LMFDB - Embedded newform 315.2.ce.a.107.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(53,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 8]))

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

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

chi := DirichletCharacter("315.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$315 = 3^{2} \cdot 5 \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	315.ce (of order $12$ , degree $4$ , 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.4
Character	$\chi$	$=$	315.107
Dual form			315.2.ce.a.53.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.494677 - 1.84616i) q^{2} +(-1.43155 + 0.826508i) q^{4} +(0.541988 - 2.16939i) q^{5} +(2.64533 - 0.0471386i) q^{7} +(-0.468944 - 0.468944i) q^{8} +(-4.27315 + 0.0725500i) q^{10} +(0.971861 - 0.561104i) q^{11} +(0.830077 - 0.830077i) q^{13} +(-1.39561 - 4.86039i) q^{14} +(-2.28679 + 3.96083i) q^{16} +(2.16001 + 0.578772i) q^{17} +(-5.19853 - 3.00137i) q^{19} +(1.01713 + 3.55355i) q^{20} +(-1.51665 - 1.51665i) q^{22} +(0.641461 - 0.171879i) q^{23} +(-4.41250 - 2.35157i) q^{25} +(-1.94308 - 1.12184i) q^{26} +(-3.74797 + 2.25387i) q^{28} -9.88857 q^{29} +(4.19734 + 7.27001i) q^{31} +(7.16237 + 1.91915i) q^{32} -4.27403i q^{34} +(1.33148 - 5.76430i) q^{35} +(5.51429 - 1.47755i) q^{37} +(-2.96942 + 11.0820i) q^{38} +(-1.27148 + 0.763160i) q^{40} +3.31153i q^{41} +(5.26014 - 5.26014i) q^{43} +(-0.927514 + 1.60650i) q^{44} +(-0.634632 - 1.09922i) q^{46} +(2.55120 + 9.52122i) q^{47} +(6.99556 - 0.249395i) q^{49} +(-2.15861 + 9.30945i) q^{50} +(-0.502235 + 1.87437i) q^{52} +(0.211894 - 0.790799i) q^{53} +(-0.690516 - 2.41246i) q^{55} +(-1.26262 - 1.21841i) q^{56} +(4.89165 + 18.2559i) q^{58} +(1.75013 + 3.03132i) q^{59} +(2.57534 - 4.46061i) q^{61} +(11.3453 - 11.3453i) q^{62} -5.02510i q^{64} +(-1.35087 - 2.25065i) q^{65} +(1.66197 - 6.20255i) q^{67} +(-3.57052 + 0.956719i) q^{68} +(-11.3005 + 0.393349i) q^{70} -12.1470i q^{71} +(-4.49672 - 1.20489i) q^{73} +(-5.45559 - 9.44935i) q^{74} +9.92263 q^{76} +(2.54444 - 1.53012i) q^{77} +(9.12881 + 5.27052i) q^{79} +(7.35317 + 7.10765i) q^{80} +(6.11362 - 1.63814i) q^{82} +(11.5106 + 11.5106i) q^{83} +(2.42628 - 4.37221i) q^{85} +(-12.3131 - 7.10899i) q^{86} +(-0.718875 - 0.192622i) q^{88} +(1.76847 - 3.06308i) q^{89} +(2.15670 - 2.23496i) q^{91} +(-0.776226 + 0.776226i) q^{92} +(16.3157 - 9.41986i) q^{94} +(-9.32868 + 9.65092i) q^{95} +(10.6773 + 10.6773i) q^{97} +(-3.92097 - 12.7916i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$64 q + 8 q^{7} + 8 q^{10} + 32 q^{16} - 48 q^{22} - 16 q^{25} + 88 q^{28} + 32 q^{31} - 16 q^{37} - 40 q^{40} - 16 q^{43} - 80 q^{52} - 32 q^{55} - 88 q^{58} + 48 q^{61} - 32 q^{67} - 112 q^{70} - 88 q^{73}+ \cdots + 208 q^{97}+O(q^{100})$ 64 * q + 8 * q^7 + 8 * q^10 + 32 * q^16 - 48 * q^22 - 16 * q^25 + 88 * q^28 + 32 * q^31 - 16 * q^37 - 40 * q^40 - 16 * q^43 - 80 * q^52 - 32 * q^55 - 88 * q^58 + 48 * q^61 - 32 * q^67 - 112 * q^70 - 88 * q^73 - 320 * q^76 - 56 * q^82 + 16 * q^85 + 120 * q^88 - 128 * q^91 + 208 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$ .

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$	$-1$

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

)

