LMFDB - Embedded newform 900.2.bj.d.523.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(127,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 1]))

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

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

chi := DirichletCharacter("900.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$900 = 2^{2} \cdot 3^{2} \cdot 5^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	900.bj (of order $20$ , degree $8$ , 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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 100)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			523.1
Character	$\chi$	$=$	900.523
Dual form			900.2.bj.d.487.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37197 - 0.343057i) q^{2} +(1.76462 + 0.941330i) q^{4} +(1.18066 - 1.89896i) q^{5} +(-1.89427 - 1.89427i) q^{7} +(-2.09809 - 1.89685i) q^{8} +(-2.27128 + 2.20029i) q^{10} +(2.99934 + 4.12824i) q^{11} +(0.433317 + 2.73586i) q^{13} +(1.94904 + 3.24872i) q^{14} +(2.22780 + 3.32219i) q^{16} +(4.16697 + 2.12318i) q^{17} +(1.55045 + 4.77181i) q^{19} +(3.87097 - 2.23956i) q^{20} +(-2.69880 - 6.69278i) q^{22} +(0.699923 - 4.41914i) q^{23} +(-2.21209 - 4.48404i) q^{25} +(0.344055 - 3.90218i) q^{26} +(-1.55954 - 5.12580i) q^{28} +(0.211843 + 0.0688321i) q^{29} +(7.01920 - 2.28068i) q^{31} +(-1.91678 - 5.32221i) q^{32} +(-4.98861 - 4.34246i) q^{34} +(-5.83362 + 1.36065i) q^{35} +(4.32186 - 0.684516i) q^{37} +(-0.490182 - 7.07869i) q^{38} +(-6.07916 + 1.74466i) q^{40} +(-2.54404 - 1.84835i) q^{41} +(-2.68807 + 2.68807i) q^{43} +(1.40668 + 10.1082i) q^{44} +(-2.47629 + 5.82283i) q^{46} +(7.84709 - 3.99829i) q^{47} +0.176489i q^{49} +(1.49665 + 6.91086i) q^{50} +(-1.81070 + 5.23565i) q^{52} +(-1.64295 + 0.837124i) q^{53} +(11.3806 - 0.821587i) q^{55} +(0.381206 + 7.56747i) q^{56} +(-0.267030 - 0.167110i) q^{58} +(-7.33328 - 5.32794i) q^{59} +(1.16375 - 0.845512i) q^{61} +(-10.4126 + 0.721044i) q^{62} +(0.803948 + 7.95950i) q^{64} +(5.70688 + 2.40726i) q^{65} +(1.53527 - 3.01313i) q^{67} +(5.35453 + 7.66911i) q^{68} +(8.47035 + 0.134481i) q^{70} +(5.45415 + 1.77216i) q^{71} +(-0.0187149 - 0.00296414i) q^{73} +(-6.16431 - 0.543507i) q^{74} +(-1.75588 + 9.87994i) q^{76} +(2.13843 - 13.5015i) q^{77} +(2.08434 - 6.41493i) q^{79} +(8.93896 - 0.308126i) q^{80} +(2.85627 + 3.40864i) q^{82} +(-2.99552 - 1.52629i) q^{83} +(8.95160 - 5.40616i) q^{85} +(4.61012 - 2.76580i) q^{86} +(1.53775 - 14.3507i) q^{88} +(0.509284 + 0.700969i) q^{89} +(4.36162 - 6.00326i) q^{91} +(5.39497 - 7.13927i) q^{92} +(-12.1376 + 2.79355i) q^{94} +(10.8920 + 2.68963i) q^{95} +(-5.07638 - 9.96296i) q^{97} +(0.0605458 - 0.242139i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$96 q + 10 q^{2} - 10 q^{4} + 20 q^{5} + 10 q^{8} - 10 q^{10} - 20 q^{13} + 10 q^{14} - 14 q^{16} + 20 q^{17} - 10 q^{20} - 10 q^{22} - 20 q^{25} + 12 q^{26} - 10 q^{28} + 20 q^{29} + 50 q^{32} - 60 q^{34}+ \cdots + 130 q^{98}+O(q^{100})$ 96 * q + 10 * q^2 - 10 * q^4 + 20 * q^5 + 10 * q^8 - 10 * q^10 - 20 * q^13 + 10 * q^14 - 14 * q^16 + 20 * q^17 - 10 * q^20 - 10 * q^22 - 20 * q^25 + 12 * q^26 - 10 * q^28 + 20 * q^29 + 50 * q^32 - 60 * q^34 + 40 * q^37 - 20 * q^38 + 40 * q^40 + 28 * q^41 - 60 * q^44 - 6 * q^46 - 80 * q^50 + 80 * q^52 + 40 * q^53 + 6 * q^56 + 60 * q^58 + 12 * q^61 - 40 * q^62 + 20 * q^64 + 100 * q^65 + 10 * q^68 - 10 * q^70 - 20 * q^73 + 20 * q^77 + 10 * q^80 - 50 * q^82 + 100 * q^85 + 6 * q^86 - 130 * q^88 - 160 * q^89 + 110 * q^92 - 170 * q^94 + 180 * q^97 + 130 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$ .

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−1.37197	−	0.343057i	−0.970132	−	0.242578i
$2$	−1.37197	−	0.343057i	−0.970132	−	0.242578i
$3$		0			0
$3$		0			0
$4$	1.76462	+	0.941330i	0.882312	+	0.470665i
$5$	1.18066	−	1.89896i	0.528006	−	0.849240i
$5$	1.18066	−	1.89896i	0.528006	−	0.849240i
$6$		0			0
$7$	−1.89427	−	1.89427i	−0.715965	−	0.715965i	0.251811	−	0.967776i	$-0.418974\pi$
$7$	−1.89427	−	1.89427i	−0.715965	−	0.715965i	−0.967776	+	0.251811i	$0.918974\pi$
$8$	−2.09809	−	1.89685i	−0.741786	−	0.670636i
$9$		0			0
$10$	−2.27128	+	2.20029i	−0.718243	+	0.695793i
$11$	2.99934	+	4.12824i	0.904336	+	1.24471i	0.969064	+	0.246809i	$0.0793819\pi$
$11$	2.99934	+	4.12824i	0.904336	+	1.24471i	−0.0647283	+	0.997903i	$0.520618\pi$
$12$		0			0
$13$	0.433317	+	2.73586i	0.120181	+	0.758790i	0.972005	+	0.234962i	$0.0754966\pi$
$13$	0.433317	+	2.73586i	0.120181	+	0.758790i	−0.851824	+	0.523828i	$0.824503\pi$
$14$	1.94904	+	3.24872i	0.520904	+	0.868258i
$15$		0			0
$16$	2.22780	+	3.32219i	0.556949	+	0.830547i
$17$	4.16697	+	2.12318i	1.01064	+	0.514947i	0.879238	−	0.476383i	$-0.158052\pi$
$17$	4.16697	+	2.12318i	1.01064	+	0.514947i	0.131402	+	0.991329i	$0.458052\pi$
$18$		0			0
$19$	1.55045	+	4.77181i	0.355699	+	1.09473i	0.955603	+	0.294657i	$0.0952052\pi$
$19$	1.55045	+	4.77181i	0.355699	+	1.09473i	−0.599905	+	0.800072i	$0.704795\pi$
$20$	3.87097	−	2.23956i	0.865574	−	0.500781i
$21$		0			0
$22$	−2.69880	−	6.69278i	−0.575386	−	1.42691i
$23$	0.699923	−	4.41914i	0.145944	−	0.921455i	−0.800675	−	0.599100i	$-0.795525\pi$
$23$	0.699923	−	4.41914i	0.145944	−	0.921455i	0.946619	−	0.322355i	$-0.104475\pi$
$24$		0			0
$25$	−2.21209	−	4.48404i	−0.442418	−	0.896809i
$26$	0.344055	−	3.90218i	0.0674747	−	0.765280i
$27$		0			0
$28$	−1.55954	−	5.12580i	−0.294725	−	0.968685i
$29$	0.211843	+	0.0688321i	0.0393383	+	0.0127818i	0.328620	−	0.944462i	$-0.393416\pi$
$29$	0.211843	+	0.0688321i	0.0393383	+	0.0127818i	−0.289282	+	0.957244i	$0.593416\pi$
$30$		0			0
$31$	7.01920	−	2.28068i	1.26069	−	0.409622i	0.398947	−	0.916974i	$-0.369376\pi$
$31$	7.01920	−	2.28068i	1.26069	−	0.409622i	0.861739	+	0.507352i	$0.169376\pi$
$32$	−1.91678	−	5.32221i	−0.338842	−	0.940843i
$33$		0			0
$34$	−4.98861	−	4.34246i	−0.855539	−	0.744725i
$35$	−5.83362	+	1.36065i	−0.986061	+	0.229992i
$36$		0			0
$37$	4.32186	−	0.684516i	0.710510	−	0.112534i	0.209290	−	0.977854i	$-0.432885\pi$
$37$	4.32186	−	0.684516i	0.710510	−	0.112534i	0.501220	+	0.865320i	$0.332885\pi$
$38$	−0.490182	−	7.07869i	−0.0795179	−	1.14832i
$39$		0			0
$40$	−6.07916	+	1.74466i	−0.961199	+	0.275854i
$41$	−2.54404	−	1.84835i	−0.397312	−	0.288664i	0.371133	−	0.928580i	$-0.378969\pi$
$41$	−2.54404	−	1.84835i	−0.397312	−	0.288664i	−0.768445	+	0.639915i	$0.778969\pi$
$42$		0			0
$43$	−2.68807	+	2.68807i	−0.409927	+	0.409927i	−0.881713	−	0.471786i	$-0.843609\pi$
$43$	−2.68807	+	2.68807i	−0.409927	+	0.409927i	0.471786	+	0.881713i	$0.343609\pi$
$44$	1.40668	+	10.1082i	0.212064	+	1.52386i
$45$		0			0
$46$	−2.47629	+	5.82283i	−0.365110	+	0.858530i
$47$	7.84709	−	3.99829i	1.14462	−	0.583211i	0.224351	−	0.974508i	$-0.427974\pi$
$47$	7.84709	−	3.99829i	1.14462	−	0.583211i	0.920264	+	0.391298i	$0.127974\pi$
$48$		0			0
$49$			0.176489i			0.0252127i
$50$	1.49665	+	6.91086i	0.211658	+	0.977344i
$51$		0			0
$52$	−1.81070	+	5.23565i	−0.251099	+	0.726055i
$53$	−1.64295	+	0.837124i	−0.225676	+	0.114988i	−0.563173	−	0.826339i	$-0.690420\pi$
$53$	−1.64295	+	0.837124i	−0.225676	+	0.114988i	0.337497	+	0.941327i	$0.390420\pi$
$54$		0			0
$55$	11.3806	−	0.821587i	1.53455	−	0.110783i
$56$	0.381206	+	7.56747i	0.0509407	+	1.01125i
$57$		0			0
$58$	−0.267030	−	0.167110i	−0.0350628	−	0.0219426i
$59$	−7.33328	−	5.32794i	−0.954712	−	0.693639i	−0.00279513	−	0.999996i	$-0.500890\pi$
$59$	−7.33328	−	5.32794i	−0.954712	−	0.693639i	−0.951917	+	0.306357i	$0.900890\pi$
$60$		0			0
$61$	1.16375	−	0.845512i	0.149003	−	0.108257i	−0.510786	−	0.859708i	$-0.670646\pi$
