LMFDB - Embedded newform 462.2.y.a.289.1

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:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			289.1
Character	$\chi$	$=$	462.289
Dual form			462.2.y.a.235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104528 + 0.994522i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-0.154851 + 0.0689440i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-2.56131 - 0.663085i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(0.104528 + 0.994522i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-0.154851 + 0.0689440i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-2.56131 - 0.663085i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-0.0847527 - 0.146796i) q^{10} +(-3.02092 - 1.36896i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.621990 - 0.451902i) q^{13} +(0.391723 - 2.61659i) q^{14} +(0.0523800 - 0.161209i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.426531 - 4.05817i) q^{17} +(0.978148 - 0.207912i) q^{18} +(-3.54823 - 0.754200i) q^{19} +(0.137133 - 0.0996327i) q^{20} +(2.20662 - 1.45974i) q^{21} +(1.04569 - 3.14747i) q^{22} +(0.717830 - 1.24332i) q^{23} +(0.913545 + 0.406737i) q^{24} +(-3.32643 + 3.69437i) q^{25} +(0.514442 + 0.571346i) q^{26} +(0.809017 + 0.587785i) q^{27} +(2.64320 + 0.116068i) q^{28} +(1.02582 - 3.15714i) q^{29} +(0.165801 + 0.0352421i) q^{30} +(-4.73369 - 2.10757i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.03872 - 1.32897i) q^{33} +4.08052 q^{34} +(0.442337 - 0.0739079i) q^{35} +(0.309017 + 0.951057i) q^{36} +(2.69612 + 2.99435i) q^{37} +(0.379177 - 3.60763i) q^{38} +(-0.0803637 + 0.764610i) q^{39} +(0.113421 + 0.125967i) q^{40} +(-1.29807 - 3.99504i) q^{41} +(1.68239 + 2.04195i) q^{42} +3.56184 q^{43} +(3.23953 + 0.710959i) q^{44} +(0.0847527 + 0.146796i) q^{45} +(1.31154 + 0.583936i) q^{46} +(-8.18793 - 1.74040i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(6.12064 + 3.39673i) q^{49} +(-4.02184 - 2.92204i) q^{50} +(2.73040 + 3.03242i) q^{51} +(-0.514442 + 0.571346i) q^{52} +(-4.29246 - 1.91113i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.562173 + 0.00371003i) q^{55} +(0.160858 + 2.64086i) q^{56} +(2.93471 - 2.13219i) q^{57} +(3.24707 + 0.690186i) q^{58} +(-3.25567 + 0.692014i) q^{59} +(-0.0177181 + 0.168577i) q^{60} +(-5.47982 + 2.43978i) q^{61} +(1.60122 - 4.92806i) q^{62} +(-0.391723 + 2.61659i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.0651597 + 0.112860i) q^{65} +(1.63932 + 2.88316i) q^{66} +(2.70447 + 4.68428i) q^{67} +(0.426531 + 4.05817i) q^{68} +(0.443644 + 1.36539i) q^{69} +(0.119740 + 0.432188i) q^{70} +(-2.83494 - 2.05970i) q^{71} +(-0.913545 + 0.406737i) q^{72} +(-2.06177 + 0.438243i) q^{73} +(-2.69612 + 2.99435i) q^{74} +(-0.519639 - 4.94403i) q^{75} +3.62750 q^{76} +(6.82978 + 5.50946i) q^{77} -0.768822 q^{78} +(1.49049 + 14.1810i) q^{79} +(-0.113421 + 0.125967i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(3.83747 - 1.70855i) q^{82} +(-13.2534 - 9.62913i) q^{83} +(-1.85490 + 1.88662i) q^{84} +(0.213738 + 0.657818i) q^{85} +(0.372313 + 3.54232i) q^{86} +(1.65981 + 2.87487i) q^{87} +(-0.368442 + 3.29610i) q^{88} +(-0.842129 + 1.45861i) q^{89} +(-0.137133 + 0.0996327i) q^{90} +(-1.89276 + 0.745030i) q^{91} +(-0.443644 + 1.36539i) q^{92} +(4.73369 - 2.10757i) q^{93} +(0.874992 - 8.32499i) q^{94} +(0.601444 - 0.127841i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(-12.4725 + 9.06181i) q^{97} +(-2.73835 + 6.44216i) q^{98} +(-1.04569 + 3.14747i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 + 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 3 q^{9} + 10 q^{10} + 6 q^{11} + 12 q^{12} - 2 q^{13} - 5 q^{14} + 3 q^{16} - 2 q^{17} - 3 q^{18} + 7 q^{19} - 10 q^{20} - 4 q^{21} + 2 q^{22} + 24 q^{23} + 3 q^{24} + 4 q^{25} + 4 q^{26} + 6 q^{27} + 14 q^{28} - 6 q^{29} - 7 q^{31} + 12 q^{32} - q^{33} - 24 q^{34} + 4 q^{35} - 6 q^{36} - q^{37} + 8 q^{38} - q^{39} + 16 q^{41} - 4 q^{42} + 52 q^{43} - 4 q^{44} - 10 q^{45} - 4 q^{46} + 27 q^{47} + 6 q^{48} - 33 q^{49} - 22 q^{50} - 8 q^{51} - 4 q^{52} + 13 q^{53} - 12 q^{54} + 30 q^{55} + 14 q^{56} - 16 q^{57} - 3 q^{58} + 14 q^{59} - 5 q^{60} + 9 q^{61} - 4 q^{62} + 5 q^{63} - 6 q^{64} - 50 q^{65} - 4 q^{66} - 20 q^{67} - 2 q^{68} - 32 q^{69} - 17 q^{70} - 18 q^{71} - 3 q^{72} + 7 q^{73} + q^{74} + 11 q^{75} - 4 q^{76} - 34 q^{77} - 12 q^{78} + q^{79} + 3 q^{81} - 2 q^{82} - 68 q^{83} - 5 q^{84} - 19 q^{86} - 8 q^{87} - q^{88} - 42 q^{89} + 10 q^{90} - 16 q^{91} + 32 q^{92} + 7 q^{93} + 8 q^{94} + 38 q^{95} + 3 q^{96} - 80 q^{97} - 2 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 + 11 * q^7 + 6 * q^8 + 3 * q^9 + 10 * q^10 + 6 * q^11 + 12 * q^12 - 2 * q^13 - 5 * q^14 + 3 * q^16 - 2 * q^17 - 3 * q^18 + 7 * q^19 - 10 * q^20 - 4 * q^21 + 2 * q^22 + 24 * q^23 + 3 * q^24 + 4 * q^25 + 4 * q^26 + 6 * q^27 + 14 * q^28 - 6 * q^29 - 7 * q^31 + 12 * q^32 - q^33 - 24 * q^34 + 4 * q^35 - 6 * q^36 - q^37 + 8 * q^38 - q^39 + 16 * q^41 - 4 * q^42 + 52 * q^43 - 4 * q^44 - 10 * q^45 - 4 * q^46 + 27 * q^47 + 6 * q^48 - 33 * q^49 - 22 * q^50 - 8 * q^51 - 4 * q^52 + 13 * q^53 - 12 * q^54 + 30 * q^55 + 14 * q^56 - 16 * q^57 - 3 * q^58 + 14 * q^59 - 5 * q^60 + 9 * q^61 - 4 * q^62 + 5 * q^63 - 6 * q^64 - 50 * q^65 - 4 * q^66 - 20 * q^67 - 2 * q^68 - 32 * q^69 - 17 * q^70 - 18 * q^71 - 3 * q^72 + 7 * q^73 + q^74 + 11 * q^75 - 4 * q^76 - 34 * q^77 - 12 * q^78 + q^79 + 3 * q^81 - 2 * q^82 - 68 * q^83 - 5 * q^84 - 19 * q^86 - 8 * q^87 - q^88 - 42 * q^89 + 10 * q^90 - 16 * q^91 + 32 * q^92 + 7 * q^93 + 8 * q^94 + 38 * q^95 + 3 * q^96 - 80 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

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
$5$	−0.154851	+	0.0689440i	−0.0692514	+	0.0308327i	−0.441070	−	0.897473i	$-0.645401\pi$
$5$	−0.154851	+	0.0689440i	−0.0692514	+	0.0308327i	0.371819	+	0.928305i	$0.378734\pi$
$6$	−0.809017	−	0.587785i	−0.330280	−	0.239962i
$7$	−2.56131	−	0.663085i	−0.968085	−	0.250623i
$7$	−2.56131	−	0.663085i	−0.968085	−	0.250623i
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	−0.0847527	−	0.146796i	−0.0268011	−	0.0464209i
$11$	−3.02092	−	1.36896i	−0.910841	−	0.412757i
$11$	−3.02092	−	1.36896i	−0.910841	−	0.412757i
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	0.621990	−	0.451902i	0.172509	−	0.125335i	−0.498181	−	0.867073i	$-0.665998\pi$
$13$	0.621990	−	0.451902i	0.172509	−	0.125335i	0.670689	+	0.741738i	$0.265998\pi$
$14$	0.391723	−	2.61659i	0.104692	−	0.699314i
$15$	0.0523800	−	0.161209i	0.0135245	−	0.0416240i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	0.426531	−	4.05817i	0.103449	−	0.984251i	−0.812502	−	0.582959i	$-0.801895\pi$
$17$	0.426531	−	4.05817i	0.103449	−	0.984251i	0.915950	−	0.401291i	$-0.131439\pi$
$18$	0.978148	−	0.207912i	0.230552	−	0.0490053i
$19$	−3.54823	−	0.754200i	−0.814020	−	0.173025i	−0.217952	−	0.975959i	$-0.569938\pi$
$19$	−3.54823	−	0.754200i	−0.814020	−	0.173025i	−0.596068	+	0.802934i	$0.703271\pi$
$20$	0.137133	−	0.0996327i	0.0306638	−	0.0222786i
$21$	2.20662	−	1.45974i	0.481524	−	0.318540i
$22$	1.04569	−	3.14747i	0.222941	−	0.671042i
$23$	0.717830	−	1.24332i	0.149678	−	0.259250i	−0.781430	−	0.623992i	$-0.785510\pi$
$23$	0.717830	−	1.24332i	0.149678	−	0.259250i	0.931108	+	0.364742i	$0.118843\pi$
$24$	0.913545	+	0.406737i	0.186477	+	0.0830248i
$25$	−3.32643	+	3.69437i	−0.665286	+	0.738874i
$26$	0.514442	+	0.571346i	0.100890	+	0.112050i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	2.64320	+	0.116068i	0.499519	+	0.0219348i
$29$	1.02582	−	3.15714i	0.190489	−	0.586266i	−0.809510	−	0.587106i	$-0.800267\pi$
$29$	1.02582	−	3.15714i	0.190489	−	0.586266i	1.00000		0.000839712i	$0.000267289\pi$
$30$	0.165801	+	0.0352421i	0.0302710	+	0.00643431i
$31$	−4.73369	−	2.10757i	−0.850196	−	0.378531i	−0.0650795	−	0.997880i	$-0.520730\pi$
$31$	−4.73369	−	2.10757i	−0.850196	−	0.378531i	−0.785116	+	0.619349i	$0.787397\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	3.03872	−	1.32897i	0.528974	−	0.231344i
$34$	4.08052			0.699804
$35$	0.442337	−	0.0739079i	0.0747686	−	0.0124927i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	2.69612	+	2.99435i	0.443240	+	0.492268i	0.922821	−	0.385230i	$-0.125878\pi$
$37$	2.69612	+	2.99435i	0.443240	+	0.492268i	−0.479581	+	0.877498i	$0.659211\pi$
$38$	0.379177	−	3.60763i	0.0615106	−	0.585234i
$39$	−0.0803637	+	0.764610i	−0.0128685	+	0.122436i
$40$	0.113421	+	0.125967i	0.0179335	+	0.0199171i
$41$	−1.29807	−	3.99504i	−0.202724	−	0.623920i	−0.999799	−	0.0200399i	$-0.993621\pi$
$41$	−1.29807	−	3.99504i	−0.202724	−	0.623920i	0.797075	−	0.603880i	$-0.206379\pi$
$42$	1.68239	+	2.04195i	0.259599	+	0.315079i
$43$	3.56184			0.543175			0.271587	−	0.962414i	$-0.412451\pi$
$43$	3.56184			0.543175			0.271587	+	0.962414i	$0.412451\pi$
$44$	3.23953	+	0.710959i	0.488377	+	0.107181i
$45$	0.0847527	+	0.146796i	0.0126342	+	0.0218830i
$46$	1.31154	+	0.583936i	0.193376	+	0.0860966i
$47$	−8.18793	−	1.74040i	−1.19433	−	0.253863i	−0.432498	−	0.901635i	$-0.642368\pi$
$47$	−8.18793	−	1.74040i	−1.19433	−	0.253863i	−0.761834	+	0.647772i	$0.775701\pi$
$48$	−0.309017	+	0.951057i	−0.0446028	+	0.137273i
$49$	6.12064	+	3.39673i	0.874377	+	0.485248i
$50$	−4.02184	−	2.92204i	−0.568774	−	0.413239i
$51$	2.73040	+	3.03242i	0.382333	+	0.424624i
$52$	−0.514442	+	0.571346i	−0.0713403	+	0.0792314i
$53$	−4.29246	−	1.91113i	−0.589614	−	0.262513i	0.0901687	−	0.995927i	$-0.471259\pi$
$53$	−4.29246	−	1.91113i	−0.589614	−	0.262513i	−0.679783	+	0.733413i	$0.737926\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	0.562173	+	0.00371003i	0.0758034	+	0.000500260i
$56$	0.160858	+	2.64086i	0.0214955	+	0.352899i
$57$	2.93471	−	2.13219i	0.388712	−	0.282416i
$58$	3.24707	+	0.690186i	0.426361	+	0.0906259i
$59$	−3.25567	+	0.692014i	−0.423852	+	0.0900925i	−0.414899	−	0.909867i	$-0.636183\pi$
