LMFDB - Embedded newform 828.2.o.a.47.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [828,2,Mod(47,828)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(828, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("828.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 828 = 2^{2} \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	828.o (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:	$6.61161328736$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$66$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.2
Character	$\chi$	$=$	828.47
Dual form			828.2.o.a.599.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40722 + 0.140428i) q^{2} +(-1.25401 + 1.19476i) q^{3} +(1.96056 - 0.395228i) q^{4} +(-0.532014 + 0.307158i) q^{5} +(1.59689 - 1.85740i) q^{6} +(1.07017 + 0.617862i) q^{7} +(-2.70345 + 0.831492i) q^{8} +(0.145075 - 2.99649i) q^{9} +O(q^{10})$	\(q+(-1.40722 + 0.140428i) q^{2} +(-1.25401 + 1.19476i) q^{3} +(1.96056 - 0.395228i) q^{4} +(-0.532014 + 0.307158i) q^{5} +(1.59689 - 1.85740i) q^{6} +(1.07017 + 0.617862i) q^{7} +(-2.70345 + 0.831492i) q^{8} +(0.145075 - 2.99649i) q^{9} +(0.705529 - 0.506950i) q^{10} +(-0.579181 + 1.00317i) q^{11} +(-1.98635 + 2.83803i) q^{12} +(1.27170 + 2.20264i) q^{13} +(-1.59273 - 0.719189i) q^{14} +(0.300168 - 1.02081i) q^{15} +(3.68759 - 1.54974i) q^{16} -5.65288i q^{17} +(0.216638 + 4.23711i) q^{18} +7.70722i q^{19} +(-0.921647 + 0.812469i) q^{20} +(-2.08020 + 0.503795i) q^{21} +(0.674164 - 1.49302i) q^{22} +(0.500000 + 0.866025i) q^{23} +(2.39671 - 4.27268i) q^{24} +(-2.31131 + 4.00330i) q^{25} +(-2.09888 - 2.92103i) q^{26} +(3.39817 + 3.93096i) q^{27} +(2.34233 + 0.788395i) q^{28} +(0.589231 + 0.340193i) q^{29} +(-0.279053 + 1.47866i) q^{30} +(7.05643 - 4.07403i) q^{31} +(-4.97164 + 2.69867i) q^{32} +(-0.472255 - 1.94997i) q^{33} +(0.793824 + 7.95488i) q^{34} -0.759126 q^{35} +(-0.899867 - 5.93214i) q^{36} -4.80087 q^{37} +(-1.08231 - 10.8458i) q^{38} +(-4.22636 - 1.24276i) q^{39} +(1.18287 - 1.27275i) q^{40} +(0.393650 - 0.227274i) q^{41} +(2.85656 - 1.00107i) q^{42} +(2.55744 + 1.47654i) q^{43} +(-0.739038 + 2.19569i) q^{44} +(0.843214 + 1.63873i) q^{45} +(-0.825226 - 1.14848i) q^{46} +(-6.50502 + 11.2670i) q^{47} +(-2.77270 + 6.34918i) q^{48} +(-2.73649 - 4.73974i) q^{49} +(2.69035 - 5.95812i) q^{50} +(6.75387 + 7.08877i) q^{51} +(3.36378 + 3.81581i) q^{52} +7.13745i q^{53} +(-5.33401 - 5.05454i) q^{54} -0.711601i q^{55} +(-3.40689 - 0.780520i) q^{56} +(-9.20832 - 9.66493i) q^{57} +(-0.876953 - 0.395983i) q^{58} +(-0.610765 - 1.05788i) q^{59} +(0.185045 - 2.11999i) q^{60} +(2.61631 - 4.53158i) q^{61} +(-9.35787 + 6.72400i) q^{62} +(2.00667 - 3.11711i) q^{63} +(6.61724 - 4.49579i) q^{64} +(-1.35312 - 0.781224i) q^{65} +(0.938399 + 2.67773i) q^{66} +(-9.95606 + 5.74813i) q^{67} +(-2.23418 - 11.0828i) q^{68} +(-1.66170 - 0.488621i) q^{69} +(1.06826 - 0.106603i) q^{70} -12.2931 q^{71} +(2.09935 + 8.22148i) q^{72} -13.6599 q^{73} +(6.75591 - 0.674178i) q^{74} +(-1.88460 - 7.78164i) q^{75} +(3.04611 + 15.1105i) q^{76} +(-1.23964 + 0.715708i) q^{77} +(6.12195 + 1.15534i) q^{78} +(-2.90485 - 1.67712i) q^{79} +(-1.48583 + 1.95715i) q^{80} +(-8.95791 - 0.869434i) q^{81} +(-0.522038 + 0.375105i) q^{82} +(-2.96563 + 5.13662i) q^{83} +(-3.87924 + 1.80987i) q^{84} +(1.73633 + 3.00741i) q^{85} +(-3.80624 - 1.71868i) q^{86} +(-1.14535 + 0.277388i) q^{87} +(0.731656 - 3.19360i) q^{88} +17.7020i q^{89} +(-1.41672 - 2.18766i) q^{90} +3.14293i q^{91} +(1.32256 + 1.50028i) q^{92} +(-3.98132 + 13.5396i) q^{93} +(7.57182 - 16.7687i) q^{94} +(-2.36734 - 4.10035i) q^{95} +(3.01021 - 9.32409i) q^{96} +(-2.82127 + 4.88659i) q^{97} +(4.51645 + 6.28560i) q^{98} +(2.92197 + 1.88105i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 9 q^{8} + 2 q^{9}+O(q^{10}) $ 132 * q - 9 * q^8 + 2 * q^9	$ 132 q - 9 q^{8} + 2 q^{9} - 29 q^{12} - 15 q^{14} - 34 q^{18} - 21 q^{20} + 66 q^{23} + 15 q^{24} + 66 q^{25} - 54 q^{26} + 12 q^{27} + 77 q^{30} + 30 q^{32} - 22 q^{33} + 36 q^{36} - 24 q^{39} - 30 q^{41} - 11 q^{42} - 65 q^{48} + 66 q^{49} - 32 q^{51} - 64 q^{54} - 42 q^{56} - 6 q^{57} + 27 q^{58} + 36 q^{59} + 58 q^{60} + 63 q^{62} - 20 q^{63} - 9 q^{64} + 78 q^{66} - 15 q^{68} - 78 q^{70} + 36 q^{72} - 12 q^{73} - 21 q^{74} + 48 q^{75} - 87 q^{76} - 11 q^{78} + 72 q^{80} - 10 q^{81} - 9 q^{82} - 157 q^{84} - 24 q^{86} + 96 q^{87} + 108 q^{88} - 63 q^{90} - 12 q^{93} + 75 q^{94} - 9 q^{96} - 6 q^{97} + 20 q^{99}+O(q^{100}) $ 132 * q - 9 * q^8 + 2 * q^9 - 29 * q^12 - 15 * q^14 - 34 * q^18 - 21 * q^20 + 66 * q^23 + 15 * q^24 + 66 * q^25 - 54 * q^26 + 12 * q^27 + 77 * q^30 + 30 * q^32 - 22 * q^33 + 36 * q^36 - 24 * q^39 - 30 * q^41 - 11 * q^42 - 65 * q^48 + 66 * q^49 - 32 * q^51 - 64 * q^54 - 42 * q^56 - 6 * q^57 + 27 * q^58 + 36 * q^59 + 58 * q^60 + 63 * q^62 - 20 * q^63 - 9 * q^64 + 78 * q^66 - 15 * q^68 - 78 * q^70 + 36 * q^72 - 12 * q^73 - 21 * q^74 + 48 * q^75 - 87 * q^76 - 11 * q^78 + 72 * q^80 - 10 * q^81 - 9 * q^82 - 157 * q^84 - 24 * q^86 + 96 * q^87 + 108 * q^88 - 63 * q^90 - 12 * q^93 + 75 * q^94 - 9 * q^96 - 6 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/828\mathbb{Z}\right)^\times$.

$n$	$415$	$461$	$649$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.40722	+	0.140428i	−0.995058	+	0.0992977i
$2$	−1.40722	+	0.140428i	−0.995058	+	0.0992977i
$3$	−1.25401	+	1.19476i	−0.724002	+	0.689798i
$3$	−1.25401	+	1.19476i	−0.724002	+	0.689798i
$4$	1.96056	−	0.395228i	0.980280	−	0.197614i
$5$	−0.532014	+	0.307158i	−0.237924	+	0.137365i	−0.614222	−	0.789133i	$-0.710530\pi$
$5$	−0.532014	+	0.307158i	−0.237924	+	0.137365i	0.376298	+	0.926499i	$0.377197\pi$
$6$	1.59689	−	1.85740i	0.651929	−	0.758280i
$7$	1.07017	+	0.617862i	0.404486	+	0.233530i	0.688418	−	0.725314i	$-0.258306\pi$
$7$	1.07017	+	0.617862i	0.404486	+	0.233530i	−0.283932	+	0.958844i	$0.591639\pi$
$8$	−2.70345	+	0.831492i	−0.955813	+	0.293977i
$9$	0.145075	−	2.99649i	0.0483584	−	0.998830i
$10$	0.705529	−	0.506950i	0.223108	−	0.160312i
$11$	−0.579181	+	1.00317i	−0.174630	+	0.302467i	−0.940033	−	0.341083i	$-0.889206\pi$
$11$	−0.579181	+	1.00317i	−0.174630	+	0.302467i	0.765403	+	0.643551i	$0.222539\pi$
$12$	−1.98635	+	2.83803i	−0.573411	+	0.819268i
$13$	1.27170	+	2.20264i	0.352705	+	0.610904i	0.986722	−	0.162415i	$-0.0519285\pi$
$13$	1.27170	+	2.20264i	0.352705	+	0.610904i	−0.634017	+	0.773319i	$0.718595\pi$
$14$	−1.59273	−	0.719189i	−0.425676	−	0.192211i
$15$	0.300168	−	1.02081i	0.0775030	−	0.263572i
$16$	3.68759	−	1.54974i	0.921897	−	0.387434i
$17$		−	5.65288i		−	1.37103i	−0.728060	−	0.685513i	$-0.759578\pi$
$17$		−	5.65288i		−	1.37103i	0.728060	−	0.685513i	$-0.240422\pi$
$18$	0.216638	+	4.23711i	0.0510621	+	0.998695i
$19$			7.70722i			1.76816i	0.467337	+	0.884079i	$0.345213\pi$
$19$			7.70722i			1.76816i	−0.467337	+	0.884079i	$0.654787\pi$
$20$	−0.921647	+	0.812469i	−0.206087	+	0.181673i
$21$	−2.08020	+	0.503795i	−0.453937	+	0.109937i
$22$	0.674164	−	1.49302i	0.143732	−	0.318313i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$	2.39671	−	4.27268i	0.489226	−	0.872157i
$25$	−2.31131	+	4.00330i	−0.462262	+	0.800660i
$26$	−2.09888	−	2.92103i	−0.411623	−	0.572861i
$27$	3.39817	+	3.93096i	0.653979	+	0.756513i
$28$	2.34233	+	0.788395i	0.442658	+	0.148993i
$29$	0.589231	+	0.340193i	0.109417	+	0.0631722i	0.553710	−	0.832710i	$-0.313212\pi$
$29$	0.589231	+	0.340193i	0.109417	+	0.0631722i	−0.444293	+	0.895882i	$0.646545\pi$
$30$	−0.279053	+	1.47866i	−0.0509479	+	0.269965i
$31$	7.05643	−	4.07403i	1.26737	−	0.731718i	0.292882	−	0.956148i	$-0.405386\pi$
$31$	7.05643	−	4.07403i	1.26737	−	0.731718i	0.974490	+	0.224431i	$0.0720522\pi$
$32$	−4.97164	+	2.69867i	−0.878870	+	0.477061i
$33$	−0.472255	−	1.94997i	−0.0822091	−	0.339446i
$34$	0.793824	+	7.95488i	0.136140	+	1.36425i
$35$	−0.759126			−0.128316
$36$	−0.899867	−	5.93214i	−0.149978	−	0.988689i
$37$	−4.80087			−0.789259			−0.394629	−	0.918840i	$-0.629127\pi$
$37$	−4.80087			−0.789259			−0.394629	+	0.918840i	$0.629127\pi$
$38$	−1.08231	−	10.8458i	−0.175574	−	1.75942i
$39$	−4.22636	−	1.24276i	−0.676759	−	0.199000i
$40$	1.18287	−	1.27275i	0.187028	−	0.201240i
$41$	0.393650	−	0.227274i	0.0614778	−	0.0354942i	−0.468946	−	0.883227i	$-0.655366\pi$
$41$	0.393650	−	0.227274i	0.0614778	−	0.0354942i	0.530424	+	0.847733i	$0.322033\pi$
$42$	2.85656	−	1.00107i	0.440777	−	0.154469i
$43$	2.55744	+	1.47654i	0.390006	+	0.225170i	0.682163	−	0.731201i	$-0.261040\pi$
$43$	2.55744	+	1.47654i	0.390006	+	0.225170i	−0.292157	+	0.956370i	$0.594373\pi$
$44$	−0.739038	+	2.19569i	−0.111414	+	0.331012i
$45$	0.843214	+	1.63873i	0.125699	+	0.244288i
$46$	−0.825226	−	1.14848i	−0.121673	−	0.169334i
$47$	−6.50502	+	11.2670i	−0.948855	+	1.64347i	−0.201013	+	0.979589i	$0.564423\pi$
$47$	−6.50502	+	11.2670i	−0.948855	+	1.64347i	−0.747842	+	0.663876i	$0.768910\pi$
$48$	−2.77270	+	6.34918i	−0.400205	+	0.916426i
$49$	−2.73649	−	4.73974i	−0.390927	−	0.677106i
$50$	2.69035	−	5.95812i	0.380473	−	0.842605i
$51$	6.75387	+	7.08877i	0.945730	+	0.992626i
$52$	3.36378	+	3.81581i	0.466473	+	0.529157i
$53$			7.13745i			0.980404i	0.871609	+	0.490202i	$0.163077\pi$
$53$			7.13745i			0.980404i	−0.871609	+	0.490202i	$0.836923\pi$
$54$	−5.33401	−	5.05454i	−0.725867	−	0.687835i
$55$		−	0.711601i		−	0.0959522i
$56$	−3.40689	−	0.780520i	−0.455265	−	0.104301i
$57$	−9.20832	−	9.66493i	−1.21967	−	1.28015i
