LMFDB - Embedded newform 432.2.l.b.107.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(107,432)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("432.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.10
Character	$\chi$	$=$	432.107
Dual form			432.2.l.b.323.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.379657 - 1.36230i) q^{2} +(-1.71172 - 1.03441i) q^{4} +(-0.463925 + 0.463925i) q^{5} -1.85883 q^{7} +(-2.05905 + 1.93916i) q^{8} +O(q^{10})$	\(q+(0.379657 - 1.36230i) q^{2} +(-1.71172 - 1.03441i) q^{4} +(-0.463925 + 0.463925i) q^{5} -1.85883 q^{7} +(-2.05905 + 1.93916i) q^{8} +(0.455873 + 0.808137i) q^{10} +(-3.73577 - 3.73577i) q^{11} +(-4.31012 + 4.31012i) q^{13} +(-0.705716 + 2.53228i) q^{14} +(1.85998 + 3.54125i) q^{16} -6.55700i q^{17} +(-1.31300 - 1.31300i) q^{19} +(1.27400 - 0.314221i) q^{20} +(-6.50754 + 3.67093i) q^{22} +0.727384i q^{23} +4.56955i q^{25} +(4.23531 + 7.50805i) q^{26} +(3.18180 + 1.92279i) q^{28} +(-0.896599 - 0.896599i) q^{29} -5.25771i q^{31} +(5.53040 - 1.18939i) q^{32} +(-8.93260 - 2.48941i) q^{34} +(0.862356 - 0.862356i) q^{35} +(3.98112 + 3.98112i) q^{37} +(-2.28719 + 1.29021i) q^{38} +(0.0556200 - 1.85487i) q^{40} -5.10406 q^{41} +(1.09445 - 1.09445i) q^{43} +(2.53027 + 10.2589i) q^{44} +(0.990915 + 0.276156i) q^{46} +6.81472 q^{47} -3.54476 q^{49} +(6.22509 + 1.73486i) q^{50} +(11.8362 - 2.91929i) q^{52} +(0.712025 - 0.712025i) q^{53} +3.46623 q^{55} +(3.82741 - 3.60456i) q^{56} +(-1.56184 + 0.881037i) q^{58} +(-1.86942 - 1.86942i) q^{59} +(5.98625 - 5.98625i) q^{61} +(-7.16257 - 1.99612i) q^{62} +(0.479345 - 7.98563i) q^{64} -3.99915i q^{65} +(-8.48245 - 8.48245i) q^{67} +(-6.78264 + 11.2238i) q^{68} +(-0.847389 - 1.50219i) q^{70} -12.4124i q^{71} +3.72969i q^{73} +(6.93493 - 3.91202i) q^{74} +(0.889307 + 3.60567i) q^{76} +(6.94415 + 6.94415i) q^{77} -0.199069i q^{79} +(-2.50577 - 0.779983i) q^{80} +(-1.93779 + 6.95326i) q^{82} +(-9.97322 + 9.97322i) q^{83} +(3.04195 + 3.04195i) q^{85} +(-1.07545 - 1.90648i) q^{86} +(14.9364 + 0.447882i) q^{88} +7.53220 q^{89} +(8.01178 - 8.01178i) q^{91} +(0.752415 - 1.24508i) q^{92} +(2.58725 - 9.28369i) q^{94} +1.21827 q^{95} +9.81958 q^{97} +(-1.34579 + 4.82903i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 8 q^{10} - 8 q^{16} - 16 q^{19} + 16 q^{22} + 24 q^{28} + 24 q^{34} - 24 q^{40} - 16 q^{43} + 32 q^{46} + 32 q^{49} + 48 q^{52} - 32 q^{55} + 32 q^{61} - 24 q^{64} - 32 q^{67} - 48 q^{76} - 80 q^{82} + 32 q^{85} - 24 q^{88} - 48 q^{91}+O(q^{100}) $ 32 * q + 8 * q^10 - 8 * q^16 - 16 * q^19 + 16 * q^22 + 24 * q^28 + 24 * q^34 - 24 * q^40 - 16 * q^43 + 32 * q^46 + 32 * q^49 + 48 * q^52 - 32 * q^55 + 32 * q^61 - 24 * q^64 - 32 * q^67 - 48 * q^76 - 80 * q^82 + 32 * q^85 - 24 * q^88 - 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.379657	−	1.36230i	0.268458	−	0.963291i
$2$	0.379657	−	1.36230i	0.268458	−	0.963291i
$3$		0			0
$3$		0			0
$4$	−1.71172	−	1.03441i	−0.855861	−	0.517206i
$5$	−0.463925	+	0.463925i	−0.207474	+	0.207474i	−0.803193	−	0.595719i	$-0.796867\pi$
$5$	−0.463925	+	0.463925i	−0.207474	+	0.207474i	0.595719	+	0.803193i	$0.296867\pi$
$6$		0			0
$7$	−1.85883			−0.702571			−0.351285	−	0.936268i	$-0.614255\pi$
$7$	−1.85883			−0.702571			−0.351285	+	0.936268i	$0.614255\pi$
$8$	−2.05905	+	1.93916i	−0.727983	+	0.685595i
$9$		0			0
$10$	0.455873	+	0.808137i	0.144160	+	0.255555i
$11$	−3.73577	−	3.73577i	−1.12638	−	1.12638i	−0.990762	−	0.135615i	$-0.956699\pi$
$11$	−3.73577	−	3.73577i	−1.12638	−	1.12638i	−0.135615	−	0.990762i	$-0.543301\pi$
$12$		0			0
$13$	−4.31012	+	4.31012i	−1.19541	+	1.19541i	−0.219888	+	0.975525i	$0.570569\pi$
$13$	−4.31012	+	4.31012i	−1.19541	+	1.19541i	−0.975525	+	0.219888i	$0.929431\pi$
$14$	−0.705716	+	2.53228i	−0.188611	+	0.676780i
$15$		0			0
$16$	1.85998	+	3.54125i	0.464995	+	0.885313i
$17$		−	6.55700i		−	1.59031i	−0.606409	−	0.795153i	$-0.707391\pi$
$17$		−	6.55700i		−	1.59031i	0.606409	−	0.795153i	$-0.292609\pi$
$18$		0			0
$19$	−1.31300	−	1.31300i	−0.301223	−	0.301223i	0.540269	−	0.841492i	$-0.318322\pi$
$19$	−1.31300	−	1.31300i	−0.301223	−	0.301223i	−0.841492	+	0.540269i	$0.818322\pi$
$20$	1.27400	−	0.314221i	0.284875	−	0.0702618i
$21$		0			0
$22$	−6.50754	+	3.67093i	−1.38741	+	0.782644i
$23$			0.727384i			0.151670i	0.997120	+	0.0758350i	$0.0241622\pi$
$23$			0.727384i			0.151670i	−0.997120	+	0.0758350i	$0.975838\pi$
$24$		0			0
$25$			4.56955i			0.913909i
$26$	4.23531	+	7.50805i	0.830613	+	1.47245i
$27$		0			0
$28$	3.18180	+	1.92279i	0.601303	+	0.363374i
$29$	−0.896599	−	0.896599i	−0.166494	−	0.166494i	0.618942	−	0.785436i	$-0.287561\pi$
$29$	−0.896599	−	0.896599i	−0.166494	−	0.166494i	−0.785436	+	0.618942i	$0.787561\pi$
$30$		0			0
$31$		−	5.25771i		−	0.944312i	−0.881515	−	0.472156i	$-0.843476\pi$
$31$		−	5.25771i		−	0.944312i	0.881515	−	0.472156i	$-0.156524\pi$
$32$	5.53040	−	1.18939i	0.977646	−	0.210257i
$33$		0			0
$34$	−8.93260	−	2.48941i	−1.53193	−	0.426930i
$35$	0.862356	−	0.862356i	0.145765	−	0.145765i
$36$		0			0
$37$	3.98112	+	3.98112i	0.654492	+	0.654492i	0.954071	−	0.299580i	$-0.0968464\pi$
$37$	3.98112	+	3.98112i	0.654492	+	0.654492i	−0.299580	+	0.954071i	$0.596846\pi$
$38$	−2.28719	+	1.29021i	−0.371031	+	0.209300i
$39$		0			0
$40$	0.0556200	−	1.85487i	0.00879430	−	0.293280i
$41$	−5.10406			−0.797121			−0.398560	−	0.917142i	$-0.630490\pi$
$41$	−5.10406			−0.797121			−0.398560	+	0.917142i	$0.630490\pi$
$42$		0			0
$43$	1.09445	−	1.09445i	0.166901	−	0.166901i	−0.618714	−	0.785616i	$-0.712346\pi$
$43$	1.09445	−	1.09445i	0.166901	−	0.166901i	0.785616	+	0.618714i	$0.212346\pi$
$44$	2.53027	+	10.2589i	0.381452	+	1.54659i
$45$		0			0
$46$	0.990915	+	0.276156i	0.146102	+	0.0407170i
$47$	6.81472			0.994029			0.497014	−	0.867742i	$-0.334430\pi$
$47$	6.81472			0.994029			0.497014	+	0.867742i	$0.334430\pi$
$48$		0			0
$49$	−3.54476			−0.506394
$50$	6.22509	+	1.73486i	0.880361	+	0.245346i
$51$		0			0
$52$	11.8362	−	2.91929i	1.64138	−	0.404832i
$53$	0.712025	−	0.712025i	0.0978042	−	0.0978042i	−0.656512	−	0.754316i	$-0.727969\pi$
$53$	0.712025	−	0.712025i	0.0978042	−	0.0978042i	0.754316	+	0.656512i	$0.227969\pi$
$54$		0			0
$55$	3.46623			0.467386
$56$	3.82741	−	3.60456i	0.511459	−	0.481679i
$57$		0			0
$58$	−1.56184	+	0.881037i	−0.205079	+	0.115686i
$59$	−1.86942	−	1.86942i	−0.243378	−	0.243378i	0.574868	−	0.818246i	$-0.305053\pi$
$59$	−1.86942	−	1.86942i	−0.243378	−	0.243378i	−0.818246	+	0.574868i	$0.805053\pi$
$60$		0			0
$61$	5.98625	−	5.98625i	0.766461	−	0.766461i	−0.211021	−	0.977482i	$-0.567679\pi$
$61$	5.98625	−	5.98625i	0.766461	−	0.766461i	0.977482	+	0.211021i	$0.0676787\pi$
$62$	−7.16257	−	1.99612i	−0.909648	−	0.253508i
$63$		0			0
$64$	0.479345	−	7.98563i	0.0599181	−	0.998203i
$65$		−	3.99915i		−	0.496033i
$66$		0			0
$67$	−8.48245	−	8.48245i	−1.03630	−	1.03630i	−0.999316	−	0.0369805i	$-0.988226\pi$
$67$	−8.48245	−	8.48245i	−1.03630	−	1.03630i	−0.0369805	−	0.999316i	$-0.511774\pi$
$68$	−6.78264	+	11.2238i	−0.822516	+	1.36108i
$69$		0			0
$70$	−0.847389	−	1.50219i	−0.101282	−	0.179546i
$71$		−	12.4124i		−	1.47308i	−0.676394	−	0.736540i	$-0.736458\pi$
$71$		−	12.4124i		−	1.47308i	0.676394	−	0.736540i	$-0.263542\pi$
$72$		0			0
