LMFDB - Embedded newform 462.2.n.f.65.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(65,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("462.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.n (of order $6$, degree $2$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.2
Character	$\chi$	$=$	462.65
Dual form			462.2.n.f.263.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.64448 - 0.543759i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.63087 + 0.941585i) q^{5} +(-1.29315 + 1.15228i) q^{6} +(1.76745 + 1.96879i) q^{7} -1.00000 q^{8} +(2.40865 + 1.78841i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.64448 - 0.543759i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.63087 + 0.941585i) q^{5} +(-1.29315 + 1.15228i) q^{6} +(1.76745 + 1.96879i) q^{7} -1.00000 q^{8} +(2.40865 + 1.78841i) q^{9} +(1.63087 - 0.941585i) q^{10} +(-0.803239 + 3.21789i) q^{11} +(0.351333 + 1.69604i) q^{12} -1.92843i q^{13} +(2.58874 - 0.546260i) q^{14} +(-2.16995 - 2.43522i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.83021 + 3.17001i) q^{17} +(2.75313 - 1.19175i) q^{18} +(2.68054 + 1.54761i) q^{19} -1.88317i q^{20} +(-1.83599 - 4.19871i) q^{21} +(2.38515 + 2.30457i) q^{22} +(3.71066 + 2.14235i) q^{23} +(1.64448 + 0.543759i) q^{24} +(-0.726834 - 1.25891i) q^{25} +(-1.67007 - 0.964214i) q^{26} +(-2.98853 - 4.25073i) q^{27} +(0.821298 - 2.51505i) q^{28} +9.69651 q^{29} +(-3.19394 + 0.661619i) q^{30} +(-5.11862 - 8.86571i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.07067 - 4.85500i) q^{33} +3.66041 q^{34} +(1.02870 + 4.87505i) q^{35} +(0.344479 - 2.98016i) q^{36} +(4.15848 - 7.20269i) q^{37} +(2.68054 - 1.54761i) q^{38} +(-1.04860 + 3.17127i) q^{39} +(-1.63087 - 0.941585i) q^{40} -6.35661 q^{41} +(-4.55418 - 0.509339i) q^{42} +6.75096i q^{43} +(3.18839 - 0.913319i) q^{44} +(2.24427 + 5.18462i) q^{45} +(3.71066 - 2.14235i) q^{46} +(-4.43228 - 2.55898i) q^{47} +(1.29315 - 1.15228i) q^{48} +(-0.752260 + 6.95946i) q^{49} -1.45367 q^{50} +(-1.28602 - 6.20822i) q^{51} +(-1.67007 + 0.964214i) q^{52} +(2.07152 - 1.19599i) q^{53} +(-5.17550 + 0.462774i) q^{54} +(-4.33990 + 4.49165i) q^{55} +(-1.76745 - 1.96879i) q^{56} +(-3.56658 - 4.00259i) q^{57} +(4.84825 - 8.39742i) q^{58} +(-9.50971 + 5.49043i) q^{59} +(-1.02399 + 3.09684i) q^{60} +(10.0627 + 5.80969i) q^{61} -10.2372 q^{62} +(0.736171 + 7.90304i) q^{63} +1.00000 q^{64} +(1.81578 - 3.14502i) q^{65} +(-2.66921 - 5.08678i) q^{66} +(5.56729 + 9.64283i) q^{67} +(1.83021 - 3.17001i) q^{68} +(-4.93720 - 5.54077i) q^{69} +(4.73627 + 1.54664i) q^{70} +9.77457i q^{71} +(-2.40865 - 1.78841i) q^{72} +(1.82066 - 1.05116i) q^{73} +(-4.15848 - 7.20269i) q^{74} +(0.510721 + 2.46549i) q^{75} -3.09522i q^{76} +(-7.75503 + 4.10604i) q^{77} +(2.22210 + 2.49375i) q^{78} +(-9.73232 - 5.61896i) q^{79} +(-1.63087 + 0.941585i) q^{80} +(2.60321 + 8.61529i) q^{81} +(-3.17830 + 5.50499i) q^{82} -2.34518 q^{83} +(-2.71819 + 3.68937i) q^{84} +6.89318i q^{85} +(5.84651 + 3.37548i) q^{86} +(-15.9457 - 5.27256i) q^{87} +(0.803239 - 3.21789i) q^{88} +(-10.7547 - 6.20926i) q^{89} +(5.61214 + 0.648713i) q^{90} +(3.79667 - 3.40839i) q^{91} -4.28470i q^{92} +(3.59668 + 17.3628i) q^{93} +(-4.43228 + 2.55898i) q^{94} +(2.91441 + 5.04791i) q^{95} +(-0.351333 - 1.69604i) q^{96} -0.0299777 q^{97} +(5.65094 + 4.13121i) q^{98} +(-7.68961 + 6.31426i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} - 8 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 - 8 * q^9	$ 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} - 8 q^{9} + 4 q^{11} + 4 q^{15} - 12 q^{16} - 4 q^{17} + 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} - 40 q^{29} + 2 q^{30} - 28 q^{31} + 12 q^{32} + 24 q^{33} - 8 q^{34} + 32 q^{35} + 16 q^{36} - 16 q^{37} + 8 q^{41} + 6 q^{42} + 4 q^{44} - 28 q^{45} - 8 q^{49} + 40 q^{50} + 34 q^{51} - 6 q^{54} + 8 q^{55} - 40 q^{57} - 20 q^{58} - 2 q^{60} - 56 q^{62} + 14 q^{63} + 24 q^{64} + 44 q^{65} - 24 q^{66} - 4 q^{68} - 20 q^{69} + 64 q^{70} + 8 q^{72} + 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} - 144 q^{83} + 6 q^{84} - 8 q^{87} - 4 q^{88} - 56 q^{90} - 32 q^{91} - 22 q^{93} + 44 q^{95} + 64 q^{97} + 8 q^{98} + 28 q^{99}+O(q^{100}) $ 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 - 8 * q^9 + 4 * q^11 + 4 * q^15 - 12 * q^16 - 4 * q^17 + 8 * q^18 + 8 * q^22 + 20 * q^25 - 12 * q^27 - 40 * q^29 + 2 * q^30 - 28 * q^31 + 12 * q^32 + 24 * q^33 - 8 * q^34 + 32 * q^35 + 16 * q^36 - 16 * q^37 + 8 * q^41 + 6 * q^42 + 4 * q^44 - 28 * q^45 - 8 * q^49 + 40 * q^50 + 34 * q^51 - 6 * q^54 + 8 * q^55 - 40 * q^57 - 20 * q^58 - 2 * q^60 - 56 * q^62 + 14 * q^63 + 24 * q^64 + 44 * q^65 - 24 * q^66 - 4 * q^68 - 20 * q^69 + 64 * q^70 + 8 * q^72 + 16 * q^74 - 26 * q^75 + 24 * q^81 + 4 * q^82 - 144 * q^83 + 6 * q^84 - 8 * q^87 - 4 * q^88 - 56 * q^90 - 32 * q^91 - 22 * q^93 + 44 * q^95 + 64 * q^97 + 8 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.64448	−	0.543759i	−0.949443	−	0.313939i
$3$	−1.64448	−	0.543759i	−0.949443	−	0.313939i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.63087	+	0.941585i	0.729349	+	0.421090i	0.818184	−	0.574957i	$-0.194981\pi$
$5$	1.63087	+	0.941585i	0.729349	+	0.421090i	−0.0888351	+	0.996046i	$0.528314\pi$
$6$	−1.29315	+	1.15228i	−0.527927	+	0.470418i
$7$	1.76745	+	1.96879i	0.668032	+	0.744132i
$7$	1.76745	+	1.96879i	0.668032	+	0.744132i
$8$	−1.00000			−0.353553
$9$	2.40865	+	1.78841i	0.802884	+	0.596135i
$10$	1.63087	−	0.941585i	0.515728	−	0.297755i
$11$	−0.803239	+	3.21789i	−0.242186	+	0.970230i
$11$	−0.803239	+	3.21789i	−0.242186	+	0.970230i
$12$	0.351333	+	1.69604i	0.101421	+	0.489606i
$13$		−	1.92843i		−	0.534849i	−0.963579	−	0.267425i	$-0.913827\pi$
$13$		−	1.92843i		−	0.534849i	0.963579	−	0.267425i	$-0.0861727\pi$
$14$	2.58874	−	0.546260i	0.691871	−	0.145994i
$15$	−2.16995	−	2.43522i	−0.560278	−	0.628772i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.83021	+	3.17001i	0.443890	+	0.768841i	0.997974	−	0.0636202i	$-0.0202646\pi$
$17$	1.83021	+	3.17001i	0.443890	+	0.768841i	−0.554084	+	0.832461i	$0.686931\pi$
$18$	2.75313	−	1.19175i	0.648919	−	0.280898i
$19$	2.68054	+	1.54761i	0.614958	+	0.355046i	0.774903	−	0.632080i	$-0.217798\pi$
$19$	2.68054	+	1.54761i	0.614958	+	0.355046i	−0.159945	+	0.987126i	$0.551132\pi$
$20$		−	1.88317i		−	0.421090i
$21$	−1.83599	−	4.19871i	−0.400646	−	0.916233i
$22$	2.38515	+	2.30457i	0.508516	+	0.491336i
$23$	3.71066	+	2.14235i	0.773726	+	0.446711i	0.834202	−	0.551459i	$-0.185929\pi$
$23$	3.71066	+	2.14235i	0.773726	+	0.446711i	−0.0604759	+	0.998170i	$0.519262\pi$
$24$	1.64448	+	0.543759i	0.335679	+	0.110994i
$25$	−0.726834	−	1.25891i	−0.145367	−	0.251783i
$26$	−1.67007	−	0.964214i	−0.327527	−	0.189098i
$27$	−2.98853	−	4.25073i	−0.575142	−	0.818053i
$28$	0.821298	−	2.51505i	0.155211	−	0.475300i
$29$	9.69651			1.80060			0.900298	−	0.435274i	$-0.143348\pi$
$29$	9.69651			1.80060			0.900298	+	0.435274i	$0.143348\pi$
$30$	−3.19394	+	0.661619i	−0.583131	+	0.120795i
$31$	−5.11862	−	8.86571i	−0.919331	−	1.59233i	−0.800433	−	0.599422i	$-0.795397\pi$
$31$	−5.11862	−	8.86571i	−0.919331	−	1.59233i	−0.118899	−	0.992906i	$-0.537936\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	3.07067	−	4.85500i	0.534535	−	0.845146i
$34$	3.66041			0.627756
$35$	1.02870	+	4.87505i	0.173882	+	0.824034i
$36$	0.344479	−	2.98016i	0.0574132	−	0.496693i
$37$	4.15848	−	7.20269i	0.683649	−	1.18412i	−0.290210	−	0.956963i	$-0.593725\pi$
$37$	4.15848	−	7.20269i	0.683649	−	1.18412i	0.973859	−	0.227152i	$-0.0729415\pi$
$38$	2.68054	−	1.54761i	0.434841	−	0.251056i
$39$	−1.04860	+	3.17127i	−0.167910	+	0.507809i
$40$	−1.63087	−	0.941585i	−0.257864	−	0.148878i
$41$	−6.35661			−0.992736			−0.496368	−	0.868112i	$-0.665333\pi$
$41$	−6.35661			−0.992736			−0.496368	+	0.868112i	$0.665333\pi$
$42$	−4.55418	−	0.509339i	−0.702726	−	0.0785927i
$43$			6.75096i			1.02951i	0.857337	+	0.514756i	$0.172118\pi$
$43$			6.75096i			1.02951i	−0.857337	+	0.514756i	$0.827882\pi$
$44$	3.18839	−	0.913319i	0.480668	−	0.137688i
$45$	2.24427	+	5.18462i	0.334556	+	0.772877i
$46$	3.71066	−	2.14235i	0.547107	−	0.315872i
$47$	−4.43228	−	2.55898i	−0.646515	−	0.373265i	0.140605	−	0.990066i	$-0.455095\pi$
$47$	−4.43228	−	2.55898i	−0.646515	−	0.373265i	−0.787120	+	0.616800i	$0.788429\pi$
$48$	1.29315	−	1.15228i	0.186650	−	0.166318i
$49$	−0.752260	+	6.95946i	−0.107466	+	0.994209i
$50$	−1.45367			−0.205580
$51$	−1.28602	−	6.20822i	−0.180079	−	0.869325i
$52$	−1.67007	+	0.964214i	−0.231597	+	0.133712i
$53$	2.07152	−	1.19599i	0.284545	−	0.164282i	−0.350934	−	0.936400i	$-0.614136\pi$
$53$	2.07152	−	1.19599i	0.284545	−	0.164282i	0.635479	+	0.772118i	$0.280803\pi$
$54$	−5.17550	+	0.462774i	−0.704297	+	0.0629756i
$55$	−4.33990	+	4.49165i	−0.585192	+	0.605654i
$56$	−1.76745	−	1.96879i	−0.236185	−	0.263090i
$57$	−3.56658	−	4.00259i	−0.472405	−	0.530156i
$58$	4.84825	−	8.39742i	0.636607	−	1.10264i
$59$	−9.50971	+	5.49043i	−1.23806	+	0.714794i	−0.968697	−	0.248246i	$-0.920146\pi$
$59$	−9.50971	+	5.49043i	−1.23806	+	0.714794i	−0.269362	+	0.963039i	$0.586813\pi$
$60$	−1.02399	+	3.09684i	−0.132197	+	0.399801i
$61$	10.0627	+	5.80969i	1.28839	+	0.743854i	0.978368	−	0.206874i	$-0.0663291\pi$