$59$	−3.25567	+	0.692014i	−0.423852	+	0.0900925i	−0.00895285	+	0.999960i	$0.502850\pi$
$60$	−0.0177181	+	0.168577i	−0.00228740	+	0.0217632i
$61$	−5.47982	+	2.43978i	−0.701620	+	0.312381i	−0.726362	−	0.687313i	$-0.758790\pi$
$61$	−5.47982	+	2.43978i	−0.701620	+	0.312381i	0.0247420	+	0.999694i	$0.492124\pi$
$62$	1.60122	−	4.92806i	0.203356	−	0.625864i
$63$	−0.391723	+	2.61659i	−0.0493524	+	0.329660i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−0.0651597	+	0.112860i	−0.00808206	+	0.0139985i
$66$	1.63932	+	2.88316i	0.201786	+	0.354893i
$67$	2.70447	+	4.68428i	0.330404	+	0.572276i	0.982591	−	0.185782i	$-0.0594817\pi$
$67$	2.70447	+	4.68428i	0.330404	+	0.572276i	−0.652187	+	0.758058i	$0.726148\pi$
$68$	0.426531	+	4.05817i	0.0517245	+	0.492125i
$69$	0.443644	+	1.36539i	0.0534084	+	0.164374i
$70$	0.119740	+	0.432188i	0.0143116	+	0.0516564i
$71$	−2.83494	−	2.05970i	−0.336445	−	0.244442i	0.406715	−	0.913555i	$-0.366674\pi$
$71$	−2.83494	−	2.05970i	−0.336445	−	0.244442i	−0.743160	+	0.669113i	$0.766674\pi$
$72$	−0.913545	+	0.406737i	−0.107662	+	0.0479344i
$73$	−2.06177	+	0.438243i	−0.241312	+	0.0512925i	−0.326980	−	0.945031i	$-0.606031\pi$
$73$	−2.06177	+	0.438243i	−0.241312	+	0.0512925i	0.0856679	+	0.996324i	$0.472698\pi$
$74$	−2.69612	+	2.99435i	−0.313418	+	0.348086i
$75$	−0.519639	−	4.94403i	−0.0600027	−	0.570888i
$76$	3.62750			0.416103
$77$	6.82978	+	5.50946i	0.778326	+	0.627861i
$78$	−0.768822			−0.0870519
$79$	1.49049	+	14.1810i	0.167693	+	1.59549i	0.677712	+	0.735327i	$0.262971\pi$
$79$	1.49049	+	14.1810i	0.167693	+	1.59549i	−0.510020	+	0.860163i	$0.670362\pi$
$80$	−0.113421	+	0.125967i	−0.0126809	+	0.0140835i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	3.83747	−	1.70855i	0.423777	−	0.188678i
$83$	−13.2534	−	9.62913i	−1.45475	−	1.05693i	−0.984693	−	0.174296i	$-0.944235\pi$
$83$	−13.2534	−	9.62913i	−1.45475	−	1.05693i	−0.470053	−	0.882638i	$-0.655765\pi$
$84$	−1.85490	+	1.88662i	−0.202387	+	0.205847i
$85$	0.213738	+	0.657818i	0.0231831	+	0.0713503i
$86$	0.372313	+	3.54232i	0.0401476	+	0.381979i
$87$	1.65981	+	2.87487i	0.177950	+	0.308218i
$88$	−0.368442	+	3.29610i	−0.0392760	+	0.351365i
$89$	−0.842129	+	1.45861i	−0.0892655	+	0.154612i	−0.907201	−	0.420698i	$-0.861785\pi$
$89$	−0.842129	+	1.45861i	−0.0892655	+	0.154612i	0.817935	+	0.575310i	$0.195119\pi$
$90$	−0.137133	+	0.0996327i	−0.0144551	+	0.0105022i
$91$	−1.89276	+	0.745030i	−0.198415	+	0.0781003i
$92$	−0.443644	+	1.36539i	−0.0462530	+	0.142352i
$93$	4.73369	−	2.10757i	0.490861	−	0.218545i
$94$	0.874992	−	8.32499i	0.0902485	−	0.858658i
$95$	0.601444	−	0.127841i	0.0617068	−	0.0131162i
$96$	−0.978148	−	0.207912i	−0.0998318	−	0.0212199i
$97$	−12.4725	+	9.06181i	−1.26639	+	0.920087i	−0.999053	−	0.0435157i	$-0.986144\pi$
$97$	−12.4725	+	9.06181i	−1.26639	+	0.920087i	−0.267338	+	0.963603i	$0.586144\pi$
$98$	−2.73835	+	6.44216i	−0.276615	+	0.650757i
$99$	−1.04569	+	3.14747i	−0.105096	+	0.316332i
$100$	2.48563	−	4.30524i	0.248563	−	0.430524i
$101$	3.48681	+	1.55243i	0.346950	+	0.154472i	0.572811	−	0.819687i	$-0.305853\pi$
$101$	3.48681	+	1.55243i	0.346950	+	0.154472i	−0.225861	+	0.974160i	$0.572520\pi$
$102$	−2.73040	+	3.03242i	−0.270350	+	0.300254i
$103$	−1.22773	−	1.36353i	−0.120971	−	0.134352i	0.679617	−	0.733567i	$-0.262146\pi$
$103$	−1.22773	−	1.36353i	−0.120971	−	0.134352i	−0.800588	+	0.599215i	$0.795479\pi$
$104$	−0.621990	−	0.451902i	−0.0609911	−	0.0443126i
$105$	−0.241057	+	0.378175i	−0.0235248	+	0.0369061i
$106$	1.45197	−	4.46871i	0.141028	−	0.434039i
$107$	11.3821	+	2.41933i	1.10034	+	0.233885i	0.722078	−	0.691811i	$-0.243187\pi$
$107$	11.3821	+	2.41933i	1.10034	+	0.233885i	0.378266	+	0.925697i	$0.376520\pi$
$108$	−0.913545	−	0.406737i	−0.0879060	−	0.0391383i
$109$	2.64921	+	4.58857i	0.253749	+	0.439505i	0.964555	−	0.263882i	$-0.0850031\pi$
$109$	2.64921	+	4.58857i	0.253749	+	0.439505i	−0.710806	+	0.703388i	$0.751670\pi$
$110$	0.0550734	+	0.559482i	0.00525104	+	0.0533445i
$111$	−4.02929			−0.382444
$112$	−2.60958	+	0.436021i	−0.246582	+	0.0412001i
$113$	−0.380030	−	1.16961i	−0.0357502	−	0.110028i	0.931589	−	0.363514i	$-0.118423\pi$
$113$	−0.380030	−	1.16961i	−0.0357502	−	0.110028i	−0.967339	+	0.253486i	$0.918423\pi$
$114$	2.42727	+	2.69576i	0.227335	+	0.252481i
$115$	−0.0254372	+	0.242019i	−0.00237203	+	0.0225684i
$116$	−0.346994	+	3.30143i	−0.0322176	+	0.306530i
$117$	−0.514442	−	0.571346i	−0.0475602	−	0.0528209i
$118$	−1.02853	−	3.16550i	−0.0946841	−	0.291408i
$119$	−3.78339	+	10.1114i	−0.346823	+	0.926911i
$120$	−0.169505			−0.0154736
$121$	7.25190	+	8.27103i	0.659264	+	0.751911i
$122$	−2.99921	−	5.19478i	−0.271535	−	0.470313i
$123$	3.83747	+	1.70855i	0.346013	+	0.154055i
$124$	5.06844	+	1.07733i	0.455159	+	0.0967470i
$125$	0.522295	−	1.60746i	0.0467155	−	0.143776i
$126$	−2.64320	−	0.116068i	−0.235475	−	0.0103402i
$127$	−16.4903	−	11.9809i	−1.46328	−	1.06313i	−0.982494	−	0.186296i	$-0.940352\pi$
$127$	−16.4903	−	11.9809i	−1.46328	−	1.06313i	−0.480785	−	0.876838i	$-0.659648\pi$
$128$	−0.669131	−	0.743145i	−0.0591433	−	0.0656853i
$129$	−2.38333	+	2.64696i	−0.209841	+	0.233052i
$130$	−0.119053	−	0.0530057i	−0.0104416	−	0.00464890i
$131$	−6.39308	+	11.0731i	−0.558566	+	0.967464i	0.439051	+	0.898462i	$0.355315\pi$
$131$	−6.39308	+	11.0731i	−0.558566	+	0.967464i	−0.997617	+	0.0690019i	$0.978019\pi$
$132$	−2.69601	+	1.93171i	−0.234658	+	0.168134i
$133$	8.58802	+	4.28452i	0.744676	+	0.371515i
$134$	−4.37593	+	3.17930i	−0.378023	+	0.274650i
$135$	−0.165801	−	0.0352421i	−0.0142699	−	0.00303316i
$136$	−3.99135	+	0.848388i	−0.342256	+	0.0727487i
$137$	1.41178	−	13.4322i	0.120617	−	1.14759i	−0.751993	−	0.659171i	$-0.770907\pi$
$137$	1.41178	−	13.4322i	0.120617	−	1.14759i	0.872609	−	0.488419i	$-0.162426\pi$
$138$	−1.31154	+	0.583936i	−0.111646	+	0.0497079i
$139$	2.09912	−	6.46043i	0.178045	−	0.547967i	−0.821714	−	0.569900i	$-0.806982\pi$
$139$	2.09912	−	6.46043i	0.178045	−	0.547967i	0.999759	+	0.0219330i	$0.00698204\pi$
$140$	−0.417305	+	0.164260i	−0.0352687	+	0.0138825i
$141$	6.77216	−	4.92026i	0.570319	−	0.414361i
$142$	1.75209	−	3.03470i	0.147032	−	0.254667i
$143$	−2.49762	+	0.513681i	−0.208861	+	0.0429562i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	0.0588173	+	0.559610i	0.00488451	+	0.0464730i
$146$	−0.651356	−	2.00467i	−0.0539066	−	0.165907i
$147$	−6.61977	+	2.27566i	−0.545990	+	0.187693i
$148$	−3.25977	−	2.36836i	−0.267951	−	0.194678i
$149$	11.8822	−	5.29028i	0.973425	−	0.433397i	0.142508	−	0.989794i	$-0.454483\pi$
$149$	11.8822	−	5.29028i	0.973425	−	0.433397i	0.830917	+	0.556397i	$0.187817\pi$
$150$	4.86263	−	1.03358i	0.397032	−	0.0843918i
$151$	4.59887	−	5.10756i	0.374251	−	0.415648i	−0.526368	−	0.850257i	$-0.676447\pi$
$151$	4.59887	−	5.10756i	0.374251	−	0.415648i	0.900619	+	0.434609i	$0.143113\pi$
$152$	0.379177	+	3.60763i	0.0307553	+	0.292617i
$153$	−4.08052			−0.329891
$154$	−4.76537	+	7.36826i	−0.384004	+	0.593751i
$155$	0.878320			0.0705484
$156$	−0.0803637	−	0.764610i	−0.00643425	−	0.0612178i
$157$	13.0801	−	14.5269i	1.04390	−	1.15937i	0.0569466	−	0.998377i	$-0.481864\pi$
$157$	13.0801	−	14.5269i	1.04390	−	1.15937i	0.986955	−	0.160993i	$-0.0514698\pi$
$158$	−13.9475	+	2.96464i	−1.10961	+	0.235854i
$159$	4.29246	−	1.91113i	0.340414	−	0.151562i
$160$	−0.137133	−	0.0996327i	−0.0108413	−	0.00787666i
$161$	−2.66301	+	2.70854i	−0.209875	+	0.213463i
$162$	−0.309017	−	0.951057i	−0.0242787	−	0.0747221i
$163$	0.362835	+	3.45215i	0.0284194	+	0.270393i	0.999499	+	0.0316384i	$0.0100725\pi$
$163$	0.362835	+	3.45215i	0.0284194	+	0.270393i	−0.971080	+	0.238755i	$0.923261\pi$
$164$	2.10031	+	3.63785i	0.164007	+	0.284068i
$165$	−0.378924	+	0.415294i	−0.0294992	+	0.0323306i
$166$	8.19103	−	14.1873i	0.635747	−	1.10115i
$167$	17.7673	−	12.9087i	1.37488	−	0.998907i	0.377539	−	0.925994i	$-0.376770\pi$
$167$	17.7673	−	12.9087i	1.37488	−	0.998907i	0.997338	−	0.0729134i	$-0.0232297\pi$
$168$	−2.07017	−	1.64754i	−0.159717	−	0.127110i
$169$	−3.83457	+	11.8016i	−0.294967	+	0.907814i
$170$	−0.631872	+	0.281328i	−0.0484624	+	0.0215768i
$171$	−0.379177	+	3.60763i	−0.0289964	+	0.275882i
$172$	−3.48400	+	0.740547i	−0.265653	+	0.0564662i
$173$	−1.43158	−	0.304292i	−0.108841	−	0.0231349i	0.153169	−	0.988200i	$-0.451052\pi$
$173$	−1.43158	−	0.304292i	−0.108841	−	0.0231349i	−0.262010	+	0.965065i	$0.584385\pi$
$174$	−2.68562	+	1.95122i	−0.203597	+	0.147922i
$175$	10.9697	−	7.25673i	0.829231	−	0.548558i
$176$	−3.31655	−	0.0218874i	−0.249995	−	0.00164982i
$177$	1.66420	−	2.88248i	0.125089	−	0.216661i
$178$	−1.53865	−	0.685049i	−0.115326	−	0.0513466i
$179$	−15.1752	+	16.8538i	−1.13425	+	1.25971i	−0.172731	+	0.984969i	$0.555259\pi$
$179$	−15.1752	+	16.8538i	−1.13425	+	1.25971i	−0.961518	+	0.274742i	$0.911407\pi$
$180$	−0.113421	−	0.125967i	−0.00845392	−	0.00938903i
$181$	−0.459054	−	0.333522i	−0.0341212	−	0.0247905i	0.570594	−	0.821232i	$-0.306713\pi$
$181$	−0.459054	−	0.333522i	−0.0341212	−	0.0247905i	−0.604715	+	0.796442i	$0.706713\pi$
$182$	−0.938796	−	1.80451i	−0.0695882	−	0.133759i
$183$	1.85361	−	5.70483i	0.137023	−	0.421713i
$184$	−1.40429	−	0.298491i	−0.103525	−	0.0220050i
$185$	−0.623940	−	0.277796i	−0.0458730	−	0.0204240i
$186$	2.59083	+	4.48746i	0.189969	+	0.329036i
$187$	−6.84398	+	11.6755i	−0.500481	+	0.853797i
$188$	8.37085			0.610507
$189$	−1.68239	−	2.04195i	−0.122376	−	0.148530i
$190$	0.190009	+	0.584786i	0.0137847	+	0.0424248i
$191$	−2.18083	−	2.42205i	−0.157799	−	0.175254i	0.659061	−	0.752089i	$-0.270954\pi$
$191$	−2.18083	−	2.42205i	−0.157799	−	0.175254i	−0.816860	+	0.576836i	$0.804287\pi$
$192$	0.104528	−	0.994522i	0.00754369	−	0.0717734i
$193$	1.09587	−	10.4265i	0.0788822	−	0.750514i	−0.881567	−	0.472059i	$-0.843511\pi$
$193$	1.09587	−	10.4265i	0.0788822	−	0.750514i	0.960449	−	0.278455i	$-0.0898224\pi$
$194$	−10.3159	−	11.4570i	−0.740638	−	0.822562i
$195$	−0.0402709	−	0.123941i	−0.00288386	−	0.00887560i
