LMFDB - Embedded newform 552.2.t.a.451.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(19,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 0, 15]))

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

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

chi := DirichletCharacter("552.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.t (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			451.23
Character	$\chi$	$=$	552.451
Dual form			552.2.t.a.235.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40862 - 0.125605i) q^{2} +(0.654861 + 0.755750i) q^{3} +(1.96845 - 0.353861i) q^{4} +(0.329554 + 2.29210i) q^{5} +(1.01738 + 0.982314i) q^{6} +(0.102068 - 0.223497i) q^{7} +(2.72836 - 0.745705i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(1.40862 - 0.125605i) q^{2} +(0.654861 + 0.755750i) q^{3} +(1.96845 - 0.353861i) q^{4} +(0.329554 + 2.29210i) q^{5} +(1.01738 + 0.982314i) q^{6} +(0.102068 - 0.223497i) q^{7} +(2.72836 - 0.745705i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.752116 + 3.18731i) q^{10} +(-1.07989 + 3.67777i) q^{11} +(1.55649 + 1.25592i) q^{12} +(-4.96634 + 2.26805i) q^{13} +(0.115703 - 0.327644i) q^{14} +(-1.51644 + 1.75006i) q^{15} +(3.74956 - 1.39311i) q^{16} +(3.16634 - 4.92692i) q^{17} +(-0.0761415 + 1.41216i) q^{18} +(-2.56041 - 3.98408i) q^{19} +(1.45979 + 4.39525i) q^{20} +(0.235748 - 0.0692219i) q^{21} +(-1.05921 + 5.31624i) q^{22} +(-0.134482 - 4.79395i) q^{23} +(2.35026 + 1.57362i) q^{24} +(-0.347630 + 0.102073i) q^{25} +(-6.71082 + 3.81863i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(0.121828 - 0.476061i) q^{28} +(5.43786 - 8.46148i) q^{29} +(-1.91628 + 2.65565i) q^{30} +(2.84031 + 2.46114i) q^{31} +(5.10675 - 2.43334i) q^{32} +(-3.48666 + 1.59230i) q^{33} +(3.84134 - 7.33789i) q^{34} +(0.545914 + 0.160295i) q^{35} +(0.0701201 + 1.99877i) q^{36} +(-0.0873580 + 0.607588i) q^{37} +(-4.10708 - 5.29047i) q^{38} +(-4.96634 - 2.26805i) q^{39} +(2.60837 + 6.00790i) q^{40} +(1.08039 + 7.51427i) q^{41} +(0.323386 - 0.127119i) q^{42} +(-4.07515 + 3.53114i) q^{43} +(-0.824289 + 7.62163i) q^{44} -2.31567 q^{45} +(-0.791578 - 6.73598i) q^{46} -7.48463i q^{47} +(3.50829 + 1.92144i) q^{48} +(4.54449 + 5.24462i) q^{49} +(-0.476859 + 0.187447i) q^{50} +(5.79703 - 0.833487i) q^{51} +(-8.97339 + 6.22193i) q^{52} +(-3.61923 + 7.92501i) q^{53} +(-1.11710 + 0.867226i) q^{54} +(-8.78569 - 1.26319i) q^{55} +(0.111814 - 0.685893i) q^{56} +(1.33425 - 4.54405i) q^{57} +(6.59710 - 12.6021i) q^{58} +(-2.19586 - 4.80827i) q^{59} +(-2.36575 + 3.98151i) q^{60} +(2.00820 - 2.31759i) q^{61} +(4.31006 + 3.11007i) q^{62} +(0.206697 + 0.132836i) q^{63} +(6.88785 - 4.06909i) q^{64} +(-6.83526 - 10.6359i) q^{65} +(-4.71139 + 2.68090i) q^{66} +(0.858092 + 2.92239i) q^{67} +(4.48932 - 10.8188i) q^{68} +(3.53496 - 3.24100i) q^{69} +(0.789122 + 0.157226i) q^{70} +(-4.30935 - 14.6763i) q^{71} +(0.349829 + 2.80671i) q^{72} +(8.82008 - 5.66832i) q^{73} +(-0.0467384 + 0.866837i) q^{74} +(-0.304791 - 0.195877i) q^{75} +(-6.44984 - 6.93642i) q^{76} +(0.711751 + 0.616736i) q^{77} +(-7.28058 - 2.57103i) q^{78} +(-2.27224 - 4.97551i) q^{79} +(4.42883 + 8.13525i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(2.46569 + 10.4491i) q^{82} +(0.0564639 + 0.00811829i) q^{83} +(0.439563 - 0.219682i) q^{84} +(12.3364 + 5.63387i) q^{85} +(-5.29683 + 5.48591i) q^{86} +(9.95580 - 1.43143i) q^{87} +(-0.203796 + 10.8396i) q^{88} +(-12.4755 + 10.8101i) q^{89} +(-3.26190 + 0.290860i) q^{90} +1.34146i q^{91} +(-1.96111 - 9.38904i) q^{92} +3.75827i q^{93} +(-0.940109 - 10.5430i) q^{94} +(8.28809 - 7.18167i) q^{95} +(5.18320 + 2.26592i) q^{96} +(-15.6973 + 2.25693i) q^{97} +(7.06024 + 6.81689i) q^{98} +(-3.48666 - 1.59230i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{21}{22}\right)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.40862	−	0.125605i	0.996048	−	0.0888163i
$2$	1.40862	−	0.125605i	0.996048	−	0.0888163i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$	1.96845	−	0.353861i	0.984223	−	0.176931i
$5$	0.329554	+	2.29210i	0.147381	+	1.02506i	0.920485	+	0.390777i	$0.127794\pi$
$5$	0.329554	+	2.29210i	0.147381	+	1.02506i	−0.773104	+	0.634279i	$0.781297\pi$
$6$	1.01738	+	0.982314i	0.415343	+	0.401028i
$7$	0.102068	−	0.223497i	0.0385780	−	0.0844741i	−0.889362	−	0.457204i	$-0.848851\pi$
$7$	0.102068	−	0.223497i	0.0385780	−	0.0844741i	0.927940	+	0.372730i	$0.121578\pi$
$8$	2.72836	−	0.745705i	0.964619	−	0.263646i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	0.752116	+	3.18731i	0.237840	+	1.00792i
$11$	−1.07989	+	3.67777i	−0.325600	+	1.10889i	0.620282	+	0.784379i	$0.287018\pi$
$11$	−1.07989	+	3.67777i	−0.325600	+	1.10889i	−0.945882	+	0.324512i	$0.894800\pi$
$12$	1.55649	+	1.25592i	0.449320	+	0.362554i
$13$	−4.96634	+	2.26805i	−1.37741	+	0.629044i	−0.960084	−	0.279712i	$-0.909761\pi$
$13$	−4.96634	+	2.26805i	−1.37741	+	0.629044i	−0.417329	+	0.908755i	$0.637034\pi$
$14$	0.115703	−	0.327644i	0.0309229	−	0.0875666i
$15$	−1.51644	+	1.75006i	−0.391543	+	0.451864i
$16$	3.74956	−	1.39311i	0.937391	−	0.348278i
$17$	3.16634	−	4.92692i	0.767950	−	1.19495i	−0.208249	−	0.978076i	$-0.566776\pi$
$17$	3.16634	−	4.92692i	0.767950	−	1.19495i	0.976199	−	0.216878i	$-0.0695872\pi$
$18$	−0.0761415	+	1.41216i	−0.0179467	+	0.332850i
$19$	−2.56041	−	3.98408i	−0.587399	−	0.914010i	−0.999995	−	0.00309641i	$-0.999014\pi$
$19$	−2.56041	−	3.98408i	−0.587399	−	0.914010i	0.412596	−	0.910914i	$-0.364622\pi$
$20$	1.45979	+	4.39525i	0.326419	+	0.982808i
$21$	0.235748	−	0.0692219i	0.0514445	−	0.0151055i
$22$	−1.05921	+	5.31624i	−0.225825	+	1.13343i
$23$	−0.134482	−	4.79395i	−0.0280413	−	0.999607i
$23$	−0.134482	−	4.79395i	−0.0280413	−	0.999607i
$24$	2.35026	+	1.57362i	0.479745	+	0.321214i
$25$	−0.347630	+	0.102073i	−0.0695260	+	0.0204147i
$26$	−6.71082	+	3.81863i	−1.31610	+	0.748894i
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$	0.121828	−	0.476061i	0.0230233	−	0.0899670i
$29$	5.43786	−	8.46148i	1.00979	−	1.57126i	0.204068	−	0.978957i	$-0.434584\pi$
$29$	5.43786	−	8.46148i	1.00979	−	1.57126i	0.805718	−	0.592300i	$-0.201780\pi$
$30$	−1.91628	+	2.65565i	−0.349862	+	0.484854i
$31$	2.84031	+	2.46114i	0.510135	+	0.442034i	0.871504	−	0.490388i	$-0.163145\pi$
$31$	2.84031	+	2.46114i	0.510135	+	0.442034i	−0.361369	+	0.932423i	$0.617691\pi$
$32$	5.10675	−	2.43334i	0.902754	−	0.430158i
$33$	−3.48666	+	1.59230i	−0.606949	+	0.277184i
$34$	3.84134	−	7.33789i	0.658784	−	1.25844i
$35$	0.545914	+	0.160295i	0.0922763	+	0.0270948i
$36$	0.0701201	+	1.99877i	0.0116867	+	0.333128i
$37$	−0.0873580	+	0.607588i	−0.0143616	+	0.0998869i	−0.995741	−	0.0921901i	$-0.970613\pi$
$37$	−0.0873580	+	0.607588i	−0.0143616	+	0.0998869i	0.981380	+	0.192077i	$0.0615223\pi$
$38$	−4.10708	−	5.29047i	−0.666256	−	0.858228i
$39$	−4.96634	−	2.26805i	−0.795250	−	0.363179i
$40$	2.60837	+	6.00790i	0.412419	+	0.949933i
$41$	1.08039	+	7.51427i	0.168728	+	1.17353i	0.881517	+	0.472153i	$0.156523\pi$
$41$	1.08039	+	7.51427i	0.168728	+	1.17353i	−0.712788	+	0.701379i	$0.752568\pi$
$42$	0.323386	−	0.127119i	0.0498996	−	0.0196149i
$43$	−4.07515	+	3.53114i	−0.621455	+	0.538494i	−0.907677	−	0.419670i	$-0.862146\pi$
$43$	−4.07515	+	3.53114i	−0.621455	+	0.538494i	0.286222	+	0.958163i	$0.407601\pi$
$44$	−0.824289	+	7.62163i	−0.124266	+	1.14900i
$45$	−2.31567			−0.345199
$46$	−0.791578	−	6.73598i	−0.116712	−	0.993166i
$47$		−	7.48463i		−	1.09175i	−0.837868	−	0.545873i	$-0.816198\pi$
$47$		−	7.48463i		−	1.09175i	0.837868	−	0.545873i	$-0.183802\pi$
$48$	3.50829	+	1.92144i	0.506378	+	0.277335i
$49$	4.54449	+	5.24462i	0.649213	+	0.749232i
$50$	−0.476859	+	0.187447i	−0.0674381	+	0.0265090i
$51$	5.79703	−	0.833487i	0.811746	−	0.116711i
$52$	−8.97339	+	6.22193i	−1.24439	+	0.862826i
$53$	−3.61923	+	7.92501i	−0.497139	+	1.08858i	0.480249	+	0.877132i	$0.340546\pi$
$53$	−3.61923	+	7.92501i	−0.497139	+	1.08858i	−0.977389	+	0.211451i	$0.932181\pi$
$54$	−1.11710	+	0.867226i	−0.152018	+	0.118014i
$55$	−8.78569	−	1.26319i	−1.18466	−	0.170329i
$56$	0.111814	−	0.685893i	0.0149418	−	0.0916563i
$57$	1.33425	−	4.54405i	0.176726	−	0.601874i
$58$	6.59710	−	12.6021i	0.866242	−	1.65473i
$59$	−2.19586	−	4.80827i	−0.285877	−	0.625983i	0.711150	−	0.703041i	$-0.248175\pi$
$59$	−2.19586	−	4.80827i	−0.285877	−	0.625983i	−0.997027	+	0.0770573i	$0.975448\pi$
$60$	−2.36575	+	3.98151i	−0.305417	+	0.514011i
$61$	2.00820	−	2.31759i	0.257124	−	0.296737i	−0.612481	−	0.790485i	$-0.709828\pi$
$61$	2.00820	−	2.31759i	0.257124	−	0.296737i	0.869605	+	0.493749i	$0.164374\pi$
$62$	4.31006	+	3.11007i	0.547379	+	0.394979i
$63$	0.206697	+	0.132836i	0.0260413	+	0.0167358i
$64$	6.88785	−	4.06909i	0.860981	−	0.508637i
$65$	−6.83526	−	10.6359i	−0.847809	−	1.31922i
$66$	−4.71139	+	2.68090i	−0.579932	+	0.329996i
$67$	0.858092	+	2.92239i	0.104833	+	0.357027i	0.995157	−	0.0982999i	$-0.0313404\pi$
$67$	0.858092	+	2.92239i	0.104833	+	0.357027i	−0.890324	+	0.455327i	$0.849522\pi$
$68$	4.48932	−	10.8188i	0.544411	−	1.31197i
$69$	3.53496	−	3.24100i	0.425559	−	0.390171i
$70$	0.789122	+	0.157226i	0.0943181	+	0.0187921i
$71$	−4.30935	−	14.6763i	−0.511426	−	1.74176i	−0.658450	−	0.752624i	$-0.728788\pi$
$71$	−4.30935	−	14.6763i	−0.511426	−	1.74176i	0.147024	−	0.989133i	$-0.453030\pi$
$72$	0.349829	+	2.80671i	0.0412277	+	0.330774i
$73$	8.82008	−	5.66832i	1.03231	−	0.663427i	0.0892386	−	0.996010i	$-0.471557\pi$
