LMFDB - Embedded newform 605.2.m.e.457.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,2,Mod(112,605)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("605.112"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.m (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,10,-4,0,-2,20,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			457.1
Character	$\chi$	$=$	605.457
Dual form			605.2.m.e.233.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30617 - 0.665529i) q^{2} +(-0.822224 + 0.130227i) q^{3} +(0.0875924 + 0.120561i) q^{4} +(-0.233059 + 2.22389i) q^{5} +(1.16064 + 0.377114i) q^{6} +(-0.659422 + 4.16343i) q^{7} +(0.424477 + 2.68004i) q^{8} +(-2.19408 + 0.712899i) q^{9} +(1.78448 - 2.74968i) q^{10} +(-0.0877208 - 0.0877208i) q^{12} +(0.420250 - 0.824787i) q^{13} +(3.63220 - 4.99930i) q^{14} +(-0.0979846 - 1.85889i) q^{15} +(1.32131 - 4.06656i) q^{16} +(-0.875188 - 1.71765i) q^{17} +(3.34030 + 0.529052i) q^{18} +(-4.39439 - 3.19271i) q^{19} +(-0.288528 + 0.166698i) q^{20} -3.50915i q^{21} +(1.95998 - 1.95998i) q^{23} +(-0.698030 - 2.14832i) q^{24} +(-4.89137 - 1.03660i) q^{25} +(-1.09784 + 0.797627i) q^{26} +(3.93640 - 2.00570i) q^{27} +(-0.559706 + 0.285184i) q^{28} +(0.810497 - 0.588860i) q^{29} +(-1.10916 + 2.49324i) q^{30} +(0.131006 + 0.403196i) q^{31} +(-0.594873 + 0.594873i) q^{32} +2.82602i q^{34} +(-9.10532 - 2.43681i) q^{35} +(-0.278132 - 0.202075i) q^{36} +(-4.87226 - 0.771690i) q^{37} +(3.61500 + 7.09483i) q^{38} +(-0.238130 + 0.732888i) q^{39} +(-6.05905 + 0.319381i) q^{40} +(-0.339428 + 0.467182i) q^{41} +(-2.33544 + 4.58356i) q^{42} +(5.05373 + 5.05373i) q^{43} +(-1.07406 - 5.04553i) q^{45} +(-3.86451 + 1.25566i) q^{46} +(-0.186094 - 1.17495i) q^{47} +(-0.556831 + 3.51569i) q^{48} +(-10.2419 - 3.32780i) q^{49} +(5.69909 + 4.60932i) q^{50} +(0.943286 + 1.29832i) q^{51} +(0.136247 - 0.0215795i) q^{52} +(8.09173 + 4.12294i) q^{53} -6.47647 q^{54} -11.4381 q^{56} +(4.02895 + 2.05285i) q^{57} +(-1.45055 + 0.229745i) q^{58} +(-5.47214 - 7.53175i) q^{59} +(0.215526 - 0.174637i) q^{60} +(-7.40093 - 2.40471i) q^{61} +(0.0972215 - 0.613832i) q^{62} +(-1.52128 - 9.60498i) q^{63} +(-6.96021 + 2.26151i) q^{64} +(1.73629 + 1.12681i) q^{65} +(-3.05526 - 3.05526i) q^{67} +(0.130421 - 0.255966i) q^{68} +(-1.35630 + 1.86679i) q^{69} +(10.2714 + 9.24275i) q^{70} +(2.65487 - 8.17086i) q^{71} +(-2.84193 - 5.57761i) q^{72} +(-5.39318 - 0.854195i) q^{73} +(5.85044 + 4.25059i) q^{74} +(4.15679 + 0.215323i) q^{75} -0.809447i q^{76} +(0.798797 - 0.798797i) q^{78} +(-0.705861 - 2.17242i) q^{79} +(8.73564 + 3.88619i) q^{80} +(2.62377 - 1.90628i) q^{81} +(0.754275 - 0.384322i) q^{82} +(-1.77193 + 0.902846i) q^{83} +(0.423065 - 0.307374i) q^{84} +(4.02384 - 1.54601i) q^{85} +(-3.23765 - 9.96446i) q^{86} +(-0.589724 + 0.589724i) q^{87} +13.9313i q^{89} +(-1.95504 + 7.30516i) q^{90} +(3.15682 + 2.29356i) q^{91} +(0.407977 + 0.0646171i) q^{92} +(-0.160224 - 0.314457i) q^{93} +(-0.538893 + 1.65854i) q^{94} +(8.12438 - 9.02854i) q^{95} +(0.411650 - 0.566587i) q^{96} +(1.50922 - 2.96200i) q^{97} +(11.1630 + 11.1630i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{2} - 4 q^{3} - 2 q^{5} + 20 q^{6} + 10 q^{8} + 12 q^{12} + 10 q^{13} + 14 q^{15} - 8 q^{16} + 10 q^{18} + 16 q^{20} - 24 q^{23} + 16 q^{25} + 20 q^{26} - 16 q^{27} - 50 q^{28} - 30 q^{30} - 28 q^{31}+ \cdots - 8 q^{97}+O(q^{100}) $ 32 * q + 10 * q^2 - 4 * q^3 - 2 * q^5 + 20 * q^6 + 10 * q^8 + 12 * q^12 + 10 * q^13 + 14 * q^15 - 8 * q^16 + 10 * q^18 + 16 * q^20 - 24 * q^23 + 16 * q^25 + 20 * q^26 - 16 * q^27 - 50 * q^28 - 30 * q^30 - 28 * q^31 + 10 * q^35 + 24 * q^36 - 8 * q^37 + 10 * q^38 + 50 * q^40 - 40 * q^41 - 10 * q^42 - 28 * q^45 - 60 * q^46 - 28 * q^47 - 54 * q^48 + 50 * q^50 - 20 * q^51 + 50 * q^52 - 24 * q^53 - 80 * q^56 - 30 * q^57 - 50 * q^58 + 34 * q^60 + 60 * q^61 - 100 * q^62 + 30 * q^63 - 8 * q^67 + 30 * q^68 + 30 * q^70 + 24 * q^71 - 80 * q^72 - 50 * q^73 + 34 * q^75 + 60 * q^78 + 98 * q^80 - 12 * q^81 - 10 * q^82 - 90 * q^83 - 30 * q^85 + 100 * q^86 + 20 * q^90 + 20 * q^91 - 68 * q^92 - 8 * q^93 + 40 * q^95 - 8 * q^97

Character values

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

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−1.30617	−	0.665529i	−0.923605	−	0.470600i	−0.0735483	−	0.997292i	$-0.523432\pi$
$2$	−1.30617	−	0.665529i	−0.923605	−	0.470600i	−0.850057	+	0.526691i	$0.823432\pi$
$3$	−0.822224	+	0.130227i	−0.474711	+	0.0751869i	−0.389206	−	0.921151i	$-0.627250\pi$
$3$	−0.822224	+	0.130227i	−0.474711	+	0.0751869i	−0.0855054	+	0.996338i	$0.527250\pi$
$4$	0.0875924	+	0.120561i	0.0437962	+	0.0602803i
$5$	−0.233059	+	2.22389i	−0.104227	+	0.994554i
$5$	−0.233059	+	2.22389i	−0.104227	+	0.994554i
$6$	1.16064	+	0.377114i	0.473829	+	0.153956i
$7$	−0.659422	+	4.16343i	−0.249238	+	1.57363i	0.472417	+	0.881375i	$0.343382\pi$
$7$	−0.659422	+	4.16343i	−0.249238	+	1.57363i	−0.721655	+	0.692253i	$0.756618\pi$
$8$	0.424477	+	2.68004i	0.150075	+	0.947538i
$9$	−2.19408	+	0.712899i	−0.731359	+	0.237633i
$10$	1.78448	−	2.74968i	0.564302	−	0.869525i
$11$		0			0
$11$		0			0
$12$	−0.0877208	−	0.0877208i	−0.0253228	−	0.0253228i
$13$	0.420250	−	0.824787i	0.116556	−	0.228755i	−0.825357	−	0.564612i	$-0.809026\pi$
$13$	0.420250	−	0.824787i	0.116556	−	0.228755i	0.941913	+	0.335857i	$0.109026\pi$
$14$	3.63220	−	4.99930i	0.970747	−	1.33612i
$15$	−0.0979846	−	1.85889i	−0.0252995	−	0.479962i
$16$	1.32131	−	4.06656i	0.330326	−	1.01664i
$17$	−0.875188	−	1.71765i	−0.212264	−	0.416592i	0.760185	−	0.649707i	$-0.225108\pi$
$17$	−0.875188	−	1.71765i	−0.212264	−	0.416592i	−0.972449	+	0.233115i	$0.925108\pi$
$18$	3.34030	+	0.529052i	0.787317	+	0.124699i
$19$	−4.39439	−	3.19271i	−1.00814	−	0.732458i	−0.0443230	−	0.999017i	$-0.514113\pi$
$19$	−4.39439	−	3.19271i	−1.00814	−	0.732458i	−0.963818	+	0.266560i	$0.914113\pi$
$20$	−0.288528	+	0.166698i	−0.0645167	+	0.0372748i
$21$		−	3.50915i		−	0.765758i
$22$		0			0
$23$	1.95998	−	1.95998i	0.408685	−	0.408685i	−0.472595	−	0.881280i	$-0.656683\pi$
$23$	1.95998	−	1.95998i	0.408685	−	0.408685i	0.881280	+	0.472595i	$0.156683\pi$
$24$	−0.698030	−	2.14832i	−0.142485	−	0.438523i
$25$	−4.89137	−	1.03660i	−0.978273	−	0.207319i
$26$	−1.09784	+	0.797627i	−0.215304	+	0.156428i
$27$	3.93640	−	2.00570i	0.757561	−	0.385996i
$28$	−0.559706	+	0.285184i	−0.105774	+	0.0538948i
$29$	0.810497	−	0.588860i	0.150505	−	0.109349i	−0.509984	−	0.860184i	$-0.670349\pi$
$29$	0.810497	−	0.588860i	0.150505	−	0.109349i	0.660490	+	0.750835i	$0.270349\pi$
$30$	−1.10916	+	2.49324i	−0.202504	+	0.455201i
$31$	0.131006	+	0.403196i	0.0235294	+	0.0724161i	0.962132	−	0.272585i	$-0.0878786\pi$
$31$	0.131006	+	0.403196i	0.0235294	+	0.0724161i	−0.938602	+	0.345001i	$0.887879\pi$
$32$	−0.594873	+	0.594873i	−0.105160	+	0.105160i
$33$		0			0
$34$			2.82602i			0.484658i
$35$	−9.10532	−	2.43681i	−1.53908	−	0.411896i
$36$	−0.278132	−	0.202075i	−0.0463553	−	0.0336791i
$37$	−4.87226	−	0.771690i	−0.800995	−	0.126865i	−0.257501	−	0.966278i	$-0.582899\pi$
$37$	−4.87226	−	0.771690i	−0.800995	−	0.126865i	−0.543494	+	0.839413i	$0.682899\pi$
$38$	3.61500	+	7.09483i	0.586430	+	1.15093i
$39$	−0.238130	+	0.732888i	−0.0381313	+	0.117356i
$40$	−6.05905	+	0.319381i	−0.958019	+	0.0504986i
$41$	−0.339428	+	0.467182i	−0.0530097	+	0.0729616i	−0.834699	−	0.550707i	$-0.814358\pi$
$41$	−0.339428	+	0.467182i	−0.0530097	+	0.0729616i	0.781689	+	0.623668i	$0.214358\pi$
$42$	−2.33544	+	4.58356i	−0.360366	+	0.707258i
$43$	5.05373	+	5.05373i	0.770687	+	0.770687i	0.978227	−	0.207540i	$-0.0665456\pi$
$43$	5.05373	+	5.05373i	0.770687	+	0.770687i	−0.207540	+	0.978227i	$0.566546\pi$
$44$		0			0
$45$	−1.07406	−	5.04553i	−0.160111	−	0.752143i
$46$	−3.86451	+	1.25566i	−0.569791	+	0.185136i
$47$	−0.186094	−	1.17495i	−0.0271446	−	0.171384i	0.970392	−	0.241537i	$-0.0776514\pi$
$47$	−0.186094	−	1.17495i	−0.0271446	−	0.171384i	−0.997536	+	0.0701524i	$0.977651\pi$
$48$	−0.556831	+	3.51569i	−0.0803717	+	0.507447i
$49$	−10.2419	−	3.32780i	−1.46313	−	0.475400i
$50$	5.69909	+	4.60932i	0.805974	+	0.651857i
$51$	0.943286	+	1.29832i	0.132086	+	0.181801i
$52$	0.136247	−	0.0215795i	0.0188941	−	0.00299254i
$53$	8.09173	+	4.12294i	1.11149	+	0.566330i	0.910602	−	0.413285i	$-0.135619\pi$
$53$	8.09173	+	4.12294i	1.11149	+	0.566330i	0.200883	+	0.979615i	$0.435619\pi$
$54$	−6.47647			−0.881337
$55$		0			0
$56$	−11.4381			−1.52848
$57$	4.02895	+	2.05285i	0.533647	+	0.271907i
$58$	−1.45055	+	0.229745i	−0.190467	+	0.0301670i
$59$	−5.47214	−	7.53175i	−0.712411	−	0.980550i	−0.999742	−	0.0227186i	$-0.992768\pi$
$59$	−5.47214	−	7.53175i	−0.712411	−	0.980550i	0.287331	−	0.957831i	$-0.407232\pi$
$60$	0.215526	−	0.174637i	0.0278242	−	0.0225456i
$61$	−7.40093	−	2.40471i	−0.947591	−	0.307891i	−0.205855	−	0.978583i	$-0.565998\pi$
$61$	−7.40093	−	2.40471i	−0.947591	−	0.307891i	−0.741737	+	0.670691i	$0.765998\pi$
$62$	0.0972215	−	0.613832i	0.0123471	−	0.0779568i
$63$	−1.52128	−	9.60498i	−0.191663	−	1.21011i
$64$	−6.96021	+	2.26151i	−0.870026	+	0.282689i
$65$	1.73629	+	1.12681i	0.215361	+	0.139764i
$66$		0			0
$67$	−3.05526	−	3.05526i	−0.373259	−	0.373259i	0.495404	−	0.868663i	$-0.335020\pi$
$67$	−3.05526	−	3.05526i	−0.373259	−	0.373259i	−0.868663	+	0.495404i	$0.835020\pi$
