LMFDB - Embedded newform 845.2.f.d.408.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(408,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.408"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,4,-12,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			408.8
Root			$1.83163i$ of defining polynomial
Character	$\chi$	$=$	845.408
Dual form			845.2.f.d.437.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.83163i q^{2} +(-1.40138 - 1.40138i) q^{3} -1.35488 q^{4} +(1.69810 + 1.45480i) q^{5} +(2.56682 - 2.56682i) q^{6} -3.53890 q^{7} +1.18163i q^{8} +0.927746i q^{9} +(-2.66466 + 3.11030i) q^{10} +(2.73940 + 2.73940i) q^{11} +(1.89870 + 1.89870i) q^{12} -6.48197i q^{14} +(-0.340953 - 4.41843i) q^{15} -4.87406 q^{16} +(-1.43251 - 1.43251i) q^{17} -1.69929 q^{18} +(0.379911 + 0.379911i) q^{19} +(-2.30072 - 1.97108i) q^{20} +(4.95936 + 4.95936i) q^{21} +(-5.01758 + 5.01758i) q^{22} +(-0.215293 + 0.215293i) q^{23} +(1.65591 - 1.65591i) q^{24} +(0.767094 + 4.94081i) q^{25} +(-2.90402 + 2.90402i) q^{27} +4.79478 q^{28} -1.97769i q^{29} +(8.09293 - 0.624501i) q^{30} +(-4.13563 + 4.13563i) q^{31} -6.56423i q^{32} -7.67790i q^{33} +(2.62382 - 2.62382i) q^{34} +(-6.00942 - 5.14841i) q^{35} -1.25698i q^{36} -5.41773 q^{37} +(-0.695857 + 0.695857i) q^{38} +(-1.71904 + 2.00652i) q^{40} +(0.475748 - 0.475748i) q^{41} +(-9.08372 + 9.08372i) q^{42} +(-6.23095 + 6.23095i) q^{43} +(-3.71155 - 3.71155i) q^{44} +(-1.34969 + 1.57541i) q^{45} +(-0.394337 - 0.394337i) q^{46} -9.75201 q^{47} +(6.83043 + 6.83043i) q^{48} +5.52385 q^{49} +(-9.04974 + 1.40503i) q^{50} +4.01498i q^{51} +(3.16254 + 3.16254i) q^{53} +(-5.31910 - 5.31910i) q^{54} +(0.666490 + 8.63708i) q^{55} -4.18167i q^{56} -1.06480i q^{57} +3.62239 q^{58} +(-8.59785 + 8.59785i) q^{59} +(0.461950 + 5.98642i) q^{60} -2.88632 q^{61} +(-7.57495 - 7.57495i) q^{62} -3.28320i q^{63} +2.27514 q^{64} +14.0631 q^{66} +2.28989i q^{67} +(1.94087 + 1.94087i) q^{68} +0.603415 q^{69} +(9.43000 - 11.0070i) q^{70} +(3.26771 - 3.26771i) q^{71} -1.09625 q^{72} -14.7546i q^{73} -9.92329i q^{74} +(5.84897 - 7.99895i) q^{75} +(-0.514732 - 0.514732i) q^{76} +(-9.69449 - 9.69449i) q^{77} -1.59718i q^{79} +(-8.27665 - 7.09080i) q^{80} +10.9225 q^{81} +(0.871396 + 0.871396i) q^{82} +7.57341 q^{83} +(-6.71932 - 6.71932i) q^{84} +(-0.348525 - 4.51655i) q^{85} +(-11.4128 - 11.4128i) q^{86} +(-2.77149 + 2.77149i) q^{87} +(-3.23695 + 3.23695i) q^{88} +(3.32661 - 3.32661i) q^{89} +(-2.88556 - 2.47213i) q^{90} +(0.291695 - 0.291695i) q^{92} +11.5912 q^{93} -17.8621i q^{94} +(0.0924314 + 1.19782i) q^{95} +(-9.19900 + 9.19900i) q^{96} +17.8254i q^{97} +10.1177i q^{98} +(-2.54147 + 2.54147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{3} - 12 q^{4} - 4 q^{6} - 4 q^{7} - 8 q^{10} - 8 q^{11} - 24 q^{12} - 28 q^{15} + 4 q^{16} - 14 q^{17} - 4 q^{19} + 12 q^{20} - 4 q^{21} - 32 q^{22} + 8 q^{23} + 4 q^{24} + 18 q^{25} + 4 q^{27}+ \cdots - 60 q^{99}+O(q^{100}) $ 20 * q + 4 * q^3 - 12 * q^4 - 4 * q^6 - 4 * q^7 - 8 * q^10 - 8 * q^11 - 24 * q^12 - 28 * q^15 + 4 * q^16 - 14 * q^17 - 4 * q^19 + 12 * q^20 - 4 * q^21 - 32 * q^22 + 8 * q^23 + 4 * q^24 + 18 * q^25 + 4 * q^27 + 36 * q^28 + 40 * q^30 - 2 * q^34 - 20 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^40 + 38 * q^41 + 16 * q^42 - 32 * q^43 + 36 * q^44 + 6 * q^45 - 4 * q^46 + 40 * q^47 + 28 * q^48 - 36 * q^49 - 42 * q^50 - 10 * q^53 - 36 * q^54 - 16 * q^55 - 8 * q^59 - 28 * q^60 + 32 * q^61 + 4 * q^62 + 20 * q^64 - 32 * q^66 - 50 * q^68 + 32 * q^69 + 12 * q^70 + 40 * q^71 + 8 * q^72 + 4 * q^75 + 16 * q^76 - 28 * q^77 - 112 * q^80 + 28 * q^81 - 34 * q^82 - 48 * q^83 - 8 * q^84 + 2 * q^85 - 60 * q^86 - 28 * q^87 - 32 * q^88 - 12 * q^89 + 46 * q^90 - 8 * q^92 + 64 * q^93 + 40 * q^95 - 56 * q^96 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.83163i			1.29516i	0.761998	+	0.647580i	$0.224219\pi$
$2$			1.83163i			1.29516i	−0.761998	+	0.647580i	$0.775781\pi$
$3$	−1.40138	−	1.40138i	−0.809089	−	0.809089i	0.175407	−	0.984496i	$-0.443876\pi$
$3$	−1.40138	−	1.40138i	−0.809089	−	0.809089i	−0.984496	+	0.175407i	$0.943876\pi$
$4$	−1.35488			−0.677439
$5$	1.69810	+	1.45480i	0.759414	+	0.650608i
$5$	1.69810	+	1.45480i	0.759414	+	0.650608i
$6$	2.56682	−	2.56682i	1.04790	−	1.04790i
$7$	−3.53890			−1.33758			−0.668790	−	0.743451i	$-0.733188\pi$
$7$	−3.53890			−1.33758			−0.668790	+	0.743451i	$0.733188\pi$
$8$			1.18163i			0.417769i
$9$			0.927746i			0.309249i
$10$	−2.66466	+	3.11030i	−0.842641	+	0.983562i
$11$	2.73940	+	2.73940i	0.825961	+	0.825961i	0.986955	−	0.160994i	$-0.0514701\pi$
$11$	2.73940	+	2.73940i	0.825961	+	0.825961i	−0.160994	+	0.986955i	$0.551470\pi$
$12$	1.89870	+	1.89870i	0.548108	+	0.548108i
$13$		0			0
$13$		0			0
$14$		−	6.48197i		−	1.73238i
$15$	−0.340953	−	4.41843i	−0.0880337	−	1.14083i
$16$	−4.87406			−1.21852
$17$	−1.43251	−	1.43251i	−0.347434	−	0.347434i	0.511719	−	0.859153i	$-0.329009\pi$
$17$	−1.43251	−	1.43251i	−0.347434	−	0.347434i	−0.859153	+	0.511719i	$0.829009\pi$
$18$	−1.69929			−0.400526
$19$	0.379911	+	0.379911i	0.0871575	+	0.0871575i	0.749341	−	0.662184i	$-0.230370\pi$
$19$	0.379911	+	0.379911i	0.0871575	+	0.0871575i	−0.662184	+	0.749341i	$0.730370\pi$
$20$	−2.30072	−	1.97108i	−0.514456	−	0.440747i
$21$	4.95936	+	4.95936i	1.08222	+	1.08222i
$22$	−5.01758	+	5.01758i	−1.06975	+	1.06975i
$23$	−0.215293	+	0.215293i	−0.0448916	+	0.0448916i	−0.729196	−	0.684305i	$-0.760106\pi$
$23$	−0.215293	+	0.215293i	−0.0448916	+	0.0448916i	0.684305	+	0.729196i	$0.260106\pi$
$24$	1.65591	−	1.65591i	0.338012	−	0.338012i
$25$	0.767094	+	4.94081i	0.153419	+	0.988161i
$26$		0			0
$27$	−2.90402	+	2.90402i	−0.558879	+	0.558879i
$28$	4.79478			0.906129
$29$		−	1.97769i		−	0.367247i	−0.982997	−	0.183624i	$-0.941217\pi$
$29$		−	1.97769i		−	0.367247i	0.982997	−	0.183624i	$-0.0587827\pi$
$30$	8.09293	−	0.624501i	1.47756	−	0.114018i
$31$	−4.13563	+	4.13563i	−0.742781	+	0.742781i	−0.973112	−	0.230331i	$-0.926019\pi$
$31$	−4.13563	+	4.13563i	−0.742781	+	0.742781i	0.230331	+	0.973112i	$0.426019\pi$
$32$		−	6.56423i		−	1.16040i
$33$		−	7.67790i		−	1.33655i
$34$	2.62382	−	2.62382i	0.449982	−	0.449982i
$35$	−6.00942	−	5.14841i	−1.01578	−	0.870240i
$36$		−	1.25698i		−	0.209497i
$37$	−5.41773			−0.890669			−0.445335	−	0.895364i	$-0.646915\pi$
$37$	−5.41773			−0.890669			−0.445335	+	0.895364i	$0.646915\pi$
$38$	−0.695857	+	0.695857i	−0.112883	+	0.112883i
$39$		0			0
$40$	−1.71904	+	2.00652i	−0.271803	+	0.317259i
$41$	0.475748	−	0.475748i	0.0742994	−	0.0742994i	−0.668981	−	0.743280i	$-0.733269\pi$
$41$	0.475748	−	0.475748i	0.0742994	−	0.0742994i	0.743280	+	0.668981i	$0.233269\pi$
$42$	−9.08372	+	9.08372i	−1.40165	+	1.40165i
$43$	−6.23095	+	6.23095i	−0.950211	+	0.950211i	−0.998818	−	0.0486066i	$-0.984522\pi$
$43$	−6.23095	+	6.23095i	−0.950211	+	0.950211i	0.0486066	+	0.998818i	$0.484522\pi$
$44$	−3.71155	−	3.71155i	−0.559538	−	0.559538i
$45$	−1.34969	+	1.57541i	−0.201200	+	0.234848i
$46$	−0.394337	−	0.394337i	−0.0581418	−	0.0581418i
$47$	−9.75201			−1.42248			−0.711238	−	0.702951i	$-0.751865\pi$
$47$	−9.75201			−1.42248			−0.711238	+	0.702951i	$0.751865\pi$
$48$	6.83043	+	6.83043i	0.985887	+	0.985887i
$49$	5.52385			0.789121
$50$	−9.04974	+	1.40503i	−1.27983	+	0.198702i
$51$			4.01498i			0.562209i
$52$		0			0
$53$	3.16254	+	3.16254i	0.434409	+	0.434409i	0.890125	−	0.455716i	$-0.150617\pi$
$53$	3.16254	+	3.16254i	0.434409	+	0.434409i	−0.455716	+	0.890125i	$0.650617\pi$
$54$	−5.31910	−	5.31910i	−0.723838	−	0.723838i
$55$	0.666490	+	8.63708i	0.0898695	+	1.16462i
$56$		−	4.18167i		−	0.558799i
$57$		−	1.06480i		−	0.141036i
$58$	3.62239			0.475644
$59$	−8.59785	+	8.59785i	−1.11934	+	1.11934i	−0.127506	+	0.991838i	$0.540697\pi$
$59$	−8.59785	+	8.59785i	−1.11934	+	1.11934i	−0.991838	+	0.127506i	$0.959303\pi$
$60$	0.461950	+	5.98642i	0.0596374	+	0.772844i
$61$	−2.88632			−0.369555			−0.184778	−	0.982780i	$-0.559157\pi$
$61$	−2.88632			−0.369555			−0.184778	+	0.982780i	$0.559157\pi$
$62$	−7.57495	−	7.57495i	−0.962020	−	0.962020i
$63$		−	3.28320i		−	0.413645i
$64$	2.27514			0.284392
$65$		0			0
$66$	14.0631			1.73105
$67$			2.28989i			0.279754i	0.990169	+	0.139877i	$0.0446708\pi$
$67$			2.28989i			0.279754i	−0.990169	+	0.139877i	$0.955329\pi$