$73$	8.82008	−	5.66832i	1.03231	−	0.663427i	0.943074	+	0.332583i	$0.107920\pi$
$74$	−0.0467384	+	0.866837i	−0.00543323	+	0.100768i
$75$	−0.304791	−	0.195877i	−0.0351942	−	0.0226180i
$76$	−6.44984	−	6.93642i	−0.739848	−	0.795662i
$77$	0.711751	+	0.616736i	0.0811115	+	0.0702835i
$78$	−7.28058	−	2.57103i	−0.824363	−	0.291112i
$79$	−2.27224	−	4.97551i	−0.255647	−	0.559789i	0.737676	−	0.675155i	$-0.235923\pi$
$79$	−2.27224	−	4.97551i	−0.255647	−	0.559789i	−0.993323	+	0.115366i	$0.963196\pi$
$80$	4.42883	+	8.13525i	0.495158	+	0.909549i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	2.46569	+	10.4491i	0.272290	+	1.15391i
$83$	0.0564639	+	0.00811829i	0.00619772	+	0.000891098i	0.145413	−	0.989371i	$-0.453549\pi$
$83$	0.0564639	+	0.00811829i	0.00619772	+	0.000891098i	−0.139215	+	0.990262i	$0.544458\pi$
$84$	0.439563	−	0.219682i	0.0479603	−	0.0239693i
$85$	12.3364	+	5.63387i	1.33808	+	0.611079i
$86$	−5.29683	+	5.48591i	−0.571172	+	0.591561i
$87$	9.95580	−	1.43143i	1.06737	−	0.153465i
$88$	−0.203796	+	10.8396i	−0.0217248	+	1.15550i
$89$	−12.4755	+	10.8101i	−1.32240	+	1.14586i	−0.344036	+	0.938956i	$0.611794\pi$
$89$	−12.4755	+	10.8101i	−1.32240	+	1.14586i	−0.978361	+	0.206907i	$0.933660\pi$
$90$	−3.26190	+	0.290860i	−0.343835	+	0.0306593i
$91$			1.34146i			0.140623i
$92$	−1.96111	−	9.38904i	−0.204460	−	0.978875i
$93$			3.75827i			0.389714i
$94$	−0.940109	−	10.5430i	−0.0969648	−	1.08743i
$95$	8.28809	−	7.18167i	0.850341	−	0.736824i
$96$	5.18320	+	2.26592i	0.529008	+	0.231265i
$97$	−15.6973	+	2.25693i	−1.59382	+	0.229156i	−0.881320	−	0.472520i	$-0.843344\pi$
$97$	−15.6973	+	2.25693i	−1.59382	+	0.229156i	−0.712496	+	0.701676i	$0.752435\pi$
$98$	7.06024	+	6.81689i	0.713191	+	0.688610i
$99$	−3.48666	−	1.59230i	−0.350422	−	0.160032i
$100$	−0.648171	+	0.323939i	−0.0648171	+	0.0323939i
$101$	−5.04761	−	0.725736i	−0.502256	−	0.0722134i	−0.113469	−	0.993541i	$-0.536196\pi$
$101$	−5.04761	−	0.725736i	−0.502256	−	0.0722134i	−0.388786	+	0.921328i	$0.627105\pi$
$102$	8.06115	−	1.90221i	0.798172	−	0.188347i
$103$	−10.7481	−	3.15593i	−1.05904	−	0.310963i	−0.294578	−	0.955628i	$-0.595179\pi$
$103$	−10.7481	−	3.15593i	−1.05904	−	0.310963i	−0.764466	+	0.644664i	$0.776997\pi$
$104$	−11.8586	+	9.89146i	−1.16283	+	0.969938i
$105$	0.236355	+	0.517545i	0.0230659	+	0.0505072i
$106$	−4.10271	+	11.6180i	−0.398491	+	1.12844i
$107$	−5.42607	−	4.70172i	−0.524558	−	0.454532i	0.351881	−	0.936045i	$-0.385542\pi$
$107$	−5.42607	−	4.70172i	−0.524558	−	0.454532i	−0.876439	+	0.481512i	$0.840088\pi$
$108$	−1.46465	+	1.36191i	−0.140936	+	0.131050i
$109$	4.48661	+	2.88337i	0.429739	+	0.276177i	0.737578	−	0.675262i	$-0.235969\pi$
$109$	4.48661	+	2.88337i	0.429739	+	0.276177i	−0.307839	+	0.951439i	$0.599606\pi$
$110$	−12.5344	−	0.675835i	−1.19511	−	0.0644383i
$111$	−0.516392	+	0.331865i	−0.0490138	+	0.0314992i
$112$	0.0713528	−	0.980210i	0.00674220	−	0.0926211i
$113$	0.779654	+	2.65526i	0.0733437	+	0.249786i	0.988002	−	0.154443i	$-0.0493582\pi$
$113$	0.779654	+	2.65526i	0.0733437	+	0.249786i	−0.914658	+	0.404228i	$0.867540\pi$
$114$	1.30871	−	6.56845i	0.122571	−	0.615191i
$115$	10.9439	−	1.88811i	1.02052	−	0.176067i
$116$	7.70995	−	18.5802i	0.715851	−	1.72513i
$117$	−1.53818	−	5.23856i	−0.142205	−	0.484305i
$118$	−3.69709	−	6.49723i	−0.340345	−	0.598119i
$119$	−0.777972	−	1.21055i	−0.0713166	−	0.110971i
$120$	−2.83235	+	5.90561i	−0.258557	+	0.539106i
$121$	−3.10607	−	1.99615i	−0.282370	−	0.181468i
$122$	2.53770	−	3.51685i	0.229753	−	0.318401i
$123$	−4.97140	+	5.73730i	−0.448256	+	0.517315i
$124$	6.46190	+	3.83955i	0.580296	+	0.344802i
$125$	4.46129	+	9.76885i	0.399030	+	0.873753i
$126$	0.307843	+	0.161154i	0.0274248	+	0.0143567i
$127$	−5.61388	+	19.1191i	−0.498152	+	1.69655i	0.199318	+	0.979935i	$0.436127\pi$
$127$	−5.61388	+	19.1191i	−0.498152	+	1.69655i	−0.697470	+	0.716614i	$0.745691\pi$
$128$	9.19130	−	6.59698i	0.812403	−	0.583096i
$129$	−5.33732	−	0.767390i	−0.469924	−	0.0675649i
$130$	−10.9642	−	14.1234i	−0.961627	−	1.23870i
$131$	−0.947155	+	2.07398i	−0.0827533	+	0.181205i	−0.946485	−	0.322747i	$-0.895394\pi$
$131$	−0.947155	+	2.07398i	−0.0827533	+	0.181205i	0.863732	+	0.503952i	$0.168121\pi$
$132$	−6.29984	+	4.36815i	−0.548331	+	0.380199i
$133$	−1.15177	+	0.165599i	−0.0998709	+	0.0143593i
$134$	1.57580	+	4.00878i	0.136128	+	0.346306i
$135$	−1.51644	−	1.75006i	−0.130514	−	0.150621i
$136$	4.96487	−	15.8035i	0.425734	−	1.35514i
$137$		−	9.20415i		−	0.786364i	−0.919461	−	0.393182i	$-0.871374\pi$
$137$		−	9.20415i		−	0.786364i	0.919461	−	0.393182i	$-0.128626\pi$
$138$	4.57234	−	5.00936i	0.389223	−	0.426425i
$139$	−6.61670			−0.561221			−0.280611	−	0.959822i	$-0.590537\pi$
$139$	−6.61670			−0.561221			−0.280611	+	0.959822i	$0.590537\pi$
$140$	1.13132	+	0.122354i	0.0956144	+	0.0103408i
$141$	5.65651	−	4.90139i	0.476364	−	0.412772i
$142$	−7.91368	−	20.1321i	−0.664101	−	1.68945i
$143$	−2.97827	−	20.7143i	−0.249055	−	1.73222i
$144$	0.845315	+	3.90966i	0.0704429	+	0.325805i
$145$	21.1866	+	9.67558i	1.75945	+	0.803514i
$146$	11.7122	−	9.09239i	0.969310	−	0.752491i
$147$	−0.987612	+	6.86900i	−0.0814569	+	0.566545i
$148$	0.0430423	+	1.22692i	0.00353805	+	0.100852i
$149$	22.0587	+	6.47702i	1.80712	+	0.530618i	0.998345	−	0.0575008i	$-0.0183132\pi$
$149$	22.0587	+	6.47702i	1.80712	+	0.530618i	0.808774	+	0.588119i	$0.200131\pi$
$150$	−0.453939	−	0.237634i	−0.0370640	−	0.0194028i
$151$	−11.0322	+	5.03826i	−0.897791	+	0.410008i	−0.810203	−	0.586149i	$-0.800643\pi$
$151$	−11.0322	+	5.03826i	−0.897791	+	0.410008i	−0.0875883	+	0.996157i	$0.527916\pi$
$152$	−9.95666	−	8.96067i	−0.807592	−	0.726807i
$153$	4.42615	+	3.83528i	0.357833	+	0.310064i
$154$	1.08005	+	0.779349i	0.0870333	+	0.0628018i
$155$	−4.70514	+	7.32134i	−0.377926	+	0.588064i
$156$	−10.5785	−	2.70714i	−0.846961	−	0.216745i
$157$	−10.4133	+	6.69225i	−0.831075	+	0.534099i	−0.885619	−	0.464412i	$-0.846266\pi$
$157$	−10.4133	+	6.69225i	−0.831075	+	0.534099i	0.0545445	+	0.998511i	$0.482629\pi$
$158$	−3.82568	−	6.72322i	−0.304355	−	0.534871i
$159$	−8.35941	+	2.45454i	−0.662944	+	0.194658i
$160$	7.26039	+	10.9032i	0.573984	+	0.861976i
$161$	−1.08516	−	0.459251i	−0.0855226	−	0.0361941i
$162$	−1.38695	−	0.276338i	−0.108969	−	0.0217112i
$163$	4.03195	−	1.18389i	0.315807	−	0.0927293i	−0.119988	−	0.992775i	$-0.538286\pi$
$163$	4.03195	−	1.18389i	0.315807	−	0.0927293i	0.435795	+	0.900046i	$0.356467\pi$
$164$	4.78570	+	14.4091i	0.373700	+	1.12516i
$165$	−4.79875	−	7.46700i	−0.373582	−	0.581305i
$166$	0.0805562	+	0.00434346i	0.00625237	+	0.000337118i
$167$	−4.94744	+	7.69837i	−0.382845	+	0.595718i	−0.978180	−	0.207759i	$-0.933383\pi$
$167$	−4.94744	+	7.69837i	−0.382845	+	0.595718i	0.595335	+	0.803477i	$0.297019\pi$
$168$	0.591586	−	0.364661i	0.0456419	−	0.0281342i
$169$	11.0072	−	12.7030i	0.846711	−	0.977157i
$170$	18.0851	+	6.38648i	1.38706	+	0.489821i
$171$	4.30791	−	1.96736i	0.329434	−	0.150448i
$172$	−6.77219	+	8.39290i	−0.516374	+	0.639953i
$173$	−0.366594	+	1.24850i	−0.0278716	+	0.0949220i	−0.972254	−	0.233927i	$-0.924842\pi$
$173$	−0.366594	+	1.24850i	−0.0278716	+	0.0949220i	0.944383	+	0.328849i	$0.106661\pi$
$174$	13.8442	−	3.26684i	1.04953	−	0.247659i
$175$	−0.0126687	+	0.0881128i	−0.000957664	+	0.00666070i
$176$	1.07443	+	15.2945i	0.0809883	+	1.15286i
$177$	2.19586	−	4.80827i	0.165051	−	0.361412i
$178$	−16.2155	+	16.7943i	−1.21540	+	1.25879i
$179$	−3.16016	−	21.9794i	−0.236202	−	1.64282i	−0.670400	−	0.742000i	$-0.733877\pi$
$179$	−3.16016	−	21.9794i	−0.236202	−	1.64282i	0.434198	−	0.900817i	$-0.357032\pi$
$180$	−4.55826	+	0.819424i	−0.339753	+	0.0610762i
$181$	4.29493	+	4.95661i	0.319240	+	0.368422i	0.892575	−	0.450898i	$-0.148896\pi$
$181$	4.29493	+	4.95661i	0.319240	+	0.368422i	−0.573336	+	0.819321i	$0.694351\pi$
$182$	0.168494	+	1.88961i	0.0124896	+	0.140067i
$183$	3.06661			0.226690
$184$	−3.94178	−	12.9793i	−0.290592	−	0.956847i
$185$	−1.42144			−0.104506
$186$	0.472058	+	5.29399i	0.0346130	+	0.388174i
$187$	14.7008	+	16.9656i	1.07503	+	1.24065i
$188$	−2.64852	−	14.7331i	−0.193163	−	1.07452i
$189$	0.0349669	+	0.243200i	0.00254347	+	0.0176902i
$190$	10.7728	−	11.1573i	0.781538	−	0.809436i
$191$	3.18374	−	6.97143i	0.230368	−	0.504435i	−0.758782	−	0.651344i	$-0.774205\pi$
$191$	3.18374	−	6.97143i	0.230368	−	0.504435i	0.989150	+	0.146910i	$0.0469326\pi$
$192$	7.58580	+	2.54080i	0.547458	+	0.183366i
$193$	−1.59729	+	11.1094i	−0.114975	+	0.799672i	0.847983	+	0.530023i	$0.177817\pi$
$193$	−1.59729	+	11.1094i	−0.114975	+	0.799672i	−0.962959	+	0.269649i	$0.913092\pi$
$194$	−21.8281	+	5.15082i	−1.56716	+	0.369807i
$195$	3.56191	−	12.1308i	0.255074	−	0.868702i
$196$	10.8015	+	8.71564i	0.771533	+	0.622546i
$197$	15.8981	−	7.26042i	1.13269	−	0.517284i	0.241271	−	0.970458i	$-0.422436\pi$
$197$	15.8981	−	7.26042i	1.13269	−	0.517284i	0.891422	+	0.453174i	$0.149708\pi$
$198$	−5.11139	−	1.80501i	−0.363251	−	0.128277i
$199$	−12.5895	+	14.5290i	−0.892444	+	1.02994i	0.106919	+	0.994268i	$0.465901\pi$
$199$	−12.5895	+	14.5290i	−0.892444	+	1.02994i	−0.999364	+	0.0356681i	$0.988644\pi$
$200$	−0.872341	+	0.537722i	−0.0616839	+	0.0380227i
$201$	−1.64667	+	2.56226i	−0.116147	+	0.180728i
$202$	−7.20134	−	0.388284i	−0.506684	−	0.0273196i
$203$	−1.33609	−	2.07899i	−0.0937749	−	0.145917i
$204$	11.1162	−	3.69202i	0.778290	−	0.258493i
$205$	−16.8674	+	4.95271i	−1.17807	+	0.345912i