$196$	−6.69311	−	2.04996i	−0.478079	−	0.146425i
$197$	26.2635			1.87119			0.935597	−	0.353069i	$-0.114862\pi$
$197$	26.2635			1.87119			0.935597	+	0.353069i	$0.114862\pi$
$198$	−3.23953	−	0.710959i	−0.230223	−	0.0505257i
$199$	9.22856	+	15.9843i	0.654195	+	1.13310i	0.982095	+	0.188387i	$0.0603259\pi$
$199$	9.22856	+	15.9843i	0.654195	+	1.13310i	−0.327900	+	0.944713i	$0.606341\pi$
$200$	4.54148	+	2.02200i	0.321131	+	0.142977i
$201$	−5.29075	−	1.12458i	−0.373180	−	0.0793220i
$202$	−1.17945	+	3.62998i	−0.0829859	+	0.255404i
$203$	−4.72089	+	7.40621i	−0.331341	+	0.519814i
$204$	−3.30121	−	2.39847i	−0.231131	−	0.167927i
$205$	0.476440	+	0.529141i	0.0332760	+	0.0369568i
$206$	1.22773	−	1.36353i	0.0855397	−	0.0950015i
$207$	−1.31154	−	0.583936i	−0.0911584	−	0.0405863i
$208$	0.384411	−	0.665819i	0.0266541	−	0.0461662i
$209$	9.68645	+	7.13576i	0.670026	+	0.493591i
$210$	−0.401300	−	0.200206i	−0.0276923	−	0.0138156i
$211$	9.34866	−	6.79220i	0.643588	−	0.467594i	−0.217493	−	0.976062i	$-0.569788\pi$
$211$	9.34866	−	6.79220i	0.643588	−	0.467594i	0.861081	+	0.508468i	$0.169788\pi$
$212$	4.59600	+	0.976910i	0.315655	+	0.0670945i
$213$	3.42760	−	0.728558i	0.234855	−	0.0499200i
$214$	−1.21633	+	11.5726i	−0.0831465	+	0.791086i
$215$	−0.551553	+	0.245567i	−0.0376156	+	0.0167475i
$216$	0.309017	−	0.951057i	0.0210259	−	0.0647112i
$217$	10.7270	+	8.53699i	0.728193	+	0.579529i
$218$	−4.28652	+	3.11434i	−0.290320	+	0.210930i
$219$	1.05392	−	1.82544i	0.0712171	−	0.123352i
$220$	−0.550660	+	0.113253i	−0.0371255	+	0.00763555i
$221$	−1.56860	−	2.71689i	−0.105515	−	0.182758i
$222$	−0.421176	−	4.00722i	−0.0282675	−	0.268947i
$223$	−8.18602	−	25.1940i	−0.548176	−	1.68711i	−0.713315	−	0.700843i	$-0.752807\pi$
$223$	−8.18602	−	25.1940i	−0.548176	−	1.68711i	0.165139	−	0.986270i	$-0.447193\pi$
$224$	−0.706408	−	2.54970i	−0.0471988	−	0.170359i
$225$	4.02184	+	2.92204i	0.268123	+	0.194803i
$226$	1.12348	−	0.500206i	0.0747329	−	0.0332732i
$227$	16.0045	−	3.40187i	1.06226	−	0.225790i	0.356539	−	0.934281i	$-0.383957\pi$
$227$	16.0045	−	3.40187i	1.06226	−	0.225790i	0.705720	+	0.708490i	$0.250623\pi$
$228$	−2.42727	+	2.69576i	−0.160750	+	0.178531i
$229$	−3.02550	−	28.7857i	−0.199931	−	1.90221i	−0.390602	−	0.920559i	$-0.627733\pi$
$229$	−3.02550	−	28.7857i	−0.199931	−	1.90221i	0.190672	−	0.981654i	$-0.438933\pi$
$230$	−0.243352			−0.0160462
$231$	−8.66434	+	1.38897i	−0.570072	+	0.0913875i
$232$	−3.31961			−0.217943
$233$	−2.70627	−	25.7484i	−0.177293	−	1.68683i	−0.615640	−	0.788027i	$-0.711103\pi$
$233$	−2.70627	−	25.7484i	−0.177293	−	1.68683i	0.438347	−	0.898806i	$-0.355564\pi$
$234$	0.514442	−	0.571346i	0.0336301	−	0.0373500i
$235$	1.38790	−	0.295007i	0.0905364	−	0.0192441i
$236$	3.04065	−	1.35378i	0.197929	−	0.0881238i
$237$	−11.5359	−	8.38131i	−0.749336	−	0.544425i
$238$	−10.4515	−	2.70573i	−0.677470	−	0.175387i
$239$	7.70973	+	23.7281i	0.498701	+	1.53484i	0.811109	+	0.584895i	$0.198864\pi$
$239$	7.70973	+	23.7281i	0.498701	+	1.53484i	−0.312408	+	0.949948i	$0.601136\pi$
$240$	−0.0177181	−	0.168577i	−0.00114370	−	0.0108816i
$241$	−4.68518	−	8.11497i	−0.301799	−	0.522731i	0.674745	−	0.738051i	$-0.264254\pi$
$241$	−4.68518	−	8.11497i	−0.301799	−	0.522731i	−0.976543	+	0.215320i	$0.930920\pi$
$242$	−7.46769	+	8.07674i	−0.480041	+	0.519192i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	4.85282	−	3.52578i	0.310670	−	0.225715i
$245$	−1.18197	−	0.104006i	−0.0755133	−	0.00664469i
$246$	−1.29807	+	3.99504i	−0.0827617	+	0.254714i
$247$	−2.54779	+	1.13435i	−0.162112	+	0.0721768i
$248$	−0.541632	+	5.15328i	−0.0343936	+	0.327234i
$249$	16.0241	−	3.40602i	1.01548	−	0.215848i
$250$	1.65325	+	0.351409i	0.104561	+	0.0222250i
$251$	0.400503	−	0.290982i	0.0252795	−	0.0183667i	−0.575074	−	0.818102i	$-0.695027\pi$
$251$	0.400503	−	0.290982i	0.0252795	−	0.0183667i	0.600353	+	0.799735i	$0.295027\pi$
$252$	−0.160858	−	2.64086i	−0.0101331	−	0.166358i
$253$	−3.87056	+	2.77329i	−0.243340	+	0.174355i
$254$	10.1916	−	17.6523i	0.639476	−	1.10761i
$255$	−0.631872	−	0.281328i	−0.0395694	−	0.0176174i
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	9.32571	+	10.3573i	0.581722	+	0.646068i	0.960124	−	0.279573i	$-0.0901930\pi$
$257$	9.32571	+	10.3573i	0.581722	+	0.646068i	−0.378402	+	0.925641i	$0.623526\pi$
$258$	−2.88159	−	2.09359i	−0.179400	−	0.130341i
$259$	−4.92011	−	9.45722i	−0.305721	−	0.587643i
$260$	0.0402709	−	0.123941i	0.00249749	−	0.00768650i
$261$	−3.24707	−	0.690186i	−0.200989	−	0.0427215i
$262$	−11.6807	−	5.20060i	−0.721638	−	0.321294i
$263$	−5.36106	−	9.28562i	−0.330577	−	0.572576i	0.652048	−	0.758178i	$-0.273910\pi$
$263$	−5.36106	−	9.28562i	−0.330577	−	0.572576i	−0.982625	+	0.185602i	$0.940577\pi$
$264$	−2.20294	−	2.47932i	−0.135582	−	0.152592i
$265$	0.796451			0.0489256
$266$	−3.36335	+	8.98883i	−0.206220	+	0.551141i
$267$	−0.520464	−	1.60182i	−0.0318519	−	0.0980300i
$268$	−3.61929	−	4.01963i	−0.221083	−	0.245538i
$269$	−1.08393	+	10.3129i	−0.0660882	+	0.628788i	0.910476	+	0.413562i	$0.135715\pi$
$269$	−1.08393	+	10.3129i	−0.0660882	+	0.628788i	−0.976564	+	0.215226i	$0.930951\pi$
$270$	0.0177181	−	0.168577i	0.00107829	−	0.0102593i
$271$	−12.2408	−	13.5948i	−0.743579	−	0.825828i	0.246083	−	0.969249i	$-0.420856\pi$
$271$	−12.2408	−	13.5948i	−0.743579	−	0.825828i	−0.989662	+	0.143421i	$0.954190\pi$
$272$	−1.26095	−	3.88081i	−0.0764564	−	0.235309i
$273$	0.712838	−	1.90512i	0.0431429	−	0.115303i
$274$	13.5062			0.815939
$275$	15.1063	−	6.60666i	0.910945	−	0.398396i
$276$	−0.717830	−	1.24332i	−0.0432083	−	0.0748390i
$277$	5.31222	+	2.36515i	0.319180	+	0.142108i	0.560072	−	0.828444i	$-0.310773\pi$
$277$	5.31222	+	2.36515i	0.319180	+	0.142108i	−0.240892	+	0.970552i	$0.577440\pi$
$278$	6.64446	+	1.41232i	0.398508	+	0.0847055i
$279$	−1.60122	+	4.92806i	−0.0958627	+	0.295035i
$280$	−0.206980	−	0.397849i	−0.0123694	−	0.0237760i
$281$	−11.3238	−	8.22722i	−0.675521	−	0.490795i	0.196348	−	0.980534i	$-0.437092\pi$
$281$	−11.3238	−	8.22722i	−0.675521	−	0.490795i	−0.871869	+	0.489740i	$0.837092\pi$
$282$	5.60119	+	6.22075i	0.333546	+	0.370441i
$283$	6.02622	−	6.69280i	0.358222	−	0.397846i	−0.536916	−	0.843636i	$-0.680411\pi$
$283$	6.02622	−	6.69280i	0.358222	−	0.397846i	0.895137	+	0.445790i	$0.147077\pi$
$284$	3.20122	+	1.42528i	0.189958	+	0.0845745i
$285$	−0.307440	+	0.532502i	−0.0182112	+	0.0315427i
$286$	−0.771939	−	2.43024i	−0.0456457	−	0.143703i
$287$	0.675703	+	11.0933i	0.0398855	+	0.654814i
$288$	0.809017	−	0.587785i	0.0476718	−	0.0346356i
$289$	0.341702	+	0.0726310i	0.0201001	+	0.00427241i
$290$	−0.550396	+	0.116990i	−0.0323204	+	0.00686990i
$291$	1.61150	−	15.3324i	0.0944679	−	0.898802i
$292$	1.92560	−	0.857333i	0.112687	−	0.0501716i
$293$	7.94954	−	24.4662i	0.464417	−	1.42933i	−0.395297	−	0.918554i	$-0.629358\pi$
$293$	7.94954	−	24.4662i	0.464417	−	1.42933i	0.859714	−	0.510776i	$-0.170642\pi$
$294$	−2.95515	−	6.34564i	−0.172348	−	0.370085i
$295$	0.456433	−	0.331618i	0.0265745	−	0.0193075i
$296$	2.01465	−	3.48947i	0.117099	−	0.202821i
$297$	−1.63932	−	2.88316i	−0.0951231	−	0.167298i
$298$	6.50333	+	11.2641i	0.376728	+	0.652511i
$299$	−0.115375	−	1.09772i	−0.00667231	−	0.0634828i
$300$	1.53621	+	4.72796i	0.0886929	+	0.272969i
$301$	−9.12297	−	2.36180i	−0.525839	−	0.136132i
$302$	5.56030	+	4.03979i	0.319959	+	0.232464i
$303$	−3.48681	+	1.55243i	−0.200312	+	0.0891845i
$304$	−3.54823	+	0.754200i	−0.203505	+	0.0432563i
$305$	0.680347	−	0.755602i	0.0389566	−	0.0432657i
$306$	−0.426531	−	4.05817i	−0.0243831	−	0.231990i
$307$	−15.4268			−0.880452			−0.440226	−	0.897887i	$-0.645102\pi$
$307$	−15.4268			−0.880452			−0.440226	+	0.897887i	$0.645102\pi$
$308$	−7.82601	−	3.96907i	−0.445928	−	0.226159i
$309$	1.83481			0.104379
$310$	0.0918095	+	0.873509i	0.00521443	+	0.0496120i
$311$	−5.30141	+	5.88781i	−0.300615	+	0.333867i	−0.874461	−	0.485097i	$-0.838784\pi$
$311$	−5.30141	+	5.88781i	−0.300615	+	0.333867i	0.573845	+	0.818964i	$0.305451\pi$
$312$	0.752021	−	0.159847i	0.0425748	−	0.00904955i
$313$	−13.6248	+	6.06616i	−0.770120	+	0.342879i	−0.753900	−	0.656989i	$-0.771830\pi$
$313$	−13.6248	+	6.06616i	−0.770120	+	0.342879i	−0.0162197	+	0.999868i	$0.505163\pi$
$314$	15.8145	+	11.4899i	0.892466	+	0.648414i
$315$	−0.119740	−	0.432188i	−0.00674658	−	0.0243511i
$316$	−4.40632	−	13.5612i	−0.247875	−	0.762880i
$317$	−0.152933	−	1.45506i	−0.00858956	−	0.0817242i	0.989387	−	0.145302i	$-0.0464155\pi$
$317$	−0.152933	−	1.45506i	−0.00858956	−	0.0817242i	−0.997977	+	0.0635781i	$0.979749\pi$
$318$	2.34934	+	4.06918i	0.131744	+	0.228188i
$319$	−7.42090	+	8.13316i	−0.415491	+	0.455370i
$320$	0.0847527	−	0.146796i	0.00473782	−	0.00820614i
$321$	−9.41399	+	6.83967i	−0.525438	+	0.381753i
$322$	−2.97207	−	2.36531i	−0.165627	−	0.131813i
$323$	−4.57410	+	14.0776i	−0.254510	+	0.783300i
$324$	0.913545	−	0.406737i	0.0507525	−	0.0225965i
$325$	−0.399510	+	3.80108i	−0.0221608	+	0.210846i
$326$	−3.39531	+	0.721695i	−0.188049	+	0.0399710i
$327$	−5.18264	−	1.10160i	−0.286601	−	0.0609189i
$328$	−3.39838	+	2.46907i	−0.187644	+	0.136331i
$329$	19.8178	+	9.88699i	1.09259	+	0.545088i
$330$	−0.452627	−	0.333439i	−0.0249163	−	0.0183552i
$331$	−14.8971	+	25.8026i	−0.818819	+	1.41824i	0.0877336	+	0.996144i	$0.472038\pi$
$331$	−14.8971	+	25.8026i	−0.818819	+	1.41824i	−0.906553	+	0.422092i	$0.861296\pi$
$332$	14.9658	+	6.66318i	0.821353	+	0.365690i
$333$	2.69612	−	2.99435i	0.147747	−	0.164089i
$334$	14.6952	+	16.3207i	0.804086	+	0.893027i
$335$	−0.741743	−	0.538908i	−0.0405258	−	0.0294437i
$336$	1.42212	−	2.23105i	0.0775830	−	0.121714i
$337$	−10.8449	+	33.3772i	−0.590759	+	1.81817i	−0.0159638	+	0.999873i	$0.505082\pi$
$337$	−10.8449	+	33.3772i	−0.590759	+	1.81817i	−0.574795	+	0.818297i	$0.694918\pi$
$338$	−12.1377	−	2.57996i	−0.660207	−	0.140331i
$339$	1.12348	+	0.500206i	0.0610191	+	0.0271675i
$340$	−0.345835	−	0.599004i	−0.0187555	−	0.0324856i