$68$	1.94087	+	1.94087i	0.235365	+	0.235365i
$69$	0.603415			0.0726426
$70$	9.43000	−	11.0070i	1.12710	−	1.31559i
$71$	3.26771	−	3.26771i	0.387806	−	0.387806i	−0.486098	−	0.873904i	$-0.661580\pi$
$71$	3.26771	−	3.26771i	0.387806	−	0.387806i	0.873904	+	0.486098i	$0.161580\pi$
$72$	−1.09625			−0.129194
$73$		−	14.7546i		−	1.72690i	−0.504436	−	0.863449i	$-0.668299\pi$
$73$		−	14.7546i		−	1.72690i	0.504436	−	0.863449i	$-0.331701\pi$
$74$		−	9.92329i		−	1.15356i
$75$	5.84897	−	7.99895i	0.675381	−	0.923639i
$76$	−0.514732	−	0.514732i	−0.0590438	−	0.0590438i
$77$	−9.69449	−	9.69449i	−1.10479	−	1.10479i
$78$		0			0
$79$		−	1.59718i		−	0.179696i	−0.995955	−	0.0898482i	$-0.971362\pi$
$79$		−	1.59718i		−	0.179696i	0.995955	−	0.0898482i	$-0.0286382\pi$
$80$	−8.27665	−	7.09080i	−0.925358	−	0.792776i
$81$	10.9225			1.21361
$82$	0.871396	+	0.871396i	0.0962296	+	0.0962296i
$83$	7.57341			0.831290			0.415645	−	0.909527i	$-0.363556\pi$
$83$	7.57341			0.831290			0.415645	+	0.909527i	$0.363556\pi$
$84$	−6.71932	−	6.71932i	−0.733138	−	0.733138i
$85$	−0.348525	−	4.51655i	−0.0378029	−	0.489889i
$86$	−11.4128	−	11.4128i	−1.23068	−	1.23068i
$87$	−2.77149	+	2.77149i	−0.297135	+	0.297135i
$88$	−3.23695	+	3.23695i	−0.345061	+	0.345061i
$89$	3.32661	−	3.32661i	0.352620	−	0.352620i	−0.508464	−	0.861083i	$-0.669786\pi$
$89$	3.32661	−	3.32661i	0.352620	−	0.352620i	0.861083	+	0.508464i	$0.169786\pi$
$90$	−2.88556	−	2.47213i	−0.304165	−	0.260586i
$91$		0			0
$92$	0.291695	−	0.291695i	0.0304113	−	0.0304113i
$93$	11.5912			1.20195
$94$		−	17.8621i		−	1.84233i
$95$	0.0924314	+	1.19782i	0.00948326	+	0.122894i
$96$	−9.19900	+	9.19900i	−0.938869	+	0.938869i
$97$			17.8254i			1.80989i	0.425528	+	0.904945i	$0.360088\pi$
$97$			17.8254i			1.80989i	−0.425528	+	0.904945i	$0.639912\pi$
$98$			10.1177i			1.02204i
$99$	−2.54147	+	2.54147i	−0.255427	+	0.255427i
$100$	−1.03932	−	6.69419i	−0.103932	−	0.669419i
$101$		−	4.55389i		−	0.453129i	−0.973996	−	0.226565i	$-0.927251\pi$
$101$		−	4.55389i		−	0.453129i	0.973996	−	0.226565i	$-0.0727494\pi$
$102$	−7.35396			−0.728151
$103$	9.79285	−	9.79285i	0.964918	−	0.964918i	−0.0344872	−	0.999405i	$-0.510980\pi$
$103$	9.79285	−	9.79285i	0.964918	−	0.964918i	0.999405	+	0.0344872i	$0.0109798\pi$
$104$		0			0
$105$	1.20660	+	15.6364i	0.117752	+	1.52596i
$106$	−5.79262	+	5.79262i	−0.562629	+	0.562629i
$107$	−4.99942	+	4.99942i	−0.483312	+	0.483312i	−0.906188	−	0.422876i	$-0.861021\pi$
$107$	−4.99942	+	4.99942i	−0.483312	+	0.483312i	0.422876	+	0.906188i	$0.361021\pi$
$108$	3.93459	−	3.93459i	0.378606	−	0.378606i
$109$	9.89281	+	9.89281i	0.947560	+	0.947560i	0.998692	−	0.0511324i	$-0.0162830\pi$
$109$	9.89281	+	9.89281i	0.947560	+	0.947560i	−0.0511324	+	0.998692i	$0.516283\pi$
$110$	−15.8199	+	1.22077i	−1.50837	+	0.116395i
$111$	7.59231	+	7.59231i	0.720630	+	0.720630i
$112$	17.2488			1.62986
$113$	1.62104	+	1.62104i	0.152494	+	0.152494i	0.779231	−	0.626737i	$-0.215610\pi$
$113$	1.62104	+	1.62104i	0.152494	+	0.152494i	−0.626737	+	0.779231i	$0.715610\pi$
$114$	1.95032			0.182664
$115$	−0.678797	+	0.0523802i	−0.0632982	+	0.00488448i
$116$			2.67952i			0.248787i
$117$		0			0
$118$	−15.7481	−	15.7481i	−1.44973	−	1.44973i
$119$	5.06950	+	5.06950i	0.464720	+	0.464720i
$120$	5.22093	−	0.402880i	0.476604	−	0.0367777i
$121$			4.00866i			0.364423i
$122$		−	5.28668i		−	0.478633i
$123$	−1.33341			−0.120230
$124$	5.60327	−	5.60327i	0.503188	−	0.503188i
$125$	−5.88530	+	9.50596i	−0.526397	+	0.850239i
$126$	6.01362			0.535736
$127$	−0.909391	−	0.909391i	−0.0806954	−	0.0806954i	0.665607	−	0.746302i	$-0.268173\pi$
$127$	−0.909391	−	0.909391i	−0.0806954	−	0.0806954i	−0.746302	+	0.665607i	$0.768173\pi$
$128$		−	8.96125i		−	0.792070i
$129$	17.4639			1.53761
$130$		0			0
$131$	−5.59439			−0.488785			−0.244392	−	0.969676i	$-0.578588\pi$
$131$	−5.59439			−0.488785			−0.244392	+	0.969676i	$0.578588\pi$
$132$			10.4026i			0.905431i
$133$	−1.34447	−	1.34447i	−0.116580	−	0.116580i
$134$	−4.19423			−0.362326
$135$	−9.15610	+	0.706541i	−0.788032	+	0.0608094i
$136$	1.69269	−	1.69269i	0.145147	−	0.145147i
$137$	14.2902			1.22089			0.610446	−	0.792058i	$-0.290990\pi$
$137$	14.2902			1.22089			0.610446	+	0.792058i	$0.290990\pi$
$138$			1.10523i			0.0940838i
$139$			17.4166i			1.47726i	0.674113	+	0.738629i	$0.264526\pi$
$139$			17.4166i			1.47726i	−0.674113	+	0.738629i	$0.735474\pi$
$140$	8.14202	+	6.97546i	0.688127	+	0.589534i
$141$	13.6663	+	13.6663i	1.15091	+	1.15091i
$142$	5.98525	+	5.98525i	0.502271	+	0.502271i
$143$		0			0
$144$		−	4.52189i		−	0.376824i
$145$	2.87714	−	3.35831i	0.238934	−	0.278893i
$146$	27.0251			2.23661
$147$	−7.74102	−	7.74102i	−0.638469	−	0.638469i
$148$	7.34036			0.603374
$149$	9.28442	+	9.28442i	0.760610	+	0.760610i	0.976433	−	0.215823i	$-0.0692434\pi$
$149$	9.28442	+	9.28442i	0.760610	+	0.760610i	−0.215823	+	0.976433i	$0.569243\pi$
$150$	14.6511	+	10.7132i	1.19626	+	0.874726i
$151$	−0.765191	−	0.765191i	−0.0622704	−	0.0622704i	0.675286	−	0.737556i	$-0.264020\pi$
$151$	−0.765191	−	0.765191i	−0.0622704	−	0.0622704i	−0.737556	+	0.675286i	$0.764020\pi$
$152$	−0.448913	+	0.448913i	−0.0364117	+	0.0364117i
$153$	1.32900	−	1.32900i	0.107443	−	0.107443i
$154$	17.7567	−	17.7567i	1.43088	−	1.43088i
$155$	−13.0392	+	1.00619i	−1.04734	+	0.0808190i
$156$		0			0
$157$	3.03481	−	3.03481i	0.242204	−	0.242204i	−0.575557	−	0.817762i	$-0.695215\pi$
$157$	3.03481	−	3.03481i	0.242204	−	0.242204i	0.817762	+	0.575557i	$0.195215\pi$
$158$	2.92544			0.232735
$159$		−	8.86386i		−	0.702950i
$160$	9.54967	−	11.1467i	0.754968	−	0.881227i
$161$	0.761901	−	0.761901i	0.0600462	−	0.0600462i
$162$			20.0061i			1.57182i
$163$		−	2.26358i		−	0.177297i	−0.996063	−	0.0886486i	$-0.971745\pi$
$163$		−	2.26358i		−	0.177297i	0.996063	−	0.0886486i	$-0.0282548\pi$
$164$	−0.644580	+	0.644580i	−0.0503333	+	0.0503333i
$165$	11.1698	−	13.0379i	0.869571	−	1.01500i
$166$			13.8717i			1.07665i
$167$	0.619569			0.0479437			0.0239719	−	0.999713i	$-0.492369\pi$
$167$	0.619569			0.0479437			0.0239719	+	0.999713i	$0.492369\pi$
$168$	−5.86012	+	5.86012i	−0.452118	+	0.452118i
$169$		0			0
$170$	8.27267	−	0.638370i	0.634485	−	0.0489608i
$171$	−0.352460	+	0.352460i	−0.0269533	+	0.0269533i
$172$	8.44218	−	8.44218i	0.643710	−	0.643710i
$173$	−4.68224	+	4.68224i	−0.355984	+	0.355984i	−0.862330	−	0.506346i	$-0.830996\pi$
$173$	−4.68224	+	4.68224i	−0.355984	+	0.355984i	0.506346	+	0.862330i	$0.330996\pi$
$174$	−5.07636	−	5.07636i	−0.384838	−	0.384838i
$175$	−2.71467	−	17.4850i	−0.205210	−	1.32175i
$176$	−13.3520	−	13.3520i	−1.00645	−	1.00645i
$177$	24.0977			1.81130
$178$	6.09312	+	6.09312i	0.456699	+	0.456699i
$179$	2.19023			0.163706			0.0818528	−	0.996644i	$-0.473916\pi$
$179$	2.19023			0.163706			0.0818528	+	0.996644i	$0.473916\pi$
$180$	1.82866	−	2.13448i	0.136300	−	0.159095i
$181$		−	9.59255i		−	0.713009i	−0.934294	−	0.356504i	$-0.883969\pi$
$181$		−	9.59255i		−	0.713009i	0.934294	−	0.356504i	$-0.116031\pi$
$182$		0			0
$183$	4.04484	+	4.04484i	0.299003	+	0.299003i
$184$	−0.254396	−	0.254396i	−0.0187543	−	0.0187543i
$185$	−9.19985	−	7.88173i	−0.676387	−	0.579477i
$186$			21.2308i			1.55672i
$187$		−	7.84842i		−	0.573933i
$188$	13.2128			0.963640
$189$	10.2771	−	10.2771i	0.747546	−	0.747546i
$190$	−2.19397	+	0.169300i	−0.159167	+	0.0122823i
$191$	3.73113			0.269975			0.134988	−	0.990847i	$-0.456901\pi$
$191$	3.73113			0.269975			0.134988	+	0.990847i	$0.456901\pi$
$192$	−3.18834	−	3.18834i	−0.230099	−	0.230099i
$193$		−	0.284086i		−	0.0204489i	−0.999948	−	0.0102245i	$-0.996745\pi$
$193$		−	0.284086i		−	0.0204489i	0.999948	−	0.0102245i	$-0.00325461\pi$
$194$	−32.6495			−2.34410
$195$		0			0
$196$	−7.48414			−0.534581
$197$			25.8492i			1.84168i	0.389946	+	0.920838i	$0.372494\pi$
$197$			25.8492i			1.84168i	−0.389946	+	0.920838i	$0.627506\pi$
$198$	−4.65504	−	4.65504i	−0.330819	−	0.330819i
$199$	5.75250			0.407784			0.203892	−	0.978993i	$-0.434641\pi$
$199$	5.75250			0.407784			0.203892	+	0.978993i	$0.434641\pi$
$200$	−5.83819	+	0.906420i	−0.412823	+	0.0640936i
$201$	3.20901	−	3.20901i	0.226346	−	0.226346i
$202$	8.34106			0.586875
$203$			6.99884i			0.491223i
$204$		−	5.43980i		−	0.380862i
$205$	1.49999	−	0.115748i	0.104764	−	0.00808422i
$206$	17.9369	+	17.9369i	1.24972	+	1.24972i
