LMFDB - Embedded newform 950.2.u.g.149.2

Newspace parameters

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			149.2
Character	$\chi$	$=$	950.149
Dual form			950.2.u.g.899.2

$q$-expansion

$f(q)$	$=$	$q+(-0.642788 + 0.766044i) q^{2} +(-0.197144 - 0.541649i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.541649 + 0.197144i) q^{6} +(4.21251 - 2.43209i) q^{7} +(0.866025 + 0.500000i) q^{8} +(2.04362 - 1.71480i) q^{9} +O(q^{10})$	\(q+(-0.642788 + 0.766044i) q^{2} +(-0.197144 - 0.541649i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.541649 + 0.197144i) q^{6} +(4.21251 - 2.43209i) q^{7} +(0.866025 + 0.500000i) q^{8} +(2.04362 - 1.71480i) q^{9} +(2.68454 - 4.64975i) q^{11} +(-0.499186 + 0.288205i) q^{12} +(-1.31923 + 3.62457i) q^{13} +(-0.844657 + 4.79029i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(0.901248 - 1.07407i) q^{17} +2.66775i q^{18} +(-4.35299 + 0.226908i) q^{19} +(-2.14781 - 1.80223i) q^{21} +(1.83633 + 5.04528i) q^{22} +(-5.25780 + 0.927092i) q^{23} +(0.100093 - 0.567654i) q^{24} +(-1.92859 - 3.34042i) q^{26} +(-2.82926 - 1.63348i) q^{27} +(-3.12664 - 3.72618i) q^{28} +(2.78364 - 2.33575i) q^{29} +(-4.10189 - 7.10468i) q^{31} +(0.342020 - 0.939693i) q^{32} +(-3.04777 - 0.537405i) q^{33} +(0.243471 + 1.38079i) q^{34} +(-2.04362 - 1.71480i) q^{36} +10.4594i q^{37} +(2.62423 - 3.48044i) q^{38} +2.22332 q^{39} +(1.79322 - 0.652678i) q^{41} +(2.76117 - 0.486869i) q^{42} +(1.45618 + 0.256764i) q^{43} +(-5.04528 - 1.83633i) q^{44} +(2.66945 - 4.62363i) q^{46} +(2.00570 + 2.39030i) q^{47} +(0.370510 + 0.441556i) q^{48} +(8.33016 - 14.4283i) q^{49} +(-0.759442 - 0.276414i) q^{51} +(3.79858 + 0.669793i) q^{52} +(1.77266 - 0.312568i) q^{53} +(3.06993 - 1.11736i) q^{54} +4.86419 q^{56} +(0.981070 + 2.31306i) q^{57} +3.63378i q^{58} +(5.61133 + 4.70846i) q^{59} +(1.40916 + 7.99176i) q^{61} +(8.07914 + 1.42457i) q^{62} +(4.43820 - 12.1939i) q^{63} +(0.500000 + 0.866025i) q^{64} +(2.37075 - 1.98929i) q^{66} +(-5.42827 - 6.46916i) q^{67} +(-1.21425 - 0.701047i) q^{68} +(1.53870 + 2.66511i) q^{69} +(1.04647 - 5.93485i) q^{71} +(2.62722 - 0.463250i) q^{72} +(0.436515 + 1.19931i) q^{73} +(-8.01234 - 6.72316i) q^{74} +(0.979350 + 4.24746i) q^{76} -26.1162i q^{77} +(-1.42912 + 1.70316i) q^{78} +(-15.6290 + 5.68848i) q^{79} +(1.06275 - 6.02717i) q^{81} +(-0.652678 + 1.79322i) q^{82} +(12.5236 - 7.23049i) q^{83} +(-1.40188 + 2.42814i) q^{84} +(-1.13271 + 0.950453i) q^{86} +(-1.81393 - 1.04727i) q^{87} +(4.64975 - 2.68454i) q^{88} +(9.02905 + 3.28630i) q^{89} +(3.25800 + 18.4770i) q^{91} +(1.82601 + 5.01693i) q^{92} +(-3.03958 + 3.62243i) q^{93} -3.12031 q^{94} -0.576411 q^{96} +(-3.90758 + 4.65687i) q^{97} +(5.69817 + 15.6556i) q^{98} +(-2.48722 - 14.1057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36q + 36q^{9} + O(q^{10}) $	$ 36q + 36q^{9} - 24q^{11} - 12q^{14} + 24q^{21} - 18q^{26} + 12q^{29} - 12q^{31} - 36q^{34} - 36q^{36} - 96q^{39} - 42q^{41} - 6q^{44} + 36q^{46} + 78q^{49} + 84q^{51} + 108q^{54} + 60q^{59} + 96q^{61} + 18q^{64} + 48q^{66} + 60q^{69} + 60q^{71} + 6q^{74} - 42q^{76} - 60q^{79} + 36q^{81} - 12q^{84} + 72q^{86} - 60q^{89} - 120q^{91} - 12q^{94} - 342q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$3$	−0.197144	−	0.541649i	−0.113821	−	0.312721i	0.869682	−	0.493613i	$-0.164324\pi$
$3$	−0.197144	−	0.541649i	−0.113821	−	0.312721i	−0.983503	+	0.180892i	$0.942102\pi$
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	0.541649	+	0.197144i	0.221127	+	0.0804837i
$7$	4.21251	−	2.43209i	1.59218	−	0.919245i	0.599247	−	0.800564i	$-0.295467\pi$
$7$	4.21251	−	2.43209i	1.59218	−	0.919245i	0.992932	−	0.118681i	$-0.0378665\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	2.04362	−	1.71480i	0.681205	−	0.571599i
$10$		0			0
$11$	2.68454	−	4.64975i	0.809418	−	1.40195i	−0.103850	−	0.994593i	$-0.533116\pi$
$11$	2.68454	−	4.64975i	0.809418	−	1.40195i	0.913268	−	0.407360i	$-0.133550\pi$
$12$	−0.499186	+	0.288205i	−0.144103	+	0.0831977i
$13$	−1.31923	+	3.62457i	−0.365890	+	1.00527i	0.611019	+	0.791616i	$0.290760\pi$
$13$	−1.31923	+	3.62457i	−0.365890	+	1.00527i	−0.976909	+	0.213658i	$0.931462\pi$
$14$	−0.844657	+	4.79029i	−0.225744	+	1.28026i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	0.901248	−	1.07407i	0.218585	−	0.260499i	−0.645598	−	0.763678i	$-0.723392\pi$
$17$	0.901248	−	1.07407i	0.218585	−	0.260499i	0.864183	+	0.503178i	$0.167836\pi$
$18$			2.66775i			0.628795i
$19$	−4.35299	+	0.226908i	−0.998644	+	0.0520563i
$19$	−4.35299	+	0.226908i	−0.998644	+	0.0520563i
$20$		0			0
$21$	−2.14781	−	1.80223i	−0.468691	−	0.393278i
$22$	1.83633	+	5.04528i	0.391507	+	1.07566i
$23$	−5.25780	+	0.927092i	−1.09633	+	0.193312i	−0.692425	−	0.721490i	$-0.743457\pi$
$23$	−5.25780	+	0.927092i	−1.09633	+	0.193312i	−0.403902	+	0.914802i	$0.632346\pi$
$24$	0.100093	−	0.567654i	0.0204313	−	0.115872i
$25$		0			0
$26$	−1.92859	−	3.34042i	−0.378228	−	0.655110i
$27$	−2.82926	−	1.63348i	−0.544492	−	0.314363i
$28$	−3.12664	−	3.72618i	−0.590879	−	0.704183i
$29$	2.78364	−	2.33575i	0.516908	−	0.433738i	−0.346644	−	0.937997i	$-0.612679\pi$
$29$	2.78364	−	2.33575i	0.516908	−	0.433738i	0.863552	+	0.504259i	$0.168234\pi$
$30$		0			0
$31$	−4.10189	−	7.10468i	−0.736721	−	1.27604i	−0.953964	−	0.299920i	$-0.903040\pi$
$31$	−4.10189	−	7.10468i	−0.736721	−	1.27604i	0.217244	−	0.976117i	$-0.430293\pi$
$32$	0.342020	−	0.939693i	0.0604612	−	0.166116i
$33$	−3.04777	−	0.537405i	−0.530549	−	0.0935501i
$34$	0.243471	+	1.38079i	0.0417549	+	0.236804i
$35$		0			0
$36$	−2.04362	−	1.71480i	−0.340603	−	0.285800i
$37$			10.4594i			1.71951i	0.510706	+	0.859755i	$0.329384\pi$
$37$			10.4594i			1.71951i	−0.510706	+	0.859755i	$0.670616\pi$
$38$	2.62423	−	3.48044i	0.425706	−	0.564601i
$39$	2.22332			0.356016
$40$		0			0
$41$	1.79322	−	0.652678i	0.280054	−	0.101931i	−0.198175	−	0.980167i	$-0.563501\pi$
$41$	1.79322	−	0.652678i	0.280054	−	0.101931i	0.478228	+	0.878236i	$0.341279\pi$
$42$	2.76117	−	0.486869i	0.426058	−	0.0751256i
$43$	1.45618	+	0.256764i	0.222065	+	0.0391561i	0.283574	−	0.958950i	$-0.408480\pi$
$43$	1.45618	+	0.256764i	0.222065	+	0.0391561i	−0.0615084	+	0.998107i	$0.519591\pi$
$44$	−5.04528	−	1.83633i	−0.760604	−	0.276837i
$45$		0			0
$46$	2.66945	−	4.62363i	0.393590	−	0.681717i
$47$	2.00570	+	2.39030i	0.292561	+	0.348661i	0.892225	−	0.451591i	$-0.149143\pi$
$47$	2.00570	+	2.39030i	0.292561	+	0.348661i	−0.599664	+	0.800252i	$0.704699\pi$
$48$	0.370510	+	0.441556i	0.0534785	+	0.0637331i
$49$	8.33016	−	14.4283i	1.19002	−	2.06118i
$50$		0			0
$51$	−0.759442	−	0.276414i	−0.106343	−	0.0387058i
$52$	3.79858	+	0.669793i	0.526769	+	0.0928835i
