LMFDB - Embedded newform 462.2.bc.a.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(95,462)]

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([15, 20, 21]))

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

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

chi := DirichletCharacter("462.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bc (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			107.3
Character	$\chi$	$=$	462.107
Dual form			462.2.bc.a.95.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104528 + 0.994522i) q^{2} +(-1.45000 + 0.947367i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(0.625478 + 1.40485i) q^{5} +(-1.09374 - 1.34303i) q^{6} +(-1.00131 + 2.44895i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(1.20499 - 2.74736i) q^{9} +O(q^{10})$	\(q+(0.104528 + 0.994522i) q^{2} +(-1.45000 + 0.947367i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(0.625478 + 1.40485i) q^{5} +(-1.09374 - 1.34303i) q^{6} +(-1.00131 + 2.44895i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(1.20499 - 2.74736i) q^{9} +(-1.33177 + 0.768898i) q^{10} +(-2.04183 + 2.61361i) q^{11} +(1.22134 - 1.22814i) q^{12} +(-1.67851 - 2.31027i) q^{13} +(-2.54020 - 0.739841i) q^{14} +(-2.23785 - 1.44447i) q^{15} +(0.913545 - 0.406737i) q^{16} +(-0.605966 + 5.76538i) q^{17} +(2.85827 + 0.911213i) q^{18} +(0.632140 - 2.97398i) q^{19} +(-0.903893 - 1.24410i) q^{20} +(-0.868158 - 4.49959i) q^{21} +(-2.81272 - 1.75745i) q^{22} +(-3.21832 - 1.85810i) q^{23} +(1.34907 + 1.08628i) q^{24} +(1.76328 - 1.95832i) q^{25} +(2.12216 - 1.91080i) q^{26} +(0.855523 + 5.12524i) q^{27} +(0.470264 - 2.60362i) q^{28} +(1.08920 - 3.35222i) q^{29} +(1.20264 - 2.37658i) q^{30} +(-7.66019 - 3.41054i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.484607 - 5.72409i) q^{33} -5.79714 q^{34} +(-4.06670 + 0.125078i) q^{35} +(-0.607451 + 2.93786i) q^{36} +(-3.75561 - 4.17102i) q^{37} +(3.02377 + 0.317811i) q^{38} +(4.62251 + 1.75972i) q^{39} +(1.14280 - 1.02899i) q^{40} +(1.91521 + 5.89442i) q^{41} +(4.38419 - 1.33374i) q^{42} +2.46157i q^{43} +(1.45381 - 2.98101i) q^{44} +(4.61331 - 0.0255853i) q^{45} +(1.51151 - 3.39491i) q^{46} +(-1.82650 + 8.59302i) q^{47} +(-0.939311 + 1.45523i) q^{48} +(-4.99475 - 4.90433i) q^{49} +(2.13191 + 1.54892i) q^{50} +(-4.58328 - 8.93386i) q^{51} +(2.12216 + 1.91080i) q^{52} +(0.878311 - 1.97272i) q^{53} +(-5.00774 + 1.38657i) q^{54} +(-4.94883 - 1.23370i) q^{55} +(2.63852 + 0.195535i) q^{56} +(1.90085 + 4.91114i) q^{57} +(3.44771 + 0.732833i) q^{58} +(0.736835 + 3.46653i) q^{59} +(2.48927 + 0.947628i) q^{60} +(3.12114 + 7.01020i) q^{61} +(2.59115 - 7.97472i) q^{62} +(5.52159 + 5.70193i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(2.19570 - 3.80307i) q^{65} +(5.74338 - 0.116378i) q^{66} +(5.97388 + 10.3471i) q^{67} +(-0.605966 - 5.76538i) q^{68} +(6.42686 - 0.354690i) q^{69} +(-0.549479 - 4.03135i) q^{70} +(-2.97099 + 4.08922i) q^{71} +(-2.98526 - 0.297034i) q^{72} +(1.41941 + 6.67780i) q^{73} +(3.75561 - 4.17102i) q^{74} +(-0.701507 + 4.51004i) q^{75} +3.04042i q^{76} +(-4.35609 - 7.61738i) q^{77} +(-1.26690 + 4.78113i) q^{78} +(-4.09443 + 0.430342i) q^{79} +(1.14280 + 1.02899i) q^{80} +(-6.09599 - 6.62110i) q^{81} +(-5.66194 + 2.52086i) q^{82} +(-0.684321 - 0.497188i) q^{83} +(1.78470 + 4.22076i) q^{84} +(-8.47849 + 2.75483i) q^{85} +(-2.44808 + 0.257304i) q^{86} +(1.59644 + 5.89259i) q^{87} +(3.11665 + 1.13425i) q^{88} +(8.42825 + 4.86605i) q^{89} +(0.507668 + 4.58537i) q^{90} +(7.33845 - 1.79729i) q^{91} +(3.53431 + 1.14837i) q^{92} +(14.3383 - 2.31174i) q^{93} +(-8.73687 - 0.918282i) q^{94} +(4.57338 - 0.972101i) q^{95} +(-1.54544 - 0.782052i) q^{96} +(-9.62720 + 6.99457i) q^{97} +(4.35537 - 5.48003i) q^{98} +(4.72013 + 8.75902i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9}+O(q^{10}) $ 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9	$ 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9} + 6 q^{11} - 12 q^{15} + 16 q^{16} + 2 q^{17} + 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} - 38 q^{29} - 6 q^{30} - 3 q^{31} + 64 q^{32} - 4 q^{33} - 16 q^{34} + 31 q^{35} + 8 q^{36} + 2 q^{37} + 22 q^{39} + 5 q^{40} - 16 q^{41} + 17 q^{42} + q^{44} + 28 q^{45} + 38 q^{49} - 34 q^{50} + 16 q^{51} - 25 q^{53} + 6 q^{54} - 42 q^{55} + 20 q^{57} - 19 q^{58} - 40 q^{59} - 4 q^{60} + 40 q^{61} + 4 q^{62} + 6 q^{63} - 32 q^{64} - 20 q^{65} - 41 q^{66} + 16 q^{67} + 2 q^{68} - 68 q^{69} - 21 q^{70} - 80 q^{71} - 16 q^{72} + 10 q^{73} - 2 q^{74} - 14 q^{75} - q^{77} - 16 q^{78} + 5 q^{80} - 88 q^{81} - 8 q^{82} + 92 q^{83} - 48 q^{84} - 100 q^{85} + 40 q^{86} + 38 q^{87} - q^{88} - 164 q^{90} + 12 q^{91} + 20 q^{92} + 47 q^{93} + 40 q^{94} - 38 q^{95} - 16 q^{97} - 18 q^{98} - 138 q^{99}+O(q^{100}) $ 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9 + 6 * q^11 - 12 * q^15 + 16 * q^16 + 2 * q^17 + 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 - 38 * q^29 - 6 * q^30 - 3 * q^31 + 64 * q^32 - 4 * q^33 - 16 * q^34 + 31 * q^35 + 8 * q^36 + 2 * q^37 + 22 * q^39 + 5 * q^40 - 16 * q^41 + 17 * q^42 + q^44 + 28 * q^45 + 38 * q^49 - 34 * q^50 + 16 * q^51 - 25 * q^53 + 6 * q^54 - 42 * q^55 + 20 * q^57 - 19 * q^58 - 40 * q^59 - 4 * q^60 + 40 * q^61 + 4 * q^62 + 6 * q^63 - 32 * q^64 - 20 * q^65 - 41 * q^66 + 16 * q^67 + 2 * q^68 - 68 * q^69 - 21 * q^70 - 80 * q^71 - 16 * q^72 + 10 * q^73 - 2 * q^74 - 14 * q^75 - q^77 - 16 * q^78 + 5 * q^80 - 88 * q^81 - 8 * q^82 + 92 * q^83 - 48 * q^84 - 100 * q^85 + 40 * q^86 + 38 * q^87 - q^88 - 164 * q^90 + 12 * q^91 + 20 * q^92 + 47 * q^93 + 40 * q^94 - 38 * q^95 - 16 * q^97 - 18 * q^98 - 138 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{10}\right)$

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
$3$	−1.45000	+	0.947367i	−0.837157	+	0.546963i
$3$	−1.45000	+	0.947367i	−0.837157	+	0.546963i
$4$	−0.978148	+	0.207912i	−0.489074	+	0.103956i
$5$	0.625478	+	1.40485i	0.279722	+	0.628266i	0.997699	−	0.0678009i	$-0.0215983\pi$
$5$	0.625478	+	1.40485i	0.279722	+	0.628266i	−0.717977	+	0.696067i	$0.754932\pi$
$6$	−1.09374	−	1.34303i	−0.446519	−	0.548289i
$7$	−1.00131	+	2.44895i	−0.378460	+	0.925618i
$7$	−1.00131	+	2.44895i	−0.378460	+	0.925618i
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	1.20499	−	2.74736i	0.401664	−	0.915787i
$10$	−1.33177	+	0.768898i	−0.421143	+	0.243147i
$11$	−2.04183	+	2.61361i	−0.615635	+	0.788032i
$11$	−2.04183	+	2.61361i	−0.615635	+	0.788032i
$12$	1.22134	−	1.22814i	0.352572	−	0.354532i
$13$	−1.67851	−	2.31027i	−0.465535	−	0.640753i	0.510110	−	0.860109i	$-0.329605\pi$
$13$	−1.67851	−	2.31027i	−0.465535	−	0.640753i	−0.975645	+	0.219356i	$0.929605\pi$
$14$	−2.54020	−	0.739841i	−0.678898	−	0.197731i
$15$	−2.23785	−	1.44447i	−0.577809	−	0.372960i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	−0.605966	+	5.76538i	−0.146968	+	1.39831i	0.633804	+	0.773494i	$0.281493\pi$
$17$	−0.605966	+	5.76538i	−0.146968	+	1.39831i	−0.780772	+	0.624816i	$0.785174\pi$
$18$	2.85827	+	0.911213i	0.673700	+	0.214775i
$19$	0.632140	−	2.97398i	0.145023	−	0.682278i	−0.844220	−	0.535997i	$-0.819936\pi$
$19$	0.632140	−	2.97398i	0.145023	−	0.682278i	0.989243	−	0.146282i	$-0.0467307\pi$
$20$	−0.903893	−	1.24410i	−0.202117	−	0.278190i
$21$	−0.868158	−	4.49959i	−0.189448	−	0.981891i
$22$	−2.81272	−	1.75745i	−0.599673	−	0.374689i
$23$	−3.21832	−	1.85810i	−0.671066	−	0.387440i	0.125415	−	0.992104i	$-0.459974\pi$
$23$	−3.21832	−	1.85810i	−0.671066	−	0.387440i	−0.796480	+	0.604664i	$0.793307\pi$
$24$	1.34907	+	1.08628i	0.275379	+	0.221736i
$25$	1.76328	−	1.95832i	0.352657	−	0.391665i
$26$	2.12216	−	1.91080i	0.416190	−	0.374739i
$27$	0.855523	+	5.12524i	0.164645	+	0.986353i
$28$	0.470264	−	2.60362i	0.0888716	−	0.492038i
$29$	1.08920	−	3.35222i	0.202260	−	0.622492i	−0.797555	−	0.603246i	$-0.793874\pi$
$29$	1.08920	−	3.35222i	0.202260	−	0.622492i	0.999815	−	0.0192455i	$-0.00612640\pi$
$30$	1.20264	−	2.37658i	0.219570	−	0.433901i
$31$	−7.66019	−	3.41054i	−1.37581	−	0.612550i	−0.420267	−	0.907400i	$-0.638064\pi$
$31$	−7.66019	−	3.41054i	−1.37581	−	0.612550i	−0.955544	+	0.294850i	$0.904730\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.484607	−	5.72409i	0.0843592	−	0.996435i
$34$	−5.79714			−0.994201
$35$	−4.06670	+	0.125078i	−0.687398	+	0.0211420i
$36$	−0.607451	+	2.93786i	−0.101242	+	0.489643i
$37$	−3.75561	−	4.17102i	−0.617418	−	0.685712i	0.350619	−	0.936518i	$-0.385971\pi$
$37$	−3.75561	−	4.17102i	−0.617418	−	0.685712i	−0.968037	+	0.250806i	$0.919304\pi$
$38$	3.02377	+	0.317811i	0.490520	+	0.0515557i
$39$	4.62251	+	1.75972i	0.740194	+	0.281781i
$40$	1.14280	−	1.02899i	0.180693	−	0.162697i
$41$	1.91521	+	5.89442i	0.299106	+	0.920555i	0.981811	+	0.189860i	$0.0608035\pi$
$41$	1.91521	+	5.89442i	0.299106	+	0.920555i	−0.682705	+	0.730694i	$0.739197\pi$
$42$	4.38419	−	1.33374i	0.676496	−	0.205800i
$43$			2.46157i			0.375386i	0.982228	+	0.187693i	$0.0601010\pi$
$43$			2.46157i			0.375386i	−0.982228	+	0.187693i	$0.939899\pi$
$44$	1.45381	−	2.98101i	0.219170	−	0.449404i
$45$	4.61331	−	0.0255853i	0.687712	−	0.00381404i
$46$	1.51151	−	3.39491i	0.222860	−	0.500552i
$47$	−1.82650	+	8.59302i	−0.266423	+	1.25342i	0.617792	+	0.786341i	$0.288027\pi$
$47$	−1.82650	+	8.59302i	−0.266423	+	1.25342i	−0.884215	+	0.467080i	$0.845306\pi$
$48$	−0.939311	+	1.45523i	−0.135578	+	0.210044i
$49$	−4.99475	−	4.90433i	−0.713536	−	0.700619i
$50$	2.13191	+	1.54892i	0.301498	+	0.219051i
$51$	−4.58328	−	8.93386i	−0.641787	−	1.25099i
$52$	2.12216	+	1.91080i	0.294291	+	0.264981i
$53$	0.878311	−	1.97272i	0.120645	−	0.270974i	−0.843120	−	0.537725i	$-0.819284\pi$
$53$	0.878311	−	1.97272i	0.120645	−	0.270974i	0.963765	+	0.266752i	$0.0859504\pi$
$54$	−5.00774	+	1.38657i	−0.681467	+	0.188688i
$55$	−4.94883	−	1.23370i	−0.667300	−	0.166353i
$56$	2.63852	+	0.195535i	0.352587	+	0.0261295i
