LMFDB - Embedded newform 144.3.v.a.43.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(43,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("144.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.v (of order $12$, degree $4$, 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:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			43.10
Character	$\chi$	$=$	144.43
Dual form			144.3.v.a.67.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59468 - 1.20706i) q^{2} +(-2.00451 - 2.23203i) q^{3} +(1.08601 + 3.84975i) q^{4} +(0.218413 - 0.815129i) q^{5} +(0.502363 + 5.97893i) q^{6} +(-4.45068 + 7.70881i) q^{7} +(2.91503 - 7.45001i) q^{8} +(-0.963885 + 8.94824i) q^{9} +O(q^{10})$	\(q+(-1.59468 - 1.20706i) q^{2} +(-2.00451 - 2.23203i) q^{3} +(1.08601 + 3.84975i) q^{4} +(0.218413 - 0.815129i) q^{5} +(0.502363 + 5.97893i) q^{6} +(-4.45068 + 7.70881i) q^{7} +(2.91503 - 7.45001i) q^{8} +(-0.963885 + 8.94824i) q^{9} +(-1.33221 + 1.03623i) q^{10} +(0.942033 + 3.51572i) q^{11} +(6.41582 - 10.1409i) q^{12} +(5.34198 + 1.43138i) q^{13} +(16.4024 - 6.92085i) q^{14} +(-2.25720 + 1.14643i) q^{15} +(-13.6411 + 8.36176i) q^{16} +20.6891 q^{17} +(12.3381 - 13.1061i) q^{18} +(1.75266 + 1.75266i) q^{19} +(3.37524 - 0.0444055i) q^{20} +(26.1277 - 5.51833i) q^{21} +(2.74144 - 6.74353i) q^{22} +(10.0379 + 17.3862i) q^{23} +(-22.4718 + 8.42718i) q^{24} +(21.0339 + 12.1439i) q^{25} +(-6.79099 - 8.73068i) q^{26} +(21.9048 - 15.7854i) q^{27} +(-34.5105 - 8.76214i) q^{28} +(-3.10032 - 11.5706i) q^{29} +(4.98332 + 0.896387i) q^{30} +(-53.3631 + 30.8092i) q^{31} +(31.8464 + 3.13133i) q^{32} +(5.95886 - 9.14993i) q^{33} +(-32.9924 - 24.9729i) q^{34} +(5.31158 + 5.31158i) q^{35} +(-35.4953 + 6.00719i) q^{36} +(16.2850 + 16.2850i) q^{37} +(-0.679367 - 4.91049i) q^{38} +(-7.51317 - 14.7926i) q^{39} +(-5.43604 - 4.00331i) q^{40} +(-46.5560 + 26.8791i) q^{41} +(-48.3263 - 22.7377i) q^{42} +(14.0229 + 52.3343i) q^{43} +(-12.5116 + 7.44471i) q^{44} +(7.08344 + 2.74010i) q^{45} +(4.97889 - 39.8418i) q^{46} +(-51.7323 - 29.8676i) q^{47} +(46.0075 + 13.6862i) q^{48} +(-15.1171 - 26.1836i) q^{49} +(-18.8839 - 44.7549i) q^{50} +(-41.4714 - 46.1785i) q^{51} +(0.291013 + 22.1198i) q^{52} +(20.3405 + 20.3405i) q^{53} +(-53.9851 - 1.26774i) q^{54} +3.07151 q^{55} +(44.4568 + 55.6290i) q^{56} +(0.398760 - 7.42520i) q^{57} +(-9.02233 + 22.1936i) q^{58} +(-0.602860 - 0.161536i) q^{59} +(-6.86482 - 7.44462i) q^{60} +(24.9988 + 93.2967i) q^{61} +(122.286 + 15.2816i) q^{62} +(-64.6903 - 47.2561i) q^{63} +(-47.0052 - 43.4340i) q^{64} +(2.33352 - 4.04177i) q^{65} +(-20.5470 + 7.39852i) q^{66} +(21.0862 - 78.6949i) q^{67} +(22.4686 + 79.6477i) q^{68} +(18.6853 - 57.2557i) q^{69} +(-2.05888 - 14.8817i) q^{70} -12.5158 q^{71} +(63.8547 + 33.2653i) q^{72} -57.3042i q^{73} +(-6.31240 - 45.6262i) q^{74} +(-15.0571 - 71.2909i) q^{75} +(-4.84388 + 8.65071i) q^{76} +(-31.2947 - 8.38538i) q^{77} +(-5.87450 + 32.6584i) q^{78} +(54.9768 + 31.7408i) q^{79} +(3.83651 + 12.9456i) q^{80} +(-79.1419 - 17.2501i) q^{81} +(106.687 + 13.3323i) q^{82} +(30.4664 - 8.16345i) q^{83} +(49.6193 + 94.5921i) q^{84} +(4.51876 - 16.8642i) q^{85} +(40.8085 - 100.383i) q^{86} +(-19.6112 + 30.1133i) q^{87} +(28.9382 + 3.23027i) q^{88} +91.2611i q^{89} +(-7.98836 - 12.9197i) q^{90} +(-34.8097 + 34.8097i) q^{91} +(-56.0312 + 57.5251i) q^{92} +(175.734 + 57.3506i) q^{93} +(46.4444 + 110.073i) q^{94} +(1.81145 - 1.04584i) q^{95} +(-56.8472 - 77.3588i) q^{96} +(43.8910 - 76.0214i) q^{97} +(-7.49821 + 60.0018i) q^{98} +(-32.3675 + 5.04079i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{8}+O(q^{10}) $ 184 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^8	\( 184 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{8} - 8 q^{10} - 2 q^{11} + 56 q^{12} - 2 q^{13} + 14 q^{14} - 2 q^{16} - 16 q^{17} + 38 q^{18} - 8 q^{19} - 44 q^{20} + 14 q^{21} - 2 q^{22} - 4 q^{23} + 120 q^{24} - 104 q^{26} - 52 q^{27} + 56 q^{28} - 2 q^{29} - 130 q^{30} - 182 q^{32} - 8 q^{33} - 10 q^{34} + 92 q^{35} - 2 q^{36} - 8 q^{37} - 254 q^{38} + 184 q^{39} - 2 q^{40} - 252 q^{42} - 2 q^{43} - 140 q^{44} - 54 q^{45} + 176 q^{46} + 162 q^{48} - 480 q^{49} - 96 q^{50} - 120 q^{51} - 2 q^{52} - 8 q^{53} + 94 q^{54} - 16 q^{55} + 260 q^{56} + 88 q^{58} + 142 q^{59} - 434 q^{60} - 2 q^{61} - 636 q^{62} + 244 q^{64} - 4 q^{65} - 100 q^{66} - 2 q^{67} - 112 q^{68} + 14 q^{69} - 100 q^{70} - 16 q^{71} + 98 q^{72} + 82 q^{74} - 296 q^{75} + 154 q^{76} + 194 q^{77} + 228 q^{78} + 592 q^{80} - 8 q^{81} - 420 q^{82} + 238 q^{83} - 22 q^{84} - 52 q^{85} - 170 q^{86} - 456 q^{87} - 26 q^{88} + 808 q^{90} + 188 q^{91} + 176 q^{92} + 26 q^{93} - 18 q^{94} - 202 q^{96} - 4 q^{97} + 408 q^{98} - 38 q^{99}+O(q^{100}) \) 184 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^8 - 8 * q^10 - 2 * q^11 + 56 * q^12 - 2 * q^13 + 14 * q^14 - 2 * q^16 - 16 * q^17 + 38 * q^18 - 8 * q^19 - 44 * q^20 + 14 * q^21 - 2 * q^22 - 4 * q^23 + 120 * q^24 - 104 * q^26 - 52 * q^27 + 56 * q^28 - 2 * q^29 - 130 * q^30 - 182 * q^32 - 8 * q^33 - 10 * q^34 + 92 * q^35 - 2 * q^36 - 8 * q^37 - 254 * q^38 + 184 * q^39 - 2 * q^40 - 252 * q^42 - 2 * q^43 - 140 * q^44 - 54 * q^45 + 176 * q^46 + 162 * q^48 - 480 * q^49 - 96 * q^50 - 120 * q^51 - 2 * q^52 - 8 * q^53 + 94 * q^54 - 16 * q^55 + 260 * q^56 + 88 * q^58 + 142 * q^59 - 434 * q^60 - 2 * q^61 - 636 * q^62 + 244 * q^64 - 4 * q^65 - 100 * q^66 - 2 * q^67 - 112 * q^68 + 14 * q^69 - 100 * q^70 - 16 * q^71 + 98 * q^72 + 82 * q^74 - 296 * q^75 + 154 * q^76 + 194 * q^77 + 228 * q^78 + 592 * q^80 - 8 * q^81 - 420 * q^82 + 238 * q^83 - 22 * q^84 - 52 * q^85 - 170 * q^86 - 456 * q^87 - 26 * q^88 + 808 * q^90 + 188 * q^91 + 176 * q^92 + 26 * q^93 - 18 * q^94 - 202 * q^96 - 4 * q^97 + 408 * q^98 - 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−1.59468	−	1.20706i	−0.797340	−	0.603530i
$2$	−1.59468	−	1.20706i	−0.797340	−	0.603530i
$3$	−2.00451	−	2.23203i	−0.668170	−	0.744009i
$3$	−2.00451	−	2.23203i	−0.668170	−	0.744009i
$4$	1.08601	+	3.84975i	0.271504	+	0.962437i
$5$	0.218413	−	0.815129i	0.0436826	−	0.163026i	−0.940639	−	0.339409i	$-0.889773\pi$
$5$	0.218413	−	0.815129i	0.0436826	−	0.163026i	0.984322	+	0.176383i	$0.0564397\pi$
$6$	0.502363	+	5.97893i	0.0837272	+	0.996489i
$7$	−4.45068	+	7.70881i	−0.635812	+	1.10126i	0.350531	+	0.936551i	$0.386001\pi$
$7$	−4.45068	+	7.70881i	−0.635812	+	1.10126i	−0.986343	+	0.164707i	$0.947332\pi$
$8$	2.91503	−	7.45001i	0.364379	−	0.931251i
$9$	−0.963885	+	8.94824i	−0.107098	+	0.994248i
$10$	−1.33221	+	1.03623i	−0.133221	+	0.103623i
$11$	0.942033	+	3.51572i	0.0856394	+	0.319610i	0.995435	−	0.0954471i	$-0.0304281\pi$
$11$	0.942033	+	3.51572i	0.0856394	+	0.319610i	−0.909795	+	0.415058i	$0.863761\pi$
$12$	6.41582	−	10.1409i	0.534652	−	0.845073i
$13$	5.34198	+	1.43138i	0.410921	+	0.110106i	0.458357	−	0.888768i	$-0.348438\pi$
$13$	5.34198	+	1.43138i	0.410921	+	0.110106i	−0.0474355	+	0.998874i	$0.515105\pi$
$14$	16.4024	−	6.92085i	1.17160	−	0.494346i
$15$	−2.25720	+	1.14643i	−0.150480	+	0.0764287i
$16$	−13.6411	+	8.36176i	−0.852572	+	0.522610i
$17$	20.6891			1.21700			0.608502	−	0.793553i	$-0.291771\pi$
$17$	20.6891			1.21700			0.608502	+	0.793553i	$0.291771\pi$
$18$	12.3381	−	13.1061i	0.685452	−	0.728117i
$19$	1.75266	+	1.75266i	0.0922452	+	0.0922452i	0.751724	−	0.659478i	$-0.229223\pi$
$19$	1.75266	+	1.75266i	0.0922452	+	0.0922452i	−0.659478	+	0.751724i	$0.729223\pi$
$20$	3.37524	−	0.0444055i	0.168762	−	0.00222028i
$21$	26.1277	−	5.51833i	1.24418	−	0.262778i
$22$	2.74144	−	6.74353i	0.124611	−	0.306524i
$23$	10.0379	+	17.3862i	0.436431	+	0.755921i	0.997411	−	0.0719081i	$-0.0229088\pi$
$23$	10.0379	+	17.3862i	0.436431	+	0.755921i	−0.560980	+	0.827829i	$0.689576\pi$
$24$	−22.4718	+	8.42718i	−0.936326	+	0.351132i
$25$	21.0339	+	12.1439i	0.841356	+	0.485757i
$26$	−6.79099	−	8.73068i	−0.261192	−	0.335795i
$27$	21.9048	−	15.7854i	0.811289	−	0.584645i
$28$	−34.5105	−	8.76214i	−1.23252	−	0.312933i
$29$	−3.10032	−	11.5706i	−0.106908	−	0.398985i	0.891647	−	0.452731i	$-0.149550\pi$
$29$	−3.10032	−	11.5706i	−0.106908	−	0.398985i	−0.998555	+	0.0537467i	$0.982884\pi$
$30$	4.98332	+	0.896387i	0.166111	+	0.0298796i
$31$	−53.3631	+	30.8092i	−1.72139	+	0.993846i	−0.805309	+	0.592855i	$0.798001\pi$
$31$	−53.3631	+	30.8092i	−1.72139	+	0.993846i	−0.916082	+	0.400991i	$0.868666\pi$
$32$	31.8464	+	3.13133i	0.995201	+	0.0978541i
$33$	5.95886	−	9.14993i	0.180571	−	0.277270i
$34$	−32.9924	−	24.9729i	−0.970366	−	0.734498i
$35$	5.31158	+	5.31158i	0.151760	+	0.151760i
$36$	−35.4953	+	6.00719i	−0.985979	+	0.166867i
$37$	16.2850	+	16.2850i	0.440134	+	0.440134i	0.892057	−	0.451923i	$-0.149262\pi$
$37$	16.2850	+	16.2850i	0.440134	+	0.440134i	−0.451923	+	0.892057i	$0.649262\pi$
$38$	−0.679367	−	4.91049i	−0.0178781	−	0.129224i
$39$	−7.51317	−	14.7926i	−0.192645	−	0.379299i
$40$	−5.43604	−	4.00331i	−0.135901	−	0.100083i
$41$	−46.5560	+	26.8791i	−1.13551	+	0.655589i	−0.945316	−	0.326157i	$-0.894246\pi$
$41$	−46.5560	+	26.8791i	−1.13551	+	0.655589i	−0.190197	+	0.981746i	$0.560913\pi$
$42$	−48.3263	−	22.7377i	−1.15063	−	0.541374i
$43$	14.0229	+	52.3343i	0.326115	+	1.21708i	0.913187	+	0.407542i	$0.133614\pi$
$43$	14.0229	+	52.3343i	0.326115	+	1.21708i	−0.587072	+	0.809535i	$0.699719\pi$
$44$	−12.5116	+	7.44471i	−0.284354	+	0.169198i
$45$	7.08344	+	2.74010i	0.157410	+	0.0608912i
$46$	4.97889	−	39.8418i	0.108237	−	0.866126i
$47$	−51.7323	−	29.8676i	−1.10069	−	0.635482i	−0.164285	−	0.986413i	$-0.552532\pi$
$47$	−51.7323	−	29.8676i	−1.10069	−	0.635482i	−0.936401	+	0.350931i	$0.885865\pi$
$48$	46.0075	+	13.6862i	0.958489	+	0.285128i
$49$	−15.1171	−	26.1836i	−0.308513	−	0.534360i
$50$	−18.8839	−	44.7549i	−0.377678	−	0.895097i
$51$	−41.4714	−	46.1785i	−0.813165	−	0.905461i
