LMFDB - Embedded newform 525.2.bc.c.82.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(82,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("525.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bc (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			82.6
Character	$\chi$	$=$	525.82
Dual form			525.2.bc.c.493.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.53443 - 0.679097i) q^{2} +(0.258819 - 0.965926i) q^{3} +(4.23009 - 2.44224i) q^{4} -2.62383i q^{6} +(-1.00739 + 2.44646i) q^{7} +(5.35166 - 5.35166i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(2.53443 - 0.679097i) q^{2} +(0.258819 - 0.965926i) q^{3} +(4.23009 - 2.44224i) q^{4} -2.62383i q^{6} +(-1.00739 + 2.44646i) q^{7} +(5.35166 - 5.35166i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.94224 - 3.36406i) q^{11} +(-1.26420 - 4.71805i) q^{12} +(0.707107 + 0.707107i) q^{13} +(-0.891779 + 6.88448i) q^{14} +(5.04461 - 8.73752i) q^{16} +(5.02738 + 1.34708i) q^{17} +(-2.53443 - 0.679097i) q^{18} +(-3.33831 + 5.78212i) q^{19} +(2.10236 + 1.60626i) q^{21} +(-7.20699 - 7.20699i) q^{22} +(-1.66292 - 6.20610i) q^{23} +(-3.78420 - 6.55442i) q^{24} +(2.27230 + 1.31191i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.71348 + 12.8090i) q^{28} +7.76897i q^{29} +(-5.56424 + 3.21251i) q^{31} +(2.93387 - 10.9493i) q^{32} +(-3.75212 + 1.00538i) q^{33} +13.6563 q^{34} -4.88448 q^{36} +(0.0497524 - 0.0133311i) q^{37} +(-4.53407 + 16.9214i) q^{38} +(0.866025 - 0.500000i) q^{39} +5.55076i q^{41} +(6.41909 + 2.64323i) q^{42} +(4.97182 - 4.97182i) q^{43} +(-16.4317 - 9.48685i) q^{44} +(-8.42909 - 14.5996i) q^{46} +(0.547536 + 2.04343i) q^{47} +(-7.13415 - 7.13415i) q^{48} +(-4.97032 - 4.92909i) q^{49} +(2.60236 - 4.50743i) q^{51} +(4.71805 + 1.26420i) q^{52} +(2.01555 + 0.540066i) q^{53} +(-1.31191 + 2.27230i) q^{54} +(7.70139 + 18.4839i) q^{56} +(4.72108 + 4.72108i) q^{57} +(5.27588 + 19.6899i) q^{58} +(-3.61565 - 6.26249i) q^{59} +(-7.50000 - 4.33013i) q^{61} +(-11.9205 + 11.9205i) q^{62} +(2.09566 - 1.61500i) q^{63} -9.56424i q^{64} +(-8.82673 + 5.09611i) q^{66} +(-0.396503 + 1.47977i) q^{67} +(24.5562 - 6.57981i) q^{68} -6.42503 q^{69} -2.64049 q^{71} +(-7.31051 + 1.95884i) q^{72} +(2.43535 - 9.08884i) q^{73} +(0.117041 - 0.0675735i) q^{74} +32.6118i q^{76} +(10.1866 - 1.36268i) q^{77} +(1.85533 - 1.85533i) q^{78} +(9.22616 + 5.32673i) q^{79} +(0.500000 + 0.866025i) q^{81} +(3.76950 + 14.0680i) q^{82} +(1.49590 + 1.49590i) q^{83} +(12.8161 + 1.66012i) q^{84} +(9.22436 - 15.9771i) q^{86} +(7.50425 + 2.01076i) q^{87} +(-28.3975 - 7.60910i) q^{88} +(7.46835 - 12.9356i) q^{89} +(-2.44224 + 1.01757i) q^{91} +(-22.1911 - 22.1911i) q^{92} +(1.66292 + 6.20610i) q^{93} +(2.77538 + 4.80709i) q^{94} +(-9.81691 - 5.66780i) q^{96} +(-3.34441 + 3.34441i) q^{97} +(-15.9442 - 9.11708i) q^{98} +3.88448i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 36 q^{16} + 12 q^{21} + 12 q^{26} - 24 q^{31} - 24 q^{36} - 24 q^{46} + 24 q^{51} - 36 q^{56} - 180 q^{61} - 72 q^{66} - 96 q^{71} + 12 q^{81} + 120 q^{86} - 12 q^{91} - 108 q^{96}+O(q^{100}) $ 24 * q + 36 * q^16 + 12 * q^21 + 12 * q^26 - 24 * q^31 - 24 * q^36 - 24 * q^46 + 24 * q^51 - 36 * q^56 - 180 * q^61 - 72 * q^66 - 96 * q^71 + 12 * q^81 + 120 * q^86 - 12 * q^91 - 108 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.53443	−	0.679097i	1.79211	−	0.480194i	0.799407	−	0.600789i	$-0.205147\pi$
$2$	2.53443	−	0.679097i	1.79211	−	0.480194i	0.992702	+	0.120595i	$0.0384803\pi$
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$	4.23009	−	2.44224i	2.11504	−	1.22112i
$5$		0			0
$5$		0			0
$6$		−	2.62383i		−	1.07117i
$7$	−1.00739	+	2.44646i	−0.380759	+	0.924674i
$7$	−1.00739	+	2.44646i	−0.380759	+	0.924674i
$8$	5.35166	−	5.35166i	1.89210	−	1.89210i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$		0			0
$11$	−1.94224	−	3.36406i	−0.585608	−	1.01430i	−0.994799	−	0.101854i	$-0.967522\pi$
$11$	−1.94224	−	3.36406i	−0.585608	−	1.01430i	0.409191	−	0.912449i	$-0.365811\pi$
$12$	−1.26420	−	4.71805i	−0.364942	−	1.36198i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i	0.798333	−	0.602217i	$-0.205716\pi$
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i	−0.602217	+	0.798333i	$0.705716\pi$
$14$	−0.891779	+	6.88448i	−0.238338	+	1.83996i
$15$		0			0
$16$	5.04461	−	8.73752i	1.26115	−	2.18438i
$17$	5.02738	+	1.34708i	1.21932	+	0.326716i	0.810412	−	0.585860i	$-0.199243\pi$
$17$	5.02738	+	1.34708i	1.21932	+	0.326716i	0.408907	+	0.912576i	$0.365910\pi$
$18$	−2.53443	−	0.679097i	−0.597370	−	0.160065i
$19$	−3.33831	+	5.78212i	−0.765860	+	1.32651i	0.173930	+	0.984758i	$0.444353\pi$
$19$	−3.33831	+	5.78212i	−0.765860	+	1.32651i	−0.939791	+	0.341751i	$0.888980\pi$
$20$		0			0
$21$	2.10236	+	1.60626i	0.458774	+	0.350514i
$22$	−7.20699	−	7.20699i	−1.53654	−	1.53654i
$23$	−1.66292	−	6.20610i	−0.346743	−	1.29406i	−0.890563	−	0.454860i	$-0.849689\pi$
$23$	−1.66292	−	6.20610i	−0.346743	−	1.29406i	0.543820	−	0.839202i	$-0.316977\pi$
$24$	−3.78420	−	6.55442i	−0.772446	−	1.33792i
$25$		0			0
$26$	2.27230	+	1.31191i	0.445635	+	0.257288i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	1.71348	+	12.8090i	0.323818	+	2.42068i
$29$			7.76897i			1.44266i	0.692591	+	0.721331i	$0.256469\pi$
$29$			7.76897i			1.44266i	−0.692591	+	0.721331i	$0.743531\pi$
$30$		0			0
$31$	−5.56424	+	3.21251i	−0.999367	+	0.576985i	−0.908061	−	0.418838i	$-0.862437\pi$
$31$	−5.56424	+	3.21251i	−0.999367	+	0.576985i	−0.0913057	+	0.995823i	$0.529104\pi$
$32$	2.93387	−	10.9493i	0.518639	−	1.93559i
$33$	−3.75212	+	1.00538i	−0.653161	+	0.175014i
$34$	13.6563			2.34204
$35$		0			0
$36$	−4.88448			−0.814081
$37$	0.0497524	−	0.0133311i	0.00817925	−	0.00219162i	−0.254727	−	0.967013i	$-0.581986\pi$
$37$	0.0497524	−	0.0133311i	0.00817925	−	0.00219162i	0.262906	+	0.964821i	$0.415319\pi$
$38$	−4.53407	+	16.9214i	−0.735523	+	2.74501i
$39$	0.866025	−	0.500000i	0.138675	−	0.0800641i
$40$		0			0
$41$			5.55076i			0.866882i	0.901182	+	0.433441i	$0.142701\pi$
$41$			5.55076i			0.866882i	−0.901182	+	0.433441i	$0.857299\pi$
$42$	6.41909	+	2.64323i	0.990487	+	0.407859i
$43$	4.97182	−	4.97182i	0.758196	−	0.758196i	−0.217798	−	0.975994i	$-0.569887\pi$
$43$	4.97182	−	4.97182i	0.758196	−	0.758196i	0.975994	+	0.217798i	$0.0698874\pi$
$44$	−16.4317	−	9.48685i	−2.47717	−	1.43020i
$45$		0			0
$46$	−8.42909	−	14.5996i	−1.24280	−	2.15260i
$47$	0.547536	+	2.04343i	0.0798663	+	0.298065i	0.994293	−	0.106687i	$-0.0340244\pi$
$47$	0.547536	+	2.04343i	0.0798663	+	0.298065i	−0.914426	+	0.404752i	$0.867358\pi$
$48$	−7.13415	−	7.13415i	−1.02973	−	1.02973i
$49$	−4.97032	−	4.92909i	−0.710046	−	0.704156i
$50$		0			0
$51$	2.60236	−	4.50743i	0.364404	−	0.631166i
$52$	4.71805	+	1.26420i	0.654276	+	0.175313i
$53$	2.01555	+	0.540066i	0.276857	+	0.0741837i	0.394576	−	0.918863i	$-0.370891\pi$
$53$	2.01555	+	0.540066i	0.276857	+	0.0741837i	−0.117719	+	0.993047i	$0.537558\pi$
$54$	−1.31191	+	2.27230i	−0.178529	+	0.309221i
$55$		0			0
$56$	7.70139	+	18.4839i	1.02914	+	2.47001i
$57$	4.72108	+	4.72108i	0.625322	+	0.625322i
$58$	5.27588	+	19.6899i	0.692757	+	2.58541i
$59$	−3.61565	−	6.26249i	−0.470717	−	0.815307i	0.528722	−	0.848795i	$-0.322672\pi$
$59$	−3.61565	−	6.26249i	−0.470717	−	0.815307i	−0.999439	+	0.0334888i	$0.989338\pi$
$60$		0			0
$61$	−7.50000	−	4.33013i	−0.960277	−	0.554416i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	−7.50000	−	4.33013i	−0.960277	−	0.554416i	−0.896258	+	0.443533i	$0.853725\pi$
$62$	−11.9205	+	11.9205i	−1.51391	+	1.51391i
$63$	2.09566	−	1.61500i	0.264028	−	0.203471i
$64$		−	9.56424i		−	1.19553i
$65$		0			0
$66$	−8.82673	+	5.09611i	−1.08649	+	0.627288i
$67$	−0.396503	+	1.47977i	−0.0484406	+	0.180783i	−0.985907	−	0.167292i	$-0.946498\pi$
$67$	−0.396503	+	1.47977i	−0.0484406	+	0.180783i	0.937467	+	0.348075i	$0.113164\pi$
$68$	24.5562	−	6.57981i	2.97787	−	0.797919i
$69$	−6.42503			−0.773482
$70$		0			0
$71$	−2.64049			−0.313369			−0.156684	−	0.987649i	$-0.550081\pi$
$71$	−2.64049			−0.313369			−0.156684	+	0.987649i	$0.550081\pi$
$72$	−7.31051	+	1.95884i	−0.861552	+	0.230852i
$73$	2.43535	−	9.08884i	0.285036	−	1.06377i	−0.663777	−	0.747930i	$-0.731048\pi$