$68$	0.130421	−	0.255966i	0.0158159	−	0.0310405i
$69$	−1.35630	+	1.86679i	−0.163280	+	0.224735i
$70$	10.2714	+	9.24275i	1.22766	+	1.10472i
$71$	2.65487	−	8.17086i	0.315075	−	0.969702i	−0.660648	−	0.750696i	$-0.729718\pi$
$71$	2.65487	−	8.17086i	0.315075	−	0.969702i	0.975723	−	0.219006i	$-0.0702816\pi$
$72$	−2.84193	−	5.57761i	−0.334925	−	0.657328i
$73$	−5.39318	−	0.854195i	−0.631224	−	0.0999760i	−0.167379	−	0.985893i	$-0.553530\pi$
$73$	−5.39318	−	0.854195i	−0.631224	−	0.0999760i	−0.463844	+	0.885917i	$0.653530\pi$
$74$	5.85044	+	4.25059i	0.680100	+	0.494122i
$75$	4.15679	+	0.215323i	0.479985	+	0.0248634i
$76$		−	0.809447i		−	0.0928499i
$77$		0			0
$78$	0.798797	−	0.798797i	0.0904460	−	0.0904460i
$79$	−0.705861	−	2.17242i	−0.0794156	−	0.244416i	0.903464	−	0.428663i	$-0.141015\pi$
$79$	−0.705861	−	2.17242i	−0.0794156	−	0.244416i	−0.982880	+	0.184247i	$0.941015\pi$
$80$	8.73564	+	3.88619i	0.976674	+	0.434489i
$81$	2.62377	−	1.90628i	0.291530	−	0.211809i
$82$	0.754275	−	0.384322i	0.0832957	−	0.0424413i
$83$	−1.77193	+	0.902846i	−0.194495	+	0.0991002i	−0.548526	−	0.836134i	$-0.684811\pi$
$83$	−1.77193	+	0.902846i	−0.194495	+	0.0991002i	0.354031	+	0.935234i	$0.384811\pi$
$84$	0.423065	−	0.307374i	0.0461601	−	0.0335373i
$85$	4.02384	−	1.54601i	0.436447	−	0.167688i
$86$	−3.23765	−	9.96446i	−0.349125	−	1.07450i
$87$	−0.589724	+	0.589724i	−0.0632250	+	0.0632250i
$88$		0			0
$89$			13.9313i			1.47671i	0.674410	+	0.738357i	$0.264398\pi$
$89$			13.9313i			1.47671i	−0.674410	+	0.738357i	$0.735602\pi$
$90$	−1.95504	+	7.30516i	−0.206079	+	0.770032i
$91$	3.15682	+	2.29356i	0.330925	+	0.240431i
$92$	0.407977	+	0.0646171i	0.0425345	+	0.00673680i
$93$	−0.160224	−	0.314457i	−0.0166144	−	0.0326076i
$94$	−0.538893	+	1.65854i	−0.0555826	+	0.171066i
$95$	8.12438	−	9.02854i	0.833544	−	0.926309i
$96$	0.411650	−	0.566587i	0.0420138	−	0.0578271i
$97$	1.50922	−	2.96200i	0.153238	−	0.300746i	−0.801607	−	0.597851i	$-0.796021\pi$
$97$	1.50922	−	2.96200i	0.153238	−	0.300746i	0.954845	+	0.297105i	$0.0960213\pi$
$98$	11.1630	+	11.1630i	1.12763	+	1.12763i
$99$		0			0
$100$	−0.303474	−	0.680504i	−0.0303474	−	0.0680504i
$101$	12.6404	−	4.10712i	1.25777	−	0.408673i	0.397069	−	0.917789i	$-0.370027\pi$
$101$	12.6404	−	4.10712i	1.25777	−	0.408673i	0.860698	+	0.509116i	$0.170027\pi$
$102$	−0.368025	−	2.32362i	−0.0364399	−	0.230073i
$103$	−1.57723	+	9.95825i	−0.155409	+	0.981215i	0.779519	+	0.626378i	$0.215464\pi$
$103$	−1.57723	+	9.95825i	−0.155409	+	0.981215i	−0.934928	+	0.354837i	$0.884536\pi$
$104$	2.38885	+	0.776185i	0.234246	+	0.0761112i
$105$	7.80395	+	0.817839i	0.761588	+	0.0798129i
$106$	−7.82528	−	10.7706i	−0.760058	−	1.04613i
$107$	6.09076	−	0.964682i	0.588816	−	0.0932593i	0.145085	−	0.989419i	$-0.453654\pi$
$107$	6.09076	−	0.964682i	0.588816	−	0.0932593i	0.443731	+	0.896160i	$0.353654\pi$
$108$	0.586606	+	0.298891i	0.0564462	+	0.0287608i
$109$	−19.9193			−1.90793			−0.953964	−	0.299922i	$-0.903039\pi$
$109$	−19.9193			−1.90793			−0.953964	+	0.299922i	$0.903039\pi$
$110$		0			0
$111$	4.10659			0.389780
$112$	16.0595	+	8.18274i	1.51748	+	0.773197i
$113$	−11.9729	+	1.89632i	−1.12632	+	0.178391i	−0.691673	−	0.722211i	$-0.743126\pi$
$113$	−11.9729	+	1.89632i	−1.12632	+	0.178391i	−0.434644	+	0.900602i	$0.643126\pi$
$114$	−3.89628	−	5.36277i	−0.364920	−	0.502269i
$115$	3.90200	+	4.81558i	0.363863	+	0.449055i
$116$	0.141987	+	0.0461342i	0.0131831	+	0.00428346i
$117$	−0.334071	+	2.10924i	−0.0308849	+	0.194999i
$118$	2.13497	+	13.4796i	0.196540	+	1.24090i
$119$	7.72845	−	2.51112i	0.708465	−	0.230194i
$120$	4.94030	−	1.05166i	0.450986	−	0.0960028i
$121$		0			0
$122$	8.06650	+	8.06650i	0.730306	+	0.730306i
$123$	0.218246	−	0.428331i	0.0196785	−	0.0386213i
$124$	−0.0371343	+	0.0511110i	−0.00333476	+	0.00458991i
$125$	3.44525	−	10.6363i	0.308153	−	0.951337i
$126$	−4.40534	+	13.5582i	−0.392459	+	1.20786i
$127$	0.526416	+	1.03315i	0.0467119	+	0.0916772i	0.913183	−	0.407551i	$-0.133617\pi$
$127$	0.526416	+	1.03315i	0.0467119	+	0.0916772i	−0.866471	+	0.499228i	$0.833617\pi$
$128$	12.2582	+	1.94151i	1.08348	+	0.171607i
$129$	−4.81343	−	3.49716i	−0.423799	−	0.307908i
$130$	−1.51797	−	2.62737i	−0.133135	−	0.230435i
$131$		−	14.4532i		−	1.26278i	−0.775465	−	0.631390i	$-0.782485\pi$
$131$		−	14.4532i		−	1.26278i	0.775465	−	0.631390i	$-0.217515\pi$
$132$		0			0
$133$	16.1904	−	16.1904i	1.40388	−	1.40388i
$134$	1.95734	+	6.02407i	0.169088	+	0.520400i
$135$	3.54303	+	9.22156i	0.304936	+	0.793666i
$136$	4.23189	−	3.07465i	0.362881	−	0.263649i
$137$	−11.0232	+	5.61663i	−0.941780	+	0.479861i	−0.856300	−	0.516479i	$-0.827242\pi$
$137$	−11.0232	+	5.61663i	−0.941780	+	0.479861i	−0.0854799	+	0.996340i	$0.527242\pi$
$138$	3.01397	−	1.53570i	0.256566	−	0.130727i
$139$	−0.816606	+	0.593299i	−0.0692636	+	0.0503229i	−0.621878	−	0.783114i	$-0.713630\pi$
$139$	−0.816606	+	0.593299i	−0.0692636	+	0.0503229i	0.552615	+	0.833437i	$0.313630\pi$
$140$	−0.503774	−	1.31119i	−0.0425766	−	0.110816i
$141$	0.306022	+	0.941839i	0.0257717	+	0.0793172i
$142$	−8.90567	+	8.90567i	−0.747347	+	0.747347i
$143$		0			0
$144$			9.86430i			0.822025i
$145$	1.12067	+	1.93969i	0.0930663	+	0.161083i
$146$	6.47594	+	4.70504i	0.535952	+	0.389392i
$147$	8.85451	+	1.40242i	0.730308	+	0.115669i
$148$	−0.333737	−	0.654997i	−0.0274331	−	0.0538404i
$149$	0.377177	−	1.16083i	0.0308996	−	0.0950990i	−0.934417	−	0.356180i	$-0.884079\pi$
$149$	0.377177	−	1.16083i	0.0308996	−	0.0950990i	0.965317	+	0.261081i	$0.0840790\pi$
$150$	−5.28619	−	3.04772i	−0.431616	−	0.248845i
$151$	−0.932668	+	1.28371i	−0.0758995	+	0.104467i	−0.845279	−	0.534326i	$-0.820566\pi$
$151$	−0.932668	+	1.28371i	−0.0758995	+	0.104467i	0.769379	+	0.638792i	$0.220566\pi$
$152$	6.69128	−	13.1324i	0.542734	−	1.06518i
$153$	3.14474	+	3.14474i	0.254237	+	0.254237i
$154$		0			0
$155$	−0.927195	+	0.197375i	−0.0744741	+	0.0158535i
$156$	−0.109216	+	0.0354863i	−0.00874425	+	0.00284118i
$157$	1.16061	+	7.32783i	0.0926271	+	0.584824i	0.989724	+	0.142991i	$0.0456719\pi$
$157$	1.16061	+	7.32783i	0.0926271	+	0.584824i	−0.897097	+	0.441834i	$0.854328\pi$
$158$	−0.523829	+	3.30733i	−0.0416736	+	0.263117i
$159$	−7.19014	−	2.33622i	−0.570215	−	0.185274i
$160$	−1.18429	−	1.46157i	−0.0936264	−	0.115547i
$161$	6.86780	+	9.45272i	0.541258	+	0.744978i
$162$	−4.69579	+	0.743741i	−0.368936	+	0.0584338i
$163$	−13.7294	−	6.99546i	−1.07537	−	0.547927i	−0.175673	−	0.984449i	$-0.556210\pi$
$163$	−13.7294	−	6.99546i	−1.07537	−	0.547927i	−0.899694	+	0.436522i	$0.856210\pi$
$164$	−0.0860550			−0.00671976
$165$		0			0
$166$	2.91533			0.226273
$167$	3.69782	+	1.88413i	0.286146	+	0.145799i	0.591172	−	0.806545i	$-0.298665\pi$
$167$	3.69782	+	1.88413i	0.286146	+	0.145799i	−0.305026	+	0.952344i	$0.598665\pi$
$168$	9.40466	−	1.48955i	0.725585	−	0.114921i
$169$	7.13754	+	9.82399i	0.549042	+	0.755691i
$170$	−6.28475	−	0.658629i	−0.482018	−	0.0505146i
$171$	11.9177	+	3.87229i	0.911369	+	0.296122i
$172$	−0.166612	+	1.05195i	−0.0127041	+	0.0802104i
$173$	−0.677320	−	4.27643i	−0.0514957	−	0.325131i	−0.999966	−	0.00826456i	$-0.997369\pi$
$173$	−0.677320	−	4.27643i	−0.0514957	−	0.325131i	0.948470	−	0.316867i	$-0.102631\pi$
$174$	1.16276	−	0.377804i	0.0881487	−	0.0286412i
$175$	7.54127	−	19.6813i	0.570066	−	1.48777i
$176$		0			0
$177$	5.48016	+	5.48016i	0.411914	+	0.411914i
$178$	9.27168	−	18.1967i	0.694942	−	1.36390i
$179$	2.18633	−	3.00922i	0.163414	−	0.224920i	−0.719456	−	0.694538i	$-0.755609\pi$
$179$	2.18633	−	3.00922i	0.163414	−	0.224920i	0.882869	+	0.469619i	$0.155609\pi$
$180$	0.514213	−	0.571439i	0.0383271	−	0.0425925i
$181$	1.86849	−	5.75062i	0.138884	−	0.427440i	−0.857290	−	0.514834i	$-0.827854\pi$
$181$	1.86849	−	5.75062i	0.138884	−	0.427440i	0.996174	+	0.0873933i	$0.0278537\pi$
$182$	−2.59692	−	5.09675i	−0.192497	−	0.377796i
$183$	6.39838	+	1.01340i	0.472982	+	0.0749129i
$184$	6.08481	+	4.42087i	0.448578	+	0.325911i
$185$	2.85168	−	10.6555i	0.209660	−	0.783409i
$186$			0.517369i			0.0379353i
$187$		0			0
$188$	0.125352	−	0.125352i	0.00914227	−	0.00914227i
$189$	5.75482	+	17.7115i	0.418602	+	1.28832i
$190$	−16.6206	+	6.38583i	−1.20579	+	0.463277i
$191$	13.3930	−	9.73057i	0.969082	−	0.704079i	0.0138398	−	0.999904i	$-0.495595\pi$
$191$	13.3930	−	9.73057i	0.969082	−	0.704079i	0.955242	+	0.295825i	$0.0955945\pi$
$192$	5.42834	−	2.76588i	0.391757	−	0.199610i
$193$	−15.1151	+	7.70155i	−1.08801	+	0.554370i	−0.903556	−	0.428471i	$-0.859052\pi$
$193$	−15.1151	+	7.70155i	−1.08801	+	0.554370i	−0.184456	+	0.982841i	$0.559052\pi$
$194$	−3.94260	+	2.86447i	−0.283062	+	0.205657i
$195$	−1.57436	−	0.700380i	−0.112742	−	0.0501553i
$196$	−0.495912	−	1.52626i	−0.0354223	−	0.109019i
$197$	−9.63624	+	9.63624i	−0.686554	+	0.686554i	−0.961469	−	0.274915i	$-0.911350\pi$
$197$	−9.63624	+	9.63624i	−0.686554	+	0.686554i	0.274915	+	0.961469i	$0.411350\pi$
$198$		0			0
$199$		−	19.4166i		−	1.37640i	−0.725519	−	0.688202i	$-0.758400\pi$
$199$		−	19.4166i		−	1.37640i	0.725519	−	0.688202i	$-0.241600\pi$
$200$	0.701848	−	13.5491i	0.0496281	−	0.958065i
$201$	2.90999	+	2.11423i	0.205255	+	0.149126i
$202$	−19.2440	−	3.04795i	−1.35400	−	0.214453i
$203$	1.91722	+	3.76275i	0.134562	+	0.264093i
$204$	−0.0739017	+	0.227446i	−0.00517416	+	0.0159244i
$205$	−0.959854	−	0.863730i	−0.0670391	−	0.0603255i
