LMFDB - Embedded newform 882.2.v.a.251.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [882,2,Mod(125,882)] 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("882.125"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(882, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.v (of order $14$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			251.10
Character	$\chi$	$=$	882.251
Dual form			882.2.v.a.629.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.781831 + 0.623490i) q^{2} +(0.222521 + 0.974928i) q^{4} +(-1.86346 - 0.897393i) q^{5} +(2.21230 - 1.45111i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(-0.897393 - 1.86346i) q^{10} +(-4.86309 - 3.87818i) q^{11} +(0.0474881 + 0.0378705i) q^{13} +(2.63440 + 0.244829i) q^{14} +(-0.900969 + 0.433884i) q^{16} +(1.28053 - 5.61037i) q^{17} -2.01809i q^{19} +(0.460236 - 2.01642i) q^{20} +(-1.38411 - 6.06417i) q^{22} +(-0.713943 + 0.162953i) q^{23} +(-0.450293 - 0.564650i) q^{25} +(0.0135158 + 0.0592167i) q^{26} +(1.90701 + 1.83394i) q^{28} +(8.50253 + 1.94065i) q^{29} -0.294432i q^{31} +(-0.974928 - 0.222521i) q^{32} +(4.49917 - 3.58797i) q^{34} +(-5.42475 + 0.718765i) q^{35} +(-0.570017 + 2.49741i) q^{37} +(1.25826 - 1.57781i) q^{38} +(1.61705 - 1.28955i) q^{40} +(-7.61862 - 3.66893i) q^{41} +(-1.03943 + 0.500565i) q^{43} +(2.69881 - 5.60413i) q^{44} +(-0.659783 - 0.317735i) q^{46} +(3.82370 - 4.79476i) q^{47} +(2.78858 - 6.42058i) q^{49} -0.722214i q^{50} +(-0.0263539 + 0.0547244i) q^{52} +(-7.87382 + 1.79715i) q^{53} +(5.58190 + 11.5909i) q^{55} +(0.347518 + 2.62283i) q^{56} +(5.43757 + 6.81850i) q^{58} +(4.79120 - 2.30732i) q^{59} +(4.45582 + 1.01701i) q^{61} +(0.183575 - 0.230196i) q^{62} +(-0.623490 - 0.781831i) q^{64} +(-0.0545073 - 0.113186i) q^{65} +4.72254 q^{67} +5.75465 q^{68} +(-4.68938 - 2.82032i) q^{70} +(-1.80731 + 0.412508i) q^{71} +(12.0502 - 9.60974i) q^{73} +(-2.00277 + 1.59715i) q^{74} +(1.96749 - 0.449067i) q^{76} +(-16.3863 - 1.52287i) q^{77} -4.58892 q^{79} +2.06828 q^{80} +(-3.66893 - 7.61862i) q^{82} +(0.413442 + 0.518440i) q^{83} +(-7.42092 + 9.30555i) q^{85} +(-1.12476 - 0.256719i) q^{86} +(5.60413 - 2.69881i) q^{88} +(6.55153 + 8.21536i) q^{89} +(0.160012 + 0.0148708i) q^{91} +(-0.317735 - 0.659783i) q^{92} +(5.97897 - 1.36466i) q^{94} +(-1.81102 + 3.76062i) q^{95} -14.0455i q^{97} +(6.18337 - 3.28115i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 16 q^{4} - 16 q^{16} + 20 q^{22} - 8 q^{25} + 76 q^{37} + 28 q^{40} - 8 q^{43} + 112 q^{49} + 28 q^{52} + 28 q^{55} + 20 q^{58} + 84 q^{61} + 16 q^{64} - 8 q^{67} + 28 q^{70} + 112 q^{85} + 8 q^{88}+ \cdots - 56 q^{94}+O(q^{100}) $ 96 * q + 16 * q^4 - 16 * q^16 + 20 * q^22 - 8 * q^25 + 76 * q^37 + 28 * q^40 - 8 * q^43 + 112 * q^49 + 28 * q^52 + 28 * q^55 + 20 * q^58 + 84 * q^61 + 16 * q^64 - 8 * q^67 + 28 * q^70 + 112 * q^85 + 8 * q^88 - 56 * q^91 - 56 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{9}{14}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$3$		0			0
$3$		0			0
$4$	0.222521	+	0.974928i	0.111260	+	0.487464i
$5$	−1.86346	−	0.897393i	−0.833363	−	0.401327i	−0.0319877	−	0.999488i	$-0.510184\pi$
$5$	−1.86346	−	0.897393i	−0.833363	−	0.401327i	−0.801375	+	0.598162i	$0.795898\pi$
$6$		0			0
$7$	2.21230	−	1.45111i	0.836173	−	0.548466i
$7$	2.21230	−	1.45111i	0.836173	−	0.548466i
$8$	−0.433884	+	0.900969i	−0.153401	+	0.318541i
$9$		0			0
$10$	−0.897393	−	1.86346i	−0.283781	−	0.589277i
$11$	−4.86309	−	3.87818i	−1.46628	−	1.16932i	−0.949736	−	0.313053i	$-0.898648\pi$
$11$	−4.86309	−	3.87818i	−1.46628	−	1.16932i	−0.516540	−	0.856263i	$-0.672780\pi$
$12$		0			0
$13$	0.0474881	+	0.0378705i	0.0131708	+	0.0105034i	0.630053	−	0.776552i	$-0.283033\pi$
$13$	0.0474881	+	0.0378705i	0.0131708	+	0.0105034i	−0.616882	+	0.787055i	$0.711605\pi$
$14$	2.63440	+	0.244829i	0.704073	+	0.0654334i
$15$		0			0
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	1.28053	−	5.61037i	0.310574	−	1.36072i	−0.542995	−	0.839736i	$-0.682710\pi$
$17$	1.28053	−	5.61037i	0.310574	−	1.36072i	0.853569	−	0.520979i	$-0.174433\pi$
$18$		0			0
$19$		−	2.01809i		−	0.462981i	−0.972837	−	0.231491i	$-0.925640\pi$
$19$		−	2.01809i		−	0.462981i	0.972837	−	0.231491i	$-0.0743603\pi$
$20$	0.460236	−	2.01642i	0.102912	−	0.450886i
$21$		0			0
$22$	−1.38411	−	6.06417i	−0.295093	−	1.29289i
$23$	−0.713943	+	0.162953i	−0.148867	+	0.0339780i	−0.296305	−	0.955093i	$-0.595755\pi$
$23$	−0.713943	+	0.162953i	−0.148867	+	0.0339780i	0.147438	+	0.989071i	$0.452897\pi$
$24$		0			0
$25$	−0.450293	−	0.564650i	−0.0900587	−	0.112930i
$26$	0.0135158	+	0.0592167i	0.00265067	+	0.0116133i
$27$		0			0
$28$	1.90701	+	1.83394i	0.360391	+	0.346581i
$29$	8.50253	+	1.94065i	1.57888	+	0.360369i	0.920012	−	0.391890i	$-0.128179\pi$
$29$	8.50253	+	1.94065i	1.57888	+	0.360369i	0.658867	+	0.752259i	$0.271036\pi$
$30$		0			0
$31$		−	0.294432i		−	0.0528815i	−0.999650	−	0.0264407i	$-0.991583\pi$
$31$		−	0.294432i		−	0.0528815i	0.999650	−	0.0264407i	$-0.00841733\pi$
$32$	−0.974928	−	0.222521i	−0.172345	−	0.0393365i
$33$		0			0
$34$	4.49917	−	3.58797i	0.771601	−	0.615331i
$35$	−5.42475	+	0.718765i	−0.916950	+	0.121493i
$36$		0			0
$37$	−0.570017	+	2.49741i	−0.0937103	+	0.410572i	−0.999925	−	0.0122462i	$-0.996102\pi$
$37$	−0.570017	+	2.49741i	−0.0937103	+	0.410572i	0.906215	+	0.422818i	$0.138959\pi$
$38$	1.25826	−	1.57781i	0.204116	−	0.255954i
$39$		0			0
$40$	1.61705	−	1.28955i	0.255678	−	0.203896i
$41$	−7.61862	−	3.66893i	−1.18983	−	0.572991i	−0.269069	−	0.963121i	$-0.586716\pi$
$41$	−7.61862	−	3.66893i	−1.18983	−	0.572991i	−0.920760	+	0.390130i	$0.872430\pi$
$42$		0			0
$43$	−1.03943	+	0.500565i	−0.158512	+	0.0763355i	−0.511458	−	0.859308i	$-0.670894\pi$
$43$	−1.03943	+	0.500565i	−0.158512	+	0.0763355i	0.352946	+	0.935644i	$0.385180\pi$
$44$	2.69881	−	5.60413i	0.406861	−	0.844855i
$45$		0			0
$46$	−0.659783	−	0.317735i	−0.0972797	−	0.0468474i
$47$	3.82370	−	4.79476i	0.557743	−	0.699388i	−0.420395	−	0.907341i	$-0.638109\pi$
$47$	3.82370	−	4.79476i	0.557743	−	0.699388i	0.978139	+	0.207953i	$0.0666801\pi$
$48$		0			0
$49$	2.78858	−	6.42058i	0.398369	−	0.917225i
$50$		−	0.722214i		−	0.102137i
$51$		0			0
$52$	−0.0263539	+	0.0547244i	−0.00365463	+	0.00758892i
$53$	−7.87382	+	1.79715i	−1.08155	+	0.246857i	−0.725928	−	0.687771i	$-0.758589\pi$
$53$	−7.87382	+	1.79715i	−1.08155	+	0.246857i	−0.355625	+	0.934629i	$0.615732\pi$
$54$		0			0
$55$	5.58190	+	11.5909i	0.752663	+	1.56292i
$56$	0.347518	+	2.62283i	0.0464390	+	0.350490i
$57$		0			0
$58$	5.43757	+	6.81850i	0.713988	+	0.895312i
$59$	4.79120	−	2.30732i	0.623762	−	0.300388i	−0.0951780	−	0.995460i	$-0.530342\pi$
$59$	4.79120	−	2.30732i	0.623762	−	0.300388i	0.718940	+	0.695073i	$0.244628\pi$
$60$		0			0
$61$	4.45582	+	1.01701i	0.570509	+	0.130215i	0.498037	−	0.867156i	$-0.334054\pi$
$61$	4.45582	+	1.01701i	0.570509	+	0.130215i	0.0724715	+	0.997370i	$0.476911\pi$
$62$	0.183575	−	0.230196i	0.0233141	−	0.0292349i
$63$		0			0
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	−0.0545073	−	0.113186i	−0.00676080	−	0.0140389i
$66$		0			0
$67$	4.72254			0.576951			0.288475	−	0.957487i	$-0.406852\pi$
$67$	4.72254			0.576951			0.288475	+	0.957487i	$0.406852\pi$
$68$	5.75465			0.697854
$69$		0			0
$70$	−4.68938	−	2.82032i	−0.560488	−	0.337093i
$71$	−1.80731	+	0.412508i	−0.214489	+	0.0489557i	−0.328415	−	0.944534i	$-0.606514\pi$
$71$	−1.80731	+	0.412508i	−0.214489	+	0.0489557i	0.113926	+	0.993489i	$0.463657\pi$
$72$		0			0
$73$	12.0502	−	9.60974i	1.41037	−	1.12474i	0.435962	−	0.899965i	$-0.356408\pi$