$58$	−0.876953	−	0.395983i	−0.115150	−	0.0519951i
$59$	−0.610765	−	1.05788i	−0.0795148	−	0.137724i	0.823526	−	0.567279i	$-0.192004\pi$
$59$	−0.610765	−	1.05788i	−0.0795148	−	0.137724i	−0.903041	+	0.429555i	$0.858670\pi$
$60$	0.185045	−	2.11999i	0.0238892	−	0.273690i
$61$	2.61631	−	4.53158i	0.334984	−	0.580210i	−0.648498	−	0.761217i	$-0.724602\pi$
$61$	2.61631	−	4.53158i	0.334984	−	0.580210i	0.983482	+	0.181007i	$0.0579357\pi$
$62$	−9.35787	+	6.72400i	−1.18845	+	0.853949i
$63$	2.00667	−	3.11711i	0.252817	−	0.392719i
$64$	6.61724	−	4.49579i	0.827155	−	0.561973i
$65$	−1.35312	−	0.781224i	−0.167834	−	0.0968989i
$66$	0.938399	+	2.67773i	0.115509	+	0.329605i
$67$	−9.95606	+	5.74813i	−1.21633	+	0.702246i	−0.964130	−	0.265430i	$-0.914486\pi$
$67$	−9.95606	+	5.74813i	−1.21633	+	0.702246i	−0.252196	+	0.967676i	$0.581153\pi$
$68$	−2.23418	−	11.0828i	−0.270934	−	1.34399i
$69$	−1.66170	−	0.488621i	−0.200045	−	0.0588231i
$70$	1.06826	−	0.106603i	0.127682	−	0.0127415i
$71$	−12.2931			−1.45892			−0.729460	−	0.684024i	$-0.760228\pi$
$71$	−12.2931			−1.45892			−0.729460	+	0.684024i	$0.760228\pi$
$72$	2.09935	+	8.22148i	0.247411	+	0.968911i
$73$	−13.6599			−1.59878			−0.799388	−	0.600815i	$-0.794843\pi$
$73$	−13.6599			−1.59878			−0.799388	+	0.600815i	$0.794843\pi$
$74$	6.75591	−	0.674178i	0.785358	−	0.0783716i
$75$	−1.88460	−	7.78164i	−0.217615	−	0.898547i
$76$	3.04611	+	15.1105i	0.349413	+	1.73329i
$77$	−1.23964	+	0.715708i	−0.141270	+	0.0815625i
$78$	6.12195	+	1.15534i	0.693175	+	0.130816i
$79$	−2.90485	−	1.67712i	−0.326821	−	0.188690i	0.327608	−	0.944814i	$-0.393758\pi$
$79$	−2.90485	−	1.67712i	−0.326821	−	0.188690i	−0.654429	+	0.756123i	$0.727091\pi$
$80$	−1.48583	+	1.95715i	−0.166121	+	0.218816i
$81$	−8.95791	−	0.869434i	−0.995323	−	0.0966037i
$82$	−0.522038	+	0.375105i	−0.0576494	+	0.0414234i
$83$	−2.96563	+	5.13662i	−0.325520	+	0.563817i	−0.981617	−	0.190859i	$-0.938873\pi$
$83$	−2.96563	+	5.13662i	−0.325520	+	0.563817i	0.656098	+	0.754676i	$0.272206\pi$
$84$	−3.87924	+	1.80987i	−0.423260	+	0.197473i
$85$	1.73633	+	3.00741i	0.188331	+	0.326200i
$86$	−3.80624	−	1.71868i	−0.410437	−	0.185330i
$87$	−1.14535	+	0.277388i	−0.122794	+	0.0297391i
$88$	0.731656	−	3.19360i	0.0779948	−	0.340439i
$89$			17.7020i			1.87640i	0.346088	+	0.938202i	$0.387510\pi$
$89$			17.7020i			1.87640i	−0.346088	+	0.938202i	$0.612490\pi$
$90$	−1.41672	−	2.18766i	−0.149335	−	0.230599i
$91$			3.14293i			0.329469i
$92$	1.32256	+	1.50028i	0.137886	+	0.156415i
$93$	−3.98132	+	13.5396i	−0.412843	+	1.40400i
$94$	7.57182	−	16.7687i	0.780973	−	1.72956i
$95$	−2.36734	−	4.10035i	−0.242884	−	0.420687i
$96$	3.01021	−	9.32409i	0.307228	−	0.951636i
$97$	−2.82127	+	4.88659i	−0.286457	+	0.496158i	−0.972961	−	0.230968i	$-0.925811\pi$
$97$	−2.82127	+	4.88659i	−0.286457	+	0.496158i	0.686505	+	0.727125i	$0.259144\pi$
$98$	4.51645	+	6.28560i	0.456231	+	0.634942i
$99$	2.92197	+	1.88105i	0.293669	+	0.189052i
$100$	−2.94924	+	8.76221i	−0.294924	+	0.876221i
$101$	−6.01926	−	3.47522i	−0.598939	−	0.345797i	0.169685	−	0.985498i	$-0.445725\pi$
$101$	−6.01926	−	3.47522i	−0.598939	−	0.345797i	−0.768624	+	0.639701i	$0.779058\pi$
$102$	−10.4997	−	9.02705i	−1.03962	−	0.893811i
$103$	5.88864	−	3.39981i	0.580225	−	0.334993i	−0.180998	−	0.983483i	$-0.557933\pi$
$103$	5.88864	−	3.39981i	0.580225	−	0.334993i	0.761223	+	0.648490i	$0.224599\pi$
$104$	−5.26945	−	4.89732i	−0.516712	−	0.480222i
$105$	0.951950	−	0.906977i	0.0929008	−	0.0885118i
$106$	−1.00230	−	10.0440i	−0.0973519	−	0.975559i
$107$	−13.1754			−1.27371			−0.636855	−	0.770983i	$-0.719765\pi$
$107$	−13.1754			−1.27371			−0.636855	+	0.770983i	$0.719765\pi$
$108$	8.21595	+	6.36382i	0.790580	+	0.612359i
$109$	−0.860360			−0.0824075			−0.0412038	−	0.999151i	$-0.513119\pi$
$109$	−0.860360			−0.0824075			−0.0412038	+	0.999151i	$0.513119\pi$
$110$	0.0999288	+	1.00138i	0.00952784	+	0.0954780i
$111$	6.02034	−	5.73592i	0.571425	−	0.544429i
$112$	4.90387	+	0.619944i	0.463372	+	0.0585792i
$113$	15.5052	−	8.95191i	1.45860	−	0.842124i	0.459660	−	0.888095i	$-0.347971\pi$
$113$	15.5052	−	8.95191i	1.45860	−	0.842124i	0.998943	+	0.0459707i	$0.0146381\pi$
$114$	14.3154	+	12.3076i	1.34076	+	1.15271i
$115$	−0.532014	−	0.307158i	−0.0496105	−	0.0286426i
$116$	1.28968	+	0.434088i	0.119743	+	0.0403040i
$117$	6.78469	−	3.49108i	0.627245	−	0.322750i
$118$	1.00804	+	1.40290i	0.0927975	+	0.129147i
$119$	3.49270	−	6.04954i	0.320176	−	0.554560i
$120$	0.0373076	+	3.00929i	0.00340570	+	0.274710i
$121$	4.82910	+	8.36424i	0.439009	+	0.760386i
$122$	−3.04537	+	6.74436i	−0.275715	+	0.610605i
$123$	−0.222102	+	0.755322i	−0.0200262	+	0.0681051i
$124$	12.2244	−	10.7763i	1.09778	−	0.967739i
$125$		−	5.91133i		−	0.528725i
$126$	−2.38611	+	4.66827i	−0.212571	+	0.415883i
$127$			18.5519i			1.64621i	0.567888	+	0.823106i	$0.307761\pi$
$127$			18.5519i			1.64621i	−0.567888	+	0.823106i	$0.692239\pi$
$128$	−8.68061	+	7.25583i	−0.767265	+	0.641331i
$129$	−4.97116	+	1.20395i	−0.437687	+	0.106001i
$130$	2.01385	+	0.909341i	0.176626	+	0.0797545i
$131$	1.12919	+	1.95581i	0.0986576	+	0.170880i	0.911129	−	0.412121i	$-0.135212\pi$
$131$	1.12919	+	1.95581i	0.0986576	+	0.170880i	−0.812472	+	0.583001i	$0.801878\pi$
$132$	−1.69657	−	3.63638i	−0.147667	−	0.316507i
$133$	−4.76200	+	8.24803i	−0.412918	+	0.715195i
$134$	13.2032	−	9.48702i	1.14058	−	0.819554i
$135$	−3.01530	−	1.04754i	−0.259516	−	0.0901583i
$136$	4.70033	+	15.2823i	0.403050	+	1.31044i
$137$	1.34750	+	0.777980i	0.115125	+	0.0664673i	0.556457	−	0.830877i	$-0.312161\pi$
$137$	1.34750	+	0.777980i	0.115125	+	0.0664673i	−0.441332	+	0.897344i	$0.645494\pi$
$138$	2.40700	+	0.454250i	0.204898	+	0.0386683i
$139$	3.96333	−	2.28823i	0.336165	−	0.194085i	−0.322410	−	0.946600i	$-0.604493\pi$
$139$	3.96333	−	2.28823i	0.336165	−	0.194085i	0.658575	+	0.752515i	$0.271160\pi$
$140$	−1.48831	+	0.300028i	−0.125785	+	0.0253570i
$141$	−5.30409	−	21.9009i	−0.446685	−	1.84439i
$142$	17.2991	−	1.72629i	1.45171	−	0.144867i
$143$	−2.94617			−0.246371
$144$	−4.10879	−	11.2747i	−0.342399	−	0.939555i
$145$	−0.417972			−0.0347107
$146$	19.2226	−	1.91824i	1.59087	−	0.158755i
$147$	9.09446	+	2.67422i	0.750099	+	0.220566i
$148$	−9.41240	+	1.89744i	−0.773695	+	0.155969i
$149$	12.4251	−	7.17363i	1.01790	−	0.587687i	0.104408	−	0.994535i	$-0.466705\pi$
$149$	12.4251	−	7.17363i	1.01790	−	0.587687i	0.913496	+	0.406848i	$0.133372\pi$
$150$	3.74482	+	10.6859i	0.305763	+	0.872497i
$151$	−14.5754	−	8.41513i	−1.18613	−	0.684814i	−0.228707	−	0.973495i	$-0.573450\pi$
$151$	−14.5754	−	8.41513i	−1.18613	−	0.684814i	−0.957425	+	0.288681i	$0.906783\pi$
$152$	−6.40850	−	20.8361i	−0.519798	−	1.69003i
$153$	−16.9388	−	0.820094i	−1.36942	−	0.0663007i
$154$	1.64395	−	1.18124i	0.132473	−	0.0951872i
$155$	−2.50274	+	4.33488i	−0.201025	+	0.348186i
$156$	−8.77720	−	0.766122i	−0.702739	−	0.0613389i
$157$	1.18664	+	2.05532i	0.0947041	+	0.164032i	0.909485	−	0.415737i	$-0.136476\pi$
$157$	1.18664	+	2.05532i	0.0947041	+	0.164032i	−0.814781	+	0.579769i	$0.803143\pi$
$158$	4.32329	+	1.95216i	0.343943	+	0.155305i
$159$	−8.52757	−	8.95042i	−0.676280	−	0.709815i
$160$	1.81606	−	2.96281i	0.143572	−	0.234230i
$161$			1.23572i			0.0973887i
$162$	12.7279	−	0.0344544i	0.999996	−	0.00270700i
$163$		−	14.5657i		−	1.14087i	−0.821341	−	0.570437i	$-0.806774\pi$
$163$		−	14.5657i		−	1.14087i	0.821341	−	0.570437i	$-0.193226\pi$
$164$	0.681949	−	0.601165i	0.0532513	−	0.0469431i
$165$	0.850195	+	0.892353i	0.0661876	+	0.0694696i
$166$	3.45198	−	7.64483i	0.267925	−	0.593354i
$167$	2.40414	+	4.16410i	0.186038	+	0.322227i	0.943926	−	0.330158i	$-0.107102\pi$
$167$	2.40414	+	4.16410i	0.186038	+	0.322227i	−0.757888	+	0.652385i	$0.773769\pi$
$168$	5.20481	−	3.09165i	0.401560	−	0.238526i
$169$	3.26557	−	5.65614i	0.251198	−	0.435088i
$170$	−2.86573	−	3.98827i	−0.219791	−	0.305886i
$171$	23.0946	+	1.11813i	1.76609	+	0.0855054i
$172$	5.59758	+	1.88407i	0.426811	+	0.143659i
$173$	6.62896	+	3.82723i	0.503991	+	0.290979i	0.730360	−	0.683062i	$-0.239352\pi$
$173$	6.62896	+	3.82723i	0.503991	+	0.290979i	−0.226369	+	0.974042i	$0.572686\pi$
$174$	1.57281	−	0.551186i	0.119235	−	0.0417853i
$175$	−4.94698	+	2.85614i	−0.373956	+	0.215904i
$176$	−0.581132	+	4.59686i	−0.0438045	+	0.346501i
$177$	2.02982	+	0.596865i	0.152570	+	0.0448631i
$178$	−2.48585	−	24.9106i	−0.186323	−	1.86713i
$179$	20.4852			1.53113			0.765567	−	0.643356i	$-0.222459\pi$
$179$	20.4852			1.53113			0.765567	+	0.643356i	$0.222459\pi$
$180$	2.30085	+	2.87958i	0.171495	+	0.214631i
$181$	11.0459			0.821035			0.410517	−	0.911853i	$-0.365348\pi$
$181$	11.0459			0.821035			0.410517	+	0.911853i	$0.365348\pi$
$182$	−0.441357	−	4.42281i	−0.0327155	−	0.327841i
$183$	2.13330	+	8.80852i	0.157698	+	0.651145i
$184$	−2.07182	−	1.92551i	−0.152736	−	0.141950i
$185$	2.55413	−	1.47463i	0.187783	−	0.108417i
$186$	3.70126	−	19.6124i	0.271389	−	1.43805i
$187$	5.67081	+	3.27404i	0.414691	+	0.239422i
$188$	−8.30044	+	24.6606i	−0.605372	+	1.79856i
$189$	1.20783	+	6.30639i	0.0878568	+	0.458722i
$190$	3.90718	+	5.43767i	0.283456	+	0.394490i
$191$	3.63815	−	6.30146i	0.263247	−	0.455958i	−0.703856	−	0.710343i	$-0.748540\pi$
$191$	3.63815	−	6.30146i	0.263247	−	0.455958i	0.967103	+	0.254385i	$0.0818731\pi$
$192$	−2.92667	+	13.5438i	−0.211214	+	0.977440i
$193$	5.39981	+	9.35274i	0.388687	+	0.673225i	0.992273	−	0.124073i	$-0.0395955\pi$
$193$	5.39981	+	9.35274i	0.388687	+	0.673225i	−0.603587	+	0.797298i	$0.706262\pi$