$207$	−0.199737	−	0.199737i	−0.0138827	−	0.0138827i
$208$		0			0
$209$			2.08146i			0.143977i
$210$	−28.6401	+	2.21005i	−1.97636	+	0.152508i
$211$	−3.22743			−0.222185			−0.111093	−	0.993810i	$-0.535435\pi$
$211$	−3.22743			−0.222185			−0.111093	+	0.993810i	$0.535435\pi$
$212$	−4.28486	−	4.28486i	−0.294285	−	0.294285i
$213$	−9.15863			−0.627539
$214$	−9.15709	−	9.15709i	−0.625966	−	0.625966i
$215$	−19.6456	+	1.51598i	−1.33982	+	0.103389i
$216$	−3.43147	−	3.43147i	−0.233482	−	0.233482i
$217$	14.6356	−	14.6356i	0.993529	−	0.993529i
$218$	−18.1200	+	18.1200i	−1.22724	+	1.22724i
$219$	−20.6769	+	20.6769i	−1.39721	+	1.39721i
$220$	−0.903013	−	11.7022i	−0.0608811	−	0.788961i
$221$		0			0
$222$	−13.9063	+	13.9063i	−0.933331	+	0.933331i
$223$	7.41523			0.496561			0.248280	−	0.968688i	$-0.420135\pi$
$223$	7.41523			0.496561			0.248280	+	0.968688i	$0.420135\pi$
$224$			23.2302i			1.55213i
$225$	−4.58381	+	0.711668i	−0.305587	+	0.0474446i
$226$	−2.96914	+	2.96914i	−0.197504	+	0.197504i
$227$		−	3.90230i		−	0.259005i	−0.991579	−	0.129502i	$-0.958662\pi$
$227$		−	3.90230i		−	0.259005i	0.991579	−	0.129502i	$-0.0413380\pi$
$228$			1.44267i			0.0955434i
$229$	−12.3946	+	12.3946i	−0.819060	+	0.819060i	−0.985972	−	0.166912i	$-0.946621\pi$
$229$	−12.3946	+	12.3946i	−0.819060	+	0.819060i	0.166912	+	0.985972i	$0.446621\pi$
$230$	−0.0959413	−	1.24331i	−0.00632618	−	0.0819813i
$231$			27.1714i			1.78774i
$232$	2.33689			0.153424
$233$	2.88962	−	2.88962i	0.189305	−	0.189305i	−0.606090	−	0.795396i	$-0.707263\pi$
$233$	2.88962	−	2.88962i	0.189305	−	0.189305i	0.795396	+	0.606090i	$0.207263\pi$
$234$		0			0
$235$	−16.5599	−	14.1873i	−1.08025	−	0.925474i
$236$	11.6490	−	11.6490i	0.758287	−	0.758287i
$237$	−2.23825	+	2.23825i	−0.145390	+	0.145390i
$238$	−9.28546	+	9.28546i	−0.601887	+	0.601887i
$239$	8.97299	+	8.97299i	0.580415	+	0.580415i	0.935017	−	0.354602i	$-0.115384\pi$
$239$	8.97299	+	8.97299i	0.580415	+	0.580415i	−0.354602	+	0.935017i	$0.615384\pi$
$240$	1.66183	+	21.5357i	0.107270	+	1.39012i
$241$	12.4080	+	12.4080i	0.799272	+	0.799272i	0.982981	−	0.183709i	$-0.0588104\pi$
$241$	12.4080	+	12.4080i	0.799272	+	0.799272i	−0.183709	+	0.982981i	$0.558810\pi$
$242$	−7.34239			−0.471986
$243$	−6.59457	−	6.59457i	−0.423042	−	0.423042i
$244$	3.91061			0.250351
$245$	9.38005	+	8.03611i	0.599270	+	0.513408i
$246$		−	2.44232i		−	0.155716i
$247$		0			0
$248$	−4.88677	−	4.88677i	−0.310311	−	0.310311i
$249$	−10.6132	−	10.6132i	−0.672587	−	0.672587i
$250$	−17.4114	−	10.7797i	−1.10120	−	0.681768i
$251$		−	21.7689i		−	1.37404i	−0.726638	−	0.687021i	$-0.758918\pi$
$251$		−	21.7689i		−	1.37404i	0.726638	−	0.687021i	$-0.241082\pi$
$252$			4.44834i			0.280219i
$253$	−1.17955			−0.0741575
$254$	1.66567	−	1.66567i	0.104513	−	0.104513i
$255$	−5.84100	+	6.81784i	−0.365778	+	0.426950i
$256$	20.9640			1.31025
$257$	9.06027	+	9.06027i	0.565164	+	0.565164i	0.930770	−	0.365606i	$-0.119138\pi$
$257$	9.06027	+	9.06027i	0.565164	+	0.565164i	−0.365606	+	0.930770i	$0.619138\pi$
$258$			31.9874i			1.99145i
$259$	19.1728			1.19134
$260$		0			0
$261$	1.83479			0.113571
$262$		−	10.2469i		−	0.633054i
$263$	11.6708	+	11.6708i	0.719650	+	0.719650i	0.968533	−	0.248884i	$-0.0800637\pi$
$263$	11.6708	+	11.6708i	0.719650	+	0.719650i	−0.248884	+	0.968533i	$0.580064\pi$
$264$	9.07242			0.558369
$265$	0.769439	+	9.97120i	0.0472663	+	0.612526i
$266$	2.46257	−	2.46257i	0.150990	−	0.150990i
$267$	−9.32370			−0.570601
$268$		−	3.10252i		−	0.189516i
$269$		−	32.3070i		−	1.96979i	−0.173150	−	0.984895i	$-0.555395\pi$
$269$		−	32.3070i		−	1.96979i	0.173150	−	0.984895i	$-0.444605\pi$
$270$	−1.29412	−	16.7706i	−0.0787579	−	1.02063i
$271$	−12.3548	−	12.3548i	−0.750503	−	0.750503i	0.224070	−	0.974573i	$-0.428065\pi$
$271$	−12.3548	−	12.3548i	−0.750503	−	0.750503i	−0.974573	+	0.224070i	$0.928065\pi$
$272$	6.98212	+	6.98212i	0.423353	+	0.423353i
$273$		0			0
$274$			26.1743i			1.58125i
$275$	−11.4335	+	15.6362i	−0.689465	+	0.942901i
$276$	−0.817553			−0.0492109
$277$	2.17391	+	2.17391i	0.130617	+	0.130617i	0.769393	−	0.638776i	$-0.220559\pi$
$277$	2.17391	+	2.17391i	0.130617	+	0.130617i	−0.638776	+	0.769393i	$0.720559\pi$
$278$	−31.9008			−1.91328
$279$	−3.83681	−	3.83681i	−0.229704	−	0.229704i
$280$	6.08351	−	7.10090i	0.363559	−	0.424360i
$281$	18.6757	+	18.6757i	1.11410	+	1.11410i	0.992590	+	0.121508i	$0.0387731\pi$
$281$	18.6757	+	18.6757i	1.11410	+	1.11410i	0.121508	+	0.992590i	$0.461227\pi$
$282$	−25.0316	+	25.0316i	−1.49061	+	1.49061i
$283$	10.8464	−	10.8464i	0.644750	−	0.644750i	−0.306969	−	0.951719i	$-0.599315\pi$
$283$	10.8464	−	10.8464i	0.644750	−	0.644750i	0.951719	+	0.306969i	$0.0993149\pi$
$284$	−4.42735	+	4.42735i	−0.262715	+	0.262715i
$285$	1.54907	−	1.80814i	0.0917593	−	0.107105i
$286$		0			0
$287$	−1.68363	+	1.68363i	−0.0993814	+	0.0993814i
$288$	6.08994			0.358853
$289$		−	12.8959i		−	0.758580i
$290$	6.15119	+	5.26987i	0.361210	+	0.309458i
$291$	24.9801	−	24.9801i	1.46436	−	1.46436i
$292$			19.9907i			1.16987i
$293$			10.3767i			0.606213i	0.952957	+	0.303107i	$0.0980238\pi$
$293$			10.3767i			0.606213i	−0.952957	+	0.303107i	$0.901976\pi$
$294$	14.1787	−	14.1787i	0.826919	−	0.826919i
$295$	−27.1082	+	2.09184i	−1.57830	+	0.121791i
$296$		−	6.40174i		−	0.372094i
$297$	−15.9106			−0.923225
$298$	−17.0057	+	17.0057i	−0.985111	+	0.985111i
$299$		0			0
$300$	−7.92463	+	10.8376i	−0.457529	+	0.625709i
$301$	22.0507	−	22.0507i	1.27098	−	1.27098i
$302$	1.40155	−	1.40155i	0.0806501	−	0.0806501i
$303$	−6.38174	+	6.38174i	−0.366622	+	0.366622i
$304$	−1.85171	−	1.85171i	−0.106203	−	0.106203i
$305$	−4.90126	−	4.19903i	−0.280646	−	0.240436i
$306$	2.43424	+	2.43424i	0.139156	+	0.139156i
$307$	−2.13935			−0.122099			−0.0610496	−	0.998135i	$-0.519445\pi$
$307$	−2.13935			−0.122099			−0.0610496	+	0.998135i	$0.519445\pi$
$308$	13.1348	+	13.1348i	0.748427	+	0.748427i
$309$	−27.4470			−1.56141
$310$	−1.84297	−	23.8831i	−0.104674	−	1.35647i
$311$			3.82084i			0.216660i	0.994115	+	0.108330i	$0.0345503\pi$
$311$			3.82084i			0.216660i	−0.994115	+	0.108330i	$0.965450\pi$
$312$		0			0
$313$	3.04531	+	3.04531i	0.172131	+	0.172131i	0.787915	−	0.615784i	$-0.211161\pi$
$313$	3.04531	+	3.04531i	0.172131	+	0.172131i	−0.615784	+	0.787915i	$0.711161\pi$
$314$	5.55866	+	5.55866i	0.313693	+	0.313693i
$315$	4.77642	−	5.57521i	0.269121	−	0.314128i
$316$			2.16398i			0.121733i
$317$		−	23.1127i		−	1.29814i	−0.760730	−	0.649068i	$-0.775159\pi$
$317$		−	23.1127i		−	1.29814i	0.760730	−	0.649068i	$-0.224841\pi$
$318$	16.2353			0.910433
$319$	5.41768	−	5.41768i	0.303332	−	0.303332i
$320$	3.86342	+	3.30988i	0.215972	+	0.185028i
$321$	14.0122			0.782084
$322$	1.39552	+	1.39552i	0.0777694	+	0.0777694i
$323$		−	1.08845i		−	0.0605629i
$324$	−14.7987			−0.822149
$325$		0			0
$326$	4.14604			0.229628
$327$		−	27.7272i		−	1.53332i
$328$	0.562157	+	0.562157i	0.0310399	+	0.0310399i
$329$	34.5114			1.90268
$330$	23.8806	+	20.4590i	1.31458	+	1.12623i
$331$	−1.41208	+	1.41208i	−0.0776150	+	0.0776150i	−0.744849	−	0.667234i	$-0.767478\pi$
$331$	−1.41208	+	1.41208i	−0.0776150	+	0.0776150i	0.667234	+	0.744849i	$0.267478\pi$
$332$	−10.2610			−0.563148
$333$		−	5.02628i		−	0.275438i
$334$			1.13482i			0.0620948i
$335$	−3.33134	+	3.88846i	−0.182010	+	0.212449i
$336$	−24.1722	−	24.1722i	−1.31870	−	1.31870i
$337$	6.12727	+	6.12727i	0.333773	+	0.333773i	0.854018	−	0.520244i	$-0.174159\pi$
$337$	6.12727	+	6.12727i	0.333773	+	0.333773i	−0.520244	+	0.854018i	$0.674159\pi$
$338$		0			0
$339$		−	4.54338i		−	0.246763i
$340$	0.472209	+	6.11938i	0.0256091	+	0.331870i
$341$	−22.6583			−1.22702
$342$	−0.645578	−	0.645578i	−0.0349089	−	0.0349089i
$343$	5.22396			0.282067
$344$	−7.36267	−	7.36267i	−0.396968	−	0.396968i
$345$	1.02466	+	0.877850i	0.0551658	+	0.0472619i
$346$	−8.57614	−	8.57614i	−0.461056	−	0.461056i
$347$	−22.9870	+	22.9870i	−1.23401	+	1.23401i	−0.271599	+	0.962411i	$0.587552\pi$
$347$	−22.9870	+	22.9870i	−1.23401	+	1.23401i	−0.962411	+	0.271599i	$0.912448\pi$
$348$	3.75504	−	3.75504i	0.201291	−	0.201291i
$349$	4.81192	−	4.81192i	0.257576	−	0.257576i	−0.566491	−	0.824068i	$-0.691700\pi$
$349$	4.81192	−	4.81192i	0.257576	−	0.257576i	0.824068	+	0.566491i	$0.191700\pi$
$350$	32.0262	−	4.97228i	1.71187	−	0.265780i
$351$		0			0
