LMFDB - Embedded newform 125.2.h.a.104.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(4,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("125.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.h (of order $50$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			104.3
Character	$\chi$	$=$	125.104
Dual form			125.2.h.a.119.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500827 - 1.95059i) q^{2} +(0.261606 - 0.0499040i) q^{3} +(-1.80137 + 0.990311i) q^{4} +(1.92710 - 1.13415i) q^{5} +(-0.228362 - 0.485293i) q^{6} +(0.923406 - 1.27096i) q^{7} +(0.0767024 + 0.0816797i) q^{8} +(-2.72338 + 1.07826i) q^{9} +O(q^{10})$	\(q+(-0.500827 - 1.95059i) q^{2} +(0.261606 - 0.0499040i) q^{3} +(-1.80137 + 0.990311i) q^{4} +(1.92710 - 1.13415i) q^{5} +(-0.228362 - 0.485293i) q^{6} +(0.923406 - 1.27096i) q^{7} +(0.0767024 + 0.0816797i) q^{8} +(-2.72338 + 1.07826i) q^{9} +(-3.17740 - 3.19097i) q^{10} +(-0.0932173 + 0.0239341i) q^{11} +(-0.421829 + 0.348967i) q^{12} +(0.949931 + 2.39925i) q^{13} +(-2.94159 - 1.16466i) q^{14} +(0.447542 - 0.392870i) q^{15} +(-2.08202 + 3.28074i) q^{16} +(1.73598 - 3.15774i) q^{17} +(3.46720 + 4.77219i) q^{18} +(-0.905011 + 4.74424i) q^{19} +(-2.34826 + 3.95145i) q^{20} +(0.178143 - 0.378572i) q^{21} +(0.0933715 + 0.169842i) q^{22} +(3.68536 + 0.231863i) q^{23} +(0.0241419 + 0.0175402i) q^{24} +(2.42742 - 4.37123i) q^{25} +(4.20421 - 3.05454i) q^{26} +(-1.33324 + 0.846097i) q^{27} +(-0.404750 + 3.20393i) q^{28} +(6.92298 + 0.874576i) q^{29} +(-0.990470 - 0.676212i) q^{30} +(-4.99189 - 2.74432i) q^{31} +(7.65526 + 2.48734i) q^{32} +(-0.0231918 + 0.0109132i) q^{33} +(-7.02889 - 1.80471i) q^{34} +(0.338038 - 3.49654i) q^{35} +(3.83800 - 4.63935i) q^{36} +(5.69623 + 3.61494i) q^{37} +(9.70732 - 0.610733i) q^{38} +(0.368240 + 0.580253i) q^{39} +(0.240450 + 0.0704130i) q^{40} +(0.510078 + 8.10746i) q^{41} +(-0.827659 - 0.157884i) q^{42} +(-8.09635 + 2.63066i) q^{43} +(0.144217 - 0.135428i) q^{44} +(-4.02531 + 5.16664i) q^{45} +(-1.39346 - 7.30476i) q^{46} +(-1.33773 + 1.42454i) q^{47} +(-0.380947 + 0.962163i) q^{48} +(1.40046 + 4.31017i) q^{49} +(-9.74220 - 2.54567i) q^{50} +(0.296559 - 0.912716i) q^{51} +(-4.08718 - 3.38121i) q^{52} +(-5.06219 - 2.38209i) q^{53} +(2.31811 + 2.17685i) q^{54} +(-0.152494 + 0.151846i) q^{55} +(0.174639 - 0.0220620i) q^{56} +1.28628i q^{57} +(-1.76127 - 13.9419i) q^{58} +(-2.15085 - 2.59993i) q^{59} +(-0.417125 + 1.15091i) q^{60} +(0.265694 - 4.22309i) q^{61} +(-2.85297 + 11.1116i) q^{62} +(-1.14436 + 4.45698i) q^{63} +(0.529873 - 8.42209i) q^{64} +(4.55172 + 3.54623i) q^{65} +(0.0329023 + 0.0397721i) q^{66} +(-0.743178 - 5.88286i) q^{67} +7.40742i q^{68} +(0.975683 - 0.123257i) q^{69} +(-6.98963 + 1.09179i) q^{70} +(-8.84989 - 8.31060i) q^{71} +(-0.296962 - 0.139740i) q^{72} +(-9.25841 - 7.65922i) q^{73} +(4.19845 - 12.9215i) q^{74} +(0.416885 - 1.26468i) q^{75} +(-3.06801 - 9.44236i) q^{76} +(-0.0556581 + 0.140576i) q^{77} +(0.947413 - 1.00889i) q^{78} +(3.13379 + 16.4279i) q^{79} +(-0.291414 + 8.68364i) q^{80} +(6.09905 - 5.72739i) q^{81} +(15.5589 - 5.05539i) q^{82} +(-14.5315 - 2.77203i) q^{83} +(0.0540038 + 0.858365i) q^{84} +(-0.235937 - 8.05414i) q^{85} +(9.18623 + 14.4752i) q^{86} +(1.85474 - 0.116690i) q^{87} +(-0.00910492 - 0.00577816i) q^{88} +(5.98097 - 7.22975i) q^{89} +(12.0940 + 5.26416i) q^{90} +(3.92652 + 1.00816i) q^{91} +(-6.86831 + 3.23198i) q^{92} +(-1.44286 - 0.468814i) q^{93} +(3.44866 + 1.89592i) q^{94} +(3.63662 + 10.1690i) q^{95} +(2.12679 + 0.268676i) q^{96} +(-0.586565 + 4.64314i) q^{97} +(7.70600 - 4.89038i) q^{98} +(0.228059 - 0.165695i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) $ 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{21}{50}\right)$

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 $

$2$	−0.500827	−	1.95059i	−0.354138	−	1.37928i	−0.857181	−	0.515016i	$-0.827786\pi$
$2$	−0.500827	−	1.95059i	−0.354138	−	1.37928i	0.503043	−	0.864262i	$-0.332214\pi$
$3$	0.261606	−	0.0499040i	0.151038	−	0.0288121i	−0.111308	−	0.993786i	$-0.535504\pi$
$3$	0.261606	−	0.0499040i	0.151038	−	0.0288121i	0.262346	+	0.964974i	$0.415504\pi$
$4$	−1.80137	+	0.990311i	−0.900685	+	0.495156i
$5$	1.92710	−	1.13415i	0.861825	−	0.507206i
$5$	1.92710	−	1.13415i	0.861825	−	0.507206i
$6$	−0.228362	−	0.485293i	−0.0932283	−	0.198120i
$7$	0.923406	−	1.27096i	0.349015	−	0.480378i	−0.598033	−	0.801472i	$-0.704051\pi$
$7$	0.923406	−	1.27096i	0.349015	−	0.480378i	0.947047	+	0.321094i	$0.104051\pi$
$8$	0.0767024	+	0.0816797i	0.0271184	+	0.0288781i
$9$	−2.72338	+	1.07826i	−0.907794	+	0.359421i
$10$	−3.17740	−	3.19097i	−1.00478	−	1.00907i
$11$	−0.0932173	+	0.0239341i	−0.0281061	+	0.00721641i	−0.262717	−	0.964873i	$-0.584618\pi$
$11$	−0.0932173	+	0.0239341i	−0.0281061	+	0.00721641i	0.234611	+	0.972089i	$0.424618\pi$
$12$	−0.421829	+	0.348967i	−0.121771	+	0.100738i
$13$	0.949931	+	2.39925i	0.263463	+	0.665432i	0.999939	−	0.0110315i	$-0.00351149\pi$
$13$	0.949931	+	2.39925i	0.263463	+	0.665432i	−0.736476	+	0.676464i	$0.763511\pi$
$14$	−2.94159	−	1.16466i	−0.786173	−	0.311268i
$15$	0.447542	−	0.392870i	0.115555	−	0.101439i
$16$	−2.08202	+	3.28074i	−0.520506	+	0.820186i
$17$	1.73598	−	3.15774i	0.421038	−	0.765865i	−0.577692	−	0.816255i	$-0.696047\pi$
$17$	1.73598	−	3.15774i	0.421038	−	0.765865i	0.998730	+	0.0503903i	$0.0160465\pi$
$18$	3.46720	+	4.77219i	0.817226	+	1.12481i
$19$	−0.905011	+	4.74424i	−0.207624	+	1.08840i	0.713949	+	0.700197i	$0.246905\pi$
$19$	−0.905011	+	4.74424i	−0.207624	+	1.08840i	−0.921573	+	0.388205i	$0.873095\pi$
$20$	−2.34826	+	3.95145i	−0.525086	+	0.883571i
$21$	0.178143	−	0.378572i	0.0388739	−	0.0826112i
$22$	0.0933715	+	0.169842i	0.0199069	+	0.0362104i
$23$	3.68536	+	0.231863i	0.768451	+	0.0483468i	0.442176	−	0.896928i	$-0.354207\pi$
$23$	3.68536	+	0.231863i	0.768451	+	0.0483468i	0.326274	+	0.945275i	$0.394207\pi$
$24$	0.0241419	+	0.0175402i	0.00492795	+	0.00358037i
$25$	2.42742	−	4.37123i	0.485483	−	0.874246i
$26$	4.20421	−	3.05454i	0.824513	−	0.599044i
$27$	−1.33324	+	0.846097i	−0.256581	+	0.162831i
$28$	−0.404750	+	3.20393i	−0.0764906	+	0.605485i
$29$	6.92298	+	0.874576i	1.28557	+	0.162405i	0.738253	−	0.674524i	$-0.235651\pi$
$29$	6.92298	+	0.874576i	1.28557	+	0.162405i	0.547312	+	0.836928i	$0.315651\pi$
$30$	−0.990470	−	0.676212i	−0.180834	−	0.123459i
$31$	−4.99189	−	2.74432i	−0.896570	−	0.492894i	−0.0343401	−	0.999410i	$-0.510933\pi$
$31$	−4.99189	−	2.74432i	−0.896570	−	0.492894i	−0.862230	+	0.506516i	$0.830933\pi$
$32$	7.65526	+	2.48734i	1.35327	+	0.439704i
$33$	−0.0231918	+	0.0109132i	−0.00403717	+	0.00189975i
$34$	−7.02889	−	1.80471i	−1.20544	−	0.309506i
$35$	0.338038	−	3.49654i	0.0571388	−	0.591024i
$36$	3.83800	−	4.63935i	0.639667	−	0.773225i
$37$	5.69623	+	3.61494i	0.936455	+	0.594292i	0.914114	−	0.405458i	$-0.132888\pi$
$37$	5.69623	+	3.61494i	0.936455	+	0.594292i	0.0223413	+	0.999750i	$0.492888\pi$
$38$	9.70732	−	0.610733i	1.57474	−	0.0990740i
$39$	0.368240	+	0.580253i	0.0589655	+	0.0929148i
$40$	0.240450	+	0.0704130i	0.0380185	+	0.0111333i
$41$	0.510078	+	8.10746i	0.0796609	+	1.26617i	0.811361	+	0.584546i	$0.198727\pi$
$41$	0.510078	+	8.10746i	0.0796609	+	1.26617i	−0.731700	+	0.681627i	$0.761273\pi$
$42$	−0.827659	−	0.157884i	−0.127711	−	0.0243621i
$43$	−8.09635	+	2.63066i	−1.23468	+	0.401173i	−0.852408	−	0.522876i	$-0.824859\pi$
$43$	−8.09635	+	2.63066i	−1.23468	+	0.401173i	−0.382274	+	0.924049i	$0.624859\pi$
$44$	0.144217	−	0.135428i	0.0217415	−	0.0204166i
$45$	−4.02531	+	5.16664i	−0.600059	+	0.770197i
$46$	−1.39346	−	7.30476i	−0.205454	−	1.07703i
$47$	−1.33773	+	1.42454i	−0.195128	+	0.207790i	−0.819091	−	0.573664i	$-0.805522\pi$
$47$	−1.33773	+	1.42454i	−0.195128	+	0.207790i	0.623963	+	0.781454i	$0.285522\pi$
$48$	−0.380947	+	0.962163i	−0.0549850	+	0.138876i
$49$	1.40046	+	4.31017i	0.200066	+	0.615739i
$50$	−9.74220	−	2.54567i	−1.37776	−	0.360012i
$51$	0.296559	−	0.912716i	0.0415266	−	0.127806i
$52$	−4.08718	−	3.38121i	−0.566790	−	0.468890i
$53$	−5.06219	−	2.38209i	−0.695345	−	0.327205i	0.0454205	−	0.998968i	$-0.485537\pi$
$53$	−5.06219	−	2.38209i	−0.695345	−	0.327205i	−0.740766	+	0.671763i	$0.765537\pi$
$54$	2.31811	+	2.17685i	0.315455	+	0.296232i
$55$	−0.152494	+	0.151846i	−0.0205623	+	0.0204749i
$56$	0.174639	−	0.0220620i	0.0233371	−	0.00294817i
$57$			1.28628i			0.170372i
$58$	−1.76127	−	13.9419i	−0.231267	−	1.83066i
$59$	−2.15085	−	2.59993i	−0.280016	−	0.338481i	0.611689	−	0.791098i	$-0.290490\pi$
$59$	−2.15085	−	2.59993i	−0.280016	−	0.338481i	−0.891705	+	0.452617i	$0.850490\pi$
$60$	−0.417125	+	1.15091i	−0.0538506	+	0.148582i
$61$	0.265694	−	4.22309i	0.0340187	−	0.540711i	−0.943701	−	0.330798i	$-0.892682\pi$
$61$	0.265694	−	4.22309i	0.0340187	−	0.540711i	0.977720	−	0.209913i	$-0.0673180\pi$
$62$	−2.85297	+	11.1116i	−0.362327	+	1.41117i
$63$	−1.14436	+	4.45698i	−0.144176	+	0.561527i
$64$	0.529873	−	8.42209i	0.0662341	−	1.05276i
$65$	4.55172	+	3.54623i	0.564571	+	0.439856i
$66$	0.0329023	+	0.0397721i	0.00405000	+	0.00489561i
$67$	−0.743178	−	5.88286i	−0.0907937	−	0.718706i	−0.970144	−	0.242530i	$-0.922023\pi$
$67$	−0.743178	−	5.88286i	−0.0907937	−	0.718706i	0.879350	−	0.476176i	$-0.157977\pi$
$68$			7.40742i			0.898282i
$69$	0.975683	−	0.123257i	0.117458	−	0.0148384i
$70$	−6.98963	+	1.09179i	−0.835421	+	0.130494i
$71$	−8.84989	−	8.31060i	−1.05029	−	0.986286i	−0.0503659	−	0.998731i	$-0.516039\pi$
$71$	−8.84989	−	8.31060i	−1.05029	−	0.986286i	−0.999923	+	0.0124444i	$0.996039\pi$
$72$	−0.296962	−	0.139740i	−0.0349973	−	0.0164685i