$52$	0.291013	+	22.1198i	0.00559641	+	0.425380i
$53$	20.3405	+	20.3405i	0.383783	+	0.383783i	0.872463	−	0.488680i	$-0.162521\pi$
$53$	20.3405	+	20.3405i	0.383783	+	0.383783i	−0.488680	+	0.872463i	$0.662521\pi$
$54$	−53.9851	−	1.26774i	−0.999724	−	0.0234766i
$55$	3.07151			0.0558457
$56$	44.4568	+	55.6290i	0.793871	+	0.993375i
$57$	0.398760	−	7.42520i	0.00699579	−	0.130267i
$58$	−9.02233	+	22.1936i	−0.155557	+	0.382649i
$59$	−0.602860	−	0.161536i	−0.0102180	−	0.00273789i	0.253706	−	0.967281i	$-0.418350\pi$
$59$	−0.602860	−	0.161536i	−0.0102180	−	0.00273789i	−0.263924	+	0.964543i	$0.585017\pi$
$60$	−6.86482	−	7.44462i	−0.114414	−	0.124077i
$61$	24.9988	+	93.2967i	0.409816	+	1.52945i	0.794997	+	0.606614i	$0.207472\pi$
$61$	24.9988	+	93.2967i	0.409816	+	1.52945i	−0.385181	+	0.922841i	$0.625861\pi$
$62$	122.286	+	15.2816i	1.97235	+	0.246478i
$63$	−64.6903	−	47.2561i	−1.02683	−	0.750098i
$64$	−47.0052	−	43.4340i	−0.734456	−	0.678656i
$65$	2.33352	−	4.04177i	0.0359003	−	0.0621811i
$66$	−20.5470	+	7.39852i	−0.311318	+	0.112099i
$67$	21.0862	−	78.6949i	0.314720	−	1.17455i	−0.609530	−	0.792763i	$-0.708642\pi$
$67$	21.0862	−	78.6949i	0.314720	−	1.17455i	0.924250	−	0.381788i	$-0.124692\pi$
$68$	22.4686	+	79.6477i	0.330421	+	1.17129i
$69$	18.6853	−	57.2557i	0.270802	−	0.829793i
$70$	−2.05888	−	14.8817i	−0.0294126	−	0.212595i
$71$	−12.5158			−0.176279			−0.0881395	−	0.996108i	$-0.528092\pi$
$71$	−12.5158			−0.176279			−0.0881395	+	0.996108i	$0.528092\pi$
$72$	63.8547	+	33.2653i	0.886870	+	0.462019i
$73$		−	57.3042i		−	0.784989i	−0.919754	−	0.392494i	$-0.871612\pi$
$73$		−	57.3042i		−	0.784989i	0.919754	−	0.392494i	$-0.128388\pi$
$74$	−6.31240	−	45.6262i	−0.0853026	−	0.616571i
$75$	−15.0571	−	71.2909i	−0.200761	−	0.950545i
$76$	−4.84388	+	8.65071i	−0.0637353	+	0.113825i
$77$	−31.2947	−	8.38538i	−0.406424	−	0.108901i
$78$	−5.87450	+	32.6584i	−0.0753141	+	0.418697i
$79$	54.9768	+	31.7408i	0.695908	+	0.401783i	0.805822	−	0.592158i	$-0.201724\pi$
$79$	54.9768	+	31.7408i	0.695908	+	0.401783i	−0.109913	+	0.993941i	$0.535057\pi$
$80$	3.83651	+	12.9456i	0.0479564	+	0.161820i
$81$	−79.1419	−	17.2501i	−0.977060	−	0.212965i
$82$	106.687	+	13.3323i	1.30106	+	0.162589i
$83$	30.4664	−	8.16345i	0.367065	−	0.0983549i	−0.0705714	−	0.997507i	$-0.522482\pi$
$83$	30.4664	−	8.16345i	0.367065	−	0.0983549i	0.437637	+	0.899152i	$0.355816\pi$
$84$	49.6193	+	94.5921i	0.590705	+	1.12610i
$85$	4.51876	−	16.8642i	0.0531619	−	0.198403i
$86$	40.8085	−	100.383i	0.474517	−	1.16724i
$87$	−19.6112	+	30.1133i	−0.225416	+	0.346130i
$88$	28.9382	+	3.23027i	0.328843	+	0.0367076i
$89$			91.2611i			1.02541i	0.858566	+	0.512703i	$0.171356\pi$
$89$			91.2611i			1.02541i	−0.858566	+	0.512703i	$0.828644\pi$
$90$	−7.98836	−	12.9197i	−0.0887596	−	0.143553i
$91$	−34.8097	+	34.8097i	−0.382524	+	0.382524i
$92$	−56.0312	+	57.5251i	−0.609034	+	0.625273i
$93$	175.734	+	57.3506i	1.88961	+	0.616673i
$94$	46.4444	+	110.073i	0.494090	+	1.17099i
$95$	1.81145	−	1.04584i	0.0190679	−	0.0110088i
$96$	−56.8472	−	77.3588i	−0.592159	−	0.805821i
$97$	43.8910	−	76.0214i	0.452485	−	0.783726i	−0.546055	−	0.837749i	$-0.683871\pi$
$97$	43.8910	−	76.0214i	0.452485	−	0.783726i	0.998540	+	0.0540230i	$0.0172044\pi$
$98$	−7.49821	+	60.0018i	−0.0765124	+	0.612264i
$99$	−32.3675	+	5.04079i	−0.326944	+	0.0509171i
$100$	−23.9080	+	94.1637i	−0.239080	+	0.941637i
$101$	−133.354	+	35.7321i	−1.32034	+	0.353783i	−0.849104	−	0.528226i	$-0.822857\pi$
$101$	−133.354	+	35.7321i	−1.32034	+	0.353783i	−0.471232	+	0.882009i	$0.656191\pi$
$102$	10.3934	+	123.698i	0.101896	+	1.21273i
$103$	55.5021	+	96.1324i	0.538855	+	0.933324i	0.998966	+	0.0454630i	$0.0144763\pi$
$103$	55.5021	+	96.1324i	0.538855	+	0.933324i	−0.460111	+	0.887861i	$0.652190\pi$
$104$	26.2358	−	35.6252i	0.252267	−	0.342550i
$105$	1.20848	−	22.5027i	0.0115093	−	0.214312i
$106$	−7.88441	−	56.9888i	−0.0743812	−	0.537630i
$107$	39.5903	−	39.5903i	0.370002	−	0.370002i	−0.497476	−	0.867478i	$-0.665740\pi$
$107$	39.5903	−	39.5903i	0.370002	−	0.370002i	0.867478	+	0.497476i	$0.165740\pi$
$108$	84.5588	+	67.1849i	0.782952	+	0.622082i
$109$	74.5749	−	74.5749i	0.684173	−	0.684173i	−0.276764	−	0.960938i	$-0.589262\pi$
$109$	74.5749	−	74.5749i	0.684173	−	0.684173i	0.960938	+	0.276764i	$0.0892621\pi$
$110$	−4.89808	−	3.70750i	−0.0445280	−	0.0337046i
$111$	3.70511	−	68.9918i	0.0333794	−	0.621548i
$112$	−3.74683	−	142.373i	−0.0334538	−	1.27118i
$113$	−75.5922	−	130.930i	−0.668958	−	1.15867i	−0.978196	−	0.207684i	$-0.933407\pi$
$113$	−75.5922	−	130.930i	−0.668958	−	1.15867i	0.309238	−	0.950985i	$-0.399926\pi$
$114$	−9.59855	+	11.3595i	−0.0841978	+	0.0996447i
$115$	16.3644	−	4.38483i	0.142299	−	0.0381289i
$116$	41.1767	−	24.5012i	0.354972	−	0.211218i
$117$	−17.9574	+	46.4216i	−0.153482	+	0.396766i
$118$	0.766386	+	0.985286i	0.00649479	+	0.00834988i
$119$	−92.0804	+	159.488i	−0.773785	+	1.34023i
$120$	1.96110	+	20.1580i	0.0163425	+	0.167984i
$121$	93.3162	−	53.8762i	0.771209	−	0.445258i
$122$	72.7496	−	178.954i	0.596309	−	1.46683i
$123$	153.317	+	50.0348i	1.24648	+	0.406787i
$124$	−176.561	−	171.975i	−1.42388	−	1.38690i
$125$	29.4109	−	29.4109i	0.235287	−	0.235287i
$126$	46.1193	+	153.443i	0.366027	+	1.21781i
$127$			109.275i			0.860432i	0.902726	+	0.430216i	$0.141563\pi$
$127$			109.275i			0.860432i	−0.902726	+	0.430216i	$0.858437\pi$
$128$	22.5308	+	126.001i	0.176022	+	0.984386i
$129$	88.7024	−	136.204i	0.687616	−	1.05585i
$130$	−8.59987	+	3.62864i	−0.0661528	+	0.0279126i
$131$	63.1083	−	235.523i	0.481743	−	1.79789i	−0.112557	−	0.993645i	$-0.535904\pi$
$131$	63.1083	−	235.523i	0.481743	−	1.79789i	0.594300	−	0.804244i	$-0.297429\pi$
$132$	41.6963	+	13.0032i	0.315881	+	0.0985087i
$133$	−21.3114	+	5.71038i	−0.160236	+	0.0429352i
$134$	−128.615	+	100.041i	−0.959816	+	0.746574i
$135$	−8.08284	−	21.3030i	−0.0598729	−	0.157800i
$136$	60.3092	−	154.134i	0.443450	−	1.13334i
$137$	−127.949	−	73.8716i	−0.933937	−	0.539209i	−0.0458824	−	0.998947i	$-0.514610\pi$
$137$	−127.949	−	73.8716i	−0.933937	−	0.539209i	−0.888055	+	0.459738i	$0.847943\pi$
$138$	−98.9082	+	68.7502i	−0.716726	+	0.498190i
$139$	−239.525	−	64.1805i	−1.72320	−	0.461730i	−0.744602	−	0.667508i	$-0.767361\pi$
$139$	−239.525	−	64.1805i	−1.72320	−	0.461730i	−0.978599	+	0.205778i	$0.934027\pi$
$140$	−14.6798	+	26.2167i	−0.104856	+	0.187262i
$141$	37.0324	+	175.338i	0.262641	+	1.24353i
$142$	19.9587	+	15.1073i	0.140554	+	0.106390i
$143$			20.1293i			0.140764i
$144$	−61.6745	−	130.124i	−0.428295	−	0.903639i
$145$	−10.1086			−0.0697148
$146$	−69.1695	+	91.3819i	−0.473764	+	0.625903i
$147$	−28.1401	+	86.2272i	−0.191430	+	0.586579i
$148$	−45.0073	+	80.3787i	−0.304104	+	0.543099i
$149$	−47.0833	+	175.717i	−0.315995	+	1.17931i	0.607064	+	0.794653i	$0.292347\pi$
$149$	−47.0833	+	175.717i	−0.315995	+	1.17931i	−0.923059	+	0.384657i	$0.874320\pi$
$150$	−62.0411	+	131.861i	−0.413607	+	0.879073i
$151$	33.2984	−	57.6745i	0.220519	−	0.381951i	−0.734446	−	0.678667i	$-0.762558\pi$
$151$	33.2984	−	57.6745i	0.220519	−	0.381951i	0.954966	+	0.296716i	$0.0958915\pi$
$152$	18.1664	−	7.94826i	0.119516	−	0.0522912i
$153$	−19.9419	+	185.131i	−0.130339	+	1.21000i
$154$	39.7833	+	51.1465i	0.258333	+	0.332120i
$155$	13.4583	+	50.2270i	0.0868276	+	0.324045i
$156$	48.7886	−	44.9888i	0.312747	−	0.288390i
$157$	−68.4158	−	18.3320i	−0.435770	−	0.116764i	0.0342637	−	0.999413i	$-0.489091\pi$
$157$	−68.4158	−	18.3320i	−0.435770	−	0.116764i	−0.470033	+	0.882649i	$0.655758\pi$
$158$	−49.3573	−	116.977i	−0.312388	−	0.740359i
$159$	4.62781	−	86.1732i	0.0291057	−	0.541970i
$160$	9.50812	−	25.2750i	0.0594257	−	0.157969i
$161$	−178.702			−1.10995
$162$	105.384	+	123.037i	0.650519	+	0.759490i
$163$	73.3398	+	73.3398i	0.449938	+	0.449938i	0.895334	−	0.445396i	$-0.146937\pi$
$163$	73.3398	+	73.3398i	0.449938	+	0.449938i	−0.445396	+	0.895334i	$0.646937\pi$
$164$	−154.038	−	150.038i	−0.939259	−	0.914865i
$165$	−6.15688	−	6.85570i	−0.0373144	−	0.0415497i
$166$	−58.4380	−	23.7567i	−0.352036	−	0.143113i
$167$	−39.9632	−	69.2182i	−0.239300	−	0.414480i	0.721213	−	0.692713i	$-0.243585\pi$
$167$	−39.9632	−	69.2182i	−0.239300	−	0.414480i	−0.960514	+	0.278233i	$0.910251\pi$
$168$	35.0514	−	210.738i	0.208639	−	1.25439i
$169$	−119.870	−	69.2072i	−0.709292	−	0.409510i
$170$	−27.5621	+	21.4387i	−0.162130	+	0.126110i
$171$	−17.3726	+	13.9938i	−0.101594	+	0.0818353i
$172$	−186.245	+	110.821i	−1.08282	+	0.644305i
$173$	−74.1988	−	276.914i	−0.428895	−	1.60066i	−0.755268	−	0.655416i	$-0.772493\pi$
$173$	−74.1988	−	276.914i	−0.428895	−	1.60066i	0.326373	−	0.945241i	$-0.394173\pi$
$174$	67.6221	−	24.3492i	0.388633	−	0.139938i
$175$	−187.230	+	108.098i	−1.06989	+	0.617700i
$176$	−42.2480	−	40.0813i	−0.240045	−	0.227735i
$177$	0.847886	+	1.66940i	0.00479031	+	0.00943163i
$178$	110.158	−	145.532i	0.618863	−	0.817598i
$179$	130.811	+	130.811i	0.730786	+	0.730786i	0.970775	−	0.239990i	$-0.0771441\pi$
$179$	130.811	+	130.811i	0.730786	+	0.730786i	−0.239990	+	0.970775i	$0.577144\pi$
$180$	−2.85599	+	30.2453i	−0.0158666	+	0.168029i
$181$	28.5332	+	28.5332i	0.157642	+	0.157642i	0.781521	−	0.623879i	$-0.214444\pi$
$181$	28.5332	+	28.5332i	0.157642	+	0.157642i	−0.623879	+	0.781521i	$0.714444\pi$
$182$	97.5276	−	13.4930i	0.535866	−	0.0741372i
$183$	158.130	−	242.812i	0.864101	−	1.32684i
$184$	158.788	−	24.1013i	0.862979	−	0.130985i
$185$	16.8312	−	9.71749i	0.0909794	−	0.0525270i
$186$	−211.014	−	303.577i	−1.13448	−	1.63214i
$187$	19.4898	+	72.7368i	0.104223	+	0.388967i
$188$	58.8010	−	231.593i	0.312771	−	1.23188i
$189$	24.1953	+	239.116i	0.128017	+	1.26516i
$190$	−4.15107	−	0.518744i	−0.0218477	−	0.00273023i
$191$	257.951	+	148.928i	1.35053	+	0.779728i	0.988323	−	0.152371i	$-0.0486908\pi$
$191$	257.951	+	148.928i	1.35053	+	0.779728i	0.362205	+	0.932099i	$0.382024\pi$