$53$	1.77266	−	0.312568i	0.243494	−	0.0429346i	−0.0505691	−	0.998721i	$-0.516104\pi$
$53$	1.77266	−	0.312568i	0.243494	−	0.0429346i	0.294063	+	0.955786i	$0.404992\pi$
$54$	3.06993	−	1.11736i	0.417765	−	0.152054i
$55$		0			0
$56$	4.86419			0.650004
$57$	0.981070	+	2.31306i	0.129946	+	0.306372i
$58$			3.63378i			0.477139i
$59$	5.61133	+	4.70846i	0.730532	+	0.612990i	0.930277	−	0.366859i	$-0.119567\pi$
$59$	5.61133	+	4.70846i	0.730532	+	0.612990i	−0.199744	+	0.979848i	$0.564011\pi$
$60$		0			0
$61$	1.40916	+	7.99176i	0.180425	+	1.02324i	0.931694	+	0.363244i	$0.118331\pi$
$61$	1.40916	+	7.99176i	0.180425	+	1.02324i	−0.751269	+	0.659996i	$0.770558\pi$
$62$	8.07914	+	1.42457i	1.02605	+	0.180921i
$63$	4.43820	−	12.1939i	0.559161	−	1.53628i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	2.37075	−	1.98929i	0.291819	−	0.244865i
$67$	−5.42827	−	6.46916i	−0.663169	−	0.790334i	0.324668	−	0.945828i	$-0.394747\pi$
$67$	−5.42827	−	6.46916i	−0.663169	−	0.790334i	−0.987837	+	0.155494i	$0.950303\pi$
$68$	−1.21425	−	0.701047i	−0.147249	−	0.0850144i
$69$	1.53870	+	2.66511i	0.185238	+	0.320842i
$70$		0			0
$71$	1.04647	−	5.93485i	0.124194	−	0.704337i	−0.857590	−	0.514334i	$-0.828039\pi$
$71$	1.04647	−	5.93485i	0.124194	−	0.704337i	0.981783	−	0.190003i	$-0.0608498\pi$
$72$	2.62722	−	0.463250i	0.309621	−	0.0545945i
$73$	0.436515	+	1.19931i	0.0510902	+	0.140369i	0.962613	−	0.270880i	$-0.0873148\pi$
$73$	0.436515	+	1.19931i	0.0510902	+	0.140369i	−0.911523	+	0.411249i	$0.865093\pi$
$74$	−8.01234	−	6.72316i	−0.931416	−	0.781551i
$75$		0			0
$76$	0.979350	+	4.24746i	0.112339	+	0.487217i
$77$		−	26.1162i		−	2.97621i
$78$	−1.42912	+	1.70316i	−0.161816	+	0.192845i
$79$	−15.6290	+	5.68848i	−1.75840	+	0.640004i	−0.999931	−	0.0117101i	$-0.996272\pi$
$79$	−15.6290	+	5.68848i	−1.75840	+	0.640004i	−0.758465	+	0.651714i	$0.774050\pi$
$80$		0			0
$81$	1.06275	−	6.02717i	0.118084	−	0.669685i
$82$	−0.652678	+	1.79322i	−0.0720762	+	0.198028i
$83$	12.5236	−	7.23049i	1.37464	−	0.793649i	0.383133	−	0.923693i	$-0.374845\pi$
$83$	12.5236	−	7.23049i	1.37464	−	0.793649i	0.991508	+	0.130044i	$0.0415119\pi$
$84$	−1.40188	+	2.42814i	−0.152958	+	0.264931i
$85$		0			0
$86$	−1.13271	+	0.950453i	−0.122143	+	0.102490i
$87$	−1.81393	−	1.04727i	−0.194474	−	0.112280i
$88$	4.64975	−	2.68454i	0.495665	−	0.286172i
$89$	9.02905	+	3.28630i	0.957077	+	0.348348i	0.772887	−	0.634543i	$-0.218812\pi$
$89$	9.02905	+	3.28630i	0.957077	+	0.348348i	0.184190	+	0.982891i	$0.441034\pi$
$90$		0			0
$91$	3.25800	+	18.4770i	0.341531	+	1.93692i
$92$	1.82601	+	5.01693i	0.190375	+	0.523051i
$93$	−3.03958	+	3.62243i	−0.315189	+	0.375628i
$94$	−3.12031			−0.321836
$95$		0			0
$96$	−0.576411			−0.0588297
$97$	−3.90758	+	4.65687i	−0.396755	+	0.472834i	−0.927028	−	0.374993i	$-0.877645\pi$
$97$	−3.90758	+	4.65687i	−0.396755	+	0.472834i	0.530273	+	0.847827i	$0.322089\pi$
$98$	5.69817	+	15.6556i	0.575602	+	1.58145i
$99$	−2.48722	−	14.1057i	−0.249975	−	1.41768i
$100$		0			0
$101$	−1.17995	−	0.429466i	−0.117409	−	0.0427335i	0.282647	−	0.959224i	$-0.408787\pi$
$101$	−1.17995	−	0.429466i	−0.117409	−	0.0427335i	−0.400057	+	0.916490i	$0.631010\pi$
$102$	0.699906	−	0.404091i	0.0693010	−	0.0400109i
$103$	−6.38005	−	3.68352i	−0.628645	−	0.362948i	0.151582	−	0.988445i	$-0.451563\pi$
$103$	−6.38005	−	3.68352i	−0.628645	−	0.362948i	−0.780227	+	0.625496i	$0.784897\pi$
$104$	−2.95477	+	2.47935i	−0.289739	+	0.243120i
$105$		0			0
$106$	−0.900005	+	1.55885i	−0.0874162	+	0.151409i
$107$	7.56108	−	4.36539i	0.730957	−	0.422018i	−0.0878153	−	0.996137i	$-0.527989\pi$
$107$	7.56108	−	4.36539i	0.730957	−	0.422018i	0.818772	+	0.574119i	$0.194655\pi$
$108$	−1.11736	+	3.06993i	−0.107518	+	0.295404i
$109$	−1.41173	+	8.00630i	−0.135219	+	0.766865i	0.839488	+	0.543378i	$0.182855\pi$
$109$	−1.41173	+	8.00630i	−0.135219	+	0.766865i	−0.974707	+	0.223487i	$0.928256\pi$
$110$		0			0
$111$	5.66531	−	2.06200i	0.537727	−	0.195717i
$112$	−3.12664	+	3.72618i	−0.295440	+	0.352091i
$113$		−	4.48210i		−	0.421640i	−0.977525	−	0.210820i	$-0.932387\pi$
$113$		−	4.48210i		−	0.421640i	0.977525	−	0.210820i	$-0.0676134\pi$
$114$	−2.40253	−	0.735261i	−0.225017	−	0.0688635i
$115$		0			0
$116$	−2.78364	−	2.33575i	−0.258454	−	0.216869i
$117$	3.51939	+	9.66944i	0.325368	+	0.893940i
$118$	−7.21378	+	1.27198i	−0.664082	+	0.117096i
$119$	1.18429	−	6.71643i	0.108564	−	0.615694i
$120$		0			0
$121$	−8.91346	−	15.4386i	−0.810314	−	1.40351i
$122$	−7.02784	−	4.05753i	−0.636271	−	0.367351i
$123$	−0.707045	−	0.842623i	−0.0637521	−	0.0759768i
$124$	−6.28445	+	5.27328i	−0.564361	+	0.473555i
$125$		0			0
$126$	6.48822	+	11.2379i	0.578017	+	1.00115i
$127$	0.0476033	−	0.130789i	0.00422411	−	0.0116057i	−0.937563	−	0.347816i	$-0.886923\pi$
$127$	0.0476033	−	0.130789i	0.00422411	−	0.0116057i	0.941787	+	0.336211i	$0.109145\pi$
$128$	−0.984808	−	0.173648i	−0.0870455	−	0.0153485i
$129$	−0.148001	−	0.839357i	−0.0130308	−	0.0739013i
$130$		0			0
$131$	9.52200	+	7.98991i	0.831941	+	0.698082i	0.955736	−	0.294226i	$-0.0950620\pi$
$131$	9.52200	+	7.98991i	0.831941	+	0.698082i	−0.123795	+	0.992308i	$0.539506\pi$
$132$			3.09479i			0.269367i
$133$	−17.7851	+	11.5427i	−1.54217	+	1.00088i
$134$	8.44489			0.729528
$135$		0			0
$136$	1.31754	−	0.479544i	0.112978	−	0.0411206i
$137$	−14.1631	+	2.49734i	−1.21004	+	0.213362i	−0.742032	−	0.670364i	$-0.766138\pi$
$137$	−14.1631	+	2.49734i	−1.21004	+	0.213362i	−0.468004	+	0.883726i	$0.655027\pi$
$138$	−3.03065	−	0.534386i	−0.257986	−	0.0454899i
$139$	16.7746	+	6.10544i	1.42280	+	0.517857i	0.934859	−	0.355020i	$-0.115526\pi$
$139$	16.7746	+	6.10544i	1.42280	+	0.517857i	0.487941	+	0.872877i	$0.337748\pi$
$140$		0			0
$141$	0.899291	−	1.55762i	0.0757340	−	0.131175i
$142$	3.87370	+	4.61650i	0.325074	+	0.387408i
$143$	13.3118	+	15.8644i	1.11319	+	1.32665i
$144$	−1.33388	+	2.31034i	−0.111156	+	0.192528i
$145$		0			0
$146$	−1.19931	−	0.436515i	−0.0992559	−	0.0361262i
$147$	−9.45729	−	1.66758i	−0.780024	−	0.137539i
$148$	10.3005	−	1.81625i	0.846694	−	0.149295i
$149$	−2.71250	+	0.987271i	−0.222217	+	0.0808804i	−0.450729	−	0.892661i	$-0.648836\pi$
$149$	−2.71250	+	0.987271i	−0.222217	+	0.0808804i	0.228512	+	0.973541i	$0.426614\pi$
$150$		0			0
$151$	2.01805			0.164226			0.0821132	−	0.996623i	$-0.473833\pi$
$151$	2.01805			0.164226			0.0821132	+	0.996623i	$0.473833\pi$
$152$	−3.88325	−	1.97999i	−0.314973	−	0.160598i
$153$		−	3.74044i		−	0.302396i
$154$	20.0061	+	16.7871i	1.61214	+	1.35275i
$155$		0			0
$156$	−0.386076	−	2.18954i	−0.0309108	−	0.175304i
$157$	10.8717	+	1.91697i	0.867655	+	0.152991i	0.589719	−	0.807609i	$-0.299239\pi$
$157$	10.8717	+	1.91697i	0.867655	+	0.152991i	0.277936	+	0.960600i	$0.410350\pi$