$73$			3.72969i			0.436527i	0.975890	+	0.218264i	$0.0700392\pi$
$73$			3.72969i			0.436527i	−0.975890	+	0.218264i	$0.929961\pi$
$74$	6.93493	−	3.91202i	0.806170	−	0.454763i
$75$		0			0
$76$	0.889307	+	3.60567i	0.102010	+	0.413599i
$77$	6.94415	+	6.94415i	0.791359	+	0.791359i
$78$		0			0
$79$		−	0.199069i		−	0.0223970i	−0.999937	−	0.0111985i	$-0.996435\pi$
$79$		−	0.199069i		−	0.0223970i	0.999937	−	0.0111985i	$-0.00356468\pi$
$80$	−2.50577	−	0.779983i	−0.280153	−	0.0872048i
$81$		0			0
$82$	−1.93779	+	6.95326i	−0.213993	+	0.767860i
$83$	−9.97322	+	9.97322i	−1.09470	+	1.09470i	−0.0996837	+	0.995019i	$0.531783\pi$
$83$	−9.97322	+	9.97322i	−1.09470	+	1.09470i	−0.995019	+	0.0996837i	$0.968217\pi$
$84$		0			0
$85$	3.04195	+	3.04195i	0.329946	+	0.329946i
$86$	−1.07545	−	1.90648i	−0.115969	−	0.205581i
$87$		0			0
$88$	14.9364	+	0.447882i	1.59222	+	0.0477444i
$89$	7.53220			0.798412			0.399206	−	0.916861i	$-0.369286\pi$
$89$	7.53220			0.798412			0.399206	+	0.916861i	$0.369286\pi$
$90$		0			0
$91$	8.01178	−	8.01178i	0.839863	−	0.839863i
$92$	0.752415	−	1.24508i	0.0784447	−	0.129808i
$93$		0			0
$94$	2.58725	−	9.28369i	0.266855	−	0.957539i
$95$	1.21827			0.124991
$96$		0			0
$97$	9.81958			0.997027			0.498514	−	0.866882i	$-0.333879\pi$
$97$	9.81958			0.997027			0.498514	+	0.866882i	$0.333879\pi$
$98$	−1.34579	+	4.82903i	−0.135946	+	0.487805i
$99$		0			0
$100$	4.72680	−	7.82179i	0.472680	−	0.782179i
$101$	−13.6195	+	13.6195i	−1.35519	+	1.35519i	−0.475454	+	0.879741i	$0.657716\pi$
$101$	−13.6195	+	13.6195i	−1.35519	+	1.35519i	−0.879741	+	0.475454i	$0.842284\pi$
$102$		0			0
$103$	1.29990			0.128083			0.0640414	−	0.997947i	$-0.479601\pi$
$103$	1.29990			0.128083			0.0640414	+	0.997947i	$0.479601\pi$
$104$	0.516742	−	17.2328i	0.0506707	−	1.68981i
$105$		0			0
$106$	−0.699667	−	1.24032i	−0.0679576	−	0.120470i
$107$	−10.6692	−	10.6692i	−1.03143	−	1.03143i	−0.999490	−	0.0319359i	$-0.989833\pi$
$107$	−10.6692	−	10.6692i	−1.03143	−	1.03143i	−0.0319359	−	0.999490i	$-0.510167\pi$
$108$		0			0
$109$	−8.11473	+	8.11473i	−0.777250	+	0.777250i	−0.979362	−	0.202112i	$-0.935220\pi$
$109$	−8.11473	+	8.11473i	−0.777250	+	0.777250i	0.202112	+	0.979362i	$0.435220\pi$
$110$	1.31598	−	4.72205i	0.125474	−	0.450229i
$111$		0			0
$112$	−3.45738	−	6.58258i	−0.326692	−	0.621995i
$113$		−	18.0982i		−	1.70253i	−0.524735	−	0.851266i	$-0.675836\pi$
$113$		−	18.0982i		−	1.70253i	0.524735	−	0.851266i	$-0.324164\pi$
$114$		0			0
$115$	−0.337451	−	0.337451i	−0.0314675	−	0.0314675i
$116$	0.607275	+	2.46218i	0.0563840	+	0.228608i
$117$		0			0
$118$	−3.25646	+	1.83698i	−0.299781	+	0.169107i
$119$			12.1883i			1.11730i
$120$		0			0
$121$			16.9119i			1.53745i
$122$	−5.88235	−	10.4278i	−0.532563	−	0.944088i
$123$		0			0
$124$	−5.43864	+	8.99973i	−0.488404	+	0.808200i
$125$	−4.43955	−	4.43955i	−0.397086	−	0.397086i
$126$		0			0
$127$		−	17.6229i		−	1.56378i	−0.623416	−	0.781891i	$-0.714256\pi$
$127$		−	17.6229i		−	1.56378i	0.623416	−	0.781891i	$-0.285744\pi$
$128$	−10.6968	−	3.68481i	−0.945475	−	0.325694i
$129$		0			0
$130$	−5.44804	−	1.51830i	−0.477825	−	0.133164i
$131$	0.516185	−	0.516185i	0.0450993	−	0.0450993i	−0.684197	−	0.729297i	$-0.739847\pi$
$131$	0.516185	−	0.516185i	0.0450993	−	0.0450993i	0.729297	+	0.684197i	$0.239847\pi$
$132$		0			0
$133$	2.44064	+	2.44064i	0.211630	+	0.211630i
$134$	−14.7761	+	8.33522i	−1.27646	+	0.720054i
$135$		0			0
$136$	12.7150	+	13.5012i	1.09031	+	1.15772i
$137$	9.51987			0.813338			0.406669	−	0.913576i	$-0.366690\pi$
$137$	9.51987			0.813338			0.406669	+	0.913576i	$0.366690\pi$
$138$		0			0
$139$	8.85424	−	8.85424i	0.751007	−	0.751007i	−0.223660	−	0.974667i	$-0.571801\pi$
$139$	8.85424	−	8.85424i	0.751007	−	0.751007i	0.974667	+	0.223660i	$0.0718007\pi$
$140$	−2.36815	+	0.584082i	−0.200145	+	0.0493639i
$141$		0			0
$142$	−16.9094	−	4.71245i	−1.41901	−	0.395460i
$143$	32.2032			2.69297
$144$		0			0
$145$	0.831909			0.0690863
$146$	5.08095	+	1.41600i	0.420503	+	0.117189i
$147$		0			0
$148$	−2.69645	−	10.9327i	−0.221647	−	0.898661i
$149$	−12.8550	+	12.8550i	−1.05313	+	1.05313i	−0.0546187	+	0.998507i	$0.517394\pi$
$149$	−12.8550	+	12.8550i	−1.05313	+	1.05313i	−0.998507	+	0.0546187i	$0.982606\pi$
$150$		0			0
$151$	−6.75375			−0.549612			−0.274806	−	0.961500i	$-0.588614\pi$
$151$	−6.75375			−0.549612			−0.274806	+	0.961500i	$0.588614\pi$
$152$	5.24964	+	0.157416i	0.425802	+	0.0127681i
$153$		0			0
$154$	12.0964	−	6.82362i	0.974756	−	0.549863i
$155$	2.43918	+	2.43918i	0.195920	+	0.195920i
$156$		0			0
$157$	−1.36386	+	1.36386i	−0.108848	+	0.108848i	−0.759433	−	0.650585i	$-0.774524\pi$
$157$	−1.36386	+	1.36386i	−0.108848	+	0.108848i	0.650585	+	0.759433i	$0.274524\pi$
$158$	−0.271192	−	0.0755780i	−0.0215749	−	0.00601266i
$159$		0			0
$160$	−2.01390	+	3.11748i	−0.159213	+	0.246458i
$161$		−	1.35208i		−	0.106559i
$162$		0			0
$163$	4.75407	+	4.75407i	0.372368	+	0.372368i	0.868339	−	0.495971i	$-0.165188\pi$
$163$	4.75407	+	4.75407i	0.372368	+	0.372368i	−0.495971	+	0.868339i	$0.665188\pi$
$164$	8.73673	+	5.27971i	0.682224	+	0.412276i
$165$		0			0
$166$	9.80011	+	17.3729i	0.760636	+	1.34840i
$167$			18.6718i			1.44487i	0.691439	+	0.722435i	$0.256977\pi$
$167$			18.6718i			1.44487i	−0.691439	+	0.722435i	$0.743023\pi$
$168$		0			0
$169$		−	24.1543i		−	1.85803i
$170$	5.29895	−	2.98916i	0.406411	−	0.229258i
$171$		0			0
$172$	−3.00550	+	0.741278i	−0.229167	+	0.0565219i
$173$	13.5409	+	13.5409i	1.02950	+	1.02950i	0.999552	+	0.0299462i	$0.00953360\pi$
$173$	13.5409	+	13.5409i	1.02950	+	1.02950i	0.0299462	+	0.999552i	$0.490466\pi$
$174$		0			0
$175$		−	8.49400i		−	0.642086i
$176$	6.28084	−	20.1778i	0.473436	−	1.52096i
$177$		0			0
$178$	2.85965	−	10.2611i	0.214340	−	0.769103i
$179$	−13.2637	+	13.2637i	−0.991375	+	0.991375i	−0.999963	−	0.00858851i	$-0.997266\pi$
$179$	−13.2637	+	13.2637i	−0.991375	+	0.991375i	0.00858851	+	0.999963i	$0.497266\pi$
$180$		0			0
$181$	0.588855	+	0.588855i	0.0437692	+	0.0437692i	0.728653	−	0.684883i	$-0.240147\pi$
$181$	0.588855	+	0.588855i	0.0437692	+	0.0437692i	−0.684883	+	0.728653i	$0.740147\pi$
$182$	−7.87272	−	13.9562i	−0.583565	−	1.03450i
$183$		0			0
$184$	−1.41051	−	1.49772i	−0.103984	−	0.110413i
$185$	−3.69388			−0.271579
$186$		0			0
$187$	−24.4954	+	24.4954i	−1.79128	+	1.79128i
$188$	−11.6649	−	7.04923i	−0.850750	−	0.514118i
$189$		0			0
$190$	0.462523	−	1.65964i	0.0335549	−	0.120403i
$191$	8.73890			0.632325			0.316162	−	0.948705i	$-0.397606\pi$
$191$	8.73890			0.632325			0.316162	+	0.948705i	$0.397606\pi$
$192$		0			0
$193$	−11.8318			−0.851673			−0.425836	−	0.904800i	$-0.640020\pi$
$193$	−11.8318			−0.851673			−0.425836	+	0.904800i	$0.640020\pi$
$194$	3.72807	−	13.3772i	0.267660	−	0.960428i
$195$		0			0
$196$	6.06764	+	3.66674i	0.433403	+	0.261910i
$197$	6.04244	−	6.04244i	0.430506	−	0.430506i	−0.458295	−	0.888800i	$-0.651540\pi$
$197$	6.04244	−	6.04244i	0.430506	−	0.430506i	0.888800	+	0.458295i	$0.151540\pi$
$198$		0			0
$199$	−11.7641			−0.833934			−0.416967	−	0.908922i	$-0.636907\pi$
$199$	−11.7641			−0.833934			−0.416967	+	0.908922i	$0.636907\pi$
$200$	−8.86107	−	9.40891i	−0.626572	−	0.665310i
$201$		0			0
$202$	13.3831	+	23.7246i	0.941635	+	1.66926i
$203$	1.66662	+	1.66662i	0.116974	+	0.116974i