$194$	3.28395	−	7.27271i	0.235774	−	0.522150i
$195$	2.63020	−	0.636998i	0.188353	−	0.0456164i
$196$	−7.23834	−	8.21101i	−0.517024	−	0.586501i
$197$			22.4271i			1.59787i	0.601420	+	0.798933i	$0.294602\pi$
$197$			22.4271i			1.59787i	−0.601420	+	0.798933i	$0.705398\pi$
$198$	−4.37601	−	2.23673i	−0.310990	−	0.158957i
$199$			8.49603i			0.602268i	0.953582	+	0.301134i	$0.0973651\pi$
$199$			8.49603i			0.602268i	−0.953582	+	0.301134i	$0.902635\pi$
$200$	2.91978	−	12.7445i	0.206460	−	0.901176i
$201$	5.61732	−	19.1034i	0.396215	−	1.34745i
$202$	8.95847	+	4.04514i	0.630315	+	0.284615i
$203$	0.420384	+	0.728127i	0.0295052	+	0.0511045i
$204$	16.0430	+	11.2286i	1.12324	+	0.786162i
$205$	−0.139618	+	0.241826i	−0.00975135	+	0.0168898i
$206$	−7.80921	+	5.61122i	−0.544093	+	0.390952i
$207$	2.66757	−	1.37261i	0.185409	−	0.0954027i
$208$	8.10301	+	6.15165i	0.561843	+	0.426540i
$209$	−7.73166	−	4.46388i	−0.534810	−	0.308773i
$210$	−1.21224	+	1.41000i	−0.0836527	+	0.0972992i
$211$	−1.11589	+	0.644260i	−0.0768212	+	0.0443527i	−0.537919	−	0.842997i	$-0.680789\pi$
$211$	−1.11589	+	0.644260i	−0.0768212	+	0.0443527i	0.461097	+	0.887350i	$0.347456\pi$
$212$	2.82092	+	13.9934i	0.193742	+	0.961071i
$213$	15.4156	−	14.6873i	1.05626	−	1.00636i
$214$	18.5407	−	1.85019i	1.26742	−	0.126477i
$215$	−1.81412			−0.123722
$216$	−12.4553	−	7.80157i	−0.847479	−	0.530830i
$217$	10.0688			0.683512
$218$	1.21072	−	0.120819i	0.0820002	−	0.00818288i
$219$	17.1297	−	16.3204i	1.15752	−	1.10283i
$220$	−0.281244	−	1.39514i	−0.0189615	−	0.0940600i
$221$	12.4513	−	7.18876i	0.837564	−	0.483568i
$222$	−7.66648	+	8.91714i	−0.514541	+	0.598479i
$223$	−14.5474	−	8.39892i	−0.974163	−	0.562433i	−0.0736604	−	0.997283i	$-0.523468\pi$
$223$	−14.5474	−	8.39892i	−0.974163	−	0.562433i	−0.900503	+	0.434850i	$0.856801\pi$
$224$	−6.98790	−	0.183759i	−0.466899	−	0.0122779i
$225$	11.6605	+	7.50659i	0.777369	+	0.500439i
$226$	−20.5621	+	14.7747i	−1.36777	+	0.982798i
$227$	−5.14797	+	8.91655i	−0.341683	+	0.591812i	−0.984745	−	0.174002i	$-0.944330\pi$
$227$	−5.14797	+	8.91655i	−0.341683	+	0.591812i	0.643062	+	0.765814i	$0.277664\pi$
$228$	−21.8733	−	15.3093i	−1.44860	−	1.01388i
$229$	−0.183411	−	0.317678i	−0.0121202	−	0.0209928i	0.859902	−	0.510460i	$-0.170525\pi$
$229$	−0.183411	−	0.317678i	−0.0121202	−	0.0209928i	−0.872022	+	0.489467i	$0.837191\pi$
$230$	0.791796	+	0.357531i	0.0522095	+	0.0235749i
$231$	0.699420	−	2.37859i	0.0460185	−	0.156499i
$232$	−1.87582	−	0.429752i	−0.123154	−	0.0282146i
$233$		−	2.86699i		−	0.187822i	−0.995581	−	0.0939112i	$-0.970063\pi$
$233$		−	2.86699i		−	0.187822i	0.995581	−	0.0939112i	$-0.0299370\pi$
$234$	−9.05734	+	5.86549i	−0.592097	+	0.383439i
$235$		−	7.99228i		−	0.521359i
$236$	−1.61554	−	1.83264i	−0.105163	−	0.119295i
$237$	5.64647	−	1.36750i	0.366778	−	0.0888284i
$238$	−4.06549	+	9.00353i	−0.263527	+	0.583612i
$239$	9.59980	+	16.6273i	0.620959	+	1.07553i	0.989307	+	0.145845i	$0.0465902\pi$
$239$	9.59980	+	16.6273i	0.620959	+	1.07553i	−0.368348	+	0.929688i	$0.620076\pi$
$240$	−0.475089	−	4.22951i	−0.0306669	−	0.273014i
$241$	9.69951	−	16.8000i	0.624801	−	1.08219i	−0.363779	−	0.931485i	$-0.618514\pi$
$241$	9.69951	−	16.8000i	0.624801	−	1.08219i	0.988579	−	0.150701i	$-0.0481530\pi$
$242$	−7.97020	−	11.0922i	−0.512344	−	0.713035i
$243$	12.2721	−	9.61231i	0.787253	−	0.616630i
$244$	3.33843	−	9.91848i	0.213721	−	0.634966i
$245$	2.91170	+	1.68107i	0.186022	+	0.107400i
$246$	0.206478	−	1.09410i	0.0131646	−	0.0697571i
$247$	−16.9763	+	9.80125i	−1.08017	+	0.623639i
$248$	−15.6892	+	16.8813i	−0.996262	+	1.07196i
$249$	−2.41813	−	9.98459i	−0.153242	−	0.632748i
$250$	0.830117	+	8.31857i	0.0525012	+	0.526112i
$251$	−7.05478			−0.445294			−0.222647	−	0.974899i	$-0.571470\pi$
$251$	−7.05478			−0.445294			−0.222647	+	0.974899i	$0.571470\pi$
$252$	2.70223	−	6.90438i	0.170225	−	0.434935i
$253$	−1.15836			−0.0728256
$254$	−2.60520	−	26.1066i	−0.163465	−	1.63808i
$255$	−5.77052	−	1.69681i	−0.361364	−	0.106259i
$256$	11.1966	−	11.4296i	0.699790	−	0.714349i
$257$	17.5036	−	10.1057i	1.09184	−	0.630376i	0.157777	−	0.987475i	$-0.449567\pi$
$257$	17.5036	−	10.1057i	1.09184	−	0.630376i	0.934067	+	0.357099i	$0.116234\pi$
$258$	6.82647	−	2.39231i	0.424998	−	0.148939i
$259$	−5.13775	−	2.96628i	−0.319244	−	0.184316i
$260$	−2.96163	−	0.996846i	−0.183673	−	0.0618218i
$261$	1.10487	−	1.71627i	0.0683895	−	0.106235i
$262$	−1.86367	−	2.59369i	−0.115138	−	0.160239i
$263$	−11.2898	+	19.5545i	−0.696157	+	1.20578i	0.273632	+	0.961834i	$0.411775\pi$
$263$	−11.2898	+	19.5545i	−0.696157	+	1.20578i	−0.969789	+	0.243945i	$0.921558\pi$
$264$	2.89810	+	4.87896i	0.178366	+	0.300279i
$265$	−2.19233	−	3.79722i	−0.134674	−	0.233261i
$266$	5.54295	−	12.2755i	0.339860	−	0.752662i
$267$	−21.1497	−	22.1984i	−1.29434	−	1.35852i
$268$	−17.2476	+	15.2045i	−1.05357	+	0.928761i
$269$		−	1.31345i		−	0.0800822i	−0.999198	−	0.0400411i	$-0.987251\pi$
$269$		−	1.31345i		−	0.0800822i	0.999198	−	0.0400411i	$-0.0127489\pi$
$270$	4.39031	+	1.05070i	0.267186	+	0.0639434i
$271$		−	1.60738i		−	0.0976414i	−0.998808	−	0.0488207i	$-0.984454\pi$
$271$		−	1.60738i		−	0.0976414i	0.998808	−	0.0488207i	$-0.0155463\pi$
$272$	−8.76048	−	20.8455i	−0.531182	−	1.26395i
$273$	−3.75507	−	3.94127i	−0.227267	−	0.238536i
$274$	−2.00549	−	0.905565i	−0.121156	−	0.0547072i
$275$	−2.67733	−	4.63727i	−0.161449	−	0.279638i
$276$	−3.45098	−	0.301220i	−0.207725	−	0.0181313i
$277$	−3.08769	+	5.34804i	−0.185521	+	0.321332i	−0.943752	−	0.330654i	$-0.892731\pi$
$277$	−3.08769	+	5.34804i	−0.185521	+	0.321332i	0.758231	+	0.651986i	$0.226064\pi$
$278$	−5.25596	+	3.77661i	−0.315231	+	0.226506i
$279$	−11.1841	−	21.7356i	−0.669574	−	1.30127i
$280$	2.05226	−	0.631207i	0.122646	−	0.0377218i
$281$	9.21222	+	5.31868i	0.549555	+	0.317286i	0.748942	−	0.662635i	$-0.230562\pi$
$281$	9.21222	+	5.31868i	0.549555	+	0.317286i	−0.199387	+	0.979921i	$0.563895\pi$
$282$	10.5396	+	30.0747i	0.627621	+	1.79092i
$283$	−0.335612	+	0.193766i	−0.0199501	+	0.0115182i	−0.509942	−	0.860209i	$-0.670333\pi$
$283$	−0.335612	+	0.193766i	−0.0199501	+	0.0115182i	0.489992	+	0.871727i	$0.337000\pi$
$284$	−24.1013	+	4.85856i	−1.43015	+	0.288303i
$285$	7.86761	+	2.31346i	0.466037	+	0.137038i
$286$	4.14592	−	0.413725i	0.245154	−	0.0244641i
$287$	0.561696			0.0331559
$288$	7.36527	+	15.2890i	0.434003	+	0.900912i
$289$	−14.9551			−0.879712
$290$	0.588180	−	0.0586950i	0.0345391	−	0.00344669i
$291$	−2.30042	−	9.49858i	−0.134853	−	0.556817i
$292$	−26.7811	+	5.39879i	−1.56725	+	0.315940i
$293$	−0.0918536	+	0.0530317i	−0.00536614	+	0.00309814i	−0.502681	−	0.864472i	$-0.667653\pi$
$293$	−0.0918536	+	0.0530317i	−0.00536614	+	0.00309814i	0.497315	+	0.867570i	$0.334320\pi$
$294$	−13.1735	−	2.48610i	−0.768293	−	0.144992i
$295$	0.649870	+	0.375203i	0.0378369	+	0.0218452i
$296$	12.9789	−	3.99189i	0.754384	−	0.232024i
$297$	−5.91158	+	1.13222i	−0.343025	+	0.0656978i
$298$	−16.4775	+	11.8397i	−0.954517	+	0.685858i
$299$	−1.27170	+	2.20264i	−0.0735441	+	0.127382i
$300$	−6.77040	−	14.5115i	−0.390889	−	0.837824i
$301$	1.82459	+	3.16029i	0.105168	+	0.182156i
$302$	21.6926	+	9.79518i	1.24827	+	0.563649i
$303$	11.7003	−	2.83364i	0.672163	−	0.162788i
$304$	11.9442	+	28.4211i	0.685045	+	1.63006i
$305$			3.21448i			0.184061i
$306$	23.9519	−	1.22463i	1.36924	−	0.0700075i
$307$		−	17.2518i		−	0.984610i	−0.870423	−	0.492305i	$-0.836154\pi$
$307$		−	17.2518i		−	0.984610i	0.870423	−	0.492305i	$-0.163846\pi$
$308$	−2.14753	+	1.89313i	−0.122367	+	0.107871i
$309$	−3.32244	+	11.2989i	−0.189007	+	0.642774i
$310$	2.91318	−	6.45161i	0.165458	−	0.366427i
$311$	−1.81814	−	3.14910i	−0.103097	−	0.178569i	0.809862	−	0.586620i	$-0.199542\pi$
$311$	−1.81814	−	3.14910i	−0.103097	−	0.178569i	−0.912959	+	0.408051i	$0.866209\pi$
$312$	12.4591	−	0.154461i	0.705356	−	0.00874463i
$313$	2.00028	−	3.46458i	0.113062	−	0.195830i	−0.803941	−	0.594709i	$-0.797267\pi$
$313$	2.00028	−	3.46458i	0.113062	−	0.195830i	0.917004	+	0.398879i	$0.130601\pi$
$314$	−1.95849	−	2.72566i	−0.110524	−	0.153818i
$315$	−0.110130	+	2.27471i	−0.00620515	+	0.128166i
$316$	−6.35798	−	2.14001i	−0.357664	−	0.120385i
$317$	14.6929	+	8.48293i	0.825233	+	0.476449i	0.852218	−	0.523187i	$-0.175257\pi$
$317$	14.6929	+	8.48293i	0.825233	+	0.476449i	−0.0269845	+	0.999636i	$0.508590\pi$
$318$	13.2571	+	11.3977i	0.743421	+	0.639154i
$319$	−0.682543	+	0.394066i	−0.0382151	+	0.0220635i
$320$	−2.13954	+	4.42436i	−0.119604	+	0.247329i
$321$	16.5220	−	15.7415i	0.922170	−	0.878603i
$322$	−0.173531	−	1.73894i	−0.00967048	−	0.0969074i
$323$	43.5680			2.42419
$324$	−17.9061	+	1.83584i	−0.994785	+	0.101991i
$325$	−11.7571			−0.652168
$326$	2.04544	+	20.4972i	0.113286	+	1.13524i
$327$	1.07890	−	1.02793i	0.0596632	−	0.0568445i
$328$	−0.875235	+	0.941739i	−0.0483268	+	0.0519989i
$329$	−13.9229	+	8.03842i	−0.767597	+	0.443172i
$330$	−1.32173	−	1.13635i	−0.0727587	−	0.0625540i
$331$	26.0155	+	15.0201i	1.42994	+	0.825578i	0.997116	−	0.0758987i	$-0.0241825\pi$
$331$	26.0155	+	15.0201i	1.42994	+	0.825578i	0.432828	+	0.901477i	$0.357516\pi$
$332$	−3.78416	+	11.2427i	−0.207683	+	0.617026i
$333$	−0.696489	+	14.3858i	−0.0381673	+	0.788336i
$334$	−3.96792	−	5.52221i	−0.217115	−	0.302162i
$335$	3.53117	−	6.11617i	0.192929	−	0.334162i
$336$	−6.89018	+	5.08155i	−0.375890	+	0.277221i
$337$	10.9061	+	18.8899i	0.594092	+	1.02900i	0.993674	+	0.112301i	$0.0358220\pi$