$158$	5.68848	−	15.6290i	0.452551	−	1.24337i
$159$	−0.518772	−	0.898540i	−0.0411413	−	0.0712589i
$160$		0			0
$161$	−19.8938	+	16.6928i	−1.56785	+	1.31558i
$162$	3.93395	+	4.68830i	0.309081	+	0.368348i
$163$	5.13439	+	2.96434i	0.402157	+	0.232185i	0.687414	−	0.726266i	$-0.258746\pi$
$163$	5.13439	+	2.96434i	0.402157	+	0.232185i	−0.285257	+	0.958451i	$0.592079\pi$
$164$	−0.954151	−	1.65264i	−0.0745067	−	0.129049i
$165$		0			0
$166$	−2.51112	+	14.2413i	−0.194901	+	1.10534i
$167$	7.11784	−	1.25507i	0.550795	−	0.0971200i	0.108677	−	0.994077i	$-0.465339\pi$
$167$	7.11784	−	1.25507i	0.550795	−	0.0971200i	0.442118	+	0.896957i	$0.354227\pi$
$168$	−0.958946	−	2.63468i	−0.0739843	−	0.203270i
$169$	−1.43852	−	1.20707i	−0.110656	−	0.0928512i
$170$		0			0
$171$	−8.50673	+	7.92821i	−0.650526	+	0.606285i
$172$		−	1.47864i		−	0.112745i
$173$	3.31585	−	3.95167i	0.252099	−	0.300440i	−0.625121	−	0.780528i	$-0.714951\pi$
$173$	3.31585	−	3.95167i	0.252099	−	0.300440i	0.877221	+	0.480087i	$0.159395\pi$
$174$	1.96823	−	0.716378i	0.149211	−	0.0543085i
$175$		0			0
$176$	−0.932329	+	5.28750i	−0.0702770	+	0.398560i
$177$	1.44409	−	3.96761i	0.108545	−	0.298224i
$178$	−8.32122	+	4.80426i	−0.623701	+	0.360094i
$179$	4.09186	−	7.08730i	0.305840	−	0.529730i	−0.671608	−	0.740906i	$-0.734396\pi$
$179$	4.09186	−	7.08730i	0.305840	−	0.529730i	0.977448	+	0.211177i	$0.0677295\pi$
$180$		0			0
$181$	−2.62934	+	2.20628i	−0.195437	+	0.163991i	−0.735255	−	0.677791i	$-0.762938\pi$
$181$	−2.62934	+	2.20628i	−0.195437	+	0.163991i	0.539818	+	0.841782i	$0.318493\pi$
$182$	−16.2484	−	9.38103i	−1.20441	−	0.695368i
$183$	4.05092	−	2.33880i	0.299453	−	0.172889i
$184$	−5.01693	−	1.82601i	−0.369853	−	0.134616i
$185$		0			0
$186$	−0.821137	−	4.65690i	−0.0602087	−	0.341461i
$187$	−2.57471	−	7.07395i	−0.188281	−	0.517298i
$188$	2.00570	−	2.39030i	0.146281	−	0.174330i
$189$	−15.8911			−1.15591
$190$		0			0
$191$	3.77584			0.273210			0.136605	−	0.990626i	$-0.456381\pi$
$191$	3.77584			0.273210			0.136605	+	0.990626i	$0.456381\pi$
$192$	0.370510	−	0.441556i	0.0267392	−	0.0318666i
$193$	−4.16508	−	11.4435i	−0.299809	−	0.823718i	−0.994531	−	0.104440i	$-0.966695\pi$
$193$	−4.16508	−	11.4435i	−0.299809	−	0.823718i	0.694722	−	0.719278i	$-0.255527\pi$
$194$	−1.05563	−	5.98676i	−0.0757896	−	0.429824i
$195$		0			0
$196$	−15.6556	−	5.69817i	−1.11826	−	0.407012i
$197$	−6.23743	+	3.60118i	−0.444399	+	0.256574i	−0.705462	−	0.708748i	$-0.749260\pi$
$197$	−6.23743	+	3.60118i	−0.444399	+	0.256574i	0.261063	+	0.965322i	$0.415927\pi$
$198$	12.4044	+	7.16167i	0.881541	+	0.508958i
$199$	−4.47147	+	3.75201i	−0.316974	+	0.265973i	−0.787367	−	0.616484i	$-0.788557\pi$
$199$	−4.47147	+	3.75201i	−0.316974	+	0.265973i	0.470393	+	0.882457i	$0.344112\pi$
$200$		0			0
$201$	−2.43386	+	4.21557i	−0.171671	+	0.297344i
$202$	1.08745	−	0.627838i	0.0765125	−	0.0441745i
$203$	6.04534	−	16.6094i	0.424299	−	1.16575i
$204$	−0.140339	+	0.795903i	−0.00982571	+	0.0557244i
$205$		0			0
$206$	6.92276	−	2.51968i	0.482332	−	0.175554i
$207$	−9.15514	+	10.9107i	−0.636327	+	0.758344i
$208$		−	3.85718i		−	0.267448i
$209$	−10.6307	+	20.8495i	−0.735340	+	1.44219i
$210$		0			0
$211$	8.17443	+	6.85916i	0.562751	+	0.472204i	0.879231	−	0.476395i	$-0.158057\pi$
$211$	8.17443	+	6.85916i	0.562751	+	0.472204i	−0.316481	+	0.948599i	$0.602501\pi$
$212$	−0.615640	−	1.69146i	−0.0422823	−	0.116170i
$213$	−3.42091	+	0.603199i	−0.234397	+	0.0413305i
$214$	−1.51608	+	8.59814i	−0.103637	+	0.587757i
$215$		0			0
$216$	−1.63348	−	2.82926i	−0.111144	−	0.192507i
$217$	−34.5585	−	19.9523i	−2.34598	−	1.35445i
$218$	−5.22574	−	6.22780i	−0.353932	−	0.421800i
$219$	0.563551	−	0.472875i	0.0380812	−	0.0319539i
$220$		0			0
$221$	2.70407	+	4.68358i	0.181895	+	0.315052i
$222$	−2.06200	+	5.66531i	−0.138393	+	0.380231i
$223$	−0.0979573	−	0.0172725i	−0.00655971	−	0.00115665i	0.170367	−	0.985381i	$-0.445505\pi$
$223$	−0.0979573	−	0.0172725i	−0.00655971	−	0.00115665i	−0.176927	+	0.984224i	$0.556616\pi$
$224$	−0.844657	−	4.79029i	−0.0564360	−	0.320065i
$225$		0			0
$226$	3.43349	+	2.88104i	0.228392	+	0.191644i
$227$			13.8262i			0.917680i	0.888519	+	0.458840i	$0.151735\pi$
$227$			13.8262i			0.917680i	−0.888519	+	0.458840i	$0.848265\pi$
$228$	2.10756	−	1.36782i	0.139576	−	0.0905864i
$229$	−15.5752			−1.02924			−0.514619	−	0.857419i	$-0.672066\pi$
$229$	−15.5752			−1.02924			−0.514619	+	0.857419i	$0.672066\pi$
$230$		0			0
$231$	−14.1458	+	5.14865i	−0.930725	+	0.338756i
$232$	3.57857	−	0.630999i	0.234945	−	0.0414271i
$233$	−15.0095	−	2.64658i	−0.983307	−	0.173384i	−0.341193	−	0.939993i	$-0.610831\pi$
$233$	−15.0095	−	2.64658i	−0.983307	−	0.173384i	−0.642113	+	0.766610i	$0.721942\pi$
$234$	−9.66944	−	3.51939i	−0.632111	−	0.230070i
$235$		0			0
$236$	3.66253	−	6.34369i	0.238411	−	0.412939i
$237$	6.16232	+	7.34396i	0.400285	+	0.477042i
$238$	4.38384	+	5.22446i	0.284162	+	0.338651i
$239$	8.41167	−	14.5694i	0.544106	−	0.942419i	−0.454557	−	0.890718i	$-0.650202\pi$
$239$	8.41167	−	14.5694i	0.544106	−	0.942419i	0.998663	−	0.0517011i	$-0.0164643\pi$
$240$		0			0
$241$	8.55776	+	3.11477i	0.551254	+	0.200640i	0.602604	−	0.798041i	$-0.294130\pi$
$241$	8.55776	+	3.11477i	0.551254	+	0.200640i	−0.0513496	+	0.998681i	$0.516352\pi$
$242$	17.5561	+	3.09561i	1.12855	+	0.198993i
$243$	−13.1261	+	2.31448i	−0.842039	+	0.148474i
$244$	7.62565	−	2.77551i	0.488182	−	0.177684i
$245$		0			0
$246$	1.09997			0.0701313
$247$	4.92017	−	16.0770i	0.313063	−	1.02296i
$248$		−	8.20377i		−	0.520940i
$249$	−6.38533	−	5.35793i	−0.404654	−	0.339545i
$250$		0			0
$251$	2.91829	+	16.5504i	0.184201	+	1.04465i	0.926978	+	0.375116i	$0.122397\pi$
$251$	2.91829	+	16.5504i	0.184201	+	1.04465i	−0.742777	+	0.669539i	$0.766492\pi$
$252$	−12.7793	−	2.25334i	−0.805020	−	0.141947i
$253$	−9.80400	+	26.9363i	−0.616372	+	1.69347i
$254$	0.0695914	+	0.120536i	0.00436655	+	0.00756309i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	6.36185	+	7.58176i	0.396841	+	0.472937i	0.927054	−	0.374927i	$-0.122332\pi$
$257$	6.36185	+	7.58176i	0.396841	+	0.472937i	−0.530213	+	0.847865i	$0.677888\pi$
$258$	0.738118	+	0.426153i	0.0459532	+	0.0265311i
$259$	25.4382	+	44.0602i	1.58065	+	2.73777i
$260$		0			0
$261$	1.68335	−	9.54674i	0.104197	−	0.590929i
$262$	−12.2412	+	2.15846i	−0.756267	+	0.133350i
$263$	7.66554	+	21.0609i	0.472677	+	1.29867i	0.915593	+	0.402107i	$0.131722\pi$
$263$	7.66554	+	21.0609i	0.472677	+	1.29867i	−0.442915	+	0.896564i	$0.646056\pi$
$264$	−2.37075	−	1.98929i	−0.145909	−	0.122432i
$265$		0			0
$266$	2.58983	−	21.0437i	0.158793	−	1.29027i
$267$		−	5.53845i		−	0.338948i
$268$	−5.42827	+	6.46916i	−0.331584	+	0.395167i