$61$	10.0627	+	5.80969i	1.28839	+	0.743854i	0.310025	+	0.950728i	$0.399662\pi$
$62$	−10.2372			−1.30013
$63$	0.736171	+	7.90304i	0.0927489	+	0.995690i
$64$	1.00000			0.125000
$65$	1.81578	−	3.14502i	0.225220	−	0.390092i
$66$	−2.66921	−	5.08678i	−0.328558	−	0.626139i
$67$	5.56729	+	9.64283i	0.680153	+	1.17806i	0.974934	+	0.222495i	$0.0714200\pi$
$67$	5.56729	+	9.64283i	0.680153	+	1.17806i	−0.294781	+	0.955565i	$0.595247\pi$
$68$	1.83021	−	3.17001i	0.221945	−	0.384420i
$69$	−4.93720	−	5.54077i	−0.594369	−	0.667030i
$70$	4.73627	+	1.54664i	0.566092	+	0.184859i
$71$			9.77457i			1.16003i	0.814607	+	0.580014i	$0.196953\pi$
$71$			9.77457i			1.16003i	−0.814607	+	0.580014i	$0.803047\pi$
$72$	−2.40865	−	1.78841i	−0.283862	−	0.210766i
$73$	1.82066	−	1.05116i	0.213092	−	0.123029i	−0.389655	−	0.920961i	$-0.627406\pi$
$73$	1.82066	−	1.05116i	0.213092	−	0.123029i	0.602748	+	0.797932i	$0.294073\pi$
$74$	−4.15848	−	7.20269i	−0.483413	−	0.837296i
$75$	0.510721	+	2.46549i	0.0589730	+	0.284690i
$76$		−	3.09522i		−	0.355046i
$77$	−7.75503	+	4.10604i	−0.883767	+	0.467927i
$78$	2.22210	+	2.49375i	0.251603	+	0.282361i
$79$	−9.73232	−	5.61896i	−1.09497	−	0.632182i	−0.160076	−	0.987105i	$-0.551174\pi$
$79$	−9.73232	−	5.61896i	−1.09497	−	0.632182i	−0.934896	+	0.354922i	$0.884507\pi$
$80$	−1.63087	+	0.941585i	−0.182337	+	0.105272i
$81$	2.60321	+	8.61529i	0.289245	+	0.957255i
$82$	−3.17830	+	5.50499i	−0.350985	+	0.607924i
$83$	−2.34518			−0.257417			−0.128709	−	0.991682i	$-0.541083\pi$
$83$	−2.34518			−0.257417			−0.128709	+	0.991682i	$0.541083\pi$
$84$	−2.71819	+	3.68937i	−0.296579	+	0.402543i
$85$			6.89318i			0.747671i
$86$	5.84651	+	3.37548i	0.630445	+	0.363988i
$87$	−15.9457	−	5.27256i	−1.70956	−	0.565278i
$88$	0.803239	−	3.21789i	0.0856256	−	0.343028i
$89$	−10.7547	−	6.20926i	−1.14000	−	0.658180i	−0.193570	−	0.981086i	$-0.562007\pi$
$89$	−10.7547	−	6.20926i	−1.14000	−	0.658180i	−0.946431	+	0.322907i	$0.895340\pi$
$90$	5.61214	+	0.648713i	0.591572	+	0.0683803i
$91$	3.79667	−	3.40839i	0.397999	−	0.357297i
$92$		−	4.28470i		−	0.446711i
$93$	3.59668	+	17.3628i	0.372958	+	1.80044i
$94$	−4.43228	+	2.55898i	−0.457155	+	0.263938i
$95$	2.91441	+	5.04791i	0.299013	+	0.517905i
$96$	−0.351333	−	1.69604i	−0.0358577	−	0.173102i
$97$	−0.0299777			−0.00304378			−0.00152189	−	0.999999i	$-0.500484\pi$
$97$	−0.0299777			−0.00304378			−0.00152189	+	0.999999i	$0.500484\pi$
$98$	5.65094	+	4.13121i	0.570831	+	0.417315i
$99$	−7.68961	+	6.31426i	−0.772835	+	0.634607i
$100$	−0.726834	+	1.25891i	−0.0726834	+	0.125891i
$101$	−3.38899	−	5.86990i	−0.337217	−	0.584077i	0.646691	−	0.762752i	$-0.276152\pi$
$101$	−3.38899	−	5.86990i	−0.337217	−	0.584077i	−0.983908	+	0.178675i	$0.942819\pi$
$102$	−6.01949	−	1.99038i	−0.596018	−	0.197077i
$103$	6.44521	−	11.1634i	0.635065	−	1.09997i	−0.351436	−	0.936212i	$-0.614307\pi$
$103$	6.44521	−	11.1634i	0.635065	−	1.09997i	0.986501	−	0.163753i	$-0.0523602\pi$
$104$			1.92843i			0.189098i
$105$	0.959172	−	8.57630i	0.0936056	−	0.836961i
$106$		−	2.39199i		−	0.232330i
$107$	2.11847	−	3.66929i	0.204800	−	0.354724i	−0.745269	−	0.666764i	$-0.767679\pi$
$107$	2.11847	−	3.66929i	0.204800	−	0.354724i	0.950069	+	0.312040i	$0.101012\pi$
$108$	−2.18698	+	4.71350i	−0.210442	+	0.453557i
$109$	1.52333	−	0.879494i	0.145908	−	0.0842403i	−0.425269	−	0.905067i	$-0.639820\pi$
$109$	1.52333	−	0.879494i	0.145908	−	0.0842403i	0.571177	+	0.820827i	$0.306487\pi$
$110$	1.71994	+	6.00429i	0.163989	+	0.572486i
$111$	−10.7551	+	9.58350i	−1.02083	+	0.909625i
$112$	−2.58874	+	0.546260i	−0.244613	+	0.0516167i
$113$		−	7.04904i		−	0.663118i	−0.943435	−	0.331559i	$-0.892425\pi$
$113$		−	7.04904i		−	0.663118i	0.943435	−	0.331559i	$-0.107575\pi$
$114$	−5.24963	+	1.08745i	−0.491673	+	0.101849i
$115$	4.03441	+	6.98781i	0.376211	+	0.651617i
$116$	−4.84825	−	8.39742i	−0.450149	−	0.779681i
$117$	3.44881	−	4.64491i	0.318843	−	0.429422i
$118$			10.9809i			1.01087i
$119$	−3.00629	+	9.20612i	−0.275586	+	0.843924i
$120$	2.16995	+	2.43522i	0.198088	+	0.222305i
$121$	−9.70961	−	5.16947i	−0.882692	−	0.469952i
$122$	10.0627	−	5.80969i	0.911031	−	0.525984i
$123$	10.4533	+	3.45646i	0.942546	+	0.311659i
$124$	−5.11862	+	8.86571i	−0.459666	+	0.796164i
$125$		−	12.1534i		−	1.08703i
$126$	7.21232	+	3.31398i	0.642525	+	0.295233i
$127$		−	12.5296i		−	1.11182i	−0.831243	−	0.555909i	$-0.812370\pi$
$127$		−	12.5296i		−	1.11182i	0.831243	−	0.555909i	$-0.187630\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	3.67090	−	11.1019i	0.323205	−	0.977463i
$130$	−1.81578	−	3.14502i	−0.159254	−	0.275837i
$131$	0.954269	−	1.65284i	0.0833749	−	0.144410i	−0.821323	−	0.570464i	$-0.806763\pi$
$131$	0.954269	−	1.65284i	0.0833749	−	0.144410i	0.904698	+	0.426054i	$0.140097\pi$
$132$	−5.73988	−	0.231780i	−0.499593	−	0.0201739i
$133$	1.69079	+	8.01274i	0.146610	+	0.694792i
$134$	11.1346			0.961882
$135$	−0.871483	−	9.74636i	−0.0750053	−	0.838833i
$136$	−1.83021	−	3.17001i	−0.156939	−	0.271826i
$137$	−0.456798	+	0.263732i	−0.0390269	+	0.0225322i	−0.519386	−	0.854539i	$-0.673839\pi$
$137$	−0.456798	+	0.263732i	−0.0390269	+	0.0225322i	0.480360	+	0.877072i	$0.340506\pi$
$138$	−7.26704	+	1.50536i	−0.618612	+	0.128144i
$139$		−	2.83391i		−	0.240369i	−0.992752	−	0.120185i	$-0.961651\pi$
$139$		−	2.83391i		−	0.240369i	0.992752	−	0.120185i	$-0.0383487\pi$
$140$	3.70757	−	3.32840i	0.313346	−	0.281302i
$141$	5.89734	+	6.61829i	0.496646	+	0.557361i
$142$	8.46502	+	4.88728i	0.710369	+	0.410132i
$143$	6.20546	+	1.54899i	0.518927	+	0.129533i
$144$	−2.75313	+	1.19175i	−0.229428	+	0.0993126i
$145$	15.8138	+	9.13009i	1.31326	+	0.758213i
$146$		−	2.10232i		−	0.173989i
$147$	5.02135	−	11.0357i	0.414154	−	0.910207i
$148$	−8.31695			−0.683649
$149$	6.58936	−	11.4131i	0.539821	−	0.934998i	−0.459092	−	0.888389i	$-0.651825\pi$
$149$	6.58936	−	11.4131i	0.539821	−	0.934998i	0.998913	−	0.0466093i	$-0.0148416\pi$
$150$	2.39053	+	0.790445i	0.195186	+	0.0645396i
$151$	−16.8439	+	9.72486i	−1.37074	+	0.791398i	−0.991021	−	0.133704i	$-0.957313\pi$
$151$	−16.8439	+	9.72486i	−1.37074	+	0.791398i	−0.379719	+	0.925102i	$0.623979\pi$
$152$	−2.68054	−	1.54761i	−0.217421	−	0.125528i
$153$	−1.26094	+	10.9086i	−0.101941	+	0.881909i
$154$	−0.321578	+	8.76907i	−0.0259135	+	0.706632i
$155$		−	19.2785i		−	1.54848i
$156$	3.27070	−	0.677519i	0.261865	−	0.0542449i
$157$	1.05398	+	1.82555i	0.0841170	+	0.145695i	0.905015	−	0.425380i	$-0.139860\pi$
$157$	1.05398	+	1.82555i	0.0841170	+	0.145695i	−0.820898	+	0.571075i	$0.806526\pi$
$158$	−9.73232	+	5.61896i	−0.774262	+	0.447020i
$159$	−4.05692	+	0.840383i	−0.321734	+	0.0666467i
$160$			1.88317i			0.148878i
$161$	2.34056	+	11.0920i	0.184462	+	0.874172i
$162$	8.76267	+	2.05320i	0.688460	+	0.161315i
$163$	1.59864	−	2.76892i	0.125215	−	0.216878i	−0.796602	−	0.604504i	$-0.793371\pi$
$163$	1.59864	−	2.76892i	0.125215	−	0.216878i	0.921817	+	0.387626i	$0.126705\pi$
$164$	3.17830	+	5.50499i	0.248184	+	0.429867i
$165$	9.57927	−	5.02659i	0.745745	−	0.391319i
$166$	−1.17259	+	2.03099i	−0.0910108	+	0.157635i
$167$	2.23560			0.172996			0.0864980	−	0.996252i	$-0.472432\pi$
$167$	2.23560			0.172996			0.0864980	+	0.996252i	$0.472432\pi$
$168$	1.83599	+	4.19871i	0.141650	+	0.323937i
$169$	9.28117			0.713936
$170$	5.96967	+	3.44659i	0.457853	+	0.264342i
$171$	3.68873	+	8.52155i	0.282084	+	0.651659i
$172$	5.84651	−	3.37548i	0.445792	−	0.257378i
$173$	−6.02196	+	10.4303i	−0.457841	+	0.793005i	−0.998847	−	0.0480147i	$-0.984711\pi$
$173$	−6.02196	+	10.4303i	−0.457841	+	0.793005i	0.541005	+	0.841019i	$0.318044\pi$
$174$	−12.5390	+	11.1731i	−0.950583	+	0.847034i
$175$	1.19389	−	3.65605i	0.0902499	−	0.276371i
$176$	−2.38515	−	2.30457i	−0.179788	−	0.173713i
$177$	18.6240	−	3.85794i	1.39987	−	0.289980i
$178$	−10.7547	+	6.20926i	−0.806102	+	0.465403i
$179$	0.922959	−	0.532870i	0.0689852	−	0.0398286i	−0.465111	−	0.885253i	$-0.653985\pi$
$179$	0.922959	−	0.532870i	0.0689852	−	0.0398286i	0.534096	+	0.845424i	$0.320652\pi$
$180$	3.36787	−	4.53590i	0.251026	−	0.338086i
$181$	−5.88043			−0.437089			−0.218544	−	0.975827i	$-0.570131\pi$
$181$	−5.88043			−0.437089			−0.218544	+	0.975827i	$0.570131\pi$
$182$	−1.05342	−	4.99221i	−0.0780848	−	0.370047i
$183$	−13.3888	−	15.0256i	−0.989730	−	1.11072i
$184$	−3.71066	−	2.14235i	−0.273554	−	0.157936i
$185$	13.5639	−	7.83112i	0.997237	−	0.575755i
$186$	16.8350	+	5.56659i	1.23440	+	0.408162i
$187$	−11.6708	+	3.34312i	−0.853456	+	0.244473i
$188$			5.11796i			0.373265i
$189$	3.08673	−	13.3967i	0.224526	−	0.974468i
$190$	5.82883			0.422868
$191$	−13.1117	−	7.57002i	−0.948726	−	0.547747i	−0.0560409	−	0.998428i	$-0.517848\pi$
$191$	−13.1117	−	7.57002i	−0.948726	−	0.547747i	−0.892685	+	0.450681i	$0.851181\pi$
$192$	−1.64448	−	0.543759i	−0.118680	−	0.0392424i
$193$	7.77762	−	4.49041i	0.559845	−	0.323227i	−0.193238	−	0.981152i	$-0.561899\pi$
$193$	7.77762	−	4.49041i	0.559845	−	0.323227i	0.753083	+	0.657925i	$0.228566\pi$
$194$	−0.0149889	+	0.0259615i	−0.00107614	+	0.00186392i
$195$	−4.69615	+	4.18459i	−0.336298	+	0.299665i
$196$	6.40320	−	2.82825i	0.457371	−	0.202018i
$197$	−26.3131			−1.87473			−0.937365	−	0.348348i	$-0.886743\pi$
$197$	−26.3131			−1.87473			−0.937365	+	0.348348i	$0.886743\pi$