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

$2$	−0.494677	−	1.84616i	−0.349790	−	1.30543i	−0.886916	−	0.461931i	$-0.847157\pi$
$2$	−0.494677	−	1.84616i	−0.349790	−	1.30543i	0.537126	−	0.843502i	$-0.319510\pi$
$3$		0			0
$3$		0			0
$4$	−1.43155	+	0.826508i	−0.715777	+	0.413254i
$5$	0.541988	−	2.16939i	0.242385	−	0.970180i
$5$	0.541988	−	2.16939i	0.242385	−	0.970180i
$6$		0			0
$7$	2.64533	−	0.0471386i	0.999841	−	0.0178167i
$7$	2.64533	−	0.0471386i	0.999841	−	0.0178167i
$8$	−0.468944	−	0.468944i	−0.165797	−	0.165797i
$9$		0			0
$10$	−4.27315	+	0.0725500i	−1.35129	+	0.0229423i
$11$	0.971861	−	0.561104i	0.293027	−	0.169179i	−0.346279	−	0.938132i	$-0.612555\pi$
$11$	0.971861	−	0.561104i	0.293027	−	0.169179i	0.639306	+	0.768952i	$0.279222\pi$
$12$		0			0
$13$	0.830077	−	0.830077i	0.230222	−	0.230222i	−0.582563	−	0.812785i	$-0.697950\pi$
$13$	0.830077	−	0.830077i	0.230222	−	0.230222i	0.812785	+	0.582563i	$0.197950\pi$
$14$	−1.39561	−	4.86039i	−0.372993	−	1.29899i
$15$		0			0
$16$	−2.28679	+	3.96083i	−0.571696	+	0.990207i
$17$	2.16001	+	0.578772i	0.523879	+	0.140373i	0.511060	−	0.859545i	$-0.329253\pi$
$17$	2.16001	+	0.578772i	0.523879	+	0.140373i	0.0128185	+	0.999918i	$0.495920\pi$
$18$		0			0
$19$	−5.19853	−	3.00137i	−1.19262	−	0.688562i	−0.233723	−	0.972303i	$-0.575091\pi$
$19$	−5.19853	−	3.00137i	−1.19262	−	0.688562i	−0.958901	+	0.283741i	$0.908424\pi$
$20$	1.01713	+	3.55355i	0.227438	+	0.794599i
$21$		0			0
$22$	−1.51665	−	1.51665i	−0.323350	−	0.323350i
$23$	0.641461	−	0.171879i	0.133754	−	0.0358392i	−0.191321	−	0.981528i	$-0.561277\pi$
$23$	0.641461	−	0.171879i	0.133754	−	0.0358392i	0.325075	+	0.945688i	$0.394610\pi$
$24$		0			0
$25$	−4.41250	−	2.35157i	−0.882499	−	0.470313i
$26$	−1.94308	−	1.12184i	−0.381069	−	0.220010i
$27$		0			0
$28$	−3.74797	+	2.25387i	−0.708300	+	0.425941i
$29$	−9.88857			−1.83626			−0.918131	−	0.396277i	$-0.870302\pi$
$29$	−9.88857			−1.83626			−0.918131	+	0.396277i	$0.870302\pi$
$30$		0			0
$31$	4.19734	+	7.27001i	0.753865	+	1.30573i	0.945937	+	0.324352i	$0.105146\pi$
$31$	4.19734	+	7.27001i	0.753865	+	1.30573i	−0.192071	+	0.981381i	$0.561521\pi$
$32$	7.16237	+	1.91915i	1.26614	+	0.339261i
$33$		0			0
$34$		−	4.27403i		−	0.732989i
$35$	1.33148	−	5.76430i	0.225061	−	0.974345i
$36$		0			0
$37$	5.51429	−	1.47755i	0.906543	−	0.242908i	0.224719	−	0.974424i	$-0.427854\pi$
$37$	5.51429	−	1.47755i	0.906543	−	0.242908i	0.681824	+	0.731516i	$0.261187\pi$
$38$	−2.96942	+	11.0820i	−0.481704	+	1.79774i
$39$		0			0
$40$	−1.27148	+	0.763160i	−0.201039	+	0.120666i
$41$			3.31153i			0.517175i	0.965988	+	0.258587i	$0.0832570\pi$
$41$			3.31153i			0.517175i	−0.965988	+	0.258587i	$0.916743\pi$
$42$		0			0
$43$	5.26014	−	5.26014i	0.802164	−	0.802164i	−0.181270	−	0.983433i	$-0.558021\pi$
$43$	5.26014	−	5.26014i	0.802164	−	0.802164i	0.983433	+	0.181270i	$0.0580207\pi$
$44$	−0.927514	+	1.60650i	−0.139828	+	0.242189i
$45$		0			0
$46$	−0.634632	−	1.09922i	−0.0935714	−	0.162070i
$47$	2.55120	+	9.52122i	0.372131	+	1.38881i	0.857491	+	0.514498i	$0.172022\pi$
$47$	2.55120	+	9.52122i	0.372131	+	1.38881i	−0.485360	+	0.874314i	$0.661311\pi$
$48$		0			0
$49$	6.99556	−	0.249395i	0.999365	−	0.0356278i
$50$	−2.15861	+	9.30945i	−0.305273	+	1.31655i
$51$		0			0
$52$	−0.502235	+	1.87437i	−0.0696474	+	0.259928i
$53$	0.211894	−	0.790799i	0.0291059	−	0.108625i	−0.949845	−	0.312722i	$-0.898759\pi$
$53$	0.211894	−	0.790799i	0.0291059	−	0.108625i	0.978951	+	0.204097i	$0.0654259\pi$
$54$		0			0
$55$	−0.690516	−	2.41246i	−0.0931092	−	0.325296i
$56$	−1.26262	−	1.21841i	−0.168724	−	0.162816i
$57$		0			0
$58$	4.89165	+	18.2559i	0.642305	+	2.39712i
$59$	1.75013	+	3.03132i	0.227848	+	0.394644i	0.957170	−	0.289526i	$-0.0934978\pi$
$59$	1.75013	+	3.03132i	0.227848	+	0.394644i	−0.729322	+	0.684170i	$0.760164\pi$
$60$		0			0
$61$	2.57534	−	4.46061i	0.329738	−	0.571123i	−0.652722	−	0.757598i	$-0.726373\pi$
$61$	2.57534	−	4.46061i	0.329738	−	0.571123i	0.982460	+	0.186475i	$0.0597063\pi$
$62$	11.3453	−	11.3453i	1.44085	−	1.44085i
$63$		0			0
$64$		−	5.02510i		−	0.628138i
$65$	−1.35087	−	2.25065i	−0.167555	−	0.279159i
$66$		0			0
$67$	1.66197	−	6.20255i	0.203042	−	0.757762i	−0.786996	−	0.616958i	$-0.788365\pi$
$67$	1.66197	−	6.20255i	0.203042	−	0.757762i	0.990038	−	0.140804i	$-0.0449687\pi$
$68$	−3.57052	+	0.956719i	−0.432990	+	0.116019i
$69$		0			0
$70$	−11.3005	+	0.393349i	−1.35067	+	0.0470142i
$71$		−	12.1470i		−	1.44159i	−0.693149	−	0.720795i	$-0.743777\pi$
$71$		−	12.1470i		−	1.44159i	0.693149	−	0.720795i	$-0.256223\pi$
$72$		0			0
$73$	−4.49672	−	1.20489i	−0.526301	−	0.141022i	−0.0141212	−	0.999900i	$-0.504495\pi$
$73$	−4.49672	−	1.20489i	−0.526301	−	0.141022i	−0.512179	+	0.858878i	$0.671162\pi$
$74$	−5.45559	−	9.44935i	−0.634199	−	1.09846i
$75$		0			0
$76$	9.92263			1.13820
$77$	2.54444	−	1.53012i	0.289966	−	0.174373i
$78$		0			0
$79$	9.12881	+	5.27052i	1.02707	+	0.592980i	0.916144	−	0.400849i	$-0.131285\pi$
$79$	9.12881	+	5.27052i	1.02707	+	0.592980i	0.110927	+	0.993829i	$0.464618\pi$
$80$	7.35317	+	7.10765i	0.822109	+	0.794659i
$81$		0			0
$82$	6.11362	−	1.63814i	0.675137	−	0.180902i
$83$	11.5106	+	11.5106i	1.26345	+	1.26345i	0.949411	+	0.314036i	$0.101681\pi$
$83$	11.5106	+	11.5106i	1.26345	+	1.26345i	0.314036	+	0.949411i	$0.398319\pi$
$84$		0			0
$85$	2.42628	−	4.37221i	0.263167	−	0.474232i
$86$	−12.3131	−	7.10899i	−1.32776	−	0.766582i
$87$		0			0
$88$	−0.718875	−	0.192622i	−0.0766323	−	0.0205336i
$89$	1.76847	−	3.06308i	0.187457	−	0.324686i	−0.756944	−	0.653479i	$-0.773309\pi$
$89$	1.76847	−	3.06308i	0.187457	−	0.324686i	0.944402	+	0.328793i	$0.106642\pi$
$90$		0			0
$91$	2.15670	−	2.23496i	0.226084	−	0.234287i
$92$	−0.776226	+	0.776226i	−0.0809272	+	0.0809272i
$93$		0			0
$94$	16.3157	−	9.41986i	1.68283	−	0.971585i
$95$	−9.32868	+	9.65092i	−0.957103	+	0.990164i
$96$		0			0
$97$	10.6773	+	10.6773i	1.08411	+	1.08411i	0.996121	+	0.0879901i	$0.0280444\pi$
$97$	10.6773	+	10.6773i	1.08411	+	1.08411i	0.0879901	+	0.996121i	$0.471956\pi$
$98$	−3.92097	−	12.7916i	−0.396077	−	1.29214i
$99$		0			0
$100$	8.26031	−	0.280570i	0.826031	−	0.0280570i
$101$	2.76599	−	1.59694i	0.275226	−	0.158902i	−0.356034	−	0.934473i	$-0.615871\pi$
$101$	2.76599	−	1.59694i	0.275226	−	0.158902i	0.631260	+	0.775571i	$0.282538\pi$
$102$		0			0
$103$	−0.554604	−	2.06981i	−0.0546468	−	0.203945i	0.933205	−	0.359345i	$-0.117000\pi$
$103$	−0.554604	−	2.06981i	−0.0546468	−	0.203945i	−0.987852	+	0.155400i	$0.950333\pi$
$104$	−0.778519			−0.0763401
$105$		0			0
$106$	−1.56476			−0.151983
$107$	−0.164185	−	0.612745i	−0.0158723	−	0.0592363i	0.957535	−	0.288315i	$-0.0930952\pi$
$107$	−0.164185	−	0.612745i	−0.0158723	−	0.0592363i	−0.973408	+	0.229079i	$0.926429\pi$
$108$		0			0
$109$	−11.9861	+	6.92020i	−1.14806	+	0.662835i	−0.948415	−	0.317033i	$-0.897314\pi$
$109$	−11.9861	+	6.92020i	−1.14806	+	0.662835i	−0.199649	+	0.979867i	$0.563980\pi$
$110$	−4.11220	+	2.46819i	−0.392083	+	0.235333i
$111$		0			0
$112$	−5.86260	+	10.5855i	−0.553963	+	1.00024i
$113$	5.75515	+	5.75515i	0.541399	+	0.541399i	0.923939	−	0.382540i	$-0.124951\pi$
$113$	5.75515	+	5.75515i	0.541399	+	0.541399i	−0.382540	+	0.923939i	$0.624951\pi$
$114$		0			0
$115$	−0.0252080	−	1.48473i	−0.00235066	−	0.138452i
$116$	14.1560	−	8.17298i	1.31435	−	0.758842i
$117$		0			0
$118$	4.73055	−	4.73055i	0.435483	−	0.435483i
$119$	5.74122	+	1.42922i	0.526296	+	0.131017i
$120$		0			0
$121$	−4.87032	+	8.43565i	−0.442757	+	0.766877i
$122$	−9.50897	−	2.54792i	−0.860901	−	0.230678i
$123$		0			0
$124$	−12.0174	−	6.93827i	−1.07920	−	0.623075i
$125$	−7.49298	+	8.29790i	−0.670193	+	0.742187i
$126$		0			0
$127$	−9.74796	−	9.74796i	−0.864992	−	0.864992i	0.126921	−	0.991913i	$-0.459490\pi$
$127$	−9.74796	−	9.74796i	−0.864992	−	0.864992i	−0.991913	+	0.126921i	$0.959490\pi$
$128$	5.04759	−	1.35250i	0.446148	−	0.119545i
$129$		0			0
$130$	−3.48682	+	3.60727i	−0.305815	+	0.316378i
$131$	12.7957	+	7.38760i	1.11796	+	0.645457i	0.940881	−	0.338738i	$-0.110000\pi$
$131$	12.7957	+	7.38760i	1.11796	+	0.645457i	0.177084	+	0.984196i	$0.443333\pi$
$132$		0			0
$133$	−13.8933	−	7.69457i	−1.20470	−	0.667204i
$134$	−12.2730			−1.06023
$135$		0			0
$136$	−0.741510	−	1.28433i	−0.0635840	−	0.110131i
$137$	−19.2723	−	5.16400i	−1.64655	−	0.441191i	−0.687903	−	0.725803i	$-0.741469\pi$
$137$	−19.2723	−	5.16400i	−1.64655	−	0.441191i	−0.958643	+	0.284612i	$0.908135\pi$
$138$		0			0
$139$		−	1.87882i		−	0.159359i	−0.996821	−	0.0796796i	$-0.974610\pi$
$139$		−	1.87882i		−	0.159359i	0.996821	−	0.0796796i	$-0.0253897\pi$
$140$	2.85816	+	9.35238i	0.241559	+	0.790420i
$141$		0			0
$142$	−22.4254	+	6.00887i	−1.88190	+	0.504253i
$143$	0.340960	−	1.27248i	0.0285125	−	0.106410i
$144$		0			0
$145$	−5.35949	+	21.4522i	−0.445081	+	1.78150i
$146$			8.89769i			0.736378i
$147$		0			0
$148$	−6.67279	+	6.67279i	−0.548500	+	0.548500i
$149$	−11.0437	+	19.1282i	−0.904731	+	1.56704i	−0.0834535	+	0.996512i	$0.526595\pi$
$149$	−11.0437	+	19.1282i	−0.904731	+	1.56704i	−0.821278	+	0.570529i	$0.806738\pi$
$150$		0			0
