LMFDB - Embedded newform 605.2.e.b.483.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,2,Mod(362,605)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("605.362"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.e (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			483.14
Character	$\chi$	$=$	605.483
Dual form			605.2.e.b.362.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.07485 + 1.07485i) q^{2} +(0.563723 + 0.563723i) q^{3} +0.310591i q^{4} +(2.23083 - 0.152980i) q^{5} +1.21183i q^{6} +(-0.135390 - 0.135390i) q^{7} +(1.81586 - 1.81586i) q^{8} -2.36443i q^{9} +(2.56223 + 2.23337i) q^{10} +(-0.175087 + 0.175087i) q^{12} +(-2.18892 + 2.18892i) q^{13} -0.291048i q^{14} +(1.34381 + 1.17133i) q^{15} +4.52471 q^{16} +(2.62090 + 2.62090i) q^{17} +(2.54140 - 2.54140i) q^{18} +0.743791 q^{19} +(0.0475140 + 0.692874i) q^{20} -0.152646i q^{21} +(-1.14886 - 1.14886i) q^{23} +2.04728 q^{24} +(4.95319 - 0.682543i) q^{25} -4.70551 q^{26} +(3.02406 - 3.02406i) q^{27} +(0.0420510 - 0.0420510i) q^{28} -9.54720 q^{29} +(0.185386 + 2.70339i) q^{30} +0.350920 q^{31} +(1.23166 + 1.23166i) q^{32} +5.63413i q^{34} +(-0.322745 - 0.281321i) q^{35} +0.734370 q^{36} +(-3.82216 + 3.82216i) q^{37} +(0.799462 + 0.799462i) q^{38} -2.46789 q^{39} +(3.77307 - 4.32865i) q^{40} +6.69597i q^{41} +(0.164071 - 0.164071i) q^{42} +(-3.72708 + 3.72708i) q^{43} +(-0.361710 - 5.27464i) q^{45} -2.46969i q^{46} +(-8.74273 + 8.74273i) q^{47} +(2.55069 + 2.55069i) q^{48} -6.96334i q^{49} +(6.05755 + 4.59030i) q^{50} +2.95493i q^{51} +(-0.679858 - 0.679858i) q^{52} +(6.38540 + 6.38540i) q^{53} +6.50079 q^{54} -0.491699 q^{56} +(0.419293 + 0.419293i) q^{57} +(-10.2618 - 10.2618i) q^{58} -9.62609i q^{59} +(-0.363805 + 0.417374i) q^{60} +5.89303i q^{61} +(0.377185 + 0.377185i) q^{62} +(-0.320122 + 0.320122i) q^{63} -6.40173i q^{64} +(-4.54825 + 5.21797i) q^{65} +(4.13426 - 4.13426i) q^{67} +(-0.814027 + 0.814027i) q^{68} -1.29528i q^{69} +(-0.0445244 - 0.649278i) q^{70} -11.4617 q^{71} +(-4.29347 - 4.29347i) q^{72} +(1.69838 - 1.69838i) q^{73} -8.21648 q^{74} +(3.17700 + 2.40747i) q^{75} +0.231015i q^{76} +(-2.65261 - 2.65261i) q^{78} -0.670485 q^{79} +(10.0939 - 0.692189i) q^{80} -3.68383 q^{81} +(-7.19714 + 7.19714i) q^{82} +(11.7967 - 11.7967i) q^{83} +0.0474103 q^{84} +(6.24773 + 5.44584i) q^{85} -8.01208 q^{86} +(-5.38198 - 5.38198i) q^{87} +7.92190i q^{89} +(5.28065 - 6.05821i) q^{90} +0.592718 q^{91} +(0.356824 - 0.356824i) q^{92} +(0.197822 + 0.197822i) q^{93} -18.7942 q^{94} +(1.65927 - 0.113785i) q^{95} +1.38863i q^{96} +(0.975091 - 0.975091i) q^{97} +(7.48452 - 7.48452i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{3} + 8 q^{5} + 12 q^{12} - 36 q^{15} - 8 q^{16} - 64 q^{20} - 24 q^{23} + 16 q^{25} - 16 q^{27} - 8 q^{31} + 24 q^{36} + 32 q^{37} - 40 q^{38} + 60 q^{42} - 28 q^{45} - 28 q^{47} + 56 q^{48}+ \cdots + 92 q^{97}+O(q^{100}) $ 32 * q - 4 * q^3 + 8 * q^5 + 12 * q^12 - 36 * q^15 - 8 * q^16 - 64 * q^20 - 24 * q^23 + 16 * q^25 - 16 * q^27 - 8 * q^31 + 24 * q^36 + 32 * q^37 - 40 * q^38 + 60 * q^42 - 28 * q^45 - 28 * q^47 + 56 * q^48 + 116 * q^53 - 80 * q^56 - 80 * q^58 + 104 * q^60 - 8 * q^67 - 80 * q^70 + 24 * q^71 - 76 * q^75 + 60 * q^78 + 8 * q^80 + 8 * q^81 - 20 * q^82 - 40 * q^86 + 80 * q^91 + 52 * q^92 + 32 * q^93 + 92 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	1.07485	+	1.07485i	0.760031	+	0.760031i	0.976328	−	0.216296i	$-0.0693978\pi$
$2$	1.07485	+	1.07485i	0.760031	+	0.760031i	−0.216296	+	0.976328i	$0.569398\pi$
$3$	0.563723	+	0.563723i	0.325466	+	0.325466i	0.850859	−	0.525394i	$-0.176082\pi$
$3$	0.563723	+	0.563723i	0.325466	+	0.325466i	−0.525394	+	0.850859i	$0.676082\pi$
$4$			0.310591i			0.155295i
$5$	2.23083	−	0.152980i	0.997657	−	0.0684146i
$5$	2.23083	−	0.152980i	0.997657	−	0.0684146i
$6$			1.21183i			0.494728i
$7$	−0.135390	−	0.135390i	−0.0511728	−	0.0511728i	0.681057	−	0.732230i	$-0.261520\pi$
$7$	−0.135390	−	0.135390i	−0.0511728	−	0.0511728i	−0.732230	+	0.681057i	$0.761520\pi$
$8$	1.81586	−	1.81586i	0.642002	−	0.642002i
$9$		−	2.36443i		−	0.788144i
$10$	2.56223	+	2.23337i	0.810248	+	0.706253i
$11$		0			0
$11$		0			0
$12$	−0.175087	+	0.175087i	−0.0505433	+	0.0505433i
$13$	−2.18892	+	2.18892i	−0.607098	+	0.607098i	−0.942186	−	0.335089i	$-0.891234\pi$
$13$	−2.18892	+	2.18892i	−0.607098	+	0.607098i	0.335089	+	0.942186i	$0.391234\pi$
$14$		−	0.291048i		−	0.0777859i
$15$	1.34381	+	1.17133i	0.346970	+	0.302437i
$16$	4.52471			1.13118
$17$	2.62090	+	2.62090i	0.635662	+	0.635662i	0.949482	−	0.313820i	$-0.101609\pi$
$17$	2.62090	+	2.62090i	0.635662	+	0.635662i	−0.313820	+	0.949482i	$0.601609\pi$
$18$	2.54140	−	2.54140i	0.599014	−	0.599014i
$19$	0.743791			0.170637			0.0853187	−	0.996354i	$-0.472809\pi$
$19$	0.743791			0.170637			0.0853187	+	0.996354i	$0.472809\pi$
$20$	0.0475140	+	0.692874i	0.0106245	+	0.154931i
$21$		−	0.152646i		−	0.0333100i
$22$		0			0
$23$	−1.14886	−	1.14886i	−0.239553	−	0.239553i	0.577112	−	0.816665i	$-0.304180\pi$
$23$	−1.14886	−	1.14886i	−0.239553	−	0.239553i	−0.816665	+	0.577112i	$0.804180\pi$
$24$	2.04728			0.417899
$25$	4.95319	−	0.682543i	0.990639	−	0.136509i
$26$	−4.70551			−0.922826
$27$	3.02406	−	3.02406i	0.581980	−	0.581980i
$28$	0.0420510	−	0.0420510i	0.00794689	−	0.00794689i
$29$	−9.54720			−1.77287			−0.886436	−	0.462852i	$-0.846826\pi$
$29$	−9.54720			−1.77287			−0.886436	+	0.462852i	$0.846826\pi$
$30$	0.185386	+	2.70339i	0.0338466	+	0.493569i
$31$	0.350920			0.0630271			0.0315136	−	0.999503i	$-0.489967\pi$
$31$	0.350920			0.0630271			0.0315136	+	0.999503i	$0.489967\pi$
$32$	1.23166	+	1.23166i	0.217729	+	0.217729i
$33$		0			0
$34$			5.63413i			0.966246i
$35$	−0.322745	−	0.281321i	−0.0545539	−	0.0475519i
$36$	0.734370			0.122395
$37$	−3.82216	+	3.82216i	−0.628360	+	0.628360i	−0.947655	−	0.319295i	$-0.896554\pi$
$37$	−3.82216	+	3.82216i	−0.628360	+	0.628360i	0.319295	+	0.947655i	$0.396554\pi$
$38$	0.799462	+	0.799462i	0.129690	+	0.129690i
$39$	−2.46789			−0.395179
$40$	3.77307	−	4.32865i	0.596576	−	0.684420i
$41$			6.69597i			1.04573i	0.852414	+	0.522867i	$0.175138\pi$
$41$			6.69597i			1.04573i	−0.852414	+	0.522867i	$0.824862\pi$
$42$	0.164071	−	0.164071i	0.0253166	−	0.0253166i
$43$	−3.72708	+	3.72708i	−0.568374	+	0.568374i	−0.931673	−	0.363299i	$-0.881650\pi$
$43$	−3.72708	+	3.72708i	−0.568374	+	0.568374i	0.363299	+	0.931673i	$0.381650\pi$
$44$		0			0
$45$	−0.361710	−	5.27464i	−0.0539205	−	0.786297i
$46$		−	2.46969i		−	0.364136i
$47$	−8.74273	+	8.74273i	−1.27526	+	1.27526i	−0.331968	+	0.943291i	$0.607713\pi$
$47$	−8.74273	+	8.74273i	−1.27526	+	1.27526i	−0.943291	+	0.331968i	$0.892287\pi$
$48$	2.55069	+	2.55069i	0.368160	+	0.368160i
$49$		−	6.96334i		−	0.994763i
$50$	6.05755	+	4.59030i	0.856667	+	0.649166i
$51$			2.95493i			0.413772i
$52$	−0.679858	−	0.679858i	−0.0942794	−	0.0942794i
$53$	6.38540	+	6.38540i	0.877102	+	0.877102i	0.993234	−	0.116132i	$-0.0370495\pi$
$53$	6.38540	+	6.38540i	0.877102	+	0.877102i	−0.116132	+	0.993234i	$0.537050\pi$
$54$	6.50079			0.884646
$55$		0			0
$56$	−0.491699			−0.0657061
$57$	0.419293	+	0.419293i	0.0555367	+	0.0555367i
$58$	−10.2618	−	10.2618i	−1.34744	−	1.34744i
$59$		−	9.62609i		−	1.25321i	−0.779337	−	0.626605i	$-0.784444\pi$
$59$		−	9.62609i		−	1.25321i	0.779337	−	0.626605i	$-0.215556\pi$
$60$	−0.363805	+	0.417374i	−0.0469670	+	0.0538828i
$61$			5.89303i			0.754525i	0.926106	+	0.377262i	$0.123134\pi$
$61$			5.89303i			0.754525i	−0.926106	+	0.377262i	$0.876866\pi$
$62$	0.377185	+	0.377185i	0.0479026	+	0.0479026i
$63$	−0.320122	+	0.320122i	−0.0403315	+	0.0403315i
$64$		−	6.40173i		−	0.800217i
$65$	−4.54825	+	5.21797i	−0.564141	+	0.647209i
$66$		0			0
$67$	4.13426	−	4.13426i	0.505081	−	0.505081i	−0.407932	−	0.913012i	$-0.633750\pi$
$67$	4.13426	−	4.13426i	0.505081	−	0.505081i	0.913012	+	0.407932i	$0.133750\pi$
$68$	−0.814027	+	0.814027i	−0.0987153	+	0.0987153i
$69$		−	1.29528i		−	0.155933i
$70$	−0.0445244	−	0.649278i	−0.00532169	−	0.0776036i
$71$	−11.4617			−1.36025			−0.680127	−	0.733094i	$-0.738075\pi$
$71$	−11.4617			−1.36025			−0.680127	+	0.733094i	$0.738075\pi$
$72$	−4.29347	−	4.29347i	−0.505990	−	0.505990i