$61$	1.16375	−	0.845512i	0.149003	−	0.108257i	0.659789	+	0.751451i	$0.270646\pi$
$62$	−10.4126	+	0.721044i	−1.32240	+	0.0915727i
$63$		0			0
$64$	0.803948	+	7.95950i	0.100493	+	0.994938i
$65$	5.70688	+	2.40726i	0.707852	+	0.298584i
$66$		0			0
$67$	1.53527	−	3.01313i	0.187563	−	0.368113i	−0.778007	−	0.628255i	$-0.783769\pi$
$67$	1.53527	−	3.01313i	0.187563	−	0.368113i	0.965570	+	0.260142i	$0.0837695\pi$
$68$	5.35453	+	7.66911i	0.649332	+	0.930016i
$69$		0			0
$70$	8.47035	+	0.134481i	1.01240	+	0.0160736i
$71$	5.45415	+	1.77216i	0.647288	+	0.210317i	0.614218	−	0.789136i	$-0.289471\pi$
$71$	5.45415	+	1.77216i	0.647288	+	0.210317i	0.0330703	+	0.999453i	$0.489471\pi$
$72$		0			0
$73$	−0.0187149	−	0.00296414i	−0.00219041	−	0.000346927i	0.155339	−	0.987861i	$-0.450353\pi$
$73$	−0.0187149	−	0.00296414i	−0.00219041	−	0.000346927i	−0.157530	+	0.987514i	$0.550353\pi$
$74$	−6.16431	−	0.543507i	−0.716586	−	0.0631814i
$75$		0			0
$76$	−1.75588	+	9.87994i	−0.201413	+	1.13331i
$77$	2.13843	−	13.5015i	0.243697	−	1.53864i
$78$		0			0
$79$	2.08434	−	6.41493i	0.234506	−	0.721736i	−0.762680	−	0.646776i	$-0.776117\pi$
$79$	2.08434	−	6.41493i	0.234506	−	0.721736i	0.997187	−	0.0749601i	$-0.0238830\pi$
$80$	8.93896	−	0.308126i	0.999406	−	0.0344495i
$81$		0			0
$82$	2.85627	+	3.40864i	0.315422	+	0.376422i
$83$	−2.99552	−	1.52629i	−0.328801	−	0.167532i	0.281795	−	0.959475i	$-0.409070\pi$
$83$	−2.99552	−	1.52629i	−0.328801	−	0.167532i	−0.610596	+	0.791942i	$0.709070\pi$
$84$		0			0
$85$	8.95160	−	5.40616i	0.970938	−	0.586381i
$86$	4.61012	−	2.76580i	0.497122	−	0.298244i
$87$		0			0
$88$	1.53775	−	14.3507i	0.163925	−	1.52979i
$89$	0.509284	+	0.700969i	0.0539840	+	0.0743026i	0.835156	−	0.550014i	$-0.185378\pi$
$89$	0.509284	+	0.700969i	0.0539840	+	0.0743026i	−0.781172	+	0.624316i	$0.785378\pi$
$90$		0			0
$91$	4.36162	−	6.00326i	0.457222	−	0.629313i
$92$	5.39497	−	7.13927i	0.562465	−	0.744320i
$93$		0			0
$94$	−12.1376	+	2.79355i	−1.25190	+	0.288133i
$95$	10.8920	+	2.68963i	1.11750	+	0.275950i
$96$		0			0
$97$	−5.07638	−	9.96296i	−0.515428	−	1.01158i	−0.991244	−	0.132040i	$-0.957847\pi$
$97$	−5.07638	−	9.96296i	−0.515428	−	1.01158i	0.475816	−	0.879545i	$-0.342153\pi$
$98$	0.0605458	−	0.242139i	0.00611605	−	0.0244597i
$99$		0			0
$100$	0.317454	−	9.99496i	0.0317454	−	0.999496i
$101$	11.8084			1.17498			0.587489	−	0.809232i	$-0.300116\pi$
$101$	11.8084			1.17498			0.587489	+	0.809232i	$0.300116\pi$
$102$		0			0
$103$	−0.880821	−	1.72871i	−0.0867899	−	0.170335i	0.843532	−	0.537079i	$-0.180472\pi$
$103$	−0.880821	−	1.72871i	−0.0867899	−	0.170335i	−0.930322	+	0.366744i	$0.880472\pi$
$104$	4.28036	−	6.56201i	0.419724	−	0.643458i
$105$		0			0
$106$	2.54126	−	0.584888i	0.246829	−	0.0568093i
$107$	8.09772	+	8.09772i	0.782836	+	0.782836i	0.980308	−	0.197472i	$-0.0632733\pi$
$107$	8.09772	+	8.09772i	0.782836	+	0.782836i	−0.197472	+	0.980308i	$0.563273\pi$
$108$		0			0
$109$	−9.13259	+	12.5699i	−0.874743	+	1.20398i	0.103106	+	0.994670i	$0.467122\pi$
$109$	−9.13259	+	12.5699i	−0.874743	+	1.20398i	−0.977849	+	0.209310i	$0.932878\pi$
$110$	−15.8957	−	2.77698i	−1.51559	−	0.264775i
$111$		0			0
$112$	2.07307	−	10.5131i	0.195887	−	0.993399i
$113$	1.26860	+	8.00964i	0.119340	+	0.753483i	0.972684	+	0.232135i	$0.0745710\pi$
$113$	1.26860	+	8.00964i	0.119340	+	0.753483i	−0.853344	+	0.521349i	$0.825429\pi$
$114$		0			0
$115$	−7.56540	−	6.54662i	−0.705477	−	0.610476i
$116$	0.309030	+	0.320877i	0.0286927	+	0.0297927i
$117$		0			0
$118$	8.23328	+	9.82552i	0.757935	+	0.904513i
$119$	−3.87149	−	11.9152i	−0.354899	−	1.09227i
$120$		0			0
$121$	−4.64713	+	14.3024i	−0.422467	+	1.30022i
$122$	−1.88669	+	0.760789i	−0.170813	+	0.0688786i
$123$		0			0
$124$	14.5331	+	2.58285i	1.30511	+	0.231947i
$125$	−11.1267	−	1.09345i	−0.995206	−	0.0978013i
$126$		0			0
$127$	15.8543	+	2.51108i	1.40684	+	0.222822i	0.813237	−	0.581932i	$-0.197703\pi$
$127$	15.8543	+	2.51108i	1.40684	+	0.222822i	0.593608	+	0.804755i	$0.297703\pi$
$128$	1.62757	−	11.1960i	0.143858	−	0.989598i
$129$		0			0
$130$	−7.00386	−	5.26048i	−0.614280	−	0.461375i
$131$	12.9418	−	4.20505i	1.13073	−	0.367397i	0.316878	−	0.948466i	$-0.397365\pi$
$131$	12.9418	−	4.20505i	1.13073	−	0.367397i	0.813854	+	0.581069i	$0.197365\pi$
$132$		0			0
$133$	6.10210	−	11.9761i	0.529119	−	1.03846i
$134$	−3.14002	+	3.60726i	−0.271257	+	0.311619i
$135$		0			0
$136$	−4.71533	−	12.3587i	−0.404337	−	1.05975i
$137$	−18.6626	+	2.95587i	−1.59445	+	0.252537i	−0.889575	−	0.456790i	$-0.848999\pi$
$137$	−18.6626	+	2.95587i	−1.59445	+	0.252537i	−0.704880	+	0.709327i	$0.748999\pi$
$138$		0			0
$139$	5.89560	−	4.28340i	0.500058	−	0.363313i	−0.308981	−	0.951068i	$-0.599988\pi$
$139$	5.89560	−	4.28340i	0.500058	−	0.363313i	0.809039	+	0.587755i	$0.199988\pi$
$140$	−11.5750	−	3.09032i	−0.978263	−	0.261179i
$141$		0			0
$142$	−6.87500	−	4.30244i	−0.576937	−	0.361053i
$143$	−9.99461	+	9.99461i	−0.835792	+	0.835792i
$144$		0			0
$145$	0.380824	−	0.321015i	0.0316257	−	0.0266588i
$146$	0.0246594	+	0.0104870i	0.00204083	+	0.000867909i
$147$		0			0
$148$	8.27082	+	2.86039i	0.679857	+	0.235122i
$149$		−	2.12851i		−	0.174375i	−0.996192	−	0.0871873i	$-0.972212\pi$
$149$		−	2.12851i		−	0.174375i	0.996192	−	0.0871873i	$-0.0277879\pi$
$150$		0			0
$151$			6.10369i			0.496712i	0.968669	+	0.248356i	$0.0798902\pi$
$151$			6.10369i			0.496712i	−0.968669	+	0.248356i	$0.920110\pi$
$152$	5.79840	−	12.9527i	0.470312	−	1.05060i
$153$		0			0
$154$	−7.56567	+	17.7902i	−0.609659	+	1.43357i
$155$	3.95637	−	16.0219i	0.317783	−	1.28691i
$156$		0			0
$157$	−11.4802	+	11.4802i	−0.916218	+	0.916218i	−0.996752	−	0.0805335i	$-0.974338\pi$
$157$	−11.4802	+	11.4802i	−0.916218	+	0.916218i	0.0805335	+	0.996752i	$0.474338\pi$
$158$	−5.06034	+	8.08607i	−0.402579	+	0.643293i
$159$		0			0
$160$	−12.3697	−	2.64383i	−0.977913	−	0.209013i
$161$	−9.69687	+	7.04519i	−0.764221	+	0.555239i
$162$		0			0
$163$	7.81379	−	1.23758i	0.612023	−	0.0969349i	0.157275	−	0.987555i	$-0.449729\pi$
$163$	7.81379	−	1.23758i	0.612023	−	0.0969349i	0.454748	+	0.890620i	$0.349729\pi$
$164$	−2.74936	−	5.65643i	−0.214689	−	0.441693i
$165$		0			0
$166$	3.58617	+	3.12167i	0.278341	+	0.242288i
$167$	−6.13600	+	12.0426i	−0.474818	+	0.931883i	0.522059	+	0.852910i	$0.325164\pi$
$167$	−6.13600	+	12.0426i	−0.474818	+	0.931883i	−0.996877	+	0.0789735i	$0.974836\pi$
$168$		0			0
$169$	5.06658	−	1.64623i	0.389737	−	0.126633i
$170$	−14.1360	+	4.34621i	−1.08418	+	0.333339i
$171$		0			0
$172$	−7.27379	+	2.21307i	−0.554621	+	0.168745i
$173$	−1.08340	−	0.171594i	−0.0823695	−	0.0130460i	0.115114	−	0.993352i	$-0.463277\pi$
$173$	−1.08340	−	0.171594i	−0.0823695	−	0.0130460i	−0.197483	+	0.980306i	$0.563277\pi$
$174$		0			0
$175$	−4.30368	+	12.6843i	−0.325328	+	0.958840i
$176$	−7.03287	+	19.1613i	−0.530122	+	1.44433i
$177$		0			0
$178$	−0.458252	−	1.13642i	−0.0343474	−	0.0851786i
$179$	−7.45601	+	22.9472i	−0.557289	+	1.71516i	0.132533	+	0.991179i	$0.457689\pi$
$179$	−7.45601	+	22.9472i	−0.557289	+	1.71516i	−0.689822	+	0.723979i	$0.742311\pi$
$180$		0			0
$181$	−2.15964	−	6.64670i	−0.160525	−	0.494045i	0.838154	−	0.545434i	$-0.183635\pi$
$181$	−2.15964	−	6.64670i	−0.160525	−	0.494045i	−0.998679	+	0.0513890i	$0.983635\pi$
$182$	−8.04349	+	6.74003i	−0.596223	+	0.499604i
$183$		0			0
$184$	−9.85094	+	7.94410i	−0.726221	+	0.585647i
$185$	3.80277	−	9.01522i	0.279586	−	0.662812i
$186$		0			0
$187$	3.73319	+	23.5704i	0.272998	+	1.72364i
$188$	17.6109	+	0.331219i	1.28440	+	0.0241566i
$189$		0			0
$190$	−14.0209	−	7.42668i	−1.01718	−	0.538788i
$191$	9.26511	−	12.7523i	0.670400	−	0.922727i	−0.329369	−	0.944201i	$-0.606836\pi$