$151$	−2.38598	−	4.13263i	−0.194168	−	0.336309i	0.752459	−	0.658639i	$-0.228867\pi$
$151$	−2.38598	−	4.13263i	−0.194168	−	0.336309i	−0.946627	+	0.322330i	$0.895534\pi$
$152$	1.03034	+	3.84529i	0.0835719	+	0.311894i
$153$		0			0
$154$	−4.08352	−	3.94054i	−0.329060	−	0.317538i
$155$	18.0464	−	5.16541i	1.44952	−	0.414896i
$156$		0			0
$157$	−3.79660	+	14.1691i	−0.303002	+	1.13082i	0.631650	+	0.775253i	$0.282378\pi$
$157$	−3.79660	+	14.1691i	−0.303002	+	1.13082i	−0.934652	+	0.355564i	$0.884289\pi$
$158$	5.21442	−	19.4605i	0.414837	−	1.54819i
$159$		0			0
$160$	8.04530	−	14.4978i	0.636037	−	1.14615i
$161$	1.68877	−	0.484914i	0.133094	−	0.0382166i
$162$		0			0
$163$	−3.19404	−	11.9203i	−0.250177	−	0.933672i	−0.970711	−	0.240252i	$-0.922770\pi$
$163$	−3.19404	−	11.9203i	−0.250177	−	0.933672i	0.720534	−	0.693420i	$-0.243897\pi$
$164$	−2.73701	−	4.74064i	−0.213724	−	0.370182i
$165$		0			0
$166$	15.5563	−	26.9443i	1.20740	−	2.09129i
$167$	2.58291	−	2.58291i	0.199871	−	0.199871i	−0.600073	−	0.799945i	$-0.704862\pi$
$167$	2.58291	−	2.58291i	0.199871	−	0.199871i	0.799945	+	0.600073i	$0.204862\pi$
$168$		0			0
$169$			11.6219i			0.893996i
$170$	−9.27202	−	2.31647i	−0.711132	−	0.177665i
$171$		0			0
$172$	−3.18262	+	11.8777i	−0.242673	+	0.905667i
$173$	2.71673	−	0.727945i	0.206549	−	0.0553446i	−0.154061	−	0.988061i	$-0.549235\pi$
$173$	2.71673	−	0.727945i	0.206549	−	0.0553446i	0.360610	+	0.932717i	$0.382569\pi$
$174$		0			0
$175$	−11.7834	−	6.01267i	−0.890739	−	0.454515i
$176$			5.13250i			0.386877i
$177$		0			0
$178$	−6.52976	−	1.74964i	−0.489426	−	0.131141i
$179$	2.82676	+	4.89609i	0.211282	+	0.365951i	0.952116	−	0.305737i	$-0.0989029\pi$
$179$	2.82676	+	4.89609i	0.211282	+	0.365951i	−0.740834	+	0.671688i	$0.765570\pi$
$180$		0			0
$181$	−22.3247			−1.65938			−0.829690	−	0.558225i	$-0.811483\pi$
$181$	−22.3247			−1.65938			−0.829690	+	0.558225i	$0.811483\pi$
$182$	−5.19296	−	2.87603i	−0.384928	−	0.213186i
$183$		0			0
$184$	−0.381411	−	0.220208i	−0.0281180	−	0.0162339i
$185$	−0.216699	−	12.7634i	−0.0159320	−	0.938387i
$186$		0			0
$187$	2.42398	−	0.649503i	0.177259	−	0.0474964i
$188$	−11.5215	−	11.5215i	−0.840295	−	0.840295i
$189$		0			0
$190$	22.4318	+	12.4482i	1.62738	+	0.903084i
$191$	5.11137	+	2.95105i	0.369846	+	0.213531i	0.673391	−	0.739286i	$-0.264837\pi$
$191$	5.11137	+	2.95105i	0.369846	+	0.213531i	−0.303545	+	0.952817i	$0.598170\pi$
$192$		0			0
$193$	−11.0380	−	2.95761i	−0.794530	−	0.212894i	−0.161349	−	0.986897i	$-0.551585\pi$
$193$	−11.0380	−	2.95761i	−0.794530	−	0.212894i	−0.633181	+	0.774004i	$0.718251\pi$
$194$	14.4301	−	24.9937i	1.03602	−	1.79445i
$195$		0			0
$196$	−9.80839	+	6.13890i	−0.700599	+	0.438493i
$197$	9.38019	−	9.38019i	0.668311	−	0.668311i	−0.289014	−	0.957325i	$-0.593327\pi$
$197$	9.38019	−	9.38019i	0.668311	−	0.668311i	0.957325	+	0.289014i	$0.0933274\pi$
$198$		0			0
$199$	10.5579	−	6.09559i	0.748428	−	0.432105i	−0.0766977	−	0.997054i	$-0.524438\pi$
$199$	10.5579	−	6.09559i	0.748428	−	0.432105i	0.825126	+	0.564949i	$0.191104\pi$
$200$	0.966461	+	3.17197i	0.0683391	+	0.224292i
$201$		0			0
$202$	−4.31648	−	4.31648i	−0.303707	−	0.303707i
$203$	−26.1586	+	0.466134i	−1.83597	+	0.0327162i
$204$		0			0
$205$	7.18401	+	1.79481i	0.501753	+	0.125355i
$206$	−3.54685	+	2.04778i	−0.247121	+	0.142675i
$207$		0			0
$208$	1.38959	+	5.18600i	0.0963504	+	0.359585i
$209$	−6.73633			−0.465962
$210$		0			0
$211$	−3.48159			−0.239683			−0.119841	−	0.992793i	$-0.538239\pi$
$211$	−3.48159			−0.239683			−0.119841	+	0.992793i	$0.538239\pi$
$212$	0.350264	+	1.30720i	0.0240562	+	0.0897791i
$213$		0			0
$214$	−1.05001	+	0.606222i	−0.0717770	+	0.0414405i
$215$	−8.56036	−	14.2622i	−0.583811	−	0.972676i
$216$		0			0
$217$	11.4461	+	19.0337i	0.777009	+	1.29209i
$218$	18.7051	+	18.7051i	1.26687	+	1.26687i
$219$		0			0
$220$	2.98242	+	2.88284i	0.201075	+	0.194361i
$221$	2.27340	−	1.31255i	0.152925	−	0.0882915i
$222$		0			0
$223$	11.8362	−	11.8362i	0.792608	−	0.792608i	−0.189310	−	0.981917i	$-0.560625\pi$
$223$	11.8362	−	11.8362i	0.792608	−	0.792608i	0.981917	+	0.189310i	$0.0606250\pi$
$224$	19.0373	+	4.73917i	1.27198	+	0.316649i
$225$		0			0
$226$	7.77799	−	13.4719i	0.517384	−	0.896135i
$227$	−25.9887	−	6.96365i	−1.72493	−	0.462194i	−0.745926	−	0.666029i	$-0.767993\pi$
$227$	−25.9887	−	6.96365i	−1.72493	−	0.462194i	−0.979005	+	0.203835i	$0.934659\pi$
$228$		0			0
$229$	−5.91912	−	3.41741i	−0.391146	−	0.225829i	0.291510	−	0.956568i	$-0.405842\pi$
$229$	−5.91912	−	3.41741i	−0.391146	−	0.225829i	−0.682657	+	0.730739i	$0.739176\pi$
$230$	−2.72859	+	0.781002i	−0.179918	+	0.0514978i
$231$		0			0
$232$	4.63719	+	4.63719i	0.304446	+	0.304446i
$233$	6.88187	−	1.84399i	0.450846	−	0.120804i	−0.0262490	−	0.999655i	$-0.508356\pi$
$233$	6.88187	−	1.84399i	0.450846	−	0.120804i	0.477095	+	0.878852i	$0.341690\pi$
$234$		0			0
$235$	22.0380	−	0.374163i	1.43760	−	0.0244077i
$236$	−5.01082	−	2.89300i	−0.326176	−	0.188318i
$237$		0			0
$238$	−0.201472	−	11.3062i	−0.0130595	−	0.732873i
$239$	18.7848			1.21509			0.607543	−	0.794287i	$-0.292155\pi$
$239$	18.7848			1.21509			0.607543	+	0.794287i	$0.292155\pi$
$240$		0			0
$241$	12.7838	+	22.1421i	0.823474	+	1.42630i	0.903080	+	0.429473i	$0.141301\pi$
$241$	12.7838	+	22.1421i	0.823474	+	1.42630i	−0.0796052	+	0.996826i	$0.525366\pi$
$242$	17.9828	+	4.81848i	1.15598	+	0.309743i
$243$		0			0
$244$			8.51414i			0.545062i
$245$	3.25048	−	15.3113i	0.207665	−	0.978200i
$246$		0			0
$247$	−6.80655	+	1.82381i	−0.433091	+	0.116046i
$248$	1.44091	−	5.37755i	0.0914978	−	0.341475i
$249$		0			0
$250$	19.0259	+	9.72847i	1.20330	+	0.615283i
$251$			2.18106i			0.137667i	0.997628	+	0.0688336i	$0.0219277\pi$
$251$			2.18106i			0.137667i	−0.997628	+	0.0688336i	$0.978072\pi$
$252$		0			0
$253$	0.526969	−	0.526969i	0.0331302	−	0.0331302i
$254$	−13.1742	+	22.8184i	−0.826623	+	1.43175i
$255$		0			0
$256$	−10.0190	−	17.3533i	−0.626185	−	1.08458i
$257$	−1.98298	−	7.40059i	−0.123695	−	0.461636i	0.876095	−	0.482139i	$-0.160140\pi$
$257$	−1.98298	−	7.40059i	−0.123695	−	0.461636i	−0.999790	+	0.0205029i	$0.993473\pi$
$258$		0			0
$259$	14.5175	−	4.16854i	0.902072	−	0.259021i
$260$	3.79402	+	2.10543i	0.235295	+	0.130573i
$261$		0			0
$262$	7.30895	−	27.2774i	0.451549	−	1.68520i
$263$	−2.35526	+	8.78994i	−0.145231	+	0.542011i	0.854514	+	0.519429i	$0.173855\pi$
$263$	−2.35526	+	8.78994i	−0.145231	+	0.542011i	−0.999745	+	0.0225820i	$0.992811\pi$
$264$		0			0
$265$	−1.60071	−	0.888285i	−0.0983307	−	0.0545669i
$266$	−7.33271	+	29.4556i	−0.449597	+	1.80604i
$267$		0			0
$268$	2.74726	+	10.2529i	0.167816	+	0.626296i
$269$	−3.66156	−	6.34200i	−0.223249	−	0.386679i	0.732544	−	0.680720i	$-0.238333\pi$
$269$	−3.66156	−	6.34200i	−0.223249	−	0.386679i	−0.955793	+	0.294041i	$0.905000\pi$
$270$		0			0
$271$	−8.97448	+	15.5443i	−0.545161	+	0.944246i	0.453436	+	0.891289i	$0.350198\pi$
$271$	−8.97448	+	15.5443i	−0.545161	+	0.944246i	−0.998597	+	0.0529575i	$0.983135\pi$
$272$	−7.23189	+	7.23189i	−0.438498	+	0.438498i
$273$		0			0
$274$			38.1343i			2.30378i
$275$	−5.60781	+	0.190475i	−0.338164	+	0.0114861i
$276$		0			0
$277$	7.24135	−	27.0251i	0.435091	−	1.62378i	−0.305758	−	0.952109i	$-0.598910\pi$
$277$	7.24135	−	27.0251i	0.435091	−	1.62378i	0.740849	−	0.671672i	$-0.234423\pi$
$278$	−3.46860	+	0.929408i	−0.208033	+	0.0557422i
$279$		0			0
$280$	−3.32752	+	2.07875i	−0.198857	+	0.124229i
$281$		−	20.0659i		−	1.19703i	−0.801111	−	0.598516i	$-0.795757\pi$
$281$		−	20.0659i		−	1.19703i	0.801111	−	0.598516i	$-0.204243\pi$
$282$		0			0
$283$	−10.1980	−	2.73254i	−0.606206	−	0.162432i	−0.0573568	−	0.998354i	$-0.518267\pi$
$283$	−10.1980	−	2.73254i	−0.606206	−	0.162432i	−0.548849	+	0.835921i	$0.684934\pi$
$284$	10.0396	+	17.3891i	0.595742	+	1.03186i
$285$		0			0
$286$	−2.51787			−0.148885
$287$	0.156101	+	8.76010i	0.00921436	+	0.517093i
$288$		0			0
$289$	−10.3918	−	5.99970i	−0.611281	−	0.352923i
$290$	42.2554	−	0.717416i	2.48132	−	0.0421281i
$291$		0			0
$292$	7.43314	−	1.99170i	0.434992	−	0.116556i
$293$	−14.8561	−	14.8561i	−0.867901	−	0.867901i	0.124339	−	0.992240i	$-0.460319\pi$
$293$	−14.8561	−	14.8561i	−0.867901	−	0.867901i	−0.992240	+	0.124339i	$0.960319\pi$
$294$		0			0
$295$	7.52466	−	2.15378i	0.438103	−	0.125398i
$296$	−3.27878	−	1.89300i	−0.190575	−	0.110029i
$297$		0			0
$298$	40.7767	+	10.9261i	2.36213	+	0.632931i
$299$	0.389789	−	0.675135i	0.0225421	−	0.0390441i
$300$		0			0
$301$	13.6669	−	14.1628i	0.787745	−	0.816328i
$302$	−6.44922	+	6.44922i	−0.371111	+	0.371111i
$303$		0			0
$304$	23.7758	−	13.7270i	1.36364	−	0.787297i
$305$	−8.28100	−	8.00450i	−0.474169	−	0.458337i
$306$		0			0
$307$	−10.5560	−	10.5560i	−0.602461	−	0.602461i	0.338504	−	0.940965i	$-0.390079\pi$
$307$	−10.5560	−	10.5560i	−0.602461	−	0.602461i	−0.940965	+	0.338504i	$0.890079\pi$
$308$	−2.37785	+	4.29345i	−0.135491	+	0.244642i
$309$		0			0
$310$	−18.4633	−	30.7613i	−1.04865	−	1.74713i
$311$	2.61258	−	1.50838i	0.148146	−	0.0855322i	−0.424095	−	0.905618i	$-0.639408\pi$
$311$	2.61258	−	1.50838i	0.148146	−	0.0855322i	0.572241	+	0.820086i	$0.306074\pi$
$312$		0			0
