LMFDB - Embedded newform 81.2.g.a.25.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,2,Mod(4,81)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("81.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(81, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.g (of order $27$, degree $18$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			25.3
Character	$\chi$	$=$	81.25
Dual form			81.2.g.a.13.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.07782 + 0.541304i) q^{2} +(-1.45923 - 0.933081i) q^{3} +(-0.325622 + 0.437386i) q^{4} +(1.12732 - 3.76550i) q^{5} +(2.07788 + 0.215810i) q^{6} +(0.736444 - 1.70727i) q^{7} +(0.533084 - 3.02327i) q^{8} +(1.25872 + 2.72317i) q^{9} +(0.823230 + 4.66877i) q^{10} +(-4.71857 - 1.11832i) q^{11} +(0.883275 - 0.334416i) q^{12} +(0.260059 - 0.171044i) q^{13} +(0.130394 + 2.23878i) q^{14} +(-5.15854 + 4.44287i) q^{15} +(0.749157 + 2.50236i) q^{16} +(3.17561 + 1.15583i) q^{17} +(-2.83074 - 2.25374i) q^{18} +(1.05997 - 0.385798i) q^{19} +(1.27990 + 1.71920i) q^{20} +(-2.66766 + 1.80414i) q^{21} +(5.69114 - 1.34882i) q^{22} +(0.902427 + 2.09206i) q^{23} +(-3.59885 + 3.91424i) q^{24} +(-8.73073 - 5.74229i) q^{25} +(-0.187712 + 0.325126i) q^{26} +(0.704172 - 5.14822i) q^{27} +(0.506934 + 0.878035i) q^{28} +(-0.166624 + 2.86083i) q^{29} +(3.15506 - 7.58096i) q^{30} +(4.82793 + 0.564304i) q^{31} +(2.05140 + 2.17436i) q^{32} +(5.84200 + 6.03470i) q^{33} +(-4.04840 + 0.473190i) q^{34} +(-5.59852 - 4.69772i) q^{35} +(-1.60094 - 0.336176i) q^{36} +(8.69541 - 7.29632i) q^{37} +(-0.933628 + 0.989588i) q^{38} +(-0.539085 + 0.00693600i) q^{39} +(-10.7832 - 5.41551i) q^{40} +(1.29097 + 0.648347i) q^{41} +(1.89869 - 3.38856i) q^{42} +(-3.07034 + 3.25437i) q^{43} +(2.02561 - 1.69969i) q^{44} +(11.6731 - 1.66984i) q^{45} +(-2.10510 - 1.76639i) q^{46} +(3.90295 - 0.456189i) q^{47} +(1.24171 - 4.35054i) q^{48} +(2.43127 + 2.57700i) q^{49} +(12.5185 + 1.46320i) q^{50} +(-3.55547 - 4.64972i) q^{51} +(-0.00986888 + 0.169442i) q^{52} +(-0.812932 - 1.40804i) q^{53} +(2.02777 + 5.93004i) q^{54} +(-9.53037 + 16.5071i) q^{55} +(-4.76895 - 3.13659i) q^{56} +(-1.90672 - 0.426070i) q^{57} +(-1.36898 - 3.17366i) q^{58} +(-9.72169 + 2.30408i) q^{59} +(-0.263514 - 3.70297i) q^{60} +(-0.456702 - 0.613457i) q^{61} +(-5.50912 + 2.00515i) q^{62} +(5.57615 - 0.143512i) q^{63} +(-8.29717 - 3.01992i) q^{64} +(-0.350896 - 1.17208i) q^{65} +(-9.56326 - 3.34205i) q^{66} +(-0.0428458 - 0.735633i) q^{67} +(-1.53959 + 1.01260i) q^{68} +(0.635212 - 3.89484i) q^{69} +(8.57712 + 2.03281i) q^{70} +(1.18078 + 6.69652i) q^{71} +(8.90386 - 2.35377i) q^{72} +(-0.692009 + 3.92458i) q^{73} +(-5.42260 + 12.5710i) q^{74} +(7.38214 + 16.5258i) q^{75} +(-0.176407 + 0.589241i) q^{76} +(-5.38424 + 7.23229i) q^{77} +(0.577284 - 0.299284i) q^{78} +(11.0976 - 5.57340i) q^{79} +10.2672 q^{80} +(-5.83126 + 6.85540i) q^{81} -1.74239 q^{82} +(6.61608 - 3.32272i) q^{83} +(0.0795440 - 1.75427i) q^{84} +(7.93219 - 10.6548i) q^{85} +(1.54768 - 5.16962i) q^{86} +(2.91253 - 4.01913i) q^{87} +(-5.89638 + 13.6693i) q^{88} +(0.943990 - 5.35363i) q^{89} +(-11.6776 + 8.11846i) q^{90} +(-0.100499 - 0.569956i) q^{91} +(-1.20889 - 0.286512i) q^{92} +(-6.51853 - 5.32830i) q^{93} +(-3.95975 + 2.60437i) q^{94} +(-0.257799 - 4.42624i) q^{95} +(-0.964619 - 5.08702i) q^{96} +(-1.32068 - 4.41138i) q^{97} +(-4.01542 - 1.46149i) q^{98} +(-2.89398 - 14.2571i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) $ 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{23}{27}\right)$

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 $

$2$	−1.07782	+	0.541304i	−0.762137	+	0.382759i	−0.787017	−	0.616931i	$-0.788376\pi$
$2$	−1.07782	+	0.541304i	−0.762137	+	0.382759i	0.0248805	+	0.999690i	$0.492079\pi$
$3$	−1.45923	−	0.933081i	−0.842488	−	0.538715i
$3$	−1.45923	−	0.933081i	−0.842488	−	0.538715i
$4$	−0.325622	+	0.437386i	−0.162811	+	0.218693i
$5$	1.12732	−	3.76550i	0.504152	−	1.68398i	−0.204863	−	0.978791i	$-0.565675\pi$
$5$	1.12732	−	3.76550i	0.504152	−	1.68398i	0.709015	−	0.705194i	$-0.249140\pi$
$6$	2.07788	+	0.215810i	0.848289	+	0.0881040i
$7$	0.736444	−	1.70727i	0.278350	−	0.645287i	−0.720489	−	0.693466i	$-0.756083\pi$
$7$	0.736444	−	1.70727i	0.278350	−	0.645287i	0.998839	+	0.0481791i	$0.0153418\pi$
$8$	0.533084	−	3.02327i	0.188474	−	1.06889i
$9$	1.25872	+	2.72317i	0.419573	+	0.907722i
$10$	0.823230	+	4.66877i	0.260328	+	1.47640i
$11$	−4.71857	−	1.11832i	−1.42270	−	0.337187i	−0.553998	−	0.832518i	$-0.686898\pi$
$11$	−4.71857	−	1.11832i	−1.42270	−	0.337187i	−0.868704	+	0.495331i	$0.835047\pi$
$12$	0.883275	−	0.334416i	0.254980	−	0.0965377i
$13$	0.260059	−	0.171044i	0.0721275	−	0.0474390i	−0.512933	−	0.858429i	$-0.671441\pi$
$13$	0.260059	−	0.171044i	0.0721275	−	0.0474390i	0.585061	+	0.810990i	$0.301071\pi$
$14$	0.130394	+	2.23878i	0.0348492	+	0.598338i
$15$	−5.15854	+	4.44287i	−1.33193	+	1.14714i
$16$	0.749157	+	2.50236i	0.187289	+	0.625589i
$17$	3.17561	+	1.15583i	0.770198	+	0.280329i	0.697079	−	0.716994i	$-0.254483\pi$
$17$	3.17561	+	1.15583i	0.770198	+	0.280329i	0.0731188	+	0.997323i	$0.476705\pi$
$18$	−2.83074	−	2.25374i	−0.667211	−	0.531213i
$19$	1.05997	−	0.385798i	0.243174	−	0.0885081i	−0.217558	−	0.976047i	$-0.569809\pi$
$19$	1.05997	−	0.385798i	0.243174	−	0.0885081i	0.460732	+	0.887539i	$0.347587\pi$
$20$	1.27990	+	1.71920i	0.286194	+	0.384426i
$21$	−2.66766	+	1.80414i	−0.582132	+	0.393696i
$22$	5.69114	−	1.34882i	1.21335	−	0.287570i
$23$	0.902427	+	2.09206i	0.188169	+	0.436225i	0.986019	−	0.166631i	$-0.0532888\pi$
$23$	0.902427	+	2.09206i	0.188169	+	0.436225i	−0.797850	+	0.602856i	$0.794030\pi$
$24$	−3.59885	+	3.91424i	−0.734612	+	0.798991i
$25$	−8.73073	−	5.74229i	−1.74615	−	1.14846i
$26$	−0.187712	+	0.325126i	−0.0368133	+	0.0637625i
$27$	0.704172	−	5.14822i	0.135518	−	0.990775i
$28$	0.506934	+	0.878035i	0.0958015	+	0.165933i
$29$	−0.166624	+	2.86083i	−0.0309413	+	0.531242i	0.946852	+	0.321670i	$0.104244\pi$
$29$	−0.166624	+	2.86083i	−0.0309413	+	0.531242i	−0.977793	+	0.209572i	$0.932793\pi$
$30$	3.15506	−	7.58096i	0.576032	−	1.38409i
$31$	4.82793	+	0.564304i	0.867122	+	0.101352i	0.538009	−	0.842939i	$-0.319176\pi$
$31$	4.82793	+	0.564304i	0.867122	+	0.101352i	0.329112	+	0.944291i	$0.393251\pi$
$32$	2.05140	+	2.17436i	0.362640	+	0.384376i
$33$	5.84200	+	6.03470i	1.01696	+	1.05051i
$34$	−4.04840	+	0.473190i	−0.694295	+	0.0811514i
$35$	−5.59852	−	4.69772i	−0.946323	−	0.794059i
$36$	−1.60094	−	0.336176i	−0.266824	−	0.0560294i
$37$	8.69541	−	7.29632i	1.42952	−	1.19951i	0.483519	−	0.875334i	$-0.339358\pi$
$37$	8.69541	−	7.29632i	1.42952	−	1.19951i	0.945998	−	0.324173i	$-0.105086\pi$
$38$	−0.933628	+	0.989588i	−0.151455	+	0.160532i
$39$	−0.539085	+	0.00693600i	−0.0863227	+	0.00111065i
$40$	−10.7832	−	5.41551i	−1.70497	−	0.856268i
$41$	1.29097	+	0.648347i	0.201615	+	0.101255i	0.546742	−	0.837301i	$-0.315868\pi$
$41$	1.29097	+	0.648347i	0.201615	+	0.101255i	−0.345127	+	0.938556i	$0.612164\pi$
$42$	1.89869	−	3.38856i	0.292974	−	0.522867i
$43$	−3.07034	+	3.25437i	−0.468222	+	0.496287i	−0.917849	−	0.396930i	$-0.870076\pi$
$43$	−3.07034	+	3.25437i	−0.468222	+	0.496287i	0.449627	+	0.893217i	$0.351557\pi$
$44$	2.02561	−	1.69969i	0.305372	−	0.256237i
$45$	11.6731	−	1.66984i	1.74012	−	0.248924i
$46$	−2.10510	−	1.76639i	−0.310380	−	0.260439i
$47$	3.90295	−	0.456189i	0.569304	−	0.0665420i	0.173429	−	0.984846i	$-0.444515\pi$
$47$	3.90295	−	0.456189i	0.569304	−	0.0665420i	0.395875	+	0.918304i	$0.370441\pi$
$48$	1.24171	−	4.35054i	0.179225	−	0.627947i
$49$	2.43127	+	2.57700i	0.347325	+	0.368142i
$50$	12.5185	+	1.46320i	1.77039	+	0.206928i
$51$	−3.55547	−	4.64972i	−0.497865	−	0.651091i
$52$	−0.00986888	+	0.169442i	−0.00136857	+	0.0234974i
$53$	−0.812932	−	1.40804i	−0.111665	−	0.193409i	0.804777	−	0.593577i	$-0.202285\pi$
$53$	−0.812932	−	1.40804i	−0.111665	−	0.193409i	−0.916442	+	0.400168i	$0.868952\pi$
$54$	2.02777	+	5.93004i	0.275945	+	0.806977i
$55$	−9.53037	+	16.5071i	−1.28507	+	2.22581i
$56$	−4.76895	−	3.13659i	−0.637278	−	0.419144i
$57$	−1.90672	−	0.426070i	−0.252552	−	0.0564344i
$58$	−1.36898	−	3.17366i	−0.179756	−	0.416722i
$59$	−9.72169	+	2.30408i	−1.26566	+	0.299966i	−0.808010	−	0.589168i	$-0.799455\pi$
$59$	−9.72169	+	2.30408i	−1.26566	+	0.299966i	−0.457646	+	0.889134i	$0.651307\pi$
$60$	−0.263514	−	3.70297i	−0.0340195	−	0.478051i
$61$	−0.456702	−	0.613457i	−0.0584747	−	0.0785451i	0.771924	−	0.635715i	$-0.219295\pi$
$61$	−0.456702	−	0.613457i	−0.0584747	−	0.0785451i	−0.830399	+	0.557170i	$0.811887\pi$
$62$	−5.50912	+	2.00515i	−0.699659	+	0.254655i
$63$	5.57615	−	0.143512i	0.702529	−	0.0180808i
$64$	−8.29717	−	3.01992i	−1.03715	−	0.377490i
$65$	−0.350896	−	1.17208i	−0.0435233	−	0.145378i
$66$	−9.56326	−	3.34205i	−1.17716	−	0.411378i
$67$	−0.0428458	−	0.735633i	−0.00523444	−	0.0898719i	0.994679	−	0.103022i	$-0.0328512\pi$
$67$	−0.0428458	−	0.735633i	−0.00523444	−	0.0898719i	−0.999914	+	0.0131499i	$0.995814\pi$
$68$	−1.53959	+	1.01260i	−0.186703	+	0.122796i
$69$	0.635212	−	3.89484i	0.0764706	−	0.468884i
$70$	8.57712	+	2.03281i	1.02516	+	0.242968i
$71$	1.18078	+	6.69652i	0.140133	+	0.794731i	0.971147	+	0.238481i	$0.0766493\pi$
$71$	1.18078	+	6.69652i	0.140133	+	0.794731i	−0.831015	+	0.556250i	$0.812240\pi$
$72$	8.90386	−	2.35377i	1.04933	−	0.277394i
$73$	−0.692009	+	3.92458i	−0.0809935	+	0.459337i	0.917156	+	0.398529i	$0.130479\pi$
