LMFDB - Embedded newform 400.2.q.f.149.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(149,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 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("400.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.q (of order $4$, degree $2$, not 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.4767670494822400.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 $ x^12 - 4x^11 + 7x^10 - 4x^9 - 8x^8 + 24x^7 - 38x^6 + 48x^5 - 32x^4 - 32x^3 + 112x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			149.5
Root			$0.719139 + 1.21772i$ of defining polynomial
Character	$\chi$	$=$	400.149
Dual form			400.2.q.f.349.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.21772 + 0.719139i) q^{2} +(1.66783 + 1.66783i) q^{3} +(0.965679 + 1.75142i) q^{4} +(0.831547 + 3.23035i) q^{6} -1.87372 q^{7} +(-0.0835873 + 2.82719i) q^{8} +2.56332i q^{9} +O(q^{10})$	\(q+(1.21772 + 0.719139i) q^{2} +(1.66783 + 1.66783i) q^{3} +(0.965679 + 1.75142i) q^{4} +(0.831547 + 3.23035i) q^{6} -1.87372 q^{7} +(-0.0835873 + 2.82719i) q^{8} +2.56332i q^{9} +(-3.29695 - 3.29695i) q^{11} +(-1.31048 + 4.53166i) q^{12} +(1.90022 + 1.90022i) q^{13} +(-2.28166 - 1.34746i) q^{14} +(-2.13493 + 3.38261i) q^{16} -2.57148i q^{17} +(-1.84338 + 3.12140i) q^{18} +(5.76636 - 5.76636i) q^{19} +(-3.12504 - 3.12504i) q^{21} +(-1.64379 - 6.38572i) q^{22} +7.58574 q^{23} +(-4.85469 + 4.57587i) q^{24} +(0.947414 + 3.68046i) q^{26} +(0.728312 - 0.728312i) q^{27} +(-1.80941 - 3.28166i) q^{28} +(-6.45786 + 6.45786i) q^{29} -0.799135 q^{31} +(-5.03231 + 2.58376i) q^{32} -10.9975i q^{33} +(1.84925 - 3.13134i) q^{34} +(-4.48944 + 2.47534i) q^{36} +(2.69652 - 2.69652i) q^{37} +(11.1686 - 2.87499i) q^{38} +6.33850i q^{39} +0.946984i q^{41} +(-1.55808 - 6.05276i) q^{42} +(-0.829986 + 0.829986i) q^{43} +(2.59054 - 8.95813i) q^{44} +(9.23730 + 5.45520i) q^{46} -1.52421i q^{47} +(-9.20233 + 2.08093i) q^{48} -3.48919 q^{49} +(4.28879 - 4.28879i) q^{51} +(-1.49308 + 5.16309i) q^{52} +(-6.97225 + 6.97225i) q^{53} +(1.41064 - 0.363122i) q^{54} +(0.156619 - 5.29735i) q^{56} +19.2346 q^{57} +(-12.5080 + 3.21976i) q^{58} +(-6.84418 - 6.84418i) q^{59} +(-6.87247 + 6.87247i) q^{61} +(-0.973121 - 0.574689i) q^{62} -4.80293i q^{63} +(-7.98603 - 0.472635i) q^{64} +(7.90874 - 13.3919i) q^{66} +(3.73647 + 3.73647i) q^{67} +(4.50373 - 2.48322i) q^{68} +(12.6517 + 12.6517i) q^{69} -9.34417i q^{71} +(-7.24699 - 0.214261i) q^{72} +0.886316 q^{73} +(5.22277 - 1.34443i) q^{74} +(15.6678 + 4.53086i) q^{76} +(6.17755 + 6.17755i) q^{77} +(-4.55826 + 7.71851i) q^{78} -3.07575 q^{79} +10.1194 q^{81} +(-0.681013 + 1.15316i) q^{82} +(-0.989393 - 0.989393i) q^{83} +(2.45547 - 8.49104i) q^{84} +(-1.60756 + 0.413814i) q^{86} -21.5412 q^{87} +(9.59670 - 9.04553i) q^{88} -10.0942i q^{89} +(-3.56048 - 3.56048i) q^{91} +(7.32539 + 13.2858i) q^{92} +(-1.33282 - 1.33282i) q^{93} +(1.09612 - 1.85606i) q^{94} +(-12.7023 - 4.08377i) q^{96} +7.16829i q^{97} +(-4.24885 - 2.50921i) q^{98} +(8.45113 - 8.45113i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 6 q^{6} + 12 q^{7} + 2 q^{8}+O(q^{10}) $ 12 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 6 * q^6 + 12 * q^7 + 2 * q^8	$ 12 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 6 q^{6} + 12 q^{7} + 2 q^{8} - 2 q^{11} - 6 q^{12} + 4 q^{13} - 14 q^{14} + 2 q^{16} - 18 q^{18} + 14 q^{19} - 20 q^{21} - 20 q^{22} + 12 q^{23} + 14 q^{24} - 16 q^{26} + 10 q^{27} - 10 q^{28} - 4 q^{31} + 2 q^{32} + 6 q^{34} + 2 q^{36} - 8 q^{37} + 28 q^{38} + 10 q^{42} + 44 q^{44} - 10 q^{46} - 58 q^{48} - 4 q^{49} + 10 q^{51} - 16 q^{53} - 10 q^{54} + 6 q^{56} - 16 q^{57} + 4 q^{58} - 20 q^{59} + 4 q^{61} + 22 q^{62} - 38 q^{64} + 32 q^{66} + 50 q^{67} + 50 q^{68} - 54 q^{72} + 40 q^{73} - 10 q^{74} + 60 q^{76} - 8 q^{77} - 48 q^{78} - 12 q^{79} - 8 q^{81} - 12 q^{82} + 2 q^{83} - 34 q^{84} + 6 q^{86} - 64 q^{87} + 56 q^{88} + 50 q^{92} + 44 q^{93} - 32 q^{94} - 34 q^{96} - 30 q^{98} - 12 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 6 * q^6 + 12 * q^7 + 2 * q^8 - 2 * q^11 - 6 * q^12 + 4 * q^13 - 14 * q^14 + 2 * q^16 - 18 * q^18 + 14 * q^19 - 20 * q^21 - 20 * q^22 + 12 * q^23 + 14 * q^24 - 16 * q^26 + 10 * q^27 - 10 * q^28 - 4 * q^31 + 2 * q^32 + 6 * q^34 + 2 * q^36 - 8 * q^37 + 28 * q^38 + 10 * q^42 + 44 * q^44 - 10 * q^46 - 58 * q^48 - 4 * q^49 + 10 * q^51 - 16 * q^53 - 10 * q^54 + 6 * q^56 - 16 * q^57 + 4 * q^58 - 20 * q^59 + 4 * q^61 + 22 * q^62 - 38 * q^64 + 32 * q^66 + 50 * q^67 + 50 * q^68 - 54 * q^72 + 40 * q^73 - 10 * q^74 + 60 * q^76 - 8 * q^77 - 48 * q^78 - 12 * q^79 - 8 * q^81 - 12 * q^82 + 2 * q^83 - 34 * q^84 + 6 * q^86 - 64 * q^87 + 56 * q^88 + 50 * q^92 + 44 * q^93 - 32 * q^94 - 34 * q^96 - 30 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	1.21772	+	0.719139i	0.861057	+	0.508508i
$2$	1.21772	+	0.719139i	0.861057	+	0.508508i
$3$	1.66783	+	1.66783i	0.962922	+	0.962922i	0.999337	−	0.0364144i	$-0.0115936\pi$
$3$	1.66783	+	1.66783i	0.962922	+	0.962922i	−0.0364144	+	0.999337i	$0.511594\pi$
$4$	0.965679	+	1.75142i	0.482839	+	0.875709i
$5$		0			0
$5$		0			0
$6$	0.831547	+	3.23035i	0.339478	+	1.31879i
$7$	−1.87372			−0.708198			−0.354099	−	0.935208i	$-0.615212\pi$
$7$	−1.87372			−0.708198			−0.354099	+	0.935208i	$0.615212\pi$
$8$	−0.0835873	+	2.82719i	−0.0295526	+	0.999563i
$9$			2.56332i			0.854439i
$10$		0			0
$11$	−3.29695	−	3.29695i	−0.994068	−	0.994068i	0.00591443	−	0.999983i	$-0.498117\pi$
$11$	−3.29695	−	3.29695i	−0.994068	−	0.994068i	−0.999983	+	0.00591443i	$0.998117\pi$
$12$	−1.31048	+	4.53166i	−0.378303	+	1.30818i
$13$	1.90022	+	1.90022i	0.527027	+	0.527027i	0.919685	−	0.392658i	$-0.128444\pi$
$13$	1.90022	+	1.90022i	0.527027	+	0.527027i	−0.392658	+	0.919685i	$0.628444\pi$
$14$	−2.28166	−	1.34746i	−0.609799	−	0.360124i
$15$		0			0
$16$	−2.13493	+	3.38261i	−0.533732	+	0.845653i
$17$		−	2.57148i		−	0.623675i	−0.950135	−	0.311838i	$-0.899056\pi$
$17$		−	2.57148i		−	0.623675i	0.950135	−	0.311838i	$-0.100944\pi$
$18$	−1.84338	+	3.12140i	−0.434489	+	0.735721i
$19$	5.76636	−	5.76636i	1.32289	−	1.32289i	0.411472	−	0.911422i	$-0.365015\pi$
$19$	5.76636	−	5.76636i	1.32289	−	1.32289i	0.911422	−	0.411472i	$-0.134985\pi$
$20$		0			0
$21$	−3.12504	−	3.12504i	−0.681940	−	0.681940i
$22$	−1.64379	−	6.38572i	−0.350458	−	1.36144i
$23$	7.58574			1.58174			0.790868	−	0.611987i	$-0.209629\pi$
$23$	7.58574			1.58174			0.790868	+	0.611987i	$0.209629\pi$
$24$	−4.85469	+	4.57587i	−0.990959	+	0.934045i
$25$		0			0
$26$	0.947414	+	3.68046i	0.185803	+	0.721798i
$27$	0.728312	−	0.728312i	0.140164	−	0.140164i
$28$	−1.80941	−	3.28166i	−0.341946	−	0.620175i
$29$	−6.45786	+	6.45786i	−1.19919	+	1.19919i	−0.224787	+	0.974408i	$0.572169\pi$
$29$	−6.45786	+	6.45786i	−1.19919	+	1.19919i	−0.974408	+	0.224787i	$0.927831\pi$
$30$		0			0
$31$	−0.799135			−0.143529			−0.0717644	−	0.997422i	$-0.522863\pi$
$31$	−0.799135			−0.143529			−0.0717644	+	0.997422i	$0.522863\pi$
$32$	−5.03231	+	2.58376i	−0.889596	+	0.456749i
$33$		−	10.9975i		−	1.91442i
$34$	1.84925	−	3.13134i	0.317144	−	0.537020i
$35$		0			0
$36$	−4.48944	+	2.47534i	−0.748240	+	0.412557i
$37$	2.69652	−	2.69652i	0.443305	−	0.443305i	−0.449816	−	0.893121i	$-0.648511\pi$
$37$	2.69652	−	2.69652i	0.443305	−	0.443305i	0.893121	+	0.449816i	$0.148511\pi$
$38$	11.1686	−	2.87499i	1.81179	−	0.466386i
$39$			6.33850i			1.01497i
$40$		0			0
$41$			0.946984i			0.147894i	0.997262	+	0.0739471i	$0.0235596\pi$
$41$			0.946984i			0.147894i	−0.997262	+	0.0739471i	$0.976440\pi$
$42$	−1.55808	−	6.05276i	−0.240417	−	0.933961i
$43$	−0.829986	+	0.829986i	−0.126572	+	0.126572i	−0.767555	−	0.640983i	$-0.778527\pi$
$43$	−0.829986	+	0.829986i	−0.126572	+	0.126572i	0.640983	+	0.767555i	$0.278527\pi$
$44$	2.59054	−	8.95813i	0.390539	−	1.35049i
$45$		0			0
$46$	9.23730	+	5.45520i	1.36197	+	0.804325i
$47$		−	1.52421i		−	0.222329i	−0.993802	−	0.111165i	$-0.964542\pi$
$47$		−	1.52421i		−	0.222329i	0.993802	−	0.111165i	$-0.0354581\pi$
$48$	−9.20233	+	2.08093i	−1.32824	+	0.300356i
$49$	−3.48919			−0.498456
$50$		0			0
$51$	4.28879	−	4.28879i	0.600551	−	0.600551i
$52$	−1.49308	+	5.16309i	−0.207053	+	0.715992i
