LMFDB - Embedded newform 462.2.y.d.235.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(25,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 24]))

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

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

chi := DirichletCharacter("462.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.y (of order $15$, degree $8$, 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:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			235.5
Character	$\chi$	$=$	462.235
Dual form			462.2.y.d.289.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104528 + 0.994522i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(2.67304 + 1.19011i) q^{5} +(0.809017 - 0.587785i) q^{6} +(2.49497 - 0.880407i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.104528 + 0.994522i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(2.67304 + 1.19011i) q^{5} +(0.809017 - 0.587785i) q^{6} +(2.49497 - 0.880407i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-1.46300 + 2.53399i) q^{10} +(-2.53399 - 2.13983i) q^{11} +(0.500000 + 0.866025i) q^{12} +(0.928329 + 0.674471i) q^{13} +(0.614789 + 2.57333i) q^{14} +(-0.904185 - 2.78280i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.159431 - 1.51689i) q^{17} +(-0.978148 - 0.207912i) q^{18} +(6.45904 - 1.37291i) q^{19} +(-2.36719 - 1.71986i) q^{20} +(-2.32373 - 1.26502i) q^{21} +(2.39298 - 2.29644i) q^{22} +(0.745007 + 1.29039i) q^{23} +(-0.913545 + 0.406737i) q^{24} +(2.38311 + 2.64671i) q^{25} +(-0.767813 + 0.852742i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-2.62350 + 0.342434i) q^{28} +(1.65246 + 5.08576i) q^{29} +(2.86206 - 0.608351i) q^{30} +(2.86210 - 1.27429i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.105370 + 3.31495i) q^{33} +1.52524 q^{34} +(7.71694 + 0.615937i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-2.53001 + 2.80986i) q^{37} +(0.690237 + 6.56717i) q^{38} +(-0.119944 - 1.14119i) q^{39} +(1.95788 - 2.17445i) q^{40} +(-3.65165 + 11.2386i) q^{41} +(1.50098 - 2.17877i) q^{42} +4.19680 q^{43} +(2.03372 + 2.61992i) q^{44} +(-1.46300 + 2.53399i) q^{45} +(-1.36120 + 0.606044i) q^{46} +(0.802005 - 0.170472i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(5.44977 - 4.39318i) q^{49} +(-2.88132 + 2.09340i) q^{50} +(-1.02059 + 1.13348i) q^{51} +(-0.767813 - 0.852742i) q^{52} +(11.3203 - 5.04011i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-4.22682 - 8.73559i) q^{55} +(-0.0663284 - 2.64492i) q^{56} +(-5.34222 - 3.88135i) q^{57} +(-5.23063 + 1.11180i) q^{58} +(-13.1746 - 2.80035i) q^{59} +(0.305851 + 2.90998i) q^{60} +(-9.69956 - 4.31852i) q^{61} +(0.968136 + 2.97962i) q^{62} +(0.614789 + 2.57333i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.67876 + 2.90770i) q^{65} +(-3.30781 - 0.241714i) q^{66} +(0.555115 - 0.961487i) q^{67} +(-0.159431 + 1.51689i) q^{68} +(0.460440 - 1.41709i) q^{69} +(-1.41920 + 7.61028i) q^{70} +(4.46737 - 3.24574i) q^{71} +(0.913545 + 0.406737i) q^{72} +(-9.18293 - 1.95189i) q^{73} +(-2.53001 - 2.80986i) q^{74} +(0.372279 - 3.54199i) q^{75} -6.60334 q^{76} +(-8.20617 - 3.10787i) q^{77} +1.14748 q^{78} +(1.04094 - 9.90391i) q^{79} +(1.95788 + 2.17445i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-10.7954 - 4.80641i) q^{82} +(-10.8334 + 7.87096i) q^{83} +(2.00994 + 1.72051i) q^{84} +(1.37910 - 4.24444i) q^{85} +(-0.438686 + 4.17381i) q^{86} +(2.67374 - 4.63106i) q^{87} +(-2.81815 + 1.74873i) q^{88} +(1.58224 + 2.74052i) q^{89} +(-2.36719 - 1.71986i) q^{90} +(2.90996 + 0.865477i) q^{91} +(-0.460440 - 1.41709i) q^{92} +(-2.86210 - 1.27429i) q^{93} +(0.0857053 + 0.815431i) q^{94} +(18.8992 + 4.01715i) q^{95} +(0.978148 - 0.207912i) q^{96} +(-6.96423 - 5.05981i) q^{97} +(3.79946 + 5.87912i) q^{98} +(2.39298 - 2.29644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9}+O(q^{10}) $ 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 20 q^{12} + 10 q^{13} + 5 q^{14} - 6 q^{15} + 5 q^{16} + 5 q^{18} - 13 q^{19} + 6 q^{20} - 2 q^{21} - 4 q^{22} - 20 q^{23} - 5 q^{24} + 12 q^{25} + 10 q^{27} - 3 q^{28} + 12 q^{29} + 3 q^{30} - 10 q^{31} - 20 q^{32} + 8 q^{33} - 13 q^{35} - 10 q^{36} + 3 q^{37} + 2 q^{38} + 5 q^{39} - 3 q^{40} - 44 q^{41} - 3 q^{42} + 36 q^{43} - 3 q^{44} + 12 q^{45} + 11 q^{47} + 10 q^{48} + 33 q^{49} - 4 q^{50} + 26 q^{53} + 20 q^{54} - 20 q^{55} + 8 q^{56} + 4 q^{57} - 6 q^{58} + 4 q^{59} + 3 q^{60} - 23 q^{61} + 5 q^{63} - 10 q^{64} - 50 q^{65} - 7 q^{66} - 108 q^{67} + 20 q^{69} - 86 q^{71} + 5 q^{72} - 35 q^{73} + 3 q^{74} - 2 q^{75} - 44 q^{76} - 37 q^{77} + 20 q^{78} + 3 q^{79} - 3 q^{80} + 5 q^{81} - 28 q^{82} - 88 q^{83} - 5 q^{84} + 96 q^{85} - 13 q^{86} + 6 q^{87} - 8 q^{88} + 6 q^{89} + 6 q^{90} + 40 q^{91} - 20 q^{92} + 10 q^{93} - 24 q^{94} + 36 q^{95} - 5 q^{96} + 60 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 20 * q^12 + 10 * q^13 + 5 * q^14 - 6 * q^15 + 5 * q^16 + 5 * q^18 - 13 * q^19 + 6 * q^20 - 2 * q^21 - 4 * q^22 - 20 * q^23 - 5 * q^24 + 12 * q^25 + 10 * q^27 - 3 * q^28 + 12 * q^29 + 3 * q^30 - 10 * q^31 - 20 * q^32 + 8 * q^33 - 13 * q^35 - 10 * q^36 + 3 * q^37 + 2 * q^38 + 5 * q^39 - 3 * q^40 - 44 * q^41 - 3 * q^42 + 36 * q^43 - 3 * q^44 + 12 * q^45 + 11 * q^47 + 10 * q^48 + 33 * q^49 - 4 * q^50 + 26 * q^53 + 20 * q^54 - 20 * q^55 + 8 * q^56 + 4 * q^57 - 6 * q^58 + 4 * q^59 + 3 * q^60 - 23 * q^61 + 5 * q^63 - 10 * q^64 - 50 * q^65 - 7 * q^66 - 108 * q^67 + 20 * q^69 - 86 * q^71 + 5 * q^72 - 35 * q^73 + 3 * q^74 - 2 * q^75 - 44 * q^76 - 37 * q^77 + 20 * q^78 + 3 * q^79 - 3 * q^80 + 5 * q^81 - 28 * q^82 - 88 * q^83 - 5 * q^84 + 96 * q^85 - 13 * q^86 + 6 * q^87 - 8 * q^88 + 6 * q^89 + 6 * q^90 + 40 * q^91 - 20 * q^92 + 10 * q^93 - 24 * q^94 + 36 * q^95 - 5 * q^96 + 60 * q^97 + 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$3$	−0.669131	−	0.743145i	−0.386323	−	0.429055i
$3$	−0.669131	−	0.743145i	−0.386323	−	0.429055i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	2.67304	+	1.19011i	1.19542	+	0.532235i	0.905307	−	0.424758i	$-0.139641\pi$
$5$	2.67304	+	1.19011i	1.19542	+	0.532235i	0.290112	+	0.956993i	$0.406307\pi$
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$	2.49497	−	0.880407i	0.943011	−	0.332763i
$7$	2.49497	−	0.880407i	0.943011	−	0.332763i
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.104528	+	0.994522i	−0.0348428	+	0.331507i
$10$	−1.46300	+	2.53399i	−0.462642	+	0.801319i
$11$	−2.53399	−	2.13983i	−0.764028	−	0.645183i
$11$	−2.53399	−	2.13983i	−0.764028	−	0.645183i
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	0.928329	+	0.674471i	0.257472	+	0.187064i	0.709032	−	0.705176i	$-0.249132\pi$
$13$	0.928329	+	0.674471i	0.257472	+	0.187064i	−0.451560	+	0.892241i	$0.649132\pi$
$14$	0.614789	+	2.57333i	0.164309	+	0.687752i
$15$	−0.904185	−	2.78280i	−0.233460	−	0.718515i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	−0.159431	−	1.51689i	−0.0386678	−	0.367900i	−0.996696	−	0.0812249i	$-0.974117\pi$
$17$	−0.159431	−	1.51689i	−0.0386678	−	0.367900i	0.958028	−	0.286675i	$-0.0925499\pi$
$18$	−0.978148	−	0.207912i	−0.230552	−	0.0490053i
$19$	6.45904	−	1.37291i	1.48181	−	0.314968i	0.605160	−	0.796104i	$-0.293109\pi$
$19$	6.45904	−	1.37291i	1.48181	−	0.314968i	0.876646	+	0.481136i	$0.159776\pi$
$20$	−2.36719	−	1.71986i	−0.529319	−	0.384573i
$21$	−2.32373	−	1.26502i	−0.507080	−	0.276050i
$22$	2.39298	−	2.29644i	0.510186	−	0.489603i
$23$	0.745007	+	1.29039i	0.155345	+	0.269065i	0.933185	−	0.359398i	$-0.117018\pi$
$23$	0.745007	+	1.29039i	0.155345	+	0.269065i	−0.777840	+	0.628463i	$0.783684\pi$
$24$	−0.913545	+	0.406737i	−0.186477	+	0.0830248i
$25$	2.38311	+	2.64671i	0.476622	+	0.529343i
$26$	−0.767813	+	0.852742i	−0.150580	+	0.167237i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−2.62350	+	0.342434i	−0.495794	+	0.0647140i
$29$	1.65246	+	5.08576i	0.306855	+	0.944402i	0.978979	+	0.203963i	$0.0653823\pi$
$29$	1.65246	+	5.08576i	0.306855	+	0.944402i	−0.672124	+	0.740439i	$0.734618\pi$
$30$	2.86206	−	0.608351i	0.522539	−	0.111069i
$31$	2.86210	−	1.27429i	0.514048	−	0.228869i	−0.133283	−	0.991078i	$-0.542552\pi$
$31$	2.86210	−	1.27429i	0.514048	−	0.228869i	0.647331	+	0.762209i	$0.275885\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.105370	+	3.31495i	0.0183425	+	0.577059i
$34$	1.52524			0.261577
$35$	7.71694	+	0.615937i	1.30440	+	0.104112i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	−2.53001	+	2.80986i	−0.415931	+	0.461938i	−0.914306	−	0.405023i	$-0.867263\pi$
$37$	−2.53001	+	2.80986i	−0.415931	+	0.461938i	0.498375	+	0.866961i	$0.333930\pi$
$38$	0.690237	+	6.56717i	0.111971	+	1.06534i
$39$	−0.119944	−	1.14119i	−0.0192064	−	0.182737i
$40$	1.95788	−	2.17445i	0.309568	−	0.343810i
$41$	−3.65165	+	11.2386i	−0.570293	+	1.75518i	0.0813833	+	0.996683i	$0.474066\pi$
$41$	−3.65165	+	11.2386i	−0.570293	+	1.75518i	−0.651676	+	0.758498i	$0.725934\pi$
$42$	1.50098	−	2.17877i	0.231607	−	0.336192i
$43$	4.19680			0.640007			0.320003	−	0.947416i	$-0.396316\pi$
$43$	4.19680			0.640007			0.320003	+	0.947416i	$0.396316\pi$
$44$	2.03372	+	2.61992i	0.306596	+	0.394967i
$45$	−1.46300	+	2.53399i	−0.218092	+	0.377746i
$46$	−1.36120	+	0.606044i	−0.200697	+	0.0893562i
$47$	0.802005	−	0.170472i	0.116985	−	0.0248658i	−0.149047	−	0.988830i	$-0.547621\pi$
$47$	0.802005	−	0.170472i	0.116985	−	0.0248658i	0.266032	+	0.963964i	$0.414287\pi$
$48$	−0.309017	−	0.951057i	−0.0446028	−	0.137273i
$49$	5.44977	−	4.39318i	0.778538	−	0.627597i
$50$	−2.88132	+	2.09340i	−0.407480	+	0.296051i
$51$	−1.02059	+	1.13348i	−0.142911	+	0.158719i
$52$	−0.767813	−	0.852742i	−0.106476	−	0.118254i
$53$	11.3203	−	5.04011i	1.55496	−	0.692313i	0.563914	−	0.825833i	$-0.309295\pi$
$53$	11.3203	−	5.04011i	1.55496	−	0.692313i	0.991046	+	0.133520i	$0.0426282\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−4.22682	−	8.73559i	−0.569945	−	1.17791i
