LMFDB - Embedded newform 525.2.bc.c.157.1

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			157.1
Character	$\chi$	$=$	525.157
Dual form			525.2.bc.c.418.1

$q$-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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

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

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	0.120595	+	0.992702i	$0.461520\pi$
$2$	−0.679097	+	2.53443i	−0.480194	+	1.79211i	−0.600789	+	0.799407i	$0.705147\pi$
$3$	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	0.409191	+	0.912449i	$0.365811\pi$
$11$	−1.94224	+	3.36406i	−0.585608	+	1.01430i	−0.994799	+	0.101854i	$0.967522\pi$
$12$	−4.71805	−	1.26420i	−1.36198	−	0.364942i
$13$	−0.707107	−	0.707107i	−0.196116	−	0.196116i	0.602217	−	0.798333i	$-0.294284\pi$
$13$	−0.707107	−	0.707107i	−0.196116	−	0.196116i	−0.798333	+	0.602217i	$0.794284\pi$
$14$	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	0.912576	+	0.408907i	$0.134090\pi$
$17$	1.34708	+	5.02738i	0.326716	+	1.21932i	−0.585860	+	0.810412i	$0.699243\pi$
$18$	0.679097	+	2.53443i	0.160065	+	0.597370i
$19$	3.33831	+	5.78212i	0.765860	+	1.32651i	0.939791	+	0.341751i	$0.111020\pi$
$19$	3.33831	+	5.78212i	0.765860	+	1.32651i	−0.173930	+	0.984758i	$0.555647\pi$
$20$		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	0.839202	−	0.543820i	$-0.183023\pi$
$23$	6.20610	+	1.66292i	1.29406	+	0.346743i	0.454860	+	0.890563i	$0.349689\pi$
$24$	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	$0.256469\pi$
$29$			7.76897i			1.44266i	−0.692591	+	0.721331i	$0.743531\pi$
$30$		0			0
$31$	−5.56424	−	3.21251i	−0.999367	−	0.576985i	−0.0913057	−	0.995823i	$-0.529104\pi$
$31$	−5.56424	−	3.21251i	−0.999367	−	0.576985i	−0.908061	+	0.418838i	$0.862437\pi$
$32$	−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	−0.967013	−	0.254727i	$-0.918014\pi$
$37$	−0.0133311	+	0.0497524i	−0.00219162	+	0.00817925i	0.964821	+	0.262906i	$0.0846810\pi$
$38$	−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	$-0.857299\pi$
$41$		−	5.55076i		−	0.866882i	0.901182	−	0.433441i	$-0.142701\pi$
$42$	2.64323	+	6.41909i	0.407859	+	0.990487i
$43$	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
$47$	2.04343	+	0.547536i	0.298065	+	0.0798663i	0.404752	−	0.914426i	$-0.367358\pi$
$47$	2.04343	+	0.547536i	0.298065	+	0.0798663i	−0.106687	+	0.994293i	$0.534024\pi$
$48$	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	0.918863	−	0.394576i	$-0.129109\pi$
$53$	−0.540066	−	2.01555i	−0.0741837	−	0.276857i	−0.993047	+	0.117719i	$0.962442\pi$
$54$	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	−0.528722	−	0.848795i	$-0.677328\pi$
$59$	3.61565	−	6.26249i	0.470717	−	0.815307i	0.999439	+	0.0334888i	$0.0106618\pi$
$60$		0			0
$61$	−7.50000	+	4.33013i	−0.960277	+	0.554416i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−7.50000	+	4.33013i	−0.960277	+	0.554416i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	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	−0.167292	−	0.985907i	$-0.553502\pi$
$67$	1.47977	−	0.396503i	0.180783	−	0.0484406i	0.348075	+	0.937467i	$0.386836\pi$
$68$	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	0.315838	−	0.948813i	$-0.397714\pi$
$73$	9.08884	−	2.43535i	1.06377	−	0.285036i	0.747930	+	0.663777i	$0.231048\pi$
$74$	−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	−0.919273	−	0.393621i	$-0.871222\pi$
$79$	−9.22616	+	5.32673i	−1.03802	+	0.599303i	−0.118751	+	0.992924i	$0.537889\pi$
$80$		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	0.620227	−	0.784423i	$-0.287041\pi$
