LMFDB - Embedded newform 409.2.h.a.5.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [409,2,Mod(5,409)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(409, base_ring=CyclotomicField(34)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("409.5"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 409 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	409.h (of order $17$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.26588144267$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{17})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{17}]$

Embedding invariants

Embedding label			5.11
Character	$\chi$	$=$	409.5
Dual form			409.2.h.a.82.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00100 + 0.619792i) q^{2} +(0.241764 + 0.0451934i) q^{3} +(-0.273621 + 0.549506i) q^{4} +(-0.624145 - 2.19364i) q^{5} +(-0.270015 + 0.104605i) q^{6} +3.32282 q^{7} +(-0.283948 - 3.06429i) q^{8} +(-2.74101 - 1.06187i) q^{9} +(1.98437 + 1.80899i) q^{10} +(-2.74561 - 1.06366i) q^{11} +(-0.0909857 + 0.120484i) q^{12} +(-5.96075 + 2.30921i) q^{13} +(-3.32613 + 2.05946i) q^{14} +(-0.0517573 - 0.558550i) q^{15} +(1.44358 + 1.91161i) q^{16} +(0.297881 + 3.21464i) q^{17} +(3.40189 - 0.635923i) q^{18} +(-3.13095 - 1.93860i) q^{19} +(1.37620 + 0.257256i) q^{20} +(0.803336 + 0.150170i) q^{21} +(3.40760 - 0.636991i) q^{22} +(-0.715350 - 7.71986i) q^{23} +(0.0698374 - 0.753665i) q^{24} +(-0.171425 + 0.106142i) q^{25} +(4.53548 - 6.00594i) q^{26} +(-1.24202 - 0.769028i) q^{27} +(-0.909194 + 1.82591i) q^{28} +(-7.22527 - 6.58670i) q^{29} +(0.397994 + 0.527029i) q^{30} +6.42923 q^{31} +(3.10938 + 1.20458i) q^{32} +(-0.615719 - 0.381237i) q^{33} +(-2.29059 - 3.03323i) q^{34} +(-2.07392 - 7.28907i) q^{35} +(1.33350 - 1.21565i) q^{36} +(2.68367 - 3.55375i) q^{37} +4.33560 q^{38} +(-1.54545 + 0.288895i) q^{39} +(-6.54472 + 2.53544i) q^{40} +(-2.32825 + 2.12248i) q^{41} +(-0.897212 + 0.347582i) q^{42} +(-2.43031 + 1.50478i) q^{43} +(1.33574 - 1.21769i) q^{44} +(-0.618582 + 6.67556i) q^{45} +(5.50077 + 7.28419i) q^{46} +(-5.01477 + 6.64063i) q^{47} +(0.262613 + 0.527399i) q^{48} +4.04112 q^{49} +(0.105810 - 0.212496i) q^{50} +(-0.0732641 + 0.790646i) q^{51} +(0.362066 - 3.90732i) q^{52} +9.00986 q^{53} +1.71990 q^{54} +(-0.619620 + 6.68677i) q^{55} +(-0.943507 - 10.1821i) q^{56} +(-0.669337 - 0.610182i) q^{57} +(11.3149 + 2.11512i) q^{58} +(3.73411 - 7.49910i) q^{59} +(0.321088 + 0.124390i) q^{60} +(-7.46017 + 1.39455i) q^{61} +(-6.43565 + 3.98479i) q^{62} +(-9.10788 - 3.52841i) q^{63} +(-8.56840 + 1.60171i) q^{64} +(8.78595 + 11.6345i) q^{65} +0.852621 q^{66} +(-1.73857 - 0.673526i) q^{67} +(-1.84797 - 0.715908i) q^{68} +(0.175941 - 1.89871i) q^{69} +(6.59370 + 6.01095i) q^{70} +(2.26383 - 7.95654i) q^{71} +(-2.47558 + 8.70075i) q^{72} +(-2.53458 - 5.09013i) q^{73} +(-0.483761 + 5.22061i) q^{74} +(-0.0462413 + 0.0179140i) q^{75} +(1.92197 - 1.19003i) q^{76} +(-9.12317 - 3.53434i) q^{77} +(1.36794 - 1.24704i) q^{78} +(1.66196 + 5.84118i) q^{79} +(3.29239 - 4.35983i) q^{80} +(6.25145 + 5.69895i) q^{81} +(1.01508 - 3.56763i) q^{82} +(0.168183 + 1.81498i) q^{83} +(-0.302329 + 0.400348i) q^{84} +(6.86586 - 2.65985i) q^{85} +(1.50008 - 3.01257i) q^{86} +(-1.44913 - 1.91896i) q^{87} +(-2.47974 + 8.71537i) q^{88} +(6.00213 + 12.0539i) q^{89} +(-3.51826 - 7.06561i) q^{90} +(-19.8065 + 7.67308i) q^{91} +(4.43784 + 1.71923i) q^{92} +(1.55435 + 0.290559i) q^{93} +(0.903968 - 9.75537i) q^{94} +(-2.29843 + 8.07815i) q^{95} +(0.697295 + 0.431747i) q^{96} +(3.00021 + 10.5446i) q^{97} +(-4.04515 + 2.50465i) q^{98} +(6.39628 + 5.83098i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q - 13 q^{2} - 11 q^{3} - 73 q^{4} - 9 q^{5} - 27 q^{6} - 22 q^{7} + q^{8} - 31 q^{9} + 5 q^{10} - 60 q^{11} - 38 q^{12} + 7 q^{13} - 37 q^{14} + 3 q^{15} - 53 q^{16} + 3 q^{17} + 16 q^{18} + 17 q^{19}+ \cdots - 103 q^{99}+O(q^{100}) $ 512 * q - 13 * q^2 - 11 * q^3 - 73 * q^4 - 9 * q^5 - 27 * q^6 - 22 * q^7 + q^8 - 31 * q^9 + 5 * q^10 - 60 * q^11 - 38 * q^12 + 7 * q^13 - 37 * q^14 + 3 * q^15 - 53 * q^16 + 3 * q^17 + 16 * q^18 + 17 * q^19 + 27 * q^20 - 120 * q^21 - q^22 + q^23 - 20 * q^24 - 5 * q^25 + 23 * q^26 + 25 * q^27 - 29 * q^28 + 13 * q^29 + 27 * q^30 + 12 * q^31 - 69 * q^32 + 55 * q^33 + 37 * q^34 - 54 * q^35 - 41 * q^36 + 25 * q^37 - 212 * q^38 - 69 * q^39 - 66 * q^40 - 117 * q^41 - 141 * q^42 - 73 * q^43 + 37 * q^44 + 75 * q^45 - q^46 + 11 * q^47 + 143 * q^48 + 318 * q^49 + 79 * q^50 + 101 * q^52 - 84 * q^53 - 8 * q^54 - 79 * q^55 - 54 * q^56 + 87 * q^57 + 61 * q^58 + 37 * q^59 + 9 * q^60 + 42 * q^61 + 45 * q^62 - 161 * q^63 - 229 * q^64 + 67 * q^65 + 112 * q^66 + 35 * q^67 + 111 * q^68 - 119 * q^69 - 96 * q^70 - 39 * q^71 + 195 * q^72 + 83 * q^73 - 47 * q^74 + 77 * q^75 + 125 * q^76 - 138 * q^77 - 87 * q^78 + 57 * q^79 - 41 * q^80 - 83 * q^81 + 149 * q^82 + 23 * q^83 - 164 * q^84 + 23 * q^85 - 111 * q^86 - 237 * q^87 - 71 * q^88 + 107 * q^89 - 38 * q^90 - 14 * q^91 - 167 * q^92 + 62 * q^93 + 147 * q^94 + 45 * q^95 + 84 * q^96 + 99 * q^97 - 151 * q^98 - 103 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/409\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{17}\right)$

Coefficient data

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

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

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

$2$	−1.00100	+	0.619792i	−0.707813	+	0.438259i	−0.832564	−	0.553929i	$-0.813128\pi$
$2$	−1.00100	+	0.619792i	−0.707813	+	0.438259i	0.124751	+	0.992188i	$0.460187\pi$
$3$	0.241764	+	0.0451934i	0.139582	+	0.0260924i	0.253077	−	0.967446i	$-0.418557\pi$
$3$	0.241764	+	0.0451934i	0.139582	+	0.0260924i	−0.113495	+	0.993539i	$0.536204\pi$
$4$	−0.273621	+	0.549506i	−0.136811	+	0.274753i
$5$	−0.624145	−	2.19364i	−0.279126	−	0.981027i	−0.966911	−	0.255113i	$-0.917887\pi$
$5$	−0.624145	−	2.19364i	−0.279126	−	0.981027i	0.687785	−	0.725914i	$-0.258583\pi$
$6$	−0.270015	+	0.104605i	−0.110233	+	0.0427046i
$7$	3.32282			1.25591			0.627954	−	0.778251i	$-0.283893\pi$
$7$	3.32282			1.25591			0.627954	+	0.778251i	$0.283893\pi$
$8$	−0.283948	−	3.06429i	−0.100391	−	1.08339i
$9$	−2.74101	−	1.06187i	−0.913670	−	0.353958i
$10$	1.98437	+	1.80899i	0.627513	+	0.572054i
$11$	−2.74561	−	1.06366i	−0.827833	−	0.320704i	−0.0902151	−	0.995922i	$-0.528755\pi$
$11$	−2.74561	−	1.06366i	−0.827833	−	0.320704i	−0.737618	+	0.675218i	$0.764050\pi$
$12$	−0.0909857	+	0.120484i	−0.0262653	+	0.0347809i
$13$	−5.96075	+	2.30921i	−1.65322	+	0.640459i	−0.993786	−	0.111307i	$-0.964496\pi$
$13$	−5.96075	+	2.30921i	−1.65322	+	0.640459i	−0.659430	+	0.751766i	$0.729202\pi$
$14$	−3.32613	+	2.05946i	−0.888947	+	0.550413i
$15$	−0.0517573	−	0.558550i	−0.0133637	−	0.144217i
$16$	1.44358	+	1.91161i	0.360896	+	0.477903i
$17$	0.297881	+	3.21464i	0.0722467	+	0.779666i	0.952375	+	0.304930i	$0.0986329\pi$
$17$	0.297881	+	3.21464i	0.0722467	+	0.779666i	−0.880128	+	0.474736i	$0.842544\pi$
$18$	3.40189	−	0.635923i	0.801832	−	0.149888i
$19$	−3.13095	−	1.93860i	−0.718289	−	0.444746i	0.118015	−	0.993012i	$-0.462347\pi$
$19$	−3.13095	−	1.93860i	−0.718289	−	0.444746i	−0.836304	+	0.548266i	$0.815288\pi$
$20$	1.37620	+	0.257256i	0.307727	+	0.0575242i
$21$	0.803336	+	0.150170i	0.175302	+	0.0327697i
$22$	3.40760	−	0.636991i	0.726503	−	0.135807i
$23$	−0.715350	−	7.71986i	−0.149161	−	1.60970i	−0.660841	−	0.750526i	$-0.729800\pi$
$23$	−0.715350	−	7.71986i	−0.149161	−	1.60970i	0.511681	−	0.859176i	$-0.329023\pi$
$24$	0.0698374	−	0.753665i	0.0142555	−	0.153841i
$25$	−0.171425	+	0.106142i	−0.0342851	+	0.0212284i
$26$	4.53548	−	6.00594i	0.889480	−	1.17786i
$27$	−1.24202	−	0.769028i	−0.239027	−	0.147999i
$28$	−0.909194	+	1.82591i	−0.171821	+	0.345064i
$29$	−7.22527	−	6.58670i	−1.34170	−	1.22312i	−0.953445	−	0.301568i	$-0.902490\pi$
$29$	−7.22527	−	6.58670i	−1.34170	−	1.22312i	−0.388255	−	0.921552i	$-0.626922\pi$
$30$	0.397994	+	0.527029i	0.0726634	+	0.0962219i
$31$	6.42923			1.15472			0.577362	−	0.816488i	$-0.304082\pi$
$31$	6.42923			1.15472			0.577362	+	0.816488i	$0.304082\pi$
$32$	3.10938	+	1.20458i	0.549666	+	0.212942i
$33$	−0.615719	−	0.381237i	−0.107183	−	0.0663648i
$34$	−2.29059	−	3.03323i	−0.392833	−	0.520194i
$35$	−2.07392	−	7.28907i	−0.350557	−	1.23208i
$36$	1.33350	−	1.21565i	0.222251	−	0.202608i
$37$	2.68367	−	3.55375i	0.441192	−	0.584233i	−0.522034	−	0.852925i	$-0.674827\pi$
$37$	2.68367	−	3.55375i	0.441192	−	0.584233i	0.963226	+	0.268692i	$0.0865913\pi$
$38$	4.33560			0.703328
$39$	−1.54545	+	0.288895i	−0.247471	+	0.0462603i
$40$	−6.54472	+	2.53544i	−1.03481	+	0.400888i
$41$	−2.32825	+	2.12248i	−0.363611	+	0.331475i	−0.834796	−	0.550559i	$-0.814415\pi$
$41$	−2.32825	+	2.12248i	−0.363611	+	0.331475i	0.471185	+	0.882034i	$0.343826\pi$
$42$	−0.897212	+	0.347582i	−0.138443	+	0.0536330i
$43$	−2.43031	+	1.50478i	−0.370618	+	0.229477i	−0.699085	−	0.715038i	$-0.746409\pi$
$43$	−2.43031	+	1.50478i	−0.370618	+	0.229477i	0.328467	+	0.944515i	$0.393468\pi$
$44$	1.33574	−	1.21769i	0.201371	−	0.183574i
$45$	−0.618582	+	6.67556i	−0.0922127	+	0.995133i
$46$	5.50077	+	7.28419i	0.811044	+	1.07400i
$47$	−5.01477	+	6.64063i	−0.731479	+	0.968635i	0.268506	+	0.963278i	$0.413470\pi$
$47$	−5.01477	+	6.64063i	−0.731479	+	0.968635i	−0.999986	+	0.00535727i	$0.998295\pi$
$48$	0.262613	+	0.527399i	0.0379050	+	0.0761235i
$49$	4.04112			0.577303
$50$	0.105810	−	0.212496i	0.0149639	−	0.0300515i
$51$	−0.0732641	+	0.790646i	−0.0102590	+	0.110713i
$52$	0.362066	−	3.90732i	0.0502095	−	0.541847i
$53$	9.00986			1.23760			0.618800	−	0.785549i	$-0.287619\pi$
$53$	9.00986			1.23760			0.618800	+	0.785549i	$0.287619\pi$
$54$	1.71990			0.234049
