LMFDB - Embedded newform 462.2.y.d.37.1

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:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			37.1
Character	$\chi$	$=$	462.37
Dual form			462.2.y.d.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.913545 - 0.406737i) q^{2} +(0.978148 - 0.207912i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.305851 - 2.90998i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-2.53596 + 0.754243i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.913545 - 0.406737i) q^{9} +O(q^{10})$	\(q+(0.913545 - 0.406737i) q^{2} +(0.978148 - 0.207912i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.305851 - 2.90998i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-2.53596 + 0.754243i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.913545 - 0.406737i) q^{9} +(-1.46300 - 2.53399i) q^{10} +(3.12014 - 1.12459i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.928329 + 0.674471i) q^{13} +(-2.00994 + 1.72051i) q^{14} +(-0.904185 - 2.78280i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(1.39338 + 0.620373i) q^{17} +(0.669131 - 0.743145i) q^{18} +(-4.41850 - 4.90724i) q^{19} +(-2.36719 - 1.71986i) q^{20} +(-2.32373 + 1.26502i) q^{21} +(2.39298 - 2.29644i) q^{22} +(0.745007 - 1.29039i) q^{23} +(0.104528 - 0.994522i) q^{24} +(-3.48368 + 0.740478i) q^{25} +(1.12240 + 0.238574i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-1.13638 + 2.38928i) q^{28} +(1.65246 + 5.08576i) q^{29} +(-1.95788 - 2.17445i) q^{30} +(-0.327483 + 3.11579i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.81815 - 1.74873i) q^{33} +1.52524 q^{34} +(2.97046 + 7.14891i) q^{35} +(0.309017 - 0.951057i) q^{36} +(3.69841 + 0.786122i) q^{37} +(-6.03245 - 2.68582i) q^{38} +(1.04827 + 0.466721i) q^{39} +(-2.86206 - 0.608351i) q^{40} +(-3.65165 + 11.2386i) q^{41} +(-1.60831 + 2.10080i) q^{42} +4.19680 q^{43} +(1.25205 - 3.07122i) q^{44} +(-1.46300 - 2.53399i) q^{45} +(0.155749 - 1.48185i) q^{46} +(-0.548635 - 0.609321i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(5.86223 - 3.82547i) q^{49} +(-2.88132 + 2.09340i) q^{50} +(1.49191 + 0.317116i) q^{51} +(1.12240 - 0.238574i) q^{52} +(-1.29527 + 12.3237i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-4.22682 - 8.73559i) q^{55} +(-0.0663284 + 2.64492i) q^{56} +(-5.34222 - 3.88135i) q^{57} +(3.57817 + 3.97396i) q^{58} +(9.01248 - 10.0094i) q^{59} +(-2.67304 - 1.19011i) q^{60} +(1.10983 + 10.5593i) q^{61} +(0.968136 + 2.97962i) q^{62} +(-2.00994 + 1.72051i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.67876 - 2.90770i) q^{65} +(1.86323 - 2.74379i) q^{66} +(0.555115 + 0.961487i) q^{67} +(1.39338 - 0.620373i) q^{68} +(0.460440 - 1.41709i) q^{69} +(5.62137 + 5.32266i) q^{70} +(4.46737 - 3.24574i) q^{71} +(-0.104528 - 0.994522i) q^{72} +(6.28185 - 6.97670i) q^{73} +(3.69841 - 0.786122i) q^{74} +(-3.25360 + 1.44859i) q^{75} -6.60334 q^{76} +(-7.06436 + 5.20526i) q^{77} +1.14748 q^{78} +(-9.09751 + 4.05047i) q^{79} +(-2.86206 + 0.608351i) q^{80} +(0.669131 - 0.743145i) q^{81} +(1.23521 + 11.7523i) q^{82} +(-10.8334 + 7.87096i) q^{83} +(-0.614789 + 2.57333i) q^{84} +(1.37910 - 4.24444i) q^{85} +(3.83397 - 1.70699i) q^{86} +(2.67374 + 4.63106i) q^{87} +(-0.105370 - 3.31495i) q^{88} +(1.58224 - 2.74052i) q^{89} +(-2.36719 - 1.71986i) q^{90} +(-2.86292 - 1.01025i) q^{91} +(-0.460440 - 1.41709i) q^{92} +(0.327483 + 3.11579i) q^{93} +(-0.749037 - 0.333493i) q^{94} +(-12.9285 + 14.3586i) q^{95} +(-0.669131 - 0.743145i) q^{96} +(-6.96423 - 5.05981i) q^{97} +(3.79946 - 5.87912i) q^{98} +(2.39298 - 2.29644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9}+O(q^{10}) $ 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 20 q^{12} + 10 q^{13} + 5 q^{14} - 6 q^{15} + 5 q^{16} + 5 q^{18} - 13 q^{19} + 6 q^{20} - 2 q^{21} - 4 q^{22} - 20 q^{23} - 5 q^{24} + 12 q^{25} + 10 q^{27} - 3 q^{28} + 12 q^{29} + 3 q^{30} - 10 q^{31} - 20 q^{32} + 8 q^{33} - 13 q^{35} - 10 q^{36} + 3 q^{37} + 2 q^{38} + 5 q^{39} - 3 q^{40} - 44 q^{41} - 3 q^{42} + 36 q^{43} - 3 q^{44} + 12 q^{45} + 11 q^{47} + 10 q^{48} + 33 q^{49} - 4 q^{50} + 26 q^{53} + 20 q^{54} - 20 q^{55} + 8 q^{56} + 4 q^{57} - 6 q^{58} + 4 q^{59} + 3 q^{60} - 23 q^{61} + 5 q^{63} - 10 q^{64} - 50 q^{65} - 7 q^{66} - 108 q^{67} + 20 q^{69} - 86 q^{71} + 5 q^{72} - 35 q^{73} + 3 q^{74} - 2 q^{75} - 44 q^{76} - 37 q^{77} + 20 q^{78} + 3 q^{79} - 3 q^{80} + 5 q^{81} - 28 q^{82} - 88 q^{83} - 5 q^{84} + 96 q^{85} - 13 q^{86} + 6 q^{87} - 8 q^{88} + 6 q^{89} + 6 q^{90} + 40 q^{91} - 20 q^{92} + 10 q^{93} - 24 q^{94} + 36 q^{95} - 5 q^{96} + 60 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 20 * q^12 + 10 * q^13 + 5 * q^14 - 6 * q^15 + 5 * q^16 + 5 * q^18 - 13 * q^19 + 6 * q^20 - 2 * q^21 - 4 * q^22 - 20 * q^23 - 5 * q^24 + 12 * q^25 + 10 * q^27 - 3 * q^28 + 12 * q^29 + 3 * q^30 - 10 * q^31 - 20 * q^32 + 8 * q^33 - 13 * q^35 - 10 * q^36 + 3 * q^37 + 2 * q^38 + 5 * q^39 - 3 * q^40 - 44 * q^41 - 3 * q^42 + 36 * q^43 - 3 * q^44 + 12 * q^45 + 11 * q^47 + 10 * q^48 + 33 * q^49 - 4 * q^50 + 26 * q^53 + 20 * q^54 - 20 * q^55 + 8 * q^56 + 4 * q^57 - 6 * q^58 + 4 * q^59 + 3 * q^60 - 23 * q^61 + 5 * q^63 - 10 * q^64 - 50 * q^65 - 7 * q^66 - 108 * q^67 + 20 * q^69 - 86 * q^71 + 5 * q^72 - 35 * q^73 + 3 * q^74 - 2 * q^75 - 44 * q^76 - 37 * q^77 + 20 * q^78 + 3 * q^79 - 3 * q^80 + 5 * q^81 - 28 * q^82 - 88 * q^83 - 5 * q^84 + 96 * q^85 - 13 * q^86 + 6 * q^87 - 8 * q^88 + 6 * q^89 + 6 * q^90 + 40 * q^91 - 20 * q^92 + 10 * q^93 - 24 * q^94 + 36 * q^95 - 5 * q^96 + 60 * q^97 + 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.913545	−	0.406737i	0.645974	−	0.287606i
$2$	0.913545	−	0.406737i	0.645974	−	0.287606i
$3$	0.978148	−	0.207912i	0.564734	−	0.120038i
$3$	0.978148	−	0.207912i	0.564734	−	0.120038i
$4$	0.669131	−	0.743145i	0.334565	−	0.371572i
$5$	−0.305851	−	2.90998i	−0.136781	−	1.30138i	−0.820505	−	0.571640i	$-0.806307\pi$
$5$	−0.305851	−	2.90998i	−0.136781	−	1.30138i	0.683724	−	0.729741i	$-0.260359\pi$
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$	−2.53596	+	0.754243i	−0.958505	+	0.285077i
$7$	−2.53596	+	0.754243i	−0.958505	+	0.285077i
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	0.913545	−	0.406737i	0.304515	−	0.135579i
$10$	−1.46300	−	2.53399i	−0.462642	−	0.801319i
$11$	3.12014	−	1.12459i	0.940759	−	0.339076i
$11$	3.12014	−	1.12459i	0.940759	−	0.339076i
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	0.928329	+	0.674471i	0.257472	+	0.187064i	0.709032	−	0.705176i	$-0.249132\pi$
$13$	0.928329	+	0.674471i	0.257472	+	0.187064i	−0.451560	+	0.892241i	$0.649132\pi$
$14$	−2.00994	+	1.72051i	−0.537179	+	0.459824i
$15$	−0.904185	−	2.78280i	−0.233460	−	0.718515i
$16$	−0.104528	−	0.994522i	−0.0261321	−	0.248630i
$17$	1.39338	+	0.620373i	0.337944	+	0.150462i	0.568691	−	0.822551i	$-0.307450\pi$
$17$	1.39338	+	0.620373i	0.337944	+	0.150462i	−0.230746	+	0.973014i	$0.574117\pi$
$18$	0.669131	−	0.743145i	0.157716	−	0.175161i
$19$	−4.41850	−	4.90724i	−1.01367	−	1.12580i	−0.992026	−	0.126032i	$-0.959776\pi$
$19$	−4.41850	−	4.90724i	−1.01367	−	1.12580i	−0.0216468	−	0.999766i	$-0.506891\pi$
$20$	−2.36719	−	1.71986i	−0.529319	−	0.384573i
$21$	−2.32373	+	1.26502i	−0.507080	+	0.276050i
$22$	2.39298	−	2.29644i	0.510186	−	0.489603i
$23$	0.745007	−	1.29039i	0.155345	−	0.269065i	−0.777840	−	0.628463i	$-0.783684\pi$
$23$	0.745007	−	1.29039i	0.155345	−	0.269065i	0.933185	+	0.359398i	$0.117018\pi$
$24$	0.104528	−	0.994522i	0.0213368	−	0.203006i
$25$	−3.48368	+	0.740478i	−0.696735	+	0.148096i
$26$	1.12240	+	0.238574i	0.220121	+	0.0467882i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−1.13638	+	2.38928i	−0.214756	+	0.451531i
$29$	1.65246	+	5.08576i	0.306855	+	0.944402i	0.978979	+	0.203963i	$0.0653823\pi$
$29$	1.65246	+	5.08576i	0.306855	+	0.944402i	−0.672124	+	0.740439i	$0.734618\pi$
$30$	−1.95788	−	2.17445i	−0.357458	−	0.396998i
$31$	−0.327483	+	3.11579i	−0.0588177	+	0.559613i	0.924940	+	0.380113i	$0.124115\pi$
$31$	−0.327483	+	3.11579i	−0.0588177	+	0.559613i	−0.983758	+	0.179500i	$0.942552\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	2.81815	−	1.74873i	0.490576	−	0.304415i
$34$	1.52524			0.261577
$35$	2.97046	+	7.14891i	0.502099	+	1.20839i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	3.69841	+	0.786122i	0.608016	+	0.129238i	0.501623	−	0.865086i	$-0.332737\pi$
$37$	3.69841	+	0.786122i	0.608016	+	0.129238i	0.106393	+	0.994324i	$0.466070\pi$
$38$	−6.03245	−	2.68582i	−0.978593	−	0.435698i
$39$	1.04827	+	0.466721i	0.167858	+	0.0747352i
$40$	−2.86206	−	0.608351i	−0.452532	−	0.0961887i
$41$	−3.65165	+	11.2386i	−0.570293	+	1.75518i	0.0813833	+	0.996683i	$0.474066\pi$
$41$	−3.65165	+	11.2386i	−0.570293	+	1.75518i	−0.651676	+	0.758498i	$0.725934\pi$
$42$	−1.60831	+	2.10080i	−0.248167	+	0.324160i
$43$	4.19680			0.640007			0.320003	−	0.947416i	$-0.396316\pi$
$43$	4.19680			0.640007			0.320003	+	0.947416i	$0.396316\pi$
$44$	1.25205	−	3.07122i	0.188754	−	0.463003i
$45$	−1.46300	−	2.53399i	−0.218092	−	0.377746i
$46$	0.155749	−	1.48185i	0.0229639	−	0.218487i
$47$	−0.548635	−	0.609321i	−0.0800267	−	0.0888786i	0.701802	−	0.712372i	$-0.252379\pi$
$47$	−0.548635	−	0.609321i	−0.0800267	−	0.0888786i	−0.781828	+	0.623494i	$0.785713\pi$
$48$	−0.309017	−	0.951057i	−0.0446028	−	0.137273i
$49$	5.86223	−	3.82547i	0.837462	−	0.546495i
$50$	−2.88132	+	2.09340i	−0.407480	+	0.296051i
$51$	1.49191	+	0.317116i	0.208910	+	0.0444051i
$52$	1.12240	−	0.238574i	0.155649	−	0.0330843i
$53$	−1.29527	+	12.3237i	−0.177920	+	1.69279i	0.433236	+	0.901281i	$0.357372\pi$
$53$	−1.29527	+	12.3237i	−0.177920	+	1.69279i	−0.611155	+	0.791511i	$0.709295\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−4.22682	−	8.73559i	−0.569945	−	1.17791i