$337$	10.9061	+	18.8899i	0.594092	+	1.02900i	−0.399582	+	0.916698i	$0.630845\pi$
$338$	−3.80111	+	8.41803i	−0.206753	+	0.457881i
$339$	−8.74818	+	29.7508i	−0.475136	+	1.61584i
$340$	4.59279	+	5.20996i	0.249079	+	0.282550i
$341$			9.43841i			0.511118i
$342$	−32.6563	+	1.66968i	−1.76585	+	0.0902859i
$343$		−	15.4132i		−	0.832233i
$344$	−8.14163	−	1.86525i	−0.438967	−	0.100568i
$345$	1.03413	−	0.250452i	0.0556758	−	0.0134839i
$346$	−9.86588	−	4.45488i	−0.530393	−	0.239496i
$347$	−4.71442	−	8.16561i	−0.253083	−	0.438353i	0.711290	−	0.702899i	$-0.248111\pi$
$347$	−4.71442	−	8.16561i	−0.253083	−	0.438353i	−0.964373	+	0.264546i	$0.914778\pi$
$348$	−2.13590	+	0.996510i	−0.114496	+	0.0534185i
$349$	−4.04905	+	7.01316i	−0.216741	+	0.375406i	−0.953810	−	0.300412i	$-0.902876\pi$
$349$	−4.04905	+	7.01316i	−0.216741	+	0.375406i	0.737069	+	0.675817i	$0.236209\pi$
$350$	6.56043	−	4.71392i	0.350670	−	0.251970i
$351$	−4.33705	+	12.4840i	−0.231494	+	0.666344i
$352$	0.172255	−	6.55042i	0.00918120	−	0.349139i
$353$	0.787791	+	0.454831i	0.0419299	+	0.0242082i	0.520818	−	0.853667i	$-0.325627\pi$
$353$	0.787791	+	0.454831i	0.0419299	+	0.0242082i	−0.478889	+	0.877876i	$0.658960\pi$
$354$	−2.94022	−	0.554880i	−0.156271	−	0.0294915i
$355$	6.54008	−	3.77592i	0.347111	−	0.200405i
$356$	6.99631	+	34.7058i	0.370804	+	1.83940i
$357$	2.84790	+	11.7591i	0.150727	+	0.622359i
$358$	−28.8272	+	2.87670i	−1.52357	+	0.152038i
$359$	21.2352			1.12075			0.560375	−	0.828239i	$-0.310657\pi$
$359$	21.2352			1.12075			0.560375	+	0.828239i	$0.310657\pi$
$360$	−3.64218	−	3.72910i	−0.191960	−	0.196541i
$361$	−40.4013			−2.12638
$362$	−15.5440	+	1.55115i	−0.816977	+	0.0815269i
$363$	−16.0490	−	4.71920i	−0.842356	−	0.247694i
$364$	1.24218	+	6.16191i	0.0651077	+	0.322972i
$365$	7.26728	−	4.19576i	0.380387	−	0.219616i
$366$	−4.23899	−	12.0960i	−0.221576	−	0.632267i
$367$	−27.4416	−	15.8434i	−1.43244	−	0.827019i	−0.435133	−	0.900366i	$-0.643298\pi$
$367$	−27.4416	−	15.8434i	−1.43244	−	0.827019i	−0.997306	+	0.0733474i	$0.976632\pi$
$368$	3.18591	+	2.41868i	0.166077	+	0.126082i
$369$	−0.623915	−	1.21254i	−0.0324797	−	0.0631223i
$370$	−3.38715	+	2.43380i	−0.176090	+	0.126527i
$371$	−4.40996	+	7.63828i	−0.228954	+	0.396560i
$372$	−2.45436	+	28.1188i	−0.127253	+	1.45789i
$373$	17.6563	+	30.5815i	0.914206	+	1.58345i	0.808059	+	0.589101i	$0.200518\pi$
$373$	17.6563	+	30.5815i	0.914206	+	1.58345i	0.106147	+	0.994350i	$0.466149\pi$
$374$	−8.43987	−	3.81097i	−0.436415	−	0.197061i
$375$	7.06265	+	7.41286i	0.364714	+	0.382798i
$376$	8.21753	−	35.8687i	0.423787	−	1.84979i
$377$			1.73049i			0.0891247i
$378$	−2.58528	−	8.70489i	−0.132973	−	0.447731i
$379$			20.6419i			1.06030i	0.847903	+	0.530152i	$0.177865\pi$
$379$			20.6419i			1.06030i	−0.847903	+	0.530152i	$0.822135\pi$
$380$	−6.26188	−	7.10334i	−0.321228	−	0.364394i
$381$	−22.1651	−	23.2642i	−1.13555	−	1.19186i
$382$	−4.23479	+	9.37847i	−0.216671	+	0.479844i
$383$	−13.4008	−	23.2109i	−0.684751	−	1.18602i	−0.973515	−	0.228623i	$-0.926578\pi$
$383$	−13.4008	−	23.2109i	−0.684751	−	1.18602i	0.288764	−	0.957400i	$-0.406756\pi$
$384$	2.21655	−	19.4702i	0.113113	−	0.993582i
$385$	0.439671	−	0.761533i	0.0224077	−	0.0388113i
$386$	−8.91213	−	12.4031i	−0.453615	−	0.631302i
$387$	4.79545	−	7.44913i	0.243767	−	0.378661i
$388$	−3.59996	+	10.6955i	−0.182760	+	0.542981i
$389$	−34.0250	−	19.6443i	−1.72513	−	0.996006i	−0.907208	−	0.420683i	$-0.861791\pi$
$389$	−34.0250	−	19.6443i	−1.72513	−	0.996006i	−0.817926	−	0.575324i	$-0.804876\pi$
$390$	−3.61183	+	1.26575i	−0.182892	+	0.0640939i
$391$	4.89554	−	2.82644i	0.247578	−	0.142939i
$392$	11.3390	+	10.5383i	0.572707	+	0.532263i
$393$	−3.75274	−	1.10349i	−0.189301	−	0.0556637i
$394$	−3.14940	−	31.5600i	−0.158665	−	1.58997i
$395$	2.06056			0.103678
$396$	6.47213	+	2.53306i	0.325237	+	0.127291i
$397$	−28.6183			−1.43631			−0.718156	−	0.695882i	$-0.755014\pi$
$397$	−28.6183			−1.43631			−0.718156	+	0.695882i	$0.755014\pi$
$398$	−1.19308	−	11.9558i	−0.0598038	−	0.599291i
$399$	−3.88286	−	16.0326i	−0.194386	−	0.802633i
$400$	−2.31909	+	18.3445i	−0.115955	+	0.917223i
$401$	15.4427	−	8.91584i	0.771171	−	0.445236i	−0.0621213	−	0.998069i	$-0.519787\pi$
$401$	15.4427	−	8.91584i	0.771171	−	0.445236i	0.833292	+	0.552833i	$0.186453\pi$
$402$	−5.22218	+	27.6715i	−0.260458	+	1.38013i
$403$	17.9473	+	10.3619i	0.894018	+	0.516162i
$404$	−13.1746	−	4.43440i	−0.655462	−	0.220620i
$405$	5.03278	−	2.28894i	0.250081	−	0.113739i
$406$	−0.693825	−	0.965604i	−0.0344339	−	0.0479221i
$407$	2.78058	−	4.81610i	0.137828	−	0.238725i
$408$	−24.1530	−	13.5483i	−1.19575	−	0.670741i
$409$	6.53070	+	11.3115i	0.322922	+	0.559318i	0.981090	−	0.193554i	$-0.0620014\pi$
$409$	6.53070	+	11.3115i	0.322922	+	0.559318i	−0.658167	+	0.752872i	$0.728668\pi$
$410$	0.162515	−	0.359909i	0.00802603	−	0.0177746i
$411$	−2.61928	+	0.634352i	−0.129200	+	0.0312903i
$412$	10.2013	−	8.99288i	0.502584	−	0.443047i
$413$		−	1.50947i		−	0.0742764i
$414$	−3.56112	+	2.30617i	−0.175020	+	0.113342i
$415$		−	3.64367i		−	0.178861i
$416$	−12.2666	−	7.51886i	−0.601421	−	0.368643i
$417$	−2.23615	+	7.60470i	−0.109505	+	0.372404i
$418$	11.5070	+	5.19593i	0.562828	+	0.254141i
$419$	4.78374	+	8.28568i	0.233701	+	0.404782i	0.958894	−	0.283763i	$-0.0915830\pi$
$419$	4.78374	+	8.28568i	0.233701	+	0.404782i	−0.725193	+	0.688545i	$0.758250\pi$
$420$	1.50789	−	2.15442i	0.0735776	−	0.105125i
$421$	−19.0509	+	32.9972i	−0.928486	+	1.60818i	−0.142629	+	0.989776i	$0.545556\pi$
$421$	−19.0509	+	32.9972i	−0.928486	+	1.60818i	−0.785857	+	0.618408i	$0.787778\pi$
$422$	1.47984	−	1.06332i	0.0720374	−	0.0517617i
$423$	32.8178	+	21.1268i	1.59566	+	1.02722i
$424$	−5.93473	−	19.2957i	−0.288216	−	0.937083i
$425$	22.6302	+	13.0656i	1.09773	+	0.633772i
$426$	−19.6307	+	22.8331i	−0.951111	+	1.10627i
$427$	5.59979	−	3.23304i	0.270993	−	0.156458i
$428$	−25.8311	+	5.20727i	−1.24859	+	0.251703i
$429$	3.69452	−	3.51998i	0.178373	−	0.169946i
$430$	2.55288	−	0.254754i	0.123111	−	0.0122853i
$431$	−14.5812			−0.702350			−0.351175	−	0.936310i	$-0.614218\pi$
$431$	−14.5812			−0.702350			−0.351175	+	0.936310i	$0.614218\pi$
$432$	18.6230	+	9.22948i	0.896000	+	0.444054i
$433$	17.6064			0.846107			0.423054	−	0.906105i	$-0.360958\pi$
$433$	17.6064			0.846107			0.423054	+	0.906105i	$0.360958\pi$
$434$	−14.1690	+	1.41394i	−0.680134	+	0.0678712i
$435$	0.524140	−	0.499378i	0.0251306	−	0.0239433i
$436$	−1.68679	+	0.340038i	−0.0807824	+	0.0162849i
$437$	−6.67465	+	3.85361i	−0.319292	+	0.184343i
$438$	−21.8135	+	25.3720i	−1.04229	+	1.21232i
$439$	−9.19061	−	5.30620i	−0.438644	−	0.253251i	0.264378	−	0.964419i	$-0.414833\pi$
$439$	−9.19061	−	5.30620i	−0.438644	−	0.253251i	−0.703022	+	0.711168i	$0.748167\pi$
$440$	0.591690	+	1.92377i	0.0282077	+	0.0917123i
$441$	−14.5996	+	7.51225i	−0.695219	+	0.357726i
$442$	−16.5123	+	11.8647i	−0.785408	+	0.564346i
$443$	−8.71052	+	15.0871i	−0.413849	+	0.716808i	−0.995307	−	0.0967688i	$-0.969149\pi$
$443$	−8.71052	+	15.0871i	−0.413849	+	0.716808i	0.581458	+	0.813577i	$0.302483\pi$
$444$	9.53624	−	13.6250i	0.452570	−	0.646614i
$445$	−5.43730	−	9.41768i	−0.257753	−	0.446441i
$446$	21.6508	+	9.77631i	1.02520	+	0.462922i
$447$	−7.01038	+	23.8409i	−0.331579	+	1.12763i
$448$	9.85934	−	0.722708i	0.465810	−	0.0341447i
$449$			17.6879i			0.834744i	0.908736	+	0.417372i	$0.137049\pi$
$449$			17.6879i			0.834744i	−0.908736	+	0.417372i	$0.862951\pi$
$450$	−17.4631	−	8.92599i	−0.823220	−	0.420775i
$451$			0.526531i			0.0247934i
$452$	26.8607	−	23.6788i	1.26342	−	1.11376i
$453$	28.3318	−	6.86157i	1.33115	−	0.322385i
$454$	5.99222	−	13.2705i	0.281229	−	0.622816i
$455$	−0.965378	−	1.67208i	−0.0452576	−	0.0783885i
$456$	32.9305	+	18.4720i	1.54211	+	0.865029i
$457$	16.9484	−	29.3555i	0.792814	−	1.37319i	−0.131404	−	0.991329i	$-0.541948\pi$
$457$	16.9484	−	29.3555i	0.792814	−	1.37319i	0.924218	−	0.381865i	$-0.124718\pi$
$458$	0.302712	+	0.421288i	0.0141448	+	0.0196855i
$459$	22.2212	−	19.2095i	1.03720	−	0.896622i
$460$	−1.16444	−	0.391935i	−0.0542924	−	0.0182741i
$461$	−16.1822	−	9.34282i	−0.753682	−	0.435139i	0.0733406	−	0.997307i	$-0.476634\pi$
$461$	−16.1822	−	9.34282i	−0.753682	−	0.435139i	−0.827023	+	0.562168i	$0.809967\pi$
$462$	−0.650221	+	3.44542i	−0.0302510	+	0.160296i
$463$	−4.70303	+	2.71529i	−0.218568	+	0.126190i	−0.605287	−	0.796007i	$-0.706942\pi$
$463$	−4.70303	+	2.71529i	−0.218568	+	0.126190i	0.386719	+	0.922198i	$0.373608\pi$
$464$	2.70005	+	0.341339i	0.125347	+	0.0158463i
$465$	−2.04070	−	8.42617i	−0.0946351	−	0.390754i
$466$	0.402605	+	4.03449i	0.0186503	+	0.186894i
$467$	33.9084			1.56910			0.784548	−	0.620069i	$-0.212895\pi$
$467$	33.9084			1.56910			0.784548	+	0.620069i	$0.212895\pi$
$468$	11.9220	−	9.52597i	0.551096	−	0.440338i
$469$	−14.2062			−0.655982
$470$	1.12234	+	11.2469i	0.0517698	+	0.518782i
$471$	−3.94368	−	1.15963i	−0.181715	−	0.0534331i
$472$	2.53078	+	2.35206i	0.116489	+	0.108263i
$473$	−2.96244	+	1.71037i	−0.136213	+	0.0786427i
$474$	−7.75382	+	2.71730i	−0.356145	+	0.124810i
$475$	−30.8543	−	17.8138i	−1.41569	−	0.817352i
$476$	4.45671	−	13.2409i	0.204273	−	0.606896i
$477$	21.3873	+	1.03547i	0.979257	+	0.0474108i
$478$	−15.8440	−	22.0503i	−0.724689	−	1.00856i
$479$	4.62146	−	8.00461i	0.211160	−	0.365740i	−0.740918	−	0.671596i	$-0.765609\pi$
$479$	4.62146	−	8.00461i	0.211160	−	0.365740i	0.952078	+	0.305856i	$0.0989425\pi$
$480$	1.26250	+	5.88515i	0.0576250	+	0.268619i