$73$	1.69838	−	1.69838i	0.198780	−	0.198780i	−0.600697	−	0.799477i	$-0.705110\pi$
$73$	1.69838	−	1.69838i	0.198780	−	0.198780i	0.799477	+	0.600697i	$0.205110\pi$
$74$	−8.21648			−0.955146
$75$	3.17700	+	2.40747i	0.366848	+	0.277990i
$76$			0.231015i			0.0264992i
$77$		0			0
$78$	−2.65261	−	2.65261i	−0.300348	−	0.300348i
$79$	−0.670485			−0.0754355			−0.0377177	−	0.999288i	$-0.512009\pi$
$79$	−0.670485			−0.0754355			−0.0377177	+	0.999288i	$0.512009\pi$
$80$	10.0939	−	0.692189i	1.12853	−	0.0773891i
$81$	−3.68383			−0.409315
$82$	−7.19714	+	7.19714i	−0.794791	+	0.794791i
$83$	11.7967	−	11.7967i	1.29485	−	1.29485i	0.363106	−	0.931748i	$-0.381716\pi$
$83$	11.7967	−	11.7967i	1.29485	−	1.29485i	0.931748	−	0.363106i	$-0.118284\pi$
$84$	0.0474103			0.00517289
$85$	6.24773	+	5.44584i	0.677661	+	0.590684i
$86$	−8.01208			−0.863964
$87$	−5.38198	−	5.38198i	−0.577009	−	0.577009i
$88$		0			0
$89$			7.92190i			0.839720i	0.907589	+	0.419860i	$0.137921\pi$
$89$			7.92190i			0.839720i	−0.907589	+	0.419860i	$0.862079\pi$
$90$	5.28065	−	6.05821i	0.556629	−	0.638592i
$91$	0.592718			0.0621338
$92$	0.356824	−	0.356824i	0.0372015	−	0.0372015i
$93$	0.197822	+	0.197822i	0.0205132	+	0.0205132i
$94$	−18.7942			−1.93847
$95$	1.65927	−	0.113785i	0.170238	−	0.0116741i
$96$			1.38863i			0.141727i
$97$	0.975091	−	0.975091i	0.0990055	−	0.0990055i	−0.655869	−	0.754875i	$-0.727698\pi$
$97$	0.975091	−	0.975091i	0.0990055	−	0.0990055i	0.754875	+	0.655869i	$0.227698\pi$
$98$	7.48452	−	7.48452i	0.756051	−	0.756051i
$99$		0			0
$100$	0.211991	+	1.53842i	0.0211991	+	0.153842i
$101$		−	4.82544i		−	0.480150i	−0.970754	−	0.240075i	$-0.922828\pi$
$101$		−	4.82544i		−	0.480150i	0.970754	−	0.240075i	$-0.0771720\pi$
$102$	−3.17609	+	3.17609i	−0.314480	+	0.314480i
$103$	2.28914	+	2.28914i	0.225556	+	0.225556i	0.810833	−	0.585277i	$-0.199014\pi$
$103$	2.28914	+	2.28914i	0.225556	+	0.225556i	−0.585277	+	0.810833i	$0.699014\pi$
$104$			7.94953i			0.779516i
$105$	−0.0233517	−	0.340526i	−0.00227889	−	0.0332319i
$106$			13.7266i			1.33325i
$107$	−7.81744	−	7.81744i	−0.755741	−	0.755741i	0.219803	−	0.975544i	$-0.429458\pi$
$107$	−7.81744	−	7.81744i	−0.755741	−	0.755741i	−0.975544	+	0.219803i	$0.929458\pi$
$108$	0.939243	+	0.939243i	0.0903787	+	0.0903787i
$109$	−9.54212			−0.913969			−0.456985	−	0.889475i	$-0.651071\pi$
$109$	−9.54212			−0.913969			−0.456985	+	0.889475i	$0.651071\pi$
$110$		0			0
$111$	−4.30929			−0.409019
$112$	−0.612603	−	0.612603i	−0.0578856	−	0.0578856i
$113$	2.93286	+	2.93286i	0.275900	+	0.275900i	0.831470	−	0.555570i	$-0.187500\pi$
$113$	2.93286	+	2.93286i	0.275900	+	0.275900i	−0.555570	+	0.831470i	$0.687500\pi$
$114$			0.901350i			0.0844192i
$115$	−2.73866	−	2.38715i	−0.255381	−	0.222603i
$116$		−	2.96527i		−	0.275319i
$117$	5.17556	+	5.17556i	0.478480	+	0.478480i
$118$	10.3466	−	10.3466i	0.952479	−	0.952479i
$119$		−	0.709690i		−	0.0650572i
$120$	4.56713	−	0.313192i	0.416920	−	0.0285904i
$121$		0			0
$122$	−6.33410	+	6.33410i	−0.573462	+	0.573462i
$123$	−3.77467	+	3.77467i	−0.340351	+	0.340351i
$124$			0.108993i			0.00978782i
$125$	10.9453	−	2.28037i	0.978979	−	0.203963i
$126$	−0.688163			−0.0613065
$127$	−10.3006	−	10.3006i	−0.914027	−	0.914027i	0.0825589	−	0.996586i	$-0.473691\pi$
$127$	−10.3006	−	10.3006i	−0.914027	−	0.914027i	−0.996586	+	0.0825589i	$0.973691\pi$
$128$	9.34421	−	9.34421i	0.825919	−	0.825919i
$129$	−4.20208			−0.369973
$130$	−10.4972	+	0.719847i	−0.920664	+	0.0631348i
$131$		−	9.76926i		−	0.853544i	−0.904359	−	0.426772i	$-0.859651\pi$
$131$		−	9.76926i		−	0.853544i	0.904359	−	0.426772i	$-0.140349\pi$
$132$		0			0
$133$	−0.100702	−	0.100702i	−0.00873200	−	0.00873200i
$134$	8.88740			0.767754
$135$	6.28353	−	7.20877i	0.540800	−	0.620432i
$136$	9.51836			0.816193
$137$	−3.06186	+	3.06186i	−0.261592	+	0.261592i	−0.825701	−	0.564109i	$-0.809220\pi$
$137$	−3.06186	+	3.06186i	−0.261592	+	0.261592i	0.564109	+	0.825701i	$0.309220\pi$
$138$	1.39222	−	1.39222i	0.118514	−	0.118514i
$139$	−10.5105			−0.891493			−0.445747	−	0.895159i	$-0.647062\pi$
$139$	−10.5105			−0.891493			−0.445747	+	0.895159i	$0.647062\pi$
$140$	0.0873757	−	0.100242i	0.00738459	−	0.00847196i
$141$	−9.85696			−0.830106
$142$	−12.3196	−	12.3196i	−1.03384	−	1.03384i
$143$		0			0
$144$		−	10.6984i		−	0.891532i
$145$	−21.2982	+	1.46053i	−1.76872	+	0.121290i
$146$	3.65099			0.302158
$147$	3.92540	−	3.92540i	0.323761	−	0.323761i
$148$	−1.18713	−	1.18713i	−0.0975813	−	0.0975813i
$149$	5.76241			0.472075			0.236038	−	0.971744i	$-0.424151\pi$
$149$	5.76241			0.472075			0.236038	+	0.971744i	$0.424151\pi$
$150$	0.827127	+	6.00244i	0.0675347	+	0.490097i
$151$		−	14.9642i		−	1.21777i	−0.793259	−	0.608885i	$-0.791617\pi$
$151$		−	14.9642i		−	1.21777i	0.793259	−	0.608885i	$-0.208383\pi$
$152$	1.35062	−	1.35062i	0.109550	−	0.109550i
$153$	6.19694	−	6.19694i	0.500993	−	0.500993i
$154$		0			0
$155$	0.782843	−	0.0536836i	0.0628795	−	0.00431197i
$156$		−	0.766504i		−	0.0613694i
$157$	3.49885	−	3.49885i	0.279239	−	0.279239i	−0.553566	−	0.832805i	$-0.686733\pi$
$157$	3.49885	−	3.49885i	0.279239	−	0.279239i	0.832805	+	0.553566i	$0.186733\pi$
$158$	−0.720669	−	0.720669i	−0.0573333	−	0.0573333i
$159$			7.19920i			0.570933i
$160$	2.93605	+	2.55921i	0.232115	+	0.202323i
$161$			0.311089i			0.0245172i
$162$	−3.95956	−	3.95956i	−0.311092	−	0.311092i
$163$	7.08286	+	7.08286i	0.554772	+	0.554772i	0.927814	−	0.373042i	$-0.121685\pi$
$163$	7.08286	+	7.08286i	0.554772	+	0.554772i	−0.373042	+	0.927814i	$0.621685\pi$
$164$	−2.07970			−0.162398
$165$		0			0
$166$	25.3592			1.96826
$167$	8.52930	+	8.52930i	0.660017	+	0.660017i	0.955384	−	0.295367i	$-0.0954419\pi$
$167$	8.52930	+	8.52930i	0.660017	+	0.660017i	−0.295367	+	0.955384i	$0.595442\pi$
$168$	−0.277182	−	0.277182i	−0.0213851	−	0.0213851i
$169$			3.41725i			0.262865i
$170$	0.861908	+	12.5688i	0.0661053	+	0.963982i
$171$		−	1.75864i		−	0.134487i
$172$	−1.15760	−	1.15760i	−0.0882658	−	0.0882658i
$173$	8.81415	−	8.81415i	0.670127	−	0.670127i	−0.287618	−	0.957745i	$-0.592863\pi$
$173$	8.81415	−	8.81415i	0.670127	−	0.670127i	0.957745	+	0.287618i	$0.0928634\pi$
$174$		−	11.5696i		−	0.877090i
$175$	−0.763025	−	0.578206i	−0.0576793	−	0.0437082i
$176$		0			0
$177$	5.42645	−	5.42645i	0.407877	−	0.407877i
$178$	−8.51483	+	8.51483i	−0.638214	+	0.638214i
$179$			20.1785i			1.50822i	0.656751	+	0.754108i	$0.271930\pi$
$179$			20.1785i			1.50822i	−0.656751	+	0.754108i	$0.728070\pi$
$180$	1.63825	−	0.112344i	0.122108	−	0.00837361i
$181$	4.60973			0.342638			0.171319	−	0.985216i	$-0.445197\pi$
$181$	4.60973			0.342638			0.171319	+	0.985216i	$0.445197\pi$
$182$	0.637081	+	0.637081i	0.0472236	+	0.0472236i
$183$	−3.32204	+	3.32204i	−0.245572	+	0.245572i
$184$	−4.17232			−0.307587
$185$	−7.94188	+	9.11131i	−0.583899	+	0.669877i
$186$			0.425256i			0.0311813i
$187$		0			0
$188$	−2.71541	−	2.71541i	−0.198042	−	0.198042i
$189$	−0.818857			−0.0595631
$190$	1.90576	+	1.66116i	0.138259	+	0.120513i
$191$	6.32630			0.457755			0.228877	−	0.973455i	$-0.426495\pi$
$191$	6.32630			0.457755			0.228877	+	0.973455i	$0.426495\pi$
$192$	3.60881	−	3.60881i	0.260443	−	0.260443i
$193$	4.19447	−	4.19447i	0.301925	−	0.301925i	−0.539842	−	0.841767i	$-0.681516\pi$
$193$	4.19447	−	4.19447i	0.301925	−	0.301925i	0.841767	+	0.539842i	$0.181516\pi$
$194$	2.09615			0.150495
$195$	−5.50545	+	0.377537i	−0.394253	+	0.0270360i
$196$	2.16275			0.154482
$197$	9.90515	+	9.90515i	0.705713	+	0.705713i	0.965631	−	0.259918i	$-0.0836955\pi$
$197$	9.90515	+	9.90515i	0.705713	+	0.705713i	−0.259918	+	0.965631i	$0.583696\pi$
$198$		0			0
$199$			13.3828i			0.948680i	0.880342	+	0.474340i	$0.157313\pi$
$199$			13.3828i			0.948680i	−0.880342	+	0.474340i	$0.842687\pi$
$200$	7.75489	−	10.2337i	0.548353	−	0.723631i
$201$	4.66116			0.328773
$202$	5.18661	−	5.18661i	0.364929	−	0.364929i
$203$	1.29260	+	1.29260i	0.0907228	+	0.0907228i
$204$	−0.917772			−0.0642569
$205$	1.02435	+	14.9376i	0.0715435	+	1.04328i
$206$			4.92095i			0.342859i
$207$	−2.71639	+	2.71639i	−0.188802	+	0.188802i
$208$	−9.90424	+	9.90424i	−0.686736	+	0.686736i
$209$		0			0
$210$	0.340914	−	0.391113i	0.0235253	−	0.0269893i
$211$			5.93238i			0.408402i	0.978929	+	0.204201i	$0.0654596\pi$
