LMFDB - Embedded newform 429.2.bq.a.29.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(29,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 21, 10]))

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

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

chi := DirichletCharacter("429.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bq (of order $30$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			29.10
Character	$\chi$	$=$	429.29
Dual form			429.2.bq.a.74.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.198720 + 1.89069i) q^{2} +(-1.52365 + 0.823714i) q^{3} +(-1.57894 - 0.335614i) q^{4} +(-0.924919 - 1.27304i) q^{5} +(-1.25461 - 3.04444i) q^{6} +(0.668009 - 3.14273i) q^{7} +(-0.226639 + 0.697522i) q^{8} +(1.64299 - 2.51010i) q^{9} +O(q^{10})$	\(q+(-0.198720 + 1.89069i) q^{2} +(-1.52365 + 0.823714i) q^{3} +(-1.57894 - 0.335614i) q^{4} +(-0.924919 - 1.27304i) q^{5} +(-1.25461 - 3.04444i) q^{6} +(0.668009 - 3.14273i) q^{7} +(-0.226639 + 0.697522i) q^{8} +(1.64299 - 2.51010i) q^{9} +(2.59073 - 1.49576i) q^{10} +(3.22328 - 0.781308i) q^{11} +(2.68220 - 0.789239i) q^{12} +(1.59927 - 3.23146i) q^{13} +(5.80920 + 1.88752i) q^{14} +(2.45787 + 1.17779i) q^{15} +(-4.22308 - 1.88024i) q^{16} +(0.287247 + 2.73297i) q^{17} +(4.41933 + 3.60520i) q^{18} +(-1.27686 + 1.14969i) q^{19} +(1.03314 + 2.32047i) q^{20} +(1.57091 + 5.33866i) q^{21} +(0.836683 + 6.24951i) q^{22} +(0.956851 - 0.552438i) q^{23} +(-0.229242 - 1.24946i) q^{24} +(0.779925 - 2.40036i) q^{25} +(5.79190 + 3.66589i) q^{26} +(-0.435731 + 5.17785i) q^{27} +(-2.10949 + 4.73800i) q^{28} +(4.12146 - 4.57734i) q^{29} +(-2.71528 + 4.41303i) q^{30} +(-4.08780 - 2.96996i) q^{31} +(3.66075 - 6.34060i) q^{32} +(-4.26757 + 3.84550i) q^{33} -5.22430 q^{34} +(-4.61868 + 2.05637i) q^{35} +(-3.43661 + 3.41188i) q^{36} +(3.97080 - 4.41002i) q^{37} +(-1.91998 - 2.64262i) q^{38} +(0.225077 + 6.24094i) q^{39} +(1.09760 - 0.356631i) q^{40} +(-6.11774 + 1.30037i) q^{41} +(-10.4059 + 1.90921i) q^{42} +(6.01953 + 3.47538i) q^{43} +(-5.35159 + 0.151859i) q^{44} +(-4.71509 + 0.230042i) q^{45} +(0.854347 + 1.91889i) q^{46} +(7.67990 + 2.49535i) q^{47} +(7.98326 - 0.613799i) q^{48} +(-3.03572 - 1.35159i) q^{49} +(4.38336 + 1.95160i) q^{50} +(-2.68885 - 3.92747i) q^{51} +(-3.60968 + 4.56555i) q^{52} +(-2.61046 + 3.59299i) q^{53} +(-9.70315 - 1.85278i) q^{54} +(-3.97591 - 3.38073i) q^{55} +(2.04073 + 1.17822i) q^{56} +(0.998467 - 2.80349i) q^{57} +(7.83534 + 8.70203i) q^{58} +(0.958686 - 4.51026i) q^{59} +(-3.48555 - 2.68457i) q^{60} +(5.47524 - 0.575471i) q^{61} +(6.42762 - 7.13859i) q^{62} +(-6.79103 - 6.84024i) q^{63} +(3.78093 + 2.74700i) q^{64} +(-5.59298 + 0.952899i) q^{65} +(-6.42262 - 8.83284i) q^{66} +(-0.278631 - 0.482604i) q^{67} +(0.463679 - 4.41161i) q^{68} +(-1.00285 + 1.62989i) q^{69} +(-2.97014 - 9.14116i) q^{70} +(-5.73518 + 0.602792i) q^{71} +(1.37848 + 1.71491i) q^{72} +(2.84681 - 0.924985i) q^{73} +(7.54892 + 8.38393i) q^{74} +(0.788884 + 4.29974i) q^{75} +(2.40194 - 1.38676i) q^{76} +(-0.302261 - 10.6518i) q^{77} +(-11.8444 - 0.814648i) q^{78} +(7.94601 - 10.9367i) q^{79} +(1.51239 + 7.11523i) q^{80} +(-3.60117 - 8.24813i) q^{81} +(-1.24288 - 11.8252i) q^{82} +(2.27286 - 1.65133i) q^{83} +(-0.688638 - 8.95665i) q^{84} +(3.21351 - 2.89346i) q^{85} +(-7.76708 + 10.6905i) q^{86} +(-2.50922 + 10.3692i) q^{87} +(-0.185541 + 2.42539i) q^{88} +(1.48471 - 0.857200i) q^{89} +(0.502044 - 8.96051i) q^{90} +(-9.08729 - 7.18473i) q^{91} +(-1.69622 + 0.551135i) q^{92} +(8.67476 + 1.15799i) q^{93} +(-6.24410 + 14.0245i) q^{94} +(2.64460 + 0.562127i) q^{95} +(-0.354837 + 12.6762i) q^{96} +(-4.71081 + 2.09739i) q^{97} +(3.15870 - 5.47103i) q^{98} +(3.33466 - 9.37443i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9}+O(q^{10}) $ 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9	$ 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9} - 52 q^{12} - 20 q^{13} - 3 q^{15} + 30 q^{16} - 20 q^{18} - 10 q^{19} + 4 q^{22} + 5 q^{24} + 60 q^{25} - 24 q^{27} - 10 q^{28} - 65 q^{30} - 8 q^{31} + 49 q^{33} - 24 q^{34} + 3 q^{36} - 6 q^{37} - 35 q^{39} - 120 q^{40} - 13 q^{42} - 32 q^{45} - 30 q^{46} - 33 q^{48} - 26 q^{49} - 100 q^{51} - 60 q^{52} - 42 q^{55} - 20 q^{57} - 34 q^{58} + 32 q^{60} - 30 q^{61} - 45 q^{63} + 40 q^{64} + 42 q^{66} + 32 q^{67} - 33 q^{69} - 268 q^{70} + 55 q^{72} - 40 q^{73} + 9 q^{75} - 32 q^{78} - 37 q^{81} + 28 q^{82} - 180 q^{84} - 10 q^{85} - 142 q^{88} - 30 q^{90} + 8 q^{91} - 26 q^{93} - 90 q^{94} + 330 q^{96} - 14 q^{97} - 4 q^{99}+O(q^{100}) $ 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9 - 52 * q^12 - 20 * q^13 - 3 * q^15 + 30 * q^16 - 20 * q^18 - 10 * q^19 + 4 * q^22 + 5 * q^24 + 60 * q^25 - 24 * q^27 - 10 * q^28 - 65 * q^30 - 8 * q^31 + 49 * q^33 - 24 * q^34 + 3 * q^36 - 6 * q^37 - 35 * q^39 - 120 * q^40 - 13 * q^42 - 32 * q^45 - 30 * q^46 - 33 * q^48 - 26 * q^49 - 100 * q^51 - 60 * q^52 - 42 * q^55 - 20 * q^57 - 34 * q^58 + 32 * q^60 - 30 * q^61 - 45 * q^63 + 40 * q^64 + 42 * q^66 + 32 * q^67 - 33 * q^69 - 268 * q^70 + 55 * q^72 - 40 * q^73 + 9 * q^75 - 32 * q^78 - 37 * q^81 + 28 * q^82 - 180 * q^84 - 10 * q^85 - 142 * q^88 - 30 * q^90 + 8 * q^91 - 26 * q^93 - 90 * q^94 + 330 * q^96 - 14 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{10}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.198720	+	1.89069i	−0.140516	+	1.33692i	0.666107	+	0.745857i	$0.267960\pi$
$2$	−0.198720	+	1.89069i	−0.140516	+	1.33692i	−0.806623	+	0.591066i	$0.798707\pi$
$3$	−1.52365	+	0.823714i	−0.879677	+	0.475572i
$3$	−1.52365	+	0.823714i	−0.879677	+	0.475572i
$4$	−1.57894	−	0.335614i	−0.789471	−	0.167807i
$5$	−0.924919	−	1.27304i	−0.413636	−	0.569322i	0.550464	−	0.834859i	$-0.314451\pi$
$5$	−0.924919	−	1.27304i	−0.413636	−	0.569322i	−0.964101	+	0.265537i	$0.914451\pi$
$6$	−1.25461	−	3.04444i	−0.512194	−	1.24289i
$7$	0.668009	−	3.14273i	0.252484	−	1.18784i	−0.650952	−	0.759118i	$-0.725630\pi$
$7$	0.668009	−	3.14273i	0.252484	−	1.18784i	0.903436	−	0.428723i	$-0.141036\pi$
$8$	−0.226639	+	0.697522i	−0.0801289	+	0.246611i
$9$	1.64299	−	2.51010i	0.547663	−	0.836699i
$10$	2.59073	−	1.49576i	0.819262	−	0.473001i
$11$	3.22328	−	0.781308i	0.971857	−	0.235573i
$11$	3.22328	−	0.781308i	0.971857	−	0.235573i
$12$	2.68220	−	0.789239i	0.774283	−	0.227834i
$13$	1.59927	−	3.23146i	0.443558	−	0.896246i
$13$	1.59927	−	3.23146i	0.443558	−	0.896246i
$14$	5.80920	+	1.88752i	1.55257	+	0.504462i
$15$	2.45787	+	1.17779i	0.634620	+	0.304105i
$16$	−4.22308	−	1.88024i	−1.05577	−	0.470059i
$17$	0.287247	+	2.73297i	0.0696676	+	0.662843i	0.972508	+	0.232868i	$0.0748110\pi$
$17$	0.287247	+	2.73297i	0.0696676	+	0.662843i	−0.902841	+	0.429975i	$0.858522\pi$
$18$	4.41933	+	3.60520i	1.04165	+	0.849753i
$19$	−1.27686	+	1.14969i	−0.292932	+	0.263757i	−0.802472	−	0.596690i	$-0.796482\pi$
$19$	−1.27686	+	1.14969i	−0.292932	+	0.263757i	0.509540	+	0.860447i	$0.329816\pi$
$20$	1.03314	+	2.32047i	0.231017	+	0.518874i
$21$	1.57091	+	5.33866i	0.342800	+	1.16499i
$22$	0.836683	+	6.24951i	0.178381	+	1.33240i
$23$	0.956851	−	0.552438i	0.199517	−	0.115191i	−0.396913	−	0.917856i	$-0.629919\pi$
$23$	0.956851	−	0.552438i	0.199517	−	0.115191i	0.596430	+	0.802665i	$0.296585\pi$
$24$	−0.229242	−	1.24946i	−0.0467938	−	0.255045i
$25$	0.779925	−	2.40036i	0.155985	−	0.480072i
$26$	5.79190	+	3.66589i	1.13588	+	0.718940i
$27$	−0.435731	+	5.17785i	−0.0838564	+	0.996478i
$28$	−2.10949	+	4.73800i	−0.398657	+	0.895397i
$29$	4.12146	−	4.57734i	0.765336	−	0.849992i	−0.226957	−	0.973905i	$-0.572878\pi$
$29$	4.12146	−	4.57734i	0.765336	−	0.849992i	0.992293	+	0.123913i	$0.0395444\pi$
$30$	−2.71528	+	4.41303i	−0.495740	+	0.805706i
$31$	−4.08780	−	2.96996i	−0.734191	−	0.533421i	0.156696	−	0.987647i	$-0.449916\pi$
$31$	−4.08780	−	2.96996i	−0.734191	−	0.533421i	−0.890886	+	0.454226i	$0.849916\pi$
$32$	3.66075	−	6.34060i	0.647135	−	1.12087i
$33$	−4.26757	+	3.84550i	−0.742888	+	0.669416i
$34$	−5.22430			−0.895960
$35$	−4.61868	+	2.05637i	−0.780700	+	0.347590i
$36$	−3.43661	+	3.41188i	−0.572768	+	0.568647i
$37$	3.97080	−	4.41002i	0.652796	−	0.725003i	−0.322337	−	0.946625i	$-0.604468\pi$
$37$	3.97080	−	4.41002i	0.652796	−	0.725003i	0.975133	+	0.221622i	$0.0711351\pi$
$38$	−1.91998	−	2.64262i	−0.311461	−	0.428690i
$39$	0.225077	+	6.24094i	0.0360412	+	0.999350i
$40$	1.09760	−	0.356631i	0.173545	−	0.0563883i
$41$	−6.11774	+	1.30037i	−0.955430	+	0.203083i	−0.659144	−	0.752016i	$-0.729081\pi$
$41$	−6.11774	+	1.30037i	−0.955430	+	0.203083i	−0.296286	+	0.955099i	$0.595748\pi$
$42$	−10.4059	+	1.90921i	−1.60567	+	0.294597i
$43$	6.01953	+	3.47538i	0.917970	+	0.529990i	0.882987	−	0.469398i	$-0.155529\pi$
$43$	6.01953	+	3.47538i	0.917970	+	0.529990i	0.0349829	+	0.999388i	$0.488862\pi$
$44$	−5.35159	+	0.151859i	−0.806783	+	0.0228936i
$45$	−4.71509	+	0.230042i	−0.702884	+	0.0342926i
$46$	0.854347	+	1.91889i	0.125967	+	0.282925i
$47$	7.67990	+	2.49535i	1.12023	+	0.363985i	0.809855	−	0.586630i	$-0.199546\pi$
$47$	7.67990	+	2.49535i	1.12023	+	0.363985i	0.310374	+	0.950614i	$0.399546\pi$
$48$	7.98326	−	0.613799i	1.15228	−	0.0885942i
$49$	−3.03572	−	1.35159i	−0.433674	−	0.193084i
$50$	4.38336	+	1.95160i	0.619901	+	0.275998i
$51$	−2.68885	−	3.92747i	−0.376515	−	0.549956i
$52$	−3.60968	+	4.56555i	−0.500573	+	0.633127i
$53$	−2.61046	+	3.59299i	−0.358575	+	0.493536i	−0.949751	−	0.313007i	$-0.898664\pi$
$53$	−2.61046	+	3.59299i	−0.358575	+	0.493536i	0.591176	+	0.806542i	$0.298664\pi$
$54$	−9.70315	−	1.85278i	−1.32043	−	0.252131i
$55$	−3.97591	−	3.38073i	−0.536112	−	0.455857i
$56$	2.04073	+	1.17822i	0.272704	+	0.157446i
$57$	0.998467	−	2.80349i	0.132250	−	0.371331i
$58$	7.83534	+	8.70203i	1.02883	+	1.14263i
