LMFDB - Embedded newform 276.2.k.a.17.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(5,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 1]))

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

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

chi := DirichletCharacter("276.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.k (of order $22$, degree $10$, 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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			17.6
Character	$\chi$	$=$	276.17
Dual form			276.2.k.a.65.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38367 + 1.04185i) q^{3} +(-2.86447 + 1.84088i) q^{5} +(-2.95914 - 0.425460i) q^{7} +(0.829091 + 2.88316i) q^{9} +O(q^{10})$	\(q+(1.38367 + 1.04185i) q^{3} +(-2.86447 + 1.84088i) q^{5} +(-2.95914 - 0.425460i) q^{7} +(0.829091 + 2.88316i) q^{9} +(1.62503 + 3.55832i) q^{11} +(0.542486 + 3.77307i) q^{13} +(-5.88140 - 0.437175i) q^{15} +(2.99087 - 3.45165i) q^{17} +(-1.65675 + 1.43558i) q^{19} +(-3.65121 - 3.67168i) q^{21} +(3.59974 - 3.16890i) q^{23} +(2.73925 - 5.99811i) q^{25} +(-1.85663 + 4.85313i) q^{27} +(-6.23639 - 5.40386i) q^{29} +(10.2658 - 3.01431i) q^{31} +(-1.45873 + 6.61659i) q^{33} +(9.25957 - 4.22870i) q^{35} +(-3.75681 + 5.84570i) q^{37} +(-3.18036 + 5.78588i) q^{39} +(4.45727 + 6.93564i) q^{41} +(0.0854712 - 0.291088i) q^{43} +(-7.68245 - 6.73245i) q^{45} -1.92803i q^{47} +(1.85902 + 0.545859i) q^{49} +(7.73448 - 1.65990i) q^{51} +(-0.0778671 + 0.541578i) q^{53} +(-11.2053 - 7.20120i) q^{55} +(-3.78806 + 0.260286i) q^{57} +(9.74390 - 1.40096i) q^{59} +(0.844930 + 2.87757i) q^{61} +(-1.22673 - 8.88441i) q^{63} +(-8.49971 - 9.80919i) q^{65} +(0.864289 + 0.394707i) q^{67} +(8.28237 - 0.634322i) q^{69} +(10.6096 + 4.84523i) q^{71} +(-0.782217 - 0.902726i) q^{73} +(10.0394 - 5.44553i) q^{75} +(-3.29477 - 11.2209i) q^{77} +(-2.71809 + 0.390802i) q^{79} +(-7.62522 + 4.78080i) q^{81} +(1.72273 + 1.10713i) q^{83} +(-2.21317 + 15.3930i) q^{85} +(-2.99909 - 13.9746i) q^{87} +(-2.53362 - 0.743938i) q^{89} -11.3958i q^{91} +(17.3450 + 6.52463i) q^{93} +(2.10297 - 7.16205i) q^{95} +(-7.53991 - 11.7323i) q^{97} +(-8.91191 + 7.63540i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + 6 q^{9}+O(q^{10}) $ 80 * q - 2 * q^3 + 6 * q^9	$ 80 q - 2 q^{3} + 6 q^{9} - 4 q^{13} + 11 q^{15} + 33 q^{21} + 25 q^{27} + 20 q^{31} + 11 q^{33} - 44 q^{37} - 18 q^{39} - 44 q^{43} - 100 q^{49} - 98 q^{55} - 33 q^{57} - 44 q^{61} - 55 q^{63} - 22 q^{67} - 41 q^{69} - 26 q^{73} - 65 q^{75} - 44 q^{79} - 42 q^{81} + 2 q^{85} - 64 q^{87} - 46 q^{93} + 66 q^{97} - 66 q^{99}+O(q^{100}) $ 80 * q - 2 * q^3 + 6 * q^9 - 4 * q^13 + 11 * q^15 + 33 * q^21 + 25 * q^27 + 20 * q^31 + 11 * q^33 - 44 * q^37 - 18 * q^39 - 44 * q^43 - 100 * q^49 - 98 * q^55 - 33 * q^57 - 44 * q^61 - 55 * q^63 - 22 * q^67 - 41 * q^69 - 26 * q^73 - 65 * q^75 - 44 * q^79 - 42 * q^81 + 2 * q^85 - 64 * q^87 - 46 * q^93 + 66 * q^97 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{7}{22}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	1.38367	+	1.04185i	0.798863	+	0.601513i
$3$	1.38367	+	1.04185i	0.798863	+	0.601513i
$4$		0			0
$5$	−2.86447	+	1.84088i	−1.28103	+	0.823267i	−0.991014	−	0.133756i	$-0.957296\pi$
$5$	−2.86447	+	1.84088i	−1.28103	+	0.823267i	−0.290014	+	0.957023i	$0.593660\pi$
$6$		0			0
$7$	−2.95914	−	0.425460i	−1.11845	−	0.160809i	−0.441799	−	0.897114i	$-0.645660\pi$
$7$	−2.95914	−	0.425460i	−1.11845	−	0.160809i	−0.676649	+	0.736305i	$0.736569\pi$
$8$		0			0
$9$	0.829091	+	2.88316i	0.276364	+	0.961053i
$10$		0			0
$11$	1.62503	+	3.55832i	0.489965	+	1.07287i	0.979602	+	0.200948i	$0.0644021\pi$
$11$	1.62503	+	3.55832i	0.489965	+	1.07287i	−0.489637	+	0.871927i	$0.662871\pi$
$12$		0			0
$13$	0.542486	+	3.77307i	0.150459	+	1.04646i	0.915453	+	0.402425i	$0.131833\pi$
$13$	0.542486	+	3.77307i	0.150459	+	1.04646i	−0.764994	+	0.644037i	$0.777258\pi$
$14$		0			0
$15$	−5.88140	−	0.437175i	−1.51857	−	0.112878i
$16$		0			0
$17$	2.99087	−	3.45165i	0.725392	−	0.837147i	−0.266552	−	0.963820i	$-0.585885\pi$
$17$	2.99087	−	3.45165i	0.725392	−	0.837147i	0.991944	+	0.126673i	$0.0404300\pi$
$18$		0			0
$19$	−1.65675	+	1.43558i	−0.380084	+	0.329345i	−0.823860	−	0.566793i	$-0.808184\pi$
$19$	−1.65675	+	1.43558i	−0.380084	+	0.329345i	0.443776	+	0.896138i	$0.353639\pi$
$20$		0			0
$21$	−3.65121	−	3.67168i	−0.796759	−	0.801226i
$22$		0			0
$23$	3.59974	−	3.16890i	0.750597	−	0.660761i
$23$	3.59974	−	3.16890i	0.750597	−	0.660761i
$24$		0			0
$25$	2.73925	−	5.99811i	0.547849	−	1.19962i
$26$		0			0
$27$	−1.85663	+	4.85313i	−0.357309	+	0.933986i
$28$		0			0
$29$	−6.23639	−	5.40386i	−1.15807	−	1.00347i	−0.999871	−	0.0160649i	$-0.994886\pi$
$29$	−6.23639	−	5.40386i	−1.15807	−	1.00347i	−0.158198	−	0.987407i	$-0.550568\pi$
$30$		0			0
$31$	10.2658	−	3.01431i	1.84379	−	0.541386i	0.843804	−	0.536652i	$-0.180311\pi$
$31$	10.2658	−	3.01431i	1.84379	−	0.541386i	0.999989	−	0.00473452i	$-0.00150705\pi$
$32$		0			0
$33$	−1.45873	+	6.61659i	−0.253933	+	1.15180i
$34$		0			0
$35$	9.25957	−	4.22870i	1.56515	−	0.714781i
$36$		0			0
$37$	−3.75681	+	5.84570i	−0.617615	+	0.961028i	0.381710	+	0.924282i	$0.375335\pi$
$37$	−3.75681	+	5.84570i	−0.617615	+	0.961028i	−0.999325	+	0.0367455i	$0.988301\pi$
$38$		0			0
$39$	−3.18036	+	5.78588i	−0.509265	+	0.926483i
$40$		0			0
$41$	4.45727	+	6.93564i	0.696108	+	1.08317i	0.991790	+	0.127879i	$0.0408168\pi$
$41$	4.45727	+	6.93564i	0.696108	+	1.08317i	−0.295682	+	0.955286i	$0.595547\pi$
$42$		0			0
$43$	0.0854712	−	0.291088i	0.0130342	−	0.0443905i	−0.952719	−	0.303852i	$-0.901727\pi$
$43$	0.0854712	−	0.291088i	0.0130342	−	0.0443905i	0.965753	+	0.259462i	$0.0835452\pi$
$44$		0			0
$45$	−7.68245	−	6.73245i	−1.14523	−	1.00361i
$46$		0			0
$47$		−	1.92803i		−	0.281232i	−0.990064	−	0.140616i	$-0.955092\pi$
$47$		−	1.92803i		−	0.281232i	0.990064	−	0.140616i	$-0.0449084\pi$
$48$		0			0
$49$	1.85902	+	0.545859i	0.265575	+	0.0779798i
$50$		0			0
$51$	7.73448	−	1.65990i	1.08304	−	0.232433i
$52$		0			0
$53$	−0.0778671	+	0.541578i	−0.0106959	+	0.0743914i	−0.994470	−	0.105019i	$-0.966510\pi$
$53$	−0.0778671	+	0.541578i	−0.0106959	+	0.0743914i	0.983774	+	0.179410i	$0.0574189\pi$
$54$		0			0
$55$	−11.2053	−	7.20120i	−1.51092	−	0.971010i
$56$		0			0
$57$	−3.78806	+	0.260286i	−0.501741	+	0.0344757i
$58$		0			0
$59$	9.74390	−	1.40096i	1.26855	−	0.182390i	0.525017	−	0.851092i	$-0.324059\pi$
$59$	9.74390	−	1.40096i	1.26855	−	0.182390i	0.743530	+	0.668702i	$0.233150\pi$
$60$		0			0
$61$	0.844930	+	2.87757i	0.108182	+	0.368435i	0.995734	−	0.0922738i	$-0.0294135\pi$
$61$	0.844930	+	2.87757i	0.108182	+	0.368435i	−0.887551	+	0.460709i	$0.847595\pi$
$62$		0			0
$63$	−1.22673	−	8.88441i	−0.154553	−	1.11933i
$64$		0			0
$65$	−8.49971	−	9.80919i	−1.05426	−	1.21668i
$66$		0			0
$67$	0.864289	+	0.394707i	0.105590	+	0.0482212i	0.467510	−	0.883988i	$-0.345151\pi$
$67$	0.864289	+	0.394707i	0.105590	+	0.0482212i	−0.361920	+	0.932209i	$0.617879\pi$