$341$	11.4149	+	12.8470i	0.618152	+	0.695706i
$342$	−3.62750			−0.196153
$343$	−13.4245	−	12.7586i	−0.724857	−	0.688900i
$344$	−1.10067	−	3.38751i	−0.0593440	−	0.182642i
$345$	−0.162834	−	0.180846i	−0.00876671	−	0.00973642i
$346$	0.152984	−	1.45554i	0.00822446	−	0.0782505i
$347$	2.01568	−	19.1779i	0.108208	−	1.02953i	−0.796833	−	0.604200i	$-0.793493\pi$
$347$	2.01568	−	19.1779i	0.108208	−	1.02953i	0.905040	−	0.425326i	$-0.139841\pi$
$348$	−2.22125	−	2.46695i	−0.119072	−	0.132243i
$349$	1.83073	+	5.63440i	0.0979967	+	0.301603i	0.988023	−	0.154306i	$-0.0493142\pi$
$349$	1.83073	+	5.63440i	0.0979967	+	0.301603i	−0.890026	+	0.455909i	$0.849314\pi$
$350$	8.36363	+	10.1511i	0.447055	+	0.542598i
$351$	0.768822			0.0410367
$352$	−0.324907	−	3.30067i	−0.0173176	−	0.175926i
$353$	−4.24471	−	7.35205i	−0.225923	−	0.391310i	0.730673	−	0.682728i	$-0.239206\pi$
$353$	−4.24471	−	7.35205i	−0.225923	−	0.391310i	−0.956596	+	0.291417i	$0.905873\pi$
$354$	3.04065	+	1.35378i	0.161609	+	0.0719528i
$355$	0.580996	+	0.123495i	0.0308361	+	0.00655441i
$356$	0.520464	−	1.60182i	0.0275845	−	0.0848965i
$357$	−4.98266	−	9.57746i	−0.263710	−	0.506893i
$358$	−18.3477	−	13.3304i	−0.969706	−	0.704533i
$359$	−4.69389	−	5.21310i	−0.247734	−	0.275137i	0.606434	−	0.795134i	$-0.292600\pi$
$359$	−4.69389	−	5.21310i	−0.247734	−	0.275137i	−0.854168	+	0.519997i	$0.825933\pi$
$360$	0.113421	−	0.125967i	0.00597782	−	0.00663904i
$361$	−5.33625	−	2.37585i	−0.280855	−	0.125045i
$362$	0.283711	−	0.491401i	0.0149115	−	0.0258275i
$363$	−10.9990	−	0.145181i	−0.577300	−	0.00762004i
$364$	1.69650	−	1.12228i	0.0889206	−	0.0588232i
$365$	0.289053	−	0.210009i	0.0151297	−	0.0109924i
$366$	5.86734	+	1.24714i	0.306691	+	0.0651891i
$367$	23.2801	−	4.94834i	1.21521	−	0.258301i	0.444672	−	0.895693i	$-0.353320\pi$
$367$	23.2801	−	4.94834i	1.21521	−	0.258301i	0.770540	+	0.637392i	$0.219987\pi$
$368$	0.150067	−	1.42780i	0.00782280	−	0.0744290i
$369$	−3.83747	+	1.70855i	−0.199770	+	0.0889435i
$370$	0.211055	−	0.649559i	0.0109722	−	0.0337690i
$371$	9.72708	+	7.74125i	0.505005	+	0.401906i
$372$	−4.19206	+	3.04571i	−0.217348	+	0.157913i
$373$	12.4054	−	21.4868i	0.642326	−	1.11254i	−0.342586	−	0.939487i	$-0.611303\pi$
$373$	12.4054	−	21.4868i	0.642326	−	1.11254i	0.984912	−	0.173055i	$-0.0553639\pi$
$374$	−12.3269	−	5.58607i	−0.637410	−	0.288849i
$375$	0.845092	+	1.46374i	0.0436403	+	0.0755873i
$376$	0.874992	+	8.32499i	0.0451243	+	0.429329i
$377$	−0.788670	−	2.42728i	−0.0406186	−	0.125011i
$378$	1.85490	−	1.88662i	0.0954060	−	0.0970372i
$379$	20.6685	+	15.0166i	1.06167	+	0.771349i	0.974397	−	0.224835i	$-0.0721843\pi$
$379$	20.6685	+	15.0166i	1.06167	+	0.771349i	0.0872745	+	0.996184i	$0.472184\pi$
$380$	−0.561721	+	0.250094i	−0.0288157	+	0.0128296i
$381$	19.9377	−	4.23790i	1.02144	−	0.217114i
$382$	2.18083	−	2.42205i	0.111581	−	0.123923i
$383$	2.26363	+	21.5370i	0.115666	+	1.10049i	0.886268	+	0.463173i	$0.153289\pi$
$383$	2.26363	+	21.5370i	0.115666	+	1.10049i	−0.770602	+	0.637317i	$0.780044\pi$
$384$	1.00000			0.0510310
$385$	−1.43744	−	0.382271i	−0.0732588	−	0.0194823i
$386$	10.4839			0.533617
$387$	−0.372313	−	3.54232i	−0.0189257	−	0.180066i
$388$	10.3159	−	11.4570i	0.523710	−	0.581639i
$389$	−12.1255	+	2.57735i	−0.614785	+	0.130677i	−0.504771	−	0.863253i	$-0.668423\pi$
$389$	−12.1255	+	2.57735i	−0.614785	+	0.130677i	−0.110014	+	0.993930i	$0.535090\pi$
$390$	0.119053	−	0.0530057i	0.00602847	−	0.00268405i
$391$	−4.73942	−	3.44339i	−0.239683	−	0.174140i
$392$	1.33911	−	6.87072i	0.0676351	−	0.347024i
$393$	−3.95114	−	12.1604i	−0.199309	−	0.613409i
$394$	2.74528	+	26.1196i	0.138305	+	1.31589i
$395$	−1.20850	−	2.09318i	−0.0608062	−	0.105319i
$396$	0.368442	−	3.29610i	0.0185149	−	0.165635i
$397$	−11.6212	+	20.1285i	−0.583250	+	1.01022i	0.411841	+	0.911256i	$0.364886\pi$
$397$	−11.6212	+	20.1285i	−0.583250	+	1.01022i	−0.995091	+	0.0989632i	$0.968447\pi$
$398$	−14.9321	+	10.8488i	−0.748480	+	0.543802i
$399$	−8.93053	+	3.51524i	−0.447086	+	0.175982i
$400$	−1.53621	+	4.72796i	−0.0768103	+	0.236398i
$401$	−33.4497	+	14.8928i	−1.67040	+	0.743709i	−0.670399	+	0.742000i	$0.733877\pi$
$401$	−33.4497	+	14.8928i	−1.67040	+	0.743709i	−0.999999	+	0.00170867i	$0.999456\pi$
$402$	0.565389	−	5.37931i	0.0281990	−	0.268296i
$403$	−3.89672	+	0.828274i	−0.194110	+	0.0412593i
$404$	−3.73338	−	0.793554i	−0.185742	−	0.0394808i
$405$	0.137133	−	0.0996327i	0.00681418	−	0.00495079i
$406$	−7.85911	−	3.92087i	−0.390041	−	0.194589i
$407$	−4.04563	−	12.7366i	−0.200535	−	0.631328i
$408$	2.04026	−	3.53384i	0.101008	−	0.174951i
$409$	−17.7387	−	7.89779i	−0.877123	−	0.390521i	−0.0817591	−	0.996652i	$-0.526054\pi$
$409$	−17.7387	−	7.89779i	−0.877123	−	0.390521i	−0.795364	+	0.606132i	$0.792720\pi$
$410$	−0.476440	+	0.529141i	−0.0235297	+	0.0261324i
$411$	9.03740	+	10.0371i	0.445782	+	0.495091i
$412$	1.48439	+	1.07847i	0.0731307	+	0.0531325i
$413$	8.79765	+	0.386322i	0.432904	+	0.0190097i
$414$	0.443644	−	1.36539i	0.0218039	−	0.0671055i
$415$	2.71617	+	0.577339i	0.133331	+	0.0283405i
$416$	0.702353	+	0.312708i	0.0344357	+	0.0153318i
$417$	3.39645	+	5.88282i	0.166325	+	0.288083i
$418$	−6.08416	+	10.3793i	−0.297586	+	0.507667i
$419$	28.6345			1.39889			0.699444	−	0.714688i	$-0.253431\pi$
$419$	28.6345			1.39889			0.699444	+	0.714688i	$0.253431\pi$
$420$	0.157162	−	0.420029i	0.00766874	−	0.0204953i
$421$	−1.45232	−	4.46977i	−0.0707816	−	0.217843i	0.909408	−	0.415905i	$-0.136535\pi$
$421$	−1.45232	−	4.46977i	−0.0707816	−	0.217843i	−0.980189	+	0.198062i	$0.936535\pi$
$422$	7.73219	+	8.58747i	0.376397	+	0.418031i
$423$	−0.874992	+	8.32499i	−0.0425436	+	0.404775i
$424$	−0.491146	+	4.67294i	−0.0238521	+	0.226938i
$425$	13.5736	+	15.0750i	0.658414	+	0.731243i
$426$	1.08285	+	3.33267i	0.0524642	+	0.161468i
$427$	15.6533	−	2.61544i	0.757517	−	0.126570i
$428$	−11.6363			−0.562463
$429$	1.28949	−	2.19981i	0.0622572	−	0.106208i
$430$	−0.301875	−	0.522863i	−0.0145577	−	0.0252147i
$431$	−19.2431	−	8.56757i	−0.926906	−	0.412685i	−0.112943	−	0.993601i	$-0.536028\pi$
$431$	−19.2431	−	8.56757i	−0.926906	−	0.412685i	−0.813963	+	0.580916i	$0.802694\pi$
$432$	0.978148	+	0.207912i	0.0470611	+	0.0100032i
$433$	−11.1498	+	34.3157i	−0.535827	+	1.64911i	0.206028	+	0.978546i	$0.433946\pi$
$433$	−11.1498	+	34.3157i	−0.535827	+	1.64911i	−0.741855	+	0.670560i	$0.766054\pi$
$434$	−7.36895	+	11.5605i	−0.353721	+	0.554924i
$435$	−0.455227	−	0.330742i	−0.0218265	−	0.0158579i
$436$	−3.54534	−	3.93750i	−0.169791	−	0.188572i
$437$	−3.48474	+	3.87019i	−0.166698	+	0.185136i
$438$	1.92560	+	0.857333i	0.0920088	+	0.0409649i
$439$	0.174396	−	0.302062i	0.00832346	−	0.0144167i	−0.861834	−	0.507191i	$-0.830684\pi$
$439$	0.174396	−	0.302062i	0.00832346	−	0.0144167i	0.870157	+	0.492774i	$0.164017\pi$
$440$	−0.170193	−	0.535805i	−0.00811362	−	0.0255435i
$441$	2.73835	−	6.44216i	0.130397	−	0.306770i
$442$	2.53804	−	1.84400i	0.120722	−	0.0877100i
$443$	−4.43705	−	0.943123i	−0.210810	−	0.0448091i	0.101296	−	0.994856i	$-0.467701\pi$
$443$	−4.43705	−	0.943123i	−0.210810	−	0.0448091i	−0.312106	+	0.950047i	$0.601034\pi$
$444$	3.94124	−	0.837737i	0.187043	−	0.0397573i
$445$	0.0298419	−	0.283927i	0.00141464	−	0.0134594i
$446$	24.2003	−	10.7747i	1.14592	−	0.510195i
$447$	−4.01928	+	12.3701i	−0.190105	+	0.585084i
$448$	2.46190	−	0.969054i	0.116314	−	0.0457835i
$449$	−12.1844	+	8.85248i	−0.575017	+	0.417774i	−0.836924	−	0.547319i	$-0.815649\pi$
$449$	−12.1844	+	8.85248i	−0.575017	+	0.417774i	0.261907	+	0.965093i	$0.415649\pi$
$450$	−2.48563	+	4.30524i	−0.117174	+	0.202951i
$451$	−1.54769	+	13.8457i	−0.0728777	+	0.651968i
$452$	0.614902	+	1.06504i	0.0289226	+	0.0500953i
$453$	0.718414	+	6.83525i	0.0337540	+	0.321148i
$454$	5.05617	+	15.5613i	0.237298	+	0.730327i
$455$	0.241730	−	0.245863i	0.0113325	−	0.0115262i
$456$	−2.93471	−	2.13219i	−0.137430	−	0.0998490i
$457$	−9.84746	+	4.38437i	−0.460645	+	0.205092i	−0.623920	−	0.781488i	$-0.714461\pi$
$457$	−9.84746	+	4.38437i	−0.460645	+	0.205092i	0.163275	+	0.986581i	$0.447794\pi$
$458$	28.3118	−	6.01785i	1.32292	−	0.281196i
$459$	2.73040	−	3.03242i	0.127444	−	0.141541i
$460$	−0.0254372	−	0.242019i	−0.00118602	−	0.0112842i
$461$	−4.41994			−0.205857			−0.102929	−	0.994689i	$-0.532821\pi$
$461$	−4.41994			−0.205857			−0.102929	+	0.994689i	$0.532821\pi$
$462$	−2.28703	−	8.47169i	−0.106402	−	0.394139i
$463$	10.3758			0.482204			0.241102	−	0.970500i	$-0.422491\pi$
$463$	10.3758			0.482204			0.241102	+	0.970500i	$0.422491\pi$
$464$	−0.346994	−	3.30143i	−0.0161088	−	0.153265i
$465$	−0.587711	+	0.652719i	−0.0272544	+	0.0302691i
$466$	25.3245	−	5.38288i	1.17313	−	0.249357i
$467$	7.04259	−	3.13556i	0.325892	−	0.145097i	−0.237268	−	0.971444i	$-0.576252\pi$
$467$	7.04259	−	3.13556i	0.325892	−	0.145097i	0.563160	+	0.826348i	$0.309585\pi$
$468$	0.621990	+	0.451902i	0.0287515	+	0.0208892i
$469$	−3.82092	−	13.7912i	−0.176434	−	0.636819i
$470$	0.438465	+	1.34946i	0.0202249	+	0.0622458i
$471$	2.04331	+	19.4408i	0.0941505	+	0.895783i
$472$	1.66420	+	2.88248i	0.0766011	+	0.132677i
$473$	−10.7600	−	4.87600i	−0.494746	−	0.224199i
$474$	7.12957	−	12.3488i	0.327472	−	0.567198i
$475$	14.5892	−	10.5997i	0.669399	−	0.486347i
$476$	1.59843	−	10.6771i	0.0732640	−	0.489382i
$477$	−1.45197	+	4.46871i	−0.0664812	+	0.204608i
$478$	−22.7922	+	10.1478i	−1.04249	+	0.464148i
$479$	−3.81514	+	36.2986i	−0.174318	+	1.65853i	0.461836	+	0.886965i	$0.347191\pi$
$479$	−3.81514	+	36.2986i	−0.174318	+	1.65853i	−0.636155	+	0.771562i	$0.719476\pi$
$480$	0.165801	−	0.0352421i	0.00756776	−	0.00160858i
$481$	3.03011	+	0.644071i	0.138161	+	0.0293671i
$482$	7.58078	−	5.50776i	0.345295	−	0.250871i
$483$	−0.230937	−	3.79137i	−0.0105080	−	0.172514i
$484$	−8.81308	−	6.58253i	−0.400594	−	0.299206i
$485$	1.30662	−	2.26313i	0.0593306	−	0.102764i
$486$	0.913545	+	0.406737i	0.0414393	+	0.0184499i
