LMFDB - Embedded newform 525.2.bc.c.418.1

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			418.1
Character	$\chi$	$=$	525.418
Dual form			525.2.bc.c.157.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.679097 - 2.53443i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-4.23009 + 2.44224i) q^{4} -2.62383i q^{6} +(2.44646 + 1.00739i) q^{7} +(5.35166 + 5.35166i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.679097 - 2.53443i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-4.23009 + 2.44224i) q^{4} -2.62383i q^{6} +(2.44646 + 1.00739i) q^{7} +(5.35166 + 5.35166i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-1.94224 - 3.36406i) q^{11} +(-4.71805 + 1.26420i) q^{12} +(-0.707107 + 0.707107i) q^{13} +(0.891779 - 6.88448i) q^{14} +(5.04461 - 8.73752i) q^{16} +(1.34708 - 5.02738i) q^{17} +(0.679097 - 2.53443i) q^{18} +(3.33831 - 5.78212i) q^{19} +(2.10236 + 1.60626i) q^{21} +(-7.20699 + 7.20699i) q^{22} +(6.20610 - 1.66292i) q^{23} +(3.78420 + 6.55442i) q^{24} +(2.27230 + 1.31191i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-12.8090 + 1.71348i) q^{28} -7.76897i q^{29} +(-5.56424 + 3.21251i) q^{31} +(-10.9493 - 2.93387i) q^{32} +(-1.00538 - 3.75212i) q^{33} -13.6563 q^{34} -4.88448 q^{36} +(-0.0133311 - 0.0497524i) q^{37} +(-16.9214 - 4.53407i) q^{38} +(-0.866025 + 0.500000i) q^{39} +5.55076i q^{41} +(2.64323 - 6.41909i) q^{42} +(4.97182 + 4.97182i) q^{43} +(16.4317 + 9.48685i) q^{44} +(-8.42909 - 14.5996i) q^{46} +(2.04343 - 0.547536i) q^{47} +(7.13415 - 7.13415i) q^{48} +(4.97032 + 4.92909i) q^{49} +(2.60236 - 4.50743i) q^{51} +(1.26420 - 4.71805i) q^{52} +(-0.540066 + 2.01555i) q^{53} +(1.31191 - 2.27230i) q^{54} +(7.70139 + 18.4839i) q^{56} +(4.72108 - 4.72108i) q^{57} +(-19.6899 + 5.27588i) q^{58} +(3.61565 + 6.26249i) q^{59} +(-7.50000 - 4.33013i) q^{61} +(11.9205 + 11.9205i) q^{62} +(1.61500 + 2.09566i) q^{63} +9.56424i q^{64} +(-8.82673 + 5.09611i) q^{66} +(1.47977 + 0.396503i) q^{67} +(6.57981 + 24.5562i) q^{68} +6.42503 q^{69} -2.64049 q^{71} +(1.95884 + 7.31051i) q^{72} +(9.08884 + 2.43535i) q^{73} +(-0.117041 + 0.0675735i) q^{74} +32.6118i q^{76} +(-1.36268 - 10.1866i) q^{77} +(1.85533 + 1.85533i) q^{78} +(-9.22616 - 5.32673i) q^{79} +(0.500000 + 0.866025i) q^{81} +(14.0680 - 3.76950i) q^{82} +(-1.49590 + 1.49590i) q^{83} +(-12.8161 - 1.66012i) q^{84} +(9.22436 - 15.9771i) q^{86} +(2.01076 - 7.50425i) q^{87} +(7.60910 - 28.3975i) q^{88} +(-7.46835 + 12.9356i) q^{89} +(-2.44224 + 1.01757i) q^{91} +(-22.1911 + 22.1911i) q^{92} +(-6.20610 + 1.66292i) q^{93} +(-2.77538 - 4.80709i) q^{94} +(-9.81691 - 5.66780i) q^{96} +(3.34441 + 3.34441i) q^{97} +(9.11708 - 15.9442i) 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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.679097	−	2.53443i	−0.480194	−	1.79211i	−0.600789	−	0.799407i	$-0.705147\pi$
$2$	−0.679097	−	2.53443i	−0.480194	−	1.79211i	0.120595	−	0.992702i	$-0.461520\pi$
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$	−4.23009	+	2.44224i	−2.11504	+	1.22112i
$5$		0			0
$5$		0			0
$6$		−	2.62383i		−	1.07117i
$7$	2.44646	+	1.00739i	0.924674	+	0.380759i
$7$	2.44646	+	1.00739i	0.924674	+	0.380759i
$8$	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	$-0.365811\pi$
$12$	−4.71805	+	1.26420i	−1.36198	+	0.364942i
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i	−0.798333	−	0.602217i	$-0.794284\pi$
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i	0.602217	+	0.798333i	$0.294284\pi$
$14$	0.891779	−	6.88448i	0.238338	−	1.83996i
$15$		0			0
$16$	5.04461	−	8.73752i	1.26115	−	2.18438i
$17$	1.34708	−	5.02738i	0.326716	−	1.21932i	−0.585860	−	0.810412i	$-0.699243\pi$
$17$	1.34708	−	5.02738i	0.326716	−	1.21932i	0.912576	−	0.408907i	$-0.134090\pi$
$18$	0.679097	−	2.53443i	0.160065	−	0.597370i
$19$	3.33831	−	5.78212i	0.765860	−	1.32651i	−0.173930	−	0.984758i	$-0.555647\pi$
$19$	3.33831	−	5.78212i	0.765860	−	1.32651i	0.939791	−	0.341751i	$-0.111020\pi$
$20$		0			0
$21$	2.10236	+	1.60626i	0.458774	+	0.350514i
$22$	−7.20699	+	7.20699i	−1.53654	+	1.53654i
$23$	6.20610	−	1.66292i	1.29406	−	0.346743i	0.454860	−	0.890563i	$-0.349689\pi$
$23$	6.20610	−	1.66292i	1.29406	−	0.346743i	0.839202	+	0.543820i	$0.183023\pi$
$24$	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
$28$	−12.8090	+	1.71348i	−2.42068	+	0.323818i
$29$		−	7.76897i		−	1.44266i	−0.692591	−	0.721331i	$-0.743531\pi$
$29$		−	7.76897i		−	1.44266i	0.692591	−	0.721331i	$-0.256469\pi$
$30$		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	$0.529104\pi$
$32$	−10.9493	−	2.93387i	−1.93559	−	0.518639i
$33$	−1.00538	−	3.75212i	−0.175014	−	0.653161i
$34$	−13.6563			−2.34204
$35$		0			0
$36$	−4.88448			−0.814081
$37$	−0.0133311	−	0.0497524i	−0.00219162	−	0.00817925i	0.964821	−	0.262906i	$-0.0846810\pi$
$37$	−0.0133311	−	0.0497524i	−0.00219162	−	0.00817925i	−0.967013	+	0.254727i	$0.918014\pi$
$38$	−16.9214	−	4.53407i	−2.74501	−	0.735523i
$39$	−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	$0.857299\pi$
$42$	2.64323	−	6.41909i	0.407859	−	0.990487i
$43$	4.97182	+	4.97182i	0.758196	+	0.758196i	0.975994	−	0.217798i	$-0.0698874\pi$
$43$	4.97182	+	4.97182i	0.758196	+	0.758196i	−0.217798	+	0.975994i	$0.569887\pi$
$44$	16.4317	+	9.48685i	2.47717	+	1.43020i
$45$		0			0
$46$	−8.42909	−	14.5996i	−1.24280	−	2.15260i
$47$	2.04343	−	0.547536i	0.298065	−	0.0798663i	−0.106687	−	0.994293i	$-0.534024\pi$
$47$	2.04343	−	0.547536i	0.298065	−	0.0798663i	0.404752	+	0.914426i	$0.367358\pi$
$48$	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
$52$	1.26420	−	4.71805i	0.175313	−	0.654276i
$53$	−0.540066	+	2.01555i	−0.0741837	+	0.276857i	−0.993047	−	0.117719i	$-0.962442\pi$
$53$	−0.540066	+	2.01555i	−0.0741837	+	0.276857i	0.918863	+	0.394576i	$0.129109\pi$
$54$	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
$58$	−19.6899	+	5.27588i	−2.58541	+	0.692757i
$59$	3.61565	+	6.26249i	0.470717	+	0.815307i	0.999439	−	0.0334888i	$-0.0106618\pi$
$59$	3.61565	+	6.26249i	0.470717	+	0.815307i	−0.528722	+	0.848795i	$0.677328\pi$
$60$		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
$63$	1.61500	+	2.09566i	0.203471	+	0.264028i
$64$			9.56424i			1.19553i
$65$		0			0