$73$	−0.692009	+	3.92458i	−0.0809935	+	0.459337i	−0.998149	+	0.0608086i	$0.980632\pi$
$74$	−5.42260	+	12.5710i	−0.630365	+	1.46135i
$75$	7.38214	+	16.5258i	0.852416	+	1.90824i
$76$	−0.176407	+	0.589241i	−0.0202353	+	0.0675906i
$77$	−5.38424	+	7.23229i	−0.613591	+	0.824196i
$78$	0.577284	−	0.299284i	0.0653646	−	0.0338873i
$79$	11.0976	−	5.57340i	1.24857	−	0.627057i	0.303162	−	0.952939i	$-0.401958\pi$
$79$	11.0976	−	5.57340i	1.24857	−	0.627057i	0.945410	+	0.325882i	$0.105661\pi$
$80$	10.2672			1.14790
$81$	−5.83126	+	6.85540i	−0.647917	+	0.761711i
$82$	−1.74239			−0.192414
$83$	6.61608	−	3.32272i	0.726209	−	0.364716i	−0.0469762	−	0.998896i	$-0.514958\pi$
$83$	6.61608	−	3.32272i	0.726209	−	0.364716i	0.773185	+	0.634180i	$0.218662\pi$
$84$	0.0795440	−	1.75427i	0.00867896	−	0.191406i
$85$	7.93219	−	10.6548i	0.860367	−	1.15567i
$86$	1.54768	−	5.16962i	0.166891	−	0.557455i
$87$	2.91253	−	4.01913i	0.312256	−	0.430896i
$88$	−5.89638	+	13.6693i	−0.628556	+	1.45716i
$89$	0.943990	−	5.35363i	0.100063	−	0.567484i	−0.893015	−	0.450027i	$-0.851414\pi$
$89$	0.943990	−	5.35363i	0.100063	−	0.567484i	0.993078	−	0.117458i	$-0.0374744\pi$
$90$	−11.6776	+	8.11846i	−1.23093	+	0.855761i
$91$	−0.100499	−	0.569956i	−0.0105351	−	0.0597476i
$92$	−1.20889	−	0.286512i	−0.126035	−	0.0298709i
$93$	−6.51853	−	5.32830i	−0.675940	−	0.552519i
$94$	−3.95975	+	2.60437i	−0.408418	+	0.268620i
$95$	−0.257799	−	4.42624i	−0.0264496	−	0.454123i
$96$	−0.964619	−	5.08702i	−0.0984510	−	0.519192i
$97$	−1.32068	−	4.41138i	−0.134095	−	0.447908i	0.864397	−	0.502810i	$-0.167701\pi$
$97$	−1.32068	−	4.41138i	−0.134095	−	0.447908i	−0.998492	+	0.0549021i	$0.982515\pi$
$98$	−4.01542	−	1.46149i	−0.405619	−	0.147633i
$99$	−2.89398	−	14.2571i	−0.290855	−	1.43289i
$100$	5.35452	−	1.94888i	0.535452	−	0.194888i
$101$	6.41627	+	8.61855i	0.638443	+	0.857578i	0.997117	−	0.0758854i	$-0.0241783\pi$
$101$	6.41627	+	8.61855i	0.638443	+	0.857578i	−0.358674	+	0.933463i	$0.616771\pi$
$102$	6.34908	+	3.08699i	0.628653	+	0.305658i
$103$	−11.4312	+	2.70923i	−1.12635	+	0.266949i	−0.751237	−	0.660032i	$-0.770543\pi$
$103$	−11.4312	+	2.70923i	−1.12635	+	0.266949i	−0.375108	+	0.926981i	$0.622394\pi$
$104$	−0.378478	−	0.877411i	−0.0371128	−	0.0860372i
$105$	3.78619	+	12.0789i	0.369495	+	1.17878i
$106$	1.63837	+	1.07758i	0.159133	+	0.104663i
$107$	3.20979	−	5.55953i	0.310302	−	0.537460i	−0.668125	−	0.744049i	$-0.732903\pi$
$107$	3.20979	−	5.55953i	0.310302	−	0.537460i	0.978428	+	0.206589i	$0.0662363\pi$
$108$	2.02247	+	1.98437i	0.194612	+	0.190946i
$109$	−1.72147	−	2.98167i	−0.164887	−	0.285592i	0.771728	−	0.635952i	$-0.219393\pi$
$109$	−1.72147	−	2.98167i	−0.164887	−	0.285592i	−0.936615	+	0.350360i	$0.886059\pi$
$110$	1.33672	−	22.9506i	0.127451	−	2.18825i
$111$	−19.4967	+	2.53349i	−1.85054	+	0.240469i
$112$	4.82391	+	0.563834i	0.455817	+	0.0532773i
$113$	−10.6387	−	11.2763i	−1.00080	−	1.06079i	−0.998150	−	0.0607914i	$-0.980638\pi$
$113$	−10.6387	−	11.2763i	−1.00080	−	1.06079i	−0.00265125	−	0.999996i	$-0.500844\pi$
$114$	2.28575	−	0.572888i	0.214080	−	0.0536559i
$115$	8.89498	−	1.03967i	0.829461	−	0.0969501i
$116$	−1.19703	−	1.00443i	−0.111141	−	0.0932587i
$117$	0.793122	+	0.492889i	0.0733242	+	0.0455676i
$118$	9.23106	−	7.74578i	0.849788	−	0.713057i
$119$	4.31197	−	4.57042i	0.395277	−	0.418969i
$120$	10.6820	+	17.9641i	0.975133	+	1.63989i
$121$	11.1843	+	5.61696i	1.01675	+	0.510633i
$122$	0.824311	+	0.413984i	0.0746296	+	0.0374804i
$123$	−1.27886	−	2.15067i	−0.115311	−	0.193919i
$124$	−1.81890	+	1.92792i	−0.163342	+	0.173132i
$125$	−16.4097	+	13.7694i	−1.46773	+	1.23157i
$126$	−5.93243	+	3.17307i	−0.528503	+	0.282680i
$127$	−9.04687	−	7.59122i	−0.802780	−	0.673612i	0.146093	−	0.989271i	$-0.453330\pi$
$127$	−9.04687	−	7.59122i	−0.802780	−	0.673612i	−0.948873	+	0.315659i	$0.897775\pi$
$128$	4.63935	−	0.542262i	0.410064	−	0.0479296i
$129$	7.51693	−	1.88400i	0.661829	−	0.165877i
$130$	1.01265	+	1.07335i	0.0888156	+	0.0941390i
$131$	17.5697	+	2.05361i	1.53507	+	0.179424i	0.841220	−	0.540693i	$-0.181838\pi$
$131$	17.5697	+	2.05361i	1.53507	+	0.179424i	0.693853	+	0.720117i	$0.255912\pi$
$132$	−4.54178	+	0.590181i	−0.395311	+	0.0513687i
$133$	0.121948	−	2.09377i	0.0105743	−	0.181553i
$134$	0.444381	+	0.769691i	0.0383887	+	0.0664911i
$135$	−18.5918	−	8.45524i	−1.60013	−	0.727711i
$136$	5.18724	−	8.98457i	0.444802	−	0.770420i
$137$	5.82369	+	3.83030i	0.497551	+	0.327245i	0.773359	−	0.633968i	$-0.218575\pi$
$137$	5.82369	+	3.83030i	0.497551	+	0.327245i	−0.275808	+	0.961213i	$0.588945\pi$
$138$	1.42364	+	4.54179i	0.121189	+	0.386623i
$139$	2.49688	+	5.78842i	0.211783	+	0.490967i	0.990684	−	0.136179i	$-0.0434822\pi$
$139$	2.49688	+	5.78842i	0.211783	+	0.490967i	−0.778902	+	0.627146i	$0.784223\pi$
$140$	3.87772	−	0.919036i	0.327727	−	0.0776728i
$141$	−6.12097	−	2.97608i	−0.515479	−	0.250631i
$142$	−4.89752	−	6.57851i	−0.410991	−	0.552057i
$143$	−1.41839	+	0.516252i	−0.118612	+	0.0431712i
$144$	−5.87135	+	5.18984i	−0.489280	+	0.432487i
$145$	10.5846	+	3.85248i	0.879004	+	0.319931i
$146$	−1.37852	−	4.60459i	−0.114088	−	0.381079i
$147$	−1.14324	−	6.02901i	−0.0942930	−	0.497265i
$148$	0.359891	+	6.17909i	0.0295829	+	0.507918i
$149$	−18.9467	+	12.4614i	−1.55217	+	1.02088i	−0.572589	+	0.819842i	$0.694061\pi$
$149$	−18.9467	+	12.4614i	−1.55217	+	1.02088i	−0.979584	+	0.201038i	$0.935569\pi$
$150$	−16.9021	−	13.8159i	−1.38005	−	1.12807i
$151$	14.1006	+	3.34191i	1.14749	+	0.271961i	0.760007	−	0.649915i	$-0.225196\pi$
$151$	14.1006	+	3.34191i	1.14749	+	0.271961i	0.387485	+	0.921876i	$0.373344\pi$
$152$	−0.601317	−	3.41024i	−0.0487733	−	0.276607i
$153$	0.849688	+	10.1026i	0.0686932	+	0.816744i
$154$	1.88840	−	10.7096i	0.152172	−	0.863008i
$155$	7.56750	−	17.5434i	0.607836	−	1.40912i
$156$	0.172504	−	0.238047i	0.0138114	−	0.0190590i
$157$	−3.26203	+	10.8960i	−0.260339	+	0.869592i	0.723468	+	0.690358i	$0.242547\pi$
$157$	−3.26203	+	10.8960i	−0.260339	+	0.869592i	−0.983807	+	0.179234i	$0.942638\pi$
$158$	−8.94431	+	12.0143i	−0.711571	+	0.955806i
$159$	−0.127559	+	2.81319i	−0.0101161	+	0.223100i
$160$	10.5001	−	5.27337i	0.830109	−	0.416897i
$161$	4.23630			0.333867
$162$	2.57422	−	10.5454i	0.202250	−	0.828524i
$163$	−0.789620			−0.0618478			−0.0309239	−	0.999522i	$-0.509845\pi$
$163$	−0.789620			−0.0618478			−0.0309239	+	0.999522i	$0.509845\pi$
$164$	−0.703945	+	0.353534i	−0.0549689	+	0.0276064i
$165$	29.3095	−	15.1951i	2.28174	−	1.18293i
$166$	−5.33237	+	7.16262i	−0.413872	+	0.555927i
$167$	1.66480	−	5.56083i	0.128826	−	0.430310i	−0.869103	−	0.494631i	$-0.835303\pi$
$167$	1.66480	−	5.56083i	0.128826	−	0.430310i	0.997929	+	0.0643213i	$0.0204882\pi$
$168$	4.03231	+	9.02683i	0.311100	+	0.696435i
$169$	−5.11066	+	11.8478i	−0.393128	+	0.911373i
$170$	−2.78203	+	15.7777i	−0.213372	+	1.21009i
$171$	2.38480	+	2.40086i	0.182370	+	0.183599i
$172$	−0.423646	−	2.40262i	−0.0323027	−	0.183198i
$173$	−3.38372	−	0.801956i	−0.257259	−	0.0609716i	0.0999623	−	0.994991i	$-0.468128\pi$
$173$	−3.38372	−	0.801956i	−0.257259	−	0.0609716i	−0.357222	+	0.934020i	$0.616276\pi$
$174$	−0.963619	+	5.90848i	−0.0730517	+	0.447921i
$175$	−16.2333	+	10.6768i	−1.22712	+	0.807093i
$176$	−0.736507	−	12.6453i	−0.0555163	−	0.953179i
$177$	16.3361	+	5.70894i	1.22790	+	0.429110i
$178$	1.88049	+	6.28126i	0.140948	+	0.470800i
$179$	7.34454	+	2.67320i	0.548957	+	0.199804i	0.601583	−	0.798810i	$-0.294537\pi$
$179$	7.34454	+	2.67320i	0.548957	+	0.199804i	−0.0526260	+	0.998614i	$0.516759\pi$
$180$	−3.07064	+	5.64937i	−0.228872	+	0.421079i
$181$	−10.9891	+	3.99971i	−0.816815	+	0.297296i	−0.716436	−	0.697653i	$-0.754228\pi$
$181$	−10.9891	+	3.99971i	−0.816815	+	0.297296i	−0.100379	+	0.994949i	$0.532006\pi$
$182$	0.416839	+	0.559912i	0.0308982	+	0.0415034i
$183$	0.0940288	+	1.32132i	0.00695081	+	0.0976745i
$184$	6.80593	−	1.61304i	0.501740	−	0.118915i
$185$	−17.6718	−	40.9679i	−1.29926	−	3.01202i
$186$	9.91006	+	2.21447i	0.726641	+	0.162373i
$187$	−13.6917	−	9.00520i	−1.00124	−	0.658525i
$188$	−1.07135	+	1.85564i	−0.0781366	+	0.135337i
$189$	−8.27081	−	4.99359i	−0.601613	−	0.363230i
$190$	2.67380	+	4.63116i	0.193978	+	0.335980i
$191$	−0.846085	+	14.5267i	−0.0612206	+	1.05112i	0.818158	+	0.574994i	$0.194995\pi$
$191$	−0.846085	+	14.5267i	−0.0612206	+	1.05112i	−0.879378	+	0.476123i	$0.842042\pi$
$192$	9.28966	+	12.1487i	0.670424	+	0.876757i
$193$	−16.9026	−	1.97563i	−1.21668	−	0.142209i	−0.516568	−	0.856246i	$-0.672791\pi$
$193$	−16.9026	−	1.97563i	−1.21668	−	0.142209i	−0.700108	+	0.714037i	$0.746865\pi$
$194$	3.81136	+	4.03981i	0.273640	+	0.290041i
$195$	−0.581602	+	2.03775i	−0.0416494	+	0.145926i
$196$	−1.91882	+	0.224278i	−0.137058	+	0.0160198i
$197$	9.53813	+	8.00344i	0.679563	+	0.570221i	0.915879	−	0.401455i	$-0.131495\pi$
$197$	9.53813	+	8.00344i	0.679563	+	0.570221i	−0.236315	+	0.971676i	$0.575940\pi$
$198$	10.8366	+	13.8001i	0.770125	+	0.980732i
$199$	−16.5214	+	13.8631i	−1.17117	+	0.982731i	−0.999997	−	0.00250896i	$-0.999201\pi$
$199$	−16.5214	+	13.8631i	−1.17117	+	0.982731i	−0.171177	+	0.985240i	$0.554757\pi$
$200$	−22.0147	+	23.3342i	−1.55667	+	1.64998i
$201$	−0.623884	+	1.11344i	−0.0440054	+	0.0785359i
$202$	−11.5809	−	5.81613i	−0.814827	−	0.409221i
$203$	4.76149	+	2.39131i	0.334191	+	0.167837i
$204$	3.19146	−	0.0410622i	0.223447	−	0.00287493i
$205$	3.89668	−	4.13024i	0.272156	−	0.288469i
$206$	10.8543	−	9.10781i	0.756252	−	0.634571i
$207$	−4.56112	+	5.09077i	−0.317020	+	0.353833i
$208$	0.622838	+	0.522623i	0.0431860	+	0.0362374i