$53$	−6.97225	+	6.97225i	−0.957712	+	0.957712i	−0.999141	−	0.0414296i	$-0.986809\pi$
$53$	−6.97225	+	6.97225i	−0.957712	+	0.957712i	0.0414296	+	0.999141i	$0.486809\pi$
$54$	1.41064	−	0.363122i	0.191963	−	0.0494147i
$55$		0			0
$56$	0.156619	−	5.29735i	0.0209291	−	0.707889i
$57$	19.2346			2.54769
$58$	−12.5080	+	3.21976i	−1.64238	+	0.422775i
$59$	−6.84418	−	6.84418i	−0.891036	−	0.891036i	0.103585	−	0.994621i	$-0.466969\pi$
$59$	−6.84418	−	6.84418i	−0.891036	−	0.891036i	−0.994621	+	0.103585i	$0.966969\pi$
$60$		0			0
$61$	−6.87247	+	6.87247i	−0.879930	+	0.879930i	−0.993527	−	0.113597i	$-0.963763\pi$
$61$	−6.87247	+	6.87247i	−0.879930	+	0.879930i	0.113597	+	0.993527i	$0.463763\pi$
$62$	−0.973121	−	0.574689i	−0.123587	−	0.0729856i
$63$		−	4.80293i		−	0.605112i
$64$	−7.98603	−	0.472635i	−0.998253	−	0.0590793i
$65$		0			0
$66$	7.90874	−	13.3919i	0.973498	−	1.64843i
$67$	3.73647	+	3.73647i	0.456483	+	0.456483i	0.897499	−	0.441016i	$-0.145382\pi$
$67$	3.73647	+	3.73647i	0.456483	+	0.456483i	−0.441016	+	0.897499i	$0.645382\pi$
$68$	4.50373	−	2.48322i	0.546158	−	0.301135i
$69$	12.6517	+	12.6517i	1.52309	+	1.52309i
$70$		0			0
$71$		−	9.34417i		−	1.10895i	−0.832201	−	0.554475i	$-0.812919\pi$
$71$		−	9.34417i		−	1.10895i	0.832201	−	0.554475i	$-0.187081\pi$
$72$	−7.24699	−	0.214261i	−0.854066	−	0.0252509i
$73$	0.886316			0.103735			0.0518677	−	0.998654i	$-0.483483\pi$
$73$	0.886316			0.103735			0.0518677	+	0.998654i	$0.483483\pi$
$74$	5.22277	−	1.34443i	0.607135	−	0.156287i
$75$		0			0
$76$	15.6678	+	4.53086i	1.79722	+	0.519725i
$77$	6.17755	+	6.17755i	0.703997	+	0.703997i
$78$	−4.55826	+	7.71851i	−0.516122	+	0.873949i
$79$	−3.07575			−0.346049			−0.173024	−	0.984918i	$-0.555354\pi$
$79$	−3.07575			−0.346049			−0.173024	+	0.984918i	$0.555354\pi$
$80$		0			0
$81$	10.1194			1.12437
$82$	−0.681013	+	1.15316i	−0.0752053	+	0.127345i
$83$	−0.989393	−	0.989393i	−0.108600	−	0.108600i	0.650719	−	0.759319i	$-0.274468\pi$
$83$	−0.989393	−	0.989393i	−0.108600	−	0.108600i	−0.759319	+	0.650719i	$0.774468\pi$
$84$	2.45547	−	8.49104i	0.267913	−	0.926448i
$85$		0			0
$86$	−1.60756	+	0.413814i	−0.173348	+	0.0446227i
$87$	−21.5412			−2.30946
$88$	9.59670	−	9.04553i	1.02301	−	0.964257i
$89$		−	10.0942i		−	1.06998i	−0.844859	−	0.534990i	$-0.820316\pi$
$89$		−	10.0942i		−	1.06998i	0.844859	−	0.534990i	$-0.179684\pi$
$90$		0			0
$91$	−3.56048	−	3.56048i	−0.373239	−	0.373239i
$92$	7.32539	+	13.2858i	0.763725	+	1.38514i
$93$	−1.33282	−	1.33282i	−0.138207	−	0.138207i
$94$	1.09612	−	1.85606i	0.113056	−	0.191438i
$95$		0			0
$96$	−12.7023	−	4.08377i	−1.29643	−	0.416798i
$97$			7.16829i			0.727830i	0.931432	+	0.363915i	$0.118560\pi$
$97$			7.16829i			0.727830i	−0.931432	+	0.363915i	$0.881440\pi$
$98$	−4.24885	−	2.50921i	−0.429199	−	0.253469i
$99$	8.45113	−	8.45113i	0.849371	−	0.849371i
$100$		0			0
$101$	−1.05091	−	1.05091i	−0.104570	−	0.104570i	0.652886	−	0.757456i	$-0.273558\pi$
$101$	−1.05091	−	1.05091i	−0.104570	−	0.104570i	−0.757456	+	0.652886i	$0.773558\pi$
$102$	8.30678	−	2.13831i	0.822493	−	0.211724i
$103$	−8.20690			−0.808649			−0.404325	−	0.914616i	$-0.632493\pi$
$103$	−8.20690			−0.808649			−0.404325	+	0.914616i	$0.632493\pi$
$104$	−5.53113	+	5.21346i	−0.542372	+	0.511222i
$105$		0			0
$106$	−13.5043	+	3.47622i	−1.31165	+	0.337641i
$107$	−2.85743	+	2.85743i	−0.276238	+	0.276238i	−0.831605	−	0.555367i	$-0.812578\pi$
$107$	−2.85743	+	2.85743i	−0.276238	+	0.276238i	0.555367	+	0.831605i	$0.312578\pi$
$108$	1.97889	+	0.572264i	0.190419	+	0.0550661i
$109$	11.3735	−	11.3735i	1.08939	−	1.08939i	0.0937940	−	0.995592i	$-0.470100\pi$
$109$	11.3735	−	11.3735i	1.08939	−	1.08939i	0.995592	−	0.0937940i	$-0.0298995\pi$
$110$		0			0
$111$	8.99467			0.853736
$112$	4.00025	−	6.33806i	0.377988	−	0.598890i
$113$		−	3.54221i		−	0.333223i	−0.986023	−	0.166611i	$-0.946717\pi$
$113$		−	3.54221i		−	0.333223i	0.986023	−	0.166611i	$-0.0532825\pi$
$114$	23.4224	+	13.8324i	2.19371	+	1.29552i
$115$		0			0
$116$	−17.5466	−	5.07419i	−1.62916	−	0.471127i
$117$	−4.87088	+	4.87088i	−0.450313	+	0.450313i
$118$	−3.41237	−	13.2562i	−0.314134	−	1.22033i
$119$			4.81822i			0.441685i
$120$		0			0
$121$			10.7398i			0.976343i
$122$	−13.3110	+	3.42648i	−1.20512	+	0.310219i
$123$	−1.57941	+	1.57941i	−0.142411	+	0.142411i
$124$	−0.771707	−	1.39962i	−0.0693014	−	0.125689i
$125$		0			0
$126$	3.45397	−	5.84862i	0.307704	−	0.521036i
$127$		−	18.0693i		−	1.60339i	−0.597735	−	0.801693i	$-0.703933\pi$
$127$		−	18.0693i		−	1.60339i	0.597735	−	0.801693i	$-0.296067\pi$
$128$	−9.38485	−	6.31860i	−0.829511	−	0.558490i
$129$	−2.76855			−0.243757
$130$		0			0
$131$	−6.39614	+	6.39614i	−0.558834	+	0.558834i	−0.928975	−	0.370142i	$-0.879309\pi$
$131$	−6.39614	+	6.39614i	−0.558834	+	0.558834i	0.370142	+	0.928975i	$0.379309\pi$
$132$	19.2612	−	10.6201i	1.67648	−	0.924358i
$133$	−10.8045	+	10.8045i	−0.936871	+	0.936871i
$134$	1.86293	+	7.23702i	0.160933	+	0.625183i
$135$		0			0
$136$	7.27006	+	0.214943i	0.623403	+	0.0184312i
$137$	−10.7357			−0.917212			−0.458606	−	0.888640i	$-0.651651\pi$
$137$	−10.7357			−0.917212			−0.458606	+	0.888640i	$0.651651\pi$
$138$	6.30790	+	24.5046i	0.536964	+	2.08597i
$139$	2.31086	+	2.31086i	0.196005	+	0.196005i	0.798285	−	0.602280i	$-0.205741\pi$
$139$	2.31086	+	2.31086i	0.196005	+	0.196005i	−0.602280	+	0.798285i	$0.705741\pi$
$140$		0			0
$141$	2.54213	−	2.54213i	0.214086	−	0.214086i
$142$	6.71976	−	11.3786i	0.563909	−	0.954869i
$143$		−	12.5299i		−	1.04780i
$144$	−8.67071	−	5.47250i	−0.722559	−	0.456042i
$145$		0			0
$146$	1.07928	+	0.637384i	0.0893221	+	0.0527503i
$147$	−5.81938	−	5.81938i	−0.479974	−	0.479974i
$148$	7.32670	+	2.11876i	0.602251	+	0.174161i
$149$	−1.38743	−	1.38743i	−0.113663	−	0.113663i	0.647988	−	0.761651i	$-0.275611\pi$
$149$	−1.38743	−	1.38743i	−0.113663	−	0.113663i	−0.761651	+	0.647988i	$0.775611\pi$
$150$		0			0
$151$		−	5.68590i		−	0.462712i	−0.972869	−	0.231356i	$-0.925684\pi$
$151$		−	5.68590i		−	0.462712i	0.972869	−	0.231356i	$-0.0743163\pi$
$152$	15.8206	+	16.7846i	1.28322	+	1.36141i
$153$	6.59152			0.532892
$154$	3.08000	+	11.9650i	0.248194	+	0.964170i
$155$		0			0
$156$	−11.1014	+	6.12096i	−0.888820	+	0.490069i
$157$	2.48874	+	2.48874i	0.198623	+	0.198623i	0.799409	−	0.600787i	$-0.205146\pi$
$157$	2.48874	+	2.48874i	0.198623	+	0.198623i	−0.600787	+	0.799409i	$0.705146\pi$
$158$	−3.74540	−	2.21189i	−0.297968	−	0.175969i
$159$	−23.2571			−1.84440
$160$		0			0
$161$	−14.2135			−1.12018
$162$	12.3225	+	7.27722i	0.968149	+	0.571753i
$163$	12.7091	+	12.7091i	0.995451	+	0.995451i	0.999990	−	0.00453842i	$-0.00144463\pi$
$163$	12.7091	+	12.7091i	0.995451	+	0.995451i	−0.00453842	+	0.999990i	$0.501445\pi$
$164$	−1.65857	+	0.914483i	−0.129512	+	0.0714091i
$165$		0			0
$166$	−0.493292	−	1.91631i	−0.0382868	−	0.148735i
$167$	−5.00982			−0.387672			−0.193836	−	0.981034i	$-0.562093\pi$
$167$	−5.00982			−0.387672			−0.193836	+	0.981034i	$0.562093\pi$
$168$	9.09630	−	8.57387i	0.701795	−	0.661489i
$169$		−	5.77830i		−	0.444485i
$170$		0			0
$171$	14.7810	+	14.7810i	1.13033	+	1.13033i
$172$	−2.25515	−	0.652152i	−0.171954	−	0.0497261i
$173$	6.19546	+	6.19546i	0.471032	+	0.471032i	0.902249	−	0.431216i	$-0.141915\pi$
$173$	6.19546	+	6.19546i	0.471032	+	0.471032i	−0.431216	+	0.902249i	$0.641915\pi$
$174$	−26.2312	−	15.4911i	−1.98858	−	1.17438i
$175$		0			0
$176$	18.1911	−	4.11356i	1.37120	−	0.310071i
$177$		−	22.8299i		−	1.71600i
$178$	7.25911	−	12.2919i	0.544093	−	0.921313i
$179$	5.51628	−	5.51628i	0.412306	−	0.412306i	−0.470235	−	0.882541i	$-0.655831\pi$
$179$	5.51628	−	5.51628i	0.412306	−	0.412306i	0.882541	+	0.470235i	$0.155831\pi$
$180$		0			0
$181$	11.8993	+	11.8993i	0.884470	+	0.884470i	0.993985	−	0.109515i	$-0.0349298\pi$
$181$	11.8993	+	11.8993i	0.884470	+	0.884470i	−0.109515	+	0.993985i	$0.534930\pi$
$182$	−1.77518	−	6.89614i	−0.131585	−	0.511176i
$183$	−22.9242			−1.69461
$184$	−0.634072	+	21.4463i	−0.0467444	+	1.58105i
$185$		0			0
$186$	−0.664518	−	2.58149i	−0.0487248	−	0.189284i
$187$	−8.47804	+	8.47804i	−0.619976	+	0.619976i
$188$	2.66954	−	1.47190i	0.194696	−	0.107349i
$189$	−1.36465	+	1.36465i	−0.0992637	+	0.0992637i
$190$		0			0
$191$	11.1278			0.805180			0.402590	−	0.915380i	$-0.368110\pi$