$56$	−0.0663284	−	2.64492i	−0.00886351	−	0.353442i
$57$	−5.34222	−	3.88135i	−0.707594	−	0.514097i
$58$	−5.23063	+	1.11180i	−0.686815	+	0.145987i
$59$	−13.1746	−	2.80035i	−1.71519	−	0.364574i	−0.757601	−	0.652719i	$-0.773628\pi$
$59$	−13.1746	−	2.80035i	−1.71519	−	0.364574i	−0.957587	+	0.288144i	$0.906962\pi$
$60$	0.305851	+	2.90998i	0.0394852	+	0.375676i
$61$	−9.69956	−	4.31852i	−1.24190	−	0.552930i	−0.322619	−	0.946529i	$-0.604563\pi$
$61$	−9.69956	−	4.31852i	−1.24190	−	0.552930i	−0.919282	+	0.393599i	$0.871230\pi$
$62$	0.968136	+	2.97962i	0.122953	+	0.378412i
$63$	0.614789	+	2.57333i	0.0774561	+	0.324209i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	1.67876	+	2.90770i	0.208225	+	0.360656i
$66$	−3.30781	−	0.241714i	−0.407163	−	0.0297530i
$67$	0.555115	−	0.961487i	0.0678181	−	0.117464i	−0.830123	−	0.557581i	$-0.811730\pi$
$67$	0.555115	−	0.961487i	0.0678181	−	0.117464i	0.897941	+	0.440117i	$0.145063\pi$
$68$	−0.159431	+	1.51689i	−0.0193339	+	0.183950i
$69$	0.460440	−	1.41709i	0.0554304	−	0.170597i
$70$	−1.41920	+	7.61028i	−0.169627	+	0.909603i
$71$	4.46737	−	3.24574i	0.530180	−	0.385198i	−0.290245	−	0.956952i	$-0.593737\pi$
$71$	4.46737	−	3.24574i	0.530180	−	0.385198i	0.820425	+	0.571754i	$0.193737\pi$
$72$	0.913545	+	0.406737i	0.107662	+	0.0479344i
$73$	−9.18293	−	1.95189i	−1.07478	−	0.228452i	−0.363667	−	0.931529i	$-0.618475\pi$
$73$	−9.18293	−	1.95189i	−1.07478	−	0.228452i	−0.711113	+	0.703077i	$0.751809\pi$
$74$	−2.53001	−	2.80986i	−0.294108	−	0.326640i
$75$	0.372279	−	3.54199i	0.0429870	−	0.408994i
$76$	−6.60334			−0.757455
$77$	−8.20617	−	3.10787i	−0.935179	−	0.354174i
$78$	1.14748			0.129926
$79$	1.04094	−	9.90391i	0.117115	−	1.11428i	−0.765257	−	0.643725i	$-0.777388\pi$
$79$	1.04094	−	9.90391i	0.117115	−	1.11428i	0.882372	−	0.470552i	$-0.155945\pi$
$80$	1.95788	+	2.17445i	0.218898	+	0.243110i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	−10.7954	−	4.80641i	−1.19215	−	0.530779i
$83$	−10.8334	+	7.87096i	−1.18912	+	0.863950i	−0.993171	−	0.116664i	$-0.962780\pi$
$83$	−10.8334	+	7.87096i	−1.18912	+	0.863950i	−0.195953	+	0.980613i	$0.562780\pi$
$84$	2.00994	+	1.72051i	0.219303	+	0.187722i
$85$	1.37910	−	4.24444i	0.149585	−	0.460374i
$86$	−0.438686	+	4.17381i	−0.0473047	+	0.450074i
$87$	2.67374	−	4.63106i	0.286655	−	0.496501i
$88$	−2.81815	+	1.74873i	−0.300415	+	0.186415i
$89$	1.58224	+	2.74052i	0.167717	+	0.290495i	0.937617	−	0.347670i	$-0.113027\pi$
$89$	1.58224	+	2.74052i	0.167717	+	0.290495i	−0.769900	+	0.638165i	$0.779694\pi$
$90$	−2.36719	−	1.71986i	−0.249523	−	0.181289i
$91$	2.90996	+	0.865477i	0.305047	+	0.0907267i
$92$	−0.460440	−	1.41709i	−0.0480042	−	0.147742i
$93$	−2.86210	−	1.27429i	−0.296786	−	0.132137i
$94$	0.0857053	+	0.815431i	0.00883982	+	0.0841053i
$95$	18.8992	+	4.01715i	1.93902	+	0.412151i
$96$	0.978148	−	0.207912i	0.0998318	−	0.0212199i
$97$	−6.96423	−	5.05981i	−0.707110	−	0.513746i	0.175130	−	0.984545i	$-0.443965\pi$
$97$	−6.96423	−	5.05981i	−0.707110	−	0.513746i	−0.882240	+	0.470800i	$0.843965\pi$
$98$	3.79946	+	5.87912i	0.383803	+	0.593881i
$99$	2.39298	−	2.29644i	0.240504	−	0.230801i
$100$	−1.78075	−	3.08435i	−0.178075	−	0.308435i
$101$	−7.59586	+	3.38189i	−0.755816	+	0.336511i	−0.748212	−	0.663460i	$-0.769087\pi$
$101$	−7.59586	+	3.38189i	−0.755816	+	0.336511i	−0.00760449	+	0.999971i	$0.502421\pi$
$102$	−1.02059	−	1.13348i	−0.101053	−	0.112231i
$103$	6.79195	−	7.54322i	0.669230	−	0.743256i	−0.308935	−	0.951083i	$-0.599973\pi$
$103$	6.79195	−	7.54322i	0.669230	−	0.743256i	0.978165	+	0.207828i	$0.0666393\pi$
$104$	0.928329	−	0.674471i	0.0910302	−	0.0661373i
$105$	−4.70591	−	6.14695i	−0.459250	−	0.599880i
$106$	3.82921	+	11.7851i	0.371926	+	1.14467i
$107$	−19.4221	+	4.12830i	−1.87761	+	0.399098i	−0.997178	−	0.0750780i	$-0.976079\pi$
$107$	−19.4221	+	4.12830i	−1.87761	+	0.399098i	−0.880430	+	0.474176i	$0.842746\pi$
$108$	−0.913545	+	0.406737i	−0.0879060	+	0.0391383i
$109$	−1.27817	+	2.21385i	−0.122426	+	0.212049i	−0.920724	−	0.390214i	$-0.872401\pi$
$109$	−1.27817	+	2.21385i	−0.122426	+	0.212049i	0.798298	+	0.602263i	$0.205734\pi$
$110$	9.12956	−	3.29055i	0.870469	−	0.313742i
$111$	3.78104			0.358880
$112$	2.63736	+	0.210504i	0.249207	+	0.0198908i
$113$	−2.37818	+	7.31928i	−0.223720	+	0.688540i	0.774699	+	0.632330i	$0.217902\pi$
$113$	−2.37818	+	7.31928i	−0.223720	+	0.688540i	−0.998419	+	0.0562096i	$0.982098\pi$
$114$	4.41850	−	4.90724i	0.413830	−	0.459605i
$115$	0.455722	+	4.33591i	0.0424963	+	0.404325i
$116$	−0.558964	−	5.31819i	−0.0518985	−	0.493782i
$117$	−0.767813	+	0.852742i	−0.0709843	+	0.0788360i
$118$	4.16213	−	12.8097i	0.383155	−	1.17923i
$119$	−1.73326	−	3.64423i	−0.158887	−	0.334066i
$120$	−2.92600			−0.267106
$121$	1.84226	+	10.8446i	0.167478	+	0.985876i
$122$	5.30875	−	9.19502i	0.480631	−	0.832478i
$123$	10.7954	−	4.80641i	0.973386	−	0.433379i
$124$	−3.06449	+	0.651378i	−0.275200	+	0.0584955i
$125$	−1.30067	−	4.00304i	−0.116335	−	0.358043i
$126$	−2.62350	+	0.342434i	−0.233720	+	0.0305065i
$127$	−6.29225	+	4.57159i	−0.558347	+	0.405663i	−0.830854	−	0.556491i	$-0.812147\pi$
$127$	−6.29225	+	4.57159i	−0.558347	+	0.405663i	0.272506	+	0.962154i	$0.412147\pi$
$128$	0.669131	−	0.743145i	0.0591433	−	0.0656853i
$129$	−2.80821	−	3.11883i	−0.247249	−	0.274598i
$130$	−3.06725	+	1.36563i	−0.269016	+	0.119774i
$131$	3.70491	+	6.41710i	0.323700	+	0.560665i	0.981248	−	0.192748i	$-0.0617399\pi$
$131$	3.70491	+	6.41710i	0.323700	+	0.560665i	−0.657549	+	0.753412i	$0.728407\pi$
$132$	0.586150	−	3.26442i	0.0510178	−	0.284131i
$133$	14.9064	−	9.11196i	1.29255	−	0.790107i
$134$	0.898195	+	0.652577i	0.0775922	+	0.0563740i
$135$	2.86206	−	0.608351i	0.246327	−	0.0523585i
$136$	−1.49191	−	0.317116i	−0.127931	−	0.0271925i
$137$	−1.25862	−	11.9749i	−0.107531	−	1.02309i	−0.906641	−	0.421903i	$-0.861362\pi$
$137$	−1.25862	−	11.9749i	−0.107531	−	1.02309i	0.799110	−	0.601185i	$-0.205305\pi$
$138$	1.36120	+	0.606044i	0.115873	+	0.0515899i
$139$	−4.74196	−	14.5943i	−0.402208	−	1.23787i	−0.923204	−	0.384310i	$-0.874440\pi$
$139$	−4.74196	−	14.5943i	−0.402208	−	1.23787i	0.520996	−	0.853559i	$-0.325560\pi$
$140$	−7.42024	−	2.20692i	−0.627125	−	0.186519i
$141$	−0.663331	−	0.481938i	−0.0558626	−	0.0405865i
$142$	2.76099	+	4.78217i	0.231697	+	0.401311i
$143$	−0.909128	−	3.69557i	−0.0760251	−	0.309039i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−1.63553	+	15.5610i	−0.135824	+	1.29227i
$146$	2.90108	−	8.92859i	0.240095	−	0.738936i
$147$	−6.91138	−	1.11035i	−0.570041	−	0.0915804i
$148$	3.05893	−	2.22244i	0.251442	−	0.182683i
$149$	−6.74481	−	3.00298i	−0.552557	−	0.246014i	0.111412	−	0.993774i	$-0.464463\pi$
$149$	−6.74481	−	3.00298i	−0.552557	−	0.246014i	−0.663969	+	0.747760i	$0.731129\pi$
$150$	3.48368	+	0.740478i	0.284441	+	0.0604598i
$151$	5.50257	+	6.11122i	0.447793	+	0.497324i	0.924204	−	0.381898i	$-0.124729\pi$
$151$	5.50257	+	6.11122i	0.447793	+	0.497324i	−0.476412	+	0.879222i	$0.658063\pi$
$152$	0.690237	−	6.56717i	0.0559856	−	0.532668i
$153$	1.52524			0.123309
$154$	3.94862	−	7.83635i	0.318189	−	0.631471i
$155$	9.16704			0.736314
$156$	−0.119944	+	1.14119i	−0.00960321	+	0.0913685i
$157$	14.7109	+	16.3381i	1.17406	+	1.30392i	0.943695	+	0.330816i	$0.107324\pi$
$157$	14.7109	+	16.3381i	1.17406	+	1.30392i	0.230360	+	0.973105i	$0.426010\pi$
$158$	9.74085	+	2.07048i	0.774940	+	0.164719i
$159$	−11.3203	−	5.04011i	−0.897757	−	0.399707i
$160$	−2.36719	+	1.71986i	−0.187143	+	0.135967i
$161$	2.99484	+	2.56358i	0.236027	+	0.202038i
$162$	0.309017	−	0.951057i	0.0242787	−	0.0747221i
$163$	−0.794290	+	7.55716i	−0.0622136	+	0.591922i	0.918357	+	0.395754i	$0.129517\pi$
$163$	−0.794290	+	7.55716i	−0.0622136	+	0.591922i	−0.980570	+	0.196169i	$0.937150\pi$
$164$	5.90850	−	10.2338i	0.461376	−	0.799127i
$165$	−3.66351	+	8.98639i	−0.285204	+	0.699590i
$166$	−6.69544	−	11.5968i	−0.519667	−	0.900089i
$167$	−12.0223	−	8.73472i	−0.930314	−	0.675913i	0.0157555	−	0.999876i	$-0.494985\pi$
$167$	−12.0223	−	8.73472i	−0.930314	−	0.675913i	−0.946070	+	0.323963i	$0.894985\pi$
$168$	−1.92118	+	1.81909i	−0.148222	+	0.140346i
$169$	−3.61034	−	11.1115i	−0.277718	−	0.854729i
$170$	4.07704	+	1.81521i	0.312694	+	0.139221i
$171$	0.690237	+	6.56717i	0.0527838	+	0.502204i
$172$	−4.10509	−	0.872565i	−0.313011	−	0.0665324i
$173$	−14.8806	+	3.16298i	−1.13135	+	0.240477i	−0.735294	−	0.677748i	$-0.762956\pi$
$173$	−14.8806	+	3.16298i	−1.13135	+	0.240477i	−0.396060	+	0.918225i	$0.629623\pi$
$174$	4.32621	+	3.14317i	0.327969	+	0.238283i
$175$	8.27598	+	4.50537i	0.625605	+	0.340574i
$176$	−1.44457	−	2.98550i	−0.108889	−	0.225041i
$177$	6.73447	+	11.6644i	0.506194	+	0.876753i
$178$	−2.89090	+	1.28711i	−0.216682	+	0.0964730i
$179$	5.41666	+	6.01581i	0.404860	+	0.449643i	0.910752	−	0.412954i	$-0.135503\pi$
$179$	5.41666	+	6.01581i	0.404860	+	0.449643i	−0.505892	+	0.862597i	$0.668836\pi$
$180$	1.95788	−	2.17445i	0.145932	−	0.162074i
$181$	2.51563	−	1.82771i	0.186986	−	0.135853i	−0.490354	−	0.871523i	$-0.663133\pi$
$181$	2.51563	−	1.82771i	0.186986	−	0.135853i	0.677340	+	0.735670i	$0.263133\pi$
$182$	−1.16491	+	2.80356i	−0.0863489	+	0.207813i
$183$	3.28099	+	10.0978i	0.242537	+	0.746453i
$184$	1.45745	−	0.309791i	0.107445	−	0.0228381i
$185$	−10.1069	+	4.49987i	−0.743071	+	0.330837i
$186$	1.56648	−	2.71322i	0.114860	−	0.198943i
$187$	−2.84189	+	4.18494i	−0.207819	+	0.306033i
$188$	−0.819923			−0.0597990
$189$	1.50098	−	2.17877i	0.109181	−	0.158482i
$190$	−5.97064	+	18.3758i	−0.433156	+	1.33312i
$191$	12.8181	−	14.2359i	0.927483	−	1.03007i	−0.0719832	−	0.997406i	$-0.522933\pi$
$191$	12.8181	−	14.2359i	0.927483	−	1.03007i	0.999466	−	0.0326684i	$-0.0104005\pi$
$192$	0.104528	+	0.994522i	0.00754369	+	0.0717734i