$192$	−2.72354	+	191.981i	−0.0141851	+	0.999899i
$193$	93.1671	+	161.370i	0.482731	+	0.836115i	0.999803	−	0.0198268i	$-0.00631147\pi$
$193$	93.1671	+	161.370i	0.482731	+	0.836115i	−0.517072	+	0.855942i	$0.672978\pi$
$194$	−161.755	+	68.2509i	−0.833786	+	0.351809i
$195$	−13.6989	+	2.89329i	−0.0702507	+	0.0148374i
$196$	84.3830	−	86.6330i	0.430526	−	0.442005i
$197$	−88.5177	−	88.5177i	−0.449329	−	0.449329i	0.445803	−	0.895131i	$-0.352918\pi$
$197$	−88.5177	−	88.5177i	−0.449329	−	0.449329i	−0.895131	+	0.445803i	$0.852918\pi$
$198$	57.7003	+	31.0310i	0.291416	+	0.156722i
$199$	285.686			1.43561			0.717804	−	0.696245i	$-0.245147\pi$
$199$	285.686			1.43561			0.717804	+	0.696245i	$0.245147\pi$
$200$	151.787	−	121.303i	0.758934	−	0.606514i
$201$	−217.917	+	110.680i	−1.08416	+	0.550645i
$202$	255.788	+	103.985i	1.26628	+	0.514777i
$203$	102.994	+	27.5971i	0.507358	+	0.135946i
$204$	132.737	−	209.805i	0.650673	−	1.02846i
$205$	11.7415	+	43.8199i	0.0572757	+	0.213756i
$206$	27.5295	−	220.295i	0.133638	−	1.06939i
$207$	−165.251	+	73.0634i	−0.798315	+	0.352963i
$208$	−84.8395	+	25.1427i	−0.407882	+	0.120878i
$209$	−4.51078	+	7.81291i	−0.0215827	+	0.0373823i
$210$	−29.0893	+	34.4260i	−0.138520	+	0.163933i
$211$	34.1510	−	127.453i	0.161853	−	0.604044i	−0.836567	−	0.547864i	$-0.815441\pi$
$211$	34.1510	−	127.453i	0.161853	−	0.604044i	0.998421	−	0.0561804i	$-0.0178922\pi$
$212$	−56.2157	+	100.396i	−0.265169	+	0.473565i
$213$	25.0880	+	27.9356i	0.117784	+	0.131153i
$214$	−110.922	+	15.3460i	−0.518325	+	0.0717104i
$215$	45.7220			0.212660
$216$	−53.7481	−	209.206i	−0.248834	−	0.968546i
$217$		−	548.488i		−	2.52759i
$218$	−208.940	+	28.9068i	−0.958438	+	0.132600i
$219$	−127.904	+	114.867i	−0.584038	+	0.524506i
$220$	3.33571	+	11.8246i	0.0151623	+	0.0537480i
$221$	110.520	+	29.6139i	0.500093	+	0.133999i
$222$	−89.1857	+	105.548i	−0.401737	+	0.475440i
$223$	123.555	+	71.3344i	0.554058	+	0.319885i	0.750757	−	0.660579i	$-0.229689\pi$
$223$	123.555	+	71.3344i	0.554058	+	0.319885i	−0.196699	+	0.980464i	$0.563022\pi$
$224$	−165.877	+	231.561i	−0.740523	+	1.03376i
$225$	−128.941	+	176.511i	−0.573071	+	0.784493i
$226$	−37.4943	+	300.035i	−0.165904	+	1.32759i
$227$	396.749	−	106.309i	1.74779	−	0.468320i	0.763641	−	0.645641i	$-0.223410\pi$
$227$	396.749	−	106.309i	1.74779	−	0.468320i	0.984153	+	0.177321i	$0.0567430\pi$
$228$	29.0182	−	6.52874i	0.127273	−	0.0286348i
$229$	32.3428	−	120.705i	0.141235	−	0.527096i	−0.858659	−	0.512547i	$-0.828702\pi$
$229$	32.3428	−	120.705i	0.141235	−	0.527096i	0.999894	−	0.0145490i	$-0.00463125\pi$
$230$	−31.3888	−	12.7604i	−0.136473	−	0.0554800i
$231$	44.0140	+	86.6591i	0.190537	+	0.375147i
$232$	−95.2382	−	10.6311i	−0.410510	−	0.0458238i
$233$			340.229i			1.46021i	0.683336	+	0.730104i	$0.260529\pi$
$233$			340.229i			1.46021i	−0.683336	+	0.730104i	$0.739471\pi$
$234$	84.6699	−	52.3520i	0.361837	−	0.223727i
$235$	−35.6450	+	35.6450i	−0.151681	+	0.151681i
$236$	−0.0328418	−	2.49629i	−0.000139160	−	0.0105775i
$237$	−39.3550	−	186.334i	−0.166055	−	0.786221i
$238$	339.350	−	143.186i	1.42584	−	0.601621i
$239$	−3.02761	+	1.74799i	−0.0126678	+	0.00731378i	−0.506321	−	0.862345i	$-0.668995\pi$
$239$	−3.02761	+	1.74799i	−0.0126678	+	0.00731378i	0.493653	+	0.869659i	$0.335661\pi$
$240$	21.2046	−	34.5128i	0.0883526	−	0.143803i
$241$	−71.2903	+	123.478i	−0.295810	+	0.512359i	−0.975173	−	0.221444i	$-0.928923\pi$
$241$	−71.2903	+	123.478i	−0.295810	+	0.512359i	0.679363	+	0.733803i	$0.262256\pi$
$242$	−213.841	−	26.7230i	−0.883642	−	0.110426i
$243$	120.138	+	211.225i	0.494394	+	0.869238i
$244$	−332.020	+	197.561i	−1.36074	+	0.809675i
$245$	−24.6448	+	6.60356i	−0.100591	+	0.0269533i
$246$	−184.097	−	264.852i	−0.748360	−	1.07664i
$247$	6.85394	+	11.8714i	0.0277488	+	0.0480623i
$248$	73.9736	+	487.366i	0.298281	+	1.96518i
$249$	−79.2913	−	51.6381i	−0.318439	−	0.207382i
$250$	−82.4016	+	11.4003i	−0.329606	+	0.0456011i
$251$	238.301	−	238.301i	0.949405	−	0.949405i	−0.0493749	−	0.998780i	$-0.515723\pi$
$251$	238.301	−	238.301i	0.949405	−	0.949405i	0.998780	+	0.0493749i	$0.0157229\pi$
$252$	111.670	−	300.362i	0.443134	−	1.19191i
$253$	−51.6688	+	51.6688i	−0.204225	+	0.204225i
$254$	131.901	−	174.259i	0.519297	−	0.686057i
$255$	−46.6994	+	23.7185i	−0.183135	+	0.0930139i
$256$	116.162	−	228.128i	0.453757	−	0.891125i
$257$	227.652	+	394.305i	0.885807	+	1.53426i	0.844786	+	0.535104i	$0.179728\pi$
$257$	227.652	+	394.305i	0.885807	+	1.53426i	0.0410206	+	0.999158i	$0.486939\pi$
$258$	−305.858	+	110.133i	−1.18550	+	0.426872i
$259$	−198.017	+	53.0584i	−0.764543	+	0.204859i
$260$	18.0940	+	4.59404i	0.0695924	+	0.0176694i
$261$	106.524	−	16.5897i	0.408139	−	0.0635621i
$262$	−384.928	+	299.409i	−1.46919	+	1.14278i
$263$	−189.300	+	327.878i	−0.719774	+	1.24668i	0.241316	+	0.970447i	$0.422421\pi$
$263$	−189.300	+	327.878i	−0.719774	+	1.24668i	−0.961089	+	0.276238i	$0.910912\pi$
$264$	−50.7968	−	71.0658i	−0.192412	−	0.269189i
$265$	21.0228	−	12.1375i	0.0793312	−	0.0458019i
$266$	40.8777	+	16.6179i	0.153676	+	0.0624734i
$267$	203.697	−	182.934i	0.762911	−	0.685145i
$268$	325.856	−	4.28704i	1.21588	−	0.0159964i
$269$	−65.2291	+	65.2291i	−0.242487	+	0.242487i	−0.817878	−	0.575391i	$-0.804850\pi$
$269$	−65.2291	+	65.2291i	−0.242487	+	0.242487i	0.575391	+	0.817878i	$0.304850\pi$
$270$	−12.8244	+	43.7279i	−0.0474979	+	0.161955i
$271$		−	32.8303i		−	0.121145i	−0.998164	−	0.0605726i	$-0.980707\pi$
$271$		−	32.8303i		−	0.121145i	0.998164	−	0.0605726i	$-0.0192927\pi$
$272$	−282.222	+	172.997i	−1.03758	+	0.636018i
$273$	147.472	+	7.91980i	0.540192	+	0.0290102i
$274$	114.871	+	272.244i	0.419237	+	0.993592i
$275$	−22.8800	+	85.3892i	−0.0831999	+	0.310506i
$276$	240.713	+	9.75337i	0.872147	+	0.0353383i
$277$	−287.712	+	77.0922i	−1.03867	+	0.278311i	−0.737563	−	0.675279i	$-0.764023\pi$
$277$	−287.712	+	77.0922i	−1.03867	+	0.278311i	−0.301109	+	0.953590i	$0.597357\pi$
$278$	304.496	+	391.468i	1.09531	+	1.40816i
$279$	−224.252	−	507.202i	−0.803771	−	1.81793i
$280$	55.0548	−	24.0879i	0.196624	−	0.0860282i
$281$	356.444	+	205.793i	1.26849	+	0.732361i	0.974701	−	0.223511i	$-0.0717519\pi$
$281$	356.444	+	205.793i	1.26849	+	0.732361i	0.293784	+	0.955872i	$0.405085\pi$
$282$	152.588	−	324.308i	0.541093	−	1.15003i
$283$	−28.4490	−	7.62288i	−0.100526	−	0.0269360i	0.208205	−	0.978085i	$-0.433238\pi$
$283$	−28.4490	−	7.62288i	−0.100526	−	0.0269360i	−0.308732	+	0.951149i	$0.599904\pi$
$284$	−13.5923	−	48.1827i	−0.0478603	−	0.169657i
$285$	−5.96540	−	1.94680i	−0.0209312	−	0.00683088i
$286$	24.2972	−	32.0998i	0.0849554	−	0.112237i
$287$		−	478.522i		−	1.66732i
$288$	−58.7162	+	281.951i	−0.203876	+	0.978997i
$289$	139.037			0.481097
$290$	16.1201	+	12.2017i	0.0555864	+	0.0420750i
$291$	−257.662	+	54.4198i	−0.885436	+	0.187010i
$292$	220.607	−	62.2331i	0.755502	−	0.213127i
$293$	56.5707	−	211.125i	0.193074	−	0.720562i	−0.799683	−	0.600422i	$-0.794999\pi$
$293$	56.5707	−	211.125i	0.193074	−	0.720562i	0.992757	−	0.120140i	$-0.0383342\pi$
$294$	148.956	−	103.538i	0.506653	−	0.352170i
$295$	−0.263345	+	0.456127i	−0.000892695	+	0.00154619i
$296$	168.794	−	73.8519i	0.570251	−	0.249500i
$297$	76.1320	+	62.1407i	0.256337	+	0.209228i
$298$	287.184	−	223.381i	0.963704	−	0.749599i
$299$	28.7361	+	107.245i	0.0961075	+	0.358678i
$300$	258.100	−	135.389i	0.860332	−	0.451296i
$301$	−465.846	−	124.823i	−1.54766	−	0.414695i
$302$	−122.717	+	51.7793i	−0.406348	+	0.171455i
$303$	347.064	+	226.024i	1.14543	+	0.745955i
$304$	−38.5636	−	9.25295i	−0.126854	−	0.0304373i
$305$	81.5089			0.267242
$306$	255.265	−	271.153i	0.834198	−	0.886121i
$307$	−383.829	−	383.829i	−1.25026	−	1.25026i	−0.955605	−	0.294652i	$-0.904796\pi$
$307$	−383.829	−	383.829i	−1.25026	−	1.25026i	−0.294652	−	0.955605i	$-0.595204\pi$
$308$	−1.70483	−	129.583i	−0.00553516	−	0.420725i
$309$	103.316	−	316.580i	0.334355	−	1.02453i
$310$	39.1653	−	96.3410i	0.126340	−	0.310777i
$311$	−35.7349	−	61.8947i	−0.114903	−	0.199018i	0.802838	−	0.596198i	$-0.203322\pi$
$311$	−35.7349	−	61.8947i	−0.114903	−	0.199018i	−0.917741	+	0.397179i	$0.869989\pi$
$312$	−132.106	+	12.8521i	−0.423418	+	0.0411927i
$313$	150.144	+	86.6859i	0.479695	+	0.276952i	0.720289	−	0.693674i	$-0.244009\pi$
$313$	150.144	+	86.6859i	0.479695	+	0.276952i	−0.240595	+	0.970626i	$0.577342\pi$
$314$	86.9736	+	111.816i	0.276986	+	0.356101i
$315$	−52.6491	+	42.4096i	−0.167140	+	0.134634i
$316$	−62.4888	+	246.118i	−0.197749	+	0.778854i
$317$	−130.260	−	486.137i	−0.410915	−	1.53355i	−0.792880	−	0.609378i	$-0.791419\pi$
$317$	−130.260	−	486.137i	−0.410915	−	1.53355i	0.381965	−	0.924177i	$-0.375247\pi$
$318$	−111.396	+	131.833i	−0.350302	+	0.414568i
$319$	37.7582	−	21.7997i	0.118364	−	0.0683376i
$320$	−45.6709	+	28.8287i	−0.142721	+	0.0900898i
$321$	−167.726	−	9.00747i	−0.522510	−	0.0280606i
$322$	284.973	+	215.704i	0.885010	+	0.669889i
$323$	36.2608	+	36.2608i	0.112263	+	0.112263i
$324$	−19.5404	−	323.410i	−0.0603100	−	0.998180i
$325$	94.9801	+	94.9801i	0.292246	+	0.292246i
$326$	−28.4281	−	205.479i	−0.0872027	−	0.630304i
$327$	−315.939	−	16.9671i	−0.966175	−	0.0518871i
$328$	64.5374	+	425.196i	0.196760	+	1.29633i
$329$	460.488	−	265.863i	1.39966	−	0.808093i
$330$	1.54302	+	18.3644i	0.00467581	+	0.0556496i
$331$	83.8273	+	312.848i	0.253255	+	0.945160i	0.969053	+	0.246853i	$0.0793963\pi$
$331$	83.8273	+	312.848i	0.253255	+	0.945160i	−0.715798	+	0.698307i	$0.753937\pi$
$332$	64.5142	+	108.422i	0.194320	+	0.326574i
$333$	−161.418	+	130.025i	−0.484740	+	0.390465i
$334$	−19.8220	+	158.619i	−0.0593474	+	0.474907i
$335$	−59.5410	−	34.3760i	−0.177734	−	0.102615i
$336$	−310.269	+	293.750i	−0.923419	+	0.874256i
$337$	−72.9816	−	126.408i	−0.216563	−	0.375098i	0.737192	−	0.675683i	$-0.236151\pi$
$337$	−72.9816	−	126.408i	−0.216563	−	0.375098i	−0.953755	+	0.300586i	$0.902818\pi$