$269$	7.02217	−	2.55586i	0.428149	−	0.155834i	−0.118952	−	0.992900i	$-0.537953\pi$
$269$	7.02217	−	2.55586i	0.428149	−	0.155834i	0.547101	+	0.837066i	$0.315731\pi$
$270$		0			0
$271$	−1.84950	+	10.4890i	−0.112349	+	0.637163i	0.875680	+	0.482893i	$0.160414\pi$
$271$	−1.84950	+	10.4890i	−0.112349	+	0.637163i	−0.988029	+	0.154271i	$0.950697\pi$
$272$	−0.479544	+	1.31754i	−0.0290766	+	0.0798874i
$273$	9.36576	−	5.40733i	0.566842	−	0.327266i
$274$	7.19080	−	12.4548i	0.434412	−	0.752424i
$275$		0			0
$276$	2.35743	−	1.97812i	0.141900	−	0.119069i
$277$	−2.01467	−	1.16317i	−0.121050	−	0.0698880i	0.438253	−	0.898852i	$-0.355598\pi$
$277$	−2.01467	−	1.16317i	−0.121050	−	0.0698880i	−0.559302	+	0.828964i	$0.688931\pi$
$278$	−15.4595	+	8.92555i	−0.927200	+	0.535319i
$279$	−20.5658	−	7.48532i	−1.23124	−	0.448135i
$280$		0			0
$281$	−2.96472	−	16.8137i	−0.176860	−	1.00302i	−0.935975	−	0.352067i	$-0.885479\pi$
$281$	−2.96472	−	16.8137i	−0.176860	−	1.00302i	0.759115	−	0.650957i	$-0.225632\pi$
$282$	0.615151	+	1.69011i	0.0366317	+	0.100645i
$283$	−5.44307	+	6.48680i	−0.323557	+	0.385600i	−0.903164	−	0.429296i	$-0.858762\pi$
$283$	−5.44307	+	6.48680i	−0.323557	+	0.385600i	0.579607	+	0.814896i	$0.303206\pi$
$284$	−6.02641			−0.357601
$285$		0			0
$286$	−20.7095			−1.22458
$287$	5.96658	−	7.11069i	0.352196	−	0.419731i
$288$	−0.912424	−	2.50687i	−0.0537651	−	0.147718i
$289$	2.61065	+	14.8057i	0.153568	+	0.870925i
$290$		0			0
$291$	3.29275	+	1.19846i	0.193024	+	0.0702551i
$292$	1.10529	−	0.638142i	0.0646824	−	0.0373444i
$293$	2.24512	+	1.29622i	0.131161	+	0.0757260i	0.564145	−	0.825676i	$-0.309206\pi$
$293$	2.24512	+	1.29622i	0.131161	+	0.0757260i	−0.432984	+	0.901402i	$0.642539\pi$
$294$	7.35647	−	6.17281i	0.429038	−	0.360006i
$295$		0			0
$296$	−5.22969	+	9.05808i	−0.303969	+	0.526490i
$297$	−15.1905	+	8.77025i	−0.881443	+	0.508901i
$298$	0.987271	−	2.71250i	0.0571911	−	0.157131i
$299$	3.57596	−	20.2803i	0.206803	−	1.17284i
$300$		0			0
$301$	6.75864	−	2.45994i	0.389562	−	0.141789i
$302$	−1.29718	+	1.54591i	−0.0746441	+	0.0889573i
$303$			0.723785i			0.0415804i
$304$	4.01286	−	1.70203i	0.230154	−	0.0976183i
$305$		0			0
$306$	2.86534	+	2.40431i	0.163801	+	0.137445i
$307$	−1.40970	−	3.87311i	−0.0804557	−	0.221050i	0.892942	−	0.450171i	$-0.148637\pi$
$307$	−1.40970	−	3.87311i	−0.0804557	−	0.221050i	−0.973398	+	0.229121i	$0.926415\pi$
$308$	−25.7194	+	4.53502i	−1.46550	+	0.258407i
$309$	−0.737387	+	4.18193i	−0.0419485	+	0.237902i
$310$		0			0
$311$	−1.24153	−	2.15040i	−0.0704008	−	0.121938i	0.828676	−	0.559728i	$-0.189094\pi$
$311$	−1.24153	−	2.15040i	−0.0704008	−	0.121938i	−0.899077	+	0.437791i	$0.855761\pi$
$312$	1.92545	+	1.11166i	0.109007	+	0.0629354i
$313$	3.45913	+	4.12243i	0.195522	+	0.233014i	0.854894	−	0.518803i	$-0.173622\pi$
$313$	3.45913	+	4.12243i	0.195522	+	0.233014i	−0.659372	+	0.751817i	$0.729178\pi$
$314$	−8.45667	+	7.09599i	−0.477238	+	0.400450i
$315$		0			0
$316$	8.31600	+	14.4037i	0.467812	+	0.810273i
$317$	−6.65753	+	18.2914i	−0.373924	+	1.02735i	0.599906	+	0.800071i	$0.295205\pi$
$317$	−6.65753	+	18.2914i	−0.373924	+	1.02735i	−0.973830	+	0.227278i	$0.927017\pi$
$318$	1.02178	+	0.180168i	0.0572987	+	0.0101033i
$319$	−3.38788	−	19.2136i	−0.189685	−	1.07576i
$320$		0			0
$321$	−3.85513	−	3.23484i	−0.215172	−	0.180551i
$322$		−	25.9695i		−	1.44722i
$323$	−3.67941	+	4.87990i	−0.204728	+	0.271525i
$324$	−6.12015			−0.340008
$325$		0			0
$326$	−5.57114	+	2.02773i	−0.308557	+	0.112306i
$327$	4.61492	−	0.813735i	0.255206	−	0.0449996i
$328$	1.87931	+	0.331373i	0.103768	+	0.0182970i
$329$	14.2625	+	5.19111i	0.786315	+	0.286195i
$330$		0			0
$331$	9.35511	−	16.2035i	0.514203	−	0.890626i	−0.485661	−	0.874147i	$-0.661421\pi$
$331$	9.35511	−	16.2035i	0.514203	−	0.890626i	0.999864	−	0.0164787i	$-0.00524557\pi$
$332$	−9.29534	−	11.0778i	−0.510148	−	0.607971i
$333$	17.9357	+	21.3749i	0.982870	+	1.17134i
$334$	−3.61382	+	6.25932i	−0.197739	+	0.342495i
$335$		0			0
$336$	2.63468	+	0.958946i	0.143734	+	0.0523148i
$337$	24.7159	+	4.35808i	1.34636	+	0.237400i	0.799924	−	0.600101i	$-0.204873\pi$
$337$	24.7159	+	4.35808i	1.34636	+	0.237400i	0.546436	+	0.837501i	$0.315984\pi$
$338$	1.84933	−	0.326087i	0.100590	−	0.0177368i
$339$	−2.42772	+	0.883619i	−0.131856	+	0.0479916i
$340$		0			0
$341$	−44.0466			−2.38526
$342$	−0.605335	−	11.6127i	−0.0327328	−	0.627942i
$343$		−	46.9896i		−	2.53720i
$344$	1.13271	+	0.950453i	0.0610714	+	0.0512450i
$345$		0			0
$346$	0.895772	+	5.08018i	0.0481570	+	0.273112i
$347$	−22.4078	−	3.95111i	−1.20292	−	0.212107i	−0.463957	−	0.885857i	$-0.653571\pi$
$347$	−22.4078	−	3.95111i	−1.20292	−	0.212107i	−0.738958	+	0.673751i	$0.764682\pi$
$348$	−0.716378	+	1.96823i	−0.0384019	+	0.105508i
$349$	6.58190	+	11.4002i	0.352321	+	0.610238i	0.986656	−	0.162820i	$-0.0520591\pi$
$349$	6.58190	+	11.4002i	0.352321	+	0.610238i	−0.634335	+	0.773059i	$0.718726\pi$
$350$		0			0
$351$	9.65310	−	8.09992i	0.515245	−	0.432341i
$352$	−3.45117	−	4.11295i	−0.183948	−	0.219221i
$353$	10.6570	+	6.15281i	0.567213	+	0.327481i	0.756036	−	0.654530i	$-0.227134\pi$
$353$	10.6570	+	6.15281i	0.567213	+	0.327481i	−0.188822	+	0.982011i	$0.560467\pi$
$354$	2.11112	+	3.65657i	0.112205	+	0.194345i
$355$		0			0
$356$	1.66850	−	9.46254i	0.0884304	−	0.501513i
$357$	−3.87142	+	0.682636i	−0.204897	+	0.0361290i
$358$	2.79899	+	7.69017i	0.147931	+	0.406438i
$359$	−9.62244	−	8.07418i	−0.507853	−	0.426139i	0.352520	−	0.935804i	$-0.385325\pi$
$359$	−9.62244	−	8.07418i	−0.507853	−	0.426139i	−0.860373	+	0.509665i	$0.829769\pi$
$360$		0			0
$361$	18.8970	−	1.97546i	0.994580	−	0.103972i
$362$		−	3.43236i		−	0.180401i
$363$	−6.60504	+	7.87158i	−0.346675	+	0.413151i
$364$	17.6306	−	6.41700i	0.924093	−	0.336342i
$365$		0			0
$366$	−0.812257	+	4.60654i	−0.0424574	+	0.240788i
$367$	−0.918156	+	2.52261i	−0.0479274	+	0.131679i	−0.961347	−	0.275340i	$-0.911210\pi$
$367$	−0.918156	+	2.52261i	−0.0479274	+	0.131679i	0.913420	+	0.407019i	$0.133432\pi$
$368$	4.62363	−	2.66945i	0.241023	−	0.139155i
$369$	2.54544	−	4.40883i	0.132510	−	0.229514i
$370$		0			0
$371$	6.70717	−	5.62798i	0.348219	−	0.292190i
$372$	4.09521	+	2.36437i	0.212327	+	0.122587i
$373$	−16.0582	+	9.27119i	−0.831461	+	0.480044i	−0.854353	−	0.519694i	$-0.826046\pi$
$373$	−16.0582	+	9.27119i	−0.831461	+	0.480044i	0.0228917	+	0.999738i	$0.492713\pi$
$374$	7.07395	+	2.57471i	0.365785	+	0.133135i
$375$		0			0
$376$	0.541837	+	3.07291i	0.0279431	+	0.158473i
$377$	4.79381	+	13.1709i	0.246894	+	0.678334i
$378$	10.2146	−	12.1733i	0.525381	−	0.626125i
$379$	−11.5855			−0.595108			−0.297554	−	0.954705i	$-0.596171\pi$
$379$	−11.5855			−0.595108			−0.297554	+	0.954705i	$0.596171\pi$
