LMFDB - Embedded newform 605.2.e.b.483.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(362,605)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.83094932229$
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			483.3
Character	$\chi$	$=$	605.483
Dual form			605.2.e.b.362.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07485 - 1.07485i) q^{2} +(0.563723 + 0.563723i) q^{3} +0.310591i q^{4} +(2.23083 - 0.152980i) q^{5} -1.21183i q^{6} +(0.135390 + 0.135390i) q^{7} +(-1.81586 + 1.81586i) q^{8} -2.36443i q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 32 * q - 4 * q^3 + 8 * q^5	$ 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}+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

Display 100 coefficients 10 coefficients

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	0.216296	−	0.976328i	$-0.430602\pi$
$2$	−1.07485	−	1.07485i	−0.760031	−	0.760031i	−0.976328	+	0.216296i	$0.930602\pi$
$3$	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	0.732230	−	0.681057i	$-0.238480\pi$
$7$	0.135390	+	0.135390i	0.0511728	+	0.0511728i	−0.681057	+	0.732230i	$0.738480\pi$
$8$	−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	−0.335089	−	0.942186i	$-0.608766\pi$
$13$	2.18892	−	2.18892i	0.607098	−	0.607098i	0.942186	+	0.335089i	$0.108766\pi$
$14$		−	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	0.313820	−	0.949482i	$-0.398391\pi$
$17$	−2.62090	−	2.62090i	−0.635662	−	0.635662i	−0.949482	+	0.313820i	$0.898391\pi$
$18$	−2.54140	+	2.54140i	−0.599014	+	0.599014i
$19$	−0.743791			−0.170637			−0.0853187	−	0.996354i	$-0.527191\pi$
$19$	−0.743791			−0.170637			−0.0853187	+	0.996354i	$0.527191\pi$
$20$	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	$-0.153174\pi$
$29$	9.54720			1.77287			0.886436	+	0.462852i	$0.153174\pi$
$30$	−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	$-0.824862\pi$
$41$		−	6.69597i		−	1.04573i	0.852414	−	0.522867i	$-0.175138\pi$
$42$	0.164071	−	0.164071i	0.0253166	−	0.0253166i
$43$	3.72708	−	3.72708i	0.568374	−	0.568374i	−0.363299	−	0.931673i	$-0.618350\pi$
$43$	3.72708	−	3.72708i	0.568374	−	0.568374i	0.931673	+	0.363299i	$0.118350\pi$
$44$		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	$-0.876866\pi$
$61$		−	5.89303i		−	0.754525i	0.926106	−	0.377262i	$-0.123134\pi$
$62$	−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	−0.799477	−	0.600697i	$-0.794890\pi$
$73$	−1.69838	+	1.69838i	−0.198780	+	0.198780i	0.600697	+	0.799477i	$0.294890\pi$
$74$	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	$-0.487991\pi$
$79$	0.670485			0.0754355			0.0377177	+	0.999288i	$0.487991\pi$
$80$	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	$0.618284\pi$
$83$	−11.7967	+	11.7967i	−1.29485	+	1.29485i	−0.931748	+	0.363106i	$0.881716\pi$
$84$	−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	$0.0771720\pi$
$101$			4.82544i			0.480150i	−0.970754	+	0.240075i	$0.922828\pi$
$102$	−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	0.975544	−	0.219803i	$-0.0705416\pi$
$107$	7.81744	+	7.81744i	0.755741	+	0.755741i	−0.219803	+	0.975544i	$0.570542\pi$
$108$	0.939243	+	0.939243i	0.0903787	+	0.0903787i
$109$	9.54212			0.913969			0.456985	−	0.889475i	$-0.348929\pi$
$109$	9.54212			0.913969			0.456985	+	0.889475i	$0.348929\pi$
$110$		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	0.996586	−	0.0825589i	$-0.0263093\pi$
$127$	10.3006	+	10.3006i	0.914027	+	0.914027i	−0.0825589	+	0.996586i	$0.526309\pi$
$128$	−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	$0.140349\pi$