$59$	0.958686	−	4.51026i	0.124810	−	0.587186i	−0.870641	−	0.491918i	$-0.836296\pi$
$59$	0.958686	−	4.51026i	0.124810	−	0.587186i	0.995452	−	0.0952678i	$-0.0303708\pi$
$60$	−3.48555	−	2.68457i	−0.449982	−	0.346576i
$61$	5.47524	−	0.575471i	0.701033	−	0.0736815i	0.252695	−	0.967546i	$-0.418683\pi$
$61$	5.47524	−	0.575471i	0.701033	−	0.0736815i	0.448337	+	0.893864i	$0.352016\pi$
$62$	6.42762	−	7.13859i	0.816308	−	0.906602i
$63$	−6.79103	−	6.84024i	−0.855590	−	0.861790i
$64$	3.78093	+	2.74700i	0.472616	+	0.343376i
$65$	−5.59298	+	0.952899i	−0.693724	+	0.118193i
$66$	−6.42262	−	8.83284i	−0.790569	−	1.08725i
$67$	−0.278631	−	0.482604i	−0.0340402	−	0.0589594i	0.848503	−	0.529190i	$-0.177504\pi$
$67$	−0.278631	−	0.482604i	−0.0340402	−	0.0589594i	−0.882544	+	0.470231i	$0.844171\pi$
$68$	0.463679	−	4.41161i	0.0562293	−	0.534986i
$69$	−1.00285	+	1.62989i	−0.120729	+	0.196216i
$70$	−2.97014	−	9.14116i	−0.355000	−	1.09258i
$71$	−5.73518	+	0.602792i	−0.680641	+	0.0715383i	−0.438539	−	0.898712i	$-0.644504\pi$
$71$	−5.73518	+	0.602792i	−0.680641	+	0.0715383i	−0.242103	+	0.970251i	$0.577837\pi$
$72$	1.37848	+	1.71491i	0.162456	+	0.202104i
$73$	2.84681	−	0.924985i	0.333194	−	0.108261i	−0.137642	−	0.990482i	$-0.543952\pi$
$73$	2.84681	−	0.924985i	0.333194	−	0.108261i	0.470836	+	0.882221i	$0.343952\pi$
$74$	7.54892	+	8.38393i	0.877545	+	0.974612i
$75$	0.788884	+	4.29974i	0.0910924	+	0.496491i
$76$	2.40194	−	1.38676i	0.275522	−	0.159072i
$77$	−0.302261	−	10.6518i	−0.0344458	−	1.21389i
$78$	−11.8444	−	0.814648i	−1.34112	−	0.0922407i
$79$	7.94601	−	10.9367i	0.893996	−	1.23048i	−0.0783479	−	0.996926i	$-0.524964\pi$
$79$	7.94601	−	10.9367i	0.893996	−	1.23048i	0.972344	−	0.233554i	$-0.0750355\pi$
$80$	1.51239	+	7.11523i	0.169090	+	0.795507i
$81$	−3.60117	−	8.24813i	−0.400130	−	0.916458i
$82$	−1.24288	−	11.8252i	−0.137253	−	1.30587i
$83$	2.27286	−	1.65133i	0.249479	−	0.181257i	−0.456017	−	0.889971i	$-0.650724\pi$
$83$	2.27286	−	1.65133i	0.249479	−	0.181257i	0.705496	+	0.708714i	$0.250724\pi$
$84$	−0.688638	−	8.95665i	−0.0751366	−	0.977250i
$85$	3.21351	−	2.89346i	0.348554	−	0.313839i
$86$	−7.76708	+	10.6905i	−0.837546	+	1.15278i
$87$	−2.50922	+	10.3692i	−0.269016	+	1.11169i
$88$	−0.185541	+	2.42539i	−0.0197788	+	0.258547i
$89$	1.48471	−	0.857200i	0.157379	−	0.0908630i	−0.419242	−	0.907875i	$-0.637704\pi$
$89$	1.48471	−	0.857200i	0.157379	−	0.0908630i	0.576621	+	0.817012i	$0.304371\pi$
$90$	0.502044	−	8.96051i	0.0529201	−	0.944521i
$91$	−9.08729	−	7.18473i	−0.952607	−	0.753164i
$92$	−1.69622	+	0.551135i	−0.176843	+	0.0574598i
$93$	8.67476	+	1.15799i	0.899530	+	0.120078i
$94$	−6.24410	+	14.0245i	−0.644030	+	1.44651i
$95$	2.64460	+	0.562127i	0.271330	+	0.0576730i
$96$	−0.354837	+	12.6762i	−0.0362154	+	1.29376i
$97$	−4.71081	+	2.09739i	−0.478311	+	0.212958i	−0.631707	−	0.775207i	$-0.717645\pi$
$97$	−4.71081	+	2.09739i	−0.478311	+	0.212958i	0.153397	+	0.988165i	$0.450979\pi$
$98$	3.15870	−	5.47103i	0.319077	−	0.552657i
$99$	3.33466	−	9.37443i	0.335146	−	0.942166i
$100$	−2.03705	+	3.52828i	−0.203705	+	0.352828i
$101$	1.41816	−	13.4929i	0.141113	−	1.34260i	−0.663224	−	0.748421i	$-0.730812\pi$
$101$	1.41816	−	13.4929i	0.141113	−	1.34260i	0.804336	−	0.594175i	$-0.202521\pi$
$102$	7.95998	−	4.30333i	0.788155	−	0.426093i
$103$	4.28789	+	13.1968i	0.422498	+	1.30032i	0.905370	+	0.424624i	$0.139594\pi$
$103$	4.28789	+	13.1968i	0.422498	+	1.30032i	−0.482872	+	0.875691i	$0.660406\pi$
$104$	1.89156	+	1.84790i	0.185482	+	0.181202i
$105$	5.34337	−	6.93766i	0.521460	−	0.677046i
$106$	−6.27450	−	5.64959i	−0.609433	−	0.548736i
$107$	−11.4246	+	2.42837i	−1.10446	+	0.234760i	−0.723837	−	0.689971i	$-0.757623\pi$
$107$	−11.4246	+	2.42837i	−1.10446	+	0.234760i	−0.380621	+	0.924731i	$0.624290\pi$
$108$	2.42575	−	8.02928i	0.233418	−	0.772618i
$109$		−	19.7610i		−	1.89276i	−0.323057	−	0.946380i	$-0.604711\pi$
$109$		−	19.7610i		−	1.89276i	0.323057	−	0.946380i	$-0.395289\pi$
$110$	7.18202	−	6.84542i	0.684779	−	0.652685i
$111$	−2.41749	+	9.99011i	−0.229458	+	0.948219i
$112$	−8.73014	+	12.0160i	−0.824921	+	1.13541i
$113$	−5.41874	+	4.87906i	−0.509753	+	0.458983i	−0.883422	−	0.468579i	$-0.844766\pi$
$113$	−5.41874	+	4.87906i	−0.509753	+	0.458983i	0.373669	+	0.927562i	$0.378100\pi$
$114$	5.10213	+	2.44491i	0.477858	+	0.228986i
$115$	−1.58829	−	0.707151i	−0.148109	−	0.0659422i
$116$	−8.04376	+	5.84414i	−0.746845	+	0.542614i
$117$	−5.48369	−	9.32358i	−0.506967	−	0.861965i
$118$	8.33702	+	2.70886i	0.767485	+	0.249371i
$119$	8.78089	+	0.922909i	0.804943	+	0.0846029i
$120$	−1.37859	+	1.44749i	−0.125847	+	0.132137i
$121$	9.77912	−	5.03675i	0.889011	−	0.457887i
$122$			10.4664i			0.947580i
$123$	8.25013	−	7.02056i	0.743890	−	0.633023i
$124$	5.45763	+	6.06132i	0.490110	+	0.544322i
$125$	−11.2599	+	3.65856i	−1.00711	+	0.327231i
$126$	14.2823	−	11.4805i	1.27237	−	1.02276i
$127$	−8.48759	+	19.0634i	−0.753152	+	1.69161i	−0.0313482	+	0.999509i	$0.509980\pi$
$127$	−8.48759	+	19.0634i	−0.753152	+	1.69161i	−0.721804	+	0.692098i	$0.756687\pi$
$128$	3.85298	−	4.27917i	0.340559	−	0.378229i
$129$	−12.0343	−	0.336869i	−1.05957	−	0.0296597i
$130$	−0.690204	−	10.7640i	−0.0605349	−	0.944063i
$131$	−18.4774			−1.61438			−0.807188	−	0.590295i	$-0.799012\pi$
$131$	−18.4774			−1.61438			−0.807188	+	0.590295i	$0.799012\pi$
$132$	8.02884	−	4.63956i	0.698821	−	0.403822i
$133$	2.76022	+	4.78084i	0.239341	+	0.414551i
$134$	0.967826	−	0.430904i	0.0836074	−	0.0372244i
$135$	6.99464	−	4.23439i	0.602002	−	0.364438i
$136$	−1.97141	−	0.419036i	−0.169047	−	0.0359321i
$137$	3.63010	−	0.381539i	0.310141	−	0.0325971i	0.0518203	−	0.998656i	$-0.483498\pi$
$137$	3.63010	−	0.381539i	0.310141	−	0.0325971i	0.258320	+	0.966059i	$0.416831\pi$
$138$	−2.88234	−	2.21998i	−0.245361	−	0.188977i
$139$	−1.95398	+	9.19274i	−0.165734	+	0.779718i	0.814230	+	0.580543i	$0.197160\pi$
$139$	−1.95398	+	9.19274i	−0.165734	+	0.779718i	−0.979964	+	0.199175i	$0.936174\pi$
$140$	7.98278	−	1.69679i	0.674668	−	0.143405i
$141$	−13.7569	+	2.52402i	−1.15854	+	0.212560i
$142$		−	10.9633i		−	0.920017i
$143$	2.63014	−	11.6654i	0.219943	−	0.975513i
$144$	−11.6581	+	7.51113i	−0.971505	+	0.625928i
$145$	−9.63917	−	1.01312i	−0.800489	−	0.0841348i
$146$	1.18315	+	5.56626i	0.0979178	+	0.460667i
$147$	5.73868	−	0.441223i	0.473318	−	0.0363914i
$148$	−7.74973	+	5.63051i	−0.637024	+	0.462825i
$149$	−2.43844	−	23.2002i	−0.199765	−	1.90064i	−0.393085	−	0.919502i	$-0.628592\pi$
$149$	−2.43844	−	23.2002i	−0.199765	−	1.90064i	0.193320	−	0.981136i	$-0.438075\pi$
$150$	−8.28625	+	0.637095i	−0.676570	+	0.0520186i
$151$	17.9876	+	5.84452i	1.46381	+	0.475621i	0.929231	−	0.369498i	$-0.120470\pi$
$151$	17.9876	+	5.84452i	1.46381	+	0.475621i	0.534578	+	0.845119i	$0.320470\pi$
$152$	−0.512549	−	1.15120i	−0.0415732	−	0.0933749i
$153$	7.33197	+	3.76923i	0.592755	+	0.304724i
$154$	20.1994	+	1.54525i	1.62772	+	0.124520i
$155$			7.95091i			0.638633i
$156$	1.73917	−	9.92962i	0.139245	−	0.795006i
$157$	−5.75649	+	17.7166i	−0.459418	+	1.41394i	0.406452	+	0.913672i	$0.366766\pi$
$157$	−5.75649	+	17.7166i	−0.459418	+	1.41394i	−0.865869	+	0.500270i	$0.833234\pi$
$158$	19.0990	+	17.1968i	1.51944	+	1.36811i
$159$	1.01782	−	7.62472i	0.0807183	−	0.604680i
$160$	−11.4577	+	1.20426i	−0.905814	+	0.0952049i
$161$	−1.09698	−	3.37616i	−0.0864542	−	0.266079i
$162$	16.3103	−	5.16965i	1.28146	−	0.406166i
$163$	16.0210	−	7.13301i	1.25486	−	0.558701i	0.331800	−	0.943350i	$-0.392344\pi$
$163$	16.0210	−	7.13301i	1.25486	−	0.558701i	0.923063	+	0.384649i	$0.125678\pi$
$164$	10.0960			0.788363
$165$	8.84264	+	1.87601i	0.688398	+	0.146047i
$166$	2.67050	+	4.62544i	0.207271	+	0.359004i
$167$	−2.49648	+	23.7524i	−0.193184	+	1.83802i	0.283534	+	0.958962i	$0.408493\pi$
$167$	−2.49648	+	23.7524i	−0.193184	+	1.83802i	−0.476717	+	0.879057i	$0.658173\pi$
$168$	−4.07986	−	0.114205i	−0.314768	−	0.00881108i
$169$	−7.88466	−	10.3360i	−0.606512	−	0.795074i
$170$	4.83205	+	6.65075i	0.370602	+	0.510089i
$171$	0.787966	+	5.09398i	0.0602573	+	0.389546i
$172$	−8.33810	−	7.50766i	−0.635774	−	0.572453i
$173$	−15.0386	−	16.7020i	−1.14336	−	1.26983i	−0.957875	−	0.287187i	$-0.907280\pi$
$173$	−15.0386	−	16.7020i	−1.14336	−	1.26983i	−0.185488	−	0.982646i	$-0.559387\pi$
$174$	−19.1063	−	6.80472i	−1.44844	−	0.515865i
$175$	−7.02270	−	4.05456i	−0.530866	−	0.306496i
$176$	−15.0812	−	2.76101i	−1.13679	−	0.208119i
$177$	2.25447	+	7.66172i	0.169456	+	0.575890i
$178$	1.32566	+	2.97748i	0.0993625	+	0.223172i
$179$	2.00273	+	9.42212i	0.149691	+	0.704243i	0.987415	+	0.158149i	$0.0505525\pi$
$179$	2.00273	+	9.42212i	0.149691	+	0.704243i	−0.837724	+	0.546094i	$0.816114\pi$
$180$	7.52205	+	1.21923i	0.560661	+	0.0908760i
$181$	−12.4533	+	9.04788i	−0.925649	+	0.672524i	−0.944924	−	0.327291i	$-0.893864\pi$
$181$	−12.4533	+	9.04788i	−0.925649	+	0.672524i	0.0192744	+	0.999814i	$0.493864\pi$
$182$	15.3899	−	15.7535i	1.14078	−	1.16773i
$183$	−7.86830	+	5.38685i	−0.581642	+	0.398207i
$184$	0.168478	+	0.792629i	0.0124204	+	0.0584334i
$185$	−9.28681	−	0.976083i	−0.682780	−	0.0717630i
$186$	−3.91325	+	16.1712i	−0.286933	+	1.18573i
$187$	3.06117	+	8.58472i	0.223855	+	0.627777i
$188$	−11.2886	−	6.51750i	−0.823309	−	0.475338i
$189$	15.9815	+	4.82823i	1.16249	+	0.351202i
$190$	−1.58834	+	4.88842i	−0.115231	+	0.354643i
$191$	−3.16111	+	14.8718i	−0.228730	+	1.07609i	0.702508	+	0.711676i	$0.252064\pi$
$191$	−3.16111	+	14.8718i	−0.228730	+	1.07609i	−0.931238	+	0.364413i	$0.881270\pi$
$192$	−8.02354	−	1.07106i	−0.579049	−	0.0772968i
$193$	−2.28266	+	5.12693i	−0.164309	+	0.369045i	−0.976871	−	0.213831i	$-0.931406\pi$
$193$	−2.28266	+	5.12693i	−0.164309	+	0.369045i	0.812561	+	0.582876i	$0.198072\pi$
$194$	−3.02939	−	9.32350i	−0.217498	−	0.669388i
$195$	7.73680	−	6.05890i	0.554044	−	0.433887i