$73$	2.43535	−	9.08884i	0.285036	−	1.06377i	0.948813	−	0.315838i	$-0.102286\pi$
$74$	0.117041	−	0.0675735i	0.0136057	−	0.00785526i
$75$		0			0
$76$			32.6118i			3.74083i
$77$	10.1866	−	1.36268i	1.16088	−	0.155292i
$78$	1.85533	−	1.85533i	0.210075	−	0.210075i
$79$	9.22616	+	5.32673i	1.03802	+	0.599303i	0.919273	−	0.393621i	$-0.128778\pi$
$79$	9.22616	+	5.32673i	1.03802	+	0.599303i	0.118751	+	0.992924i	$0.462111\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	3.76950	+	14.0680i	0.416272	+	1.55355i
$83$	1.49590	+	1.49590i	0.164196	+	0.164196i	0.784423	−	0.620227i	$-0.212959\pi$
$83$	1.49590	+	1.49590i	0.164196	+	0.164196i	−0.620227	+	0.784423i	$0.712959\pi$
$84$	12.8161	+	1.66012i	1.39835	+	0.181134i
$85$		0			0
$86$	9.22436	−	15.9771i	0.994688	−	1.72285i
$87$	7.50425	+	2.01076i	0.804540	+	0.215576i
$88$	−28.3975	−	7.60910i	−3.02719	−	0.811133i
$89$	7.46835	−	12.9356i	0.791644	−	1.37117i	−0.133304	−	0.991075i	$-0.542559\pi$
$89$	7.46835	−	12.9356i	0.791644	−	1.37117i	0.924948	−	0.380093i	$-0.124108\pi$
$90$		0			0
$91$	−2.44224	+	1.01757i	−0.256017	+	0.106671i
$92$	−22.1911	−	22.1911i	−2.31358	−	2.31358i
$93$	1.66292	+	6.20610i	0.172437	+	0.643543i
$94$	2.77538	+	4.80709i	0.286258	+	0.495814i
$95$		0			0
$96$	−9.81691	−	5.66780i	−1.00193	−	0.578467i
$97$	−3.34441	+	3.34441i	−0.339573	+	0.339573i	−0.856207	−	0.516634i	$-0.827185\pi$
$97$	−3.34441	+	3.34441i	−0.339573	+	0.339573i	0.516634	+	0.856207i	$0.327185\pi$
$98$	−15.9442	−	9.11708i	−1.61061	−	0.920964i
$99$			3.88448i			0.390405i
$100$		0			0
$101$	3.75714	−	2.16919i	0.373850	−	0.215842i	−0.301289	−	0.953533i	$-0.597417\pi$
$101$	3.75714	−	2.16919i	0.373850	−	0.215842i	0.675139	+	0.737691i	$0.264084\pi$
$102$	3.53452	−	13.1910i	0.349969	−	1.30610i
$103$	2.35277	−	0.630422i	0.231825	−	0.0621173i	−0.141036	−	0.990004i	$-0.545043\pi$
$103$	2.35277	−	0.630422i	0.231825	−	0.0621173i	0.372861	+	0.927887i	$0.378377\pi$
$104$	7.56839			0.742142
$105$		0			0
$106$	5.47502			0.531781
$107$	6.59837	−	1.76803i	0.637889	−	0.170922i	0.0746418	−	0.997210i	$-0.476219\pi$
$107$	6.59837	−	1.76803i	0.637889	−	0.170922i	0.563247	+	0.826289i	$0.309552\pi$
$108$	−1.26420	+	4.71805i	−0.121647	+	0.453994i
$109$	2.56407	−	1.48037i	0.245594	−	0.141794i	−0.372151	−	0.928172i	$-0.621380\pi$
$109$	2.56407	−	1.48037i	0.245594	−	0.141794i	0.617745	+	0.786378i	$0.288046\pi$
$110$		0			0
$111$		−	0.0515075i		−	0.00488888i
$112$	16.2941	+	21.1435i	1.53964	+	1.99788i
$113$	−4.54318	+	4.54318i	−0.427387	+	0.427387i	−0.887737	−	0.460351i	$-0.847724\pi$
$113$	−4.54318	+	4.54318i	−0.427387	+	0.427387i	0.460351	+	0.887737i	$0.347724\pi$
$114$	15.1713	+	8.75915i	1.42092	+	0.820370i
$115$		0			0
$116$	18.9737	+	32.8634i	1.76166	+	3.05129i
$117$	−0.258819	−	0.965926i	−0.0239278	−	0.0892999i
$118$	−13.4164	−	13.4164i	−1.23508	−	1.23508i
$119$	−8.36013	+	10.9422i	−0.766372	+	1.00307i
$120$		0			0
$121$	−2.04461	+	3.54136i	−0.185873	+	0.321942i
$122$	−21.9488	−	5.88115i	−1.98715	−	0.532455i
$123$	5.36162	+	1.43664i	0.483441	+	0.129538i
$124$	−15.6915	+	27.1784i	−1.40914	+	2.44069i
$125$		0			0
$126$	4.21455	−	5.51625i	0.375462	−	0.491426i
$127$	−12.5710	−	12.5710i	−1.11550	−	1.11550i	−0.992394	−	0.123105i	$-0.960715\pi$
$127$	−12.5710	−	12.5710i	−1.11550	−	1.11550i	−0.123105	−	0.992394i	$-0.539285\pi$
$128$	−0.627313	−	2.34116i	−0.0554471	−	0.206931i
$129$	−3.51561	−	6.08921i	−0.309532	−	0.536125i
$130$		0			0
$131$	−3.52498	−	2.03515i	−0.307979	−	0.177812i	0.338043	−	0.941131i	$-0.390235\pi$
$131$	−3.52498	−	2.03515i	−0.307979	−	0.177812i	−0.646022	+	0.763319i	$0.723568\pi$
$132$	−13.4164	+	13.4164i	−1.16775	+	1.16775i
$133$	−10.7827	−	13.9919i	−0.934981	−	1.21325i
$134$			4.01963i			0.347243i
$135$		0			0
$136$	34.1140	−	19.6957i	2.92525	−	1.68889i
$137$	−1.81981	+	6.79164i	−0.155477	+	0.580249i	0.843587	+	0.536993i	$0.180440\pi$
$137$	−1.81981	+	6.79164i	−0.155477	+	0.580249i	−0.999064	+	0.0432559i	$0.986227\pi$
$138$	−16.2838	+	4.36322i	−1.38617	+	0.371422i
$139$	−18.9555			−1.60778			−0.803892	−	0.594775i	$-0.797241\pi$
$139$	−18.9555			−1.60778			−0.803892	+	0.594775i	$0.797241\pi$
$140$		0			0
$141$	2.11552			0.178159
$142$	−6.69213	+	1.79315i	−0.561591	+	0.150478i
$143$	1.00538	−	3.75212i	0.0840740	−	0.313768i
$144$	−8.73752	+	5.04461i	−0.728126	+	0.420384i
$145$		0			0
$146$		−	24.6888i		−	2.04326i
$147$	−6.04755	+	3.52522i	−0.498793	+	0.290755i
$148$	0.177899	−	0.177899i	0.0146232	−	0.0146232i
$149$	−0.688724	−	0.397635i	−0.0564225	−	0.0325755i	0.471523	−	0.881854i	$-0.343704\pi$
$149$	−0.688724	−	0.397635i	−0.0564225	−	0.0325755i	−0.527946	+	0.849278i	$0.677038\pi$
$150$		0			0
$151$	−4.96722	−	8.60347i	−0.404226	−	0.700141i	0.590005	−	0.807400i	$-0.299126\pi$
$151$	−4.96722	−	8.60347i	−0.404226	−	0.700141i	−0.994231	+	0.107259i	$0.965793\pi$
$152$	13.0785	+	48.8095i	1.06080	+	3.95897i
$153$	−3.68030	−	3.68030i	−0.297535	−	0.297535i
$154$	24.8919	−	10.3713i	2.00584	−	0.835746i
$155$		0			0
$156$	2.44224	−	4.23009i	0.195536	−	0.338678i
$157$	−2.24119	−	0.600524i	−0.178866	−	0.0479270i	0.168274	−	0.985740i	$-0.446181\pi$
$157$	−2.24119	−	0.600524i	−0.178866	−	0.0479270i	−0.347140	+	0.937813i	$0.612847\pi$
$158$	27.0004	+	7.23473i	2.14803	+	0.575564i
$159$	1.04333	−	1.80709i	0.0827412	−	0.143312i
$160$		0			0
$161$	16.8582	+	2.18372i	1.32861	+	0.172101i
$162$	1.85533	+	1.85533i	0.145768	+	0.145768i
$163$	−1.26642	−	4.72633i	−0.0991934	−	0.370195i	0.898428	−	0.439120i	$-0.144710\pi$
$163$	−1.26642	−	4.72633i	−0.0991934	−	0.370195i	−0.997622	+	0.0689252i	$0.978043\pi$
$164$	13.5563	+	23.4802i	1.05857	+	1.83349i
$165$		0			0
$166$	4.80709	+	2.77538i	0.373103	+	0.215411i
$167$	9.98118	−	9.98118i	0.772367	−	0.772367i	−0.206153	−	0.978520i	$-0.566094\pi$
$167$	9.98118	−	9.98118i	0.772367	−	0.772367i	0.978520	+	0.206153i	$0.0660945\pi$
$168$	19.8473	−	2.65500i	1.53125	−	0.204838i
$169$		−	12.0000i		−	0.923077i
$170$		0			0
$171$	5.78212	−	3.33831i	0.442170	−	0.255287i
$172$	8.88885	−	33.1736i	0.677768	−	2.52947i
$173$	−5.79555	+	1.55291i	−0.440628	+	0.118066i	−0.472311	−	0.881432i	$-0.656580\pi$
$173$	−5.79555	+	1.55291i	−0.440628	+	0.118066i	0.0316829	+	0.999498i	$0.489913\pi$
$174$	20.3844			1.54534
$175$		0			0
$176$	−39.1914			−2.95416
$177$	−6.98490	+	1.87160i	−0.525017	+	0.140678i
$178$	10.1435	−	37.8560i	0.760286	−	2.83743i
$179$	10.3923	−	6.00000i	0.776757	−	0.448461i	−0.0585225	−	0.998286i	$-0.518639\pi$
$179$	10.3923	−	6.00000i	0.776757	−	0.448461i	0.835280	+	0.549825i	$0.185306\pi$
$180$		0			0
$181$			16.2462i			1.20757i	0.797148	+	0.603784i	$0.206341\pi$
$181$			16.2462i			1.20757i	−0.797148	+	0.603784i	$0.793659\pi$
$182$	−5.49865	+	4.23748i	−0.407587	+	0.314103i
$183$	−6.12372	+	6.12372i	−0.452679	+	0.452679i
$184$	−42.1123	−	24.3136i	−3.10456	−	1.79242i
$185$		0			0
$186$	8.42909	+	14.5996i	0.618051	+	1.07050i
$187$	−5.23272	−	19.5288i	−0.382655	−	1.42809i
$188$	7.30668	+	7.30668i	0.532894	+	0.532894i
$189$	−1.01757	−	2.44224i	−0.0740175	−	0.177647i
$190$		0			0
$191$	−4.50648	+	7.80545i	−0.326077	+	0.564783i	−0.981730	−	0.190280i	$-0.939060\pi$
$191$	−4.50648	+	7.80545i	−0.326077	+	0.564783i	0.655652	+	0.755063i	$0.272394\pi$
$192$	−9.23834	−	2.47541i	−0.666720	−	0.178647i
$193$	7.82938	+	2.09788i	0.563571	+	0.151008i	0.529347	−	0.848406i	$-0.322437\pi$
$193$	7.82938	+	2.09788i	0.563571	+	0.151008i	0.0342247	+	0.999414i	$0.489104\pi$
$194$	−6.20497	+	10.7473i	−0.445491	+	0.771613i
$195$		0			0
$196$	−33.0629	−	8.71176i	−2.36164	−	0.622269i
$197$	5.04466	+	5.04466i	0.359417	+	0.359417i	0.863598	−	0.504181i	$-0.168205\pi$
$197$	5.04466	+	5.04466i	0.359417	+	0.359417i	−0.504181	+	0.863598i	$0.668205\pi$
$198$	2.63794	+	9.84493i	0.187470	+	0.699649i
$199$	−11.2098	−	19.4159i	−0.794641	−	1.37636i	−0.923067	−	0.384640i	$-0.874326\pi$
$199$	−11.2098	−	19.4159i	−0.794641	−	1.37636i	0.128425	−	0.991719i	$-0.459008\pi$
$200$		0			0
$201$	1.32673	+	0.765985i	0.0935800	+	0.0540284i
$202$	8.04911	−	8.04911i	0.566333	−	0.566333i
$203$	−19.0065	−	7.82640i	−1.33399	−	0.549306i
$204$		−	25.4224i		−	1.77993i
$205$		0			0