$131$			9.76926i			0.853544i	−0.904359	+	0.426772i	$0.859651\pi$
$132$		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	$-0.352938\pi$
$139$	10.5105			0.891493			0.445747	+	0.895159i	$0.352938\pi$
$140$	−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	$-0.575849\pi$
$149$	−5.76241			−0.472075			−0.236038	+	0.971744i	$0.575849\pi$
$150$	−0.827127	−	6.00244i	−0.0675347	−	0.490097i
$151$			14.9642i			1.21777i	0.793259	+	0.608885i	$0.208383\pi$
$151$			14.9642i			1.21777i	−0.793259	+	0.608885i	$0.791617\pi$
$152$	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	0.295367	−	0.955384i	$-0.404558\pi$
$167$	−8.52930	−	8.52930i	−0.660017	−	0.660017i	−0.955384	+	0.295367i	$0.904558\pi$
$168$	−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	−0.957745	−	0.287618i	$-0.907137\pi$
$173$	−8.81415	+	8.81415i	−0.670127	+	0.670127i	0.287618	+	0.957745i	$0.407137\pi$
$174$		−	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	−0.841767	−	0.539842i	$-0.818484\pi$
$193$	−4.19447	+	4.19447i	−0.301925	+	0.301925i	0.539842	+	0.841767i	$0.318484\pi$
$194$	−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	0.259918	−	0.965631i	$-0.416304\pi$
$197$	−9.90515	−	9.90515i	−0.705713	−	0.705713i	−0.965631	+	0.259918i	$0.916304\pi$
$198$		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	$-0.934540\pi$
$211$		−	5.93238i		−	0.408402i	0.978929	−	0.204201i	$-0.0654596\pi$
$212$	−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	0.943834	−	0.330421i	$-0.107191\pi$
$227$	9.24199	+	9.24199i	0.613412	+	0.613412i	−0.330421	+	0.943834i	$0.607191\pi$
$228$	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	−0.969554	−	0.244878i	$-0.921252\pi$
$233$	−11.0617	+	11.0617i	−0.724676	+	0.724676i	0.244878	+	0.969554i	$0.421252\pi$
$234$			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	$-0.445357\pi$
$239$	5.28173			0.341647			0.170823	+	0.985302i	$0.445357\pi$
$240$	6.08035	+	5.29994i	0.392485	+	0.342110i
$241$		−	16.1676i		−	1.04144i	−0.853726	−	0.520722i	$-0.825663\pi$
$241$		−	16.1676i		−	1.04144i	0.853726	−	0.520722i	$-0.174337\pi$
$242$		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	−0.962664	−	0.270700i	$-0.912745\pi$
$263$	−11.2218	+	11.2218i	−0.691964	+	0.691964i	0.270700	+	0.962664i	$0.412745\pi$
$264$		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	$0.182141\pi$
$271$			17.8282i			1.08298i	−0.840706	+	0.541492i	$0.817859\pi$
$272$	−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	0.799529	−	0.600628i	$-0.205083\pi$
$277$	3.31038	+	3.31038i	0.198901	+	0.198901i	−0.600628	+	0.799529i	$0.705083\pi$
$278$	−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	$-0.871297\pi$
$281$		−	13.1893i		−	0.786808i	0.919366	−	0.393404i	$-0.128703\pi$
$282$	10.5947	+	10.5947i	0.630907	+	0.630907i
$283$	16.1125	−	16.1125i	0.957789	−	0.957789i	−0.0413554	−	0.999145i	$-0.513168\pi$
$283$	16.1125	−	16.1125i	0.957789	−	0.957789i	0.999145	+	0.0413554i	$0.0131676\pi$
$284$		−	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	−0.541881	−	0.840456i	$-0.682287\pi$
$293$	5.11078	−	5.11078i	0.298575	−	0.298575i	0.840456	+	0.541881i	$0.182287\pi$
$294$	−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	$-0.948232\pi$
$307$	−20.1272	−	20.1272i	−1.14872	−	1.14872i	−0.161918	−	0.986804i	$-0.551768\pi$
$308$		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	0.838467	−	0.544952i	$-0.183452\pi$
$337$	5.38821	+	5.38821i	0.293515	+	0.293515i	−0.544952	+	0.838467i	$0.683452\pi$
$338$	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	0.507405	−	0.861708i	$-0.330605\pi$