$206$	8.68764	−	11.9575i	0.605297	−	0.833119i
$207$	−2.90309	+	5.69763i	−0.201778	+	0.396012i
$208$	−2.79877	−	2.79877i	−0.194060	−	0.194060i
$209$		0			0
$210$	−9.64903	−	6.26200i	−0.665846	−	0.432119i
$211$	−6.07815	+	1.97491i	−0.418437	+	0.135959i	−0.510666	−	0.859779i	$-0.670601\pi$
$211$	−6.07815	+	1.97491i	−0.418437	+	0.135959i	0.0922284	+	0.995738i	$0.470601\pi$
$212$	0.211710	+	1.33668i	0.0145403	+	0.0918037i
$213$	−1.11883	+	7.06401i	−0.0766609	+	0.484018i
$214$	−8.59762	−	2.79354i	−0.587721	−	0.190962i
$215$	−12.4168	+	10.0611i	−0.846816	+	0.686163i
$216$	7.04626	+	9.69835i	0.479437	+	0.659889i
$217$	−1.76507	+	0.279559i	−0.119820	+	0.0189777i
$218$	26.0181	+	13.2569i	1.76217	+	0.897871i
$219$	4.54564			0.307166
$220$		0			0
$221$	−1.78450			−0.120038
$222$	−5.36392	−	2.73305i	−0.360003	−	0.183430i
$223$	−14.0202	+	2.22058i	−0.938860	+	0.148701i	−0.607066	−	0.794651i	$-0.707654\pi$
$223$	−14.0202	+	2.22058i	−0.938860	+	0.148701i	−0.331794	+	0.943352i	$0.607654\pi$
$224$	−2.08444	−	2.86898i	−0.139272	−	0.191692i
$225$	11.4710	−	1.21268i	0.764735	−	0.0808452i
$226$	16.9008	+	5.49139i	1.12422	+	0.365282i
$227$	1.29499	−	8.17622i	0.0859512	−	0.542675i	−0.906711	−	0.421753i	$-0.861415\pi$
$227$	1.29499	−	8.17622i	0.0859512	−	0.542675i	0.992662	−	0.120922i	$-0.0385850\pi$
$228$	0.105412	+	0.665546i	0.00698109	+	0.0440769i
$229$	−18.6401	+	6.05655i	−1.23178	+	0.400228i	−0.851357	−	0.524587i	$-0.824220\pi$
$229$	−18.6401	+	6.05655i	−1.23178	+	0.400228i	−0.380418	+	0.924815i	$0.624220\pi$
$230$	−1.89178	−	8.88688i	−0.124740	−	0.585984i
$231$		0			0
$232$	1.92221	+	1.92221i	0.126199	+	0.126199i
$233$	−1.68573	+	3.30844i	−0.110436	+	0.216743i	−0.939609	−	0.342249i	$-0.888812\pi$
$233$	−1.68573	+	3.30844i	−0.110436	+	0.216743i	0.829173	+	0.558991i	$0.188812\pi$
$234$	1.84012	−	2.53270i	0.120292	−	0.165568i
$235$	2.65633	−	0.140019i	0.173280	−	0.00913385i
$236$	0.428714	−	1.31945i	0.0279069	−	0.0858887i
$237$	0.863285	+	1.69429i	0.0560764	+	0.110056i
$238$	−11.7659	−	1.86354i	−0.762672	−	0.120795i
$239$	−2.59930	−	1.88850i	−0.168135	−	0.122157i	0.500536	−	0.865716i	$-0.333136\pi$
$239$	−2.59930	−	1.88850i	−0.168135	−	0.122157i	−0.668671	+	0.743559i	$0.733136\pi$
$240$	−7.68874	−	2.05770i	−0.496306	−	0.132824i
$241$			25.4119i			1.63693i	0.574559	+	0.818463i	$0.305174\pi$
$241$			25.4119i			1.63693i	−0.574559	+	0.818463i	$0.694826\pi$
$242$		0			0
$243$	−11.2809	+	11.2809i	−0.723671	+	0.723671i
$244$	−0.358352	−	1.10289i	−0.0229411	−	0.0706055i
$245$	9.78763	−	22.0013i	0.625309	−	1.40561i
$246$	−0.570133	+	0.414226i	−0.0363504	+	0.0264101i
$247$	−4.48005	+	2.28270i	−0.285059	+	0.145245i
$248$	−1.02497	+	0.522250i	−0.0650858	+	0.0331629i
$249$	1.33935	−	0.973096i	0.0848780	−	0.0616674i
$250$	−11.5788	+	11.5999i	−0.732311	+	0.733643i
$251$	5.03867	+	15.5074i	0.318038	+	0.978820i	0.974486	+	0.224448i	$0.0720580\pi$
$251$	5.03867	+	15.5074i	0.318038	+	0.978820i	−0.656448	+	0.754371i	$0.727942\pi$
$252$	1.02473	−	1.02473i	0.0645519	−	0.0645519i
$253$		0			0
$254$		−	1.69982i		−	0.106656i
$255$	−3.10717	+	1.79518i	−0.194578	+	0.112418i
$256$	−2.87779	−	2.09084i	−0.179862	−	0.130677i
$257$	−16.0045	−	2.53487i	−0.998335	−	0.158121i	−0.364182	−	0.931328i	$-0.618651\pi$
$257$	−16.0045	−	2.53487i	−0.998335	−	0.158121i	−0.634154	+	0.773207i	$0.718651\pi$
$258$	3.95972	+	7.77139i	0.246521	+	0.483825i
$259$	6.42576	−	19.7764i	0.399277	−	1.22885i
$260$	0.0162366	+	0.308029i	0.00100695	+	0.0191031i
$261$	−1.35849	+	1.86981i	−0.0840887	+	0.115738i
$262$	−9.61901	+	18.8784i	−0.594265	+	1.16631i
$263$	−0.677874	−	0.677874i	−0.0417995	−	0.0417995i	0.685898	−	0.727698i	$-0.259410\pi$
$263$	−0.677874	−	0.677874i	−0.0417995	−	0.0417995i	−0.727698	+	0.685898i	$0.759410\pi$
$264$		0			0
$265$	−11.0548	+	17.0342i	−0.679092	+	1.04640i
$266$	−31.9226	+	10.3723i	−1.95730	+	0.635966i
$267$	−1.81424	−	11.4546i	−0.111030	−	0.701013i
$268$	0.100726	−	0.635961i	0.00615284	−	0.0388475i
$269$	27.0327	+	8.78345i	1.64821	+	0.535536i	0.978351	−	0.206951i	$-0.0663541\pi$
$269$	27.0327	+	8.78345i	1.64821	+	0.535536i	0.669860	+	0.742487i	$0.266354\pi$
$270$	1.50940	−	14.4030i	0.0918593	−	0.876536i
$271$	−18.0744	−	24.8772i	−1.09794	−	1.51118i	−0.838087	−	0.545536i	$-0.816326\pi$
$271$	−18.0744	−	24.8772i	−1.09794	−	1.51118i	−0.259853	−	0.965648i	$-0.583674\pi$
$272$	−8.14133	+	1.28946i	−0.493641	+	0.0781850i
$273$	−2.89430	−	1.47472i	−0.175171	−	0.0892540i
$274$	18.1363			1.09565
$275$		0			0
$276$	−0.343863			−0.0206981
$277$	−26.8625	−	13.6871i	−1.61401	−	0.822379i	−0.999438	−	0.0335176i	$-0.989329\pi$
$277$	−26.8625	−	13.6871i	−1.61401	−	0.822379i	−0.614571	−	0.788861i	$-0.710671\pi$
$278$	1.46149	−	0.231477i	0.0876542	−	0.0138831i
$279$	−0.574875	−	0.791248i	−0.0344169	−	0.0473708i
$280$	2.66575	−	25.4370i	0.159309	−	1.52015i
$281$	−8.10210	−	2.63253i	−0.483331	−	0.157044i	0.0572089	−	0.998362i	$-0.481780\pi$
$281$	−8.10210	−	2.63253i	−0.483331	−	0.157044i	−0.540540	+	0.841319i	$0.681780\pi$
$282$	0.227103	−	1.43387i	0.0135238	−	0.0853859i
$283$	1.49267	+	9.42432i	0.0887297	+	0.560218i	0.991501	+	0.130097i	$0.0415289\pi$
$283$	1.49267	+	9.42432i	0.0887297	+	0.560218i	−0.902772	+	0.430120i	$0.858471\pi$
$284$	1.21763	−	0.395632i	0.0722530	−	0.0234764i
$285$	−5.50430	+	8.48150i	−0.326046	+	0.502401i
$286$		0			0
$287$	−1.72125	−	1.72125i	−0.101602	−	0.101602i
$288$	0.881112	−	1.72928i	0.0519200	−	0.101899i
$289$	7.80797	−	10.7468i	0.459292	−	0.632162i
$290$	−0.172863	−	3.27941i	−0.0101509	−	0.192574i
$291$	−0.855180	+	2.63197i	−0.0501315	+	0.154289i
$292$	−0.369419	−	0.725025i	−0.0216186	−	0.0424289i
$293$	−2.27904	−	0.360965i	−0.133143	−	0.0210878i	0.0895072	−	0.995986i	$-0.471471\pi$
$293$	−2.27904	−	0.360965i	−0.133143	−	0.0210878i	−0.222650	+	0.974898i	$0.571471\pi$
$294$	−10.6322	−	7.72474i	−0.620082	−	0.450516i
$295$	18.0251	−	10.4141i	1.04946	−	0.606331i
$296$		−	13.3854i		−	0.778013i
$297$		0			0
$298$	−1.26523	+	1.26523i	−0.0732926	+	0.0732926i
$299$	−0.792887	−	2.44025i	−0.0458538	−	0.141124i
$300$	0.338144	+	0.520006i	0.0195227	+	0.0300225i
$301$	−24.3734	+	17.7083i	−1.40486	+	1.02069i
$302$	2.07257	−	1.05603i	0.119263	−	0.0607676i
$303$	−9.85838	+	5.02310i	−0.566349	+	0.288569i
$304$	−18.7897	+	13.6515i	−1.07766	+	0.782967i
$305$	7.07265	−	15.8984i	0.404979	−	0.910340i
$306$	−2.01466	−	6.20050i	−0.115171	−	0.354459i
$307$	12.4635	−	12.4635i	0.711327	−	0.711327i	−0.255486	−	0.966813i	$-0.582235\pi$
$307$	12.4635	−	12.4635i	0.711327	−	0.711327i	0.966813	+	0.255486i	$0.0822353\pi$
$308$		0			0
$309$		−	8.39331i		−	0.477479i
$310$	1.34244	+	0.359269i	0.0762453	+	0.0204051i
$311$	−12.2271	−	8.88353i	−0.693337	−	0.503739i	0.184419	−	0.982848i	$-0.440960\pi$
$311$	−12.2271	−	8.88353i	−0.693337	−	0.503739i	−0.877755	+	0.479109i	$0.840960\pi$
$312$	−2.06525	−	0.327104i	−0.116922	−	0.0185186i
$313$	−11.8565	−	23.2697i	−0.670169	−	1.31528i	−0.936251	−	0.351331i	$-0.885729\pi$
$313$	−11.8565	−	23.2697i	−0.670169	−	1.31528i	0.266082	−	0.963950i	$-0.414271\pi$
$314$	3.36092	−	10.3438i	0.189668	−	0.583737i
$315$	21.7150	−	1.14463i	1.22350	−	0.0644925i
$316$	0.200080	−	0.275386i	0.0112554	−	0.0154917i
$317$	−12.8603	+	25.2398i	−0.722307	+	1.41761i	0.178744	+	0.983896i	$0.442797\pi$
$317$	−12.8603	+	25.2398i	−0.722307	+	1.41761i	−0.901051	+	0.433712i	$0.857203\pi$
$318$	7.83675	+	7.83675i	0.439463	+	0.439463i
$319$		0			0
$320$	−3.40720	−	16.0058i	−0.190469	−	0.894751i
$321$	−4.88234	+	1.58637i	−0.272506	+	0.0885425i
$322$	−2.67949	−	16.9176i	−0.149322	−	0.942782i
$323$	−1.63805	+	10.3423i	−0.0911436	+	0.575458i
$324$	0.459645	+	0.149348i	0.0255358	+	0.00829710i
$325$	−2.91057	+	3.59871i	−0.161449	+	0.199620i
$326$	13.2773	+	18.2746i	0.735360	+	1.01214i
$327$	16.3782	−	2.59405i	0.905714	−	0.143451i
$328$	−1.39615	−	0.711372i	−0.0770893	−	0.0392790i
$329$	5.01454			0.276461
$330$		0			0
$331$	−24.6455			−1.35464			−0.677319	−	0.735690i	$-0.736858\pi$
$331$	−24.6455			−1.35464			−0.677319	+	0.735690i	$0.736858\pi$
$332$	−0.264055	−	0.134543i	−0.0144919	−	0.00738401i
$333$	11.2403	−	1.78028i	0.615962	−	0.0975588i
$334$	−3.57605	−	4.92202i	−0.195673	−	0.269321i
$335$	7.50662	−	6.08250i	0.410130	−	0.332323i
$336$	−14.2702	−	4.63665i	−0.778501	−	0.252950i
$337$	−4.85195	+	30.6340i	−0.264302	+	1.66874i	0.396390	+	0.918082i	$0.370263\pi$
$337$	−4.85195	+	30.6340i	−0.264302	+	1.66874i	−0.660692	+	0.750657i	$0.729737\pi$
$338$	−2.78473	−	17.5821i	−0.151469	−	0.956339i
$339$	9.59746	−	3.11840i	0.521263	−	0.169369i
$340$	0.538845	+	0.349698i	0.0292230	+	0.0189650i
$341$		0			0
$342$	−12.9895	−	12.9895i	−0.702390	−	0.702390i
$343$	7.21277	−	14.1559i	0.389453	−	0.764345i
$344$	−11.3990	+	15.6894i	−0.614594	+	0.845916i
$345$	−3.83544	−	3.45134i	−0.206493	−	0.185814i
$346$	−1.96139	+	6.03654i	−0.105445	+	0.324527i
$347$	13.7041	+	26.8957i	0.735672	+	1.44384i	0.890068	+	0.455829i	$0.150657\pi$
$347$	13.7041	+	26.8957i	0.735672	+	1.44384i	−0.154395	+	0.988009i	$0.549343\pi$
$348$	−0.122753	−	0.0194421i	−0.00658024	−	0.00104221i
$349$	17.2865	+	12.5594i	0.925323	+	0.672287i	0.944843	−	0.327523i	$-0.106214\pi$
$349$	17.2865	+	12.5594i	0.925323	+	0.672287i	−0.0195201	+	0.999809i	$0.506214\pi$
$350$	−22.9487	+	20.6883i	−1.22666	+	1.10584i