$56$	−0.0663284	+	2.64492i	−0.00886351	+	0.353442i
$57$	−5.34222	−	3.88135i	−0.707594	−	0.514097i
$58$	3.57817	+	3.97396i	0.469836	+	0.521806i
$59$	9.01248	−	10.0094i	1.17332	−	1.30311i	0.229253	−	0.973367i	$-0.426372\pi$
$59$	9.01248	−	10.0094i	1.17332	−	1.30311i	0.944071	−	0.329742i	$-0.106962\pi$
$60$	−2.67304	−	1.19011i	−0.345088	−	0.153643i
$61$	1.10983	+	10.5593i	0.142099	+	1.35198i	0.800508	+	0.599323i	$0.204563\pi$
$61$	1.10983	+	10.5593i	0.142099	+	1.35198i	−0.658408	+	0.752661i	$0.728770\pi$
$62$	0.968136	+	2.97962i	0.122953	+	0.378412i
$63$	−2.00994	+	1.72051i	−0.253229	+	0.216763i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	1.67876	−	2.90770i	0.208225	−	0.360656i
$66$	1.86323	−	2.74379i	0.229348	−	0.337737i
$67$	0.555115	+	0.961487i	0.0678181	+	0.117464i	0.897941	−	0.440117i	$-0.145063\pi$
$67$	0.555115	+	0.961487i	0.0678181	+	0.117464i	−0.830123	+	0.557581i	$0.811730\pi$
$68$	1.39338	−	0.620373i	0.168972	−	0.0752312i
$69$	0.460440	−	1.41709i	0.0554304	−	0.170597i
$70$	5.62137	+	5.32266i	0.671882	+	0.636180i
$71$	4.46737	−	3.24574i	0.530180	−	0.385198i	−0.290245	−	0.956952i	$-0.593737\pi$
$71$	4.46737	−	3.24574i	0.530180	−	0.385198i	0.820425	+	0.571754i	$0.193737\pi$
$72$	−0.104528	−	0.994522i	−0.0123188	−	0.117206i
$73$	6.28185	−	6.97670i	0.735235	−	0.816561i	−0.253326	−	0.967381i	$-0.581525\pi$
$73$	6.28185	−	6.97670i	0.735235	−	0.816561i	0.988561	+	0.150820i	$0.0481913\pi$
$74$	3.69841	−	0.786122i	0.429932	−	0.0913849i
$75$	−3.25360	+	1.44859i	−0.375693	+	0.167269i
$76$	−6.60334			−0.757455
$77$	−7.06436	+	5.20526i	−0.805059	+	0.593195i
$78$	1.14748			0.129926
$79$	−9.09751	+	4.05047i	−1.02355	+	0.455714i	−0.848696	−	0.528881i	$-0.822612\pi$
$79$	−9.09751	+	4.05047i	−1.02355	+	0.455714i	−0.174854	+	0.984594i	$0.555945\pi$
$80$	−2.86206	+	0.608351i	−0.319989	+	0.0680157i
$81$	0.669131	−	0.743145i	0.0743478	−	0.0825716i
$82$	1.23521	+	11.7523i	0.136406	+	1.29782i
$83$	−10.8334	+	7.87096i	−1.18912	+	0.863950i	−0.993171	−	0.116664i	$-0.962780\pi$
$83$	−10.8334	+	7.87096i	−1.18912	+	0.863950i	−0.195953	+	0.980613i	$0.562780\pi$
$84$	−0.614789	+	2.57333i	−0.0670790	+	0.280773i
$85$	1.37910	−	4.24444i	0.149585	−	0.460374i
$86$	3.83397	−	1.70699i	0.413428	−	0.184070i
$87$	2.67374	+	4.63106i	0.286655	+	0.496501i
$88$	−0.105370	−	3.31495i	−0.0112325	−	0.353375i
$89$	1.58224	−	2.74052i	0.167717	−	0.290495i	−0.769900	−	0.638165i	$-0.779694\pi$
$89$	1.58224	−	2.74052i	0.167717	−	0.290495i	0.937617	+	0.347670i	$0.113027\pi$
$90$	−2.36719	−	1.71986i	−0.249523	−	0.181289i
$91$	−2.86292	−	1.01025i	−0.300116	−	0.105903i
$92$	−0.460440	−	1.41709i	−0.0480042	−	0.147742i
$93$	0.327483	+	3.11579i	0.0339584	+	0.323093i
$94$	−0.749037	−	0.333493i	−0.0772572	−	0.0343971i
$95$	−12.9285	+	14.3586i	−1.32644	+	1.47316i
$96$	−0.669131	−	0.743145i	−0.0682929	−	0.0758469i
$97$	−6.96423	−	5.05981i	−0.707110	−	0.513746i	0.175130	−	0.984545i	$-0.443965\pi$
$97$	−6.96423	−	5.05981i	−0.707110	−	0.513746i	−0.882240	+	0.470800i	$0.843965\pi$
$98$	3.79946	−	5.87912i	0.383803	−	0.593881i
$99$	2.39298	−	2.29644i	0.240504	−	0.230801i
$100$	−1.78075	+	3.08435i	−0.178075	+	0.308435i
$101$	0.869123	−	8.26915i	0.0864810	−	0.822812i	−0.862198	−	0.506571i	$-0.830913\pi$
$101$	0.869123	−	8.26915i	0.0864810	−	0.822812i	0.948679	−	0.316240i	$-0.102421\pi$
$102$	1.49191	−	0.317116i	0.147721	−	0.0313992i
$103$	−9.92859	−	2.11039i	−0.978293	−	0.207943i	−0.309099	−	0.951030i	$-0.600027\pi$
$103$	−9.92859	−	2.11039i	−0.978293	−	0.207943i	−0.669195	+	0.743087i	$0.733361\pi$
$104$	0.928329	−	0.674471i	0.0910302	−	0.0661373i
$105$	4.39189	+	6.37510i	0.428604	+	0.622146i
$106$	3.82921	+	11.7851i	0.371926	+	1.14467i
$107$	13.2863	+	14.7559i	1.28443	+	1.42651i	0.850863	+	0.525387i	$0.176079\pi$
$107$	13.2863	+	14.7559i	1.28443	+	1.42651i	0.433569	+	0.901120i	$0.357254\pi$
$108$	0.104528	−	0.994522i	0.0100583	−	0.0956979i
$109$	−1.27817	−	2.21385i	−0.122426	−	0.212049i	0.798298	−	0.602263i	$-0.205734\pi$
$109$	−1.27817	−	2.21385i	−0.122426	−	0.212049i	−0.920724	+	0.390214i	$0.872401\pi$
$110$	−7.41448	−	6.26115i	−0.706943	−	0.596977i
$111$	3.78104			0.358880
$112$	1.01519	+	2.44323i	0.0959266	+	0.230864i
$113$	−2.37818	+	7.31928i	−0.223720	+	0.688540i	0.774699	+	0.632330i	$0.217902\pi$
$113$	−2.37818	+	7.31928i	−0.223720	+	0.688540i	−0.998419	+	0.0562096i	$0.982098\pi$
$114$	−6.45904	−	1.37291i	−0.604945	−	0.128585i
$115$	−3.98287	−	1.77329i	−0.371404	−	0.165360i
$116$	4.88517	+	2.17502i	0.453577	+	0.201945i
$117$	1.12240	+	0.238574i	0.103766	+	0.0220562i
$118$	4.16213	−	12.8097i	0.383155	−	1.17923i
$119$	−4.00147	−	0.522296i	−0.366815	−	0.0478788i
$120$	−2.92600			−0.267106
$121$	8.47060	−	7.01776i	0.770055	−	0.637978i
$122$	5.30875	+	9.19502i	0.480631	+	0.832478i
$123$	−1.23521	+	11.7523i	−0.111375	+	1.05967i
$124$	2.09636	+	2.32824i	0.188258	+	0.209082i
$125$	−1.30067	−	4.00304i	−0.116335	−	0.358043i
$126$	−1.13638	+	2.38928i	−0.101237	+	0.212854i
$127$	−6.29225	+	4.57159i	−0.558347	+	0.405663i	−0.830854	−	0.556491i	$-0.812147\pi$
$127$	−6.29225	+	4.57159i	−0.558347	+	0.405663i	0.272506	+	0.962154i	$0.412147\pi$
$128$	−0.978148	−	0.207912i	−0.0864569	−	0.0183770i
$129$	4.10509	−	0.872565i	0.361433	−	0.0768250i
$130$	0.350957	−	3.33913i	0.0307810	−	0.292861i
$131$	3.70491	−	6.41710i	0.323700	−	0.560665i	−0.657549	−	0.753412i	$-0.728407\pi$
$131$	3.70491	−	6.41710i	0.323700	−	0.560665i	0.981248	+	0.192748i	$0.0617399\pi$
$132$	0.586150	−	3.26442i	0.0510178	−	0.284131i
$133$	14.9064	+	9.11196i	1.29255	+	0.790107i
$134$	0.898195	+	0.652577i	0.0775922	+	0.0563740i
$135$	−1.95788	−	2.17445i	−0.168507	−	0.187146i
$136$	1.02059	−	1.13348i	0.0875147	−	0.0971949i
$137$	10.9999	+	4.89748i	0.939786	+	0.418420i	0.818700	−	0.574222i	$-0.194695\pi$
$137$	10.9999	+	4.89748i	0.939786	+	0.418420i	0.121087	+	0.992642i	$0.461362\pi$
$138$	−0.155749	−	1.48185i	−0.0132582	−	0.126144i
$139$	−4.74196	−	14.5943i	−0.402208	−	1.23787i	−0.923204	−	0.384310i	$-0.874440\pi$
$139$	−4.74196	−	14.5943i	−0.402208	−	1.23787i	0.520996	−	0.853559i	$-0.325560\pi$
$140$	7.30030	+	2.57608i	0.616988	+	0.217718i
$141$	−0.663331	−	0.481938i	−0.0558626	−	0.0405865i
$142$	2.76099	−	4.78217i	0.231697	−	0.401311i
$143$	3.65502	+	1.06046i	0.305648	+	0.0886799i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	14.2940	−	6.36411i	1.18705	−	0.528511i
$146$	2.90108	−	8.92859i	0.240095	−	0.738936i
$147$	4.93877	−	4.96070i	0.407343	−	0.409152i
$148$	3.05893	−	2.22244i	0.251442	−	0.182683i
$149$	0.771746	+	7.34267i	0.0632239	+	0.601535i	0.979564	+	0.201134i	$0.0644626\pi$
$149$	0.771746	+	7.34267i	0.0632239	+	0.601535i	−0.916340	+	0.400401i	$0.868871\pi$
$150$	−2.38311	+	2.64671i	−0.194580	+	0.216103i
$151$	−8.04376	+	1.70975i	−0.654592	+	0.139138i	−0.523223	−	0.852196i	$-0.675271\pi$
$151$	−8.04376	+	1.70975i	−0.654592	+	0.139138i	−0.131369	+	0.991334i	$0.541937\pi$
$152$	−6.03245	+	2.68582i	−0.489297	+	0.217849i
$153$	1.52524			0.123309
$154$	−4.33644	+	7.62858i	−0.349441	+	0.614729i
$155$	9.16704			0.736314
$156$	1.04827	−	0.466721i	0.0839290	−	0.0373676i
$157$	−21.5046	+	4.57095i	−1.71626	+	0.364802i	−0.957914	−	0.287055i	$-0.907324\pi$
$157$	−21.5046	+	4.57095i	−1.71626	+	0.364802i	−0.758342	+	0.651856i	$0.773990\pi$
$158$	−6.66351	+	7.40058i	−0.530121	+	0.588759i
$159$	1.29527	+	12.3237i	0.102722	+	0.977334i
$160$	−2.36719	+	1.71986i	−0.187143	+	0.135967i
$161$	−0.916044	+	3.83430i	−0.0721944	+	0.302185i
$162$	0.309017	−	0.951057i	0.0242787	−	0.0747221i
$163$	6.94184	−	3.09071i	0.543727	−	0.242083i	−0.116445	−	0.993197i	$-0.537150\pi$
$163$	6.94184	−	3.09071i	0.543727	−	0.242083i	0.660172	+	0.751114i	$0.270483\pi$
$164$	5.90850	+	10.2338i	0.461376	+	0.799127i
$165$	−5.95069	−	7.66589i	−0.463261	−	0.596789i
$166$	−6.69544	+	11.5968i	−0.519667	+	0.900089i
$167$	−12.0223	−	8.73472i	−0.930314	−	0.675913i	0.0157555	−	0.999876i	$-0.494985\pi$
$167$	−12.0223	−	8.73472i	−0.930314	−	0.675913i	−0.946070	+	0.323963i	$0.894985\pi$
$168$	0.485031	+	2.60091i	0.0374209	+	0.200665i
$169$	−3.61034	−	11.1115i	−0.277718	−	0.854729i
$170$	−0.466497	−	4.43842i	−0.0357787	−	0.340412i
$171$	−6.03245	−	2.68582i	−0.461313	−	0.205390i
$172$	2.80821	−	3.11883i	0.214124	−	0.237809i
$173$	10.1795	+	11.3055i	0.773936	+	0.859543i	0.993236	−	0.116114i	$-0.0370439\pi$
$173$	10.1795	+	11.3055i	0.773936	+	0.859543i	−0.219300	+	0.975658i	$0.570377\pi$
$174$	4.32621	+	3.14317i	0.327969	+	0.238283i
$175$	8.27598	−	4.50537i	0.625605	−	0.340574i
$176$	−1.44457	−	2.98550i	−0.108889	−	0.225041i
$177$	6.73447	−	11.6644i	0.506194	−	0.876753i
$178$	0.330778	−	3.14715i	0.0247929	−	0.235889i
$179$	−7.91817	+	1.68306i	−0.591832	+	0.125798i	−0.494085	−	0.869413i	$-0.664497\pi$
$179$	−7.91817	+	1.68306i	−0.591832	+	0.125798i	−0.0977470	+	0.995211i	$0.531164\pi$
$180$	−2.86206	−	0.608351i	−0.213326	−	0.0453438i
$181$	2.51563	−	1.82771i	0.186986	−	0.135853i	−0.490354	−	0.871523i	$-0.663133\pi$
$181$	2.51563	−	1.82771i	0.186986	−	0.135853i	0.677340	+	0.735670i	$0.263133\pi$
$182$	−3.02632	+	0.241549i	−0.224326	+	0.0179048i
$183$	3.28099	+	10.0978i	0.242537	+	0.746453i
$184$	−0.997014	−	1.10730i	−0.0735009	−	0.0816310i
$185$	1.15643	−	11.0027i	0.0850227	−	0.808937i
$186$	1.56648	+	2.71322i	0.114860	+	0.198943i
$187$	5.04521	+	0.368673i	0.368942	+	0.0269600i
$188$	−0.819923			−0.0597990
$189$	−1.60831	+	2.10080i	−0.116987	+	0.152811i
$190$	−5.97064	+	18.3758i	−0.433156	+	1.33312i
$191$	−18.7377	−	3.98282i	−1.35581	−	0.288187i	−0.528025	−	0.849229i	$-0.677067\pi$
$191$	−18.7377	−	3.98282i	−1.35581	−	0.288187i	−0.827787	+	0.561042i	$0.810401\pi$
$192$	−0.913545	−	0.406737i	−0.0659295	−	0.0293537i
$193$	−19.0193	−	8.46793i	−1.36904	−	0.609535i	−0.415166	−	0.909746i	$-0.636276\pi$