$193$	2.17620	+	20.7052i	0.156646	+	1.49039i	0.736926	+	0.675973i	$0.236276\pi$
$193$	2.17620	+	20.7052i	0.156646	+	1.49039i	−0.580280	+	0.814417i	$0.697057\pi$
$194$	5.76005	−	6.39718i	0.413547	−	0.459291i
$195$	1.03753	−	3.19320i	0.0742992	−	0.228670i
$196$	−6.24407	+	3.16411i	−0.446005	+	0.226008i
$197$	5.42608			0.386592			0.193296	−	0.981140i	$-0.438082\pi$
$197$	5.42608			0.386592			0.193296	+	0.981140i	$0.438082\pi$
$198$	2.03372	+	2.61992i	0.144531	+	0.186189i
$199$	−4.64296	+	8.04185i	−0.329131	+	0.570071i	−0.982340	−	0.187106i	$-0.940089\pi$
$199$	−4.64296	+	8.04185i	−0.329131	+	0.570071i	0.653209	+	0.757178i	$0.273422\pi$
$200$	3.25360	−	1.44859i	0.230064	−	0.102431i
$201$	−1.08597	+	0.230830i	−0.0765983	+	0.0162815i
$202$	−2.56938	−	7.90775i	−0.180781	−	0.556388i
$203$	8.60039	+	11.2340i	0.603629	+	0.788471i
$204$	1.23395	−	0.896516i	0.0863937	−	0.0627687i
$205$	−23.1363	+	25.6954i	−1.61591	+	1.79465i
$206$	6.79195	+	7.54322i	0.473217	+	0.525561i
$207$	−1.36120	+	0.606044i	−0.0946097	+	0.0421229i
$208$	0.573739	+	0.993745i	0.0397816	+	0.0689038i
$209$	−19.3050	−	10.3423i	−1.33535	−	0.715392i
$210$	6.60517	−	4.03760i	0.455800	−	0.278621i
$211$	−11.5909	−	8.42129i	−0.797951	−	0.579745i	0.112361	−	0.993667i	$-0.464159\pi$
$211$	−11.5909	−	8.42129i	−0.797951	−	0.579745i	−0.910312	+	0.413922i	$0.864159\pi$
$212$	−12.1208	+	2.57636i	−0.832460	+	0.176945i
$213$	−5.40131	−	1.14808i	−0.370092	−	0.0786654i
$214$	−2.07552	−	19.7473i	−0.141880	−	1.34989i
$215$	11.2182	+	4.99467i	0.765076	+	0.340634i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	6.01896	−	5.69912i	0.408593	−	0.386882i
$218$	−2.06812	−	1.50258i	−0.140071	−	0.101767i
$219$	4.69404	+	8.13032i	0.317194	+	0.549396i
$220$	2.31823	+	9.42350i	0.156295	+	0.635332i
$221$	0.875092	−	1.51570i	0.0588650	−	0.101957i
$222$	−0.395226	+	3.76033i	−0.0265258	+	0.252377i
$223$	−3.10067	+	9.54289i	−0.207636	+	0.639039i	0.791958	+	0.610575i	$0.209062\pi$
$223$	−3.10067	+	9.54289i	−0.207636	+	0.639039i	−0.999595	+	0.0284642i	$0.990938\pi$
$224$	−0.485031	+	2.60091i	−0.0324075	+	0.173781i
$225$	−2.88132	+	2.09340i	−0.192088	+	0.139560i
$226$	−7.03060	−	3.13022i	−0.467668	−	0.208219i
$227$	−4.17162	−	0.886704i	−0.276880	−	0.0588526i	0.0673788	−	0.997727i	$-0.478536\pi$
$227$	−4.17162	−	0.886704i	−0.276880	−	0.0588526i	−0.344259	+	0.938875i	$0.611870\pi$
$228$	4.41850	+	4.90724i	0.292622	+	0.324990i
$229$	0.602339	−	5.73087i	0.0398036	−	0.378706i	−0.956428	−	0.291970i	$-0.905689\pi$
$229$	0.602339	−	5.73087i	0.0398036	−	0.378706i	0.996231	−	0.0867369i	$-0.0276439\pi$
$230$	−4.35979			−0.287476
$231$	3.18140	+	8.17794i	0.209321	+	0.538069i
$232$	5.34748			0.351080
$233$	−2.54497	+	24.2138i	−0.166726	+	1.58630i	0.516629	+	0.856210i	$0.327187\pi$
$233$	−2.54497	+	24.2138i	−0.166726	+	1.58630i	−0.683355	+	0.730086i	$0.739480\pi$
$234$	−0.767813	−	0.852742i	−0.0501935	−	0.0557455i
$235$	2.34667	+	0.498800i	0.153080	+	0.0325382i
$236$	12.3045	+	5.47831i	0.800954	+	0.356608i
$237$	−8.05657	+	5.85344i	−0.523330	+	0.380222i
$238$	3.80544	−	1.34284i	0.246670	−	0.0870431i
$239$	5.03819	−	15.5060i	0.325894	−	1.00300i	−0.645142	−	0.764063i	$-0.723202\pi$
$239$	5.03819	−	15.5060i	0.325894	−	1.00300i	0.971036	−	0.238935i	$-0.0767982\pi$
$240$	0.305851	−	2.90998i	0.0197426	−	0.187838i
$241$	9.99434	−	17.3107i	0.643792	−	1.11508i	−0.340787	−	0.940141i	$-0.610693\pi$
$241$	9.99434	−	17.3107i	0.643792	−	1.11508i	0.984579	−	0.174940i	$-0.0559733\pi$
$242$	−10.9778	+	0.698591i	−0.705679	+	0.0449071i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	8.58973	+	6.24081i	0.549901	+	0.399527i
$245$	19.7958	−	5.25730i	1.26471	−	0.335877i
$246$	3.65165	+	11.2386i	0.232821	+	0.716549i
$247$	6.92211	+	3.08192i	0.440443	+	0.196098i
$248$	−0.327483	−	3.11579i	−0.0207952	−	0.197853i
$249$	13.0982	+	2.78412i	0.830068	+	0.176436i
$250$	4.11707	−	0.875110i	0.260386	−	0.0553468i
$251$	−2.68953	−	1.95406i	−0.169762	−	0.123339i	0.499660	−	0.866221i	$-0.333458\pi$
$251$	−2.68953	−	1.95406i	−0.169762	−	0.123339i	−0.669422	+	0.742882i	$0.733458\pi$
$252$	−0.0663284	−	2.64492i	−0.00417830	−	0.166614i
$253$	0.873372	−	4.86403i	0.0549084	−	0.305799i
$254$	−3.88883	−	6.73565i	−0.244007	−	0.422632i
$255$	−4.07704	+	1.81521i	−0.255314	+	0.113673i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	10.5100	−	11.6726i	0.655598	−	0.728115i	−0.320064	−	0.947396i	$-0.603704\pi$
$257$	10.5100	−	11.6726i	0.655598	−	0.728115i	0.975662	+	0.219281i	$0.0703711\pi$
$258$	3.39529	−	2.46682i	0.211381	−	0.153577i
$259$	−3.83848	+	9.23796i	−0.238512	+	0.574019i
$260$	−1.03753	−	3.19320i	−0.0643450	−	0.198034i
$261$	−5.23063	+	1.11180i	−0.323768	+	0.0688190i
$262$	−6.76921	+	3.01385i	−0.418203	+	0.186196i
$263$	1.24355	−	2.15389i	0.0766804	−	0.132814i	−0.825135	−	0.564935i	$-0.808901\pi$
$263$	1.24355	−	2.15389i	0.0766804	−	0.132814i	0.901816	+	0.432121i	$0.142235\pi$
$264$	3.18527	+	0.924163i	0.196040	+	0.0568783i
$265$	36.2579			2.22730
$266$	7.50390	+	15.7772i	0.460094	+	0.967363i
$267$	0.977878	−	3.00960i	0.0598452	−	0.184185i
$268$	−0.742889	+	0.825061i	−0.0453791	+	0.0503986i
$269$	−0.189684	−	1.80472i	−0.0115652	−	0.110036i	0.987216	−	0.159386i	$-0.0509515\pi$
$269$	−0.189684	−	1.80472i	−0.0115652	−	0.110036i	−0.998782	+	0.0493505i	$0.984285\pi$
$270$	0.305851	+	2.90998i	0.0186135	+	0.177095i
$271$	−16.5880	+	18.4228i	−1.00765	+	1.11911i	−0.0147786	+	0.999891i	$0.504704\pi$
$271$	−16.5880	+	18.4228i	−1.00765	+	1.11911i	−0.992868	+	0.119215i	$0.961962\pi$
$272$	0.471326	−	1.45059i	0.0285784	−	0.0879551i
$273$	−1.30397	−	2.74164i	−0.0789199	−	0.165932i
$274$	12.0409			0.727418
$275$	−0.375275	−	11.8062i	−0.0226299	−	0.711941i
$276$	−0.745007	+	1.29039i	−0.0448442	+	0.0776724i
$277$	−4.36898	+	1.94519i	−0.262507	+	0.116875i	−0.533770	−	0.845630i	$-0.679225\pi$
$277$	−4.36898	+	1.94519i	−0.262507	+	0.116875i	0.271263	+	0.962505i	$0.412559\pi$
$278$	15.0100	−	3.19047i	0.900238	−	0.191352i
$279$	0.968136	+	2.97962i	0.0579608	+	0.178385i
$280$	2.97046	−	7.14891i	0.177519	−	0.427229i
$281$	14.1543	−	10.2837i	0.844373	−	0.613473i	−0.0792155	−	0.996858i	$-0.525242\pi$
$281$	14.1543	−	10.2837i	0.844373	−	0.613473i	0.923589	+	0.383384i	$0.125242\pi$
$282$	0.548635	−	0.609321i	0.0326708	−	0.0362846i
$283$	18.9322	+	21.0264i	1.12540	+	1.24989i	0.964833	+	0.262863i	$0.0846668\pi$
$283$	18.9322	+	21.0264i	1.12540	+	1.24989i	0.160571	+	0.987024i	$0.448667\pi$
$284$	−5.04458	+	2.24599i	−0.299341	+	0.133275i
$285$	−9.66070	−	16.7328i	−0.572251	−	0.991167i
$286$	3.77036	−	0.517856i	0.222946	−	0.0306215i
$287$	0.783803	+	31.2550i	0.0462665	+	1.84493i
$288$	−0.809017	−	0.587785i	−0.0476718	−	0.0346356i
$289$	14.3530	−	3.05082i	0.844293	−	0.179460i
$290$	−15.3048	−	3.25315i	−0.898731	−	0.191031i
$291$	0.899808	+	8.56110i	0.0527477	+	0.501861i
$292$	8.57644	+	3.81848i	0.501898	+	0.223459i
$293$	4.17657	+	12.8541i	0.243998	+	0.750947i	0.995800	+	0.0915585i	$0.0291848\pi$
$293$	4.17657	+	12.8541i	0.243998	+	0.750947i	−0.751802	+	0.659389i	$0.770815\pi$
$294$	1.82671	−	6.75745i	0.106536	−	0.394103i
$295$	−31.8835	−	23.1647i	−1.85633	−	1.34870i
$296$	1.89052	+	3.27448i	0.109884	+	0.190325i
$297$	−3.30781	−	0.241714i	−0.191938	−	0.0140257i
$298$	3.69156	−	6.39397i	0.213846	−	0.370393i
$299$	−0.178718	+	1.70039i	−0.0103356	+	0.0983362i
$300$	−1.10057	+	3.38719i	−0.0635412	+	0.195560i
$301$	10.4709	−	3.69490i	0.603533	−	0.212970i
$302$	−6.65292	+	4.83363i	−0.382832	+	0.278144i
$303$	7.59586	+	3.38189i	0.436371	+	0.194285i
$304$	6.45904	+	1.37291i	0.370451	+	0.0787419i
$305$	−20.7878	−	23.0872i	−1.19030	−	1.32197i
$306$	−0.159431	+	1.51689i	−0.00911409	+	0.0867148i
$307$	9.52605			0.543680			0.271840	−	0.962342i	$-0.412368\pi$
$307$	9.52605			0.543680			0.271840	+	0.962342i	$0.412368\pi$
$308$	7.38068	+	4.74611i	0.420553	+	0.270435i
$309$	−10.1504			−0.577436
$310$	−0.958217	+	9.11682i	−0.0544230	+	0.517801i
$311$	−8.89421	−	9.87802i	−0.504344	−	0.560131i	0.436179	−	0.899860i	$-0.356331\pi$
$311$	−8.89421	−	9.87802i	−0.504344	−	0.560131i	−0.940523	+	0.339729i	$0.889665\pi$
$312$	−1.12240	−	0.238574i	−0.0635435	−	0.0135066i
$313$	−27.2851	−	12.1481i	−1.54225	−	0.686652i	−0.553036	−	0.833158i	$-0.686531\pi$
$313$	−27.2851	−	12.1481i	−1.54225	−	0.686652i	−0.989210	+	0.146506i	$0.953197\pi$
$314$	−17.7863	+	12.9225i	−1.00374	+	0.729259i
$315$	−1.41920	+	7.61028i	−0.0799630	+	0.428791i
$316$	−3.07733	+	9.47106i	−0.173114	+	0.532789i
$317$	−1.20427	+	11.4578i	−0.0676384	+	0.643537i	0.907212	+	0.420675i	$0.138207\pi$
$317$	−1.20427	+	11.4578i	−0.0676384	+	0.643537i	−0.974850	+	0.222862i	$0.928460\pi$
$318$	6.19580	−	10.7314i	0.347443	−	0.601789i
$319$	6.69533	−	16.4233i	0.374866	−	0.919527i
$320$	−1.46300	−	2.53399i	−0.0817843	−	0.141655i
$321$	16.0639	+	11.6711i	0.896597	+	0.651416i
$322$	−2.86258	+	2.71047i	−0.159525	+	0.151048i
$323$	−3.11233	−	9.57876i	−0.173175	−	0.532977i
$324$	0.913545	+	0.406737i	0.0507525	+	0.0225965i
$325$	0.427181	+	4.06436i	0.0236958	+	0.225450i
$326$	−7.43274	−	1.57988i	−0.411661	−	0.0875013i
$327$	2.50048	−	0.531493i	0.138277	−	0.0293916i
$328$	9.56016	+	6.94586i	0.527871	+	0.383521i
$329$	1.85090	−	1.13141i	0.102043	−	0.0623768i
$330$	−8.55422	−	4.58277i	−0.470894	−	0.252273i
$331$	−9.97943	−	17.2849i	−0.548519	−	0.950063i	−0.998376	−	0.0569624i	$-0.981858\pi$
$331$	−9.97943	−	17.2849i	−0.548519	−	0.950063i	0.449857	−	0.893100i	$-0.351475\pi$
$332$	12.2332	−	5.44656i	0.671382	−	0.298919i
$333$	−2.53001	−	2.80986i	−0.138644	−	0.153979i
$334$	9.94354	−	11.0434i	0.544086	−	0.604269i
$335$	2.62812	−	1.90944i	0.143590	−	0.104324i
$336$	−1.60831	−	2.10080i	−0.0877403	−	0.114608i
$337$	3.23547	+	9.95776i	0.176247	+	0.542434i	0.999688	−	0.0249685i	$-0.00794855\pi$