$196$	4.33961	+	3.15291i	0.309972	+	0.225208i
$197$	−0.656595	−	1.13726i	−0.0467805	−	0.0810261i	0.841687	−	0.539966i	$-0.181563\pi$
$197$	−0.656595	−	1.13726i	−0.0467805	−	0.0810261i	−0.888468	+	0.458940i	$0.848229\pi$
$198$	17.0615	+	8.16772i	1.21251	+	0.580454i
$199$	−8.54698	+	14.8038i	−0.605879	+	1.04941i	0.386032	+	0.922485i	$0.373845\pi$
$199$	−8.54698	+	14.8038i	−0.605879	+	1.04941i	−0.991912	+	0.126929i	$0.959488\pi$
$200$	1.49754	+	1.08803i	0.105892	+	0.0769353i
$201$	0.822063	+	0.505804i	0.0579839	+	0.0356767i
$202$	25.2292	+	5.36263i	1.77512	+	0.377313i
$203$	−11.6322	−	16.0104i	−0.816421	−	1.12371i
$204$	2.92742	+	7.10366i	0.204961	+	0.497356i
$205$	7.31383	+	6.58540i	0.510820	+	0.459945i
$206$	−25.8031	+	5.48462i	−1.79779	+	0.382132i
$207$	0.185423	−	3.30944i	0.0128878	−	0.230022i
$208$	−12.8298	+	10.6397i	−0.889584	+	0.737731i
$209$	−3.21742	+	4.70340i	−0.222554	+	0.325341i
$210$	12.0552	+	11.4813i	0.831885	+	0.792288i
$211$	−4.06587	−	0.427340i	−0.279906	−	0.0294193i	−0.0364648	−	0.999335i	$-0.511610\pi$
$211$	−4.06587	−	0.427340i	−0.279906	−	0.0294193i	−0.243441	+	0.969916i	$0.578276\pi$
$212$	5.32763	−	4.79702i	0.365903	−	0.329460i
$213$	8.24186	−	5.64259i	0.564723	−	0.386624i
$214$	−2.32102	−	22.0830i	−0.158661	−	1.50956i
$215$	−1.14328	−	10.8776i	−0.0779708	−	0.741843i
$216$	−3.51291	−	1.47743i	−0.239023	−	0.100527i
$217$	−12.0645	+	10.8629i	−0.818990	+	0.737422i
$218$	37.3620	+	3.92690i	2.53047	+	0.265963i
$219$	−3.57561	+	3.75431i	−0.241617	+	0.253693i
$220$	5.14311	+	6.67234i	0.346749	+	0.449849i
$221$	9.29088	+	3.44254i	0.624972	+	0.231570i
$222$	−18.4078	−	6.55598i	−1.23545	−	0.440008i
$223$	9.56121	−	2.03230i	0.640266	−	0.136093i	0.123672	−	0.992323i	$-0.460533\pi$
$223$	9.56121	−	2.03230i	0.640266	−	0.136093i	0.516594	+	0.856230i	$0.327200\pi$
$224$	−17.4814	−	15.7403i	−1.16803	−	1.05169i
$225$	−4.74373	−	5.90146i	−0.316249	−	0.393430i
$226$	−8.14800	−	11.2148i	−0.541997	−	0.745994i
$227$	−1.44509	−	0.307163i	−0.0959138	−	0.0203871i	0.159705	−	0.987165i	$-0.448946\pi$
$227$	−1.44509	−	0.307163i	−0.0959138	−	0.0203871i	−0.255619	+	0.966778i	$0.582279\pi$
$228$	−2.51741	+	4.09145i	−0.166720	+	0.270963i
$229$	12.3774	+	8.99268i	0.817919	+	0.594253i	0.916116	−	0.400914i	$-0.131307\pi$
$229$	12.3774	+	8.99268i	0.817919	+	0.594253i	−0.0981964	+	0.995167i	$0.531307\pi$
$230$	1.65263	−	2.86244i	0.108971	−	0.188744i
$231$	9.23461	+	15.9807i	0.607593	+	1.05145i
$232$	2.25872	+	3.91221i	0.148292	+	0.256849i
$233$	13.0157	+	9.45647i	0.852688	+	0.619514i	0.925886	−	0.377803i	$-0.123321\pi$
$233$	13.0157	+	9.45647i	0.852688	+	0.619514i	−0.0731980	+	0.997317i	$0.523321\pi$
$234$	18.7178	−	8.51520i	1.22362	−	0.556656i
$235$	−3.92660	−	12.0848i	−0.256143	−	0.788328i
$236$	−3.02742	+	6.79969i	−0.197068	+	0.442622i
$237$	−3.09815	+	23.2090i	−0.201246	+	1.50758i
$238$	−3.48988	+	16.4186i	−0.226215	+	1.06426i
$239$	0.0409999	−	0.126185i	0.00265207	−	0.00816222i	−0.949722	−	0.313095i	$-0.898634\pi$
$239$	0.0409999	−	0.126185i	0.00265207	−	0.00816222i	0.952374	+	0.304933i	$0.0986341\pi$
$240$	−8.16526	−	9.59531i	−0.527065	−	0.619374i
$241$	−13.1696	−	7.60345i	−0.848326	−	0.489781i	0.0117595	−	0.999931i	$-0.496257\pi$
$241$	−13.1696	−	7.60345i	−0.848326	−	0.489781i	−0.860086	+	0.510149i	$0.829590\pi$
$242$	7.57966	+	19.4902i	0.487239	+	1.25288i
$243$	12.2810	+	9.60088i	0.787827	+	0.615897i
$244$	−8.83822	−	0.928934i	−0.565809	−	0.0594689i
$245$	1.08716	+	5.11471i	0.0694564	+	0.326767i
$246$	11.6343	+	16.9936i	0.741774	+	1.08347i
$247$	1.67313	+	5.96479i	0.106459	+	0.379531i
$248$	2.99807	−	2.17822i	0.190377	−	0.138317i
$249$	−2.10281	+	4.38823i	−0.133260	+	0.278093i
$250$	−4.67965	−	22.0160i	−0.295967	−	1.39242i
$251$	10.6397	+	23.8972i	0.671574	+	1.50838i	0.851309	+	0.524664i	$0.175809\pi$
$251$	10.6397	+	23.8972i	0.671574	+	1.50838i	−0.179736	+	0.983715i	$0.557524\pi$
$252$	8.42696	+	13.0795i	0.530848	+	0.823932i
$253$	2.65258	−	2.52826i	0.166766	−	0.158950i
$254$	−34.3565	−	19.8357i	−2.15572	−	1.24460i
$255$	−2.51287	+	7.05561i	−0.157362	+	0.441840i
$256$	13.5793	+	15.0813i	0.848705	+	0.942582i
$257$	−8.34432	−	7.51326i	−0.520504	−	0.468664i	0.366505	−	0.930416i	$-0.380554\pi$
$257$	−8.34432	−	7.51326i	−0.520504	−	0.468664i	−0.887009	+	0.461752i	$0.847221\pi$
$258$	3.02838	−	22.6863i	0.188539	−	1.41239i
$259$	−11.2070	−	15.4251i	−0.696368	−	0.958469i
$260$	9.15079	+	0.372513i	0.567508	+	0.0231022i
$261$	−4.71806	−	17.8658i	−0.292041	−	1.10586i
$262$	3.67182	−	34.9351i	0.226846	−	2.15830i
$263$	7.86553	+	13.6235i	0.485009	+	0.840060i	0.999852	−	0.0172244i	$-0.00548297\pi$
$263$	7.86553	+	13.6235i	0.485009	+	0.840060i	−0.514843	+	0.857285i	$0.672150\pi$
$264$	−1.71513	−	3.84826i	−0.105559	−	0.236844i
$265$	6.98850			0.429300
$266$	−9.58762	+	4.26868i	−0.587854	+	0.261730i
$267$	−1.55609	+	2.52905i	−0.0952311	+	0.154775i
$268$	0.277974	+	0.855516i	0.0169800	+	0.0522589i
$269$	19.9629	−	2.09819i	1.21716	−	0.127929i	0.525909	−	0.850541i	$-0.323725\pi$
$269$	19.9629	−	2.09819i	1.21716	−	0.127929i	0.691254	+	0.722612i	$0.257059\pi$
$270$	6.61596	+	14.0662i	0.402635	+	0.856040i
$271$	−9.33430	−	8.40464i	−0.567018	−	0.510546i	0.335015	−	0.942213i	$-0.391259\pi$
$271$	−9.33430	−	8.40464i	−0.567018	−	0.510546i	−0.902033	+	0.431667i	$0.857925\pi$
$272$	3.92557	−	12.0817i	0.238023	−	0.732558i
$273$	19.7640	+	3.46164i	1.19617	+	0.209508i
$274$			6.93923i			0.419215i
$275$	0.638498	−	8.34641i	0.0385029	−	0.503307i
$276$	2.13046	−	2.23693i	0.128238	−	0.134648i
$277$	−4.41743	−	9.92171i	−0.265418	−	0.596138i	0.730842	−	0.682546i	$-0.239128\pi$
$277$	−4.41743	−	9.92171i	−0.265418	−	0.596138i	−0.996260	+	0.0864089i	$0.972461\pi$
$278$	−16.9924	−	5.52115i	−1.01913	−	0.331137i
$279$	−14.1711	+	5.38116i	−0.848402	+	0.322162i
$280$	−0.387592	−	3.68769i	−0.0231630	−	0.220381i
$281$	−2.00784	+	1.45878i	−0.119778	+	0.0870235i	−0.646061	−	0.763286i	$-0.723585\pi$
$281$	−2.00784	+	1.45878i	−0.119778	+	0.0870235i	0.526284	+	0.850309i	$0.323585\pi$
$282$	−2.03837	−	26.5117i	−0.121383	−	1.57875i
$283$	−2.14837	−	10.1073i	−0.127707	−	0.600814i	−0.994729	−	0.102544i	$-0.967302\pi$
$283$	−2.14837	−	10.1073i	−0.127707	−	0.600814i	0.867021	−	0.498271i	$-0.166031\pi$
$284$	9.25782	+	0.973036i	0.549351	+	0.0577391i
$285$	−4.49246	+	1.32191i	−0.266110	+	0.0783033i
$286$	21.5331	+	7.29095i	1.27328	+	0.431123i
$287$			20.0951i			1.18617i
$288$	−9.90095	−	19.6064i	−0.583419	−	1.15532i
$289$	9.24188	−	1.96442i	0.543640	−	0.115554i
$290$	3.83099	−	18.0234i	0.224963	−	1.05837i
$291$	5.44996	−	7.07604i	0.319482	−	0.414805i
$292$	−4.80538	+	0.505066i	−0.281214	+	0.0295568i
$293$	19.5240	+	4.14996i	1.14061	+	0.242443i	0.739219	−	0.673465i	$-0.235195\pi$
$293$	19.5240	+	4.14996i	1.14061	+	0.242443i	0.401387	+	0.915909i	$0.368528\pi$
$294$	−0.306173	+	10.9378i	−0.0178564	+	0.637904i
$295$	−6.62846	+	2.95118i	−0.385924	+	0.171824i
$296$	2.17615	+	3.76920i	0.126486	+	0.219080i
$297$	2.64101	+	17.0301i	0.153247	+	0.988188i
$298$	44.3491			2.56908
$299$	−0.254917	−	3.97552i	−0.0147422	−	0.229911i
$300$	0.197452	−	7.05379i	0.0113999	−	0.407251i
$301$	14.9433	−	16.5962i	0.861316	−	0.956589i
$302$	−14.6247	+	32.8476i	−0.841557	+	1.89017i
$303$	8.95354	+	21.7266i	0.514367	+	1.24816i
$304$	7.55398	−	2.45444i	0.433251	−	0.140772i
$305$	−5.79675	−	6.43795i	−0.331921	−	0.368636i
$306$	−8.58347	+	13.1135i	−0.490684	+	0.749649i
$307$		−	11.3321i		−	0.646758i	−0.946270	−	0.323379i	$-0.895181\pi$
$307$		−	11.3321i		−	0.646758i	0.946270	−	0.323379i	$-0.104819\pi$
$308$	−3.09766	+	16.9201i	−0.176505	+	0.964111i
$309$	−17.4036	−	16.5752i	−0.990055	−	0.942929i
$310$	−15.0327	−	1.58001i	−0.853803	−	0.0897383i
$311$	16.2196	+	5.27007i	0.919730	+	0.298838i	0.730356	−	0.683067i	$-0.239354\pi$
$311$	16.2196	+	5.27007i	0.919730	+	0.298838i	0.189374	+	0.981905i	$0.439354\pi$
$312$	−4.40420	−	1.25744i	−0.249339	−	0.0711886i
$313$	−5.86538	+	4.26145i	−0.331531	+	0.240871i	−0.741080	−	0.671417i	$-0.765686\pi$
$313$	−5.86538	+	4.26145i	−0.331531	+	0.240871i	0.409549	+	0.912288i	$0.365686\pi$
$314$	−32.3528	−	14.4044i	−1.82578	−	0.812888i
$315$	−2.42676	+	14.9719i	−0.136732	+	0.843573i
$316$	−16.2168	+	14.6017i	−0.912267	+	0.821409i
$317$	−4.86826	+	6.70058i	−0.273429	+	0.376342i	−0.923543	−	0.383494i	$-0.874721\pi$
$317$	−4.86826	+	6.70058i	−0.273429	+	0.376342i	0.650115	+	0.759836i	$0.274721\pi$
$318$	14.2138	+	3.43957i	0.797068	+	0.192881i
$319$	9.70832	−	17.9742i	0.543561	−	1.00636i
$320$		−	7.35403i		−	0.411103i
$321$	15.4067	−	13.1106i	0.859921	−	0.731761i
$322$	6.60128	−	1.40315i	0.367875	−	0.0781943i
$323$	−3.50885	−	3.15938i	−0.195238	−	0.175793i
$324$	2.91785	+	14.2319i	0.162103	+	0.790662i
$325$	−6.50936	−	6.35913i	−0.361074	−	0.352741i
$326$	10.3027	+	31.7083i	0.570611	+	1.75616i
$327$	16.2774	+	30.1087i	0.900143	+	1.66502i
$328$	0.479482	−	4.56197i	0.0264750	−	0.251893i
$329$	12.9725	−	22.4690i	0.715195	−	1.23875i
$330$	−5.30418	+	16.3459i	−0.291985	+	0.899813i
$331$	−1.80969	+	3.13448i	−0.0994698	+	0.172287i	−0.911465	−	0.411377i	$-0.865048\pi$
$331$	−1.80969	+	3.13448i	−0.0994698	+	0.172287i	0.811996	+	0.583664i	$0.198381\pi$
$332$	−4.14293	+	1.84455i	−0.227373	+	0.101233i
$333$	−4.54559	−	17.2127i	−0.249097	−	0.943251i
$334$	−44.4125	−	9.44017i	−2.43014	−	0.516543i
$335$	−0.356663	+	0.801079i	−0.0194866	+	0.0437676i
$336$	3.40388	−	25.4993i	0.185697	−	1.39110i
$337$	−13.5928	+	4.41655i	−0.740445	+	0.240585i	−0.654865	−	0.755746i	$-0.727274\pi$
$337$	−13.5928	+	4.41655i	−0.740445	+	0.240585i	−0.0855801	+	0.996331i	$0.527274\pi$
$338$	21.1090	−	12.8535i	1.14818	−	0.699140i
$339$	4.23729	−	11.8975i	0.230138	−	0.646181i
$340$	−6.04503	+	3.49010i	−0.327838	+	0.189277i
$341$	−15.4966	−	6.37920i	−0.839187	−	0.345453i