$313$	7.27876	+	27.1647i	0.411420	+	1.53544i	0.791900	+	0.610650i	$0.209092\pi$
$313$	7.27876	+	27.1647i	0.411420	+	1.53544i	−0.380480	+	0.924789i	$0.624241\pi$
$314$	28.0365			1.58219
$315$		0			0
$316$	−17.4245			−0.980205
$317$	4.43708	+	16.5594i	0.249211	+	0.930069i	0.971220	+	0.238185i	$0.0765524\pi$
$317$	4.43708	+	16.5594i	0.249211	+	0.930069i	−0.722009	+	0.691884i	$0.756781\pi$
$318$		0			0
$319$	−9.61032	+	5.54852i	−0.538075	+	0.310657i
$320$	−10.9014	−	2.72355i	−0.609407	−	0.152251i
$321$		0			0
$322$	−1.73063	−	2.87787i	−0.0964441	−	0.160378i
$323$	−9.49175	−	9.49175i	−0.528135	−	0.528135i
$324$		0			0
$325$	−5.61470	+	1.71073i	−0.311447	+	0.0948943i
$326$	−20.4268	+	11.7934i	−1.13134	+	0.653177i
$327$		0			0
$328$	1.55292	−	1.55292i	0.0857459	−	0.0857459i
$329$	7.19760	+	25.0665i	0.396816	+	1.38196i
$330$		0			0
$331$	−7.37160	+	12.7680i	−0.405180	+	0.701792i	−0.994342	−	0.106223i	$-0.966124\pi$
$331$	−7.37160	+	12.7680i	−0.405180	+	0.701792i	0.589163	+	0.808014i	$0.299458\pi$
$332$	−25.9915	−	6.96441i	−1.42647	−	0.382222i
$333$		0			0
$334$	−6.04617	−	3.49076i	−0.330832	−	0.191006i
$335$	−12.5550	−	6.96717i	−0.685952	−	0.380657i
$336$		0			0
$337$	−20.2173	−	20.2173i	−1.10131	−	1.10131i	−0.994253	−	0.107055i	$-0.965858\pi$
$337$	−20.2173	−	20.2173i	−1.10131	−	1.10131i	−0.107055	−	0.994253i	$-0.534142\pi$
$338$	21.4560	−	5.74911i	1.16705	−	0.312710i
$339$		0			0
$340$	0.140314	+	8.26439i	0.00760958	+	0.448199i
$341$	8.15847	+	4.71029i	0.441806	+	0.255077i
$342$		0			0
$343$	18.4938	−	0.989492i	0.998572	−	0.0534275i
$344$	−4.93342			−0.265992
$345$		0			0
$346$	−2.68781	−	4.65542i	−0.144497	−	0.250277i
$347$	18.7190	+	5.01575i	1.00489	+	0.269260i	0.723493	−	0.690332i	$-0.242535\pi$
$347$	18.7190	+	5.01575i	1.00489	+	0.269260i	0.281397	+	0.959591i	$0.409202\pi$
$348$		0			0
$349$			19.5132i			1.04452i	0.852787	+	0.522258i	$0.174910\pi$
$349$			19.5132i			1.04452i	−0.852787	+	0.522258i	$0.825090\pi$
$350$	−5.27140	+	24.7283i	−0.281768	+	1.32178i
$351$		0			0
$352$	8.03767	−	2.15369i	0.428409	−	0.114792i
$353$	−5.15540	+	19.2402i	−0.274394	+	1.02405i	0.681852	+	0.731491i	$0.261175\pi$
$353$	−5.15540	+	19.2402i	−0.274394	+	1.02405i	−0.956246	+	0.292564i	$0.905492\pi$
$354$		0			0
$355$	−26.3517	−	6.58356i	−1.39860	−	0.349419i
$356$			5.84662i			0.309870i
$357$		0			0
$358$	7.64064	−	7.64064i	0.403820	−	0.403820i
$359$	3.47927	−	6.02627i	0.183629	−	0.318054i	−0.759485	−	0.650525i	$-0.774549\pi$
$359$	3.47927	−	6.02627i	0.183629	−	0.318054i	0.943114	+	0.332471i	$0.107882\pi$
$360$		0			0
$361$	8.51646	+	14.7509i	0.448235	+	0.776366i
$362$	11.0435	+	41.2149i	0.580434	+	2.16621i
$363$		0			0
$364$	−1.24022	+	4.98199i	−0.0650053	+	0.261127i
$365$	−5.05104	+	9.10209i	−0.264384	+	0.476425i
$366$		0			0
$367$	1.03003	−	3.84412i	0.0537671	−	0.200662i	−0.933817	−	0.357750i	$-0.883544\pi$
$367$	1.03003	−	3.84412i	0.0537671	−	0.200662i	0.987585	+	0.157088i	$0.0502107\pi$
$368$	−0.786100	+	2.93377i	−0.0409783	+	0.152933i
$369$		0			0
$370$	−23.4562	+	6.71385i	−1.21943	+	0.349036i
$371$	0.523253	−	2.10191i	0.0271659	−	0.109126i
$372$		0			0
$373$	2.78464	+	10.3924i	0.144183	+	0.538099i	0.999790	+	0.0204732i	$0.00651727\pi$
$373$	2.78464	+	10.3924i	0.144183	+	0.538099i	−0.855607	+	0.517625i	$0.826816\pi$
$374$	−2.39817	−	4.15376i	−0.124007	−	0.214786i
$375$		0			0
$376$	3.26855	−	5.66129i	0.168562	−	0.291959i
$377$	−8.20828	+	8.20828i	−0.422748	+	0.422748i
$378$		0			0
$379$			13.4948i			0.693180i	0.938017	+	0.346590i	$0.112661\pi$
$379$			13.4948i			0.693180i	−0.938017	+	0.346590i	$0.887339\pi$
$380$	5.37795	−	21.5260i	0.275883	−	1.10426i
$381$		0			0
$382$	2.91964	−	10.8962i	0.149382	−	0.557500i
$383$	2.67081	−	0.715640i	0.136472	−	0.0365675i	−0.189937	−	0.981796i	$-0.560828\pi$
$383$	2.67081	−	0.715640i	0.136472	−	0.0365675i	0.326408	+	0.945229i	$0.394162\pi$
$384$		0			0
$385$	−1.94036	−	6.34920i	−0.0988901	−	0.323585i
$386$			21.8409i			1.11167i
$387$		0			0
$388$	−24.1099	−	6.46023i	−1.22399	−	0.327968i
$389$	−8.29427	−	14.3661i	−0.420536	−	0.728390i	0.575456	−	0.817833i	$-0.304825\pi$
$389$	−8.29427	−	14.3661i	−0.420536	−	0.728390i	−0.995992	+	0.0894428i	$0.971491\pi$
$390$		0			0
$391$	1.48504			0.0751016
$392$	−3.39748	−	3.16357i	−0.171598	−	0.159784i
$393$		0			0
$394$	−21.9575	−	12.6772i	−1.10620	−	0.638667i
$395$	16.3815	−	16.9474i	0.824244	−	0.852715i
$396$		0			0
$397$	13.5010	−	3.61757i	0.677594	−	0.181561i	0.0964210	−	0.995341i	$-0.469260\pi$
$397$	13.5010	−	3.61757i	0.677594	−	0.181561i	0.581173	+	0.813780i	$0.302594\pi$
$398$	−16.4762	−	16.4762i	−0.825876	−	0.825876i
$399$		0			0
$400$	19.4046	−	12.0996i	0.970229	−	0.604981i
$401$	−7.99139	−	4.61383i	−0.399071	−	0.230404i	0.287012	−	0.957927i	$-0.407338\pi$
$401$	−7.99139	−	4.61383i	−0.399071	−	0.230404i	−0.686083	+	0.727523i	$0.740671\pi$
$402$		0			0
$403$	9.51879	+	2.55055i	0.474165	+	0.127052i
$404$	−2.63977	+	4.57222i	−0.131333	+	0.227476i
$405$		0			0
$406$	13.8006	+	48.0623i	0.684912	+	2.38529i
$407$	4.53006	−	4.53006i	0.224547	−	0.224547i
$408$		0			0
$409$	−14.8468	+	8.57179i	−0.734125	+	0.423848i	−0.819929	−	0.572465i	$-0.805987\pi$
$409$	−14.8468	+	8.57179i	−0.734125	+	0.423848i	0.0858041	+	0.996312i	$0.472654\pi$
$410$	−0.240252	−	14.1507i	−0.0118652	−	0.698852i
$411$		0			0
$412$	2.50466	+	2.50466i	0.123396	+	0.123396i
$413$	4.77257	+	7.93634i	0.234843	+	0.390522i
$414$		0			0
$415$	31.2094	−	18.7323i	1.53201	−	0.919531i
$416$	7.53836	−	4.35228i	0.369599	−	0.213388i
$417$		0			0
$418$	3.33231	+	12.4363i	0.162989	+	0.608282i
$419$	22.7475			1.11129			0.555645	−	0.831420i	$-0.312471\pi$
$419$	22.7475			1.11129			0.555645	+	0.831420i	$0.312471\pi$
$420$		0			0
$421$	−8.08528			−0.394052			−0.197026	−	0.980398i	$-0.563128\pi$
$421$	−8.08528			−0.394052			−0.197026	+	0.980398i	$0.563128\pi$
$422$	1.72227	+	6.42758i	0.0838386	+	0.312890i
$423$		0			0
$424$	−0.470207	+	0.271474i	−0.0228353	+	0.0131839i
$425$	−8.17000	−	7.63323i	−0.396303	−	0.370266i
$426$		0			0
$427$	6.60235	−	11.9212i	0.319510	−	0.576907i
$428$	0.741478	+	0.741478i	0.0358407	+	0.0358407i
$429$		0			0
$430$	−22.0957	+	22.8590i	−1.06555	+	1.10236i
$431$	−23.4131	+	13.5176i	−1.12777	+	0.651119i	−0.943373	−	0.331733i	$-0.892367\pi$
$431$	−23.4131	+	13.5176i	−1.12777	+	0.651119i	−0.184398	+	0.982852i	$0.559034\pi$
$432$		0			0
$433$	−1.13772	+	1.13772i	−0.0546754	+	0.0546754i	−0.733916	−	0.679240i	$-0.762309\pi$
$433$	−1.13772	+	1.13772i	−0.0546754	+	0.0546754i	0.679240	+	0.733916i	$0.262309\pi$
$434$	29.4772	−	30.5468i	1.41495	−	1.46629i
$435$		0			0
$436$	11.4392	−	19.8133i	0.547838	−	0.948883i
$437$	−3.85052	−	1.03174i	−0.184196	−	0.0493551i
$438$		0			0
$439$	−27.2646	−	15.7412i	−1.30127	−	0.751287i	−0.320646	−	0.947199i	$-0.603900\pi$
$439$	−27.2646	−	15.7412i	−1.30127	−	0.751287i	−0.980621	+	0.195912i	$0.937233\pi$
$440$	−0.807493	+	1.45512i	−0.0384957	+	0.0693701i
$441$		0			0
$442$	−3.54777	−	3.54777i	−0.168750	−	0.168750i
$443$	13.9059	−	3.72608i	0.660690	−	0.177031i	0.0871324	−	0.996197i	$-0.472230\pi$
$443$	13.9059	−	3.72608i	0.660690	−	0.177031i	0.573557	+	0.819166i	$0.305563\pi$
$444$		0			0
$445$	−5.68652	−	5.49665i	−0.269567	−	0.260566i
$446$	−27.7065	−	15.9964i	−1.31194	−	0.757450i
$447$		0			0
$448$	−0.236876	−	13.2931i	−0.0111914	−	0.628038i
$449$	−13.1001			−0.618230			−0.309115	−	0.951025i	$-0.600033\pi$
$449$	−13.1001			−0.618230			−0.309115	+	0.951025i	$0.600033\pi$
$450$		0			0
$451$	1.85812	+	3.21835i	0.0874953	+	0.151546i
$452$	−12.9955	−	3.48213i	−0.611256	−	0.163785i
$453$		0			0
$454$			51.4241i			2.41345i
$455$	−3.67959	−	5.89004i	−0.172502	−	0.276130i
$456$		0			0
$457$	5.00463	−	1.34099i	0.234107	−	0.0627288i	−0.139858	−	0.990172i	$-0.544665\pi$
$457$	5.00463	−	1.34099i	0.234107	−	0.0627288i	0.373965	+	0.927443i	$0.377998\pi$
$458$	−3.38103	+	12.6182i	−0.157985	+	0.589608i
$459$		0			0
$460$	1.26323	+	2.10464i	0.0588985	+	0.0981294i
$461$		−	26.5137i		−	1.23486i	−0.786624	−	0.617432i	$-0.788173\pi$
$461$		−	26.5137i		−	1.23486i	0.786624	−	0.617432i	$-0.211827\pi$
$462$		0			0
$463$	−8.59270	+	8.59270i	−0.399337	+	0.399337i	−0.877999	−	0.478662i	$-0.841122\pi$
$463$	−8.59270	+	8.59270i	−0.399337	+	0.399337i	0.478662	+	0.877999i	$0.341122\pi$
$464$	22.6130	−	39.1669i	1.04978	−	1.81828i
$465$		0			0
$466$	−6.80861	−	11.7929i	−0.315403	−	0.546294i
$467$	−2.64464	−	9.86992i	−0.122379	−	0.456726i	0.877353	−	0.479845i	$-0.159307\pi$
$467$	−2.64464	−	9.86992i	−0.122379	−	0.456726i	−0.999733	+	0.0231190i	$0.992640\pi$
$468$		0			0
$469$	4.10408	−	16.4861i	0.189509	−	0.761259i
$470$	−11.5924	−	40.5005i	−0.534719	−	1.86815i
$471$		0			0
$472$	0.600804	−	2.24223i	0.0276543	−	0.103207i
$473$	2.16064	−	8.06361i	0.0993462	−	0.370765i
$474$		0			0
$475$	15.8806	+	25.4682i	0.728650	+	1.16856i
$476$	−9.40012	+	2.69915i	−0.430854	+	0.123715i
$477$		0			0
$478$	−9.29240	−	34.6797i	−0.425025	−	1.58621i
$479$	−2.60300	−	4.50853i	−0.118934	−	0.206000i	0.800411	−	0.599451i	$-0.204614\pi$
$479$	−2.60300	−	4.50853i	−0.118934	−	0.206000i	−0.919346	+	0.393451i	$0.871281\pi$