$83$	−1.49590	−	1.49590i	−0.164196	−	0.164196i	−0.784423	+	0.620227i	$0.787041\pi$
$84$	−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	−0.924948	−	0.380093i	$-0.875892\pi$
$89$	−7.46835	−	12.9356i	−0.791644	−	1.37117i	0.133304	−	0.991075i	$-0.457441\pi$
$90$		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	−0.516634	−	0.856207i	$-0.672815\pi$
$97$	3.34441	−	3.34441i	0.339573	−	0.339573i	0.856207	+	0.516634i	$0.172815\pi$
$98$	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	0.675139	−	0.737691i	$-0.264084\pi$
$101$	3.75714	+	2.16919i	0.373850	+	0.215842i	−0.301289	+	0.953533i	$0.597417\pi$
$102$	−13.1910	+	3.53452i	−1.30610	+	0.349969i
$103$	0.630422	−	2.35277i	0.0621173	−	0.231825i	−0.927887	−	0.372861i	$-0.878377\pi$
$103$	0.630422	−	2.35277i	0.0621173	−	0.231825i	0.990004	+	0.141036i	$0.0450434\pi$
$104$	−7.56839			−0.742142
$105$		0			0
$106$	5.47502			0.531781
$107$	−1.76803	+	6.59837i	−0.170922	+	0.637889i	0.826289	+	0.563247i	$0.190448\pi$
$107$	−1.76803	+	6.59837i	−0.170922	+	0.637889i	−0.997210	+	0.0746418i	$0.976219\pi$
$108$	−4.71805	+	1.26420i	−0.453994	+	0.121647i
$109$	−2.56407	−	1.48037i	−0.245594	−	0.141794i	0.372151	−	0.928172i	$-0.378620\pi$
$109$	−2.56407	−	1.48037i	−0.245594	−	0.141794i	−0.617745	+	0.786378i	$0.711954\pi$
$110$		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	−0.887737	−	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
$117$	−0.965926	−	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	−0.992394	−	0.123105i	$-0.960715\pi$
$127$	−12.5710	−	12.5710i	−1.11550	−	1.11550i	−0.123105	−	0.992394i	$-0.539285\pi$
$128$	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	−0.646022	−	0.763319i	$-0.723568\pi$
$131$	−3.52498	+	2.03515i	−0.307979	+	0.177812i	0.338043	+	0.941131i	$0.390235\pi$
$132$	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	0.0432559	−	0.999064i	$-0.486227\pi$
$137$	6.79164	−	1.81981i	0.580249	−	0.155477i	0.536993	+	0.843587i	$0.319560\pi$
$138$	−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	−0.471523	−	0.881854i	$-0.656296\pi$
$149$	0.688724	−	0.397635i	0.0564225	−	0.0325755i	0.527946	+	0.849278i	$0.322962\pi$
$150$		0			0
$151$	−4.96722	+	8.60347i	−0.404226	+	0.700141i	−0.994231	−	0.107259i	$-0.965793\pi$
$151$	−4.96722	+	8.60347i	−0.404226	+	0.700141i	0.590005	+	0.807400i	$0.299126\pi$
$152$	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	0.937813	−	0.347140i	$-0.112847\pi$
$157$	−0.600524	−	2.24119i	−0.0479270	−	0.178866i	−0.985740	+	0.168274i	$0.946181\pi$
$158$	−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	0.439120	−	0.898428i	$-0.355290\pi$
$163$	4.72633	+	1.26642i	0.370195	+	0.0991934i	−0.0689252	+	0.997622i	$0.521957\pi$
$164$	−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	−0.978520	−	0.206153i	$-0.933906\pi$
$167$	−9.98118	+	9.98118i	−0.772367	+	0.772367i	0.206153	+	0.978520i	$0.433906\pi$
$168$	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	−0.999498	−	0.0316829i	$-0.989913\pi$
$173$	−1.55291	+	5.79555i	−0.118066	+	0.440628i	0.881432	+	0.472311i	$0.156580\pi$
$174$	−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	0.0585225	−	0.998286i	$-0.481361\pi$
$179$	−10.3923	−	6.00000i	−0.776757	−	0.448461i	−0.835280	+	0.549825i	$0.814694\pi$
$180$		0			0
$181$		−	16.2462i		−	1.20757i	−0.797148	−	0.603784i	$-0.793659\pi$
$181$		−	16.2462i		−	1.20757i	0.797148	−	0.603784i	$-0.206341\pi$
$182$	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	0.655652	−	0.755063i	$-0.272394\pi$