$198$	1.62350	+	9.81653i	0.115377	+	0.697630i
$199$	−11.1870	−	19.3764i	−0.793023	−	1.37356i	−0.924087	−	0.382183i	$-0.875172\pi$
$199$	−11.1870	−	19.3764i	−0.793023	−	1.37356i	0.131063	−	0.991374i	$-0.458161\pi$
$200$	0.726834	+	1.25891i	0.0513949	+	0.0890186i
$201$	−3.91194	−	18.8847i	−0.275927	−	1.33203i
$202$	−6.77798			−0.476897
$203$	17.1381	+	19.0904i	1.20286	+	1.33988i
$204$	−4.73347	+	4.21784i	−0.331409	+	0.295308i
$205$	−10.3668	−	5.98529i	−0.724051	−	0.418031i
$206$	−6.44521	−	11.1634i	−0.449059	−	0.777793i
$207$	5.10630	+	11.7963i	0.354912	+	0.819903i
$208$	1.67007	+	0.964214i	0.115798	+	0.0668562i
$209$	−7.13315	+	7.38258i	−0.493411	+	0.510664i
$210$	−6.94771	−	5.11882i	−0.479438	−	0.353232i
$211$		−	3.09207i		−	0.212867i	−0.994320	−	0.106434i	$-0.966057\pi$
$211$		−	3.09207i		−	0.212867i	0.994320	−	0.106434i	$-0.0339432\pi$
$212$	−2.07152	−	1.19599i	−0.142273	−	0.0821412i
$213$	5.31501	−	16.0741i	0.364178	−	1.10138i
$214$	−2.11847	−	3.66929i	−0.144815	−	0.250827i
$215$	−6.35661	+	11.0100i	−0.433517	+	0.750874i
$216$	2.98853	+	4.25073i	0.203343	+	0.289226i
$217$	8.40782	−	25.7472i	0.570760	−	1.74783i
$218$		−	1.75899i		−	0.119134i
$219$	−3.56562	+	0.738613i	−0.240943	+	0.0499108i
$220$	6.05983	+	1.51264i	0.408554	+	0.101982i
$221$	6.11314	−	3.52942i	0.411214	−	0.237415i
$222$	2.92202	+	14.1059i	0.196113	+	0.946727i
$223$	17.5862			1.17766			0.588829	−	0.808258i	$-0.299589\pi$
$223$	17.5862			1.17766			0.588829	+	0.808258i	$0.299589\pi$
$224$	−0.821298	+	2.51505i	−0.0548753	+	0.168044i
$225$	0.500758	−	4.33216i	0.0333839	−	0.288811i
$226$	−6.10465	−	3.52452i	−0.406075	−	0.234448i
$227$	−2.91997	−	5.05754i	−0.193805	−	0.335681i	0.752703	−	0.658360i	$-0.228750\pi$
$227$	−2.91997	−	5.05754i	−0.193805	−	0.335681i	−0.946508	+	0.322680i	$0.895416\pi$
$228$	−1.68305	+	5.09004i	−0.111463	+	0.337096i
$229$	−9.77062	+	16.9232i	−0.645661	+	1.11832i	0.338488	+	0.940971i	$0.390085\pi$
$229$	−9.77062	+	16.9232i	−0.645661	+	1.11832i	−0.984149	+	0.177346i	$0.943249\pi$
$230$	8.06883			0.532043
$231$	14.9857	−	2.53545i	0.985987	−	0.166820i
$232$	−9.69651			−0.636607
$233$	−7.60946	+	13.1800i	−0.498512	+	0.863448i	−0.999999	−	0.00171719i	$-0.999453\pi$
$233$	−7.60946	+	13.1800i	−0.498512	+	0.863448i	0.501486	+	0.865166i	$0.332787\pi$
$234$	−2.29820	−	5.30921i	−0.150238	−	0.347074i
$235$	−4.81899	−	8.34674i	−0.314356	−	0.544481i
$236$	9.50971	+	5.49043i	0.619029	+	0.357397i
$237$	12.9493	+	14.5323i	0.841146	+	0.943976i
$238$	6.46959	+	7.20658i	0.419361	+	0.467133i
$239$	7.81811			0.505712			0.252856	−	0.967504i	$-0.418630\pi$
$239$	7.81811			0.505712			0.252856	+	0.967504i	$0.418630\pi$
$240$	3.19394	−	0.661619i	0.206168	−	0.0427073i
$241$	−17.1878	+	9.92339i	−1.10717	+	0.639222i	−0.938094	−	0.346382i	$-0.887410\pi$
$241$	−17.1878	+	9.92339i	−1.10717	+	0.639222i	−0.169071	+	0.985604i	$0.554077\pi$
$242$	−9.33170	+	5.82404i	−0.599864	+	0.374383i
$243$	0.403712	−	15.5832i	0.0258981	−	0.999665i
$244$		−	11.6194i		−	0.743854i
$245$	−7.77977	+	10.6417i	−0.497031	+	0.679872i
$246$	8.22006	−	7.32462i	0.524092	−	0.467001i
$247$	2.98445	−	5.16923i	0.189896	−	0.328910i
$248$	5.11862	+	8.86571i	0.325033	+	0.562973i
$249$	3.85662	+	1.27521i	0.244403	+	0.0808135i
$250$	−10.5251	−	6.07668i	−0.665667	−	0.384323i
$251$		−	8.52934i		−	0.538367i	−0.963089	−	0.269184i	$-0.913246\pi$
$251$		−	8.52934i		−	0.538367i	0.963089	−	0.269184i	$-0.0867538\pi$
$252$	6.47615	−	4.58906i	0.407959	−	0.289084i
$253$	−9.87440	+	10.2197i	−0.620798	+	0.642505i
$254$	−10.8509	−	6.26478i	−0.680847	−	0.393087i
$255$	3.74823	−	11.3357i	0.234723	−	0.709871i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.21369	−	2.43278i	−0.262843	−	0.151752i	0.362788	−	0.931872i	$-0.381825\pi$
$257$	−4.21369	−	2.43278i	−0.262843	−	0.151752i	−0.625631	+	0.780119i	$0.715158\pi$
$258$	−7.77903	−	8.73002i	−0.484302	−	0.543507i
$259$	21.5305	−	4.54322i	1.33784	−	0.282302i
$260$	−3.63156			−0.225220
$261$	23.3555	+	17.3413i	1.44567	+	1.07340i
$262$	−0.954269	−	1.65284i	−0.0589549	−	0.102113i
$263$	4.34326	+	7.52274i	0.267817	+	0.463872i	0.968298	−	0.249799i	$-0.0803645\pi$
$263$	4.34326	+	7.52274i	0.267817	+	0.463872i	−0.700481	+	0.713671i	$0.747031\pi$
$264$	−3.07067	+	4.85500i	−0.188987	+	0.298804i
$265$	4.50452			0.276711
$266$	7.78463	+	2.54210i	0.477306	+	0.155866i
$267$	14.3097	+	16.0590i	0.875737	+	0.982796i
$268$	5.56729	−	9.64283i	0.340077	−	0.589030i
$269$	4.58369	−	2.64640i	0.279473	−	0.161354i	−0.353712	−	0.935354i	$-0.615081\pi$
$269$	4.58369	−	2.64640i	0.279473	−	0.161354i	0.633185	+	0.774001i	$0.281747\pi$
$270$	−8.87633	−	4.11845i	−0.540197	−	0.250641i
$271$	11.7299	+	6.77227i	0.712541	+	0.411386i	0.812001	−	0.583656i	$-0.198378\pi$
$271$	11.7299	+	6.77227i	0.712541	+	0.411386i	−0.0994600	+	0.995042i	$0.531712\pi$
$272$	−3.66041			−0.221945
$273$	−8.09690	+	3.54057i	−0.490047	+	0.214285i
$274$			0.527465i			0.0318653i
$275$	4.63487	−	1.32766i	0.279493	−	0.0800611i
$276$	−2.32985	+	7.04612i	−0.140240	+	0.424127i
$277$	3.05634	−	1.76458i	0.183637	−	0.106023i	−0.405363	−	0.914156i	$-0.632855\pi$
$277$	3.05634	−	1.76458i	0.183637	−	0.106023i	0.589001	+	0.808133i	$0.299522\pi$
$278$	−2.45424	−	1.41696i	−0.147196	−	0.0849834i
$279$	3.52651	−	30.5086i	0.211127	−	1.82650i
$280$	−1.02870	−	4.87505i	−0.0614766	−	0.291340i
$281$	0.0460619			0.00274782			0.00137391	−	0.999999i	$-0.499563\pi$
$281$	0.0460619			0.00274782			0.00137391	+	0.999999i	$0.499563\pi$
$282$	8.68028	−	1.79810i	0.516903	−	0.107076i
$283$	17.9928	−	10.3882i	1.06956	−	0.617513i	0.141501	−	0.989938i	$-0.454807\pi$
$283$	17.9928	−	10.3882i	1.06956	−	0.617513i	0.928062	+	0.372425i	$0.121474\pi$
$284$	8.46502	−	4.88728i	0.502307	−	0.290007i
$285$	−2.04786	−	9.88595i	−0.121305	−	0.585593i
$286$	4.44419	−	4.59960i	0.262791	−	0.271980i
$287$	−11.2350	−	12.5148i	−0.663179	−	0.738727i
$288$	−0.344479	+	2.98016i	−0.0202986	+	0.175607i
$289$	1.80069	−	3.11888i	0.105923	−	0.183464i
$290$	15.8138	−	9.13009i	0.928617	−	0.536137i
$291$	0.0492979	+	0.0163007i	0.00288989	+	0.000955562i
$292$	−1.82066	−	1.05116i	−0.106546	−	0.0615144i
$293$	4.89347			0.285879			0.142940	−	0.989731i	$-0.454344\pi$
$293$	4.89347			0.285879			0.142940	+	0.989731i	$0.454344\pi$
$294$	−7.04650	−	9.86645i	−0.410960	−	0.575423i
$295$	−20.6788			−1.20397
$296$	−4.15848	+	7.20269i	−0.241706	+	0.418648i
$297$	16.0789	−	6.20239i	0.932991	−	0.359899i
$298$	−6.58936	−	11.4131i	−0.381711	−	0.661144i
$299$	4.13137	−	7.15574i	0.238923	−	0.413827i
$300$	1.87981	−	1.67504i	0.108531	−	0.0967085i
$301$	−13.2912	+	11.9320i	−0.766093	+	0.687748i
$302$			19.4497i			1.11921i
$303$	2.38132	+	11.4957i	0.136803	+	0.660413i
$304$	−2.68054	+	1.54761i	−0.153740	+	0.0887616i
$305$	10.9406	+	18.9497i	0.626459	+	1.08506i
$306$	8.81666	+	6.54631i	0.504015	+	0.374227i
$307$		−	25.7355i		−	1.46880i	−0.678715	−	0.734402i	$-0.737463\pi$
$307$		−	25.7355i		−	1.46880i	0.678715	−	0.734402i	$-0.262537\pi$
$308$	7.43345	+	4.66303i	0.423560	+	0.265701i
$309$	−16.6693	+	14.8534i	−0.948281	+	0.844982i
$310$	−16.6956	−	9.63924i	−0.948249	−	0.547472i
$311$	−2.38671	+	1.37797i	−0.135338	+	0.0781373i	−0.566140	−	0.824309i	$-0.691564\pi$
$311$	−2.38671	+	1.37797i	−0.135338	+	0.0781373i	0.430802	+	0.902446i	$0.358231\pi$
$312$	1.04860	−	3.17127i	0.0593653	−	0.179538i
$313$	−6.72689	+	11.6513i	−0.380226	+	0.658571i	−0.991094	−	0.133161i	$-0.957487\pi$
$313$	−6.72689	+	11.6513i	−0.380226	+	0.658571i	0.610868	+	0.791732i	$0.290820\pi$
$314$	2.10797			0.118959
$315$	−6.24078	+	13.5820i	−0.351628	+	0.765261i
$316$			11.2379i			0.632182i
$317$	−4.97256	−	2.87091i	−0.279287	−	0.161246i	0.353814	−	0.935316i	$-0.384885\pi$
$317$	−4.97256	−	2.87091i	−0.279287	−	0.161246i	−0.633101	+	0.774070i	$0.718218\pi$
$318$	−1.30067	+	3.93358i	−0.0729377	+	0.220584i
$319$	−7.78861	+	31.2023i	−0.436079	+	1.74699i
$320$	1.63087	+	0.941585i	0.0911686	+	0.0526362i
$321$	−5.47899	+	4.88215i	−0.305807	+	0.272495i
$322$	10.7762	+	3.51902i	0.600536	+	0.196107i
$323$			11.3298i			0.630406i
$324$	6.15946	−	6.56209i	0.342192	−	0.364561i
$325$	−2.42772	+	1.40165i	−0.134666	+	0.0777494i
$326$	−1.59864	−	2.76892i	−0.0885403	−	0.153356i
$327$	−2.98332	+	0.617990i	−0.164978	+	0.0341749i
$328$	6.35661			0.350985
$329$	−2.79573	−	13.2491i	−0.154134	−	0.730446i
$330$	0.436482	−	10.8092i	0.0240275	−	0.595026i
$331$	4.29871	−	7.44558i	0.236278	−	0.409246i	−0.723365	−	0.690466i	$-0.757406\pi$
$331$	4.29871	−	7.44558i	0.236278	−	0.409246i	0.959643	+	0.281220i	$0.0907389\pi$
$332$	1.17259	+	2.03099i	0.0643543	+	0.111465i
$333$	22.8977	−	9.91173i	1.25478	−	0.543160i
$334$	1.11780	−	1.93609i	0.0611633	−	0.105938i
$335$			20.9683i			1.14562i
$336$	4.55418	+	0.509339i	0.248451	+	0.0277867i
$337$		−	8.82385i		−	0.480666i	−0.970691	−	0.240333i	$-0.922743\pi$
$337$		−	8.82385i		−	0.480666i	0.970691	−	0.240333i	$-0.0772566\pi$
$338$	4.64058	−	8.03773i	0.252415	−	0.437195i
$339$	−3.83298	+	11.5920i	−0.208179	+	0.629592i
$340$	5.96967	−	3.44659i	0.323751	−	0.186918i
$341$	32.6403	−	9.34987i	1.76757	−	0.506324i
$342$	9.22424	+	1.06624i	0.498790	+	0.0576556i
$343$	−15.0313	+	10.8194i	−0.811613	+	0.584195i
$344$		−	6.75096i		−	0.363988i
$345$	−2.83484	−	13.6851i	−0.152623	−	0.736780i