$347$	−6.59993	−	6.59993i	−0.354303	−	0.354303i	−0.861708	+	0.507405i	$0.830605\pi$
$348$	−1.67159	+	1.67159i	−0.0896068	+	0.0896068i
$349$	−1.50177			−0.0803880			−0.0401940	−	0.999192i	$-0.512798\pi$
$349$	−1.50177			−0.0803880			−0.0401940	+	0.999192i	$0.512798\pi$
$350$	−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	$-0.744216\pi$
$359$	−26.3042			−1.38828			−0.694142	+	0.719838i	$0.744216\pi$
$360$	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	−0.847662	−	0.530536i	$-0.821991\pi$
$373$	−6.12473	+	6.12473i	−0.317126	+	0.317126i	0.530536	+	0.847662i	$0.321991\pi$
$374$		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	$-0.466131\pi$
$409$	4.29562			0.212405			0.106202	+	0.994345i	$0.466131\pi$
$410$	−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	$0.0765650\pi$
$431$			9.89129i			0.476446i	−0.971210	+	0.238223i	$0.923435\pi$
$432$	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	$-0.300420\pi$
$439$	24.5862			1.17344			0.586718	+	0.809791i	$0.300420\pi$
$440$		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	0.586880	−	0.809674i	$-0.300356\pi$
$457$	−4.76277	−	4.76277i	−0.222793	−	0.222793i	−0.809674	+	0.586880i	$0.800356\pi$
$458$	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	$0.236806\pi$
$461$			29.0801i			1.35440i	−0.735801	+	0.677198i	$0.763194\pi$
$462$		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	$-0.295241\pi$
$479$	26.2551			1.19963			0.599814	+	0.800140i	$0.295241\pi$
$480$	−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	$0.135872\pi$
$491$			18.3477i			0.828019i	−0.910273	+	0.414009i	$0.864128\pi$
$492$	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	−0.786268	−	0.617886i	$-0.787989\pi$
$503$	−3.77641	+	3.77641i	−0.168382	+	0.168382i	0.617886	+	0.786268i	$0.287989\pi$
$504$			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	−0.666057	−	0.745901i	$-0.732019\pi$
$523$	1.82596	−	1.82596i	0.0798437	−	0.0798437i	0.745901	+	0.666057i	$0.232019\pi$
$524$	−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	$-0.936385\pi$
$541$		−	9.23515i		−	0.397050i	0.980096	−	0.198525i	$-0.0636151\pi$
$542$	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	0.690731	−	0.723112i	$-0.257289\pi$
$547$	−0.757332	−	0.757332i	−0.0323812	−	0.0323812i	−0.723112	+	0.690731i	$0.757289\pi$
$548$	−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	$-0.884718\pi$
$557$	−30.4317	−	30.4317i	−1.28943	−	1.28943i	−0.354304	−	0.935130i	$-0.615282\pi$
$558$	−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	−0.978233	−	0.207511i	$-0.933464\pi$
$563$	−18.2874	+	18.2874i	−0.770722	+	0.770722i	0.207511	+	0.978233i	$0.433464\pi$
$564$		−	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	$-0.692882\pi$
$569$	−27.1717			−1.13910			−0.569548	+	0.821958i	$0.692882\pi$
$570$	0.137888	+	2.01076i	0.00577550	+	0.0842214i
$571$			40.5475i			1.69686i	0.529308	+	0.848430i	$0.322451\pi$
$571$			40.5475i			1.69686i	−0.529308	+	0.848430i	$0.677549\pi$
$572$		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	−0.357243	−	0.934012i	$-0.616283\pi$
$593$	14.0452	−	14.0452i	0.576769	−	0.576769i	0.934012	+	0.357243i	$0.116283\pi$
$594$		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	$-0.945345\pi$
$601$		−	8.37748i		−	0.341725i	0.985295	−	0.170862i	$-0.0546553\pi$
$602$	−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	0.808661	−	0.588275i	$-0.200193\pi$
$607$	5.42972	+	5.42972i	0.220386	+	0.220386i	−0.588275	+	0.808661i	$0.700193\pi$
$608$	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	$-0.416115\pi$