$352$	17.9821	−	17.9821i	0.958448	−	0.958448i
$353$	−27.3262			−1.45443			−0.727213	−	0.686412i	$-0.759185\pi$
$353$	−27.3262			−1.45443			−0.727213	+	0.686412i	$0.759185\pi$
$354$			44.1382i			2.34592i
$355$	10.3028	−	0.795027i	0.546815	−	0.0421957i
$356$	−4.50714	+	4.50714i	−0.238878	+	0.238878i
$357$		−	14.2086i		−	0.752000i
$358$			4.01170i			0.212025i
$359$	−3.89871	+	3.89871i	−0.205766	+	0.205766i	−0.802465	−	0.596699i	$-0.796479\pi$
$359$	−3.89871	+	3.89871i	−0.205766	+	0.205766i	0.596699	+	0.802465i	$0.296479\pi$
$360$	−1.86154	−	1.59483i	−0.0981120	−	0.0840548i
$361$		−	18.7113i		−	0.984807i
$362$	17.5700			0.923460
$363$	5.61766	−	5.61766i	0.294851	−	0.294851i
$364$		0			0
$365$	21.4651	−	25.0548i	1.12353	−	1.31143i
$366$	−7.40866	+	7.40866i	−0.387257	+	0.387257i
$367$	12.7812	−	12.7812i	0.667175	−	0.667175i	−0.289886	−	0.957061i	$-0.593617\pi$
$367$	12.7812	−	12.7812i	0.667175	−	0.667175i	0.957061	+	0.289886i	$0.0936174\pi$
$368$	1.04935	−	1.04935i	0.0547012	−	0.0547012i
$369$	0.441373	+	0.441373i	0.0229770	+	0.0229770i
$370$	14.4364	−	16.8508i	0.750515	−	0.876029i
$371$	−11.1919	−	11.1919i	−0.581057	−	0.581057i
$372$	−15.7046			−0.814248
$373$	10.9702	+	10.9702i	0.568014	+	0.568014i	0.931572	−	0.363558i	$-0.118438\pi$
$373$	10.9702	+	10.9702i	0.568014	+	0.568014i	−0.363558	+	0.931572i	$0.618438\pi$
$374$	14.3754			0.743335
$375$	21.5690	−	5.07393i	1.11382	−	0.262017i
$376$		−	11.5232i		−	0.594266i
$377$		0			0
$378$	18.8238	+	18.8238i	0.968191	+	0.968191i
$379$	15.1090	+	15.1090i	0.776099	+	0.776099i	0.979165	−	0.203066i	$-0.0650905\pi$
$379$	15.1090	+	15.1090i	0.776099	+	0.776099i	−0.203066	+	0.979165i	$0.565091\pi$
$380$	−0.125233	−	1.62290i	−0.00642433	−	0.0832531i
$381$			2.54881i			0.130579i
$382$			6.83407i			0.349661i
$383$	−19.4072			−0.991664			−0.495832	−	0.868419i	$-0.665137\pi$
$383$	−19.4072			−0.991664			−0.495832	+	0.868419i	$0.665137\pi$
$384$	−12.5581	+	12.5581i	−0.640855	+	0.640855i
$385$	−2.35865	−	30.5658i	−0.120208	−	1.55778i
$386$	0.520340			0.0264846
$387$	−5.78074	−	5.78074i	−0.293852	−	0.293852i
$388$		−	24.1512i		−	1.22609i
$389$	−14.8591			−0.753387			−0.376693	−	0.926338i	$-0.622939\pi$
$389$	−14.8591			−0.753387			−0.376693	+	0.926338i	$0.622939\pi$
$390$		0			0
$391$	0.616816			0.0311937
$392$			6.52713i			0.329670i
$393$	7.83989	+	7.83989i	0.395470	+	0.395470i
$394$	−47.3461			−2.38526
$395$	2.32358	−	2.71217i	0.116912	−	0.136464i
$396$	3.44338	−	3.44338i	0.173036	−	0.173036i
$397$	−5.27779			−0.264884			−0.132442	−	0.991191i	$-0.542282\pi$
$397$	−5.27779			−0.264884			−0.132442	+	0.991191i	$0.542282\pi$
$398$			10.5365i			0.528145i
$399$			3.76823i			0.188647i
$400$	−3.73887	−	24.0818i	−0.186943	−	1.20409i
$401$	−19.7133	−	19.7133i	−0.984435	−	0.984435i	0.0154455	−	0.999881i	$-0.495083\pi$
$401$	−19.7133	−	19.7133i	−0.984435	−	0.984435i	−0.999881	+	0.0154455i	$0.995083\pi$
$402$	5.87772	+	5.87772i	0.293154	+	0.293154i
$403$		0			0
$404$			6.16996i			0.306967i
$405$	18.5476	+	15.8901i	0.921635	+	0.789587i
$406$	−12.8193			−0.636212
$407$	−14.8413	−	14.8413i	−0.735658	−	0.735658i
$408$	−4.74421			−0.234873
$409$	1.86330	+	1.86330i	0.0921344	+	0.0921344i	0.751672	−	0.659537i	$-0.229248\pi$
$409$	1.86330	+	1.86330i	0.0921344	+	0.0921344i	−0.659537	+	0.751672i	$0.729248\pi$
$410$	0.212009	+	2.74743i	0.0104704	+	0.135686i
$411$	−20.0260	−	20.0260i	−0.987810	−	0.987810i
$412$	−13.2681	+	13.2681i	−0.653673	+	0.653673i
$413$	30.4270	−	30.4270i	1.49721	−	1.49721i
$414$	0.365845	−	0.365845i	0.0179803	−	0.0179803i
$415$	12.8604	+	11.0178i	0.631293	+	0.540844i
$416$		0			0
$417$	24.4073	−	24.4073i	1.19523	−	1.19523i
$418$	−3.81246			−0.186474
$419$			19.6701i			0.960948i	0.877009	+	0.480474i	$0.159535\pi$
$419$			19.6701i			0.960948i	−0.877009	+	0.480474i	$0.840465\pi$
$420$	−1.63480	−	21.1854i	−0.0797699	−	1.03374i
$421$	−10.4427	+	10.4427i	−0.508948	+	0.508948i	−0.914203	−	0.405256i	$-0.867183\pi$
$421$	−10.4427	+	10.4427i	−0.508948	+	0.508948i	0.405256	+	0.914203i	$0.367183\pi$
$422$		−	5.91147i		−	0.287766i
$423$		−	9.04738i		−	0.439899i
$424$	−3.73695	+	3.73695i	−0.181482	+	0.181482i
$425$	5.97887	−	8.17660i	0.290018	−	0.396623i
$426$		−	16.7752i		−	0.812763i
$427$	10.2144			0.494310
$428$	6.77359	−	6.77359i	0.327414	−	0.327414i
$429$		0			0
$430$	−2.77671	−	35.9835i	−0.133905	−	1.73528i
$431$	12.1144	−	12.1144i	0.583532	−	0.583532i	−0.352340	−	0.935872i	$-0.614614\pi$
$431$	12.1144	−	12.1144i	0.583532	−	0.583532i	0.935872	+	0.352340i	$0.114614\pi$
$432$	14.1544	−	14.1544i	0.681003	−	0.681003i
$433$	7.94551	−	7.94551i	0.381837	−	0.381837i	−0.489927	−	0.871764i	$-0.662977\pi$
$433$	7.94551	−	7.94551i	0.381837	−	0.381837i	0.871764	+	0.489927i	$0.162977\pi$
$434$	26.8070	+	26.8070i	1.28678	+	1.28678i
$435$	−8.73826	+	0.674298i	−0.418967	+	0.0323301i
$436$	−13.4035	−	13.4035i	−0.641913	−	0.641913i
$437$	−0.163584			−0.00782528
$438$	−37.8724	−	37.8724i	−1.80962	−	1.80962i
$439$	−4.24435			−0.202572			−0.101286	−	0.994857i	$-0.532296\pi$
$439$	−4.24435			−0.202572			−0.101286	+	0.994857i	$0.532296\pi$
$440$	−10.2058	+	0.787544i	−0.486543	+	0.0375447i
$441$			5.12473i			0.244035i
$442$		0			0
$443$	15.1569	+	15.1569i	0.720126	+	0.720126i	0.968631	−	0.248505i	$-0.0799392\pi$
$443$	15.1569	+	15.1569i	0.720126	+	0.720126i	−0.248505	+	0.968631i	$0.579939\pi$
$444$	−10.2867	−	10.2867i	−0.488183	−	0.488183i
$445$	10.4885	−	0.809356i	0.497201	−	0.0383671i
$446$			13.5820i			0.643126i
$447$		−	26.0221i		−	1.23080i
$448$	−8.05150			−0.380398
$449$	10.2868	−	10.2868i	0.485466	−	0.485466i	−0.421406	−	0.906872i	$-0.638463\pi$
$449$	10.2868	−	10.2868i	0.485466	−	0.485466i	0.906872	+	0.421406i	$0.138463\pi$
$450$	−1.30351	−	8.39586i	−0.0614483	−	0.395785i
$451$	2.60653			0.122737
$452$	−2.19631	−	2.19631i	−0.103306	−	0.103306i
$453$			2.14465i			0.100764i
$454$	7.14758			0.335453
$455$		0			0
$456$	1.25820			0.0589205
$457$			30.2953i			1.41715i	0.705634	+	0.708576i	$0.250662\pi$
$457$			30.2953i			1.41715i	−0.705634	+	0.708576i	$0.749338\pi$
$458$	−22.7024	−	22.7024i	−1.06081	−	1.06081i
$459$	8.32005			0.388347
$460$	0.919687	−	0.0709688i	0.0428806	−	0.00330894i
$461$	−4.90581	+	4.90581i	−0.228486	+	0.228486i	−0.812060	−	0.583574i	$-0.801654\pi$
$461$	−4.90581	+	4.90581i	−0.228486	+	0.228486i	0.583574	+	0.812060i	$0.301654\pi$
$462$	−49.7680			−2.31541
$463$		−	31.4463i		−	1.46143i	−0.682680	−	0.730717i	$-0.739186\pi$
$463$		−	31.4463i		−	1.46143i	0.682680	−	0.730717i	$-0.260814\pi$
$464$			9.63937i			0.447496i
$465$	19.6830	+	16.8629i	0.912778	+	0.781999i
$466$	5.29272	+	5.29272i	0.245180	+	0.245180i
$467$	−3.69622	−	3.69622i	−0.171041	−	0.171041i	0.616396	−	0.787436i	$-0.288592\pi$
$467$	−3.69622	−	3.69622i	−0.171041	−	0.171041i	−0.787436	+	0.616396i	$0.788592\pi$
$468$		0			0
$469$		−	8.10369i		−	0.374194i
$470$	25.9858	−	30.3316i	1.19864	−	1.39909i
$471$	−8.50587			−0.391930
$472$	−10.1595	−	10.1595i	−0.467627	−	0.467627i
$473$	−34.1382			−1.56968
$474$	−4.09966	−	4.09966i	−0.188304	−	0.188304i
$475$	−1.58564	+	2.16849i	−0.0727540	+	0.0994972i
$476$	−6.86855	−	6.86855i	−0.314820	−	0.314820i
$477$	−2.93404	+	2.93404i	−0.134340	+	0.134340i
$478$	−16.4352	+	16.4352i	−0.751730	+	0.751730i
$479$	−13.6849	+	13.6849i	−0.625281	+	0.625281i	−0.946877	−	0.321596i	$-0.895781\pi$
$479$	−13.6849	+	13.6849i	−0.625281	+	0.625281i	0.321596	+	0.946877i	$0.395781\pi$
$480$	−29.0036	+	2.23810i	−1.32383	+	0.102155i
$481$		0			0
$482$	−22.7270	+	22.7270i	−1.03518	+	1.03518i
$483$	−2.13543			−0.0971654
$484$		−	5.43124i		−	0.246874i
$485$	−25.9324	+	30.2693i	−1.17753	+	1.37446i
$486$	12.0788	−	12.0788i	0.547907	−	0.547907i
$487$		−	23.3627i		−	1.05866i	−0.848415	−	0.529332i	$-0.822443\pi$
$487$		−	23.3627i		−	1.05866i	0.848415	−	0.529332i	$-0.177557\pi$
$488$		−	3.41056i		−	0.154389i
$489$	−3.17214	+	3.17214i	−0.143449	+	0.143449i
$490$	−14.7192	+	17.1808i	−0.664946	+	0.776150i
$491$			21.3186i			0.962094i	0.876695	+	0.481047i	$0.159743\pi$
$491$			21.3186i			0.962094i	−0.876695	+	0.481047i	$0.840257\pi$
$492$	1.80661			0.0814481
$493$	−2.83305	+	2.83305i	−0.127594	+	0.127594i
$494$		0			0
$495$	−8.01301	+	0.618334i	−0.360158	+	0.0277920i
$496$	20.1573	−	20.1573i	0.905090	−	0.905090i
$497$	−11.5641	+	11.5641i	−0.518722	+	0.518722i