$342$	−9.78774	+	0.477528i	−0.529260	+	0.0258218i
$343$	6.94408	−	9.55770i	0.374945	−	0.516067i
$344$	−3.78841	+	3.41110i	−0.204257	+	0.183914i
$345$	3.00248	−	0.230848i	0.161648	−	0.0124284i
$346$	34.5669	−	25.1144i	1.85833	−	1.35016i
$347$	1.70115	+	16.1854i	0.0913225	+	0.868875i	0.940277	+	0.340410i	$0.110566\pi$
$347$	1.70115	+	16.1854i	0.0913225	+	0.868875i	−0.848955	+	0.528466i	$0.822768\pi$
$348$	7.44194	−	15.5302i	0.398930	−	0.832504i
$349$	2.13050	+	10.0232i	0.114043	+	0.536531i	0.997663	+	0.0683261i	$0.0217658\pi$
$349$	2.13050	+	10.0232i	0.114043	+	0.536531i	−0.883620	+	0.468205i	$0.844901\pi$
$350$	9.06148	−	12.4721i	0.484357	−	0.666660i
$351$	16.0352	+	9.68883i	0.855894	+	0.517152i
$352$	6.84567	−	23.2977i	0.364875	−	1.24177i
$353$	−12.1349	+	7.00607i	−0.645874	+	0.372896i	−0.786874	−	0.617114i	$-0.788302\pi$
$353$	−12.1349	+	7.00607i	−0.645874	+	0.372896i	0.141000	+	0.990010i	$0.454968\pi$
$354$	−14.9340	+	2.73998i	−0.793732	+	0.145628i
$355$	6.07196	+	6.74359i	0.322266	+	0.357913i
$356$	−2.63196	+	0.855177i	−0.139494	+	0.0453243i
$357$	−14.1392	+	5.82676i	−0.748324	+	0.308385i
$358$	−18.2123	+	1.91419i	−0.962552	+	0.101168i
$359$	−8.61919	−	26.5271i	−0.454904	−	1.40005i	−0.871248	−	0.490843i	$-0.836689\pi$
$359$	−8.61919	−	26.5271i	−0.454904	−	1.40005i	0.416345	−	0.909207i	$-0.363311\pi$
$360$	0.908162	−	3.34102i	0.0478644	−	0.176087i
$361$	−1.67746	+	15.9599i	−0.0882871	+	0.839996i
$362$	−14.6321	−	25.3435i	−0.769044	−	1.33202i
$363$	−10.7511	+	15.7294i	−0.564284	+	0.825581i
$364$	11.9370	+	14.3941i	0.625669	+	0.754455i
$365$	−3.81061	−	2.76857i	−0.199457	−	0.144914i
$366$	−8.62130	−	15.9470i	−0.450642	−	0.833565i
$367$	0.534048	−	0.593120i	0.0278771	−	0.0309606i	−0.729045	−	0.684466i	$-0.760036\pi$
$367$	0.534048	−	0.593120i	0.0278771	−	0.0309606i	0.756922	+	0.653505i	$0.226702\pi$
$368$	−5.07958	+	0.533885i	−0.264791	+	0.0278307i
$369$	−6.78734	+	17.4926i	−0.353335	+	0.910629i
$370$	3.69095	−	17.3646i	0.191883	−	0.902740i
$371$	9.54801	+	10.6041i	0.495708	+	0.550539i
$372$	−13.3083	−	4.73977i	−0.690003	−	0.245745i
$373$	3.87238	+	2.23572i	0.200504	+	0.115761i	0.596891	−	0.802323i	$-0.296403\pi$
$373$	3.87238	+	2.23572i	0.200504	+	0.115761i	−0.396387	+	0.918084i	$0.629736\pi$
$374$	−16.8394	+	4.08179i	−0.870745	+	0.211064i
$375$	14.1425	−	14.8493i	0.730313	−	0.766813i
$376$	−3.48113	+	4.79136i	−0.179525	+	0.247095i
$377$	−8.20017	−	20.6387i	−0.422330	−	1.06295i
$378$	−12.3046	+	29.2567i	−0.632879	+	1.50480i
$379$	0.732188	+	0.325991i	0.0376099	+	0.0167450i	0.425455	−	0.904979i	$-0.360114\pi$
$379$	0.732188	+	0.325991i	0.0376099	+	0.0167450i	−0.387845	+	0.921724i	$0.626781\pi$
$380$	−3.98701	−	1.77513i	−0.204529	−	0.0910622i
$381$	−2.77075	−	36.0373i	−0.141950	−	1.84624i
$382$	−27.4899	−	8.93202i	−1.40651	−	0.457002i
$383$	−2.30932	−	5.18682i	−0.118001	−	0.265034i	0.844883	−	0.534952i	$-0.179670\pi$
$383$	−2.30932	−	5.18682i	−0.118001	−	0.265034i	−0.962883	+	0.269918i	$0.913004\pi$
$384$	−2.34576	+	9.69369i	−0.119707	+	0.494679i
$385$	−13.2807	+	10.2369i	−0.676846	+	0.521720i
$386$	−9.23985	−	5.33463i	−0.470296	−	0.271526i
$387$	18.6136	−	9.39959i	0.946180	−	0.477808i
$388$	8.14201	−	1.73064i	0.413348	−	0.0878598i
$389$	26.0965	−	8.47927i	1.32315	−	0.429916i	0.439572	−	0.898208i	$-0.355130\pi$
$389$	26.0965	−	8.47927i	1.32315	−	0.429916i	0.883574	+	0.468292i	$0.155130\pi$
$390$	9.91807	+	15.8319i	0.502221	+	0.801682i
$391$	1.78465	+	2.45636i	0.0902537	+	0.124224i
$392$	1.63077	−	1.81116i	0.0823665	−	0.0914773i
$393$	28.1530	−	15.2201i	1.42013	−	0.767751i
$394$	2.28068	−	1.01543i	0.114899	−	0.0511564i
$395$	−21.2723			−1.07033
$396$	−8.41143	+	13.6825i	−0.422690	+	0.687572i
$397$	14.6034	−	25.2939i	0.732925	−	1.26946i	−0.222702	−	0.974886i	$-0.571488\pi$
$397$	14.6034	−	25.2939i	0.732925	−	1.26946i	0.955628	−	0.294577i	$-0.0951789\pi$
$398$	−26.2910	−	19.1015i	−1.31785	−	0.957474i
$399$	−8.14364	−	5.01067i	−0.407692	−	0.250847i
$400$	−7.80694	+	8.67048i	−0.390347	+	0.433524i
$401$	−8.19725	+	18.4113i	−0.409351	+	0.919417i	0.584776	+	0.811195i	$0.301183\pi$
$401$	−8.19725	+	18.4113i	−0.409351	+	0.919417i	−0.994127	+	0.108222i	$0.965484\pi$
$402$	−1.11968	+	1.45376i	−0.0558446	+	0.0725068i
$403$	−16.1348	+	8.45979i	−0.803732	+	0.421412i
$404$	−6.76761	+	20.8286i	−0.336701	+	1.03626i
$405$	−7.16942	+	12.2133i	−0.356251	+	0.606883i
$406$	32.5822	−	18.8114i	1.61703	−	0.933592i
$407$	9.35343	−	17.3172i	0.463632	−	0.858380i
$408$	3.34890	−	0.985416i	0.165795	−	0.0487854i
$409$	12.4200	+	27.8958i	0.614131	+	1.37936i	0.906153	+	0.422949i	$0.139005\pi$
$409$	12.4200	+	27.8958i	0.614131	+	1.37936i	−0.292023	+	0.956411i	$0.594328\pi$
$410$	−13.9044	+	12.5196i	−0.686689	+	0.618298i
$411$	−5.21671	+	3.57150i	−0.257321	+	0.176169i
$412$	−2.34130	−	22.2760i	−0.115348	−	1.09746i
$413$	−13.5341	−	6.02579i	−0.665971	−	0.296510i
$414$	6.22029	+	1.00823i	0.305711	+	0.0495518i
$415$	−4.20443	−	1.36610i	−0.206387	−	0.0670593i
$416$	−14.6349	−	21.9699i	−0.717533	−	1.07716i
$417$	−4.59502	−	15.6160i	−0.225019	−	0.764718i
$418$	−8.25333	−	7.01783i	−0.403684	−	0.343253i
$419$	27.1045	−	15.6488i	1.32414	−	0.764494i	0.339755	−	0.940514i	$-0.389656\pi$
$419$	27.1045	−	15.6488i	1.32414	−	0.764494i	0.984387	+	0.176020i	$0.0563224\pi$
$420$	−10.7653	+	9.16084i	−0.525290	+	0.447003i
$421$	−6.70814	+	20.6455i	−0.326935	+	1.00620i	0.643625	+	0.765341i	$0.277430\pi$
$421$	−6.70814	+	20.6455i	−0.326935	+	1.00620i	−0.970560	+	0.240861i	$0.922570\pi$
$422$	1.61594	−	7.60240i	0.0786627	−	0.370079i
$423$	18.8816	−	15.1775i	0.918054	−	0.737954i
$424$	−1.91456	−	2.63517i	−0.0929793	−	0.127975i
$425$	6.78416	+	1.44202i	0.329080	+	0.0699481i
$426$	9.03060	+	16.7041i	0.437534	+	0.809318i
$427$	1.84896	−	17.5916i	0.0894773	−	0.851319i
$428$	18.8538			0.911331
$429$	5.60158	+	19.9405i	0.270447	+	0.962735i
$430$	20.7933			1.00274
$431$	−0.828321	+	7.88094i	−0.0398988	+	0.379612i	0.956292	+	0.292413i	$0.0944582\pi$
$431$	−0.828321	+	7.88094i	−0.0398988	+	0.379612i	−0.996191	+	0.0871987i	$0.972208\pi$
$432$	11.5757	−	21.0472i	0.556937	−	1.01263i
$433$	9.97050	+	2.11930i	0.479152	+	0.101847i	0.441155	−	0.897431i	$-0.354569\pi$
$433$	9.97050	+	2.11930i	0.479152	+	0.101847i	0.0379970	+	0.999278i	$0.487902\pi$
$434$	−18.1410	−	24.9689i	−0.870795	−	1.19855i
$435$	15.5212	−	6.39629i	0.744184	−	0.306679i
$436$	−6.63207	+	31.2014i	−0.317619	+	1.49428i
$437$	−0.586633	+	1.80547i	−0.0280625	+	0.0863674i
$438$	−6.38770	−	7.50643i	−0.305216	−	0.358671i
$439$	−1.88799	+	1.09003i	−0.0901091	+	0.0520245i	−0.544377	−	0.838840i	$-0.683234\pi$
$439$	−1.88799	+	1.09003i	−0.0901091	+	0.0520245i	0.454268	+	0.890865i	$0.349901\pi$
$440$	3.25923	−	2.00708i	0.155378	−	0.0956840i
$441$	−8.38027	+	5.39930i	−0.399061	+	0.257110i
$442$	−8.35507	+	16.8821i	−0.397410	+	0.803000i
$443$	−26.5158	−	8.61549i	−1.25980	−	0.409334i	−0.398378	−	0.917221i	$-0.630427\pi$
$443$	−26.5158	−	8.61549i	−1.25980	−	0.409334i	−0.861424	+	0.507887i	$0.830427\pi$
$444$	7.16990	−	14.9625i	0.340269	−	0.710087i
$445$	−2.46449	−	1.09726i	−0.116828	−	0.0520152i
$446$	1.94245	+	18.4812i	0.0919778	+	0.875110i
$447$	22.8257	+	33.3404i	1.07962	+	1.57694i
$448$	11.1588	−	10.0474i	0.527203	−	0.474696i
$449$	11.4189	+	25.6472i	0.538889	+	1.21037i	0.953783	+	0.300495i	$0.0971520\pi$
$449$	11.4189	+	25.6472i	0.538889	+	1.21037i	−0.414894	+	0.909870i	$0.636181\pi$
$450$	12.1005	−	7.79621i	0.570424	−	0.367517i
$451$	−18.7032	+	8.97128i	−0.880700	+	0.422441i
$452$	10.1934	−	5.88514i	0.479455	−	0.276814i
$453$	−32.2209	+	5.91166i	−1.51387	+	0.277754i
$454$	0.867919	−	2.67118i	0.0407335	−	0.125365i
$455$	−0.741451	+	18.2138i	−0.0347598	+	0.853875i
$456$	1.72921	+	1.33183i	0.0809775	+	0.0623687i
$457$	11.6892	−	26.2545i	0.546800	−	1.22813i	−0.402978	−	0.915209i	$-0.632025\pi$
$457$	11.6892	−	26.2545i	0.546800	−	1.22813i	0.949778	−	0.312923i	$-0.101308\pi$
$458$	−19.4620	+	21.6148i	−0.909402	+	1.00999i
$459$	−14.2761	+	0.296482i	−0.666351	+	0.0138386i
$460$	2.27048	+	1.64960i	0.105862	+	0.0769131i
$461$	−3.66386	+	6.34599i	−0.170643	+	0.295562i	−0.938645	−	0.344885i	$-0.887918\pi$
$461$	−3.66386	+	6.34599i	−0.170643	+	0.295562i	0.768002	+	0.640448i	$0.221251\pi$
$462$	−32.0496	+	14.2842i	−1.49108	+	0.664559i
$463$	−14.7862			−0.687173			−0.343587	−	0.939121i	$-0.611642\pi$
$463$	−14.7862			−0.687173			−0.343587	+	0.939121i	$0.611642\pi$
$464$	−26.0118	+	11.5812i	−1.20757	+	0.537643i
$465$	−6.54928	−	12.1144i	−0.303716	−	0.561790i
$466$	−20.4658	+	22.7296i	−0.948059	+	1.05293i
$467$	−14.5505	−	20.0270i	−0.673317	−	0.926741i	0.326513	−	0.945193i	$-0.394126\pi$
$467$	−14.5505	−	20.0270i	−0.673317	−	0.926741i	−0.999830	+	0.0184519i	$0.994126\pi$
$468$	5.52930	+	16.5618i	0.255592	+	0.765569i
$469$	−1.70282	+	0.553281i	−0.0786291	+	0.0255481i
$470$	23.6290	−	5.02251i	1.08993	−	0.231671i
$471$	−5.82261	−	31.7356i	−0.268292	−	1.46230i
$472$	2.92873	+	1.69090i	0.134806	+	0.0778302i
$473$	22.1180	+	6.49902i	1.01699	+	0.298825i
$474$	−43.2654	−	10.4697i	−1.98725	−	0.480891i
$475$	1.76382	+	3.96160i	0.0809296	+	0.181771i
$476$	−13.5548	−	4.40421i	−0.621282	−	0.201867i
$477$	4.72980	+	12.4558i	0.216563	+	0.570310i
$478$	0.230430	+	0.102594i	0.0105396	+	0.00469253i
$479$	−21.2657	−	9.46808i	−0.971653	−	0.432608i	−0.141374	−	0.989956i	$-0.545152\pi$
$479$	−21.2657	−	9.46808i	−0.971653	−	0.432608i	−0.830279	+	0.557348i	$0.811819\pi$
$480$	16.4656	−	11.2728i	0.751547	−	0.514529i
$481$	−7.90041	−	19.8843i	−0.360228	−	0.906646i
$482$	16.9929	−	23.3887i	0.774004	−	1.06532i
$483$	4.45240	+	4.24047i	0.202591	+	0.192948i
$484$	−17.1311	+	4.67073i	−0.778684	+	0.212306i
$485$	7.02718	+	4.05715i	0.319088	+	0.184226i