$57$	1.90085	+	4.91114i	0.251774	+	0.650496i
$58$	3.44771	+	0.732833i	0.452706	+	0.0962257i
$59$	0.736835	+	3.46653i	0.0959277	+	0.451304i	0.999727	+	0.0233486i	$0.00743276\pi$
$59$	0.736835	+	3.46653i	0.0959277	+	0.451304i	−0.903800	+	0.427956i	$0.859234\pi$
$60$	2.48927	+	0.947628i	0.321363	+	0.122338i
$61$	3.12114	+	7.01020i	0.399622	+	0.897565i	0.995524	+	0.0945080i	$0.0301278\pi$
$61$	3.12114	+	7.01020i	0.399622	+	0.897565i	−0.595903	+	0.803057i	$0.703206\pi$
$62$	2.59115	−	7.97472i	0.329076	−	1.01279i
$63$	5.52159	+	5.70193i	0.695655	+	0.718376i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	2.19570	−	3.80307i	0.272343	−	0.471712i
$66$	5.74338	−	0.116378i	0.706962	−	0.0143251i
$67$	5.97388	+	10.3471i	0.729826	+	1.26410i	0.956957	+	0.290231i	$0.0937321\pi$
$67$	5.97388	+	10.3471i	0.729826	+	1.26410i	−0.227131	+	0.973864i	$0.572935\pi$
$68$	−0.605966	−	5.76538i	−0.0734841	−	0.699155i
$69$	6.42686	−	0.354690i	0.773702	−	0.0426997i
$70$	−0.549479	−	4.03135i	−0.0656753	−	0.481838i
$71$	−2.97099	+	4.08922i	−0.352592	+	0.485301i	−0.948066	−	0.318073i	$-0.896964\pi$
$71$	−2.97099	+	4.08922i	−0.352592	+	0.485301i	0.595474	+	0.803374i	$0.296964\pi$
$72$	−2.98526	−	0.297034i	−0.351816	−	0.0350058i
$73$	1.41941	+	6.67780i	0.166129	+	0.781577i	0.979757	+	0.200191i	$0.0641562\pi$
$73$	1.41941	+	6.67780i	0.166129	+	0.781577i	−0.813628	+	0.581386i	$0.802510\pi$
$74$	3.75561	−	4.17102i	0.436580	−	0.484872i
$75$	−0.701507	+	4.51004i	−0.0810030	+	0.520775i
$76$			3.04042i			0.348760i
$77$	−4.35609	−	7.61738i	−0.496423	−	0.868081i
$78$	−1.26690	+	4.78113i	−0.143448	+	0.541356i
$79$	−4.09443	+	0.430342i	−0.460660	+	0.0484173i	−0.332016	−	0.943274i	$-0.607729\pi$
$79$	−4.09443	+	0.430342i	−0.460660	+	0.0484173i	−0.128643	+	0.991691i	$0.541062\pi$
$80$	1.14280	+	1.02899i	0.127769	+	0.115044i
$81$	−6.09599	−	6.62110i	−0.677332	−	0.735677i
$82$	−5.66194	+	2.52086i	−0.625257	+	0.278382i
$83$	−0.684321	−	0.497188i	−0.0751140	−	0.0545735i	0.549595	−	0.835432i	$-0.314782\pi$
$83$	−0.684321	−	0.497188i	−0.0751140	−	0.0545735i	−0.624709	+	0.780858i	$0.714782\pi$
$84$	1.78470	+	4.22076i	0.194727	+	0.460523i
$85$	−8.47849	+	2.75483i	−0.919621	+	0.298803i
$86$	−2.44808	+	0.257304i	−0.263984	+	0.0277458i
$87$	1.59644	+	5.89259i	0.171156	+	0.631752i
$88$	3.11665	+	1.13425i	0.332236	+	0.120911i
$89$	8.42825	+	4.86605i	0.893393	+	0.515800i	0.875051	−	0.484031i	$-0.160828\pi$
$89$	8.42825	+	4.86605i	0.893393	+	0.515800i	0.0183419	+	0.999832i	$0.494161\pi$
$90$	0.507668	+	4.58537i	0.0535129	+	0.483340i
$91$	7.33845	−	1.79729i	0.769279	−	0.188407i
$92$	3.53431	+	1.14837i	0.368477	+	0.119726i
$93$	14.3383	−	2.31174i	1.48681	−	0.239716i
$94$	−8.73687	−	0.918282i	−0.901140	−	0.0947136i
$95$	4.57338	−	0.972101i	0.469219	−	0.0997355i
$96$	−1.54544	−	0.782052i	−0.157731	−	0.0798179i
$97$	−9.62720	+	6.99457i	−0.977494	+	0.710191i	−0.957147	−	0.289602i	$-0.906477\pi$
$97$	−9.62720	+	6.99457i	−0.977494	+	0.710191i	−0.0203472	+	0.999793i	$0.506477\pi$
$98$	4.35537	−	5.48003i	0.439959	−	0.553567i
$99$	4.72013	+	8.75902i	0.474391	+	0.880314i
$100$	−1.31759	+	2.28214i	−0.131759	+	0.228214i
$101$	−0.550878	−	0.245267i	−0.0548144	−	0.0244049i	0.379146	−	0.925337i	$-0.376218\pi$
$101$	−0.550878	−	0.245267i	−0.0548144	−	0.0244049i	−0.433961	+	0.900932i	$0.642884\pi$
$102$	8.40584	−	5.49201i	0.832302	−	0.543790i
$103$	13.3497	+	14.8263i	1.31538	+	1.46088i	0.794523	+	0.607234i	$0.207721\pi$
$103$	13.3497	+	14.8263i	1.31538	+	1.46088i	0.520858	+	0.853643i	$0.325612\pi$
$104$	−1.67851	+	2.31027i	−0.164591	+	0.226540i
$105$	5.77822	−	4.03402i	0.563896	−	0.393680i
$106$	2.05372	+	0.667294i	0.199475	+	0.0648133i
$107$	9.38657	+	1.99518i	0.907434	+	0.192881i	0.637909	−	0.770112i	$-0.279800\pi$
$107$	9.38657	+	1.99518i	0.907434	+	0.192881i	0.269526	+	0.962993i	$0.413133\pi$
$108$	−1.90242	−	4.83537i	−0.183061	−	0.465283i
$109$	2.60120	−	1.50180i	0.249150	−	0.143847i	−0.370225	−	0.928942i	$-0.620719\pi$
$109$	2.60120	−	1.50180i	0.249150	−	0.143847i	0.619375	+	0.785095i	$0.287386\pi$
$110$	0.709652	−	5.05068i	0.0676627	−	0.481563i
$111$	9.39711	+	2.49004i	0.891935	+	0.236344i
$112$	0.0813359	+	2.64450i	0.00768552	+	0.249882i
$113$	−16.3395	+	5.30902i	−1.53709	+	0.499431i	−0.950571	−	0.310506i	$-0.899502\pi$
$113$	−16.3395	+	5.30902i	−1.53709	+	0.499431i	−0.586518	+	0.809936i	$0.699502\pi$
$114$	−4.68554	+	2.40379i	−0.438841	+	0.225136i
$115$	0.597353	−	5.68344i	0.0557035	−	0.529983i
$116$	−0.368435	+	3.50542i	−0.0342083	+	0.325471i
$117$	−8.36973	+	1.82761i	−0.773782	+	0.168963i
$118$	−3.37052	+	1.09515i	−0.310282	+	0.100817i
$119$	−13.5124	−	7.25692i	−1.23868	−	0.665241i
$120$	−0.682238	+	2.57468i	−0.0622795	+	0.235035i
$121$	−2.66186	−	10.6731i	−0.241988	−	0.970279i
$122$	−6.64555	+	3.83681i	−0.601660	+	0.347369i
$123$	−8.36124	−	6.73250i	−0.753908	−	0.607049i
$124$	8.20189	+	1.74336i	0.736551	+	0.156559i
$125$	11.1667	+	3.62828i	0.998779	+	0.324523i
$126$	−5.09353	+	6.08736i	−0.453768	+	0.542305i
$127$	1.02656	−	1.41294i	0.0910925	−	0.125378i	−0.761038	−	0.648707i	$-0.775310\pi$
$127$	1.02656	−	1.41294i	0.0910925	−	0.125378i	0.852131	+	0.523329i	$0.175310\pi$
$128$	−0.669131	−	0.743145i	−0.0591433	−	0.0656853i
$129$	−2.33201	−	3.56927i	−0.205322	−	0.314257i
$130$	4.01175	+	1.78614i	0.351854	+	0.156655i
$131$	−3.07127	+	5.31960i	−0.268338	+	0.464776i	−0.968433	−	0.249274i	$-0.919808\pi$
$131$	−3.07127	+	5.31960i	−0.268338	+	0.464776i	0.700094	+	0.714050i	$0.253141\pi$
$132$	0.716087	+	5.69976i	0.0623274	+	0.496100i
$133$	6.65018	+	4.52596i	0.576644	+	0.392451i
$134$	−9.66594	+	7.02272i	−0.835010	+	0.606670i
$135$	−6.66506	+	4.40760i	−0.573637	+	0.379346i
$136$	5.67045	−	1.20529i	0.486237	−	0.103353i
$137$	−22.9208	−	2.40907i	−1.95825	−	0.205821i	−0.960807	−	0.277220i	$-0.910587\pi$
$137$	−22.9208	−	2.40907i	−1.95825	−	0.205821i	−0.997448	+	0.0713990i	$0.977254\pi$
$138$	1.02454	+	6.35457i	0.0872143	+	0.540937i
$139$	−20.1869	−	6.55912i	−1.71223	−	0.556337i	−0.721528	−	0.692385i	$-0.756560\pi$
$139$	−20.1869	−	6.55912i	−1.71223	−	0.556337i	−0.990702	+	0.136048i	$0.956560\pi$
$140$	3.95183	−	0.967859i	0.333990	−	0.0817991i
$141$	−5.49232	−	14.1902i	−0.462537	−	1.19503i
$142$	−4.37737	−	2.52728i	−0.367341	−	0.212084i
$143$	9.46536	+	0.330216i	0.791533	+	0.0276141i
$144$	−0.0166377	−	2.99995i	−0.00138647	−	0.249996i
$145$	5.39063	−	0.566578i	0.447667	−	0.0470517i
$146$	−6.49285	+	2.10965i	−0.537352	+	0.174596i
$147$	11.8886	+	2.37941i	0.980554	+	0.196250i
$148$	4.54074	+	3.29904i	0.373247	+	0.271180i
$149$	10.9261	−	4.86460i	0.895099	−	0.398524i	0.0929661	−	0.995669i	$-0.470365\pi$
$149$	10.9261	−	4.86460i	0.895099	−	0.398524i	0.802133	+	0.597145i	$0.203699\pi$
$150$	−4.55867	−	0.226236i	−0.372213	−	0.0184721i
$151$	8.08810	+	7.28256i	0.658201	+	0.592646i	0.929041	−	0.369978i	$-0.120635\pi$
$151$	8.08810	+	7.28256i	0.658201	+	0.592646i	−0.270840	+	0.962624i	$0.587301\pi$
$152$	−3.02377	+	0.317811i	−0.245260	+	0.0257779i
$153$	15.1094	+	8.61204i	1.22152	+	0.696242i
$154$	7.12031	−	5.12846i	0.573771	−	0.413263i
$155$		−	12.8946i		−	1.03572i
$156$	−4.88736	−	0.760196i	−0.391302	−	0.0608644i
$157$	2.01310	−	2.23577i	0.160663	−	0.178434i	−0.657439	−	0.753508i	$-0.728360\pi$
$157$	2.01310	−	2.23577i	0.160663	−	0.178434i	0.818101	+	0.575074i	$0.195027\pi$
$158$	−0.855969	−	4.02702i	−0.0680973	−	0.320372i
$159$	0.595339	+	3.69252i	0.0472134	+	0.292836i
$160$	−0.903893	+	1.24410i	−0.0714590	+	0.0983549i
$161$	7.77293	−	6.02098i	0.612593	−	0.474520i
$162$	5.94762	−	6.75469i	0.467289	−	0.530698i
$163$	−2.34022	−	22.2657i	−0.183300	−	1.74399i	−0.569878	−	0.821729i	$-0.693010\pi$
$163$	−2.34022	−	22.2657i	−0.183300	−	1.74399i	0.386578	−	0.922257i	$-0.373657\pi$
$164$	−3.09888	−	5.36742i	−0.241982	−	0.419125i
$165$	8.34457	−	2.89949i	0.649624	−	0.225725i
$166$	0.422934	−	0.732542i	0.0328260	−	0.0568563i
$167$	−5.77320	+	4.19447i	−0.446743	+	0.324578i	−0.788309	−	0.615280i	$-0.789043\pi$
$167$	−5.77320	+	4.19447i	−0.446743	+	0.324578i	0.341565	+	0.939858i	$0.389043\pi$
$168$	−4.01109	+	2.21612i	−0.309462	+	0.170977i
$169$	1.49727	−	4.60812i	0.115175	−	0.354471i
$170$	−3.62598	−	8.14408i	−0.278100	−	0.624623i
$171$	−7.40888	−	5.32034i	−0.566571	−	0.406857i
$172$	−0.511789	−	2.40778i	−0.0390235	−	0.183591i
$173$	12.1730	+	2.58745i	0.925494	+	0.196720i	0.645921	−	0.763404i	$-0.276474\pi$
$173$	12.1730	+	2.58745i	0.925494	+	0.196720i	0.279573	+	0.960124i	$0.409807\pi$
$174$	−5.69344	+	2.20364i	−0.431618	+	0.167057i
$175$	3.03025	+	6.27909i	0.229065	+	0.474655i
$176$	−0.802255	+	3.21813i	−0.0604722	+	0.242576i
$177$	−4.35249	−	4.32842i	−0.327153	−	0.325344i
$178$	−3.95840	+	8.89072i	−0.296695	+	0.666388i
$179$	6.74311	+	6.07153i	0.504004	+	0.453807i	0.881486	−	0.472210i	$-0.156543\pi$
$179$	6.74311	+	6.07153i	0.504004	+	0.453807i	−0.377482	+	0.926017i	$0.623210\pi$
$180$	−4.50718	+	0.984188i	−0.335946	+	0.0733571i
$181$	5.75748	+	4.18305i	0.427950	+	0.310924i	0.780829	−	0.624745i	$-0.214797\pi$
$181$	5.75748	+	4.18305i	0.427950	+	0.310924i	−0.352879	+	0.935669i	$0.614797\pi$
$182$	2.55452	+	7.11038i	0.189354	+	0.527057i
$183$	−11.1669	−	7.20792i	−0.825480	−	0.532825i
$184$	−0.772640	+	3.63499i	−0.0569598	+	0.267975i
$185$	3.51060	−	7.88493i	0.258104	−	0.579712i
$186$	3.79783	+	14.0181i	0.278471	+	1.02786i
$187$	−13.8311	−	13.3557i	−1.01143	−	0.976664i
$188$		−	8.78500i		−	0.640712i
$189$	−13.4081	−	3.03682i	−0.975297	−	0.220896i
$190$	1.44482	+	4.44671i	0.104819	+	0.322598i
$191$	−5.81307	+	5.23412i	−0.420619	+	0.378727i	−0.852086	−	0.523401i	$-0.824663\pi$
$191$	−5.81307	+	5.23412i	−0.420619	+	0.378727i	0.431467	+	0.902129i	$0.357996\pi$
$192$	0.616225	−	1.61872i	0.0444722	−	0.116821i
$193$	5.05645	+	0.531454i	0.363971	+	0.0382549i	0.284749	−	0.958602i	$-0.408090\pi$