$206$	−15.5365	−	3.09550i	−1.08248	−	0.215674i
$207$	4.76429	+	0.549137i	0.331141	+	0.0381676i
$208$	−15.4619	+	15.4229i	−1.07209	+	1.06938i
$209$	17.4175	−	5.11424i	1.20479	−	0.353760i
$210$	0.397942	+	0.699339i	0.0274606	+	0.0482590i
$211$	−15.2536	+	9.80288i	−1.05010	+	0.674858i	−0.947465	−	0.319861i	$-0.896364\pi$
$211$	−15.2536	+	9.80288i	−1.05010	+	0.674858i	−0.102635	+	0.994719i	$0.532727\pi$
$212$	−4.31991	+	16.8807i	−0.296693	+	1.15937i
$213$	8.26959	−	12.8677i	0.566623	−	0.881682i
$214$	−8.23386	−	5.94141i	−0.562855	−	0.406147i
$215$	−9.43669	−	8.17694i	−0.643577	−	0.557663i
$216$	−1.89208	+	2.10239i	−0.128740	+	0.143049i
$217$	0.839964	−	0.383599i	0.0570204	−	0.0260404i
$218$	6.68212	+	3.49805i	0.452570	+	0.236918i
$219$	10.0598	+	2.95381i	0.679775	+	0.199600i
$220$	−17.7412	+	0.622389i	−1.19611	+	0.0419614i
$221$	−4.55060	+	31.6501i	−0.306107	+	2.12902i
$222$	−0.685719	+	0.532335i	−0.0460224	+	0.0357280i
$223$	0.259914	+	0.118699i	0.0174051	+	0.00794866i	0.424099	−	0.905616i	$-0.360591\pi$
$223$	0.259914	+	0.118699i	0.0174051	+	0.00794866i	−0.406693	+	0.913565i	$0.633318\pi$
$224$	−0.0226102	−	1.38971i	−0.00151071	−	0.0928539i
$225$	−0.0515615	−	0.358618i	−0.00343743	−	0.0239079i
$226$	1.43175	+	3.64233i	0.0952389	+	0.242284i
$227$	−6.25148	+	5.41694i	−0.414925	+	0.359535i	−0.837166	−	0.546949i	$-0.815789\pi$
$227$	−6.25148	+	5.41694i	−0.414925	+	0.359535i	0.422241	+	0.906484i	$0.361244\pi$
$228$	1.01844	−	9.41685i	0.0674481	−	0.623646i
$229$	−6.86772			−0.453832			−0.226916	−	0.973914i	$-0.572864\pi$
$229$	−6.86772			−0.453832			−0.226916	+	0.973914i	$0.572864\pi$
$230$	15.1786	−	4.03424i	1.00085	−	0.266010i
$231$			0.941781i			0.0619647i
$232$	8.52666	−	27.1410i	0.559802	−	1.78189i
$233$	−6.26603	−	7.23139i	−0.410502	−	0.473744i	0.512418	−	0.858736i	$-0.328750\pi$
$233$	−6.26603	−	7.23139i	−0.410502	−	0.473744i	−0.922920	+	0.384992i	$0.874204\pi$
$234$	−2.82471	−	7.18596i	−0.184657	−	0.469761i
$235$	17.1555	−	2.46659i	1.11910	−	0.160902i
$236$	−6.02390	−	8.68779i	−0.392122	−	0.565527i
$237$	2.27224	−	4.97551i	0.147598	−	0.323194i
$238$	−1.24792	−	1.60749i	−0.0808908	−	0.104198i
$239$	18.8926	+	2.71635i	1.22206	+	0.175706i	0.722993	−	0.690855i	$-0.242766\pi$
$239$	18.8926	+	2.71635i	1.22206	+	0.175706i	0.499070	+	0.866561i	$0.333675\pi$
$240$	−3.24795	+	8.67455i	−0.209654	+	0.559939i
$241$	−2.54752	+	8.67604i	−0.164100	+	0.558873i	0.835851	+	0.548957i	$0.184975\pi$
$241$	−2.54752	+	8.67604i	−0.164100	+	0.558873i	−0.999951	+	0.00991652i	$0.996843\pi$
$242$	−4.62601	−	2.42169i	−0.297371	−	0.155672i
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$	3.13293	−	5.27267i	0.200565	−	0.337548i
$245$	−10.5235	+	12.1448i	−0.672323	+	0.775902i
$246$	−6.28220	+	8.70614i	−0.400539	+	0.555083i
$247$	21.7520	+	13.9791i	1.38404	+	0.889471i
$248$	9.58467	+	4.59684i	0.608627	+	0.291900i
$249$	0.0308406	+	0.0479889i	0.00195444	+	0.00304117i
$250$	7.51130	+	13.2003i	0.475056	+	0.834860i
$251$	2.65594	+	9.04530i	0.167641	+	0.570934i	0.999864	+	0.0164924i	$0.00524994\pi$
$251$	2.65594	+	9.04530i	0.167641	+	0.570934i	−0.832223	+	0.554442i	$0.812932\pi$
$252$	0.453877	+	0.188339i	0.0285916	+	0.0118642i
$253$	17.7763	+	4.68235i	1.11758	+	0.294377i
$254$	−5.50639	+	27.6368i	−0.345502	+	1.73409i
$255$	3.82086	+	13.0127i	0.239272	+	0.814884i
$256$	12.1185	−	10.4471i	0.757404	−	0.652946i
$257$	16.8486	−	10.8279i	1.05098	−	0.675426i	0.103304	−	0.994650i	$-0.467058\pi$
$257$	16.8486	−	10.8279i	1.05098	−	0.675426i	0.947679	+	0.319223i	$0.103422\pi$
$258$	−7.61466	−	0.410570i	−0.474068	−	0.0255610i
$259$	0.126878	+	0.0815395i	0.00788381	+	0.00506662i
$260$	−17.2185	−	18.5174i	−1.06784	−	1.14840i
$261$	7.60146	+	6.58670i	0.470519	+	0.407707i
$262$	−1.07368	+	3.04043i	−0.0663324	+	0.187838i
$263$	4.39390	+	9.62131i	0.270940	+	0.593275i	0.995375	−	0.0960678i	$-0.0306266\pi$
$263$	4.39390	+	9.62131i	0.270940	+	0.593275i	−0.724435	+	0.689343i	$0.757899\pi$
$264$	−8.32545	+	6.94438i	−0.512396	+	0.427397i
$265$	−19.3576	−	5.68390i	−1.18913	−	0.349159i
$266$	−1.60161	+	0.377935i	−0.0982008	+	0.0231727i
$267$	−16.3394	−	2.34925i	−0.999954	−	0.143772i
$268$	2.72323	+	5.44893i	0.166348	+	0.332847i
$269$	−11.8601	−	5.41632i	−0.723123	−	0.330239i	0.0196279	−	0.999807i	$-0.493752\pi$
$269$	−11.8601	−	5.41632i	−0.723123	−	0.330239i	−0.742750	+	0.669568i	$0.766479\pi$
$270$	−2.35591	−	2.27471i	−0.143376	−	0.138434i
$271$	7.53634	−	1.08356i	0.457800	−	0.0658217i	0.0904429	−	0.995902i	$-0.471172\pi$
$271$	7.53634	−	1.08356i	0.457800	−	0.0658217i	0.367357	+	0.930080i	$0.380263\pi$
$272$	5.00863	−	22.8849i	0.303693	−	1.38760i
$273$	−1.01381	+	0.878468i	−0.0613583	+	0.0531673i
$274$	−1.15609	−	12.9652i	−0.0698419	−	0.783256i
$275$		−	1.38873i		−	0.0837437i
$276$	5.81151	−	7.63062i	0.349812	−	0.459309i
$277$		−	2.35003i		−	0.141200i	−0.997505	−	0.0705999i	$-0.977509\pi$
$277$		−	2.35003i		−	0.141200i	0.997505	−	0.0705999i	$-0.0224914\pi$
$278$	−9.32045	+	0.831092i	−0.559003	+	0.0498456i
$279$	−2.84031	+	2.46114i	−0.170045	+	0.147345i
$280$	1.60898	+	0.0302507i	0.0961550	+	0.00180783i
$281$	31.7278	−	4.56178i	1.89272	−	0.272133i	0.904656	−	0.426144i	$-0.140128\pi$
$281$	31.7278	−	4.56178i	1.89272	−	0.272133i	0.988069	+	0.154011i	$0.0492191\pi$
$282$	7.35226	−	7.61471i	0.437821	−	0.453449i
$283$	−6.61258	−	3.01986i	−0.393077	−	0.179512i	0.209064	−	0.977902i	$-0.432958\pi$
$283$	−6.61258	−	3.01986i	−0.393077	−	0.179512i	−0.602141	+	0.798390i	$0.705686\pi$
$284$	−13.6761	−	27.3646i	−0.811527	−	1.62379i
$285$	10.8551	+	1.56073i	0.643000	+	0.0924495i
$286$	−6.79709	−	28.8046i	−0.401920	−	1.70325i
$287$	1.78969	+	0.525501i	0.105642	+	0.0310194i
$288$	1.68180	+	5.40107i	0.0991013	+	0.318261i
$289$	−7.18678	−	15.7368i	−0.422752	−	0.925697i
$290$	31.0592	+	10.9681i	1.82386	+	0.644070i
$291$	−11.9852	−	10.3852i	−0.702585	−	0.608793i
$292$	15.3561	−	14.2789i	0.898646	−	0.835608i
$293$	−5.28346	−	3.39547i	−0.308663	−	0.198366i	0.377134	−	0.926159i	$-0.376910\pi$
$293$	−5.28346	−	3.39547i	−0.308663	−	0.198366i	−0.685797	+	0.727793i	$0.740546\pi$
$294$	−0.528394	+	9.79989i	−0.0308166	+	0.571541i
$295$	10.2974	−	6.61771i	0.599535	−	0.385298i
$296$	0.214738	+	1.72286i	0.0124814	+	0.100139i
$297$	−1.07989	−	3.67777i	−0.0626617	−	0.213406i
$298$	31.8860	+	6.35300i	1.84711	+	0.368020i
$299$	11.5408	+	23.5033i	0.667421	+	1.35923i
$300$	−0.669278	−	0.277720i	−0.0386408	−	0.0160342i
$301$	0.373259	+	1.27120i	0.0215143	+	0.0732709i
$302$	−14.9075	+	8.48272i	−0.857828	+	0.488126i
$303$	−2.75700	−	4.28998i	−0.158386	−	0.246453i
$304$	−15.1507	−	11.3716i	−0.868952	−	0.652207i
$305$	5.97394	+	3.83922i	0.342067	+	0.219833i
$306$	6.71652	+	4.84653i	0.383958	+	0.277058i
$307$	17.6507	−	20.3700i	1.00738	−	1.16258i	0.0207169	−	0.999785i	$-0.493405\pi$
$307$	17.6507	−	20.3700i	1.00738	−	1.16258i	0.986661	−	0.162790i	$-0.0520494\pi$
$308$	1.61928	+	0.962150i	0.0922672	+	0.0548236i
$309$	−4.65343	−	10.1896i	−0.264724	−	0.579665i
$310$	−5.70818	+	10.9040i	−0.324203	+	0.619306i
$311$	−2.86856	+	9.76941i	−0.162661	+	0.553973i	0.837313	+	0.546724i	$0.184125\pi$
$311$	−2.86856	+	9.76941i	−0.162661	+	0.553973i	−0.999974	+	0.00724833i	$0.997693\pi$
$312$	−15.2412	−	2.48463i	−0.862864	−	0.140664i
$313$	−8.32160	−	1.19647i	−0.470365	−	0.0676282i	−0.0969430	−	0.995290i	$-0.530906\pi$
$313$	−8.32160	−	1.19647i	−0.470365	−	0.0676282i	−0.373422	+	0.927662i	$0.621816\pi$
$314$	−13.8279	+	10.7348i	−0.780354	+	0.605802i
$315$	−0.236355	+	0.517545i	−0.0133171	+	0.0291604i
$316$	−6.23342	−	8.98997i	−0.350657	−	0.505725i
$317$	−17.8163	+	2.56160i	−1.00066	+	0.143874i	−0.623126	−	0.782121i	$-0.714138\pi$
$317$	−17.8163	+	2.56160i	−1.00066	+	0.143874i	−0.377536	+	0.925995i	$0.623229\pi$
$318$	−11.4670	+	4.50752i	−0.643036	+	0.252769i
$319$	25.2471	+	29.1367i	1.41357	+	1.63134i
$320$	11.5967	+	14.4466i	0.648273	+	0.807591i
$321$		−	7.17972i		−	0.400733i
$322$	−1.58627	−	0.510611i	−0.0883993	−	0.0284552i
$323$	−27.7364			−1.54329
$324$	−1.98840	−	0.215048i	−0.110467	−	0.0119471i
$325$	1.49494	−	1.29537i	0.0829243	−	0.0718543i
$326$	5.53081	−	2.17409i	0.306323	−	0.120412i
$327$	0.759000	+	5.27896i	0.0419728	+	0.291927i
$328$	8.55111	+	19.6959i	0.472156	+	1.08753i
$329$	−1.67280	−	0.763940i	−0.0922242	−	0.0421174i
$330$	−7.69753	−	9.91545i	−0.423735	−	0.545827i
$331$	−0.544538	+	3.78734i	−0.0299305	+	0.208171i	−0.999299	−	0.0374402i	$-0.988080\pi$
$331$	−0.544538	+	3.78734i	−0.0299305	+	0.208171i	0.969368	+	0.245611i	$0.0789887\pi$
$332$	0.114019	−	0.00399997i	0.00625760	−	0.000219527i
$333$	−0.588972	−	0.172938i	−0.0322755	−	0.00947693i
$334$	−6.00214	+	11.4655i	−0.328422	+	0.627367i
$335$	−6.41562	+	2.92992i	−0.350523	+	0.160078i
$336$	0.787519	−	0.587976i	0.0429627	−	0.0320767i
$337$	−3.82404	−	3.31355i	−0.208309	−	0.180500i	0.544458	−	0.838788i	$-0.316736\pi$
$337$	−3.82404	−	3.31355i	−0.208309	−	0.180500i	−0.752766	+	0.658288i	$0.771281\pi$
$338$	13.9095	−	19.2764i	0.756578	−	1.04850i
$339$	−1.49615	+	2.32805i	−0.0812595	+	0.126442i
$340$	26.2772	+	6.72458i	1.42508	+	0.364691i
$341$	−12.1188	+	7.78825i	−0.656268	+	0.421758i
$342$	5.82112	−	3.31236i	0.314770	−	0.179112i
$343$	3.28624	−	0.964928i	0.177440	−	0.0521012i
$344$	−8.48528	+	12.6731i	−0.457496	+	0.683286i
$345$	8.59364	+	7.03437i	0.462666	+	0.378718i