$486$	−20.5928	+	21.3117i	−0.934109	+	0.966720i
$487$	19.6403	+	21.8128i	0.889987	+	0.988431i	0.999985	−	0.00550090i	$-0.00175100\pi$
$487$	19.6403	+	21.8128i	0.889987	+	0.988431i	−0.109998	+	0.993932i	$0.535084\pi$
$488$	−0.839498	+	3.94953i	−0.0380023	+	0.178787i
$489$	−18.5348	+	24.0649i	−0.838171	+	1.08825i
$490$	−9.88639	+	1.03910i	−0.446622	+	0.0469418i
$491$	0.874850	−	0.971619i	0.0394814	−	0.0438485i	−0.723081	−	0.690764i	$-0.757275\pi$
$491$	0.874850	−	0.971619i	0.0394814	−	0.0438485i	0.762562	+	0.646915i	$0.223941\pi$
$492$	−15.3827	+	8.31620i	−0.693505	+	0.374923i
$493$	13.6936	+	9.94901i	0.616730	+	0.448081i
$494$	−11.6101	+	1.97806i	−0.522363	+	0.0889971i
$495$	−15.0183	+	4.42543i	−0.675024	+	0.198908i
$496$	11.6789	+	20.2284i	0.524397	+	0.908283i
$497$	−1.93674	+	18.4268i	−0.0868745	+	0.826556i
$498$	−7.87894	−	4.84780i	−0.353064	−	0.217235i
$499$	3.38536	+	10.4191i	0.151550	+	0.466422i	0.997795	−	0.0663715i	$-0.0211422\pi$
$499$	3.38536	+	10.4191i	0.151550	+	0.466422i	−0.846245	+	0.532794i	$0.821142\pi$
$500$	19.0066	−	1.99767i	0.849999	−	0.0893385i
$501$	−15.7615	−	38.2467i	−0.704171	−	1.70874i
$502$	−47.2967	+	15.3676i	−2.11095	+	0.685890i
$503$	−13.1269	−	14.5789i	−0.585300	−	0.650042i	0.375650	−	0.926761i	$-0.377419\pi$
$503$	−13.1269	−	14.5789i	−0.585300	−	0.650042i	−0.960951	+	0.276720i	$0.910753\pi$
$504$	6.31033	−	3.18663i	0.281085	−	0.141944i
$505$	−18.4887	+	10.6745i	−0.822738	+	0.475008i
$506$	4.25305	+	5.51763i	0.189071	+	0.245289i
$507$	20.5273	+	9.25363i	0.911650	+	0.410968i
$508$	19.7994	−	27.2515i	0.878455	−	1.20909i
$509$	2.90478	+	13.6659i	0.128752	+	0.605732i	0.994454	+	0.105172i	$0.0335392\pi$
$509$	2.90478	+	13.6659i	0.128752	+	0.605732i	−0.865702	+	0.500560i	$0.833127\pi$
$510$	−12.8407	−	6.15315i	−0.568594	−	0.272466i
$511$	−1.00529	−	9.56466i	−0.0444713	−	0.423116i
$512$	−21.8957	+	15.9081i	−0.967662	+	0.703048i
$513$	−5.39656	−	7.11235i	−0.238264	−	0.314018i
$514$	15.8635	−	14.2835i	0.699707	−	0.630019i
$515$	12.8341	−	17.6646i	0.565537	−	0.778395i
$516$	18.8885	+	4.57080i	0.831518	+	0.201218i
$517$	26.7041	+	2.04286i	1.17445	+	0.0898449i
$518$	31.3912	−	18.1237i	1.37925	−	0.796310i
$519$	36.6712	+	13.0605i	1.60969	+	0.573292i
$520$	0.602917	−	4.11719i	0.0264397	−	0.180551i
$521$	−36.6415	+	11.9055i	−1.60529	+	0.521591i	−0.968408	−	0.249370i	$-0.919777\pi$
$521$	−36.6415	+	11.9055i	−1.60529	+	0.521591i	−0.636883	+	0.770960i	$0.719777\pi$
$522$	34.7163	−	5.37012i	1.51949	−	0.235044i
$523$	−3.81367	+	8.56564i	−0.166760	+	0.374549i	−0.977524	−	0.210824i	$-0.932385\pi$
$523$	−3.81367	+	8.56564i	−0.166760	+	0.374549i	0.810764	+	0.585373i	$0.199052\pi$
$524$	29.1747	+	6.20127i	1.27450	+	0.270904i
$525$	14.0399	+	0.393009i	0.612752	+	0.0171523i
$526$	−27.3209	+	12.1640i	−1.19125	+	0.530378i
$527$	6.94261	−	12.0250i	0.302425	−	0.523815i
$528$	25.2527	−	8.21583i	1.09898	−	0.357548i
$529$	−10.8896	+	18.8614i	−0.473462	+	0.820060i
$530$	−1.38875	+	13.2131i	−0.0603236	+	0.573941i
$531$	−9.74608	−	9.81671i	−0.422944	−	0.426009i
$532$	−2.75370	−	8.47503i	−0.119388	−	0.367439i
$533$	−5.58185	+	21.8489i	−0.241777	+	0.946379i
$534$	−4.47243	−	3.44466i	−0.193541	−	0.149065i
$535$	13.6582	+	12.2979i	0.590497	+	0.531686i
$536$	0.399775	−	0.0849749i	0.0172677	−	0.00367036i
$537$	−10.8126	−	12.7063i	−0.466598	−	0.548317i
$538$			38.1608i			1.64523i
$539$	−10.8410	−	1.98472i	−0.466954	−	0.0854881i
$540$	−12.4652	+	4.33835i	−0.536419	+	0.186693i
$541$	16.9791	−	23.3697i	0.729987	−	1.00474i	−0.269146	−	0.963100i	$-0.586741\pi$
$541$	16.9791	−	23.3697i	0.729987	−	1.00474i	0.999133	−	0.0416414i	$-0.0132587\pi$
$542$	17.7455	−	15.9781i	0.762235	−	0.686320i
$543$	11.5216	−	24.0438i	0.494439	−	1.03182i
$544$	18.3802	+	8.18341i	0.788046	+	0.350861i
$545$	−25.1566	+	18.2773i	−1.07759	+	0.782914i
$546$	−10.4724	+	36.6797i	−0.448178	+	1.56975i
$547$	36.5575	+	11.8783i	1.56309	+	0.507877i	0.957630	−	0.288001i	$-0.0929907\pi$
$547$	36.5575	+	11.8783i	1.56309	+	0.507877i	0.605456	+	0.795879i	$0.292991\pi$
$548$	−5.85977	−	0.615887i	−0.250317	−	0.0263094i
$549$	7.55128	−	14.6889i	0.322281	−	0.626906i
$550$	15.6536	+	2.86580i	0.667473	+	0.122198i
$551$			10.5830i			0.450853i
$552$	−0.909601	−	1.06891i	−0.0387152	−	0.0454957i
$553$	−29.0633	−	32.2780i	−1.23590	−	1.37260i
$554$	19.6367	−	6.38037i	0.834286	−	0.271076i
$555$	14.9538	−	6.16247i	0.634754	−	0.261582i
$556$	6.17043	−	13.8590i	0.261684	−	0.587753i
$557$	2.44637	−	2.71697i	0.103656	−	0.115122i	−0.689084	−	0.724681i	$-0.741987\pi$
$557$	2.44637	−	2.71697i	0.103656	−	0.115122i	0.792740	+	0.609560i	$0.208654\pi$
$558$	−7.35805	−	27.8626i	−0.311491	−	1.17952i
$559$	20.8574	−	13.8938i	0.882174	−	0.587645i
$560$	23.3715			0.987628
$561$	−11.7355	−	10.5585i	−0.495473	−	0.445782i
$562$	−2.35911	−	4.08610i	−0.0995130	−	0.172362i
$563$	25.4743	−	11.3419i	1.07361	−	0.478003i	0.207697	−	0.978193i	$-0.433403\pi$
$563$	25.4743	−	11.3419i	1.07361	−	0.478003i	0.865916	+	0.500190i	$0.166736\pi$
$564$	22.5684	+	0.631743i	0.950303	+	0.0266012i
$565$	11.2231	+	2.38555i	0.472161	+	0.100361i
$566$	19.5367	−	2.05339i	0.821188	−	0.0863103i
$567$	−28.3273	+	5.80770i	−1.18963	+	0.243901i
$568$	0.879354	−	4.13703i	0.0368969	−	0.173586i
$569$	6.54623	−	1.39144i	0.274432	−	0.0583324i	−0.0686396	−	0.997642i	$-0.521866\pi$
$569$	6.54623	−	1.39144i	0.274432	−	0.0583324i	0.343072	+	0.939309i	$0.388533\pi$
$570$	−1.60659	−	8.75656i	−0.0672926	−	0.366772i
$571$			17.5766i			0.735558i	0.929913	+	0.367779i	$0.119882\pi$
$571$			17.5766i			0.735558i	−0.929913	+	0.367779i	$0.880118\pi$
$572$	−8.06793	+	17.5363i	−0.337337	+	0.733230i
$573$	−7.43374	−	25.2633i	−0.310549	−	1.05539i
$574$	−37.9937	−	3.99329i	−1.58582	−	0.166677i
$575$	−0.579780	−	2.72765i	−0.0241785	−	0.113751i
$576$	13.1073	−	4.97719i	0.546136	−	0.207383i
$577$	−26.1228	+	18.9793i	−1.08751	+	0.790121i	−0.978977	−	0.203973i	$-0.934615\pi$
$577$	−26.1228	+	18.9793i	−1.08751	+	0.790121i	−0.108531	+	0.994093i	$0.534615\pi$
$578$	1.87758	+	17.8639i	0.0780969	+	0.743042i
$579$	−0.745167	−	9.69188i	−0.0309681	−	0.402781i
$580$	14.8797	+	4.83469i	0.617844	+	0.200750i
$581$	−3.67140	−	8.24611i	−0.152315	−	0.342106i
$582$	12.2956	+	11.7104i	0.509670	+	0.485410i
$583$	−5.60703	+	13.6208i	−0.232219	+	0.564116i
$584$			2.19535i			0.0908442i
$585$	−6.79734	+	15.6045i	−0.281035	+	0.645168i
$586$	−11.7261	+	36.0893i	−0.484402	+	1.49083i
$587$	7.27290	+	6.54855i	0.300185	+	0.270288i	0.805434	−	0.592686i	$-0.201933\pi$
$587$	7.27290	+	6.54855i	0.300185	+	0.270288i	−0.505249	+	0.862974i	$0.668599\pi$
$588$	−9.20912	−	1.22932i	−0.379778	−	0.0506963i
$589$	8.63409	−	0.907480i	0.355762	−	0.0373920i
$590$	−4.26257	−	13.1188i	−0.175487	−	0.540094i
$591$	1.93719	+	1.19193i	0.0796854	+	0.0490294i
$592$	−25.0609	+	11.1578i	−1.03000	+	0.458584i
$593$	10.0561			0.412955			0.206478	−	0.978451i	$-0.433800\pi$
$593$	10.0561			0.412955			0.206478	+	0.978451i	$0.433800\pi$
$594$	−32.7236	+	1.60912i	−1.34266	+	0.0660230i
$595$	−6.94671	−	12.0321i	−0.284787	−	0.493266i
$596$	−3.93617	+	37.4502i	−0.161232	+	1.53402i
$597$	0.828461	−	29.5960i	0.0339066	−	1.21128i
$598$	7.56716	+	0.308046i	0.309444	+	0.0125969i
$599$	8.24459	+	11.3477i	0.336865	+	0.463654i	0.943522	−	0.331309i	$-0.107490\pi$
$599$	8.24459	+	11.3477i	0.336865	+	0.463654i	−0.606658	+	0.794963i	$0.707490\pi$
$600$	−3.17795	−	0.424222i	−0.129739	−	0.0173188i
$601$	2.28206	+	2.05478i	0.0930873	+	0.0838162i	0.714361	−	0.699778i	$-0.246718\pi$
$601$	2.28206	+	2.05478i	0.0930873	+	0.0838162i	−0.621273	+	0.783594i	$0.713384\pi$
$602$	28.4088	+	31.5512i	1.15786	+	1.28593i
$603$	−1.66917	−	0.0935211i	−0.0679739	−	0.00380848i
$604$	−26.4398	−	15.2651i	−1.07582	−	0.621126i
$605$	−15.4569	−	7.79063i	−0.628412	−	0.316734i
$606$	−42.8576	+	12.6109i	−1.74097	+	0.512283i
$607$	6.28187	+	14.1093i	0.254973	+	0.572679i	0.994997	−	0.0999010i	$-0.0318526\pi$
$607$	6.28187	+	14.1093i	0.254973	+	0.572679i	−0.740024	+	0.672580i	$0.765186\pi$
$608$	2.61547	+	12.3048i	0.106071	+	0.499025i
$609$	30.9113	+	14.8125i	1.25259	+	0.600232i
$610$	13.3241	−	9.68054i	0.539478	−	0.391954i
$611$	20.3459	−	20.8266i	0.823106	−	0.842552i
$612$	−10.3117	−	8.41210i	−0.416827	−	0.340039i
$613$	−0.629473	−	2.96144i	−0.0254242	−	0.119611i	0.963605	−	0.267328i	$-0.0861408\pi$
$613$	−0.629473	−	2.96144i	−0.0254242	−	0.119611i	−0.989030	+	0.147717i	$0.952808\pi$
$614$	21.4256	+	2.25192i	0.864666	+	0.0908800i
$615$	−16.5682	−	4.00931i	−0.668093	−	0.161671i
$616$	7.49840	+	2.20329i	0.302119	+	0.0887729i
$617$	23.5962	+	13.6233i	0.949949	+	0.548453i	0.893065	−	0.449928i	$-0.148550\pi$
$617$	23.5962	+	13.6233i	0.949949	+	0.548453i	0.0568839	+	0.998381i	$0.481884\pi$
$618$	34.7970	−	29.6110i	1.39974	−	1.19113i
$619$	14.0711	−	43.3065i	0.565566	−	1.74063i	−0.100696	−	0.994917i	$-0.532107\pi$
$619$	14.0711	−	43.3065i	0.565566	−	1.74063i	0.666262	−	0.745717i	$-0.267893\pi$
$620$	2.66844	−	12.5540i	0.107167	−	0.504182i
$621$	2.44351	+	5.19515i	0.0980548	+	0.208474i
$622$	−13.1873	+	29.6191i	−0.528761	+	1.18762i
$623$	−1.70215	−	5.23868i	−0.0681952	−	0.209883i
$624$	10.7839	−	26.7792i	0.431703	−	1.07203i
$625$	4.86262	+	3.53290i	0.194505	+	0.141316i
$626$	−6.89153	−	11.9365i	−0.275441	−	0.477078i
$627$	1.02795	−	9.81655i	0.0410525	−	0.392035i
$628$	15.0351	−	26.0416i	0.599966	−	1.03917i
$629$	13.1931	+	9.58532i	0.526042	+	0.382192i
$630$	−27.8251	−	7.56349i	−1.10858	−	0.301337i
$631$	−4.11204	−	0.874041i	−0.163698	−	0.0347950i	0.125334	−	0.992115i	$-0.460000\pi$
$631$	−4.11204	−	0.874041i	−0.163698	−	0.0347950i	−0.289031	+	0.957320i	$0.593333\pi$
$632$	5.82775	+	8.02121i	0.231815	+	0.319066i
$633$	6.54695	−	2.69800i	0.260218	−	0.107236i
$634$	−11.7013	−	10.5359i	−0.464719	−	0.418435i