$487$	7.58313	−	8.42192i	0.343625	−	0.381634i	−0.546417	−	0.837513i	$-0.684009\pi$
$487$	7.58313	−	8.42192i	0.343625	−	0.381634i	0.890041	+	0.455880i	$0.150675\pi$
$488$	4.01372	+	4.45769i	0.181693	+	0.201790i
$489$	−2.80823	−	2.04030i	−0.126992	−	0.0922655i
$490$	−0.0201135	−	1.18637i	−0.000908634	−	0.0535946i
$491$	−5.25020	+	16.1585i	−0.236938	+	0.729221i	0.759920	+	0.650017i	$0.225238\pi$
$491$	−5.25020	+	16.1585i	−0.236938	+	0.729221i	−0.996858	+	0.0792048i	$0.974762\pi$
$492$	−4.10884	−	0.873360i	−0.185241	−	0.0393741i
$493$	−12.3747	−	5.50955i	−0.557327	−	0.248138i
$494$	−1.39445	−	2.41526i	−0.0627393	−	0.108668i
$495$	−0.0550734	−	0.559482i	−0.00247537	−	0.0251468i
$496$	−5.18167			−0.232664
$497$	5.89540	+	7.15534i	0.264445	+	0.320961i
$498$	5.06234	+	15.5803i	0.226849	+	0.698168i
$499$	−13.6186	−	15.1250i	−0.609653	−	0.677088i	0.356726	−	0.934209i	$-0.383893\pi$
$499$	−13.6186	−	15.1250i	−0.609653	−	0.677088i	−0.966379	+	0.257121i	$0.917226\pi$
$500$	−0.176672	+	1.68092i	−0.00790102	+	0.0751732i
$501$	−2.29562	+	21.8413i	−0.102561	+	0.975798i
$502$	0.331252	+	0.367893i	0.0147845	+	0.0164199i
$503$	1.29370	+	3.98160i	0.0576832	+	0.177531i	0.975747	−	0.218903i	$-0.0702478\pi$
$503$	1.29370	+	3.98160i	0.0576832	+	0.177531i	−0.918063	+	0.396433i	$0.870248\pi$
$504$	2.60958	−	0.436021i	0.116240	−	0.0194219i
$505$	−0.646965			−0.0287896
$506$	−3.16268	−	3.55947i	−0.140598	−	0.158238i
$507$	−6.20446	−	10.7464i	−0.275550	−	0.477266i
$508$	18.6209	+	8.29058i	0.826170	+	0.367835i
$509$	−3.50764	−	0.745571i	−0.155473	−	0.0330469i	0.129517	−	0.991577i	$-0.458657\pi$
$509$	−3.50764	−	0.745571i	−0.155473	−	0.0330469i	−0.284991	+	0.958530i	$0.591991\pi$
$510$	0.213738	−	0.657818i	0.00946447	−	0.0291287i
$511$	5.57143	+	0.244652i	0.246466	+	0.0108228i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−2.42727	−	2.69576i	−0.107167	−	0.119021i
$514$	−9.32571	+	10.3573i	−0.411340	+	0.456839i
$515$	0.284121	+	0.126499i	0.0125199	+	0.00557421i
$516$	1.78092	−	3.08464i	0.0784005	−	0.135794i
$517$	22.3525	+	16.4665i	0.983063	+	0.724197i
$518$	8.89112	−	5.88170i	0.390654	−	0.258427i
$519$	1.18405	−	0.860260i	0.0519739	−	0.0377612i
$520$	0.127472	+	0.0270949i	0.00559000	+	0.00118819i
$521$	−14.8953	+	3.16610i	−0.652577	+	0.138710i	−0.522292	−	0.852767i	$-0.674923\pi$
$521$	−14.8953	+	3.16610i	−0.652577	+	0.138710i	−0.130286	+	0.991477i	$0.541589\pi$
$522$	0.346994	−	3.30143i	0.0151875	−	0.144500i
$523$	4.51269	−	2.00918i	0.197326	−	0.0878552i	−0.305695	−	0.952130i	$-0.598889\pi$
$523$	4.51269	−	2.00918i	0.197326	−	0.0878552i	0.503021	+	0.864274i	$0.332222\pi$
$524$	3.95114	−	12.1604i	0.172606	−	0.531228i
$525$	−1.94736	+	13.0078i	−0.0849897	+	0.567706i
$526$	8.67437	−	6.30230i	0.378221	−	0.274793i
$527$	−10.5720	+	18.3112i	−0.460522	+	0.797647i
$528$	2.23547	−	2.45003i	0.0972864	−	0.106624i
$529$	10.4694	+	18.1336i	0.455193	+	0.788417i
$530$	0.0832518	+	0.792088i	0.00361623	+	0.0344061i
$531$	1.02853	+	3.16550i	0.0446345	+	0.137371i
$532$	−9.29116	−	2.40534i	−0.402823	−	0.104285i
$533$	−2.61275	−	1.89827i	−0.113171	−	0.0822233i
$534$	1.53865	−	0.685049i	0.0665837	−	0.0296450i
$535$	−1.92932	+	0.410089i	−0.0834117	+	0.0177297i
$536$	3.61929	−	4.01963i	0.156330	−	0.173622i
$537$	−2.37060	−	22.5548i	−0.102299	−	0.973310i
$538$	−10.3697			−0.447069
$539$	−13.8400	−	18.6402i	−0.596129	−	0.802888i
$540$	0.169505			0.00729435
$541$	−1.19785	−	11.3968i	−0.0514998	−	0.489988i	−0.989623	−	0.143687i	$-0.954104\pi$
$541$	−1.19785	−	11.3968i	−0.0514998	−	0.489988i	0.938123	−	0.346301i	$-0.112562\pi$
$542$	12.2408	−	13.5948i	0.525790	−	0.583948i
$543$	0.555022	−	0.117974i	0.0238183	−	0.00506273i
$544$	3.72774	−	1.65970i	0.159826	−	0.0711590i
$545$	−0.726587	−	0.527897i	−0.0311236	−	0.0226126i
$546$	1.96919	+	0.509794i	0.0842736	+	0.0218172i
$547$	3.04448	+	9.36993i	0.130172	+	0.400629i	0.994808	−	0.101770i	$-0.0324506\pi$
$547$	3.04448	+	9.36993i	0.130172	+	0.400629i	−0.864636	+	0.502400i	$0.832451\pi$
$548$	1.41178	+	13.4322i	0.0603083	+	0.573795i
$549$	2.99921	+	5.19478i	0.128003	+	0.221708i
$550$	8.14951	+	14.3330i	0.347496	+	0.611160i
$551$	−6.02095	+	10.4286i	−0.256501	+	0.444273i
$552$	1.16147	−	0.843860i	0.0494356	−	0.0359171i
$553$	5.58562	−	37.3103i	0.237525	−	1.58660i
$554$	−1.79692	+	5.53035i	−0.0763438	+	0.234962i
$555$	0.623940	−	0.277796i	0.0264848	−	0.0117918i
$556$	−0.710052	+	6.75569i	−0.0301129	+	0.286505i
$557$	25.3808	−	5.39485i	1.07542	−	0.228587i	0.364030	−	0.931387i	$-0.381401\pi$
$557$	25.3808	−	5.39485i	1.07542	−	0.228587i	0.711387	+	0.702800i	$0.248067\pi$
$558$	−5.06844	−	1.07733i	−0.214564	−	0.0456070i
$559$	2.21542	−	1.60960i	0.0937025	−	0.0680788i
$560$	0.374034	−	0.247433i	0.0158058	−	0.0104559i
$561$	−4.09707	−	12.8985i	−0.172978	−	0.544575i
$562$	6.99849	−	12.1217i	0.295213	−	0.511325i
$563$	−9.94250	−	4.42669i	−0.419027	−	0.186563i	0.186382	−	0.982477i	$-0.440324\pi$
$563$	−9.94250	−	4.42669i	−0.419027	−	0.186563i	−0.605409	+	0.795915i	$0.706990\pi$
$564$	−5.60119	+	6.22075i	−0.235853	+	0.261941i
$565$	0.139486	+	0.154915i	0.00586821	+	0.00651731i
$566$	7.28605	+	5.29362i	0.306255	+	0.222508i
$567$	2.64320	+	0.116068i	0.111004	+	0.00487441i
$568$	−1.08285	+	3.33267i	−0.0454353	+	0.139836i
$569$	−12.0906	−	2.56993i	−0.506864	−	0.107737i	−0.0526201	−	0.998615i	$-0.516757\pi$
$569$	−12.0906	−	2.56993i	−0.506864	−	0.107737i	−0.454244	+	0.890877i	$0.650091\pi$
$570$	−0.561721	−	0.250094i	−0.0235279	−	0.0104753i
$571$	−20.3296	−	35.2118i	−0.850765	−	1.47357i	−0.880519	−	0.474012i	$-0.842805\pi$
$571$	−20.3296	−	35.2118i	−0.850765	−	1.47357i	0.0297532	−	0.999557i	$-0.490528\pi$
$572$	2.33624	−	1.02174i	0.0976830	−	0.0427211i
$573$	3.25919			0.136155
$574$	−10.9619	+	1.83156i	−0.457539	+	0.0764480i
$575$	2.20547	+	6.78774i	0.0919745	+	0.283068i
$576$	0.669131	+	0.743145i	0.0278804	+	0.0309644i
$577$	0.204311	−	1.94389i	0.00850557	−	0.0809251i	−0.989446	−	0.144904i	$-0.953713\pi$
$577$	0.204311	−	1.94389i	0.00850557	−	0.0809251i	0.997951	+	0.0639793i	$0.0203792\pi$
$578$	−0.0365156	+	0.347422i	−0.00151885	+	0.0144509i
$579$	7.01510	+	7.79106i	0.291538	+	0.323786i
$580$	−0.173881	−	0.535152i	−0.00722003	−	0.0222210i
$581$	27.5611	+	33.4513i	1.14343	+	1.38779i
$582$	15.4169			0.639050
$583$	10.3509	+	11.6495i	0.428691	+	0.482475i
$584$	1.05392	+	1.82544i	0.0436114	+	0.0755371i
$585$	0.119053	+	0.0530057i	0.00492222	+	0.00219151i
$586$	25.1631	+	5.34858i	1.03948	+	0.220948i
$587$	7.47396	−	23.0025i	0.308484	−	0.949415i	−0.669871	−	0.742478i	$-0.733651\pi$
$587$	7.47396	−	23.0025i	0.308484	−	0.949415i	0.978354	−	0.206937i	$-0.0663495\pi$
$588$	6.00198	−	3.60226i	0.247517	−	0.148555i
$589$	15.2067	+	11.0483i	0.626580	+	0.455237i
$590$	0.377511	+	0.419269i	0.0155419	+	0.0172610i
$591$	−17.5737	+	19.5176i	−0.722885	+	0.802845i
$592$	3.68094	+	1.63886i	0.151286	+	0.0673568i
$593$	−7.03620	+	12.1871i	−0.288942	+	0.500462i	−0.973558	−	0.228442i	$-0.926637\pi$
$593$	−7.03620	+	12.1871i	−0.288942	+	0.500462i	0.684615	+	0.728905i	$0.259970\pi$
$594$	2.69601	−	1.93171i	0.110619	−	0.0792592i
$595$	−0.111260	−	1.82660i	−0.00456123	−	0.0748834i
$596$	−10.5226	+	7.64512i	−0.431023	+	0.313156i
$597$	−18.0538	−	3.83745i	−0.738892	−	0.157056i
$598$	1.07965	−	0.229486i	0.0441500	−	0.00938438i
$599$	3.42066	−	32.5454i	0.139764	−	1.32977i	−0.669713	−	0.742620i	$-0.733583\pi$
$599$	3.42066	−	32.5454i	0.139764	−	1.32977i	0.809478	−	0.587151i	$-0.199750\pi$
$600$	−4.54148	+	2.02200i	−0.185405	+	0.0825477i
$601$	−10.2215	+	31.4584i	−0.416942	+	1.28322i	0.493560	+	0.869712i	$0.335695\pi$
$601$	−10.2215	+	31.4584i	−0.416942	+	1.28322i	−0.910502	+	0.413504i	$0.864305\pi$
$602$	1.39525	−	9.31987i	0.0568662	−	0.379850i
$603$	4.37593	−	3.17930i	0.178202	−	0.129471i
$604$	−3.43645	+	5.95211i	−0.139827	+	0.242188i
$605$	−1.69320	−	0.780800i	−0.0688384	−	0.0317440i
$606$	−1.90839	−	3.30543i	−0.0775231	−	0.134274i
$607$	−4.24648	−	40.4025i	−0.172359	−	1.63989i	−0.648999	−	0.760789i	$-0.724812\pi$
$607$	−4.24648	−	40.4025i	−0.172359	−	1.63989i	0.476640	−	0.879099i	$-0.341855\pi$
$608$	−1.12096	−	3.44996i	−0.0454609	−	0.139914i
$609$	−2.34500	−	8.46403i	−0.0950242	−	0.342980i
$610$	0.822579	+	0.597638i	0.0333052	+	0.0241977i
$611$	−5.87930	+	2.61763i	−0.237851	+	0.105898i
$612$	3.99135	−	0.848388i	0.161341	−	0.0342941i
$613$	21.7051	−	24.1060i	0.876662	−	0.973632i	−0.123162	−	0.992387i	$-0.539303\pi$
$613$	21.7051	−	24.1060i	0.876662	−	0.973632i	0.999824	+	0.0187547i	$0.00597014\pi$
$614$	−1.61254	−	15.3423i	−0.0650767	−	0.619163i
$615$	−0.712029			−0.0287118
$616$	3.12929	−	8.19802i	0.126083	−	0.330308i
$617$	−31.1313			−1.25330			−0.626649	−	0.779302i	$-0.715574\pi$
$617$	−31.1313			−1.25330			−0.626649	+	0.779302i	$0.715574\pi$
$618$	0.191790	+	1.82476i	0.00771491	+	0.0734024i
$619$	14.6745	−	16.2977i	0.589819	−	0.655060i	−0.372165	−	0.928167i	$-0.621384\pi$
$619$	14.6745	−	16.2977i	0.589819	−	0.655060i	0.961984	+	0.273106i	$0.0880511\pi$
$620$	−0.859127	+	0.182613i	−0.0345034	+	0.00733392i
$621$	1.31154	−	0.583936i	0.0526303	−	0.0234325i
$622$	−6.40971	−	4.65693i	−0.257006	−	0.186726i
$623$	3.12414	−	3.17755i	0.125166	−	0.127306i
$624$	0.237579	+	0.731193i	0.00951077	+	0.0292711i
$625$	−2.56825	−	24.4352i	−0.102730	−	0.977410i
$626$	−7.45711	−	12.9161i	−0.298046	−	0.516231i
$627$	−11.7844	+	2.42368i	−0.470624	+	0.0967925i
$628$	−9.77392	+	16.9289i	−0.390022	+	0.675538i
$629$	13.3016	−	9.66415i	0.530368	−	0.385335i
$630$	0.417305	−	0.164260i	0.0166258	−	0.00654427i
$631$	10.1468	−	31.2285i	0.403936	−	1.24319i	−0.517844	−	0.855475i	$-0.673265\pi$
$631$	10.1468	−	31.2285i	0.403936	−	1.24319i	0.921780	−	0.387713i	$-0.126735\pi$
$632$	13.0264	−	5.79971i	0.518161	−	0.230700i
$633$	−1.20789	+	11.4923i	−0.0480092	+	0.456777i
$634$	1.43110	−	0.304190i	0.0568363	−	0.0120809i
$635$	3.37955	+	0.718346i	0.134113	+	0.0285067i
