LMFDB - Embedded newform 950.2.e.m.201.3

Newspace parameters

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.e (of order $3$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.39075800976.1
Defining polynomial:	$x^{8} - x^{7} + 12 x^{6} - 13 x^{5} + 125 x^{4} - 116 x^{3} + 232 x^{2} + 96 x + 64$
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.3
Root			$-0.236942 + 0.410396i$ of defining polynomial
Character	$\chi$	$=$	950.201
Dual form			950.2.e.m.501.3

$q$-expansion

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.236942 - 0.410396i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.236942 - 0.410396i) q^{6} -2.19155 q^{7} -1.00000 q^{8} +(1.38772 + 2.40360i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.236942 - 0.410396i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.236942 - 0.410396i) q^{6} -2.19155 q^{7} -1.00000 q^{8} +(1.38772 + 2.40360i) q^{9} -4.96699 q^{11} -0.473885 q^{12} +(-1.14116 - 1.97656i) q^{13} +(-1.09578 + 1.89794i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.38772 + 5.86770i) q^{17} +2.77543 q^{18} +(-3.12466 + 3.03916i) q^{19} +(-0.519272 + 0.899406i) q^{21} +(-2.48349 + 4.30154i) q^{22} +(-3.84233 - 6.65511i) q^{23} +(-0.236942 + 0.410396i) q^{24} -2.28233 q^{26} +2.73689 q^{27} +(1.09578 + 1.89794i) q^{28} +(-0.983494 - 1.70346i) q^{29} +7.58388 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.17689 + 2.03843i) q^{33} +(3.38772 + 5.86770i) q^{34} +(1.38772 - 2.40360i) q^{36} -7.38864 q^{37} +(1.06966 + 4.22562i) q^{38} -1.08156 q^{39} +(-5.70393 + 9.87950i) q^{41} +(0.519272 + 0.899406i) q^{42} +(5.07927 - 8.79756i) q^{43} +(2.48349 + 4.30154i) q^{44} -7.68466 q^{46} +(-2.09578 - 3.62999i) q^{47} +(0.236942 + 0.410396i) q^{48} -2.19709 q^{49} +(1.60539 + 2.78061i) q^{51} +(-1.14116 + 1.97656i) q^{52} +(2.09578 + 3.62999i) q^{53} +(1.36844 - 2.37022i) q^{54} +2.19155 q^{56} +(0.506896 + 2.00245i) q^{57} -1.96699 q^{58} +(-1.72044 + 2.97988i) q^{59} +(2.36160 + 4.09041i) q^{61} +(3.79194 - 6.56783i) q^{62} +(-3.04126 - 5.26761i) q^{63} +1.00000 q^{64} +(1.17689 + 2.03843i) q^{66} +(-0.404223 - 0.700134i) q^{67} +6.77543 q^{68} -3.64164 q^{69} +(5.59854 - 9.69696i) q^{71} +(-1.38772 - 2.40360i) q^{72} +(2.42850 - 4.20628i) q^{73} +(-3.69432 + 6.39875i) q^{74} +(4.19432 + 1.18645i) q^{76} +10.8854 q^{77} +(-0.540781 + 0.936659i) q^{78} +(-7.63427 + 13.2229i) q^{79} +(-3.51467 + 6.08758i) q^{81} +(5.70393 + 9.87950i) q^{82} +12.7232 q^{83} +1.03854 q^{84} +(-5.07927 - 8.79756i) q^{86} -0.932126 q^{87} +4.96699 q^{88} +(1.78233 + 3.08709i) q^{89} +(2.50093 + 4.33173i) q^{91} +(-3.84233 + 6.65511i) q^{92} +(1.79694 - 3.11239i) q^{93} -4.19155 q^{94} +0.473885 q^{96} +(0.0861680 - 0.149247i) q^{97} +(-1.09854 + 1.90273i) q^{98} +(-6.89277 - 11.9386i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8q + 4q^{2} - q^{3} - 4q^{4} + q^{6} - 12q^{7} - 8q^{8} - 11q^{9} + O(q^{10}) $	$ 8q + 4q^{2} - q^{3} - 4q^{4} + q^{6} - 12q^{7} - 8q^{8} - 11q^{9} + 10q^{11} + 2q^{12} - 9q^{13} - 6q^{14} - 4q^{16} - 5q^{17} - 22q^{18} - q^{21} + 5q^{22} - 6q^{23} + q^{24} - 18q^{26} - 16q^{27} + 6q^{28} + 17q^{29} + 22q^{31} + 4q^{32} + 4q^{33} + 5q^{34} - 11q^{36} + 8q^{37} - 36q^{39} + 7q^{41} + q^{42} + 13q^{43} - 5q^{44} - 12q^{46} - 14q^{47} - q^{48} + 44q^{49} - 9q^{51} - 9q^{52} + 14q^{53} - 8q^{54} + 12q^{56} + 48q^{57} + 34q^{58} + 14q^{59} - 9q^{61} + 11q^{62} + 45q^{63} + 8q^{64} - 4q^{66} - 6q^{67} + 10q^{68} + 54q^{69} + 14q^{71} + 11q^{72} + 11q^{73} + 4q^{74} + 10q^{77} - 18q^{78} - 17q^{79} - 36q^{81} - 7q^{82} + 46q^{83} + 2q^{84} - 13q^{86} + 2q^{87} - 10q^{88} + 14q^{89} - 25q^{91} - 6q^{92} - 13q^{93} - 28q^{94} - 2q^{96} + 17q^{97} + 22q^{98} - 60q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.236942	−	0.410396i	0.136799	−	0.236942i	−0.789484	−	0.613771i	$-0.789652\pi$
$3$	0.236942	−	0.410396i	0.136799	−	0.236942i	0.926283	+	0.376828i	$0.122985\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.236942	−	0.410396i	−0.0967313	−	0.167544i
$7$	−2.19155			−0.828330			−0.414165	−	0.910202i	$-0.635926\pi$
$7$	−2.19155			−0.828330			−0.414165	+	0.910202i	$0.635926\pi$
$8$	−1.00000			−0.353553
$9$	1.38772	+	2.40360i	0.462572	+	0.801199i
$10$		0			0
$11$	−4.96699			−1.49760			−0.748802	−	0.662794i	$-0.769370\pi$
$11$	−4.96699			−1.49760			−0.748802	+	0.662794i	$0.769370\pi$
$12$	−0.473885			−0.136799
$13$	−1.14116	−	1.97656i	−0.316502	−	0.548198i	0.663253	−	0.748395i	$-0.269175\pi$
$13$	−1.14116	−	1.97656i	−0.316502	−	0.548198i	−0.979756	+	0.200197i	$0.935842\pi$
$14$	−1.09578	+	1.89794i	−0.292859	+	0.507246i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.38772	+	5.86770i	−0.821642	+	1.42313i	0.0828169	+	0.996565i	$0.473608\pi$
$17$	−3.38772	+	5.86770i	−0.821642	+	1.42313i	−0.904459	+	0.426561i	$0.859725\pi$
$18$	2.77543			0.654176
$19$	−3.12466	+	3.03916i	−0.716846	+	0.697232i
$19$	−3.12466	+	3.03916i	−0.716846	+	0.697232i
$20$		0			0
$21$	−0.519272	+	0.899406i	−0.113314	+	0.196266i
$22$	−2.48349	+	4.30154i	−0.529483	+	0.917091i
$23$	−3.84233	−	6.65511i	−0.801181	−	1.38769i	−0.918839	−	0.394632i	$-0.870872\pi$
$23$	−3.84233	−	6.65511i	−0.801181	−	1.38769i	0.117658	−	0.993054i	$-0.462461\pi$
$24$	−0.236942	+	0.410396i	−0.0483656	+	0.0837718i
$25$		0			0
$26$	−2.28233			−0.447602
$27$	2.73689			0.526715
$28$	1.09578	+	1.89794i	0.207082	+	0.358677i
$29$	−0.983494	−	1.70346i	−0.182630	−	0.316325i	0.760145	−	0.649753i	$-0.225128\pi$
$29$	−0.983494	−	1.70346i	−0.182630	−	0.316325i	−0.942775	+	0.333428i	$0.891794\pi$
$30$		0			0
$31$	7.58388			1.36210			0.681052	−	0.732235i	$-0.261523\pi$
$31$	7.58388			1.36210			0.681052	+	0.732235i	$0.261523\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.17689	+	2.03843i	−0.204870	+	0.354846i
$34$	3.38772	+	5.86770i	0.580989	+	1.00630i
$35$		0			0
$36$	1.38772	−	2.40360i	0.231286	−	0.400599i
$37$	−7.38864			−1.21469			−0.607343	−	0.794440i	$-0.707764\pi$
$37$	−7.38864			−1.21469			−0.607343	+	0.794440i	$0.707764\pi$
$38$	1.06966	+	4.22562i	0.173522	+	0.685485i
$39$	−1.08156			−0.173188
$40$		0			0
$41$	−5.70393	+	9.87950i	−0.890804	+	1.54292i	−0.0518913	+	0.998653i	$0.516525\pi$
$41$	−5.70393	+	9.87950i	−0.890804	+	1.54292i	−0.838913	+	0.544266i	$0.816808\pi$
$42$	0.519272	+	0.899406i	0.0801254	+	0.138781i