$209$	−5.43299	+	0.635026i	−0.375808	+	0.0439256i
$210$	−10.6192	−	10.9695i	−0.732796	−	0.756967i
$211$	8.69998	+	9.22144i	0.598931	+	0.634830i	0.953927	−	0.300038i	$-0.0969993\pi$
$211$	8.69998	+	9.22144i	0.598931	+	0.634830i	−0.354996	+	0.934868i	$0.615518\pi$
$212$	0.880565	+	0.102923i	0.0604775	+	0.00706880i
$213$	4.52537	−	10.8735i	0.310073	−	0.745043i
$214$	−0.450202	+	7.72966i	−0.0307752	+	0.528389i
$215$	8.79309	+	15.2301i	0.599684	+	1.03868i
$216$	−15.1891	−	4.87333i	−1.03348	−	0.331588i
$217$	4.51892	−	7.82700i	0.306764	−	0.531331i
$218$	3.46943	+	2.28188i	0.234979	+	0.154548i
$219$	4.67175	−	5.08117i	0.315688	−	0.343354i
$220$	−4.11667	−	9.54352i	−0.277546	−	0.643424i
$221$	1.02354	−	0.242584i	0.0688510	−	0.0163180i
$222$	19.6426	−	13.2843i	1.31833	−	0.891583i
$223$	−2.94086	−	3.95026i	−0.196934	−	0.264529i	0.692676	−	0.721249i	$-0.256432\pi$
$223$	−2.94086	−	3.95026i	−0.196934	−	0.264529i	−0.889611	+	0.456720i	$0.849024\pi$
$224$	5.22297	−	1.90100i	0.348974	−	0.127016i
$225$	4.64768	−	31.0031i	0.309845	−	2.06688i
$226$	17.5705	+	6.39515i	1.16877	+	0.425399i
$227$	1.84316	+	6.15657i	0.122335	+	0.408626i	0.997116	−	0.0758915i	$-0.0241803\pi$
$227$	1.84316	+	6.15657i	0.122335	+	0.408626i	−0.874781	+	0.484518i	$0.838995\pi$
$228$	0.807229	−	0.695237i	0.0534600	−	0.0460432i
$229$	−1.72908	−	29.6872i	−0.114261	−	1.96178i	−0.242795	−	0.970078i	$-0.578064\pi$
$229$	−1.72908	−	29.6872i	−0.114261	−	1.96178i	0.128534	−	0.991705i	$-0.458973\pi$
$230$	−9.02445	+	5.93547i	−0.595054	+	0.391373i
$231$	14.6052	−	5.52966i	0.960950	−	0.363825i
$232$	8.56022	+	2.02881i	0.562006	+	0.133198i
$233$	3.77489	+	21.4085i	0.247301	+	1.40252i	0.815087	+	0.579339i	$0.196689\pi$
$233$	3.77489	+	21.4085i	0.247301	+	1.40252i	−0.567786	+	0.823176i	$0.692200\pi$
$234$	−1.12165	−	0.101928i	−0.0733245	−	0.00666322i
$235$	2.68208	−	15.2108i	0.174960	−	0.992245i
$236$	2.15782	−	5.00239i	0.140462	−	0.325628i
$237$	−21.3944	−	2.22203i	−1.38971	−	0.144337i
$238$	−2.17356	+	7.26019i	−0.140891	+	0.470608i
$239$	3.55200	−	4.77116i	0.229760	−	0.308621i	−0.672261	−	0.740315i	$-0.734677\pi$
$239$	3.55200	−	4.77116i	0.229760	−	0.308621i	0.902020	+	0.431694i	$0.142084\pi$
$240$	−14.9822	−	9.58011i	−0.967096	−	0.618393i
$241$	−1.05990	+	0.532302i	−0.0682741	+	0.0342886i	−0.482609	−	0.875836i	$-0.660311\pi$
$241$	−1.05990	+	0.532302i	−0.0682741	+	0.0342886i	0.414335	+	0.910125i	$0.364014\pi$
$242$	−15.0952			−0.970355
$243$	14.9058	−	4.56258i	0.956208	−	0.292689i
$244$	0.417030			0.0266976
$245$	12.4445	−	6.24987i	0.795050	−	0.399289i
$246$	2.54255	+	1.62579i	0.162107	+	0.103656i
$247$	0.209667	−	0.281632i	0.0133408	−	0.0179198i
$248$	4.27973	−	14.2953i	0.271763	−	0.907753i
$249$	−12.7548	−	1.32472i	−0.808301	−	0.0839507i
$250$	10.2334	−	23.7236i	0.647216	−	1.50041i
$251$	2.34580	−	13.3037i	0.148066	−	0.839722i	−0.816789	−	0.576937i	$-0.804248\pi$
$251$	2.34580	−	13.3037i	0.148066	−	0.839722i	0.964854	−	0.262785i	$-0.0846410\pi$
$252$	−1.75295	+	2.48566i	−0.110425	+	0.156582i
$253$	−1.91857	−	10.8807i	−0.120619	−	0.684066i
$254$	13.8601	+	3.28490i	0.869659	+	0.206113i
$255$	−21.5167	+	8.14642i	−1.34743	+	0.510149i
$256$	10.0473	−	6.60820i	0.627955	−	0.413013i
$257$	1.42333	+	24.4376i	0.0887849	+	1.52438i	0.689130	+	0.724637i	$0.257993\pi$
$257$	1.42333	+	24.4376i	0.0887849	+	1.52438i	−0.600345	+	0.799741i	$0.704970\pi$
$258$	−7.08211	+	6.09957i	−0.440913	+	0.379742i
$259$	−6.05309	−	20.2187i	−0.376121	−	1.25633i
$260$	0.626909	+	0.228176i	0.0388793	+	0.0141509i
$261$	−8.00023	+	3.14723i	−0.495202	+	0.194809i
$262$	−20.0487	+	7.29712i	−1.23861	+	0.450818i
$263$	−12.9529	−	17.3987i	−0.798708	−	1.07285i	−0.995717	−	0.0924498i	$-0.970530\pi$
$263$	−12.9529	−	17.3987i	−0.798708	−	1.07285i	0.197009	−	0.980402i	$-0.436877\pi$
$264$	21.3588	−	14.4449i	1.31454	−	0.889025i
$265$	−6.21841	+	1.47379i	−0.381994	+	0.0905342i
$266$	1.00193	+	2.32273i	0.0614322	+	0.142416i
$267$	−6.37288	+	6.93138i	−0.390014	+	0.424193i
$268$	0.335707	+	0.220798i	0.0205066	+	0.0134874i
$269$	−2.87056	+	4.97195i	−0.175021	+	0.303145i	−0.940169	−	0.340710i	$-0.889333\pi$
$269$	−2.87056	+	4.97195i	−0.175021	+	0.303145i	0.765148	+	0.643855i	$0.222666\pi$
$270$	24.6155	−	0.950549i	1.49805	−	0.0578486i
$271$	7.23998	+	12.5400i	0.439798	+	0.761752i	0.997674	−	0.0681726i	$-0.0217169\pi$
$271$	7.23998	+	12.5400i	0.439798	+	0.761752i	−0.557876	+	0.829924i	$0.688384\pi$
$272$	−0.513264	+	8.81240i	−0.0311212	+	0.534330i
$273$	−0.385164	+	0.925471i	−0.0233112	+	0.0560121i
$274$	−8.35027	−	0.976006i	−0.504458	−	0.0589627i
$275$	34.7748	+	36.8592i	2.09700	+	2.22269i
$276$	1.49671	+	1.54608i	0.0900914	+	0.0930630i
$277$	−11.7722	+	1.37598i	−0.707325	+	0.0826744i	−0.462146	−	0.886804i	$-0.652921\pi$
$277$	−11.7722	+	1.37598i	−0.707325	+	0.0826744i	−0.245178	+	0.969478i	$0.578846\pi$
$278$	−5.82449	−	4.88733i	−0.349330	−	0.293122i
$279$	4.54031	+	13.8575i	0.271821	+	0.829630i
$280$	−17.1870	+	14.4216i	−1.02712	+	0.861853i
$281$	10.4252	−	11.0501i	0.621915	−	0.659192i	−0.337455	−	0.941342i	$-0.609566\pi$
$281$	10.4252	−	11.0501i	0.621915	−	0.659192i	0.959370	+	0.282150i	$0.0910475\pi$
$282$	8.20829	−	0.105610i	0.488797	−	0.00628898i
$283$	22.2931	+	11.1960i	1.32519	+	0.665535i	0.963737	−	0.266856i	$-0.0859847\pi$
$283$	22.2931	+	11.1960i	1.32519	+	0.665535i	0.361452	+	0.932391i	$0.382281\pi$
$284$	−3.31345	−	1.66408i	−0.196617	−	0.0987449i
$285$	−3.75385	+	6.69946i	−0.222359	+	0.396842i
$286$	1.24933	−	1.32421i	0.0738742	−	0.0783021i
$287$	2.05763	−	1.72655i	0.121458	−	0.101915i
$288$	−3.33900	+	8.32322i	−0.196753	+	0.490450i
$289$	−4.27421	−	3.58648i	−0.251424	−	0.210970i
$290$	−13.4937	+	1.57719i	−0.792378	+	0.0926157i
$291$	−2.18900	+	7.66954i	−0.128321	+	0.449596i
$292$	−1.49122	−	1.58060i	−0.0872672	−	0.0924979i
$293$	8.51771	+	0.995577i	0.497610	+	0.0581622i	0.361196	−	0.932490i	$-0.382368\pi$
$293$	8.51771	+	0.995577i	0.497610	+	0.0581622i	0.136413	+	0.990652i	$0.456442\pi$
$294$	4.49574	+	5.87937i	0.262197	+	0.342892i
$295$	−2.28340	+	39.2045i	−0.132945	+	2.28257i
$296$	−17.4233	−	30.1781i	−1.01271	−	1.75407i
$297$	−9.08005	+	23.5047i	−0.526878	+	1.36388i
$298$	13.6758	−	23.6871i	0.792216	−	1.37216i
$299$	0.592519	+	0.389706i	0.0342662	+	0.0225373i
$300$	−9.63195	−	2.15232i	−0.556101	−	0.124265i
$301$	3.29495	+	7.63856i	0.189918	+	0.440279i
$302$	−17.0070	+	4.03073i	−0.978641	+	0.231942i
$303$	−1.32102	−	18.5634i	−0.0758909	−	1.06644i
$304$	1.75949	+	2.36340i	0.100914	+	0.135550i
$305$	−2.82482	+	1.02815i	−0.161749	+	0.0588718i
$306$	−6.38437	−	10.4288i	−0.364970	−	0.596178i
$307$	1.80059	+	0.655362i	0.102765	+	0.0374035i	0.392891	−	0.919585i	$-0.371475\pi$
$307$	1.80059	+	0.655362i	0.102765	+	0.0374035i	−0.290126	+	0.956989i	$0.593697\pi$
$308$	−1.41008	−	4.70998i	−0.0803466	−	0.268376i
$309$	19.2087	+	6.71280i	1.09274	+	0.381878i
$310$	1.33989	+	23.0050i	0.0761007	+	1.30660i
$311$	12.7439	−	8.38182i	0.722643	−	0.475290i	−0.134143	−	0.990962i	$-0.542828\pi$
$311$	12.7439	−	8.38182i	0.722643	−	0.475290i	0.856786	+	0.515672i	$0.172458\pi$
$312$	−0.266408	+	1.63350i	−0.0150824	+	0.0924785i
$313$	−29.8816	−	7.08206i	−1.68901	−	0.400302i	−0.729947	−	0.683504i	$-0.760455\pi$
$313$	−29.8816	−	7.08206i	−1.68901	−	0.400302i	−0.959060	+	0.283202i	$0.908603\pi$
$314$	−2.38212	−	13.5097i	−0.134431	−	0.762395i
$315$	5.74570	−	21.1588i	0.323734	−	1.19216i
$316$	−1.17588	+	6.66874i	−0.0661484	+	0.375146i
$317$	−9.09096	+	21.0752i	−0.510599	+	1.18370i	0.446721	+	0.894673i	$0.352592\pi$
$317$	−9.09096	+	21.0752i	−0.510599	+	1.18370i	−0.957320	+	0.289029i	$0.906668\pi$
$318$	−1.38530	−	3.10117i	−0.0776839	−	0.173905i
$319$	3.98555	−	13.3127i	0.223148	−	0.745366i
$320$	−20.7251	+	27.8386i	−1.15857	+	1.55623i
$321$	−9.87133	+	5.11764i	−0.550964	+	0.285639i
$322$	−4.56598	+	2.29312i	−0.254452	+	0.127791i
$323$	3.81197			0.212104
$324$	−1.09967	−	4.78278i	−0.0610928	−	0.265710i
$325$	−3.25269			−0.180427
$326$	0.851071	−	0.427424i	0.0471365	−	0.0236728i
$327$	−0.270119	+	5.95722i	−0.0149376	+	0.329435i
$328$	2.64832	−	3.55731i	0.146229	−	0.196420i
$329$	2.09547	−	6.99934i	0.115527	−	0.385886i
$330$	−23.3653	+	32.2429i	−1.28622	+	1.77491i
$331$	−0.356898	+	0.827382i	−0.0196169	+	0.0454770i	−0.927743	−	0.373220i	$-0.878254\pi$
$331$	−0.356898	+	0.827382i	−0.0196169	+	0.0454770i	0.908126	+	0.418697i	$0.137513\pi$
$332$	−0.701029	+	3.97573i	−0.0384740	+	0.218197i
$333$	30.8141	+	14.4950i	1.68860	+	0.794323i
$334$	1.21573	+	6.89476i	0.0665219	+	0.377265i
$335$	−2.81833	−	0.667956i	−0.153982	−	0.0364944i
$336$	−6.51310	−	5.32387i	−0.355319	−	0.290441i
$337$	29.3783	−	19.3224i	1.60034	−	1.05256i	0.642082	−	0.766636i	$-0.278071\pi$
$337$	29.3783	−	19.3224i	1.60034	−	1.05256i	0.958253	−	0.285921i	$-0.0922996\pi$
$338$	−0.904887	−	15.5363i	−0.0492194	−	0.845064i
$339$	5.00256	+	26.3815i	0.271702	+	1.43285i
$340$	2.07736	+	6.93886i	0.112661	+	0.376313i
$341$	−22.1498	−	8.06188i	−1.19948	−	0.436575i
$342$	−3.86999	−	1.29681i	−0.209265	−	0.0701235i
$343$	18.4205	−	6.70453i	0.994616	−	0.362010i
$344$	8.20209	+	11.0173i	0.442227	+	0.594014i
$345$	−13.9499	−	6.78262i	−0.751040	−	0.365164i
$346$	4.08116	−	0.967252i	0.219404	−	0.0519998i
$347$	−6.01061	−	13.9342i	−0.322666	−	0.748025i	−0.999925	−	0.0122793i	$-0.996091\pi$
$347$	−6.01061	−	13.9342i	−0.322666	−	0.748025i	0.677258	−	0.735745i	$-0.263168\pi$