$380$		0			0
$381$	−0.0802265			−0.00411013
$382$	−2.42706	+	2.89246i	−0.124179	+	0.147991i
$383$	−9.94564	−	27.3254i	−0.508199	−	1.39626i	−0.883094	−	0.469197i	$-0.844543\pi$
$383$	−9.94564	−	27.3254i	−0.508199	−	1.39626i	0.374895	−	0.927067i	$-0.377679\pi$
$384$	0.100093	+	0.567654i	0.00510783	+	0.0289680i
$385$		0			0
$386$	11.4435	+	4.16508i	0.582457	+	0.211997i
$387$	3.41617	−	1.97233i	0.173654	−	0.100259i
$388$	5.26467	+	3.03956i	0.267273	+	0.154310i
$389$	−22.8144	+	19.1436i	−1.15674	+	0.970618i	−0.999856	−	0.0169993i	$-0.994589\pi$
$389$	−22.8144	+	19.1436i	−1.15674	+	0.970618i	−0.156882	+	0.987617i	$0.550144\pi$
$390$		0			0
$391$	−3.74282	+	6.48276i	−0.189283	+	0.327847i
$392$	14.4283	−	8.33016i	0.728737	−	0.420737i
$393$	2.45052	−	6.73274i	0.123612	−	0.339622i
$394$	1.25068	−	7.09294i	0.0630082	−	0.357337i
$395$		0			0
$396$	−13.4595	+	4.89887i	−0.676367	+	0.246178i
$397$	4.03025	−	4.80307i	0.202273	−	0.241059i	−0.655367	−	0.755311i	$-0.727486\pi$
$397$	4.03025	−	4.80307i	0.202273	−	0.241059i	0.857639	+	0.514252i	$0.171930\pi$
$398$		−	5.83709i		−	0.292587i
$399$	9.75834	+	7.35772i	0.488528	+	0.368347i
$400$		0			0
$401$	7.58485	+	6.36445i	0.378769	+	0.317825i	0.812219	−	0.583353i	$-0.198259\pi$
$401$	7.58485	+	6.36445i	0.378769	+	0.317825i	−0.433450	+	0.901178i	$0.642704\pi$
$402$	−1.66486	−	4.57417i	−0.0830357	−	0.228139i
$403$	31.1627	−	5.49483i	1.55233	−	0.273717i
$404$	−0.218046	+	1.23660i	−0.0108482	+	0.0615231i
$405$		0			0
$406$	8.83769	+	15.3073i	0.438607	+	0.759690i
$407$	48.6335	+	28.0786i	2.41067	+	1.39180i
$408$	−0.519489	−	0.619103i	−0.0257185	−	0.0306502i
$409$	23.4859	−	19.7070i	1.16130	−	0.974449i	0.161380	−	0.986892i	$-0.448405\pi$
$409$	23.4859	−	19.7070i	1.16130	−	0.974449i	0.999923	+	0.0124433i	$0.00396092\pi$
$410$		0			0
$411$	4.14486	+	7.17910i	0.204451	+	0.354119i
$412$	−2.51968	+	6.92276i	−0.124136	+	0.341060i
$413$	35.0892	+	6.18717i	1.72663	+	0.304451i
$414$	−2.47325	−	14.0265i	−0.121554	−	0.689365i
$415$		0			0
$416$	2.95477	+	2.47935i	0.144870	+	0.121560i
$417$		−	10.2896i		−	0.503882i
$418$	−9.13834	−	21.5454i	−0.446971	−	1.05382i
$419$	−17.9296			−0.875916			−0.437958	−	0.898995i	$-0.644298\pi$
$419$	−17.9296			−0.875916			−0.437958	+	0.898995i	$0.644298\pi$
$420$		0			0
$421$	30.2850	−	11.0228i	1.47600	−	0.537220i	0.526278	−	0.850313i	$-0.323587\pi$
$421$	30.2850	−	11.0228i	1.47600	−	0.537220i	0.949723	+	0.313093i	$0.101365\pi$
$422$	−10.5088	+	1.85299i	−0.511562	+	0.0902022i
$423$	8.19775	+	1.44549i	0.398588	+	0.0702819i
$424$	1.69146	+	0.615640i	0.0821444	+	0.0298981i
$425$		0			0
$426$	1.73684	−	3.00830i	0.0841503	−	0.145753i
$427$	25.3728	+	30.2382i	1.22788	+	1.46333i
$428$	−5.61204	−	6.68816i	−0.271268	−	0.323285i
$429$	5.96858	−	10.3379i	0.288166	−	0.499118i
$430$		0			0
$431$	1.30703	+	0.475720i	0.0629575	+	0.0229146i	0.373307	−	0.927708i	$-0.378224\pi$
$431$	1.30703	+	0.475720i	0.0629575	+	0.0229146i	−0.310349	+	0.950623i	$0.600446\pi$
$432$	3.21732	+	0.567300i	0.154793	+	0.0272942i
$433$	−32.7483	+	5.77441i	−1.57378	+	0.277500i	−0.891304	−	0.453406i	$-0.850209\pi$
$433$	−32.7483	+	5.77441i	−1.57378	+	0.277500i	−0.682478	+	0.730906i	$0.739098\pi$
$434$	37.4981	−	13.6482i	1.79997	−	0.655135i
$435$		0			0
$436$	8.12981			0.389347
$437$	22.6768	−	5.22866i	1.08478	−	0.250121i
$438$			0.735663i			0.0351513i
$439$	27.6648	+	23.2135i	1.32037	+	1.10792i	0.986227	+	0.165397i	$0.0528906\pi$
$439$	27.6648	+	23.2135i	1.32037	+	1.10792i	0.334141	+	0.942523i	$0.391554\pi$
$440$		0			0
$441$	−7.71789	−	43.7704i	−0.367519	−	2.08430i
$442$	−5.32597	−	0.939112i	−0.253330	−	0.0446690i
$443$	10.9404	−	30.0586i	0.519795	−	1.42813i	−0.350951	−	0.936394i	$-0.614142\pi$
$443$	10.9404	−	30.0586i	0.519795	−	1.42813i	0.870746	−	0.491732i	$-0.163636\pi$
$444$	−3.01445	−	5.22118i	−0.143059	−	0.247786i
$445$		0			0
$446$	0.0761973	−	0.0639371i	0.00360805	−	0.00302751i
$447$	1.06951	+	1.27459i	0.0505860	+	0.0602860i
$448$	4.21251	+	2.43209i	0.199022	+	0.114906i
$449$	−1.09116	−	1.88995i	−0.0514951	−	0.0891922i	0.839129	−	0.543933i	$-0.183065\pi$
$449$	−1.09116	−	1.88995i	−0.0514951	−	0.0891922i	−0.890624	+	0.454741i	$0.849732\pi$
$450$		0			0
$451$	1.77917	−	10.0902i	0.0837777	−	0.475127i
$452$	−4.41400	+	0.778308i	−0.207617	+	0.0366085i
$453$	−0.397846	−	1.09307i	−0.0186924	−	0.0513570i
$454$	−10.5915	−	8.88734i	−0.497084	−	0.417103i
$455$		0			0
$456$	−0.306897	+	2.49370i	−0.0143718	+	0.116778i
$457$			37.2037i			1.74031i	0.492774	+	0.870157i	$0.335983\pi$
$457$			37.2037i			1.74031i	−0.492774	+	0.870157i	$0.664017\pi$
$458$	10.0115	−	11.9313i	0.467808	−	0.557512i
$459$	−4.30433	+	1.56665i	−0.200909	+	0.0731248i
$460$		0			0
$461$	−0.847556	+	4.80673i	−0.0394746	+	0.223872i	−0.998163	−	0.0605870i	$-0.980703\pi$
$461$	−0.847556	+	4.80673i	−0.0394746	+	0.223872i	0.958688	+	0.284459i	$0.0918138\pi$
$462$	5.14865	−	14.1458i	0.239537	−	0.658122i
$463$	−17.5133	+	10.1113i	−0.813914	+	0.469913i	−0.848313	−	0.529495i	$-0.822381\pi$
$463$	−17.5133	+	10.1113i	−0.813914	+	0.469913i	0.0343994	+	0.999408i	$0.489048\pi$
$464$	−1.81689	+	3.14694i	−0.0843470	+	0.146093i
$465$		0			0
$466$	11.6753	−	9.79677i	0.540850	−	0.453827i
$467$	33.7859	+	19.5063i	1.56342	+	0.902644i	0.996907	+	0.0785944i	$0.0250432\pi$
$467$	33.7859	+	19.5063i	1.56342	+	0.902644i	0.566518	+	0.824049i	$0.308290\pi$
$468$	8.91140	−	5.14500i	0.411930	−	0.237828i
$469$	−38.6003	−	14.0493i	−1.78239	−	0.648739i
$470$		0			0
$471$	−1.10496	−	6.26656i	−0.0509140	−	0.288748i
$472$	2.50532	+	6.88331i	0.115317	+	0.316830i
$473$	5.10305	−	6.08158i	0.234639	−	0.279631i
$474$	−9.58686			−0.440339
$475$		0			0
$476$	−6.82004			−0.312596
$477$	3.08665	−	3.67853i	0.141328	−	0.168428i
$478$	5.75392	+	15.8088i	0.263178	+	0.723076i
$479$	5.39865	+	30.6172i	0.246670	+	1.39894i	0.816581	+	0.577231i	$0.195867\pi$
$479$	5.39865	+	30.6172i	0.246670	+	1.39894i	−0.569911	+	0.821707i	$0.693022\pi$
$480$		0			0
$481$	−37.9107	−	13.7984i	−1.72858	−	0.629151i
$482$	−7.88688	+	4.55349i	−0.359237	+	0.207406i
$483$	12.9636	+	7.48453i	0.589864	+	0.340558i
$484$	−13.6562	+	11.4589i	−0.620737	+	0.520860i
$485$		0			0
$486$	6.66429	−	11.5429i	0.302298	−	0.523596i
$487$	24.2263	−	13.9870i	1.09780	−	0.633813i	0.162155	−	0.986765i	$-0.448155\pi$
$487$	24.2263	−	13.9870i	1.09780	−	0.633813i	0.935641	+	0.352952i	$0.114822\pi$
$488$	−2.77551	+	7.62565i	−0.125641	+	0.345197i
$489$	0.593418	−	3.36544i	0.0268353	−	0.152191i
$490$		0			0
$491$	−2.79400	+	1.01693i	−0.126091	+	0.0458935i	−0.404295	−	0.914629i	$-0.632483\pi$
$491$	−2.79400	+	1.01693i	−0.126091	+	0.0458935i	0.278204	+	0.960522i	$0.410261\pi$