$191$	11.1278			0.805180			0.402590	+	0.915380i	$0.368110\pi$
$192$	−12.5311	−	14.1076i	−0.904352	−	1.01813i
$193$			20.7821i			1.49593i	0.663738	+	0.747965i	$0.268969\pi$
$193$			20.7821i			1.49593i	−0.663738	+	0.747965i	$0.731031\pi$
$194$	−5.15500	+	8.72896i	−0.370107	+	0.626703i
$195$		0			0
$196$	−3.36944	−	6.11103i	−0.240674	−	0.436502i
$197$	−14.0309	+	14.0309i	−0.999663	+	0.999663i	−1.00000		0.000337236i	$-0.999893\pi$
$197$	−14.0309	+	14.0309i	−0.999663	+	0.999663i	0.000337236		1.00000i	$0.499893\pi$
$198$	16.3686	−	4.21357i	1.16327	−	0.299445i
$199$			3.24727i			0.230193i	0.993354	+	0.115096i	$0.0367177\pi$
$199$			3.24727i			0.230193i	−0.993354	+	0.115096i	$0.963282\pi$
$200$		0			0
$201$			12.4636i			0.879115i
$202$	−0.523964	−	2.03547i	−0.0368660	−	0.143215i
$203$	12.1002	−	12.1002i	0.849267	−	0.849267i
$204$	11.6531	+	3.36987i	0.815877	+	0.235938i
$205$		0			0
$206$	−9.99369	−	5.90190i	−0.696294	−	0.411205i
$207$			19.4447i			1.35150i
$208$	−10.4846	+	2.37088i	−0.726974	+	0.164391i
$209$	−38.0228			−2.63009
$210$		0			0
$211$	−10.1821	+	10.1821i	−0.700964	+	0.700964i	−0.964617	−	0.263654i	$-0.915072\pi$
$211$	−10.1821	+	10.1821i	−0.700964	+	0.700964i	0.263654	+	0.964617i	$0.415072\pi$
$212$	−18.9443	−	5.47837i	−1.30110	−	0.376256i
$213$	15.5845	−	15.5845i	1.06783	−	1.06783i
$214$	−5.53443	+	1.42466i	−0.378326	+	0.0973876i
$215$		0			0
$216$	1.99820	+	2.11996i	0.135960	+	0.144245i
$217$	1.49735			0.101647
$218$	22.0289	−	5.67061i	1.49198	−	0.384062i
$219$	1.47822	+	1.47822i	0.0998892	+	0.0998892i
$220$		0			0
$221$	4.88638	−	4.88638i	0.328694	−	0.328694i
$222$	10.9530	+	6.46842i	0.735116	+	0.434132i
$223$			24.0469i			1.61030i	0.593070	+	0.805151i	$0.297916\pi$
$223$			24.0469i			1.61030i	−0.593070	+	0.805151i	$0.702084\pi$
$224$	9.42912	−	4.84124i	0.630010	−	0.323469i
$225$		0			0
$226$	2.54734	−	4.31341i	0.169446	−	0.286924i
$227$	11.9863	+	11.9863i	0.795562	+	0.795562i	0.982392	−	0.186830i	$-0.0598215\pi$
$227$	11.9863	+	11.9863i	0.795562	+	0.795562i	−0.186830	+	0.982392i	$0.559821\pi$
$228$	18.5745	+	33.6879i	1.23012	+	2.23103i
$229$	20.1972	+	20.1972i	1.33467	+	1.33467i	0.901140	+	0.433529i	$0.142732\pi$
$229$	20.1972	+	20.1972i	1.33467	+	1.33467i	0.433529	+	0.901140i	$0.357268\pi$
$230$		0			0
$231$			20.6062i			1.35579i
$232$	−17.7178	−	18.7974i	−1.16323	−	1.23411i
$233$	−10.0655			−0.659410			−0.329705	−	0.944084i	$-0.606949\pi$
$233$	−10.0655			−0.659410			−0.329705	+	0.944084i	$0.606949\pi$
$234$	−9.43419	+	2.42852i	−0.616733	+	0.158757i
$235$		0			0
$236$	5.37774	−	18.5963i	0.350061	−	1.21052i
$237$	−5.12983	−	5.12983i	−0.333218	−	0.333218i
$238$	−3.46497	+	5.86724i	−0.224601	+	0.380316i
$239$	−0.992801			−0.0642189			−0.0321095	−	0.999484i	$-0.510223\pi$
$239$	−0.992801			−0.0642189			−0.0321095	+	0.999484i	$0.510223\pi$
$240$		0			0
$241$	14.1229			0.909738			0.454869	−	0.890558i	$-0.349686\pi$
$241$	14.1229			0.909738			0.454869	+	0.890558i	$0.349686\pi$
$242$	−7.72339	+	13.0780i	−0.496478	+	0.840687i
$243$	14.6924	+	14.6924i	0.942520	+	0.942520i
$244$	−18.6732	−	5.39997i	−1.19543	−	0.345698i
$245$		0			0
$246$	−3.05909	+	0.787462i	−0.195041	+	0.0502068i
$247$	21.9148			1.39440
$248$	0.0667975	−	2.25931i	0.00424165	−	0.143466i
$249$		−	3.30028i		−	0.209147i
$250$		0			0
$251$	1.56681	+	1.56681i	0.0988961	+	0.0988961i	0.754824	−	0.655928i	$-0.227722\pi$
$251$	1.56681	+	1.56681i	0.0988961	+	0.0988961i	−0.655928	+	0.754824i	$0.727722\pi$
$252$	8.41193	−	4.63809i	0.529902	−	0.292172i
$253$	−25.0098	−	25.0098i	−1.57235	−	1.57235i
$254$	12.9943	−	22.0033i	0.815335	−	1.38061i
$255$		0			0
$256$	−6.88415	−	14.4433i	−0.430260	−	0.902705i
$257$		−	10.2593i		−	0.639960i	−0.947424	−	0.319980i	$-0.896324\pi$
$257$		−	10.2593i		−	0.639960i	0.947424	−	0.319980i	$-0.103676\pi$
$258$	−3.37132	−	1.99097i	−0.209889	−	0.123953i
$259$	−5.05251	+	5.05251i	−0.313948	+	0.313948i
$260$		0			0
$261$	−16.5535	−	16.5535i	−1.02464	−	1.02464i
$262$	−12.3884	+	3.18899i	−0.765359	+	0.197016i
$263$	−19.0630			−1.17548			−0.587739	−	0.809051i	$-0.699982\pi$
$263$	−19.0630			−1.17548			−0.587739	+	0.809051i	$0.699982\pi$
$264$	31.0921	+	0.919252i	1.91358	+	0.0565761i
$265$		0			0
$266$	−20.9268	+	5.38692i	−1.28311	+	0.330293i
$267$	16.8354	−	16.8354i	1.03031	−	1.03031i
$268$	−2.93589	+	10.1524i	−0.179338	+	0.620154i
$269$	−3.48459	+	3.48459i	−0.212459	+	0.212459i	−0.805311	−	0.592852i	$-0.798002\pi$
$269$	−3.48459	+	3.48459i	−0.212459	+	0.212459i	0.592852	+	0.805311i	$0.298002\pi$
$270$		0			0
$271$	−30.0045			−1.82264			−0.911322	−	0.411695i	$-0.864937\pi$
$271$	−30.0045			−1.82264			−0.911322	+	0.411695i	$0.864937\pi$
$272$	8.69832	+	5.48992i	0.527413	+	0.332876i
$273$		−	11.8765i		−	0.718801i
$274$	−13.0731	−	7.72045i	−0.789772	−	0.466409i
$275$		0			0
$276$	−9.94096	+	34.3760i	−0.598375	+	2.06919i
$277$	−8.43732	+	8.43732i	−0.506949	+	0.506949i	−0.913589	−	0.406639i	$-0.866701\pi$
$277$	−8.43732	+	8.43732i	−0.506949	+	0.506949i	0.406639	+	0.913589i	$0.366701\pi$
$278$	1.15215	+	4.47581i	0.0691014	+	0.268441i
$279$		−	2.04844i		−	0.122637i
$280$		0			0
$281$		−	6.44714i		−	0.384604i	−0.981336	−	0.192302i	$-0.938405\pi$
$281$		−	6.44714i		−	0.384604i	0.981336	−	0.192302i	$-0.0615954\pi$
$282$	4.92375	−	1.26746i	0.293205	−	0.0754759i
$283$	2.61000	−	2.61000i	0.155148	−	0.155148i	−0.625264	−	0.780413i	$-0.715009\pi$
$283$	2.61000	−	2.61000i	0.155148	−	0.155148i	0.780413	+	0.625264i	$0.215009\pi$
$284$	16.3656	−	9.02347i	0.971117	−	0.535444i
$285$		0			0
$286$	9.01073	−	15.2579i	0.532815	−	0.902217i
$287$		−	1.77438i		−	0.104738i
$288$	−6.62300	−	12.8994i	−0.390264	−	0.760105i
$289$	10.3875			0.611029
$290$		0			0
$291$	−11.9555	+	11.9555i	−0.700844	+	0.700844i
$292$	0.855896	+	1.55231i	0.0500875	+	0.0908420i
$293$	−7.52428	+	7.52428i	−0.439573	+	0.439573i	−0.891868	−	0.452295i	$-0.850605\pi$
$293$	−7.52428	+	7.52428i	−0.439573	+	0.439573i	0.452295	+	0.891868i	$0.350605\pi$
$294$	−2.90143	−	11.2713i	−0.169215	−	0.657356i
$295$		0			0
$296$	7.39818	+	7.84897i	0.430010	+	0.456212i
$297$	−4.80242			−0.278665
$298$	−0.691746	−	2.68726i	−0.0400718	−	0.155669i
$299$	14.4146	+	14.4146i	0.833618	+	0.833618i
$300$		0			0
$301$	1.55516	−	1.55516i	0.0896377	−	0.0896377i
$302$	4.08895	−	6.92383i	0.235293	−	0.398422i
$303$		−	3.50549i		−	0.201385i
$304$	7.19460	+	31.8162i	0.412639	+	1.82478i
$305$		0			0
$306$	8.02661	+	4.74021i	0.458851	+	0.270980i
$307$	12.7130	+	12.7130i	0.725571	+	0.725571i	0.969734	−	0.244163i	$-0.0785133\pi$
$307$	12.7130	+	12.7130i	0.725571	+	0.725571i	−0.244163	+	0.969734i	$0.578513\pi$
$308$	−4.85394	+	16.7850i	−0.276579	+	0.956414i
$309$	−13.6877	−	13.6877i	−0.778667	−	0.778667i
$310$		0			0
$311$		−	11.9313i		−	0.676563i	−0.941045	−	0.338281i	$-0.890154\pi$
$311$		−	11.9313i		−	0.676563i	0.941045	−	0.338281i	$-0.109846\pi$
$312$	−17.9202	−	0.529818i	−1.01453	−	0.0299951i
$313$	34.3458			1.94134			0.970670	−	0.240414i	$-0.0772832\pi$
$313$	34.3458			1.94134			0.970670	+	0.240414i	$0.0772832\pi$
$314$	1.24083	+	4.82033i	0.0700244	+	0.272027i
$315$		0			0
$316$	−2.97019	−	5.38692i	−0.167086	−	0.303038i
$317$	−17.1112	−	17.1112i	−0.961060	−	0.961060i	0.0382097	−	0.999270i	$-0.487835\pi$
$317$	−17.1112	−	17.1112i	−0.961060	−	0.961060i	−0.999270	+	0.0382097i	$0.987835\pi$
$318$	−28.3206	−	16.7251i	−1.58814	−	0.937894i
$319$	42.5825			2.38416
$320$		0			0
$321$	−9.53141			−0.531992
$322$	−17.3081	−	10.2215i	−0.964541	−	0.569622i
$323$	−14.8281	−	14.8281i	−0.825056	−	0.825056i
$324$	9.77205	+	17.7232i	0.542891	+	0.984623i
$325$		0			0
$326$	6.33649	+	24.6157i	0.350946	+	1.36334i
$327$	37.9382			2.09799
$328$	−2.67731	−	0.0791559i	−0.147830	−	0.00437065i
$329$			2.85594i			0.157453i
$330$		0			0
$331$	9.80246	+	9.80246i	0.538792	+	0.538792i	0.923174	−	0.384382i	$-0.125585\pi$
$331$	9.80246	+	9.80246i	0.538792	+	0.538792i	−0.384382	+	0.923174i	$0.625585\pi$
$332$	0.777405	−	2.68828i	0.0426656	−	0.147538i
$333$	6.91203	+	6.91203i	0.378777	+	0.378777i
$334$	−6.10056	−	3.60276i	−0.333808	−	0.197134i
$335$		0			0
$336$	17.2425	−	3.89906i	0.940658	−	0.212711i
$337$			6.07501i			0.330927i	0.986216	+	0.165463i	$0.0529120\pi$
$337$			6.07501i			0.330927i	−0.986216	+	0.165463i	$0.947088\pi$
