LMFDB - Embedded newform 446.2.g.b.53.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [446,2,Mod(9,446)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(446, base_ring=CyclotomicField(222)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("446.9"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 446 = 2 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	446.g (of order $111$, degree $72$, minimal)

Newform invariants

comment:select newform

sage:traces = [648,18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$3.56132793015$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$9$ over $\Q(\zeta_{111})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{111}]$

Embedding invariants

Embedding label			53.9
Character	$\chi$	$=$	446.53
Dual form			446.2.g.b.101.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.911228 - 0.411901i) q^{2} +(1.38592 + 2.95390i) q^{3} +(0.660675 - 0.750672i) q^{4} +(1.40613 + 0.323933i) q^{5} +(2.47960 + 2.12082i) q^{6} +(0.477253 - 0.775108i) q^{7} +(0.292823 - 0.956167i) q^{8} +(-4.88725 + 5.88051i) q^{9} +(1.41474 - 0.284011i) q^{10} +(0.868844 - 4.66942i) q^{11} +(3.13305 + 0.911197i) q^{12} +(1.22106 - 0.103928i) q^{13} +(0.115618 - 0.902881i) q^{14} +(0.991919 + 4.60252i) q^{15} +(-0.127018 - 0.991900i) q^{16} +(0.334237 - 0.118094i) q^{17} +(-2.03121 + 7.37155i) q^{18} +(-2.51363 + 0.142437i) q^{19} +(1.17217 - 0.841532i) q^{20} +(2.95102 + 0.335521i) q^{21} +(-1.13163 - 4.61279i) q^{22} +(-4.34950 + 4.66868i) q^{23} +(3.23025 - 0.460199i) q^{24} +(-2.62375 - 1.27663i) q^{25} +(1.06986 - 0.597658i) q^{26} +(-14.6710 - 3.82003i) q^{27} +(-0.266543 - 0.870355i) q^{28} +(-5.06958 - 2.12093i) q^{29} +(2.79965 + 3.78538i) q^{30} +(-0.0852665 + 0.543327i) q^{31} +(-0.524307 - 0.851529i) q^{32} +(14.9971 - 3.90495i) q^{33} +(0.255924 - 0.245283i) q^{34} +(0.922165 - 0.935308i) q^{35} +(1.18545 + 7.55382i) q^{36} +(-2.13716 + 1.82792i) q^{37} +(-2.23182 + 1.16516i) q^{38} +(1.99928 + 3.46285i) q^{39} +(0.721482 - 1.24964i) q^{40} +(0.390423 - 9.19086i) q^{41} +(2.82726 - 0.909793i) q^{42} +(0.0491717 - 0.693782i) q^{43} +(-2.93118 - 3.73719i) q^{44} +(-8.77702 + 6.68564i) q^{45} +(-2.04035 + 6.04580i) q^{46} +(10.5108 + 0.595602i) q^{47} +(2.75394 - 1.74989i) q^{48} +(2.77840 + 5.51064i) q^{49} +(-2.91668 - 0.0825719i) q^{50} +(0.812061 + 0.823635i) q^{51} +(0.728708 - 0.985279i) q^{52} +(-2.75907 + 1.64544i) q^{53} +(-14.9421 + 2.56208i) q^{54} +(2.73429 - 6.28439i) q^{55} +(-0.601382 - 0.683303i) q^{56} +(-3.90442 - 7.22759i) q^{57} +(-5.49316 + 0.155512i) q^{58} +(8.94861 + 8.57655i) q^{59} +(4.11032 + 2.29616i) q^{60} +(-3.29382 - 4.72775i) q^{61} +(0.146100 + 0.530216i) q^{62} +(2.22557 + 6.59463i) q^{63} +(-0.828510 - 0.559975i) q^{64} +(1.75064 + 0.249406i) q^{65} +(12.0574 - 9.73565i) q^{66} +(13.2379 + 2.65754i) q^{67} +(0.132173 - 0.328924i) q^{68} +(-19.8188 - 6.37758i) q^{69} +(0.455048 - 1.23212i) q^{70} +(2.80105 - 11.4178i) q^{71} +(4.19165 + 6.39497i) q^{72} +(-4.99668 - 11.4842i) q^{73} +(-1.19452 + 2.54596i) q^{74} +(0.134724 - 9.51960i) q^{75} +(-1.55377 + 1.98101i) q^{76} +(-3.20465 - 2.90194i) q^{77} +(3.24815 + 2.33195i) q^{78} +(-2.15862 - 1.37162i) q^{79} +(0.142705 - 1.43589i) q^{80} +(-4.85256 - 26.0791i) q^{81} +(-3.42996 - 8.53579i) q^{82} +(0.820241 + 11.5731i) q^{83} +(2.20153 - 1.99358i) q^{84} +(0.508237 - 0.0577849i) q^{85} +(-0.240963 - 0.652447i) q^{86} +(-0.760996 - 17.9144i) q^{87} +(-4.21033 - 2.19807i) q^{88} +(-0.00522727 + 0.00120421i) q^{89} +(-5.24405 + 9.70741i) q^{90} +(0.502200 - 0.996054i) q^{91} +(0.631045 + 6.34953i) q^{92} +(-1.72310 + 0.501137i) q^{93} +(9.82305 - 3.78667i) q^{94} +(-3.58064 - 0.613962i) q^{95} +(1.78868 - 2.72890i) q^{96} +(7.59717 + 8.15468i) q^{97} +(4.80160 + 3.87702i) q^{98} +(23.2123 + 27.9299i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q + 18 q^{2} - 4 q^{3} - 18 q^{4} + 3 q^{5} + 4 q^{6} - 8 q^{7} + 18 q^{8} + 13 q^{9} - 3 q^{10} + 29 q^{11} - 4 q^{12} - 6 q^{13} - 66 q^{14} - 10 q^{15} - 18 q^{16} + 10 q^{17} - 13 q^{18} - 5 q^{19}+ \cdots + 301 q^{99}+O(q^{100}) $ 648 * q + 18 * q^2 - 4 * q^3 - 18 * q^4 + 3 * q^5 + 4 * q^6 - 8 * q^7 + 18 * q^8 + 13 * q^9 - 3 * q^10 + 29 * q^11 - 4 * q^12 - 6 * q^13 - 66 * q^14 - 10 * q^15 - 18 * q^16 + 10 * q^17 - 13 * q^18 - 5 * q^19 + 3 * q^20 + q^21 + 8 * q^22 + 7 * q^23 - 33 * q^24 + 14 * q^25 + 6 * q^26 + 26 * q^27 - 8 * q^28 - 328 * q^29 + 121 * q^30 + 23 * q^31 + 18 * q^32 + 14 * q^33 - 10 * q^34 + 7 * q^35 + 13 * q^36 + 47 * q^37 + 5 * q^38 + 3 * q^39 - 3 * q^40 - 55 * q^41 - q^42 + 32 * q^43 - 8 * q^44 + 13 * q^45 + 30 * q^46 - 124 * q^47 - 4 * q^48 + 18 * q^49 - 14 * q^50 - 97 * q^51 - 6 * q^52 + 12 * q^53 - 26 * q^54 + 10 * q^55 + 8 * q^56 - 105 * q^57 - 79 * q^58 - 172 * q^59 - 10 * q^60 - 23 * q^61 - 23 * q^62 + 22 * q^63 - 18 * q^64 + 3 * q^65 + 97 * q^66 + 79 * q^67 + 10 * q^68 + 241 * q^69 - 81 * q^70 - 6 * q^71 - 87 * q^72 + 5 * q^73 - 158 * q^74 - 155 * q^75 - 5 * q^76 - 27 * q^77 - 3 * q^78 - 246 * q^79 + 3 * q^80 - 189 * q^81 + 18 * q^82 + 142 * q^83 + q^84 - 63 * q^85 + 5 * q^86 - 112 * q^87 + 8 * q^88 - 162 * q^89 - 13 * q^90 + 12 * q^91 + 81 * q^92 - 64 * q^93 + 50 * q^94 + 180 * q^95 + 4 * q^96 - 48 * q^97 + 19 * q^98 + 301 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/446\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{40}{111}\right)$

Coefficient data

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

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

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

$2$	0.911228	−	0.411901i	0.644336	−	0.291258i
$2$	0.911228	−	0.411901i	0.644336	−	0.291258i