$191$	−4.50648	−	7.80545i	−0.326077	−	0.564783i	−0.981730	+	0.190280i	$0.939060\pi$
$192$	−2.47541	−	9.23834i	−0.178647	−	0.666720i
$193$	−2.09788	−	7.82938i	−0.151008	−	0.563571i	−0.999414	−	0.0342247i	$-0.989104\pi$
$193$	−2.09788	−	7.82938i	−0.151008	−	0.563571i	0.848406	−	0.529347i	$-0.177563\pi$
$194$	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	$0.668205\pi$
$198$	−9.84493	−	2.63794i	−0.699649	−	0.187470i
$199$	11.2098	−	19.4159i	0.794641	−	1.37636i	−0.128425	−	0.991719i	$-0.540992\pi$
$199$	11.2098	−	19.4159i	0.794641	−	1.37636i	0.923067	−	0.384640i	$-0.125674\pi$
$200$		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	−0.972263	−	0.233888i	$-0.924855\pi$
$223$	−18.0117	−	18.0117i	−1.20615	−	1.20615i	−0.233888	−	0.972263i	$-0.575145\pi$
$224$	−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	0.982732	+	0.185033i	$0.0592392\pi$
$227$	3.37758	+	12.6053i	0.224178	+	0.836642i	−0.758555	+	0.651609i	$0.774094\pi$
$228$	−8.44056	−	31.5006i	−0.558990	−	2.08618i
$229$	5.22191	+	9.04461i	0.345073	+	0.597684i	0.985367	−	0.170446i	$-0.0545207\pi$
$229$	5.22191	+	9.04461i	0.345073	+	0.597684i	−0.640294	+	0.768130i	$0.721187\pi$
$230$		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	0.321034	−	0.947068i	$-0.395970\pi$
$233$	1.91605	+	0.513403i	0.125524	+	0.0336342i	−0.195510	+	0.980702i	$0.562636\pi$
$234$	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	$-0.930272\pi$
$239$		−	6.71902i		−	0.434617i	0.976103	−	0.217308i	$-0.0697278\pi$
$240$		0			0
$241$	21.2230	+	12.2531i	1.36710	+	0.789293i	0.990556	−	0.137107i	$-0.0437805\pi$
$241$	21.2230	+	12.2531i	1.36710	+	0.789293i	0.376540	+	0.926401i	$0.377114\pi$
$242$	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	$-0.913795\pi$
$251$		−	8.47667i		−	0.535043i	0.963552	−	0.267521i	$-0.0862046\pi$
$252$	−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	−0.124921	−	0.992167i	$-0.539868\pi$
$257$	−11.6898	−	3.13227i	−0.729190	−	0.195386i	−0.604268	+	0.796781i	$0.706535\pi$
$258$	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	−0.958031	−	0.286664i	$-0.907454\pi$
$263$	−4.40597	−	16.4433i	−0.271684	−	1.01394i	0.686347	−	0.727274i	$-0.259213\pi$
$264$	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	−0.894677	−	0.446714i	$-0.852594\pi$
$269$	−0.991819	+	1.71788i	−0.0604723	+	0.104741i	0.834204	+	0.551455i	$0.185927\pi$
$270$		0			0
$271$	1.63382	−	0.943287i	0.0992475	−	0.0573006i	−0.449555	−	0.893253i	$-0.648417\pi$
$271$	1.63382	−	0.943287i	0.0992475	−	0.0573006i	0.548802	+	0.835952i	$0.315084\pi$
$272$	−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	0.307383	−	0.951586i	$-0.400547\pi$
$277$	17.4651	−	4.67976i	1.04938	−	0.281180i	0.741994	+	0.670406i	$0.233880\pi$
$278$	−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	0.538266	−	0.842775i	$-0.319080\pi$
$283$	23.9858	−	6.42696i	1.42580	−	0.382043i	0.887539	+	0.460732i	$0.152413\pi$
$284$	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	0.368291	−	0.929711i	$-0.379943\pi$
$293$	−9.60996	−	9.60996i	−0.561420	−	0.561420i	−0.929711	+	0.368291i	$0.879943\pi$
$294$	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	−0.310892	−	0.950445i	$-0.600628\pi$
$307$	11.2059	−	11.2059i	0.639553	−	0.639553i	0.950445	+	0.310892i	$0.100628\pi$
$308$	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	−0.317035	−	0.948414i	$-0.602687\pi$
$311$	−22.8711	−	13.2047i	−1.29690	−	0.748767i	−0.979868	+	0.199646i	$0.936021\pi$
$312$	−7.31051	+	1.95884i	−0.413876	+	0.110898i