$635$	32.1189	−	6.82708i	1.27460	−	0.270924i
$636$	−4.16604	+	11.6974i	−0.165194	+	0.463832i
$637$	−9.22254	+	7.64824i	−0.365410	+	0.303034i
$638$	32.0545	+	21.9273i	1.26905	+	0.868110i
$639$	−7.90978	+	15.3862i	−0.312906	+	0.608671i
$640$	−9.01126	−	0.947121i	−0.356201	−	0.0374383i
$641$	6.56003	−	5.90668i	0.259106	−	0.233300i	−0.529331	−	0.848415i	$-0.677557\pi$
$641$	6.56003	−	5.90668i	0.259106	−	0.233300i	0.788437	+	0.615115i	$0.210891\pi$
$642$	21.7265	+	31.7348i	0.857476	+	1.25247i
$643$	−1.10259	−	10.4904i	−0.0434817	−	0.413701i	−0.994514	−	0.104608i	$-0.966641\pi$
$643$	−1.10259	−	10.4904i	−0.0434817	−	0.413701i	0.951032	−	0.309093i	$-0.100025\pi$
$644$	0.598981	+	5.69892i	0.0236032	+	0.224569i
$645$	10.7019	+	15.6318i	0.421389	+	0.615502i
$646$	6.67071	−	6.00633i	0.262455	−	0.236316i
$647$	21.3609	+	2.24513i	0.839785	+	0.0882650i	0.514648	−	0.857402i	$-0.327923\pi$
$647$	21.3609	+	2.24513i	0.839785	+	0.0882650i	0.325138	+	0.945667i	$0.394589\pi$
$648$	6.56941	−	0.642552i	0.258071	−	0.0252418i
$649$	−0.433786	−	15.2869i	−0.0170276	−	0.600063i
$650$	13.3167	−	11.0435i	0.522324	−	0.433163i
$651$	9.43405	−	26.4889i	0.369750	−	1.03818i
$652$	−27.6902	+	5.88573i	−1.08443	+	0.230503i
$653$	17.8296	+	16.0539i	0.697727	+	0.628236i	0.939681	−	0.342052i	$-0.111122\pi$
$653$	17.8296	+	16.0539i	0.697727	+	0.628236i	−0.241954	+	0.970288i	$0.577788\pi$
$654$	−60.1611	+	24.7924i	−2.35248	+	0.969459i
$655$	17.0901	+	23.5225i	0.667764	+	0.919099i
$656$	28.2807	+	6.01125i	1.10418	+	0.234700i
$657$	2.35548	−	8.66551i	0.0918960	−	0.338074i
$658$	39.9041	+	28.9920i	1.55562	+	1.13023i
$659$	−14.8961	+	25.8007i	−0.580268	+	1.00505i	0.415180	+	0.909739i	$0.363719\pi$
$659$	−14.8961	+	25.8007i	−0.580268	+	1.00505i	−0.995447	+	0.0953137i	$0.969615\pi$
$660$	−13.3324	−	5.92983i	−0.518962	−	0.230818i
$661$	−15.2127	−	26.3492i	−0.591706	−	1.02486i	−0.994003	−	0.109356i	$-0.965121\pi$
$661$	−15.2127	−	26.3492i	−0.591706	−	1.02486i	0.402297	−	0.915509i	$-0.368212\pi$
$662$	−5.56673	−	4.04446i	−0.216357	−	0.157193i
$663$	−16.9917	+	2.40782i	−0.659902	+	0.0935120i
$664$	0.636722	+	1.95963i	0.0247096	+	0.0760483i
$665$	3.53323	−	7.93576i	0.137013	−	0.307736i
$666$	33.4473	−	5.17382i	1.29606	−	0.200481i
$667$	1.41492	−	6.65669i	0.0547860	−	0.257748i
$668$	11.9135	−	36.6658i	0.460945	−	1.41864i
$669$	−12.8939	+	10.9722i	−0.498506	+	0.424210i
$670$	−1.44372	−	0.833532i	−0.0557757	−	0.0322021i
$671$	17.1986	−	6.13275i	0.663946	−	0.236752i
$672$	39.6010	+	9.58299i	1.52764	+	0.369672i
$673$	45.8714	+	4.82128i	1.76821	+	0.185847i	0.931975	−	0.362522i	$-0.118084\pi$
$673$	45.8714	+	4.82128i	1.76821	+	0.185847i	0.836237	+	0.548369i	$0.184751\pi$
$674$	−5.64920	−	26.5774i	−0.217599	−	1.02372i
$675$	12.0889	+	5.08425i	0.465301	+	0.195693i
$676$	8.98052	+	18.9661i	0.345405	+	0.729465i
$677$	37.3974	−	27.1708i	1.43730	−	1.04426i	0.448701	−	0.893682i	$-0.351887\pi$
$677$	37.3974	−	27.1708i	1.43730	−	1.04426i	0.988598	−	0.150577i	$-0.0481132\pi$
$678$	21.6524	+	10.3757i	0.831556	+	0.398476i
$679$	3.44467	+	16.2059i	0.132194	+	0.621926i
$680$	1.28994	+	2.89726i	0.0494671	+	0.111105i
$681$	2.45482	−	0.722332i	0.0940687	−	0.0276798i
$682$	15.1406	−	28.0316i	0.579763	−	1.07339i
$683$	−33.7456	−	19.4830i	−1.29124	−	0.745497i	−0.312365	−	0.949962i	$-0.601121\pi$
$683$	−33.7456	−	19.4830i	−1.29124	−	0.745497i	−0.978874	+	0.204465i	$0.934455\pi$
$684$	0.465459	−	8.30754i	0.0177973	−	0.317647i
$685$	−3.84327	−	4.26838i	−0.146844	−	0.163086i
$686$	16.6908	+	15.0284i	0.637256	+	0.573788i
$687$	−26.2661	−	3.50624i	−1.00211	−	0.133772i
$688$	−18.8864	−	25.9949i	−0.720039	−	0.991048i
$689$	7.43577	+	14.1818i	0.283280	+	0.540283i
$690$	−0.160190	+	5.72264i	−0.00609832	+	0.217857i
$691$	−4.11962	+	39.1955i	−0.156718	+	1.49107i	0.579861	+	0.814716i	$0.303107\pi$
$691$	−4.11962	+	39.1955i	−0.156718	+	1.49107i	−0.736578	+	0.676352i	$0.763560\pi$
$692$	18.1396	+	31.4187i	0.689564	+	1.19436i
$693$	−27.2338	−	16.7422i	−1.03453	−	0.635982i
$694$	−30.9396			−1.17445
$695$	13.5100	−	6.01504i	0.512464	−	0.228164i
$696$	−6.66403	−	4.10029i	−0.252599	−	0.155421i
$697$	−5.31117	−	16.3461i	−0.201175	−	0.619152i
$698$	−19.3742	+	2.03632i	−0.733326	+	0.0770757i
$699$	−27.6208	−	3.68708i	−1.04471	−	0.139458i
$700$	9.72766	+	8.75883i	0.367671	+	0.331053i
$701$	−8.81132	+	27.1184i	−0.332799	+	1.02425i	0.634997	+	0.772514i	$0.281001\pi$
$701$	−8.81132	+	27.1184i	−0.332799	+	1.02425i	−0.967796	+	0.251735i	$0.918999\pi$
$702$	−21.5051	+	28.3922i	−0.811659	+	1.07160i
$703$			10.1962i			0.384556i
$704$	14.3333	+	5.90031i	0.540205	+	0.222376i
$705$	15.9372	+	15.1786i	0.600230	+	0.571659i
$706$	−10.8349	−	24.3356i	−0.407777	−	0.915882i
$707$	−41.4573	−	13.4703i	−1.55916	−	0.506603i
$708$	−0.988292	−	12.8540i	−0.0371423	−	0.483084i
$709$	2.17934	+	20.7350i	0.0818468	+	0.778721i	0.956059	+	0.293176i	$0.0947121\pi$
$709$	2.17934	+	20.7350i	0.0818468	+	0.778721i	−0.874212	+	0.485545i	$0.838621\pi$
$710$	−13.9567	+	10.1401i	−0.523786	+	0.380552i
$711$	−14.3971	−	37.9142i	−0.539933	−	1.42189i
$712$	0.261422	+	1.22989i	0.00979721	+	0.0460923i
$713$	−5.55214	−	0.583553i	−0.207929	−	0.0218542i
$714$	−8.20688	−	27.8907i	−0.307135	−	1.04379i
$715$	−17.2833	+	7.44130i	−0.646357	+	0.278289i
$716$		−	15.5491i		−	0.581098i
$717$	0.0414709	+	0.226033i	0.00154876	+	0.00844136i
$718$	51.8675	−	11.0248i	1.93568	−	0.411441i
$719$	4.18577	−	19.6925i	0.156103	−	0.734406i	−0.828555	−	0.559908i	$-0.810836\pi$
$719$	4.18577	−	19.6925i	0.156103	−	0.734406i	0.984658	−	0.174498i	$-0.0558302\pi$
$720$	20.3447	+	7.89400i	0.758204	+	0.294192i
$721$	44.3382	−	4.66014i	1.65124	−	0.173553i
$722$	−29.8420	−	6.34311i	−1.11060	−	0.236066i
$723$	26.3288	+	0.737004i	0.979179	+	0.0274095i
$724$	22.6997	−	10.1066i	0.843627	−	0.375607i
$725$	−7.77285	−	13.4630i	−0.288677	−	0.500002i
$726$	−27.6031	−	23.4527i	−1.02445	−	0.870412i
$727$	−37.9010			−1.40567			−0.702835	−	0.711353i	$-0.748083\pi$
$727$	−37.9010			−1.40567			−0.702835	+	0.711353i	$0.748083\pi$
$728$	7.07104	−	4.71025i	0.262070	−	0.174573i
$729$	−26.6203	−	4.51230i	−0.985936	−	0.167122i
$730$	5.99177	−	6.65453i	0.221765	−	0.246295i
$731$	−7.76902	+	17.4495i	−0.287348	+	0.645393i
$732$	14.2315	−	5.86480i	0.526011	−	0.216769i
$733$	−5.58394	+	1.81433i	−0.206248	+	0.0670139i	−0.410319	−	0.911942i	$-0.634583\pi$
$733$	−5.58394	+	1.81433i	−0.206248	+	0.0670139i	0.204071	+	0.978956i	$0.434583\pi$
$734$	1.01528	+	1.12759i	0.0374748	+	0.0416200i
$735$	−5.86951	−	6.89749i	−0.216500	−	0.254418i
$736$		−	8.08935i		−	0.298177i
$737$	−1.27517	−	1.33787i	−0.0469715	−	0.0492811i
$738$	−31.7244	−	16.3089i	−1.16779	−	0.600339i
$739$	12.6615	+	1.33077i	0.465760	+	0.0489533i	0.334502	−	0.942395i	$-0.391432\pi$
$739$	12.6615	+	1.33077i	0.465760	+	0.0489533i	0.131258	+	0.991348i	$0.458098\pi$
$740$	14.3357	+	4.65796i	0.526992	+	0.171230i
$741$	−7.46255	−	7.71005i	−0.274143	−	0.283236i
$742$	−21.9466	+	15.9451i	−0.805684	+	0.585364i
$743$	18.3115	+	8.15281i	0.671784	+	0.299098i	0.714138	−	0.700005i	$-0.246819\pi$
$743$	18.3115	+	8.15281i	0.671784	+	0.299098i	−0.0423535	+	0.999103i	$0.513486\pi$
$744$	−2.77376	+	5.78839i	−0.101691	+	0.212213i
$745$	−27.2795	+	24.5626i	−0.999444	+	0.899904i
$746$	−4.99658	+	6.87720i	−0.182938	+	0.251792i
$747$	−0.410712	−	8.41823i	−0.0150272	−	0.308007i
$748$	−1.95226	−	14.5821i	−0.0713815	−	0.533176i
$749$			37.5266i			1.37119i
$750$	25.2650	+	29.6899i	0.922549	+	1.08412i
$751$	−25.8559	+	5.49585i	−0.943496	+	0.200546i	−0.653881	−	0.756597i	$-0.726860\pi$
$751$	−25.8559	+	5.49585i	−0.943496	+	0.200546i	−0.289615	+	0.957143i	$0.593527\pi$
$752$	−27.7410	−	24.9781i	−1.01161	−	0.910858i
$753$	−35.8956	−	27.6468i	−1.30811	−	1.00750i
$754$	40.6511	−	11.4027i	1.48043	−	0.415261i
$755$	−9.19674	−	28.3047i	−0.334704	−	1.03011i
$756$	−23.6135	−	12.9871i	−0.858814	−	0.472337i
$757$	−3.07625	+	29.2686i	−0.111808	+	1.06378i	0.784432	+	0.620215i	$0.212955\pi$
$757$	−3.07625	+	29.2686i	−0.111808	+	1.06378i	−0.896240	+	0.443569i	$0.853712\pi$
$758$	−0.761850	+	1.31956i	−0.0276716	+	0.0479287i
$759$	−1.95902	+	6.03714i	−0.0711081	+	0.219134i
$760$	−0.991464	+	1.71727i	−0.0359642	+	0.0622918i
$761$	42.1535	−	18.7680i	1.52806	−	0.680338i	0.541053	−	0.840988i	$-0.318026\pi$
$761$	42.1535	−	18.7680i	1.52806	−	0.680338i	0.987011	+	0.160650i	$0.0513592\pi$
$762$	68.6861	+	1.92268i	2.48823	+	0.0696514i
$763$	−62.1035	−	13.2005i	−2.24830	−	0.477890i
$764$	9.98240	−	22.4208i	0.361151	−	0.811158i
$765$	−1.98309	−	12.8201i	−0.0716989	−	0.463513i
$766$	10.2656	−	3.33549i	0.370911	−	0.120516i
$767$	−13.0415	−	10.3111i	−0.470902	−	0.372312i
$768$	−33.1127	−	11.7931i	−1.19485	−	0.425548i
$769$	−26.3967	+	15.2401i	−0.951888	+	0.549573i	−0.893667	−	0.448731i	$-0.851876\pi$
$769$	−26.3967	+	15.2401i	−0.951888	+	0.549573i	−0.0582209	+	0.998304i	$0.518543\pi$
$770$	−16.7157	−	27.1440i	−0.602391	−	0.978201i
$771$	18.9026	+	4.57420i	0.680759	+	0.164736i
$772$	5.32485	−	7.32903i	0.191646	−	0.263778i
$773$	−18.7792	+	16.9089i	−0.675441	+	0.608170i	−0.933764	−	0.357889i	$-0.883497\pi$
$773$	−18.7792	+	16.9089i	−0.675441	+	0.608170i	0.258323	+	0.966059i	$0.416830\pi$
$774$	14.0729	+	37.0604i	0.505839	+	1.33211i
$775$	−10.3172	+	7.49585i	−0.370603	+	0.269259i
$776$	−0.395323	−	3.76125i	−0.0141913	−	0.135021i
$777$	29.7813	+	14.2710i	1.06840	+	0.511970i
$778$	10.8458	+	51.0255i	0.388841	+	1.82935i
$779$	6.31649	−	8.69390i	0.226312	−	0.311491i
$780$	−14.2494	+	6.97006i	−0.510211	+	0.249568i
$781$	−18.0152	+	6.42391i	−0.644633	+	0.229866i
$782$	−4.99888	+	2.88610i	−0.178759	+	0.103207i
$783$	21.9050	+	23.3348i	0.782819	+	0.833917i
$784$	10.2788	+	11.4157i	0.367099	+	0.407705i
$785$	27.8783	−	9.05821i	0.995020	−	0.323302i