$3$	1.38592	+	2.95390i	0.800159	+	1.70543i	0.704148	+	0.710053i	$0.251329\pi$
$3$	1.38592	+	2.95390i	0.800159	+	1.70543i	0.0960114	+	0.995380i	$0.469391\pi$
$4$	0.660675	−	0.750672i	0.330337	−	0.375336i
$5$	1.40613	+	0.323933i	0.628843	+	0.144867i	0.526906	−	0.849924i	$-0.323352\pi$
$5$	1.40613	+	0.323933i	0.628843	+	0.144867i	0.101937	+	0.994791i	$0.467496\pi$
$6$	2.47960	+	2.12082i	1.01229	+	0.865819i
$7$	0.477253	−	0.775108i	0.180385	−	0.292963i	−0.748643	−	0.662973i	$-0.769294\pi$
$7$	0.477253	−	0.775108i	0.180385	−	0.292963i	0.929028	+	0.370010i	$0.120646\pi$
$8$	0.292823	−	0.956167i	0.103528	−	0.338056i
$9$	−4.88725	+	5.88051i	−1.62908	+	1.96017i
$10$	1.41474	−	0.284011i	0.447380	−	0.0898123i
$11$	0.868844	−	4.66942i	0.261966	−	1.40788i	−0.555313	−	0.831642i	$-0.687401\pi$
$11$	0.868844	−	4.66942i	0.261966	−	1.40788i	0.817279	−	0.576242i	$-0.195481\pi$
$12$	3.13305	+	0.911197i	0.904433	+	0.263040i
$13$	1.22106	−	0.103928i	0.338661	−	0.0288243i	0.0857583	−	0.996316i	$-0.472669\pi$
$13$	1.22106	−	0.103928i	0.338661	−	0.0288243i	0.252903	+	0.967492i	$0.418615\pi$
$14$	0.115618	−	0.902881i	0.0309003	−	0.241305i
$15$	0.991919	+	4.60252i	0.256113	+	1.18837i
$16$	−0.127018	−	0.991900i	−0.0317545	−	0.247975i
$17$	0.334237	−	0.118094i	0.0810644	−	0.0286419i	−0.292300	−	0.956327i	$-0.594420\pi$
$17$	0.334237	−	0.118094i	0.0810644	−	0.0286419i	0.373364	+	0.927685i	$0.378204\pi$
$18$	−2.03121	+	7.37155i	−0.478761	+	1.73749i
$19$	−2.51363	+	0.142437i	−0.576665	+	0.0326772i	−0.342497	−	0.939519i	$-0.611273\pi$
$19$	−2.51363	+	0.142437i	−0.576665	+	0.0326772i	−0.234168	+	0.972196i	$0.575237\pi$
$20$	1.17217	−	0.841532i	0.262104	−	0.188172i
$21$	2.95102	+	0.335521i	0.643966	+	0.0732168i
$22$	−1.13163	−	4.61279i	−0.241263	−	0.983450i
$23$	−4.34950	+	4.66868i	−0.906933	+	0.973487i	−0.999754	−	0.0221958i	$-0.992934\pi$
$23$	−4.34950	+	4.66868i	−0.906933	+	0.973487i	0.0928204	+	0.995683i	$0.470412\pi$
$24$	3.23025	−	0.460199i	0.659371	−	0.0939376i
$25$	−2.62375	−	1.27663i	−0.524751	−	0.255326i
$26$	1.06986	−	0.597658i	0.209816	−	0.117210i
$27$	−14.6710	−	3.82003i	−2.82343	−	0.735165i
$28$	−0.266543	−	0.870355i	−0.0503719	−	0.164482i
$29$	−5.06958	−	2.12093i	−0.941397	−	0.393847i	−0.138767	−	0.990325i	$-0.544314\pi$
$29$	−5.06958	−	2.12093i	−0.941397	−	0.393847i	−0.802629	+	0.596478i	$0.796566\pi$
$30$	2.79965	+	3.78538i	0.511144	+	0.691112i
$31$	−0.0852665	+	0.543327i	−0.0153143	+	0.0975843i	−0.994360	−	0.106055i	$-0.966178\pi$
$31$	−0.0852665	+	0.543327i	−0.0153143	+	0.0975843i	0.979046	+	0.203640i	$0.0652771\pi$
$32$	−0.524307	−	0.851529i	−0.0926853	−	0.150531i
$33$	14.9971	−	3.90495i	2.61067	−	0.679765i
$34$	0.255924	−	0.245283i	0.0438905	−	0.0420657i
$35$	0.922165	−	0.935308i	0.155874	−	0.158096i
$36$	1.18545	+	7.55382i	0.197575	+	1.25897i
$37$	−2.13716	+	1.82792i	−0.351347	+	0.300509i	−0.808054	−	0.589108i	$-0.799479\pi$
$37$	−2.13716	+	1.82792i	−0.351347	+	0.300509i	0.456707	+	0.889617i	$0.349029\pi$
$38$	−2.23182	+	1.16516i	−0.362049	+	0.189014i
$39$	1.99928	+	3.46285i	0.320141	+	0.554500i
$40$	0.721482	−	1.24964i	0.114076	−	0.197586i
$41$	0.390423	−	9.19086i	0.0609738	−	1.43537i	−0.664585	−	0.747212i	$-0.731392\pi$
$41$	0.390423	−	9.19086i	0.0609738	−	1.43537i	0.725559	−	0.688160i	$-0.241581\pi$
$42$	2.82726	−	0.909793i	0.436255	−	0.140384i
$43$	0.0491717	−	0.693782i	0.00749861	−	0.105801i	−0.992345	−	0.123498i	$-0.960589\pi$
$43$	0.0491717	−	0.693782i	0.00749861	−	0.105801i	0.999843	+	0.0176977i	$0.00563366\pi$
$44$	−2.93118	−	3.73719i	−0.441892	−	0.563402i
$45$	−8.77702	+	6.68564i	−1.30840	+	0.996637i
$46$	−2.04035	+	6.04580i	−0.300834	+	0.891404i
$47$	10.5108	+	0.595602i	1.53315	+	0.0868774i	0.802824	−	0.596217i	$-0.203330\pi$
$47$	10.5108	+	0.595602i	1.53315	+	0.0868774i	0.730330	+	0.683094i	$0.239366\pi$
$48$	2.75394	−	1.74989i	0.397496	−	0.252575i
$49$	2.77840	+	5.51064i	0.396915	+	0.787234i
$50$	−2.91668	−	0.0825719i	−0.412481	−	0.0116774i
$51$	0.812061	+	0.823635i	0.113711	+	0.115332i
$52$	0.728708	−	0.985279i	0.101054	−	0.136634i
$53$	−2.75907	+	1.64544i	−0.378988	+	0.226019i	−0.689076	−	0.724689i	$-0.741984\pi$
$53$	−2.75907	+	1.64544i	−0.378988	+	0.226019i	0.310089	+	0.950708i	$0.399641\pi$
$54$	−14.9421	+	2.56208i	−2.03336	+	0.348655i
$55$	2.73429	−	6.28439i	0.368692	−	0.847387i
$56$	−0.601382	−	0.683303i	−0.0803630	−	0.0913101i
$57$	−3.90442	−	7.22759i	−0.517153	−	0.957318i
$58$	−5.49316	+	0.155512i	−0.721287	+	0.0204198i
$59$	8.94861	+	8.57655i	1.16501	+	1.11657i	0.991279	+	0.131778i	$0.0420686\pi$
$59$	8.94861	+	8.57655i	1.16501	+	1.11657i	0.173730	+	0.984793i	$0.444418\pi$
$60$	4.11032	+	2.29616i	0.530640	+	0.296433i
$61$	−3.29382	−	4.72775i	−0.421730	−	0.605327i	0.551775	−	0.833993i	$-0.313951\pi$
$61$	−3.29382	−	4.72775i	−0.421730	−	0.605327i	−0.973505	+	0.228666i	$0.926563\pi$
$62$	0.146100	+	0.530216i	0.0185547	+	0.0673375i
$63$	2.22557	+	6.59463i	0.280396	+	0.830846i
$64$	−0.828510	−	0.559975i	−0.103564	−	0.0699968i
$65$	1.75064	+	0.249406i	0.217140	+	0.0309350i
$66$	12.0574	−	9.73565i	1.48416	−	1.19838i
$67$	13.2379	+	2.65754i	1.61727	+	0.324671i	0.919935	−	0.392072i	$-0.128242\pi$
$67$	13.2379	+	2.65754i	1.61727	+	0.324671i	0.697338	+	0.716743i	$0.254368\pi$
$68$	0.132173	−	0.328924i	0.0160283	−	0.0398879i
$69$	−19.8188	−	6.37758i	−2.38591	−	0.767770i
$70$	0.455048	−	1.23212i	0.0543887	−	0.147267i
$71$	2.80105	−	11.4178i	0.332424	−	1.35504i	−0.529631	−	0.848228i	$-0.677670\pi$
$71$	2.80105	−	11.4178i	0.332424	−	1.35504i	0.862055	−	0.506815i	$-0.169177\pi$
$72$	4.19165	+	6.39497i	0.493990	+	0.753654i
$73$	−4.99668	−	11.4842i	−0.584817	−	1.34412i	−0.916237	−	0.400636i	$-0.868789\pi$
