LMFDB - Embedded newform 62.2.g.b.51.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [62,2,Mod(7,62)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(62, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([28]))

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

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

chi := DirichletCharacter("62.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	62.g (of order $15$, degree $8$, 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:	$0.495072492532$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			51.1
Root			$-0.978148 - 0.207912i$ of defining polynomial
Character	$\chi$	$=$	62.51
Dual form			62.2.g.b.45.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(-1.75181 - 1.94558i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.169131 + 0.292943i) q^{5} +(-1.30902 + 2.26728i) q^{6} +(-0.352722 - 3.35592i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.402863 + 3.83299i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(-1.75181 - 1.94558i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.169131 + 0.292943i) q^{5} +(-1.30902 + 2.26728i) q^{6} +(-0.352722 - 3.35592i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.402863 + 3.83299i) q^{9} +(0.226341 - 0.251377i) q^{10} +(3.61426 + 1.60917i) q^{11} +(2.56082 + 0.544320i) q^{12} +(5.53062 - 1.17557i) q^{13} +(-3.08268 + 1.37250i) q^{14} +(0.273659 - 0.842236i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-5.71044 + 2.54245i) q^{17} +(3.76988 - 0.801313i) q^{18} +(-0.942790 - 0.200396i) q^{19} +(-0.309017 - 0.137583i) q^{20} +(-5.91131 + 6.56518i) q^{21} +(0.413545 - 3.93462i) q^{22} +(0.657170 + 0.477462i) q^{23} +(-0.273659 - 2.60369i) q^{24} +(2.44279 - 4.23104i) q^{25} +(-2.82709 - 4.89667i) q^{26} +(1.80902 - 1.31433i) q^{27} +(2.25792 + 2.50767i) q^{28} +(1.43997 + 4.43176i) q^{29} -0.885579 q^{30} +(-4.26988 + 3.57325i) q^{31} -1.00000 q^{32} +(-3.20071 - 9.85077i) q^{33} +(4.18264 + 4.64529i) q^{34} +(0.923438 - 0.670917i) q^{35} +(-1.92705 - 3.33775i) q^{36} +(-0.991653 + 1.71759i) q^{37} +(0.100750 + 0.958572i) q^{38} +(-11.9757 - 8.70089i) q^{39} +(-0.0353579 + 0.336408i) q^{40} +(4.63048 - 5.14267i) q^{41} +(8.07055 + 3.59324i) q^{42} +(7.95156 + 1.69016i) q^{43} +(-3.86984 + 0.822560i) q^{44} +(-1.19098 + 0.530260i) q^{45} +(0.251017 - 0.772550i) q^{46} +(-0.462897 + 1.42465i) q^{47} +(-2.39169 + 1.06485i) q^{48} +(-4.29078 + 0.912033i) q^{49} +(-4.77882 - 1.01577i) q^{50} +(14.9501 + 6.65622i) q^{51} +(-3.78339 + 4.20188i) q^{52} +(-0.929449 + 8.84312i) q^{53} +(-1.80902 - 1.31433i) q^{54} +(0.139886 + 1.33093i) q^{55} +(1.68720 - 2.92232i) q^{56} +(1.26170 + 2.18533i) q^{57} +(3.76988 - 2.73898i) q^{58} +(-5.22995 - 5.80845i) q^{59} +(0.273659 + 0.842236i) q^{60} +7.56231 q^{61} +(4.71783 + 2.95670i) q^{62} +13.0053 q^{63} +(0.309017 + 0.951057i) q^{64} +(1.27977 + 1.42133i) q^{65} +(-8.37957 + 6.08811i) q^{66} +(-0.288120 - 0.499038i) q^{67} +(3.12543 - 5.41340i) q^{68} +(-0.222295 - 2.11500i) q^{69} +(-0.923438 - 0.670917i) q^{70} +(-0.783084 + 7.45055i) q^{71} +(-2.57890 + 2.86416i) q^{72} +(-10.0803 - 4.48803i) q^{73} +(1.93997 + 0.412353i) q^{74} +(-12.5111 + 2.65932i) q^{75} +(0.880523 - 0.392034i) q^{76} +(4.12543 - 12.6968i) q^{77} +(-4.57433 + 14.0783i) q^{78} +(-13.2795 + 5.91243i) q^{79} +(0.330869 - 0.0703285i) q^{80} +(5.58347 + 1.18680i) q^{81} +(-6.32187 - 2.81468i) q^{82} +(1.06460 - 1.18236i) q^{83} +(0.923438 - 8.78592i) q^{84} +(-1.71060 - 1.24283i) q^{85} +(-0.849733 - 8.08467i) q^{86} +(6.09979 - 10.5652i) q^{87} +(1.97815 + 3.42625i) q^{88} +(6.02090 - 4.37444i) q^{89} +(0.872341 + 0.968833i) q^{90} +(-5.89590 - 18.1457i) q^{91} -0.812307 q^{92} +(14.4320 + 2.04774i) q^{93} +1.49797 q^{94} +(-0.100750 - 0.310077i) q^{95} +(1.75181 + 1.94558i) q^{96} +(-0.0600337 + 0.0436171i) q^{97} +(2.19332 + 3.79894i) q^{98} +(-7.62398 + 13.2051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + q^{3} - 2 q^{4} - 3 q^{5} - 6 q^{6} - 16 q^{7} + 2 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + q^3 - 2 * q^4 - 3 * q^5 - 6 * q^6 - 16 * q^7 + 2 * q^8 + 8 * q^9	\( 8 q + 2 q^{2} + q^{3} - 2 q^{4} - 3 q^{5} - 6 q^{6} - 16 q^{7} + 2 q^{8} + 8 q^{9} + 8 q^{10} + 3 q^{11} + q^{12} - 14 q^{14} - 4 q^{15} - 2 q^{16} - 2 q^{17} + 7 q^{18} + 3 q^{19} + 2 q^{20} - 31 q^{21} - 3 q^{22} + 15 q^{23} + 4 q^{24} + 9 q^{25} - 10 q^{26} + 10 q^{27} + 9 q^{28} + 13 q^{29} + 14 q^{30} - 11 q^{31} - 8 q^{32} - 6 q^{33} + 22 q^{34} + 24 q^{35} - 2 q^{36} + 8 q^{37} - 18 q^{38} - 30 q^{39} - 2 q^{40} + 13 q^{41} + 21 q^{42} - 7 q^{44} - 14 q^{45} + 5 q^{46} + 9 q^{47} - 4 q^{48} + 9 q^{49} - 9 q^{50} + 28 q^{51} - 51 q^{53} - 10 q^{54} + q^{55} + q^{56} + 18 q^{57} + 7 q^{58} - 18 q^{59} - 4 q^{60} - 20 q^{61} - 19 q^{62} - 14 q^{63} - 2 q^{64} + 10 q^{65} - 19 q^{66} - 18 q^{67} + 3 q^{68} + 35 q^{69} - 24 q^{70} + 7 q^{71} + 7 q^{72} - 13 q^{73} + 17 q^{74} - 36 q^{75} - 12 q^{76} + 11 q^{77} - 10 q^{78} + 9 q^{79} + 7 q^{80} + 16 q^{81} + 7 q^{82} + 6 q^{83} + 24 q^{84} - 17 q^{85} + 15 q^{86} + q^{87} + 7 q^{88} + 28 q^{89} + 19 q^{90} + 20 q^{91} - 20 q^{92} + 32 q^{93} + 6 q^{94} + 18 q^{95} - q^{96} + q^{97} + 11 q^{98} - 11 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + q^3 - 2 * q^4 - 3 * q^5 - 6 * q^6 - 16 * q^7 + 2 * q^8 + 8 * q^9 + 8 * q^10 + 3 * q^11 + q^12 - 14 * q^14 - 4 * q^15 - 2 * q^16 - 2 * q^17 + 7 * q^18 + 3 * q^19 + 2 * q^20 - 31 * q^21 - 3 * q^22 + 15 * q^23 + 4 * q^24 + 9 * q^25 - 10 * q^26 + 10 * q^27 + 9 * q^28 + 13 * q^29 + 14 * q^30 - 11 * q^31 - 8 * q^32 - 6 * q^33 + 22 * q^34 + 24 * q^35 - 2 * q^36 + 8 * q^37 - 18 * q^38 - 30 * q^39 - 2 * q^40 + 13 * q^41 + 21 * q^42 - 7 * q^44 - 14 * q^45 + 5 * q^46 + 9 * q^47 - 4 * q^48 + 9 * q^49 - 9 * q^50 + 28 * q^51 - 51 * q^53 - 10 * q^54 + q^55 + q^56 + 18 * q^57 + 7 * q^58 - 18 * q^59 - 4 * q^60 - 20 * q^61 - 19 * q^62 - 14 * q^63 - 2 * q^64 + 10 * q^65 - 19 * q^66 - 18 * q^67 + 3 * q^68 + 35 * q^69 - 24 * q^70 + 7 * q^71 + 7 * q^72 - 13 * q^73 + 17 * q^74 - 36 * q^75 - 12 * q^76 + 11 * q^77 - 10 * q^78 + 9 * q^79 + 7 * q^80 + 16 * q^81 + 7 * q^82 + 6 * q^83 + 24 * q^84 - 17 * q^85 + 15 * q^86 + q^87 + 7 * q^88 + 28 * q^89 + 19 * q^90 + 20 * q^91 - 20 * q^92 + 32 * q^93 + 6 * q^94 + 18 * q^95 - q^96 + q^97 + 11 * q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{15}\right)$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	−1.75181	−	1.94558i	−1.01141	−	1.12328i	−0.992349	−	0.123462i	$-0.960600\pi$
$3$	−1.75181	−	1.94558i	−1.01141	−	1.12328i	−0.0190567	−	0.999818i	$-0.506066\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.169131	+	0.292943i	0.0756375	+	0.131008i	0.901363	−	0.433064i	$-0.142567\pi$
$5$	0.169131	+	0.292943i	0.0756375	+	0.131008i	−0.825726	+	0.564072i	$0.809234\pi$
$6$	−1.30902	+	2.26728i	−0.534404	+	0.925615i
$7$	−0.352722	−	3.35592i	−0.133316	−	1.26842i	−0.832721	−	0.553694i	$-0.813218\pi$
$7$	−0.352722	−	3.35592i	−0.133316	−	1.26842i	0.699404	−	0.714726i	$-0.253449\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−0.402863	+	3.83299i	−0.134288	+	1.27766i
$10$	0.226341	−	0.251377i	0.0715753	−	0.0794924i
$11$	3.61426	+	1.60917i	1.08974	+	0.485183i	0.871342	−	0.490677i	$-0.163250\pi$
$11$	3.61426	+	1.60917i	1.08974	+	0.485183i	0.218397	+	0.975860i	$0.429917\pi$
$12$	2.56082	+	0.544320i	0.739246	+	0.157132i
$13$	5.53062	−	1.17557i	1.53392	−	0.326045i	0.637921	−	0.770102i	$-0.279795\pi$
$13$	5.53062	−	1.17557i	1.53392	−	0.326045i	0.895998	+	0.444057i	$0.146461\pi$
$14$	−3.08268	+	1.37250i	−0.823880	+	0.366815i
$15$	0.273659	−	0.842236i	0.0706585	−	0.217464i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−5.71044	+	2.54245i	−1.38498	+	0.616635i	−0.957775	−	0.287518i	$-0.907170\pi$
$17$	−5.71044	+	2.54245i	−1.38498	+	0.616635i	−0.427209	+	0.904153i	$0.640503\pi$
$18$	3.76988	−	0.801313i	0.888569	−	0.188871i
$19$	−0.942790	−	0.200396i	−0.216291	−	0.0459740i	0.0984917	−	0.995138i	$-0.468598\pi$
$19$	−0.942790	−	0.200396i	−0.216291	−	0.0459740i	−0.314782	+	0.949164i	$0.601932\pi$
$20$	−0.309017	−	0.137583i	−0.0690983	−	0.0307645i
$21$	−5.91131	+	6.56518i	−1.28995	+	1.43264i
$22$	0.413545	−	3.93462i	0.0881682	−	0.838864i
$23$	0.657170	+	0.477462i	0.137029	+	0.0995578i	0.654188	−	0.756332i	$-0.273010\pi$
$23$	0.657170	+	0.477462i	0.137029	+	0.0995578i	−0.517159	+	0.855889i	$0.673010\pi$
$24$	−0.273659	−	2.60369i	−0.0558604	−	0.531476i
$25$	2.44279	−	4.23104i	0.488558	−	0.846207i
$26$	−2.82709	−	4.89667i	−0.554438	−	0.960315i
$27$	1.80902	−	1.31433i	0.348145	−	0.252942i
$28$	2.25792	+	2.50767i	0.426707	+	0.473906i
$29$	1.43997	+	4.43176i	0.267395	+	0.822957i	0.991132	+	0.132881i	$0.0424229\pi$
$29$	1.43997	+	4.43176i	0.267395	+	0.822957i	−0.723737	+	0.690076i	$0.757577\pi$
$30$	−0.885579			−0.161684
$31$	−4.26988	+	3.57325i	−0.766893	+	0.641775i
$31$	−4.26988	+	3.57325i	−0.766893	+	0.641775i
$32$	−1.00000			−0.176777
$33$	−3.20071	−	9.85077i	−0.557172	−	1.71480i
$34$	4.18264	+	4.64529i	0.717316	+	0.796660i
$35$	0.923438	−	0.670917i	0.156089	−	0.113406i
$36$	−1.92705	−	3.33775i	−0.321175	−	0.556292i
$37$	−0.991653	+	1.71759i	−0.163027	+	0.282371i	−0.935953	−	0.352125i	$-0.885459\pi$
$37$	−0.991653	+	1.71759i	−0.163027	+	0.282371i	0.772926	+	0.634496i	$0.218792\pi$
$38$	0.100750	+	0.958572i	0.0163438	+	0.155501i
$39$	−11.9757	−	8.70089i	−1.91765	−	1.39326i
$40$	−0.0353579	+	0.336408i	−0.00559058	+	0.0531908i
$41$	4.63048	−	5.14267i	0.723160	−	0.803150i	−0.263721	−	0.964599i	$-0.584950\pi$
$41$	4.63048	−	5.14267i	0.723160	−	0.803150i	0.986881	+	0.161449i	$0.0516166\pi$
$42$	8.07055	+	3.59324i	1.24531	+	0.554449i
$43$	7.95156	+	1.69016i	1.21260	+	0.257746i	0.769454	−	0.638702i	$-0.220528\pi$
$43$	7.95156	+	1.69016i	1.21260	+	0.257746i	0.443148	+	0.896449i	$0.353862\pi$
$44$	−3.86984	+	0.822560i	−0.583400	+	0.124006i
$45$	−1.19098	+	0.530260i	−0.177541	+	0.0790465i
$46$	0.251017	−	0.772550i	0.0370104	−	0.113906i