$338$	4.15540	−	7.03635i	0.226024	−	0.382727i
$339$	5.90780	−	5.90780i	0.320868	−	0.320868i
$340$		0			0
$341$	2.63471	+	2.63471i	0.142677	+	0.142677i
$342$	7.36952	+	28.6287i	0.398498	+	1.54806i
$343$	19.6538			1.06120
$344$	−2.27715	−	2.41590i	−0.122776	−	0.130257i
$345$		0			0
$346$	3.08894	+	11.9997i	0.166062	+	0.645110i
$347$	−5.77231	+	5.77231i	−0.309874	+	0.309874i	−0.844860	−	0.534987i	$-0.820317\pi$
$347$	−5.77231	+	5.77231i	−0.309874	+	0.309874i	0.534987	+	0.844860i	$0.320317\pi$
$348$	−20.8019	−	37.7277i	−1.11510	−	2.02242i
$349$	7.58851	−	7.58851i	0.406203	−	0.406203i	−0.474209	−	0.880412i	$-0.657266\pi$
$349$	7.58851	−	7.58851i	0.406203	−	0.406203i	0.880412	+	0.474209i	$0.157266\pi$
$350$		0			0
$351$	2.76791			0.147740
$352$	25.1098	+	8.07275i	1.33836	+	0.430279i
$353$			16.2285i			0.863753i	0.901933	+	0.431877i	$0.142148\pi$
$353$			16.2285i			0.863753i	−0.901933	+	0.431877i	$0.857852\pi$
$354$	16.4178	−	27.8003i	0.872598	−	1.47757i
$355$		0			0
$356$	17.6791	−	9.74772i	0.936990	−	0.516628i
$357$	−8.03597	+	8.03597i	−0.425309	+	0.425309i
$358$	10.6843	−	2.75031i	0.564680	−	0.145358i
$359$			6.77298i			0.357464i	0.983898	+	0.178732i	$0.0571996\pi$
$359$			6.77298i			0.357464i	−0.983898	+	0.178732i	$0.942800\pi$
$360$		0			0
$361$		−	47.5019i		−	2.50010i
$362$	5.93277	+	23.0473i	0.311819	+	1.21134i
$363$	−17.9121	+	17.9121i	−0.940142	+	0.940142i
$364$	2.79761	−	9.67416i	0.146634	−	0.507064i
$365$		0			0
$366$	−27.9153	−	16.4857i	−1.45915	−	0.861722i
$367$		−	6.35705i		−	0.331835i	−0.986140	−	0.165918i	$-0.946941\pi$
$367$		−	6.35705i		−	0.331835i	0.986140	−	0.165918i	$-0.0530586\pi$
$368$	−16.1950	+	25.6596i	−0.844224	+	1.33760i
$369$	−2.42742			−0.126367
$370$		0			0
$371$	13.0640	−	13.0640i	0.678250	−	0.678250i
$372$	1.04725	−	3.62140i	0.0542974	−	0.187761i
$373$	9.20937	−	9.20937i	0.476843	−	0.476843i	−0.427278	−	0.904121i	$-0.640527\pi$
$373$	9.20937	−	9.20937i	0.476843	−	0.476843i	0.904121	+	0.427278i	$0.140527\pi$
$374$	−16.4208	+	4.22698i	−0.849097	+	0.218572i
$375$		0			0
$376$	4.30925	+	0.127405i	0.222232	+	0.00657041i
$377$	−24.5428			−1.26402
$378$	−2.64313	+	0.680387i	−0.135948	+	0.0349954i
$379$	−5.41600	−	5.41600i	−0.278201	−	0.278201i	0.554189	−	0.832391i	$-0.313028\pi$
$379$	−5.41600	−	5.41600i	−0.278201	−	0.278201i	−0.832391	+	0.554189i	$0.813028\pi$
$380$		0			0
$381$	30.1365	−	30.1365i	1.54394	−	1.54394i
$382$	13.5505	+	8.00244i	0.693306	+	0.409440i
$383$		−	28.1626i		−	1.43904i	−0.694472	−	0.719520i	$-0.744362\pi$
$383$		−	28.1626i		−	1.43904i	0.694472	−	0.719520i	$-0.255638\pi$
$384$	−5.11398	−	26.1907i	−0.260972	−	1.33654i
$385$		0			0
$386$	−14.9452	+	25.3068i	−0.760693	+	1.28808i
$387$	−2.12752	−	2.12752i	−0.108148	−	0.108148i
$388$	−12.5547	+	6.92227i	−0.637367	+	0.351425i
$389$	−9.59783	−	9.59783i	−0.486629	−	0.486629i	0.420611	−	0.907241i	$-0.361816\pi$
$389$	−9.59783	−	9.59783i	−0.486629	−	0.486629i	−0.907241	+	0.420611i	$0.861816\pi$
$390$		0			0
$391$		−	19.5066i		−	0.986490i
$392$	0.291652	−	9.86461i	0.0147307	−	0.498238i
$393$	−21.3354			−1.07623
$394$	−27.1759	+	6.99554i	−1.36910	+	0.352430i
$395$		0			0
$396$	22.9625	+	6.64039i	1.15391	+	0.333692i
$397$	10.4884	+	10.4884i	0.526399	+	0.526399i	0.919497	−	0.393098i	$-0.128597\pi$
$397$	10.4884	+	10.4884i	0.526399	+	0.526399i	−0.393098	+	0.919497i	$0.628597\pi$
$398$	−2.33524	+	3.95426i	−0.117055	+	0.198209i
$399$	−36.0402			−1.80427
$400$		0			0
$401$	−2.44221			−0.121958			−0.0609791	−	0.998139i	$-0.519422\pi$
$401$	−2.44221			−0.121958			−0.0609791	+	0.998139i	$0.519422\pi$
$402$	−8.96306	+	15.1772i	−0.447037	+	0.756969i
$403$	−1.51853	−	1.51853i	−0.0756436	−	0.0756436i
$404$	0.825743	−	2.85543i	0.0410823	−	0.142063i
$405$		0			0
$406$	23.4364	−	6.03292i	1.16313	−	0.299409i
$407$	−17.7806			−0.881350
$408$	11.7667	+	12.4837i	0.582541	+	0.618036i
$409$		−	24.6628i		−	1.21950i	−0.792596	−	0.609748i	$-0.791271\pi$
$409$		−	24.6628i		−	1.21950i	0.792596	−	0.609748i	$-0.208729\pi$
$410$		0			0
$411$	−17.9053	−	17.9053i	−0.883204	−	0.883204i
$412$	−7.92522	−	14.3737i	−0.390448	−	0.708142i
$413$	12.8240	+	12.8240i	0.631030	+	0.631030i
$414$	−13.9834	+	23.6781i	−0.687247	+	1.16372i
$415$		0			0
$416$	−14.4722	−	4.65279i	−0.709560	−	0.228122i
$417$			7.70826i			0.377475i
$418$	−46.3011	−	27.3437i	−2.26466	−	1.33742i
$419$	−19.1661	+	19.1661i	−0.936326	+	0.936326i	−0.998091	−	0.0617649i	$-0.980327\pi$
$419$	−19.1661	+	19.1661i	−0.936326	+	0.936326i	0.0617649	+	0.998091i	$0.480327\pi$
$420$		0			0
$421$	−7.43469	−	7.43469i	−0.362345	−	0.362345i	0.502331	−	0.864676i	$-0.332476\pi$
$421$	−7.43469	−	7.43469i	−0.362345	−	0.362345i	−0.864676	+	0.502331i	$0.832476\pi$
$422$	−19.7213	+	5.07659i	−0.960016	+	0.247124i
$423$	3.90704			0.189967
$424$	−19.1291	−	20.2947i	−0.928991	−	0.985596i
$425$		0			0
$426$	30.1850	−	7.77012i	1.46247	−	0.376464i
$427$	12.8771	−	12.8771i	0.623164	−	0.623164i
$428$	−7.76391	−	2.24519i	−0.375283	−	0.108526i
$429$	20.8977	−	20.8977i	1.00895	−	1.00895i
$430$		0			0
$431$	22.5647			1.08690			0.543451	−	0.839441i	$-0.317117\pi$
$431$	22.5647			1.08690			0.543451	+	0.839441i	$0.317117\pi$
$432$	0.908704	+	4.01849i	0.0437201	+	0.193340i
$433$		−	26.4811i		−	1.27260i	−0.771441	−	0.636301i	$-0.780464\pi$
$433$		−	26.4811i		−	1.27260i	0.771441	−	0.636301i	$-0.219536\pi$
$434$	1.82335	+	1.07680i	0.0875237	+	0.0516882i
$435$		0			0
$436$	30.9030	+	8.93662i	1.47998	+	0.427986i
$437$	43.7421	−	43.7421i	2.09247	−	2.09247i
$438$	0.737013	+	2.86311i	0.0352159	+	0.136805i
$439$		−	0.765288i		−	0.0365252i	−0.999833	−	0.0182626i	$-0.994187\pi$
$439$		−	0.765288i		−	0.0365252i	0.999833	−	0.0182626i	$-0.00581349\pi$
$440$		0			0
$441$		−	8.94390i		−	0.425900i
$442$	9.46423	−	2.43625i	0.450167	−	0.115881i
$443$	20.2685	−	20.2685i	0.962985	−	0.962985i	−0.0363537	−	0.999339i	$-0.511574\pi$
$443$	20.2685	−	20.2685i	0.962985	−	0.962985i	0.999339	+	0.0363537i	$0.0115743\pi$
$444$	8.68596	+	15.7534i	0.412218	+	0.747625i
$445$		0			0
$446$	−17.2931	+	29.2824i	−0.818851	+	1.38656i
$447$		−	4.62800i		−	0.218897i
$448$	14.9635	+	0.885583i	0.706961	+	0.0418399i
$449$	35.2717			1.66457			0.832287	−	0.554345i	$-0.187031\pi$
$449$	35.2717			1.66457			0.832287	+	0.554345i	$0.187031\pi$
$450$		0			0
$451$	3.12216	−	3.12216i	0.147017	−	0.147017i
$452$	6.20388	−	3.42063i	0.291806	−	0.160893i
$453$	9.48312	−	9.48312i	0.445556	−	0.445556i
$454$	5.97615	+	23.2158i	0.280475	+	1.08957i
$455$		0			0
$456$	−1.60777	+	54.3800i	−0.0752908	+	2.54658i
$457$	−9.01188			−0.421558			−0.210779	−	0.977534i	$-0.567600\pi$
$457$	−9.01188			−0.421558			−0.210779	+	0.977534i	$0.567600\pi$
$458$	10.0699	+	39.1191i	0.470537	+	1.82792i
$459$	−1.87284	−	1.87284i	−0.0874167	−	0.0874167i
$460$		0			0
$461$	−22.8247	+	22.8247i	−1.06305	+	1.06305i	−0.0651807	+	0.997873i	$0.520762\pi$
$461$	−22.8247	+	22.8247i	−1.06305	+	1.06305i	−0.997873	+	0.0651807i	$0.979238\pi$
$462$	−14.8187	+	25.0926i	−0.689429	+	1.16741i
$463$		−	3.72721i		−	0.173218i	−0.996242	−	0.0866090i	$-0.972397\pi$
$463$		−	3.72721i		−	0.173218i	0.996242	−	0.0866090i	$-0.0276031\pi$
$464$	−8.05738	−	35.6315i	−0.374054	−	1.65415i
$465$		0			0
$466$	−12.2569	−	7.23846i	−0.567790	−	0.335315i
$467$	−3.23477	−	3.23477i	−0.149687	−	0.149687i	0.628291	−	0.777978i	$-0.283755\pi$
$467$	−3.23477	−	3.23477i	−0.149687	−	0.149687i	−0.777978	+	0.628291i	$0.783755\pi$
$468$	−13.2346	−	3.82724i	−0.611771	−	0.176914i
$469$	−7.00109	−	7.00109i	−0.323280	−	0.323280i
$470$		0			0
$471$			8.30158i			0.382517i
$472$	19.9219	−	18.7777i	0.916979	−	0.864314i
$473$	5.47284			0.251642
$474$	−2.55763	−	9.93575i	−0.117476	−	0.456364i
$475$		0			0
$476$	−8.43871	+	4.65285i	−0.386788	+	0.213263i
$477$	−17.8721	−	17.8721i	−0.818307	−	0.818307i
$478$	−1.20895	−	0.713961i	−0.0552962	−	0.0326558i
$479$	11.0636			0.505508			0.252754	−	0.967531i	$-0.418664\pi$
$479$	11.0636			0.505508			0.252754	+	0.967531i	$0.418664\pi$
$480$		0			0
$481$	10.2480			0.467267
$482$	17.1978	+	10.1563i	0.783336	+	0.462609i
$483$	−23.7057	−	23.7057i	−1.07865	−	1.07865i
$484$	−18.8098	+	10.3712i	−0.854992	+	0.471417i
$485$		0			0
$486$	7.32536	+	28.4572i	0.332285	+	1.29084i
