LMFDB - Embedded newform 462.2.n.e.65.8

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			65.8
Character	$\chi$	$=$	462.65
Dual form			462.2.n.e.263.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.351333 - 1.69604i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.63087 - 0.941585i) q^{5} +(1.29315 + 1.15228i) q^{6} +(1.76745 + 1.96879i) q^{7} +1.00000 q^{8} +(-2.75313 - 1.19175i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.351333 - 1.69604i) 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} +(-2.75313 - 1.19175i) q^{9} +(1.63087 - 0.941585i) q^{10} +(0.803239 - 3.21789i) q^{11} +(-1.64448 + 0.543759i) 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} +(2.40865 - 1.78841i) q^{18} +(2.68054 + 1.54761i) q^{19} +1.88317i q^{20} +(3.96011 - 2.30597i) q^{21} +(2.38515 + 2.30457i) q^{22} +(-3.71066 - 2.14235i) q^{23} +(0.351333 - 1.69604i) 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} +(-1.02399 - 3.09684i) q^{30} +(-5.11862 - 8.86571i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-5.17548 - 2.49288i) 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} +(-3.27070 - 0.677519i) q^{39} +(-1.63087 - 0.941585i) q^{40} +6.35661 q^{41} +(0.0169703 + 4.58254i) q^{42} +6.75096i q^{43} +(-3.18839 + 0.913319i) q^{44} +(3.36787 + 4.53590i) 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} +(-6.01949 + 1.99038i) q^{51} +(-1.67007 + 0.964214i) q^{52} +(-2.07152 + 1.19599i) q^{53} +(-2.18698 - 4.71350i) 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} +(3.19394 + 0.661619i) q^{60} +(10.0627 + 5.80969i) q^{61} +10.2372 q^{62} +(-2.51971 - 7.52669i) q^{63} +1.00000 q^{64} +(-1.81578 + 3.14502i) q^{65} +(4.74663 - 3.23566i) 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} +(-2.75313 - 1.19175i) q^{72} +(1.82066 - 1.05116i) q^{73} +(4.15848 + 7.20269i) q^{74} +(-2.39053 + 0.790445i) 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} +(6.15946 + 6.56209i) q^{81} +(-3.17830 + 5.50499i) q^{82} +2.34518 q^{83} +(-3.97708 - 2.27658i) q^{84} +6.89318i q^{85} +(-5.84651 - 3.37548i) q^{86} +(-3.40670 + 16.4457i) 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} +(-16.8350 + 5.56659i) q^{93} +(-4.43228 + 2.55898i) q^{94} +(-2.91441 - 5.04791i) q^{95} +(-1.64448 + 0.543759i) q^{96} -0.0299777 q^{97} +(-5.65094 - 4.13121i) q^{98} +(-6.04634 + 7.90201i) 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} + 32 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} + 32 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} - 52 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 + 32 * 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 + 32 * 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 - 52 * 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
$3$	0.351333	−	1.69604i	0.202842	−	0.979211i
$3$	0.351333	−	1.69604i	0.202842	−	0.979211i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.63087	−	0.941585i	−0.729349	−	0.421090i	0.0888351	−	0.996046i	$-0.471686\pi$
$5$	−1.63087	−	0.941585i	−0.729349	−	0.421090i	−0.818184	+	0.574957i	$0.805019\pi$
$6$	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
$9$	−2.75313	−	1.19175i	−0.917710	−	0.397250i
$10$	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
$12$	−1.64448	+	0.543759i	−0.474721	+	0.156970i
$13$		−	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	0.554084	−	0.832461i	$-0.313069\pi$
$17$	−1.83021	−	3.17001i	−0.443890	−	0.768841i	−0.997974	+	0.0636202i	$0.979735\pi$
$18$	2.40865	−	1.78841i	0.567725	−	0.421531i
$19$	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
$21$	3.96011	−	2.30597i	0.864168	−	0.503204i
$22$	2.38515	+	2.30457i	0.508516	+	0.491336i
$23$	−3.71066	−	2.14235i	−0.773726	−	0.446711i	0.0604759	−	0.998170i	$-0.480738\pi$
$23$	−3.71066	−	2.14235i	−0.773726	−	0.446711i	−0.834202	+	0.551459i	$0.814071\pi$
$24$	0.351333	−	1.69604i	0.0717154	−	0.346204i
$25$	−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	$-0.856652\pi$
$29$	−9.69651			−1.80060			−0.900298	+	0.435274i	$0.856652\pi$
$30$	−1.02399	−	3.09684i	−0.186954	−	0.565404i
$31$	−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
$33$	−5.17548	−	2.49288i	−0.900935	−	0.433954i
$34$	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
$39$	−3.27070	−	0.677519i	−0.523731	−	0.108490i
$40$	−1.63087	−	0.941585i	−0.257864	−	0.148878i
$41$	6.35661			0.992736			0.496368	−	0.868112i	$-0.334667\pi$
$41$	6.35661			0.992736			0.496368	+	0.868112i	$0.334667\pi$
$42$	0.0169703	+	4.58254i	0.00261858	+	0.707102i
$43$			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
$45$	3.36787	+	4.53590i	0.502053	+	0.676172i
$46$	3.71066	−	2.14235i	0.547107	−	0.315872i
$47$	4.43228	+	2.55898i	0.646515	+	0.373265i	0.787120	−	0.616800i	$-0.211571\pi$
$47$	4.43228	+	2.55898i	0.646515	+	0.373265i	−0.140605	+	0.990066i	$0.544905\pi$
$48$	1.29315	+	1.15228i	0.186650	+	0.166318i
$49$	−0.752260	+	6.95946i	−0.107466	+	0.994209i
$50$	1.45367			0.205580
$51$	−6.01949	+	1.99038i	−0.842897	+	0.278709i
$52$	−1.67007	+	0.964214i	−0.231597	+	0.133712i
$53$	−2.07152	+	1.19599i	−0.284545	+	0.164282i	−0.635479	−	0.772118i	$-0.719197\pi$
$53$	−2.07152	+	1.19599i	−0.284545	+	0.164282i	0.350934	+	0.936400i	$0.385864\pi$
$54$	−2.18698	−	4.71350i	−0.297610	−	0.641427i
$55$	−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	0.269362	−	0.963039i	$-0.413187\pi$
$59$	9.50971	−	5.49043i	1.23806	−	0.714794i	0.968697	+	0.248246i	$0.0798540\pi$
$60$	3.19394	+	0.661619i	0.412336	+	0.0854147i
$61$	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
$63$	−2.51971	−	7.52669i	−0.317453	−	0.948274i
$64$	1.00000			0.125000
$65$	−1.81578	+	3.14502i	−0.225220	+	0.390092i
$66$	4.74663	−	3.23566i	0.584270	−	0.398282i
$67$	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	$-0.803047\pi$
$71$		−	9.77457i		−	1.16003i	0.814607	−	0.580014i	$-0.196953\pi$