$73$	−9.25841	−	7.65922i	−1.08362	−	0.896444i	−0.0885899	−	0.996068i	$-0.528236\pi$
$73$	−9.25841	−	7.65922i	−1.08362	−	0.896444i	−0.995025	+	0.0996238i	$0.968236\pi$
$74$	4.19845	−	12.9215i	0.488059	−	1.50209i
$75$	0.416885	−	1.26468i	0.0481377	−	0.146032i
$76$	−3.06801	−	9.44236i	−0.351925	−	1.08311i
$77$	−0.0556581	+	0.140576i	−0.00634283	+	0.0160202i
$78$	0.947413	−	1.00889i	0.107273	−	0.114235i
$79$	3.13379	+	16.4279i	0.352578	+	1.84828i	0.509235	+	0.860628i	$0.329928\pi$
$79$	3.13379	+	16.4279i	0.352578	+	1.84828i	−0.156656	+	0.987653i	$0.550072\pi$
$80$	−0.291414	+	8.68364i	−0.0325811	+	0.970860i
$81$	6.09905	−	5.72739i	0.677672	−	0.636376i
$82$	15.5589	−	5.05539i	1.71819	−	0.558275i
$83$	−14.5315	−	2.77203i	−1.59504	−	0.304270i	−0.688127	−	0.725590i	$-0.741567\pi$
$83$	−14.5315	−	2.77203i	−1.59504	−	0.304270i	−0.906912	+	0.421320i	$0.861567\pi$
$84$	0.0540038	+	0.858365i	0.00589229	+	0.0936553i
$85$	−0.235937	−	8.05414i	−0.0255909	−	0.873594i
$86$	9.18623	+	14.4752i	0.990576	+	1.56090i
$87$	1.85474	−	0.116690i	0.198849	−	0.0125105i
$88$	−0.00910492	−	0.00577816i	−0.000970588	−	0.000615954i
$89$	5.98097	−	7.22975i	0.633982	−	0.766352i	−0.351490	−	0.936192i	$-0.614325\pi$
$89$	5.98097	−	7.22975i	0.633982	−	0.766352i	0.985472	+	0.169840i	$0.0543249\pi$
$90$	12.0940	+	5.26416i	1.27482	+	0.554891i
$91$	3.92652	+	1.00816i	0.411611	+	0.105684i
$92$	−6.86831	+	3.23198i	−0.716071	+	0.336957i
$93$	−1.44286	−	0.468814i	−0.149618	−	0.0486138i
$94$	3.44866	+	1.89592i	0.355702	+	0.195549i
$95$	3.63662	+	10.1690i	0.373109	+	1.04332i
$96$	2.12679	+	0.268676i	0.217064	+	0.0274216i
$97$	−0.586565	+	4.64314i	−0.0595566	+	0.471439i	0.933927	+	0.357464i	$0.116358\pi$
$97$	−0.586565	+	4.64314i	−0.0595566	+	0.471439i	−0.993484	+	0.113975i	$0.963642\pi$
$98$	7.70600	−	4.89038i	0.778424	−	0.494003i
$99$	0.228059	−	0.165695i	0.0229208	−	0.0166529i
$100$	−0.0437944	+	10.2781i	−0.00437944	+	1.02781i
$101$	5.15615	+	3.74616i	0.513056	+	0.372757i	0.813981	−	0.580891i	$-0.197296\pi$
$101$	5.15615	+	3.74616i	0.513056	+	0.372757i	−0.300926	+	0.953648i	$0.597296\pi$
$102$	−1.92886	−	0.121354i	−0.190986	−	0.0120158i
$103$	0.174922	+	0.318182i	0.0172356	+	0.0313514i	0.884784	−	0.466001i	$-0.154306\pi$
$103$	0.174922	+	0.318182i	0.0172356	+	0.0313514i	−0.867549	+	0.497352i	$0.834306\pi$
$104$	−0.123108	+	0.261618i	−0.0120718	+	0.0256538i
$105$	−0.0860588	−	0.931586i	−0.00839848	−	0.0909135i
$106$	−2.11120	+	11.0673i	−0.205058	+	1.07495i
$107$	−3.98839	−	5.48955i	−0.385573	−	0.530695i	0.571478	−	0.820618i	$-0.306370\pi$
$107$	−3.98839	−	5.48955i	−0.385573	−	0.530695i	−0.957050	+	0.289923i	$0.906370\pi$
$108$	1.56375	−	2.84445i	0.150472	−	0.273708i
$109$	−2.52787	+	3.98328i	−0.242126	+	0.381529i	−0.943558	−	0.331207i	$-0.892544\pi$
$109$	−2.52787	+	3.98328i	−0.242126	+	0.381529i	0.701432	+	0.712736i	$0.252544\pi$
$110$	0.372562	+	0.221405i	0.0355224	+	0.0211102i
$111$	1.67057	+	0.661425i	0.158563	+	0.0627797i
$112$	2.24714	+	5.67563i	0.212335	+	0.536296i
$113$	8.52650	−	7.05373i	0.802105	−	0.663559i	−0.143219	−	0.989691i	$-0.545745\pi$
$113$	8.52650	−	7.05373i	0.802105	−	0.663559i	0.945324	+	0.326132i	$0.105745\pi$
$114$	2.50902	−	0.644206i	0.234991	−	0.0603354i
$115$	7.36502	−	3.73292i	0.686791	−	0.348097i
$116$	−13.3370	+	5.28047i	−1.23830	+	0.490280i
$117$	−5.17405	−	5.50980i	−0.478341	−	0.509381i
$118$	−3.99419	+	5.49754i	−0.367695	+	0.506089i
$119$	−2.41034	−	5.12224i	−0.220956	−	0.469555i
$120$	0.0664170	+	0.00642105i	0.00606302	+	0.000586159i
$121$	−9.63126	+	5.29483i	−0.875569	+	0.481348i
$122$	−8.37059	+	1.59678i	−0.757838	+	0.144565i
$123$	0.538034	+	2.09551i	0.0485129	+	0.188945i
$124$	11.7100			1.05159
$125$	−0.279754	−	11.1768i	−0.0250219	−	0.999687i
$126$	9.26688			0.825560
$127$	−4.07627	−	15.8760i	−0.361711	−	1.40877i	−0.845682	−	0.533687i	$-0.820806\pi$
$127$	−4.07627	−	15.8760i	−0.361711	−	1.40877i	0.483971	−	0.875084i	$-0.339194\pi$
$128$	−0.880169	+	0.167901i	−0.0777967	+	0.0148405i
$129$	−1.98677	+	1.09224i	−0.174926	+	0.0961662i
$130$	4.63763	−	10.6546i	0.406747	−	0.934469i
$131$	1.89214	+	4.02100i	0.165317	+	0.351316i	0.970271	−	0.242021i	$-0.0778102\pi$
$131$	1.89214	+	4.02100i	0.165317	+	0.351316i	−0.804954	+	0.593337i	$0.797810\pi$
$132$	0.0309695	−	0.0426258i	0.00269555	−	0.00371010i
$133$	5.19404	+	5.53109i	0.450380	+	0.479606i
$134$	−11.1029	+	4.39593i	−0.959141	+	0.379751i
$135$	−1.60968	+	3.14260i	−0.138539	+	0.270472i
$136$	0.391077	−	0.100412i	0.0335346	−	0.00861022i
$137$	−9.35565	+	7.73966i	−0.799307	+	0.661244i	−0.944629	−	0.328140i	$-0.893578\pi$
$137$	−9.35565	+	7.73966i	−0.799307	+	0.661244i	0.145322	+	0.989384i	$0.453578\pi$
$138$	−0.729073	−	1.84143i	−0.0620628	−	0.156753i
$139$	6.14401	+	2.43258i	0.521128	+	0.206329i	0.613937	−	0.789355i	$-0.289585\pi$
$139$	6.14401	+	2.43258i	0.521128	+	0.206329i	−0.0928096	+	0.995684i	$0.529585\pi$
$140$	2.85374	+	6.63333i	0.241185	+	0.560619i
$141$	−0.278868	+	0.439425i	−0.0234849	+	0.0370063i
$142$	−11.7783	+	21.4247i	−0.988415	+	1.79792i
$143$	−0.145974	−	0.200916i	−0.0122070	−	0.0168014i
$144$	2.13264	−	11.1797i	0.177720	−	0.931641i
$145$	14.3332	−	6.16629i	1.19030	−	0.512083i
$146$	−10.3032	+	21.8953i	−0.852696	+	1.81207i
$147$	0.581464	+	1.05768i	0.0479583	+	0.0872358i
$148$	−13.8409	−	0.870798i	−1.13772	−	0.0715792i
$149$	−5.58217	−	4.05568i	−0.457309	−	0.332254i	0.335166	−	0.942159i	$-0.391208\pi$
$149$	−5.58217	−	4.05568i	−0.457309	−	0.332254i	−0.792475	+	0.609905i	$0.791208\pi$
$150$	−2.67566	−	0.179787i	−0.218467	−	0.0146796i
$151$	−13.5350	+	9.83374i	−1.10146	+	0.800258i	−0.981298	−	0.192496i	$-0.938342\pi$
$151$	−13.5350	+	9.83374i	−1.10146	+	0.800258i	−0.120163	+	0.992754i	$0.538342\pi$
$152$	−0.456924	+	0.289973i	−0.0370615	+	0.0235199i
$153$	−1.32287	+	10.4716i	−0.106948	+	0.846577i
$154$	0.302082	+	0.0381618i	0.0243425	+	0.00307517i
$155$	−12.7323	+	0.372979i	−1.02269	+	0.0299584i
$156$	−1.23797	−	0.680578i	−0.0991167	−	0.0544899i
$157$	2.20072	+	0.715057i	0.175637	+	0.0570678i	0.395515	−	0.918459i	$-0.370566\pi$
$157$	2.20072	+	0.715057i	0.175637	+	0.0570678i	−0.219879	+	0.975527i	$0.570566\pi$
$158$	30.4746	−	14.3403i	2.42443	−	1.14085i
$159$	−1.44318	−	0.370544i	−0.114451	−	0.0293861i
$160$	17.5734	−	3.88884i	1.38930	−	0.307440i
$161$	3.69777	−	4.46984i	0.291425	−	0.352273i
$162$	−14.2264	−	9.02832i	−1.11773	−	0.709332i
$163$	23.2521	−	1.46290i	1.82124	−	0.114583i	0.884925	−	0.465734i	$-0.154210\pi$
$163$	23.2521	−	1.46290i	1.82124	−	0.114583i	0.936319	+	0.351151i	$0.114210\pi$
$164$	−8.94775	−	14.0994i	−0.698702	−	1.10098i
$165$	−0.0323156	+	0.0473338i	−0.00251577	+	0.00368493i
$166$	1.87066	+	29.7333i	0.145192	+	2.30776i
$167$	3.04632	+	0.581117i	0.235732	+	0.0449682i	0.303893	−	0.952706i	$-0.401713\pi$
$167$	3.04632	+	0.581117i	0.235732	+	0.0449682i	−0.0681617	+	0.997674i	$0.521713\pi$
$168$	0.0445856	−	0.0144868i	0.00343986	−	0.00111768i
$169$	4.62256	−	4.34087i	0.355581	−	0.333913i
$170$	−15.5922	+	4.49395i	−1.19587	+	0.344670i
$171$	−2.65084	−	13.8962i	−0.202715	−	1.06267i
$172$	11.9794	−	12.7567i	0.913417	−	0.972690i
$173$	−5.56535	+	14.0565i	−0.423126	+	1.06869i	0.549330	+	0.835605i	$0.314883\pi$
$173$	−5.56535	+	14.0565i	−0.423126	+	1.06869i	−0.972456	+	0.233088i	$0.925117\pi$
$174$	−1.15652	−	3.55940i	−0.0876754	−	0.269837i
$175$	−3.31417	−	7.12157i	−0.250527	−	0.538340i
$176$	0.115559	−	0.355653i	0.00871057	−	0.0268084i
$177$	−0.692421	−	0.572820i	−0.0520455	−	0.0430558i
$178$	−17.0977	−	8.04558i	−1.28153	−	0.603042i
$179$	−5.86372	−	5.50640i	−0.438275	−	0.411567i	0.433747	−	0.901035i	$-0.357191\pi$
$179$	−5.86372	−	5.50640i	−0.438275	−	0.411567i	−0.872022	+	0.489467i	$0.837191\pi$
$180$	2.13450	−	13.2933i	0.159096	−	0.990827i
$181$	22.0246	−	2.78236i	1.63708	−	0.206811i	0.747718	−	0.664017i	$-0.231150\pi$
$181$	22.0246	−	2.78236i	1.63708	−	0.206811i	0.889361	+	0.457205i	$0.151150\pi$
$182$		−	8.16396i		−	0.605153i
$183$	−0.141242	−	1.11804i	−0.0104409	−	0.0826482i
$184$	0.263737	+	0.318804i	0.0194430	+	0.0235025i
$185$	15.0771	+	0.505971i	1.10849	+	0.0371998i
$186$	−0.191841	+	3.04923i	−0.0140665	+	0.223580i
$187$	−0.0862458	+	0.335905i	−0.00630692	+	0.0245638i
$188$	0.999009	−	3.89088i	0.0728602	−	0.283772i
$189$	−0.155763	+	2.47578i	−0.0113301	+	0.180087i
$190$	18.0143	−	12.1865i	1.30690	−	0.884101i
$191$	−15.4385	−	18.6620i	−1.11709	−	1.35033i	−0.929816	−	0.368024i	$-0.880034\pi$
$191$	−15.4385	−	18.6620i	−1.11709	−	1.35033i	−0.187276	−	0.982307i	$-0.559966\pi$
$192$	−0.281678	−	2.22971i	−0.0203284	−	0.160916i
$193$		−	14.7466i		−	1.06148i	−0.847533	−	0.530742i	$-0.821913\pi$
$193$		−	14.7466i		−	1.06148i	0.847533	−	0.530742i	$-0.178087\pi$
$194$	9.35064	−	1.18126i	0.671337	−	0.0848095i
$195$	1.36773	+	0.700566i	0.0979450	+	0.0501686i
$196$	−6.79116	−	6.37732i	−0.485083	−	0.455523i
$197$	−14.8094	−	6.96875i	−1.05512	−	0.496503i	−0.181644	−	0.983364i	$-0.558142\pi$
$197$	−14.8094	−	6.96875i	−1.05512	−	0.496503i	−0.873479	+	0.486861i	$0.838142\pi$
$198$	−0.437421	−	0.361866i	−0.0310861	−	0.0257167i
$199$	−6.04605	+	18.6078i	−0.428593	+	1.31907i	0.470919	+	0.882177i	$0.343923\pi$
$199$	−6.04605	+	18.6078i	−0.428593	+	1.31907i	−0.899512	+	0.436897i	$0.856077\pi$
$200$	0.543230	−	0.137013i	0.0384121	−	0.00968829i
$201$	−0.487998	−	1.50190i	−0.0344208	−	0.105936i
$202$	4.72489	−	11.9337i	0.332442	−	0.839653i
$203$	7.50427	−	7.99124i	0.526697	−	0.560875i
$204$	0.369660	+	1.93783i	0.0258814	+	0.135675i
$205$	10.1780	+	15.0454i	0.710865	+	1.05081i