$786$	23.1820	+	56.2532i	0.826873	+	2.00648i
$787$	−5.51858	+	0.580026i	−0.196716	+	0.0206757i	−0.202374	−	0.979308i	$-0.564866\pi$
$787$	−5.51858	+	0.580026i	−0.196716	+	0.0206757i	0.00565798	+	0.999984i	$0.498199\pi$
$788$	0.655045	+	2.01602i	0.0233350	+	0.0718178i
$789$	−23.2061	−	14.2784i	−0.826160	−	0.508325i
$790$	4.22724	−	40.2195i	0.150398	−	1.43095i
$791$	11.7138	+	20.2889i	0.416495	+	0.721391i
$792$	5.78311	+	4.45061i	0.205494	+	0.158146i
$793$	6.89679	−	18.6134i	0.244912	−	0.660980i
$794$	44.9210	+	32.6370i	1.59419	+	1.15824i
$795$	−10.6480	+	5.75652i	−0.377645	+	0.204163i
$796$	18.4636	−	20.5059i	0.654423	−	0.726811i
$797$	−9.06103	+	0.952352i	−0.320958	+	0.0337341i	−0.263638	−	0.964622i	$-0.584922\pi$
$797$	−9.06103	+	0.952352i	−0.320958	+	0.0337341i	−0.0573204	+	0.998356i	$0.518256\pi$
$798$	11.0920	−	14.4014i	0.392651	−	0.509804i
$799$	−4.61370	+	21.7058i	−0.163221	+	0.767894i
$800$	−12.3646	−	13.7323i	−0.437156	−	0.485511i
$801$	0.287715	−	5.13514i	0.0101659	−	0.181441i
$802$	−33.1812	−	19.1572i	−1.17167	−	0.676464i
$803$	8.45338	−	5.20572i	0.298313	−	0.183706i
$804$	−1.12823	−	1.07453i	−0.0397897	−	0.0378958i
$805$	−3.28338	+	4.51918i	−0.115724	+	0.159280i
$806$	−12.7886	−	32.1871i	−0.450458	−	1.13374i
$807$	−28.6881	+	19.6407i	−1.00987	+	0.691384i
$808$	9.09020	+	4.04722i	0.319792	+	0.142381i
$809$	26.3528	+	11.7330i	0.926516	+	0.412511i	0.813819	−	0.581118i	$-0.197385\pi$
$809$	26.3528	+	11.7330i	0.926516	+	0.412511i	0.112696	+	0.993629i	$0.464051\pi$
$810$	−21.6669	−	15.9822i	−0.761297	−	0.561557i
$811$	−21.8623	−	7.10349i	−0.767689	−	0.249437i	−0.101114	−	0.994875i	$-0.532241\pi$
$811$	−21.8623	−	7.10349i	−0.767689	−	0.249437i	−0.666575	+	0.745438i	$0.732241\pi$
$812$	12.9933	+	29.1833i	0.455974	+	1.02413i
$813$	21.1452	+	5.11689i	0.741594	+	0.179457i
$814$	30.8828	+	21.1258i	1.08244	+	0.740457i
$815$	−23.8988	−	13.7980i	−0.837137	−	0.483321i
$816$	3.97066	+	21.6417i	0.139001	+	0.757612i
$817$	−11.6817	+	2.48303i	−0.408691	+	0.0868701i
$818$	−55.2106	+	17.9390i	−1.93039	+	0.627223i
$819$	−32.9647	+	11.0055i	−1.15188	+	0.384565i
$820$	−9.33795	−	12.8526i	−0.326096	−	0.448832i
$821$	−12.3010	+	13.6616i	−0.429308	+	0.476795i	−0.918522	−	0.395369i	$-0.870617\pi$
$821$	−12.3010	+	13.6616i	−0.429308	+	0.476795i	0.489215	+	0.872163i	$0.337283\pi$
$822$	−5.71595	−	10.5729i	−0.199367	−	0.368773i
$823$	−40.9343	+	18.2251i	−1.42688	+	0.635287i	−0.967481	−	0.252944i	$-0.918601\pi$
$823$	−40.9343	+	18.2251i	−1.42688	+	0.635287i	−0.459398	+	0.888231i	$0.651935\pi$
$824$	−10.1768			−0.354527
$825$	5.90221	+	13.2429i	0.205489	+	0.461059i
$826$	14.0824	−	24.3915i	0.489990	−	0.848688i
$827$	−38.8245	−	28.2077i	−1.35006	−	0.980877i	−0.999008	−	0.0445217i	$-0.985824\pi$
$827$	−38.8245	−	28.2077i	−1.35006	−	0.980877i	−0.351053	−	0.936355i	$-0.614176\pi$
$828$	−1.40347	+	5.16318i	−0.0487739	+	0.179433i
$829$	−18.1060	+	20.1088i	−0.628848	+	0.698407i	−0.970413	−	0.241451i	$-0.922377\pi$
$829$	−18.1060	+	20.1088i	−0.628848	+	0.698407i	0.341564	+	0.939858i	$0.389043\pi$
$830$	3.41839	−	7.67782i	0.118654	−	0.266501i
$831$	14.9032	+	11.4785i	0.516988	+	0.398183i
$832$	14.9236	−	7.82471i	0.517381	−	0.271273i
$833$	2.82186	−	8.68478i	0.0977715	−	0.300910i
$834$	30.4382	−	5.58457i	1.05399	−	0.193378i
$835$	32.5469	−	18.7910i	1.12633	−	0.650288i
$836$	6.65865	−	6.34658i	0.230294	−	0.219501i
$837$	17.1592	−	19.8719i	0.593108	−	0.686874i
$838$	24.2009	+	54.3561i	0.836006	+	1.87770i
$839$	−18.3232	+	16.4983i	−0.632587	+	0.569584i	−0.921793	−	0.387683i	$-0.873275\pi$
$839$	−18.3232	+	16.4983i	−0.632587	+	0.569584i	0.289206	+	0.957267i	$0.406609\pi$
$840$	3.62815	+	5.29946i	0.125183	+	0.182849i
$841$	−0.934329	−	8.88954i	−0.0322182	−	0.306536i
$842$	−37.7014	−	16.7857i	−1.29928	−	0.578475i
$843$	1.85762	−	3.87655i	0.0639797	−	0.133515i
$844$	6.27635	+	2.03931i	0.216041	+	0.0701960i
$845$	−5.86544	+	19.5974i	−0.201777	+	0.674172i
$846$	24.9438	+	38.7154i	0.857586	+	1.33106i
$847$	−9.29664	−	34.0977i	−0.319436	−	1.17161i
$848$	17.7799	−	10.2652i	0.610564	−	0.352509i
$849$	11.5988	+	13.6302i	0.398071	+	0.467789i
$850$	−4.07456	+	12.5402i	−0.139756	+	0.430126i
$851$	1.36320	−	6.41336i	0.0467299	−	0.219847i
$852$	−14.9071	+	6.14324i	−0.510710	+	0.210464i
$853$	−9.26266	−	12.7490i	−0.317147	−	0.436516i	0.620446	−	0.784249i	$-0.286952\pi$
$853$	−9.26266	−	12.7490i	−0.317147	−	0.436516i	−0.937594	+	0.347733i	$0.886952\pi$
$854$	32.8930	+	6.99162i	1.12558	+	0.239248i
$855$	5.75604	−	5.71463i	0.196852	−	0.195436i
$856$	0.895411	−	8.51927i	0.0306045	−	0.291183i
$857$	−41.6760			−1.42363			−0.711813	−	0.702369i	$-0.752126\pi$
$857$	−41.6760			−1.42363			−0.711813	+	0.702369i	$0.752126\pi$
$858$	−38.8145	+	6.62831i	−1.32510	+	0.226287i
$859$	−6.49589			−0.221637			−0.110819	−	0.993841i	$-0.535347\pi$
$859$	−6.49589			−0.221637			−0.110819	+	0.993841i	$0.535347\pi$
$860$	−1.84550	+	17.5587i	−0.0629309	+	0.598747i
$861$	−16.5526	−	30.6178i	−0.564111	−	1.04345i
$862$	−14.7359	−	3.13220i	−0.501905	−	0.106683i
$863$	−5.53496	−	7.61821i	−0.188412	−	0.259327i	0.704353	−	0.709850i	$-0.251237\pi$
$863$	−5.53496	−	7.61821i	−0.188412	−	0.259327i	−0.892765	+	0.450523i	$0.851237\pi$
$864$	31.2356	+	21.7176i	1.06266	+	0.738848i
$865$	−7.35293	+	34.5928i	−0.250007	+	1.17619i
$866$	−5.98828	+	18.4300i	−0.203490	+	0.626278i
$867$	−12.4632	+	10.6058i	−0.423273	+	0.360190i
$868$	22.6948	−	13.1029i	0.770313	−	0.444741i
$869$	17.0673	−	41.4605i	0.578968	−	1.40645i
$870$	9.00906	+	30.6169i	0.305436	+	1.03801i
$871$	−2.00512	+	0.128572i	−0.0679410	+	0.00435649i
$872$	13.7837	+	4.47860i	0.466776	+	0.151665i
$873$	−2.47517	+	15.2706i	−0.0837717	+	0.516831i
$874$	−3.29702	−	1.46793i	−0.111523	−	0.0496534i
$875$	3.97617	+	37.8307i	0.134419	+	1.27891i
$876$	6.90567	−	4.72781i	0.233321	−	0.159738i
$877$	5.90317	−	5.31524i	0.199336	−	0.179483i	−0.563417	−	0.826172i	$-0.690514\pi$
$877$	5.90317	−	5.31524i	0.199336	−	0.179483i	0.762753	+	0.646690i	$0.223847\pi$
$878$	−1.68574	−	3.78623i	−0.0568910	−	0.127779i
$879$	−33.1661	+	9.75915i	−1.11866	+	0.329168i
$880$	10.4340	+	21.7528i	0.351731	+	0.733285i
$881$	−4.30108	+	2.48323i	−0.144907	+	0.0836622i	−0.570701	−	0.821158i	$-0.693328\pi$
$881$	−4.30108	+	2.48323i	−0.144907	+	0.0836622i	0.425794	+	0.904820i	$0.359995\pi$
$882$	−8.54310	−	16.9175i	−0.287661	−	0.569641i
$883$	−9.32263	+	28.6921i	−0.313732	+	0.965567i	0.662542	+	0.749025i	$0.269478\pi$
$883$	−9.32263	+	28.6921i	−0.313732	+	0.965567i	−0.976273	+	0.216542i	$0.930522\pi$
$884$	−13.5144	−	8.55372i	−0.454538	−	0.287693i
$885$	7.66849	−	9.95651i	0.257773	−	0.334684i
$886$	21.5585	−	48.4211i	0.724271	−	1.62674i
$887$	−37.7408	+	41.9154i	−1.26721	+	1.40738i	−0.394683	+	0.918817i	$0.629146\pi$
$887$	−37.7408	+	41.9154i	−1.26721	+	1.40738i	−0.872528	+	0.488564i	$0.837521\pi$
$888$	−6.42043	−	3.95040i	−0.215455	−	0.132567i
$889$	54.2415	+	39.4088i	1.81920	+	1.32173i
$890$	2.56433	−	4.44155i	0.0859566	−	0.148881i
$891$	−18.0519	−	23.7724i	−0.604762	−	0.796406i
$892$	−15.7787			−0.528309
$893$	−12.6751	+	5.64330i	−0.424155	+	0.188846i
$894$	−67.5724	+	36.5310i	−2.25996	+	1.22178i
$895$	10.1424	−	11.2643i	0.339023	−	0.376523i
$896$	−10.8745	−	14.9674i	−0.363290	−	0.500026i
$897$	3.66310	+	5.84731i	0.122307	+	0.195236i
$898$	−50.7601	+	16.4930i	−1.69389	+	0.550377i
$899$	−30.4422	+	6.47070i	−1.01531	+	0.215810i
$900$	5.50946	+	10.9101i	0.183649	+	0.363671i
$901$	−10.5694	−	6.10225i	−0.352118	−	0.203295i
$902$	−13.2453	−	37.1449i	−0.441019	−	1.23679i
$903$	−9.09774	+	37.5957i	−0.302754	+	1.25111i
$904$	−2.17515	−	4.88548i	−0.0723446	−	0.162489i
$905$	23.0367	+	7.48506i	0.765764	+	0.248812i
$906$	−4.77420	−	62.0947i	−0.158612	−	2.06296i
$907$	32.6868	+	14.5531i	1.08535	+	0.483228i	0.869870	−	0.493280i	$-0.164202\pi$
$907$	32.6868	+	14.5531i	1.08535	+	0.483228i	0.215478	+	0.976509i	$0.430869\pi$
$908$	2.17862	+	0.969984i	0.0723000	+	0.0321901i
$909$	−31.5385	−	25.7285i	−1.04607	−	0.853359i
$910$	−34.2894	−	5.02130i	−1.13668	−	0.166455i
$911$	−14.8072	+	20.3804i	−0.490586	+	0.675233i	−0.980496	−	0.196540i	$-0.937030\pi$
$911$	−14.8072	+	20.3804i	−0.490586	+	0.675233i	0.489910	+	0.871773i	$0.337030\pi$
$912$	−9.48783	+	9.96202i	−0.314174	+	0.329875i
$913$	6.03588	−	7.09852i	0.199759	−	0.234927i
$914$	47.3163	+	27.3181i	1.56508	+	0.903602i
$915$	14.1352	+	5.03428i	0.467296	+	0.166428i
$916$	−16.5251	−	18.3529i	−0.546003	−	0.606398i
$917$	−12.3430	+	58.0695i	−0.407603	+	1.91762i
$918$	2.27639	−	27.0506i	0.0751320	−	0.892804i
$919$	29.6837	−	3.11988i	0.979173	−	0.102915i	0.398602	−	0.917124i	$-0.369496\pi$
$919$	29.6837	−	3.11988i	0.979173	−	0.102915i	0.580572	+	0.814209i	$0.302829\pi$
$920$	0.853220	−	0.947597i	0.0281298	−	0.0312414i
$921$	9.33443	+	17.2661i	0.307580	+	0.568938i
$922$	−11.2702	−	8.18831i	−0.371166	−	0.269668i
$923$	−7.22422	+	19.4970i	−0.237788	+	0.641753i
$924$	−9.21757	−	28.3318i	−0.303236	−	0.932047i
$925$	−7.48872	−	12.9708i	−0.246228	−	0.426479i
$926$	2.93831	−	27.9562i	0.0965590	−	0.918697i
$927$	40.1701	+	10.9191i	1.31936	+	0.358631i
$928$	−13.9355	−	42.8890i	−0.457455	−	1.40790i
$929$	35.1563	−	3.69508i	1.15344	−	0.121232i	0.491563	−	0.870842i	$-0.336426\pi$
$929$	35.1563	−	3.69508i	1.15344	−	0.121232i	0.661879	+	0.749610i	$0.269759\pi$
$930$	24.2060	−	9.97532i	0.793747	−	0.327104i
$931$	5.43010	−	1.76435i	0.177964	−	0.0578241i
$932$	−17.3773	−	19.2995i	−0.569213	−	0.632175i
$933$	−29.0540	+	5.33061i	−0.951185	+	0.174516i
$934$	40.7565	−	23.5308i	1.33359	−	0.769950i
$935$	8.09737	−	11.8372i	0.264812	−	0.387117i
$936$	7.74622	−	1.71191i	0.253193	−	0.0559556i
$937$	14.4899	−	19.9437i	0.473365	−	0.651531i	−0.503848	−	0.863792i	$-0.668083\pi$