$43$	5.07927	−	8.79756i	0.774582	−	1.34161i	−0.160448	−	0.987044i	$-0.551294\pi$
$43$	5.07927	−	8.79756i	0.774582	−	1.34161i	0.935029	−	0.354570i	$-0.115373\pi$
$44$	2.48349	+	4.30154i	0.374401	+	0.648481i
$45$		0			0
$46$	−7.68466			−1.13304
$47$	−2.09578	−	3.62999i	−0.305701	−	0.529489i	0.671717	−	0.740808i	$-0.265557\pi$
$47$	−2.09578	−	3.62999i	−0.305701	−	0.529489i	−0.977417	+	0.211319i	$0.932224\pi$
$48$	0.236942	+	0.410396i	0.0341997	+	0.0592356i
$49$	−2.19709			−0.313870
$50$		0			0
$51$	1.60539	+	2.78061i	0.224799	+	0.389364i
$52$	−1.14116	+	1.97656i	−0.158251	+	0.274099i
$53$	2.09578	+	3.62999i	0.287877	+	0.498618i	0.973303	−	0.229525i	$-0.0737172\pi$
$53$	2.09578	+	3.62999i	0.287877	+	0.498618i	−0.685426	+	0.728143i	$0.740384\pi$
$54$	1.36844	−	2.37022i	0.186222	−	0.322545i
$55$		0			0
$56$	2.19155			0.292859
$57$	0.506896	+	2.00245i	0.0671401	+	0.265232i
$58$	−1.96699			−0.258278
$59$	−1.72044	+	2.97988i	−0.223982	+	0.387948i	−0.956013	−	0.293323i	$-0.905239\pi$
$59$	−1.72044	+	2.97988i	−0.223982	+	0.387948i	0.732032	+	0.681271i	$0.238572\pi$
$60$		0			0
$61$	2.36160	+	4.09041i	0.302372	+	0.523724i	0.976673	−	0.214733i	$-0.0688882\pi$
$61$	2.36160	+	4.09041i	0.302372	+	0.523724i	−0.674301	+	0.738457i	$0.735555\pi$
$62$	3.79194	−	6.56783i	0.481577	−	0.834115i
$63$	−3.04126	−	5.26761i	−0.383162	−	0.663657i
$64$	1.00000			0.125000
$65$		0			0
$66$	1.17689	+	2.03843i	0.144865	+	0.250914i
$67$	−0.404223	−	0.700134i	−0.0493836	−	0.0855350i	0.840277	−	0.542157i	$-0.182392\pi$
$67$	−0.404223	−	0.700134i	−0.0493836	−	0.0855350i	−0.889661	+	0.456622i	$0.849059\pi$
$68$	6.77543			0.821642
$69$	−3.64164			−0.438402
$70$		0			0
$71$	5.59854	−	9.69696i	0.664425	−	1.15082i	−0.315016	−	0.949086i	$-0.602010\pi$
$71$	5.59854	−	9.69696i	0.664425	−	1.15082i	0.979441	−	0.201731i	$-0.0646568\pi$
$72$	−1.38772	−	2.40360i	−0.163544	−	0.283266i
$73$	2.42850	−	4.20628i	0.284234	−	0.492308i	−0.688189	−	0.725531i	$-0.741594\pi$
$73$	2.42850	−	4.20628i	0.284234	−	0.492308i	0.972423	+	0.233224i	$0.0749274\pi$
$74$	−3.69432	+	6.39875i	−0.429456	+	0.743840i
$75$		0			0
$76$	4.19432	+	1.18645i	0.481122	+	0.136095i
$77$	10.8854			1.24051
$78$	−0.540781	+	0.936659i	−0.0612313	+	0.106056i
$79$	−7.63427	+	13.2229i	−0.858922	+	1.48770i	0.0140356	+	0.999901i	$0.495532\pi$
$79$	−7.63427	+	13.2229i	−0.858922	+	1.48770i	−0.872958	+	0.487796i	$0.837801\pi$
$80$		0			0
$81$	−3.51467	+	6.08758i	−0.390518	+	0.676398i
$82$	5.70393	+	9.87950i	0.629894	+	1.09101i
$83$	12.7232			1.39655			0.698276	−	0.715828i	$-0.253951\pi$
$83$	12.7232			1.39655			0.698276	+	0.715828i	$0.253951\pi$
$84$	1.03854			0.113314
$85$		0			0
$86$	−5.07927	−	8.79756i	−0.547712	−	0.948665i
$87$	−0.932126			−0.0999343
$88$	4.96699			0.529483
$89$	1.78233	+	3.08709i	0.188927	+	0.327230i	0.944893	−	0.327380i	$-0.106166\pi$
$89$	1.78233	+	3.08709i	0.188927	+	0.327230i	−0.755966	+	0.654611i	$0.772833\pi$
$90$		0			0
$91$	2.50093	+	4.33173i	0.262168	+	0.454089i
$92$	−3.84233	+	6.65511i	−0.400591	+	0.693843i
$93$	1.79694	−	3.11239i	0.186334	−	0.322740i
$94$	−4.19155			−0.432326
$95$		0			0
$96$	0.473885			0.0483656
$97$	0.0861680	−	0.149247i	0.00874903	−	0.0151538i	−0.861618	−	0.507558i	$-0.830548\pi$
$97$	0.0861680	−	0.149247i	0.00874903	−	0.0151538i	0.870367	+	0.492404i	$0.163882\pi$
$98$	−1.09854	+	1.90273i	−0.110970	+	0.192205i
$99$	−6.89277	−	11.9386i	−0.692750	−	1.19988i
$100$		0			0
$101$	−7.41199	−	12.8379i	−0.737521	−	1.27742i	−0.953609	−	0.301049i	$-0.902663\pi$
$101$	−7.41199	−	12.8379i	−0.737521	−	1.27742i	0.216088	−	0.976374i	$-0.430670\pi$
$102$	3.21077			0.317914
$103$	−14.6031			−1.43889			−0.719443	−	0.694552i	$-0.755603\pi$
$103$	−14.6031			−1.43889			−0.719443	+	0.694552i	$0.755603\pi$
$104$	1.14116	+	1.97656i	0.111900	+	0.193817i
$105$		0			0
$106$	4.19155			0.407120
$107$	0.363891			0.0351787			0.0175893	−	0.999845i	$-0.494401\pi$
$107$	0.363891			0.0351787			0.0175893	+	0.999845i	$0.494401\pi$
$108$	−1.36844	−	2.37022i	−0.131679	−	0.228074i
$109$	6.61776	−	11.4623i	0.633867	−	1.09789i	−0.352887	−	0.935666i	$-0.614800\pi$
$109$	6.61776	−	11.4623i	0.633867	−	1.09789i	0.986754	−	0.162224i	$-0.0518666\pi$
$110$		0			0
$111$	−1.75068	+	3.03227i	−0.166167	+	0.287810i
$112$	1.09578	−	1.89794i	0.103541	−	0.179339i
$113$	−17.4894			−1.64527			−0.822633	−	0.568572i	$-0.807496\pi$
$113$	−17.4894			−1.64527			−0.822633	+	0.568572i	$0.807496\pi$
$114$	1.98762	+	0.562242i	0.186158	+	0.0526588i
$115$		0			0
$116$	−0.983494	+	1.70346i	−0.0913151	+	0.158162i
$117$	3.16723	−	5.48580i	0.292810	−	0.507162i
$118$	1.72044	+	2.97988i	0.158379	+	0.274320i
$119$	7.42437	−	12.8594i	0.680591	−	1.17882i
$120$		0			0
$121$	13.6710			1.24282
$122$	4.72320			0.427619
$123$	2.70301	+	4.68174i	0.243722	+	0.422138i
$124$	−3.79194	−	6.56783i	−0.340526	−	0.589809i
$125$		0			0
$126$	−6.08251			−0.541873
$127$	−2.33272	−	4.04039i	−0.206995	−	0.358527i	0.743771	−	0.668434i	$-0.233035\pi$
$127$	−2.33272	−	4.04039i	−0.206995	−	0.358527i	−0.950767	+	0.309908i	$0.899702\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−2.40699	−	4.16903i	−0.211924	−	0.367062i
$130$		0			0
$131$	−0.449610	+	0.778747i	−0.0392826	+	0.0680395i	−0.884998	−	0.465594i	$-0.845841\pi$
$131$	−0.449610	+	0.778747i	−0.0392826	+	0.0680395i	0.845716	+	0.533634i	$0.179174\pi$
$132$	2.35378			0.204870
$133$	6.84786	−	6.66049i	0.593785	−	0.577538i
$134$	−0.808445			−0.0698390
$135$		0			0
$136$	3.38772	−	5.86770i	0.290494	−	0.503151i
$137$	3.73787	+	6.47418i	0.319348	+	0.553126i	0.980352	−	0.197256i	$-0.0632029\pi$
$137$	3.73787	+	6.47418i	0.319348	+	0.553126i	−0.661004	+	0.750382i	$0.729870\pi$
$138$	−1.82082	+	3.15375i	−0.154999	+	0.268465i
$139$	3.00961	+	5.21280i	0.255272	+	0.442144i	0.964969	−	0.262363i	$-0.0845017\pi$
$139$	3.00961	+	5.21280i	0.255272	+	0.442144i	−0.709698	+	0.704506i	$0.751168\pi$
$140$		0			0
$141$	−1.98631			−0.167278
$142$	−5.59854	−	9.69696i	−0.469819	−	0.813751i
$143$	5.66815	+	9.81753i	0.473995	+	0.820983i
$144$	−2.77543			−0.231286
$145$		0			0
$146$	−2.42850	−	4.20628i	−0.200984	−	0.348114i
$147$	−0.520583	+	0.901676i	−0.0429370	+	0.0743690i
$148$	3.69432	+	6.39875i	0.303671	+	0.525974i
$149$	−2.99034	+	5.17942i	−0.244978	+	0.424314i	−0.962125	−	0.272607i	$-0.912114\pi$