$191$	9.26511	−	12.7523i	0.670400	−	0.922727i	0.999769	+	0.0214746i	$0.00683611\pi$
$192$		0			0
$193$	6.44920	+	6.44920i	0.464223	+	0.464223i	0.900037	−	0.435814i	$-0.143539\pi$
$193$	6.44920	+	6.44920i	0.464223	+	0.464223i	−0.435814	+	0.900037i	$0.643539\pi$
$194$	3.54680	+	15.4104i	0.254645	+	1.10640i
$195$		0			0
$196$	−0.166135	+	0.311437i	−0.0118668	+	0.0222455i
$197$	2.59555	+	5.09406i	0.184925	+	0.362936i	0.964794	−	0.263007i	$-0.0847142\pi$
$197$	2.59555	+	5.09406i	0.184925	+	0.362936i	−0.779869	+	0.625943i	$0.784714\pi$
$198$		0			0
$199$	−24.6399			−1.74668			−0.873338	−	0.487115i	$-0.838049\pi$
$199$	−24.6399			−1.74668			−0.873338	+	0.487115i	$0.838049\pi$
$200$	−3.86438	+	13.6039i	−0.273253	+	0.961942i
$201$		0			0
$202$	−16.2008	−	4.05095i	−1.13988	−	0.285024i
$203$	−0.270901	−	0.531674i	−0.0190136	−	0.0373162i
$204$		0			0
$205$	−6.51359	+	2.64875i	−0.454929	+	0.184997i
$206$	0.615418	+	2.67391i	0.0428782	+	0.186300i
$207$		0			0
$208$	−8.12369	+	7.53449i	−0.563276	+	0.522423i
$209$	−15.0488	+	20.7129i	−1.04095	+	1.43274i
$210$		0			0
$211$	11.6703	+	16.0628i	0.803419	+	1.10581i	0.992306	+	0.123813i	$0.0395122\pi$
$211$	11.6703	+	16.0628i	0.803419	+	1.10581i	−0.188886	+	0.981999i	$0.560488\pi$
$212$	−3.68720	−	0.0693474i	−0.253238	−	0.00476280i
$213$		0			0
$214$	−8.33188	−	13.8878i	−0.569556	−	0.949353i
$215$	1.93084	+	8.27822i	0.131682	+	0.564570i
$216$		0			0
$217$	−17.6165	−	8.97603i	−1.19588	−	0.609333i
$218$	16.8419	−	14.1126i	1.14068	−	0.955827i
$219$		0			0
$220$	20.8558	+	9.26307i	1.40610	+	0.624516i
$221$	−4.00309	+	12.3203i	−0.269277	+	0.828750i
$222$		0			0
$223$	1.81060	−	11.4317i	0.121247	−	0.765524i	−0.849883	−	0.526972i	$-0.823327\pi$
$223$	1.81060	−	11.4317i	0.121247	−	0.765524i	0.971130	−	0.238552i	$-0.0766727\pi$
$224$	−6.45080	+	13.7126i	−0.431012	+	0.916210i
$225$		0			0
$226$	1.00727	−	11.4242i	0.0670028	−	0.759928i
$227$	−15.3359	−	2.42897i	−1.01788	−	0.161216i	−0.374872	−	0.927077i	$-0.622313\pi$
$227$	−15.3359	−	2.42897i	−1.01788	−	0.161216i	−0.643007	+	0.765861i	$0.722313\pi$
$228$		0			0
$229$	−16.0312	−	5.20884i	−1.05937	−	0.344210i	−0.273030	−	0.962006i	$-0.588026\pi$
$229$	−16.0312	−	5.20884i	−1.05937	−	0.344210i	−0.786339	+	0.617796i	$0.788026\pi$
$230$	8.13367	+	11.5772i	0.536318	+	0.763375i
$231$		0			0
$232$	−0.313902	−	0.546250i	−0.0206087	−	0.0358631i
$233$	13.2595	−	26.0233i	0.868660	−	1.70484i	0.174963	−	0.984575i	$-0.444019\pi$
$233$	13.2595	−	26.0233i	0.868660	−	1.70484i	0.693697	−	0.720267i	$-0.255981\pi$
$234$		0			0
$235$	1.67214	−	19.6219i	0.109078	−	1.27999i
$236$	−7.92513	−	16.3048i	−0.515882	−	1.06136i
$237$		0			0
$238$	1.22399	+	17.6755i	0.0793392	+	1.14573i
$239$	0.369981	−	0.268807i	0.0239321	−	0.0173877i	−0.575755	−	0.817622i	$-0.695292\pi$
$239$	0.369981	−	0.268807i	0.0239321	−	0.0173877i	0.599687	+	0.800235i	$0.295292\pi$
$240$		0			0
$241$	17.6697	+	12.8378i	1.13820	+	0.826953i	0.986868	−	0.161530i	$-0.0516429\pi$
$241$	17.6697	+	12.8378i	1.13820	+	0.826953i	0.151335	+	0.988483i	$0.451643\pi$
$242$	11.2823	−	18.0283i	0.725252	−	1.15890i
$243$		0			0
$244$	2.84948	−	0.396541i	0.182419	−	0.0253859i
$245$	0.335146	+	0.208373i	0.0214117	+	0.0133125i
$246$		0			0
$247$	−12.3832	+	6.30953i	−0.787921	+	0.401466i
$248$	−19.0530	−	8.52929i	−1.20987	−	0.541610i
$249$		0			0
$250$	14.8905	+	5.31729i	0.941757	+	0.336295i
$251$			5.42259i			0.342271i	0.985248	+	0.171135i	$0.0547436\pi$
$251$			5.42259i			0.342271i	−0.985248	+	0.171135i	$0.945256\pi$
$252$		0			0
$253$	20.3426	−	10.3651i	1.27893	−	0.651647i
$254$	−20.8903	−	8.88407i	−1.31077	−	0.557436i
$255$		0			0
$256$	−6.07385	+	14.8023i	−0.379616	+	0.925144i
$257$	−8.02192	+	8.02192i	−0.500394	+	0.500394i	−0.911560	−	0.411166i	$-0.865121\pi$
$257$	−8.02192	+	8.02192i	−0.500394	+	0.500394i	0.411166	+	0.911560i	$0.365121\pi$
$258$		0			0
$259$	−9.48341	−	6.89010i	−0.589271	−	0.428130i
$260$	7.80447	+	9.61997i	0.484013	+	0.596605i
$261$		0			0
$262$	−19.1984	+	1.32944i	−1.18608	+	0.0821332i
$263$	−19.6441	+	3.11132i	−1.21131	+	0.191852i	−0.729224	−	0.684275i	$-0.760119\pi$
$263$	−19.6441	+	3.11132i	−1.21131	+	0.191852i	−0.482081	+	0.876127i	$0.660119\pi$
$264$		0			0
$265$	−0.350096	+	4.10825i	−0.0215063	+	0.252368i
$266$	−12.4804	+	14.3375i	−0.765222	+	0.879086i
$267$		0			0
$268$	5.54552	−	3.87185i	0.338747	−	0.236511i
$269$	9.63789	−	3.13154i	0.587633	−	0.190933i	−8.44003e−5	−	1.00000i	$-0.500027\pi$
$269$	9.63789	−	3.13154i	0.587633	−	0.190933i	0.587717	+	0.809067i	$0.300027\pi$
$270$		0			0
$271$	−1.79674	−	0.583795i	−0.109144	−	0.0354630i	0.253936	−	0.967221i	$-0.418275\pi$
$271$	−1.79674	−	0.583795i	−0.109144	−	0.0354630i	−0.363080	+	0.931758i	$0.618275\pi$
$272$	2.22957	+	18.5735i	0.135187	+	1.12618i
$273$		0			0
$274$	26.6186	+	2.34696i	1.60809	+	0.141785i
$275$	11.8764	−	22.5812i	0.716173	−	1.36170i
$276$		0			0
$277$	1.79116	−	11.3089i	0.107620	−	0.679488i	−0.873607	−	0.486632i	$-0.838225\pi$
$277$	1.79116	−	11.3089i	0.107620	−	0.679488i	0.981227	−	0.192855i	$-0.0617748\pi$
$278$	−9.55805	+	3.85419i	−0.573254	+	0.231159i
$279$		0			0
$280$	14.8204	+	8.21070i	0.885688	+	0.490683i
$281$	−7.15917	−	22.0337i	−0.427080	−	1.31442i	−0.900988	−	0.433844i	$-0.857157\pi$
$281$	−7.15917	−	22.0337i	−0.427080	−	1.31442i	0.473908	−	0.880574i	$-0.342843\pi$
$282$		0			0
$283$	−16.9779	−	8.65065i	−1.00923	−	0.514228i	−0.130449	−	0.991455i	$-0.541642\pi$
$283$	−16.9779	−	8.65065i	−1.00923	−	0.514228i	−0.878780	+	0.477227i	$0.841642\pi$
$284$	7.95633	+	8.26135i	0.472122	+	0.490221i
$285$		0			0
$286$	17.1411	−	10.2836i	1.01357	−	0.608084i
$287$	1.31782	+	8.32036i	0.0777882	+	0.491135i
$288$		0			0
$289$	2.86343	+	3.94118i	0.168437	+	0.231834i
$290$	−0.632607	+	0.309780i	−0.0371479	+	0.0181909i
$291$		0			0
$292$	−0.0302344	−	0.0228475i	−0.00176934	−	0.00133705i
$293$	9.23047	+	9.23047i	0.539250	+	0.539250i	0.923309	−	0.384059i	$-0.125474\pi$
$293$	9.23047	+	9.23047i	0.539250	+	0.539250i	−0.384059	+	0.923309i	$0.625474\pi$
$294$		0			0
$295$	−18.7756	+	7.63512i	−1.09316	+	0.444534i
$296$	−10.3661	−	6.76173i	−0.602515	−	0.393018i
$297$		0			0
$298$	−0.730201	+	2.92026i	−0.0422994	+	0.169166i
$299$	12.3934			0.716731
$300$		0			0
$301$	10.1838			0.586986
$302$	2.09391	−	8.37411i	0.120491	−	0.481876i
$303$		0			0
$304$	−12.3987	+	15.7815i	−0.711117	+	0.905132i
$305$	−0.231605	−	3.20817i	−0.0132616	−	0.183699i
$306$		0			0
$307$	−9.17187	−	9.17187i	−0.523466	−	0.523466i	0.395150	−	0.918616i	$-0.370692\pi$
$307$	−9.17187	−	9.17187i	−0.523466	−	0.523466i	−0.918616	+	0.395150i	$0.870692\pi$
$308$	16.4829	−	21.8122i	0.939203	−	1.24286i
$309$		0			0
$310$	−10.9245	+	20.6243i	−0.620467	+	1.17138i
$311$	2.44643	+	3.36722i	0.138724	+	0.190938i	0.872726	−	0.488209i	$-0.162350\pi$
$311$	2.44643	+	3.36722i	0.138724	+	0.190938i	−0.734002	+	0.679147i	$0.762350\pi$
$312$		0			0
$313$	3.50477	+	22.1282i	0.198101	+	1.25076i	0.863529	+	0.504300i	$0.168249\pi$
$313$	3.50477	+	22.1282i	0.198101	+	1.25076i	−0.665427	+	0.746462i	$0.731751\pi$
$314$	19.6889	−	11.8122i	1.11111	−	0.666598i
$315$		0			0
$316$	9.71663	−	9.35789i	0.546603	−	0.526422i
$317$	−5.61291	−	2.85992i	−0.315252	−	0.160629i	0.289204	−	0.957268i	$-0.406609\pi$
$317$	−5.61291	−	2.85992i	−0.315252	−	0.160629i	−0.604456	+	0.796639i	$0.706609\pi$
$318$		0			0
$319$	0.351235	+	1.08099i	0.0196654	+	0.0605239i
$320$	16.0640	+	7.87079i	0.898002	+	0.439990i
$321$		0			0
$322$	15.7208	−	6.33924i	0.876084	−	0.353272i
$323$	−3.67070	+	23.1759i	−0.204243	+	1.28954i
$324$		0			0
$325$	11.3092	−	7.99498i	0.627320	−	0.443482i
$326$	−11.1449	−	0.982643i	−0.617257	−	0.0544235i