$338$	107.618	+	255.054i	0.318396	+	0.754598i
$339$	−140.713	+	431.174i	−0.415083	+	1.27190i
$340$	69.8306	−	0.918709i	0.205384	−	0.00270208i
$341$	−158.586	−	158.586i	−0.465062	−	0.465062i
$342$	44.5951	−	1.34599i	0.130395	−	0.00393564i
$343$	−167.041			−0.486999
$344$	430.768	+	48.0852i	1.25223	+	0.139783i
$345$	−42.5897	−	27.7364i	−0.123448	−	0.0803952i
$346$	−215.928	+	531.151i	−0.624069	+	1.53512i
$347$	−403.536	−	108.127i	−1.16293	−	0.311605i	−0.374792	−	0.927109i	$-0.622286\pi$
$347$	−403.536	−	108.127i	−1.16293	−	0.311605i	−0.788134	+	0.615504i	$0.788953\pi$
$348$	−137.227	−	42.7946i	−0.394329	−	0.122973i
$349$	−10.4683	−	39.0684i	−0.0299952	−	0.111944i	0.949305	−	0.314356i	$-0.101789\pi$
$349$	−10.4683	−	39.0684i	−0.0299952	−	0.111944i	−0.979300	+	0.202412i	$0.935122\pi$
$350$	429.053	+	53.6172i	1.22587	+	0.153192i
$351$	139.610	−	52.9712i	0.397749	−	0.150915i
$352$	18.9915	+	114.913i	0.0539532	+	0.326457i
$353$	76.7780	−	132.983i	0.217501	−	0.376723i	−0.736542	−	0.676392i	$-0.763543\pi$
$353$	76.7780	−	132.983i	0.217501	−	0.376723i	0.954043	+	0.299668i	$0.0968760\pi$
$354$	0.662957	−	3.68561i	0.00187276	−	0.0104113i
$355$	−2.73362	+	10.2020i	−0.00770033	+	0.0287380i
$356$	−351.333	+	99.1109i	−0.986889	+	0.278401i
$357$	540.557	−	114.169i	1.51417	−	0.319801i
$358$	−50.7050	−	366.497i	−0.141634	−	1.02374i
$359$	−167.258			−0.465898			−0.232949	−	0.972489i	$-0.574838\pi$
$359$	−167.258			−0.465898			−0.232949	+	0.972489i	$0.574838\pi$
$360$	41.0622	−	44.7842i	0.114062	−	0.124401i
$361$		−	354.856i		−	0.982982i
$362$	−11.0601	−	79.9427i	−0.0305527	−	0.220836i
$363$	−307.306	−	100.289i	−0.846574	−	0.276278i
$364$	−171.812	−	96.2047i	−0.472012	−	0.264299i
$365$	−46.7103	−	12.5160i	−0.127973	−	0.0342904i
$366$	−545.256	+	196.335i	−1.48977	+	0.536434i
$367$	−522.360	−	301.585i	−1.42332	−	0.821757i	−0.426743	−	0.904373i	$-0.640339\pi$
$367$	−522.360	−	301.585i	−1.42332	−	0.821757i	−0.996581	+	0.0826158i	$0.973673\pi$
$368$	−282.308	−	153.233i	−0.767141	−	0.416394i
$369$	−195.646	−	442.503i	−0.530206	−	1.19919i
$370$	−38.5700	−	4.81995i	−0.104243	−	0.0130269i
$371$	−247.330	+	66.2719i	−0.666658	+	0.178630i
$372$	−29.9358	+	738.815i	−0.0804727	+	1.98606i
$373$	−65.6128	+	244.870i	−0.175906	+	0.656489i	0.820490	+	0.571661i	$0.193701\pi$
$373$	−65.6128	+	244.870i	−0.175906	+	0.656489i	−0.996396	+	0.0848279i	$0.972966\pi$
$374$	56.7177	−	139.517i	0.151652	−	0.373041i
$375$	−124.600	−	6.69148i	−0.332267	−	0.0178439i
$376$	−373.315	+	298.341i	−0.992860	+	0.793459i
$377$		−	66.2474i		−	0.175722i
$378$	250.043	−	410.519i	0.661490	−	1.08603i
$379$	294.019	−	294.019i	0.775775	−	0.775775i	−0.203335	−	0.979109i	$-0.565178\pi$
$379$	294.019	−	294.019i	0.775775	−	0.775775i	0.979109	+	0.203335i	$0.0651779\pi$
$380$	5.99347	+	5.83782i	0.0157723	+	0.0153627i
$381$	243.904	−	219.043i	0.640169	−	0.574915i
$382$	−231.584	−	548.855i	−0.606242	−	1.43679i
$383$	245.435	−	141.702i	0.640823	−	0.369980i	−0.144108	−	0.989562i	$-0.546031\pi$
$383$	245.435	−	141.702i	0.640823	−	0.369980i	0.784932	+	0.619582i	$0.212698\pi$
$384$	236.075	−	302.860i	0.614779	−	0.788699i
$385$	−13.6703	+	23.6777i	−0.0355074	+	0.0615005i
$386$	46.2116	−	369.792i	0.119719	−	0.958011i
$387$	−481.816	+	75.0362i	−1.24500	+	0.193892i
$388$	340.330	+	86.4090i	0.877139	+	0.222704i
$389$	230.319	−	61.7139i	0.592080	−	0.158647i	0.0496765	−	0.998765i	$-0.484181\pi$
$389$	230.319	−	61.7139i	0.592080	−	0.158647i	0.542404	+	0.840118i	$0.317514\pi$
$390$	25.3377	+	11.9215i	0.0649686	+	0.0305679i
$391$	207.675	+	359.704i	0.531138	+	0.919959i
$392$	−239.135	+	36.2966i	−0.610039	+	0.0925933i
$393$	−652.196	+	331.250i	−1.65953	+	0.842874i
$394$	34.3114	+	248.004i	0.0870847	+	0.629451i
$395$	37.8805	−	37.8805i	0.0959001	−	0.0959001i
$396$	−54.5573	−	119.132i	−0.137771	−	0.300839i
$397$	−311.353	+	311.353i	−0.784265	+	0.784265i	−0.980547	−	0.196282i	$-0.937113\pi$
$397$	−311.353	+	311.353i	−0.784265	+	0.784265i	0.196282	+	0.980547i	$0.437113\pi$
$398$	−455.578	−	344.840i	−1.14467	−	0.866432i
$399$	55.4647	+	36.1212i	0.139009	+	0.0905292i
$400$	−388.471	+	10.2234i	−0.971178	+	0.0255586i
$401$	155.020	+	268.503i	0.386585	+	0.669584i	0.991988	−	0.126335i	$-0.0403214\pi$
$401$	155.020	+	268.503i	0.386585	+	0.669584i	−0.605403	+	0.795919i	$0.706988\pi$
$402$	481.105	+	86.5398i	1.19678	+	0.215273i
$403$	−329.164	+	88.1993i	−0.816785	+	0.218857i
$404$	−282.384	−	474.574i	−0.698970	−	1.17469i
$405$	−31.3467	+	60.7432i	−0.0773993	+	0.149983i
$406$	−130.931	−	168.328i	−0.322490	−	0.414601i
$407$	−41.9123	+	72.5942i	−0.102979	+	0.178364i
$408$	−464.921	+	174.350i	−1.13951	+	0.427329i
$409$	−1.96843	+	1.13647i	−0.00481279	+	0.00277867i	−0.502404	−	0.864633i	$-0.667551\pi$
$409$	−1.96843	+	1.13647i	−0.00481279	+	0.00277867i	0.497592	+	0.867411i	$0.334218\pi$
$410$	34.1693	−	84.0515i	0.0833397	−	0.205004i
$411$	91.5923	+	433.663i	0.222852	+	1.05514i
$412$	−309.810	+	318.070i	−0.751965	+	0.772015i
$413$	3.92838	−	3.92838i	0.00951183	−	0.00951183i
$414$	351.715	+	82.9552i	0.849552	+	0.200375i
$415$		−	26.6171i		−	0.0641375i
$416$	165.641	+	62.3118i	0.398175	+	0.149788i
$417$	336.877	+	663.276i	0.807859	+	1.59059i
$418$	16.6239	−	7.01431i	0.0397701	−	0.0167806i
$419$	−69.6605	+	259.977i	−0.166254	+	0.620469i	0.831623	+	0.555341i	$0.187412\pi$
$419$	−69.6605	+	259.977i	−0.166254	+	0.620469i	−0.997877	+	0.0651281i	$0.979254\pi$
$420$	87.9423	−	19.7859i	0.209386	−	0.0471094i
$421$	312.830	−	83.8227i	0.743065	−	0.199104i	0.132625	−	0.991166i	$-0.457659\pi$
$421$	312.830	−	83.8227i	0.743065	−	0.199104i	0.610440	+	0.792063i	$0.290993\pi$
$422$	−208.304	+	162.025i	−0.493611	+	0.383946i
$423$	317.127	−	434.123i	0.749708	−	1.02630i
$424$	210.830	−	92.2436i	0.497240	−	0.217556i
$425$	435.172	+	251.246i	1.02393	+	0.591168i
$426$	−6.28748	−	74.8311i	−0.0147593	−	0.175660i
$427$	−830.468	−	222.523i	−1.94489	−	0.521132i
$428$	195.408	+	109.417i	0.456561	+	0.255647i
$429$	44.9291	−	40.3493i	0.104730	−	0.0940544i
$430$	−72.9120	−	55.1892i	−0.169563	−	0.128347i
$431$		−	129.427i		−	0.300295i	−0.988664	−	0.150148i	$-0.952025\pi$
$431$		−	129.427i		−	0.300295i	0.988664	−	0.150148i	$-0.0479749\pi$
$432$	−166.813	+	398.494i	−0.386141	+	0.922440i
$433$	264.692			0.611299			0.305649	−	0.952144i	$-0.401127\pi$
$433$	264.692			0.611299			0.305649	+	0.952144i	$0.401127\pi$
$434$	−662.058	+	874.663i	−1.52548	+	2.01535i
$435$	20.2629	+	22.5628i	0.0465813	+	0.0518684i
$436$	368.084	+	206.105i	0.844230	+	0.472719i
$437$	−12.8790	+	48.0651i	−0.0294714	+	0.109989i
$438$	342.618	−	28.7875i	0.782232	−	0.0657249i
$439$	200.080	−	346.549i	0.455764	−	0.789406i	−0.542968	−	0.839753i	$-0.682700\pi$
$439$	200.080	−	346.549i	0.455764	−	0.789406i	0.998732	+	0.0503476i	$0.0160329\pi$
$440$	8.95356	−	22.8828i	0.0203490	−	0.0520064i
$441$	248.869	−	110.034i	0.564328	−	0.249509i
$442$	−140.499	−	180.629i	−0.317871	−	0.408664i
$443$	−16.5605	−	61.8045i	−0.0373825	−	0.139514i	0.944712	−	0.327900i	$-0.106341\pi$
$443$	−16.5605	−	61.8045i	−0.0373825	−	0.139514i	−0.982095	+	0.188386i	$0.939674\pi$
$444$	269.625	−	60.6623i	0.607264	−	0.136627i
$445$	74.3896	+	19.9326i	0.167168	+	0.0447924i
$446$	−110.926	−	262.894i	−0.248712	−	0.589448i
$447$	486.584	−	247.136i	1.08856	−	0.552876i
$448$	544.029	−	169.043i	1.21435	−	0.377328i
$449$	−482.324			−1.07422			−0.537109	−	0.843513i	$-0.680484\pi$
$449$	−482.324			−1.07422			−0.537109	+	0.843513i	$0.680484\pi$
$450$	418.679	−	125.839i	0.930398	−	0.279643i
$451$	−138.357	−	138.357i	−0.306778	−	0.306778i
$452$	421.952	−	433.203i	0.933522	−	0.958413i
$453$	−195.478	+	41.2862i	−0.431519	+	0.0911396i
$454$	−761.009	−	309.372i	−1.67623	−	0.681436i
$455$	20.7715	+	35.9773i	0.0456516	+	0.0790709i
$456$	−54.1554	−	24.6155i	−0.118762	−	0.0539813i
$457$	639.822	+	369.402i	1.40005	+	0.808319i	0.994397	−	0.105709i	$-0.0337112\pi$
$457$	639.822	+	369.402i	1.40005	+	0.808319i	0.405652	+	0.914028i	$0.367045\pi$
$458$	−197.275	+	153.446i	−0.430730	+	0.335035i
$459$	453.190	−	326.585i	0.987342	−	0.711514i
$460$	34.6525	+	58.2369i	0.0753315	+	0.126602i
$461$	−12.6966	−	47.3843i	−0.0275414	−	0.102786i	0.950787	−	0.309845i	$-0.100277\pi$
$461$	−12.6966	−	47.3843i	−0.0275414	−	0.102786i	−0.978328	+	0.207059i	$0.933611\pi$
$462$	34.4143	−	191.321i	0.0744899	−	0.414115i
$463$	732.511	−	422.916i	1.58210	−	0.913424i	0.587545	−	0.809192i	$-0.300095\pi$
$463$	732.511	−	422.916i	1.58210	−	0.913424i	0.994553	−	0.104233i	$-0.0332387\pi$
$464$	139.042	+	131.911i	0.299660	+	0.284292i
$465$	85.1307	−	130.720i	0.183077	−	0.281118i
$466$	410.676	−	542.556i	0.881279	−	1.16428i
$467$	208.036	+	208.036i	0.445472	+	0.445472i	0.893846	−	0.448374i	$-0.147997\pi$
$467$	208.036	+	208.036i	0.445472	+	0.445472i	−0.448374	+	0.893846i	$0.647997\pi$
$468$	−198.213	−	18.7169i	−0.423533	−	0.0399933i
$469$	512.796	+	512.796i	1.09338	+	1.09338i
$470$	99.8680	−	13.8168i	0.212485	−	0.0293973i
$471$	96.2227	+	189.453i	0.204295	+	0.402235i
$472$	−2.96080	+	4.02043i	−0.00627288	+	0.00851785i
$473$	−170.782	+	98.6012i	−0.361062	+	0.208459i
$474$	−162.158	+	344.648i	−0.342106	+	0.727105i
$475$	15.5811	+	58.1494i	0.0328023	+	0.122420i
$476$	−713.989	−	181.280i	−1.49998	−	0.380841i
$477$	−201.617	+	162.406i	−0.422678	+	0.340473i
$478$	6.93801	+	0.867018i	0.0145147	+	0.00181385i
$479$	104.675	+	60.4344i	0.218529	+	0.126168i	0.605269	−	0.796021i	$-0.293066\pi$
$479$	104.675	+	60.4344i	0.218529	+	0.126168i	−0.386740	+	0.922189i	$0.626399\pi$
$480$	−75.4736	+	29.4416i	−0.157237	+	0.0613368i
$481$	63.6839	+	110.304i	0.132399	+	0.229322i
$482$	262.731	−	110.857i	0.545085	−	0.229994i
$483$	358.211	+	398.868i	0.741637	+	0.825815i
$484$	308.752	+	300.734i	0.637918	+	0.621351i
$485$	−52.3809	−	52.3809i	−0.108002	−	0.108002i