$346$	6.02196	+	10.4303i	0.323743	+	0.560739i
$347$	9.43262	+	16.3378i	0.506369	+	0.877058i	0.999973	+	0.00737048i	$0.00234612\pi$
$347$	9.43262	+	16.3378i	0.506369	+	0.877058i	−0.493603	+	0.869687i	$0.664321\pi$
$348$	3.40670	+	16.4457i	0.182618	+	0.881582i
$349$		−	5.90640i		−	0.316162i	−0.987426	−	0.158081i	$-0.949469\pi$
$349$		−	5.90640i		−	0.316162i	0.987426	−	0.158081i	$-0.0505307\pi$
$350$	−2.56928	−	2.86197i	−0.137334	−	0.152979i
$351$	−8.19722	+	5.76316i	−0.437535	+	0.307614i
$352$	−3.18839	+	0.913319i	−0.169942	+	0.0486801i
$353$	7.42132	−	4.28470i	0.394997	−	0.228052i	−0.289326	−	0.957231i	$-0.593431\pi$
$353$	7.42132	−	4.28470i	0.394997	−	0.228052i	0.684323	+	0.729179i	$0.260098\pi$
$354$	5.97095	−	18.0579i	0.317352	−	0.959764i
$355$	−9.20359	+	15.9411i	−0.488476	+	0.846065i
$356$			12.4185i			0.658180i
$357$	9.94970	−	13.5046i	0.526594	−	0.714740i
$358$		−	1.06574i		−	0.0563262i
$359$	14.6090	−	25.3035i	0.771033	−	1.33547i	−0.165964	−	0.986132i	$-0.553073\pi$
$359$	14.6090	−	25.3035i	0.771033	−	1.33547i	0.936997	−	0.349337i	$-0.113593\pi$
$360$	−2.24427	−	5.18462i	−0.118283	−	0.273253i
$361$	−4.70980	−	8.15762i	−0.247884	−	0.429348i
$362$	−2.94021	+	5.09260i	−0.154534	+	0.267661i
$363$	13.1564	+	13.7808i	0.690529	+	0.723304i
$364$	−4.85009	−	1.58381i	−0.254214	−	0.0830143i
$365$	3.95902			0.207225
$366$	−19.7070	+	4.08226i	−1.03010	+	0.213383i
$367$	1.05133	+	1.82095i	0.0548789	+	0.0950530i	0.892160	−	0.451720i	$-0.149189\pi$
$367$	1.05133	+	1.82095i	0.0548789	+	0.0950530i	−0.837281	+	0.546773i	$0.815856\pi$
$368$	−3.71066	+	2.14235i	−0.193432	+	0.111678i
$369$	−15.3109	−	11.3682i	−0.797052	−	0.591805i
$370$		−	15.6622i		−	0.814241i
$371$	6.01597	+	1.96453i	0.312333	+	0.101994i
$372$	13.2383	−	11.7962i	0.686374	−	0.611606i
$373$	24.2451	+	13.9979i	1.25536	+	0.724784i	0.972169	−	0.234280i	$-0.0752731\pi$
$373$	24.2451	+	13.9979i	1.25536	+	0.724784i	0.283193	+	0.959063i	$0.408606\pi$
$374$	−2.94019	+	11.7788i	−0.152033	+	0.609067i
$375$	−6.60850	+	19.9860i	−0.341261	+	1.03207i
$376$	4.43228	+	2.55898i	0.228577	+	0.131969i
$377$		−	18.6990i		−	0.963048i
$378$	−10.0585	−	9.37155i	−0.517355	−	0.482020i
$379$	−15.4596			−0.794105			−0.397053	−	0.917796i	$-0.629967\pi$
$379$	−15.4596			−0.794105			−0.397053	+	0.917796i	$0.629967\pi$
$380$	2.91441	−	5.04791i	0.149506	−	0.258953i
$381$	−6.81306	+	20.6046i	−0.349044	+	1.05561i
$382$	−13.1117	+	7.57002i	−0.670850	+	0.387316i
$383$	2.54013	+	1.46654i	0.129794	+	0.0749369i	0.563491	−	0.826122i	$-0.309458\pi$
$383$	2.54013	+	1.46654i	0.129794	+	0.0749369i	−0.433697	+	0.901059i	$0.642791\pi$
$384$	−1.29315	+	1.15228i	−0.0659908	+	0.0588023i
$385$	−16.5137	−	0.605587i	−0.841614	−	0.0308636i
$386$		−	8.98082i		−	0.457112i
$387$	−12.0735	+	16.2607i	−0.613729	+	0.826579i
$388$	0.0149889	+	0.0259615i	0.000760944	+	0.00131799i
$389$	−20.9725	+	12.1085i	−1.06335	+	0.613925i	−0.926357	−	0.376647i	$-0.877077\pi$
$389$	−20.9725	+	12.1085i	−1.06335	+	0.613925i	−0.136993	+	0.990572i	$0.543744\pi$
$390$	1.27588	+	6.15928i	0.0646069	+	0.311887i
$391$			15.6838i			0.793163i
$392$	0.752260	−	6.95946i	0.0379949	−	0.351506i
$393$	−2.46803	+	2.19918i	−0.124496	+	0.110934i
$394$	−13.1565	+	22.7878i	−0.662817	+	1.14803i
$395$	−10.5815	−	18.3276i	−0.532411	−	0.922163i
$396$	9.31311	+	3.50227i	0.468002	+	0.175996i
$397$	7.83756	−	13.5750i	0.393356	−	0.681312i	−0.599534	−	0.800349i	$-0.704647\pi$
$397$	7.83756	−	13.5750i	0.393356	−	0.681312i	0.992890	+	0.119037i	$0.0379808\pi$
$398$	−22.3739			−1.12150
$399$	1.57652	−	14.0962i	0.0789245	−	0.705693i
$400$	1.45367			0.0726834
$401$	−11.1027	−	6.41014i	−0.554442	−	0.320107i	0.196470	−	0.980510i	$-0.437052\pi$
$401$	−11.1027	−	6.41014i	−0.554442	−	0.320107i	−0.750911	+	0.660403i	$0.770386\pi$
$402$	−18.3106	−	6.05453i	−0.913252	−	0.301973i
$403$	−17.0969	+	9.87089i	−0.851656	+	0.491704i
$404$	−3.38899	+	5.86990i	−0.168608	+	0.292038i
$405$	−3.86653	+	16.5016i	−0.192129	+	0.819971i
$406$	25.1018	−	5.29681i	1.24578	−	0.262876i
$407$	19.8372	+	19.1670i	0.983294	+	0.950073i
$408$	1.28602	+	6.20822i	0.0636676	+	0.307353i
$409$	−26.5370	+	15.3212i	−1.31217	+	0.757583i	−0.982456	−	0.186497i	$-0.940287\pi$
$409$	−26.5370	+	15.3212i	−1.31217	+	0.757583i	−0.329717	+	0.944080i	$0.606953\pi$
$410$	−10.3668	+	5.98529i	−0.511981	+	0.295592i
$411$	0.894603	−	0.185316i	0.0441275	−	0.00914094i
$412$	−12.8904			−0.635065
$413$	−27.6174	−	9.01856i	−1.35896	−	0.443774i
$414$	12.7691	+	1.47599i	0.627566	+	0.0725410i
$415$	−3.82470	−	2.20819i	−0.187747	−	0.108396i
$416$	1.67007	−	0.964214i	0.0818818	−	0.0472745i
$417$	−1.54097	+	4.66032i	−0.0754614	+	0.228217i
$418$	2.82692	+	9.86878i	0.138269	+	0.482698i
$419$		−	5.27534i		−	0.257717i	−0.991663	−	0.128859i	$-0.958869\pi$
$419$		−	5.27534i		−	0.257717i	0.991663	−	0.128859i	$-0.0411313\pi$
$420$	−7.90688	+	3.45748i	−0.385816	+	0.168708i
$421$	−4.07368			−0.198539			−0.0992695	−	0.995061i	$-0.531651\pi$
$421$	−4.07368			−0.198539			−0.0992695	+	0.995061i	$0.531651\pi$
$422$	−2.67782	−	1.54604i	−0.130354	−	0.0752599i
$423$	−6.09933	−	14.0904i	−0.296560	−	0.685099i
$424$	−2.07152	+	1.19599i	−0.100602	+	0.0580826i
$425$	2.66051	−	4.60814i	0.129054	−	0.223528i
$426$	−11.2631	−	12.6400i	−0.545698	−	0.612409i
$427$	6.34719	+	30.0796i	0.307162	+	1.45565i
$428$	−4.23693			−0.204800
$429$	−9.36251	−	5.92156i	−0.452026	−	0.285896i
$430$	6.35661	+	11.0100i	0.306543	+	0.530948i
$431$	−9.11020	−	15.7793i	−0.438823	−	0.760064i	0.558776	−	0.829319i	$-0.311271\pi$
$431$	−9.11020	−	15.7793i	−0.438823	−	0.760064i	−0.997599	+	0.0692548i	$0.977938\pi$
$432$	5.17550	−	0.462774i	0.249007	−	0.0222652i
$433$	37.1564			1.78562			0.892811	−	0.450431i	$-0.148730\pi$
$433$	37.1564			1.78562			0.892811	+	0.450431i	$0.148730\pi$
$434$	−18.0938	−	20.1550i	−0.868530	−	0.967470i
$435$	−21.0409	−	23.6132i	−1.00884	−	1.13216i
$436$	−1.52333	−	0.879494i	−0.0729542	−	0.0421201i
$437$	6.63105	+	11.4853i	0.317206	+	0.549417i
$438$	−1.14315	+	3.45723i	−0.0546220	+	0.165193i
$439$	−32.2063	−	18.5943i	−1.53712	−	0.887459i	−0.999005	−	0.0445907i	$-0.985802\pi$
$439$	−32.2063	−	18.5943i	−1.53712	−	0.887459i	−0.538119	−	0.842869i	$-0.680865\pi$
$440$	4.33990	−	4.49165i	0.206897	−	0.214131i
$441$	−14.2583	+	15.4176i	−0.678965	+	0.734170i
$442$		−	7.05884i		−	0.335755i
$443$	5.90271	+	3.40793i	0.280446	+	0.161916i	0.633625	−	0.773640i	$-0.281566\pi$
$443$	5.90271	+	3.40793i	0.280446	+	0.161916i	−0.353179	+	0.935556i	$0.614899\pi$
$444$	13.6771	+	4.52242i	0.649086	+	0.214624i
$445$	−11.6931	−	20.2530i	−0.554306	−	0.960085i
$446$	8.79309	−	15.2301i	0.416365	−	0.721165i
$447$	−17.0421	+	15.1856i	−0.806062	+	0.718256i
$448$	1.76745	+	1.96879i	0.0835040	+	0.0930165i
$449$		−	2.92958i		−	0.138255i	−0.997608	−	0.0691277i	$-0.977978\pi$
$449$		−	2.92958i		−	0.138255i	0.997608	−	0.0691277i	$-0.0220216\pi$
$450$	−3.50138	−	2.59975i	−0.165057	−	0.122553i
$451$	5.10588	−	20.4549i	0.240426	−	0.963182i
$452$	−6.10465	+	3.52452i	−0.287138	+	0.165779i
$453$	32.9876	−	6.83332i	1.54989	−	0.321057i
$454$	−5.83994			−0.274082
$455$	9.40118	−	1.98377i	0.440734	−	0.0930007i
$456$	3.56658	+	4.00259i	0.167020	+	0.187438i
$457$	−6.48607	−	3.74473i	−0.303406	−	0.175171i	0.340566	−	0.940221i	$-0.389381\pi$
$457$	−6.48607	−	3.74473i	−0.303406	−	0.175171i	−0.643972	+	0.765049i	$0.722715\pi$
$458$	9.77062	+	16.9232i	0.456551	+	0.790770i
$459$	8.00524	−	17.2534i	0.373653	−	0.805319i
$460$	4.03441	−	6.98781i	0.188105	−	0.325808i
$461$	17.0494			0.794068			0.397034	−	0.917804i	$-0.370040\pi$
$461$	17.0494			0.794068			0.397034	+	0.917804i	$0.370040\pi$
$462$	5.29709	−	14.2457i	0.246443	−	0.662771i
$463$	−0.105850			−0.00491928			−0.00245964	−	0.999997i	$-0.500783\pi$
$463$	−0.105850			−0.00491928			−0.00245964	+	0.999997i	$0.500783\pi$
$464$	−4.84825	+	8.39742i	−0.225075	+	0.389841i
$465$	−10.4828	+	31.7031i	−0.486130	+	1.47020i
$466$	7.60946	+	13.1800i	0.352501	+	0.610550i
$467$	0.545934	+	0.315195i	0.0252628	+	0.0145855i	0.512578	−	0.858641i	$-0.328690\pi$
$467$	0.545934	+	0.315195i	0.0252628	+	0.0145855i	−0.487315	+	0.873226i	$0.662024\pi$
$468$	−5.74702	−	0.664303i	−0.265656	−	0.0307074i
$469$	−9.14481	+	28.0040i	−0.422268	+	1.29311i
$470$	−9.63799			−0.444567
$471$	−0.740597	−	3.57520i	−0.0341249	−	0.164737i
$472$	9.50971	−	5.49043i	0.437720	−	0.252718i
$473$	−21.7239	−	5.42264i	−0.998864	−	0.249333i
$474$	19.0600	−	3.94825i	0.875455	−	0.181349i
$475$		−	4.49942i		−	0.206448i
$476$	9.47588	−	1.99954i	0.434326	−	0.0916486i
$477$	7.12850	+	0.823989i	0.326391	+	0.0377279i
$478$	3.90906	−	6.77068i	0.178796	−	0.309684i
$479$	17.3889	+	30.1185i	0.794519	+	1.37615i	0.923144	+	0.384454i	$0.125610\pi$
$479$	17.3889	+	30.1185i	0.794519	+	1.37615i	−0.128625	+	0.991693i	$0.541056\pi$
$480$	1.02399	−	3.09684i	0.0467386	−	0.141351i
$481$	−13.8899	−	8.01932i	−0.633323	−	0.365649i
$482$			19.8468i			0.903996i
$483$	2.18236	−	19.5133i	0.0993010	−	0.887887i
$484$	0.377916	+	10.9935i	0.0171780	+	0.499705i
$485$	−0.0488899	−	0.0282266i	−0.00221997	−	0.00128170i
$486$	−13.2936	−	8.14124i	−0.603011	−	0.369294i
$487$	−10.2036	−	17.6732i	−0.462371	−	0.800850i	0.536708	−	0.843768i	$-0.319668\pi$