$149$	−2.99034	+	5.17942i	−0.244978	+	0.424314i	0.717147	+	0.696921i	$0.245447\pi$
$150$		0			0
$151$	6.06777			0.493788			0.246894	−	0.969042i	$-0.420590\pi$
$151$	6.06777			0.493788			0.246894	+	0.969042i	$0.420590\pi$
$152$	3.12466	−	3.03916i	0.253443	−	0.246509i
$153$	−18.8048			−1.52028
$154$	5.44271	−	9.42706i	0.438586	−	0.759654i
$155$		0			0
$156$	0.540781	+	0.936659i	0.0432971	+	0.0749928i
$157$	0.954613	−	1.65344i	0.0761864	−	0.131959i	−0.825415	−	0.564526i	$-0.809059\pi$
$157$	0.954613	−	1.65344i	0.0761864	−	0.131959i	0.901602	+	0.432567i	$0.142392\pi$
$158$	7.63427	+	13.2229i	0.607350	+	1.05196i
$159$	1.98631			0.157525
$160$		0			0
$161$	8.42068	+	14.5850i	0.663642	+	1.14946i
$162$	3.51467	+	6.08758i	0.276138	+	0.478285i
$163$	−7.54533			−0.590996			−0.295498	−	0.955343i	$-0.595486\pi$
$163$	−7.54533			−0.590996			−0.295498	+	0.955343i	$0.595486\pi$
$164$	11.4079			0.890804
$165$		0			0
$166$	6.36160	−	11.0186i	0.493756	−	0.855211i
$167$	2.67782	+	4.63811i	0.207216	+	0.358908i	0.950836	−	0.309694i	$-0.100227\pi$
$167$	2.67782	+	4.63811i	0.207216	+	0.358908i	−0.743621	+	0.668602i	$0.766893\pi$
$168$	0.519272	−	0.899406i	0.0400627	−	0.0693907i
$169$	3.89549	−	6.74718i	0.299653	−	0.519014i
$170$		0			0
$171$	−11.6411	−	3.29292i	−0.890214	−	0.251816i
$172$	−10.1585			−0.774582
$173$	−0.790099	+	1.36849i	−0.0600701	+	0.104044i	−0.894497	−	0.447075i	$-0.852466\pi$
$173$	−0.790099	+	1.36849i	−0.0600701	+	0.104044i	0.834426	+	0.551119i	$0.185799\pi$
$174$	−0.466063	+	0.807244i	−0.0353321	+	0.0611970i
$175$		0			0
$176$	2.48349	−	4.30154i	0.187200	−	0.324241i
$177$	0.815288	+	1.41212i	0.0612808	+	0.106142i
$178$	3.56466			0.267183
$179$	−4.18155			−0.312544			−0.156272	−	0.987714i	$-0.549948\pi$
$179$	−4.18155			−0.312544			−0.156272	+	0.987714i	$0.549948\pi$
$180$		0			0
$181$	1.87350	+	3.24500i	0.139256	+	0.241199i	0.927215	−	0.374529i	$-0.122196\pi$
$181$	1.87350	+	3.24500i	0.139256	+	0.241199i	−0.787959	+	0.615728i	$0.788862\pi$
$182$	5.00185			0.370762
$183$	2.23825			0.165456
$184$	3.84233	+	6.65511i	0.283260	+	0.490621i
$185$		0			0
$186$	−1.79694	−	3.11239i	−0.131758	−	0.228212i
$187$	16.8267	−	29.1448i	1.23049	−	2.13128i
$188$	−2.09578	+	3.62999i	−0.152850	+	0.264744i
$189$	−5.99804			−0.436293
$190$		0			0
$191$	−1.96699			−0.142326			−0.0711631	−	0.997465i	$-0.522671\pi$
$191$	−1.96699			−0.142326			−0.0711631	+	0.997465i	$0.522671\pi$
$192$	0.236942	−	0.410396i	0.0170998	−	0.0296178i
$193$	6.92621	−	11.9965i	0.498559	−	0.863530i	−0.501439	−	0.865193i	$-0.667196\pi$
$193$	6.92621	−	11.9965i	0.498559	−	0.863530i	0.999999	+	0.00166273i	$0.000529265\pi$
$194$	−0.0861680	−	0.149247i	−0.00618650	−	0.0107153i
$195$		0			0
$196$	1.09854	+	1.90273i	0.0784674	+	0.135910i
$197$	−17.2218			−1.22701			−0.613503	−	0.789693i	$-0.710240\pi$
$197$	−17.2218			−1.22701			−0.613503	+	0.789693i	$0.710240\pi$
$198$	−13.7855			−0.979696
$199$	−4.60723	−	7.97995i	−0.326598	−	0.565684i	0.655237	−	0.755424i	$-0.272569\pi$
$199$	−4.60723	−	7.97995i	−0.326598	−	0.565684i	−0.981834	+	0.189740i	$0.939236\pi$
$200$		0			0
$201$	−0.383110			−0.0270225
$202$	−14.8240			−1.04301
$203$	2.15538	+	3.73323i	0.151278	+	0.262021i
$204$	1.60539	−	2.78061i	0.112400	−	0.194682i
$205$		0			0
$206$	−7.30155	+	12.6467i	−0.508723	+	0.881134i
$207$	10.6641	−	18.4708i	0.741208	−	1.28381i
$208$	2.28233			0.158251
$209$	15.5201	−	15.0955i	1.07355	−	1.04418i
$210$		0			0
$211$	5.89048	−	10.2026i	0.405518	−	0.702377i	−0.588864	−	0.808232i	$-0.700425\pi$
$211$	5.89048	−	10.2026i	0.405518	−	0.702377i	0.994382	+	0.105855i	$0.0337580\pi$
$212$	2.09578	−	3.62999i	0.143939	−	0.249309i
$213$	−2.65306	−	4.59524i	−0.181785	−	0.314861i
$214$	0.181945	−	0.315139i	0.0124375	−	0.0215424i
$215$		0			0
$216$	−2.73689			−0.186222
$217$	−16.6205			−1.12827
$218$	−6.61776	−	11.4623i	−0.448211	−	0.776325i
$219$	−1.15083	−	1.99329i	−0.0777657	−	0.134694i
$220$		0			0
$221$	15.4638			1.04021
$222$	1.75068	+	3.03227i	0.117498	+	0.203513i
$223$	−0.298836	+	0.517599i	−0.0200115	+	0.0346610i	−0.875858	−	0.482569i	$-0.839704\pi$
$223$	−0.298836	+	0.517599i	−0.0200115	+	0.0346610i	0.855846	+	0.517230i	$0.173037\pi$
$224$	−1.09578	−	1.89794i	−0.0732147	−	0.126812i
$225$		0			0
$226$	−8.74471	+	15.1463i	−0.581690	+	1.00752i
$227$	−15.3364			−1.01791			−0.508957	−	0.860792i	$-0.669969\pi$
$227$	−15.3364			−1.01791			−0.508957	+	0.860792i	$0.669969\pi$
$228$	1.48073	−	1.44021i	0.0980636	−	0.0953804i
$229$	15.5802			1.02957			0.514784	−	0.857320i	$-0.327872\pi$
$229$	15.5802			1.02957			0.514784	+	0.857320i	$0.327872\pi$
$230$		0			0
$231$	2.57922	−	4.46734i	0.169700	−	0.293929i
$232$	0.983494	+	1.70346i	0.0645696	+	0.111838i
$233$	−14.7310	+	25.5148i	−0.965058	+	1.67153i	−0.255599	+	0.966783i	$0.582273\pi$
$233$	−14.7310	+	25.5148i	−0.965058	+	1.67153i	−0.709459	+	0.704747i	$0.751061\pi$
$234$	−3.16723	−	5.48580i	−0.207048	−	0.358618i
$235$		0			0
$236$	3.44087			0.223982
$237$	3.61776	+	6.26615i	0.234999	+	0.407030i
$238$	−7.42437	−	12.8594i	−0.481250	−	0.833550i
$239$	1.34825			0.0872108			0.0436054	−	0.999049i	$-0.486116\pi$
$239$	1.34825			0.0872108			0.0436054	+	0.999049i	$0.486116\pi$
$240$		0			0
$241$	−13.9331	−	24.1328i	−0.897507	−	1.55453i	−0.830671	−	0.556763i	$-0.812043\pi$
$241$	−13.9331	−	24.1328i	−0.897507	−	1.55453i	−0.0668355	−	0.997764i	$-0.521290\pi$
$242$	6.83549	−	11.8394i	0.439402	−	0.761066i
$243$	5.77088	+	9.99546i	0.370202	+	0.641209i
$244$	2.36160	−	4.09041i	0.151186	−	0.261862i
$245$		0			0
$246$	5.40601			0.344675
$247$	9.57282	+	2.70788i	0.609104	+	0.172298i
$248$	−7.58388			−0.481577
$249$	3.01467	−	5.22155i	0.191047	−	0.330902i
$250$		0			0
$251$	−14.4166	−	24.9703i	−0.909968	−	1.57611i	−0.814107	−	0.580715i	$-0.802773\pi$
$251$	−14.4166	−	24.9703i	−0.909968	−	1.57611i	−0.0958610	−	0.995395i	$-0.530560\pi$
$252$	−3.04126	+	5.26761i	−0.191581	+	0.331828i
$253$	19.0848	+	33.0559i	1.19985	+	2.07820i
$254$	−4.66544			−0.292736
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.65083	+	2.85932i	0.102976	+	0.178359i	0.912909	−	0.408162i	$-0.133830\pi$
$257$	1.65083	+	2.85932i	0.102976	+	0.178359i	−0.809934	+	0.586522i	$0.800497\pi$
$258$	−4.81398			−0.299705
$259$	16.1926			1.00616
$260$		0			0
$261$	2.72962	−	4.72784i	0.168959	−	0.292646i