$193$	5.05645	+	0.531454i	0.363971	+	0.0382549i	0.0792219	+	0.996857i	$0.474756\pi$
$194$	−7.96257	−	8.84333i	−0.571679	−	0.634914i
$195$	0.419135	+	7.59458i	0.0300149	+	0.543859i
$196$	5.90527	+	3.75869i	0.421805	+	0.268478i
$197$	25.9981			1.85229			0.926146	−	0.377166i	$-0.123101\pi$
$197$	25.9981			1.85229			0.926146	+	0.377166i	$0.123101\pi$
$198$	−8.21765	+	5.60984i	−0.584003	+	0.398674i
$199$	−9.18570	−	15.9101i	−0.651157	−	1.12784i	−0.982843	−	0.184447i	$-0.940951\pi$
$199$	−9.18570	−	15.9101i	−0.651157	−	1.12784i	0.331686	−	0.943390i	$-0.392383\pi$
$200$	−2.40736	−	1.07183i	−0.170226	−	0.0757896i
$201$	−18.4646	−	9.34377i	−1.30239	−	0.659059i
$202$	0.186341	−	0.573497i	0.0131109	−	0.0403511i
$203$	7.11880	+	6.02402i	0.499642	+	0.422804i
$204$	6.34058	+	7.78572i	0.443929	+	0.545109i
$205$	−7.08283	+	6.37741i	−0.494687	+	0.445418i
$206$	−13.3497	+	14.8263i	−0.930114	+	1.03300i
$207$	−8.98291	+	6.60289i	−0.624355	+	0.458933i
$208$	−2.47306	−	1.42782i	−0.171476	−	0.0990018i
$209$	6.48210	+	7.72453i	0.448376	+	0.534317i
$210$	4.61591	+	5.32489i	0.318528	+	0.367452i
$211$	7.87519	+	10.8393i	0.542151	+	0.746206i	0.988921	−	0.148442i	$-0.0474259\pi$
$211$	7.87519	+	10.8393i	0.542151	+	0.746206i	−0.446770	+	0.894649i	$0.647426\pi$
$212$	−0.448966	+	2.11222i	−0.0308351	+	0.145068i
$213$	0.433943	−	8.74398i	0.0297333	−	0.599128i
$214$	−1.00308	+	9.54371i	−0.0685694	+	0.652394i
$215$	−3.45812	+	1.53966i	−0.235842	+	0.105004i
$216$	4.61002	−	2.39744i	0.313672	−	0.163125i
$217$	16.0225	−	15.3444i	1.08768	−	1.04165i
$218$	1.76547	+	2.42997i	0.119573	+	0.164578i
$219$	−8.38447	−	8.33810i	−0.566570	−	0.563436i
$220$	5.09719	+	0.177825i	0.343652	+	0.0119889i
$221$	14.3367	−	8.27729i	0.964390	−	0.556791i
$222$	−1.49413	+	9.60592i	−0.100280	+	0.644707i
$223$	2.64203	+	8.13135i	0.176924	+	0.544515i	0.999716	−	0.0238268i	$-0.00758503\pi$
$223$	2.64203	+	8.13135i	0.176924	+	0.544515i	−0.822792	+	0.568342i	$0.807585\pi$
$224$	−2.62151	+	0.357316i	−0.175157	+	0.0238742i
$225$	−3.25548	−	7.20414i	−0.217032	−	0.480276i
$226$	−6.98788	−	15.6950i	−0.464827	−	1.04402i
$227$	10.8932	−	2.31542i	0.723007	−	0.153680i	0.168312	−	0.985734i	$-0.446168\pi$
$227$	10.8932	−	2.31542i	0.723007	−	0.153680i	0.554695	+	0.832054i	$0.312835\pi$
$228$	−2.88040	−	4.40861i	−0.190759	−	0.291967i
$229$	−0.445552	−	4.23915i	−0.0294429	−	0.280131i	−0.999331	−	0.0365788i	$-0.988354\pi$
$229$	−0.445552	−	4.23915i	−0.0294429	−	0.280131i	0.969888	−	0.243552i	$-0.0783126\pi$
$230$	5.71474			0.376819
$231$	13.5328	+	6.91837i	0.890392	+	0.455195i
$232$	−3.52473			−0.231410
$233$	2.91797	+	27.7626i	0.191162	+	1.81879i	0.498167	+	0.867081i	$0.334007\pi$
$233$	2.91797	+	27.7626i	0.191162	+	1.81879i	−0.307005	+	0.951708i	$0.599327\pi$
$234$	−2.69248	−	8.13284i	−0.176013	−	0.531661i
$235$	−13.2143	+	2.80879i	−0.862007	+	0.183225i
$236$	−1.44147	−	3.23759i	−0.0938314	−	0.210749i
$237$	5.52923	−	4.50293i	0.359162	−	0.292496i
$238$	5.80474	−	14.1969i	0.376265	−	0.920250i
$239$	−6.97039	−	21.4526i	−0.450877	−	1.38766i	−0.875908	−	0.482478i	$-0.839737\pi$
$239$	−6.97039	−	21.4526i	−0.450877	−	1.38766i	0.425031	−	0.905179i	$-0.360263\pi$
$240$	−2.63189	−	0.409373i	−0.169888	−	0.0264249i
$241$	−10.2188	+	5.89982i	−0.658250	+	0.380041i	−0.791610	−	0.611027i	$-0.790757\pi$
$241$	−10.2188	+	5.89982i	−0.658250	+	0.380041i	0.133360	+	0.991068i	$0.457423\pi$
$242$	10.3364	−	3.76292i	0.664447	−	0.241890i
$243$	15.1118	+	3.82544i	0.969421	+	0.245402i
$244$	−4.51044	−	6.20809i	−0.288752	−	0.397432i
$245$	3.76572	−	10.0844i	0.240583	−	0.644269i
$246$	5.82163	−	9.01918i	0.371173	−	0.575042i
$247$	−7.93175	+	3.53144i	−0.504685	+	0.224700i
$248$	−0.876484	+	8.33919i	−0.0556568	+	0.529539i
$249$	1.46328	+	0.0726193i	0.0927318	+	0.00460206i
$250$	−2.44116	+	11.4848i	−0.154393	+	0.726361i
$251$	−15.9115	−	21.9003i	−1.00433	−	1.38234i	−0.922633	−	0.385679i	$-0.873967\pi$
$251$	−15.9115	−	21.9003i	−1.00433	−	1.38234i	−0.0816933	−	0.996658i	$-0.526033\pi$
$252$	−6.58643	−	4.42933i	−0.414906	−	0.279022i
$253$	11.4276	−	4.61750i	0.718446	−	0.290299i
$254$	1.51250	+	0.873245i	0.0949029	+	0.0547922i
$255$	9.68396	−	12.0267i	0.606433	−	0.753143i
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	−2.62786	+	2.36614i	−0.163922	+	0.147596i	−0.747009	−	0.664813i	$-0.768511\pi$
$257$	−2.62786	+	2.36614i	−0.163922	+	0.147596i	0.583088	+	0.812409i	$0.301844\pi$
$258$	3.30596	−	2.69232i	0.205820	−	0.167617i
$259$	13.9752	−	5.02081i	0.868375	−	0.311978i
$260$	−1.35702	+	4.17647i	−0.0841587	+	0.259014i
$261$	−7.89728	−	7.03183i	−0.488829	−	0.435259i
$262$	−5.61150	−	2.49840i	−0.346679	−	0.154352i
$263$	−7.29140	−	12.6291i	−0.449607	−	0.778742i	0.548753	−	0.835984i	$-0.315103\pi$
$263$	−7.29140	−	12.6291i	−0.449607	−	0.778742i	−0.998360	+	0.0572421i	$0.981769\pi$
$264$	−5.59368	+	1.30795i	−0.344267	+	0.0804988i
$265$	3.32073			0.203991
$266$	−3.80604	+	7.08684i	−0.233363	+	0.434522i
$267$	−16.8309	+	0.928876i	−1.03003	+	0.0568463i
$268$	−7.99461	−	8.87892i	−0.488349	−	0.542366i
$269$	−32.0505	−	3.36864i	−1.95415	−	0.205390i	−0.957585	−	0.288152i	$-0.906959\pi$
$269$	−32.0505	−	3.36864i	−1.95415	−	0.205390i	−0.996569	+	0.0827620i	$0.973626\pi$
$270$	−5.08014	−	6.16783i	−0.309168	−	0.375362i
$271$	11.9967	−	10.8018i	0.728745	−	0.656165i	−0.218806	−	0.975768i	$-0.570216\pi$
$271$	11.9967	−	10.8018i	0.728745	−	0.656165i	0.947551	+	0.319603i	$0.103550\pi$
$272$	1.79141	+	5.51340i	0.108620	+	0.334299i
$273$	−8.93805	+	9.55828i	−0.540955	+	0.578493i
$274$		−	23.0470i		−	1.39232i
$275$	1.51796	+	8.60709i	0.0915366	+	0.519027i
$276$	−6.21267	+	1.68316i	−0.373959	+	0.101314i
$277$	−3.47917	+	7.81433i	−0.209043	+	0.469518i	−0.987388	−	0.158319i	$-0.949393\pi$
$277$	−3.47917	+	7.81433i	−0.209043	+	0.469518i	0.778345	+	0.627836i	$0.216059\pi$
$278$	4.41308	−	20.7619i	0.264679	−	1.24522i
$279$	−18.6004	+	16.9356i	−1.11358	+	1.01391i
$280$	1.37564	+	3.82901i	0.0822100	+	0.228827i
$281$	14.8669	+	10.8015i	0.886886	+	0.644361i	0.935064	−	0.354478i	$-0.115341\pi$
$281$	14.8669	+	10.8015i	0.886886	+	0.644361i	−0.0481780	+	0.998839i	$0.515341\pi$
$282$	13.5384	−	6.94552i	0.806200	−	0.413599i
$283$	19.7415	+	17.7753i	1.17351	+	1.05663i	0.997386	+	0.0722638i	$0.0230224\pi$
$283$	19.7415	+	17.7753i	1.17351	+	1.05663i	0.176123	+	0.984368i	$0.443644\pi$
$284$	2.05587	−	4.61756i	0.121994	−	0.274002i
$285$	−5.71045	+	5.74221i	−0.338258	+	0.340139i
$286$	0.660992	+	9.44802i	0.0390853	+	0.558673i
$287$	−16.3529	−	1.21188i	−0.965281	−	0.0715351i
$288$	2.98178	−	0.330127i	0.175703	−	0.0194529i
$289$	−16.2439	−	3.45274i	−0.955523	−	0.203103i
$290$	1.12695	+	5.30187i	0.0661766	+	0.311337i
$291$	7.33301	−	19.2626i	0.429868	−	1.12919i
$292$	−2.77678	−	6.23676i	−0.162499	−	0.364979i
$293$	5.07903	−	15.6317i	0.296720	−	0.913211i	−0.685918	−	0.727679i	$-0.740599\pi$
$293$	5.07903	−	15.6317i	0.296720	−	0.913211i	0.982638	−	0.185532i	$-0.0594009\pi$
$294$	−1.12368	+	12.0722i	−0.0655344	+	0.704063i
$295$	−4.40907	+	3.20338i	−0.256706	+	0.186508i
$296$	−2.80633	+	4.86071i	−0.163115	+	0.282523i
$297$	−15.1422	−	8.22887i	−0.878639	−	0.477487i
$298$	5.98004	+	10.3577i	0.346414	+	0.600007i
$299$	1.10927	+	10.5540i	0.0641508	+	0.610354i
$300$	−0.251514	−	4.55734i	−0.0145212	−	0.263118i
$301$	−6.02827	−	2.46480i	−0.347464	−	0.142069i
$302$	−6.39723	+	8.80503i	−0.368119	+	0.506673i
$303$	1.03113	−	0.166247i	0.0592368	−	0.00955065i
$304$	−0.632140	−	2.97398i	−0.0362557	−	0.170570i
$305$	−7.89605	+	8.76945i	−0.452127	+	0.502137i
$306$	−6.98550	+	15.9268i	−0.399335	+	0.910476i
$307$			5.44813i			0.310941i	0.987841	+	0.155471i	$0.0496894\pi$
$307$			5.44813i			0.310941i	−0.987841	+	0.155471i	$0.950311\pi$
$308$	5.84464	+	6.54524i	0.333029	+	0.372950i
$309$	−33.4029	−	8.85108i	−1.90023	−	0.503521i
$310$	12.8240	−	1.34785i	0.728352	−	0.0765529i
$311$	0.153058	+	0.137814i	0.00867911	+	0.00781471i	0.673459	−	0.739225i	$-0.264808\pi$
$311$	0.153058	+	0.137814i	0.00867911	+	0.00781471i	−0.664780	+	0.747040i	$0.731475\pi$
$312$	0.245163	−	4.94005i	0.0138796	−	0.279675i
$313$	12.1422	−	5.40605i	0.686317	−	0.305568i	−0.0337923	−	0.999429i	$-0.510758\pi$
$313$	12.1422	−	5.40605i	0.686317	−	0.305568i	0.720109	+	0.693861i	$0.244092\pi$
$314$	2.43395	+	1.76837i	0.137356	+	0.0997947i
$315$	−4.55671	+	11.3234i	−0.256741	+	0.638002i
$316$	3.91549	−	1.27222i	0.220263	−	0.0715679i
$317$	−16.7375	+	1.75918i	−0.940073	+	0.0988056i	−0.562153	−	0.827033i	$-0.690027\pi$
$317$	−16.7375	+	1.75918i	−0.940073	+	0.0988056i	−0.377919	+	0.925839i	$0.623360\pi$
$318$	−3.61006	+	0.978051i	−0.202442	+	0.0548464i
$319$	6.53742	+	9.69141i	0.366025	+	0.542615i
$320$	−1.33177	−	0.768898i	−0.0744482	−	0.0429827i
$321$	−15.5007	+	5.99952i	−0.865164	+	0.334861i
$322$	6.80049	+	7.10099i	0.378976	+	0.395722i
$323$	16.7631	+	5.44666i	0.932723	+	0.303060i
$324$	7.33938	+	5.20898i	0.407743	+	0.289388i
$325$	−7.48394	−	0.786594i	−0.415134	−	0.0436324i
$326$	21.8991	−	4.65480i	1.21288	−	0.257806i
$327$	−2.34898	+	4.64190i	−0.129899	+	0.256698i
$328$	5.01410	−	3.64295i	0.276857	−	0.201149i
$329$	−19.2150	−	13.0773i	−1.05936	−	0.720976i
$330$	3.75585	+	7.99578i	0.206753	+	0.440153i
$331$	−2.59582	+	4.49610i	−0.142679	+	0.247128i	−0.928505	−	0.371321i	$-0.878905\pi$
$331$	−2.59582	+	4.49610i	−0.142679	+	0.247128i	0.785825	+	0.618448i	$0.212238\pi$
$332$	0.772738	+	0.344045i	0.0424095	+	0.0188819i
$333$	−15.9848	+	5.29196i	−0.875961	+	0.289998i
$334$	−4.77496	−	5.30313i	−0.261274	−	0.290174i
$335$	−10.7995	+	14.8642i	−0.590040	+	0.812120i
$336$	−2.62325	−	3.75747i	−0.143110	−	0.204987i
$337$	9.96836	+	3.23892i	0.543011	+	0.176435i	0.567663	−	0.823261i	$-0.307848\pi$
$337$	9.96836	+	3.23892i	0.543011	+	0.176435i	−0.0246518	+	0.999696i	$0.507848\pi$
$338$	4.73939	+	1.00739i	0.257789	+	0.0547947i
$339$	18.6626	−	23.1776i	1.01362	−	1.25883i