$73$	−4.99668	−	11.4842i	−0.584817	−	1.34412i	0.331421	−	0.943483i	$-0.392472\pi$
$74$	−1.19452	+	2.54596i	−0.138860	+	0.295961i
$75$	0.134724	−	9.51960i	0.0155566	−	1.09923i
$76$	−1.55377	+	1.98101i	−0.178229	+	0.227238i
$77$	−3.20465	−	2.90194i	−0.365204	−	0.330707i
$78$	3.24815	+	2.33195i	0.367781	+	0.264041i
$79$	−2.15862	−	1.37162i	−0.242864	−	0.154319i	0.409293	−	0.912403i	$-0.365775\pi$
$79$	−2.15862	−	1.37162i	−0.242864	−	0.154319i	−0.652157	+	0.758084i	$0.726136\pi$
$80$	0.142705	−	1.43589i	0.0159549	−	0.160537i
$81$	−4.85256	−	26.0791i	−0.539174	−	2.89768i
$82$	−3.42996	−	8.53579i	−0.378776	−	0.942621i
$83$	0.820241	+	11.5731i	0.0900332	+	1.27031i	0.814159	+	0.580643i	$0.197199\pi$
$83$	0.820241	+	11.5731i	0.0900332	+	1.27031i	−0.724125	+	0.689668i	$0.757756\pi$
$84$	2.20153	−	1.99358i	0.240207	−	0.217517i
$85$	0.508237	−	0.0577849i	0.0551260	−	0.00626765i
$86$	−0.240963	−	0.652447i	−0.0259837	−	0.0703552i
$87$	−0.760996	−	17.9144i	−0.0815874	−	1.92063i
$88$	−4.21033	−	2.19807i	−0.448823	−	0.234315i
$89$	−0.00522727	+	0.00120421i	−0.000554090	+	0.000127646i	−0.224768	−	0.974412i	$-0.572163\pi$
$89$	−0.00522727	+	0.00120421i	−0.000554090	+	0.000127646i	0.224214	+	0.974540i	$0.428018\pi$
$90$	−5.24405	+	9.70741i	−0.552771	+	1.02325i
$91$	0.502200	−	0.996054i	0.0526448	−	0.104415i
$92$	0.631045	+	6.34953i	0.0657910	+	0.661984i
$93$	−1.72310	+	0.501137i	−0.178678	+	0.0519655i
$94$	9.82305	−	3.78667i	1.01317	−	0.390565i
$95$	−3.58064	−	0.613962i	−0.367366	−	0.0629912i
$96$	1.78868	−	2.72890i	0.182557	−	0.278517i
$97$	7.59717	+	8.15468i	0.771376	+	0.827982i	0.988979	−	0.148055i	$-0.0473014\pi$
$97$	7.59717	+	8.15468i	0.771376	+	0.827982i	−0.217603	+	0.976037i	$0.569824\pi$
$98$	4.80160	+	3.87702i	0.485035	+	0.391638i
$99$	23.2123	+	27.9299i	2.33293	+	2.80706i
$100$	−2.69178	+	1.12614i	−0.269178	+	0.112614i
$101$	5.44306	+	3.24610i	0.541604	+	0.322999i	0.756880	−	0.653554i	$-0.226723\pi$
$101$	5.44306	+	3.24610i	0.541604	+	0.322999i	−0.215276	+	0.976553i	$0.569065\pi$
$102$	1.07923	+	0.416031i	0.106860	+	0.0411932i
$103$	2.37623	+	0.202247i	0.234137	+	0.0199280i	0.201287	−	0.979532i	$-0.435488\pi$
$103$	2.37623	+	0.202247i	0.234137	+	0.0199280i	0.0328501	+	0.999460i	$0.489542\pi$
$104$	0.258182	−	1.19797i	0.0253169	−	0.117471i
$105$	4.04085	+	1.42772i	0.394346	+	0.139331i
$106$	−1.83638	+	2.63584i	−0.178365	+	0.256015i
$107$	−9.19888	+	4.47586i	−0.889289	+	0.432697i	−0.824934	−	0.565230i	$-0.808788\pi$
$107$	−9.19888	+	4.47586i	−0.889289	+	0.432697i	−0.0643557	+	0.997927i	$0.520499\pi$
$108$	−12.5603	+	8.48931i	−1.20862	+	0.816884i
$109$	−13.5329	−	10.3083i	−1.29622	−	0.987356i	−0.999475	−	0.0323983i	$-0.989685\pi$
$109$	−13.5329	−	10.3083i	−1.29622	−	0.987356i	−0.296742	−	0.954958i	$-0.595900\pi$
$110$	−0.0969823	−	6.85277i	−0.00924689	−	0.653386i
$111$	−8.36143	−	3.77960i	−0.793632	−	0.358744i
$112$	−0.829450	−	0.374935i	−0.0783756	−	0.0354280i
$113$	0.156450	+	11.0548i	0.0147176	+	1.03994i	0.861425	+	0.507885i	$0.169573\pi$
$113$	0.156450	+	11.0548i	0.0147176	+	1.03994i	−0.846707	+	0.532059i	$0.821418\pi$
$114$	−6.53487	−	4.97775i	−0.612047	−	0.466209i
$115$	−7.62832	+	5.15585i	−0.711345	+	0.480785i
$116$	−4.94147	+	2.40435i	−0.458804	+	0.223238i
$117$	−5.35648	+	7.68838i	−0.495207	+	0.710791i
$118$	11.6869	+	4.12925i	1.07587	+	0.380128i
$119$	0.0679804	−	0.315430i	0.00623176	−	0.0289155i
$120$	4.69124	+	0.399283i	0.428249	+	0.0364494i
$121$	−10.7848	−	4.15742i	−0.980438	−	0.377948i
$122$	−4.94879	−	2.95134i	−0.448042	−	0.267201i
$123$	27.6900	−	11.5845i	2.49672	−	1.04454i
$124$	0.351527	+	0.422969i	0.0315680	+	0.0379838i
$125$	−8.88920	−	7.17753i	−0.795074	−	0.641978i
$126$	4.74434	+	5.09250i	0.422660	+	0.453676i
$127$	−7.49253	+	11.4310i	−0.664855	+	1.01433i	0.332602	+	0.943067i	$0.392073\pi$
$127$	−7.49253	+	11.4310i	−0.664855	+	1.01433i	−0.997457	+	0.0712660i	$0.977296\pi$
$128$	−0.985616	−	0.169001i	−0.0871170	−	0.0149377i
$129$	2.11751	−	0.816275i	0.186436	−	0.0718690i
$130$	1.69796	−	0.493826i	0.148921	−	0.0433114i
$131$	−0.940623	−	9.46449i	−0.0821826	−	0.826916i	−0.946228	−	0.323501i	$-0.895140\pi$
$131$	−0.940623	−	9.46449i	−0.0821826	−	0.826916i	0.864045	−	0.503415i	$-0.167923\pi$
$132$	6.97689	−	13.8378i	0.607261	−	1.20443i
$133$	−1.08923	+	2.01631i	−0.0944484	+	0.174836i
$134$	13.1574	−	3.03110i	1.13663	−	0.261847i
$135$	−19.3920	−	10.1239i	−1.66899	−	0.871326i
$136$	−0.0150448	−	0.354167i	−0.00129008	−	0.0303696i
$137$	2.29836	+	6.22320i	0.196362	+	0.531684i	0.997793	−	0.0664040i	$-0.0211526\pi$
$137$	2.29836	+	6.22320i	0.196362	+	0.531684i	−0.801431	+	0.598088i	$0.795927\pi$
$138$	−20.6864	+	2.35198i	−1.76095	+	0.200214i
$139$	−6.68037	+	6.04936i	−0.566622	+	0.513100i	−0.903580	−	0.428420i	$-0.859070\pi$
$139$	−6.68037	+	6.04936i	−0.566622	+	0.513100i	0.336958	+	0.941520i	$0.390602\pi$
$140$	−0.0928588	−	1.31018i	−0.00784800	−	0.110730i
$141$	12.8077	+	31.8732i	1.07860	+	2.68421i
$142$	−2.15060	−	11.5580i	−0.180475	−	0.969924i
$143$	0.575630	−	5.79195i	0.0481366	−	0.484347i
$144$	6.45364	+	4.10073i	0.537804	+	0.341728i
$145$	−6.44147	−	4.62452i	−0.534935	−	0.384045i
$146$	−9.28345	−	8.40656i	−0.768304	−	0.695732i
$147$	−12.4272	+	15.8444i	−1.02498	+	1.30682i
$148$	−0.0397958	+	2.81197i	−0.00327119	+	0.231143i
$149$	9.87553	−	21.0484i	0.809035	−	1.72435i	0.128406	−	0.991722i	$-0.459014\pi$
$149$	9.87553	−	21.0484i	0.809035	−	1.72435i	0.680628	−	0.732629i	$-0.261707\pi$
$150$	−3.79837	−	8.73002i	−0.310136	−	0.712803i
$151$	9.97746	+	15.2221i	0.811954	+	1.23875i	0.967987	+	0.251002i	$0.0807601\pi$
$151$	9.97746	+	15.2221i	0.811954	+	1.23875i	−0.156033	+	0.987752i	$0.549871\pi$
$152$	−0.599854	+	2.44515i	−0.0486546	+	0.198328i