$348$	0.809532	+	2.58262i	0.0433955	+	0.138443i
$349$	23.6602	+	15.5615i	1.26650	+	0.832989i	0.991708	−	0.128514i	$-0.0410208\pi$
$349$	23.6602	+	15.5615i	1.26650	+	0.832989i	0.274791	+	0.961504i	$0.411391\pi$
$350$	11.7173	−	20.2949i	0.626315	−	1.08481i
$351$	−0.697444	−	1.45929i	−0.0372268	−	0.0778910i
$352$	−7.24806	−	12.5540i	−0.386323	−	0.669131i
$353$	0.966039	−	16.5863i	0.0514171	−	0.882797i	−0.869717	−	0.493551i	$-0.835699\pi$
$353$	0.966039	−	16.5863i	0.0514171	−	0.882797i	0.921134	−	0.389246i	$-0.127264\pi$
$354$	−20.6977	+	2.68956i	−1.10007	+	0.142949i
$355$	26.5469	+	3.10289i	1.40896	+	0.164684i
$356$	2.03422	+	2.15615i	0.107814	+	0.114276i
$357$	−10.5567	+	2.64589i	−0.558722	+	0.140035i
$358$	−9.36314	+	1.09439i	−0.494857	+	0.0578405i
$359$	−10.7593	−	9.02816i	−0.567856	−	0.476488i	0.313077	−	0.949728i	$-0.398640\pi$
$359$	−10.7593	−	9.02816i	−0.567856	−	0.476488i	−0.880934	+	0.473239i	$0.843085\pi$
$360$	1.17436	−	36.1810i	0.0618942	−	1.90690i
$361$	−13.5801	+	11.3951i	−0.714745	+	0.599742i
$362$	9.67928	−	10.2594i	0.508732	−	0.539224i
$363$	−11.0794	−	18.6323i	−0.581518	−	0.977943i
$364$	0.282015	+	0.141633i	0.0147816	+	0.00742361i
$365$	13.9979	+	7.03001i	0.732684	+	0.367968i
$366$	−0.816580	−	1.37325i	−0.0426833	−	0.0717808i
$367$	−3.75380	+	3.97880i	−0.195947	+	0.207692i	−0.817896	−	0.575366i	$-0.804860\pi$
$367$	−3.75380	+	3.97880i	−0.195947	+	0.207692i	0.621949	+	0.783058i	$0.286341\pi$
$368$	−4.55902	+	3.82547i	−0.237656	+	0.199417i
$369$	−0.140595	+	4.33160i	−0.00731907	+	0.225494i
$370$	41.2232	+	34.5903i	2.14309	+	1.79827i
$371$	−3.00258	+	0.350951i	−0.155886	+	0.0182205i
$372$	4.45310	−	1.11610i	0.230883	−	0.0578672i
$373$	−19.4174	−	20.5812i	−1.00540	−	1.06566i	−0.997840	−	0.0656851i	$-0.979077\pi$
$373$	−19.4174	−	20.5812i	−1.00540	−	1.06566i	−0.00755468	−	0.999971i	$-0.502405\pi$
$374$	19.6318	+	2.29463i	1.01514	+	0.118653i
$375$	36.7936	−	4.78114i	1.90001	−	0.246897i
$376$	0.701416	−	12.0429i	0.0361728	−	0.621063i
$377$	0.445994	+	0.772485i	0.0229699	+	0.0397850i
$378$	11.6175	+	0.905188i	0.597541	+	0.0465579i
$379$	−8.11043	+	14.0477i	−0.416605	+	0.721580i	−0.995595	−	0.0937537i	$-0.970113\pi$
$379$	−8.11043	+	14.0477i	−0.416605	+	0.721580i	0.578991	+	0.815334i	$0.303447\pi$
$380$	2.01992	+	1.32852i	0.103620	+	0.0681518i
$381$	6.11825	+	19.5188i	0.313448	+	0.999980i
$382$	−6.95144	−	16.1152i	−0.355667	−	0.824528i
$383$	−14.4122	+	3.41575i	−0.736427	+	0.174536i	−0.581680	−	0.813418i	$-0.697604\pi$
$383$	−14.4122	+	3.41575i	−0.736427	+	0.174536i	−0.154747	+	0.987954i	$0.549456\pi$
$384$	−7.27586	−	3.53760i	−0.371295	−	0.180528i
$385$	21.1635	+	28.4275i	1.07859	+	1.44880i
$386$	19.2874	−	7.02006i	0.981705	−	0.357311i
$387$	−12.7269	−	4.26471i	−0.646944	−	0.216787i
$388$	2.35952	+	0.858795i	0.119787	+	0.0435987i
$389$	2.14188	+	7.15437i	0.108598	+	0.362741i	0.994963	−	0.100246i	$-0.0319629\pi$
$389$	2.14188	+	7.15437i	0.108598	+	0.362741i	−0.886365	+	0.462987i	$0.846778\pi$
$390$	−0.476174	−	2.51115i	−0.0241120	−	0.127157i
$391$	0.447694	+	7.68661i	0.0226409	+	0.388729i
$392$	9.08703	−	5.97663i	0.458964	−	0.301866i
$393$	−23.7221	−	19.3907i	−1.19662	−	0.978129i
$394$	−14.6127	−	3.46328i	−0.736178	−	0.174477i
$395$	−8.47619	−	48.0709i	−0.426484	−	2.41871i
$396$	7.17820	+	3.37664i	0.360718	+	0.169682i
$397$	−5.20739	+	29.5326i	−0.261351	+	1.48220i	0.517876	+	0.855455i	$0.326723\pi$
$397$	−5.20739	+	29.5326i	−0.261351	+	1.48220i	−0.779228	+	0.626741i	$0.784388\pi$
$398$	10.3030	−	23.8851i	0.516445	−	1.19725i
$399$	−2.13161	+	2.94152i	−0.106714	+	0.147260i
$400$	7.82858	−	26.1493i	0.391429	−	1.30746i
$401$	−3.91254	+	5.25545i	−0.195383	+	0.262445i	−0.889008	−	0.457891i	$-0.848605\pi$
$401$	−3.91254	+	5.25545i	−0.195383	+	0.262445i	0.693625	+	0.720336i	$0.256012\pi$
$402$	0.0697287	−	1.53780i	0.00347775	−	0.0766985i
$403$	1.35207	−	0.679035i	0.0673514	−	0.0338251i
$404$	−5.85891			−0.291492
$405$	19.2403	+	29.6858i	0.956060	+	1.47510i
$406$	−6.42647			−0.318941
$407$	−49.1895	+	24.7039i	−2.43823	+	1.22453i
$408$	−15.9527	+	8.27045i	−0.789777	+	0.409448i
$409$	1.06650	−	1.43255i	0.0527348	−	0.0708352i	−0.774973	−	0.631994i	$-0.782237\pi$
$409$	1.06650	−	1.43255i	0.0527348	−	0.0708352i	0.827708	+	0.561159i	$0.189644\pi$
$410$	−1.96422	+	6.56096i	−0.0970061	+	0.324023i
$411$	−4.92413	−	11.0233i	−0.242890	−	0.543738i
$412$	2.53726	−	5.88202i	0.125002	−	0.289786i
$413$	−3.22579	+	18.2944i	−0.158731	+	0.900207i
$414$	2.16044	−	7.95591i	0.106180	−	0.391012i
$415$	−5.05329	−	28.6586i	−0.248056	−	1.40680i
$416$	0.905398	+	0.214583i	0.0443908	+	0.0105208i
$417$	1.75754	−	10.7764i	0.0860670	−	0.527724i
$418$	5.51207	−	3.62534i	0.269604	−	0.177321i
$419$	−1.20481	−	20.6857i	−0.0588587	−	1.01056i	−0.890422	−	0.455135i	$-0.849591\pi$
$419$	−1.20481	−	20.6857i	−0.0588587	−	1.01056i	0.831564	−	0.555429i	$-0.187446\pi$
$420$	−6.51603	−	2.27714i	−0.317950	−	0.111113i
$421$	−5.43755	−	18.1627i	−0.265010	−	0.885196i	−0.982123	−	0.188239i	$-0.939722\pi$
$421$	−5.43755	−	18.1627i	−0.265010	−	0.885196i	0.717113	−	0.696957i	$-0.245463\pi$
$422$	−14.3686	−	5.22976i	−0.699454	−	0.254581i
$423$	6.15499	+	10.0542i	0.299266	+	0.488850i
$424$	−4.69024	+	1.70711i	−0.227778	+	0.0829045i
$425$	−21.0883	−	28.3265i	−1.02293	−	1.37404i
$426$	1.00833	+	14.1694i	0.0488539	+	0.686508i
$427$	−1.38367	+	0.327936i	−0.0669606	+	0.0158700i
$428$	1.38648	+	3.21422i	0.0670181	+	0.155365i
$429$	2.55147	+	0.570142i	0.123186	+	0.0275267i
$430$	−17.7215	−	11.6556i	−0.854607	−	0.562084i
$431$	−0.254281	+	0.440427i	−0.0122483	+	0.0212146i	−0.872085	−	0.489355i	$-0.837232\pi$
$431$	−0.254281	+	0.440427i	−0.0122483	+	0.0212146i	0.859836	+	0.510570i	$0.170566\pi$
$432$	13.4102	−	2.09473i	0.645199	−	0.100783i
$433$	10.9606	+	18.9844i	0.526734	+	0.912330i	0.999515	+	0.0311498i	$0.00991689\pi$
$433$	10.9606	+	18.9844i	0.526734	+	0.912330i	−0.472781	+	0.881180i	$0.656750\pi$
$434$	−0.633818	+	10.8822i	−0.0304242	+	0.522364i
$435$	−11.8507	−	15.4980i	−0.568199	−	0.743071i
$436$	1.86469	+	0.217951i	0.0893025	+	0.0104380i
$437$	1.76366	+	1.86937i	0.0843672	+	0.0894240i
$438$	−2.28487	+	8.00545i	−0.109175	+	0.382515i
$439$	33.4327	−	3.90773i	1.59566	−	0.186506i	0.728680	−	0.684854i	$-0.240134\pi$
$439$	33.4327	−	3.90773i	1.59566	−	0.186506i	0.866977	+	0.498348i	$0.166060\pi$
$440$	44.8249	+	37.6125i	2.13694	+	1.79311i
$441$	−3.95730	+	9.86447i	−0.188443	+	0.469737i
$442$	−0.971889	+	0.815511i	−0.0462280	+	0.0387899i
$443$	8.41216	−	8.91636i	0.399674	−	0.423629i	−0.496013	−	0.868315i	$-0.665203\pi$
$443$	8.41216	−	8.91636i	0.399674	−	0.423629i	0.895687	+	0.444686i	$0.146685\pi$
$444$	5.24043	−	9.35254i	0.248700	−	0.443852i
$445$	−19.0950	−	9.58985i	−0.905188	−	0.454602i
$446$	5.30802	+	2.66579i	0.251342	+	0.126229i
$447$	39.2751	−	0.505324i	1.85765	−	0.0239010i
$448$	−11.2662	+	11.9415i	−0.532279	+	0.564183i
$449$	19.3898	−	16.2699i	0.915060	−	0.767826i	−0.0580153	−	0.998316i	$-0.518477\pi$
$449$	19.3898	−	16.2699i	0.915060	−	0.767826i	0.973075	+	0.230490i	$0.0740328\pi$
$450$	11.7727	+	35.9317i	0.554972	+	1.69384i
$451$	−5.36645	−	4.50299i	−0.252696	−	0.212037i
$452$	8.39630	−	0.981386i	0.394929	−	0.0461605i
$453$	−17.4578	−	18.0336i	−0.820239	−	0.847294i
$454$	−5.31918	−	5.63800i	−0.249641	−	0.264604i
$455$	−2.25946	−	0.264094i	−0.105925	−	0.0123809i
$456$	−2.30457	+	5.53741i	−0.107921	+	0.259313i
$457$	1.70347	−	29.2475i	0.0796850	−	1.36814i	−0.687253	−	0.726418i	$-0.741184\pi$
$457$	1.70347	−	29.2475i	0.0796850	−	1.36814i	0.766938	−	0.641721i	$-0.221779\pi$
$458$	17.9334	+	31.0616i	0.837973	+	1.45141i
$459$	8.18662	−	15.5348i	0.382119	−	0.725103i
$460$	−2.44166	+	4.22908i	−0.113843	+	0.197182i
$461$	−10.7092	−	7.04356i	−0.498778	−	0.328051i	0.275069	−	0.961425i	$-0.411299\pi$
$461$	−10.7092	−	7.04356i	−0.498778	−	0.328051i	−0.773846	+	0.633373i	$0.781670\pi$
$462$	−12.7486	+	13.8658i	−0.593118	+	0.645097i
$463$	4.08935	+	9.48017i	0.190048	+	0.440581i	0.986423	−	0.164222i	$-0.0525112\pi$
$463$	4.08935	+	9.48017i	0.190048	+	0.440581i	−0.796375	+	0.604803i	$0.793252\pi$
$464$	−7.28363	+	1.72625i	−0.338134	+	0.0801393i
$465$	−27.4122	+	18.5389i	−1.27121	+	0.859719i
$466$	−15.6571	−	21.0312i	−0.725303	−	0.974251i
$467$	−6.54957	+	2.38385i	−0.303078	+	0.110311i	−0.489083	−	0.872238i	$-0.662668\pi$
$467$	−6.54957	+	2.38385i	−0.303078	+	0.110311i	0.186005	+	0.982549i	$0.440446\pi$
$468$	−0.473841	+	0.186405i	−0.0219033	+	0.00861658i
$469$	−1.28748	−	0.468604i	−0.0594502	−	0.0216381i
$470$	5.34287	+	17.8464i	0.246448	+	0.823194i
$471$	14.9269	−	12.8560i	0.687794	−	0.592372i
$472$	1.78339	+	30.6196i	0.0820870	+	1.40938i
$473$	18.1270	−	11.9223i	0.833482	−	0.548190i
$474$	24.2621	−	9.18588i	1.11440	−	0.421921i
$475$	−11.4697	−	2.71836i	−0.526265	−	0.124727i
$476$	0.594967	+	3.37422i	0.0272702	+	0.154657i
$477$	2.81107	−	3.98607i	0.128710	−	0.182510i
$478$	−1.24578	+	7.06518i	−0.0569807	+	0.323154i
$479$	−13.2430	+	30.7006i	−0.605086	+	1.40275i	0.290075	+	0.957004i	$0.406320\pi$
$479$	−13.2430	+	30.7006i	−0.605086	+	1.40275i	−0.895161	+	0.445743i	$0.852939\pi$
$480$	−20.2426	−	2.10242i	−0.923946	−	0.0959617i
$481$	1.01333	−	3.38477i	0.0462041	−	0.154332i
$482$	0.854249	−	1.14746i	0.0389100	−	0.0522651i
$483$	−6.18174	−	3.95281i	−0.281279	−	0.179859i
$484$	−6.09863	+	3.06285i	−0.277211	+	0.139220i
$485$	−18.0999			−0.821874
$486$	−13.5961	+	12.9862i	−0.616731	+	0.589067i