$337$	3.23547	+	9.95776i	0.176247	+	0.542434i	−0.823441	+	0.567402i	$0.807949\pi$
$338$	11.4280	−	2.42909i	0.621601	−	0.132125i
$339$	7.03060	−	3.13022i	0.381850	−	0.170010i
$340$	−2.23144	+	3.86496i	−0.121017	+	0.209607i
$341$	−9.97930	−	2.89536i	−0.540409	−	0.156793i
$342$	−6.60334			−0.357068
$343$	9.72922	−	15.7589i	0.525329	−	0.850899i
$344$	1.29688	−	3.99140i	0.0699233	−	0.215202i
$345$	2.91727	−	3.23996i	0.157060	−	0.174433i
$346$	−1.59020	−	15.1297i	−0.0854897	−	0.813380i
$347$	0.166114	+	1.58047i	0.00891745	+	0.0848439i	0.998075	−	0.0620114i	$-0.0197515\pi$
$347$	0.166114	+	1.58047i	0.00891745	+	0.0848439i	−0.989158	+	0.146855i	$0.953085\pi$
$348$	−3.57817	+	3.97396i	−0.191810	+	0.213026i
$349$	0.555278	−	1.70897i	0.0297234	−	0.0914791i	−0.935094	−	0.354399i	$-0.884685\pi$
$349$	0.555278	−	1.70897i	0.0297234	−	0.0914791i	0.964818	+	0.262920i	$0.0846855\pi$
$350$	−5.34576	+	7.75970i	−0.285743	+	0.414774i
$351$	1.14748			0.0612478
$352$	3.12014	−	1.12459i	0.166304	−	0.0599408i
$353$	−2.90566	+	5.03275i	−0.154653	+	0.267866i	−0.932932	−	0.360051i	$-0.882759\pi$
$353$	−2.90566	+	5.03275i	−0.154653	+	0.267866i	0.778280	+	0.627918i	$0.216092\pi$
$354$	−12.3045	+	5.47831i	−0.653976	+	0.291169i
$355$	15.8043	−	3.35930i	0.838803	−	0.178293i
$356$	−0.977878	−	3.00960i	−0.0518275	−	0.159508i
$357$	−1.54842	+	3.72653i	−0.0819508	+	0.197229i
$358$	−6.54905	+	4.75816i	−0.346128	+	0.251477i
$359$	13.3641	−	14.8423i	0.705328	−	0.783347i	−0.278886	−	0.960324i	$-0.589965\pi$
$359$	13.3641	−	14.8423i	0.705328	−	0.783347i	0.984215	+	0.176977i	$0.0566320\pi$
$360$	1.95788	+	2.17445i	0.103189	+	0.114603i
$361$	22.4770	−	10.0074i	1.18300	−	0.526705i
$362$	1.55475	+	2.69290i	0.0817157	+	0.141536i
$363$	6.82642	−	8.62554i	0.358294	−	0.452723i
$364$	−2.66643	−	1.45158i	−0.139759	−	0.0760835i
$365$	−22.2233	−	16.1462i	−1.16322	−	0.845131i
$366$	−10.3855	+	2.20750i	−0.542857	+	0.115388i
$367$	−27.3974	−	5.82350i	−1.43013	−	0.303984i	−0.573202	−	0.819414i	$-0.694299\pi$
$367$	−27.3974	−	5.82350i	−1.43013	−	0.303984i	−0.856932	+	0.515430i	$0.827632\pi$
$368$	0.155749	+	1.48185i	0.00811897	+	0.0772469i
$369$	−10.7954	−	4.80641i	−0.561985	−	0.250212i
$370$	−3.41876	−	10.5219i	−0.177733	−	0.547006i
$371$	23.8064	−	22.5414i	1.23597	−	1.17029i
$372$	2.53461	+	1.84150i	0.131414	+	0.0954776i
$373$	2.97342	+	5.15011i	0.153958	+	0.266663i	0.932679	−	0.360707i	$-0.117465\pi$
$373$	2.97342	+	5.15011i	0.153958	+	0.266663i	−0.778721	+	0.627370i	$0.784131\pi$
$374$	−3.86496	−	3.26376i	−0.199852	−	0.168765i
$375$	−2.10452	+	3.64514i	−0.108677	+	0.188234i
$376$	0.0857053	−	0.815431i	0.00441991	−	0.0420526i
$377$	−1.89617	+	5.83580i	−0.0976575	+	0.300559i
$378$	2.00994	+	1.72051i	0.103380	+	0.0884932i
$379$	−17.9697	+	13.0558i	−0.923041	+	0.670629i	−0.944279	−	0.329146i	$-0.893239\pi$
$379$	−17.9697	+	13.0558i	−0.923041	+	0.670629i	0.0212377	+	0.999774i	$0.493239\pi$
$380$	−17.6510	−	7.85872i	−0.905476	−	0.403144i
$381$	7.60769	+	1.61707i	0.389754	+	0.0828448i
$382$	12.8181	+	14.2359i	0.655830	+	0.728372i
$383$	−0.794260	+	7.55688i	−0.0405848	+	0.386139i	0.955309	+	0.295609i	$0.0955226\pi$
$383$	−0.794260	+	7.55688i	−0.0405848	+	0.386139i	−0.995894	+	0.0905294i	$0.971144\pi$
$384$	−1.00000			−0.0510310
$385$	−18.2367	−	18.0737i	−0.929427	−	0.921122i
$386$	−20.8192			−1.05967
$387$	−0.438686	+	4.17381i	−0.0222996	+	0.212167i
$388$	5.76005	+	6.39718i	0.292422	+	0.324768i
$389$	−23.1554	−	4.92182i	−1.17402	−	0.249546i	−0.420702	−	0.907199i	$-0.638216\pi$
$389$	−23.1554	−	4.92182i	−1.17402	−	0.249546i	−0.753321	+	0.657653i	$0.771549\pi$
$390$	3.06725	+	1.36563i	0.155316	+	0.0691513i
$391$	1.83860	−	1.33582i	0.0929821	−	0.0675554i
$392$	−2.49409	−	6.54060i	−0.125971	−	0.330350i
$393$	2.28976	−	7.04716i	0.115503	−	0.355482i
$394$	−0.567180	+	5.39635i	−0.0285741	+	0.271864i
$395$	14.5693	−	25.2347i	0.733059	−	1.26970i
$396$	−2.81815	+	1.74873i	−0.141617	+	0.0878769i
$397$	8.60312	+	14.9010i	0.431778	+	0.747862i	0.997027	−	0.0770589i	$-0.0245530\pi$
$397$	8.60312	+	14.9010i	0.431778	+	0.747862i	−0.565248	+	0.824921i	$0.691220\pi$
$398$	−7.51247	−	5.45813i	−0.376566	−	0.273591i
$399$	−16.7458	−	4.98052i	−0.838341	−	0.249338i
$400$	1.10057	+	3.38719i	0.0550283	+	0.169360i
$401$	19.3873	+	8.63178i	0.968155	+	0.431050i	0.829017	−	0.559223i	$-0.188900\pi$
$401$	19.3873	+	8.63178i	0.968155	+	0.431050i	0.139138	+	0.990273i	$0.455567\pi$
$402$	−0.116051	−	1.10415i	−0.00578808	−	0.0550699i
$403$	3.51644	+	0.747442i	0.175166	+	0.0372327i
$404$	8.13301	−	1.72872i	0.404632	−	0.0860072i
$405$	−2.36719	−	1.71986i	−0.117626	−	0.0854607i
$406$	−12.0714	+	7.37900i	−0.599095	+	0.366214i
$407$	12.4237	−	1.70638i	0.615818	−	0.0845821i
$408$	0.762622	+	1.32090i	0.0377554	+	0.0653943i
$409$	11.6191	−	5.17317i	0.574529	−	0.255797i	−0.0988402	−	0.995103i	$-0.531513\pi$
$409$	11.6191	−	5.17317i	0.574529	−	0.255797i	0.673369	+	0.739307i	$0.264847\pi$
$410$	−23.1363	−	25.6954i	−1.14262	−	1.26901i
$411$	−8.05694	+	8.94814i	−0.397419	+	0.441379i
$412$	−8.21185	+	5.96626i	−0.404569	+	0.293936i
$413$	−35.3357	+	4.61223i	−1.73876	+	0.226953i
$414$	−0.460440	−	1.41709i	−0.0226294	−	0.0696461i
$415$	−38.3255	+	8.14634i	−1.88133	+	0.399888i
$416$	−1.04827	+	0.466721i	−0.0513958	+	0.0228829i
$417$	−7.67265	+	13.2894i	−0.375731	+	0.650786i
$418$	12.3036	−	18.1182i	0.601787	−	0.886188i
$419$	17.5889			0.859273			0.429637	−	0.903002i	$-0.358642\pi$
$419$	17.5889			0.859273			0.429637	+	0.903002i	$0.358642\pi$
$420$	3.32505	+	6.99103i	0.162246	+	0.341128i
$421$	−11.0434	+	33.9881i	−0.538223	+	1.65648i	0.198358	+	0.980130i	$0.436439\pi$
$421$	−11.0434	+	33.9881i	−0.538223	+	1.65648i	−0.736581	+	0.676350i	$0.763561\pi$
$422$	9.58674	−	10.6471i	0.466675	−	0.518295i
$423$	0.0857053	+	0.815431i	0.00416713	+	0.0396476i
$424$	−1.29527	−	12.3237i	−0.0629041	−	0.598492i
$425$	3.63483	−	4.03688i	0.176315	−	0.195818i
$426$	1.70639	−	5.25171i	0.0826746	−	0.254446i
$427$	−28.0022	−	2.23503i	−1.35512	−	0.108161i
$428$	19.8560			0.959777
$429$	−2.13802	+	3.14843i	−0.103225	+	0.152008i
$430$	−6.13994	+	10.6347i	−0.296094	+	0.512850i
$431$	28.0563	−	12.4915i	1.35142	−	0.601692i	0.401985	−	0.915646i	$-0.368320\pi$
$431$	28.0563	−	12.4915i	1.35142	−	0.601692i	0.949438	+	0.313954i	$0.101654\pi$
$432$	0.978148	−	0.207912i	0.0470611	−	0.0100032i
$433$	9.06549	+	27.9007i	0.435660	+	1.34082i	0.892409	+	0.451227i	$0.149014\pi$
$433$	9.06549	+	27.9007i	0.435660	+	1.34082i	−0.456750	+	0.889595i	$0.650986\pi$
$434$	5.03875	+	6.58171i	0.241868	+	0.315932i
$435$	12.6585	−	9.19694i	0.606929	−	0.440959i
$436$	1.71052	−	1.89973i	0.0819193	−	0.0909806i
$437$	6.58363	+	7.31186i	0.314938	+	0.349774i
$438$	−8.57644	+	3.81848i	−0.409798	+	0.182454i
$439$	3.72017	+	6.44352i	0.177554	+	0.307532i	0.941042	−	0.338289i	$-0.109848\pi$
$439$	3.72017	+	6.44352i	0.177554	+	0.307532i	−0.763488	+	0.645822i	$0.776515\pi$
$440$	−9.61420	+	1.32050i	−0.458339	+	0.0629525i
$441$	3.79946	+	5.87912i	0.180927	+	0.279958i
$442$	1.41593	+	1.02873i	0.0673488	+	0.0489318i
$443$	−36.4140	+	7.74003i	−1.73008	+	0.367740i	−0.962092	−	0.272724i	$-0.912075\pi$
$443$	−36.4140	+	7.74003i	−1.73008	+	0.367740i	−0.767988	+	0.640464i	$0.778742\pi$
$444$	−3.69841	−	0.786122i	−0.175519	−	0.0373077i
$445$	0.967859	+	9.20856i	0.0458809	+	0.436528i
$446$	−9.16651	−	4.08119i	−0.434047	−	0.193250i
$447$	2.28151	+	7.02176i	0.107912	+	0.332118i
$448$	−2.53596	−	0.754243i	−0.119813	−	0.0356346i
$449$	−10.0582	−	7.30773i	−0.474677	−	0.344873i	0.324584	−	0.945857i	$-0.394776\pi$
$449$	−10.0582	−	7.30773i	−0.474677	−	0.344873i	−0.799261	+	0.600984i	$0.794776\pi$
$450$	−1.78075	−	3.08435i	−0.0839454	−	0.145398i
$451$	33.3020	−	20.6647i	1.56813	−	0.973064i
$452$	3.84797	−	6.66489i	0.180993	−	0.313490i
$453$	0.859586	−	8.17841i	0.0403869	−	0.384255i
$454$	1.31790	−	4.05608i	0.0618521	−	0.190361i
$455$	6.74843	+	5.77664i	0.316371	+	0.270813i
$456$	−5.34222	+	3.88135i	−0.250172	+	0.181761i
$457$	28.3265	+	12.6118i	1.32506	+	0.589953i	0.942570	−	0.334008i	$-0.108401\pi$
$457$	28.3265	+	12.6118i	1.32506	+	0.589953i	0.382487	+	0.923961i	$0.375068\pi$
$458$	5.63651	+	1.19808i	0.263377	+	0.0559825i
$459$	−1.02059	−	1.13348i	−0.0476369	−	0.0529062i
$460$	0.455722	−	4.33591i	0.0212482	−	0.202163i
$461$	−33.2674			−1.54942			−0.774709	−	0.632318i	$-0.782104\pi$
$461$	−33.2674			−1.54942			−0.774709	+	0.632318i	$0.782104\pi$
$462$	−8.46569	+	2.30915i	−0.393859	+	0.107431i
$463$	14.9784			0.696104			0.348052	−	0.937475i	$-0.386843\pi$
$463$	14.9784			0.696104			0.348052	+	0.937475i	$0.386843\pi$
$464$	−0.558964	+	5.31819i	−0.0259493	+	0.246891i
$465$	−6.13395	−	6.81244i	−0.284455	−	0.315919i
$466$	−23.8151	−	5.06205i	−1.10321	−	0.234495i
$467$	−27.1802	−	12.1014i	−1.25775	−	0.559986i	−0.333852	−	0.942626i	$-0.608348\pi$
$467$	−27.1802	−	12.1014i	−1.25775	−	0.559986i	−0.923898	+	0.382640i	$0.875015\pi$
$468$	0.928329	−	0.674471i	0.0429120	−	0.0311774i
$469$	0.538496	−	2.88761i	0.0248654	−	0.133337i
$470$	−0.741362	+	2.28168i	−0.0341965	+	0.105246i
$471$	2.29806	−	21.8646i	0.105889	−	1.00747i
$472$	−6.73447	+	11.6644i	−0.309979	+	0.536899i
$473$	−10.6347	−	8.98045i	−0.488983	−	0.412921i
$474$	−4.97923	−	8.62428i	−0.228704	−	0.396126i
$475$	19.0263	+	13.8234i	0.872987	+	0.634262i
$476$	0.937703	+	3.92496i	0.0429795	+	0.179900i
$477$	3.82921	+	11.7851i	0.175328	+	0.539603i
$478$	14.8944	+	6.63141i	0.681253	+	0.303314i
$479$	−0.326854	−	3.10981i	−0.0149343	−	0.142091i	0.984514	−	0.175307i	$-0.0560917\pi$
$479$	−0.326854	−	3.10981i	−0.0149343	−	0.142091i	−0.999448	+	0.0332161i	$0.989425\pi$
$480$	2.86206	+	0.608351i	0.130635	+	0.0277673i
$481$	−4.24385	+	0.902058i	−0.193503	+	0.0411303i
$482$	16.1712	+	11.7491i	0.736577	+	0.535155i