$340$	7.72045	−	4.45740i	0.418700	−	0.241737i
$341$	24.5546	−	13.0570i	1.32971	−	0.707075i
$342$	4.51676	−	7.92442i	0.244238	−	0.428504i
$343$	17.0118	−	7.32115i	0.918550	−	0.395305i
$344$	2.34109	−	0.760667i	0.126223	−	0.0410124i
$345$	4.51814	+	8.80689i	0.243248	+	0.474147i
$346$	−1.30085	+	12.3768i	−0.0699341	+	0.665378i
$347$	−2.19708	+	20.9038i	−0.117945	+	1.12217i	0.762158	+	0.647391i	$0.224140\pi$
$347$	−2.19708	+	20.9038i	−0.117945	+	1.12217i	−0.880103	+	0.474783i	$0.842527\pi$
$348$	−2.78669	−	5.43190i	−0.149382	−	0.291181i
$349$	−22.6164	+	7.34851i	−1.21063	+	0.393357i	−0.843660	−	0.536877i	$-0.819604\pi$
$349$	−22.6164	+	7.34851i	−1.21063	+	0.393357i	−0.366967	+	0.930234i	$0.619604\pi$
$350$	−5.92795	+	3.67000i	−0.316862	+	0.196169i
$351$	10.4047	−	10.5792i	0.555361	−	0.564678i
$352$	−3.28436	−	0.461474i	−0.175057	−	0.0245966i
$353$	−13.4986	+	7.79343i	−0.718459	+	0.414803i	−0.814185	−	0.580605i	$-0.802816\pi$
$353$	−13.4986	+	7.79343i	−0.718459	+	0.414803i	0.0957262	+	0.995408i	$0.469483\pi$
$354$	3.84975	−	4.78109i	0.204612	−	0.254112i
$355$	−7.60301	−	1.61607i	−0.403526	−	0.0857721i
$356$	−9.25578	−	3.00739i	−0.490555	−	0.159391i
$357$	26.4679	−	2.27866i	1.40083	−	0.120600i
$358$	−5.33342	+	7.34082i	−0.281880	+	0.387975i
$359$	−1.94638	−	2.16167i	−0.102726	−	0.114089i	0.689589	−	0.724201i	$-0.257791\pi$
$359$	−1.94638	−	2.16167i	−0.102726	−	0.114089i	−0.792315	+	0.610112i	$0.791124\pi$
$360$	−1.44993	−	4.37962i	−0.0764178	−	0.230826i
$361$	8.91239	+	3.96805i	0.469073	+	0.208845i
$362$	−3.55832	+	6.16318i	−0.187021	+	0.323930i
$363$	13.9710	+	12.9542i	0.733288	+	0.679918i
$364$	−6.80441	+	3.28377i	−0.356648	+	0.172116i
$365$	−8.49347	+	6.17087i	−0.444568	+	0.322998i
$366$	6.00117	−	11.8592i	0.313686	−	0.619888i
$367$	14.4830	−	3.07845i	0.756004	−	0.160694i	0.186243	−	0.982504i	$-0.440369\pi$
$367$	14.4830	−	3.07845i	0.756004	−	0.160694i	0.569761	+	0.821810i	$0.307036\pi$
$368$	−3.69584	−	0.388448i	−0.192659	−	0.0202492i
$369$	18.5019	+	1.84095i	0.963172	+	0.0958359i
$370$	8.20869	+	2.66717i	0.426750	+	0.138659i
$371$	3.95163	+	4.12625i	0.205159	+	0.214224i
$372$	−13.5443	+	5.24232i	−0.702241	+	0.271802i
$373$	16.2860	+	9.40275i	0.843259	+	0.486856i	0.858371	−	0.513030i	$-0.171477\pi$
$373$	16.2860	+	9.40275i	0.843259	+	0.486856i	−0.0151118	+	0.999886i	$0.504810\pi$
$374$	11.8368	−	15.1514i	0.612064	−	0.783462i
$375$	−19.6290	+	5.31796i	−1.01364	+	0.274618i
$376$	8.73687	−	0.918282i	0.450570	−	0.0473568i
$377$	−9.57277	+	3.11038i	−0.493023	+	0.160193i
$378$	1.61866	−	13.6521i	0.0832548	−	0.702188i
$379$	−3.58670	−	2.60589i	−0.184236	−	0.133856i	0.491844	−	0.870683i	$-0.336323\pi$
$379$	−3.58670	−	2.60589i	−0.184236	−	0.133856i	−0.676081	+	0.736828i	$0.736323\pi$
$380$	−4.27133	+	1.90172i	−0.219114	+	0.0975560i
$381$	−0.149939	+	3.02129i	−0.00768163	+	0.154785i
$382$	−5.81307	−	5.23412i	−0.297423	−	0.267801i
$383$	−16.0454	+	1.68644i	−0.819884	+	0.0861733i	−0.505177	−	0.863016i	$-0.668573\pi$
$383$	−16.0454	+	1.68644i	−0.819884	+	0.0861733i	−0.314707	+	0.949189i	$0.601906\pi$
$384$	1.67427	+	0.443647i	0.0854397	+	0.0226398i
$385$	7.97661	−	10.8841i	0.406525	−	0.554707i
$386$			5.08430i			0.258784i
$387$	6.76282	+	2.96617i	0.343773	+	0.150779i
$388$	7.96257	−	8.84333i	0.404238	−	0.448952i
$389$	2.04013	+	9.59804i	0.103439	+	0.486640i	0.999120	+	0.0419439i	$0.0133551\pi$
$389$	2.04013	+	9.59804i	0.103439	+	0.486640i	−0.895681	+	0.444696i	$0.853312\pi$
$390$	−7.50916	+	1.21069i	−0.380241	+	0.0613056i
$391$	12.6628	−	17.4289i	0.640386	−	0.881416i
$392$	−3.12083	+	6.26581i	−0.157626	+	0.316471i
$393$	−0.586272	−	10.6230i	−0.0295735	−	0.535861i
$394$	2.71755	+	25.8557i	0.136908	+	1.30259i
$395$	−3.16554	−	5.48288i	−0.159276	−	0.275873i
$396$	−6.43809	−	7.58624i	−0.323526	−	0.381223i
$397$	15.4632	−	26.7830i	0.776076	−	1.34420i	−0.158112	−	0.987421i	$-0.550541\pi$
$397$	15.4632	−	26.7830i	0.776076	−	1.34420i	0.934188	−	0.356781i	$-0.116126\pi$
$398$	14.8628	−	10.7984i	0.745003	−	0.541277i
$399$	−13.9305	−	0.262481i	−0.697397	−	0.0131405i
$400$	0.814317	−	2.50621i	0.0407159	−	0.125311i
$401$	5.08300	+	11.4166i	0.253833	+	0.570118i	0.994849	−	0.101369i	$-0.0323224\pi$
$401$	5.08300	+	11.4166i	0.253833	+	0.570118i	−0.741016	+	0.671487i	$0.765656\pi$
$402$	7.36251	−	19.3401i	0.367209	−	0.964598i
$403$	4.97844	+	23.4217i	0.247994	+	1.16672i
$404$	0.589834	+	0.125373i	0.0293453	+	0.00623754i
$405$	5.48871	−	12.7053i	0.272736	−	0.631330i
$406$	−5.24691	+	7.70949i	−0.260400	+	0.382615i
$407$	18.5697	−	1.29915i	0.920467	−	0.0643967i
$408$	−7.08030	+	7.11967i	−0.350527	+	0.352476i
$409$	−1.88231	+	4.22774i	−0.0930744	+	0.209049i	−0.954083	−	0.299541i	$-0.903166\pi$
$409$	−1.88231	+	4.22774i	−0.0930744	+	0.209049i	0.861009	+	0.508590i	$0.169833\pi$
$410$	−7.08283	−	6.37741i	−0.349796	−	0.314958i
$411$	35.5174	−	18.2212i	1.75194	−	0.898787i
$412$	−16.1405	−	11.7268i	−0.795185	−	0.577736i
$413$	−9.22718	−	1.66661i	−0.454040	−	0.0820083i
$414$	−7.50569	−	8.24351i	−0.368884	−	0.405146i
$415$	0.270445	−	1.27235i	0.0132756	−	0.0624570i
$416$	1.16150	−	2.60877i	0.0569471	−	0.127905i
$417$	35.4849	−	9.61368i	1.73770	−	0.470784i
$418$	−7.00465	+	7.25402i	−0.342609	+	0.354806i
$419$			18.6281i			0.910045i	0.890480	+	0.455022i	$0.150369\pi$
$419$			18.6281i			0.910045i	−0.890480	+	0.455022i	$0.849631\pi$
$420$	−4.81323	+	5.14723i	−0.234861	+	0.251159i
$421$	0.740760	+	2.27983i	0.0361024	+	0.111112i	0.967484	−	0.252933i	$-0.0813953\pi$
$421$	0.740760	+	2.27983i	0.0361024	+	0.111112i	−0.931381	+	0.364045i	$0.881395\pi$
$422$	−9.95671	+	8.96507i	−0.484685	+	0.436413i
$423$	21.4072	+	15.3726i	1.04085	+	0.747441i
$424$	−2.14758	−	0.225720i	−0.104296	−	0.0109619i
$425$	10.2220	+	11.3527i	0.495840	+	0.550686i
$426$	8.74144	−	0.482429i	0.423524	−	0.0233738i
$427$	−20.2929	+	0.624142i	−0.982043	+	0.0302043i
$428$	−9.59628			−0.463854
$429$	−14.0376	+	8.48835i	−0.677741	+	0.409822i
$430$	−1.89269	−	3.27824i	−0.0912738	−	0.158091i
$431$	6.01065	+	2.67611i	0.289523	+	0.128904i	0.546359	−	0.837551i	$-0.316013\pi$
$431$	6.01065	+	2.67611i	0.289523	+	0.128904i	−0.256836	+	0.966455i	$0.582680\pi$
$432$	2.86618	+	4.33417i	0.137899	+	0.208528i
$433$	2.81285	−	8.65706i	0.135177	−	0.416032i	−0.860441	−	0.509551i	$-0.829812\pi$
$433$	2.81285	−	8.65706i	0.135177	−	0.416032i	0.995617	+	0.0935190i	$0.0298116\pi$
$434$	16.9352	+	14.3308i	0.812915	+	0.687899i
$435$	−7.27964	+	5.92844i	−0.349032	+	0.284247i
$436$	−2.23211	+	2.00980i	−0.106899	+	0.0962522i
$437$	−7.56037	+	8.39665i	−0.361662	+	0.401666i
$438$	7.41600	−	9.21011i	0.354350	−	0.440076i
$439$	29.1172	+	16.8108i	1.38969	+	0.802338i	0.993280	−	0.115736i	$-0.0369227\pi$
$439$	29.1172	+	16.8108i	1.38969	+	0.802338i	0.396410	+	0.918074i	$0.370256\pi$
$440$	0.355951	+	5.08785i	0.0169693	+	0.242554i
$441$	−19.4926	+	7.81271i	−0.928219	+	0.372034i
$442$	9.73054	+	13.3929i	0.462835	+	0.637037i
$443$	7.18896	−	33.8214i	0.341558	−	1.60690i	−0.387109	−	0.922034i	$-0.626526\pi$
$443$	7.18896	−	33.8214i	0.341558	−	1.60690i	0.728667	−	0.684868i	$-0.240140\pi$
$444$	−9.70947	−	0.481858i	−0.460791	−	0.0228680i
$445$	−1.56437	+	14.8840i	−0.0741583	+	0.705569i
$446$	−7.81063	+	3.47752i	−0.369844	+	0.164665i
$447$	−11.2342	+	17.4047i	−0.531361	+	0.823213i
$448$	−0.629381	−	2.56980i	−0.0297355	−	0.121412i
$449$	20.6335	+	28.3995i	0.973753	+	1.34026i	0.940128	+	0.340822i	$0.110705\pi$
$449$	20.6335	+	28.3995i	0.973753	+	1.34026i	0.0336257	+	0.999434i	$0.489295\pi$
$450$	6.82439	−	3.99069i	0.321705	−	0.188123i
$451$	−19.3162	−	7.02980i	−0.909566	−	0.331020i
$452$	14.8786	−	8.59017i	0.699831	−	0.404048i
$453$	−18.6270	−	2.89730i	−0.875173	−	0.136127i
$454$	3.44139	+	10.5915i	0.161512	+	0.497084i
$455$	7.11496	+	9.18523i	0.333554	+	0.430610i
$456$	4.08338	−	3.32544i	0.191222	−	0.155728i
$457$	16.5405	+	37.1505i	0.773731	+	1.73783i	0.668918	+	0.743336i	$0.266758\pi$
$457$	16.5405	+	37.1505i	0.773731	+	1.73783i	0.104813	+	0.994492i	$0.466576\pi$
$458$	4.16935	−	0.886223i	0.194821	−	0.0414105i
$459$	−30.0674	+	1.82669i	−1.40342	+	0.0852627i
$460$	0.597353	+	5.68344i	0.0278517	+	0.264992i
$461$	5.11725			0.238334			0.119167	−	0.992874i	$-0.461978\pi$
$461$	5.11725			0.238334			0.119167	+	0.992874i	$0.461978\pi$
$462$	−5.46591	+	14.1818i	−0.254297	+	0.659798i
$463$	19.5779			0.909864			0.454932	−	0.890526i	$-0.349664\pi$
$463$	19.5779			0.909864			0.454932	+	0.890526i	$0.349664\pi$
$464$	−0.368435	−	3.50542i	−0.0171042	−	0.162735i
$465$	12.2159	+	18.6972i	0.566500	+	0.867060i
$466$	−27.3055	+	5.80397i	−1.26490	+	0.268864i
$467$	−9.67112	−	21.7217i	−0.447526	−	1.00516i	−0.986638	−	0.162926i	$-0.947907\pi$
$467$	−9.67112	−	21.7217i	−0.447526	−	1.00516i	0.539112	−	0.842234i	$-0.318760\pi$
$468$	7.80685	−	3.52784i	0.360872	−	0.163075i
$469$	−31.3212	+	4.26913i	−1.44628	+	0.197130i
$470$	−4.17467	−	12.8483i	−0.192563	−	0.592649i
$471$	−0.800893	+	5.14900i	−0.0369032	+	0.237254i
$472$	3.06918	−	1.77199i	0.141270	−	0.0815624i
$473$	−6.43357	−	5.02610i	−0.295816	−	0.231100i
$474$	5.05622	+	5.02826i	0.232240	+	0.230955i
$475$	−4.70938	−	6.48191i	−0.216081	−	0.297410i
$476$	14.7259	+	4.28896i	0.674961	+	0.196584i
$477$	−4.36141	−	4.79015i	−0.199695	−	0.219326i
$478$	20.6065	−	9.17461i	0.942520	−	0.419637i
$479$	−1.06765	+	10.1580i	−0.0487821	+	0.464131i	0.942676	+	0.333708i	$0.108300\pi$
$479$	−1.06765	+	10.1580i	−0.0487821	+	0.464131i	−0.991459	+	0.130422i	$0.958367\pi$
$480$	0.132023	−	2.66027i	0.00602598	−	0.121424i
$481$	−3.33237	+	15.6776i	−0.151943	+	0.714835i
$482$	−6.93565	−	9.54610i	−0.315910	−	0.434813i
$483$	−5.56666	+	16.0942i	−0.253292	+	0.732313i
$484$	4.82275	+	9.88641i	0.219216	+	0.449382i
$485$	−15.8479	−	9.14979i	−0.719616	−	0.415471i
$486$	−2.22487	+	15.4289i	−0.100922	+	0.699868i
$487$	−12.1923	+	13.5410i	−0.552487	+	0.613599i	−0.953103	−	0.302647i	$-0.902130\pi$