$636$	−3.80131	+	2.76181i	−0.150732	+	0.109513i
$637$	5.34196	−	0.653194i	0.211656	−	0.0258805i
$638$	−8.86430	−	6.53010i	−0.350941	−	0.258529i
$639$	−1.75209	+	3.03470i	−0.0693115	+	0.120051i
$640$	0.154851	+	0.0689440i	0.00612102	+	0.00272525i
$641$	0.884942	−	0.982827i	0.0349531	−	0.0388193i	−0.725415	−	0.688312i	$-0.758352\pi$
$641$	0.884942	−	0.982827i	0.0349531	−	0.0388193i	0.760368	+	0.649493i	$0.225019\pi$
$642$	−7.78623	−	8.64748i	−0.307298	−	0.341289i
$643$	23.0084	+	16.7166i	0.907363	+	0.659238i	0.940347	−	0.340218i	$-0.110501\pi$
$643$	23.0084	+	16.7166i	0.907363	+	0.659238i	−0.0329835	+	0.999456i	$0.510501\pi$
$644$	2.04168	−	3.20303i	0.0804535	−	0.126217i
$645$	0.186569	−	0.574200i	0.00734615	−	0.0226091i
$646$	−14.4786	−	3.07753i	−0.569654	−	0.121084i
$647$	−38.0995	−	16.9630i	−1.49785	−	0.666884i	−0.516005	−	0.856586i	$-0.672581\pi$
$647$	−38.0995	−	16.9630i	−1.49785	−	0.666884i	−0.981842	+	0.189701i	$0.939248\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	10.7825	+	2.36636i	0.423248	+	0.0928877i
$650$	−3.82202			−0.149912
$651$	−13.5220	+	2.25932i	−0.529967	+	0.0885496i
$652$	−1.07265	−	3.30127i	−0.0420081	−	0.129288i
$653$	−29.5850	−	32.8575i	−1.15775	−	1.28581i	−0.951617	−	0.307288i	$-0.900579\pi$
$653$	−29.5850	−	32.8575i	−1.15775	−	1.28581i	−0.206133	−	0.978524i	$-0.566088\pi$
$654$	0.553836	−	5.26940i	0.0216567	−	0.206050i
$655$	0.226547	−	2.15545i	0.00885191	−	0.0842203i
$656$	−2.81077	−	3.12168i	−0.109742	−	0.121881i
$657$	0.651356	+	2.00467i	0.0254118	+	0.0782095i
$658$	−7.76131	+	20.7427i	−0.302567	+	0.808635i
$659$	11.9772			0.466564			0.233282	−	0.972409i	$-0.425054\pi$
$659$	11.9772			0.466564			0.233282	+	0.972409i	$0.425054\pi$
$660$	0.284300	−	0.485001i	0.0110663	−	0.0188787i
$661$	4.90965	+	8.50376i	0.190963	+	0.330758i	0.945570	−	0.325420i	$-0.105506\pi$
$661$	4.90965	+	8.50376i	0.190963	+	0.330758i	−0.754607	+	0.656177i	$0.772172\pi$
$662$	−27.2184	−	12.1184i	−1.05787	−	0.470995i
$663$	3.06864	+	0.652259i	0.119176	+	0.0253316i
$664$	−5.06234	+	15.5803i	−0.196457	+	0.604632i
$665$	−1.62525	−	0.0713681i	−0.0630247	−	0.00276754i
$666$	3.25977	+	2.36836i	0.126313	+	0.0917721i
$667$	−3.18897	−	3.54171i	−0.123477	−	0.137135i
$668$	−14.6952	+	16.3207i	−0.568574	+	0.631466i
$669$	24.2003	+	10.7747i	0.935637	+	0.416573i
$670$	0.458422	−	0.794011i	0.0177104	−	0.0306753i
$671$	19.8941	+	0.131290i	0.768002	+	0.00506838i
$672$	2.36748	+	1.18112i	0.0913274	+	0.0455628i
$673$	−18.9080	+	13.7375i	−0.728851	+	0.529541i	−0.889200	−	0.457519i	$-0.848738\pi$
$673$	−18.9080	+	13.7375i	−0.728851	+	0.529541i	0.160349	+	0.987060i	$0.448738\pi$
$674$	−34.3279	−	7.29662i	−1.32226	−	0.281055i
$675$	−4.86263	+	1.03358i	−0.187163	+	0.0397827i
$676$	1.29708	−	12.3409i	0.0498879	−	0.474651i
$677$	−14.6786	+	6.53532i	−0.564143	+	0.251173i	−0.668934	−	0.743321i	$-0.733249\pi$
$677$	−14.6786	+	6.53532i	−0.564143	+	0.251173i	0.104791	+	0.994494i	$0.466583\pi$
$678$	−0.380030	+	1.16961i	−0.0145950	+	0.0449187i
$679$	37.9547	−	14.9398i	1.45657	−	0.573336i
$680$	0.559573	−	0.406554i	0.0214586	−	0.0155906i
$681$	−8.18105	+	14.1700i	−0.313498	+	0.542995i
$682$	−11.5835	+	12.6953i	−0.443554	+	0.486127i
$683$	−16.9084	−	29.2861i	−0.646980	−	1.12060i	−0.983840	−	0.179048i	$-0.942698\pi$
$683$	−16.9084	−	29.2861i	−0.646980	−	1.12060i	0.336860	−	0.941555i	$-0.390635\pi$
$684$	−0.379177	−	3.60763i	−0.0144982	−	0.137941i
$685$	0.707455	+	2.17732i	0.0270304	+	0.0831912i
$686$	11.2855	−	14.6846i	0.430881	−	0.560662i
$687$	23.4164	+	17.0130i	0.893392	+	0.649087i
$688$	3.25390	−	1.44873i	0.124054	−	0.0552323i
$689$	−3.53351	+	0.751070i	−0.134616	+	0.0286135i
$690$	0.162834	−	0.180846i	0.00619900	−	0.00688469i
$691$	−4.48673	−	42.6884i	−0.170683	−	1.62394i	−0.659604	−	0.751614i	$-0.729276\pi$
$691$	−4.48673	−	42.6884i	−0.170683	−	1.62394i	0.488921	−	0.872328i	$-0.337391\pi$
$692$	1.46356			0.0556363
$693$	4.76537	−	7.36826i	0.181021	−	0.279897i
$694$	19.2836			0.731995
$695$	0.120358	+	1.14513i	0.00456542	+	0.0434371i
$696$	2.22125	−	2.46695i	0.0841964	−	0.0935096i
$697$	−16.7662	+	3.56376i	−0.635065	+	0.134987i
$698$	−5.41217	+	2.40966i	−0.204854	+	0.0912068i
$699$	20.9456	+	15.2179i	0.792236	+	0.575593i
$700$	−9.22123	+	9.37889i	−0.348530	+	0.354489i
$701$	−10.2167	−	31.4437i	−0.385879	−	1.18761i	−0.935841	−	0.352424i	$-0.885358\pi$
$701$	−10.2167	−	31.4437i	−0.385879	−	1.18761i	0.549962	−	0.835190i	$-0.314642\pi$
$702$	0.0803637	+	0.764610i	0.00303313	+	0.0288583i
$703$	−7.30813	−	12.6581i	−0.275631	−	0.477408i
$704$	3.24863	−	0.668141i	0.122437	−	0.0251815i
$705$	−0.709452	+	1.22881i	−0.0267195	+	0.0462795i
$706$	6.86808	−	4.98996i	0.258484	−	0.187799i
$707$	−7.90141	−	6.28829i	−0.297163	−	0.236496i
$708$	−1.02853	+	3.16550i	−0.0386546	+	0.118967i
$709$	−37.8178	+	16.8376i	−1.42028	+	0.632349i	−0.966007	−	0.258515i	$-0.916767\pi$
$709$	−37.8178	+	16.8376i	−1.42028	+	0.632349i	−0.454271	+	0.890864i	$0.650100\pi$
$710$	−0.0620874	+	0.590722i	−0.00233010	+	0.0221694i
$711$	13.9475	−	2.96464i	0.523074	−	0.111183i
$712$	1.64745	+	0.350177i	0.0617409	+	0.0131234i
$713$	−6.01837	+	4.37260i	−0.225390	+	0.163755i
$714$	9.00416	−	5.95648i	0.336972	−	0.222916i
$715$	0.351343	−	0.251740i	0.0131395	−	0.00941453i
$716$	11.3395	−	19.6406i	0.423777	−	0.734004i
$717$	−22.7922	−	10.1478i	−0.851192	−	0.378975i
$718$	4.69389	−	5.21310i	0.175175	−	0.194551i
$719$	−6.73876	−	7.48415i	−0.251313	−	0.279112i	0.604267	−	0.796782i	$-0.293466\pi$
$719$	−6.73876	−	7.48415i	−0.251313	−	0.279112i	−0.855580	+	0.517670i	$0.826799\pi$
$720$	0.137133	+	0.0996327i	0.00511063	+	0.00371309i
$721$	2.24045	+	4.30651i	0.0834389	+	0.160383i
$722$	1.80505	−	5.55536i	0.0671768	−	0.206749i
$723$	9.16559	+	1.94821i	0.340872	+	0.0724546i
$724$	0.518365	+	0.230791i	0.0192649	+	0.00857729i
$725$	8.25134	+	14.2917i	0.306447	+	0.530782i
$726$	−1.00533	−	10.9540i	−0.0373112	−	0.406540i
$727$	−7.56139			−0.280436			−0.140218	−	0.990121i	$-0.544780\pi$
$727$	−7.56139			−0.280436			−0.140218	+	0.990121i	$0.544780\pi$
$728$	1.29346	+	1.56989i	0.0479388	+	0.0581841i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	0.239073	+	0.265517i	0.00884848	+	0.00982724i
$731$	1.51923	−	14.4545i	0.0561908	−	0.534620i
$732$	−0.627005	+	5.96555i	−0.0231748	+	0.220493i
$733$	−10.4788	−	11.6378i	−0.387042	−	0.429854i	0.517865	−	0.855462i	$-0.326727\pi$
$733$	−10.4788	−	11.6378i	−0.387042	−	0.429854i	−0.904907	+	0.425608i	$0.860060\pi$
$734$	7.35467	+	22.6353i	0.271466	+	0.835486i
$735$	0.868184	−	0.808782i	0.0320234	−	0.0298324i
$736$	1.43566			0.0529192
$737$	−1.75740	−	17.8532i	−0.0647347	−	0.657629i
$738$	−2.10031	−	3.63785i	−0.0773136	−	0.133911i
$739$	27.3867	+	12.1934i	1.00744	+	0.448540i	0.843038	−	0.537854i	$-0.180765\pi$
$739$	27.3867	+	12.1934i	1.00744	+	0.448540i	0.164399	+	0.986394i	$0.447431\pi$
$740$	0.668062	+	0.142001i	0.0245584	+	0.00522006i
$741$	0.861817	−	2.65240i	0.0316597	−	0.0974384i
$742$	−6.68209	+	10.4830i	−0.245307	+	0.384842i
$743$	−32.1566	−	23.3631i	−1.17971	−	0.857110i	−0.187571	−	0.982251i	$-0.560062\pi$
$743$	−32.1566	−	23.3631i	−1.17971	−	0.857110i	−0.992139	+	0.125141i	$0.960062\pi$
$744$	−3.46721	−	3.85073i	−0.127114	−	0.141175i
$745$	−1.47523	+	1.63841i	−0.0540483	+	0.0600267i
$746$	22.6658	+	10.0914i	0.829853	+	0.369474i
$747$	−8.19103	+	14.1873i	−0.299694	+	0.519085i
$748$	4.26695	−	12.8433i	0.156015	−	0.469598i
$749$	−27.5488	−	13.7439i	−1.00661	−	0.502192i
$750$	−1.36739	+	0.993465i	−0.0499299	+	0.0362762i
$751$	32.9055	+	6.99427i	1.20074	+	0.255225i	0.764510	−	0.644612i	$-0.222981\pi$
$751$	32.9055	+	6.99427i	1.20074	+	0.255225i	0.436227	+	0.899836i	$0.356314\pi$
$752$	−8.18793	+	1.74040i	−0.298583	+	0.0634658i
$753$	−0.0517467	+	0.492337i	−0.00188575	+	0.0179418i
$754$	2.33154	−	1.03807i	0.0849097	−	0.0378042i
$755$	−0.360003	+	1.10798i	−0.0131018	+	0.0403233i
$756$	2.07017	+	1.64754i	0.0752915	+	0.0599204i
$757$	24.6600	−	17.9166i	0.896284	−	0.651189i	−0.0412245	−	0.999150i	$-0.513126\pi$
$757$	24.6600	−	17.9166i	0.896284	−	0.651189i	0.937509	+	0.347961i	$0.113126\pi$
$758$	−12.7739	+	22.1250i	−0.463967	+	0.803615i
$759$	0.528957	−	4.73208i	0.0191999	−	0.171763i
$760$	−0.307440	−	0.532502i	−0.0111520	−	0.0193159i
$761$	0.526013	+	5.00468i	0.0190680	+	0.181419i	0.999910	−	0.0133830i	$-0.00426007\pi$
$761$	0.526013	+	5.00468i	0.0190680	+	0.181419i	−0.980842	+	0.194803i	$0.937593\pi$
$762$	6.29874	+	19.3855i	0.228179	+	0.702264i
$763$	−3.74285	−	13.5094i	−0.135500	−	0.489074i
$764$	2.63674	+	1.91571i	0.0953940	+	0.0693078i
$765$	0.631872	−	0.281328i	0.0228454	−	0.0101714i
$766$	−21.1824	+	4.50246i	−0.765352	+	0.162681i
$767$	−1.71227	+	1.90167i	−0.0618265	+	0.0686653i
$768$	0.104528	+	0.994522i	0.00377185	+	0.0358867i
$769$	−14.4532			−0.521194			−0.260597	−	0.965448i	$-0.583919\pi$
$769$	−14.4532			−0.521194			−0.260597	+	0.965448i	$0.583919\pi$
$770$	0.229924	−	1.46952i	0.00828587	−	0.0529580i
$771$	−13.9371			−0.501931
$772$	1.09587	+	10.4265i	0.0394411	+	0.375257i
$773$	6.71492	−	7.45767i	0.241519	−	0.268234i	−0.610183	−	0.792260i	$-0.708904\pi$
$773$	6.71492	−	7.45767i	0.241519	−	0.268234i	0.851702	+	0.524027i	$0.175571\pi$
$774$	3.48400	−	0.740547i	0.125230	−	0.0266184i
$775$	23.5324	−	10.4773i	0.845310	−	0.376356i
$776$	12.4725	+	9.06181i	0.447737	+	0.325300i
$777$	10.3203	+	2.67176i	0.370238	+	0.0958490i
$778$	−3.83068	−	11.7896i	−0.137337	−	0.422679i
$779$	1.59278	+	15.1543i	0.0570673	+	0.542959i
$780$	0.0651597	+	0.112860i	0.00233309	+	0.00404103i
$781$	5.74446	+	10.1031i	0.205553	+	0.361517i
$782$	2.92912	−	5.07339i	0.104745	−	0.181424i
$783$	2.68562	−	1.95122i	0.0959763	−	0.0697309i
$784$	6.97306	+	0.613584i	0.249038	+	0.0219137i
$785$	−1.02392	+	3.15129i	−0.0365451	+	0.112474i
$786$	11.6807	−	5.20060i	0.416638	−	0.185499i