$327$		0			0
$328$	1.83158	+	8.70366i	0.101132	+	0.480579i
$329$	−22.4383	−	7.29065i	−1.23706	−	0.401946i
$330$		0			0
$331$	−15.4106	+	5.00720i	−0.847042	+	0.275221i	−0.700206	−	0.713940i	$-0.746909\pi$
$331$	−15.4106	+	5.00720i	−0.847042	+	0.275221i	−0.146835	+	0.989161i	$0.546909\pi$
$332$	−3.84922	−	5.51311i	−0.211253	−	0.302571i
$333$		0			0
$334$	12.5497	−	14.4171i	0.686690	−	0.788869i
$335$	−3.90919	−	6.47289i	−0.213582	−	0.353652i
$336$		0			0
$337$	−19.9748	+	3.16369i	−1.08809	+	0.172337i	−0.674610	−	0.738174i	$-0.735688\pi$
$337$	−19.9748	+	3.16369i	−1.08809	+	0.172337i	−0.413484	+	0.910511i	$0.635688\pi$
$338$	−7.51597	+	0.520462i	−0.408815	+	0.0283094i
$339$		0			0
$340$	20.8852	−	1.11343i	1.13266	−	0.0603845i
$341$	30.4682	+	22.1364i	1.64995	+	1.19876i
$342$		0			0
$343$	−12.9255	+	12.9255i	−0.697914	+	0.697914i
$344$	10.7387	−	0.540952i	0.578990	−	0.0291662i
$345$		0			0
$346$	1.42753	+	0.607091i	0.0767446	+	0.0326374i
$347$	−5.16571	+	2.63206i	−0.277310	+	0.141296i	−0.587115	−	0.809504i	$-0.699736\pi$
$347$	−5.16571	+	2.63206i	−0.277310	+	0.141296i	0.309805	+	0.950800i	$0.399736\pi$
$348$		0			0
$349$			0.0528810i			0.00283065i	0.999999	+	0.00141533i	$0.000450513\pi$
$349$			0.0528810i			0.00283065i	−0.999999	+	0.00141533i	$0.999549\pi$
$350$	10.2560	−	15.9261i	0.548204	−	0.851284i
$351$		0			0
$352$	16.2223	−	23.8761i	0.864652	−	1.27260i
$353$	3.66865	−	1.86927i	0.195263	−	0.0994913i	−0.353626	−	0.935387i	$-0.615051\pi$
$353$	3.66865	−	1.86927i	0.195263	−	0.0994913i	0.548888	+	0.835896i	$0.315051\pi$
$354$		0			0
$355$	9.80475	−	8.26489i	0.520382	−	0.438655i
$356$	0.238851	+	1.71635i	0.0126591	+	0.0909664i
$357$		0			0
$358$	18.1017	−	28.9252i	0.956703	−	1.52874i
$359$	−22.3556	−	16.2423i	−1.17989	−	0.857237i	−0.187726	−	0.982221i	$-0.560112\pi$
$359$	−22.3556	−	16.2423i	−1.17989	−	0.857237i	−0.992159	+	0.124985i	$0.960112\pi$
$360$		0			0
$361$	−4.99493	+	3.62903i	−0.262891	+	0.191002i
$362$	0.682778	+	9.85997i	0.0358860	+	0.518229i
$363$		0			0
$364$	13.3477	−	6.48777i	0.699608	−	0.340052i
$365$	−0.0277246	+	0.0320391i	−0.00145117	+	0.00167700i
$366$		0			0
$367$	3.08204	−	6.04885i	0.160881	−	0.315747i	−0.796468	−	0.604681i	$-0.793301\pi$
$367$	3.08204	−	6.04885i	0.160881	−	0.315747i	0.957349	+	0.288934i	$0.0933007\pi$
$368$	16.2405	−	7.51967i	0.846595	−	0.391990i
$369$		0			0
$370$	−8.31004	+	11.0641i	−0.432018	+	0.575194i
$371$	4.69792	+	1.52645i	0.243904	+	0.0792492i
$372$		0			0
$373$	−11.3458	−	1.79701i	−0.587466	−	0.0930454i	−0.144376	−	0.989523i	$-0.546118\pi$
$373$	−11.3458	−	1.79701i	−0.587466	−	0.0930454i	−0.443089	+	0.896477i	$0.646118\pi$
$374$	2.96416	−	33.6187i	0.153273	−	1.73838i
$375$		0			0
$376$	−24.0480	−	6.49595i	−1.24018	−	0.335003i
$377$	−0.0965194	+	0.609399i	−0.00497100	+	0.0313857i
$378$		0			0
$379$	−3.95657	+	12.1771i	−0.203235	+	0.625494i	0.796546	+	0.604578i	$0.206658\pi$
$379$	−3.95657	+	12.1771i	−0.203235	+	0.625494i	−0.999781	+	0.0209157i	$0.993342\pi$
$380$	16.6885	+	14.9992i	0.856102	+	0.769441i
$381$		0			0
$382$	−17.0863	+	14.3174i	−0.874210	+	0.732542i
$383$	−16.4227	−	8.36780i	−0.839163	−	0.427575i	−0.0190788	−	0.999818i	$-0.506073\pi$
$383$	−16.4227	−	8.36780i	−0.839163	−	0.427575i	−0.820084	+	0.572243i	$0.806073\pi$
$384$		0			0
$385$	−23.1141	−	20.0015i	−1.17800	−	1.01937i
$386$	−6.63569	−	11.0606i	−0.337748	−	0.562968i
$387$		0			0
$388$	0.420528	−	22.3594i	0.0213491	−	1.13513i
$389$	14.6199	+	20.1226i	0.741258	+	1.02025i	0.998545	+	0.0539190i	$0.0171713\pi$
$389$	14.6199	+	20.1226i	0.741258	+	1.02025i	−0.257287	+	0.966335i	$0.582829\pi$
$390$		0			0
$391$	12.2992	−	16.9284i	0.621997	−	0.856105i
$392$	0.334773	−	0.370290i	0.0169086	−	0.0187025i
$393$		0			0
$394$	−1.81348	−	7.87933i	−0.0913617	−	0.396955i
$395$	−9.72080	−	11.5319i	−0.489106	−	0.580233i
$396$		0			0
$397$	12.6438	+	24.8148i	0.634574	+	1.24542i	0.954566	+	0.298001i	$0.0963199\pi$
$397$	12.6438	+	24.8148i	0.634574	+	1.24542i	−0.319992	+	0.947420i	$0.603680\pi$
$398$	33.8053	+	8.45289i	1.69451	+	0.423705i
$399$		0			0
$400$	9.96874	−	17.3385i	0.498437	−	0.866926i
$401$	−10.4612			−0.522406			−0.261203	−	0.965284i	$-0.584119\pi$
$401$	−10.4612			−0.522406			−0.261203	+	0.965284i	$0.584119\pi$
$402$		0			0
$403$	9.28115	+	18.2153i	0.462327	+	0.907368i
$404$	20.8374	+	11.1156i	1.03670	+	0.553021i
$405$		0			0
$406$	0.189275	+	0.822377i	0.00939357	+	0.0408139i
$407$	15.7886	+	15.7886i	0.782611	+	0.782611i
$408$		0			0
$409$	−9.12365	+	12.5576i	−0.451136	+	0.620935i	−0.972641	−	0.232313i	$-0.925371\pi$
$409$	−9.12365	+	12.5576i	−0.451136	+	0.620935i	0.521505	+	0.853248i	$0.325371\pi$
$410$	9.84515	−	1.39949i	0.486217	−	0.0691159i
$411$		0			0
$412$	0.0729673	−	3.87966i	0.00359484	−	0.191137i
$413$	3.79865	+	23.9837i	0.186919	+	1.18016i
$414$		0			0
$415$	−6.43505	+	3.88634i	−0.315884	+	0.190773i
$416$	13.7302	−	7.55024i	0.673181	−	0.370181i
$417$		0			0
$418$	27.7523	−	23.2550i	1.35741	−	1.13744i
$419$	−11.1568	−	34.3371i	−0.545045	−	1.67748i	−0.720883	−	0.693056i	$-0.756264\pi$
$419$	−11.1568	−	34.3371i	−0.545045	−	1.67748i	0.175838	−	0.984419i	$-0.443736\pi$
$420$		0			0
$421$	4.95128	−	15.2385i	0.241311	−	0.742678i	−0.754911	−	0.655828i	$-0.772320\pi$
$421$	4.95128	−	15.2385i	0.241311	−	0.742678i	0.996221	−	0.0868504i	$-0.0276802\pi$
$422$	−10.5009	−	26.0414i	−0.511177	−	1.26768i
$423$		0			0
$424$	5.03495	+	1.36006i	0.244519	+	0.0660504i
$425$	0.302700	−	23.3816i	0.0146831	−	1.13417i
$426$		0			0
$427$	−3.80607	−	0.602823i	−0.184189	−	0.0291726i
$428$	6.66680	+	21.9121i	0.322252	+	1.05916i
$429$		0			0
$430$	0.190836	−	12.0199i	0.00920295	−	0.579651i
$431$	−6.40797	+	2.08208i	−0.308661	+	0.100290i	−0.459252	−	0.888306i	$-0.651882\pi$
$431$	−6.40797	+	2.08208i	−0.308661	+	0.100290i	0.150591	+	0.988596i	$0.451882\pi$
$432$		0			0
$433$	4.78847	−	9.39790i	0.230119	−	0.451634i	−0.746857	−	0.664985i	$-0.768438\pi$
$433$	4.78847	−	9.39790i	0.230119	−	0.451634i	0.976976	+	0.213351i	$0.0684378\pi$
$434$	21.0900	+	18.3583i	1.01235	+	0.881228i
$435$		0			0
$436$	−27.9480	+	13.5844i	−1.33847	+	0.650576i
$437$	22.1725	−	3.51178i	1.06065	−	0.167991i
$438$		0			0
$439$	8.47207	−	6.15532i	0.404350	−	0.293778i	−0.366960	−	0.930237i	$-0.619602\pi$
$439$	8.47207	−	6.15532i	0.404350	−	0.293778i	0.771311	+	0.636459i	$0.219602\pi$
$440$	−25.4358	−	19.8634i	−1.21261	−	0.946951i
$441$		0			0
$442$	9.71869	−	15.5298i	0.462271	−	0.738676i
$443$	−3.27124	+	3.27124i	−0.155421	+	0.155421i	−0.780534	−	0.625113i	$-0.785053\pi$
$443$	−3.27124	+	3.27124i	−0.155421	+	0.155421i	0.625113	+	0.780534i	$0.285053\pi$
$444$		0			0
$445$	1.93240	−	0.139504i	0.0916046	−	0.00661314i
$446$	−6.40583	+	15.0629i	−0.303325	+	0.713247i
$447$		0			0
$448$	13.5545	−	16.6003i	0.640391	−	0.784291i
$449$		−	18.0931i		−	0.853868i	−0.904283	−	0.426934i	$-0.859594\pi$
$449$		−	18.0931i		−	0.853868i	0.904283	−	0.426934i	$-0.140406\pi$
$450$		0			0
$451$		−	16.0463i		−	0.755589i
$452$	−5.30111	+	15.3282i	−0.249343	+	0.720977i
$453$		0			0
$454$	20.2072	+	8.59356i	0.948369	+	0.403316i
$455$	−6.25036	−	15.3703i	−0.293021	−	0.720573i
$456$		0			0
$457$	23.4612	−	23.4612i	1.09747	−	1.09747i	0.102764	−	0.994706i	$-0.467231\pi$
$457$	23.4612	−	23.4612i	1.09747	−	1.09747i	0.994706	−	0.102764i	$-0.0327687\pi$
$458$	20.2074	+	12.6460i	0.944230	+	0.590908i
$459$		0			0
$460$	−7.18756	−	18.6739i	−0.335122	−	0.870674i
$461$	26.1799	−	19.0208i	1.21932	−	0.885887i	0.223275	−	0.974755i	$-0.428325\pi$
$461$	26.1799	−	19.0208i	1.21932	−	0.885887i	0.996043	+	0.0888686i	$0.0283251\pi$
$462$		0			0