$351$		−	4.08959i		−	0.218286i
$352$		0			0
$353$	−2.82626	+	2.82626i	−0.150427	+	0.150427i	−0.778309	−	0.627882i	$-0.783922\pi$
$353$	−2.82626	+	2.82626i	−0.150427	+	0.150427i	0.627882	+	0.778309i	$0.283922\pi$
$354$	−3.51084	−	10.8053i	−0.186599	−	0.574293i
$355$	17.5523	+	7.80843i	0.931581	+	0.414429i
$356$	−1.67956	+	1.22027i	−0.0890167	+	0.0646744i
$357$	−6.02750	+	3.07116i	−0.319009	+	0.162543i
$358$	−4.85844	+	2.47550i	−0.256777	+	0.130834i
$359$	−8.68908	+	6.31298i	−0.458592	+	0.333187i	−0.792979	−	0.609249i	$-0.791471\pi$
$359$	−8.68908	+	6.31298i	−0.458592	+	0.333187i	0.334387	+	0.942436i	$0.391471\pi$
$360$	13.0663	−	5.02023i	0.688656	−	0.264590i
$361$	3.24592	+	9.98992i	0.170838	+	0.525785i
$362$	−6.26778	+	6.26778i	−0.329427	+	0.329427i
$363$		0			0
$364$			0.581487i			0.0304782i
$365$	3.15656	−	11.7947i	0.165222	−	0.617365i
$366$	−7.68295	−	5.58199i	−0.401594	−	0.291775i
$367$	34.1783	+	5.41331i	1.78409	+	0.282572i	0.959202	−	0.282721i	$-0.0912370\pi$
$367$	34.1783	+	5.41331i	1.78409	+	0.282572i	0.824890	+	0.565293i	$0.191237\pi$
$368$	−5.38066	−	10.5601i	−0.280486	−	0.550485i
$369$	0.411677	−	1.26701i	0.0214310	−	0.0659579i
$370$	−10.8164	+	12.0201i	−0.562315	+	0.624895i
$371$	−22.5015	+	30.9706i	−1.16822	+	1.60791i
$372$	0.0238767	−	0.0468606i	0.00123795	−	0.00242961i
$373$	−9.90454	−	9.90454i	−0.512838	−	0.512838i	0.402557	−	0.915395i	$-0.368121\pi$
$373$	−9.90454	−	9.90454i	−0.512838	−	0.512838i	−0.915395	+	0.402557i	$0.868121\pi$
$374$		0			0
$375$	−1.44763	+	9.19406i	−0.0747555	+	0.474779i
$376$	3.06993	−	0.997480i	0.158319	−	0.0514411i
$377$	−0.145073	−	0.915956i	−0.00747165	−	0.0471741i
$378$	4.27073	−	26.9643i	0.219663	−	1.38690i
$379$	25.2037	+	8.18919i	1.29463	+	0.420651i	0.873710	−	0.486447i	$-0.161708\pi$
$379$	25.2037	+	8.18919i	1.29463	+	0.420651i	0.420919	+	0.907098i	$0.361708\pi$
$380$	1.80012	+	0.188649i	0.0923442	+	0.00967749i
$381$	−0.567376	−	0.780926i	−0.0290676	−	0.0400081i
$382$	−23.9695	+	3.79640i	−1.22639	+	0.194241i
$383$	−21.4177	−	10.9129i	−1.09439	−	0.557622i	−0.188907	−	0.981995i	$-0.560495\pi$
$383$	−21.4177	−	10.9129i	−1.09439	−	0.557622i	−0.905487	+	0.424373i	$0.860495\pi$
$384$	−10.3318			−0.527243
$385$		0			0
$386$	24.8686			1.26578
$387$	−14.6911	−	7.48548i	−0.746789	−	0.380508i
$388$	0.489297	−	0.0774970i	0.0248403	−	0.00393431i
$389$	−4.43509	−	6.10438i	−0.224868	−	0.309505i	0.681644	−	0.731684i	$-0.261265\pi$
$389$	−4.43509	−	6.10438i	−0.224868	−	0.309505i	−0.906512	+	0.422179i	$0.861265\pi$
$390$	1.59027	+	1.96260i	0.0805264	+	0.0993803i
$391$	−5.08193	−	1.65122i	−0.257004	−	0.0835057i
$392$	4.57119	−	28.8613i	0.230880	−	1.45772i
$393$	1.88220	+	11.8838i	0.0949445	+	0.599456i
$394$	18.9998	−	6.17342i	0.957197	−	0.311012i
$395$	4.99573	−	1.06346i	0.251362	−	0.0535083i
$396$		0			0
$397$	16.0995	+	16.0995i	0.808008	+	0.808008i	0.984332	−	0.176324i	$-0.0564206\pi$
$397$	16.0995	+	16.0995i	0.808008	+	0.808008i	−0.176324	+	0.984332i	$0.556421\pi$
$398$	−12.9223	+	25.3614i	−0.647736	+	1.27125i
$399$	−11.2037	+	15.4205i	−0.560886	+	0.771993i
$400$	−10.6784	+	18.5214i	−0.533918	+	0.926069i
$401$	−7.46030	+	22.9604i	−0.372550	+	1.14659i	0.572568	+	0.819858i	$0.305947\pi$
$401$	−7.46030	+	22.9604i	−0.372550	+	1.14659i	−0.945117	+	0.326732i	$0.894053\pi$
$402$	−2.39387	−	4.69823i	−0.119395	−	0.234327i
$403$	0.387606	+	0.0613908i	0.0193080	+	0.00305809i
$404$	1.60236	+	1.16418i	0.0797203	+	0.0579202i
$405$	3.62787	+	6.27926i	0.180270	+	0.312019i
$406$		−	6.19078i		−	0.307243i
$407$		0			0
$408$	−3.07915	+	3.07915i	−0.152441	+	0.152441i
$409$	1.80956	+	5.56925i	0.0894769	+	0.275382i	0.985775	−	0.168070i	$-0.0537536\pi$
$409$	1.80956	+	5.56925i	0.0894769	+	0.275382i	−0.896298	+	0.443452i	$0.853754\pi$
$410$	0.678899	+	1.76699i	0.0335284	+	0.0872656i
$411$	8.33214	−	6.05365i	0.410994	−	0.298605i
$412$	−1.33872	+	0.682114i	−0.0659542	+	0.0336054i
$413$	34.9663	−	17.8162i	1.72058	−	0.876680i
$414$	7.58387	−	5.51001i	0.372727	−	0.270802i
$415$	−1.59486	−	4.15100i	−0.0782888	−	0.203765i
$416$	0.240648	+	0.740639i	0.0117987	+	0.0363128i
$417$	0.594169	−	0.594169i	0.0290966	−	0.0290966i
$418$		0			0
$419$		−	11.0599i		−	0.540311i	−0.962817	−	0.270155i	$-0.912925\pi$
$419$		−	11.0599i		−	0.540311i	0.962817	−	0.270155i	$-0.0870751\pi$
$420$	0.584968	+	1.01249i	0.0285435	+	0.0494042i
$421$	−6.36944	−	4.62767i	−0.310428	−	0.225539i	0.421652	−	0.906758i	$-0.361450\pi$
$421$	−6.36944	−	4.62767i	−0.310428	−	0.225539i	−0.732080	+	0.681219i	$0.761450\pi$
$422$	9.25349	+	1.46561i	0.450453	+	0.0713447i
$423$	1.24593	+	2.44527i	0.0605790	+	0.118893i
$424$	−7.61491	+	23.4363i	−0.369813	+	1.13817i
$425$	2.50035	+	9.30889i	0.121285	+	0.451547i
$426$	6.16269	−	8.48222i	0.298583	−	0.410965i
$427$	14.8922	−	29.2275i	0.720682	−	1.41442i
$428$	0.649807	+	0.649807i	0.0314096	+	0.0314096i
$429$		0			0
$430$	22.9144	−	4.87787i	1.10503	−	0.235232i
$431$	6.94552	−	2.25674i	0.334554	−	0.108703i	−0.136923	−	0.990582i	$-0.543721\pi$
$431$	6.94552	−	2.25674i	0.334554	−	0.108703i	0.471477	+	0.881879i	$0.343721\pi$
$432$	−2.95510	−	18.6577i	−0.142177	−	0.897671i
$433$	0.789604	−	4.98536i	0.0379460	−	0.239581i	−0.961424	−	0.275070i	$-0.911299\pi$
$433$	0.789604	−	4.98536i	0.0379460	−	0.239581i	0.999370	+	0.0354890i	$0.0112989\pi$
$434$	2.49154	+	0.809550i	0.119598	+	0.0388596i
$435$	−1.17404	−	1.44892i	−0.0562909	−	0.0694705i
$436$	−1.74478	−	2.40149i	−0.0835599	−	0.115010i
$437$	−14.8706	+	2.35527i	−0.711357	+	0.112668i
$438$	−5.93740	−	3.02525i	−0.283700	−	0.144552i
$439$	1.29778			0.0619394			0.0309697	−	0.999520i	$-0.490140\pi$
$439$	1.29778			0.0619394			0.0309697	+	0.999520i	$0.490140\pi$
$440$		0			0
$441$	24.8439			1.18304
$442$	2.33086	+	1.18763i	0.110868	+	0.0564900i
$443$	15.2112	−	2.40922i	0.722707	−	0.114466i	0.215764	−	0.976445i	$-0.430776\pi$
$443$	15.2112	−	2.40922i	0.722707	−	0.114466i	0.506942	+	0.861980i	$0.330776\pi$
$444$	0.359706	+	0.495092i	0.0170709	+	0.0234960i
$445$	−30.9817	−	3.24682i	−1.46867	−	0.153914i
$446$	19.7907	+	6.43037i	0.937115	+	0.304487i
$447$	−0.158952	+	1.00358i	−0.00751816	+	0.0474678i
$448$	−4.82591	−	30.4696i	−0.228003	−	1.43955i
$449$	−11.5295	+	3.74615i	−0.544109	+	0.176792i	−0.568159	−	0.822919i	$-0.692344\pi$
$449$	−11.5295	+	3.74615i	−0.544109	+	0.176792i	0.0240497	+	0.999711i	$0.492344\pi$
$450$	−15.7902	−	6.05033i	−0.744359	−	0.285215i
$451$		0			0
$452$	−1.27736	−	1.27736i	−0.0600818	−	0.0600818i
$453$	0.599688	−	1.17695i	0.0281758	−	0.0552981i
$454$	−7.13299	+	9.81772i	−0.334768	+	0.460768i
$455$	−5.83636	+	6.48588i	−0.273613	+	0.304063i
$456$	−3.79153	+	11.6691i	−0.177555	+	0.546458i
$457$	−1.59383	−	3.12807i	−0.0745563	−	0.146325i	0.850720	−	0.525620i	$-0.176167\pi$
$457$	−1.59383	−	3.12807i	−0.0745563	−	0.146325i	−0.925276	+	0.379295i	$0.876167\pi$
$458$	28.3781	+	4.49465i	1.32602	+	0.210021i
$459$	−6.89018	−	5.00601i	−0.321606	−	0.233660i
$460$	−0.238784	+	0.892235i	−0.0111334	+	0.0416007i
$461$			5.45336i			0.253988i	0.991903	+	0.126994i	$0.0405329\pi$
$461$			5.45336i			0.253988i	−0.991903	+	0.126994i	$0.959467\pi$
$462$		0			0
$463$	15.3996	−	15.3996i	0.715681	−	0.715681i	−0.252037	−	0.967718i	$-0.581100\pi$
$463$	15.3996	−	15.3996i	0.715681	−	0.715681i	0.967718	+	0.252037i	$0.0811005\pi$
$464$	−1.32372	−	4.07400i	−0.0614523	−	0.189131i
$465$	0.736658	−	0.283033i	0.0341617	−	0.0131253i
$466$	4.40372	−	3.19949i	0.203998	−	0.148214i
$467$	−13.0834	+	6.66632i	−0.605427	+	0.308481i	−0.729700	−	0.683768i	$-0.760340\pi$
$467$	−13.0834	+	6.66632i	−0.605427	+	0.308481i	0.124273	+	0.992248i	$0.460340\pi$
$468$	−0.283553	+	0.144478i	−0.0131073	+	0.00667848i
$469$	14.7351	−	10.7057i	0.680402	−	0.494341i
$470$	−3.56282	−	1.58498i	−0.164341	−	0.0731096i
$471$	−1.90857	−	5.87397i	−0.0879422	−	0.270658i
$472$	17.8626	−	17.8626i	0.822193	−	0.822193i
$473$		0			0
$474$		−	2.78758i		−	0.128038i
$475$	18.1850	+	20.1719i	0.834385	+	0.925551i
$476$	0.979695	+	0.711790i	0.0449043	+	0.0326249i
$477$	−20.6931	−	3.27747i	−0.947473	−	0.150065i
$478$	2.13829	+	4.19663i	0.0978030	+	0.191949i
$479$	1.51842	−	4.67321i	0.0693783	−	0.213524i	−0.910356	−	0.413826i	$-0.864192\pi$
$479$	1.51842	−	4.67321i	0.0693783	−	0.213524i	0.979734	+	0.200302i	$0.0641922\pi$
$480$	1.16409	+	1.04751i	0.0531331	+	0.0478122i
$481$	−2.68405	+	3.69428i	−0.122382	+	0.168444i
$482$	16.9124	−	33.1924i	0.770338	−	1.51187i
$483$	−6.87787	−	6.87787i	−0.312954	−	0.312954i
$484$		0			0
$485$	6.23543	+	4.04665i	0.283136	+	0.183749i
$486$	22.2426	−	7.22706i	1.00895	−	0.327826i
$487$	1.67972	+	10.6054i	0.0761155	+	0.480574i	0.996071	+	0.0885527i	$0.0282242\pi$
$487$	1.67972	+	10.6054i	0.0761155	+	0.480574i	−0.919956	+	0.392022i	$0.871776\pi$
$488$	3.30319	−	20.8555i	0.149529	−	0.944086i
$489$	12.1996	+	3.96390i	0.551686	+	0.179254i
$490$	−27.4269	+	22.2236i	−1.23902	+	1.00396i
$491$	−1.91387	−	2.63421i	−0.0863715	−	0.118880i	0.763645	−	0.645637i	$-0.223408\pi$
$491$	−1.91387	−	2.63421i	−0.0863715	−	0.118880i	−0.850016	+	0.526757i	$0.823408\pi$
$492$	0.0707565	−	0.0112067i	0.00318995	−	0.000505238i
$493$	−1.72079	−	0.876788i	−0.0775007	−	0.0394886i
$494$	7.37092			0.331634
$495$		0			0
$496$	1.81272			0.0813935
$497$	32.2681	+	16.4414i	1.44742	+	0.737498i