$47$	−0.462897	+	1.42465i	−0.0675205	+	0.207807i	−0.979124	−	0.203264i	$-0.934845\pi$
$47$	−0.462897	+	1.42465i	−0.0675205	+	0.207807i	0.911603	+	0.411071i	$0.134845\pi$
$48$	−2.39169	+	1.06485i	−0.345211	+	0.153698i
$49$	−4.29078	+	0.912033i	−0.612968	+	0.130290i
$50$	−4.77882	−	1.01577i	−0.675827	−	0.143651i
$51$	14.9501	+	6.65622i	2.09344	+	0.932057i
$52$	−3.78339	+	4.20188i	−0.524661	+	0.582695i
$53$	−0.929449	+	8.84312i	−0.127670	+	1.21470i	0.723694	+	0.690121i	$0.242443\pi$
$53$	−0.929449	+	8.84312i	−0.127670	+	1.21470i	−0.851364	+	0.524575i	$0.824224\pi$
$54$	−1.80902	−	1.31433i	−0.246176	−	0.178857i
$55$	0.139886	+	1.33093i	0.0188623	+	0.179463i
$56$	1.68720	−	2.92232i	0.225462	−	0.390512i
$57$	1.26170	+	2.18533i	0.167116	+	0.289454i
$58$	3.76988	−	2.73898i	0.495010	−	0.359646i
$59$	−5.22995	−	5.80845i	−0.680882	−	0.756196i	0.299329	−	0.954150i	$-0.403237\pi$
$59$	−5.22995	−	5.80845i	−0.680882	−	0.756196i	−0.980211	+	0.197954i	$0.936570\pi$
$60$	0.273659	+	0.842236i	0.0353292	+	0.108732i
$61$	7.56231			0.968254			0.484127	−	0.874998i	$-0.339137\pi$
$61$	7.56231			0.968254			0.484127	+	0.874998i	$0.339137\pi$
$62$	4.71783	+	2.95670i	0.599165	+	0.375502i
$63$	13.0053			1.63852
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	1.27977	+	1.42133i	0.158736	+	0.176294i
$66$	−8.37957	+	6.08811i	−1.03145	+	0.749395i
$67$	−0.288120	−	0.499038i	−0.0351994	−	0.0609672i	0.847889	−	0.530174i	$-0.177873\pi$
$67$	−0.288120	−	0.499038i	−0.0351994	−	0.0609672i	−0.883088	+	0.469207i	$0.844540\pi$
$68$	3.12543	−	5.41340i	0.379014	−	0.656471i
$69$	−0.222295	−	2.11500i	−0.0267612	−	0.254616i
$70$	−0.923438	−	0.670917i	−0.110372	−	0.0801899i
$71$	−0.783084	+	7.45055i	−0.0929350	+	0.884218i	0.844382	+	0.535741i	$0.179968\pi$
$71$	−0.783084	+	7.45055i	−0.0929350	+	0.884218i	−0.937317	+	0.348477i	$0.886699\pi$
$72$	−2.57890	+	2.86416i	−0.303926	+	0.337544i
$73$	−10.0803	−	4.48803i	−1.17981	−	0.525284i	−0.279333	−	0.960194i	$-0.590113\pi$
$73$	−10.0803	−	4.48803i	−1.17981	−	0.525284i	−0.900474	+	0.434910i	$0.856780\pi$
$74$	1.93997	+	0.412353i	0.225516	+	0.0479350i
$75$	−12.5111	+	2.65932i	−1.44466	+	0.307072i
$76$	0.880523	−	0.392034i	0.101003	−	0.0449694i
$77$	4.12543	−	12.6968i	0.470136	−	1.44693i
$78$	−4.57433	+	14.0783i	−0.517941	+	1.59406i
$79$	−13.2795	+	5.91243i	−1.49407	+	0.665201i	−0.981152	−	0.193239i	$-0.938101\pi$
$79$	−13.2795	+	5.91243i	−1.49407	+	0.665201i	−0.512914	+	0.858440i	$0.671434\pi$
$80$	0.330869	−	0.0703285i	0.0369923	−	0.00786296i
$81$	5.58347	+	1.18680i	0.620385	+	0.131867i
$82$	−6.32187	−	2.81468i	−0.698134	−	0.310829i
$83$	1.06460	−	1.18236i	0.116855	−	0.129781i	−0.681879	−	0.731465i	$-0.738837\pi$
$83$	1.06460	−	1.18236i	0.116855	−	0.129781i	0.798734	+	0.601684i	$0.205503\pi$
$84$	0.923438	−	8.78592i	0.100755	−	0.958623i
$85$	−1.71060	−	1.24283i	−0.185541	−	0.134803i
$86$	−0.849733	−	8.08467i	−0.0916291	−	0.871793i
$87$	6.09979	−	10.5652i	0.653967	−	1.13270i
$88$	1.97815	+	3.42625i	0.210871	+	0.365240i
$89$	6.02090	−	4.37444i	0.638214	−	0.463689i	−0.221022	−	0.975269i	$-0.570939\pi$
$89$	6.02090	−	4.37444i	0.638214	−	0.463689i	0.859236	+	0.511579i	$0.170939\pi$
$90$	0.872341	+	0.968833i	0.0919528	+	0.102124i
$91$	−5.89590	−	18.1457i	−0.618058	−	1.90219i
$92$	−0.812307			−0.0846889
$93$	14.4320	+	2.04774i	1.49653	+	0.212341i
$94$	1.49797			0.154503
$95$	−0.100750	−	0.310077i	−0.0103367	−	0.0318132i
$96$	1.75181	+	1.94558i	0.178793	+	0.198570i
$97$	−0.0600337	+	0.0436171i	−0.00609550	+	0.00442864i	−0.590829	−	0.806797i	$-0.701199\pi$
$97$	−0.0600337	+	0.0436171i	−0.00609550	+	0.00442864i	0.584733	+	0.811226i	$0.301199\pi$
$98$	2.19332	+	3.79894i	0.221559	+	0.383751i
$99$	−7.62398	+	13.2051i	−0.766239	+	1.32717i
$100$	0.510682	+	4.85882i	0.0510682	+	0.485882i
$101$	−4.17274	−	3.03168i	−0.415204	−	0.301663i	0.360502	−	0.932759i	$-0.382606\pi$
$101$	−4.17274	−	3.03168i	−0.415204	−	0.301663i	−0.775705	+	0.631096i	$0.782606\pi$
$102$	1.71060	−	16.2753i	0.169375	−	1.61149i
$103$	−2.62855	+	2.91930i	−0.258999	+	0.287647i	−0.858594	−	0.512656i	$-0.828662\pi$
$103$	−2.62855	+	2.91930i	−0.258999	+	0.287647i	0.599595	+	0.800303i	$0.295328\pi$
$104$	5.16535	+	2.29976i	0.506504	+	0.225510i
$105$	−2.92301	−	0.621304i	−0.285256	−	0.0606331i
$106$	8.69752	−	1.84872i	0.844778	−	0.179563i
$107$	0.533023	−	0.237317i	0.0515292	−	0.0229423i	−0.380810	−	0.924653i	$-0.624355\pi$
$107$	0.533023	−	0.237317i	0.0515292	−	0.0229423i	0.432339	+	0.901711i	$0.357688\pi$
$108$	−0.690983	+	2.12663i	−0.0664899	+	0.204635i
$109$	−1.19302	+	3.67173i	−0.114270	+	0.351688i	−0.991794	−	0.127845i	$-0.959194\pi$
$109$	−1.19302	+	3.67173i	−0.114270	+	0.351688i	0.877524	+	0.479533i	$0.159194\pi$
$110$	1.22256	−	0.544320i	0.116567	−	0.0518989i
$111$	5.07890	−	1.07955i	0.482068	−	0.102467i
$112$	−3.30067	−	0.701579i	−0.311884	−	0.0662930i
$113$	−15.2609	−	6.79458i	−1.43562	−	0.639180i	−0.466223	−	0.884667i	$-0.654386\pi$
$113$	−15.2609	−	6.79458i	−1.43562	−	0.639180i	−0.969400	+	0.245487i	$0.921052\pi$
$114$	1.68848	−	1.87525i	0.158141	−	0.175633i
$115$	−0.0287215	+	0.273267i	−0.00267829	+	0.0254823i
$116$	−3.76988	−	2.73898i	−0.350025	−	0.254308i
$117$	2.27786	+	21.6724i	0.210588	+	2.00362i
$118$	−3.90802	+	6.76889i	−0.359763	+	0.623127i
$119$	10.5465	+	18.2670i	0.966793	+	1.67453i
$120$	0.716449	−	0.520530i	0.0654025	−	0.0475177i
$121$	3.11298	+	3.45731i	0.282998	+	0.314301i
$122$	−2.33688	−	7.19218i	−0.211571	−	0.651149i
$123$	−18.1172			−1.63357
$124$	1.35410	−	5.40059i	0.121602	−	0.484988i
$125$	3.34391			0.299088
$126$	−4.01886	−	12.3688i	−0.358029	−	1.10190i
$127$	4.50168	+	4.99962i	0.399460	+	0.443645i	0.908996	−	0.416804i	$-0.136850\pi$
$127$	4.50168	+	4.99962i	0.399460	+	0.443645i	−0.509537	+	0.860449i	$0.670183\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	−10.6413	−	18.4312i	−0.936911	−	1.62278i
$130$	0.956295	−	1.65635i	0.0838726	−	0.145272i
$131$	0.758243	+	7.21420i	0.0662480	+	0.630308i	0.976391	+	0.216013i	$0.0693053\pi$
$131$	0.758243	+	7.21420i	0.0662480	+	0.630308i	−0.910143	+	0.414295i	$0.864028\pi$
$132$	8.37957	+	6.08811i	0.729348	+	0.529902i
$133$	−0.339972	+	3.23461i	−0.0294793	+	0.280477i
$134$	−0.385579	+	0.428229i	−0.0333090	+	0.0369934i
$135$	0.690983	+	0.307645i	0.0594703	+	0.0264779i
$136$	−6.11426	−	1.29963i	−0.524293	−	0.111442i
$137$	−1.21363	+	0.257964i	−0.103687	+	0.0220394i	−0.259463	−	0.965753i	$-0.583546\pi$
$137$	−1.21363	+	0.257964i	−0.103687	+	0.0220394i	0.155776	+	0.987792i	$0.450212\pi$
$138$	−1.94279	+	0.864986i	−0.165381	+	0.0736325i
$139$	−5.76291	+	17.7364i	−0.488804	+	1.50438i	0.337591	+	0.941293i	$0.390388\pi$
$139$	−5.76291	+	17.7364i	−0.488804	+	1.50438i	−0.826395	+	0.563091i	$0.809612\pi$
$140$	−0.352722	+	1.08557i	−0.0298104	+	0.0917471i
$141$	3.58268	−	1.59511i	0.301716	−	0.134333i
$142$	7.32788	−	1.55759i	0.614942	−	0.130710i
$143$	21.8808	+	4.65090i	1.82976	+	0.388928i
$144$	3.52090	+	1.56760i	0.293408	+	0.130634i
$145$	−1.05471	+	1.17137i	−0.0875889	+	0.0972773i
$146$	−1.15339	+	10.9738i	−0.0954554	+	0.908197i
$147$	9.29105	+	6.75034i	0.766312	+	0.556759i
$148$	−0.207312	−	1.97244i	−0.0170409	−	0.162134i
$149$	3.41365	−	5.91261i	0.279657	−	0.484380i	−0.691643	−	0.722240i	$-0.743113\pi$
$149$	3.41365	−	5.91261i	0.279657	−	0.484380i	0.971299	+	0.237860i	$0.0764460\pi$
$150$	6.39531	+	11.0770i	0.522175	+	0.904433i
$151$	−0.376642	+	0.273647i	−0.0306507	+	0.0222690i	−0.603005	−	0.797737i	$-0.706030\pi$
$151$	−0.376642	+	0.273647i	−0.0306507	+	0.0222690i	0.572354	+	0.820006i	$0.306030\pi$
$152$	−0.644943	−	0.716282i	−0.0523118	−	0.0580981i
$153$	−7.44466	−	22.9123i	−0.601865	−	1.85235i
$154$	−13.3502			−1.07579
$155$	−1.76893	−	0.646485i	−0.142084	−	0.0519269i
$156$	14.8028			1.18518
$157$	−0.906154	−	2.78885i	−0.0723189	−	0.222575i	0.908363	−	0.418182i	$-0.137332\pi$
$157$	−0.906154	−	2.78885i	−0.0723189	−	0.222575i	−0.980682	+	0.195607i	$0.937332\pi$
$158$	9.72666	+	10.8026i	0.773812	+	0.859405i
$159$	18.8332	−	13.6831i	1.49357	−	1.08514i
$160$	−0.169131	−	0.292943i	−0.0133709	−	0.0231592i
$161$	1.37053	−	2.37383i	0.108013	−	0.187084i
$162$	−0.596670	−	5.67693i	−0.0468788	−	0.446022i
$163$	2.52090	+	1.83154i	0.197452	+	0.143457i	0.682118	−	0.731242i	$-0.261059\pi$
$163$	2.52090	+	1.83154i	0.197452	+	0.143457i	−0.484666	+	0.874699i	$0.661059\pi$
$164$	−0.723352	+	6.88224i	−0.0564843	+	0.537413i
$165$	2.34437	−	2.60369i	0.182509	−	0.202697i
$166$	−1.45347	−	0.647127i	−0.112811	−	0.0502268i
$167$	−6.27504	−	1.33380i	−0.485577	−	0.103213i	−0.0413833	−	0.999143i	$-0.513176\pi$
$167$	−6.27504	−	1.33380i	−0.485577	−	0.103213i	−0.444194	+	0.895931i	$0.646510\pi$
$168$	−8.64127	+	1.83676i	−0.666688	+	0.141709i
$169$	17.3297	−	7.71570i	1.33306	−	0.593515i
$170$	−0.653392	+	2.01093i	−0.0501129	+	0.154232i
$171$	1.14793	−	3.53297i	0.0877845	−	0.270173i
$172$	−7.42640	+	3.30645i	−0.566258	+	0.252114i
$173$	−14.0292	+	2.98199i	−1.06662	+	0.226717i	−0.707600	−	0.706613i	$-0.750222\pi$
$173$	−14.0292	+	2.98199i	−1.06662	+	0.226717i	−0.359019	+	0.933330i	$0.616889\pi$
$174$	−11.9330	−	2.53644i	−0.904638	−	0.192287i
$175$	−15.0607	−	6.70544i	−1.13848	−	0.506883i
$176$	2.64728	−	2.94010i	0.199546	−	0.221618i
$177$	−2.13893	+	20.3506i	−0.160772	+	1.52964i
$178$	−6.02090	−	4.37444i	−0.451285	−	0.327878i
$179$	−1.99874	−	19.0168i	−0.149393	−	1.42138i	−0.770393	−	0.637569i	$-0.779940\pi$
$179$	−1.99874	−	19.0168i	−0.149393	−	1.42138i	0.621000	−	0.783811i	$-0.286727\pi$
$180$	0.651847	−	1.12903i	0.0485858	−	0.0841530i
$181$	−3.10278	−	5.37418i	−0.230628	−	0.399460i	0.727365	−	0.686251i	$-0.240745\pi$
$181$	−3.10278	−	5.37418i	−0.230628	−	0.399460i	−0.957993	+	0.286791i	$0.907411\pi$
$182$	−15.4357	+	11.2147i	−1.14417	+	0.831286i
$183$	−13.2477	−	14.7131i	−0.979298	−	1.08762i
$184$	0.251017	+	0.772550i	0.0185052	+	0.0569532i
$185$	−0.670876			−0.0493238
$186$	−2.51223	−	14.3585i	−0.184205	−	1.05281i
$187$	−24.7302			−1.80845