$613$	30.3535	−	30.3535i	1.22597	−	1.22597i	0.965476	−	0.260492i	$-0.0838848\pi$
$614$			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	$-0.479068\pi$
$659$	3.37375			0.131423			0.0657113	+	0.997839i	$0.479068\pi$
$660$		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	$0.513889\pi$
$673$	−27.0491	+	27.0491i	−1.04267	+	1.04267i	−0.999048	+	0.0436186i	$0.986111\pi$
$674$		−	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	0.118140	−	0.992997i	$-0.462307\pi$
$677$	−22.7631	−	22.7631i	−0.874857	−	0.874857i	−0.992997	+	0.118140i	$0.962307\pi$
$678$	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	$-0.821040\pi$
$701$		−	28.2273i		−	1.06613i	0.846074	−	0.533066i	$-0.178960\pi$
$702$	−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	$0.569523\pi$
$733$	−32.2972	+	32.2972i	−1.19292	+	1.19292i	−0.976243	+	0.216680i	$0.930477\pi$
$734$	−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	$-0.522247\pi$
$739$	−3.79675			−0.139666			−0.0698329	+	0.997559i	$0.522247\pi$
$740$	−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	$-0.466090\pi$
$743$	30.0019	−	30.0019i	1.10066	−	1.10066i	0.994331	−	0.106331i	$-0.0339103\pi$
$744$	−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	$0.185421\pi$
$761$			30.3518i			1.10025i	−0.835081	+	0.550127i	$0.814579\pi$
$762$	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	$-0.737458\pi$
$769$	−37.6421			−1.35741			−0.678705	+	0.734411i	$0.737458\pi$
$770$		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	0.455039	−	0.890472i	$-0.349625\pi$
$787$	−12.2154	−	12.2154i	−0.435433	−	0.435433i	−0.890472	+	0.455039i	$0.849625\pi$
$788$	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	$-0.413697\pi$
$809$	15.2351			0.535638			0.267819	+	0.963469i	$0.413697\pi$
$810$	9.43883	+	8.22736i	0.331647	+	0.289080i
$811$			45.5573i			1.59973i	0.600178	+	0.799866i	$0.295096\pi$
$811$			45.5573i			1.59973i	−0.600178	+	0.799866i	$0.704904\pi$
$812$	−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	$-0.832953\pi$
$821$		−	28.7123i		−	1.00207i	0.865428	−	0.501034i	$-0.167047\pi$
$822$	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	0.0239670	−	0.999713i	$-0.492370\pi$
$827$	−28.0601	−	28.0601i	−0.975746	−	0.975746i	−0.999713	+	0.0239670i	$0.992370\pi$
$828$	−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	−0.855575	−	0.517679i	$-0.826796\pi$
$853$	−9.86864	+	9.86864i	−0.337896	+	0.337896i	0.517679	+	0.855575i	$0.326796\pi$
$854$	−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	0.0773373	−	0.997005i	$-0.475358\pi$
$857$	−26.9229	−	26.9229i	−0.919668	−	0.919668i	−0.997005	+	0.0773373i	$0.975358\pi$
$858$		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	0.843537	−	0.537071i	$-0.180469\pi$
$877$	9.07573	+	9.07573i	0.306466	+	0.306466i	−0.537071	+	0.843537i	$0.680469\pi$
$878$	−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	0.572796	−	0.819698i	$-0.305859\pi$
$887$	−7.35335	−	7.35335i	−0.246901	−	0.246901i	−0.819698	+	0.572796i	$0.805859\pi$
$888$	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	$-0.548116\pi$
$919$	−9.13000			−0.301171			−0.150585	+	0.988597i	$0.548116\pi$
$920$	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	0.509996	−	0.860177i	$-0.329647\pi$
$937$	−10.7192	−	10.7192i	−0.350181	−	0.350181i	−0.860177	+	0.509996i	$0.829647\pi$
$938$	−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	$-0.884208\pi$
$941$		−	21.8290i		−	0.711605i	0.934561	−	0.355803i	$-0.115792\pi$
$942$	−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	−0.541767	−	0.840529i	$-0.682244\pi$