$498$	−2.39705	+	0.379656i	−0.107414	+	0.0170128i
$499$	5.25588	+	7.23410i	0.235285	+	0.323843i	0.910290	−	0.413971i	$-0.135858\pi$
$499$	5.25588	+	7.23410i	0.235285	+	0.323843i	−0.675005	+	0.737813i	$0.735858\pi$
$500$	1.58409	−	0.516295i	0.0708428	−	0.0230894i
$501$	−3.28580	−	1.06762i	−0.146799	−	0.0476978i
$502$	3.73926	−	23.6088i	0.166891	−	1.05371i
$503$	3.02441	+	19.0954i	0.134852	+	0.851421i	0.958660	+	0.284553i	$0.0918451\pi$
$503$	3.02441	+	19.0954i	0.134852	+	0.851421i	−0.823808	+	0.566868i	$0.808155\pi$
$504$	25.0960	−	8.15419i	1.11787	−	0.363217i
$505$	6.18781	+	29.0681i	0.275354	+	1.29351i
$506$		0			0
$507$	−7.14801	−	7.14801i	−0.317454	−	0.317454i
$508$	−0.0784471	+	0.153961i	−0.00348053	+	0.00683092i
$509$	1.65845	−	2.28267i	0.0735097	−	0.101177i	−0.770679	−	0.637224i	$-0.780083\pi$
$509$	1.65845	−	2.28267i	0.0735097	−	0.101177i	0.844189	+	0.536046i	$0.180083\pi$
$510$	5.25324	−	0.276906i	0.232618	−	0.0122616i
$511$	7.11276	−	21.8908i	0.314650	−	0.968393i
$512$	−8.90156	−	17.4703i	−0.393397	−	0.772085i
$513$	−23.7017	−	3.75398i	−1.04645	−	0.165742i
$514$	19.2177	+	13.9625i	0.847656	+	0.615858i
$515$	−21.7784	−	5.82845i	−0.959673	−	0.256832i
$516$		−	0.886635i		−	0.0390319i
$517$		0			0
$518$	−21.5550	+	21.5550i	−0.947071	+	0.947071i
$519$	1.11382	+	3.42798i	0.0488912	+	0.150472i
$520$	−2.28289	+	5.13164i	−0.100111	+	0.225037i
$521$	−7.68839	+	5.58594i	−0.336835	+	0.244725i	−0.743325	−	0.668930i	$-0.766752\pi$
$521$	−7.68839	+	5.58594i	−0.336835	+	0.244725i	0.406491	+	0.913655i	$0.366752\pi$
$522$	3.01884	−	1.53818i	0.132131	−	0.0673241i
$523$	13.2194	−	6.73563i	0.578045	−	0.294528i	−0.140420	−	0.990092i	$-0.544845\pi$
$523$	13.2194	−	6.73563i	0.578045	−	0.294528i	0.718465	+	0.695564i	$0.244845\pi$
$524$	1.74248	−	1.26599i	0.0761207	−	0.0553049i
$525$	−3.63757	+	17.1645i	−0.158756	+	0.749121i
$526$	0.434277	+	1.33657i	0.0189354	+	0.0582771i
$527$	0.577895	−	0.577895i	0.0251735	−	0.0251735i
$528$		0			0
$529$			15.3169i			0.665953i
$530$	25.7763	−	14.8924i	1.11965	−	0.646883i
$531$	17.3757	+	12.6242i	0.754039	+	0.547842i
$532$	3.37007	+	0.533767i	0.146111	+	0.0231417i
$533$	0.242681	+	0.476289i	0.0105117	+	0.0206304i
$534$	−5.25369	+	16.1692i	−0.227349	+	0.699709i
$535$	0.725838	+	13.7700i	0.0313807	+	0.595329i
$536$	6.89134	−	9.48511i	0.297661	−	0.409695i
$537$	−1.40577	+	2.75897i	−0.0606633	+	0.119058i
$538$	−29.4638	−	29.4638i	−1.27027	−	1.27027i
$539$		0			0
$540$	−0.801414	+	1.23489i	−0.0344874	+	0.0531411i
$541$	29.7351	−	9.66153i	1.27841	−	0.415381i	0.410392	−	0.911909i	$-0.365392\pi$
$541$	29.7351	−	9.66153i	1.27841	−	0.415381i	0.868021	+	0.496528i	$0.165392\pi$
$542$	7.05176	+	44.5230i	0.302899	+	1.91243i
$543$	−0.787429	+	4.97163i	−0.0337918	+	0.213353i
$544$	1.54241	+	0.501159i	0.0661303	+	0.0214870i
$545$	4.64239	−	44.2984i	0.198858	−	1.89754i
$546$	2.79899	+	3.85248i	0.119786	+	0.164871i
$547$	31.1772	−	4.93799i	1.33304	−	0.211133i	0.551076	−	0.834455i	$-0.314217\pi$
$547$	31.1772	−	4.93799i	1.33304	−	0.211133i	0.781966	+	0.623322i	$0.214217\pi$
$548$	−1.64270	−	0.836995i	−0.0701725	−	0.0357547i
$549$	17.9525			0.766194
$550$		0			0
$551$	−5.44169			−0.231824
$552$	−5.57880	−	2.84254i	−0.237449	−	0.120987i
$553$	9.51017	−	1.50626i	0.404414	−	0.0640528i
$554$	25.9779	+	35.7555i	1.10370	+	1.51911i
$555$	−0.957078	+	9.13259i	−0.0406257	+	0.387657i
$556$	−0.143057	−	0.0464820i	−0.00606696	−	0.00197128i
$557$	−2.07471	+	13.0992i	−0.0879082	+	0.555030i	0.903945	+	0.427648i	$0.140658\pi$
$557$	−2.07471	+	13.0992i	−0.0879082	+	0.555030i	−0.991854	+	0.127383i	$0.959342\pi$
$558$	0.224289	+	1.41610i	0.00949491	+	0.0599485i
$559$	6.29208	−	2.04442i	0.266127	−	0.0864698i
$560$	−21.9403	+	33.8076i	−0.927149	+	1.42863i
$561$		0			0
$562$	8.83073	+	8.83073i	0.372502	+	0.372502i
$563$	−13.3342	+	26.1698i	−0.561968	+	1.10292i	0.418860	+	0.908051i	$0.362430\pi$
$563$	−13.3342	+	26.1698i	−0.561968	+	1.10292i	−0.980828	+	0.194874i	$0.937570\pi$
$564$	−0.0867434	+	0.119392i	−0.00365256	+	0.00502731i
$565$	−1.42682	−	27.0684i	−0.0600266	−	1.13878i
$566$	4.32248	−	13.3032i	0.181687	−	0.559176i
$567$	6.20650	+	12.1809i	0.260648	+	0.511551i
$568$	23.0252	+	3.64683i	0.966115	+	0.153018i
$569$	−17.3540	−	12.6084i	−0.727518	−	0.528573i	0.161259	−	0.986912i	$-0.448445\pi$
$569$	−17.3540	−	12.6084i	−0.727518	−	0.528573i	−0.888777	+	0.458339i	$0.848445\pi$
$570$	12.8343	−	7.41505i	0.537568	−	0.310582i
$571$			28.7176i			1.20179i	0.799326	+	0.600897i	$0.205190\pi$
$571$			28.7176i			1.20179i	−0.799326	+	0.600897i	$0.794810\pi$
$572$		0			0
$573$	−9.74484	+	9.74484i	−0.407097	+	0.407097i
$574$	1.10271	+	3.39380i	0.0460263	+	0.141654i
$575$	−11.6187	+	7.55529i	−0.484534	+	0.315077i
$576$	13.6590	−	9.92385i	0.569125	−	0.413494i
$577$	−5.96290	+	3.03825i	−0.248239	+	0.126484i	−0.573683	−	0.819077i	$-0.694486\pi$
$577$	−5.96290	+	3.03825i	−0.248239	+	0.126484i	0.325445	+	0.945561i	$0.394486\pi$
$578$	−17.3509	+	8.84070i	−0.721700	+	0.367725i
$579$	11.4251	−	8.30081i	0.474810	−	0.344970i
$580$	−0.135689	+	0.305010i	−0.00563417	+	0.0126649i
$581$	−2.59048	−	7.97268i	−0.107471	−	0.330763i
$582$	2.86867	−	2.86867i	0.118910	−	0.118910i
$583$		0			0
$584$		−	14.8165i		−	0.613112i
$585$	−4.61286	−	1.23452i	−0.190718	−	0.0510409i
$586$	2.73660	+	1.98825i	0.113048	+	0.0821340i
$587$	36.0485	+	5.70952i	1.48788	+	0.235657i	0.846839	−	0.531849i	$-0.178503\pi$
$587$	36.0485	+	5.70952i	1.48788	+	0.235657i	0.641041	+	0.767506i	$0.278503\pi$
$588$	0.606512	+	1.19035i	0.0250121	+	0.0490890i
$589$	0.711594	−	2.19006i	0.0293207	−	0.0902400i
$590$	−30.4748	+	1.60637i	−1.25463	+	0.0661333i
$591$	6.66825	−	9.17805i	0.274295	−	0.377535i
$592$	−9.57587	+	18.7937i	−0.393566	+	0.772417i
$593$	−26.6656	−	26.6656i	−1.09502	−	1.09502i	−0.994983	−	0.100040i	$-0.968103\pi$
$593$	−26.6656	−	26.6656i	−1.09502	−	1.09502i	−0.100040	−	0.994983i	$-0.531897\pi$
$594$		0			0
$595$	3.78328	+	17.7724i	0.155099	+	0.728599i
$596$	0.172988	−	0.0562073i	0.00708588	−	0.00230234i
$597$	2.52857	+	15.9648i	0.103487	+	0.653394i
$598$	−0.588412	+	3.71509i	−0.0240620	+	0.151921i
$599$	−36.7124	−	11.9286i	−1.50003	−	0.487388i	−0.560002	−	0.828492i	$-0.689199\pi$
$599$	−36.7124	−	11.9286i	−1.50003	−	0.487388i	−0.940026	+	0.341103i	$0.889199\pi$
$600$	1.18739	+	11.2318i	0.0484749	+	0.458536i
$601$	−22.4050	−	30.8379i	−0.913920	−	1.25790i	−0.965810	−	0.259250i	$-0.916525\pi$
$601$	−22.4050	−	30.8379i	−0.913920	−	1.25790i	0.0518905	−	0.998653i	$-0.483475\pi$
$602$	43.6213	−	6.90894i	1.77787	−	0.281587i
$603$	8.88156	+	4.52538i	0.361685	+	0.184288i
$604$	−0.236459			−0.00962138
$605$		0			0
$606$	16.2198			0.658884
$607$	−32.2834	−	16.4492i	−1.31034	−	0.667653i	−0.347491	−	0.937683i	$-0.612966\pi$
$607$	−32.2834	−	16.4492i	−1.31034	−	0.667653i	−0.962852	+	0.270031i	$0.912966\pi$
$608$	4.51336	−	0.714845i	0.183041	−	0.0289908i
$609$	−2.06640	−	2.84415i	−0.0837346	−	0.115251i
$610$	−19.8190	+	16.0590i	−0.802447	+	0.650211i
$611$	−1.04729	−	0.340286i	−0.0423689	−	0.0137665i
$612$	−0.103676	+	0.654587i	−0.00419087	+	0.0264601i
$613$	0.376892	+	2.37960i	0.0152225	+	0.0961113i	0.994130	−	0.108194i	$-0.0345066\pi$
$613$	0.376892	+	2.37960i	0.0152225	+	0.0961113i	−0.978907	+	0.204305i	$0.934507\pi$
$614$	−24.5743	+	7.98466i	−0.991736	+	0.322235i
$615$	0.901696	+	0.585180i	0.0363599	+	0.0235967i
$616$		0			0
$617$	−25.5598	−	25.5598i	−1.02900	−	1.02900i	−0.999567	−	0.0294325i	$-0.990630\pi$
$617$	−25.5598	−	25.5598i	−1.02900	−	1.02900i	−0.0294325	−	0.999567i	$-0.509370\pi$
$618$	−5.58599	+	10.9631i	−0.224701	+	0.441001i
$619$	0.537145	−	0.739317i	0.0215897	−	0.0297157i	−0.798086	−	0.602544i	$-0.794154\pi$
$619$	0.537145	−	0.739317i	0.0215897	−	0.0297157i	0.819675	+	0.572828i	$0.194154\pi$
$620$	−0.105011	−	0.0944946i	−0.00421734	−	0.00379499i
$621$	3.78415	−	11.6464i	0.151853	−	0.467355i
$622$	10.0585	+	19.7409i	0.403310	+	0.791540i
$623$	−58.0020	−	9.18661i	−2.32380	−	0.368054i
$624$	2.66569	+	1.93674i	0.106713	+	0.0775316i
$625$	22.8509	+	10.1407i	0.914038	+	0.405630i
$626$			38.2851i			1.53018i
$627$		0			0
$628$	−0.781786	+	0.781786i	−0.0311967	+	0.0311967i
$629$	2.93865	+	9.04423i	0.117172	+	0.360617i
$630$	−29.1253	−	12.9569i	−1.16038	−	0.516214i
$631$	−18.6941	+	13.5820i	−0.744199	+	0.540692i	−0.894023	−	0.448020i	$-0.852129\pi$
$631$	−18.6941	+	13.5820i	−0.744199	+	0.540692i	0.149824	+	0.988713i	$0.452129\pi$
$632$	5.52255	−	2.81388i	0.219675	−	0.111930i
$633$	4.74042	−	2.41536i	0.188415	−	0.0960020i
$634$	33.5956	−	24.4087i	1.33425	−	0.969392i
$635$	−2.42030	+	0.929906i	−0.0960465	+	0.0369022i
$636$	−0.348145	−	1.07148i	−0.0138049	−	0.0424870i
$637$	−7.04889	+	7.04889i	−0.279287	+	0.279287i
$638$		0			0
$639$			19.8201i			0.784072i
$640$	−7.17458	+	26.8084i	−0.283600	+	1.05969i
$641$	−7.06172	−	5.13064i	−0.278921	−	0.202648i	0.439525	−	0.898230i	$-0.355147\pi$
$641$	−7.06172	−	5.13064i	−0.278921	−	0.202648i	−0.718447	+	0.695582i	$0.755147\pi$
$642$	7.43296	+	1.17727i	0.293356	+	0.0464630i
$643$	14.3186	+	28.1018i	0.564670	+	1.10823i	0.980082	+	0.198594i	$0.0636376\pi$
$643$	14.3186	+	28.1018i	0.564670	+	1.10823i	−0.415412	+	0.909634i	$0.636362\pi$
$644$	−0.538058	+	1.65597i	−0.0212024	+	0.0652544i