$480$		0			0
$481$	3.35081	−	5.80377i	0.152784	−	0.264629i
$482$	34.5541	−	34.5541i	1.57390	−	1.57390i
$483$		0			0
$484$		−	16.1014i		−	0.731884i
$485$	28.9501	−	17.3762i	1.31456	−	0.789012i
$486$		0			0
$487$	−6.88081	+	25.6796i	−0.311799	+	1.16365i	0.615133	+	0.788423i	$0.289102\pi$
$487$	−6.88081	+	25.6796i	−0.311799	+	1.16365i	−0.926932	+	0.375228i	$0.877564\pi$
$488$	−3.29946	+	0.884089i	−0.149360	+	0.0400208i
$489$		0			0
$490$	−29.8750	+	1.57323i	−1.34961	+	0.0710712i
$491$		−	5.16035i		−	0.232883i	−0.993198	−	0.116442i	$-0.962851\pi$
$491$		−	5.16035i		−	0.232883i	0.993198	−	0.116442i	$-0.0371488\pi$
$492$		0			0
$493$	−21.3594	−	5.72323i	−0.961978	−	0.257761i
$494$	6.73409	+	11.6638i	0.302981	+	0.524779i
$495$		0			0
$496$	−38.3937			−1.72393
$497$	−0.572595	−	32.1330i	−0.0256844	−	1.44136i
$498$		0			0
$499$	6.70115	+	3.86891i	0.299985	+	0.173196i	0.642436	−	0.766339i	$-0.277924\pi$
$499$	6.70115	+	3.86891i	0.299985	+	0.173196i	−0.342451	+	0.939536i	$0.611257\pi$
$500$	3.86833	−	18.0719i	0.172997	−	0.808200i
$501$		0			0
$502$	4.02658	−	1.07892i	0.179715	−	0.0481545i
$503$	−3.22778	−	3.22778i	−0.143920	−	0.143920i	0.631476	−	0.775395i	$-0.282449\pi$
$503$	−3.22778	−	3.22778i	−0.143920	−	0.143920i	−0.775395	+	0.631476i	$0.782449\pi$
$504$		0			0
$505$	−1.96526	−	6.86602i	−0.0874528	−	0.305534i
$506$	−1.23355	−	0.712190i	−0.0548379	−	0.0316607i
$507$		0			0
$508$	22.0115	+	5.89796i	0.976602	+	0.261680i
$509$	−8.98621	+	15.5646i	−0.398307	+	0.689887i	−0.993517	−	0.113682i	$-0.963735\pi$
$509$	−8.98621	+	15.5646i	−0.398307	+	0.689887i	0.595210	+	0.803570i	$0.297069\pi$
$510$		0			0
$511$	−11.9521	−	2.97537i	−0.528730	−	0.131623i
$512$	−19.6907	+	19.6907i	−0.870216	+	0.870216i
$513$		0			0
$514$	−12.6817	+	7.32181i	−0.559368	+	0.322951i
$515$	−4.79081	+	0.0813390i	−0.211109	+	0.00358422i
$516$		0			0
$517$	7.82181	+	7.82181i	0.344003	+	0.344003i
$518$	−14.8773	−	24.7395i	−0.653669	−	1.08699i
$519$		0			0
$520$	−0.421948	+	1.68891i	−0.0185037	+	0.0740637i
$521$	−24.8083	+	14.3231i	−1.08687	+	0.627505i	−0.932741	−	0.360546i	$-0.882590\pi$
$521$	−24.8083	+	14.3231i	−1.08687	+	0.627505i	−0.154129	+	0.988051i	$0.549257\pi$
$522$		0			0
$523$	−0.195886	−	0.731058i	−0.00856551	−	0.0319669i	0.961511	−	0.274767i	$-0.0886007\pi$
$523$	−0.195886	−	0.731058i	−0.00856551	−	0.0319669i	−0.970076	+	0.242800i	$0.921934\pi$
$524$	−24.4236			−1.06695
$525$		0			0
$526$	17.3927			0.758359
$527$	4.85861	+	18.1326i	0.211644	+	0.789868i
$528$		0			0
$529$	−19.5367	+	11.2795i	−0.849420	+	0.490413i
$530$	−0.848083	+	3.39458i	−0.0368384	+	0.147451i
$531$		0			0
$532$	26.2486	−	0.467739i	1.13802	−	0.0202791i
$533$	2.74883	+	2.74883i	0.119065	+	0.119065i
$534$		0			0
$535$	−1.41827	+	0.0240795i	−0.0613171	+	0.00104105i
$536$	−3.68802	+	2.12928i	−0.159298	+	0.0919708i
$537$		0			0
$538$	−9.89706	+	9.89706i	−0.426693	+	0.426693i
$539$	6.65877	−	4.16761i	0.286814	−	0.179512i
$540$		0			0
$541$	20.4118	−	35.3542i	0.877571	−	1.52000i	0.0235718	−	0.999722i	$-0.492496\pi$
$541$	20.4118	−	35.3542i	0.877571	−	1.52000i	0.853999	−	0.520275i	$-0.174170\pi$
$542$	33.1367	+	8.87895i	1.42334	+	0.381383i
$543$		0			0
$544$	14.3600	+	8.29076i	0.615681	+	0.355463i
$545$	8.51626	+	29.7533i	0.364796	+	1.27449i
$546$		0			0
$547$	−15.8647	−	15.8647i	−0.678325	−	0.678325i	0.281296	−	0.959621i	$-0.409236\pi$
$547$	−15.8647	−	15.8647i	−0.678325	−	0.678325i	−0.959621	+	0.281296i	$0.909236\pi$
$548$	31.8574	−	8.53618i	1.36088	−	0.364647i
$549$		0			0
$550$	3.12570	+	10.2587i	0.133280	+	0.437432i
$551$	51.4060	+	29.6793i	2.18997	+	1.26438i
$552$		0			0
$553$	24.3972	+	13.5120i	1.03747	+	0.574587i
$554$	−53.4748			−2.27193
$555$		0			0
$556$	1.55286	+	2.68963i	0.0658558	+	0.114066i
$557$	5.32480	+	1.42678i	0.225619	+	0.0604544i	0.369857	−	0.929089i	$-0.379407\pi$
$557$	5.32480	+	1.42678i	0.225619	+	0.0604544i	−0.144238	+	0.989543i	$0.546073\pi$
$558$		0			0
$559$		−	8.73265i		−	0.369352i
$560$	19.7866	+	18.4555i	0.836137	+	0.779886i
$561$		0			0
$562$	−37.0449	+	9.92615i	−1.56264	+	0.418709i
$563$	−10.0547	+	37.5245i	−0.423753	+	1.58147i	0.342877	+	0.939380i	$0.388599\pi$
$563$	−10.0547	+	37.5245i	−0.423753	+	1.58147i	−0.766630	+	0.642089i	$0.778068\pi$
$564$		0			0
$565$	15.6044	−	9.36593i	0.656481	−	0.394028i
$566$			20.1788i			0.848179i
$567$		0			0
$568$	−5.69628	+	5.69628i	−0.239011	+	0.239011i
$569$	−2.56024	+	4.43446i	−0.107331	+	0.185902i	−0.914688	−	0.404161i	$-0.867564\pi$
$569$	−2.56024	+	4.43446i	−0.107331	+	0.185902i	0.807357	+	0.590063i	$0.200897\pi$
$570$		0			0
$571$	17.4000	+	30.1377i	0.728169	+	1.26123i	0.957656	+	0.287914i	$0.0929617\pi$
$571$	17.4000	+	30.1377i	0.728169	+	1.26123i	−0.229487	+	0.973312i	$0.573705\pi$
$572$	0.563612	+	2.10343i	0.0235658	+	0.0879488i
$573$		0			0
$574$	16.0953	−	4.62161i	0.671807	−	0.192902i
$575$	−3.23463	−	0.750023i	−0.134893	−	0.0312781i
$576$		0			0
$577$	−1.89014	+	7.05409i	−0.0786874	+	0.293666i	−0.994044	−	0.108978i	$-0.965242\pi$
$577$	−1.89014	+	7.05409i	−0.0786874	+	0.293666i	0.915357	+	0.402644i	$0.131909\pi$
$578$	−5.93583	+	22.1528i	−0.246898	+	0.921435i
$579$		0			0
$580$	−10.0580	−	35.1396i	−0.417635	−	1.45909i
$581$	30.9918	+	29.9066i	1.28576	+	1.24074i
$582$		0			0
$583$	−0.237789	−	0.887442i	−0.00984823	−	0.0367541i
$584$	1.54368	+	2.67373i	0.0638780	+	0.110640i
$585$		0			0
$586$	−20.0777	+	34.7757i	−0.829403	+	1.43657i
$587$	−21.2623	+	21.2623i	−0.877588	+	0.877588i	−0.993285	−	0.115696i	$-0.963090\pi$
$587$	−21.2623	+	21.2623i	−0.877588	+	0.877588i	0.115696	+	0.993285i	$0.463090\pi$
$588$		0			0
$589$		−	50.3912i		−	2.07633i
$590$	−7.69850	−	12.8263i	−0.316942	−	0.528051i
$591$		0			0
$592$	−6.75767	+	25.2200i	−0.277739	+	1.03653i
$593$	−23.5608	+	6.31310i	−0.967527	+	0.259248i	−0.707783	−	0.706430i	$-0.750305\pi$
$593$	−23.5608	+	6.31310i	−0.967527	+	0.259248i	−0.259744	+	0.965678i	$0.583638\pi$
$594$		0			0
$595$	6.21222	−	11.6803i	0.254676	−	0.478846i
$596$		−	36.5107i		−	1.49553i
$597$		0			0
$598$	−1.43923	−	0.385640i	−0.0588544	−	0.0157700i
$599$	6.90412	+	11.9583i	0.282095	+	0.488602i	0.971900	−	0.235392i	$-0.0756374\pi$
$599$	6.90412	+	11.9583i	0.282095	+	0.488602i	−0.689806	+	0.723994i	$0.742304\pi$
$600$		0			0
$601$	2.66574			0.108738			0.0543690	−	0.998521i	$-0.482685\pi$
$601$	2.66574			0.108738			0.0543690	+	0.998521i	$0.482685\pi$
$602$	−32.9074	−	18.2252i	−1.34121	−	0.742804i
$603$		0			0
$604$	6.83130	+	3.94406i	0.277962	+	0.160481i
$605$	15.6605	+	15.1377i	0.636692	+	0.615433i
$606$		0			0
$607$	4.14832	−	1.11154i	0.168375	−	0.0451159i	−0.173647	−	0.984808i	$-0.555555\pi$
$607$	4.14832	−	1.11154i	0.168375	−	0.0451159i	0.342022	+	0.939692i	$0.388888\pi$
$608$	−31.4737	−	31.4737i	−1.27643	−	1.27643i
$609$		0			0
$610$	−10.6812	+	19.2477i	−0.432468	+	0.779317i
$611$	10.0210	+	5.78565i	0.405408	+	0.234062i
$612$		0			0
$613$	−24.4122	−	6.54122i	−0.985998	−	0.264197i	−0.270429	−	0.962740i	$-0.587166\pi$
$613$	−24.4122	−	6.54122i	−0.985998	−	0.264197i	−0.715568	+	0.698543i	$0.753832\pi$
$614$	−14.2662	+	24.7098i	−0.575738	+	0.997208i
$615$		0			0
$616$	−1.91074	−	0.475662i	−0.0769860	−	0.0191650i
$617$	−10.0544	+	10.0544i	−0.404774	+	0.404774i	−0.879911	−	0.475138i	$-0.842398\pi$
$617$	−10.0544	+	10.0544i	−0.404774	+	0.404774i	0.475138	+	0.879911i	$0.342398\pi$
$618$		0			0
$619$	−9.47268	+	5.46905i	−0.380739	+	0.219820i	−0.678140	−	0.734933i	$-0.737214\pi$
$619$	−9.47268	+	5.46905i	−0.380739	+	0.219820i	0.297401	+	0.954753i	$0.403880\pi$
$620$	−21.5651	+	22.3100i	−0.866076	+	0.895993i
$621$		0			0
$622$	−4.07709	−	4.07709i	−0.163476	−	0.163476i
$623$	4.53380	−	8.18622i	0.181643	−	0.327974i
$624$		0			0
$625$	13.9403	+	20.7526i	0.557611	+	0.830103i
$626$	46.5498	−	26.8755i	1.86050	−	1.07416i
$627$		0			0
$628$	−6.27584	−	23.4217i	−0.250433	−	0.934629i
$629$	12.7661			0.509016
$630$		0			0
$631$	−14.9321			−0.594439			−0.297219	−	0.954809i	$-0.596059\pi$
$631$	−14.9321			−0.594439			−0.297219	+	0.954809i	$0.596059\pi$
$632$	−1.80932	−	6.75248i	−0.0719709	−	0.268599i
$633$		0			0
$634$	28.3764	−	16.3831i	1.12697	−	0.650657i
$635$	−26.4304	+	15.8638i	−1.04886	+	0.629537i
$636$		0			0
$637$	5.59984	−	6.01387i	0.221874	−	0.238278i
$638$	14.9975	+	14.9975i	0.593755	+	0.593755i
$639$		0			0
$640$	−0.198359	−	11.6832i	−0.00784083	−	0.461820i
$641$	8.48248	−	4.89736i	0.335038	−	0.193434i	−0.323038	−	0.946386i	$-0.604704\pi$
$641$	8.48248	−	4.89736i	0.335038	−	0.193434i	0.658075	+	0.752952i	$0.271371\pi$
$642$		0			0
$643$	−3.43776	+	3.43776i	−0.135572	+	0.135572i	−0.771636	−	0.636064i	$-0.780561\pi$
$643$	−3.43776	+	3.43776i	−0.135572	+	0.135572i	0.636064	+	0.771636i	$0.280561\pi$
$644$	−2.01679	+	2.08997i	−0.0794725	+	0.0823562i
$645$		0			0
$646$	−12.8279	+	22.2186i	−0.504709	+	0.874181i
$647$	18.7678	+	5.02881i	0.737837	+	0.197703i	0.608117	−	0.793848i	$-0.291925\pi$
$647$	18.7678	+	5.02881i	0.737837	+	0.197703i	0.129720	+	0.991551i	$0.458592\pi$
$648$		0			0
$649$	3.40177	+	1.96401i	0.133531	+	0.0770943i