$204$		0			0
$205$	2.36790	−	2.36790i	0.165381	−	0.165381i
$206$	0.493515	−	1.77085i	0.0343848	−	0.123381i
$207$		0			0
$208$	−23.2800	−	7.24649i	−1.61418	−	0.502453i
$209$			9.81012i			0.678580i
$210$		0			0
$211$	14.2861	+	14.2861i	0.983498	+	0.983498i	0.999866	−	0.0163680i	$-0.00521031\pi$
$211$	14.2861	+	14.2861i	0.983498	+	0.983498i	−0.0163680	+	0.999866i	$0.505210\pi$
$212$	−1.95532	+	0.482261i	−0.134292	+	0.0331218i
$213$		0			0
$214$	−18.5852	+	10.4840i	−1.27046	+	0.716669i
$215$			1.01548i			0.0692553i
$216$		0			0
$217$			9.77317i			0.663446i
$218$	7.97389	+	14.1355i	0.540060	+	0.957378i
$219$		0			0
$220$	−5.93322	−	3.58551i	−0.400018	−	0.241735i
$221$	28.2615	+	28.2615i	1.90107	+	1.90107i
$222$		0			0
$223$			25.2083i			1.68807i	0.536286	+	0.844036i	$0.319827\pi$
$223$			25.2083i			1.68807i	−0.536286	+	0.844036i	$0.680173\pi$
$224$	−10.2801	+	2.21088i	−0.686866	+	0.147720i
$225$		0			0
$226$	−24.6551	−	6.87109i	−1.64003	−	0.457058i
$227$	−5.31259	+	5.31259i	−0.352609	+	0.352609i	−0.861080	−	0.508470i	$-0.830211\pi$
$227$	−5.31259	+	5.31259i	−0.352609	+	0.352609i	0.508470	+	0.861080i	$0.330211\pi$
$228$		0			0
$229$	−6.10498	−	6.10498i	−0.403429	−	0.403429i	0.476011	−	0.879439i	$-0.342082\pi$
$229$	−6.10498	−	6.10498i	−0.403429	−	0.403429i	−0.879439	+	0.476011i	$0.842082\pi$
$230$	−0.587826	+	0.331594i	−0.0387601	+	0.0218647i
$231$		0			0
$232$	3.58478	+	0.107493i	0.235353	+	0.00705729i
$233$	8.03106			0.526132			0.263066	−	0.964778i	$-0.415266\pi$
$233$	8.03106			0.526132			0.263066	+	0.964778i	$0.415266\pi$
$234$		0			0
$235$	−3.16152	+	3.16152i	−0.206235	+	0.206235i
$236$	1.26618	+	5.13369i	0.0824212	+	0.334175i
$237$		0			0
$238$	16.6042	+	4.62738i	1.07629	+	0.299948i
$239$	−16.4509			−1.06412			−0.532060	−	0.846706i	$-0.678582\pi$
$239$	−16.4509			−1.06412			−0.532060	+	0.846706i	$0.678582\pi$
$240$		0			0
$241$	3.21157			0.206876			0.103438	−	0.994636i	$-0.467016\pi$
$241$	3.21157			0.206876			0.103438	+	0.994636i	$0.467016\pi$
$242$	23.0391	+	6.42072i	1.48101	+	0.412740i
$243$		0			0
$244$	−16.4390	+	4.05454i	−1.05240	+	0.259565i
$245$	1.64450	−	1.64450i	0.105063	−	0.105063i
$246$		0			0
$247$	11.3184			0.720172
$248$	10.1955	+	10.8259i	0.647416	+	0.687443i
$249$		0			0
$250$	−7.73350	+	4.36249i	−0.489110	+	0.275908i
$251$	0.155779	+	0.155779i	0.00983268	+	0.00983268i	0.712006	−	0.702173i	$-0.247787\pi$
$251$	0.155779	+	0.155779i	0.00983268	+	0.00983268i	−0.702173	+	0.712006i	$0.747787\pi$
$252$		0			0
$253$	2.71734	−	2.71734i	0.170837	−	0.170837i
$254$	−24.0077	−	6.69066i	−1.50638	−	0.419809i
$255$		0			0
$256$	−9.08094	+	13.1733i	−0.567559	+	0.823333i
$257$		−	13.0277i		−	0.812646i	−0.913729	−	0.406323i	$-0.866811\pi$
$257$		−	13.0277i		−	0.812646i	0.913729	−	0.406323i	$-0.133189\pi$
$258$		0			0
$259$	−7.40021	−	7.40021i	−0.459827	−	0.459827i
$260$	−4.13677	+	6.84543i	−0.256552	+	0.424535i
$261$		0			0
$262$	−0.507226	−	0.899172i	−0.0313365	−	0.0555510i
$263$		−	14.3366i		−	0.884032i	−0.897007	−	0.442016i	$-0.854264\pi$
$263$		−	14.3366i		−	0.884032i	0.897007	−	0.442016i	$-0.145736\pi$
$264$		0			0
$265$			0.660652i			0.0405835i
$266$	4.25149	−	2.39828i	0.260676	−	0.147048i
$267$		0			0
$268$	5.74524	+	23.2940i	0.350947	+	1.42290i
$269$	−9.05831	−	9.05831i	−0.552295	−	0.552295i	0.374807	−	0.927103i	$-0.377709\pi$
$269$	−9.05831	−	9.05831i	−0.552295	−	0.552295i	−0.927103	+	0.374807i	$0.877709\pi$
$270$		0			0
$271$			25.2882i			1.53615i	0.640360	+	0.768075i	$0.278785\pi$
$271$			25.2882i			1.53615i	−0.640360	+	0.768075i	$0.721215\pi$
$272$	23.2200	−	12.1959i	1.40792	−	0.739485i
$273$		0			0
$274$	3.61428	−	12.9689i	0.218347	−	0.783481i
$275$	17.0708	−	17.0708i	1.02941	−	1.02941i
$276$		0			0
$277$	−4.54879	−	4.54879i	−0.273310	−	0.273310i	0.557121	−	0.830431i	$-0.311906\pi$
$277$	−4.54879	−	4.54879i	−0.273310	−	0.273310i	−0.830431	+	0.557121i	$0.811906\pi$
$278$	−8.70056	−	15.4237i	−0.521825	−	0.925052i
$279$		0			0
$280$	−0.103388	+	3.44788i	−0.00617862	+	0.206050i
$281$	−18.3548			−1.09495			−0.547477	−	0.836820i	$-0.684412\pi$
$281$	−18.3548			−1.09495			−0.547477	+	0.836820i	$0.684412\pi$
$282$		0			0
$283$	10.0643	−	10.0643i	0.598259	−	0.598259i	−0.341590	−	0.939849i	$-0.610965\pi$
$283$	10.0643	−	10.0643i	0.598259	−	0.598259i	0.939849	+	0.341590i	$0.110965\pi$
$284$	−12.8395	+	21.2466i	−0.761887	+	1.26075i
$285$		0			0
$286$	12.2262	−	43.8705i	0.722949	−	2.59412i
$287$	9.48757			0.560034
$288$		0			0
$289$	−25.9942			−1.52907
$290$	0.315840	−	1.13331i	0.0185468	−	0.0665502i
$291$		0			0
$292$	3.85804	−	6.38419i	0.225775	−	0.373606i
$293$	0.876200	−	0.876200i	0.0511882	−	0.0511882i	−0.681049	−	0.732238i	$-0.738476\pi$
$293$	0.876200	−	0.876200i	0.0511882	−	0.0511882i	0.732238	+	0.681049i	$0.238476\pi$
$294$		0			0
$295$	1.73454			0.100989
$296$	−15.9173	−	0.477297i	−0.925175	−	0.0277423i
$297$		0			0
$298$	12.6319	+	22.3929i	0.731747	+	1.29719i
$299$	−3.13511	−	3.13511i	−0.181308	−	0.181308i
$300$		0			0
$301$	−2.03439	+	2.03439i	−0.117260	+	0.117260i
$302$	−2.56411	+	9.20063i	−0.147548	+	0.529437i
$303$		0			0
$304$	2.20751	−	7.09182i	0.126609	−	0.406744i
$305$			5.55434i			0.318041i
$306$		0			0
$307$	−13.8024	−	13.8024i	−0.787744	−	0.787744i	0.193380	−	0.981124i	$-0.438055\pi$
$307$	−13.8024	−	13.8024i	−0.787744	−	0.787744i	−0.981124	+	0.193380i	$0.938055\pi$
$308$	−4.70333	−	19.0696i	−0.267997	−	1.08659i
$309$		0			0
$310$	4.24895	−	2.39684i	0.241324	−	0.136132i
$311$			12.4588i			0.706472i	0.935534	+	0.353236i	$0.114919\pi$
$311$			12.4588i			0.706472i	−0.935534	+	0.353236i	$0.885081\pi$
$312$		0			0
$313$		−	12.1941i		−	0.689249i	−0.938741	−	0.344625i	$-0.888006\pi$
$313$		−	12.1941i		−	0.689249i	0.938741	−	0.344625i	$-0.111994\pi$
$314$	1.34019	+	2.37579i	0.0756312	+	0.134073i
$315$		0			0
$316$	−0.205920	+	0.340751i	−0.0115839	+	0.0191688i
$317$	−18.9130	−	18.9130i	−1.06226	−	1.06226i	−0.997929	−	0.0643287i	$-0.979509\pi$
$317$	−18.9130	−	18.9130i	−1.06226	−	1.06226i	−0.0643287	−	0.997929i	$-0.520491\pi$
$318$		0			0
$319$			6.69897i			0.375070i
$320$	3.48235	+	3.92711i	0.194669	+	0.219532i
$321$		0			0
$322$	−1.84194	−	0.513327i	−0.102647	−	0.0286066i
$323$	−8.60934	+	8.60934i	−0.479036	+	0.479036i
$324$		0			0
$325$	−19.6953	−	19.6953i	−1.09250	−	1.09250i
$326$	8.28138	−	4.67155i	0.458663	−	0.258733i
$327$		0			0
$328$	10.5095	−	9.89758i	0.580290	−	0.546502i
$329$	−12.6674			−0.698375
$330$		0			0
$331$	0.852960	−	0.852960i	0.0468829	−	0.0468829i	−0.683277	−	0.730160i	$-0.739446\pi$
$331$	0.852960	−	0.852960i	0.0468829	−	0.0468829i	0.730160	+	0.683277i	$0.239446\pi$
$332$	27.3878	−	6.75495i	1.50310	−	0.370726i
$333$		0			0
$334$	25.4366	+	7.08888i	1.39183	+	0.387887i
$335$	7.87044			0.430008
$336$		0			0
$337$	32.9286			1.79374			0.896869	−	0.442297i	$-0.145836\pi$
$337$	32.9286			1.79374			0.896869	+	0.442297i	$0.145836\pi$
$338$	−32.9055	−	9.17036i	−1.78982	−	0.498802i
$339$		0			0
$340$	−2.06034	−	8.35361i	−0.111738	−	0.453038i
$341$	−19.6416	+	19.6416i	−1.06365	+	1.06365i
$342$		0			0
$343$	19.6009			1.05835
$344$	−0.131213	+	4.37582i	−0.00707455	+	0.235928i
$345$		0			0
$346$	23.5877	−	13.3059i	1.26808	−	0.715330i