$346$	−0.359575	+	1.80472i	−0.0193308	+	0.0970223i
$347$	21.6332	−	6.35207i	1.16133	−	0.340997i	0.356380	−	0.934341i	$-0.384011\pi$
$347$	21.6332	−	6.35207i	1.16133	−	0.340997i	0.804949	+	0.593344i	$0.202193\pi$
$348$	19.0909	−	6.34066i	1.02338	−	0.339895i
$349$	7.37582	+	11.4770i	0.394818	+	0.614350i	0.980577	−	0.196136i	$-0.0628395\pi$
$349$	7.37582	+	11.4770i	0.394818	+	0.614350i	−0.585758	+	0.810486i	$0.699203\pi$
$350$	−0.00677803	+	0.125709i	−0.000362301	+	0.00671943i
$351$	2.95175	−	4.59301i	0.157553	−	0.245157i
$352$	3.43454	+	21.4092i	0.183061	+	1.14111i
$353$	−20.8656	+	24.0802i	−1.11057	+	1.28166i	−0.154667	+	0.987967i	$0.549430\pi$
$353$	−20.8656	+	24.0802i	−1.11057	+	1.28166i	−0.955899	+	0.293695i	$0.905115\pi$
$354$	2.48920	−	7.04886i	0.132300	−	0.374643i
$355$	32.2193	−	14.7141i	1.71002	−	0.780942i
$356$	−20.7320	+	25.6936i	−1.09880	+	1.36176i
$357$	0.405408	−	1.38069i	0.0214565	−	0.0730740i
$358$	−7.21221	−	30.5638i	−0.381177	−	1.61535i
$359$	−1.97633	+	13.7456i	−0.104306	+	0.725467i	0.868809	+	0.495148i	$0.164886\pi$
$359$	−1.97633	+	13.7456i	−0.104306	+	0.725467i	−0.973115	+	0.230319i	$0.926023\pi$
$360$	−6.31796	+	1.72680i	−0.332986	+	0.0910105i
$361$	−1.42429	+	3.11876i	−0.0749626	+	0.164145i
$362$	6.67252	+	6.44254i	0.350700	+	0.338612i
$363$	−0.525453	−	3.65461i	−0.0275792	−	0.191817i
$364$	0.474690	+	2.64059i	0.0248805	+	0.138404i
$365$	15.8990	+	18.3485i	0.832193	+	0.960402i
$366$	4.31970	−	0.385182i	0.225794	−	0.0201338i
$367$	6.60690			0.344877			0.172439	−	0.985020i	$-0.444835\pi$
$367$	6.60690			0.344877			0.172439	+	0.985020i	$0.444835\pi$
$368$	−7.18276	−	17.7879i	−0.374427	−	0.927256i
$369$	−7.59154			−0.395200
$370$	−2.00228	+	0.178540i	−0.104093	+	0.00928186i
$371$	1.40181	+	1.61778i	0.0727784	+	0.0839908i
$372$	1.32991	+	7.39795i	0.0689524	+	0.383566i
$373$	−5.13674	−	35.7268i	−0.265970	−	1.84986i	−0.485473	−	0.874252i	$-0.661352\pi$
$373$	−5.13674	−	35.7268i	−0.265970	−	1.84986i	0.219502	−	0.975612i	$-0.429557\pi$
$374$	22.8389	+	22.0517i	1.18097	+	1.14027i
$375$	−4.46129	+	9.76885i	−0.230380	+	0.504461i
$376$	−5.58133	−	20.4207i	−0.287835	−	1.05312i
$377$	−7.81519	+	54.3559i	−0.402503	+	2.79947i
$378$	0.0798024	+	0.338185i	0.00410459	+	0.0173944i
$379$	2.66267	−	9.06822i	0.136772	−	0.465803i	−0.862411	−	0.506208i	$-0.831047\pi$
$379$	2.66267	−	9.06822i	0.136772	−	0.465803i	0.999183	+	0.0404050i	$0.0128648\pi$
$380$	13.7734	−	17.0696i	0.706558	−	0.875651i
$381$	−18.1256	+	8.27768i	−0.928602	+	0.424078i
$382$	3.60905	−	10.2200i	0.184655	−	0.522902i
$383$	15.3049	−	17.6628i	0.782044	−	0.902527i	−0.215211	−	0.976568i	$-0.569044\pi$
$383$	15.3049	−	17.6628i	0.782044	−	0.902527i	0.997255	+	0.0740403i	$0.0235894\pi$
$384$	11.0047	+	2.62622i	0.561580	+	0.134019i
$385$	−1.17906	+	1.83465i	−0.0600903	+	0.0935023i
$386$	−0.854584	+	15.8496i	−0.0434972	+	0.806723i
$387$	−2.91524	−	4.53621i	−0.148190	−	0.230588i
$388$	−30.1006	+	9.99729i	−1.52813	+	0.507536i
$389$	−3.60626	+	1.05889i	−0.182844	+	0.0536880i	−0.371873	−	0.928284i	$-0.621284\pi$
$389$	−3.60626	+	1.05889i	−0.182844	+	0.0536880i	0.189029	+	0.981972i	$0.439466\pi$
$390$	3.49371	−	17.5351i	0.176911	−	0.887923i
$391$	−24.0452	−	14.5167i	−1.21602	−	0.734140i
$392$	16.3099	+	10.9203i	0.823776	+	0.551561i
$393$	−2.18766	+	0.642356i	−0.110353	+	0.0324026i
$394$	21.4825	−	12.2241i	1.08227	−	0.615841i
$395$	10.6555	−	6.84789i	0.536137	−	0.344555i
$396$	−7.42675	−	1.90057i	−0.373208	−	0.0955072i
$397$	1.31518	−	2.04646i	0.0660070	−	0.102709i	−0.806681	−	0.590987i	$-0.798738\pi$
$397$	1.31518	−	2.04646i	0.0660070	−	0.102709i	0.872688	+	0.488278i	$0.162375\pi$
$398$	−15.9089	+	22.0473i	−0.797442	+	1.10513i
$399$	−0.879398	−	0.762003i	−0.0440250	−	0.0381479i
$400$	−1.16126	+	0.867019i	−0.0580631	+	0.0433509i
$401$	15.8212	−	7.22529i	0.790072	−	0.360814i	0.0208394	−	0.999783i	$-0.493366\pi$
$401$	15.8212	−	7.22529i	0.790072	−	0.360814i	0.769232	+	0.638969i	$0.220639\pi$
$402$	−1.99770	+	3.81610i	−0.0996363	+	0.190330i
$403$	−19.6879	−	5.78090i	−0.980726	−	0.287967i
$404$	−10.1928	+	0.357578i	−0.507108	+	0.0177902i
$405$	0.329554	−	2.29210i	0.0163756	−	0.113895i
$406$	−2.14318	−	2.76070i	−0.106364	−	0.137011i
$407$	−2.14024	−	0.977413i	−0.106088	−	0.0484486i
$408$	15.1948	−	6.59692i	0.752256	−	0.326596i
$409$	1.30062	+	9.04602i	0.0643116	+	0.447297i	0.996380	+	0.0850140i	$0.0270935\pi$
$409$	1.30062	+	9.04602i	0.0643116	+	0.447297i	−0.932068	+	0.362283i	$0.881997\pi$
$410$	−23.1377	+	9.09514i	−1.14269	+	0.449177i
$411$	6.95603	−	6.02744i	0.343116	−	0.297312i
$412$	−22.2739	−	2.40894i	−1.09735	−	0.118680i
$413$	−1.29876			−0.0639079
$414$	6.78007	+	0.175108i	0.333222	+	0.00860610i
$415$			0.132096i			0.00648434i
$416$	−19.8429	+	23.6671i	−0.972877	+	1.16038i
$417$	−4.33302	−	5.00057i	−0.212189	−	0.244879i
$418$	23.8924	−	9.39178i	1.16861	−	0.459367i
$419$	9.44017	−	1.35729i	0.461183	−	0.0663080i	0.0921921	−	0.995741i	$-0.470613\pi$
$419$	9.44017	−	1.35729i	0.461183	−	0.0663080i	0.368990	+	0.929433i	$0.379704\pi$
$420$	0.648391	+	0.935123i	0.0316383	+	0.0456293i
$421$	6.94145	−	15.1997i	0.338306	−	0.740786i	−0.661654	−	0.749810i	$-0.730145\pi$
$421$	6.94145	−	15.1997i	0.338306	−	0.740786i	0.999959	+	0.00902344i	$0.00287229\pi$
$422$	−20.2553	+	15.7245i	−0.986012	+	0.765457i
$423$	7.40845	+	1.06517i	0.360211	+	0.0517906i
$424$	−3.96483	+	24.3211i	−0.192549	+	1.18114i
$425$	−0.597807	+	2.03594i	−0.0289979	+	0.0987578i
$426$	10.0325	−	19.1645i	0.486076	−	0.928523i
$427$	−0.313002	−	0.685379i	−0.0151472	−	0.0331678i
$428$	−12.3447	−	7.33501i	−0.596703	−	0.354551i
$429$	13.7045	−	15.8158i	0.661658	−	0.763595i
$430$	−14.3198	−	10.3329i	−0.690563	−	0.498299i
$431$	23.9841	+	15.4137i	1.15528	+	0.742450i	0.970683	−	0.240365i	$-0.0772671\pi$
$431$	23.9841	+	15.4137i	1.15528	+	0.742450i	0.184593	+	0.982815i	$0.440903\pi$
$432$	−2.40116	+	3.19913i	−0.115526	+	0.153918i
$433$	−7.70302	−	11.9861i	−0.370184	−	0.576017i	0.605325	−	0.795979i	$-0.293043\pi$
$433$	−7.70302	−	11.9861i	−0.370184	−	0.576017i	−0.975509	+	0.219961i	$0.929407\pi$
$434$	1.13501	−	0.645850i	0.0544823	−	0.0310018i
$435$	6.56194	+	22.3479i	0.314621	+	1.07150i
$436$	9.85197	+	4.08812i	0.471824	+	0.195786i
$437$	−18.7551	+	12.8103i	−0.897179	+	0.612798i
$438$	14.5414	+	2.89725i	0.694817	+	0.138436i
$439$	6.40785	+	21.8231i	0.305830	+	1.04156i	0.958777	+	0.284158i	$0.0917141\pi$
$439$	6.40785	+	21.8231i	0.305830	+	1.04156i	−0.652947	+	0.757403i	$0.726468\pi$
$440$	−24.9125	+	3.10509i	−1.18765	+	0.148030i
$441$	−5.83799	+	3.75185i	−0.277999	+	0.178659i
$442$	−2.43467	+	45.1548i	−0.115805	+	2.14779i
$443$	−7.07225	−	4.54506i	−0.336013	−	0.215942i	0.361743	−	0.932278i	$-0.382182\pi$
$443$	−7.07225	−	4.54506i	−0.336013	−	0.215942i	−0.697756	+	0.716336i	$0.745818\pi$
$444$	−0.899056	+	0.835990i	−0.0426673	+	0.0396743i
$445$	−28.8890	−	25.0325i	−1.36947	−	1.18665i
$446$	0.381030	+	0.134555i	0.0180423	+	0.00637139i
$447$	9.55038	+	20.9124i	0.451717	+	0.989123i
$448$	−0.206404	−	1.95474i	−0.00975168	−	0.0923528i
$449$	14.5361	+	4.26818i	0.686000	+	0.201428i	0.606116	−	0.795376i	$-0.292727\pi$
$449$	14.5361	+	4.26818i	0.686000	+	0.201428i	0.0798844	+	0.996804i	$0.474545\pi$
$450$	−0.117675	−	0.498682i	−0.00554726	−	0.0235081i
$451$	−28.8025	−	4.14117i	−1.35626	−	0.195000i
$452$	2.47430	+	4.95084i	0.116381	+	0.232868i
$453$	−11.0322	−	5.03826i	−0.518340	−	0.236718i
$454$	−8.12559	+	8.41565i	−0.381353	+	0.394966i
$455$	−3.07475	+	0.442082i	−0.144146	+	0.0207251i
$456$	0.251799	−	13.3927i	0.0117916	−	0.627172i
$457$	1.87103	−	1.62126i	0.0875233	−	0.0758394i	−0.610000	−	0.792401i	$-0.708831\pi$
$457$	1.87103	−	1.62126i	0.0875233	−	0.0758394i	0.697524	+	0.716562i	$0.254285\pi$
$458$	−9.67404	+	0.862621i	−0.452038	+	0.0403076i
$459$			5.85664i			0.273365i
$460$	20.8743	−	7.58924i	0.973268	−	0.353850i
$461$			2.76849i			0.128941i	0.997920	+	0.0644707i	$0.0205359\pi$
$461$			2.76849i			0.128941i	−0.997920	+	0.0644707i	$0.979464\pi$
$462$	0.118293	+	1.32662i	0.00550347	+	0.0617198i
$463$	7.58995	−	6.57673i	0.352735	−	0.305647i	−0.460412	−	0.887706i	$-0.652298\pi$
$463$	7.58995	−	6.57673i	0.352735	−	0.305647i	0.813147	+	0.582059i	$0.197753\pi$
$464$	8.60181	−	39.3024i	0.399329	−	1.82457i
$465$	−8.61431	+	1.23855i	−0.399479	+	0.0574364i
$466$	−9.73479	−	9.39927i	−0.450955	−	0.435413i
$467$	32.1428	+	14.6791i	1.48739	+	0.679269i	0.982899	−	0.184146i	$-0.0589519\pi$
$467$	32.1428	+	14.6791i	1.48739	+	0.679269i	0.504494	+	0.863415i	$0.331679\pi$
$468$	−4.88155	−	9.76753i	−0.225650	−	0.451504i
$469$	0.740731	+	0.106501i	0.0342038	+	0.00491776i
$470$	23.8558	−	5.62931i	1.10039	−	0.259661i
$471$	−11.8769	−	3.48739i	−0.547261	−	0.160690i
$472$	−9.57664	−	11.4812i	−0.440801	−	0.528465i
$473$	−8.58601	−	18.8007i	−0.394785	−	0.864459i
$474$	2.57578	−	7.29403i	0.118310	−	0.335026i
$475$	1.29674	+	1.12364i	0.0594987	+	0.0515559i
$476$	−1.95976	−	2.10761i	−0.0898256	−	0.0966020i
$477$	−7.32927	−	4.71024i	−0.335584	−	0.215667i
$478$	26.9538	+	1.45331i	1.23284	+	0.0664727i
$479$	3.93364	−	2.52799i	0.179732	−	0.115507i	−0.447681	−	0.894193i	$-0.647750\pi$
$479$	3.93364	−	2.52799i	0.179732	−	0.115507i	0.627413	+	0.778686i	$0.284114\pi$
$480$	−3.48557	+	12.6271i	−0.159094	+	0.576347i
$481$	−0.944191	−	3.21562i	−0.0430514	−	0.146620i
$482$	−2.49874	+	12.5413i	−0.113814	+	0.571239i