$211$			5.93238i			0.408402i	−0.978929	+	0.204201i	$0.934540\pi$
$212$	−1.98324	+	1.98324i	−0.136210	+	0.136210i
$213$	−6.46123	−	6.46123i	−0.442716	−	0.442716i
$214$		−	16.8051i		−	1.14877i
$215$	−7.74431	+	8.88464i	−0.528157	+	0.605928i
$216$		−	10.9825i		−	0.747264i
$217$	−0.0475113	−	0.0475113i	−0.00322527	−	0.00322527i
$218$	−10.2563	−	10.2563i	−0.694645	−	0.694645i
$219$	1.91483			0.129392
$220$		0			0
$221$	−11.4739			−0.771818
$222$	−4.63182	−	4.63182i	−0.310867	−	0.310867i
$223$	−15.0300	−	15.0300i	−1.00648	−	1.00648i	−0.999979	−	0.00650292i	$-0.997930\pi$
$223$	−15.0300	−	15.0300i	−1.00648	−	1.00648i	−0.00650292	−	0.999979i	$-0.502070\pi$
$224$		−	0.333511i		−	0.0222836i
$225$	−1.61383	−	11.7115i	−0.107588	−	0.780766i
$226$			6.30474i			0.419385i
$227$	−9.24199	−	9.24199i	−0.613412	−	0.613412i	0.330421	−	0.943834i	$-0.392809\pi$
$227$	−9.24199	−	9.24199i	−0.613412	−	0.613412i	−0.943834	+	0.330421i	$0.892809\pi$
$228$	−0.130228	+	0.130228i	−0.00862458	+	0.00862458i
$229$			16.4311i			1.08580i	0.839798	+	0.542899i	$0.182673\pi$
$229$			16.4311i			1.08580i	−0.839798	+	0.542899i	$0.817327\pi$
$230$	−0.377812	−	5.50946i	−0.0249122	−	0.363283i
$231$		0			0
$232$	−17.3363	+	17.3363i	−1.13819	+	1.13819i
$233$	11.0617	−	11.0617i	0.724676	−	0.724676i	−0.244878	−	0.969554i	$-0.578748\pi$
$233$	11.0617	−	11.0617i	0.724676	−	0.724676i	0.969554	+	0.244878i	$0.0787480\pi$
$234$			11.1259i			0.727320i
$235$	−18.1661	+	20.8410i	−1.18502	+	1.35952i
$236$	2.98977			0.194618
$237$	−0.377968	−	0.377968i	−0.0245517	−	0.0245517i
$238$	0.762808	−	0.762808i	0.0494455	−	0.0494455i
$239$	−5.28173			−0.341647			−0.170823	−	0.985302i	$-0.554643\pi$
$239$	−5.28173			−0.341647			−0.170823	+	0.985302i	$0.554643\pi$
$240$	6.08035	+	5.29994i	0.392485	+	0.342110i
$241$			16.1676i			1.04144i	0.853726	+	0.520722i	$0.174337\pi$
$241$			16.1676i			1.04144i	−0.853726	+	0.520722i	$0.825663\pi$
$242$		0			0
$243$	−11.1488	−	11.1488i	−0.715198	−	0.715198i
$244$	−1.83032			−0.117174
$245$	−1.06525	−	15.5340i	−0.0680563	−	0.992432i
$246$	−8.11439			−0.517354
$247$	−1.62810	+	1.62810i	−0.103594	+	0.103594i
$248$	0.637221	−	0.637221i	0.0404635	−	0.0404635i
$249$	13.3001			0.842861
$250$	14.2156	+	9.31348i	0.899073	+	0.589036i
$251$	19.3427			1.22090			0.610450	−	0.792055i	$-0.290989\pi$
$251$	19.3427			1.22090			0.610450	+	0.792055i	$0.290989\pi$
$252$	−0.0994268	−	0.0994268i	−0.00626330	−	0.00626330i
$253$		0			0
$254$		−	22.1431i		−	1.38938i
$255$	0.452044	+	6.59194i	0.0283081	+	0.412803i
$256$	7.28371			0.455232
$257$	−3.32773	+	3.32773i	−0.207578	+	0.207578i	−0.803237	−	0.595659i	$-0.796891\pi$
$257$	−3.32773	+	3.32773i	−0.207578	+	0.207578i	0.595659	+	0.803237i	$0.296891\pi$
$258$	−4.51659	−	4.51659i	−0.281191	−	0.281191i
$259$	1.03497			0.0643099
$260$	−1.62065	−	1.41264i	−0.100509	−	0.0876084i
$261$			22.5737i			1.39728i
$262$	10.5005	−	10.5005i	0.648720	−	0.648720i
$263$	11.2218	−	11.2218i	0.691964	−	0.691964i	−0.270700	−	0.962664i	$-0.587255\pi$
$263$	11.2218	−	11.2218i	0.691964	−	0.691964i	0.962664	+	0.270700i	$0.0872550\pi$
$264$		0			0
$265$	15.2216	+	13.2679i	0.935053	+	0.815040i
$266$		−	0.216479i		−	0.0132732i
$267$	−4.46576	+	4.46576i	−0.273300	+	0.273300i
$268$	1.28406	+	1.28406i	0.0784366	+	0.0784366i
$269$			11.3124i			0.689729i	0.938653	+	0.344864i	$0.112075\pi$
$269$			11.3124i			0.689729i	−0.938653	+	0.344864i	$0.887925\pi$
$270$	14.5022	−	0.994489i	0.882573	−	0.0605227i
$271$		−	17.8282i		−	1.08298i	−0.840706	−	0.541492i	$-0.817859\pi$
$271$		−	17.8282i		−	1.08298i	0.840706	−	0.541492i	$-0.182141\pi$
$272$	11.8588	+	11.8588i	0.719047	+	0.719047i
$273$	0.334129	+	0.334129i	0.0202224	+	0.0202224i
$274$	−6.58205			−0.397636
$275$		0			0
$276$	0.402300			0.0242156
$277$	−3.31038	−	3.31038i	−0.198901	−	0.198901i	0.600628	−	0.799529i	$-0.294917\pi$
$277$	−3.31038	−	3.31038i	−0.198901	−	0.198901i	−0.799529	+	0.600628i	$0.794917\pi$
$278$	−11.2972	−	11.2972i	−0.677563	−	0.677563i
$279$		−	0.829727i		−	0.0496744i
$280$	−1.09690	+	0.0752200i	−0.0655521	+	0.00449525i
$281$			13.1893i			0.786808i	0.919366	+	0.393404i	$0.128703\pi$
$281$			13.1893i			0.786808i	−0.919366	+	0.393404i	$0.871297\pi$
$282$	−10.5947	−	10.5947i	−0.630907	−	0.630907i
$283$	−16.1125	+	16.1125i	−0.957789	+	0.957789i	−0.999145	−	0.0413554i	$-0.986832\pi$
$283$	−16.1125	+	16.1125i	−0.957789	+	0.957789i	0.0413554	+	0.999145i	$0.486832\pi$
$284$		−	3.55990i		−	0.211241i
$285$	0.999513	+	0.871227i	0.0592061	+	0.0516070i
$286$		0			0
$287$	0.906570	−	0.906570i	0.0535131	−	0.0535131i
$288$	2.91218	−	2.91218i	0.171602	−	0.171602i
$289$		−	3.26175i		−	0.191868i
$290$	−24.4621	−	21.3224i	−1.43646	−	1.25210i
$291$	1.09936			0.0644458
$292$	0.527499	+	0.527499i	0.0308696	+	0.0308696i
$293$	−5.11078	+	5.11078i	−0.298575	+	0.298575i	−0.840456	−	0.541881i	$-0.817713\pi$
$293$	−5.11078	+	5.11078i	−0.298575	+	0.298575i	0.541881	+	0.840456i	$0.317713\pi$
$294$	8.43840			0.492137
$295$	−1.47260	−	21.4742i	−0.0857378	−	1.25027i
$296$			13.8810i			0.806817i
$297$		0			0
$298$	6.19371	+	6.19371i	0.358792	+	0.358792i
$299$	5.02952			0.290864
$300$	−0.747736	+	0.986745i	−0.0431706	+	0.0569698i
$301$	1.00922			0.0581706
$302$	16.0842	−	16.0842i	0.925543	−	0.925543i
$303$	2.72022	−	2.72022i	0.156272	−	0.156272i
$304$	3.36544			0.193021
$305$	0.901513	+	13.1463i	0.0516205	+	0.752757i
$306$	13.3215			0.761541
$307$	20.1272	+	20.1272i	1.14872	+	1.14872i	0.986804	+	0.161918i	$0.0517681\pi$
$307$	20.1272	+	20.1272i	1.14872	+	1.14872i	0.161918	+	0.986804i	$0.448232\pi$
$308$		0			0
$309$			2.58088i			0.146821i
$310$	0.899138	+	0.783734i	0.0510676	+	0.0445131i
$311$	−7.51588			−0.426187			−0.213093	−	0.977032i	$-0.568354\pi$
$311$	−7.51588			−0.426187			−0.213093	+	0.977032i	$0.568354\pi$
$312$	−4.48134	+	4.48134i	−0.253706	+	0.253706i
$313$	0.951824	+	0.951824i	0.0538003	+	0.0538003i	0.733495	−	0.679695i	$-0.237888\pi$
$313$	0.951824	+	0.951824i	0.0538003	+	0.0538003i	−0.679695	+	0.733495i	$0.737888\pi$
$314$	7.52146			0.424460
$315$	−0.665164	+	0.763109i	−0.0374778	+	0.0429963i
$316$		−	0.208246i		−	0.0117148i
$317$	8.01290	−	8.01290i	0.450049	−	0.450049i	−0.445322	−	0.895371i	$-0.646911\pi$
$317$	8.01290	−	8.01290i	0.450049	−	0.450049i	0.895371	+	0.445322i	$0.146911\pi$
$318$	−7.73803	+	7.73803i	−0.433927	+	0.433927i
$319$		0			0
$320$	−0.979335	−	14.2812i	−0.0547465	−	0.798342i
$321$		−	8.81375i		−	0.491936i
$322$	−0.334373	+	0.334373i	−0.0186339	+	0.0186339i
$323$	1.94940	+	1.94940i	0.108468	+	0.108468i
$324$		−	1.14416i		−	0.0635647i
$325$	−9.34812	+	12.3362i	−0.518540	+	0.684288i
$326$			15.2260i			0.843289i
$327$	−5.37912	−	5.37912i	−0.297466	−	0.297466i
$328$	12.1589	+	12.1589i	0.671364	+	0.671364i
$329$	2.36737			0.130517
$330$		0			0
$331$	−17.7048			−0.973145			−0.486572	−	0.873640i	$-0.661753\pi$
$331$	−17.7048			−0.973145			−0.486572	+	0.873640i	$0.661753\pi$
$332$	3.66394	+	3.66394i	0.201085	+	0.201085i
$333$	9.03725	+	9.03725i	0.495238	+	0.495238i
$334$			18.3354i			1.00327i
$335$	8.59037	−	9.85529i	0.469342	−	0.538452i
$336$		−	0.690678i		−	0.0376796i
$337$	−5.38821	−	5.38821i	−0.293515	−	0.293515i	0.544952	−	0.838467i	$-0.316548\pi$
$337$	−5.38821	−	5.38821i	−0.293515	−	0.293515i	−0.838467	+	0.544952i	$0.816548\pi$
$338$	−3.67302	+	3.67302i	−0.199786	+	0.199786i
$339$			3.30664i			0.179592i
$340$	−1.69143	+	1.94049i	−0.0917305	+	0.105238i
$341$		0			0
$342$	1.89027	−	1.89027i	0.102214	−	0.102214i
$343$	−1.89050	+	1.89050i	−0.102078	+	0.102078i
$344$			13.5357i			0.729795i
$345$	−0.198151	−	2.88954i	−0.0106681	−	0.155567i
$346$	18.9477			1.01864
$347$	6.59993	+	6.59993i	0.354303	+	0.354303i	0.861708	−	0.507405i	$-0.169395\pi$
$347$	6.59993	+	6.59993i	0.354303	+	0.354303i	−0.507405	+	0.861708i	$0.669395\pi$
$348$	1.67159	−	1.67159i	0.0896068	−	0.0896068i
$349$	1.50177			0.0803880			0.0401940	−	0.999192i	$-0.487202\pi$
$349$	1.50177			0.0803880			0.0401940	+	0.999192i	$0.487202\pi$
$350$	−0.198653	−	1.44162i	−0.0106184	−	0.0770577i
$351$			13.2388i			0.706637i
$352$		0			0
$353$	4.40229	+	4.40229i	0.234310	+	0.234310i	0.814489	−	0.580179i	$-0.197017\pi$