$347$	−13.8785	−	13.8785i	−0.745036	−	0.745036i	0.228506	−	0.973542i	$-0.426616\pi$
$347$	−13.8785	−	13.8785i	−0.745036	−	0.745036i	−0.973542	+	0.228506i	$0.926616\pi$
$348$		0			0
$349$	19.2311	−	19.2311i	1.02942	−	1.02942i	0.0298648	−	0.999554i	$-0.490492\pi$
$349$	19.2311	−	19.2311i	1.02942	−	1.02942i	0.999554	−	0.0298648i	$-0.00950766\pi$
$350$	−11.5714	−	3.22480i	−0.618516	−	0.172373i
$351$		0			0
$352$	−25.1036	−	16.2170i	−1.33803	−	0.864369i
$353$		−	12.1549i		−	0.646939i	−0.946239	−	0.323469i	$-0.895151\pi$
$353$		−	12.1549i		−	0.646939i	0.946239	−	0.323469i	$-0.104849\pi$
$354$		0			0
$355$	5.75842	+	5.75842i	0.305625	+	0.305625i
$356$	−12.8930	−	7.79141i	−0.683330	−	0.412944i
$357$		0			0
$358$	13.0335	+	23.1048i	0.688840	+	1.22112i
$359$			2.82558i			0.149128i	0.997216	+	0.0745642i	$0.0237566\pi$
$359$			2.82558i			0.149128i	−0.997216	+	0.0745642i	$0.976243\pi$
$360$		0			0
$361$		−	15.5521i		−	0.818530i
$362$	1.02576	−	0.578634i	0.0539127	−	0.0304123i
$363$		0			0
$364$	−22.0014	+	5.42645i	−1.15319	+	0.284423i
$365$	−1.73030	−	1.73030i	−0.0905678	−	0.0905678i
$366$		0			0
$367$			9.20981i			0.480748i	0.970680	+	0.240374i	$0.0772701\pi$
$367$			9.20981i			0.480748i	−0.970680	+	0.240374i	$0.922730\pi$
$368$	−2.57585	+	1.35292i	−0.134275	+	0.0705259i
$369$		0			0
$370$	−1.40241	+	5.03217i	−0.0729076	+	0.261610i
$371$	−1.32353	+	1.32353i	−0.0687143	+	0.0687143i
$372$		0			0
$373$	15.4719	+	15.4719i	0.801107	+	0.801107i	0.983269	−	0.182162i	$-0.0583094\pi$
$373$	15.4719	+	15.4719i	0.801107	+	0.801107i	−0.182162	+	0.983269i	$0.558309\pi$
$374$	24.0703	+	42.6699i	1.24464	+	2.20641i
$375$		0			0
$376$	−14.0318	+	13.2148i	−0.723636	+	0.681501i
$377$	7.72891			0.398059
$378$		0			0
$379$	−6.10456	+	6.10456i	−0.313570	+	0.313570i	−0.846291	−	0.532721i	$-0.821170\pi$
$379$	−6.10456	+	6.10456i	−0.313570	+	0.313570i	0.532721	+	0.846291i	$0.321170\pi$
$380$	−2.08533	−	1.26019i	−0.106975	−	0.0646464i
$381$		0			0
$382$	3.31778	−	11.9050i	0.169753	−	0.609113i
$383$	1.66755			0.0852078			0.0426039	−	0.999092i	$-0.486435\pi$
$383$	1.66755			0.0852078			0.0426039	+	0.999092i	$0.486435\pi$
$384$		0			0
$385$	−6.44313			−0.328372
$386$	−4.49203	+	16.1185i	−0.228638	+	0.820409i
$387$		0			0
$388$	−16.8084	−	10.1575i	−0.853317	−	0.515669i
$389$	18.2598	−	18.2598i	0.925810	−	0.925810i	−0.0716217	−	0.997432i	$-0.522817\pi$
$389$	18.2598	−	18.2598i	0.925810	−	0.925810i	0.997432	+	0.0716217i	$0.0228174\pi$
$390$		0			0
$391$	4.76945			0.241202
$392$	7.29883	−	6.87384i	0.368646	−	0.347182i
$393$		0			0
$394$	−5.93756	−	10.5257i	−0.299130	−	0.530275i
$395$	0.0923532	+	0.0923532i	0.00464679	+	0.00464679i
$396$		0			0
$397$	7.45587	−	7.45587i	0.374199	−	0.374199i	−0.494805	−	0.869004i	$-0.664760\pi$
$397$	7.45587	−	7.45587i	0.374199	−	0.374199i	0.869004	+	0.494805i	$0.164760\pi$
$398$	−4.46632	+	16.0262i	−0.223876	+	0.803322i
$399$		0			0
$400$	−16.1819	+	8.49927i	−0.809096	+	0.424964i
$401$		−	26.1001i		−	1.30338i	−0.758487	−	0.651688i	$-0.774061\pi$
$401$		−	26.1001i		−	1.30338i	0.758487	−	0.651688i	$-0.225939\pi$
$402$		0			0
$403$	22.6614	+	22.6614i	1.12884	+	1.12884i
$404$	37.4011	−	9.22464i	1.86077	−	0.458943i
$405$		0			0
$406$	2.90318	−	1.63770i	0.144083	−	0.0812775i
$407$		−	29.7451i		−	1.47441i
$408$		0			0
$409$		−	26.4012i		−	1.30546i	−0.757592	−	0.652728i	$-0.773624\pi$
$409$		−	26.4012i		−	1.30546i	0.757592	−	0.652728i	$-0.226376\pi$
$410$	−2.32680	−	4.12478i	−0.114913	−	0.203708i
$411$		0			0
$412$	−2.22506	−	1.34463i	−0.109621	−	0.0662452i
$413$	3.47494	+	3.47494i	0.170990	+	0.170990i
$414$		0			0
$415$		−	9.25365i		−	0.454244i
$416$	−18.7103	+	28.9632i	−0.917348	+	1.42004i
$417$		0			0
$418$	13.3643	+	3.72448i	0.653671	+	0.182170i
$419$	12.4672	−	12.4672i	0.609061	−	0.609061i	−0.333640	−	0.942701i	$-0.608277\pi$
$419$	12.4672	−	12.4672i	0.609061	−	0.609061i	0.942701	+	0.333640i	$0.108277\pi$
$420$		0			0
$421$	−16.2503	−	16.2503i	−0.791992	−	0.791992i	0.189826	−	0.981818i	$-0.439208\pi$
$421$	−16.2503	−	16.2503i	−0.791992	−	0.791992i	−0.981818	+	0.189826i	$0.939208\pi$
$422$	24.8858	−	14.0382i	1.21142	−	0.683368i
$423$		0			0
$424$	−0.0853648	+	2.84682i	−0.00414568	+	0.138254i
$425$	29.9625			1.45340
$426$		0			0
$427$	−11.1274	+	11.1274i	−0.538493	+	0.538493i
$428$	7.22631	+	29.2989i	0.349297	+	1.41622i
$429$		0			0
$430$	1.38339	+	0.385534i	0.0667130	+	0.0185921i
$431$	−25.7670			−1.24115			−0.620576	−	0.784146i	$-0.713101\pi$
$431$	−25.7670			−1.24115			−0.620576	+	0.784146i	$0.713101\pi$
$432$		0			0
$433$	21.5016			1.03330			0.516652	−	0.856196i	$-0.327178\pi$
$433$	21.5016			1.03330			0.516652	+	0.856196i	$0.327178\pi$
$434$	13.3140	+	3.71045i	0.639092	+	0.178107i
$435$		0			0
$436$	22.2841	−	5.49618i	1.06722	−	0.263219i
$437$	0.955055	−	0.955055i	0.0456865	−	0.0456865i
$438$		0			0
$439$	−22.7689			−1.08670			−0.543349	−	0.839507i	$-0.682844\pi$
$439$	−22.7689			−1.08670			−0.543349	+	0.839507i	$0.682844\pi$
$440$	−7.13713	+	6.72156i	−0.340249	+	0.320438i
$441$		0			0
$442$	49.2303	−	27.7709i	2.34164	−	1.32093i
$443$	−10.2897	−	10.2897i	−0.488878	−	0.488878i	0.419074	−	0.907952i	$-0.362355\pi$
$443$	−10.2897	−	10.2897i	−0.488878	−	0.488878i	−0.907952	+	0.419074i	$0.862355\pi$
$444$		0			0
$445$	−3.49438	+	3.49438i	−0.165649	+	0.165649i
$446$	34.3413	+	9.57050i	1.62611	+	0.453176i
$447$		0			0
$448$	−0.891020	+	14.8439i	−0.0420967	+	0.701308i
$449$			21.5190i			1.01555i	0.861491	+	0.507773i	$0.169531\pi$
$449$			21.5190i			1.01555i	−0.861491	+	0.507773i	$0.830469\pi$
$450$		0			0
$451$	19.0676	+	19.0676i	0.897858	+	0.897858i
$452$	−18.7210	+	30.9790i	−0.880560	+	1.45713i
$453$		0			0
$454$	5.22038	+	9.25431i	0.245005	+	0.434326i
$455$			7.43373i			0.348498i
$456$		0			0
$457$		−	6.79833i		−	0.318012i	−0.987278	−	0.159006i	$-0.949171\pi$
$457$		−	6.79833i		−	0.318012i	0.987278	−	0.159006i	$-0.0508290\pi$
$458$	−10.6346	+	5.99902i	−0.496923	+	0.280316i
$459$		0			0
$460$	0.228559	+	0.926687i	0.0106566	+	0.0432070i
$461$	−19.4466	−	19.4466i	−0.905720	−	0.905720i	0.0902034	−	0.995923i	$-0.471248\pi$
$461$	−19.4466	−	19.4466i	−0.905720	−	0.905720i	−0.995923	+	0.0902034i	$0.971248\pi$
$462$		0			0
$463$		−	10.1469i		−	0.471566i	−0.971806	−	0.235783i	$-0.924235\pi$
$463$		−	10.1469i		−	0.471566i	0.971806	−	0.235783i	$-0.0757654\pi$
$464$	1.50743	−	4.84274i	0.0699805	−	0.224819i
$465$		0			0
$466$	3.04905	−	10.9407i	0.141244	−	0.506819i
$467$	−2.71845	+	2.71845i	−0.125795	+	0.125795i	−0.767201	−	0.641406i	$-0.778351\pi$
$467$	−2.71845	+	2.71845i	−0.125795	+	0.125795i	0.641406	+	0.767201i	$0.278351\pi$
$468$		0			0
$469$	15.7674	+	15.7674i	0.728072	+	0.728072i
$470$	3.10664	+	5.50722i	0.143299	+	0.254029i
$471$		0			0
$472$	7.47434	+	0.224126i	0.344034	+	0.0103162i
$473$	−8.17719			−0.375988
$474$		0			0
$475$	5.99981	−	5.99981i	0.275290	−	0.275290i
$476$	12.6078	−	20.8630i	0.577876	−	0.956255i
$477$		0			0
$478$	−6.24570	+	22.4111i	−0.285672	+	1.02506i
$479$	−2.18580			−0.0998716			−0.0499358	−	0.998752i	$-0.515902\pi$
$479$	−2.18580			−0.0998716			−0.0499358	+	0.998752i	$0.515902\pi$
$480$		0			0
$481$	−34.3182			−1.56478
$482$	1.21930	−	4.37513i	0.0555374	−	0.199282i
$483$		0			0
$484$	17.4939	−	28.9485i	0.795177	−	1.31584i