$787$	−4.30257	+	40.9362i	−0.153370	+	1.45922i	0.599144	+	0.800641i	$0.295508\pi$
$787$	−4.30257	+	40.9362i	−0.153370	+	1.45922i	−0.752514	+	0.658576i	$0.771159\pi$
$788$	−25.6895	+	5.46048i	−0.915152	+	0.194522i
$789$	10.4878	+	2.22925i	0.373376	+	0.0793635i
$790$	1.95539	−	1.42068i	0.0695698	−	0.0505454i
$791$	0.197823	+	3.24774i	0.00703379	+	0.115476i
$792$	3.31655	+	0.0218874i	0.117849	+	0.000777734i
$793$	−2.30586	+	3.99386i	−0.0818833	+	0.141826i
$794$	−21.2329	−	9.45352i	−0.753529	−	0.335493i
$795$	−0.532930	+	0.591879i	−0.0189011	+	0.0209918i
$796$	−12.3502	−	13.7163i	−0.437742	−	0.486162i
$797$	−15.5866	−	11.3243i	−0.552106	−	0.401129i	0.276455	−	0.961027i	$-0.410840\pi$
$797$	−15.5866	−	11.3243i	−0.552106	−	0.401129i	−0.828561	+	0.559898i	$0.810840\pi$
$798$	−4.42948	−	8.51416i	−0.156802	−	0.301398i
$799$	−10.5552	+	32.4857i	−0.373417	+	1.14926i
$800$	−4.86263	−	1.03358i	−0.171920	−	0.0365427i
$801$	1.53865	+	0.685049i	0.0543654	+	0.0242050i
$802$	−18.3076	−	31.7097i	−0.646465	−	1.11971i
$803$	6.82838	+	1.49858i	0.240968	+	0.0528838i
$804$	5.40894			0.190759
$805$	0.225632	−	0.603019i	0.00795248	−	0.0212536i
$806$	−1.23105	−	3.78880i	−0.0433621	−	0.133455i
$807$	−6.93868	−	7.70618i	−0.244253	−	0.271270i
$808$	0.398963	−	3.79587i	0.0140355	−	0.133538i
$809$	−1.31811	+	12.5410i	−0.0463423	+	0.440918i	0.946608	+	0.322387i	$0.104485\pi$
$809$	−1.31811	+	12.5410i	−0.0463423	+	0.440918i	−0.992950	+	0.118531i	$0.962182\pi$
$810$	0.113421	+	0.125967i	0.00398522	+	0.00442603i
$811$	−2.26954	−	6.98491i	−0.0796942	−	0.245273i	0.903269	−	0.429074i	$-0.141160\pi$
$811$	−2.26954	−	6.98491i	−0.0796942	−	0.245273i	−0.982964	+	0.183800i	$0.941160\pi$
$812$	3.07789	−	8.22590i	0.108013	−	0.288672i
$813$	18.2937			0.641587
$814$	12.2439	−	5.35480i	0.429149	−	0.187686i
$815$	−0.294190	−	0.509552i	−0.0103050	−	0.0178488i
$816$	3.72774	+	1.65970i	0.130497	+	0.0581011i
$817$	−12.6382	−	2.68633i	−0.442155	−	0.0939829i
$818$	6.00032	−	18.4671i	0.209796	−	0.645687i
$819$	0.938796	+	1.80451i	0.0328042	+	0.0630548i
$820$	−0.576044	−	0.418520i	−0.0201163	−	0.0146154i
$821$	−15.0706	−	16.7376i	−0.525967	−	0.584145i	0.420360	−	0.907358i	$-0.361904\pi$
$821$	−15.0706	−	16.7376i	−0.525967	−	0.584145i	−0.946326	+	0.323212i	$0.895237\pi$
$822$	−9.03740	+	10.0371i	−0.315216	+	0.350082i
$823$	−0.227550	−	0.101312i	−0.00793191	−	0.00353151i	0.402767	−	0.915303i	$-0.368049\pi$
$823$	−0.227550	−	0.101312i	−0.00793191	−	0.00353151i	−0.410699	+	0.911771i	$0.634715\pi$
$824$	−0.917404	+	1.58899i	−0.0319593	+	0.0553551i
$825$	−5.19839	+	15.6469i	−0.180985	+	0.544755i
$826$	0.535399	+	8.78984i	0.0186289	+	0.305837i
$827$	11.7921	−	8.56749i	0.410053	−	0.297921i	−0.363570	−	0.931567i	$-0.618442\pi$
$827$	11.7921	−	8.56749i	0.410053	−	0.297921i	0.773623	+	0.633646i	$0.218442\pi$
$828$	1.40429	+	0.298491i	0.0488024	+	0.0103733i
$829$	25.8971	−	5.50459i	0.899443	−	0.191182i	0.265088	−	0.964224i	$-0.414599\pi$
$829$	25.8971	−	5.50459i	0.899443	−	0.191182i	0.634355	+	0.773042i	$0.281266\pi$
$830$	−0.290260	+	2.76163i	−0.0100751	+	0.0958577i
$831$	−5.31222	+	2.36515i	−0.184279	+	0.0820463i
$832$	−0.237579	+	0.731193i	−0.00823657	+	0.0253495i
$833$	16.3952	−	23.3898i	0.568059	−	0.810407i
$834$	−5.49557	+	3.99277i	−0.190296	+	0.138258i
$835$	−1.86131	+	3.22388i	−0.0644132	+	0.111567i
$836$	−10.9584	−	4.96590i	−0.379004	−	0.171749i
$837$	−2.59083	−	4.48746i	−0.0895523	−	0.155109i
$838$	2.99312	+	28.4776i	0.103396	+	0.983744i
$839$	16.6616	+	51.2791i	0.575221	+	1.77035i	0.635424	+	0.772163i	$0.280825\pi$
$839$	16.6616	+	51.2791i	0.575221	+	1.77035i	−0.0602026	+	0.998186i	$0.519175\pi$
$840$	0.434156	+	0.112396i	0.0149798	+	0.00387805i
$841$	14.5463	+	10.5685i	0.501595	+	0.364430i
$842$	4.29348	−	1.91158i	0.147963	−	0.0658774i
$843$	13.6911	−	2.91014i	0.471547	−	0.100230i
$844$	−7.73219	+	8.58747i	−0.266153	+	0.295593i
$845$	−0.219863	−	2.09185i	−0.00756351	−	0.0719620i
$846$	−8.37085			−0.287796
$847$	−13.0900	−	25.9933i	−0.449778	−	0.893141i
$848$	−4.69868			−0.161353
$849$	0.941389	+	8.95671i	0.0323084	+	0.307394i
$850$	−13.5736	+	15.0750i	−0.465569	+	0.517067i
$851$	5.65829	−	1.20271i	0.193964	−	0.0412283i
$852$	−3.20122	+	1.42528i	−0.109672	+	0.0488291i
$853$	26.0914	+	18.9565i	0.893354	+	0.649060i	0.936750	−	0.349998i	$-0.113818\pi$
$853$	26.0914	+	18.9565i	0.893354	+	0.649060i	−0.0433962	+	0.999058i	$0.513818\pi$
$854$	4.23733	+	15.2942i	0.144998	+	0.523356i
$855$	−0.190009	−	0.584786i	−0.00649815	−	0.0199993i
$856$	−1.21633	−	11.5726i	−0.0415732	−	0.395543i
$857$	−5.70709	−	9.88497i	−0.194951	−	0.337664i	0.751934	−	0.659239i	$-0.229121\pi$
$857$	−5.70709	−	9.88497i	−0.194951	−	0.337664i	−0.946884	+	0.321574i	$0.895788\pi$
$858$	2.32255	+	1.05248i	0.0792905	+	0.0359312i
$859$	19.2673	−	33.3719i	0.657391	−	1.13863i	−0.323898	−	0.946092i	$-0.604994\pi$
$859$	19.2673	−	33.3719i	0.657391	−	1.13863i	0.981289	−	0.192542i	$-0.0616731\pi$
$860$	0.488444	−	0.354875i	0.0166558	−	0.0121011i
$861$	−8.69603	−	6.92069i	−0.296360	−	0.235857i
$862$	6.50918	−	20.0332i	0.221704	−	0.682334i
$863$	−8.35298	+	3.71898i	−0.284339	+	0.126596i	−0.543950	−	0.839117i	$-0.683072\pi$
$863$	−8.35298	+	3.71898i	−0.284339	+	0.126596i	0.259612	+	0.965713i	$0.416405\pi$
$864$	−0.104528	+	0.994522i	−0.00355613	+	0.0338343i
$865$	0.242660	−	0.0515790i	0.00825070	−	0.00175374i
$866$	−35.2932	−	7.50179i	−1.19931	−	0.254921i
$867$	−0.282619	+	0.205335i	−0.00959824	+	0.00697353i
$868$	−12.2675	−	6.12018i	−0.416385	−	0.207732i
$869$	14.9106	−	44.8801i	0.505807	−	1.52245i
$870$	0.281346	−	0.487306i	0.00953852	−	0.0165212i
$871$	3.79899	+	1.69142i	0.128724	+	0.0573116i
$872$	3.54534	−	3.93750i	0.120060	−	0.133341i
$873$	10.3159	+	11.4570i	0.349140	+	0.387759i
$874$	−4.21325	−	3.06110i	−0.142515	−	0.103543i
$875$	−2.40364	+	3.77088i	−0.0812580	+	0.127479i
$876$	−0.651356	+	2.00467i	−0.0220073	+	0.0677314i
$877$	15.9908	+	3.39895i	0.539971	+	0.114774i	0.469820	−	0.882762i	$-0.344319\pi$
$877$	15.9908	+	3.39895i	0.539971	+	0.114774i	0.0701505	+	0.997536i	$0.477652\pi$
$878$	0.318637	+	0.141866i	0.0107535	+	0.00478776i
$879$	12.8626	+	22.2787i	0.433846	+	0.751443i
$880$	0.515080	−	0.225267i	0.0173633	−	0.00759376i
$881$	−39.2188			−1.32132			−0.660658	−	0.750687i	$-0.729723\pi$
$881$	−39.2188			−1.32132			−0.660658	+	0.750687i	$0.729723\pi$
$882$	6.69311	+	2.04996i	0.225369	+	0.0690256i
$883$	6.84129	+	21.0553i	0.230228	+	0.708568i	0.997719	+	0.0675086i	$0.0215050\pi$
$883$	6.84129	+	21.0553i	0.230228	+	0.708568i	−0.767491	+	0.641060i	$0.778495\pi$
$884$	2.09919	+	2.33139i	0.0706035	+	0.0784131i
$885$	−0.0589731	+	0.561091i	−0.00198236	+	0.0188609i
$886$	0.474159	−	4.51132i	0.0159297	−	0.151561i
$887$	28.1877	+	31.3056i	0.946451	+	1.05114i	0.998621	+	0.0525018i	$0.0167195\pi$
$887$	28.1877	+	31.3056i	0.946451	+	1.05114i	−0.0521701	+	0.998638i	$0.516614\pi$
$888$	1.24512	+	3.83209i	0.0417835	+	0.128596i
$889$	34.2925	+	41.6213i	1.15013	+	1.39594i
$890$	0.285491			0.00956967
$891$	3.23953	+	0.710959i	0.108528	+	0.0238180i
$892$	13.2453	+	22.9415i	0.443484	+	0.768137i
$893$	27.7400	+	12.3507i	0.928285	+	0.413299i
$894$	−12.7224	−	2.70424i	−0.425502	−	0.0904431i
$895$	1.18793	−	3.65606i	0.0397080	−	0.122209i
$896$	1.22108	+	2.34712i	0.0407936	+	0.0784116i
$897$	0.892966	+	0.648778i	0.0298153	+	0.0216621i
$898$	−10.0776	−	11.1923i	−0.336294	−	0.373492i
$899$	−11.5098	+	12.7829i	−0.383873	+	0.426335i
$900$	−4.54148	−	2.02200i	−0.151383	−	0.0673999i
$901$	−9.58653	+	16.6044i	−0.319374	+	0.553172i
$902$	−13.9316	−	0.0919407i	−0.463872	−	0.00306129i
$903$	7.85962	−	5.19934i	0.261552	−	0.173023i
$904$	−0.994932	+	0.722861i	−0.0330910	+	0.0240420i
$905$	0.0940792	+	0.0199972i	0.00312730	+	0.000664728i
$906$	−6.72271	+	1.42896i	−0.223347	+	0.0474739i
$907$	−3.54885	+	33.7651i	−0.117838	+	1.12115i	0.762561	+	0.646916i	$0.223942\pi$
$907$	−3.54885	+	33.7651i	−0.117838	+	1.12115i	−0.880399	+	0.474234i	$0.842725\pi$
$908$	−14.9475	+	6.65507i	−0.496051	+	0.220856i
$909$	1.17945	−	3.62998i	0.0391199	−	0.120399i
$910$	0.269784	+	0.214706i	0.00894324	+	0.00711744i
$911$	43.1445	−	31.3463i	1.42944	−	1.03855i	0.439321	−	0.898330i	$-0.355219\pi$
$911$	43.1445	−	31.3463i	1.42944	−	1.03855i	0.990120	−	0.140220i	$-0.0447810\pi$
$912$	1.81375	−	3.14151i	0.0600593	−	0.104026i
$913$	26.8555	+	47.2321i	0.888786	+	1.56316i
$914$	−5.38969	−	9.33522i	−0.178275	−	0.308782i
$915$	0.106281	+	1.01119i	0.00351353	+	0.0334290i
$916$	8.94427	+	27.5276i	0.295527	+	0.909539i
$917$	23.7171	−	24.1226i	0.783207	−	0.796598i
$918$	3.30121	+	2.39847i	0.108956	+	0.0791613i
$919$	42.4371	−	18.8942i	1.39987	−	0.623263i	0.438554	−	0.898705i	$-0.355491\pi$
$919$	42.4371	−	18.8942i	1.39987	−	0.623263i	0.961318	+	0.275441i	$0.0888240\pi$
$920$	0.238034	−	0.0505958i	0.00784776	−	0.00166809i
$921$	10.3225	−	11.4643i	0.340139	−	0.377762i
$922$	−0.462009	−	4.39572i	−0.0152155	−	0.144765i
$923$	−2.69408			−0.0886768
$924$	8.18622	−	3.16004i	0.269307	−	0.103958i
$925$	−20.0307			−0.658605
$926$	1.08456	+	10.3189i	0.0356410	+	0.339102i
$927$	−1.22773	+	1.36353i	−0.0403238	+	0.0447841i
$928$	3.24707	−	0.690186i	0.106590	−	0.0226565i
$929$	46.6313	−	20.7616i	1.52992	−	0.681166i	0.542616	−	0.839981i	$-0.317434\pi$
$929$	46.6313	−	20.7616i	1.52992	−	0.681166i	0.987308	+	0.158814i	$0.0507671\pi$
$930$	−0.710576	−	0.516264i	−0.0233007	−	0.0169290i
$931$	−19.1556	−	16.6686i	−0.627800	−	0.546291i
$932$	8.00052	+	24.6231i	0.262066	+	0.806555i
$933$	−0.828162	−	7.87943i	−0.0271128	−	0.257961i
$934$	3.85454	+	6.67626i	0.126124	+	0.218454i
$935$	0.254840	−	2.27981i	0.00833416	−	0.0745578i
$936$	−0.384411	+	0.665819i	−0.0125649	+	0.0217630i
$937$	−35.3107	+	25.6547i	−1.15355	+	0.838104i	−0.988949	−	0.148257i	$-0.952634\pi$
$937$	−35.3107	+	25.6547i	−1.15355	+	0.838104i	−0.164602	+	0.986360i	$0.552634\pi$
$938$	13.3163	−	5.24156i	0.434791	−	0.171143i