$313$	−4.42301	+	16.5069i	−0.250004	+	0.933026i	0.720799	+	0.693144i	$0.243775\pi$
$313$	−4.42301	+	16.5069i	−0.250004	+	0.933026i	−0.970802	+	0.239881i	$0.922891\pi$
$314$	6.08793			0.343562
$315$		0			0
$316$	52.0366			2.92729
$317$	3.76986	−	14.0693i	0.211736	−	0.790211i	−0.775554	−	0.631282i	$-0.782529\pi$
$317$	3.76986	−	14.0693i	0.211736	−	0.790211i	0.987290	−	0.158929i	$-0.0508041\pi$
$318$	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	0.735407	−	0.677625i	$-0.236991\pi$
$331$	−3.98685	−	6.90542i	−0.219137	−	0.379556i	−0.954544	+	0.298069i	$0.903658\pi$
$332$	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	0.854695	−	0.519130i	$-0.173744\pi$
$337$	6.16015	+	6.16015i	0.335565	+	0.335565i	−0.519130	+	0.854695i	$0.673744\pi$
$338$	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	−0.940626	−	0.339443i	$-0.889761\pi$
$347$	−29.5348	+	7.91383i	−1.58551	+	0.424836i	−0.644885	+	0.764280i	$0.723095\pi$
$348$	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	0.593978	−	0.804481i	$-0.297557\pi$
$353$	28.3820	−	7.60492i	1.51062	−	0.404769i	0.916641	+	0.399712i	$0.130890\pi$
$354$	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	−0.977336	−	0.211692i	$-0.932102\pi$
$359$	−24.3032	+	14.0315i	−1.28267	+	0.740552i	−0.305337	+	0.952244i	$0.598769\pi$
$360$		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	−0.870298	−	0.492526i	$-0.836074\pi$
$367$	−6.95141	−	25.9430i	−0.362861	−	1.35421i	0.507437	−	0.861689i	$-0.330593\pi$
$368$	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	0.182699	−	0.983169i	$-0.441517\pi$
$373$	−2.90979	−	0.779675i	−0.150663	−	0.0403701i	−0.333362	+	0.942799i	$0.608183\pi$
$374$	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	$0.370999\pi$
$379$			35.7819i			1.83799i	−0.394264	+	0.918997i	$0.629001\pi$
$380$		0			0
$381$	−15.3963	−	8.88906i	−0.788777	−	0.455400i
$382$	22.8427	−	6.12067i	1.16873	−	0.313161i
$383$	5.30268	−	19.7899i	0.270954	−	1.01122i	−0.687550	−	0.726137i	$-0.741314\pi$
$383$	5.30268	−	19.7899i	0.270954	−	1.01122i	0.958504	−	0.285078i	$-0.0920196\pi$
$384$	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	0.210188	−	0.977661i	$-0.432592\pi$
$389$	−10.4808	−	6.05109i	−0.531397	−	0.306802i	−0.741585	+	0.670859i	$0.765926\pi$
$390$		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	0.952529	−	0.304448i	$-0.0984719\pi$
$397$	32.3823	+	8.67680i	1.62522	+	0.435476i	0.672690	+	0.739924i	$0.265139\pi$
$398$	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	0.763297	+	0.646047i	$0.223579\pi$
$401$	18.8464	+	32.6428i	0.941142	+	1.63011i	0.177845	+	0.984059i	$0.443087\pi$
$402$	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	−0.841073	−	0.540922i	$-0.818075\pi$
$409$	0.969040	−	1.67843i	0.0479160	−	0.0829929i	0.888989	+	0.457929i	$0.151409\pi$
$410$		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	−0.914227	−	0.405202i	$-0.867201\pi$
$431$	−2.20473	+	3.81870i	−0.106198	+	0.183941i	0.808029	+	0.589143i	$0.200534\pi$
$432$	9.74543	+	2.61128i	0.468877	+	0.125635i
$433$	−12.0839	−	12.0839i	−0.580715	−	0.580715i	0.354385	−	0.935100i	$-0.384690\pi$
$433$	−12.0839	−	12.0839i	−0.580715	−	0.580715i	−0.935100	+	0.354385i	$0.884690\pi$
$434$	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	0.999210	−	0.0397376i	$-0.0126522\pi$
$439$	9.74684	+	16.8820i	0.465191	+	0.805735i	−0.534019	+	0.845473i	$0.679319\pi$
$440$		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	−0.482572	−	0.875856i	$-0.660297\pi$
$443$	−28.1705	−	7.54825i	−1.33842	−	0.358628i	−0.855848	+	0.517228i	$0.826964\pi$