$487$	−8.67546			−0.393122			−0.196561	−	0.980492i	$-0.562977\pi$
$487$	−8.67546			−0.393122			−0.196561	+	0.980492i	$0.562977\pi$
$488$	−2.09811	+	1.05371i	−0.0949768	+	0.0476991i
$489$	1.15224	+	0.736779i	0.0521060	+	0.0333183i
$490$	−10.0299	+	13.4725i	−0.453105	+	0.608626i
$491$	−4.61063	+	15.4006i	−0.208075	+	0.695018i	0.788701	+	0.614777i	$0.210754\pi$
$491$	−4.61063	+	15.4006i	−0.208075	+	0.695018i	−0.996775	+	0.0802410i	$0.974431\pi$
$492$	1.35710	+	0.140949i	0.0611826	+	0.00635447i
$493$	−3.83575	+	8.89227i	−0.172754	+	0.400488i
$494$	−0.0735360	+	0.417043i	−0.00330854	+	0.0187637i
$495$	−56.9476	−	5.17500i	−2.55960	−	0.232599i
$496$	2.20478	+	12.5040i	0.0989977	+	0.561444i
$497$	12.3023	+	2.91571i	0.551836	+	0.130787i
$498$	14.4645	−	5.47639i	0.648168	−	0.245403i
$499$	−6.45428	+	4.24505i	−0.288933	+	0.190034i	−0.685698	−	0.727886i	$-0.740503\pi$
$499$	−6.45428	+	4.24505i	−0.288933	+	0.190034i	0.396765	+	0.917920i	$0.370133\pi$
$500$	−0.679177	−	11.6610i	−0.0303737	−	0.521496i
$501$	−7.61804	+	6.56115i	−0.340349	+	0.293131i
$502$	4.67298	+	15.6088i	0.208565	+	0.696656i
$503$	30.5447	+	11.1174i	1.36192	+	0.495698i	0.916647	−	0.399697i	$-0.130885\pi$
$503$	30.5447	+	11.1174i	1.36192	+	0.495698i	0.445272	+	0.895395i	$0.353107\pi$
$504$	2.53868	−	16.9347i	0.113082	−	0.754332i
$505$	39.6864	−	14.4447i	1.76602	−	0.642778i
$506$	7.95766	+	10.6890i	0.353761	+	0.475184i
$507$	18.5126	−	12.5201i	0.822176	−	0.556037i
$508$	6.26616	−	1.48511i	0.278016	−	0.0658909i
$509$	0.494855	+	1.14720i	0.0219340	+	0.0508488i	0.928831	−	0.370503i	$-0.120815\pi$
$509$	0.494855	+	1.14720i	0.0219340	+	0.0508488i	−0.906897	+	0.421352i	$0.861556\pi$
$510$	18.7815	−	20.4275i	0.831659	−	0.904543i
$511$	6.19069	+	4.07168i	0.273860	+	0.180121i
$512$	−11.9231	+	20.6514i	−0.526931	+	0.912671i
$513$	−1.23977	−	5.72863i	−0.0547371	−	0.252925i
$514$	−14.7623	−	25.5690i	−0.651136	−	1.12780i
$515$	−2.68492	+	46.0982i	−0.118312	+	2.03133i
$516$	−1.62364	+	3.90128i	−0.0714768	+	0.171744i
$517$	−18.9265	−	2.21219i	−0.832386	−	0.0972920i
$518$	17.4686	+	18.5157i	0.767528	+	0.813533i
$519$	4.18934	+	4.32753i	0.183892	+	0.189957i
$520$	−3.73056	+	0.436040i	−0.163596	+	0.0191216i
$521$	−17.9588	−	15.0692i	−0.786787	−	0.660193i	0.158161	−	0.987413i	$-0.449444\pi$
$521$	−17.9588	−	15.0692i	−0.786787	−	0.660193i	−0.944948	+	0.327220i	$0.893888\pi$
$522$	6.91924	−	7.72271i	0.302847	−	0.338014i
$523$	26.2642	−	22.0383i	1.14845	−	0.963666i	0.148770	−	0.988872i	$-0.452469\pi$
$523$	26.2642	−	22.0383i	1.14845	−	0.963666i	0.999682	+	0.0252058i	$0.00802411\pi$
$524$	−6.61930	+	7.01605i	−0.289166	+	0.306498i
$525$	33.6506	−	0.432957i	1.46863	−	0.0188958i
$526$	23.3789	+	11.7413i	1.01937	+	0.511946i
$527$	14.6794	+	7.37226i	0.639443	+	0.321141i
$528$	−10.7244	+	19.1397i	−0.466720	+	0.832949i
$529$	12.2212	−	12.9537i	0.531357	−	0.563206i
$530$	5.90458	−	4.95453i	0.256479	−	0.215211i
$531$	−18.5113	−	23.5736i	−0.803321	−	1.02301i
$532$	0.876079	+	0.735118i	0.0379828	+	0.0318714i
$533$	0.446624	−	0.0522028i	0.0193454	−	0.00226115i
$534$	3.11686	−	10.9205i	0.134880	−	0.472575i
$535$	−17.3160	−	18.3538i	−0.748634	−	0.793506i
$536$	−2.24686	−	0.262620i	−0.0970495	−	0.0113435i
$537$	−8.22309	−	10.7539i	−0.354852	−	0.464064i
$538$	0.402621	−	6.91273i	0.0173582	−	0.298029i
$539$	−8.59021	−	14.8787i	−0.370007	−	0.640870i
$540$	9.75211	−	5.37859i	0.419664	−	0.231458i
$541$	7.30619	−	12.6547i	0.314118	−	0.544068i	−0.665132	−	0.746726i	$-0.731625\pi$
$541$	7.30619	−	12.6547i	0.314118	−	0.544068i	0.979250	+	0.202658i	$0.0649580\pi$
$542$	−14.5914	−	9.59690i	−0.626754	−	0.412222i
$543$	19.7677	+	4.41723i	0.848315	+	0.189562i
$544$	4.00127	+	9.27599i	0.171553	+	0.397705i
$545$	−13.1681	+	3.12091i	−0.564061	+	0.133685i
$546$	−0.0858215	−	1.20599i	−0.00367282	−	0.0516115i
$547$	−9.06430	−	12.1755i	−0.387561	−	0.520585i	0.564935	−	0.825136i	$-0.308901\pi$
$547$	−9.06430	−	12.1755i	−0.387561	−	0.520585i	−0.952496	+	0.304550i	$0.901494\pi$
$548$	−3.57164	+	1.29997i	−0.152573	+	0.0555320i
$549$	1.09569	−	2.01584i	0.0467627	−	0.0860341i
$550$	−57.4331	−	20.9040i	−2.44896	−	0.891348i
$551$	0.927083	+	3.09667i	0.0394951	+	0.131923i
$552$	−11.4365	−	3.99669i	−0.486771	−	0.170111i
$553$	−1.34257	−	23.0510i	−0.0570918	−	0.980229i
$554$	11.9436	−	7.85541i	0.507434	−	0.333744i
$555$	−12.4391	+	76.2709i	−0.528009	+	3.23752i
$556$	−3.34481	−	0.792735i	−0.141852	−	0.0336195i
$557$	2.44666	+	13.8757i	0.103668	+	0.587931i	0.991744	+	0.128234i	$0.0409309\pi$
$557$	2.44666	+	13.8757i	0.103668	+	0.587931i	−0.888076	+	0.459697i	$0.847958\pi$
$558$	−12.3948	−	12.4783i	−0.524713	−	0.528249i
$559$	−0.241831	+	1.37149i	−0.0102284	+	0.0580079i
$560$	7.56120	−	17.5288i	0.319519	−	0.740728i
$561$	11.5768	+	25.9162i	0.488775	+	1.09418i
$562$	−5.25509	+	17.5532i	−0.221673	+	0.740438i
$563$	−21.3884	+	28.7296i	−0.901413	+	1.21081i	0.0754952	+	0.997146i	$0.475946\pi$
$563$	−21.3884	+	28.7296i	−0.901413	+	1.21081i	−0.976908	+	0.213661i	$0.931461\pi$
$564$	3.29482	−	1.70815i	0.138737	−	0.0719261i
$565$	−54.4542	+	27.3479i	−2.29091	+	1.15054i
$566$	−30.0885			−1.26471
$567$	7.40961	+	15.0041i	0.311175	+	0.630115i
$568$	20.8748			0.875889
$569$	25.0852	−	12.5982i	1.05162	−	0.528146i	0.162926	−	0.986638i	$-0.447907\pi$
$569$	25.0852	−	12.5982i	1.05162	−	0.528146i	0.888698	+	0.458493i	$0.151610\pi$
$570$	0.419552	−	9.25281i	0.0175731	−	0.387558i
$571$	−27.9334	+	37.5211i	−1.16898	+	1.57021i	−0.420136	+	0.907461i	$0.638018\pi$
$571$	−27.9334	+	37.5211i	−1.16898	+	1.57021i	−0.748842	+	0.662749i	$0.769390\pi$
$572$	0.236058	−	0.788487i	0.00987007	−	0.0329683i
$573$	14.7893	−	20.4084i	0.617830	−	0.852573i
$574$	−1.28317	+	2.97472i	−0.0535585	+	0.124163i
$575$	4.13438	−	23.4472i	0.172415	−	0.977816i
$576$	−2.22005	−	26.3958i	−0.0925021	−	1.09982i
$577$	3.26382	+	18.5100i	0.135875	+	0.770583i	0.974247	+	0.225485i	$0.0723966\pi$
$577$	3.26382	+	18.5100i	0.135875	+	0.770583i	−0.838372	+	0.545098i	$0.816492\pi$
$578$	6.54822	+	1.55196i	0.272370	+	0.0645529i
$579$	22.8214	+	18.6544i	0.948425	+	0.775251i
$580$	−5.13160	+	3.37511i	−0.213078	+	0.140144i
$581$	−0.800406	−	13.7424i	−0.0332064	−	0.570132i
$582$	−1.79219	−	9.45132i	−0.0742888	−	0.391770i
$583$	2.26123	+	7.55305i	0.0936507	+	0.312815i
$584$	11.4962	+	4.18426i	0.475714	+	0.173146i
$585$	2.75008	−	2.43086i	0.113702	−	0.100504i
$586$	−9.71950	+	3.53761i	−0.401509	+	0.146137i
$587$	0.583716	+	0.784066i	0.0240925	+	0.0323619i	0.814006	−	0.580856i	$-0.197282\pi$
$587$	0.583716	+	0.784066i	0.0240925	+	0.0323619i	−0.789914	+	0.613218i	$0.789875\pi$
$588$	3.00927	+	1.46314i	0.124100	+	0.0603389i
$589$	5.33517	−	1.26446i	0.219832	−	0.0521011i
$590$	−18.7604	−	43.4916i	−0.772355	−	1.79052i
$591$	−6.45048	−	20.5787i	−0.265337	−	0.846496i
$592$	24.7722	+	16.2929i	1.01813	+	0.669636i
$593$	−19.3929	+	33.5896i	−0.796372	+	1.37936i	0.125592	+	0.992082i	$0.459917\pi$
$593$	−19.3929	+	33.5896i	−0.796372	+	1.37936i	−0.921964	+	0.387276i	$0.873416\pi$
$594$	−2.93650	−	30.2490i	−0.120486	−	1.24113i
$595$	−12.3490	−	21.3890i	−0.506258	−	0.876865i
$596$	0.718999	−	12.3447i	0.0294513	−	0.505660i
$597$	37.0440	−	4.81369i	1.51611	−	0.197011i
$598$	−0.849580	−	0.0993016i	−0.0347419	−	0.00406075i
$599$	−22.8341	−	24.2028i	−0.932978	−	0.988899i	0.0669827	−	0.997754i	$-0.478663\pi$
$599$	−22.8341	−	24.2028i	−0.932978	−	0.988899i	−0.999961	+	0.00885515i	$0.997181\pi$
$600$	53.8973	−	13.5085i	2.20035	−	0.551484i
$601$	20.2207	−	2.36346i	0.824820	−	0.0964076i	0.306797	−	0.951775i	$-0.400743\pi$
$601$	20.2207	−	2.36346i	0.824820	−	0.0964076i	0.518022	+	0.855367i	$0.326668\pi$
$602$	−7.68616	−	6.44945i	−0.313264	−	0.262860i
$603$	1.94932	−	1.04263i	0.0793824	−	0.0424592i
$604$	−6.05317	+	5.07922i	−0.246300	+	0.206670i
$605$	33.7589	−	35.7824i	1.37250	−	1.45476i
$606$	11.4723	+	19.2930i	0.466028	+	0.783723i
$607$	−1.41785	−	0.712069i	−0.0575486	−	0.0289020i	0.419792	−	0.907620i	$-0.362103\pi$
$607$	−1.41785	−	0.712069i	−0.0575486	−	0.0289020i	−0.477341	+	0.878718i	$0.658399\pi$
$608$	3.01329	+	1.51333i	0.122205	+	0.0613737i
$609$	−4.71683	−	7.93234i	−0.191136	−	0.321434i
$610$	2.48812	−	2.63725i	0.100741	−	0.106779i
$611$	0.936970	−	0.786211i	0.0379058	−	0.0318067i
$612$	−4.69540	−	2.91798i	−0.189800	−	0.117952i
$613$	−5.23563	−	4.39322i	−0.211465	−	0.177440i	0.530903	−	0.847433i	$-0.321853\pi$
$613$	−5.23563	−	4.39322i	−0.211465	−	0.177440i	−0.742368	+	0.669992i	$0.766297\pi$
$614$	−2.29547	+	0.268302i	−0.0926377	+	0.0108278i
$615$	−9.54002	+	2.39106i	−0.384691	+	0.0964169i
$616$	18.9949	+	20.1334i	0.765327	+	0.811199i
$617$	0.404239	+	0.0472487i	0.0162740	+	0.00190216i	0.124226	−	0.992254i	$-0.460355\pi$
$617$	0.404239	+	0.0472487i	0.0162740	+	0.00190216i	−0.107952	+	0.994156i	$0.534429\pi$
$618$	−24.3372	+	3.16250i	−0.978986	+	0.127214i
$619$	−0.582923	+	10.0084i	−0.0234297	+	0.402272i	0.966121	+	0.258088i	$0.0830926\pi$
$619$	−0.582923	+	10.0084i	−0.0234297	+	0.402272i	−0.989551	+	0.144183i	$0.953944\pi$
$620$	5.20911	+	9.02245i	0.209203	+	0.362350i
$621$	11.4058	−	3.17272i	0.457701	−	0.127317i
$622$	−9.19862	+	15.9325i	−0.368831	+	0.638834i
$623$	−8.44490	−	5.55430i	−0.338338	−	0.222528i
$624$	−0.421215	−	1.34379i	−0.0168621	−	0.0537945i
$625$	12.6549	+	29.3373i	0.506194	+	1.17349i
$626$	36.0406	−	8.54179i	1.44047	−	0.341398i
$627$	8.52053	+	4.14277i	0.340277	+	0.165446i
$628$	−3.70355	−	4.97473i	−0.147788	−	0.198513i