$645$	8.89912	−	9.88950i	0.350403	−	0.389399i
$646$	9.02265	−	12.4186i	0.354991	−	0.488604i
$647$	6.23845	−	12.2437i	0.245259	−	0.481348i	−0.735257	−	0.677789i	$-0.762938\pi$
$647$	6.23845	−	12.2437i	0.245259	−	0.481348i	0.980516	+	0.196441i	$0.0629384\pi$
$648$	6.22265	+	6.22265i	0.244449	+	0.244449i
$649$		0			0
$650$	6.19675	−	2.76347i	0.243057	−	0.108392i
$651$	1.41487	−	0.459720i	0.0554532	−	0.0180178i
$652$	−0.359211	−	2.26797i	−0.0140678	−	0.0888205i
$653$	−0.851181	+	5.37414i	−0.0333093	+	0.210307i	−0.998730	−	0.0503921i	$-0.983953\pi$
$653$	−0.851181	+	5.37414i	−0.0333093	+	0.210307i	0.965420	+	0.260699i	$0.0839529\pi$
$654$	−23.1192	−	7.51187i	−0.904030	−	0.293737i
$655$	32.1423	+	3.36845i	1.25590	+	0.131616i
$656$	1.45134	+	1.99759i	0.0566652	+	0.0779929i
$657$	12.4420	−	1.97062i	0.485408	−	0.0768812i
$658$	−6.54987	−	3.33733i	−0.255341	−	0.130102i
$659$	42.1160			1.64061			0.820304	−	0.571928i	$-0.193805\pi$
$659$	42.1160			1.64061			0.820304	+	0.571928i	$0.193805\pi$
$660$		0			0
$661$	−19.5844			−0.761745			−0.380872	−	0.924628i	$-0.624376\pi$
$661$	−19.5844			−0.761745			−0.380872	+	0.924628i	$0.624376\pi$
$662$	32.1913	+	16.4023i	1.25115	+	0.637493i
$663$	1.46726	−	0.232390i	0.0569835	−	0.00902529i
$664$	−3.17181	−	4.36562i	−0.123090	−	0.169419i
$665$	32.2323	+	39.7789i	1.24991	+	1.54256i
$666$	−15.8666	−	5.15536i	−0.614817	−	0.199766i
$667$	0.434404	−	2.74272i	0.0168202	−	0.106198i
$668$	0.0967487	+	0.610847i	0.00374332	+	0.0236344i
$669$	11.2385	−	3.65162i	0.434507	−	0.141180i
$670$	−13.8530	+	2.94894i	−0.535189	+	0.113927i
$671$		0			0
$672$	2.08750	+	2.08750i	0.0805269	+	0.0805269i
$673$	2.51797	−	4.94179i	0.0970605	−	0.190492i	−0.837371	−	0.546635i	$-0.815908\pi$
$673$	2.51797	−	4.94179i	0.0970605	−	0.190492i	0.934431	+	0.356143i	$0.115908\pi$
$674$	26.7253	−	36.7842i	1.02942	−	1.41687i
$675$	−21.3335	+	5.73014i	−0.821126	+	0.220553i
$676$	−0.559191	+	1.72101i	−0.0215073	+	0.0661928i
$677$	1.05927	+	2.07893i	0.0407110	+	0.0798999i	0.910466	−	0.413584i	$-0.135723\pi$
$677$	1.05927	+	2.07893i	0.0407110	+	0.0798999i	−0.869755	+	0.493484i	$0.835723\pi$
$678$	−14.6114	−	2.31421i	−0.561146	−	0.0888767i
$679$	11.3369	+	8.23673i	0.435070	+	0.316097i
$680$	5.85139	+	10.1278i	0.224391	+	0.388384i
$681$			6.89132i			0.264076i
$682$		0			0
$683$	−25.0400	+	25.0400i	−0.958127	+	0.958127i	−0.999158	−	0.0410307i	$-0.986936\pi$
$683$	−25.0400	+	25.0400i	−0.958127	+	0.958127i	0.0410307	+	0.999158i	$0.486936\pi$
$684$	0.577053	+	1.77599i	0.0220642	+	0.0679066i
$685$	−9.92168	−	25.8235i	−0.379088	−	0.986665i
$686$	−18.8423	+	13.6897i	−0.719401	+	0.522676i
$687$	14.5376	−	7.40730i	0.554646	−	0.282606i
$688$	27.2288	−	13.8738i	1.03809	−	0.528933i
$689$	6.80110	−	4.94129i	0.259101	−	0.188248i
$690$	2.71278	+	7.06065i	0.103274	+	0.268794i
$691$	−0.556172	−	1.71172i	−0.0211578	−	0.0651170i	0.939920	−	0.341394i	$-0.110899\pi$
$691$	−0.556172	−	1.71172i	−0.0211578	−	0.0651170i	−0.961078	+	0.276277i	$0.910899\pi$
$692$	0.456241	−	0.456241i	0.0173437	−	0.0173437i
$693$		0			0
$694$		−	44.2510i		−	1.67974i
$695$	−1.12911	−	1.95431i	−0.0428297	−	0.0741314i
$696$	−1.83081	−	1.33016i	−0.0693967	−	0.0504196i
$697$	1.09952	+	0.174147i	0.0416473	+	0.00659628i
$698$	−14.2205	−	27.9094i	−0.538255	−	1.05638i
$699$	0.955200	−	2.93980i	0.0361290	−	0.111194i
$700$	3.03335	−	0.814752i	0.114650	−	0.0307947i
$701$	−10.4715	+	14.4128i	−0.395502	+	0.544362i	−0.959608	−	0.281340i	$-0.909221\pi$
$701$	−10.4715	+	14.4128i	−0.395502	+	0.544362i	0.564106	+	0.825703i	$0.309221\pi$
$702$	−2.72174	+	5.34171i	−0.102725	+	0.201610i
$703$	18.9468	+	18.9468i	0.714593	+	0.714593i
$704$		0			0
$705$	−2.16587	+	0.461055i	−0.0815713	+	0.0173643i
$706$	5.57255	−	1.81063i	0.209726	−	0.0681440i
$707$	8.76432	+	55.3357i	0.329616	+	2.08111i
$708$	−0.180671	+	1.14071i	−0.00679003	+	0.0428706i
$709$	−9.55567	−	3.10483i	−0.358871	−	0.116604i	0.124032	−	0.992278i	$-0.460417\pi$
$709$	−9.55567	−	3.10483i	−0.358871	−	0.116604i	−0.482903	+	0.875674i	$0.660417\pi$
$710$	−17.7297	−	21.8808i	−0.665383	−	0.821171i
$711$	3.09743	+	4.26324i	0.116163	+	0.159884i
$712$	−37.3365	+	5.91351i	−1.39924	+	0.221618i
$713$	1.04703	+	0.533487i	0.0392115	+	0.0199793i
$714$	9.91691			0.371131
$715$		0			0
$716$	0.554298			0.0207151
$717$	2.38314	+	1.21427i	0.0890001	+	0.0453478i
$718$	15.5509	−	2.46302i	0.580355	−	0.0919193i
$719$	4.03181	+	5.54931i	0.150361	+	0.206954i	0.877553	−	0.479480i	$-0.159175\pi$
$719$	4.03181	+	5.54931i	0.150361	+	0.206954i	−0.727191	+	0.686435i	$0.759175\pi$
$720$	−21.9371	−	2.29897i	−0.817548	−	0.0856774i
$721$	−40.4204	−	13.1334i	−1.50533	−	0.489113i
$722$	2.40884	−	15.2088i	0.0896478	−	0.566014i
$723$	−3.30933	−	20.8943i	−0.123075	−	0.777067i
$724$	0.856964	−	0.278444i	0.0318488	−	0.0103483i
$725$	−4.57485	+	2.04017i	−0.169906	+	0.0757702i
$726$		0			0
$727$	−25.2212	−	25.2212i	−0.935401	−	0.935401i	0.0626351	−	0.998036i	$-0.480050\pi$
$727$	−25.2212	−	25.2212i	−0.935401	−	0.935401i	−0.998036	+	0.0626351i	$0.980050\pi$
$728$	−4.80685	+	9.43398i	−0.178154	+	0.349647i
$729$	2.08750	−	2.87320i	0.0773149	−	0.106415i
$730$	−11.9728	+	13.3052i	−0.443132	+	0.492448i
$731$	4.25759	−	13.1035i	0.157473	−	0.484651i
$732$	0.438272	+	0.860158i	0.0161990	+	0.0317924i
$733$	7.61562	+	1.20620i	0.281289	+	0.0445519i	0.295485	−	0.955347i	$-0.404519\pi$
$733$	7.61562	+	1.20620i	0.281289	+	0.0445519i	−0.0141956	+	0.999899i	$0.504519\pi$
$734$	−41.0401	−	29.8174i	−1.51482	−	1.10058i
$735$	−5.18245	+	19.3646i	−0.191157	+	0.714275i
$736$			2.33188i			0.0859543i
$737$		0			0
$738$	−1.38095	+	1.38095i	−0.0508336	+	0.0508336i
$739$	−12.6089	−	38.8062i	−0.463825	−	1.42751i	−0.860454	−	0.509528i	$-0.829820\pi$
$739$	−12.6089	−	38.8062i	−0.463825	−	1.42751i	0.396629	−	0.917979i	$-0.370180\pi$
$740$	1.53442	−	0.589542i	0.0564064	−	0.0216720i
$741$	3.38633	−	2.46031i	0.124400	−	0.0903819i
$742$	50.0027	−	25.4776i	1.83566	−	0.935313i
$743$	−39.5290	+	20.1411i	−1.45018	+	0.738904i	−0.988932	−	0.148368i	$-0.952598\pi$
$743$	−39.5290	+	20.1411i	−1.45018	+	0.738904i	−0.461248	+	0.887271i	$0.652598\pi$
$744$	0.774746	−	0.562886i	0.0284036	−	0.0206364i
$745$	2.49366	+	1.10934i	0.0913605	+	0.0406432i
$746$	6.34530	+	19.5288i	0.232318	+	0.715001i
$747$	3.24412	−	3.24412i	0.118696	−	0.118696i
$748$		0			0
$749$			25.9946i			0.949821i
$750$	8.00978	−	11.0456i	0.292476	−	0.403329i
$751$	10.6518	+	7.73896i	0.388688	+	0.282399i	0.764918	−	0.644128i	$-0.222780\pi$
$751$	10.6518	+	7.73896i	0.388688	+	0.282399i	−0.376229	+	0.926527i	$0.622780\pi$
$752$	−5.02390	−	0.795708i	−0.183203	−	0.0290165i
$753$	−6.16240	−	12.0944i	−0.224570	−	0.440744i
$754$	−0.420104	+	1.29295i	−0.0152993	+	0.0470864i
$755$	−2.63746	−	2.37333i	−0.0959869	−	0.0863743i
$756$	−1.63123	+	2.24520i	−0.0593274	+	0.0816571i
$757$	9.02166	−	17.7060i	0.327898	−	0.643535i	−0.666929	−	0.745121i	$-0.732392\pi$
$757$	9.02166	−	17.7060i	0.327898	−	0.643535i	0.994827	+	0.101586i	$0.0323916\pi$
$758$	−27.4703	−	27.4703i	−0.997768	−	0.997768i
$759$		0			0
$760$	27.6455	+	17.9413i	1.00281	+	0.650799i
$761$	−16.8706	+	5.48158i	−0.611558	+	0.198707i	−0.598389	−	0.801206i	$-0.704192\pi$
$761$	−16.8706	+	5.48158i	−0.611558	+	0.198707i	−0.0131694	+	0.999913i	$0.504192\pi$
$762$	0.221363	+	1.39763i	0.00801914	+	0.0506309i
$763$	13.1353	−	82.9328i	0.475528	−	3.00237i
$764$	2.34625	+	0.762341i	0.0848842	+	0.0275805i
$765$	−7.72647	+	6.26065i	−0.279351	+	0.226354i
$766$	20.7124	+	28.5082i	0.748371	+	1.03004i
$767$	−8.51175	+	1.34813i	−0.307342	+	0.0486781i
$768$	2.63847	+	1.34437i	0.0952076	+	0.0485107i
$769$	−33.4001			−1.20444			−0.602218	−	0.798331i	$-0.705716\pi$
$769$	−33.4001			−1.20444			−0.602218	+	0.798331i	$0.705716\pi$
$770$		0			0
$771$	13.4894			0.485810
$772$	−2.25247	−	1.14769i	−0.0810683	−	0.0413064i
$773$	−37.6915	+	5.96974i	−1.35567	+	0.214717i	−0.791614	−	0.611021i	$-0.790759\pi$
$773$	−37.6915	+	5.96974i	−1.35567	+	0.214717i	−0.564054	+	0.825738i	$0.690759\pi$
$774$	14.2073	+	19.5547i	0.510671	+	0.702878i
$775$	−0.222849	−	2.10798i	−0.00800496	−	0.0757208i
$776$	8.57893	+	2.78746i	0.307966	+	0.100064i
$777$	−2.70797	+	17.0975i	−0.0971480	+	0.613369i
$778$	1.73036	+	10.9251i	0.0620365	+	0.391683i
$779$	2.98315	−	0.969285i	0.106882	−	0.0347282i
$780$	−0.0534639	−	0.251154i	−0.00191432	−	0.00899276i
$781$		0			0
$782$	5.53895	+	5.53895i	0.198072	+	0.198072i
$783$	2.00936	−	3.94360i	0.0718088	−	0.140933i
$784$	−27.0654	+	37.2523i	−0.966621	+	1.33044i
$785$	−16.5668	+	0.873259i	−0.591293	+	0.0311680i
$786$	5.45050	−	16.7749i	0.194413	−	0.598341i
$787$	−16.6820	−	32.7403i	−0.594649	−	1.16706i	−0.970662	−	0.240450i	$-0.922705\pi$
$787$	−16.6820	−	32.7403i	−0.594649	−	1.16706i	0.376013	−	0.926614i	$-0.377295\pi$
$788$	−2.00581	−	0.317689i	−0.0714541	−	0.0113172i
$789$	0.645642	+	0.469086i	0.0229855	+	0.0166999i
$790$	−7.23305	−	1.93574i	−0.257340	−	0.0688706i
$791$		−	51.0989i		−	1.81687i
$792$		0			0
$793$	−5.09361	+	5.09361i	−0.180879	+	0.180879i
$794$	−10.3140	−	31.7434i	−0.366032	−	1.12653i
$795$	6.87122	−	15.4456i	0.243697	−	0.547799i
$796$	2.34087	−	1.70074i	0.0829700	−	0.0602812i
$797$	17.9460	−	9.14395i	0.635680	−	0.323895i	−0.106283	−	0.994336i	$-0.533895\pi$
$797$	17.9460	−	9.14395i	0.635680	−	0.323895i	0.741963	+	0.670441i	$0.233895\pi$