$73$	12.0502	−	9.60974i	1.41037	−	1.12474i	0.974412	−	0.224770i	$-0.0721631\pi$
$74$	−2.00277	+	1.59715i	−0.232817	+	0.185665i
$75$		0			0
$76$	1.96749	−	0.449067i	0.225687	−	0.0515115i
$77$	−16.3863	−	1.52287i	−1.86739	−	0.173547i
$78$		0			0
$79$	−4.58892			−0.516294			−0.258147	−	0.966106i	$-0.583112\pi$
$79$	−4.58892			−0.516294			−0.258147	+	0.966106i	$0.583112\pi$
$80$	2.06828			0.231241
$81$		0			0
$82$	−3.66893	−	7.61862i	−0.405166	−	0.841336i
$83$	0.413442	+	0.518440i	0.0453812	+	0.0569062i	0.804004	−	0.594624i	$-0.202699\pi$
$83$	0.413442	+	0.518440i	0.0453812	+	0.0569062i	−0.758623	+	0.651530i	$0.774128\pi$
$84$		0			0
$85$	−7.42092	+	9.30555i	−0.804912	+	1.00933i
$86$	−1.12476	−	0.256719i	−0.121286	−	0.0276827i
$87$		0			0
$88$	5.60413	−	2.69881i	0.597403	−	0.287694i
$89$	6.55153	+	8.21536i	0.694461	+	0.870827i	0.996596	−	0.0824385i	$-0.0262708\pi$
$89$	6.55153	+	8.21536i	0.694461	+	0.870827i	−0.302135	+	0.953265i	$0.597699\pi$
$90$		0			0
$91$	0.160012	+	0.0148708i	0.0167738	+	0.00155889i
$92$	−0.317735	−	0.659783i	−0.0331261	−	0.0687871i
$93$		0			0
$94$	5.97897	−	1.36466i	0.616684	−	0.140754i
$95$	−1.81102	+	3.76062i	−0.185807	+	0.385832i
$96$		0			0
$97$		−	14.0455i		−	1.42611i	−0.701109	−	0.713054i	$-0.747311\pi$
$97$		−	14.0455i		−	1.42611i	0.701109	−	0.713054i	$-0.252689\pi$
$98$	6.18337	−	3.28115i	0.624614	−	0.331447i
$99$		0			0
$100$	0.450293	−	0.564650i	0.0450293	−	0.0564650i
$101$	5.45360	+	2.62631i	0.542653	+	0.261328i	0.685068	−	0.728479i	$-0.259772\pi$
$101$	5.45360	+	2.62631i	0.542653	+	0.261328i	−0.142415	+	0.989807i	$0.545487\pi$
$102$		0			0
$103$	−5.39776	+	11.2086i	−0.531857	+	1.10441i	0.445979	+	0.895043i	$0.352856\pi$
$103$	−5.39776	+	11.2086i	−0.531857	+	1.10441i	−0.977836	+	0.209370i	$0.932859\pi$
$104$	−0.0547244	+	0.0263539i	−0.00536617	+	0.00258421i
$105$		0			0
$106$	−7.27651	−	3.50418i	−0.706757	−	0.340356i
$107$	−13.5743	+	10.8252i	−1.31228	+	1.04651i	−0.317106	+	0.948390i	$0.602711\pi$
$107$	−13.5743	+	10.8252i	−1.31228	+	1.04651i	−0.995175	+	0.0981193i	$0.968717\pi$
$108$		0			0
$109$	−3.44317	+	4.31760i	−0.329796	+	0.413551i	−0.918890	−	0.394513i	$-0.870913\pi$
$109$	−3.44317	+	4.31760i	−0.329796	+	0.413551i	0.589094	+	0.808064i	$0.299485\pi$
$110$	−2.86272	+	12.5424i	−0.272950	+	1.19587i
$111$		0			0
$112$	−1.36361	+	2.26728i	−0.128849	+	0.214238i
$113$	−14.2669	+	11.3775i	−1.34212	+	1.07030i	−0.351131	+	0.936326i	$0.614203\pi$
$113$	−14.2669	+	11.3775i	−1.34212	+	1.07030i	−0.990985	+	0.133975i	$0.957226\pi$
$114$		0			0
$115$	1.47664	+	0.337032i	0.137697	+	0.0314284i
$116$			8.72118i			0.809742i
$117$		0			0
$118$	5.18451	+	1.18333i	0.477272	+	0.108934i
$119$	−5.30832	−	14.2700i	−0.486613	−	1.30813i
$120$		0			0
$121$	6.16158	+	26.9957i	0.560144	+	2.45415i
$122$	2.84960	+	3.57329i	0.257991	+	0.323510i
$123$		0			0
$124$	0.287050	−	0.0655172i	0.0257778	−	0.00588362i
$125$	2.63357	+	11.5384i	0.235553	+	1.03203i
$126$		0			0
$127$	1.16385	−	5.09916i	0.103275	−	0.452478i	−0.896677	−	0.442685i	$-0.854026\pi$
$127$	1.16385	−	5.09916i	0.103275	−	0.452478i	0.999952	−	0.00979215i	$-0.00311699\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	0.0279545	−	0.122477i	0.00245177	−	0.0107419i
$131$	9.23890	−	4.44922i	0.807206	−	0.388730i	0.0156892	−	0.999877i	$-0.495006\pi$
$131$	9.23890	−	4.44922i	0.807206	−	0.388730i	0.791517	+	0.611147i	$0.209291\pi$
$132$		0			0
$133$	−2.92846	−	4.46463i	−0.253930	−	0.387132i
$134$	3.69223	+	2.94446i	0.318960	+	0.254362i
$135$		0			0
$136$	4.49917	+	3.58797i	0.385801	+	0.307666i
$137$	1.55204	+	3.22284i	0.132600	+	0.275346i	0.956688	−	0.291115i	$-0.0940264\pi$
$137$	1.55204	+	3.22284i	0.132600	+	0.275346i	−0.824088	+	0.566461i	$0.808312\pi$
$138$		0			0
$139$	−8.13878	+	16.9004i	−0.690323	+	1.43347i	0.200766	+	0.979639i	$0.435657\pi$
$139$	−8.13878	+	16.9004i	−0.690323	+	1.43347i	−0.891088	+	0.453830i	$0.850057\pi$
$140$	−1.90786	−	5.12880i	−0.161244	−	0.433462i
$141$		0			0
$142$	−1.67021	−	0.804331i	−0.140161	−	0.0674979i
$143$	−0.0840700	−	0.368335i	−0.00703029	−	0.0308017i
$144$		0			0
$145$	−14.1026	−	11.2464i	−1.17115	−	0.933964i
$146$	15.4128			1.27557
$147$		0			0
$148$	−2.56164			−0.210565
$149$	10.0903	+	8.04671i	0.826626	+	0.659212i	0.942557	−	0.334045i	$-0.108414\pi$
$149$	10.0903	+	8.04671i	0.826626	+	0.659212i	−0.115931	+	0.993257i	$0.536985\pi$
$150$		0			0
$151$	−3.33084	−	14.5934i	−0.271060	−	1.18759i	−0.908764	−	0.417310i	$-0.862973\pi$
$151$	−3.33084	−	14.5934i	−0.271060	−	1.18759i	0.637705	−	0.770281i	$-0.279884\pi$
$152$	1.81824	+	0.875616i	0.147478	+	0.0710219i
$153$		0			0
$154$	−11.8618	−	11.4073i	−0.955852	−	0.919227i
$155$	−0.264221	+	0.548661i	−0.0212227	+	0.0440695i
$156$		0			0
$157$	2.58460	+	5.36697i	0.206273	+	0.428331i	0.978281	−	0.207282i	$-0.0664617\pi$
$157$	2.58460	+	5.36697i	0.206273	+	0.428331i	−0.772008	+	0.635613i	$0.780747\pi$
$158$	−3.58776	−	2.86114i	−0.285427	−	0.227620i
$159$		0			0
$160$	1.61705	+	1.28955i	0.127839	+	0.101948i
$161$	−1.34300	+	1.39651i	−0.105843	+	0.110060i
$162$		0			0
$163$	−11.4562	+	5.51701i	−0.897319	+	0.432126i	−0.824920	−	0.565250i	$-0.808780\pi$
$163$	−11.4562	+	5.51701i	−0.897319	+	0.432126i	−0.0723990	+	0.997376i	$0.523065\pi$
$164$	1.88164	−	8.24402i	0.146932	−	0.643750i
$165$		0			0
$166$			0.663110i			0.0514673i
$167$	3.77483	−	16.5386i	0.292105	−	1.27980i	−0.589485	−	0.807779i	$-0.700669\pi$
$167$	3.77483	−	16.5386i	0.292105	−	1.27980i	0.881590	−	0.472016i	$-0.156474\pi$
$168$		0			0
$169$	−2.89195	−	12.6705i	−0.222458	−	0.974651i
$170$	−11.6038	+	2.64850i	−0.889973	+	0.203130i
$171$		0			0
$172$	−0.719311	−	0.901987i	−0.0548469	−	0.0687759i
$173$	−2.83438	−	12.4182i	−0.215494	−	0.944142i	−0.960761	−	0.277376i	$-0.910535\pi$
$173$	−2.83438	−	12.4182i	−0.215494	−	0.944142i	0.745267	−	0.666766i	$-0.232322\pi$
$174$		0			0
$175$	−1.81555	−	0.595755i	−0.137243	−	0.0450348i
$176$	6.06417	+	1.38411i	0.457104	+	0.104331i
$177$		0			0
$178$			10.5078i			0.787596i
$179$	−0.193832	−	0.0442410i	−0.0144877	−	0.00330672i	0.215271	−	0.976554i	$-0.430937\pi$
$179$	−0.193832	−	0.0442410i	−0.0144877	−	0.00330672i	−0.229759	+	0.973248i	$0.573794\pi$
$180$		0			0
$181$	−7.74260	+	6.17452i	−0.575503	+	0.458948i	−0.867477	−	0.497478i	$-0.834259\pi$
$181$	−7.74260	+	6.17452i	−0.575503	+	0.458948i	0.291974	+	0.956426i	$0.405688\pi$
$182$	0.115831	+	0.111392i	0.00858595	+	0.00825696i
$183$		0			0
$184$	0.162953	−	0.713943i	0.0120130	−	0.0526326i
$185$	3.30336	−	4.14228i	0.242868	−	0.304547i
$186$		0			0
$187$	−27.9854	+	22.3176i	−2.04649	+	1.63202i
$188$	5.52540	+	2.66089i	0.402981	+	0.194066i
$189$		0			0
$190$	−3.76062	+	1.81102i	−0.272824	+	0.131385i
$191$	11.1089	−	23.0678i	0.803809	−	1.66913i	0.0624224	−	0.998050i	$-0.480117\pi$
$191$	11.1089	−	23.0678i	0.803809	−	1.66913i	0.741387	−	0.671078i	$-0.234168\pi$
$192$		0			0
$193$	1.42186	+	0.684733i	0.102348	+	0.0492881i	0.484357	−	0.874870i	$-0.339054\pi$
$193$	1.42186	+	0.684733i	0.102348	+	0.0492881i	−0.382009	+	0.924158i	$0.624768\pi$
$194$	8.75725	−	10.9812i	0.628734	−	0.788408i
$195$		0			0
$196$	6.88012	+	1.28996i	0.491437	+	0.0921397i
$197$			18.5328i			1.32040i	0.751088	+	0.660202i	$0.229529\pi$
$197$			18.5328i			1.32040i	−0.751088	+	0.660202i	$0.770471\pi$
$198$		0			0
$199$	10.0992	−	20.9713i	0.715917	−	1.48662i	−0.151196	−	0.988504i	$-0.548312\pi$
$199$	10.0992	−	20.9713i	0.715917	−	1.48662i	0.867112	−	0.498112i	$-0.165973\pi$
$200$	0.704107	−	0.160708i	0.0497879	−	0.0113638i
$201$		0			0
$202$	2.62631	+	5.45360i	0.184787	+	0.383714i
$203$	21.6263	−	8.04476i	1.51787	−	0.564632i