$487$	−12.1923	+	13.5410i	−0.552487	+	0.613599i	0.400615	+	0.916246i	$0.368796\pi$
$488$	5.70261	−	5.13466i	0.258145	−	0.232435i
$489$	24.4871	+	30.0682i	1.10735	+	1.35973i
$490$	10.4228	+	2.69099i	0.470854	+	0.121566i
$491$	12.5746	−	38.7006i	0.567483	−	1.74653i	−0.0929749	−	0.995668i	$-0.529638\pi$
$491$	12.5746	−	38.7006i	0.567483	−	1.74653i	0.660458	−	0.750863i	$-0.270362\pi$
$492$	9.57829	+	4.84698i	0.431823	+	0.218519i
$493$	18.6668	+	8.31100i	0.840711	+	0.374308i
$494$	−4.34119	−	7.51916i	−0.195319	−	0.338303i
$495$	−9.35273	+	12.1096i	−0.420374	+	0.544287i
$496$	−8.38512			−0.376503
$497$	−7.03942	−	11.3704i	−0.315761	−	0.510032i
$498$	0.0807334	+	1.46286i	0.00361775	+	0.0655523i
$499$	24.4819	+	27.1899i	1.09596	+	1.21719i	0.974452	+	0.224597i	$0.0721065\pi$
$499$	24.4819	+	27.1899i	1.09596	+	1.21719i	0.121509	+	0.992590i	$0.461227\pi$
$500$	−11.6770	−	1.22731i	−0.522213	−	0.0548868i
$501$	4.39742	−	11.5513i	0.196462	−	0.516075i
$502$	20.1172	−	18.1136i	0.897872	−	0.808448i
$503$	−7.83301	−	24.1075i	−0.349256	−	1.07490i	−0.959265	−	0.282506i	$-0.908834\pi$
$503$	−7.83301	−	24.1075i	−0.349256	−	1.07490i	0.610009	−	0.792395i	$-0.291166\pi$
$504$	3.71660	−	7.01334i	0.165550	−	0.312399i
$505$		−	0.927307i		−	0.0412646i
$506$	5.78671	+	10.8823i	0.257251	+	0.483778i
$507$	2.19454	+	8.10024i	0.0974631	+	0.359744i
$508$	−0.710361	+	1.59550i	−0.0315172	+	0.0707887i
$509$	−0.850616	+	4.00183i	−0.0377029	+	0.177378i	−0.992970	−	0.118366i	$-0.962234\pi$
$509$	−0.850616	+	4.00183i	−0.0377029	+	0.177378i	0.955267	+	0.295744i	$0.0955677\pi$
$510$	12.9731	+	8.37378i	0.574458	+	0.370797i
$511$	−17.7749	−	3.21049i	−0.786315	−	0.142024i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	15.7832	+	0.695557i	0.696845	+	0.0307096i
$514$	−2.62786	−	2.36614i	−0.115910	−	0.104366i
$515$	−12.4787	+	28.0277i	−0.549879	+	1.23505i
$516$	3.02314	+	3.00642i	0.133086	+	0.132350i
$517$	−18.7294	−	22.3192i	−0.823716	−	0.981599i
$518$	6.45411	+	13.3738i	0.283577	+	0.587611i
$519$	−20.1021	+	7.78048i	−0.882382	+	0.341525i
$520$	−4.29544	−	0.913024i	−0.188368	−	0.0400388i
$521$	−2.19412	−	10.3225i	−0.0961261	−	0.452238i	−0.999716	−	0.0238389i	$-0.992411\pi$
$521$	−2.19412	−	10.3225i	−0.0961261	−	0.452238i	0.903590	−	0.428399i	$-0.140922\pi$
$522$	6.16782	−	8.58905i	0.269958	−	0.375932i
$523$	−13.6552	−	30.6700i	−0.597099	−	1.34111i	−0.918972	−	0.394323i	$-0.870979\pi$
$523$	−13.6552	−	30.6700i	−0.597099	−	1.34111i	0.321873	−	0.946783i	$-0.395687\pi$
$524$	1.89815	−	5.84191i	0.0829211	−	0.255205i
$525$	−10.3425	−	6.23392i	−0.451382	−	0.272070i
$526$	11.7977	−	8.57156i	0.514406	−	0.373738i
$527$	24.3048	−	42.0972i	1.05874	−	1.83378i
$528$	−1.88549	−	5.42632i	−0.0820552	−	0.236150i
$529$	−4.59495	−	7.95869i	−0.199781	−	0.346030i
$530$	0.347111	+	3.30254i	0.0150775	+	0.143453i
$531$	10.4117	+	2.15279i	0.451829	+	0.0934233i
$532$	−7.44586	−	3.04441i	−0.322819	−	0.131992i
$533$	10.4030	−	14.3185i	0.450604	−	0.620203i
$534$	−2.68309	−	16.6416i	−0.116109	−	0.720152i
$535$	3.06818	+	14.4346i	0.132649	+	0.624063i
$536$	7.99461	−	8.87892i	0.345315	−	0.383511i
$537$	−15.5295	−	2.41550i	−0.670146	−	0.104237i
$538$		−	32.2271i		−	1.38941i
$539$	23.0164	−	3.04050i	0.991387	−	0.130964i
$540$	5.60302	−	5.69703i	0.241116	−	0.245161i
$541$	10.7475	−	1.12961i	0.462071	−	0.0485657i	0.129367	−	0.991597i	$-0.458706\pi$
$541$	10.7475	−	1.12961i	0.462071	−	0.0485657i	0.332704	+	0.943031i	$0.392039\pi$
$542$	11.9967	+	10.8018i	0.515301	+	0.463979i
$543$	−12.3112	−	0.610976i	−0.528325	−	0.0262195i
$544$	−5.29595	+	2.35791i	−0.227062	+	0.101094i
$545$	3.73679	+	2.71494i	0.160067	+	0.116295i
$546$	−10.4402	−	7.88997i	−0.446799	−	0.337660i
$547$	−15.5636	+	5.05692i	−0.665451	+	0.216218i	−0.622215	−	0.782847i	$-0.713767\pi$
$547$	−15.5636	+	5.05692i	−0.665451	+	0.216218i	−0.0432365	+	0.999065i	$0.513767\pi$
$548$	22.9208	−	2.40907i	0.979127	−	0.102910i
$549$	23.0205	−	0.127671i	0.982492	−	0.00544888i
$550$	−8.40127	+	2.40933i	−0.358231	+	0.102734i
$551$	−9.28092	−	5.35834i	−0.395380	−	0.228273i
$552$	−2.32334	−	6.00270i	−0.0988878	−	0.255492i
$553$	3.04591	−	10.4580i	0.129525	−	0.444719i
$554$	−8.13520	−	2.64329i	−0.345631	−	0.112302i
$555$	2.37956	+	14.7590i	0.101007	+	0.626483i
$556$	21.1095	+	2.21870i	0.895241	+	0.0940937i
$557$	4.39280	−	0.933718i	0.186129	−	0.0395629i	−0.113904	−	0.993492i	$-0.536336\pi$
$557$	4.39280	−	0.933718i	0.186129	−	0.0395629i	0.300033	+	0.953929i	$0.403002\pi$
$558$	−18.7871	−	16.7283i	−0.795323	−	0.708165i
$559$	5.68688	−	4.13176i	0.240530	−	0.174755i
$560$	−3.66424	+	1.76834i	−0.154842	+	0.0747260i
$561$	32.7079	+	6.26254i	1.38093	+	0.264405i
$562$	−9.18826	+	15.9145i	−0.387584	+	0.671314i
$563$	−3.87105	−	1.72350i	−0.163145	−	0.0726369i	0.323539	−	0.946215i	$-0.395127\pi$
$563$	−3.87105	−	1.72350i	−0.163145	−	0.0726369i	−0.486685	+	0.873578i	$0.661794\pi$
$564$	8.32262	+	12.7382i	0.350445	+	0.536376i
$565$	−17.6783	−	19.6338i	−0.743733	−	0.825999i
$566$	−15.6144	+	21.4914i	−0.656321	+	0.903349i
$567$	22.3187	−	8.29902i	0.937299	−	0.348526i
$568$	4.80717	+	1.56194i	0.201704	+	0.0655377i
$569$	22.6666	+	4.81794i	0.950235	+	0.201979i	0.656855	−	0.754017i	$-0.271887\pi$
$569$	22.6666	+	4.81794i	0.950235	+	0.201979i	0.293380	+	0.955996i	$0.405220\pi$
$570$	−6.30766	−	5.07895i	−0.264199	−	0.212734i
$571$	25.0279	−	14.4499i	1.04739	−	0.604709i	0.125470	−	0.992097i	$-0.459956\pi$
$571$	25.0279	−	14.4499i	1.04739	−	0.604709i	0.921917	+	0.387388i	$0.126623\pi$
$572$	−9.32717	+	1.64496i	−0.389989	+	0.0687792i
$573$	3.47032	−	13.0966i	0.144975	−	0.547117i
$574$	−0.504101	−	16.3900i	−0.0210408	−	0.684105i
$575$	−9.31356	+	3.02616i	−0.388402	+	0.126200i
$576$	0.640000	+	2.93094i	0.0266666	+	0.122122i
$577$	−1.81210	+	17.2409i	−0.0754385	+	0.717750i	0.889795	+	0.456361i	$0.150847\pi$
$577$	−1.81210	+	17.2409i	−0.0754385	+	0.717750i	−0.965233	+	0.261389i	$0.915819\pi$
$578$	1.73588	−	16.5158i	0.0722032	−	0.686967i
$579$	−7.83532	+	4.01970i	−0.325625	+	0.167053i
$580$	−5.15503	+	1.67497i	−0.214051	+	0.0695494i
$581$	1.90281	−	1.17803i	0.0789418	−	0.0488729i
$582$	19.9236	+	5.27934i	0.825860	+	0.218836i
$583$	3.36255	+	6.32351i	0.139262	+	0.261893i
$584$	5.91234	−	3.41349i	0.244654	−	0.141251i
$585$	−7.80260	−	10.6151i	−0.322598	−	0.438878i
$586$	16.0769	+	3.41726i	0.664132	+	0.141166i
$587$	−8.66389	−	2.81507i	−0.357597	−	0.116190i	0.124708	−	0.992193i	$-0.460200\pi$
$587$	−8.66389	−	2.81507i	−0.357597	−	0.116190i	−0.482305	+	0.876003i	$0.660200\pi$
$588$	−12.1235	+	0.144361i	−0.499965	+	0.00595334i
$589$	−14.9852	+	20.6253i	−0.617454	+	0.849852i
$590$	−3.64670	−	4.05008i	−0.150132	−	0.166739i
$591$	−37.6973	+	24.6298i	−1.55066	+	1.01313i
$592$	−5.12743	−	2.28288i	−0.210736	−	0.0938257i
$593$	−23.8397	+	41.2916i	−0.978981	+	1.69564i	−0.312863	+	0.949798i	$0.601288\pi$
$593$	−23.8397	+	41.2916i	−0.978981	+	1.69564i	−0.666118	+	0.745846i	$0.732045\pi$
$594$	6.60100	−	15.9194i	0.270842	−	0.653180i
$595$	1.74316	−	23.5219i	0.0714626	−	0.964302i
$596$	−9.67591	+	7.02996i	−0.396341	+	0.287958i
$597$	28.3919	+	14.3674i	1.16200	+	0.588018i
$598$	−10.3802	+	2.20639i	−0.424480	+	0.0902260i
$599$	−16.2633	−	1.70934i	−0.664501	−	0.0698418i	−0.233728	−	0.972302i	$-0.575092\pi$
$599$	−16.2633	−	1.70934i	−0.664501	−	0.0698418i	−0.430773	+	0.902460i	$0.641759\pi$
$600$	4.50608	−	0.726508i	0.183960	−	0.0296596i
$601$	1.81854	+	0.590879i	0.0741797	+	0.0241025i	0.345872	−	0.938282i	$-0.387583\pi$
$601$	1.81854	+	0.590879i	0.0741797	+	0.0241025i	−0.271692	+	0.962384i	$0.587583\pi$
$602$	1.82117	−	6.25289i	0.0742253	−	0.254849i
$603$	35.6256	−	3.94428i	1.45079	−	0.160623i
$604$	−9.42549	−	5.44181i	−0.383518	−	0.221424i
$605$	13.3291	−	10.4153i	0.541904	−	0.423441i
$606$	0.273119	+	1.00810i	0.0110947	+	0.0409514i
$607$	−17.4553	+	1.83462i	−0.708487	+	0.0744650i	−0.451916	−	0.892060i	$-0.649259\pi$
$607$	−17.4553	+	1.83462i	−0.708487	+	0.0744650i	−0.256571	+	0.966525i	$0.582593\pi$
$608$	2.89161	−	0.939542i	0.117270	−	0.0381035i
$609$	−16.0292	−	1.99071i	−0.649537	−	0.0806675i
$610$	−9.54678	−	6.93614i	−0.386538	−	0.280836i
$611$	22.9180	−	10.2037i	0.927163	−	0.412800i
$612$	−16.5698	−	5.28243i	−0.669793	−	0.213529i
$613$	−14.1860	−	12.7731i	−0.572967	−	0.515902i	0.330928	−	0.943656i	$-0.392638\pi$
$613$	−14.1860	−	12.7731i	−0.572967	−	0.515902i	−0.903895	+	0.427754i	$0.859305\pi$
$614$	−5.41828	+	0.569485i	−0.218664	+	0.0229825i
$615$	4.22835	−	15.9573i	0.170504	−	0.643460i
$616$	−5.89845	+	6.49679i	−0.237655	+	0.261763i
$617$			25.9415i			1.04436i	0.852834	+	0.522182i	$0.174882\pi$
$617$			25.9415i			1.04436i	−0.852834	+	0.522182i	$0.825118\pi$
$618$	5.31104	−	34.1451i	0.213641	−	1.37352i
$619$	1.86804	−	2.07467i	0.0750829	−	0.0833880i	−0.704433	−	0.709771i	$-0.748799\pi$
$619$	1.86804	−	2.07467i	0.0750829	−	0.0833880i	0.779516	+	0.626383i	$0.215465\pi$
$620$	2.68094	+	12.6128i	0.107669	+	0.506543i
$621$	6.76985	−	18.0843i	0.271665	−	0.725698i
$622$	−0.121060	+	0.166625i	−0.00485406	+	0.00668105i
$623$	−20.3560	+	15.7680i	−0.815547	+	0.631730i
$624$	4.93861	−	0.272556i	0.197703	−	0.0109110i
$625$	0.510085	+	4.85314i	0.0204034	+	0.194125i
$626$	6.64564	+	11.5106i	0.265613	+	0.460055i
$627$	−16.7170	−	5.05963i	−0.667612	−	0.202062i
$628$	−1.50426	+	2.60546i	−0.0600266	+	0.103969i
$629$	26.3233	−	19.1250i	1.04958	−	0.762564i
$630$	−11.7377	−	3.34813i	−0.467641	−	0.133393i
$631$	5.73594	−	17.6534i	0.228344	−	0.702771i	−0.769591	−	0.638537i	$-0.779540\pi$
$631$	5.73594	−	17.6534i	0.228344	−	0.702771i	0.997935	−	0.0642336i	$-0.0204603\pi$
$632$	1.67453	+	3.76105i	0.0666092	+	0.149607i
$633$	−21.6878	−	8.25623i	−0.862012	−	0.328156i
$634$	−3.49909	−	16.4619i	−0.138967	−	0.653787i
$635$	2.62705	+	0.558397i	0.104251	+	0.0221593i
$636$	−1.35005	−	3.48805i	−0.0535329	−	0.138310i