$492$	−0.707045	+	0.842623i	−0.0318760	+	0.0379884i
$493$		−	5.09490i		−	0.229463i
$494$	9.15311	+	14.1032i	0.411818	+	0.634533i
$495$		0			0
$496$	6.28445	+	5.27328i	0.282180	+	0.236777i
$497$	−10.0258	−	27.5458i	−0.449720	−	1.23560i
$498$	8.20883	−	1.44744i	0.367846	−	0.0648612i
$499$	−3.20155	+	18.1569i	−0.143321	+	0.812815i	0.825379	+	0.564580i	$0.190962\pi$
$499$	−3.20155	+	18.1569i	−0.143321	+	0.812815i	−0.968700	+	0.248235i	$0.920149\pi$
$500$		0			0
$501$	−2.08304	−	3.60794i	−0.0930636	−	0.161191i
$502$	−14.5542	−	8.40288i	−0.649586	−	0.375039i
$503$	2.10120	+	2.50412i	0.0936881	+	0.111653i	0.810852	−	0.585252i	$-0.199004\pi$
$503$	2.10120	+	2.50412i	0.0936881	+	0.111653i	−0.717163	+	0.696905i	$0.754560\pi$
$504$	9.94053	−	8.34110i	0.442786	−	0.371542i
$505$		0			0
$506$	−14.3325	−	24.8246i	−0.637157	−	1.10359i
$507$	−0.370209	+	1.01714i	−0.0164416	+	0.0451728i
$508$	−0.137068	−	0.0241688i	−0.00608142	−	0.00107232i
$509$	−6.53272	−	37.0489i	−0.289558	−	1.64216i	−0.688536	−	0.725202i	$-0.741746\pi$
$509$	−6.53272	−	37.0489i	−0.289558	−	1.64216i	0.398978	−	0.916960i	$-0.369365\pi$
$510$		0			0
$511$	4.75567	+	3.99048i	0.210378	+	0.176528i
$512$			1.00000i			0.0441942i
$513$	12.6864	+	6.46852i	0.560118	+	0.285592i
$514$	−9.89728			−0.436550
$515$		0			0
$516$	−0.800905	+	0.291506i	−0.0352579	+	0.0128328i
$517$	16.4987	−	2.90916i	0.725610	−	0.127945i
$518$	−50.1034	−	8.83459i	−2.20142	−	0.388169i
$519$	−2.79412	−	1.01698i	−0.122648	−	0.0446403i
$520$		0			0
$521$	−15.7203	+	27.2284i	−0.688719	+	1.19290i	0.283533	+	0.958962i	$0.408493\pi$
$521$	−15.7203	+	27.2284i	−0.688719	+	1.19290i	−0.972252	+	0.233934i	$0.924840\pi$
$522$	6.23119	+	7.42605i	0.272732	+	0.325029i
$523$	2.88381	+	3.43679i	0.126100	+	0.150280i	0.825400	−	0.564548i	$-0.190949\pi$
$523$	2.88381	+	3.43679i	0.126100	+	0.150280i	−0.699300	+	0.714828i	$0.746505\pi$
$524$	6.21505	−	10.7648i	0.271506	−	0.470261i
$525$		0			0
$526$	−21.0609	−	7.66554i	−0.918299	−	0.334233i
$527$	−11.3277	−	1.99738i	−0.493443	−	0.0870073i
$528$	3.04777	−	0.537405i	0.132637	−	0.0233875i
$529$	5.17201	−	1.88246i	0.224870	−	0.0818460i
$530$		0			0
$531$	19.5415			0.848027
$532$	14.4557	+	15.5106i	0.626735	+	0.672469i
$533$			7.36067i			0.318826i
$534$	4.24270	+	3.56005i	0.183599	+	0.154058i
$535$		0			0
$536$	−1.46644	−	8.31660i	−0.0633406	−	0.359222i
$537$	−4.64551	−	0.819129i	−0.200469	−	0.0353480i
$538$	−2.55586	+	7.02217i	−0.110191	+	0.302747i
$539$	−44.7252	−	77.4664i	−1.92645	−	3.33671i
$540$		0			0
$541$	17.0269	−	14.2873i	0.732045	−	0.614259i	−0.198643	−	0.980072i	$-0.563653\pi$
$541$	17.0269	−	14.2873i	0.732045	−	0.614259i	0.930688	+	0.365813i	$0.119209\pi$
$542$	−6.84623	−	8.15902i	−0.294071	−	0.350460i
$543$	1.71339	+	0.989225i	0.0735285	+	0.0424517i
$544$	−0.701047	−	1.21425i	−0.0300571	−	0.0520605i
$545$		0			0
$546$	−1.87794	+	10.6504i	−0.0803686	+	0.455793i
$547$	−28.4071	+	5.00894i	−1.21460	+	0.214167i	−0.744000	−	0.668180i	$-0.767074\pi$
$547$	−28.4071	+	5.00894i	−1.21460	+	0.214167i	−0.470600	+	0.882347i	$0.655962\pi$
$548$	4.91880	+	13.5143i	0.210121	+	0.577302i
$549$	16.5840	+	13.9157i	0.707790	+	0.593906i
$550$		0			0
$551$	−11.5871	+	10.7991i	−0.493629	+	0.460058i
$552$			3.07740i			0.130983i
$553$	−52.0023	+	61.9739i	−2.21136	+	2.63540i
$554$	2.18604	−	0.795654i	0.0928760	−	0.0338041i
$555$		0			0
$556$	3.09981	−	17.5799i	0.131461	−	0.745554i
$557$	9.58721	−	26.3406i	0.406223	−	1.11609i	−0.552937	−	0.833223i	$-0.686493\pi$
$557$	9.58721	−	26.3406i	0.406223	−	1.11609i	0.959160	−	0.282865i	$-0.0912850\pi$
$558$	18.9535	−	10.9428i	0.802366	−	0.463246i
$559$	−2.85170	+	4.93929i	−0.120614	+	0.208910i
$560$		0			0
$561$	−3.32401	+	2.78917i	−0.140340	+	0.117759i
$562$	14.7858	+	8.53656i	0.623699	+	0.360093i
$563$	−5.69177	+	3.28614i	−0.239879	+	0.138494i	−0.615121	−	0.788432i	$-0.710893\pi$
$563$	−5.69177	+	3.28614i	−0.239879	+	0.138494i	0.375242	+	0.926927i	$0.377560\pi$
$564$	−1.69011	−	0.615151i	−0.0711666	−	0.0259025i
$565$		0			0
$566$	−1.47044	−	8.33927i	−0.0618071	−	0.350526i
$567$	−10.1818	−	27.9742i	−0.427595	−	1.17481i
$568$	3.87370	−	4.61650i	0.162537	−	0.193704i
$569$	−3.90032			−0.163510			−0.0817549	−	0.996652i	$-0.526052\pi$
$569$	−3.90032			−0.163510			−0.0817549	+	0.996652i	$0.526052\pi$
$570$		0			0
$571$	18.1559			0.759802			0.379901	−	0.925027i	$-0.375958\pi$
$571$	18.1559			0.759802			0.379901	+	0.925027i	$0.375958\pi$
$572$	13.3118	−	15.8644i	0.556594	−	0.663323i
$573$	−0.744385	−	2.04518i	−0.0310971	−	0.0854386i
$574$	1.61186	+	9.14132i	0.0672778	+	0.381551i
$575$		0			0
$576$	2.50687	+	0.912424i	0.104453	+	0.0380177i
$577$	−12.1402	+	7.00915i	−0.505403	+	0.291795i	−0.730942	−	0.682439i	$-0.760919\pi$
$577$	−12.1402	+	7.00915i	−0.505403	+	0.291795i	0.225539	+	0.974234i	$0.427586\pi$
$578$	−13.0199	−	7.51707i	−0.541558	−	0.312669i
$579$	−5.37721	+	4.51202i	−0.223469	+	0.187513i
$580$		0			0
$581$	35.1705	−	60.9170i	1.45912	−	2.52726i
$582$	−3.03461	+	1.75203i	−0.125789	+	0.0726241i
$583$	3.30541	−	9.08155i	0.136896	−	0.376119i
$584$	−0.221624	+	1.25689i	−0.00917088	+	0.0520106i
$585$		0			0
$586$	−2.43610	+	0.886667i	−0.100634	+	0.0366279i
$587$	−4.89246	+	5.83061i	−0.201933	+	0.240655i	−0.857502	−	0.514481i	$-0.827985\pi$
$587$	−4.89246	+	5.83061i	−0.201933	+	0.240655i	0.655568	+	0.755136i	$0.272429\pi$
$588$			9.60319i			0.396029i
$589$	19.4676	+	29.9958i	0.802148	+	1.23596i
$590$		0			0
$591$	3.18025	+	2.66855i	0.130818	+	0.109769i
$592$	−3.57732	−	9.82860i	−0.147027	−	0.403953i
$593$	9.27933	−	1.63620i	0.381056	−	0.0671905i	0.0201608	−	0.999797i	$-0.493582\pi$
$593$	9.27933	−	1.63620i	0.381056	−	0.0671905i	0.360896	+	0.932606i	$0.382471\pi$
$594$	3.04587	−	17.2740i	0.124974	−	0.708761i
$595$		0			0
$596$	1.44329	+	2.49986i	0.0591196	+	0.102398i
$597$	2.91380	+	1.68228i	0.119254	+	0.0688512i
$598$	13.2370	+	15.7753i	0.541302	+	0.645099i
$599$	−10.7502	+	9.02053i	−0.439243	+	0.368569i	−0.835426	−	0.549603i	$-0.814779\pi$
$599$	−10.7502	+	9.02053i	−0.439243	+	0.368569i	0.396183	+	0.918172i	$0.370335\pi$
$600$		0			0
$601$	6.78599	+	11.7537i	0.276806	+	0.479443i	0.970589	−	0.240742i	$-0.0773906\pi$
$601$	6.78599	+	11.7537i	0.276806	+	0.479443i	−0.693783	+	0.720184i	$0.744057\pi$
$602$	−2.45994	+	6.75864i	−0.100260	+	0.275462i
$603$	−22.1866	−	3.91210i	−0.903508	−	0.159313i
$604$	−0.350430	−	1.98739i	−0.0142588	−	0.0808657i
$605$		0			0
$606$	−0.554451	−	0.465240i	−0.0225231	−	0.0188991i
$607$		−	2.07689i		−	0.0842984i	−0.999111	−	0.0421492i	$-0.986580\pi$
$607$		−	2.07689i		−	0.0842984i	0.999111	−	0.0421492i	$-0.0134205\pi$
$608$	−1.27559	+	4.16808i	−0.0517318	+	0.169038i