$206$	5.53479	−	3.19551i	0.385627	−	0.222642i
$207$	−1.66292	+	6.20610i	−0.115581	+	0.431354i
$208$	9.74543	−	2.61128i	0.675724	−	0.181060i
$209$	25.9352			1.79398
$210$		0			0
$211$	−18.6927			−1.28686			−0.643430	−	0.765505i	$-0.722489\pi$
$211$	−18.6927			−1.28686			−0.643430	+	0.765505i	$0.722489\pi$
$212$	9.84493	−	2.63794i	0.676153	−	0.181175i
$213$	−0.683410	+	2.55052i	−0.0468265	+	0.174759i
$214$	15.5224	−	8.96187i	1.06109	−	0.612621i
$215$		0			0
$216$			7.56839i			0.514964i
$217$	−2.25391	−	16.8489i	−0.153005	−	1.14378i
$218$	5.49314	−	5.49314i	0.372042	−	0.372042i
$219$	−8.14883	−	4.70473i	−0.550647	−	0.317916i
$220$		0			0
$221$	2.60236	+	4.50743i	0.175054	+	0.303202i
$222$	−0.0349786	−	0.130542i	−0.00234761	−	0.00876140i
$223$	18.0117	+	18.0117i	1.20615	+	1.20615i	0.972263	+	0.233888i	$0.0751450\pi$
$223$	18.0117	+	18.0117i	1.20615	+	1.20615i	0.233888	+	0.972263i	$0.424855\pi$
$224$	23.8316	+	18.2079i	1.59231	+	1.21656i
$225$		0			0
$226$	−8.42909	+	14.5996i	−0.560695	+	0.971152i
$227$	12.6053	+	3.37758i	0.836642	+	0.224178i	0.651609	−	0.758555i	$-0.274094\pi$
$227$	12.6053	+	3.37758i	0.836642	+	0.224178i	0.185033	+	0.982732i	$0.440761\pi$
$228$	31.5006	+	8.44056i	2.08618	+	0.558990i
$229$	−5.22191	+	9.04461i	−0.345073	+	0.597684i	−0.985367	−	0.170446i	$-0.945479\pi$
$229$	−5.22191	+	9.04461i	−0.345073	+	0.597684i	0.640294	+	0.768130i	$0.278813\pi$
$230$		0			0
$231$	1.32025	−	10.1922i	0.0868658	−	0.670599i
$232$	41.5769	+	41.5769i	2.72966	+	2.72966i
$233$	−0.513403	−	1.91605i	−0.0336342	−	0.125524i	0.947068	−	0.321034i	$-0.104030\pi$
$233$	−0.513403	−	1.91605i	−0.0336342	−	0.125524i	−0.980702	+	0.195510i	$0.937364\pi$
$234$	−1.31191	−	2.27230i	−0.0857626	−	0.148545i
$235$		0			0
$236$	−30.5890	−	17.6606i	−1.99118	−	1.14961i
$237$	7.53313	−	7.53313i	0.489329	−	0.489329i
$238$	−13.7573	+	33.4096i	−0.891753	+	2.16563i
$239$		−	6.71902i		−	0.434617i	−0.976103	−	0.217308i	$-0.930272\pi$
$239$		−	6.71902i		−	0.434617i	0.976103	−	0.217308i	$-0.0697278\pi$
$240$		0			0
$241$	21.2230	−	12.2531i	1.36710	−	0.789293i	0.376540	−	0.926401i	$-0.377114\pi$
$241$	21.2230	−	12.2531i	1.36710	−	0.789293i	0.990556	+	0.137107i	$0.0437805\pi$
$242$	−2.77697	+	10.3638i	−0.178511	+	0.666211i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	−42.3009			−2.70804
$245$		0			0
$246$	14.5642			0.928582
$247$	−6.44912	+	1.72804i	−0.410347	+	0.109952i
$248$	−12.5856	+	46.9702i	−0.799188	+	2.98261i
$249$	1.83209	−	1.05776i	0.116104	−	0.0670327i
$250$		0			0
$251$			8.47667i			0.535043i	0.963552	+	0.267521i	$0.0862046\pi$
$251$			8.47667i			0.535043i	−0.963552	+	0.267521i	$0.913795\pi$
$252$	4.92059	−	11.9497i	0.309968	−	0.752760i
$253$	−17.6479	+	17.6479i	−1.10951	+	1.10951i
$254$	−40.3973	−	23.3234i	−2.53475	−	1.46344i
$255$		0			0
$256$	6.38448	+	11.0583i	0.399030	+	0.691141i
$257$	−3.13227	−	11.6898i	−0.195386	−	0.729190i	−0.992167	−	0.124921i	$-0.960132\pi$
$257$	−3.13227	−	11.6898i	−0.195386	−	0.729190i	0.796781	−	0.604268i	$-0.206535\pi$
$258$	−13.0452	−	13.0452i	−0.812160	−	0.812160i
$259$	−0.0175062	+	0.135147i	−0.00108778	+	0.00839762i
$260$		0			0
$261$	3.88448	−	6.72812i	0.240444	−	0.416460i
$262$	−10.3158	−	2.76412i	−0.637315	−	0.170768i
$263$	16.4433	+	4.40597i	1.01394	+	0.271684i	0.727274	−	0.686347i	$-0.240787\pi$
$263$	16.4433	+	4.40597i	1.01394	+	0.271684i	0.286664	+	0.958031i	$0.407454\pi$
$264$	−14.6997	+	25.4605i	−0.904701	+	1.56699i
$265$		0			0
$266$	−36.8299	−	28.1389i	−2.25818	−	1.72531i
$267$	−10.5618	−	10.5618i	−0.646375	−	0.646375i
$268$	1.93671	+	7.22791i	0.118304	+	0.441515i
$269$	0.991819	+	1.71788i	0.0604723	+	0.104741i	0.894677	−	0.446714i	$-0.147406\pi$
$269$	0.991819	+	1.71788i	0.0604723	+	0.104741i	−0.834204	+	0.551455i	$0.814073\pi$
$270$		0			0
$271$	1.63382	+	0.943287i	0.0992475	+	0.0573006i	0.548802	−	0.835952i	$-0.315084\pi$
$271$	1.63382	+	0.943287i	0.0992475	+	0.0573006i	−0.449555	+	0.893253i	$0.648417\pi$
$272$	37.1313	−	37.1313i	2.25142	−	2.25142i
$273$	0.350801	+	2.62239i	0.0212315	+	0.158714i
$274$			18.4487i			1.11453i
$275$		0			0
$276$	−27.1784	+	15.6915i	−1.63595	+	0.944516i
$277$	−4.67976	+	17.4651i	−0.281180	+	1.04938i	0.670406	+	0.741994i	$0.266120\pi$
$277$	−4.67976	+	17.4651i	−0.281180	+	1.04938i	−0.951586	+	0.307383i	$0.900547\pi$
$278$	−48.0413	+	12.8726i	−2.88132	+	0.772049i
$279$	6.42503			0.384656
$280$		0			0
$281$	19.1521			1.14252			0.571260	−	0.820769i	$-0.306455\pi$
$281$	19.1521			1.14252			0.571260	+	0.820769i	$0.306455\pi$
$282$	5.36162	−	1.43664i	0.319280	−	0.0855507i
$283$	6.42696	−	23.9858i	0.382043	−	1.42580i	−0.460732	−	0.887539i	$-0.652413\pi$
$283$	6.42696	−	23.9858i	0.382043	−	1.42580i	0.842775	−	0.538266i	$-0.180920\pi$
$284$	−11.1695	+	6.44872i	−0.662789	+	0.382661i
$285$		0			0
$286$		−	10.1922i		−	0.602679i
$287$	−13.5797	−	5.59179i	−0.801584	−	0.330073i
$288$	−8.01547	+	8.01547i	−0.472316	+	0.472316i
$289$	8.73752	+	5.04461i	0.513971	+	0.296742i
$290$		0			0
$291$	2.36485	+	4.09605i	0.138630	+	0.240114i
$292$	−11.8954	−	44.3943i	−0.696126	−	2.59798i
$293$	9.60996	+	9.60996i	0.561420	+	0.561420i	0.929711	−	0.368291i	$-0.120057\pi$
$293$	9.60996	+	9.60996i	0.561420	+	0.561420i	−0.368291	+	0.929711i	$0.620057\pi$
$294$	−12.9331	+	13.0413i	−0.754273	+	0.760582i
$295$		0			0
$296$	0.194915	−	0.337602i	0.0113292	−	0.0196227i
$297$	3.75212	+	1.00538i	0.217720	+	0.0583380i
$298$	−2.01555	−	0.540066i	−0.116758	−	0.0312852i
$299$	3.21251	−	5.56424i	0.185784	−	0.321788i
$300$		0			0
$301$	7.15478	+	17.1719i	0.412395	+	0.989774i
$302$	−18.4316	−	18.4316i	−1.06062	−	1.06062i
$303$	−1.12285	−	4.19055i	−0.0645063	−	0.240741i
$304$	33.6809	+	58.3370i	1.93173	+	3.34586i
$305$		0			0
$306$	−11.8267	−	6.82816i	−0.676089	−	0.390340i
$307$	−11.2059	+	11.2059i	−0.639553	+	0.639553i	−0.950445	−	0.310892i	$-0.899372\pi$
$307$	−11.2059	+	11.2059i	−0.639553	+	0.639553i	0.310892	+	0.950445i	$0.399372\pi$
$308$	39.7624	−	30.6425i	2.26567	−	1.74602i
$309$		−	2.43576i		−	0.138566i
$310$		0			0
$311$	−22.8711	+	13.2047i	−1.29690	+	0.748767i	−0.979868	−	0.199646i	$-0.936021\pi$
$311$	−22.8711	+	13.2047i	−1.29690	+	0.748767i	−0.317035	+	0.948414i	$0.602687\pi$
$312$	1.95884	−	7.31051i	0.110898	−	0.413876i
$313$	−16.5069	+	4.42301i	−0.933026	+	0.250004i	−0.693144	−	0.720799i	$-0.743775\pi$
$313$	−16.5069	+	4.42301i	−0.933026	+	0.250004i	−0.239881	+	0.970802i	$0.577109\pi$
$314$	−6.08793			−0.343562
$315$		0			0
$316$	52.0366			2.92729
$317$	−14.0693	+	3.76986i	−0.790211	+	0.211736i	−0.631282	−	0.775554i	$-0.717471\pi$
$317$	−14.0693	+	3.76986i	−0.790211	+	0.211736i	−0.158929	+	0.987290i	$0.550804\pi$
$318$	1.41704	−	5.28847i	0.0794637	−	0.296562i
$319$	26.1353	−	15.0892i	1.46330	−	0.844834i
$320$		0			0
$321$		−	6.83114i		−	0.381277i
$322$	44.2088	−	5.91387i	2.46366	−	0.329567i
$323$	−24.5719	+	24.5719i	−1.36722	+	1.36722i
$324$	4.23009	+	2.44224i	0.235005	+	0.135680i
$325$		0			0
$326$	−6.41928	−	11.1185i	−0.355531	−	0.615797i
$327$	−0.766296	−	2.85985i	−0.0423762	−	0.158150i
$328$	29.7058	+	29.7058i	1.64023	+	1.64023i
$329$	−5.55076	−	0.719015i	−0.306023	−	0.0396406i
$330$		0			0
$331$	−3.98685	+	6.90542i	−0.219137	+	0.379556i	−0.954544	−	0.298069i	$-0.903658\pi$
$331$	−3.98685	+	6.90542i	−0.219137	+	0.379556i	0.735407	+	0.677625i	$0.236991\pi$
$332$	9.98111	+	2.67443i	0.547785	+	0.146778i
$333$	−0.0497524	−	0.0133311i	−0.00272642	−	0.000730541i
$334$	18.5184	−	32.0747i	1.01328	−	1.75505i
$335$		0			0
$336$	24.6403	−	10.2665i	1.34424	−	0.560084i
$337$	6.16015	+	6.16015i	0.335565	+	0.335565i	0.854695	−	0.519130i	$-0.173744\pi$
$337$	6.16015	+	6.16015i	0.335565	+	0.335565i	−0.519130	+	0.854695i	$0.673744\pi$
$338$	−8.14917	−	30.4131i	−0.443256	−	1.65425i
$339$	3.21251	+	5.56424i	0.174480	+	0.302208i
$340$		0			0
$341$	21.6142	+	12.4790i	1.17047	+	0.675773i
$342$	12.3873	−	12.3873i	0.669829	−	0.669829i
$343$	17.0659	−	7.19415i	0.921471	−	0.388447i
$344$		−	53.2150i		−	2.86916i
$345$		0			0
$346$	−13.6338	+	7.87149i	−0.732959	+	0.423174i
$347$	7.91383	−	29.5348i	0.424836	−	1.58551i	−0.339443	−	0.940626i	$-0.610239\pi$