$188$	−0.462897	−	1.42465i	−0.0337602	−	0.103903i
$189$	−5.04886	−	5.60733i	−0.367251	−	0.407873i
$190$	−0.263767	+	0.191638i	−0.0191357	+	0.0139029i
$191$	6.85867	+	11.8796i	0.496276	+	0.859575i	0.999991	−	0.00429481i	$-0.00136709\pi$
$191$	6.85867	+	11.8796i	0.496276	+	0.859575i	−0.503715	+	0.863870i	$0.668034\pi$
$192$	1.30902	−	2.26728i	0.0944702	−	0.163627i
$193$	1.57653	+	14.9997i	0.113481	+	1.07970i	0.891987	+	0.452062i	$0.149311\pi$
$193$	1.57653	+	14.9997i	0.113481	+	1.07970i	−0.778506	+	0.627638i	$0.784022\pi$
$194$	0.0600337	+	0.0436171i	0.00431017	+	0.00313152i
$195$	0.523398	−	4.97980i	0.0374813	−	0.356611i
$196$	2.93523	−	3.25991i	0.209659	−	0.232850i
$197$	−6.11564	−	2.72286i	−0.435721	−	0.193995i	0.177141	−	0.984185i	$-0.443315\pi$
$197$	−6.11564	−	2.72286i	−0.435721	−	0.193995i	−0.612862	+	0.790190i	$0.709982\pi$
$198$	14.9148	+	3.17023i	1.05995	+	0.225298i
$199$	20.8648	−	4.43495i	1.47906	−	0.314385i	0.603452	−	0.797399i	$-0.293791\pi$
$199$	20.8648	−	4.43495i	1.47906	−	0.314385i	0.875613	+	0.483014i	$0.160458\pi$
$200$	4.46320	−	1.98714i	0.315596	−	0.140512i
$201$	−0.466187	+	1.43478i	−0.0328823	+	0.101201i
$202$	−1.59385	+	4.90535i	−0.112143	+	0.345140i
$203$	14.3647	−	6.39560i	1.00821	−	0.448883i
$204$	−16.0073	+	3.40246i	−1.12074	+	0.238220i
$205$	2.28966	+	0.486683i	0.159917	+	0.0339914i
$206$	3.58869	+	1.59779i	0.250036	+	0.111323i
$207$	−2.09486	+	2.32657i	−0.145603	+	0.161708i
$208$	0.591023	−	5.62321i	0.0409801	−	0.389899i
$209$	−3.08501	−	2.24139i	−0.213395	−	0.155040i
$210$	0.312363	+	2.97194i	0.0215551	+	0.205083i
$211$	8.78542	−	15.2168i	0.604813	−	1.04757i	−0.387268	−	0.921967i	$-0.626581\pi$
$211$	8.78542	−	15.2168i	0.604813	−	1.04757i	0.992081	−	0.125600i	$-0.0400856\pi$
$212$	−4.44591	−	7.70055i	−0.305347	−	0.528876i
$213$	15.8674	−	11.5284i	1.08722	−	0.789911i
$214$	−0.390415	−	0.433600i	−0.0266882	−	0.0296403i
$215$	0.849733	+	2.61521i	0.0579513	+	0.178356i
$216$	2.23607			0.152145
$217$	13.4976	+	13.0690i	0.916279	+	0.887184i
$218$	3.86068			0.261478
$219$	8.92689	+	27.4741i	0.603223	+	1.85653i
$220$	−0.895472	−	0.994522i	−0.0603727	−	0.0670507i
$221$	−28.5935	+	20.7744i	−1.92340	+	1.39743i
$222$	−2.59618	−	4.49672i	−0.174244	−	0.301800i
$223$	3.63910	−	6.30310i	0.243692	−	0.422087i	−0.718071	−	0.695970i	$-0.754975\pi$
$223$	3.63910	−	6.30310i	0.243692	−	0.422087i	0.961763	+	0.273883i	$0.0883081\pi$
$224$	0.352722	+	3.35592i	0.0235672	+	0.224227i
$225$	15.2334	+	11.0677i	1.01556	+	0.737848i
$226$	−1.74616	+	16.6136i	−0.116153	+	1.10512i
$227$	−0.111949	+	0.124332i	−0.00743031	+	0.00825219i	−0.746849	−	0.664994i	$-0.768434\pi$
$227$	−0.111949	+	0.124332i	−0.00743031	+	0.00825219i	0.739418	+	0.673246i	$0.235101\pi$
$228$	−2.30524	−	1.02636i	−0.152668	−	0.0679722i
$229$	0.738301	+	0.156931i	0.0487883	+	0.0103703i	0.232241	−	0.972658i	$-0.425394\pi$
$229$	0.738301	+	0.156931i	0.0487883	+	0.0103703i	−0.183453	+	0.983029i	$0.558727\pi$
$230$	0.268768	−	0.0571283i	0.0177220	−	0.00376693i
$231$	−31.9295	+	14.2159i	−2.10081	+	0.935339i
$232$	−1.43997	+	4.43176i	−0.0945384	+	0.290959i
$233$	2.15185	−	6.62270i	0.140972	−	0.433868i	−0.855499	−	0.517805i	$-0.826749\pi$
$233$	2.15185	−	6.62270i	0.140972	−	0.433868i	0.996471	+	0.0839369i	$0.0267494\pi$
$234$	19.9078	−	8.86352i	1.30141	−	0.579426i
$235$	−0.495631	+	0.105350i	−0.0323314	+	0.00687226i
$236$	7.64524	+	1.62505i	0.497663	+	0.105782i
$237$	34.7663	+	15.4790i	2.25831	+	1.00547i
$238$	14.1139	−	15.6751i	0.914870	−	1.01607i
$239$	1.91367	−	18.2073i	0.123785	−	1.17774i	−0.739549	−	0.673102i	$-0.764961\pi$
$239$	1.91367	−	18.2073i	0.123785	−	1.17774i	0.863334	−	0.504633i	$-0.168372\pi$
$240$	−0.716449	−	0.520530i	−0.0462466	−	0.0336001i
$241$	1.03079	+	9.80731i	0.0663990	+	0.631744i	0.976226	+	0.216756i	$0.0695476\pi$
$241$	1.03079	+	9.80731i	0.0663990	+	0.631744i	−0.909827	+	0.414988i	$0.863786\pi$
$242$	2.32614	−	4.02899i	0.149530	−	0.258993i
$243$	−10.8262	−	18.7516i	−0.694503	−	1.20292i
$244$	−6.11803	+	4.44501i	−0.391667	+	0.284563i
$245$	−0.992875	−	1.10270i	−0.0634325	−	0.0704489i
$246$	5.59852	+	17.2305i	0.356948	+	1.09857i
$247$	−5.44980			−0.346762
$248$	−5.55471	+	0.381048i	−0.352724	+	0.0241965i
$249$	−4.16535			−0.263968
$250$	−1.03332	−	3.18025i	−0.0653532	−	0.201136i
$251$	−5.72683	−	6.36029i	−0.361474	−	0.401458i	0.534785	−	0.844988i	$-0.320393\pi$
$251$	−5.72683	−	6.36029i	−0.361474	−	0.401458i	−0.896259	+	0.443530i	$0.853726\pi$
$252$	−10.5215	+	7.64433i	−0.662794	+	0.481548i
$253$	1.60686	+	2.78317i	0.101023	+	0.174976i
$254$	3.36383	−	5.82632i	0.211065	−	0.365576i
$255$	0.578630	+	5.50530i	0.0362352	+	0.344755i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	2.71188	−	25.8018i	0.169162	−	1.60947i	−0.499776	−	0.866155i	$-0.666584\pi$
$257$	2.71188	−	25.8018i	0.169162	−	1.60947i	0.668938	−	0.743318i	$-0.266749\pi$
$258$	−14.2408	+	15.8160i	−0.886593	+	0.984661i
$259$	6.11389	+	2.72208i	0.379899	+	0.169142i
$260$	−1.87080	−	0.397650i	−0.116022	−	0.0246612i
$261$	−17.5670	+	3.73398i	−1.08737	+	0.231128i
$262$	6.62681	−	2.95044i	0.409405	−	0.182279i
$263$	0.229343	−	0.705844i	0.0141419	−	0.0435242i	−0.943737	−	0.330698i	$-0.892716\pi$
$263$	0.229343	−	0.705844i	0.0141419	−	0.0435242i	0.957878	+	0.287174i	$0.0927158\pi$
$264$	3.20071	−	9.85077i	0.196990	−	0.606273i
$265$	−2.74773	+	1.22337i	−0.168791	+	0.0751508i
$266$	3.18136	−	0.676219i	0.195062	−	0.0414616i
$267$	−19.0583	−	4.05096i	−1.16635	−	0.247915i
$268$	0.526421	+	0.234378i	0.0321563	+	0.0143169i
$269$	−12.2513	+	13.6064i	−0.746972	+	0.829597i	−0.990095	−	0.140399i	$-0.955162\pi$
$269$	−12.2513	+	13.6064i	−0.746972	+	0.829597i	0.243123	+	0.969996i	$0.421828\pi$
$270$	0.0790627	−	0.752232i	0.00481160	−	0.0457794i
$271$	9.75759	+	7.08930i	0.592731	+	0.430645i	0.843291	−	0.537456i	$-0.180615\pi$
$271$	9.75759	+	7.08930i	0.592731	+	0.430645i	−0.250560	+	0.968101i	$0.580615\pi$
$272$	0.653392	+	6.21661i	0.0396177	+	0.376937i
$273$	−24.9754	+	43.2587i	−1.51158	+	2.61814i
$274$	0.620369	+	1.07451i	0.0374779	+	0.0649136i
$275$	15.6373	−	11.3612i	0.942966	−	0.685105i
$276$	1.42301	+	1.58041i	0.0856549	+	0.0951294i
$277$	6.08930	+	18.7409i	0.365871	+	1.12603i	0.949434	+	0.313966i	$0.101658\pi$
$277$	6.08930	+	18.7409i	0.365871	+	1.12603i	−0.583564	+	0.812067i	$0.698342\pi$
$278$	18.6492			1.11850
$279$	−11.9761	−	17.8059i	−0.716987	−	1.06601i
$280$	1.14143			0.0682136
$281$	8.20288	+	25.2459i	0.489343	+	1.50604i	0.825591	+	0.564269i	$0.190842\pi$
$281$	8.20288	+	25.2459i	0.489343	+	1.50604i	−0.336248	+	0.941773i	$0.609158\pi$
$282$	−2.62415	−	2.91441i	−0.156266	−	0.173551i
$283$	22.7012	−	16.4934i	1.34945	−	0.980432i	0.350410	−	0.936597i	$-0.386042\pi$
$283$	22.7012	−	16.4934i	1.34945	−	0.980432i	0.999039	−	0.0438352i	$-0.0139576\pi$
$284$	−3.74580	−	6.48791i	−0.222272	−	0.384986i
$285$	−0.426784	+	0.739211i	−0.0252805	+	0.0437871i
$286$	−2.33826	−	22.2471i	−0.138264	−	1.31550i
$287$	−18.8917	−	13.7256i	−1.11514	−	0.810197i
$288$	0.402863	−	3.83299i	0.0237390	−	0.225861i
$289$	14.7698	−	16.4035i	0.868813	−	0.964914i
$290$	1.43997	+	0.641114i	0.0845577	+	0.0376475i
$291$	0.190028	+	0.0403917i	0.0111396	+	0.00236780i
$292$	10.7931	−	2.29415i	0.631619	−	0.134255i
$293$	−17.6253	+	7.84729i	−1.02968	+	0.458444i	−0.850835	−	0.525434i	$-0.823903\pi$
$293$	−17.6253	+	7.84729i	−1.02968	+	0.458444i	−0.178846	+	0.983877i	$0.557236\pi$
$294$	3.54886	−	10.9223i	0.206974	−	0.637000i
$295$	0.816999	−	2.51446i	0.0475675	−	0.146398i
$296$	−1.81184	+	0.806683i	−0.105311	+	0.0468875i
$297$	8.65323	−	1.83930i	0.502111	−	0.106727i
$298$	−6.67810	−	1.41947i	−0.386852	−	0.0822279i
$299$	4.19585	+	1.86811i	0.242652	+	0.108036i
$300$	8.55859	−	9.50528i	0.494130	−	0.548787i
$301$	2.86735	−	27.2810i	0.165271	−	1.57245i
$302$	0.376642	+	0.273647i	0.0216733	+	0.0157466i
$303$	1.41148	+	13.4293i	0.0810873	+	0.771494i
$304$	−0.481926	+	0.834720i	−0.0276404	+	0.0478745i
$305$	1.27902	+	2.21532i	0.0732363	+	0.126849i
$306$	−19.4904	+	14.1606i	−1.11419	+	0.809507i
$307$	8.84886	+	9.82766i	0.505031	+	0.560894i	0.940712	−	0.339207i	$-0.110159\pi$
$307$	8.84886	+	9.82766i	0.505031	+	0.560894i	−0.435680	+	0.900101i	$0.643492\pi$
$308$	4.12543	+	12.6968i	0.235068	+	0.723465i
$309$	10.2844			0.585062
$310$	−0.0682155	+	1.88212i	−0.00387438	+	0.106897i
$311$	−33.7062			−1.91130			−0.955651	−	0.294502i	$-0.904846\pi$
$311$	−33.7062			−1.91130			−0.955651	+	0.294502i	$0.904846\pi$
$312$	−4.57433	−	14.0783i	−0.258970	−	0.797029i
$313$	−14.7147	−	16.3423i	−0.831723	−	0.923722i	0.166332	−	0.986070i	$-0.446808\pi$
$313$	−14.7147	−	16.3423i	−0.831723	−	0.923722i	−0.998054	+	0.0623483i	$0.980141\pi$
$314$	−2.37234	+	1.72361i	−0.133879	+	0.0972688i
$315$	2.19960	+	3.80981i	0.123933	+	0.214659i
$316$	7.26814	−	12.5888i	0.408865	−	0.708174i
$317$	−2.61698	−	24.8989i	−0.146984	−	1.39846i	−0.780705	−	0.624900i	$-0.785140\pi$
$317$	−2.61698	−	24.8989i	−0.146984	−	1.39846i	0.633720	−	0.773562i	$-0.281527\pi$
$318$	−18.8332	−	13.6831i	−1.05611	−	0.767311i
$319$	−1.92705	+	18.3347i	−0.107894	+	1.02654i
$320$	−0.226341	+	0.251377i	−0.0126528	+	0.0140524i
$321$	−1.39547	−	0.621304i	−0.0778876	−	0.0346778i
$322$	−2.68116	−	0.569898i	−0.149415	−	0.0317592i
$323$	5.89324	−	1.25265i	0.327909	−	0.0696991i
$324$	−5.21470	+	2.32174i	−0.289706	+	0.128985i
$325$	8.53627	−	26.2719i	0.473507	−	1.45731i
$326$	0.962897	−	2.96349i	0.0533299	−	0.164133i
$327$	9.23357	−	4.11105i	0.510617	−	0.227342i
$328$	6.76893	−	1.43878i	0.373751	−	0.0794433i
$329$	4.94429	+	1.05094i	0.272588	+	0.0579403i
$330$	−3.20071	−	1.42505i	−0.176193	−	0.0784463i
$331$	4.61026	−	5.12021i	0.253403	−	0.281432i	−0.602999	−	0.797742i	$-0.706028\pi$
$331$	4.61026	−	5.12021i	0.253403	−	0.281432i	0.856402	+	0.516309i	$0.172695\pi$
$332$	−0.166307	+	1.58231i	−0.00912729	+	0.0868404i
$333$	−6.18402	−	4.49295i	−0.338882	−	0.246212i
$334$	0.670574	+	6.38008i	0.0366922	+	0.349103i