$481$	−6.10526	−	10.5746i	−0.278376	−	0.482161i
$482$	−11.2902	+	25.0035i	−0.514254	+	1.13888i
$483$	−1.47640	−	1.54961i	−0.0671785	−	0.0705097i
$484$	12.7735	+	14.4900i	0.580615	+	0.658637i
$485$		−	3.46631i		−	0.157397i
$486$	−15.9197	+	15.2500i	−0.722132	+	0.691755i
$487$		−	36.2086i		−	1.64077i	−0.571812	−	0.820384i	$-0.693759\pi$
$487$		−	36.2086i		−	1.64077i	0.571812	−	0.820384i	$-0.306241\pi$
$488$	−3.30508	+	14.4263i	−0.149614	+	0.653049i
$489$	17.4026	+	18.2655i	0.786972	+	0.825995i
$490$	−4.33349	−	1.95676i	−0.195767	−	0.0883974i
$491$	2.02666	+	3.51028i	0.0914619	+	0.158417i	0.908126	−	0.418696i	$-0.137513\pi$
$491$	2.02666	+	3.51028i	0.0914619	+	0.158417i	−0.816665	+	0.577113i	$0.804179\pi$
$492$	−0.136919	+	1.56864i	−0.00617279	+	0.0707195i
$493$	1.92307	−	3.33085i	0.0866107	−	0.150014i
$494$	22.5130	−	16.1765i	1.01291	−	0.727816i
$495$	−2.13230	−	0.103236i	−0.0958400	−	0.00464010i
$496$	19.7076	−	25.9590i	0.884895	−	1.16559i
$497$	−13.1557	−	7.59542i	−0.590112	−	0.340701i
$498$	4.80496	+	13.7110i	0.215316	+	0.614404i
$499$	5.79444	−	3.34542i	0.259395	−	0.149762i	−0.364664	−	0.931139i	$-0.618816\pi$
$499$	5.79444	−	3.34542i	0.259395	−	0.149762i	0.624058	+	0.781378i	$0.285483\pi$
$500$	−2.33632	−	11.5895i	−0.104484	−	0.518299i
$501$	−7.98993	−	2.34943i	−0.356964	−	0.104965i
$502$	9.92765	−	0.990690i	0.443093	−	0.0442166i
$503$	43.0762			1.92067			0.960337	−	0.278842i	$-0.0899506\pi$
$503$	43.0762			1.92067			0.960337	+	0.278842i	$0.0899506\pi$
$504$	−2.83308	+	10.0955i	−0.126195	+	0.449689i
$505$	4.26977			0.190002
$506$	1.63007	−	0.162667i	0.0724657	−	0.00723142i
$507$	2.66270	+	10.9944i	0.118255	+	0.488280i
$508$	7.33221	+	36.3720i	0.325314	+	1.61375i
$509$	−7.97002	+	4.60149i	−0.353265	+	0.203958i	−0.666122	−	0.745843i	$-0.732047\pi$
$509$	−7.97002	+	4.60149i	−0.353265	+	0.203958i	0.312857	+	0.949800i	$0.398714\pi$
$510$	8.35870	+	1.57745i	0.370129	+	0.0698509i
$511$	−14.6185	−	8.43997i	−0.646682	−	0.373362i
$512$	−14.1511	+	17.6563i	−0.625398	+	0.780306i
$513$	−30.2968	+	26.1905i	−1.33763	+	1.15634i
$514$	−23.2123	+	16.6790i	−1.02385	+	0.735678i
$515$	−2.08856	+	3.61749i	−0.0920328	+	0.159406i
$516$	−9.27043	+	4.32515i	−0.408108	+	0.190404i
$517$	−7.53517	−	13.0513i	−0.331396	−	0.573995i
$518$	7.64651	+	3.45274i	0.335968	+	0.151704i
$519$	−12.8854	+	3.12066i	−0.565607	+	0.136982i
$520$	4.30767	+	0.986889i	0.188904	+	0.0432779i
$521$		−	22.5458i		−	0.987749i	−0.869533	−	0.493874i	$-0.835580\pi$
$521$		−	22.5458i		−	0.987749i	0.869533	−	0.493874i	$-0.164420\pi$
$522$	−1.31378	+	2.57033i	−0.0575027	+	0.112500i
$523$		−	21.9098i		−	0.958048i	−0.877802	−	0.479024i	$-0.840991\pi$
$523$		−	21.9098i		−	0.958048i	0.877802	−	0.479024i	$-0.159009\pi$
$524$	2.98683	+	3.38820i	0.130480	+	0.148014i
$525$	2.79114	−	9.49210i	0.121815	−	0.414269i
$526$	13.1412	−	29.1029i	0.572985	−	1.26895i
$527$	−23.0300	−	39.8892i	−1.00320	−	1.73760i
$528$	−4.76342	−	6.45882i	−0.207301	−	0.281084i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	3.61833	+	5.03568i	0.157170	+	0.218736i
$531$	−3.25852	+	1.67668i	−0.141408	+	0.0727617i
$532$	−6.07634	+	18.0528i	−0.263443	+	0.782690i
$533$	1.00121	+	0.578047i	0.0433671	+	0.0250380i
$534$	32.8796	+	28.2681i	1.42284	+	1.22328i
$535$	7.00947	−	4.04692i	0.303046	−	0.174964i
$536$	22.1361	−	23.8182i	0.956136	−	1.02879i
$537$	−25.6886	+	24.4750i	−1.10854	+	1.05617i
$538$	0.184445	+	1.84831i	0.00795198	+	0.0796864i
$539$	6.33970			0.273070
$540$	−6.32569	−	0.862043i	−0.272215	−	0.0370964i
$541$	11.9733			0.514772			0.257386	−	0.966309i	$-0.417139\pi$
$541$	11.9733			0.514772			0.257386	+	0.966309i	$0.417139\pi$
$542$	0.225721	+	2.26194i	0.00969557	+	0.0971588i
$543$	−13.8516	+	13.1972i	−0.594431	+	0.566348i
$544$	15.2553	+	28.1041i	0.654064	+	1.20495i
$545$	0.457723	−	0.264267i	0.0196067	−	0.0113199i
$546$	5.83769	+	5.01893i	0.249830	+	0.214790i
$547$	6.85376	+	3.95702i	0.293046	+	0.169190i	0.639315	−	0.768945i	$-0.279218\pi$
$547$	6.85376	+	3.95702i	0.293046	+	0.169190i	−0.346269	+	0.938135i	$0.612551\pi$
$548$	2.94933	+	0.992706i	0.125989	+	0.0424063i
$549$	−13.1993	−	8.49717i	−0.563332	−	0.362650i
$550$	4.41881	+	6.14971i	0.188419	+	0.262225i
$551$	−2.62194	+	4.54133i	−0.111698	+	0.193467i
$552$	4.89860	−	0.0607302i	0.208498	−	0.00258485i
$553$	−2.07246	−	3.58960i	−0.0881298	−	0.152645i
$554$	3.59406	−	7.95949i	0.152697	−	0.338166i
$555$	−1.44107	+	4.90078i	−0.0611700	+	0.208027i
$556$	6.86597	−	6.05263i	0.291182	−	0.256689i
$557$		−	30.4629i		−	1.29076i	−0.763863	−	0.645378i	$-0.776700\pi$
$557$		−	30.4629i		−	1.29076i	0.763863	−	0.645378i	$-0.223300\pi$
$558$	18.7908	+	29.0163i	0.795478	+	1.22836i
$559$			7.51083i			0.317674i
$560$	−2.79934	+	1.17644i	−0.118294	+	0.0497138i
$561$	−11.0230	+	2.66960i	−0.465389	+	0.112711i
$562$	−13.7106	−	6.19092i	−0.578345	−	0.261148i
$563$	8.38168	+	14.5175i	0.353246	+	0.611840i	0.986816	−	0.161845i	$-0.0517446\pi$
$563$	8.38168	+	14.5175i	0.353246	+	0.611840i	−0.633570	+	0.773685i	$0.718411\pi$
$564$	−19.0548	−	40.8417i	−0.802354	−	1.71975i
$565$	−5.49930	+	9.52507i	−0.231357	+	0.400723i
$566$	0.445071	−	0.319801i	0.0187077	−	0.0134422i
$567$	−9.04928	−	6.46519i	−0.380034	−	0.271513i
$568$	33.2337	−	10.2216i	1.39445	−	0.428888i
$569$	21.6469	+	12.4978i	0.907485	+	0.523936i	0.879621	−	0.475675i	$-0.157796\pi$
$569$	21.6469	+	12.4978i	0.907485	+	0.523936i	0.0278636	+	0.999612i	$0.491130\pi$
$570$	−11.3964	−	2.15072i	−0.477341	−	0.0900839i
$571$	13.3888	−	7.73000i	0.560302	−	0.323490i	−0.192965	−	0.981206i	$-0.561810\pi$
$571$	13.3888	−	7.73000i	0.560302	−	0.323490i	0.753267	+	0.657715i	$0.228477\pi$
$572$	−5.77614	+	1.16441i	−0.241513	+	0.0486864i
$573$	2.96649	+	12.2488i	0.123927	+	0.511702i
$574$	−0.790432	+	0.0788779i	−0.0329920	+	0.00329230i
$575$	−4.62262			−0.192776
$576$	−12.5116	−	20.4807i	−0.521316	−	0.853364i
$577$	−25.4084			−1.05777			−0.528883	−	0.848695i	$-0.677389\pi$
$577$	−25.4084			−1.05777			−0.528883	+	0.848695i	$0.677389\pi$
$578$	21.0452	−	2.10012i	0.875364	−	0.0873534i
$579$	−17.9457	−	5.27692i	−0.745799	−	0.219301i
$580$	−0.819459	+	0.165194i	−0.0340262	+	0.00685931i
$581$	−6.34744	+	3.66470i	−0.263336	+	0.152037i
$582$	4.57108	+	13.0436i	0.189477	+	0.540674i
$583$	−7.16008	−	4.13388i	−0.296540	−	0.171208i
$584$	36.9289	−	11.3581i	1.52813	−	0.470003i
$585$	−2.53724	+	3.94127i	−0.104902	+	0.162952i
$586$	0.121811	−	0.0875263i	0.00503198	−	0.00361568i
$587$	7.77549	−	13.4675i	0.320929	−	0.555865i	−0.659751	−	0.751484i	$-0.729338\pi$
$587$	7.77549	−	13.4675i	0.320929	−	0.555865i	0.980680	+	0.195619i	$0.0626717\pi$
$588$	18.8872	+	1.64857i	0.778894	+	0.0679861i
$589$	31.3995	+	54.3855i	1.29379	+	2.24092i
$590$	−0.967202	−	0.436734i	−0.0398191	−	0.0179801i
$591$	−26.7951	−	28.1238i	−1.10220	−	1.15686i
$592$	−17.7037	+	7.44009i	−0.727616	+	0.305786i
$593$		−	1.96941i		−	0.0808741i	−0.999182	−	0.0404370i	$-0.987125\pi$
$593$		−	1.96941i		−	0.0808741i	0.999182	−	0.0404370i	$-0.0128750\pi$
$594$	8.15992	−	2.42343i	0.334806	−	0.0994346i
$595$			4.29125i			0.175924i
$596$	21.5249	−	18.9751i	0.881695	−	0.777250i
$597$	−10.1508	−	10.6541i	−0.415443	−	0.436043i
$598$	1.48025	−	3.27820i	0.0605319	−	0.134055i
$599$	5.60432	+	9.70697i	0.228986	+	0.396616i	0.957508	−	0.288407i	$-0.0931255\pi$
$599$	5.60432	+	9.70697i	0.228986	+	0.396616i	−0.728522	+	0.685023i	$0.759792\pi$
$600$	11.5653	+	19.4702i	0.472151	+	0.794869i
$601$	10.6262	−	18.4052i	0.433453	−	0.750762i	−0.563715	−	0.825969i	$-0.690628\pi$
$601$	10.6262	−	18.4052i	0.433453	−	0.750762i	0.997168	+	0.0752072i	$0.0239618\pi$
$602$	−3.01141	−	4.19101i	−0.122736	−	0.170813i
$603$	15.7798	+	30.6671i	0.642605	+	1.24886i
$604$	−31.9019	−	10.7378i	−1.29807	−	0.436913i
$605$	−5.13829	−	2.96659i	−0.208901	−	0.120609i
$606$	−16.0670	+	5.63062i	−0.652677	+	0.228728i
$607$	6.30708	−	3.64139i	0.255997	−	0.147800i	−0.366510	−	0.930414i	$-0.619448\pi$
$607$	6.30708	−	3.64139i	0.255997	−	0.147800i	0.622507	+	0.782614i	$0.286114\pi$
$608$	−20.7992	−	38.3175i	−0.843520	−	1.55398i
$609$	−1.39711	−	0.410817i	−0.0566136	−	0.0166472i
$610$	−0.451404	−	4.52350i	−0.0182768	−	0.183151i
$611$	−33.0897			−1.33866
$612$	−33.5337	+	5.08685i	−1.35552	+	0.205624i
$613$	26.1843			1.05757			0.528787	−	0.848754i	$-0.322647\pi$
$613$	26.1843			1.05757			0.528787	+	0.848754i	$0.322647\pi$
$614$	2.42263	+	24.2771i	0.0977696	+	0.979744i
$615$	−0.113842	−	0.470062i	−0.00459057	−	0.0189547i
$616$	2.75620	−	2.96563i	0.111051	−	0.119489i
$617$	8.74246	−	5.04746i	0.351958	−	0.203203i	−0.313589	−	0.949559i	$-0.601531\pi$
$617$	8.74246	−	5.04746i	0.351958	−	0.203203i	0.665547	+	0.746356i	$0.268198\pi$
$618$	3.08872	−	16.3667i	0.124247	−	0.658365i
$619$	−10.8288	−	6.25198i	−0.435244	−	0.251288i	0.266334	−	0.963881i	$-0.414188\pi$
$619$	−10.8288	−	6.25198i	−0.435244	−	0.251288i	−0.701578	+	0.712592i	$0.747521\pi$
$620$	−3.19352	+	9.48795i	−0.128255	+	0.381045i
$621$	−1.70522	+	4.90838i	−0.0684281	+	0.196967i
$622$	3.00075	+	4.17618i	0.120319	+	0.167449i
$623$	−10.9374	+	18.9441i	−0.438197	+	0.758979i
$624$	−17.5110	+	1.96697i	−0.701002	+	0.0787417i
$625$	−9.74083	−	16.8716i	−0.389633	−	0.674864i
$626$	−2.32831	+	5.15634i	−0.0930582	+	0.206089i
$627$	15.0289	−	3.63978i	0.600195	−	0.145359i
$628$	3.13880	+	3.56058i	0.125252	+	0.142083i
$629$			27.1388i			1.08209i
$630$	−0.164456	−	3.21650i	−0.00655207	−	0.128148i