$486$	63.3794	−	481.850i	0.130410	−	0.991460i
$487$	568.859			1.16809			0.584044	−	0.811722i	$-0.301469\pi$
$487$	568.859			1.16809			0.584044	+	0.811722i	$0.301469\pi$
$488$	767.933	+	85.7219i	1.57363	+	0.175660i
$489$	16.6861	−	310.707i	0.0341228	−	0.635392i
$490$	47.2715	+	19.2172i	0.0964725	+	0.0392188i
$491$	−658.128	−	176.345i	−1.34038	−	0.359154i	−0.483806	−	0.875175i	$-0.660746\pi$
$491$	−658.128	−	176.345i	−1.34038	−	0.359154i	−0.856576	+	0.516021i	$0.827413\pi$
$492$	−26.1172	+	644.570i	−0.0530837	+	1.31010i
$493$	−64.1427	−	239.384i	−0.130107	−	0.485566i
$494$	3.39961	−	27.2042i	0.00688180	−	0.0550692i
$495$	−2.96059	+	27.4846i	−0.00598098	+	0.0555245i
$496$	470.315	−	866.483i	0.948215	−	1.74694i
$497$	55.7038	−	96.4819i	0.112080	−	0.194129i
$498$	64.1139	+	178.056i	0.128743	+	0.357541i
$499$	−64.9520	+	242.404i	−0.130164	+	0.485780i	−0.999971	−	0.00761290i	$-0.997577\pi$
$499$	−64.9520	+	242.404i	−0.130164	+	0.485780i	0.869807	+	0.493393i	$0.164243\pi$
$500$	145.165	+	81.2838i	0.290330	+	0.162568i
$501$	−74.3904	+	227.947i	−0.148484	+	0.454985i
$502$	−667.657	+	92.3704i	−1.32999	+	0.184005i
$503$	−471.584			−0.937544			−0.468772	−	0.883319i	$-0.655303\pi$
$503$	−471.584			−0.937544			−0.468772	+	0.883319i	$0.655303\pi$
$504$	−540.633	+	344.190i	−1.07268	+	0.682916i
$505$			116.505i			0.230703i
$506$	144.763	−	20.0279i	0.286092	−	0.0395809i
$507$	85.8090	+	406.280i	0.169249	+	0.801342i
$508$	−420.681	+	118.674i	−0.828112	+	0.233610i
$509$	326.239	+	87.4154i	0.640941	+	0.171740i	0.564630	−	0.825344i	$-0.309019\pi$
$509$	326.239	+	87.4154i	0.640941	+	0.171740i	0.0763113	+	0.997084i	$0.475686\pi$
$510$	103.100	+	18.5454i	0.202157	+	0.0363635i
$511$	441.747	+	255.043i	0.864475	+	0.499105i
$512$	−460.605	+	223.577i	−0.899620	+	0.436675i
$513$	66.0581	+	10.7252i	0.128768	+	0.0209069i
$514$	112.917	−	903.581i	0.219684	−	1.75794i
$515$	90.4827	−	24.2448i	0.175695	−	0.0470772i
$516$	620.684	+	193.563i	1.20288	+	0.375121i
$517$	56.2726	−	210.012i	0.108844	−	0.406213i
$518$	379.818	+	154.407i	0.733240	+	0.298083i
$519$	−469.346	+	720.690i	−0.904328	+	1.38861i
$520$	−23.3089	−	29.1666i	−0.0448249	−	0.0560896i
$521$			231.484i			0.444307i	0.975012	+	0.222153i	$0.0713085\pi$
$521$			231.484i			0.444307i	−0.975012	+	0.222153i	$0.928691\pi$
$522$	−189.897	−	102.126i	−0.363788	−	0.195644i
$523$	208.858	−	208.858i	0.399346	−	0.399346i	−0.478657	−	0.878002i	$-0.658876\pi$
$523$	208.858	−	208.858i	0.399346	−	0.399346i	0.878002	+	0.478657i	$0.158876\pi$
$524$	975.243	−	12.8305i	1.86115	−	0.0244858i
$525$	616.582	+	201.221i	1.17444	+	0.383278i
$526$	697.642	−	294.364i	1.32632	−	0.559627i
$527$	−1104.03	+	637.414i	−2.09494	+	1.20951i
$528$	−4.77609	+	174.642i	−0.00904563	+	0.330761i
$529$	62.9803	−	109.085i	0.119055	−	0.206210i
$530$	−48.1753	−	6.02029i	−0.0908967	−	0.0113590i
$531$	2.02655	−	5.23883i	0.00381647	−	0.00986597i
$532$	−45.1280	−	75.8421i	−0.0848271	−	0.142560i
$533$	−287.175	+	76.9484i	−0.538791	+	0.144369i
$534$	−545.644	+	45.8463i	−1.02181	+	0.0858544i
$535$	−23.6241	−	40.9182i	−0.0441573	−	0.0764826i
$536$	−524.811	−	386.491i	−0.979124	−	0.721065i
$537$	29.7617	−	554.184i	0.0554221	−	1.03200i
$538$	182.755	−	25.2842i	0.339693	−	0.0469966i
$539$	77.8134	−	77.8134i	0.144366	−	0.144366i
$540$	73.2331	−	54.2523i	0.135617	−	0.100467i
$541$	−647.189	+	647.189i	−1.19628	+	1.19628i	−0.221011	+	0.975271i	$0.570936\pi$
$541$	−647.189	+	647.189i	−1.19628	+	1.19628i	−0.975271	+	0.221011i	$0.929064\pi$
$542$	−39.6282	+	52.3539i	−0.0731147	+	0.0965940i
$543$	6.49180	−	120.882i	0.0119554	−	0.222619i
$544$	658.872	+	64.7843i	1.21116	+	0.119089i
$545$	−44.5000	−	77.0763i	−0.0816514	−	0.141424i
$546$	−225.612	−	190.637i	−0.413208	−	0.349153i
$547$	654.150	−	175.279i	1.19589	−	0.320437i	0.394677	−	0.918820i	$-0.370856\pi$
$547$	654.150	−	175.279i	1.19589	−	0.320437i	0.801210	+	0.598383i	$0.204190\pi$
$548$	145.432	−	572.799i	0.265388	−	1.04525i
$549$	−858.937	+	133.768i	−1.56455	+	0.243657i
$550$	139.556	−	108.551i	0.253738	−	0.197366i
$551$	14.8454	−	25.7130i	0.0269427	−	0.0466661i
$552$	−372.087	−	306.108i	−0.674070	−	0.554543i
$553$	−489.368	+	282.537i	−0.884933	+	0.510916i
$554$	551.864	+	224.348i	0.996144	+	0.404960i
$555$	−55.4280	−	18.0889i	−0.0998702	−	0.0325925i
$556$	−13.0485	−	991.812i	−0.0234686	−	1.78383i
$557$	13.1728	−	13.1728i	0.0236496	−	0.0236496i	−0.695183	−	0.718833i	$-0.744677\pi$
$557$	13.1728	−	13.1728i	0.0236496	−	0.0236496i	0.718833	+	0.695183i	$0.244677\pi$
$558$	−254.613	+	1079.51i	−0.456295	+	1.93461i
$559$			299.641i			0.536030i
$560$	−116.870	−	28.0419i	−0.208697	−	0.0500748i
$561$	123.283	−	189.303i	0.219756	−	0.337439i
$562$	−320.010	−	758.424i	−0.569413	−	1.34951i
$563$	−164.872	+	615.310i	−0.292845	+	1.09291i	0.650068	+	0.759876i	$0.274740\pi$
$563$	−164.872	+	615.310i	−0.292845	+	1.09291i	−0.942914	+	0.333037i	$0.891926\pi$
$564$	−634.789	+	332.985i	−1.12551	+	0.590399i
$565$	−123.235	+	33.0207i	−0.218115	+	0.0584437i
$566$	36.1658	+	46.4957i	0.0638971	+	0.0821479i
$567$	485.213	−	533.314i	0.855755	−	0.940590i
$568$	−36.4840	+	93.2428i	−0.0642323	+	0.164160i
$569$	−42.6950	−	24.6500i	−0.0750352	−	0.0433216i	0.462013	−	0.886873i	$-0.347127\pi$
$569$	−42.6950	−	24.6500i	−0.0750352	−	0.0433216i	−0.537048	+	0.843552i	$0.680461\pi$
$570$	7.16300	+	10.3051i	0.0125667	+	0.0180792i
$571$	487.424	+	130.605i	0.853632	+	0.228730i	0.658997	−	0.752146i	$-0.270981\pi$
$571$	487.424	+	130.605i	0.853632	+	0.228730i	0.194635	+	0.980876i	$0.437648\pi$
$572$	−77.4927	+	21.8607i	−0.135477	+	0.0382180i
$573$	−184.654	−	874.281i	−0.322258	−	1.52580i
$574$	−577.604	+	763.090i	−1.00628	+	1.32942i
$575$			487.599i			0.847999i
$576$	433.965	−	378.748i	0.753412	−	0.657549i
$577$	−260.550			−0.451559			−0.225780	−	0.974178i	$-0.572493\pi$
$577$	−260.550			−0.451559			−0.225780	+	0.974178i	$0.572493\pi$
$578$	−221.720	−	167.826i	−0.383598	−	0.290356i
$579$	173.428	−	531.420i	0.299531	−	0.917823i
$580$	−10.9781	−	38.9158i	−0.0189278	−	0.0670961i
$581$	−72.6659	+	271.193i	−0.125070	+	0.466769i
$582$	476.576	+	224.231i	0.818860	+	0.385276i
$583$	−52.3500	+	90.6728i	−0.0897941	+	0.155528i
$584$	−426.916	−	167.043i	−0.731021	−	0.286033i
$585$	33.9175	+	24.7767i	0.0579786	+	0.0423533i
$586$	−345.052	+	268.392i	−0.588826	+	0.458007i
$587$	−179.335	−	669.287i	−0.305511	−	1.14018i	−0.932505	−	0.361158i	$-0.882381\pi$
$587$	−179.335	−	669.287i	−0.305511	−	1.14018i	0.626994	−	0.779024i	$-0.284285\pi$
$588$	−362.514	−	14.6886i	−0.616520	−	0.0249806i
$589$	−147.525	−	39.5293i	−0.250467	−	0.0671126i
$590$	0.970524	−	0.409504i	0.00164496	−	0.000694074i
$591$	−20.1393	+	375.009i	−0.0340767	+	0.634532i
$592$	−358.317	−	85.9745i	−0.605264	−	0.145227i
$593$	−403.282			−0.680070			−0.340035	−	0.940413i	$-0.610439\pi$
$593$	−403.282			−0.680070			−0.340035	+	0.940413i	$0.610439\pi$
$594$	−46.3988	−	190.991i	−0.0781124	−	0.321533i
$595$	109.892	+	109.892i	0.184692	+	0.184692i
$596$	−727.600	+	9.57249i	−1.22081	+	0.0160612i
$597$	−572.660	−	637.659i	−0.959230	−	1.06811i
$598$	83.6258	−	205.707i	0.139842	−	0.343992i
$599$	−141.868	−	245.723i	−0.236842	−	0.410222i	0.722965	−	0.690885i	$-0.242779\pi$
$599$	−141.868	−	245.723i	−0.236842	−	0.410222i	−0.959806	+	0.280663i	$0.909446\pi$
$600$	−575.009	−	95.6398i	−0.958349	−	0.159400i
$601$	69.0537	+	39.8682i	0.114898	+	0.0663364i	0.556348	−	0.830950i	$-0.312202\pi$
$601$	69.0537	+	39.8682i	0.114898	+	0.0663364i	−0.441450	+	0.897286i	$0.645536\pi$
$602$	592.207	+	761.358i	0.983733	+	1.26471i
$603$	683.856	+	264.538i	1.13409	+	0.438702i
$604$	258.195	+	65.5552i	0.427475	+	0.108535i
$605$	−23.5345	−	87.8321i	−0.0389000	−	0.145177i
$606$	−280.632	−	779.364i	−0.463089	−	1.28608i
$607$	372.619	−	215.132i	0.613869	−	0.354418i	−0.160609	−	0.987018i	$-0.551346\pi$
$607$	372.619	−	215.132i	0.613869	−	0.354418i	0.774478	+	0.632600i	$0.218012\pi$
$608$	50.3277	+	61.3040i	0.0827759	+	0.100829i
$609$	−144.854	−	285.203i	−0.237856	−	0.468314i
$610$	−129.981	−	98.3862i	−0.213083	−	0.161289i
$611$	−233.601	−	233.601i	−0.382325	−	0.382325i
$612$	−734.363	+	124.283i	−1.19994	+	0.203077i
$613$	437.066	+	437.066i	0.712995	+	0.712995i	0.967161	−	0.254165i	$-0.0818007\pi$
$613$	437.066	+	437.066i	0.712995	+	0.712995i	−0.254165	+	0.967161i	$0.581801\pi$
$614$	148.780	+	1075.39i	0.242313	+	1.75145i
$615$	74.2713	−	114.045i	0.120766	−	0.185439i
$616$	−153.696	+	208.702i	−0.249507	+	0.338802i
$617$	370.468	−	213.890i	0.600435	−	0.346661i	−0.168778	−	0.985654i	$-0.553982\pi$
$617$	370.468	−	213.890i	0.600435	−	0.346661i	0.769213	+	0.638993i	$0.220649\pi$
$618$	−546.887	+	380.137i	−0.884930	+	0.615108i
$619$	46.1198	+	172.121i	0.0745069	+	0.278064i	0.993121	−	0.117092i	$-0.0373573\pi$
$619$	46.1198	+	172.121i	0.0745069	+	0.278064i	−0.918614	+	0.395156i	$0.870691\pi$
$620$	−178.745	+	106.358i	−0.288299	+	0.171546i
$621$	494.327	+	222.389i	0.796018	+	0.358114i
$622$	−17.7248	+	141.836i	−0.0284965	+	0.228033i
$623$	−703.515	−	406.174i	−1.12924	−	0.651965i
$624$	226.181	+	138.965i	0.362469	+	0.222701i
$625$	286.048	+	495.450i	0.457677	+	0.792720i
$626$	−134.797	−	319.470i	−0.215331	−	0.510335i
$627$	26.4805	−	5.59286i	0.0422337	−	0.00892003i
$628$	−3.72707	−	283.293i	−0.00593482	−	0.451103i
$629$	336.920	+	336.920i	0.535644	+	0.535644i
$630$	135.149	−	4.07914i	0.214523	−	0.00647483i
$631$	−544.768			−0.863341			−0.431671	−	0.902031i	$-0.642076\pi$
$631$	−544.768			−0.863341			−0.431671	+	0.902031i	$0.642076\pi$
$632$	396.729	−	317.052i	0.627735	−	0.501664i
$633$	−352.935	+	179.255i	−0.557560	+	0.283184i
$634$	−379.073	+	932.464i	−0.597907	+	1.47076i
$635$	89.0731	+	23.8671i	0.140273	+	0.0375859i
$636$	336.771	−	75.7694i	0.529514	−	0.119134i
$637$	−43.2767	−	161.511i	−0.0679383	−	0.253549i