$463$	−30.2882	+	4.79718i	−1.40761	+	0.222944i	−0.813560	−	0.581481i	$-0.802473\pi$
$463$	−30.2882	+	4.79718i	−1.40761	+	0.222944i	−0.594054	+	0.804425i	$0.702473\pi$
$464$	0.243271	+	0.857127i	0.0112936	+	0.0397911i
$465$		0			0
$466$	−27.1192	+	31.1545i	−1.25627	+	1.44320i
$467$	−7.07648	+	13.8884i	−0.327460	+	0.642677i	−0.994774	−	0.102100i	$-0.967444\pi$
$467$	−7.07648	+	13.8884i	−0.327460	+	0.642677i	0.667314	+	0.744777i	$0.267444\pi$
$468$		0			0
$469$	−8.61588	+	2.79947i	−0.397844	+	0.129268i
$470$	−9.02556	+	26.3471i	−0.416318	+	1.21530i
$471$		0			0
$472$	5.27958	+	25.0886i	0.243013	+	1.15480i
$473$	−19.1594	−	3.03456i	−0.880952	−	0.139529i
$474$		0			0
$475$	17.9673	−	17.5080i	0.824394	−	0.803322i
$476$	4.38443	−	24.6702i	0.200960	−	1.13076i
$477$		0			0
$478$	−0.599821	+	0.241872i	−0.0274352	+	0.0110630i
$479$	2.15249	−	6.62469i	0.0983498	−	0.302690i	−0.889762	−	0.456424i	$-0.849130\pi$
$479$	2.15249	−	6.62469i	0.0983498	−	0.302690i	0.988112	+	0.153734i	$0.0491300\pi$
$480$		0			0
$481$	3.74547	+	11.5274i	0.170779	+	0.525604i
$482$	−19.8382	−	23.6748i	−0.903606	−	1.07836i
$483$		0			0
$484$	−21.6637	+	20.8639i	−0.984715	+	0.948358i
$485$	−24.9127	−	2.12301i	−1.13123	−	0.0964009i
$486$		0			0
$487$	3.26215	+	20.5964i	0.147822	+	0.933313i	0.944405	+	0.328784i	$0.106639\pi$
$487$	3.26215	+	20.5964i	0.147822	+	0.933313i	−0.796583	+	0.604529i	$0.793361\pi$
$488$	−4.04545	−	0.433491i	−0.183129	−	0.0196232i
$489$		0			0
$490$	−0.388327	−	0.400857i	−0.0175428	−	0.0181089i
$491$	2.89183	−	3.98026i	0.130506	−	0.179627i	−0.738763	−	0.673965i	$-0.764590\pi$
$491$	2.89183	−	3.98026i	0.130506	−	0.179627i	0.869269	+	0.494339i	$0.164590\pi$
$492$		0			0
$493$	0.736603	+	0.736603i	0.0331749	+	0.0331749i
$494$	19.1539	−	4.40839i	0.861774	−	0.198343i
$495$		0			0
$496$	23.2142	+	18.2382i	1.04235	+	0.818921i
$497$	−6.97467	−	13.6886i	−0.312857	−	0.614016i
$498$		0			0
$499$	19.8140			0.886994			0.443497	−	0.896276i	$-0.353738\pi$
$499$	19.8140			0.886994			0.443497	+	0.896276i	$0.353738\pi$
$500$	−18.6052	−	12.4035i	−0.832051	−	0.554700i
$501$		0			0
$502$	1.86026	−	7.43965i	0.0830273	−	0.332048i
$503$	12.4717	+	24.4770i	0.556084	+	1.09138i	0.982398	+	0.186801i	$0.0598118\pi$
$503$	12.4717	+	24.4770i	0.556084	+	1.09138i	−0.426314	+	0.904575i	$0.640188\pi$
$504$		0			0
$505$	13.9417	−	22.4237i	0.620396	−	0.997839i
$506$	−31.4653	+	7.24194i	−1.39880	+	0.321943i
$507$		0			0
$508$	25.6132	+	19.3553i	1.13640	+	0.858751i
$509$	8.04575	−	11.0740i	0.356622	−	0.490847i	−0.592582	−	0.805510i	$-0.701891\pi$
$509$	8.04575	−	11.0740i	0.356622	−	0.490847i	0.949204	+	0.314663i	$0.101891\pi$
$510$		0			0
$511$	0.0298360	+	0.0410658i	0.00131987	+	0.00181664i
$512$	13.4112	−	18.2247i	0.592697	−	0.805426i
$513$		0			0
$514$	13.7578	−	8.25389i	0.606832	−	0.364064i
$515$	−4.32270	−	0.368371i	−0.190481	−	0.0162324i
$516$		0			0
$517$	40.0420	+	20.4024i	1.76105	+	0.897298i
$518$	10.6473	+	12.7064i	0.467815	+	0.558287i
$519$		0			0
$520$	−7.40734	−	15.8757i	−0.324833	−	0.696197i
$521$	−1.41202	+	4.34576i	−0.0618618	+	0.190391i	−0.977211	−	0.212270i	$-0.931915\pi$
$521$	−1.41202	+	4.34576i	−0.0618618	+	0.190391i	0.915349	+	0.402661i	$0.131915\pi$
$522$		0			0
$523$	−5.67302	+	35.8180i	−0.248064	+	1.56621i	0.477859	+	0.878437i	$0.341413\pi$
$523$	−5.67302	+	35.8180i	−0.248064	+	1.56621i	−0.725923	+	0.687776i	$0.758587\pi$
$524$	26.7958	+	4.76219i	1.17058	+	0.208037i
$525$		0			0
$526$	28.0185	+	2.47039i	1.22167	+	0.107714i
$527$	34.0911	+	5.39950i	1.48503	+	0.235206i
$528$		0			0
$529$	2.83537	+	0.921267i	0.123277	+	0.0400551i
$530$	1.88969	−	5.51631i	0.0820828	−	0.239613i
$531$		0			0
$532$	22.0413	−	15.3891i	0.955613	−	0.667204i
$533$	3.95446	−	7.76106i	0.171286	−	0.336169i
$534$		0			0
$535$	24.9379	−	5.81660i	1.07816	−	0.251473i
$536$	−8.93658	+	3.40965i	−0.386001	+	0.147274i
$537$		0			0
$538$	−14.2972	+	0.990047i	−0.616397	+	0.0426840i
$539$	−0.728590	+	0.529352i	−0.0313826	+	0.0228008i
$540$		0			0
$541$	−23.6895	−	17.2114i	−1.01849	−	0.739976i	−0.0525174	−	0.998620i	$-0.516724\pi$
$541$	−23.6895	−	17.2114i	−1.01849	−	0.739976i	−0.965973	+	0.258644i	$0.916724\pi$
$542$	2.26480	+	1.41733i	0.0972815	+	0.0608797i
$543$		0			0
$544$	3.31285	−	26.2472i	0.142037	−	1.12534i
$545$	13.0873	+	32.1832i	0.560599	+	1.37858i
$546$		0			0
$547$	−31.1849	+	15.8895i	−1.33337	+	0.679385i	−0.967876	−	0.251429i	$-0.919100\pi$
$547$	−31.1849	+	15.8895i	−1.33337	+	0.679385i	−0.365493	+	0.930814i	$0.619100\pi$
$548$	−35.7149	−	12.3517i	−1.52567	−	0.527638i
$549$		0			0
$550$	−24.0407	+	26.9066i	−1.02510	+	1.14730i
$551$			1.11760i			0.0476112i
$552$		0			0
$553$	−16.0999	+	8.20329i	−0.684636	+	0.348839i
$554$	−6.33703	+	14.9011i	−0.269235	+	0.633086i
$555$		0			0
$556$	14.4356	−	2.00889i	0.612206	−	0.0851960i
$557$	25.1416	−	25.1416i	1.06528	−	1.06528i	0.0675692	−	0.997715i	$-0.478476\pi$
$557$	25.1416	−	25.1416i	1.06528	−	1.06528i	0.997715	−	0.0675692i	$-0.0215243\pi$
$558$		0			0
$559$	−8.51896	−	6.18939i	−0.360314	−	0.261783i
$560$	−17.5164	−	16.3491i	−0.740205	−	0.690876i
$561$		0			0
$562$	2.26340	+	32.6856i	0.0954756	+	1.37876i
$563$	27.3038	−	4.32450i	1.15072	−	0.182256i	0.448208	−	0.893929i	$-0.352063\pi$
$563$	27.3038	−	4.32450i	1.15072	−	0.182256i	0.702510	+	0.711674i	$0.252063\pi$
$564$		0			0
$565$	16.7078	+	7.04762i	0.702901	+	0.296496i
$566$	20.3255	+	17.6928i	0.854345	+	0.743686i
$567$		0			0
$568$	−8.08177	−	14.0638i	−0.339104	−	0.590105i
$569$	−8.77237	+	2.85032i	−0.367757	+	0.119491i	−0.487065	−	0.873366i	$-0.661932\pi$
$569$	−8.77237	+	2.85032i	−0.367757	+	0.119491i	0.119308	+	0.992857i	$0.461932\pi$
$570$		0			0
$571$	−17.2235	−	5.59625i	−0.720780	−	0.234196i	−0.0744189	−	0.997227i	$-0.523710\pi$
$571$	−17.2235	−	5.59625i	−0.720780	−	0.234196i	−0.646362	+	0.763031i	$0.723710\pi$
$572$	−27.0450	+	8.22851i	−1.13081	+	0.344051i
$573$		0			0
$574$	1.04635	−	11.8674i	0.0436737	−	0.495336i
$575$	−21.3639	+	6.63706i	−0.890937	+	0.276785i
$576$		0			0
$577$	1.72312	−	10.8794i	0.0717345	−	0.452914i	−0.925510	−	0.378724i	$-0.876363\pi$
$577$	1.72312	−	10.8794i	0.0717345	−	0.452914i	0.997244	−	0.0741898i	$-0.0236371\pi$
$578$	−2.57651	−	6.38951i	−0.107169	−	0.265769i
$579$		0			0
$580$	0.974192	−	0.207989i	0.0404511	−	0.00863629i
$581$	2.78310	+	8.56552i	0.115463	+	0.355357i
$582$		0			0
$583$	−8.38362	−	4.27167i	−0.347214	−	0.176914i
$584$	0.0336429	+	0.0417182i	0.00139215	+	0.00172631i
$585$		0			0
$586$	−9.49738	−	15.8305i	−0.392333	−	0.653953i
$587$	7.33025	+	46.2814i	0.302552	+	1.91024i	0.402825	+	0.915277i	$0.368028\pi$
$587$	7.33025	+	46.2814i	0.302552	+	1.91024i	−0.100273	+	0.994960i	$0.531972\pi$
$588$		0			0
$589$	21.7659	+	29.9582i	0.896849	+	1.23441i
$590$	28.3790	−	4.03408i	1.16834	−	0.166080i
$591$		0			0
$592$	11.9023	+	12.8331i	0.489182	+	0.527436i
$593$	11.5238	+	11.5238i	0.473225	+	0.473225i	0.902957	−	0.429731i	$-0.141392\pi$
$593$	11.5238	+	11.5238i	0.473225	+	0.473225i	−0.429731	+	0.902957i	$0.641392\pi$
$594$		0			0
$595$	−27.1974	−	6.71601i	−1.11499	−	0.275329i
$596$	2.00363	−	3.75603i	0.0820720	−	0.153853i
$597$		0			0
$598$	−17.0035	−	4.25165i	−0.695324	−	0.173863i
$599$	−7.21615			−0.294844			−0.147422	−	0.989074i	$-0.547098\pi$
$599$	−7.21615			−0.294844			−0.147422	+	0.989074i	$0.547098\pi$
$600$		0			0
$601$	−15.0642			−0.614483			−0.307241	−	0.951632i	$-0.599406\pi$
$601$	−15.0642			−0.614483			−0.307241	+	0.951632i	$0.599406\pi$
$602$	−13.9720	−	3.49363i	−0.569454	−	0.142390i
$603$		0			0
$604$	−5.74559	+	10.7707i	−0.233785	+	0.438255i
$605$	21.6730	+	25.7110i	0.881133	+	1.04530i
$606$		0			0