$193$	−19.0193	−	8.46793i	−1.36904	−	0.609535i	−0.953873	+	0.300211i	$0.902943\pi$
$194$	−8.42015	−	1.78976i	−0.604531	−	0.128497i
$195$	1.03753	−	3.19320i	0.0742992	−	0.228670i
$196$	1.07972	−	6.91623i	0.0771232	−	0.494016i
$197$	5.42608			0.386592			0.193296	−	0.981140i	$-0.438082\pi$
$197$	5.42608			0.386592			0.193296	+	0.981140i	$0.438082\pi$
$198$	1.25205	−	3.07122i	0.0889794	−	0.218262i
$199$	−4.64296	−	8.04185i	−0.329131	−	0.570071i	0.653209	−	0.757178i	$-0.273422\pi$
$199$	−4.64296	−	8.04185i	−0.329131	−	0.570071i	−0.982340	+	0.187106i	$0.940089\pi$
$200$	−0.372279	+	3.54199i	−0.0263241	+	0.250457i
$201$	0.742889	+	0.825061i	0.0523993	+	0.0581953i
$202$	−2.56938	−	7.90775i	−0.180781	−	0.556388i
$203$	−8.02649	−	11.6509i	−0.563349	−	0.817736i
$204$	1.23395	−	0.896516i	0.0863937	−	0.0627687i
$205$	33.8210	+	7.18888i	2.36216	+	0.502093i
$206$	−9.92859	+	2.11039i	−0.691758	+	0.147038i
$207$	0.155749	−	1.48185i	0.0108253	−	0.102996i
$208$	0.573739	−	0.993745i	0.0397816	−	0.0689038i
$209$	−19.3050	−	10.3423i	−1.33535	−	0.715392i
$210$	6.60517	+	4.03760i	0.455800	+	0.278621i
$211$	−11.5909	−	8.42129i	−0.797951	−	0.579745i	0.112361	−	0.993667i	$-0.464159\pi$
$211$	−11.5909	−	8.42129i	−0.797951	−	0.579745i	−0.910312	+	0.413922i	$0.864159\pi$
$212$	8.29159	+	9.20875i	0.569469	+	0.632459i
$213$	3.69493	−	4.10363i	0.253172	−	0.281176i
$214$	18.1394	+	8.07617i	1.23998	+	0.552076i
$215$	−1.28360	−	12.2126i	−0.0875405	−	0.832892i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	−1.51958	−	8.14854i	−0.103156	−	0.553159i
$218$	−2.06812	−	1.50258i	−0.140071	−	0.101767i
$219$	4.69404	−	8.13032i	0.317194	−	0.549396i
$220$	−9.32010	−	2.70411i	−0.628361	−	0.182311i
$221$	0.875092	+	1.51570i	0.0588650	+	0.101957i
$222$	3.45415	−	1.53789i	0.231827	−	0.103216i
$223$	−3.10067	+	9.54289i	−0.207636	+	0.639039i	0.791958	+	0.610575i	$0.209062\pi$
$223$	−3.10067	+	9.54289i	−0.207636	+	0.639039i	−0.999595	+	0.0284642i	$0.990938\pi$
$224$	1.92118	+	1.81909i	0.128364	+	0.121543i
$225$	−2.88132	+	2.09340i	−0.192088	+	0.139560i
$226$	0.804446	+	7.65379i	0.0535109	+	0.509122i
$227$	2.85372	−	3.16937i	0.189408	−	0.210359i	−0.640960	−	0.767574i	$-0.721464\pi$
$227$	2.85372	−	3.16937i	0.189408	−	0.210359i	0.830368	+	0.557215i	$0.188130\pi$
$228$	−6.45904	+	1.37291i	−0.427761	+	0.0909233i
$229$	−5.26425	+	2.34379i	−0.347871	+	0.154882i	−0.573232	−	0.819393i	$-0.694311\pi$
$229$	−5.26425	+	2.34379i	−0.347871	+	0.154882i	0.225361	+	0.974275i	$0.427644\pi$
$230$	−4.35979			−0.287476
$231$	−5.82775	+	6.56028i	−0.383438	+	0.431635i
$232$	5.34748			0.351080
$233$	22.2422	−	9.90287i	1.45714	−	0.648759i	0.483185	−	0.875518i	$-0.339480\pi$
$233$	22.2422	−	9.90287i	1.45714	−	0.648759i	0.973951	+	0.226760i	$0.0728132\pi$
$234$	1.12240	−	0.238574i	0.0733738	−	0.0155961i
$235$	−1.60531	+	1.78288i	−0.104719	+	0.116302i
$236$	−1.40789	−	13.3952i	−0.0916456	−	0.871950i
$237$	−8.05657	+	5.85344i	−0.523330	+	0.380222i
$238$	−3.86797	+	1.15040i	−0.250723	+	0.0745697i
$239$	5.03819	−	15.5060i	0.325894	−	1.00300i	−0.645142	−	0.764063i	$-0.723202\pi$
$239$	5.03819	−	15.5060i	0.325894	−	1.00300i	0.971036	−	0.238935i	$-0.0767982\pi$
$240$	−2.67304	+	1.19011i	−0.172544	+	0.0768215i
$241$	9.99434	+	17.3107i	0.643792	+	1.11508i	0.984579	+	0.174940i	$0.0559733\pi$
$241$	9.99434	+	17.3107i	0.643792	+	1.11508i	−0.340787	+	0.940141i	$0.610693\pi$
$242$	4.88390	−	9.85634i	0.313949	−	0.633590i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	8.58973	+	6.24081i	0.549901	+	0.399527i
$245$	−12.9250	−	15.8889i	−0.825747	−	1.01511i
$246$	3.65165	+	11.2386i	0.232821	+	0.716549i
$247$	−0.792032	−	7.53568i	−0.0503958	−	0.479484i
$248$	2.86210	+	1.27429i	0.181743	+	0.0809173i
$249$	−8.96024	+	9.95136i	−0.567832	+	0.630642i
$250$	−2.81640	−	3.12793i	−0.178125	−	0.197828i
$251$	−2.68953	−	1.95406i	−0.169762	−	0.123339i	0.499660	−	0.866221i	$-0.333458\pi$
$251$	−2.68953	−	1.95406i	−0.169762	−	0.123339i	−0.669422	+	0.742882i	$0.733458\pi$
$252$	−0.0663284	+	2.64492i	−0.00417830	+	0.166614i
$253$	0.873372	−	4.86403i	0.0549084	−	0.305799i
$254$	−3.88883	+	6.73565i	−0.244007	+	0.422632i
$255$	0.466497	−	4.43842i	0.0292132	−	0.277945i
$256$	−0.978148	+	0.207912i	−0.0611342	+	0.0129945i
$257$	−15.3638	−	3.26567i	−0.958365	−	0.203707i	−0.297928	−	0.954588i	$-0.596296\pi$
$257$	−15.3638	−	3.26567i	−0.958365	−	0.203707i	−0.660437	+	0.750881i	$0.729629\pi$
$258$	3.39529	−	2.46682i	0.211381	−	0.153577i
$259$	−9.97198	+	0.795925i	−0.619629	+	0.0494564i
$260$	−1.03753	−	3.19320i	−0.0643450	−	0.198034i
$261$	3.57817	+	3.97396i	0.221483	+	0.245982i
$262$	0.774538	−	7.36924i	0.0478511	−	0.455273i
$263$	1.24355	+	2.15389i	0.0766804	+	0.132814i	0.901816	−	0.432121i	$-0.142235\pi$
$263$	1.24355	+	2.15389i	0.0766804	+	0.132814i	−0.825135	+	0.564935i	$0.808901\pi$
$264$	−0.792284	−	3.22060i	−0.0487617	−	0.198214i
$265$	36.2579			2.22730
$266$	17.3238	+	2.26121i	1.06219	+	0.138644i
$267$	0.977878	−	3.00960i	0.0598452	−	0.184185i
$268$	1.08597	+	0.230830i	0.0663361	+	0.0141002i
$269$	1.65778	+	0.738090i	0.101076	+	0.0450021i	0.456652	−	0.889645i	$-0.349048\pi$
$269$	1.65778	+	0.738090i	0.101076	+	0.0450021i	−0.355576	+	0.934648i	$0.615715\pi$
$270$	−2.67304	−	1.19011i	−0.162676	−	0.0724280i
$271$	24.2486	+	5.15420i	1.47300	+	0.313095i	0.873320	−	0.487147i	$-0.161962\pi$
$271$	24.2486	+	5.15420i	1.47300	+	0.313095i	0.599677	+	0.800242i	$0.295296\pi$
$272$	0.471326	−	1.45059i	0.0285784	−	0.0879551i
$273$	−3.01041	−	0.392936i	−0.182198	−	0.0237816i
$274$	12.0409			0.727418
$275$	−10.0368	+	6.22810i	−0.605244	+	0.375569i
$276$	−0.745007	−	1.29039i	−0.0448442	−	0.0776724i
$277$	0.499901	−	4.75624i	0.0300362	−	0.285775i	−0.969186	−	0.246331i	$-0.920775\pi$
$277$	0.499901	−	4.75624i	0.0300362	−	0.285775i	0.999222	−	0.0394435i	$-0.0125585\pi$
$278$	−10.2680	−	11.4038i	−0.615835	−	0.683954i
$279$	0.968136	+	2.97962i	0.0579608	+	0.178385i
$280$	7.71694	−	0.615937i	0.461175	−	0.0368093i
$281$	14.1543	−	10.2837i	0.844373	−	0.613473i	−0.0792155	−	0.996858i	$-0.525242\pi$
$281$	14.1543	−	10.2837i	0.844373	−	0.613473i	0.923589	+	0.383384i	$0.125242\pi$
$282$	−0.802005	−	0.170472i	−0.0477587	−	0.0101514i
$283$	−27.6755	+	5.88260i	−1.64514	+	0.349685i	−0.935074	−	0.354454i	$-0.884667\pi$
$283$	−27.6755	+	5.88260i	−1.64514	+	0.349685i	−0.710063	+	0.704138i	$0.751333\pi$
$284$	0.577204	−	5.49173i	0.0342508	−	0.325874i
$285$	−9.66070	+	16.7328i	−0.572251	+	0.991167i
$286$	3.77036	−	0.517856i	0.222946	−	0.0306215i
$287$	0.783803	−	31.2550i	0.0462665	−	1.84493i
$288$	−0.809017	−	0.587785i	−0.0476718	−	0.0346356i
$289$	−9.81858	−	10.9046i	−0.577563	−	0.641449i
$290$	10.4697	−	11.6278i	0.614804	−	0.682809i
$291$	−7.86403	−	3.50129i	−0.460998	−	0.205249i
$292$	−0.981322	−	9.33665i	−0.0574275	−	0.546386i
$293$	4.17657	+	12.8541i	0.243998	+	0.750947i	0.995800	+	0.0915585i	$0.0291848\pi$
$293$	4.17657	+	12.8541i	0.243998	+	0.750947i	−0.751802	+	0.659389i	$0.770815\pi$
$294$	2.49409	−	6.54060i	0.145459	−	0.381456i
$295$	−31.8835	−	23.1647i	−1.85633	−	1.34870i
$296$	1.89052	−	3.27448i	0.109884	−	0.190325i
$297$	1.86323	−	2.74379i	0.108116	−	0.159211i
$298$	3.69156	+	6.39397i	0.213846	+	0.370393i
$299$	1.56194	−	0.695422i	0.0903295	−	0.0402173i
$300$	−1.10057	+	3.38719i	−0.0635412	+	0.195560i
$301$	−10.6429	+	3.16541i	−0.613449	+	0.182451i
$302$	−6.65292	+	4.83363i	−0.382832	+	0.278144i
$303$	−0.869123	−	8.26915i	−0.0499298	−	0.475050i
$304$	−4.41850	+	4.90724i	−0.253418	+	0.281449i
$305$	30.3879	−	6.45916i	1.74001	−	0.369850i
$306$	1.39338	−	0.620373i	0.0796542	−	0.0354643i
$307$	9.52605			0.543680			0.271840	−	0.962342i	$-0.412368\pi$
$307$	9.52605			0.543680			0.271840	+	0.962342i	$0.412368\pi$
$308$	−0.858716	+	8.73285i	−0.0489299	+	0.497600i
$309$	−10.1504			−0.577436
$310$	8.37451	−	3.72857i	0.475640	−	0.211769i
$311$	13.0017	−	2.76360i	0.737260	−	0.156709i	0.176048	−	0.984382i	$-0.443669\pi$
$311$	13.0017	−	2.76360i	0.737260	−	0.156709i	0.561212	+	0.827672i	$0.310335\pi$
$312$	0.767813	−	0.852742i	0.0434688	−	0.0482770i
$313$	3.12198	+	29.7037i	0.176465	+	1.67895i	0.621483	+	0.783428i	$0.286531\pi$
$313$	3.12198	+	29.7037i	0.176465	+	1.67895i	−0.445018	+	0.895522i	$0.646803\pi$
$314$	−17.7863	+	12.9225i	−1.00374	+	0.729259i
$315$	5.62137	+	5.32266i	0.316728	+	0.299898i
$316$	−3.07733	+	9.47106i	−0.173114	+	0.532789i
$317$	10.5249	−	4.68600i	0.591138	−	0.263192i	−0.0892908	−	0.996006i	$-0.528460\pi$
$317$	10.5249	−	4.68600i	0.591138	−	0.263192i	0.680429	+	0.732814i	$0.261793\pi$
$318$	6.19580	+	10.7314i	0.347443	+	0.601789i
$319$	10.8753	+	14.0100i	0.608901	+	0.784407i
$320$	−1.46300	+	2.53399i	−0.0817843	+	0.141655i
$321$	16.0639	+	11.6711i	0.896597	+	0.651416i
$322$	0.722703	+	3.87540i	0.0402747	+	0.215967i
$323$	−3.11233	−	9.57876i	−0.173175	−	0.532977i
$324$	−0.104528	−	0.994522i	−0.00580714	−	0.0552512i
$325$	−3.73343	−	1.66223i	−0.207093	−	0.0922039i
$326$	5.08458	−	5.64700i	0.281609	−	0.312758i
$327$	−1.71052	−	1.89973i	−0.0945922	−	0.105055i
$328$	9.56016	+	6.94586i	0.527871	+	0.383521i
$329$	1.85090	+	1.13141i	0.102043	+	0.0623768i
$330$	−8.55422	−	4.58277i	−0.470894	−	0.252273i
$331$	−9.97943	+	17.2849i	−0.548519	+	0.950063i	0.449857	+	0.893100i	$0.351475\pi$
$331$	−9.97943	+	17.2849i	−0.548519	+	0.950063i	−0.998376	+	0.0569624i	$0.981858\pi$
$332$	−1.39973	+	13.3175i	−0.0768200	+	0.730894i
$333$	3.69841	−	0.786122i	0.202672	−	0.0430792i
$334$	−14.5357	−	3.08965i	−0.795356	−	0.169058i
$335$	2.62812	−	1.90944i	0.143590	−	0.104324i
$336$	1.50098	+	2.17877i	0.0818854	+	0.118862i
$337$	3.23547	+	9.95776i	0.176247	+	0.542434i	0.999688	−	0.0249685i	$-0.00794855\pi$
$337$	3.23547	+	9.95776i	0.176247	+	0.542434i	−0.823441	+	0.567402i	$0.807949\pi$
$338$	−7.81765	−	8.68238i	−0.425224	−	0.472259i