$638$	−86.5258	−	10.8128i	−0.135620	−	0.0169480i
$639$	12.0638	−	111.994i	0.0188792	−	0.175265i
$640$	107.628	+	9.15485i	0.168169	+	0.0143044i
$641$	−26.0886	+	45.1867i	−0.0406998	+	0.0704941i	−0.885658	−	0.464339i	$-0.846292\pi$
$641$	−26.0886	+	45.1867i	−0.0406998	+	0.0704941i	0.844958	+	0.534833i	$0.179625\pi$
$642$	256.596	+	216.819i	0.399683	+	0.337724i
$643$	257.044	−	959.303i	0.399758	−	1.49192i	−0.413765	−	0.910384i	$-0.635786\pi$
$643$	257.044	−	959.303i	0.399758	−	1.49192i	0.813523	−	0.581533i	$-0.197547\pi$
$644$	−194.073	−	687.959i	−0.301356	−	1.06826i
$645$	−91.6501	−	102.053i	−0.142093	−	0.158221i
$646$	−14.0555	−	101.593i	−0.0217577	−	0.157265i
$647$	556.919			0.860771			0.430386	−	0.902645i	$-0.358378\pi$
$647$	556.919			0.860771			0.430386	+	0.902645i	$0.358378\pi$
$648$	−359.215	+	539.323i	−0.554344	+	0.832288i
$649$		−	2.27165i		−	0.00350024i
$650$	−36.8163	−	266.110i	−0.0566404	−	0.409399i
$651$	−1224.24	+	1099.45i	−1.88055	+	1.68886i
$652$	−202.692	+	361.988i	−0.310877	+	0.555196i
$653$	40.9007	+	10.9593i	0.0626350	+	0.0167830i	0.290000	−	0.957026i	$-0.406345\pi$
$653$	40.9007	+	10.9593i	0.0626350	+	0.0167830i	−0.227365	+	0.973810i	$0.573011\pi$
$654$	483.342	+	408.415i	0.739055	+	0.624487i
$655$	−178.198	−	102.883i	−0.272059	−	0.157073i
$656$	410.321	−	755.953i	0.625489	−	1.15237i
$657$	512.771	+	55.2346i	0.780474	+	0.0840710i
$658$	−1055.24	−	131.870i	−1.60371	−	0.200410i
$659$	−151.791	+	40.6723i	−0.230335	+	0.0617181i	−0.372140	−	0.928176i	$-0.621376\pi$
$659$	−151.791	+	40.6723i	−0.230335	+	0.0617181i	0.141805	+	0.989895i	$0.454709\pi$
$660$	19.7063	−	31.1478i	0.0298580	−	0.0471937i
$661$	192.713	−	719.215i	0.291548	−	1.08807i	−0.652372	−	0.757899i	$-0.726226\pi$
$661$	192.713	−	719.215i	0.291548	−	1.08807i	0.943920	−	0.330173i	$-0.107107\pi$
$662$	243.948	−	600.077i	0.368502	−	0.906461i
$663$	−155.440	−	306.046i	−0.234450	−	0.461608i
$664$	27.9928	−	250.772i	0.0421578	−	0.377668i
$665$			18.6188i			0.0279982i
$666$	414.359	−	12.5064i	0.622160	−	0.0187783i
$667$	170.047	−	170.047i	0.254943	−	0.254943i
$668$	223.072	−	229.020i	0.333940	−	0.342844i
$669$	−88.4465	−	418.768i	−0.132207	−	0.625962i
$670$	53.4550	+	126.688i	0.0797836	+	0.189087i
$671$	−304.455	+	175.777i	−0.453733	+	0.261963i
$672$	849.353	−	93.9248i	1.26392	−	0.139769i
$673$	109.309	−	189.330i	0.162421	−	0.281322i	−0.773315	−	0.634022i	$-0.781403\pi$
$673$	109.309	−	189.330i	0.162421	−	0.281322i	0.935736	+	0.352700i	$0.114736\pi$
$674$	−36.1995	+	289.673i	−0.0537084	+	0.429783i
$675$	652.441	−	66.0181i	0.966579	−	0.0978047i
$676$	136.250	−	536.631i	0.201553	−	0.793833i
$677$	676.788	−	181.345i	0.999686	−	0.267865i	0.278372	−	0.960473i	$-0.410205\pi$
$677$	676.788	−	181.345i	0.999686	−	0.267865i	0.721314	+	0.692608i	$0.243538\pi$
$678$	744.844	−	517.735i	1.09859	−	0.763621i
$679$	390.690	+	676.694i	0.575390	+	0.996604i
$680$	−112.466	−	82.8246i	−0.165392	−	0.121801i
$681$	−1032.57	−	672.458i	−1.51626	−	0.987457i
$682$	61.4714	+	444.318i	0.0901340	+	0.651492i
$683$	128.298	−	128.298i	0.187845	−	0.187845i	−0.606919	−	0.794764i	$-0.707595\pi$
$683$	128.298	−	128.298i	0.187845	−	0.187845i	0.794764	+	0.606919i	$0.207595\pi$
$684$	−72.7396	−	51.6825i	−0.106344	−	0.0755592i
$685$	−88.1607	+	88.1607i	−0.128702	+	0.128702i
$686$	266.377	+	201.628i	0.388304	+	0.293918i
$687$	−334.248	+	169.764i	−0.486533	+	0.247109i
$688$	−628.896	−	596.643i	−0.914093	−	0.867214i
$689$	79.5435	+	137.773i	0.115448	+	0.199961i
$690$	34.4375	+	95.6389i	0.0499094	+	0.138607i
$691$	−92.2110	+	24.7079i	−0.133446	+	0.0357567i	−0.324924	−	0.945740i	$-0.605339\pi$
$691$	−92.2110	+	24.7079i	−0.133446	+	0.0357567i	0.191478	+	0.981497i	$0.438672\pi$
$692$	985.467	−	586.379i	1.42409	−	0.847368i
$693$	105.199	−	271.949i	0.151802	−	0.392423i
$694$	512.995	+	659.520i	0.739185	+	0.950316i
$695$	−104.631	+	181.226i	−0.150548	+	0.260757i
$696$	167.177	+	233.884i	0.240197	+	0.336041i
$697$	−963.200	+	556.104i	−1.38192	+	0.797853i
$698$	−30.4642	+	74.9375i	−0.0436450	+	0.107360i
$699$	759.399	−	681.991i	1.08641	−	0.975667i
$700$	−619.483	−	603.395i	−0.884976	−	0.861993i
$701$	−162.682	+	162.682i	−0.232071	+	0.232071i	−0.813557	−	0.581486i	$-0.802472\pi$
$701$	−162.682	+	162.682i	−0.232071	+	0.232071i	0.581486	+	0.813557i	$0.302472\pi$
$702$	−286.573	−	84.0454i	−0.408223	−	0.119723i
$703$			57.0839i			0.0812005i
$704$	108.421	−	206.173i	0.154007	−	0.292860i
$705$	151.011	+	8.10985i	0.214200	+	0.0115033i
$706$	−282.955	+	119.390i	−0.400786	+	0.169108i
$707$	318.064	−	1187.03i	0.449879	−	1.67897i
$708$	−5.50595	+	5.07714i	−0.00777677	+	0.00717110i
$709$	−846.251	+	226.752i	−1.19358	+	0.319820i	−0.800301	−	0.599598i	$-0.795327\pi$
$709$	−846.251	+	226.752i	−1.19358	+	0.319820i	−0.393283	+	0.919418i	$0.628661\pi$
$710$	16.6737	−	12.9693i	0.0234840	−	0.0182666i
$711$	−337.016	+	461.351i	−0.474003	+	0.648876i
$712$	679.896	+	266.029i	0.954910	+	0.373636i
$713$	−1071.31	−	618.521i	−1.50254	−	0.867491i
$714$	−999.825	−	470.421i	−1.40032	−	0.658854i
$715$	16.4080	+	4.39650i	0.0229482	+	0.00614895i
$716$	−361.526	+	645.650i	−0.504925	+	0.901746i
$717$	9.97045	+	3.25384i	0.0139058	+	0.00453814i
$718$	266.722	+	201.890i	0.371480	+	0.281184i
$719$			229.456i			0.319133i	0.987187	+	0.159566i	$0.0510096\pi$
$719$			229.456i			0.319133i	−0.987187	+	0.159566i	$0.948990\pi$
$720$	−119.538	+	21.8519i	−0.166026	+	0.0303499i
$721$	−988.088			−1.37044
$722$	−428.333	+	565.883i	−0.593259	+	0.783771i
$723$	418.509	−	88.3918i	0.578851	−	0.122257i
$724$	−78.8583	+	140.833i	−0.108920	+	0.194521i
$725$	75.3002	−	281.024i	0.103862	−	0.387619i
$726$	369.001	+	530.866i	0.508265	+	0.731221i
$727$	439.328	−	760.939i	0.604303	−	1.04668i	−0.387858	−	0.921719i	$-0.626785\pi$
$727$	439.328	−	760.939i	0.604303	−	1.04668i	0.992161	−	0.124964i	$-0.0398817\pi$
$728$	157.861	+	360.803i	0.216842	+	0.495609i
$729$	230.642	−	691.553i	0.316381	−	0.948632i
$730$	59.3805	+	76.3411i	0.0813431	+	0.104577i
$731$	290.121	+	1082.75i	0.396882	+	1.48119i
$732$	1106.50	+	345.065i	1.51161	+	0.471401i
$733$	1051.88	+	281.850i	1.43503	+	0.384516i	0.890792	−	0.454412i	$-0.150151\pi$
$733$	1051.88	+	281.850i	1.43503	+	0.384516i	0.544242	+	0.838928i	$0.316817\pi$
$734$	468.967	+	1111.45i	0.638920	+	1.51424i
$735$	64.1401	+	41.7710i	0.0872655	+	0.0568313i
$736$	265.230	+	585.120i	0.360367	+	0.795000i
$737$	296.533			0.402351
$738$	−222.134	+	941.807i	−0.300994	+	1.27616i
$739$	62.5587	+	62.5587i	0.0846532	+	0.0846532i	0.748165	−	0.663512i	$-0.230935\pi$
$739$	62.5587	+	62.5587i	0.0846532	+	0.0846532i	−0.663512	+	0.748165i	$0.730935\pi$
$740$	55.6888	+	54.2425i	0.0752552	+	0.0733007i
$741$	12.7584	−	39.0945i	0.0172179	−	0.0527591i
$742$	474.406	+	192.860i	0.639362	+	0.259919i
$743$	16.0083	+	27.7272i	0.0215455	+	0.0373179i	0.876597	−	0.481225i	$-0.159808\pi$
$743$	16.0083	+	27.7272i	0.0215455	+	0.0373179i	−0.855052	+	0.518543i	$0.826475\pi$
$744$	939.532	−	1142.04i	1.26281	−	1.53500i
$745$	132.949	+	76.7579i	0.178454	+	0.103031i
$746$	400.205	−	311.291i	0.536467	−	0.417281i
$747$	43.6824	+	280.489i	0.0584771	+	0.375488i
$748$	−258.852	+	154.024i	−0.346059	+	0.205914i
$749$	128.990	+	481.397i	0.172216	+	0.642720i
$750$	190.620	+	161.071i	0.254161	+	0.214761i
$751$	−237.459	+	137.097i	−0.316191	+	0.182553i	−0.649693	−	0.760196i	$-0.725103\pi$
$751$	−237.459	+	137.097i	−0.316191	+	0.182553i	0.333503	+	0.942749i	$0.391769\pi$
$752$	955.433	−	25.1442i	1.27052	−	0.0334364i
$753$	−1009.57	−	54.2175i	−1.34073	−	0.0720020i
$754$	−79.9645	+	105.643i	−0.106054	+	0.140111i
$755$	−39.7394	−	39.7394i	−0.0526350	−	0.0526350i
$756$	−894.260	+	352.829i	−1.18288	+	0.466705i
$757$	−430.086	−	430.086i	−0.568145	−	0.568145i	0.363464	−	0.931608i	$-0.381594\pi$
$757$	−430.086	−	430.086i	−0.568145	−	0.568145i	−0.931608	+	0.363464i	$0.881594\pi$
$758$	−823.764	+	113.968i	−1.08676	+	0.150353i
$759$	218.897	+	11.7556i	0.288402	+	0.0154882i
$760$	−2.51108	−	16.5439i	−0.00330406	−	0.0217683i
$761$	66.6438	−	38.4768i	0.0875739	−	0.0505608i	−0.455574	−	0.890198i	$-0.650566\pi$
$761$	66.6438	−	38.4768i	0.0875739	−	0.0505608i	0.543147	+	0.839637i	$0.317232\pi$
$762$	−653.347	+	54.8957i	−0.857411	+	0.0720416i
$763$	242.974	+	906.793i	0.318446	+	1.18846i
$764$	−293.197	+	1154.78i	−0.383766	+	1.51150i
$765$	146.550	+	56.6901i	0.191568	+	0.0741048i
$766$	−562.434	−	70.2854i	−0.734248	−	0.0917564i
$767$	−2.98924	−	1.72584i	−0.00389732	−	0.00225012i
$768$	−742.035	+	198.009i	−0.966192	+	0.257824i
$769$	−225.462	−	390.512i	−0.293189	−	0.507818i	0.681373	−	0.731936i	$-0.261383\pi$
$769$	−225.462	−	390.512i	−0.293189	−	0.507818i	−0.974562	+	0.224118i	$0.928050\pi$
$770$	50.3802	−	21.2575i	0.0654289	−	0.0276071i
$771$	423.769	−	1298.51i	0.549635	−	1.68420i
$772$	−520.054	+	533.920i	−0.673645	+	0.691607i
$773$	−998.533	−	998.533i	−1.29176	−	1.29176i	−0.933696	−	0.358067i	$-0.883436\pi$
$773$	−998.533	−	998.533i	−1.29176	−	1.29176i	−0.358067	−	0.933696i	$-0.616564\pi$
$774$	858.916	+	461.922i	1.10971	+	0.596798i
$775$	−1496.58			−1.93107
$776$	−438.417	−	548.593i	−0.564970	−	0.706950i
$777$	515.354	+	335.623i	0.663262	+	0.431947i
$778$	−441.778	−	179.595i	−0.567838	−	0.230842i
$779$	−128.707	−	34.4869i	−0.165220	−	0.0442707i
$780$	−26.0156	−	49.5951i	−0.0333534	−	0.0635835i
$781$	−11.7903	−	44.0020i	−0.0150964	−	0.0563406i
$782$	103.008	−	824.289i	0.131724	−	1.05408i
$783$	−250.558	−	204.511i	−0.319997	−	0.261189i
$784$	425.156	+	230.769i	0.542291	+	0.294348i
$785$	−29.8858	+	51.7638i	−0.0380711	+	0.0659411i
$786$	1439.88	+	259.002i	1.83191	+	0.329519i
$787$	11.5597	−	43.1414i	0.0146883	−	0.0548176i	−0.958193	−	0.286124i	$-0.907633\pi$
$787$	11.5597	−	43.1414i	0.0146883	−	0.0548176i	0.972881	+	0.231306i	$0.0742999\pi$