$262$	0.449610	+	0.778747i	0.0277770	+	0.0481112i
$263$	−5.59854	+	9.69696i	−0.345221	+	0.597940i	−0.985394	−	0.170291i	$-0.945529\pi$
$263$	−5.59854	+	9.69696i	−0.345221	+	0.597940i	0.640173	+	0.768231i	$0.278863\pi$
$264$	1.17689	−	2.03843i	0.0724326	−	0.125457i
$265$		0			0
$266$	−2.34422	−	9.26067i	−0.143734	−	0.567808i
$267$	1.68924			0.103380
$268$	−0.404223	+	0.700134i	−0.0246918	+	0.0427675i
$269$	14.1998	−	24.5948i	0.865777	−	1.49957i	−0.000496384	−	1.00000i	$-0.500158\pi$
$269$	14.1998	−	24.5948i	0.865777	−	1.49957i	0.866273	−	0.499570i	$-0.166509\pi$
$270$		0			0
$271$	−10.2850	+	17.8142i	−0.624772	+	1.08214i	0.363813	+	0.931472i	$0.381475\pi$
$271$	−10.2850	+	17.8142i	−0.624772	+	1.08214i	−0.988585	+	0.150665i	$0.951859\pi$
$272$	−3.38772	−	5.86770i	−0.205410	−	0.355781i
$273$	2.37030			0.143457
$274$	7.47574			0.451626
$275$		0			0
$276$	1.82082	+	3.15375i	0.109601	+	0.189834i
$277$	−8.99447			−0.540425			−0.270213	−	0.962801i	$-0.587094\pi$
$277$	−8.99447			−0.540425			−0.270213	+	0.962801i	$0.587094\pi$
$278$	6.01922			0.361009
$279$	10.5243	+	18.2286i	0.630072	+	1.09132i
$280$		0			0
$281$	4.78233	+	8.28324i	0.285290	+	0.494137i	0.972679	−	0.232152i	$-0.0745768\pi$
$281$	4.78233	+	8.28324i	0.285290	+	0.494137i	−0.687390	+	0.726289i	$0.741243\pi$
$282$	−0.993157	+	1.72020i	−0.0591416	+	0.102436i
$283$	1.25806	−	2.17902i	0.0747836	−	0.129529i	−0.826209	−	0.563364i	$-0.809507\pi$
$283$	1.25806	−	2.17902i	0.0747836	−	0.129529i	0.900992	+	0.433835i	$0.142840\pi$
$284$	−11.1971			−0.664425
$285$		0			0
$286$	11.3363			0.670330
$287$	12.5005	−	21.6515i	0.737880	−	1.27805i
$288$	−1.38772	+	2.40360i	−0.0817720	+	0.141633i
$289$	−14.4532	−	25.0338i	−0.850191	−	1.47257i
$290$		0			0
$291$	−0.0408337	−	0.0707260i	−0.00239371	−	0.00414603i
$292$	−4.85699			−0.284234
$293$	−0.406116			−0.0237256			−0.0118628	−	0.999930i	$-0.503776\pi$
$293$	−0.406116			−0.0237256			−0.0118628	+	0.999930i	$0.503776\pi$
$294$	0.520583	+	0.901676i	0.0303610	+	0.0525868i
$295$		0			0
$296$	7.38864			0.429456
$297$	−13.5941			−0.788809
$298$	2.99034	+	5.17942i	0.173226	+	0.300036i
$299$	−8.76946	+	15.1892i	−0.507151	+	0.878411i
$300$		0			0
$301$	−11.1315	+	19.2803i	−0.641609	+	1.11130i
$302$	3.03388	−	5.25484i	0.174580	−	0.302382i
$303$	−7.02486			−0.403568
$304$	−1.06966	−	4.22562i	−0.0613493	−	0.242356i
$305$		0			0
$306$	−9.40238	+	16.2854i	−0.537498	+	0.930975i
$307$	−10.4555	+	18.1095i	−0.596729	+	1.03357i	0.396571	+	0.918004i	$0.370200\pi$
$307$	−10.4555	+	18.1095i	−0.596729	+	1.03357i	−0.993300	+	0.115561i	$0.963133\pi$
$308$	−5.44271	−	9.42706i	−0.310127	−	0.537156i
$309$	−3.46009	+	5.99305i	−0.196838	+	0.340933i
$310$		0			0
$311$	−9.92397			−0.562737			−0.281368	−	0.959600i	$-0.590788\pi$
$311$	−9.92397			−0.562737			−0.281368	+	0.959600i	$0.590788\pi$
$312$	1.08156			0.0612313
$313$	7.32766	+	12.6919i	0.414184	+	0.717388i	0.995342	−	0.0964027i	$-0.0307336\pi$
$313$	7.32766	+	12.6919i	0.414184	+	0.717388i	−0.581158	+	0.813790i	$0.697400\pi$
$314$	−0.954613	−	1.65344i	−0.0538719	−	0.0933089i
$315$		0			0
$316$	15.2685			0.858922
$317$	17.5220	+	30.3490i	0.984133	+	1.70457i	0.645729	+	0.763567i	$0.276554\pi$
$317$	17.5220	+	30.3490i	0.984133	+	1.70457i	0.338404	+	0.941001i	$0.390113\pi$
$318$	0.993157	−	1.72020i	0.0556935	−	0.0964639i
$319$	4.88500	+	8.46107i	0.273508	+	0.473729i
$320$		0			0
$321$	0.0862211	−	0.149339i	0.00481239	−	0.00833531i
$322$	16.8414			0.938532
$323$	−7.24742	−	28.6304i	−0.403257	−	1.59304i
$324$	7.02933			0.390518
$325$		0			0
$326$	−3.77267	+	6.53445i	−0.208949	+	0.361910i
$327$	−3.13606	−	5.43181i	−0.173424	−	0.300380i
$328$	5.70393	−	9.87950i	0.314947	−	0.545504i
$329$	4.59301	+	7.95533i	0.253221	+	0.438591i
$330$		0			0
$331$	21.4464			1.17880			0.589401	−	0.807841i	$-0.299364\pi$
$331$	21.4464			1.17880			0.589401	+	0.807841i	$0.299364\pi$
$332$	−6.36160	−	11.0186i	−0.349138	−	0.604725i
$333$	−10.2533	−	17.7593i	−0.561880	−	0.973204i
$334$	5.35563			0.293047
$335$		0			0
$336$	−0.519272	−	0.899406i	−0.0283286	−	0.0490666i
$337$	−14.8593	+	25.7371i	−0.809438	+	1.40199i	0.103815	+	0.994597i	$0.466895\pi$
$337$	−14.8593	+	25.7371i	−0.809438	+	1.40199i	−0.913254	+	0.407392i	$0.866438\pi$
$338$	−3.89549	−	6.74718i	−0.211886	−	0.366998i
$339$	−4.14398	+	7.17759i	−0.225070	+	0.389833i
$340$		0			0
$341$	−37.6690			−2.03989
$342$	−8.67228	+	8.43499i	−0.468943	+	0.456112i
$343$	20.1559			1.08832
$344$	−5.07927	+	8.79756i	−0.273856	+	0.474332i
$345$		0			0
$346$	0.790099	+	1.36849i	0.0424760	+	0.0735705i
$347$	1.07651	−	1.86456i	0.0577898	−	0.100095i	−0.835683	−	0.549212i	$-0.814928\pi$
$347$	1.07651	−	1.86456i	0.0577898	−	0.100095i	0.893473	+	0.449117i	$0.148261\pi$
$348$	0.466063	+	0.807244i	0.0249836	+	0.0432728i
$349$	17.5031			0.936920			0.468460	−	0.883485i	$-0.344809\pi$
$349$	17.5031			0.936920			0.468460	+	0.883485i	$0.344809\pi$
$350$		0			0
$351$	−3.12324	−	5.40961i	−0.166706	−	0.288744i
$352$	−2.48349	−	4.30154i	−0.132371	−	0.229273i
$353$	21.3171			1.13459			0.567297	−	0.823513i	$-0.307989\pi$
$353$	21.3171			1.13459			0.567297	+	0.823513i	$0.307989\pi$
$354$	1.63058			0.0866642
$355$		0			0
$356$	1.78233	−	3.08709i	0.0944633	−	0.163615i
$357$	−3.51829	−	6.09386i	−0.186208	−	0.322521i
$358$	−2.09077	+	3.62133i	−0.110501	+	0.191393i
$359$	−12.8547	+	22.2650i	−0.678445	+	1.17510i	0.297004	+	0.954876i	$0.404013\pi$
$359$	−12.8547	+	22.2650i	−0.678445	+	1.17510i	−0.975449	+	0.220226i	$0.929321\pi$
$360$		0			0
$361$	0.526988	−	18.9927i	0.0277362	−	0.999615i
$362$	3.74700			0.196938
$363$	3.23923	−	5.61051i	0.170016	−	0.294476i
$364$	2.50093	−	4.33173i	0.131084	−	0.227044i
$365$		0			0
$366$	1.11913	−	1.93838i	0.0584977	−	0.101321i
$367$	−7.17092	−	12.4204i	−0.374319	−	0.648339i	0.615906	−	0.787820i	$-0.288790\pi$
$367$	−7.17092	−	12.4204i	−0.374319	−	0.648339i	−0.990225	+	0.139480i	$0.955457\pi$
$368$	7.68466			0.400591
$369$	−31.6618			−1.64825
$370$		0			0
$371$	−4.59301	−	7.95533i	−0.238457	−	0.413020i
$372$	−3.59388			−0.186334
$373$	−0.646114			−0.0334545			−0.0167273	−	0.999860i	$-0.505325\pi$
$373$	−0.646114			−0.0334545			−0.0167273	+	0.999860i	$0.505325\pi$
$374$	−16.8267	−	29.1448i	−0.870090	−	1.50704i
$375$		0			0
$376$	2.09578	+	3.62999i	0.108081	+	0.187203i