$68$		0			0
$69$	8.28237	−	0.634322i	0.997080	−	0.0763634i
$70$		0			0
$71$	10.6096	+	4.84523i	1.25913	+	0.575023i	0.929407	−	0.369056i	$-0.120319\pi$
$71$	10.6096	+	4.84523i	1.25913	+	0.575023i	0.329718	+	0.944079i	$0.393046\pi$
$72$		0			0
$73$	−0.782217	−	0.902726i	−0.0915516	−	0.105656i	0.708125	−	0.706087i	$-0.249541\pi$
$73$	−0.782217	−	0.902726i	−0.0915516	−	0.105656i	−0.799677	+	0.600431i	$0.794996\pi$
$74$		0			0
$75$	10.0394	−	5.44553i	1.15925	−	0.628795i
$76$		0			0
$77$	−3.29477	−	11.2209i	−0.375474	−	1.27875i
$78$		0			0
$79$	−2.71809	+	0.390802i	−0.305809	+	0.0439686i	−0.293511	−	0.955956i	$-0.594824\pi$
$79$	−2.71809	+	0.390802i	−0.305809	+	0.0439686i	−0.0122977	+	0.999924i	$0.503915\pi$
$80$		0			0
$81$	−7.62522	+	4.78080i	−0.847246	+	0.531200i
$82$		0			0
$83$	1.72273	+	1.10713i	0.189094	+	0.121524i	0.631763	−	0.775162i	$-0.282332\pi$
$83$	1.72273	+	1.10713i	0.189094	+	0.121524i	−0.442668	+	0.896685i	$0.645968\pi$
$84$		0			0
$85$	−2.21317	+	15.3930i	−0.240052	+	1.66960i
$86$		0			0
$87$	−2.99909	−	13.9746i	−0.321536	−	1.49823i
$88$		0			0
$89$	−2.53362	−	0.743938i	−0.268563	−	0.0788573i	0.144678	−	0.989479i	$-0.453785\pi$
$89$	−2.53362	−	0.743938i	−0.268563	−	0.0788573i	−0.413242	+	0.910621i	$0.635603\pi$
$90$		0			0
$91$		−	11.3958i		−	1.19461i
$92$		0			0
$93$	17.3450	+	6.52463i	1.79859	+	0.676572i
$94$		0			0
$95$	2.10297	−	7.16205i	0.215760	−	0.734811i
$96$		0			0
$97$	−7.53991	−	11.7323i	−0.765562	−	1.19124i	−0.976873	−	0.213818i	$-0.931410\pi$
$97$	−7.53991	−	11.7323i	−0.765562	−	1.19124i	0.211312	−	0.977419i	$-0.432226\pi$
$98$		0			0
$99$	−8.91191	+	7.63540i	−0.895681	+	0.767386i
$100$		0			0
$101$	−5.25905	+	8.18324i	−0.523295	+	0.814263i	−0.997821	−	0.0659785i	$-0.978983\pi$
$101$	−5.25905	+	8.18324i	−0.523295	+	0.814263i	0.474526	+	0.880241i	$0.342619\pi$
$102$		0			0
$103$	6.92555	−	3.16279i	0.682395	−	0.311639i	−0.0438869	−	0.999037i	$-0.513974\pi$
$103$	6.92555	−	3.16279i	0.682395	−	0.311639i	0.726282	+	0.687397i	$0.241247\pi$
$104$		0			0
$105$	17.2179	+	3.79596i	1.68029	+	0.370448i
$106$		0			0
$107$	5.41925	−	1.59124i	0.523899	−	0.153831i	−0.00908065	−	0.999959i	$-0.502891\pi$
$107$	5.41925	−	1.59124i	0.523899	−	0.153831i	0.532979	+	0.846128i	$0.321072\pi$
$108$		0			0
$109$	−7.44839	−	6.45407i	−0.713426	−	0.618187i	0.220611	−	0.975362i	$-0.429195\pi$
$109$	−7.44839	−	6.45407i	−0.713426	−	0.618187i	−0.934038	+	0.357174i	$0.883740\pi$
$110$		0			0
$111$	−11.2885	+	4.17450i	−1.07146	+	0.396226i
$112$		0			0
$113$	−3.00794	+	6.58648i	−0.282964	+	0.619604i	−0.996732	−	0.0807778i	$-0.974260\pi$
$113$	−3.00794	+	6.58648i	−0.282964	+	0.619604i	0.713768	+	0.700382i	$0.246987\pi$
$114$		0			0
$115$	−4.47776	+	15.7039i	−0.417553	+	1.46439i
$116$		0			0
$117$	−10.4286	+	4.69230i	−0.964125	+	0.433803i
$118$		0			0
$119$	−10.3189	+	8.94140i	−0.945934	+	0.819657i
$120$		0			0
$121$	−2.81746	+	3.25152i	−0.256133	+	0.295593i
$122$		0			0
$123$	−1.05852	+	14.2405i	−0.0954433	+	1.28402i
$124$		0			0
$125$	0.772423	+	5.37232i	0.0690876	+	0.480515i
$126$		0			0
$127$	2.76720	+	6.05932i	0.245549	+	0.537677i	0.991772	−	0.128019i	$-0.0408619\pi$
$127$	2.76720	+	6.05932i	0.245549	+	0.537677i	−0.746223	+	0.665696i	$0.768135\pi$
$128$		0			0
$129$	0.421535	−	0.313722i	0.0371141	−	0.0276217i
$130$		0			0
$131$	−4.98158	−	0.716244i	−0.435243	−	0.0625785i	−0.0787889	−	0.996891i	$-0.525105\pi$
$131$	−4.98158	−	0.716244i	−0.435243	−	0.0625785i	−0.356454	+	0.934313i	$0.616014\pi$
$132$		0			0
$133$	5.51333	−	3.54320i	0.478066	−	0.307235i
$134$		0			0
$135$	−3.61577	−	17.3195i	−0.311196	−	1.49062i
$136$		0			0
$137$	−6.95643			−0.594328			−0.297164	−	0.954826i	$-0.596041\pi$
$137$	−6.95643			−0.594328			−0.297164	+	0.954826i	$0.596041\pi$
$138$		0			0
$139$	5.37578			0.455968			0.227984	−	0.973665i	$-0.426787\pi$
$139$	5.37578			0.455968			0.227984	+	0.973665i	$0.426787\pi$
$140$		0			0
$141$	2.00872	−	2.66776i	0.169165	−	0.224666i
$142$		0			0
$143$	−12.5443	+	8.06170i	−1.04900	+	0.674153i
$144$		0			0
$145$	27.8118	+	3.99873i	2.30964	+	0.332077i
$146$		0			0
$147$	2.00357	+	2.69212i	0.165252	+	0.222042i
$148$		0			0
$149$	8.32132	+	18.2212i	0.681709	+	1.49274i	0.860822	+	0.508907i	$0.169950\pi$
$149$	8.32132	+	18.2212i	0.681709	+	1.49274i	−0.179112	+	0.983829i	$0.557323\pi$
$150$		0			0
$151$	2.81257	+	19.5618i	0.228883	+	1.59192i	0.702825	+	0.711363i	$0.251922\pi$
$151$	2.81257	+	19.5618i	0.228883	+	1.59192i	−0.473942	+	0.880556i	$0.657169\pi$
$152$		0			0
$153$	12.4313	+	5.76142i	1.00501	+	0.465783i
$154$		0			0
$155$	−23.8570	+	27.5325i	−1.91624	+	2.21146i
$156$		0			0
$157$	14.0729	−	12.1943i	1.12314	−	0.973208i	0.123325	−	0.992366i	$-0.460644\pi$
$157$	14.0729	−	12.1943i	1.12314	−	0.973208i	0.999816	+	0.0191585i	$0.00609871\pi$
$158$		0			0
$159$	−0.671986	+	0.668240i	−0.0532920	+	0.0529948i
$160$		0			0
$161$	−12.0003	+	7.84566i	−0.945760	+	0.618324i
$162$		0			0
$163$	6.35455	−	13.9145i	0.497727	−	1.08987i	−0.479474	−	0.877556i	$-0.659173\pi$
$163$	6.35455	−	13.9145i	0.497727	−	1.08987i	0.977201	−	0.212314i	$-0.0681001\pi$
$164$		0			0
$165$	−8.00185	−	21.6383i	−0.622943	−	1.68454i
$166$		0			0
$167$	−3.69780	−	3.20416i	−0.286145	−	0.247946i	0.499947	−	0.866056i	$-0.333353\pi$
$167$	−3.69780	−	3.20416i	−0.286145	−	0.247946i	−0.786091	+	0.618111i	$0.787898\pi$
$168$		0			0
$169$	−1.46839	+	0.431158i	−0.112953	+	0.0331660i
$170$		0			0
$171$	−5.51261	−	3.58644i	−0.421560	−	0.274262i
$172$		0			0
$173$	5.29172	−	2.41665i	0.402322	−	0.183734i	−0.203969	−	0.978977i	$-0.565384\pi$
$173$	5.29172	−	2.41665i	0.402322	−	0.183734i	0.606291	+	0.795243i	$0.292657\pi$
$174$		0			0
$175$	−10.6578	+	16.5838i	−0.805651	+	1.25362i
$176$		0			0
$177$	14.9419	+	8.21322i	1.12311	+	0.617344i
$178$		0			0
$179$	−2.91024	−	4.52843i	−0.217522	−	0.338470i	0.715294	−	0.698823i	$-0.246293\pi$
$179$	−2.91024	−	4.52843i	−0.217522	−	0.338470i	−0.932816	+	0.360353i	$0.882656\pi$
$180$		0			0
$181$	1.04094	−	3.54512i	0.0773726	−	0.263507i	−0.911718	−	0.410817i	$-0.865243\pi$
$181$	1.04094	−	3.54512i	0.0773726	−	0.263507i	0.989090	+	0.147310i	$0.0470616\pi$
$182$		0			0
$183$	−1.82889	+	4.86190i	−0.135196	+	0.359402i
$184$		0			0
$185$		−	23.6606i		−	1.73957i
$186$		0			0
$187$	17.1423	+	5.03344i	1.25357	+	0.368082i
$188$		0			0
$189$	7.55885	−	13.5712i	0.549825	−	0.987157i
$190$		0			0
$191$	3.21612	−	22.3686i	0.232710	−	1.61854i	−0.453584	−	0.891213i	$-0.649855\pi$
$191$	3.21612	−	22.3686i	0.232710	−	1.61854i	0.686295	−	0.727324i	$-0.259236\pi$
$192$		0			0
$193$	−19.2442	−	12.3675i	−1.38523	−	0.890234i	−0.385755	−	0.922601i	$-0.626059\pi$
$193$	−19.2442	−	12.3675i	−1.38523	−	0.890234i	−0.999476	+	0.0323673i	$0.989695\pi$
$194$		0			0
$195$	−1.54109	−	22.4281i	−0.110359	−	1.60611i
$196$		0			0
$197$	−14.8010	+	2.12806i	−1.05453	+	0.151618i	−0.647706	−	0.761891i	$-0.724271\pi$