$487$	−10.2036	−	17.6732i	−0.462371	−	0.800850i	−0.999079	+	0.0429182i	$0.986335\pi$
$488$	−10.0627	−	5.80969i	−0.455516	−	0.262992i
$489$	−4.13456	+	3.68417i	−0.186971	+	0.166604i
$490$	5.32609	+	12.0583i	0.240608	+	0.544739i
$491$	−32.5970			−1.47108			−0.735542	−	0.677480i	$-0.763072\pi$
$491$	−32.5970			−1.47108			−0.735542	+	0.677480i	$0.763072\pi$
$492$	−2.23328	−	10.7811i	−0.100684	−	0.486049i
$493$	17.7466	+	30.7380i	0.799267	+	1.38437i
$494$	−2.98445	−	5.16923i	−0.134277	−	0.232574i
$495$	−18.4862	+	3.05733i	−0.830893	+	0.137417i
$496$	10.2372			0.459666
$497$	−19.2441	+	17.2760i	−0.863214	+	0.774936i
$498$	3.03268	−	2.70232i	0.135897	−	0.121094i
$499$	−4.61628	+	7.99563i	−0.206653	+	0.357934i	−0.950658	−	0.310240i	$-0.899590\pi$
$499$	−4.61628	+	7.99563i	−0.206653	+	0.357934i	0.744005	+	0.668174i	$0.232924\pi$
$500$	−10.5251	+	6.07668i	−0.470698	+	0.271757i
$501$	−3.67641	−	1.21563i	−0.164250	−	0.0543103i
$502$	−7.38662	−	4.26467i	−0.329681	−	0.190341i
$503$	19.5451			0.871472			0.435736	−	0.900074i	$-0.356488\pi$
$503$	19.5451			0.871472			0.435736	+	0.900074i	$0.356488\pi$
$504$	−0.736171	−	7.90304i	−0.0327917	−	0.352029i
$505$		−	12.7641i		−	0.567994i
$506$	3.91330	+	13.6613i	0.173967	+	0.607320i
$507$	−15.2627	−	5.04672i	−0.677842	−	0.224133i
$508$	−10.8509	+	6.26478i	−0.481431	+	0.277954i
$509$	−14.9595	−	8.63689i	−0.663069	−	0.382823i	0.130376	−	0.991465i	$-0.458382\pi$
$509$	−14.9595	−	8.63689i	−0.663069	−	0.382823i	−0.793446	+	0.608641i	$0.791715\pi$
$510$	−7.94291	−	8.91393i	−0.351718	−	0.394715i
$511$	5.28743	+	1.72663i	0.233902	+	0.0763816i
$512$	−1.00000			−0.0441942
$513$	−1.43239	−	16.0193i	−0.0632415	−	0.707271i
$514$	−4.21369	+	2.43278i	−0.185858	+	0.107305i
$515$	21.0226	−	12.1374i	0.926368	−	0.534839i
$516$	−11.4499	+	2.37183i	−0.504055	+	0.104414i
$517$	11.7947	−	12.2071i	0.518730	−	0.536868i
$518$	6.83069	−	20.9175i	0.300123	−	0.919064i
$519$	15.5746	−	13.8780i	0.683650	−	0.609178i
$520$	−1.81578	+	3.14502i	−0.0796272	+	0.137918i
$521$	−36.9007	+	21.3046i	−1.61665	+	0.933373i	−0.628871	+	0.777509i	$0.716483\pi$
$521$	−36.9007	+	21.3046i	−1.61665	+	0.933373i	−0.987779	+	0.155864i	$0.950184\pi$
$522$	26.6958	−	11.5558i	1.16844	−	0.505785i
$523$	22.0386	+	12.7240i	0.963679	+	0.556381i	0.897303	−	0.441414i	$-0.145523\pi$
$523$	22.0386	+	12.7240i	0.963679	+	0.556381i	0.0663759	+	0.997795i	$0.478856\pi$
$524$	−1.90854			−0.0833749
$525$	−3.95135	+	5.36312i	−0.172451	+	0.234066i
$526$	8.68651			0.378750
$527$	18.7363	−	32.4522i	0.816165	−	1.41364i
$528$	2.66921	+	5.08678i	0.116163	+	0.221374i
$529$	−2.32066	−	4.01950i	−0.100898	−	0.174761i
$530$	2.25226	−	3.90103i	0.0978319	−	0.169450i
$531$	−32.7247	−	3.78268i	−1.42013	−	0.164154i
$532$	6.09384	−	5.47064i	0.264201	−	0.237182i
$533$			12.2583i			0.530964i
$534$	21.0623	−	4.36303i	0.911457	−	0.188807i
$535$	6.90990	−	3.98943i	0.298741	−	0.172478i
$536$	−5.56729	−	9.64283i	−0.240470	−	0.416507i
$537$	−1.80754	+	0.374429i	−0.0780013	+	0.0161578i
$538$		−	5.29279i		−	0.228188i
$539$	−21.7905	−	8.01080i	−0.938584	−	0.345050i
$540$	−8.00485	+	5.62791i	−0.344474	+	0.242186i
$541$	8.03990	+	4.64184i	0.345662	+	0.199568i	0.662773	−	0.748820i	$-0.269379\pi$
$541$	8.03990	+	4.64184i	0.345662	+	0.199568i	−0.317111	+	0.948388i	$0.602713\pi$
$542$	11.7299	−	6.77227i	0.503843	−	0.290894i
$543$	9.67026	+	3.19754i	0.414991	+	0.137219i
$544$	−1.83021	+	3.17001i	−0.0784695	+	0.135913i
$545$	3.31248			0.141891
$546$	−0.982222	+	8.78241i	−0.0420352	+	0.375852i
$547$			24.0593i			1.02870i	0.857580	+	0.514351i	$0.171967\pi$
$547$			24.0593i			1.02870i	−0.857580	+	0.514351i	$0.828033\pi$
$548$	0.456798	+	0.263732i	0.0195134	+	0.0112661i
$549$	13.8474	+	31.9896i	0.590992	+	1.36528i
$550$	1.16764	−	4.67774i	0.0497885	−	0.199460i
$551$	25.9919	+	15.0064i	1.10729	+	0.639295i
$552$	4.93720	+	5.54077i	0.210141	+	0.235831i
$553$	−6.13882	−	29.0921i	−0.261049	−	1.23712i
$554$		−	3.52915i		−	0.149939i
$555$	−26.5638	+	5.50265i	−1.12757	+	0.233575i
$556$	−2.45424	+	1.41696i	−0.104083	+	0.0600923i
$557$	0.991345	+	1.71706i	0.0420046	+	0.0727542i	0.886263	−	0.463182i	$-0.153292\pi$
$557$	0.991345	+	1.71706i	0.0420046	+	0.0727542i	−0.844259	+	0.535936i	$0.819959\pi$
$558$	−24.6580	−	18.3083i	−1.04385	−	0.775054i
$559$	13.0187			0.550634
$560$	−4.73627	−	1.54664i	−0.200144	−	0.0653576i
$561$	21.0104	+	0.848411i	0.887058	+	0.0358200i
$562$	0.0230310	−	0.0398908i	0.000971503	−	0.00168269i
$563$	−8.74927	−	15.1542i	−0.368738	−	0.638672i	0.620631	−	0.784103i	$-0.286877\pi$
$563$	−8.74927	−	15.1542i	−0.368738	−	0.638672i	−0.989368	+	0.145431i	$0.953543\pi$
$564$	2.78294	−	8.41639i	0.117183	−	0.354394i
$565$	6.63727	−	11.4961i	0.279232	−	0.483644i
$566$		−	20.7763i		−	0.873295i
$567$	−12.3607	+	20.3522i	−0.519099	+	0.854714i
$568$		−	9.77457i		−	0.410132i
$569$	−17.2132	+	29.8142i	−0.721616	+	1.24988i	0.238735	+	0.971085i	$0.423267\pi$
$569$	−17.2132	+	29.8142i	−0.721616	+	1.24988i	−0.960352	+	0.278792i	$0.910066\pi$
$570$	−9.58541	−	3.16948i	−0.401489	−	0.132755i
$571$	−38.1519	+	22.0270i	−1.59661	+	0.921802i	−0.604473	+	0.796625i	$0.706616\pi$
$571$	−38.1519	+	22.0270i	−1.59661	+	0.921802i	−0.992134	+	0.125177i	$0.960050\pi$
$572$	−1.76127	−	6.14858i	−0.0736423	−	0.257085i
$573$	17.4456	+	19.5783i	0.728802	+	0.817897i
$574$	−16.4556	+	3.47236i	−0.686845	+	0.144933i
$575$		−	6.22854i		−	0.259748i
$576$	2.40865	+	1.78841i	0.100360	+	0.0745169i
$577$	−8.80997	−	15.2593i	−0.366764	−	0.635254i	0.622294	−	0.782784i	$-0.286201\pi$
$577$	−8.80997	−	15.2593i	−0.366764	−	0.635254i	−0.989058	+	0.147530i	$0.952868\pi$
$578$	−1.80069	−	3.11888i	−0.0748987	−	0.129728i
$579$	−15.2319	+	3.15525i	−0.633015	+	0.131128i
$580$		−	18.2602i		−	0.758213i
$581$	−4.14499	−	4.61717i	−0.171963	−	0.191553i
$582$	0.0387657	−	0.0345429i	0.00160689	−	0.00143185i
$583$	2.18465	+	7.62660i	0.0904788	+	0.315861i
$584$	−1.82066	+	1.05116i	−0.0753395	+	0.0434973i
$585$	9.99815	−	4.32791i	0.413373	−	0.178937i
$586$	2.44673	−	4.23787i	0.101074	−	0.175065i
$587$			23.7907i			0.981945i	0.871175	+	0.490973i	$0.163359\pi$
$587$			23.7907i			0.981945i	−0.871175	+	0.490973i	$0.836641\pi$
$588$	−12.0678	+	1.16922i	−0.497670	+	0.0482178i
$589$		−	31.6865i		−	1.30562i
$590$	−10.3394	+	17.9084i	−0.425667	+	0.737277i
$591$	43.2715	+	14.3080i	1.77995	+	0.588552i
$592$	4.15848	+	7.20269i	0.170912	+	0.296029i
$593$	−15.9838	+	27.6848i	−0.656377	+	1.13688i	0.325170	+	0.945656i	$0.394579\pi$
$593$	−15.9838	+	27.6848i	−0.656377	+	1.13688i	−0.981547	+	0.191223i	$0.938755\pi$
$594$	2.66801	−	17.0259i	0.109470	−	0.698582i
$595$	−13.5712	+	12.1833i	−0.556366	+	0.499468i
$596$	−13.1787			−0.539821
$597$	7.86069	+	37.9472i	0.321717	+	1.55308i
$598$	−4.13137	−	7.15574i	−0.168944	−	0.292620i
$599$	29.5373	−	17.0534i	1.20686	−	0.696782i	0.244790	−	0.969576i	$-0.421281\pi$
$599$	29.5373	−	17.0534i	1.20686	−	0.696782i	0.962072	+	0.272794i	$0.0879478\pi$
$600$	−0.510721	−	2.46549i	−0.0208501	−	0.100653i
$601$		−	6.42758i		−	0.262186i	−0.991370	−	0.131093i	$-0.958151\pi$
$601$		−	6.42758i		−	0.262186i	0.991370	−	0.131093i	$-0.0418487\pi$
$602$	3.68778	+	17.4765i	0.150303	+	0.712290i
$603$	−3.83563	+	33.1828i	−0.156199	+	1.35131i
$604$	16.8439	+	9.72486i	0.685370	+	0.395699i
$605$	−10.9677	−	17.5732i	−0.445899	−	0.714451i
$606$	11.1463	+	3.68559i	0.452786	+	0.149717i
$607$	37.8030	+	21.8256i	1.53438	+	0.885872i	0.999153	+	0.0411611i	$0.0131057\pi$
$607$	37.8030	+	21.8256i	1.53438	+	0.885872i	0.535223	+	0.844711i	$0.320228\pi$
$608$			3.09522i			0.125528i
$609$	−17.8027	−	40.7128i	−0.721402	−	1.64977i
$610$	21.8813			0.885946
$611$	−4.93480	+	8.54733i	−0.199641	+	0.345788i
$612$	10.0776	−	4.36230i	0.407363	−	0.176336i
$613$	28.9843	−	16.7341i	1.17067	−	0.675884i	0.216829	−	0.976210i	$-0.430428\pi$
$613$	28.9843	−	16.7341i	1.17067	−	0.675884i	0.953837	+	0.300325i	$0.0970951\pi$
$614$	−22.2876	−	12.8678i	−0.899455	−	0.519301i
$615$	13.7935	+	15.4798i	0.556208	+	0.624204i
$616$	7.75503	−	4.10604i	0.312459	−	0.165437i
$617$		−	38.2908i		−	1.54153i	−0.637119	−	0.770766i	$-0.719874\pi$
$617$		−	38.2908i		−	1.54153i	0.637119	−	0.770766i	$-0.280126\pi$
$618$	4.52882	+	21.8627i	0.182176	+	0.879447i
$619$	0.394181	+	0.682741i	0.0158435	+	0.0274417i	0.873838	−	0.486216i	$-0.161623\pi$
$619$	0.394181	+	0.682741i	0.0158435	+	0.0274417i	−0.857995	+	0.513658i	$0.828290\pi$
$620$	−16.6956	+	9.63924i	−0.670513	+	0.387121i
$621$	−1.98285	−	22.1755i	−0.0795691	−	0.889872i
$622$			2.75593i			0.110503i
$623$	−6.78373	−	32.1484i	−0.271785	−	1.28800i
$624$	−2.22210	−	2.49375i	−0.0889551	−	0.0998298i
$625$	7.80925	−	13.5260i	0.312370	−	0.541041i
$626$	6.72689	+	11.6513i	0.268860	+	0.465680i
$627$	15.7447	−	8.26181i	0.628783	−	0.329945i
$628$	1.05398	−	1.82555i	0.0420585	−	0.0728474i
$629$	30.4435			1.21386
$630$	8.64199	+	12.1957i	0.344305	+	0.485888i
$631$	−29.1733			−1.16137			−0.580686	−	0.814128i	$-0.697215\pi$
$631$	−29.1733			−1.16137			−0.580686	+	0.814128i	$0.697215\pi$
$632$	9.73232	+	5.61896i	0.387131	+	0.223510i
$633$	−1.68134	+	5.08487i	−0.0668274	+	0.202105i
$634$	−4.97256	+	2.87091i	−0.197486	+	0.114018i
$635$	11.7976	−	20.4341i	0.468175	−	0.810903i