$939$	4.60874	−	14.1843i	0.150401	−	0.462886i
$940$	−1.29623	+	0.577120i	−0.0422785	+	0.0188236i
$941$	−2.55441	+	24.3036i	−0.0832713	+	0.792273i	0.870587	+	0.492015i	$0.163739\pi$
$941$	−2.55441	+	24.3036i	−0.0832713	+	0.792273i	−0.953858	+	0.300258i	$0.902927\pi$
$942$	−19.1207	+	4.06422i	−0.622985	+	0.132420i
$943$	−5.89889	−	1.25385i	−0.192094	−	0.0408309i
$944$	−2.69273	+	1.95639i	−0.0876410	+	0.0636749i
$945$	0.401300	+	0.200206i	0.0130543	+	0.00651272i
$946$	3.72457	−	11.2108i	0.121096	−	0.364493i
$947$	−23.2323	+	40.2396i	−0.754949	+	1.30761i	0.190450	+	0.981697i	$0.439005\pi$
$947$	−23.2323	+	40.2396i	−0.754949	+	1.30761i	−0.945399	+	0.325914i	$0.894328\pi$
$948$	13.0264	+	5.79971i	0.423077	+	0.188366i
$949$	−1.08436	+	1.20430i	−0.0351997	+	0.0390933i
$950$	12.0666	+	13.4013i	0.391493	+	0.434797i
$951$	1.18365	+	0.859973i	0.0383825	+	0.0278865i
$952$	10.7857	+	0.473619i	0.349565	+	0.0153501i
$953$	−15.8972	+	48.9265i	−0.514960	+	1.58488i	0.268394	+	0.963309i	$0.413507\pi$
$953$	−15.8972	+	48.9265i	−0.514960	+	1.58488i	−0.783354	+	0.621576i	$0.786493\pi$
$954$	−4.59600	−	0.976910i	−0.148801	−	0.0316286i
$955$	0.504689	+	0.224702i	0.0163314	+	0.00727119i
$956$	−12.4746	−	21.6066i	−0.403458	−	0.698809i
$957$	−1.07856	−	10.9570i	−0.0348650	−	0.354188i
$958$	−36.4986			−1.17922
$959$	−12.5227	+	33.4679i	−0.404379	+	1.08074i
$960$	0.0523800	+	0.161209i	0.00169056	+	0.00520300i
$961$	−2.77711	−	3.08429i	−0.0895842	−	0.0994933i
$962$	−0.323809	+	3.08084i	−0.0104400	+	0.0993302i
$963$	1.21633	−	11.5726i	0.0391956	−	0.372921i
$964$	6.26999	+	6.96353i	0.201943	+	0.224280i
$965$	0.549147	+	1.69010i	0.0176777	+	0.0544063i
$966$	3.74647	−	0.625978i	0.120541	−	0.0201405i
$967$	11.5691			0.372038			0.186019	−	0.982546i	$-0.440441\pi$
$967$	11.5691			0.372038			0.186019	+	0.982546i	$0.440441\pi$
$968$	5.62525	−	9.45286i	0.180802	−	0.303826i
$969$	−7.40105	−	12.8190i	−0.237756	−	0.411805i
$970$	2.38731	+	1.06290i	0.0766520	+	0.0341277i
$971$	21.7300	+	4.61886i	0.697349	+	0.148226i	0.542928	−	0.839779i	$-0.317315\pi$
$971$	21.7300	+	4.61886i	0.697349	+	0.148226i	0.154421	+	0.988005i	$0.450649\pi$
$972$	−0.309017	+	0.951057i	−0.00991172	+	0.0305052i
$973$	−9.66032	+	15.1553i	−0.309696	+	0.485856i
$974$	9.16844	+	6.66126i	0.293776	+	0.213441i
$975$	−2.55743	−	2.84031i	−0.0819033	−	0.0909628i
$976$	−4.01372	+	4.45769i	−0.128476	+	0.142687i
$977$	21.2678	+	9.46903i	0.680417	+	0.302941i	0.717689	−	0.696364i	$-0.245200\pi$
$977$	21.2678	+	9.46903i	0.680417	+	0.302941i	−0.0372717	+	0.999305i	$0.511867\pi$
$978$	1.73558	−	3.00611i	0.0554978	−	0.0961249i
$979$	4.54078	−	3.25350i	0.145124	−	0.103982i
$980$	1.17777	−	0.144012i	0.0376223	−	0.00460031i
$981$	4.28652	−	3.11434i	0.136858	−	0.0994331i
$982$	−16.6187	−	3.53242i	−0.530325	−	0.112724i
$983$	37.8739	−	8.05036i	1.20799	−	0.256766i	0.440457	−	0.897774i	$-0.354817\pi$
$983$	37.8739	−	8.05036i	1.20799	−	0.256766i	0.767535	+	0.641007i	$0.221483\pi$
$984$	0.439085	−	4.17762i	0.0139975	−	0.133178i
$985$	−4.06692	+	1.81071i	−0.129583	+	0.0576940i
$986$	4.18587	−	12.8828i	0.133305	−	0.410271i
$987$	−20.6082	+	8.11181i	−0.655965	+	0.258202i
$988$	2.25627	−	1.63927i	0.0717814	−	0.0521523i
$989$	2.55679	−	4.42850i	0.0813013	−	0.140818i
$990$	0.550660	−	0.113253i	0.0175011	−	0.00359943i
$991$	−1.62630	−	2.81684i	−0.0516612	−	0.0894798i	0.839038	−	0.544072i	$-0.183118\pi$
$991$	−1.62630	−	2.81684i	−0.0516612	−	0.0894798i	−0.890700	+	0.454592i	$0.849785\pi$
$992$	−0.541632	−	5.15328i	−0.0171968	−	0.163617i
$993$	−9.20692	−	28.3360i	−0.292173	−	0.899215i
$994$	−6.49990	+	6.61104i	−0.206164	+	0.209689i
$995$	−2.53107	−	1.83893i	−0.0802405	−	0.0582981i
$996$	−14.9658	+	6.66318i	−0.474208	+	0.211131i
$997$	−28.2647	+	6.00785i	−0.895152	+	0.190270i	−0.632445	−	0.774605i	$-0.717949\pi$
$997$	−28.2647	+	6.00785i	−0.895152	+	0.190270i	−0.262707	+	0.964876i	$0.584615\pi$
$998$	13.6186	−	15.1250i	0.431090	−	0.478774i
$999$	0.421176	+	4.00722i	0.0133254	+	0.126783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.a.289.1	yes	24
7.4	even	3	inner	462.2.y.a.25.3	✓	24
11.4	even	5	inner	462.2.y.a.37.3	yes	24
77.4	even	15	inner	462.2.y.a.235.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.a.25.3	✓	24	7.4	even	3	inner
462.2.y.a.37.3	yes	24	11.4	even	5	inner
462.2.y.a.235.1	yes	24	77.4	even	15	inner
462.2.y.a.289.1	yes	24	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.104528 + 0.994522i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-0.154851 + 0.0689440i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-2.56131 - 0.663085i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(0.104528 + 0.994522i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-0.154851 + 0.0689440i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-2.56131 - 0.663085i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-0.0847527 - 0.146796i) q^{10} +(-3.02092 - 1.36896i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.621990 - 0.451902i) q^{13} +(0.391723 - 2.61659i) q^{14} +(0.0523800 - 0.161209i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.426531 - 4.05817i) q^{17} +(0.978148 - 0.207912i) q^{18} +(-3.54823 - 0.754200i) q^{19} +(0.137133 - 0.0996327i) q^{20} +(2.20662 - 1.45974i) q^{21} +(1.04569 - 3.14747i) q^{22} +(0.717830 - 1.24332i) q^{23} +(0.913545 + 0.406737i) q^{24} +(-3.32643 + 3.69437i) q^{25} +(0.514442 + 0.571346i) q^{26} +(0.809017 + 0.587785i) q^{27} +(2.64320 + 0.116068i) q^{28} +(1.02582 - 3.15714i) q^{29} +(0.165801 + 0.0352421i) q^{30} +(-4.73369 - 2.10757i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.03872 - 1.32897i) q^{33} +4.08052 q^{34} +(0.442337 - 0.0739079i) q^{35} +(0.309017 + 0.951057i) q^{36} +(2.69612 + 2.99435i) q^{37} +(0.379177 - 3.60763i) q^{38} +(-0.0803637 + 0.764610i) q^{39} +(0.113421 + 0.125967i) q^{40} +(-1.29807 - 3.99504i) q^{41} +(1.68239 + 2.04195i) q^{42} +3.56184 q^{43} +(3.23953 + 0.710959i) q^{44} +(0.0847527 + 0.146796i) q^{45} +(1.31154 + 0.583936i) q^{46} +(-8.18793 - 1.74040i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(6.12064 + 3.39673i) q^{49} +(-4.02184 - 2.92204i) q^{50} +(2.73040 + 3.03242i) q^{51} +(-0.514442 + 0.571346i) q^{52} +(-4.29246 - 1.91113i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.562173 + 0.00371003i) q^{55} +(0.160858 + 2.64086i) q^{56} +(2.93471 - 2.13219i) q^{57} +(3.24707 + 0.690186i) q^{58} +(-3.25567 + 0.692014i) q^{59} +(-0.0177181 + 0.168577i) q^{60} +(-5.47982 + 2.43978i) q^{61} +(1.60122 - 4.92806i) q^{62} +(-0.391723 + 2.61659i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.0651597 + 0.112860i) q^{65} +(1.63932 + 2.88316i) q^{66} +(2.70447 + 4.68428i) q^{67} +(0.426531 + 4.05817i) q^{68} +(0.443644 + 1.36539i) q^{69} +(0.119740 + 0.432188i) q^{70} +(-2.83494 - 2.05970i) q^{71} +(-0.913545 + 0.406737i) q^{72} +(-2.06177 + 0.438243i) q^{73} +(-2.69612 + 2.99435i) q^{74} +(-0.519639 - 4.94403i) q^{75} +3.62750 q^{76} +(6.82978 + 5.50946i) q^{77} -0.768822 q^{78} +(1.49049 + 14.1810i) q^{79} +(-0.113421 + 0.125967i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(3.83747 - 1.70855i) q^{82} +(-13.2534 - 9.62913i) q^{83} +(-1.85490 + 1.88662i) q^{84} +(0.213738 + 0.657818i) q^{85} +(0.372313 + 3.54232i) q^{86} +(1.65981 + 2.87487i) q^{87} +(-0.368442 + 3.29610i) q^{88} +(-0.842129 + 1.45861i) q^{89} +(-0.137133 + 0.0996327i) q^{90} +(-1.89276 + 0.745030i) q^{91} +(-0.443644 + 1.36539i) q^{92} +(4.73369 - 2.10757i) q^{93} +(0.874992 - 8.32499i) q^{94} +(0.601444 - 0.127841i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(-12.4725 + 9.06181i) q^{97} +(-2.73835 + 6.44216i) q^{98} +(-1.04569 + 3.14747i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 + 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 3 q^{9} + 10 q^{10} + 6 q^{11} + 12 q^{12} - 2 q^{13} - 5 q^{14} + 3 q^{16} - 2 q^{17} - 3 q^{18} + 7 q^{19} - 10 q^{20} - 4 q^{21} + 2 q^{22} + 24 q^{23} + 3 q^{24} + 4 q^{25} + 4 q^{26} + 6 q^{27} + 14 q^{28} - 6 q^{29} - 7 q^{31} + 12 q^{32} - q^{33} - 24 q^{34} + 4 q^{35} - 6 q^{36} - q^{37} + 8 q^{38} - q^{39} + 16 q^{41} - 4 q^{42} + 52 q^{43} - 4 q^{44} - 10 q^{45} - 4 q^{46} + 27 q^{47} + 6 q^{48} - 33 q^{49} - 22 q^{50} - 8 q^{51} - 4 q^{52} + 13 q^{53} - 12 q^{54} + 30 q^{55} + 14 q^{56} - 16 q^{57} - 3 q^{58} + 14 q^{59} - 5 q^{60} + 9 q^{61} - 4 q^{62} + 5 q^{63} - 6 q^{64} - 50 q^{65} - 4 q^{66} - 20 q^{67} - 2 q^{68} - 32 q^{69} - 17 q^{70} - 18 q^{71} - 3 q^{72} + 7 q^{73} + q^{74} + 11 q^{75} - 4 q^{76} - 34 q^{77} - 12 q^{78} + q^{79} + 3 q^{81} - 2 q^{82} - 68 q^{83} - 5 q^{84} - 19 q^{86} - 8 q^{87} - q^{88} - 42 q^{89} + 10 q^{90} - 16 q^{91} + 32 q^{92} + 7 q^{93} + 8 q^{94} + 38 q^{95} + 3 q^{96} - 80 q^{97} - 2 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 + 11 * q^7 + 6 * q^8 + 3 * q^9 + 10 * q^10 + 6 * q^11 + 12 * q^12 - 2 * q^13 - 5 * q^14 + 3 * q^16 - 2 * q^17 - 3 * q^18 + 7 * q^19 - 10 * q^20 - 4 * q^21 + 2 * q^22 + 24 * q^23 + 3 * q^24 + 4 * q^25 + 4 * q^26 + 6 * q^27 + 14 * q^28 - 6 * q^29 - 7 * q^31 + 12 * q^32 - q^33 - 24 * q^34 + 4 * q^35 - 6 * q^36 - q^37 + 8 * q^38 - q^39 + 16 * q^41 - 4 * q^42 + 52 * q^43 - 4 * q^44 - 10 * q^45 - 4 * q^46 + 27 * q^47 + 6 * q^48 - 33 * q^49 - 22 * q^50 - 8 * q^51 - 4 * q^52 + 13 * q^53 - 12 * q^54 + 30 * q^55 + 14 * q^56 - 16 * q^57 - 3 * q^58 + 14 * q^59 - 5 * q^60 + 9 * q^61 - 4 * q^62 + 5 * q^63 - 6 * q^64 - 50 * q^65 - 4 * q^66 - 20 * q^67 - 2 * q^68 - 32 * q^69 - 17 * q^70 - 18 * q^71 - 3 * q^72 + 7 * q^73 + q^74 + 11 * q^75 - 4 * q^76 - 34 * q^77 - 12 * q^78 + q^79 + 3 * q^81 - 2 * q^82 - 68 * q^83 - 5 * q^84 - 19 * q^86 - 8 * q^87 - q^88 - 42 * q^89 + 10 * q^90 - 16 * q^91 + 32 * q^92 + 7 * q^93 + 8 * q^94 + 38 * q^95 + 3 * q^96 - 80 * q^97 - 2 * q^99

Introduction

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