$485$	−4.55555	+	4.55555i	−0.206857	+	0.206857i
$486$		0			0
$487$	6.03958			0.273679			0.136840	−	0.990593i	$-0.456305\pi$
$487$	6.03958			0.273679			0.136840	+	0.990593i	$0.456305\pi$
$488$	−0.717693	+	23.9342i	−0.0324884	+	1.08345i
$489$		0			0
$490$	−1.61596	−	2.86465i	−0.0730016	−	0.129412i
$491$	15.4395	+	15.4395i	0.696777	+	0.696777i	0.963714	−	0.266937i	$-0.0860116\pi$
$491$	15.4395	+	15.4395i	0.696777	+	0.696777i	−0.266937	+	0.963714i	$0.586012\pi$
$492$		0			0
$493$	−5.87900	+	5.87900i	−0.264777	+	0.264777i
$494$	4.29710	−	15.4190i	0.193336	−	0.693735i
$495$		0			0
$496$	18.6189	−	9.77924i	0.836012	−	0.439101i
$497$			23.0725i			1.03494i
$498$		0			0
$499$	−9.67414	−	9.67414i	−0.433074	−	0.433074i	0.456599	−	0.889673i	$-0.349068\pi$
$499$	−9.67414	−	9.67414i	−0.433074	−	0.433074i	−0.889673	+	0.456599i	$0.849068\pi$
$500$	3.00695	+	12.1916i	0.134475	+	0.545225i
$501$		0			0
$502$	0.271360	−	0.153075i	0.0121114	−	0.00683207i
$503$		−	31.7197i		−	1.41431i	−0.707057	−	0.707156i	$-0.749978\pi$
$503$		−	31.7197i		−	1.41431i	0.707057	−	0.707156i	$-0.250022\pi$
$504$		0			0
$505$		−	12.6369i		−	0.562334i
$506$	−2.67017	−	4.73348i	−0.118704	−	0.210429i
$507$		0			0
$508$	−18.2294	+	30.1655i	−0.808797	+	1.33838i
$509$	−4.16082	−	4.16082i	−0.184425	−	0.184425i	0.608856	−	0.793281i	$-0.291629\pi$
$509$	−4.16082	−	4.16082i	−0.184425	−	0.184425i	−0.793281	+	0.608856i	$0.791629\pi$
$510$		0			0
$511$		−	6.93285i		−	0.306691i
$512$	14.4984	+	17.3723i	0.640744	+	0.767755i
$513$		0			0
$514$	−17.7476	−	4.94606i	−0.782815	−	0.218161i
$515$	−0.603055	+	0.603055i	−0.0265738	+	0.0265738i
$516$		0			0
$517$	−25.4582	−	25.4582i	−1.11965	−	1.11965i
$518$	−12.8908	+	7.27177i	−0.566391	+	0.319503i
$519$		0			0
$520$	7.75497	+	8.23443i	0.340078	+	0.361104i
$521$	0.107484			0.00470896			0.00235448	−	0.999997i	$-0.499251\pi$
$521$	0.107484			0.00470896			0.00235448	+	0.999997i	$0.499251\pi$
$522$		0			0
$523$	−3.02020	+	3.02020i	−0.132064	+	0.132064i	−0.770049	−	0.637985i	$-0.779768\pi$
$523$	−3.02020	+	3.02020i	−0.132064	+	0.132064i	0.637985	+	0.770049i	$0.279768\pi$
$524$	−1.41751	+	0.349617i	−0.0619244	+	0.0152731i
$525$		0			0
$526$	−19.5307	−	5.44298i	−0.851580	−	0.237325i
$527$	−34.4748			−1.50174
$528$		0			0
$529$	22.4709			0.976996
$530$	0.900007	+	0.250821i	0.0390938	+	0.0108950i
$531$		0			0
$532$	−1.65307	−	6.70232i	−0.0716696	−	0.290583i
$533$	21.9991	−	21.9991i	0.952889	−	0.952889i
$534$		0			0
$535$	9.89937			0.427987
$536$	33.9146	+	1.01696i	1.46489	+	0.0439261i
$537$		0			0
$538$	−15.7792	+	8.90109i	−0.680289	+	0.383753i
$539$	13.2424	+	13.2424i	0.570391	+	0.570391i
$540$		0			0
$541$	−5.72807	+	5.72807i	−0.246269	+	0.246269i	−0.819437	−	0.573169i	$-0.805714\pi$
$541$	−5.72807	+	5.72807i	−0.246269	+	0.246269i	0.573169	+	0.819437i	$0.305714\pi$
$542$	34.4501	+	9.60084i	1.47976	+	0.412391i
$543$		0			0
$544$	−7.79884	−	36.2628i	−0.334373	−	1.55476i
$545$		−	7.52925i		−	0.322518i
$546$		0			0
$547$	13.2259	+	13.2259i	0.565500	+	0.565500i	0.930865	−	0.365365i	$-0.119056\pi$
$547$	13.2259	+	13.2259i	0.565500	+	0.565500i	−0.365365	+	0.930865i	$0.619056\pi$
$548$	−16.2954	−	9.84747i	−0.696104	−	0.420663i
$549$		0			0
$550$	−16.7745	−	29.7365i	−0.715266	−	1.26797i
$551$			2.35447i			0.100304i
$552$		0			0
$553$			0.370036i			0.0157355i
$554$	−7.92379	+	4.46984i	−0.336650	+	0.189905i
$555$		0			0
$556$	−24.3149	+	5.99706i	−1.03118	+	0.254332i
$557$	−21.4603	−	21.4603i	−0.909301	−	0.909301i	0.0869144	−	0.996216i	$-0.472299\pi$
$557$	−21.4603	−	21.4603i	−0.909301	−	0.909301i	−0.996216	+	0.0869144i	$0.972299\pi$
$558$		0			0
$559$			9.43440i			0.399032i
$560$	4.65779	+	1.44985i	0.196827	+	0.0612675i
$561$		0			0
$562$	−6.96852	+	25.0047i	−0.293949	+	1.05476i
$563$	29.5192	−	29.5192i	1.24409	−	1.24409i	0.285797	−	0.958290i	$-0.407742\pi$
$563$	29.5192	−	29.5192i	1.24409	−	1.24409i	0.958290	−	0.285797i	$-0.0922582\pi$
$564$		0			0
$565$	8.39618	+	8.39618i	0.353230	+	0.353230i
$566$	−9.88960	−	17.5315i	−0.415691	−	0.736906i
$567$		0			0
$568$	24.0696	+	25.5577i	1.00994	+	1.07238i
$569$	−11.3544			−0.476003			−0.238001	−	0.971265i	$-0.576492\pi$
$569$	−11.3544			−0.476003			−0.238001	+	0.971265i	$0.576492\pi$
$570$		0			0
$571$	−1.37894	+	1.37894i	−0.0577066	+	0.0577066i	−0.735371	−	0.677665i	$-0.762992\pi$
$571$	−1.37894	+	1.37894i	−0.0577066	+	0.0577066i	0.677665	+	0.735371i	$0.262992\pi$
$572$	−55.1230	−	33.3114i	−2.30481	−	1.39282i
$573$		0			0
$574$	3.60202	−	12.9249i	0.150345	−	0.539476i
$575$	−3.32381			−0.138613
$576$		0			0
$577$	6.63854			0.276366			0.138183	−	0.990407i	$-0.455874\pi$
$577$	6.63854			0.276366			0.138183	+	0.990407i	$0.455874\pi$
$578$	−9.86888	+	35.4119i	−0.410491	+	1.47294i
$579$		0			0
$580$	−1.42400	−	0.860537i	−0.0591282	−	0.0357319i
$581$	18.5385	−	18.5385i	0.769106	−	0.769106i
$582$		0			0
$583$	−5.31992			−0.220329
$584$	−7.23245	−	7.67960i	−0.299281	−	0.317784i
$585$		0			0
$586$	−0.860992	−	1.52630i	−0.0355673	−	0.0630510i
$587$	21.0123	+	21.0123i	0.867269	+	0.867269i	0.992169	−	0.124900i	$-0.0398611\pi$
$587$	21.0123	+	21.0123i	0.867269	+	0.867269i	−0.124900	+	0.992169i	$0.539861\pi$
$588$		0			0
$589$	−6.90337	+	6.90337i	−0.284448	+	0.284448i
$590$	0.658531	−	2.36297i	0.0271113	−	0.0972819i
$591$		0			0
$592$	−6.69334	+	21.5030i	−0.275094	+	0.883766i
$593$			33.0340i			1.35654i	0.734812	+	0.678271i	$0.237271\pi$
$593$			33.0340i			1.35654i	−0.734812	+	0.678271i	$0.762729\pi$
$594$		0			0
$595$	−5.65447	−	5.65447i	−0.231811	−	0.231811i
$596$	35.3017	−	8.70684i	1.44601	−	0.356646i
$597$		0			0
$598$	−5.46123	+	3.08070i	−0.223326	+	0.125979i
$599$		−	16.4107i		−	0.670522i	−0.942125	−	0.335261i	$-0.891176\pi$
$599$		−	16.4107i		−	0.670522i	0.942125	−	0.335261i	$-0.108824\pi$
$600$		0			0
$601$			34.3301i			1.40035i	0.713969	+	0.700177i	$0.246896\pi$
$601$			34.3301i			1.40035i	−0.713969	+	0.700177i	$0.753104\pi$
$602$	1.99908	+	3.54381i	0.0814762	+	0.144435i
$603$		0			0
$604$	11.5605	+	6.98616i	0.470391	+	0.284263i
$605$	−7.84586	−	7.84586i	−0.318980	−	0.318980i
$606$		0			0
$607$			42.5123i			1.72552i	0.505614	+	0.862760i	$0.331266\pi$
$607$			42.5123i			1.72552i	−0.505614	+	0.862760i	$0.668734\pi$
$608$	−8.82309	−	5.69974i	−0.357823	−	0.231155i
$609$		0			0
$610$	7.56668	+	2.10874i	0.306366	+	0.0853805i
$611$	−29.3723	+	29.3723i	−1.18828	+	1.18828i
$612$		0			0
$613$	−11.1129	−	11.1129i	−0.448845	−	0.448845i	0.446126	−	0.894970i	$-0.352803\pi$
$613$	−11.1129	−	11.1129i	−0.448845	−	0.448845i	−0.894970	+	0.446126i	$0.852803\pi$
$614$	−24.0432	+	13.5628i	−0.970304	+	0.547351i
$615$		0			0
$616$	−27.7641	−	0.832535i	−1.11865	−	0.0335438i
$617$	−33.8647			−1.36334			−0.681671	−	0.731659i	$-0.738746\pi$
$617$	−33.8647			−1.36334			−0.681671	+	0.731659i	$0.738746\pi$
$618$		0			0
$619$	0.960938	−	0.960938i	0.0386234	−	0.0386234i	−0.687531	−	0.726155i	$-0.741306\pi$
$619$	0.960938	−	0.960938i	0.0386234	−	0.0386234i	0.726155	+	0.687531i	$0.241306\pi$
$620$	−1.65208	−	6.69832i	−0.0663491	−	0.269011i
$621$		0			0
$622$	16.9726	+	4.73005i	0.680538	+	0.189658i
$623$	−14.0011			−0.560941
$624$		0			0
$625$	−18.7285			−0.749140
$626$	−16.6120	−	4.62956i	−0.663948	−	0.185034i