$609$	−10.1883			−0.412850
$610$		0			0
$611$	−11.3098	+	4.11642i	−0.457545	+	0.166533i
$612$	−3.68361	+	0.649520i	−0.148901	+	0.0262553i
$613$	−16.2680	−	2.86849i	−0.657059	−	0.115857i	−0.164828	−	0.986322i	$-0.552707\pi$
$613$	−16.2680	−	2.86849i	−0.657059	−	0.115857i	−0.492230	+	0.870465i	$0.663818\pi$
$614$	3.87311	+	1.40970i	0.156306	+	0.0568908i
$615$		0			0
$616$	13.0581	−	22.6173i	0.526125	−	0.911275i
$617$	−14.7080	−	17.5283i	−0.592120	−	0.705661i	0.383892	−	0.923378i	$-0.374583\pi$
$617$	−14.7080	−	17.5283i	−0.592120	−	0.705661i	−0.976012	+	0.217717i	$0.930139\pi$
$618$	−2.72956	−	3.25297i	−0.109799	−	0.130853i
$619$	−6.66514	+	11.5444i	−0.267895	+	0.464007i	−0.968318	−	0.249721i	$-0.919661\pi$
$619$	−6.66514	+	11.5444i	−0.267895	+	0.464007i	0.700423	+	0.713728i	$0.252995\pi$
$620$		0			0
$621$	16.3901	+	5.96550i	0.657711	+	0.239387i
$622$	2.44534	+	0.431179i	0.0980492	+	0.0172887i
$623$	46.0276	−	8.11590i	1.84406	−	0.325157i
$624$	−2.08924	+	0.760421i	−0.0836365	+	0.0304412i
$625$		0			0
$626$	−5.38145			−0.215086
$627$	13.3889	+	1.64775i	0.534700	+	0.0658048i
$628$		−	11.0394i		−	0.440520i
$629$	11.2341	+	9.42649i	0.447931	+	0.375859i
$630$		0			0
$631$	1.51546	+	8.59462i	0.0603297	+	0.342147i	1.00000		6.52024e-5i	$2.07546e-5\pi$
$631$	1.51546	+	8.59462i	0.0603297	+	0.342147i	−0.939670	+	0.342081i	$0.888868\pi$
$632$	−16.3793	−	2.88812i	−0.651534	−	0.114883i
$633$	2.10372	−	5.77991i	0.0836152	−	0.229731i
$634$	−9.73266	−	16.8575i	−0.386533	−	0.669495i
$635$		0			0
$636$	−0.794805	+	0.666921i	−0.0315161	+	0.0264451i
$637$	41.3068	+	49.2275i	1.63663	+	1.95046i
$638$	16.8962	+	9.75501i	0.668926	+	0.386204i
$639$	−8.03848	−	13.9230i	−0.317997	−	0.550787i
$640$		0			0
$641$	−0.151753	+	0.860632i	−0.00599387	+	0.0339929i	−0.987658	−	0.156626i	$-0.949938\pi$
$641$	−0.151753	+	0.860632i	−0.00599387	+	0.0339929i	0.981664	+	0.190619i	$0.0610494\pi$
$642$	4.95606	−	0.873887i	0.195600	−	0.0344896i
$643$	6.50122	+	17.8620i	0.256383	+	0.704407i	0.999383	+	0.0351158i	$0.0111800\pi$
$643$	6.50122	+	17.8620i	0.256383	+	0.704407i	−0.743000	+	0.669291i	$0.766598\pi$
$644$	19.8938	+	16.6928i	0.783924	+	0.657790i
$645$		0			0
$646$	−1.37314	−	5.95533i	−0.0540255	−	0.234309i
$647$		−	14.4175i		−	0.566810i	−0.959000	−	0.283405i	$-0.908536\pi$
$647$		−	14.4175i		−	0.566810i	0.959000	−	0.283405i	$-0.0914641\pi$
$648$	3.93395	−	4.68830i	0.154540	−	0.184174i
$649$	36.9570	−	13.4512i	1.45069	−	0.528007i
$650$		0			0
$651$	−3.99417	+	22.6520i	−0.156544	+	0.887804i
$652$	2.02773	−	5.57114i	0.0794121	−	0.218183i
$653$	9.06528	−	5.23384i	0.354752	−	0.204816i	−0.312024	−	0.950074i	$-0.601007\pi$
$653$	9.06528	−	5.23384i	0.354752	−	0.204816i	0.666776	+	0.745258i	$0.267674\pi$
$654$	−2.34306	+	4.05829i	−0.0916207	+	0.158692i
$655$		0			0
$656$	−1.46184	+	1.22663i	−0.0570755	+	0.0478920i
$657$	2.94865	+	1.70240i	0.115038	+	0.0664171i
$658$	−13.1444	+	7.58889i	−0.512420	+	0.295846i
$659$	5.20991	+	1.89625i	0.202949	+	0.0738675i	0.441495	−	0.897264i	$-0.354448\pi$
$659$	5.20991	+	1.89625i	0.202949	+	0.0738675i	−0.238545	+	0.971131i	$0.576671\pi$
$660$		0			0
$661$	5.00125	+	28.3635i	0.194526	+	1.10321i	0.913092	+	0.407753i	$0.133688\pi$
$661$	5.00125	+	28.3635i	0.194526	+	1.10321i	−0.718566	+	0.695459i	$0.755201\pi$
$662$	6.39927	+	17.5818i	0.248715	+	0.683338i
$663$	2.00376	−	2.38799i	0.0778198	−	0.0927420i
$664$	14.4610			0.561195
$665$		0			0
$666$	−27.9030			−1.08122
$667$	−12.4703	+	14.8616i	−0.482854	+	0.575443i
$668$	−2.47200	−	6.79176i	−0.0956445	−	0.262781i
$669$	0.00995606	+	0.0564636i	0.000384924	+	0.00218301i
$670$		0			0
$671$	40.9427	+	14.9019i	1.58057	+	0.575282i
$672$	−2.42814	+	1.40188i	−0.0936674	+	0.0540789i
$673$	−34.5899	−	19.9705i	−1.33334	−	0.769807i	−0.347533	−	0.937668i	$-0.612981\pi$
$673$	−34.5899	−	19.9705i	−1.33334	−	0.769807i	−0.985811	+	0.167861i	$0.946314\pi$
$674$	−19.2255	+	16.1322i	−0.740540	+	0.621387i
$675$		0			0
$676$	−0.938930	+	1.62627i	−0.0361127	+	0.0625490i
$677$	−12.6270	+	7.29022i	−0.485296	+	0.280186i	−0.722621	−	0.691245i	$-0.757063\pi$
$677$	−12.6270	+	7.29022i	−0.485296	+	0.280186i	0.237325	+	0.971430i	$0.423729\pi$
$678$	0.883619	−	2.42772i	0.0339352	−	0.0932361i
$679$	−5.13477	+	29.1207i	−0.197054	+	1.11755i
$680$		0			0
$681$	7.48897	−	2.72576i	0.286978	−	0.104451i
$682$	28.3126	−	33.7417i	1.08415	−	1.29204i
$683$		−	26.6159i		−	1.01843i	−0.860640	−	0.509214i	$-0.829936\pi$
$683$		−	26.6159i		−	1.01843i	0.860640	−	0.509214i	$-0.170064\pi$
$684$	9.28494	+	7.00078i	0.355018	+	0.267681i
$685$		0			0
$686$	35.9961	+	30.2043i	1.37434	+	1.15321i
$687$	3.07056	+	8.43628i	0.117149	+	0.321864i
$688$	−1.45618	+	0.256764i	−0.0555163	+	0.00978902i
$689$	−1.20563	+	6.83749i	−0.0459310	+	0.260488i
$690$		0			0
$691$	−18.6248	−	32.2591i	−0.708521	−	1.22719i	−0.965406	−	0.260752i	$-0.916029\pi$
$691$	−18.6248	−	32.2591i	−0.708521	−	1.22719i	0.256885	−	0.966442i	$-0.417304\pi$
$692$	−4.46743	−	2.57927i	−0.169826	−	0.0980492i
$693$	−44.7839	−	53.3714i	−1.70120	−	2.02741i
$694$	17.4302	−	14.6257i	0.661642	−	0.555183i
$695$		0			0
$696$	−1.04727	−	1.81393i	−0.0396968	−	0.0687569i
$697$	0.915115	−	2.51426i	0.0346625	−	0.0952344i
$698$	−12.9638	−	2.28587i	−0.490688	−	0.0865215i
$699$	1.52552	+	8.65165i	0.0577004	+	0.327235i
$700$		0			0
$701$	−30.3425	−	25.4604i	−1.14602	−	0.961626i	−0.146402	−	0.989225i	$-0.546769\pi$
$701$	−30.3425	−	25.4604i	−1.14602	−	0.961626i	−0.999619	+	0.0275989i	$0.991214\pi$
$702$			12.6012i			0.475603i
$703$	−2.37332	−	45.5295i	−0.0895114	−	1.71718i
$704$	5.36907			0.202354
$705$		0			0
$706$	−11.5635	+	4.20877i	−0.435198	+	0.158399i
$707$	−6.01505	+	1.06062i	−0.226219	+	0.0398886i
$708$	−4.15810	−	0.733185i	−0.156271	−	0.0275548i
$709$	−34.4453	−	12.5371i	−1.29362	−	0.470839i	−0.398707	−	0.917079i	$-0.630541\pi$
$709$	−34.4453	−	12.5371i	−1.29362	−	0.470839i	−0.894914	+	0.446239i	$0.852763\pi$
$710$		0			0
$711$	−22.1850	+	38.4256i	−0.832003	+	1.44107i
$712$	6.17623	+	7.36055i	0.231464	+	0.275848i
$713$	28.1536	+	33.5521i	1.05436	+	1.25654i
$714$	1.96557	−	3.40447i	0.0735597	−	0.127409i
$715$		0			0
$716$	−7.69017	−	2.79899i	−0.287395	−	0.104603i
$717$	−9.54983	−	1.68389i	−0.356645	−	0.0628861i
$718$	12.3704	−	2.18123i	0.461658	−	0.0814028i
$719$	10.3333	−	3.76101i	0.385367	−	0.140262i	−0.142069	−	0.989857i	$-0.545376\pi$
$719$	10.3333	−	3.76101i	0.385367	−	0.140262i	0.527436	+	0.849595i	$0.323153\pi$
$720$		0			0
$721$	−35.8347			−1.33455
$722$	−10.6335	+	15.7458i	−0.395737	+	0.585997i
$723$		−	5.24936i		−	0.195226i
$724$	2.62934	+	2.20628i	0.0977187	+	0.0819957i
$725$		0			0