$204$		0			0
$205$	10.9045	+	13.6738i	0.761603	+	0.955019i
$206$	−11.2086	+	5.39776i	−0.780938	+	0.376080i
$207$		0			0
$208$	−0.0592167	−	0.0135158i	−0.00410594	−	0.000937154i
$209$	−7.82652	+	9.81414i	−0.541372	+	0.678858i
$210$		0			0
$211$	−1.26466	−	1.58583i	−0.0870625	−	0.109173i	0.736392	−	0.676555i	$-0.236528\pi$
$211$	−1.26466	−	1.58583i	−0.0870625	−	0.109173i	−0.823455	+	0.567382i	$0.807956\pi$
$212$	−3.50418	−	7.27651i	−0.240668	−	0.499753i
$213$		0			0
$214$	−17.3622			−1.18686
$215$	2.38614			0.162734
$216$		0			0
$217$	−0.427252	−	0.651373i	−0.0290037	−	0.0442181i
$218$	−5.38396	+	1.22885i	−0.364648	+	0.0832285i
$219$		0			0
$220$	−10.0582	+	8.02117i	−0.678126	+	0.540787i
$221$	0.273278	−	0.217932i	0.0183826	−	0.0146597i
$222$		0			0
$223$	27.3521	−	6.24293i	1.83163	−	0.418057i	0.839509	−	0.543346i	$-0.182843\pi$
$223$	27.3521	−	6.24293i	1.83163	−	0.418057i	0.992120	+	0.125289i	$0.0399858\pi$
$224$	−2.47974	+	0.922439i	−0.165685	+	0.0616331i
$225$		0			0
$226$	−18.2480			−1.21384
$227$	−11.2079			−0.743894			−0.371947	−	0.928254i	$-0.621310\pi$
$227$	−11.2079			−0.743894			−0.371947	+	0.928254i	$0.621310\pi$
$228$		0			0
$229$	0.439466	+	0.912561i	0.0290408	+	0.0603038i	0.914985	−	0.403489i	$-0.132203\pi$
$229$	0.439466	+	0.912561i	0.0290408	+	0.0603038i	−0.885944	+	0.463793i	$0.846488\pi$
$230$	0.944344	+	1.18417i	0.0622682	+	0.0780818i
$231$		0			0
$232$	−5.43757	+	6.81850i	−0.356994	+	0.447656i
$233$	28.8486	+	6.58450i	1.88993	+	0.431365i	0.999708	−	0.0241544i	$-0.00768934\pi$
$233$	28.8486	+	6.58450i	1.88993	+	0.431365i	0.890226	+	0.455520i	$0.150546\pi$
$234$		0			0
$235$	−11.4281	+	5.50347i	−0.745486	+	0.359007i
$236$	3.31562	+	4.15765i	0.215828	+	0.270640i
$237$		0			0
$238$	4.74701	−	14.4664i	0.307703	−	0.937721i
$239$	6.83495	+	14.1929i	0.442116	+	0.918064i	0.996322	+	0.0856846i	$0.0273077\pi$
$239$	6.83495	+	14.1929i	0.442116	+	0.918064i	−0.554206	+	0.832380i	$0.686978\pi$
$240$		0			0
$241$	9.88232	−	2.25558i	0.636576	−	0.145294i	0.107960	−	0.994155i	$-0.465568\pi$
$241$	9.88232	−	2.25558i	0.636576	−	0.145294i	0.528616	+	0.848861i	$0.322711\pi$
$242$	−12.0142	+	24.9477i	−0.772302	+	1.60370i
$243$		0			0
$244$			4.57041i			0.292590i
$245$	−10.9582	+	9.46201i	−0.700093	+	0.604505i
$246$		0			0
$247$	0.0764260	−	0.0958352i	0.00486287	−	0.00609785i
$248$	0.265274	+	0.127749i	0.0168449	+	0.00811208i
$249$		0			0
$250$	−5.13508	+	10.6631i	−0.324771	+	0.674394i
$251$	0.807332	−	0.388791i	0.0509583	−	0.0245402i	−0.408231	−	0.912879i	$-0.633854\pi$
$251$	0.807332	−	0.388791i	0.0509583	−	0.0245402i	0.459189	+	0.888338i	$0.348140\pi$
$252$		0			0
$253$	4.10393	+	1.97635i	0.258012	+	0.124252i
$254$	4.08921	−	3.26104i	0.256580	−	0.204616i
$255$		0			0
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	−2.81500	+	12.3333i	−0.175595	+	0.769331i	0.808036	+	0.589133i	$0.200531\pi$
$257$	−2.81500	+	12.3333i	−0.175595	+	0.769331i	−0.983630	+	0.180197i	$0.942326\pi$
$258$		0			0
$259$	2.36295	+	6.35219i	0.146827	+	0.394706i
$260$	0.0982187	−	0.0783268i	0.00609127	−	0.00485762i
$261$		0			0
$262$	9.99731	+	2.28182i	0.617636	+	0.140971i
$263$		−	12.3187i		−	0.759603i	−0.925068	−	0.379801i	$-0.875992\pi$
$263$		−	12.3187i		−	0.759603i	0.925068	−	0.379801i	$-0.124008\pi$
$264$		0			0
$265$	16.2853	+	3.71701i	1.00040	+	0.228334i
$266$	0.494088	−	5.31645i	0.0302945	−	0.325973i
$267$		0			0
$268$	1.05086	+	4.60414i	0.0641918	+	0.281243i
$269$	−0.416618	−	0.522423i	−0.0254017	−	0.0318527i	0.768968	−	0.639287i	$-0.220770\pi$
$269$	−0.416618	−	0.522423i	−0.0254017	−	0.0318527i	−0.794370	+	0.607434i	$0.792199\pi$
$270$		0			0
$271$	−29.7211	+	6.78365i	−1.80543	+	0.412077i	−0.986760	−	0.162188i	$-0.948145\pi$
$271$	−29.7211	+	6.78365i	−1.80543	+	0.412077i	−0.818669	+	0.574266i	$0.805288\pi$
$272$	1.28053	+	5.61037i	0.0776436	+	0.340179i
$273$		0			0
$274$	−0.795976	+	3.48740i	−0.0480866	+	0.210681i
$275$			4.49226i			0.270894i
$276$		0			0
$277$	3.09232	−	13.5483i	0.185800	−	0.814041i	−0.793000	−	0.609221i	$-0.791482\pi$
$277$	3.09232	−	13.5483i	0.185800	−	0.814041i	0.978800	−	0.204820i	$-0.0656608\pi$
$278$	−16.9004	+	8.13878i	−1.01362	+	0.488132i
$279$		0			0
$280$	1.70612	−	5.19939i	0.101960	−	0.310723i
$281$	24.3841	+	19.4457i	1.45464	+	1.16003i	0.956054	+	0.293191i	$0.0947173\pi$
$281$	24.3841	+	19.4457i	1.45464	+	1.16003i	0.498582	+	0.866842i	$0.333854\pi$
$282$		0			0
$283$	−24.2602	−	19.3469i	−1.44212	−	1.15005i	−0.962067	−	0.272814i	$-0.912045\pi$
$283$	−24.2602	−	19.3469i	−1.44212	−	1.15005i	−0.480054	−	0.877239i	$-0.659383\pi$
$284$	−0.804331	−	1.67021i	−0.0477282	−	0.0991087i
$285$		0			0
$286$	0.163924	−	0.340393i	0.00969306	−	0.0201278i
$287$	−22.1787	+	2.93862i	−1.30917	+	0.173461i
$288$		0			0
$289$	−14.5200	−	6.99249i	−0.854120	−	0.411323i
$290$	−4.01380	−	17.5856i	−0.235699	−	1.03266i
$291$		0			0
$292$	12.0502	+	9.60974i	0.705187	+	0.562368i
$293$	13.1726			0.769549			0.384774	−	0.923011i	$-0.374279\pi$
$293$	13.1726			0.769549			0.384774	+	0.923011i	$0.374279\pi$
$294$		0			0
$295$	−10.9988			−0.640373
$296$	−2.00277	−	1.59715i	−0.116408	−	0.0928327i
$297$		0			0
$298$	2.87184	+	12.5823i	0.166361	+	0.728875i
$299$	−0.0400749	−	0.0192991i	−0.00231759	−	0.00111609i
$300$		0			0
$301$	−1.57317	+	2.61573i	−0.0906762	+	0.150768i
$302$	6.49466	−	13.4863i	0.373725	−	0.776049i
$303$		0			0
$304$	0.875616	+	1.81824i	0.0502200	+	0.104283i
$305$	−7.39056	−	5.89378i	−0.423182	−	0.337477i
$306$		0			0
$307$	14.2043	+	11.3276i	0.810683	+	0.646498i	0.938492	−	0.345300i	$-0.112223\pi$
$307$	14.2043	+	11.3276i	0.810683	+	0.646498i	−0.127809	+	0.991799i	$0.540794\pi$
$308$	−2.16160	−	16.3143i	−0.123169	−	0.929594i
$309$		0			0
$310$	−0.548661	+	0.264221i	−0.0311618	+	0.0150067i
$311$	3.66913	−	16.0755i	0.208057	−	0.911559i	−0.757801	−	0.652486i	$-0.773726\pi$
$311$	3.66913	−	16.0755i	0.208057	−	0.911559i	0.965858	−	0.259072i	$-0.0834168\pi$
$312$		0			0
$313$			22.0392i			1.24573i	0.782330	+	0.622864i	$0.214031\pi$
$313$			22.0392i			1.24573i	−0.782330	+	0.622864i	$0.785969\pi$
$314$	−1.32553	+	5.80754i	−0.0748042	+	0.327738i
$315$		0			0
$316$	−1.02113	−	4.47387i	−0.0574431	−	0.251675i
$317$	17.3501	−	3.96005i	0.974480	−	0.222419i	0.294502	−	0.955651i	$-0.404846\pi$
$317$	17.3501	−	3.96005i	0.974480	−	0.222419i	0.679978	+	0.733232i	$0.261989\pi$
$318$		0			0
$319$	−33.8223	−	42.4119i	−1.89369	−	2.37461i
$320$	0.460236	+	2.01642i	0.0257280	+	0.112722i
$321$		0			0
$322$	−1.92071	+	0.254489i	−0.107037	+	0.0141821i
$323$	−11.3222	−	2.58423i	−0.629986	−	0.143790i
$324$		0			0
$325$		−	0.0438670i		−	0.00243330i
$326$	−12.3966	−	2.82945i	−0.686585	−	0.156709i
$327$		0			0
$328$	6.61119	−	5.27225i	0.365042	−	0.291111i
$329$	1.50147	−	16.1561i	0.0827789	−	0.890713i
$330$		0			0
$331$	6.02818	−	26.4112i	0.331339	−	1.45169i	−0.485202	−	0.874402i	$-0.661254\pi$
$331$	6.02818	−	26.4112i	0.331339	−	1.45169i	0.816541	−	0.577288i	$-0.195889\pi$
$332$	−0.413442	+	0.518440i	−0.0226906	+	0.0284531i
$333$		0			0
$334$	13.2629	−	10.5768i	0.725715	−	0.578739i
$335$	−8.80026	−	4.23798i	−0.480809	−	0.231546i
$336$		0			0
$337$	8.85257	−	4.26317i	0.482230	−	0.232230i	−0.176943	−	0.984221i	$-0.556621\pi$
$337$	8.85257	−	4.26317i	0.482230	−	0.232230i	0.659173	+	0.751991i	$0.270906\pi$
$338$	5.63889	−	11.7093i	0.306715	−	0.636900i
$339$		0			0
$340$	−10.7235	−	5.16419i	−0.581566	−	0.280067i
$341$	−1.14186	+	1.43185i	−0.0618352	+	0.0775388i
$342$		0			0
$343$	−3.14774	−	18.2508i	−0.169962	−	0.985451i
$344$		−	1.15368i		−	0.0622025i
$345$		0			0