$637$	−2.94659	+	19.7712i	−0.116748	+	0.783363i
$638$	−8.95497	+	7.51463i	−0.354531	+	0.297507i
$639$	7.65454	+	13.0899i	0.302809	+	0.517827i
$640$	0.625478	−	1.40485i	0.0247242	−	0.0555314i
$641$	−16.4752	−	14.8344i	−0.650732	−	0.585922i	0.276223	−	0.961093i	$-0.410917\pi$
$641$	−16.4752	−	14.8344i	−0.650732	−	0.585922i	−0.926955	+	0.375172i	$0.877584\pi$
$642$	−7.58692	−	14.7886i	−0.299432	−	0.583661i
$643$	−7.51353	−	5.45890i	−0.296305	−	0.215278i	0.429693	−	0.902975i	$-0.358622\pi$
$643$	−7.51353	−	5.45890i	−0.296305	−	0.215278i	−0.725998	+	0.687697i	$0.758622\pi$
$644$	−6.35124	+	7.50549i	−0.250274	+	0.295758i
$645$	3.55566	−	5.50861i	0.140004	−	0.216901i
$646$	−3.66460	+	17.2406i	−0.144182	+	0.678322i
$647$	17.3277	−	38.9187i	0.681224	−	1.53005i	−0.158687	−	0.987329i	$-0.550726\pi$
$647$	17.3277	−	38.9187i	0.681224	−	1.53005i	0.839911	−	0.542724i	$-0.182607\pi$
$648$	−4.41327	+	7.84366i	−0.173370	+	0.308128i
$649$	−10.5646	−	5.15228i	−0.414699	−	0.202245i
$650$		−	7.52517i		−	0.295161i
$651$	−8.69576	+	37.4286i	−0.340814	+	1.46694i
$652$	6.91839	+	21.2926i	0.270945	+	0.833883i
$653$	−32.6782	+	29.4236i	−1.27880	+	1.15143i	−0.298390	+	0.954444i	$0.596449\pi$
$653$	−32.6782	+	29.4236i	−1.27880	+	1.15143i	−0.980406	+	0.196988i	$0.936884\pi$
$654$	−4.86201	−	1.85090i	−0.190119	−	0.0723758i
$655$	−9.39423	−	0.987374i	−0.367063	−	0.0385799i
$656$	4.14711	+	4.60584i	0.161918	+	0.179828i
$657$	20.0567	+	4.14706i	0.782487	+	0.161792i
$658$	10.9972	−	20.4767i	0.428714	−	0.798265i
$659$	−40.0931			−1.56180			−0.780902	−	0.624654i	$-0.785240\pi$
$659$	−40.0931			−1.56180			−0.780902	+	0.624654i	$0.785240\pi$
$660$	−7.55938	+	4.57106i	−0.294249	+	0.177928i
$661$	−7.52716	−	13.0374i	−0.292773	−	0.507097i	0.681692	−	0.731640i	$-0.261245\pi$
$661$	−7.52716	−	13.0374i	−0.292773	−	0.507097i	−0.974464	+	0.224543i	$0.927911\pi$
$662$	−4.74280	−	2.11163i	−0.184334	−	0.0820709i
$663$	−12.9466	+	25.5842i	−0.502802	+	0.993607i
$664$	−0.261387	+	0.804467i	−0.0101438	+	0.0312194i
$665$	−2.19874	+	12.1734i	−0.0852636	+	0.472063i
$666$	−6.93383	−	15.3441i	−0.268681	−	0.594570i
$667$	−9.73415	+	8.76467i	−0.376908	+	0.339369i
$668$	4.77496	−	5.30313i	0.184749	−	0.205184i
$669$	−11.5343	−	9.28747i	−0.445942	−	0.359074i
$670$	−15.9117	−	9.18660i	−0.614721	−	0.354909i
$671$	−24.6948	−	6.15620i	−0.953330	−	0.237658i
$672$	3.46268	−	3.00164i	0.133576	−	0.115791i
$673$	−4.60337	−	6.33599i	−0.177447	−	0.244235i	0.711024	−	0.703168i	$-0.248232\pi$
$673$	−4.60337	−	6.33599i	−0.177447	−	0.244235i	−0.888471	+	0.458933i	$0.848232\pi$
$674$	−2.17920	+	10.2523i	−0.0839395	+	0.394904i
$675$	11.5454	+	7.36186i	0.444383	+	0.283358i
$676$	−0.506468	+	4.81872i	−0.0194796	+	0.185336i
$677$	4.41635	−	1.96628i	0.169734	−	0.0755705i	−0.320111	−	0.947380i	$-0.603720\pi$
$677$	4.41635	−	1.96628i	0.169734	−	0.0755705i	0.489845	+	0.871810i	$0.337053\pi$
$678$	25.0014	+	16.1377i	0.960172	+	0.619764i
$679$	−7.48956	−	30.5803i	−0.287423	−	1.17357i
$680$	5.23999	+	7.21223i	0.200945	+	0.276576i
$681$	−13.6016	+	13.6772i	−0.521213	+	0.524112i
$682$	15.5521	+	23.0553i	0.595521	+	0.882831i
$683$	25.9588	−	14.9873i	0.993286	−	0.573474i	0.0870310	−	0.996206i	$-0.472262\pi$
$683$	25.9588	−	14.9873i	0.993286	−	0.573474i	0.906255	+	0.422732i	$0.138929\pi$
$684$	8.35314	+	3.66369i	0.319390	+	0.140085i
$685$	−10.9521	−	33.7070i	−0.418457	−	1.28788i
$686$	9.05926	+	16.1533i	0.345884	+	0.616737i
$687$	4.66208	+	5.72466i	0.177869	+	0.218409i
$688$	1.00121	+	2.24875i	0.0381708	+	0.0857330i
$689$	−6.03176	+	1.28209i	−0.229792	+	0.0488437i
$690$	−8.28637	+	5.41396i	−0.315457	+	0.206106i
$691$	1.57506	+	14.9857i	0.0599179	+	0.570081i	0.982758	+	0.184897i	$0.0591953\pi$
$691$	1.57506	+	14.9857i	0.0599179	+	0.570081i	−0.922840	+	0.385184i	$0.874138\pi$
$692$	−12.4449			−0.473085
$693$	−26.1767	+	2.78888i	−0.994372	+	0.105941i
$694$	−21.0189			−0.797867
$695$	−3.41190	−	32.4621i	−0.129421	−	1.23136i
$696$	5.11086	−	3.33922i	0.193727	−	0.126573i
$697$	−35.1441	+	7.47012i	−1.33118	+	0.282951i
$698$	−9.67231	−	21.7244i	−0.366102	−	0.822279i
$699$	−30.5324	−	37.4914i	−1.15484	−	1.41805i
$700$	−4.26953	−	5.51185i	−0.161373	−	0.208329i
$701$	−11.9132	−	36.6650i	−0.449955	−	1.38482i	−0.876957	−	0.480568i	$-0.840430\pi$
$701$	−11.9132	−	36.6650i	−0.449955	−	1.38482i	0.427003	−	0.904250i	$-0.359570\pi$
$702$	11.6089	+	9.24185i	0.438149	+	0.348811i
$703$	−14.7786	+	8.53244i	−0.557386	+	0.321807i
$704$	0.115636	−	3.31461i	0.00435820	−	0.124924i
$705$	16.4998	−	16.5915i	0.621418	−	0.624874i
$706$	−9.16173	−	12.6100i	−0.344806	−	0.474585i
$707$	1.15225	−	1.10349i	0.0433347	−	0.0415009i
$708$	5.15731	+	3.32890i	0.193823	+	0.125108i
$709$	−2.85997	+	1.27334i	−0.107408	+	0.0478213i	−0.459737	−	0.888055i	$-0.652056\pi$
$709$	−2.85997	+	1.27334i	−0.107408	+	0.0478213i	0.352329	+	0.935876i	$0.385390\pi$
$710$	0.812486	−	7.73029i	0.0304921	−	0.290113i
$711$	−3.75145	+	11.7674i	−0.140690	+	0.441314i
$712$	2.02342	−	9.51943i	0.0758308	−	0.356756i
$713$	18.3158	+	25.2096i	0.685933	+	0.944106i
$714$	5.03283	+	26.0847i	0.188349	+	0.976196i
$715$	5.45647	+	13.5039i	0.204060	+	0.505018i
$716$	−7.85810	−	4.53688i	−0.293671	−	0.169551i
$717$	30.4306	+	24.5028i	1.13645	+	0.915074i
$718$	1.94638	−	2.16167i	0.0726382	−	0.0806729i
$719$	17.6956	−	15.9332i	0.659934	−	0.594207i	−0.269587	−	0.962976i	$-0.586887\pi$
$719$	17.6956	−	15.9332i	0.659934	−	0.594207i	0.929521	+	0.368769i	$0.120221\pi$
$720$	4.20407	−	1.89978i	0.156676	−	0.0708005i
$721$	−49.6761	+	17.8470i	−1.85003	+	0.664655i
$722$	−3.01472	+	9.27834i	−0.112196	+	0.345304i
$723$	9.22793	−	18.2357i	0.343190	−	0.678191i
$724$	−6.50137	−	2.89459i	−0.241621	−	0.107577i
$725$	−4.64416	−	8.04393i	−0.172480	−	0.298744i
$726$	−11.4228	+	15.2486i	−0.423942	+	0.565927i
$727$	11.6051			0.430410			0.215205	−	0.976569i	$-0.430958\pi$
$727$	11.6051			0.430410			0.215205	+	0.976569i	$0.430958\pi$
$728$	−3.97703	−	6.42389i	−0.147399	−	0.238085i
$729$	−25.5362	+	8.76952i	−0.945784	+	0.324797i
$730$	−7.02487	−	7.80191i	−0.260002	−	0.288762i
$731$	−14.1919	−	1.49163i	−0.524905	−	0.0551698i
$732$	12.4215	+	4.72868i	0.459111	+	0.174777i
$733$	10.5769	−	9.52348i	0.390667	−	0.351758i	−0.450269	−	0.892893i	$-0.648672\pi$
$733$	10.5769	−	9.52348i	0.390667	−	0.351758i	0.840936	+	0.541135i	$0.182005\pi$
$734$	4.57546	+	14.0818i	0.168883	+	0.519770i
$735$	4.09334	+	18.1899i	0.150985	+	0.670944i
$736$		−	3.71619i		−	0.136981i
$737$	−39.2408	−	5.51358i	−1.44545	−	0.203095i
$738$	0.103116	+	18.5930i	0.00379577	+	0.684418i
$739$	3.07755	−	6.91228i	0.113209	−	0.254272i	−0.848051	−	0.529915i	$-0.822224\pi$
$739$	3.07755	−	6.91228i	0.113209	−	0.254272i	0.961260	+	0.275642i	$0.0888906\pi$
$740$	−1.79451	+	8.44252i	−0.0659676	+	0.310353i
$741$	8.15546	−	12.6349i	0.299598	−	0.464153i
$742$	−3.69058	+	4.36130i	−0.135486	+	0.160108i
$743$	−13.0117	−	9.45356i	−0.477354	−	0.346818i	0.322947	−	0.946417i	$-0.395327\pi$
$743$	−13.0117	−	9.45356i	−0.477354	−	0.346818i	−0.800300	+	0.599600i	$0.795327\pi$
$744$	−6.62937	−	12.9222i	−0.243044	−	0.473749i
$745$	13.6680	+	12.3068i	0.500758	+	0.450885i
$746$	−7.64888	+	17.1797i	−0.280045	+	0.628992i
$747$	−2.19056	+	1.28097i	−0.0801483	+	0.0468682i
$748$	16.3057	+	10.1882i	0.596196	+	0.372516i
$749$	−14.2850	+	20.9895i	−0.521962	+	0.766939i
$750$	−7.34061	−	18.9656i	−0.268041	−	0.692525i
$751$	−40.1294	−	8.52977i	−1.46434	−	0.311256i	−0.594304	−	0.804240i	$-0.702573\pi$
$751$	−40.1294	−	8.52977i	−1.46434	−	0.311256i	−0.870038	+	0.492985i	$0.835906\pi$
$752$	1.82650	+	8.59302i	0.0666057	+	0.313355i
$753$	43.8193	+	16.6814i	1.59687	+	0.607904i
$754$	−4.09397	−	9.19520i	−0.149094	−	0.334870i
$755$	−5.17195	+	15.9176i	−0.188226	+	0.579301i
$756$	13.7465	+	0.182758i	0.499956	+	0.00664683i
$757$	26.2442	−	19.0675i	0.953862	−	0.693021i	0.00214449	−	0.999998i	$-0.499317\pi$
$757$	26.2442	−	19.0675i	0.953862	−	0.693021i	0.951717	+	0.306977i	$0.0993174\pi$
$758$	2.21670	−	3.83944i	0.0805142	−	0.139455i
$759$	−12.1955	+	17.5215i	−0.442669	+	0.635989i
$760$	−2.33777	−	4.04914i	−0.0848000	−	0.146878i
$761$	2.53232	+	24.0934i	0.0917964	+	0.873385i	0.939416	+	0.342780i	$0.111369\pi$
$761$	2.53232	+	24.0934i	0.0917964	+	0.873385i	−0.847619	+	0.530605i	$0.821965\pi$
$762$	−3.02041	+	0.166693i	−0.109418	+	0.00603864i
$763$	1.07324	+	7.87399i	0.0388538	+	0.285057i
$764$	4.59781	−	6.32834i	0.166343	−	0.228951i
$765$	−2.64800	+	26.6130i	−0.0957387	+	0.962195i
$766$	−3.35441	−	15.7813i	−0.121200	−	0.570200i
$767$	6.77184	−	7.52089i	0.244517	−	0.271564i
$768$	−0.266208	+	1.71147i	−0.00960594	+	0.0617574i
$769$		−	32.4846i		−	1.17142i	−0.810519	−	0.585712i	$-0.800815\pi$
$769$		−	32.4846i		−	1.17142i	0.810519	−	0.585712i	$-0.199185\pi$
$770$	11.6583	+	6.79521i	0.420136	+	0.244882i
$771$	1.56880	−	5.92045i	0.0564989	−	0.213220i
$772$	−5.05645	+	0.531454i	−0.181985	+	0.0191274i
$773$	37.5209	+	33.7839i	1.34953	+	1.21512i	0.955131	+	0.296185i	$0.0957146\pi$
$773$	37.5209	+	33.7839i	1.34953	+	1.21512i	0.394401	+	0.918938i	$0.370952\pi$
$774$	−2.24301	+	7.03582i	−0.0806235	+	0.252897i
$775$	−20.1860	+	8.98740i	−0.725103	+	0.322837i
$776$	9.62720	+	6.99457i	0.345596	+	0.251091i
$777$	−15.5074	+	20.5198i	−0.556326	+	0.736143i
$778$	−9.33221	+	3.03222i	−0.334576	+	0.108710i
$779$	18.7406	−	1.96972i	0.671452	−	0.0705724i
$780$	−1.98898	−	7.34148i	−0.0712168	−	0.262867i
$781$	−4.62135	−	16.1145i	−0.165365	−	0.576622i
$782$	18.6570	+	10.7716i	0.667174	+	0.385193i
$783$	18.1128	+	2.71452i	0.647298	+	0.0970091i
$784$	−6.55770	−	2.44878i	−0.234204	−	0.0874564i
$785$	4.40006	+	1.42967i	0.157045	+	0.0510270i
$786$	10.5036	−	1.69347i	0.374650	−	0.0604041i
$787$	9.61482	+	1.01056i	0.342731	+	0.0360225i	0.274331	−	0.961635i	$-0.411544\pi$
$787$	9.61482	+	1.01056i	0.342731	+	0.0360225i	0.0684007	+	0.997658i	$0.478210\pi$
