LMFDB - Embedded newform 845.2.k.e.268.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(268,845)] 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("845.268"); 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, 1])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [20,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == 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			268.8
Root			$1.83163i$ of defining polynomial
Character	$\chi$	$=$	845.268
Dual form			845.2.k.e.577.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.83163 q^{2} +(-1.40138 - 1.40138i) q^{3} +1.35488 q^{4} +(1.45480 - 1.69810i) q^{5} +(-2.56682 - 2.56682i) q^{6} -3.53890i q^{7} -1.18163 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} +(-4.41843 + 0.340953i) q^{15} -4.87406 q^{16} +(1.43251 + 1.43251i) q^{17} +1.69929i q^{18} +(0.379911 - 0.379911i) q^{19} +(1.97108 - 2.30072i) 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} -4.79478i q^{28} -1.97769i q^{29} +(-8.09293 + 0.624501i) q^{30} +(4.13563 + 4.13563i) q^{31} -6.56423 q^{32} +7.67790 q^{33} +(2.62382 + 2.62382i) q^{34} +(-6.00942 - 5.14841i) q^{35} +1.25698i q^{36} -5.41773i 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} +(1.57541 + 1.34969i) q^{45} +(0.394337 - 0.394337i) q^{46} -9.75201i q^{47} +(6.83043 + 6.83043i) q^{48} -5.52385 q^{49} +(-1.40503 - 9.04974i) 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} -1.06480 q^{57} -3.62239i q^{58} +(-8.59785 - 8.59785i) q^{59} +(-5.98642 + 0.461950i) q^{60} -2.88632 q^{61} +(7.57495 + 7.57495i) q^{62} +3.28320 q^{63} -2.27514 q^{64} +14.0631 q^{66} +2.28989 q^{67} +(1.94087 + 1.94087i) q^{68} -0.603415 q^{69} +(-11.0070 - 9.43000i) q^{70} +(-3.26771 - 3.26771i) q^{71} -1.09625i q^{72} +14.7546 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} +(-7.09080 + 8.27665i) q^{80} +10.9225 q^{81} +(-0.871396 - 0.871396i) q^{82} -7.57341i q^{83} +(-6.71932 + 6.71932i) q^{84} +(4.51655 - 0.348525i) 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} -11.5912i q^{93} -17.8621i q^{94} +(-0.0924314 - 1.19782i) q^{95} +(9.19900 + 9.19900i) q^{96} +17.8254 q^{97} -10.1177 q^{98} +(-2.54147 - 2.54147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 8 q^{2} + 4 q^{3} + 12 q^{4} - 6 q^{5} + 4 q^{6} + 12 q^{8} + 8 q^{10} + 8 q^{11} + 24 q^{12} - 24 q^{15} + 4 q^{16} + 14 q^{17} - 4 q^{19} - 22 q^{20} + 4 q^{21} - 32 q^{22} - 8 q^{23} + 4 q^{24}+ \cdots - 60 q^{99}+O(q^{100}) $ 20 * q + 8 * q^2 + 4 * q^3 + 12 * q^4 - 6 * q^5 + 4 * q^6 + 12 * q^8 + 8 * q^10 + 8 * q^11 + 24 * q^12 - 24 * q^15 + 4 * q^16 + 14 * q^17 - 4 * q^19 - 22 * q^20 + 4 * q^21 - 32 * q^22 - 8 * q^23 + 4 * q^24 - 18 * q^25 + 4 * q^27 - 40 * q^30 + 12 * q^32 + 36 * q^33 - 2 * q^34 - 20 * q^35 + 8 * q^38 - 16 * q^40 - 38 * q^41 + 16 * q^42 + 32 * q^43 + 36 * q^44 - 20 * q^45 + 4 * q^46 + 28 * q^48 + 36 * q^49 - 52 * q^50 - 10 * q^53 - 36 * q^54 - 16 * q^55 - 12 * q^57 - 8 * q^59 - 92 * q^60 + 32 * q^61 - 4 * q^62 + 64 * q^63 - 20 * q^64 - 32 * q^66 + 116 * q^67 - 50 * q^68 - 32 * q^69 + 32 * q^70 - 40 * q^71 + 72 * q^73 - 4 * q^75 - 16 * q^76 + 28 * q^77 - 34 * q^80 + 28 * q^81 + 34 * q^82 - 8 * q^84 + 60 * q^86 - 28 * q^87 + 32 * q^88 - 12 * q^89 - 46 * q^90 - 8 * q^92 - 40 * q^95 + 56 * q^96 + 44 * q^97 - 8 * q^98 - 60 * q^99

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.83163			1.29516			0.647580	−	0.761998i	$-0.275781\pi$
$2$	1.83163			1.29516			0.647580	+	0.761998i	$0.275781\pi$
$3$	−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
$5$	1.45480	−	1.69810i	0.650608	−	0.759414i
$5$	1.45480	−	1.69810i	0.650608	−	0.759414i
$6$	−2.56682	−	2.56682i	−1.04790	−	1.04790i
$7$		−	3.53890i		−	1.33758i	−0.743451	−	0.668790i	$-0.766812\pi$
$7$		−	3.53890i		−	1.33758i	0.743451	−	0.668790i	$-0.233188\pi$
$8$	−1.18163			−0.417769
$9$			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	$-0.948530\pi$
$11$	−2.73940	+	2.73940i	−0.825961	+	0.825961i	0.160994	+	0.986955i	$0.448530\pi$
$12$	−1.89870	−	1.89870i	−0.548108	−	0.548108i
$13$		0			0
$13$		0			0
$14$		−	6.48197i		−	1.73238i
$15$	−4.41843	+	0.340953i	−1.14083	+	0.0880337i
$16$	−4.87406			−1.21852
$17$	1.43251	+	1.43251i	0.347434	+	0.347434i	0.859153	−	0.511719i	$-0.170991\pi$
$17$	1.43251	+	1.43251i	0.347434	+	0.347434i	−0.511719	+	0.859153i	$0.670991\pi$
$18$			1.69929i			0.400526i
$19$	0.379911	−	0.379911i	0.0871575	−	0.0871575i	−0.662184	−	0.749341i	$-0.730370\pi$
$19$	0.379911	−	0.379911i	0.0871575	−	0.0871575i	0.749341	+	0.662184i	$0.230370\pi$
$20$	1.97108	−	2.30072i	0.440747	−	0.514456i
$21$	−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	−0.684305	−	0.729196i	$-0.739894\pi$
$23$	0.215293	−	0.215293i	0.0448916	−	0.0448916i	0.729196	+	0.684305i	$0.239894\pi$
$24$	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
$28$		−	4.79478i		−	0.906129i
$29$		−	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	$-0.0739810\pi$
$31$	4.13563	+	4.13563i	0.742781	+	0.742781i	−0.230331	+	0.973112i	$0.573981\pi$
$32$	−6.56423			−1.16040
$33$	7.67790			1.33655
$34$	2.62382	+	2.62382i	0.449982	+	0.449982i
$35$	−6.00942	−	5.14841i	−1.01578	−	0.870240i
$36$			1.25698i			0.209497i
$37$		−	5.41773i		−	0.890669i	−0.895364	−	0.445335i	$-0.853085\pi$
$37$		−	5.41773i		−	0.890669i	0.895364	−	0.445335i	$-0.146915\pi$
$38$	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	$-0.266731\pi$
$41$	−0.475748	−	0.475748i	−0.0742994	−	0.0742994i	−0.743280	+	0.668981i	$0.766731\pi$
$42$	−9.08372	+	9.08372i	−1.40165	+	1.40165i
$43$	6.23095	−	6.23095i	0.950211	−	0.950211i	−0.0486066	−	0.998818i	$-0.515478\pi$
$43$	6.23095	−	6.23095i	0.950211	−	0.950211i	0.998818	+	0.0486066i	$0.0154781\pi$
$44$	−3.71155	+	3.71155i	−0.559538	+	0.559538i
$45$	1.57541	+	1.34969i	0.234848	+	0.201200i
$46$	0.394337	−	0.394337i	0.0581418	−	0.0581418i
$47$		−	9.75201i		−	1.42248i	−0.702951	−	0.711238i	$-0.748135\pi$
$47$		−	9.75201i		−	1.42248i	0.702951	−	0.711238i	$-0.251865\pi$
$48$	6.83043	+	6.83043i	0.985887	+	0.985887i
$49$	−5.52385			−0.789121
$50$	−1.40503	−	9.04974i	−0.198702	−	1.27983i
$51$		−	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
$57$	−1.06480			−0.141036
$58$		−	3.62239i		−	0.475644i
$59$	−8.59785	−	8.59785i	−1.11934	−	1.11934i	−0.991838	−	0.127506i	$-0.959303\pi$