$55$	−0.619620	+	6.68677i	−0.0835496	+	0.901644i
$56$	−0.943507	−	10.1821i	−0.126081	−	1.36064i
$57$	−0.669337	−	0.610182i	−0.0886559	−	0.0808205i
$58$	11.3149	+	2.11512i	1.48572	+	0.277728i
$59$	3.73411	−	7.49910i	0.486139	−	0.976300i	−0.507282	−	0.861780i	$-0.669350\pi$
$59$	3.73411	−	7.49910i	0.486139	−	0.976300i	0.993421	−	0.114519i	$-0.0365327\pi$
$60$	0.321088	+	0.124390i	0.0414523	+	0.0160587i
$61$	−7.46017	+	1.39455i	−0.955177	+	0.178553i	−0.638192	−	0.769877i	$-0.720317\pi$
$61$	−7.46017	+	1.39455i	−0.955177	+	0.178553i	−0.316985	+	0.948431i	$0.602670\pi$
$62$	−6.43565	+	3.98479i	−0.817328	+	0.506068i
$63$	−9.10788	−	3.52841i	−1.14748	−	0.444538i
$64$	−8.56840	+	1.60171i	−1.07105	+	0.200214i
$65$	8.78595	+	11.6345i	1.08976	+	1.44308i
$66$	0.852621			0.104950
$67$	−1.73857	−	0.673526i	−0.212400	−	0.0822843i	0.252691	−	0.967547i	$-0.418684\pi$
$67$	−1.73857	−	0.673526i	−0.212400	−	0.0822843i	−0.465091	+	0.885263i	$0.653979\pi$
$68$	−1.84797	−	0.715908i	−0.224099	−	0.0868166i
$69$	0.175941	−	1.89871i	0.0211808	−	0.228578i
$70$	6.59370	+	6.01095i	0.788098	+	0.718446i
$71$	2.26383	−	7.95654i	0.268667	−	0.944267i	−0.703639	−	0.710557i	$-0.748443\pi$
$71$	2.26383	−	7.95654i	0.268667	−	0.944267i	0.972306	−	0.233710i	$-0.0750866\pi$
$72$	−2.47558	+	8.70075i	−0.291750	+	1.02539i
$73$	−2.53458	−	5.09013i	−0.296650	−	0.595754i	0.695823	−	0.718213i	$-0.255040\pi$
$73$	−2.53458	−	5.09013i	−0.296650	−	0.595754i	−0.992474	+	0.122459i	$0.960922\pi$
$74$	−0.483761	+	5.22061i	−0.0562361	+	0.606884i
$75$	−0.0462413	+	0.0179140i	−0.00533948	+	0.00206853i
$76$	1.92197	−	1.19003i	0.220465	−	0.136506i
$77$	−9.12317	−	3.53434i	−1.03968	−	0.402775i
$78$	1.36794	−	1.24704i	0.154889	−	0.141200i
$79$	1.66196	+	5.84118i	0.186985	+	0.657185i	0.997448	+	0.0713948i	$0.0227450\pi$
$79$	1.66196	+	5.84118i	0.186985	+	0.657185i	−0.810463	+	0.585790i	$0.800784\pi$
$80$	3.29239	−	4.35983i	0.368101	−	0.487444i
$81$	6.25145	+	5.69895i	0.694605	+	0.633216i
$82$	1.01508	−	3.56763i	0.112097	−	0.393978i
$83$	0.168183	+	1.81498i	0.0184604	+	0.199220i	0.999970	+	0.00780447i	$0.00248427\pi$
$83$	0.168183	+	1.81498i	0.0184604	+	0.199220i	−0.981509	+	0.191416i	$0.938692\pi$
$84$	−0.302329	+	0.400348i	−0.0329868	+	0.0436816i
$85$	6.86586	−	2.65985i	0.744707	−	0.288501i
$86$	1.50008	−	3.01257i	0.161758	−	0.324854i
$87$	−1.44913	−	1.91896i	−0.155363	−	0.205734i
$88$	−2.47974	+	8.71537i	−0.264341	+	0.929061i
$89$	6.00213	+	12.0539i	0.636225	+	1.27771i	0.945154	+	0.326626i	$0.105912\pi$
$89$	6.00213	+	12.0539i	0.636225	+	1.27771i	−0.308929	+	0.951085i	$0.599970\pi$
$90$	−3.51826	−	7.06561i	−0.370857	−	0.744781i
$91$	−19.8065	+	7.67308i	−2.07629	+	0.804357i
$92$	4.43784	+	1.71923i	0.462677	+	0.179242i
$93$	1.55435	+	0.290559i	0.161179	+	0.0301296i
$94$	0.903968	−	9.75537i	0.0932372	−	1.00619i
$95$	−2.29843	+	8.07815i	−0.235814	+	0.828801i
$96$	0.697295	+	0.431747i	0.0711674	+	0.0440650i
$97$	3.00021	+	10.5446i	0.304625	+	1.07065i	0.951398	+	0.307964i	$0.0996476\pi$
$97$	3.00021	+	10.5446i	0.304625	+	1.07065i	−0.646773	+	0.762683i	$0.723882\pi$
$98$	−4.04515	+	2.50465i	−0.408622	+	0.253008i
$99$	6.39628	+	5.83098i	0.642851	+	0.586036i
$100$	−0.0114200	−	0.123242i	−0.00114200	−	0.0123242i
$101$	1.14343	−	1.04238i	0.113776	−	0.103720i	−0.614809	−	0.788676i	$-0.710767\pi$
$101$	1.14343	−	1.04238i	0.113776	−	0.103720i	0.728585	+	0.684956i	$0.240179\pi$
$102$	−0.416699	−	0.836843i	−0.0412593	−	0.0828598i
$103$	−0.919179	−	3.23058i	−0.0905694	−	0.318318i	0.903281	−	0.429049i	$-0.141151\pi$
$103$	−0.919179	−	3.23058i	−0.0905694	−	0.318318i	−0.993850	+	0.110731i	$0.964681\pi$
$104$	8.76862	+	17.6098i	0.859834	+	1.72678i
$105$	−0.171980	−	1.85596i	−0.0167835	−	0.181123i
$106$	−9.01885	+	5.58424i	−0.875988	+	0.542389i
$107$	0.551124	−	5.94757i	0.0532791	−	0.574974i	−0.926690	−	0.375826i	$-0.877359\pi$
$107$	0.551124	−	5.94757i	0.0532791	−	0.574974i	0.979969	−	0.199148i	$-0.0638174\pi$
$108$	0.762429	−	0.472076i	0.0733647	−	0.0454255i
$109$	0.278764	−	3.00834i	0.0267008	−	0.288147i	−0.971906	−	0.235371i	$-0.924370\pi$
$109$	0.278764	−	3.00834i	0.0267008	−	0.288147i	0.998606	−	0.0527761i	$-0.0168070\pi$
$110$	−3.52417	−	7.07748i	−0.336016	−	0.674811i
$111$	0.809419	−	0.737883i	0.0768267	−	0.0700368i
$112$	4.79676	+	6.35194i	0.453252	+	0.600202i
$113$	−2.84066	−	1.75886i	−0.267227	−	0.165460i	0.386278	−	0.922383i	$-0.373761\pi$
$113$	−2.84066	−	1.75886i	−0.267227	−	0.165460i	−0.653504	+	0.756923i	$0.726702\pi$
$114$	1.04819	+	0.195941i	0.0981721	+	0.0183515i
$115$	−16.4881	+	6.38753i	−1.53753	+	0.595641i
$116$	5.59642	−	2.16806i	0.519614	−	0.201300i
$117$	18.7906			1.73719
$118$	0.910045	+	9.82095i	0.0837765	+	0.904092i
$119$	0.989803	+	10.6817i	0.0907351	+	0.979187i
$120$	−1.69686	+	0.317198i	−0.154901	+	0.0289561i
$121$	−1.72207	−	1.56988i	−0.156552	−	0.142716i
$122$	6.60329	−	6.01969i	0.597833	−	0.544997i
$123$	−0.658808	+	0.407916i	−0.0594027	+	0.0367806i
$124$	−1.75917	+	3.53290i	−0.157979	+	0.317264i
$125$	−8.08748	−	7.37271i	−0.723366	−	0.659436i
$126$	11.3038	−	2.11306i	1.00703	−	0.188246i
$127$	1.49321	−	5.24808i	0.132501	−	0.465692i	−0.866965	−	0.498369i	$-0.833933\pi$
$127$	1.49321	−	5.24808i	0.132501	−	0.465692i	0.999466	+	0.0326767i	$0.0104032\pi$
$128$	2.65570	−	2.42099i	0.234733	−	0.213987i
$129$	−0.655566	+	0.253968i	−0.0577194	+	0.0223606i
$130$	−16.0057	−	6.20063i	−1.40379	−	0.543832i
$131$	11.7680	+	10.7280i	1.02818	+	0.937306i	0.998061	−	0.0622405i	$-0.0198246\pi$
$131$	11.7680	+	10.7280i	1.02818	+	0.937306i	0.0301145	+	0.999546i	$0.490413\pi$
$132$	0.377965	−	0.234026i	0.0328977	−	0.0203694i
$133$	−10.4036	−	6.44162i	−0.902104	−	0.558559i
$134$	2.15775	−	0.403354i	0.186401	−	0.0348445i
$135$	−0.911770	+	3.20454i	−0.0784726	+	0.275803i
$136$	9.76600	−	1.82558i	0.837428	−	0.156542i
$137$	−9.30039	+	8.47843i	−0.794586	+	0.724361i	−0.965352	−	0.260951i	$-0.915964\pi$
$137$	−9.30039	+	8.47843i	−0.794586	+	0.724361i	0.170766	+	0.985312i	$0.445376\pi$
$138$	1.00069	+	2.00965i	0.0851842	+	0.171073i
$139$	−2.32809	−	8.18239i	−0.197466	−	0.694021i	−0.995779	−	0.0917791i	$-0.970745\pi$
$139$	−2.32809	−	8.18239i	−0.197466	−	0.694021i	0.798313	−	0.602242i	$-0.205726\pi$
$140$	4.57286	+	0.854815i	0.386477	+	0.0722450i
$141$	−1.51250	+	1.37883i	−0.127376	+	0.116118i
$142$	2.66531	+	9.36758i	0.223668	+	0.786110i
$143$	18.8221			1.57399
$144$	−1.92699	−	6.77265i	−0.160582	−	0.564388i
$145$	−9.93926	+	19.9607i	−0.825411	+	1.65765i
$146$	5.69193	+	3.52429i	0.471067	+	0.291673i
$147$	0.976995	+	0.182632i	0.0805812	+	0.0150632i
$148$	1.21850	+	2.44707i	0.100160	+	0.201148i
$149$	5.58495	−	1.04401i	0.457537	−	0.0855285i	0.0500645	−	0.998746i	$-0.484057\pi$
$149$	5.58495	−	1.04401i	0.457537	−	0.0855285i	0.407472	+	0.913218i	$0.366410\pi$
$150$	0.0351845	−	0.0465918i	0.00287280	−	0.00380421i
$151$	−10.1801	+	13.4807i	−0.828446	+	1.09704i	0.165395	+	0.986227i	$0.447110\pi$
$151$	−10.1801	+	13.4807i	−0.828446	+	1.09704i	−0.993841	+	0.110813i	$0.964655\pi$
$152$	−5.05140	+	10.1446i	−0.409723	+	0.822835i
$153$	2.59705	−	9.12768i	0.209959	−	0.737929i
$154$	11.3228	−	2.11660i	0.912420	−	0.170561i
$155$	−4.01277	−	14.1034i	−0.322314	−	1.13282i
$156$	0.264119	−	0.928283i	0.0211465	−	0.0743221i
$157$	8.90267	−	8.11586i	0.710510	−	0.647716i	−0.235492	−	0.971876i	$-0.575670\pi$
$157$	8.90267	−	8.11586i	0.710510	−	0.647716i	0.946002	+	0.324161i	$0.105082\pi$
$158$	−5.28394	−	4.81695i	−0.420368	−	0.383216i
$159$	2.17825	+	0.407186i	0.172747	+	0.0322920i
$160$	0.701714	−	7.57270i	0.0554753	−	0.598674i
$161$	−2.37698	−	25.6517i	−0.187332	−	2.02164i
$162$	−9.78985	−	1.83004i	−0.769163	−	0.143782i
$163$	−7.65707	+	15.3775i	−0.599748	+	1.20446i	0.362424	+	0.932013i	$0.381949\pi$
$163$	−7.65707	+	15.3775i	−0.599748	+	1.20446i	−0.962172	+	0.272443i	$0.912168\pi$
$164$	−0.529256	−	1.86014i	−0.0413279	−	0.145253i
$165$	−0.452000	+	1.58861i	−0.0351881	+	0.123673i
$166$	−1.29326	−	1.71255i	−0.100376	−	0.132920i
$167$	−10.4078	−	1.94555i	−0.805379	−	0.150551i	−0.235066	−	0.971979i	$-0.575531\pi$
$167$	−10.4078	−	1.94555i	−0.805379	−	0.150551i	−0.570312	+	0.821428i	$0.693178\pi$
$168$	0.232057	−	2.50429i	0.0179036	−	0.193210i
$169$	20.5910	−	18.7712i	1.58393	−	1.44394i
$170$	−5.22416	+	6.91791i	−0.400675	+	0.530579i
$171$	6.52341	+	8.63840i	0.498858	+	0.660595i
$172$	−0.161903	−	1.74721i	−0.0123450	−	0.133223i
$173$	−12.0975	−	16.0197i	−0.919759	−	1.21796i	−0.975608	−	0.219518i	$-0.929551\pi$
$173$	−12.0975	−	16.0197i	−0.919759	−	1.21796i	0.0558494	−	0.998439i	$-0.482213\pi$
$174$	2.63993	+	1.02272i	0.200133	+	0.0775319i
$175$	−0.569615	+	0.352691i	−0.0430588	+	0.0266609i
$176$	−1.93022	−	6.78403i	−0.145496	−	0.511365i
$177$	1.24168	−	1.64425i	0.0933305	−	0.123589i
$178$	−13.4790	−	8.34587i	−1.01030	−	0.625549i
$179$	−7.01296	+	9.28666i	−0.524173	+	0.694118i	−0.980684	−	0.195600i	$-0.937334\pi$
$179$	−7.01296	+	9.28666i	−0.524173	+	0.694118i	0.456510	+	0.889718i	$0.349099\pi$
$180$	−3.49900	−	2.16649i	−0.260800	−	0.161481i
$181$	0.581641	−	0.225329i	0.0432330	−	0.0167486i	−0.339528	−	0.940596i	$-0.610267\pi$
$181$	0.581641	−	0.225329i	0.0432330	−	0.0167486i	0.382761	+	0.923847i	$0.374973\pi$
$182$	15.0706	−	19.9566i	1.11710	−	1.47928i
$183$	−1.86662			−0.137985
$184$	−23.4527	+	4.38407i	−1.72896	+	0.323198i
$185$	−9.47066	−	3.66895i	−0.696297	−	0.269747i
$186$	−1.73599	+	0.672527i	−0.127289	+	0.0493121i
$187$	2.60141	−	9.14301i	0.190234	−	0.668603i
$188$	−2.27691	−	4.57266i	−0.166061	−	0.333496i
$189$	−4.12701	−	2.55534i	−0.300196	−	0.185874i
$190$	−2.70605	−	9.51077i	−0.196317	−	0.689984i
$191$	−1.71450	−	3.44319i	−0.124057	−	0.249140i	0.824425	−	0.565972i	$-0.191499\pi$