$726$	−1.78434	−	10.1195i	−0.0662232	−	0.375570i
$727$	−44.7236	−	7.88597i	−1.65871	−	0.292475i	−0.735714	−	0.677293i	$-0.763153\pi$
$727$	−44.7236	−	7.88597i	−1.65871	−	0.292475i	−0.922992	+	0.384818i	$0.874264\pi$
$728$	−6.41700	+	17.6306i	−0.237830	+	0.653432i
$729$	−5.33885	−	9.24717i	−0.197735	−	0.342488i
$730$		0			0
$731$	1.58816	−	1.33262i	0.0587402	−	0.0492889i
$732$	−3.00670	−	3.58325i	−0.111131	−	0.132441i
$733$	23.4118	+	13.5168i	0.864735	+	0.499255i	0.865595	−	0.500744i	$-0.166940\pi$
$733$	23.4118	+	13.5168i	0.864735	+	0.499255i	−0.000859816		1.00000i	$0.500274\pi$
$734$	−1.34225	−	2.32485i	−0.0495435	−	0.0858119i
$735$		0			0
$736$	−0.927092	+	5.25780i	−0.0341731	+	0.193805i
$737$	−44.6524	+	7.87342i	−1.64479	+	0.290021i
$738$	1.74118	+	4.78386i	0.0640938	+	0.176096i
$739$	0.964167	+	0.809032i	0.0354675	+	0.0297607i	0.660349	−	0.750959i	$-0.270408\pi$
$739$	0.964167	+	0.809032i	0.0354675	+	0.0297607i	−0.624882	+	0.780720i	$0.714853\pi$
$740$		0			0
$741$	−9.67809	+	0.504490i	−0.355534	+	0.0185329i
$742$			8.75559i			0.321428i
$743$	−33.5678	+	40.0045i	−1.23148	+	1.46762i	−0.395867	+	0.918308i	$0.629556\pi$
$743$	−33.5678	+	40.0045i	−1.23148	+	1.46762i	−0.835615	+	0.549315i	$0.814889\pi$
$744$	−4.44356	+	1.61733i	−0.162909	+	0.0592940i
$745$		0			0
$746$	3.21985	−	18.2607i	0.117887	−	0.668571i
$747$	13.1945	−	36.2517i	0.482763	−	1.32638i
$748$	−6.51938	+	3.76397i	−0.238372	+	0.137624i
$749$	21.2341	−	36.7785i	0.775876	−	1.34386i
$750$		0			0
$751$	0.810409	−	0.680014i	0.0295723	−	0.0248141i	−0.627882	−	0.778309i	$-0.716078\pi$
$751$	0.810409	−	0.680014i	0.0295723	−	0.0248141i	0.657454	+	0.753495i	$0.271633\pi$
$752$	−2.70227	−	1.56016i	−0.0985417	−	0.0568931i
$753$	8.38920	−	4.84351i	0.305720	−	0.176507i
$754$	−13.1709	−	4.79381i	−0.479655	−	0.174580i
$755$		0			0
$756$	2.75945	+	15.6496i	0.100360	+	0.569172i
$757$	0.632944	+	1.73900i	0.0230047	+	0.0632050i	0.950663	−	0.310224i	$-0.100404\pi$
$757$	0.632944	+	1.73900i	0.0230047	+	0.0632050i	−0.927659	+	0.373429i	$0.878182\pi$
$758$	7.44703	−	8.87503i	0.270488	−	0.322355i
$759$	16.5228			0.599739
$760$		0			0
$761$	−31.8442			−1.15435			−0.577176	−	0.816620i	$-0.695845\pi$
$761$	−31.8442			−1.15435			−0.577176	+	0.816620i	$0.695845\pi$
$762$	0.0515686	−	0.0614570i	0.00186813	−	0.00222635i
$763$	13.5252	+	37.1601i	0.489644	+	1.34529i
$764$	−0.655668	−	3.71848i	−0.0237212	−	0.134530i
$765$		0			0
$766$	27.3254	+	9.94564i	0.987308	+	0.359351i
$767$	−24.4688	+	14.1271i	−0.883517	+	0.510099i
$768$	−0.499186	−	0.288205i	−0.0180128	−	0.0103997i
$769$	−0.0929228	+	0.0779715i	−0.00335088	+	0.00281172i	−0.644462	−	0.764637i	$-0.722918\pi$
$769$	−0.0929228	+	0.0779715i	−0.00335088	+	0.00281172i	0.641111	+	0.767448i	$0.278474\pi$
$770$		0			0
$771$	2.85245	−	4.94059i	0.102728	−	0.177931i
$772$	−10.5463	+	6.08894i	−0.379571	+	0.219146i
$773$	−11.9131	+	32.7308i	−0.428483	+	1.17725i	0.518251	+	0.855229i	$0.326583\pi$
$773$	−11.9131	+	32.7308i	−0.428483	+	1.17725i	−0.946734	+	0.322018i	$0.895639\pi$
$774$	−0.684981	+	3.88472i	−0.0246211	+	0.139633i
$775$		0			0
$776$	−5.71250	+	2.07918i	−0.205067	+	0.0746382i
$777$	18.8502	−	22.4648i	0.676246	−	0.805919i
$778$		−	29.7821i		−	1.06774i
$779$	−7.65776	+	3.24800i	−0.274368	+	0.116372i
$780$		0			0
$781$	−24.7863	−	20.7982i	−0.886923	−	0.744217i
$782$	−2.56024	−	7.03421i	−0.0915541	−	0.251543i
$783$	−

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.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.642788 + 0.766044i) q^{2} +(-0.197144 - 0.541649i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.541649 + 0.197144i) q^{6} +(4.21251 - 2.43209i) q^{7} +(0.866025 + 0.500000i) q^{8} +(2.04362 - 1.71480i) q^{9} +O(q^{10})\)	\(q+(-0.642788 + 0.766044i) q^{2} +(-0.197144 - 0.541649i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.541649 + 0.197144i) q^{6} +(4.21251 - 2.43209i) q^{7} +(0.866025 + 0.500000i) q^{8} +(2.04362 - 1.71480i) q^{9} +(2.68454 - 4.64975i) q^{11} +(-0.499186 + 0.288205i) q^{12} +(-1.31923 + 3.62457i) q^{13} +(-0.844657 + 4.79029i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(0.901248 - 1.07407i) q^{17} +2.66775i q^{18} +(-4.35299 + 0.226908i) q^{19} +(-2.14781 - 1.80223i) q^{21} +(1.83633 + 5.04528i) q^{22} +(-5.25780 + 0.927092i) q^{23} +(0.100093 - 0.567654i) q^{24} +(-1.92859 - 3.34042i) q^{26} +(-2.82926 - 1.63348i) q^{27} +(-3.12664 - 3.72618i) q^{28} +(2.78364 - 2.33575i) q^{29} +(-4.10189 - 7.10468i) q^{31} +(0.342020 - 0.939693i) q^{32} +(-3.04777 - 0.537405i) q^{33} +(0.243471 + 1.38079i) q^{34} +(-2.04362 - 1.71480i) q^{36} +10.4594i q^{37} +(2.62423 - 3.48044i) q^{38} +2.22332 q^{39} +(1.79322 - 0.652678i) q^{41} +(2.76117 - 0.486869i) q^{42} +(1.45618 + 0.256764i) q^{43} +(-5.04528 - 1.83633i) q^{44} +(2.66945 - 4.62363i) q^{46} +(2.00570 + 2.39030i) q^{47} +(0.370510 + 0.441556i) q^{48} +(8.33016 - 14.4283i) q^{49} +(-0.759442 - 0.276414i) q^{51} +(3.79858 + 0.669793i) q^{52} +(1.77266 - 0.312568i) q^{53} +(3.06993 - 1.11736i) q^{54} +4.86419 q^{56} +(0.981070 + 2.31306i) q^{57} +3.63378i q^{58} +(5.61133 + 4.70846i) q^{59} +(1.40916 + 7.99176i) q^{61} +(8.07914 + 1.42457i) q^{62} +(4.43820 - 12.1939i) q^{63} +(0.500000 + 0.866025i) q^{64} +(2.37075 - 1.98929i) q^{66} +(-5.42827 - 6.46916i) q^{67} +(-1.21425 - 0.701047i) q^{68} +(1.53870 + 2.66511i) q^{69} +(1.04647 - 5.93485i) q^{71} +(2.62722 - 0.463250i) q^{72} +(0.436515 + 1.19931i) q^{73} +(-8.01234 - 6.72316i) q^{74} +(0.979350 + 4.24746i) q^{76} -26.1162i q^{77} +(-1.42912 + 1.70316i) q^{78} +(-15.6290 + 5.68848i) q^{79} +(1.06275 - 6.02717i) q^{81} +(-0.652678 + 1.79322i) q^{82} +(12.5236 - 7.23049i) q^{83} +(-1.40188 + 2.42814i) q^{84} +(-1.13271 + 0.950453i) q^{86} +(-1.81393 - 1.04727i) q^{87} +(4.64975 - 2.68454i) q^{88} +(9.02905 + 3.28630i) q^{89} +(3.25800 + 18.4770i) q^{91} +(1.82601 + 5.01693i) q^{92} +(-3.03958 + 3.62243i) q^{93} -3.12031 q^{94} -0.576411 q^{96} +(-3.90758 + 4.65687i) q^{97} +(5.69817 + 15.6556i) q^{98} +(-2.48722 - 14.1057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36q + 36q^{9} + O(q^{10}) \)	\( 36q + 36q^{9} - 24q^{11} - 12q^{14} + 24q^{21} - 18q^{26} + 12q^{29} - 12q^{31} - 36q^{34} - 36q^{36} - 96q^{39} - 42q^{41} - 6q^{44} + 36q^{46} + 78q^{49} + 84q^{51} + 108q^{54} + 60q^{59} + 96q^{61} + 18q^{64} + 48q^{66} + 60q^{69} + 60q^{71} + 6q^{74} - 42q^{76} - 60q^{79} + 36q^{81} - 12q^{84} + 72q^{86} - 60q^{89} - 120q^{91} - 12q^{94} - 342q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

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Groups

Properties

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