$487$	6.68176			0.302779			0.151390	−	0.988474i	$-0.451625\pi$
$487$	6.68176			0.302779			0.151390	+	0.988474i	$0.451625\pi$
$488$	−18.8553	−	20.0042i	−0.853541	−	0.905550i
$489$			42.3932i			1.91708i
$490$		0			0
$491$	−18.4274	−	18.4274i	−0.831618	−	0.831618i	0.156120	−	0.987738i	$-0.450101\pi$
$491$	−18.4274	−	18.4274i	−0.831618	−	0.831618i	−0.987738	+	0.156120i	$0.950101\pi$
$492$	−4.29141	−	1.24100i	−0.193472	−	0.0559488i
$493$	16.6063	+	16.6063i	0.747908	+	0.747908i
$494$	26.6860	+	15.7597i	1.20066	+	0.709065i
$495$		0			0
$496$	1.70610	−	2.70316i	0.0766060	−	0.121376i
$497$			17.5083i			0.785356i
$498$	2.37336	−	4.01881i	0.106353	−	0.180087i
$499$	−8.84615	+	8.84615i	−0.396008	+	0.396008i	−0.876822	−	0.480814i	$-0.840341\pi$
$499$	−8.84615	+	8.84615i	−0.396008	+	0.396008i	0.480814	+	0.876822i	$0.340341\pi$
$500$		0			0
$501$	−8.35554	−	8.35554i	−0.373298	−	0.373298i
$502$	0.781180	+	3.03469i	0.0348658	+	0.135445i
$503$	16.8746			0.752401			0.376201	−	0.926538i	$-0.377230\pi$
$503$	16.8746			0.752401			0.376201	+	0.926538i	$0.377230\pi$
$504$	13.5788	+	0.401464i	0.604848	+	0.0178826i
$505$		0			0
$506$	−12.4694	−	48.4405i	−0.554332	−	2.15344i
$507$	9.63723	−	9.63723i	0.428004	−	0.428004i
$508$	31.6468	−	17.4491i	1.40410	−	0.774178i
$509$	−20.5691	+	20.5691i	−0.911707	+	0.911707i	−0.996407	−	0.0846994i	$-0.973007\pi$
$509$	−20.5691	+	20.5691i	−0.911707	+	0.911707i	0.0846994	+	0.996407i	$0.473007\pi$
$510$		0			0
$511$	−1.66070			−0.0734652
$512$	2.00376	−	22.5385i	0.0885545	−	0.996071i
$513$		−	8.39943i		−	0.370844i
$514$	7.37788	−	12.4930i	0.325425	−	0.551042i
$515$		0			0
$516$	−2.67353	−	4.84889i	−0.117696	−	0.213460i
$517$	−5.02526	+	5.02526i	−0.221011	+	0.221011i
$518$	−9.78599	+	2.51908i	−0.429972	+	0.110682i
$519$			20.6660i			0.907135i
$520$		0			0
$521$			12.6708i			0.555118i	0.960709	+	0.277559i	$0.0895253\pi$
$521$			12.6708i			0.555118i	−0.960709	+	0.277559i	$0.910475\pi$
$522$	−8.25327	−	32.0619i	−0.361236	−	1.40331i
$523$	−27.8509	+	27.8509i	−1.21784	+	1.21784i	−0.249448	+	0.968388i	$0.580249\pi$
$523$	−27.8509	+	27.8509i	−1.21784	+	1.21784i	−0.968388	+	0.249448i	$0.919751\pi$
$524$	−17.3789	−	5.02570i	−0.759202	−	0.219549i
$525$		0			0
$526$	−23.2134	−	13.7090i	−1.01215	−	0.597740i
$527$			2.05496i			0.0895154i
$528$	37.2003	+	23.4789i	1.61894	+	1.02179i
$529$	34.5435			1.50189
$530$		0			0
$531$	17.5438	−	17.5438i	0.761336	−	0.761336i
$532$	−29.3569	−	8.48954i	−1.27278	−	0.368068i
$533$	−1.79948	+	1.79948i	−0.0779442	+	0.0779442i
$534$	32.6077	−	8.39377i	1.41107	−	0.363234i
$535$		0			0
$536$	−10.8760	+	10.2514i	−0.469774	+	0.442793i
$537$	18.4005			0.794038
$538$	−6.74915	+	1.73734i	−0.290976	+	0.0749023i
$539$	11.5037	+	11.5037i	0.495499	+	0.495499i
$540$		0			0
$541$	−23.4122	+	23.4122i	−1.00657	+	1.00657i	−0.00659048	+	0.999978i	$0.502098\pi$
$541$	−23.4122	+	23.4122i	−1.00657	+	1.00657i	−0.999978	+	0.00659048i	$0.997902\pi$
$542$	−36.5370	−	21.5774i	−1.56940	−	0.926829i
$543$			39.6921i			1.70335i
$544$	6.64409	+	12.9405i	0.284863	+	0.554819i
$545$		0			0
$546$	8.54089	−	14.4623i	0.365516	−	0.618929i
$547$	17.3745	+	17.3745i	0.742878	+	0.742878i	0.973131	−	0.230253i	$-0.0739552\pi$
$547$	17.3745	+	17.3745i	0.742878	+	0.742878i	−0.230253	+	0.973131i	$0.573955\pi$
$548$	−10.3672	−	18.8027i	−0.442866	−	0.803211i
$549$	−17.6163	−	17.6163i	−0.751846	−	0.751846i
$550$		0			0
$551$			74.4767i			3.17282i
$552$	−36.8264	+	34.7113i	−1.56744	+	1.47741i
$553$	5.76308			0.245071
$554$	−16.3419	+	4.20668i	−0.694300	+	0.178725i
$555$		0			0
$556$	−1.81574	+	6.27884i	−0.0770043	+	0.266282i
$557$	22.8889	+	22.8889i	0.969832	+	0.969832i	0.999558	−	0.0297261i	$-0.00946351\pi$
$557$	22.8889	+	22.8889i	0.969832	+	0.969832i	−0.0297261	+	0.999558i	$0.509464\pi$
$558$	1.47311	−	2.49442i	0.0623617	−	0.105597i
$559$	−3.15432			−0.133413
$560$		0			0
$561$	−28.2799			−1.19398
$562$	4.63639	−	7.85081i	0.195574	−	0.331166i
$563$	−19.2489	−	19.2489i	−0.811246	−	0.811246i	0.173574	−	0.984821i	$-0.444468\pi$
$563$	−19.2489	−	19.2489i	−0.811246	−	0.811246i	−0.984821	+	0.173574i	$0.944468\pi$
$564$	6.90721	+	1.99745i	0.290846	+	0.0841079i
$565$		0			0
$566$	5.05520	−	1.30129i	0.212486	−	0.0546975i
$567$	−18.9608			−0.796278
$568$	26.4178	+	0.781054i	1.10846	+	0.0327723i
$569$		−	34.4274i		−	1.44327i	−0.692273	−	0.721635i	$-0.743391\pi$
$569$		−	34.4274i		−	1.44327i	0.692273	−	0.721635i	$-0.256609\pi$
$570$		0			0
$571$	5.85059	+	5.85059i	0.244840	+	0.244840i	0.818849	−	0.574009i	$-0.194613\pi$
$571$	5.85059	+	5.85059i	0.244840	+	0.244840i	−0.574009	+	0.818849i	$0.694613\pi$
$572$	21.9451	−	12.0998i	0.917569	−	0.505920i
$573$	18.5593	+	18.5593i	0.775326	+	0.775326i
$574$	1.27603	−	2.16070i	0.0532603	−	0.0901857i
$575$		0			0
$576$	1.21151	−	20.4707i	0.0504797	−	0.852947i
$577$			32.5042i			1.35317i	0.736365	+	0.676585i	$0.236541\pi$
$577$			32.5042i			1.35317i	−0.736365	+	0.676585i	$0.763459\pi$
$578$	12.6491	+	7.47005i	0.526131	+	0.310713i
$579$	−34.6611	+	34.6611i	−1.44047	+	1.44047i
$580$		0			0
$581$	1.85384	+	1.85384i	0.0769103	+	0.0769103i
$582$	−23.1561	+	5.96077i	−0.959851	+	0.247082i
$583$	45.9743			1.90406
$584$	−0.0740848	+	2.50578i	−0.00306565	+	0.103690i
$585$		0			0
$586$	−14.5735	+	3.75146i	−0.602024	+	0.154971i
$587$	14.7519	−	14.7519i	0.608875	−	0.608875i	−0.333777	−	0.942652i	$-0.608323\pi$
$587$	14.7519	−	14.7519i	0.608875	−	0.608875i	0.942652	+	0.333777i	$0.108323\pi$
$588$	4.57251	−	15.8118i	0.188567	−	0.652068i
$589$	−4.60810	+	4.60810i	−0.189873	+	0.189873i
$590$		0			0
$591$	−46.8024			−1.92520
$592$	3.36440	+	14.8782i	0.138276	+	0.611488i
$593$			20.5310i			0.843108i	0.906803	+	0.421554i	$0.138515\pi$
$593$			20.5310i			0.843108i	−0.906803	+	0.421554i	$0.861485\pi$
$594$	−5.84800	−	3.45361i	−0.239946	−	0.141703i
$595$		0			0
$596$	1.09016	−	3.76979i	0.0446547	−	0.154416i
$597$	−5.41590	+	5.41590i	−0.221658	+	0.221658i
$598$	7.18683	+	27.9190i	0.293891	+	1.14169i
$599$		−	12.3998i		−	0.506644i	−0.967382	−	0.253322i	$-0.918477\pi$
$599$		−	12.3998i		−	0.506644i	0.967382	−	0.253322i	$-0.0815232\pi$
$600$		0			0
$601$			12.3980i			0.505723i	0.967502	+	0.252862i	$0.0813718\pi$
$601$			12.3980i			0.505723i	−0.967502	+	0.252862i	$0.918628\pi$
$602$	3.01212	−	0.775370i	0.122765	−	0.0316017i
$603$	−9.57777	+	9.57777i	−0.390037	+	0.390037i
$604$	9.95839	−	5.49076i	0.405201	−	0.223416i
$605$		0			0
$606$	2.52093	−	4.26870i	0.102406	−	0.173404i
$607$			4.90398i			0.199046i	0.995035	+	0.0995232i	$0.0317318\pi$
$607$			4.90398i			0.199046i	−0.995035	+	0.0995232i	$0.968268\pi$
$608$	−14.1192	+	43.9171i	−0.572610	+	1.78107i
$609$	40.3621			1.63556
$610$		0			0
$611$	2.89635	−	2.89635i	0.117174	−	0.117174i
$612$	6.36529	+	11.5445i	0.257301	+	0.466659i
$613$	−0.408547	+	0.408547i	−0.0165011	+	0.0165011i	−0.715309	−	0.698808i	$-0.753714\pi$
$613$	−0.408547	+	0.408547i	−0.0165011	+	0.0165011i	0.698808	+	0.715309i	$0.253714\pi$
$614$	6.33846	+	24.6233i	0.255800	+	0.993717i
$615$		0			0
$616$	−17.9815	+	16.9487i	−0.724494	+	0.682884i
$617$	6.17186			0.248470			0.124235	−	0.992253i	$-0.460352\pi$
$617$	6.17186			0.248470			0.124235	+	0.992253i	$0.460352\pi$
$618$	−6.82442	−	26.5111i	−0.274518	−	1.06643i
$619$	−18.5138	−	18.5138i	−0.744132	−	0.744132i	0.229238	−	0.973370i	$-0.426377\pi$
$619$	−18.5138	−	18.5138i	−0.744132	−	0.744132i	−0.973370	+	0.229238i	$0.926377\pi$
$620$		0			0
$621$	5.52479	−	5.52479i	0.221702	−	0.221702i
$622$	8.58027	−	14.5290i	0.344037	−	0.582559i
$623$			18.9136i			0.757757i
$624$	−21.4407	−	13.5323i	−0.858315	−	0.541724i
$625$		0			0
$626$	41.8236	+	24.6994i	1.67161	+	0.987187i
$627$	−63.4156	−	63.4156i	−2.53258	−	2.53258i
$628$	−1.95550	+	6.76214i	−0.0780329	+	0.269839i
$629$	−6.93404	−	6.93404i	−0.276478	−	0.276478i
$630$		0			0
$631$		−	20.7940i		−	0.827795i	−0.910323	−	0.413897i	$-0.864167\pi$
$631$		−	20.7940i		−	0.827795i	0.910323	−	0.413897i	$-0.135833\pi$
$632$	0.257094	−	8.69574i	0.0102266	−	0.345898i
$633$	−33.9640			−1.34995
$634$	−8.53130	−	33.1419i	−0.338821	−	1.31623i
$635$		0			0
$636$	−22.4588	−	40.7328i	−0.890551	−	1.61516i
$637$	−6.63024	−	6.63024i	−0.262700	−	0.262700i
$638$	51.8535	+	30.6227i	2.05290	+	1.21237i