$191$	−1.71450	−	3.44319i	−0.124057	−	0.249140i	−0.948482	+	0.316831i	$0.897381\pi$
$192$	−2.14391			−0.154724
$193$	11.8256	−	23.7489i	0.851222	−	1.70949i	0.159656	−	0.987173i	$-0.448962\pi$
$193$	11.8256	−	23.7489i	0.851222	−	1.70949i	0.691567	−	0.722312i	$-0.256921\pi$
$194$	−9.53869	−	8.69567i	−0.684838	−	0.624313i
$195$	1.59832	+	3.20986i	0.114458	+	0.229863i
$196$	−1.10574	+	2.22062i	−0.0789811	+	0.158615i
$197$	9.67487	−	19.4298i	0.689306	−	1.38431i	−0.223006	−	0.974817i	$-0.571587\pi$
$197$	9.67487	−	19.4298i	0.689306	−	1.38431i	0.912312	−	0.409496i	$-0.134295\pi$
$198$	−10.0167	−	1.87244i	−0.711853	−	0.133068i
$199$	13.8820	+	18.3827i	0.984067	+	1.30312i	0.952798	+	0.303604i	$0.0981901\pi$
$199$	13.8820	+	18.3827i	0.984067	+	1.30312i	0.0312689	+	0.999511i	$0.490045\pi$
$200$	0.373925	+	0.495157i	0.0264405	+	0.0350129i
$201$	−0.389884	−	0.241406i	−0.0275003	−	0.0170275i
$202$	−0.498517	+	1.75211i	−0.0350756	+	0.123278i
$203$	−24.0083	−	21.8864i	−1.68505	−	1.53613i
$204$	−0.414418	−	0.256596i	−0.0290150	−	0.0179653i
$205$	6.10912	+	3.78261i	0.426680	+	0.264189i
$206$	2.92238	+	2.66410i	0.203612	+	0.185617i
$207$	−6.23672	+	21.9198i	−0.433482	+	1.52353i
$208$	−13.0192	−	8.06112i	−0.902716	−	0.558938i
$209$	6.53437	+	8.65290i	0.451992	+	0.598534i
$210$	1.32246	+	1.75122i	0.0912584	+	0.120846i
$211$	9.32806	+	1.74372i	0.642170	+	0.120042i	0.494755	−	0.869032i	$-0.335258\pi$
$211$	9.32806	+	1.74372i	0.642170	+	0.120042i	0.147415	+	0.989075i	$0.452905\pi$
$212$	−2.46529	+	4.95097i	−0.169317	+	0.340034i
$213$	0.906895	−	1.82129i	0.0621394	−	0.124793i
$214$	3.13458	+	6.29509i	0.214276	+	0.430324i
$215$	4.81782	+	4.39202i	0.328573	+	0.299534i
$216$	−2.00385	+	4.02428i	−0.136345	+	0.273817i
$217$	21.3632			1.45023
$218$	1.58550	+	3.18412i	0.107384	+	0.215656i
$219$	−0.382729	−	1.34515i	−0.0258624	−	0.0908970i
$220$	−3.50488	−	2.17013i	−0.236299	−	0.146310i
$221$	−9.19887	−	18.4738i	−0.618783	−	1.24268i
$222$	−0.352893	+	1.24029i	−0.0236846	+	0.0832429i
$223$	12.0048	−	4.65070i	0.803904	−	0.311434i	0.0759952	−	0.997108i	$-0.475787\pi$
$223$	12.0048	−	4.65070i	0.803904	−	0.311434i	0.727909	+	0.685674i	$0.240493\pi$
$224$	10.3319	+	4.00260i	0.690329	+	0.267435i
$225$	0.582588	−	0.108904i	0.0388392	−	0.00726030i
$226$	3.93362			0.261661
$227$	−2.60645	+	3.45150i	−0.172996	+	0.229084i	−0.876252	−	0.481853i	$-0.839964\pi$
$227$	−2.60645	+	3.45150i	−0.172996	+	0.229084i	0.703256	+	0.710937i	$0.251729\pi$
$228$	0.518443	−	0.200846i	0.0343347	−	0.0133013i
$229$	10.1218	+	6.26717i	0.668869	+	0.414146i	0.818430	−	0.574606i	$-0.194845\pi$
$229$	10.1218	+	6.26717i	0.668869	+	0.414146i	−0.149561	+	0.988753i	$0.547786\pi$
$230$	12.5456	−	16.6131i	0.827235	−	1.09544i
$231$	−2.04592	−	1.26678i	−0.134612	−	0.0833481i
$232$	−18.1319	+	24.0106i	−1.19042	+	1.57637i
$233$	−7.25792	−	25.5090i	−0.475482	−	1.67115i	−0.714108	−	0.700036i	$-0.753167\pi$
$233$	−7.25792	−	25.5090i	−0.475482	−	1.67115i	0.238625	−	0.971112i	$-0.423303\pi$
$234$	−18.8093	+	11.6462i	−1.22960	+	0.761339i
$235$	17.6971	+	6.85590i	1.15443	+	0.447229i
$236$	3.09907	+	4.10383i	0.201732	+	0.267136i
$237$	0.137818	+	1.48729i	0.00895225	+	0.0966102i
$238$	−7.61121	−	10.0789i	−0.493361	−	0.653316i
$239$	−4.18263	+	5.53869i	−0.270552	+	0.358268i	−0.912928	−	0.408121i	$-0.866184\pi$
$239$	−4.18263	+	5.53869i	−0.270552	+	0.358268i	0.642376	+	0.766390i	$0.277949\pi$
$240$	0.993016	−	0.905253i	0.0640989	−	0.0584339i
$241$	−0.172095	+	1.85720i	−0.0110856	+	0.119633i	−0.999479	−	0.0322855i	$-0.989721\pi$
$241$	−0.172095	+	1.85720i	−0.0110856	+	0.119633i	0.988393	+	0.151918i	$0.0485450\pi$
$242$	2.69679	+	0.504117i	0.173356	+	0.0324059i
$243$	3.89486	+	5.15762i	0.249855	+	0.330862i
$244$	1.27495	−	4.48098i	0.0816203	−	0.286865i
$245$	−2.52224	−	8.86477i	−0.161140	−	0.566349i
$246$	0.406642	−	0.816647i	0.0259265	−	0.0520675i
$247$	23.1395	+	4.32551i	1.47233	+	0.275226i
$248$	−1.82557	−	19.7010i	−0.115924	−	1.25102i
$249$	−0.0413648	+	0.446397i	−0.00262138	+	0.0282892i
$250$	12.6651	+	2.36752i	0.801012	+	0.149735i
$251$	3.42059	+	3.11828i	0.215906	+	0.196824i	0.774422	−	0.632670i	$-0.218041\pi$
$251$	3.42059	+	3.11828i	0.215906	+	0.196824i	−0.558516	+	0.829494i	$0.688629\pi$
$252$	4.43099	−	4.03938i	0.279126	−	0.254457i
$253$	−6.24720	+	21.9566i	−0.392758	+	1.38040i
$254$	1.75802	+	6.17880i	0.110308	+	0.387692i
$255$	1.78012	−	0.332762i	0.111476	−	0.0208384i
$256$	3.61310	−	12.6987i	0.225819	−	0.793672i
$257$	3.54868	−	7.12671i	0.221361	−	0.444552i	−0.756447	−	0.654054i	$-0.773067\pi$
$257$	3.54868	−	7.12671i	0.221361	−	0.444552i	0.977808	+	0.209502i	$0.0671844\pi$
$258$	0.498813	−	0.660536i	0.0310548	−	0.0411232i
$259$	8.91734	−	11.8085i	0.554097	−	0.733742i
$260$	−8.79724	+	1.64449i	−0.545581	+	0.101987i
$261$	12.8103	+	25.7265i	0.792937	+	1.59243i
$262$	−18.4289	−	3.44495i	−1.13854	−	0.212830i
$263$	1.96905	+	1.21918i	0.121417	+	0.0751780i	0.585797	−	0.810458i	$-0.300782\pi$
$263$	1.96905	+	1.21918i	0.121417	+	0.0751780i	−0.464380	+	0.885636i	$0.653723\pi$
$264$	−0.993387	+	1.99499i	−0.0611387	+	0.122783i
$265$	−5.62346	−	19.7644i	−0.345446	−	1.21412i
$266$	14.4064			0.883315
$267$	0.906339	+	3.18545i	0.0554671	+	0.194946i
$268$	0.845816	−	0.771063i	0.0516664	−	0.0471002i
$269$	15.3617	+	2.87160i	0.936621	+	0.175085i	0.629866	−	0.776704i	$-0.283110\pi$
$269$	15.3617	+	2.87160i	0.936621	+	0.175085i	0.306755	+	0.951789i	$0.400757\pi$
$270$	−1.07347	−	3.77284i	−0.0653291	−	0.229608i
$271$	−10.3087	−	20.7027i	−0.626211	−	1.25760i	−0.950230	−	0.311550i	$-0.899152\pi$
$271$	−10.3087	−	20.7027i	−0.626211	−	1.25760i	0.324019	−	0.946051i	$-0.394966\pi$
$272$	−5.71514	+	5.21004i	−0.346531	+	0.315905i
$273$	−5.13526	+	0.959947i	−0.310800	+	0.0580986i
$274$	4.05482	−	14.2512i	0.244960	−	0.860946i
$275$	0.583566	−	0.109087i	0.0351904	−	0.00657822i
$276$	0.995210	+	0.616208i	0.0599046	+	0.0370913i
$277$	0.813982	−	0.503996i	0.0489074	−	0.0302822i	−0.501761	−	0.865006i	$-0.667314\pi$
$277$	0.813982	−	0.503996i	0.0489074	−	0.0302822i	0.550668	+	0.834724i	$0.314373\pi$
$278$	7.40180	+	6.74763i	0.443930	+	0.404696i
$279$	−17.6226	−	6.82703i	−1.05504	−	0.408723i
$280$	−21.7469	+	8.42480i	−1.29963	+	0.503478i
$281$	−6.72330	+	6.12910i	−0.401078	+	0.365631i	−0.848956	−	0.528464i	$-0.822768\pi$
$281$	−6.72330	+	6.12910i	−0.401078	+	0.365631i	0.447878	+	0.894095i	$0.352180\pi$
$282$	0.659425	−	2.31764i	0.0392682	−	0.138013i
$283$	2.73012	−	0.510347i	0.162289	−	0.0303370i	−0.101978	−	0.994787i	$-0.532517\pi$
$283$	2.73012	−	0.510347i	0.162289	−	0.0303370i	0.264267	+	0.964450i	$0.414870\pi$
$284$	3.75273	+	3.42106i	0.222684	+	0.203003i
$285$	−0.920757	+	1.84913i	−0.0545409	+	0.109533i
$286$	−18.8409	+	11.6658i	−1.11409	+	0.689813i
$287$	−7.73634	+	7.05261i	−0.456662	+	0.416302i
$288$	−7.24373	−	6.60353i	−0.426841	−	0.389117i
$289$	6.46534	−	1.20858i	0.380314	−	0.0710931i
$290$	−2.42231	−	26.1409i	−0.142243	−	1.53505i
$291$	0.248793	+	2.68490i	0.0145845	+	0.157392i
$292$	3.49057			0.204270
$293$	−15.5395	+	6.02004i	−0.907828	+	0.351694i	−0.769466	−	0.638687i	$-0.779478\pi$
$293$	−15.5395	+	6.02004i	−0.907828	+	0.351694i	−0.138362	+	0.990382i	$0.544184\pi$
$294$	−1.09116	+	0.422719i	−0.0636380	+	0.0246535i
$295$	−18.7810	−	3.51077i	−1.09347	−	0.204405i
$296$	−11.6517	−	7.21445i	−0.677243	−	0.419331i
$297$	2.59213	+	3.43254i	0.150411	+	0.199176i
$298$	−4.94346	+	4.50656i	−0.286367	+	0.261058i
$299$	22.0908	+	44.3643i	1.27754	+	2.56565i
$300$	0.00280877	−	0.0303115i	0.000162165	−	0.00175003i
$301$	−8.07547	+	5.00012i	−0.465462	+	0.288202i
$302$	1.83508	−	19.8037i	0.105597	−	1.13957i
$303$	0.323549	−	0.200333i	0.0185874	−	0.0115088i
$304$	−0.813930	−	8.78370i	−0.0466821	−	0.503780i
$305$	7.71537	+	15.4945i	0.441781	+	0.887215i
$306$	3.05762	+	10.7464i	0.174793	+	0.614332i
$307$	−13.5143	−	27.1403i	−0.771301	−	1.54898i	−0.834518	−	0.550981i	$-0.814254\pi$
$307$	−13.5143	−	27.1403i	−0.771301	−	1.54898i	0.0632165	−	0.998000i	$-0.479864\pi$
$308$	4.43843	−	4.04616i	0.252903	−	0.230552i
$309$	−0.0762229	−	0.822577i	−0.00433617	−	0.0467947i
$310$	12.7580	+	11.6304i	0.724604	+	0.660564i
$311$	6.71274	−	4.15635i	0.380645	−	0.235685i	−0.322751	−	0.946484i	$-0.604608\pi$
$311$	6.71274	−	4.15635i	0.380645	−	0.235685i	0.703395	+	0.710799i	$0.251666\pi$
$312$	1.32409	+	4.65368i	0.0749616	+	0.263463i
$313$	0.171323	+	0.106079i	0.00968375	+	0.00599592i	0.531266	−	0.847205i	$-0.321717\pi$
$313$	0.171323	+	0.106079i	0.00968375	+	0.00599592i	−0.521582	+	0.853201i	$0.674658\pi$
$314$	−3.88142	+	13.6418i	−0.219041	+	0.769849i
$315$	−2.05543	+	22.1817i	−0.115811	+	1.24980i
$316$	−3.66451	−	0.685016i	−0.206145	−	0.0385351i
$317$	−16.5333	−	6.40503i	−0.928602	−	0.359742i	−0.151025	−	0.988530i	$-0.548257\pi$
$317$	−16.5333	−	6.40503i	−0.928602	−	0.359742i	−0.777577	+	0.628788i	$0.783552\pi$
$318$	−2.43280	+	0.942472i	−0.136425	+	0.0528512i
$319$	12.8318	+	25.7697i	0.718443	+	1.44283i
$320$	8.86151	+	17.7963i	0.495374	+	0.994844i
$321$	0.402033	−	1.41300i	0.0224393	−	0.0788659i
$322$	18.2781	+	24.2041i	1.01860	+	1.34884i
$323$	5.29926	−	10.6424i	0.294859	−	0.592157i
$324$	−4.84213	+	1.87585i	−0.269007	+	0.104214i
$325$	0.776720	−	1.02854i	0.0430847	−	0.0570533i
$326$	−1.86612	−	20.1386i	−0.103355	−	1.11537i
$327$	0.203352	−	0.714709i	0.0112454	−	0.0395235i
$328$	7.16498	+	6.53175i	0.395620	+	0.360655i
$329$	−16.6632	+	22.0656i	−0.918670	+	1.21652i
$330$	−0.532159	−	1.87035i	−0.0292944	−	0.102959i
$331$	−18.6424	+	16.9948i	−1.02468	+	0.934119i	−0.997851	−	0.0655210i	$-0.979129\pi$
$331$	−18.6424	+	16.9948i	−1.02468	+	0.934119i	−0.0268286	+	0.999640i	$0.508541\pi$