$353$	4.40229	+	4.40229i	0.234310	+	0.234310i	−0.580179	+	0.814489i	$0.697017\pi$
$354$	11.6652			0.619999
$355$	−25.5691	+	1.75341i	−1.35707	+	0.0930612i
$356$	−2.46047			−0.130405
$357$	0.400069	−	0.400069i	0.0211739	−	0.0211739i
$358$	−21.6888	+	21.6888i	−1.14629	+	1.14629i
$359$	26.3042			1.38828			0.694142	−	0.719838i	$-0.255784\pi$
$359$	26.3042			1.38828			0.694142	+	0.719838i	$0.255784\pi$
$360$	−10.2348	−	8.92118i	−0.539422	−	0.470187i
$361$	−18.4468			−0.970883
$362$	4.95475	+	4.95475i	0.260416	+	0.260416i
$363$		0			0
$364$			0.184093i			0.00964908i
$365$	3.52897	−	4.04860i	0.184715	−	0.211913i
$366$	−7.14136			−0.373285
$367$	5.77642	−	5.77642i	0.301527	−	0.301527i	−0.540084	−	0.841611i	$-0.681608\pi$
$367$	5.77642	−	5.77642i	0.301527	−	0.301527i	0.841611	+	0.540084i	$0.181608\pi$
$368$	−5.19825	−	5.19825i	−0.270978	−	0.270978i
$369$	15.8322			0.824189
$370$	−18.3296	+	1.25695i	−0.952908	+	0.0653459i
$371$		−	1.72904i		−	0.0897675i
$372$	−0.0614416	+	0.0614416i	−0.00318560	+	0.00318560i
$373$	6.12473	−	6.12473i	0.317126	−	0.317126i	−0.530536	−	0.847662i	$-0.678009\pi$
$373$	6.12473	−	6.12473i	0.317126	−	0.317126i	0.847662	+	0.530536i	$0.178009\pi$
$374$		0			0
$375$	7.45563	+	4.88463i	0.385007	+	0.252241i
$376$			31.7511i			1.63744i
$377$	20.8981	−	20.8981i	1.07631	−	1.07631i
$378$	−0.880145	−	0.880145i	−0.0452698	−	0.0452698i
$379$			0.618390i			0.0317646i	0.999874	+	0.0158823i	$0.00505570\pi$
$379$			0.618390i			0.0317646i	−0.999874	+	0.0158823i	$0.994944\pi$
$380$	0.0353405	+	0.515354i	0.00181293	+	0.0264371i
$381$		−	11.6133i		−	0.594969i
$382$	6.79980	+	6.79980i	0.347908	+	0.347908i
$383$	−7.33899	−	7.33899i	−0.375005	−	0.375005i	0.494292	−	0.869296i	$-0.335428\pi$
$383$	−7.33899	−	7.33899i	−0.375005	−	0.375005i	−0.869296	+	0.494292i	$0.835428\pi$
$384$	10.5351			0.537617
$385$		0			0
$386$	9.01683			0.458945
$387$	8.81242	+	8.81242i	0.447961	+	0.447961i
$388$	0.302854	+	0.302854i	0.0153751	+	0.0153751i
$389$			22.1469i			1.12289i	0.827513	+	0.561447i	$0.189755\pi$
$389$			22.1469i			1.12289i	−0.827513	+	0.561447i	$0.810245\pi$
$390$	−6.32330	−	5.51171i	−0.320193	−	0.279097i
$391$		−	6.02208i		−	0.304550i
$392$	−12.6444	−	12.6444i	−0.638640	−	0.638640i
$393$	5.50716	−	5.50716i	0.277799	−	0.277799i
$394$			21.2930i			1.07273i
$395$	−1.49574	+	0.102571i	−0.0752587	+	0.00516089i
$396$		0			0
$397$	10.7769	−	10.7769i	0.540876	−	0.540876i	−0.382910	−	0.923786i	$-0.625078\pi$
$397$	10.7769	−	10.7769i	0.540876	−	0.540876i	0.923786	+	0.382910i	$0.125078\pi$
$398$	−14.3844	+	14.3844i	−0.721027	+	0.721027i
$399$		−	0.113536i		−	0.00568393i
$400$	22.4118	−	3.08831i	1.12059	−	0.154416i
$401$	−4.28172			−0.213819			−0.106909	−	0.994269i	$-0.534096\pi$
$401$	−4.28172			−0.213819			−0.106909	+	0.994269i	$0.534096\pi$
$402$	5.01003	+	5.01003i	0.249878	+	0.249878i
$403$	−0.768137	+	0.768137i	−0.0382636	+	0.0382636i
$404$	1.49874			0.0745650
$405$	−8.21800	+	0.563552i	−0.408356	+	0.0280031i
$406$			2.77869i			0.137904i
$407$		0			0
$408$	5.36572	+	5.36572i	0.265643	+	0.265643i
$409$	−4.29562			−0.212405			−0.106202	−	0.994345i	$-0.533869\pi$
$409$	−4.29562			−0.212405			−0.106202	+	0.994345i	$0.533869\pi$
$410$	−14.9546	+	17.1566i	−0.738553	+	0.847304i
$411$	−3.45208			−0.170279
$412$	−0.710985	+	0.710985i	−0.0350277	+	0.0350277i
$413$	−1.30328	+	1.30328i	−0.0641303	+	0.0641303i
$414$	−5.83942			−0.286992
$415$	24.5117	−	28.1210i	1.20323	−	1.38041i
$416$	−5.39202			−0.264366
$417$	−5.92504	−	5.92504i	−0.290151	−	0.290151i
$418$		0			0
$419$		−	1.20241i		−	0.0587414i	−0.999569	−	0.0293707i	$-0.990650\pi$
$419$		−	1.20241i		−	0.0587414i	0.999569	−	0.0293707i	$-0.00935032\pi$
$420$	0.105764	−	0.00725281i	0.00516077	−	0.000353901i
$421$	31.3087			1.52589			0.762947	−	0.646461i	$-0.223752\pi$
$421$	31.3087			1.52589			0.762947	+	0.646461i	$0.223752\pi$
$422$	−6.37639	+	6.37639i	−0.310398	+	0.310398i
$423$	20.6716	+	20.6716i	1.00509	+	1.00509i
$424$	23.1899			1.12620
$425$	14.7707	+	11.1930i	0.716485	+	0.542938i
$426$		−	13.8897i		−	0.672957i
$427$	0.797860	−	0.797860i	0.0386111	−	0.0386111i
$428$	2.42802	−	2.42802i	0.117363	−	0.117363i
$429$		0			0
$430$	−17.8736	+	1.22568i	−0.861940	+	0.0591078i
$431$		−	9.89129i		−	0.476446i	−0.971210	−	0.238223i	$-0.923435\pi$
$431$		−	9.89129i		−	0.476446i	0.971210	−	0.238223i	$-0.0765650\pi$
$432$	13.6830	−	13.6830i	0.658323	−	0.658323i
$433$	−19.0794	−	19.0794i	−0.916896	−	0.916896i	0.0799066	−	0.996802i	$-0.474538\pi$
$433$	−19.0794	−	19.0794i	−0.916896	−	0.916896i	−0.996802	+	0.0799066i	$0.974538\pi$
$434$		−	0.102135i		−	0.00490262i
$435$	−12.8296	−	11.1829i	−0.615133	−	0.536181i
$436$		−	2.96369i		−	0.141935i
$437$	−0.854510	−	0.854510i	−0.0408768	−	0.0408768i
$438$	2.05815	+	2.05815i	0.0983420	+	0.0983420i
$439$	−24.5862			−1.17344			−0.586718	−	0.809791i	$-0.699580\pi$
$439$	−24.5862			−1.17344			−0.586718	+	0.809791i	$0.699580\pi$
$440$		0			0
$441$	−16.4643			−0.784016
$442$	−12.3327	−	12.3327i	−0.586606	−	0.586606i
$443$	21.7769	+	21.7769i	1.03465	+	1.03465i	0.999378	+	0.0352717i	$0.0112296\pi$
$443$	21.7769	+	21.7769i	1.03465	+	1.03465i	0.0352717	+	0.999378i	$0.488770\pi$
$444$		−	1.33842i		−	0.0635188i
$445$	1.21189	+	17.6724i	0.0574491	+	0.837753i
$446$		−	32.3098i		−	1.52992i
$447$	3.24841	+	3.24841i	0.153644	+	0.153644i
$448$	−0.866734	+	0.866734i	−0.0409493	+	0.0409493i
$449$		−	7.32471i		−	0.345674i	−0.984950	−	0.172837i	$-0.944707\pi$
$449$		−	7.32471i		−	0.345674i	0.984950	−	0.172837i	$-0.0552935\pi$
$450$	10.8534	−	14.3227i	0.511636	−	0.675177i
$451$		0			0
$452$	−0.910918	+	0.910918i	−0.0428460	+	0.0428460i
$453$	8.43567	−	8.43567i	0.396342	−	0.396342i
$454$		−	19.8674i		−	0.932425i
$455$	1.32225	−	0.0906738i	0.0619882	−	0.00425085i
$456$	1.52275			0.0713093
$457$	4.76277	+	4.76277i	0.222793	+	0.222793i	0.809674	−	0.586880i	$-0.199644\pi$
$457$	4.76277	+	4.76277i	0.222793	+	0.222793i	−0.586880	+	0.809674i	$0.699644\pi$
$458$	−17.6609	+	17.6609i	−0.825240	+	0.825240i
$459$	15.8515			0.739885
$460$	0.741427	−	0.850601i	0.0345692	−	0.0396595i
$461$		−	29.0801i		−	1.35440i	−0.735801	−	0.677198i	$-0.763194\pi$
$461$		−	29.0801i		−	1.35440i	0.735801	−	0.677198i	$-0.236806\pi$
$462$		0			0
$463$	17.5146	+	17.5146i	0.813970	+	0.813970i	0.985227	−	0.171256i	$-0.0547826\pi$
$463$	17.5146	+	17.5146i	0.813970	+	0.813970i	−0.171256	+	0.985227i	$0.554783\pi$
$464$	−43.1984			−2.00543
$465$	0.471570	+	0.411044i	0.0218685	+	0.0190617i
$466$	23.7792			1.10155
$467$	18.7084	−	18.7084i	0.865723	−	0.865723i	−0.126273	−	0.991996i	$-0.540302\pi$
$467$	18.7084	−	18.7084i	0.865723	−	0.865723i	0.991996	+	0.126273i	$0.0403015\pi$
$468$	−1.60748	+	1.60748i	−0.0743057	+	0.0743057i
$469$	−1.11948			−0.0516928
$470$	−41.9266	+	2.87513i	−1.93393	+	0.132620i
$471$	3.94477			0.181765
$472$	−17.4796	−	17.4796i	−0.804563	−	0.804563i
$473$		0			0
$474$		−	0.812515i		−	0.0373201i
$475$	3.68414	−	0.507669i	0.169040	−	0.0232935i
$476$	0.220423			0.0101031
$477$	15.0978	−	15.0978i	0.691283	−	0.691283i
$478$	−5.67705	−	5.67705i	−0.259662	−	0.259662i
$479$	−26.2551			−1.19963			−0.599814	−	0.800140i	$-0.704759\pi$
$479$	−26.2551			−1.19963			−0.599814	+	0.800140i	$0.704759\pi$
$480$	0.212433	+	3.09780i	0.00969618	+	0.141395i
$481$		−	16.7328i		−	0.762951i
$482$	−17.3776	+	17.3776i	−0.791530	+	0.791530i
$483$	−0.175368	+	0.175368i	−0.00797952	+	0.00797952i
$484$		0			0
$485$	2.02609	−	2.32443i	0.0920001	−	0.105547i
$486$		−	23.9666i		−	1.08715i
$487$	−16.5004	+	16.5004i	−0.747705	+	0.747705i	−0.974048	−	0.226343i	$-0.927323\pi$
$487$	−16.5004	+	16.5004i	−0.747705	+	0.747705i	0.226343	+	0.974048i	$0.427323\pi$
$488$	10.7009	+	10.7009i	0.484406	+	0.484406i
$489$			7.98555i			0.361119i
$490$	15.5517	−	17.8417i	0.702554	−	0.806004i
$491$		−	18.3477i		−	0.828019i	−0.910273	−	0.414009i	$-0.864128\pi$
$491$		−	18.3477i		−	0.828019i	0.910273	−	0.414009i	$-0.135872\pi$
$492$	−1.17238	−	1.17238i	−0.0528549	−	0.0528549i
$493$	−25.0223	−	25.0223i	−1.12695	−	1.12695i
$494$	−3.49992			−0.157469
$495$		0			0
$496$	1.58781			0.0712949
$497$	1.55181	+	1.55181i	0.0696080	+	0.0696080i
$498$	14.2956	+	14.2956i	0.640601	+	0.640601i