$483$	−0.363550	−	1.12086i	−0.0165421	−	0.0510007i
$484$	−6.82049	−	2.83020i	−0.310022	−	0.128645i
$485$	−10.3462	−	35.2359i	−0.469796	−	1.59998i
$486$	−0.699418	−	1.22915i	−0.0317263	−	0.0557555i
$487$	−0.391580	−	0.609311i	−0.0177442	−	0.0276105i	0.832268	−	0.554373i	$-0.187042\pi$
$487$	−0.391580	−	0.609311i	−0.0177442	−	0.0276105i	−0.850012	+	0.526763i	$0.823406\pi$
$488$	3.75085	−	7.82073i	0.169793	−	0.354028i
$489$	3.53509	+	2.27186i	0.159862	+	0.102737i
$490$	−13.2982	+	18.4293i	−0.600753	+	0.832549i
$491$	11.7670	−	13.5799i	0.531038	−	0.612851i	−0.425321	−	0.905042i	$-0.639839\pi$
$491$	11.7670	−	13.5799i	0.531038	−	0.612851i	0.956360	+	0.292191i	$0.0943844\pi$
$492$	−7.75573	+	13.0528i	−0.349655	+	0.588464i
$493$	−24.4709	−	53.5838i	−1.10211	−	2.41329i
$494$	32.3962	+	16.9592i	1.45757	+	0.763030i
$495$	2.50067	−	8.51649i	0.112397	−	0.382788i
$496$	14.0786	+	5.27134i	0.632147	+	0.236690i
$497$	−3.71996	−	0.534850i	−0.166863	−	0.0239913i
$498$	0.0494705	+	0.0637246i	0.00221683	+	0.00285557i
$499$	−15.6642	+	34.2999i	−0.701227	+	1.53547i	0.137249	+	0.990537i	$0.456174\pi$
$499$	−15.6642	+	34.2999i	−0.701227	+	1.53547i	−0.838477	+	0.544937i	$0.816553\pi$
$500$	12.2386	+	17.6508i	0.547328	+	0.789367i
$501$	−9.05793	+	1.30233i	−0.404678	+	0.0581840i
$502$	4.87736	+	12.4078i	0.217687	+	0.553788i
$503$	−23.9448	−	27.6337i	−1.06764	−	1.23213i	−0.971570	−	0.236754i	$-0.923917\pi$
$503$	−23.9448	−	27.6337i	−1.06764	−	1.23213i	−0.0960750	−	0.995374i	$-0.530629\pi$
$504$	0.662999	+	0.208289i	0.0295323	+	0.00927793i
$505$		−	11.8088i		−	0.525483i
$506$	25.6282	+	4.36288i	1.13931	+	0.193954i
$507$	16.8085			0.746493
$508$	−4.28511	+	39.6215i	−0.190121	+	1.75792i
$509$	−11.1005	+	9.61865i	−0.492022	+	0.426339i	−0.865205	−	0.501419i	$-0.832812\pi$
$509$	−11.1005	+	9.61865i	−0.492022	+	0.426339i	0.373183	+	0.927758i	$0.378266\pi$
$510$	7.01662	+	17.8500i	0.310701	+	0.790413i
$511$	−0.366609	−	2.54982i	−0.0162178	−	0.112797i
$512$	15.7582	−	16.2382i	0.696419	−	0.717635i
$513$	4.30791	+	1.96736i	0.190199	+	0.0868609i
$514$	22.3732	−	17.3687i	0.986842	−	0.766102i
$515$	3.69162	−	25.6758i	0.162672	−	1.13141i
$516$	−10.7778	+	0.378102i	−0.474465	+	0.0166450i
$517$	27.5268	+	8.08260i	1.21063	+	0.355472i
$518$	0.188965	+	0.0989221i	0.00830266	+	0.00434639i
$519$	−1.18362	+	0.540543i	−0.0519553	+	0.0237272i
$520$	−26.5802	−	23.9214i	−1.16562	−	1.04902i
$521$	−26.9410	−	23.3445i	−1.18031	−	1.02274i	−0.999228	−	0.0392736i	$-0.987496\pi$
$521$	−26.9410	−	23.3445i	−1.18031	−	1.02274i	−0.181079	−	0.983469i	$-0.557959\pi$
$522$	11.5349	+	8.32341i	0.504870	+	0.364306i
$523$	−3.78195	+	5.88483i	−0.165373	+	0.257325i	−0.914043	−	0.405618i	$-0.867056\pi$
$523$	−3.78195	+	5.88483i	−0.165373	+	0.257325i	0.748670	+	0.662943i	$0.230693\pi$
$524$	−1.13052	+	4.41768i	−0.0493871	+	0.192987i
$525$	−0.0748874	+	0.0481272i	−0.00326836	+	0.00210044i
$526$	7.39785	+	13.0009i	0.322561	+	0.566867i
$527$	21.1192	−	6.20117i	0.919969	−	0.270127i
$528$	−10.8552	+	10.8277i	−0.472411	+	0.471217i
$529$	−22.9638	+	1.28939i	−0.998427	+	0.0560606i
$530$	−27.9815	−	5.57507i	−1.21544	−	0.242166i
$531$	5.07183	−	1.48922i	0.220099	−	0.0646268i
$532$	−2.20859	+	0.733538i	−0.0957546	+	0.0318029i
$533$	−22.4083	−	34.8680i	−0.970612	−	1.51030i
$534$	−23.3111	−	1.25690i	−1.00877	−	0.0543913i
$535$	8.98861	−	13.9865i	0.388611	−	0.604691i
$536$	4.52042	+	7.33345i	0.195253	+	0.316757i
$537$	14.5415	−	16.7817i	0.627510	−	0.724185i
$538$	−17.3867	−	6.13988i	−0.749595	−	0.264709i
$539$	−24.1961	+	11.0500i	−1.04220	+	0.475957i
$540$	−3.60431	−	2.90830i	−0.155105	−	0.125153i
$541$	8.95509	−	30.4982i	0.385009	−	1.31122i	−0.508067	−	0.861317i	$-0.669640\pi$
$541$	8.95509	−	30.4982i	0.385009	−	1.31122i	0.893077	−	0.449904i	$-0.148542\pi$
$542$	10.4798	−	2.47294i	0.450145	−	0.106222i
$543$	−0.933377	+	6.49178i	−0.0400551	+	0.278589i
$544$	4.18083	−	32.8653i	0.179252	−	1.40909i
$545$	−5.13038	+	11.2340i	−0.219761	+	0.481210i
$546$	−1.31773	+	1.36477i	−0.0563937	+	0.0584068i
$547$	1.84641	+	12.8421i	0.0789467	+	0.549087i	0.990458	+	0.137812i	$0.0440071\pi$
$547$	1.84641	+	12.8421i	0.0789467	+	0.549087i	−0.911512	+	0.411274i	$0.865084\pi$
$548$	−3.25699	−	18.1179i	−0.139132	−	0.773957i
$549$	2.00820	+	2.31759i	0.0857079	+	0.0989122i
$550$	−0.174432	−	1.95620i	−0.00743781	−	0.0834128i
$551$	−47.6344			−2.02929
$552$	7.22779	−	11.4786i	0.307635	−	0.488563i
$553$	−1.34394			−0.0571500
$554$	−0.295176	−	3.31031i	−0.0125408	−	0.140642i
$555$	−0.930845	−	1.07425i	−0.0395122	−	0.0455995i
$556$	−13.0246	+	2.34139i	−0.552367	+	0.0992972i
$557$	2.22989	+	15.5092i	0.0944835	+	0.657147i	0.980937	+	0.194328i	$0.0622528\pi$
$557$	2.22989	+	15.5092i	0.0944835	+	0.657147i	−0.886453	+	0.462819i	$0.846838\pi$
$558$	−3.69180	+	3.82359i	−0.156286	+	0.161865i
$559$	12.2298	−	26.7795i	0.517264	−	1.13265i
$560$	2.27025	−	0.159484i	0.0959355	−	0.00673944i
$561$	−3.19479	+	22.2202i	−0.134884	+	0.938139i
$562$	44.1196	−	10.4110i	1.86107	−	0.439162i
$563$	−0.264712	+	0.901527i	−0.0111563	+	0.0379948i	−0.964883	−	0.262680i	$-0.915394\pi$
$563$	−0.264712	+	0.901527i	−0.0111563	+	0.0379948i	0.953727	+	0.300675i	$0.0972119\pi$
$564$	9.40012	−	11.6497i	0.395817	−	0.490543i
$565$	−5.82917	+	2.66209i	−0.245235	+	0.111995i
$566$	−9.69395	−	3.42328i	−0.407467	−	0.143891i
$567$	−0.160900	+	0.185688i	−0.00675716	+	0.00779818i
$568$	−22.7016	−	36.8287i	−0.952539	−	1.54530i
$569$	−13.3941	+	20.8417i	−0.561511	+	0.873728i	−0.999683	−	0.0251630i	$-0.991990\pi$
$569$	−13.3941	+	20.8417i	−0.561511	+	0.873728i	0.438173	+	0.898891i	$0.355626\pi$
$570$	15.4868	+	0.835022i	0.648670	+	0.0349752i
$571$	−21.1207	−	32.8644i	−0.883872	−	1.37533i	−0.926521	−	0.376242i	$-0.877216\pi$
$571$	−21.1207	−	32.8644i	−0.883872	−	1.37533i	0.0426490	−	0.999090i	$-0.486420\pi$
$572$	−13.1925	−	39.7211i	−0.551608	−	1.66082i
$573$	7.35356	−	2.15920i	0.307200	−	0.0902019i
$574$	2.58701	+	0.515439i	0.107980	+	0.0215140i
$575$	0.536084	+	1.65279i	0.0223562	+	0.0689262i
$576$	3.04743	+	7.39683i	0.126976	+	0.308201i
$577$	1.40373	−	0.412173i	0.0584382	−	0.0171590i	−0.252383	−	0.967627i	$-0.581214\pi$
$577$	1.40373	−	0.412173i	0.0584382	−	0.0171590i	0.310821	+	0.950468i	$0.399396\pi$
$578$	−12.1001	−	21.2646i	−0.503298	−	0.884491i
$579$	−9.44192	+	6.06796i	−0.392393	+	0.252176i
$580$	45.1285	+	11.5488i	1.87386	+	0.479537i
$581$	0.00757757	−	0.0117909i	0.000314370	−	0.000489170i
$582$	−18.1871	−	13.1235i	−0.753879	−	0.543986i
$583$	−25.2380	−	21.8689i	−1.04525	−	0.905716i
$584$	19.8374	−	22.0424i	0.820879	−	0.912120i
$585$	11.5004	−	5.25204i	0.475482	−	0.217145i
$586$	−7.86890	−	4.11932i	−0.325061	−	0.170167i
$587$	−43.8926	−	12.8880i	−1.81164	−	0.531946i	−0.812913	−	0.582384i	$-0.802120\pi$
$587$	−43.8926	−	12.8880i	−1.81164	−	0.531946i	−0.998727	+	0.0504388i	$0.983938\pi$
$588$	0.486608	+	13.8707i	0.0200674	+	0.572019i
$589$	2.53302	−	17.6176i	0.104371	−	0.725919i
$590$	13.6739	−	10.6153i	0.562945	−	0.437024i
$591$	15.8981	+	7.26042i	0.653961	+	0.298654i
$592$	0.518885	+	2.39989i	0.0213260	+	0.0986349i
$593$	1.70202	+	11.8378i	0.0698937	+	0.486121i	0.994461	+	0.105103i	$0.0335173\pi$
$593$	1.70202	+	11.8378i	0.0698937	+	0.486121i	−0.924568	+	0.381018i	$0.875574\pi$
$594$	−1.98311	−	5.04496i	−0.0813680	−	0.206997i
$595$	2.51831	−	2.18213i	0.103241	−	0.0894585i
$596$	45.7134	+	4.94395i	1.87249	+	0.202512i
$597$	−19.2247			−0.786813
$598$	19.2088	+	31.6578i	0.785505	+	1.29458i
$599$		−	3.62324i		−	0.148042i	−0.997257	−	0.0740208i	$-0.976417\pi$
$599$		−	3.62324i		−	0.148042i	0.997257	−	0.0740208i	$-0.0235831\pi$
$600$	−0.977645	−	0.307139i	−0.0399122	−	0.0125389i
$601$	6.55041	+	7.55957i	0.267197	+	0.308361i	0.873454	−	0.486907i	$-0.161875\pi$
$601$	6.55041	+	7.55957i	0.267197	+	0.308361i	−0.606257	+	0.795269i	$0.707330\pi$
$602$	0.685451	+	1.74376i	0.0279369	+	0.0710705i
$603$	−3.01477	+	0.433458i	−0.122771	+	0.0176518i
$604$	−19.9335	+	13.8214i	−0.811084	+	0.562386i
$605$	3.55175	−	7.77724i	0.144399	−	0.316190i
$606$	−4.42243	−	5.69668i	−0.179649	−	0.231412i
$607$	31.2262	+	4.48965i	1.26743	+	0.182229i	0.743040	−	0.669247i	$-0.233383\pi$
$607$	31.2262	+	4.48965i	1.26743	+	0.182229i	0.524393	+	0.851476i	$0.324292\pi$
$608$	−22.7700	−	14.1153i	−0.923445	−	0.572452i
$609$	0.696246	−	2.37120i	0.0282133	−	0.0960858i
$610$	8.89726	+	4.65766i	0.360240	+	0.188583i
$611$	16.9755	+	37.1712i	0.686756	+	1.50379i
$612$	10.0698	+	5.98331i	0.407048	+	0.241861i
$613$	−6.02669	+	6.95517i	−0.243416	+	0.280917i	−0.864290	−	0.502993i	$-0.832232\pi$
$613$	−6.02669	+	6.95517i	−0.243416	+	0.280917i	0.620875	+	0.783910i	$0.286778\pi$
$614$	22.3046	−	30.9107i	0.900141	−	1.24745i
$615$	−14.7888	−	9.50418i	−0.596342	−	0.383245i
$616$	2.40181	+	1.15192i	0.0967717	+	0.0464121i
$617$	−3.95322	−	6.15133i	−0.159151	−	0.247643i	0.752516	−	0.658574i	$-0.228840\pi$
$617$	−3.95322	−	6.15133i	−0.159151	−	0.247643i	−0.911667	+	0.410931i	$0.865204\pi$
$618$	−7.83480	−	13.7688i	−0.315162	−	0.553862i
$619$	−0.659273	−	2.24528i	−0.0264984	−	0.0902453i	0.945182	−	0.326544i	$-0.105884\pi$
$619$	−0.659273	−	2.24528i	−0.0264984	−	0.0902453i	−0.971681	+	0.236298i	$0.924066\pi$
$620$	−6.67108	+	16.0766i	−0.267917	+	0.645653i
$621$	2.70494	+	3.96022i	0.108545	+	0.158918i
$622$	−2.81363	+	14.1217i	−0.112816	+	0.566230i
$623$	1.14267	+	3.89159i	0.0457803	+	0.155913i