$66$	−8.82673	+	5.09611i	−1.08649	+	0.627288i
$67$	1.47977	+	0.396503i	0.180783	+	0.0484406i	0.348075	−	0.937467i	$-0.386836\pi$
$67$	1.47977	+	0.396503i	0.180783	+	0.0484406i	−0.167292	+	0.985907i	$0.553502\pi$
$68$	6.57981	+	24.5562i	0.797919	+	2.97787i
$69$	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	$0.550081\pi$
$72$	1.95884	+	7.31051i	0.230852	+	0.861552i
$73$	9.08884	+	2.43535i	1.06377	+	0.285036i	0.747930	−	0.663777i	$-0.231048\pi$
$73$	9.08884	+	2.43535i	1.06377	+	0.285036i	0.315838	+	0.948813i	$0.397714\pi$
$74$	−0.117041	+	0.0675735i	−0.0136057	+	0.00785526i
$75$		0			0
$76$			32.6118i			3.74083i
$77$	−1.36268	−	10.1866i	−0.155292	−	1.16088i
$78$	1.85533	+	1.85533i	0.210075	+	0.210075i
$79$	−9.22616	−	5.32673i	−1.03802	−	0.599303i	−0.118751	−	0.992924i	$-0.537889\pi$
$79$	−9.22616	−	5.32673i	−1.03802	−	0.599303i	−0.919273	+	0.393621i	$0.871222\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	14.0680	−	3.76950i	1.55355	−	0.416272i
$83$	−1.49590	+	1.49590i	−0.164196	+	0.164196i	−0.784423	−	0.620227i	$-0.787041\pi$
$83$	−1.49590	+	1.49590i	−0.164196	+	0.164196i	0.620227	+	0.784423i	$0.287041\pi$
$84$	−12.8161	−	1.66012i	−1.39835	−	0.181134i
$85$		0			0
$86$	9.22436	−	15.9771i	0.994688	−	1.72285i
$87$	2.01076	−	7.50425i	0.215576	−	0.804540i
$88$	7.60910	−	28.3975i	0.811133	−	3.02719i
$89$	−7.46835	+	12.9356i	−0.791644	+	1.37117i	0.133304	+	0.991075i	$0.457441\pi$
$89$	−7.46835	+	12.9356i	−0.791644	+	1.37117i	−0.924948	+	0.380093i	$0.875892\pi$
$90$		0			0
$91$	−2.44224	+	1.01757i	−0.256017	+	0.106671i
$92$	−22.1911	+	22.1911i	−2.31358	+	2.31358i
$93$	−6.20610	+	1.66292i	−0.643543	+	0.172437i
$94$	−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	$-0.172815\pi$
$97$	3.34441	+	3.34441i	0.339573	+	0.339573i	−0.516634	+	0.856207i	$0.672815\pi$
$98$	9.11708	−	15.9442i	0.920964	−	1.61061i
$99$		−	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	$0.264084\pi$
$102$	−13.1910	−	3.53452i	−1.30610	−	0.349969i
$103$	0.630422	+	2.35277i	0.0621173	+	0.231825i	0.990004	−	0.141036i	$-0.0450434\pi$
$103$	0.630422	+	2.35277i	0.0621173	+	0.231825i	−0.927887	+	0.372861i	$0.878377\pi$
$104$	−7.56839			−0.742142
$105$		0			0
$106$	5.47502			0.531781
$107$	−1.76803	−	6.59837i	−0.170922	−	0.637889i	−0.997210	−	0.0746418i	$-0.976219\pi$
$107$	−1.76803	−	6.59837i	−0.170922	−	0.637889i	0.826289	−	0.563247i	$-0.190448\pi$
$108$	−4.71805	−	1.26420i	−0.453994	−	0.121647i
$109$	−2.56407	+	1.48037i	−0.245594	+	0.141794i	−0.617745	−	0.786378i	$-0.711954\pi$
$109$	−2.56407	+	1.48037i	−0.245594	+	0.141794i	0.372151	+	0.928172i	$0.378620\pi$
$110$		0			0
$111$		−	0.0515075i		−	0.00488888i
$112$	21.1435	−	16.2941i	1.99788	−	1.53964i
$113$	−4.54318	−	4.54318i	−0.427387	−	0.427387i	0.460351	−	0.887737i	$-0.347724\pi$
$113$	−4.54318	−	4.54318i	−0.427387	−	0.427387i	−0.887737	+	0.460351i	$0.847724\pi$
$114$	−15.1713	−	8.75915i	−1.42092	−	0.820370i
$115$		0			0
$116$	18.9737	+	32.8634i	1.76166	+	3.05129i
$117$	−0.965926	+	0.258819i	−0.0892999	+	0.0239278i
$118$	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
$122$	−5.88115	+	21.9488i	−0.532455	+	1.98715i
$123$	−1.43664	+	5.36162i	−0.129538	+	0.483441i
$124$	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	−0.123105	+	0.992394i	$0.539285\pi$
$127$	−12.5710	+	12.5710i	−1.11550	+	1.11550i	−0.992394	+	0.123105i	$0.960715\pi$
$128$	2.34116	−	0.627313i	0.206931	−	0.0554471i
$129$	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
$133$	13.9919	−	10.7827i	1.21325	−	0.934981i
$134$		−	4.01963i		−	0.347243i
$135$		0			0
$136$	34.1140	−	19.6957i	2.92525	−	1.68889i
$137$	6.79164	+	1.81981i	0.580249	+	0.155477i	0.536993	−	0.843587i	$-0.319560\pi$
$137$	6.79164	+	1.81981i	0.580249	+	0.155477i	0.0432559	+	0.999064i	$0.486227\pi$
$138$	−4.36322	−	16.2838i	−0.371422	−	1.38617i
$139$	18.9555			1.60778			0.803892	−	0.594775i	$-0.202759\pi$
$139$	18.9555			1.60778			0.803892	+	0.594775i	$0.202759\pi$
$140$		0			0
$141$	2.11552			0.178159
$142$	1.79315	+	6.69213i	0.150478	+	0.561591i
$143$	3.75212	+	1.00538i	0.313768	+	0.0840740i
$144$	8.73752	−	5.04461i	0.728126	−	0.420384i
$145$		0			0
$146$		−	24.6888i		−	2.04326i
$147$	3.52522	+	6.04755i	0.290755	+	0.498793i
$148$	0.177899	+	0.177899i	0.0146232	+	0.0146232i
$149$	0.688724	+	0.397635i	0.0564225	+	0.0325755i	0.527946	−	0.849278i	$-0.322962\pi$
$149$	0.688724	+	0.397635i	0.0564225	+	0.0325755i	−0.471523	+	0.881854i	$0.656296\pi$
$150$		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	$0.965793\pi$
$152$	48.8095	−	13.0785i	3.95897	−	1.06080i
$153$	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
$157$	−0.600524	+	2.24119i	−0.0479270	+	0.178866i	−0.985740	−	0.168274i	$-0.946181\pi$
$157$	−0.600524	+	2.24119i	−0.0479270	+	0.178866i	0.937813	+	0.347140i	$0.112847\pi$
$158$	−7.23473	+	27.0004i	−0.575564	+	2.14803i
$159$	−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
$163$	4.72633	−	1.26642i	0.370195	−	0.0991934i	−0.0689252	−	0.997622i	$-0.521957\pi$
$163$	4.72633	−	1.26642i	0.370195	−	0.0991934i	0.439120	+	0.898428i	$0.355290\pi$
$164$	−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	$-0.433906\pi$
$167$	−9.98118	−	9.98118i	−0.772367	−	0.772367i	−0.978520	+	0.206153i	$0.933906\pi$
$168$	2.65500	+	19.8473i	0.204838	+	1.53125i
$169$			12.0000i			0.923077i
$170$		0			0
$171$	5.78212	−	3.33831i	0.442170	−	0.255287i
$172$	−33.1736	−	8.88885i	−2.52947	−	0.677768i
$173$	−1.55291	−	5.79555i	−0.118066	−	0.440628i	0.881432	−	0.472311i	$-0.156580\pi$
$173$	−1.55291	−	5.79555i	−0.118066	−	0.440628i	−0.999498	+	0.0316829i	$0.989913\pi$
$174$	−20.3844			−1.54534
$175$		0			0
$176$	−39.1914			−2.95416
$177$	1.87160	+	6.98490i	0.140678	+	0.525017i
$178$	37.8560	+	10.1435i	2.83743	+	0.760286i
$179$	−10.3923	+	6.00000i	−0.776757	+	0.448461i	−0.835280	−	0.549825i	$-0.814694\pi$
$179$	−10.3923	+	6.00000i	−0.776757	+	0.448461i	0.0585225	+	0.998286i	$0.481361\pi$
$180$		0			0
$181$			16.2462i			1.20757i	0.797148	+	0.603784i	$0.206341\pi$
$181$			16.2462i			1.20757i	−0.797148	+	0.603784i	$0.793659\pi$
$182$	4.23748	+	5.49865i	0.314103	+	0.407587i
$183$	−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
$187$	−19.5288	+	5.23272i	−1.42809	+	0.382655i