$607$	−3.59194	−	3.59194i	−0.145792	−	0.145792i	0.630443	−	0.776235i	$-0.282873\pi$
$607$	−3.59194	−	3.59194i	−0.145792	−	0.145792i	−0.776235	+	0.630443i	$0.782873\pi$
$608$	22.4247	−	17.3984i	0.909442	−	0.705596i
$609$		0			0
$610$	−0.782829	+	4.48098i	−0.0316958	+	0.181430i
$611$	14.3390	+	19.7360i	0.580095	+	0.798433i
$612$		0			0
$613$	−0.788465	−	4.97817i	−0.0318458	−	0.201066i	0.966636	−	0.256155i	$-0.0824558\pi$
$613$	−0.788465	−	4.97817i	−0.0318458	−	0.201066i	−0.998481	+	0.0550888i	$0.982456\pi$
$614$	9.43709	+	15.7300i	0.380850	+	0.634812i
$615$		0			0
$616$	−30.0970	+	24.2711i	−1.21264	+	0.977912i
$617$	16.5627	+	8.43913i	0.666790	+	0.339746i	0.754406	−	0.656408i	$-0.227925\pi$
$617$	16.5627	+	8.43913i	0.666790	+	0.339746i	−0.0876162	+	0.996154i	$0.527925\pi$
$618$		0			0
$619$	−6.54265	−	20.1362i	−0.262971	−	0.809343i	−0.992154	−	0.125024i	$-0.960099\pi$
$619$	−6.54265	−	20.1362i	−0.262971	−	0.809343i	0.729182	−	0.684320i	$-0.239901\pi$
$620$	22.0634	−	24.5484i	0.886087	−	0.985886i
$621$		0			0
$622$	−2.20129	−	5.45901i	−0.0882637	−	0.218886i
$623$	0.363103	−	2.29254i	0.0145474	−	0.0918487i
$624$		0			0
$625$	−15.2133	+	19.8382i	−0.608532	+	0.793529i
$626$	2.78279	−	31.5617i	0.111223	−	1.26146i
$627$		0			0
$628$	−31.0648	+	9.45157i	−1.23962	+	0.377159i
$629$	19.4624	+	6.32373i	0.776018	+	0.252144i
$630$		0			0
$631$	3.22756	−	1.04870i	0.128487	−	0.0417480i	−0.244068	−	0.969758i	$-0.578482\pi$
$631$	3.22756	−	1.04870i	0.128487	−	0.0417480i	0.372555	+	0.928010i	$0.378482\pi$
$632$	−16.5413	+	9.50542i	−0.657976	+	0.378105i
$633$		0			0
$634$	6.71965	+	5.84928i	0.266871	+	0.232305i
$635$	23.4870	−	27.1420i	0.932053	−	1.07710i
$636$		0			0
$637$	−0.482849	+	0.0764758i	−0.0191312	+	0.00303008i
$638$	−0.111044	−	1.60359i	−0.00439629	−	0.0634866i
$639$		0			0
$640$	−19.3392	−	16.3094i	−0.764449	−	0.644684i
$641$	−31.0401	−	22.5519i	−1.22601	−	0.890748i	−0.229425	−	0.973326i	$-0.573685\pi$
$641$	−31.0401	−	22.5519i	−1.22601	−	0.890748i	−0.996585	+	0.0825780i	$0.973685\pi$
$642$		0			0
$643$	6.79295	−	6.79295i	0.267888	−	0.267888i	−0.560361	−	0.828249i	$-0.689338\pi$
$643$	6.79295	−	6.79295i	0.267888	−	0.267888i	0.828249	+	0.560361i	$0.189338\pi$
$644$	−23.7432	+	3.30416i	−0.935613	+	0.130202i
$645$		0			0
$646$	12.9868	−	30.5375i	0.510957	−	1.20148i
$647$	−30.3148	+	15.4461i	−1.19180	+	0.607251i	−0.933417	−	0.358793i	$-0.883188\pi$
$647$	−30.3148	+	15.4461i	−1.19180	+	0.607251i	−0.258379	+	0.966044i	$0.583188\pi$
$648$		0			0
$649$		−	46.2539i		−	1.81562i
$650$	−18.2586	+	7.08922i	−0.716162	+	0.278062i
$651$		0			0
$652$	14.9534	+	5.17148i	0.585619	+	0.202531i
$653$	−5.70477	+	2.90673i	−0.223245	+	0.113749i	−0.562036	−	0.827112i	$-0.689982\pi$
$653$	−5.70477	+	2.90673i	−0.223245	+	0.113749i	0.338791	+	0.940862i	$0.389982\pi$
$654$		0			0
$655$	7.29465	−	29.5407i	0.285025	−	1.15425i
$656$	0.472973	−	12.5695i	0.0184665	−	0.490758i
$657$		0			0
$658$	28.2837	+	17.7002i	1.10261	+	0.690025i
$659$	−11.5792	−	8.41281i	−0.451063	−	0.327716i	0.338952	−	0.940804i	$-0.389927\pi$
$659$	−11.5792	−	8.41281i	−0.451063	−	0.327716i	−0.790015	+	0.613087i	$0.789927\pi$
$660$		0			0
$661$	−0.382235	+	0.277710i	−0.0148672	+	0.0108017i	−0.595194	−	0.803582i	$-0.702925\pi$
$661$	−0.382235	+	0.277710i	−0.0148672	+	0.0108017i	0.580327	+	0.814384i	$0.302925\pi$
$662$	22.8607	−	1.58304i	0.888505	−	0.0615267i
$663$		0			0
$664$	3.38972	+	8.88434i	0.131547	+	0.344779i
$665$	−15.5375	−	25.7273i	−0.602520	−	0.997661i
$666$		0			0
$667$	0.452453	−	0.887989i	0.0175190	−	0.0343831i
$668$	−22.1638	+	15.4746i	−0.857543	+	0.598731i
$669$		0			0
$670$	3.14274	+	10.2217i	0.121414	+	0.394899i
$671$	6.98096	+	2.26825i	0.269497	+	0.0875648i
$672$		0			0
$673$	−21.1799	−	3.35456i	−0.816424	−	0.129309i	−0.265764	−	0.964038i	$-0.585624\pi$
$673$	−21.1799	−	3.35456i	−0.816424	−	0.129309i	−0.550660	+	0.834729i	$0.685624\pi$
$674$	28.4902	+	2.51198i	1.09740	+	0.0967578i
$675$		0			0
$676$	10.4903	+	1.86434i	0.403471	+	0.0717055i
$677$	−6.95245	+	43.8961i	−0.267204	+	1.68706i	0.380191	+	0.924908i	$0.375858\pi$
$677$	−6.95245	+	43.8961i	−0.267204	+	1.68706i	−0.647395	+	0.762155i	$0.724142\pi$
$678$		0			0
$679$	−9.25648	+	28.4885i	−0.355231	+	1.09329i
$680$	−29.0359	−	5.63721i	−1.11348	−	0.216177i
$681$		0			0
$682$	−34.2075	−	40.8229i	−1.30987	−	1.56319i
$683$	−21.8180	−	11.1168i	−0.834843	−	0.425374i	−0.0163335	−	0.999867i	$-0.505199\pi$
$683$	−21.8180	−	11.1168i	−0.834843	−	0.425374i	−0.818510	+	0.574493i	$0.805199\pi$
$684$		0			0
$685$	−16.4211	+	38.9294i	−0.627418	+	1.48742i
$686$	22.1677	−	13.2993i	0.846367	−	0.507770i
$687$		0			0
$688$	−14.9187	−	2.94180i	−0.568771	−	0.112155i
$689$	−3.00217	−	4.13213i	−0.114374	−	0.157422i
$690$		0			0
$691$	9.83947	−	13.5429i	0.374311	−	0.515195i	−0.579755	−	0.814791i	$-0.696852\pi$
$691$	9.83947	−	13.5429i	0.374311	−	0.515195i	0.954066	+	0.299596i	$0.0968518\pi$
$692$	−1.75027	−	1.32264i	−0.0665353	−	0.0502791i
$693$		0			0
$694$	7.99017	−	1.83899i	0.303303	−	0.0698070i
$695$	−1.17332	−	16.2527i	−0.0445065	−	0.616501i
$696$		0			0
$697$	−6.67656	−	13.1035i	−0.252893	−	0.496330i
$698$	0.0181412	−	0.0725513i	0.000686654	−	0.00274611i
$699$		0			0
$700$	−19.5345	+	18.3318i	−0.738333	+	0.692876i
$701$	−50.9450			−1.92417			−0.962083	−	0.272757i	$-0.912064\pi$
$701$	−50.9450			−1.92417			−0.962083	+	0.272757i	$0.912064\pi$
$702$		0			0
$703$	9.96723	+	19.5618i	0.375921	+	0.737787i
$704$	−30.4474	+	27.1922i	−1.14753	+	1.02484i
$705$		0			0
$706$	−5.67456	+	1.30604i	−0.213565	+	0.0491533i
$707$	−22.3682	−	22.3682i	−0.841244	−	0.841244i
$708$		0			0
$709$	23.6335	−	32.5288i	0.887576	−	1.22164i	−0.0866885	−	0.996235i	$-0.527628\pi$
$709$	23.6335	−	32.5288i	0.887576	−	1.22164i	0.974264	−	0.225408i	$-0.0723715\pi$
$710$	−16.2872	+	7.97563i	−0.611247	+	0.299320i
$711$		0			0
$712$	0.261108	−	2.43673i	0.00978544	−	0.0913202i
$713$	−5.16574	−	32.6152i	−0.193458	−	1.22145i
$714$		0			0
$715$	7.17914	+	30.7796i	0.268485	+	1.15109i
$716$	−34.7580	+	33.4747i	−1.29897	+	1.25101i
$717$		0			0
$718$	25.0993	+	29.9533i	0.936698	+	1.11785i
$719$	3.14270	+	9.67223i	0.117203	+	0.360713i	0.992400	−	0.123053i	$-0.0392685\pi$
$719$	3.14270	+	9.67223i	0.117203	+	0.360713i	−0.875197	+	0.483766i	$0.839269\pi$
$720$		0			0
$721$	−1.60612	+	4.94314i	−0.0598152	+	0.184092i
$722$	8.09788	−	3.26539i	0.301372	−	0.121525i
$723$		0			0
$724$	2.44578	−	13.7619i	0.0908966	−	0.511455i
$725$	−0.159971	−	1.10218i	−0.00594117	−	0.0409339i
$726$		0			0
$727$	8.65722	+	1.37117i	0.321078	+	0.0508538i	0.314893	−	0.949127i	$-0.398031\pi$
$727$	8.65722	+	1.37117i	0.321078	+	0.0508538i	0.00618506	+	0.999981i	$0.498031\pi$
$728$	−20.5383	+	4.32204i	−0.761201	+	0.160185i
$729$		0			0
$730$	0.0490287	−	0.0344457i	0.00181463	−	0.00127489i
$731$	−16.9084	+	5.49386i	−0.625378	+	0.203198i
$732$		0			0
$733$	−0.119518	+	0.234567i	−0.00441450	+	0.00866394i	−0.893203	−	0.449653i	$-0.851548\pi$
$733$	−0.119518	+	0.234567i	−0.00441450	+	0.00866394i	0.888789	+	0.458317i	$0.151548\pi$
$734$	−6.30358	+	7.24154i	−0.232669	+	0.267290i
$735$		0			0
$736$	−24.8612	+	4.74538i	−0.916397	+	0.174917i
$737$	17.0437	−	2.69946i	0.627814	−	0.0994360i
$738$		0			0
$739$	−5.97506	+	4.34113i	−0.219796	+	0.159691i	−0.692235	−	0.721672i	$-0.743374\pi$
$739$	−5.97506	+	4.34113i	−0.219796	+	0.159691i	0.472439	+	0.881363i	$0.343374\pi$
$740$	15.1968	−	12.3288i	0.558644	−	0.453216i
$741$		0			0
$742$	−5.92176	−	3.70590i	−0.217395	−	0.136048i
$743$	−7.03452	+	7.03452i	−0.258071	+	0.258071i	−0.824269	−	0.566198i	$-0.808414\pi$
$743$	−7.03452	+	7.03452i	−0.258071	+	0.258071i	0.566198	+	0.824269i	$0.308414\pi$