$636$	2.75625	+	3.09320i	0.109292	+	0.122653i
$637$	13.4208	+	1.45068i	0.531752	+	0.0574780i
$638$	23.1277	+	22.3463i	0.915633	+	0.884698i
$639$	−17.4809	+	23.5435i	−0.691533	+	0.931367i
$640$	1.63087	−	0.941585i	0.0644659	−	0.0372194i
$641$	40.2975	−	23.2658i	1.59166	−	0.918943i	0.598633	−	0.801024i	$-0.295711\pi$
$641$	40.2975	−	23.2658i	1.59166	−	0.918943i	0.993023	−	0.117919i	$-0.0376224\pi$
$642$	1.48857	+	7.18602i	0.0587492	+	0.283610i
$643$	20.8634			0.822772			0.411386	−	0.911461i	$-0.365045\pi$
$643$	20.8634			0.822772			0.411386	+	0.911461i	$0.365045\pi$
$644$	8.43568	−	7.57299i	0.332412	−	0.298417i
$645$	16.4401	−	14.6492i	0.647329	−	0.576814i
$646$	9.81189	+	5.66489i	0.386043	+	0.222882i
$647$	15.0854	−	8.70958i	0.593069	−	0.342409i	−0.173241	−	0.984879i	$-0.555424\pi$
$647$	15.0854	−	8.70958i	0.593069	−	0.342409i	0.766310	+	0.642471i	$0.222091\pi$
$648$	−2.60321	−	8.61529i	−0.102264	−	0.338441i
$649$	−10.0290	−	35.0113i	−0.393674	−	1.37431i
$650$			2.80329i			0.109954i
$651$	−27.8268	+	37.7690i	−1.09062	+	1.48028i
$652$	−3.19727			−0.125215
$653$	33.2503	+	19.1970i	1.30118	+	0.751239i	0.980607	−	0.195984i	$-0.0627901\pi$
$653$	33.2503	+	19.1970i	1.30118	+	0.751239i	0.320576	+	0.947223i	$0.396123\pi$
$654$	−0.956466	+	2.89263i	−0.0374008	+	0.113111i
$655$	3.11258	−	1.79705i	0.121619	−	0.0702166i
$656$	3.17830	−	5.50499i	0.124092	−	0.214934i
$657$	6.26524	+	0.724204i	0.244430	+	0.0282539i
$658$	−12.8719	−	4.20337i	−0.501799	−	0.163864i
$659$	26.8196			1.04474			0.522372	−	0.852718i	$-0.325047\pi$
$659$	26.8196			1.04474			0.522372	+	0.852718i	$0.325047\pi$
$660$	−9.14279	−	5.78260i	−0.355882	−	0.225087i
$661$	8.71664	+	15.0977i	0.339038	+	0.587231i	0.984252	−	0.176771i	$-0.0565652\pi$
$661$	8.71664	+	15.0977i	0.339038	+	0.587231i	−0.645214	+	0.764002i	$0.723232\pi$
$662$	−4.29871	−	7.44558i	−0.167074	−	0.289381i
$663$	−11.9721	+	2.48000i	−0.464958	+	0.0963152i
$664$	2.34518			0.0910108
$665$	−4.78720	+	14.6598i	−0.185640	+	0.568482i
$666$	2.86501	−	24.7858i	0.111017	−	0.960431i
$667$	35.9805	+	20.7733i	1.39317	+	0.804346i
$668$	−1.11780	−	1.93609i	−0.0432490	−	0.0749095i
$669$	−28.9202	−	9.56265i	−1.11812	−	0.369713i
$670$	18.1591	+	10.4842i	0.701547	+	0.405039i
$671$	−26.7776	+	27.7140i	−1.03374	+	1.06989i
$672$	2.71819	−	3.68937i	0.104857	−	0.142320i
$673$			48.1928i			1.85770i	0.370460	+	0.928849i	$0.379200\pi$
$673$			48.1928i			1.85770i	−0.370460	+	0.928849i	$0.620800\pi$
$674$	−7.64168	−	4.41192i	−0.294346	−	0.169941i
$675$	−3.17914	+	6.85187i	−0.122365	+	0.263729i
$676$	−4.64058	−	8.03773i	−0.178484	−	0.309143i
$677$	1.34824	−	2.33522i	0.0518171	−	0.0897499i	−0.838953	−	0.544203i	$-0.816832\pi$
$677$	1.34824	−	2.33522i	0.0518171	−	0.0897499i	0.890771	+	0.454453i	$0.150165\pi$
$678$	8.12250	+	9.11547i	0.311943	+	0.350078i
$679$	−0.0529840	−	0.0590198i	−0.00203334	−	0.00226497i
$680$		−	6.89318i		−	0.264342i
$681$	2.05176	+	9.90480i	0.0786237	+	0.379553i
$682$	8.22295	−	32.9423i	0.314873	−	1.26143i
$683$	20.6454	−	11.9196i	0.789973	−	0.456091i	−0.0499797	−	0.998750i	$-0.515916\pi$
$683$	20.6454	−	11.9196i	0.789973	−	0.456091i	0.839953	+	0.542659i	$0.182582\pi$
$684$	5.53551	−	7.45531i	0.211656	−	0.285061i
$685$	−0.993306			−0.0379523
$686$	1.85426	+	18.4272i	0.0707961	+	0.703554i
$687$	25.2698	−	22.5171i	0.964102	−	0.859080i
$688$	−5.84651	−	3.37548i	−0.222896	−	0.128689i
$689$	−2.30639	−	3.99478i	−0.0878663	−	0.152189i
$690$	−13.2691	−	4.38750i	−0.505144	−	0.167029i
$691$	19.4649	−	33.7142i	0.740479	−	1.28255i	−0.211799	−	0.977313i	$-0.567932\pi$
$691$	19.4649	−	33.7142i	0.740479	−	1.28255i	0.952278	−	0.305234i	$-0.0987345\pi$
$692$	12.0439			0.457841
$693$	−26.0224	−	3.97911i	−0.988510	−	0.151154i
$694$	18.8652			0.716115
$695$	2.66837	−	4.62175i	0.101217	−	0.175313i
$696$	15.9457	+	5.27256i	0.604422	+	0.199856i
$697$	−11.6339	−	20.1505i	−0.440666	−	0.763255i
$698$	−5.11509	−	2.95320i	−0.193609	−	0.111780i
$699$	19.6804	−	17.5365i	0.744379	−	0.663292i
$700$	−3.76318	+	0.794080i	−0.142235	+	0.0300134i
$701$	34.2114			1.29215			0.646073	−	0.763275i	$-0.276410\pi$
$701$	34.2114			1.29215			0.646073	+	0.763275i	$0.276410\pi$
$702$	0.892427	+	9.98058i	0.0336825	+	0.376693i
$703$	22.2939	−	12.8714i	0.840831	−	0.485454i
$704$	−0.803239	+	3.21789i	−0.0302732	+	0.121279i
$705$	3.38614	+	16.3464i	0.127529	+	0.615643i
$706$		−	8.56941i		−	0.322514i
$707$	5.56674	−	17.0469i	0.209359	−	0.641116i
$708$	−12.6531	−	14.1999i	−0.475532	−	0.533666i
$709$	−13.2642	+	22.9743i	−0.498148	+	0.862817i	−0.999998	−	0.00213754i	$-0.999320\pi$
$709$	−13.2642	+	22.9743i	−0.498148	+	0.862817i	0.501850	+	0.864955i	$0.332653\pi$
$710$	9.20359	+	15.9411i	0.345404	+	0.598258i
$711$	−13.3928	−	30.9395i	−0.502269	−	1.16032i
$712$	10.7547	+	6.20926i	0.403051	+	0.232702i
$713$		−	43.8635i		−	1.64270i
$714$	−6.72049	−	15.3690i	−0.251508	−	0.575170i
$715$	8.66182	+	8.36918i	0.323934	+	0.312989i
$716$	−0.922959	−	0.532870i	−0.0344926	−	0.0199143i
$717$	−12.8568	−	4.25117i	−0.480144	−	0.158763i
$718$	−14.6090	−	25.3035i	−0.545203	−	0.944319i
$719$	37.2542	+	21.5087i	1.38935	+	0.802139i	0.993242	−	0.116066i	$-0.0370284\pi$
$719$	37.2542	+	21.5087i	1.38935	+	0.802139i	0.396105	+	0.918205i	$0.370362\pi$
$720$	−5.61214	−	0.648713i	−0.209152	−	0.0241761i
$721$	33.3700	−	7.04152i	1.24276	−	0.262240i
$722$	−9.41961			−0.350561
$723$	33.6610	−	6.97282i	1.25187	−	0.259322i
$724$	2.94021	+	5.09260i	0.109272	+	0.189265i
$725$	−7.04775	−	12.2071i	−0.261747	−	0.453359i
$726$	18.5127	−	4.50334i	0.687071	−	0.167135i
$727$	2.36652			0.0877693			0.0438847	−	0.999037i	$-0.486027\pi$
$727$	2.36652			0.0877693			0.0438847	+	0.999037i	$0.486027\pi$
$728$	−3.79667	+	3.40839i	−0.140714	+	0.126323i
$729$	−9.13742	+	25.4068i	−0.338423	+	0.940994i
$730$	1.97951	−	3.42861i	0.0732650	−	0.126899i
$731$	−21.4006	+	12.3557i	−0.791531	+	0.456991i
$732$	−6.31814	+	19.1079i	−0.233525	+	0.706247i
$733$	25.4862	+	14.7145i	0.941355	+	0.543491i	0.890385	−	0.455209i	$-0.150435\pi$
$733$	25.4862	+	14.7145i	0.941355	+	0.543491i	0.0509699	+	0.998700i	$0.483769\pi$
$734$	2.10266			0.0776104
$735$	18.5802	−	13.2698i	0.685342	−	0.489462i
$736$			4.28470i			0.157936i
$737$	−35.5014	+	10.1694i	−1.30771	+	0.374596i
$738$	−17.5006	+	7.57549i	−0.644205	+	0.278858i
$739$	18.2469	−	10.5349i	0.671224	−	0.387532i	−0.125316	−	0.992117i	$-0.539994\pi$
$739$	18.2469	−	10.5349i	0.671224	−	0.387532i	0.796540	+	0.604585i	$0.206661\pi$
$740$	−13.5639	−	7.83112i	−0.498619	−	0.287878i
$741$	−7.71870	+	6.87788i	−0.283554	+	0.252665i
$742$	4.70932	−	4.22771i	0.172885	−	0.155204i
$743$	−28.9793			−1.06315			−0.531573	−	0.847013i	$-0.678399\pi$
$743$	−28.9793			−1.06315			−0.531573	+	0.847013i	$0.678399\pi$
$744$	−3.59668	−	17.3628i	−0.131861	−	0.636552i
$745$	21.4928	−	12.4089i	0.787436	−	0.454627i
$746$	24.2451	−	13.9979i	0.887675	−	0.512499i
$747$	−5.64873	−	4.19414i	−0.206676	−	0.153456i
$748$	8.73065	+	8.43568i	0.319224	+	0.308439i
$749$	10.9683	−	2.31446i	0.400774	−	0.0845687i
$750$	14.0041	+	15.7161i	0.511359	+	0.573872i
$751$	1.85140	−	3.20672i	0.0675586	−	0.117015i	−0.830268	−	0.557365i	$-0.811812\pi$
$751$	1.85140	−	3.20672i	0.0675586	−	0.117015i	0.897826	+	0.440350i	$0.145146\pi$
$752$	4.43228	−	2.55898i	0.161629	−	0.0933163i
$753$	−4.63791	+	14.0264i	−0.169015	+	0.511149i
$754$	−16.1938	−	9.34950i	−0.589744	−	0.340489i
$755$	−36.6271			−1.33300
$756$	−13.1453	+	4.02517i	−0.478089	+	0.146394i
$757$	−15.7188			−0.571308			−0.285654	−	0.958333i	$-0.592211\pi$
$757$	−15.7188			−0.571308			−0.285654	+	0.958333i	$0.592211\pi$
$758$	−7.72979	+	13.3884i	−0.280759	+	0.486288i
$759$	21.7953	−	11.4368i	0.791120	−	0.415129i
$760$	−2.91441	−	5.04791i	−0.105717	−	0.183107i
$761$	−10.5972	+	18.3548i	−0.384147	+	0.665362i	−0.991650	−	0.128955i	$-0.958838\pi$
$761$	−10.5972	+	18.3548i	−0.384147	+	0.665362i	0.607504	+	0.794317i	$0.292171\pi$
$762$	14.4376	+	16.2026i	0.523020	+	0.586958i
$763$	4.42394	+	1.44465i	0.160157	+	0.0523000i
$764$			15.1400i			0.547747i
$765$	−12.3278	+	16.6033i	−0.445713	+	0.600293i
$766$	2.54013	−	1.46654i	0.0917786	−	0.0529884i
$767$	10.5879	+	18.3388i	0.382307	+	0.662175i
$768$	0.351333	+	1.69604i	0.0126776	+	0.0612007i
$769$			16.9681i			0.611884i	0.952050	+	0.305942i	$0.0989714\pi$
$769$			16.9681i			0.611884i	−0.952050	+	0.305942i	$0.901029\pi$
$770$	−8.78128	+	13.9985i	−0.316455	+	0.504469i
$771$	5.60651	+	6.29190i	0.201913	+	0.226597i
$772$	−7.77762	−	4.49041i	−0.279923	−	0.161613i
$773$	−24.6916	+	14.2557i	−0.888096	+	0.512743i	−0.873319	−	0.487148i	$-0.838037\pi$
$773$	−24.6916	+	14.2557i	−0.888096	+	0.512743i	−0.0147769	+	0.999891i	$0.504704\pi$
$774$	8.04547	+	18.5863i	0.289188	+	0.668070i
$775$	−7.44078	+	12.8878i	−0.267281	+	0.462944i
$776$	0.0299777			0.00107614
$777$	−37.8769	−	4.23614i	−1.35883	−	0.151971i
$778$			24.2170i			0.868222i
$779$	−17.0391	−	9.83756i	−0.610491	−	0.352467i
$780$	5.97204	+	1.97469i	0.213833	+	0.0707053i
$781$	−31.4535	−	7.85131i	−1.12549	−	0.280942i
$782$	13.5826	+	7.84189i	0.485711	+	0.280425i
$783$	−28.9783	−	41.2172i	−1.03560	−	1.47298i
$784$	−5.65094	−	4.13121i	−0.201819	−	0.147543i
$785$			3.96966i			0.141683i
$786$	0.670531	+	3.23696i	0.0239171	+	0.115459i