$59$	−8.59785	−	8.59785i	−1.11934	−	1.11934i	−0.127506	−	0.991838i	$-0.540697\pi$
$60$	−5.98642	+	0.461950i	−0.772844	+	0.0596374i
$61$	−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
$63$	3.28320			0.413645
$64$	−2.27514			−0.284392
$65$		0			0
$66$	14.0631			1.73105
$67$	2.28989			0.279754			0.139877	−	0.990169i	$-0.455329\pi$
$67$	2.28989			0.279754			0.139877	+	0.990169i	$0.455329\pi$
$68$	1.94087	+	1.94087i	0.235365	+	0.235365i
$69$	−0.603415			−0.0726426
$70$	−11.0070	−	9.43000i	−1.31559	−	1.12710i
$71$	−3.26771	−	3.26771i	−0.387806	−	0.387806i	0.486098	−	0.873904i	$-0.338420\pi$
$71$	−3.26771	−	3.26771i	−0.387806	−	0.387806i	−0.873904	+	0.486098i	$0.838420\pi$
$72$		−	1.09625i		−	0.129194i
$73$	14.7546			1.72690			0.863449	−	0.504436i	$-0.168299\pi$
$73$	14.7546			1.72690			0.863449	+	0.504436i	$0.168299\pi$
$74$		−	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	$-0.0286382\pi$
$80$	−7.09080	+	8.27665i	−0.792776	+	0.925358i
$81$	10.9225			1.21361
$82$	−0.871396	−	0.871396i	−0.0962296	−	0.0962296i
$83$		−	7.57341i		−	0.831290i	−0.909527	−	0.415645i	$-0.863556\pi$
$83$		−	7.57341i		−	0.831290i	0.909527	−	0.415645i	$-0.136444\pi$
$84$	−6.71932	+	6.71932i	−0.733138	+	0.733138i
$85$	4.51655	−	0.348525i	0.489889	−	0.0378029i
$86$	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	0.861083	−	0.508464i	$-0.169786\pi$
$89$	3.32661	+	3.32661i	0.352620	+	0.352620i	−0.508464	+	0.861083i	$0.669786\pi$
$90$	2.88556	+	2.47213i	0.304165	+	0.260586i
$91$		0			0
$92$	0.291695	−	0.291695i	0.0304113	−	0.0304113i
$93$		−	11.5912i		−	1.20195i
$94$		−	17.8621i		−	1.84233i
$95$	−0.0924314	−	1.19782i	−0.00948326	−	0.122894i
$96$	9.19900	+	9.19900i	0.938869	+	0.938869i
$97$	17.8254			1.80989			0.904945	−	0.425528i	$-0.139912\pi$
$97$	17.8254			1.80989			0.904945	+	0.425528i	$0.139912\pi$
$98$	−10.1177			−1.02204
$99$	−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	$0.0727494\pi$
$101$			4.55389i			0.453129i	−0.973996	+	0.226565i	$0.927251\pi$
$102$		−	7.35396i		−	0.728151i
$103$	−9.79285	+	9.79285i	−0.964918	+	0.964918i	−0.999405	−	0.0344872i	$-0.989020\pi$
$103$	−9.79285	+	9.79285i	−0.964918	+	0.964918i	0.0344872	+	0.999405i	$0.489020\pi$
$104$		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	−0.0511324	−	0.998692i	$-0.516283\pi$
$109$	9.89281	−	9.89281i	0.947560	−	0.947560i	0.998692	+	0.0511324i	$0.0162830\pi$
$110$	1.22077	+	15.8199i	0.116395	+	1.50837i
$111$	−7.59231	+	7.59231i	−0.720630	+	0.720630i
$112$			17.2488i			1.62986i
$113$	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
$115$	−0.0523802	−	0.678797i	−0.00488448	−	0.0632982i
$116$		−	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
$122$	−5.28668			−0.478633
$123$			1.33341i			0.120230i
$124$	5.60327	+	5.60327i	0.503188	+	0.503188i
$125$	−9.50596	−	5.88530i	−0.850239	−	0.526397i
$126$	6.01362			0.535736
$127$	0.909391	+	0.909391i	0.0806954	+	0.0806954i	0.746302	−	0.665607i	$-0.231827\pi$
$127$	0.909391	+	0.909391i	0.0806954	+	0.0806954i	−0.665607	+	0.746302i	$0.731827\pi$
$128$	8.96125			0.792070
$129$	−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	$0.578588\pi$
$132$	10.4026			0.905431
$133$	−1.34447	−	1.34447i	−0.116580	−	0.116580i
$134$	4.19423			0.362326
$135$	0.706541	+	9.15610i	0.0608094	+	0.788032i
$136$	−1.69269	−	1.69269i	−0.145147	−	0.145147i
$137$			14.2902i			1.22089i	0.792058	+	0.610446i	$0.209010\pi$
$137$			14.2902i			1.22089i	−0.792058	+	0.610446i	$0.790990\pi$
$138$	−1.10523			−0.0940838
$139$			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
$145$	−3.35831	−	2.87714i	−0.278893	−	0.238934i
$146$	27.0251			2.23661
$147$	7.74102	+	7.74102i	0.638469	+	0.638469i
$148$		−	7.34036i		−	0.603374i
$149$	9.28442	−	9.28442i	0.760610	−	0.760610i	−0.215823	−	0.976433i	$-0.569243\pi$
$149$	9.28442	−	9.28442i	0.760610	−	0.760610i	0.976433	+	0.215823i	$0.0692434\pi$
$150$	−10.7132	+	14.6511i	−0.874726	+	1.19626i
$151$	0.765191	−	0.765191i	0.0622704	−	0.0622704i	−0.675286	−	0.737556i	$-0.735980\pi$
$151$	0.765191	−	0.765191i	0.0622704	−	0.0622704i	0.737556	+	0.675286i	$0.235980\pi$
$152$	−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	$0.195215\pi$
$158$		−	2.92544i		−	0.232735i
$159$		−	8.86386i		−	0.702950i
$160$	−9.54967	+	11.1467i	−0.754968	+	0.881227i
$161$	−0.761901	−	0.761901i	−0.0600462	−	0.0600462i
$162$	20.0061			1.57182
$163$	2.26358			0.177297			0.0886486	−	0.996063i	$-0.471745\pi$
$163$	2.26358			0.177297			0.0886486	+	0.996063i	$0.471745\pi$
$164$	−0.644580	−	0.644580i	−0.0503333	−	0.0503333i
$165$	11.1698	−	13.0379i	0.869571	−	1.01500i
$166$		−	13.8717i		−	1.07665i
$167$			0.619569i			0.0479437i	0.999713	+	0.0239719i	$0.00763121\pi$
$167$			0.619569i			0.0479437i	−0.999713	+	0.0239719i	$0.992369\pi$
$168$	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	−0.506346	−	0.862330i	$-0.669004\pi$
$173$	4.68224	−	4.68224i	0.355984	−	0.355984i	0.862330	+	0.506346i	$0.169004\pi$
$174$	−5.07636	+	5.07636i	−0.384838	+	0.384838i
$175$	−17.4850	+	2.71467i	−1.32175	+	0.205210i
$176$	13.3520	−	13.3520i	1.00645	−	1.00645i
$177$			24.0977i			1.81130i
$178$	6.09312	+	6.09312i	0.456699	+	0.456699i
$179$	−2.19023			−0.163706			−0.0818528	−	0.996644i	$-0.526084\pi$
$179$	−2.19023			−0.163706			−0.0818528	+	0.996644i	$0.526084\pi$
$180$	2.13448	+	1.82866i	0.159095	+	0.136300i
$181$			9.59255i			0.713009i	0.934294	+	0.356504i	$0.116031\pi$
$181$			9.59255i			0.713009i	−0.934294	+	0.356504i	$0.883969\pi$
$182$		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
$187$	−7.84842			−0.573933
$188$		−	13.2128i		−	0.963640i
$189$	10.2771	+	10.2771i	0.747546	+	0.747546i
$190$	−0.169300	−	2.19397i	−0.0122823	−	0.159167i
$191$	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
$193$	0.284086			0.0204489			0.0102245	−	0.999948i	$-0.496745\pi$
$193$	0.284086			0.0204489			0.0102245	+	0.999948i	$0.496745\pi$
$194$	32.6495			2.34410
$195$		0			0
$196$	−7.48414			−0.534581
$197$	25.8492			1.84168			0.920838	−	0.389946i	$-0.127506\pi$
$197$	25.8492			1.84168			0.920838	+	0.389946i	$0.127506\pi$
$198$	−4.65504	−	4.65504i	−0.330819	−	0.330819i
$199$	−5.75250			−0.407784			−0.203892	−	0.978993i	$-0.565359\pi$
$199$	−5.75250			−0.407784			−0.203892	+	0.978993i	$0.565359\pi$