$197$	−14.8010	+	2.12806i	−1.05453	+	0.151618i	−0.406820	+	0.913509i	$0.633362\pi$
$198$		0			0
$199$	3.26918	+	11.1338i	0.231746	+	0.789255i	0.990456	+	0.137827i	$0.0440117\pi$
$199$	3.26918	+	11.1338i	0.231746	+	0.789255i	−0.758710	+	0.651428i	$0.774170\pi$
$200$		0			0
$201$	0.784665	+	1.44661i	0.0553460	+	0.102036i
$202$		0			0
$203$	16.1552	+	18.6441i	1.13387	+	1.30856i
$204$		0			0
$205$	−25.5354	−	11.6616i	−1.78347	−	0.814482i
$206$		0			0
$207$	12.1209	+	7.75131i	0.842464	+	0.538753i
$208$		0			0
$209$	−7.80053	−	3.56238i	−0.539574	−	0.246415i
$210$		0			0
$211$	−15.9998	−	18.4648i	−1.10147	−	1.27117i	−0.959626	−	0.281281i	$-0.909241\pi$
$211$	−15.9998	−	18.4648i	−1.10147	−	1.27117i	−0.141849	−	0.989888i	$-0.545305\pi$
$212$		0			0
$213$	9.63215	+	17.7578i	0.659984	+	1.21675i
$214$		0			0
$215$	0.291029	+	0.991154i	0.0198480	+	0.0675962i
$216$		0			0
$217$	−31.6604	+	4.55208i	−2.14925	+	0.309015i
$218$		0			0
$219$	−0.141824	−	2.06403i	−0.00958358	−	0.139474i
$220$		0			0
$221$	14.6458	+	9.41230i	0.985185	+	0.633140i
$222$		0			0
$223$	0.820932	−	5.70971i	0.0549737	−	0.382350i	−0.943697	−	0.330810i	$-0.892678\pi$
$223$	0.820932	−	5.70971i	0.0549737	−	0.382350i	0.998671	−	0.0515399i	$-0.0164129\pi$
$224$		0			0
$225$	19.5646	+	2.92470i	1.30431	+	0.194980i
$226$		0			0
$227$	−0.659378	−	0.193611i	−0.0437644	−	0.0128504i	0.259777	−	0.965669i	$-0.416351\pi$
$227$	−0.659378	−	0.193611i	−0.0437644	−	0.0128504i	−0.303541	+	0.952818i	$0.598169\pi$
$228$		0			0
$229$			15.7780i			1.04264i	0.853362	+	0.521319i	$0.174560\pi$
$229$			15.7780i			1.04264i	−0.853362	+	0.521319i	$0.825440\pi$
$230$		0			0
$231$	7.13168	−	18.9588i	0.469230	−	1.24739i
$232$		0			0
$233$	3.09597	−	10.5439i	0.202824	−	0.690754i	−0.793765	−	0.608224i	$-0.791882\pi$
$233$	3.09597	−	10.5439i	0.202824	−	0.690754i	0.996589	−	0.0825292i	$-0.0262998\pi$
$234$		0			0
$235$	3.54928	+	5.52278i	0.231529	+	0.360266i
$236$		0			0
$237$	−4.16809	−	2.29110i	−0.270747	−	0.148823i
$238$		0			0
$239$	−6.42062	+	9.99069i	−0.415316	+	0.646244i	−0.984382	−	0.176048i	$-0.943669\pi$
$239$	−6.42062	+	9.99069i	−0.415316	+	0.646244i	0.569066	+	0.822292i	$0.307305\pi$
$240$		0			0
$241$	20.6830	−	9.44559i	1.33231	−	0.608444i	0.383277	−	0.923633i	$-0.374795\pi$
$241$	20.6830	−	9.44559i	1.33231	−	0.608444i	0.949029	+	0.315190i	$0.102068\pi$
$242$		0			0
$243$	−15.5317	−	1.32928i	−0.996358	−	0.0852734i
$244$		0			0
$245$	−6.32997	+	1.85865i	−0.404407	+	0.118745i
$246$		0			0
$247$	−6.31532	−	5.47226i	−0.401834	−	0.348191i
$248$		0			0
$249$	1.23023	+	3.32674i	0.0779624	+	0.210823i
$250$		0			0
$251$	0.225005	−	0.492693i	0.0142022	−	0.0310985i	−0.902398	−	0.430904i	$-0.858195\pi$
$251$	0.225005	−	0.492693i	0.0142022	−	0.0310985i	0.916600	+	0.399805i	$0.130922\pi$
$252$		0			0
$253$	17.1256	+	7.65946i	1.07668	+	0.481546i
$254$		0			0
$255$	−19.0995	+	18.9930i	−1.19606	+	1.18939i
$256$		0			0
$257$	16.4766	−	14.2771i	1.02778	−	0.890579i	0.0337252	−	0.999431i	$-0.489263\pi$
$257$	16.4766	−	14.2771i	1.02778	−	0.890579i	0.994058	+	0.108852i	$0.0347174\pi$
$258$		0			0
$259$	13.6040	−	15.6999i	0.845312	−	0.975542i
$260$		0			0
$261$	10.4097	−	22.4608i	0.644342	−	1.39029i
$262$		0			0
$263$	−3.00836	−	20.9236i	−0.185503	−	1.29020i	−0.843478	−	0.537164i	$-0.819496\pi$
$263$	−3.00836	−	20.9236i	−0.185503	−	1.29020i	0.657974	−	0.753040i	$-0.271413\pi$
$264$		0			0
$265$	−0.773932	−	1.69467i	−0.0475423	−	0.104103i
$266$		0			0
$267$	−2.73063	−	3.66902i	−0.167112	−	0.224541i
$268$		0			0
$269$	26.0162	+	3.74056i	1.58623	+	0.228066i	0.878264	−	0.478176i	$-0.158702\pi$
$269$	26.0162	+	3.74056i	1.58623	+	0.228066i	0.707971	+	0.706242i	$0.249611\pi$
$270$		0			0
$271$	−13.4236	+	8.62684i	−0.815427	+	0.524043i	−0.880617	−	0.473830i	$-0.842871\pi$
$271$	−13.4236	+	8.62684i	−0.815427	+	0.524043i	0.0651892	+	0.997873i	$0.479235\pi$
$272$		0			0
$273$	11.8728	−	15.7681i	0.718573	−	0.954329i
$274$		0			0
$275$	25.7946			1.55547
$276$		0			0
$277$	−8.36257			−0.502458			−0.251229	−	0.967928i	$-0.580835\pi$
$277$	−8.36257			−0.502458			−0.251229	+	0.967928i	$0.580835\pi$
$278$		0			0
$279$	17.2020	+	27.0988i	1.02986	+	1.62236i
$280$		0			0
$281$	−19.7159	+	12.6706i	−1.17615	+	0.755866i	−0.974675	−	0.223627i	$-0.928210\pi$
$281$	−19.7159	+	12.6706i	−1.17615	+	0.755866i	−0.201476	+	0.979493i	$0.564574\pi$
$282$		0			0
$283$	9.95437	+	1.43122i	0.591726	+	0.0850773i	0.431672	−	0.902031i	$-0.357924\pi$
$283$	9.95437	+	1.43122i	0.591726	+	0.0850773i	0.160054	+	0.987108i	$0.448833\pi$
$284$		0			0
$285$	10.3716	−	7.71894i	0.614361	−	0.457231i
$286$		0			0
$287$	−10.2388	−	22.4199i	−0.604379	−	1.32340i
$288$		0			0
$289$	−0.549215	−	3.81987i	−0.0323068	−	0.224699i
$290$		0			0
$291$	1.79059	−	24.0891i	0.104966	−	1.41213i
$292$		0			0
$293$	11.5999	−	13.3870i	0.677673	−	0.782076i	−0.307884	−	0.951424i	$-0.599621\pi$
$293$	11.5999	−	13.3870i	0.677673	−	0.782076i	0.985556	+	0.169348i	$0.0541662\pi$
$294$		0			0
$295$	−25.3321	+	21.9504i	−1.47489	+	1.27800i
$296$		0			0
$297$	−20.2861	+	1.27999i	−1.17712	+	0.0742727i
$298$		0			0
$299$	13.9093	+	11.8630i	0.804395	+	0.686054i
$300$		0			0
$301$	−0.376767	+	0.825005i	−0.0217165	+	0.0475525i
$302$		0			0
$303$	−15.8025	+	5.84377i	−0.907831	+	0.335716i
$304$		0			0
$305$	−7.71753	−	6.68728i	−0.441904	−	0.382912i
$306$		0			0
$307$	−6.52779	+	1.91673i	−0.372561	+	0.109394i	−0.462652	−	0.886540i	$-0.653102\pi$
$307$	−6.52779	+	1.91673i	−0.372561	+	0.109394i	0.0900916	+	0.995933i	$0.471284\pi$
$308$		0			0
$309$	12.8778	+	2.83913i	0.732595	+	0.161512i
$310$		0			0
$311$	−10.2245	+	4.66937i	−0.579777	+	0.264775i	−0.683644	−	0.729816i	$-0.739606\pi$
$311$	−10.2245	+	4.66937i	−0.579777	+	0.264775i	0.103866	+	0.994591i	$0.466879\pi$
$312$		0			0
$313$	4.57884	−	7.12481i	0.258811	−	0.402718i	−0.687394	−	0.726284i	$-0.741246\pi$
$313$	4.57884	−	7.12481i	0.258811	−	0.402718i	0.946205	+	0.323566i	$0.104882\pi$
$314$		0			0
$315$	19.8690	+	23.1908i	1.11949	+	1.30665i
$316$		0			0
$317$	−16.9261	−	26.3375i	−0.950665	−	1.47926i	−0.876147	−	0.482044i	$-0.839894\pi$
$317$	−16.9261	−	26.3375i	−0.950665	−	1.47926i	−0.0745181	−	0.997220i	$-0.523742\pi$
$318$		0			0
$319$	9.09436	−	30.9725i	0.509186	−	1.73413i
$320$		0			0
$321$	9.15629	+	3.44431i	0.511054	+	0.192242i
$322$		0			0
$323$			10.0121i			0.557091i
$324$		0			0
$325$	24.1173	+	7.08149i	1.33779	+	0.392810i
$326$		0			0
$327$	−3.58194	−	16.6904i	−0.198082	−	0.922982i
$328$		0			0
$329$	−0.820300	+	5.70531i	−0.0452246	+	0.314544i
$330$		0			0
$331$	−6.39842	−	4.11202i	−0.351689	−	0.226017i	0.352853	−	0.935679i	$-0.385211\pi$
$331$	−6.39842	−	4.11202i	−0.351689	−	0.226017i	−0.704543	+	0.709662i	$0.748848\pi$
$332$		0			0
$333$	−19.9688	−	5.98485i	−1.09429	−	0.327968i
$334$		0			0
$335$	−3.20233	+	0.460426i	−0.174962	+	0.0251558i
$336$		0			0
$337$	7.56804	+	25.7744i	0.412258	+	1.40402i	0.860200	+	0.509958i	$0.170339\pi$
$337$	7.56804	+	25.7744i	0.412258	+	1.40402i	−0.447942	+	0.894063i	$0.647843\pi$