$444$	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	$0.171922\pi$
$449$			21.7926i			1.02846i	−0.857653	+	0.514229i	$0.828078\pi$
$450$		0			0
$451$	18.6731	+	10.7809i	0.879281	+	0.507653i
$452$	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	−0.955832	−	0.293913i	$-0.905042\pi$
$457$	0.404025	−	1.50784i	0.0188995	−	0.0705339i	0.974732	+	0.223380i	$0.0717089\pi$
$458$	−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	$-0.999236\pi$
$461$		−	0.103015i		−	0.00479789i	0.999997	−	0.00239894i	$-0.000763608\pi$
$462$	−26.7280	−	3.57545i	−1.24350	−	0.166345i
$463$	−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
$467$	−19.2677	−	5.16277i	−0.891603	−	0.238904i	−0.216196	−	0.976350i	$-0.569365\pi$
$467$	−19.2677	−	5.16277i	−0.891603	−	0.238904i	−0.675407	+	0.737446i	$0.736032\pi$
$468$	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	−0.912618	−	0.408814i	$-0.865943\pi$
$479$	−2.23820	+	3.87668i	−0.102266	+	0.177130i	0.810352	+	0.585944i	$0.199276\pi$
$480$		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	0.116549	−	0.993185i	$-0.462817\pi$
$487$	15.7583	−	4.22241i	0.714075	−	0.191336i	0.597527	+	0.801849i	$0.296150\pi$
$488$	−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	−0.955531	−	0.294891i	$-0.904717\pi$
$499$	−26.3126	+	15.1916i	−1.17791	+	0.680068i	−0.222382	+	0.974960i	$0.571383\pi$
$500$		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	0.760676	−	0.649131i	$-0.224867\pi$
$503$	2.50170	+	2.50170i	0.111545	+	0.111545i	−0.649131	+	0.760676i	$0.724867\pi$
$504$	−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	0.684124	+	0.729366i	$0.260185\pi$
$509$	21.9679	+	38.0496i	0.973711	+	1.68652i	0.289587	+	0.957152i	$0.406482\pi$
$510$		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	−0.0417148	−	0.999130i	$-0.513282\pi$
$521$	−21.1784	−	12.2274i	−0.927844	−	0.535691i	−0.886129	+	0.463439i	$0.846615\pi$
$522$	−19.6899	+	5.27588i	−0.861802	+	0.230919i
$523$	1.65889	−	6.19106i	0.0725382	−	0.270716i	−0.920126	−	0.391623i	$-0.871914\pi$
$523$	1.65889	−	6.19106i	0.0725382	−	0.270716i	0.992664	+	0.120907i	$0.0385803\pi$
$524$	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	0.793643	−	0.608383i	$-0.208182\pi$
$541$	−3.02498	−	5.23941i	−0.130054	−	0.225260i	−0.923697	+	0.383123i	$0.874848\pi$
$542$	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	0.746557	−	0.665322i	$-0.231706\pi$
$547$	1.89992	+	1.89992i	0.0812347	+	0.0812347i	−0.665322	+	0.746557i	$0.731706\pi$
$548$	−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	0.446277	−	0.894895i	$-0.352750\pi$
$557$	30.2141	−	8.09584i	1.28021	−	0.343032i	0.833935	+	0.551863i	$0.186083\pi$
$558$	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	0.319741	−	0.947505i	$-0.396404\pi$
$563$	25.3980	−	6.80537i	1.07040	−	0.286812i	0.750657	+	0.660693i	$0.229737\pi$
$564$	−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	−0.942551	−	0.334062i	$-0.891581\pi$
$569$	−26.8240	+	15.4868i	−1.12452	+	0.649242i	−0.181970	+	0.983304i	$0.558247\pi$
$570$		0			0
$571$	−0.993521	+	1.72083i	−0.0415775	+	0.0720144i	−0.886065	−	0.463560i	$-0.846572\pi$
$571$	−0.993521	+	1.72083i	−0.0415775	+	0.0720144i	0.844488	+	0.535575i	$0.179905\pi$
$572$	−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	0.889591	+	0.456758i	$0.150989\pi$
$577$	8.34871	+	31.1578i	0.347561	+	1.29712i	−0.542030	+	0.840359i	$0.682344\pi$
$578$	−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	−0.696537	−	0.717521i	$-0.745277\pi$
$587$	0.508420	−	0.508420i	0.0209848	−	0.0209848i	0.717521	+	0.696537i	$0.245277\pi$