$206$	0.533037	−	0.500555i	0.0371385	−	0.0348753i
$207$	−10.2867	+	3.34234i	−0.714972	+	0.232308i
$208$	−9.84910	−	1.87882i	−0.682912	−	0.130273i
$209$	−0.0291864	−	0.463905i	−0.00201887	−	0.0320890i
$210$	−1.77404	+	0.634429i	−0.122421	+	0.0437798i
$211$	6.94381	+	10.9417i	0.478031	+	0.753257i	0.994688	−	0.102936i	$-0.0328236\pi$
$211$	6.94381	+	10.9417i	0.478031	+	0.753257i	−0.516657	+	0.856193i	$0.672824\pi$
$212$	11.4779	−	0.722127i	0.788304	−	0.0495959i
$213$	−2.72992	−	1.73246i	−0.187051	−	0.118706i
$214$	−8.71038	+	10.5290i	−0.595430	+	0.719751i
$215$	−12.6189	+	14.2520i	−0.860602	+	0.971979i
$216$	−0.171371	−	0.0440007i	−0.0116603	−	0.00299387i
$217$	−8.09746	+	3.81037i	−0.549691	+	0.258665i
$218$	9.03578	+	2.93590i	0.611980	+	0.198844i
$219$	−2.80428	−	1.54167i	−0.189496	−	0.104176i
$220$	0.124324	−	0.424547i	0.00838190	−	0.0286229i
$221$	9.22527	+	1.16542i	0.620559	+	0.0783948i
$222$	0.453505	−	3.58986i	0.0304372	−	0.240936i
$223$	−16.5922	+	10.5297i	−1.11109	+	0.705121i	−0.959046	−	0.283252i	$-0.908587\pi$
$223$	−16.5922	+	10.5297i	−1.11109	+	0.705121i	−0.152048	+	0.988373i	$0.548587\pi$
$224$	10.2302	−	7.43269i	0.683536	−	0.496618i
$225$	−1.89744	+	14.5219i	−0.126496	+	0.968128i
$226$	−18.0293	−	13.0990i	−1.19929	−	0.871334i
$227$	20.3099	+	1.27779i	1.34802	+	0.0848099i	0.720316	−	0.693646i	$-0.243997\pi$
$227$	20.3099	+	1.27779i	1.34802	+	0.0848099i	0.627699	+	0.778456i	$0.283997\pi$
$228$	−1.27382	−	2.31707i	−0.0843609	−	0.153452i
$229$	3.25931	−	6.92638i	0.215381	−	0.457708i	−0.767717	−	0.640789i	$-0.778607\pi$
$229$	3.25931	−	6.92638i	0.215381	−	0.457708i	0.983098	+	0.183081i	$0.0586072\pi$
$230$	−10.9700	−	12.4966i	−0.723341	−	0.824001i
$231$	−0.00754517	+	0.0395532i	−0.000496436	+	0.00260241i
$232$	0.459574	+	0.632549i	0.0301725	+	0.0415289i
$233$	−12.4007	+	22.5569i	−0.812400	+	1.47775i	0.0649443	+	0.997889i	$0.479313\pi$
$233$	−12.4007	+	22.5569i	−0.812400	+	1.47775i	−0.877344	+	0.479861i	$0.840687\pi$
$234$	−8.15607	+	12.8519i	−0.533179	+	0.840156i
$235$	−0.962299	+	4.26240i	−0.0627735	+	0.278048i
$236$	6.44920	+	2.55342i	0.419807	+	0.166214i
$237$	1.63963	+	4.14124i	0.106506	+	0.269003i
$238$	−8.78424	+	7.26695i	−0.569398	+	0.471047i
$239$	−10.1639	+	2.60966i	−0.657451	+	0.168805i	−0.562655	−	0.826692i	$-0.690220\pi$
$239$	−10.1639	+	2.60966i	−0.657451	+	0.168805i	−0.0947964	+	0.995497i	$0.530220\pi$
$240$	0.357113	+	2.28623i	0.0230515	+	0.147576i
$241$	23.3293	−	9.23672i	1.50277	−	0.594989i	0.534562	−	0.845129i	$-0.320477\pi$
$241$	23.3293	−	9.23672i	1.50277	−	0.594989i	0.968210	+	0.250140i	$0.0804766\pi$
$242$	15.1516	+	16.1349i	0.973985	+	1.03719i
$243$	4.09415	−	5.63512i	0.262640	−	0.361493i
$244$	3.70356	+	7.87047i	0.237096	+	0.503855i
$245$	7.58720	+	6.71780i	0.484728	+	0.429184i
$246$	3.81802	−	2.09897i	0.243428	−	0.133826i
$247$	−12.2423	+	2.33534i	−0.778959	+	0.148594i
$248$	−0.158735	−	0.618232i	−0.0100797	−	0.0392578i
$249$	−3.93986			−0.249679
$250$	−21.6614	+	6.14335i	−1.36998	+	0.388539i
$251$	18.2046			1.14907			0.574533	−	0.818482i	$-0.305184\pi$
$251$	18.2046			1.14907			0.574533	+	0.818482i	$0.305184\pi$
$252$	−2.35239	−	9.16195i	−0.148187	−	0.577148i
$253$	−0.349089	+	0.0665922i	−0.0219470	+	0.00418662i
$254$	−28.9262	+	15.9023i	−1.81499	+	0.997799i
$255$	−0.463656	−	2.09524i	−0.0290353	−	0.131209i
$256$	−6.41777	−	13.6384i	−0.401110	−	0.852403i
$257$	−2.35287	+	3.23844i	−0.146768	+	0.202008i	−0.876071	−	0.482182i	$-0.839844\pi$
$257$	−2.35287	+	3.23844i	−0.146768	+	0.202008i	0.729303	+	0.684191i	$0.239844\pi$
$258$	3.12554	+	3.32836i	0.194588	+	0.207215i
$259$	9.85438	−	3.90162i	0.612321	−	0.242435i
$260$	−11.7112	−	1.88046i	−0.726297	−	0.116621i
$261$	−19.7969	+	5.08299i	−1.22540	+	0.314629i
$262$	6.89569	−	5.70461i	0.426017	−	0.352432i
$263$	0.194656	+	0.491646i	0.0120030	+	0.0303162i	0.935654	−	0.352918i	$-0.114810\pi$
$263$	0.194656	+	0.491646i	0.0120030	+	0.0303162i	−0.923651	+	0.383234i	$0.874810\pi$
$264$	−0.00267025	−	0.00105723i	−0.000164343	−	6.50679e-5i
$265$	−12.4570	+	1.15076i	−0.765226	+	0.0706906i
$266$	8.18758	−	12.9016i	0.502013	−	0.791046i
$267$	1.20386	−	2.18982i	0.0736753	−	0.134015i
$268$	7.16461	+	9.86123i	0.437648	+	0.602371i
$269$	4.55111	−	23.8577i	0.277486	−	1.45463i	−0.521484	−	0.853261i	$-0.674621\pi$
$269$	4.55111	−	23.8577i	0.277486	−	1.45463i	0.798970	−	0.601371i	$-0.205379\pi$
$270$	6.93610	+	1.56593i	0.422118	+	0.0952992i
$271$	−1.32904	+	2.82436i	−0.0807335	+	0.171567i	−0.941118	−	0.338078i	$-0.890223\pi$
$271$	−1.32904	+	2.82436i	−0.0807335	+	0.171567i	0.860385	+	0.509645i	$0.170223\pi$
$272$	6.74538	+	12.2698i	0.408999	+	0.743966i
$273$	1.07751	+	0.0677914i	0.0652140	+	0.00410292i
$274$	19.7825	+	14.3728i	1.19510	+	0.868294i
$275$	−0.121656	+	0.465572i	−0.00733610	+	0.0280751i
$276$	−1.63550	+	1.18826i	−0.0984457	+	0.0715250i
$277$	−8.52732	+	5.41160i	−0.512357	+	0.325152i	−0.766746	−	0.641950i	$-0.778126\pi$
$277$	−8.52732	+	5.41160i	−0.512357	+	0.325152i	0.254389	+	0.967102i	$0.418126\pi$
$278$	1.66790	−	13.2028i	0.100034	−	0.791849i
$279$	16.5539	+	2.09125i	0.991058	+	0.125200i
$280$	0.311525	−	0.240582i	0.0186172	−	0.0143775i
$281$	−4.83086	−	2.65579i	−0.288185	−	0.158431i	0.331104	−	0.943594i	$-0.392579\pi$
$281$	−4.83086	−	2.65579i	−0.288185	−	0.158431i	−0.619289	+	0.785163i	$0.712579\pi$
$282$	0.996804	+	0.323881i	0.0593588	+	0.0192868i
$283$	27.9104	−	13.1336i	1.65910	−	0.780713i	0.659522	−	0.751685i	$-0.270759\pi$
$283$	27.9104	−	13.1336i	1.65910	−	0.780713i	0.999579	−	0.0290283i	$-0.00924128\pi$
$284$	24.1720	+	6.20631i	1.43434	+	0.368277i
$285$	1.45884	+	2.47880i	0.0864140	+	0.146831i
$286$	−0.318797	+	0.385360i	−0.0188509	+	0.0227868i
$287$	10.7753	+	6.83819i	0.636044	+	0.403646i
$288$	−23.5302	+	1.48039i	−1.38653	+	0.0872331i
$289$	2.15137	+	3.39001i	0.126551	+	0.199412i
$290$	−19.2064	−	24.8699i	−1.12784	−	1.46041i
$291$	0.0782624	+	1.24394i	0.00458782	+	0.0729213i
$292$	24.2628	+	4.62838i	1.41988	+	0.270856i
$293$	4.20809	−	1.36729i	0.245839	−	0.0798779i	−0.183506	−	0.983019i	$-0.558745\pi$
$293$	4.20809	−	1.36729i	0.245839	−	0.0798779i	0.429345	+	0.903141i	$0.358745\pi$
$294$	1.77189	−	1.66391i	0.103339	−	0.0970413i
$295$	−7.09359	−	2.57093i	−0.413005	−	0.149686i
$296$	0.141647	+	0.742541i	0.00823308	+	0.0431593i
$297$	0.104030	−	0.110781i	0.00603643	−	0.00642815i
$298$	−5.11528	+	12.9197i	−0.296320	+	0.748420i
$299$	2.94454	+	9.06235i	0.170287	+	0.524090i
$300$	0.501461	+	2.69100i	0.0289519	+	0.155365i
$301$	−4.13275	+	12.7193i	−0.238208	+	0.733129i
$302$	25.9603	+	21.4762i	1.49385	+	1.23582i
$303$	1.53583	+	0.722705i	0.0882309	+	0.0415183i
$304$	−13.6804	−	12.8467i	−0.784623	−	0.736810i
$305$	−4.27759	−	8.43965i	−0.244934	−	0.483253i
$306$	21.0883	−	2.66407i	1.20554	−	0.152295i
$307$			12.2612i			0.699785i	0.936790	+	0.349893i	$0.113782\pi$
$307$			12.2612i			0.699785i	−0.936790	+	0.349893i	$0.886218\pi$
$308$	−0.0389535	−	0.308349i	−0.00221958	−	0.0175698i
$309$	0.0616391	+	0.0745089i	0.00350653	+	0.00423866i
$310$	7.10422	+	24.6488i	0.403493	+	1.39996i
$311$	0.579964	−	9.21826i	0.0328867	−	0.522720i	−0.946754	−	0.321959i	$-0.895659\pi$
$311$	0.579964	−	9.21826i	0.0328867	−	0.522720i	0.979640	−	0.200761i	$-0.0643413\pi$
$312$	−0.0191500	+	0.0745845i	−0.00108416	+	0.00422252i
$313$	−3.64986	+	14.2153i	−0.206302	+	0.803495i	0.778184	+	0.628036i	$0.216141\pi$
$313$	−3.64986	+	14.2153i	−0.206302	+	0.803495i	−0.984487	+	0.175459i	$0.943859\pi$
$314$	0.292605	−	4.65083i	0.0165127	−	0.262461i
$315$	2.84959	+	9.88692i	0.160556	+	0.557065i
$316$	−21.9138	−	26.4893i	−1.23275	−	1.49014i
$317$	−0.0604509	−	0.478518i	−0.00339526	−	0.0268763i	0.990326	−	0.138760i	$-0.0443116\pi$
$317$	−0.0604509	−	0.478518i	−0.00339526	−	0.0268763i	−0.993721	+	0.111884i	$0.964312\pi$
$318$			3.00063i			0.168267i
$319$	−0.666274	+	0.0841699i	−0.0373042	+	0.00471261i
$320$	−8.53078	−	16.8312i	−0.476885	−	0.940890i
$321$	−1.31734	−	1.23706i	−0.0735267	−	0.0690461i
$322$	−10.5708	−	4.97423i	−0.589086	−	0.277203i
$323$	13.4100	+	11.0937i	0.746151	+	0.617270i
$324$	−5.31474	+	16.3571i	−0.295263	+	0.908727i
$325$	12.7936	+	1.67161i	0.709659	+	0.0927245i
$326$	−14.4988	−	44.6227i	−0.803013	−	2.47142i
$327$	−0.462523	+	1.16820i	−0.0255776	+	0.0646017i
$328$	−0.623091	+	0.663525i	−0.0344045	+	0.0366370i
$329$	0.575261	+	3.01562i	0.0317152	+	0.166257i
$330$	0.108513	+	0.0393286i	0.00597347	+	0.00216497i
$331$	16.8345	−	15.8086i	0.925307	−	0.868921i	−0.0663540	−	0.997796i	$-0.521137\pi$
$331$	16.8345	−	15.8086i	0.925307	−	0.868921i	0.991661	+	0.128875i	$0.0411367\pi$
$332$	28.9218	−	9.39726i	1.58729	−	0.515741i
$333$	−19.4109	−	3.70282i	−1.06371	−	0.202913i
$334$	−0.392158	−	6.23317i	−0.0214579	−	0.341064i
$335$	−8.10422	−	10.4940i	−0.442781	−	0.573347i
$336$	0.871102	+	1.37264i	0.0475225	+	0.0748835i
$337$	29.5852	−	1.86134i	1.61161	−	0.101394i	0.768756	−	0.639542i	$-0.220876\pi$
$337$	29.5852	−	1.86134i	1.61161	−	0.101394i	0.842850	+	0.538149i	$0.180876\pi$
$338$	−10.7824	−	6.84270i	−0.586484	−	0.372194i
$339$	1.87857	−	2.27080i	0.102030	−	0.123333i
$340$	8.40111	+	14.2748i	0.455614	+	0.774161i
$341$	0.531013	+	0.136341i	0.0287560	+	0.00738328i
$342$	−25.7782	+	12.1303i	−1.39393	+	0.655932i
$343$	17.2300	+	5.59835i	0.930331	+	0.302283i
$344$	−0.835882	−	0.459530i	−0.0450677	−	0.0247762i
$345$	1.74044	−	1.34410i	0.0937024	−	0.0723638i
$346$	30.2057	+	3.81587i	1.62387	+	0.205142i
$347$	0.860316	−	6.81010i	0.0461842	−	0.365585i	−0.952038	−	0.305980i	$-0.901016\pi$