$72$	−2.75313	−	1.19175i	−0.324460	−	0.140449i
$73$	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
$75$	−2.39053	+	0.790445i	−0.276035	+	0.0912728i
$76$		−	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
$81$	6.15946	+	6.56209i	0.684384	+	0.729121i
$82$	−3.17830	+	5.50499i	−0.350985	+	0.607924i
$83$	2.34518			0.257417			0.128709	−	0.991682i	$-0.458917\pi$
$83$	2.34518			0.257417			0.128709	+	0.991682i	$0.458917\pi$
$84$	−3.97708	−	2.27658i	−0.433936	−	0.248395i
$85$			6.89318i			0.747671i
$86$	−5.84651	−	3.37548i	−0.630445	−	0.363988i
$87$	−3.40670	+	16.4457i	−0.365236	+	1.76316i
$88$	0.803239	−	3.21789i	0.0856256	−	0.343028i
$89$	10.7547	+	6.20926i	1.14000	+	0.658180i	0.946431	−	0.322907i	$-0.104660\pi$
$89$	10.7547	+	6.20926i	1.14000	+	0.658180i	0.193570	+	0.981086i	$0.437993\pi$
$90$	−5.61214	+	0.648713i	−0.591572	+	0.0683803i
$91$	3.79667	−	3.40839i	0.397999	−	0.357297i
$92$			4.28470i			0.446711i
$93$	−16.8350	+	5.56659i	−1.74571	+	0.577229i
$94$	−4.43228	+	2.55898i	−0.457155	+	0.263938i
$95$	−2.91441	−	5.04791i	−0.299013	−	0.517905i
$96$	−1.64448	+	0.543759i	−0.167839	+	0.0554972i
$97$	−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
$99$	−6.04634	+	7.90201i	−0.607680	+	0.794182i
$100$	−0.726834	+	1.25891i	−0.0726834	+	0.125891i
$101$	3.38899	+	5.86990i	0.337217	+	0.584077i	0.983908	−	0.178675i	$-0.0571811\pi$
$101$	3.38899	+	5.86990i	0.337217	+	0.584077i	−0.646691	+	0.762752i	$0.723848\pi$
$102$	1.28602	−	6.20822i	0.127335	−	0.614706i
$103$	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
$105$	−8.62971	+	0.0319580i	−0.842174	+	0.00311878i
$106$		−	2.39199i		−	0.232330i
$107$	−2.11847	+	3.66929i	−0.204800	+	0.354724i	−0.950069	−	0.312040i	$-0.898988\pi$
$107$	−2.11847	+	3.66929i	−0.204800	+	0.354724i	0.745269	+	0.666764i	$0.232321\pi$
$108$	5.17550	+	0.462774i	0.498013	+	0.0445305i
$109$	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	$0.107575\pi$
$113$			7.04904i			0.663118i	−0.943435	+	0.331559i	$0.892425\pi$
$114$	1.68305	+	5.09004i	0.157633	+	0.476726i
$115$	4.03441	+	6.98781i	0.376211	+	0.651617i
$116$	4.84825	+	8.39742i	0.450149	+	0.779681i
$117$	−2.29820	+	5.30921i	−0.212469	+	0.490837i
$118$			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
$123$	2.23328	−	10.7811i	0.201368	−	0.972098i
$124$	−5.11862	+	8.86571i	−0.459666	+	0.796164i
$125$			12.1534i			1.08703i
$126$	7.77816	+	1.58121i	0.692933	+	0.140866i
$127$		−	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
$129$	11.4499	+	2.37183i	1.00811	+	0.208828i
$130$	−1.81578	−	3.14502i	−0.159254	−	0.275837i
$131$	−0.954269	+	1.65284i	−0.0833749	+	0.144410i	−0.904698	−	0.426054i	$-0.859903\pi$
$131$	−0.954269	+	1.65284i	−0.0833749	+	0.144410i	0.821323	+	0.570464i	$0.193237\pi$
$132$	0.428843	+	5.72853i	0.0373260	+	0.498605i
$133$	1.69079	+	8.01274i	0.146610	+	0.694792i
$134$	−11.1346			−0.961882
$135$	8.87633	−	4.11845i	0.763953	−	0.354460i
$136$	−1.83021	−	3.17001i	−0.156939	−	0.271826i
$137$	0.456798	−	0.263732i	0.0390269	−	0.0225322i	−0.480360	−	0.877072i	$-0.659494\pi$
$137$	0.456798	−	0.263732i	0.0390269	−	0.0225322i	0.519386	+	0.854539i	$0.326161\pi$
$138$	−2.32985	−	7.04612i	−0.198330	−	0.599806i
$139$		−	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
$144$	2.40865	−	1.78841i	0.200721	−	0.149034i
$145$	15.8138	+	9.13009i	1.31326	+	0.758213i
$146$			2.10232i			0.173989i
$147$	11.5393	+	3.72095i	0.951742	+	0.306899i
$148$	−8.31695			−0.683649
$149$	−6.58936	+	11.4131i	−0.539821	+	0.934998i	0.459092	+	0.888389i	$0.348175\pi$
$149$	−6.58936	+	11.4131i	−0.539821	+	0.934998i	−0.998913	+	0.0466093i	$0.985158\pi$
$150$	0.510721	−	2.46549i	0.0417002	−	0.201306i
$151$	−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
$156$	1.04860	+	3.17127i	0.0839552	+	0.253905i
$157$	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
$159$	1.30067	+	3.93358i	0.103149	+	0.311954i
$160$			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
$165$	6.09329	+	8.93872i	0.474362	+	0.695879i
$166$	−1.17259	+	2.03099i	−0.0910108	+	0.157635i
$167$	−2.23560			−0.172996			−0.0864980	−	0.996252i	$-0.527568\pi$
$167$	−2.23560			−0.172996			−0.0864980	+	0.996252i	$0.527568\pi$
$168$	3.96011	−	2.30597i	0.305529	−	0.177909i
$169$	9.28117			0.713936
$170$	−5.96967	−	3.44659i	−0.457853	−	0.264342i
$171$	−5.53551	−	7.45531i	−0.423311	−	0.570122i
$172$	5.84651	−	3.37548i	0.445792	−	0.257378i
$173$	6.02196	−	10.4303i	0.457841	−	0.793005i	−0.541005	−	0.841019i	$-0.681956\pi$
$173$	6.02196	−	10.4303i	0.457841	−	0.793005i	0.998847	+	0.0480147i	$0.0152894\pi$
$174$	−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
$177$	−5.97095	−	18.0579i	−0.448804	−	1.35731i
$178$	−10.7547	+	6.20926i	−0.806102	+	0.465403i
$179$	−0.922959	+	0.532870i	−0.0689852	+	0.0398286i	−0.534096	−	0.845424i	$-0.679348\pi$
$179$	−0.922959	+	0.532870i	−0.0689852	+	0.0398286i	0.465111	+	0.885253i	$0.346015\pi$
$180$	2.24427	−	5.18462i	0.167278	−	0.386438i
$181$	−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
$186$	3.59668	−	17.3628i	0.263721	−	1.27310i
$187$	−11.6708	+	3.34312i	−0.853456	+	0.244473i
$188$		−	5.11796i		−	0.373265i
$189$	−13.6509	+	1.62916i	−0.992954	+	0.118504i
$190$	5.82883			0.422868
$191$	13.1117	+	7.57002i	0.948726	+	0.547747i	0.892685	−	0.450681i	$-0.148819\pi$
$191$	13.1117	+	7.57002i	0.948726	+	0.547747i	0.0560409	+	0.998428i	$0.482152\pi$
$192$	0.351333	−	1.69604i	0.0253552	−	0.122401i
$193$	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	$-0.113257\pi$
$197$	26.3131			1.87473			0.937365	+	0.348348i	$0.113257\pi$
$198$	−3.82017	−	9.18729i	−0.271487	−	0.652912i
$199$	−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
$201$	18.3106	−	6.05453i	1.29153	−	0.427054i
$202$	−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
$207$	7.66279	+	10.3204i	0.532601	+	0.717314i
$208$	1.67007	+	0.964214i	0.115798	+	0.0668562i