$200$	0.906420	+	5.83819i	0.0640936	+	0.412823i
$201$	−3.20901	−	3.20901i	−0.226346	−	0.226346i
$202$			8.34106i			0.586875i
$203$	−6.99884			−0.491223
$204$		−	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
$210$	2.21005	+	28.6401i	0.152508	+	1.97636i
$211$	−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
$213$			9.15863i			0.627539i
$214$	−9.15709	+	9.15709i	−0.625966	+	0.625966i
$215$	−1.51598	−	19.6456i	−0.103389	−	1.33982i
$216$	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
$223$		−	7.41523i		−	0.496561i	−0.968688	−	0.248280i	$-0.920135\pi$
$223$		−	7.41523i		−	0.496561i	0.968688	−	0.248280i	$-0.0798654\pi$
$224$			23.2302i			1.55213i
$225$	4.58381	−	0.711668i	0.305587	−	0.0474446i
$226$	2.96914	+	2.96914i	0.197504	+	0.197504i
$227$	−3.90230			−0.259005			−0.129502	−	0.991579i	$-0.541338\pi$
$227$	−3.90230			−0.259005			−0.129502	+	0.991579i	$0.541338\pi$
$228$	−1.44267			−0.0955434
$229$	−12.3946	−	12.3946i	−0.819060	−	0.819060i	0.166912	−	0.985972i	$-0.446621\pi$
$229$	−12.3946	−	12.3946i	−0.819060	−	0.819060i	−0.985972	+	0.166912i	$0.946621\pi$
$230$	−0.0959413	−	1.24331i	−0.00632618	−	0.0819813i
$231$		−	27.1714i		−	1.78774i
$232$			2.33689i			0.153424i
$233$	−2.88962	+	2.88962i	−0.189305	+	0.189305i	−0.795396	−	0.606090i	$-0.792737\pi$
$233$	−2.88962	+	2.88962i	−0.189305	+	0.189305i	0.606090	+	0.795396i	$0.292737\pi$
$234$		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	−0.354602	−	0.935017i	$-0.615384\pi$
$239$	8.97299	−	8.97299i	0.580415	−	0.580415i	0.935017	+	0.354602i	$0.115384\pi$
$240$	21.5357	−	1.66183i	1.39012	−	0.107270i
$241$	−12.4080	+	12.4080i	−0.799272	+	0.799272i	−0.982981	−	0.183709i	$-0.941190\pi$
$241$	−12.4080	+	12.4080i	−0.799272	+	0.799272i	0.183709	+	0.982981i	$0.441190\pi$
$242$		−	7.34239i		−	0.471986i
$243$	−6.59457	−	6.59457i	−0.423042	−	0.423042i
$244$	−3.91061			−0.250351
$245$	−8.03611	+	9.38005i	−0.513408	+	0.599270i
$246$			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	$0.241082\pi$
$251$			21.7689i			1.37404i	−0.726638	+	0.687021i	$0.758918\pi$
$252$	4.44834			0.280219
$253$			1.17955i			0.0741575i
$254$	1.66567	+	1.66567i	0.104513	+	0.104513i
$255$	−6.81784	−	5.84100i	−0.426950	−	0.365778i
$256$	20.9640			1.31025
$257$	−9.06027	−	9.06027i	−0.565164	−	0.565164i	0.365606	−	0.930770i	$-0.380862\pi$
$257$	−9.06027	−	9.06027i	−0.565164	−	0.565164i	−0.930770	+	0.365606i	$0.880862\pi$
$258$	−31.9874			−1.99145
$259$	−19.1728			−1.19134
$260$		0			0
$261$	1.83479			0.113571
$262$	−10.2469			−0.633054
$263$	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
$265$	9.97120	−	0.769439i	0.612526	−	0.0472663i
$266$	−2.46257	−	2.46257i	−0.150990	−	0.150990i
$267$		−	9.32370i		−	0.570601i
$268$	3.10252			0.189516
$269$		−	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	$-0.571935\pi$
$271$	12.3548	−	12.3548i	0.750503	−	0.750503i	0.974573	+	0.224070i	$0.0719346\pi$
$272$	−6.98212	−	6.98212i	−0.423353	−	0.423353i
$273$		0			0
$274$			26.1743i			1.58125i
$275$	15.6362	+	11.4335i	0.942901	+	0.689465i
$276$	−0.817553			−0.0492109
$277$	−2.17391	−	2.17391i	−0.130617	−	0.130617i	0.638776	−	0.769393i	$-0.279441\pi$
$277$	−2.17391	−	2.17391i	−0.130617	−	0.130617i	−0.769393	+	0.638776i	$0.779441\pi$
$278$			31.9008i			1.91328i
$279$	−3.83681	+	3.83681i	−0.229704	+	0.229704i
$280$	7.10090	+	6.08351i	0.424360	+	0.363559i
$281$	−18.6757	+	18.6757i	−1.11410	+	1.11410i	−0.121508	+	0.992590i	$0.538773\pi$
$281$	−18.6757	+	18.6757i	−1.11410	+	1.11410i	−0.992590	+	0.121508i	$0.961227\pi$
$282$	−25.0316	+	25.0316i	−1.49061	+	1.49061i
$283$	−10.8464	+	10.8464i	−0.644750	+	0.644750i	−0.951719	−	0.306969i	$-0.900685\pi$
$283$	−10.8464	+	10.8464i	−0.644750	+	0.644750i	0.306969	+	0.951719i	$0.400685\pi$
$284$	−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
$288$		−	6.08994i		−	0.358853i
$289$		−	12.8959i		−	0.758580i
$290$	−6.15119	−	5.26987i	−0.361210	−	0.309458i
$291$	−24.9801	−	24.9801i	−1.46436	−	1.46436i
$292$	19.9907			1.16987
$293$	−10.3767			−0.606213			−0.303107	−	0.952957i	$-0.598024\pi$
$293$	−10.3767			−0.606213			−0.303107	+	0.952957i	$0.598024\pi$
$294$	14.1787	+	14.1787i	0.826919	+	0.826919i
$295$	−27.1082	+	2.09184i	−1.57830	+	0.121791i
$296$			6.40174i			0.372094i
$297$		−	15.9106i		−	0.923225i
$298$	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
$305$	−4.19903	+	4.90126i	−0.240436	+	0.280646i
$306$	−2.43424	+	2.43424i	−0.139156	+	0.139156i
$307$		−	2.13935i		−	0.122099i	−0.998135	−	0.0610496i	$-0.980555\pi$
$307$		−	2.13935i		−	0.122099i	0.998135	−	0.0610496i	$-0.0194448\pi$
$308$	13.1348	+	13.1348i	0.748427	+	0.748427i
$309$	27.4470			1.56141
$310$	23.8831	−	1.84297i	1.35647	−	0.104674i
$311$		−	3.82084i		−	0.216660i	−0.994115	−	0.108330i	$-0.965450\pi$
$311$		−	3.82084i		−	0.216660i	0.994115	−	0.108330i	$-0.0345503\pi$
$312$		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
$317$	−23.1127			−1.29814			−0.649068	−	0.760730i	$-0.724841\pi$
$317$	−23.1127			−1.29814			−0.649068	+	0.760730i	$0.724841\pi$
$318$		−	16.2353i		−	0.910433i
$319$	5.41768	+	5.41768i	0.303332	+	0.303332i
$320$	−3.30988	+	3.86342i	−0.185028	+	0.215972i
$321$	14.0122			0.782084
$322$	−1.39552	−	1.39552i	−0.0777694	−	0.0777694i
$323$	1.08845			0.0605629
$324$	14.7987			0.822149
$325$		0			0
$326$	4.14604			0.229628
$327$	−27.7272			−1.53332
$328$	0.562157	+	0.562157i	0.0310399	+	0.0310399i
$329$	−34.5114			−1.90268
$330$	20.4590	−	23.8806i	1.12623	−	1.31458i
$331$	1.41208	+	1.41208i	0.0776150	+	0.0776150i	0.744849	−	0.667234i	$-0.232522\pi$
$331$	1.41208	+	1.41208i	0.0776150	+	0.0776150i	−0.667234	+	0.744849i	$0.732522\pi$
$332$		−	10.2610i		−	0.563148i
$333$	5.02628			0.275438
$334$			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	0.520244	−	0.854018i	$-0.325841\pi$
$337$	−6.12727	−	6.12727i	−0.333773	−	0.333773i	−0.854018	+	0.520244i	$0.825841\pi$
$338$		0			0
$339$		−	4.54338i		−	0.246763i
$340$	6.11938	−	0.472209i	0.331870	−	0.0256091i
$341$	−22.6583			−1.22702
$342$	0.645578	+	0.645578i	0.0349089	+	0.0349089i
$343$		−	5.22396i		−	0.282067i
$344$	−7.36267	+	7.36267i	−0.396968	+	0.396968i
$345$	−0.877850	+	1.02466i	−0.0472619	+	0.0551658i
$346$	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	0.824068	−	0.566491i	$-0.191700\pi$