$347$	0.860316	−	6.81010i	0.0461842	−	0.365585i	0.998222	−	0.0596052i	$-0.0189842\pi$
$348$	−3.22551	+	2.04697i	−0.172905	+	0.109729i
$349$	−10.1392	+	7.36658i	−0.542740	+	0.394324i	−0.825102	−	0.564984i	$-0.808882\pi$
$349$	−10.1392	+	7.36658i	−0.542740	+	0.394324i	0.282361	+	0.959308i	$0.408882\pi$
$350$	−12.2315	+	10.0313i	−0.653799	+	0.536193i
$351$	−3.29648	−	2.39503i	−0.175953	−	0.127837i
$352$	−0.773134	−	0.0486415i	−0.0412082	−	0.00259260i
$353$	−9.54331	−	17.3592i	−0.507939	−	0.923938i	−0.998616	−	0.0525960i	$-0.983250\pi$
$353$	−9.54331	−	17.3592i	−0.507939	−	0.923938i	0.490677	−	0.871342i	$-0.336750\pi$
$354$	−0.770556	+	1.63751i	−0.0409546	+	0.0870329i
$355$	−26.4801	−	5.97825i	−1.40542	−	0.317293i
$356$	−3.61423	+	18.9465i	−0.191554	+	1.00416i
$357$	−0.886181	−	1.21972i	−0.0469016	−	0.0645546i
$358$	−7.80403	+	14.1955i	−0.412456	+	0.750254i
$359$	9.88080	−	15.5696i	0.521489	−	0.821735i	−0.476872	−	0.878973i	$-0.658229\pi$
$359$	9.88080	−	15.5696i	0.521489	−	0.821735i	0.998361	+	0.0572382i	$0.0182294\pi$
$360$	−0.730761	+	0.0675068i	−0.0385145	+	0.00355792i
$361$	−4.02297	−	1.59281i	−0.211735	−	0.0838319i
$362$	−16.4578	−	41.5676i	−0.865002	−	2.18475i
$363$	−2.25536	+	1.86580i	−0.118376	+	0.0979289i
$364$	−8.07151	+	2.07241i	−0.423062	+	0.108624i
$365$	−26.5286	−	4.25967i	−1.38857	−	0.222961i
$366$	−2.11011	+	0.835452i	−0.110297	+	0.0436698i
$367$	−3.58144	−	3.81385i	−0.186950	−	0.199081i	0.628666	−	0.777676i	$-0.283601\pi$
$367$	−3.58144	−	3.81385i	−0.186950	−	0.199081i	−0.815615	+	0.578594i	$0.803601\pi$
$368$	−8.43369	+	11.6080i	−0.439636	+	0.605107i
$369$	−10.1311	−	21.5297i	−0.527405	−	1.12079i
$370$	−6.56406	−	29.6626i	−0.341249	−	1.54209i
$371$	−7.70199	+	4.23421i	−0.399868	+	0.219829i
$372$	3.06340	−	0.584375i	0.158830	−	0.0302984i
$373$	−1.11661	−	4.34890i	−0.0578158	−	0.225178i	0.933109	−	0.359593i	$-0.117084\pi$
$373$	−1.11661	−	4.34890i	−0.0578158	−	0.225178i	−0.990925	+	0.134415i	$0.957084\pi$
$374$	0.698408			0.0361138
$375$	−0.630954	−	2.90997i	−0.0325823	−	0.150270i
$376$	−0.218963			−0.0112921
$377$	4.47802	+	17.4408i	0.230630	+	0.898245i
$378$	4.90725	−	0.936108i	0.252402	−	0.0481482i
$379$	20.9322	−	11.5076i	1.07522	−	0.591105i	0.157167	−	0.987572i	$-0.449764\pi$
$379$	20.9322	−	11.5076i	1.07522	−	0.591105i	0.918049	+	0.396467i	$0.129764\pi$
$380$	−16.6214	−	14.7168i	−0.852660	−	0.754955i
$381$	−1.85866	−	3.94984i	−0.0952218	−	0.202357i
$382$	−28.6698	+	39.4607i	−1.46688	+	2.01898i
$383$	19.9030	+	21.1945i	1.01699	+	1.08299i	0.996533	+	0.0831976i	$0.0265133\pi$
$383$	19.9030	+	21.1945i	1.01699	+	1.08299i	0.0204606	+	0.999791i	$0.493487\pi$
$384$	−0.221878	+	0.0878479i	−0.0113227	+	0.00448297i
$385$	0.0521757	+	0.334029i	0.00265912	+	0.0170237i
$386$	−28.7646	+	7.38550i	−1.46408	+	0.375912i
$387$	19.2129	−	15.8943i	0.976647	−	0.807953i
$388$	−3.54153	−	8.94489i	−0.179794	−	0.454108i
$389$	−29.3506	−	11.6207i	−1.48814	−	0.589194i	−0.523323	−	0.852134i	$-0.675308\pi$
$389$	−29.3506	−	11.6207i	−1.48814	−	0.589194i	−0.964812	+	0.262940i	$0.915308\pi$
$390$	0.681524	−	3.01874i	0.0345103	−	0.152860i
$391$	7.12988	−	11.2349i	0.360574	−	0.568173i
$392$	−0.244635	+	0.444990i	−0.0123559	+	0.0224754i
$393$	0.695658	+	0.957491i	0.0350913	+	0.0482990i
$394$	−6.17627	+	32.3772i	−0.311156	+	1.63114i
$395$	24.6708	+	28.1040i	1.24132	+	1.41406i
$396$	−0.246729	+	0.524327i	−0.0123986	+	0.0263484i
$397$	−11.7735	−	21.4160i	−0.590897	−	1.07484i	−0.987615	−	0.156896i	$-0.949851\pi$
$397$	−11.7735	−	21.4160i	−0.590897	−	1.07484i	0.396719	−	0.917940i	$-0.370149\pi$
$398$	39.3243	+	2.47408i	1.97115	+	0.124014i
$399$	1.63481	+	1.18776i	0.0818431	+	0.0594625i
$400$	9.28695	+	17.0647i	0.464347	+	0.853237i
$401$	−6.03188	+	4.38242i	−0.301218	+	0.218847i	−0.728119	−	0.685451i	$-0.759605\pi$
$401$	−6.03188	+	4.38242i	−0.301218	+	0.218847i	0.426901	+	0.904298i	$0.359605\pi$
$402$	−2.68520	+	1.70408i	−0.133926	+	0.0849918i
$403$	1.84235	−	14.5837i	0.0917740	−	0.726466i
$404$	−12.9980	−	1.64203i	−0.646674	−	0.0816939i
$405$	5.25776	−	17.9545i	0.261260	−	0.892164i
$406$	−19.3460	−	10.6356i	−0.960126	−	0.527834i
$407$	−0.617508	−	0.200640i	−0.0306087	−	0.00994538i
$408$	0.0972972	−	0.0457846i	0.00481693	−	0.00226668i
$409$	−17.1017	−	4.39098i	−0.845626	−	0.217120i	−0.199069	−	0.979985i	$-0.563792\pi$
$409$	−17.1017	−	4.39098i	−0.845626	−	0.217120i	−0.646557	+	0.762866i	$0.723792\pi$
$410$	24.2500	−	27.3883i	1.19762	−	1.35261i
$411$	−2.06125	+	2.49163i	−0.101674	+	0.122903i
$412$	−0.630198	−	0.399936i	−0.0310476	−	0.0197034i
$413$	−5.29050	+	0.332850i	−0.260329	+	0.0163785i
$414$	11.6714	+	18.3911i	0.573616	+	0.903875i
$415$	−31.1475	+	11.1389i	−1.52897	+	0.546787i
$416$	1.30420	+	20.7297i	0.0639437	+	1.01636i
$417$	1.72870	+	0.329768i	0.0846550	+	0.0161488i
$418$	−0.890273	+	0.289267i	−0.0435447	+	0.0141485i
$419$	−13.0231	+	12.2295i	−0.636221	+	0.597451i	−0.934039	−	0.357171i	$-0.883741\pi$
$419$	−13.0231	+	12.2295i	−0.636221	+	0.597451i	0.297818	+	0.954623i	$0.403741\pi$
$420$	1.07758	+	1.59291i	0.0525807	+	0.0777259i
$421$	1.24410	+	6.52182i	0.0606339	+	0.317854i	0.999662	−	0.0259854i	$-0.00827235\pi$
$421$	1.24410	+	6.52182i	0.0606339	+	0.317854i	−0.939028	+	0.343840i	$0.888272\pi$
$422$	17.8651	−	19.0244i	0.869661	−	0.926095i
$423$	2.10712	−	5.32198i	0.102452	−	0.258763i
$424$	−0.193714	−	0.596190i	−0.00940758	−	0.0289536i
$425$	−9.58926	−	15.2535i	−0.465147	−	0.739905i
$426$	−2.01210	+	6.19261i	−0.0974867	+	0.300033i
$427$	−5.12203	−	4.23731i	−0.247873	−	0.205058i
$428$	12.6209	+	5.93896i	0.610056	+	0.287071i
$429$	−0.0482142	−	0.0452761i	−0.00232780	−	0.00218595i
$430$	34.1198	+	17.4765i	1.64540	+	0.842794i
$431$	2.47687	−	0.312902i	0.119307	−	0.0150719i	−0.0654531	−	0.997856i	$-0.520849\pi$
$431$	2.47687	−	0.312902i	0.119307	−	0.0150719i	0.184760	+	0.982784i	$0.440849\pi$
$432$		−	6.13560i		−	0.295199i
$433$	−0.385188	−	3.04908i	−0.0185109	−	0.146529i	0.980150	−	0.198256i	$-0.0635276\pi$
$433$	−0.385188	−	3.04908i	−0.0185109	−	0.146529i	−0.998661	+	0.0517264i	$0.983528\pi$
$434$	11.4879	+	13.8865i	0.551438	+	0.666573i
$435$	3.44192	−	2.32842i	0.165027	−	0.111639i
$436$	0.608935	−	9.67874i	0.0291627	−	0.463527i
$437$	−4.43530	+	17.2744i	−0.212169	+	0.826345i
$438$	−1.60270	+	6.24212i	−0.0765802	+	0.298260i
$439$	−1.47332	+	23.4178i	−0.0703178	+	1.11767i	0.791739	+	0.610859i	$0.209176\pi$
$439$	−1.47332	+	23.4178i	−0.0703178	+	1.11767i	−0.862057	+	0.506811i	$0.830824\pi$
$440$	−0.0240994		0.000808750i	−0.00114889		3.85556e-5i
$441$	−8.46149	−	10.2282i	−0.402928	−	0.487056i
$442$	−2.34700	−	18.5784i	−0.111635	−	0.883686i
$443$		−	16.3151i		−	0.775153i	−0.921838	−	0.387576i	$-0.873312\pi$
$443$		−	16.3151i		−	0.775153i	0.921838	−	0.387576i	$-0.126688\pi$
$444$	−3.66433	+	0.462912i	−0.173901	+	0.0219688i
$445$	3.32631	−	20.7157i	0.157682	−	0.982021i
$446$	28.8490	+	27.0910i	1.36604	+	1.28280i
$447$	−1.66272	−	0.782418i	−0.0786441	−	0.0370071i
$448$	−10.2149	−	8.45046i	−0.482606	−	0.399247i
$449$	2.47580	−	7.61971i	0.116840	−	0.359597i	−0.875486	−	0.483243i	$-0.839459\pi$
$449$	2.47580	−	7.61971i	0.116840	−	0.359597i	0.992326	+	0.123646i	$0.0394588\pi$
$450$	29.2766	−	3.57183i	1.38011	−	0.168378i
$451$	−0.241593	−	0.743547i	−0.0113762	−	0.0350123i
$452$	−8.37398	+	21.1503i	−0.393879	+	0.994825i
$453$	−3.05009	+	3.24801i	−0.143306	+	0.152605i
$454$	−7.67930	−	40.2563i	−0.360407	−	1.88932i
$455$	8.71020	−	2.51044i	0.408340	−	0.117691i
$456$	−0.105063	+	0.0986610i	−0.00492004	+	0.00462023i
$457$	−17.5219	+	5.69322i	−0.819641	+	0.266318i	−0.688676	−	0.725069i	$-0.741808\pi$
$457$	−17.5219	+	5.69322i	−0.819641	+	0.266318i	−0.130965	+	0.991387i	$0.541808\pi$
$458$	−15.1429	−	2.88866i	−0.707581	−	0.134978i
$459$	0.357281	+	5.67882i	0.0166765	+	0.265065i
$460$	−9.57037	+	14.0180i	−0.446221	+	0.653594i
$461$	14.5180	+	22.8768i	0.676172	+	1.06548i	0.993128	+	0.117037i	$0.0373395\pi$
$461$	14.5180	+	22.8768i	0.676172	+	1.06548i	−0.316955	+	0.948441i	$0.602660\pi$
$462$	0.0809309	−	0.00509174i	0.00376525	−	0.000236889i
$463$	20.5245	+	13.0252i	0.953852	+	0.605333i	0.919084	−	0.394062i	$-0.128931\pi$
$463$	20.5245	+	13.0252i	0.953852	+	0.605333i	0.0347685	+	0.999395i	$0.488931\pi$
$464$	−17.2831	+	20.8916i	−0.802346	+	0.969870i
$465$	−3.31224	+	0.732968i	−0.153601	+	0.0339906i
$466$	50.2099	+	12.8917i	2.32593	+	0.597197i
$467$	34.5793	−	16.2718i	1.60014	−	0.752968i	0.601202	−	0.799097i	$-0.294689\pi$
$467$	34.5793	−	16.2718i	1.60014	−	0.752968i	0.998935	+	0.0461295i	$0.0146887\pi$
$468$	14.7768	+	4.80127i	0.683057	+	0.221939i
$469$	−8.16314	−	4.48772i	−0.376939	−	0.207224i
$470$	8.79616	−	0.257673i	0.405736	−	0.0118856i
$471$	0.611406	+	0.0772385i	0.0281721	+	0.00355896i
$472$	0.0473863	−	0.375101i	0.00218113	−	0.0172654i
$473$	0.691757	−	0.439003i	0.0318070	−	0.0201854i
$474$	7.25670	−	5.27230i	0.333311	−	0.242165i
$475$	18.5413	+	15.4722i	0.850733	+	0.709915i
$476$	9.41453	+	6.84006i	0.431514	+	0.313514i
$477$	16.3548	+	1.02896i	0.748835	+	0.0471127i
$478$	10.1808	+	18.5187i	0.465657	+	0.847027i
$479$	−5.30863	+	11.2814i	−0.242558	+	0.515461i	−0.988624	−	0.150411i	$-0.951940\pi$
$479$	−5.30863	+	11.2814i	−0.242558	+	0.515461i	0.746066	+	0.665872i	$0.231940\pi$
$480$	4.40325	−	1.89433i	0.200980	−	0.0864639i
$481$	−3.26212	+	17.1006i	−0.148740	+	0.779722i
$482$	−29.7010	−	40.8799i	−1.35284	−	1.86203i
$483$	0.744296	−	1.35387i	0.0338667	−	0.0616032i
$484$	12.1059	−	19.0759i	0.550269	−	0.867086i
$485$	4.13564	+	9.61303i	0.187790	+	0.436505i