$629$	36.0465	−	13.1199i	1.43727	−	0.523123i
$630$	5.26048	+	25.9156i	0.209583	+	1.03250i
$631$	−14.7754	−	5.37779i	−0.588198	−	0.214086i	0.0307388	−	0.999527i	$-0.490214\pi$
$631$	−14.7754	−	5.37779i	−0.588198	−	0.214086i	−0.618937	+	0.785441i	$0.712436\pi$
$632$	−10.9340	−	36.5220i	−0.434930	−	1.45277i
$633$	−4.09094	−	21.5740i	−0.162600	−	0.857490i
$634$	−1.60963	−	27.6363i	−0.0639267	−	1.09758i
$635$	−38.7835	+	25.5083i	−1.53908	+	1.01227i
$636$	−1.18891	−	0.971828i	−0.0471435	−	0.0385355i
$637$	1.07305	+	0.254319i	0.0425160	+	0.0100765i
$638$	2.91047	+	16.5061i	0.115227	+	0.653483i
$639$	−16.7495	+	11.6445i	−0.662599	+	0.460649i
$640$	3.18813	−	18.0808i	0.126022	−	0.714706i
$641$	3.18622	−	7.38649i	0.125848	−	0.291749i	−0.843631	−	0.536924i	$-0.819586\pi$
$641$	3.18622	−	7.38649i	0.125848	−	0.291749i	0.969479	+	0.245175i	$0.0788455\pi$
$642$	7.86935	−	10.8593i	0.310579	−	0.428582i
$643$	2.73923	−	9.14968i	0.108025	−	0.360828i	−0.886835	−	0.462085i	$-0.847101\pi$
$643$	2.73923	−	9.14968i	0.108025	−	0.360828i	0.994860	+	0.101257i	$0.0322865\pi$
$644$	−1.37943	+	1.85290i	−0.0543572	+	0.0730144i
$645$	1.37974	−	30.4289i	0.0543273	−	1.19814i
$646$	−4.10863	+	2.06343i	−0.161652	+	0.0811846i
$647$	36.6579			1.44117			0.720586	−	0.693365i	$-0.243873\pi$
$647$	36.6579			1.44117			0.720586	+	0.693365i	$0.243873\pi$
$648$	17.6172	+	21.2840i	0.692067	+	0.836113i
$649$	48.4492			1.90180
$650$	3.50583	−	1.76069i	0.137510	−	0.0690601i
$651$	−13.8974	+	7.20489i	−0.544681	+	0.282382i
$652$	0.257118	−	0.345369i	0.0100695	−	0.0135257i
$653$	−5.54195	+	18.5114i	−0.216873	+	0.724407i	0.778441	+	0.627717i	$0.216011\pi$
$653$	−5.54195	+	18.5114i	−0.216873	+	0.724407i	−0.995315	+	0.0966895i	$0.969175\pi$
$654$	−2.93352	−	6.56705i	−0.114710	−	0.256792i
$655$	27.5395	−	63.8438i	1.07606	−	2.49458i
$656$	−0.655261	+	3.71617i	−0.0255836	+	0.145092i
$657$	−11.5583	+	3.05548i	−0.450933	+	0.119206i
$658$	1.53023	+	8.67834i	0.0596544	+	0.338317i
$659$	−30.0112	−	7.11279i	−1.16907	−	0.277075i	−0.400169	−	0.916441i	$-0.631049\pi$
$659$	−30.0112	−	7.11279i	−1.16907	−	0.277075i	−0.768902	+	0.639367i	$0.779197\pi$
$660$	−2.89770	+	17.7674i	−0.112793	+	0.691595i
$661$	−13.3404	+	8.77415i	−0.518883	+	0.341275i	−0.781785	−	0.623548i	$-0.785691\pi$
$661$	−13.3404	+	8.77415i	−0.518883	+	0.341275i	0.262902	+	0.964822i	$0.415320\pi$
$662$	−0.0631919	−	1.08496i	−0.00245602	−	0.0421683i
$663$	−1.71994	−	0.601063i	−0.0667969	−	0.0233433i
$664$	−6.51855	−	21.7735i	−0.252969	−	0.844975i
$665$	−7.74664	−	2.81955i	−0.300402	−	0.109337i
$666$	−41.0584	+	1.05671i	−1.59098	+	0.0409467i
$667$	−6.13538	+	2.23310i	−0.237563	+	0.0864659i
$668$	1.89013	+	2.53889i	0.0731315	+	0.0982327i
$669$	0.605483	+	8.50841i	0.0234093	+	0.328954i
$670$	3.39923	−	0.805633i	0.131324	−	0.0311243i
$671$	1.46894	+	3.40538i	0.0567077	+	0.131463i
$672$	−9.39531	−	2.09945i	−0.362432	−	0.0809879i
$673$	32.1238	+	21.1281i	1.23828	+	0.814430i	0.988107	−	0.153771i	$-0.0491417\pi$
$673$	32.1238	+	21.1281i	1.23828	+	0.814430i	0.250174	+	0.968201i	$0.419512\pi$
$674$	−21.2053	+	36.7287i	−0.816798	+	1.41474i
$675$	−35.7105	+	40.9041i	−1.37450	+	1.57440i
$676$	−3.51794	−	6.09325i	−0.135305	−	0.234356i
$677$	−0.758942	+	13.0305i	−0.0291685	+	0.500804i	0.951810	+	0.306688i	$0.0992208\pi$
$677$	−0.758942	+	13.0305i	−0.0291685	+	0.500804i	−0.980979	+	0.194116i	$0.937816\pi$
$678$	−19.6723	−	25.7267i	−0.755510	−	0.988030i
$679$	−8.50403	−	0.993978i	−0.326355	−	0.0381454i
$680$	−27.9837	−	29.6610i	−1.07313	−	1.13745i
$681$	3.05499	−	10.7037i	0.117067	−	0.410166i
$682$	28.2376	−	3.30050i	1.08127	−	0.126383i
$683$	−6.97390	−	5.85180i	−0.266849	−	0.223913i	0.499538	−	0.866292i	$-0.333503\pi$
$683$	−6.97390	−	5.85180i	−0.266849	−	0.223913i	−0.766387	+	0.642379i	$0.777947\pi$
$684$	−1.82665	+	0.261302i	−0.0698436	+	0.00999115i
$685$	20.9882	−	17.6112i	0.801916	−	0.672888i
$686$	−16.2249	+	17.1974i	−0.619470	+	0.656600i
$687$	−25.1774	+	44.9338i	−0.960578	+	1.71433i
$688$	−10.4438	−	5.24505i	−0.398165	−	0.199966i
$689$	−0.452247	−	0.227127i	−0.0172292	−	0.00865285i
$690$	18.7070	−	0.240690i	0.712165	−	0.00916290i
$691$	−8.21347	+	8.70577i	−0.312455	+	0.331183i	−0.864501	−	0.502630i	$-0.832366\pi$
$691$	−8.21347	+	8.70577i	−0.312455	+	0.331183i	0.552046	+	0.833813i	$0.313847\pi$
$692$	1.45258	−	1.21886i	0.0552187	−	0.0463340i
$693$	−26.4720	−	5.55876i	−1.00559	−	0.211160i
$694$	14.0210	+	11.7650i	0.532229	+	0.446594i
$695$	24.6111	−	2.87662i	0.933552	−	0.109117i
$696$	−10.5983	−	10.9479i	−0.401728	−	0.414979i
$697$	3.35022	+	3.55103i	0.126899	+	0.134505i
$698$	−33.9250	−	3.96526i	−1.28408	−	0.150087i
$699$	14.4674	−	34.7622i	0.547207	−	1.31483i
$700$	0.616031	−	10.5769i	0.0232838	−	0.399767i
$701$	0.441721	+	0.765084i	0.0166836	+	0.0288968i	0.874247	−	0.485482i	$-0.161356\pi$
$701$	0.441721	+	0.765084i	0.0166836	+	0.0288968i	−0.857563	+	0.514379i	$0.828023\pi$
$702$	1.54164	+	1.19533i	0.0581854	+	0.0451147i
$703$	6.40198	−	11.0886i	0.241455	−	0.418213i
$704$	35.7735	+	23.5286i	1.34827	+	0.886768i
$705$	−18.1067	+	19.6935i	−0.681939	+	0.741702i
$706$	7.93698	+	18.4000i	0.298712	+	0.692493i
$707$	19.4394	−	4.60723i	0.731094	−	0.173273i
$708$	−7.81640	+	5.28623i	−0.293758	+	0.198669i
$709$	14.1307	+	18.9808i	0.530689	+	0.712838i	0.983931	−	0.178549i	$-0.0571402\pi$
$709$	14.1307	+	18.9808i	0.530689	+	0.712838i	−0.453242	+	0.891387i	$0.649733\pi$
$710$	−30.2925	+	11.0256i	−1.13686	+	0.413782i
$711$	29.1460	+	23.2051i	1.09306	+	0.870261i
$712$	−15.6823	−	5.70787i	−0.587717	−	0.213912i
$713$	3.17629	+	10.6096i	0.118953	+	0.397331i
$714$	9.94607	−	8.56620i	0.372222	−	0.320582i
$715$	0.344972	+	5.92293i	0.0129012	+	0.221505i
$716$	−3.56076	+	2.34195i	−0.133072	+	0.0875228i
$717$	−9.63507	+	3.64793i	−0.359828	+	0.136234i
$718$	16.4837	+	3.90670i	0.615165	+	0.145797i
$719$	4.25311	+	24.1206i	0.158614	+	0.899547i	0.955407	+	0.295293i	$0.0954174\pi$
$719$	4.25311	+	24.1206i	0.158614	+	0.899547i	−0.796792	+	0.604253i	$0.793471\pi$
$720$	12.9235	+	27.9592i	0.481630	+	1.04198i
$721$	−3.79302	+	21.5113i	−0.141259	+	0.801122i
$722$	8.46880	−	19.6329i	0.315176	−	0.730661i
$723$	2.04332	+	0.212221i	0.0759919	+	0.00789258i
$724$	1.82888	−	6.10888i	0.0679698	−	0.227035i
$725$	17.8824	−	24.0203i	0.664137	−	0.892091i
$726$	22.0274	+	14.0850i	0.817513	+	0.522745i
$727$	−7.38654	+	3.70966i	−0.273952	+	0.137584i	−0.580471	−	0.814281i	$-0.697132\pi$
$727$	−7.38654	+	3.70966i	−0.273952	+	0.137584i	0.306520	+	0.951864i	$0.400835\pi$
$728$	−1.77670			−0.0658490
$729$	−26.0083	−	7.25046i	−0.963270	−	0.268536i
$730$	−18.8926			−0.699248
$731$	−13.5117	+	6.78582i	−0.499748	+	0.250983i
$732$	−0.608543	−	0.389123i	−0.0224924	−	0.0143824i
$733$	−9.09837	+	12.2212i	−0.336056	+	0.451402i	−0.937743	−	0.347331i	$-0.887088\pi$
$733$	−9.09837	+	12.2212i	−0.336056	+	0.451402i	0.601687	+	0.798732i	$0.294496\pi$
$734$	1.89220	−	6.32039i	0.0698424	−	0.233290i
$735$	−23.9911	−	2.49173i	−0.884924	−	0.0919089i
$736$	−2.69765	+	6.25386i	−0.0994368	+	0.230520i
$737$	−0.620504	+	3.51905i	−0.0228565	+	0.129626i
$738$	−2.19317	−	4.74481i	−0.0807318	−	0.174659i
$739$	4.97375	+	28.2075i	0.182962	+	1.03763i	0.928545	+	0.371219i	$0.121060\pi$
$739$	4.97375	+	28.2075i	0.182962	+	1.03763i	−0.745583	+	0.666413i	$0.767829\pi$
$740$	23.6731	+	5.61063i	0.870241	+	0.206251i
$741$	−0.568738	+	0.215330i	−0.0208931	+	0.00791034i
$742$	3.04628	−	2.00357i	0.111833	−	0.0735534i
$743$	−0.857991	−	14.7311i	−0.0314766	−	0.540433i	−0.976781	−	0.214242i	$-0.931272\pi$
$743$	−0.857991	−	14.7311i	−0.0314766	−	0.540433i	0.945304	−	0.326191i	$-0.105765\pi$
$744$	−19.5838	+	16.8668i	−0.717977	+	0.618368i
$745$	25.5646	+	85.3918i	0.936615	+	3.12851i
$746$	32.0692	+	11.6723i	1.17414	+	0.427352i
$747$	17.3761	+	13.8343i	0.635758	+	0.506171i
$748$	8.39708	−	3.05629i	0.307028	−	0.111749i
$749$	−7.12778	−	9.57426i	−0.260443	−	0.349836i
$750$	−37.0690	+	25.0697i	−1.35357	+	0.915417i
$751$	−7.24039	+	1.71600i	−0.264206	+	0.0626179i	−0.360583	−	0.932727i	$-0.617422\pi$
$751$	−7.24039	+	1.71600i	−0.264206	+	0.0626179i	0.0963779	+	0.995345i	$0.469274\pi$
$752$	4.06547	+	9.42481i	0.148252	+	0.343688i
$753$	−15.8365	+	17.2244i	−0.577114	+	0.627691i
$754$	−0.898852	−	0.591184i	−0.0327343	−	0.0215297i
$755$	28.4798	−	49.3285i	1.03649	−	1.79525i
$756$	4.87728	−	1.99152i	0.177385	−	0.0724308i
$757$	−5.40930	−	9.36918i	−0.196604	−	0.340529i	0.750821	−	0.660506i	$-0.229658\pi$
$757$	−5.40930	−	9.36918i	−0.196604	−	0.340529i	−0.947425	+	0.319977i	$0.896325\pi$
$758$	1.13756	−	19.5311i	0.0413180	−	0.709402i
$759$	−7.35298	+	17.6677i	−0.266896	+	0.641297i
$760$	−13.5191	−	1.58016i	−0.490391	−	0.0573185i
$761$	3.90961	+	4.14394i	0.141723	+	0.150218i	0.794347	−	0.607464i	$-0.207813\pi$
$761$	3.90961	+	4.14394i	0.141723	+	0.150218i	−0.652624	+	0.757682i	$0.726332\pi$
$762$	−17.1600	−	17.7260i	−0.621642	−	0.642146i
$763$	−6.35828	+	0.743177i	−0.230185	+	0.0269048i
$764$	−6.07829	−	5.10029i	−0.219905	−	0.184522i
$765$	38.9991	+	8.18930i	1.41002	+	0.296085i
$766$	13.6848	−	11.4829i	0.494453	−	0.414895i
$767$	−2.13412	+	2.26203i	−0.0770586	+	0.0816773i
$768$	−20.8273	+	0.267969i	−0.751541	+	0.00966951i
$769$	−14.7408	−	7.40311i	−0.531567	−	0.266963i	0.162706	−	0.986675i	$-0.447978\pi$
$769$	−14.7408	−	7.40311i	−0.531567	−	0.266963i	−0.694273	+	0.719712i	$0.744274\pi$
$770$	−38.1984	−	19.1839i	−1.37657	−	0.691341i