$377$	−2.24466	+	3.88786i	−0.115606	+	0.200235i
$378$	−2.99902	+	5.19446i	−0.154253	+	0.267174i
$379$	13.1255			0.674213			0.337107	−	0.941466i	$-0.390552\pi$
$379$	13.1255			0.674213			0.337107	+	0.941466i	$0.390552\pi$
$380$		0			0
$381$	−2.21088			−0.113267
$382$	−0.983494	+	1.70346i	−0.0503199	+	0.0871567i
$383$	−5.59854	+	9.69696i	−0.286072	+	0.495492i	−0.972869	−	0.231358i	$-0.925683\pi$
$383$	−5.59854	+	9.69696i	−0.286072	+	0.495492i	0.686796	+	0.726850i	$0.259016\pi$
$384$	−0.236942	−	0.410396i	−0.0120914	−	0.0209429i
$385$		0			0
$386$	−6.92621	−	11.9965i	−0.352535	−	0.610608i
$387$	28.1944			1.43320
$388$	−0.172336			−0.00874903
$389$	11.0037	+	19.0590i	0.557909	+	0.966327i	0.997671	+	0.0682127i	$0.0217296\pi$
$389$	11.0037	+	19.0590i	0.557909	+	0.966327i	−0.439761	+	0.898115i	$0.644937\pi$
$390$		0			0
$391$	52.0669			2.63314
$392$	2.19709			0.110970
$393$	0.213063	+	0.369036i	0.0107476	+	0.0186154i
$394$	−8.61092	+	14.9145i	−0.433812	+	0.751384i
$395$		0			0
$396$	−6.89277	+	11.9386i	−0.346375	+	0.599939i
$397$	−4.78044	+	8.27996i	−0.239923	+	0.415559i	−0.960692	−	0.277616i	$-0.910456\pi$
$397$	−4.78044	+	8.27996i	−0.239923	+	0.415559i	0.720769	+	0.693176i	$0.243789\pi$
$398$	−9.21446			−0.461879
$399$	−1.11089	−	4.38849i	−0.0556141	−	0.219699i
$400$		0			0
$401$	−7.71543	+	13.3635i	−0.385290	+	0.667343i	−0.991809	−	0.127726i	$-0.959232\pi$
$401$	−7.71543	+	13.3635i	−0.385290	+	0.667343i	0.606519	+	0.795069i	$0.292565\pi$
$402$	−0.191555	+	0.331783i	−0.00955389	+	0.0165478i
$403$	−8.65446	−	14.9900i	−0.431109	−	0.746703i
$404$	−7.41199	+	12.8379i	−0.368760	+	0.638712i
$405$		0			0
$406$	4.31076			0.213940
$407$	36.6993			1.81912
$408$	−1.60539	−	2.78061i	−0.0794785	−	0.137661i
$409$	7.70164	+	13.3396i	0.380822	+	0.659602i	0.991180	−	0.132523i	$-0.0423079\pi$
$409$	7.70164	+	13.3396i	0.380822	+	0.659602i	−0.610358	+	0.792125i	$0.708975\pi$
$410$		0			0
$411$	3.54264			0.174745
$412$	7.30155	+	12.6467i	0.359721	+	0.623056i
$413$	3.77043	−	6.53058i	0.185531	−	0.321349i
$414$	−10.6641	−	18.4708i	−0.524113	−	0.907791i
$415$		0			0
$416$	1.14116	−	1.97656i	0.0559502	−	0.0969086i
$417$	2.85242			0.139683
$418$	−5.31300	−	20.9886i	−0.259867	−	1.02659i
$419$	−37.5581			−1.83484			−0.917418	−	0.397926i	$-0.869730\pi$
$419$	−37.5581			−1.83484			−0.917418	+	0.397926i	$0.869730\pi$
$420$		0			0
$421$	1.91844	−	3.32283i	0.0934990	−	0.161945i	−0.815482	−	0.578782i	$-0.803528\pi$
$421$	1.91844	−	3.32283i	0.0934990	−	0.161945i	0.908981	+	0.416837i	$0.136861\pi$
$422$	−5.89048	−	10.2026i	−0.286744	−	0.496656i
$423$	5.81669	−	10.0748i	0.282817	−	0.489854i
$424$	−2.09578	−	3.62999i	−0.101780	−	0.176288i
$425$		0			0
$426$	−5.30613			−0.257083
$427$	−5.17558	−	8.96437i	−0.250464	−	0.433816i
$428$	−0.181945	−	0.315139i	−0.00879466	−	0.0152328i
$429$	5.37210			0.259367
$430$		0			0
$431$	−4.56282	−	7.90303i	−0.219783	−	0.380676i	0.734958	−	0.678112i	$-0.237202\pi$
$431$	−4.56282	−	7.90303i	−0.219783	−	0.380676i	−0.954742	+	0.297436i	$0.903868\pi$
$432$	−1.36844	+	2.37022i	−0.0658393	+	0.114037i
$433$	4.32766	+	7.49573i	0.207974	+	0.360222i	0.951076	−	0.308956i	$-0.0999796\pi$
$433$	4.32766	+	7.49573i	0.207974	+	0.360222i	−0.743102	+	0.669178i	$0.766646\pi$
$434$	−8.31024	+	14.3938i	−0.398904	+	0.690923i
$435$		0			0
$436$	−13.2355			−0.633867
$437$	32.2319	+	9.11749i	1.54186	+	0.436149i
$438$	−2.30166			−0.109977
$439$	2.03757	−	3.52917i	0.0972477	−	0.168438i	−0.813297	−	0.581849i	$-0.802329\pi$
$439$	2.03757	−	3.52917i	0.0972477	−	0.168438i	0.910544	+	0.413411i	$0.135663\pi$
$440$		0			0
$441$	−3.04893	−	5.28091i	−0.145187	−	0.251472i
$442$	7.73189	−	13.3920i	0.367768	−	0.636993i
$443$	1.37121	+	2.37501i	0.0651482	+	0.112840i	0.896760	−	0.442518i	$-0.145915\pi$
$443$	1.37121	+	2.37501i	0.0651482	+	0.112840i	−0.831612	+	0.555358i	$0.812581\pi$
$444$	3.50136			0.166167
$445$		0			0
$446$	0.298836	+	0.517599i	0.0141503	+	0.0245090i
$447$	1.41707	+	2.45445i	0.0670253	+	0.116091i
$448$	−2.19155			−0.103541
$449$	−20.7753			−0.980448			−0.490224	−	0.871596i	$-0.663085\pi$
$449$	−20.7753			−0.980448			−0.490224	+	0.871596i	$0.663085\pi$
$450$		0			0
$451$	28.3314	−	49.0713i	1.33407	−	2.31068i
$452$	8.74471	+	15.1463i	0.411317	+	0.712421i
$453$	1.43771	−	2.49019i	0.0675496	−	0.116999i
$454$	−7.66821	+	13.2817i	−0.359887	+	0.623342i
$455$		0			0
$456$	−0.506896	−	2.00245i	−0.0237376	−	0.0937735i
$457$	5.15669			0.241220			0.120610	−	0.992700i	$-0.461515\pi$
$457$	5.15669			0.241220			0.120610	+	0.992700i	$0.461515\pi$
$458$	7.79010	−	13.4928i	0.364007	−	0.630479i
$459$	−9.27181	+	16.0592i	−0.432771	+	0.749581i
$460$		0			0
$461$	−17.7397	+	30.7261i	−0.826221	+	1.43106i	0.0747623	+	0.997201i	$0.476180\pi$
$461$	−17.7397	+	30.7261i	−0.826221	+	1.43106i	−0.900983	+	0.433855i	$0.857153\pi$
$462$	−2.57922	−	4.46734i	−0.119996	−	0.207839i
$463$	39.3280			1.82773			0.913865	−	0.406019i	$-0.133083\pi$
$463$	39.3280			1.82773			0.913865	+	0.406019i	$0.133083\pi$
$464$	1.96699			0.0913151
$465$		0			0
$466$	14.7310	+	25.5148i	0.682399	+	1.18195i
$467$	−9.87174			−0.456810			−0.228405	−	0.973566i	$-0.573351\pi$
$467$	−9.87174			−0.456810			−0.228405	+	0.973566i	$0.573351\pi$
$468$	−6.33445			−0.292810
$469$	0.885876	+	1.53438i	0.0409059	+	0.0708512i
$470$		0			0
$471$	−0.452376	−	0.783539i	−0.0208444	−	0.0361036i
$472$	1.72044	−	2.97988i	0.0791895	−	0.137160i
$473$	−25.2287	+	43.6974i	−1.16002	+	2.00921i
$474$	7.23553			0.332339
$475$		0			0
$476$	−14.8487			−0.680591
$477$	−5.81669	+	10.0748i	−0.266328	+	0.461294i
$478$	0.674124	−	1.16762i	0.0308337	−	0.0534055i
$479$	9.36431	+	16.2195i	0.427866	+	0.741086i	0.996683	−	0.0813778i	$-0.0259320\pi$
$479$	9.36431	+	16.2195i	0.427866	+	0.741086i	−0.568817	+	0.822464i	$0.692599\pi$
$480$		0			0
$481$	8.43166	+	14.6041i	0.384451	+	0.665888i
$482$	−27.8661			−1.26927
$483$	7.98086			0.363142
$484$	−6.83549	−	11.8394i	−0.310704	−	0.538155i
$485$		0			0
$486$	11.5418			0.523545
$487$	−17.9129			−0.811711			−0.405856	−	0.913937i	$-0.633026\pi$
$487$	−17.9129			−0.811711			−0.405856	+	0.913937i	$0.633026\pi$
$488$	−2.36160	−	4.09041i	−0.106905	−	0.185164i
$489$	−1.78781	+	3.09658i	−0.0808475	+	0.140032i
$490$		0			0
$491$	−15.0101	+	25.9982i	−0.677396	+	1.17328i	0.298367	+	0.954451i	$0.403558\pi$