$188$	−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	$0.272394\pi$
$192$	−2.47541	+	9.23834i	−0.178647	+	0.666720i
$193$	−2.09788	+	7.82938i	−0.151008	+	0.563571i	0.848406	+	0.529347i	$0.177563\pi$
$193$	−2.09788	+	7.82938i	−0.151008	+	0.563571i	−0.999414	+	0.0342247i	$0.989104\pi$
$194$	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	−0.504181	−	0.863598i	$-0.668205\pi$
$197$	5.04466	−	5.04466i	0.359417	−	0.359417i	0.863598	+	0.504181i	$0.168205\pi$
$198$	−9.84493	+	2.63794i	−0.699649	+	0.187470i
$199$	11.2098	+	19.4159i	0.794641	+	1.37636i	0.923067	+	0.384640i	$0.125674\pi$
$199$	11.2098	+	19.4159i	0.794641	+	1.37636i	−0.128425	+	0.991719i	$0.540992\pi$
$200$		0			0
$201$	1.32673	+	0.765985i	0.0935800	+	0.0540284i
$202$	−8.04911	−	8.04911i	−0.566333	−	0.566333i
$203$	7.82640	−	19.0065i	0.549306	−	1.33399i
$204$			25.4224i			1.77993i
$205$		0			0
$206$	5.53479	−	3.19551i	0.385627	−	0.222642i
$207$	6.20610	+	1.66292i	0.431354	+	0.115581i
$208$	2.61128	+	9.74543i	0.181060	+	0.675724i
$209$	−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	$0.722489\pi$
$212$	−2.63794	−	9.84493i	−0.181175	−	0.676153i
$213$	−2.55052	−	0.683410i	−0.174759	−	0.0468265i
$214$	−15.5224	+	8.96187i	−1.06109	+	0.612621i
$215$		0			0
$216$			7.56839i			0.514964i
$217$	−16.8489	+	2.25391i	−1.14378	+	0.153005i
$218$	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
$222$	−0.130542	+	0.0349786i	−0.00876140	+	0.00234761i
$223$	−18.0117	+	18.0117i	−1.20615	+	1.20615i	−0.233888	+	0.972263i	$0.575145\pi$
$223$	−18.0117	+	18.0117i	−1.20615	+	1.20615i	−0.972263	+	0.233888i	$0.924855\pi$
$224$	−23.8316	−	18.2079i	−1.59231	−	1.21656i
$225$		0			0
$226$	−8.42909	+	14.5996i	−0.560695	+	0.971152i
$227$	3.37758	−	12.6053i	0.224178	−	0.836642i	−0.758555	−	0.651609i	$-0.774094\pi$
$227$	3.37758	−	12.6053i	0.224178	−	0.836642i	0.982732	−	0.185033i	$-0.0592392\pi$
$228$	−8.44056	+	31.5006i	−0.558990	+	2.08618i
$229$	5.22191	−	9.04461i	0.345073	−	0.597684i	−0.640294	−	0.768130i	$-0.721187\pi$
$229$	5.22191	−	9.04461i	0.345073	−	0.597684i	0.985367	+	0.170446i	$0.0545207\pi$
$230$		0			0
$231$	1.32025	−	10.1922i	0.0868658	−	0.670599i
$232$	41.5769	−	41.5769i	2.72966	−	2.72966i
$233$	1.91605	−	0.513403i	0.125524	−	0.0336342i	−0.195510	−	0.980702i	$-0.562636\pi$
$233$	1.91605	−	0.513403i	0.125524	−	0.0336342i	0.321034	+	0.947068i	$0.395970\pi$
$234$	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
$238$	−33.4096	−	13.7573i	−2.16563	−	0.891753i
$239$			6.71902i			0.434617i	0.976103	+	0.217308i	$0.0697278\pi$
$239$			6.71902i			0.434617i	−0.976103	+	0.217308i	$0.930272\pi$
$240$		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	$0.0437805\pi$
$242$	10.3638	+	2.77697i	0.666211	+	0.178511i
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	42.3009			2.70804
$245$		0			0
$246$	14.5642			0.928582
$247$	1.72804	+	6.44912i	0.109952	+	0.410347i
$248$	−46.9702	−	12.5856i	−2.98261	−	0.799188i
$249$	−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	$0.913795\pi$
$252$	−11.9497	−	4.92059i	−0.752760	−	0.309968i
$253$	−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
$257$	−11.6898	+	3.13227i	−0.729190	+	0.195386i	−0.604268	−	0.796781i	$-0.706535\pi$
$257$	−11.6898	+	3.13227i	−0.729190	+	0.195386i	−0.124921	+	0.992167i	$0.539868\pi$
$258$	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
$262$	−2.76412	+	10.3158i	−0.170768	+	0.637315i
$263$	−4.40597	+	16.4433i	−0.271684	+	1.01394i	0.686347	+	0.727274i	$0.259213\pi$
$263$	−4.40597	+	16.4433i	−0.271684	+	1.01394i	−0.958031	+	0.286664i	$0.907454\pi$
$264$	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
$268$	−7.22791	+	1.93671i	−0.441515	+	0.118304i
$269$	−0.991819	−	1.71788i	−0.0604723	−	0.104741i	0.834204	−	0.551455i	$-0.185927\pi$
$269$	−0.991819	−	1.71788i	−0.0604723	−	0.104741i	−0.894677	+	0.446714i	$0.852594\pi$
$270$		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
$273$	−2.62239	+	0.350801i	−0.158714	+	0.0212315i
$274$		−	18.4487i		−	1.11453i
$275$		0			0
$276$	−27.1784	+	15.6915i	−1.63595	+	0.944516i
$277$	17.4651	+	4.67976i	1.04938	+	0.281180i	0.741994	−	0.670406i	$-0.233880\pi$
$277$	17.4651	+	4.67976i	1.04938	+	0.281180i	0.307383	+	0.951586i	$0.400547\pi$
$278$	−12.8726	−	48.0413i	−0.772049	−	2.88132i
$279$	−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	$0.306455\pi$
$282$	−1.43664	−	5.36162i	−0.0855507	−	0.319280i
$283$	23.9858	+	6.42696i	1.42580	+	0.382043i	0.887539	−	0.460732i	$-0.152413\pi$
$283$	23.9858	+	6.42696i	1.42580	+	0.382043i	0.538266	+	0.842775i	$0.319080\pi$
$284$	11.1695	−	6.44872i	0.662789	−	0.382661i
$285$		0			0
$286$		−	10.1922i		−	0.602679i
$287$	−5.59179	+	13.5797i	−0.330073	+	0.801584i
$288$	−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
$292$	−44.3943	+	11.8954i	−2.59798	+	0.696126i
$293$	−9.60996	+	9.60996i	−0.561420	+	0.561420i	−0.929711	−	0.368291i	$-0.879943\pi$
$293$	−9.60996	+	9.60996i	−0.561420	+	0.561420i	0.368291	+	0.929711i	$0.379943\pi$
$294$	12.9331	−	13.0413i	0.754273	−	0.760582i
$295$		0			0
$296$	0.194915	−	0.337602i	0.0113292	−	0.0196227i
$297$	1.00538	−	3.75212i	0.0583380	−	0.217720i
$298$	0.540066	−	2.01555i	0.0312852	−	0.116758i
$299$	−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
$303$	4.19055	−	1.12285i	0.240741	−	0.0645063i
$304$	−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	$-0.100628\pi$
$307$	11.2059	+	11.2059i	0.639553	+	0.639553i	−0.310892	+	0.950445i	$0.600628\pi$
$308$	30.6425	+	39.7624i	1.74602	+	2.26567i
$309$			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	$0.602687\pi$
$312$	−7.31051	−	1.95884i	−0.413876	−	0.110898i
$313$	−4.42301	−	16.5069i	−0.250004	−	0.933026i	−0.970802	−	0.239881i	$-0.922891\pi$
$313$	−4.42301	−	16.5069i	−0.250004	−	0.933026i	0.720799	−	0.693144i	$-0.243775\pi$
$314$	6.08793			0.343562
$315$		0			0
$316$	52.0366			2.92729
$317$	3.76986	+	14.0693i	0.211736	+	0.790211i	0.987290	+	0.158929i	$0.0508041\pi$
$317$	3.76986	+	14.0693i	0.211736	+	0.790211i	−0.775554	+	0.631282i	$0.782529\pi$
$318$	5.28847	+	1.41704i	0.296562	+	0.0794637i
$319$	−26.1353	+	15.0892i	−1.46330	+	0.844834i
$320$		0			0
$321$		−	6.83114i		−	0.381277i
$322$	−5.91387	−	44.2088i	−0.329567	−	2.46366i