$624$	−21.7812	−	1.58553i	−0.871948	−	0.0634720i
$625$	−22.4449	+	14.4244i	−0.897795	+	0.576978i
$626$	−11.8723	−	0.640135i	−0.474512	−	0.0255849i
$627$	15.2711	+	9.81416i	0.609870	+	0.391940i
$628$	−18.1300	+	16.8582i	−0.723465	+	0.672716i
$629$	2.71693	+	2.35424i	0.108331	+	0.0938696i
$630$	−0.267929	+	0.758714i	−0.0106745	+	0.0302279i
$631$	−3.97806	−	8.71073i	−0.158364	−	0.346769i	0.813773	−	0.581183i	$-0.197410\pi$
$631$	−3.97806	−	8.71073i	−0.158364	−	0.346769i	−0.972137	+	0.234415i	$0.924683\pi$
$632$	−9.90974	−	11.8805i	−0.394188	−	0.472583i
$633$	−17.3975	−	5.10837i	−0.691488	−	0.203039i
$634$	−24.7747	+	5.84615i	−0.983930	+	0.232180i
$635$	−45.6729	−	6.56678i	−1.81248	−	0.260595i
$636$	−15.5865	+	7.78971i	−0.618044	+	0.308882i
$637$	−34.4645	−	15.7394i	−1.36553	−	0.623619i
$638$	39.2234	+	37.8715i	1.55287	+	1.49935i
$639$	15.1402	−	2.17683i	0.598937	−	0.0861142i
$640$	18.1499	+	18.8933i	0.717439	+	0.746822i
$641$	2.11100	−	1.82919i	0.0833794	−	0.0722486i	−0.612174	−	0.790723i	$-0.709705\pi$
$641$	2.11100	−	1.82919i	0.0833794	−	0.0722486i	0.695553	+	0.718475i	$0.255159\pi$
$642$	−0.901811	−	10.1135i	−0.0355916	−	0.399149i
$643$			21.9936i			0.867344i	0.901071	+	0.433672i	$0.142782\pi$
$643$			21.9936i			0.867344i	−0.901071	+	0.433672i	$0.857218\pi$
$644$	−2.29859	−	0.520016i	−0.0905772	−	0.0204915i
$645$		−	12.4865i		−	0.491657i
$646$	−39.0701	+	3.48383i	−1.53719	+	0.137070i
$647$	24.7258	−	21.4250i	0.972070	−	0.842303i	−0.0154368	−	0.999881i	$-0.504914\pi$
$647$	24.7258	−	21.4250i	0.972070	−	0.842303i	0.987507	+	0.157578i	$0.0503684\pi$
$648$	−2.82793	−	0.0531684i	−0.111091	−	0.00208865i
$649$	20.0550	−	2.88348i	0.787229	−	0.113186i
$650$	1.94310	−	2.01247i	0.0762148	−	0.0789354i
$651$	0.839964	+	0.383599i	0.0329208	+	0.0150344i
$652$	7.51775	−	3.75717i	0.294418	−	0.147142i
$653$	25.1880	+	3.62149i	0.985682	+	0.141720i	0.616261	−	0.787542i	$-0.288647\pi$
$653$	25.1880	+	3.62149i	0.985682	+	0.141720i	0.369421	+	0.929262i	$0.379556\pi$
$654$	1.73221	+	7.34074i	0.0677348	+	0.287046i
$655$	−5.06590	−	1.48748i	−0.197941	−	0.0581207i
$656$	14.5192	+	26.6701i	0.566880	+	1.04129i
$657$	4.35540	+	9.53699i	0.169920	+	0.372074i
$658$	−2.45230	−	0.865993i	−0.0956005	−	0.0337599i
$659$	1.51932	+	1.31650i	0.0591843	+	0.0512835i	0.683951	−	0.729528i	$-0.260260\pi$
$659$	1.51932	+	1.31650i	0.0591843	+	0.0512835i	−0.624766	+	0.780812i	$0.714806\pi$
$660$	−12.0884	−	13.0003i	−0.470539	−	0.506036i
$661$	35.0333	+	22.5146i	1.36264	+	0.875715i	0.998453	−	0.0556109i	$-0.0177106\pi$
$661$	35.0333	+	22.5146i	1.36264	+	0.875715i	0.364187	+	0.931326i	$0.381347\pi$
$662$	−0.291339	+	5.40334i	−0.0113232	+	0.210007i
$663$	−26.8996	+	17.2873i	−1.04469	+	0.671384i
$664$	0.160108	−	0.0199558i	0.00621338	−	0.000774436i
$665$	−0.759138	−	2.58539i	−0.0294381	−	0.100257i
$666$	−0.851362	−	0.169626i	−0.0329896	−	0.00657289i
$667$	−41.2952	−	24.9309i	−1.59895	−	0.965328i
$668$	−7.01463	+	16.9045i	−0.271404	+	0.654057i
$669$	0.0805010	+	0.274161i	0.00311235	+	0.0105997i
$670$	−8.66919	+	4.93299i	−0.334920	+	0.190578i
$671$	6.35492	+	9.88845i	0.245329	+	0.381739i
$672$	1.03547	−	0.927154i	0.0399440	−	0.0357658i
$673$	−6.37562	−	4.09736i	−0.245762	−	0.157942i	0.411961	−	0.911201i	$-0.364844\pi$
$673$	−6.37562	−	4.09736i	−0.245762	−	0.157942i	−0.657723	+	0.753260i	$0.728480\pi$
$674$	−5.80283	−	4.18723i	−0.223517	−	0.161286i
$675$	0.237260	−	0.273812i	0.00913214	−	0.0105390i
$676$	17.1721	−	28.9003i	0.660464	−	1.11155i
$677$	1.67051	+	3.65791i	0.0642030	+	0.140585i	0.939013	−	0.343880i	$-0.111741\pi$
$677$	1.67051	+	3.65791i	0.0642030	+	0.140585i	−0.874810	+	0.484465i	$0.839014\pi$
$678$	−1.81509	+	3.46727i	−0.0697082	+	0.133160i
$679$	−1.09777	+	3.73866i	−0.0421285	+	0.143477i
$680$	37.8594	+	6.17185i	1.45184	+	0.236680i
$681$	−8.18770	−	1.17721i	−0.313753	−	0.0451109i
$682$	−16.0925	+	12.4929i	−0.616215	+	0.478378i
$683$	0.944631	−	2.06845i	0.0361453	−	0.0791471i	−0.890698	−	0.454595i	$-0.849784\pi$
$683$	0.944631	−	2.06845i	0.0361453	−	0.0791471i	0.926843	+	0.375448i	$0.122511\pi$
$684$	7.78372	−	5.39704i	0.297618	−	0.206361i
$685$	21.0968	−	3.03326i	0.806067	−	0.115895i
$686$	4.50788	−	1.77199i	0.172112	−	0.0676549i
$687$	−4.49740	−	5.19028i	−0.171586	−	0.198021i
$688$	−10.3608	+	18.9174i	−0.395001	+	0.721219i
$689$		−	47.5668i		−	1.81215i
$690$	12.9888	+	8.82938i	0.494474	+	0.336129i
$691$	−27.9299			−1.06250			−0.531251	−	0.847214i	$-0.678278\pi$
$691$	−27.9299			−1.06250			−0.531251	+	0.847214i	$0.678278\pi$
$692$	−0.279823	+	2.58734i	−0.0106373	+	0.0983558i
$693$	−0.711751	+	0.616736i	−0.0270372	+	0.0234278i
$694$	29.6751	−	11.6649i	1.12645	−	0.442794i
$695$	−2.18056	−	15.1661i	−0.0827132	−	0.575283i
$696$	26.0955	−	11.3295i	0.989149	−	0.429445i
$697$	40.4431	+	18.4697i	1.53189	+	0.699591i
$698$	11.8313	+	15.2403i	0.447822	+	0.576855i
$699$	1.36174	−	9.47111i	0.0515057	−	0.358230i
$700$	0.00624201	+	0.177928i	0.000235926	+	0.00672506i
$701$	−41.9637	−	12.3217i	−1.58495	−	0.465382i	−0.633640	−	0.773628i	$-0.718440\pi$
$701$	−41.9637	−	12.3217i	−1.58495	−	0.465382i	−0.951307	+	0.308245i	$0.900258\pi$
$702$	3.58100	−	6.84058i	0.135156	−	0.258181i
$703$	2.64435	−	1.20764i	0.0997337	−	0.0455468i
$704$	7.52708	+	29.7261i	0.283687	+	1.12035i
$705$	13.0986	+	11.3500i	0.493321	+	0.427465i
$706$	−26.3673	+	36.5408i	−0.992345	+	1.37523i
$707$	−0.677398	+	1.05405i	−0.0254762	+	0.0396417i
$708$	2.62098	−	10.2419i	0.0985025	−	0.384912i
$709$	−17.0653	+	10.9672i	−0.640902	+	0.411883i	−0.820332	−	0.571888i	$-0.806211\pi$
$709$	−17.0653	+	10.9672i	−0.640902	+	0.411883i	0.179430	+	0.983771i	$0.442575\pi$
$710$	43.5368	−	24.7735i	1.63391	−	0.929734i
$711$	5.24824	−	1.54102i	0.196824	−	0.0577929i
$712$	−25.9764	+	38.7967i	−0.973507	+	1.45397i
$713$	11.4166	−	13.9473i	0.427556	−	0.522330i
$714$	0.397646	−	1.99580i	0.0148815	−	0.0746909i
$715$	46.4977	−	13.6529i	1.73891	−	0.510591i
$716$	−13.9983	−	42.1470i	−0.523140	−	1.57511i
$717$	10.3192	+	16.0569i	0.385376	+	0.599657i
$718$	−1.05738	+	19.6107i	−0.0394609	+	0.731864i
$719$	−15.1905	+	23.6369i	−0.566510	+	0.881506i	−0.999805	−	0.0197458i	$-0.993714\pi$
$719$	−15.1905	+	23.6369i	−0.566510	+	0.881506i	0.433295	+	0.901252i	$0.357351\pi$
$720$	−8.68274	+	3.22598i	−0.323586	+	0.120225i
$721$	−1.80238	+	2.08006i	−0.0671241	+	0.0774654i
$722$	−1.61456	+	4.57206i	−0.0600876	+	0.170154i
$723$	−8.22518	+	3.75632i	−0.305898	+	0.139699i
$724$	10.2083	+	8.23702i	0.379388	+	0.306126i
$725$	−1.02667	+	3.49652i	−0.0381296	+	0.129858i
$726$	−1.19920	−	5.08197i	−0.0445067	−	0.188610i
$727$	−3.80952	+	26.4958i	−0.141287	+	0.982676i	0.788620	+	0.614881i	$0.210796\pi$
$727$	−3.80952	+	26.4958i	−0.141287	+	0.982676i	−0.929907	+	0.367794i	$0.880113\pi$
$728$	1.00033	+	3.65997i	0.0370747	+	0.135648i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	24.7004	+	23.8491i	0.914203	+	0.882694i
$731$	4.49433	+	31.2587i	0.166229	+	1.15615i
$732$	6.03645	−	1.08515i	0.223114	−	0.0401084i
$733$	−21.2943	−	24.5749i	−0.786522	−	0.907694i	0.211040	−	0.977477i	$-0.432315\pi$
$733$	−21.2943	−	24.5749i	−0.786522	−	0.907694i	−0.997562	+	0.0697828i	$0.977769\pi$
$734$	9.30664	−	0.829860i	0.343514	−	0.0306307i
$735$	−16.0699			−0.592746
$736$	−12.3521	−	24.1542i	−0.455303	−	0.890337i
$737$	−11.6746			−0.430038
$738$	−10.6936	+	0.953537i	−0.393638	+	0.0351002i
$739$	24.2312	+	27.9643i	0.891358	+	1.02868i	0.999403	+	0.0345357i	$0.0109952\pi$
$739$	24.2312	+	27.9643i	0.891358	+	1.02868i	−0.108046	+	0.994146i	$0.534459\pi$
$740$	−2.79803	+	0.502992i	−0.102858	+	0.0184904i
$741$	3.67978	+	25.5934i	0.135180	+	0.940197i
$742$	2.17783	+	2.10277i	0.0799506	+	0.0771949i
$743$	−14.3515	+	31.4254i	−0.526505	+	1.15289i	0.440412	+	0.897796i	$0.354832\pi$
$743$	−14.3515	+	31.4254i	−0.526505	+	1.15289i	−0.966917	+	0.255090i	$0.917895\pi$
$744$	2.80256	+	10.2539i	0.102747	+	0.375926i
$745$	−7.57642	+	52.6952i	−0.277579	+	1.93060i
$746$	−11.7232	−	49.6805i	−0.429217	−	1.81893i
$747$	−0.0160713	+	0.0547338i	−0.000588018	+	0.00200261i
$748$	34.9412	+	28.1939i	1.27758	+	1.03087i
$749$	−1.60465	+	0.732819i	−0.0586326	+	0.0267766i
$750$	−5.05726	+	14.3210i	−0.184665	+	0.522929i
$751$	−16.5892	+	19.1449i	−0.605348	+	0.698609i	−0.972856	−	0.231412i	$-0.925666\pi$
$751$	−16.5892	+	19.1449i	−0.605348	+	0.698609i	0.367508	+	0.930020i	$0.380211\pi$
$752$	−10.4269	−	28.0641i	−0.380232	−	1.02339i
$753$	−5.09671	+	7.93063i	−0.185734	+	0.289008i
$754$	−4.18130	+	77.5486i	−0.152274	+	2.82415i
$755$	−15.1839	−	23.6266i	−0.552598	−	0.859859i
$756$	0.154889	+	0.466353i	0.00563328	+	0.0169611i
$757$	8.85149	−	2.59903i	0.321713	−	0.0944634i	−0.116889	−	0.993145i	$-0.537292\pi$
$757$	8.85149	−	2.59903i	0.321713	−	0.0944634i	0.438602	+	0.898682i	$0.355474\pi$
$758$	2.61169	−	13.1082i	0.0948608	−	0.476110i
$759$	8.10230	+	16.5007i	0.294095	+	0.598937i
$760$	17.2575	−	25.7746i	0.625994	−	0.934944i
$761$	−3.10797	+	0.912583i	−0.112664	+	0.0330811i	−0.337579	−	0.941297i	$-0.609608\pi$
$761$	−3.10797	+	0.912583i	−0.112664	+	0.0330811i	0.224915	+	0.974378i	$0.427790\pi$
$762$	−24.4924	+	13.9368i	−0.887267	+	0.504877i
$763$	1.10236	−	0.708447i	0.0399083	−	0.0256475i
$764$	3.80011	−	14.8495i	0.137483	−	0.537236i
$765$	−7.33218	+	11.4091i	−0.265096	+	0.412497i
$766$	19.3403	−	26.8026i	0.698795	−	0.968419i
$767$	21.8108	+	18.8992i	0.787542	+	0.682409i
