	0.322731i	0.909114	−	0.416547i	$-0.136760\pi$
$977$	−2.70297	−	10.0876i	−0.0864755	−	0.322731i	−0.995590	+	0.0938164i	$0.970093\pi$
$978$	−3.34301	+	17.5728i	−0.106898	+	0.561917i
$979$	−14.0049	+	8.08574i	−0.447599	+	0.258421i
$980$		0			0
$981$	38.5574	+	15.2209i	1.23104	+	0.485967i
$982$	−7.44133	+	27.7714i	−0.237462	+	0.886221i
$983$	15.8387	+	15.8387i	0.505176	+	0.505176i	0.913042	−	0.407866i	$-0.133727\pi$
$983$	15.8387	+	15.8387i	0.505176	+	0.505176i	−0.407866	+	0.913042i	$0.633727\pi$
$984$	5.35419	−	0.395904i	0.170685	−	0.0126210i
$985$		0			0
$986$	1.91359	−	3.31444i	0.0609413	−	0.105553i
$987$	10.2174	+	29.2926i	0.325222	+	0.932395i
$988$	1.65448	−	2.50428i	0.0526361	−	0.0796717i
$989$	−28.7786			−0.915107
$990$		0			0
$991$	12.4412	−	21.5489i	0.395209	−	0.684523i	−0.597919	−	0.801557i	$-0.704005\pi$
$991$	12.4412	−	21.5489i	0.395209	−	0.684523i	0.993128	+	0.117034i	$0.0373387\pi$
$992$	0.650592	−	2.42804i	0.0206563	−	0.0770905i
$993$	−23.1940	+	8.09012i	−0.736038	+	0.256732i
$994$	−26.5950	−	46.0638i	−0.843541	−	1.46106i
$995$		0			0
$996$	−2.35144	−	1.13527i	−0.0745082	−	0.0359723i
$997$	−49.9090	−	13.3731i	−1.58063	−	0.423529i	−0.641511	−	0.767114i	$-0.721692\pi$
$997$	−49.9090	−	13.3731i	−1.58063	−	0.423529i	−0.939122	+	0.343585i	$0.888359\pi$
$998$	−2.87868	−	10.7434i	−0.0911231	−	0.340076i
$999$	4.90513	+	1.52902i	0.155191	+	0.0483761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bn.d.368.7		96
3.2	odd	2	inner	975.2.bn.d.368.18		96
5.2	odd	4	inner	975.2.bn.d.407.18		96
5.3	odd	4		195.2.bf.a.17.7	✓	96
5.4	even	2		195.2.bf.a.173.18	yes	96
13.10	even	6	inner	975.2.bn.d.218.7		96
15.2	even	4	inner	975.2.bn.d.407.7		96
15.8	even	4		195.2.bf.a.17.18	yes	96
15.14	odd	2		195.2.bf.a.173.7	yes	96
39.23	odd	6	inner	975.2.bn.d.218.18		96
65.23	odd	12		195.2.bf.a.62.7	yes	96
65.49	even	6		195.2.bf.a.23.18	yes	96
65.62	odd	12	inner	975.2.bn.d.257.18		96
195.23	even	12		195.2.bf.a.62.18	yes	96
195.62	even	12	inner	975.2.bn.d.257.7		96
195.179	odd	6		195.2.bf.a.23.7	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.7	✓	96	5.3	odd	4
195.2.bf.a.17.18	yes	96	15.8	even	4
195.2.bf.a.23.7	yes	96	195.179	odd	6
195.2.bf.a.23.18	yes	96	65.49	even	6
195.2.bf.a.62.7	yes	96	65.23	odd	12
195.2.bf.a.62.18	yes	96	195.23	even	12
195.2.bf.a.173.7	yes	96	15.14	odd	2
195.2.bf.a.173.18	yes	96	5.4	even	2
975.2.bn.d.218.7		96	13.10	even	6	inner
975.2.bn.d.218.18		96	39.23	odd	6	inner
975.2.bn.d.257.7		96	195.62	even	12	inner
975.2.bn.d.257.18		96	65.62	odd	12	inner
975.2.bn.d.368.7		96	1.1	even	1	trivial