$650$	5.93575	+	9.51937i	0.232819	+	0.373381i
$651$		0			0
$652$	14.4247	+	14.4247i	0.564914	+	0.564914i
$653$	12.5364	−	3.35912i	0.490588	−	0.131453i	−0.00504043	−	0.999987i	$-0.501604\pi$
$653$	12.5364	−	3.35912i	0.490588	−	0.131453i	0.495629	+	0.868535i	$0.334938\pi$
$654$		0			0
$655$	22.9617	−	23.7548i	0.897187	−	0.928179i
$656$	−13.1164	−	7.57277i	−0.512110	−	0.295667i
$657$		0			0
$658$	42.7163	−	25.6878i	1.66526	−	1.00141i
$659$	−1.48624			−0.0578959			−0.0289479	−	0.999581i	$-0.509216\pi$
$659$	−1.48624			−0.0578959			−0.0289479	+	0.999581i	$0.509216\pi$
$660$		0			0
$661$	−9.29471	−	16.0989i	−0.361522	−	0.626175i	0.626689	−	0.779269i	$-0.284410\pi$
$661$	−9.29471	−	16.0989i	−0.361522	−	0.626175i	−0.988212	+	0.153094i	$0.951076\pi$
$662$	27.2183	+	7.29312i	1.05787	+	0.283455i
$663$		0			0
$664$		−	10.7956i		−	0.418951i
$665$	−24.2225	+	25.9696i	−0.939309	+	1.00706i
$666$		0			0
$667$	−6.34313	+	1.69964i	−0.245607	+	0.0658102i
$668$	−1.56278	+	5.83237i	−0.0604657	+	0.225661i
$669$		0			0
$670$	−6.65185	+	26.6250i	−0.256983	+	1.02861i
$671$		−	5.78013i		−	0.223139i
$672$		0			0
$673$	9.44812	−	9.44812i	0.364198	−	0.364198i	−0.501158	−	0.865356i	$-0.667092\pi$
$673$	9.44812	−	9.44812i	0.364198	−	0.364198i	0.865356	+	0.501158i	$0.167092\pi$
$674$	−27.3234	+	47.3255i	−1.05246	+	1.82291i
$675$		0			0
$676$	−9.60563	−	16.6374i	−0.369447	−	0.639901i
$677$	−11.0601	−	41.2767i	−0.425072	−	1.58639i	−0.763765	−	0.645495i	$-0.776651\pi$
$677$	−11.0601	−	41.2767i	−0.425072	−	1.58639i	0.338692	−	0.940897i	$-0.390015\pi$
$678$		0			0
$679$	28.7482	+	27.7416i	1.10325	+	1.06462i
$680$	−3.18811	+	0.912531i	−0.122258	+	0.0349940i
$681$		0			0
$682$	4.66015	−	17.3919i	0.178446	−	0.665971i
$683$	−0.687686	+	2.56648i	−0.0263136	+	0.0982036i	−0.977834	−	0.209383i	$-0.932855\pi$
$683$	−0.687686	+	2.56648i	−0.0263136	+	0.0982036i	0.951520	+	0.307586i	$0.0995213\pi$
$684$		0			0
$685$	−21.6481	+	39.0103i	−0.827132	+	1.49051i
$686$	−10.9752	−	33.6531i	−0.419036	−	1.28488i
$687$		0			0
$688$	8.80570	+	32.8633i	0.335714	+	1.25290i
$689$	−0.480536	−	0.832313i	−0.0183070	−	0.0317086i
$690$		0			0
$691$	15.5622	−	26.9545i	0.592014	−	1.02540i	−0.401947	−	0.915663i	$-0.631667\pi$
$691$	15.5622	−	26.9545i	0.592014	−	1.02540i	0.993961	−	0.109735i	$-0.0350002\pi$
$692$	−3.28749	+	3.28749i	−0.124972	+	0.124972i
$693$		0			0
$694$		−	37.0395i		−	1.40600i
$695$	−4.07588	−	1.01830i	−0.154607	−	0.0386262i
$696$		0			0
$697$	−1.91662	+	7.15294i	−0.0725973	+	0.270937i
$698$	36.0245	−	9.65273i	1.36355	−	0.365361i
$699$		0			0
$700$	21.8380	−	1.13158i	0.825400	−	0.0427697i
$701$			24.8143i			0.937224i	0.883404	+	0.468612i	$0.155246\pi$
$701$			24.8143i			0.937224i	−0.883404	+	0.468612i	$0.844754\pi$
$702$		0			0
$703$	−33.1009	−	8.86935i	−1.24842	−	0.334514i
$704$	−2.81961	−	4.88370i	−0.106268	−	0.184061i
$705$		0			0
$706$	38.0708			1.43281
$707$	7.24167	−	4.35483i	0.272351	−	0.163780i
$708$		0			0
$709$	−14.3464	−	8.28290i	−0.538791	−	0.311071i	0.205798	−	0.978594i	$-0.434021\pi$
$709$	−14.3464	−	8.28290i	−0.538791	−	0.311071i	−0.744589	+	0.667524i	$0.767354\pi$
$710$	0.881269	+	51.9062i	0.0330734	+	1.94800i
$711$		0			0
$712$	−2.26573	+	0.607099i	−0.0849117	+	0.0227520i
$713$	3.94199	+	3.94199i	0.147629	+	0.147629i
$714$		0			0
$715$	−2.57571	−	1.42934i	−0.0963260	−	0.0534544i
$716$	−8.09331	−	4.67268i	−0.302461	−	0.174626i
$717$		0			0
$718$	−12.8466	−	3.44223i	−0.479430	−	0.128463i
$719$	8.28531	−	14.3506i	0.308990	−	0.535186i	−0.669152	−	0.743126i	$-0.733342\pi$
$719$	8.28531	−	14.3506i	0.308990	−	0.535186i	0.978142	+	0.207939i	$0.0666757\pi$
$720$		0			0
$721$	−1.56468	−	5.44919i	−0.0582717	−	0.202939i
$722$	23.0197	−	23.0197i	0.856705	−	0.856705i
$723$		0			0
$724$	31.9589	−	18.4515i	1.18774	−	0.685745i
$725$	43.6333	+	23.2536i	1.62050	+	0.863618i
$726$		0			0
$727$	10.4810	+	10.4810i	0.388721	+	0.388721i	0.874231	−	0.485510i	$-0.161366\pi$
$727$	10.4810	+	10.4810i	0.388721	+	0.388721i	−0.485510	+	0.874231i	$0.661366\pi$
$728$	−2.05944	+	0.0366983i	−0.0763280	+	0.00136013i
$729$		0			0
$730$	19.3026	+	4.82244i	0.714420	+	0.178487i
$731$	14.4064	−	8.31752i	0.532838	−	0.307634i
$732$		0			0
$733$	7.08056	+	26.4250i	0.261527	+	0.976030i	0.964342	+	0.264658i	$0.0852592\pi$
$733$	7.08056	+	26.4250i	0.261527	+	0.976030i	−0.702816	+	0.711372i	$0.748074\pi$
$734$	−7.60640			−0.280757
$735$		0			0
$736$	4.92424			0.181510
$737$	−1.86508	−	6.96055i	−0.0687009	−	0.256395i
$738$		0			0
$739$	24.2950	−	14.0267i	0.893707	−	0.515982i	0.0185537	−	0.999828i	$-0.494094\pi$
$739$	24.2950	−	14.0267i	0.893707	−	0.515982i	0.875153	+	0.483846i	$0.160760\pi$
$740$	10.8593	+	18.0925i	0.399196	+	0.665092i
$741$		0			0
$742$	−4.13931	+	0.0737607i	−0.151959	+	0.00270784i
$743$	−13.7752	−	13.7752i	−0.505363	−	0.505363i	0.407737	−	0.913100i	$-0.366318\pi$
$743$	−13.7752	−	13.7752i	−0.505363	−	0.505363i	−0.913100	+	0.407737i	$0.866318\pi$
$744$		0			0
$745$	35.5109	+	34.3252i	1.30102	+	1.25758i
$746$	17.8086	−	10.2818i	0.652018	−	0.376443i
$747$		0			0
$748$	−2.93323	+	2.93323i	−0.107250	+	0.107250i
$749$	−0.463207	−	1.61317i	−0.0169252	−	0.0589441i
$750$		0			0
$751$	17.1719	−	29.7426i	0.626611	−	1.08532i	−0.361617	−	0.932327i	$-0.617775\pi$
$751$	17.1719	−	29.7426i	0.626611	−	1.08532i	0.988227	−	0.152994i	$-0.0488916\pi$
$752$	−43.5460	−	11.6681i	−1.58796	−	0.425492i
$753$		0			0
$754$	19.2143	+	11.0934i	0.699742	+	0.403996i
$755$	−10.2585	+	2.93627i	−0.373344	+	0.106862i
$756$		0			0
$757$	14.6354	+	14.6354i	0.531932	+	0.531932i	0.921147	−	0.389215i	$-0.127254\pi$
$757$	14.6354	+	14.6354i	0.531932	+	0.531932i	−0.389215	+	0.921147i	$0.627254\pi$
$758$	24.9135	−	6.67556i	0.904900	−	0.242467i
$759$		0			0
$760$	8.90037	−	0.151111i	0.322850	−	0.00548139i
$761$	−31.8819	−	18.4070i	−1.15572	−	0.667254i	−0.205443	−	0.978669i	$-0.565864\pi$
$761$	−31.8819	−	18.4070i	−1.15572	−	0.667254i	−0.950274	+	0.311415i	$0.899197\pi$
$762$		0			0
$763$	−31.3811	+	18.8712i	−1.13607	+	0.683184i
$764$	−9.75627			−0.352969
$765$		0			0
$766$	−2.64237	−	4.57673i	−0.0954728	−	0.165364i
$767$	3.96897	+	1.06348i	0.143311	+	0.0384002i
$768$		0			0
$769$		−	24.6011i		−	0.887139i	−0.896240	−	0.443569i	$-0.853712\pi$
$769$		−	24.6011i		−	0.887139i	0.896240	−	0.443569i	$-0.146288\pi$
$770$	−10.7618	+	6.72303i	−0.387828	+	0.242281i
$771$		0			0
$772$	18.2459	−	4.88898i	0.656685	−	0.175958i
$773$	2.47156	−	9.22398i	0.0888958	−	0.331764i	−0.907128	−	0.420856i	$-0.861730\pi$
$773$	2.47156	−	9.22398i	0.0888958	−	0.331764i	0.996023	+	0.0890921i	$0.0283966\pi$
$774$		0			0
$775$	−1.42485	−	41.9492i	−0.0511821	−	1.50686i
$776$		−	10.0141i		−	0.359484i
$777$		0			0
$778$	−22.4191	+	22.4191i	−0.803765	+	0.803765i
$779$	9.93914	−	17.2151i	0.356107	−	0.616795i
$780$		0			0
$781$	−6.81576	−	11.8052i	−0.243887	−	0.422425i
$782$	−0.734615	−	2.74162i	−0.0262698	−	0.0980401i
$783$		0			0
$784$	−15.0095	+	28.2785i	−0.536055	+	1.00995i
$785$	28.6806	+	15.9158i	1.02365	+	0.568059i
$786$		0			0
$787$	−10.2341	+	38.1941i	−0.364806	+	1.36147i	0.502879	+	0.864357i	$0.332274\pi$
$787$	−10.2341	+	38.1941i	−0.364806	+	1.36147i	−0.867684	+	0.497116i	$0.834392\pi$
$788$	−5.67545	+	21.1810i	−0.202179	+	0.754544i
$789$		0			0
$790$	−39.3912	−	21.8594i	−1.40147	−	0.777724i
$791$	15.4956	+	14.9530i	0.550959	+	0.531667i
$792$		0			0
$793$	−1.56493	−	5.84038i	−0.0555721	−	0.207398i
$794$	−13.3572	−	23.1354i	−0.474031	−	0.821046i
$795$		0			0
$796$	−10.0761	+	17.4523i	−0.357138	+	0.618581i
$797$	10.0038	−	10.0038i	0.354354	−	0.354354i	−0.507373	−	0.861727i	$-0.669383\pi$
$797$	10.0038	−	10.0038i	0.354354	−	0.354354i	0.861727	+	0.507373i	$0.169383\pi$
$798$		0			0
$799$			22.0425i			0.779806i
$800$	−27.0909	−	25.3110i	−0.957809	−	0.894880i
$801$		0			0
$802$	−4.56472	+	17.0358i	−0.161186	+	0.601553i
$803$	−5.04625	+	1.35214i	−0.178078	+	0.0477160i
$804$		0			0
$805$	−0.136672	−	3.92643i	−0.00481705	−	0.138388i
$806$		−	18.8349i		−	0.663432i
$807$		0			0
$808$	−2.04597	−	0.548215i	−0.0719769	−	0.0192862i
$809$	−2.99072	−	5.18008i	−0.105148	−	0.182122i	0.808651	−	0.588289i	$-0.200198\pi$
$809$	−2.99072	−	5.18008i	−0.105148	−	0.182122i	−0.913799	+	0.406167i	$0.866865\pi$
$810$		0			0
$811$	4.80074			0.168577			0.0842883	−	0.996441i	$-0.473138\pi$
$811$	4.80074			0.168577			0.0842883	+	0.996441i	$0.473138\pi$
$812$	37.0621	−	22.2875i	1.30062	−	0.782139i
$813$		0			0
$814$	−10.6041	−	6.12230i	−0.371675	−	0.214587i
$815$	−27.5910	+	0.468442i	−0.966469	+	0.0164088i
$816$		0			0
$817$	−43.1326	+	11.5574i	−1.50902	+	0.404340i
$818$	23.1693	+	23.1693i	0.810094	+	0.810094i
$819$		0			0
$820$	−11.7677	+	3.36827i	−0.410946	+	0.117625i
$821$	−22.5254	−	13.0050i	−0.786142	−	0.453879i	0.0524609	−	0.998623i	$-0.483294\pi$
$821$	−22.5254	−	13.0050i	−0.786142	−	0.453879i	−0.838602	+	0.544744i	$0.816627\pi$
$822$		0			0
$823$	11.2027	+	3.00174i	0.390500	+	0.104634i	0.448726	−	0.893669i	$-0.351878\pi$
$823$	11.2027	+	3.00174i	0.390500	+	0.104634i	−0.0582263	+	0.998303i	$0.518545\pi$
$824$	−0.710547	+	1.23070i	−0.0247531	+	0.0428736i