$798$	24.8968	−	12.6855i	0.881337	−	0.449063i
$799$	−1.85529	+	1.34795i	−0.0656355	+	0.0476870i
$800$	3.52638	−	2.29310i	0.124676	−	0.0810733i
$801$	−9.93160	−	30.5663i	−0.350916	−	1.08001i
$802$	25.0253	−	25.0253i	0.883674	−	0.883674i
$803$		0			0
$804$			0.536020i			0.0189040i
$805$	−22.6224	+	13.0702i	−0.797335	+	0.460663i
$806$	−0.465424	−	0.338150i	−0.0163939	−	0.0119108i
$807$	−23.3708	−	3.70156i	−0.822690	−	0.130301i
$808$	16.3728	+	32.1334i	0.575993	+	1.13045i
$809$	−16.0484	+	49.3920i	−0.564233	+	1.73653i	0.105987	+	0.994367i	$0.466200\pi$
$809$	−16.0484	+	49.3920i	−0.564233	+	1.73653i	−0.670220	+	0.742162i	$0.733800\pi$
$810$	−0.559599	−	10.6163i	−0.0196623	−	0.373017i
$811$	23.0252	−	31.6914i	0.808523	−	1.11284i	−0.183027	−	0.983108i	$-0.558590\pi$
$811$	23.0252	−	31.6914i	0.808523	−	1.11284i	0.991550	−	0.129728i	$-0.0414104\pi$
$812$	−0.285706	+	0.560729i	−0.0100263	+	0.0196777i
$813$	18.1009	+	18.1009i	0.634826	+	0.634826i
$814$		0			0
$815$	18.7569	−	28.9022i	0.657025	−	1.01240i
$816$	6.52607	−	2.12045i	0.228458	−	0.0742306i
$817$	−6.07296	−	38.3431i	−0.212466	−	1.34146i
$818$	1.34290	−	8.47873i	0.0469533	−	0.296452i
$819$	−8.56139	−	2.78176i	−0.299159	−	0.0972027i
$820$	0.0200559	−	0.191377i	0.000700382	−	0.00668316i
$821$	14.6926	+	20.2226i	0.512775	+	0.705774i	0.984384	−	0.176034i	$-0.0563268\pi$
$821$	14.6926	+	20.2226i	0.512775	+	0.705774i	−0.471609	+	0.881808i	$0.656327\pi$
$822$	−14.9121	+	2.36185i	−0.520120	+	0.0823789i
$823$	−20.4719	−	10.4310i	−0.713606	−	0.363600i	0.0591972	−	0.998246i	$-0.481146\pi$
$823$	−20.4719	−	10.4310i	−0.713606	−	0.363600i	−0.772803	+	0.634646i	$0.781146\pi$
$824$	−27.3580			−0.953062
$825$		0			0
$826$	−57.5294			−2.00170
$827$	4.93382	+	2.51391i	0.171566	+	0.0874171i	0.537664	−	0.843159i	$-0.319307\pi$
$827$	4.93382	+	2.51391i	0.171566	+	0.0874171i	−0.366099	+	0.930576i	$0.619307\pi$
$828$	−0.941197	+	0.149071i	−0.0327089	+	0.00518057i
$829$	−8.80126	−	12.1139i	−0.305680	−	0.420733i	0.628348	−	0.777933i	$-0.283732\pi$
$829$	−8.80126	−	12.1139i	−0.305680	−	0.420733i	−0.934028	+	0.357200i	$0.883732\pi$
$830$	−0.679443	+	6.48336i	−0.0235838	+	0.225041i
$831$	23.8694	+	7.75564i	0.828020	+	0.269040i
$832$	−1.05976	+	6.69109i	−0.0367407	+	0.231972i
$833$	3.24759	+	20.5045i	0.112522	+	0.710439i
$834$	−1.17153	+	0.380652i	−0.0405666	+	0.0131809i
$835$	−5.05192	+	7.78443i	−0.174829	+	0.269391i
$836$		0			0
$837$	1.32438	+	1.32438i	0.0457773	+	0.0457773i
$838$	−7.36068	+	14.4461i	−0.254270	+	0.499034i
$839$	7.40356	−	10.1901i	0.255599	−	0.351802i	−0.661863	−	0.749625i	$-0.730234\pi$
$839$	7.40356	−	10.1901i	0.255599	−	0.351802i	0.917462	+	0.397823i	$0.130234\pi$
$840$	1.12076	+	21.2621i	0.0386698	+	0.733612i
$841$	−8.65134	+	26.6261i	−0.298322	+	0.918141i
$842$	5.23975	+	10.2836i	0.180574	+	0.354396i
$843$	7.00457	+	1.10941i	0.241250	+	0.0382103i
$844$	−0.770496	−	0.559798i	−0.0265216	−	0.0192691i
$845$	−23.5109	+	13.5835i	−0.808801	+	0.467288i
$846$		−	4.02315i		−	0.138319i
$847$		0			0
$848$	27.4579	−	27.4579i	0.942907	−	0.942907i
$849$	−2.45461	−	7.55451i	−0.0842420	−	0.259270i
$850$	2.92944	−	13.8231i	0.100479	−	0.474128i
$851$	−11.0621	+	8.03706i	−0.379203	+	0.275507i
$852$	−0.949642	+	0.483867i	−0.0325342	+	0.0165770i
$853$	44.3481	−	22.5965i	1.51845	−	0.773689i	0.521614	−	0.853181i	$-0.325330\pi$
$853$	44.3481	−	22.5965i	1.51845	−	0.773689i	0.996835	+	0.0794926i	$0.0253300\pi$
$854$	−38.9035	+	28.2651i	−1.33125	+	0.967211i
$855$	−11.3891	+	25.6012i	−0.389498	+	0.875541i
$856$	5.17078	+	15.9140i	0.176734	+	0.543930i
$857$	21.2860	−	21.2860i	0.727117	−	0.727117i	−0.242927	−	0.970044i	$-0.578108\pi$
$857$	21.2860	−	21.2860i	0.727117	−	0.727117i	0.970044	+	0.242927i	$0.0781077\pi$
$858$		0			0
$859$		−	9.31402i		−	0.317790i	−0.987295	−	0.158895i	$-0.949207\pi$
$859$		−	9.31402i		−	0.317790i	0.987295	−	0.158895i	$-0.0507932\pi$
$860$	−2.30059	−	0.615694i	−0.0784494	−	0.0209950i
$861$	1.63941	+	1.19110i	0.0558709	+	0.0405926i
$862$	−10.5740	−	1.67475i	−0.360151	−	0.0570424i
$863$	−16.0664	−	31.5320i	−0.546905	−	1.07336i	−0.984695	−	0.174285i	$-0.944239\pi$
$863$	−16.0664	−	31.5320i	−0.546905	−	1.07336i	0.437790	−	0.899077i	$-0.355761\pi$
$864$	−1.14852	+	3.53479i	−0.0390735	+	0.120256i
$865$	9.66817	−	0.509623i	0.328727	−	0.0173277i
$866$	−4.34927	+	5.98625i	−0.147794	+	0.203421i
$867$	−5.02038	+	9.85305i	−0.170501	+	0.334627i
$868$	−0.188310	−	0.188310i	−0.00639166	−	0.00639166i
$869$		0			0
$870$	0.569202	+	2.67390i	0.0192978	+	0.0906538i
$871$	−3.80391	+	1.23597i	−0.128891	+	0.0418791i
$872$	−8.45531	−	53.3847i	−0.286333	−	1.80783i
$873$	−1.19973	+	7.57478i	−0.0406046	+	0.256368i
$874$	20.9911	+	6.82042i	0.710034	+	0.230704i
$875$	42.0115	+	21.3579i	1.42025	+	0.722027i
$876$	0.398163	+	0.548025i	0.0134527	+	0.0185160i
$877$	−21.5902	+	3.41955i	−0.729048	+	0.115470i	−0.509915	−	0.860225i	$-0.670323\pi$
$877$	−21.5902	+	3.41955i	−0.729048	+	0.115470i	−0.219133	+	0.975695i	$0.570323\pi$
$878$	−1.69512	−	0.863707i	−0.0572076	−	0.0291487i
$879$	1.92089			0.0647901
$880$		0			0
$881$	46.4810			1.56599			0.782993	−	0.622031i	$-0.213692\pi$
$881$	46.4810			1.56599			0.782993	+	0.622031i	$0.213692\pi$
$882$	−32.4505	−	16.5344i	−1.09267	−	0.556741i
$883$	27.5798	−	4.36822i	0.928135	−	0.147002i	0.325976	−	0.945378i	$-0.394307\pi$
$883$	27.5798	−	4.36822i	0.928135	−	0.147002i	0.602159	+	0.798376i	$0.294307\pi$
$884$	−0.156308	−	0.215140i	−0.00525721	−	0.00723593i
$885$	−13.4645	+	10.9101i	−0.452603	+	0.366738i
$886$	−21.4719	−	6.97665i	−0.721363	−	0.234385i
$887$	−1.10133	+	6.95351i	−0.0369790	+	0.233476i	−0.999255	−	0.0385999i	$-0.987710\pi$
$887$	−1.10133	+	6.95351i	−0.0369790	+	0.233476i	0.962276	+	0.272076i	$0.0877102\pi$
$888$	1.74315	+	11.0058i	0.0584963	+	0.369331i
$889$	−4.64858	+	1.51041i	−0.155908	+	0.0506577i
$890$	38.3066	+	24.8601i	1.28404	+	0.833313i
$891$		0			0
$892$	−1.49577	−	1.49577i	−0.0500822	−	0.0500822i
$893$	−2.93351	+	5.75734i	−0.0981662	+	0.192662i
$894$	0.875532	−	1.20507i	0.0292822	−	0.0403035i
$895$	6.18263	+	5.56347i	0.206662	+	0.185966i
$896$	−16.1666	+	49.7558i	−0.540090	+	1.66223i
$897$	0.969718	+	1.90318i	0.0323780	+	0.0635453i
$898$	17.5527	+	2.78007i	0.585740	+	0.0927721i
$899$	0.343606	+	0.249644i	0.0114599	+	0.00832611i
$900$	1.15098	+	1.27673i	0.0383658	+	0.0425577i
$901$		−	17.5071i		−	0.583247i
$902$		0			0
$903$	17.7343	−	17.7343i	0.590160	−	0.590160i
$904$	−10.1645	−	31.2830i	−0.338065	−	1.04046i
$905$	12.3533	+	5.49555i	0.410637	+	0.182678i
$906$	−1.56659	+	1.13820i	−0.0520466	+	0.0378141i
$907$	−26.3281	+	13.4148i	−0.874211	+	0.445433i	−0.832712	−	0.553706i	$-0.813213\pi$
$907$	−26.3281	+	13.4148i	−0.874211	+	0.445433i	−0.0414984	+	0.999139i	$0.513213\pi$
$908$	1.09916	−	0.560050i	0.0364769	−	0.0185859i
$909$	−24.8061	+	18.0227i	−0.822765	+	0.597774i
$910$	11.9398	−	4.58743i	0.395802	−	0.152072i
$911$	5.23886	+	16.1236i	0.173571	+	0.534198i	0.999565	−	0.0294813i	$-0.00938555\pi$
$911$	5.23886	+	16.1236i	0.173571	+	0.534198i	−0.825994	+	0.563679i	$0.809386\pi$
$912$	13.6715	−	13.6715i	0.452709	−	0.452709i
$913$		0			0
$914$			5.14655i			0.170233i
$915$	−3.74490	+	13.9931i	−0.123802	+	0.462598i
$916$	−2.36292	−	1.71676i	−0.0780729	−	0.0567233i
$917$	60.1748	+	9.53075i	1.98715	+	0.314733i
$918$	5.66813	+	11.1243i	0.187076	+	0.367158i
$919$	−1.55222	+	4.77725i	−0.0512030	+	0.157587i	−0.973388	−	0.229161i	$-0.926402\pi$
$919$	−1.55222	+	4.77725i	−0.0512030	+	0.157587i	0.922185	+	0.386748i	$0.126402\pi$
$920$	−11.2497	+	12.5016i	−0.370890	+	0.412166i
$921$	−8.62467	+	11.8708i	−0.284193	+	0.391158i
$922$	3.62937	−	7.12304i	0.119527	−	0.234585i
$923$	−5.62351	−	5.62351i	−0.185100	−	0.185100i
$924$		0			0
$925$	23.0321	+	8.82519i	0.757290	+	0.290170i
$926$	−30.3635	+	9.86569i	−0.997805	+	0.324207i
$927$	−3.63865	−	22.9736i	−0.119509	−	0.754551i
$928$	−0.131845	+	0.832439i	−0.00432804	+	0.0273262i
$929$	−11.2348	−	3.65041i	−0.368602	−	0.119766i	0.118858	−	0.992911i	$-0.462077\pi$
$929$	−11.2348	−	3.65041i	−0.368602	−	0.119766i	−0.487460	+	0.873145i	$0.662077\pi$
$930$	−1.15057	−	0.120578i	−0.0377287	−	0.00395389i
$931$	34.3822	+	47.3231i	1.12683	+	1.55095i
$932$	−0.546524	+	0.0865609i	−0.0179020	+	0.00283540i
$933$	11.2103	+	5.71194i	0.367009	+	0.187001i
$934$	21.5258			0.704346
$935$		0			0
$936$	−5.79466			−0.189405
$937$	2.04229	+	1.04060i	0.0667187	+	0.0339949i	0.487032	−	0.873384i	$-0.338080\pi$
$937$	2.04229	+	1.04060i	0.0667187	+	0.0339949i	−0.420313	+	0.907379i	$0.638080\pi$
$938$	−26.3715	+	4.17683i	−0.861060	+	0.136378i
$939$	12.7791	+	17.5889i	0.417029	+	0.573991i
$940$	0.249555	+	0.307984i	0.00813960	+	0.0100453i
$941$	−1.68653	−	0.547988i	−0.0549794	−	0.0178639i	0.281398	−	0.959591i	$-0.409202\pi$
$941$	−1.68653	−	0.547988i	−0.0549794	−	0.0178639i	−0.336378	+	0.941727i	$0.609202\pi$
$942$	−1.41638	+	8.94264i	−0.0461480	+	0.291367i
$943$	0.250397	+	1.58094i	0.00815404	+	0.0514826i
$944$	−37.8587	+	12.3010i	−1.23219	+	0.400364i
$945$	−40.7297	+	8.67026i	−1.32494	+	0.282043i
$946$		0			0
$947$	−8.63289	−	8.63289i	−0.280531	−	0.280531i	0.552790	−	0.833321i	$-0.313563\pi$
$947$	−8.63289	−	8.63289i	−0.280531	−	0.280531i	−0.833321	+	0.552790i	$0.813563\pi$