$349$	4.81192	+	4.81192i	0.257576	+	0.257576i	−0.566491	+	0.824068i	$0.691700\pi$
$350$	−32.0262	+	4.97228i	−1.71187	+	0.265780i
$351$		0			0
$352$	17.9821	−	17.9821i	0.958448	−	0.958448i
$353$			27.3262i			1.45443i	0.686412	+	0.727213i	$0.259185\pi$
$353$			27.3262i			1.45443i	−0.686412	+	0.727213i	$0.740815\pi$
$354$			44.1382i			2.34592i
$355$	−10.3028	+	0.795027i	−0.546815	+	0.0421957i
$356$	4.50714	+	4.50714i	0.238878	+	0.238878i
$357$	−14.2086			−0.752000
$358$	−4.01170			−0.212025
$359$	−3.89871	−	3.89871i	−0.205766	−	0.205766i	0.596699	−	0.802465i	$-0.296479\pi$
$359$	−3.89871	−	3.89871i	−0.205766	−	0.205766i	−0.802465	+	0.596699i	$0.796479\pi$
$360$	−1.86154	−	1.59483i	−0.0981120	−	0.0840548i
$361$			18.7113i			0.984807i
$362$			17.5700i			0.923460i
$363$	−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
$370$	−16.8508	−	14.4364i	−0.876029	−	0.750515i
$371$	11.1919	−	11.1919i	0.581057	−	0.581057i
$372$		−	15.7046i		−	0.814248i
$373$	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
$375$	5.07393	+	21.5690i	0.262017	+	1.11382i
$376$			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	−0.203066	−	0.979165i	$-0.565091\pi$
$379$	15.1090	−	15.1090i	0.776099	−	0.776099i	0.979165	+	0.203066i	$0.0650905\pi$
$380$	−0.125233	−	1.62290i	−0.00642433	−	0.0832531i
$381$		−	2.54881i		−	0.130579i
$382$	6.83407			0.349661
$383$			19.4072i			0.991664i	0.868419	+	0.495832i	$0.165137\pi$
$383$			19.4072i			0.991664i	−0.868419	+	0.495832i	$0.834863\pi$
$384$	−12.5581	−	12.5581i	−0.640855	−	0.640855i
$385$	30.5658	−	2.35865i	1.55778	−	0.120208i
$386$	0.520340			0.0264846
$387$	5.78074	+	5.78074i	0.293852	+	0.293852i
$388$	24.1512			1.22609
$389$	14.8591			0.753387			0.376693	−	0.926338i	$-0.377061\pi$
$389$	14.8591			0.753387			0.376693	+	0.926338i	$0.377061\pi$
$390$		0			0
$391$	0.616816			0.0311937
$392$	6.52713			0.329670
$393$	7.83989	+	7.83989i	0.395470	+	0.395470i
$394$	47.3461			2.38526
$395$	−2.71217	−	2.32358i	−0.136464	−	0.116912i
$396$	−3.44338	−	3.44338i	−0.173036	−	0.173036i
$397$		−	5.27779i		−	0.264884i	−0.991191	−	0.132442i	$-0.957718\pi$
$397$		−	5.27779i		−	0.264884i	0.991191	−	0.132442i	$-0.0422819\pi$
$398$	−10.5365			−0.528145
$399$			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	$-0.504917\pi$
$401$	19.7133	−	19.7133i	0.984435	−	0.984435i	0.999881	+	0.0154455i	$0.00491664\pi$
$402$	−5.87772	−	5.87772i	−0.293154	−	0.293154i
$403$		0			0
$404$			6.16996i			0.306967i
$405$	15.8901	−	18.5476i	0.789587	−	0.921635i
$406$	−12.8193			−0.636212
$407$	14.8413	+	14.8413i	0.735658	+	0.735658i
$408$			4.74421i			0.234873i
$409$	1.86330	−	1.86330i	0.0921344	−	0.0921344i	−0.659537	−	0.751672i	$-0.729248\pi$
$409$	1.86330	−	1.86330i	0.0921344	−	0.0921344i	0.751672	+	0.659537i	$0.229248\pi$
$410$	−2.74743	+	0.212009i	−0.135686	+	0.0104704i
$411$	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
$418$			3.81246i			0.186474i
$419$			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	$-0.132817\pi$
$421$	10.4427	+	10.4427i	0.508948	+	0.508948i	−0.405256	+	0.914203i	$0.632817\pi$
$422$	−5.91147			−0.287766
$423$	9.04738			0.439899
$424$	−3.73695	−	3.73695i	−0.181482	−	0.181482i
$425$	5.97887	−	8.17660i	0.290018	−	0.396623i
$426$			16.7752i			0.812763i
$427$			10.2144i			0.494310i
$428$	−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	$-0.385386\pi$
$431$	−12.1144	−	12.1144i	−0.583532	−	0.583532i	−0.935872	+	0.352340i	$0.885386\pi$
$432$	14.1544	−	14.1544i	0.681003	−	0.681003i
$433$	−7.94551	+	7.94551i	−0.381837	+	0.381837i	−0.871764	−	0.489927i	$-0.837023\pi$
$433$	−7.94551	+	7.94551i	−0.381837	+	0.381837i	0.489927	+	0.871764i	$0.337023\pi$
$434$	26.8070	−	26.8070i	1.28678	−	1.28678i
$435$	0.674298	+	8.73826i	0.0323301	+	0.418967i
$436$	13.4035	−	13.4035i	0.641913	−	0.641913i
$437$		−	0.163584i		−	0.00782528i
$438$	−37.8724	−	37.8724i	−1.80962	−	1.80962i
$439$	4.24435			0.202572			0.101286	−	0.994857i	$-0.467704\pi$
$439$	4.24435			0.202572			0.101286	+	0.994857i	$0.467704\pi$
$440$	−0.787544	−	10.2058i	−0.0375447	−	0.486543i
$441$		−	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
$447$	−26.0221			−1.23080
$448$			8.05150i			0.380398i
$449$	10.2868	+	10.2868i	0.485466	+	0.485466i	0.906872	−	0.421406i	$-0.138463\pi$
$449$	10.2868	+	10.2868i	0.485466	+	0.485466i	−0.421406	+	0.906872i	$0.638463\pi$
$450$	8.39586	−	1.30351i	0.395785	−	0.0614483i
$451$	2.60653			0.122737
$452$	2.19631	+	2.19631i	0.103306	+	0.103306i
$453$	−2.14465			−0.100764
$454$	−7.14758			−0.335453
$455$		0			0
$456$	1.25820			0.0589205
$457$	30.2953			1.41715			0.708576	−	0.705634i	$-0.249338\pi$
$457$	30.2953			1.41715			0.708576	+	0.705634i	$0.249338\pi$
$458$	−22.7024	−	22.7024i	−1.06081	−	1.06081i
$459$	−8.32005			−0.388347
$460$	−0.0709688	−	0.919687i	−0.00330894	−	0.0428806i
$461$	4.90581	+	4.90581i	0.228486	+	0.228486i	0.812060	−	0.583574i	$-0.198346\pi$
$461$	4.90581	+	4.90581i	0.228486	+	0.228486i	−0.583574	+	0.812060i	$0.698346\pi$
$462$		−	49.7680i		−	2.31541i
$463$	31.4463			1.46143			0.730717	−	0.682680i	$-0.239186\pi$
$463$	31.4463			1.46143			0.730717	+	0.682680i	$0.239186\pi$
$464$			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	0.787436	−	0.616396i	$-0.211408\pi$
$467$	3.69622	+	3.69622i	0.171041	+	0.171041i	−0.616396	+	0.787436i	$0.711408\pi$
$468$		0			0
$469$		−	8.10369i		−	0.374194i
$470$	−30.3316	−	25.9858i	−1.39909	−	1.19864i
$471$	−8.50587			−0.391930
$472$	10.1595	+	10.1595i	0.467627	+	0.467627i
$473$			34.1382i			1.56968i
$474$	−4.09966	+	4.09966i	−0.188304	+	0.188304i
$475$	−2.16849	−	1.58564i	−0.0994972	−	0.0727540i
$476$	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	0.321596	−	0.946877i	$-0.395781\pi$
$479$	−13.6849	−	13.6849i	−0.625281	−	0.625281i	−0.946877	+	0.321596i	$0.895781\pi$
$480$	29.0036	−	2.23810i	1.32383	−	0.102155i
$481$		0			0
$482$	−22.7270	+	22.7270i	−1.03518	+	1.03518i
$483$			2.13543i			0.0971654i
$484$		−	5.43124i		−	0.246874i
$485$	25.9324	−	30.2693i	1.17753	−	1.37446i
$486$	−12.0788	−	12.0788i	−0.547907	−	0.547907i
$487$	−23.3627			−1.05866			−0.529332	−	0.848415i	$-0.677557\pi$
$487$	−23.3627			−1.05866			−0.529332	+	0.848415i	$0.677557\pi$
$488$	3.41056			0.154389