$825$		0			0
$826$	12.2909	−	12.7369i	0.427655	−	0.443172i
$827$	−9.82938	+	9.82938i	−0.341801	+	0.341801i	−0.857044	−	0.515243i	$-0.827702\pi$
$827$	−9.82938	+	9.82938i	−0.341801	+	0.341801i	0.515243	+	0.857044i	$0.327702\pi$
$828$		0			0
$829$	33.1815	−	19.1573i	1.15244	−	0.665362i	0.202960	−	0.979187i	$-0.434944\pi$
$829$	33.1815	−	19.1573i	1.15244	−	0.665362i	0.949481	+	0.313825i	$0.101611\pi$
$830$	−50.0214	−	48.3512i	−1.73627	−	1.67830i
$831$		0			0
$832$	−4.17123	−	4.17123i	−0.144611	−	0.144611i
$833$	15.2548	+	3.51014i	0.528547	+	0.121619i
$834$		0			0
$835$	−4.20343	−	7.00324i	−0.145466	−	0.242357i
$836$	9.64341	−	5.56763i	0.333524	−	0.192560i
$837$		0			0
$838$	−11.2527	−	41.9956i	−0.388718	−	1.45071i
$839$	23.9846			0.828039			0.414020	−	0.910268i	$-0.364124\pi$
$839$	23.9846			0.828039			0.414020	+	0.910268i	$0.364124\pi$
$840$		0			0
$841$	68.7839			2.37186
$842$	3.99960	+	14.9267i	0.137835	+	0.514409i
$843$		0			0
$844$	4.98409	−	2.87756i	0.171559	−	0.0990498i
$845$	25.2125	+	6.29896i	0.867337	+	0.216691i
$846$		0			0
$847$	−12.4860	+	22.5447i	−0.429023	+	0.774644i
$848$	2.64766	+	2.64766i	0.0909212	+	0.0909212i
$849$		0			0
$850$	−10.0507	+	18.8591i	−0.344735	+	0.646863i
$851$	3.28324	−	1.89558i	0.112548	−	0.0649796i
$852$		0			0
$853$	32.7833	−	32.7833i	1.12248	−	1.12248i	0.131111	−	0.991368i	$-0.458146\pi$
$853$	32.7833	−	32.7833i	1.12248	−	1.12248i	0.991368	−	0.131111i	$-0.0418544\pi$
$854$	−25.2745	−	6.29185i	−0.864875	−	0.215303i
$855$		0			0
$856$	−0.210350	+	0.364336i	−0.00718961	+	0.0124528i
$857$	−6.84801	−	1.83492i	−0.233924	−	0.0626796i	0.139953	−	0.990158i	$-0.455305\pi$
$857$	−6.84801	−	1.83492i	−0.233924	−	0.0626796i	−0.373876	+	0.927479i	$0.621972\pi$
$858$		0			0
$859$	35.3255	+	20.3952i	1.20529	+	0.695874i	0.961727	−	0.274011i	$-0.0883504\pi$
$859$	35.3255	+	20.3952i	1.20529	+	0.695874i	0.243563	+	0.969885i	$0.421684\pi$
$860$	24.0424	+	13.3419i	0.819841	+	0.454956i
$861$		0			0
$862$	36.5376	+	36.5376i	1.24448	+	1.24448i
$863$	−26.6975	+	7.15357i	−0.908793	+	0.243510i	−0.682789	−	0.730616i	$-0.739233\pi$
$863$	−26.6975	+	7.15357i	−0.908793	+	0.243510i	−0.226004	+	0.974126i	$0.572566\pi$
$864$		0			0
$865$	−0.106761	−	6.28818i	−0.00363000	−	0.213804i
$866$	2.66322	+	1.53761i	0.0904999	+	0.0522501i
$867$		0			0
$868$	−32.1172	−	17.7875i	−1.09013	−	0.603749i
$869$	11.8292			0.401280
$870$		0			0
$871$	−3.76903	−	6.52816i	−0.127709	−	0.221198i
$872$	8.86601	+	2.37564i	0.300241	+	0.0804493i
$873$		0			0
$874$			7.61907i			0.257719i
$875$	−19.4303	+	22.3039i	−0.656863	+	0.754010i
$876$		0			0
$877$	6.53819	−	1.75190i	0.220779	−	0.0591576i	−0.146734	−	0.989176i	$-0.546876\pi$
$877$	6.53819	−	1.75190i	0.220779	−	0.0591576i	0.367513	+	0.930018i	$0.380209\pi$
$878$	−15.5736	+	58.1216i	−0.525585	+	1.96151i
$879$		0			0
$880$	11.1344	+	2.78175i	0.375340	+	0.0937729i
$881$		−	54.4886i		−	1.83577i	−0.396848	−	0.917884i	$-0.629896\pi$
$881$		−	54.4886i		−	1.83577i	0.396848	−	0.917884i	$-0.370104\pi$
$882$		0			0
$883$	−26.9366	+	26.9366i	−0.906490	+	0.906490i	−0.995987	−	0.0894971i	$-0.971474\pi$
$883$	−26.9366	+	26.9366i	−0.906490	+	0.906490i	0.0894971	+	0.995987i	$0.471474\pi$
$884$	−2.16966	+	3.75796i	−0.0729736	+	0.126394i
$885$		0			0
$886$	−13.7579	−	23.8293i	−0.462205	−	0.800562i
$887$	−11.7970	−	44.0271i	−0.396105	−	1.47829i	−0.819889	−	0.572522i	$-0.805965\pi$
$887$	−11.7970	−	44.0271i	−0.396105	−	1.47829i	0.423784	−	0.905763i	$-0.360702\pi$
$888$		0			0
$889$	−26.2461	−	25.3271i	−0.880266	−	0.849443i
$890$	−7.33471	+	13.2173i	−0.245860	+	0.443045i
$891$		0			0
$892$	−7.16142	+	26.7268i	−0.239782	+	0.894879i
$893$	15.3142	−	57.1534i	0.512471	−	1.91257i
$894$		0			0
$895$	12.1536	−	3.47872i	0.406250	−	0.116281i
$896$	13.2888	−	3.81574i	0.443947	−	0.127475i
$897$		0			0
$898$	6.48030	+	24.1848i	0.216251	+	0.807058i
$899$	−41.5057	−	71.8900i	−1.38429	−	2.39767i
$900$		0			0
$901$	0.915385	−	1.58549i	0.0304959	−	0.0528205i
$902$	5.02243	−	5.02243i	0.167228	−	0.167228i
$903$		0			0
$904$		−	5.39768i		−	0.179524i
$905$	−12.0997	+	48.4309i	−0.402208	+	1.60990i
$906$		0			0
$907$	0.102828	−	0.383760i	0.00341435	−	0.0127425i	−0.964198	−	0.265185i	$-0.914567\pi$
$907$	0.102828	−	0.383760i	0.00341435	−	0.0127425i	0.967612	+	0.252442i	$0.0812337\pi$
$908$	42.9597	−	11.5110i	1.42567	−	0.382007i
$909$		0			0
$910$	−9.05376	+	9.70678i	−0.300129	+	0.321777i
$911$			21.8995i			0.725562i	0.931874	+	0.362781i	$0.118173\pi$
$911$			21.8995i			0.725562i	−0.931874	+	0.362781i	$0.881827\pi$
$912$		0			0
$913$	17.6453	+	4.72804i	0.583973	+	0.156475i
$914$	−4.95136	−	8.57600i	−0.163776	−	0.283669i
$915$		0			0
$916$	11.2980			0.373298
$917$	34.1971	+	18.9395i	1.12929	+	0.625436i
$918$		0			0
$919$	−27.8860	−	16.1000i	−0.919875	−	0.531090i	−0.0362798	−	0.999342i	$-0.511551\pi$
$919$	−27.8860	−	16.1000i	−0.919875	−	0.531090i	−0.883595	+	0.468252i	$0.844884\pi$
$920$	−0.684436	+	0.708078i	−0.0225652	+	0.0233446i
$921$		0			0
$922$	−48.9485	+	13.1157i	−1.61203	+	0.431943i
$923$	−10.0830	−	10.0830i	−0.331886	−	0.331886i
$924$		0			0
$925$	−27.8063	−	6.44753i	−0.914267	−	0.211994i
$926$	20.1141	+	11.6129i	0.660991	+	0.381623i
$927$		0			0
$928$	−70.8256	−	18.9777i	−2.32496	−	0.622972i
$929$	−27.1770	+	47.0719i	−0.891647	+	1.54438i	−0.0537466	+	0.998555i	$0.517116\pi$
$929$	−27.1770	+	47.0719i	−0.891647	+	1.54438i	−0.837900	+	0.545823i	$0.816217\pi$
$930$		0			0
$931$	−37.1151	−	19.6998i	−1.21640	−	0.645634i
$932$	−8.32769	+	8.32769i	−0.272783	+	0.272783i
$933$		0			0
$934$	−16.9132	+	9.76486i	−0.553418	+	0.319516i
$935$	−0.0952570	−	5.61057i	−0.00311524	−	0.183485i
$936$		0			0
$937$	−16.8346	−	16.8346i	−0.549964	−	0.549964i	0.376467	−	0.926430i	$-0.377139\pi$
$937$	−16.8346	−	16.8346i	−0.549964	−	0.549964i	−0.926430	+	0.376467i	$0.877139\pi$
$938$	−32.4663	+	0.578534i	−1.06006	+	0.0188898i
$939$		0			0
$940$	−31.2393	+	18.7502i	−1.01891	+	0.611563i
$941$	10.4837	−	6.05274i	0.341757	−	0.197314i	−0.319292	−	0.947657i	$-0.603445\pi$
$941$	10.4837	−	6.05274i	0.341757	−	0.197314i	0.661049	+	0.750343i	$0.270112\pi$
$942$		0			0
$943$	0.569183	+	2.12422i	0.0185351	+	0.0691741i
$944$	−16.0087			−0.521039
$945$		0			0
$946$	−15.9555			−0.518759
$947$	5.75096	+	21.4629i	0.186881	+	0.697450i	0.994220	+	0.107362i	$0.0342404\pi$
$947$	5.75096	+	21.4629i	0.186881	+	0.697450i	−0.807339	+	0.590088i	$0.799093\pi$
$948$		0			0
$949$	−4.73278	+	2.73247i	−0.153632	+	0.0886997i
$950$	39.1627	−	41.9166i	1.27061	−	1.35996i
$951$		0			0
$952$	−2.02208	−	3.36253i	−0.0655361	−	0.108980i
$953$	20.5298	+	20.5298i	0.665024	+	0.665024i	0.956560	−	0.291536i	$-0.0941663\pi$
$953$	20.5298	+	20.5298i	0.665024	+	0.665024i	−0.291536	+	0.956560i	$0.594166\pi$
$954$		0			0
$955$	9.17228	−	9.48911i	0.296808	−	0.307061i
$956$	−26.8914	+	15.5258i	−0.869730	+	0.502139i
$957$		0			0
$958$	−7.03582	+	7.03582i	−0.227317	+	0.227317i
$959$	−51.2251	−	12.7520i	−1.65414	−	0.411785i
$960$		0			0
$961$	−19.7354	+	34.1827i	−0.636625	+	1.10267i
$962$	−12.3723	−	3.31513i	−0.398897	−	0.106884i
$963$		0			0
$964$	−36.6013	−	21.1318i	−1.17885	−	0.680608i
$965$	−12.3987	+	22.3427i	−0.399127	+	0.719236i
$966$		0			0
$967$	−12.1981	−	12.1981i	−0.392263	−	0.392263i	0.483230	−	0.875493i	$-0.339463\pi$
$967$	−12.1981	−	12.1981i	−0.392263	−	0.392263i	−0.875493	+	0.483230i	$0.839463\pi$
$968$	6.23975	−	1.67194i	0.200553	−	0.0537381i
$969$		0			0
$970$	−46.4002	−	44.8509i	−1.48982	−	1.44008i
$971$	−16.6289	−	9.60073i	−0.533648	−	0.308102i	0.208853	−	0.977947i	$-0.433027\pi$
$971$	−16.6289	−	9.60073i	−0.533648	−	0.308102i	−0.742501	+	0.669845i	$0.766360\pi$
$972$		0			0
$973$	−0.0885648	−	4.97009i	−0.00283926	−	0.159334i
$974$	50.8124			1.62813
$975$		0			0
$976$	11.7785	+	20.4009i	0.377020	+	0.653018i
$977$	8.86259	+	2.37472i	0.283539	+	0.0759741i	0.397786	−	0.917478i	$-0.369779\pi$
$977$	8.86259	+	2.37472i	0.283539	+	0.0759741i	−0.114247	+	0.993452i	$0.536445\pi$
$978$		0			0
$979$		−	3.96918i		−	0.126856i
$980$	8.00164	+	24.6054i	0.255603	+	0.785991i
$981$		0			0
$982$	−9.52683	+	2.55271i	−0.304013	+	0.0814601i
$983$	11.5884	−	43.2486i	0.369614	−	1.37942i	−0.491443	−	0.870910i	$-0.663531\pi$
$983$	11.5884	−	43.2486i	0.369614	−	1.37942i	0.861057	−	0.508508i	$-0.169803\pi$
$984$		0			0
$985$	−15.2653	−	25.4332i	−0.486394	−	0.810371i
$986$			42.2640i			1.34596i
$987$		0			0
$988$	8.23655	−	8.23655i	0.262040	−	0.262040i
$989$	2.47007	−	4.27828i	0.0785435	−	0.136041i
$990$		0			0
$991$	22.5543	+	39.0653i	0.716462	+	1.24095i	0.962393	+	0.271662i	$0.0875732\pi$
$991$	22.5543	+	39.0653i	0.716462	+	1.24095i	−0.245930	+	0.969287i	$0.579093\pi$
$992$	16.1107	+	60.1258i	0.511514	+	1.90900i
$993$		0			0
$994$	−59.0394	+	16.9525i	−1.87262	+	0.537702i
$995$	−7.50147	−	26.2079i	−0.237812	−	0.830845i
$996$		0			0
$997$	13.3278	−	49.7401i	0.422096	−	1.57529i	−0.348087	−	0.937462i	$-0.613169\pi$
$997$	13.3278	−	49.7401i	0.422096	−	1.57529i	0.770183	−	0.637823i	$-0.220165\pi$
$998$	3.82772	−	14.2853i	0.121164	−	0.452192i
$999$		0			0