$339$	−0.804446	+	7.65379i	−0.0436915	+	0.415697i
$340$	−2.23144	−	3.86496i	−0.121017	−	0.209607i
$341$	2.48219	+	10.0900i	0.134418	+	0.546404i
$342$	−6.60334			−0.357068
$343$	−11.9811	+	14.1228i	−0.646918	+	0.762560i
$344$	1.29688	−	3.99140i	0.0699233	−	0.215202i
$345$	−4.26452	−	0.906451i	−0.229594	−	0.0488017i
$346$	13.8978	+	6.18772i	0.747153	+	0.332654i
$347$	−1.45178	−	0.646374i	−0.0779357	−	0.0346992i	0.367399	−	0.930064i	$-0.380248\pi$
$347$	−1.45178	−	0.646374i	−0.0779357	−	0.0346992i	−0.445334	+	0.895364i	$0.646915\pi$
$348$	5.23063	+	1.11180i	0.280391	+	0.0595990i
$349$	0.555278	−	1.70897i	0.0297234	−	0.0914791i	−0.935094	−	0.354399i	$-0.884685\pi$
$349$	0.555278	−	1.70897i	0.0297234	−	0.0914791i	0.964818	+	0.262920i	$0.0846855\pi$
$350$	5.72799	−	7.48200i	0.306174	−	0.399930i
$351$	1.14748			0.0612478
$352$	−2.53399	−	2.13983i	−0.135062	−	0.114053i
$353$	−2.90566	−	5.03275i	−0.154653	−	0.267866i	0.778280	−	0.627918i	$-0.216092\pi$
$353$	−2.90566	−	5.03275i	−0.154653	−	0.267866i	−0.932932	+	0.360051i	$0.882759\pi$
$354$	1.40789	−	13.3952i	0.0748283	−	0.711944i
$355$	−10.8114	−	12.0072i	−0.573808	−	0.637278i
$356$	−0.977878	−	3.00960i	−0.0518275	−	0.159508i
$357$	−4.02262	+	0.321070i	−0.212900	+	0.0169929i
$358$	−6.54905	+	4.75816i	−0.346128	+	0.251477i
$359$	−19.5358	−	4.15247i	−1.03106	−	0.219159i	−0.338840	−	0.940844i	$-0.610035\pi$
$359$	−19.5358	−	4.15247i	−1.03106	−	0.219159i	−0.692222	+	0.721685i	$0.743368\pi$
$360$	−2.86206	+	0.608351i	−0.150844	+	0.0320629i
$361$	−2.57183	+	24.4693i	−0.135360	+	1.28786i
$362$	1.55475	−	2.69290i	0.0817157	−	0.141536i
$363$	6.82642	−	8.62554i	0.358294	−	0.452723i
$364$	−2.66643	+	1.45158i	−0.139759	+	0.0760835i
$365$	−22.2233	−	16.1462i	−1.16322	−	0.845131i
$366$	7.10449	+	7.89033i	0.371358	+	0.412434i
$367$	18.7420	−	20.8151i	0.978325	−	1.08654i	−0.0179098	−	0.999840i	$-0.505701\pi$
$367$	18.7420	−	20.8151i	0.978325	−	1.08654i	0.996234	−	0.0867001i	$-0.0276322\pi$
$368$	−1.36120	−	0.606044i	−0.0709573	−	0.0315922i
$369$	1.23521	+	11.7523i	0.0643026	+	0.611799i
$370$	−3.41876	−	10.5219i	−0.177733	−	0.547006i
$371$	−6.01030	−	32.2294i	−0.312039	−	1.67327i
$372$	2.53461	+	1.84150i	0.131414	+	0.0954776i
$373$	2.97342	−	5.15011i	0.153958	−	0.266663i	−0.778721	−	0.627370i	$-0.784131\pi$
$373$	2.97342	−	5.15011i	0.153958	−	0.266663i	0.932679	+	0.360707i	$0.117465\pi$
$374$	4.75898	−	1.71527i	0.246081	−	0.0886946i
$375$	−2.10452	−	3.64514i	−0.108677	−	0.188234i
$376$	−0.749037	+	0.333493i	−0.0386286	+	0.0171986i
$377$	−1.89617	+	5.83580i	−0.0976575	+	0.300559i
$378$	−0.614789	+	2.57333i	−0.0316213	+	0.132358i
$379$	−17.9697	+	13.0558i	−0.923041	+	0.670629i	−0.944279	−	0.329146i	$-0.893239\pi$
$379$	−17.9697	+	13.0558i	−0.923041	+	0.670629i	0.0212377	+	0.999774i	$0.493239\pi$
$380$	2.01964	+	19.2156i	0.103605	+	0.985738i
$381$	−5.20427	+	5.77992i	−0.266623	+	0.296114i
$382$	−18.7377	+	3.98282i	−0.958704	+	0.203779i
$383$	6.94158	−	3.09059i	0.354698	−	0.157922i	−0.221649	−	0.975126i	$-0.571144\pi$
$383$	6.94158	−	3.09059i	0.354698	−	0.157922i	0.576348	+	0.817205i	$0.304477\pi$
$384$	−1.00000			−0.0510310
$385$	17.3078	+	18.9651i	0.882089	+	0.966551i
$386$	−20.8192			−1.05967
$387$	3.83397	−	1.70699i	0.194892	−	0.0867714i
$388$	−8.42015	+	1.78976i	−0.427468	+	0.0908612i
$389$	15.8401	−	17.5922i	0.803125	−	0.891961i	−0.192883	−	0.981222i	$-0.561784\pi$
$389$	15.8401	−	17.5922i	0.803125	−	0.891961i	0.996008	+	0.0892611i	$0.0284506\pi$
$390$	−0.350957	−	3.33913i	−0.0177714	−	0.169084i
$391$	1.83860	−	1.33582i	0.0929821	−	0.0675554i
$392$	−1.82671	−	6.75745i	−0.0922626	−	0.341303i
$393$	2.28976	−	7.04716i	0.115503	−	0.355482i
$394$	4.95697	−	2.20698i	0.249728	−	0.111186i
$395$	14.5693	+	25.2347i	0.733059	+	1.26970i
$396$	−0.105370	−	3.31495i	−0.00529503	−	0.166583i
$397$	8.60312	−	14.9010i	0.431778	−	0.747862i	−0.565248	−	0.824921i	$-0.691220\pi$
$397$	8.60312	−	14.9010i	0.431778	−	0.747862i	0.997027	+	0.0770589i	$0.0245530\pi$
$398$	−7.51247	−	5.45813i	−0.376566	−	0.273591i
$399$	16.4751	+	5.81363i	0.824789	+	0.291046i
$400$	1.10057	+	3.38719i	0.0550283	+	0.169360i
$401$	−2.21831	−	21.1058i	−0.110777	−	1.05397i	−0.898810	−	0.438339i	$-0.855567\pi$
$401$	−2.21831	−	21.1058i	−0.110777	−	1.05397i	0.788033	−	0.615633i	$-0.211100\pi$
$402$	1.01425	+	0.451571i	0.0505860	+	0.0225223i
$403$	−2.40552	+	2.67160i	−0.119828	+	0.133082i
$404$	−5.56362	−	6.17903i	−0.276801	−	0.307418i
$405$	−2.36719	−	1.71986i	−0.117626	−	0.0854607i
$406$	−12.0714	−	7.37900i	−0.599095	−	0.366214i
$407$	12.4237	−	1.70638i	0.615818	−	0.0845821i
$408$	0.762622	−	1.32090i	0.0377554	−	0.0653943i
$409$	−1.32947	+	12.6490i	−0.0657379	+	0.625455i	0.911205	+	0.411954i	$0.135153\pi$
$409$	−1.32947	+	12.6490i	−0.0657379	+	0.625455i	−0.976943	+	0.213501i	$0.931513\pi$
$410$	33.8210	−	7.18888i	1.67030	−	0.355034i
$411$	11.7778	+	2.50345i	0.580955	+	0.123486i
$412$	−8.21185	+	5.96626i	−0.404569	+	0.293936i
$413$	−15.3058	+	32.1810i	−0.753150	+	1.58352i
$414$	−0.460440	−	1.41709i	−0.0226294	−	0.0696461i
$415$	26.2177	+	29.1177i	1.28698	+	1.42933i
$416$	0.119944	−	1.14119i	0.00588074	−	0.0559515i
$417$	−7.67265	−	13.2894i	−0.375731	−	0.650786i
$418$	−21.8426	−	1.59612i	−1.06835	−	0.0780688i
$419$	17.5889			0.859273			0.429637	−	0.903002i	$-0.358642\pi$
$419$	17.5889			0.859273			0.429637	+	0.903002i	$0.358642\pi$
$420$	7.67637	+	1.00196i	0.374568	+	0.0488909i
$421$	−11.0434	+	33.9881i	−0.538223	+	1.65648i	0.198358	+	0.980130i	$0.436439\pi$
$421$	−11.0434	+	33.9881i	−0.538223	+	1.65648i	−0.736581	+	0.676350i	$0.763561\pi$
$422$	−14.0141	−	2.97878i	−0.682194	−	0.145005i
$423$	−0.749037	−	0.333493i	−0.0364194	−	0.0162150i
$424$	11.3203	+	5.04011i	0.549761	+	0.244770i
$425$	−5.31346	−	1.12941i	−0.257741	−	0.0547844i
$426$	1.70639	−	5.25171i	0.0826746	−	0.254446i
$427$	−10.7788	−	25.9410i	−0.521622	−	1.25537i
$428$	19.8560			0.959777
$429$	3.79563	+	0.277362i	0.183255	+	0.0133911i
$430$	−6.13994	−	10.6347i	−0.296094	−	0.512850i
$431$	−3.21022	+	30.5432i	−0.154631	+	1.47121i	0.591980	+	0.805952i	$0.298346\pi$
$431$	−3.21022	+	30.5432i	−0.154631	+	1.47121i	−0.746611	+	0.665261i	$0.768320\pi$
$432$	−0.669131	−	0.743145i	−0.0321936	−	0.0357546i
$433$	9.06549	+	27.9007i	0.435660	+	1.34082i	0.892409	+	0.451227i	$0.149014\pi$
$433$	9.06549	+	27.9007i	0.435660	+	1.34082i	−0.456750	+	0.889595i	$0.650986\pi$
$434$	−4.70251	−	6.82599i	−0.225728	−	0.327658i
$435$	12.6585	−	9.19694i	0.606929	−	0.440959i
$436$	−2.50048	−	0.531493i	−0.119751	−	0.0254539i
$437$	−9.62407	+	2.04566i	−0.460382	+	0.0978571i
$438$	0.981322	−	9.33665i	0.0468894	−	0.446122i
$439$	3.72017	−	6.44352i	0.177554	−	0.307532i	−0.763488	−	0.645822i	$-0.776515\pi$
$439$	3.72017	−	6.44352i	0.177554	−	0.307532i	0.941042	+	0.338289i	$0.109848\pi$
$440$	−9.61420	+	1.32050i	−0.458339	+	0.0629525i
$441$	3.79946	−	5.87912i	0.180927	−	0.279958i
$442$	1.41593	+	1.02873i	0.0673488	+	0.0489318i
$443$	24.9100	+	27.6654i	1.18351	+	1.31442i	0.938652	+	0.344865i	$0.112075\pi$
$443$	24.9100	+	27.6654i	1.18351	+	1.31442i	0.244860	+	0.969559i	$0.421258\pi$
$444$	2.53001	−	2.80986i	0.120069	−	0.133350i
$445$	−8.45878	−	3.76609i	−0.400985	−	0.178530i
$446$	1.04884	+	9.97902i	0.0496639	+	0.472520i
$447$	2.28151	+	7.02176i	0.107912	+	0.332118i
$448$	2.49497	+	0.880407i	0.117876	+	0.0415953i
$449$	−10.0582	−	7.30773i	−0.474677	−	0.344873i	0.324584	−	0.945857i	$-0.394776\pi$
$449$	−10.0582	−	7.30773i	−0.474677	−	0.344873i	−0.799261	+	0.600984i	$0.794776\pi$
$450$	−1.78075	+	3.08435i	−0.0839454	+	0.145398i
$451$	1.24516	+	39.1728i	0.0586321	+	1.84457i
$452$	3.84797	+	6.66489i	0.180993	+	0.313490i
$453$	−7.51250	+	3.34478i	−0.352968	+	0.157152i
$454$	1.31790	−	4.05608i	0.0618521	−	0.190361i
$455$	−2.06417	+	8.64003i	−0.0967697	+	0.405051i
$456$	−5.34222	+	3.88135i	−0.250172	+	0.181761i
$457$	−3.24113	−	30.8373i	−0.151614	−	1.44251i	−0.760544	−	0.649286i	$-0.775068\pi$
$457$	−3.24113	−	30.8373i	−0.151614	−	1.44251i	0.608930	−	0.793224i	$-0.291599\pi$
$458$	−3.85582	+	4.28232i	−0.180171	+	0.200100i
$459$	1.49191	−	0.317116i	0.0696366	−	0.0148017i
$460$	−3.98287	+	1.77329i	−0.185702	+	0.0826799i
$461$	−33.2674			−1.54942			−0.774709	−	0.632318i	$-0.782104\pi$
$461$	−33.2674			−1.54942			−0.774709	+	0.632318i	$0.782104\pi$
$462$	−2.65561	+	8.36348i	−0.123550	+	0.389104i
$463$	14.9784			0.696104			0.348052	−	0.937475i	$-0.386843\pi$
$463$	14.9784			0.696104			0.348052	+	0.937475i	$0.386843\pi$
$464$	4.88517	−	2.17502i	0.226788	−	0.100973i
$465$	8.96672	−	1.90593i	0.415822	−	0.0883856i
$466$	16.2914	−	18.0934i	0.754685	−	0.838163i
$467$	3.10998	+	29.5894i	0.143912	+	1.36924i	0.793324	+	0.608799i	$0.208348\pi$
$467$	3.10998	+	29.5894i	0.143912	+	1.36924i	−0.649412	+	0.760437i	$0.724985\pi$
$468$	0.928329	−	0.674471i	0.0429120	−	0.0311774i
$469$	−2.13295	−	2.01961i	−0.0984903	−	0.0932567i
$470$	−0.741362	+	2.28168i	−0.0341965	+	0.105246i
$471$	−20.0844	+	8.94213i	−0.925438	+	0.412032i
$472$	−6.73447	−	11.6644i	−0.309979	−	0.536899i
$473$	13.0946	−	4.71968i	0.602092	−	0.217011i
$474$	−4.97923	+	8.62428i	−0.228704	+	0.396126i
$475$	19.0263	+	13.8234i	0.872987	+	0.634262i
$476$	−3.06565	+	2.62419i	−0.140514	+	0.120280i
$477$	3.82921	+	11.7851i	0.175328	+	0.539603i
$478$	−1.70423	−	16.2146i	−0.0779495	−	0.741640i
$479$	2.85660	+	1.27184i	0.130521	+	0.0581118i	0.470958	−	0.882156i	$-0.343908\pi$
$479$	2.85660	+	1.27184i	0.130521	+	0.0581118i	−0.340437	+	0.940267i	$0.610575\pi$
$480$	−1.95788	+	2.17445i	−0.0893646	+	0.0992494i
$481$	2.90313	+	3.22425i	0.132371	+	0.147013i
$482$	16.1712	+	11.7491i	0.736577	+	0.535155i
$483$	−0.0988303	+	3.94097i	−0.00449694	+	0.179320i
$484$	0.452728	−	10.9907i	0.0205785	−	0.499576i