$498$	19.4396	−	19.4396i	0.871108	−	0.871108i
$499$	−23.0389	−	23.0389i	−1.03136	−	1.03136i	−0.999492	−	0.0318687i	$-0.989854\pi$
$499$	−23.0389	−	23.0389i	−1.03136	−	1.03136i	−0.0318687	−	0.999492i	$-0.510146\pi$
$500$	7.97386	−	12.8794i	0.356602	−	0.575985i
$501$	−0.868254	−	0.868254i	−0.0387907	−	0.0387907i
$502$	39.8727			1.77960
$503$	0.464437	+	0.464437i	0.0207082	+	0.0207082i	0.717385	−	0.696677i	$-0.245339\pi$
$503$	0.464437	+	0.464437i	0.0207082	+	0.0207082i	−0.696677	+	0.717385i	$0.745339\pi$
$504$	3.87953			0.172808
$505$	6.62502	−	7.73297i	0.294809	−	0.344113i
$506$		−	2.16050i		−	0.0960458i
$507$		0			0
$508$	1.23211	+	1.23211i	0.0546662	+	0.0546662i
$509$	−22.6497	−	22.6497i	−1.00393	−	1.00393i	−0.999992	−	0.00393669i	$-0.998747\pi$
$509$	−22.6497	−	22.6497i	−1.00393	−	1.00393i	−0.00393669	−	0.999992i	$-0.501253\pi$
$510$	−12.4878	−	10.6986i	−0.552968	−	0.473741i
$511$			52.2152i			2.30987i
$512$			20.4758i			0.904912i
$513$	−2.20654			−0.0974210
$514$	−16.5951	+	16.5951i	−0.731978	+	0.731978i
$515$	30.8759	−	2.38258i	1.36056	−	0.104989i
$516$	−23.6614			−1.04164
$517$	−26.7147	−	26.7147i	−1.17491	−	1.17491i
$518$			35.1176i			1.54298i
$519$	13.1232			0.576046
$520$		0			0
$521$	−23.4746			−1.02844			−0.514220	−	0.857658i	$-0.671919\pi$
$521$	−23.4746			−1.02844			−0.514220	+	0.857658i	$0.671919\pi$
$522$			3.36066i			0.147092i
$523$	17.4961	+	17.4961i	0.765049	+	0.765049i	0.977230	−	0.212181i	$-0.0680568\pi$
$523$	17.4961	+	17.4961i	0.765049	+	0.765049i	−0.212181	+	0.977230i	$0.568057\pi$
$524$	7.57972			0.331121
$525$	−20.6989	+	28.3075i	−0.903376	+	1.23544i
$526$	−21.3765	+	21.3765i	−0.932061	+	0.932061i
$527$	11.8486			0.516134
$528$			37.4226i			1.62861i
$529$			22.9073i			0.995969i
$530$	−18.2636	+	1.40933i	−0.793319	+	0.0612174i
$531$	−7.97661	−	7.97661i	−0.346156	−	0.346156i
$532$	1.82159	+	1.82159i	0.0789759	+	0.0789759i
$533$		0			0
$534$		−	17.0776i		−	0.739019i
$535$	−15.7627	+	1.21635i	−0.681480	+	0.0525872i
$536$	−2.70579			−0.116873
$537$	−3.06935	−	3.06935i	−0.132452	−	0.132452i
$538$	59.1745			2.55119
$539$	15.1320	+	15.1320i	0.651783	+	0.651783i
$540$	12.4054	−	0.957277i	0.533843	−	0.0411946i
$541$	27.6908	+	27.6908i	1.19052	+	1.19052i	0.976922	+	0.213597i	$0.0685180\pi$
$541$	27.6908	+	27.6908i	1.19052	+	1.19052i	0.213597	+	0.976922i	$0.431482\pi$
$542$	22.6295	−	22.6295i	0.972021	−	0.972021i
$543$	−13.4428	+	13.4428i	−0.576887	+	0.576887i
$544$	−9.40330	+	9.40330i	−0.403163	+	0.403163i
$545$	2.40690	+	31.1911i	0.103100	+	1.33608i
$546$		0			0
$547$	6.53914	−	6.53914i	0.279593	−	0.279593i	−0.553353	−	0.832947i	$-0.686652\pi$
$547$	6.53914	−	6.53914i	0.279593	−	0.279593i	0.832947	+	0.553353i	$0.186652\pi$
$548$	−19.3614			−0.827079
$549$		−	2.67777i		−	0.114284i
$550$	−28.6398	−	20.9419i	−1.22121	−	0.892967i
$551$	0.751344	−	0.751344i	0.0320083	−	0.0320083i
$552$			0.713012i			0.0303478i
$553$			5.65225i			0.240358i
$554$	−3.98180	+	3.98180i	−0.169170	+	0.169170i
$555$	1.84719	+	23.9378i	0.0784089	+	1.01610i
$556$		−	23.5974i		−	1.00075i
$557$	−16.2486			−0.688475			−0.344237	−	0.938883i	$-0.611862\pi$
$557$	−16.2486			−0.688475			−0.344237	+	0.938883i	$0.611862\pi$
$558$	7.02763	−	7.02763i	0.297503	−	0.297503i
$559$		0			0
$560$	29.2903	+	25.0937i	1.23774	+	1.06040i
$561$	−10.9986	+	10.9986i	−0.464363	+	0.464363i
$562$	−34.2070	+	34.2070i	−1.44294	+	1.44294i
$563$	22.9991	−	22.9991i	0.969298	−	0.969298i	−0.0302442	−	0.999543i	$-0.509628\pi$
$563$	22.9991	−	22.9991i	0.969298	−	0.969298i	0.999543	+	0.0302442i	$0.00962850\pi$
$564$	−18.5161	−	18.5161i	−0.779670	−	0.779670i
$565$	0.394394	+	5.11097i	0.0165923	+	0.215020i
$566$	19.8666	+	19.8666i	0.835054	+	0.835054i
$567$	−38.6538			−1.62331
$568$	3.86122	+	3.86122i	0.162013	+	0.162013i
$569$	−32.8329			−1.37642			−0.688212	−	0.725509i	$-0.741604\pi$
$569$	−32.8329			−1.37642			−0.688212	+	0.725509i	$0.741604\pi$
$570$	3.31184	+	2.83734i	0.138718	+	0.118843i
$571$			31.7967i			1.33065i	0.746554	+	0.665325i	$0.231707\pi$
$571$			31.7967i			1.33065i	−0.746554	+	0.665325i	$0.768293\pi$
$572$		0			0
$573$	−5.22875	−	5.22875i	−0.218434	−	0.218434i
$574$	−3.08379	−	3.08379i	−0.128715	−	0.128715i
$575$	−1.22887	−	0.898570i	−0.0512474	−	0.0374730i
$576$			2.11075i			0.0879480i
$577$			39.9389i			1.66268i	0.555767	+	0.831338i	$0.312425\pi$
$577$			39.9389i			1.66268i	−0.555767	+	0.831338i	$0.687575\pi$
$578$	23.6205			0.982482
$579$	−0.398113	+	0.398113i	−0.0165450	+	0.0165450i
$580$	−3.89818	+	4.55010i	−0.161863	+	0.188933i
$581$	−26.8016			−1.11192
$582$	45.7544	+	45.7544i	1.89658	+	1.89658i
$583$			17.3270i			0.717609i
$584$	17.4345			0.721444
$585$		0			0
$586$	−19.0063			−0.785143
$587$		−	18.6555i		−	0.769993i	−0.922918	−	0.384997i	$-0.874203\pi$
$587$		−	18.6555i		−	0.769993i	0.922918	−	0.384997i	$-0.125797\pi$
$588$	10.4881	+	10.4881i	0.432523	+	0.432523i
$589$	−3.14234			−0.129478
$590$	−3.83147	−	49.6522i	−0.157739	−	2.04415i
$591$	36.2245	−	36.2245i	1.49008	−	1.49008i
$592$	26.4064			1.08529
$593$		−	8.65172i		−	0.355284i	−0.984095	−	0.177642i	$-0.943153\pi$
$593$		−	8.65172i		−	0.355284i	0.984095	−	0.177642i	$-0.0568468\pi$
$594$		−	29.1423i		−	1.19572i
$595$	1.23340	+	15.9837i	0.0505644	+	0.655266i
$596$	−12.5793	−	12.5793i	−0.515266	−	0.515266i
$597$	−8.06145	−	8.06145i	−0.329933	−	0.329933i
$598$		0			0
$599$			35.1779i			1.43733i	0.695356	+	0.718666i	$0.255247\pi$
$599$			35.1779i			1.43733i	−0.695356	+	0.718666i	$0.744753\pi$
$600$	9.45178	+	6.91130i	0.385867	+	0.282153i
$601$	−40.0769			−1.63477			−0.817385	−	0.576091i	$-0.804577\pi$
$601$	−40.0769			−1.63477			−0.817385	+	0.576091i	$0.804577\pi$
$602$	40.3889	+	40.3889i	1.64613	+	1.64613i
$603$	−2.12443			−0.0865136
$604$	1.03674	+	1.03674i	0.0421843	+	0.0421843i
$605$	−5.83181	+	6.80711i	−0.237097	+	0.276748i
$606$	−11.6890	−	11.6890i	−0.474834	−	0.474834i
$607$	30.4484	−	30.4484i	1.23586	−	1.23586i	0.274188	−	0.961676i	$-0.411591\pi$
$607$	30.4484	−	30.4484i	1.23586	−	1.23586i	0.961676	−	0.274188i	$-0.0884092\pi$
$608$	2.49382	−	2.49382i	0.101138	−	0.101138i
$609$	9.80806	−	9.80806i	0.397443	−	0.397443i
$610$	7.69108	−	8.97731i	0.311403	−	0.363481i
$611$		0			0
$612$	−1.80063	+	1.80063i	−0.0727863	+	0.0727863i
$613$	20.2795			0.819080			0.409540	−	0.912292i	$-0.365689\pi$
$613$	20.2795			0.819080			0.409540	+	0.912292i	$0.365689\pi$
$614$		−	3.91850i		−	0.158138i
$615$	−2.26427	−	1.93985i	−0.0913040	−	0.0782223i
$616$	11.4553	−	11.4553i	0.461546	−	0.461546i
$617$			8.67054i			0.349063i	0.984652	+	0.174531i	$0.0558410\pi$
$617$			8.67054i			0.349063i	−0.984652	+	0.174531i	$0.944159\pi$
$618$		−	50.2729i		−	2.02227i
$619$	−21.3034	+	21.3034i	−0.856257	+	0.856257i	−0.990895	−	0.134638i	$-0.957013\pi$
$619$	−21.3034	+	21.3034i	−0.856257	+	0.856257i	0.134638	+	0.990895i	$0.457013\pi$
$620$	17.6666	−	1.36326i	0.709507	−	0.0547499i
$621$		−	1.25043i		−	0.0501780i
$622$	−6.99837			−0.280609
$623$	−11.7725	+	11.7725i	−0.471657	+	0.471657i
$624$		0			0
$625$	−23.8231	+	7.58013i	−0.952925	+	0.303205i
$626$	−5.57789	+	5.57789i	−0.222937	+	0.222937i
$627$	2.91692	−	2.91692i	0.116490	−	0.116490i
$628$	−4.11180	+	4.11180i	−0.164079	+	0.164079i
$629$	7.76093	+	7.76093i	0.309449	+	0.309449i
$630$	10.2117	+	8.74864i	0.406845	+	0.348554i
$631$	−20.0819	−	20.0819i	−0.799449	−	0.799449i	0.183560	−	0.983009i	$-0.441238\pi$
$631$	−20.0819	−	20.0819i	−0.799449	−	0.799449i	−0.983009	+	0.183560i	$0.941238\pi$
$632$	1.88727			0.0750715
$633$	4.52286	+	4.52286i	0.179768	+	0.179768i
$634$	42.3339			1.68129
$635$	−0.221253	−	2.86722i	−0.00878015	−	0.113782i
$636$			12.0094i			0.476206i
$637$		0			0
$638$	9.92320	+	9.92320i	0.392863	+	0.392863i
$639$	3.03161	+	3.03161i	0.119929	+	0.119929i
$640$	13.0369	−	15.2171i	0.515327	−	0.601509i
$641$		−	16.3686i		−	0.646520i	−0.946310	−	0.323260i	$-0.895221\pi$
$641$		−	16.3686i		−	0.646520i	0.946310	−	0.323260i	$-0.104779\pi$
$642$			25.6652i			1.01292i
$643$	41.0517			1.61892			0.809460	−	0.587175i	$-0.199760\pi$
$643$	41.0517			1.61892			0.809460	+	0.587175i	$0.199760\pi$
$644$	−1.03228	+	1.03228i	−0.0406776	+	0.0406776i
$645$	29.6555	+	25.4065i	1.16768	+	1.00038i
$646$	1.99364			0.0784386