$486$	−13.0423	−	5.16381i	−0.591610	−	0.234235i
$487$	−4.58165	−	11.5719i	−0.207614	−	0.524374i	0.788237	−	0.615372i	$-0.210994\pi$
$487$	−4.58165	−	11.5719i	−0.207614	−	0.524374i	−0.995851	+	0.0909984i	$0.970994\pi$
$488$	0.365320	−	0.302219i	0.0165373	−	0.0136808i
$489$	6.00988	−	1.54307i	0.271776	−	0.0697802i
$490$	9.30381	−	18.1640i	0.420303	−	0.820565i
$491$	−8.61106	+	3.40936i	−0.388612	+	0.153862i	−0.554302	−	0.832316i	$-0.687015\pi$
$491$	−8.61106	+	3.40936i	−0.388612	+	0.153862i	0.165690	+	0.986178i	$0.447015\pi$
$492$	−3.04440	−	3.24196i	−0.137252	−	0.146159i
$493$	14.7799	−	20.3427i	0.665651	−	0.916190i
$494$	10.6866	+	22.7101i	0.480812	+	1.02178i
$495$	0.251570	−	0.577962i	0.0113072	−	0.0259775i
$496$	19.3966	−	10.6634i	0.870935	−	0.478800i
$497$	−18.7345	+	3.57379i	−0.840356	+	0.160306i
$498$	1.97319	+	7.68507i	0.0884208	+	0.344376i
$499$	−30.3925			−1.36056			−0.680278	−	0.732954i	$-0.738141\pi$
$499$	−30.3925			−1.36056			−0.680278	+	0.732954i	$0.738141\pi$
$500$	11.5725	+	19.8566i	0.517538	+	0.888013i
$501$	0.825936			0.0369001
$502$	−9.11736	−	35.5098i	−0.406928	−	1.58488i
$503$	−12.2693	+	2.34050i	−0.547062	+	0.104358i	−0.453501	−	0.891256i	$-0.649825\pi$
$503$	−12.2693	+	2.34050i	−0.547062	+	0.104358i	−0.0935614	+	0.995614i	$0.529825\pi$
$504$	−0.451820	+	0.248390i	−0.0201257	+	0.0110642i
$505$	14.1851	+	1.37138i	0.631229	+	0.0610258i
$506$	0.304727	+	0.647578i	0.0135468	+	0.0287884i
$507$	0.992662	−	1.36628i	0.0440856	−	0.0606787i
$508$	23.0651	+	24.5618i	1.02335	+	1.08976i
$509$	18.2702	−	7.23367i	0.809811	−	0.320627i	0.0735215	−	0.997294i	$-0.476576\pi$
$509$	18.2702	−	7.23367i	0.809811	−	0.320627i	0.736289	+	0.676667i	$0.236576\pi$
$510$	−3.85474	+	1.95376i	−0.170691	+	0.0865137i
$511$	−18.2838	+	4.69449i	−0.808829	+	0.207672i
$512$	−24.7697	+	20.4913i	−1.09468	+	0.905595i
$513$	−2.80749	−	7.09091i	−0.123954	−	0.313071i
$514$	7.49526	+	2.96758i	0.330602	+	0.130894i
$515$	0.697957	+	0.414780i	0.0307556	+	0.0182774i
$516$	2.49726	−	3.93505i	0.109936	−	0.173231i
$517$	0.0906043	−	0.164809i	0.00398477	−	0.00724828i
$518$	−12.5458	−	17.2678i	−0.551232	−	0.758705i
$519$	−0.754454	+	3.95499i	−0.0331169	+	0.173605i
$520$	0.0594723	+	0.643787i	0.00260803	+	0.0282319i
$521$	−13.5647	+	28.8265i	−0.594282	+	1.26291i	0.350914	+	0.936408i	$0.385871\pi$
$521$	−13.5647	+	28.8265i	−0.594282	+	1.26291i	−0.945195	+	0.326505i	$0.894129\pi$
$522$	19.8297	+	36.0701i	0.867922	+	1.57874i
$523$	−17.2633	−	1.08611i	−0.754871	−	0.0474925i	−0.319309	−	0.947651i	$-0.603451\pi$
$523$	−17.2633	−	1.08611i	−0.754871	−	0.0474925i	−0.435563	+	0.900158i	$0.643451\pi$
$524$	−7.39048	−	5.36950i	−0.322854	−	0.234567i
$525$	−1.22240	−	1.69765i	−0.0533499	−	0.0740917i
$526$	0.861512	−	0.625925i	0.0375637	−	0.0272916i
$527$	−17.3317	+	10.9990i	−0.754980	+	0.479125i
$528$	0.0124823	−	0.0988079i	0.000543224	−	0.00430006i
$529$	−9.29053	−	1.17367i	−0.403936	−	0.0510290i
$530$	8.48346	+	23.7222i	0.368498	+	1.03042i
$531$	8.66098	+	4.76141i	0.375854	+	0.206628i
$532$	−14.8339	−	4.81982i	−0.643130	−	0.208966i
$533$	−18.9673	+	8.92533i	−0.821565	+	0.386599i
$534$	−4.87437	−	1.25153i	−0.210935	−	0.0541589i
$535$	−13.9120	−	6.05548i	−0.601468	−	0.261801i
$536$	0.423507	−	0.511932i	0.0182927	−	0.0221121i
$537$	−1.80877	−	1.14788i	−0.0780544	−	0.0495348i
$538$	−48.8160	+	3.07124i	−2.10461	+	0.132411i
$539$	−0.233707	−	0.368264i	−0.0100665	−	0.0158622i
$540$	−0.212529	−	7.25507i	−0.00914578	−	0.312208i
$541$	1.33106	+	21.1565i	0.0572266	+	0.909590i	0.916993	+	0.398903i	$0.130609\pi$
$541$	1.33106	+	21.1565i	0.0572266	+	0.909590i	−0.859767	+	0.510687i	$0.829391\pi$
$542$	6.17479	+	1.17790i	0.265230	+	0.0505953i
$543$	5.62293	−	1.82700i	0.241303	−	0.0784041i
$544$	21.1438	−	19.8553i	0.906532	−	0.851290i
$545$	−0.353817	+	10.5432i	−0.0151559	+	0.451619i
$546$	−0.407414	−	2.13574i	−0.0174357	−	0.0914012i
$547$	8.26217	−	8.79831i	0.353265	−	0.376189i	−0.527652	−	0.849461i	$-0.676927\pi$
$547$	8.26217	−	8.79831i	0.353265	−	0.376189i	0.880916	+	0.473272i	$0.156927\pi$
$548$	9.18830	−	23.2070i	0.392505	−	0.991354i
$549$	3.83002	+	11.7876i	0.163461	+	0.503081i
$550$	0.969070	+	0.00412915i	0.0413213	+	0.000176068i
$551$	−10.4146	+	32.0527i	−0.443676	+	1.36549i
$552$	0.0849048	+	0.0702394i	0.00361379	+	0.00298959i
$553$	23.7729	+	11.1867i	1.01093	+	0.475706i
$554$	14.8265	+	13.9231i	0.629920	+	0.591534i
$555$	3.96950	−	0.620042i	0.168496	−	0.0263193i
$556$	−13.4766	+	1.70250i	−0.571537	+	0.0722019i
$557$			37.2663i			1.57902i	0.613735	+	0.789512i	$0.289666\pi$
$557$			37.2663i			1.57902i	−0.613735	+	0.789512i	$0.710334\pi$
$558$	−4.21148	−	33.3373i	−0.178286	−	1.41128i
$559$	−14.0026	−	16.9262i	−0.592247	−	0.715903i
$560$	10.7675	+	8.38890i	0.455008	+	0.354496i
$561$	−0.00579940	+	0.0921788i	−0.000244851	+	0.00389179i
$562$	−2.76093	+	10.7531i	−0.116463	+	0.453593i
$563$	3.76090	−	14.6477i	0.158503	−	0.617329i	−0.838833	−	0.544388i	$-0.816762\pi$
$563$	3.76090	−	14.6477i	0.158503	−	0.617329i	0.997336	−	0.0729402i	$-0.0232382\pi$
$564$	0.0671761	−	1.06773i	0.00282862	−	0.0449597i
$565$	8.43142	−	23.2635i	0.354713	−	0.978705i
$566$	−39.5966	−	47.8641i	−1.66437	−	2.01188i
$567$	−1.64738	−	13.0403i	−0.0691834	−	0.547643i
$568$		−	1.36030i		−	0.0570769i
$569$	−6.01416	+	0.759765i	−0.252127	+	0.0318510i	−0.250381	−	0.968147i	$-0.580556\pi$
$569$	−6.01416	+	0.759765i	−0.252127	+	0.0318510i	−0.00174597	+	0.999998i	$0.500556\pi$
$570$	4.10450	−	4.08704i	0.171918	−	0.171187i
$571$	−19.7939	−	18.5877i	−0.828348	−	0.777870i	0.149150	−	0.988815i	$-0.452346\pi$
$571$	−19.7939	−	18.5877i	−0.828348	−	0.777870i	−0.977498	+	0.210944i	$0.932346\pi$
$572$	0.461922	+	0.217364i	0.0193139	+	0.00908845i
$573$	−4.97011	−	4.11164i	−0.207629	−	0.171766i
$574$	7.94198	−	24.4429i	0.331492	−	1.02023i
$575$	9.95943	−	15.5467i	0.415337	−	0.648343i
$576$	7.63819	+	23.5079i	0.318258	+	0.979497i
$577$	−2.85568	+	7.21263i	−0.118884	+	0.300266i	−0.977017	−	0.213161i	$-0.931624\pi$
$577$	−2.85568	+	7.21263i	−0.118884	+	0.300266i	0.858133	+	0.513427i	$0.171624\pi$
$578$	5.53507	−	5.89425i	0.230228	−	0.245168i
$579$	−0.735915	−	3.85780i	−0.0305836	−	0.160325i
$580$	−19.7128	+	25.3021i	−0.818529	+	1.05061i
$581$	−16.9416	+	15.9092i	−0.702857	+	0.660026i
$582$	2.38723	−	0.775659i	0.0989540	−	0.0321521i
$583$	0.528897	+	0.100892i	0.0219047	+	0.00417854i
$584$	−0.0845388	−	1.34371i	−0.00349824	−	0.0556029i
$585$	−16.2198	−	4.74979i	−0.670607	−	0.196380i
$586$	−4.77455	−	7.52348i	−0.197235	−	0.310792i
$587$	6.37641	−	0.401170i	0.263183	−	0.0165581i	0.0693491	−	0.997592i	$-0.477908\pi$
$587$	6.37641	−	0.401170i	0.263183	−	0.0165581i	0.193834	+	0.981034i	$0.437908\pi$
$588$	−2.09486	−	1.32944i	−0.0863906	−	0.0548252i
$589$	17.5374	−	21.1991i	0.722616	−	0.873493i
$590$	−1.46218	+	15.1243i	−0.0601971	+	0.622658i
$591$	−4.22198	−	1.08402i	−0.173669	−	0.0445907i
$592$	−23.7194	+	11.1615i	−0.974861	+	0.458735i
$593$	−45.2119	−	14.6903i	−1.85663	−	0.603256i	−0.995487	−	0.0948968i	$-0.969748\pi$
$593$	−45.2119	−	14.6903i	−1.85663	−	0.603256i	−0.861145	−	0.508360i	$-0.830252\pi$
$594$	−0.268189	−	0.147438i	−0.0110039	−	0.00604946i
$595$	−10.4543	−	7.13737i	−0.428587	−	0.292604i
$596$	14.0719	+	1.77770i	0.576409	+	0.0728174i
$597$	−0.653077	+	5.16964i	−0.0267287	+	0.211579i
$598$	16.2023	−	10.2823i	0.662560	−	0.420473i
$599$	11.1833	−	8.12515i	0.456937	−	0.331985i	−0.335391	−	0.942079i	$-0.608869\pi$
$599$	11.1833	−	8.12515i	0.456937	−	0.331985i	0.792329	+	0.610094i	$0.208869\pi$
$600$	0.135275	−	0.0629528i	0.00552256	−	0.00257004i
$601$	1.02012	+	0.741159i	0.0416115	+	0.0302325i	0.608397	−	0.793633i	$-0.291813\pi$
$601$	1.02012	+	0.741159i	0.0416115	+	0.0302325i	−0.566785	+	0.823866i	$0.691813\pi$
$602$	26.8800	+	1.69115i	1.09555	+	0.0689259i
$603$	8.36723	+	15.2199i	0.340740	+	0.619804i
$604$	14.6430	−	31.1180i	0.595817	−	1.26617i
$605$	−12.5553	+	21.1269i	−0.510444	+	0.858932i
$606$	0.640520	−	3.35772i	0.0260193	−	0.136398i
$607$	−12.4239	−	17.1000i	−0.504270	−	0.694069i	0.478670	−	0.877995i	$-0.341119\pi$
$607$	−12.4239	−	17.1000i	−0.504270	−	0.694069i	−0.982940	+	0.183927i	$0.941119\pi$
$608$	−18.7286	+	34.0673i	−0.759546	+	1.38161i
$609$	1.56437	−	2.46505i	0.0633914	−	0.0998888i
$610$	−14.3200	+	12.5706i	−0.579799	+	0.508970i
$611$	−4.68857	−	1.85634i	−0.189679	−	0.0750993i
$612$	−7.98715	−	20.1732i	−0.322861	−	0.815455i
$613$	14.9559	−	12.3726i	0.604064	−	0.499725i	−0.284379	−	0.958712i	$-0.591787\pi$
$613$	14.9559	−	12.3726i	0.604064	−	0.499725i	0.888443	+	0.458987i	$0.151787\pi$
$614$	23.9167	−	6.14075i	0.965198	−	0.247821i
$615$	3.41346	+	3.42804i	0.137644	+	0.138232i
$616$	−0.0157513	+	0.00623640i	−0.000634640	+	0.000251272i
$617$	−0.377514	−	0.402011i	−0.0151981	−	0.0161844i	0.721325	−	0.692597i	$-0.243534\pi$
$617$	−0.377514	−	0.402011i	−0.0151981	−	0.0161844i	−0.736523	+	0.676413i	$0.763534\pi$
$618$	0.114466	−	0.157549i	0.00460450	−	0.00633755i
$619$	−3.09449	−	6.57613i	−0.124378	−	0.264317i	0.832934	−	0.553372i	$-0.186659\pi$
$619$	−3.09449	−	6.57613i	−0.124378	−	0.264317i	−0.957313	+	0.289055i	$0.906659\pi$
$620$	22.5663	−	13.2808i	0.906283	−	0.533371i
$621$	−5.10963	+	2.80904i	−0.205042	+	0.112723i
$622$	−18.2715	+	3.48548i	−0.732622	+	0.139755i
$623$	−3.66586	−	14.2776i	−0.146869	−	0.572019i
$624$	−2.67034			−0.106899
$625$	−13.2153	−	21.2216i	−0.528612	−	0.848863i
$626$	29.5561			1.18130
$627$	−0.0307861	−	0.119904i	−0.00122948	−	0.00478850i
$628$	−4.67244	+	0.891316i	−0.186451	+	0.0355674i