$485$	−12.5939	+	21.8133i	−0.571860	+	0.990490i
$486$	0.104528	−	0.994522i	0.00474151	−	0.0451124i
$487$	18.6235	−	3.95855i	0.843911	−	0.179379i	0.234384	−	0.972144i	$-0.424693\pi$
$487$	18.6235	−	3.95855i	0.843911	−	0.179379i	0.609527	+	0.792765i	$0.291359\pi$
$488$	10.3855	+	2.20750i	0.470128	+	0.0999289i
$489$	6.14755	−	4.46646i	0.278002	−	0.201980i
$490$	−18.2702	−	9.25820i	−0.825362	−	0.418243i
$491$	3.32782	+	10.2420i	0.150183	+	0.462215i	0.997641	−	0.0686473i	$-0.0218683\pi$
$491$	3.32782	+	10.2420i	0.150183	+	0.462215i	−0.847458	+	0.530862i	$0.821868\pi$
$492$	7.90712	+	8.78174i	0.356480	+	0.395912i
$493$	−0.852557	+	8.11154i	−0.0383972	+	0.365325i
$494$	−3.78859	−	6.56204i	−0.170457	−	0.295240i
$495$	−7.41448	−	6.26115i	−0.333256	−	0.281418i
$496$	3.13295			0.140674
$497$	−8.88103	+	11.6006i	−0.398369	+	0.520356i
$498$	−4.13801	+	12.7355i	−0.185429	+	0.570690i
$499$	−31.3660	−	6.66706i	−1.40414	−	0.298458i	−0.557300	−	0.830311i	$-0.688163\pi$
$499$	−31.3660	−	6.66706i	−1.40414	−	0.298458i	−0.846837	+	0.531853i	$0.821496\pi$
$500$	−3.84516	−	1.71197i	−0.171961	−	0.0765618i
$501$	−13.5756	−	6.04427i	−0.606515	−	0.270038i
$502$	−3.25180	−	0.691191i	−0.145135	−	0.0308494i
$503$	−11.1920	+	34.4454i	−0.499027	+	1.53585i	0.311560	+	0.950227i	$0.399149\pi$
$503$	−11.1920	+	34.4454i	−0.499027	+	1.53585i	−0.810586	+	0.585619i	$0.800851\pi$
$504$	1.01519	+	2.44323i	0.0452202	+	0.108830i
$505$	−24.3289			−1.08262
$506$	−1.18051	−	4.79875i	−0.0524803	−	0.213330i
$507$	−5.84165	−	10.1180i	−0.259437	−	0.449357i
$508$	−0.812986	+	7.73505i	−0.0360704	+	0.343187i
$509$	−9.70247	−	10.7757i	−0.430055	−	0.477624i	0.488701	−	0.872451i	$-0.337471\pi$
$509$	−9.70247	−	10.7757i	−0.430055	−	0.477624i	−0.918755	+	0.394828i	$0.870804\pi$
$510$	−1.37910	−	4.24444i	−0.0610677	−	0.187947i
$511$	−10.6684	+	22.4307i	−0.471943	+	0.992276i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−6.45904	−	1.37291i	−0.285174	−	0.0606155i
$514$	−15.3638	+	3.26567i	−0.677667	+	0.144042i
$515$	−3.10451	+	29.5374i	−0.136801	+	1.30157i
$516$	2.09840	−	3.63454i	0.0923770	−	0.160002i
$517$	−2.39706	−	1.28418i	−0.105422	−	0.0564782i
$518$	−8.78612	+	4.78308i	−0.386040	+	0.210157i
$519$	12.3076	+	8.94203i	0.540246	+	0.392511i
$520$	−2.24662	−	2.49513i	−0.0985209	−	0.109419i
$521$	−15.5172	+	17.2336i	−0.679819	+	0.755016i	−0.980028	−	0.198858i	$-0.936277\pi$
$521$	−15.5172	+	17.2336i	−0.679819	+	0.755016i	0.300209	+	0.953873i	$0.402944\pi$
$522$	4.88517	+	2.17502i	0.213818	+	0.0951979i
$523$	0.463907	+	4.41378i	0.0202852	+	0.193001i	0.999972	−	0.00753469i	$-0.00239839\pi$
$523$	0.463907	+	4.41378i	0.0202852	+	0.193001i	−0.979686	+	0.200536i	$0.935732\pi$
$524$	−2.28976	−	7.04716i	−0.100029	−	0.307857i
$525$	7.15841	−	6.12759i	0.312419	−	0.267430i
$526$	2.01210	+	1.46188i	0.0877318	+	0.0637409i
$527$	−2.38926	+	4.13832i	−0.104078	+	0.180268i
$528$	−2.03372	−	2.61992i	−0.0885065	−	0.114017i
$529$	10.3899	+	17.9959i	0.451736	+	0.782430i
$530$	33.1232	−	14.7474i	1.43878	−	0.640586i
$531$	4.16213	−	12.8097i	0.180621	−	0.555894i
$532$	16.7458	−	4.98052i	0.726024	−	0.215933i
$533$	−10.9701	+	7.97022i	−0.475166	+	0.345229i
$534$	−0.330778	−	3.14715i	−0.0143142	−	0.136190i
$535$	38.8757	−	43.1758i	1.68074	−	1.86665i
$536$	1.08597	−	0.230830i	0.0469067	−	0.00997033i
$537$	−7.39522	+	3.29256i	−0.319127	+	0.142085i
$538$	1.81466			0.0782357
$539$	13.9889	−	18.5286i	0.602546	−	0.798084i
$540$	−2.92600			−0.125915
$541$	−18.5181	+	8.24479i	−0.796155	+	0.354471i	−0.764168	−	0.645017i	$-0.776850\pi$
$541$	−18.5181	+	8.24479i	−0.796155	+	0.354471i	−0.0319871	+	0.999488i	$0.510184\pi$
$542$	24.2486	−	5.15420i	1.04157	−	0.221392i
$543$	2.08066	−	2.31080i	0.0892896	−	0.0991661i
$544$	−0.159431	−	1.51689i	−0.00683557	−	0.0650361i
$545$	−6.05133	+	4.39655i	−0.259211	+	0.188328i
$546$	−2.90996	+	0.865477i	−0.124535	+	0.0370390i
$547$	−5.53350	+	17.0304i	−0.236595	+	0.728165i	0.760311	+	0.649560i	$0.225047\pi$
$547$	−5.53350	+	17.0304i	−0.236595	+	0.728165i	−0.996906	+	0.0786056i	$0.974953\pi$
$548$	10.9999	−	4.89748i	0.469893	−	0.209210i
$549$	5.30875	+	9.19502i	0.226572	+	0.392434i
$550$	−6.63591	+	9.77200i	−0.282956	+	0.416680i
$551$	17.6556	−	30.5805i	0.752155	−	1.30277i
$552$	−1.20545	−	0.875809i	−0.0513072	−	0.0372769i
$553$	20.0159	−	17.1336i	0.851164	−	0.728594i
$554$	−1.47786	−	4.54837i	−0.0627881	−	0.193242i
$555$	−1.15643	−	11.0027i	−0.0490879	−	0.467040i
$556$	−14.0186	−	6.24150i	−0.594523	−	0.264698i
$557$	−8.73077	+	9.69650i	−0.369935	+	0.410854i	−0.899155	−	0.437630i	$-0.855818\pi$
$557$	−8.73077	+	9.69650i	−0.369935	+	0.410854i	0.529220	+	0.848484i	$0.322484\pi$
$558$	2.09636	+	2.32824i	0.0887458	+	0.0985622i
$559$	3.89602	+	2.83062i	0.164784	+	0.119723i
$560$	6.79925	−	3.70145i	0.287321	−	0.156415i
$561$	5.01161	−	0.688341i	0.211590	−	0.0290618i
$562$	8.74782	−	15.1517i	0.369005	−	0.639135i
$563$	−1.21336	+	11.5443i	−0.0511370	+	0.486536i	0.938742	+	0.344621i	$0.111993\pi$
$563$	−1.21336	+	11.5443i	−0.0511370	+	0.486536i	−0.989879	+	0.141915i	$0.954674\pi$
$564$	−0.802005	+	0.170472i	−0.0337705	+	0.00717815i
$565$	22.0263	+	4.68183i	0.926653	+	0.196966i
$566$	−22.8901	+	16.6307i	−0.962144	+	0.699039i
$567$	−1.13638	+	2.38928i	−0.0477235	+	0.100340i
$568$	−1.70639	−	5.25171i	−0.0715983	−	0.220357i
$569$	−17.9961	−	19.9867i	−0.754436	−	0.837886i	0.236582	−	0.971612i	$-0.423973\pi$
$569$	−17.9961	−	19.9867i	−0.754436	−	0.837886i	−0.991018	+	0.133725i	$0.957306\pi$
$570$	−2.01964	+	19.2156i	−0.0845933	+	0.804851i
$571$	−23.1911	−	40.1681i	−0.970517	−	1.68098i	−0.694000	−	0.719975i	$-0.744153\pi$
$571$	−23.1911	−	40.1681i	−0.970517	−	1.68098i	−0.276516	−	0.961009i	$-0.589180\pi$
$572$	3.23376	−	2.00663i	0.135210	−	0.0839013i
$573$	−19.1563			−0.800266
$574$	−11.9965	−	28.8717i	−0.500725	−	1.20508i
$575$	−1.63986	+	5.04696i	−0.0683868	+	0.210473i
$576$	−0.978148	−	0.207912i	−0.0407562	−	0.00866299i
$577$	26.1462	+	11.6410i	1.08848	+	0.484622i	0.870920	−	0.491425i	$-0.163524\pi$
$577$	26.1462	+	11.6410i	1.08848	+	0.484622i	0.217559	+	0.976047i	$0.430191\pi$
$578$	−13.4050	−	5.96830i	−0.557576	−	0.248249i
$579$	−20.3643	−	4.32856i	−0.846310	−	0.179889i
$580$	4.83512	−	14.8810i	0.200767	−	0.617898i
$581$	21.5366	−	28.1315i	0.893489	−	1.16709i
$582$	−8.60826			−0.356824
$583$	9.81766	+	39.9084i	0.406606	+	1.65284i
$584$	−4.69404	−	8.13032i	−0.194241	−	0.336435i
$585$	0.350957	−	3.33913i	0.0145103	−	0.138056i
$586$	9.04373	+	10.0441i	0.373593	+	0.414917i
$587$	−2.74496	−	8.44812i	−0.113297	−	0.348691i	0.878291	−	0.478126i	$-0.158684\pi$
$587$	−2.74496	−	8.44812i	−0.113297	−	0.348691i	−0.991588	+	0.129435i	$0.958684\pi$
$588$	−0.381835	−	6.98958i	−0.0157466	−	0.288245i
$589$	16.7369	−	12.1601i	0.689633	−	0.501047i
$590$	−38.5490	−	8.19383i	−1.58704	−	0.337335i
$591$	5.30750	−	1.12814i	0.218322	−	0.0464057i
$592$	0.395226	−	3.76033i	0.0162437	−	0.154548i
$593$	−1.50460	+	2.60604i	−0.0617863	+	0.107017i	−0.895264	−	0.445536i	$-0.853013\pi$
$593$	−1.50460	+	2.60604i	−0.0617863	+	0.107017i	0.833478	+	0.552553i	$0.186346\pi$
$594$	0.586150	−	3.26442i	0.0240500	−	0.133941i
$595$	−0.296015	+	11.8039i	−0.0121354	+	0.483914i
$596$	5.97307	+	4.33969i	0.244666	+	0.177761i
$597$	−6.21350	−	6.90079i	−0.254301	−	0.282430i
$598$	1.14405	−	1.27060i	0.0467838	−	0.0519586i
$599$	−27.0999	−	12.0657i	−1.10727	−	0.492989i	−0.230101	−	0.973167i	$-0.573906\pi$
$599$	−27.0999	−	12.0657i	−1.10727	−	0.492989i	−0.877171	+	0.480177i	$0.840572\pi$
$600$	0.372279	+	3.54199i	0.0151982	+	0.144601i
$601$	−7.97445	−	24.5428i	−0.325285	−	1.00112i	−0.971312	−	0.237809i	$-0.923571\pi$
$601$	−7.97445	−	24.5428i	−0.325285	−	1.00112i	0.646027	−	0.763314i	$-0.276429\pi$
$602$	−8.43533	+	7.22062i	−0.343798	+	0.294291i
$603$	0.898195	+	0.652577i	0.0365773	+	0.0265750i
$604$	−4.11173	+	7.12173i	−0.167304	+	0.289779i
$605$	−23.0122	−	22.5029i	−0.935581	−	0.914871i
$606$	−4.15735	−	7.20074i	−0.168881	−	0.292510i
$607$	−13.6714	+	6.08690i	−0.554905	+	0.247059i	−0.664977	−	0.746864i	$-0.731559\pi$
$607$	−13.6714	+	6.08690i	−0.554905	+	0.247059i	0.110072	+	0.993924i	$0.464892\pi$
$608$	−2.04054	+	6.28015i	−0.0827550	+	0.254694i
$609$	−10.2735	−	9.72755i	−0.416302	−	0.394180i
$610$	25.1336	−	18.2606i	1.01763	−	0.739351i
$611$	−0.0983449	−	0.935689i	−0.00397861	−	0.0378539i
$612$	1.02059	−	1.13348i	0.0412548	−	0.0458181i
$613$	−23.0825	+	4.90633i	−0.932293	+	0.198165i	−0.648930	−	0.760848i	$-0.724783\pi$
$613$	−23.0825	+	4.90633i	−0.932293	+	0.198165i	−0.283363	+	0.959013i	$0.591450\pi$
$614$	8.70248	−	3.87459i	0.351203	−	0.156366i
$615$	34.5766			1.39426
$616$	2.76749	+	8.32712i	0.111505	+	0.335509i
$617$	43.2502			1.74119			0.870595	−	0.492001i	$-0.163734\pi$
$617$	43.2502			1.74119			0.870595	+	0.492001i	$0.163734\pi$
$618$	−9.27286	+	4.12854i	−0.373009	+	0.166074i
$619$	17.5182	−	3.72361i	0.704116	−	0.149665i	0.158080	−	0.987426i	$-0.449469\pi$
$619$	17.5182	−	3.72361i	0.704116	−	0.149665i	0.546036	+	0.837762i	$0.316136\pi$
$620$	6.13395	−	6.81244i	0.246345	−	0.273594i
$621$	−0.155749	−	1.48185i	−0.00624999	−	0.0594647i
$622$	10.7536	−	7.81295i	0.431180	−	0.313271i
$623$	−1.94549	+	8.14326i	−0.0779443	+	0.326253i
$624$	0.354590	−	1.09132i	0.0141950	−	0.0436876i
$625$	−27.5189	+	12.2522i	−1.10076	+	0.490089i
$626$	14.9336	+	25.8658i	0.596868	+	1.03381i
$627$	−21.0334	−	6.10257i	−0.839993	−	0.243713i
$628$	−10.9925	+	19.0396i	−0.438650	+	0.759764i
$629$	4.66561	+	3.38976i	0.186030	+	0.135159i
$630$	7.30030	+	2.57608i	0.290851	+	0.102633i
$631$	−3.77694	−	11.6242i	−0.150358	−	0.462753i	0.847303	−	0.531109i	$-0.178225\pi$
$631$	−3.77694	−	11.6242i	−0.150358	−	0.462753i	−0.997661	+	0.0683561i	$0.978225\pi$
$632$	1.04094	+	9.90391i	0.0414065	+	0.393956i