$346$	5.52664	−	11.4762i	0.297114	−	0.616963i
$347$	1.05288	−	0.240312i	0.0565214	−	0.0129006i	−0.194167	−	0.980969i	$-0.562200\pi$
$347$	1.05288	−	0.240312i	0.0565214	−	0.0129006i	0.250688	+	0.968068i	$0.419343\pi$
$348$		0			0
$349$	12.8678	+	26.7202i	0.688796	+	1.43030i	0.892399	+	0.451247i	$0.149021\pi$
$349$	12.8678	+	26.7202i	0.688796	+	1.43030i	−0.203603	+	0.979054i	$0.565265\pi$
$350$	−1.04801	−	1.59776i	−0.0560185	−	0.0854038i
$351$		0			0
$352$	3.87818	+	4.86309i	0.206708	+	0.259203i
$353$	18.9935	−	9.14679i	1.01092	−	0.486835i	0.146291	−	0.989242i	$-0.453266\pi$
$353$	18.9935	−	9.14679i	1.01092	−	0.486835i	0.864631	+	0.502407i	$0.167552\pi$
$354$		0			0
$355$	3.73803	+	0.853182i	0.198394	+	0.0452822i
$356$	−6.55153	+	8.21536i	−0.347231	+	0.435413i
$357$		0			0
$358$	−0.123960	−	0.155441i	−0.00655151	−	0.00821533i
$359$	6.00746	+	12.4746i	0.317061	+	0.658385i	0.997207	−	0.0746926i	$-0.0237975\pi$
$359$	6.00746	+	12.4746i	0.317061	+	0.658385i	−0.680145	+	0.733077i	$0.738083\pi$
$360$		0			0
$361$	14.9273			0.785648
$362$	−9.90316			−0.520498
$363$		0			0
$364$	0.0211081	+	0.159309i	0.00110636	+	0.00835008i
$365$	−31.0788	+	7.09354i	−1.62674	+	0.371293i
$366$		0			0
$367$	−2.44696	+	1.95139i	−0.127731	+	0.101862i	−0.685271	−	0.728288i	$-0.740316\pi$
$367$	−2.44696	+	1.95139i	−0.127731	+	0.101862i	0.557541	+	0.830149i	$0.311745\pi$
$368$	0.572538	−	0.456584i	0.0298456	−	0.0238011i
$369$		0			0
$370$	5.16534	−	1.17896i	0.268533	−	0.0612910i
$371$	−14.8114	+	15.4016i	−0.768972	+	0.799611i
$372$		0			0
$373$	16.6140			0.860240			0.430120	−	0.902772i	$-0.358471\pi$
$373$	16.6140			0.860240			0.430120	+	0.902772i	$0.358471\pi$
$374$	−35.7946			−1.85090
$375$		0			0
$376$	2.66089	+	5.52540i	0.137225	+	0.284951i
$377$	0.330276	+	0.414152i	0.0170101	+	0.0213299i
$378$		0			0
$379$	3.04806	−	3.82214i	0.156568	−	0.196330i	−0.697360	−	0.716721i	$-0.745642\pi$
$379$	3.04806	−	3.82214i	0.156568	−	0.196330i	0.853928	+	0.520391i	$0.174214\pi$
$380$	−4.06933	−	0.928797i	−0.208752	−	0.0476463i
$381$		0			0
$382$	23.0678	−	11.1089i	1.18025	−	0.568379i
$383$	8.31374	+	10.4251i	0.424812	+	0.532698i	0.947470	−	0.319845i	$-0.103631\pi$
$383$	8.31374	+	10.4251i	0.424812	+	0.532698i	−0.522658	+	0.852543i	$0.675059\pi$
$384$		0			0
$385$	29.1685	+	17.5427i	1.48656	+	0.894061i
$386$	0.684733	+	1.42186i	0.0348520	+	0.0723709i
$387$		0			0
$388$	13.6934	−	3.12543i	0.695177	−	0.158670i
$389$	−1.46399	+	3.04000i	−0.0742272	+	0.154134i	−0.934780	−	0.355226i	$-0.884404\pi$
$389$	−1.46399	+	3.04000i	−0.0742272	+	0.154134i	0.860553	+	0.509361i	$0.170118\pi$
$390$		0			0
$391$			4.21415i			0.213119i
$392$	4.57482	+	5.29821i	0.231063	+	0.267600i
$393$		0			0
$394$	−11.5550	+	14.4895i	−0.582132	+	0.729970i
$395$	8.55125	+	4.11807i	0.430260	+	0.207202i
$396$		0			0
$397$	10.2920	−	21.3715i	0.516538	−	1.07260i	−0.465696	−	0.884945i	$-0.654196\pi$
$397$	10.2920	−	21.3715i	0.516538	−	1.07260i	0.982234	−	0.187658i	$-0.0600897\pi$
$398$	20.9713	−	10.0992i	1.05120	−	0.506230i
$399$		0			0
$400$	0.650693	+	0.313357i	0.0325346	+	0.0156679i
$401$	15.2960	−	12.1981i	0.763844	−	0.609145i	−0.162114	−	0.986772i	$-0.551831\pi$
$401$	15.2960	−	12.1981i	0.763844	−	0.609145i	0.925958	+	0.377627i	$0.123260\pi$
$402$		0			0
$403$	0.0111503	−	0.0139820i	0.000555435	−	0.000696493i
$404$	−1.34693	+	5.90128i	−0.0670122	+	0.293599i
$405$		0			0
$406$	21.9239	+	7.19410i	1.08807	+	0.357037i
$407$	12.4575	−	9.93449i	0.617493	−	0.492434i
$408$		0			0
$409$	6.08252	+	1.38829i	0.300761	+	0.0686468i	0.370238	−	0.928937i	$-0.379276\pi$
$409$	6.08252	+	1.38829i	0.300761	+	0.0686468i	−0.0694773	+	0.997584i	$0.522133\pi$
$410$			17.4894i			0.863742i
$411$		0			0
$412$	−12.1287	−	2.76829i	−0.597536	−	0.136384i
$413$	7.25143	−	12.0570i	0.356820	−	0.593288i
$414$		0			0
$415$	−0.305187	−	1.33711i	−0.0149810	−	0.0656362i
$416$	−0.0378705	−	0.0474881i	−0.00185675	−	0.00232830i
$417$		0			0
$418$	−12.2380	+	2.79325i	−0.598582	+	0.136622i
$419$	−3.65547	−	16.0157i	−0.178582	−	0.782417i	−0.982286	−	0.187388i	$-0.939998\pi$
$419$	−3.65547	−	16.0157i	−0.178582	−	0.782417i	0.803704	−	0.595029i	$-0.202859\pi$
$420$		0			0
$421$	0.839528	−	3.67821i	0.0409161	−	0.179265i	−0.950341	−	0.311211i	$-0.899265\pi$
$421$	0.839528	−	3.67821i	0.0409161	−	0.179265i	0.991257	+	0.131946i	$0.0421225\pi$
$422$		−	2.02835i		−	0.0987385i
$423$		0			0
$424$	1.79715	−	7.87382i	0.0872773	−	0.382387i
$425$	−3.74451	+	1.80326i	−0.181635	+	0.0874710i
$426$		0			0
$427$	11.3334	−	4.21592i	0.548462	−	0.204023i
$428$	−13.5743	−	10.8252i	−0.656141	−	0.523255i
$429$		0			0
$430$	1.86556	+	1.48774i	0.0899654	+	0.0717450i
$431$	10.5837	+	21.9772i	0.509797	+	1.05861i	0.983997	+	0.178187i	$0.0570233\pi$
$431$	10.5837	+	21.9772i	0.509797	+	1.05861i	−0.474199	+	0.880418i	$0.657262\pi$
$432$		0			0
$433$	3.71242	−	7.70891i	0.178407	−	0.370467i	−0.792518	−	0.609848i	$-0.791230\pi$
$433$	3.71242	−	7.70891i	0.178407	−	0.370467i	0.970926	+	0.239382i	$0.0769447\pi$
$434$	0.0720855	−	0.775651i	0.00346022	−	0.0372324i
$435$		0			0
$436$	−4.97553	−	2.39609i	−0.238285	−	0.114752i
$437$	0.328853	+	1.44080i	0.0157312	+	0.0689229i
$438$		0			0
$439$	−11.7053	−	9.33467i	−0.558664	−	0.445520i	0.303006	−	0.952989i	$-0.402010\pi$
$439$	−11.7053	−	9.33467i	−0.558664	−	0.445520i	−0.861670	+	0.507469i	$0.830581\pi$
$440$	−12.8650			−0.613313
$441$		0			0
$442$	0.349535			0.0166257
$443$	−16.0922	−	12.8331i	−0.764564	−	0.609720i	0.161593	−	0.986857i	$-0.448337\pi$
$443$	−16.0922	−	12.8331i	−0.764564	−	0.609720i	−0.926157	+	0.377138i	$0.876908\pi$
$444$		0			0
$445$	−4.83609	−	21.1883i	−0.229252	−	1.00442i
$446$	25.2771	+	12.1728i	1.19691	+	0.576399i
$447$		0			0
$448$	−2.51387	−	0.824900i	−0.118769	−	0.0389729i
$449$	−10.0138	+	20.7939i	−0.472580	+	0.981323i	0.519353	+	0.854560i	$0.326173\pi$
$449$	−10.0138	+	20.7939i	−0.472580	+	0.981323i	−0.991933	+	0.126763i	$0.959541\pi$
$450$		0			0
$451$	22.8212	+	47.3887i	1.07461	+	2.23145i
$452$	−14.2669	−	11.3775i	−0.671058	−	0.535151i
$453$		0			0
$454$	−8.76269	−	6.98801i	−0.411253	−	0.327963i
$455$	−0.284831	−	0.171305i	−0.0133531	−	0.00803090i
$456$		0			0
$457$	16.4861	−	7.93930i	0.771189	−	0.371385i	−0.00654516	−	0.999979i	$-0.502083\pi$
$457$	16.4861	−	7.93930i	0.771189	−	0.371385i	0.777734	+	0.628594i	$0.216369\pi$
$458$	−0.225384	+	0.987472i	−0.0105315	+	0.0461415i
$459$		0			0
$460$			1.51461i			0.0706190i
$461$	8.24425	−	36.1204i	0.383973	−	1.68230i	−0.300917	−	0.953650i	$-0.597293\pi$
$461$	8.24425	−	36.1204i	0.383973	−	1.68230i	0.684890	−	0.728646i	$-0.259850\pi$
$462$		0			0
$463$	−0.557431	−	2.44227i	−0.0259060	−	0.113502i	0.960322	−	0.278894i	$-0.0899680\pi$
$463$	−0.557431	−	2.44227i	−0.0259060	−	0.113502i	−0.986228	+	0.165393i	$0.947111\pi$
$464$	−8.50253	+	1.94065i	−0.394720	+	0.0900922i
$465$		0			0
$466$	18.4494	+	23.1348i	0.854650	+	1.07170i
$467$	−4.49444	−	19.6914i	−0.207978	−	0.911210i	−0.965910	−	0.258877i	$-0.916648\pi$
$467$	−4.49444	−	19.6914i	−0.207978	−	0.911210i	0.757933	−	0.652333i	$-0.226210\pi$
$468$		0			0
$469$	10.4477	−	6.85291i	0.482430	−	0.316438i
$470$	−12.3662	−	2.82250i	−0.570410	−	0.130192i
$471$		0			0
$472$			5.31783i			0.244773i
$473$	6.99614	+	1.59682i	0.321683	+	0.0734220i
$474$		0			0
$475$	−1.13951	+	0.908732i	−0.0522845	+	0.0416955i
$476$	12.7310	−	8.35061i	0.583527	−	0.382750i
$477$		0			0
$478$	−3.50536	+	15.3580i	−0.160332	+	0.702459i
$479$	−5.90009	+	7.39847i	−0.269582	+	0.338045i	−0.898133	−	0.439723i	$-0.855077\pi$
$479$	−5.90009	+	7.39847i	−0.269582	+	0.338045i	0.628552	+	0.777768i	$0.283648\pi$