$499$		−	11.7579i		−	0.526356i	−0.964747	−	0.263178i	$-0.915229\pi$
$499$		−	11.7579i		−	0.526356i	0.964747	−	0.263178i	$-0.0847707\pi$
$500$	0.708263	+	3.39951i	0.0316745	+	0.152031i
$501$			9.61633i			0.429626i
$502$	20.7904	+	20.7904i	0.927922	+	0.927922i
$503$	3.77641	−	3.77641i	0.168382	−	0.168382i	−0.617886	−	0.786268i	$-0.712011\pi$
$503$	3.77641	−	3.77641i	0.168382	−	0.168382i	0.786268	+	0.617886i	$0.212011\pi$
$504$			1.16259i			0.0517859i
$505$	−0.738195	−	10.7647i	−0.0328492	−	0.479025i
$506$		0			0
$507$	−1.92638	+	1.92638i	−0.0855536	+	0.0855536i
$508$	3.19926	−	3.19926i	0.141944	−	0.141944i
$509$		−	19.5870i		−	0.868179i	−0.900870	−	0.434089i	$-0.857070\pi$
$509$		−	19.5870i		−	0.868179i	0.900870	−	0.434089i	$-0.142930\pi$
$510$	−6.59944	+	7.57120i	−0.292228	+	0.335258i
$511$	−0.459888			−0.0203442
$512$	−10.8595	−	10.8595i	−0.479928	−	0.479928i
$513$	2.24927	−	2.24927i	0.0993075	−	0.0993075i
$514$	−7.15359			−0.315532
$515$	5.45687	+	4.75649i	0.240459	+	0.209596i
$516$		−	1.30513i		−	0.0574550i
$517$		0			0
$518$	1.11243	+	1.11243i	0.0488775	+	0.0488775i
$519$	9.93748			0.436207
$520$	1.21612	+	17.7340i	0.0533302	+	0.777689i
$521$	18.7340			0.820752			0.410376	−	0.911916i	$-0.365397\pi$
$521$	18.7340			0.820752			0.410376	+	0.911916i	$0.365397\pi$
$522$	−24.2633	+	24.2633i	−1.06197	+	1.06197i
$523$	−1.82596	+	1.82596i	−0.0798437	+	0.0798437i	−0.745901	−	0.666057i	$-0.767981\pi$
$523$	−1.82596	+	1.82596i	−0.0798437	+	0.0798437i	0.666057	+	0.745901i	$0.267981\pi$
$524$	3.03424			0.132551
$525$	−0.104187	−	0.756083i	−0.00454710	−	0.0329982i
$526$	24.1234			1.05183
$527$	0.919727	+	0.919727i	0.0400639	+	0.0400639i
$528$		0			0
$529$		−	20.3603i		−	0.885228i
$530$	2.09990	+	30.6218i	0.0912137	+	1.33013i
$531$	−22.7602			−0.987710
$532$	0.0312772	−	0.0312772i	0.00135604	−	0.00135604i
$533$	−14.6569	−	14.6569i	−0.634863	−	0.634863i
$534$	−9.60002			−0.415433
$535$	−18.6353	−	16.2435i	−0.805674	−	0.702266i
$536$		−	15.0145i		−	0.648526i
$537$	−11.3751	+	11.3751i	−0.490873	+	0.490873i
$538$	−12.1591	+	12.1591i	−0.524216	+	0.524216i
$539$		0			0
$540$	2.23898	+	1.95161i	0.0963502	+	0.0839837i
$541$			9.23515i			0.397050i	0.980096	+	0.198525i	$0.0636151\pi$
$541$			9.23515i			0.397050i	−0.980096	+	0.198525i	$0.936385\pi$
$542$	19.1626	−	19.1626i	0.823102	−	0.823102i
$543$	2.59861	+	2.59861i	0.111517	+	0.111517i
$544$			6.45613i			0.276804i
$545$	−21.2868	+	1.45975i	−0.911828	+	0.0625288i
$546$			0.718275i			0.0307393i
$547$	0.757332	+	0.757332i	0.0323812	+	0.0323812i	0.723112	−	0.690731i	$-0.242711\pi$
$547$	0.757332	+	0.757332i	0.0323812	+	0.0323812i	−0.690731	+	0.723112i	$0.742711\pi$
$548$	−0.950984	−	0.950984i	−0.0406240	−	0.0406240i
$549$	13.9337			0.594674
$550$		0			0
$551$	−7.10113			−0.302518
$552$	−2.35203	−	2.35203i	−0.100109	−	0.100109i
$553$	0.0907773	+	0.0907773i	0.00386024	+	0.00386024i
$554$		−	7.11630i		−	0.302343i
$555$	−9.61328	+	0.659233i	−0.408061	+	0.0279829i
$556$		−	3.26448i		−	0.138445i
$557$	30.4317	+	30.4317i	1.28943	+	1.28943i	0.935130	+	0.354304i	$0.115282\pi$
$557$	30.4317	+	30.4317i	1.28943	+	1.28943i	0.354304	+	0.935130i	$0.384718\pi$
$558$	0.891829	−	0.891829i	0.0377541	−	0.0377541i
$559$		−	16.3166i		−	0.690117i
$560$	−1.46033	−	1.27290i	−0.0617102	−	0.0537897i
$561$		0			0
$562$	−14.1765	+	14.1765i	−0.597998	+	0.597998i
$563$	18.2874	−	18.2874i	0.770722	−	0.770722i	−0.207511	−	0.978233i	$-0.566536\pi$
$563$	18.2874	−	18.2874i	0.770722	−	0.770722i	0.978233	+	0.207511i	$0.0665362\pi$
$564$		−	3.06148i		−	0.128912i
$565$	6.99137	+	6.09404i	0.294129	+	0.256378i
$566$	−34.6369			−1.45590
$567$	0.498756	+	0.498756i	0.0209458	+	0.0209458i
$568$	−20.8128	+	20.8128i	−0.873286	+	0.873286i
$569$	27.1717			1.13910			0.569548	−	0.821958i	$-0.307118\pi$
$569$	27.1717			1.13910			0.569548	+	0.821958i	$0.307118\pi$
$570$	0.137888	+	2.01076i	0.00577550	+	0.0842214i
$571$		−	40.5475i		−	1.69686i	−0.529308	−	0.848430i	$-0.677549\pi$
$571$		−	40.5475i		−	1.69686i	0.529308	−	0.848430i	$-0.322451\pi$
$572$		0			0
$573$	3.56628	+	3.56628i	0.148984	+	0.148984i
$574$	1.94885			0.0813433
$575$	−6.47466	−	4.90637i	−0.270012	−	0.204610i
$576$	−15.1365			−0.630686
$577$	−23.9058	+	23.9058i	−0.995212	+	0.995212i	−0.999989	−	0.00477680i	$-0.998479\pi$
$577$	−23.9058	+	23.9058i	−0.995212	+	0.995212i	0.00477680	+	0.999989i	$0.498479\pi$
$578$	3.50588	−	3.50588i	0.145826	−	0.145826i
$579$	4.72905			0.196532
$580$	−0.453626	−	6.61501i	−0.0188358	−	0.274673i
$581$	−3.19432			−0.132523
$582$	1.18165	+	1.18165i	0.0489808	+	0.0489808i
$583$		0			0
$584$		−	6.16801i		−	0.255234i
$585$	12.3375	+	10.7540i	0.510094	+	0.444624i
$586$	−10.9866			−0.453853
$587$	6.84769	−	6.84769i	0.282634	−	0.282634i	−0.551524	−	0.834159i	$-0.685954\pi$
$587$	6.84769	−	6.84769i	0.282634	−	0.282634i	0.834159	+	0.551524i	$0.185954\pi$
$588$	1.21919	+	1.21919i	0.0502786	+	0.0502786i
$589$	0.261011			0.0107548
$590$	21.4986	−	24.6642i	0.885084	−	1.01541i
$591$			11.1675i			0.459371i
$592$	−17.2942	+	17.2942i	−0.710787	+	0.710787i
$593$	−14.0452	+	14.0452i	−0.576769	+	0.576769i	−0.934012	−	0.357243i	$-0.883717\pi$
$593$	−14.0452	+	14.0452i	−0.576769	+	0.576769i	0.357243	+	0.934012i	$0.383717\pi$
$594$		0			0
$595$	−0.108568	−	1.58320i	−0.00445086	−	0.0649048i
$596$			1.78975i			0.0733111i
$597$	−7.54419	+	7.54419i	−0.308763	+	0.308763i
$598$	5.40596	+	5.40596i	0.221066	+	0.221066i
$599$		−	4.51582i		−	0.184512i	−0.995735	−	0.0922558i	$-0.970592\pi$
$599$		−	4.51582i		−	0.184512i	0.995735	−	0.0922558i	$-0.0294077\pi$
$600$	10.1406	−	1.39736i	0.413987	−	0.0570469i
$601$			8.37748i			0.341725i	0.985295	+	0.170862i	$0.0546553\pi$
$601$			8.37748i			0.341725i	−0.985295	+	0.170862i	$0.945345\pi$
$602$	1.08476	+	1.08476i	0.0442115	+	0.0442115i
$603$	−9.77518	−	9.77518i	−0.398076	−	0.398076i
$604$	4.64774			0.189114
$605$		0			0
$606$	5.84763			0.237544
$607$	−5.42972	−	5.42972i	−0.220386	−	0.220386i	0.588275	−	0.808661i	$-0.299807\pi$
$607$	−5.42972	−	5.42972i	−0.220386	−	0.220386i	−0.808661	+	0.588275i	$0.799807\pi$
$608$	0.916100	+	0.916100i	0.0371528	+	0.0371528i
$609$			1.45734i			0.0590543i
$610$	−13.1613	+	15.0993i	−0.532886	+	0.611352i
$611$		−	38.2743i		−	1.54841i
$612$	1.92471	+	1.92471i	0.0778019	+	0.0778019i
$613$	−30.3535	+	30.3535i	−1.22597	+	1.22597i	−0.260492	+	0.965476i	$0.583885\pi$
$613$	−30.3535	+	30.3535i	−1.22597	+	1.22597i	−0.965476	+	0.260492i	$0.916115\pi$
$614$			43.2674i			1.74613i
$615$	−7.84320	+	8.99810i	−0.316268	+	0.362838i
$616$		0			0
$617$	33.4407	−	33.4407i	1.34627	−	1.34627i	0.456601	−	0.889671i	$-0.349067\pi$
$617$	33.4407	−	33.4407i	1.34627	−	1.34627i	0.889671	−	0.456601i	$-0.150933\pi$
$618$	−2.77405	+	2.77405i	−0.111589	+	0.111589i
$619$		−	21.1001i		−	0.848084i	−0.905642	−	0.424042i	$-0.860611\pi$
$619$		−	21.1001i		−	0.848084i	0.905642	−	0.424042i	$-0.139389\pi$
$620$	0.0166736	+	0.243144i	0.000669629	+	0.00976488i
$621$	−6.94842			−0.278830
$622$	−8.07842	−	8.07842i	−0.323915	−	0.323915i
$623$	1.07255	−	1.07255i	0.0429708	−	0.0429708i
$624$	−11.1665			−0.447018
$625$	24.0683	−	6.76153i	0.962731	−	0.270461i
$626$			2.04613i			0.0817798i
$627$		0			0
$628$	1.08671	+	1.08671i	0.0433645	+	0.0433645i
$629$	−20.0350			−0.798849
$630$	−1.53517	+	0.105275i	−0.0611628	+	0.00419426i
$631$	−28.2199			−1.12342			−0.561708	−	0.827335i	$-0.689856\pi$
$631$	−28.2199			−1.12342			−0.561708	+	0.827335i	$0.689856\pi$
$632$	−1.21750	+	1.21750i	−0.0484297	+	0.0484297i
$633$	−3.34422	+	3.34422i	−0.132921	+	0.132921i
$634$	17.2253			0.684103
$635$	−24.5546	−	21.4030i	−0.974418	−	0.849353i
$636$	−2.23600			−0.0886633
$637$	15.2422	+	15.2422i	0.603918	+	0.603918i
$638$		0			0
$639$			27.1004i			1.07208i
$640$	19.4159	−	22.2748i	0.767479	−	0.880489i
$641$	−16.9387			−0.669040			−0.334520	−	0.942389i	$-0.608574\pi$
$641$	−16.9387			−0.669040			−0.334520	+	0.942389i	$0.608574\pi$
$642$	9.47343	−	9.47343i	0.373886	−	0.373886i
$643$	−4.43755	−	4.43755i	−0.175000	−	0.175000i	0.614172	−	0.789172i	$-0.289490\pi$
$643$	−4.43755	−	4.43755i	−0.175000	−	0.175000i	−0.789172	+	0.614172i	$0.789490\pi$
$644$	−0.0966212			−0.00380741
$645$	−9.37413	+	0.642833i	−0.369106	+	0.0253115i