Display

a_p

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a_n

instead) (See

a_n

instead) Display

a_n

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up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.ce.a.107.4	yes	64
3.2	odd	2	inner	315.2.ce.a.107.13	yes	64
5.3	odd	4	inner	315.2.ce.a.233.4	yes	64
7.4	even	3	inner	315.2.ce.a.242.13	yes	64
15.8	even	4	inner	315.2.ce.a.233.13	yes	64
21.11	odd	6	inner	315.2.ce.a.242.4	yes	64
35.18	odd	12	inner	315.2.ce.a.53.13	yes	64
105.53	even	12	inner	315.2.ce.a.53.4	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.ce.a.53.4	✓	64	105.53	even	12	inner
315.2.ce.a.53.13	yes	64	35.18	odd	12	inner
315.2.ce.a.107.4	yes	64	1.1	even	1	trivial
315.2.ce.a.107.13	yes	64	3.2	odd	2	inner
315.2.ce.a.233.4	yes	64	5.3	odd	4	inner
315.2.ce.a.233.13	yes	64	15.8	even	4	inner
315.2.ce.a.242.4	yes	64	21.11	odd	6	inner
315.2.ce.a.242.13	yes	64	7.4	even	3	inner

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	315.2.ce.a.107.4

Level	$315$
Weight	$2$
Character	315.107
Analytic conductor	$2.515$
Analytic rank	$0$
Dimension	$64$
Inner twists	$8$