$937$	14.4899	−	19.9437i	0.473365	−	0.651531i	0.977213	+	0.212261i	$0.0680827\pi$
$938$	−0.707700	−	3.32947i	−0.0231072	−	0.108711i
$939$	5.42654	−	11.3243i	0.177089	−	0.369556i
$940$	2.14403	+	20.3991i	0.0699305	+	0.665344i
$941$	24.1623	−	17.5549i	0.787667	−	0.572274i	−0.119603	−	0.992822i	$-0.538162\pi$
$941$	24.1623	−	17.5549i	0.787667	−	0.572274i	0.907270	+	0.420548i	$0.138162\pi$
$942$	61.1594	−	4.70228i	1.99268	−	0.153209i
$943$	−5.13539	+	4.62393i	−0.167231	+	0.150576i
$944$	−12.5290	+	17.2446i	−0.407783	+	0.561265i
$945$	−8.63508	−	24.8109i	−0.280899	−	0.807098i
$946$	−16.6830	+	40.5269i	−0.542410	+	1.31764i
$947$	−17.5802	+	10.1499i	−0.571279	+	0.329828i	−0.757660	−	0.652649i	$-0.773657\pi$
$947$	−17.5802	+	10.1499i	−0.571279	+	0.329828i	0.186381	+	0.982478i	$0.440324\pi$
$948$	12.6811	−	35.6058i	0.411861	−	1.15642i
$949$	1.56377	−	10.6787i	0.0507622	−	0.346644i
$950$	−7.84069	+	2.54759i	−0.254385	+	0.0826548i
$951$	1.89813	−	14.2194i	0.0615512	−	0.461095i
$952$	−2.63384	+	5.91570i	−0.0853632	+	0.191729i
$953$	−26.7535	−	5.68663i	−0.866631	−	0.184208i	−0.246918	−	0.969036i	$-0.579418\pi$
$953$	−26.7535	−	5.68663i	−0.866631	−	0.184208i	−0.619713	+	0.784828i	$0.712751\pi$
$954$	−24.4900	+	6.46739i	−0.792891	+	0.209390i
$955$	21.8562	−	9.73102i	0.707251	−	0.314889i
$956$	−0.107086	+	0.185478i	−0.00346341	+	0.00599880i
$957$	0.0135787	+	35.3832i	0.000438936	+	1.14378i
$958$	22.1272	−	38.3254i	0.714896	−	1.23824i
$959$	1.22586	−	11.6633i	0.0395852	−	0.376628i
$960$	6.05762	+	11.2049i	0.195509	+	0.361638i
$961$	−1.69008	−	5.20155i	−0.0545189	−	0.167792i
$962$	39.1651	−	10.9859i	1.26273	−	0.354198i
$963$	−12.6750	+	32.6666i	−0.408448	+	1.05267i
$964$	18.2421	+	16.4253i	0.587540	+	0.529023i
$965$	8.63807	−	1.83608i	0.278069	−	0.0591055i
$966$	−8.90222	+	7.57547i	−0.286424	+	0.243737i
$967$		−	38.6123i		−	1.24169i	−0.783934	−	0.620844i	$-0.786790\pi$
$967$		−	38.6123i		−	1.24169i	0.783934	−	0.620844i	$-0.213210\pi$
$968$	1.29692	+	7.96267i	0.0416846	+	0.255930i
$969$	7.94867	+	1.92349i	0.255348	+	0.0617913i
$970$	−9.06727	+	12.4800i	−0.291132	+	0.400709i
$971$	30.3225	−	27.3025i	0.973095	−	0.876178i	−0.0192328	−	0.999815i	$-0.506122\pi$
$971$	30.3225	−	27.3025i	0.973095	−	0.876178i	0.992328	+	0.123637i	$0.0394557\pi$
$972$	−16.1688	−	19.2809i	−0.518614	−	0.618435i
$973$	27.5850	+	12.2817i	0.884336	+	0.393732i
$974$	−45.1442	+	32.7992i	−1.44651	+	1.05095i
$975$	15.1561	+	4.32720i	0.485382	+	0.138581i
$976$	−24.2044	−	7.86449i	−0.774764	−	0.251736i
$977$	−8.90784	−	0.936252i	−0.284987	−	0.0299534i	−0.0390436	−	0.999238i	$-0.512431\pi$
$977$	−8.90784	−	0.936252i	−0.284987	−	0.0299534i	−0.245944	+	0.969284i	$0.579098\pi$
$978$	−41.8162	−	39.8258i	−1.33713	−	1.27349i
$979$	4.11592	−	3.92302i	0.131545	−	0.125380i
$980$		−	8.44069i		−	0.269628i
$981$	−49.6020	−	32.4671i	−1.58367	−	1.03659i
$982$	1.66318	+	1.84715i	0.0530743	+	0.0589450i
$983$	57.1038	−	18.5542i	1.82133	−	0.591786i	0.821565	−	0.570115i	$-0.193102\pi$
$983$	57.1038	−	18.5542i	1.82133	−	0.591786i	0.999765	−	0.0216706i	$-0.00689849\pi$
$984$	3.02720	+	7.34578i	0.0965036	+	0.234175i
$985$	−0.840477	+	1.88774i	−0.0267798	+	0.0601485i
$986$	−21.5317	+	23.9134i	−0.685710	+	0.761558i
$987$	−1.25742	+	44.9204i	−0.0400243	+	1.42983i
$988$	−0.639908	−	9.97959i	−0.0203582	−	0.317493i
$989$	7.67973			0.244201
$990$	−5.38268	−	29.2745i	−0.171073	−	0.930405i
$991$	−21.1164	−	36.5746i	−0.670784	−	1.16183i	−0.977682	−	0.210089i	$-0.932625\pi$
$991$	−21.1164	−	36.5746i	−0.670784	−	1.16183i	0.306898	−	0.951742i	$-0.400709\pi$
$992$	−33.7957	+	15.0468i	−1.07302	+	0.477737i
$993$	0.175414	−	6.26651i	0.00556660	−	0.198862i
$994$	−34.4546	−	7.32356i	−1.09283	−	0.232289i
$995$	26.7511	−	2.81166i	0.848068	−	0.0891355i
$996$	4.79297	−	6.22303i	0.151871	−	0.197184i
$997$	1.14643	−	5.39352i	0.0363077	−	0.170814i	−0.956258	−	0.292525i	$-0.905505\pi$
$997$	1.14643	−	5.39352i	0.0363077	−	0.170814i	0.992566	+	0.121710i	$0.0388379\pi$
$998$	−20.3720	+	4.33021i	−0.644866	+	0.137070i
$999$	21.1042	+	22.4818i	0.667708	+	0.711292i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bq.a.29.10	✓	416
3.2	odd	2	inner	429.2.bq.a.29.43	yes	416
11.8	odd	10	inner	429.2.bq.a.107.10	yes	416
13.9	even	3	inner	429.2.bq.a.425.43	yes	416
33.8	even	10	inner	429.2.bq.a.107.43	yes	416
39.35	odd	6	inner	429.2.bq.a.425.10	yes	416
143.74	odd	30	inner	429.2.bq.a.74.43	yes	416
429.74	even	30	inner	429.2.bq.a.74.10	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bq.a.29.10	✓	416	1.1	even	1	trivial
429.2.bq.a.29.43	yes	416	3.2	odd	2	inner
429.2.bq.a.74.10	yes	416	429.74	even	30	inner
429.2.bq.a.74.43	yes	416	143.74	odd	30	inner
429.2.bq.a.107.10	yes	416	11.8	odd	10	inner
429.2.bq.a.107.43	yes	416	33.8	even	10	inner
429.2.bq.a.425.10	yes	416	39.35	odd	6	inner
429.2.bq.a.425.43	yes	416	13.9	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bq (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.198720 + 1.89069i) q^{2} +(-1.52365 + 0.823714i) q^{3} +(-1.57894 - 0.335614i) q^{4} +(-0.924919 - 1.27304i) q^{5} +(-1.25461 - 3.04444i) q^{6} +(0.668009 - 3.14273i) q^{7} +(-0.226639 + 0.697522i) q^{8} +(1.64299 - 2.51010i) q^{9} +O(q^{10})\)	\(q+(-0.198720 + 1.89069i) q^{2} +(-1.52365 + 0.823714i) q^{3} +(-1.57894 - 0.335614i) q^{4} +(-0.924919 - 1.27304i) q^{5} +(-1.25461 - 3.04444i) q^{6} +(0.668009 - 3.14273i) q^{7} +(-0.226639 + 0.697522i) q^{8} +(1.64299 - 2.51010i) q^{9} +(2.59073 - 1.49576i) q^{10} +(3.22328 - 0.781308i) q^{11} +(2.68220 - 0.789239i) q^{12} +(1.59927 - 3.23146i) q^{13} +(5.80920 + 1.88752i) q^{14} +(2.45787 + 1.17779i) q^{15} +(-4.22308 - 1.88024i) q^{16} +(0.287247 + 2.73297i) q^{17} +(4.41933 + 3.60520i) q^{18} +(-1.27686 + 1.14969i) q^{19} +(1.03314 + 2.32047i) q^{20} +(1.57091 + 5.33866i) q^{21} +(0.836683 + 6.24951i) q^{22} +(0.956851 - 0.552438i) q^{23} +(-0.229242 - 1.24946i) q^{24} +(0.779925 - 2.40036i) q^{25} +(5.79190 + 3.66589i) q^{26} +(-0.435731 + 5.17785i) q^{27} +(-2.10949 + 4.73800i) q^{28} +(4.12146 - 4.57734i) q^{29} +(-2.71528 + 4.41303i) q^{30} +(-4.08780 - 2.96996i) q^{31} +(3.66075 - 6.34060i) q^{32} +(-4.26757 + 3.84550i) q^{33} -5.22430 q^{34} +(-4.61868 + 2.05637i) q^{35} +(-3.43661 + 3.41188i) q^{36} +(3.97080 - 4.41002i) q^{37} +(-1.91998 - 2.64262i) q^{38} +(0.225077 + 6.24094i) q^{39} +(1.09760 - 0.356631i) q^{40} +(-6.11774 + 1.30037i) q^{41} +(-10.4059 + 1.90921i) q^{42} +(6.01953 + 3.47538i) q^{43} +(-5.35159 + 0.151859i) q^{44} +(-4.71509 + 0.230042i) q^{45} +(0.854347 + 1.91889i) q^{46} +(7.67990 + 2.49535i) q^{47} +(7.98326 - 0.613799i) q^{48} +(-3.03572 - 1.35159i) q^{49} +(4.38336 + 1.95160i) q^{50} +(-2.68885 - 3.92747i) q^{51} +(-3.60968 + 4.56555i) q^{52} +(-2.61046 + 3.59299i) q^{53} +(-9.70315 - 1.85278i) q^{54} +(-3.97591 - 3.38073i) q^{55} +(2.04073 + 1.17822i) q^{56} +(0.998467 - 2.80349i) q^{57} +(7.83534 + 8.70203i) q^{58} +(0.958686 - 4.51026i) q^{59} +(-3.48555 - 2.68457i) q^{60} +(5.47524 - 0.575471i) q^{61} +(6.42762 - 7.13859i) q^{62} +(-6.79103 - 6.84024i) q^{63} +(3.78093 + 2.74700i) q^{64} +(-5.59298 + 0.952899i) q^{65} +(-6.42262 - 8.83284i) q^{66} +(-0.278631 - 0.482604i) q^{67} +(0.463679 - 4.41161i) q^{68} +(-1.00285 + 1.62989i) q^{69} +(-2.97014 - 9.14116i) q^{70} +(-5.73518 + 0.602792i) q^{71} +(1.37848 + 1.71491i) q^{72} +(2.84681 - 0.924985i) q^{73} +(7.54892 + 8.38393i) q^{74} +(0.788884 + 4.29974i) q^{75} +(2.40194 - 1.38676i) q^{76} +(-0.302261 - 10.6518i) q^{77} +(-11.8444 - 0.814648i) q^{78} +(7.94601 - 10.9367i) q^{79} +(1.51239 + 7.11523i) q^{80} +(-3.60117 - 8.24813i) q^{81} +(-1.24288 - 11.8252i) q^{82} +(2.27286 - 1.65133i) q^{83} +(-0.688638 - 8.95665i) q^{84} +(3.21351 - 2.89346i) q^{85} +(-7.76708 + 10.6905i) q^{86} +(-2.50922 + 10.3692i) q^{87} +(-0.185541 + 2.42539i) q^{88} +(1.48471 - 0.857200i) q^{89} +(0.502044 - 8.96051i) q^{90} +(-9.08729 - 7.18473i) q^{91} +(-1.69622 + 0.551135i) q^{92} +(8.67476 + 1.15799i) q^{93} +(-6.24410 + 14.0245i) q^{94} +(2.64460 + 0.562127i) q^{95} +(-0.354837 + 12.6762i) q^{96} +(-4.71081 + 2.09739i) q^{97} +(3.15870 - 5.47103i) q^{98} +(3.33466 - 9.37443i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9}+O(q^{10}) \) 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9	\( 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9} - 52 q^{12} - 20 q^{13} - 3 q^{15} + 30 q^{16} - 20 q^{18} - 10 q^{19} + 4 q^{22} + 5 q^{24} + 60 q^{25} - 24 q^{27} - 10 q^{28} - 65 q^{30} - 8 q^{31} + 49 q^{33} - 24 q^{34} + 3 q^{36} - 6 q^{37} - 35 q^{39} - 120 q^{40} - 13 q^{42} - 32 q^{45} - 30 q^{46} - 33 q^{48} - 26 q^{49} - 100 q^{51} - 60 q^{52} - 42 q^{55} - 20 q^{57} - 34 q^{58} + 32 q^{60} - 30 q^{61} - 45 q^{63} + 40 q^{64} + 42 q^{66} + 32 q^{67} - 33 q^{69} - 268 q^{70} + 55 q^{72} - 40 q^{73} + 9 q^{75} - 32 q^{78} - 37 q^{81} + 28 q^{82} - 180 q^{84} - 10 q^{85} - 142 q^{88} - 30 q^{90} + 8 q^{91} - 26 q^{93} - 90 q^{94} + 330 q^{96} - 14 q^{97} - 4 q^{99}+O(q^{100}) \) 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9 - 52 * q^12 - 20 * q^13 - 3 * q^15 + 30 * q^16 - 20 * q^18 - 10 * q^19 + 4 * q^22 + 5 * q^24 + 60 * q^25 - 24 * q^27 - 10 * q^28 - 65 * q^30 - 8 * q^31 + 49 * q^33 - 24 * q^34 + 3 * q^36 - 6 * q^37 - 35 * q^39 - 120 * q^40 - 13 * q^42 - 32 * q^45 - 30 * q^46 - 33 * q^48 - 26 * q^49 - 100 * q^51 - 60 * q^52 - 42 * q^55 - 20 * q^57 - 34 * q^58 + 32 * q^60 - 30 * q^61 - 45 * q^63 + 40 * q^64 + 42 * q^66 + 32 * q^67 - 33 * q^69 - 268 * q^70 + 55 * q^72 - 40 * q^73 + 9 * q^75 - 32 * q^78 - 37 * q^81 + 28 * q^82 - 180 * q^84 - 10 * q^85 - 142 * q^88 - 30 * q^90 + 8 * q^91 - 26 * q^93 - 90 * q^94 + 330 * q^96 - 14 * q^97 - 4 * q^99

Introduction

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