$347$	7.91383	−	29.5348i	0.424836	−	1.58551i	0.764280	−	0.644885i	$-0.223095\pi$
$348$	36.6544	−	9.82151i	1.96488	−	0.526488i
$349$	−2.78991			−0.149340			−0.0746702	−	0.997208i	$-0.523790\pi$
$349$	−2.78991			−0.149340			−0.0746702	+	0.997208i	$0.523790\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$	−42.5325	+	11.3966i	−2.26699	+	0.607439i
$353$	7.60492	−	28.3820i	0.404769	−	1.51062i	−0.399712	−	0.916641i	$-0.630890\pi$
$353$	7.60492	−	28.3820i	0.404769	−	1.51062i	0.804481	−	0.593978i	$-0.202443\pi$
$354$	−16.4317	+	9.48685i	−0.873335	+	0.504220i
$355$		0			0
$356$		−	72.9581i		−	3.86677i
$357$	8.40563	+	10.9073i	0.444873	+	0.577277i
$358$	22.2639	−	22.2639i	1.17669	−	1.17669i
$359$	24.3032	+	14.0315i	1.28267	+	0.740552i	0.977336	−	0.211692i	$-0.0678975\pi$
$359$	24.3032	+	14.0315i	1.28267	+	0.740552i	0.305337	+	0.952244i	$0.401231\pi$
$360$		0			0
$361$	−12.7886	−	22.1505i	−0.673084	−	1.16582i
$362$	11.0327	+	41.1747i	0.579867	+	2.16409i
$363$	2.89151	+	2.89151i	0.151765	+	0.151765i
$364$	−7.84574	+	10.2690i	−0.411228	+	0.538240i
$365$		0			0
$366$	−11.3615	+	19.6787i	−0.593876	+	1.02862i
$367$	−25.9430	−	6.95141i	−1.35421	−	0.362861i	−0.492526	−	0.870298i	$-0.663926\pi$
$367$	−25.9430	−	6.95141i	−1.35421	−	0.362861i	−0.861689	+	0.507437i	$0.830593\pi$
$368$	−62.6147	−	16.7776i	−3.26402	−	0.874590i
$369$	2.77538	−	4.80709i	0.144480	−	0.250247i
$370$		0			0
$371$	−3.35170	+	4.38691i	−0.174012	+	0.227757i
$372$	22.1911	+	22.1911i	1.15055	+	1.15055i
$373$	0.779675	+	2.90979i	0.0403701	+	0.150663i	0.983169	−	0.182699i	$-0.0584834\pi$
$373$	0.779675	+	2.90979i	0.0403701	+	0.150663i	−0.942799	+	0.333362i	$0.891817\pi$
$374$	−26.5239	−	45.9407i	−1.37152	−	2.37554i
$375$		0			0
$376$	13.8660	+	8.00553i	0.715084	+	0.412854i
$377$	−5.49349	+	5.49349i	−0.282929	+	0.282929i
$378$	−4.23748	−	5.49865i	−0.217953	−	0.282820i
$379$			35.7819i			1.83799i	0.394264	+	0.918997i	$0.370999\pi$
$379$			35.7819i			1.83799i	−0.394264	+	0.918997i	$0.629001\pi$
$380$		0			0
$381$	−15.3963	+	8.88906i	−0.788777	+	0.455400i
$382$	−6.12067	+	22.8427i	−0.313161	+	1.16873i
$383$	19.7899	−	5.30268i	1.01122	−	0.270954i	0.285078	−	0.958504i	$-0.407980\pi$
$383$	19.7899	−	5.30268i	1.01122	−	0.270954i	0.726137	+	0.687550i	$0.241314\pi$
$384$	−2.42375			−0.123686
$385$		0			0
$386$	21.2676			1.08249
$387$	−6.79164	+	1.81981i	−0.345238	+	0.0925063i
$388$	−5.97928	+	22.3150i	−0.303552	+	1.13287i
$389$	10.4808	−	6.05109i	0.531397	−	0.306802i	−0.210188	−	0.977661i	$-0.567408\pi$
$389$	10.4808	−	6.05109i	0.531397	−	0.306802i	0.741585	+	0.670859i	$0.234074\pi$
$390$		0			0
$391$		−	33.4405i		−	1.69116i
$392$	−52.9783	+	0.220639i	−2.67581	+	0.0111439i
$393$	−2.87813	+	2.87813i	−0.145183	+	0.145183i
$394$	16.2111	+	9.35951i	0.816706	+	0.471525i
$395$		0			0
$396$	9.48685	+	16.4317i	0.476732	+	0.825724i
$397$	8.67680	+	32.3823i	0.435476	+	1.62522i	0.739924	+	0.672690i	$0.234861\pi$
$397$	8.67680	+	32.3823i	0.435476	+	1.62522i	−0.304448	+	0.952529i	$0.598472\pi$
$398$	−41.5957	−	41.5957i	−2.08500	−	2.08500i
$399$	−16.3059	+	6.79394i	−0.816317	+	0.340123i
$400$		0			0
$401$	18.8464	−	32.6428i	0.941142	−	1.63011i	0.177845	−	0.984059i	$-0.443087\pi$
$401$	18.8464	−	32.6428i	0.941142	−	1.63011i	0.763297	−	0.646047i	$-0.223579\pi$
$402$	3.88267	+	1.04036i	0.193650	+	0.0518883i
$403$	−6.20610	−	1.66292i	−0.309148	−	0.0828359i
$404$	10.5954	−	18.3517i	0.527139	−	0.913031i
$405$		0			0
$406$	−53.4853	−	6.92820i	−2.65443	−	0.343841i
$407$	−0.141478	−	0.141478i	−0.00701280	−	0.00701280i
$408$	−10.1953	−	38.0492i	−0.504740	−	1.88372i
$409$	−0.969040	−	1.67843i	−0.0479160	−	0.0829929i	0.841073	−	0.540922i	$-0.181925\pi$
$409$	−0.969040	−	1.67843i	−0.0479160	−	0.0829929i	−0.888989	+	0.457929i	$0.848591\pi$
$410$		0			0
$411$	6.08921	+	3.51561i	0.300359	+	0.173412i
$412$	8.41276	−	8.41276i	0.414467	−	0.414467i
$413$	18.9633	−	2.53675i	0.933123	−	0.124825i
$414$			16.8582i			0.828534i
$415$		0			0
$416$	9.81691	−	5.66780i	0.481314	−	0.277887i
$417$	−4.90604	+	18.3096i	−0.240250	+	0.896625i
$418$	65.7308	−	17.6125i	3.21500	−	0.861457i
$419$	−19.9783			−0.976006			−0.488003	−	0.872842i	$-0.662274\pi$
$419$	−19.9783			−0.976006			−0.488003	+	0.872842i	$0.662274\pi$
$420$		0			0
$421$	7.44872			0.363028			0.181514	−	0.983388i	$-0.441900\pi$
$421$	7.44872			0.363028			0.181514	+	0.983388i	$0.441900\pi$
$422$	−47.3753	+	12.6942i	−2.30619	+	0.617942i
$423$	0.547536	−	2.04343i	0.0266221	−	0.0993551i
$424$	13.6768	−	7.89631i	0.664204	−	0.383479i
$425$		0			0
$426$			6.92820i			0.335673i
$427$	18.1489	−	13.9863i	0.878288	−	0.676844i
$428$	23.5937	−	23.5937i	1.14045	−	1.14045i
$429$	−3.36406	−	1.94224i	−0.162418	−	0.0937723i
$430$		0			0
$431$	−2.20473	−	3.81870i	−0.106198	−	0.183941i	0.808029	−	0.589143i	$-0.200534\pi$
$431$	−2.20473	−	3.81870i	−0.106198	−	0.183941i	−0.914227	+	0.405202i	$0.867201\pi$
$432$	2.61128	+	9.74543i	0.125635	+	0.468877i
$433$	12.0839	+	12.0839i	0.580715	+	0.580715i	0.935100	−	0.354385i	$-0.115310\pi$
$433$	12.0839	+	12.0839i	0.580715	+	0.580715i	−0.354385	+	0.935100i	$0.615310\pi$
$434$	−17.1544	−	41.1718i	−0.823439	−	1.97631i
$435$		0			0
$436$	7.23084	−	12.5242i	0.346294	−	0.599800i
$437$	41.4357	+	11.1027i	1.98214	+	0.531113i
$438$	−23.8476	−	6.38994i	−1.13948	−	0.305323i
$439$	−9.74684	+	16.8820i	−0.465191	+	0.805735i	−0.999210	−	0.0397376i	$-0.987348\pi$
$439$	−9.74684	+	16.8820i	−0.465191	+	0.805735i	0.534019	+	0.845473i	$0.320681\pi$
$440$		0			0
$441$	1.83988	+	6.75388i	0.0876132	+	0.321613i
$442$	9.65648	+	9.65648i	0.459312	+	0.459312i
$443$	7.54825	+	28.1705i	0.358628	+	1.33842i	0.875856	+	0.482572i	$0.160297\pi$
$443$	7.54825	+	28.1705i	0.358628	+	1.33842i	−0.517228	+	0.855848i	$0.673036\pi$
$444$	−0.125794	−	0.217881i	−0.00596991	−	0.0103402i
$445$		0			0
$446$	57.8810	+	33.4176i	2.74074	+	1.58237i
$447$	−0.562341	+	0.562341i	−0.0265978	+	0.0265978i
$448$	23.3985	+	9.63495i	1.10548	+	0.455208i
$449$			21.7926i			1.02846i	0.857653	+	0.514229i	$0.171922\pi$
$449$			21.7926i			1.02846i	−0.857653	+	0.514229i	$0.828078\pi$
$450$		0			0
$451$	18.6731	−	10.7809i	0.879281	−	0.507653i
$452$	−8.12250	+	30.3136i	−0.382050	+	1.42583i
$453$	−9.59593	+	2.57122i	−0.450856	+	0.120807i
$454$	34.2409			1.60700
$455$		0			0
$456$	50.5313			2.36634
$457$	−1.50784	+	0.404025i	−0.0705339	+	0.0188995i	−0.293913	−	0.955832i	$-0.594958\pi$
$457$	−1.50784	+	0.404025i	−0.0705339	+	0.0188995i	0.223380	+	0.974732i	$0.428291\pi$
$458$	−7.09236	+	26.4691i	−0.331404	+	1.23682i
$459$	−4.50743	+	2.60236i	−0.210389	+	0.121468i
$460$		0			0
$461$			0.103015i			0.00479789i	0.999997	+	0.00239894i	$0.000763608\pi$
$461$			0.103015i			0.00479789i	−0.999997	+	0.00239894i	$0.999236\pi$
$462$	−3.57545	−	26.7280i	−0.166345	−	1.24350i
$463$	−14.0423	+	14.0423i	−0.652602	+	0.652602i	−0.953619	−	0.301017i	$-0.902674\pi$
$463$	−14.0423	+	14.0423i	−0.652602	+	0.652602i	0.301017	+	0.953619i	$0.402674\pi$
$464$	67.8815	+	39.1914i	3.15132	+	1.81941i
$465$		0			0
$466$	−2.60236	−	4.50743i	−0.120552	−	0.208803i
$467$	−5.16277	−	19.2677i	−0.238904	−	0.891603i	−0.976350	−	0.216196i	$-0.930635\pi$
$467$	−5.16277	−	19.2677i	−0.238904	−	0.891603i	0.737446	−	0.675407i	$-0.236032\pi$
$468$	−3.45385	−	3.45385i	−0.159654	−	0.159654i
$469$	−3.22076	−	2.46074i	−0.148721	−	0.113626i
$470$		0			0
$471$	−1.16012	+	2.00939i	−0.0534557	+	0.0925879i
$472$	−52.8645	−	14.1650i	−2.43328	−	0.651997i
$473$	−26.3820	−	7.06903i	−1.21305	−	0.325035i
$474$	13.9764	−	24.2079i	0.641958	−	1.11190i
$475$		0			0
$476$	−8.64049	+	66.7041i	−0.396036	+	3.05738i
$477$	−1.47549	−	1.47549i	−0.0675579	−	0.0675579i
$478$	−4.56286	−	17.0288i	−0.208701	−	0.778881i
$479$	2.23820	+	3.87668i	0.102266	+	0.177130i	0.912618	−	0.408814i	$-0.134057\pi$
$479$	2.23820	+	3.87668i	0.102266	+	0.177130i	−0.810352	+	0.585944i	$0.800724\pi$
$480$		0			0
$481$	0.0446068	+	0.0257538i	0.00203390	+	0.00117427i
$482$	45.4671	−	45.4671i	2.07097	−	2.07097i
$483$	6.47253	−	15.7186i	0.294510	−	0.715219i
$484$			19.9737i			0.907895i
$485$		0			0
$486$	2.27230	−	1.31191i	0.103074	−	0.0595097i
$487$	−4.22241	+	15.7583i	−0.191336	+	0.714075i	0.801849	+	0.597527i	$0.203850\pi$