$744$		0			0
$745$	−4.04196	−	2.51305i	−0.148086	−	0.0920709i
$746$	14.9497	+	6.35772i	0.547349	+	0.232772i
$747$		0			0
$748$	−15.5999	+	45.1071i	−0.570388	+	1.64928i
$749$		−	30.6785i		−	1.12097i
$750$		0			0
$751$			29.2029i			1.06563i	0.846232	+	0.532814i	$0.178866\pi$
$751$			29.2029i			1.06563i	−0.846232	+	0.532814i	$0.821134\pi$
$752$	30.7648	+	17.1621i	1.12188	+	0.625838i
$753$		0			0
$754$	0.341481	−	0.802968i	0.0124360	−	0.0292424i
$755$	11.5907	+	7.20638i	0.421827	+	0.262267i
$756$		0			0
$757$	−20.1848	+	20.1848i	−0.733630	+	0.733630i	−0.971337	−	0.237707i	$-0.923604\pi$
$757$	−20.1848	+	20.1848i	−0.733630	+	0.733630i	0.237707	+	0.971337i	$0.423604\pi$
$758$	9.60573	−	15.3493i	0.348896	−	0.557511i
$759$		0			0
$760$	−17.7506	−	26.3036i	−0.643883	−	0.954131i
$761$	−7.93313	+	5.76375i	−0.287576	+	0.208936i	−0.722215	−	0.691669i	$-0.756876\pi$
$761$	−7.93313	+	5.76375i	−0.287576	+	0.208936i	0.434639	+	0.900605i	$0.356876\pi$
$762$		0			0
$763$	41.1103	−	6.51124i	1.48829	−	0.235723i
$764$	28.3536	−	13.7815i	1.02580	−	0.498599i
$765$		0			0
$766$	19.6609	+	17.1143i	0.710378	+	0.618366i
$767$	11.3988	−	22.3715i	0.411589	−	0.807788i
$768$		0			0
$769$	17.2976	−	5.62032i	0.623766	−	0.202674i	0.0199544	−	0.999801i	$-0.493648\pi$
$769$	17.2976	−	5.62032i	0.623766	−	0.202674i	0.603812	+	0.797127i	$0.293648\pi$
$770$	24.8503	+	35.3710i	0.895543	+	1.27468i
$771$		0			0
$772$	5.30959	+	17.4512i	0.191096	+	0.628084i
$773$	−42.7233	−	6.76671i	−1.53665	−	0.243382i	−0.670025	−	0.742339i	$-0.733717\pi$
$773$	−42.7233	−	6.76671i	−1.53665	−	0.243382i	−0.866627	+	0.498957i	$0.833717\pi$
$774$		0			0
$775$	−25.7538	−	26.4294i	−0.925103	−	0.949370i
$776$	−8.24751	+	30.5323i	−0.296068	+	1.09604i
$777$		0			0
$778$	−13.1549	−	32.6231i	−0.471627	−	1.16959i
$779$	4.87557	−	15.0055i	0.174685	−	0.537626i
$780$		0			0
$781$	9.04296	+	27.8314i	0.323582	+	0.995884i
$782$	−22.6816	+	19.0060i	−0.811091	+	0.679653i
$783$		0			0
$784$	−0.586330	+	0.393182i	−0.0209404	+	0.0140422i
$785$	8.24623	+	35.3546i	0.294320	+	1.26186i
$786$		0			0
$787$	−1.89589	−	11.9702i	−0.0675813	−	0.426691i	−0.998162	−	0.0606043i	$-0.980697\pi$
$787$	−1.89589	−	11.9702i	−0.0675813	−	0.426691i	0.930581	−	0.366087i	$-0.119303\pi$
$788$	−0.215016	+	11.4324i	−0.00765962	+	0.407261i
$789$		0			0
$790$	9.38058	+	19.1563i	0.333746	+	0.681549i
$791$	12.7693	−	17.5755i	0.454025	−	0.624911i
$792$		0			0
$793$	2.81747	+	2.81747i	0.100051	+	0.100051i
$794$	−8.83405	−	38.3829i	−0.313509	−	1.36216i
$795$		0			0
$796$	−43.4802	−	23.1943i	−1.54111	−	0.822099i
$797$	7.47486	+	14.6702i	0.264773	+	0.519646i	0.984668	−	0.174436i	$-0.0558103\pi$
$797$	7.47486	+	14.6702i	0.264773	+	0.519646i	−0.719895	+	0.694083i	$0.755810\pi$
$798$		0			0
$799$	41.1877			1.45712
$800$	−19.6250	+	20.3681i	−0.693847	+	0.720123i
$801$		0			0
$802$	14.3525	+	3.58878i	0.506803	+	0.126724i
$803$	−0.0438956	−	0.0861499i	−0.00154904	−	0.00304016i
$804$		0			0
$805$	1.92984	+	26.7319i	0.0680178	+	0.942177i
$806$	−6.48462	−	28.1749i	−0.228411	−	0.992417i
$807$		0			0
$808$	−24.7750	−	22.3987i	−0.871583	−	0.787984i
$809$	−12.5671	+	17.2972i	−0.441837	+	0.608136i	−0.970619	−	0.240621i	$-0.922649\pi$
$809$	−12.5671	+	17.2972i	−0.441837	+	0.608136i	0.528782	+	0.848757i	$0.322649\pi$
$810$		0			0
$811$	18.5355	+	25.5120i	0.650871	+	0.895847i	0.999136	−	0.0415488i	$-0.0132292\pi$
$811$	18.5355	+	25.5120i	0.650871	+	0.895847i	−0.348265	+	0.937396i	$0.613229\pi$
$812$	0.0224415	−	1.19321i	0.000787542	−	0.0418735i
$813$		0			0
$814$	−16.2451	−	27.0779i	−0.569392	−	0.949080i
$815$	6.87529	−	16.2992i	0.240831	−	0.570937i
$816$		0			0
$817$	−16.9947	−	8.65922i	−0.594569	−	0.302948i
$818$	16.8254	−	14.0988i	0.588286	−	0.492953i
$819$		0			0
$820$	−13.9874	−	1.45738i	−0.488461	−	0.0508940i
$821$	6.22378	−	19.1548i	0.217211	−	0.668508i	−0.781778	−	0.623557i	$-0.785687\pi$
$821$	6.22378	−	19.1548i	0.217211	−	0.668508i	0.998989	−	0.0449507i	$-0.0143131\pi$
$822$		0			0
$823$	6.60034	−	41.6729i	0.230073	−	1.45263i	−0.554289	−	0.832324i	$-0.687010\pi$
$823$	6.60034	−	41.6729i	0.230073	−	1.45263i	0.784363	−	0.620302i	$-0.212990\pi$
$824$	−1.43105	+	5.29776i	−0.0498531	+	0.184556i
$825$		0			0
$826$	3.01613	−	34.2082i	0.104945	−	1.19026i
$827$	13.5996	+	2.15397i	0.472905	+	0.0749008i	0.388338	−	0.921517i	$-0.373049\pi$
$827$	13.5996	+	2.15397i	0.472905	+	0.0749008i	0.0845669	+	0.996418i	$0.473049\pi$
$828$		0			0
$829$	35.5980	+	11.5665i	1.23637	+	0.401721i	0.853018	−	0.521881i	$-0.174770\pi$
$829$	35.5980	+	11.5665i	1.23637	+	0.401721i	0.383352	+	0.923602i	$0.374770\pi$
$830$	10.1620	−	3.12436i	0.352727	−	0.108448i
$831$		0			0
$832$	−21.4277	+	5.64848i	−0.742872	+	0.195826i
$833$	−0.374718	+	0.735426i	−0.0129832	+	0.0254810i
$834$		0			0
$835$	15.6239	+	25.8702i	0.540686	+	0.895275i
$836$	−46.0533	+	22.3846i	−1.59279	+	0.774189i
$837$		0			0
$838$	3.52726	+	50.9370i	0.121847	+	1.75959i
$839$	−6.53213	+	4.74587i	−0.225514	+	0.163846i	−0.694805	−	0.719198i	$-0.744509\pi$
$839$	−6.53213	+	4.74587i	−0.225514	+	0.163846i	0.469291	+	0.883044i	$0.344509\pi$
$840$		0			0
$841$	−23.4214	−	17.0166i	−0.807633	−	0.586780i
$842$	−12.0207	+	19.2082i	−0.414260	+	0.661959i
$843$		0			0
$844$	5.47332	+	39.3305i	0.188400	+	1.35381i
$845$	2.85577	−	11.5649i	0.0982416	−	0.397844i
$846$		0			0
$847$	35.8955	−	18.2897i	1.23338	−	0.628440i
$848$	−6.44124	−	3.59324i	−0.221193	−	0.123392i
$849$		0			0
$850$	−8.43650	+	31.9750i	−0.289370	+	1.09674i
$851$		−	19.5780i		−	0.671126i
$852$		0			0
$853$	−31.0768	+	15.8344i	−1.06405	+	0.542160i	−0.896199	−	0.443652i	$-0.853683\pi$
$853$	−31.0768	+	15.8344i	−1.06405	+	0.542160i	−0.167851	+	0.985812i	$0.553683\pi$
$854$	5.01503	+	2.13276i	0.171611	+	0.0729814i
$855$		0			0
$856$	−1.62960	−	32.3499i	−0.0556986	−	1.10570i
$857$	−31.7738	+	31.7738i	−1.08537	+	1.08537i	−0.0893726	+	0.995998i	$0.528486\pi$
$857$	−31.7738	+	31.7738i	−1.08537	+	1.08537i	−0.995998	+	0.0893726i	$0.971514\pi$
$858$		0			0
$859$	−34.2690	−	24.8979i	−1.16924	−	0.849504i	−0.178324	−	0.983972i	$-0.557068\pi$
$859$	−34.2690	−	24.8979i	−1.16924	−	0.849504i	−0.990918	+	0.134468i	$0.957068\pi$
$860$	−4.38533	+	16.4255i	−0.149538	+	0.560105i
$861$		0			0
$862$	9.50584	−	0.658255i	0.323770	−	0.0224203i
$863$	−16.4649	+	2.60778i	−0.560472	+	0.0887700i	−0.430242	−	0.902714i	$-0.641572\pi$
$863$	−16.4649	+	2.60778i	−0.560472	+	0.0887700i	−0.130230	+	0.991484i	$0.541572\pi$
$864$		0			0
$865$	−1.60498	+	1.85474i	−0.0545708	+	0.0630631i
$866$	−9.79367	+	11.2510i	−0.332802	+	0.382323i
$867$		0			0
$868$	−22.6370	−	32.4222i	−0.768350	−	1.10048i
$869$	32.7340	−	10.6359i	1.11043	−	0.360799i
$870$		0			0
$871$	8.90876	+	2.89463i	0.301862	+	0.0980809i
$872$	43.0042	−	9.04970i	1.45631	−	0.306462i
$873$		0			0
$874$	−31.6248	−	2.78836i	−1.06973	−	0.0943177i
$875$	19.0057	+	23.1483i	0.642511	+	0.782555i
$876$		0			0
$877$	−2.32444	+	14.6759i	−0.0784907	+	0.495571i	0.916856	+	0.399217i	$0.130718\pi$
$877$	−2.32444	+	14.6759i	−0.0784907	+	0.495571i	−0.995347	+	0.0963539i	$0.969282\pi$
$878$	−13.7351	+	5.53854i	−0.463537	+	0.186917i
$879$		0			0
$880$	28.0830	+	35.9780i	0.946679	+	1.21282i
$881$	15.1162	+	46.5230i	0.509279	+	1.56740i	0.793456	+	0.608628i	$0.208280\pi$
$881$	15.1162	+	46.5230i	0.509279	+	1.56740i	−0.284177	+	0.958772i	$0.591720\pi$
$882$		0			0
$883$	−1.45332	−	0.740506i	−0.0489083	−	0.0249200i	0.429365	−	0.903131i	$-0.358737\pi$
$883$	−1.45332	−	0.740506i	−0.0489083	−	0.0249200i	−0.478274	+	0.878211i	$0.658737\pi$
$884$	−18.6614	+	17.9724i	−0.627650	+	0.604477i
$885$		0			0