$631$			2.50411i			0.0996872i	0.998757	+	0.0498436i	$0.0158723\pi$
$631$			2.50411i			0.0996872i	−0.998757	+	0.0498436i	$0.984128\pi$
$632$	9.24762	+	2.11863i	0.367851	+	0.0842748i
$633$	0.629598	−	2.14114i	0.0250243	−	0.0851025i
$634$	−21.8674	−	9.87409i	−0.868465	−	0.392150i
$635$	−5.69836	−	9.86984i	−0.226132	−	0.391673i
$636$	−20.2563	−	14.1775i	−0.803213	−	0.562175i
$637$	6.95998	−	12.0550i	0.275764	−	0.477638i
$638$	0.905153	−	0.650388i	0.0358353	−	0.0257491i
$639$	−1.78342	+	36.8361i	−0.0705511	+	1.45721i
$640$	2.38951	−	6.52652i	0.0944538	−	0.257983i
$641$	−1.78269	−	1.02923i	−0.0704119	−	0.0406523i	0.464381	−	0.885636i	$-0.346277\pi$
$641$	−1.78269	−	1.02923i	−0.0704119	−	0.0406523i	−0.534793	+	0.844983i	$0.679610\pi$
$642$	−21.0396	+	24.4719i	−0.830369	+	0.965830i
$643$	−15.4801	+	8.93741i	−0.610474	+	0.352457i	−0.773151	−	0.634222i	$-0.781320\pi$
$643$	−15.4801	+	8.93741i	−0.610474	+	0.352457i	0.162677	+	0.986679i	$0.447987\pi$
$644$	0.488393	+	2.42271i	0.0192454	+	0.0954682i
$645$	2.27493	−	2.16745i	0.0895751	−	0.0853432i
$646$	−61.3100	+	6.11818i	−2.41221	+	0.240717i
$647$	−1.58845			−0.0624483			−0.0312242	−	0.999512i	$-0.509941\pi$
$647$	−1.58845			−0.0624483			−0.0312242	+	0.999512i	$0.509941\pi$
$648$	24.9401	−	5.09796i	0.979741	−	0.200267i
$649$	1.41497			0.0555426
$650$	16.5449	−	1.65103i	0.648945	−	0.0647588i
$651$	−12.6263	+	12.0298i	−0.494864	+	0.471485i
$652$	−5.75677	−	28.5569i	−0.225453	−	1.11838i
$653$	10.8551	−	6.26720i	0.424793	−	0.245254i	−0.272333	−	0.962203i	$-0.587795\pi$
$653$	10.8551	−	6.26720i	0.424793	−	0.245254i	0.697126	+	0.716949i	$0.254462\pi$
$654$	−1.37390	+	1.59803i	−0.0537238	+	0.0624880i
$655$	−1.20149	−	0.693678i	−0.0469460	−	0.0271043i
$656$	1.09940	−	1.44815i	0.0429245	−	0.0565406i
$657$	−1.98172	+	40.9319i	−0.0773143	+	1.59691i
$658$	18.4639	−	13.2670i	0.719797	−	0.517203i
$659$	1.98565	−	3.43925i	0.0773500	−	0.133974i	−0.824756	−	0.565489i	$-0.808687\pi$
$659$	1.98565	−	3.43925i	0.0773500	−	0.133974i	0.902106	+	0.431515i	$0.142021\pi$
$660$	2.01954	+	1.41349i	0.0786106	+	0.0550201i
$661$	−16.3279	−	28.2807i	−0.635082	−	1.09999i	−0.986498	−	0.163774i	$-0.947633\pi$
$661$	−16.3279	−	28.2807i	−0.635082	−	1.09999i	0.351416	−	0.936219i	$-0.385700\pi$
$662$	−38.7189	−	17.4833i	−1.50485	−	0.679508i
$663$	−7.02516	+	23.8911i	−0.272834	+	0.927854i
$664$	3.74636	−	16.3525i	0.145387	−	0.634599i
$665$		−	5.85075i		−	0.226882i
$666$	−1.04005	−	20.3418i	−0.0403012	−	0.788229i
$667$			0.680385i			0.0263446i
$668$	6.35923	+	7.21378i	0.246046	+	0.279109i
$669$	28.2773	−	6.84835i	1.09326	−	0.264772i
$670$	−4.11027	+	9.10270i	−0.158794	+	0.351668i
$671$	3.03063	+	5.24921i	0.116996	+	0.202644i
$672$	8.98243	−	8.11846i	0.346505	−	0.313176i
$673$	24.9330	−	43.1852i	0.961097	−	1.66467i	0.241342	−	0.970440i	$-0.422412\pi$
$673$	24.9330	−	43.1852i	0.961097	−	1.66467i	0.719755	−	0.694228i	$-0.244254\pi$
$674$	−18.0000	−	25.0508i	−0.693334	−	0.964921i
$675$	−23.5910	+	4.51827i	−0.908019	+	0.173908i
$676$	4.16689	−	12.3798i	0.160265	−	0.476148i
$677$	32.1591	+	18.5671i	1.23597	+	0.713590i	0.968269	−	0.249910i	$-0.0804011\pi$
$677$	32.1591	+	18.5671i	1.23597	+	0.713590i	0.267706	+	0.963501i	$0.413734\pi$
$678$	8.13280	−	43.0945i	0.312338	−	1.65503i
$679$	−6.03848	+	3.48632i	−0.231735	+	0.133793i
$680$	−7.19471	−	6.68663i	−0.275905	−	0.256421i
$681$	−4.19758	−	17.3320i	−0.160851	−	0.664165i
$682$	−1.32542	−	13.2820i	−0.0507529	−	0.508592i
$683$	−14.7789			−0.565497			−0.282749	−	0.959194i	$-0.591246\pi$
$683$	−14.7789			−0.565497			−0.282749	+	0.959194i	$0.591246\pi$
$684$	45.7203	−	6.93548i	1.74816	−	0.265185i
$685$	−0.955851			−0.0365212
$686$	2.16444	+	21.6898i	0.0826388	+	0.828120i
$687$	0.609550	+	0.179237i	0.0232558	+	0.00683833i
$688$	11.7190	+	1.48151i	0.446784	+	0.0564821i
$689$	−15.7213	+	9.07667i	−0.598932	+	0.345794i
$690$	−1.42008	+	0.497663i	−0.0540617	+	0.0189457i
$691$	37.4456	+	21.6192i	1.42450	+	0.822434i	0.996679	−	0.0814306i	$-0.0259489\pi$
$691$	37.4456	+	21.6192i	1.42450	+	0.822434i	0.427819	+	0.903865i	$0.359282\pi$
$692$	14.5091	+	4.88357i	0.551553	+	0.185645i
$693$	1.96477	+	3.81841i	0.0746355	+	0.145049i
$694$	7.78093	+	10.8288i	0.295360	+	0.411056i
$695$	−1.40570	+	2.43474i	−0.0533211	+	0.0923548i
$696$	2.86575	−	1.70225i	0.108626	−	0.0645237i
$697$	−1.28475	−	2.22526i	−0.0486635	−	0.0842876i
$698$	4.71307	−	10.4377i	0.178392	−	0.395072i
$699$	3.42537	+	3.59522i	0.129559	+	0.135984i
$700$	−8.57002	+	7.55482i	−0.323916	+	0.285545i
$701$		−	21.4085i		−	0.808586i	−0.914629	−	0.404293i	$-0.867518\pi$
$701$		−	21.4085i		−	0.808586i	0.914629	−	0.404293i	$-0.132482\pi$
$702$	4.35010	−	18.1768i	0.164184	−	0.686038i
$703$		−	37.0014i		−	1.39553i
$704$	0.677463	+	9.24210i	0.0255328	+	0.348325i
$705$	9.54890	+	10.0224i	0.359632	+	0.377465i
$706$	−1.17247	−	0.529421i	−0.0441265	−	0.0199250i
$707$	−4.29442	−	7.43815i	−0.161508	−	0.279740i
$708$	4.21547	+	0.367950i	0.158427	+	0.0138284i
$709$	−19.7463	+	34.2016i	−0.741588	+	1.28447i	0.210184	+	0.977662i	$0.432594\pi$
$709$	−19.7463	+	34.2016i	−0.741588	+	1.28447i	−0.951772	+	0.306806i	$0.900740\pi$
$710$	−8.67311	+	6.23197i	−0.325496	+	0.233882i
$711$	−5.44689	+	8.46105i	−0.204274	+	0.317314i
$712$	−14.7190	−	47.8563i	−0.551619	−	1.79349i
$713$	7.05643	+	4.07403i	0.264265	+	0.152574i
$714$	−5.65894	−	16.1478i	−0.211781	−	0.604317i
$715$	1.56740	−	0.904940i	0.0586175	−	0.0338429i
$716$	40.1624	−	8.09631i	1.50094	−	0.302573i
$717$	−31.9040	−	9.38133i	−1.19148	−	0.350352i
$718$	−29.8827	+	2.98202i	−1.11521	+	0.111288i
$719$	−12.9949			−0.484627			−0.242314	−	0.970198i	$-0.577906\pi$
$719$	−12.9949			−0.484627			−0.242314	+	0.970198i	$0.577906\pi$
$720$	5.64903	+	4.73622i	0.210527	+	0.176509i
$721$	8.40245			0.312924
$722$	56.8537	−	5.67348i	2.11588	−	0.211145i
$723$	7.90883	+	32.6560i	0.294133	+	1.21449i
$724$	21.6561	−	4.36564i	0.804844	−	0.162248i
$725$	−2.72379	+	1.57258i	−0.101159	+	0.0584041i
$726$	23.2473	+	4.38723i	0.862788	+	0.162826i
$727$	0.518910	+	0.299593i	0.0192453	+	0.0111113i	0.509592	−	0.860416i	$-0.329796\pi$
$727$	0.518910	+	0.299593i	0.0192453	+	0.0111113i	−0.490346	+	0.871528i	$0.663130\pi$
$728$	−2.61332	−	8.49675i	−0.0968563	−	0.314911i
$729$	−3.90482	+	26.7161i	−0.144623	+	0.989487i
$730$	−9.63749	+	6.92491i	−0.356699	+	0.256303i
$731$	8.34670	−	14.4569i	0.308714	−	0.534708i
$732$	7.66383	+	16.4265i	0.283263	+	0.607141i
$733$	−21.2333	−	36.7771i	−0.784270	−	1.35839i	−0.929434	−	0.368987i	$-0.879705\pi$
$733$	−21.2333	−	36.7771i	−0.784270	−	1.35839i	0.145165	−	0.989408i	$-0.453629\pi$
$734$	40.8413	+	18.4417i	1.50748	+	0.680694i
$735$	−5.65978	+	1.37072i	−0.208764	+	0.0505598i
$736$	−4.82293	−	2.95623i	−0.177776	−	0.108968i
$737$		−	13.3168i		−	0.490532i
$738$	1.04826	+	1.61870i	0.0385871	+	0.0595852i
$739$		−	13.8092i		−	0.507981i	−0.967207	−	0.253990i	$-0.918257\pi$
$739$		−	13.8092i		−	0.507981i	0.967207	−	0.253990i	$-0.0817432\pi$
$740$	4.42471	−	3.90056i	0.162656	−	0.143387i
$741$	9.57820	−	32.5735i	0.351864	−	1.19662i
$742$	5.13317	−	11.3681i	0.188445	−	0.417334i
$743$	−11.5510	−	20.0069i	−0.423765	−	0.733983i	0.572539	−	0.819877i	$-0.305958\pi$
$743$	−11.5510	−	20.0069i	−0.423765	−	0.733983i	−0.996304	+	0.0858946i	$0.972625\pi$
$744$	−0.494834	−	39.9141i	−0.0181415	−	1.46332i
$745$	−4.40688	+	7.63294i	−0.161456	+	0.279649i
$746$	−29.1408	−	40.5556i	−1.06692	−	1.48485i
$747$	14.9616	+	9.63167i	0.547416	+	0.352404i
$748$	12.4120	+	4.17770i	0.453826	+	0.152752i
$749$	−14.0999	−	8.14056i	−0.515198	−	0.297450i
$750$	−10.9797	−	9.43976i	−0.400922	−	0.344691i
$751$	10.5707	−	6.10301i	0.385731	−	0.222702i	−0.294578	−	0.955628i	$-0.595179\pi$
$751$	10.5707	−	6.10301i	0.385731	−	0.222702i	0.680309	+	0.732925i	$0.261846\pi$
$752$	−6.52694	+	51.6292i	−0.238013	+	1.88272i
$753$	8.84675	−	8.42880i	0.322394	−	0.307162i
$754$	−0.243009	−	2.43518i	−0.00884988	−	0.0886842i
$755$	10.3391			0.376279
$756$	4.86049	+	11.8867i	0.176774	+	0.432315i
$757$	24.8777			0.904196			0.452098	−	0.891968i	$-0.350676\pi$
$757$	24.8777			0.904196			0.452098	+	0.891968i	$0.350676\pi$
$758$	−2.89871	−	29.0478i	−0.105286	−	1.05506i
$759$	1.45260	−	1.38397i	0.0527259	−	0.0502349i
$760$	9.80937	+	9.11665i	0.355823	+	0.330696i
$761$	11.9099	−	6.87619i	0.431734	−	0.249262i	−0.268351	−	0.963321i	$-0.586479\pi$
$761$	11.9099	−	6.87619i	0.431734	−	0.249262i	0.700085	+	0.714059i	$0.253145\pi$
$762$	34.4582	+	29.6253i	1.24829	+	1.07321i
$763$	−0.920730	−	0.531584i	−0.0333327	−	0.0192446i
$764$	4.64230	−	13.7923i	0.167953	−	0.498988i
$765$	9.26358	−	4.76659i	0.334925	−	0.172337i
$766$	22.1174	+	30.7811i	0.799136	+	1.11217i
$767$	1.55342	−	2.69059i	0.0560906	−	0.0971517i
$768$	−0.385025	+	27.7101i	−0.0138934	+	0.999903i
$769$	6.25675	+	10.8370i	0.225624	+	0.390793i	0.956507	−	0.291711i	$-0.0942245\pi$
$769$	6.25675	+	10.8370i	0.225624	+	0.390793i	−0.730882	+	0.682504i	$0.760891\pi$
$770$	−0.511775	+	1.13339i	−0.0184431	+	0.0408445i
$771$	−9.87571	+	33.5853i	−0.355665	+	1.20954i
$772$	14.2831	+	16.2025i	0.514060	+	0.583139i
$773$		−	21.4529i		−	0.771607i	−0.922581	−	0.385803i	$-0.873924\pi$
$773$		−	21.4529i		−	0.771607i	0.922581	−	0.385803i	$-0.126076\pi$
$774$	−5.70221	+	11.1560i	−0.204962	+	0.400995i
$775$			37.6654i			1.35298i
$776$	3.56400	−	15.5565i	0.127940	−	0.558446i
$777$	9.98678	−	2.41866i	0.358274	−	0.0867689i