$487$	−4.22241	+	15.7583i	−0.191336	+	0.714075i	−0.993185	+	0.116549i	$0.962817\pi$
$488$	−63.3109	+	16.9641i	−2.86595	+	0.767928i
$489$	−4.89306			−0.221272
$490$		0			0
$491$	−40.4095			−1.82365			−0.911827	−	0.410575i	$-0.865328\pi$
$491$	−40.4095			−1.82365			−0.911827	+	0.410575i	$0.865328\pi$
$492$	26.1887	−	7.01725i	1.18068	−	0.316362i
$493$	−10.4654	+	39.0576i	−0.471340	+	1.75906i
$494$	−15.1713	+	8.75915i	−0.682589	+	0.394093i
$495$		0			0
$496$			64.8235i			2.91066i
$497$	2.66001	−	6.45986i	0.119318	−	0.289764i
$498$	3.92498	−	3.92498i	0.175882	−	0.175882i
$499$	26.3126	+	15.1916i	1.17791	+	0.680068i	0.955531	−	0.294891i	$-0.0952834\pi$
$499$	26.3126	+	15.1916i	1.17791	+	0.680068i	0.222382	+	0.974960i	$0.428617\pi$
$500$		0			0
$501$	−7.05776	−	12.2244i	−0.315317	−	0.546146i
$502$	5.75648	+	21.4835i	0.256924	+	0.958855i
$503$	−2.50170	−	2.50170i	−0.111545	−	0.111545i	0.649131	−	0.760676i	$-0.275133\pi$
$503$	−2.50170	−	2.50170i	−0.111545	−	0.111545i	−0.760676	+	0.649131i	$0.775133\pi$
$504$	2.57232	−	19.8582i	0.114580	−	0.884554i
$505$		0			0
$506$	−32.7427	+	56.7120i	−1.45559	+	2.52115i
$507$	−11.5911	−	3.10583i	−0.514779	−	0.137935i
$508$	−83.8781	−	22.4751i	−3.72149	−	0.997170i
$509$	−21.9679	+	38.0496i	−0.973711	+	1.68652i	−0.289587	+	0.957152i	$0.593518\pi$
$509$	−21.9679	+	38.0496i	−0.973711	+	1.68652i	−0.684124	+	0.729366i	$0.739815\pi$
$510$		0			0
$511$	19.7821	+	15.1140i	0.875109	+	0.668604i
$512$	27.1183	+	27.1183i	1.19847	+	1.19847i
$513$	−1.72804	−	6.44912i	−0.0762946	−	0.284735i
$514$	−15.8770	−	27.4998i	−0.700305	−	1.21296i
$515$		0			0
$516$	−29.7427	−	17.1719i	−1.30935	−	0.755952i
$517$	5.81078	−	5.81078i	0.255558	−	0.255558i
$518$	0.0474097	+	0.354408i	0.00208306	+	0.0155718i
$519$			6.00000i			0.263371i
$520$		0			0
$521$	−21.1784	+	12.2274i	−0.927844	+	0.535691i	−0.886129	−	0.463439i	$-0.846615\pi$
$521$	−21.1784	+	12.2274i	−0.927844	+	0.535691i	−0.0417148	+	0.999130i	$0.513282\pi$
$522$	5.27588	−	19.6899i	0.230919	−	0.861802i
$523$	6.19106	−	1.65889i	0.270716	−	0.0725382i	−0.120907	−	0.992664i	$-0.538580\pi$
$523$	6.19106	−	1.65889i	0.270716	−	0.0725382i	0.391623	+	0.920126i	$0.371914\pi$
$524$	−19.8813			−0.868517
$525$		0			0
$526$	44.6664			1.94755
$527$	−32.3011	+	8.65505i	−1.40706	+	0.377020i
$528$	−10.1435	+	37.8560i	−0.441438	+	1.64747i
$529$	−15.8318	+	9.14049i	−0.688339	+	0.397413i
$530$		0			0
$531$			7.23130i			0.313812i
$532$	−79.7835	−	32.8529i	−3.45905	−	1.42435i
$533$	−3.92498	+	3.92498i	−0.170010	+	0.170010i
$534$	−33.9407	−	19.5957i	−1.46876	−	0.847989i
$535$		0			0
$536$	5.79728	+	10.0412i	0.250404	+	0.433713i
$537$	−3.10583	−	11.5911i	−0.134026	−	0.500193i
$538$	3.68030	+	3.68030i	0.158669	+	0.158669i
$539$	−6.92820	+	26.2939i	−0.298419	+	1.13256i
$540$		0			0
$541$	−3.02498	+	5.23941i	−0.130054	+	0.225260i	−0.923697	−	0.383123i	$-0.874848\pi$
$541$	−3.02498	+	5.23941i	−0.130054	+	0.225260i	0.793643	+	0.608383i	$0.208182\pi$
$542$	4.78138	+	1.28117i	0.205378	+	0.0550308i
$543$	15.6926	+	4.20481i	0.673433	+	0.180446i
$544$	29.4993	−	51.0944i	1.26477	−	2.19065i
$545$		0			0
$546$	2.66994	+	6.40803i	0.114263	+	0.274238i
$547$	1.89992	+	1.89992i	0.0812347	+	0.0812347i	0.746557	−	0.665322i	$-0.231706\pi$
$547$	1.89992	+	1.89992i	0.0812347	+	0.0812347i	−0.665322	+	0.746557i	$0.731706\pi$
$548$	8.88885	+	33.1736i	0.379713	+	1.41711i
$549$	4.33013	+	7.50000i	0.184805	+	0.320092i
$550$		0			0
$551$	−44.9211	−	25.9352i	−1.91370	−	1.10488i
$552$	−34.3846	+	34.3846i	−1.46351	+	1.46351i
$553$	−22.3260	+	17.2053i	−0.949397	+	0.731644i
$554$			47.4420i			2.01562i
$555$		0			0
$556$	−80.1834	+	46.2939i	−3.40053	+	1.96330i
$557$	−8.09584	+	30.2141i	−0.343032	+	1.28021i	0.551863	+	0.833935i	$0.313917\pi$
$557$	−8.09584	+	30.2141i	−0.343032	+	1.28021i	−0.894895	+	0.446277i	$0.852750\pi$
$558$	16.2838	−	4.36322i	0.689346	−	0.184710i
$559$	7.03122			0.297389
$560$		0			0
$561$	−20.2177			−0.853591
$562$	48.5396	−	13.0062i	2.04752	−	0.548631i
$563$	6.80537	−	25.3980i	0.286812	−	1.07040i	−0.660693	−	0.750657i	$-0.729737\pi$
$563$	6.80537	−	25.3980i	0.286812	−	1.07040i	0.947505	−	0.319741i	$-0.103596\pi$
$564$	8.94882	−	5.16660i	0.376813	−	0.217553i
$565$		0			0
$566$		−	65.1546i		−	2.73865i
$567$	−2.62239	+	0.350801i	−0.110130	+	0.0147323i
$568$	−14.1310	+	14.1310i	−0.592925	+	0.592925i
$569$	26.8240	+	15.4868i	1.12452	+	0.649242i	0.942551	−	0.334062i	$-0.108419\pi$
$569$	26.8240	+	15.4868i	1.12452	+	0.649242i	0.181970	+	0.983304i	$0.441753\pi$
$570$		0			0
$571$	−0.993521	−	1.72083i	−0.0415775	−	0.0720144i	0.844488	−	0.535575i	$-0.179905\pi$
$571$	−0.993521	−	1.72083i	−0.0415775	−	0.0720144i	−0.886065	+	0.463560i	$0.846572\pi$
$572$	−4.91075	−	18.3272i	−0.205329	−	0.766298i
$573$	6.37312	+	6.37312i	0.266241	+	0.266241i
$574$	−38.2141	−	4.95005i	−1.59502	−	0.206611i
$575$		0			0
$576$	−4.78212	+	8.28287i	−0.199255	+	0.345120i
$577$	31.1578	+	8.34871i	1.29712	+	0.347561i	0.840359	−	0.542030i	$-0.182344\pi$
$577$	31.1578	+	8.34871i	1.29712	+	0.347561i	0.456758	+	0.889591i	$0.349011\pi$
$578$	25.5704	+	6.85156i	1.06359	+	0.284987i
$579$	4.05279	−	7.01963i	0.168428	−	0.291726i
$580$		0			0
$581$	−5.16660	+	2.15269i	−0.214347	+	0.0893087i
$582$	8.77516	+	8.77516i	0.363742	+	0.363742i
$583$	−2.09788	−	7.82938i	−0.0868852	−	0.324260i
$584$	−35.6073	−	61.6736i	−1.47344	−	2.55207i
$585$		0			0
$586$	30.8818	+	17.8296i	1.27572	+	0.736535i
$587$	−0.508420	+	0.508420i	−0.0209848	+	0.0209848i	−0.717521	−	0.696537i	$-0.754723\pi$
$587$	−0.508420	+	0.508420i	−0.0209848	+	0.0209848i	0.696537	+	0.717521i	$0.254723\pi$
$588$	−16.9722	+	29.6815i	−0.699923	+	1.22405i
$589$		−	42.8974i		−	1.76756i
$590$		0			0
$591$	6.17843	−	3.56712i	0.254147	−	0.146732i
$592$	0.134501	−	0.501963i	0.00552794	−	0.0206306i
$593$	−14.8361	+	3.97533i	−0.609247	+	0.163247i	−0.550235	−	0.835010i	$-0.685462\pi$
$593$	−14.8361	+	3.97533i	−0.609247	+	0.163247i	−0.0590125	+	0.998257i	$0.518795\pi$
$594$	10.1922			0.418192
$595$		0			0
$596$	−3.88448			−0.159115
$597$	−21.6557	+	5.80262i	−0.886307	+	0.237485i
$598$	4.36322	−	16.2838i	0.178425	−	0.665892i
$599$	20.6390	−	11.9159i	0.843287	−	0.486872i	−0.0150931	−	0.999886i	$-0.504804\pi$
$599$	20.6390	−	11.9159i	0.843287	−	0.486872i	0.858380	+	0.513014i	$0.171471\pi$
$600$		0			0
$601$			13.8729i			0.565887i	0.959137	+	0.282944i	$0.0913110\pi$
$601$			13.8729i			0.565887i	−0.959137	+	0.282944i	$0.908689\pi$
$602$	29.7947	+	38.6622i	1.21434	+	1.57575i
$603$	1.08327	−	1.08327i	0.0441140	−	0.0441140i
$604$	−42.0235	−	24.2623i	−1.70991	−	0.987219i
$605$		0			0
$606$	−5.69158	−	9.85810i	−0.231205	−	0.400458i
$607$	10.7542	+	40.1351i	0.436498	+	1.62903i	0.737456	+	0.675395i	$0.236027\pi$
$607$	10.7542	+	40.1351i	0.436498	+	1.62903i	−0.300958	+	0.953637i	$0.597306\pi$
$608$	53.5162	+	53.5162i	2.17037	+	2.17037i
$609$	−12.4790	+	16.3332i	−0.505673	+	0.661855i
$610$		0			0
$611$	−1.05776	+	1.83209i	−0.0427923	+	0.0741185i
$612$	−24.5562	−	6.57981i	−0.992624	−	0.265973i
$613$	46.8226	+	12.5461i	1.89115	+	0.506731i	0.998424	+	0.0561248i	$0.0178745\pi$
$613$	46.8226	+	12.5461i	1.89115	+	0.506731i	0.892723	+	0.450606i	$0.148792\pi$
$614$	−20.7906	+	36.0103i	−0.839039	+	1.45326i
$615$		0			0
$616$	47.2228	−	61.8081i	1.90266	−	2.49032i
$617$	4.18738	+	4.18738i	0.168578	+	0.168578i	0.786354	−	0.617776i	$-0.211966\pi$
$617$	4.18738	+	4.18738i	0.168578	+	0.168578i	−0.617776	+	0.786354i	$0.711966\pi$
$618$	−1.65412	−	6.17326i	−0.0665384	−	0.248325i
$619$	−7.48289	−	12.9607i	−0.300763	−	0.520936i	0.675546	−	0.737318i	$-0.263908\pi$
$619$	−7.48289	−	12.9607i	−0.300763	−	0.520936i	−0.976309	+	0.216381i	$0.930575\pi$
$620$		0			0
$621$	5.56424	+	3.21251i	0.223285	+	0.128914i
$622$	−48.9979	+	48.9979i	−1.96464	+	1.96464i
$623$	24.1228	+	31.3022i	0.966458	+	1.25410i
$624$		−	10.0892i		−	0.403892i
$625$		0			0
$626$	−38.8319	+	22.4196i	−1.55203	+	0.896067i
$627$	6.71252	−	25.0515i	0.268072	−	1.00046i
$628$	−10.9470	+	2.93325i	−0.436834	+	0.117049i
$629$	0.268083			0.0106892
$630$		0			0
$631$	28.8319			1.14778			0.573889	−	0.818933i	$-0.305434\pi$