$323$	−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
$327$	−2.85985	+	0.766296i	−0.158150	+	0.0423762i
$328$	−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	$0.236991\pi$
$332$	2.67443	−	9.98111i	0.146778	−	0.547785i
$333$	0.0133311	−	0.0497524i	0.000730541	−	0.00272642i
$334$	−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	−0.519130	−	0.854695i	$-0.673744\pi$
$337$	6.16015	−	6.16015i	0.335565	−	0.335565i	0.854695	+	0.519130i	$0.173744\pi$
$338$	30.4131	−	8.14917i	1.65425	−	0.443256i
$339$	−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
$343$	7.19415	+	17.0659i	0.388447	+	0.921471i
$344$			53.2150i			2.86916i
$345$		0			0
$346$	−13.6338	+	7.87149i	−0.732959	+	0.423174i
$347$	−29.5348	−	7.91383i	−1.58551	−	0.424836i	−0.644885	−	0.764280i	$-0.723095\pi$
$347$	−29.5348	−	7.91383i	−1.58551	−	0.424836i	−0.940626	+	0.339443i	$0.889761\pi$
$348$	9.82151	+	36.6544i	0.526488	+	1.96488i
$349$	2.78991			0.149340			0.0746702	−	0.997208i	$-0.476210\pi$
$349$	2.78991			0.149340			0.0746702	+	0.997208i	$0.476210\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$	11.3966	+	42.5325i	0.607439	+	2.26699i
$353$	28.3820	+	7.60492i	1.51062	+	0.404769i	0.916641	−	0.399712i	$-0.130890\pi$
$353$	28.3820	+	7.60492i	1.51062	+	0.404769i	0.593978	+	0.804481i	$0.297557\pi$
$354$	16.4317	−	9.48685i	0.873335	−	0.504220i
$355$		0			0
$356$		−	72.9581i		−	3.86677i
$357$	10.9073	−	8.40563i	0.577277	−	0.444873i
$358$	22.2639	+	22.2639i	1.17669	+	1.17669i
$359$	−24.3032	−	14.0315i	−1.28267	−	0.740552i	−0.305337	−	0.952244i	$-0.598769\pi$
$359$	−24.3032	−	14.0315i	−1.28267	−	0.740552i	−0.977336	+	0.211692i	$0.932102\pi$
$360$		0			0
$361$	−12.7886	−	22.1505i	−0.673084	−	1.16582i
$362$	41.1747	−	11.0327i	2.16409	−	0.579867i
$363$	−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
$367$	−6.95141	+	25.9430i	−0.362861	+	1.35421i	0.507437	+	0.861689i	$0.330593\pi$
$367$	−6.95141	+	25.9430i	−0.362861	+	1.35421i	−0.870298	+	0.492526i	$0.836074\pi$
$368$	16.7776	−	62.6147i	0.874590	−	3.26402i
$369$	−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
$373$	−2.90979	+	0.779675i	−0.150663	+	0.0403701i	−0.333362	−	0.942799i	$-0.608183\pi$
$373$	−2.90979	+	0.779675i	−0.150663	+	0.0403701i	0.182699	+	0.983169i	$0.441517\pi$
$374$	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
$378$	5.49865	−	4.23748i	0.282820	−	0.217953i
$379$		−	35.7819i		−	1.83799i	−0.394264	−	0.918997i	$-0.629001\pi$
$379$		−	35.7819i		−	1.83799i	0.394264	−	0.918997i	$-0.370999\pi$
$380$		0			0
$381$	−15.3963	+	8.88906i	−0.788777	+	0.455400i
$382$	22.8427	+	6.12067i	1.16873	+	0.313161i
$383$	5.30268	+	19.7899i	0.270954	+	1.01122i	0.958504	+	0.285078i	$0.0920196\pi$
$383$	5.30268	+	19.7899i	0.270954	+	1.01122i	−0.687550	+	0.726137i	$0.741314\pi$
$384$	2.42375			0.123686
$385$		0			0
$386$	21.2676			1.08249
$387$	1.81981	+	6.79164i	0.0925063	+	0.345238i
$388$	−22.3150	−	5.97928i	−1.13287	−	0.303552i
$389$	−10.4808	+	6.05109i	−0.531397	+	0.306802i	−0.741585	−	0.670859i	$-0.765926\pi$
$389$	−10.4808	+	6.05109i	−0.531397	+	0.306802i	0.210188	+	0.977661i	$0.432592\pi$
$390$		0			0
$391$		−	33.4405i		−	1.69116i
$392$	0.220639	+	52.9783i	0.0111439	+	2.67581i
$393$	−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
$397$	32.3823	−	8.67680i	1.62522	−	0.435476i	0.672690	−	0.739924i	$-0.265139\pi$
$397$	32.3823	−	8.67680i	1.62522	−	0.435476i	0.952529	+	0.304448i	$0.0984719\pi$
$398$	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	$-0.223579\pi$
$402$	1.04036	−	3.88267i	0.0518883	−	0.193650i
$403$	1.66292	−	6.20610i	0.0828359	−	0.309148i
$404$	−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
$408$	38.0492	−	10.1953i	1.88372	−	0.504740i
$409$	0.969040	+	1.67843i	0.0479160	+	0.0829929i	0.888989	−	0.457929i	$-0.151409\pi$
$409$	0.969040	+	1.67843i	0.0479160	+	0.0829929i	−0.841073	+	0.540922i	$0.818075\pi$
$410$		0			0
$411$	6.08921	+	3.51561i	0.300359	+	0.173412i
$412$	−8.41276	−	8.41276i	−0.414467	−	0.414467i
$413$	2.53675	+	18.9633i	0.124825	+	0.933123i
$414$		−	16.8582i		−	0.828534i
$415$		0			0
$416$	9.81691	−	5.66780i	0.481314	−	0.277887i
$417$	18.3096	+	4.90604i	0.896625	+	0.240250i
$418$	17.6125	+	65.7308i	0.861457	+	3.21500i
$419$	19.9783			0.976006			0.488003	−	0.872842i	$-0.337726\pi$
$419$	19.9783			0.976006			0.488003	+	0.872842i	$0.337726\pi$
$420$		0			0
$421$	7.44872			0.363028			0.181514	−	0.983388i	$-0.441900\pi$
$421$	7.44872			0.363028			0.181514	+	0.983388i	$0.441900\pi$
$422$	12.6942	+	47.3753i	0.617942	+	2.30619i
$423$	2.04343	+	0.547536i	0.0993551	+	0.0266221i
$424$	−13.6768	+	7.89631i	−0.664204	+	0.383479i
$425$		0			0
$426$			6.92820i			0.335673i
$427$	−13.9863	−	18.1489i	−0.676844	−	0.878288i
$428$	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	$0.867201\pi$
$432$	9.74543	−	2.61128i	0.468877	−	0.125635i
$433$	−12.0839	+	12.0839i	−0.580715	+	0.580715i	−0.935100	−	0.354385i	$-0.884690\pi$
$433$	−12.0839	+	12.0839i	−0.580715	+	0.580715i	0.354385	+	0.935100i	$0.384690\pi$
$434$	17.1544	+	41.1718i	0.823439	+	1.97631i
$435$		0			0
$436$	7.23084	−	12.5242i	0.346294	−	0.599800i
$437$	11.1027	−	41.4357i	0.531113	−	1.98214i
$438$	6.38994	−	23.8476i	0.305323	−	1.13948i
$439$	9.74684	−	16.8820i	0.465191	−	0.805735i	−0.534019	−	0.845473i	$-0.679319\pi$
$439$	9.74684	−	16.8820i	0.465191	−	0.805735i	0.999210	+	0.0397376i	$0.0126522\pi$
$440$		0			0
$441$	1.83988	+	6.75388i	0.0876132	+	0.321613i
$442$	9.65648	−	9.65648i	0.459312	−	0.459312i
$443$	−28.1705	+	7.54825i	−1.33842	+	0.358628i	−0.855848	−	0.517228i	$-0.826964\pi$
$443$	−28.1705	+	7.54825i	−1.33842	+	0.358628i	−0.482572	+	0.875856i	$0.660297\pi$
$444$	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
$448$	−9.63495	+	23.3985i	−0.455208	+	1.10548i
$449$		−	21.7926i		−	1.02846i	−0.857653	−	0.514229i	$-0.828078\pi$
$449$		−	21.7926i		−	1.02846i	0.857653	−	0.514229i	$-0.171922\pi$
$450$		0			0
$451$	18.6731	−	10.7809i	0.879281	−	0.507653i
$452$	30.3136	+	8.12250i	1.42583	+	0.382050i
$453$	−2.57122	−	9.59593i	−0.120807	−	0.450856i
$454$	−34.2409			−1.60700
$455$		0			0
$456$	50.5313			2.36634
$457$	0.404025	+	1.50784i	0.0188995	+	0.0705339i	0.974732	−	0.223380i	$-0.0717089\pi$