$335$	0.0974597	−	0.168805i	0.00532479	−	0.00922281i
$336$	4.41716	+	7.65074i	0.240976	+	0.417382i
$337$	−23.6299	+	17.1681i	−1.28720	+	0.935209i	−0.999745	−	0.0225841i	$-0.992811\pi$
$337$	−23.6299	+	17.1681i	−1.28720	+	0.935209i	−0.287459	+	0.957793i	$0.592811\pi$
$338$	−12.6933	−	14.0973i	−0.690422	−	0.766791i
$339$	13.5147	+	41.5940i	0.734019	+	2.25908i
$340$	2.11442			0.114671
$341$	−21.1824	+	6.04368i	−1.14709	+	0.327283i
$342$	−3.71478			−0.200873
$343$	−2.72508	−	8.38695i	−0.147141	−	0.452853i
$344$	5.43950	+	6.04118i	0.293278	+	0.325718i
$345$	0.581977	−	0.422831i	0.0313326	−	0.0227644i
$346$	7.17130	+	12.4211i	0.385532	+	0.667760i
$347$	6.89337	−	11.9397i	0.370056	−	0.640955i	−0.619518	−	0.784982i	$-0.712672\pi$
$347$	6.89337	−	11.9397i	0.370056	−	0.640955i	0.989574	+	0.144027i	$0.0460052\pi$
$348$	1.27520	+	12.1328i	0.0683581	+	0.650384i
$349$	27.4754	+	19.9621i	1.47073	+	1.06854i	0.980403	+	0.197004i	$0.0631211\pi$
$349$	27.4754	+	19.9621i	1.47073	+	1.06854i	0.490323	+	0.871541i	$0.336879\pi$
$350$	−1.72325	+	16.3956i	−0.0921116	+	0.876383i
$351$	8.45991	−	9.39568i	0.451557	−	0.501504i
$352$	−3.61426	−	1.60917i	−0.192640	−	0.0857691i
$353$	−1.38686	−	0.294786i	−0.0738150	−	0.0156899i	0.170856	−	0.985296i	$-0.445347\pi$
$353$	−1.38686	−	0.294786i	−0.0738150	−	0.0156899i	−0.244671	+	0.969606i	$0.578680\pi$
$354$	20.0155	−	4.25443i	1.06381	−	0.226120i
$355$	−2.31503	+	1.03072i	−0.122869	+	0.0547048i
$356$	−2.29978	+	7.07799i	−0.121888	+	0.375133i
$357$	17.0645	−	52.5193i	0.903151	−	2.77961i
$358$	−17.4684	+	7.77742i	−0.923233	+	0.411050i
$359$	−2.48972	+	0.529206i	−0.131402	+	0.0279304i	−0.273143	−	0.961973i	$-0.588063\pi$
$359$	−2.48972	+	0.529206i	−0.131402	+	0.0279304i	0.141741	+	0.989904i	$0.454730\pi$
$360$	−1.27520	−	0.271053i	−0.0672092	−	0.0142858i
$361$	−16.5087	−	7.35013i	−0.868877	−	0.386849i
$362$	−4.15233	+	4.61163i	−0.218242	+	0.242382i
$363$	1.27314	−	12.1131i	0.0668223	−	0.635772i
$364$	15.4357	+	11.2147i	0.809048	+	0.587808i
$365$	−0.390148	−	3.71201i	−0.0204213	−	0.194295i
$366$	−9.89919	+	17.1459i	−0.517439	+	0.896230i
$367$	4.76686	+	8.25644i	0.248828	+	0.430983i	0.963201	−	0.268783i	$-0.0866213\pi$
$367$	4.76686	+	8.25644i	0.248828	+	0.430983i	−0.714373	+	0.699765i	$0.753288\pi$
$368$	0.657170	−	0.477462i	0.0342574	−	0.0248894i
$369$	17.8464	+	19.8204i	0.929044	+	1.03181i
$370$	0.207312	+	0.638041i	0.0107776	+	0.0331702i
$371$	30.0047			1.55776
$372$	−12.8794	+	6.82628i	−0.667766	+	0.353926i
$373$	−22.2606			−1.15261			−0.576306	−	0.817234i	$-0.695506\pi$
$373$	−22.2606			−1.15261			−0.576306	+	0.817234i	$0.695506\pi$
$374$	7.64206	+	23.5198i	0.395161	+	1.21618i
$375$	−5.85788	−	6.50584i	−0.302500	−	0.335960i
$376$	−1.21188	+	0.880483i	−0.0624980	+	0.0454074i
$377$	13.1738	+	22.8176i	0.678483	+	1.17517i
$378$	−3.77270	+	6.53452i	−0.194047	+	0.336099i
$379$	−0.395450	−	3.76246i	−0.0203129	−	0.193264i	0.979660	−	0.200666i	$-0.0643106\pi$
$379$	−0.395450	−	3.76246i	−0.0203129	−	0.193264i	−0.999973	+	0.00740164i	$0.997644\pi$
$380$	0.263767	+	0.191638i	0.0135310	+	0.00983081i
$381$	1.84108	−	17.5168i	0.0943216	−	0.897410i
$382$	9.17869	−	10.1940i	0.469623	−	0.521569i
$383$	15.6586	+	6.97167i	0.800118	+	0.356236i	0.765721	−	0.643173i	$-0.222382\pi$
$383$	15.6586	+	6.97167i	0.800118	+	0.356236i	0.0343971	+	0.999408i	$0.489049\pi$
$384$	−2.56082	−	0.544320i	−0.130681	−	0.0277772i
$385$	4.41716	−	0.938896i	0.225119	−	0.0478506i
$386$	13.7784	−	6.13452i	0.701300	−	0.312239i
$387$	−9.68174	+	29.7973i	−0.492151	+	1.51468i
$388$	0.0229309	−	0.0705739i	0.00116414	−	0.00358285i
$389$	6.58243	−	2.93069i	0.333742	−	0.148592i	−0.233022	−	0.972471i	$-0.574862\pi$
$389$	6.58243	−	2.93069i	0.333742	−	0.148592i	0.566765	+	0.823880i	$0.308195\pi$
$390$	−4.89781	+	1.04106i	−0.248010	+	0.0527162i
$391$	−4.96665	−	1.05569i	−0.251175	−	0.0533888i
$392$	−4.00739	−	1.78421i	−0.202404	−	0.0901160i
$393$	12.7075	−	14.1131i	0.641009	−	0.711912i
$394$	−0.699755	+	6.65772i	−0.0352531	+	0.335411i
$395$	−3.97798	−	2.89017i	−0.200154	−	0.145420i
$396$	−1.59385	−	15.1644i	−0.0800938	−	0.762042i
$397$	−7.32091	+	12.6802i	−0.367426	+	0.636401i	−0.989162	−	0.146826i	$-0.953094\pi$
$397$	−7.32091	+	12.6802i	−0.367426	+	0.636401i	0.621736	+	0.783227i	$0.286428\pi$
$398$	−10.6655	−	18.4731i	−0.534611	−	0.925973i
$399$	6.88876	−	5.00498i	0.344869	−	0.250562i
$400$	−3.26909	−	3.63069i	−0.163455	−	0.181535i
$401$	−7.69654	−	23.6875i	−0.384347	−	1.18290i	−0.936953	−	0.349456i	$-0.886367\pi$
$401$	−7.69654	−	23.6875i	−0.384347	−	1.18290i	0.552606	−	0.833443i	$-0.313633\pi$
$402$	1.50861			0.0752428
$403$	−19.4145	+	24.7819i	−0.967105	+	1.23447i
$404$	5.15780			0.256610
$405$	0.596670	+	1.83636i	0.0296488	+	0.0912495i
$406$	−10.5215	−	11.6853i	−0.522174	−	0.579933i
$407$	−6.34799	+	4.61208i	−0.314658	+	0.228612i
$408$	8.18247	+	14.1725i	0.405093	+	0.701641i
$409$	−17.1148	+	29.6437i	−0.846271	+	1.46578i	0.0382412	+	0.999269i	$0.487824\pi$
$409$	−17.1148	+	29.6437i	−0.846271	+	1.46578i	−0.884513	+	0.466516i	$0.845509\pi$
$410$	−0.244682	−	2.32799i	−0.0120840	−	0.114971i
$411$	2.62793	+	1.90930i	0.129626	+	0.0941788i
$412$	0.410620	−	3.90679i	0.0202298	−	0.192474i
$413$	−17.6480	+	19.6001i	−0.868402	+	0.964458i
$414$	2.86005	+	1.27338i	0.140564	+	0.0625830i
$415$	0.526421	+	0.111894i	0.0258410	+	0.00549267i
$416$	−5.53062	+	1.17557i	−0.271161	+	0.0576371i
$417$	44.6031	−	19.8586i	2.18422	−	0.972479i
$418$	−1.17837	+	3.62665i	−0.0576359	+	0.177385i
$419$	−5.95186	+	18.3180i	−0.290768	+	0.894891i	0.693843	+	0.720126i	$0.255916\pi$
$419$	−5.95186	+	18.3180i	−0.290768	+	0.894891i	−0.984610	+	0.174764i	$0.944084\pi$
$420$	2.72995	−	1.21545i	0.133208	−	0.0593081i
$421$	24.6360	−	5.23655i	1.20069	−	0.255214i	0.436198	−	0.899851i	$-0.356325\pi$
$421$	24.6360	−	5.23655i	1.20069	−	0.255214i	0.764489	+	0.644637i	$0.222991\pi$
$422$	−17.1869	−	3.65318i	−0.836644	−	0.177834i
$423$	−5.27419	−	2.34822i	−0.256440	−	0.114174i
$424$	−5.94980	+	6.60792i	−0.288948	+	0.320909i
$425$	−3.19220	+	30.3717i	−0.154844	+	1.47325i
$426$	−15.8674	−	11.5284i	−0.768780	−	0.558551i
$427$	−2.66739	−	25.3785i	−0.129084	−	1.22815i
$428$	−0.291733	+	0.505296i	−0.0141014	+	0.0244244i
$429$	−29.2822	−	50.7183i	−1.41376	−	2.44870i
$430$	2.22463	−	1.61629i	0.107281	−	0.0779444i
$431$	17.4323	+	19.3605i	0.839683	+	0.932562i	0.998500	−	0.0547458i	$-0.0174349\pi$
$431$	17.4323	+	19.3605i	0.839683	+	0.932562i	−0.158818	+	0.987308i	$0.550768\pi$
$432$	−0.690983	−	2.12663i	−0.0332449	−	0.102317i
$433$	−7.86224			−0.377835			−0.188917	−	0.981993i	$-0.560498\pi$
$433$	−7.86224			−0.377835			−0.188917	+	0.981993i	$0.560498\pi$
$434$	8.25839	−	16.8756i	0.396415	−	0.810053i
$435$	4.12665			0.197858
$436$	−1.19302	−	3.67173i	−0.0571351	−	0.175844i
$437$	−0.523892	−	0.581841i	−0.0250611	−	0.0278332i
$438$	23.3709	−	16.9799i	1.11670	−	0.811333i
$439$	−14.5359	−	25.1770i	−0.693762	−	1.20163i	−0.970596	−	0.240713i	$-0.922619\pi$
$439$	−14.5359	−	25.1770i	−0.693762	−	1.20163i	0.276835	−	0.960918i	$-0.410715\pi$
$440$	−0.669131	+	1.15897i	−0.0318996	+	0.0552516i
$441$	−1.76722	−	16.8139i	−0.0841531	−	0.800663i
$442$	28.5935	+	20.7744i	1.36005	+	0.988136i
$443$	−2.62268	+	24.9532i	−0.124607	+	1.18556i	0.736248	+	0.676711i	$0.236596\pi$
$443$	−2.62268	+	24.9532i	−0.124607	+	1.18556i	−0.860856	+	0.508849i	$0.830071\pi$
$444$	−3.47437	+	3.85868i	−0.164886	+	0.183125i
$445$	2.29978	+	1.02393i	0.109020	+	0.0485388i
$446$	−7.11915	−	1.51322i	−0.337101	−	0.0716531i
$447$	−17.4835	+	3.71623i	−0.826941	+	0.175772i
$448$	3.08268	−	1.37250i	0.145643	−	0.0648443i
$449$	8.21822	−	25.2931i	0.387842	−	1.19365i	−0.546556	−	0.837423i	$-0.684061\pi$
$449$	8.21822	−	25.2931i	0.387842	−	1.19365i	0.934398	−	0.356232i	$-0.115939\pi$
$450$	5.81864	−	17.9079i	0.274293	−	0.844188i
$451$	25.0112	−	11.1357i	1.17773	−	0.524359i
$452$	16.3401	−	3.47319i	0.768572	−	0.163365i
$453$	1.19221	+	0.253411i	0.0560147	+	0.0119063i
$454$	0.152841	+	0.0680490i	0.00717317	+	0.00319370i
$455$	4.31848	−	4.79615i	0.202453	−	0.224847i
$456$	−0.263767	+	2.50957i	−0.0123520	+	0.117522i
$457$	−5.72315	−	4.15811i	−0.267718	−	0.194508i	0.445825	−	0.895120i	$-0.352910\pi$
$457$	−5.72315	−	4.15811i	−0.267718	−	0.194508i	−0.713543	+	0.700612i	$0.752910\pi$
$458$	−0.0788976	−	0.750660i	−0.00368664	−	0.0350761i
$459$	−6.98866	+	12.1047i	−0.326203	+	0.565000i
$460$	−0.137386	−	0.237960i	−0.00640566	−	0.0110949i
$461$	−15.8777	+	11.5358i	−0.739496	+	0.537275i	−0.892553	−	0.450942i	$-0.851088\pi$
$461$	−15.8777	+	11.5358i	−0.739496	+	0.537275i	0.153057	+	0.988217i	$0.451088\pi$
$462$	23.3869	+	25.9738i	1.08806	+	1.20841i
$463$	1.17047	+	3.60234i	0.0543964	+	0.167415i	0.974564	−	0.224110i	$-0.0719476\pi$
$463$	1.17047	+	3.60234i	0.0543964	+	0.167415i	−0.920167	+	0.391525i	$0.871948\pi$
$464$	4.65983			0.216327
$465$	1.84103	+	4.57410i	0.0853757	+	0.212119i
$466$	−6.96352			−0.322579
$467$	1.06497	+	3.27763i	0.0492808	+	0.151671i	0.972669	−	0.232198i	$-0.0745916\pi$
$467$	1.06497	+	3.27763i	0.0492808	+	0.151671i	−0.923388	+	0.383868i	$0.874592\pi$
$468$	−14.5816	−	16.1945i	−0.674033	−	0.748589i
$469$	−1.57311	+	1.14293i	−0.0726393	+	0.0527756i
$470$	0.253352	+	0.438819i	0.0116863	+	0.0202412i
$471$	−3.83853	+	6.64853i	−0.176870	+	0.306348i
$472$	−0.816999	−	7.77323i	−0.0376054	−	0.357792i
$473$	26.0192	+	18.9041i	1.19637	+	0.869210i
$474$	3.97798	−	37.8480i	0.182715	−	1.73842i
$475$	−3.15092	+	3.49945i	−0.144574	+	0.160566i
$476$	−19.2694	−	8.57927i	−0.883209	−	0.393230i
$477$	−33.5211	−	7.12514i	−1.53483	−	0.326238i
$478$	−17.9076	+	3.80637i	−0.819073	+	0.174099i
$479$	−0.262489	+	0.116868i	−0.0119934	+	0.00533981i	−0.412725	−	0.910856i	$-0.635423\pi$
$479$	−0.262489	+	0.116868i	−0.0119934	+	0.00533981i	0.400731	+	0.916196i	$0.368756\pi$
$480$	−0.273659	+	0.842236i	−0.0124908	+	0.0384426i
$481$	−3.46531	+	10.6651i	−0.158004	+	0.486288i
$482$	9.00877	−	4.01096i	0.410338	−	0.182694i