$489$	−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	$-0.840257\pi$
$491$		−	21.3186i		−	0.962094i	0.876695	−	0.481047i	$-0.159743\pi$
$492$			1.80661i			0.0814481i
$493$	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	−0.0318687	+	0.999492i	$0.510146\pi$
$499$	−23.0389	+	23.0389i	−1.03136	+	1.03136i	−0.999492	+	0.0318687i	$0.989854\pi$
$500$	−12.8794	−	7.97386i	−0.575985	−	0.356602i
$501$	0.868254	−	0.868254i	0.0387907	−	0.0387907i
$502$			39.8727i			1.77960i
$503$	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
$505$	7.73297	+	6.62502i	0.344113	+	0.294809i
$506$			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	−0.00393669	+	0.999992i	$0.501253\pi$
$509$	−22.6497	+	22.6497i	−1.00393	+	1.00393i	−0.999992	+	0.00393669i	$0.998747\pi$
$510$	−12.4878	−	10.6986i	−0.552968	−	0.473741i
$511$		−	52.2152i		−	2.30987i
$512$	20.4758			0.904912
$513$			2.20654i			0.0974210i
$514$	−16.5951	−	16.5951i	−0.731978	−	0.731978i
$515$	2.38258	+	30.8759i	0.104989	+	1.36056i
$516$	−23.6614			−1.04164
$517$	26.7147	+	26.7147i	1.17491	+	1.17491i
$518$	−35.1176			−1.54298
$519$	−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	$0.671919\pi$
$522$	3.36066			0.147092
$523$	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
$525$	28.3075	+	20.6989i	1.23544	+	0.903376i
$526$	21.3765	+	21.3765i	0.932061	+	0.932061i
$527$			11.8486i			0.516134i
$528$	−37.4226			−1.62861
$529$			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
$535$	1.21635	+	15.7627i	0.0525872	+	0.681480i
$536$	−2.70579			−0.116873
$537$	3.06935	+	3.06935i	0.132452	+	0.132452i
$538$		−	59.1745i		−	2.55119i
$539$	15.1320	−	15.1320i	0.651783	−	0.651783i
$540$	0.957277	+	12.4054i	0.0411946	+	0.533843i
$541$	−27.6908	+	27.6908i	−1.19052	+	1.19052i	−0.213597	+	0.976922i	$0.568518\pi$
$541$	−27.6908	+	27.6908i	−1.19052	+	1.19052i	−0.976922	+	0.213597i	$0.931482\pi$
$542$	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	$0.186652\pi$
$548$			19.3614i			0.827079i
$549$		−	2.67777i		−	0.114284i
$550$	28.6398	+	20.9419i	1.22121	+	0.892967i
$551$	−0.751344	−	0.751344i	−0.0320083	−	0.0320083i
$552$	0.713012			0.0303478
$553$	−5.65225			−0.240358
$554$	−3.98180	−	3.98180i	−0.169170	−	0.169170i
$555$	1.84719	+	23.9378i	0.0784089	+	1.01610i
$556$			23.5974i			1.00075i
$557$		−	16.2486i		−	0.688475i	−0.938883	−	0.344237i	$-0.888138\pi$
$557$		−	16.2486i		−	0.688475i	0.938883	−	0.344237i	$-0.111862\pi$
$558$	−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	−0.999543	−	0.0302442i	$-0.990372\pi$
$563$	−22.9991	+	22.9991i	−0.969298	+	0.969298i	0.0302442	+	0.999543i	$0.490372\pi$
$564$	−18.5161	+	18.5161i	−0.779670	+	0.779670i
$565$	5.11097	−	0.394394i	0.215020	−	0.0165923i
$566$	−19.8666	+	19.8666i	−0.835054	+	0.835054i
$567$		−	38.6538i		−	1.62331i
$568$	3.86122	+	3.86122i	0.162013	+	0.162013i
$569$	32.8329			1.37642			0.688212	−	0.725509i	$-0.258396\pi$
$569$	32.8329			1.37642			0.688212	+	0.725509i	$0.258396\pi$
$570$	−2.83734	+	3.31184i	−0.118843	+	0.138718i
$571$		−	31.7967i		−	1.33065i	−0.746554	−	0.665325i	$-0.768293\pi$
$571$		−	31.7967i		−	1.33065i	0.746554	−	0.665325i	$-0.231707\pi$
$572$		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
$577$	39.9389			1.66268			0.831338	−	0.555767i	$-0.187575\pi$
$577$	39.9389			1.66268			0.831338	+	0.555767i	$0.187575\pi$
$578$		−	23.6205i		−	0.982482i
$579$	−0.398113	−	0.398113i	−0.0165450	−	0.0165450i
$580$	−4.55010	−	3.89818i	−0.188933	−	0.161863i
$581$	−26.8016			−1.11192
$582$	−45.7544	−	45.7544i	−1.89658	−	1.89658i
$583$	−17.3270			−0.717609
$584$	−17.4345			−0.721444
$585$		0			0
$586$	−19.0063			−0.785143
$587$	−18.6555			−0.769993			−0.384997	−	0.922918i	$-0.625797\pi$
$587$	−18.6555			−0.769993			−0.384997	+	0.922918i	$0.625797\pi$
$588$	10.4881	+	10.4881i	0.432523	+	0.432523i
$589$	3.14234			0.129478
$590$	−49.6522	+	3.83147i	−2.04415	+	0.157739i
$591$	−36.2245	−	36.2245i	−1.49008	−	1.49008i
$592$			26.4064i			1.08529i
$593$	8.65172			0.355284			0.177642	−	0.984095i	$-0.443153\pi$
$593$	8.65172			0.355284			0.177642	+	0.984095i	$0.443153\pi$
$594$		−	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	$0.744753\pi$
$600$	6.91130	−	9.45178i	0.282153	−	0.385867i
$601$	−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
$603$			2.12443i			0.0865136i
$604$	1.03674	−	1.03674i	0.0421843	−	0.0421843i
$605$	−6.80711	−	5.83181i	−0.276748	−	0.237097i
$606$	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
$613$		−	20.2795i		−	0.819080i	−0.912292	−	0.409540i	$-0.865689\pi$
$613$		−	20.2795i		−	0.819080i	0.912292	−	0.409540i	$-0.134311\pi$
$614$		−	3.91850i		−	0.158138i
$615$	2.26427	+	1.93985i	0.0913040	+	0.0782223i
$616$	−11.4553	−	11.4553i	−0.461546	−	0.461546i
$617$	8.67054			0.349063			0.174531	−	0.984652i	$-0.444159\pi$
$617$	8.67054			0.349063			0.174531	+	0.984652i	$0.444159\pi$
$618$	50.2729			2.02227
$619$	−21.3034	−	21.3034i	−0.856257	−	0.856257i	0.134638	−	0.990895i	$-0.457013\pi$
$619$	−21.3034	−	21.3034i	−0.856257	−	0.856257i	−0.990895	+	0.134638i	$0.957013\pi$
$620$	17.6666	−	1.36326i	0.709507	−	0.0547499i
$621$			1.25043i			0.0501780i
$622$		−	6.99837i		−	0.280609i
$623$	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
$630$	8.74864	−	10.2117i	0.348554	−	0.406845i
$631$	20.0819	−	20.0819i	0.799449	−	0.799449i	−0.183560	−	0.983009i	$-0.558762\pi$
$631$	20.0819	−	20.0819i	0.799449	−	0.799449i	0.983009	+	0.183560i	$0.0587620\pi$
$632$			1.88727i			0.0750715i
$633$	4.52286	+	4.52286i	0.179768	+	0.179768i
$634$	−42.3339			−1.68129
$635$	2.86722	−	0.221253i	0.113782	−	0.00878015i
$636$		−	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	$0.104779\pi$
$641$			16.3686i			0.646520i	−0.946310	+	0.323260i	$0.895221\pi$
$642$	25.6652			1.01292
$643$		−	41.0517i		−	1.61892i	−0.587175	−	0.809460i	$-0.699760\pi$
$643$		−	41.0517i		−	1.61892i	0.587175	−	0.809460i	$-0.300240\pi$
$644$	−1.03228	−	1.03228i	−0.0406776	−	0.0406776i
$645$	−25.4065	+	29.6555i	−1.00038	+	1.16768i
$646$	1.99364			0.0784386
$647$	−2.00480	−	2.00480i	−0.0788168	−	0.0788168i	0.666599	−	0.745416i	$-0.267749\pi$
$647$	−2.00480	−	2.00480i	−0.0788168	−	0.0788168i	−0.745416	+	0.666599i	$0.767749\pi$
$648$	−12.9064			−0.507010
$649$	47.1059			1.84907
$650$		0			0
$651$	−41.0201			−1.60771