$480$		0			0
$481$	−0.121647	+	0.0970104i	−0.00554663	+	0.00442329i
$482$	9.13264	+	4.39805i	0.415980	+	0.200326i
$483$		0			0
$484$	−24.9477	+	12.0142i	−1.13399	+	0.546100i
$485$	−12.6044	+	26.1733i	−0.572335	+	1.18847i
$486$		0			0
$487$	11.7143	+	5.64132i	0.530827	+	0.255633i	0.680043	−	0.733172i	$-0.261961\pi$
$487$	11.7143	+	5.64132i	0.530827	+	0.255633i	−0.149217	+	0.988805i	$0.547675\pi$
$488$	−2.84960	+	3.57329i	−0.128995	+	0.161755i
$489$		0			0
$490$	−14.4669	+	0.565376i	−0.653549	+	0.0255411i
$491$		−	16.7834i		−	0.757426i	−0.925514	−	0.378713i	$-0.876367\pi$
$491$		−	16.7834i		−	0.757426i	0.925514	−	0.378713i	$-0.123633\pi$
$492$		0			0
$493$	21.7755	−	45.2173i	0.980719	−	2.03648i
$494$	0.119505	−	0.0272761i	0.00537676	−	0.00122721i
$495$		0			0
$496$	0.127749	+	0.265274i	0.00573611	+	0.0119111i
$497$	−3.39974	+	3.53520i	−0.152499	+	0.158575i
$498$		0			0
$499$	6.85163	+	8.59167i	0.306721	+	0.384616i	0.911172	−	0.412027i	$-0.135179\pi$
$499$	6.85163	+	8.59167i	0.306721	+	0.384616i	−0.604451	+	0.796642i	$0.706607\pi$
$500$	−10.6631	+	5.13508i	−0.476868	+	0.229648i
$501$		0			0
$502$	0.873604	+	0.199394i	0.0389909	+	0.00889941i
$503$	19.6882	−	24.6882i	0.877853	−	1.10079i	−0.116343	−	0.993209i	$-0.537117\pi$
$503$	19.6882	−	24.6882i	0.877853	−	1.10079i	0.994196	−	0.107584i	$-0.0343113\pi$
$504$		0			0
$505$	−7.80571	−	9.78805i	−0.347349	−	0.435562i
$506$	1.97635	+	4.10393i	0.0878594	+	0.182442i
$507$		0			0
$508$	5.23030			0.232057
$509$	0.401795			0.0178093			0.00890463	−	0.999960i	$-0.497166\pi$
$509$	0.401795			0.0178093			0.00890463	+	0.999960i	$0.497166\pi$
$510$		0			0
$511$	12.7140	−	38.7458i	0.562436	−	1.71402i
$512$	0.974928	−	0.222521i	0.0430861	−	0.00983413i
$513$		0			0
$514$	−9.89055	+	7.88745i	−0.436253	+	0.347900i
$515$	20.1170	−	16.0428i	0.886461	−	0.706929i
$516$		0			0
$517$	−37.1899	+	8.48836i	−1.63561	+	0.373318i
$518$	−2.11309	+	6.43962i	−0.0928440	+	0.282941i
$519$		0			0
$520$	0.125626			0.00550908
$521$	−26.6577			−1.16789			−0.583947	−	0.811792i	$-0.698492\pi$
$521$	−26.6577			−1.16789			−0.583947	+	0.811792i	$0.698492\pi$
$522$		0			0
$523$	−2.70653	−	5.62016i	−0.118348	−	0.245752i	0.833376	−	0.552706i	$-0.186405\pi$
$523$	−2.70653	−	5.62016i	−0.118348	−	0.245752i	−0.951725	+	0.306953i	$0.900690\pi$
$524$	6.39352	+	8.01722i	0.279302	+	0.350234i
$525$		0			0
$526$	7.68058	−	9.63114i	0.334889	−	0.419938i
$527$	−1.65187	−	0.377029i	−0.0719567	−	0.0164236i
$528$		0			0
$529$	−20.2391	+	9.74665i	−0.879962	+	0.423767i
$530$	10.4148	+	13.0598i	0.452391	+	0.567281i
$531$		0			0
$532$	3.70105	−	3.84851i	0.160461	−	0.166854i
$533$	−0.222849	−	0.462752i	−0.00965268	−	0.0200440i
$534$		0			0
$535$	35.0096	−	7.99072i	1.51360	−	0.345469i
$536$	−2.04903	+	4.25486i	−0.0885048	+	0.183782i
$537$		0			0
$538$		−	0.668204i		−	0.0288083i
$539$	−38.4613	+	20.4092i	−1.65664	+	0.879085i
$540$		0			0
$541$	3.68283	−	4.61812i	0.158337	−	0.198549i	−0.696335	−	0.717717i	$-0.745187\pi$
$541$	3.68283	−	4.61812i	0.158337	−	0.198549i	0.854672	+	0.519169i	$0.173758\pi$
$542$	−27.4664	−	13.2271i	−1.17978	−	0.568154i
$543$		0			0
$544$	−2.49685	+	5.18476i	−0.107052	+	0.222295i
$545$	10.2908	−	4.95578i	0.440809	−	0.212282i
$546$		0			0
$547$	22.7008	+	10.9321i	0.970614	+	0.467423i	0.850867	−	0.525381i	$-0.176077\pi$
$547$	22.7008	+	10.9321i	0.970614	+	0.467423i	0.119747	+	0.992804i	$0.461792\pi$
$548$	−2.79668	+	2.23027i	−0.119468	+	0.0952726i
$549$		0			0
$550$	−2.80088	+	3.51219i	−0.119430	+	0.149760i
$551$	3.91640	−	17.1589i	0.166844	−	0.730992i
$552$		0			0
$553$	−10.1521	+	6.65901i	−0.431711	+	0.283170i
$554$	10.8649	−	8.66449i	0.461607	−	0.368119i
$555$		0			0
$556$	−18.2877	−	4.17404i	−0.775570	−	0.177019i
$557$			11.2130i			0.475112i	0.971374	+	0.237556i	$0.0763463\pi$
$557$			11.2130i			0.475112i	−0.971374	+	0.237556i	$0.923654\pi$
$558$		0			0
$559$	−0.0683174	−	0.0155930i	−0.00288952	−	0.000659514i
$560$	4.57567	−	3.00129i	0.193357	−	0.126828i
$561$		0			0
$562$	6.94009	+	30.4065i	0.292750	+	1.28262i
$563$	19.9187	+	24.9772i	0.839472	+	1.05267i	0.997866	+	0.0652891i	$0.0207969\pi$
$563$	19.9187	+	24.9772i	0.839472	+	1.05267i	−0.158394	+	0.987376i	$0.550632\pi$
$564$		0			0
$565$	36.7958	−	8.39840i	1.54801	−	0.353323i
$566$	−6.90482	−	30.2520i	−0.290231	−	1.27159i
$567$		0			0
$568$	0.412508	−	1.80731i	0.0173084	−	0.0758332i
$569$			40.5576i			1.70026i	0.526570	+	0.850132i	$0.323478\pi$
$569$			40.5576i			1.70026i	−0.526570	+	0.850132i	$0.676522\pi$
$570$		0			0
$571$	1.97675	−	8.66073i	0.0827246	−	0.362440i	−0.916575	−	0.399863i	$-0.869058\pi$
$571$	1.97675	−	8.66073i	0.0827246	−	0.362440i	0.999300	+	0.0374229i	$0.0119149\pi$
$572$	0.340393	−	0.163924i	0.0142325	−	0.00685403i
$573$		0			0
$574$	−19.1722	−	11.5307i	−0.800233	−	0.481282i
$575$	0.413495	+	0.329751i	0.0172439	+	0.0137516i
$576$		0			0
$577$	−1.13066	−	0.901669i	−0.0470699	−	0.0375370i	0.599672	−	0.800246i	$-0.295298\pi$
$577$	−1.13066	−	0.901669i	−0.0470699	−	0.0375370i	−0.646742	+	0.762709i	$0.723869\pi$
$578$	−6.99249	−	14.5200i	−0.290849	−	0.603954i
$579$		0			0
$580$	7.82633	−	16.2515i	0.324971	−	0.674809i
$581$	1.66697	+	0.546999i	0.0691576	+	0.0226934i
$582$		0			0
$583$	45.2608	+	21.7964i	1.87451	+	0.902716i
$584$	3.42968	+	15.0264i	0.141921	+	0.621797i
$585$		0			0
$586$	10.2987	+	8.21295i	0.425436	+	0.339274i
$587$	−36.5168			−1.50721			−0.753605	−	0.657327i	$-0.771687\pi$
$587$	−36.5168			−1.50721			−0.753605	+	0.657327i	$0.771687\pi$
$588$		0			0
$589$	−0.594190			−0.0244832
$590$	−8.59919	−	6.85762i	−0.354023	−	0.282324i
$591$		0			0
$592$	−0.570017	−	2.49741i	−0.0234276	−	0.102643i
$593$	19.7361	+	9.50441i	0.810465	+	0.390299i	0.792752	−	0.609544i	$-0.208647\pi$
$593$	19.7361	+	9.50441i	0.810465	+	0.390299i	0.0177126	+	0.999843i	$0.494362\pi$
$594$		0			0
$595$	−2.91402	+	31.3552i	−0.119463	+	1.28544i
$596$	−5.59967	+	11.6278i	−0.229371	+	0.476294i
$597$		0			0
$598$	−0.0192991	−	0.0400749i	−0.000789197	−	0.00163878i
$599$	−18.9930	−	15.1464i	−0.776032	−	0.618865i	0.153270	−	0.988184i	$-0.451019\pi$
$599$	−18.9930	−	15.1464i	−0.776032	−	0.618865i	−0.929303	+	0.369319i	$0.879591\pi$
$600$		0			0
$601$	−24.5896	−	19.6096i	−1.00303	−	0.799892i	−0.0232038	−	0.999731i	$-0.507387\pi$
$601$	−24.5896	−	19.6096i	−1.00303	−	0.799892i	−0.979829	+	0.199839i	$0.935958\pi$
$602$	−2.86084	+	1.06420i	−0.116599	+	0.0433737i
$603$		0			0
$604$	13.4863	−	6.49466i	0.548749	−	0.264264i
$605$	12.7439	−	55.8346i	0.518112	−	2.27000i
$606$		0			0
$607$			24.6260i			0.999540i	0.866158	+	0.499770i	$0.166582\pi$
$607$			24.6260i			0.999540i	−0.866158	+	0.499770i	$0.833418\pi$
$608$	−0.449067	+	1.96749i	−0.0182121	+	0.0797923i
$609$		0			0
$610$	−2.10346	−	9.21588i	−0.0851668	−	0.373140i
$611$	0.363160	−	0.0828889i	0.0146919	−	0.00335333i
$612$		0			0
$613$	−16.4714	−	20.6545i	−0.665274	−	0.834227i	0.328632	−	0.944458i	$-0.393412\pi$
$613$	−16.4714	−	20.6545i	−0.665274	−	0.834227i	−0.993906	+	0.110231i	$0.964841\pi$
$614$	4.04276	+	17.7125i	0.163153	+	0.714818i
$615$		0			0
$616$	8.48180	−	14.1028i	0.341741	−	0.568217i
$617$	−23.5219	−	5.36873i	−0.946957	−	0.216137i	−0.278962	−	0.960302i	$-0.589990\pi$
$617$	−23.5219	−	5.36873i	−0.946957	−	0.216137i	−0.667995	+	0.744165i	$0.732847\pi$
$618$		0			0
$619$			11.1701i			0.448965i	0.974478	+	0.224482i	$0.0720691\pi$
$619$			11.1701i			0.448965i	−0.974478	+	0.224482i	$0.927931\pi$
$620$	−0.593699	−	0.135508i	−0.0238435	−	0.00544213i
$621$		0			0
$622$	12.8916	−	10.2807i	0.516904	−	0.412217i