$338$		0			0
$339$	−11.0241	+	5.97969i	−0.598749	+	0.324772i
$340$		0			0
$341$	27.4081	+	31.6307i	1.48423	+	1.71290i
$342$		0			0
$343$	13.7670	+	6.28716i	0.743346	+	0.339475i
$344$		0			0
$345$	−22.5568	+	17.0638i	−1.21442	+	0.918686i
$346$		0			0
$347$	−20.3111	−	9.27576i	−1.09036	−	0.497949i	−0.212641	−	0.977130i	$-0.568206\pi$
$347$	−20.3111	−	9.27576i	−1.09036	−	0.497949i	−0.877716	+	0.479181i	$0.840934\pi$
$348$		0			0
$349$	0.0970529	+	0.112005i	0.00519512	+	0.00599549i	0.758341	−	0.651858i	$-0.226010\pi$
$349$	0.0970529	+	0.112005i	0.00519512	+	0.00599549i	−0.753146	+	0.657853i	$0.771465\pi$
$350$		0			0
$351$	−19.3184	−	4.37246i	−1.03114	−	0.233385i
$352$		0			0
$353$	1.52276	+	5.18604i	0.0810483	+	0.276025i	0.990039	−	0.140790i	$-0.0449643\pi$
$353$	1.52276	+	5.18604i	0.0810483	+	0.276025i	−0.908991	+	0.416815i	$0.863146\pi$
$354$		0			0
$355$	−39.3103	+	5.65196i	−2.08637	+	0.299975i
$356$		0			0
$357$	−23.5936	+	1.62117i	−1.24871	+	0.0858014i
$358$		0			0
$359$	10.3640	+	6.66054i	0.546991	+	0.351530i	0.784768	−	0.619790i	$-0.212782\pi$
$359$	10.3640	+	6.66054i	0.546991	+	0.351530i	−0.237776	+	0.971320i	$0.576419\pi$
$360$		0			0
$361$	−2.02006	+	14.0498i	−0.106319	+	0.739464i
$362$		0			0
$363$	−7.28604	+	1.56366i	−0.382418	+	0.0820709i
$364$		0			0
$365$	3.90244	+	1.14586i	0.204263	+	0.0599771i
$366$		0			0
$367$		−	27.2067i		−	1.42018i	−0.704112	−	0.710088i	$-0.748655\pi$
$367$		−	27.2067i		−	1.42018i	0.704112	−	0.710088i	$-0.251345\pi$
$368$		0			0
$369$	−16.3011	+	18.6013i	−0.848600	+	0.968344i
$370$		0			0
$371$	0.460839	−	1.56947i	0.0239256	−	0.0814830i
$372$		0			0
$373$	−14.1406	−	22.0033i	−0.732175	−	1.13929i	−0.985130	−	0.171809i	$-0.945039\pi$
$373$	−14.1406	−	22.0033i	−0.732175	−	1.13929i	0.252955	−	0.967478i	$-0.418597\pi$
$374$		0			0
$375$	−4.52838	+	8.23828i	−0.233845	+	0.425423i
$376$		0			0
$377$	17.0060	−	26.4619i	0.875855	−	1.36286i
$378$		0			0
$379$	28.0766	−	12.8222i	1.44220	−	0.658631i	0.467879	−	0.883792i	$-0.345018\pi$
$379$	28.0766	−	12.8222i	1.44220	−	0.658631i	0.974321	+	0.225161i	$0.0722910\pi$
$380$		0			0
$381$	−2.48402	+	11.2671i	−0.127260	+	0.577231i
$382$		0			0
$383$	6.56957	−	1.92900i	0.335689	−	0.0985673i	−0.109544	−	0.993982i	$-0.534939\pi$
$383$	6.56957	−	1.92900i	0.335689	−	0.0985673i	0.445233	+	0.895415i	$0.353121\pi$
$384$		0			0
$385$	30.0942	+	26.0767i	1.53374	+	1.32899i
$386$		0			0
$387$	0.910117	+	0.00508843i	0.0462639	+	0.000258659i
$388$		0			0
$389$	−8.30247	+	18.1799i	−0.420952	+	0.921756i	0.573757	+	0.819025i	$0.305485\pi$
$389$	−8.30247	+	18.1799i	−0.420952	+	0.921756i	−0.994709	+	0.102731i	$0.967242\pi$
$390$		0			0
$391$	−0.171577	−	21.9028i	−0.00867701	−	1.10767i
$392$		0			0
$393$	−6.14665	−	6.18112i	−0.310058	−	0.311796i
$394$		0			0
$395$	7.06644	−	6.12311i	0.355551	−	0.308087i
$396$		0			0
$397$	7.27775	−	8.39898i	0.365260	−	0.421533i	−0.543135	−	0.839645i	$-0.682763\pi$
$397$	7.27775	−	8.39898i	0.365260	−	0.421533i	0.908395	+	0.418113i	$0.137308\pi$
$398$		0			0
$399$	11.3201	+	0.841445i	0.566715	+	0.0421249i
$400$		0			0
$401$	4.07046	+	28.3107i	0.203269	+	1.41377i	0.794499	+	0.607265i	$0.207734\pi$
$401$	4.07046	+	28.3107i	0.203269	+	1.41377i	−0.591230	+	0.806503i	$0.701357\pi$
$402$		0			0
$403$	16.9423	+	37.0984i	0.843955	+	1.84800i
$404$		0			0
$405$	13.0413	−	27.7316i	0.648026	−	1.37799i
$406$		0			0
$407$	−26.9058	−	3.86847i	−1.33367	−	0.191753i
$408$		0			0
$409$	0.828026	−	0.532140i	0.0409432	−	0.0263126i	−0.520009	−	0.854161i	$-0.674071\pi$
$409$	0.828026	−	0.532140i	0.0409432	−	0.0263126i	0.560952	+	0.827848i	$0.310435\pi$
$410$		0			0
$411$	−9.62541	−	7.24757i	−0.474786	−	0.357496i
$412$		0			0
$413$	−29.4296			−1.44813
$414$		0			0
$415$	−6.97280			−0.342281
$416$		0			0
$417$	7.43832	+	5.60077i	0.364256	+	0.274271i
$418$		0			0
$419$	18.7030	−	12.0197i	0.913702	−	0.587201i	0.00287821	−	0.999996i	$-0.499084\pi$
$419$	18.7030	−	12.0197i	0.913702	−	0.587201i	0.910824	+	0.412795i	$0.135447\pi$
$420$		0			0
$421$	21.8392	+	3.14000i	1.06438	+	0.153034i	0.652183	−	0.758061i	$-0.273853\pi$
$421$	21.8392	+	3.14000i	1.06438	+	0.153034i	0.412195	+	0.911096i	$0.364762\pi$
$422$		0			0
$423$	5.55882	−	1.59851i	0.270279	−	0.0777224i
$424$		0			0
$425$	−12.5106	−	27.3945i	−0.606855	−	1.32883i
$426$		0			0
$427$	−1.27597	−	8.87460i	−0.0617488	−	0.429472i
$428$		0			0
$429$	−25.7562	−	1.91450i	−1.24352	−	0.0924331i
$430$		0			0
$431$	6.22491	−	7.18393i	0.299843	−	0.346038i	−0.585756	−	0.810487i	$-0.699202\pi$
$431$	6.22491	−	7.18393i	0.299843	−	0.346038i	0.885600	+	0.464450i	$0.153748\pi$
$432$		0			0
$433$	−20.1501	+	17.4602i	−0.968353	+	0.839083i	−0.986996	−	0.160744i	$-0.948611\pi$
$433$	−20.1501	+	17.4602i	−0.968353	+	0.839083i	0.0186433	+	0.999826i	$0.494065\pi$
$434$		0			0
$435$	34.3163	+	34.5087i	1.64534	+	1.65456i
$436$		0			0
$437$	−1.41465	+	10.4178i	−0.0676718	+	0.498350i
$438$		0			0
$439$	12.0364	−	26.3561i	0.574468	−	1.25791i	−0.369916	−	0.929065i	$-0.620614\pi$
$439$	12.0364	−	26.3561i	0.574468	−	1.25791i	0.944384	−	0.328844i	$-0.106659\pi$
$440$		0			0
$441$	−0.0324971	+	5.81243i	−0.00154748	+	0.276782i
$442$		0			0
$443$	10.9119	+	9.45519i	0.518439	+	0.449230i	0.874354	−	0.485288i	$-0.161285\pi$
$443$	10.9119	+	9.45519i	0.518439	+	0.449230i	−0.355915	+	0.934518i	$0.615831\pi$
$444$		0			0
$445$	8.62697	−	2.53311i	0.408958	−	0.120081i
$446$		0			0
$447$	−7.46976	+	33.8817i	−0.353308	+	1.60255i
$448$		0			0
$449$	9.10020	−	4.15592i	0.429465	−	0.196130i	−0.188942	−	0.981988i	$-0.560506\pi$
$449$	9.10020	−	4.15592i	0.429465	−	0.196130i	0.618407	+	0.785858i	$0.287778\pi$
$450$		0			0
$451$	−17.4360	+	27.1310i	−0.821031	+	1.27755i
$452$		0			0
$453$	−16.4888	+	29.9974i	−0.774714	+	1.40940i
$454$		0			0
$455$	20.9784	+	32.6430i	0.983482	+	1.53033i
$456$		0			0
$457$	−5.07186	+	17.2732i	−0.237251	+	0.808004i	0.751667	+	0.659543i	$0.229250\pi$
$457$	−5.07186	+	17.2732i	−0.237251	+	0.808004i	−0.988918	+	0.148461i	$0.952568\pi$
$458$		0			0
$459$	11.1984	+	20.9235i	0.522694	+	0.976627i
$460$		0			0
$461$			17.7515i			0.826770i	0.910556	+	0.413385i	$0.135654\pi$
$461$			17.7515i			0.826770i	−0.910556	+	0.413385i	$0.864346\pi$
$462$		0			0
$463$	−8.06685	−	2.36864i	−0.374898	−	0.110080i	0.0888548	−	0.996045i	$-0.471679\pi$
$463$	−8.06685	−	2.36864i	−0.374898	−	0.110080i	−0.463753	+	0.885965i	$0.653497\pi$
$464$		0			0
$465$	−61.6951	+	13.2404i	−2.86104	+	0.614010i
$466$		0			0
$467$	0.273762	−	1.90405i	0.0126682	−	0.0881091i	−0.982506	−	0.186228i	$-0.940374\pi$
$467$	0.273762	−	1.90405i	0.0126682	−	0.0881091i	0.995175	+	0.0981193i	$0.0312827\pi$
$468$		0			0
$469$	−2.38962	−	1.53571i	−0.110342	−	0.0709127i
$470$		0			0
$471$	32.1769	−	2.21095i	1.48263	−	0.101875i
$472$		0			0
$473$	1.17468	−	0.168893i	0.0540118	−	0.00776572i
$474$		0			0
$475$	4.07254	+	13.8698i	0.186861	+	0.636389i
$476$		0			0