$768$	15.8313	+	2.31711i	0.571264	+	0.0836115i
$769$	46.5847	−	21.2745i	1.67989	−	0.767179i	0.680481	−	0.732766i	$-0.261771\pi$
$769$	46.5847	−	21.2745i	1.67989	−	0.767179i	0.999408	−	0.0344138i	$-0.0109564\pi$
$770$	−1.43041	+	2.73243i	−0.0515483	+	0.0984698i
$771$	19.2166	+	5.64252i	0.692071	+	0.203210i
$772$	0.787003	+	22.4335i	0.0283248	+	0.807398i
$773$	3.61887	−	25.1698i	0.130162	−	0.905294i	−0.815179	−	0.579209i	$-0.803361\pi$
$773$	3.61887	−	25.1698i	0.130162	−	0.905294i	0.945341	−	0.326085i	$-0.105730\pi$
$774$	−4.67625	−	6.02364i	−0.168085	−	0.216515i
$775$	−1.23859	−	0.565647i	−0.0444916	−	0.0203186i
$776$	−41.1447	+	17.8632i	−1.47701	+	0.641252i
$777$	0.0214639	+	0.149285i	0.000770015	+	0.00535557i
$778$	−4.94686	+	1.94455i	−0.177353	+	0.0697154i
$779$	27.1712	−	23.5440i	0.973509	−	0.843551i
$780$	2.71883	−	25.1392i	0.0973497	−	0.900127i
$781$	58.6298			2.09794
$782$	−35.6940	−	17.4283i	−1.27642	−	0.623236i
$783$			10.0582i			0.359450i
$784$	24.3462	+	13.3341i	0.869508	+	0.476216i
$785$	−18.7710	−	21.6629i	−0.669966	−	0.773182i
$786$	−3.00092	+	1.17962i	−0.107039	+	0.0420757i
$787$	20.9552	−	3.01290i	0.746973	−	0.107398i	0.241691	−	0.970353i	$-0.422298\pi$
$787$	20.9552	−	3.01290i	0.746973	−	0.107398i	0.505281	+	0.862955i	$0.331389\pi$
$788$	28.7254	−	19.9175i	1.02330	−	0.709531i
$789$	−4.39390	+	9.62131i	−0.156427	+	0.342528i
$790$	14.1495	−	10.9845i	0.503416	−	0.390811i
$791$	0.673021	+	0.0967658i	0.0239299	+	0.00344060i
$792$	−10.7002	−	1.74435i	−0.380216	−	0.0619828i
$793$	−4.71700	+	16.0646i	−0.167505	+	0.570471i
$794$	1.59555	−	3.04789i	0.0566239	−	0.108166i
$795$	−8.38092	−	18.3517i	−0.297241	−	0.650866i
$796$	−19.6405	+	33.0546i	−0.696138	+	1.17159i
$797$	14.2101	−	16.3994i	0.503349	−	0.580896i	−0.446034	−	0.895016i	$-0.647164\pi$
$797$	14.2101	−	16.3994i	0.503349	−	0.580896i	0.949383	+	0.314120i	$0.101710\pi$
$798$	−1.33445	−	0.962919i	−0.0472391	−	0.0340870i
$799$	−36.8762	−	23.6989i	−1.30459	−	0.838406i
$800$	−1.52688	+	1.36716i	−0.0539833	+	0.0483365i
$801$	−8.92458	−	13.8869i	−0.315335	−	0.490670i
$802$	21.3786	−	12.1649i	0.754903	−	0.429559i
$803$	11.3221	+	38.5594i	0.399547	+	1.36073i
$804$	−2.33469	+	5.62637i	−0.0823382	+	0.198427i
$805$	0.695029	−	2.63864i	0.0244966	−	0.0929998i
$806$	−28.4590	−	5.67021i	−1.00243	−	0.199725i
$807$	−3.67333	−	12.5102i	−0.129307	−	0.440380i
$808$	−14.3128	+	1.78396i	−0.503524	+	0.0627594i
$809$	4.67455	−	3.00415i	0.164348	−	0.105620i	−0.455881	−	0.890041i	$-0.650676\pi$
$809$	4.67455	−	3.00415i	0.164348	−	0.105620i	0.620230	+	0.784420i	$0.287039\pi$
$810$	0.176318	−	3.27010i	0.00619519	−	0.114899i
$811$	26.1612	+	16.8128i	0.918643	+	0.590376i	0.912263	−	0.409604i	$-0.134333\pi$
$811$	26.1612	+	16.8128i	0.918643	+	0.590376i	0.00637917	+	0.999980i	$0.497969\pi$
$812$	−3.36569	−	3.61960i	−0.118113	−	0.127023i
$813$	5.75416	+	4.98600i	0.201807	+	0.174867i
$814$	−3.13756	−	1.10798i	−0.109971	−	0.0388348i
$815$	4.04233	+	8.85147i	0.141597	+	0.310053i
$816$	20.5752	−	11.2011i	0.720276	−	0.392118i
$817$	24.5024	+	7.19456i	0.857231	+	0.251706i
$818$	2.96831	+	12.5791i	0.103785	+	0.439817i
$819$	−1.32780	−	0.190909i	−0.0463972	−	0.00667091i
$820$	−31.4500	+	15.7179i	−1.09828	+	0.548891i
$821$	42.9116	+	19.5971i	1.49763	+	0.683943i	0.984663	−	0.174468i	$-0.0558205\pi$
$821$	42.9116	+	19.5971i	1.49763	+	0.683943i	0.512963	+	0.858411i	$0.328548\pi$
$822$	9.04136	−	9.36411i	0.315354	−	0.326611i
$823$	−29.7617	+	4.27909i	−1.03743	+	0.149160i	−0.639922	−	0.768440i	$-0.721033\pi$
$823$	−29.7617	+	4.27909i	−1.03743	+	0.149160i	−0.397506	+	0.917600i	$0.630124\pi$
$824$	−31.6781	−	0.595585i	−1.10356	−	0.0207482i
$825$	1.04953	−	0.909426i	0.0365401	−	0.0316622i
$826$	−1.82947	+	0.163131i	−0.0636554	+	0.00567606i
$827$		−	53.1681i		−	1.84884i	−0.381379	−	0.924419i	$-0.624551\pi$
$827$		−	53.1681i		−	1.84884i	0.381379	−	0.924419i	$-0.375449\pi$
$828$	9.57257	−	0.604950i	0.332670	−	0.0210235i
$829$			24.7194i			0.858540i	0.903176	+	0.429270i	$0.141229\pi$
$829$			24.7194i			0.858540i	−0.903176	+	0.429270i	$0.858771\pi$
$830$	0.0165920	+	0.186074i	0.000575915	+	0.00645872i
$831$	1.77604	−	1.53894i	0.0616100	−	0.0533854i
$832$	−24.9785	+	35.8305i	−0.865972	+	1.24220i
$833$	40.2292	−	5.78409i	1.39386	−	0.200407i
$834$	−6.73169	−	6.49967i	−0.233099	−	0.225065i
$835$	−19.2759	−	8.80299i	−0.667068	−	0.304640i
$836$	32.4757	−	16.2305i	1.12320	−	0.561343i
$837$	−3.72002	−	0.534858i	−0.128583	−	0.0184874i
$838$	13.1272	−	3.09765i	0.453471	−	0.107007i
$839$	33.4076	+	9.80936i	1.15336	+	0.338657i	0.801849	−	0.597527i	$-0.203850\pi$
$839$	33.4076	+	9.80936i	1.15336	+	0.338657i	0.351511	+	0.936184i	$0.385668\pi$
$840$	1.03080	+	1.23580i	0.0355658	+	0.0426390i
$841$	−29.9792	−	65.6453i	−1.03377	−	2.26363i
$842$	7.86875	−	22.2825i	0.271175	−	0.767906i
$843$	24.2249	+	20.9910i	0.834349	+	0.722968i
$844$	−26.5570	+	24.6941i	−0.914130	+	0.850006i
$845$	32.7441	+	21.0433i	1.12643	+	0.723913i
$846$	10.5695	+	0.569891i	0.363388	+	0.0195933i
$847$	−0.763164	+	0.490456i	−0.0262226	+	0.0168523i
$848$	−2.53010	+	34.7573i	−0.0868840	+	1.19357i
$849$	−2.04806	−	6.97504i	−0.0702892	−	0.239383i
$850$	−0.586361	+	2.94297i	−0.0201120	+	0.100943i
$851$	2.92449	+	0.337080i	0.100250	+	0.0115550i
$852$	11.7249	−	28.2557i	0.401687	−	0.968025i
$853$	−6.78171	−	23.0964i	−0.232201	−	0.790806i	−0.990334	−	0.138705i	$-0.955706\pi$
$853$	−6.78171	−	23.0964i	−0.232201	−	0.790806i	0.758132	−	0.652101i	$-0.226112\pi$
$854$	−0.526989	−	0.926127i	−0.0180332	−	0.0316914i
$855$	5.92906	+	9.22579i	0.202769	+	0.315515i
$856$	−18.3104	−	8.78172i	−0.625835	−	0.300153i
$857$	−5.22283	−	3.35651i	−0.178409	−	0.114656i	0.448388	−	0.893839i	$-0.351998\pi$
$857$	−5.22283	−	3.35651i	−0.178409	−	0.114656i	−0.626797	+	0.779183i	$0.715634\pi$
$858$	17.3179	−	23.9999i	0.591224	−	0.819343i
$859$	5.18658	−	5.98564i	0.176964	−	0.204227i	−0.660337	−	0.750969i	$-0.729587\pi$
$859$	5.18658	−	5.98564i	0.176964	−	0.204227i	0.837301	+	0.546742i	$0.184132\pi$
$860$	−21.4691	−	12.7566i	−0.732091	−	0.434996i
$861$	0.774852	+	1.69669i	0.0264069	+	0.0578230i
$862$	35.7207	+	18.6995i	1.21665	+	0.636909i
$863$	−2.74038	+	9.33289i	−0.0932838	+	0.317695i	−0.992895	−	0.118997i	$-0.962032\pi$
$863$	−2.74038	+	9.33289i	−0.0932838	+	0.317695i	0.899611	+	0.436693i	$0.143850\pi$
$864$	−2.98051	+	4.80797i	−0.101399	+	0.163570i
$865$	−2.98250	−	0.428819i	−0.101408	−	0.0145803i
$866$	−12.3562	−	15.9164i	−0.419880	−	0.540862i
$867$	7.18678	−	15.7368i	0.244076	−	0.534451i
$868$	1.51768	−	1.05232i	0.0515135	−	0.0357182i
$869$	20.7526	−	2.98377i	0.703983	−	0.101217i
$870$	12.0503	+	30.6556i	0.408544	+	1.03932i
$871$	−10.8897	−	12.5674i	−0.368984	−	0.425830i
$872$	14.3912	+	4.52117i	0.487348	+	0.153106i
$873$		−	15.8587i		−	0.536735i
$874$	−24.8099	+	20.4006i	−0.839207	+	0.690060i
$875$	2.63867			0.0892032
$876$	20.8473	+	2.25466i	0.704366	+	0.0761780i
$877$	−28.0371	+	24.2943i	−0.946745	+	0.820359i	−0.983858	−	0.178952i	$-0.942729\pi$
$877$	−28.0371	+	24.2943i	−0.946745	+	0.820359i	0.0371132	+	0.999311i	$0.488184\pi$
$878$	11.7674	+	29.9358i	0.397129	+	1.01028i
$879$	−0.893802	−	6.21653i	−0.0301472	−	0.209678i
$880$	−34.7023	+	7.50304i	−1.16981	+	0.252928i
$881$	26.2752	+	11.9995i	0.885234	+	0.404273i	0.805536	−	0.592546i	$-0.201877\pi$
$881$	26.2752	+	11.9995i	0.885234	+	0.404273i	0.0796974	+	0.996819i	$0.474605\pi$
$882$	−7.75228	+	6.01823i	−0.261033	+	0.202644i
$883$	−3.23119	+	22.4734i	−0.108738	+	0.756291i	0.860373	+	0.509666i	$0.170231\pi$
$883$	−3.23119	+	22.4734i	−0.108738	+	0.756291i	−0.969111	+	0.246626i	$0.920678\pi$
$884$	2.24213	+	63.9119i	0.0754111	+	2.14959i
$885$	11.7447	+	3.44854i	0.394793	+	0.115922i
$886$	−10.5330	−	5.51397i	−0.353864	−	0.185245i
$887$	20.5751	−	9.39633i	0.690844	−	0.315498i	−0.0388759	−	0.999244i	$-0.512378\pi$
$887$	20.5751	−	9.39633i	0.690844	−	0.315498i	0.729720	+	0.683746i	$0.239650\pi$
$888$	−1.16143	+	1.29052i	−0.0389750	+	0.0433071i
$889$	3.70008	+	3.20614i	0.124097	+	0.107530i
$890$	−43.8380	−	31.6327i	−1.46945	−	1.06033i
$891$	2.07230	−	3.22456i	0.0694246	−	0.108027i
$892$	0.553630	+	0.141679i	0.0185369	+	0.00474375i
$893$	−29.8194	+	19.1637i	−0.997867	+	0.641290i
$894$	16.0796	+	28.2582i	0.537782	+	0.945094i
$895$	49.3374	−	14.4868i	1.64917	−	0.484240i
$896$	−0.536271	−	2.72757i	−0.0179156	−	0.0911217i
$897$	−10.2050	+	24.1134i	−0.340736	+	0.805121i
$898$	21.0120	+	4.18646i	0.701179	+	0.139704i
$899$	36.2701	−	10.6499i	1.20968	−	0.355193i
$900$	−0.228397	−	0.687675i	−0.00761324	−	0.0229225i
$901$	27.5862	+	42.9249i	0.919028	+	1.43004i
$902$	−41.0921	−	2.21562i	−1.36822	−	0.0737720i
$903$	−0.716278	+	1.11455i	−0.0238362	+	0.0370899i
$904$	4.10721	+	6.66310i	0.136604	+	0.221611i
$905$	−9.94562	+	11.4779i	−0.330604	+	0.381537i
$906$	−16.1731	−	5.71131i	−0.537316	−	0.189745i
$907$	−51.6205	+	23.5743i	−1.71403	+	0.782771i	−0.717778	+	0.696272i	$0.754841\pi$
$907$	−51.6205	+	23.5743i	−1.71403	+	0.782771i	−0.996252	+	0.0864989i	$0.972432\pi$
$908$	−10.3889	+	12.8751i	−0.344766	+	0.427275i
$909$	1.43670	−	4.89295i	0.0476523	−	0.162289i
$910$	−4.27564	+	1.00893i	−0.141736	+	0.0334458i
$911$	4.76175	−	33.1187i	0.157764	−	1.09727i	−0.744978	−	0.667089i	$-0.767540\pi$
$911$	4.76175	−	33.1187i	0.157764	−	1.09727i	0.902742	−	0.430182i	$-0.141551\pi$