$787$	−22.5484	+	13.0183i	−0.803763	+	0.464053i	−0.844785	−	0.535106i	$-0.820272\pi$
$787$	−22.5484	+	13.0183i	−0.803763	+	0.464053i	0.0410223	+	0.999158i	$0.486939\pi$
$788$	13.1565	+	22.7878i	0.468683	+	0.811782i
$789$	−3.05186	−	14.7327i	−0.108649	−	0.524498i
$790$	−21.1629			−0.752943
$791$	13.8781	−	12.4588i	0.493447	−	0.442984i
$792$	7.68961	−	6.31426i	0.273239	−	0.224367i
$793$	11.2036	−	19.4051i	0.397850	−	0.689096i
$794$	−7.83756	−	13.5750i	−0.278144	−	0.481760i
$795$	−7.40761	−	2.44937i	−0.262721	−	0.0868704i
$796$	−11.1870	+	19.3764i	−0.396512	+	0.686778i
$797$		−	4.80180i		−	0.170089i	−0.996377	−	0.0850443i	$-0.972897\pi$
$797$		−	4.80180i		−	0.170089i	0.996377	−	0.0850443i	$-0.0271032\pi$
$798$	−11.4194	−	8.41340i	−0.404243	−	0.297831i
$799$		−	18.7338i		−	0.662756i
$800$	0.726834	−	1.25891i	0.0256975	−	0.0445093i
$801$	−14.7998	−	34.1898i	−0.522924	−	1.20804i
$802$	−11.1027	+	6.41014i	−0.392049	+	0.226350i
$803$	1.92009	+	6.70302i	0.0677584	+	0.236544i
$804$	−14.3987	+	12.8302i	−0.507803	+	0.452487i
$805$	−6.62691	+	20.2935i	−0.233568	+	0.715252i
$806$			19.7418i			0.695374i
$807$	−8.97681	+	1.85953i	−0.315999	+	0.0654586i
$808$	3.38899	+	5.86990i	0.119224	+	0.206502i
$809$	−16.5190	−	28.6117i	−0.580776	−	1.00593i	−0.995388	−	0.0959356i	$-0.969416\pi$
$809$	−16.5190	−	28.6117i	−0.580776	−	1.00593i	0.414611	−	0.909999i	$-0.363918\pi$
$810$	12.3575	+	11.5993i	0.434200	+	0.407558i
$811$		−	26.1823i		−	0.919383i	−0.888079	−	0.459692i	$-0.847960\pi$
$811$		−	26.1823i		−	0.919383i	0.888079	−	0.459692i	$-0.152040\pi$
$812$	7.96372	−	24.3872i	0.279472	−	0.855823i
$813$	−15.6072	−	17.5151i	−0.547367	−	0.614282i
$814$	26.5177	−	7.59603i	0.929445	−	0.266241i
$815$	5.21435	−	3.01050i	0.182651	−	0.105453i
$816$	6.01949	+	1.99038i	0.210724	+	0.0696774i
$817$	−10.4479	+	18.0962i	−0.365524	+	0.633107i
$818$			30.6423i			1.07138i
$819$	15.2404	−	1.41965i	0.532544	−	0.0496067i
$820$			11.9706i			0.418031i
$821$	−19.6060	+	33.9586i	−0.684255	+	1.18516i	0.289415	+	0.957204i	$0.406539\pi$
$821$	−19.6060	+	33.9586i	−0.684255	+	1.18516i	−0.973670	+	0.227961i	$0.926794\pi$
$822$	0.286814	−	0.867407i	0.0100038	−	0.0302543i
$823$	−4.36167	−	7.55463i	−0.152038	−	0.263338i	0.779938	−	0.625856i	$-0.215250\pi$
$823$	−4.36167	−	7.55463i	−0.152038	−	0.263338i	−0.931977	+	0.362518i	$0.881917\pi$
$824$	−6.44521	+	11.1634i	−0.224529	+	0.388896i
$825$	−8.34389	−	0.336932i	−0.290497	−	0.0117304i
$826$	−21.6190	+	19.4081i	−0.752222	+	0.675294i
$827$	44.8575			1.55985			0.779925	−	0.625873i	$-0.215257\pi$
$827$	44.8575			1.55985			0.779925	+	0.625873i	$0.215257\pi$
$828$	7.66279	−	10.3204i	0.266300	−	0.358657i
$829$	11.8646	+	20.5500i	0.412074	+	0.713733i	0.995116	−	0.0987089i	$-0.0314713\pi$
$829$	11.8646	+	20.5500i	0.412074	+	0.713733i	−0.583043	+	0.812442i	$0.698138\pi$
$830$	−3.82470	+	2.20819i	−0.132757	+	0.0766474i
$831$	−5.98560	+	1.23991i	−0.207638	+	0.0430119i
$832$		−	1.92843i		−	0.0668562i
$833$	−23.4384	+	10.3526i	−0.812091	+	0.358696i
$834$	3.26547	+	3.66468i	0.113074	+	0.126897i
$835$	3.64598	+	2.10501i	0.126174	+	0.0728469i
$836$	9.96008	+	2.48620i	0.344476	+	0.0859871i
$837$	−22.3886	+	48.2533i	−0.773864	+	1.66788i
$838$	−4.56858	−	2.63767i	−0.157819	−	0.0911168i
$839$			40.8769i			1.41123i	0.708597	+	0.705613i	$0.249328\pi$
$839$			40.8769i			1.41123i	−0.708597	+	0.705613i	$0.750672\pi$
$840$	−0.959172	+	8.57630i	−0.0330946	+	0.295911i
$841$	65.0223			2.24215
$842$	−2.03684	+	3.52791i	−0.0701941	+	0.121580i
$843$	−0.0757481	−	0.0250466i	−0.00260890	−	0.000862651i
$844$	−2.67782	+	1.54604i	−0.0921742	+	0.0532168i
$845$	15.1364	+	8.73901i	0.520708	+	0.300631i
$846$	−15.2523	−	1.76303i	−0.524385	−	0.0606142i
$847$	−6.98364	−	28.2529i	−0.239961	−	0.970783i
$848$			2.39199i			0.0821412i
$849$	−35.2376	+	7.29941i	−1.20935	+	0.250515i
$850$	−2.66051	−	4.60814i	−0.0912549	−	0.158058i
$851$	30.8614	−	17.8178i	1.05791	−	0.610787i
$852$	−16.5781	+	3.43412i	−0.567956	+	0.117651i
$853$			4.60065i			0.157523i	0.996893	+	0.0787616i	$0.0250966\pi$
$853$			4.60065i			0.157523i	−0.996893	+	0.0787616i	$0.974903\pi$
$854$	29.2233	+	9.54296i	1.00000	+	0.326553i
$855$	−2.00791	+	17.3708i	−0.0686690	+	0.594070i
$856$	−2.11847	+	3.66929i	−0.0724077	+	0.125414i
$857$	4.67390	+	8.09543i	0.159657	+	0.276535i	0.934745	−	0.355319i	$-0.115628\pi$
$857$	4.67390	+	8.09543i	0.159657	+	0.276535i	−0.775088	+	0.631854i	$0.782294\pi$
$858$	−9.80948	+	5.14739i	−0.334890	+	0.175729i
$859$	−9.47884	+	16.4178i	−0.323414	+	0.560169i	−0.981190	−	0.193044i	$-0.938164\pi$
$859$	−9.47884	+	16.4178i	−0.323414	+	0.560169i	0.657776	+	0.753213i	$0.271497\pi$
$860$	12.7132			0.433517
$861$	11.6707	+	26.6895i	0.397736	+	0.909577i
$862$	−18.2204			−0.620590
$863$	−43.1545	−	24.9152i	−1.46900	−	0.848125i	−0.469600	−	0.882880i	$-0.655602\pi$
$863$	−43.1545	−	24.9152i	−1.46900	−	0.848125i	−0.999396	+	0.0347546i	$0.988935\pi$
$864$	2.18698	−	4.71350i	0.0744025	−	0.160357i
$865$	−19.6421	+	11.3404i	−0.667852	+	0.385585i
$866$	18.5782	−	32.1784i	0.631313	−	1.09347i
$867$	−4.65712	+	4.14981i	−0.158164	+	0.140935i
$868$	−26.5016	+	5.59219i	−0.899523	+	0.189811i
$869$	25.8986	−	26.8042i	0.878549	−	0.909269i
$870$	−30.9701	+	6.41539i	−1.04998	+	0.217502i
$871$	18.5955	−	10.7361i	0.630085	−	0.363780i
$872$	−1.52333	+	0.879494i	−0.0515864	+	0.0297834i
$873$	−0.0722059	−	0.0536123i	−0.00244380	−	0.00181450i
$874$	13.2621			0.448597
$875$	23.9274	−	21.4804i	0.808894	−	0.726171i
$876$	2.42247	+	2.71861i	0.0818476	+	0.0918535i
$877$	−39.0886	−	22.5678i	−1.31993	−	0.762060i	−0.336210	−	0.941787i	$-0.609145\pi$
$877$	−39.0886	−	22.5678i	−1.31993	−	0.762060i	−0.983717	+	0.179727i	$0.942479\pi$
$878$	−32.2063	+	18.5943i	−1.08691	+	0.627529i
$879$	−8.04723	−	2.66087i	−0.271426	−	0.0897488i
$880$	−1.71994	−	6.00429i	−0.0579790	−	0.202405i
$881$		−	42.3927i		−	1.42825i	−0.700020	−	0.714123i	$-0.746826\pi$
$881$		−	42.3927i		−	1.42825i	0.700020	−	0.714123i	$-0.253174\pi$
$882$	6.22287	+	20.0568i	0.209535	+	0.675348i
$883$	54.9147			1.84803			0.924013	−	0.382360i	$-0.124889\pi$
$883$	54.9147			1.84803			0.924013	+	0.382360i	$0.124889\pi$
$884$	−6.11314	−	3.52942i	−0.205607	−	0.118707i
$885$	34.0060	+	11.2443i	1.14310	+	0.377973i
$886$	5.90271	−	3.40793i	0.198305	−	0.114492i
$887$	−4.16485	+	7.21373i	−0.139842	+	0.242213i	−0.927437	−	0.373980i	$-0.877993\pi$
$887$	−4.16485	+	7.21373i	−0.139842	+	0.242213i	0.787595	+	0.616194i	$0.211326\pi$
$888$	10.7551	−	9.58350i	0.360917	−	0.321601i
$889$	24.6680	−	22.1453i	0.827340	−	0.742730i
$890$	−23.3862			−0.783907
$891$	−29.8141	+	1.45669i	−0.998809	+	0.0488010i
$892$	−8.79309	−	15.2301i	−0.294414	−	0.509941i
$893$	−7.92060	−	13.7189i	−0.265053	−	0.459085i
$894$	4.63011	+	22.3517i	0.154854	+	0.747552i
$895$	2.00697			0.0670857
$896$	2.58874	−	0.546260i	0.0864839	−	0.0182493i
$897$	−10.6850	+	9.52103i	−0.356761	+	0.317898i
$898$	−2.53709	−	1.46479i	−0.0846637	−	0.0488806i
$899$	−49.6327	−	85.9664i	−1.65534	−	2.86714i
$900$	−4.00214	+	1.73241i	−0.133405	+	0.0577470i
$901$	7.58263	+	4.37783i	0.252614	+	0.145847i
$902$	−15.1615	−	14.6492i	−0.504822	−	0.487767i
$903$	28.3453	−	12.3947i	0.943273	−	0.412470i
$904$			7.04904i			0.234448i
$905$	−9.59023	−	5.53692i	−0.318790	−	0.184054i
$906$	10.5760	−	31.9847i	0.351363	−	1.06262i
$907$	−7.78469	−	13.4835i	−0.258486	−	0.447712i	0.707350	−	0.706863i	$-0.249890\pi$
$907$	−7.78469	−	13.4835i	−0.258486	−	0.447712i	−0.965837	+	0.259152i	$0.916557\pi$
$908$	−2.91997	+	5.05754i	−0.0969027	+	0.167840i
$909$	2.33487	−	20.1994i	0.0774428	−	0.669973i
$910$	2.98259	−	9.13354i	0.0988719	−	0.302774i
$911$		−	21.4845i		−	0.711812i	−0.934522	−	0.355906i	$-0.884172\pi$
$911$		−	21.4845i		−	0.711812i	0.934522	−	0.355906i	$-0.115828\pi$
$912$	5.24963	−	1.08745i	0.173833	−	0.0360091i
$913$	1.88374	−	7.54654i	0.0623428	−	0.249754i
$914$	−6.48607	+	3.74473i	−0.214540	+	0.123865i
$915$	−7.68760	−	37.1116i	−0.254144	−	1.22687i
$916$	19.5412			0.645661
$917$	4.94072	−	1.04256i	0.163157	−	0.0344283i
$918$	−10.9392	−	15.5594i	−0.361049	−	0.513538i
$919$	44.7656	+	25.8455i	1.47668	+	0.852563i	0.999653	−	0.0263245i	$-0.00838033\pi$
$919$	44.7656	+	25.8455i	1.47668	+	0.852563i	0.477029	+	0.878888i	$0.341714\pi$
$920$	−4.03441	−	6.98781i	−0.133011	−	0.230381i
$921$	−13.9939	+	42.3217i	−0.461116	+	1.39455i
$922$	8.52468	−	14.7652i	0.280745	−	0.486265i
$923$	18.8495			0.620440
$924$	−9.68862	−	11.7103i	−0.318732	−	0.385240i
$925$	−12.0901			−0.397520
$926$	−0.0529251	+	0.0916690i	−0.00173923	+	0.00301243i
$927$	35.4890	−	15.3622i	1.16561	−	0.504560i
$928$	4.84825	+	8.39742i	0.159152	+	0.275659i
$929$	−26.8652	−	15.5107i	−0.881420	−	0.508888i	−0.0102936	−	0.999947i	$-0.503277\pi$
$929$	−26.8652	−	15.5107i	−0.881420	−	0.508888i	−0.871126	+	0.491059i	$0.836610\pi$
$930$	22.2143	+	24.9300i	0.728435	+	0.817486i
$931$	−12.7870	+	17.4909i	−0.419077	+	0.573241i
$932$	15.2189			0.498512
$933$	4.67418	−	0.968248i	0.153026	−	0.0316990i
$934$	0.545934	−	0.315195i	0.0178635	−	0.0103135i
$935$	−22.1815	−	5.53688i	−0.725412	−	0.181075i
$936$	−3.44881	+	4.64491i	−0.112728	+	0.151824i
$937$		−	31.6686i		−	1.03457i	−0.855814	−	0.517283i	$-0.826943\pi$