$788$	244.640	−	436.903i	0.310456	−	0.554445i
$789$	1111.29	−	234.711i	1.40848	−	0.297479i
$790$	−106.131	+	14.6833i	−0.134344	+	0.0185865i
$791$	1345.75			1.70132
$792$	−56.7983	+	255.832i	−0.0717150	+	0.323020i
$793$			534.172i			0.673609i
$794$	872.331	−	120.687i	1.09865	−	0.151999i
$795$	−69.2315	−	22.5936i	−0.0870837	−	0.0284197i
$796$	310.259	+	1099.82i	0.389773	+	1.38168i
$797$	1354.81	+	363.021i	1.69989	+	0.455484i	0.972912	−	0.231177i	$-0.0742576\pi$
$797$	1354.81	+	363.021i	1.69989	+	0.455484i	0.726978	+	0.686661i	$0.240924\pi$
$798$	−44.8481	−	124.551i	−0.0562006	−	0.156079i
$799$	−1070.29	−	617.933i	−1.33954	−	0.773383i
$800$	631.828	+	452.605i	0.789785	+	0.565756i
$801$	−816.626	−	87.9652i	−1.01951	−	0.109819i
$802$	76.8913	−	615.296i	0.0958745	−	0.767202i
$803$	201.465	−	53.9824i	0.250891	−	0.0672259i
$804$	−662.750	−	718.725i	−0.824316	−	0.893937i
$805$	−39.0310	+	145.666i	−0.0484857	+	0.180951i
$806$	631.374	+	256.671i	0.783342	+	0.318451i
$807$	276.345	+	14.8407i	0.342435	+	0.0183900i
$808$	−122.527	+	1097.65i	−0.151642	+	1.35847i
$809$		−	494.014i		−	0.610647i	−0.952249	−	0.305324i	$-0.901235\pi$
$809$		−	494.014i		−	0.610647i	0.952249	−	0.305324i	$-0.0987646\pi$
$810$	123.309	−	59.0286i	0.152233	−	0.0728748i
$811$	104.644	−	104.644i	0.129031	−	0.129031i	−0.639642	−	0.768673i	$-0.720917\pi$
$811$	104.644	−	104.644i	0.129031	−	0.129031i	0.768673	+	0.639642i	$0.220917\pi$
$812$	5.61076	+	426.471i	0.00690980	+	0.525210i
$813$	−73.2782	+	65.8087i	−0.0901331	+	0.0809456i
$814$	154.462	−	65.1740i	0.189757	−	0.0800663i
$815$	75.7998	−	43.7630i	0.0930059	−	0.0536970i
$816$	951.851	+	283.154i	1.16648	+	0.347002i
$817$	−67.1467	+	116.301i	−0.0821869	+	0.142352i
$818$	4.51081	+	0.563700i	0.00551444	+	0.000689120i
$819$	−277.933	−	345.038i	−0.339356	−	0.421291i
$820$	−155.944	+	92.7909i	−0.190176	+	0.113160i
$821$	−947.981	+	254.011i	−1.15467	+	0.309392i	−0.784834	−	0.619707i	$-0.787252\pi$
$821$	−947.981	+	254.011i	−1.15467	+	0.309392i	−0.369833	+	0.929098i	$0.620585\pi$
$822$	377.396	−	802.111i	0.459119	−	0.975804i
$823$	317.667	+	550.216i	0.385987	+	0.668549i	0.991906	−	0.126977i	$-0.0405276\pi$
$823$	317.667	+	550.216i	0.385987	+	0.668549i	−0.605919	+	0.795527i	$0.707194\pi$
$824$	877.977	−	133.262i	1.06551	−	0.161725i
$825$	236.454	−	120.095i	0.286611	−	0.145569i
$826$	−11.0063	+	1.52273i	−0.0133248	+	0.00184349i
$827$	277.677	−	277.677i	0.335764	−	0.335764i	−0.519006	−	0.854770i	$-0.673698\pi$
$827$	277.677	−	277.677i	0.335764	−	0.335764i	0.854770	+	0.519006i	$0.173698\pi$
$828$	−460.741	−	556.828i	−0.556450	−	0.672497i
$829$	−102.849	+	102.849i	−0.124064	+	0.124064i	−0.766413	−	0.642349i	$-0.777960\pi$
$829$	−102.849	+	102.849i	−0.124064	+	0.124064i	0.642349	+	0.766413i	$0.277960\pi$
$830$	−32.1284	+	42.4457i	−0.0387089	+	0.0511394i
$831$	748.793	+	487.649i	0.901075	+	0.586822i
$832$	−188.930	−	299.306i	−0.227079	−	0.359742i
$833$	−312.759	−	541.715i	−0.375461	−	0.650318i
$834$	263.402	−	1464.35i	0.315830	−	1.75581i
$835$	−65.1503	+	17.4570i	−0.0780243	+	0.0209065i
$836$	−34.9765	−	8.88046i	−0.0418379	−	0.0106226i
$837$	−682.574	+	1517.23i	−0.815500	+	1.81270i
$838$	424.894	−	330.495i	0.507033	−	0.394386i
$839$	−28.1867	+	48.8208i	−0.0335956	+	0.0581893i	−0.882334	−	0.470623i	$-0.844029\pi$
$839$	−28.1867	+	48.8208i	−0.0335956	+	0.0581893i	0.848739	+	0.528812i	$0.177362\pi$
$840$	−164.123	−	74.5993i	−0.195384	−	0.0888087i
$841$	604.062	−	348.755i	0.718266	−	0.414691i
$842$	−600.044	−	243.935i	−0.712641	−	0.289709i
$843$	−255.160	−	1208.11i	−0.302681	−	1.43311i
$844$	527.752	−	6.94324i	0.625299	−	0.00822659i
$845$	−82.5941	+	82.5941i	−0.0977445	+	0.0977445i
$846$	−1029.73	+	309.498i	−1.21717	+	0.365837i
$847$			959.143i			1.13240i
$848$	−447.550	−	107.385i	−0.527771	−	0.126634i
$849$	40.0118	+	78.7790i	0.0471281	+	0.0927904i
$850$	−390.690	−	925.936i	−0.459636	−	1.08934i
$851$	−119.666	+	446.601i	−0.140618	+	0.524795i
$852$	−80.2991	+	126.921i	−0.0942478	+	0.148968i
$853$	−518.429	+	138.913i	−0.607771	+	0.162852i	−0.549563	−	0.835453i	$-0.685206\pi$
$853$	−518.429	+	138.913i	−0.607771	+	0.162852i	−0.0582088	+	0.998304i	$0.518539\pi$
$854$	1055.73	+	1357.28i	1.23622	+	1.58932i
$855$	7.61239	+	17.2173i	0.00890338	+	0.0201372i
$856$	−179.541	−	410.355i	−0.209744	−	0.479386i
$857$	−239.819	−	138.460i	−0.279836	−	0.161563i	0.353513	−	0.935429i	$-0.384987\pi$
$857$	−239.819	−	138.460i	−0.279836	−	0.161563i	−0.633349	+	0.773866i	$0.718320\pi$
$858$	−120.352	+	10.1122i	−0.140270	+	0.0117858i
$859$	451.454	+	120.967i	0.525558	+	0.140823i	0.511836	−	0.859083i	$-0.328965\pi$
$859$	451.454	+	120.967i	0.525558	+	0.140823i	0.0137216	+	0.999906i	$0.495632\pi$
$860$	49.6547	+	176.018i	0.0577380	+	0.204672i
$861$	−1068.07	+	959.201i	−1.24050	+	1.11406i
$862$	−156.226	+	206.395i	−0.181237	+	0.239437i
$863$		−	510.271i		−	0.591275i	−0.955300	−	0.295638i	$-0.904468\pi$
$863$		−	510.271i		−	0.591275i	0.955300	−	0.295638i	$-0.0955321\pi$
$864$	747.019	−	434.117i	0.864606	−	0.502451i
$865$	−241.926			−0.279684
$866$	−422.100	−	319.499i	−0.487413	−	0.368937i
$867$	−278.701	−	310.334i	−0.321454	−	0.357940i
$868$	2111.54	−	595.666i	2.43265	−	0.686251i
$869$	−59.8019	+	223.184i	−0.0688169	+	0.256828i
$870$	−5.07821	−	60.4389i	−0.00583703	−	0.0694700i
$871$	225.284	−	390.204i	0.258650	−	0.447996i
$872$	−338.195	−	772.972i	−0.387839	−	0.886435i
$873$	637.952	+	466.023i	0.730758	+	0.533818i
$874$	78.5553	−	61.1028i	0.0898802	−	0.0699116i
$875$	95.8242	+	357.621i	0.109513	+	0.408710i
$876$	−581.114	−	367.653i	−0.663372	−	0.419695i
$877$	1519.08	+	407.035i	1.73213	+	0.464122i	0.980671	−	0.195662i	$-0.0626855\pi$
$877$	1519.08	+	407.035i	1.73213	+	0.464122i	0.751456	+	0.659784i	$0.229352\pi$
$878$	−737.369	+	311.126i	−0.839829	+	0.354358i
$879$	−584.632	+	296.934i	−0.665111	+	0.337809i
$880$	−41.8990	+	25.6833i	−0.0476125	+	0.0291855i
$881$	1147.38			1.30236			0.651180	−	0.758923i	$-0.274274\pi$
$881$	1147.38			1.30236			0.651180	+	0.758923i	$0.274274\pi$
$882$	−529.683	−	124.931i	−0.600548	−	0.141645i
$883$	606.164	+	606.164i	0.686482	+	0.686482i	0.961453	−	0.274970i	$-0.0886680\pi$
$883$	606.164	+	606.164i	0.686482	+	0.686482i	−0.274970	+	0.961453i	$0.588668\pi$
$884$	6.02079	+	457.637i	0.00681085	+	0.517689i
$885$	1.54596	−	0.326518i	0.00174685	−	0.000368946i
$886$	−48.1931	+	118.548i	−0.0543940	+	0.133801i
$887$	−525.452	−	910.109i	−0.592392	−	1.02605i	−0.993909	−	0.110201i	$-0.964850\pi$
$887$	−525.452	−	910.109i	−0.592392	−	1.02605i	0.401517	−	0.915851i	$-0.368483\pi$
$888$	−503.189	−	228.716i	−0.566654	−	0.257564i
$889$	−842.379	−	486.348i	−0.947558	−	0.547073i
$890$	−94.5678	−	121.579i	−0.106256	−	0.136606i
$891$	−13.9077	−	294.490i	−0.0156090	−	0.330517i
$892$	−140.437	+	553.126i	−0.157441	+	0.620096i
$893$	−38.3212	−	143.017i	−0.0429129	−	0.160153i
$894$	−1074.25	−	193.234i	−1.20163	−	0.216145i
$895$	135.198	−	78.0568i	0.151060	−	0.0872143i
$896$	−1071.60	−	387.107i	−1.19598	−	0.432039i
$897$	181.771	−	279.113i	0.202643	−	0.311163i
$898$	769.152	+	582.193i	0.856517	+	0.648322i
$899$	521.923	+	521.923i	0.580559	+	0.580559i
$900$	−819.555	−	304.697i	−0.910617	−	0.338552i
$901$	420.825	+	420.825i	0.467065	+	0.467065i
$902$	53.6300	+	387.640i	0.0594567	+	0.429756i
$903$	655.185	+	1289.99i	0.725565	+	1.42856i
$904$	−1195.78	+	181.499i	−1.32277	+	0.200773i
$905$	29.4903	−	17.0262i	0.0325860	−	0.0188135i
$906$	361.560	+	170.115i	0.399073	+	0.187765i
$907$	−297.923	−	1111.87i	−0.328471	−	1.22587i	−0.910776	−	0.412901i	$-0.864516\pi$
$907$	−297.923	−	1111.87i	−0.328471	−	1.22587i	0.582305	−	0.812971i	$-0.302151\pi$
$908$	840.137	+	1411.93i	0.925261	+	1.55499i
$909$	−191.201	−	1227.72i	−0.210342	−	1.35063i
$910$	10.3028	−	82.4446i	0.0113218	−	0.0905985i
$911$	897.442	+	518.138i	0.985117	+	0.568758i	0.903811	−	0.427931i	$-0.140758\pi$
$911$	897.442	+	518.138i	0.985117	+	0.568758i	0.0813062	+	0.996689i	$0.474091\pi$
$912$	56.6482	+	104.623i	0.0621143	+	0.114718i
$913$	57.4007	+	99.4210i	0.0628705	+	0.108895i
$914$	−574.423	−	1361.38i	−0.628471	−	1.48948i
$915$	−163.385	−	181.930i	−0.178563	−	0.198831i
$916$	499.809	−	6.57561i	0.545643	−	0.00717861i
$917$	1534.73	+	1534.73i	1.67364	+	1.67364i
$918$	−1116.90	−	26.2283i	−1.21667	−	0.0285711i
$919$	−886.991			−0.965170			−0.482585	−	0.875849i	$-0.660302\pi$
$919$	−886.991			−0.965170			−0.482585	+	0.875849i	$0.660302\pi$
$920$	15.0358	−	134.697i	0.0163432	−	0.146410i
$921$	−87.3277	+	1626.10i	−0.0948183	+	1.76559i
$922$	−36.9487	+	90.8884i	−0.0400745	+	0.0985775i
$923$	−66.8591	−	17.9148i	−0.0724368	−	0.0194094i
$924$	−285.816	+	263.556i	−0.309325	+	0.285234i
$925$	144.773	+	540.300i	0.156511	+	0.584108i
$926$	−1678.61	−	209.769i	−1.81275	−	0.226533i
$927$	−913.713	+	403.985i	−0.985667	+	0.435798i
$928$	−62.5029	−	378.189i	−0.0673522	−	0.407531i
$929$	598.063	−	1035.88i	0.643771	−	1.11504i	−0.340813	−	0.940131i	$-0.610702\pi$
$929$	598.063	−	1035.88i	0.643771	−	1.11504i	0.984584	−	0.174913i	$-0.0559644\pi$
$930$	−293.543	+	105.698i	−0.315637	+	0.113654i
$931$	19.3958	−	72.3861i	0.0208333	−	0.0777509i
$932$	−1309.80	+	369.493i	−1.40536	+	0.396452i
$933$	−66.5196	+	203.830i	−0.0712965	+	0.218467i
$934$	−80.6390	−	582.862i	−0.0863373	−	0.624049i
$935$	63.5467			0.0679644
$936$	293.495	+	269.103i	0.313563	+	0.287503i
$937$			769.784i			0.821541i	0.911739	+	0.410771i	$0.134740\pi$
$937$			769.784i			0.821541i	−0.911739	+	0.410771i	$0.865260\pi$
$938$	−198.771	−	1436.72i	−0.211909	−	1.53169i
$939$	−107.481	−	508.889i	−0.114463	−	0.541948i
$940$	−175.935	−	98.5133i	−0.187165	−	0.104801i
$941$	−164.170	−	43.9893i	−0.174464	−	0.0467474i	0.170530	−	0.985353i	$-0.445452\pi$
$941$	−164.170	−	43.9893i	−0.174464	−	0.0467474i	−0.344993	+	0.938605i	$0.612119\pi$