$483$	−7.01936	+	1.49201i	−0.319392	+	0.0678889i
$484$	−4.55061	−	0.967262i	−0.206846	−	0.0439664i
$485$	−0.0229309	−	0.0102095i	−0.00104124	−	0.000463588i
$486$	−14.4883	+	16.0909i	−0.657204	+	0.729899i
$487$	1.37741	−	13.1052i	0.0624164	−	0.593853i	−0.917954	−	0.396687i	$-0.870160\pi$
$487$	1.37741	−	13.1052i	0.0624164	−	0.593853i	0.980370	−	0.197165i	$-0.0631736\pi$
$488$	6.11803	+	4.44501i	0.276950	+	0.201216i
$489$	−0.852722	−	8.11311i	−0.0385614	−	0.366887i
$490$	−0.741914	+	1.28503i	−0.0335163	+	0.0580519i
$491$	−12.1208	−	20.9938i	−0.547004	−	0.947438i	−0.998478	−	0.0551541i	$-0.982435\pi$
$491$	−12.1208	−	20.9938i	−0.547004	−	0.947438i	0.451474	−	0.892284i	$-0.350898\pi$
$492$	14.6571	−	10.6490i	0.660793	−	0.480095i
$493$	−19.4904	−	21.6462i	−0.877802	−	0.974898i
$494$	1.68408	+	5.18306i	0.0757703	+	0.233197i
$495$	−5.15780			−0.231826
$496$	2.07890	+	5.16509i	0.0933453	+	0.231920i
$497$	25.2797			1.13395
$498$	1.28716	+	3.96149i	0.0576792	+	0.177518i
$499$	−10.0806	−	11.1957i	−0.451271	−	0.501187i	0.473984	−	0.880534i	$-0.342815\pi$
$499$	−10.0806	−	11.1957i	−0.451271	−	0.501187i	−0.925255	+	0.379347i	$0.876149\pi$
$500$	−2.70528	+	1.96550i	−0.120984	+	0.0878998i
$501$	8.39764	+	14.5451i	0.375179	+	0.649829i
$502$	−4.27931	+	7.41198i	−0.190995	+	0.330813i
$503$	1.79262	+	17.0557i	0.0799292	+	0.760476i	0.958928	+	0.283651i	$0.0915457\pi$
$503$	1.79262	+	17.0557i	0.0799292	+	0.760476i	−0.878998	+	0.476825i	$0.841788\pi$
$504$	10.5215	+	7.64433i	0.468666	+	0.340506i
$505$	0.182369	−	1.73512i	0.00811531	−	0.0772120i
$506$	2.15040	−	2.38826i	0.0955971	−	0.106171i
$507$	−45.3699	−	20.2000i	−2.01495	−	0.897112i
$508$	−6.58064	−	1.39876i	−0.291969	−	0.0620599i
$509$	−0.578498	+	0.122964i	−0.0256415	+	0.00545027i	−0.220715	−	0.975338i	$-0.570839\pi$
$509$	−0.578498	+	0.122964i	−0.0256415	+	0.00545027i	0.195073	+	0.980789i	$0.437506\pi$
$510$	5.05705	−	2.25154i	0.223930	−	0.0996999i
$511$	−11.5059	+	35.4117i	−0.508993	+	1.56652i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−1.96891	+	0.876615i	−0.0869294	+	0.0387035i
$514$	−25.3770	+	5.39405i	−1.11933	+	0.237921i
$515$	−1.29976	−	0.276272i	−0.0572741	−	0.0121740i
$516$	19.4426	+	8.65639i	0.855911	+	0.381076i
$517$	−3.96553	+	4.40417i	−0.174404	+	0.193695i
$518$	0.699555	−	6.65582i	0.0307367	−	0.292440i
$519$	30.3781	+	22.0710i	1.33345	+	0.968809i
$520$	0.199920	+	1.90211i	0.00876708	+	0.0834132i
$521$	15.5570	−	26.9454i	0.681563	−	1.18050i	−0.292941	−	0.956131i	$-0.594634\pi$
$521$	15.5570	−	26.9454i	0.681563	−	1.18050i	0.974504	−	0.224371i	$-0.0720327\pi$
$522$	8.97973	+	15.5533i	0.393032	+	0.680751i
$523$	−34.2082	+	24.8537i	−1.49582	+	1.08678i	−0.523811	+	0.851835i	$0.675490\pi$
$523$	−34.2082	+	24.8537i	−1.49582	+	1.08678i	−0.972009	+	0.234942i	$0.924510\pi$
$524$	−4.85383	−	5.39073i	−0.212041	−	0.235495i
$525$	13.3374	+	41.0483i	0.582092	+	1.79150i
$526$	−0.742168			−0.0323601
$527$	15.2981	−	31.2608i	0.666394	−	1.36174i
$528$	−10.3577			−0.450762
$529$	−6.90349	−	21.2468i	−0.300152	−	0.923772i
$530$	2.01258	+	2.23520i	0.0874211	+	0.0970910i
$531$	24.3707	−	17.7063i	1.05760	−	0.768390i
$532$	−1.62622	−	2.81669i	−0.0705054	−	0.122119i
$533$	19.5639	−	33.8856i	0.847406	−	1.46775i
$534$	2.03664	+	19.3773i	0.0881339	+	0.838538i
$535$	0.159671	+	0.116008i	0.00690317	+	0.00501545i
$536$	0.0602334	−	0.573083i	0.00260169	−	0.0247534i
$537$	−33.4972	+	37.2024i	−1.44551	+	1.60540i
$538$	16.7263	+	7.44703i	0.721122	+	0.321064i
$539$	−16.9756	−	3.60827i	−0.731190	−	0.155419i
$540$	−0.739846	+	0.157259i	−0.0318379	+	0.00676736i
$541$	21.6703	−	9.64823i	0.931678	−	0.414810i	0.115956	−	0.993254i	$-0.463007\pi$
$541$	21.6703	−	9.64823i	0.931678	−	0.414810i	0.815722	+	0.578444i	$0.196340\pi$
$542$	3.72707	−	11.4707i	0.160091	−	0.492710i
$543$	−5.02041	+	15.4512i	−0.215446	+	0.663076i
$544$	5.71044	−	2.54245i	0.244833	−	0.109007i
$545$	−1.27738	+	0.271516i	−0.0547170	+	0.0116305i
$546$	48.8593	+	10.3854i	2.09098	+	0.444453i
$547$	−28.9725	−	12.8994i	−1.23877	−	0.551538i	−0.320412	−	0.947278i	$-0.603821\pi$
$547$	−28.9725	−	12.8994i	−1.23877	−	0.551538i	−0.918362	+	0.395741i	$0.870488\pi$
$548$	0.830216	−	0.922048i	0.0354651	−	0.0393880i
$549$	−3.04658	+	28.9862i	−0.130025	+	1.23710i
$550$	−15.6373	−	11.3612i	−0.666778	−	0.484442i
$551$	−0.469478	−	4.46678i	−0.0200004	−	0.190291i
$552$	1.06332	−	1.84173i	0.0452581	−	0.0783893i
$553$	24.5257	+	42.4797i	1.04294	+	1.80642i
$554$	15.9420	−	11.5825i	0.677310	−	0.492095i
$555$	1.17524	+	1.30524i	0.0498863	+	0.0554044i
$556$	−5.76291	−	17.7364i	−0.244402	−	0.752192i
$557$	22.9754			0.973500			0.486750	−	0.873541i	$-0.338182\pi$
$557$	22.9754			0.973500			0.486750	+	0.873541i	$0.338182\pi$
$558$	−13.2336	+	16.8922i	−0.560225	+	0.715105i
$559$	45.9640			1.94407
$560$	−0.352722	−	1.08557i	−0.0149052	−	0.0458735i
$561$	43.3226	+	48.1146i	1.82908	+	2.03140i
$562$	21.4754	−	15.6028i	0.905886	−	0.658165i
$563$	16.6877	+	28.9040i	0.703304	+	1.21816i	0.967300	+	0.253634i	$0.0816260\pi$
$563$	16.6877	+	28.9040i	0.703304	+	1.21816i	−0.263996	+	0.964524i	$0.585041\pi$
$564$	−1.96086	+	3.39632i	−0.0825673	+	0.143011i
$565$	−0.590658	−	5.61974i	−0.0248492	−	0.236424i
$566$	−22.7012	−	16.4934i	−0.954204	−	0.693270i
$567$	2.01341	−	19.1563i	0.0845552	−	0.804489i
$568$	−5.01285	+	5.56734i	−0.210335	+	0.233600i
$569$	−23.1538	−	10.3088i	−0.970659	−	0.432165i	−0.140739	−	0.990047i	$-0.544948\pi$
$569$	−23.1538	−	10.3088i	−0.970659	−	0.432165i	−0.829921	+	0.557881i	$0.811614\pi$
$570$	0.834915	+	0.177467i	0.0349707	+	0.00743326i
$571$	15.0919	−	3.20788i	0.631575	−	0.134245i	0.119009	−	0.992893i	$-0.462028\pi$
$571$	15.0919	−	3.20788i	0.631575	−	0.134245i	0.512566	+	0.858648i	$0.328695\pi$
$572$	−20.4357	+	9.09854i	−0.854458	+	0.380429i
$573$	11.0976	−	34.1548i	0.463607	−	1.42684i
$574$	−7.21598	+	22.2085i	−0.301189	+	0.926965i
$575$	3.62549	−	1.61417i	0.151193	−	0.0673156i
$576$	−3.76988	+	0.801313i	−0.157078	+	0.0333880i
$577$	26.3521	+	5.60130i	1.09705	+	0.233185i	0.720669	−	0.693279i	$-0.243835\pi$
$577$	26.3521	+	5.60130i	1.09705	+	0.233185i	0.376382	+	0.926465i	$0.377168\pi$
$578$	−20.1648	−	8.97796i	−0.838746	−	0.373434i
$579$	26.4212	−	29.3438i	1.09803	−	1.21949i
$580$	0.164762	−	1.56760i	0.00684136	−	0.0650912i
$581$	−4.34342	−	3.15568i	−0.180195	−	0.130920i
$582$	−0.0203071	−	0.193209i	−0.000841756	−	0.00800877i
$583$	−17.5894	+	30.4657i	−0.728477	+	1.26176i
$584$	−5.51712	−	9.55593i	−0.228300	−	0.395427i
$585$	−5.96352	+	4.33275i	−0.246561	+	0.179137i
$586$	12.9097	+	14.3377i	0.533296	+	0.592285i
$587$	5.72519	+	17.6203i	0.236304	+	0.727268i	0.996946	+	0.0780966i	$0.0248843\pi$
$587$	5.72519	+	17.6203i	0.236304	+	0.727268i	−0.760642	+	0.649171i	$0.775116\pi$
$588$	−11.4844			−0.473607
$589$	4.74166	−	2.51316i	0.195377	−	0.103553i
$590$	−2.64386			−0.108846
$591$	5.41588	+	16.6684i	0.222780	+	0.685645i
$592$	1.32709	+	1.47388i	0.0545431	+	0.0605763i
$593$	20.4260	−	14.8404i	0.838797	−	0.609421i	−0.0832376	−	0.996530i	$-0.526526\pi$
$593$	20.4260	−	14.8404i	0.838797	−	0.609421i	0.922034	+	0.387108i	$0.126526\pi$
$594$	−4.42327	−	7.66133i	−0.181489	−	0.314348i
$595$	−3.56746	+	6.17902i	−0.146252	+	0.253315i
$596$	0.713647	+	6.78989i	0.0292321	+	0.278125i
$597$	−45.1796	−	32.8249i	−1.84908	−	1.34343i
$598$	0.480092	−	4.56777i	0.0196324	−	0.186790i
$599$	−5.48810	+	6.09515i	−0.224238	+	0.249041i	−0.844757	−	0.535150i	$-0.820255\pi$
$599$	−5.48810	+	6.09515i	−0.224238	+	0.249041i	0.620520	+	0.784191i	$0.286922\pi$
$600$	−11.6848	−	5.20241i	−0.477030	−	0.212388i
$601$	−44.1755	−	9.38980i	−1.80196	−	0.383018i	−0.820037	−	0.572310i	$-0.806047\pi$
$601$	−44.1755	−	9.38980i	−1.80196	−	0.383018i	−0.981921	+	0.189292i	$0.939381\pi$
$602$	−26.8318	+	5.70328i	−1.09358	+	0.232448i
$603$	2.02888	−	0.903315i	0.0826224	−	0.0367858i
$604$	0.143865	−	0.442769i	0.00585376	−	0.0180160i
$605$	−0.486295	+	1.49666i	−0.0197707	+	0.0608479i
$606$	12.3359	−	5.49228i	0.501110	−	0.223109i
$607$	7.84293	−	1.66707i	0.318335	−	0.0676641i	−0.0459732	−	0.998943i	$-0.514639\pi$
$607$	7.84293	−	1.66707i	0.318335	−	0.0676641i	0.364308	+	0.931279i	$0.381306\pi$
$608$	0.942790	+	0.200396i	0.0382352	+	0.00812714i
$609$	−37.6074	−	16.7439i	−1.52393	−	0.678496i
$610$	1.71166	−	1.90099i	0.0693031	−	0.0769688i
$611$	−0.885333	+	8.42338i	−0.0358167	+	0.340773i
$612$	19.4904	+	14.1606i	0.787851	+	0.572408i
$613$	−0.448861	−	4.27062i	−0.0181293	−	0.172489i	0.981711	−	0.190379i	$-0.0609717\pi$
$613$	−0.448861	−	4.27062i	−0.0181293	−	0.172489i	−0.999840	+	0.0178902i	$0.994305\pi$
$614$	6.61221	−	11.4527i	0.266847	−	0.462193i
$615$	−3.06417	−	5.30730i	−0.123559	−	0.214011i
$616$	10.8005	−	7.84703i	0.435165	−	0.316166i
$617$	2.57049	+	2.85482i	0.103484	+	0.114931i	0.792662	−	0.609662i	$-0.208695\pi$
$617$	2.57049	+	2.85482i	0.103484	+	0.114931i	−0.689178	+	0.724593i	$0.742028\pi$
$618$	−3.17807	−	9.78109i	−0.127841	−	0.393453i
$619$	20.6266			0.829055			0.414527	−	0.910037i	$-0.363947\pi$
$619$	20.6266			0.829055			0.414527	+	0.910037i	$0.363947\pi$
$620$	1.81109	−	0.516731i	0.0727349	−	0.0207524i
$621$	1.81637			0.0728886
$622$	10.4158	+	32.0565i	0.417635	+	1.28535i
$623$	−16.8040	−	18.6627i	−0.673237	−	0.747706i
$624$	−11.9757	+	8.70089i	−0.479414	+	0.348314i
$625$	−11.6484	−	20.1756i	−0.465936	−	0.807024i
$626$	−10.9954	+	19.0445i	−0.439463	+	0.761173i
$627$	1.04354	+	9.92862i	0.0416750	+	0.396511i
$628$	2.37234	+	1.72361i	0.0946667	+	0.0687794i
$629$	1.29588	−	12.3294i	0.0516700	−	0.491607i
$630$	2.94364	−	3.26924i	0.117277	−	0.130250i
$631$	−12.5263	−	5.57707i	−0.498664	−	0.222019i	0.141963	−	0.989872i	$-0.454659\pi$
$631$	−12.5263	−	5.57707i	−0.498664	−	0.222019i	−0.640627	+	0.767853i	$0.721325\pi$
$632$	−14.2186	−	3.02226i	−0.565586	−	0.120219i
$633$	−44.9958	+	9.56416i	−1.78842	+	0.380141i
$634$	−22.8716	+	10.1831i	−0.908347	+	0.404422i
$635$	−0.703232	+	2.16432i	−0.0279069	+	0.0858886i
$636$	−7.19364	+	22.1398i	−0.285246	+	0.877898i