$646$			4.19062i			0.164878i
$647$	30.7501	−	30.7501i	1.20891	−	1.20891i	0.237529	−	0.971380i	$-0.423662\pi$
$647$	30.7501	−	30.7501i	1.20891	−	1.20891i	0.971380	−	0.237529i	$-0.0763375\pi$
$648$	−6.68931	+	6.68931i	−0.262781	+	0.262781i
$649$		0			0
$650$	−23.3073	+	3.21171i	−0.914188	+	0.125974i
$651$		−	0.0535664i		−	0.00209943i
$652$	−2.19987	+	2.19987i	−0.0861535	+	0.0861535i
$653$	6.88088	+	6.88088i	0.269270	+	0.269270i	0.828806	−	0.559536i	$-0.189021\pi$
$653$	6.88088	+	6.88088i	0.269270	+	0.269270i	−0.559536	+	0.828806i	$0.689021\pi$
$654$		−	11.5634i		−	0.452167i
$655$	−1.49450	−	21.7935i	−0.0583948	−	0.851544i
$656$			30.2973i			1.18291i
$657$	−4.01569	−	4.01569i	−0.156667	−	0.156667i
$658$	2.54455	+	2.54455i	0.0991971	+	0.0991971i
$659$	−3.37375			−0.131423			−0.0657113	−	0.997839i	$-0.520932\pi$
$659$	−3.37375			−0.131423			−0.0657113	+	0.997839i	$0.520932\pi$
$660$		0			0
$661$	9.93056			0.386254			0.193127	−	0.981174i	$-0.438137\pi$
$661$	9.93056			0.386254			0.193127	+	0.981174i	$0.438137\pi$
$662$	−19.0300	−	19.0300i	−0.739620	−	0.739620i
$663$	−6.46810	−	6.46810i	−0.251200	−	0.251200i
$664$		−	42.8421i		−	1.66260i
$665$	−0.240055	−	0.209244i	−0.00930893	−	0.00811414i
$666$			19.4273i			0.752793i
$667$	10.9684	+	10.9684i	0.424697	+	0.424697i
$668$	−2.64912	+	2.64912i	−0.102498	+	0.102498i
$669$		−	16.9455i		−	0.655151i
$670$	19.8263	−	1.35959i	0.765955	−	0.0525256i
$671$		0			0
$672$	0.188008	−	0.188008i	0.00725256	−	0.00725256i
$673$	27.0491	−	27.0491i	1.04267	−	1.04267i	0.0436186	−	0.999048i	$-0.486111\pi$
$673$	27.0491	−	27.0491i	1.04267	−	1.04267i	0.999048	−	0.0436186i	$-0.0138886\pi$
$674$		−	11.5830i		−	0.446161i
$675$	12.9147	−	17.0428i	0.497087	−	0.655977i
$676$	−1.06136			−0.0408217
$677$	22.7631	+	22.7631i	0.874857	+	0.874857i	0.992997	−	0.118140i	$-0.0376931\pi$
$677$	22.7631	+	22.7631i	0.874857	+	0.874857i	−0.118140	+	0.992997i	$0.537693\pi$
$678$	−3.55413	+	3.55413i	−0.136496	+	0.136496i
$679$	−0.264036			−0.0101328
$680$	21.2338	−	1.45612i	0.814280	−	0.0558395i
$681$		−	10.4198i		−	0.399289i
$682$		0			0
$683$	−28.7223	−	28.7223i	−1.09903	−	1.09903i	−0.994524	−	0.104505i	$-0.966674\pi$
$683$	−28.7223	−	28.7223i	−1.09903	−	1.09903i	−0.104505	−	0.994524i	$-0.533326\pi$
$684$	0.546218			0.0208852
$685$	−6.36208	+	7.29888i	−0.243082	+	0.278876i
$686$	−4.06400			−0.155164
$687$	−9.26259	+	9.26259i	−0.353390	+	0.353390i
$688$	−16.8640	+	16.8640i	−0.642933	+	0.642933i
$689$	−27.9543			−1.06497
$690$	2.89283	−	3.31879i	0.110128	−	0.126344i
$691$	−25.2649			−0.961122			−0.480561	−	0.876961i	$-0.659567\pi$
$691$	−25.2649			−0.961122			−0.480561	+	0.876961i	$0.659567\pi$
$692$	2.73759	+	2.73759i	0.104068	+	0.104068i
$693$		0			0
$694$			14.1878i			0.538562i
$695$	−23.4472	+	1.60790i	−0.889404	+	0.0609911i
$696$	−19.5458			−0.740882
$697$	−17.5495	+	17.5495i	−0.664733	+	0.664733i
$698$	1.61418	+	1.61418i	0.0610974	+	0.0610974i
$699$	12.4715			0.471714
$700$	0.179585	−	0.236988i	0.00678768	−	0.00895732i
$701$			28.2273i			1.06613i	0.846074	+	0.533066i	$0.178960\pi$
$701$			28.2273i			1.06613i	−0.846074	+	0.533066i	$0.821040\pi$
$702$	−14.2297	+	14.2297i	−0.537066	+	0.537066i
$703$	−2.84289	+	2.84289i	−0.107222	+	0.107222i
$704$		0			0
$705$	−21.9892	+	1.50791i	−0.828161	+	0.0567914i
$706$			9.46358i			0.356167i
$707$	−0.653319	+	0.653319i	−0.0245706	+	0.0245706i
$708$	1.68540	+	1.68540i	0.0633414	+	0.0633414i
$709$		−	8.15970i		−	0.306444i	−0.988192	−	0.153222i	$-0.951035\pi$
$709$		−	8.15970i		−	0.306444i	0.988192	−	0.153222i	$-0.0489650\pi$
$710$	−29.3675	−	25.5982i	−1.10214	−	0.960684i
$711$			1.58532i			0.0594540i
$712$	14.3850	+	14.3850i	0.539102	+	0.539102i
$713$	−0.403157	−	0.403157i	−0.0150984	−	0.0150984i
$714$	0.860026			0.0321856
$715$		0			0
$716$	−6.26727			−0.234219
$717$	−2.97744	−	2.97744i	−0.111194	−	0.111194i
$718$	28.2730	+	28.2730i	1.05514	+	1.05514i
$719$		−	1.03764i		−	0.0386975i	−0.999813	−	0.0193487i	$-0.993841\pi$
$719$		−	1.03764i		−	0.0386975i	0.999813	−	0.0193487i	$-0.00615928\pi$
$720$	−1.63663	−	23.8663i	−0.0609938	−	0.889443i
$721$		−	0.619856i		−	0.0230846i
$722$	−19.8275	−	19.8275i	−0.737901	−	0.737901i
$723$	−9.11403	+	9.11403i	−0.338954	+	0.338954i
$724$			1.43174i			0.0532101i
$725$	−47.2892	+	6.51637i	−1.75627	+	0.242012i
$726$		0			0
$727$	−3.27903	+	3.27903i	−0.121612	+	0.121612i	−0.765294	−	0.643681i	$-0.777406\pi$
$727$	−3.27903	+	3.27903i	−0.121612	+	0.121612i	0.643681	+	0.765294i	$0.277406\pi$
$728$	1.07629	−	1.07629i	0.0398900	−	0.0398900i
$729$		−	1.51821i		−	0.0562300i
$730$	8.14472	−	0.558526i	0.301450	−	0.0206720i
$731$	−19.5366			−0.722588
$732$	−1.03179	−	1.03179i	−0.0381362	−	0.0381362i
$733$	32.2972	−	32.2972i	1.19292	−	1.19292i	0.216680	−	0.976243i	$-0.430477\pi$
$733$	32.2972	−	32.2972i	1.19292	−	1.19292i	0.976243	−	0.216680i	$-0.0695229\pi$
$734$	12.4175			0.458340
$735$	8.15638	−	9.35739i	0.300853	−	0.345153i
$736$		−	2.83001i		−	0.104315i
$737$		0			0
$738$	17.0171	+	17.0171i	0.626410	+	0.626410i
$739$	3.79675			0.139666			0.0698329	−	0.997559i	$-0.477753\pi$
$739$	3.79675			0.139666			0.0698329	+	0.997559i	$0.477753\pi$
$740$	−2.82989	−	2.46667i	−0.104029	−	0.0906767i
$741$	−1.83560			−0.0674323
$742$	1.85846	−	1.85846i	0.0682261	−	0.0682261i
$743$	−30.0019	+	30.0019i	−1.10066	+	1.10066i	−0.106331	+	0.994331i	$0.533910\pi$
$743$	−30.0019	+	30.0019i	−1.10066	+	1.10066i	−0.994331	+	0.106331i	$0.966090\pi$
$744$	0.718432			0.0263390
$745$	12.8550	−	0.881532i	0.470969	−	0.0322968i
$746$	13.1663			0.482052
$747$	−27.8924	−	27.8924i	−1.02053	−	1.02053i
$748$		0			0
$749$			2.11681i			0.0773467i
$750$	2.76343	+	13.2639i	0.100906	+	0.484329i
$751$	−9.99217			−0.364619			−0.182310	−	0.983241i	$-0.558357\pi$
$751$	−9.99217			−0.364619			−0.182310	+	0.983241i	$0.558357\pi$
$752$	−39.5584	+	39.5584i	−1.44255	+	1.44255i
$753$	10.9039	+	10.9039i	0.397361	+	0.397361i
$754$	44.9245			1.63605
$755$	−2.28922	−	33.3826i	−0.0833132	−	1.21492i
$756$		−	0.254329i		−	0.00924986i
$757$	−20.7772	+	20.7772i	−0.755161	+	0.755161i	−0.975437	−	0.220277i	$-0.929304\pi$
$757$	−20.7772	+	20.7772i	−0.755161	+	0.755161i	0.220277	+	0.975437i	$0.429304\pi$
$758$	−0.664675	+	0.664675i	−0.0241421	+	0.0241421i
$759$		0			0
$760$	2.80638	−	3.21961i	0.101798	−	0.116788i
$761$		−	30.3518i		−	1.10025i	−0.835081	−	0.550127i	$-0.814579\pi$
$761$		−	30.3518i		−	1.10025i	0.835081	−	0.550127i	$-0.185421\pi$
$762$	12.4826	−	12.4826i	0.452195	−	0.452195i
$763$	1.29191	+	1.29191i	0.0467704	+	0.0467704i
$764$			1.96489i			0.0710872i
$765$	12.8763	−	14.7723i	0.465544	−	0.534095i
$766$		−	15.7766i		−	0.570031i
$767$	21.0708	+	21.0708i	0.760821	+	0.760821i
$768$	4.10600	+	4.10600i	0.148162	+	0.148162i
$769$	37.6421			1.35741			0.678705	−	0.734411i	$-0.262542\pi$
$769$	37.6421			1.35741			0.678705	+	0.734411i	$0.262542\pi$
$770$		0			0
$771$	−3.75184			−0.135119
$772$	1.30276	+	1.30276i	0.0468875	+	0.0468875i
$773$	18.2525	+	18.2525i	0.656497	+	0.656497i	0.954549	−	0.298053i	$-0.0963371\pi$
$773$	18.2525	+	18.2525i	0.656497	+	0.656497i	−0.298053	+	0.954549i	$0.596337\pi$
$774$			18.9440i			0.680928i
$775$	1.73818	−	0.239518i	0.0624371	−	0.00860374i
$776$		−	3.54125i		−	0.127123i
$777$	0.583436	+	0.583436i	0.0209307	+	0.0209307i
$778$	−23.8045	+	23.8045i	−0.853434	+	0.853434i
$779$			4.98040i			0.178441i
$780$	−0.117260	−	1.70994i	−0.00419856	−	0.0612257i
$781$		0			0
$782$	6.47282	−	6.47282i	0.231467	−	0.231467i
$783$	−28.8713	+	28.8713i	−1.03178	+	1.03178i
$784$		−	31.5071i		−	1.12525i
$785$	7.27008	−	8.34059i	0.259480	−	0.297688i
$786$	11.8387			0.422272
$787$	12.2154	+	12.2154i	0.435433	+	0.435433i	0.890472	−	0.455039i	$-0.150375\pi$
$787$	12.2154	+	12.2154i	0.435433	+	0.435433i	−0.455039	+	0.890472i	$0.650375\pi$
$788$	−3.07645	+	3.07645i	−0.109594	+	0.109594i
$789$	12.6520			0.450421
$790$	−1.71794	−	1.49744i	−0.0611214	−	0.0532765i
$791$		−	0.794162i		−	0.0282372i
$792$		0			0
$793$	−12.8994	−	12.8994i	−0.458070	−	0.458070i
$794$	23.1670			0.822165
$795$	1.10133	+	16.0602i	0.0390602	+	0.569596i
$796$	−4.15657			−0.147326
$797$	31.5150	−	31.5150i	1.11632	−	1.11632i	0.124043	−	0.992277i	$-0.460414\pi$