$457$	0.404025	+	1.50784i	0.0188995	+	0.0705339i	−0.955832	+	0.293913i	$0.905042\pi$
$458$	−26.4691	−	7.09236i	−1.23682	−	0.331404i
$459$	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	$0.999236\pi$
$462$	−26.7280	+	3.57545i	−1.24350	+	0.166345i
$463$	−14.0423	−	14.0423i	−0.652602	−	0.652602i	0.301017	−	0.953619i	$-0.402674\pi$
$463$	−14.0423	−	14.0423i	−0.652602	−	0.652602i	−0.953619	+	0.301017i	$0.902674\pi$
$464$	−67.8815	−	39.1914i	−3.15132	−	1.81941i
$465$		0			0
$466$	−2.60236	−	4.50743i	−0.120552	−	0.208803i
$467$	−19.2677	+	5.16277i	−0.891603	+	0.238904i	−0.675407	−	0.737446i	$-0.736032\pi$
$467$	−19.2677	+	5.16277i	−0.891603	+	0.238904i	−0.216196	+	0.976350i	$0.569365\pi$
$468$	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
$472$	−14.1650	+	52.8645i	−0.651997	+	2.43328i
$473$	7.06903	−	26.3820i	0.325035	−	1.21305i
$474$	−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
$478$	17.0288	−	4.56286i	0.778881	−	0.208701i
$479$	−2.23820	−	3.87668i	−0.102266	−	0.177130i	0.810352	−	0.585944i	$-0.199276\pi$
$479$	−2.23820	−	3.87668i	−0.102266	−	0.177130i	−0.912618	+	0.408814i	$0.865943\pi$
$480$		0			0
$481$	0.0446068	+	0.0257538i	0.00203390	+	0.00117427i
$482$	−45.4671	−	45.4671i	−2.07097	−	2.07097i
$483$	15.7186	+	6.47253i	0.715219	+	0.294510i
$484$		−	19.9737i		−	0.907895i
$485$		0			0
$486$	2.27230	−	1.31191i	0.103074	−	0.0595097i
$487$	15.7583	+	4.22241i	0.714075	+	0.191336i	0.597527	−	0.801849i	$-0.296150\pi$
$487$	15.7583	+	4.22241i	0.714075	+	0.191336i	0.116549	+	0.993185i	$0.462817\pi$
$488$	−16.9641	−	63.3109i	−0.767928	−	2.86595i
$489$	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	$0.865328\pi$
$492$	−7.01725	−	26.1887i	−0.316362	−	1.18068i
$493$	−39.0576	−	10.4654i	−1.75906	−	0.471340i
$494$	15.1713	−	8.75915i	0.682589	−	0.394093i
$495$		0			0
$496$			64.8235i			2.91066i
$497$	−6.45986	−	2.66001i	−0.289764	−	0.119318i
$498$	3.92498	+	3.92498i	0.175882	+	0.175882i
$499$	−26.3126	−	15.1916i	−1.17791	−	0.680068i	−0.222382	−	0.974960i	$-0.571383\pi$
$499$	−26.3126	−	15.1916i	−1.17791	−	0.680068i	−0.955531	+	0.294891i	$0.904717\pi$
$500$		0			0
$501$	−7.05776	−	12.2244i	−0.315317	−	0.546146i
$502$	21.4835	−	5.75648i	0.958855	−	0.256924i
$503$	2.50170	−	2.50170i	0.111545	−	0.111545i	−0.649131	−	0.760676i	$-0.724867\pi$
$503$	2.50170	−	2.50170i	0.111545	−	0.111545i	0.760676	+	0.649131i	$0.224867\pi$
$504$	−2.57232	+	19.8582i	−0.114580	+	0.884554i
$505$		0			0
$506$	−32.7427	+	56.7120i	−1.45559	+	2.52115i
$507$	−3.10583	+	11.5911i	−0.137935	+	0.514779i
$508$	22.4751	−	83.8781i	0.997170	−	3.72149i
$509$	21.9679	−	38.0496i	0.973711	−	1.68652i	0.289587	−	0.957152i	$-0.406482\pi$
$509$	21.9679	−	38.0496i	0.973711	−	1.68652i	0.684124	−	0.729366i	$-0.260185\pi$
$510$		0			0
$511$	19.7821	+	15.1140i	0.875109	+	0.668604i
$512$	27.1183	−	27.1183i	1.19847	−	1.19847i
$513$	6.44912	−	1.72804i	0.284735	−	0.0762946i
$514$	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
$518$	−0.354408	+	0.0474097i	−0.0155718	+	0.00208306i
$519$		−	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	$0.513282\pi$
$522$	−19.6899	−	5.27588i	−0.861802	−	0.230919i
$523$	1.65889	+	6.19106i	0.0725382	+	0.270716i	0.992664	−	0.120907i	$-0.0385803\pi$
$523$	1.65889	+	6.19106i	0.0725382	+	0.270716i	−0.920126	+	0.391623i	$0.871914\pi$
$524$	19.8813			0.868517
$525$		0			0
$526$	44.6664			1.94755
$527$	8.65505	+	32.3011i	0.377020	+	1.40706i
$528$	−37.8560	−	10.1435i	−1.64747	−	0.441438i
$529$	15.8318	−	9.14049i	0.688339	−	0.397413i
$530$		0			0
$531$			7.23130i			0.313812i
$532$	−32.8529	+	79.7835i	−1.42435	+	3.45905i
$533$	−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
$537$	−11.5911	+	3.10583i	−0.500193	+	0.134026i
$538$	−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	$0.208182\pi$
$542$	1.28117	−	4.78138i	0.0550308	−	0.205378i
$543$	−4.20481	+	15.6926i	−0.180446	+	0.673433i
$544$	−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	−0.665322	−	0.746557i	$-0.731706\pi$
$547$	1.89992	−	1.89992i	0.0812347	−	0.0812347i	0.746557	+	0.665322i	$0.231706\pi$
$548$	−33.1736	+	8.88885i	−1.41711	+	0.379713i
$549$	−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
$553$	−17.2053	−	22.3260i	−0.731644	−	0.949397i
$554$		−	47.4420i		−	2.01562i
$555$		0			0
$556$	−80.1834	+	46.2939i	−3.40053	+	1.96330i
$557$	30.2141	+	8.09584i	1.28021	+	0.343032i	0.833935	−	0.551863i	$-0.186083\pi$
$557$	30.2141	+	8.09584i	1.28021	+	0.343032i	0.446277	+	0.894895i	$0.352750\pi$
$558$	4.36322	+	16.2838i	0.184710	+	0.689346i
$559$	−7.03122			−0.297389
$560$		0			0
$561$	−20.2177			−0.853591
$562$	−13.0062	−	48.5396i	−0.548631	−	2.04752i
$563$	25.3980	+	6.80537i	1.07040	+	0.286812i	0.750657	−	0.660693i	$-0.229737\pi$
$563$	25.3980	+	6.80537i	1.07040	+	0.286812i	0.319741	+	0.947505i	$0.396404\pi$
$564$	−8.94882	+	5.16660i	−0.376813	+	0.217553i
$565$		0			0
$566$		−	65.1546i		−	2.73865i
$567$	0.350801	+	2.62239i	0.0147323	+	0.110130i
$568$	−14.1310	−	14.1310i	−0.592925	−	0.592925i
$569$	−26.8240	−	15.4868i	−1.12452	−	0.649242i	−0.181970	−	0.983304i	$-0.558247\pi$
$569$	−26.8240	−	15.4868i	−1.12452	−	0.649242i	−0.942551	+	0.334062i	$0.891581\pi$
$570$		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	$0.846572\pi$
$572$	−18.3272	+	4.91075i	−0.766298	+	0.205329i
$573$	−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
$577$	8.34871	−	31.1578i	0.347561	−	1.29712i	−0.542030	−	0.840359i	$-0.682344\pi$
$577$	8.34871	−	31.1578i	0.347561	−	1.29712i	0.889591	−	0.456758i	$-0.150989\pi$
$578$	−6.85156	+	25.5704i	−0.284987	+	1.06359i
$579$	−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
$583$	7.82938	−	2.09788i	0.324260	−	0.0868852i
$584$	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	$-0.245277\pi$
$587$	0.508420	+	0.508420i	0.0209848	+	0.0209848i	−0.696537	+	0.717521i	$0.745277\pi$
$588$	−29.6815	−	16.9722i	−1.22405	−	0.699923i
$589$			42.8974i			1.76756i
$590$		0			0
$591$	6.17843	−	3.56712i	0.254147	−	0.146732i
$592$	−0.501963	−	0.134501i	−0.0206306	−	0.00552794i
$593$	−3.97533	−	14.8361i	−0.163247	−	0.609247i	−0.998257	−	0.0590125i	$-0.981205\pi$
$593$	−3.97533	−	14.8361i	−0.163247	−	0.609247i	0.835010	−	0.550235i	$-0.185462\pi$