$637$	−22.6585	+	10.0882i	−0.897763	+	0.399710i
$638$	18.0328	−	3.83299i	0.713925	−	0.151749i
$639$	−28.2424	−	6.00311i	−1.11725	−	0.237479i
$640$	0.309017	+	0.137583i	0.0122150	+	0.00543845i
$641$	15.5867	−	17.3108i	0.615639	−	0.683737i	−0.352021	−	0.935992i	$-0.614506\pi$
$641$	15.5867	−	17.3108i	0.615639	−	0.683737i	0.967661	+	0.252255i	$0.0811722\pi$
$642$	−0.159671	+	1.51917i	−0.00630170	+	0.0599567i
$643$	−12.3482	−	8.97146i	−0.486964	−	0.353800i	0.317052	−	0.948408i	$-0.397307\pi$
$643$	−12.3482	−	8.97146i	−0.486964	−	0.353800i	−0.804015	+	0.594608i	$0.797307\pi$
$644$	0.286518	+	2.72604i	0.0112904	+	0.107421i
$645$	3.59953	−	6.23456i	0.141731	−	0.245486i
$646$	−3.01245	−	5.21771i	−0.118523	−	0.205288i
$647$	22.5689	−	16.3973i	0.887274	−	0.644643i	−0.0478915	−	0.998853i	$-0.515250\pi$
$647$	22.5689	−	16.3973i	0.887274	−	0.644643i	0.935166	+	0.354210i	$0.115250\pi$
$648$	3.81953	+	4.24202i	0.150045	+	0.166642i
$649$	−9.55560	−	29.4091i	−0.375090	−	1.15441i
$650$	−27.6240			−1.08350
$651$	1.78157	−	49.1551i	0.0698254	−	1.92654i
$652$	−3.11600			−0.122032
$653$	−2.29978	−	7.07799i	−0.0899973	−	0.276983i	0.895920	−	0.444215i	$-0.146517\pi$
$653$	−2.29978	−	7.07799i	−0.0899973	−	0.276983i	−0.985918	+	0.167232i	$0.946517\pi$
$654$	−6.76317	−	7.51126i	−0.264461	−	0.293714i
$655$	−1.98511	+	1.44226i	−0.0775646	+	0.0563539i
$656$	−3.46007	−	5.99302i	−0.135093	−	0.233988i
$657$	21.2635	−	36.8295i	0.829570	−	1.43686i
$658$	−0.528365	−	5.02706i	−0.0205978	−	0.195975i
$659$	−14.8418	−	10.7832i	−0.578155	−	0.420054i	0.259904	−	0.965635i	$-0.416309\pi$
$659$	−14.8418	−	10.7832i	−0.578155	−	0.420054i	−0.838058	+	0.545580i	$0.816309\pi$
$660$	−0.366227	+	3.48442i	−0.0142554	+	0.135631i
$661$	1.28377	−	1.42577i	0.0499330	−	0.0554562i	−0.717661	−	0.696393i	$-0.754787\pi$
$661$	1.28377	−	1.42577i	0.0499330	−	0.0554562i	0.767594	+	0.640937i	$0.221454\pi$
$662$	−6.29425	−	2.80238i	−0.244633	−	0.108918i
$663$	90.5083	+	19.2381i	3.51505	+	0.747148i
$664$	1.55626	−	0.330792i	0.0603944	−	0.0128372i
$665$	−1.00506	+	0.447480i	−0.0389744	+	0.0173525i
$666$	−2.36208	+	7.26975i	−0.0915289	+	0.281697i
$667$	−1.16970	+	3.59995i	−0.0452908	+	0.139391i
$668$	5.86060	−	2.60931i	0.226753	−	0.100957i
$669$	−18.6382	+	3.96167i	−0.720593	+	0.153167i
$670$	−0.190660	−	0.0405260i	−0.00736584	−	0.00156566i
$671$	27.3321	+	12.1690i	1.05514	+	0.469780i
$672$	5.91131	−	6.56518i	0.228034	−	0.253257i
$673$	1.81727	−	17.2902i	0.0700508	−	0.666489i	−0.902003	−	0.431730i	$-0.857903\pi$
$673$	1.81727	−	17.2902i	0.0700508	−	0.666489i	0.972054	−	0.234759i	$-0.0754300\pi$
$674$	23.6299	+	17.1681i	0.910191	+	0.661292i
$675$	−1.14192	−	10.8646i	−0.0439525	−	0.418180i
$676$	−9.48489	+	16.4283i	−0.364803	+	0.631858i
$677$	24.0827	+	41.7124i	0.925572	+	1.60314i	0.790638	+	0.612283i	$0.209749\pi$
$677$	24.0827	+	41.7124i	0.925572	+	1.60314i	0.134934	+	0.990855i	$0.456918\pi$
$678$	35.3820	−	25.7065i	1.35884	−	0.987253i
$679$	0.167551	+	0.186084i	0.00643001	+	0.00714125i
$680$	−0.653392	−	2.01093i	−0.0250564	−	0.0771158i
$681$	0.438010			0.0167846
$682$	12.2936	+	18.2781i	0.470746	+	0.699903i
$683$	30.1537			1.15380			0.576900	−	0.816815i	$-0.304262\pi$
$683$	30.1537			1.15380			0.576900	+	0.816815i	$0.304262\pi$
$684$	1.14793	+	3.53297i	0.0438923	+	0.135086i
$685$	−0.280830	−	0.311893i	−0.0107300	−	0.0119168i
$686$	−7.13436	+	5.18342i	−0.272391	+	0.197904i
$687$	−0.988040	−	1.71134i	−0.0376961	−	0.0652915i
$688$	4.06460	−	7.04010i	0.154962	−	0.268401i
$689$	5.25528	+	50.0006i	0.200210	+	1.90487i
$690$	−0.581977	−	0.422831i	−0.0221555	−	0.0160969i
$691$	2.01890	−	19.2085i	0.0768025	−	0.730727i	−0.886576	−	0.462582i	$-0.846923\pi$
$691$	2.01890	−	19.2085i	0.0768025	−	0.730727i	0.963379	−	0.268144i	$-0.0864104\pi$
$692$	9.59707	−	10.6586i	0.364826	−	0.405180i
$693$	47.0045	+	20.9278i	1.78555	+	0.794980i
$694$	−13.4855	−	2.86643i	−0.511902	−	0.108808i
$695$	−6.17044	+	1.31157i	−0.234058	+	0.0497506i
$696$	11.1449	−	4.96202i	0.422446	−	0.188085i
$697$	−13.3671	+	41.1397i	−0.506315	+	1.55828i
$698$	10.4947	−	32.2993i	0.397229	−	1.22255i
$699$	−16.6546	+	7.41511i	−0.629935	+	0.280465i
$700$	16.1257	−	3.42762i	0.609494	−	0.129552i
$701$	−29.3881	−	6.24663i	−1.10997	−	0.235932i	−0.383781	−	0.923424i	$-0.625378\pi$
$701$	−29.3881	−	6.24663i	−1.10997	−	0.235932i	−0.726192	+	0.687492i	$0.758711\pi$
$702$	−11.5501	−	5.14243i	−0.435930	−	0.194088i
$703$	1.27912	−	1.42061i	0.0482429	−	0.0535792i
$704$	−0.413545	+	3.93462i	−0.0155861	+	0.148292i
$705$	1.07322	+	0.779737i	0.0404197	+	0.0293666i
$706$	0.148205	+	1.41007i	0.00557776	+	0.0530688i
$707$	−8.70226	+	15.0727i	−0.327282	+	0.566869i
$708$	−10.2313	−	17.7212i	−0.384517	−	0.666003i
$709$	−10.1724	+	7.39065i	−0.382031	+	0.277562i	−0.762182	−	0.647363i	$-0.775872\pi$
$709$	−10.1724	+	7.39065i	−0.382031	+	0.277562i	0.380151	+	0.924924i	$0.375872\pi$
$710$	1.69565	+	1.88321i	0.0636367	+	0.0706758i
$711$	−17.3125	−	53.2822i	−0.649268	−	1.99824i
$712$	7.44224			0.278910
$713$	−4.51213	+	0.309528i	−0.168981	+	0.0115919i
$714$	−55.2220			−2.06663
$715$	2.33826	+	7.19643i	0.0874460	+	0.269131i
$716$	12.7948	+	14.2101i	0.478164	+	0.531055i
$717$	−38.7762	+	28.1726i	−1.44812	+	1.05212i
$718$	1.27267	+	2.20433i	0.0474956	+	0.0822648i
$719$	−9.55091	+	16.5427i	−0.356189	+	0.616937i	−0.987321	−	0.158738i	$-0.949257\pi$
$719$	−9.55091	+	16.5427i	−0.356189	+	0.616937i	0.631132	+	0.775676i	$0.282591\pi$
$720$	0.136273	+	1.29655i	0.00507860	+	0.0483196i
$721$	10.7241	+	7.79152i	0.399386	+	0.290171i
$722$	−1.88893	+	17.9720i	−0.0702988	+	0.668848i
$723$	17.2751	−	19.1860i	0.642469	−	0.713535i
$724$	5.66907	+	2.52403i	0.210689	+	0.0938049i
$725$	22.2685	+	4.73331i	0.827030	+	0.175791i
$726$	−11.9136	+	2.53232i	−0.442157	+	0.0939834i
$727$	2.12061	−	0.944155i	0.0786490	−	0.0350168i	−0.367035	−	0.930207i	$-0.619627\pi$
$727$	2.12061	−	0.944155i	0.0786490	−	0.0350168i	0.445684	+	0.895190i	$0.352960\pi$
$728$	5.89590	−	18.1457i	0.218516	−	0.672525i
$729$	−12.2254	+	37.6260i	−0.452794	+	1.39356i
$730$	−3.40977	+	1.51813i	−0.126201	+	0.0561884i
$731$	−49.7040	+	10.5649i	−1.83837	+	0.390758i
$732$	19.3657	+	4.11631i	0.715778	+	0.152143i
$733$	23.1320	+	10.2990i	0.854399	+	0.380403i	0.786724	−	0.617304i	$-0.211775\pi$
$733$	23.1320	+	10.2990i	0.854399	+	0.380403i	0.0676749	+	0.997707i	$0.478442\pi$
$734$	6.37930	−	7.08493i	0.235464	−	0.261510i
$735$	−0.406063	+	3.86343i	−0.0149779	+	0.142505i
$736$	−0.657170	−	0.477462i	−0.0242236	−	0.0175995i
$737$	−0.238301	−	2.26728i	−0.00877794	−	0.0835165i
$738$	13.3355	−	23.0977i	0.490886	−	0.850239i
$739$	7.49675	+	12.9847i	0.275772	+	0.477652i	0.970330	−	0.241786i	$-0.0777331\pi$
$739$	7.49675	+	12.9847i	0.275772	+	0.477652i	−0.694557	+	0.719437i	$0.744400\pi$
$740$	0.542750	−	0.394331i	0.0199519	−	0.0144959i
$741$	9.54699	+	10.6030i	0.350717	+	0.389511i
$742$	−9.27195	−	28.5361i	−0.340384	−	1.04759i
$743$	−45.0197			−1.65161			−0.825807	−	0.563953i	$-0.809280\pi$
$743$	−45.0197			−1.65161			−0.825807	+	0.563953i	$0.809280\pi$
$744$	10.4721	+	10.1396i	0.383927	+	0.371736i
$745$	2.30941			0.0846102
$746$	6.87891	+	21.1711i	0.251855	+	0.775130i
$747$	4.10309	+	4.55694i	0.150124	+	0.166730i
$748$	20.0072	−	14.5361i	0.731534	−	0.531491i
$749$	−0.984426	−	1.70508i	−0.0359702	−	0.0623021i
$750$	−4.37723	+	7.58159i	−0.159834	+	0.276840i
$751$	−3.08054	−	29.3093i	−0.112410	−	1.06951i	−0.894721	−	0.446625i	$-0.852626\pi$
$751$	−3.08054	−	29.3093i	−0.112410	−	1.06951i	0.782311	−	0.622888i	$-0.214041\pi$
$752$	1.21188	+	0.880483i	0.0441927	+	0.0321079i
$753$	−2.34214	+	22.2840i	−0.0853524	+	0.812074i
$754$	17.6299	−	19.5800i	0.642044	−	0.713062i
$755$	−0.143865	−	0.0640526i	−0.00523577	−	0.00233111i
$756$	7.38052	+	1.56878i	0.268427	+	0.0570559i
$757$	35.9297	−	7.63709i	1.30589	−	0.277575i	0.498136	−	0.867099i	$-0.334018\pi$
$757$	35.9297	−	7.63709i	1.30589	−	0.277575i	0.807751	+	0.589524i	$0.200685\pi$
$758$	−3.45611	+	1.53876i	−0.125532	+	0.0558902i
$759$	2.59996	−	8.00185i	0.0943726	−	0.290449i
$760$	0.100750	−	0.310077i	0.00365459	−	0.0112477i
$761$	15.5184	−	6.90925i	0.562543	−	0.250460i	−0.105707	−	0.994397i	$-0.533710\pi$
$761$	15.5184	−	6.90925i	0.562543	−	0.250460i	0.668250	+	0.743937i	$0.267044\pi$
$762$	−17.2283	+	3.66200i	−0.624117	+	0.132660i
$763$	12.7428	+	2.70857i	0.461322	+	0.0980570i
$764$	−12.5314	−	5.57935i	−0.453371	−	0.201854i
$765$	5.45287	−	6.05603i	0.197149	−	0.218956i
$766$	1.79167	−	17.0466i	0.0647357	−	0.615919i
$767$	−35.7532	−	25.9762i	−1.29097	−	0.937946i
$768$	0.273659	+	2.60369i	0.00987482	+	0.0939526i
$769$	0.489819	−	0.848392i	0.0176633	−	0.0305938i	−0.857059	−	0.515219i	$-0.827711\pi$
$769$	0.489819	−	0.848392i	0.0176633	−	0.0305938i	0.874722	+	0.484625i	$0.161044\pi$
$770$	−2.25792	−	3.91083i	−0.0813698	−	0.140937i
$771$	−54.9502	+	39.9236i	−1.97898	+	1.43781i
$772$	−10.0920	−	11.2083i	−0.363220	−	0.403396i
$773$	11.0234	+	33.9266i	0.396484	+	1.22025i	0.927799	+	0.373079i	$0.121698\pi$
$773$	11.0234	+	33.9266i	0.396484	+	1.22025i	−0.531315	+	0.847174i	$0.678302\pi$
$774$	31.3308			1.12616
$775$	4.68813	+	26.7947i	0.168403	+	0.962495i
$776$	−0.0742058			−0.00266383
$777$	−5.41434	−	16.6636i	−0.194238	−	0.597804i
$778$	−4.82133	−	5.35463i	−0.172853	−	0.191973i
$779$	−5.39614	+	3.92053i	−0.193337	+	0.140467i
$780$	2.50361	+	4.33639i	0.0896437	+	0.155268i
$781$	−14.8195	+	25.6681i	−0.530282	+	0.918476i
$782$	0.530755	+	5.04980i	0.0189798	+	0.180580i
$783$	8.42971	+	6.12454i	0.301253	+	0.218873i
$784$	−0.458528	+	4.36261i	−0.0163760	+	0.155807i
$785$	0.663716	−	0.737132i	0.0236891	−	0.0263094i
$786$	−17.3492	−	7.72436i	−0.618826	−	0.275519i
$787$	20.8326	+	4.42810i	0.742600	+	0.157845i	0.563650	−	0.826014i	$-0.309397\pi$
$787$	20.8326	+	4.42810i	0.742600	+	0.157845i	0.178950	+	0.983858i	$0.442730\pi$
$788$	6.54811	−	1.39184i	0.233267	−	0.0495824i
$789$	−1.77504	+	0.790298i	−0.0631931	+	0.0281354i