$629$	21.3036	−	11.7118i	0.849430	−	0.466978i
$630$	17.8582	−	10.5100i	0.711488	−	0.418729i
$631$	2.51731	+	5.34955i	0.100212	+	0.212962i	0.948646	−	0.316340i	$-0.102454\pi$
$631$	2.51731	+	5.34955i	0.100212	+	0.212962i	−0.848434	+	0.529302i	$0.822454\pi$
$632$	−1.10146	+	1.51602i	−0.0438136	+	0.0603042i
$633$	2.36258	+	2.51589i	0.0939040	+	0.0999976i
$634$	−0.903119	+	0.357570i	−0.0358674	+	0.0142009i
$635$	−25.8612	−	25.9716i	−1.02627	−	1.03065i
$636$	2.96665	−	0.761705i	0.117635	−	0.0302036i
$637$	−9.01084	+	7.45442i	−0.357023	+	0.295355i
$638$	0.497869	+	1.25747i	0.0197108	+	0.0497839i
$639$	33.0626	+	13.0904i	1.30794	+	0.517849i
$640$	−1.50575	+	1.32180i	−0.0595199	+	0.0522489i
$641$	1.19941	−	1.88997i	0.0473739	−	0.0746493i	−0.819816	−	0.572628i	$-0.805924\pi$
$641$	1.19941	−	1.88997i	0.0473739	−	0.0746493i	0.867189	+	0.497978i	$0.165924\pi$
$642$	−1.75325	+	3.18914i	−0.0691951	+	0.125865i
$643$	−9.58777	−	13.1964i	−0.378105	−	0.520417i	0.576976	−	0.816761i	$-0.304232\pi$
$643$	−9.58777	−	13.1964i	−0.378105	−	0.520417i	−0.955081	+	0.296344i	$0.904232\pi$
$644$	−2.23452	+	11.7138i	−0.0880525	+	0.461588i
$645$	−2.58995	+	4.35815i	−0.101979	+	0.171602i
$646$	14.9232	−	31.7134i	0.587146	−	1.24775i
$647$	22.1367	+	40.2665i	0.870284	+	1.58304i	0.811185	+	0.584789i	$0.198823\pi$
$647$	22.1367	+	40.2665i	0.870284	+	1.58304i	0.0590987	+	0.998252i	$0.481177\pi$
$648$	0.935623	+	0.0588644i	0.0367547	+	0.00231241i
$649$	0.262723	+	0.190879i	0.0103128	+	0.00749267i
$650$	−3.14672	−	25.7922i	−0.123424	−	1.01165i
$651$	−1.92819	+	1.40091i	−0.0755717	+	0.0549061i
$652$	−40.4369	+	25.6620i	−1.58363	+	1.00500i
$653$	1.48746	−	11.7744i	0.0582086	−	0.460769i	−0.935890	−	0.352291i	$-0.885403\pi$
$653$	1.48746	−	11.7744i	0.0582086	−	0.460769i	0.994099	−	0.108477i	$-0.0345974\pi$
$654$	2.51033	+	0.317128i	0.0981616	+	0.0124007i
$655$	8.20674	+	5.60289i	0.320664	+	0.218923i
$656$	−27.6605	−	15.2065i	−1.07996	−	0.593714i
$657$	33.4729	+	10.8760i	1.30590	+	0.424313i
$658$	5.59415	−	2.63241i	0.218083	−	0.102622i
$659$	33.8432	+	8.68945i	1.31834	+	0.338493i	0.841386	−	0.540434i	$-0.181740\pi$
$659$	33.8432	+	8.68945i	1.31834	+	0.338493i	0.476956	+	0.878927i	$0.341740\pi$
$660$	0.0113372	−	0.117268i	0.000441301	−	0.00456466i
$661$	25.3219	−	30.6089i	0.984906	−	1.19055i	0.00322922	−	0.999995i	$-0.498972\pi$
$661$	25.3219	−	30.6089i	0.984906	−	1.19055i	0.981677	−	0.190552i	$-0.0610279\pi$
$662$	−39.2674	−	24.9198i	−1.52617	−	0.968536i
$663$	2.47155	−	0.155496i	0.0959869	−	0.00603898i
$664$	−0.888182	−	1.39955i	−0.0344681	−	0.0543131i
$665$	16.2825	+	4.76814i	0.631408	+	0.184901i
$666$	2.49879	+	39.7172i	0.0968263	+	1.53901i
$667$	25.3109	+	4.82831i	0.980042	+	0.186953i
$668$	−6.06304	+	1.97000i	−0.234586	+	0.0762216i
$669$	−3.81513	+	3.58265i	−0.147502	+	0.138513i
$670$	−16.4107	+	21.0637i	−0.633999	+	0.813761i
$671$	0.0763087	+	0.400024i	0.00294586	+	0.0154428i
$672$	2.30537	−	2.45497i	0.0889314	−	0.0947024i
$673$	9.12213	−	23.0399i	0.351632	−	0.888122i	−0.641065	−	0.767487i	$-0.721507\pi$
$673$	9.12213	−	23.0399i	0.351632	−	0.888122i	0.992697	−	0.120635i	$-0.0384931\pi$
$674$	−18.4478	−	56.7764i	−0.710581	−	2.18694i
$675$	0.462168	+	7.88171i	0.0177888	+	0.303367i
$676$	−4.02812	+	12.3973i	−0.154928	+	0.476819i
$677$	11.7586	+	9.72760i	0.451922	+	0.373862i	0.835359	−	0.549705i	$-0.185260\pi$
$677$	11.7586	+	9.72760i	0.451922	+	0.373862i	−0.383437	+	0.923567i	$0.625260\pi$
$678$	−5.37026	−	2.52705i	−0.206243	−	0.0970508i
$679$	5.35960	+	5.03300i	0.205683	+	0.193149i
$680$	0.639763	−	0.637043i	0.0245338	−	0.0244295i
$681$	5.37696	−	0.679268i	0.206045	−	0.0260296i
$682$		−	1.10407i		−	0.0422772i
$683$	−1.47394	−	11.6674i	−0.0563986	−	0.446441i	−0.994876	−	0.101101i	$-0.967764\pi$
$683$	−1.47394	−	11.6674i	−0.0563986	−	0.446441i	0.938478	−	0.345340i	$-0.112236\pi$
$684$	18.5367	+	22.4070i	0.708769	+	0.856755i
$685$	−9.25132	+	25.5258i	−0.353475	+	0.975290i
$686$	2.29088	−	36.4124i	0.0874661	−	1.39023i
$687$	0.507000	−	1.97463i	0.0193433	−	0.0753370i
$688$	8.22626	−	32.0392i	0.313623	−	1.22148i
$689$	0.906492	−	14.4083i	0.0345346	−	0.548912i
$690$	−3.49345	−	2.72174i	−0.132993	−	0.103615i
$691$	−0.330652	−	0.399690i	−0.0125786	−	0.0152049i	0.764186	−	0.644995i	$-0.223141\pi$
$691$	−0.330652	−	0.399690i	−0.0125786	−	0.0152049i	−0.776765	+	0.629791i	$0.783141\pi$
$692$	−3.89503	−	30.8323i	−0.148067	−	1.17207i
$693$		−	0.442857i		−	0.0168227i
$694$	−13.7146	+	1.73256i	−0.520599	+	0.0657670i
$695$	14.5990	−	2.28038i	0.553772	−	0.0864999i
$696$	0.151794	+	0.142544i	0.00575374	+	0.00540312i
$697$	26.4868	+	12.4637i	1.00326	+	0.472097i
$698$	19.4472	+	16.0881i	0.736087	+	0.608944i
$699$	−2.11843	+	6.51986i	−0.0801264	+	0.246604i
$700$	13.0226	+	9.54652i	0.492208	+	0.360825i
$701$	2.72346	+	8.38194i	0.102864	+	0.316581i	0.989223	−	0.146416i	$-0.0467739\pi$
$701$	2.72346	+	8.38194i	0.102864	+	0.316581i	−0.886360	+	0.462998i	$0.846774\pi$
$702$	−3.02077	+	7.62959i	−0.114012	+	0.287960i
$703$	−22.3053	+	23.7527i	−0.841260	+	0.895850i
$704$	0.152182	+	0.797767i	0.00573558	+	0.0300670i
$705$	−0.0390322	+	1.16309i	−0.00147004	+	0.0438046i
$706$	−29.0812	+	27.3091i	−1.09449	+	1.02779i
$707$	9.52243	−	3.09403i	0.358128	−	0.116363i
$708$	1.81458	+	0.346149i	0.0681959	+	0.0130091i
$709$	−0.197603	−	3.14081i	−0.00742114	−	0.117956i	0.992572	−	0.121659i	$-0.0388213\pi$
$709$	−0.197603	−	3.14081i	−0.00742114	−	0.117956i	−0.999993	+	0.00370295i	$0.998821\pi$
$710$	1.60079	+	54.6459i	0.0600765	+	2.05082i
$711$	−26.2481	−	41.3603i	−0.984380	−	1.55113i
$712$	1.04928	−	0.0660150i	0.0393234	−	0.00247402i
$713$	−17.7606	−	11.2712i	−0.665140	−	0.422111i
$714$	−1.93536	+	2.33945i	−0.0724290	+	0.0875516i
$715$	−0.509174	−	0.221629i	−0.0190420	−	0.00828844i
$716$	16.0158	+	4.11215i	0.598537	+	0.153678i
$717$	−2.52872	+	1.18992i	−0.0944367	+	0.0444385i
$718$	−35.3186	−	11.4757i	−1.31808	−	0.428270i
$719$	36.5837	+	20.1121i	1.36434	+	0.750054i	0.984564	−	0.175023i	$-0.0560000\pi$
$719$	36.5837	+	20.1121i	1.36434	+	0.750054i	0.379779	+	0.925077i	$0.376000\pi$
$720$	−8.56962	−	23.9631i	−0.319371	−	0.893052i
$721$	0.565920	+	0.0714923i	0.0210760	+	0.00266251i
$722$	−1.09210	+	8.64489i	−0.0406439	+	0.321730i
$723$	5.64213	−	3.58061i	0.209833	−	0.133164i
$724$	−36.9191	+	26.8233i	−1.37209	+	0.996881i
$725$	20.6279	−	28.1390i	0.766102	−	1.04506i
$726$	4.76896	+	3.46485i	0.176993	+	0.128593i
$727$	−30.4553	−	1.91609i	−1.12953	−	0.0710637i	−0.512993	−	0.858393i	$-0.671463\pi$
$727$	−30.4553	−	1.91609i	−1.12953	−	0.0710637i	−0.616533	+	0.787329i	$0.711463\pi$
$728$	0.218827	+	0.398046i	0.00811028	+	0.0147525i
$729$	−9.89723	+	21.0327i	−0.366564	+	0.778989i
$730$	4.97735	+	53.8798i	0.184220	+	1.99418i
$731$	−5.74817	+	30.1330i	−0.212604	+	1.11451i
$732$	1.36164	+	1.87414i	0.0503277	+	0.0692702i
$733$	−1.90806	+	3.47075i	−0.0704758	+	0.128195i	−0.909197	−	0.416366i	$-0.863304\pi$
$733$	−1.90806	+	3.47075i	−0.0704758	+	0.128195i	0.838721	+	0.544561i	$0.183304\pi$
$734$	−5.64558	+	8.89601i	−0.208382	+	0.328358i
$735$	2.32010	+	1.37878i	0.0855782	+	0.0508572i
$736$	27.6356	+	10.9417i	1.01866	+	0.403317i
$737$	0.210078	+	0.530597i	0.00773833	+	0.0195448i
$738$	−36.9218	+	30.5444i	−1.35911	+	1.12435i
$739$	2.50927	−	0.644270i	0.0923048	−	0.0236999i	−0.202255	−	0.979333i	$-0.564827\pi$
$739$	2.50927	−	0.644270i	0.0923048	−	0.0236999i	0.294560	+	0.955633i	$0.404827\pi$
$740$	−27.6605	+	14.0196i	−1.01682	+	0.515369i
$741$	−3.08612	+	1.22188i	−0.113371	+	0.0448869i
$742$	12.1166	+	12.9028i	0.444814	+	0.473678i
$743$	−5.21932	+	7.18378i	−0.191478	+	0.263547i	−0.893952	−	0.448162i	$-0.852079\pi$
$743$	−5.21932	+	7.18378i	−0.191478	+	0.263547i	0.702474	+	0.711709i	$0.252079\pi$
$744$	−0.0723783	−	0.153812i	−0.00265352	−	0.00563901i
$745$	−15.3571	−	1.48469i	−0.562642	−	0.0543950i
$746$	−7.92371	+	4.35609i	−0.290108	+	0.159488i
$747$	42.5638	−	8.11948i	1.55733	−	0.297076i
$748$	−0.177290	−	0.690500i	−0.00648237	−	0.0252472i
$749$	−10.6599			−0.389504
$750$	−5.36016	+	2.68812i	−0.195725	+	0.0981564i
$751$	3.34863			0.122193			0.0610966	−	0.998132i	$-0.480540\pi$
$751$	3.34863			0.122193			0.0610966	+	0.998132i	$0.480540\pi$
$752$	−1.88836	−	7.35466i	−0.0688612	−	0.268197i
$753$	4.76244	−	0.908483i	0.173553	−	0.0331070i
$754$	31.7771	−	17.4696i	1.15725	−	0.636205i
$755$	−14.9303	+	34.3012i	−0.543370	+	1.24835i
$756$	−2.17121	−	4.61405i	−0.0789660	−	0.167811i
$757$	3.51064	−	4.83199i	0.127597	−	0.175622i	−0.740439	−	0.672123i	$-0.765382\pi$
$757$	3.51064	−	4.83199i	0.127597	−	0.175622i	0.868036	+	0.496502i	$0.165382\pi$
$758$	−32.9300	−	35.0669i	−1.19607	−	1.27369i
$759$	−0.0880004	+	0.0348418i	−0.00319421	+	0.00126468i
$760$	−0.551666	+	1.07703i	−0.0200110	+	0.0390679i
$761$	49.5736	−	12.7283i	1.79704	−	0.461401i	0.805656	−	0.592384i	$-0.201813\pi$
$761$	49.5736	−	12.7283i	1.79704	−	0.461401i	0.991385	+	0.130983i	$0.0418133\pi$
$762$	−6.77367	+	5.60367i	−0.245384	+	0.202999i
$763$	2.72834	+	6.89100i	0.0987726	+	0.249471i
$764$	46.2916	+	18.3281i	1.67477	+	0.663089i
$765$	9.32703	+	21.6801i	0.337219	+	0.783845i
$766$	31.3739	−	49.4373i	1.13358	−	1.78624i
$767$	4.19472	−	7.63017i	0.151463	−	0.275509i
$768$	−2.35954	−	3.24763i	−0.0851425	−	0.117189i
$769$	−0.760893	+	3.98874i	−0.0274385	+	0.143838i	−0.993370	−	0.114960i	$-0.963326\pi$
$769$	−0.760893	+	3.98874i	−0.0274385	+	0.143838i	0.965932	+	0.258797i	$0.0833261\pi$
$770$	0.625423	−	0.269064i	0.0225387	−	0.00969640i