$477$	−1.62601	+	0.224514i	−0.0744501	+	0.0102798i
$478$		0			0
$479$	−3.20887	−	3.70323i	−0.146617	−	0.169205i	0.677691	−	0.735347i	$-0.262981\pi$
$479$	−3.20887	−	3.70323i	−0.146617	−	0.169205i	−0.824308	+	0.566142i	$0.808435\pi$
$480$		0			0
$481$	−24.0943	−	11.0035i	−1.09861	−	0.501716i
$482$		0			0
$483$	−24.7785	−	1.64677i	−1.12746	−	0.0749306i
$484$		0			0
$485$	43.1956	+	19.7268i	1.96141	+	0.895747i
$486$		0			0
$487$	10.5871	+	12.2182i	0.479749	+	0.553660i	0.943098	−	0.332516i	$-0.107898\pi$
$487$	10.5871	+	12.2182i	0.479749	+	0.553660i	−0.463348	+	0.886176i	$0.653352\pi$
$488$		0			0
$489$	23.2895	−	12.6326i	1.05319	−	0.571268i
$490$		0			0
$491$	−7.25855	−	24.7203i	−0.327574	−	1.11561i	−0.944478	−	0.328575i	$-0.893432\pi$
$491$	−7.25855	−	24.7203i	−0.327574	−	1.11561i	0.616904	−	0.787038i	$-0.288387\pi$
$492$		0			0
$493$	−37.3045	+	5.36357i	−1.68011	+	0.241563i
$494$		0			0
$495$	11.4720	−	38.2771i	0.515628	−	1.72043i
$496$		0			0
$497$	−29.3337	−	18.8517i	−1.31580	−	0.845612i
$498$		0			0
$499$	−3.67618	+	25.5684i	−0.164569	+	1.14460i	0.725317	+	0.688415i	$0.241693\pi$
$499$	−3.67618	+	25.5684i	−0.164569	+	1.14460i	−0.889885	+	0.456184i	$0.849216\pi$
$500$		0			0
$501$	−1.77828	−	8.28607i	−0.0794477	−	0.370194i
$502$		0			0
$503$	−15.0054	−	4.40600i	−0.669060	−	0.196454i	−0.0704754	−	0.997514i	$-0.522452\pi$
$503$	−15.0054	−	4.40600i	−0.669060	−	0.196454i	−0.598584	+	0.801060i	$0.704270\pi$
$504$		0			0
$505$		−	33.1219i		−	1.47390i
$506$		0			0
$507$	−2.48097	−	0.933262i	−0.110184	−	0.0414476i
$508$		0			0
$509$	10.4892	−	35.7230i	0.464927	−	1.58339i	−0.309609	−	0.950864i	$-0.600198\pi$
$509$	10.4892	−	35.7230i	0.464927	−	1.58339i	0.774536	−	0.632530i	$-0.217984\pi$
$510$		0			0
$511$	1.93061	+	3.00409i	0.0854053	+	0.132893i
$512$		0			0
$513$	−3.89109	−	10.7058i	−0.171796	−	0.472672i
$514$		0			0
$515$	−14.0157	+	21.8088i	−0.617604	+	0.961011i
$516$		0			0
$517$	6.86056	−	3.13311i	0.301727	−	0.137794i
$518$		0			0
$519$	9.83979	+	2.16934i	0.431919	+	0.0952235i
$520$		0			0
$521$	7.22476	−	2.12138i	0.316522	−	0.0929394i	−0.119612	−	0.992821i	$-0.538165\pi$
$521$	7.22476	−	2.12138i	0.316522	−	0.0929394i	0.436135	+	0.899881i	$0.356347\pi$
$522$		0			0
$523$	0.120667	+	0.104559i	0.00527640	+	0.00457203i	0.657495	−	0.753459i	$-0.271616\pi$
$523$	0.120667	+	0.104559i	0.00527640	+	0.00457203i	−0.652219	+	0.758031i	$0.726162\pi$
$524$		0			0
$525$	−32.0247	+	11.8427i	−1.39767	+	0.516859i
$526$		0			0
$527$	20.2993	−	44.4493i	0.884253	−	1.93624i
$528$		0			0
$529$	2.91619	−	22.8144i	0.126791	−	0.991929i
$530$		0			0
$531$	12.1178	+	26.9317i	0.525867	+	1.16874i
$532$		0			0
$533$	−23.7507	+	20.5801i	−1.02876	+	0.891422i
$534$		0			0
$535$	−12.5940	+	14.5342i	−0.544485	+	0.628370i
$536$		0			0
$537$	0.691128	−	9.29789i	0.0298244	−	0.401234i
$538$		0			0
$539$	1.07863	+	7.50204i	0.0464599	+	0.323136i
$540$		0			0
$541$	−13.7347	−	30.0749i	−0.590502	−	1.29302i	−0.935138	−	0.354283i	$-0.884725\pi$
$541$	−13.7347	−	30.0749i	−0.590502	−	1.29302i	0.344636	−	0.938736i	$-0.388002\pi$
$542$		0			0
$543$	5.13381	−	3.82078i	0.220313	−	0.163965i
$544$		0			0
$545$	33.2168	+	4.77586i	1.42285	+	0.204575i
$546$		0			0
$547$	−6.32275	+	4.06338i	−0.270341	+	0.173738i	−0.668787	−	0.743454i	$-0.733186\pi$
$547$	−6.32275	+	4.06338i	−0.270341	+	0.173738i	0.398446	+	0.917192i	$0.369550\pi$
$548$		0			0
$549$	−7.59596	+	4.82183i	−0.324188	+	0.205791i
$550$		0			0
$551$	18.0898			0.770652
$552$		0			0
$553$	8.20946			0.349102
$554$		0			0
$555$	24.6509	−	32.7385i	1.04637	−	1.38967i
$556$		0			0
$557$	30.9244	−	19.8739i	1.31031	−	0.842085i	0.316016	−	0.948754i	$-0.397655\pi$
$557$	30.9244	−	19.8739i	1.31031	−	0.842085i	0.994295	+	0.106669i	$0.0340184\pi$
$558$		0			0
$559$	1.14466	+	0.164578i	0.0484141	+	0.00696090i
$560$		0			0
$561$	18.4752	+	24.8244i	0.780025	+	1.04809i
$562$		0			0
$563$	1.07116	+	2.34552i	0.0451442	+	0.0988519i	0.930860	−	0.365375i	$-0.119059\pi$
$563$	1.07116	+	2.34552i	0.0451442	+	0.0988519i	−0.885716	+	0.464227i	$0.846332\pi$
$564$		0			0
$565$	−3.50877	−	24.4040i	−0.147615	−	1.02668i
$566$		0			0
$567$	24.5981	−	10.9028i	1.03302	−	0.457876i
$568$		0			0
$569$	9.76060	−	11.2643i	0.409185	−	0.472225i	−0.513327	−	0.858193i	$-0.671587\pi$
$569$	9.76060	−	11.2643i	0.409185	−	0.472225i	0.922512	+	0.385968i	$0.126133\pi$
$570$		0			0
$571$	29.2368	−	25.3338i	1.22352	−	1.06019i	0.227257	−	0.973835i	$-0.427024\pi$
$571$	29.2368	−	25.3338i	1.22352	−	1.06019i	0.996265	−	0.0863526i	$-0.0275212\pi$
$572$		0			0
$573$	27.7548	−	27.6001i	1.15948	−	1.15301i
$574$		0			0
$575$	−9.14684	−	30.2720i	−0.381450	−	1.26243i
$576$		0			0
$577$	−8.87440	+	19.4322i	−0.369446	+	0.808974i	0.630029	+	0.776572i	$0.283043\pi$
$577$	−8.87440	+	19.4322i	−0.369446	+	0.808974i	−0.999475	+	0.0324023i	$0.989684\pi$
$578$		0			0
$579$	−13.7426	−	37.1622i	−0.571122	−	1.54441i
$580$		0			0
$581$	−4.62676	−	4.00911i	−0.191950	−	0.166326i
$582$		0			0
$583$	−2.05364	+	0.603004i	−0.0850533	+	0.0249739i
$584$		0			0
$585$	21.2344	−	32.6387i	0.877935	−	1.34945i
$586$		0			0
$587$	−9.94359	+	4.54109i	−0.410416	+	0.187431i	−0.609914	−	0.792468i	$-0.708796\pi$
$587$	−9.94359	+	4.54109i	−0.410416	+	0.187431i	0.199498	+	0.979898i	$0.436069\pi$
$588$		0			0
$589$	−12.6806	+	19.7314i	−0.522494	+	0.813016i
$590$		0			0
$591$	−22.6968	−	12.4759i	−0.933621	−	0.513189i
$592$		0			0
$593$	1.09110	+	1.69778i	0.0448060	+	0.0697195i	0.862934	−	0.505317i	$-0.168624\pi$
$593$	1.09110	+	1.69778i	0.0448060	+	0.0697195i	−0.818128	+	0.575036i	$0.804988\pi$
$594$		0			0
$595$	13.0982	−	44.6082i	0.536972	−	1.82876i
$596$		0			0
$597$	−7.07630	+	18.8115i	−0.289614	+	0.769905i
$598$		0			0
$599$			29.9101i			1.22209i	0.791595	+	0.611047i	$0.209251\pi$
$599$			29.9101i			1.22209i	−0.791595	+	0.611047i	$0.790749\pi$
$600$		0			0
$601$	−11.9786	−	3.51724i	−0.488618	−	0.143471i	0.0281376	−	0.999604i	$-0.491042\pi$
$601$	−11.9786	−	3.51724i	−0.488618	−	0.143471i	−0.516756	+	0.856133i	$0.672861\pi$
$602$		0			0
$603$	−0.421430	+	2.81913i	−0.0171620	+	0.114804i
$604$		0			0
$605$	2.08485	−	14.5005i	0.0847613	−	0.589528i
$606$		0			0
$607$	19.3432	+	12.4311i	0.785115	+	0.504562i	0.870727	−	0.491766i	$-0.163648\pi$
$607$	19.3432	+	12.4311i	0.785115	+	0.504562i	−0.0856129	+	0.996328i	$0.527285\pi$
$608$		0			0
$609$	2.92911	+	42.6286i	0.118693	+	1.72740i
$610$		0			0
$611$	7.27461	−	1.04593i	0.294299	−	0.0423138i
$612$		0			0
$613$	−2.71963	−	9.26220i	−0.109845	−	0.374097i	0.886162	−	0.463376i	$-0.153362\pi$
$613$	−2.71963	−	9.26220i	−0.109845	−	0.374097i	−0.996007	+	0.0892788i	$0.971544\pi$
$614$		0			0
$615$	−23.1829	−	42.7399i	−0.934824	−	1.72344i
$616$		0			0
$617$	−26.0916	−	30.1113i	−1.05041	−	1.21224i	−0.976623	−	0.214962i	$-0.931037\pi$
$617$	−26.0916	−	30.1113i	−1.05041	−	1.21224i	−0.0737857	−	0.997274i	$-0.523508\pi$
$618$		0			0
$619$	−28.0651	−	12.8169i	−1.12803	−	0.515155i	−0.238097	−	0.971241i	$-0.576524\pi$