$153$	−0.939050	+	2.54264i	−0.0759177	+	0.205560i
$154$	−4.11548	−	1.32433i	−0.331635	−	0.106718i
$155$	−0.295898	+	0.736370i	−0.0237671	+	0.0591466i
$156$	3.92034	+	0.787016i	0.313879	+	0.0630117i
$157$	−9.08885	+	7.33873i	−0.725369	+	0.585695i	−0.918473	−	0.395484i	$-0.870577\pi$
$157$	−9.08885	+	7.33873i	−0.725369	+	0.585695i	0.193104	+	0.981178i	$0.438145\pi$
$158$	−2.53197	−	0.360718i	−0.201433	−	0.0286972i
$159$	−8.68431	−	5.86957i	−0.688711	−	0.465487i
$160$	−0.461408	−	1.36721i	−0.0364775	−	0.108087i
$161$	1.54292	+	5.59947i	0.121599	+	0.441300i
$162$	−15.1638	−	21.7652i	−1.19138	−	1.71004i
$163$	2.20296	+	1.23065i	0.172549	+	0.0963917i	0.571582	−	0.820545i	$-0.306330\pi$
$163$	2.20296	+	1.23065i	0.172549	+	0.0963917i	−0.399033	+	0.916937i	$0.630654\pi$
$164$	−6.64138	−	6.36525i	−0.518605	−	0.497043i
$165$	22.3529	−	0.632816i	1.74017	−	0.0492647i
$166$	5.51439	+	10.2079i	0.428000	+	0.792284i
$167$	−4.59683	−	5.22301i	−0.355713	−	0.404169i	0.545103	−	0.838369i	$-0.316491\pi$
$167$	−4.59683	−	5.22301i	−0.355713	−	0.404169i	−0.900816	+	0.434200i	$0.857031\pi$
$168$	1.18494	−	2.72342i	0.0914202	−	0.210116i
$169$	−11.3328	+	1.94321i	−0.871755	+	0.149477i
$170$	0.439318	−	0.261999i	0.0336942	−	0.0200944i
$171$	11.4471	−	15.4775i	0.875383	−	1.18360i
$172$	−0.488316	−	0.495276i	−0.0372338	−	0.0377644i
$173$	10.8478	+	0.307104i	0.824745	+	0.0233487i	0.438151	−	0.898901i	$-0.355633\pi$
$173$	10.8478	+	0.307104i	0.824745	+	0.0233487i	0.386594	+	0.922250i	$0.373651\pi$
$174$	−8.07242	−	16.0107i	−0.611969	−	1.21377i
$175$	−2.24172	+	1.42442i	−0.169458	+	0.107676i
$176$	−4.74196	−	0.268707i	−0.357439	−	0.0202546i
$177$	−12.9322	+	38.3197i	−0.972045	+	2.88028i
$178$	−0.00426722	+	0.00325044i	−0.000319842	+	0.000243630i
$179$	8.66646	+	11.0495i	0.647762	+	0.825880i	0.993664	−	0.112390i	$-0.0358506\pi$
$179$	8.66646	+	11.0495i	0.647762	+	0.825880i	−0.345902	+	0.938270i	$0.612427\pi$
$180$	−0.780028	+	11.0057i	−0.0581399	+	0.820316i
$181$	−20.3786	+	6.55771i	−1.51473	+	0.487431i	−0.942939	−	0.332966i	$-0.891950\pi$
$181$	−20.3786	+	6.55771i	−1.51473	+	0.487431i	−0.571794	+	0.820397i	$0.693752\pi$
$182$	0.0473429	−	1.11449i	0.00350929	−	0.0826114i
$183$	9.40035	−	16.2819i	0.694894	−	1.20359i
$184$	3.19040	+	5.52594i	0.235200	+	0.407378i
$185$	−3.59726	+	1.87801i	−0.264476	+	0.138074i
$186$	−1.36372	+	1.16640i	−0.0999930	+	0.0855245i
$187$	−0.261028	−	1.66330i	−0.0190883	−	0.121632i
$188$	7.39130	−	7.49665i	0.539066	−	0.546749i
$189$	−9.96271	+	9.54848i	−0.724680	+	0.694550i
$190$	−3.51567	+	0.915409i	−0.255054	+	0.0664108i
$191$	4.47024	+	7.26014i	0.323456	+	0.525325i	0.971734	−	0.236078i	$-0.0758621\pi$
$191$	4.47024	+	7.26014i	0.323456	+	0.525325i	−0.648279	+	0.761403i	$0.724511\pi$
$192$	0.505863	−	3.22341i	0.0365075	−	0.232630i
$193$	4.43906	+	6.00201i	0.319531	+	0.432034i	0.934199	−	0.356751i	$-0.116116\pi$
$193$	4.43906	+	6.00201i	0.319531	+	0.432034i	−0.614669	+	0.788785i	$0.710710\pi$
$194$	10.2817	+	4.30149i	0.738181	+	0.308829i
$195$	1.68952	+	5.51687i	0.120989	+	0.395071i
$196$	5.97230	+	1.55507i	0.426593	+	0.111076i
$197$	16.2669	−	9.08725i	1.15897	−	0.647440i	0.214722	−	0.976675i	$-0.431115\pi$
$197$	16.2669	−	9.08725i	1.15897	−	0.647440i	0.944248	+	0.329235i	$0.106791\pi$
$198$	32.6561	+	15.8893i	2.32077	+	1.12920i
$199$	−15.3146	+	2.18181i	−1.08563	+	0.154664i	−0.660764	−	0.750594i	$-0.729768\pi$
$199$	−15.3146	+	2.18181i	−1.08563	+	0.154664i	−0.424863	+	0.905258i	$0.639678\pi$
$200$	−1.98896	+	2.13492i	−0.140641	+	0.150962i
$201$	10.4966	+	42.7867i	0.740371	+	3.01794i
$202$	6.29694	+	0.715941i	0.443051	+	0.0503735i
$203$	−4.06342	+	2.91725i	−0.285196	+	0.204751i
$204$	1.15479	−	0.0654370i	0.0808513	−	0.00458151i
$205$	3.52621	−	12.7971i	0.246281	−	0.893790i
$206$	2.24860	−	0.794480i	0.156667	−	0.0553541i
$207$	−6.19713	−	48.3943i	−0.430730	−	3.36363i
$208$	−0.258182	−	1.19797i	−0.0179017	−	0.0830643i
$209$	−1.51885	+	11.8609i	−0.105061	+	0.820438i
$210$	4.27022	−	0.363449i	0.294673	−	0.0250804i
$211$	2.96916	+	0.863532i	0.204405	+	0.0594480i	0.379879	−	0.925036i	$-0.375966\pi$
$211$	2.96916	+	0.863532i	0.204405	+	0.0594480i	−0.175474	+	0.984484i	$0.556146\pi$
$212$	−0.587661	+	3.15826i	−0.0403607	+	0.216910i
$213$	37.6090	−	7.55009i	2.57693	−	0.517323i
$214$	−6.53867	+	7.86756i	−0.446974	+	0.537815i
$215$	0.293881	−	0.959622i	0.0200425	−	0.0654457i
$216$	−7.94858	+	12.9093i	−0.540833	+	0.878368i
$217$	0.380443	+	0.325395i	0.0258262	+	0.0220892i
$218$	−16.5776	−	3.81900i	−1.12277	−	0.258655i
$219$	26.9981	−	30.6758i	1.82436	−	2.07288i
$220$	−2.91104	−	6.20450i	−0.196262	−	0.418307i
$221$	0.395851	−	0.178936i	0.0266278	−	0.0120365i
$222$	−9.17600			−0.615853
$223$	−13.7038	−	5.93346i	−0.917674	−	0.397334i
$223$	−13.7038	−	5.93346i	−0.917674	−	0.397334i
$224$	−0.910254			−0.0608189
$225$	20.3302	−	9.18981i	1.35534	−	0.612654i
$226$	4.69603	+	10.0090i	0.312375	+	0.665786i
$227$	10.0741	−	11.4464i	0.668639	−	0.759721i	−0.313148	−	0.949704i	$-0.601384\pi$
$227$	10.0741	−	11.4464i	0.668639	−	0.759721i	0.981787	+	0.189983i	$0.0608432\pi$
$228$	−8.00510	−	1.84415i	−0.530151	−	0.122132i
$229$	0.245438	+	0.209924i	0.0162190	+	0.0138722i	0.658058	−	0.752967i	$-0.271378\pi$
$229$	0.245438	+	0.209924i	0.0162190	+	0.0138722i	−0.641839	+	0.766839i	$0.721828\pi$
$230$	−4.82745	+	7.84027i	−0.318312	+	0.516972i
$231$	4.13067	−	13.4881i	0.271778	−	0.887449i
$232$	−3.51245	+	4.22630i	−0.230604	+	0.277470i
$233$	13.5416	−	2.71849i	0.887137	−	0.178095i	0.268039	−	0.963408i	$-0.413624\pi$
$233$	13.5416	−	2.71849i	0.887137	−	0.178095i	0.619098	+	0.785314i	$0.287498\pi$
$234$	−1.71412	+	9.21221i	−0.112056	+	0.602221i
$235$	14.5866	+	4.24228i	0.951527	+	0.276736i