$623$	26.4153	+	8.66792i	1.05831	+	0.347273i
$624$		0			0
$625$	4.64342	−	20.3441i	0.185737	−	0.813766i
$626$	−13.7412	+	17.2309i	−0.549209	+	0.688686i
$627$		0			0
$628$	−4.65729	+	3.71406i	−0.185846	+	0.148207i
$629$	13.2815	+	6.39602i	0.529567	+	0.255026i
$630$		0			0
$631$	−38.7310	+	18.6519i	−1.54186	+	0.742520i	−0.995476	−	0.0950162i	$-0.969710\pi$
$631$	−38.7310	+	18.6519i	−1.54186	+	0.742520i	−0.546382	+	0.837536i	$0.683995\pi$
$632$	1.99106	−	4.13447i	0.0792000	−	0.164461i
$633$		0			0
$634$	16.0339	+	7.72153i	0.636789	+	0.306661i
$635$	−6.74474	+	8.45764i	−0.267657	+	0.335631i
$636$		0			0
$637$	0.375575	−	0.199296i	0.0148808	−	0.00789639i
$638$		−	54.2468i		−	2.14765i
$639$		0			0
$640$	−0.897393	+	1.86346i	−0.0354726	+	0.0736596i
$641$	8.49213	−	1.93827i	0.335419	−	0.0765572i	−0.0514942	−	0.998673i	$-0.516398\pi$
$641$	8.49213	−	1.93827i	0.335419	−	0.0765572i	0.386913	+	0.922116i	$0.373541\pi$
$642$		0			0
$643$	0.109941	+	0.228294i	0.00433564	+	0.00900304i	0.903125	−	0.429377i	$-0.141267\pi$
$643$	0.109941	+	0.228294i	0.00433564	+	0.00900304i	−0.898790	+	0.438380i	$0.855552\pi$
$644$	−1.66034	−	0.998574i	−0.0654266	−	0.0393493i
$645$		0			0
$646$	−7.24084	−	9.07973i	−0.284887	−	0.357237i
$647$	30.9739	−	14.9163i	1.21771	−	0.586418i	0.289037	−	0.957318i	$-0.406665\pi$
$647$	30.9739	−	14.9163i	1.21771	−	0.586418i	0.928673	+	0.370900i	$0.120951\pi$
$648$		0			0
$649$	−32.2482	−	7.36045i	−1.26585	−	0.288923i
$650$	0.0273506	−	0.0342966i	0.00107278	−	0.00134522i
$651$		0			0
$652$	−7.92794	−	9.94132i	−0.310482	−	0.389332i
$653$	5.11565	+	10.6227i	0.200191	+	0.415700i	0.976761	−	0.214330i	$-0.0687568\pi$
$653$	5.11565	+	10.6227i	0.200191	+	0.415700i	−0.776571	+	0.630030i	$0.783042\pi$
$654$		0			0
$655$	−21.2090			−0.828704
$656$	8.45603			0.330152
$657$		0			0
$658$	11.2470	−	11.6952i	0.438455	−	0.455925i
$659$	10.8696	−	2.48092i	0.423420	−	0.0966428i	−0.00550115	−	0.999985i	$-0.501751\pi$
$659$	10.8696	−	2.48092i	0.423420	−	0.0966428i	0.428921	+	0.903342i	$0.358894\pi$
$660$		0			0
$661$	−17.7313	+	14.1402i	−0.689667	+	0.549991i	−0.904402	−	0.426681i	$-0.859683\pi$
$661$	−17.7313	+	14.1402i	−0.689667	+	0.549991i	0.214735	+	0.976672i	$0.431111\pi$
$662$	21.1801	−	16.8906i	0.823189	−	0.656471i
$663$		0			0
$664$	−0.646484	+	0.147556i	−0.0250885	+	0.00572628i
$665$	1.45053	+	10.9476i	0.0562492	+	0.424531i
$666$		0			0
$667$	−6.38655			−0.247288
$668$	16.9639			0.656354
$669$		0			0
$670$	−4.23798	−	8.80026i	−0.163727	−	0.339984i
$671$	−17.7249	−	22.2263i	−0.684261	−	0.858036i
$672$		0			0
$673$	−31.5426	+	39.5531i	−1.21588	+	1.52466i	−0.434407	+	0.900717i	$0.643042\pi$
$673$	−31.5426	+	39.5531i	−1.21588	+	1.52466i	−0.781469	+	0.623944i	$0.785529\pi$
$674$	9.57926	+	2.18640i	0.368979	+	0.0842172i
$675$		0			0
$676$	11.7093	−	5.63889i	0.450357	−	0.216880i
$677$	−14.2437	−	17.8610i	−0.547428	−	0.686454i	0.428750	−	0.903423i	$-0.358954\pi$
$677$	−14.2437	−	17.8610i	−0.547428	−	0.686454i	−0.976178	+	0.216970i	$0.930383\pi$
$678$		0			0
$679$	−20.3816	−	31.0730i	−0.782173	−	1.19247i
$680$	−5.16419	−	10.7235i	−0.198038	−	0.411229i
$681$		0			0
$682$	−1.78548	+	0.407525i	−0.0683697	+	0.0156049i
$683$	9.61362	−	19.9629i	0.367855	−	0.763859i	−0.632084	−	0.774900i	$-0.717800\pi$
$683$	9.61362	−	19.9629i	0.367855	−	0.763859i	0.999939	+	0.0110412i	$0.00351460\pi$
$684$		0			0
$685$		−	7.39841i		−	0.282679i
$686$	8.91819	−	16.2316i	0.340498	−	0.619727i
$687$		0			0
$688$	0.719311	−	0.901987i	0.0274235	−	0.0343879i
$689$	−0.441972	−	0.212842i	−0.0168378	−	0.00810865i
$690$		0			0
$691$	18.0948	−	37.5742i	0.688359	−	1.42939i	−0.204414	−	0.978884i	$-0.565529\pi$
$691$	18.0948	−	37.5742i	0.688359	−	1.42939i	0.892773	−	0.450507i	$-0.148757\pi$
$692$	11.4762	−	5.52664i	0.436259	−	0.210091i
$693$		0			0
$694$	0.973005	+	0.468574i	0.0369348	+	0.0177868i
$695$	30.3325	−	24.1894i	1.15058	−	0.917556i
$696$		0			0
$697$	−30.3400	+	38.0451i	−1.14921	+	1.44106i
$698$	−6.59935	+	28.9136i	−0.249789	+	1.09440i
$699$		0			0
$700$	0.176819	−	1.90260i	0.00668314	−	0.0719116i
$701$	−21.0216	+	16.7642i	−0.793975	+	0.633174i	−0.934121	−	0.356957i	$-0.883814\pi$
$701$	−21.0216	+	16.7642i	−0.793975	+	0.633174i	0.140146	+	0.990131i	$0.455243\pi$
$702$		0			0
$703$	5.04000	+	1.15035i	0.190087	+	0.0433861i
$704$			6.22012i			0.234430i
$705$		0			0
$706$	20.5527	+	4.69101i	0.773509	+	0.176548i
$707$	15.8761	−	2.10354i	0.597082	−	0.0791117i
$708$		0			0
$709$	−8.23796	−	36.0928i	−0.309383	−	1.35550i	−0.855507	−	0.517791i	$-0.826754\pi$
$709$	−8.23796	−	36.0928i	−0.309383	−	1.35550i	0.546124	−	0.837704i	$-0.316103\pi$
$710$	2.39056	+	2.99767i	0.0897162	+	0.112501i
$711$		0			0
$712$	−10.2444	+	2.33822i	−0.383925	+	0.0876283i
$713$	0.0479785	+	0.210208i	0.00179681	+	0.00787233i
$714$		0			0
$715$	−0.173880	+	0.761820i	−0.00650276	+	0.0284905i
$716$		−	0.198817i		−	0.00743014i
$717$		0			0
$718$	−3.08098	+	13.4986i	−0.114981	+	0.503765i
$719$	11.3640	−	5.47263i	0.423807	−	0.204095i	−0.209809	−	0.977742i	$-0.567284\pi$
$719$	11.3640	−	5.47263i	0.423807	−	0.204095i	0.633616	+	0.773648i	$0.281570\pi$
$720$		0			0
$721$	4.32332	+	32.6295i	0.161009	+	1.21519i
$722$	11.6706	+	9.30703i	0.434336	+	0.346372i
$723$		0			0
$724$	−7.74260	−	6.17452i	−0.287751	−	0.229474i
$725$	−2.73285	−	5.67481i	−0.101495	−	0.210757i
$726$		0			0
$727$	−12.4954	+	25.9469i	−0.463428	+	0.962318i	0.530015	+	0.847988i	$0.322186\pi$
$727$	−12.4954	+	25.9469i	−0.463428	+	0.962318i	−0.993443	+	0.114330i	$0.963528\pi$
$728$	−0.0828249	+	0.137714i	−0.00306969	+	0.00510401i
$729$		0			0
$730$	−28.7211	−	13.8314i	−1.06302	−	0.511922i
$731$	1.47733	+	6.47260i	0.0546410	+	0.239398i
$732$		0			0
$733$	33.9425	+	27.0682i	1.25369	+	0.999788i	0.999467	+	0.0326431i	$0.0103925\pi$
$733$	33.9425	+	27.0682i	1.25369	+	0.999788i	0.254227	+	0.967145i	$0.418179\pi$
$734$	−3.12979			−0.115522
$735$		0			0
$736$	0.732304			0.0269931
$737$	−22.9661	−	18.3149i	−0.845968	−	0.674637i
$738$		0			0
$739$	−3.95219	−	17.3157i	−0.145384	−	0.636967i	−0.994132	−	0.108171i	$-0.965501\pi$
$739$	−3.95219	−	17.3157i	−0.145384	−	0.636967i	0.848749	−	0.528797i	$-0.177357\pi$
$740$	4.77350	+	2.29879i	0.175477	+	0.0845054i
$741$		0			0
$742$	−21.1828	+	2.80666i	−0.777645	+	0.103036i
$743$	12.9283	−	26.8460i	0.474294	−	0.984883i	−0.517337	−	0.855782i	$-0.673077\pi$
$743$	12.9283	−	26.8460i	0.474294	−	0.984883i	0.991631	−	0.129101i	$-0.0412091\pi$
$744$		0			0
$745$	−11.5817	−	24.0496i	−0.424320	−	0.881110i
$746$	12.9893	+	10.3587i	0.475574	+	0.379257i
$747$		0			0
$748$	−27.9854	−	22.3176i	−1.02325	−	0.816012i
$749$	−14.3221	+	43.6464i	−0.523318	+	1.59480i
$750$		0			0
$751$	−28.4427	+	13.6973i	−1.03789	+	0.499821i	−0.873628	−	0.486595i	$-0.838239\pi$
$751$	−28.4427	+	13.6973i	−1.03789	+	0.499821i	−0.164262	+	0.986417i	$0.552524\pi$
$752$	−1.36466	+	5.97897i	−0.0497641	+	0.218031i
$753$		0			0
$754$			0.529721i			0.0192913i
$755$	−6.88911	+	30.1832i	−0.250720	+	1.09848i
$756$		0			0
$757$	−7.49894	−	32.8550i	−0.272554	−	1.19413i	−0.906987	−	0.421158i	$-0.861624\pi$
$757$	−7.49894	−	32.8550i	−0.272554	−	1.19413i	0.634434	−	0.772977i	$-0.281233\pi$
$758$	4.76613	−	1.08784i	0.173114	−	0.0395121i
$759$		0			0
$760$	−2.60243	−	3.26335i	−0.0944001	−	0.118374i
$761$	−1.64697	−	7.21584i	−0.0597026	−	0.261574i	0.936264	−	0.351297i	$-0.114259\pi$
$761$	−1.64697	−	7.21584i	−0.0597026	−	0.261574i	−0.995967	+	0.0897225i	$0.971402\pi$
$762$		0			0
$763$	−1.35205	+	14.5483i	−0.0489475	+	0.526682i
$764$	24.9614	+	5.69728i	0.903072	+	0.206120i
$765$		0			0