$491$	−15.0101	+	25.9982i	−0.677396	+	1.17328i	−0.975762	+	0.218832i	$0.929775\pi$
$492$	2.70301	−	4.68174i	0.121861	−	0.211069i
$493$	13.3272			0.600227
$494$	7.13150	−	6.93637i	0.320861	−	0.312082i
$495$		0			0
$496$	−3.79194	+	6.56783i	−0.170263	+	0.294904i
$497$	−12.2695	+	21.2514i	−0.550363	+	0.953257i
$498$	−3.01467	−	5.22155i	−0.135090	−	0.233983i
$499$	−4.73966	+	8.20932i	−0.212176	+	0.367500i	−0.952395	−	0.304866i	$-0.901388\pi$
$499$	−4.73966	+	8.20932i	−0.212176	+	0.367500i	0.740219	+	0.672366i	$0.234722\pi$
$500$		0			0
$501$	2.53795			0.113387
$502$	−28.8332			−1.28689
$503$	2.43034	+	4.20947i	0.108363	+	0.187691i	0.915107	−	0.403210i	$-0.132106\pi$
$503$	2.43034	+	4.20947i	0.108363	+	0.187691i	−0.806744	+	0.590901i	$0.798772\pi$
$504$	3.04126	+	5.26761i	0.135468	+	0.234638i
$505$		0			0
$506$	38.1696			1.69685
$507$	−1.84601	−	3.19738i	−0.0819842	−	0.142001i
$508$	−2.33272	+	4.04039i	−0.103498	+	0.179263i
$509$	14.5467	+	25.1957i	0.644773	+	1.11678i	0.984354	+	0.176202i	$0.0563813\pi$
$509$	14.5467	+	25.1957i	0.644773	+	1.11678i	−0.339581	+	0.940577i	$0.610285\pi$
$510$		0			0
$511$	−5.32218	+	9.21829i	−0.235440	+	0.407793i
$512$	−1.00000			−0.0441942
$513$	−8.55185	+	8.31785i	−0.377573	+	0.367242i
$514$	3.30166			0.145630
$515$		0			0
$516$	−2.40699	+	4.16903i	−0.105962	+	0.183531i
$517$	10.4097	+	18.0301i	0.457818	+	0.792964i
$518$	8.09631	−	14.0232i	0.355731	−	0.616145i
$519$	0.374416	+	0.648507i	0.0164350	+	0.0284663i
$520$		0			0
$521$	−8.76175			−0.383859			−0.191930	−	0.981409i	$-0.561475\pi$
$521$	−8.76175			−0.383859			−0.191930	+	0.981409i	$0.561475\pi$
$522$	−2.72962	−	4.72784i	−0.119472	−	0.206932i
$523$	1.34733	+	2.33365i	0.0589147	+	0.102043i	0.893978	−	0.448110i	$-0.147903\pi$
$523$	1.34733	+	2.33365i	0.0589147	+	0.102043i	−0.835064	+	0.550153i	$0.814569\pi$
$524$	0.899220			0.0392826
$525$		0			0
$526$	5.59854	+	9.69696i	0.244108	+	0.422808i
$527$	−25.6920	+	44.4999i	−1.11916	+	1.93845i
$528$	−1.17689	−	2.03843i	−0.0512176	−	0.0887114i
$529$	−18.0270	+	31.2237i	−0.783782	+	1.35755i
$530$		0			0
$531$	−9.54991			−0.414431
$532$	−9.19208	−	2.60018i	−0.398527	−	0.112732i
$533$	26.0365			1.12777
$534$	0.844619	−	1.46292i	0.0365502	−	0.0633068i
$535$		0			0
$536$	0.404223	+	0.700134i	0.0174598	+	0.0302412i
$537$	−0.990786	+	1.71609i	−0.0427556	+	0.0740548i
$538$	−14.1998	−	24.5948i	−0.612197	−	1.06036i
$539$	10.9129			0.470052
$540$		0			0
$541$	21.9890	+	38.0861i	0.945382	+	1.63745i	0.754984	+	0.655743i	$0.227644\pi$
$541$	21.9890	+	38.0861i	0.945382	+	1.63745i	0.190398	+	0.981707i	$0.439022\pi$
$542$	10.2850	+	17.8142i	0.441780	+	0.765186i
$543$	1.77565			0.0762003
$544$	−6.77543			−0.290494
$545$		0			0
$546$	1.18515	−	2.05274i	0.0507197	−	0.0878492i
$547$	−9.49121	−	16.4393i	−0.405815	−	0.702892i	0.588601	−	0.808424i	$-0.299679\pi$
$547$	−9.49121	−	16.4393i	−0.405815	−	0.702892i	−0.994416	+	0.105532i	$0.966346\pi$
$548$	3.73787	−	6.47418i	0.159674	−	0.276563i
$549$	−6.55447	+	11.3527i	−0.279738	+	0.484520i
$550$		0			0
$551$	8.25018	+	2.33374i	0.351469	+	0.0994206i
$552$	3.64164			0.154999
$553$	16.7309	−	28.9788i	0.711471	−	1.23230i
$554$	−4.49723	+	7.78944i	−0.191069	+	0.330941i
$555$		0			0
$556$	3.00961	−	5.21280i	0.127636	−	0.221072i
$557$	−2.51927	−	4.36351i	−0.106745	−	0.184888i	0.807705	−	0.589587i	$-0.200710\pi$
$557$	−2.51927	−	4.36351i	−0.106745	−	0.184888i	−0.914450	+	0.404699i	$0.867376\pi$
$558$	21.0485			0.891056
$559$	−23.1851			−0.980627
$560$		0			0
$561$	−7.97394	−	13.8113i	−0.336660	−	0.583112i
$562$	9.56466			0.403461
$563$	0.334560			0.0141000			0.00705002	−	0.999975i	$-0.497756\pi$
$563$	0.334560			0.0141000			0.00705002	+	0.999975i	$0.497756\pi$
$564$	0.993157	+	1.72020i	0.0418194	+	0.0724334i
$565$		0			0
$566$	−1.25806	−	2.17902i	−0.0528800	−	0.0915909i
$567$	7.70258	−	13.3413i	0.323478	−	0.560280i
$568$	−5.59854	+	9.69696i	−0.234910	+	0.406875i
$569$	2.30155			0.0964859			0.0482430	−	0.998836i	$-0.484638\pi$
$569$	2.30155			0.0964859			0.0482430	+	0.998836i	$0.484638\pi$
$570$		0			0
$571$	−23.6131			−0.988178			−0.494089	−	0.869411i	$-0.664498\pi$
$571$	−23.6131			−0.988178			−0.494089	+	0.869411i	$0.664498\pi$
$572$	5.66815	−	9.81753i	0.236997	−	0.410491i
$573$	−0.466063	+	0.807244i	−0.0194701	+	0.0337231i
$574$	−12.5005	−	21.6515i	−0.521760	−	0.903715i
$575$		0			0
$576$	1.38772	+	2.40360i	0.0578215	+	0.100150i
$577$	−1.59399			−0.0663587			−0.0331793	−	0.999449i	$-0.510563\pi$
$577$	−1.59399			−0.0663587			−0.0331793	+	0.999449i	$0.510563\pi$
$578$	−28.9065			−1.20235
$579$	−3.28222	−	5.68498i	−0.136405	−	0.236260i
$580$		0			0
$581$	−27.8836			−1.15681
$582$	−0.0816674			−0.00338522
$583$	−10.4097	−	18.0301i	−0.431126	−	0.746732i
$584$	−2.42850	+	4.20628i	−0.100492	+	0.174057i
$585$		0			0
$586$	−0.203058	+	0.351707i	−0.00838826	+	0.0145289i
$587$	4.86431	−	8.42524i	0.200772	−	0.347747i	−0.748006	−	0.663692i	$-0.768988\pi$
$587$	4.86431	−	8.42524i	0.200772	−	0.347747i	0.948777	+	0.315946i	$0.102322\pi$
$588$	1.04117			0.0429370
$589$	−23.6970	+	23.0486i	−0.976419	+	0.949702i
$590$		0			0
$591$	−4.08058	+	7.06778i	−0.167853	+	0.290729i
$592$	3.69432	−	6.39875i	0.151836	−	0.262987i
$593$	−8.09757	−	14.0254i	−0.332527	−	0.575954i	0.650480	−	0.759524i	$-0.274568\pi$
$593$	−8.09757	−	14.0254i	−0.332527	−	0.575954i	−0.983007	+	0.183570i	$0.941235\pi$
$594$	−6.79705	+	11.7728i	−0.278886	+	0.483045i
$595$		0			0
$596$	5.98067			0.244978
$597$	−4.36659			−0.178713
$598$	8.76946	+	15.1892i	0.358610	+	0.621131i
$599$	−11.6159	−	20.1194i	−0.474614	−	0.822055i	0.524964	−	0.851125i	$-0.324079\pi$
$599$	−11.6159	−	20.1194i	−0.474614	−	0.822055i	−0.999577	+	0.0290696i	$0.990746\pi$
$600$		0			0
$601$	44.9899			1.83518			0.917588	−	0.397532i	$-0.130133\pi$
$601$	44.9899			1.83518			0.917588	+	0.397532i	$0.130133\pi$
$602$	11.1315	+	19.2803i	0.453686	+	0.785807i
$603$	1.12189	−	1.94318i	0.0456870	−	0.0791322i
$604$	−3.03388	−	5.25484i	−0.123447	−	0.213816i
$605$		0			0
$606$	−3.51243	+	6.08371i	−0.142683	+	0.247134i
$607$	36.6965			1.48947			0.744733	−	0.667363i	$-0.232577\pi$
$607$	36.6965			1.48947			0.744733	+	0.667363i	$0.232577\pi$
$608$	−4.19432	−	1.18645i	−0.170102	−	0.0481170i
$609$	2.04280			0.0827786
$610$		0			0