$652$	3.06687			0.120108
$653$	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
$655$	−8.13874	+	9.49985i	−0.318007	+	0.371190i
$656$	2.31883	+	2.31883i	0.0905349	+	0.0905349i
$657$			13.6885i			0.534041i
$658$	−63.2122			−2.46427
$659$			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	$-0.916389\pi$
$661$	−18.1521	+	18.1521i	−0.706037	+	0.706037i	0.259663	+	0.965699i	$0.416389\pi$
$662$	2.58641	+	2.58641i	0.100524	+	0.100524i
$663$		0			0
$664$			8.94896i			0.347287i
$665$	−4.23898	+	0.327106i	−0.164381	+	0.0126846i
$666$	9.20629			0.356736
$667$	−0.425782	−	0.425782i	−0.0164863	−	0.0164863i
$668$			0.839440i			0.0324789i
$669$	−10.3916	+	10.3916i	−0.401762	+	0.401762i
$670$	6.10178	−	7.12223i	0.235732	−	0.275156i
$671$	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	$-0.456590\pi$
$673$	29.2283	−	29.2283i	1.12667	−	1.12667i	0.990715	−	0.135955i	$-0.0434103\pi$
$674$	−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	$0.111290\pi$
$678$		−	8.32181i		−	0.319597i
$679$		−	63.0822i		−	2.42087i
$680$	−5.33689	+	0.411827i	−0.204660	+	0.0157929i
$681$	5.46862	+	5.46862i	0.209558	+	0.209558i
$682$	−41.5017			−1.58918
$683$	−6.65304			−0.254571			−0.127286	−	0.991866i	$-0.540627\pi$
$683$	−6.65304			−0.254571			−0.127286	+	0.991866i	$0.540627\pi$
$684$	0.477541	+	0.477541i	0.0182592	+	0.0182592i
$685$	24.2662	+	20.7894i	0.927162	+	0.794322i
$686$		−	9.56838i		−	0.365322i
$687$			34.7392i			1.32538i
$688$	−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	0.999925	+	0.0122158i	$0.00388850\pi$
$691$	26.6060	+	26.6060i	1.01214	+	1.01214i	0.0122158	+	0.999925i	$0.496111\pi$
$692$	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
$695$	29.5752	+	25.3377i	1.12185	+	0.961115i
$696$	3.27488	−	3.27488i	0.124134	−	0.124134i
$697$		−	1.36302i		−	0.0516282i
$698$	8.81368	+	8.81368i	0.333603	+	0.333603i
$699$	8.09892			0.306329
$700$	−23.6901	+	3.67805i	−0.895401	+	0.139017i
$701$			40.3398i			1.52361i	0.647804	+	0.761807i	$0.275688\pi$
$701$			40.3398i			1.52361i	−0.647804	+	0.761807i	$0.724312\pi$
$702$		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
$707$	16.1158			0.606097
$708$			32.6495i			1.22704i
$709$	−31.5318	−	31.5318i	−1.18420	−	1.18420i	−0.978645	−	0.205559i	$-0.934099\pi$
$709$	−31.5318	−	31.5318i	−1.18420	−	1.18420i	−0.205559	−	0.978645i	$-0.565901\pi$
$710$	−18.8709	+	1.45620i	−0.708213	+	0.0546501i
$711$	1.48177			0.0555708
$712$	−3.93081	−	3.93081i	−0.147313	−	0.147313i
$713$	1.78074			0.0666893
$714$	−26.0250			−0.973960
$715$		0			0
$716$	−2.96749			−0.110900
$717$	−25.1492			−0.939214
$718$	−7.14100	−	7.14100i	−0.266500	−	0.266500i
$719$	27.5650			1.02800			0.514001	−	0.857790i	$-0.328163\pi$
$719$	27.5650			1.02800			0.514001	+	0.857790i	$0.328163\pi$
$720$	−7.67863	−	6.57846i	−0.286166	−	0.245165i
$721$	34.6560	+	34.6560i	1.29066	+	1.29066i
$722$			34.2723i			1.27548i
$723$	34.7768			1.29336
$724$			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	$0.0310716\pi$
$727$	29.4624	+	29.4624i	1.09270	+	1.09270i	0.0974593	+	0.995240i	$0.468928\pi$
$728$		0			0
$729$		−	14.2845i		−	0.529057i
$730$	39.3161	−	45.8913i	1.45516	−	1.69851i
$731$	17.8518			0.660271
$732$	5.48026	+	5.48026i	0.202556	+	0.202556i
$733$		−	23.3958i		−	0.864144i	−0.901839	−	0.432072i	$-0.857783\pi$
$733$		−	23.3958i		−	0.864144i	0.901839	−	0.432072i	$-0.142217\pi$
$734$	23.4105	−	23.4105i	0.864098	−	0.864098i
$735$	24.4067	−	1.88337i	0.900255	−	0.0694693i
$736$	−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	0.884418	−	0.466695i	$-0.154556\pi$
$739$	11.3556	+	11.3556i	0.417723	+	0.417723i	−0.466695	+	0.884418i	$0.654556\pi$
$740$	−12.4647	−	10.6788i	−0.458210	−	0.392560i
$741$		0			0
$742$	20.4995	−	20.4995i	0.752561	−	0.752561i
$743$			52.2801i			1.91797i	0.283457	+	0.958985i	$0.408519\pi$
$743$			52.2801i			1.91797i	−0.283457	+	0.958985i	$0.591481\pi$
$744$			13.6965i			0.502137i
$745$	−2.25888	−	29.2729i	−0.0827589	−	1.07248i
$746$	20.0933	+	20.0933i	0.735669	+	0.735669i
$747$	7.02620			0.257075
$748$	−10.6336			−0.388805
$749$	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	$-0.833124\pi$
$751$		−	27.4355i		−	1.00114i	0.865697	−	0.500569i	$-0.166876\pi$
$752$			47.5319i			1.73331i
$753$	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
$760$	0.109219	+	1.41538i	0.00396181	+	0.0513412i
$761$	−1.72762	+	1.72762i	−0.0626260	+	0.0626260i	−0.737726	−	0.675100i	$-0.764100\pi$
$761$	−1.72762	+	1.72762i	−0.0626260	+	0.0626260i	0.675100	+	0.737726i	$0.264100\pi$
$762$		−	4.66848i		−	0.169121i
$763$	−35.0097	−	35.0097i	−1.26744	−	1.26744i
$764$	5.05523			0.182892
$765$	0.323343	+	4.19021i	0.0116905	+	0.151497i
$766$			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	−0.858494	−	0.512824i	$-0.828600\pi$
$769$	−9.58574	+	9.58574i	−0.345670	+	0.345670i	0.512824	+	0.858494i	$0.328600\pi$
$770$	55.9853	−	4.32017i	2.01757	−	0.155688i
$771$			25.3938i			0.914536i
$772$	0.384901			0.0138529
$773$			22.4445i			0.807272i	0.914920	+	0.403636i	$0.132254\pi$
$773$			22.4445i			0.807272i	−0.914920	+	0.403636i	$0.867746\pi$
$774$	10.5882	+	10.5882i	0.380585	+	0.380585i
$775$	17.2609	−	23.6058i	0.620031	−	0.847944i
$776$	−21.0629			−0.756115
$777$	26.8685	+	26.8685i	0.963901	+	0.963901i
$778$	27.2164			0.975756
$779$	−0.361484			−0.0129515
$780$		0			0
$781$	17.9032			0.640626
$782$	1.12978			0.0404009
$783$	5.74324	+	5.74324i	0.205247	+	0.205247i
$784$	26.9236			0.961556
$785$	−0.738363	−	9.56847i	−0.0263533	−	0.341513i
$786$	14.3598	+	14.3598i	0.512197	+	0.512197i
$787$			13.4958i			0.481074i	0.970640	+	0.240537i	$0.0773235\pi$
$787$			13.4958i			0.481074i	−0.970640	+	0.240537i	$0.922676\pi$
$788$	35.0224			1.24762
$789$		−	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
$795$	−15.0517	−	12.8952i	−0.533830	−	0.457345i
$796$	−7.79393			−0.276248
$797$	−4.43678	−	4.43678i	−0.157159	−	0.157159i	0.624148	−	0.781307i	$-0.285446\pi$
$797$	−4.43678	−	4.43678i	−0.157159	−	0.157159i	−0.781307	+	0.624148i	$0.785446\pi$
$798$			6.90201i			0.244328i
$799$	13.9698	−	13.9698i	0.494216	−	0.494216i
$800$	5.03539	+	32.4326i	0.178028	+	1.14667i
$801$	−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
$808$		−	5.38101i		−	0.189303i