$948$	−0.128648	+	0.252485i	−0.00417828	+	0.00820033i
$949$	−2.97101	+	4.08925i	−0.0964431	+	0.132743i
$950$	−10.3278	−	38.4507i	−0.335078	−	1.24751i
$951$	7.28714	−	22.4275i	0.236302	−	0.727262i
$952$	10.0105	+	19.6466i	0.324441	+	0.636752i
$953$	18.2074	+	2.88376i	0.589794	+	0.0934143i	0.444196	−	0.895930i	$-0.353489\pi$
$953$	18.2074	+	2.88376i	0.589794	+	0.0934143i	0.145598	+	0.989344i	$0.453489\pi$
$954$	24.8476	+	18.0528i	0.804470	+	0.584482i
$955$	18.5184	+	32.0523i	0.599240	+	1.03719i
$956$		−	0.478792i		−	0.0154852i
$957$		0			0
$958$	−5.09348	+	5.09348i	−0.164563	+	0.164563i
$959$	−16.1154	−	49.5982i	−0.520395	−	1.60161i
$960$	4.88588	+	12.7166i	0.157691	+	0.410428i
$961$	24.9341	−	18.1157i	0.804327	−	0.584377i
$962$	5.96448	−	3.03906i	0.192303	−	0.0979831i
$963$	−12.6759	+	6.45868i	−0.408474	+	0.208128i
$964$	−3.06368	+	2.22589i	−0.0986743	+	0.0716911i
$965$	−13.6047	−	35.4093i	−0.437950	−	1.13987i
$966$	4.40628	+	13.5611i	0.141770	+	0.436322i
$967$	9.49113	−	9.49113i	0.305214	−	0.305214i	−0.537836	−	0.843050i	$-0.680758\pi$
$967$	9.49113	−	9.49113i	0.305214	−	0.305214i	0.843050	+	0.537836i	$0.180758\pi$
$968$		0			0
$969$		−	8.71697i		−	0.280029i
$970$	−5.45140	−	9.43550i	−0.175034	−	0.302956i
$971$	−41.4379	−	30.1064i	−1.32981	−	0.966161i	−0.999754	−	0.0221983i	$-0.992933\pi$
$971$	−41.4379	−	30.1064i	−1.32981	−	0.966161i	−0.330053	−	0.943963i	$-0.607067\pi$
$972$	−2.34815	−	0.371911i	−0.0753171	−	0.0119291i
$973$	−1.93167	−	3.79111i	−0.0619265	−	0.121538i
$974$	4.86416	−	14.9703i	0.155858	−	0.479681i
$975$	1.92449	−	3.33798i	0.0616329	−	0.106901i
$976$	−19.5578	+	26.9190i	−0.626029	+	0.861655i
$977$	−6.57391	+	12.9020i	−0.210318	+	0.412772i	−0.971933	−	0.235257i	$-0.924407\pi$
$977$	−6.57391	+	12.9020i	−0.210318	+	0.412772i	0.761615	+	0.648030i	$0.224407\pi$
$978$	−13.2967	−	13.2967i	−0.425183	−	0.425183i
$979$		0			0
$980$	3.50981	−	0.747144i	0.112117	−	0.0238666i
$981$	43.7046	−	14.2005i	1.39538	−	0.453386i
$982$	0.746699	+	4.71447i	0.0238281	+	0.150445i
$983$	−9.00238	+	56.8388i	−0.287131	+	1.81288i	0.248734	+	0.968572i	$0.419986\pi$
$983$	−9.00238	+	56.8388i	−0.287131	+	1.81288i	−0.535865	+	0.844304i	$0.680014\pi$
$984$	1.24059	+	0.403091i	0.0395484	+	0.0128501i
$985$	−19.1841	−	23.6758i	−0.611257	−	0.754372i
$986$	1.66413	+	2.29048i	0.0529967	+	0.0729437i
$987$	−4.12308	+	0.653031i	−0.131239	+	0.0207862i
$988$	−0.667621	−	0.340170i	−0.0212399	−	0.0108222i
$989$	19.8105			0.629936
$990$		0			0
$991$	13.1102			0.416458			0.208229	−	0.978080i	$-0.433230\pi$
$991$	13.1102			0.416458			0.208229	+	0.978080i	$0.433230\pi$
$992$	−0.317782	−	0.161918i	−0.0100896	−	0.00514090i
$993$	20.2641	−	3.20952i	0.643062	−	0.101851i
$994$	−31.2055	−	42.9507i	−0.989779	−	1.36231i
$995$	43.1803	+	4.52521i	1.36891	+	0.143459i
$996$	0.234634	+	0.0762372i	0.00743466	+	0.00241567i
$997$	0.352744	−	2.22714i	0.0111715	−	0.0705343i	−0.981473	−	0.191602i	$-0.938632\pi$
$997$	0.352744	−	2.22714i	0.0111715	−	0.0705343i	0.992644	+	0.121068i	$0.0386318\pi$
$998$	−2.05059	−	12.9469i	−0.0649104	−	0.409828i
$999$	−20.7269	+	6.73459i	−0.655772	+	0.213073i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.m.e.457.1		32
5.3	odd	4	inner	605.2.m.e.578.1		32
11.2	odd	10	inner	605.2.m.e.112.1		32
11.3	even	5		605.2.e.b.362.4		32
11.4	even	5		605.2.m.c.602.4		32
11.5	even	5		605.2.m.d.282.4		32
11.6	odd	10		605.2.m.c.282.1		32
11.7	odd	10		605.2.m.d.602.1		32
11.8	odd	10		605.2.e.b.362.13		32
11.9	even	5		55.2.l.a.2.4	✓	32
11.10	odd	2		55.2.l.a.17.4	yes	32
33.20	odd	10		495.2.bj.a.442.1		32
33.32	even	2		495.2.bj.a.127.1		32
44.31	odd	10		880.2.cm.a.497.3		32
44.43	even	2		880.2.cm.a.17.3		32
55.3	odd	20		605.2.e.b.483.13		32
55.8	even	20		605.2.e.b.483.4		32
55.9	even	10		275.2.bm.b.57.1		32
55.13	even	20	inner	605.2.m.e.233.1		32
55.18	even	20		605.2.m.d.118.4		32
55.28	even	20		605.2.m.c.403.4		32
55.32	even	4		275.2.bm.b.193.1		32
55.38	odd	20		605.2.m.d.403.1		32
55.42	odd	20		275.2.bm.b.68.1		32
55.43	even	4		55.2.l.a.28.4	yes	32
55.48	odd	20		605.2.m.c.118.1		32
55.53	odd	20		55.2.l.a.13.4	yes	32
55.54	odd	2		275.2.bm.b.182.1		32
165.53	even	20		495.2.bj.a.343.1		32
165.98	odd	4		495.2.bj.a.28.1		32
220.43	odd	4		880.2.cm.a.193.3		32
220.163	even	20		880.2.cm.a.673.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.2.4	✓	32	11.9	even	5
55.2.l.a.13.4	yes	32	55.53	odd	20
55.2.l.a.17.4	yes	32	11.10	odd	2
55.2.l.a.28.4	yes	32	55.43	even	4
275.2.bm.b.57.1		32	55.9	even	10
275.2.bm.b.68.1		32	55.42	odd	20
275.2.bm.b.182.1		32	55.54	odd	2
275.2.bm.b.193.1		32	55.32	even	4
495.2.bj.a.28.1		32	165.98	odd	4
495.2.bj.a.127.1		32	33.32	even	2
495.2.bj.a.343.1		32	165.53	even	20
495.2.bj.a.442.1		32	33.20	odd	10
605.2.e.b.362.4		32	11.3	even	5
605.2.e.b.362.13		32	11.8	odd	10
605.2.e.b.483.4		32	55.8	even	20
605.2.e.b.483.13		32	55.3	odd	20
605.2.m.c.118.1		32	55.48	odd	20
605.2.m.c.282.1		32	11.6	odd	10
605.2.m.c.403.4		32	55.28	even	20
605.2.m.c.602.4		32	11.4	even	5
605.2.m.d.118.4		32	55.18	even	20
605.2.m.d.282.4		32	11.5	even	5
605.2.m.d.403.1		32	55.38	odd	20
605.2.m.d.602.1		32	11.7	odd	10
605.2.m.e.112.1		32	11.2	odd	10	inner
605.2.m.e.233.1		32	55.13	even	20	inner
605.2.m.e.457.1		32	1.1	even	1	trivial
605.2.m.e.578.1		32	5.3	odd	4	inner
880.2.cm.a.17.3		32	44.43	even	2
880.2.cm.a.193.3		32	220.43	odd	4
880.2.cm.a.497.3		32	44.31	odd	10
880.2.cm.a.673.3		32	220.163	even	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.m (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.30617 - 0.665529i) q^{2} +(-0.822224 + 0.130227i) q^{3} +(0.0875924 + 0.120561i) q^{4} +(-0.233059 + 2.22389i) q^{5} +(1.16064 + 0.377114i) q^{6} +(-0.659422 + 4.16343i) q^{7} +(0.424477 + 2.68004i) q^{8} +(-2.19408 + 0.712899i) q^{9} +(1.78448 - 2.74968i) q^{10} +(-0.0877208 - 0.0877208i) q^{12} +(0.420250 - 0.824787i) q^{13} +(3.63220 - 4.99930i) q^{14} +(-0.0979846 - 1.85889i) q^{15} +(1.32131 - 4.06656i) q^{16} +(-0.875188 - 1.71765i) q^{17} +(3.34030 + 0.529052i) q^{18} +(-4.39439 - 3.19271i) q^{19} +(-0.288528 + 0.166698i) q^{20} -3.50915i q^{21} +(1.95998 - 1.95998i) q^{23} +(-0.698030 - 2.14832i) q^{24} +(-4.89137 - 1.03660i) q^{25} +(-1.09784 + 0.797627i) q^{26} +(3.93640 - 2.00570i) q^{27} +(-0.559706 + 0.285184i) q^{28} +(0.810497 - 0.588860i) q^{29} +(-1.10916 + 2.49324i) q^{30} +(0.131006 + 0.403196i) q^{31} +(-0.594873 + 0.594873i) q^{32} +2.82602i q^{34} +(-9.10532 - 2.43681i) q^{35} +(-0.278132 - 0.202075i) q^{36} +(-4.87226 - 0.771690i) q^{37} +(3.61500 + 7.09483i) q^{38} +(-0.238130 + 0.732888i) q^{39} +(-6.05905 + 0.319381i) q^{40} +(-0.339428 + 0.467182i) q^{41} +(-2.33544 + 4.58356i) q^{42} +(5.05373 + 5.05373i) q^{43} +(-1.07406 - 5.04553i) q^{45} +(-3.86451 + 1.25566i) q^{46} +(-0.186094 - 1.17495i) q^{47} +(-0.556831 + 3.51569i) q^{48} +(-10.2419 - 3.32780i) q^{49} +(5.69909 + 4.60932i) q^{50} +(0.943286 + 1.29832i) q^{51} +(0.136247 - 0.0215795i) q^{52} +(8.09173 + 4.12294i) q^{53} -6.47647 q^{54} -11.4381 q^{56} +(4.02895 + 2.05285i) q^{57} +(-1.45055 + 0.229745i) q^{58} +(-5.47214 - 7.53175i) q^{59} +(0.215526 - 0.174637i) q^{60} +(-7.40093 - 2.40471i) q^{61} +(0.0972215 - 0.613832i) q^{62} +(-1.52128 - 9.60498i) q^{63} +(-6.96021 + 2.26151i) q^{64} +(1.73629 + 1.12681i) q^{65} +(-3.05526 - 3.05526i) q^{67} +(0.130421 - 0.255966i) q^{68} +(-1.35630 + 1.86679i) q^{69} +(10.2714 + 9.24275i) q^{70} +(2.65487 - 8.17086i) q^{71} +(-2.84193 - 5.57761i) q^{72} +(-5.39318 - 0.854195i) q^{73} +(5.85044 + 4.25059i) q^{74} +(4.15679 + 0.215323i) q^{75} -0.809447i q^{76} +(0.798797 - 0.798797i) q^{78} +(-0.705861 - 2.17242i) q^{79} +(8.73564 + 3.88619i) q^{80} +(2.62377 - 1.90628i) q^{81} +(0.754275 - 0.384322i) q^{82} +(-1.77193 + 0.902846i) q^{83} +(0.423065 - 0.307374i) q^{84} +(4.02384 - 1.54601i) q^{85} +(-3.23765 - 9.96446i) q^{86} +(-0.589724 + 0.589724i) q^{87} +13.9313i q^{89} +(-1.95504 + 7.30516i) q^{90} +(3.15682 + 2.29356i) q^{91} +(0.407977 + 0.0646171i) q^{92} +(-0.160224 - 0.314457i) q^{93} +(-0.538893 + 1.65854i) q^{94} +(8.12438 - 9.02854i) q^{95} +(0.411650 - 0.566587i) q^{96} +(1.50922 - 2.96200i) q^{97} +(11.1630 + 11.1630i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{2} - 4 q^{3} - 2 q^{5} + 20 q^{6} + 10 q^{8} + 12 q^{12} + 10 q^{13} + 14 q^{15} - 8 q^{16} + 10 q^{18} + 16 q^{20} - 24 q^{23} + 16 q^{25} + 20 q^{26} - 16 q^{27} - 50 q^{28} - 30 q^{30} - 28 q^{31}+ \cdots - 8 q^{97}+O(q^{100}) \) 32 * q + 10 * q^2 - 4 * q^3 - 2 * q^5 + 20 * q^6 + 10 * q^8 + 12 * q^12 + 10 * q^13 + 14 * q^15 - 8 * q^16 + 10 * q^18 + 16 * q^20 - 24 * q^23 + 16 * q^25 + 20 * q^26 - 16 * q^27 - 50 * q^28 - 30 * q^30 - 28 * q^31 + 10 * q^35 + 24 * q^36 - 8 * q^37 + 10 * q^38 + 50 * q^40 - 40 * q^41 - 10 * q^42 - 28 * q^45 - 60 * q^46 - 28 * q^47 - 54 * q^48 + 50 * q^50 - 20 * q^51 + 50 * q^52 - 24 * q^53 - 80 * q^56 - 30 * q^57 - 50 * q^58 + 34 * q^60 + 60 * q^61 - 100 * q^62 + 30 * q^63 - 8 * q^67 + 30 * q^68 + 30 * q^70 + 24 * q^71 - 80 * q^72 - 50 * q^73 + 34 * q^75 + 60 * q^78 + 98 * q^80 - 12 * q^81 - 10 * q^82 - 90 * q^83 - 30 * q^85 + 100 * q^86 + 20 * q^90 + 20 * q^91 - 68 * q^92 - 8 * q^93 + 40 * q^95 - 8 * q^97

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