$332$	−1.04336	−	0.404200i	−0.0572618	−	0.0221833i
$333$	−11.1296	+	6.89115i	−0.609898	+	0.377633i
$334$	11.6240	−	4.50317i	0.636038	−	0.246402i
$335$	−0.392355	+	4.23418i	−0.0214366	+	0.231338i
$336$	0.872617	+	1.75245i	0.0476051	+	0.0956040i
$337$	−0.940663	+	3.30609i	−0.0512412	+	0.180094i	−0.983222	−	0.182414i	$-0.941609\pi$
$337$	−0.940663	+	3.30609i	−0.0512412	+	0.180094i	0.931981	+	0.362508i	$0.118079\pi$
$338$	−8.97734	+	31.5521i	−0.488303	+	1.71621i
$339$	−0.607278	−	0.553607i	−0.0329828	−	0.0300678i
$340$	−0.417044	+	4.50062i	−0.0226174	+	0.244080i
$341$	−17.6522	−	6.83849i	−0.955919	−	0.370325i
$342$	−11.8839	−	4.60386i	−0.642610	−	0.248948i
$343$	−9.83183			−0.530869
$344$	5.30117	+	7.01988i	0.285820	+	0.378486i
$345$	−4.27490	+	0.799118i	−0.230153	+	0.0430230i
$346$	22.0385	+	8.53777i	1.18480	+	0.458993i
$347$	−12.0548	+	7.46400i	−0.647134	+	0.400688i	−0.810386	−	0.585896i	$-0.800743\pi$
$347$	−12.0548	+	7.46400i	−0.647134	+	0.400688i	0.163252	+	0.986584i	$0.447801\pi$
$348$	1.45099	−	0.271237i	0.0777813	−	0.0145399i
$349$	25.4121	+	9.84471i	1.36028	+	0.526975i	0.927263	−	0.374410i	$-0.122155\pi$
$349$	25.4121	+	9.84471i	1.36028	+	0.526975i	0.433017	+	0.901386i	$0.357449\pi$
$350$	0.351589	−	0.706085i	0.0187932	−	0.0377418i
$351$	9.17924	+	1.71590i	0.489951	+	0.0915878i
$352$	−7.25589	−	6.61462i	−0.386740	−	0.352560i
$353$	−2.42088	−	26.1255i	−0.128851	−	1.39052i	−0.777237	−	0.629208i	$-0.783379\pi$
$353$	−2.42088	−	26.1255i	−0.128851	−	1.39052i	0.648386	−	0.761312i	$-0.275444\pi$
$354$	−0.223827	+	2.41548i	−0.0118963	+	0.128381i
$355$	−18.8668			−1.00134
$356$	−8.26600			−0.438097
$357$	−0.243443	+	2.62717i	−0.0128844	+	0.139045i
$358$	1.26416	−	13.6425i	0.0668132	−	0.721029i
$359$	9.56210	−	19.2033i	0.504668	−	1.01351i	−0.485580	−	0.874192i	$-0.661391\pi$
$359$	9.56210	−	19.2033i	0.504668	−	1.01351i	0.990248	−	0.139318i	$-0.0444909\pi$
$360$	20.6315			1.08737
$361$	−2.42436	−	4.86877i	−0.127598	−	0.256251i
$362$	−0.442564	+	0.586050i	−0.0232607	+	0.0308021i
$363$	−0.345386	−	0.457365i	−0.0181281	−	0.0240055i
$364$	1.20308	−	12.9833i	0.0630585	−	0.680510i
$365$	−9.58397	+	8.73694i	−0.501648	+	0.457312i
$366$	1.86848	−	1.15692i	0.0976672	−	0.0604730i
$367$	8.49590	−	3.29133i	0.443482	−	0.171806i	−0.129138	−	0.991627i	$-0.541221\pi$
$367$	8.49590	−	3.29133i	0.443482	−	0.171806i	0.572620	+	0.819821i	$0.305927\pi$
$368$	13.7247	−	12.5117i	0.715450	−	0.652219i
$369$	8.63555	−	3.34543i	0.449549	−	0.174156i
$370$	11.7541	−	2.19722i	0.611066	−	0.114228i
$371$	29.9381			1.55431
$372$	−0.584968	+	0.774623i	−0.0303292	+	0.0401623i
$373$	−17.9793	+	16.3903i	−0.930932	+	0.848657i	−0.988736	−	0.149671i	$-0.952178\pi$
$373$	−17.9793	+	16.3903i	−0.930932	+	0.848657i	0.0578039	+	0.998328i	$0.481590\pi$
$374$	3.06276	+	10.7645i	0.158371	+	0.556617i
$375$	−1.62206	−	2.14795i	−0.0837628	−	0.110920i
$376$	21.7727	+	13.4811i	1.12284	+	0.695234i
$377$	58.2781	+	22.5771i	3.00148	+	1.16278i
$378$	5.71491			0.293943
$379$	−9.51131	−	12.5950i	−0.488563	−	0.646962i	0.485233	−	0.874385i	$-0.338735\pi$
$379$	−9.51131	−	12.5950i	−0.488563	−	0.646962i	−0.973796	+	0.227423i	$0.926970\pi$
$380$	−3.81009	−	3.47336i	−0.195453	−	0.178179i
$381$	0.598182	−	1.20131i	0.0306458	−	0.0615451i
$382$	3.85028	+	2.38399i	0.196997	+	0.121976i
$383$	−4.64114	+	6.14586i	−0.237151	+	0.314039i	−0.900993	−	0.433835i	$-0.857160\pi$
$383$	−4.64114	+	6.14586i	−0.237151	+	0.314039i	0.663842	+	0.747873i	$0.268925\pi$
$384$	0.751464	−	0.465287i	0.0383480	−	0.0237441i
$385$	−2.05889	+	22.2189i	−0.104931	+	1.13238i
$386$	2.88203	+	31.1020i	0.146691	+	1.58305i
$387$	8.25938	−	1.54395i	0.419848	−	0.0784832i
$388$	−6.61526	−	1.23661i	−0.335839	−	0.0627792i
$389$	16.3861	+	3.06310i	0.830810	+	0.155305i	0.581940	−	0.813231i	$-0.302294\pi$
$389$	16.3861	+	3.06310i	0.830810	+	0.155305i	0.248870	+	0.968537i	$0.419941\pi$
$390$	−3.58936	−	2.22244i	−0.181754	−	0.112538i
$391$	24.6035	−	4.59919i	1.24425	−	0.232591i
$392$	−1.14747	−	12.3831i	−0.0579558	−	0.625443i
$393$	2.36024	+	3.12547i	0.119058	+	0.157659i
$394$	2.35788	+	25.4456i	0.118788	+	1.28193i
$395$	11.7762	−	7.29149i	0.592523	−	0.366875i
$396$	−4.95432	+	1.91931i	−0.248964	+	0.0964491i
$397$	18.4091	−	24.3776i	0.923926	−	1.22348i	−0.0504896	−	0.998725i	$-0.516078\pi$
$397$	18.4091	−	24.3776i	0.923926	−	1.22348i	0.974416	−	0.224752i	$-0.0721571\pi$
$398$	−25.2893	−	9.79712i	−1.26764	−	0.491085i
$399$	−2.22409	−	2.02752i	−0.111344	−	0.101503i
$400$	−0.450369	−	0.174474i	−0.0225185	−	0.00872370i
$401$	2.25579	+	24.3438i	0.112649	+	1.21567i	0.845008	+	0.534754i	$0.179596\pi$
$401$	2.25579	+	24.3438i	0.112649	+	1.21567i	−0.732359	+	0.680918i	$0.761581\pi$
$402$	0.539895			0.0269275
$403$	−38.3231	+	14.8464i	−1.90901	+	0.739554i
$404$	0.259924	+	0.913539i	0.0129317	+	0.0454502i
$405$	8.59964	−	17.2704i	0.427320	−	0.858174i
$406$	37.5972	+	7.02814i	1.86592	+	0.348801i
$407$	−11.1483	+	6.90272i	−0.552600	+	0.342155i
$408$	2.44357			0.120975
$409$	−2.47297	−	20.0720i	−0.122280	−	0.992496i
$409$	−2.47297	−	20.0720i	−0.122280	−	0.992496i
$410$	−8.45965			−0.417793
$411$	−2.63166	+	1.62946i	−0.129810	+	0.0803752i
$412$	2.02673	+	0.378861i	0.0998497	+	0.0186651i
$413$	12.4078	−	24.9181i	0.610546	−	1.22614i
$414$	−7.34277	−	25.8072i	−0.360878	−	1.26835i
$415$	3.87645	−	1.50174i	0.190287	−	0.0737177i
$416$	−21.3159			−1.04510
$417$	−0.193057	−	2.08342i	−0.00945405	−	0.102025i
$418$	−11.9039	−	4.61159i	−0.582238	−	0.225560i
$419$	−16.0489	−	14.6305i	−0.784038	−	0.714745i	0.179077	−	0.983835i	$-0.442689\pi$
$419$	−16.0489	−	14.6305i	−0.784038	−	0.714745i	−0.963115	+	0.269090i	$0.913277\pi$
$420$	1.06692	+	0.413326i	0.0520602	+	0.0201682i
$421$	16.5019	−	21.8520i	0.804251	−	1.06500i	−0.192244	−	0.981347i	$-0.561576\pi$
$421$	16.5019	−	21.8520i	0.804251	−	1.06500i	0.996495	−	0.0836535i	$-0.0266589\pi$
$422$	−10.4181	+	4.03600i	−0.507146	+	0.196469i
$423$	20.7970	−	12.8770i	1.01119	−	0.626100i
$424$	−2.55833	−	27.6088i	−0.124243	−	1.34080i
$425$	−0.392273	−	0.519453i	−0.0190280	−	0.0251972i
$426$	0.221021	+	2.38519i	0.0107085	+	0.115563i
$427$	−24.7888	+	4.63383i	−1.19961	+	0.224247i
$428$	3.11742	+	1.93023i	0.150686	+	0.0933011i
$429$	4.55050	+	0.850636i	0.219700	+	0.0410691i
$430$	−7.54477	−	1.41036i	−0.363841	−	0.0680137i
$431$	−38.3713	+	7.17284i	−1.84828	+	0.345504i	−0.986756	−	0.162210i	$-0.948138\pi$
$431$	−38.3713	+	7.17284i	−1.84828	+	0.345504i	−0.861526	+	0.507714i	$0.830491\pi$
$432$	−0.322879	−	3.48442i	−0.0155345	−	0.167644i
$433$	3.23419	−	34.9025i	0.155425	−	1.67731i	−0.459081	−	0.888394i	$-0.651821\pi$
$433$	3.23419	−	34.9025i	0.155425	−	1.67731i	0.614507	−	0.788912i	$-0.289355\pi$
$434$	−21.3845	+	13.2407i	−1.02649	+	0.635575i
$435$	−3.30504	+	4.37659i	−0.158465	+	0.209841i
$436$	1.57683	+	0.976329i	0.0755163	+	0.0467577i
$437$	−12.7260	+	25.5573i	−0.608767	+	1.22257i
$438$	1.21683	+	1.10928i	0.0581422	+	0.0530036i
$439$	5.19981	+	6.88565i	0.248173	+	0.328634i	0.905004	−	0.425404i	$-0.139868\pi$
$439$	5.19981	+	6.88565i	0.248173	+	0.328634i	−0.656830	+	0.754038i	$0.728103\pi$
$440$	20.6661			0.985218
$441$	−11.0767	−	4.29115i	−0.527464	−	0.204341i
$442$	20.6580	+	12.7909i	0.982600	+	0.608400i
$443$	−7.51196	−	9.94744i	−0.356904	−	0.472617i	0.583775	−	0.811916i	$-0.301575\pi$
$443$	−7.51196	−	9.94744i	−0.356904	−	0.472617i	−0.940679	+	0.339298i	$0.889810\pi$
$444$	0.183997	+	0.646681i	0.00873209	+	0.0306901i
$445$	22.6958	−	20.6899i	1.07588	−	0.980796i
$446$	−9.13436	+	12.0958i	−0.432524	+	0.572755i
$447$	1.39742			0.0660957
$448$	−28.4712	+	5.32220i	−1.34514	+	0.251450i
$449$	−22.0666	+	8.54865i	−1.04139	+	0.403436i	−0.820369	−	0.571834i	$-0.806232\pi$
$449$	−22.0666	+	8.54865i	−1.04139	+	0.403436i	−0.221018	+	0.975270i	$0.570938\pi$
$450$	−0.515671	+	0.470096i	−0.0243090	+	0.0221605i
$451$	8.65006	−	3.35105i	0.407315	−	0.157795i
$452$	1.74377	−	1.07970i	0.0820199	−	0.0507846i
$453$	−3.07042	+	2.79906i	−0.144261	+	0.131511i
$454$	0.469842	−	5.07040i	0.0220508	−	0.237966i
$455$	29.1941	+	38.6593i	1.36864	+	1.81237i
$456$	−1.67971	+	2.22430i	−0.0786598	+	0.104162i
$457$	−9.66863	−	19.4172i	−0.452280	−	0.908300i	−0.997544	−	0.0700361i	$-0.977689\pi$
$457$	−9.66863	−	19.4172i	−0.452280	−	0.908300i	0.545265	−	0.838264i	$-0.316429\pi$
$458$	−14.0163			−0.654938
$459$	2.10218	−	4.22174i	0.0981212	−	0.197054i
$460$	1.00152	−	10.8081i	0.0466959	−	0.503929i
$461$	−3.70321	+	39.9640i	−0.172476	+	1.86131i	0.267838	+	0.963464i	$0.413691\pi$
$461$	−3.70321	+	39.9640i	−0.172476	+	1.86131i	−0.440314	+	0.897844i	$0.645133\pi$
$462$	2.83310			0.131808
$463$	32.8166			1.52512			0.762558	−	0.646920i	$-0.223943\pi$
$463$	32.8166			1.52512			0.762558	+	0.646920i	$0.223943\pi$
$464$	2.16095	−	23.3204i	0.100320	−	1.08262i
$465$	−0.332760	−	3.59105i	−0.0154314	−	0.166531i
$466$	23.0754	+	21.0360i	1.06895	+	0.974475i
$467$	24.0781	+	4.50098i	1.11420	+	0.208280i	0.708490	−	0.705721i	$-0.249377\pi$
$467$	24.0781	+	4.50098i	1.11420	+	0.208280i	0.405712	+	0.914001i	$0.367024\pi$
$468$	−5.14150	+	10.3255i	−0.237666	+	0.477297i
$469$	−5.77695	−	2.23800i	−0.266755	−	0.103341i
$470$	−21.9640	+	4.10578i	−1.01312	+	0.189386i
$471$	2.51912	−	1.55978i	0.116075	−	0.0718707i
$472$	−24.0397	−	9.31302i	−1.10652	−	0.428666i
$473$	8.27326	−	1.54654i	0.380405	−	0.0711100i
$474$	−1.05977	−	1.40336i	−0.0486768	−	0.0644585i
$475$	0.742491			0.0340678
$476$	−6.14047	−	2.37883i	−0.281448	−	0.109034i
$477$	−24.6961	−	9.56732i	−1.13076	−	0.438058i
$478$	0.753965	−	8.13658i	0.0344856	−	0.372159i
$479$	9.15530	+	8.34615i	0.418316	+	0.381346i	0.855308	−	0.518120i	$-0.173368\pi$