$236$	12.3503	−	1.05117i	0.803936	−	0.0684250i
$237$	1.05995	−	8.27729i	0.0688511	−	0.537668i
$238$	−0.0679804	−	0.315430i	−0.00440652	−	0.0204463i
$239$	3.02464	+	23.6198i	0.195648	+	1.52784i	0.730511	+	0.682901i	$0.239282\pi$
$239$	3.02464	+	23.6198i	0.195648	+	1.52784i	−0.534863	+	0.844939i	$0.679637\pi$
$240$	4.43925	−	1.56849i	0.286553	−	0.101245i
$241$	4.71285	−	17.1036i	0.303581	−	1.10174i	−0.639395	−	0.768879i	$-0.720815\pi$
$241$	4.71285	−	17.1036i	0.303581	−	1.10174i	0.942976	−	0.332861i	$-0.108014\pi$
$242$	−11.5399	+	0.653917i	−0.741812	+	0.0420354i
$243$	33.3645	−	23.9534i	2.14033	−	1.53661i
$244$	−5.72514	−	0.650929i	−0.366514	−	0.0416715i
$245$	2.12173	+	8.64871i	0.135553	+	0.552546i
$246$	20.4602	−	21.9617i	1.30450	−	1.40022i
$247$	−3.05449	+	0.435159i	−0.194352	+	0.0276885i
$248$	0.494543	+	0.240627i	0.0314035	+	0.0152799i
$249$	−33.0489	+	18.4622i	−2.09439	+	1.17000i
$250$	−11.0565	−	2.87890i	−0.699276	−	0.182077i
$251$	1.72831	+	5.64352i	0.109090	+	0.356216i	0.993977	−	0.109590i	$-0.0349538\pi$
$251$	1.72831	+	5.64352i	0.109090	+	0.356216i	−0.884887	+	0.465806i	$0.845765\pi$
$252$	6.42079	+	2.68623i	0.404472	+	0.169217i
$253$	18.0210	+	24.3660i	1.13297	+	1.53188i
$254$	−2.11899	+	13.5024i	−0.132957	+	0.847216i
$255$	0.875064	+	1.42119i	0.0547987	+	0.0889987i
$256$	−0.967733	+	0.251978i	−0.0604833	+	0.0157486i
$257$	16.3832	−	15.7020i	1.02196	−	0.979466i	0.0221625	−	0.999754i	$-0.492945\pi$
$257$	16.3832	−	15.7020i	1.02196	−	0.979466i	0.999794	+	0.0202882i	$0.00645838\pi$
$258$	1.59331	−	1.61602i	0.0991951	−	0.100609i
$259$	0.396873	+	2.52891i	0.0246605	+	0.157139i
$260$	1.34383	−	1.14938i	0.0833406	−	0.0712816i
$261$	37.2484	−	19.4462i	2.30562	−	1.20369i
$262$	−4.75556	−	8.23686i	−0.293799	−	0.508875i
$263$	14.4900	−	25.0974i	0.893492	−	1.54757i	0.0578329	−	0.998326i	$-0.481581\pi$
$263$	14.4900	−	25.0974i	0.893492	−	1.54757i	0.835659	−	0.549248i	$-0.185086\pi$
$264$	0.657719	−	15.4832i	0.0404798	−	0.952927i
$265$	−4.41264	+	1.41996i	−0.271066	+	0.0872274i
$266$	−0.162018	+	2.28598i	−0.00993398	+	0.140162i
$267$	−0.0108017	−	0.0137719i	−0.000661053	−	0.000842826i
$268$	10.7409	−	8.18159i	0.656106	−	0.499770i
$269$	1.66468	−	4.93263i	0.101497	−	0.300748i	−0.884740	−	0.466085i	$-0.845664\pi$
$269$	1.66468	−	4.93263i	0.101497	−	0.300748i	0.986237	+	0.165337i	$0.0528713\pi$
$270$	−21.8405	−	1.23761i	−1.32917	−	0.0753187i
$271$	−14.4270	+	9.16712i	−0.876378	+	0.556863i	−0.896554	−	0.442934i	$-0.853938\pi$
$271$	−14.4270	+	9.16712i	−0.876378	+	0.556863i	0.0201759	+	0.999796i	$0.493577\pi$
$272$	−0.159591	−	0.316530i	−0.00967663	−	0.0191925i
$273$	3.63825	+	0.102999i	0.220197	+	0.00623381i
$274$	4.65768	+	4.72406i	0.281381	+	0.285391i
$275$	−8.24075	+	11.1422i	−0.496936	+	0.671901i
$276$	−17.8813	+	10.6640i	−1.07633	+	0.641895i
$277$	−18.3015	+	3.13811i	−1.09963	+	0.188550i	−0.690077	−	0.723736i	$-0.742423\pi$
$277$	−18.3015	+	3.13811i	−1.09963	+	0.188550i	−0.409553	+	0.912286i	$0.634315\pi$
$278$	−3.59561	+	8.26400i	−0.215650	+	0.495642i
$279$	−2.77832	−	3.15678i	−0.166334	−	0.188992i
$280$	−0.624280	−	1.15562i	−0.0373078	−	0.0690617i
$281$	−29.0362	+	0.822019i	−1.73215	+	0.0490376i	−0.880206	−	0.474592i	$-0.842596\pi$
$281$	−29.0362	+	0.822019i	−1.73215	+	0.0490376i	−0.851946	+	0.523630i	$0.824578\pi$
$282$	24.7994	+	23.7683i	1.47678	+	1.41538i
$283$	−0.494158	−	0.276053i	−0.0293747	−	0.0164097i	0.472939	−	0.881095i	$-0.343193\pi$
$283$	−0.494158	−	0.276053i	−0.0293747	−	0.0164097i	−0.502313	+	0.864686i	$0.667518\pi$
$284$	−6.72044	−	9.64612i	−0.398785	−	0.572392i
$285$	−3.14888	−	11.4277i	−0.186524	−	0.676921i
$286$	−1.86118	−	5.51489i	−0.110054	−	0.326102i
$287$	−6.93758	−	4.68899i	−0.409512	−	0.276782i
$288$	7.56984	+	1.07844i	0.446057	+	0.0635477i
$289$	−13.1288	+	10.6008i	−0.772285	+	0.623576i
$290$	−7.77450	−	1.56074i	−0.456534	−	0.0916501i
$291$	−13.5590	+	33.7430i	−0.794845	+	1.97805i
$292$	−11.9220	−	3.83643i	−0.697683	−	0.224510i
$293$	−8.96039	+	24.2618i	−0.523472	+	1.41739i	0.352858	+	0.935677i	$0.385210\pi$
$293$	−8.96039	+	24.2618i	−0.523472	+	1.41739i	−0.876330	+	0.481711i	$0.840015\pi$
$294$	−4.79771	+	19.5567i	−0.279808	+	1.14057i
$295$	9.80472	+	14.9585i	0.570853	+	0.870919i
$296$	1.12199	+	2.57874i	0.0652144	+	0.149886i
$297$	−30.5841	+	65.1860i	−1.77467	+	3.78248i
$298$	0.329006	−	23.2476i	0.0190588	−	1.34670i
$299$	−4.82580	+	6.15277i	−0.279083	+	0.355824i
$300$	−7.05709	−	6.39049i	−0.407441	−	0.368955i
$301$	−0.514288	−	0.369223i	−0.0296431	−	0.0212816i
$302$	15.3617	+	9.76105i	0.883968	+	0.561685i
$303$	−2.04504	+	20.5771i	−0.117485	+	1.18212i
$304$	0.460558	+	2.47518i	0.0264148	+	0.141961i
$305$	−3.10008	−	7.71484i	−0.177510	−	0.441750i
$306$	0.191626	+	2.70372i	0.0109545	+	0.154561i
$307$	4.21297	−	3.81502i	0.240447	−	0.217735i	−0.542120	−	0.840301i	$-0.682378\pi$
$307$	4.21297	−	3.81502i	0.240447	−	0.217735i	0.782567	+	0.622566i	$0.213910\pi$
$308$	−4.29564	+	0.488400i	−0.244767	+	0.0278292i
$309$	2.69584	+	7.29945i	0.153361	+	0.415251i
$310$	0.0336812	+	0.792882i	0.00191296	+	0.0450327i
$311$	14.6811	+	7.66451i	0.832488	+	0.434614i	0.824847	−	0.565357i	$-0.191261\pi$
$311$	14.6811	+	7.66451i	0.832488	+	0.434614i	0.00764118	+	0.999971i	$0.497568\pi$
$312$	3.89650	−	0.897642i	0.220596	−	0.0508190i
$313$	−3.64051	+	6.73906i	−0.205774	+	0.380914i	−0.961853	−	0.273565i	$-0.911797\pi$
$313$	−3.64051	+	6.73906i	−0.205774	+	0.380914i	0.756080	+	0.654480i	$0.227112\pi$
$314$	−5.25919	+	10.4310i	−0.296793	+	0.588654i
$315$	0.993237	+	9.99388i	0.0559626	+	0.563091i
$316$	−2.45578	+	0.714224i	−0.138148	+	0.0401782i
$317$	−15.5672	+	6.00099i	−0.874343	+	0.337049i	−0.754938	−	0.655796i	$-0.772333\pi$