$594$	−10.1922			−0.418192
$595$		0			0
$596$	−3.88448			−0.159115
$597$	5.80262	+	21.6557i	0.237485	+	0.886307i
$598$	16.2838	+	4.36322i	0.665892	+	0.178425i
$599$	−20.6390	+	11.9159i	−0.843287	+	0.486872i	−0.858380	−	0.513014i	$-0.828529\pi$
$599$	−20.6390	+	11.9159i	−0.843287	+	0.486872i	0.0150931	+	0.999886i	$0.495196\pi$
$600$		0			0
$601$			13.8729i			0.565887i	0.959137	+	0.282944i	$0.0913110\pi$
$601$			13.8729i			0.565887i	−0.959137	+	0.282944i	$0.908689\pi$
$602$	38.6622	−	29.7947i	1.57575	−	1.21434i
$603$	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
$607$	40.1351	−	10.7542i	1.62903	−	0.436498i	0.675395	−	0.737456i	$-0.263973\pi$
$607$	40.1351	−	10.7542i	1.62903	−	0.436498i	0.953637	+	0.300958i	$0.0973064\pi$
$608$	−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
$612$	−6.57981	+	24.5562i	−0.265973	+	0.992624i
$613$	−12.5461	+	46.8226i	−0.506731	+	1.89115i	−0.0561248	+	0.998424i	$0.517874\pi$
$613$	−12.5461	+	46.8226i	−0.506731	+	1.89115i	−0.450606	+	0.892723i	$0.648792\pi$
$614$	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	−0.617776	−	0.786354i	$-0.711966\pi$
$617$	4.18738	−	4.18738i	0.168578	−	0.168578i	0.786354	+	0.617776i	$0.211966\pi$
$618$	6.17326	−	1.65412i	0.248325	−	0.0665384i
$619$	7.48289	+	12.9607i	0.300763	+	0.520936i	0.976309	−	0.216381i	$-0.0694255\pi$
$619$	7.48289	+	12.9607i	0.300763	+	0.520936i	−0.675546	+	0.737318i	$0.736092\pi$
$620$		0			0
$621$	5.56424	+	3.21251i	0.223285	+	0.128914i
$622$	48.9979	+	48.9979i	1.96464	+	1.96464i
$623$	−31.3022	+	24.1228i	−1.25410	+	0.966458i
$624$			10.0892i			0.403892i
$625$		0			0
$626$	−38.8319	+	22.4196i	−1.55203	+	0.896067i
$627$	−25.0515	−	6.71252i	−1.00046	−	0.268072i
$628$	−2.93325	−	10.9470i	−0.117049	−	0.436834i
$629$	−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	$0.305434\pi$
$632$	−20.8685	−	77.8821i	−0.830103	−	3.09799i
$633$	−18.0558	−	4.83803i	−0.717653	−	0.192294i
$634$	33.0975	−	19.1088i	1.31447	−	0.758909i
$635$		0			0
$636$		−	10.1922i		−	0.404148i
$637$	−6.99994	+	0.0291526i	−0.277348	+	0.00115507i
$638$	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	$0.709348\pi$
$642$	−17.3130	+	4.63901i	−0.683290	+	0.183087i
$643$	23.6685	−	23.6685i	0.933396	−	0.933396i	−0.0645203	−	0.997916i	$-0.520552\pi$
$643$	23.6685	−	23.6685i	0.933396	−	0.933396i	0.997916	+	0.0645203i	$0.0205517\pi$
$644$	−76.6447	+	31.9344i	−3.02023	+	1.25839i
$645$		0			0
$646$	−45.5890	+	78.9625i	−1.79368	+	3.10674i
$647$	−1.00538	+	3.75212i	−0.0395255	+	0.147511i	−0.982869	−	0.184308i	$-0.940996\pi$
$647$	−1.00538	+	3.75212i	−0.0395255	+	0.147511i	0.943343	+	0.331819i	$0.107662\pi$
$648$	−1.95884	+	7.31051i	−0.0769507	+	0.287184i
$649$	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
$653$	26.7404	−	7.16508i	1.04643	−	0.280391i	0.305657	−	0.952142i	$-0.401124\pi$
$653$	26.7404	−	7.16508i	1.04643	−	0.280391i	0.740778	+	0.671750i	$0.234457\pi$
$654$	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
$658$	−1.94721	−	14.5563i	−0.0759102	−	0.567462i
$659$			11.1129i			0.432896i	0.976294	+	0.216448i	$0.0694471\pi$
$659$			11.1129i			0.432896i	−0.976294	+	0.216448i	$0.930553\pi$
$660$		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	$0.260544\pi$
$662$	20.2087	+	5.41492i	0.785435	+	0.210457i
$663$	1.34708	+	5.02738i	0.0523164	+	0.195247i
$664$	−16.0111			−0.621350
$665$		0			0
$666$	−0.135147			−0.00523684
$667$	−12.9192	−	48.2150i	−0.500232	−	1.86689i
$668$	66.5977	+	17.8448i	2.57674	+	0.690436i
$669$	−22.0597	+	12.7362i	−0.852878	+	0.492409i
$670$		0			0
$671$			33.6406i			1.29868i
$672$	−18.3070	−	23.7555i	−0.706207	−	0.916389i
$673$	−13.2621	−	13.2621i	−0.511216	−	0.511216i	0.403683	−	0.914899i	$-0.367730\pi$
$673$	−13.2621	−	13.2621i	−0.511216	−	0.511216i	−0.914899	+	0.403683i	$0.867730\pi$
$674$	−19.7958	−	11.4291i	−0.762504	−	0.440232i
$675$		0			0
$676$	−29.3069	−	50.7610i	−1.12719	−	1.95235i
$677$	−19.7899	+	5.30268i	−0.760587	+	0.203799i	−0.618209	−	0.786014i	$-0.712141\pi$
$677$	−19.7899	+	5.30268i	−0.760587	+	0.203799i	−0.142378	+	0.989812i	$0.545475\pi$
$678$	−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
$682$	16.9489	−	63.2540i	0.649005	−	2.42212i
$683$	1.07859	−	4.02536i	0.0412712	−	0.154026i	−0.942215	−	0.335008i	$-0.891261\pi$
$683$	1.07859	−	4.02536i	0.0412712	−	0.154026i	0.983486	+	0.180982i	$0.0579276\pi$
$684$	−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
$688$	68.5223	−	18.3605i	2.61239	−	0.699987i
$689$	−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
$693$	3.91320	−	9.50323i	0.148650	−	0.360998i
$694$			80.2280i			3.04541i
$695$		0			0
$696$	50.9211	−	29.3993i	1.93016	−	1.11438i
$697$	27.9058	+	7.47733i	1.05701	+	0.283224i
$698$	−1.89462	−	7.07081i	−0.0717124	−	0.267634i
$699$	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	$0.632662\pi$
$702$	0.679097	+	2.53443i	0.0256309	+	0.0956557i
$703$	−0.332178	−	0.0890068i	−0.0125283	−	0.00335696i
$704$	32.1747	−	18.5761i	1.21263	−	0.700112i
$705$		0			0
$706$		−	77.0964i		−	2.90156i
$707$	11.3769	−	1.52191i	0.427873	−	0.0572372i
$708$	−24.9758	−	24.9758i	−0.938649	−	0.938649i
$709$	2.78660	+	1.60884i	0.104653	+	0.0604214i	0.551413	−	0.834232i	$-0.314089\pi$
$709$	2.78660	+	1.60884i	0.104653	+	0.0604214i	−0.446760	+	0.894654i	$0.647422\pi$
$710$		0			0
$711$	−5.32673	−	9.22616i	−0.199768	−	0.346008i
$712$	−109.195	+	29.2587i	−4.09225	+	1.09652i
$713$	−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
$717$	−1.73901	+	6.49007i	−0.0649445	+	0.242376i
$718$	−19.0574	+	71.1233i	−0.711217	+	2.65430i
$719$	−18.1298	+	31.4017i	−0.676126	+	1.17108i	0.300013	+	0.953935i	$0.403009\pi$
$719$	−18.1298	+	31.4017i	−0.676126	+	1.17108i	−0.976138	+	0.217149i	$0.930324\pi$
$720$		0			0
$721$	−0.827859	+	6.39103i	−0.0308311	+	0.238014i
$722$	−47.4541	+	47.4541i	−1.76606	+	1.76606i
$723$	23.6712	−	6.34268i	0.880342	−	0.235887i
$724$	−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	−0.977192	−	0.212357i	$-0.931886\pi$
$727$	−32.0737	−	32.0737i	−1.18955	−	1.18955i	−0.212357	−	0.977192i	$-0.568114\pi$
$728$	−18.5158	−	7.62435i	−0.686240	−	0.282577i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	31.6927	−	18.2978i	1.17220	−	0.676768i