$483$	−0.0988303	−	3.94097i	−0.00449694	−	0.179320i
$484$	0.452728	−	10.9907i	0.0205785	−	0.499576i
$485$	−12.5939	−	21.8133i	−0.571860	−	0.990490i
$486$	−0.913545	+	0.406737i	−0.0414393	+	0.0184499i
$487$	−12.7399	−	14.1491i	−0.577302	−	0.641159i	0.381791	−	0.924249i	$-0.375307\pi$
$487$	−12.7399	−	14.1491i	−0.577302	−	0.641159i	−0.959093	+	0.283090i	$0.908641\pi$
$488$	−7.10449	+	7.89033i	−0.321605	+	0.357179i
$489$	6.14755	−	4.46646i	0.278002	−	0.201980i
$490$	3.15928	+	20.2369i	0.142722	+	0.914211i
$491$	3.32782	+	10.2420i	0.150183	+	0.462215i	0.997641	−	0.0686473i	$-0.0218683\pi$
$491$	3.32782	+	10.2420i	0.150183	+	0.462215i	−0.847458	+	0.530862i	$0.821868\pi$
$492$	−11.5588	+	2.45689i	−0.521110	+	0.110765i
$493$	7.45108	−	3.31743i	0.335580	−	0.149410i
$494$	−3.78859	+	6.56204i	−0.170457	+	0.295240i
$495$	9.12956	−	3.29055i	0.410343	−	0.147899i
$496$	3.13295			0.140674
$497$	8.28840	−	12.0311i	0.371786	−	0.539670i
$498$	−4.13801	+	12.7355i	−0.185429	+	0.570690i
$499$	21.4569	−	23.8303i	0.960541	−	1.06679i	−0.0371798	−	0.999309i	$-0.511837\pi$
$499$	21.4569	−	23.8303i	0.960541	−	1.06679i	0.997721	−	0.0674801i	$-0.0214959\pi$
$500$	0.439965	+	4.18599i	0.0196758	+	0.187203i
$501$	1.55333	+	14.7790i	0.0693978	+	0.660276i
$502$	2.22449	−	2.47054i	0.0992838	−	0.110266i
$503$	−11.1920	+	34.4454i	−0.499027	+	1.53585i	0.311560	+	0.950227i	$0.399149\pi$
$503$	−11.1920	+	34.4454i	−0.499027	+	1.53585i	−0.810586	+	0.585619i	$0.800851\pi$
$504$	2.63736	+	0.210504i	0.117478	+	0.00937661i
$505$	−24.3289			−1.08262
$506$	4.74609	+	1.37702i	0.210990	+	0.0612159i
$507$	−5.84165	+	10.1180i	−0.259437	+	0.449357i
$508$	7.10524	−	3.16346i	0.315244	−	0.140356i
$509$	14.1833	−	3.01474i	0.628662	−	0.133626i	0.117447	−	0.993079i	$-0.462529\pi$
$509$	14.1833	−	3.01474i	0.628662	−	0.133626i	0.511215	+	0.859453i	$0.329196\pi$
$510$	−1.37910	−	4.24444i	−0.0610677	−	0.187947i
$511$	−24.6296	+	3.21480i	−1.08955	+	0.142214i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	4.41850	−	4.90724i	0.195081	−	0.216660i
$514$	10.5100	+	11.6726i	0.463578	+	0.514855i
$515$	27.1324	−	12.0801i	1.19560	−	0.532314i
$516$	2.09840	+	3.63454i	0.0923770	+	0.160002i
$517$	−2.39706	−	1.28418i	−0.105422	−	0.0564782i
$518$	−8.78612	−	4.78308i	−0.386040	−	0.210157i
$519$	12.3076	+	8.94203i	0.540246	+	0.392511i
$520$	3.28416	−	0.698069i	0.144020	−	0.0306123i
$521$	22.6833	+	4.82148i	0.993773	+	0.211233i	0.675974	−	0.736925i	$-0.263723\pi$
$521$	22.6833	+	4.82148i	0.993773	+	0.211233i	0.317799	+	0.948158i	$0.397056\pi$
$522$	−0.558964	−	5.31819i	−0.0244652	−	0.232771i
$523$	−4.05440	−	1.80513i	−0.177286	−	0.0789330i	0.316174	−	0.948701i	$-0.397602\pi$
$523$	−4.05440	−	1.80513i	−0.177286	−	0.0789330i	−0.493461	+	0.869768i	$0.664268\pi$
$524$	−2.28976	−	7.04716i	−0.100029	−	0.307857i
$525$	−2.18957	−	9.16493i	−0.0955608	−	0.399990i
$526$	2.01210	+	1.46188i	0.0877318	+	0.0637409i
$527$	−2.38926	−	4.13832i	−0.104078	−	0.180268i
$528$	−1.25205	+	3.07122i	−0.0544886	+	0.133658i
$529$	10.3899	−	17.9959i	0.451736	−	0.782430i
$530$	−3.78998	+	36.0592i	−0.164626	+	1.56631i
$531$	4.16213	−	12.8097i	0.180621	−	0.555894i
$532$	−16.4751	+	5.81363i	−0.714288	+	0.252053i
$533$	−10.9701	+	7.97022i	−0.475166	+	0.345229i
$534$	2.89090	+	1.28711i	0.125101	+	0.0556987i
$535$	−56.8292	−	12.0794i	−2.45694	−	0.522239i
$536$	−0.742889	−	0.825061i	−0.0320879	−	0.0356372i
$537$	0.846165	−	8.05073i	0.0365147	−	0.347414i
$538$	1.81466			0.0782357
$539$	−23.2103	−	0.529273i	−0.999740	−	0.0227974i
$540$	−2.92600			−0.125915
$541$	2.11885	−	20.1595i	0.0910966	−	0.866726i	−0.849589	−	0.527446i	$-0.823150\pi$
$541$	2.11885	−	20.1595i	0.0910966	−	0.866726i	0.940685	−	0.339280i	$-0.110184\pi$
$542$	−16.5880	−	18.4228i	−0.712514	−	0.791327i
$543$	−3.04154	−	0.646500i	−0.130525	−	0.0277440i
$544$	1.39338	+	0.620373i	0.0597407	+	0.0265983i
$545$	−6.05133	+	4.39655i	−0.259211	+	0.188328i
$546$	2.86292	−	1.01025i	0.122522	−	0.0432346i
$547$	−5.53350	+	17.0304i	−0.236595	+	0.728165i	0.760311	+	0.649560i	$0.225047\pi$
$547$	−5.53350	+	17.0304i	−0.236595	+	0.728165i	−0.996906	+	0.0786056i	$0.974953\pi$
$548$	−1.25862	+	11.9749i	−0.0537655	+	0.511544i
$549$	5.30875	−	9.19502i	0.226572	−	0.392434i
$550$	11.7808	+	0.860866i	0.502333	+	0.0367074i
$551$	17.6556	+	30.5805i	0.752155	+	1.30277i
$552$	−1.20545	−	0.875809i	−0.0513072	−	0.0372769i
$553$	−6.12235	−	25.6264i	−0.260349	−	1.08975i
$554$	−1.47786	−	4.54837i	−0.0627881	−	0.193242i
$555$	10.1069	+	4.49987i	0.429012	+	0.191009i
$556$	1.60402	+	15.2612i	0.0680257	+	0.647221i
$557$	12.7628	+	2.71282i	0.540777	+	0.114946i	0.470199	−	0.882560i	$-0.344182\pi$
$557$	12.7628	+	2.71282i	0.540777	+	0.114946i	0.0705784	+	0.997506i	$0.477516\pi$
$558$	−3.06449	+	0.651378i	−0.129730	+	0.0275750i
$559$	3.89602	+	2.83062i	0.164784	+	0.119723i
$560$	6.79925	+	3.70145i	0.287321	+	0.156415i
$561$	5.01161	−	0.688341i	0.211590	−	0.0290618i
$562$	8.74782	+	15.1517i	0.369005	+	0.639135i
$563$	10.6044	−	4.72137i	0.446921	−	0.198982i	−0.170920	−	0.985285i	$-0.554674\pi$
$563$	10.6044	−	4.72137i	0.446921	−	0.198982i	0.617841	+	0.786303i	$0.288007\pi$
$564$	0.548635	+	0.609321i	0.0231017	+	0.0256571i
$565$	−15.0677	+	16.7344i	−0.633904	+	0.704022i
$566$	−22.8901	+	16.6307i	−0.962144	+	0.699039i
$567$	−2.62350	+	0.342434i	−0.110177	+	0.0143809i
$568$	−1.70639	−	5.25171i	−0.0715983	−	0.220357i
$569$	26.3071	−	5.59174i	1.10285	−	0.234418i	0.379700	−	0.925110i	$-0.376027\pi$
$569$	26.3071	−	5.59174i	1.10285	−	0.234418i	0.723149	+	0.690692i	$0.242694\pi$
$570$	17.6510	−	7.85872i	0.739318	−	0.329166i
$571$	−23.1911	+	40.1681i	−0.970517	+	1.68098i	−0.276516	+	0.961009i	$0.589180\pi$
$571$	−23.1911	+	40.1681i	−0.970517	+	1.68098i	−0.694000	+	0.719975i	$0.744153\pi$
$572$	0.120909	+	3.80383i	0.00505548	+	0.159046i
$573$	−19.1563			−0.800266
$574$	−31.1657	−	2.48753i	−1.30083	−	0.103828i
$575$	−1.63986	+	5.04696i	−0.0683868	+	0.210473i
$576$	0.669131	−	0.743145i	0.0278804	−	0.0309644i
$577$	−2.99166	−	28.4637i	−0.124544	−	1.18496i	−0.861047	−	0.508526i	$-0.830191\pi$
$577$	−2.99166	−	28.4637i	−0.124544	−	1.18496i	0.736502	−	0.676435i	$-0.236476\pi$
$578$	1.53381	+	14.5932i	0.0637982	+	0.606999i
$579$	13.9308	−	15.4717i	0.578943	−	0.642981i
$580$	4.83512	−	14.8810i	0.200767	−	0.617898i
$581$	−20.0995	+	29.1757i	−0.833867	+	1.21041i
$582$	−8.60826			−0.356824
$583$	−39.4705	−	11.4519i	−1.63470	−	0.474287i
$584$	−4.69404	+	8.13032i	−0.194241	+	0.336435i
$585$	−3.06725	+	1.36563i	−0.126815	+	0.0564618i
$586$	−13.2203	+	2.81006i	−0.546126	+	0.116083i
$587$	−2.74496	−	8.44812i	−0.113297	−	0.348691i	0.878291	−	0.478126i	$-0.158684\pi$
$587$	−2.74496	−	8.44812i	−0.113297	−	0.348691i	−0.991588	+	0.129435i	$0.958684\pi$
$588$	6.52949	+	2.52304i	0.269272	+	0.104049i
$589$	16.7369	−	12.1601i	0.689633	−	0.501047i
$590$	26.3705	−	29.2875i	1.08566	−	1.20575i
$591$	−3.63075	−	4.03236i	−0.149349	−	0.165869i
$592$	−3.45415	+	1.53789i	−0.141965	+	0.0632068i
$593$	−1.50460	−	2.60604i	−0.0617863	−	0.107017i	0.833478	−	0.552553i	$-0.186346\pi$
$593$	−1.50460	−	2.60604i	−0.0617863	−	0.107017i	−0.895264	+	0.445536i	$0.853013\pi$
$594$	0.586150	−	3.26442i	0.0240500	−	0.133941i
$595$	−0.296015	−	11.8039i	−0.0121354	−	0.483914i
$596$	5.97307	+	4.33969i	0.244666	+	0.177761i
$597$	9.08301	−	1.93065i	0.371743	−	0.0790163i
$598$	−1.67240	−	0.355479i	−0.0683894	−	0.0145366i
$599$	3.10079	+	29.5020i	0.126695	+	1.20542i	0.854431	+	0.519564i	$0.173906\pi$
$599$	3.10079	+	29.5020i	0.126695	+	1.20542i	−0.727737	+	0.685857i	$0.759428\pi$
$600$	−3.25360	−	1.44859i	−0.132827	−	0.0591386i
$601$	−7.97445	−	24.5428i	−0.325285	−	1.00112i	−0.971312	−	0.237809i	$-0.923571\pi$
$601$	−7.97445	−	24.5428i	−0.325285	−	1.00112i	0.646027	−	0.763314i	$-0.276429\pi$
$602$	2.58015	+	10.7998i	0.105159	+	0.440166i
$603$	0.898195	+	0.652577i	0.0365773	+	0.0265750i
$604$	−4.11173	−	7.12173i	−0.167304	−	0.289779i
$605$	−7.98192	+	31.1806i	−0.324511	+	1.26767i
$606$	−4.15735	+	7.20074i	−0.168881	+	0.292510i
$607$	1.56429	−	14.8832i	0.0634926	−	0.604091i	−0.915799	−	0.401637i	$-0.868441\pi$
$607$	1.56429	−	14.8832i	0.0634926	−	0.604091i	0.979292	−	0.202455i	$-0.0648919\pi$
$608$	−2.04054	+	6.28015i	−0.0827550	+	0.254694i
$609$	2.59369	−	13.9083i	0.105102	−	0.563594i
$610$	25.1336	−	18.2606i	1.01763	−	0.739351i
$611$	0.859503	+	0.382675i	0.0347718	+	0.0154814i
$612$	−1.49191	−	0.317116i	−0.0603070	−	0.0128187i
$613$	15.7903	+	17.5369i	0.637762	+	0.708307i	0.972211	−	0.234107i	$-0.0752167\pi$
$613$	15.7903	+	17.5369i	0.637762	+	0.708307i	−0.334448	+	0.942414i	$0.608550\pi$
$614$	−0.995743	+	9.47386i	−0.0401849	+	0.382334i
$615$	34.5766			1.39426
$616$	−5.49160	+	6.84414i	−0.221263	+	0.275758i
$617$	43.2502			1.74119			0.870595	−	0.492001i	$-0.163734\pi$
$617$	43.2502			1.74119			0.870595	+	0.492001i	$0.163734\pi$
$618$	1.06101	−	10.0948i	0.0426799	−	0.406072i
$619$	−11.9838	−	13.3094i	−0.481671	−	0.534950i	0.452505	−	0.891762i	$-0.350531\pi$
$619$	−11.9838	−	13.3094i	−0.481671	−	0.534950i	−0.934176	+	0.356812i	$0.883864\pi$
$620$	−8.96672	−	1.90593i	−0.360112	−	0.0765442i
$621$	1.36120	+	0.606044i	0.0546229	+	0.0243197i
$622$	10.7536	−	7.81295i	0.431180	−	0.313271i
$623$	6.36042	+	5.44451i	0.254825	+	0.218130i
$624$	0.354590	−	1.09132i	0.0141950	−	0.0436876i
$625$	3.14873	−	29.9582i	0.125949	−	1.19833i
$626$	14.9336	−	25.8658i	0.596868	−	1.03381i
$627$	5.23172	+	21.2667i	0.208935	+	0.849312i
$628$	−10.9925	−	19.0396i	−0.438650	−	0.759764i
$629$	4.66561	+	3.38976i	0.186030	+	0.135159i
$630$	−7.42024	−	2.20692i	−0.295630	−	0.0879257i
$631$	−3.77694	−	11.6242i	−0.150358	−	0.462753i	0.847303	−	0.531109i	$-0.178225\pi$
$631$	−3.77694	−	11.6242i	−0.150358	−	0.462753i	−0.997661	+	0.0683561i	$0.978225\pi$