$797$	31.5150	−	31.5150i	1.11632	−	1.11632i	0.992277	−	0.124043i	$-0.0395862\pi$
$798$	0.122034	−	0.122034i	0.00431997	−	0.00431997i
$799$	−45.8277			−1.62127
$800$	6.94133	+	5.26000i	0.245413	+	0.185969i
$801$	18.7308			0.661820
$802$	−4.60219	−	4.60219i	−0.162509	−	0.162509i
$803$		0			0
$804$			1.44771i			0.0510569i
$805$	0.0475902	+	0.693986i	0.00167734	+	0.0244598i
$806$	−1.65126			−0.0581631
$807$	−6.37706	+	6.37706i	−0.224483	+	0.224483i
$808$	−8.76231	−	8.76231i	−0.308257	−	0.308257i
$809$	−15.2351			−0.535638			−0.267819	−	0.963469i	$-0.586303\pi$
$809$	−15.2351			−0.535638			−0.267819	+	0.963469i	$0.586303\pi$
$810$	−9.43883	−	8.22736i	−0.331647	−	0.289080i
$811$		−	45.5573i		−	1.59973i	−0.600178	−	0.799866i	$-0.704904\pi$
$811$		−	45.5573i		−	1.59973i	0.600178	−	0.799866i	$-0.295096\pi$
$812$	−0.401470	+	0.401470i	−0.0140888	+	0.0140888i
$813$	10.0502	−	10.0502i	0.352475	−	0.352475i
$814$		0			0
$815$	16.8842	+	14.7171i	0.591427	+	0.515518i
$816$			13.3702i			0.468051i
$817$	−2.77217	+	2.77217i	−0.0969859	+	0.0969859i
$818$	−4.61714	−	4.61714i	−0.161434	−	0.161434i
$819$		−	1.40144i		−	0.0489703i
$820$	−4.63946	+	0.318152i	−0.162017	+	0.0111104i
$821$			28.7123i			1.00207i	0.865428	+	0.501034i	$0.167047\pi$
$821$			28.7123i			1.00207i	−0.865428	+	0.501034i	$0.832953\pi$
$822$	−3.71046	−	3.71046i	−0.129417	−	0.129417i
$823$	19.0615	+	19.0615i	0.664443	+	0.664443i	0.956424	−	0.291981i	$-0.0943145\pi$
$823$	19.0615	+	19.0615i	0.664443	+	0.664443i	−0.291981	+	0.956424i	$0.594314\pi$
$824$	8.31350			0.289614
$825$		0			0
$826$	−2.80165			−0.0974820
$827$	28.0601	+	28.0601i	0.975746	+	0.975746i	0.999713	−	0.0239670i	$-0.00762967\pi$
$827$	28.0601	+	28.0601i	0.975746	+	0.975746i	−0.0239670	+	0.999713i	$0.507630\pi$
$828$	−0.843687	−	0.843687i	−0.0293201	−	0.0293201i
$829$		−	10.8672i		−	0.377432i	−0.982032	−	0.188716i	$-0.939567\pi$
$829$		−	10.8672i		−	0.377432i	0.982032	−	0.188716i	$-0.0604326\pi$
$830$	56.5721	−	3.87945i	1.96365	−	0.134658i
$831$		−	3.73228i		−	0.129471i
$832$	14.0129	+	14.0129i	0.485810	+	0.485810i
$833$	18.2502	−	18.2502i	0.632333	−	0.632333i
$834$		−	12.7370i		−	0.441047i
$835$	20.3322	+	17.7226i	0.703625	+	0.613316i
$836$		0			0
$837$	1.06120	−	1.06120i	0.0366805	−	0.0366805i
$838$	1.29240	−	1.29240i	0.0446453	−	0.0446453i
$839$		−	40.3158i		−	1.39186i	−0.718112	−	0.695928i	$-0.754993\pi$
$839$		−	40.3158i		−	1.39186i	0.718112	−	0.695928i	$-0.245007\pi$
$840$	−0.660750	−	0.575943i	−0.0227980	−	0.0198719i
$841$	62.1491			2.14307
$842$	33.6521	+	33.6521i	1.15973	+	1.15973i
$843$	−7.43512	+	7.43512i	−0.256079	+	0.256079i
$844$	−1.84254			−0.0634229
$845$	0.522769	+	7.62329i	0.0179838	+	0.262249i
$846$			44.4376i			1.52780i
$847$		0			0
$848$	28.8921	+	28.8921i	0.992159	+	0.992159i
$849$	−18.1660			−0.623455
$850$	3.84554	+	27.9070i	0.131901	+	0.957201i
$851$	8.78224			0.301051
$852$	2.00680	−	2.00680i	0.0687518	−	0.0687518i
$853$	9.86864	−	9.86864i	0.337896	−	0.337896i	−0.517679	−	0.855575i	$-0.673204\pi$
$853$	9.86864	−	9.86864i	0.337896	−	0.337896i	0.855575	+	0.517679i	$0.173204\pi$
$854$	1.71515			0.0586913
$855$	−0.269037	−	3.92323i	−0.00920086	−	0.134172i
$856$	−28.3907			−0.970374
$857$	26.9229	+	26.9229i	0.919668	+	0.919668i	0.997005	−	0.0773373i	$-0.0246418\pi$
$857$	26.9229	+	26.9229i	0.919668	+	0.919668i	−0.0773373	+	0.997005i	$0.524642\pi$
$858$		0			0
$859$		−	18.3200i		−	0.625071i	−0.949906	−	0.312535i	$-0.898822\pi$
$859$		−	18.3200i		−	0.625071i	0.949906	−	0.312535i	$-0.101178\pi$
$860$	−2.75949	−	2.40531i	−0.0940977	−	0.0820204i
$861$	1.02211			0.0348334
$862$	10.6316	−	10.6316i	0.362114	−	0.362114i
$863$	8.59342	+	8.59342i	0.292523	+	0.292523i	0.838076	−	0.545553i	$-0.183680\pi$
$863$	8.59342	+	8.59342i	0.292523	+	0.292523i	−0.545553	+	0.838076i	$0.683680\pi$
$864$	7.44923			0.253428
$865$	18.3145	−	21.0112i	0.622711	−	0.714404i
$866$		−	41.0148i		−	1.39374i
$867$	1.83873	−	1.83873i	0.0624464	−	0.0624464i
$868$	0.0147565	−	0.0147565i	0.000500870	−	0.000500870i
$869$		0			0
$870$	−1.76991	−	25.8098i	−0.0600057	−	0.875035i
$871$			18.0992i			0.613266i
$872$	−17.3271	+	17.3271i	−0.586770	+	0.586770i
$873$	−2.30554	−	2.30554i	−0.0780306	−	0.0780306i
$874$		−	1.83693i		−	0.0621352i
$875$	−1.79063	−	1.17315i	−0.0605344	−	0.0396597i
$876$			0.594727i			0.0200940i
$877$	−9.07573	−	9.07573i	−0.306466	−	0.306466i	0.537071	−	0.843537i	$-0.319531\pi$
$877$	−9.07573	−	9.07573i	−0.306466	−	0.306466i	−0.843537	+	0.537071i	$0.819531\pi$
$878$	−26.4264	−	26.4264i	−0.891848	−	0.891848i
$879$	−5.76213			−0.194352
$880$		0			0
$881$	13.8380			0.466216			0.233108	−	0.972451i	$-0.425110\pi$
$881$	13.8380			0.466216			0.233108	+	0.972451i	$0.425110\pi$
$882$	−17.6966	−	17.6966i	−0.595877	−	0.595877i
$883$	30.8218	+	30.8218i	1.03724	+	1.03724i	0.999279	+	0.0379569i	$0.0120850\pi$
$883$	30.8218	+	30.8218i	1.03724	+	1.03724i	0.0379569	+	0.999279i	$0.487915\pi$
$884$		−	3.56368i		−	0.119860i
$885$	11.2753	−	12.9356i	0.379017	−	0.434826i
$886$			46.8136i			1.57273i
$887$	7.35335	+	7.35335i	0.246901	+	0.246901i	0.819698	−	0.572796i	$-0.194141\pi$
$887$	7.35335	+	7.35335i	0.246901	+	0.246901i	−0.572796	+	0.819698i	$0.694141\pi$
$888$	−7.82504	+	7.82504i	−0.262591	+	0.262591i
$889$			2.78920i			0.0935467i
$890$	−17.6925	+	20.2977i	−0.593055	+	0.680381i
$891$		0			0
$892$	4.66817	−	4.66817i	0.156302	−	0.156302i
$893$	−6.50277	+	6.50277i	−0.217607	+	0.217607i
$894$			6.98308i			0.233549i
$895$	3.08691	+	45.0149i	0.103184	+	1.50468i
$896$	−2.53023			−0.0845292
$897$	2.83526	+	2.83526i	0.0946664	+	0.0946664i
$898$	7.87294	−	7.87294i	0.262723	−	0.262723i
$899$	−3.35031			−0.111739
$900$	3.63748	−	0.501239i	0.121249	−	0.0167080i
$901$			33.4710i			1.11508i
$902$		0			0
$903$	0.568922	+	0.568922i	0.0189325	+	0.0189325i
$904$	10.6513			0.354257
$905$	10.2835	−	0.705194i	0.341835	−	0.0234414i
$906$	18.1341			0.602465
$907$	−11.5308	+	11.5308i	−0.382873	+	0.382873i	−0.872136	−	0.489263i	$-0.837266\pi$
$907$	−11.5308	+	11.5308i	−0.382873	+	0.382873i	0.489263	+	0.872136i	$0.337266\pi$
$908$	2.87047	−	2.87047i	0.0952600	−	0.0952600i
$909$	−11.4094			−0.378427
$910$	1.51868	+	1.32376i	0.0503437	+	0.0438822i
$911$	−17.7104			−0.586773			−0.293387	−	0.955994i	$-0.594782\pi$
$911$	−17.7104			−0.586773			−0.293387	+	0.955994i	$0.594782\pi$
$912$	1.89718	+	1.89718i	0.0628219	+	0.0628219i
$913$		0			0
$914$			10.2385i			0.338659i
$915$	−6.90269	+	7.91910i	−0.228196	+	0.261797i
$916$	−5.10334			−0.168619
$917$	−1.32266	+	1.32266i	−0.0436782	+	0.0436782i
$918$	17.0379	+	17.0379i	0.562336	+	0.562336i
$919$	9.13000			0.301171			0.150585	−	0.988597i	$-0.451884\pi$
$919$	9.13000			0.301171			0.150585	+	0.988597i	$0.451884\pi$
$920$	−9.30773	+	0.638280i	−0.306867	+	0.0210435i
$921$			22.6924i			0.747740i
$922$	31.2567	−	31.2567i	1.02938	−	1.02938i
$923$	25.0888	−	25.0888i	0.825807	−	0.825807i
$924$		0			0
$925$	−16.3231	+	21.5407i	−0.536701	+	0.708254i
$926$			37.6509i			1.23729i
$927$	5.41252	−	5.41252i	0.177770	−	0.177770i
$928$	−11.7589	−	11.7589i	−0.386006	−	0.386006i
$929$		−	1.81238i		−	0.0594624i	−0.999558	−	0.0297312i	$-0.990535\pi$
$929$		−	1.81238i		−	0.0594624i	0.999558	−	0.0297312i	$-0.00946512\pi$
$930$	0.0650556	+	0.948674i	0.00213326	+	0.0311083i
$931$		−	5.17927i		−	0.169744i
$932$	3.43566	+	3.43566i	0.112539	+	0.112539i
$933$	−4.23688	−	4.23688i	−0.138709	−	0.138709i
$934$	40.2174			1.31595
$935$		0			0
$936$	18.7961			0.614371
$937$	10.7192	+	10.7192i	0.350181	+	0.350181i	0.860177	−	0.509996i	$-0.170353\pi$
$937$	10.7192	+	10.7192i	0.350181	+	0.350181i	−0.509996	+	0.860177i	$0.670353\pi$
$938$	−1.20327	−	1.20327i	−0.0392881	−	0.0392881i
$939$			1.07313i			0.0350203i
$940$	−6.47302	−	5.64221i	−0.211127	−	0.184029i
$941$			21.8290i			0.711605i	0.934561	+	0.355803i	$0.115792\pi$
$941$			21.8290i			0.711605i	−0.934561	+	0.355803i	$0.884208\pi$
$942$	4.24002	+	4.24002i	0.138147	+	0.138147i
$943$	7.69271	−	7.69271i	0.250509	−	0.250509i
$944$		−	43.5553i		−	1.41760i
$945$	−1.82673	+	0.125268i	−0.0594235	+	0.00407498i
$946$		0			0
$947$	6.90662	−	6.90662i	0.224435	−	0.224435i	−0.585928	−	0.810363i	$-0.699270\pi$