$611$	−4.78326	+	8.28484i	−0.193510	+	0.335169i
$612$	9.40238	+	16.2854i	0.380069	+	0.658298i
$613$	−11.7090	+	20.2806i	−0.472921	+	0.819124i	−0.999520	−	0.0309903i	$-0.990134\pi$
$613$	−11.7090	+	20.2806i	−0.472921	+	0.819124i	0.526598	+	0.850114i	$0.323467\pi$
$614$	10.4555	+	18.1095i	0.421951	+	0.730841i
$615$		0			0
$616$	−10.8854			−0.438586
$617$	−8.56777	−	14.8398i	−0.344925	−	0.597428i	0.640415	−	0.768029i	$-0.278762\pi$
$617$	−8.56777	−	14.8398i	−0.344925	−	0.597428i	−0.985340	+	0.170601i	$0.945429\pi$
$618$	3.46009	+	5.99305i	0.139185	+	0.241076i
$619$	25.3556			1.01913			0.509564	−	0.860433i	$-0.329807\pi$
$619$	25.3556			1.01913			0.509564	+	0.860433i	$0.329807\pi$
$620$		0			0
$621$	−10.5160	−	18.2143i	−0.421994	−	0.730915i
$622$	−4.96199	+	8.59441i	−0.198957	+	0.344604i
$623$	−3.90607	−	6.76552i	−0.156494	−	0.271055i
$624$	0.540781	−	0.936659i	0.0216485	−	0.0374964i
$625$		0			0
$626$	14.6553			0.585745
$627$	−2.51775	−	9.94617i	−0.100549	−	0.397212i
$628$	−1.90923			−0.0761864
$629$	25.0306	−	43.3543i	0.998036	−	1.72865i
$630$		0			0
$631$	−14.2956	−	24.7607i	−0.569098	−	0.985707i	−0.996655	−	0.0817184i	$-0.973959\pi$
$631$	−14.2956	−	24.7607i	−0.569098	−	0.985707i	0.427557	−	0.903988i	$-0.359374\pi$
$632$	7.63427	−	13.2229i	0.303675	−	0.525980i
$633$	−2.79141	−	4.83486i	−0.110949	−	0.192169i
$634$	35.0440			1.39177
$635$		0			0
$636$	−0.993157	−	1.72020i	−0.0393812	−	0.0682103i
$637$	2.50724	+	4.34267i	0.0993404	+	0.172063i
$638$	9.77001			0.386798
$639$	31.0768			1.22938
$640$		0			0
$641$	−1.82404	+	3.15932i	−0.0720451	+	0.124786i	−0.899797	−	0.436308i	$-0.856286\pi$
$641$	−1.82404	+	3.15932i	−0.0720451	+	0.124786i	0.827752	+	0.561094i	$0.189619\pi$
$642$	−0.0862211	−	0.149339i	−0.00340288	−	0.00589396i
$643$	−14.9459	+	25.8870i	−0.589408	+	1.02088i	0.404902	+	0.914360i	$0.367306\pi$
$643$	−14.9459	+	25.8870i	−0.589408	+	1.02088i	−0.994310	+	0.106524i	$0.966028\pi$
$644$	8.42068	−	14.5850i	0.331821	−	0.574731i
$645$		0			0
$646$	−28.4183	−	8.03873i	−1.11810	−	0.316280i
$647$	−30.0091			−1.17978			−0.589890	−	0.807483i	$-0.700829\pi$
$647$	−30.0091			−1.17978			−0.589890	+	0.807483i	$0.700829\pi$
$648$	3.51467	−	6.08758i	0.138069	−	0.239143i
$649$	8.54539	−	14.8010i	0.335436	−	0.580992i
$650$		0			0
$651$	−3.93810	+	6.82098i	−0.154346	+	0.267335i
$652$	3.77267	+	6.53445i	0.147749	+	0.255909i
$653$	26.4776			1.03615			0.518074	−	0.855336i	$-0.326649\pi$
$653$	26.4776			1.03615			0.518074	+	0.855336i	$0.326649\pi$
$654$	−6.27211			−0.245259
$655$		0			0
$656$	−5.70393	−	9.87950i	−0.222701	−	0.385730i
$657$	13.4803			0.525915
$658$	9.18602			0.358108
$659$	−0.581112	−	1.00652i	−0.0226369	−	0.0392083i	0.854485	−	0.519476i	$-0.173873\pi$
$659$	−0.581112	−	1.00652i	−0.0226369	−	0.0392083i	−0.877122	+	0.480268i	$0.840540\pi$
$660$		0			0
$661$	−15.9899	−	27.6953i	−0.621935	−	1.07722i	−0.989125	−	0.147077i	$-0.953013\pi$
$661$	−15.9899	−	27.6953i	−0.621935	−	1.07722i	0.367190	−	0.930146i	$-0.380320\pi$
$662$	10.7232	−	18.5731i	0.416769	−	0.721865i
$663$	3.66402	−	6.34627i	0.142299	−	0.246469i
$664$	−12.7232			−0.493756
$665$		0			0
$666$	−20.5067			−0.794618
$667$	−7.55782	+	13.0905i	−0.292640	+	0.506867i
$668$	2.67782	−	4.63811i	0.103608	−	0.179454i
$669$	0.141614	+	0.245282i	0.00547510	+	0.00948315i
$670$		0			0
$671$	−11.7300	−	20.3170i	−0.452833	−	0.784330i
$672$	−1.03854			−0.0400627
$673$	−48.3529			−1.86387			−0.931934	−	0.362629i	$-0.881879\pi$
$673$	−48.3529			−1.86387			−0.931934	+	0.362629i	$0.881879\pi$
$674$	14.8593	+	25.7371i	0.572359	+	0.991355i
$675$		0			0
$676$	−7.79097			−0.299653
$677$	−33.6964			−1.29506			−0.647529	−	0.762041i	$-0.724198\pi$
$677$	−33.6964			−1.29506			−0.647529	+	0.762041i	$0.724198\pi$
$678$	4.14398	+	7.17759i	0.159149	+	0.275654i
$679$	−0.188842	+	0.327084i	−0.00724708	+	0.0125523i
$680$		0			0
$681$	−3.63384	+	6.29400i	−0.139249	+	0.241187i
$682$	−18.8345	+	32.6223i	−0.721211	+	1.24917i
$683$	−18.3886			−0.703622			−0.351811	−	0.936071i	$-0.614434\pi$
$683$	−18.3886			−0.703622			−0.351811	+	0.936071i	$0.614434\pi$
$684$	2.96878	+	11.7279i	0.113514	+	0.448428i
$685$		0			0
$686$	10.0780	−	17.4555i	0.384778	−	0.666456i
$687$	3.69161	−	6.39405i	0.140844	−	0.243948i
$688$	5.07927	+	8.79756i	0.193645	+	0.335404i
$689$	4.78326	−	8.28484i	0.182228	−	0.315627i
$690$		0			0
$691$	18.2779			0.695322			0.347661	−	0.937620i	$-0.386976\pi$
$691$	18.2779			0.695322			0.347661	+	0.937620i	$0.386976\pi$
$692$	1.58020			0.0600701
$693$	15.1059	+	26.1642i	0.573825	+	0.993895i
$694$	−1.07651	−	1.86456i	−0.0408636	−	0.0707778i
$695$		0			0
$696$	0.932126			0.0353321
$697$	−38.6466	−	66.9379i	−1.46384	−	2.53545i
$698$	8.75155	−	15.1581i	0.331251	−	0.573744i
$699$	6.98078	+	12.0911i	0.264037	+	0.457326i
$700$		0			0
$701$	4.80292	−	8.31891i	0.181404	−	0.314201i	−0.760955	−	0.648805i	$-0.775269\pi$
$701$	4.80292	−	8.31891i	0.181404	−	0.314201i	0.942359	+	0.334604i	$0.108603\pi$
$702$	−6.24648			−0.235758
$703$	23.0870	−	22.4553i	0.870742	−	0.846917i
$704$	−4.96699			−0.187200
$705$		0			0
$706$	10.6585	−	18.4611i	0.401140	−	0.694794i
$707$	16.2438	+	28.1351i	0.610910	+	1.05813i
$708$	0.815288	−	1.41212i	0.0306404	−	0.0530708i
$709$	−10.2630	−	17.7760i	−0.385435	−	0.667593i	0.606394	−	0.795164i	$-0.292615\pi$
$709$	−10.2630	−	17.7760i	−0.385435	−	0.667593i	−0.991829	+	0.127571i	$0.959282\pi$
$710$		0			0
$711$	−42.3768			−1.58925
$712$	−1.78233	−	3.08709i	−0.0667956	−	0.115693i
$713$	−29.1398	−	50.4715i	−1.09129	−	1.89017i
$714$	−7.03659			−0.263338
$715$		0			0
$716$	2.09077	+	3.62133i	0.0781359	+	0.135335i
$717$	0.319457	−	0.553315i	0.0119303	−	0.0206639i
$718$	12.8547	+	22.2650i	0.479733	+	0.830922i
$719$	4.32220	−	7.48626i	0.161191	−	0.279190i	−0.774105	−	0.633057i	$-0.781800\pi$
$719$	4.32220	−	7.48626i	0.161191	−	0.279190i	0.935296	+	0.353866i	$0.115133\pi$
$720$		0			0
$721$	32.0035			1.19187
$722$	−16.1847	−	9.95273i	−0.602331	−	0.370402i
$723$	−13.2053			−0.491111
$724$	1.87350	−	3.24500i	0.0696281	−	0.120599i
$725$		0			0
$726$	−3.23923	−	5.61051i	−0.120219	−	0.208226i
$727$	−10.3547	+	17.9348i	−0.384033	+	0.665164i	−0.991634	−	0.129078i	$-0.958798\pi$
$727$	−10.3547	+	17.9348i	−0.384033	+	0.665164i	0.607602	+	0.794242i	$0.292132\pi$
$728$	−2.50093	−	4.33173i	−0.0926905	−	0.160545i