$619$	−28.0651	−	12.8169i	−1.12803	−	0.515155i	−0.889936	+	0.456086i	$0.849251\pi$
$620$		0			0
$621$	8.69569	+	23.3535i	0.348946	+	0.937143i
$622$		0			0
$623$	7.18082	+	3.27937i	0.287693	+	0.131385i
$624$		0			0
$625$	9.48838	+	10.9502i	0.379535	+	0.438007i
$626$		0			0
$627$	−7.08189	−	13.0562i	−0.282824	−	0.521413i
$628$		0			0
$629$	8.94119	+	30.4509i	0.356509	+	1.21416i
$630$		0			0
$631$	10.4665	−	1.50486i	0.416665	−	0.0599074i	0.0692059	−	0.997602i	$-0.477953\pi$
$631$	10.4665	−	1.50486i	0.416665	−	0.0599074i	0.347460	+	0.937695i	$0.387044\pi$
$632$		0			0
$633$	−2.90094	−	42.2187i	−0.115302	−	1.67804i
$634$		0			0
$635$	−19.0810	−	12.2626i	−0.757207	−	0.486627i
$636$		0			0
$637$	−1.05107	+	7.31036i	−0.0416449	+	0.289647i
$638$		0			0
$639$	−5.17327	+	34.6062i	−0.204651	+	1.36900i
$640$		0			0
$641$	−21.2644	−	6.24380i	−0.839894	−	0.246615i	−0.166632	−	0.986019i	$-0.553289\pi$
$641$	−21.2644	−	6.24380i	−0.839894	−	0.246615i	−0.673262	+	0.739404i	$0.735107\pi$
$642$		0			0
$643$			17.0391i			0.671955i	0.941870	+	0.335977i	$0.109067\pi$
$643$			17.0391i			0.671955i	−0.941870	+	0.335977i	$0.890933\pi$
$644$		0			0
$645$	−0.629947	+	1.67464i	−0.0248041	+	0.0659389i
$646$		0			0
$647$	−2.11553	+	7.20482i	−0.0831699	+	0.283251i	−0.990568	−	0.137021i	$-0.956247\pi$
$647$	−2.11553	+	7.20482i	−0.0831699	+	0.283251i	0.907398	+	0.420272i	$0.138065\pi$
$648$		0			0
$649$	20.8192	+	32.3953i	0.817225	+	1.27163i
$650$		0			0
$651$	−48.5501	−	26.6868i	−1.90283	−	1.04594i
$652$		0			0
$653$	−5.98234	+	9.30870i	−0.234107	+	0.364277i	−0.938353	−	0.345678i	$-0.887649\pi$
$653$	−5.98234	+	9.30870i	−0.234107	+	0.364277i	0.704246	+	0.709956i	$0.251285\pi$
$654$		0			0
$655$	15.5881	−	7.11884i	0.609077	−	0.278156i
$656$		0			0
$657$	1.95418	−	3.00370i	0.0762396	−	0.117185i
$658$		0			0
$659$	4.38869	−	1.28864i	0.170959	−	0.0501982i	−0.195133	−	0.980777i	$-0.562514\pi$
$659$	4.38869	−	1.28864i	0.170959	−	0.0501982i	0.366092	+	0.930579i	$0.380696\pi$
$660$		0			0
$661$	24.2050	+	20.9738i	0.941466	+	0.815785i	0.983048	−	0.183350i	$-0.0586943\pi$
$661$	24.2050	+	20.9738i	0.941466	+	0.815785i	−0.0415819	+	0.999135i	$0.513240\pi$
$662$		0			0
$663$	10.4588	+	28.2823i	0.406185	+	1.09839i
$664$		0			0
$665$	−9.27013	+	20.2988i	−0.359480	+	0.787152i
$666$		0			0
$667$	−39.5736	+	0.310003i	−1.53230	+	0.0120034i
$668$		0			0
$669$	7.08456	−	7.04507i	0.273905	−	0.272378i
$670$		0			0
$671$	−8.86627	+	7.68267i	−0.342279	+	0.296586i
$672$		0			0
$673$	2.71503	−	3.13331i	0.104657	−	0.120780i	−0.701004	−	0.713157i	$-0.747265\pi$
$673$	2.71503	−	3.13331i	0.104657	−	0.120780i	0.805661	+	0.592376i	$0.201810\pi$
$674$		0			0
$675$	24.0239	+	24.4302i	0.924679	+	0.940320i
$676$		0			0
$677$	0.0551295	+	0.383434i	0.00211880	+	0.0147366i	0.990853	−	0.134943i	$-0.0430850\pi$
$677$	0.0551295	+	0.383434i	0.00211880	+	0.0147366i	−0.988735	+	0.149679i	$0.952176\pi$
$678$		0			0
$679$	17.3200	+	37.9255i	0.664680	+	1.45545i
$680$		0			0
$681$	−0.710648	−	0.954867i	−0.0272321	−	0.0365906i
$682$		0			0
$683$	12.3601	+	1.77712i	0.472947	+	0.0679996i	0.374668	−	0.927159i	$-0.377757\pi$
$683$	12.3601	+	1.77712i	0.472947	+	0.0679996i	0.0982799	+	0.995159i	$0.468666\pi$
$684$		0			0
$685$	19.9265	−	12.8060i	0.761351	−	0.489290i
$686$		0			0
$687$	−16.4383	+	21.8315i	−0.627161	+	0.832925i
$688$		0			0
$689$	−2.08565			−0.0794571
$690$		0			0
$691$	−13.1496			−0.500236			−0.250118	−	0.968215i	$-0.580469\pi$
$691$	−13.1496			−0.500236			−0.250118	+	0.968215i	$0.580469\pi$
$692$		0			0
$693$	29.6201	−	18.8025i	1.12517	−	0.714249i
$694$		0			0
$695$	−15.3987	+	9.89617i	−0.584108	+	0.375383i
$696$		0			0
$697$	37.2705	+	5.35868i	1.41172	+	0.202975i
$698$		0			0
$699$	15.2690	−	11.3637i	0.577526	−	0.429816i
$700$		0			0
$701$	13.4957	+	29.5515i	0.509726	+	1.11614i	0.973185	+	0.230025i	$0.0738808\pi$
$701$	13.4957	+	29.5515i	0.509726	+	1.11614i	−0.463459	+	0.886118i	$0.653392\pi$
$702$		0			0
$703$	−2.16790	−	15.0781i	−0.0817639	−	0.568680i
$704$		0			0
$705$	−0.842887	+	11.3395i	−0.0317450	+	0.427071i
$706$		0			0
$707$	19.0439	−	21.9778i	0.716219	−	0.826561i
$708$		0			0
$709$	−5.33000	+	4.61847i	−0.200172	+	0.173450i	−0.749179	−	0.662368i	$-0.769552\pi$
$709$	−5.33000	+	4.61847i	−0.200172	+	0.173450i	0.549007	+	0.835818i	$0.315006\pi$
$710$		0			0
$711$	−3.38028	−	7.51266i	−0.126771	−	0.281747i
$712$		0			0
$713$	27.4021	−	43.3820i	1.02622	−	1.62467i
$714$		0			0
$715$	21.0920	−	46.1849i	0.788794	−	1.72722i
$716$		0			0
$717$	−19.2928	+	7.13449i	−0.720504	+	0.266442i
$718$		0			0
$719$	8.57532	+	7.43055i	0.319805	+	0.277113i	0.799938	−	0.600083i	$-0.204866\pi$
$719$	8.57532	+	7.43055i	0.319805	+	0.277113i	−0.480132	+	0.877196i	$0.659411\pi$
$720$		0			0
$721$	−21.8393	+	6.41259i	−0.813338	+	0.238817i
$722$		0			0
$723$	38.4593	+	8.47898i	1.43032	+	0.315336i
$724$		0			0
$725$	−49.4960	+	22.6041i	−1.83824	+	0.839494i
$726$		0			0
$727$	−5.54326	+	8.62548i	−0.205588	+	0.319901i	−0.928702	−	0.370828i	$-0.879074\pi$
$727$	−5.54326	+	8.62548i	−0.205588	+	0.319901i	0.723113	+	0.690729i	$0.242710\pi$
$728$		0			0
$729$	−20.1058	−	18.0210i	−0.744660	−	0.667444i
$730$		0			0
$731$	−0.749100	−	1.16562i	−0.0277065	−	0.0431121i
$732$		0			0
$733$	−2.45839	+	8.37252i	−0.0908029	+	0.309246i	−0.992354	−	0.123427i	$-0.960611\pi$
$733$	−2.45839	+	8.37252i	−0.0908029	+	0.309246i	0.901551	+	0.432673i	$0.142430\pi$
$734$		0			0
$735$	−10.6950	−	4.02313i	−0.394492	−	0.148396i
$736$		0			0
$737$			3.71683i			0.136911i
$738$		0			0
$739$	−1.82118	−	0.534746i	−0.0669931	−	0.0196709i	0.248064	−	0.968744i	$-0.420206\pi$
$739$	−1.82118	−	0.534746i	−0.0669931	−	0.0196709i	−0.315057	+	0.949073i	$0.602024\pi$
$740$		0			0
$741$	−3.03705	−	14.1514i	−0.111569	−	0.519866i
$742$		0			0
$743$	−6.24739	+	43.4516i	−0.229195	+	1.59408i	0.472319	+	0.881428i	$0.343417\pi$
$743$	−6.24739	+	43.4516i	−0.229195	+	1.59408i	−0.701513	+	0.712656i	$0.747492\pi$
$744$		0			0
$745$	−57.3791	−	36.8753i	−2.10221	−	1.35101i
$746$		0			0
$747$	−1.76374	+	5.88482i	−0.0645318	+	0.215314i
$748$		0			0
$749$	−16.7133	+	2.40301i	−0.610691	+	0.0878041i
$750$		0			0
$751$	9.05913	+	30.8526i	0.330572	+	1.12583i	0.942303	+	0.334760i	$0.108655\pi$
$751$	9.05913	+	30.8526i	0.330572	+	1.12583i	−0.611731	+	0.791066i	$0.709527\pi$
$752$		0			0
$753$	0.824646	−	0.447303i	0.0300518	−	0.0163006i
$754$		0			0
$755$	−44.0675	−	50.8566i	−1.60378	−	1.85086i
$756$		0			0
$757$	−18.8533	−	8.61002i	−0.685235	−	0.312936i	0.0422036	−	0.999109i	$-0.486562\pi$
$757$	−18.8533	−	8.61002i	−0.685235	−	0.312936i	−0.727439	+	0.686173i	$0.759289\pi$
$758$		0			0
$759$	15.7162	+	28.4405i	0.570463	+	1.03233i
$760$		0			0
$761$	−9.62875	−	4.39730i	−0.349042	−	0.159402i	0.233177	−	0.972434i	$-0.425088\pi$
$761$	−9.62875	−	4.39730i	−0.349042	−	0.159402i	−0.582219	+	0.813032i	$0.697815\pi$
$762$		0			0
$763$	19.2949	+	22.2675i	0.698521	+	0.806136i
$764$		0			0