$627$		0			0
$628$	3.74535	−	0.923756i	0.149456	−	0.0368619i
$629$	26.1042	−	26.1042i	1.04084	−	1.04084i
$630$		0			0
$631$	−15.2529			−0.607210			−0.303605	−	0.952798i	$-0.598190\pi$
$631$	−15.2529			−0.607210			−0.303605	+	0.952798i	$0.598190\pi$
$632$	0.386027	+	0.409893i	0.0153553	+	0.0163047i
$633$		0			0
$634$	−32.9455	+	18.5847i	−1.30843	+	0.738092i
$635$	8.17571	+	8.17571i	0.324443	+	0.324443i
$636$		0			0
$637$	15.2784	−	15.2784i	0.605351	−	0.605351i
$638$	9.12601	+	2.54331i	0.361302	+	0.100691i
$639$		0			0
$640$	6.67200	−	3.25305i	0.263734	−	0.128588i
$641$			8.86880i			0.350297i	0.984542	+	0.175148i	$0.0560405\pi$
$641$			8.86880i			0.350297i	−0.984542	+	0.175148i	$0.943960\pi$
$642$		0			0
$643$	−22.1302	−	22.1302i	−0.872730	−	0.872730i	0.120039	−	0.992769i	$-0.461698\pi$
$643$	−22.1302	−	22.1302i	−0.872730	−	0.872730i	−0.992769	+	0.120039i	$0.961698\pi$
$644$	−1.39861	+	2.31439i	−0.0551129	+	0.0911996i
$645$		0			0
$646$	8.45990	+	14.9971i	0.332850	+	0.590053i
$647$			28.2219i			1.10952i	0.832011	+	0.554759i	$0.187190\pi$
$647$			28.2219i			1.10952i	−0.832011	+	0.554759i	$0.812810\pi$
$648$		0			0
$649$			13.9675i			0.548271i
$650$	−34.3084	+	19.3535i	−1.34569	+	0.759106i
$651$		0			0
$652$	−3.21998	−	13.0553i	−0.126104	−	0.511286i
$653$	21.7199	+	21.7199i	0.849964	+	0.849964i	0.990128	−	0.140164i	$-0.0447631\pi$
$653$	21.7199	+	21.7199i	0.849964	+	0.849964i	−0.140164	+	0.990128i	$0.544763\pi$
$654$		0			0
$655$			0.478942i			0.0187138i
$656$	−9.49346	−	18.0748i	−0.370657	−	0.705701i
$657$		0			0
$658$	−4.80926	+	17.2568i	−0.187484	+	0.672739i
$659$	18.3081	−	18.3081i	0.713181	−	0.713181i	−0.254018	−	0.967199i	$-0.581752\pi$
$659$	18.3081	−	18.3081i	0.713181	−	0.713181i	0.967199	+	0.254018i	$0.0817523\pi$
$660$		0			0
$661$	14.2270	+	14.2270i	0.553366	+	0.553366i	0.927411	−	0.374045i	$-0.122029\pi$
$661$	14.2270	+	14.2270i	0.553366	+	0.553366i	−0.374045	+	0.927411i	$0.622029\pi$
$662$	−0.838155	−	1.48582i	−0.0325758	−	0.0577480i
$663$		0			0
$664$	1.19569	−	39.8749i	0.0464018	−	1.54745i
$665$	−2.26455			−0.0878154
$666$		0			0
$667$	0.652171	−	0.652171i	0.0252522	−	0.0252522i
$668$	19.3144	−	31.9610i	0.747296	−	1.23661i
$669$		0			0
$670$	2.98807	−	10.7219i	0.115439	−	0.414223i
$671$	−44.7265			−1.72665
$672$		0			0
$673$	−24.8456			−0.957727			−0.478863	−	0.877889i	$-0.658951\pi$
$673$	−24.8456			−0.957727			−0.478863	+	0.877889i	$0.658951\pi$
$674$	12.5016	−	44.8587i	0.481543	−	1.72789i
$675$		0			0
$676$	−24.9856	+	41.3455i	−0.960983	+	1.59021i
$677$	−19.3414	+	19.3414i	−0.743350	+	0.743350i	−0.973221	−	0.229871i	$-0.926170\pi$
$677$	−19.3414	+	19.3414i	−0.743350	+	0.743350i	0.229871	+	0.973221i	$0.426170\pi$
$678$		0			0
$679$	−18.2529			−0.700482
$680$	−12.1623	−	0.364700i	−0.466405	−	0.0139856i
$681$		0			0
$682$	19.3007	+	34.2148i	0.739060	+	1.31015i
$683$	12.6585	+	12.6585i	0.484363	+	0.484363i	0.906522	−	0.422159i	$-0.138728\pi$
$683$	12.6585	+	12.6585i	0.484363	+	0.484363i	−0.422159	+	0.906522i	$0.638728\pi$
$684$		0			0
$685$	−4.41651	+	4.41651i	−0.168746	+	0.168746i
$686$	7.44161	−	26.7023i	0.284122	−	1.01950i
$687$		0			0
$688$	5.91136	+	1.84006i	0.225368	+	0.0701516i
$689$			6.13783i			0.233833i
$690$		0			0
$691$	−24.0824	−	24.0824i	−0.916137	−	0.916137i	0.0806084	−	0.996746i	$-0.474314\pi$
$691$	−24.0824	−	24.0824i	−0.916137	−	0.916137i	−0.996746	+	0.0806084i	$0.974314\pi$
$692$	−9.17139	−	37.1852i	−0.348644	−	1.41357i
$693$		0			0
$694$	−24.1757	+	13.6376i	−0.917698	+	0.517676i
$695$			8.21540i			0.311628i
$696$		0			0
$697$			33.4673i			1.26767i
$698$	−18.8973	−	33.4998i	−0.715275	−	1.26799i
$699$		0			0
$700$	−8.78630	+	14.5394i	−0.332091	+	0.549536i
$701$	−22.8729	−	22.8729i	−0.863896	−	0.863896i	0.127892	−	0.991788i	$-0.459179\pi$
$701$	−22.8729	−	22.8729i	−0.863896	−	0.863896i	−0.991788	+	0.127892i	$0.959179\pi$
$702$		0			0
$703$		−	10.4544i		−	0.394296i
$704$	−31.6232	+	28.0417i	−1.19184	+	1.05686i
$705$		0			0
$706$	−16.5586	−	4.61468i	−0.623190	−	0.173676i
$707$	25.3164	−	25.3164i	0.952120	−	0.952120i
$708$		0			0
$709$	8.29714	+	8.29714i	0.311606	+	0.311606i	0.845531	−	0.533926i	$-0.179284\pi$
$709$	8.29714	+	8.29714i	0.311606	+	0.311606i	−0.533926	+	0.845531i	$0.679284\pi$
$710$	10.0309	−	5.65847i	0.376454	−	0.212359i
$711$		0			0
$712$	−15.5092	+	14.6061i	−0.581230	+	0.547388i
$713$	3.82437			0.143224
$714$		0			0
$715$	−14.9399	+	14.9399i	−0.558720	+	0.558720i
$716$	36.4239	−	8.98362i	1.36122	−	0.335734i
$717$		0			0
$718$	3.84929	+	1.07275i	0.143654	+	0.0400347i
$719$	4.37297			0.163084			0.0815421	−	0.996670i	$-0.474015\pi$
$719$	4.37297			0.163084			0.0815421	+	0.996670i	$0.474015\pi$
$720$		0			0
$721$	−2.41629			−0.0899872
$722$	−21.1866	−	5.90445i	−0.788483	−	0.219741i
$723$		0			0
$724$	−0.398837	−	1.61707i	−0.0148226	−	0.0600981i
$725$	4.09705	−	4.09705i	0.152161	−	0.152161i
$726$		0			0
$727$	11.7071			0.434193			0.217096	−	0.976150i	$-0.430341\pi$
$727$	11.7071			0.434193			0.217096	+	0.976150i	$0.430341\pi$
$728$	−0.960533	+	32.0327i	−0.0355997	+	1.18721i
$729$		0			0
$730$	−3.01410	+	1.70026i	−0.111557	+	0.0629295i
$731$	−7.17628	−	7.17628i	−0.265424	−	0.265424i
$732$		0			0
$733$	16.9853	−	16.9853i	0.627367	−	0.627367i	−0.320038	−	0.947405i	$-0.603696\pi$
$733$	16.9853	−	16.9853i	0.627367	−	0.627367i	0.947405	+	0.320038i	$0.103696\pi$
$734$	12.5465	+	3.49657i	0.463100	+	0.129061i
$735$		0			0
$736$	0.865145	+	4.02272i	0.0318897	+	0.148280i
$737$			63.3769i			2.33452i
$738$		0			0
$739$	−7.66564	−	7.66564i	−0.281985	−	0.281985i	0.551915	−	0.833900i	$-0.313897\pi$
$739$	−7.66564	−	7.66564i	−0.281985	−	0.281985i	−0.833900	+	0.551915i	$0.813897\pi$
$740$	6.32289	+	3.82100i	0.232434	+	0.140463i
$741$		0			0
$742$	1.30056	+	2.30553i	0.0477450	+	0.0846388i
$743$			3.54776i			0.130155i	0.997880	+	0.0650774i	$0.0207294\pi$
$743$			3.54776i			0.130155i	−0.997880	+	0.0650774i	$0.979271\pi$
$744$		0			0
$745$		−	11.9275i		−	0.436992i
$746$	26.9515	−	15.2034i	0.986763	−	0.556636i
$747$		0			0
$748$	67.2677	−	16.5910i	2.45955	−	0.606626i
$749$	19.8321	+	19.8321i	0.724650	+	0.724650i
$750$		0			0
$751$		−	37.9479i		−	1.38474i	−0.721543	−	0.692370i	$-0.756567\pi$
$751$		−	37.9479i		−	1.38474i	0.721543	−	0.692370i	$-0.243433\pi$
$752$	12.6752	+	24.1326i	0.462219	+	0.880027i
$753$		0			0
$754$	2.93433	−	10.5291i	0.106862	−	0.383447i
$755$	3.13323	−	3.13323i	0.114030	−	0.114030i
$756$		0			0
$757$	25.8295	+	25.8295i	0.938789	+	0.938789i	0.998232	−	0.0594425i	$-0.0189323\pi$
$757$	25.8295	+	25.8295i	0.938789	+	0.938789i	−0.0594425	+	0.998232i	$0.518932\pi$
$758$	5.99860	+	10.6339i	0.217879	+	0.386240i
$759$		0			0
$760$	−2.50847	+	2.36241i	−0.0909917	+	0.0856936i
$761$	12.7041			0.460523			0.230261	−	0.973129i	$-0.426042\pi$
$761$	12.7041			0.460523			0.230261	+	0.973129i	$0.426042\pi$
$762$		0			0
$763$	15.0839	−	15.0839i	0.546073	−	0.546073i
$764$	−14.9586	−	9.03963i	−0.541182	−	0.327042i
$765$		0			0
$766$	0.633096	−	2.27170i	0.0228747	−	0.0820799i
$767$	16.1149			0.581875
$768$		0			0
$769$	0.366691			0.0132232			0.00661161	−	0.999978i	$-0.497895\pi$
$769$	0.366691			0.0132232			0.00661161	+	0.999978i	$0.497895\pi$