$317$	−15.5672	+	6.00099i	−0.874343	+	0.337049i	−0.119405	+	0.992846i	$0.538099\pi$
$318$	−10.3311	−	1.77144i	−0.579338	−	0.0993374i
$319$	−14.3082	+	21.8292i	−0.801105	+	1.22220i
$320$	−0.983602	−	1.05578i	−0.0549850	−	0.0590200i
$321$	−25.9701	−	20.9694i	−1.44951	−	1.17040i
$322$	3.71238	+	4.46687i	0.206883	+	0.248929i
$323$	−0.823327	+	0.344451i	−0.0458111	+	0.0191657i
$324$	−22.7828	−	13.5871i	−1.26571	−	0.754840i
$325$	−3.33644	−	1.28616i	−0.185072	−	0.0713433i
$326$	2.51430	+	0.213999i	0.139254	+	0.0118523i
$327$	11.6942	−	54.2612i	0.646690	−	3.00065i
$328$	−8.67367	−	3.06460i	−0.478924	−	0.169214i
$329$	5.47795	−	7.86273i	0.302009	−	0.433486i
$330$	20.1080	−	9.78385i	1.10691	−	0.538583i
$331$	29.1072	−	19.6730i	1.59987	−	1.08133i	0.654147	−	0.756368i	$-0.273028\pi$
$331$	29.1072	−	19.6730i	1.59987	−	1.08133i	0.945728	−	0.324959i	$-0.105351\pi$
$332$	9.22951	+	7.03031i	0.506535	+	0.385838i
$333$	−0.304289	−	21.5011i	−0.0166750	−	1.17825i
$334$	−6.34013	−	2.86592i	−0.346916	−	0.156816i
$335$	17.7535	+	8.02507i	0.969976	+	0.438457i
$336$	−0.0420285	−	2.96974i	−0.00229284	−	0.162012i
$337$	2.72734	+	2.07747i	0.148568	+	0.113167i	0.677587	−	0.735443i	$-0.263026\pi$
$337$	2.72734	+	2.07747i	0.148568	+	0.113167i	−0.529019	+	0.848610i	$0.677440\pi$
$338$	−9.52638	+	6.43871i	−0.518167	+	0.350220i
$339$	−32.4378	+	15.7831i	−1.76178	+	0.857220i
$340$	0.292402	−	0.419696i	0.0158577	−	0.0227612i
$341$	2.46294	+	0.870211i	0.133376	+	0.0471246i
$342$	4.05573	−	18.8186i	0.219309	−	1.01760i
$343$	11.9462	+	1.01677i	0.645032	+	0.0549003i
$344$	−0.648972	−	0.250171i	−0.0349902	−	0.0134883i
$345$	−25.8021	−	15.3877i	−1.38914	−	0.828447i
$346$	10.0114	−	4.18839i	0.538214	−	0.225169i
$347$	17.2175	+	20.7167i	0.924286	+	1.11213i	0.993420	+	0.114526i	$0.0365349\pi$
$347$	17.2175	+	20.7167i	0.924286	+	1.11213i	−0.0691343	+	0.997607i	$0.522024\pi$
$348$	−13.9507	−	11.2644i	−0.747833	−	0.603833i
$349$	−3.90365	−	4.19011i	−0.208958	−	0.224292i	0.618551	−	0.785745i	$-0.287720\pi$
$349$	−3.90365	−	4.19011i	−0.208958	−	0.224292i	−0.827509	+	0.561453i	$0.810243\pi$
$350$	−1.45600	+	2.22134i	−0.0778264	+	0.118735i
$351$	−18.3112	−	3.13977i	−0.977378	−	0.167588i
$352$	−4.43169	+	1.70837i	−0.236210	+	0.0910562i
$353$	9.97718	−	2.90170i	0.531032	−	0.154442i	−0.00285827	−	0.999996i	$-0.500910\pi$
$353$	9.97718	−	2.90170i	0.531032	−	0.154442i	0.533890	+	0.845554i	$0.320730\pi$
$354$	3.99971	+	40.2448i	0.212582	+	2.13898i
$355$	7.63726	−	15.1476i	0.405344	−	0.803951i
$356$	−0.00254956	+	0.00471956i	−0.000135126	+	0.000250136i
$357$	1.02596	−	0.236353i	0.0542998	−	0.0125091i
$358$	12.4484	+	6.49892i	0.657921	+	0.343478i
$359$	−0.0799571	−	1.88225i	−0.00421997	−	0.0993414i	−0.999973	−	0.00728199i	$-0.997682\pi$
$359$	−0.0799571	−	1.88225i	−0.00421997	−	0.0993414i	0.995754	−	0.0920594i	$-0.0293450\pi$
$360$	3.82248	+	10.3500i	0.201462	+	0.545493i
$361$	−12.5803	+	1.43034i	−0.662123	+	0.0752812i
$362$	−15.8685	+	14.3696i	−0.834028	+	0.755247i
$363$	−2.66625	−	37.6191i	−0.139942	−	1.97449i
$364$	−0.415919	−	1.03505i	−0.0218001	−	0.0542516i
$365$	−3.30590	−	17.7669i	−0.173039	−	0.929960i
$366$	1.85934	−	18.7085i	0.0971891	−	0.977910i
$367$	−13.2958	−	8.44834i	−0.694036	−	0.441000i	0.141861	−	0.989887i	$-0.454691\pi$
$367$	−13.2958	−	8.44834i	−0.694036	−	0.441000i	−0.835897	+	0.548887i	$0.815052\pi$
$368$	5.18333	+	3.72126i	0.270200	+	0.193984i
$369$	52.1388	+	47.2139i	2.71424	+	2.45786i
$370$	−2.50437	+	3.19301i	−0.130196	+	0.165997i
$371$	−0.0413794	+	2.92387i	−0.00214831	+	0.151800i
$372$	−0.762222	+	1.62457i	−0.0395193	+	0.0842303i
$373$	−9.84894	−	22.6364i	−0.509959	−	1.17207i	−0.960238	−	0.279181i	$-0.909937\pi$
$373$	−9.84894	−	22.6364i	−0.509959	−	1.17207i	0.450280	−	0.892887i	$-0.351324\pi$
$374$	−0.922972	−	1.40813i	−0.0477257	−	0.0728126i
$375$	8.88200	−	36.2052i	0.458664	−	1.86963i
$376$	3.64729	−	9.87565i	0.188095	−	0.509298i
$377$	−6.41068	−	2.06292i	−0.330167	−	0.106246i
$378$	−5.14527	+	12.8045i	−0.264644	+	0.658592i
$379$	−1.83759	−	0.368900i	−0.0943907	−	0.0189491i	0.149401	−	0.988777i	$-0.452265\pi$
$379$	−1.83759	−	0.368900i	−0.0943907	−	0.0189491i	−0.243792	+	0.969828i	$0.578391\pi$
$380$	−2.82652	+	2.28226i	−0.144997	+	0.117077i
$381$	−44.1499	−	6.28984i	−2.26187	−	0.322238i
$382$	7.06387	+	4.77435i	0.361419	+	0.244277i
$383$	−5.06558	−	15.0099i	−0.258839	−	0.766969i	−0.995843	−	0.0910816i	$-0.970968\pi$
$383$	−5.06558	−	15.0099i	−0.258839	−	0.766969i	0.737005	−	0.675888i	$-0.236240\pi$
$384$	−0.866770	−	3.14563i	−0.0442322	−	0.160525i
$385$	−3.56613	−	5.11862i	−0.181747	−	0.260869i
$386$	6.51724	+	3.64075i	0.331719	+	0.185309i
$387$	3.83947	+	3.67984i	0.195171	+	0.187057i
$388$	11.1407	−	0.315397i	0.565586	−	0.0160118i
$389$	−4.49040	−	8.31233i	−0.227673	−	0.421452i	0.740384	−	0.672184i	$-0.234644\pi$
$389$	−4.49040	−	8.31233i	−0.227673	−	0.421452i	−0.968056	+	0.250733i	$0.919328\pi$
$390$	3.81195	+	4.33121i	0.193025	+	0.219320i
$391$	−0.902423	+	2.07409i	−0.0456375	+	0.104891i
$392$	6.08267	−	1.04298i	0.307221	−	0.0526783i
$393$	26.6535	−	15.8955i	1.34449	−	0.801821i
$394$	11.0798	−	14.9809i	0.558194	−	0.754728i
$395$	−2.59100	−	2.62793i	−0.130367	−	0.132225i
$396$	36.3020	+	1.02772i	1.82424	+	0.0516447i
$397$	2.14484	+	4.25405i	0.107647	+	0.213504i	0.940345	−	0.340223i	$-0.110502\pi$
$397$	2.14484	+	4.25405i	0.107647	+	0.213504i	−0.832698	+	0.553727i	$0.813205\pi$
$398$	−13.0565	+	8.29625i	−0.654461	+	0.415853i
$399$	−7.46556	−	0.423042i	−0.373745	−	0.0211786i
$400$	−0.933024	+	2.76466i	−0.0466512	+	0.138233i
$401$	11.0276	−	8.39994i	0.550691	−	0.419473i	−0.293150	−	0.956066i	$-0.594704\pi$