$732$	40.8595	+	10.9483i	1.51021	+	0.404660i
$733$	−0.0129286	−	0.0482502i	−0.000477529	−	0.00178216i	0.965687	−	0.259710i	$-0.0836270\pi$
$733$	−0.0129286	−	0.0482502i	−0.000477529	−	0.00178216i	−0.966164	+	0.257928i	$0.916960\pi$
$734$	70.4713			2.60114
$735$		0			0
$736$	−72.8315			−2.68460
$737$	−1.54021	−	5.74814i	−0.0567344	−	0.211736i
$738$	14.0680	+	3.76950i	0.517849	+	0.138757i
$739$	1.70927	−	0.986849i	0.0628766	−	0.0363018i	−0.468232	−	0.883605i	$-0.655109\pi$
$739$	1.70927	−	0.986849i	0.0628766	−	0.0363018i	0.531109	+	0.847304i	$0.321776\pi$
$740$		0			0
$741$			6.67662i			0.245272i
$742$	13.3944	+	5.51550i	0.491725	+	0.202480i
$743$	−0.784440	−	0.784440i	−0.0287783	−	0.0287783i	0.692571	−	0.721350i	$-0.256478\pi$
$743$	−0.784440	−	0.784440i	−0.0287783	−	0.0287783i	−0.721350	+	0.692571i	$0.756478\pi$
$744$	−42.1123	−	24.3136i	−1.54391	−	0.891379i
$745$		0			0
$746$	3.95206	+	6.84516i	0.144695	+	0.250619i
$747$	−2.04343	+	0.547536i	−0.0747653	+	0.0200333i
$748$	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	$-0.102092\pi$
$752$	5.52421	−	20.6166i	0.201447	−	0.751811i
$753$	−2.19392	+	8.18783i	−0.0799510	+	0.298381i
$754$	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	−0.825368	−	0.564596i	$-0.809032\pi$
$757$	−7.17478	+	7.17478i	−0.260772	+	0.260772i	0.564596	+	0.825368i	$0.309032\pi$
$758$	−90.6866	+	24.2994i	−3.29389	+	0.882594i
$759$	−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
$763$	−7.76422	+	1.03863i	−0.281084	+	0.0376010i
$764$		−	44.0236i		−	1.59272i
$765$		0			0
$766$	46.5549	−	26.8785i	1.68210	−	0.971159i
$767$	−6.98490	−	1.87160i	−0.252210	−	0.0675795i
$768$	3.30485	+	12.3339i	0.119254	+	0.445060i
$769$	14.0274			0.505842			0.252921	−	0.967487i	$-0.418609\pi$
$769$	14.0274			0.505842			0.252921	+	0.967487i	$0.418609\pi$
$770$		0			0
$771$	−12.1022			−0.435849
$772$	−10.2470	−	38.2425i	−0.368799	−	1.37638i
$773$	38.0434	+	10.1937i	1.36833	+	0.366642i	0.866867	−	0.498540i	$-0.166130\pi$
$773$	38.0434	+	10.1937i	1.36833	+	0.366642i	0.501459	+	0.865181i	$0.332797\pi$
$774$	15.9771	−	9.22436i	0.574284	−	0.331563i
$775$		0			0
$776$			35.7963i			1.28501i
$777$	0.0518883	−	0.126011i	0.00186148	−	0.00452062i
$778$	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
$782$	−84.7525	+	22.7094i	−3.03074	+	0.812086i
$783$	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
$787$	−13.5183	+	50.4509i	−0.481875	+	1.79838i	0.111864	+	0.993724i	$0.464318\pi$
$787$	−13.5183	+	50.4509i	−0.481875	+	1.79838i	−0.593739	+	0.804658i	$0.702349\pi$
$788$	−9.01908	+	33.6597i	−0.321291	+	1.19908i
$789$	−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
$793$	8.36516	−	2.24144i	0.297056	−	0.0795958i
$794$	−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	$-0.0585607\pi$
$797$	22.5902	+	22.5902i	0.800187	+	0.800187i	−0.182938	+	0.983124i	$0.558561\pi$
$798$	−28.2920	−	36.7124i	−1.00153	−	1.29960i
$799$		−	11.0107i		−	0.389530i
$800$		0			0
$801$	−12.9356	+	7.46835i	−0.457056	+	0.263881i
$802$	−95.5294	−	25.5970i	−3.37326	−	0.903862i
$803$	−9.46007	−	35.3055i	−0.333839	−	1.24590i
$804$	−7.48289			−0.263901
$805$		0			0
$806$	−16.8582			−0.593804
$807$	−0.513403	−	1.91605i	−0.0180727	−	0.0674481i
$808$	31.7157	+	8.49820i	1.11576	+	0.298966i
$809$	40.8145	−	23.5642i	1.43496	−	0.828474i	0.437467	−	0.899235i	$-0.355876\pi$
$809$	40.8145	−	23.5642i	1.43496	−	0.828474i	0.997493	+	0.0707602i	$0.0225425\pi$
$810$		0			0
$811$			41.4206i			1.45448i	0.686386	+	0.727238i	$0.259196\pi$
$811$			41.4206i			1.45448i	−0.686386	+	0.727238i	$0.740804\pi$
$812$	13.3120	+	99.5129i	0.467159	+	3.49222i
$813$	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
$817$	45.3451	−	12.1502i	1.58643	−	0.425081i
$818$	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	$0.0121229\pi$
$822$	4.77488	−	17.8201i	0.166543	−	0.621547i
$823$	3.26072	−	12.1692i	0.113662	−	0.424191i	−0.885522	−	0.464598i	$-0.846199\pi$
$823$	3.26072	−	12.1692i	0.113662	−	0.424191i	0.999183	+	0.0404070i	$0.0128655\pi$
$824$	−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	−0.449804	−	0.893127i	$-0.648506\pi$
$827$	12.7489	−	12.7489i	0.443324	−	0.443324i	0.893127	+	0.449804i	$0.148506\pi$
$828$	−30.3136	+	8.12250i	−1.05347	+	0.282277i
$829$	−0.174326	−	0.301942i	−0.00605460	−	0.0104869i	0.862982	−	0.505234i	$-0.168594\pi$
$829$	−0.174326	−	0.301942i	−0.00605460	−	0.0104869i	−0.869037	+	0.494747i	$0.835261\pi$
$830$		0			0
$831$	15.6588	+	9.04061i	0.543198	+	0.313615i
$832$	−6.76294	−	6.76294i	−0.234463	−	0.234463i
$833$	31.4759	−	18.3478i	1.09057	−	0.635714i
$834$		−	49.7360i		−	1.72222i
$835$		0			0
$836$	109.708	−	63.3400i	3.79434	−	2.19066i
$837$	−6.20610	−	1.66292i	−0.214514	−	0.0574789i
$838$	−13.5672	−	50.6336i	−0.468672	−	1.74911i
$839$	−51.9734			−1.79432			−0.897161	−	0.441704i	$-0.854374\pi$
$839$	−51.9734			−1.79432			−0.897161	+	0.441704i	$0.854374\pi$
$840$		0			0
$841$	−31.3569			−1.08127
$842$	−5.05841	−	18.8782i	−0.174324	−	0.650587i
$843$	18.4995	+	4.95693i	0.637158	+	0.170726i
$844$	79.0718	−	45.6521i	2.72176	−	1.57141i
$845$		0			0
$846$		−	5.55076i		−	0.190839i
$847$	−8.56959	+	6.60407i	−0.294455	+	0.226919i
$848$	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
$852$	12.4580	−	3.33810i	0.426803	−	0.114362i
$853$	−3.33685	+	3.33685i	−0.114251	+	0.114251i	−0.761921	−	0.647670i	$-0.775744\pi$
$853$	−3.33685	+	3.33685i	−0.114251	+	0.114251i	0.647670	+	0.761921i	$0.275744\pi$
$854$	−36.4990	+	47.7721i	−1.24897	+	1.63473i
$855$		0			0
$856$	25.8504	−	44.7742i	0.883548	−	1.53035i
$857$	−8.64078	+	32.2478i	−0.295164	+	1.10157i	0.645924	+	0.763402i	$0.276472\pi$
$857$	−8.64078	+	32.2478i	−0.295164	+	1.10157i	−0.941087	+	0.338164i	$0.890194\pi$
$858$	2.63794	−	9.84493i	0.0900579	−	0.336100i
$859$	2.81235	−	4.87114i	0.0959563	−	0.166201i	−0.814051	−	0.580793i	$-0.802742\pi$
$859$	2.81235	−	4.87114i	0.0959563	−	0.166201i	0.910007	+	0.414592i	$0.136076\pi$
$860$		0			0
$861$	−8.91594	+	11.6697i	−0.303854	+	0.397703i
$862$	−8.18099	+	8.18099i	−0.278646	+	0.278646i
$863$	−24.0137	+	6.43446i	−0.817437	+	0.219032i	−0.643226	−	0.765677i	$-0.722404\pi$
$863$	−24.0137	+	6.43446i	−0.817437	+	0.219032i	−0.174211	+	0.984708i	$0.555738\pi$