$647$	2.00480	+	2.00480i	0.0788168	+	0.0788168i	0.745416	−	0.666599i	$-0.232251\pi$
$647$	2.00480	+	2.00480i	0.0788168	+	0.0788168i	−0.666599	+	0.745416i	$0.732251\pi$
$648$			12.9064i			0.507010i
$649$	−47.1059			−1.84907
$650$		0			0
$651$	−41.0201			−1.60771
$652$			3.06687i			0.120108i
$653$	0.887856	+	0.887856i	0.0347445	+	0.0347445i	0.724266	−	0.689521i	$-0.242179\pi$
$653$	0.887856	+	0.887856i	0.0347445	+	0.0347445i	−0.689521	+	0.724266i	$0.742179\pi$
$654$	50.7861			1.98589
$655$	−9.49985	−	8.13874i	−0.371190	−	0.318007i
$656$	−2.31883	+	2.31883i	−0.0905349	+	0.0905349i
$657$	13.6885			0.534041
$658$			63.2122i			2.46427i
$659$			9.35210i			0.364306i	0.983270	+	0.182153i	$0.0583066\pi$
$659$			9.35210i			0.364306i	−0.983270	+	0.182153i	$0.941693\pi$
$660$	−15.1338	+	17.6647i	−0.589081	+	0.687597i
$661$	18.1521	+	18.1521i	0.706037	+	0.706037i	0.965699	−	0.259663i	$-0.0836114\pi$
$661$	18.1521	+	18.1521i	0.706037	+	0.706037i	−0.259663	+	0.965699i	$0.583611\pi$
$662$	−2.58641	−	2.58641i	−0.100524	−	0.100524i
$663$		0			0
$664$			8.94896i			0.347287i
$665$	−0.327106	−	4.23898i	−0.0126846	−	0.164381i
$666$	9.20629			0.356736
$667$	0.425782	+	0.425782i	0.0164863	+	0.0164863i
$668$	−0.839440			−0.0324789
$669$	−10.3916	−	10.3916i	−0.401762	−	0.401762i
$670$	−7.12223	−	6.10178i	−0.275156	−	0.235732i
$671$	−7.90679	−	7.90679i	−0.305238	−	0.305238i
$672$	32.5544	−	32.5544i	1.25581	−	1.25581i
$673$	−29.2283	+	29.2283i	−1.12667	+	1.12667i	−0.135955	+	0.990715i	$0.543410\pi$
$673$	−29.2283	+	29.2283i	−1.12667	+	1.12667i	−0.990715	+	0.135955i	$0.956590\pi$
$674$	−11.2229	+	11.2229i	−0.432290	+	0.432290i
$675$	−16.5759	−	12.1205i	−0.638005	−	0.466520i
$676$		0			0
$677$	15.5322	−	15.5322i	0.596950	−	0.596950i	−0.342549	−	0.939500i	$-0.611290\pi$
$677$	15.5322	−	15.5322i	0.596950	−	0.596950i	0.939500	+	0.342549i	$0.111290\pi$
$678$	8.32181			0.319597
$679$		−	63.0822i		−	2.42087i
$680$	5.33689	−	0.411827i	0.204660	−	0.0157929i
$681$	−5.46862	+	5.46862i	−0.209558	+	0.209558i
$682$		−	41.5017i		−	1.58918i
$683$			6.65304i			0.254571i	0.991866	+	0.127286i	$0.0406265\pi$
$683$			6.65304i			0.254571i	−0.991866	+	0.127286i	$0.959373\pi$
$684$	0.477541	−	0.477541i	0.0182592	−	0.0182592i
$685$	24.2662	+	20.7894i	0.927162	+	0.794322i
$686$			9.56838i			0.365322i
$687$	34.7392			1.32538
$688$	30.3701	−	30.3701i	1.15785	−	1.15785i
$689$		0			0
$690$	−1.60790	+	1.87680i	−0.0612117	+	0.0714485i
$691$	−26.6060	+	26.6060i	−1.01214	+	1.01214i	−0.0122158	+	0.999925i	$0.503889\pi$
$691$	−26.6060	+	26.6060i	−1.01214	+	1.01214i	−0.999925	+	0.0122158i	$0.996111\pi$
$692$	6.34386	−	6.34386i	0.241157	−	0.241157i
$693$	8.99402	−	8.99402i	0.341655	−	0.341655i
$694$	−42.1038	−	42.1038i	−1.59824	−	1.59824i
$695$	−25.3377	+	29.5752i	−0.961115	+	1.12185i
$696$	−3.27488	−	3.27488i	−0.124134	−	0.124134i
$697$	−1.36302			−0.0516282
$698$	8.81368	+	8.81368i	0.333603	+	0.333603i
$699$	−8.09892			−0.306329
$700$	3.67805	+	23.6901i	0.139017	+	0.895401i
$701$		−	40.3398i		−	1.52361i	−0.647804	−	0.761807i	$-0.724312\pi$
$701$		−	40.3398i		−	1.52361i	0.647804	−	0.761807i	$-0.275688\pi$
$702$		0			0
$703$	−2.05825	−	2.05825i	−0.0776285	−	0.0776285i
$704$	6.23252	+	6.23252i	0.234897	+	0.234897i
$705$	3.32498	+	43.0885i	0.125226	+	1.62281i
$706$		−	50.0515i		−	1.88371i
$707$			16.1158i			0.606097i
$708$	−32.6495			−1.22704
$709$	−31.5318	+	31.5318i	−1.18420	+	1.18420i	−0.205559	+	0.978645i	$0.565901\pi$
$709$	−31.5318	+	31.5318i	−1.18420	+	1.18420i	−0.978645	+	0.205559i	$0.934099\pi$
$710$	1.45620	+	18.8709i	0.0546501	+	0.708213i
$711$	1.48177			0.0555708
$712$	3.93081	+	3.93081i	0.147313	+	0.147313i
$713$		−	1.78074i		−	0.0666893i
$714$	26.0250			0.973960
$715$		0			0
$716$	−2.96749			−0.110900
$717$		−	25.1492i		−	0.939214i
$718$	−7.14100	−	7.14100i	−0.266500	−	0.266500i
$719$	−27.5650			−1.02800			−0.514001	−	0.857790i	$-0.671837\pi$
$719$	−27.5650			−1.02800			−0.514001	+	0.857790i	$0.671837\pi$
$720$	6.57846	−	7.67863i	0.245165	−	0.286166i
$721$	−34.6560	+	34.6560i	−1.29066	+	1.29066i
$722$	34.2723			1.27548
$723$		−	34.7768i		−	1.29336i
$724$			12.9967i			0.483020i
$725$	9.77136	−	1.51707i	0.362899	−	0.0563426i
$726$	10.2895	+	10.2895i	0.381879	+	0.381879i
$727$	−29.4624	−	29.4624i	−1.09270	−	1.09270i	−0.995240	−	0.0974593i	$-0.968928\pi$
$727$	−29.4624	−	29.4624i	−1.09270	−	1.09270i	−0.0974593	−	0.995240i	$-0.531072\pi$
$728$		0			0
$729$		−	14.2845i		−	0.529057i
$730$	45.8913	+	39.3161i	1.69851	+	1.45516i
$731$	17.8518			0.660271
$732$	−5.48026	−	5.48026i	−0.202556	−	0.202556i
$733$	23.3958			0.864144			0.432072	−	0.901839i	$-0.357783\pi$
$733$	23.3958			0.864144			0.432072	+	0.901839i	$0.357783\pi$
$734$	23.4105	+	23.4105i	0.864098	+	0.864098i
$735$	−1.88337	−	24.4067i	−0.0694693	−	0.900255i
$736$	1.41323	+	1.41323i	0.0520924	+	0.0520924i
$737$	−6.27292	+	6.27292i	−0.231066	+	0.231066i
$738$	−0.808434	+	0.808434i	−0.0297589	+	0.0297589i
$739$	11.3556	−	11.3556i	0.417723	−	0.417723i	−0.466695	−	0.884418i	$-0.654556\pi$
$739$	11.3556	−	11.3556i	0.417723	−	0.417723i	0.884418	+	0.466695i	$0.154556\pi$
$740$	12.4647	+	10.6788i	0.458210	+	0.392560i
$741$		0			0
$742$	20.4995	−	20.4995i	0.752561	−	0.752561i
$743$	−52.2801			−1.91797			−0.958985	−	0.283457i	$-0.908519\pi$
$743$	−52.2801			−1.91797			−0.958985	+	0.283457i	$0.908519\pi$
$744$			13.6965i			0.502137i
$745$	2.25888	+	29.2729i	0.0827589	+	1.07248i
$746$	−20.0933	+	20.0933i	−0.735669	+	0.735669i
$747$			7.02620i			0.257075i
$748$			10.6336i			0.388805i
$749$	17.6925	−	17.6925i	0.646468	−	0.646468i
$750$	9.29358	+	39.5065i	0.339353	+	1.44258i
$751$			27.4355i			1.00114i	0.865697	+	0.500569i	$0.166876\pi$
$751$			27.4355i			1.00114i	−0.865697	+	0.500569i	$0.833124\pi$
$752$	47.5319			1.73331
$753$	−30.5066	+	30.5066i	−1.11172	+	1.11172i
$754$		0			0
$755$	−0.186169	−	2.41257i	−0.00677539	−	0.0878026i
$756$	−13.9241	+	13.9241i	−0.506416	+	0.506416i
$757$	1.70159	−	1.70159i	0.0618452	−	0.0618452i	−0.675508	−	0.737353i	$-0.736075\pi$
$757$	1.70159	−	1.70159i	0.0618452	−	0.0618452i	0.737353	+	0.675508i	$0.236075\pi$
$758$	−27.6742	+	27.6742i	−1.00517	+	1.00517i
$759$	1.65300	+	1.65300i	0.0600000	+	0.0600000i
$760$	−1.41538	+	0.109219i	−0.0513412	+	0.00396181i
$761$	1.72762	+	1.72762i	0.0626260	+	0.0626260i	0.737726	−	0.675100i	$-0.235900\pi$
$761$	1.72762	+	1.72762i	0.0626260	+	0.0626260i	−0.675100	+	0.737726i	$0.735900\pi$
$762$	−4.66848			−0.169121
$763$	−35.0097	−	35.0097i	−1.26744	−	1.26744i
$764$	−5.05523			−0.182892
$765$	4.19021	−	0.323343i	0.151497	−	0.0116905i
$766$		−	35.5469i		−	1.28436i
$767$		0			0
$768$	−29.3786	−	29.3786i	−1.06011	−	1.06011i
$769$	−9.58574	−	9.58574i	−0.345670	−	0.345670i	0.512824	−	0.858494i	$-0.328600\pi$
$769$	−9.58574	−	9.58574i	−0.345670	−	0.345670i	−0.858494	+	0.512824i	$0.828600\pi$
$770$	55.9853	−	4.32017i	2.01757	−	0.155688i
$771$		−	25.3938i		−	0.914536i
$772$			0.384901i			0.0138529i
$773$	−22.4445			−0.807272			−0.403636	−	0.914920i	$-0.632254\pi$
$773$	−22.4445			−0.807272			−0.403636	+	0.914920i	$0.632254\pi$
$774$	10.5882	−	10.5882i	0.380585	−	0.380585i
$775$	−23.6058	−	17.2609i	−0.847944	−	0.620031i
$776$	−21.0629			−0.756115
$777$	−26.8685	−	26.8685i	−0.963901	−	0.963901i
$778$		−	27.2164i		−	0.975756i
$779$	0.361484			0.0129515
$780$		0			0
$781$	17.9032			0.640626
$782$			1.12978i			0.0404009i
$783$	5.74324	+	5.74324i	0.205247	+	0.205247i
$784$	−26.9236			−0.961556
$785$	9.56847	−	0.738363i	0.341513	−	0.0263533i
$786$	−14.3598	+	14.3598i	−0.512197	+	0.512197i
$787$	13.4958			0.481074			0.240537	−	0.970640i	$-0.422676\pi$
$787$	13.4958			0.481074			0.240537	+	0.970640i	$0.422676\pi$
$788$		−	35.0224i		−	1.24762i
$789$		−	32.7104i		−	1.16452i
$790$	4.96769	+	4.25594i	0.176743	+	0.151420i
$791$	−5.73669	−	5.73669i	−0.203973	−	0.203973i
$792$	−3.00307	−	3.00307i	−0.106709	−	0.106709i
$793$		0			0
$794$		−	9.66696i		−	0.343068i
$795$	12.8952	−	15.0517i	0.457345	−	0.533830i
$796$	−7.79393			−0.276248
$797$	4.43678	+	4.43678i	0.157159	+	0.157159i	0.781307	−	0.624148i	$-0.214554\pi$
$797$	4.43678	+	4.43678i	0.157159	+	0.157159i	−0.624148	+	0.781307i	$0.714554\pi$
$798$	−6.90201			−0.244328
$799$	13.9698	+	13.9698i	0.494216	+	0.494216i
$800$	32.4326	−	5.03539i	1.14667	−	0.178028i