$766$			13.3342i			0.481784i
$767$	0.314905	+	0.0718749i	0.0113705	+	0.00259525i
$768$		0			0
$769$	−22.7162	+	18.1155i	−0.819166	+	0.653263i	−0.940668	−	0.339328i	$-0.889800\pi$
$769$	−22.7162	+	18.1155i	−0.819166	+	0.653263i	0.121502	+	0.992591i	$0.461229\pi$
$770$	11.8671	+	31.9017i	0.427662	+	1.14966i
$771$		0			0
$772$	−0.351171	+	1.53858i	−0.0126389	+	0.0553747i
$773$	−16.0019	+	20.0658i	−0.575548	+	0.721715i	−0.981346	−	0.192248i	$-0.938422\pi$
$773$	−16.0019	+	20.0658i	−0.575548	+	0.721715i	0.405798	+	0.913963i	$0.366994\pi$
$774$		0			0
$775$	−0.166251	+	0.132581i	−0.00597191	+	0.00476244i
$776$	12.6546	+	6.09413i	0.454274	+	0.218767i
$777$		0			0
$778$	−3.04000	+	1.46399i	−0.108989	+	0.0524865i
$779$	−7.40424	+	15.3751i	−0.265284	+	0.550868i
$780$		0			0
$781$	10.3889	+	5.00303i	0.371744	+	0.179023i
$782$	−2.62748	+	3.29476i	−0.0939586	+	0.117820i
$783$		0			0
$784$	0.273356	+	6.99466i	0.00976270	+	0.249809i
$785$		−	12.3205i		−	0.439738i
$786$		0			0
$787$	−14.1208	+	29.3222i	−0.503353	+	1.04522i	0.482233	+	0.876043i	$0.339826\pi$
$787$	−14.1208	+	29.3222i	−0.503353	+	1.04522i	−0.985585	+	0.169179i	$0.945888\pi$
$788$	−18.0681	+	4.12393i	−0.643650	+	0.146909i
$789$		0			0
$790$	4.11807	+	8.55125i	0.146514	+	0.304240i
$791$	−15.0528	+	45.8732i	−0.535216	+	1.63106i
$792$		0			0
$793$	0.173084	+	0.217040i	0.00614638	+	0.00770731i
$794$	21.3715	−	10.2920i	0.758445	−	0.365248i
$795$		0			0
$796$	22.6928	+	5.17948i	0.804325	+	0.183582i
$797$	−0.858869	+	1.07699i	−0.0304227	+	0.0381489i	−0.796810	−	0.604230i	$-0.793481\pi$
$797$	−0.858869	+	1.07699i	−0.0304227	+	0.0381489i	0.766387	+	0.642379i	$0.222052\pi$
$798$		0			0
$799$	−22.0040	−	27.5922i	−0.778447	−	0.976142i
$800$	0.313357	+	0.650693i	0.0110788	+	0.0230055i
$801$		0			0
$802$	19.5643			0.690838
$803$	−95.8697			−3.38317
$804$		0			0
$805$	3.75584	−	1.39714i	0.132376	−	0.0492425i
$806$	0.0174353	−	0.00397949i	0.000614131	−	0.000140171i
$807$		0			0
$808$	−4.73246	+	3.77401i	−0.166487	+	0.132769i
$809$	10.4326	−	8.31969i	0.366789	−	0.292505i	−0.422699	−	0.906270i	$-0.638917\pi$
$809$	10.4326	−	8.31969i	0.366789	−	0.292505i	0.789488	+	0.613765i	$0.210346\pi$
$810$		0			0
$811$	−48.0814	+	10.9743i	−1.68837	+	0.385359i	−0.955495	−	0.295008i	$-0.904678\pi$
$811$	−48.0814	+	10.9743i	−1.68837	+	0.385359i	−0.732872	+	0.680367i	$0.761821\pi$
$812$	12.6554	+	19.2939i	0.444116	+	0.677084i
$813$		0			0
$814$	15.9337			0.558475
$815$	26.2991			0.921216
$816$		0			0
$817$	1.01019	+	2.09767i	0.0353419	+	0.0733882i
$818$	3.88992	+	4.87780i	0.136008	+	0.170548i
$819$		0			0
$820$	−10.9045	+	13.6738i	−0.380801	+	0.477510i
$821$	37.2145	+	8.49398i	1.29880	+	0.296442i	0.815369	−	0.578942i	$-0.196534\pi$
$821$	37.2145	+	8.49398i	1.29880	+	0.296442i	0.483428	+	0.875384i	$0.339391\pi$
$822$		0			0
$823$	11.9115	−	5.73630i	0.415210	−	0.199955i	−0.214603	−	0.976701i	$-0.568846\pi$
$823$	11.9115	−	5.73630i	0.415210	−	0.199955i	0.629813	+	0.776747i	$0.283131\pi$
$824$	−7.75657	−	9.72643i	−0.270213	−	0.338836i
$825$		0			0
$826$	13.1868	−	4.90538i	0.458829	−	0.170680i
$827$	2.02758	+	4.21031i	0.0705057	+	0.146407i	0.933243	−	0.359246i	$-0.116966\pi$
$827$	2.02758	+	4.21031i	0.0705057	+	0.146407i	−0.862737	+	0.505653i	$0.831252\pi$
$828$		0			0
$829$	−41.7610	+	9.53168i	−1.45042	+	0.331049i	−0.873929	−	0.486054i	$-0.838436\pi$
$829$	−41.7610	+	9.53168i	−1.45042	+	0.331049i	−0.576492	+	0.817103i	$0.695579\pi$
$830$	0.595070	−	1.23568i	0.0206552	−	0.0428910i
$831$		0			0
$832$		−	0.0607396i		−	0.00210577i
$833$	−32.4510	−	23.8667i	−1.12436	−	0.826934i
$834$		0			0
$835$	−21.8759	+	27.4315i	−0.757046	+	0.949305i
$836$	−11.3096	−	5.44644i	−0.391152	−	0.188369i
$837$		0			0
$838$	7.12764	−	14.8007i	0.246220	−	0.511282i
$839$	−34.2077	+	16.4736i	−1.18098	+	0.568730i	−0.918197	−	0.396124i	$-0.870355\pi$
$839$	−34.2077	+	16.4736i	−1.18098	+	0.568730i	−0.262784	+	0.964855i	$0.584641\pi$
$840$		0			0
$841$	42.3987	+	20.4182i	1.46203	+	0.704074i
$842$	2.94970	−	2.35230i	0.101653	−	0.0810658i
$843$		0			0
$844$	1.26466	−	1.58583i	0.0435312	−	0.0545865i
$845$	−5.98137	+	26.2061i	−0.205765	+	0.901517i
$846$		0			0
$847$	52.8048	+	50.7815i	1.81440	+	1.74487i
$848$	6.31432	−	5.03550i	0.216835	−	0.172920i
$849$		0			0
$850$	−4.05189	−	0.924818i	−0.138979	−	0.0317210i
$851$		−	1.87589i		−	0.0643048i
$852$		0			0
$853$	50.4358	+	11.5117i	1.72689	+	0.394151i	0.966773	−	0.255635i	$-0.0822846\pi$
$853$	50.4358	+	11.5117i	1.72689	+	0.394151i	0.760117	+	0.649787i	$0.225142\pi$
$854$	11.4894	+	3.77013i	0.393159	+	0.129011i
$855$		0			0
$856$	−3.86346	−	16.9269i	−0.132050	−	0.578550i
$857$	13.0344	+	16.3446i	0.445246	+	0.558321i	0.952917	−	0.303230i	$-0.0980650\pi$
$857$	13.0344	+	16.3446i	0.445246	+	0.558321i	−0.507671	+	0.861551i	$0.669494\pi$
$858$		0			0
$859$	−22.9528	+	5.23883i	−0.783140	+	0.178747i	−0.595354	−	0.803463i	$-0.702988\pi$
$859$	−22.9528	+	5.23883i	−0.783140	+	0.178747i	−0.187786	+	0.982210i	$0.560131\pi$
$860$	0.530967	+	2.32632i	0.0181058	+	0.0793268i
$861$		0			0
$862$	−5.42792	+	23.7813i	−0.184876	+	0.809994i
$863$			42.4340i			1.44447i	0.691648	+	0.722235i	$0.256885\pi$
$863$			42.4340i			1.44447i	−0.691648	+	0.722235i	$0.743115\pi$
$864$		0			0
$865$	−5.86230	+	25.6844i	−0.199324	+	0.873296i
$866$	7.70891	−	3.71242i	0.261959	−	0.126153i
$867$		0			0
$868$	0.539969	−	0.561484i	0.0183277	−	0.0190580i
$869$	22.3163	+	17.7967i	0.757029	+	0.603711i
$870$		0			0
$871$	0.224265	+	0.178845i	0.00759892	+	0.00605993i
$872$	−2.39609	−	4.97553i	−0.0811418	−	0.168493i
$873$		0			0
$874$	−0.641217	+	1.33150i	−0.0216895	+	0.0450387i
$875$	22.5697	+	21.7049i	0.762996	+	0.733760i
$876$		0			0
$877$	−24.4019	−	11.7513i	−0.823993	−	0.396814i	−0.0261339	−	0.999658i	$-0.508320\pi$
$877$	−24.4019	−	11.7513i	−0.823993	−	0.396814i	−0.797859	+	0.602845i	$0.794034\pi$
$878$	−3.33151	−	14.5963i	−0.112433	−	0.492601i
$879$		0			0
$880$	−10.0582	−	8.02117i	−0.339063	−	0.270394i
$881$	−47.6241			−1.60450			−0.802248	−	0.596992i	$-0.796363\pi$
$881$	−47.6241			−1.60450			−0.802248	+	0.596992i	$0.796363\pi$
$882$		0			0
$883$	54.7776			1.84341			0.921707	−	0.387887i	$-0.126795\pi$
$883$	54.7776			1.84341			0.921707	+	0.387887i	$0.126795\pi$
$884$	0.273278	+	0.217932i	0.00919132	+	0.00732983i
$885$		0			0
$886$	−4.58008	−	20.0667i	−0.153871	−	0.674153i
$887$	19.4603	+	9.37160i	0.653414	+	0.314667i	0.731060	−	0.682314i	$-0.239026\pi$
$887$	19.4603	+	9.37160i	0.653414	+	0.314667i	−0.0776460	+	0.996981i	$0.524740\pi$
$888$		0			0
$889$	−4.82463	−	12.9698i	−0.161813	−	0.434992i
$890$	9.42967	−	19.5809i	0.316083	−	0.656354i
$891$		0			0
$892$	12.1728	+	25.2771i	0.407576	+	0.846340i
$893$	−9.67626	−	7.71656i	−0.323804	−	0.258225i
$894$		0			0
$895$	0.321497	+	0.256385i	0.0107464	+	0.00857000i
$896$	−1.45111	−	2.21230i	−0.0484780	−	0.0739079i
$897$		0			0
$898$	−20.7939	+	10.0138i	−0.693900	+	0.334165i
$899$	0.571388	−	2.50341i	0.0190568	−	0.0834935i
$900$		0			0
$901$			46.4764i			1.54835i
$902$	−11.7040	+	51.2788i	−0.389702	+	1.70740i
$903$		0			0
$904$	−4.06057	−	17.7905i	−0.135053	−	0.591704i
$905$	19.9690	−	4.55779i	0.663791	−	0.151506i
$906$		0			0
$907$	21.5734	+	27.0522i	0.716332	+	0.898252i	0.998124	−	0.0612232i	$-0.0195001\pi$
$907$	21.5734	+	27.0522i	0.716332	+	0.898252i	−0.281792	+	0.959476i	$0.590929\pi$
$908$	−2.49399	−	10.9269i	−0.0827660	−	0.362622i
$909$		0			0
$910$	−0.115883	−	0.311521i	−0.00384148	−	0.0103268i
$911$	22.3771	+	5.10743i	0.741387	+	0.169217i	0.576502	−	0.817096i	$-0.304417\pi$
$911$	22.3771	+	5.10743i	0.741387	+	0.169217i	0.164886	+	0.986313i	$0.447275\pi$