$209$	7.13315	−	7.38258i	0.493411	−	0.510664i
$210$	4.28718	−	7.48953i	0.295844	−	0.516827i
$211$		−	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
$213$	−16.5781	−	3.43412i	−1.13591	−	0.235302i
$214$	−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
$219$	−1.14315	−	3.45723i	−0.0772472	−	0.233618i
$220$	6.05983	+	1.51264i	0.408554	+	0.101982i
$221$	−6.11314	+	3.52942i	−0.411214	+	0.237415i
$222$	13.6771	−	4.52242i	0.917946	−	0.303525i
$223$	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	0.946508	−	0.322680i	$-0.104584\pi$
$227$	2.91997	+	5.05754i	0.193805	+	0.335681i	−0.752703	+	0.658360i	$0.771250\pi$
$228$	−5.24963	−	1.08745i	−0.347665	−	0.0720183i
$229$	−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
$231$	−4.23943	−	14.5955i	−0.278934	−	0.960310i
$232$	−9.69651			−0.636607
$233$	7.60946	−	13.1800i	0.498512	−	0.863448i	−0.501486	−	0.865166i	$-0.667213\pi$
$233$	7.60946	−	13.1800i	0.498512	−	0.863448i	0.999999	+	0.00171719i	$0.000546597\pi$
$234$	−3.44881	−	4.64491i	−0.225456	−	0.303647i
$235$	−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	$-0.581370\pi$
$239$	−7.81811			−0.505712			−0.252856	+	0.967504i	$0.581370\pi$
$240$	−1.02399	−	3.09684i	−0.0660984	−	0.199900i
$241$	−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
$243$	13.2936	−	8.14124i	0.852786	−	0.522261i
$244$		−	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
$249$	0.823939	−	3.97753i	0.0522150	−	0.252066i
$250$	−10.5251	−	6.07668i	−0.665667	−	0.384323i
$251$			8.52934i			0.538367i	0.963089	+	0.269184i	$0.0867538\pi$
$251$			8.52934i			0.538367i	−0.963089	+	0.269184i	$0.913246\pi$
$252$	−5.25845	+	5.94548i	−0.331251	+	0.374530i
$253$	−9.87440	+	10.2197i	−0.620798	+	0.642505i
$254$	10.8509	+	6.26478i	0.680847	+	0.393087i
$255$	11.6911	+	2.42180i	0.732128	+	0.151659i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.21369	+	2.43278i	0.262843	+	0.151752i	0.625631	−	0.780119i	$-0.284842\pi$
$257$	4.21369	+	2.43278i	0.262843	+	0.151752i	−0.362788	+	0.931872i	$0.618175\pi$
$258$	−7.77903	+	8.73002i	−0.484302	+	0.543507i
$259$	21.5305	−	4.54322i	1.33784	−	0.282302i
$260$	3.63156			0.225220
$261$	26.6958	+	11.5558i	1.65243	+	0.715287i
$262$	−0.954269	−	1.65284i	−0.0589549	−	0.102113i
$263$	−4.34326	−	7.52274i	−0.267817	−	0.463872i	0.700481	−	0.713671i	$-0.252969\pi$
$263$	−4.34326	−	7.52274i	−0.267817	−	0.463872i	−0.968298	+	0.249799i	$0.919636\pi$
$264$	−5.17548	−	2.49288i	−0.318529	−	0.153426i
$265$	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	−0.633185	−	0.774001i	$-0.718253\pi$
$269$	−4.58369	+	2.64640i	−0.279473	+	0.161354i	0.353712	+	0.935354i	$0.384919\pi$
$270$	−0.871483	+	9.74636i	−0.0530368	+	0.593144i
$271$	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
$273$	−4.44689	−	7.63679i	−0.269138	−	0.462200i
$274$			0.527465i			0.0318653i
$275$	−4.63487	+	1.32766i	−0.279493	+	0.0800611i
$276$	7.26704	+	1.50536i	0.437425	+	0.0906117i
$277$	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	$-0.500437\pi$
$281$	−0.0460619			−0.00274782			−0.00137391	+	0.999999i	$0.500437\pi$
$282$	2.78294	+	8.41639i	0.165721	+	0.501189i
$283$	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
$285$	−9.58541	+	3.16948i	−0.567791	+	0.187744i
$286$	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
$291$	−0.0105321	+	0.0508435i	−0.000617405	+	0.00298050i
$292$	−1.82066	−	1.05116i	−0.106546	−	0.0615144i
$293$	−4.89347			−0.285879			−0.142940	−	0.989731i	$-0.545656\pi$
$293$	−4.89347			−0.285879			−0.142940	+	0.989731i	$0.545656\pi$
$294$	−8.99207	+	8.13282i	−0.524428	+	0.474315i
$295$	−20.6788			−1.20397
$296$	4.15848	−	7.20269i	0.241706	−	0.418648i
$297$	11.2779	+	13.0311i	0.654409	+	0.756141i
$298$	−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
$303$	11.1463	−	3.68559i	0.640337	−	0.211731i
$304$	−2.68054	+	1.54761i	−0.153740	+	0.0887616i
$305$	−10.9406	−	18.9497i	−0.626459	−	1.08506i
$306$	−10.0776	−	4.36230i	−0.576098	−	0.249376i
$307$		−	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	−0.430802	−	0.902446i	$-0.641769\pi$
$311$	2.38671	−	1.37797i	0.135338	−	0.0781373i	0.566140	+	0.824309i	$0.308436\pi$
$312$	−3.27070	−	0.677519i	−0.185167	−	0.0383570i
$313$	−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
$315$	−2.97770	+	14.6476i	−0.167774	+	0.825299i
$316$			11.2379i			0.632182i
$317$	4.97256	+	2.87091i	0.279287	+	0.161246i	0.633101	−	0.774070i	$-0.281782\pi$
$317$	4.97256	+	2.87091i	0.279287	+	0.161246i	−0.353814	+	0.935316i	$0.615115\pi$
$318$	−4.05692	−	0.840383i	−0.227501	−	0.0471263i
$319$	−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
$324$	2.60321	−	8.61529i	0.144623	−	0.478627i
$325$	−2.42772	+	1.40165i	−0.134666	+	0.0777494i
$326$	1.59864	+	2.76892i	0.0885403	+	0.153356i
$327$	−0.956466	−	2.89263i	−0.0528927	−	0.159963i
$328$	6.35661			0.350985
$329$	2.79573	+	13.2491i	0.154134	+	0.730446i
$330$	−10.7878	+	0.807584i	−0.593849	+	0.0444560i
$331$	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
$333$	−20.0326	+	14.8741i	−1.09778	+	0.815095i
$334$	1.11780	−	1.93609i	0.0611633	−	0.105938i
$335$		−	20.9683i		−	1.14562i
$336$	0.0169703	+	4.58254i	0.000925807	+	0.249998i
$337$		−	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
$339$	11.9555	+	2.47656i	0.649332	+	0.134508i
$340$	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
$345$	13.2691	−	4.38750i	0.714382	−	0.236215i
$346$	6.02196	+	10.4303i	0.323743	+	0.560739i
$347$	−9.43262	−	16.3378i	−0.506369	−	0.877058i	−0.999973	−	0.00737048i	$-0.997654\pi$
$347$	−9.43262	−	16.3378i	−0.506369	−	0.877058i	0.493603	−	0.869687i	$-0.335679\pi$
$348$	15.9457	−	5.27256i	0.854782	−	0.282639i
$349$		−	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	−0.684323	−	0.729179i	$-0.739902\pi$
$353$	−7.42132	+	4.28470i	−0.394997	+	0.228052i	0.289326	+	0.957231i	$0.406569\pi$
$354$	18.6240	+	3.85794i	0.989856	+	0.205047i