$790$	−1.51945	+	4.67640i	−0.0540598	+	0.166379i
$791$	−17.4193	+	53.6109i	−0.619357	+	1.90619i
$792$	−13.9297	+	6.20191i	−0.494971	+	0.220375i
$793$	41.8243	−	8.89002i	1.48522	−	0.315694i
$794$	14.3219	+	3.04421i	0.508264	+	0.108035i
$795$	7.19364	+	3.20282i	0.255132	+	0.113592i
$796$	−14.2732	+	15.8520i	−0.505899	+	0.561858i
$797$	−0.502701	+	4.78288i	−0.0178066	+	0.169418i	−0.999811	−	0.0194394i	$-0.993812\pi$
$797$	−0.502701	+	4.78288i	−0.0178066	+	0.169418i	0.982004	+	0.188858i	$0.0604785\pi$
$798$	−6.88876	−	5.00498i	−0.243859	−	0.177174i
$799$	−0.978759	−	9.31227i	−0.0346260	−	0.329444i
$800$	−2.44279	+	4.23104i	−0.0863657	+	0.149590i
$801$	14.3416	+	24.8403i	0.506735	+	0.877690i
$802$	−20.1498	+	14.6397i	−0.711514	+	0.516945i
$803$	−29.2107	−	32.4418i	−1.03082	−	1.14485i
$804$	−0.466187	−	1.43478i	−0.0164412	−	0.0506007i
$805$	0.927193			0.0326793
$806$	29.5684	+	10.8063i	1.04150	+	0.380635i
$807$	47.9341			1.68736
$808$	−1.59385	−	4.90535i	−0.0560713	−	0.172570i
$809$	2.76904	+	3.07534i	0.0973544	+	0.108123i	0.789853	−	0.613296i	$-0.210157\pi$
$809$	2.76904	+	3.07534i	0.0973544	+	0.108123i	−0.692499	+	0.721419i	$0.743490\pi$
$810$	1.56210	−	1.13493i	0.0548867	−	0.0398775i
$811$	−17.4509	−	30.2259i	−0.612784	−	1.06137i	−0.990769	−	0.135562i	$-0.956716\pi$
$811$	−17.4509	−	30.2259i	−0.612784	−	1.06137i	0.377985	−	0.925812i	$-0.376617\pi$
$812$	−7.86208	+	13.6175i	−0.275905	+	0.477882i
$813$	−3.30061	−	31.4032i	−0.115758	−	1.10136i
$814$	6.34799	+	4.61208i	0.222497	+	0.161653i
$815$	−0.110175	+	1.04825i	−0.00385927	+	0.0367185i
$816$	10.9503	−	12.1615i	0.383337	−	0.425738i
$817$	−7.15795	−	3.18692i	−0.250425	−	0.111496i
$818$	33.4816	+	7.11672i	1.17066	+	0.248830i
$819$	71.9275	−	15.2887i	2.51335	−	0.534229i
$820$	−2.13844	+	0.952096i	−0.0746777	+	0.0332486i
$821$	−1.64222	+	5.05424i	−0.0573139	+	0.176394i	−0.975615	−	0.219488i	$-0.929561\pi$
$821$	−1.64222	+	5.05424i	−0.0573139	+	0.176394i	0.918301	+	0.395882i	$0.129561\pi$
$822$	1.00378	−	3.08931i	0.0350108	−	0.107752i
$823$	−14.0813	+	6.26939i	−0.490843	+	0.218537i	−0.637206	−	0.770694i	$-0.719910\pi$
$823$	−14.0813	+	6.26939i	−0.490843	+	0.218537i	0.146363	+	0.989231i	$0.453243\pi$
$824$	−3.84246	+	0.816741i	−0.133859	+	0.0284525i
$825$	−49.4976	−	10.5210i	−1.72329	−	0.366296i
$826$	24.0943	+	10.7275i	0.838349	+	0.373257i
$827$	−26.7671	+	29.7279i	−0.930785	+	1.03374i	0.0685635	+	0.997647i	$0.478158\pi$
$827$	−26.7671	+	29.7279i	−0.930785	+	1.03374i	−0.999348	+	0.0360946i	$0.988508\pi$
$828$	0.327249	−	3.11356i	0.0113727	−	0.108204i
$829$	−17.6691	−	12.8373i	−0.613672	−	0.445859i	0.237033	−	0.971502i	$-0.423825\pi$
$829$	−17.6691	−	12.8373i	−0.613672	−	0.445859i	−0.850705	+	0.525643i	$0.823825\pi$
$830$	−0.0562553	−	0.535233i	−0.00195265	−	0.0185782i
$831$	25.7947	−	44.6777i	0.894808	−	1.54985i
$832$	2.82709	+	4.89667i	0.0980117	+	0.169761i
$833$	22.1834	−	16.1172i	0.768610	−	0.558428i
$834$	−32.6698	−	36.2834i	−1.13126	−	1.25639i
$835$	−0.670574	−	2.06381i	−0.0232062	−	0.0714212i
$836$	3.81328			0.131885
$837$	−3.02786	+	12.0761i	−0.104658	+	0.417411i
$838$	19.2606			0.665348
$839$	−16.8853	−	51.9677i	−0.582947	−	1.79413i	−0.607364	−	0.794424i	$-0.707773\pi$
$839$	−16.8853	−	51.9677i	−0.582947	−	1.79413i	0.0244170	−	0.999702i	$-0.492227\pi$
$840$	−1.99957	−	2.22074i	−0.0689916	−	0.0766230i
$841$	5.89450	−	4.28260i	0.203258	−	0.147676i
$842$	−12.5932	−	21.8121i	−0.433991	−	0.751694i
$843$	34.7480	−	60.1852i	1.19678	−	2.07289i
$844$	1.83665	+	17.4746i	0.0632202	+	0.601500i
$845$	5.19125	+	3.77166i	0.178584	+	0.129749i
$846$	−0.603476	+	5.74169i	−0.0207479	+	0.197403i
$847$	10.5045	−	11.6664i	0.360937	−	0.400862i
$848$	8.12309	+	3.61663i	0.278948	+	0.124196i
$849$	−71.8574	−	15.2738i	−2.46614	−	0.524194i
$850$	29.8717	−	6.34942i	1.02459	−	0.217783i
$851$	−1.47177	+	0.655275i	−0.0504517	+	0.0224625i
$852$	−6.06082	+	18.6533i	−0.207640	+	0.639051i
$853$	14.7273	−	45.3260i	0.504253	−	1.55193i	−0.297769	−	0.954638i	$-0.596242\pi$
$853$	14.7273	−	45.3260i	0.504253	−	1.55193i	0.802022	−	0.597294i	$-0.203758\pi$
$854$	−23.3121	+	10.3792i	−0.797725	+	0.355170i
$855$	1.22911	−	0.261255i	0.0420346	−	0.00893474i
$856$	0.570716	+	0.121309i	0.0195067	+	0.00414627i
$857$	35.3560	+	15.7415i	1.20774	+	0.537720i	0.909073	−	0.416638i	$-0.136792\pi$
$857$	35.3560	+	15.7415i	1.20774	+	0.537720i	0.298666	+	0.954358i	$0.403458\pi$
$858$	−39.1872	+	43.5218i	−1.33783	+	1.48581i
$859$	0.520212	−	4.94949i	0.0177494	−	0.168874i	−0.982056	−	0.188588i	$-0.939609\pi$
$859$	0.520212	−	4.94949i	0.0177494	−	0.168874i	0.999806	+	0.0197138i	$0.00627552\pi$
$860$	−2.22463	−	1.61629i	−0.0758593	−	0.0551150i
$861$	6.39032	+	60.7999i	0.217782	+	2.07205i
$862$	13.0261	−	22.5618i	0.443669	−	0.768458i
$863$	−25.7100	−	44.5311i	−0.875179	−	1.51586i	−0.856572	−	0.516028i	$-0.827410\pi$
$863$	−25.7100	−	44.5311i	−0.875179	−	1.51586i	−0.0186078	−	0.999827i	$-0.505923\pi$
$864$	−1.80902	+	1.31433i	−0.0615440	+	0.0447143i
$865$	−3.24632	−	3.60540i	−0.110378	−	0.122587i
$866$	2.42956	+	7.47743i	0.0825600	+	0.254093i
$867$	−57.7882			−1.96259
$868$	−18.6016	−	2.63936i	−0.631379	−	0.0895856i
$869$	−57.5098			−1.95089
$870$	−1.27520	−	3.92468i	−0.0432335	−	0.133059i
$871$	−2.18014	−	2.42129i	−0.0738711	−	0.0820421i
$872$	−3.12336	+	2.26925i	−0.105770	+	0.0768466i
$873$	−0.142998	−	0.247680i	−0.00483976	−	0.00838271i
$874$	−0.391472	+	0.678049i	−0.0132417	+	0.0229354i
$875$	−1.17947	−	11.2219i	−0.0398733	−	0.379369i
$876$	−23.3709	−	16.9799i	−0.789629	−	0.573699i
$877$	−5.67031	+	53.9494i	−0.191473	+	1.82174i	0.303499	+	0.952832i	$0.401845\pi$
$877$	−5.67031	+	53.9494i	−0.191473	+	1.82174i	−0.494972	+	0.868909i	$0.664822\pi$
$878$	−19.4529	+	21.6046i	−0.656502	+	0.729119i
$879$	46.1436	+	20.5445i	1.55639	+	0.692948i
$880$	1.30902	+	0.278240i	0.0441270	+	0.00937947i
$881$	−10.3373	+	2.19727i	−0.348273	+	0.0740278i	−0.378727	−	0.925508i	$-0.623638\pi$
$881$	−10.3373	+	2.19727i	−0.348273	+	0.0740278i	0.0304537	+	0.999536i	$0.490305\pi$
$882$	−15.4449	+	6.87651i	−0.520057	+	0.231544i
$883$	4.45680	−	13.7166i	0.149983	−	0.461601i	−0.847635	−	0.530580i	$-0.821974\pi$
$883$	4.45680	−	13.7166i	0.149983	−	0.461601i	0.997618	+	0.0689792i	$0.0219742\pi$
$884$	10.9217	−	33.6136i	0.367337	−	1.13055i
$885$	−6.32331	+	2.81532i	−0.212556	+	0.0946359i
$886$	24.5423	−	5.21663i	0.824515	−	0.175256i
$887$	19.4065	+	4.12498i	0.651606	+	0.138503i	0.521843	−	0.853042i	$-0.325245\pi$
$887$	19.4065	+	4.12498i	0.651606	+	0.138503i	0.129764	+	0.991545i	$0.458578\pi$
$888$	4.74346	+	2.11192i	0.159180	+	0.0708715i
$889$	15.1905	−	16.8708i	0.509474	−	0.565828i
$890$	0.263142	−	2.50363i	0.00882054	−	0.0839219i
$891$	18.2703	+	13.2742i	0.612078	+	0.444701i
$892$	0.760778	+	7.23832i	0.0254727	+	0.242357i
$893$	0.721909	−	1.25038i	0.0241578	−	0.0418425i
$894$	8.93705	+	15.4794i	0.298900	+	0.517709i
$895$	5.23278	−	3.80184i	0.174912	−	0.127081i
$896$	−2.25792	−	2.50767i	−0.0754318	−	0.0837755i
$897$	−3.71576	−	11.4359i	−0.124066	−	0.381835i
$898$	−26.5947			−0.887477
$899$	−21.9843	−	13.7777i	−0.733217	−	0.459513i
$900$	−18.8295			−0.627651
$901$	−17.1756	−	52.8612i	−0.572203	−	1.76106i
$902$	−18.3196	−	20.3459i	−0.609974	−	0.677445i
$903$	−58.1003	+	42.2124i	−1.93346	+	1.40474i
$904$	−8.35256	−	14.4671i	−0.277802	−	0.481167i
$905$	1.04955	−	1.81788i	0.0348883	−	0.0604282i
$906$	−0.127403	−	1.21216i	−0.00423270	−	0.0402714i
$907$	22.4227	+	16.2911i	0.744535	+	0.540936i	0.894128	−	0.447811i	$-0.147796\pi$
$907$	22.4227	+	16.2911i	0.744535	+	0.540936i	−0.149593	+	0.988748i	$0.547796\pi$
$908$	0.0174881	−	0.166388i	0.000580364	−	0.00552179i
$909$	13.3014	−	14.7727i	0.441180	−	0.489981i
$910$	−5.89590	−	2.62502i	−0.195447	−	0.0870186i
$911$	34.8211	+	7.40145i	1.15367	+	0.245221i	0.744748	−	0.667346i	$-0.232570\pi$
$911$	34.8211	+	7.40145i	1.15367	+	0.245221i	0.408927	+	0.912567i	$0.365903\pi$
$912$	2.46826	−	0.524644i	0.0817321	−	0.0173727i
$913$	5.75036	−	2.56023i	0.190309	−	0.0847311i
$914$	−2.18605	+	6.72797i	−0.0723081	+	0.222541i
$915$	2.06949	−	6.36925i	0.0684153	−	0.210561i
$916$	−0.689540	+	0.307003i	−0.0227830	+	0.0101437i
$917$	23.9429	−	5.08921i	0.790663	−	0.168061i
$918$	13.6719	+	2.90605i	0.451240	+	0.0959139i
$919$	29.7890	+	13.2629i	0.982648	+	0.437503i	0.834227	−	0.551421i	$-0.185914\pi$
$919$	29.7890	+	13.2629i	0.982648	+	0.437503i	0.148421	+	0.988924i	$0.452581\pi$
$920$	−0.183858	+	0.204195i	−0.00606163	+	0.00673212i
$921$	3.61898	−	34.4323i	0.119250	−	1.13458i
$922$	15.8777	+	11.5358i	0.522903	+	0.379911i
$923$	4.42770	+	42.1268i	0.145740	+	1.38662i
$924$	17.4756	−	30.2686i	0.574905	−	0.995764i
$925$	4.84480	+	8.39144i	0.159296	+	0.275909i
$926$	3.06433	−	2.22637i	0.100700	−	0.0731630i
$927$	−10.1307	−	11.2513i	−0.332736	−	0.369541i
$928$	−1.43997	−	4.43176i	−0.0472692	−	0.145480i
$929$	1.46885			0.0481914			0.0240957	−	0.999710i	$-0.492329\pi$
$929$	1.46885			0.0481914			0.0240957	+	0.999710i	$0.492329\pi$
$930$	3.78132	−	3.16440i	0.123994	−	0.103765i
$931$	4.22807			0.138569
$932$	2.15185	+	6.62270i	0.0704861	+	0.216934i
$933$	59.0467	+	65.5780i	1.93310	+	2.14693i
$934$	2.78812	−	2.02569i	0.0912301	−	0.0662825i
$935$	−4.18264	−	7.24454i	−0.136787	−	0.236922i
$936$	−10.8959	+	18.8722i	−0.356144	+	0.616859i
$937$	−0.547971	−	5.21360i	−0.0179014	−	0.170321i	0.981918	−	0.189305i	$-0.0606235\pi$
$937$	−0.547971	−	5.21360i	−0.0179014	−	0.170321i	−0.999820	+	0.0189841i	$0.993957\pi$
$938$	1.57311	+	1.14293i	0.0513638	+	0.0373180i
$939$	−6.01796	+	57.2571i	−0.196389	+	1.86852i
$940$	0.339051	−	0.376554i	0.0110586	−	0.0122819i
$941$	49.1188	+	21.8691i	1.60123	+	0.712912i	0.996506	−	0.0835265i	$-0.0266183\pi$
$941$	49.1188	+	21.8691i	1.60123	+	0.712912i	0.604720	+	0.796438i	$0.293285\pi$
$942$	7.50929	+	1.59615i	0.244666	+	0.0520054i
$943$	5.49845	−	1.16873i	0.179054	−	0.0380591i
$944$	−7.14031	+	3.17907i	−0.232397	+	0.103470i
$945$	0.788710	−	2.42740i	0.0256567	−	0.0789633i