$631$	28.8319			1.14778			0.573889	+	0.818933i	$0.305434\pi$
$632$	77.8821	−	20.8685i	3.09799	−	0.830103i
$633$	−4.83803	+	18.0558i	−0.192294	+	0.717653i
$634$	−33.0975	+	19.1088i	−1.31447	+	0.758909i
$635$		0			0
$636$		−	10.1922i		−	0.404148i
$637$	−0.0291526	−	6.99994i	−0.00115507	−	0.277348i
$638$	55.9909	−	55.9909i	2.21670	−	2.21670i
$639$	2.28673	+	1.32025i	0.0904618	+	0.0522281i
$640$		0			0
$641$	9.61419	+	16.6523i	0.379738	+	0.657725i	0.991024	−	0.133685i	$-0.0426809\pi$
$641$	9.61419	+	16.6523i	0.379738	+	0.657725i	−0.611286	+	0.791410i	$0.709348\pi$
$642$	−4.63901	−	17.3130i	−0.183087	−	0.683290i
$643$	−23.6685	−	23.6685i	−0.933396	−	0.933396i	0.0645203	−	0.997916i	$-0.479448\pi$
$643$	−23.6685	−	23.6685i	−0.933396	−	0.933396i	−0.997916	+	0.0645203i	$0.979448\pi$
$644$	76.6447	−	31.9344i	3.02023	−	1.25839i
$645$		0			0
$646$	−45.5890	+	78.9625i	−1.79368	+	3.10674i
$647$	−3.75212	−	1.00538i	−0.147511	−	0.0395255i	0.184308	−	0.982869i	$-0.440996\pi$
$647$	−3.75212	−	1.00538i	−0.147511	−	0.0395255i	−0.331819	+	0.943343i	$0.607662\pi$
$648$	7.31051	+	1.95884i	0.287184	+	0.0769507i
$649$	−14.0449	+	24.3265i	−0.551312	+	0.954900i
$650$		0			0
$651$	−16.8582	−	2.18372i	−0.660724	−	0.0855867i
$652$	−16.8999	−	16.8999i	−0.661851	−	0.661851i
$653$	−7.16508	−	26.7404i	−0.280391	−	1.04643i	−0.952142	−	0.305657i	$-0.901124\pi$
$653$	−7.16508	−	26.7404i	−0.280391	−	1.04643i	0.671750	−	0.740778i	$-0.265543\pi$
$654$	−3.88424	−	6.72770i	−0.151886	−	0.263074i
$655$		0			0
$656$	48.4998	+	28.0014i	1.89360	+	1.09327i
$657$	−6.65349	+	6.65349i	−0.259577	+	0.259577i
$658$	−14.5563	+	1.94721i	−0.567462	+	0.0759102i
$659$		−	11.1129i		−	0.432896i	−0.976294	−	0.216448i	$-0.930553\pi$
$659$		−	11.1129i		−	0.432896i	0.976294	−	0.216448i	$-0.0694471\pi$
$660$		0			0
$661$	10.0946	−	5.82810i	0.392633	−	0.226687i	−0.290667	−	0.956824i	$-0.593877\pi$
$661$	10.0946	−	5.82810i	0.392633	−	0.226687i	0.683300	+	0.730137i	$0.260544\pi$
$662$	−5.41492	+	20.2087i	−0.210457	+	0.785435i
$663$	5.02738	−	1.34708i	0.195247	−	0.0523164i
$664$	16.0111			0.621350
$665$		0			0
$666$	−0.135147			−0.00523684
$667$	48.2150	−	12.9192i	1.86689	−	0.500232i
$668$	17.8448	−	66.5977i	0.690436	−	2.57674i
$669$	22.0597	−	12.7362i	0.852878	−	0.492409i
$670$		0			0
$671$			33.6406i			1.29868i
$672$	23.7555	−	18.3070i	0.916389	−	0.706207i
$673$	−13.2621	+	13.2621i	−0.511216	+	0.511216i	−0.914899	−	0.403683i	$-0.867730\pi$
$673$	−13.2621	+	13.2621i	−0.511216	+	0.511216i	0.403683	+	0.914899i	$0.367730\pi$
$674$	19.7958	+	11.4291i	0.762504	+	0.440232i
$675$		0			0
$676$	−29.3069	−	50.7610i	−1.12719	−	1.95235i
$677$	−5.30268	−	19.7899i	−0.203799	−	0.760587i	−0.989812	−	0.142378i	$-0.954525\pi$
$677$	−5.30268	−	19.7899i	−0.203799	−	0.760587i	0.786014	−	0.618209i	$-0.212141\pi$
$678$	11.9205	+	11.9205i	0.457805	+	0.457805i
$679$	−4.81282	−	11.5511i	−0.184699	−	0.443290i
$680$		0			0
$681$	6.52498	−	11.3016i	0.250038	−	0.433078i
$682$	63.2540	+	16.9489i	2.42212	+	0.649005i
$683$	−4.02536	−	1.07859i	−0.154026	−	0.0412712i	0.180982	−	0.983486i	$-0.442072\pi$
$683$	−4.02536	−	1.07859i	−0.154026	−	0.0412712i	−0.335008	+	0.942215i	$0.608739\pi$
$684$	16.3059	−	28.2427i	0.623472	−	1.07989i
$685$		0			0
$686$	38.3667	−	29.8224i	1.46485	−	1.13863i
$687$	7.38489	+	7.38489i	0.281751	+	0.281751i
$688$	−18.3605	−	68.5223i	−0.699987	−	2.61239i
$689$	1.04333	+	1.80709i	0.0397476	+	0.0688448i
$690$		0			0
$691$	−23.7032	−	13.6851i	−0.901713	−	0.520604i	−0.0239572	−	0.999713i	$-0.507627\pi$
$691$	−23.7032	−	13.6851i	−0.901713	−	0.520604i	−0.877755	+	0.479109i	$0.840960\pi$
$692$	−20.7231	+	20.7231i	−0.787774	+	0.787774i
$693$	−9.50323	−	3.91320i	−0.360998	−	0.148650i
$694$		−	80.2280i		−	3.04541i
$695$		0			0
$696$	50.9211	−	29.3993i	1.93016	−	1.11438i
$697$	−7.47733	+	27.9058i	−0.283224	+	1.05701i
$698$	−7.07081	+	1.89462i	−0.267634	+	0.0717124i
$699$	−1.98364			−0.0750281
$700$		0			0
$701$	−21.4358			−0.809618			−0.404809	−	0.914401i	$-0.632662\pi$
$701$	−21.4358			−0.809618			−0.404809	+	0.914401i	$0.632662\pi$
$702$	−2.53443	+	0.679097i	−0.0956557	+	0.0256309i
$703$	−0.0890068	+	0.332178i	−0.00335696	+	0.0125283i
$704$	−32.1747	+	18.5761i	−1.21263	+	0.700112i
$705$		0			0
$706$		−	77.0964i		−	2.90156i
$707$	1.52191	+	11.3769i	0.0572372	+	0.427873i
$708$	−24.9758	+	24.9758i	−0.938649	+	0.938649i
$709$	−2.78660	−	1.60884i	−0.104653	−	0.0604214i	0.446760	−	0.894654i	$-0.352578\pi$
$709$	−2.78660	−	1.60884i	−0.104653	−	0.0604214i	−0.551413	+	0.834232i	$0.685911\pi$
$710$		0			0
$711$	−5.32673	−	9.22616i	−0.199768	−	0.346008i
$712$	−29.2587	−	109.195i	−1.09652	−	4.09225i
$713$	29.1901	+	29.1901i	1.09318	+	1.09318i
$714$	28.7106	+	21.9356i	1.07447	+	0.820918i
$715$		0			0
$716$	29.3069	−	50.7610i	1.09525	−	1.89703i
$717$	−6.49007	−	1.73901i	−0.242376	−	0.0649445i
$718$	71.1233	+	19.0574i	2.65430	+	0.711217i
$719$	18.1298	−	31.4017i	0.676126	−	1.17108i	−0.300013	−	0.953935i	$-0.596991\pi$
$719$	18.1298	−	31.4017i	0.676126	−	1.17108i	0.976138	−	0.217149i	$-0.0696757\pi$
$720$		0			0
$721$	−0.827859	+	6.39103i	−0.0308311	+	0.238014i
$722$	−47.4541	−	47.4541i	−1.76606	−	1.76606i
$723$	−6.34268	−	23.6712i	−0.235887	−	0.880342i
$724$	39.6770	+	68.7226i	1.47459	+	2.55406i
$725$		0			0
$726$	9.29193	+	5.36470i	0.344856	+	0.199103i
$727$	32.0737	−	32.0737i	1.18955	−	1.18955i	0.212357	−	0.977192i	$-0.431886\pi$
$727$	32.0737	−	32.0737i	1.18955	−	1.18955i	0.977192	−	0.212357i	$-0.0681140\pi$
$728$	−7.62435	+	18.5158i	−0.282577	+	0.686240i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	31.6927	−	18.2978i	1.17220	−	0.676768i
$732$	−10.9483	+	40.8595i	−0.404660	+	1.51021i
$733$	−0.0482502	+	0.0129286i	−0.00178216	+	0.000477529i	−0.259710	−	0.965687i	$-0.583627\pi$
$733$	−0.0482502	+	0.0129286i	−0.00178216	+	0.000477529i	0.257928	+	0.966164i	$0.416960\pi$
$734$	−70.4713			−2.60114
$735$		0			0
$736$	−72.8315			−2.68460
$737$	5.74814	−	1.54021i	0.211736	−	0.0567344i
$738$	3.76950	−	14.0680i	0.138757	−	0.517849i
$739$	−1.70927	+	0.986849i	−0.0628766	+	0.0363018i	−0.531109	−	0.847304i	$-0.678224\pi$
$739$	−1.70927	+	0.986849i	−0.0628766	+	0.0363018i	0.468232	+	0.883605i	$0.344891\pi$
$740$		0			0
$741$			6.67662i			0.245272i
$742$	−5.51550	+	13.3944i	−0.202480	+	0.491725i
$743$	−0.784440	+	0.784440i	−0.0287783	+	0.0287783i	−0.721350	−	0.692571i	$-0.756478\pi$
$743$	−0.784440	+	0.784440i	−0.0287783	+	0.0287783i	0.692571	+	0.721350i	$0.256478\pi$
$744$	42.1123	+	24.3136i	1.54391	+	0.891379i
$745$		0			0
$746$	3.95206	+	6.84516i	0.144695	+	0.250619i
$747$	−0.547536	−	2.04343i	−0.0200333	−	0.0747653i
$748$	−69.8289	−	69.8289i	−2.55320	−	2.55320i
$749$	−2.32175	+	17.9237i	−0.0848348	+	0.654919i
$750$		0			0
$751$	20.4855	−	35.4820i	0.747527	−	1.29476i	−0.201477	−	0.979493i	$-0.564574\pi$
$751$	20.4855	−	35.4820i	0.747527	−	1.29476i	0.949005	−	0.315262i	$-0.102092\pi$
$752$	20.6166	+	5.52421i	0.751811	+	0.201447i
$753$	8.18783	+	2.19392i	0.298381	+	0.0799510i
$754$	−10.1922	+	17.6535i	−0.371179	+	0.642901i
$755$		0			0
$756$	−10.2690	−	7.84574i	−0.373479	−	0.285347i
$757$	−7.17478	−	7.17478i	−0.260772	−	0.260772i	0.564596	−	0.825368i	$-0.309032\pi$
$757$	−7.17478	−	7.17478i	−0.260772	−	0.260772i	−0.825368	+	0.564596i	$0.809032\pi$
$758$	24.2994	+	90.6866i	0.882594	+	3.29389i
$759$	12.4790	+	21.6142i	0.452957	+	0.784545i
$760$		0			0
$761$	23.7678	+	13.7224i	0.861583	+	0.497435i	0.864542	−	0.502560i	$-0.167609\pi$
$761$	23.7678	+	13.7224i	0.861583	+	0.497435i	−0.00295888	+	0.999996i	$0.500942\pi$
$762$	−32.9843	+	32.9843i	−1.19489	+	1.19489i
$763$	1.03863	+	7.76422i	0.0376010	+	0.281084i
$764$			44.0236i			1.59272i
$765$		0			0
$766$	46.5549	−	26.8785i	1.68210	−	0.971159i
$767$	1.87160	−	6.98490i	0.0675795	−	0.252210i
$768$	12.3339	−	3.30485i	0.445060	−	0.119254i
$769$	−14.0274			−0.505842			−0.252921	−	0.967487i	$-0.581391\pi$
$769$	−14.0274			−0.505842			−0.252921	+	0.967487i	$0.581391\pi$
$770$		0			0
$771$	−12.1022			−0.435849
$772$	38.2425	−	10.2470i	1.37638	−	0.368799i
$773$	10.1937	−	38.0434i	0.366642	−	1.36833i	−0.498540	−	0.866867i	$-0.666130\pi$