$355$	−9.20359	+	15.9411i	−0.488476	+	0.846065i
$356$		−	12.4185i		−	0.658180i
$357$	−14.5578	−	8.33321i	−0.770479	−	0.441040i
$358$		−	1.06574i		−	0.0563262i
$359$	−14.6090	+	25.3035i	−0.771033	+	1.33547i	0.165964	+	0.986132i	$0.446927\pi$
$359$	−14.6090	+	25.3035i	−0.771033	+	1.33547i	−0.936997	+	0.349337i	$0.886407\pi$
$360$	3.36787	+	4.53590i	0.177503	+	0.239063i
$361$	−4.70980	−	8.15762i	−0.247884	−	0.429348i
$362$	2.94021	−	5.09260i	0.154534	−	0.267661i
$363$	−12.1789	+	14.6517i	−0.639229	+	0.769016i
$364$	−4.85009	−	1.58381i	−0.254214	−	0.0830143i
$365$	−3.95902			−0.207225
$366$	6.31814	+	19.1079i	0.330254	+	0.998784i
$367$	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
$369$	−17.5006	−	7.57549i	−0.911044	−	0.394364i
$370$		−	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
$375$	20.6126	+	4.26987i	1.06443	+	0.220495i
$376$	4.43228	+	2.55898i	0.228577	+	0.131969i
$377$			18.6990i			0.963048i
$378$	5.41453	−	12.6366i	0.278493	−	0.649955i
$379$	−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
$381$	−21.2507	−	4.40204i	−1.08870	−	0.225523i
$382$	−13.1117	+	7.57002i	−0.670850	+	0.387316i
$383$	−2.54013	−	1.46654i	−0.129794	−	0.0749369i	0.433697	−	0.901059i	$-0.357209\pi$
$383$	−2.54013	−	1.46654i	−0.129794	−	0.0749369i	−0.563491	+	0.826122i	$0.690542\pi$
$384$	1.29315	+	1.15228i	0.0659908	+	0.0588023i
$385$	−16.5137	−	0.605587i	−0.841614	−	0.0308636i
$386$			8.98082i			0.457112i
$387$	8.04547	−	18.5863i	0.408974	−	0.944794i
$388$	0.0149889	+	0.0259615i	0.000760944	+	0.00131799i
$389$	20.9725	−	12.1085i	1.06335	−	0.613925i	0.136993	−	0.990572i	$-0.456256\pi$
$389$	20.9725	−	12.1085i	1.06335	−	0.613925i	0.926357	+	0.376647i	$0.122923\pi$
$390$	−5.97204	+	1.97469i	−0.302406	+	0.0999924i
$391$			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
$396$	9.86651	+	1.28528i	0.495811	+	0.0645879i
$397$	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
$399$	14.1840	−	0.0525269i	0.710088	−	0.00262963i
$400$	1.45367			0.0726834
$401$	11.1027	+	6.41014i	0.554442	+	0.320107i	0.750911	−	0.660403i	$-0.229614\pi$
$401$	11.1027	+	6.41014i	0.554442	+	0.320107i	−0.196470	+	0.980510i	$0.562948\pi$
$402$	−3.91194	+	18.8847i	−0.195110	+	0.941886i
$403$	−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
$408$	−6.01949	+	1.99038i	−0.298009	+	0.0985387i
$409$	−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
$411$	−0.286814	−	0.867407i	−0.0141475	−	0.0427860i
$412$	−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
$417$	−4.80644	−	0.995646i	−0.235372	−	0.0487570i
$418$	2.82692	+	9.86878i	0.138269	+	0.482698i
$419$			5.27534i			0.257717i	0.991663	+	0.128859i	$0.0411313\pi$
$419$			5.27534i			0.257717i	−0.991663	+	0.128859i	$0.958869\pi$
$420$	4.34253	+	7.45757i	0.211894	+	0.363892i
$421$	−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
$423$	−9.15298	−	12.3274i	−0.445033	−	0.599378i
$424$	−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
$429$	−4.80733	+	9.98053i	−0.232100	+	0.481865i
$430$	6.35661	+	11.0100i	0.306543	+	0.530948i
$431$	9.11020	+	15.7793i	0.438823	+	0.760064i	0.997599	−	0.0692548i	$-0.0220622\pi$
$431$	9.11020	+	15.7793i	0.438823	+	0.760064i	−0.558776	+	0.829319i	$0.688729\pi$
$432$	−2.18698	−	4.71350i	−0.105221	−	0.226779i
$433$	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
$438$	3.56562	+	0.738613i	0.170372	+	0.0352923i
$439$	−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
$441$	10.3650	−	18.2638i	0.493572	−	0.869705i
$442$		−	7.05884i		−	0.335755i
$443$	−5.90271	−	3.40793i	−0.280446	−	0.161916i	0.353179	−	0.935556i	$-0.385101\pi$
$443$	−5.90271	−	3.40793i	−0.280446	−	0.161916i	−0.633625	+	0.773640i	$0.718434\pi$
$444$	−2.92202	+	14.1059i	−0.138673	+	0.669437i
$445$	−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	$0.0220216\pi$
$449$			2.92958i			0.138255i	−0.997608	+	0.0691277i	$0.977978\pi$
$450$	−4.00214	−	1.73241i	−0.188663	−	0.0816666i
$451$	5.10588	−	20.4549i	0.240426	−	0.963182i
$452$	6.10465	−	3.52452i	0.287138	−	0.165779i
$453$	10.5760	+	31.9847i	0.496902	+	1.50277i
$454$	−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
$459$	18.9445	+	1.69395i	0.884253	+	0.0790666i
$460$	4.03441	−	6.98781i	0.188105	−	0.325808i
$461$	−17.0494			−0.794068			−0.397034	−	0.917804i	$-0.629960\pi$
$461$	−17.0494			−0.794068			−0.397034	+	0.917804i	$0.629960\pi$
$462$	14.7597	+	3.62627i	0.686686	+	0.168709i
$463$	−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
$465$	32.6971	+	6.77315i	1.51629	+	0.314098i
$466$	7.60946	+	13.1800i	0.352501	+	0.610550i
$467$	−0.545934	−	0.315195i	−0.0252628	−	0.0145855i	0.487315	−	0.873226i	$-0.337976\pi$
$467$	−0.545934	−	0.315195i	−0.0252628	−	0.0145855i	−0.512578	+	0.858641i	$0.671310\pi$
$468$	5.74702	−	0.664303i	0.265656	−	0.0307074i
$469$	−9.14481	+	28.0040i	−0.422268	+	1.29311i
$470$	9.63799			0.444567
$471$	3.46651	−	1.14623i	0.159729	−	0.0528153i
$472$	9.50971	−	5.49043i	0.437720	−	0.252718i
$473$	21.7239	+	5.42264i	0.998864	+	0.249333i
$474$	−6.11072	−	18.4806i	−0.280675	−	0.848841i
$475$		−	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	$-0.874390\pi$
$479$	−17.3889	−	30.1185i	−0.794519	−	1.37615i	0.128625	−	0.991693i	$-0.458944\pi$
$480$	3.19394	+	0.661619i	0.145783	+	0.0301986i
$481$	−13.8899	−	8.01932i	−0.633323	−	0.365649i
$482$		−	19.8468i		−	0.903996i
$483$	−19.6348	+	0.0727128i	−0.893416	+	0.00330855i
$484$	0.377916	+	10.9935i	0.0171780	+	0.499705i
$485$	0.0488899	+	0.0282266i	0.00221997	+	0.00128170i
$486$	0.403712	+	15.5832i	0.0183127	+	0.706870i
$487$	−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	$-0.236928\pi$
$491$	32.5970			1.47108			0.735542	+	0.677480i	$0.236928\pi$
$492$	−10.4533	+	3.45646i	−0.471273	+	0.155829i
$493$	17.7466	+	30.7380i	0.799267	+	1.38437i
$494$	2.98445	+	5.16923i	0.134277	+	0.232574i
$495$	17.3012	−	7.19403i	0.777633	−	0.323347i