$771$	−0.453913	+	0.964613i	−0.0163473	+	0.0347397i
$772$	14.6037	+	26.5641i	0.525600	+	0.956063i
$773$	−11.9163	−	0.749712i	−0.428601	−	0.0269653i	−0.152974	−	0.988230i	$-0.548885\pi$
$773$	−11.9163	−	0.749712i	−0.428601	−	0.0269653i	−0.275626	+	0.961265i	$0.588885\pi$
$774$	−40.6257	−	29.5163i	−1.46026	−	1.06094i
$775$	−24.1134	+	15.1591i	−0.866180	+	0.544531i
$776$	−0.424241	+	0.308229i	−0.0152294	+	0.0110648i
$777$	2.38326	−	1.51246i	0.0854989	−	0.0542592i
$778$	−7.96773	+	63.0711i	−0.285657	+	2.26121i
$779$	−38.9253	−	4.91741i	−1.39465	−	0.176185i
$780$	−3.15756	+	0.0924971i	−0.113059	+	0.00331193i
$781$	1.02387	+	0.562877i	0.0366369	+	0.0201413i
$782$	−25.4855	−	8.28076i	−0.911361	−	0.296119i
$783$	−9.96994	+	4.69150i	−0.356297	+	0.167661i
$784$	−17.0564	−	4.37933i	−0.609156	−	0.156405i
$785$	5.05199	−	1.11796i	0.180313	−	0.0399016i
$786$	1.51927	−	1.83648i	0.0541906	−	0.0655052i
$787$	−7.63075	−	4.84262i	−0.272007	−	0.172621i	0.392826	−	0.919613i	$-0.371497\pi$
$787$	−7.63075	−	4.84262i	−0.272007	−	0.172621i	−0.664833	+	0.746992i	$0.731497\pi$
$788$	33.5784	−	2.11257i	1.19618	−	0.0752572i
$789$	0.0754584	+	0.118903i	0.00268639	+	0.00423307i
$790$	42.4636	−	62.1978i	1.51079	−	2.21290i
$791$	−1.09159	−	17.3503i	−0.0388124	−	0.616905i
$792$	0.0310266	+	0.00591863i	0.00110248	+	0.000210309i
$793$	10.3846	−	3.37417i	0.368769	−	0.119820i
$794$	−35.8773	+	33.6911i	−1.27324	+	1.19565i
$795$	−3.20139	+	0.922699i	−0.113542	+	0.0327248i
$796$	−7.53637	−	39.5070i	−0.267120	−	1.40029i
$797$	−1.38216	+	1.47185i	−0.0489585	+	0.0521355i	−0.752982	−	0.658042i	$-0.771385\pi$
$797$	−1.38216	+	1.47185i	−0.0489585	+	0.0521355i	0.704023	+	0.710177i	$0.251385\pi$
$798$	1.49808	−	3.78372i	0.0530315	−	0.133942i
$799$	2.17604	+	6.69717i	0.0769828	+	0.236929i
$800$	29.4552	−	27.4251i	1.04140	−	0.969623i
$801$	−8.49289	+	26.1384i	−0.300082	+	0.923556i
$802$	11.5692	+	9.57091i	0.408524	+	0.337960i
$803$	1.04636	+	0.492380i	0.0369253	+	0.0173757i
$804$	2.36642	+	2.22222i	0.0834572	+	0.0783715i
$805$	2.05651	−	12.8076i	0.0724825	−	0.451410i
$806$	−29.3696	+	3.71024i	−1.03450	+	0.130688i
$807$		−	6.46844i		−	0.227700i
$808$	0.0895033	+	0.708492i	0.00314872	+	0.0249247i
$809$	9.09669	+	10.9960i	0.319823	+	0.386599i	0.905784	−	0.423740i	$-0.139283\pi$
$809$	9.09669	+	10.9960i	0.319823	+	0.386599i	−0.585961	+	0.810339i	$0.699283\pi$
$810$	−37.6551	−	1.26366i	−1.32306	−	0.0444007i
$811$	−1.13998	+	18.1194i	−0.0400300	+	0.636258i	0.925951	+	0.377644i	$0.123266\pi$
$811$	−1.13998	+	18.1194i	−0.0400300	+	0.636258i	−0.965981	+	0.258614i	$0.916734\pi$
$812$	−5.60416	+	21.8267i	−0.196667	+	0.765969i
$813$	−0.206738	+	0.805193i	−0.00725063	+	0.0282394i
$814$	−0.0821031	+	1.30499i	−0.00287771	+	0.0457400i
$815$	43.1499	−	29.1905i	1.51148	−	1.02250i
$816$	2.37694	+	2.87323i	0.0832097	+	0.100583i
$817$	−5.15320	−	40.7918i	−0.180288	−	1.42712i
$818$			35.5576i			1.24324i
$819$	−11.7805	+	1.48822i	−0.411643	+	0.0520026i
$820$	−33.2340	−	17.0229i	−1.16058	−	0.594464i
$821$	−10.5198	−	9.87877i	−0.367144	−	0.344771i	0.478914	−	0.877862i	$-0.341031\pi$
$821$	−10.5198	−	9.87877i	−0.367144	−	0.344771i	−0.846058	+	0.533090i	$0.821031\pi$
$822$	5.89248	+	2.77279i	0.205524	+	0.0967122i
$823$	9.86331	+	8.15964i	0.343813	+	0.284427i	0.793264	−	0.608878i	$-0.208380\pi$
$823$	9.86331	+	8.15964i	0.343813	+	0.284427i	−0.449450	+	0.893305i	$0.648380\pi$
$824$	−0.0125721	+	0.0386929i	−0.000437969	+	0.00134793i
$825$	−0.00859189	+	0.127868i	−0.000299131	+	0.00445178i
$826$	3.29888	+	10.1529i	0.114783	+	0.353265i
$827$	4.48118	−	11.3182i	0.155826	−	0.393572i	−0.830800	−	0.556571i	$-0.812117\pi$
$827$	4.48118	−	11.3182i	0.155826	−	0.393572i	0.986626	+	0.162999i	$0.0521168\pi$
$828$	15.2201	−	16.2078i	0.528935	−	0.563259i
$829$	7.32286	+	38.3878i	0.254333	+	1.33326i	0.848618	+	0.529007i	$0.177435\pi$
$829$	7.32286	+	38.3878i	0.254333	+	1.33326i	−0.594284	+	0.804255i	$0.702565\pi$
$830$	37.3270	+	55.1775i	1.29564	+	1.91524i
$831$	−1.96074	+	1.84126i	−0.0680173	+	0.0638725i
$832$	20.7101	−	6.72910i	0.717992	−	0.233290i
$833$	16.0416	+	3.06009i	0.555808	+	0.106026i
$834$	−0.222539	−	3.53715i	−0.00770589	−	0.122482i
$835$	6.52964	−	2.33511i	0.225967	−	0.0808099i
$836$	0.511986	+	0.806761i	0.0177074	+	0.0279024i
$837$	8.97733	−	0.564806i	0.310302	−	0.0195225i
$838$	30.3772	+	19.2779i	1.04936	+	0.665945i
$839$	30.9653	−	37.4306i	1.06904	−	1.29225i	0.114740	−	0.993396i	$-0.463396\pi$
$839$	30.9653	−	37.4306i	1.06904	−	1.29225i	0.954300	−	0.298852i	$-0.0966035\pi$
$840$	0.0694908	−	0.0784841i	0.00239766	−	0.00270796i
$841$	19.0739	+	4.89734i	0.657720	+	0.168874i
$842$	12.0983	−	5.69305i	0.416936	−	0.196195i
$843$	−1.39632	−	0.453690i	−0.0480917	−	0.0156259i
$844$	−23.3440	−	12.8335i	−0.803535	−	0.441747i
$845$	3.98493	−	13.6079i	0.137086	−	0.468128i
$846$	−11.4363	−	1.44474i	−0.393189	−	0.0496713i
$847$	−2.16405	+	17.1302i	−0.0743576	+	0.588601i
$848$	18.3546	−	11.6482i	0.630300	−	0.400001i
$849$	6.64610	−	4.82868i	0.228094	−	0.165720i
$850$	−24.9509	+	26.3441i	−0.855807	+	0.903596i
$851$	20.1545	+	14.6431i	0.690887	+	0.501959i
$852$	6.63326	+	0.417329i	0.227252	+	0.0142975i
$853$	16.7739	+	30.5116i	0.574328	+	1.04470i	0.990772	+	0.135538i	$0.0432761\pi$
$853$	16.7739	+	30.5116i	0.574328	+	1.04470i	−0.416444	+	0.909161i	$0.636724\pi$
$854$	−5.70002	+	12.1132i	−0.195051	+	0.414504i
$855$	−20.8688	−	23.7729i	−0.713698	−	0.813016i
$856$	0.142466	−	0.746833i	0.00486939	−	0.0255262i
$857$	−8.96365	−	12.3374i	−0.306192	−	0.421438i	0.627997	−	0.778216i	$-0.283875\pi$
$857$	−8.96365	−	12.3374i	−0.306192	−	0.421438i	−0.934189	+	0.356778i	$0.883875\pi$
$858$	−0.0641683	+	0.116722i	−0.00219067	+	0.00398481i
$859$	−10.6219	+	16.7374i	−0.362414	+	0.571072i	−0.975788	−	0.218720i	$-0.929812\pi$
$859$	−10.6219	+	16.7374i	−0.362414	+	0.571072i	0.613374	+	0.789793i	$0.289812\pi$
$860$	8.61738	−	38.1698i	0.293850	−	1.30158i
$861$	3.16013	+	1.25118i	0.107697	+	0.0426402i
$862$	−1.85083	−	4.67466i	−0.0630394	−	0.159219i
$863$	13.7354	−	11.3629i	0.467557	−	0.386797i	−0.373598	−	0.927591i	$-0.621876\pi$
$863$	13.7354	−	11.3629i	0.467557	−	0.386797i	0.841155	+	0.540794i	$0.181876\pi$
$864$	−12.3108	+	3.16088i	−0.418822	+	0.107535i
$865$	5.21714	+	33.4001i	0.177388	+	1.13564i
$866$	−5.75459	+	2.27840i	−0.195549	+	0.0774233i
$867$	0.731985	+	0.779485i	0.0248595	+	0.0264727i
$868$	10.8131	−	14.8829i	0.367019	−	0.505159i
$869$	−0.685310	−	1.45636i	−0.0232475	−	0.0494036i
$870$	−6.26561	−	5.54764i	−0.212424	−	0.188083i
$871$	13.4085	−	7.37138i	0.454330	−	0.249770i
$872$	−0.519247	+	0.0990516i	−0.0175839	+	0.00335431i
$873$	−3.40909	−	13.2775i	−0.115380	−	0.449376i
$874$	35.9166			1.21490
$875$	−14.4636	−	9.96521i	−0.488960	−	0.336885i
$876$	6.57828			0.222259
$877$	−5.06760	−	19.7370i	−0.171121	−	0.666471i	−0.995015	−	0.0997272i	$-0.968203\pi$
$877$	−5.06760	−	19.7370i	−0.171121	−	0.666471i	0.823894	−	0.566744i	$-0.191797\pi$
$878$	46.4164	−	8.85441i	1.56648	−	0.298822i
$879$	1.03263	−	0.567691i	0.0348296	−	0.0191478i
$880$	−0.180670	−	0.816440i	−0.00609040	−	0.0275222i
$881$	−9.12063	−	19.3823i	−0.307282	−	0.653007i	0.690224	−	0.723596i	$-0.257512\pi$
$881$	−9.12063	−	19.3823i	−0.307282	−	0.653007i	−0.997505	+	0.0705892i	$0.977512\pi$
$882$	−15.7133	+	21.6275i	−0.529093	+	0.728235i
$883$	22.6606	+	24.1311i	0.762590	+	0.812076i	0.986711	−	0.162486i	$-0.0519511\pi$
$883$	22.6606	+	24.1311i	0.762590	+	0.812076i	−0.224121	+	0.974561i	$0.571951\pi$
$884$	−17.7723	+	7.03654i	−0.597746	+	0.236664i
$885$	−1.98403	−	0.318573i	−0.0666923	−	0.0107087i
$886$	−31.8241	+	8.17103i	−1.06915	+	0.274511i
$887$	−9.73209	+	8.05108i	−0.326772	+	0.270329i	−0.786314	−	0.617827i	$-0.788013\pi$
$887$	−9.73209	+	8.05108i	−0.326772	+	0.270329i	0.459543	+	0.888156i	$0.348013\pi$
$888$	0.0741116	+	0.187184i	0.00248702	+	0.00628150i
$889$	−23.9419	−	9.47925i	−0.802984	−	0.317924i
$890$	−42.0739	+	3.88673i	−1.41032	+	0.130284i
$891$	−0.431456	+	0.679867i	−0.0144543	+	0.0227764i
$892$	19.4609	−	35.3993i	0.651600	−	1.18526i
$893$	−5.54767	−	7.63572i	−0.185646	−	0.255520i
$894$	−0.693442	+	3.63515i	−0.0231922	+	0.121578i
$895$	−17.5450	−	3.96104i	−0.586466	−	0.132403i
$896$	−0.599358	+	1.27370i	−0.0200231	+	0.0425513i
$897$	1.22256	+	2.22382i	0.0408200	+	0.0742513i
$898$	−16.1029	−	1.01311i	−0.537361	−	0.0338079i
$899$	−32.1587	−	23.3646i	−1.07255	−	0.779254i
$900$	−10.9632	−	28.0384i	−0.365441	−	0.934614i
$901$	−16.3099	+	11.8498i	−0.543361	+	0.394775i
$902$	−1.32936	+	0.843638i	−0.0442629	+	0.0280901i
$903$	−0.446409	+	3.53369i	−0.0148556	+	0.117594i
$904$	1.23015	+	0.155404i	0.0409142	+	0.00516866i
$905$	39.2880	−	30.3411i	1.30598	−	1.00857i
$906$	7.86312	+	4.32279i	0.261235	+	0.143615i
$907$	20.9701	+	6.81360i	0.696301	+	0.226242i	0.635718	−	0.771921i	$-0.280704\pi$
$907$	20.9701	+	6.81360i	0.696301	+	0.226242i	0.0605827	+	0.998163i	$0.480704\pi$
$908$	−37.8511	+	17.8114i	−1.25613	+	0.591090i
$909$	−18.0815	−	4.64254i	−0.599725	−	0.153983i
$910$	−9.25914	−	15.7327i	−0.306937	−	0.521536i
$911$	−1.87663	+	2.26846i	−0.0621756	+	0.0751574i	−0.800684	−	0.599087i	$-0.795530\pi$
$911$	−1.87663	+	2.26846i	−0.0621756	+	0.0751574i	0.738508	+	0.674244i	$0.235530\pi$
$912$	−4.21997	−	2.67807i	−0.139737	−	0.0886799i
$913$	1.42093	−	0.0893975i	0.0470260	−	0.00295863i
$914$	19.8806	+	31.3268i	0.657592	+	1.03620i
$915$	−1.54022	−	1.99439i	−0.0509179	−	0.0659326i
$916$	0.988056	+	15.7047i	0.0326463	+	0.518898i
$917$	6.85773	+	1.30818i	0.226462	+	0.0432000i
$918$	10.8981	−	3.54102i	0.359692	−	0.116871i