$778$	50.6394	+	22.8659i	1.81551	+	0.819782i
$779$	1.75165	+	3.03395i	0.0627594	+	0.108702i
$780$	4.90491	−	2.28840i	0.175624	−	0.0819379i
$781$	7.11991	−	12.3321i	0.254771	−	0.441275i
$782$	−6.49221	+	4.66491i	−0.232161	+	0.166817i
$783$	0.665027	+	3.47227i	0.0237661	+	0.124089i
$784$	−17.4364	−	13.2374i	−0.622729	−	0.472764i
$785$	−1.26262	−	0.728972i	−0.0450647	−	0.0260181i
$786$	5.43591	+	1.02587i	0.193893	+	0.0365914i
$787$	22.2862	−	12.8670i	0.794418	−	0.458657i	−0.0470977	−	0.998890i	$-0.514997\pi$
$787$	22.2862	−	12.8670i	0.794418	−	0.458657i	0.841516	+	0.540233i	$0.181664\pi$
$788$	8.86383	+	43.9697i	0.315761	+	1.56636i
$789$	−9.20550	−	38.0101i	−0.327724	−	1.35319i
$790$	−2.89967	+	0.289361i	−0.103166	+	0.0102950i
$791$	22.1242			0.786645
$792$	−9.46345	−	2.65571i	−0.336269	−	0.0943667i
$793$	13.3086			0.472603
$794$	40.2724	−	4.01882i	1.42921	−	0.142623i
$795$	7.28598	+	2.14243i	0.258407	+	0.0759843i
$796$	3.35787	+	16.6570i	0.119016	+	0.590391i
$797$	7.11282	−	4.10659i	0.251949	−	0.145463i	−0.368707	−	0.929546i	$-0.620200\pi$
$797$	7.11282	−	4.10659i	0.251949	−	0.145463i	0.620656	+	0.784083i	$0.286866\pi$
$798$	7.71548	+	22.0162i	0.273125	+	0.779364i
$799$	63.6912	+	36.7721i	2.25323	+	1.30090i
$800$	0.687407	−	26.1404i	0.0243035	−	0.924204i
$801$	53.0438	+	2.56812i	1.87421	+	0.0907400i
$802$	−20.4793	+	14.7152i	−0.723149	+	0.519611i
$803$	7.91158	−	13.7033i	0.279194	−	0.483578i
$804$	3.46291	−	39.6734i	0.122127	−	1.39917i
$805$	−0.379563	−	0.657422i	−0.0133778	−	0.0231711i
$806$	−26.7110	−	12.0612i	−0.940853	−	0.424837i
$807$	1.56926	+	1.64707i	0.0552405	+	0.0579797i
$808$	19.1624	+	4.39011i	0.674130	+	0.154443i
$809$			43.7072i			1.53666i	0.640053	+	0.768331i	$0.278912\pi$
$809$			43.7072i			1.53666i	−0.640053	+	0.768331i	$0.721088\pi$
$810$	−6.76082	+	3.92780i	−0.237551	+	0.138009i
$811$			5.96976i			0.209627i	0.994492	+	0.104813i	$0.0334245\pi$
$811$			5.96976i			0.209627i	−0.994492	+	0.104813i	$0.966575\pi$
$812$	1.11196	+	1.26139i	0.0390223	+	0.0442661i
$813$	1.92044	+	2.01567i	0.0673528	+	0.0706926i
$814$	−3.23658	+	7.16780i	−0.113442	+	0.251231i
$815$	4.47398	+	7.74915i	0.156717	+	0.271441i
$816$	35.8912	+	15.6738i	1.25644	+	0.548691i
$817$	−11.3800	+	19.7107i	−0.398136	+	0.689592i
$818$	−10.7786	−	15.0007i	−0.376866	−	0.524488i
$819$	9.41777	+	0.455962i	0.329084	+	0.0159326i
$820$	−0.178153	+	0.529294i	−0.00622138	+	0.0184838i
$821$	−39.3264	−	22.7051i	−1.37250	−	0.792413i	−0.381257	−	0.924469i	$-0.624509\pi$
$821$	−39.3264	−	22.7051i	−1.37250	−	0.792413i	−0.991242	+	0.132056i	$0.957842\pi$
$822$	3.59683	−	1.26050i	0.125454	−	0.0439649i
$823$	2.15227	−	1.24262i	0.0750235	−	0.0433149i	−0.462019	−	0.886870i	$-0.652875\pi$
$823$	2.15227	−	1.24262i	0.0750235	−	0.0433149i	0.537043	+	0.843555i	$0.319541\pi$
$824$	−13.0927	+	14.0876i	−0.456106	+	0.490763i
$825$	8.89785	+	2.61640i	0.309783	+	0.0910914i
$826$	0.211973	+	2.12417i	0.00737547	+	0.0739093i
$827$	27.4835			0.955696			0.477848	−	0.878443i	$-0.341417\pi$
$827$	27.4835			0.955696			0.477848	+	0.878443i	$0.341417\pi$
$828$	4.68745	−	3.74538i	0.162900	−	0.130161i
$829$	1.06711			0.0370621			0.0185311	−	0.999828i	$-0.494101\pi$
$829$	1.06711			0.0370621			0.0185311	+	0.999828i	$0.494101\pi$
$830$	0.511673	+	5.12746i	0.0177604	+	0.177977i
$831$	−2.51765	−	10.3955i	−0.0873365	−	0.360618i
$832$	18.3177	+	8.85815i	0.635054	+	0.307101i
$833$	−26.7932	+	15.4691i	−0.928330	+	0.535972i
$834$	2.07885	−	11.0155i	0.0719848	−	0.381437i
$835$	−2.55807	−	1.47690i	−0.0885258	−	0.0511104i
$836$	−16.9226	−	5.69593i	−0.585282	−	0.196998i
$837$	39.9938	+	13.8942i	1.38239	+	0.480255i
$838$	−7.89534	−	10.9880i	−0.272740	−	0.379575i
$839$	−12.1992	+	21.1296i	−0.421163	+	0.729476i	−0.996054	−	0.0887544i	$-0.971711\pi$
$839$	−12.1992	+	21.1296i	−0.421163	+	0.729476i	0.574890	+	0.818230i	$0.305045\pi$
$840$	−1.81940	+	3.24350i	−0.0627753	+	0.111911i
$841$	−14.2685	−	24.7138i	−0.492019	−	0.852201i
$842$	22.1752	−	49.1097i	0.764208	−	1.69243i
$843$	−17.9068	+	4.33677i	−0.616742	+	0.149366i
$844$	−1.93314	+	1.70414i	−0.0665415	+	0.0586590i
$845$			4.01219i			0.138024i
$846$	−49.1488	−	25.1216i	−1.68977	−	0.863698i
$847$			11.9349i			0.410087i
$848$	11.0612	+	26.3200i	0.379842	+	0.903832i
$849$	0.189356	−	0.643961i	0.00649868	−	0.0221007i
$850$	−33.6805	−	15.2082i	−1.15523	−	0.521639i
$851$	−2.40044	−	4.15768i	−0.0822859	−	0.142523i
$852$	24.4184	−	34.8881i	0.836561	−	1.19525i
$853$	−7.09016	+	12.2805i	−0.242762	+	0.420477i	−0.961500	−	0.274805i	$-0.911387\pi$
$853$	−7.09016	+	12.2805i	−0.242762	+	0.420477i	0.718738	+	0.695281i	$0.244720\pi$
$854$	−7.42615	+	5.33598i	−0.254118	+	0.182593i
$855$	−12.6301	+	6.49884i	−0.431940	+	0.222256i
$856$	35.6189	−	10.9552i	1.21743	−	0.374441i
$857$	18.9876	+	10.9625i	0.648604	+	0.374471i	0.787921	−	0.615776i	$-0.211157\pi$
$857$	18.9876	+	10.9625i	0.648604	+	0.374471i	−0.139317	+	0.990248i	$0.544491\pi$
$858$	−4.70472	+	5.47222i	−0.160616	+	0.186818i
$859$	−43.3062	+	25.0028i	−1.47759	+	0.853085i	−0.999679	−	0.0253249i	$-0.991938\pi$
$859$	−43.3062	+	25.0028i	−1.47759	+	0.853085i	−0.477908	+	0.878410i	$0.658605\pi$
$860$	−3.55670	+	0.716992i	−0.121282	+	0.0244492i
$861$	−0.704371	+	0.671094i	−0.0240049	+	0.0228708i
$862$	20.5190	−	2.04761i	0.698879	−	0.0697418i
$863$	−5.24350			−0.178491			−0.0892454	−	0.996010i	$-0.528446\pi$
$863$	−5.24350			−0.178491			−0.0892454	+	0.996010i	$0.528446\pi$
$864$	−27.5028	−	10.3727i	−0.935666	−	0.352888i
$865$	−4.70226			−0.159882
$866$	−24.7761	+	2.47243i	−0.841926	+	0.0840165i
$867$	18.7538	−	17.8678i	0.636913	−	0.606823i
$868$	19.7404	−	3.97946i	0.670033	−	0.135072i
$869$	3.36487	−	1.94271i	0.114145	−	0.0659019i
$870$	−0.667456	+	0.776341i	−0.0226289	+	0.0263204i
$871$	−25.3222	−	14.6198i	−0.858009	−	0.495372i
$872$	2.32594	−	0.715382i	0.0787661	−	0.0242259i
$873$	14.2333	+	9.16284i	0.481725	+	0.310115i
$874$	8.85158	−	6.36021i	0.299409	−	0.215137i
$875$	3.65239	−	6.32612i	0.123473	−	0.213862i
$876$	27.1335	−	38.7673i	0.916756	−	1.30983i
$877$	12.2048	+	21.1393i	0.412125	+	0.713822i	0.995122	−	0.0986527i	$-0.0314533\pi$
$877$	12.2048	+	21.1393i	0.412125	+	0.713822i	−0.582997	+	0.812475i	$0.698120\pi$
$878$	13.6784	+	6.17639i	0.461623	+	0.208443i
$879$	0.0518248	−	0.176246i	0.00174801	−	0.00594461i
$880$	−1.10279	−	2.62409i	−0.0371751	−	0.0884581i
$881$		−	38.0073i		−	1.28050i	−0.768167	−	0.640249i	$-0.778831\pi$
$881$		−	38.0073i		−	1.28050i	0.768167	−	0.640249i	$-0.221169\pi$
$882$	19.4900	−	12.6216i	0.656261	−	0.424992i
$883$			50.7254i			1.70705i	0.521055	+	0.853523i	$0.325539\pi$
$883$			50.7254i			1.70705i	−0.521055	+	0.853523i	$0.674461\pi$
$884$	21.5703	−	19.0151i	0.725488	−	0.639546i
$885$	−1.26322	+	0.305934i	−0.0424627	+	0.0102839i
$886$	10.1390	−	22.4541i	0.340626	−	0.754360i
$887$	−11.3444	−	19.6490i	−0.380906	−	0.659749i	0.610286	−	0.792181i	$-0.291055\pi$
$887$	−11.3444	−	19.6490i	−0.380906	−	0.659749i	−0.991192	+	0.132432i	$0.957721\pi$
$888$	−11.5063	+	20.5126i	−0.386126	+	0.688358i
$889$	−11.4625	+	19.8536i	−0.384440	+	0.665869i
$890$	8.97401	+	12.4892i	0.300810	+	0.418640i
$891$	6.06044	−	8.48275i	0.203032	−	0.284183i
$892$	−31.8405	−	10.7171i	−1.06610	−	0.358834i
$893$	−86.8375	−	50.1357i	−2.90591	−	1.67773i
$894$	6.51724	−	34.5339i	0.217969	−	1.15499i
$895$	−10.8984	+	6.29219i	−0.364293	+	0.210325i
$896$	−13.7728	+	2.40154i	−0.460118	+	0.0802299i
$897$	−1.03692	−	4.28151i	−0.0346218	−	0.142956i
$898$	−2.48388	−	24.8909i	−0.0828882	−	0.830619i
$899$	5.54382			0.184897
$900$	25.8280	+	10.1086i	0.860934	+	0.336952i
$901$	40.3472			1.34416
$902$	−0.0739398	−	0.740947i	−0.00246192	−	0.0246708i
$903$	−6.06386	−	1.78307i	−0.201793	−	0.0593368i
$904$	−34.4739	+	37.0934i	−1.14659	+	1.23371i
$905$	−5.87656	+	3.39284i	−0.195344	+	0.112782i
$906$	−38.9057	+	13.6344i	−1.29255	+	0.452971i
$907$	42.5525	+	24.5677i	1.41293	+	0.815758i	0.995664	−	0.0930249i	$-0.0296536\pi$
$907$	42.5525	+	24.5677i	1.41293	+	0.815758i	0.417270	+	0.908783i	$0.362987\pi$
$908$	−6.56884	+	19.5161i	−0.217995	+	0.647663i
$909$	−11.2867	+	17.5325i	−0.374357	+	0.581516i
$910$	1.59331	+	2.21743i	0.0528177	+	0.0735071i
$911$	−4.44982	+	7.70731i	−0.147429	+	0.255355i	−0.930277	−	0.366859i	$-0.880433\pi$
$911$	−4.44982	+	7.70731i	−0.147429	+	0.255355i	0.782847	+	0.622214i	$0.213766\pi$
$912$	−48.9346	−	21.3698i	−1.62039	−	0.707626i
$913$	−3.43527	−	5.95006i	−0.113691	−	0.196918i
$914$	−19.7279	+	43.6899i	−0.652541	+	1.44513i
$915$	−3.84055	−	4.03099i	−0.126965	−	0.133260i
$916$	−0.485144	−	0.550337i	−0.0160296	−	0.0181837i
$917$			2.79073i			0.0921580i
$918$	−28.5727	+	30.1525i	−0.943040	+	0.995182i
$919$			34.5061i			1.13825i	0.822250	+	0.569126i	$0.192718\pi$
$919$			34.5061i			1.13825i	−0.822250	+	0.569126i	$0.807282\pi$
$920$	1.69367	+	0.388021i	0.0558386	+	0.0127927i
$921$	20.6118	+	21.6339i	0.679182	+	0.712860i
$922$	24.0840	+	10.8750i	0.793166	+	0.358149i
$923$	−15.6331	−	27.0773i	−0.514568	−	0.891259i
$924$	0.431172	−	4.93979i	0.0141845	−	0.162507i
$925$	11.0963	−	19.2194i	0.364844	−	0.631928i
$926$	6.23691	−	4.48147i	0.204958	−	0.147270i
$927$	−9.33319	−	18.1385i	−0.306542	−	0.595746i
$928$	−3.84751	−	0.101177i	−0.126301	−	0.00332129i
$929$	−12.8251	−	7.40460i	−0.420779	−	0.242937i	0.274631	−	0.961550i	$-0.411444\pi$
$929$	−12.8251	−	7.40460i	−0.420779	−	0.242937i	−0.695411	+	0.718612i	$0.744778\pi$