$788$	−25.4300	+	5.40532i	−0.905907	+	0.192556i
$789$	22.5369	+	11.4045i	0.802335	+	0.406011i
$790$	5.12195	−	3.72132i	0.182231	−	0.132398i
$791$	3.35936	−	45.3306i	0.119445	−	1.61177i
$792$	6.87172	−	7.19580i	0.244176	−	0.255691i
$793$	10.9566	−	18.9774i	0.389080	−	0.673906i
$794$	28.2527	+	12.5789i	1.00265	+	0.446408i
$795$	−4.81505	+	3.14595i	−0.170772	+	0.111575i
$796$	12.2929	+	13.6526i	0.435709	+	0.483904i
$797$	15.0586	−	20.7263i	0.533401	−	0.734164i	−0.454243	−	0.890878i	$-0.650090\pi$
$797$	15.0586	−	20.7263i	0.533401	−	0.734164i	0.987644	+	0.156714i	$0.0500901\pi$
$798$	−1.19509	−	13.8816i	−0.0423057	−	0.491404i
$799$	−48.4352	−	15.7376i	−1.71352	−	0.556755i
$800$	2.57760	+	0.547886i	0.0911319	+	0.0193707i
$801$	23.5248	−	17.2919i	0.831207	−	0.610979i
$802$	−10.8227	+	6.24851i	−0.382164	+	0.220643i
$803$	−20.3513	−	9.92515i	−0.718183	−	0.350251i
$804$	20.0038	+	5.30059i	0.705478	+	0.186937i
$805$	13.3203	+	7.15378i	0.469480	+	0.252138i
$806$	−22.7730	+	7.39940i	−0.802145	+	0.260633i
$807$	49.6645	−	25.4791i	1.74827	−	0.896905i
$808$	−0.0630318	+	0.599707i	−0.00221745	+	0.0210976i
$809$	−4.13435	+	39.3357i	−0.145356	+	1.38297i	0.642110	+	0.766612i	$0.278059\pi$
$809$	−4.13435	+	39.3357i	−0.145356	+	1.38297i	−0.787466	+	0.616358i	$0.788608\pi$
$810$	13.2094	+	4.13058i	0.464131	+	0.145134i
$811$	6.05170	−	1.96632i	0.212504	−	0.0690467i	−0.200830	−	0.979626i	$-0.564364\pi$
$811$	6.05170	−	1.96632i	0.212504	−	0.0690467i	0.413334	+	0.910579i	$0.364364\pi$
$812$	−8.21571	−	4.41230i	−0.288315	−	0.154841i
$813$	−7.16183	+	27.0279i	−0.251176	+	0.947909i
$814$	3.23310	+	18.3322i	0.113320	+	0.642543i
$815$	29.8162	−	17.2144i	1.04441	−	0.602993i
$816$	−7.82076	−	6.29730i	−0.273781	−	0.220450i
$817$	7.32066	+	1.55605i	0.256118	+	0.0544395i
$818$	−4.40134	−	1.43008i	−0.153889	−	0.0500016i
$819$	3.90496	−	22.3271i	0.136450	−	0.780172i
$820$	5.60212	−	7.71066i	0.195634	−	0.269268i
$821$	1.54876	+	1.72007i	0.0540520	+	0.0600308i	0.769564	−	0.638569i	$-0.220473\pi$
$821$	1.54876	+	1.72007i	0.0540520	+	0.0600308i	−0.715512	+	0.698600i	$0.753807\pi$
$822$	21.8340	+	33.4182i	0.761548	+	1.16559i
$823$	−26.6972	−	11.8864i	−0.930607	−	0.414333i	−0.115280	−	0.993333i	$-0.536776\pi$
$823$	−26.6972	−	11.8864i	−0.930607	−	0.414333i	−0.815328	+	0.579000i	$0.803443\pi$
$824$	9.97537	−	17.2779i	0.347509	−	0.601902i
$825$	−10.3551	−	11.0422i	−0.360519	−	0.384440i
$826$	0.692973	−	9.35084i	0.0241116	−	0.325357i
$827$	17.9867	−	13.0681i	0.625459	−	0.454423i	−0.229365	−	0.973341i	$-0.573665\pi$
$827$	17.9867	−	13.0681i	0.625459	−	0.454423i	0.854824	+	0.518918i	$0.173665\pi$
$828$	7.41379	−	8.32625i	0.257647	−	0.289357i
$829$	29.6381	−	6.29977i	1.02937	−	0.218800i	0.337885	−	0.941188i	$-0.390289\pi$
$829$	29.6381	−	6.29977i	1.02937	−	0.218800i	0.691488	+	0.722388i	$0.256955\pi$
$830$	1.29364	+	0.135968i	0.0449031	+	0.00471950i
$831$	−2.35826	−	14.6268i	−0.0818070	−	0.507399i
$832$	2.71588	+	0.882444i	0.0941563	+	0.0305932i
$833$	31.3020	−	25.8248i	1.08455	−	0.894775i
$834$	13.2702	+	34.2856i	0.459509	+	1.18721i
$835$	−9.50359	−	5.48690i	−0.328885	−	0.189882i
$836$	−7.94647	−	6.20803i	−0.274834	−	0.214709i
$837$	10.9263	−	42.1781i	0.377670	−	1.45789i
$838$	−18.5261	+	1.94717i	−0.639974	+	0.0672639i
$839$	8.71380	−	2.83129i	0.300834	−	0.0977468i	−0.154711	−	0.987960i	$-0.549445\pi$
$839$	8.71380	−	2.83129i	0.300834	−	0.0977468i	0.455545	+	0.890213i	$0.349445\pi$
$840$	−5.62215	−	4.24883i	−0.193983	−	0.146599i
$841$	13.4105	+	9.74328i	0.462430	+	0.335975i
$842$	−2.18991	+	0.975009i	−0.0754691	+	0.0336010i
$843$	−31.7900	−	1.57766i	−1.09490	−	0.0543375i
$844$	−9.95671	−	8.96507i	−0.342724	−	0.308590i
$845$	7.41021	−	0.778845i	0.254919	−	0.0267931i
$846$	−13.0507	+	22.8968i	−0.448693	+	0.787209i
$847$	28.8032	+	4.16828i	0.989690	+	0.143224i
$848$		−	2.15941i		−	0.0741544i
$849$	−45.4648	−	7.07174i	−1.56035	−	0.242702i
$850$	−10.2220	+	11.3527i	−0.350611	+	0.389393i
$851$	4.33657	+	20.4020i	0.148656	+	0.699370i
$852$	1.39352	+	8.64313i	0.0477411	+	0.296109i
$853$	−3.55547	+	4.89368i	−0.121737	+	0.167556i	−0.865536	−	0.500847i	$-0.833022\pi$
$853$	−3.55547	+	4.89368i	−0.121737	+	0.167556i	0.743799	+	0.668403i	$0.233022\pi$
$854$	−2.74191	−	20.1165i	−0.0938262	−	0.688372i
$855$	2.84017	−	13.7361i	0.0971317	−	0.469764i
$856$	−1.00308	−	9.54371i	−0.0342847	−	0.326197i
$857$	−20.7960	−	36.0197i	−0.710378	−	1.23041i	−0.964715	−	0.263295i	$-0.915191\pi$
$857$	−20.7960	−	36.0197i	−0.710378	−	1.23041i	0.254338	−	0.967115i	$-0.418143\pi$
$858$	−9.90918	−	13.0734i	−0.338294	−	0.446319i
$859$	1.12045	−	1.94067i	0.0382291	−	0.0662148i	−0.846278	−	0.532742i	$-0.821162\pi$
$859$	1.12045	−	1.94067i	0.0382291	−	0.0662148i	0.884507	+	0.466527i	$0.154495\pi$
$860$	3.06244	−	2.22500i	0.104428	−	0.0758717i
$861$	24.8598	−	13.7350i	0.847219	−	0.468087i
$862$	−2.03317	+	6.25745i	−0.0692500	+	0.213130i
$863$	1.35643	+	3.04660i	0.0461735	+	0.103707i	0.935159	−	0.354227i	$-0.115256\pi$
$863$	1.35643	+	3.04660i	0.0461735	+	0.103707i	−0.888986	+	0.457935i	$0.848589\pi$
$864$	−4.01083	+	3.30352i	−0.136451	+	0.112388i
$865$	3.97896	+	18.7195i	0.135289	+	0.636484i
$866$	8.90366	+	1.89253i	0.302559	+	0.0643108i
$867$	26.8246	−	10.3824i	0.911012	−	0.352606i
$868$	−12.4821	+	18.3404i	−0.423669	+	0.622513i
$869$	7.23539	−	11.5799i	0.245444	−	0.392822i
$870$	−6.65689	−	6.62007i	−0.225690	−	0.224442i
$871$	13.8773	−	31.1689i	0.470214	−	1.05612i
$872$	−2.23211	−	2.00980i	−0.0755889	−	0.0680605i
$873$	7.61592	+	34.8778i	0.257760	+	1.18044i
$874$	−9.14092	−	6.64127i	−0.309196	−	0.224644i
$875$	−20.0668	+	23.7137i	−0.678382	+	0.801669i
$876$	9.93484	+	6.41266i	0.335667	+	0.216664i
$877$	−8.38729	+	39.4591i	−0.283219	+	1.33244i	0.574578	+	0.818450i	$0.305166\pi$
$877$	−8.38729	+	39.4591i	−0.283219	+	1.33244i	−0.857797	+	0.513989i	$0.828167\pi$
$878$	−13.6752	+	30.7149i	−0.461515	+	1.03658i
$879$	7.44432	+	27.4776i	0.251091	+	0.926796i
$880$	−5.02278	+	0.885826i	−0.169318	+	0.0298612i
$881$			3.97269i			0.133843i	0.997758	+	0.0669217i	$0.0213178\pi$
$881$			3.97269i			0.133843i	−0.997758	+	0.0669217i	$0.978682\pi$
$882$	−9.80744	−	18.5692i	−0.330234	−	0.625256i
$883$	−1.44215	−	4.43849i	−0.0485323	−	0.149367i	0.923853	−	0.382746i	$-0.125022\pi$
$883$	−1.44215	−	4.43849i	−0.0485323	−	0.149367i	−0.972386	+	0.233379i	$0.925022\pi$
$884$	−12.3025	+	11.0772i	−0.413776	+	0.372566i
$885$	3.35837	−	8.82191i	0.112891	−	0.296545i
$886$	34.3876	+	3.61428i	1.15527	+	0.121424i
$887$	28.7066	+	31.8819i	0.963874	+	1.07049i	0.997472	+	0.0710553i	$0.0226367\pi$
$887$	28.7066	+	31.8819i	0.963874	+	1.07049i	−0.0335982	+	0.999435i	$0.510697\pi$
$888$	−0.535698	−	9.70665i	−0.0179769	−	0.325734i
$889$	2.43232	+	3.92879i	0.0815773	+	0.131767i
$890$	−14.9660			−0.501661
$891$	29.7519	−	2.41336i	0.996726	−	0.0808506i
$892$	−4.27490	−	7.40435i	−0.143134	−	0.247916i
$893$	24.4009	+	10.8640i	0.816545	+	0.363549i
$894$	−18.4836	−	9.35341i	−0.618185	−	0.312825i
$895$	−4.31189	+	13.2706i	−0.144131	+	0.443589i
$896$	2.48994	−	0.894551i	0.0831829	−	0.0298848i
$897$	−11.6070	−	14.2524i	−0.387545	−	0.475874i
$898$	−26.0872	+	23.4890i	−0.870540	+	0.783838i
$899$	−19.7764	+	21.9639i	−0.659579	+	0.732537i
$900$	4.68217	+	6.36986i	0.156072	+	0.212329i
$901$	10.8412	+	6.25919i	0.361174	+	0.208524i
$902$	4.97219	−	19.9452i	0.165556	−	0.664104i
$903$	11.0760	−	2.13703i	0.368588	−	0.0711159i
$904$	10.0984	+	13.8992i	0.335866	+	0.462280i
$905$	−2.27537	+	10.7048i	−0.0756358	+	0.355839i
$906$	0.934379	−	18.8278i	0.0310427	−	0.625512i
$907$	−0.400534	+	3.81083i	−0.0132995	+	0.126537i	−0.999157	−	0.0410485i	$-0.986930\pi$
$907$	−0.400534	+	3.81083i	−0.0132995	+	0.126537i	0.985858	+	0.167585i	$0.0535969\pi$
$908$	−10.1738	+	4.52965i	−0.337628	+	0.150322i
$909$	−1.33764	+	1.21792i	−0.0443667	+	0.0403957i
$910$	−8.39119	+	8.03610i	−0.278165	+	0.266394i
$911$	20.2122	+	27.8197i	0.669660	+	0.921709i	0.999753	−	0.0222401i	$-0.00707984\pi$
$911$	20.2122	+	27.8197i	0.669660	+	0.921709i	−0.330092	+	0.943949i	$0.607080\pi$
$912$	3.73405	+	3.71340i	0.123647	+	0.122963i
$913$	2.69672	−	0.773371i	0.0892484	−	0.0255948i
$914$	−35.2181	+	20.3332i	−1.16491	+	0.672561i
$915$	3.14137	−	20.1962i	0.103851	−	0.667664i
$916$	1.31718	+	4.05388i	0.0435210	+	0.133944i
$917$	−9.95216	−	12.8480i	−0.328649	−	0.424278i
$918$	−4.95958	−	29.7117i	−0.163691	−	0.980633i
$919$	4.90275	+	11.0117i	0.161727	+	0.363244i	0.976173	−	0.216995i	$-0.0696256\pi$
$919$	4.90275	+	11.0117i	0.161727	+	0.363244i	−0.814446	+	0.580239i	$0.802959\pi$
$920$	−5.58986	+	1.18816i	−0.184292	+	0.0391725i
$921$	−5.16138	−	7.89978i	−0.170073	−	0.260307i
$922$	0.534898	+	5.08922i	0.0176159	+	0.167604i
$923$	14.4340			0.475102
$924$	−14.6755	−	3.95357i	−0.482787	−	0.130063i
$925$	−14.7904			−0.486306
$926$	2.04645	+	19.4707i	0.0672506	+	0.639847i
$927$	56.8194	−	18.8108i	1.86619	−	0.617826i
$928$	3.44771	−	0.732833i	0.113177	−	0.0240564i
$929$	−11.7342	−	26.3554i	−0.384986	−	0.864694i	−0.997255	−	0.0740437i	$-0.976410\pi$
$929$	−11.7342	−	26.3554i	−0.384986	−	0.864694i	0.612269	−	0.790650i	$-0.290257\pi$
$930$	−17.3178	+	14.1034i	−0.567874	+	0.462468i
$931$	−17.7428	+	11.7541i	−0.581496	+	0.385225i
$932$	−8.62637	−	26.5493i	−0.282566	−	0.869650i
$933$	−0.352494	−	0.0548280i	−0.0115401	−	0.00179499i
$934$	20.5918	−	11.8887i	0.673784	−	0.389009i
$935$	10.1116	−	27.7843i	0.330684	−	0.908644i
$936$	4.32455	+	7.39532i	0.141352	+	0.241724i
$937$	6.99152	+	9.62300i	0.228403	+	0.314370i	0.907802	−	0.419400i	$-0.137759\pi$
$937$	6.99152	+	9.62300i	0.228403	+	0.314370i	−0.679399	+	0.733769i	$0.737759\pi$
$938$	−7.51970	−	30.7034i	−0.245527	−	1.00250i
$939$	−12.4846	+	19.3419i	−0.407421	+	0.631198i
$940$	12.3416	−	5.49482i	0.402538	−	0.179221i
$941$	−2.95244	+	28.0906i	−0.0962467	+	0.915727i	0.834733	+	0.550655i	$0.185622\pi$