$770$	−2.44618	+	8.77747i	−0.0881541	+	0.316318i
$771$		0			0
$772$	20.2528	+	12.2390i	0.728913	+	0.440490i
$773$	7.31241	−	7.31241i	0.263009	−	0.263009i	−0.563266	−	0.826275i	$-0.690455\pi$
$773$	7.31241	−	7.31241i	0.263009	−	0.263009i	0.826275	+	0.563266i	$0.190455\pi$
$774$		0			0
$775$	24.0253			0.863016
$776$	−20.2190	+	19.0417i	−0.725819	+	0.683557i
$777$		0			0
$778$	−17.9429	−	31.8078i	−0.643284	−	1.14037i
$779$	6.70163	+	6.70163i	0.240111	+	0.240111i
$780$		0			0
$781$	−46.3698	+	46.3698i	−1.65924	+	1.65924i
$782$	1.81075	−	6.49743i	0.0647525	−	0.232347i
$783$		0			0
$784$	−6.59319	−	12.5529i	−0.235471	−	0.448318i
$785$		−	1.26546i		−	0.0451661i
$786$		0			0
$787$	15.3004	+	15.3004i	0.545401	+	0.545401i	0.925107	−	0.379706i	$-0.123975\pi$
$787$	15.3004	+	15.3004i	0.545401	+	0.545401i	−0.379706	+	0.925107i	$0.623975\pi$
$788$	−16.5933	+	4.09260i	−0.591113	+	0.145793i
$789$		0			0
$790$	0.160875	−	0.0907502i	0.00572369	−	0.00322875i
$791$			33.6413i			1.19615i
$792$		0			0
$793$			51.6030i			1.83248i
$794$	−7.32646	−	12.9878i	−0.260006	−	0.460920i
$795$		0			0
$796$	20.1368	+	12.1689i	0.713732	+	0.431316i
$797$	8.26831	+	8.26831i	0.292878	+	0.292878i	0.838216	−	0.545338i	$-0.183599\pi$
$797$	8.26831	+	8.26831i	0.292878	+	0.292878i	−0.545338	+	0.838216i	$0.683599\pi$
$798$		0			0
$799$		−	44.6841i		−	1.58081i
$800$	5.43498	+	25.2714i	0.192156	+	0.893480i
$801$		0			0
$802$	−35.5562	−	9.90907i	−1.25553	−	0.349902i
$803$	13.9332	−	13.9332i	0.491694	−	0.491694i
$804$		0			0
$805$	0.627264	+	0.627264i	0.0221082	+	0.0221082i
$806$	39.4751	−	22.2680i	1.39045	−	0.784358i
$807$		0			0
$808$	1.63285	−	54.4537i	0.0574434	−	1.91567i
$809$	−5.41620			−0.190424			−0.0952118	−	0.995457i	$-0.530353\pi$
$809$	−5.41620			−0.190424			−0.0952118	+	0.995457i	$0.530353\pi$
$810$		0			0
$811$	23.5526	−	23.5526i	0.827044	−	0.827044i	−0.160063	−	0.987107i	$-0.551170\pi$
$811$	23.5526	−	23.5526i	0.827044	−	0.827044i	0.987107	+	0.160063i	$0.0511697\pi$
$812$	−1.12882	−	4.57677i	−0.0396138	−	0.160613i
$813$		0			0
$814$	−40.5217	−	11.2929i	−1.42028	−	0.395816i
$815$	−4.41106			−0.154513
$816$		0			0
$817$	−2.87401			−0.100549
$818$	−35.9664	−	10.0234i	−1.25753	−	0.350460i
$819$		0			0
$820$	−6.50258	+	1.60380i	−0.227080	+	0.0560072i
$821$	−0.586621	+	0.586621i	−0.0204732	+	0.0204732i	−0.717269	−	0.696796i	$-0.754608\pi$
$821$	−0.586621	+	0.586621i	−0.0204732	+	0.0204732i	0.696796	+	0.717269i	$0.254608\pi$
$822$		0			0
$823$	−42.9664			−1.49772			−0.748858	−	0.662731i	$-0.769397\pi$
$823$	−42.9664			−1.49772			−0.748858	+	0.662731i	$0.769397\pi$
$824$	−2.67655	+	2.52071i	−0.0932421	+	0.0878130i
$825$		0			0
$826$	6.05319	−	3.41462i	0.210617	−	0.118810i
$827$	−4.76551	−	4.76551i	−0.165713	−	0.165713i	0.619379	−	0.785092i	$-0.287384\pi$
$827$	−4.76551	−	4.76551i	−0.165713	−	0.165713i	−0.785092	+	0.619379i	$0.787384\pi$
$828$		0			0
$829$	18.7283	−	18.7283i	0.650460	−	0.650460i	−0.302644	−	0.953104i	$-0.597869\pi$
$829$	18.7283	−	18.7283i	0.650460	−	0.650460i	0.953104	+	0.302644i	$0.0978692\pi$
$830$	−12.6062	−	3.51321i	−0.437569	−	0.121945i
$831$		0			0
$832$	32.3530	+	36.4851i	1.12164	+	1.26489i
$833$			23.2430i			0.805322i
$834$		0			0
$835$	−8.66233	−	8.66233i	−0.299772	−	0.299772i
$836$	10.1477	−	16.7922i	0.350966	−	0.580770i
$837$		0			0
$838$	−12.2508	−	21.7173i	−0.423196	−	0.750210i
$839$			1.97689i			0.0682499i	0.999418	+	0.0341249i	$0.0108644\pi$
$839$			1.97689i			0.0682499i	−0.999418	+	0.0341249i	$0.989136\pi$
$840$		0			0
$841$		−	27.3922i		−	0.944559i
$842$	−28.3073	+	15.9683i	−0.975535	+	0.550303i
$843$		0			0
$844$	−9.67613	−	39.2316i	−0.333066	−	1.35041i
$845$	11.2058	+	11.2058i	0.385491	+	0.385491i
$846$		0			0
$847$		−	31.4363i		−	1.08017i
$848$	3.84581	+	1.19711i	0.132066	+	0.0411088i
$849$		0			0
$850$	11.3755	−	40.8179i	0.390175	−	1.40004i
$851$	−2.89580	+	2.89580i	−0.0992668	+	0.0992668i
$852$		0			0
$853$	23.8260	+	23.8260i	0.815787	+	0.815787i	0.985495	−	0.169707i	$-0.0542822\pi$
$853$	23.8260	+	23.8260i	0.815787	+	0.815787i	−0.169707	+	0.985495i	$0.554282\pi$
$854$	10.9343	+	19.3835i	0.374163	+	0.663288i
$855$		0			0
$856$	42.6574	+	1.27913i	1.45800	+	0.0437196i
$857$	56.6389			1.93475			0.967375	−	0.253350i	$-0.0815323\pi$
$857$	56.6389			1.93475			0.967375	+	0.253350i	$0.0815323\pi$
$858$		0			0
$859$	10.4303	−	10.4303i	0.355877	−	0.355877i	−0.506414	−	0.862291i	$-0.669029\pi$
$859$	10.4303	−	10.4303i	0.355877	−	0.355877i	0.862291	+	0.506414i	$0.169029\pi$
$860$	1.05043	−	1.73822i	0.0358193	−	0.0592729i
$861$		0			0
$862$	−9.78261	+	35.1024i	−0.333197	+	1.19559i
$863$	16.2869			0.554412			0.277206	−	0.960810i	$-0.410592\pi$
$863$	16.2869			0.554412			0.277206	+	0.960810i	$0.410592\pi$
$864$		0			0
$865$	−12.5639			−0.427187
$866$	8.16324	−	29.2917i	0.277398	−	0.995372i
$867$		0			0
$868$	10.1095	−	16.7289i	0.343138	−	0.567818i
$869$	−0.743677	+	0.743677i	−0.0252275	+	0.0252275i
$870$		0			0
$871$	73.1209			2.47761
$872$	0.972877	−	32.4443i	0.0329458	−	1.09870i
$873$		0			0
$874$	−0.938478	−	1.66366i	−0.0317445	−	0.0562743i
$875$	8.25236	+	8.25236i	0.278981	+	0.278981i
$876$		0			0
$877$	−2.12318	+	2.12318i	−0.0716946	+	0.0716946i	−0.742045	−	0.670350i	$-0.766144\pi$
$877$	−2.12318	+	2.12318i	−0.0716946	+	0.0716946i	0.670350	+	0.742045i	$0.266144\pi$
$878$	−8.64435	+	31.0180i	−0.291733	+	1.04681i
$879$		0			0
$880$	6.44713	+	12.2748i	0.217333	+	0.413783i
$881$			17.3923i			0.585963i	0.956118	+	0.292981i	$0.0946474\pi$
$881$			17.3923i			0.585963i	−0.956118	+	0.292981i	$0.905353\pi$
$882$		0			0
$883$	8.04441	+	8.04441i	0.270716	+	0.270716i	0.829388	−	0.558672i	$-0.188689\pi$
$883$	8.04441	+	8.04441i	0.270716	+	0.270716i	−0.558672	+	0.829388i	$0.688689\pi$
$884$	−19.1418	−	77.6098i	−0.643807	−	2.61030i
$885$		0			0
$886$	−17.9242	+	10.1111i	−0.602175	+	0.339689i
$887$			42.1906i			1.41662i	0.705901	+	0.708311i	$0.250542\pi$
$887$			42.1906i			1.41662i	−0.705901	+	0.708311i	$0.749458\pi$
$888$		0			0
$889$			32.7580i			1.09867i
$890$	3.43373	+	6.08705i	0.115099	+	0.204038i
$891$		0			0
$892$	26.0758	−	43.1496i	0.873082	−	1.44475i
$893$	−8.94772	−	8.94772i	−0.299424	−	0.299424i
$894$		0			0
$895$		−	12.3067i		−	0.411368i
$896$	19.8836	+	6.84942i	0.664263	+	0.228823i
$897$		0			0
$898$	29.3154	+	8.16985i	0.978267	+	0.272631i
$899$	−4.71405	+	4.71405i	−0.157223	+	0.157223i
$900$		0			0
$901$	−4.66875	−	4.66875i	−0.155538	−	0.155538i
$902$	33.2149	−	18.7366i	1.10594	−	0.623862i
$903$		0			0
$904$	35.0952	+	37.2649i	1.16725	+	1.23941i
$905$	−0.546369			−0.0181619
$906$		0			0
$907$	5.05861	−	5.05861i	0.167968	−	0.167968i	−0.618117	−	0.786086i	$-0.712104\pi$
$907$	5.05861	−	5.05861i	0.167968	−	0.167968i	0.786086	+	0.618117i	$0.212104\pi$
$908$	14.5891	−	3.59827i	0.484156	−	0.119413i
$909$		0			0
$910$	10.1270	+	2.82226i	0.335706	+	0.0935571i
$911$	−40.8990			−1.35505			−0.677523	−	0.735502i	$-0.736946\pi$
$911$	−40.8990			−1.35505			−0.677523	+	0.735502i	$0.736946\pi$
$912$		0			0
$913$	74.5152			2.46609
$914$	−9.26136	−	2.58103i	−0.306339	−	0.0853729i
$915$		0			0
$916$	4.13496	+	16.7651i	0.136623	+	0.553935i
$917$	−0.959499	+	0.959499i	−0.0316854	+	0.0316854i
$918$		0			0