$801$	3.08625	+	3.08625i	0.109047	+	0.109047i
$802$	36.1075	−	36.1075i	1.27500	−	1.27500i
$803$	40.4189	−	40.4189i	1.42635	−	1.42635i
$804$	−4.34781	+	4.34781i	−0.153335	+	0.153335i
$805$	2.40220	−	0.185369i	0.0846664	−	0.00653339i
$806$		0			0
$807$	−45.2744	+	45.2744i	−1.59374	+	1.59374i
$808$	5.38101			0.189303
$809$		−	21.5781i		−	0.758645i	−0.925265	−	0.379322i	$-0.876157\pi$
$809$		−	21.5781i		−	0.758645i	0.925265	−	0.379322i	$-0.123843\pi$
$810$	−29.1049	+	33.9723i	−1.02264	+	1.19366i
$811$	−22.5473	+	22.5473i	−0.791743	+	0.791743i	−0.981777	−	0.190035i	$-0.939140\pi$
$811$	−22.5473	+	22.5473i	−0.791743	+	0.791743i	0.190035	+	0.981777i	$0.439140\pi$
$812$		−	9.48257i		−	0.332773i
$813$			34.6277i			1.21445i
$814$	27.1839	−	27.1839i	0.952795	−	0.952795i
$815$	3.29306	−	3.84379i	0.115351	−	0.134642i
$816$		−	19.5692i		−	0.685061i
$817$	−4.73441			−0.165636
$818$	−3.41289	+	3.41289i	−0.119329	+	0.119329i
$819$		0			0
$820$	−2.03230	+	0.156825i	−0.0709710	+	0.00547656i
$821$	−12.6803	+	12.6803i	−0.442544	+	0.442544i	−0.892866	−	0.450322i	$-0.851309\pi$
$821$	−12.6803	+	12.6803i	−0.442544	+	0.442544i	0.450322	+	0.892866i	$0.351309\pi$
$822$	36.6803	−	36.6803i	1.27937	−	1.27937i
$823$	0.814658	−	0.814658i	0.0283972	−	0.0283972i	−0.692766	−	0.721163i	$-0.743608\pi$
$823$	0.814658	−	0.814658i	0.0283972	−	0.0283972i	0.721163	+	0.692766i	$0.243608\pi$
$824$	11.5715	+	11.5715i	0.403112	+	0.403112i
$825$	37.9350	−	5.88968i	1.32073	−	0.205052i
$826$	55.7310	+	55.7310i	1.93913	+	1.93913i
$827$	4.45029			0.154752			0.0773759	−	0.997002i	$-0.475346\pi$
$827$	4.45029			0.154752			0.0773759	+	0.997002i	$0.475346\pi$
$828$	0.270619	+	0.270619i	0.00940466	+	0.00940466i
$829$	29.1274			1.01164			0.505819	−	0.862640i	$-0.331191\pi$
$829$	29.1274			1.01164			0.505819	+	0.862640i	$0.331191\pi$
$830$	−20.1806	+	23.5556i	−0.700479	+	0.817625i
$831$		−	6.09295i		−	0.211362i
$832$		0			0
$833$	−7.91294	−	7.91294i	−0.274167	−	0.274167i
$834$	44.7052	+	44.7052i	1.54802	+	1.54802i
$835$	1.05209	+	0.901352i	0.0364091	+	0.0311926i
$836$		−	2.82012i		−	0.0975358i
$837$		−	24.0199i		−	0.830249i
$838$	−36.0284			−1.24458
$839$	22.8596	−	22.8596i	0.789200	−	0.789200i	−0.192163	−	0.981363i	$-0.561550\pi$
$839$	22.8596	−	22.8596i	0.789200	−	0.789200i	0.981363	+	0.192163i	$0.0615502\pi$
$840$	−18.4764	+	1.42575i	−0.637496	+	0.0491931i
$841$	25.0888			0.865130
$842$	−19.1273	−	19.1273i	−0.659169	−	0.659169i
$843$		−	52.3436i		−	1.80281i
$844$	4.37277			0.150517
$845$		0			0
$846$	16.5715			0.569739
$847$		−	14.1863i		−	0.487446i
$848$	−15.4144	−	15.4144i	−0.529334	−	0.529334i
$849$	−30.3998			−1.04332
$850$	14.9765	+	10.9511i	0.513691	+	0.375619i
$851$	1.16640	−	1.16640i	0.0399836	−	0.0399836i
$852$	12.4088			0.425119
$853$		−	9.24230i		−	0.316450i	−0.987403	−	0.158225i	$-0.949423\pi$
$853$		−	9.24230i		−	0.316450i	0.987403	−	0.158225i	$-0.0505772\pi$
$854$			18.7091i			0.640211i
$855$	−1.11127	+	0.0857528i	−0.0380048	+	0.00293268i
$856$	−5.90745	−	5.90745i	−0.201912	−	0.201912i
$857$	37.7913	+	37.7913i	1.29093	+	1.29093i	0.934214	+	0.356713i	$0.116103\pi$
$857$	37.7913	+	37.7913i	1.29093	+	1.29093i	0.356713	+	0.934214i	$0.383897\pi$
$858$		0			0
$859$		−	6.16263i		−	0.210266i	−0.994458	−	0.105133i	$-0.966473\pi$
$859$		−	6.16263i		−	0.210266i	0.994458	−	0.105133i	$-0.0335269\pi$
$860$	26.6174	−	2.05396i	0.907645	−	0.0700395i
$861$	4.71881			0.160817
$862$	22.1892	+	22.1892i	0.755767	+	0.755767i
$863$	33.7740			1.14968			0.574840	−	0.818266i	$-0.305064\pi$
$863$	33.7740			1.14968			0.574840	+	0.818266i	$0.305064\pi$
$864$	19.0627	+	19.0627i	0.648525	+	0.648525i
$865$	−14.7627	+	1.13918i	−0.501945	+	0.0387332i
$866$	14.5532	+	14.5532i	0.494539	+	0.494539i
$867$	−18.0720	+	18.0720i	−0.613758	+	0.613758i
$868$	−19.8294	+	19.8294i	−0.673055	+	0.673055i
$869$	4.37531	−	4.37531i	0.148422	−	0.148422i
$870$	−1.23507	−	16.0053i	−0.0418727	−	0.542630i
$871$		0			0
$872$	−11.6896	+	11.6896i	−0.395861	+	0.395861i
$873$	−16.5374			−0.559706
$874$		−	0.299626i		−	0.0101350i
$875$	20.8275	−	33.6407i	0.704098	−	1.13726i
$876$	28.0146	−	28.0146i	0.946527	−	0.946527i
$877$			22.6972i			0.766429i	0.923659	+	0.383214i	$0.125183\pi$
$877$			22.6972i			0.766429i	−0.923659	+	0.383214i	$0.874817\pi$
$878$		−	7.77409i		−	0.262363i
$879$	14.5417	−	14.5417i	0.490480	−	0.490480i
$880$	−3.24852	−	42.0976i	−0.109507	−	1.41911i
$881$		−	7.83247i		−	0.263883i	−0.991258	−	0.131941i	$-0.957879\pi$
$881$		−	7.83247i		−	0.263883i	0.991258	−	0.131941i	$-0.0421210\pi$
$882$	−9.38661			−0.316064
$883$	−18.9296	+	18.9296i	−0.637032	+	0.637032i	−0.949822	−	0.312790i	$-0.898736\pi$
$883$	−18.9296	+	18.9296i	−0.637032	+	0.637032i	0.312790	+	0.949822i	$0.398736\pi$
$884$		0			0
$885$	40.9204	+	35.0575i	1.37552	+	1.17844i
$886$	−27.7619	+	27.7619i	−0.932678	+	0.932678i
$887$	25.1275	−	25.1275i	0.843698	−	0.843698i	−0.145640	−	0.989338i	$-0.546524\pi$
$887$	25.1275	−	25.1275i	0.843698	−	0.843698i	0.989338	+	0.145640i	$0.0465241\pi$
$888$	−8.97129	+	8.97129i	−0.301057	+	0.301057i
$889$	3.21825	+	3.21825i	0.107937	+	0.107937i
$890$	1.48244	+	19.2110i	0.0496916	+	0.643955i
$891$	29.9212	+	29.9212i	1.00240	+	1.00240i
$892$	−10.0467			−0.336389
$893$	−3.70489	−	3.70489i	−0.123979	−	0.123979i
$894$	47.6628			1.59408
$895$	3.71923	+	3.18636i	0.124320	+	0.106508i
$896$			31.7130i			1.05946i
$897$		0			0
$898$	18.8417	+	18.8417i	0.628755	+	0.628755i
$899$	8.17898	+	8.17898i	0.272784	+	0.272784i
$900$	6.21050	−	0.964223i	0.207017	−	0.0321408i
$901$		−	9.06072i		−	0.301856i
$902$			4.77421i			0.158964i
$903$	−61.8031			−2.05668
$904$	−1.91546	+	1.91546i	−0.0637073	+	0.0637073i
$905$	13.9553	−	16.2891i	0.463889	−	0.541469i
$906$	−3.92821			−0.130506
$907$	32.8817	+	32.8817i	1.09182	+	1.09182i	0.995334	+	0.0964844i	$0.0307598\pi$
$907$	32.8817	+	32.8817i	1.09182	+	1.09182i	0.0964844	+	0.995334i	$0.469240\pi$
$908$			5.28714i			0.175460i
$909$	4.22485			0.140130
$910$		0			0
$911$	17.7325			0.587504			0.293752	−	0.955882i	$-0.405096\pi$
$911$	17.7325			0.587504			0.293752	+	0.955882i	$0.405096\pi$
$912$			5.18990i			0.171855i
$913$	20.7466	+	20.7466i	0.686613	+	0.686613i
$914$	−55.4898			−1.83544
$915$	0.984100	+	12.7530i	0.0325333	+	0.421601i
$916$	16.7932	−	16.7932i	0.554863	−	0.554863i
$917$	19.7980			0.653789
$918$			15.2393i			0.502971i
$919$			48.7954i			1.60961i	0.593538	+	0.804806i	$0.297730\pi$
$919$			48.7954i			1.60961i	−0.593538	+	0.804806i	$0.702270\pi$
$920$	−0.0618939	−	0.802086i	−0.00204058	−	0.0264440i
$921$	2.99805	+	2.99805i	0.0987891	+	0.0987891i
$922$	−8.98564	−	8.98564i	−0.295926	−	0.295926i
$923$		0			0
$924$		−	36.8139i		−	1.21109i
$925$	−4.15591	−	26.7680i	−0.136645	−	0.880125i
$926$	57.5981			1.89279
$927$	9.08527	+	9.08527i	0.298399	+	0.298399i
$928$	−12.9820			−0.426155
$929$	−7.34465	−	7.34465i	−0.240970	−	0.240970i	0.576281	−	0.817251i	$-0.304503\pi$
$929$	−7.34465	−	7.34465i	−0.240970	−	0.240970i	−0.817251	+	0.576281i	$0.804503\pi$
$930$	−30.8867	+	36.0521i	−1.01281	+	1.18219i
$931$	2.09857	+	2.09857i	0.0687778	+	0.0687778i
$932$	−3.91508	+	3.91508i	−0.128243	+	0.128243i
$933$	5.35446	−	5.35446i	0.175297	−	0.175297i
$934$	6.77011	−	6.77011i	0.221525	−	0.221525i
$935$	11.4179	−	13.3274i	0.373406	−	0.435853i
$936$		0			0
$937$	5.31856	−	5.31856i	0.173750	−	0.173750i	−0.614875	−	0.788625i	$-0.710794\pi$
$937$	5.31856	−	5.31856i	0.173750	−	0.173750i	0.788625	+	0.614875i	$0.210794\pi$
$938$	14.8430			0.484641
$939$		−	8.53529i		−	0.278539i
$940$	22.4366	+	19.2220i	0.731802	+	0.626952i
$941$	38.9093	−	38.9093i	1.26841	−	1.26841i	0.321497	−	0.946911i	$-0.395814\pi$
$941$	38.9093	−	38.9093i	1.26841	−	1.26841i	0.946911	−	0.321497i	$-0.104186\pi$
$942$		−	15.5796i		−	0.507611i
$943$			0.204850i			0.00667084i
$944$	41.9064	−	41.9064i	1.36394	−	1.36394i
$945$	32.4026	−	2.50038i	1.05406	−	0.0813375i
$946$		−	62.5286i		−	2.03298i
$947$	−33.7517			−1.09678			−0.548392	−	0.836222i	$-0.684760\pi$
$947$	−33.7517			−1.09678			−0.548392	+	0.836222i	$0.684760\pi$
$948$	3.03256	−	3.03256i	0.0984930	−	0.0984930i
$949$		0			0
$950$	−3.97188	−	2.90431i	−0.128865	−	0.0942281i
$951$	−32.3897	+	32.3897i	−1.05031	+	1.05031i
$952$	−5.99026	+	5.99026i	−0.194146	+	0.194146i