$941$	−2.95244	+	28.0906i	−0.0962467	+	0.915727i	−0.930980	+	0.365071i	$0.881045\pi$
$942$	−5.20451	−	0.258288i	−0.169572	−	0.00841546i
$943$	4.78864	−	22.5288i	0.155940	−	0.733638i
$944$	2.08310	+	2.86714i	0.0677991	+	0.0933174i
$945$	−4.12021	−	20.7358i	−0.134030	−	0.674536i
$946$	4.32608	−	6.92370i	0.140653	−	0.225109i
$947$	−10.4876	−	6.05504i	−0.340803	−	0.196763i	0.319824	−	0.947477i	$-0.396376\pi$
$947$	−10.4876	−	6.05504i	−0.340803	−	0.196763i	−0.660627	+	0.750714i	$0.729709\pi$
$948$	−4.47219	+	5.55412i	−0.145250	+	0.180389i
$949$	13.0450	−	14.4880i	0.423459	−	0.470299i
$950$	5.95414	−	5.36113i	0.193178	−	0.173938i
$951$	22.6028	−	18.4074i	0.732945	−	0.596900i
$952$	−2.72618	+	15.0936i	−0.0883562	+	0.489185i
$953$	−13.8596	+	42.6554i	−0.448956	+	1.38174i	0.429131	+	0.903242i	$0.358820\pi$
$953$	−13.8596	+	42.6554i	−0.448956	+	1.38174i	−0.878087	+	0.478501i	$0.841180\pi$
$954$	4.30801	−	4.83823i	0.139477	−	0.156643i
$955$	−10.9891	−	4.89265i	−0.355598	−	0.158322i
$956$	11.2783	+	19.5346i	0.364767	+	0.631795i
$957$	−18.6606	−	7.85920i	−0.603210	−	0.254052i
$958$	−10.2139			−0.329998
$959$	28.8505	−	53.7197i	0.931633	−	1.73470i
$960$	2.65949	−	0.146774i	0.0858348	−	0.00473711i
$961$	26.3037	+	29.2132i	0.848507	+	0.942362i
$962$	−15.9400	−	1.67536i	−0.513926	−	0.0540158i
$963$	16.7922	−	23.3841i	0.541122	−	0.753543i
$964$	8.76884	−	7.89549i	0.282425	−	0.254297i
$965$	2.41608	+	7.43594i	0.0777765	+	0.239371i
$966$	−16.5879	−	3.85386i	−0.533708	−	0.123996i
$967$			42.3317i			1.36129i	0.732611	+	0.680647i	$0.238301\pi$
$967$			42.3317i			1.36129i	−0.732611	+	0.680647i	$0.761699\pi$
$968$	−9.32813	+	5.82974i	−0.299818	+	0.187375i
$969$	−29.4664	+	7.98315i	−0.946598	+	0.256456i
$970$	7.44311	−	16.7175i	0.238984	−	0.536766i
$971$	−0.103111	+	0.485100i	−0.00330900	+	0.0155676i	−0.979771	−	0.200121i	$-0.935866\pi$
$971$	−0.103111	+	0.485100i	−0.00330900	+	0.0155676i	0.976462	+	0.215689i	$0.0691997\pi$
$972$	−15.5769	−	0.599931i	−0.499630	−	0.0192428i
$973$	36.2764	−	42.8691i	1.16297	−	1.37432i
$974$	−14.7412	−	10.7101i	−0.472339	−	0.343175i
$975$	11.5969	−	5.94948i	0.371398	−	0.190536i
$976$	5.70261	+	5.13466i	0.182536	+	0.164356i
$977$	5.55445	−	12.4755i	0.177702	−	0.399126i	−0.802631	−	0.596476i	$-0.796567\pi$
$977$	5.55445	−	12.4755i	0.177702	−	0.399126i	0.980333	+	0.197350i	$0.0632336\pi$
$978$	−27.3439	+	27.4960i	−0.874361	+	0.879224i
$979$	−29.9270	+	12.0925i	−0.956471	+	0.386477i
$980$	−1.58677	+	10.6470i	−0.0506874	+	0.340105i
$981$	−0.991571	−	8.95609i	−0.0316584	−	0.285946i
$982$	39.8030	+	8.46038i	1.27016	+	0.269982i
$983$	−11.7639	−	55.3450i	−0.375212	−	1.76523i	−0.609224	−	0.792999i	$-0.708519\pi$
$983$	−11.7639	−	55.3450i	−0.375212	−	1.76523i	0.234012	−	0.972234i	$-0.424815\pi$
$984$	−3.81922	+	10.0325i	−0.121752	+	0.319823i
$985$	16.2613	+	36.5234i	0.518127	+	1.16373i
$986$	−6.31426	+	19.4333i	−0.201087	+	0.618882i
$987$	40.2508	+	0.758413i	1.28120	+	0.0241406i
$988$	7.02420	−	5.10338i	0.223469	−	0.162360i
$989$	4.57383	−	7.92211i	0.145439	−	0.251908i
$990$	−13.0209	−	8.03570i	−0.413832	−	0.255391i
$991$	10.9736	+	19.0068i	0.348588	+	0.603772i	0.985999	−	0.166752i	$-0.0533280\pi$
$991$	10.9736	+	19.0068i	0.348588	+	0.603772i	−0.637411	+	0.770524i	$0.719995\pi$
$992$	−0.876484	−	8.33919i	−0.0278284	−	0.264769i
$993$	−0.495514	−	8.97853i	−0.0157247	−	0.284925i
$994$	10.5723	−	8.18939i	0.335333	−	0.259752i
$995$	16.6058	−	22.8559i	0.526439	−	0.724581i
$996$	−1.44641	+	0.233201i	−0.0458311	+	0.00738927i
$997$	1.91129	+	8.99194i	0.0605313	+	0.284777i	0.997994	−	0.0633083i	$-0.0201651\pi$
$997$	1.91129	+	8.99194i	0.0605313	+	0.284777i	−0.937463	+	0.348086i	$0.886832\pi$
$998$	−24.4819	+	27.1899i	−0.774961	+	0.860681i
$999$	18.1645	−	22.8168i	0.574699	−	0.721891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bc.a.107.3	yes	128
3.2	odd	2		462.2.bc.b.107.7	yes	128
7.4	even	3	inner	462.2.bc.a.305.14	yes	128
11.7	odd	10		462.2.bc.b.359.15	yes	128
21.11	odd	6		462.2.bc.b.305.15	yes	128
33.29	even	10	inner	462.2.bc.a.359.14	yes	128
77.18	odd	30		462.2.bc.b.95.7	yes	128
231.95	even	30	inner	462.2.bc.a.95.3	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.3	✓	128	231.95	even	30	inner
462.2.bc.a.107.3	yes	128	1.1	even	1	trivial
462.2.bc.a.305.14	yes	128	7.4	even	3	inner
462.2.bc.a.359.14	yes	128	33.29	even	10	inner
462.2.bc.b.95.7	yes	128	77.18	odd	30
462.2.bc.b.107.7	yes	128	3.2	odd	2
462.2.bc.b.305.15	yes	128	21.11	odd	6
462.2.bc.b.359.15	yes	128	11.7	odd	10

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.bc (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.104528 + 0.994522i) q^{2} +(-1.45000 + 0.947367i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(0.625478 + 1.40485i) q^{5} +(-1.09374 - 1.34303i) q^{6} +(-1.00131 + 2.44895i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(1.20499 - 2.74736i) q^{9} +O(q^{10})\)	\(q+(0.104528 + 0.994522i) q^{2} +(-1.45000 + 0.947367i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(0.625478 + 1.40485i) q^{5} +(-1.09374 - 1.34303i) q^{6} +(-1.00131 + 2.44895i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(1.20499 - 2.74736i) q^{9} +(-1.33177 + 0.768898i) q^{10} +(-2.04183 + 2.61361i) q^{11} +(1.22134 - 1.22814i) q^{12} +(-1.67851 - 2.31027i) q^{13} +(-2.54020 - 0.739841i) q^{14} +(-2.23785 - 1.44447i) q^{15} +(0.913545 - 0.406737i) q^{16} +(-0.605966 + 5.76538i) q^{17} +(2.85827 + 0.911213i) q^{18} +(0.632140 - 2.97398i) q^{19} +(-0.903893 - 1.24410i) q^{20} +(-0.868158 - 4.49959i) q^{21} +(-2.81272 - 1.75745i) q^{22} +(-3.21832 - 1.85810i) q^{23} +(1.34907 + 1.08628i) q^{24} +(1.76328 - 1.95832i) q^{25} +(2.12216 - 1.91080i) q^{26} +(0.855523 + 5.12524i) q^{27} +(0.470264 - 2.60362i) q^{28} +(1.08920 - 3.35222i) q^{29} +(1.20264 - 2.37658i) q^{30} +(-7.66019 - 3.41054i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.484607 - 5.72409i) q^{33} -5.79714 q^{34} +(-4.06670 + 0.125078i) q^{35} +(-0.607451 + 2.93786i) q^{36} +(-3.75561 - 4.17102i) q^{37} +(3.02377 + 0.317811i) q^{38} +(4.62251 + 1.75972i) q^{39} +(1.14280 - 1.02899i) q^{40} +(1.91521 + 5.89442i) q^{41} +(4.38419 - 1.33374i) q^{42} +2.46157i q^{43} +(1.45381 - 2.98101i) q^{44} +(4.61331 - 0.0255853i) q^{45} +(1.51151 - 3.39491i) q^{46} +(-1.82650 + 8.59302i) q^{47} +(-0.939311 + 1.45523i) q^{48} +(-4.99475 - 4.90433i) q^{49} +(2.13191 + 1.54892i) q^{50} +(-4.58328 - 8.93386i) q^{51} +(2.12216 + 1.91080i) q^{52} +(0.878311 - 1.97272i) q^{53} +(-5.00774 + 1.38657i) q^{54} +(-4.94883 - 1.23370i) q^{55} +(2.63852 + 0.195535i) q^{56} +(1.90085 + 4.91114i) q^{57} +(3.44771 + 0.732833i) q^{58} +(0.736835 + 3.46653i) q^{59} +(2.48927 + 0.947628i) q^{60} +(3.12114 + 7.01020i) q^{61} +(2.59115 - 7.97472i) q^{62} +(5.52159 + 5.70193i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(2.19570 - 3.80307i) q^{65} +(5.74338 - 0.116378i) q^{66} +(5.97388 + 10.3471i) q^{67} +(-0.605966 - 5.76538i) q^{68} +(6.42686 - 0.354690i) q^{69} +(-0.549479 - 4.03135i) q^{70} +(-2.97099 + 4.08922i) q^{71} +(-2.98526 - 0.297034i) q^{72} +(1.41941 + 6.67780i) q^{73} +(3.75561 - 4.17102i) q^{74} +(-0.701507 + 4.51004i) q^{75} +3.04042i q^{76} +(-4.35609 - 7.61738i) q^{77} +(-1.26690 + 4.78113i) q^{78} +(-4.09443 + 0.430342i) q^{79} +(1.14280 + 1.02899i) q^{80} +(-6.09599 - 6.62110i) q^{81} +(-5.66194 + 2.52086i) q^{82} +(-0.684321 - 0.497188i) q^{83} +(1.78470 + 4.22076i) q^{84} +(-8.47849 + 2.75483i) q^{85} +(-2.44808 + 0.257304i) q^{86} +(1.59644 + 5.89259i) q^{87} +(3.11665 + 1.13425i) q^{88} +(8.42825 + 4.86605i) q^{89} +(0.507668 + 4.58537i) q^{90} +(7.33845 - 1.79729i) q^{91} +(3.53431 + 1.14837i) q^{92} +(14.3383 - 2.31174i) q^{93} +(-8.73687 - 0.918282i) q^{94} +(4.57338 - 0.972101i) q^{95} +(-1.54544 - 0.782052i) q^{96} +(-9.62720 + 6.99457i) q^{97} +(4.35537 - 5.48003i) q^{98} +(4.72013 + 8.75902i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9}+O(q^{10}) \) 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9	\( 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9} + 6 q^{11} - 12 q^{15} + 16 q^{16} + 2 q^{17} + 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} - 38 q^{29} - 6 q^{30} - 3 q^{31} + 64 q^{32} - 4 q^{33} - 16 q^{34} + 31 q^{35} + 8 q^{36} + 2 q^{37} + 22 q^{39} + 5 q^{40} - 16 q^{41} + 17 q^{42} + q^{44} + 28 q^{45} + 38 q^{49} - 34 q^{50} + 16 q^{51} - 25 q^{53} + 6 q^{54} - 42 q^{55} + 20 q^{57} - 19 q^{58} - 40 q^{59} - 4 q^{60} + 40 q^{61} + 4 q^{62} + 6 q^{63} - 32 q^{64} - 20 q^{65} - 41 q^{66} + 16 q^{67} + 2 q^{68} - 68 q^{69} - 21 q^{70} - 80 q^{71} - 16 q^{72} + 10 q^{73} - 2 q^{74} - 14 q^{75} - q^{77} - 16 q^{78} + 5 q^{80} - 88 q^{81} - 8 q^{82} + 92 q^{83} - 48 q^{84} - 100 q^{85} + 40 q^{86} + 38 q^{87} - q^{88} - 164 q^{90} + 12 q^{91} + 20 q^{92} + 47 q^{93} + 40 q^{94} - 38 q^{95} - 16 q^{97} - 18 q^{98} - 138 q^{99}+O(q^{100}) \) 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9 + 6 * q^11 - 12 * q^15 + 16 * q^16 + 2 * q^17 + 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 - 38 * q^29 - 6 * q^30 - 3 * q^31 + 64 * q^32 - 4 * q^33 - 16 * q^34 + 31 * q^35 + 8 * q^36 + 2 * q^37 + 22 * q^39 + 5 * q^40 - 16 * q^41 + 17 * q^42 + q^44 + 28 * q^45 + 38 * q^49 - 34 * q^50 + 16 * q^51 - 25 * q^53 + 6 * q^54 - 42 * q^55 + 20 * q^57 - 19 * q^58 - 40 * q^59 - 4 * q^60 + 40 * q^61 + 4 * q^62 + 6 * q^63 - 32 * q^64 - 20 * q^65 - 41 * q^66 + 16 * q^67 + 2 * q^68 - 68 * q^69 - 21 * q^70 - 80 * q^71 - 16 * q^72 + 10 * q^73 - 2 * q^74 - 14 * q^75 - q^77 - 16 * q^78 + 5 * q^80 - 88 * q^81 - 8 * q^82 + 92 * q^83 - 48 * q^84 - 100 * q^85 + 40 * q^86 + 38 * q^87 - q^88 - 164 * q^90 + 12 * q^91 + 20 * q^92 + 47 * q^93 + 40 * q^94 - 38 * q^95 - 16 * q^97 - 18 * q^98 - 138 * q^99

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