$765$	−46.2153	+	6.38123i	−1.67092	+	0.230714i
$766$		0			0
$767$	10.5719	+	36.0044i	0.381728	+	1.30005i
$768$		0			0
$769$	22.6795	−	3.26082i	0.817844	−	0.117588i	0.279320	−	0.960198i	$-0.409891\pi$
$769$	22.6795	−	3.26082i	0.817844	−	0.117588i	0.538524	+	0.842610i	$0.318982\pi$
$770$		0			0
$771$	37.6728	−	2.58858i	1.35675	−	0.0932255i
$772$		0			0
$773$	14.7557	+	9.48292i	0.530726	+	0.341077i	0.778402	−	0.627766i	$-0.216031\pi$
$773$	14.7557	+	9.48292i	0.530726	+	0.341077i	−0.247676	+	0.968843i	$0.579667\pi$
$774$		0			0
$775$	10.0404	−	69.8324i	0.360661	−	2.50845i
$776$		0			0
$777$	35.1804	−	7.55009i	1.26209	−	0.270858i
$778$		0			0
$779$	−17.3412	−	5.09185i	−0.621315	−	0.182434i
$780$		0			0
$781$			45.6259i			1.63262i
$782$		0			0
$783$	37.8044	−	20.2330i	1.35102	−	0.723070i
$784$		0			0
$785$	−17.8632	+	60.8366i	−0.637566	+	2.17135i
$786$		0			0
$787$	−1.08549	−	1.68906i	−0.0386937	−	0.0602085i	0.821368	−	0.570399i	$-0.193211\pi$
$787$	−1.08549	−	1.68906i	−0.0386937	−	0.0602085i	−0.860062	+	0.510190i	$0.829575\pi$
$788$		0			0
$789$	17.6367	−	32.0856i	0.627883	−	1.14228i
$790$		0			0
$791$	11.7032	−	18.2105i	0.416118	−	0.647492i
$792$		0			0
$793$	−10.3989	+	4.74902i	−0.369276	+	0.168643i
$794$		0			0
$795$	0.694732	−	3.15119i	0.0246396	−	0.111761i
$796$		0			0
$797$	−2.98344	+	0.876017i	−0.105679	+	0.0310301i	−0.334144	−	0.942522i	$-0.608447\pi$
$797$	−2.98344	+	0.876017i	−0.105679	+	0.0310301i	0.228466	+	0.973552i	$0.426629\pi$
$798$		0			0
$799$	−6.65488	−	5.76649i	−0.235433	−	0.204004i
$800$		0			0
$801$	0.0442895	−	7.92163i	0.00156489	−	0.279897i
$802$		0			0
$803$	1.94106	−	4.25034i	0.0684987	−	0.149991i
$804$		0			0
$805$	19.9317	−	44.5648i	0.702499	−	1.57070i
$806$		0			0
$807$	32.1007	+	32.2807i	1.13000	+	1.13633i
$808$		0			0
$809$	−23.6771	+	20.5163i	−0.832442	+	0.721315i	−0.962818	−	0.270149i	$-0.912927\pi$
$809$	−23.6771	+	20.5163i	−0.832442	+	0.721315i	0.130376	+	0.991465i	$0.458381\pi$
$810$		0			0
$811$	−16.8150	+	19.4055i	−0.590454	+	0.681421i	−0.969819	−	0.243827i	$-0.921597\pi$
$811$	−16.8150	+	19.4055i	−0.590454	+	0.681421i	0.379365	+	0.925247i	$0.376143\pi$
$812$		0			0
$813$	−27.5618	−	2.04871i	−0.966634	−	0.0718516i
$814$		0			0
$815$	7.41259	+	51.5557i	0.259652	+	1.80592i
$816$		0			0
$817$	0.276276	+	0.604961i	0.00966569	+	0.0211649i
$818$		0			0
$819$	32.8560	−	9.44820i	1.14808	−	0.330147i
$820$		0			0
$821$	−56.1185	−	8.06862i	−1.95855	−	0.281597i	−0.958555	−	0.284909i	$-0.908037\pi$
$821$	−56.1185	−	8.06862i	−1.95855	−	0.281597i	−0.999995	+	0.00331182i	$0.998946\pi$
$822$		0			0
$823$	−38.5755	+	24.7910i	−1.34466	+	0.864159i	−0.997290	−	0.0735703i	$-0.976561\pi$
$823$	−38.5755	+	24.7910i	−1.34466	+	0.864159i	−0.347367	+	0.937729i	$0.612924\pi$
$824$		0			0
$825$	35.6912	+	26.8741i	1.24261	+	0.935637i
$826$		0			0
$827$	−48.9487			−1.70211			−0.851056	−	0.525075i	$-0.824037\pi$
$827$	−48.9487			−1.70211			−0.851056	+	0.525075i	$0.824037\pi$
$828$		0			0
$829$	8.05151			0.279640			0.139820	−	0.990177i	$-0.455348\pi$
$829$	8.05151			0.279640			0.139820	+	0.990177i	$0.455348\pi$
$830$		0			0
$831$	−11.5710	−	8.71256i	−0.401395	−	0.302235i
$832$		0			0
$833$	7.44421	−	4.78410i	0.257927	−	0.165759i
$834$		0			0
$835$	16.4907	+	2.37101i	0.570684	+	0.0820520i
$836$		0			0
$837$	−4.43098	+	55.4178i	−0.153157	+	1.91552i
$838$		0			0
$839$	−21.2282	−	46.4832i	−0.732878	−	1.60478i	−0.794926	−	0.606707i	$-0.792490\pi$
$839$	−21.2282	−	46.4832i	−0.732878	−	1.60478i	0.0620476	−	0.998073i	$-0.480237\pi$
$840$		0			0
$841$	5.56370	+	38.6964i	0.191852	+	1.33436i
$842$		0			0
$843$	−40.4812	−	3.00904i	−1.39425	−	0.103637i
$844$		0			0
$845$	3.41244	−	3.93816i	0.117391	−	0.135477i
$846$		0			0
$847$	9.72063	−	8.42298i	0.334005	−	0.289417i
$848$		0			0
$849$	12.2825	+	12.3513i	0.421533	+	0.423896i
$850$		0			0
$851$	5.00093	+	32.9479i	0.171430	+	1.12944i
$852$		0			0
$853$	5.66105	−	12.3960i	0.193831	−	0.424430i	−0.787616	−	0.616167i	$-0.788685\pi$
$853$	5.66105	−	12.3960i	0.193831	−	0.424430i	0.981446	+	0.191737i	$0.0614120\pi$
$854$		0			0
$855$	22.3929	+	0.125198i	0.765820	+	0.00428167i
$856$		0			0
$857$	39.7111	+	34.4099i	1.35651	+	1.17542i	0.967113	+	0.254346i	$0.0818603\pi$
$857$	39.7111	+	34.4099i	1.35651	+	1.17542i	0.389392	+	0.921072i	$0.372685\pi$
$858$		0			0
$859$	−40.9690	+	12.0296i	−1.39784	+	0.410444i	−0.891943	−	0.452148i	$-0.850658\pi$
$859$	−40.9690	+	12.0296i	−1.39784	+	0.410444i	−0.505900	+	0.862592i	$0.668840\pi$
$860$		0			0
$861$	9.19104	−	41.6891i	0.313230	−	1.42076i
$862$		0			0
$863$	6.02463	−	2.75136i	0.205081	−	0.0936572i	−0.310227	−	0.950663i	$-0.600405\pi$
$863$	6.02463	−	2.75136i	0.205081	−	0.0936572i	0.515308	+	0.857005i	$0.327678\pi$
$864$		0			0
$865$	−10.7092	+	16.6638i	−0.364123	+	0.566587i
$866$		0			0
$867$	3.21981	−	5.85765i	0.109350	−	0.198936i
$868$		0			0
$869$	−5.80757	−	9.03676i	−0.197008	−	0.306551i
$870$		0			0
$871$	−1.02040	+	3.47515i	−0.0345748	+	0.117751i
$872$		0			0
$873$	27.5749	−	31.4659i	0.933269	−	1.06496i
$874$		0			0
$875$		−	16.2261i		−	0.548541i
$876$		0			0
$877$	−41.8413	−	12.2857i	−1.41288	−	0.414859i	−0.515794	−	0.856713i	$-0.672503\pi$
$877$	−41.8413	−	12.2857i	−1.41288	−	0.414859i	−0.897087	+	0.441853i	$0.854321\pi$
$878$		0			0
$879$	29.9977	−	6.43782i	1.01180	−	0.217142i
$880$		0			0
$881$	−5.35428	+	37.2398i	−0.180390	+	1.25464i	0.675452	+	0.737404i	$0.263949\pi$
$881$	−5.35428	+	37.2398i	−0.180390	+	1.25464i	−0.855842	+	0.517237i	$0.826960\pi$
$882$		0			0
$883$	−20.0971	−	12.9156i	−0.676321	−	0.434645i	0.156878	−	0.987618i	$-0.449857\pi$
$883$	−20.0971	−	12.9156i	−0.676321	−	0.434645i	−0.833199	+	0.552973i	$0.813493\pi$
$884$		0			0
$885$	−57.9202	+	3.97983i	−1.94697	+	0.133780i
$886$		0			0
$887$	37.0217	−	5.32291i	1.24307	−	0.178726i	0.510773	−	0.859716i	$-0.329359\pi$
$887$	37.0217	−	5.32291i	1.24307	−	0.178726i	0.732293	+	0.680990i	$0.238450\pi$
$888$		0			0
$889$	−5.61052	−	19.1077i	−0.188171	−	0.640851i
$890$		0			0
$891$	−29.4029	−	19.3640i	−0.985033	−	0.648719i
$892$		0			0
$893$	2.76785	+	3.19427i	0.0926225	+	0.106892i
$894$		0			0
$895$	16.6726	+	7.61411i	0.557303	+	0.254512i
$896$		0			0
$897$	6.88641	+	30.9059i	0.229931	+	1.03192i
$898$		0			0
$899$	−80.3105	−	36.6766i	−2.67850	−	1.22323i
$900$		0			0
$901$	1.63644	+	1.88856i	0.0545179	+	0.0629170i
$902$		0			0
$903$	−1.38086	+	0.749000i	−0.0459520	+	0.0249252i
$904$		0			0
$905$	3.54440	+	12.0711i	0.117820	+	0.401258i
$906$		0			0
$907$	−3.11147	+	0.447362i	−0.103315	+	0.0148544i	−0.193778	−	0.981045i	$-0.562074\pi$
$907$	−3.11147	+	0.447362i	−0.103315	+	0.0148544i	0.0904636	+	0.995900i	$0.471165\pi$
$908$		0			0
$909$	−27.9538	−	8.37802i	−0.927170	−	0.277882i
$910$		0			0
$911$	13.4070	+	8.61616i	0.444194	+	0.285466i	0.743556	−	0.668673i	$-0.233138\pi$
$911$	13.4070	+	8.61616i	0.444194	+	0.285466i	−0.299362	+	0.954140i	$0.596774\pi$
$912$		0			0
$913$	−1.14004	+	7.92916i	−0.0377298	+	0.262417i