$588$	−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	0.835010	+	0.550235i	$0.185462\pi$
$593$	−3.97533	+	14.8361i	−0.163247	+	0.609247i	−0.998257	+	0.0590125i	$0.981205\pi$
$594$	−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	0.0150931	−	0.999886i	$-0.495196\pi$
$599$	−20.6390	−	11.9159i	−0.843287	−	0.486872i	−0.858380	+	0.513014i	$0.828529\pi$
$600$		0			0
$601$		−	13.8729i		−	0.565887i	−0.959137	−	0.282944i	$-0.908689\pi$
$601$		−	13.8729i		−	0.565887i	0.959137	−	0.282944i	$-0.0913110\pi$
$602$	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	0.953637	−	0.300958i	$-0.0973064\pi$
$607$	40.1351	+	10.7542i	1.62903	+	0.436498i	0.675395	+	0.737456i	$0.263973\pi$
$608$	−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	−0.450606	−	0.892723i	$-0.648792\pi$
$613$	−12.5461	−	46.8226i	−0.506731	−	1.89115i	−0.0561248	−	0.998424i	$-0.517874\pi$
$614$	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	$0.711966\pi$
$618$	6.17326	+	1.65412i	0.248325	+	0.0665384i
$619$	7.48289	−	12.9607i	0.300763	−	0.520936i	−0.675546	−	0.737318i	$-0.736092\pi$
$619$	7.48289	−	12.9607i	0.300763	−	0.520936i	0.976309	+	0.216381i	$0.0694255\pi$
$620$		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	−0.611286	−	0.791410i	$-0.709348\pi$
$641$	9.61419	−	16.6523i	0.379738	−	0.657725i	0.991024	+	0.133685i	$0.0426809\pi$
$642$	−17.3130	−	4.63901i	−0.683290	−	0.183087i
$643$	23.6685	+	23.6685i	0.933396	+	0.933396i	0.997916	−	0.0645203i	$-0.0205517\pi$
$643$	23.6685	+	23.6685i	0.933396	+	0.933396i	−0.0645203	+	0.997916i	$0.520552\pi$
$644$	−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	0.943343	−	0.331819i	$-0.107662\pi$
$647$	−1.00538	−	3.75212i	−0.0395255	−	0.147511i	−0.982869	+	0.184308i	$0.940996\pi$
$648$	−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	0.740778	−	0.671750i	$-0.234457\pi$
$653$	26.7404	+	7.16508i	1.04643	+	0.280391i	0.305657	+	0.952142i	$0.401124\pi$
$654$	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	$-0.930553\pi$
$659$		−	11.1129i		−	0.432896i	0.976294	−	0.216448i	$-0.0694471\pi$
$660$		0			0
$661$	10.0946	+	5.82810i	0.392633	+	0.226687i	0.683300	−	0.730137i	$-0.260544\pi$
$661$	10.0946	+	5.82810i	0.392633	+	0.226687i	−0.290667	+	0.956824i	$0.593877\pi$
$662$	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	−0.914899	−	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
$677$	−19.7899	−	5.30268i	−0.760587	−	0.203799i	−0.142378	−	0.989812i	$-0.545475\pi$
$677$	−19.7899	−	5.30268i	−0.760587	−	0.203799i	−0.618209	+	0.786014i	$0.712141\pi$
$678$	−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	0.983486	−	0.180982i	$-0.0579276\pi$
$683$	1.07859	+	4.02536i	0.0412712	+	0.154026i	−0.942215	+	0.335008i	$0.891261\pi$
$684$	−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	−0.877755	−	0.479109i	$-0.840960\pi$
$691$	−23.7032	+	13.6851i	−0.901713	+	0.520604i	−0.0239572	+	0.999713i	$0.507627\pi$
$692$	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	−0.446760	−	0.894654i	$-0.647422\pi$
$709$	2.78660	−	1.60884i	0.104653	−	0.0604214i	0.551413	+	0.834232i	$0.314089\pi$
$710$		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	−0.976138	−	0.217149i	$-0.930324\pi$
$719$	−18.1298	−	31.4017i	−0.676126	−	1.17108i	0.300013	−	0.953935i	$-0.403009\pi$
$720$		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	−0.212357	+	0.977192i	$0.568114\pi$
$727$	−32.0737	+	32.0737i	−1.18955	+	1.18955i	−0.977192	+	0.212357i	$0.931886\pi$