$919$	−40.5613	+	38.0896i	−1.33799	+	1.25646i	−0.397094	+	0.917778i	$0.629981\pi$
$919$	−40.5613	+	38.0896i	−1.33799	+	1.25646i	−0.940901	+	0.338682i	$0.890019\pi$
$920$	0.869818	+	0.315249i	0.0286771	+	0.0103934i
$921$	0.611884	+	3.20761i	0.0201623	+	0.105694i
$922$	37.3522	−	39.7761i	1.23013	−	1.30996i
$923$	11.5324	−	29.1276i	0.379594	−	0.958746i
$924$	−0.0255783	−	0.0787219i	−0.000841465	−	0.00258976i
$925$	29.6289	−	16.1246i	0.974191	−	0.530173i
$926$	15.1277	−	46.5582i	0.497126	−	1.53000i
$927$	−0.819463	−	0.677918i	−0.0269147	−	0.0222658i
$928$	50.8218	+	23.9149i	1.66831	+	0.785046i
$929$	6.70258	+	6.29414i	0.219905	+	0.206504i	0.786668	−	0.617377i	$-0.211805\pi$
$929$	6.70258	+	6.29414i	0.219905	+	0.206504i	−0.566763	+	0.823881i	$0.691805\pi$
$930$	3.08858	+	6.09374i	0.101279	+	0.199822i
$931$	−21.7159	+	2.74336i	−0.711710	+	0.0899099i
$932$		−	52.9139i		−	1.73325i
$933$	−0.308306	−	2.44049i	−0.0100935	−	0.0798982i
$934$	−49.0578	−	59.3007i	−1.60522	−	1.94038i
$935$	0.214762	+	0.745138i	0.00702347	+	0.0243686i
$936$	0.0531773	−	0.845230i	0.00173816	−	0.0276272i
$937$	−5.19196	+	20.2213i	−0.169614	+	0.660602i	0.825717	+	0.564084i	$0.190771\pi$
$937$	−5.19196	+	20.2213i	−0.169614	+	0.660602i	−0.995331	+	0.0965183i	$0.969229\pi$
$938$	−4.66540	+	18.1705i	−0.152331	+	0.593289i
$939$	−0.245426	+	3.90094i	−0.00800919	+	0.127302i
$940$	−2.48765	−	8.63114i	−0.0811382	−	0.281517i
$941$	−0.0743429	−	0.0898652i	−0.00242351	−	0.00292952i	0.769300	−	0.638888i	$-0.220605\pi$
$941$	−0.0743429	−	0.0898652i	−0.00242351	−	0.00292952i	−0.771724	+	0.635958i	$0.780605\pi$
$942$	−0.155548	−	1.23129i	−0.00506802	−	0.0401175i
$943$			29.9972i			0.976843i
$944$	13.0078	−	1.64327i	0.423368	−	0.0534838i
$945$	2.50773	+	4.94773i	0.0815765	+	0.160950i
$946$	−1.20277	−	1.12947i	−0.0391053	−	0.0367223i
$947$	−44.9686	−	21.1606i	−1.46128	−	0.687628i	−0.479484	−	0.877550i	$-0.659176\pi$
$947$	−44.9686	−	21.1606i	−1.46128	−	0.687628i	−0.981799	+	0.189923i	$0.939176\pi$
$948$	−7.05471	−	5.83616i	−0.229126	−	0.189550i
$949$	9.58155	−	29.4890i	0.311030	−	0.957253i
$950$	20.8941	−	43.9154i	0.677893	−	1.42481i
$951$	−0.0396943	−	0.122167i	−0.00128718	−	0.00396152i
$952$	0.233504	−	0.589764i	0.00756791	−	0.0191144i
$953$	−36.9997	+	39.4007i	−1.19854	+	1.27631i	−0.246918	+	0.969036i	$0.579418\pi$
$953$	−36.9997	+	39.4007i	−1.19854	+	1.27631i	−0.951620	+	0.307277i	$0.900582\pi$
$954$	−6.18385	−	32.4169i	−0.200210	−	1.04954i
$955$	−50.9170	−	18.4539i	−1.64763	−	0.597153i
$956$	15.7247	−	14.7664i	0.508572	−	0.477581i
$957$	−0.170101	+	0.0552691i	−0.00549858	+	0.00178660i
$958$	24.6642	+	4.70494i	0.796863	+	0.152010i
$959$	1.19774	+	19.0375i	0.0386770	+	0.614753i
$960$	−3.07165	−	3.97741i	−0.0991370	−	0.128370i
$961$	0.777088	+	1.22450i	0.0250674	+	0.0394998i
$962$	34.9901	−	2.20139i	1.12813	−	0.0709757i
$963$	16.7811	+	10.6496i	0.540763	+	0.343179i
$964$	−32.8775	+	39.7420i	−1.05891	+	1.28000i
$965$	−16.7248	−	28.4182i	−0.538392	−	0.914813i
$966$	−3.01361	−	0.773764i	−0.0969614	−	0.0248955i
$967$	−15.2587	+	7.18022i	−0.490688	+	0.230900i	−0.655172	−	0.755479i	$-0.727404\pi$
$967$	−15.2587	+	7.18022i	−0.490688	+	0.230900i	0.164484	+	0.986380i	$0.447404\pi$
$968$	−1.17122	−	0.380553i	−0.0376445	−	0.0122314i
$969$	4.06175	+	2.23297i	0.130482	+	0.0717332i
$970$	16.6799	−	12.8814i	0.535558	−	0.413597i
$971$	2.78003	+	0.351200i	0.0892154	+	0.0112705i	0.169814	−	0.985476i	$-0.445683\pi$
$971$	2.78003	+	0.351200i	0.0892154	+	0.0112705i	−0.0805988	+	0.996747i	$0.525683\pi$
$972$	−1.79456	+	14.2054i	−0.0575606	+	0.455639i
$973$	8.76513	−	5.56252i	0.280997	−	0.178326i
$974$	−20.2775	+	14.7325i	−0.649732	+	0.472058i
$975$	3.43029	−	0.201145i	0.109857	−	0.00644181i
$976$	13.3017	+	9.66425i	0.425777	+	0.309345i
$977$	−39.1572	−	2.46356i	−1.25275	−	0.0788163i	−0.577491	−	0.816397i	$-0.695968\pi$
$977$	−39.1572	−	2.46356i	−1.25275	−	0.0788163i	−0.675259	+	0.737581i	$0.735968\pi$
$978$	−6.01982	−	10.9500i	−0.192493	−	0.350143i
$979$	−0.384492	+	0.817087i	−0.0122884	+	0.0261142i
$980$	−20.3201	−	4.58755i	−0.649100	−	0.146544i
$981$	2.58932	−	13.5737i	0.0826707	−	0.433375i
$982$	10.9629	+	15.0892i	0.349841	+	0.481515i
$983$	7.34143	−	13.3540i	0.234155	−	0.425927i	−0.732958	−	0.680274i	$-0.761861\pi$
$983$	7.34143	−	13.3540i	0.234155	−	0.425927i	0.967113	+	0.254348i	$0.0818607\pi$
$984$	−0.129892	+	0.204677i	−0.00414080	+	0.00652486i
$985$	−36.4427	+	3.36653i	−1.16116	+	0.107267i
$986$	−47.0825	−	18.6413i	−1.49941	−	0.593660i
$987$	0.300983	+	0.760197i	0.00958041	+	0.0241973i
$988$	19.7402	−	16.3305i	0.628020	−	0.519543i
$989$	−30.4479	+	7.81770i	−0.968188	+	0.248588i
$990$	−1.25336	−	0.201251i	−0.0398345	−	0.00639618i
$991$	−44.7465	+	17.7164i	−1.42142	+	0.562780i	−0.948061	−	0.318089i	$-0.896959\pi$
$991$	−44.7465	+	17.7164i	−1.42142	+	0.562780i	−0.473360	+	0.880869i	$0.656959\pi$
$992$	−31.3882	−	33.4250i	−0.996575	−	1.06124i
$993$	3.61509	−	4.97574i	0.114721	−	0.157900i
$994$	16.3537	+	34.7535i	0.518709	+	1.10231i
$995$	9.45270	+	42.7162i	0.299671	+	1.35419i
$996$	7.09715	−	3.90169i	0.224882	−	0.123630i
$997$	8.66840	−	1.65359i	0.274531	−	0.0523696i	−0.0482773	−	0.998834i	$-0.515373\pi$
$997$	8.66840	−	1.65359i	0.274531	−	0.0523696i	0.322808	+	0.946464i	$0.395373\pi$
$998$	15.2214	+	59.2834i	0.481825	+	1.87658i
$999$	−10.6530			−0.337046

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.h.a.104.3	✓	240
5.2	odd	4		625.2.g.b.351.19		480
5.3	odd	4		625.2.g.b.351.6		480
5.4	even	2		625.2.h.a.274.10		240
125.6	even	25		625.2.h.a.349.10		240
125.33	odd	100		625.2.g.b.276.6		480
125.92	odd	100		625.2.g.b.276.19		480
125.119	even	50	inner	125.2.h.a.119.3	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.h.a.104.3	✓	240	1.1	even	1	trivial
125.2.h.a.119.3	yes	240	125.119	even	50	inner
625.2.g.b.276.6		480	125.33	odd	100
625.2.g.b.276.19		480	125.92	odd	100
625.2.g.b.351.6		480	5.3	odd	4
625.2.g.b.351.19		480	5.2	odd	4
625.2.h.a.274.10		240	5.4	even	2
625.2.h.a.349.10		240	125.6	even	25

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.h (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500827 - 1.95059i) q^{2} +(0.261606 - 0.0499040i) q^{3} +(-1.80137 + 0.990311i) q^{4} +(1.92710 - 1.13415i) q^{5} +(-0.228362 - 0.485293i) q^{6} +(0.923406 - 1.27096i) q^{7} +(0.0767024 + 0.0816797i) q^{8} +(-2.72338 + 1.07826i) q^{9} +O(q^{10})\)	\(q+(-0.500827 - 1.95059i) q^{2} +(0.261606 - 0.0499040i) q^{3} +(-1.80137 + 0.990311i) q^{4} +(1.92710 - 1.13415i) q^{5} +(-0.228362 - 0.485293i) q^{6} +(0.923406 - 1.27096i) q^{7} +(0.0767024 + 0.0816797i) q^{8} +(-2.72338 + 1.07826i) q^{9} +(-3.17740 - 3.19097i) q^{10} +(-0.0932173 + 0.0239341i) q^{11} +(-0.421829 + 0.348967i) q^{12} +(0.949931 + 2.39925i) q^{13} +(-2.94159 - 1.16466i) q^{14} +(0.447542 - 0.392870i) q^{15} +(-2.08202 + 3.28074i) q^{16} +(1.73598 - 3.15774i) q^{17} +(3.46720 + 4.77219i) q^{18} +(-0.905011 + 4.74424i) q^{19} +(-2.34826 + 3.95145i) q^{20} +(0.178143 - 0.378572i) q^{21} +(0.0933715 + 0.169842i) q^{22} +(3.68536 + 0.231863i) q^{23} +(0.0241419 + 0.0175402i) q^{24} +(2.42742 - 4.37123i) q^{25} +(4.20421 - 3.05454i) q^{26} +(-1.33324 + 0.846097i) q^{27} +(-0.404750 + 3.20393i) q^{28} +(6.92298 + 0.874576i) q^{29} +(-0.990470 - 0.676212i) q^{30} +(-4.99189 - 2.74432i) q^{31} +(7.65526 + 2.48734i) q^{32} +(-0.0231918 + 0.0109132i) q^{33} +(-7.02889 - 1.80471i) q^{34} +(0.338038 - 3.49654i) q^{35} +(3.83800 - 4.63935i) q^{36} +(5.69623 + 3.61494i) q^{37} +(9.70732 - 0.610733i) q^{38} +(0.368240 + 0.580253i) q^{39} +(0.240450 + 0.0704130i) q^{40} +(0.510078 + 8.10746i) q^{41} +(-0.827659 - 0.157884i) q^{42} +(-8.09635 + 2.63066i) q^{43} +(0.144217 - 0.135428i) q^{44} +(-4.02531 + 5.16664i) q^{45} +(-1.39346 - 7.30476i) q^{46} +(-1.33773 + 1.42454i) q^{47} +(-0.380947 + 0.962163i) q^{48} +(1.40046 + 4.31017i) q^{49} +(-9.74220 - 2.54567i) q^{50} +(0.296559 - 0.912716i) q^{51} +(-4.08718 - 3.38121i) q^{52} +(-5.06219 - 2.38209i) q^{53} +(2.31811 + 2.17685i) q^{54} +(-0.152494 + 0.151846i) q^{55} +(0.174639 - 0.0220620i) q^{56} +1.28628i q^{57} +(-1.76127 - 13.9419i) q^{58} +(-2.15085 - 2.59993i) q^{59} +(-0.417125 + 1.15091i) q^{60} +(0.265694 - 4.22309i) q^{61} +(-2.85297 + 11.1116i) q^{62} +(-1.14436 + 4.45698i) q^{63} +(0.529873 - 8.42209i) q^{64} +(4.55172 + 3.54623i) q^{65} +(0.0329023 + 0.0397721i) q^{66} +(-0.743178 - 5.88286i) q^{67} +7.40742i q^{68} +(0.975683 - 0.123257i) q^{69} +(-6.98963 + 1.09179i) q^{70} +(-8.84989 - 8.31060i) q^{71} +(-0.296962 - 0.139740i) q^{72} +(-9.25841 - 7.65922i) q^{73} +(4.19845 - 12.9215i) q^{74} +(0.416885 - 1.26468i) q^{75} +(-3.06801 - 9.44236i) q^{76} +(-0.0556581 + 0.140576i) q^{77} +(0.947413 - 1.00889i) q^{78} +(3.13379 + 16.4279i) q^{79} +(-0.291414 + 8.68364i) q^{80} +(6.09905 - 5.72739i) q^{81} +(15.5589 - 5.05539i) q^{82} +(-14.5315 - 2.77203i) q^{83} +(0.0540038 + 0.858365i) q^{84} +(-0.235937 - 8.05414i) q^{85} +(9.18623 + 14.4752i) q^{86} +(1.85474 - 0.116690i) q^{87} +(-0.00910492 - 0.00577816i) q^{88} +(5.98097 - 7.22975i) q^{89} +(12.0940 + 5.26416i) q^{90} +(3.92652 + 1.00816i) q^{91} +(-6.86831 + 3.23198i) q^{92} +(-1.44286 - 0.468814i) q^{93} +(3.44866 + 1.89592i) q^{94} +(3.63662 + 10.1690i) q^{95} +(2.12679 + 0.268676i) q^{96} +(-0.586565 + 4.64314i) q^{97} +(7.70600 - 4.89038i) q^{98} +(0.228059 - 0.165695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Introduction

L-functions

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