$773$	10.1937	−	38.0434i	0.366642	−	1.36833i	0.865181	−	0.501459i	$-0.167203\pi$
$774$	−15.9771	+	9.22436i	−0.574284	+	0.331563i
$775$		0			0
$776$			35.7963i			1.28501i
$777$	0.126011	+	0.0518883i	0.00452062	+	0.00186148i
$778$	22.4535	−	22.4535i	0.804997	−	0.804997i
$779$	−32.0951	−	18.5301i	−1.14993	−	0.663911i
$780$		0			0
$781$	5.12847	+	8.88278i	0.183511	+	0.317851i
$782$	−22.7094	−	84.7525i	−0.812086	−	3.03074i
$783$	−5.49349	−	5.49349i	−0.196321	−	0.196321i
$784$	−68.1413	+	18.5629i	−2.43362	+	0.662961i
$785$		0			0
$786$	−5.33988	+	9.24894i	−0.190467	+	0.329899i
$787$	−50.4509	−	13.5183i	−1.79838	−	0.481875i	−0.804658	−	0.593739i	$-0.797651\pi$
$787$	−50.4509	−	13.5183i	−1.79838	−	0.481875i	−0.993724	+	0.111864i	$0.964318\pi$
$788$	33.6597	+	9.01908i	1.19908	+	0.321291i
$789$	8.51168	−	14.7427i	0.303024	−	0.524853i
$790$		0			0
$791$	−6.53793	−	15.6915i	−0.232462	−	0.557925i
$792$	20.7884	+	20.7884i	0.738685	+	0.738685i
$793$	−2.24144	−	8.36516i	−0.0795958	−	0.297056i
$794$	43.9814	+	76.1780i	1.56084	+	2.70346i
$795$		0			0
$796$	−94.8368	−	54.7541i	−3.36140	−	1.94071i
$797$	−22.5902	+	22.5902i	−0.800187	+	0.800187i	−0.983124	−	0.182938i	$-0.941439\pi$
$797$	−22.5902	+	22.5902i	−0.800187	+	0.800187i	0.182938	+	0.983124i	$0.441439\pi$
$798$	−36.7124	+	28.2920i	−1.29960	+	1.00153i
$799$			11.0107i			0.389530i
$800$		0			0
$801$	−12.9356	+	7.46835i	−0.457056	+	0.263881i
$802$	25.5970	−	95.5294i	0.903862	−	3.37326i
$803$	−35.3055	+	9.46007i	−1.24590	+	0.333839i
$804$	7.48289			0.263901
$805$		0			0
$806$	−16.8582			−0.593804
$807$	1.91605	−	0.513403i	0.0674481	−	0.0180727i
$808$	8.49820	−	31.7157i	0.298966	−	1.11576i
$809$	−40.8145	+	23.5642i	−1.43496	+	0.828474i	−0.997493	−	0.0707602i	$-0.977457\pi$
$809$	−40.8145	+	23.5642i	−1.43496	+	0.828474i	−0.437467	+	0.899235i	$0.644124\pi$
$810$		0			0
$811$			41.4206i			1.45448i	0.686386	+	0.727238i	$0.259196\pi$
$811$			41.4206i			1.45448i	−0.686386	+	0.727238i	$0.740804\pi$
$812$	−99.5129	+	13.3120i	−3.49222	+	0.467159i
$813$	1.33401	−	1.33401i	0.0467857	−	0.0467857i
$814$	−0.454643	−	0.262488i	−0.0159352	−	0.00920020i
$815$		0			0
$816$	−26.2558	−	45.4764i	−0.919137	−	1.59199i
$817$	12.1502	+	45.3451i	0.425081	+	1.58643i
$818$	−3.59578	−	3.59578i	−0.125723	−	0.125723i
$819$	2.62383	+	0.339877i	0.0916840	+	0.0118763i
$820$		0			0
$821$	13.3713	−	23.1598i	0.466663	−	0.808284i	−0.532612	−	0.846359i	$-0.678790\pi$
$821$	13.3713	−	23.1598i	0.466663	−	0.808284i	0.999275	+	0.0380759i	$0.0121229\pi$
$822$	17.8201	+	4.77488i	0.621547	+	0.166543i
$823$	−12.1692	−	3.26072i	−0.424191	−	0.113662i	0.0404070	−	0.999183i	$-0.487135\pi$
$823$	−12.1692	−	3.26072i	−0.424191	−	0.113662i	−0.464598	+	0.885522i	$0.653801\pi$
$824$	9.21741	−	15.9650i	0.321104	−	0.556168i
$825$		0			0
$826$	46.3384	−	19.3071i	1.61232	−	0.671781i
$827$	12.7489	+	12.7489i	0.443324	+	0.443324i	0.893127	−	0.449804i	$-0.148506\pi$
$827$	12.7489	+	12.7489i	0.443324	+	0.443324i	−0.449804	+	0.893127i	$0.648506\pi$
$828$	8.12250	+	30.3136i	0.282277	+	1.05347i
$829$	0.174326	+	0.301942i	0.00605460	+	0.0104869i	0.869037	−	0.494747i	$-0.164739\pi$
$829$	0.174326	+	0.301942i	0.00605460	+	0.0104869i	−0.862982	+	0.505234i	$0.831406\pi$
$830$		0			0
$831$	15.6588	+	9.04061i	0.543198	+	0.313615i
$832$	6.76294	−	6.76294i	0.234463	−	0.234463i
$833$	−18.3478	−	31.4759i	−0.635714	−	1.09057i
$834$			49.7360i			1.72222i
$835$		0			0
$836$	109.708	−	63.3400i	3.79434	−	2.19066i
$837$	1.66292	−	6.20610i	0.0574789	−	0.214514i
$838$	−50.6336	+	13.5672i	−1.74911	+	0.468672i
$839$	51.9734			1.79432			0.897161	−	0.441704i	$-0.145626\pi$
$839$	51.9734			1.79432			0.897161	+	0.441704i	$0.145626\pi$
$840$		0			0
$841$	−31.3569			−1.08127
$842$	18.8782	−	5.05841i	0.650587	−	0.174324i
$843$	4.95693	−	18.4995i	0.170726	−	0.637158i
$844$	−79.0718	+	45.6521i	−2.72176	+	1.57141i
$845$		0			0
$846$		−	5.55076i		−	0.190839i
$847$	−6.60407	−	8.56959i	−0.226919	−	0.294455i
$848$	14.8865	−	14.8865i	0.511205	−	0.511205i
$849$	−21.5050	−	12.4159i	−0.738051	−	0.426114i
$850$		0			0
$851$	−0.165469	−	0.286600i	−0.00567219	−	0.00982452i
$852$	3.33810	+	12.4580i	0.114362	+	0.426803i
$853$	3.33685	+	3.33685i	0.114251	+	0.114251i	0.761921	−	0.647670i	$-0.224256\pi$
$853$	3.33685	+	3.33685i	0.114251	+	0.114251i	−0.647670	+	0.761921i	$0.724256\pi$
$854$	36.4990	−	47.7721i	1.24897	−	1.63473i
$855$		0			0
$856$	25.8504	−	44.7742i	0.883548	−	1.53035i
$857$	−32.2478	−	8.64078i	−1.10157	−	0.295164i	−0.338164	−	0.941087i	$-0.609806\pi$
$857$	−32.2478	−	8.64078i	−1.10157	−	0.295164i	−0.763402	+	0.645924i	$0.776472\pi$
$858$	−9.84493	−	2.63794i	−0.336100	−	0.0900579i
$859$	−2.81235	+	4.87114i	−0.0959563	+	0.166201i	−0.910007	−	0.414592i	$-0.863924\pi$
$859$	−2.81235	+	4.87114i	−0.0959563	+	0.166201i	0.814051	+	0.580793i	$0.197258\pi$
$860$		0			0
$861$	−8.91594	+	11.6697i	−0.303854	+	0.397703i
$862$	−8.18099	−	8.18099i	−0.278646	−	0.278646i
$863$	6.43446	+	24.0137i	0.219032	+	0.817437i	0.984708	+	0.174211i	$0.0557376\pi$
$863$	6.43446	+	24.0137i	0.219032	+	0.817437i	−0.765677	+	0.643226i	$0.777596\pi$
$864$	5.66780	+	9.81691i	0.192822	+	0.333978i
$865$		0			0
$866$	38.8319	+	22.4196i	1.31956	+	0.761849i
$867$	7.13415	−	7.13415i	0.242288	−	0.242288i
$868$	−50.6834	−	65.7679i	−1.72031	−	2.23231i
$869$		−	41.3832i		−	1.40383i
$870$		0			0
$871$	−1.32673	+	0.765985i	−0.0449544	+	0.0259544i
$872$	5.79963	−	21.6445i	0.196400	−	0.732975i
$873$	4.56855	−	1.22414i	0.154622	−	0.0414308i
$874$	112.556			3.80725
$875$		0			0
$876$	−45.9604			−1.55286
$877$	32.9587	−	8.83125i	1.11294	−	0.298210i	0.344914	−	0.938634i	$-0.387908\pi$
$877$	32.9587	−	8.83125i	1.11294	−	0.298210i	0.768022	+	0.640424i	$0.221241\pi$
$878$	−13.2381	+	49.4053i	−0.446764	+	1.66735i
$879$	11.7698	−	6.79527i	0.396984	−	0.229199i
$880$		0			0
$881$		−	7.67040i		−	0.258422i	−0.991617	−	0.129211i	$-0.958755\pi$
$881$		−	7.67040i		−	0.258422i	0.991617	−	0.129211i	$-0.0412445\pi$
$882$	9.24957	+	15.8677i	0.311449	+	0.534295i
$883$	−17.8491	+	17.8491i	−0.600671	+	0.600671i	−0.940491	−	0.339819i	$-0.889634\pi$
$883$	−17.8491	+	17.8491i	−0.600671	+	0.600671i	0.339819	+	0.940491i	$0.389634\pi$
$884$	22.0165	+	12.7112i	0.740494	+	0.427524i
$885$		0			0
$886$	38.2610	+	66.2699i	1.28540	+	2.22638i
$887$	−3.83542	−	14.3140i	−0.128781	−	0.480616i	0.871165	−	0.490990i	$-0.163365\pi$
$887$	−3.83542	−	14.3140i	−0.128781	−	0.480616i	−0.999946	+	0.0103733i	$0.996698\pi$
$888$	−0.275651	−	0.275651i	−0.00925024	−	0.00925024i
$889$	43.4185	−	18.0905i	1.45621	−	0.606737i
$890$		0			0
$891$	1.94224	−	3.36406i	0.0650676	−	0.112700i
$892$	120.180	+	32.2021i	4.02392	+	1.07821i
$893$	−13.6432	−	3.65569i	−0.456553	−	0.122333i
$894$	−1.04333	+	1.80709i	−0.0348941	+	0.0604383i
$895$		0			0
$896$	6.35951	+	0.823777i	0.212456	+	0.0275204i
$897$	−4.54318	−	4.54318i	−0.151692	−	0.151692i
$898$	14.7993	+	55.2318i	0.493859	+	1.84311i
$899$	−24.9579	−	43.2284i	−0.832393	−	1.44175i
$900$		0			0
$901$	9.40544	+	5.43023i	0.313341	+	0.180907i
$902$	40.0042	−	40.0042i	1.33200	−	1.33200i
$903$	18.4386	−	2.46656i	0.613598	−	0.0820820i
$904$			48.6271i			1.61731i
$905$		0			0
$906$	−22.5741	+	13.0331i	−0.749973	+	0.432997i
$907$	3.26072	−	12.1692i	0.108271	−	0.404071i	−0.890425	−	0.455130i	$-0.849593\pi$
$907$	3.26072	−	12.1692i	0.108271	−	0.404071i	0.998696	+	0.0510586i	$0.0162595\pi$
$908$	61.5703	−	16.4977i	2.04328	−	0.547496i
$909$	−4.33837			−0.143895
$910$		0			0
$911$	−20.6405			−0.683850			−0.341925	−	0.939727i	$-0.611079\pi$
$911$	−20.6405			−0.683850			−0.341925	+	0.939727i	$0.611079\pi$
$912$	65.0665	−	17.4345i	2.15457	−	0.577315i
$913$	2.12689	−	7.93768i	0.0703899	−	0.262699i
$914$	−3.54714	+	2.04794i	−0.117329	+	0.0677399i
$915$		0			0
$916$			51.0126i			1.68550i
$917$	8.52994	−	6.57352i	0.281683	−	0.217077i
$918$	−9.65648	+	9.65648i	−0.318711	+	0.318711i
$919$	6.15100	+	3.55128i	0.202903	+	0.117146i	0.598009	−	0.801490i	$-0.295959\pi$
$919$	6.15100	+	3.55128i	0.202903	+	0.117146i	−0.395106	+	0.918636i	$0.629292\pi$
$920$		0			0
$921$	7.92375	+	13.7243i	0.261096	+	0.452232i
$922$	0.0699572	+	0.261084i	0.00230392	+	0.00859834i