$809$		−	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	$-0.0608601\pi$
$811$	22.5473	+	22.5473i	0.791743	+	0.791743i	−0.190035	+	0.981777i	$0.560860\pi$
$812$	−9.48257			−0.332773
$813$	−34.6277			−1.21445
$814$	27.1839	+	27.1839i	0.952795	+	0.952795i
$815$	3.29306	−	3.84379i	0.115351	−	0.134642i
$816$			19.5692i			0.685061i
$817$		−	4.73441i		−	0.165636i
$818$	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	$-0.148691\pi$
$821$	12.6803	+	12.6803i	0.442544	+	0.442544i	−0.450322	+	0.892866i	$0.648691\pi$
$822$	36.6803	−	36.6803i	1.27937	−	1.27937i
$823$	−0.814658	+	0.814658i	−0.0283972	+	0.0283972i	−0.721163	−	0.692766i	$-0.756392\pi$
$823$	−0.814658	+	0.814658i	−0.0283972	+	0.0283972i	0.692766	+	0.721163i	$0.256392\pi$
$824$	11.5715	−	11.5715i	0.403112	−	0.403112i
$825$	−5.88968	−	37.9350i	−0.205052	−	1.32073i
$826$	−55.7310	+	55.7310i	−1.93913	+	1.93913i
$827$			4.45029i			0.154752i	0.997002	+	0.0773759i	$0.0246542\pi$
$827$			4.45029i			0.154752i	−0.997002	+	0.0773759i	$0.975346\pi$
$828$	0.270619	+	0.270619i	0.00940466	+	0.00940466i
$829$	−29.1274			−1.01164			−0.505819	−	0.862640i	$-0.668809\pi$
$829$	−29.1274			−1.01164			−0.505819	+	0.862640i	$0.668809\pi$
$830$	−23.5556	−	20.1806i	−0.817625	−	0.700479i
$831$			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
$837$	−24.0199			−0.830249
$838$			36.0284i			1.24458i
$839$	22.8596	+	22.8596i	0.789200	+	0.789200i	0.981363	−	0.192163i	$-0.0615502\pi$
$839$	22.8596	+	22.8596i	0.789200	+	0.789200i	−0.192163	+	0.981363i	$0.561550\pi$
$840$	−1.42575	−	18.4764i	−0.0491931	−	0.637496i
$841$	25.0888			0.865130
$842$	19.1273	+	19.1273i	0.659169	+	0.659169i
$843$	52.3436			1.80281
$844$	−4.37277			−0.150517
$845$		0			0
$846$	16.5715			0.569739
$847$	−14.1863			−0.487446
$848$	−15.4144	−	15.4144i	−0.529334	−	0.529334i
$849$	30.3998			1.04332
$850$	10.9511	−	14.9765i	0.375619	−	0.513691i
$851$	−1.16640	−	1.16640i	−0.0399836	−	0.0399836i
$852$			12.4088i			0.425119i
$853$	9.24230			0.316450			0.158225	−	0.987403i	$-0.449423\pi$
$853$	9.24230			0.316450			0.158225	+	0.987403i	$0.449423\pi$
$854$			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	$-0.883897\pi$
$857$	−37.7913	−	37.7913i	−1.29093	−	1.29093i	−0.356713	−	0.934214i	$-0.616103\pi$
$858$		0			0
$859$		−	6.16263i		−	0.210266i	−0.994458	−	0.105133i	$-0.966473\pi$
$859$		−	6.16263i		−	0.210266i	0.994458	−	0.105133i	$-0.0335269\pi$
$860$	−2.05396	−	26.6174i	−0.0700395	−	0.907645i
$861$	4.71881			0.160817
$862$	−22.1892	−	22.1892i	−0.755767	−	0.755767i
$863$		−	33.7740i		−	1.14968i	−0.818266	−	0.574840i	$-0.805064\pi$
$863$		−	33.7740i		−	1.14968i	0.818266	−	0.574840i	$-0.194936\pi$
$864$	19.0627	−	19.0627i	0.648525	−	0.648525i
$865$	−1.13918	−	14.7627i	−0.0387332	−	0.501945i
$866$	−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
$873$			16.5374i			0.559706i
$874$		−	0.299626i		−	0.0101350i
$875$	−20.8275	+	33.6407i	−0.704098	+	1.13726i
$876$	−28.0146	−	28.0146i	−0.946527	−	0.946527i
$877$	22.6972			0.766429			0.383214	−	0.923659i	$-0.374817\pi$
$877$	22.6972			0.766429			0.383214	+	0.923659i	$0.374817\pi$
$878$	7.77409			0.262363
$879$	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	$0.0421210\pi$
$881$			7.83247i			0.263883i	−0.991258	+	0.131941i	$0.957879\pi$
$882$		−	9.38661i		−	0.316064i
$883$	18.9296	−	18.9296i	0.637032	−	0.637032i	−0.312790	−	0.949822i	$-0.601264\pi$
$883$	18.9296	−	18.9296i	0.637032	−	0.637032i	0.949822	+	0.312790i	$0.101264\pi$
$884$		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
$890$	19.2110	−	1.48244i	0.643955	−	0.0496916i
$891$	−29.9212	+	29.9212i	−1.00240	+	1.00240i
$892$		−	10.0467i		−	0.336389i
$893$	−3.70489	−	3.70489i	−0.123979	−	0.123979i
$894$	−47.6628			−1.59408
$895$	−3.18636	+	3.71923i	−0.106508	+	0.124320i
$896$		−	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
$902$	4.77421			0.158964
$903$			61.8031i			2.05668i
$904$	−1.91546	−	1.91546i	−0.0637073	−	0.0637073i
$905$	16.2891	+	13.9553i	0.541469	+	0.463889i
$906$	−3.92821			−0.130506
$907$	−32.8817	−	32.8817i	−1.09182	−	1.09182i	−0.995334	−	0.0964844i	$-0.969240\pi$
$907$	−32.8817	−	32.8817i	−1.09182	−	1.09182i	−0.0964844	−	0.995334i	$-0.530760\pi$
$908$	−5.28714			−0.175460
$909$	−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	$0.405096\pi$
$912$	5.18990			0.171855
$913$	20.7466	+	20.7466i	0.686613	+	0.686613i
$914$	55.4898			1.83544
$915$	12.7530	−	0.984100i	0.421601	−	0.0325333i
$916$	−16.7932	−	16.7932i	−0.554863	−	0.554863i
$917$			19.7980i			0.653789i
$918$	−15.2393			−0.502971
$919$			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
$925$	−26.7680	+	4.15591i	−0.880125	+	0.136645i
$926$	57.5981			1.89279
$927$	−9.08527	−	9.08527i	−0.298399	−	0.298399i
$928$			12.9820i			0.426155i
$929$	−7.34465	+	7.34465i	−0.240970	+	0.240970i	−0.817251	−	0.576281i	$-0.804503\pi$
$929$	−7.34465	+	7.34465i	−0.240970	+	0.240970i	0.576281	+	0.817251i	$0.304503\pi$
$930$	−36.0521	−	30.8867i	−1.18219	−	1.01281i
$931$	−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	$0.210794\pi$
$938$		−	14.8430i		−	0.484641i
$939$		−	8.53529i		−	0.278539i
$940$	−22.4366	−	19.2220i	−0.731802	−	0.626952i
$941$	−38.9093	−	38.9093i	−1.26841	−	1.26841i	−0.946911	−	0.321497i	$-0.895814\pi$
$941$	−38.9093	−	38.9093i	−1.26841	−	1.26841i	−0.321497	−	0.946911i	$-0.604186\pi$
$942$	−15.5796			−0.507611
$943$	−0.204850			−0.00667084
$944$	41.9064	+	41.9064i	1.36394	+	1.36394i
$945$	32.4026	−	2.50038i	1.05406	−	0.0813375i
$946$			62.5286i			2.03298i
$947$		−	33.7517i		−	1.09678i	−0.836222	−	0.548392i	$-0.815240\pi$
$947$		−	33.7517i		−	1.09678i	0.836222	−	0.548392i	$-0.184760\pi$
$948$	−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	−0.755874	−	0.654717i	$-0.772788\pi$
$953$	−3.12279	+	3.12279i	−0.101157	+	0.101157i	0.654717	+	0.755874i	$0.272788\pi$
$954$	−5.37407	+	5.37407i	−0.173992	+	0.173992i
$955$	5.42807	−	6.33584i	0.175648	−	0.205023i
$956$	12.1573	−	12.1573i	0.393195	−	0.393195i
$957$		−	15.1845i		−	0.490845i
$958$	−25.0658	−	25.0658i	−0.809839	−	0.809839i
$959$	50.5716			1.63304
$960$	10.0525	−	0.775716i	0.324444	−	0.0250361i
$961$			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
$967$	16.2803			0.523540			0.261770	−	0.965130i	$-0.415694\pi$