$632$	−9.09751	−	4.05047i	−0.361880	−	0.161119i
$633$	1.49760	+	14.2487i	0.0595241	+	0.566334i
$634$	−11.2692	−	2.39534i	−0.447557	−	0.0951312i
$635$	−22.2601	+	4.73154i	−0.883367	+	0.187765i
$636$	10.0250	+	7.28359i	0.397517	+	0.288813i
$637$	8.02225	−	0.402612i	0.317853	−	0.0159521i
$638$	15.6335	+	8.37535i	0.618935	+	0.331583i
$639$	2.76099	+	4.78217i	0.109223	+	0.189180i
$640$	2.67304	−	1.19011i	0.105661	−	0.0470434i
$641$	−6.42143	−	7.13172i	−0.253631	−	0.281686i	0.602861	−	0.797846i	$-0.294027\pi$
$641$	−6.42143	−	7.13172i	−0.253631	−	0.281686i	−0.856492	+	0.516160i	$0.827361\pi$
$642$	−13.2863	+	14.7559i	−0.524367	+	0.582369i
$643$	18.9801	−	13.7898i	0.748501	−	0.543818i	−0.146861	−	0.989157i	$-0.546917\pi$
$643$	18.9801	−	13.7898i	0.748501	−	0.543818i	0.895362	+	0.445339i	$0.146917\pi$
$644$	−2.39640	−	3.13022i	−0.0944313	−	0.123348i
$645$	−3.79469	−	11.6789i	−0.149416	−	0.459854i
$646$	9.85162	−	2.09403i	0.387607	−	0.0823883i
$647$	26.3096	−	11.7138i	1.03434	−	0.460517i	0.181885	−	0.983320i	$-0.441780\pi$
$647$	26.3096	−	11.7138i	1.03434	−	0.460517i	0.852454	+	0.522802i	$0.175113\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	27.3921	+	35.2875i	1.07523	+	1.38515i
$650$	−4.08675			−0.160295
$651$	−8.26274	−	0.659500i	−0.323842	−	0.0258479i
$652$	2.34815	−	7.22688i	0.0919608	−	0.283026i
$653$	17.9951	−	19.9856i	0.704202	−	0.782096i	−0.279837	−	0.960048i	$-0.590280\pi$
$653$	17.9951	−	19.9856i	0.704202	−	0.782096i	0.984039	+	0.177952i	$0.0569471\pi$
$654$	0.267210	+	2.54233i	0.0104487	+	0.0994132i
$655$	2.26630	+	21.5624i	0.0885517	+	0.842513i
$656$	−7.90712	+	8.78174i	−0.308721	+	0.342870i
$657$	2.90108	−	8.92859i	0.113182	−	0.348338i
$658$	0.931744	+	1.95902i	0.0363231	+	0.0763706i
$659$	15.1694			0.590914			0.295457	−	0.955356i	$-0.404528\pi$
$659$	15.1694			0.590914			0.295457	+	0.955356i	$0.404528\pi$
$660$	5.45183	−	8.02833i	0.212212	−	0.312502i
$661$	−1.61796	+	2.80238i	−0.0629312	+	0.109000i	−0.895774	−	0.444509i	$-0.853378\pi$
$661$	−1.61796	+	2.80238i	−0.0629312	+	0.109000i	0.832843	+	0.553509i	$0.186712\pi$
$662$	18.2333	−	8.11800i	0.708658	−	0.315515i
$663$	−1.71194	+	0.363884i	−0.0664862	+	0.0141321i
$664$	4.13801	+	12.7355i	0.160586	+	0.494232i
$665$	50.6897	−	6.61632i	1.96566	−	0.256570i
$666$	3.05893	−	2.22244i	0.118531	−	0.0861178i
$667$	−5.33152	+	5.92125i	−0.206437	+	0.229272i
$668$	9.94354	+	11.0434i	0.384727	+	0.427283i
$669$	9.16651	−	4.08119i	0.354398	−	0.157788i
$670$	1.62427	+	2.81332i	0.0627510	+	0.108688i
$671$	15.3377	+	31.6985i	0.592107	+	1.22371i
$672$	2.25740	−	1.37990i	0.0870812	−	0.0532309i
$673$	31.7876	+	23.0950i	1.22532	+	0.890247i	0.996530	−	0.0832285i	$-0.0265231\pi$
$673$	31.7876	+	23.0950i	1.22532	+	0.890247i	0.228790	+	0.973476i	$0.426523\pi$
$674$	−10.2414	+	2.17688i	−0.394484	+	0.0838502i
$675$	3.48368	+	0.740478i	0.134087	+	0.0285010i
$676$	1.22124	+	11.6193i	0.0469706	+	0.446896i
$677$	21.5698	+	9.60351i	0.828997	+	0.369093i	0.776958	−	0.629552i	$-0.216762\pi$
$677$	21.5698	+	9.60351i	0.828997	+	0.369093i	0.0520383	+	0.998645i	$0.483428\pi$
$678$	2.37818	+	7.31928i	0.0913334	+	0.281095i
$679$	−21.8302	−	6.49272i	−0.837768	−	0.249168i
$680$	−3.61054	−	2.62321i	−0.138458	−	0.100596i
$681$	2.13241	+	3.69344i	0.0817140	+	0.141533i
$682$	3.92262	−	9.62198i	0.150205	−	0.368445i
$683$	−14.6635	+	25.3980i	−0.561085	+	0.971828i	0.436317	+	0.899793i	$0.356283\pi$
$683$	−14.6635	+	25.3980i	−0.561085	+	0.971828i	−0.997402	+	0.0720349i	$0.977051\pi$
$684$	0.690237	−	6.56717i	0.0263919	−	0.251102i
$685$	10.8872	−	33.5074i	0.415979	−	1.28025i
$686$	14.6556	+	11.3232i	0.559552	+	0.432321i
$687$	−4.66191	+	3.38707i	−0.177863	+	0.129225i
$688$	3.83397	+	1.70699i	0.146169	+	0.0650785i
$689$	13.9084	+	2.95631i	0.529866	+	0.112627i
$690$	2.91727	+	3.23996i	0.111059	+	0.123343i
$691$	−2.86252	+	27.2351i	−0.108895	+	1.03607i	0.794501	+	0.607263i	$0.207733\pi$
$691$	−2.86252	+	27.2351i	−0.108895	+	1.03607i	−0.903396	+	0.428807i	$0.858934\pi$
$692$	15.2131			0.578315
$693$	3.94862	−	7.83635i	0.149996	−	0.297678i
$694$	−1.58917			−0.0603241
$695$	4.69337	−	44.6545i	0.178030	−	1.69384i
$696$	−3.57817	−	3.97396i	−0.135630	−	0.150632i
$697$	17.6300	+	3.74736i	0.667782	+	0.141941i
$698$	1.64157	+	0.730873i	0.0621342	+	0.0276639i
$699$	19.6972	−	14.3109i	0.745018	−	0.541287i
$700$	−7.15841	−	6.12759i	−0.270563	−	0.231601i
$701$	6.60359	−	20.3237i	0.249414	−	0.767617i	−0.745465	−	0.666545i	$-0.767773\pi$
$701$	6.60359	−	20.3237i	0.249414	−	0.767617i	0.994879	−	0.101073i	$-0.0322275\pi$
$702$	−0.119944	+	1.14119i	−0.00452700	+	0.0430715i
$703$	−12.4837	+	21.6225i	−0.470833	+	0.815507i
$704$	0.792284	+	3.22060i	0.0298603	+	0.121381i
$705$	−1.19955	−	2.07768i	−0.0451776	−	0.0782499i
$706$	−4.70145	−	3.41581i	−0.176942	−	0.128556i
$707$	−15.9740	+	15.1252i	−0.600764	+	0.568841i
$708$	−4.16213	−	12.8097i	−0.156422	−	0.481419i
$709$	29.8065	+	13.2707i	1.11941	+	0.498392i	0.881162	−	0.472814i	$-0.156762\pi$
$709$	29.8065	+	13.2707i	1.11941	+	0.498392i	0.238244	+	0.971205i	$0.423428\pi$
$710$	1.68890	+	16.0688i	0.0633833	+	0.603052i
$711$	9.74085	+	2.07048i	0.365310	+	0.0776491i
$712$	3.09533	−	0.657933i	0.116002	−	0.0246571i
$713$	3.77661	+	2.74387i	0.141435	+	0.102759i
$714$	−3.54426	−	1.92946i	−0.132641	−	0.0722083i
$715$	1.96801	−	10.9604i	0.0735995	−	0.409895i
$716$	−4.04754	−	7.01054i	−0.151264	−	0.261996i
$717$	−14.8944	+	6.63141i	−0.556241	+	0.247654i
$718$	13.3641	+	14.8423i	0.498743	+	0.553910i
$719$	−1.92979	+	2.14325i	−0.0719692	+	0.0799299i	−0.778054	−	0.628197i	$-0.783793\pi$
$719$	−1.92979	+	2.14325i	−0.0719692	+	0.0799299i	0.706085	+	0.708127i	$0.250460\pi$
$720$	−2.36719	+	1.71986i	−0.0882199	+	0.0640955i
$721$	10.3046	−	24.7998i	0.383764	−	0.923593i
$722$	7.60309	+	23.3999i	0.282958	+	0.870854i
$723$	−19.5519	+	4.15588i	−0.727143	+	0.154559i
$724$	−2.84066	+	1.26475i	−0.105572	+	0.0470039i
$725$	−9.52254	+	16.4935i	−0.353658	+	0.612554i
$726$	7.86473	+	7.69064i	0.291888	+	0.285427i
$727$	0.0274808			0.00101921			0.000509604	−	1.00000i	$-0.499838\pi$
$727$	0.0274808			0.00101921			0.000509604		1.00000i	$0.499838\pi$
$728$	1.72235	−	2.50009i	0.0638344	−	0.0926596i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	18.3807	−	20.4139i	0.680301	−	0.755551i
$731$	−0.669103	−	6.36609i	−0.0247477	−	0.235458i
$732$	−1.10983	−	10.5593i	−0.0410205	−	0.390284i
$733$	−29.4025	+	32.6548i	−1.08601	+	1.20613i	−0.108749	+	0.994069i	$0.534684\pi$
$733$	−29.4025	+	32.6548i	−1.08601	+	1.20613i	−0.977256	+	0.212062i	$0.931982\pi$
$734$	8.65541	−	26.6386i	0.319477	−	0.983249i
$735$	−17.1529	−	11.1933i	−0.632695	−	0.412872i
$736$	−1.49001			−0.0549227
$737$	−3.46408	+	1.24855i	−0.127601	+	0.0459910i
$738$	5.90850	−	10.2338i	0.217495	−	0.376712i
$739$	−34.5459	+	15.3808i	−1.27079	+	0.565792i	−0.927635	−	0.373487i	$-0.878162\pi$
$739$	−34.5459	+	15.3808i	−1.27079	+	0.565792i	−0.343154	+	0.939279i	$0.611495\pi$
$740$	10.8216	−	2.30020i	0.397809	−	0.0845569i
$741$	−2.34148	−	7.20633i	−0.0860164	−	0.264731i
$742$	19.9295	+	26.0322i	0.731634	+	0.955673i
$743$	24.6493	−	17.9088i	0.904295	−	0.657009i	−0.0352708	−	0.999378i	$-0.511229\pi$
$743$	24.6493	−	17.9088i	0.904295	−	0.657009i	0.939565	+	0.342369i	$0.111229\pi$
$744$	−2.09636	+	2.32824i	−0.0768561	+	0.0853574i
$745$	−14.4553	−	16.0542i	−0.529599	−	0.588180i
$746$	−5.43271	+	2.41880i	−0.198906	+	0.0885585i
$747$	−6.69544	−	11.5968i	−0.244973	−	0.424306i
$748$	3.64988	−	3.50263i	0.133453	−	0.128069i
$749$	−44.8231	+	27.3994i	−1.63780	+	1.00115i
$750$	−3.40519	−	2.47402i	−0.124340	−	0.0903383i
$751$	48.5982	−	10.3299i	1.77337	−	0.376942i	0.798904	−	0.601458i	$-0.205413\pi$
$751$	48.5982	−	10.3299i	1.77337	−	0.376942i	0.974471	+	0.224515i	$0.0720799\pi$
$752$	0.802005	+	0.170472i	0.0292461	+	0.00621646i
$753$	0.347499	+	3.30623i	0.0126636	+	0.120486i
$754$	−5.60562	−	2.49578i	−0.204145	−	0.0908911i
$755$	7.43553	+	22.8842i	0.270607	+	0.832842i
$756$	−1.92118	+	1.81909i	−0.0698725	+	0.0661596i
$757$	−33.1432	−	24.0799i	−1.20461	−	0.875200i	−0.209880	−	0.977727i	$-0.567307\pi$
$757$	−33.1432	−	24.0799i	−1.20461	−	0.875200i	−0.994730	+	0.102527i	$0.967307\pi$
$758$	−11.1059	−	19.2360i	−0.403384	−	0.698681i
$759$	−4.19908	+	2.60563i	−0.152417	+	0.0945784i
$760$	9.66070	−	16.7328i	0.350431	−	0.606964i
$761$	2.29977	−	21.8808i	0.0833665	−	0.793179i	−0.870342	−	0.492447i	$-0.836102\pi$
$761$	2.29977	−	21.8808i	0.0833665	−	0.793179i	0.953709	−	0.300732i	$-0.0972309\pi$
$762$	−2.40343	+	7.39699i	−0.0870670	+	0.267965i
$763$	−1.23990	+	6.64881i	−0.0448875	+	0.240703i
$764$	−15.4978	+	11.2598i	−0.560690	+	0.407365i
$765$	4.07704	+	1.81521i	0.147406	+	0.0656292i
$766$	−7.43246	−	1.57982i	−0.268546	−	0.0570812i
$767$	−10.3416	−	11.4855i	−0.373414	−	0.414718i
$768$	0.104528	−	0.994522i	0.00377185	−	0.0358867i
$769$	−39.4988			−1.42436			−0.712182	−	0.701994i	$-0.752293\pi$
$769$	−39.4988			−1.42436			−0.712182	+	0.701994i	$0.752293\pi$
$770$	19.8810	−	16.2476i	0.716460	−	0.585521i
$771$	−15.7070			−0.565674
$772$	2.17620	−	20.7052i	0.0783231	−	0.745195i
$773$	−3.03926	−	3.37545i	−0.109315	−	0.121406i	0.686004	−	0.727598i	$-0.259363\pi$
$773$	−3.03926	−	3.37545i	−0.109315	−	0.121406i	−0.795319	+	0.606191i	$0.792697\pi$
$774$	−4.10509	−	0.872565i	−0.147555	−	0.0313637i
$775$	10.1934	+	4.53838i	0.366157	+	0.163023i
$776$	−6.96423	+	5.05981i	−0.250001	+	0.181636i
$777$	9.43359	−	3.32885i	0.338428	−	0.119422i
$778$	7.31525	−	22.5140i	0.262265	−	0.807167i
$779$	−8.15653	+	77.6042i	−0.292238	+	2.78046i
$780$	−1.67876	+	2.90770i	−0.0601093	+	0.104112i
$781$	−18.2656	−	1.33474i	−0.653596	−	0.0477608i
$782$	1.13632	+	1.96816i	0.0406346	+	0.0703813i
$783$	4.32621	+	3.14317i	0.154606	+	0.112328i
$784$	6.76548	−	1.79675i	0.241624	−	0.0641697i