975.2.bn.d.368.18		96	3.2	odd	2	inner
975.2.bn.d.407.7		96	15.2	even	4	inner
975.2.bn.d.407.18		96	5.2	odd	4	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+(-0.381405 - 1.42342i) q^{2} +(1.70154 + 0.323695i) q^{3} +(-0.148609 + 0.0857994i) q^{4} +(-0.188219 - 2.54546i) q^{6} +(-1.06453 + 3.97287i) q^{7} +(-1.90523 - 1.90523i) q^{8} +(2.79044 + 1.10156i) q^{9} +(-2.13830 + 3.70364i) q^{11} +(-0.280636 + 0.0978867i) q^{12} +(-0.217053 + 3.59901i) q^{13} +6.06108 q^{14} +(-2.15688 + 3.73582i) q^{16} +(-0.606673 + 2.26413i) q^{17} +(0.503692 - 4.39212i) q^{18} +(2.42558 + 4.20123i) q^{19} +(-3.09733 + 6.41539i) q^{21} +(6.08741 + 1.63112i) q^{22} +(-0.730756 - 2.72722i) q^{23} +(-2.62510 - 3.85852i) q^{24} +(5.20570 - 1.06372i) q^{26} +(4.39147 + 2.77759i) q^{27} +(-0.182671 - 0.681739i) q^{28} +(0.553990 - 0.959539i) q^{29} -2.59652i q^{31} +(0.935116 + 0.250564i) q^{32} +(-4.83724 + 5.60972i) q^{33} +3.45421 q^{34} +(-0.509198 + 0.0757171i) q^{36} +(0.955101 - 0.255918i) q^{37} +(5.05499 - 5.05499i) q^{38} +(-1.53431 + 6.05359i) q^{39} +(-0.575209 + 0.996292i) q^{41} +(10.3131 + 1.96194i) q^{42} +(2.63809 - 9.84550i) q^{43} -0.733860i q^{44} +(-3.60327 + 2.08035i) q^{46} +(3.07931 - 3.07931i) q^{47} +(-4.87927 + 5.65846i) q^{48} +(-8.58827 - 4.95844i) q^{49} +(-1.76516 + 3.65613i) q^{51} +(-0.276537 - 0.553469i) q^{52} +(2.89463 - 2.89463i) q^{53} +(2.27876 - 7.31030i) q^{54} +(9.59737 - 5.54104i) q^{56} +(2.76729 + 7.93368i) q^{57} +(-1.57712 - 0.422589i) q^{58} +(-7.54722 + 4.35739i) q^{59} +(1.64416 + 2.84776i) q^{61} +(-3.69594 + 0.990323i) q^{62} +(-7.34684 + 9.91342i) q^{63} +7.20087i q^{64} +(9.82995 + 4.74586i) q^{66} +(-5.95621 + 1.59596i) q^{67} +(-0.104104 - 0.388523i) q^{68} +(-0.360619 - 4.87700i) q^{69} +(-4.38783 - 7.59994i) q^{71} +(-3.21771 - 7.41514i) q^{72} +(8.00201 - 8.00201i) q^{73} +(-0.728560 - 1.26190i) q^{74} +(-0.720926 - 0.416227i) q^{76} +(-12.4378 - 12.4378i) q^{77} +(9.20200 - 0.124901i) q^{78} -2.06111i q^{79} +(6.57314 + 6.14767i) q^{81} +(1.63753 + 0.438775i) q^{82} +(6.21215 + 6.21215i) q^{83} +(-0.0901463 - 1.21913i) q^{84} -15.0205 q^{86} +(1.25323 - 1.45336i) q^{87} +(11.1302 - 2.98233i) q^{88} +(3.27478 + 1.89069i) q^{89} +(-14.0673 - 4.69357i) q^{91} +(0.342591 + 0.342591i) q^{92} +(0.840480 - 4.41806i) q^{93} +(-5.55763 - 3.20870i) q^{94} +(1.51003 + 0.729035i) q^{96} +(-1.31670 + 4.91400i) q^{97} +(-3.78234 + 14.1159i) q^{98} +(-10.0466 + 7.97935i) 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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