$479$	9.15530	+	8.34615i	0.418316	+	0.381346i	−0.436992	+	0.899465i	$0.643956\pi$
$480$	0.511885	−	1.79909i	0.0233642	−	0.0821168i
$481$	−7.79033	+	27.3802i	−0.355209	+	1.24843i
$482$	−0.978809	−	1.96571i	−0.0445835	−	0.0895358i
$483$	0.584621	−	6.30906i	0.0266012	−	0.287072i
$484$	1.33385	−	0.516737i	0.0606296	−	0.0234880i
$485$	21.2586	−	13.1628i	0.965304	−	0.597691i
$486$	−7.09540	−	2.74877i	−0.321854	−	0.124687i
$487$	3.56167	−	3.24689i	0.161395	−	0.147131i	−0.588970	−	0.808155i	$-0.700466\pi$
$487$	3.56167	−	3.24689i	0.161395	−	0.147131i	0.750364	+	0.661024i	$0.229878\pi$
$488$	6.39159	+	22.4641i	0.289334	+	1.01690i
$489$	−2.54616	+	3.37166i	−0.115141	+	0.152472i
$490$	8.01907	+	7.31035i	0.362265	+	0.330248i
$491$	9.81506	−	34.4964i	0.442948	−	1.55680i	−0.343506	−	0.939150i	$-0.611615\pi$
$491$	9.81506	−	34.4964i	0.442948	−	1.55680i	0.786454	−	0.617649i	$-0.211915\pi$
$492$	−0.0438886	−	0.473633i	−0.00197865	−	0.0213530i
$493$	19.0216	−	25.1887i	0.856692	−	1.13444i
$494$	−25.8435	+	10.0118i	−1.16275	+	0.450453i
$495$	8.79888	−	17.6705i	0.395480	−	0.794232i
$496$	9.28113	+	12.2902i	0.416735	+	0.551847i
$497$	7.52230	−	26.4381i	0.337421	−	1.18591i
$498$	−0.235267	−	0.472480i	−0.0105426	−	0.0211723i
$499$	14.0441	+	28.2044i	0.628702	+	1.26260i	0.948997	+	0.315285i	$0.102100\pi$
$499$	14.0441	+	28.2044i	0.628702	+	1.26260i	−0.320295	+	0.947318i	$0.603782\pi$
$500$	6.26425	−	2.42679i	0.280146	−	0.108529i
$501$	−2.42830	−	0.940727i	−0.108488	−	0.0420286i
$502$	−5.35669	−	1.00134i	−0.239081	−	0.0446920i
$503$	−0.137417	+	1.48297i	−0.00612714	+	0.0661224i	−0.998249	−	0.0591563i	$-0.981159\pi$
$503$	−0.137417	+	1.48297i	−0.00612714	+	0.0661224i	0.992122	+	0.125279i	$0.0399825\pi$
$504$	−8.22589	+	28.9110i	−0.366410	+	1.28780i
$505$	−3.00027	−	1.85769i	−0.133510	−	0.0826660i
$506$	−7.35510	−	25.8505i	−0.326974	−	1.14920i
$507$	5.82649	−	3.60761i	0.258764	−	0.160220i
$508$	2.47528	+	2.25651i	0.109823	+	0.100117i
$509$	0.127693	+	1.37803i	0.00565989	+	0.0610800i	0.998096	−	0.0616850i	$-0.0196474\pi$
$509$	0.127693	+	1.37803i	0.00565989	+	0.0610800i	−0.992436	+	0.122765i	$0.960824\pi$
$510$	−1.57566	+	1.43640i	−0.0697712	+	0.0636048i
$511$	−8.42195	−	16.9136i	−0.372565	−	0.748212i
$512$	6.22074	+	21.8636i	0.274920	+	0.966245i
$513$	2.39787	+	4.81557i	0.105869	+	0.212613i
$514$	0.864855	+	9.33327i	0.0381471	+	0.411673i
$515$	−6.51303	+	4.03270i	−0.286998	+	0.177702i
$516$	0.0398202	−	0.429728i	0.00175299	−	0.0189177i
$517$	20.8320	−	12.8986i	0.916189	−	0.567280i
$518$	−1.60745	+	17.3471i	−0.0706273	+	0.762190i
$519$	−2.20076	−	4.41972i	−0.0966025	−	0.194004i
$520$	33.1566	−	30.2263i	1.45401	−	1.32551i
$521$	−6.91128	−	9.15201i	−0.302789	−	0.400957i	0.621030	−	0.783786i	$-0.286714\pi$
$521$	−6.91128	−	9.15201i	−0.302789	−	0.400957i	−0.923819	+	0.382830i	$0.874950\pi$
$522$	−28.7682	−	17.8125i	−1.25915	−	0.779632i
$523$	−19.5178	−	3.64852i	−0.853456	−	0.159539i	−0.261196	−	0.965286i	$-0.584117\pi$
$523$	−19.5178	−	3.64852i	−0.853456	−	0.159539i	−0.592260	+	0.805747i	$0.701764\pi$
$524$	−9.11505	+	3.53119i	−0.398193	+	0.154261i
$525$	−0.153651	+	0.0595249i	−0.00670590	+	0.00259788i
$526$	−2.72665			−0.118888
$527$	1.91514	+	20.6677i	0.0834250	+	0.900299i
$528$	−0.160064	−	1.72736i	−0.00696588	−	0.0751738i
$529$	−36.4761	+	6.81856i	−1.58592	+	0.296459i
$530$	17.8789	+	16.2988i	0.776609	+	0.707973i
$531$	−18.1983	+	16.5900i	−0.789740	+	0.719943i
$532$	6.38635	−	3.95426i	0.276883	−	0.171439i
$533$	8.97687	−	18.0280i	0.388831	−	0.780879i
$534$	−2.88156	−	2.62689i	−0.124697	−	0.113677i
$535$	−13.3908	+	2.50318i	−0.578936	+	0.108222i
$536$	−1.57021	+	5.51872i	−0.0678229	+	0.238373i
$537$	−2.11517	+	1.92824i	−0.0912765	+	0.0832095i
$538$	−17.1569	+	6.64660i	−0.739684	+	0.286555i
$539$	−11.0953	−	4.29836i	−0.477910	−	0.185143i
$540$	−1.51143	−	1.37785i	−0.0650417	−	0.0592933i
$541$	−11.8595	+	7.34311i	−0.509881	+	0.315705i	−0.757149	−	0.653242i	$-0.773408\pi$
$541$	−11.8595	+	7.34311i	−0.509881	+	0.315705i	0.247268	+	0.968947i	$0.420467\pi$
$542$	23.1504	+	14.3341i	0.994395	+	0.615703i
$543$	0.150803	−	0.0281899i	0.00647157	−	0.00120975i
$544$	−2.94607	+	10.3544i	−0.126312	+	0.443940i
$545$	−6.77322	+	1.26613i	−0.290133	+	0.0542352i
$546$	4.54542	−	4.14370i	0.194526	−	0.177334i
$547$	−5.63462	−	11.3158i	−0.240919	−	0.483831i	0.741396	−	0.671068i	$-0.234164\pi$
$547$	−5.63462	−	11.3158i	−0.240919	−	0.483831i	−0.982315	+	0.187238i	$0.940047\pi$
$548$	−2.11416	−	7.43049i	−0.0903123	−	0.317415i
$549$	21.9292	+	4.09928i	0.935916	+	0.174953i
$550$	−0.516537	+	0.470886i	−0.0220252	+	0.0200786i
$551$	9.85296	+	34.6296i	0.419750	+	1.47527i
$552$	−5.86814			−0.249765
$553$	5.52239	+	19.4092i	0.234836	+	0.825363i
$554$	−0.502422	+	1.00900i	−0.0213458	+	0.0428682i
$555$	−2.12385	−	1.31503i	−0.0901523	−	0.0558199i
$556$	5.13329	+	0.959577i	0.217700	+	0.0406951i
$557$	3.33137	+	6.69030i	0.141155	+	0.283477i	0.954448	−	0.298377i	$-0.0964452\pi$
$557$	3.33137	+	6.69030i	0.141155	+	0.283477i	−0.813293	+	0.581854i	$0.802328\pi$
$558$	21.8715	−	4.08849i	0.925895	−	0.173080i
$559$	11.0116	−	14.5817i	0.465741	−	0.616741i
$560$	10.9400	−	14.4869i	0.462300	−	0.612184i
$561$	1.04213	−	2.09288i	0.0439988	−	0.0883614i
$562$	2.93125	−	10.3023i	0.123647	−	0.434575i
$563$	−33.4071	+	6.24486i	−1.40794	+	0.263190i	−0.832215	−	0.554454i	$-0.812927\pi$
$563$	−33.4071	+	6.24486i	−1.40794	+	0.263190i	−0.575725	+	0.817643i	$0.695280\pi$
$564$	−0.343821	−	1.20840i	−0.0144775	−	0.0508830i
$565$	−2.08533	+	7.32917i	−0.0877305	+	0.308341i
$566$	−2.41653	+	2.20296i	−0.101574	+	0.0925974i
$567$	20.7724	+	18.9366i	0.872360	+	0.795261i
$568$	−25.0239	−	4.67778i	−1.04998	−	0.196275i
$569$	3.15885	−	34.0894i	0.132426	−	1.42910i	−0.627259	−	0.778811i	$-0.715823\pi$
$569$	3.15885	−	34.0894i	0.132426	−	1.42910i	0.759685	−	0.650292i	$-0.225353\pi$
$570$	−0.224399	−	2.42165i	−0.00939904	−	0.101432i
$571$	−33.4236	−	6.24795i	−1.39873	−	0.261468i	−0.570245	−	0.821475i	$-0.693152\pi$
$571$	−33.4236	−	6.24795i	−1.39873	−	0.261468i	−0.828488	+	0.560006i	$0.810799\pi$
$572$	−5.15013	+	10.3429i	−0.215338	+	0.432457i
$573$	−0.258895	−	0.909922i	−0.0108155	−	0.0380125i
$574$	3.37292	−	11.8546i	0.140783	−	0.494800i
$575$	0.942030	+	1.24745i	0.0392854	+	0.0520222i
$576$	25.1869	+	4.70825i	1.04945	+	0.196177i
$577$	−2.40215	+	25.9233i	−0.100003	+	1.07920i	0.786849	+	0.617146i	$0.211711\pi$
$577$	−2.40215	+	25.9233i	−0.100003	+	1.07920i	−0.886851	+	0.462055i	$0.847112\pi$
$578$	−5.72273	+	5.21696i	−0.238034	+	0.216997i
$579$	3.93228	−	5.20719i	0.163420	−	0.216403i
$580$	−8.24893	−	10.9234i	−0.342518	−	0.453568i
$581$	0.558840	+	6.03085i	0.0231846	+	0.250202i
$582$	−1.91312	−	2.53338i	−0.0793014	−	0.105012i
$583$	−24.7376	−	9.58339i	−1.02453	−	0.396903i
$584$	−14.8779	+	9.21201i	−0.615652	+	0.381196i
$585$	−11.7280	−	41.2198i	−0.484895	−	1.70423i
$586$	11.8239	−	15.6573i	0.488439	−	0.646797i
$587$	−34.5291	−	21.3795i	−1.42517	−	0.882426i	−0.425422	−	0.904995i	$-0.639874\pi$
$587$	−34.5291	−	21.3795i	−1.42517	−	0.882426i	−0.999745	+	0.0225688i	$0.992816\pi$
$588$	−0.367684	+	0.486892i	−0.0151630	+	0.0200791i
$589$	−20.1296	−	12.4637i	−0.829426	−	0.513559i
$590$	20.9757	−	8.12602i	0.863554	−	0.334543i
$591$	3.21713	−	4.26016i	0.132335	−	0.175240i
$592$	10.6675			0.438431
$593$	24.1957	−	4.52296i	0.993597	−	0.185736i	0.338244	−	0.941058i	$-0.390167\pi$
$593$	24.1957	−	4.52296i	0.993597	−	0.185736i	0.655353	+	0.755323i	$0.272520\pi$
$594$	−4.72218	−	1.82938i	−0.193753	−	0.0750604i
$595$	22.8140	−	8.83819i	0.935283	−	0.362330i
$596$	−0.954473	+	3.35462i	−0.0390967	+	0.137411i
$597$	2.52538	+	5.07164i	0.103357	+	0.207568i
$598$	−49.6095	−	30.7169i	−2.02868	−	1.25611i
$599$	−9.42126	−	33.1123i	−0.384942	−	1.35293i	−0.876213	−	0.481925i	$-0.839938\pi$
$599$	−9.42126	−	33.1123i	−0.384942	−	1.35293i	0.491270	−	0.871007i	$-0.336533\pi$
$600$	0.0680237	+	0.136610i	0.00277705	+	0.00557708i
$601$	47.4710			1.93638			0.968192	−	0.250208i	$-0.0804989\pi$
$601$	47.4710			1.93638			0.968192	+	0.250208i	$0.0804989\pi$
$602$	4.98450	−	10.0102i	0.203153	−	0.407986i
$603$	4.05024	+	3.69228i	0.164939	+	0.150361i
$604$	−4.62220	−	9.28262i	−0.188075	−	0.377705i
$605$	−2.36893	+	4.75744i	−0.0963105	+	0.193418i
$606$	−0.199707	+	0.401066i	−0.00811254	+	0.0162922i
$607$	9.08493	+	1.69827i	0.368746	+	0.0689305i	0.364861	−	0.931062i	$-0.381116\pi$
$607$	9.08493	+	1.69827i	0.368746	+	0.0689305i	0.00388461	+	0.999992i	$0.498763\pi$
$608$	−7.40011	−	9.79933i	−0.300114	−	0.397415i
$609$	−4.81520	−	6.37635i	−0.195122	−	0.258383i
$610$	−17.3265	−	10.7281i	−0.701528	−	0.434368i
$611$	14.5572	−	51.1633i	0.588922	−	2.06985i
$612$	4.30510	+	3.92462i	0.174023	+	0.158643i
$613$	28.3400	+	17.5474i	1.14464	+	0.708733i	0.961622	−	0.274377i	$-0.0884715\pi$
$613$	28.3400	+	17.5474i	1.14464	+	0.708733i	0.183020	+	0.983109i	$0.441413\pi$
$614$	30.3491	+	18.7914i	1.22479	+	0.758359i
$615$	1.30601	+	1.19059i	0.0526636	+	0.0480092i
$616$	−8.23971	+	28.9596i	−0.331987	+	1.16681i
$617$	−8.26128	−	5.11517i	−0.332587	−	0.205929i	0.349971	−	0.936760i	$-0.386191\pi$
$617$	−8.26128	−	5.11517i	−0.332587	−	0.205929i	−0.682558	+	0.730831i	$0.739133\pi$
$618$	0.586125	+	0.776155i	0.0235774	+	0.0312215i
$619$	−5.81379	−	7.69871i	−0.233676	−	0.309437i	0.666037	−	0.745919i	$-0.267989\pi$
$619$	−5.81379	−	7.69871i	−0.233676	−	0.309437i	−0.899713	+	0.436481i	$0.856224\pi$
$620$	8.84790	+	1.65396i	0.355340	+	0.0664246i
$621$	−5.04830	+	10.1384i	−0.202581	+	0.406838i
$622$	−4.14337	+	8.32100i	−0.166134	+	0.333642i
$623$	19.9440	+	40.0529i	0.799039	+	1.60469i
$624$	−2.78325	−	2.53727i	−0.111419	−	0.101572i