$930$	4.05499	+	11.5709i	0.132968	+	0.379426i
$931$	36.5303	−	21.0908i	1.19723	−	0.691222i
$932$	−1.13311	−	5.62090i	−0.0371163	−	0.184119i
$933$	6.04240	+	1.77676i	0.197819	+	0.0581685i
$934$	−47.7168	+	4.76170i	−1.56134	+	0.155808i
$935$	−4.02260			−0.131553
$936$	−15.4392	+	15.0794i	−0.504648	+	0.492884i
$937$	10.2099			0.333544			0.166772	−	0.985995i	$-0.446666\pi$
$937$	10.2099			0.333544			0.166772	+	0.985995i	$0.446666\pi$
$938$	19.9913	−	1.99495i	0.652740	−	0.0651375i
$939$	1.63100	+	6.73448i	0.0532255	+	0.219771i
$940$	−3.15877	−	15.6693i	−0.103028	−	0.511078i
$941$	−24.5910	+	14.1976i	−0.801643	+	0.462829i	−0.844045	−	0.536272i	$-0.819832\pi$
$941$	−24.5910	+	14.1976i	−0.801643	+	0.462829i	0.0424023	+	0.999101i	$0.486499\pi$
$942$	5.71248	+	1.07806i	0.186123	+	0.0351251i
$943$	0.393650	+	0.227274i	0.0128190	+	0.00740105i
$944$	−3.89168	−	2.95449i	−0.126663	−	0.0961604i
$945$	−2.57964	−	2.98409i	−0.0839158	−	0.0970724i
$946$	3.92863	−	2.82288i	0.127731	−	0.0917796i
$947$	−27.6267	+	47.8508i	−0.897747	+	1.55494i	−0.0673795	+	0.997727i	$0.521464\pi$
$947$	−27.6267	+	47.8508i	−0.897747	+	1.55494i	−0.830368	+	0.557216i	$0.811870\pi$
$948$	10.5298	−	4.91270i	0.341991	−	0.159557i
$949$	−17.3713	−	30.0880i	−0.563897	−	0.976698i
$950$	45.9205	+	20.7351i	1.48986	+	0.672737i
$951$	−28.5601	+	6.91685i	−0.926124	+	0.224294i
$952$	−4.41219	+	19.2588i	−0.143000	+	0.624180i
$953$			25.4714i			0.825099i	0.910935	+	0.412549i	$0.135362\pi$
$953$			25.4714i			0.825099i	−0.910935	+	0.412549i	$0.864638\pi$
$954$	−30.2421	+	1.54624i	−0.979125	+	0.0500615i
$955$			4.46995i			0.144644i
$956$	25.3926	+	28.8048i	0.821254	+	0.931613i
$957$	0.385098	−	1.30964i	0.0124485	−	0.0423347i
$958$	−5.37936	+	11.9133i	−0.173799	+	0.384900i
$959$	0.961369	+	1.66514i	0.0310442	+	0.0537701i
$960$	−2.60306	−	8.10444i	−0.0840134	−	0.261570i
$961$	17.6955	−	30.6495i	0.570822	−	0.988693i
$962$	10.0764	+	14.0235i	0.324878	+	0.452136i
$963$	−1.91142	+	39.4799i	−0.0615947	+	1.27222i
$964$	12.3766	−	36.7710i	0.398624	−	1.18431i
$965$	−5.74554	−	3.31719i	−0.184956	−	0.106784i
$966$	2.29523	+	1.97332i	0.0738480	+	0.0634905i
$967$	−26.4952	+	15.2970i	−0.852029	+	0.491919i	−0.861335	−	0.508038i	$-0.830371\pi$
$967$	−26.4952	+	15.2970i	−0.852029	+	0.491919i	0.00930620	+	0.999957i	$0.497038\pi$
$968$	−20.0100	−	18.5969i	−0.643146	−	0.597728i
$969$	−54.6347	+	52.0536i	−1.75512	+	1.67220i
$970$	0.486767	+	4.87787i	0.0156292	+	0.156619i
$971$	16.7422			0.537283			0.268642	−	0.963240i	$-0.413425\pi$
$971$	16.7422			0.537283			0.268642	+	0.963240i	$0.413425\pi$
$972$	20.2611	−	23.6958i	0.649874	−	0.760042i
$973$	5.65524			0.181299
$974$	5.08471	+	50.9536i	0.162925	+	1.63266i
$975$	14.7435	−	14.0470i	0.472171	−	0.449864i
$976$	2.62512	−	20.7652i	0.0840282	−	0.664678i
$977$	37.7214	−	21.7785i	1.20681	−	0.696754i	0.244752	−	0.969586i	$-0.421293\pi$
$977$	37.7214	−	21.7785i	1.20681	−	0.696754i	0.962062	+	0.272831i	$0.0879601\pi$
$978$	−27.0543	−	23.2599i	−0.865102	−	0.743769i
$979$	−17.7581	−	10.2526i	−0.567551	−	0.327676i
$980$	6.37297	+	2.14506i	0.203577	+	0.0685213i
$981$	−0.124817	+	2.57806i	−0.00398510	+	0.0823111i
$982$	−3.34491	−	4.65515i	−0.106740	−	0.148552i
$983$	−14.4268	+	24.9880i	−0.460144	+	0.796993i	−0.998968	−	0.0454259i	$-0.985535\pi$
$983$	−14.4268	+	24.9880i	−0.460144	+	0.796993i	0.538824	+	0.842418i	$0.318869\pi$
$984$	−0.0276048	−	2.22665i	−0.000880009	−	0.0709830i
$985$	−6.88868	−	11.9315i	−0.219491	−	0.380170i
$986$	−2.23844	+	4.95731i	−0.0712866	+	0.157873i
$987$	7.85548	−	26.7149i	0.250043	−	0.850344i
$988$	−29.4093	+	25.9254i	−0.935633	+	0.824798i
$989$			2.95308i			0.0939023i
$990$	3.01513	−	0.154160i	0.0958270	−	0.00489952i
$991$		−	30.4371i		−	0.966866i	−0.875381	−	0.483433i	$-0.839390\pi$
$991$		−	30.4371i		−	0.966866i	0.875381	−	0.483433i	$-0.160610\pi$
$992$	−24.0876	+	39.2976i	−0.764781	+	1.24770i
$993$	−50.5692	+	12.2471i	−1.60476	+	0.388651i
$994$	19.5796	+	8.84104i	0.621026	+	0.280421i
$995$	−2.60962	−	4.52000i	−0.0827307	−	0.143294i
$996$	−8.68707	−	18.6197i	−0.275260	−	0.589987i
$997$	21.6718	−	37.5367i	0.686354	−	1.18880i	−0.286655	−	0.958034i	$-0.592543\pi$
$997$	21.6718	−	37.5367i	0.686354	−	1.18880i	0.973009	−	0.230766i	$-0.0741232\pi$
$998$	−7.68429	+	5.52146i	−0.243242	+	0.174779i
$999$	−16.3142	−	18.8720i	−0.516159	−	0.597084i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	828.2.o.a.47.2	✓	132
4.3	odd	2		828.2.o.b.47.25	yes	132
9.5	odd	6		828.2.o.b.599.25	yes	132
36.23	even	6	inner	828.2.o.a.599.2	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
828.2.o.a.47.2	✓	132	1.1	even	1	trivial
828.2.o.a.599.2	yes	132	36.23	even	6	inner
828.2.o.b.47.25	yes	132	4.3	odd	2
828.2.o.b.599.25	yes	132	9.5	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:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40722 + 0.140428i) q^{2} +(-1.25401 + 1.19476i) q^{3} +(1.96056 - 0.395228i) q^{4} +(-0.532014 + 0.307158i) q^{5} +(1.59689 - 1.85740i) q^{6} +(1.07017 + 0.617862i) q^{7} +(-2.70345 + 0.831492i) q^{8} +(0.145075 - 2.99649i) q^{9} +O(q^{10})\)	\(q+(-1.40722 + 0.140428i) q^{2} +(-1.25401 + 1.19476i) q^{3} +(1.96056 - 0.395228i) q^{4} +(-0.532014 + 0.307158i) q^{5} +(1.59689 - 1.85740i) q^{6} +(1.07017 + 0.617862i) q^{7} +(-2.70345 + 0.831492i) q^{8} +(0.145075 - 2.99649i) q^{9} +(0.705529 - 0.506950i) q^{10} +(-0.579181 + 1.00317i) q^{11} +(-1.98635 + 2.83803i) q^{12} +(1.27170 + 2.20264i) q^{13} +(-1.59273 - 0.719189i) q^{14} +(0.300168 - 1.02081i) q^{15} +(3.68759 - 1.54974i) q^{16} -5.65288i q^{17} +(0.216638 + 4.23711i) q^{18} +7.70722i q^{19} +(-0.921647 + 0.812469i) q^{20} +(-2.08020 + 0.503795i) q^{21} +(0.674164 - 1.49302i) q^{22} +(0.500000 + 0.866025i) q^{23} +(2.39671 - 4.27268i) q^{24} +(-2.31131 + 4.00330i) q^{25} +(-2.09888 - 2.92103i) q^{26} +(3.39817 + 3.93096i) q^{27} +(2.34233 + 0.788395i) q^{28} +(0.589231 + 0.340193i) q^{29} +(-0.279053 + 1.47866i) q^{30} +(7.05643 - 4.07403i) q^{31} +(-4.97164 + 2.69867i) q^{32} +(-0.472255 - 1.94997i) q^{33} +(0.793824 + 7.95488i) q^{34} -0.759126 q^{35} +(-0.899867 - 5.93214i) q^{36} -4.80087 q^{37} +(-1.08231 - 10.8458i) q^{38} +(-4.22636 - 1.24276i) q^{39} +(1.18287 - 1.27275i) q^{40} +(0.393650 - 0.227274i) q^{41} +(2.85656 - 1.00107i) q^{42} +(2.55744 + 1.47654i) q^{43} +(-0.739038 + 2.19569i) q^{44} +(0.843214 + 1.63873i) q^{45} +(-0.825226 - 1.14848i) q^{46} +(-6.50502 + 11.2670i) q^{47} +(-2.77270 + 6.34918i) q^{48} +(-2.73649 - 4.73974i) q^{49} +(2.69035 - 5.95812i) q^{50} +(6.75387 + 7.08877i) q^{51} +(3.36378 + 3.81581i) q^{52} +7.13745i q^{53} +(-5.33401 - 5.05454i) q^{54} -0.711601i q^{55} +(-3.40689 - 0.780520i) q^{56} +(-9.20832 - 9.66493i) q^{57} +(-0.876953 - 0.395983i) q^{58} +(-0.610765 - 1.05788i) q^{59} +(0.185045 - 2.11999i) q^{60} +(2.61631 - 4.53158i) q^{61} +(-9.35787 + 6.72400i) q^{62} +(2.00667 - 3.11711i) q^{63} +(6.61724 - 4.49579i) q^{64} +(-1.35312 - 0.781224i) q^{65} +(0.938399 + 2.67773i) q^{66} +(-9.95606 + 5.74813i) q^{67} +(-2.23418 - 11.0828i) q^{68} +(-1.66170 - 0.488621i) q^{69} +(1.06826 - 0.106603i) q^{70} -12.2931 q^{71} +(2.09935 + 8.22148i) q^{72} -13.6599 q^{73} +(6.75591 - 0.674178i) q^{74} +(-1.88460 - 7.78164i) q^{75} +(3.04611 + 15.1105i) q^{76} +(-1.23964 + 0.715708i) q^{77} +(6.12195 + 1.15534i) q^{78} +(-2.90485 - 1.67712i) q^{79} +(-1.48583 + 1.95715i) q^{80} +(-8.95791 - 0.869434i) q^{81} +(-0.522038 + 0.375105i) q^{82} +(-2.96563 + 5.13662i) q^{83} +(-3.87924 + 1.80987i) q^{84} +(1.73633 + 3.00741i) q^{85} +(-3.80624 - 1.71868i) q^{86} +(-1.14535 + 0.277388i) q^{87} +(0.731656 - 3.19360i) q^{88} +17.7020i q^{89} +(-1.41672 - 2.18766i) q^{90} +3.14293i q^{91} +(1.32256 + 1.50028i) q^{92} +(-3.98132 + 13.5396i) q^{93} +(7.57182 - 16.7687i) q^{94} +(-2.36734 - 4.10035i) q^{95} +(3.01021 - 9.32409i) q^{96} +(-2.82127 + 4.88659i) q^{97} +(4.51645 + 6.28560i) q^{98} +(2.92197 + 1.88105i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 9 q^{8} + 2 q^{9}+O(q^{10}) \) 132 * q - 9 * q^8 + 2 * q^9	\( 132 q - 9 q^{8} + 2 q^{9} - 29 q^{12} - 15 q^{14} - 34 q^{18} - 21 q^{20} + 66 q^{23} + 15 q^{24} + 66 q^{25} - 54 q^{26} + 12 q^{27} + 77 q^{30} + 30 q^{32} - 22 q^{33} + 36 q^{36} - 24 q^{39} - 30 q^{41} - 11 q^{42} - 65 q^{48} + 66 q^{49} - 32 q^{51} - 64 q^{54} - 42 q^{56} - 6 q^{57} + 27 q^{58} + 36 q^{59} + 58 q^{60} + 63 q^{62} - 20 q^{63} - 9 q^{64} + 78 q^{66} - 15 q^{68} - 78 q^{70} + 36 q^{72} - 12 q^{73} - 21 q^{74} + 48 q^{75} - 87 q^{76} - 11 q^{78} + 72 q^{80} - 10 q^{81} - 9 q^{82} - 157 q^{84} - 24 q^{86} + 96 q^{87} + 108 q^{88} - 63 q^{90} - 12 q^{93} + 75 q^{94} - 9 q^{96} - 6 q^{97} + 20 q^{99}+O(q^{100}) \) 132 * q - 9 * q^8 + 2 * q^9 - 29 * q^12 - 15 * q^14 - 34 * q^18 - 21 * q^20 + 66 * q^23 + 15 * q^24 + 66 * q^25 - 54 * q^26 + 12 * q^27 + 77 * q^30 + 30 * q^32 - 22 * q^33 + 36 * q^36 - 24 * q^39 - 30 * q^41 - 11 * q^42 - 65 * q^48 + 66 * q^49 - 32 * q^51 - 64 * q^54 - 42 * q^56 - 6 * q^57 + 27 * q^58 + 36 * q^59 + 58 * q^60 + 63 * q^62 - 20 * q^63 - 9 * q^64 + 78 * q^66 - 15 * q^68 - 78 * q^70 + 36 * q^72 - 12 * q^73 - 21 * q^74 + 48 * q^75 - 87 * q^76 - 11 * q^78 + 72 * q^80 - 10 * q^81 - 9 * q^82 - 157 * q^84 - 24 * q^86 + 96 * q^87 + 108 * q^88 - 63 * q^90 - 12 * q^93 + 75 * q^94 - 9 * q^96 - 6 * q^97 + 20 * q^99

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