$728$	−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	−0.966164	−	0.257928i	$-0.916960\pi$
$733$	−0.0129286	+	0.0482502i	−0.000477529	+	0.00178216i	0.965687	+	0.259710i	$0.0836270\pi$
$734$	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	0.531109	−	0.847304i	$-0.321776\pi$
$739$	1.70927	+	0.986849i	0.0628766	+	0.0363018i	−0.468232	+	0.883605i	$0.655109\pi$
$740$		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	−0.721350	−	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
$747$	−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	0.949005	+	0.315262i	$0.102092\pi$
$751$	20.4855	+	35.4820i	0.747527	+	1.29476i	−0.201477	+	0.979493i	$0.564574\pi$
$752$	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	0.564596	−	0.825368i	$-0.309032\pi$
$757$	−7.17478	−	7.17478i	−0.260772	−	0.260772i	−0.825368	+	0.564596i	$0.809032\pi$
$758$	−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	−0.00295888	−	0.999996i	$-0.500942\pi$
$761$	23.7678	−	13.7224i	0.861583	−	0.497435i	0.864542	+	0.502560i	$0.167609\pi$
$762$	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	0.501459	−	0.865181i	$-0.332797\pi$
$773$	38.0434	−	10.1937i	1.36833	−	0.366642i	0.866867	+	0.498540i	$0.166130\pi$
$774$	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	−0.593739	−	0.804658i	$-0.702349\pi$
$787$	−13.5183	−	50.4509i	−0.481875	−	1.79838i	0.111864	−	0.993724i	$-0.464318\pi$
$788$	−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	−0.182938	−	0.983124i	$-0.558561\pi$
$797$	22.5902	−	22.5902i	0.800187	−	0.800187i	0.983124	+	0.182938i	$0.0585607\pi$
$798$	−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	0.997493	−	0.0707602i	$-0.0225425\pi$
$809$	40.8145	+	23.5642i	1.43496	+	0.828474i	0.437467	+	0.899235i	$0.355876\pi$
$810$		0			0
$811$		−	41.4206i		−	1.45448i	−0.686386	−	0.727238i	$-0.740804\pi$
$811$		−	41.4206i		−	1.45448i	0.686386	−	0.727238i	$-0.259196\pi$
$812$	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	0.999275	−	0.0380759i	$-0.0121229\pi$
$821$	13.3713	+	23.1598i	0.466663	+	0.808284i	−0.532612	+	0.846359i	$0.678790\pi$
$822$	4.77488	+	17.8201i	0.166543	+	0.621547i
$823$	3.26072	+	12.1692i	0.113662	+	0.424191i	0.999183	−	0.0404070i	$-0.0128655\pi$
$823$	3.26072	+	12.1692i	0.113662	+	0.424191i	−0.885522	+	0.464598i	$0.846199\pi$
$824$	−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	$0.648506\pi$
$828$	−30.3136	−	8.12250i	−1.05347	−	0.282277i
$829$	−0.174326	+	0.301942i	−0.00605460	+	0.0104869i	−0.869037	−	0.494747i	$-0.835261\pi$
$829$	−0.174326	+	0.301942i	−0.00605460	+	0.0104869i	0.862982	+	0.505234i	$0.168594\pi$
$830$		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	0.647670	−	0.761921i	$-0.275744\pi$
$853$	−3.33685	−	3.33685i	−0.114251	−	0.114251i	−0.761921	+	0.647670i	$0.775744\pi$
$854$	−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	−0.941087	−	0.338164i	$-0.890194\pi$
$857$	−8.64078	−	32.2478i	−0.295164	−	1.10157i	0.645924	−	0.763402i	$-0.276472\pi$
$858$	2.63794	+	9.84493i	0.0900579	+	0.336100i
$859$	2.81235	+	4.87114i	0.0959563	+	0.166201i	0.910007	−	0.414592i	$-0.136076\pi$
$859$	2.81235	+	4.87114i	0.0959563	+	0.166201i	−0.814051	+	0.580793i	$0.802742\pi$
$860$		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	−0.174211	−	0.984708i	$-0.555738\pi$
$863$	−24.0137	−	6.43446i	−0.817437	−	0.219032i	−0.643226	+	0.765677i	$0.722404\pi$
$864$	−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	0.640424	+	0.768022i	$0.278759\pi$
$877$	−8.83125	+	32.9587i	−0.298210	+	1.11294i	−0.938634	+	0.344914i	$0.887908\pi$