$942$	75.2360	−	418.263i	0.0798683	−	0.444016i
$943$	−934.651	−	539.621i	−0.991147	−	0.572239i
$944$	9.57442	−	2.83744i	0.0101424	−	0.00300576i
$945$	200.195	+	32.5038i	0.211846	+	0.0343955i
$946$	391.361	+	48.9070i	0.413701	+	0.0516987i
$947$	−482.998	+	129.419i	−0.510029	+	0.136662i	−0.504651	−	0.863324i	$-0.668379\pi$
$947$	−482.998	+	129.419i	−0.510029	+	0.136662i	−0.00537861	+	0.999986i	$0.501712\pi$
$948$	674.601	−	353.869i	0.711604	−	0.373279i
$949$	82.0239	−	306.118i	0.0864320	−	0.322569i
$950$	45.3429	−	111.537i	0.0477294	−	0.117407i
$951$	−823.963	+	1265.21i	−0.866417	+	1.33040i
$952$	919.769	+	1150.91i	0.966144	+	1.20894i
$953$			1294.44i			1.35828i	0.734010	+	0.679139i	$0.237647\pi$
$953$			1294.44i			1.35828i	−0.734010	+	0.679139i	$0.762353\pi$
$954$	517.549	−	15.6209i	0.542504	−	0.0163741i
$955$	177.735	−	177.735i	0.186110	−	0.186110i
$956$	−10.0174	−	9.75721i	−0.0104784	−	0.0102063i
$957$	−124.344	−	40.5796i	−0.129931	−	0.0424029i
$958$	−93.9760	−	222.723i	−0.0980960	−	0.232488i
$959$	1138.92	−	657.558i	1.18762	−	0.685670i
$960$	155.894	+	44.1512i	0.162390	+	0.0459908i
$961$	1417.92	−	2455.90i	1.47546	−	2.55557i
$962$	31.5877	−	252.770i	0.0328355	−	0.262754i
$963$	316.103	+	392.423i	0.328248	+	0.407501i
$964$	−552.783	−	140.351i	−0.573427	−	0.145592i
$965$	151.886	−	40.6979i	0.157395	−	0.0421739i
$966$	−89.7735	−	1068.45i	−0.0929333	−	1.10606i
$967$	−49.2735	−	85.3442i	−0.0509550	−	0.0882567i	0.839423	−	0.543479i	$-0.182893\pi$
$967$	−49.2735	−	85.3442i	−0.0509550	−	0.0882567i	−0.890378	+	0.455222i	$0.849560\pi$
$968$	−129.358	−	852.257i	−0.133634	−	0.880431i
$969$	8.24997	−	153.620i	0.00851390	−	0.158535i
$970$	20.3040	+	146.758i	0.0209319	+	0.151297i
$971$	−712.041	+	712.041i	−0.733307	+	0.733307i	−0.971273	−	0.237966i	$-0.923519\pi$
$971$	−712.041	+	712.041i	−0.733307	+	0.733307i	0.237966	+	0.971273i	$0.423519\pi$
$972$	−682.691	+	691.894i	−0.702357	+	0.711825i
$973$	1560.80	−	1560.80i	1.60412	−	1.60412i
$974$	−907.149	−	686.647i	−0.931364	−	0.704976i
$975$	21.6096	−	402.386i	0.0221637	−	0.412704i
$976$	−1121.14	−	1063.64i	−1.14871	−	1.08980i
$977$	12.5757	+	21.7818i	0.0128718	+	0.0222946i	0.872390	−	0.488811i	$-0.162569\pi$
$977$	12.5757	+	21.7818i	0.0128718	+	0.0222946i	−0.859518	+	0.511106i	$0.829236\pi$
$978$	−401.651	+	475.337i	−0.410686	+	0.486030i
$979$	−320.848	+	85.9710i	−0.327731	+	0.0878151i
$980$	−52.1867	−	87.7049i	−0.0532517	−	0.0894947i
$981$	595.432	+	739.195i	0.606965	+	0.753512i
$982$	836.645	+	1075.61i	0.851980	+	1.09533i
$983$	82.8778	−	143.549i	0.0843111	−	0.146031i	−0.820786	−	0.571235i	$-0.806464\pi$
$983$	82.8778	−	143.549i	0.0843111	−	0.146031i	0.905097	+	0.425204i	$0.139798\pi$
$984$	819.683	−	996.359i	0.833011	−	1.01256i
$985$	−91.4868	+	52.8199i	−0.0928800	+	0.0536243i
$986$	−186.663	+	459.165i	−0.189314	+	0.465684i
$987$	−1516.46	−	494.896i	−1.53644	−	0.501415i
$988$	−38.2584	+	39.2784i	−0.0387230	+	0.0397555i
$989$	−769.133	+	769.133i	−0.777687	+	0.777687i
$990$	37.8968	−	40.2556i	0.0382796	−	0.0406622i
$991$		−	824.626i		−	0.832115i	−0.909338	−	0.416057i	$-0.863412\pi$
$991$		−	824.626i		−	0.832115i	0.909338	−	0.416057i	$-0.136588\pi$
$992$	−1795.90	+	814.066i	−1.81038	+	0.820631i
$993$	530.252	−	814.211i	0.533990	−	0.819951i
$994$	−205.289	+	86.6200i	−0.206528	+	0.0871428i
$995$	62.3976	−	232.871i	0.0627112	−	0.234041i
$996$	112.682	−	361.331i	0.113135	−	0.362782i
$997$	−391.985	+	105.032i	−0.393165	+	0.105348i	−0.449985	−	0.893036i	$-0.648571\pi$
$997$	−391.985	+	105.032i	−0.393165	+	0.105348i	0.0568198	+	0.998384i	$0.481904\pi$
$998$	396.174	−	308.156i	0.396968	−	0.308774i
$999$	613.784	+	99.6544i	0.614398	+	0.0997541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.v.a.43.10	✓	184
3.2	odd	2		432.3.w.a.235.37		184
9.4	even	3	inner	144.3.v.a.139.40	yes	184
9.5	odd	6		432.3.w.a.91.7		184
16.3	odd	4	inner	144.3.v.a.115.40	yes	184
48.35	even	4		432.3.w.a.19.7		184
144.67	odd	12	inner	144.3.v.a.67.10	yes	184
144.131	even	12		432.3.w.a.307.37		184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.v.a.43.10	✓	184	1.1	even	1	trivial
144.3.v.a.67.10	yes	184	144.67	odd	12	inner
144.3.v.a.115.40	yes	184	16.3	odd	4	inner
144.3.v.a.139.40	yes	184	9.4	even	3	inner
432.3.w.a.19.7		184	48.35	even	4
432.3.w.a.91.7		184	9.5	odd	6
432.3.w.a.235.37		184	3.2	odd	2
432.3.w.a.307.37		184	144.131	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.59468 - 1.20706i) q^{2} +(-2.00451 - 2.23203i) q^{3} +(1.08601 + 3.84975i) q^{4} +(0.218413 - 0.815129i) q^{5} +(0.502363 + 5.97893i) q^{6} +(-4.45068 + 7.70881i) q^{7} +(2.91503 - 7.45001i) q^{8} +(-0.963885 + 8.94824i) q^{9} +O(q^{10})\)	\(q+(-1.59468 - 1.20706i) q^{2} +(-2.00451 - 2.23203i) q^{3} +(1.08601 + 3.84975i) q^{4} +(0.218413 - 0.815129i) q^{5} +(0.502363 + 5.97893i) q^{6} +(-4.45068 + 7.70881i) q^{7} +(2.91503 - 7.45001i) q^{8} +(-0.963885 + 8.94824i) q^{9} +(-1.33221 + 1.03623i) q^{10} +(0.942033 + 3.51572i) q^{11} +(6.41582 - 10.1409i) q^{12} +(5.34198 + 1.43138i) q^{13} +(16.4024 - 6.92085i) q^{14} +(-2.25720 + 1.14643i) q^{15} +(-13.6411 + 8.36176i) q^{16} +20.6891 q^{17} +(12.3381 - 13.1061i) q^{18} +(1.75266 + 1.75266i) q^{19} +(3.37524 - 0.0444055i) q^{20} +(26.1277 - 5.51833i) q^{21} +(2.74144 - 6.74353i) q^{22} +(10.0379 + 17.3862i) q^{23} +(-22.4718 + 8.42718i) q^{24} +(21.0339 + 12.1439i) q^{25} +(-6.79099 - 8.73068i) q^{26} +(21.9048 - 15.7854i) q^{27} +(-34.5105 - 8.76214i) q^{28} +(-3.10032 - 11.5706i) q^{29} +(4.98332 + 0.896387i) q^{30} +(-53.3631 + 30.8092i) q^{31} +(31.8464 + 3.13133i) q^{32} +(5.95886 - 9.14993i) q^{33} +(-32.9924 - 24.9729i) q^{34} +(5.31158 + 5.31158i) q^{35} +(-35.4953 + 6.00719i) q^{36} +(16.2850 + 16.2850i) q^{37} +(-0.679367 - 4.91049i) q^{38} +(-7.51317 - 14.7926i) q^{39} +(-5.43604 - 4.00331i) q^{40} +(-46.5560 + 26.8791i) q^{41} +(-48.3263 - 22.7377i) q^{42} +(14.0229 + 52.3343i) q^{43} +(-12.5116 + 7.44471i) q^{44} +(7.08344 + 2.74010i) q^{45} +(4.97889 - 39.8418i) q^{46} +(-51.7323 - 29.8676i) q^{47} +(46.0075 + 13.6862i) q^{48} +(-15.1171 - 26.1836i) q^{49} +(-18.8839 - 44.7549i) q^{50} +(-41.4714 - 46.1785i) q^{51} +(0.291013 + 22.1198i) q^{52} +(20.3405 + 20.3405i) q^{53} +(-53.9851 - 1.26774i) q^{54} +3.07151 q^{55} +(44.4568 + 55.6290i) q^{56} +(0.398760 - 7.42520i) q^{57} +(-9.02233 + 22.1936i) q^{58} +(-0.602860 - 0.161536i) q^{59} +(-6.86482 - 7.44462i) q^{60} +(24.9988 + 93.2967i) q^{61} +(122.286 + 15.2816i) q^{62} +(-64.6903 - 47.2561i) q^{63} +(-47.0052 - 43.4340i) q^{64} +(2.33352 - 4.04177i) q^{65} +(-20.5470 + 7.39852i) q^{66} +(21.0862 - 78.6949i) q^{67} +(22.4686 + 79.6477i) q^{68} +(18.6853 - 57.2557i) q^{69} +(-2.05888 - 14.8817i) q^{70} -12.5158 q^{71} +(63.8547 + 33.2653i) q^{72} -57.3042i q^{73} +(-6.31240 - 45.6262i) q^{74} +(-15.0571 - 71.2909i) q^{75} +(-4.84388 + 8.65071i) q^{76} +(-31.2947 - 8.38538i) q^{77} +(-5.87450 + 32.6584i) q^{78} +(54.9768 + 31.7408i) q^{79} +(3.83651 + 12.9456i) q^{80} +(-79.1419 - 17.2501i) q^{81} +(106.687 + 13.3323i) q^{82} +(30.4664 - 8.16345i) q^{83} +(49.6193 + 94.5921i) q^{84} +(4.51876 - 16.8642i) q^{85} +(40.8085 - 100.383i) q^{86} +(-19.6112 + 30.1133i) q^{87} +(28.9382 + 3.23027i) q^{88} +91.2611i q^{89} +(-7.98836 - 12.9197i) q^{90} +(-34.8097 + 34.8097i) q^{91} +(-56.0312 + 57.5251i) q^{92} +(175.734 + 57.3506i) q^{93} +(46.4444 + 110.073i) q^{94} +(1.81145 - 1.04584i) q^{95} +(-56.8472 - 77.3588i) q^{96} +(43.8910 - 76.0214i) q^{97} +(-7.49821 + 60.0018i) q^{98} +(-32.3675 + 5.04079i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{8}+O(q^{10}) \) 184 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^8	\( 184 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{8} - 8 q^{10} - 2 q^{11} + 56 q^{12} - 2 q^{13} + 14 q^{14} - 2 q^{16} - 16 q^{17} + 38 q^{18} - 8 q^{19} - 44 q^{20} + 14 q^{21} - 2 q^{22} - 4 q^{23} + 120 q^{24} - 104 q^{26} - 52 q^{27} + 56 q^{28} - 2 q^{29} - 130 q^{30} - 182 q^{32} - 8 q^{33} - 10 q^{34} + 92 q^{35} - 2 q^{36} - 8 q^{37} - 254 q^{38} + 184 q^{39} - 2 q^{40} - 252 q^{42} - 2 q^{43} - 140 q^{44} - 54 q^{45} + 176 q^{46} + 162 q^{48} - 480 q^{49} - 96 q^{50} - 120 q^{51} - 2 q^{52} - 8 q^{53} + 94 q^{54} - 16 q^{55} + 260 q^{56} + 88 q^{58} + 142 q^{59} - 434 q^{60} - 2 q^{61} - 636 q^{62} + 244 q^{64} - 4 q^{65} - 100 q^{66} - 2 q^{67} - 112 q^{68} + 14 q^{69} - 100 q^{70} - 16 q^{71} + 98 q^{72} + 82 q^{74} - 296 q^{75} + 154 q^{76} + 194 q^{77} + 228 q^{78} + 592 q^{80} - 8 q^{81} - 420 q^{82} + 238 q^{83} - 22 q^{84} - 52 q^{85} - 170 q^{86} - 456 q^{87} - 26 q^{88} + 808 q^{90} + 188 q^{91} + 176 q^{92} + 26 q^{93} - 18 q^{94} - 202 q^{96} - 4 q^{97} + 408 q^{98} - 38 q^{99}+O(q^{100}) \) 184 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^8 - 8 * q^10 - 2 * q^11 + 56 * q^12 - 2 * q^13 + 14 * q^14 - 2 * q^16 - 16 * q^17 + 38 * q^18 - 8 * q^19 - 44 * q^20 + 14 * q^21 - 2 * q^22 - 4 * q^23 + 120 * q^24 - 104 * q^26 - 52 * q^27 + 56 * q^28 - 2 * q^29 - 130 * q^30 - 182 * q^32 - 8 * q^33 - 10 * q^34 + 92 * q^35 - 2 * q^36 - 8 * q^37 - 254 * q^38 + 184 * q^39 - 2 * q^40 - 252 * q^42 - 2 * q^43 - 140 * q^44 - 54 * q^45 + 176 * q^46 + 162 * q^48 - 480 * q^49 - 96 * q^50 - 120 * q^51 - 2 * q^52 - 8 * q^53 + 94 * q^54 - 16 * q^55 + 260 * q^56 + 88 * q^58 + 142 * q^59 - 434 * q^60 - 2 * q^61 - 636 * q^62 + 244 * q^64 - 4 * q^65 - 100 * q^66 - 2 * q^67 - 112 * q^68 + 14 * q^69 - 100 * q^70 - 16 * q^71 + 98 * q^72 + 82 * q^74 - 296 * q^75 + 154 * q^76 + 194 * q^77 + 228 * q^78 + 592 * q^80 - 8 * q^81 - 420 * q^82 + 238 * q^83 - 22 * q^84 - 52 * q^85 - 170 * q^86 - 456 * q^87 - 26 * q^88 + 808 * q^90 + 188 * q^91 + 176 * q^92 + 26 * q^93 - 18 * q^94 - 202 * q^96 - 4 * q^97 + 408 * q^98 - 38 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more