$729$	−15.6185			−0.578464
$730$		0			0
$731$	34.4143	+	59.6073i	1.27286	+	2.20465i
$732$	−1.11913	−	1.93838i	−0.0413641	−	0.0716447i
$733$	24.8157			0.916590			0.458295	−	0.888800i	$-0.348460\pi$
$733$	24.8157			0.916590			0.458295	+	0.888800i	$0.348460\pi$
$734$	−14.3418			−0.529367
$735$		0			0
$736$	3.84233	−	6.65511i	0.141630	−	0.245311i
$737$	2.00777	+	3.47756i	0.0739571	+	0.128097i
$738$	−15.8309	+	27.4199i	−0.582743	+	1.00934i
$739$	−2.07422	+	3.59265i	−0.0763013	+	0.132158i	−0.901651	−	0.432464i	$-0.857644\pi$
$739$	−2.07422	+	3.59265i	−0.0763013	+	0.132158i	0.825350	+	0.564621i	$0.190978\pi$
$740$		0			0
$741$	3.37951	−	3.28704i	0.124149	−	0.120752i
$742$	−9.18602			−0.337229
$743$	−0.401456	+	0.695343i	−0.0147280	+	0.0255097i	−0.873295	−	0.487191i	$-0.838022\pi$
$743$	−0.401456	+	0.695343i	−0.0147280	+	0.0255097i	0.858567	+	0.512701i	$0.171355\pi$
$744$	−1.79694	+	3.11239i	−0.0658791	+	0.114106i
$745$		0			0
$746$	−0.323057	+	0.559551i	−0.0118280	+	0.0204866i
$747$	17.6562	+	30.5814i	0.646007	+	1.11892i
$748$	−33.6535			−1.23049
$749$	−0.797487			−0.0291395
$750$		0			0
$751$	−16.1292	−	27.9366i	−0.588563	−	1.01942i	−0.994421	−	0.105485i	$-0.966360\pi$
$751$	−16.1292	−	27.9366i	−0.588563	−	1.01942i	0.405858	−	0.913936i	$-0.366973\pi$
$752$	4.19155			0.152850
$753$	−13.6636			−0.497930
$754$	2.24466	+	3.88786i	0.0817456	+	0.141588i
$755$		0			0
$756$	2.99902	+	5.19446i	0.109073	+	0.188921i
$757$	18.0531	−	31.2689i	0.656151	−	1.13649i	−0.325453	−	0.945558i	$-0.605517\pi$
$757$	18.0531	−	31.2689i	0.656151	−	1.13649i	0.981604	−	0.190929i	$-0.0611500\pi$
$758$	6.56277	−	11.3670i	0.238370	−	0.412870i
$759$	18.0880			0.656552
$760$		0			0
$761$	3.07513			0.111473			0.0557367	−	0.998446i	$-0.482249\pi$
$761$	3.07513			0.111473			0.0557367	+	0.998446i	$0.482249\pi$
$762$	−1.10544	+	1.91468i	−0.0400459	+	0.0693615i
$763$	−14.5032	+	25.1203i	−0.525051	+	0.909415i
$764$	0.983494	+	1.70346i	0.0355816	+	0.0616291i
$765$		0			0
$766$	5.59854	+	9.69696i	0.202284	+	0.350365i
$767$	7.85321			0.283563
$768$	−0.473885			−0.0170998
$769$	−0.423890	−	0.734199i	−0.0152859	−	0.0264759i	0.858281	−	0.513180i	$-0.171533\pi$
$769$	−0.423890	−	0.734199i	−0.0152859	−	0.0264759i	−0.873567	+	0.486704i	$0.838199\pi$
$770$		0			0
$771$	1.56460			0.0563478
$772$	−13.8524			−0.498559
$773$	3.51743	+	6.09237i	0.126513	+	0.219127i	0.922323	−	0.386419i	$-0.126288\pi$
$773$	3.51743	+	6.09237i	0.126513	+	0.219127i	−0.795810	+	0.605546i	$0.792955\pi$
$774$	14.0972	−	24.4170i	0.506713	−	0.877652i
$775$		0			0
$776$	−0.0861680	+	0.149247i	−0.00309325	+	0.00535767i
$777$	3.83672	−	6.64539i	0.137641	−	0.238402i
$778$	22.0074			0.789003
$779$	−12.2026	−	48.2052i	−0.437202	−	1.72713i
$780$		0			0
$781$	−27.8079	+	48.1647i	−0.995045	+	1.72347i
$782$	26.0334	−	45.0913i	0.930954	−	1.61246i
$783$	−2.69171	−	4.66219i	−0.0961940	−	0.166613i
$784$	1.09854	−	1.90273i	0.0392337	−	0.0679548i
$785$		0			0

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.236942 - 0.410396i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.236942 - 0.410396i) q^{6} -2.19155 q^{7} -1.00000 q^{8} +(1.38772 + 2.40360i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.236942 - 0.410396i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.236942 - 0.410396i) q^{6} -2.19155 q^{7} -1.00000 q^{8} +(1.38772 + 2.40360i) q^{9} -4.96699 q^{11} -0.473885 q^{12} +(-1.14116 - 1.97656i) q^{13} +(-1.09578 + 1.89794i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.38772 + 5.86770i) q^{17} +2.77543 q^{18} +(-3.12466 + 3.03916i) q^{19} +(-0.519272 + 0.899406i) q^{21} +(-2.48349 + 4.30154i) q^{22} +(-3.84233 - 6.65511i) q^{23} +(-0.236942 + 0.410396i) q^{24} -2.28233 q^{26} +2.73689 q^{27} +(1.09578 + 1.89794i) q^{28} +(-0.983494 - 1.70346i) q^{29} +7.58388 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.17689 + 2.03843i) q^{33} +(3.38772 + 5.86770i) q^{34} +(1.38772 - 2.40360i) q^{36} -7.38864 q^{37} +(1.06966 + 4.22562i) q^{38} -1.08156 q^{39} +(-5.70393 + 9.87950i) q^{41} +(0.519272 + 0.899406i) q^{42} +(5.07927 - 8.79756i) q^{43} +(2.48349 + 4.30154i) q^{44} -7.68466 q^{46} +(-2.09578 - 3.62999i) q^{47} +(0.236942 + 0.410396i) q^{48} -2.19709 q^{49} +(1.60539 + 2.78061i) q^{51} +(-1.14116 + 1.97656i) q^{52} +(2.09578 + 3.62999i) q^{53} +(1.36844 - 2.37022i) q^{54} +2.19155 q^{56} +(0.506896 + 2.00245i) q^{57} -1.96699 q^{58} +(-1.72044 + 2.97988i) q^{59} +(2.36160 + 4.09041i) q^{61} +(3.79194 - 6.56783i) q^{62} +(-3.04126 - 5.26761i) q^{63} +1.00000 q^{64} +(1.17689 + 2.03843i) q^{66} +(-0.404223 - 0.700134i) q^{67} +6.77543 q^{68} -3.64164 q^{69} +(5.59854 - 9.69696i) q^{71} +(-1.38772 - 2.40360i) q^{72} +(2.42850 - 4.20628i) q^{73} +(-3.69432 + 6.39875i) q^{74} +(4.19432 + 1.18645i) q^{76} +10.8854 q^{77} +(-0.540781 + 0.936659i) q^{78} +(-7.63427 + 13.2229i) q^{79} +(-3.51467 + 6.08758i) q^{81} +(5.70393 + 9.87950i) q^{82} +12.7232 q^{83} +1.03854 q^{84} +(-5.07927 - 8.79756i) q^{86} -0.932126 q^{87} +4.96699 q^{88} +(1.78233 + 3.08709i) q^{89} +(2.50093 + 4.33173i) q^{91} +(-3.84233 + 6.65511i) q^{92} +(1.79694 - 3.11239i) q^{93} -4.19155 q^{94} +0.473885 q^{96} +(0.0861680 - 0.149247i) q^{97} +(-1.09854 + 1.90273i) q^{98} +(-6.89277 - 11.9386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8q + 4q^{2} - q^{3} - 4q^{4} + q^{6} - 12q^{7} - 8q^{8} - 11q^{9} + O(q^{10}) \)	\( 8q + 4q^{2} - q^{3} - 4q^{4} + q^{6} - 12q^{7} - 8q^{8} - 11q^{9} + 10q^{11} + 2q^{12} - 9q^{13} - 6q^{14} - 4q^{16} - 5q^{17} - 22q^{18} - q^{21} + 5q^{22} - 6q^{23} + q^{24} - 18q^{26} - 16q^{27} + 6q^{28} + 17q^{29} + 22q^{31} + 4q^{32} + 4q^{33} + 5q^{34} - 11q^{36} + 8q^{37} - 36q^{39} + 7q^{41} + q^{42} + 13q^{43} - 5q^{44} - 12q^{46} - 14q^{47} - q^{48} + 44q^{49} - 9q^{51} - 9q^{52} + 14q^{53} - 8q^{54} + 12q^{56} + 48q^{57} + 34q^{58} + 14q^{59} - 9q^{61} + 11q^{62} + 45q^{63} + 8q^{64} - 4q^{66} - 6q^{67} + 10q^{68} + 54q^{69} + 14q^{71} + 11q^{72} + 11q^{73} + 4q^{74} + 10q^{77} - 18q^{78} - 17q^{79} - 36q^{81} - 7q^{82} + 46q^{83} + 2q^{84} - 13q^{86} + 2q^{87} - 10q^{88} + 14q^{89} - 25q^{91} - 6q^{92} - 13q^{93} - 28q^{94} - 2q^{96} + 17q^{97} + 22q^{98} - 60q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

Downloads

Learn more about