$633$	−13.0885	−	5.82738i	−0.520221	−	0.231617i
$634$	7.70903	−	8.56174i	0.306165	−	0.340030i
$635$	15.2277	+	16.9121i	0.604293	+	0.671136i
$636$	10.0250	+	7.28359i	0.397517	+	0.288813i
$637$	8.02225	+	0.402612i	0.317853	+	0.0159521i
$638$	15.6335	+	8.37535i	0.618935	+	0.331583i
$639$	2.76099	−	4.78217i	0.109223	−	0.189180i
$640$	−0.305851	+	2.90998i	−0.0120898	+	0.115027i
$641$	9.38697	−	1.99526i	0.370763	−	0.0788081i	−0.0187621	−	0.999824i	$-0.505973\pi$
$641$	9.38697	−	1.99526i	0.370763	−	0.0788081i	0.389525	+	0.921016i	$0.372639\pi$
$642$	19.4221	+	4.12830i	0.766530	+	0.162931i
$643$	18.9801	−	13.7898i	0.748501	−	0.543818i	−0.146861	−	0.989157i	$-0.546917\pi$
$643$	18.9801	−	13.7898i	0.748501	−	0.543818i	0.895362	+	0.445339i	$0.146917\pi$
$644$	2.23649	+	3.24640i	0.0881300	+	0.127926i
$645$	−3.79469	−	11.6789i	−0.149416	−	0.459854i
$646$	−6.73929	−	7.48474i	−0.265154	−	0.294483i
$647$	−3.01037	+	28.6417i	−0.118350	+	1.12602i	0.760637	+	0.649177i	$0.224887\pi$
$647$	−3.01037	+	28.6417i	−0.118350	+	1.12602i	−0.878987	+	0.476846i	$0.841780\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	16.8638	−	41.3660i	0.661962	−	1.62376i
$650$	−4.08675			−0.160295
$651$	−3.18055	−	7.65454i	−0.124656	−	0.300005i
$652$	2.34815	−	7.22688i	0.0919608	−	0.283026i
$653$	−26.3056	−	5.59142i	−1.02942	−	0.218809i	−0.337909	−	0.941179i	$-0.609720\pi$
$653$	−26.3056	−	5.59142i	−1.02942	−	0.218809i	−0.691507	+	0.722370i	$0.743053\pi$
$654$	−2.33533	−	1.03976i	−0.0913187	−	0.0406577i
$655$	−19.8068	−	8.81853i	−0.773914	−	0.344569i
$656$	11.5588	+	2.45689i	0.451294	+	0.0959256i
$657$	2.90108	−	8.92859i	0.113182	−	0.348338i
$658$	2.15107	+	0.280770i	0.0838572	+	0.0109455i
$659$	15.1694			0.590914			0.295457	−	0.955356i	$-0.404528\pi$
$659$	15.1694			0.590914			0.295457	+	0.955356i	$0.404528\pi$
$660$	−9.67865	−	0.707257i	−0.376741	−	0.0275299i
$661$	−1.61796	−	2.80238i	−0.0629312	−	0.109000i	0.832843	−	0.553509i	$-0.186712\pi$
$661$	−1.61796	−	2.80238i	−0.0629312	−	0.109000i	−0.895774	+	0.444509i	$0.853378\pi$
$662$	−2.08627	+	19.8495i	−0.0810851	+	0.771474i
$663$	1.17110	+	1.30064i	0.0454818	+	0.0505127i
$664$	4.13801	+	12.7355i	0.160586	+	0.494232i
$665$	21.9565	−	46.1642i	0.851435	−	1.79017i
$666$	3.05893	−	2.22244i	0.118531	−	0.0861178i
$667$	7.79371	+	1.65660i	0.301774	+	0.0641440i
$668$	−14.5357	+	3.08965i	−0.562401	+	0.119542i
$669$	−1.04884	+	9.97902i	−0.0405504	+	0.385811i
$670$	1.62427	−	2.81332i	0.0627510	−	0.108688i
$671$	15.3377	+	31.6985i	0.592107	+	1.22371i
$672$	2.25740	+	1.37990i	0.0870812	+	0.0532309i
$673$	31.7876	+	23.0950i	1.22532	+	0.890247i	0.996530	−	0.0832285i	$-0.0265231\pi$
$673$	31.7876	+	23.0950i	1.22532	+	0.890247i	0.228790	+	0.973476i	$0.426523\pi$
$674$	7.00593	+	7.78088i	0.269859	+	0.299708i
$675$	−2.38311	+	2.64671i	−0.0917260	+	0.101872i
$676$	−10.6732	−	4.75202i	−0.410508	−	0.182770i
$677$	−2.46804	−	23.4818i	−0.0948543	−	0.902479i	−0.933687	−	0.358090i	$-0.883428\pi$
$677$	−2.46804	−	23.4818i	−0.0948543	−	0.902479i	0.838833	−	0.544389i	$-0.183238\pi$
$678$	2.37818	+	7.31928i	0.0913334	+	0.281095i
$679$	21.4774	+	7.57877i	0.824225	+	0.290847i
$680$	−3.61054	−	2.62321i	−0.138458	−	0.100596i
$681$	2.13241	−	3.69344i	0.0817140	−	0.141533i
$682$	6.37157	+	8.20808i	0.243980	+	0.314304i
$683$	−14.6635	−	25.3980i	−0.561085	−	0.971828i	−0.997402	−	0.0720349i	$-0.977051\pi$
$683$	−14.6635	−	25.3980i	−0.561085	−	0.971828i	0.436317	−	0.899793i	$-0.356283\pi$
$684$	−6.03245	+	2.68582i	−0.230657	+	0.102695i
$685$	10.8872	−	33.5074i	0.415979	−	1.28025i
$686$	−5.20101	+	17.7750i	−0.198575	+	0.678651i
$687$	−4.66191	+	3.38707i	−0.177863	+	0.129225i
$688$	−0.438686	−	4.17381i	−0.0167247	−	0.159125i
$689$	−9.51442	+	10.5668i	−0.362470	+	0.402564i
$690$	−4.26452	+	0.906451i	−0.162347	+	0.0345080i
$691$	25.0175	−	11.1385i	0.951711	−	0.423729i	0.128655	−	0.991689i	$-0.458934\pi$
$691$	25.0175	−	11.1385i	0.951711	−	0.423729i	0.823056	+	0.567960i	$0.192267\pi$
$692$	15.2131			0.578315
$693$	−4.33644	+	7.62858i	−0.164728	+	0.289786i
$694$	−1.58917			−0.0603241
$695$	−41.0186	+	18.2627i	−1.55592	+	0.692742i
$696$	5.23063	−	1.11180i	0.198266	−	0.0421428i
$697$	−12.0603	+	13.3943i	−0.456816	+	0.507345i
$698$	−0.187829	−	1.78708i	−0.00710944	−	0.0676418i
$699$	19.6972	−	14.3109i	0.745018	−	0.541287i
$700$	2.18957	−	9.16493i	0.0827581	−	0.346402i
$701$	6.60359	−	20.3237i	0.249414	−	0.767617i	−0.745465	−	0.666545i	$-0.767773\pi$
$701$	6.60359	−	20.3237i	0.249414	−	0.767617i	0.994879	−	0.101073i	$-0.0322275\pi$
$702$	1.04827	−	0.466721i	0.0395645	−	0.0176153i
$703$	−12.4837	−	21.6225i	−0.470833	−	0.815507i
$704$	−3.18527	−	0.924163i	−0.120049	−	0.0348307i
$705$	−1.19955	+	2.07768i	−0.0451776	+	0.0782499i
$706$	−4.70145	−	3.41581i	−0.176942	−	0.128556i
$707$	4.03289	+	21.6258i	0.151672	+	0.813322i
$708$	−4.16213	−	12.8097i	−0.156422	−	0.481419i
$709$	−3.41048	−	32.4485i	−0.128083	−	1.21863i	−0.850050	−	0.526702i	$-0.823428\pi$
$709$	−3.41048	−	32.4485i	−0.128083	−	1.21863i	0.721967	−	0.691928i	$-0.243238\pi$
$710$	−14.7605	−	6.57178i	−0.553950	−	0.246635i
$711$	−6.66351	+	7.40058i	−0.249901	+	0.277543i
$712$	−2.11745	−	2.35167i	−0.0793548	−	0.0881325i
$713$	3.77661	+	2.74387i	0.141435	+	0.102759i
$714$	−3.54426	+	1.92946i	−0.132641	+	0.0722083i
$715$	1.96801	−	10.9604i	0.0735995	−	0.409895i
$716$	−4.04754	+	7.01054i	−0.151264	+	0.261996i
$717$	1.70423	−	16.2146i	0.0636455	−	0.605546i
$718$	−19.5358	+	4.15247i	−0.729071	+	0.154969i
$719$	2.82101	+	0.599624i	0.105206	+	0.0223622i	0.260214	−	0.965551i	$-0.416207\pi$
$719$	2.82101	+	0.599624i	0.105206	+	0.0223622i	−0.155008	+	0.987913i	$0.549540\pi$
$720$	−2.36719	+	1.71986i	−0.0882199	+	0.0640955i
$721$	26.7703	−	2.13670i	0.996978	−	0.0795750i
$722$	7.60309	+	23.3999i	0.282958	+	0.870854i
$723$	13.3750	+	14.8545i	0.497423	+	0.552444i
$724$	0.325031	−	3.09246i	0.0120797	−	0.114930i
$725$	−9.52254	−	16.4935i	−0.353658	−	0.612554i
$726$	2.72793	−	10.6564i	0.101243	−	0.395495i
$727$	0.0274808			0.00101921			0.000509604	−	1.00000i	$-0.499838\pi$
$727$	0.0274808			0.00101921			0.000509604		1.00000i	$0.499838\pi$
$728$	−1.84550	+	2.41062i	−0.0683986	+	0.0893435i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−26.8693	−	5.71124i	−0.994477	−	0.211383i
$731$	5.84774	+	2.60358i	0.216287	+	0.0962970i
$732$	9.69956	+	4.31852i	0.358506	+	0.159617i
$733$	42.9811	+	9.13591i	1.58754	+	0.337443i	0.915264	−	0.402855i	$-0.131982\pi$
$733$	42.9811	+	9.13591i	1.58754	+	0.337443i	0.672279	+	0.740298i	$0.265316\pi$
$734$	8.65541	−	26.6386i	0.319477	−	0.983249i
$735$	−15.9460	−	12.8545i	−0.588179	−	0.474144i
$736$	−1.49001			−0.0549227
$737$	2.81332	+	2.37570i	0.103630	+	0.0875101i
$738$	5.90850	+	10.2338i	0.217495	+	0.376712i
$739$	3.95276	−	37.6080i	0.145405	−	1.38343i	−0.641862	−	0.766820i	$-0.721838\pi$
$739$	3.95276	−	37.6080i	0.145405	−	1.38343i	0.787267	−	0.616612i	$-0.211495\pi$
$740$	−7.40282	−	8.22166i	−0.272133	−	0.302234i
$741$	−2.34148	−	7.20633i	−0.0860164	−	0.264731i
$742$	−18.5996	−	26.9985i	−0.682812	−	0.991144i
$743$	24.6493	−	17.9088i	0.904295	−	0.657009i	−0.0352708	−	0.999378i	$-0.511229\pi$
$743$	24.6493	−	17.9088i	0.904295	−	0.657009i	0.939565	+	0.342369i	$0.111229\pi$
$744$	3.06449	+	0.651378i	0.112350	+	0.0238807i
$745$	21.1310	−	4.49152i	0.774178	−	0.164557i
$746$	0.621614	−	5.91426i	0.0227589	−	0.216537i
$747$	−6.69544	+	11.5968i	−0.244973	+	0.424306i
$748$	3.64988	−	3.50263i	0.133453	−	0.128069i
$749$	−44.8231	−	27.3994i	−1.63780	−	1.00115i
$750$	−3.40519	−	2.47402i	−0.124340	−	0.0903383i
$751$	−33.2451	−	36.9224i	−1.21313	−	1.34732i	−0.920330	−	0.391143i	$-0.872080\pi$
$751$	−33.2451	−	36.9224i	−1.21313	−	1.34732i	−0.292799	−	0.956174i	$-0.594587\pi$
$752$	−0.548635	+	0.609321i	−0.0200067	+	0.0222197i
$753$	−3.03703	−	1.35217i	−0.110676	−	0.0492760i
$754$	0.641399	+	6.10251i	0.0233584	+	0.222240i
$755$	7.43553	+	22.8842i	0.270607	+	0.832842i
$756$	0.485031	+	2.60091i	0.0176404	+	0.0945943i
$757$	−33.1432	−	24.0799i	−1.20461	−	0.875200i	−0.209880	−	0.977727i	$-0.567307\pi$
$757$	−33.1432	−	24.0799i	−1.20461	−	0.875200i	−0.994730	+	0.102527i	$0.967307\pi$
$758$	−11.1059	+	19.2360i	−0.403384	+	0.698681i
$759$	−0.157003	−	4.93932i	−0.00569883	−	0.179286i
$760$	9.66070	+	16.7328i	0.350431	+	0.606964i
$761$	−20.0992	+	8.94875i	−0.728596	+	0.324392i	−0.737296	−	0.675570i	$-0.763898\pi$
$761$	−20.0992	+	8.94875i	−0.728596	+	0.324392i	0.00869926	+	0.999962i	$0.497231\pi$
$762$	−2.40343	+	7.39699i	−0.0870670	+	0.267965i
$763$	4.91118	+	4.65021i	0.177797	+	0.168349i
$764$	−15.4978	+	11.2598i	−0.560690	+	0.407365i
$765$	−0.466497	−	4.43842i	−0.0168662	−	0.160472i
$766$	5.08439	−	5.64679i	0.183707	−	0.204027i
$767$	15.1176	−	3.21334i	0.545864	−	0.116027i
$768$	−0.913545	+	0.406737i	−0.0329647	+	0.0146768i
$769$	−39.4988			−1.42436			−0.712182	−	0.701994i	$-0.752293\pi$
$769$	−39.4988			−1.42436			−0.712182	+	0.701994i	$0.752293\pi$
$770$	23.5253	+	10.2857i	0.847793	+	0.370672i
$771$	−15.7070			−0.565674
$772$	−19.0193	+	8.46793i	−0.684519	+	0.304768i
$773$	4.44285	−	0.944358i	0.159798	−	0.0339662i	−0.127318	−	0.991862i	$-0.540637\pi$
$773$	4.44285	−	0.944358i	0.159798	−	0.0339662i	0.287116	+	0.957896i	$0.407303\pi$
$774$	2.80821	−	3.11883i	0.100939	−	0.112104i
$775$	−1.16633	−	11.0969i	−0.0418959	−	0.398613i
$776$	−6.96423	+	5.05981i	−0.250001	+	0.181636i
$777$	−9.58858	+	2.85182i	−0.343989	+	0.102309i
$778$	7.31525	−	22.5140i	0.262265	−	0.807167i
$779$	71.2855	−	31.7384i	2.55407	−	1.13714i
$780$	−1.67876	−	2.90770i	−0.0601093	−	0.104112i
$781$	10.2887	−	15.1511i	0.368160	−	0.542150i
$782$	1.13632	−	1.96816i	0.0406346	−	0.0703813i
$783$	4.32621	+	3.14317i	0.154606	+	0.112328i
$784$	−4.41728	−	5.43025i	−0.157760	−	0.193938i