$947$	6.90662	−	6.90662i	0.224435	−	0.224435i	0.810363	+	0.585928i	$0.199270\pi$
$948$	0.117393	−	0.117393i	0.00381276	−	0.00381276i
$949$			7.43522i			0.241357i
$950$	4.50556	+	3.41422i	0.146180	+	0.110772i
$951$	9.03412			0.292951
$952$	−1.28870	−	1.28870i	−0.0417669	−	0.0417669i
$953$	−9.22299	+	9.22299i	−0.298762	+	0.298762i	−0.840529	−	0.541767i	$-0.817756\pi$
$953$	−9.22299	+	9.22299i	−0.298762	+	0.298762i	0.541767	+	0.840529i	$0.317756\pi$
$954$	32.4557			1.05079
$955$	14.1129	−	0.967795i	0.456682	−	0.0313171i
$956$		−	1.64046i		−	0.0530561i
$957$		0			0
$958$	−28.2202	−	28.2202i	−0.911755	−	0.911755i
$959$	0.829093			0.0267728
$960$	7.49856	−	8.60270i	0.242015	−	0.277651i
$961$	−30.8769			−0.996028
$962$	17.9852	−	17.9852i	0.579867	−	0.579867i
$963$	−18.4838	+	18.4838i	−0.595633	+	0.595633i
$964$	−5.02149			−0.161731
$965$	8.71548	−	9.99882i	0.280561	−	0.321873i
$966$	−0.376987			−0.0121294
$967$	−13.6319	−	13.6319i	−0.438372	−	0.438372i	0.453092	−	0.891464i	$-0.350321\pi$
$967$	−13.6319	−	13.6319i	−0.438372	−	0.438372i	−0.891464	+	0.453092i	$0.850321\pi$
$968$		0			0
$969$			2.19785i			0.0706051i
$970$	4.67615	−	0.320668i	0.150142	−	0.0102960i
$971$	4.10875			0.131856			0.0659280	−	0.997824i	$-0.478999\pi$
$971$	4.10875			0.131856			0.0659280	+	0.997824i	$0.478999\pi$
$972$	3.46272	−	3.46272i	0.111067	−	0.111067i
$973$	1.42303	+	1.42303i	0.0456202	+	0.0456202i
$974$	−35.4708			−1.13656
$975$	−12.2239	+	1.68444i	−0.391480	+	0.0539453i
$976$			26.6643i			0.853502i
$977$	−21.7149	+	21.7149i	−0.694720	+	0.694720i	−0.963267	−	0.268547i	$-0.913457\pi$
$977$	−21.7149	+	21.7149i	−0.694720	+	0.694720i	0.268547	+	0.963267i	$0.413457\pi$
$978$	−8.58324	+	8.58324i	−0.274462	+	0.274462i
$979$		0			0
$980$	4.82472	−	0.330856i	0.154120	−	0.0105688i
$981$			22.5617i			0.720339i
$982$	19.7209	−	19.7209i	0.629320	−	0.629320i
$983$	19.6048	+	19.6048i	0.625296	+	0.625296i	0.946881	−	0.321585i	$-0.104215\pi$
$983$	19.6048	+	19.6048i	0.625296	+	0.625296i	−0.321585	+	0.946881i	$0.604215\pi$
$984$			13.7085i			0.437012i
$985$	23.6120	+	20.5814i	0.752340	+	0.655778i
$986$		−	53.7902i		−	1.71303i
$987$	1.33454	+	1.33454i	0.0424789	+	0.0424789i
$988$	−0.505673	−	0.505673i	−0.0160876	−	0.0160876i
$989$	8.56376			0.272312
$990$		0			0
$991$	9.10087			0.289099			0.144549	−	0.989498i	$-0.453827\pi$
$991$	9.10087			0.289099			0.144549	+	0.989498i	$0.453827\pi$
$992$	0.432215	+	0.432215i	0.0137228	+	0.0137228i
$993$	−9.98062	−	9.98062i	−0.316725	−	0.316725i
$994$			3.33591i			0.105809i
$995$	2.04729	+	29.8547i	0.0649035	+	0.946457i
$996$			4.13089i			0.130892i
$997$	−20.4146	−	20.4146i	−0.646537	−	0.646537i	0.305617	−	0.952155i	$-0.401137\pi$
$997$	−20.4146	−	20.4146i	−0.646537	−	0.646537i	−0.952155	+	0.305617i	$0.901137\pi$
$998$	12.6379	−	12.6379i	0.400047	−	0.400047i
$999$			23.1169i			0.731385i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.e.b.483.14		32
5.2	odd	4	inner	605.2.e.b.362.3		32
11.2	odd	10		605.2.m.e.403.4		32
11.3	even	5		605.2.m.c.233.4		32
11.4	even	5		605.2.m.d.578.1		32
11.5	even	5		605.2.m.e.118.1		32
11.6	odd	10		55.2.l.a.8.4	yes	32
11.7	odd	10		605.2.m.c.578.4		32
11.8	odd	10		605.2.m.d.233.1		32
11.9	even	5		55.2.l.a.18.1	yes	32
11.10	odd	2	inner	605.2.e.b.483.3		32
33.17	even	10		495.2.bj.a.118.1		32
33.20	odd	10		495.2.bj.a.73.4		32
44.31	odd	10		880.2.cm.a.513.1		32
44.39	even	10		880.2.cm.a.833.4		32
55.2	even	20		605.2.m.e.282.1		32
55.7	even	20		605.2.m.c.457.4		32
55.9	even	10		275.2.bm.b.18.4		32
55.17	even	20		55.2.l.a.52.1	yes	32
55.27	odd	20		605.2.m.e.602.4		32
55.28	even	20		275.2.bm.b.107.4		32
55.32	even	4	inner	605.2.e.b.362.14		32
55.37	odd	20		605.2.m.d.457.1		32
55.39	odd	10		275.2.bm.b.118.1		32
55.42	odd	20		55.2.l.a.7.4	✓	32
55.47	odd	20		605.2.m.c.112.4		32
55.52	even	20		605.2.m.d.112.1		32
55.53	odd	20		275.2.bm.b.7.1		32
165.17	odd	20		495.2.bj.a.217.4		32
165.152	even	20		495.2.bj.a.172.1		32
220.127	odd	20		880.2.cm.a.657.1		32
220.207	even	20		880.2.cm.a.337.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.4	✓	32	55.42	odd	20
55.2.l.a.8.4	yes	32	11.6	odd	10
55.2.l.a.18.1	yes	32	11.9	even	5
55.2.l.a.52.1	yes	32	55.17	even	20
275.2.bm.b.7.1		32	55.53	odd	20
275.2.bm.b.18.4		32	55.9	even	10
275.2.bm.b.107.4		32	55.28	even	20
275.2.bm.b.118.1		32	55.39	odd	10
495.2.bj.a.73.4		32	33.20	odd	10
495.2.bj.a.118.1		32	33.17	even	10
495.2.bj.a.172.1		32	165.152	even	20
495.2.bj.a.217.4		32	165.17	odd	20
605.2.e.b.362.3		32	5.2	odd	4	inner
605.2.e.b.362.14		32	55.32	even	4	inner
605.2.e.b.483.3		32	11.10	odd	2	inner
605.2.e.b.483.14		32	1.1	even	1	trivial
605.2.m.c.112.4		32	55.47	odd	20
605.2.m.c.233.4		32	11.3	even	5
605.2.m.c.457.4		32	55.7	even	20
605.2.m.c.578.4		32	11.7	odd	10
605.2.m.d.112.1		32	55.52	even	20
605.2.m.d.233.1		32	11.8	odd	10
605.2.m.d.457.1		32	55.37	odd	20
605.2.m.d.578.1		32	11.4	even	5
605.2.m.e.118.1		32	11.5	even	5
605.2.m.e.282.1		32	55.2	even	20
605.2.m.e.403.4		32	11.2	odd	10
605.2.m.e.602.4		32	55.27	odd	20
880.2.cm.a.337.4		32	220.207	even	20
880.2.cm.a.513.1		32	44.31	odd	10
880.2.cm.a.657.1		32	220.127	odd	20
880.2.cm.a.833.4		32	44.39	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.07485 + 1.07485i) q^{2} +(0.563723 + 0.563723i) q^{3} +0.310591i q^{4} +(2.23083 - 0.152980i) q^{5} +1.21183i q^{6} +(-0.135390 - 0.135390i) q^{7} +(1.81586 - 1.81586i) q^{8} -2.36443i q^{9} +(2.56223 + 2.23337i) q^{10} +(-0.175087 + 0.175087i) q^{12} +(-2.18892 + 2.18892i) q^{13} -0.291048i q^{14} +(1.34381 + 1.17133i) q^{15} +4.52471 q^{16} +(2.62090 + 2.62090i) q^{17} +(2.54140 - 2.54140i) q^{18} +0.743791 q^{19} +(0.0475140 + 0.692874i) q^{20} -0.152646i q^{21} +(-1.14886 - 1.14886i) q^{23} +2.04728 q^{24} +(4.95319 - 0.682543i) q^{25} -4.70551 q^{26} +(3.02406 - 3.02406i) q^{27} +(0.0420510 - 0.0420510i) q^{28} -9.54720 q^{29} +(0.185386 + 2.70339i) q^{30} +0.350920 q^{31} +(1.23166 + 1.23166i) q^{32} +5.63413i q^{34} +(-0.322745 - 0.281321i) q^{35} +0.734370 q^{36} +(-3.82216 + 3.82216i) q^{37} +(0.799462 + 0.799462i) q^{38} -2.46789 q^{39} +(3.77307 - 4.32865i) q^{40} +6.69597i q^{41} +(0.164071 - 0.164071i) q^{42} +(-3.72708 + 3.72708i) q^{43} +(-0.361710 - 5.27464i) q^{45} -2.46969i q^{46} +(-8.74273 + 8.74273i) q^{47} +(2.55069 + 2.55069i) q^{48} -6.96334i q^{49} +(6.05755 + 4.59030i) q^{50} +2.95493i q^{51} +(-0.679858 - 0.679858i) q^{52} +(6.38540 + 6.38540i) q^{53} +6.50079 q^{54} -0.491699 q^{56} +(0.419293 + 0.419293i) q^{57} +(-10.2618 - 10.2618i) q^{58} -9.62609i q^{59} +(-0.363805 + 0.417374i) q^{60} +5.89303i q^{61} +(0.377185 + 0.377185i) q^{62} +(-0.320122 + 0.320122i) q^{63} -6.40173i q^{64} +(-4.54825 + 5.21797i) q^{65} +(4.13426 - 4.13426i) q^{67} +(-0.814027 + 0.814027i) q^{68} -1.29528i q^{69} +(-0.0445244 - 0.649278i) q^{70} -11.4617 q^{71} +(-4.29347 - 4.29347i) q^{72} +(1.69838 - 1.69838i) q^{73} -8.21648 q^{74} +(3.17700 + 2.40747i) q^{75} +0.231015i q^{76} +(-2.65261 - 2.65261i) q^{78} -0.670485 q^{79} +(10.0939 - 0.692189i) q^{80} -3.68383 q^{81} +(-7.19714 + 7.19714i) q^{82} +(11.7967 - 11.7967i) q^{83} +0.0474103 q^{84} +(6.24773 + 5.44584i) q^{85} -8.01208 q^{86} +(-5.38198 - 5.38198i) q^{87} +7.92190i q^{89} +(5.28065 - 6.05821i) q^{90} +0.592718 q^{91} +(0.356824 - 0.356824i) q^{92} +(0.197822 + 0.197822i) q^{93} -18.7942 q^{94} +(1.65927 - 0.113785i) q^{95} +1.38863i q^{96} +(0.975091 - 0.975091i) q^{97} +(7.48452 - 7.48452i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} + 8 q^{5} + 12 q^{12} - 36 q^{15} - 8 q^{16} - 64 q^{20} - 24 q^{23} + 16 q^{25} - 16 q^{27} - 8 q^{31} + 24 q^{36} + 32 q^{37} - 40 q^{38} + 60 q^{42} - 28 q^{45} - 28 q^{47} + 56 q^{48}+ \cdots + 92 q^{97}+O(q^{100}) \) 32 * q - 4 * q^3 + 8 * q^5 + 12 * q^12 - 36 * q^15 - 8 * q^16 - 64 * q^20 - 24 * q^23 + 16 * q^25 - 16 * q^27 - 8 * q^31 + 24 * q^36 + 32 * q^37 - 40 * q^38 + 60 * q^42 - 28 * q^45 - 28 * q^47 + 56 * q^48 + 116 * q^53 - 80 * q^56 - 80 * q^58 + 104 * q^60 - 8 * q^67 - 80 * q^70 + 24 * q^71 - 76 * q^75 + 60 * q^78 + 8 * q^80 + 8 * q^81 - 20 * q^82 - 40 * q^86 + 80 * q^91 + 52 * q^92 + 32 * q^93 + 92 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more