$785$	19.8786	+	61.1799i	0.709496	+	2.18361i
$786$	6.76921	+	3.01385i	0.241450	+	0.107500i
$787$	2.58840	+	24.6270i	0.0922666	+	0.877858i	0.938554	+	0.345132i	$0.112166\pi$
$787$	2.58840	+	24.6270i	0.0922666	+	0.877858i	−0.846288	+	0.532726i	$0.821168\pi$
$788$	−5.30750	−	1.12814i	−0.189072	−	0.0401885i
$789$	−2.43274	+	0.517096i	−0.0866080	+	0.0184091i
$790$	23.5736	+	17.1272i	0.838709	+	0.609358i
$791$	0.510460	+	20.3552i	0.0181499	+	0.723746i
$792$	−1.44457	−	2.98550i	−0.0513306	−	0.106085i
$793$	−6.09167	−	10.5511i	−0.216321	−	0.374680i
$794$	−15.7187	+	6.99841i	−0.557835	+	0.248364i
$795$	−24.2612	−	26.9448i	−0.860458	−	0.955635i
$796$	6.21350	−	6.90079i	0.220232	−	0.244592i
$797$	0.563517	−	0.409419i	0.0199608	−	0.0145024i	−0.577760	−	0.816207i	$-0.696073\pi$
$797$	0.563517	−	0.409419i	0.0199608	−	0.0145024i	0.597721	+	0.801704i	$0.296073\pi$
$798$	6.70366	−	16.1335i	0.237307	−	0.571120i
$799$	−0.386451	−	1.18937i	−0.0136717	−	0.0420770i
$800$	−3.48368	+	0.740478i	−0.123167	+	0.0261799i
$801$	−2.89090	+	1.28711i	−0.102145	+	0.0454778i
$802$	−10.6110	+	18.3788i	−0.374688	+	0.648979i
$803$	19.0928	+	24.5960i	0.673769	+	0.867973i
$804$	1.11023			0.0391548
$805$	4.95438	+	10.4167i	0.174619	+	0.367142i
$806$	−1.11091	+	3.41904i	−0.0391303	+	0.120431i
$807$	−1.21425	+	1.34856i	−0.0427435	+	0.0474715i
$808$	0.869123	+	8.26915i	0.0305756	+	0.290908i
$809$	−4.33366	−	41.2320i	−0.152363	−	1.44964i	−0.757144	−	0.653247i	$-0.773406\pi$
$809$	−4.33366	−	41.2320i	−0.152363	−	1.44964i	0.604781	−	0.796392i	$-0.293261\pi$
$810$	1.95788	−	2.17445i	0.0687929	−	0.0764022i
$811$	−15.8140	+	48.6704i	−0.555304	+	1.70905i	0.139834	+	0.990175i	$0.455343\pi$
$811$	−15.8140	+	48.6704i	−0.555304	+	1.70905i	−0.695139	+	0.718876i	$0.744657\pi$
$812$	−6.07677	−	12.7766i	−0.213253	−	0.448371i
$813$	24.7903			0.869435
$814$	0.398407	+	12.5340i	0.0139642	+	0.439315i
$815$	−11.1170	+	19.2553i	−0.389413	+	0.674483i
$816$	−1.39338	+	0.620373i	−0.0487780	+	0.0217174i
$817$	27.1073	−	5.76184i	0.948366	−	0.201581i
$818$	3.93030	+	12.0962i	0.137420	+	0.422934i
$819$	−1.16491	+	2.80356i	−0.0407052	+	0.0979641i
$820$	27.9731	−	20.3236i	0.976862	−	0.709732i
$821$	0.693247	−	0.769929i	0.0241945	−	0.0268707i	−0.730926	−	0.682457i	$-0.760912\pi$
$821$	0.693247	−	0.769929i	0.0241945	−	0.0268707i	0.755121	+	0.655586i	$0.227578\pi$
$822$	−8.05694	−	8.94814i	−0.281018	−	0.312102i
$823$	−43.0091	+	19.1489i	−1.49920	+	0.667488i	−0.982087	−	0.188428i	$-0.939661\pi$
$823$	−43.0091	+	19.1489i	−1.49920	+	0.667488i	−0.517115	+	0.855916i	$0.672994\pi$
$824$	−5.07520	−	8.79051i	−0.176803	−	0.306232i
$825$	−8.52261	+	8.17878i	−0.296719	+	0.284749i
$826$	−0.893373	−	35.6243i	−0.0310844	−	1.23953i
$827$	−30.5206	−	22.1745i	−1.06130	−	0.771083i	−0.0869753	−	0.996210i	$-0.527720\pi$
$827$	−30.5206	−	22.1745i	−1.06130	−	0.771083i	−0.974329	+	0.225128i	$0.927720\pi$
$828$	1.45745	−	0.309791i	0.0506500	−	0.0107660i
$829$	26.0224	+	5.53122i	0.903794	+	0.192107i	0.636290	−	0.771450i	$-0.280468\pi$
$829$	26.0224	+	5.53122i	0.903794	+	0.192107i	0.267503	+	0.963557i	$0.413801\pi$
$830$	−4.09561	−	38.9671i	−0.142161	−	1.35257i
$831$	4.36898	+	1.94519i	0.151558	+	0.0674781i
$832$	−0.354590	−	1.09132i	−0.0122932	−	0.0378346i
$833$	−7.53283	−	7.56628i	−0.260997	−	0.262156i
$834$	−12.4146	−	9.01974i	−0.429883	−	0.312328i
$835$	−21.7408	−	37.6561i	−0.752371	−	1.30314i
$836$	16.7328	+	14.1300i	0.578717	+	0.488697i
$837$	1.56648	−	2.71322i	0.0541454	−	0.0937825i
$838$	−1.83854	+	17.4925i	−0.0635113	+	0.604269i
$839$	0.332153	−	1.02226i	0.0114672	−	0.0352924i	−0.945159	−	0.326610i	$-0.894094\pi$
$839$	0.332153	−	1.02226i	0.0114672	−	0.0352924i	0.956626	+	0.291318i	$0.0940936\pi$
$840$	−7.30030	+	2.57608i	−0.251884	+	0.0888831i
$841$	0.327176	−	0.237707i	0.0112819	−	0.00819680i
$842$	−32.6476	−	14.5356i	−1.12511	−	0.500931i
$843$	−17.1133	−	3.63755i	−0.589414	−	0.125284i
$844$	9.58674	+	10.6471i	0.329989	+	0.366490i
$845$	3.57334	−	33.9981i	0.122927	−	1.16957i
$846$	−0.819923			−0.0281895
$847$	14.1441	+	25.4351i	0.485996	+	0.873961i
$848$	12.3916			0.425529
$849$	2.95750	−	28.1388i	0.101501	−	0.965720i
$850$	3.63483	+	4.03688i	0.124674	+	0.138464i
$851$	−5.51069	−	1.17133i	−0.188904	−	0.0401528i
$852$	5.04458	+	2.24599i	0.172824	+	0.0769464i
$853$	−40.6836	+	29.5584i	−1.39298	+	1.01206i	−0.397451	+	0.917624i	$0.630105\pi$
$853$	−40.6836	+	29.5584i	−1.39298	+	1.01206i	−0.995531	+	0.0944367i	$0.969895\pi$
$854$	5.14981	−	27.6152i	0.176223	−	0.944972i
$855$	−5.97064	+	18.3758i	−0.204192	+	0.628437i
$856$	−2.07552	+	19.7473i	−0.0709398	+	0.674947i
$857$	10.1365	−	17.5570i	0.346257	−	0.599735i	−0.639324	−	0.768937i	$-0.720786\pi$
$857$	10.1365	−	17.5570i	0.346257	−	0.599735i	0.985581	+	0.169202i	$0.0541191\pi$
$858$	−2.90770	−	2.45541i	−0.0992673	−	0.0838262i
$859$	−15.0153	−	26.0072i	−0.512314	−	0.887354i	−0.999898	−	0.0142782i	$-0.995455\pi$
$859$	−15.0153	−	26.0072i	−0.512314	−	0.887354i	0.487584	−	0.873076i	$-0.337878\pi$
$860$	−9.93462	−	7.21793i	−0.338768	−	0.246129i
$861$	22.7025	−	21.4962i	0.773701	−	0.732588i
$862$	9.49035	+	29.2083i	0.323243	+	0.994839i
$863$	−43.4759	−	19.3567i	−1.47994	−	0.658911i	−0.501444	−	0.865190i	$-0.667198\pi$
$863$	−43.4759	−	19.3567i	−1.47994	−	0.658911i	−0.978493	+	0.206279i	$0.933864\pi$
$864$	0.104528	+	0.994522i	0.00355613	+	0.0338343i
$865$	−43.5408	−	9.25489i	−1.48043	−	0.314676i
$866$	−28.6955	+	6.09941i	−0.975111	+	0.207266i
$867$	−11.8712	−	8.62494i	−0.403168	−	0.292918i
$868$	−7.07234	+	4.32317i	−0.240051	+	0.146738i
$869$	−23.8304	+	22.8690i	−0.808392	+	0.775778i
$870$	7.82338	+	13.5505i	0.265237	+	0.459405i
$871$	1.16382	−	0.518168i	0.0394347	−	0.0175574i
$872$	1.71052	+	1.89973i	0.0579257	+	0.0643330i
$873$	5.76005	−	6.39718i	0.194948	−	0.216512i
$874$	−7.95998	+	5.78326i	−0.269250	+	0.195622i
$875$	−6.76943	−	8.84236i	−0.228849	−	0.298926i
$876$	−2.90108	−	8.92859i	−0.0980183	−	0.301669i
$877$	40.8879	−	8.69099i	1.38069	−	0.293474i	0.543049	−	0.839701i	$-0.317270\pi$
$877$	40.8879	−	8.69099i	1.38069	−	0.293474i	0.837637	+	0.546227i	$0.183936\pi$
$878$	−6.79709	+	3.02626i	−0.229391	+	0.102131i
$879$	6.75782	−	11.7049i	0.227936	−	0.394796i
$880$	−0.308312	−	9.69956i	−0.0103932	−	0.326972i
$881$	17.3067			0.583079			0.291540	−	0.956559i	$-0.405832\pi$
$881$	17.3067			0.583079			0.291540	+	0.956559i	$0.405832\pi$
$882$	−6.24407	+	3.16411i	−0.210249	+	0.106541i
$883$	−7.52678	+	23.1651i	−0.253296	+	0.779566i	0.740864	+	0.671655i	$0.234416\pi$
$883$	−7.52678	+	23.1651i	−0.253296	+	0.779566i	−0.994161	+	0.107911i	$0.965584\pi$
$884$	−1.17110	+	1.30064i	−0.0393884	+	0.0437453i
$885$	4.11948	+	39.1943i	0.138475	+	1.31750i
$886$	−3.89133	−	37.0235i	−0.130732	−	1.24383i
$887$	−10.2086	+	11.3378i	−0.342772	+	0.380687i	−0.889741	−	0.456466i	$-0.849115\pi$
$887$	−10.2086	+	11.3378i	−0.342772	+	0.380687i	0.546969	+	0.837153i	$0.315782\pi$
$888$	1.16841	−	3.59598i	0.0392091	−	0.120673i
$889$	−11.6741	+	16.9457i	−0.391538	+	0.568342i
$890$	−9.25929			−0.310372
$891$	2.03372	+	2.61992i	0.0681324	+	0.0877705i
$892$	5.01699	−	8.68969i	0.167981	−	0.290952i
$893$	4.94614	−	2.20217i	0.165516	−	0.0736927i
$894$	−7.22178	+	1.53504i	−0.241532	+	0.0513393i
$895$	7.31944	+	22.5269i	0.244662	+	0.752992i
$896$	1.01519	−	2.44323i	0.0339152	−	0.0816227i
$897$	1.38322	−	1.00497i	0.0461845	−	0.0335550i
$898$	8.31907	−	9.23926i	0.277611	−	0.308318i
$899$	11.2102	+	12.4502i	0.373882	+	0.415238i
$900$	3.25360	−	1.44859i	0.108453	−	0.0482865i
$901$	−9.45010	−	16.3681i	−0.314828	−	0.545299i
$902$	17.0705	+	35.2797i	0.568386	+	1.17468i
$903$	−9.75225	−	5.30903i	−0.324535	−	0.176674i
$904$	6.22615	+	4.52356i	0.207079	+	0.150452i
$905$	8.89957	−	1.89166i	0.295832	−	0.0628810i
$906$	8.04376	+	1.70975i	0.267236	+	0.0568028i
$907$	0.344156	+	3.27443i	0.0114275	+	0.108726i	0.998749	−	0.0500094i	$-0.0159251\pi$
$907$	0.344156	+	3.27443i	0.0114275	+	0.108726i	−0.987321	+	0.158735i	$0.949258\pi$
$908$	3.89610	+	1.73466i	0.129297	+	0.0575666i
$909$	−2.56938	−	7.90775i	−0.0852211	−	0.262284i
$910$	−6.45040	+	6.10764i	−0.213829	+	0.202466i
$911$	34.2584	+	24.8902i	1.13503	+	0.824649i	0.986419	−	0.164247i	$-0.0525194\pi$
$911$	34.2584	+	24.8902i	1.13503	+	0.824649i	0.148612	+	0.988896i	$0.452519\pi$
$912$	−3.30167	−	5.71866i	−0.109329	−	0.189364i
$913$	44.2944	+	3.23676i	1.46593	+	0.107121i
$914$	−15.5036	+	26.8530i	−0.512813	+	0.888219i
$915$	−3.24737	+	30.8966i	−0.107355	+	1.02141i
$916$	−1.78069	+	5.48040i	−0.0588357	+	0.181078i
$917$	14.8933	+	12.7486i	0.491821	+	0.420997i
$918$	1.23395	−	0.896516i	0.0407264	−	0.0295894i
$919$	−22.7982	−	10.1504i	−0.752043	−	0.334831i	−0.00533741	−	0.999986i	$-0.501699\pi$
$919$	−22.7982	−	10.1504i	−0.752043	−	0.334831i	−0.746706	+	0.665155i	$0.768366\pi$
$920$	4.26452	+	0.906451i	0.140597	+	0.0298848i
$921$	−6.37417	−	7.07923i	−0.210036	−	0.233269i
$922$	3.47739	−	33.0852i	0.114522	−	1.08960i
$923$	6.33635			0.208563
$924$	−1.41159	−	8.66068i	−0.0464379	−	0.284916i
$925$	−13.4662			−0.442765
$926$	−1.56567	+	14.8963i	−0.0514510	+	0.489523i
$927$	6.79195	+	7.54322i	0.223077	+	0.247752i
$928$	−5.23063	−	1.11180i	−0.171704	−	0.0364968i
$929$	32.4000	+	14.4254i	1.06301	+	0.473282i	0.862315	−	0.506372i	$-0.169014\pi$
$929$	32.4000	+	14.4254i	1.06301	+	0.473282i	0.200694	+	0.979654i	$0.435680\pi$
$930$	7.41629	−	5.38825i	0.243190	−	0.176688i
$931$	29.1688	−	35.8578i	0.955969	−	1.17519i
$932$	7.52368	−	23.1555i	0.246446	−	0.758484i
$933$	−1.38941	+	13.2194i	−0.0454873	+	0.432783i
$934$	14.8762	−	25.7664i	0.486765	−	0.843101i
$935$	−12.5770	+	7.80435i	−0.411313	+	0.255230i
$936$	0.573739	+	0.993745i	0.0187532	+	0.0324816i
$937$	−4.64241	−	3.37291i	−0.151661	−	0.110188i	0.509367	−	0.860549i	$-0.329880\pi$