$785$	19.8786	+	61.1799i	0.709496	+	2.18361i
$786$	−0.774538	−	7.36924i	−0.0276269	−	0.262852i
$787$	−22.6218	−	10.0719i	−0.806381	−	0.359024i	−0.0382106	−	0.999270i	$-0.512166\pi$
$787$	−22.6218	−	10.0719i	−0.806381	−	0.359024i	−0.768170	+	0.640246i	$0.778832\pi$
$788$	3.63075	−	4.03236i	0.129340	−	0.143647i
$789$	1.66419	+	1.84827i	0.0592467	+	0.0658002i
$790$	23.5736	+	17.1272i	0.838709	+	0.609358i
$791$	0.510460	−	20.3552i	0.0181499	−	0.723746i
$792$	−1.44457	−	2.98550i	−0.0513306	−	0.106085i
$793$	−6.09167	+	10.5511i	−0.216321	+	0.374680i
$794$	1.79854	−	17.1120i	0.0638279	−	0.607282i
$795$	35.4655	−	7.53843i	1.25783	−	0.267361i
$796$	−9.08301	−	1.93065i	−0.321939	−	0.0684302i
$797$	0.563517	−	0.409419i	0.0199608	−	0.0145024i	−0.577760	−	0.816207i	$-0.696073\pi$
$797$	0.563517	−	0.409419i	0.0199608	−	0.0145024i	0.597721	+	0.801704i	$0.296073\pi$
$798$	17.4154	−	1.39003i	0.616499	−	0.0492066i
$799$	−0.386451	−	1.18937i	−0.0136717	−	0.0420770i
$800$	2.38311	+	2.64671i	0.0842557	+	0.0935754i
$801$	0.330778	−	3.14715i	0.0116875	−	0.111199i
$802$	−10.6110	−	18.3788i	−0.374688	−	0.648979i
$803$	11.7544	−	28.8328i	0.414802	−	1.01749i
$804$	1.11023			0.0391548
$805$	11.4379	+	1.49294i	0.403133	+	0.0526193i
$806$	−1.11091	+	3.41904i	−0.0391303	+	0.120431i
$807$	1.77501	+	0.377290i	0.0624833	+	0.0132812i
$808$	−7.59586	−	3.38189i	−0.267221	−	0.118975i
$809$	37.8748	+	16.8629i	1.33161	+	0.592869i	0.944301	−	0.329083i	$-0.106739\pi$
$809$	37.8748	+	16.8629i	1.33161	+	0.592869i	0.387305	+	0.921952i	$0.373406\pi$
$810$	−2.86206	−	0.608351i	−0.100563	−	0.0213753i
$811$	−15.8140	+	48.6704i	−0.555304	+	1.70905i	0.139834	+	0.990175i	$0.455343\pi$
$811$	−15.8140	+	48.6704i	−0.555304	+	1.70905i	−0.695139	+	0.718876i	$0.744657\pi$
$812$	−14.0291	−	1.83116i	−0.492325	−	0.0642612i
$813$	24.7903			0.869435
$814$	10.6555	−	6.61201i	0.373476	−	0.231751i
$815$	−11.1170	−	19.2553i	−0.389413	−	0.674483i
$816$	0.159431	−	1.51689i	0.00558122	−	0.0531017i
$817$	−18.5436	−	20.5947i	−0.648757	−	0.720518i
$818$	3.93030	+	12.0962i	0.137420	+	0.422934i
$819$	−3.02632	+	0.241549i	−0.105748	+	0.00844041i
$820$	27.9731	−	20.3236i	0.976862	−	0.709732i
$821$	−1.01340	−	0.215405i	−0.0353679	−	0.00751769i	0.190194	−	0.981747i	$-0.439088\pi$
$821$	−1.01340	−	0.215405i	−0.0353679	−	0.00751769i	−0.225562	+	0.974229i	$0.572422\pi$
$822$	11.7778	−	2.50345i	0.410797	−	0.0873177i
$823$	4.92113	−	46.8214i	0.171540	−	1.63209i	−0.482687	−	0.875793i	$-0.660339\pi$
$823$	4.92113	−	46.8214i	0.171540	−	1.63209i	0.654227	−	0.756298i	$-0.272994\pi$
$824$	−5.07520	+	8.79051i	−0.176803	+	0.306232i
$825$	−8.52261	+	8.17878i	−0.296719	+	0.284749i
$826$	−0.893373	+	35.6243i	−0.0310844	+	1.23953i
$827$	−30.5206	−	22.1745i	−1.06130	−	0.771083i	−0.0869753	−	0.996210i	$-0.527720\pi$
$827$	−30.5206	−	22.1745i	−1.06130	−	0.771083i	−0.974329	+	0.225128i	$0.927720\pi$
$828$	−0.997014	−	1.10730i	−0.0346486	−	0.0384812i
$829$	−17.8014	+	19.7704i	−0.618267	+	0.686655i	−0.968216	−	0.250114i	$-0.919532\pi$
$829$	−17.8014	+	19.7704i	−0.618267	+	0.686655i	0.349950	+	0.936769i	$0.386199\pi$
$830$	35.7943	+	15.9367i	1.24244	+	0.553169i
$831$	−0.499901	−	4.75624i	−0.0173414	−	0.164992i
$832$	−0.354590	−	1.09132i	−0.0122932	−	0.0378346i
$833$	10.5415	−	1.69356i	0.365243	−	0.0586783i
$834$	−12.4146	−	9.01974i	−0.429883	−	0.312328i
$835$	−21.7408	+	37.6561i	−0.752371	+	1.30314i
$836$	−20.6034	+	7.42604i	−0.712583	+	0.256835i
$837$	1.56648	+	2.71322i	0.0541454	+	0.0937825i
$838$	16.0682	−	7.15404i	0.555068	−	0.247132i
$839$	0.332153	−	1.02226i	0.0114672	−	0.0352924i	−0.945159	−	0.326610i	$-0.894094\pi$
$839$	0.332153	−	1.02226i	0.0114672	−	0.0352924i	0.956626	+	0.291318i	$0.0940936\pi$
$840$	7.42024	−	2.20692i	0.256023	−	0.0761459i
$841$	0.327176	−	0.237707i	0.0112819	−	0.00819680i
$842$	3.73556	+	35.5414i	0.128736	+	1.22484i
$843$	11.7069	−	13.0018i	0.403206	−	0.447806i
$844$	−14.0141	+	2.97878i	−0.482384	+	0.102534i
$845$	−31.2299	+	13.9044i	−1.07434	+	0.478327i
$846$	−0.819923			−0.0281895
$847$	−16.1880	+	24.1857i	−0.556228	+	0.831030i
$848$	12.3916			0.425529
$849$	−25.8476	+	11.5081i	−0.887089	+	0.394957i
$850$	−5.31346	+	1.12941i	−0.182250	+	0.0387384i
$851$	3.76975	−	4.18673i	0.129225	−	0.143519i
$852$	−0.577204	−	5.49173i	−0.0197747	−	0.188144i
$853$	−40.6836	+	29.5584i	−1.39298	+	1.01206i	−0.397451	+	0.917624i	$0.630105\pi$
$853$	−40.6836	+	29.5584i	−1.39298	+	1.01206i	−0.995531	+	0.0944367i	$0.969895\pi$
$854$	−20.3981	−	19.3142i	−0.698008	−	0.660917i
$855$	−5.97064	+	18.3758i	−0.204192	+	0.628437i
$856$	18.1394	−	8.07617i	0.619991	−	0.276038i
$857$	10.1365	+	17.5570i	0.346257	+	0.599735i	0.985581	−	0.169202i	$-0.0541191\pi$
$857$	10.1365	+	17.5570i	0.346257	+	0.599735i	−0.639324	+	0.768937i	$0.720786\pi$
$858$	3.58030	−	1.29044i	0.122229	−	0.0440549i
$859$	−15.0153	+	26.0072i	−0.512314	+	0.887354i	0.487584	+	0.873076i	$0.337878\pi$
$859$	−15.0153	+	26.0072i	−0.512314	+	0.887354i	−0.999898	+	0.0142782i	$0.995455\pi$
$860$	−9.93462	−	7.21793i	−0.338768	−	0.246129i
$861$	−5.73161	−	30.7350i	−0.195333	−	1.04745i
$862$	9.49035	+	29.2083i	0.323243	+	0.994839i
$863$	4.97454	+	47.3296i	0.169335	+	1.61112i	0.667890	+	0.744260i	$0.267198\pi$
$863$	4.97454	+	47.3296i	0.169335	+	1.61112i	−0.498554	+	0.866858i	$0.666136\pi$
$864$	−0.913545	−	0.406737i	−0.0310794	−	0.0138375i
$865$	29.7854	−	33.0800i	1.01273	−	1.12475i
$866$	19.6300	+	21.8013i	0.667054	+	0.740838i
$867$	−11.8712	−	8.62494i	−0.403168	−	0.292918i
$868$	−7.07234	−	4.32317i	−0.240051	−	0.146738i
$869$	−23.8304	+	22.8690i	−0.808392	+	0.775778i
$870$	7.82338	−	13.5505i	0.265237	−	0.459405i
$871$	−0.133165	+	1.26699i	−0.00451214	+	0.0429302i
$872$	−2.50048	+	0.531493i	−0.0846768	+	0.0179986i
$873$	−8.42015	−	1.78976i	−0.284979	−	0.0605741i
$874$	−7.95998	+	5.78326i	−0.269250	+	0.195622i
$875$	6.31771	+	9.17055i	0.213578	+	0.310021i
$876$	−2.90108	−	8.92859i	−0.0980183	−	0.301669i
$877$	−27.9706	−	31.0645i	−0.944499	−	1.04897i	−0.998727	−	0.0504438i	$-0.983936\pi$
$877$	−27.9706	−	31.0645i	−0.944499	−	1.04897i	0.0542279	−	0.998529i	$-0.482730\pi$
$878$	0.777727	−	7.39958i	0.0262470	−	0.249724i
$879$	6.75782	+	11.7049i	0.227936	+	0.394796i
$880$	−8.24591	+	5.11679i	−0.277970	+	0.172487i
$881$	17.3067			0.583079			0.291540	−	0.956559i	$-0.405832\pi$
$881$	17.3067			0.583079			0.291540	+	0.956559i	$0.405832\pi$
$882$	1.07972	−	6.91623i	0.0363562	−	0.232881i
$883$	−7.52678	+	23.1651i	−0.253296	+	0.779566i	0.740864	+	0.671655i	$0.234416\pi$
$883$	−7.52678	+	23.1651i	−0.253296	+	0.779566i	−0.994161	+	0.107911i	$0.965584\pi$
$884$	1.71194	+	0.363884i	0.0575787	+	0.0122387i
$885$	−36.0030	−	16.0296i	−1.21023	−	0.538828i
$886$	34.0090	+	15.1418i	1.14255	+	0.508698i
$887$	14.9232	+	3.17202i	0.501071	+	0.106506i	0.451511	−	0.892265i	$-0.350885\pi$
$887$	14.9232	+	3.17202i	0.501071	+	0.106506i	0.0495593	+	0.998771i	$0.484218\pi$
$888$	1.16841	−	3.59598i	0.0392091	−	0.120673i
$889$	12.5088	−	16.3393i	0.419533	−	0.548002i
$890$	−9.25929			−0.310372
$891$	1.25205	−	3.07122i	0.0419453	−	0.102890i
$892$	5.01699	+	8.68969i	0.167981	+	0.290952i
$893$	−0.565941	+	5.38457i	−0.0189385	+	0.180188i
$894$	4.94027	+	5.48673i	0.165227	+	0.183504i
$895$	7.31944	+	22.5269i	0.244662	+	0.752992i
$896$	2.63736	−	0.210504i	0.0881081	−	0.00703246i
$897$	1.38322	−	1.00497i	0.0461845	−	0.0335550i
$898$	−12.1610	−	2.58489i	−0.405817	−	0.0862590i
$899$	−16.3873	+	3.48323i	−0.546548	+	0.116172i
$900$	−0.372279	+	3.54199i	−0.0124093	+	0.118066i
$901$	−9.45010	+	16.3681i	−0.314828	+	0.545299i
$902$	17.0705	+	35.2797i	0.568386	+	1.17468i
$903$	−9.75225	+	5.30903i	−0.324535	+	0.176674i
$904$	6.22615	+	4.52356i	0.207079	+	0.150452i
$905$	−6.08801	−	6.76143i	−0.202372	−	0.224757i
$906$	−5.50257	+	6.11122i	−0.182811	+	0.203032i
$907$	−3.00782	−	1.33917i	−0.0998729	−	0.0444663i	0.356192	−	0.934413i	$-0.384075\pi$
$907$	−3.00782	−	1.33917i	−0.0998729	−	0.0444663i	−0.456065	+	0.889946i	$0.650742\pi$
$908$	−0.445794	−	4.24145i	−0.0147942	−	0.140757i
$909$	−2.56938	−	7.90775i	−0.0852211	−	0.262284i
$910$	1.62850	+	8.73263i	0.0539844	+	0.289484i
$911$	34.2584	+	24.8902i	1.13503	+	0.824649i	0.986419	−	0.164247i	$-0.0525194\pi$
$911$	34.2584	+	24.8902i	1.13503	+	0.824649i	0.148612	+	0.988896i	$0.452519\pi$
$912$	−3.30167	+	5.71866i	−0.109329	+	0.189364i
$913$	−24.9503	+	36.7417i	−0.825735	+	1.21597i
$914$	−15.5036	−	26.8530i	−0.512813	−	0.888219i
$915$	28.3810	−	12.6360i	0.938246	−	0.417734i
$916$	−1.78069	+	5.48040i	−0.0588357	+	0.181078i
$917$	−4.55548	+	19.0679i	−0.150435	+	0.629679i
$918$	1.23395	−	0.896516i	0.0407264	−	0.0295894i
$919$	2.60858	+	24.8190i	0.0860493	+	0.818704i	0.949394	+	0.314089i	$0.101699\pi$
$919$	2.60858	+	24.8190i	0.0860493	+	0.818704i	−0.863344	+	0.504615i	$0.831634\pi$
$920$	−2.91727	+	3.23996i	−0.0961795	+	0.106818i
$921$	9.31788	−	1.98058i	0.307035	−	0.0652622i
$922$	−30.3913	+	13.5311i	−1.00088	+	0.445622i
$923$	6.33635			0.208563
$924$	0.975710	+	8.72055i	0.0320985	+	0.286885i
$925$	−13.4662			−0.442765
$926$	13.6834	−	6.09225i	0.449665	−	0.200204i
$927$	−9.92859	+	2.11039i	−0.326098	+	0.0693142i
$928$	3.57817	−	3.97396i	0.117459	−	0.130451i
$929$	−3.70723	−	35.2719i	−0.121630	−	1.15723i	−0.869689	−	0.493601i	$-0.835680\pi$
$929$	−3.70723	−	35.2719i	−0.121630	−	1.15723i	0.748058	−	0.663633i	$-0.230986\pi$
$930$	7.41629	−	5.38825i	0.243190	−	0.176688i
$931$	−44.6748	−	11.8646i	−1.46416	−	0.388845i
$932$	7.52368	−	23.1555i	0.246446	−	0.758484i
$933$	12.1430	−	5.40642i	0.397545	−	0.176998i
$934$	14.8762	+	25.7664i	0.486765	+	0.843101i
$935$	−0.470252	−	14.7942i	−0.0153789	−	0.483822i
$936$	0.573739	−	0.993745i	0.0187532	−	0.0324816i
$937$	−4.64241	−	3.37291i	−0.151661	−	0.110188i	0.509367	−	0.860549i	$-0.329880\pi$