$914$		0			0
$915$	−3.71137	−	17.2935i	−0.122694	−	0.571706i
$916$		0			0
$917$	14.4365	+	4.23893i	0.476734	+	0.139982i
$918$		0			0
$919$		−	1.89850i		−	0.0626257i	−0.999510	−	0.0313129i	$-0.990031\pi$
$919$		−	1.89850i		−	0.0626257i	0.999510	−	0.0313129i	$-0.00996882\pi$
$920$		0			0
$921$	−11.0293	−	4.14886i	−0.363427	−	0.136710i
$922$		0			0
$923$	−12.5259	+	42.6592i	−0.412294	+	1.40414i
$924$		0			0
$925$	24.7724	+	38.5466i	0.814511	+	1.26740i
$926$		0			0
$927$	14.8607	+	17.3452i	0.488091	+	0.569692i
$928$		0			0
$929$	19.8701	−	30.9184i	0.651915	−	1.01440i	−0.345202	−	0.938528i	$-0.612190\pi$
$929$	19.8701	−	30.9184i	0.651915	−	1.01440i	0.997118	−	0.0758716i	$-0.0241739\pi$
$930$		0			0
$931$	−3.86356	+	1.76443i	−0.126623	+	0.0578269i
$932$		0			0
$933$	−19.0121	−	4.19153i	−0.622429	−	0.137224i
$934$		0			0
$935$	−58.3695	+	17.1388i	−1.90889	+	0.560500i
$936$		0			0
$937$	−15.8004	−	13.6911i	−0.516175	−	0.447269i	0.357404	−	0.933950i	$-0.383662\pi$
$937$	−15.8004	−	13.6911i	−0.516175	−	0.447269i	−0.873580	+	0.486681i	$0.838207\pi$
$938$		0			0
$939$	13.7586	−	5.08793i	0.448995	−	0.166038i
$940$		0			0
$941$	−5.12550	+	11.2233i	−0.167086	+	0.365868i	−0.974591	−	0.223994i	$-0.928091\pi$
$941$	−5.12550	+	11.2233i	−0.167086	+	0.365868i	0.807504	+	0.589862i	$0.200818\pi$
$942$		0			0
$943$	38.0233	+	10.8419i	1.23821	+	0.353059i
$944$		0			0
$945$	3.33083	+	52.7891i	0.108352	+	1.71723i
$946$		0			0
$947$	−20.9164	+	18.1242i	−0.679693	+	0.588957i	−0.924761	−	0.380549i	$-0.875735\pi$
$947$	−20.9164	+	18.1242i	−0.679693	+	0.588957i	0.245068	+	0.969506i	$0.421190\pi$
$948$		0			0
$949$	2.98171	−	3.44108i	0.0967905	−	0.111702i
$950$		0			0
$951$	4.01964	−	54.0770i	0.130346	−	1.75357i
$952$		0			0
$953$	−5.04079	−	35.0595i	−0.163287	−	1.13569i	−0.892384	−	0.451277i	$-0.850969\pi$
$953$	−5.04079	−	35.0595i	−0.163287	−	1.13569i	0.729097	−	0.684411i	$-0.239940\pi$
$954$		0			0
$955$	31.9655	+	69.9946i	1.03438	+	2.26497i
$956$		0			0
$957$	44.8524	−	33.3808i	1.44987	−	1.07905i
$958$		0			0
$959$	20.5850	+	2.95968i	0.664725	+	0.0955731i
$960$		0			0
$961$	70.2218	−	45.1288i	2.26522	−	1.45577i
$962$		0			0
$963$	9.08084	+	14.3053i	0.292626	+	0.460981i
$964$		0			0
$965$	77.8916			2.50742
$966$		0			0
$967$	26.6053			0.855568			0.427784	−	0.903881i	$-0.359294\pi$
$967$	26.6053			0.855568			0.427784	+	0.903881i	$0.359294\pi$
$968$		0			0
$969$	−10.4312	+	13.8535i	−0.335097	+	0.445039i
$970$		0			0
$971$	−7.98182	+	5.12961i	−0.256149	+	0.164617i	−0.662413	−	0.749139i	$-0.730468\pi$
$971$	−7.98182	+	5.12961i	−0.256149	+	0.164617i	0.406264	+	0.913756i	$0.366831\pi$
$972$		0			0
$973$	−15.9077	−	2.28718i	−0.509977	−	0.0733236i
$974$		0			0
$975$	25.9926	+	34.9251i	0.832429	+	1.11850i
$976$		0			0
$977$	−0.786556	−	1.72232i	−0.0251642	−	0.0551018i	0.896633	−	0.442775i	$-0.146006\pi$
$977$	−0.786556	−	1.72232i	−0.0251642	−	0.0551018i	−0.921797	+	0.387674i	$0.873279\pi$
$978$		0			0
$979$	−1.47004	−	10.2244i	−0.0469827	−	0.326772i
$980$		0			0
$981$	12.4327	−	26.8259i	0.396946	−	0.856485i
$982$		0			0
$983$	−25.5871	+	29.5290i	−0.816100	+	0.941830i	−0.999148	−	0.0412739i	$-0.986858\pi$
$983$	−25.5871	+	29.5290i	−0.816100	+	0.941830i	0.183047	+	0.983104i	$0.441404\pi$
$984$		0			0
$985$	38.4794	−	33.3426i	1.22605	−	1.06238i
$986$		0			0
$987$	−7.07911	+	7.03964i	−0.225331	+	0.224074i
$988$		0			0
$989$	−0.614755	−	1.31869i	−0.0195481	−	0.0419319i
$990$		0			0
$991$	−4.04453	+	8.85629i	−0.128479	+	0.281329i	−0.962929	−	0.269753i	$-0.913058\pi$
$991$	−4.04453	+	8.85629i	−0.128479	+	0.281329i	0.834451	+	0.551083i	$0.185785\pi$
$992$		0			0
$993$	−4.56920	−	12.3559i	−0.144999	−	0.392102i
$994$		0			0
$995$	−29.8605	−	25.8742i	−0.946640	−	0.820268i
$996$		0			0
$997$	26.2907	−	7.71964i	0.832634	−	0.244483i	0.162486	−	0.986711i	$-0.448049\pi$
$997$	26.2907	−	7.71964i	0.832634	−	0.244483i	0.670148	+	0.742227i	$0.266231\pi$
$998$		0			0
$999$	−21.3950	−	29.0856i	−0.676907	−	0.920228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.k.a.17.6	✓	80
3.2	odd	2	inner	276.2.k.a.17.8	yes	80
23.19	odd	22	inner	276.2.k.a.65.8	yes	80
69.65	even	22	inner	276.2.k.a.65.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.k.a.17.6	✓	80	1.1	even	1	trivial
276.2.k.a.17.8	yes	80	3.2	odd	2	inner
276.2.k.a.65.6	yes	80	69.65	even	22	inner
276.2.k.a.65.8	yes	80	23.19	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.k (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38367 + 1.04185i) q^{3} +(-2.86447 + 1.84088i) q^{5} +(-2.95914 - 0.425460i) q^{7} +(0.829091 + 2.88316i) q^{9} +O(q^{10})\)	\(q+(1.38367 + 1.04185i) q^{3} +(-2.86447 + 1.84088i) q^{5} +(-2.95914 - 0.425460i) q^{7} +(0.829091 + 2.88316i) q^{9} +(1.62503 + 3.55832i) q^{11} +(0.542486 + 3.77307i) q^{13} +(-5.88140 - 0.437175i) q^{15} +(2.99087 - 3.45165i) q^{17} +(-1.65675 + 1.43558i) q^{19} +(-3.65121 - 3.67168i) q^{21} +(3.59974 - 3.16890i) q^{23} +(2.73925 - 5.99811i) q^{25} +(-1.85663 + 4.85313i) q^{27} +(-6.23639 - 5.40386i) q^{29} +(10.2658 - 3.01431i) q^{31} +(-1.45873 + 6.61659i) q^{33} +(9.25957 - 4.22870i) q^{35} +(-3.75681 + 5.84570i) q^{37} +(-3.18036 + 5.78588i) q^{39} +(4.45727 + 6.93564i) q^{41} +(0.0854712 - 0.291088i) q^{43} +(-7.68245 - 6.73245i) q^{45} -1.92803i q^{47} +(1.85902 + 0.545859i) q^{49} +(7.73448 - 1.65990i) q^{51} +(-0.0778671 + 0.541578i) q^{53} +(-11.2053 - 7.20120i) q^{55} +(-3.78806 + 0.260286i) q^{57} +(9.74390 - 1.40096i) q^{59} +(0.844930 + 2.87757i) q^{61} +(-1.22673 - 8.88441i) q^{63} +(-8.49971 - 9.80919i) q^{65} +(0.864289 + 0.394707i) q^{67} +(8.28237 - 0.634322i) q^{69} +(10.6096 + 4.84523i) q^{71} +(-0.782217 - 0.902726i) q^{73} +(10.0394 - 5.44553i) q^{75} +(-3.29477 - 11.2209i) q^{77} +(-2.71809 + 0.390802i) q^{79} +(-7.62522 + 4.78080i) q^{81} +(1.72273 + 1.10713i) q^{83} +(-2.21317 + 15.3930i) q^{85} +(-2.99909 - 13.9746i) q^{87} +(-2.53362 - 0.743938i) q^{89} -11.3958i q^{91} +(17.3450 + 6.52463i) q^{93} +(2.10297 - 7.16205i) q^{95} +(-7.53991 - 11.7323i) q^{97} +(-8.91191 + 7.63540i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 6 q^{9}+O(q^{10}) \) 80 * q - 2 * q^3 + 6 * q^9	\( 80 q - 2 q^{3} + 6 q^{9} - 4 q^{13} + 11 q^{15} + 33 q^{21} + 25 q^{27} + 20 q^{31} + 11 q^{33} - 44 q^{37} - 18 q^{39} - 44 q^{43} - 100 q^{49} - 98 q^{55} - 33 q^{57} - 44 q^{61} - 55 q^{63} - 22 q^{67} - 41 q^{69} - 26 q^{73} - 65 q^{75} - 44 q^{79} - 42 q^{81} + 2 q^{85} - 64 q^{87} - 46 q^{93} + 66 q^{97} - 66 q^{99}+O(q^{100}) \) 80 * q - 2 * q^3 + 6 * q^9 - 4 * q^13 + 11 * q^15 + 33 * q^21 + 25 * q^27 + 20 * q^31 + 11 * q^33 - 44 * q^37 - 18 * q^39 - 44 * q^43 - 100 * q^49 - 98 * q^55 - 33 * q^57 - 44 * q^61 - 55 * q^63 - 22 * q^67 - 41 * q^69 - 26 * q^73 - 65 * q^75 - 44 * q^79 - 42 * q^81 + 2 * q^85 - 64 * q^87 - 46 * q^93 + 66 * q^97 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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