$953$	9.22299	−	9.22299i	0.298762	−	0.298762i	0.840529	+	0.541767i	$0.182244\pi$
$954$	−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	0.891464	−	0.453092i	$-0.149679\pi$
$967$	13.6319	+	13.6319i	0.438372	+	0.438372i	−0.453092	+	0.891464i	$0.649679\pi$
$968$		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	0.952155	−	0.305617i	$-0.0988627\pi$
$997$	20.4146	+	20.4146i	0.646537	+	0.646537i	−0.305617	+	0.952155i	$0.598863\pi$
$998$	−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.483.3		32
5.2	odd	4	inner	605.2.e.b.362.14		32
11.2	odd	10		55.2.l.a.18.1	yes	32
11.3	even	5		605.2.m.d.233.1		32
11.4	even	5		605.2.m.c.578.4		32
11.5	even	5		55.2.l.a.8.4	yes	32
11.6	odd	10		605.2.m.e.118.1		32
11.7	odd	10		605.2.m.d.578.1		32
11.8	odd	10		605.2.m.c.233.4		32
11.9	even	5		605.2.m.e.403.4		32
11.10	odd	2	inner	605.2.e.b.483.14		32
33.2	even	10		495.2.bj.a.73.4		32
33.5	odd	10		495.2.bj.a.118.1		32
44.27	odd	10		880.2.cm.a.833.4		32
44.35	even	10		880.2.cm.a.513.1		32
55.2	even	20		55.2.l.a.7.4	✓	32
55.7	even	20		605.2.m.d.457.1		32
55.13	even	20		275.2.bm.b.7.1		32
55.17	even	20		605.2.m.e.602.4		32
55.24	odd	10		275.2.bm.b.18.4		32
55.27	odd	20		55.2.l.a.52.1	yes	32
55.32	even	4	inner	605.2.e.b.362.3		32
55.37	odd	20		605.2.m.c.457.4		32
55.38	odd	20		275.2.bm.b.107.4		32
55.42	odd	20		605.2.m.e.282.1		32
55.47	odd	20		605.2.m.d.112.1		32
55.49	even	10		275.2.bm.b.118.1		32
55.52	even	20		605.2.m.c.112.4		32
165.2	odd	20		495.2.bj.a.172.1		32
165.137	even	20		495.2.bj.a.217.4		32
220.27	even	20		880.2.cm.a.657.1		32
220.167	odd	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	55.2	even	20
55.2.l.a.8.4	yes	32	11.5	even	5
55.2.l.a.18.1	yes	32	11.2	odd	10
55.2.l.a.52.1	yes	32	55.27	odd	20
275.2.bm.b.7.1		32	55.13	even	20
275.2.bm.b.18.4		32	55.24	odd	10
275.2.bm.b.107.4		32	55.38	odd	20
275.2.bm.b.118.1		32	55.49	even	10
495.2.bj.a.73.4		32	33.2	even	10
495.2.bj.a.118.1		32	33.5	odd	10
495.2.bj.a.172.1		32	165.2	odd	20
495.2.bj.a.217.4		32	165.137	even	20
605.2.e.b.362.3		32	55.32	even	4	inner
605.2.e.b.362.14		32	5.2	odd	4	inner
605.2.e.b.483.3		32	1.1	even	1	trivial
605.2.e.b.483.14		32	11.10	odd	2	inner
605.2.m.c.112.4		32	55.52	even	20
605.2.m.c.233.4		32	11.8	odd	10
605.2.m.c.457.4		32	55.37	odd	20
605.2.m.c.578.4		32	11.4	even	5
605.2.m.d.112.1		32	55.47	odd	20
605.2.m.d.233.1		32	11.3	even	5
605.2.m.d.457.1		32	55.7	even	20
605.2.m.d.578.1		32	11.7	odd	10
605.2.m.e.118.1		32	11.6	odd	10
605.2.m.e.282.1		32	55.42	odd	20
605.2.m.e.403.4		32	11.9	even	5
605.2.m.e.602.4		32	55.17	even	20
880.2.cm.a.337.4		32	220.167	odd	20
880.2.cm.a.513.1		32	44.35	even	10
880.2.cm.a.657.1		32	220.27	even	20
880.2.cm.a.833.4		32	44.27	odd	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.07485 - 1.07485i) q^{2} +(0.563723 + 0.563723i) q^{3} +0.310591i q^{4} +(2.23083 - 0.152980i) q^{5} -1.21183i q^{6} +(0.135390 + 0.135390i) q^{7} +(-1.81586 + 1.81586i) q^{8} -2.36443i q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} + 8 q^{5}+O(q^{10}) \) 32 * q - 4 * q^3 + 8 * q^5	\( 32 q - 4 q^{3} + 8 q^{5} + 12 q^{12} - 36 q^{15} - 8 q^{16} - 64 q^{20} - 24 q^{23} + 16 q^{25} - 16 q^{27} - 8 q^{31} + 24 q^{36} + 32 q^{37} - 40 q^{38} + 60 q^{42} - 28 q^{45} - 28 q^{47} + 56 q^{48} + 116 q^{53} - 80 q^{56} - 80 q^{58} + 104 q^{60} - 8 q^{67} - 80 q^{70} + 24 q^{71} - 76 q^{75} + 60 q^{78} + 8 q^{80} + 8 q^{81} - 20 q^{82} - 40 q^{86} + 80 q^{91} + 52 q^{92} + 32 q^{93} + 92 q^{97}+O(q^{100}) \) 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