$496$	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
$501$	−0.785439	+	3.79168i	−0.0350908	+	0.169400i
$502$	−7.38662	−	4.26467i	−0.329681	−	0.190341i
$503$	−19.5451			−0.871472			−0.435736	−	0.900074i	$-0.643512\pi$
$503$	−19.5451			−0.871472			−0.435736	+	0.900074i	$0.643512\pi$
$504$	−2.51971	−	7.52669i	−0.112237	−	0.335265i
$505$		−	12.7641i		−	0.567994i
$506$	−3.91330	−	13.6613i	−0.173967	−	0.607320i
$507$	3.26078	−	15.7413i	0.144816	−	0.699094i
$508$	−10.8509	+	6.26478i	−0.481431	+	0.277954i
$509$	14.9595	+	8.63689i	0.663069	+	0.382823i	0.793446	−	0.608641i	$-0.208285\pi$
$509$	14.9595	+	8.63689i	0.663069	+	0.382823i	−0.130376	+	0.991465i	$0.541618\pi$
$510$	−7.94291	+	8.91393i	−0.351718	+	0.394715i
$511$	5.28743	+	1.72663i	0.233902	+	0.0763816i
$512$	1.00000			0.0441942
$513$	−14.5893	+	6.76918i	−0.644135	+	0.298867i
$514$	−4.21369	+	2.43278i	−0.185858	+	0.107305i
$515$	−21.0226	+	12.1374i	−0.926368	+	0.534839i
$516$	−3.67090	−	11.1019i	−0.161602	−	0.488732i
$517$	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	$-0.283517\pi$
$521$	36.9007	−	21.3046i	1.61665	−	0.933373i	0.987779	−	0.155864i	$-0.0498162\pi$
$522$	−23.3555	+	17.3413i	−1.02224	+	0.759008i
$523$	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
$525$	−5.78136	−	3.30939i	−0.252319	−	0.144433i
$526$	8.68651			0.378750
$527$	−18.7363	+	32.4522i	−0.816165	+	1.41364i
$528$	4.74663	−	3.23566i	0.206571	−	0.140814i
$529$	−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
$534$	6.75268	+	20.4220i	0.292217	+	0.883748i
$535$	6.90990	−	3.98943i	0.298741	−	0.172478i
$536$	5.56729	+	9.64283i	0.240470	+	0.416507i
$537$	0.579506	+	1.75259i	0.0250075	+	0.0756300i
$538$		−	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
$543$	−2.06598	+	9.97346i	−0.0886599	+	0.428002i
$544$	−1.83021	+	3.17001i	−0.0784695	+	0.135913i
$545$	−3.31248			−0.141891
$546$	8.83710	−	0.0327260i	0.378193	−	0.00140054i
$547$			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
$549$	−20.7802	−	27.9870i	−0.886875	−	1.19446i
$550$	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
$555$	8.51649	+	25.7563i	0.361505	+	1.09329i
$556$	−2.45424	+	1.41696i	−0.104083	+	0.0600923i
$557$	−0.991345	−	1.71706i	−0.0420046	−	0.0727542i	0.844259	−	0.535936i	$-0.180041\pi$
$557$	−0.991345	−	1.71706i	−0.0420046	−	0.0727542i	−0.886263	+	0.463182i	$0.846708\pi$
$558$	−28.1845	−	12.2002i	−1.19314	−	0.516477i
$559$	13.0187			0.550634
$560$	4.73627	+	1.54664i	0.200144	+	0.0653576i
$561$	1.56974	+	20.9688i	0.0662746	+	0.885303i
$562$	0.0230310	−	0.0398908i	0.000971503	−	0.00168269i
$563$	8.74927	+	15.1542i	0.368738	+	0.638672i	0.989368	−	0.145431i	$-0.0464567\pi$
$563$	8.74927	+	15.1542i	0.368738	+	0.638672i	−0.620631	+	0.784103i	$0.713123\pi$
$564$	−8.68028	−	1.79810i	−0.365506	−	0.0757139i
$565$	6.63727	−	11.4961i	0.279232	−	0.483644i
$566$			20.7763i			0.873295i
$567$	−2.03285	+	23.7248i	−0.0853719	+	0.996349i
$568$		−	9.77457i		−	0.410132i
$569$	17.2132	−	29.8142i	0.721616	−	1.24988i	−0.238735	−	0.971085i	$-0.576733\pi$
$569$	17.2132	−	29.8142i	0.721616	−	1.24988i	0.960352	−	0.278792i	$-0.0899339\pi$
$570$	2.04786	−	9.88595i	0.0857753	−	0.414077i
$571$	−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
$576$	−2.75313	−	1.19175i	−0.114714	−	0.0496563i
$577$	−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
$579$	−4.88340	−	14.7688i	−0.202947	−	0.613771i
$580$		−	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
$585$	8.74716	−	6.49470i	0.361650	−	0.268523i
$586$	2.44673	−	4.23787i	0.101074	−	0.175065i
$587$		−	23.7907i		−	0.981945i	−0.871175	−	0.490973i	$-0.836641\pi$
$587$		−	23.7907i		−	0.981945i	0.871175	−	0.490973i	$-0.163359\pi$
$588$	−2.54719	−	11.8538i	−0.105044	−	0.488841i
$589$		−	31.6865i		−	1.30562i
$590$	10.3394	−	17.9084i	0.425667	−	0.737277i
$591$	9.24465	−	44.6282i	0.380274	−	1.83576i
$592$	4.15848	+	7.20269i	0.170912	+	0.296029i
$593$	15.9838	−	27.6848i	0.656377	−	1.13688i	−0.325170	−	0.945656i	$-0.605421\pi$
$593$	15.9838	−	27.6848i	0.656377	−	1.13688i	0.981547	−	0.191223i	$-0.0612452\pi$
$594$	−16.9242	+	3.25138i	−0.694408	+	0.133406i
$595$	−13.5712	+	12.1833i	−0.556366	+	0.499468i
$596$	13.1787			0.539821
$597$	−36.7936	+	12.1660i	−1.50586	+	0.497923i
$598$	−4.13137	−	7.15574i	−0.168944	−	0.292620i
$599$	−29.5373	+	17.0534i	−1.20686	+	0.696782i	−0.962072	−	0.272794i	$-0.912052\pi$
$599$	−29.5373	+	17.0534i	−1.20686	+	0.696782i	−0.244790	+	0.969576i	$0.578719\pi$
$600$	−2.39053	+	0.790445i	−0.0975931	+	0.0322698i
$601$		−	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
$606$	−2.38132	+	11.4957i	−0.0967347	+	0.466983i
$607$	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
$609$	−38.3993	+	22.3598i	−1.55602	+	0.906067i
$610$	21.8813			0.885946
$611$	4.93480	−	8.54733i	0.199641	−	0.345788i
$612$	8.81666	−	6.54631i	0.356392	−	0.264619i
$613$	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	$0.280126\pi$
$617$			38.2908i			1.54153i	−0.637119	+	0.770766i	$0.719874\pi$
$618$	21.1981	−	7.00928i	0.852712	−	0.281955i
$619$	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
$621$	20.1960	−	9.37055i	0.810436	−	0.376027i
$622$			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
$627$	−10.0151	−	14.6919i	−0.399963	−	0.586737i
$628$	1.05398	−	1.82555i	0.0420585	−	0.0728474i
$629$	−30.4435			−1.21386
$630$	−11.1963	−	9.90256i	−0.446073	−	0.394527i
$631$	−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
$633$	−5.24430	−	1.08635i	−0.208442	−	0.0431784i
$634$	−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
$639$	−11.6488	+	26.9107i	−0.460821	+	1.06457i
$640$	1.63087	−	0.941585i	0.0644659	−	0.0372194i
$641$	−40.2975	+	23.2658i	−1.59166	+	0.918943i	−0.598633	+	0.801024i	$0.704289\pi$
$641$	−40.2975	+	23.2658i	−1.59166	+	0.918943i	−0.993023	+	0.117919i	$0.962378\pi$
$642$	−6.96756	+	2.30387i	−0.274988	+	0.0909265i