$771$	20.7253	−	36.9883i	0.746405	−	1.33210i
$772$	6.36797	−	6.74966i	0.229188	−	0.242925i
$773$	−1.26612	+	1.06240i	−0.0455393	+	0.0382121i	−0.665273	−	0.746600i	$-0.731685\pi$
$773$	−1.26612	+	1.06240i	−0.0455393	+	0.0382121i	0.619734	+	0.784812i	$0.287241\pi$
$774$	16.0258	−	2.29250i	0.576037	−	0.0824023i
$775$	−38.9109	−	32.6502i	−1.39772	−	1.17283i
$776$	−14.0408	+	1.64114i	−0.504037	+	0.0589134i
$777$	−10.0329	+	35.1519i	−0.359927	+	1.26107i
$778$	−6.18126	−	6.55175i	−0.221609	−	0.234892i
$779$	1.61852	+	0.189177i	0.0579894	+	0.00677799i
$780$	−0.701899	−	0.917920i	−0.0251320	−	0.0328668i
$781$	1.91728	−	32.9185i	0.0686058	−	1.17792i
$782$	−4.64333	−	8.04248i	−0.166045	−	0.287598i
$783$	14.6108	+	2.87233i	0.522148	+	0.102649i
$784$	−4.62716	+	8.01448i	−0.165256	+	0.286232i
$785$	37.3514	+	24.5664i	1.33313	+	0.876812i
$786$	36.0645	+	8.05885i	1.28638	+	0.287450i
$787$	−16.5047	−	38.2623i	−0.588331	−	1.36390i	−0.909033	−	0.416724i	$-0.863178\pi$
$787$	−16.5047	−	38.2623i	−0.588331	−	1.36390i	0.320702	−	0.947180i	$-0.396081\pi$
$788$	−6.60642	+	1.56575i	−0.235344	+	0.0557775i
$789$	2.66682	+	37.4749i	0.0949414	+	1.33414i
$790$	35.1568	+	47.2238i	1.25082	+	1.68015i
$791$	−27.0865	+	9.85869i	−0.963086	+	0.350535i
$792$	−44.6458	+	1.14904i	−1.58642	+	0.0408293i
$793$	−0.223698	−	0.0814193i	−0.00794374	−	0.00289128i
$794$	−10.3734	−	34.6497i	−0.368139	−	1.22967i
$795$	10.4493	+	3.65168i	0.370597	+	0.129512i
$796$	−0.683800	−	11.7404i	−0.0242366	−	0.416127i
$797$	38.8546	−	25.5551i	1.37630	−	0.905207i	0.376525	−	0.926407i	$-0.377119\pi$
$797$	38.8546	−	25.5551i	1.37630	−	0.905207i	0.999775	+	0.0212000i	$0.00674869\pi$
$798$	0.705251	−	4.32429i	0.0249656	−	0.153078i
$799$	12.9215	+	3.06245i	0.457130	+	0.108342i
$800$	−5.42444	−	30.7635i	−0.191783	−	1.08765i
$801$	15.7670	−	4.16808i	0.557101	−	0.147272i
$802$	1.37223	−	7.78232i	0.0484553	−	0.274803i
$803$	7.65423	−	17.7445i	0.270112	−	0.626190i
$804$	−0.283852	−	0.635438i	−0.0100107	−	0.0224102i
$805$	4.77565	−	15.9518i	0.168320	−	0.562227i
$806$	−1.08973	+	1.46376i	−0.0383841	+	0.0515587i
$807$	8.82805	−	4.57677i	0.310762	−	0.161110i
$808$	29.4766	−	14.8037i	1.03698	−	0.520793i
$809$	−25.7135			−0.904038			−0.452019	−	0.892008i	$-0.649296\pi$
$809$	−25.7135			−0.904038			−0.452019	+	0.892008i	$0.649296\pi$
$810$	−36.8067	−	21.5812i	−1.29326	−	0.758287i
$811$	−33.1951			−1.16564			−0.582818	−	0.812602i	$-0.698050\pi$
$811$	−33.1951			−1.16564			−0.582818	+	0.812602i	$0.698050\pi$
$812$	−2.59637	+	1.30395i	−0.0911148	+	0.0457596i
$813$	1.13604	−	25.0543i	0.0398427	−	0.878692i
$814$	39.6453	−	53.2529i	1.38957	−	1.86651i
$815$	−0.890152	+	2.97332i	−0.0311807	+	0.104151i
$816$	8.97166	−	12.3804i	0.314071	−	0.433401i
$817$	−1.99894	+	4.63407i	−0.0699341	+	0.162125i
$818$	−0.374049	+	2.12134i	−0.0130783	+	0.0741708i
$819$	1.42558	−	0.991088i	0.0498140	−	0.0346314i
$820$	0.537666	+	3.04925i	0.0187761	+	0.106485i
$821$	0.212213	+	0.0502955i	0.00740630	+	0.00175532i	0.234317	−	0.972160i	$-0.424715\pi$
$821$	0.212213	+	0.0502955i	0.00740630	+	0.00175532i	−0.226911	+	0.973915i	$0.572863\pi$
$822$	11.2743	+	9.21570i	0.393236	+	0.321434i
$823$	−12.9464	+	8.51501i	−0.451285	+	0.296815i	−0.754731	−	0.656034i	$-0.772233\pi$
$823$	−12.9464	+	8.51501i	−0.451285	+	0.296815i	0.303447	+	0.952848i	$0.401862\pi$
$824$	2.09698	+	36.0037i	0.0730517	+	1.25425i
$825$	−16.3520	−	86.2338i	−0.569302	−	3.00228i
$826$	−6.42598	−	21.4643i	−0.223588	−	0.746837i
$827$	−43.9974	−	16.0138i	−1.52994	−	0.556853i	−0.566334	−	0.824176i	$-0.691639\pi$
$827$	−43.9974	−	16.0138i	−1.52994	−	0.556853i	−0.963607	+	0.267323i	$0.913861\pi$
$828$	−0.741431	−	3.65264i	−0.0257665	−	0.126938i
$829$	−12.5795	+	4.57858i	−0.436905	+	0.159021i	−0.551103	−	0.834438i	$-0.685793\pi$
$829$	−12.5795	+	4.57858i	−0.436905	+	0.159021i	0.114197	+	0.993458i	$0.463570\pi$
$830$	20.9596	+	28.1536i	0.727518	+	0.977226i
$831$	18.4623	+	8.97658i	0.640451	+	0.311394i
$832$	−2.67430	+	0.633820i	−0.0927146	+	0.0219738i
$833$	4.74220	+	10.9937i	0.164308	+	0.380908i
$834$	3.93901	+	12.5665i	0.136397	+	0.435141i
$835$	−19.0626	−	12.5376i	−0.659687	−	0.433883i
$836$	1.49135	−	2.58309i	0.0515794	−	0.0893382i
$837$	6.30485	−	24.4579i	0.217928	−	0.845387i
$838$	12.4958	+	21.6434i	0.431661	+	0.747659i
$839$	1.37589	−	23.6231i	0.0475009	−	0.815559i	−0.887477	−	0.460852i	$-0.847544\pi$
$839$	1.37589	−	23.6231i	0.0475009	−	0.815559i	0.934978	−	0.354706i	$-0.115419\pi$
$840$	38.5363	−	5.00759i	1.32963	−	0.172778i
$841$	20.6474	+	2.41333i	0.711978	+	0.0832183i
$842$	15.6923	+	16.6328i	0.540791	+	0.573205i
$843$	−25.5234	+	6.39706i	−0.879073	+	0.220326i
$844$	−6.86623	+	0.802547i	−0.236345	+	0.0276248i
$845$	38.8518	+	32.6005i	1.33654	+	1.12149i
$846$	−12.0763	−	7.50490i	−0.415193	−	0.258024i
$847$	17.8263	−	14.9580i	0.612518	−	0.513964i
$848$	2.91440	−	3.08909i	0.100081	−	0.106080i
$849$	−22.0840	−	37.1389i	−0.757923	−	1.27460i
$850$	38.0627	+	19.1158i	1.30554	+	0.655666i
$851$	23.1113	+	11.6069i	0.792245	+	0.397881i
$852$	3.28238	+	5.52000i	0.112452	+	0.189112i
$853$	20.6100	−	21.8453i	0.705673	−	0.747970i	−0.271029	−	0.962571i	$-0.587364\pi$
$853$	20.6100	−	21.8453i	0.705673	−	0.747970i	0.976702	+	0.214601i	$0.0688452\pi$
$854$	1.31384	−	1.10244i	0.0449587	−	0.0377249i
$855$	11.7289	−	6.27342i	0.401119	−	0.214546i
$856$	−15.0969	−	12.6678i	−0.516000	−	0.432975i
$857$	12.3003	−	1.43770i	0.420171	−	0.0491110i	0.0966193	−	0.995321i	$-0.469197\pi$
$857$	12.3003	−	1.43770i	0.420171	−	0.0491110i	0.323552	+	0.946210i	$0.395123\pi$
$858$	−3.05865	+	0.766605i	−0.104421	+	0.0261715i
$859$	26.2139	+	27.7851i	0.894408	+	0.948017i	0.998918	−	0.0465072i	$-0.0148090\pi$
$859$	26.2139	+	27.7851i	0.894408	+	0.948017i	−0.104510	+	0.994524i	$0.533328\pi$
$860$	−9.52465	−	1.11327i	−0.324788	−	0.0379623i
$861$	−4.61357	+	0.599510i	−0.157230	+	0.0204313i
$862$	0.0356651	−	0.612346i	0.00121476	−	0.0208566i
$863$	1.57263	+	2.72387i	0.0535329	+	0.0927217i	0.891550	−	0.452922i	$-0.149618\pi$
$863$	1.57263	+	2.72387i	0.0535329	+	0.0927217i	−0.838017	+	0.545644i	$0.816285\pi$
$864$	12.6386	−	9.02995i	0.429975	−	0.307205i
$865$	−6.83429	+	11.8373i	−0.232373	+	0.402482i
$866$	−22.0899	−	14.5288i	−0.750646	−	0.493708i
$867$	2.89058	+	9.22170i	0.0981691	+	0.313185i
$868$	1.95196	+	4.52516i	0.0662539	+	0.153594i
$869$	−58.5974	+	13.8878i	−1.98778	+	0.471113i
$870$	21.1621	+	10.2892i	0.717462	+	0.348838i
$871$	−0.136968	−	0.183980i	−0.00464098	−	0.00623392i
$872$	−9.93208	+	3.61498i	−0.336343	+	0.122419i
$873$	10.3506	−	9.14912i	0.350313	−	0.309651i
$874$	−2.91281	−	1.06018i	−0.0985272	−	0.0358610i
$875$	11.4232	+	38.1562i	0.386176	+	1.28992i
$876$	0.701209	+	3.69790i	0.0236917	+	0.124941i
$877$	2.18119	+	37.4496i	0.0736536	+	1.26458i	0.809372	+	0.587296i	$0.199807\pi$
$877$	2.18119	+	37.4496i	0.0736536	+	1.26458i	−0.735719	+	0.677287i	$0.763156\pi$
$878$	−33.9193	+	22.3091i	−1.14472	+	0.752896i
$879$	−11.5004	−	9.40049i	−0.387898	−	0.317071i
$880$	−48.4464	−	11.4820i	−1.63313	−	0.387058i
$881$	−4.15332	−	23.5546i	−0.139929	−	0.793576i	−0.971300	−	0.237858i	$-0.923555\pi$
$881$	−4.15332	−	23.5546i	−0.139929	−	0.793576i	0.831371	−	0.555718i	$-0.187556\pi$
$882$	−1.07439	−	12.7743i	−0.0361768	−	0.430132i
$883$	2.98131	−	16.9078i	0.100329	−	0.568994i	−0.892655	−	0.450742i	$-0.851160\pi$
$883$	2.98131	−	16.9078i	0.100329	−	0.568994i	0.992984	−	0.118253i	$-0.0377293\pi$
$884$	−0.227185	+	0.526675i	−0.00764107	+	0.0177140i
$885$	39.9130	−	55.0779i	1.34166	−	1.85142i
$886$	−4.24036	+	14.1638i	−0.142458	+	0.475842i
$887$	2.87407	−	3.86055i	0.0965020	−	0.129625i	−0.751249	−	0.660018i	$-0.770548\pi$
$887$	2.87407	−	3.86055i	0.0965020	−	0.129625i	0.847751	+	0.530394i	$0.177956\pi$
$888$	−2.73393	+	60.2943i	−0.0917448	+	2.02334i
$889$	−19.6228	+	9.85493i	−0.658127	+	0.330524i
$890$	25.7720			0.863880
$891$	35.1817	−	25.8264i	1.17863	−	0.865218i
$892$	2.68540			0.0899137
$893$	3.96101	−	1.98930i	0.132550	−	0.0665693i
$894$	−42.0582	+	21.8044i	−1.40664	+	0.729249i
$895$	18.3456	−	24.6424i	0.613224	−	0.823703i
$896$	2.49083	−	8.31996i	0.0832129	−	0.277950i
$897$	−0.500995	−	1.12154i	−0.0167277	−	0.0374471i
$898$	−12.0918	+	28.0319i	−0.403508	+	0.935436i
$899$	−2.41882	+	13.7178i	−0.0806723	+	0.457515i
$900$	12.0470	+	12.1281i	0.401565	+	0.404271i
$901$	−0.954103	−	5.41099i	−0.0317858	−	0.180266i
$902$	8.22157	+	1.94855i	0.273748	+	0.0648796i
$903$	2.31930	−	14.2209i	0.0771813	−	0.473242i
$904$	−39.7627	+	26.1523i	−1.32249	+	0.869814i
$905$	2.67270	+	45.8885i	0.0888436	+	1.52539i
$906$	28.5781	+	9.98712i	0.949444	+	0.331800i
$907$	−6.02455	−	20.1234i	−0.200042	−	0.668187i	−0.997866	−	0.0652962i	$-0.979201\pi$
$907$	−6.02455	−	20.1234i	−0.200042	−	0.668187i	0.797824	−	0.602890i	$-0.205984\pi$
$908$	−3.29297	−	1.19854i	−0.109281	−	0.0397751i
$909$	−15.3935	+	28.3209i	−0.510569	+	0.939345i
$910$	2.57826	−	0.938410i	0.0854685	−	0.0311080i
$911$	−15.1128	−	20.3001i	−0.500710	−	0.672571i	0.477871	−	0.878430i	$-0.341409\pi$
$911$	−15.1128	−	20.3001i	−0.500710	−	0.672571i	−0.978582	+	0.205859i	$0.934001\pi$
$912$	−0.362255	−	5.09050i	−0.0119955	−	0.168563i
$913$	−34.9343	+	8.27958i	−1.15616	+	0.274014i
$914$	13.9957	+	32.4457i	0.462937	+	1.07321i
$915$	5.08142	+	1.13548i	0.167987	+	0.0375377i
$916$	13.5478	+	8.91052i	0.447631	+	0.294412i
$917$	16.4452	−	28.4839i	0.543067	−	0.940620i
$918$	−0.414686	+	21.1753i	−0.0136867	+	0.698887i