$625$	−11.5747	+	23.2451i	−0.462988	+	0.929805i
$626$	−0.237241			−0.00948205
$627$	1.18872	+	2.38727i	0.0474728	+	0.0953383i
$628$	2.02375	+	7.11274i	0.0807563	+	0.283829i
$629$	12.2235	+	7.56844i	0.487381	+	0.301774i
$630$	−11.6905	−	23.4777i	−0.465762	−	0.935376i
$631$	7.00469	−	24.6189i	0.278852	−	0.980064i	−0.688207	−	0.725514i	$-0.741602\pi$
$631$	7.00469	−	24.6189i	0.278852	−	0.980064i	0.967060	−	0.254550i	$-0.0819274\pi$
$632$	17.4271	−	6.75131i	0.693215	−	0.268553i
$633$	2.17638	+	0.843134i	0.0865033	+	0.0335116i
$634$	20.5196	−	3.83577i	0.814937	−	0.152338i
$635$	−12.4444			−0.493841
$636$	−0.819768	+	1.08555i	−0.0325059	+	0.0430448i
$637$	−24.0881	+	9.33178i	−0.954406	+	0.369739i
$638$	−28.8165	−	17.8424i	−1.14086	−	0.706388i
$639$	−14.6540	+	19.4050i	−0.579704	+	0.767652i
$640$	−6.96833	−	4.31461i	−0.275447	−	0.170550i
$641$	−13.0447	+	17.2740i	−0.515236	+	0.682283i	−0.979043	−	0.203654i	$-0.934718\pi$
$641$	−13.0447	+	17.2740i	−0.515236	+	0.682283i	0.463807	+	0.885936i	$0.346483\pi$
$642$	0.473331	+	1.66359i	0.0186809	+	0.0656565i
$643$	24.7269	−	15.3102i	0.975134	−	0.603777i	0.0562965	−	0.998414i	$-0.482071\pi$
$643$	24.7269	−	15.3102i	0.975134	−	0.603777i	0.918837	+	0.394637i	$0.129130\pi$
$644$	14.7461	+	5.71268i	0.581079	+	0.225111i
$645$	0.966283	+	1.27956i	0.0380473	+	0.0503828i
$646$	1.29149	+	13.9374i	0.0508131	+	0.548361i
$647$	−17.5210	−	23.2015i	−0.688821	−	0.912147i	0.310439	−	0.950593i	$-0.399524\pi$
$647$	−17.5210	−	23.2015i	−0.688821	−	0.912147i	−0.999261	+	0.0384465i	$0.987759\pi$
$648$	15.6881	−	20.7744i	0.616287	−	0.816097i
$649$	−18.2289	+	16.6178i	−0.715546	+	0.652306i
$650$	−0.140012	+	1.51097i	−0.00549174	+	0.0592653i
$651$	5.16483	+	0.965475i	0.202426	+	0.0378399i
$652$	−6.35487	−	8.41521i	−0.248876	−	0.329565i
$653$	−9.18018	+	32.2650i	−0.359248	+	1.26263i	0.546015	+	0.837775i	$0.316144\pi$
$653$	−9.18018	+	32.2650i	−0.359248	+	1.26263i	−0.905263	+	0.424851i	$0.860326\pi$
$654$	0.239416	+	0.841459i	0.00936190	+	0.0329036i
$655$	16.1884	−	32.5106i	0.632532	−	1.27029i
$656$	−7.41838	−	1.38674i	−0.289639	−	0.0541429i
$657$	1.54225	+	16.6435i	0.0601687	+	0.649324i
$658$	3.00372	−	32.4153i	0.117097	−	1.26368i
$659$	2.67239	+	0.499556i	0.104102	+	0.0194599i	0.235542	−	0.971864i	$-0.424313\pi$
$659$	2.67239	+	0.499556i	0.104102	+	0.0194599i	−0.131441	+	0.991324i	$0.541960\pi$
$660$	−0.749275	−	0.683055i	−0.0291655	−	0.0265879i
$661$	−14.6252	+	13.3326i	−0.568854	+	0.518579i	−0.906227	−	0.422792i	$-0.861050\pi$
$661$	−14.6252	+	13.3326i	−0.568854	+	0.518579i	0.337373	+	0.941371i	$0.390462\pi$
$662$	8.12778	−	28.5662i	0.315895	−	1.11026i
$663$	−1.38906	−	4.88203i	−0.0539465	−	0.189602i
$664$	5.51386	−	1.03072i	0.213979	−	0.0399997i
$665$	−7.63727	+	26.8422i	−0.296161	+	1.04090i
$666$	6.86962	−	13.7961i	0.266192	−	0.534586i
$667$	−45.6798	+	60.4899i	−1.76873	+	2.34218i
$668$	3.91688	−	5.18679i	0.151549	−	0.200683i
$669$	3.11251	−	0.581830i	0.120337	−	0.0224948i
$670$	−2.23156	−	4.48159i	−0.0862129	−	0.173139i
$671$	21.9661	+	4.10617i	0.847990	+	0.158517i
$672$	2.31698	+	1.43462i	0.0893796	+	0.0553415i
$673$	7.52999	−	15.1223i	0.290260	−	0.582921i	−0.701255	−	0.712910i	$-0.747377\pi$
$673$	7.52999	−	15.1223i	0.290260	−	0.582921i	0.991515	+	0.129990i	$0.0414944\pi$
$674$	−1.10748	−	3.89240i	−0.0426587	−	0.149930i
$675$	0.294540			0.0113369
$676$	4.68074	+	16.4511i	0.180028	+	0.632734i
$677$	−25.3197	+	23.0819i	−0.973113	+	0.887110i	−0.993631	−	0.112680i	$-0.964057\pi$
$677$	−25.3197	+	23.0819i	−0.973113	+	0.887110i	0.0205181	+	0.999789i	$0.493468\pi$
$678$	0.951006	+	0.177774i	0.0365232	+	0.00682736i
$679$	9.96915	+	35.0379i	0.382581	+	1.34463i
$680$	−10.1001	−	20.2837i	−0.387320	−	0.777844i
$681$	−0.786129	+	0.716652i	−0.0301245	+	0.0274621i
$682$	21.9082	−	4.09536i	0.838910	−	0.156819i
$683$	−9.59637	+	33.7277i	−0.367195	+	1.29056i	0.529652	+	0.848215i	$0.322323\pi$
$683$	−9.59637	+	33.7277i	−0.367195	+	1.29056i	−0.896847	+	0.442341i	$0.854148\pi$
$684$	−6.53179	+	1.22100i	−0.249749	+	0.0466862i
$685$	24.4034	+	15.1100i	0.932407	+	0.577322i
$686$	9.84164	−	6.09369i	0.375756	−	0.232658i
$687$	2.16385	+	1.97261i	0.0825562	+	0.0752599i
$688$	−6.38491	−	2.47353i	−0.243423	−	0.0943024i
$689$	−53.7055	+	20.8056i	−2.04602	+	0.792632i
$690$	3.78388	−	3.44946i	0.144050	−	0.131319i
$691$	13.5296	−	47.5516i	0.514690	−	1.80895i	−0.0698161	−	0.997560i	$-0.522241\pi$
$691$	13.5296	−	47.5516i	0.514690	−	1.80895i	0.584506	−	0.811389i	$-0.301288\pi$
$692$	12.1131	−	2.26433i	0.460470	−	0.0860768i
$693$	21.2537	+	19.3753i	0.807361	+	0.736007i
$694$	7.44068	−	14.9429i	0.282444	−	0.567224i
$695$	−16.4962	+	10.2140i	−0.625736	+	0.387439i
$696$	−5.46876	+	4.98544i	−0.207293	+	0.188972i
$697$	−7.51655	−	6.85224i	−0.284710	−	0.259547i
$698$	−31.5392	+	5.89569i	−1.19378	+	0.223155i
$699$	−0.601864	−	6.49515i	−0.0227646	−	0.245669i
$700$	−0.0379467	−	0.409510i	−0.00143425	−	0.0154780i
$701$	31.3030			1.18230			0.591150	−	0.806562i	$-0.298674\pi$
$701$	31.3030			1.18230			0.591150	+	0.806562i	$0.298674\pi$
$702$	−10.2519	+	3.97161i	−0.386933	+	0.149899i
$703$	−15.2917	+	5.92405i	−0.576739	+	0.223430i
$704$	25.2292	+	4.71615i	0.950861	+	0.177747i
$705$	3.96867	+	2.45730i	0.149469	+	0.0925472i
$706$	18.6157	+	24.6511i	0.700610	+	0.927757i
$707$	3.79942	−	3.46363i	0.142892	−	0.130263i
$708$	0.563775	+	1.13221i	0.0211880	+	0.0425512i
$709$	0.490561	−	5.29400i	0.0184234	−	0.198820i	−0.981548	−	0.191218i	$-0.938756\pi$
$709$	0.490561	−	5.29400i	0.0184234	−	0.198820i	0.999971	−	0.00760279i	$-0.00242007\pi$
$710$	18.8856	−	11.6935i	0.708764	−	0.438848i
$711$	1.64715	−	17.7755i	0.0617728	−	0.666635i
$712$	35.2323	−	21.8149i	1.32039	−	0.817549i
$713$	−4.59915	−	49.6328i	−0.172240	−	1.85876i
$714$	−1.38461	−	2.78068i	−0.0518179	−	0.104064i
$715$	−11.7477	−	41.2890i	−0.439341	−	1.54412i
$716$	−3.18418	−	6.39469i	−0.118998	−	0.238981i
$717$	−1.26152	+	1.15003i	−0.0471123	+	0.0429485i
$718$	2.33039	+	25.1490i	0.0869695	+	0.938551i
$719$	−0.683070	−	0.622701i	−0.0254742	−	0.0232228i	0.660858	−	0.750511i	$-0.270192\pi$
$719$	−0.683070	−	0.622701i	−0.0254742	−	0.0232228i	−0.686333	+	0.727288i	$0.740781\pi$
$720$	−13.6541	+	8.45424i	−0.508857	+	0.315071i
$721$	−3.05426	−	10.7346i	−0.113747	−	0.399778i
$722$	5.44441	+	3.37103i	0.202620	+	0.125457i
$723$	−0.125539	+	0.441225i	−0.00466886	+	0.0164093i
$724$	−0.0353298	+	0.381270i	−0.00131302	+	0.0141698i
$725$	1.93772	+	0.362223i	0.0719651	+	0.0134526i
$726$	0.629202	+	0.243754i	0.0233519	+	0.00904657i
$727$	−40.7304	+	15.7790i	−1.51061	+	0.585212i	−0.967146	−	0.254222i	$-0.918181\pi$
$727$	−40.7304	+	15.7790i	−1.51061	+	0.585212i	−0.543461	+	0.839434i	$0.682886\pi$
$728$	29.1365	+	58.5140i	1.07987	+	2.16867i
$729$	−10.6033	−	21.2942i	−0.392714	−	0.788675i
$730$	4.17845	−	14.6857i	0.154651	−	0.543543i
$731$	−5.56128	−	7.36433i	−0.205691	−	0.272379i
$732$	0.510747	−	1.02572i	0.0188778	−	0.0379116i
$733$	2.19956	−	0.852113i	0.0812425	−	0.0314735i	−0.320277	−	0.947324i	$-0.603776\pi$
$733$	2.19956	−	0.852113i	0.0812425	−	0.0314735i	0.401520	+	0.915850i	$0.368482\pi$
$734$	−6.46444	+	8.56031i	−0.238607	+	0.315967i
$735$	−0.209157	−	2.25717i	−0.00771488	−	0.0832568i
$736$	7.07489	−	24.8657i	0.260784	−	0.916560i
$737$	4.05704	+	3.69848i	0.149443	+	0.136235i
$738$	−6.57070	+	8.70102i	−0.241871	+	0.320289i
$739$	−11.3843	−	40.0117i	−0.418779	−	1.47186i	−0.828678	−	0.559725i	$-0.810907\pi$
$739$	−11.3843	−	40.0117i	−0.418779	−	1.47186i	0.409899	−	0.912131i	$-0.365564\pi$
$740$	4.60748	−	4.20028i	0.169374	−	0.154405i
$741$	5.39879	+	2.09150i	0.198330	+	0.0768333i
$742$	−29.9680	+	18.5554i	−1.10016	+	0.681190i
$743$	−47.0688	+	18.2345i	−1.72679	+	0.668960i	−0.999843	−	0.0177370i	$-0.994354\pi$
$743$	−47.0688	+	18.2345i	−1.72679	+	0.668960i	−0.726943	+	0.686697i	$0.759060\pi$
$744$	0.449001	−	4.84549i	0.0164612	−	0.177644i
$745$	−5.77600	−	11.5998i	−0.211616	−	0.424983i
$746$	7.83867	−	27.5501i	0.286994	−	1.00868i
$747$	1.46629	−	5.15347i	0.0536487	−	0.188556i
$748$	4.31233	+	3.93121i	0.157674	+	0.143739i
$749$	1.83128	−	19.7627i	0.0669137	−	0.722113i
$750$	2.95496	+	1.14476i	0.107900	+	0.0418007i
$751$	−8.14489	−	3.15535i	−0.297211	−	0.115140i	0.208019	−	0.978125i	$-0.433298\pi$
$751$	−8.14489	−	3.15535i	−0.297211	−	0.115140i	−0.505230	+	0.862984i	$0.668592\pi$
$752$	−19.9336			−0.726902
$753$	0.686049	+	0.908475i	0.0250010	+	0.0331067i
$754$	−72.3294	+	13.5207i	−2.63408	+	0.492395i
$755$	35.9256	+	13.9177i	1.30747	+	0.506515i
$756$	2.53341	−	1.56862i	0.0921393	−	0.0570502i
$757$	32.3483	−	6.04695i	1.17572	−	0.219780i	0.440591	−	0.897708i	$-0.354769\pi$
$757$	32.3483	−	6.04695i	1.17572	−	0.219780i	0.735128	+	0.677928i	$0.237122\pi$
$758$	17.3271	+	6.71255i	0.629348	+	0.243811i
$759$	−2.50264	+	5.02598i	−0.0908401	+	0.182431i
$760$	25.4064	+	4.74928i	0.921587	+	0.172275i
$761$	−8.02129	−	7.31237i	−0.290772	−	0.265073i	0.515144	−	0.857104i	$-0.327738\pi$
$761$	−8.02129	−	7.31237i	−0.290772	−	0.265073i	−0.805916	+	0.592030i	$0.798327\pi$
$762$	0.145784	+	1.57326i	0.00528119	+	0.0569932i
$763$	0.926282	−	9.99618i	0.0335337	−	0.361886i
$764$	2.36118			0.0854244
$765$	−21.6438			−0.782533
$766$	0.836617	−	9.02853i	0.0302282	−	0.326214i
$767$	−4.94111	+	53.3231i	−0.178413	+	1.92539i
$768$	1.44742	−	2.90680i	0.0522291	−	0.104890i
$769$	−27.6133			−0.995761			−0.497881	−	0.867246i	$-0.665888\pi$
$769$	−27.6133			−0.995761			−0.497881	+	0.867246i	$0.665888\pi$
$770$	−11.7102	−	23.5172i	−0.422005	−	0.847500i
$771$	1.18002	−	1.56260i	0.0424975	−	0.0562757i
$772$	9.81444	+	12.9964i	0.353229	+	0.467751i