$401$	11.0276	−	8.39994i	0.550691	−	0.419473i	0.843841	+	0.536593i	$0.180289\pi$
$402$	27.1887	+	34.6649i	1.35605	+	1.72893i
$403$	−0.0476489	+	0.672296i	−0.00237356	+	0.0334895i
$404$	6.03285	−	1.94133i	0.300145	−	0.0965849i
$405$	1.62453	−	38.2426i	0.0807234	−	1.90029i
$406$	−2.50109	+	4.33201i	−0.124127	+	0.214994i
$407$	6.67849	+	11.5675i	0.331041	+	0.573379i
$408$	1.02532	−	0.535287i	0.0507610	−	0.0265006i
$409$	−14.4394	+	12.3501i	−0.713984	+	0.610674i	−0.930796	−	0.365539i	$-0.880885\pi$
$409$	−14.4394	+	12.3501i	−0.713984	+	0.610674i	0.216812	+	0.976213i	$0.430434\pi$
$410$	−2.05796	−	13.1136i	−0.101636	−	0.647632i
$411$	−15.1974	+	15.4140i	−0.749631	+	0.760315i
$412$	1.72174	−	1.65015i	0.0848240	−	0.0812972i
$413$	10.9185	−	2.84296i	0.537264	−	0.139893i
$414$	−25.5807	−	41.5456i	−1.25722	−	2.04186i
$415$	−2.59554	+	16.5390i	−0.127410	+	0.811868i
$416$	−0.728708	−	0.985279i	−0.0357279	−	0.0483073i
$417$	−27.1276	−	11.3492i	−1.32844	−	0.555774i
$418$	3.50151	+	11.4336i	0.171265	+	0.559238i
$419$	21.2397	+	5.53038i	1.03763	+	0.270177i	0.731519	−	0.681821i	$-0.238812\pi$
$419$	21.2397	+	5.53038i	1.03763	+	0.270177i	0.306106	+	0.951997i	$0.400974\pi$
$420$	3.74144	−	2.09009i	0.182563	−	0.101986i
$421$	17.7368	+	8.63011i	0.864438	+	0.420606i	0.815885	−	0.578215i	$-0.196250\pi$
$421$	17.7368	+	8.63011i	0.864438	+	0.420606i	0.0485539	+	0.998821i	$0.484539\pi$
$422$	3.06127	−	0.436126i	0.149020	−	0.0212303i
$423$	−54.8712	+	58.8978i	−2.66793	+	2.86371i
$424$	0.765398	+	3.11995i	0.0371710	+	0.151518i
$425$	−1.02772	−	0.116848i	−0.0498516	−	0.00566796i
$426$	31.1605	−	22.3711i	1.50973	−	1.08388i
$427$	−5.23650	+	0.296731i	−0.253412	+	0.0143598i
$428$	−2.71757	+	9.86243i	−0.131359	+	0.476718i
$429$	17.9066	−	6.32680i	0.864538	−	0.305461i
$430$	−0.127477	−	0.995485i	−0.00614748	−	0.0480065i
$431$	−7.92606	−	36.7771i	−0.381785	−	1.77149i	−0.604500	−	0.796605i	$-0.706627\pi$
$431$	−7.92606	−	36.7771i	−0.381785	−	1.77149i	0.222715	−	0.974884i	$-0.428508\pi$
$432$	−1.92561	+	15.0374i	−0.0926460	+	0.723486i
$433$	−8.88216	+	0.755984i	−0.426850	+	0.0363303i	−0.296262	−	0.955107i	$-0.595740\pi$
$433$	−8.88216	+	0.755984i	−0.426850	+	0.0363303i	−0.130587	+	0.991437i	$0.541686\pi$
$434$	0.480701	+	0.139804i	0.0230744	+	0.00671081i
$435$	4.73302	−	25.4366i	0.226931	−	1.21959i
$436$	−16.6790	+	3.34834i	−0.798779	+	0.160356i
$437$	10.2680	−	12.3548i	0.491186	−	0.591012i
$438$	11.9660	−	39.0732i	0.571759	−	1.86699i
$439$	6.20472	−	10.0771i	0.296135	−	0.480954i	−0.668800	−	0.743442i	$-0.733192\pi$
$439$	6.20472	−	10.0771i	0.296135	−	0.480954i	0.964935	+	0.262488i	$0.0845432\pi$
$440$	−5.20826	−	4.45465i	−0.248294	−	0.212367i
$441$	−45.9841	−	10.5934i	−2.18972	−	0.504448i
$442$	0.287007	−	0.326103i	0.0136515	−	0.0155111i
$443$	14.6947	+	31.3199i	0.698168	+	1.48805i	0.864844	+	0.502041i	$0.167417\pi$
$443$	14.6947	+	31.3199i	0.698168	+	1.48805i	−0.166676	+	0.986012i	$0.553303\pi$
$444$	−8.36143	+	3.77960i	−0.396816	+	0.179372i
$445$	−0.00774034			−0.000366927
$446$	−14.9313	+	0.237878i	−0.707017	+	0.0112638i
$447$	75.8614			3.58812
$448$	−0.829450	+	0.374935i	−0.0391878	+	0.0177140i
$449$	−16.2958	−	34.7324i	−0.769047	−	1.63912i	−0.769105	−	0.639123i	$-0.779298\pi$
$449$	−16.2958	−	34.7324i	−0.769047	−	1.63912i	5.75138e−5	−	1.00000i	$-0.499982\pi$
$450$	14.7401	−	16.7480i	0.694856	−	0.789510i
$451$	−42.5768	−	9.80848i	−2.00486	−	0.461863i
$452$	8.40186	+	7.18615i	0.395190	+	0.338008i
$453$	−31.1365	+	50.5689i	−1.46292	+	2.37593i
$454$	4.46500	−	14.5798i	0.209553	−	0.684262i
$455$	1.02882	−	1.23791i	0.0482316	−	0.0580339i
$456$	−8.05408	+	1.61687i	−0.377167	+	0.0757170i
$457$	−0.378933	+	2.03650i	−0.0177258	+	0.0952634i	−0.990834	−	0.135085i	$-0.956869\pi$
$457$	−0.378933	+	2.03650i	−0.0177258	+	0.0952634i	0.973108	+	0.230348i	$0.0739865\pi$
$458$	0.310118	+	0.0901928i	0.0144909	+	0.00421443i
$459$	−5.35471	+	0.455753i	−0.249936	+	0.0212727i
$460$	−1.16949	+	9.13271i	−0.0545277	+	0.425815i
$461$	4.66487	+	21.6451i	0.217265	+	1.00811i	0.946213	+	0.323543i	$0.104874\pi$
$461$	4.66487	+	21.6451i	0.217265	+	1.00811i	−0.728949	+	0.684568i	$0.759991\pi$
$462$	−1.79176	−	13.9921i	−0.0833603	−	0.650973i
$463$	−12.1474	+	4.29195i	−0.564537	+	0.199464i	−0.600130	−	0.799903i	$-0.704884\pi$
$463$	−12.1474	+	4.29195i	−0.564537	+	0.199464i	0.0355926	+	0.999366i	$0.488668\pi$
$464$	−1.45983	+	5.29791i	−0.0677707	+	0.245949i
$465$	−2.58525	+	0.146495i	−0.119888	+	0.00679356i
$466$	11.2197	−	8.05496i	0.519743	−	0.373139i
$467$	17.3824	+	1.97632i	0.804363	+	0.0914534i	0.505482	−	0.862837i	$-0.331315\pi$
$467$	17.3824	+	1.97632i	0.804363	+	0.0914534i	0.298881	+	0.954290i	$0.403387\pi$
$468$	2.23256	+	9.10048i	0.103200	+	0.420670i
$469$	8.37773	−	8.99252i	0.386848	−	0.415236i
$470$	15.0392	−	2.14256i	0.693704	−	0.0988289i
$471$	−34.2743	−	16.6767i	−1.57927	−	0.768420i
$472$	10.8210	−	6.04495i	0.498075	−	0.278242i
$473$	−3.19684	−	0.832391i	−0.146991	−	0.0382734i
$474$	−2.44357	−	7.97910i	−0.112237	−	0.366492i
$475$	6.77698	+	2.83525i	0.310949	+	0.130090i
$476$	−0.191872	−	0.259428i	−0.00879443	−	0.0118909i
$477$	3.80823	−	24.2664i	0.174367	−	1.11108i
$478$	12.4852	+	20.2772i	0.571058	+	0.927458i
$479$	−10.2371	+	2.66554i	−0.467746	+	0.121792i	−0.478382	−	0.878152i	$-0.658777\pi$
$479$	−10.2371	+	2.66554i	−0.467746	+	0.121792i	0.0106360	+	0.999943i	$0.496614\pi$
$480$	3.39911	−	3.25778i	0.155148	−	0.148697i
$481$	−2.41963	+	2.45412i	−0.110326	+	0.111898i
$482$	−2.75051	−	17.5265i	−0.125282	−	0.798311i
$483$	−14.4019	+	12.3180i	−0.655310	+	0.560490i
$484$	−10.2461	+	5.34916i	−0.465733	+	0.243144i
$485$	8.04107	+	13.9275i	0.365126	+	0.632417i
$486$	20.5363	−	35.5699i	0.931544	−	1.61348i