$639$	23.9521			0.947530
$640$		0			0
$641$	16.1179			0.636620			0.318310	−	0.947987i	$-0.396885\pi$
$641$	16.1179			0.636620			0.318310	+	0.947987i	$0.396885\pi$
$642$	−11.6066	−	6.85441i	−0.458075	−	0.270522i
$643$	−10.3733	−	10.3733i	−0.409082	−	0.409082i	0.472336	−	0.881419i	$-0.343411\pi$
$643$	−10.3733	−	10.3733i	−0.409082	−	0.409082i	−0.881419	+	0.472336i	$0.843411\pi$
$644$	−13.7257	−	24.8938i	−0.540868	−	0.980954i
$645$		0			0
$646$	−7.39298	−	28.7199i	−0.290873	−	1.12997i
$647$	32.5724			1.28055			0.640276	−	0.768145i	$-0.278820\pi$
$647$	32.5724			1.28055			0.640276	+	0.768145i	$0.278820\pi$
$648$	−0.845850	+	28.6094i	−0.0332281	+	1.12388i
$649$			45.1298i			1.77150i
$650$		0			0
$651$	2.49733	+	2.49733i	0.0978780	+	0.0978780i
$652$	−9.98601	+	34.5318i	−0.391083	+	1.35237i
$653$	−4.31962	−	4.31962i	−0.169040	−	0.169040i	0.617517	−	0.786557i	$-0.288139\pi$
$653$	−4.31962	−	4.31962i	−0.169040	−	0.169040i	−0.786557	+	0.617517i	$0.788139\pi$
$654$	46.1981	+	27.2828i	1.80649	+	1.06684i
$655$		0			0
$656$	−3.20328	−	2.02174i	−0.125067	−	0.0789359i
$657$			2.27191i			0.0886356i
$658$	−2.05382	+	3.47774i	−0.0800662	+	0.135576i
$659$	4.19711	−	4.19711i	0.163496	−	0.163496i	−0.620617	−	0.784114i	$-0.713118\pi$
$659$	4.19711	−	4.19711i	0.163496	−	0.163496i	0.784114	+	0.620617i	$0.213118\pi$
$660$		0			0
$661$	21.2310	+	21.2310i	0.825790	+	0.825790i	0.986931	−	0.161141i	$-0.0515175\pi$
$661$	21.2310	+	21.2310i	0.825790	+	0.825790i	−0.161141	+	0.986931i	$0.551518\pi$
$662$	4.88731	+	18.9860i	0.189951	+	0.737911i
$663$	16.2993			0.633013
$664$	2.87990	−	2.71450i	0.111762	−	0.105343i
$665$		0			0
$666$	3.44620	+	13.3876i	0.133538	+	0.518760i
$667$	−48.9877	+	48.9877i	−1.89681	+	1.89681i
$668$	−4.83788	−	8.77429i	−0.187183	−	0.339488i
$669$	−40.1062	+	40.1062i	−1.55060	+	1.55060i
$670$		0			0
$671$	45.3164			1.74942
$672$	23.8005	+	7.65182i	0.918126	+	0.295175i
$673$			6.08317i			0.234489i	0.993103	+	0.117244i	$0.0374061\pi$
$673$			6.08317i			0.234489i	−0.993103	+	0.117244i	$0.962594\pi$
$674$	−4.36877	+	7.39765i	−0.168279	+	0.284947i
$675$		0			0
$676$	10.1202	−	5.57998i	0.389239	−	0.214615i
$677$	8.42443	−	8.42443i	0.323777	−	0.323777i	−0.526437	−	0.850214i	$-0.676472\pi$
$677$	8.42443	−	8.42443i	0.323777	−	0.323777i	0.850214	+	0.526437i	$0.176472\pi$
$678$	11.4426	−	2.94551i	0.439449	−	0.113122i
$679$		−	13.4313i		−	0.515447i
$680$		0			0
$681$			39.9824i			1.53213i
$682$	1.31361	+	5.10305i	0.0503008	+	0.195406i
$683$	14.7609	−	14.7609i	0.564812	−	0.564812i	−0.365859	−	0.930670i	$-0.619225\pi$
$683$	14.7609	−	14.7609i	0.564812	−	0.564812i	0.930670	+	0.365859i	$0.119225\pi$
$684$	−11.6140	+	40.1615i	−0.444073	+	1.53561i
$685$		0			0
$686$	23.9328	+	14.1338i	0.913757	+	0.539630i
$687$			67.3710i			2.57036i
$688$	−1.03556	−	4.57948i	−0.0394804	−	0.174591i
$689$	−26.4977			−1.00948
$690$		0			0
$691$	−4.06268	+	4.06268i	−0.154552	+	0.154552i	−0.780147	−	0.625596i	$-0.784856\pi$
$691$	−4.06268	+	4.06268i	−0.154552	+	0.154552i	0.625596	+	0.780147i	$0.284856\pi$
$692$	−4.86802	+	16.8337i	−0.185054	+	0.639920i
$693$	−15.8350	+	15.8350i	−0.601523	+	0.601523i
$694$	−11.1801	+	2.87796i	−0.424392	+	0.109246i
$695$		0			0
$696$	1.80057	−	60.9012i	0.0682506	−	2.30845i
$697$	2.43515			0.0922379
$698$	14.6979	−	3.78348i	0.556322	−	0.143207i
$699$	−16.7875	−	16.7875i	−0.634961	−	0.634961i
$700$		0			0
$701$	11.1049	−	11.1049i	0.419428	−	0.419428i	−0.465578	−	0.885007i	$-0.654154\pi$
$701$	11.1049	−	11.1049i	0.419428	−	0.419428i	0.885007	+	0.465578i	$0.154154\pi$
$702$	3.37054	+	1.99051i	0.127213	+	0.0751271i
$703$		−	31.0982i		−	1.17289i
$704$	24.7713	+	27.8878i	0.933603	+	1.05106i
$705$		0			0
$706$	−11.6705	+	19.7617i	−0.439225	+	0.743741i
$707$	1.96911	+	1.96911i	0.0740561	+	0.0740561i
$708$	39.9846	−	22.0463i	1.50271	−	0.828551i
$709$	−13.0114	−	13.0114i	−0.488652	−	0.488652i	0.419229	−	0.907881i	$-0.362300\pi$
$709$	−13.0114	−	13.0114i	−0.488652	−	0.488652i	−0.907881	+	0.419229i	$0.862300\pi$
$710$		0			0
$711$		−	7.88412i		−	0.295678i
$712$	28.5381	+	0.843744i	1.06951	+	0.0316206i
$713$	−6.06203			−0.227025
$714$	−15.5645	+	4.00658i	−0.582488	+	0.149942i
$715$		0			0
$716$	14.9883	+	4.33436i	0.560138	+	0.161983i
$717$	−1.65582	−	1.65582i	−0.0618378	−	0.0618378i
$718$	−4.87071	+	8.24759i	−0.181773	+	0.307797i
$719$	50.0570			1.86681			0.933406	−	0.358821i	$-0.116821\pi$
$719$	50.0570			1.86681			0.933406	+	0.358821i	$0.116821\pi$
$720$		0			0
$721$	15.3774			0.572684
$722$	34.1604	−	57.8439i	1.27132	−	2.15273i
$723$	23.5547	+	23.5547i	0.876007	+	0.876007i
$724$	−9.34977	+	32.3316i	−0.347481	+	1.20160i
$725$		0			0
$726$	−34.6932	+	8.93062i	−1.28759	+	0.331447i
$727$	−27.7141			−1.02786			−0.513930	−	0.857832i	$-0.671811\pi$
$727$	−27.7141			−1.02786			−0.513930	+	0.857832i	$0.671811\pi$
$728$	10.3638	−	9.76854i	0.384107	−	0.362046i
$729$			18.6509i			0.690775i
$730$		0			0
$731$	2.13429	+	2.13429i	0.0789396	+	0.0789396i
$732$	−22.1374	−	40.1499i	−0.818224	−	1.48398i
$733$	−16.8860	−	16.8860i	−0.623698	−	0.623698i	0.322777	−	0.946475i	$-0.395384\pi$
$733$	−16.8860	−	16.8860i	−0.623698	−	0.623698i	−0.946475	+	0.322777i	$0.895384\pi$
$734$	4.57160	−	7.74110i	0.168741	−	0.285729i
$735$		0			0
$736$	−38.1738	+	19.5998i	−1.40711	+	0.722457i
$737$		−	24.6379i		−	0.907550i
$738$	−2.95592	−	1.74565i	−0.108809	−	0.0642584i
$739$	23.6286	−	23.6286i	0.869193	−	0.869193i	−0.123190	−	0.992383i	$-0.539312\pi$
$739$	23.6286	−	23.6286i	0.869193	−	0.869193i	0.992383	+	0.123190i	$0.0393124\pi$
$740$		0			0
$741$	36.5501	+	36.5501i	1.34270	+	1.34270i
$742$	25.3031	−	6.51345i	0.928907	−	0.239116i
$743$	−6.53356			−0.239693			−0.119846	−	0.992792i	$-0.538240\pi$
$743$	−6.53356			−0.239693			−0.119846	+	0.992792i	$0.538240\pi$
$744$	3.87955	−	3.65673i	0.142231	−	0.134062i
$745$		0			0
$746$	17.8372	−	4.59161i	0.653068	−	0.168111i
$747$	2.53613	−	2.53613i	0.0927921	−	0.0927921i
$748$	−23.0356	−	6.66153i	−0.842267	−	0.243570i
$749$	5.35401	−	5.35401i	0.195631	−	0.195631i
$750$		0			0
$751$	−22.8483			−0.833746			−0.416873	−	0.908965i	$-0.636874\pi$
$751$	−22.8483			−0.833746			−0.416873	+	0.908965i	$0.636874\pi$
$752$	5.15583	+	3.25409i	0.188014	+	0.118664i
$753$			5.22634i			0.190459i
$754$	−29.8862	−	17.6496i	−1.08839	−	0.642762i
$755$		0			0
$756$	−3.70789	−	1.07226i	−0.134855	−	0.0389977i
$757$	24.0190	−	24.0190i	0.872985	−	0.872985i	−0.119811	−	0.992797i	$-0.538229\pi$
$757$	24.0190	−	24.0190i	0.872985	−	0.872985i	0.992797	+	0.119811i	$0.0382290\pi$
$758$	−2.70031	−	10.4900i	−0.0980797	−	0.381015i
$759$		−	83.4243i		−	3.02811i
$760$		0			0
$761$		−	5.51772i		−	0.200017i	−0.994987	−	0.100009i	$-0.968113\pi$
$761$		−	5.51772i		−	0.200017i	0.994987	−	0.100009i	$-0.0318871\pi$
$762$	58.3700	−	15.0254i	2.11452	−	0.544314i
$763$	−21.3107	+	21.3107i	−0.771501	+	0.771501i
$764$	10.7459	+	19.4894i	0.388772	+	0.705103i
$765$		0			0
$766$	20.2528	−	34.2941i	0.731763	−	1.23910i
$767$		−	26.0109i		−	0.939200i
$768$	12.6073	−	35.5706i	0.454928	−	1.28354i
$769$	−14.0124			−0.505299			−0.252649	−	0.967558i	$-0.581302\pi$
$769$	−14.0124			−0.505299			−0.252649	+	0.967558i	$0.581302\pi$
$770$		0			0
$771$	17.1108	−	17.1108i	0.616231	−	0.616231i
$772$	−36.3982	+	20.0689i	−1.31000	+	0.722294i
$773$	0.753043	−	0.753043i	0.0270851	−	0.0270851i	−0.693435	−	0.720520i	$-0.743903\pi$
$773$	0.753043	−	0.753043i	0.0270851	−	0.0270851i	0.720520	+	0.693435i	$0.243903\pi$
$774$	−1.06074	−	4.12070i	−0.0381274	−	0.148115i
$775$		0			0
$776$	−20.2661	−	0.599178i	−0.727512	−	0.0215092i
$777$	−16.8535			−0.604614
$778$	−4.78529	−	18.5896i	−0.171561	−	0.666471i
$779$	5.46066	+	5.46066i	0.195648	+	0.195648i
$780$		0			0
$781$	−30.8073	+	30.8073i	−1.10237	+	1.10237i
$782$	14.0279	−	23.7535i	0.501638	−	0.849424i
$783$			9.40668i			0.336167i
$784$	7.44917	−	11.8026i	0.266042	−	0.421521i
$785$		0			0
$786$	−25.9805	−	15.3431i	−0.926693	−	0.547270i
$787$	−29.2752	−	29.2752i	−1.04355	−	1.04355i	−0.999008	−	0.0445395i	$-0.985818\pi$
$787$	−29.2752	−	29.2752i	−1.04355	−	1.04355i	−0.0445395	−	0.999008i	$-0.514182\pi$
$788$	−38.1234	−	11.0247i	−1.35809	−	0.392737i
$789$	−31.7939	−	31.7939i	−1.13189	−	1.13189i
$790$		0			0