$967$	16.2803			0.523540			0.261770	+	0.965130i	$0.415694\pi$
$968$			4.73674i			0.152245i
$969$	−1.52533	−	1.52533i	−0.0490007	−	0.0490007i
$970$	47.4986	−	55.4421i	1.52509	−	1.78014i
$971$	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
$973$	61.6357			1.97595
$974$	−42.7918			−1.37114
$975$		0			0
$976$	14.0681			0.450309
$977$	−16.0487			−0.513444			−0.256722	−	0.966485i	$-0.582642\pi$
$977$	−16.0487			−0.513444			−0.256722	+	0.966485i	$0.582642\pi$
$978$	−5.81019	−	5.81019i	−0.185790	−	0.185790i
$979$	−18.2258			−0.582500
$980$	−10.8879	+	12.7088i	−0.347803	+	0.405968i
$981$	9.17801	+	9.17801i	0.293031	+	0.293031i
$982$		−	39.0478i		−	1.24607i
$983$	−34.3036			−1.09411			−0.547057	−	0.837096i	$-0.684252\pi$
$983$	−34.3036			−1.09411			−0.547057	+	0.837096i	$0.684252\pi$
$984$		−	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
$990$	−14.6769	+	1.13256i	−0.466462	+	0.0359951i
$991$	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
$993$		−	3.95773i		−	0.125595i
$994$	−21.1812	+	21.1812i	−0.671828	+	0.671828i
$995$	−8.36875	+	9.76832i	−0.265307	+	0.309677i
$996$	−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.k.e.268.8		20
5.2	odd	4		845.2.f.e.437.8		20
13.2	odd	12		845.2.t.f.188.4		20
13.3	even	3		65.2.o.a.33.2	yes	20
13.4	even	6		845.2.o.f.258.4		20
13.5	odd	4		845.2.f.e.408.3		20
13.6	odd	12		65.2.t.a.28.2	yes	20
13.7	odd	12		845.2.t.g.418.4		20
13.8	odd	4		845.2.f.d.408.8		20
13.9	even	3		845.2.o.e.258.2		20
13.10	even	6		845.2.o.g.488.4		20
13.11	odd	12		845.2.t.e.188.2		20
13.12	even	2		845.2.k.d.268.3		20
39.29	odd	6		585.2.cf.a.163.4		20
39.32	even	12		585.2.dp.a.28.4		20
65.2	even	12		845.2.o.e.357.2		20
65.3	odd	12		325.2.x.b.7.4		20
65.7	even	12		845.2.o.g.587.4		20
65.12	odd	4		845.2.f.d.437.3		20
65.17	odd	12		845.2.t.e.427.2		20
65.19	odd	12		325.2.x.b.93.4		20
65.22	odd	12		845.2.t.f.427.4		20
65.29	even	6		325.2.s.b.293.4		20
65.32	even	12		65.2.o.a.2.2	✓	20
65.37	even	12		845.2.o.f.357.4		20
65.42	odd	12		65.2.t.a.7.2	yes	20
65.47	even	4		845.2.k.d.577.3		20
65.57	even	4	inner	845.2.k.e.577.8		20
65.58	even	12		325.2.s.b.132.4		20
65.62	odd	12		845.2.t.g.657.4		20
195.32	odd	12		585.2.cf.a.262.4		20
195.107	even	12		585.2.dp.a.397.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.2	✓	20	65.32	even	12
65.2.o.a.33.2	yes	20	13.3	even	3
65.2.t.a.7.2	yes	20	65.42	odd	12
65.2.t.a.28.2	yes	20	13.6	odd	12
325.2.s.b.132.4		20	65.58	even	12
325.2.s.b.293.4		20	65.29	even	6
325.2.x.b.7.4		20	65.3	odd	12
325.2.x.b.93.4		20	65.19	odd	12
585.2.cf.a.163.4		20	39.29	odd	6
585.2.cf.a.262.4		20	195.32	odd	12
585.2.dp.a.28.4		20	39.32	even	12
585.2.dp.a.397.4		20	195.107	even	12
845.2.f.d.408.8		20	13.8	odd	4
845.2.f.d.437.3		20	65.12	odd	4
845.2.f.e.408.3		20	13.5	odd	4
845.2.f.e.437.8		20	5.2	odd	4
845.2.k.d.268.3		20	13.12	even	2
845.2.k.d.577.3		20	65.47	even	4
845.2.k.e.268.8		20	1.1	even	1	trivial
845.2.k.e.577.8		20	65.57	even	4	inner
845.2.o.e.258.2		20	13.9	even	3
845.2.o.e.357.2		20	65.2	even	12
845.2.o.f.258.4		20	13.4	even	6
845.2.o.f.357.4		20	65.37	even	12
845.2.o.g.488.4		20	13.10	even	6
845.2.o.g.587.4		20	65.7	even	12
845.2.t.e.188.2		20	13.11	odd	12
845.2.t.e.427.2		20	65.17	odd	12
845.2.t.f.188.4		20	13.2	odd	12
845.2.t.f.427.4		20	65.22	odd	12
845.2.t.g.418.4		20	13.7	odd	12
845.2.t.g.657.4		20	65.62	odd	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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.83163 q^{2} +(-1.40138 - 1.40138i) q^{3} +1.35488 q^{4} +(1.45480 - 1.69810i) q^{5} +(-2.56682 - 2.56682i) q^{6} -3.53890i q^{7} -1.18163 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} +(-4.41843 + 0.340953i) q^{15} -4.87406 q^{16} +(1.43251 + 1.43251i) q^{17} +1.69929i q^{18} +(0.379911 - 0.379911i) q^{19} +(1.97108 - 2.30072i) 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} -4.79478i q^{28} -1.97769i q^{29} +(-8.09293 + 0.624501i) q^{30} +(4.13563 + 4.13563i) q^{31} -6.56423 q^{32} +7.67790 q^{33} +(2.62382 + 2.62382i) q^{34} +(-6.00942 - 5.14841i) q^{35} +1.25698i q^{36} -5.41773i 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} +(1.57541 + 1.34969i) q^{45} +(0.394337 - 0.394337i) q^{46} -9.75201i q^{47} +(6.83043 + 6.83043i) q^{48} -5.52385 q^{49} +(-1.40503 - 9.04974i) 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} -1.06480 q^{57} -3.62239i q^{58} +(-8.59785 - 8.59785i) q^{59} +(-5.98642 + 0.461950i) q^{60} -2.88632 q^{61} +(7.57495 + 7.57495i) q^{62} +3.28320 q^{63} -2.27514 q^{64} +14.0631 q^{66} +2.28989 q^{67} +(1.94087 + 1.94087i) q^{68} -0.603415 q^{69} +(-11.0070 - 9.43000i) q^{70} +(-3.26771 - 3.26771i) q^{71} -1.09625i q^{72} +14.7546 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} +(-7.09080 + 8.27665i) q^{80} +10.9225 q^{81} +(-0.871396 - 0.871396i) q^{82} -7.57341i q^{83} +(-6.71932 + 6.71932i) q^{84} +(4.51655 - 0.348525i) 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} -11.5912i q^{93} -17.8621i q^{94} +(-0.0924314 - 1.19782i) q^{95} +(9.19900 + 9.19900i) q^{96} +17.8254 q^{97} -10.1177 q^{98} +(-2.54147 - 2.54147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 8 q^{2} + 4 q^{3} + 12 q^{4} - 6 q^{5} + 4 q^{6} + 12 q^{8} + 8 q^{10} + 8 q^{11} + 24 q^{12} - 24 q^{15} + 4 q^{16} + 14 q^{17} - 4 q^{19} - 22 q^{20} + 4 q^{21} - 32 q^{22} - 8 q^{23} + 4 q^{24}+ \cdots - 60 q^{99}+O(q^{100}) \) 20 * q + 8 * q^2 + 4 * q^3 + 12 * q^4 - 6 * q^5 + 4 * q^6 + 12 * q^8 + 8 * q^10 + 8 * q^11 + 24 * q^12 - 24 * q^15 + 4 * q^16 + 14 * q^17 - 4 * q^19 - 22 * q^20 + 4 * q^21 - 32 * q^22 - 8 * q^23 + 4 * q^24 - 18 * q^25 + 4 * q^27 - 40 * q^30 + 12 * q^32 + 36 * q^33 - 2 * q^34 - 20 * q^35 + 8 * q^38 - 16 * q^40 - 38 * q^41 + 16 * q^42 + 32 * q^43 + 36 * q^44 - 20 * q^45 + 4 * q^46 + 28 * q^48 + 36 * q^49 - 52 * q^50 - 10 * q^53 - 36 * q^54 - 16 * q^55 - 12 * q^57 - 8 * q^59 - 92 * q^60 + 32 * q^61 - 4 * q^62 + 64 * q^63 - 20 * q^64 - 32 * q^66 + 116 * q^67 - 50 * q^68 - 32 * q^69 + 32 * q^70 - 40 * q^71 + 72 * q^73 - 4 * q^75 - 16 * q^76 + 28 * q^77 - 34 * q^80 + 28 * q^81 + 34 * q^82 - 8 * q^84 + 60 * q^86 - 28 * q^87 + 32 * q^88 - 12 * q^89 - 46 * q^90 - 8 * q^92 - 40 * q^95 + 56 * q^96 + 44 * q^97 - 8 * q^98 - 60 * q^99

Introduction

L-functions

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