$919$	−30.9766			−1.02182			−0.510912	−	0.859633i	$-0.670692\pi$
$919$	−30.9766			−1.02182			−0.510912	+	0.859633i	$0.670692\pi$
$920$	1.34920	+	0.0404571i	0.0444818	+	0.00133383i
$921$		0			0
$922$	−33.8752	+	19.1091i	−1.11562	+	0.629325i
$923$	53.4990	+	53.4990i	1.76094	+	1.76094i
$924$		0			0
$925$	−18.1919	+	18.1919i	−0.598146	+	0.598146i
$926$	−13.8231	−	3.85233i	−0.454255	−	0.126595i
$927$		0			0
$928$	−6.02496	−	3.89214i	−0.197779	−	0.127766i
$929$			16.8850i			0.553980i	0.960873	+	0.276990i	$0.0893368\pi$
$929$			16.8850i			0.553980i	−0.960873	+	0.276990i	$0.910663\pi$
$930$		0			0
$931$	4.65427	+	4.65427i	0.152538	+	0.152538i
$932$	−13.7469	−	8.30743i	−0.450296	−	0.272119i
$933$		0			0
$934$	2.67127	+	4.73543i	0.0874067	+	0.154948i
$935$		−	22.7281i		−	0.743287i
$936$		0			0
$937$		−	53.1410i		−	1.73604i	−0.496528	−	0.868020i	$-0.665392\pi$
$937$		−	53.1410i		−	1.73604i	0.496528	−	0.868020i	$-0.334608\pi$
$938$	27.4662	−	15.4937i	0.896802	−	0.505889i
$939$		0			0
$940$	8.68195	−	2.14132i	0.283174	−	0.0698423i
$941$	−9.89314	−	9.89314i	−0.322507	−	0.322507i	0.527221	−	0.849728i	$-0.323234\pi$
$941$	−9.89314	−	9.89314i	−0.322507	−	0.322507i	−0.849728	+	0.527221i	$0.823234\pi$
$942$		0			0
$943$		−	3.71261i		−	0.120899i
$944$	3.14301	−	10.0972i	0.102296	−	0.328636i
$945$		0			0
$946$	−3.10453	+	11.1398i	−0.100937	+	0.362186i
$947$	−14.3740	+	14.3740i	−0.467093	+	0.467093i	−0.900971	−	0.433878i	$-0.857145\pi$
$947$	−14.3740	+	14.3740i	−0.467093	+	0.467093i	0.433878	+	0.900971i	$0.357145\pi$
$948$		0			0
$949$	−16.0754	−	16.0754i	−0.521830	−	0.521830i
$950$	−5.89568	−	10.4514i	−0.191281	−	0.339089i
$951$		0			0
$952$	−23.6351	−	25.0963i	−0.766017	−	0.813377i
$953$	5.12058			0.165872			0.0829360	−	0.996555i	$-0.473570\pi$
$953$	5.12058			0.165872			0.0829360	+	0.996555i	$0.473570\pi$
$954$		0			0
$955$	−4.05419	+	4.05419i	−0.131191	+	0.131191i
$956$	28.1594	+	17.0170i	0.910739	+	0.550370i
$957$		0			0
$958$	−0.829852	+	2.97771i	−0.0268113	+	0.0962054i
$959$	−17.6958			−0.571427
$960$		0			0
$961$	3.35651			0.108275
$962$	−13.0291	+	46.7517i	−0.420077	+	1.50734i
$963$		0			0
$964$	−5.49732	−	3.32209i	−0.177057	−	0.106997i
$965$	5.48907	−	5.48907i	0.176699	−	0.176699i
$966$		0			0
$967$	−52.7411			−1.69604			−0.848019	−	0.529965i	$-0.822205\pi$
$967$	−52.7411			−1.69604			−0.848019	+	0.529965i	$0.822205\pi$
$968$	−32.7949	−	34.8224i	−1.05407	−	1.11924i
$969$		0			0
$970$	4.47648	+	7.93557i	0.143731	+	0.254796i
$971$	22.7551	+	22.7551i	0.730246	+	0.730246i	0.970668	−	0.240423i	$-0.0772861\pi$
$971$	22.7551	+	22.7551i	0.730246	+	0.730246i	−0.240423	+	0.970668i	$0.577286\pi$
$972$		0			0
$973$	−16.4585	+	16.4585i	−0.527635	+	0.527635i
$974$	2.29297	−	8.22771i	0.0734714	−	0.263633i
$975$		0			0
$976$	32.3331	+	10.0645i	1.03496	+	0.322157i
$977$			16.3452i			0.522929i	0.965213	+	0.261465i	$0.0842055\pi$
$977$			16.3452i			0.522929i	−0.965213	+	0.261465i	$0.915795\pi$
$978$		0			0
$979$	−28.1386	−	28.1386i	−0.899312	−	0.899312i
$980$	−4.51602	+	1.11384i	−0.144259	+	0.0355802i
$981$		0			0
$982$	26.8950	−	15.1716i	0.858255	−	0.484144i
$983$		−	6.62052i		−	0.211162i	−0.994411	−	0.105581i	$-0.966330\pi$
$983$		−	6.62052i		−	0.211162i	0.994411	−	0.105581i	$-0.0336702\pi$
$984$		0			0
$985$			5.60647i			0.178637i
$986$	5.77696	+	10.2410i	0.183976	+	0.326138i
$987$		0			0
$988$	−19.3739	−	11.7079i	−0.616367	−	0.372477i
$989$	0.796082	+	0.796082i	0.0253139	+	0.0253139i
$990$		0			0
$991$			41.3701i			1.31417i	0.753818	+	0.657083i	$0.228210\pi$
$991$			41.3701i			1.31417i	−0.753818	+	0.657083i	$0.771790\pi$
$992$	−6.25348	−	29.0772i	−0.198548	−	0.923203i
$993$		0			0
$994$	31.4317	+	8.75963i	0.996952	+	0.277839i
$995$	5.45765	−	5.45765i	0.173019	−	0.173019i
$996$		0			0
$997$	1.44258	+	1.44258i	0.0456871	+	0.0456871i	0.729581	−	0.683894i	$-0.239715\pi$
$997$	1.44258	+	1.44258i	0.0456871	+	0.0456871i	−0.683894	+	0.729581i	$0.739715\pi$
$998$	−16.8519	+	9.50623i	−0.533439	+	0.300914i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.l.b.107.10	yes	32
3.2	odd	2	inner	432.2.l.b.107.7	✓	32
4.3	odd	2		1728.2.l.b.1295.7		32
12.11	even	2		1728.2.l.b.1295.10		32
16.3	odd	4	inner	432.2.l.b.323.7	yes	32
16.13	even	4		1728.2.l.b.431.10		32
48.29	odd	4		1728.2.l.b.431.7		32
48.35	even	4	inner	432.2.l.b.323.10	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.l.b.107.7	✓	32	3.2	odd	2	inner
432.2.l.b.107.10	yes	32	1.1	even	1	trivial
432.2.l.b.323.7	yes	32	16.3	odd	4	inner
432.2.l.b.323.10	yes	32	48.35	even	4	inner
1728.2.l.b.431.7		32	48.29	odd	4
1728.2.l.b.431.10		32	16.13	even	4
1728.2.l.b.1295.7		32	4.3	odd	2
1728.2.l.b.1295.10		32	12.11	even	2

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.379657 - 1.36230i) q^{2} +(-1.71172 - 1.03441i) q^{4} +(-0.463925 + 0.463925i) q^{5} -1.85883 q^{7} +(-2.05905 + 1.93916i) q^{8} +O(q^{10})\)	\(q+(0.379657 - 1.36230i) q^{2} +(-1.71172 - 1.03441i) q^{4} +(-0.463925 + 0.463925i) q^{5} -1.85883 q^{7} +(-2.05905 + 1.93916i) q^{8} +(0.455873 + 0.808137i) q^{10} +(-3.73577 - 3.73577i) q^{11} +(-4.31012 + 4.31012i) q^{13} +(-0.705716 + 2.53228i) q^{14} +(1.85998 + 3.54125i) q^{16} -6.55700i q^{17} +(-1.31300 - 1.31300i) q^{19} +(1.27400 - 0.314221i) q^{20} +(-6.50754 + 3.67093i) q^{22} +0.727384i q^{23} +4.56955i q^{25} +(4.23531 + 7.50805i) q^{26} +(3.18180 + 1.92279i) q^{28} +(-0.896599 - 0.896599i) q^{29} -5.25771i q^{31} +(5.53040 - 1.18939i) q^{32} +(-8.93260 - 2.48941i) q^{34} +(0.862356 - 0.862356i) q^{35} +(3.98112 + 3.98112i) q^{37} +(-2.28719 + 1.29021i) q^{38} +(0.0556200 - 1.85487i) q^{40} -5.10406 q^{41} +(1.09445 - 1.09445i) q^{43} +(2.53027 + 10.2589i) q^{44} +(0.990915 + 0.276156i) q^{46} +6.81472 q^{47} -3.54476 q^{49} +(6.22509 + 1.73486i) q^{50} +(11.8362 - 2.91929i) q^{52} +(0.712025 - 0.712025i) q^{53} +3.46623 q^{55} +(3.82741 - 3.60456i) q^{56} +(-1.56184 + 0.881037i) q^{58} +(-1.86942 - 1.86942i) q^{59} +(5.98625 - 5.98625i) q^{61} +(-7.16257 - 1.99612i) q^{62} +(0.479345 - 7.98563i) q^{64} -3.99915i q^{65} +(-8.48245 - 8.48245i) q^{67} +(-6.78264 + 11.2238i) q^{68} +(-0.847389 - 1.50219i) q^{70} -12.4124i q^{71} +3.72969i q^{73} +(6.93493 - 3.91202i) q^{74} +(0.889307 + 3.60567i) q^{76} +(6.94415 + 6.94415i) q^{77} -0.199069i q^{79} +(-2.50577 - 0.779983i) q^{80} +(-1.93779 + 6.95326i) q^{82} +(-9.97322 + 9.97322i) q^{83} +(3.04195 + 3.04195i) q^{85} +(-1.07545 - 1.90648i) q^{86} +(14.9364 + 0.447882i) q^{88} +7.53220 q^{89} +(8.01178 - 8.01178i) q^{91} +(0.752415 - 1.24508i) q^{92} +(2.58725 - 9.28369i) q^{94} +1.21827 q^{95} +9.81958 q^{97} +(-1.34579 + 4.82903i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 8 q^{10} - 8 q^{16} - 16 q^{19} + 16 q^{22} + 24 q^{28} + 24 q^{34} - 24 q^{40} - 16 q^{43} + 32 q^{46} + 32 q^{49} + 48 q^{52} - 32 q^{55} + 32 q^{61} - 24 q^{64} - 32 q^{67} - 48 q^{76} - 80 q^{82} + 32 q^{85} - 24 q^{88} - 48 q^{91}+O(q^{100}) \) 32 * q + 8 * q^10 - 8 * q^16 - 16 * q^19 + 16 * q^22 + 24 * q^28 + 24 * q^34 - 24 * q^40 - 16 * q^43 + 32 * q^46 + 32 * q^49 + 48 * q^52 - 32 * q^55 + 32 * q^61 - 24 * q^64 - 32 * q^67 - 48 * q^76 - 80 * q^82 + 32 * q^85 - 24 * q^88 - 48 * q^91

Introduction

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