$864$	−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
$868$	65.7679	−	50.6834i	2.23231	−	1.72031i
$869$			41.3832i			1.40383i
$870$		0			0
$871$	−1.32673	+	0.765985i	−0.0449544	+	0.0259544i
$872$	−21.6445	−	5.79963i	−0.732975	−	0.196400i
$873$	1.22414	+	4.56855i	0.0414308	+	0.154622i
$874$	−112.556			−3.80725
$875$		0			0
$876$	−45.9604			−1.55286
$877$	−8.83125	−	32.9587i	−0.298210	−	1.11294i	−0.938634	−	0.344914i	$-0.887908\pi$
$877$	−8.83125	−	32.9587i	−0.298210	−	1.11294i	0.640424	−	0.768022i	$-0.278759\pi$
$878$	−49.4053	−	13.2381i	−1.66735	−	0.446764i
$879$	−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	$-0.0412445\pi$
$882$	15.8677	−	9.24957i	0.534295	−	0.311449i
$883$	−17.8491	−	17.8491i	−0.600671	−	0.600671i	0.339819	−	0.940491i	$-0.389634\pi$
$883$	−17.8491	−	17.8491i	−0.600671	−	0.600671i	−0.940491	+	0.339819i	$0.889634\pi$
$884$	−22.0165	−	12.7112i	−0.740494	−	0.427524i
$885$		0			0
$886$	38.2610	+	66.2699i	1.28540	+	2.22638i
$887$	−14.3140	+	3.83542i	−0.480616	+	0.128781i	−0.490990	−	0.871165i	$-0.663365\pi$
$887$	−14.3140	+	3.83542i	−0.480616	+	0.128781i	0.0103733	+	0.999946i	$0.496698\pi$
$888$	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
$892$	32.2021	−	120.180i	1.07821	−	4.02392i
$893$	3.65569	−	13.6432i	0.122333	−	0.456553i
$894$	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
$898$	−55.2318	+	14.7993i	−1.84311	+	0.493859i
$899$	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
$903$	2.46656	+	18.4386i	0.0820820	+	0.613598i
$904$		−	48.6271i		−	1.61731i
$905$		0			0
$906$	−22.5741	+	13.0331i	−0.749973	+	0.432997i
$907$	−12.1692	−	3.26072i	−0.404071	−	0.108271i	0.0510586	−	0.998696i	$-0.483740\pi$
$907$	−12.1692	−	3.26072i	−0.404071	−	0.108271i	−0.455130	+	0.890425i	$0.650407\pi$
$908$	16.4977	+	61.5703i	0.547496	+	2.04328i
$909$	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	$0.611079\pi$
$912$	−17.4345	−	65.0665i	−0.577315	−	2.15457i
$913$	7.93768	+	2.12689i	0.262699	+	0.0703899i
$914$	3.54714	−	2.04794i	0.117329	−	0.0677399i
$915$		0			0
$916$			51.0126i			1.68550i
$917$	−6.57352	−	8.52994i	−0.217077	−	0.281683i
$918$	−9.65648	−	9.65648i	−0.318711	−	0.318711i
$919$	−6.15100	−	3.55128i	−0.202903	−	0.117146i	0.395106	−	0.918636i	$-0.370708\pi$
$919$	−6.15100	−	3.55128i	−0.202903	−	0.117146i	−0.598009	+	0.801490i	$0.704041\pi$
$920$		0			0
$921$	7.92375	+	13.7243i	0.261096	+	0.452232i
$922$	0.261084	−	0.0699572i	0.00859834	−	0.00230392i
$923$	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
$927$	−0.630422	+	2.35277i	−0.0207058	+	0.0772750i
$928$	−22.7931	+	85.0651i	−0.748221	+	2.79240i
$929$	−26.2178	+	45.4106i	−0.860179	+	1.48987i	0.0115773	+	0.999933i	$0.496315\pi$
$929$	−26.2178	+	45.4106i	−0.860179	+	1.48987i	−0.871756	+	0.489940i	$0.837019\pi$
$930$		0			0
$931$	45.0930	−	12.2842i	1.47786	−	0.402597i
$932$	−6.85119	+	6.85119i	−0.224418	+	0.224418i
$933$	−25.5094	+	6.83523i	−0.835142	+	0.223776i
$934$	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	$-0.116909\pi$
$937$	17.5774	+	17.5774i	0.574228	+	0.574228i	−0.359079	+	0.933307i	$0.616909\pi$
$938$	4.04935	−	9.83386i	0.132216	−	0.321087i
$939$		−	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	$0.220474\pi$
$942$	5.88049	+	1.57567i	0.191597	+	0.0513382i
$943$	9.23046	+	34.4485i	0.300585	+	1.12180i
$944$	72.9581			2.37458
$945$		0			0
$946$	−71.6638			−2.32999
$947$	9.65519	+	36.0337i	0.313752	+	1.17094i	0.925146	+	0.379611i	$0.123942\pi$
$947$	9.65519	+	36.0337i	0.313752	+	1.17094i	−0.611395	+	0.791326i	$0.709391\pi$
$948$	50.2635	+	13.4681i	1.63248	+	0.437422i
$949$	−8.14883	+	4.70473i	−0.264522	+	0.152722i
$950$		0			0
$951$			14.5656i			0.472322i
$952$	103.300	−	13.8186i	3.34797	−	0.447863i
$953$	22.4302	+	22.4302i	0.726585	+	0.726585i	0.969938	−	0.243353i	$-0.0782474\pi$
$953$	22.4302	+	22.4302i	0.726585	+	0.726585i	−0.243353	+	0.969938i	$0.578247\pi$
$954$	4.74151	+	2.73751i	0.153512	+	0.0886302i
$955$		0			0
$956$	−16.4095	−	28.4220i	−0.530720	−	0.919234i
$957$	−29.1501	+	7.81075i	−0.942290	+	0.252486i
$958$	−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
$962$	0.0349786	−	0.130542i	0.00112776	−	0.00420884i
$963$	1.76803	−	6.59837i	0.0569739	−	0.212630i
$964$	−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	−0.836001	−	0.548728i	$-0.815112\pi$
$967$	−8.93322	+	8.93322i	−0.287273	+	0.287273i	0.548728	+	0.836001i	$0.315112\pi$
$968$	−29.8942	+	8.01013i	−0.960837	+	0.257455i
$969$	−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
$973$	46.3738	+	19.0956i	1.48668	+	0.612178i
$974$		−	42.8056i		−	1.37158i
$975$		0			0
$976$	−75.6691	+	43.6876i	−2.42211	+	1.39841i
$977$	−53.9070	−	14.4443i	−1.72464	−	0.462115i	−0.745701	−	0.666281i	$-0.767885\pi$
$977$	−53.9070	−	14.4443i	−1.72464	−	0.462115i	−0.978936	+	0.204165i	$0.934552\pi$
$978$	−3.32286	−	12.4011i	−0.106253	−	0.396543i
$979$	58.0214			1.85437
$980$		0			0
$981$	−2.96074			−0.0945291
$982$	27.4419	+	102.415i	0.875708	+	3.26819i
$983$	−33.0746	−	8.86231i	−1.05492	−	0.282664i	−0.310634	−	0.950530i	$-0.600541\pi$
$983$	−33.0746	−	8.86231i	−1.05492	−	0.282664i	−0.744282	+	0.667866i	$0.767208\pi$
$984$	−36.3820	+	21.0052i	−1.15982	+	0.669620i
$985$		0			0
$986$			106.096i			3.37877i
$987$	5.17552	+	2.13116i	0.164739	+	0.0678355i
$988$	−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	$0.642050\pi$
$992$	70.3498	−	18.8502i	2.23361	−	0.598494i
$993$	−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
$997$	0.0828858	−	0.309334i	0.00262502	−	0.00979671i	−0.964601	−	0.263714i	$-0.915052\pi$
$997$	0.0828858	−	0.309334i	0.00262502	−	0.00979671i	0.967226	+	0.253917i	$0.0817191\pi$
$998$	−20.6331	+	77.0038i	−0.653130	+	2.43751i
$999$	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.418.1	yes	24
5.2	odd	4	inner	525.2.bc.c.82.6	yes	24
5.3	odd	4	inner	525.2.bc.c.82.1	✓	24
5.4	even	2	inner	525.2.bc.c.418.6	yes	24
7.3	odd	6	inner	525.2.bc.c.493.6	yes	24
35.3	even	12	inner	525.2.bc.c.157.6	yes	24
35.17	even	12	inner	525.2.bc.c.157.1	yes	24
35.24	odd	6	inner	525.2.bc.c.493.1	yes	24

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

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