$923$	−1.86711	−	1.86711i	−0.0614567	−	0.0614567i
$924$	−19.3071	−	46.3384i	−0.635158	−	1.52442i
$925$		0			0
$926$	−26.0531	+	45.1253i	−0.856158	+	1.48291i
$927$	−2.35277	−	0.630422i	−0.0772750	−	0.0207058i
$928$	85.0651	+	22.7931i	2.79240	+	0.748221i
$929$	26.2178	−	45.4106i	0.860179	−	1.48987i	−0.0115773	−	0.999933i	$-0.503685\pi$
$929$	26.2178	−	45.4106i	0.860179	−	1.48987i	0.871756	−	0.489940i	$-0.162981\pi$
$930$		0			0
$931$	45.0930	−	12.2842i	1.47786	−	0.402597i
$932$	−6.85119	−	6.85119i	−0.224418	−	0.224418i
$933$	6.83523	+	25.5094i	0.223776	+	0.835142i
$934$	−26.1693	−	45.3265i	−0.856285	−	1.48313i
$935$		0			0
$936$	−6.55442	−	3.78420i	−0.214238	−	0.123690i
$937$	−17.5774	+	17.5774i	−0.574228	+	0.574228i	−0.933307	−	0.359079i	$-0.883091\pi$
$937$	−17.5774	+	17.5774i	−0.574228	+	0.574228i	0.359079	+	0.933307i	$0.383091\pi$
$938$	−9.83386	−	4.04935i	−0.321087	−	0.132216i
$939$			17.0892i			0.557685i
$940$		0			0
$941$	18.4461	−	10.6498i	0.601325	−	0.347175i	−0.168238	−	0.985746i	$-0.553808\pi$
$941$	18.4461	−	10.6498i	0.601325	−	0.347175i	0.769563	+	0.638571i	$0.220474\pi$
$942$	−1.57567	+	5.88049i	−0.0513382	+	0.191597i
$943$	34.4485	−	9.23046i	1.12180	−	0.300585i
$944$	−72.9581			−2.37458
$945$		0			0
$946$	−71.6638			−2.32999
$947$	−36.0337	+	9.65519i	−1.17094	+	0.313752i	−0.791326	−	0.611395i	$-0.790609\pi$
$947$	−36.0337	+	9.65519i	−1.17094	+	0.313752i	−0.379611	+	0.925146i	$0.623942\pi$
$948$	13.4681	−	50.2635i	0.437422	−	1.63248i
$949$	8.14883	−	4.70473i	0.264522	−	0.152722i
$950$		0			0
$951$			14.5656i			0.472322i
$952$	13.8186	+	103.300i	0.447863	+	3.34797i
$953$	22.4302	−	22.4302i	0.726585	−	0.726585i	−0.243353	−	0.969938i	$-0.578247\pi$
$953$	22.4302	−	22.4302i	0.726585	−	0.726585i	0.969938	+	0.243353i	$0.0782474\pi$
$954$	−4.74151	−	2.73751i	−0.153512	−	0.0886302i
$955$		0			0
$956$	−16.4095	−	28.4220i	−0.530720	−	0.919234i
$957$	−7.81075	−	29.1501i	−0.252486	−	0.942290i
$958$	8.30519	+	8.30519i	0.268329	+	0.268329i
$959$	−14.7822	−	11.2939i	−0.477342	−	0.364700i
$960$		0			0
$961$	5.14049	−	8.90359i	0.165822	−	0.287213i
$962$	0.130542	+	0.0349786i	0.00420884	+	0.00112776i
$963$	−6.59837	−	1.76803i	−0.212630	−	0.0569739i
$964$	59.8502	−	103.664i	1.92764	−	3.33878i
$965$		0			0
$966$	5.72971	−	44.2330i	0.184350	−	1.42317i
$967$	−8.93322	−	8.93322i	−0.287273	−	0.287273i	0.548728	−	0.836001i	$-0.315112\pi$
$967$	−8.93322	−	8.93322i	−0.287273	−	0.287273i	−0.836001	+	0.548728i	$0.815112\pi$
$968$	8.01013	+	29.8942i	0.257455	+	0.960837i
$969$	17.3750	+	30.0944i	0.558165	+	0.966770i
$970$		0			0
$971$	8.91594	+	5.14762i	0.286126	+	0.165195i	0.636194	−	0.771530i	$-0.280508\pi$
$971$	8.91594	+	5.14762i	0.286126	+	0.165195i	−0.350067	+	0.936725i	$0.613841\pi$
$972$	3.45385	−	3.45385i	0.110782	−	0.110782i
$973$	19.0956	−	46.3738i	0.612178	−	1.48668i
$974$			42.8056i			1.37158i
$975$		0			0
$976$	−75.6691	+	43.6876i	−2.42211	+	1.39841i
$977$	14.4443	−	53.9070i	0.462115	−	1.72464i	−0.204165	−	0.978936i	$-0.565448\pi$
$977$	14.4443	−	53.9070i	0.462115	−	1.72464i	0.666281	−	0.745701i	$-0.267885\pi$
$978$	−12.4011	+	3.32286i	−0.396543	+	0.106253i
$979$	−58.0214			−1.85437
$980$		0			0
$981$	−2.96074			−0.0945291
$982$	−102.415	+	27.4419i	−3.26819	+	0.875708i
$983$	−8.86231	+	33.0746i	−0.282664	+	1.05492i	0.667866	+	0.744282i	$0.267208\pi$
$983$	−8.86231	+	33.0746i	−0.282664	+	1.05492i	−0.950530	+	0.310634i	$0.899459\pi$
$984$	36.3820	−	21.0052i	1.15982	−	0.669620i
$985$		0			0
$986$			106.096i			3.37877i
$987$	−2.13116	+	5.17552i	−0.0678355	+	0.164739i
$988$	−23.0600	+	23.0600i	−0.733638	+	0.733638i
$989$	−39.1234	−	22.5879i	−1.24405	−	0.718253i
$990$		0			0
$991$	17.7993	+	30.8293i	0.565413	+	0.979324i	0.997011	+	0.0772581i	$0.0246166\pi$
$991$	17.7993	+	30.8293i	0.565413	+	0.979324i	−0.431598	+	0.902066i	$0.642050\pi$
$992$	18.8502	+	70.3498i	0.598494	+	2.23361i
$993$	5.63826	+	5.63826i	0.178925	+	0.178925i
$994$	2.35474	−	18.1784i	0.0746877	−	0.576585i
$995$		0			0
$996$	5.16660	−	8.94882i	0.163710	−	0.283554i
$997$	0.309334	+	0.0828858i	0.00979671	+	0.00262502i	0.263714	−	0.964601i	$-0.415052\pi$
$997$	0.309334	+	0.0828858i	0.00979671	+	0.00262502i	−0.253917	+	0.967226i	$0.581719\pi$
$998$	77.0038	+	20.6331i	2.43751	+	0.653130i
$999$	−0.0257538	+	0.0446068i	−0.000814813	+	0.00141130i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bc.c.82.6	yes	24
5.2	odd	4	inner	525.2.bc.c.418.6	yes	24
5.3	odd	4	inner	525.2.bc.c.418.1	yes	24
5.4	even	2	inner	525.2.bc.c.82.1	✓	24
7.3	odd	6	inner	525.2.bc.c.157.1	yes	24
35.3	even	12	inner	525.2.bc.c.493.6	yes	24
35.17	even	12	inner	525.2.bc.c.493.1	yes	24
35.24	odd	6	inner	525.2.bc.c.157.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bc.c.82.1	✓	24	5.4	even	2	inner
525.2.bc.c.82.6	yes	24	1.1	even	1	trivial
525.2.bc.c.157.1	yes	24	7.3	odd	6	inner
525.2.bc.c.157.6	yes	24	35.24	odd	6	inner
525.2.bc.c.418.1	yes	24	5.3	odd	4	inner
525.2.bc.c.418.6	yes	24	5.2	odd	4	inner
525.2.bc.c.493.1	yes	24	35.17	even	12	inner
525.2.bc.c.493.6	yes	24	35.3	even	12	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.53443 - 0.679097i) q^{2} +(0.258819 - 0.965926i) q^{3} +(4.23009 - 2.44224i) q^{4} -2.62383i q^{6} +(-1.00739 + 2.44646i) q^{7} +(5.35166 - 5.35166i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(2.53443 - 0.679097i) q^{2} +(0.258819 - 0.965926i) q^{3} +(4.23009 - 2.44224i) q^{4} -2.62383i q^{6} +(-1.00739 + 2.44646i) q^{7} +(5.35166 - 5.35166i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.94224 - 3.36406i) q^{11} +(-1.26420 - 4.71805i) q^{12} +(0.707107 + 0.707107i) q^{13} +(-0.891779 + 6.88448i) q^{14} +(5.04461 - 8.73752i) q^{16} +(5.02738 + 1.34708i) q^{17} +(-2.53443 - 0.679097i) q^{18} +(-3.33831 + 5.78212i) q^{19} +(2.10236 + 1.60626i) q^{21} +(-7.20699 - 7.20699i) q^{22} +(-1.66292 - 6.20610i) q^{23} +(-3.78420 - 6.55442i) q^{24} +(2.27230 + 1.31191i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.71348 + 12.8090i) q^{28} +7.76897i q^{29} +(-5.56424 + 3.21251i) q^{31} +(2.93387 - 10.9493i) q^{32} +(-3.75212 + 1.00538i) q^{33} +13.6563 q^{34} -4.88448 q^{36} +(0.0497524 - 0.0133311i) q^{37} +(-4.53407 + 16.9214i) q^{38} +(0.866025 - 0.500000i) q^{39} +5.55076i q^{41} +(6.41909 + 2.64323i) q^{42} +(4.97182 - 4.97182i) q^{43} +(-16.4317 - 9.48685i) q^{44} +(-8.42909 - 14.5996i) q^{46} +(0.547536 + 2.04343i) q^{47} +(-7.13415 - 7.13415i) q^{48} +(-4.97032 - 4.92909i) q^{49} +(2.60236 - 4.50743i) q^{51} +(4.71805 + 1.26420i) q^{52} +(2.01555 + 0.540066i) q^{53} +(-1.31191 + 2.27230i) q^{54} +(7.70139 + 18.4839i) q^{56} +(4.72108 + 4.72108i) q^{57} +(5.27588 + 19.6899i) q^{58} +(-3.61565 - 6.26249i) q^{59} +(-7.50000 - 4.33013i) q^{61} +(-11.9205 + 11.9205i) q^{62} +(2.09566 - 1.61500i) q^{63} -9.56424i q^{64} +(-8.82673 + 5.09611i) q^{66} +(-0.396503 + 1.47977i) q^{67} +(24.5562 - 6.57981i) q^{68} -6.42503 q^{69} -2.64049 q^{71} +(-7.31051 + 1.95884i) q^{72} +(2.43535 - 9.08884i) q^{73} +(0.117041 - 0.0675735i) q^{74} +32.6118i q^{76} +(10.1866 - 1.36268i) q^{77} +(1.85533 - 1.85533i) q^{78} +(9.22616 + 5.32673i) q^{79} +(0.500000 + 0.866025i) q^{81} +(3.76950 + 14.0680i) q^{82} +(1.49590 + 1.49590i) q^{83} +(12.8161 + 1.66012i) q^{84} +(9.22436 - 15.9771i) q^{86} +(7.50425 + 2.01076i) q^{87} +(-28.3975 - 7.60910i) q^{88} +(7.46835 - 12.9356i) q^{89} +(-2.44224 + 1.01757i) q^{91} +(-22.1911 - 22.1911i) q^{92} +(1.66292 + 6.20610i) q^{93} +(2.77538 + 4.80709i) q^{94} +(-9.81691 - 5.66780i) q^{96} +(-3.34441 + 3.34441i) q^{97} +(-15.9442 - 9.11708i) q^{98} +3.88448i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 36 q^{16} + 12 q^{21} + 12 q^{26} - 24 q^{31} - 24 q^{36} - 24 q^{46} + 24 q^{51} - 36 q^{56} - 180 q^{61} - 72 q^{66} - 96 q^{71} + 12 q^{81} + 120 q^{86} - 12 q^{91} - 108 q^{96}+O(q^{100}) \) 24 * q + 36 * q^16 + 12 * q^21 + 12 * q^26 - 24 * q^31 - 24 * q^36 - 24 * q^46 + 24 * q^51 - 36 * q^56 - 180 * q^61 - 72 * q^66 - 96 * q^71 + 12 * q^81 + 120 * q^86 - 12 * q^91 - 108 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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