$912$	−1.32751	−	18.8970i	−0.0439581	−	0.625741i
$913$	−0.0908322	+	0.198895i	−0.00300611	+	0.00658245i
$914$	2.43195	−	2.51876i	0.0804416	−	0.0833132i
$915$	1.01061	+	7.02896i	0.0334098	+	0.232370i
$916$	−13.5187	+	2.43022i	−0.446672	+	0.0802967i
$917$	0.366855	+	0.423373i	0.0121146	+	0.0139810i
$918$	0.735624	+	8.24981i	0.0242792	+	0.272284i
$919$	12.1795			0.401766			0.200883	−	0.979615i	$-0.435619\pi$
$919$	12.1795			0.401766			0.200883	+	0.979615i	$0.435619\pi$
$920$	28.4508	−	13.3123i	0.937994	−	0.438894i
$921$	26.9533			0.888143
$922$	0.347736	+	3.89976i	0.0114521	+	0.128432i
$923$	54.6883	+	63.1136i	1.80009	+	2.07741i
$924$	0.333260	+	1.85385i	0.0109634	+	0.0609871i
$925$	−0.0316503	−	0.220133i	−0.00104066	−	0.00723792i
$926$	9.86532	−	10.2175i	0.324195	−	0.335767i
$927$	4.65343	−	10.1896i	0.152839	−	0.334670i
$928$	7.18014	−	56.4428i	0.235700	−	1.85282i
$929$	0.429550	−	2.98759i	0.0140931	−	0.0980196i	−0.981561	−	0.191150i	$-0.938778\pi$
$929$	0.429550	−	2.98759i	0.0140931	−	0.0980196i	0.995654	+	0.0931305i	$0.0296874\pi$
$930$	−11.9788	+	2.82666i	−0.392799	+	0.0926897i
$931$	9.25922	−	31.5340i	0.303459	−	1.03349i
$932$	−14.8933	−	12.0173i	−0.487845	−	0.393640i
$933$	−9.26174	+	4.22969i	−0.303216	+	0.138474i
$934$	47.1210	+	16.6401i	1.54184	+	0.544480i
$935$	−34.0421	+	39.2867i	−1.11330	+	1.28481i
$936$	−8.10312	−	13.1456i	−0.264859	−	0.429678i
$937$	20.3496	−	31.6646i	0.664794	−	1.03444i	−0.331073	−	0.943605i	$-0.607410\pi$
$937$	20.3496	−	31.6646i	0.664794	−	1.03444i	0.995866	−	0.0908336i	$-0.0289531\pi$
$938$	1.05679	+	0.0569804i	0.0345054	+	0.00186047i
$939$	−4.54526	−	7.07256i	−0.148329	−	0.230804i
$940$	32.8968	−	10.9260i	1.07298	−	0.356367i
$941$	36.5227	−	10.7240i	1.19061	−	0.349594i	0.374353	−	0.927286i	$-0.377865\pi$
$941$	36.5227	−	10.7240i	1.19061	−	0.349594i	0.816254	+	0.577693i	$0.196047\pi$
$942$	−17.1682	−	3.42061i	−0.559370	−	0.111450i
$943$	35.8777	−	6.18986i	1.16834	−	0.201569i
$944$	−14.9320	−	14.9698i	−0.485995	−	0.487226i
$945$	−0.545914	+	0.160295i	−0.0177586	+	0.00521439i
$946$	−14.4559	−	25.4047i	−0.470003	−	0.825979i
$947$	−12.9933	+	8.35026i	−0.422224	+	0.271347i	−0.734452	−	0.678660i	$-0.762561\pi$
$947$	−12.9933	+	8.35026i	−0.422224	+	0.271347i	0.312228	+	0.950007i	$0.398925\pi$
$948$	2.71214	−	10.5981i	0.0880863	−	0.344210i
$949$	−30.9474	+	48.1552i	−1.00460	+	1.56318i
$950$	1.96776	+	1.41990i	0.0638426	+	0.0460677i
$951$	−13.6031	−	11.7872i	−0.441111	−	0.382225i
$952$	−3.02530	−	2.72267i	−0.0980504	−	0.0882422i
$953$	−29.5971	+	13.5166i	−0.958745	+	0.437844i	−0.832420	−	0.554145i	$-0.813045\pi$
$953$	−29.5971	+	13.5166i	−0.958745	+	0.437844i	−0.126325	+	0.991989i	$0.540318\pi$
$954$	−10.9158	−	5.71436i	−0.353413	−	0.185009i
$955$	17.0284	+	4.99999i	0.551026	+	0.161796i
$956$	38.1504	−	1.33838i	1.23387	−	0.0432862i
$957$	−5.48672	+	38.1610i	−0.177360	+	1.23357i
$958$	5.22349	−	4.05508i	0.168763	−	0.131014i
$959$	−2.05710	−	0.939448i	−0.0664273	−	0.0303363i
$960$	−3.32383	+	18.2247i	−0.107276	+	0.588200i
$961$	−2.40162	−	16.7036i	−0.0774716	−	0.538827i
$962$	−1.73391	−	4.41101i	−0.0559035	−	0.142217i
$963$	5.42607	−	4.70172i	0.174853	−	0.151511i
$964$	−1.94454	+	17.9798i	−0.0626293	+	0.579090i
$965$	−25.9902			−0.836654
$966$	−0.652891	−	1.53320i	−0.0210064	−	0.0493299i
$967$			28.8772i			0.928627i	0.885671	+	0.464314i	$0.153699\pi$
$967$			28.8772i			0.928627i	−0.885671	+	0.464314i	$0.846301\pi$
$968$	−9.96300	−	3.12999i	−0.320223	−	0.100602i
$969$	−18.1635	−	20.9617i	−0.583494	−	0.673388i
$970$	−18.9997	−	48.3346i	−0.610043	−	1.55193i
$971$	5.71633	−	0.821885i	0.183446	−	0.0263755i	−0.0499796	−	0.998750i	$-0.515916\pi$
$971$	5.71633	−	0.821885i	0.183446	−	0.0263755i	0.233425	+	0.972375i	$0.425007\pi$
$972$	−1.13961	−	1.64356i	−0.0365529	−	0.0527173i
$973$	−0.675352	+	1.47882i	−0.0216508	+	0.0474086i
$974$	−0.628123	−	0.809106i	−0.0201263	−	0.0259254i
$975$	1.95795	+	0.281511i	0.0627047	+	0.00901558i
$976$	4.30122	−	11.4876i	0.137679	−	0.367709i
$977$	−8.09022	+	27.5527i	−0.258829	+	0.881491i	0.722859	+	0.690995i	$0.242828\pi$
$977$	−8.09022	+	27.5527i	−0.258829	+	0.881491i	−0.981688	+	0.190495i	$0.938991\pi$
$978$	5.26497	+	2.75618i	0.168355	+	0.0881329i
$979$	−26.2848	−	57.5556i	−0.840065	−	1.83949i
$980$	−16.4174	+	27.6302i	−0.524435	+	0.882616i
$981$	−3.49253	+	4.03060i	−0.111508	+	0.128687i
$982$	14.8696	−	20.6069i	0.474509	−	0.657594i
$983$	−50.2722	−	32.3080i	−1.60343	−	1.03046i	−0.965510	−	0.260366i	$-0.916157\pi$
$983$	−50.2722	−	32.3080i	−1.60343	−	1.03046i	−0.637924	−	0.770099i	$-0.720207\pi$
$984$	−9.28542	+	19.3606i	−0.296008	+	0.617193i
$985$	21.8809	+	34.0473i	0.697182	+	1.08484i
$986$	−41.2007	−	72.4058i	−1.31210	−	2.30587i
$987$	−0.518101	−	1.76449i	−0.0164913	−	0.0561643i
$988$	47.7642	+	19.8200i	1.51958	+	0.630558i
$989$	17.4761	+	19.0612i	0.555708	+	0.606111i
$990$	2.45279	−	12.3106i	0.0779547	−	0.391258i
$991$	−1.17398	−	3.99822i	−0.0372928	−	0.127008i	0.938743	−	0.344619i	$-0.111992\pi$
$991$	−1.17398	−	3.99822i	−0.0372928	−	0.127008i	−0.976036	+	0.217611i	$0.930174\pi$
$992$	20.4935	+	5.65700i	0.650671	+	0.179610i
$993$	−3.21888	+	2.06865i	−0.102148	+	0.0656466i
$994$	−5.30721	−	0.286156i	−0.168335	−	0.00907632i
$995$	−37.4508	−	24.0682i	−1.18727	−	0.763013i
$996$	0.0776895	+	0.0835504i	0.00246169	+	0.00264739i
$997$	7.28974	+	6.31659i	0.230868	+	0.200049i	0.762611	−	0.646858i	$-0.223917\pi$
$997$	7.28974	+	6.31659i	0.230868	+	0.200049i	−0.531743	+	0.846906i	$0.678463\pi$
$998$	−17.7568	+	50.2832i	−0.562081	+	1.59169i
$999$	−0.254997	−	0.558365i	−0.00806774	−	0.0176659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.t.a.451.23	yes	240
8.3	odd	2	inner	552.2.t.a.451.21	yes	240
23.5	odd	22	inner	552.2.t.a.235.21	✓	240
184.51	even	22	inner	552.2.t.a.235.23	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.t.a.235.21	✓	240	23.5	odd	22	inner
552.2.t.a.235.23	yes	240	184.51	even	22	inner
552.2.t.a.451.21	yes	240	8.3	odd	2	inner
552.2.t.a.451.23	yes	240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40862 - 0.125605i) q^{2} +(0.654861 + 0.755750i) q^{3} +(1.96845 - 0.353861i) q^{4} +(0.329554 + 2.29210i) q^{5} +(1.01738 + 0.982314i) q^{6} +(0.102068 - 0.223497i) q^{7} +(2.72836 - 0.745705i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(1.40862 - 0.125605i) q^{2} +(0.654861 + 0.755750i) q^{3} +(1.96845 - 0.353861i) q^{4} +(0.329554 + 2.29210i) q^{5} +(1.01738 + 0.982314i) q^{6} +(0.102068 - 0.223497i) q^{7} +(2.72836 - 0.745705i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.752116 + 3.18731i) q^{10} +(-1.07989 + 3.67777i) q^{11} +(1.55649 + 1.25592i) q^{12} +(-4.96634 + 2.26805i) q^{13} +(0.115703 - 0.327644i) q^{14} +(-1.51644 + 1.75006i) q^{15} +(3.74956 - 1.39311i) q^{16} +(3.16634 - 4.92692i) q^{17} +(-0.0761415 + 1.41216i) q^{18} +(-2.56041 - 3.98408i) q^{19} +(1.45979 + 4.39525i) q^{20} +(0.235748 - 0.0692219i) q^{21} +(-1.05921 + 5.31624i) q^{22} +(-0.134482 - 4.79395i) q^{23} +(2.35026 + 1.57362i) q^{24} +(-0.347630 + 0.102073i) q^{25} +(-6.71082 + 3.81863i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(0.121828 - 0.476061i) q^{28} +(5.43786 - 8.46148i) q^{29} +(-1.91628 + 2.65565i) q^{30} +(2.84031 + 2.46114i) q^{31} +(5.10675 - 2.43334i) q^{32} +(-3.48666 + 1.59230i) q^{33} +(3.84134 - 7.33789i) q^{34} +(0.545914 + 0.160295i) q^{35} +(0.0701201 + 1.99877i) q^{36} +(-0.0873580 + 0.607588i) q^{37} +(-4.10708 - 5.29047i) q^{38} +(-4.96634 - 2.26805i) q^{39} +(2.60837 + 6.00790i) q^{40} +(1.08039 + 7.51427i) q^{41} +(0.323386 - 0.127119i) q^{42} +(-4.07515 + 3.53114i) q^{43} +(-0.824289 + 7.62163i) q^{44} -2.31567 q^{45} +(-0.791578 - 6.73598i) q^{46} -7.48463i q^{47} +(3.50829 + 1.92144i) q^{48} +(4.54449 + 5.24462i) q^{49} +(-0.476859 + 0.187447i) q^{50} +(5.79703 - 0.833487i) q^{51} +(-8.97339 + 6.22193i) q^{52} +(-3.61923 + 7.92501i) q^{53} +(-1.11710 + 0.867226i) q^{54} +(-8.78569 - 1.26319i) q^{55} +(0.111814 - 0.685893i) q^{56} +(1.33425 - 4.54405i) q^{57} +(6.59710 - 12.6021i) q^{58} +(-2.19586 - 4.80827i) q^{59} +(-2.36575 + 3.98151i) q^{60} +(2.00820 - 2.31759i) q^{61} +(4.31006 + 3.11007i) q^{62} +(0.206697 + 0.132836i) q^{63} +(6.88785 - 4.06909i) q^{64} +(-6.83526 - 10.6359i) q^{65} +(-4.71139 + 2.68090i) q^{66} +(0.858092 + 2.92239i) q^{67} +(4.48932 - 10.8188i) q^{68} +(3.53496 - 3.24100i) q^{69} +(0.789122 + 0.157226i) q^{70} +(-4.30935 - 14.6763i) q^{71} +(0.349829 + 2.80671i) q^{72} +(8.82008 - 5.66832i) q^{73} +(-0.0467384 + 0.866837i) q^{74} +(-0.304791 - 0.195877i) q^{75} +(-6.44984 - 6.93642i) q^{76} +(0.711751 + 0.616736i) q^{77} +(-7.28058 - 2.57103i) q^{78} +(-2.27224 - 4.97551i) q^{79} +(4.42883 + 8.13525i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(2.46569 + 10.4491i) q^{82} +(0.0564639 + 0.00811829i) q^{83} +(0.439563 - 0.219682i) q^{84} +(12.3364 + 5.63387i) q^{85} +(-5.29683 + 5.48591i) q^{86} +(9.95580 - 1.43143i) q^{87} +(-0.203796 + 10.8396i) q^{88} +(-12.4755 + 10.8101i) q^{89} +(-3.26190 + 0.290860i) q^{90} +1.34146i q^{91} +(-1.96111 - 9.38904i) q^{92} +3.75827i q^{93} +(-0.940109 - 10.5430i) q^{94} +(8.28809 - 7.18167i) q^{95} +(5.18320 + 2.26592i) q^{96} +(-15.6973 + 2.25693i) q^{97} +(7.06024 + 6.81689i) q^{98} +(-3.48666 - 1.59230i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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