$791$			6.63709i			0.235988i
$792$	23.1866	+	24.5994i	0.823899	+	0.874101i
$793$	−26.1185			−0.927494
$794$	5.22932	+	20.3146i	0.185581	+	0.720937i
$795$		0			0
$796$	−5.68733	+	3.13582i	−0.201582	+	0.111146i
$797$	−6.09658	−	6.09658i	−0.215952	−	0.215952i	0.590838	−	0.806790i	$-0.298797\pi$
$797$	−6.09658	−	6.09658i	−0.215952	−	0.215952i	−0.806790	+	0.590838i	$0.798797\pi$
$798$	−43.8869	−	25.9179i	−1.55358	−	0.917485i
$799$	−3.91948			−0.138661
$800$		0			0
$801$	25.8745			0.914232
$802$	−2.97393	−	1.75629i	−0.105013	−	0.0620167i
$803$	−2.92214	−	2.92214i	−0.103120	−	0.103120i
$804$	−21.8290	+	12.0358i	−0.769849	+	0.424471i
$805$		0			0
$806$	−0.757111	−	2.94119i	−0.0266681	−	0.103599i
$807$	−11.6234			−0.409163
$808$	3.05897	−	2.88329i	0.107614	−	0.101434i
$809$			31.5083i			1.10777i	0.832592	+	0.553886i	$0.186856\pi$
$809$			31.5083i			1.10777i	−0.832592	+	0.553886i	$0.813144\pi$
$810$		0			0
$811$	20.2317	+	20.2317i	0.710431	+	0.710431i	0.966625	−	0.256194i	$-0.0824686\pi$
$811$	20.2317	+	20.2317i	0.710431	+	0.710431i	−0.256194	+	0.966625i	$0.582469\pi$
$812$	32.8774	+	9.50760i	1.15377	+	0.333651i
$813$	−50.0424	−	50.0424i	−1.75506	−	1.75506i
$814$	−21.6517	−	12.7867i	−0.758893	−	0.448174i
$815$		0			0
$816$	5.35106	+	23.6636i	0.187325	+	0.828391i
$817$			9.57200i			0.334882i
$818$	17.7359	−	30.0323i	0.620123	−	1.05006i
$819$	9.12664	−	9.12664i	0.318910	−	0.318910i
$820$		0			0
$821$	−19.1821	−	19.1821i	−0.669459	−	0.669459i	0.288132	−	0.957591i	$-0.406966\pi$
$821$	−19.1821	−	19.1821i	−0.669459	−	0.669459i	−0.957591	+	0.288132i	$0.906966\pi$
$822$	−8.92723	−	34.6800i	−0.311373	−	1.20961i
$823$	−11.4746			−0.399979			−0.199989	−	0.979798i	$-0.564091\pi$
$823$	−11.4746			−0.399979			−0.199989	+	0.979798i	$0.564091\pi$
$824$	0.685992	−	23.2025i	0.0238977	−	0.808296i
$825$		0			0
$826$	6.39381	+	24.8383i	0.222469	+	0.864236i
$827$	−17.7573	+	17.7573i	−0.617482	+	0.617482i	−0.944885	−	0.327403i	$-0.893827\pi$
$827$	−17.7573	+	17.7573i	−0.617482	+	0.617482i	0.327403	+	0.944885i	$0.393827\pi$
$828$	−34.0557	+	18.7773i	−1.18352	+	0.652556i
$829$	20.0071	−	20.0071i	0.694876	−	0.694876i	−0.268424	−	0.963301i	$-0.586503\pi$
$829$	20.0071	−	20.0071i	0.694876	−	0.694876i	0.963301	+	0.268424i	$0.0865030\pi$
$830$		0			0
$831$	−28.1440			−0.976306
$832$	−14.2771	−	16.0733i	−0.494970	−	0.557243i
$833$			8.97238i			0.310874i
$834$	−5.54331	+	9.38649i	−0.191949	+	0.325028i
$835$		0			0
$836$	−36.7178	−	66.5939i	−1.26991	−	2.30320i
$837$	−0.582020	+	0.582020i	−0.0201175	+	0.0201175i
$838$	−37.1220	+	9.55584i	−1.28236	+	0.330101i
$839$		−	20.3936i		−	0.704065i	−0.935988	−	0.352033i	$-0.885491\pi$
$839$		−	20.3936i		−	0.704065i	0.935988	−	0.352033i	$-0.114509\pi$
$840$		0			0
$841$		−	54.4079i		−	1.87614i
$842$	−3.70679	−	14.3999i	−0.127744	−	0.496255i
$843$	10.7527	−	10.7527i	0.370344	−	0.370344i
$844$	−27.6657	−	8.00047i	−0.952293	−	0.275387i
$845$		0			0
$846$	4.75768	+	2.80971i	0.163572	+	0.0965997i
$847$		−	20.1233i		−	0.691444i
$848$	−8.69917	−	38.4697i	−0.298731	−	1.32105i
$849$	8.70608			0.298792
$850$		0			0
$851$	20.4551	−	20.4551i	0.701191	−	0.701191i
$852$	42.3446	+	12.2453i	1.45070	+	0.419519i
$853$	37.4481	−	37.4481i	1.28220	−	1.28220i	0.342784	−	0.939414i	$-0.388630\pi$
$853$	37.4481	−	37.4481i	1.28220	−	1.28220i	0.939414	−	0.342784i	$-0.111370\pi$
$854$	24.9410	−	6.42024i	0.853464	−	0.219696i
$855$		0			0
$856$	−7.83965	−	8.31734i	−0.267954	−	0.284281i
$857$	−12.7258			−0.434706			−0.217353	−	0.976093i	$-0.569742\pi$
$857$	−12.7258			−0.434706			−0.217353	+	0.976093i	$0.569742\pi$
$858$	40.4759	−	10.4192i	1.38183	−	0.355705i
$859$	−17.4318	−	17.4318i	−0.594766	−	0.594766i	0.344149	−	0.938915i	$-0.388167\pi$
$859$	−17.4318	−	17.4318i	−0.594766	−	0.594766i	−0.938915	+	0.344149i	$0.888167\pi$
$860$		0			0
$861$	2.95936	−	2.95936i	0.100855	−	0.100855i
$862$	27.4774	+	16.2271i	0.935885	+	0.552699i
$863$			33.6976i			1.14708i	0.819178	+	0.573540i	$0.194430\pi$
$863$			33.6976i			1.14708i	−0.819178	+	0.573540i	$0.805570\pi$
$864$	−1.78331	+	5.54688i	−0.0606694	+	0.188709i
$865$		0			0
$866$	19.0436	−	32.2466i	0.647128	−	1.09578i
$867$	17.3246	+	17.3246i	0.588374	+	0.588374i
$868$	1.44596	+	2.62249i	0.0490791	+	0.0890130i
$869$	10.1406	+	10.1406i	0.343996	+	0.343996i
$870$		0			0
$871$			14.2003i			0.481158i
$872$	31.2044	+	33.1058i	1.05672	+	1.12110i
$873$	−18.3746			−0.621886
$874$	84.7223	−	21.8090i	2.86577	−	0.737699i
$875$		0			0
$876$	−1.16150	+	4.01648i	−0.0392434	+	0.135704i
$877$	−21.8386	−	21.8386i	−0.737436	−	0.737436i	0.234645	−	0.972081i	$-0.424607\pi$
$877$	−21.8386	−	21.8386i	−0.737436	−	0.737436i	−0.972081	+	0.234645i	$0.924607\pi$
$878$	0.550349	−	0.931906i	0.0185734	−	0.0314503i
$879$	−25.0985			−0.846550
$880$		0			0
$881$	−39.3274			−1.32497			−0.662487	−	0.749073i	$-0.730499\pi$
$881$	−39.3274			−1.32497			−0.662487	+	0.749073i	$0.730499\pi$
$882$	6.43191	−	10.8912i	0.216574	−	0.366724i
$883$	6.80206	+	6.80206i	0.228907	+	0.228907i	0.812236	−	0.583329i	$-0.198250\pi$
$883$	6.80206	+	6.80206i	0.228907	+	0.228907i	−0.583329	+	0.812236i	$0.698250\pi$
$884$	13.2768	+	3.83942i	0.446546	+	0.129134i
$885$		0			0
$886$	39.2572	−	10.1055i	1.31887	−	0.339500i
$887$	−29.4190			−0.987793			−0.493897	−	0.869521i	$-0.664428\pi$
$887$	−29.4190			−0.987793			−0.493897	+	0.869521i	$0.664428\pi$
$888$	−0.751840	+	25.4297i	−0.0252301	+	0.853363i
$889$			33.8566i			1.13552i
$890$		0			0
$891$	−33.3630	−	33.3630i	−1.11770	−	1.11770i
$892$	−42.1162	+	23.2216i	−1.41016	+	0.777517i
$893$	−8.78917	−	8.78917i	−0.294118	−	0.294118i
$894$	3.32818	−	5.63561i	0.111311	−	0.188483i
$895$		0			0
$896$	17.5845	+	11.8393i	0.587458	+	0.395522i
$897$			48.0822i			1.60542i
$898$	42.9510	+	25.3652i	1.43329	+	0.846449i
$899$	5.16070	−	5.16070i	0.172119	−	0.172119i
$900$		0			0
$901$	17.9290	+	17.9290i	0.597301	+	0.597301i
$902$	6.04718	−	1.55665i	0.201349	−	0.0518307i
$903$	5.18748			0.172628
$904$	10.0145	+	0.296084i	0.333077	+	0.00984759i
$905$		0			0
$906$	18.3675	−	4.72810i	0.610218	−	0.157081i
$907$	−16.6137	+	16.6137i	−0.551649	+	0.551649i	−0.926917	−	0.375267i	$-0.877551\pi$
$907$	−16.6137	+	16.6137i	−0.551649	+	0.551649i	0.375267	+	0.926917i	$0.377551\pi$
$908$	−9.41814	+	32.5681i	−0.312552	+	1.08081i
$909$	2.69382	−	2.69382i	0.0893485	−	0.0893485i
$910$		0			0
$911$	40.7299			1.34944			0.674721	−	0.738073i	$-0.264264\pi$
$911$	40.7299			1.34944			0.674721	+	0.738073i	$0.264264\pi$
$912$	−41.0646	+	65.0633i	−1.35978	+	2.15446i
$913$			6.52396i			0.215912i
$914$	−10.9739	−	6.48079i	−0.362985	−	0.214365i
$915$		0			0
$916$	−15.8697	+	54.8777i	−0.524351	+	1.81321i
$917$	11.9846	−	11.9846i	0.395765	−	0.395765i
$918$	−0.933760	−	3.62742i	−0.0308187	−	0.119723i
$919$		−	35.6125i		−	1.17475i	−0.809316	−	0.587373i	$-0.800162\pi$
$919$		−	35.6125i		−	1.17475i	0.809316	−	0.587373i	$-0.199838\pi$
$920$		0			0
$921$			42.4064i			1.39734i
$922$	−44.2083	+	11.3800i	−1.45592	+	0.374779i
$923$	17.7560	−	17.7560i	0.584446	−	0.584446i
$924$	−36.0901	+	19.8990i	−1.18728	+	0.654628i
$925$		0			0
$926$	2.68038	−	4.53869i	0.0880828	−	0.149151i
$927$		−	21.0369i		−	0.690942i
$928$	15.8124	−	49.1836i	0.519067	−	1.61453i
$929$	0.570971			0.0187329			0.00936647	−	0.999956i	$-0.497019\pi$
$929$	0.570971			0.0187329			0.00936647	+	0.999956i	$0.497019\pi$
$930$		0			0
$931$	−20.1199	+	20.1199i	−0.659404	+	0.659404i
$932$	−9.72000	−	17.6288i	−0.318389	−	0.577451i
$933$	19.8994	−	19.8994i	0.651477	−	0.651477i
$934$	−1.61279	−	6.26529i	−0.0527722	−	0.205007i
$935$		0			0
$936$	−13.3638	−	14.1780i	−0.436808	−	0.463424i
$937$	21.3585			0.697750			0.348875	−	0.937169i	$-0.386564\pi$
$937$	21.3585			0.697750			0.348875	+	0.937169i	$0.386564\pi$
$938$	−3.49060	−	13.5601i	−0.113972	−	0.442753i
$939$	57.2830	+	57.2830i	1.86936	+	1.86936i
$940$		0			0
$941$	33.6914	−	33.6914i	1.09831	−	1.09831i	0.103700	−	0.994609i	$-0.466932\pi$
$941$	33.6914	−	33.6914i	1.09831	−	1.09831i	0.994609	−	0.103700i	$-0.0330681\pi$
$942$	−5.96999	+	10.1090i	−0.194513	+	0.329369i
$943$			7.18358i			0.233929i
$944$	37.7630	−	8.53937i	1.22908	−	0.277933i
$945$		0			0
$946$	6.66438	+	3.93573i	0.216678	+	0.127962i