$773$	3.61077	−	38.9664i	0.129870	−	1.40152i	−0.642468	−	0.766312i	$-0.722089\pi$
$773$	3.61077	−	38.9664i	0.129870	−	1.40152i	0.772338	−	0.635211i	$-0.219087\pi$
$774$	−7.31070	+	6.66459i	−0.262778	+	0.239554i
$775$	−1.10213	+	0.682412i	−0.0395898	+	0.0245130i
$776$	31.4599	−	12.1876i	1.12935	−	0.437511i
$777$	2.68955	−	2.45185i	0.0964872	−	0.0879597i
$778$	−18.3010	+	7.08984i	−0.656122	+	0.254183i
$779$	11.4043	−	2.13183i	0.408600	−	0.0763806i
$780$	−2.20117			−0.0788146
$781$	−14.6786	+	19.4376i	−0.525242	+	0.695533i
$782$	−21.7775	+	19.8528i	−0.778762	+	0.709936i
$783$	3.90859	+	13.7373i	0.139682	+	0.490930i
$784$	5.83369	+	7.72506i	0.208346	+	0.275895i
$785$	−23.3598	−	14.4638i	−0.833749	−	0.516235i
$786$	−4.29974	−	1.66573i	−0.153366	−	0.0594145i
$787$	35.8995			1.27968			0.639839	−	0.768509i	$-0.279001\pi$
$787$	35.8995			1.27968			0.639839	+	0.768509i	$0.279001\pi$
$788$	8.02951	+	10.6328i	0.286039	+	0.378777i
$789$	0.420945	+	0.383742i	0.0149860	+	0.0136616i
$790$	−7.26871	+	14.5975i	−0.258609	+	0.519357i
$791$	−9.43899	−	5.84437i	−0.335612	−	0.207802i
$792$	16.0516	−	21.2557i	0.570368	−	0.755290i
$793$	41.2479	−	25.5396i	1.46476	−	0.906939i
$794$	−3.31845	+	35.8117i	−0.117767	+	1.27091i
$795$	−0.466326	−	5.03246i	−0.0165389	−	0.178483i
$796$	−13.8998	+	2.59832i	−0.492665	+	0.0920951i
$797$	12.3704	+	2.31243i	0.438182	+	0.0819104i	0.398218	−	0.917291i	$-0.369629\pi$
$797$	12.3704	+	2.31243i	0.438182	+	0.0819104i	0.0399637	+	0.999201i	$0.487276\pi$
$798$	3.48295	+	0.651076i	0.123295	+	0.0230478i
$799$	−22.8411	−	14.1426i	−0.808058	−	0.500329i
$800$	−0.660883	+	0.123540i	−0.0233657	+	0.00436781i
$801$	−3.65219	−	39.4134i	−0.129044	−	1.39260i
$802$	−17.3461	−	22.9700i	−0.612513	−	0.811099i
$803$	1.54484	+	16.6714i	0.0545161	+	0.588322i
$804$	0.239334	−	0.148190i	0.00844068	−	0.00522625i
$805$	−54.7870	+	21.2246i	−1.93099	+	0.748069i
$806$	29.1596	−	38.6136i	1.02710	−	1.36011i
$807$	3.58413	+	1.38850i	0.126167	+	0.0488774i
$808$	−3.51881	−	3.20782i	−0.123791	−	0.112851i
$809$	13.6597	+	5.29180i	0.480250	+	0.186050i	0.589184	−	0.807999i	$-0.299449\pi$
$809$	13.6597	+	5.29180i	0.480250	+	0.186050i	−0.108934	+	0.994049i	$0.534744\pi$
$810$	2.09583	+	22.6176i	0.0736401	+	0.794703i
$811$	4.44491			0.156082			0.0780409	−	0.996950i	$-0.475134\pi$
$811$	4.44491			0.156082			0.0780409	+	0.996950i	$0.475134\pi$
$812$	18.5959	−	7.20408i	0.652587	−	0.252814i
$813$	−1.55665	−	5.47105i	−0.0545940	−	0.191878i
$814$	6.88116	−	13.8192i	0.241184	−	0.484364i
$815$	38.5118	+	7.19910i	1.34901	+	0.252174i
$816$	−1.61717	+	1.00131i	−0.0566123	+	0.0350529i
$817$	10.5263			0.368270
$818$	14.9159	+	18.5593i	0.521522	+	0.648910i
$819$	62.4376			2.18175
$820$	−3.75015	+	2.32200i	−0.130961	+	0.0810876i
$821$	31.6885	+	5.92360i	1.10594	+	0.206735i	0.704886	−	0.709321i	$-0.250998\pi$
$821$	31.6885	+	5.92360i	1.10594	+	0.206735i	0.401050	+	0.916056i	$0.368645\pi$
$822$	1.62437	−	3.26217i	0.0566563	−	0.113781i
$823$	9.83398	+	34.5629i	0.342791	+	1.20479i	0.921216	+	0.389050i	$0.127197\pi$
$823$	9.83398	+	34.5629i	0.342791	+	1.20479i	−0.578425	+	0.815735i	$0.696333\pi$
$824$	−9.63841	+	3.73394i	−0.335770	+	0.130078i
$825$	0.146015			0.00508359
$826$	3.02392	+	32.6332i	0.105215	+	1.13546i
$827$	−1.68521	−	0.652852i	−0.0586004	−	0.0227019i	0.331763	−	0.943363i	$-0.392357\pi$
$827$	−1.68521	−	0.652852i	−0.0586004	−	0.0227019i	−0.390363	+	0.920661i	$0.627651\pi$
$828$	−10.3386	−	9.42484i	−0.359290	−	0.327536i
$829$	8.18658	+	3.17150i	0.284332	+	0.110151i	0.499184	−	0.866496i	$-0.333633\pi$
$829$	8.18658	+	3.17150i	0.284332	+	0.110151i	−0.214853	+	0.976646i	$0.568927\pi$
$830$	−2.94955	+	3.90583i	−0.102380	+	0.135573i
$831$	0.219568	−	0.0850612i	0.00761674	−	0.00295074i
$832$	47.3755	−	29.3336i	1.64245	−	1.01696i
$833$	1.20377	+	12.9908i	0.0417082	+	0.450103i
$834$	1.48454	+	1.96584i	0.0514053	+	0.0680716i
$835$	2.22812	+	24.0453i	0.0771073	+	0.832121i
$836$	−6.54276	+	1.22305i	−0.226286	+	0.0423002i
$837$	−7.98525	−	4.94426i	−0.276011	−	0.170899i
$838$	25.1327	+	4.69812i	0.868195	+	0.162294i
$839$	3.34091	+	0.624525i	0.115341	+	0.0215610i	0.241104	−	0.970499i	$-0.422491\pi$
$839$	3.34091	+	0.624525i	0.115341	+	0.0215610i	−0.125762	+	0.992060i	$0.540138\pi$
$840$	−5.63836	+	1.05399i	−0.194542	+	0.0363662i
$841$	6.14408	+	66.3052i	0.211865	+	2.28639i
$842$	−2.97464	+	32.1015i	−0.102513	+	1.10629i
$843$	−1.90244	+	1.17794i	−0.0655236	+	0.0405705i
$844$	−3.51054	+	4.64870i	−0.120838	+	0.160015i
$845$	−54.0291	−	33.4534i	−1.85866	−	1.15083i
$846$	−12.8367	+	25.7797i	−0.441336	+	0.886323i
$847$	−5.72213	−	5.21641i	−0.196615	−	0.179238i
$848$	13.0065	+	17.2234i	0.446644	+	0.591453i
$849$	0.683107			0.0234442
$850$	0.714618	+	0.276844i	0.0245112	+	0.00949568i
$851$	−29.3542	−	18.1754i	−1.00625	−	0.623043i
$852$	0.752663	+	0.996687i	0.0257858	+	0.0341459i
$853$	6.87470	+	24.1621i	0.235385	+	0.827293i	0.986027	+	0.166584i	$0.0532737\pi$
$853$	6.87470	+	24.1621i	0.235385	+	0.827293i	−0.750642	+	0.660709i	$0.770256\pi$
$854$	21.9415	−	20.0023i	0.750823	−	0.684466i
$855$	14.8780	−	19.7017i	0.508817	−	0.673782i
$856$	−18.3816			−0.628269
$857$	27.9150	−	5.21822i	0.953558	−	0.178251i	0.316091	−	0.948729i	$-0.397629\pi$
$857$	27.9150	−	5.21822i	0.953558	−	0.178251i	0.637467	+	0.770478i	$0.279982\pi$
$858$	−5.08226	+	1.96888i	−0.173506	+	0.0672164i
$859$	−6.14082	+	5.59810i	−0.209522	+	0.191005i	−0.771653	−	0.636044i	$-0.780570\pi$
$859$	−6.14082	+	5.59810i	−0.209522	+	0.191005i	0.562131	+	0.827048i	$0.309982\pi$
$860$	−3.73170	+	1.44567i	−0.127250	+	0.0492969i
$861$	−2.18910	+	1.35543i	−0.0746042	+	0.0461930i
$862$	33.9640	−	30.9622i	1.15682	−	1.05458i
$863$	−0.497350	+	5.36726i	−0.0169300	+	0.182704i	−1.00000		0.000527456i	$-0.999832\pi$
$863$	−0.497350	+	5.36726i	−0.0169300	+	0.182704i	0.983070	+	0.183231i	$0.0586556\pi$
$864$	−2.93556	−	3.88731i	−0.0998699	−	0.132249i
$865$	−27.5909	+	36.5363i	−0.938120	+	1.24227i
$866$	18.3948	+	36.9418i	0.625082	+	1.25533i
$867$	1.61770			0.0549401
$868$	−5.84542	+	11.7392i	−0.198406	+	0.398454i
$869$	1.64991	−	17.8054i	0.0559694	−	0.604006i
$870$	0.595771	−	6.42939i	0.0201985	−	0.217977i
$871$	11.9185			0.403843
$872$	−9.29758			−0.314856
$873$	2.97347	−	32.0888i	0.100637	−	1.08604i
$874$	−3.10148	−	33.4702i	−0.104909	−	1.13215i
$875$	−26.8732	−	24.4982i	−0.908481	−	0.828190i
$876$	0.843892	+	0.157751i	0.0285125	+	0.00532990i
$877$	−7.22151	+	14.5027i	−0.243853	+	0.489723i	−0.982949	−	0.183877i	$-0.941135\pi$
$877$	−7.22151	+	14.5027i	−0.243853	+	0.489723i	0.739096	+	0.673600i	$0.235253\pi$
$878$	−9.47267	−	3.66973i	−0.319687	−	0.123847i
$879$	−4.02895	+	0.753142i	−0.135893	+	0.0254028i
$880$	−13.6770	+	8.46843i	−0.461051	+	0.285471i
$881$	15.4285	+	5.97702i	0.519798	+	0.201371i	0.606826	−	0.794835i	$-0.292443\pi$
$881$	15.4285	+	5.97702i	0.519798	+	0.201371i	−0.0870272	+	0.996206i	$0.527737\pi$
$882$	13.7474	−	2.56984i	0.462900	−	0.0865310i
$883$	16.6136	+	21.9999i	0.559092	+	0.740357i	0.986511	−	0.163696i	$-0.0523418\pi$
$883$	16.6136	+	21.9999i	0.559092	+	0.740357i	−0.427419	+	0.904054i	$0.640577\pi$
$884$	12.6685			0.426087
$885$	−4.38189	−	1.69755i	−0.147296	−	0.0570626i
$886$	13.6848	+	5.30152i	0.459750	+	0.178108i
$887$	0.345372	−	3.72715i	0.0115964	−	0.125146i	−0.987968	−	0.154659i	$-0.950572\pi$
$887$	0.345372	−	3.72715i	0.0115964	−	0.125146i	0.999564	+	0.0295132i	$0.00939572\pi$
$888$	−2.49092	−	2.27077i	−0.0835897	−	0.0762021i
$889$	4.96166	−	17.4384i	0.166409	−	0.584866i
$890$	−9.89497	+	34.7772i	−0.331680	+	1.16574i
$891$	−11.1023	−	22.2965i	−0.371942	−	0.746961i
$892$	−0.729194	+	7.86926i	−0.0244152	+	0.263482i
$893$	28.5745	−	11.0698i	0.956210	−	0.370438i
$894$	−1.39881	+	0.866109i	−0.0467833	+	0.0289670i
$895$	24.7487	+	9.58771i	0.827259	+	0.320482i
$896$	8.82441	−	8.04451i	0.294803	−	0.268748i
$897$	3.33577	+	11.7240i	0.111378	+	0.391454i
$898$	16.7903	−	22.2339i	0.560298	−	0.741955i
$899$	−46.4529	−	42.3475i	−1.54929	−	1.41237i
$900$	−0.0995647	+	0.349934i	−0.00331882	+	0.0116645i
$901$	2.68386	+	28.9635i	0.0894124	+	0.964913i
$902$	−6.58174	+	8.71563i	−0.219148	+	0.290199i
$903$	−2.17833	+	0.843888i	−0.0724902	+	0.0280828i
$904$	−4.58305	+	9.20401i	−0.152430	+	0.306121i
$905$	−0.857319	−	1.13527i	−0.0284983	−	0.0377378i
$906$	1.33865	−	4.70487i	0.0444737	−	0.156309i
$907$	8.66934	+	17.4104i	0.287861	+	0.578102i	0.991142	−	0.132810i	$-0.0424000\pi$
$907$	8.66934	+	17.4104i	0.287861	+	0.578102i	−0.703281	+	0.710912i	$0.748282\pi$
$908$	−1.18344	−	2.37666i	−0.0392737	−	0.0788723i
$909$	−4.24103	+	1.64298i	−0.140666	+	0.0544943i
$910$	−53.1840	−	20.6036i	−1.76303	−	0.683002i
$911$	20.1923	+	3.77460i	0.669002	+	0.125058i	0.507284	−	0.861779i	$-0.330649\pi$
$911$	20.1923	+	3.77460i	0.669002	+	0.125058i	0.161718	+	0.986837i	$0.448296\pi$
$912$	0.200187	−	2.16036i	0.00662886	−	0.0715367i
$913$	1.46875	−	5.16212i	0.0486085	−	0.170841i
$914$	21.7129	+	13.4441i	0.718200	+	0.444691i
$915$	1.16504	+	4.09470i	0.0385151	+	0.135367i
$916$	−6.21339	+	3.84717i	−0.205296	+	0.127114i
$917$	39.1029	+	35.6470i	1.29129	+	1.17717i
$918$	0.512325	+	5.52886i	0.0169092	+	0.182480i
$919$	32.1076	−	29.2700i	1.05913	−	0.965528i	0.0596677	−	0.998218i	$-0.480996\pi$
$919$	32.1076	−	29.2700i	1.05913	−	0.965528i	0.999466	+	0.0326908i	$0.0104076\pi$
$920$	24.2550	+	48.7106i	0.799664	+	1.60594i
$921$	−2.04070	−	7.17230i	−0.0672432	−	0.236335i
$922$	−21.0624	−	42.2991i	−0.693655	−	1.39305i
$923$	4.87917	+	52.6546i	0.160600	+	1.73315i
$924$	1.25591	−	0.777627i	0.0413164	−	0.0255820i
$925$	−0.0828462	+	0.894053i	−0.00272397	+	0.0293963i
$926$	−32.8494	+	20.3395i	−1.07950	+	0.668396i