$937$	−4.64241	−	3.37291i	−0.151661	−	0.110188i	−0.661028	+	0.750361i	$0.729880\pi$
$938$	−2.76999	−	0.977454i	−0.0904434	−	0.0319150i
$939$	9.22949	+	28.4055i	0.301193	+	0.926977i
$940$	0.250774	+	2.38596i	0.00817935	+	0.0778213i
$941$	−9.59602	−	4.27243i	−0.312821	−	0.139277i	0.244320	−	0.969695i	$-0.421435\pi$
$941$	−9.59602	−	4.27243i	−0.312821	−	0.139277i	−0.557142	+	0.830418i	$0.688102\pi$
$942$	−14.7109	+	16.3381i	−0.479306	+	0.532324i
$943$	11.7817	+	13.0849i	0.383666	+	0.426104i
$944$	−10.8966	−	7.91684i	−0.354654	−	0.257671i
$945$	6.60517	+	4.03760i	0.214866	+	0.131343i
$946$	10.0429	−	9.63771i	0.326522	−	0.313349i
$947$	−22.6783	+	39.2800i	−0.736946	+	1.27643i	0.216918	+	0.976190i	$0.430400\pi$
$947$	−22.6783	+	39.2800i	−0.736946	+	1.27643i	−0.953864	+	0.300238i	$0.902934\pi$
$948$	−1.04094	+	9.90391i	−0.0338083	+	0.321664i
$949$	10.5372	−	2.23975i	0.342052	−	0.0727054i
$950$	23.0039	+	4.88963i	0.746345	+	0.158641i
$951$	9.32065	−	6.77185i	0.302243	−	0.219592i
$952$	−1.73326	+	3.64423i	−0.0561752	+	0.118110i
$953$	−6.62476	−	20.3889i	−0.214597	−	0.660462i	−0.999182	−	0.0404406i	$-0.987124\pi$
$953$	−6.62476	−	20.3889i	−0.214597	−	0.660462i	0.784585	−	0.620022i	$-0.212876\pi$
$954$	8.29159	+	9.20875i	0.268450	+	0.298144i
$955$	−5.85897	+	55.7444i	−0.189592	+	1.80385i
$956$	−8.15197	−	14.1196i	−0.263654	−	0.456661i
$957$	13.5505	+	11.4427i	0.438025	+	0.369890i
$958$	3.12694			0.101027
$959$	−31.5893	−	4.12322i	−1.02007	−	0.133146i
$960$	−0.904185	+	2.78280i	−0.0291825	+	0.0898144i
$961$	20.7217	+	4.40453i	0.668441	+	0.142081i
$962$	3.96356	+	1.76469i	0.127790	+	0.0568959i
$963$	18.1394	+	8.07617i	0.584533	+	0.260251i
$964$	19.5519	+	4.15588i	0.629724	+	0.133852i
$965$	−18.8244	+	57.9356i	−0.605979	+	1.86501i
$966$	1.51265	+	3.64045i	0.0486687	+	0.117130i
$967$	6.38864			0.205445			0.102722	−	0.994710i	$-0.467245\pi$
$967$	6.38864			0.205445			0.102722	+	0.994710i	$0.467245\pi$
$968$	−4.05672	−	10.2246i	−0.130388	−	0.328632i
$969$	−5.03585	−	8.72235i	−0.161775	−	0.280202i
$970$	−2.63284	+	25.0498i	−0.0845355	+	0.804301i
$971$	−10.0228	−	11.1314i	−0.321647	−	0.357225i	0.560538	−	0.828129i	$-0.310595\pi$
$971$	−10.0228	−	11.1314i	−0.321647	−	0.357225i	−0.882185	+	0.470904i	$0.843928\pi$
$972$	−0.309017	−	0.951057i	−0.00991172	−	0.0305052i
$973$	23.0331	+	33.4339i	0.738406	+	1.07184i
$974$	15.4033	−	11.1912i	0.493554	−	0.358588i
$975$	−3.99744	−	0.849682i	−0.128021	−	0.0272116i
$976$	10.3855	−	2.20750i	0.332431	−	0.0706604i
$977$	−4.22573	+	40.2051i	−0.135193	+	1.28628i	0.690986	+	0.722868i	$0.257177\pi$
$977$	−4.22573	+	40.2051i	−0.135193	+	1.28628i	−0.826179	+	0.563408i	$0.809490\pi$
$978$	3.79939	−	6.58074i	0.121491	−	0.210429i
$979$	1.85486	−	10.3302i	0.0592816	−	0.330154i
$980$	−20.4563	−	1.02664i	−0.653452	−	0.0327947i
$981$	−2.06812	−	1.50258i	−0.0660300	−	0.0479736i
$982$	7.20591	+	8.00297i	0.229950	+	0.255385i
$983$	17.5035	−	19.4396i	0.558275	−	0.620027i	−0.396256	−	0.918140i	$-0.629691\pi$
$983$	17.5035	−	19.4396i	0.558275	−	0.620027i	0.954531	+	0.298113i	$0.0963573\pi$
$984$	10.7954	+	4.80641i	0.344144	+	0.153223i
$985$	−1.65957	−	15.7898i	−0.0528783	−	0.503103i
$986$	2.52041	+	7.75703i	0.0802662	+	0.247034i
$987$	2.04568	+	0.721866i	0.0651148	+	0.0229772i
$988$	−6.13007	−	4.45376i	−0.195024	−	0.141693i
$989$	3.12665	−	5.41552i	0.0994217	−	0.172203i
$990$	−9.32010	−	2.70411i	−0.296212	−	0.0859421i
$991$	−16.7308	−	28.9786i	−0.531471	−	0.920534i	−0.999325	−	0.0367287i	$-0.988306\pi$
$991$	−16.7308	−	28.9786i	−0.531471	−	0.920534i	0.467855	−	0.883805i	$-0.345027\pi$
$992$	2.86210	−	1.27429i	0.0908717	−	0.0404587i
$993$	−6.16763	+	18.9820i	−0.195724	+	0.602376i
$994$	−3.39485	+	14.2099i	−0.107678	+	0.450710i
$995$	−21.9815	+	15.9705i	−0.696861	+	0.506299i
$996$	1.39973	+	13.3175i	0.0443521	+	0.421982i
$997$	15.4135	−	17.1184i	0.488150	−	0.542146i	−0.447867	−	0.894100i	$-0.647816\pi$
$997$	15.4135	−	17.1184i	0.488150	−	0.542146i	0.936017	+	0.351954i	$0.114483\pi$
$998$	−31.3660	+	6.66706i	−0.992874	+	0.211042i
$999$	3.45415	−	1.53789i	0.109285	−	0.0486566i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.d.25.1	✓	40	77.25	even	15	inner
462.2.y.d.37.1	yes	40	1.1	even	1	trivial
462.2.y.d.235.5	yes	40	7.4	even	3	inner
462.2.y.d.289.5	yes	40	11.3	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.913545 - 0.406737i) q^{2} +(0.978148 - 0.207912i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.305851 - 2.90998i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-2.53596 + 0.754243i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.913545 - 0.406737i) q^{9} +O(q^{10})\)	\(q+(0.913545 - 0.406737i) q^{2} +(0.978148 - 0.207912i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.305851 - 2.90998i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-2.53596 + 0.754243i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.913545 - 0.406737i) q^{9} +(-1.46300 - 2.53399i) q^{10} +(3.12014 - 1.12459i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.928329 + 0.674471i) q^{13} +(-2.00994 + 1.72051i) q^{14} +(-0.904185 - 2.78280i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(1.39338 + 0.620373i) q^{17} +(0.669131 - 0.743145i) q^{18} +(-4.41850 - 4.90724i) q^{19} +(-2.36719 - 1.71986i) q^{20} +(-2.32373 + 1.26502i) q^{21} +(2.39298 - 2.29644i) q^{22} +(0.745007 - 1.29039i) q^{23} +(0.104528 - 0.994522i) q^{24} +(-3.48368 + 0.740478i) q^{25} +(1.12240 + 0.238574i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-1.13638 + 2.38928i) q^{28} +(1.65246 + 5.08576i) q^{29} +(-1.95788 - 2.17445i) q^{30} +(-0.327483 + 3.11579i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.81815 - 1.74873i) q^{33} +1.52524 q^{34} +(2.97046 + 7.14891i) q^{35} +(0.309017 - 0.951057i) q^{36} +(3.69841 + 0.786122i) q^{37} +(-6.03245 - 2.68582i) q^{38} +(1.04827 + 0.466721i) q^{39} +(-2.86206 - 0.608351i) q^{40} +(-3.65165 + 11.2386i) q^{41} +(-1.60831 + 2.10080i) q^{42} +4.19680 q^{43} +(1.25205 - 3.07122i) q^{44} +(-1.46300 - 2.53399i) q^{45} +(0.155749 - 1.48185i) q^{46} +(-0.548635 - 0.609321i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(5.86223 - 3.82547i) q^{49} +(-2.88132 + 2.09340i) q^{50} +(1.49191 + 0.317116i) q^{51} +(1.12240 - 0.238574i) q^{52} +(-1.29527 + 12.3237i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-4.22682 - 8.73559i) q^{55} +(-0.0663284 + 2.64492i) q^{56} +(-5.34222 - 3.88135i) q^{57} +(3.57817 + 3.97396i) q^{58} +(9.01248 - 10.0094i) q^{59} +(-2.67304 - 1.19011i) q^{60} +(1.10983 + 10.5593i) q^{61} +(0.968136 + 2.97962i) q^{62} +(-2.00994 + 1.72051i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.67876 - 2.90770i) q^{65} +(1.86323 - 2.74379i) q^{66} +(0.555115 + 0.961487i) q^{67} +(1.39338 - 0.620373i) q^{68} +(0.460440 - 1.41709i) q^{69} +(5.62137 + 5.32266i) q^{70} +(4.46737 - 3.24574i) q^{71} +(-0.104528 - 0.994522i) q^{72} +(6.28185 - 6.97670i) q^{73} +(3.69841 - 0.786122i) q^{74} +(-3.25360 + 1.44859i) q^{75} -6.60334 q^{76} +(-7.06436 + 5.20526i) q^{77} +1.14748 q^{78} +(-9.09751 + 4.05047i) q^{79} +(-2.86206 + 0.608351i) q^{80} +(0.669131 - 0.743145i) q^{81} +(1.23521 + 11.7523i) q^{82} +(-10.8334 + 7.87096i) q^{83} +(-0.614789 + 2.57333i) q^{84} +(1.37910 - 4.24444i) q^{85} +(3.83397 - 1.70699i) q^{86} +(2.67374 + 4.63106i) q^{87} +(-0.105370 - 3.31495i) q^{88} +(1.58224 - 2.74052i) q^{89} +(-2.36719 - 1.71986i) q^{90} +(-2.86292 - 1.01025i) q^{91} +(-0.460440 - 1.41709i) q^{92} +(0.327483 + 3.11579i) q^{93} +(-0.749037 - 0.333493i) q^{94} +(-12.9285 + 14.3586i) q^{95} +(-0.669131 - 0.743145i) q^{96} +(-6.96423 - 5.05981i) q^{97} +(3.79946 - 5.87912i) q^{98} +(2.39298 - 2.29644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9}+O(q^{10}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 20 q^{12} + 10 q^{13} + 5 q^{14} - 6 q^{15} + 5 q^{16} + 5 q^{18} - 13 q^{19} + 6 q^{20} - 2 q^{21} - 4 q^{22} - 20 q^{23} - 5 q^{24} + 12 q^{25} + 10 q^{27} - 3 q^{28} + 12 q^{29} + 3 q^{30} - 10 q^{31} - 20 q^{32} + 8 q^{33} - 13 q^{35} - 10 q^{36} + 3 q^{37} + 2 q^{38} + 5 q^{39} - 3 q^{40} - 44 q^{41} - 3 q^{42} + 36 q^{43} - 3 q^{44} + 12 q^{45} + 11 q^{47} + 10 q^{48} + 33 q^{49} - 4 q^{50} + 26 q^{53} + 20 q^{54} - 20 q^{55} + 8 q^{56} + 4 q^{57} - 6 q^{58} + 4 q^{59} + 3 q^{60} - 23 q^{61} + 5 q^{63} - 10 q^{64} - 50 q^{65} - 7 q^{66} - 108 q^{67} + 20 q^{69} - 86 q^{71} + 5 q^{72} - 35 q^{73} + 3 q^{74} - 2 q^{75} - 44 q^{76} - 37 q^{77} + 20 q^{78} + 3 q^{79} - 3 q^{80} + 5 q^{81} - 28 q^{82} - 88 q^{83} - 5 q^{84} + 96 q^{85} - 13 q^{86} + 6 q^{87} - 8 q^{88} + 6 q^{89} + 6 q^{90} + 40 q^{91} - 20 q^{92} + 10 q^{93} - 24 q^{94} + 36 q^{95} - 5 q^{96} + 60 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 20 * q^12 + 10 * q^13 + 5 * q^14 - 6 * q^15 + 5 * q^16 + 5 * q^18 - 13 * q^19 + 6 * q^20 - 2 * q^21 - 4 * q^22 - 20 * q^23 - 5 * q^24 + 12 * q^25 + 10 * q^27 - 3 * q^28 + 12 * q^29 + 3 * q^30 - 10 * q^31 - 20 * q^32 + 8 * q^33 - 13 * q^35 - 10 * q^36 + 3 * q^37 + 2 * q^38 + 5 * q^39 - 3 * q^40 - 44 * q^41 - 3 * q^42 + 36 * q^43 - 3 * q^44 + 12 * q^45 + 11 * q^47 + 10 * q^48 + 33 * q^49 - 4 * q^50 + 26 * q^53 + 20 * q^54 - 20 * q^55 + 8 * q^56 + 4 * q^57 - 6 * q^58 + 4 * q^59 + 3 * q^60 - 23 * q^61 + 5 * q^63 - 10 * q^64 - 50 * q^65 - 7 * q^66 - 108 * q^67 + 20 * q^69 - 86 * q^71 + 5 * q^72 - 35 * q^73 + 3 * q^74 - 2 * q^75 - 44 * q^76 - 37 * q^77 + 20 * q^78 + 3 * q^79 - 3 * q^80 + 5 * q^81 - 28 * q^82 - 88 * q^83 - 5 * q^84 + 96 * q^85 - 13 * q^86 + 6 * q^87 - 8 * q^88 + 6 * q^89 + 6 * q^90 + 40 * q^91 - 20 * q^92 + 10 * q^93 - 24 * q^94 + 36 * q^95 - 5 * q^96 + 60 * q^97 + 2 * q^98 - 4 * q^99

Introduction

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