$953$	3.12279	−	3.12279i	0.101157	−	0.101157i	−0.654717	−	0.755874i	$-0.727212\pi$
$953$	3.12279	−	3.12279i	0.101157	−	0.101157i	0.755874	+	0.654717i	$0.227212\pi$
$954$	−5.37407	−	5.37407i	−0.173992	−	0.173992i
$955$	6.33584	+	5.42807i	0.205023	+	0.175648i
$956$	−12.1573	−	12.1573i	−0.393195	−	0.393195i
$957$	−15.1845			−0.490845
$958$	−25.0658	−	25.0658i	−0.809839	−	0.809839i
$959$	−50.5716			−1.63304
$960$	−0.775716	−	10.0525i	−0.0250361	−	0.324444i
$961$		−	3.20686i		−	0.103447i
$962$		0			0
$963$	−4.63819	−	4.63819i	−0.149463	−	0.149463i
$964$	−16.8114	−	16.8114i	−0.541457	−	0.541457i
$965$	0.413289	−	0.482406i	0.0133042	−	0.0155292i
$966$		−	3.91132i		−	0.125845i
$967$			16.2803i			0.523540i	0.965130	+	0.261770i	$0.0843061\pi$
$967$			16.2803i			0.523540i	−0.965130	+	0.261770i	$0.915694\pi$
$968$	−4.73674			−0.152245
$969$	−1.52533	+	1.52533i	−0.0490007	+	0.0490007i
$970$	−55.4421	−	47.4986i	−1.78014	−	1.52509i
$971$	12.8029			0.410865			0.205433	−	0.978671i	$-0.434140\pi$
$971$	12.8029			0.410865			0.205433	+	0.978671i	$0.434140\pi$
$972$	8.93484	+	8.93484i	0.286585	+	0.286585i
$973$		−	61.6357i		−	1.97595i
$974$	42.7918			1.37114
$975$		0			0
$976$	14.0681			0.450309
$977$		−	16.0487i		−	0.513444i	−0.966485	−	0.256722i	$-0.917358\pi$
$977$		−	16.0487i		−	0.513444i	0.966485	−	0.256722i	$-0.0826425\pi$
$978$	−5.81019	−	5.81019i	−0.185790	−	0.185790i
$979$	18.2258			0.582500
$980$	−12.7088	−	10.8879i	−0.405968	−	0.347803i
$981$	−9.17801	+	9.17801i	−0.293031	+	0.293031i
$982$	−39.0478			−1.24607
$983$			34.3036i			1.09411i	0.837096	+	0.547057i	$0.184252\pi$
$983$			34.3036i			1.09411i	−0.837096	+	0.547057i	$0.815748\pi$
$984$		−	1.57559i		−	0.0502281i
$985$	−37.6054	+	43.8945i	−1.19821	+	1.39859i
$986$	−5.18910	−	5.18910i	−0.165255	−	0.165255i
$987$	−48.3637	−	48.3637i	−1.53943	−	1.53943i
$988$		0			0
$989$		−	2.68296i		−	0.0853131i
$990$	−1.13256	−	14.6769i	−0.0359951	−	0.466462i
$991$	22.3545			0.710114			0.355057	−	0.934845i	$-0.384461\pi$
$991$	22.3545			0.710114			0.355057	+	0.934845i	$0.384461\pi$
$992$	27.1472	+	27.1472i	0.861926	+	0.861926i
$993$	3.95773			0.125595
$994$	−21.1812	−	21.1812i	−0.671828	−	0.671828i
$995$	9.76832	+	8.36875i	0.309677	+	0.265307i
$996$	14.3796	+	14.3796i	0.455637	+	0.455637i
$997$	8.41794	−	8.41794i	0.266599	−	0.266599i	−0.561129	−	0.827728i	$-0.689633\pi$
$997$	8.41794	−	8.41794i	0.266599	−	0.266599i	0.827728	+	0.561129i	$0.189633\pi$
$998$	42.1987	−	42.1987i	1.33578	−	1.33578i
$999$	15.7332	−	15.7332i	0.497776	−	0.497776i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.f.d.408.8		20
5.2	odd	4		845.2.k.d.577.3		20
13.2	odd	12		65.2.o.a.33.2	yes	20
13.3	even	3		845.2.t.e.188.2		20
13.4	even	6		65.2.t.a.28.2	yes	20
13.5	odd	4		845.2.k.e.268.8		20
13.6	odd	12		845.2.o.e.258.2		20
13.7	odd	12		845.2.o.f.258.4		20
13.8	odd	4		845.2.k.d.268.3		20
13.9	even	3		845.2.t.g.418.4		20
13.10	even	6		845.2.t.f.188.4		20
13.11	odd	12		845.2.o.g.488.4		20
13.12	even	2		845.2.f.e.408.3		20
39.2	even	12		585.2.cf.a.163.4		20
39.17	odd	6		585.2.dp.a.28.4		20
65.2	even	12		65.2.t.a.7.2	yes	20
65.4	even	6		325.2.x.b.93.4		20
65.7	even	12		845.2.t.e.427.2		20
65.12	odd	4		845.2.k.e.577.8		20
65.17	odd	12		65.2.o.a.2.2	✓	20
65.22	odd	12		845.2.o.g.587.4		20
65.28	even	12		325.2.x.b.7.4		20
65.32	even	12		845.2.t.f.427.4		20
65.37	even	12		845.2.t.g.657.4		20
65.42	odd	12		845.2.o.f.357.4		20
65.43	odd	12		325.2.s.b.132.4		20
65.47	even	4	inner	845.2.f.d.437.3		20
65.54	odd	12		325.2.s.b.293.4		20
65.57	even	4		845.2.f.e.437.8		20
65.62	odd	12		845.2.o.e.357.2		20
195.2	odd	12		585.2.dp.a.397.4		20
195.17	even	12		585.2.cf.a.262.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.2	✓	20	65.17	odd	12
65.2.o.a.33.2	yes	20	13.2	odd	12
65.2.t.a.7.2	yes	20	65.2	even	12
65.2.t.a.28.2	yes	20	13.4	even	6
325.2.s.b.132.4		20	65.43	odd	12
325.2.s.b.293.4		20	65.54	odd	12
325.2.x.b.7.4		20	65.28	even	12
325.2.x.b.93.4		20	65.4	even	6
585.2.cf.a.163.4		20	39.2	even	12
585.2.cf.a.262.4		20	195.17	even	12
585.2.dp.a.28.4		20	39.17	odd	6
585.2.dp.a.397.4		20	195.2	odd	12
845.2.f.d.408.8		20	1.1	even	1	trivial
845.2.f.d.437.3		20	65.47	even	4	inner
845.2.f.e.408.3		20	13.12	even	2
845.2.f.e.437.8		20	65.57	even	4
845.2.k.d.268.3		20	13.8	odd	4
845.2.k.d.577.3		20	5.2	odd	4
845.2.k.e.268.8		20	13.5	odd	4
845.2.k.e.577.8		20	65.12	odd	4
845.2.o.e.258.2		20	13.6	odd	12
845.2.o.e.357.2		20	65.62	odd	12
845.2.o.f.258.4		20	13.7	odd	12
845.2.o.f.357.4		20	65.42	odd	12
845.2.o.g.488.4		20	13.11	odd	12
845.2.o.g.587.4		20	65.22	odd	12
845.2.t.e.188.2		20	13.3	even	3
845.2.t.e.427.2		20	65.7	even	12
845.2.t.f.188.4		20	13.10	even	6
845.2.t.f.427.4		20	65.32	even	12
845.2.t.g.418.4		20	13.9	even	3
845.2.t.g.657.4		20	65.37	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.83163i q^{2} +(-1.40138 - 1.40138i) q^{3} -1.35488 q^{4} +(1.69810 + 1.45480i) q^{5} +(2.56682 - 2.56682i) q^{6} -3.53890 q^{7} +1.18163i q^{8} +0.927746i q^{9} +(-2.66466 + 3.11030i) q^{10} +(2.73940 + 2.73940i) q^{11} +(1.89870 + 1.89870i) q^{12} -6.48197i q^{14} +(-0.340953 - 4.41843i) q^{15} -4.87406 q^{16} +(-1.43251 - 1.43251i) q^{17} -1.69929 q^{18} +(0.379911 + 0.379911i) q^{19} +(-2.30072 - 1.97108i) q^{20} +(4.95936 + 4.95936i) q^{21} +(-5.01758 + 5.01758i) q^{22} +(-0.215293 + 0.215293i) q^{23} +(1.65591 - 1.65591i) q^{24} +(0.767094 + 4.94081i) q^{25} +(-2.90402 + 2.90402i) q^{27} +4.79478 q^{28} -1.97769i q^{29} +(8.09293 - 0.624501i) q^{30} +(-4.13563 + 4.13563i) q^{31} -6.56423i q^{32} -7.67790i q^{33} +(2.62382 - 2.62382i) q^{34} +(-6.00942 - 5.14841i) q^{35} -1.25698i q^{36} -5.41773 q^{37} +(-0.695857 + 0.695857i) q^{38} +(-1.71904 + 2.00652i) q^{40} +(0.475748 - 0.475748i) q^{41} +(-9.08372 + 9.08372i) q^{42} +(-6.23095 + 6.23095i) q^{43} +(-3.71155 - 3.71155i) q^{44} +(-1.34969 + 1.57541i) q^{45} +(-0.394337 - 0.394337i) q^{46} -9.75201 q^{47} +(6.83043 + 6.83043i) q^{48} +5.52385 q^{49} +(-9.04974 + 1.40503i) q^{50} +4.01498i q^{51} +(3.16254 + 3.16254i) q^{53} +(-5.31910 - 5.31910i) q^{54} +(0.666490 + 8.63708i) q^{55} -4.18167i q^{56} -1.06480i q^{57} +3.62239 q^{58} +(-8.59785 + 8.59785i) q^{59} +(0.461950 + 5.98642i) q^{60} -2.88632 q^{61} +(-7.57495 - 7.57495i) q^{62} -3.28320i q^{63} +2.27514 q^{64} +14.0631 q^{66} +2.28989i q^{67} +(1.94087 + 1.94087i) q^{68} +0.603415 q^{69} +(9.43000 - 11.0070i) q^{70} +(3.26771 - 3.26771i) q^{71} -1.09625 q^{72} -14.7546i q^{73} -9.92329i q^{74} +(5.84897 - 7.99895i) q^{75} +(-0.514732 - 0.514732i) q^{76} +(-9.69449 - 9.69449i) q^{77} -1.59718i q^{79} +(-8.27665 - 7.09080i) q^{80} +10.9225 q^{81} +(0.871396 + 0.871396i) q^{82} +7.57341 q^{83} +(-6.71932 - 6.71932i) q^{84} +(-0.348525 - 4.51655i) q^{85} +(-11.4128 - 11.4128i) q^{86} +(-2.77149 + 2.77149i) q^{87} +(-3.23695 + 3.23695i) q^{88} +(3.32661 - 3.32661i) q^{89} +(-2.88556 - 2.47213i) q^{90} +(0.291695 - 0.291695i) q^{92} +11.5912 q^{93} -17.8621i q^{94} +(0.0924314 + 1.19782i) q^{95} +(-9.19900 + 9.19900i) q^{96} +17.8254i q^{97} +10.1177i q^{98} +(-2.54147 + 2.54147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} - 12 q^{4} - 4 q^{6} - 4 q^{7} - 8 q^{10} - 8 q^{11} - 24 q^{12} - 28 q^{15} + 4 q^{16} - 14 q^{17} - 4 q^{19} + 12 q^{20} - 4 q^{21} - 32 q^{22} + 8 q^{23} + 4 q^{24} + 18 q^{25} + 4 q^{27}+ \cdots - 60 q^{99}+O(q^{100}) \) 20 * q + 4 * q^3 - 12 * q^4 - 4 * q^6 - 4 * q^7 - 8 * q^10 - 8 * q^11 - 24 * q^12 - 28 * q^15 + 4 * q^16 - 14 * q^17 - 4 * q^19 + 12 * q^20 - 4 * q^21 - 32 * q^22 + 8 * q^23 + 4 * q^24 + 18 * q^25 + 4 * q^27 + 36 * q^28 + 40 * q^30 - 2 * q^34 - 20 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^40 + 38 * q^41 + 16 * q^42 - 32 * q^43 + 36 * q^44 + 6 * q^45 - 4 * q^46 + 40 * q^47 + 28 * q^48 - 36 * q^49 - 42 * q^50 - 10 * q^53 - 36 * q^54 - 16 * q^55 - 8 * q^59 - 28 * q^60 + 32 * q^61 + 4 * q^62 + 20 * q^64 - 32 * q^66 - 50 * q^68 + 32 * q^69 + 12 * q^70 + 40 * q^71 + 8 * q^72 + 4 * q^75 + 16 * q^76 - 28 * q^77 - 112 * q^80 + 28 * q^81 - 34 * q^82 - 48 * q^83 - 8 * q^84 + 2 * q^85 - 60 * q^86 - 28 * q^87 - 32 * q^88 - 12 * q^89 + 46 * q^90 - 8 * q^92 + 64 * q^93 + 40 * q^95 - 56 * q^96 - 60 * q^99

Introduction

L-functions

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