$643$	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	−0.766310	−	0.642471i	$-0.777909\pi$
$647$	−15.0854	+	8.70958i	−0.593069	+	0.342409i	0.173241	+	0.984879i	$0.444576\pi$
$648$	6.15946	+	6.56209i	0.241966	+	0.257783i
$649$	−10.0290	−	35.0113i	−0.393674	−	1.37431i
$650$		−	2.80329i		−	0.109954i
$651$	−40.7144	−	23.3059i	−1.59572	−	0.913428i
$652$	−3.19727			−0.125215
$653$	−33.2503	−	19.1970i	−1.30118	−	0.751239i	−0.320576	−	0.947223i	$-0.603877\pi$
$653$	−33.2503	−	19.1970i	−1.30118	−	0.751239i	−0.980607	+	0.195984i	$0.937210\pi$
$654$	2.98332	+	0.617990i	0.116657	+	0.0241653i
$655$	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	$-0.674953\pi$
$659$	−26.8196			−1.04474			−0.522372	+	0.852718i	$0.674953\pi$
$660$	4.69451	−	9.74631i	0.182734	−	0.379374i
$661$	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
$663$	3.83831	+	11.6081i	0.149068	+	0.450823i
$664$	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
$669$	6.17860	−	29.8269i	0.238878	−	1.15318i
$670$	18.1591	+	10.4842i	0.701547	+	0.405039i
$671$	26.7776	−	27.7140i	1.03374	−	1.06989i
$672$	−3.97708	−	2.27658i	−0.153419	−	0.0878208i
$673$			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
$675$	7.52347	+	0.672720i	0.289578	+	0.0258930i
$676$	−4.64058	−	8.03773i	−0.178484	−	0.309143i
$677$	−1.34824	+	2.33522i	−0.0518171	+	0.0897499i	−0.890771	−	0.454453i	$-0.849835\pi$
$677$	−1.34824	+	2.33522i	−0.0518171	+	0.0897499i	0.838953	+	0.544203i	$0.183168\pi$
$678$	−8.12250	+	9.11547i	−0.311943	+	0.350078i
$679$	−0.0529840	−	0.0590198i	−0.00203334	−	0.00226497i
$680$			6.89318i			0.264342i
$681$	9.60369	−	3.17552i	0.368014	−	0.121686i
$682$	8.22295	−	32.9423i	0.314873	−	1.26143i
$683$	−20.6454	+	11.9196i	−0.789973	+	0.456091i	−0.839953	−	0.542659i	$-0.817418\pi$
$683$	−20.6454	+	11.9196i	−0.789973	+	0.456091i	0.0499797	+	0.998750i	$0.484084\pi$
$684$	−3.68873	+	8.52155i	−0.141042	+	0.325830i
$685$	−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
$690$	−2.83484	+	13.6851i	−0.107921	+	0.520982i
$691$	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
$693$	−26.2440	+	2.06241i	−0.996926	+	0.0783443i
$694$	18.8652			0.716115
$695$	−2.66837	+	4.62175i	−0.101217	+	0.175313i
$696$	−3.40670	+	16.4457i	−0.129131	+	0.623373i
$697$	−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	$-0.723590\pi$
$701$	−34.2114			−1.29215			−0.646073	+	0.763275i	$0.723590\pi$
$702$	−9.08965	+	4.21743i	−0.343067	+	0.159177i
$703$	22.2939	−	12.8714i	0.840831	−	0.485454i
$704$	0.803239	−	3.21789i	0.0302732	−	0.121279i
$705$	−15.8495	+	5.24074i	−0.596927	+	0.197378i
$706$		−	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
$711$	20.0980	+	27.0682i	0.753732	+	1.01514i
$712$	10.7547	+	6.20926i	0.403051	+	0.232702i
$713$			43.8635i			1.64270i
$714$	14.4957	−	8.44080i	0.542486	−	0.315889i
$715$	8.66182	+	8.36918i	0.323934	+	0.312989i
$716$	0.922959	+	0.532870i	0.0344926	+	0.0199143i
$717$	−2.74676	+	13.2599i	−0.102579	+	0.495199i
$718$	−14.6090	−	25.3035i	−0.545203	−	0.944319i
$719$	−37.2542	−	21.5087i	−1.38935	−	0.802139i	−0.396105	−	0.918205i	$-0.629638\pi$
$719$	−37.2542	−	21.5087i	−1.38935	−	0.802139i	−0.993242	+	0.116066i	$0.962972\pi$
$720$	−5.61214	+	0.648713i	−0.209152	+	0.0241761i
$721$	33.3700	−	7.04152i	1.24276	−	0.262240i
$722$	9.41961			0.350561
$723$	10.7919	+	32.6377i	0.401354	+	1.21381i
$724$	2.94021	+	5.09260i	0.109272	+	0.189265i
$725$	7.04775	+	12.2071i	0.261747	+	0.453359i
$726$	−6.59930	−	17.8731i	−0.244923	−	0.663335i
$727$	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
$732$	−19.7070	−	4.08226i	−0.728390	−	0.150885i
$733$	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
$735$	−15.3155	−	16.9336i	−0.564920	−	0.624605i
$736$			4.28470i			0.157936i
$737$	35.5014	−	10.1694i	1.30771	−	0.374596i
$738$	15.3109	−	11.3682i	0.563601	−	0.418469i
$739$	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	$-0.321601\pi$
$743$	28.9793			1.06315			0.531573	+	0.847013i	$0.321601\pi$
$744$	−16.8350	+	5.56659i	−0.617200	+	0.204081i
$745$	21.4928	−	12.4089i	0.787436	−	0.454627i
$746$	−24.2451	+	13.9979i	−0.887675	+	0.512499i
$747$	−6.45660	−	2.79487i	−0.236235	−	0.102259i
$748$	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
$753$	14.4661	+	2.99663i	0.527175	+	0.109203i
$754$	−16.1938	−	9.34950i	−0.589744	−	0.340489i
$755$	36.6271			1.33300
$756$	8.23632	+	11.0074i	0.299552	+	0.400335i
$757$	−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
$759$	13.8638	+	20.3379i	0.503225	+	0.738220i
$760$	−2.91441	−	5.04791i	−0.105717	−	0.183107i
$761$	10.5972	−	18.3548i	0.384147	−	0.665362i	−0.607504	−	0.794317i	$-0.707829\pi$
$761$	10.5972	−	18.3548i	0.384147	−	0.665362i	0.991650	+	0.128955i	$0.0411624\pi$
$762$	14.4376	−	16.2026i	0.523020	−	0.586958i
$763$	4.42394	+	1.44465i	0.160157	+	0.0523000i
$764$		−	15.1400i		−	0.547747i
$765$	8.21496	−	18.9778i	0.297012	−	0.686145i
$766$	2.54013	−	1.46654i	0.0917786	−	0.0529884i
$767$	−10.5879	−	18.3388i	−0.382307	−	0.662175i
$768$	−1.64448	+	0.543759i	−0.0593402	+	0.0196212i
$769$			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	0.0147769	−	0.999891i	$-0.495296\pi$
$773$	24.6916	−	14.2557i	0.888096	−	0.512743i	0.873319	+	0.487148i	$0.161963\pi$
$774$	12.0735	+	16.2607i	0.433972	+	0.584480i
$775$	−7.44078	+	12.8878i	−0.267281	+	0.462944i
$776$	−0.0299777			−0.00107614
$777$	−0.141141	−	38.1128i	−0.00506342	−	1.36729i
$778$			24.2170i			0.868222i
$779$	17.0391	+	9.83756i	0.610491	+	0.352467i
$780$	1.27588	−	6.15928i	0.0456840	−	0.220538i
$781$	−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
$786$	−3.13856	+	1.03779i	−0.111949	+	0.0370166i
$787$	−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
$789$	−14.2848	+	4.72337i	−0.508553	+	0.168156i
$790$	−21.1629			−0.752943
$791$	−13.8781	+	12.4588i	−0.493447	+	0.442984i
$792$	−6.04634	+	7.90201i	−0.214847	+	0.280786i
$793$	11.2036	−	19.4051i	0.397850	−	0.689096i