$912$		0			0
$913$		−	4.12462i		−	0.136505i
$914$	17.8395	+	4.07174i	0.590077	+	0.134681i
$915$		0			0
$916$	−0.791891	+	0.631512i	−0.0261648	+	0.0208657i
$917$	13.9830	−	23.2497i	0.461759	−	0.767771i
$918$		0			0
$919$	0.261764	−	1.14686i	0.00863478	−	0.0378315i	−0.970427	−	0.241395i	$-0.922395\pi$
$919$	0.261764	−	1.14686i	0.00863478	−	0.0378315i	0.979062	+	0.203563i	$0.0652523\pi$
$920$	−0.944344	+	1.18417i	−0.0311341	+	0.0390409i
$921$		0			0
$922$	28.9663	−	23.0999i	0.953956	−	0.760754i
$923$	−0.101448	−	0.0488547i	−0.00333920	−	0.00160807i
$924$		0			0
$925$	1.66684	−	0.802707i	0.0548053	−	0.0263928i
$926$	1.08691	−	2.25699i	0.0357181	−	0.0741694i
$927$		0			0
$928$	−7.85752	−	3.78398i	−0.257936	−	0.124215i
$929$	−6.24270	+	7.82810i	−0.204816	+	0.256832i	−0.873621	−	0.486606i	$-0.838235\pi$
$929$	−6.24270	+	7.82810i	−0.204816	+	0.256832i	0.668805	+	0.743438i	$0.266806\pi$
$930$		0			0
$931$	−12.9573	−	5.62761i	−0.424658	−	0.184438i
$932$			29.5905i			0.969269i
$933$		0			0
$934$	8.76350	−	18.1976i	0.286751	−	0.595444i
$935$	72.1772	−	16.4740i	2.36045	−	0.538757i
$936$		0			0
$937$	3.82527	+	7.94326i	0.124966	+	0.259495i	0.954061	−	0.299614i	$-0.0968578\pi$
$937$	3.82527	+	7.94326i	0.124966	+	0.259495i	−0.829094	+	0.559109i	$0.811143\pi$
$938$	12.4411	+	1.15622i	0.406215	+	0.0377518i
$939$		0			0
$940$	−7.90848	−	9.91692i	−0.257946	−	0.323454i
$941$	−22.1371	+	10.6607i	−0.721650	+	0.347528i	−0.758394	−	0.651796i	$-0.774016\pi$
$941$	−22.1371	+	10.6607i	−0.721650	+	0.347528i	0.0367439	+	0.999325i	$0.488301\pi$
$942$		0			0
$943$	6.03712	+	1.37793i	0.196596	+	0.0448717i
$944$	−3.31562	+	4.15765i	−0.107914	+	0.135320i
$945$		0			0
$946$	4.47420	+	5.61047i	0.145469	+	0.182412i
$947$	3.92040	+	8.14079i	0.127396	+	0.264540i	0.954905	−	0.296912i	$-0.0959569\pi$
$947$	3.92040	+	8.14079i	0.127396	+	0.264540i	−0.827509	+	0.561453i	$0.810243\pi$
$948$		0			0
$949$	0.936168			0.0303893
$950$	−1.45749			−0.0472873
$951$		0			0
$952$	15.1601	+	1.40891i	0.491340	+	0.0456630i
$953$	−22.2693	+	5.08282i	−0.721373	+	0.164649i	−0.567419	−	0.823429i	$-0.692058\pi$
$953$	−22.2693	+	5.08282i	−0.721373	+	0.164649i	−0.153954	+	0.988078i	$0.549201\pi$
$954$		0			0
$955$	−41.4018	+	33.0168i	−1.33973	+	1.06840i
$956$	−12.3162	+	9.82181i	−0.398333	+	0.317660i
$957$		0			0
$958$	−9.22574	+	2.10572i	−0.298070	+	0.0680326i
$959$	8.11026	+	4.87773i	0.261894	+	0.157510i
$960$		0			0
$961$	30.9133			0.997204
$962$	−0.155593			−0.00501651
$963$		0			0
$964$	4.39805	+	9.13264i	0.141652	+	0.294143i
$965$	−2.03510	−	2.55194i	−0.0655123	−	0.0821498i
$966$		0			0
$967$	−19.0578	+	23.8977i	−0.612856	+	0.768498i	−0.987320	−	0.158744i	$-0.949256\pi$
$967$	−19.0578	+	23.8977i	−0.612856	+	0.768498i	0.374463	+	0.927242i	$0.377827\pi$
$968$	−26.9957	−	6.16158i	−0.867673	−	0.198041i
$969$		0			0
$970$	−26.1733	+	12.6044i	−0.840373	+	0.404702i
$971$	−28.9287	−	36.2755i	−0.928367	−	1.16414i	−0.986158	−	0.165807i	$-0.946977\pi$
$971$	−28.9287	−	36.2755i	−0.928367	−	1.16414i	0.0577908	−	0.998329i	$-0.481594\pi$
$972$		0			0
$973$	6.51874	+	49.1990i	0.208981	+	1.57725i
$974$	5.64132	+	11.7143i	0.180760	+	0.375351i
$975$		0			0
$976$	−4.45582	+	1.01701i	−0.142627	+	0.0325537i
$977$	−4.66538	+	9.68776i	−0.149259	+	0.309939i	−0.962171	−	0.272448i	$-0.912167\pi$
$977$	−4.66538	+	9.68776i	−0.149259	+	0.309939i	0.812912	+	0.582387i	$0.197881\pi$
$978$		0			0
$979$		−	65.3600i		−	2.08892i
$980$	−11.6632	−	8.57795i	−0.372567	−	0.274013i
$981$		0			0
$982$	10.4643	−	13.1218i	0.333929	−	0.418734i
$983$	−11.1575	−	5.37316i	−0.355868	−	0.171377i	0.247404	−	0.968912i	$-0.420422\pi$
$983$	−11.1575	−	5.37316i	−0.355868	−	0.171377i	−0.603272	+	0.797535i	$0.706137\pi$
$984$		0			0
$985$	16.6312	−	34.5350i	0.529913	−	1.10038i
$986$	45.2173	−	21.7755i	1.44001	−	0.693473i
$987$		0			0
$988$	0.110439	+	0.0531845i	0.00351353	+	0.00169203i
$989$	0.660529	−	0.526754i	0.0210036	−	0.0167498i
$990$		0			0
$991$	21.3102	−	26.7222i	0.676942	−	0.848858i	−0.318127	−	0.948048i	$-0.603054\pi$
$991$	21.3102	−	26.7222i	0.676942	−	0.848858i	0.995069	+	0.0991901i	$0.0316252\pi$
$992$	−0.0655172	+	0.287050i	−0.00208017	+	0.00911384i
$993$		0			0
$994$	−4.86218	+	0.644226i	−0.154219	+	0.0204336i
$995$	−37.6390	+	30.0161i	−1.19324	+	0.951575i
$996$		0			0
$997$	−23.4335	−	5.34855i	−0.742148	−	0.169390i	−0.165301	−	0.986243i	$-0.552860\pi$
$997$	−23.4335	−	5.34855i	−0.742148	−	0.169390i	−0.576846	+	0.816853i	$0.695717\pi$
$998$			10.9892i			0.347856i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.v.a.251.10	yes	96
3.2	odd	2	inner	882.2.v.a.251.7	✓	96
49.41	odd	14	inner	882.2.v.a.629.7	yes	96
147.41	even	14	inner	882.2.v.a.629.10	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.v.a.251.7	✓	96	3.2	odd	2	inner
882.2.v.a.251.10	yes	96	1.1	even	1	trivial
882.2.v.a.629.7	yes	96	49.41	odd	14	inner
882.2.v.a.629.10	yes	96	147.41	even	14	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.v (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.781831 + 0.623490i) q^{2} +(0.222521 + 0.974928i) q^{4} +(-1.86346 - 0.897393i) q^{5} +(2.21230 - 1.45111i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(-0.897393 - 1.86346i) q^{10} +(-4.86309 - 3.87818i) q^{11} +(0.0474881 + 0.0378705i) q^{13} +(2.63440 + 0.244829i) q^{14} +(-0.900969 + 0.433884i) q^{16} +(1.28053 - 5.61037i) q^{17} -2.01809i q^{19} +(0.460236 - 2.01642i) q^{20} +(-1.38411 - 6.06417i) q^{22} +(-0.713943 + 0.162953i) q^{23} +(-0.450293 - 0.564650i) q^{25} +(0.0135158 + 0.0592167i) q^{26} +(1.90701 + 1.83394i) q^{28} +(8.50253 + 1.94065i) q^{29} -0.294432i q^{31} +(-0.974928 - 0.222521i) q^{32} +(4.49917 - 3.58797i) q^{34} +(-5.42475 + 0.718765i) q^{35} +(-0.570017 + 2.49741i) q^{37} +(1.25826 - 1.57781i) q^{38} +(1.61705 - 1.28955i) q^{40} +(-7.61862 - 3.66893i) q^{41} +(-1.03943 + 0.500565i) q^{43} +(2.69881 - 5.60413i) q^{44} +(-0.659783 - 0.317735i) q^{46} +(3.82370 - 4.79476i) q^{47} +(2.78858 - 6.42058i) q^{49} -0.722214i q^{50} +(-0.0263539 + 0.0547244i) q^{52} +(-7.87382 + 1.79715i) q^{53} +(5.58190 + 11.5909i) q^{55} +(0.347518 + 2.62283i) q^{56} +(5.43757 + 6.81850i) q^{58} +(4.79120 - 2.30732i) q^{59} +(4.45582 + 1.01701i) q^{61} +(0.183575 - 0.230196i) q^{62} +(-0.623490 - 0.781831i) q^{64} +(-0.0545073 - 0.113186i) q^{65} +4.72254 q^{67} +5.75465 q^{68} +(-4.68938 - 2.82032i) q^{70} +(-1.80731 + 0.412508i) q^{71} +(12.0502 - 9.60974i) q^{73} +(-2.00277 + 1.59715i) q^{74} +(1.96749 - 0.449067i) q^{76} +(-16.3863 - 1.52287i) q^{77} -4.58892 q^{79} +2.06828 q^{80} +(-3.66893 - 7.61862i) q^{82} +(0.413442 + 0.518440i) q^{83} +(-7.42092 + 9.30555i) q^{85} +(-1.12476 - 0.256719i) q^{86} +(5.60413 - 2.69881i) q^{88} +(6.55153 + 8.21536i) q^{89} +(0.160012 + 0.0148708i) q^{91} +(-0.317735 - 0.659783i) q^{92} +(5.97897 - 1.36466i) q^{94} +(-1.81102 + 3.76062i) q^{95} -14.0455i q^{97} +(6.18337 - 3.28115i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 16 q^{4} - 16 q^{16} + 20 q^{22} - 8 q^{25} + 76 q^{37} + 28 q^{40} - 8 q^{43} + 112 q^{49} + 28 q^{52} + 28 q^{55} + 20 q^{58} + 84 q^{61} + 16 q^{64} - 8 q^{67} + 28 q^{70} + 112 q^{85} + 8 q^{88}+ \cdots - 56 q^{94}+O(q^{100}) \) 96 * q + 16 * q^4 - 16 * q^16 + 20 * q^22 - 8 * q^25 + 76 * q^37 + 28 * q^40 - 8 * q^43 + 112 * q^49 + 28 * q^52 + 28 * q^55 + 20 * q^58 + 84 * q^61 + 16 * q^64 - 8 * q^67 + 28 * q^70 + 112 * q^85 + 8 * q^88 - 56 * q^91 - 56 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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