$946$	9.93846	−	30.5874i	0.323127	−	0.994483i
$947$	34.6324	−	15.4193i	1.12540	−	0.501061i	0.242281	−	0.970206i	$-0.422104\pi$
$947$	34.6324	−	15.4193i	1.12540	−	0.501061i	0.883121	+	0.469145i	$0.155438\pi$
$948$	−37.2248	+	7.91238i	−1.20901	+	0.256982i
$949$	−61.0262	−	12.9715i	−1.98100	−	0.421074i
$950$	4.30186	+	1.91531i	0.139571	+	0.0621410i
$951$	−43.8583	+	48.7096i	−1.42220	+	1.57952i
$952$	−2.20481	+	20.9774i	−0.0714584	+	0.679881i
$953$	−25.3455	−	18.4146i	−0.821021	−	0.596506i	0.0959840	−	0.995383i	$-0.469400\pi$
$953$	−25.3455	−	18.4146i	−0.821021	−	0.596506i	−0.917005	+	0.398876i	$0.869400\pi$
$954$	3.58219	+	34.0823i	0.115978	+	1.10345i
$955$	−2.32002	+	4.01840i	−0.0750742	+	0.130032i
$956$	9.15382	+	15.8549i	0.296056	+	0.512783i
$957$	39.0473	−	28.3696i	1.26222	−	0.917058i
$958$	0.192261	+	0.213528i	0.00621167	+	0.00689876i
$959$	1.29378	+	3.98184i	0.0417783	+	0.128580i
$960$	0.885579			0.0285820
$961$	5.46376	−	30.5147i	0.176250	−	0.984345i
$962$	11.2140			0.361553
$963$	0.694898	+	2.13868i	0.0223928	+	0.0689179i
$964$	−6.59852	−	7.32840i	−0.212524	−	0.236032i
$965$	−4.12740	+	2.99873i	−0.132866	+	0.0965327i
$966$	3.58809	+	6.21475i	0.115445	+	0.199956i
$967$	−3.59754	+	6.23112i	−0.115689	+	0.200379i	−0.918055	−	0.396453i	$-0.870241\pi$
$967$	−3.59754	+	6.23112i	−0.115689	+	0.200379i	0.802366	+	0.596832i	$0.203574\pi$
$968$	0.486295	+	4.62679i	0.0156301	+	0.148711i
$969$	−12.7609	−	9.27136i	−0.409940	−	0.297839i
$970$	−0.00262376	+	0.0249634i	−8.42439e−5	+	0.000801528i
$971$	−10.4849	+	11.6447i	−0.336478	+	0.373696i	−0.887511	−	0.460787i	$-0.847567\pi$
$971$	−10.4849	+	11.6447i	−0.336478	+	0.373696i	0.551033	+	0.834483i	$0.314234\pi$
$972$	19.7805	+	8.80686i	0.634461	+	0.282480i
$973$	61.5548	+	13.0839i	1.97336	+	0.419450i
$974$	−12.8894	+	2.73973i	−0.413004	+	0.0877866i
$975$	−66.0680	+	29.4154i	−2.11587	+	0.942046i
$976$	2.33688	−	7.19218i	0.0748017	−	0.230216i
$977$	3.42627	−	10.5450i	0.109616	−	0.337364i	−0.881170	−	0.472800i	$-0.843243\pi$
$977$	3.42627	−	10.5450i	0.109616	−	0.337364i	0.990786	+	0.135436i	$0.0432434\pi$
$978$	−7.45252	+	3.31807i	−0.238305	+	0.106100i
$979$	28.8003	−	6.12169i	0.920461	−	0.195650i
$980$	1.45140	+	0.308505i	0.0463634	+	0.00985484i
$981$	−13.5931	−	6.05202i	−0.433993	−	0.193226i
$982$	−16.2208	+	18.0150i	−0.517626	+	0.574882i
$983$	1.25391	−	11.9302i	0.0399936	−	0.380514i	−0.956157	−	0.292855i	$-0.905395\pi$
$983$	1.25391	−	11.9302i	0.0399936	−	0.380514i	0.996151	−	0.0876591i	$-0.0279386\pi$
$984$	−14.6571	−	10.6490i	−0.467252	−	0.339478i
$985$	−0.236700	−	2.25205i	−0.00754189	−	0.0717563i
$986$	−14.5639	+	25.2255i	−0.463811	+	0.803344i
$987$	−6.61676	−	11.4606i	−0.210614	−	0.364794i
$988$	4.40898	−	3.20331i	0.140268	−	0.101911i
$989$	4.41854	+	4.90729i	0.140502	+	0.156043i
$990$	1.59385	+	4.90535i	0.0506558	+	0.155902i
$991$	−35.5304			−1.12866			−0.564330	−	0.825550i	$-0.690865\pi$
$991$	−35.5304			−1.12866			−0.564330	+	0.825550i	$0.690865\pi$
$992$	4.26988	−	3.57325i	0.135569	−	0.113451i
$993$	−18.0380			−0.572420
$994$	−7.81185	−	24.0424i	−0.247777	−	0.762579i
$995$	4.82806	+	5.36210i	0.153060	+	0.169990i
$996$	3.36984	−	2.44833i	0.106777	−	0.0775784i
$997$	11.5479	+	20.0015i	0.365725	+	0.633454i	0.988892	−	0.148634i	$-0.0474877\pi$
$997$	11.5479	+	20.0015i	0.365725	+	0.633454i	−0.623167	+	0.782089i	$0.714154\pi$
$998$	−7.53263	+	13.0469i	−0.238441	+	0.412992i
$999$	0.463564	+	4.41051i	0.0146665	+	0.139542i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.2.g.b.51.1	yes	8
3.2	odd	2		558.2.ba.c.361.1		8
4.3	odd	2		496.2.bg.b.113.1		8
31.13	odd	30		1922.2.a.m.1.3		4
31.14	even	15	inner	62.2.g.b.45.1	✓	8
31.18	even	15		1922.2.a.h.1.1		4
93.14	odd	30		558.2.ba.c.541.1		8
124.107	odd	30		496.2.bg.b.417.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.2.g.b.45.1	✓	8	31.14	even	15	inner
62.2.g.b.51.1	yes	8	1.1	even	1	trivial
496.2.bg.b.113.1		8	4.3	odd	2
496.2.bg.b.417.1		8	124.107	odd	30
558.2.ba.c.361.1		8	3.2	odd	2
558.2.ba.c.541.1		8	93.14	odd	30
1922.2.a.h.1.1		4	31.18	even	15
1922.2.a.m.1.3		4	31.13	odd	30

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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	62.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-1.75181 - 1.94558i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.169131 + 0.292943i) q^{5} +(-1.30902 + 2.26728i) q^{6} +(-0.352722 - 3.35592i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.402863 + 3.83299i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-1.75181 - 1.94558i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.169131 + 0.292943i) q^{5} +(-1.30902 + 2.26728i) q^{6} +(-0.352722 - 3.35592i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.402863 + 3.83299i) q^{9} +(0.226341 - 0.251377i) q^{10} +(3.61426 + 1.60917i) q^{11} +(2.56082 + 0.544320i) q^{12} +(5.53062 - 1.17557i) q^{13} +(-3.08268 + 1.37250i) q^{14} +(0.273659 - 0.842236i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-5.71044 + 2.54245i) q^{17} +(3.76988 - 0.801313i) q^{18} +(-0.942790 - 0.200396i) q^{19} +(-0.309017 - 0.137583i) q^{20} +(-5.91131 + 6.56518i) q^{21} +(0.413545 - 3.93462i) q^{22} +(0.657170 + 0.477462i) q^{23} +(-0.273659 - 2.60369i) q^{24} +(2.44279 - 4.23104i) q^{25} +(-2.82709 - 4.89667i) q^{26} +(1.80902 - 1.31433i) q^{27} +(2.25792 + 2.50767i) q^{28} +(1.43997 + 4.43176i) q^{29} -0.885579 q^{30} +(-4.26988 + 3.57325i) q^{31} -1.00000 q^{32} +(-3.20071 - 9.85077i) q^{33} +(4.18264 + 4.64529i) q^{34} +(0.923438 - 0.670917i) q^{35} +(-1.92705 - 3.33775i) q^{36} +(-0.991653 + 1.71759i) q^{37} +(0.100750 + 0.958572i) q^{38} +(-11.9757 - 8.70089i) q^{39} +(-0.0353579 + 0.336408i) q^{40} +(4.63048 - 5.14267i) q^{41} +(8.07055 + 3.59324i) q^{42} +(7.95156 + 1.69016i) q^{43} +(-3.86984 + 0.822560i) q^{44} +(-1.19098 + 0.530260i) q^{45} +(0.251017 - 0.772550i) q^{46} +(-0.462897 + 1.42465i) q^{47} +(-2.39169 + 1.06485i) q^{48} +(-4.29078 + 0.912033i) q^{49} +(-4.77882 - 1.01577i) q^{50} +(14.9501 + 6.65622i) q^{51} +(-3.78339 + 4.20188i) q^{52} +(-0.929449 + 8.84312i) q^{53} +(-1.80902 - 1.31433i) q^{54} +(0.139886 + 1.33093i) q^{55} +(1.68720 - 2.92232i) q^{56} +(1.26170 + 2.18533i) q^{57} +(3.76988 - 2.73898i) q^{58} +(-5.22995 - 5.80845i) q^{59} +(0.273659 + 0.842236i) q^{60} +7.56231 q^{61} +(4.71783 + 2.95670i) q^{62} +13.0053 q^{63} +(0.309017 + 0.951057i) q^{64} +(1.27977 + 1.42133i) q^{65} +(-8.37957 + 6.08811i) q^{66} +(-0.288120 - 0.499038i) q^{67} +(3.12543 - 5.41340i) q^{68} +(-0.222295 - 2.11500i) q^{69} +(-0.923438 - 0.670917i) q^{70} +(-0.783084 + 7.45055i) q^{71} +(-2.57890 + 2.86416i) q^{72} +(-10.0803 - 4.48803i) q^{73} +(1.93997 + 0.412353i) q^{74} +(-12.5111 + 2.65932i) q^{75} +(0.880523 - 0.392034i) q^{76} +(4.12543 - 12.6968i) q^{77} +(-4.57433 + 14.0783i) q^{78} +(-13.2795 + 5.91243i) q^{79} +(0.330869 - 0.0703285i) q^{80} +(5.58347 + 1.18680i) q^{81} +(-6.32187 - 2.81468i) q^{82} +(1.06460 - 1.18236i) q^{83} +(0.923438 - 8.78592i) q^{84} +(-1.71060 - 1.24283i) q^{85} +(-0.849733 - 8.08467i) q^{86} +(6.09979 - 10.5652i) q^{87} +(1.97815 + 3.42625i) q^{88} +(6.02090 - 4.37444i) q^{89} +(0.872341 + 0.968833i) q^{90} +(-5.89590 - 18.1457i) q^{91} -0.812307 q^{92} +(14.4320 + 2.04774i) q^{93} +1.49797 q^{94} +(-0.100750 - 0.310077i) q^{95} +(1.75181 + 1.94558i) q^{96} +(-0.0600337 + 0.0436171i) q^{97} +(2.19332 + 3.79894i) q^{98} +(-7.62398 + 13.2051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + q^{3} - 2 q^{4} - 3 q^{5} - 6 q^{6} - 16 q^{7} + 2 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + q^3 - 2 * q^4 - 3 * q^5 - 6 * q^6 - 16 * q^7 + 2 * q^8 + 8 * q^9	\( 8 q + 2 q^{2} + q^{3} - 2 q^{4} - 3 q^{5} - 6 q^{6} - 16 q^{7} + 2 q^{8} + 8 q^{9} + 8 q^{10} + 3 q^{11} + q^{12} - 14 q^{14} - 4 q^{15} - 2 q^{16} - 2 q^{17} + 7 q^{18} + 3 q^{19} + 2 q^{20} - 31 q^{21} - 3 q^{22} + 15 q^{23} + 4 q^{24} + 9 q^{25} - 10 q^{26} + 10 q^{27} + 9 q^{28} + 13 q^{29} + 14 q^{30} - 11 q^{31} - 8 q^{32} - 6 q^{33} + 22 q^{34} + 24 q^{35} - 2 q^{36} + 8 q^{37} - 18 q^{38} - 30 q^{39} - 2 q^{40} + 13 q^{41} + 21 q^{42} - 7 q^{44} - 14 q^{45} + 5 q^{46} + 9 q^{47} - 4 q^{48} + 9 q^{49} - 9 q^{50} + 28 q^{51} - 51 q^{53} - 10 q^{54} + q^{55} + q^{56} + 18 q^{57} + 7 q^{58} - 18 q^{59} - 4 q^{60} - 20 q^{61} - 19 q^{62} - 14 q^{63} - 2 q^{64} + 10 q^{65} - 19 q^{66} - 18 q^{67} + 3 q^{68} + 35 q^{69} - 24 q^{70} + 7 q^{71} + 7 q^{72} - 13 q^{73} + 17 q^{74} - 36 q^{75} - 12 q^{76} + 11 q^{77} - 10 q^{78} + 9 q^{79} + 7 q^{80} + 16 q^{81} + 7 q^{82} + 6 q^{83} + 24 q^{84} - 17 q^{85} + 15 q^{86} + q^{87} + 7 q^{88} + 28 q^{89} + 19 q^{90} + 20 q^{91} - 20 q^{92} + 32 q^{93} + 6 q^{94} + 18 q^{95} - q^{96} + q^{97} + 11 q^{98} - 11 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + q^3 - 2 * q^4 - 3 * q^5 - 6 * q^6 - 16 * q^7 + 2 * q^8 + 8 * q^9 + 8 * q^10 + 3 * q^11 + q^12 - 14 * q^14 - 4 * q^15 - 2 * q^16 - 2 * q^17 + 7 * q^18 + 3 * q^19 + 2 * q^20 - 31 * q^21 - 3 * q^22 + 15 * q^23 + 4 * q^24 + 9 * q^25 - 10 * q^26 + 10 * q^27 + 9 * q^28 + 13 * q^29 + 14 * q^30 - 11 * q^31 - 8 * q^32 - 6 * q^33 + 22 * q^34 + 24 * q^35 - 2 * q^36 + 8 * q^37 - 18 * q^38 - 30 * q^39 - 2 * q^40 + 13 * q^41 + 21 * q^42 - 7 * q^44 - 14 * q^45 + 5 * q^46 + 9 * q^47 - 4 * q^48 + 9 * q^49 - 9 * q^50 + 28 * q^51 - 51 * q^53 - 10 * q^54 + q^55 + q^56 + 18 * q^57 + 7 * q^58 - 18 * q^59 - 4 * q^60 - 20 * q^61 - 19 * q^62 - 14 * q^63 - 2 * q^64 + 10 * q^65 - 19 * q^66 - 18 * q^67 + 3 * q^68 + 35 * q^69 - 24 * q^70 + 7 * q^71 + 7 * q^72 - 13 * q^73 + 17 * q^74 - 36 * q^75 - 12 * q^76 + 11 * q^77 - 10 * q^78 + 9 * q^79 + 7 * q^80 + 16 * q^81 + 7 * q^82 + 6 * q^83 + 24 * q^84 - 17 * q^85 + 15 * q^86 + q^87 + 7 * q^88 + 28 * q^89 + 19 * q^90 + 20 * q^91 - 20 * q^92 + 32 * q^93 + 6 * q^94 + 18 * q^95 - q^96 + q^97 + 11 * q^98 - 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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