$927$	−0.910985	+	9.83109i	−0.0299207	+	0.322895i
$928$	−14.5319	−	29.1840i	−0.477033	−	0.958011i
$929$	16.7802	−	15.2972i	0.550540	−	0.501883i	−0.349945	−	0.936770i	$-0.613800\pi$
$929$	16.7802	−	15.2972i	0.550540	−	0.501883i	0.900485	+	0.434887i	$0.143212\pi$
$930$	2.55879	+	3.38839i	0.0839062	+	0.111110i
$931$	−12.6525	−	7.83412i	−0.414670	−	0.256753i
$932$	16.0032	+	2.99152i	0.524203	+	0.0979906i
$933$	1.81074	−	0.701483i	0.0592808	−	0.0229655i
$934$	−26.8918	+	10.4179i	−0.879927	+	0.340885i
$935$	−21.6802			−0.709017
$936$	−5.33554	−	57.5797i	−0.174398	−	1.88205i
$937$	0.147679	+	1.59371i	0.00482445	+	0.0520641i	0.997806	−	0.0662048i	$-0.0210891\pi$
$937$	0.147679	+	1.59371i	0.00482445	+	0.0520641i	−0.992982	+	0.118269i	$0.962266\pi$
$938$	7.16982	−	1.34027i	0.234103	−	0.0437614i
$939$	0.0366256	+	0.0333886i	0.00119523	+	0.00108960i
$940$	−8.60966	+	7.84874i	−0.280816	+	0.255998i
$941$	2.25912	−	1.39879i	0.0736451	−	0.0455991i	−0.489116	−	0.872219i	$-0.662680\pi$
$941$	2.25912	−	1.39879i	0.0736451	−	0.0455991i	0.562761	+	0.826620i	$0.309739\pi$
$942$	−1.55490	+	3.12267i	−0.0506615	+	0.101742i
$943$	18.0507	+	16.4554i	0.587813	+	0.535862i
$944$	19.7259	−	3.68740i	0.642023	−	0.120015i
$945$	−3.02964	+	10.6481i	−0.0985544	+	0.346383i
$946$	−7.32298	+	6.67578i	−0.238091	+	0.217048i
$947$	−38.1268	+	14.7704i	−1.23895	+	0.479973i	−0.889480	−	0.456973i	$-0.848933\pi$
$947$	−38.1268	+	14.7704i	−1.23895	+	0.479973i	−0.349473	+	0.936946i	$0.613639\pi$
$948$	−0.854987	−	0.331224i	−0.0277687	−	0.0107576i
$949$	26.8622	+	24.4881i	0.871983	+	0.794918i
$950$	−0.743232	+	0.460190i	−0.0241136	+	0.0149305i
$951$	−3.70768	−	2.29570i	−0.120230	−	0.0744431i
$952$	32.4507	−	6.06608i	1.05173	−	0.196603i
$953$	0.753767	−	2.64922i	0.0244169	−	0.0858166i	−0.948660	−	0.316299i	$-0.897560\pi$
$953$	0.753767	−	2.64922i	0.0244169	−	0.0858166i	0.973077	+	0.230482i	$0.0740304\pi$
$954$	30.6505	−	5.72957i	0.992347	−	0.185502i
$955$	−6.48303	+	5.91006i	−0.209786	+	0.191245i
$956$	−1.89909	−	3.81388i	−0.0614209	−	0.123350i
$957$	1.93764	+	6.81010i	0.0626350	+	0.220139i
$958$	−14.3373	−	2.68011i	−0.463218	−	0.0865904i
$959$	−30.9035	+	28.1723i	−0.997926	+	0.909730i
$960$	1.33811	+	4.70298i	0.0431874	+	0.151788i
$961$	10.3350			0.333388
$962$	−9.17190	−	32.2359i	−0.295714	−	1.03933i
$963$	−7.82620	+	15.7171i	−0.252196	+	0.506477i
$964$	−0.973451	−	0.602735i	−0.0313527	−	0.0194128i
$965$	−59.4775	−	11.1183i	−1.91465	−	0.357910i
$966$	3.32510	+	6.67770i	0.106983	+	0.214852i
$967$	32.9843	−	6.16583i	1.06070	−	0.198280i	0.375641	−	0.926765i	$-0.377422\pi$
$967$	32.9843	−	6.16583i	1.06070	−	0.198280i	0.685061	+	0.728485i	$0.259775\pi$
$968$	−4.32157	+	5.72269i	−0.138901	+	0.183934i
$969$	1.76213	−	2.33344i	0.0566079	−	0.0749610i
$970$	−13.1217	+	26.3518i	−0.421311	+	0.846107i
$971$	−3.78683	+	13.3093i	−0.121525	+	0.427117i	−0.998580	−	0.0532735i	$-0.983035\pi$
$971$	−3.78683	+	13.3093i	−0.121525	+	0.427117i	0.877055	+	0.480391i	$0.159505\pi$
$972$	−3.89986	+	0.729010i	−0.125088	+	0.0233830i
$973$	−7.73582	−	27.1886i	−0.247999	−	0.871626i
$974$	−1.55283	+	5.45762i	−0.0497558	+	0.174874i
$975$	0.234266	−	0.213562i	0.00750251	−	0.00683944i
$976$	−13.4352	−	12.2478i	−0.430051	−	0.392043i
$977$	41.9732	+	7.84615i	1.34284	+	0.251021i	0.805626	−	0.592424i	$-0.201829\pi$
$977$	41.9732	+	7.84615i	1.34284	+	0.251021i	0.537216	+	0.843445i	$0.319476\pi$
$978$	0.458974	−	4.95312i	0.0146764	−	0.158383i
$979$	−3.65832	−	39.4796i	−0.116920	−	1.26177i
$980$	5.56138	+	1.03960i	0.177652	+	0.0332089i
$981$	−3.95857	+	7.94989i	−0.126388	+	0.253820i
$982$	11.5557	+	40.6141i	0.368757	+	1.29605i
$983$	−16.7489	+	58.8662i	−0.534206	+	1.87754i	−0.0577725	+	0.998330i	$0.518400\pi$
$983$	−16.7489	+	58.8662i	−0.534206	+	1.87754i	−0.476434	+	0.879210i	$0.658071\pi$
$984$	1.43704	+	1.90295i	0.0458111	+	0.0606638i
$985$	−48.6605	−	9.09622i	−1.55045	−	0.289830i
$986$	−3.42886	+	37.0033i	−0.109197	+	1.17843i
$987$	−5.02577	+	4.58159i	−0.159972	+	0.145834i
$988$	−8.70834	+	11.5317i	−0.277049	+	0.366872i
$989$	13.3552	+	17.6852i	0.424672	+	0.562356i
$990$	2.14439	+	23.1417i	0.0681532	+	0.735490i
$991$	28.9508	+	38.3371i	0.919653	+	1.21782i	0.975638	+	0.219386i	$0.0704055\pi$
$991$	28.9508	+	38.3371i	0.919653	+	1.21782i	−0.0559846	+	0.998432i	$0.517830\pi$
$992$	19.9909	+	7.74452i	0.634712	+	0.245889i
$993$	−5.27511	+	3.26621i	−0.167401	+	0.103650i
$994$	8.85633	+	31.1268i	0.280906	+	0.987281i
$995$	31.6607	−	41.9256i	1.00371	−	1.32913i
$996$	−0.233979	−	0.144874i	−0.00741392	−	0.00459050i
$997$	−21.4242	+	28.3702i	−0.678511	+	0.898494i	−0.998807	−	0.0488231i	$-0.984453\pi$
$997$	−21.4242	+	28.3702i	−0.678511	+	0.898494i	0.320296	+	0.947318i	$0.396218\pi$
$998$	−31.5390	−	19.5281i	−0.998350	−	0.618152i
$999$	−6.06611	+	2.35002i	−0.191923	+	0.0743514i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	409.2.h.a.5.11	✓	512
409.82	even	17	inner	409.2.h.a.82.11	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
409.2.h.a.5.11	✓	512	1.1	even	1	trivial
409.2.h.a.82.11	yes	512	409.82	even	17	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 409 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	409.h (of order \(17\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00100 + 0.619792i) q^{2} +(0.241764 + 0.0451934i) q^{3} +(-0.273621 + 0.549506i) q^{4} +(-0.624145 - 2.19364i) q^{5} +(-0.270015 + 0.104605i) q^{6} +3.32282 q^{7} +(-0.283948 - 3.06429i) q^{8} +(-2.74101 - 1.06187i) q^{9} +(1.98437 + 1.80899i) q^{10} +(-2.74561 - 1.06366i) q^{11} +(-0.0909857 + 0.120484i) q^{12} +(-5.96075 + 2.30921i) q^{13} +(-3.32613 + 2.05946i) q^{14} +(-0.0517573 - 0.558550i) q^{15} +(1.44358 + 1.91161i) q^{16} +(0.297881 + 3.21464i) q^{17} +(3.40189 - 0.635923i) q^{18} +(-3.13095 - 1.93860i) q^{19} +(1.37620 + 0.257256i) q^{20} +(0.803336 + 0.150170i) q^{21} +(3.40760 - 0.636991i) q^{22} +(-0.715350 - 7.71986i) q^{23} +(0.0698374 - 0.753665i) q^{24} +(-0.171425 + 0.106142i) q^{25} +(4.53548 - 6.00594i) q^{26} +(-1.24202 - 0.769028i) q^{27} +(-0.909194 + 1.82591i) q^{28} +(-7.22527 - 6.58670i) q^{29} +(0.397994 + 0.527029i) q^{30} +6.42923 q^{31} +(3.10938 + 1.20458i) q^{32} +(-0.615719 - 0.381237i) q^{33} +(-2.29059 - 3.03323i) q^{34} +(-2.07392 - 7.28907i) q^{35} +(1.33350 - 1.21565i) q^{36} +(2.68367 - 3.55375i) q^{37} +4.33560 q^{38} +(-1.54545 + 0.288895i) q^{39} +(-6.54472 + 2.53544i) q^{40} +(-2.32825 + 2.12248i) q^{41} +(-0.897212 + 0.347582i) q^{42} +(-2.43031 + 1.50478i) q^{43} +(1.33574 - 1.21769i) q^{44} +(-0.618582 + 6.67556i) q^{45} +(5.50077 + 7.28419i) q^{46} +(-5.01477 + 6.64063i) q^{47} +(0.262613 + 0.527399i) q^{48} +4.04112 q^{49} +(0.105810 - 0.212496i) q^{50} +(-0.0732641 + 0.790646i) q^{51} +(0.362066 - 3.90732i) q^{52} +9.00986 q^{53} +1.71990 q^{54} +(-0.619620 + 6.68677i) q^{55} +(-0.943507 - 10.1821i) q^{56} +(-0.669337 - 0.610182i) q^{57} +(11.3149 + 2.11512i) q^{58} +(3.73411 - 7.49910i) q^{59} +(0.321088 + 0.124390i) q^{60} +(-7.46017 + 1.39455i) q^{61} +(-6.43565 + 3.98479i) q^{62} +(-9.10788 - 3.52841i) q^{63} +(-8.56840 + 1.60171i) q^{64} +(8.78595 + 11.6345i) q^{65} +0.852621 q^{66} +(-1.73857 - 0.673526i) q^{67} +(-1.84797 - 0.715908i) q^{68} +(0.175941 - 1.89871i) q^{69} +(6.59370 + 6.01095i) q^{70} +(2.26383 - 7.95654i) q^{71} +(-2.47558 + 8.70075i) q^{72} +(-2.53458 - 5.09013i) q^{73} +(-0.483761 + 5.22061i) q^{74} +(-0.0462413 + 0.0179140i) q^{75} +(1.92197 - 1.19003i) q^{76} +(-9.12317 - 3.53434i) q^{77} +(1.36794 - 1.24704i) q^{78} +(1.66196 + 5.84118i) q^{79} +(3.29239 - 4.35983i) q^{80} +(6.25145 + 5.69895i) q^{81} +(1.01508 - 3.56763i) q^{82} +(0.168183 + 1.81498i) q^{83} +(-0.302329 + 0.400348i) q^{84} +(6.86586 - 2.65985i) q^{85} +(1.50008 - 3.01257i) q^{86} +(-1.44913 - 1.91896i) q^{87} +(-2.47974 + 8.71537i) q^{88} +(6.00213 + 12.0539i) q^{89} +(-3.51826 - 7.06561i) q^{90} +(-19.8065 + 7.67308i) q^{91} +(4.43784 + 1.71923i) q^{92} +(1.55435 + 0.290559i) q^{93} +(0.903968 - 9.75537i) q^{94} +(-2.29843 + 8.07815i) q^{95} +(0.697295 + 0.431747i) q^{96} +(3.00021 + 10.5446i) q^{97} +(-4.04515 + 2.50465i) q^{98} +(6.39628 + 5.83098i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q - 13 q^{2} - 11 q^{3} - 73 q^{4} - 9 q^{5} - 27 q^{6} - 22 q^{7} + q^{8} - 31 q^{9} + 5 q^{10} - 60 q^{11} - 38 q^{12} + 7 q^{13} - 37 q^{14} + 3 q^{15} - 53 q^{16} + 3 q^{17} + 16 q^{18} + 17 q^{19}+ \cdots - 103 q^{99}+O(q^{100}) \) 512 * q - 13 * q^2 - 11 * q^3 - 73 * q^4 - 9 * q^5 - 27 * q^6 - 22 * q^7 + q^8 - 31 * q^9 + 5 * q^10 - 60 * q^11 - 38 * q^12 + 7 * q^13 - 37 * q^14 + 3 * q^15 - 53 * q^16 + 3 * q^17 + 16 * q^18 + 17 * q^19 + 27 * q^20 - 120 * q^21 - q^22 + q^23 - 20 * q^24 - 5 * q^25 + 23 * q^26 + 25 * q^27 - 29 * q^28 + 13 * q^29 + 27 * q^30 + 12 * q^31 - 69 * q^32 + 55 * q^33 + 37 * q^34 - 54 * q^35 - 41 * q^36 + 25 * q^37 - 212 * q^38 - 69 * q^39 - 66 * q^40 - 117 * q^41 - 141 * q^42 - 73 * q^43 + 37 * q^44 + 75 * q^45 - q^46 + 11 * q^47 + 143 * q^48 + 318 * q^49 + 79 * q^50 + 101 * q^52 - 84 * q^53 - 8 * q^54 - 79 * q^55 - 54 * q^56 + 87 * q^57 + 61 * q^58 + 37 * q^59 + 9 * q^60 + 42 * q^61 + 45 * q^62 - 161 * q^63 - 229 * q^64 + 67 * q^65 + 112 * q^66 + 35 * q^67 + 111 * q^68 - 119 * q^69 - 96 * q^70 - 39 * q^71 + 195 * q^72 + 83 * q^73 - 47 * q^74 + 77 * q^75 + 125 * q^76 - 138 * q^77 - 87 * q^78 + 57 * q^79 - 41 * q^80 - 83 * q^81 + 149 * q^82 + 23 * q^83 - 164 * q^84 + 23 * q^85 - 111 * q^86 - 237 * q^87 - 71 * q^88 + 107 * q^89 - 38 * q^90 - 14 * q^91 - 167 * q^92 + 62 * q^93 + 147 * q^94 + 45 * q^95 + 84 * q^96 + 99 * q^97 - 151 * q^98 - 103 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more