$886$	5.61028	−	3.36584i	0.188481	−	0.113078i
$887$	−4.23212	−	26.7206i	−0.142101	−	0.897189i	−0.950989	−	0.309226i	$-0.899930\pi$
$887$	−4.23212	−	26.7206i	−0.142101	−	0.897189i	0.808888	−	0.587963i	$-0.200070\pi$
$888$		0			0
$889$	−25.2757	−	34.7890i	−0.847719	−	1.16679i
$890$	−2.69906	−	0.471527i	−0.0904728	−	0.0158056i
$891$		0			0
$892$	13.9560	−	18.4683i	0.467283	−	0.618364i
$893$	31.2456	+	31.2456i	1.04560	+	1.04560i
$894$		0			0
$895$	34.7729	+	41.2515i	1.16233	+	1.37889i
$896$	−24.2913	+	18.1252i	−0.811515	+	0.605521i
$897$		0			0
$898$	−6.20698	+	24.8233i	−0.207130	+	0.828365i
$899$	1.64396			0.0548290
$900$		0			0
$901$	−8.62349			−0.287290
$902$	−5.50478	+	22.0150i	−0.183289	+	0.733021i
$903$		0			0
$904$	12.5314	−	19.2113i	0.416789	−	0.638957i
$905$	−15.1716	−	3.74640i	−0.504321	−	0.124535i
$906$		0			0
$907$	35.5508	+	35.5508i	1.18045	+	1.18045i	0.979629	+	0.200818i	$0.0643600\pi$
$907$	35.5508	+	35.5508i	1.18045	+	1.18045i	0.200818	+	0.979629i	$0.435640\pi$
$908$	−24.7756	−	18.7223i	−0.822208	−	0.621323i
$909$		0			0
$910$	3.30243	+	23.2319i	0.109474	+	0.770131i
$911$	3.41319	+	4.69785i	0.113084	+	0.155647i	0.861807	−	0.507236i	$-0.169333\pi$
$911$	3.41319	+	4.69785i	0.113084	+	0.155647i	−0.748723	+	0.662883i	$0.769333\pi$
$912$		0			0
$913$	−2.68368	−	16.9441i	−0.0888169	−	0.560768i
$914$	−40.2367	+	24.1397i	−1.33091	+	0.798469i
$915$		0			0
$916$	−23.3857	−	24.2822i	−0.772686	−	0.802308i
$917$	−32.4808	−	16.5498i	−1.07261	−	0.546522i
$918$		0			0
$919$	−13.3369	−	41.0468i	−0.439944	−	1.35401i	−0.887934	−	0.459971i	$-0.847860\pi$
$919$	−13.3369	−	41.0468i	−0.439944	−	1.35401i	0.447990	−	0.894039i	$-0.352140\pi$
$920$	3.45494	+	28.0858i	0.113906	+	0.925961i
$921$		0			0
$922$	−42.4433	+	17.1148i	−1.39780	+	0.563647i
$923$	−2.48500	+	15.6897i	−0.0817948	+	0.516432i
$924$		0			0
$925$	−12.6298	−	17.8652i	−0.415264	−	0.587404i
$926$	43.2004	+	3.80897i	1.41965	+	0.125171i
$927$		0			0
$928$	−0.0397177	−	1.25941i	−0.00130380	−	0.0413422i
$929$	−34.3019	−	11.1453i	−1.12541	−	0.365667i	−0.313578	−	0.949562i	$-0.601528\pi$
$929$	−34.3019	−	11.1453i	−1.12541	−	0.365667i	−0.811829	+	0.583895i	$0.801528\pi$
$930$		0			0
$931$	−0.842173	+	0.273639i	−0.0276011	+	0.00896814i
$932$	47.8946	−	33.4397i	1.56884	−	1.09535i
$933$		0			0
$934$	14.4732	−	16.6268i	0.473579	−	0.544047i
$935$	49.1669	+	20.7394i	1.60793	+	0.678252i
$936$		0			0
$937$	37.4056	−	5.92447i	1.22199	−	0.193544i	0.488084	−	0.872796i	$-0.337696\pi$
$937$	37.4056	−	5.92447i	1.22199	−	0.193544i	0.733905	+	0.679252i	$0.237696\pi$
$938$	12.7811	−	0.885062i	0.417319	−	0.0288983i
$939$		0			0
$940$	21.4214	−	33.0513i	0.698689	−	1.07801i
$941$	−25.8261	−	18.7637i	−0.841906	−	0.611680i	0.0809965	−	0.996714i	$-0.474190\pi$
$941$	−25.8261	−	18.7637i	−0.841906	−	0.611680i	−0.922902	+	0.385034i	$0.874190\pi$
$942$		0			0
$943$	−9.94877	+	9.94877i	−0.323977	+	0.323977i
$944$	1.36336	−	36.2321i	0.0443736	−	1.17925i
$945$		0			0
$946$	25.2452	+	10.7361i	0.820793	+	0.349061i
$947$	−3.14898	+	1.60449i	−0.102328	+	0.0521388i	−0.504405	−	0.863467i	$-0.668288\pi$
$947$	−3.14898	+	1.60449i	−0.102328	+	0.0521388i	0.402077	+	0.915606i	$0.368288\pi$
$948$		0			0
$949$		−	0.0524856i		−	0.00170375i
$950$	−30.6568	+	17.8567i	−0.994639	+	0.579348i
$951$		0			0
$952$	−14.4786	+	32.3428i	−0.469255	+	1.04824i
$953$	−48.0361	+	24.4756i	−1.55604	+	0.792843i	−0.999284	−	0.0378308i	$-0.987955\pi$
$953$	−48.0361	+	24.4756i	−1.55604	+	0.792843i	−0.556759	+	0.830674i	$0.687955\pi$
$954$		0			0
$955$	−13.2772	−	32.6502i	−0.429641	−	1.05654i
$956$	0.905914	−	0.126069i	0.0292994	−	0.00407736i
$957$		0			0
$958$	−5.22581	+	8.35047i	−0.168838	+	0.269791i
$959$	40.9512	+	29.7528i	1.32238	+	0.960767i
$960$		0			0
$961$	18.9882	−	13.7957i	0.612523	−	0.445024i
$962$	−1.18414	−	17.1002i	−0.0381783	−	0.551332i
$963$		0			0
$964$	19.0957	+	39.2868i	0.615032	+	1.26534i
$965$	19.8611	−	4.63246i	0.639350	−	0.149124i
$966$		0			0
$967$	7.03165	−	13.8004i	0.226123	−	0.443791i	−0.749873	−	0.661582i	$-0.769885\pi$
$967$	7.03165	−	13.8004i	0.226123	−	0.443791i	0.975995	+	0.217792i	$0.0698853\pi$
$968$	36.8796	−	21.1928i	1.18535	−	0.681163i
$969$		0			0
$970$	33.4513	+	11.4592i	1.07406	+	0.367932i
$971$	−16.7721	−	5.44959i	−0.538242	−	0.174886i	0.0272659	−	0.999628i	$-0.491320\pi$
$971$	−16.7721	−	5.44959i	−0.538242	−	0.174886i	−0.565508	+	0.824743i	$0.691320\pi$
$972$		0			0
$973$	−19.2817	−	3.05393i	−0.618144	−	0.0979044i
$974$	2.59016	−	29.3769i	0.0829940	−	0.941295i
$975$		0			0
$976$	5.40154	+	1.98256i	0.172899	+	0.0634602i
$977$	8.24291	−	52.0437i	0.263714	−	1.66502i	−0.399605	−	0.916687i	$-0.630853\pi$
$977$	8.24291	−	52.0437i	0.263714	−	1.66502i	0.663319	−	0.748337i	$-0.269147\pi$
$978$		0			0
$979$	−1.36625	+	4.20489i	−0.0436656	+	0.134389i
$980$	0.395258	+	0.683183i	0.0126261	+	0.0218235i
$981$		0			0
$982$	−5.33297	+	4.46875i	−0.170182	+	0.142603i
$983$	15.6381	+	7.96803i	0.498779	+	0.254141i	0.685234	−	0.728323i	$-0.259700\pi$
$983$	15.6381	+	7.96803i	0.498779	+	0.254141i	−0.186455	+	0.982463i	$0.559700\pi$
$984$		0			0
$985$	12.7379	+	1.08549i	0.405862	+	0.0345867i
$986$	−0.757903	−	1.26330i	−0.0241366	−	0.0402316i
$987$		0			0
$988$	−27.7910	−	0.522682i	−0.884148	−	0.0166287i
$989$	9.99752	+	13.7604i	0.317903	+	0.437555i
$990$		0			0
$991$	20.0939	−	27.6568i	0.638302	−	0.878548i	−0.360221	−	0.932867i	$-0.617299\pi$
$991$	20.0939	−	27.6568i	0.638302	−	0.878548i	0.998524	+	0.0543192i	$0.0172988\pi$
$992$	−25.5925	−	32.9862i	−0.812563	−	1.04731i
$993$		0			0
$994$	4.87311	+	21.1730i	0.154566	+	0.671568i
$995$	−29.0913	+	46.7902i	−0.922256	+	1.48335i
$996$		0			0
$997$	0.954518	+	1.87335i	0.0302299	+	0.0593295i	0.905628	−	0.424074i	$-0.139400\pi$
$997$	0.954518	+	1.87335i	0.0302299	+	0.0593295i	−0.875398	+	0.483404i	$0.839400\pi$
$998$	−27.1842	−	6.79731i	−0.860502	−	0.215165i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.d.523.1		96
3.2	odd	2		100.2.l.b.23.12	yes	96
4.3	odd	2	inner	900.2.bj.d.523.12		96
12.11	even	2		100.2.l.b.23.1	✓	96
15.2	even	4		500.2.l.e.407.7		96
15.8	even	4		500.2.l.d.407.6		96
15.14	odd	2		500.2.l.f.343.1		96
25.12	odd	20	inner	900.2.bj.d.487.12		96
60.23	odd	4		500.2.l.d.407.5		96
60.47	odd	4		500.2.l.e.407.8		96
60.59	even	2		500.2.l.f.343.12		96
75.38	even	20		500.2.l.f.207.12		96
75.41	odd	10		500.2.l.e.43.8		96
75.59	odd	10		500.2.l.d.43.5		96
75.62	even	20		100.2.l.b.87.1	yes	96
100.87	even	20	inner	900.2.bj.d.487.1		96
300.59	even	10		500.2.l.d.43.6		96
300.191	even	10		500.2.l.e.43.7		96
300.263	odd	20		500.2.l.f.207.1		96
300.287	odd	20		100.2.l.b.87.12	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.2.l.b.23.1	✓	96	12.11	even	2
100.2.l.b.23.12	yes	96	3.2	odd	2
100.2.l.b.87.1	yes	96	75.62	even	20
100.2.l.b.87.12	yes	96	300.287	odd	20
500.2.l.d.43.5		96	75.59	odd	10
500.2.l.d.43.6		96	300.59	even	10
500.2.l.d.407.5		96	60.23	odd	4
500.2.l.d.407.6		96	15.8	even	4
500.2.l.e.43.7		96	300.191	even	10
500.2.l.e.43.8		96	75.41	odd	10
500.2.l.e.407.7		96	15.2	even	4
500.2.l.e.407.8		96	60.47	odd	4
500.2.l.f.207.1		96	300.263	odd	20
500.2.l.f.207.12		96	75.38	even	20
500.2.l.f.343.1		96	15.14	odd	2
500.2.l.f.343.12		96	60.59	even	2
900.2.bj.d.487.1		96	100.87	even	20	inner
900.2.bj.d.487.12		96	25.12	odd	20	inner
900.2.bj.d.523.1		96	1.1	even	1	trivial
900.2.bj.d.523.12		96	4.3	odd	2	inner

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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	900.2.bj.d.523.1

Level	$900$
Weight	$2$
Character	900.523
Analytic conductor	$7.187$
Analytic rank	$0$
Dimension	$96$
Inner twists	$4$