$794$	7.83756	+	13.5750i	0.278144	+	0.481760i
$795$	1.58258	−	7.63987i	0.0561285	−	0.270958i
$796$	−11.1870	+	19.3764i	−0.396512	+	0.686778i
$797$			4.80180i			0.170089i	0.996377	+	0.0850443i	$0.0271032\pi$
$797$			4.80180i			0.170089i	−0.996377	+	0.0850443i	$0.972897\pi$
$798$	−7.04650	+	12.3100i	−0.249444	+	0.435768i
$799$		−	18.7338i		−	0.662756i
$800$	−0.726834	+	1.25891i	−0.0256975	+	0.0445093i
$801$	−22.2093	−	29.9119i	−0.784729	−	1.05688i
$802$	−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
$807$	2.87800	+	8.70391i	0.101311	+	0.306392i
$808$	3.38899	+	5.86990i	0.119224	+	0.206502i
$809$	16.5190	+	28.6117i	0.580776	+	1.00593i	0.995388	+	0.0959356i	$0.0305843\pi$
$809$	16.5190	+	28.6117i	0.580776	+	1.00593i	−0.414611	+	0.909999i	$0.636082\pi$
$810$	16.2241	+	4.90229i	0.570056	+	0.172249i
$811$		−	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
$816$	1.28602	−	6.20822i	0.0450198	−	0.217331i
$817$	−10.4479	+	18.0962i	−0.365524	+	0.633107i
$818$		−	30.6423i		−	1.07138i
$819$	−14.5147	+	4.85907i	−0.507184	+	0.169790i
$820$			11.9706i			0.418031i
$821$	19.6060	−	33.9586i	0.684255	−	1.18516i	−0.289415	−	0.957204i	$-0.593461\pi$
$821$	19.6060	−	33.9586i	0.684255	−	1.18516i	0.973670	−	0.227961i	$-0.0732059\pi$
$822$	0.894603	+	0.185316i	0.0312029	+	0.00646362i
$823$	−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
$825$	0.623395	+	8.32739i	0.0217038	+	0.289922i
$826$	−21.6190	+	19.4081i	−0.752222	+	0.675294i
$827$	−44.8575			−1.55985			−0.779925	−	0.625873i	$-0.784743\pi$
$827$	−44.8575			−1.55985			−0.779925	+	0.625873i	$0.784743\pi$
$828$	5.10630	−	11.7963i	0.177456	−	0.409951i
$829$	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
$831$	−1.91901	−	5.80363i	−0.0665697	−	0.201326i
$832$		−	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
$837$	52.9829	+	4.73753i	1.83136	+	0.163753i
$838$	−4.56858	−	2.63767i	−0.157819	−	0.0911168i
$839$		−	40.8769i		−	1.41123i	−0.708597	−	0.705613i	$-0.750672\pi$
$839$		−	40.8769i		−	1.41123i	0.708597	−	0.705613i	$-0.249328\pi$
$840$	−8.62971	+	0.0319580i	−0.297753	+	0.00110266i
$841$	65.0223			2.24215
$842$	2.03684	−	3.52791i	0.0701941	−	0.121580i
$843$	−0.0161831	+	0.0781231i	−0.000557374	+	0.00269070i
$844$	−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
$849$	−11.2973	−	34.1664i	−0.387723	−	1.17259i
$850$	−2.66051	−	4.60814i	−0.0912549	−	0.158058i
$851$	−30.8614	+	17.8178i	−1.05791	+	0.610787i
$852$	5.31501	+	16.0741i	0.182089	+	0.550690i
$853$			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	0.775088	−	0.631854i	$-0.217706\pi$
$857$	−4.67390	−	8.09543i	−0.159657	−	0.276535i	−0.934745	+	0.355319i	$0.884372\pi$
$858$	−6.23973	−	9.15354i	−0.213021	−	0.312497i
$859$	−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
$861$	25.1729	−	14.6581i	0.857890	−	0.499548i
$862$	−18.2204			−0.620590
$863$	43.1545	+	24.9152i	1.46900	+	0.848125i	0.999396	−	0.0347546i	$-0.0110650\pi$
$863$	43.1545	+	24.9152i	1.46900	+	0.848125i	0.469600	+	0.882880i	$0.344398\pi$
$864$	5.17550	+	0.462774i	0.176074	+	0.0157439i
$865$	−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
$870$	9.92914	+	30.0286i	0.336629	+	1.01806i
$871$	18.5955	−	10.7361i	0.630085	−	0.363780i
$872$	1.52333	−	0.879494i	0.0515864	−	0.0297834i
$873$	0.0825326	+	0.0357260i	0.00279330	+	0.00120914i
$874$	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
$879$	−1.71923	+	8.29954i	−0.0579883	+	0.279936i
$880$	−1.71994	−	6.00429i	−0.0579790	−	0.202405i
$881$			42.3927i			1.42825i	0.700020	+	0.714123i	$0.253174\pi$
$881$			42.3927i			1.42825i	−0.700020	+	0.714123i	$0.746826\pi$
$882$	10.6344	+	18.1083i	0.358079	+	0.609737i
$883$	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
$885$	−7.26515	+	35.0722i	−0.244215	+	1.17894i
$886$	5.90271	−	3.40793i	0.198305	−	0.114492i
$887$	4.16485	−	7.21373i	0.139842	−	0.242213i	−0.787595	−	0.616194i	$-0.788674\pi$
$887$	4.16485	−	7.21373i	0.139842	−	0.242213i	0.927437	+	0.373980i	$0.122007\pi$
$888$	−10.7551	−	9.58350i	−0.360917	−	0.321601i
$889$	24.6680	−	22.1453i	0.827340	−	0.742730i
$890$	23.3862			0.783907
$891$	26.0636	−	14.5495i	0.873163	−	0.487427i
$892$	−8.79309	−	15.2301i	−0.294414	−	0.509941i
$893$	7.92060	+	13.7189i	0.265053	+	0.459085i
$894$	−21.6722	+	7.16605i	−0.724826	+	0.239669i
$895$	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
$900$	3.50138	−	2.59975i	0.116713	−	0.0866583i
$901$	7.58263	+	4.37783i	0.252614	+	0.145847i
$902$	15.1615	+	14.6492i	0.504822	+	0.487767i
$903$	15.5675	+	26.7346i	0.518054	+	0.889672i
$904$			7.04904i			0.234448i
$905$	9.59023	+	5.53692i	0.318790	+	0.184054i
$906$	−32.9876	−	6.83332i	−1.09594	−	0.227022i
$907$	−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	$0.115828\pi$
$911$			21.4845i			0.711812i	−0.934522	+	0.355906i	$0.884172\pi$
$912$	1.68305	+	5.09004i	0.0557315	+	0.168548i
$913$	1.88374	−	7.54654i	0.0623428	−	0.249754i
$914$	6.48607	−	3.74473i	0.214540	−	0.123865i
$915$	−35.9834	+	11.8981i	−1.18957	+	0.393340i
$916$	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
$921$	−43.6486	−	9.04173i	−1.43827	−	0.297935i
$922$	8.52468	−	14.7652i	0.280745	−	0.486265i
$923$	−18.8495			−0.620440
$924$	−10.5203	+	10.9692i	−0.346093	+	0.360860i
$925$	−12.0901			−0.397520
$926$	0.0529251	−	0.0916690i	0.00173923	−	0.00301243i
$927$	−31.0485	+	23.0533i	−1.01977	+	0.757170i
$928$	4.84825	+	8.39742i	0.159152	+	0.275659i
$929$	26.8652	+	15.5107i	0.881420	+	0.508888i	0.871126	−	0.491059i	$-0.163390\pi$
$929$	26.8652	+	15.5107i	0.881420	+	0.508888i	0.0102936	+	0.999947i	$0.496723\pi$
$930$	−22.2143	+	24.9300i	−0.728435	+	0.817486i
$931$	−12.7870	+	17.4909i	−0.419077	+	0.573241i
$932$	−15.2189			−0.498512
$933$	−1.49856	−	4.53208i	−0.0490608	−	0.148374i
$934$	0.545934	−	0.315195i	0.0178635	−	0.0103135i
$935$	22.1815	+	5.53688i	0.725412	+	0.181075i
$936$	−2.29820	+	5.30921i	−0.0751192	+	0.173537i