$878$	−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	$0.0412445\pi$
$881$			7.67040i			0.258422i	−0.991617	+	0.129211i	$0.958755\pi$
$882$	15.8677	+	9.24957i	0.534295	+	0.311449i
$883$	−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
$887$	−14.3140	−	3.83542i	−0.480616	−	0.128781i	0.0103733	−	0.999946i	$-0.496698\pi$
$887$	−14.3140	−	3.83542i	−0.480616	−	0.128781i	−0.490990	+	0.871165i	$0.663365\pi$
$888$	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	−0.455130	−	0.890425i	$-0.650407\pi$
$907$	−12.1692	+	3.26072i	−0.404071	+	0.108271i	0.0510586	+	0.998696i	$0.483740\pi$
$908$	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	−0.598009	−	0.801490i	$-0.704041\pi$
$919$	−6.15100	+	3.55128i	−0.202903	+	0.117146i	0.395106	+	0.918636i	$0.370708\pi$
$920$		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	−0.871756	−	0.489940i	$-0.837019\pi$
$929$	−26.2178	−	45.4106i	−0.860179	−	1.48987i	0.0115773	−	0.999933i	$-0.496315\pi$
$930$		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	−0.359079	−	0.933307i	$-0.616909\pi$
$937$	17.5774	−	17.5774i	0.574228	−	0.574228i	0.933307	+	0.359079i	$0.116909\pi$
$938$	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	0.769563	−	0.638571i	$-0.220474\pi$
$941$	18.4461	+	10.6498i	0.601325	+	0.347175i	−0.168238	+	0.985746i	$0.553808\pi$
$942$	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	−0.611395	−	0.791326i	$-0.709391\pi$
$947$	9.65519	−	36.0337i	0.313752	−	1.17094i	0.925146	−	0.379611i	$-0.123942\pi$
$948$	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	−0.243353	−	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
$957$	−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	0.548728	−	0.836001i	$-0.315112\pi$
$967$	−8.93322	−	8.93322i	−0.287273	−	0.287273i	−0.836001	+	0.548728i	$0.815112\pi$
$968$	−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	−0.350067	−	0.936725i	$-0.613841\pi$
$971$	8.91594	−	5.14762i	0.286126	−	0.165195i	0.636194	+	0.771530i	$0.280508\pi$
$972$	−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	−0.978936	−	0.204165i	$-0.934552\pi$
$977$	−53.9070	+	14.4443i	−1.72464	+	0.462115i	−0.745701	+	0.666281i	$0.767885\pi$
$978$	−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	−0.744282	−	0.667866i	$-0.767208\pi$
$983$	−33.0746	+	8.86231i	−1.05492	+	0.282664i	−0.310634	+	0.950530i	$0.600541\pi$
$984$	−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	−0.431598	−	0.902066i	$-0.642050\pi$
$991$	17.7993	−	30.8293i	0.565413	−	0.979324i	0.997011	−	0.0772581i	$-0.0246166\pi$
$992$	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	0.967226	−	0.253917i	$-0.0817191\pi$
$997$	0.0828858	+	0.309334i	0.00262502	+	0.00979671i	−0.964601	+	0.263714i	$0.915052\pi$
$998$	−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.157.1	yes	24
5.2	odd	4	inner	525.2.bc.c.493.1	yes	24
5.3	odd	4	inner	525.2.bc.c.493.6	yes	24
5.4	even	2	inner	525.2.bc.c.157.6	yes	24
7.5	odd	6	inner	525.2.bc.c.82.6	yes	24
35.12	even	12	inner	525.2.bc.c.418.6	yes	24
35.19	odd	6	inner	525.2.bc.c.82.1	✓	24
35.33	even	12	inner	525.2.bc.c.418.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bc.c.82.1	✓	24	35.19	odd	6	inner
525.2.bc.c.82.6	yes	24	7.5	odd	6	inner
525.2.bc.c.157.1	yes	24	1.1	even	1	trivial
525.2.bc.c.157.6	yes	24	5.4	even	2	inner
525.2.bc.c.418.1	yes	24	35.33	even	12	inner
525.2.bc.c.418.6	yes	24	35.12	even	12	inner
525.2.bc.c.493.1	yes	24	5.2	odd	4	inner
525.2.bc.c.493.6	yes	24	5.3	odd	4	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

Related objects

Downloads

Learn more