$947$	0.421834	+	0.421834i	0.0137078	+	0.0137078i	0.713927	−	0.700220i	$-0.246915\pi$
$947$	0.421834	+	0.421834i	0.0137078	+	0.0137078i	−0.700220	+	0.713927i	$0.746915\pi$
$948$	4.03071	−	13.9382i	0.130911	−	0.452693i
$949$	1.68420	+	1.68420i	0.0546714	+	0.0546714i
$950$		0			0
$951$		−	57.0771i		−	1.85085i
$952$	−13.6220	−	0.402742i	−0.441492	−	0.0130529i
$953$	−27.7261			−0.898137			−0.449069	−	0.893497i	$-0.648244\pi$
$953$	−27.7261			−0.898137			−0.449069	+	0.893497i	$0.648244\pi$
$954$	−8.91067	−	34.6157i	−0.288493	−	1.12072i
$955$		0			0
$956$	−0.958726	−	1.73881i	−0.0310074	−	0.0562371i
$957$	71.0204	+	71.0204i	2.29576	+	2.29576i
$958$	13.4723	+	7.95625i	0.435271	+	0.257055i
$959$	20.1156			0.649567
$960$		0			0
$961$	−30.3614			−0.979399
$962$	12.4792	+	7.36972i	0.402344	+	0.237609i
$963$	−7.32450	−	7.32450i	−0.236029	−	0.236029i
$964$	13.6382	+	24.7352i	0.439257	+	0.796666i
$965$		0			0
$966$	−11.8192	−	45.9147i	−0.380277	−	1.47728i
$967$	41.9640			1.34947			0.674735	−	0.738060i	$-0.264258\pi$
$967$	41.9640			1.34947			0.674735	+	0.738060i	$0.264258\pi$
$968$	−30.3634	−	0.897709i	−0.975916	−	0.0288534i
$969$		−	49.4614i		−	1.58893i
$970$		0			0
$971$	30.0549	+	30.0549i	0.964508	+	0.964508i	0.999391	−	0.0348833i	$-0.0111059\pi$
$971$	30.0549	+	30.0549i	0.964508	+	0.964508i	−0.0348833	+	0.999391i	$0.511106\pi$
$972$	−11.5444	+	39.9208i	−0.370287	+	1.28046i
$973$	−4.32990	−	4.32990i	−0.138810	−	0.138810i
$974$	8.13651	+	4.80511i	0.260710	+	0.153966i
$975$		0			0
$976$	−8.57468	−	37.9192i	−0.274469	−	1.21376i
$977$		−	44.3389i		−	1.41853i	−0.704944	−	0.709263i	$-0.749028\pi$
$977$		−	44.3389i		−	1.41853i	0.704944	−	0.709263i	$-0.250972\pi$
$978$	−30.4866	+	51.6229i	−0.974853	+	1.65072i
$979$	−33.2800	+	33.2800i	−1.06363	+	1.06363i
$980$		0			0
$981$	29.1539	+	29.1539i	0.930814	+	0.930814i
$982$	−9.18755	−	35.6913i	−0.293186	−	1.13896i
$983$	−27.0764			−0.863604			−0.431802	−	0.901968i	$-0.642122\pi$
$983$	−27.0764			−0.863604			−0.431802	+	0.901968i	$0.642122\pi$
$984$	−4.33327	−	4.59731i	−0.138140	−	0.146557i
$985$		0			0
$986$	8.27955	+	32.1639i	0.263674	+	1.02431i
$987$	−4.76323	+	4.76323i	−0.151615	+	0.151615i
$988$	21.1626	+	38.3819i	0.673272	+	1.22109i
$989$	−6.29606	+	6.29606i	−0.200203	+	0.200203i
$990$		0			0
$991$	19.3780			0.615564			0.307782	−	0.951457i	$-0.400413\pi$
$991$	19.3780			0.615564			0.307782	+	0.951457i	$0.400413\pi$
$992$	4.02150	−	2.06477i	0.127683	−	0.0655567i
$993$			32.6977i			1.03763i
$994$	−12.5909	+	21.3202i	−0.399360	+	0.676236i
$995$		0			0
$996$	5.78017	−	3.18701i	0.183152	−	0.100984i
$997$	8.69453	−	8.69453i	0.275359	−	0.275359i	−0.555894	−	0.831253i	$-0.687624\pi$
$997$	8.69453	−	8.69453i	0.275359	−	0.275359i	0.831253	+	0.555894i	$0.187624\pi$
$998$	−17.1337	+	4.41051i	−0.542359	+	0.139612i
$999$		−	3.92782i		−	0.124271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.q.f.149.5		12
4.3	odd	2		1600.2.q.f.49.1		12
5.2	odd	4		400.2.l.f.101.3	✓	12
5.3	odd	4		400.2.l.g.101.4	yes	12
5.4	even	2		400.2.q.e.149.2		12
16.3	odd	4		1600.2.q.e.849.6		12
16.13	even	4		400.2.q.e.349.2		12
20.3	even	4		1600.2.l.f.1201.6		12
20.7	even	4		1600.2.l.g.1201.1		12
20.19	odd	2		1600.2.q.e.49.6		12
80.3	even	4		1600.2.l.f.401.6		12
80.13	odd	4		400.2.l.g.301.4	yes	12
80.19	odd	4		1600.2.q.f.849.1		12
80.29	even	4	inner	400.2.q.f.349.5		12
80.67	even	4		1600.2.l.g.401.1		12
80.77	odd	4		400.2.l.f.301.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.l.f.101.3	✓	12	5.2	odd	4
400.2.l.f.301.3	yes	12	80.77	odd	4
400.2.l.g.101.4	yes	12	5.3	odd	4
400.2.l.g.301.4	yes	12	80.13	odd	4
400.2.q.e.149.2		12	5.4	even	2
400.2.q.e.349.2		12	16.13	even	4
400.2.q.f.149.5		12	1.1	even	1	trivial
400.2.q.f.349.5		12	80.29	even	4	inner
1600.2.l.f.401.6		12	80.3	even	4
1600.2.l.f.1201.6		12	20.3	even	4
1600.2.l.g.401.1		12	80.67	even	4
1600.2.l.g.1201.1		12	20.7	even	4
1600.2.q.e.49.6		12	20.19	odd	2
1600.2.q.e.849.6		12	16.3	odd	4
1600.2.q.f.49.1		12	4.3	odd	2
1600.2.q.f.849.1		12	80.19	odd	4

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.q (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.21772 + 0.719139i) q^{2} +(1.66783 + 1.66783i) q^{3} +(0.965679 + 1.75142i) q^{4} +(0.831547 + 3.23035i) q^{6} -1.87372 q^{7} +(-0.0835873 + 2.82719i) q^{8} +2.56332i q^{9} +O(q^{10})\)	\(q+(1.21772 + 0.719139i) q^{2} +(1.66783 + 1.66783i) q^{3} +(0.965679 + 1.75142i) q^{4} +(0.831547 + 3.23035i) q^{6} -1.87372 q^{7} +(-0.0835873 + 2.82719i) q^{8} +2.56332i q^{9} +(-3.29695 - 3.29695i) q^{11} +(-1.31048 + 4.53166i) q^{12} +(1.90022 + 1.90022i) q^{13} +(-2.28166 - 1.34746i) q^{14} +(-2.13493 + 3.38261i) q^{16} -2.57148i q^{17} +(-1.84338 + 3.12140i) q^{18} +(5.76636 - 5.76636i) q^{19} +(-3.12504 - 3.12504i) q^{21} +(-1.64379 - 6.38572i) q^{22} +7.58574 q^{23} +(-4.85469 + 4.57587i) q^{24} +(0.947414 + 3.68046i) q^{26} +(0.728312 - 0.728312i) q^{27} +(-1.80941 - 3.28166i) q^{28} +(-6.45786 + 6.45786i) q^{29} -0.799135 q^{31} +(-5.03231 + 2.58376i) q^{32} -10.9975i q^{33} +(1.84925 - 3.13134i) q^{34} +(-4.48944 + 2.47534i) q^{36} +(2.69652 - 2.69652i) q^{37} +(11.1686 - 2.87499i) q^{38} +6.33850i q^{39} +0.946984i q^{41} +(-1.55808 - 6.05276i) q^{42} +(-0.829986 + 0.829986i) q^{43} +(2.59054 - 8.95813i) q^{44} +(9.23730 + 5.45520i) q^{46} -1.52421i q^{47} +(-9.20233 + 2.08093i) q^{48} -3.48919 q^{49} +(4.28879 - 4.28879i) q^{51} +(-1.49308 + 5.16309i) q^{52} +(-6.97225 + 6.97225i) q^{53} +(1.41064 - 0.363122i) q^{54} +(0.156619 - 5.29735i) q^{56} +19.2346 q^{57} +(-12.5080 + 3.21976i) q^{58} +(-6.84418 - 6.84418i) q^{59} +(-6.87247 + 6.87247i) q^{61} +(-0.973121 - 0.574689i) q^{62} -4.80293i q^{63} +(-7.98603 - 0.472635i) q^{64} +(7.90874 - 13.3919i) q^{66} +(3.73647 + 3.73647i) q^{67} +(4.50373 - 2.48322i) q^{68} +(12.6517 + 12.6517i) q^{69} -9.34417i q^{71} +(-7.24699 - 0.214261i) q^{72} +0.886316 q^{73} +(5.22277 - 1.34443i) q^{74} +(15.6678 + 4.53086i) q^{76} +(6.17755 + 6.17755i) q^{77} +(-4.55826 + 7.71851i) q^{78} -3.07575 q^{79} +10.1194 q^{81} +(-0.681013 + 1.15316i) q^{82} +(-0.989393 - 0.989393i) q^{83} +(2.45547 - 8.49104i) q^{84} +(-1.60756 + 0.413814i) q^{86} -21.5412 q^{87} +(9.59670 - 9.04553i) q^{88} -10.0942i q^{89} +(-3.56048 - 3.56048i) q^{91} +(7.32539 + 13.2858i) q^{92} +(-1.33282 - 1.33282i) q^{93} +(1.09612 - 1.85606i) q^{94} +(-12.7023 - 4.08377i) q^{96} +7.16829i q^{97} +(-4.24885 - 2.50921i) q^{98} +(8.45113 - 8.45113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 6 q^{6} + 12 q^{7} + 2 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 6 * q^6 + 12 * q^7 + 2 * q^8	\( 12 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 6 q^{6} + 12 q^{7} + 2 q^{8} - 2 q^{11} - 6 q^{12} + 4 q^{13} - 14 q^{14} + 2 q^{16} - 18 q^{18} + 14 q^{19} - 20 q^{21} - 20 q^{22} + 12 q^{23} + 14 q^{24} - 16 q^{26} + 10 q^{27} - 10 q^{28} - 4 q^{31} + 2 q^{32} + 6 q^{34} + 2 q^{36} - 8 q^{37} + 28 q^{38} + 10 q^{42} + 44 q^{44} - 10 q^{46} - 58 q^{48} - 4 q^{49} + 10 q^{51} - 16 q^{53} - 10 q^{54} + 6 q^{56} - 16 q^{57} + 4 q^{58} - 20 q^{59} + 4 q^{61} + 22 q^{62} - 38 q^{64} + 32 q^{66} + 50 q^{67} + 50 q^{68} - 54 q^{72} + 40 q^{73} - 10 q^{74} + 60 q^{76} - 8 q^{77} - 48 q^{78} - 12 q^{79} - 8 q^{81} - 12 q^{82} + 2 q^{83} - 34 q^{84} + 6 q^{86} - 64 q^{87} + 56 q^{88} + 50 q^{92} + 44 q^{93} - 32 q^{94} - 34 q^{96} - 30 q^{98} - 12 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 6 * q^6 + 12 * q^7 + 2 * q^8 - 2 * q^11 - 6 * q^12 + 4 * q^13 - 14 * q^14 + 2 * q^16 - 18 * q^18 + 14 * q^19 - 20 * q^21 - 20 * q^22 + 12 * q^23 + 14 * q^24 - 16 * q^26 + 10 * q^27 - 10 * q^28 - 4 * q^31 + 2 * q^32 + 6 * q^34 + 2 * q^36 - 8 * q^37 + 28 * q^38 + 10 * q^42 + 44 * q^44 - 10 * q^46 - 58 * q^48 - 4 * q^49 + 10 * q^51 - 16 * q^53 - 10 * q^54 + 6 * q^56 - 16 * q^57 + 4 * q^58 - 20 * q^59 + 4 * q^61 + 22 * q^62 - 38 * q^64 + 32 * q^66 + 50 * q^67 + 50 * q^68 - 54 * q^72 + 40 * q^73 - 10 * q^74 + 60 * q^76 - 8 * q^77 - 48 * q^78 - 12 * q^79 - 8 * q^81 - 12 * q^82 + 2 * q^83 - 34 * q^84 + 6 * q^86 - 64 * q^87 + 56 * q^88 + 50 * q^92 + 44 * q^93 - 32 * q^94 - 34 * q^96 - 30 * q^98 - 12 * q^99

Introduction

L-functions

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