$937$		−	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	0.547555	−	0.836770i	$-0.315559\pi$
$941$	−13.8313	−	23.9564i	−0.450886	−	0.780958i	−0.998441	+	0.0558120i	$0.982225\pi$
$942$	−0.740597	+	3.57520i	−0.0241299	+	0.116486i
$943$	−23.5872	−	13.6181i	−0.768106	−	0.443466i
$944$			10.9809i			0.357397i
$945$	23.7968	+	10.1965i	0.774110	+	0.331692i
$946$	−15.5581	+	16.1021i	−0.505836	+	0.523524i
$947$	−18.7065	−	10.8002i	−0.607879	−	0.350959i	0.164256	−	0.986418i	$-0.447478\pi$
$947$	−18.7065	−	10.8002i	−0.607879	−	0.350959i	−0.772135	+	0.635459i	$0.780811\pi$
$948$	19.0600	+	3.94825i	0.619040	+	0.128233i
$949$	−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	$-0.462849\pi$
$953$	7.18964			0.232895			0.116448	+	0.993197i	$0.462849\pi$
$954$	−2.85065	+	6.58545i	−0.0922933	+	0.213212i
$955$	−14.2556	−	24.6915i	−0.461301	−	0.798997i
$956$	3.90906	+	6.77068i	0.126428	+	0.218980i
$957$	50.1840	+	24.1722i	1.62222	+	0.781377i
$958$	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
$963$	10.2053	−	7.57735i	0.328861	−	0.244177i
$964$	17.1878	+	9.92339i	0.553583	+	0.319611i
$965$	−16.9124			−0.544430
$966$	9.75445	−	17.0406i	0.313844	−	0.548273i
$967$		−	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
$969$	−19.2158	−	3.98052i	−0.617301	−	0.127873i
$970$	−0.0488899	+	0.0282266i	−0.00156976	+	0.000906301i
$971$	−13.2167	−	7.63066i	−0.424144	−	0.244879i	0.272705	−	0.962098i	$-0.412082\pi$
$971$	−13.2167	−	7.63066i	−0.424144	−	0.244879i	−0.696849	+	0.717218i	$0.745415\pi$
$972$	−13.6973	−	7.44199i	−0.439342	−	0.238702i
$973$	5.57938	−	5.00879i	0.178867	−	0.160574i
$974$	20.4073			0.653891
$975$	1.52432	+	4.60997i	0.0488172	+	0.147637i
$976$	−10.0627	+	5.80969i	−0.322098	+	0.185963i
$977$	49.3619	−	28.4991i	1.57923	−	0.911768i	0.584262	−	0.811565i	$-0.301384\pi$
$977$	49.3619	−	28.4991i	1.57923	−	0.911768i	0.994967	−	0.100203i	$-0.0319491\pi$
$978$	5.25786	−	1.73855i	0.168128	−	0.0555926i
$979$	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	0.179311	−	0.983793i	$-0.442613\pi$
$983$	35.1451	−	20.2910i	1.12096	−	0.647184i	0.941645	+	0.336609i	$0.109280\pi$
$984$	2.23328	−	10.7811i	0.0711945	−	0.343689i
$985$	−42.9133	−	24.7760i	−1.36733	−	0.789430i
$986$	−35.4932			−1.13033
$987$	23.4533	−	0.0868534i	0.746526	−	0.00276457i
$988$	−5.96891			−0.189896
$989$	14.4629	−	25.0505i	0.459895	−	0.796561i
$990$	−2.42041	+	18.5803i	−0.0769256	+	0.590521i
$991$	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
$996$	−3.85662	+	1.27521i	−0.122202	+	0.0404067i
$997$	−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
$999$	18.1890	+	39.2020i	0.575474	+	1.24030i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.351333 - 1.69604i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.63087 - 0.941585i) q^{5} +(1.29315 + 1.15228i) q^{6} +(1.76745 + 1.96879i) q^{7} +1.00000 q^{8} +(-2.75313 - 1.19175i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.351333 - 1.69604i) 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} +(-2.75313 - 1.19175i) q^{9} +(1.63087 - 0.941585i) q^{10} +(0.803239 - 3.21789i) q^{11} +(-1.64448 + 0.543759i) 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} +(2.40865 - 1.78841i) q^{18} +(2.68054 + 1.54761i) q^{19} +1.88317i q^{20} +(3.96011 - 2.30597i) q^{21} +(2.38515 + 2.30457i) q^{22} +(-3.71066 - 2.14235i) q^{23} +(0.351333 - 1.69604i) 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} +(-1.02399 - 3.09684i) q^{30} +(-5.11862 - 8.86571i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-5.17548 - 2.49288i) 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} +(-3.27070 - 0.677519i) q^{39} +(-1.63087 - 0.941585i) q^{40} +6.35661 q^{41} +(0.0169703 + 4.58254i) q^{42} +6.75096i q^{43} +(-3.18839 + 0.913319i) q^{44} +(3.36787 + 4.53590i) 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} +(-6.01949 + 1.99038i) q^{51} +(-1.67007 + 0.964214i) q^{52} +(-2.07152 + 1.19599i) q^{53} +(-2.18698 - 4.71350i) 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} +(3.19394 + 0.661619i) q^{60} +(10.0627 + 5.80969i) q^{61} +10.2372 q^{62} +(-2.51971 - 7.52669i) q^{63} +1.00000 q^{64} +(-1.81578 + 3.14502i) q^{65} +(4.74663 - 3.23566i) 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} +(-2.75313 - 1.19175i) q^{72} +(1.82066 - 1.05116i) q^{73} +(4.15848 + 7.20269i) q^{74} +(-2.39053 + 0.790445i) 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} +(6.15946 + 6.56209i) q^{81} +(-3.17830 + 5.50499i) q^{82} +2.34518 q^{83} +(-3.97708 - 2.27658i) q^{84} +6.89318i q^{85} +(-5.84651 - 3.37548i) q^{86} +(-3.40670 + 16.4457i) 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} +(-16.8350 + 5.56659i) q^{93} +(-4.43228 + 2.55898i) q^{94} +(-2.91441 - 5.04791i) q^{95} +(-1.64448 + 0.543759i) q^{96} -0.0299777 q^{97} +(-5.65094 - 4.13121i) q^{98} +(-6.04634 + 7.90201i) 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	\( 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9} - 4 q^{11} + 4 q^{15} - 12 q^{16} + 4 q^{17} - 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} + 40 q^{29} - 2 q^{30} - 28 q^{31} - 12 q^{32} + 32 q^{33} - 8 q^{34} - 32 q^{35} + 16 q^{36} - 16 q^{37} - 8 q^{41} + 6 q^{42} - 4 q^{44} - 28 q^{45} - 8 q^{49} - 40 q^{50} - 34 q^{51} + 6 q^{54} + 8 q^{55} + 40 q^{57} - 20 q^{58} - 2 q^{60} + 56 q^{62} - 14 q^{63} + 24 q^{64} - 44 q^{65} + 32 q^{66} + 4 q^{68} - 20 q^{69} + 64 q^{70} - 8 q^{72} - 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} + 144 q^{83} - 6 q^{84} + 8 q^{87} - 4 q^{88} + 56 q^{90} - 32 q^{91} - 22 q^{93} - 44 q^{95} + 64 q^{97} - 8 q^{98} - 52 q^{99}+O(q^{100}) \) 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 + 32 * 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 + 32 * 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 - 52 * q^99

Introduction

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