$937$		−	31.6686i		−	1.03457i	0.855814	−	0.517283i	$-0.173057\pi$
$938$	19.6798	+	21.9217i	0.642568	+	0.715767i
$939$	17.3978	−	15.5026i	0.567754	−	0.505908i
$940$	−4.81899	+	8.34674i	−0.157178	+	0.272241i
$941$	13.8313	+	23.9564i	0.450886	+	0.780958i	0.998441	−	0.0558120i	$-0.0177747\pi$
$941$	13.8313	+	23.9564i	0.450886	+	0.780958i	−0.547555	+	0.836770i	$0.684441\pi$
$942$	−3.46651	−	1.14623i	−0.112945	−	0.0373460i
$943$	−23.5872	−	13.6181i	−0.768106	−	0.443466i
$944$		−	10.9809i		−	0.357397i
$945$	17.6482	−	18.9419i	0.574097	−	0.616181i
$946$	−15.5581	+	16.1021i	−0.505836	+	0.523524i
$947$	18.7065	+	10.8002i	0.607879	+	0.350959i	0.772135	−	0.635459i	$-0.219189\pi$
$947$	18.7065	+	10.8002i	0.607879	+	0.350959i	−0.164256	+	0.986418i	$0.552522\pi$
$948$	6.11072	−	18.4806i	0.198467	−	0.600221i
$949$	−2.02708	−	3.51101i	−0.0658019	−	0.113972i
$950$	−3.89662	−	2.24971i	−0.126423	−	0.0729903i
$951$	6.61622	+	7.42504i	0.214546	+	0.240774i
$952$	3.00629	−	9.20612i	0.0974344	−	0.298372i
$953$	−7.18964			−0.232895			−0.116448	−	0.993197i	$-0.537151\pi$
$953$	−7.18964			−0.232895			−0.116448	+	0.993197i	$0.537151\pi$
$954$	4.27784	−	5.76147i	0.138500	−	0.186534i
$955$	−14.2556	−	24.6915i	−0.461301	−	0.798997i
$956$	−3.90906	−	6.77068i	−0.126428	−	0.218980i
$957$	29.7748	−	47.0765i	0.962482	−	1.52177i
$958$	34.7778			1.12362
$959$	−1.32660	−	0.433206i	−0.0428381	−	0.0139889i
$960$	−2.16995	−	2.43522i	−0.0700348	−	0.0785965i
$961$	−36.9006	+	63.9137i	−1.19034	+	2.06173i
$962$	−13.8899	+	8.01932i	−0.447827	+	0.258553i
$963$	11.6648	−	5.04937i	0.375894	−	0.162714i
$964$	17.1878	+	9.92339i	0.553583	+	0.319611i
$965$	16.9124			0.544430
$966$	−15.8078	−	11.6466i	−0.508609	−	0.374725i
$967$		−	45.6617i		−	1.46838i	−0.678944	−	0.734190i	$-0.737562\pi$
$967$		−	45.6617i		−	1.46838i	0.678944	−	0.734190i	$-0.262438\pi$
$968$	9.70961	+	5.16947i	0.312079	+	0.166153i
$969$	6.16068	−	18.6317i	0.197909	−	0.598535i
$970$	−0.0488899	+	0.0282266i	−0.00156976	+	0.000906301i
$971$	13.2167	+	7.63066i	0.424144	+	0.244879i	0.696849	−	0.717218i	$-0.254585\pi$
$971$	13.2167	+	7.63066i	0.424144	+	0.244879i	−0.272705	+	0.962098i	$0.587918\pi$
$972$	−13.6973	+	7.44199i	−0.439342	+	0.238702i
$973$	5.57938	−	5.00879i	0.178867	−	0.160574i
$974$	−20.4073			−0.653891
$975$	4.75451	−	0.984888i	0.152266	−	0.0315417i
$976$	−10.0627	+	5.80969i	−0.322098	+	0.185963i
$977$	−49.3619	+	28.4991i	−1.57923	+	0.911768i	−0.584262	+	0.811565i	$0.698616\pi$
$977$	−49.3619	+	28.4991i	−1.57923	+	0.911768i	−0.994967	+	0.100203i	$0.968051\pi$
$978$	1.12331	+	5.42271i	0.0359194	+	0.173399i
$979$	28.6193	−	29.6201i	0.914678	−	0.946661i
$980$	13.1059	+	1.41663i	0.418651	+	0.0452527i
$981$	5.24206	+	0.605935i	0.167366	+	0.0193460i
$982$	−16.2985	+	28.2298i	−0.520106	+	0.900851i
$983$	−35.1451	+	20.2910i	−1.12096	+	0.647184i	−0.941645	−	0.336609i	$-0.890720\pi$
$983$	−35.1451	+	20.2910i	−1.12096	+	0.647184i	−0.179311	+	0.983793i	$0.557387\pi$
$984$	−10.4533	−	3.45646i	−0.333240	−	0.110188i
$985$	−42.9133	−	24.7760i	−1.36733	−	0.789430i
$986$	35.4932			1.13033
$987$	−2.60677	+	23.3081i	−0.0829745	+	0.741905i
$988$	−5.96891			−0.189896
$989$	−14.4629	+	25.0505i	−0.459895	+	0.796561i
$990$	−6.59538	+	17.5382i	−0.209615	+	0.557400i
$991$	24.3227	+	42.1282i	0.772637	+	1.33825i	0.936113	+	0.351699i	$0.114396\pi$
$991$	24.3227	+	42.1282i	0.772637	+	1.33825i	−0.163476	+	0.986547i	$0.552271\pi$
$992$	5.11862	−	8.86571i	0.162516	−	0.281487i
$993$	−11.1178	+	9.90667i	−0.352811	+	0.314379i
$994$	5.33945	+	25.3039i	0.169357	+	0.802590i
$995$		−	42.1340i		−	1.33574i
$996$	−0.823939	−	3.97753i	−0.0261075	−	0.126033i
$997$	−23.2261	+	13.4096i	−0.735577	+	0.424686i	−0.820459	−	0.571705i	$-0.806282\pi$
$997$	−23.2261	+	13.4096i	−0.735577	+	0.424686i	0.0848819	+	0.996391i	$0.472949\pi$
$998$	4.61628	+	7.99563i	0.146126	+	0.253097i
$999$	−43.0444	+	3.84887i	−1.36186	+	0.121773i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.n.f.65.2	yes	24
3.2	odd	2		462.2.n.e.65.8	yes	24
7.4	even	3	inner	462.2.n.f.263.8	yes	24
11.10	odd	2		462.2.n.e.65.2	✓	24
21.11	odd	6		462.2.n.e.263.2	yes	24
33.32	even	2	inner	462.2.n.f.65.8	yes	24
77.32	odd	6		462.2.n.e.263.8	yes	24
231.32	even	6	inner	462.2.n.f.263.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.n.e.65.2	✓	24	11.10	odd	2
462.2.n.e.65.8	yes	24	3.2	odd	2
462.2.n.e.263.2	yes	24	21.11	odd	6
462.2.n.e.263.8	yes	24	77.32	odd	6
462.2.n.f.65.2	yes	24	1.1	even	1	trivial
462.2.n.f.65.8	yes	24	33.32	even	2	inner
462.2.n.f.263.2	yes	24	231.32	even	6	inner
462.2.n.f.263.8	yes	24	7.4	even	3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.64448 - 0.543759i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.63087 + 0.941585i) q^{5} +(-1.29315 + 1.15228i) q^{6} +(1.76745 + 1.96879i) q^{7} -1.00000 q^{8} +(2.40865 + 1.78841i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.64448 - 0.543759i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.63087 + 0.941585i) q^{5} +(-1.29315 + 1.15228i) q^{6} +(1.76745 + 1.96879i) q^{7} -1.00000 q^{8} +(2.40865 + 1.78841i) q^{9} +(1.63087 - 0.941585i) q^{10} +(-0.803239 + 3.21789i) q^{11} +(0.351333 + 1.69604i) q^{12} -1.92843i q^{13} +(2.58874 - 0.546260i) q^{14} +(-2.16995 - 2.43522i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.83021 + 3.17001i) q^{17} +(2.75313 - 1.19175i) q^{18} +(2.68054 + 1.54761i) q^{19} -1.88317i q^{20} +(-1.83599 - 4.19871i) q^{21} +(2.38515 + 2.30457i) q^{22} +(3.71066 + 2.14235i) q^{23} +(1.64448 + 0.543759i) q^{24} +(-0.726834 - 1.25891i) q^{25} +(-1.67007 - 0.964214i) q^{26} +(-2.98853 - 4.25073i) q^{27} +(0.821298 - 2.51505i) q^{28} +9.69651 q^{29} +(-3.19394 + 0.661619i) q^{30} +(-5.11862 - 8.86571i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.07067 - 4.85500i) q^{33} +3.66041 q^{34} +(1.02870 + 4.87505i) q^{35} +(0.344479 - 2.98016i) q^{36} +(4.15848 - 7.20269i) q^{37} +(2.68054 - 1.54761i) q^{38} +(-1.04860 + 3.17127i) q^{39} +(-1.63087 - 0.941585i) q^{40} -6.35661 q^{41} +(-4.55418 - 0.509339i) q^{42} +6.75096i q^{43} +(3.18839 - 0.913319i) q^{44} +(2.24427 + 5.18462i) q^{45} +(3.71066 - 2.14235i) q^{46} +(-4.43228 - 2.55898i) q^{47} +(1.29315 - 1.15228i) q^{48} +(-0.752260 + 6.95946i) q^{49} -1.45367 q^{50} +(-1.28602 - 6.20822i) q^{51} +(-1.67007 + 0.964214i) q^{52} +(2.07152 - 1.19599i) q^{53} +(-5.17550 + 0.462774i) q^{54} +(-4.33990 + 4.49165i) q^{55} +(-1.76745 - 1.96879i) q^{56} +(-3.56658 - 4.00259i) q^{57} +(4.84825 - 8.39742i) q^{58} +(-9.50971 + 5.49043i) q^{59} +(-1.02399 + 3.09684i) q^{60} +(10.0627 + 5.80969i) q^{61} -10.2372 q^{62} +(0.736171 + 7.90304i) q^{63} +1.00000 q^{64} +(1.81578 - 3.14502i) q^{65} +(-2.66921 - 5.08678i) q^{66} +(5.56729 + 9.64283i) q^{67} +(1.83021 - 3.17001i) q^{68} +(-4.93720 - 5.54077i) q^{69} +(4.73627 + 1.54664i) q^{70} +9.77457i q^{71} +(-2.40865 - 1.78841i) q^{72} +(1.82066 - 1.05116i) q^{73} +(-4.15848 - 7.20269i) q^{74} +(0.510721 + 2.46549i) q^{75} -3.09522i q^{76} +(-7.75503 + 4.10604i) q^{77} +(2.22210 + 2.49375i) q^{78} +(-9.73232 - 5.61896i) q^{79} +(-1.63087 + 0.941585i) q^{80} +(2.60321 + 8.61529i) q^{81} +(-3.17830 + 5.50499i) q^{82} -2.34518 q^{83} +(-2.71819 + 3.68937i) q^{84} +6.89318i q^{85} +(5.84651 + 3.37548i) q^{86} +(-15.9457 - 5.27256i) q^{87} +(0.803239 - 3.21789i) q^{88} +(-10.7547 - 6.20926i) q^{89} +(5.61214 + 0.648713i) q^{90} +(3.79667 - 3.40839i) q^{91} -4.28470i q^{92} +(3.59668 + 17.3628i) q^{93} +(-4.43228 + 2.55898i) q^{94} +(2.91441 + 5.04791i) q^{95} +(-0.351333 - 1.69604i) q^{96} -0.0299777 q^{97} +(5.65094 + 4.13121i) q^{98} +(-7.68961 + 6.31426i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} - 8 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 - 8 * q^9	\( 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} - 8 q^{9} + 4 q^{11} + 4 q^{15} - 12 q^{16} - 4 q^{17} + 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} - 40 q^{29} + 2 q^{30} - 28 q^{31} + 12 q^{32} + 24 q^{33} - 8 q^{34} + 32 q^{35} + 16 q^{36} - 16 q^{37} + 8 q^{41} + 6 q^{42} + 4 q^{44} - 28 q^{45} - 8 q^{49} + 40 q^{50} + 34 q^{51} - 6 q^{54} + 8 q^{55} - 40 q^{57} - 20 q^{58} - 2 q^{60} - 56 q^{62} + 14 q^{63} + 24 q^{64} + 44 q^{65} - 24 q^{66} - 4 q^{68} - 20 q^{69} + 64 q^{70} + 8 q^{72} + 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} - 144 q^{83} + 6 q^{84} - 8 q^{87} - 4 q^{88} - 56 q^{90} - 32 q^{91} - 22 q^{93} + 44 q^{95} + 64 q^{97} + 8 q^{98} + 28 q^{99}+O(q^{100}) \) 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 - 8 * q^9 + 4 * q^11 + 4 * q^15 - 12 * q^16 - 4 * q^17 + 8 * q^18 + 8 * q^22 + 20 * q^25 - 12 * q^27 - 40 * q^29 + 2 * q^30 - 28 * q^31 + 12 * q^32 + 24 * q^33 - 8 * q^34 + 32 * q^35 + 16 * q^36 - 16 * q^37 + 8 * q^41 + 6 * q^42 + 4 * q^44 - 28 * q^45 - 8 * q^49 + 40 * q^50 + 34 * q^51 - 6 * q^54 + 8 * q^55 - 40 * q^57 - 20 * q^58 - 2 * q^60 - 56 * q^62 + 14 * q^63 + 24 * q^64 + 44 * q^65 - 24 * q^66 - 4 * q^68 - 20 * q^69 + 64 * q^70 + 8 * q^72 + 16 * q^74 - 26 * q^75 + 24 * q^81 + 4 * q^82 - 144 * q^83 + 6 * q^84 - 8 * q^87 - 4 * q^88 - 56 * q^90 - 32 * q^91 - 22 * q^93 + 44 * q^95 + 64 * q^97 + 8 * q^98 + 28 * q^99

Introduction

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