$937$	−4.64241	−	3.37291i	−0.151661	−	0.110188i	−0.661028	+	0.750361i	$0.729880\pi$
$938$	2.81550	+	0.837383i	0.0919294	+	0.0273415i
$939$	9.22949	+	28.4055i	0.301193	+	0.926977i
$940$	−2.19168	−	0.975801i	−0.0714849	−	0.0318271i
$941$	1.09798	+	10.4466i	0.0357932	+	0.340550i	0.997733	+	0.0672899i	$0.0214352\pi$
$941$	1.09798	+	10.4466i	0.0357932	+	0.340550i	−0.961940	+	0.273260i	$0.911898\pi$
$942$	21.5046	+	4.57095i	0.700659	+	0.148930i
$943$	−17.2227	+	3.66081i	−0.560850	+	0.119212i
$944$	−10.8966	−	7.91684i	−0.354654	−	0.257671i
$945$	6.60517	−	4.03760i	0.214866	−	0.131343i
$946$	10.0429	−	9.63771i	0.326522	−	0.313349i
$947$	−22.6783	−	39.2800i	−0.736946	−	1.27643i	−0.953864	−	0.300238i	$-0.902934\pi$
$947$	−22.6783	−	39.2800i	−0.736946	−	1.27643i	0.216918	−	0.976190i	$-0.430400\pi$
$948$	9.09751	−	4.05047i	0.295473	−	0.131553i
$949$	−7.20829	−	8.00561i	−0.233991	−	0.259873i
$950$	−15.7365	+	17.4771i	−0.510559	+	0.567034i
$951$	9.32065	−	6.77185i	0.302243	−	0.219592i
$952$	−4.00147	+	0.522296i	−0.129689	+	0.0169277i
$953$	−6.62476	−	20.3889i	−0.214597	−	0.660462i	−0.999182	−	0.0404406i	$-0.987124\pi$
$953$	−6.62476	−	20.3889i	−0.214597	−	0.660462i	0.784585	−	0.620022i	$-0.212876\pi$
$954$	−12.1208	+	2.57636i	−0.392426	+	0.0834126i
$955$	51.2055	−	22.7982i	1.65697	−	0.737732i
$956$	−8.15197	+	14.1196i	−0.263654	+	0.456661i
$957$	−16.6849	+	6.01372i	−0.539347	+	0.194396i
$958$	3.12694			0.101027
$959$	−13.6830	−	28.7691i	−0.441849	−	0.929001i
$960$	−0.904185	+	2.78280i	−0.0291825	+	0.0898144i
$961$	−14.1753	+	15.7432i	−0.457266	+	0.507846i
$962$	−0.453513	−	4.31489i	−0.0146219	−	0.139118i
$963$	−2.07552	−	19.7473i	−0.0668827	−	0.636346i
$964$	−13.3750	+	14.8545i	−0.430781	+	0.478431i
$965$	−18.8244	+	57.9356i	−0.605979	+	1.86501i
$966$	3.92971	+	0.313654i	0.126436	+	0.0100917i
$967$	6.38864			0.205445			0.102722	−	0.994710i	$-0.467245\pi$
$967$	6.38864			0.205445			0.102722	+	0.994710i	$0.467245\pi$
$968$	10.8831	+	1.59909i	0.349798	+	0.0513966i
$969$	−5.03585	+	8.72235i	−0.161775	+	0.280202i
$970$	23.0102	−	10.2448i	0.738813	−	0.328941i
$971$	14.6515	−	3.11428i	0.470190	−	0.0999419i	0.0332776	−	0.999446i	$-0.489405\pi$
$971$	14.6515	−	3.11428i	0.470190	−	0.0999419i	0.436912	+	0.899504i	$0.356072\pi$
$972$	−0.309017	−	0.951057i	−0.00991172	−	0.0305052i
$973$	−24.6799	−	32.2374i	−0.791203	−	1.03348i
$974$	15.4033	−	11.1912i	0.493554	−	0.358588i
$975$	2.73457	−	3.03704i	0.0875762	−	0.0972633i
$976$	−7.10449	−	7.89033i	−0.227409	−	0.252563i
$977$	36.9315	−	16.4430i	1.18154	−	0.526057i	0.280529	−	0.959846i	$-0.409490\pi$
$977$	36.9315	−	16.4430i	1.18154	−	0.526057i	0.901015	+	0.433788i	$0.142823\pi$
$978$	3.79939	+	6.58074i	0.121491	+	0.210429i
$979$	1.85486	−	10.3302i	0.0592816	−	0.330154i
$980$	−20.4563	+	1.02664i	−0.653452	+	0.0327947i
$981$	−2.06812	−	1.50258i	−0.0660300	−	0.0479736i
$982$	−10.5337	+	2.23901i	−0.336145	+	0.0714498i
$983$	−25.5869	−	5.43867i	−0.816096	−	0.173467i	−0.219092	−	0.975704i	$-0.570309\pi$
$983$	−25.5869	−	5.43867i	−0.816096	−	0.173467i	−0.597005	+	0.802238i	$0.703643\pi$
$984$	−1.23521	−	11.7523i	−0.0393772	−	0.374649i
$985$	14.5041	+	6.45765i	0.462139	+	0.205758i
$986$	2.52041	+	7.75703i	0.0802662	+	0.247034i
$987$	−2.07930	−	0.618421i	−0.0661847	−	0.0196846i
$988$	−6.13007	−	4.45376i	−0.195024	−	0.141693i
$989$	3.12665	+	5.41552i	0.0994217	+	0.172203i
$990$	2.31823	+	9.42350i	0.0736781	+	0.299499i
$991$	−16.7308	+	28.9786i	−0.531471	+	0.920534i	0.467855	+	0.883805i	$0.345027\pi$
$991$	−16.7308	+	28.9786i	−0.531471	+	0.920534i	−0.999325	+	0.0367287i	$0.988306\pi$
$992$	−0.327483	+	3.11579i	−0.0103976	+	0.0989265i
$993$	−6.16763	+	18.9820i	−0.195724	+	0.602376i
$994$	11.0989	+	9.50059i	0.352034	+	0.301341i
$995$	−21.9815	+	15.9705i	−0.696861	+	0.506299i
$996$	−12.2332	−	5.44656i	−0.387623	−	0.172581i
$997$	−22.5317	−	4.78927i	−0.713587	−	0.151678i	−0.163207	−	0.986592i	$-0.552184\pi$
$997$	−22.5317	−	4.78927i	−0.713587	−	0.151678i	−0.550380	+	0.834914i	$0.685517\pi$
$998$	21.4569	+	23.8303i	0.679205	+	0.754333i
$999$	−0.395226	+	3.76033i	−0.0125044	+	0.118971i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.d.235.5	yes	40
7.2	even	3	inner	462.2.y.d.37.1	yes	40
11.3	even	5	inner	462.2.y.d.25.1	✓	40
77.58	even	15	inner	462.2.y.d.289.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.d.25.1	✓	40	11.3	even	5	inner
462.2.y.d.37.1	yes	40	7.2	even	3	inner
462.2.y.d.235.5	yes	40	1.1	even	1	trivial
462.2.y.d.289.5	yes	40	77.58	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 + 0.994522i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(2.67304 + 1.19011i) q^{5} +(0.809017 - 0.587785i) q^{6} +(2.49497 - 0.880407i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.104528 + 0.994522i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(2.67304 + 1.19011i) q^{5} +(0.809017 - 0.587785i) q^{6} +(2.49497 - 0.880407i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-1.46300 + 2.53399i) q^{10} +(-2.53399 - 2.13983i) q^{11} +(0.500000 + 0.866025i) q^{12} +(0.928329 + 0.674471i) q^{13} +(0.614789 + 2.57333i) q^{14} +(-0.904185 - 2.78280i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.159431 - 1.51689i) q^{17} +(-0.978148 - 0.207912i) q^{18} +(6.45904 - 1.37291i) q^{19} +(-2.36719 - 1.71986i) q^{20} +(-2.32373 - 1.26502i) q^{21} +(2.39298 - 2.29644i) q^{22} +(0.745007 + 1.29039i) q^{23} +(-0.913545 + 0.406737i) q^{24} +(2.38311 + 2.64671i) q^{25} +(-0.767813 + 0.852742i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-2.62350 + 0.342434i) q^{28} +(1.65246 + 5.08576i) q^{29} +(2.86206 - 0.608351i) q^{30} +(2.86210 - 1.27429i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.105370 + 3.31495i) q^{33} +1.52524 q^{34} +(7.71694 + 0.615937i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-2.53001 + 2.80986i) q^{37} +(0.690237 + 6.56717i) q^{38} +(-0.119944 - 1.14119i) q^{39} +(1.95788 - 2.17445i) q^{40} +(-3.65165 + 11.2386i) q^{41} +(1.50098 - 2.17877i) q^{42} +4.19680 q^{43} +(2.03372 + 2.61992i) q^{44} +(-1.46300 + 2.53399i) q^{45} +(-1.36120 + 0.606044i) q^{46} +(0.802005 - 0.170472i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(5.44977 - 4.39318i) q^{49} +(-2.88132 + 2.09340i) q^{50} +(-1.02059 + 1.13348i) q^{51} +(-0.767813 - 0.852742i) q^{52} +(11.3203 - 5.04011i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-4.22682 - 8.73559i) q^{55} +(-0.0663284 - 2.64492i) q^{56} +(-5.34222 - 3.88135i) q^{57} +(-5.23063 + 1.11180i) q^{58} +(-13.1746 - 2.80035i) q^{59} +(0.305851 + 2.90998i) q^{60} +(-9.69956 - 4.31852i) q^{61} +(0.968136 + 2.97962i) q^{62} +(0.614789 + 2.57333i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.67876 + 2.90770i) q^{65} +(-3.30781 - 0.241714i) q^{66} +(0.555115 - 0.961487i) q^{67} +(-0.159431 + 1.51689i) q^{68} +(0.460440 - 1.41709i) q^{69} +(-1.41920 + 7.61028i) q^{70} +(4.46737 - 3.24574i) q^{71} +(0.913545 + 0.406737i) q^{72} +(-9.18293 - 1.95189i) q^{73} +(-2.53001 - 2.80986i) q^{74} +(0.372279 - 3.54199i) q^{75} -6.60334 q^{76} +(-8.20617 - 3.10787i) q^{77} +1.14748 q^{78} +(1.04094 - 9.90391i) q^{79} +(1.95788 + 2.17445i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-10.7954 - 4.80641i) q^{82} +(-10.8334 + 7.87096i) q^{83} +(2.00994 + 1.72051i) q^{84} +(1.37910 - 4.24444i) q^{85} +(-0.438686 + 4.17381i) q^{86} +(2.67374 - 4.63106i) q^{87} +(-2.81815 + 1.74873i) q^{88} +(1.58224 + 2.74052i) q^{89} +(-2.36719 - 1.71986i) q^{90} +(2.90996 + 0.865477i) q^{91} +(-0.460440 - 1.41709i) q^{92} +(-2.86210 - 1.27429i) q^{93} +(0.0857053 + 0.815431i) q^{94} +(18.8992 + 4.01715i) q^{95} +(0.978148 - 0.207912i) q^{96} +(-6.96423 - 5.05981i) q^{97} +(3.79946 + 5.87912i) q^{98} +(2.39298 - 2.29644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9}+O(q^{10}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 20 q^{12} + 10 q^{13} + 5 q^{14} - 6 q^{15} + 5 q^{16} + 5 q^{18} - 13 q^{19} + 6 q^{20} - 2 q^{21} - 4 q^{22} - 20 q^{23} - 5 q^{24} + 12 q^{25} + 10 q^{27} - 3 q^{28} + 12 q^{29} + 3 q^{30} - 10 q^{31} - 20 q^{32} + 8 q^{33} - 13 q^{35} - 10 q^{36} + 3 q^{37} + 2 q^{38} + 5 q^{39} - 3 q^{40} - 44 q^{41} - 3 q^{42} + 36 q^{43} - 3 q^{44} + 12 q^{45} + 11 q^{47} + 10 q^{48} + 33 q^{49} - 4 q^{50} + 26 q^{53} + 20 q^{54} - 20 q^{55} + 8 q^{56} + 4 q^{57} - 6 q^{58} + 4 q^{59} + 3 q^{60} - 23 q^{61} + 5 q^{63} - 10 q^{64} - 50 q^{65} - 7 q^{66} - 108 q^{67} + 20 q^{69} - 86 q^{71} + 5 q^{72} - 35 q^{73} + 3 q^{74} - 2 q^{75} - 44 q^{76} - 37 q^{77} + 20 q^{78} + 3 q^{79} - 3 q^{80} + 5 q^{81} - 28 q^{82} - 88 q^{83} - 5 q^{84} + 96 q^{85} - 13 q^{86} + 6 q^{87} - 8 q^{88} + 6 q^{89} + 6 q^{90} + 40 q^{91} - 20 q^{92} + 10 q^{93} - 24 q^{94} + 36 q^{95} - 5 q^{96} + 60 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 20 * q^12 + 10 * q^13 + 5 * q^14 - 6 * q^15 + 5 * q^16 + 5 * q^18 - 13 * q^19 + 6 * q^20 - 2 * q^21 - 4 * q^22 - 20 * q^23 - 5 * q^24 + 12 * q^25 + 10 * q^27 - 3 * q^28 + 12 * q^29 + 3 * q^30 - 10 * q^31 - 20 * q^32 + 8 * q^33 - 13 * q^35 - 10 * q^36 + 3 * q^37 + 2 * q^38 + 5 * q^39 - 3 * q^40 - 44 * q^41 - 3 * q^42 + 36 * q^43 - 3 * q^44 + 12 * q^45 + 11 * q^47 + 10 * q^48 + 33 * q^49 - 4 * q^50 + 26 * q^53 + 20 * q^54 - 20 * q^55 + 8 * q^56 + 4 * q^57 - 6 * q^58 + 4 * q^59 + 3 * q^60 - 23 * q^61 + 5 * q^63 - 10 * q^64 - 50 * q^65 - 7 * q^66 - 108 * q^67 + 20 * q^69 - 86 * q^71 + 5 * q^72 - 35 * q^73 + 3 * q^74 - 2 * q^75 - 44 * q^76 - 37 * q^77 + 20 * q^78 + 3 * q^79 - 3 * q^80 + 5 * q^81 - 28 * q^82 - 88 * q^83 - 5 * q^84 + 96 * q^85 - 13 * q^86 + 6 * q^87 - 8 * q^88 + 6 * q^89 + 6 * q^90 + 40 * q^91 - 20 * q^92 + 10 * q^93 - 24 * q^94 + 36 * q^95 - 5 * q^96 + 60 * q^97 + 2 * q^98 - 4 * q^99

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