$919$	−20.2378	−	35.0529i	−0.667583	−	1.15629i	−0.978578	−	0.205876i	$-0.933996\pi$
$919$	−20.2378	−	35.0529i	−0.667583	−	1.15629i	0.310995	−	0.950411i	$-0.399338\pi$
$920$	1.59856	−	27.4462i	0.0527029	−	0.904873i
$921$	−2.01598	−	2.63642i	−0.0664287	−	0.0868731i
$922$	15.3554	+	1.79478i	0.505702	+	0.0591080i
$923$	1.45247	+	1.53953i	0.0478087	+	0.0506742i
$924$	−2.33717	+	8.18868i	−0.0768872	+	0.269388i
$925$	−117.815	+	13.7706i	−3.87373	+	0.452774i
$926$	−9.53925	−	8.00438i	−0.313479	−	0.263040i
$927$	−21.7663	−	27.7188i	−0.714899	−	0.910404i
$928$	−6.56228	+	5.50641i	−0.215417	+	0.180757i
$929$	−10.3432	+	10.9632i	−0.339351	+	0.359691i	−0.874465	−	0.485089i	$-0.838787\pi$
$929$	−10.3432	+	10.9632i	−0.339351	+	0.359691i	0.535114	+	0.844780i	$0.320269\pi$
$930$	19.5104	−	34.8199i	0.639770	−	1.14179i
$931$	3.57128	+	1.79356i	0.117044	+	0.0587816i
$932$	−10.5930	−	5.31998i	−0.346984	−	0.174262i
$933$	−26.4173	+	0.339892i	−0.864864	+	0.0111276i
$934$	5.76890	−	6.11468i	0.188764	−	0.200078i
$935$	−49.3440	+	41.4046i	−1.61372	+	1.35407i
$936$	1.91294	−	2.13507i	0.0625263	−	0.0697870i
$937$	10.3708	+	8.70215i	0.338800	+	0.284287i	0.796274	−	0.604936i	$-0.206801\pi$
$937$	10.3708	+	8.70215i	0.338800	+	0.284287i	−0.457474	+	0.889223i	$0.651246\pi$
$938$	1.64133	−	0.191844i	0.0535914	−	0.00626393i
$939$	36.9960	+	38.2163i	1.20732	+	1.24714i
$940$	5.77967	+	6.12609i	0.188512	+	0.199811i
$941$	30.6082	+	3.57758i	0.997798	+	0.116626i	0.599284	−	0.800536i	$-0.295452\pi$
$941$	30.6082	+	3.57758i	0.997798	+	0.116626i	0.398514	+	0.917162i	$0.369526\pi$
$942$	−9.12955	+	21.9365i	−0.297457	+	0.714728i
$943$	−0.191380	+	3.28586i	−0.00623218	+	0.107002i
$944$	−13.0487	−	22.6010i	−0.424699	−	0.735601i
$945$	−28.1272	+	25.5144i	−0.914978	+	0.829984i
$946$	−13.0842	+	22.6624i	−0.425403	+	0.736819i
$947$	−41.5068	−	27.2995i	−1.34879	−	0.887114i	−0.350023	−	0.936741i	$-0.613826\pi$
$947$	−41.5068	−	27.2995i	−1.34879	−	0.887114i	−0.998768	+	0.0496273i	$0.984197\pi$
$948$	7.93836	−	8.63405i	0.257826	−	0.280421i
$949$	0.491311	+	1.13899i	0.0159486	+	0.0369731i
$950$	13.8338	−	3.27866i	0.448826	−	0.106374i
$951$	32.9307	−	22.2710i	1.06785	−	0.722188i
$952$	−11.5190	−	15.4727i	−0.373332	−	0.501472i
$953$	21.4128	−	7.79362i	0.693629	−	0.252460i	0.0289406	−	0.999581i	$-0.490787\pi$
$953$	21.4128	−	7.79362i	0.693629	−	0.252460i	0.664688	+	0.747121i	$0.268564\pi$
$954$	−0.872165	+	5.81793i	−0.0282374	+	0.188362i
$955$	53.7466	+	19.5622i	1.73920	+	0.633017i
$956$	0.930231	+	3.10719i	0.0300858	+	0.100494i
$957$	−18.2376	+	15.7074i	−0.589539	+	0.507749i
$958$	−2.34478	−	40.2583i	−0.0757564	−	1.30069i
$959$	10.8282	−	7.12180i	0.349660	−	0.229975i
$960$	56.2184	−	21.2848i	1.81444	−	0.686964i
$961$	−7.17393	−	1.70025i	−0.231417	−	0.0548469i
$962$	0.739993	+	4.19671i	0.0238583	+	0.135307i
$963$	19.1797	+	1.74292i	0.618058	+	0.0561649i
$964$	0.112305	−	0.636915i	0.00361711	−	0.0205136i
$965$	−26.4938	+	61.4196i	−0.852867	+	1.97717i
$966$	8.80250	+	0.914235i	0.283216	+	0.0294150i
$967$	−16.3536	+	54.6249i	−0.525897	+	1.75662i	0.119565	+	0.992826i	$0.461850\pi$
$967$	−16.3536	+	54.6249i	−0.525897	+	1.75662i	−0.645462	+	0.763793i	$0.723335\pi$
$968$	22.9438	−	30.8188i	0.737440	−	0.990554i
$969$	−5.56255	−	3.55688i	−0.178695	−	0.114263i
$970$	19.5085	−	9.79754i	0.626381	−	0.314580i
$971$	38.8020			1.24521			0.622607	−	0.782535i	$-0.286074\pi$
$971$	38.8020			1.24521			0.622607	+	0.782535i	$0.286074\pi$
$972$	−2.85805	+	8.00527i	−0.0916719	+	0.256769i
$973$	11.7212			0.375765
$974$	9.35062	−	4.69606i	0.299613	−	0.150471i
$975$	4.74643	+	3.03503i	0.152008	+	0.0971987i
$976$	1.19295	−	1.60241i	0.0381853	−	0.0512918i
$977$	12.5244	−	41.8345i	0.400692	−	1.33840i	−0.485155	−	0.874428i	$-0.661237\pi$
$977$	12.5244	−	41.8345i	0.400692	−	1.33840i	0.885847	−	0.463977i	$-0.153578\pi$
$978$	−1.64073	−	0.170408i	−0.0524648	−	0.00544904i
$979$	−10.4414	+	24.2058i	−0.333708	+	0.773621i
$980$	−1.31860	+	7.47815i	−0.0421211	+	0.238881i
$981$	5.95274	−	8.44093i	0.190056	−	0.269498i
$982$	−3.36694	−	19.0949i	−0.107443	−	0.609342i
$983$	34.1022	+	8.08236i	1.08769	+	0.257787i	0.735078	−	0.677982i	$-0.237145\pi$
$983$	34.1022	+	8.08236i	1.08769	+	0.257787i	0.352612	+	0.935770i	$0.385293\pi$
$984$	−7.18378	+	2.71985i	−0.229011	+	0.0867056i
$985$	40.8895	−	26.8934i	1.30285	−	0.856896i
$986$	−0.679153	−	11.6606i	−0.0216286	−	0.371349i
$987$	−9.58873	+	8.25843i	−0.305213	+	0.262869i
$988$	0.0549097	+	0.183411i	0.00174691	+	0.00583508i
$989$	−9.57909	−	3.48651i	−0.304597	−	0.110864i
$990$	64.1807	−	25.2482i	2.03980	−	0.802440i
$991$	−0.299988	+	0.109187i	−0.00952943	+	0.00346843i	−0.346780	−	0.937946i	$-0.612725\pi$
$991$	−0.299988	+	0.109187i	−0.00952943	+	0.00346843i	0.337251	+	0.941415i	$0.390503\pi$
$992$	8.67703	+	11.6553i	0.275496	+	0.370055i
$993$	1.29281	−	0.874328i	0.0410261	−	0.0277460i
$994$	−14.8381	+	3.51668i	−0.470634	+	0.111542i
$995$	33.5768	+	77.8397i	1.06445	+	2.46768i
$996$	4.73265	−	5.14740i	0.149960	−	0.163102i
$997$	−8.98796	−	5.91148i	−0.284652	−	0.187218i	0.399151	−	0.916885i	$-0.369305\pi$
$997$	−8.98796	−	5.91148i	−0.284652	−	0.187218i	−0.683803	+	0.729667i	$0.739675\pi$
$998$	4.65872	−	8.06914i	0.147469	−	0.255424i
$999$	−31.4400	−	49.9037i	−0.994716	−	1.57888i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.g.a.25.3	yes	144
3.2	odd	2		243.2.g.a.73.6		144
9.2	odd	6		729.2.g.b.703.3		144
9.4	even	3		729.2.g.d.217.6		144
9.5	odd	6		729.2.g.a.217.3		144
9.7	even	3		729.2.g.c.703.6		144
81.13	even	27	inner	81.2.g.a.13.3	✓	144
81.14	odd	54		729.2.g.a.514.3		144
81.16	even	27		6561.2.a.c.1.24		72
81.40	even	27		729.2.g.c.28.6		144
81.41	odd	54		729.2.g.b.28.3		144
81.65	odd	54		6561.2.a.d.1.49		72
81.67	even	27		729.2.g.d.514.6		144
81.68	odd	54		243.2.g.a.10.6		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.3	✓	144	81.13	even	27	inner
81.2.g.a.25.3	yes	144	1.1	even	1	trivial
243.2.g.a.10.6		144	81.68	odd	54
243.2.g.a.73.6		144	3.2	odd	2
729.2.g.a.217.3		144	9.5	odd	6
729.2.g.a.514.3		144	81.14	odd	54
729.2.g.b.28.3		144	81.41	odd	54
729.2.g.b.703.3		144	9.2	odd	6
729.2.g.c.28.6		144	81.40	even	27
729.2.g.c.703.6		144	9.7	even	3
729.2.g.d.217.6		144	9.4	even	3
729.2.g.d.514.6		144	81.67	even	27
6561.2.a.c.1.24		72	81.16	even	27
6561.2.a.d.1.49		72	81.65	odd	54

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07782 + 0.541304i) q^{2} +(-1.45923 - 0.933081i) q^{3} +(-0.325622 + 0.437386i) q^{4} +(1.12732 - 3.76550i) q^{5} +(2.07788 + 0.215810i) q^{6} +(0.736444 - 1.70727i) q^{7} +(0.533084 - 3.02327i) q^{8} +(1.25872 + 2.72317i) q^{9} +(0.823230 + 4.66877i) q^{10} +(-4.71857 - 1.11832i) q^{11} +(0.883275 - 0.334416i) q^{12} +(0.260059 - 0.171044i) q^{13} +(0.130394 + 2.23878i) q^{14} +(-5.15854 + 4.44287i) q^{15} +(0.749157 + 2.50236i) q^{16} +(3.17561 + 1.15583i) q^{17} +(-2.83074 - 2.25374i) q^{18} +(1.05997 - 0.385798i) q^{19} +(1.27990 + 1.71920i) q^{20} +(-2.66766 + 1.80414i) q^{21} +(5.69114 - 1.34882i) q^{22} +(0.902427 + 2.09206i) q^{23} +(-3.59885 + 3.91424i) q^{24} +(-8.73073 - 5.74229i) q^{25} +(-0.187712 + 0.325126i) q^{26} +(0.704172 - 5.14822i) q^{27} +(0.506934 + 0.878035i) q^{28} +(-0.166624 + 2.86083i) q^{29} +(3.15506 - 7.58096i) q^{30} +(4.82793 + 0.564304i) q^{31} +(2.05140 + 2.17436i) q^{32} +(5.84200 + 6.03470i) q^{33} +(-4.04840 + 0.473190i) q^{34} +(-5.59852 - 4.69772i) q^{35} +(-1.60094 - 0.336176i) q^{36} +(8.69541 - 7.29632i) q^{37} +(-0.933628 + 0.989588i) q^{38} +(-0.539085 + 0.00693600i) q^{39} +(-10.7832 - 5.41551i) q^{40} +(1.29097 + 0.648347i) q^{41} +(1.89869 - 3.38856i) q^{42} +(-3.07034 + 3.25437i) q^{43} +(2.02561 - 1.69969i) q^{44} +(11.6731 - 1.66984i) q^{45} +(-2.10510 - 1.76639i) q^{46} +(3.90295 - 0.456189i) q^{47} +(1.24171 - 4.35054i) q^{48} +(2.43127 + 2.57700i) q^{49} +(12.5185 + 1.46320i) q^{50} +(-3.55547 - 4.64972i) q^{51} +(-0.00986888 + 0.169442i) q^{52} +(-0.812932 - 1.40804i) q^{53} +(2.02777 + 5.93004i) q^{54} +(-9.53037 + 16.5071i) q^{55} +(-4.76895 - 3.13659i) q^{56} +(-1.90672 - 0.426070i) q^{57} +(-1.36898 - 3.17366i) q^{58} +(-9.72169 + 2.30408i) q^{59} +(-0.263514 - 3.70297i) q^{60} +(-0.456702 - 0.613457i) q^{61} +(-5.50912 + 2.00515i) q^{62} +(5.57615 - 0.143512i) q^{63} +(-8.29717 - 3.01992i) q^{64} +(-0.350896 - 1.17208i) q^{65} +(-9.56326 - 3.34205i) q^{66} +(-0.0428458 - 0.735633i) q^{67} +(-1.53959 + 1.01260i) q^{68} +(0.635212 - 3.89484i) q^{69} +(8.57712 + 2.03281i) q^{70} +(1.18078 + 6.69652i) q^{71} +(8.90386 - 2.35377i) q^{72} +(-0.692009 + 3.92458i) q^{73} +(-5.42260 + 12.5710i) q^{74} +(7.38214 + 16.5258i) q^{75} +(-0.176407 + 0.589241i) q^{76} +(-5.38424 + 7.23229i) q^{77} +(0.577284 - 0.299284i) q^{78} +(11.0976 - 5.57340i) q^{79} +10.2672 q^{80} +(-5.83126 + 6.85540i) q^{81} -1.74239 q^{82} +(6.61608 - 3.32272i) q^{83} +(0.0795440 - 1.75427i) q^{84} +(7.93219 - 10.6548i) q^{85} +(1.54768 - 5.16962i) q^{86} +(2.91253 - 4.01913i) q^{87} +(-5.89638 + 13.6693i) q^{88} +(0.943990 - 5.35363i) q^{89} +(-11.6776 + 8.11846i) q^{90} +(-0.100499 - 0.569956i) q^{91} +(-1.20889 - 0.286512i) q^{92} +(-6.51853 - 5.32830i) q^{93} +(-3.95975 + 2.60437i) q^{94} +(-0.257799 - 4.42624i) q^{95} +(-0.964619 - 5.08702i) q^{96} +(-1.32068 - 4.41138i) q^{97} +(-4.01542 - 1.46149i) q^{98} +(-2.89398 - 14.2571i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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