$487$	0.926364	−	21.8073i	0.0419775	−	0.988184i	−0.847384	−	0.530980i	$-0.821824\pi$
$487$	0.926364	−	21.8073i	0.0419775	−	0.988184i	0.889362	−	0.457204i	$-0.151149\pi$
$488$	−5.48503	+	1.76505i	−0.248295	+	0.0798999i
$489$	−0.582088	+	8.21289i	−0.0263229	+	0.371400i
$490$	5.49580	+	7.00701i	0.248275	+	0.316544i
$491$	−15.2314	+	11.6021i	−0.687385	+	0.523596i	−0.890171	−	0.455627i	$-0.849415\pi$
$491$	−15.2314	+	11.6021i	−0.687385	+	0.523596i	0.202785	+	0.979223i	$0.435001\pi$
$492$	9.59790	−	28.4397i	0.432707	−	1.28216i
$493$	−1.94491	−	0.110210i	−0.0875943	−	0.00496360i
$494$	−2.60409	+	1.65468i	−0.117164	+	0.0744474i
$495$	23.5922	+	46.7924i	1.06039	+	2.10316i
$496$	0.549756	+	0.0155637i	0.0246848	+	0.000698831i
$497$	−7.51321	−	7.62030i	−0.337014	−	0.341817i
$498$	−22.5105	+	30.4362i	−1.00872	+	1.36388i
$499$	30.5239	−	18.2037i	1.36644	−	0.814910i	0.372842	−	0.927895i	$-0.378383\pi$
$499$	30.5239	−	18.2037i	1.36644	−	0.814910i	0.993597	+	0.112984i	$0.0360410\pi$
$500$	−11.2608	+	1.93087i	−0.503600	+	0.0863509i
$501$	9.05743	−	20.8172i	0.404656	−	0.930045i
$502$	3.89945	+	4.43064i	0.174041	+	0.197749i
$503$	−8.29294	−	15.3513i	−0.369764	−	0.684481i	0.625654	−	0.780101i	$-0.284832\pi$
$503$	−8.29294	−	15.3513i	−0.369764	−	0.684481i	−0.995418	+	0.0956195i	$0.969517\pi$
$504$	6.95727	−	0.196962i	0.309901	−	0.00877337i
$505$	6.60215	+	6.32765i	0.293792	+	0.281577i
$506$	26.4576	+	14.7801i	1.17619	+	0.657057i
$507$	−21.4464	−	30.7829i	−0.952467	−	1.36712i
$508$	3.63077	+	13.1766i	0.161089	+	0.584616i
$509$	−4.39418	−	13.0204i	−0.194768	−	0.577121i	0.805103	−	0.593135i	$-0.202110\pi$
$509$	−4.39418	−	13.0204i	−0.194768	−	0.577121i	−0.999872	+	0.0160134i	$0.994903\pi$
$510$	1.38278	+	0.934593i	0.0612303	+	0.0413845i
$511$	−11.2861	−	1.60789i	−0.499269	−	0.0711287i
$512$	−0.778036	+	0.628220i	−0.0343846	+	0.0277637i
$513$	37.4215	+	7.51244i	1.65220	+	0.331682i
$514$	8.46116	−	21.0564i	0.373206	−	0.928758i
$515$	3.27579	+	1.05413i	0.144349	+	0.0464504i
$516$	0.786229	−	2.12885i	0.0346118	−	0.0937172i
$517$	11.9133	−	48.5618i	0.523948	−	2.13574i
$518$	1.40330	+	2.14095i	0.0616576	+	0.0940677i
$519$	14.1270	+	32.4690i	0.620108	+	1.42523i
$520$	0.751101	−	1.60087i	0.0329380	−	0.0702029i
$521$	−0.559017	+	39.5002i	−0.0244910	+	1.73053i	0.488866	+	0.872359i	$0.337411\pi$
$521$	−0.559017	+	39.5002i	−0.0244910	+	1.73053i	−0.513357	+	0.858175i	$0.671598\pi$
$522$	25.9319	−	33.0626i	1.13501	−	1.44711i
$523$	−17.9957	−	16.2959i	−0.786899	−	0.712570i	0.175420	−	0.984494i	$-0.443872\pi$
$523$	−17.9957	−	16.2959i	−0.786899	−	0.712570i	−0.962319	+	0.271924i	$0.912340\pi$
$524$	−7.72617	−	5.54685i	−0.337519	−	0.242315i
$525$	−7.31442	−	4.64768i	−0.319227	−	0.202841i
$526$	2.86605	−	28.8380i	0.124966	−	1.25739i
$527$	0.0356641	+	0.191669i	0.00155355	+	0.00834925i
$528$	−5.77823	−	14.3797i	−0.251465	−	0.625795i
$529$	−1.25239	−	17.6704i	−0.0544516	−	0.768278i
$530$	−3.43604	+	3.11148i	−0.149252	+	0.135154i
$531$	−94.1685	+	10.7066i	−4.08657	+	0.464629i
$532$	0.793960	+	2.14978i	0.0344225	+	0.0932048i
$533$	−0.478454	−	11.2632i	−0.0207241	−	0.487862i
$534$	−0.0155155	−	0.00810011i	−0.000671420	−	0.000350526i
$535$	−14.3847	+	3.31383i	−0.621907	+	0.143269i
$536$	6.41743	−	11.8795i	0.277191	−	0.513116i
$537$	−20.6282	+	40.9136i	−0.890172	+	1.76555i
$538$	−0.514855	−	5.18043i	−0.0221970	−	0.223344i
$539$	28.1455	−	8.18566i	1.21231	−	0.352581i
$540$	−20.4115	+	7.86840i	−0.878371	+	0.338602i
$541$	45.0225	+	7.71989i	1.93567	+	0.331904i	0.999791	−	0.0204210i	$-0.00650067\pi$
$541$	45.0225	+	7.71989i	1.93567	+	0.331904i	0.935878	+	0.352325i	$0.114609\pi$
$542$	−9.37036	+	14.2958i	−0.402491	+	0.614059i
$543$	−47.6139	−	51.1080i	−2.04331	−	2.19325i
$544$	−0.275803	−	0.222695i	−0.0118250	−	0.00954799i
$545$	−15.6899	−	18.8786i	−0.672081	−	0.808671i
$546$	3.35770	−	1.40474i	0.143696	−	0.0601174i
$547$	4.16881	+	2.48618i	0.178245	+	0.106301i	0.598563	−	0.801076i	$-0.295739\pi$
$547$	4.16881	+	2.48618i	0.178245	+	0.106301i	−0.420317	+	0.907377i	$0.638081\pi$
$548$	6.19005	+	2.38619i	0.264426	+	0.101933i
$549$	43.8993	+	3.73638i	1.87358	+	0.159465i
$550$	−2.91971	+	13.5475i	−0.124497	+	0.577667i
$551$	13.0451	+	4.60913i	0.555741	+	0.196356i
$552$	−11.9014	+	17.0826i	−0.506559	+	0.727085i
$553$	−2.09336	+	1.01856i	−0.0890187	+	0.0433134i
$554$	−15.3842	+	10.3979i	−0.653614	+	0.441766i
$555$	−10.5330	−	8.02318i	−0.447099	−	0.340565i
$556$	0.127532	+	9.01143i	0.00540856	+	0.382170i
$557$	10.7943	+	4.87932i	0.457368	+	0.206743i	0.627403	−	0.778695i	$-0.284118\pi$
$557$	10.7943	+	4.87932i	0.457368	+	0.206743i	−0.170035	+	0.985438i	$0.554388\pi$
$558$	−3.83196	−	1.73216i	−0.162220	−	0.0733281i
$559$	−0.0120614	−	0.852260i	−0.000510143	−	0.0360467i
$560$	−1.04486	−	0.795895i	−0.0441536	−	0.0336327i
$561$	4.55145	−	3.07625i	0.192162	−	0.129879i
$562$	−26.1200	+	12.7091i	−1.10180	+	0.536100i
$563$	−6.48536	+	9.30871i	−0.273325	+	0.392315i	−0.933373	−	0.358909i	$-0.883149\pi$
$563$	−6.48536	+	9.30871i	−0.273325	+	0.392315i	0.660047	+	0.751224i	$0.270536\pi$
$564$	32.3881	+	11.4434i	1.36378	+	0.481855i
$565$	−3.36101	+	15.5952i	−0.141399	+	0.656093i
$566$	−0.563998	−	0.0480033i	−0.0237066	−	0.00201773i
$567$	−22.5300	−	8.68506i	−0.946172	−	0.364738i
$568$	−10.0971	−	6.02167i	−0.423665	−	0.252663i
$569$	25.8211	−	10.8026i	1.08248	−	0.452870i	0.228694	−	0.973498i	$-0.426554\pi$
$569$	25.8211	−	10.8026i	1.08248	−	0.452870i	0.853784	+	0.520628i	$0.174302\pi$
$570$	−7.57645	−	9.11625i	−0.317343	−	0.381838i
$571$	10.2336	+	8.26302i	0.428261	+	0.345796i	0.818090	−	0.575091i	$-0.195033\pi$
$571$	10.2336	+	8.26302i	0.428261	+	0.345796i	−0.389829	+	0.920887i	$0.627466\pi$
$572$	−3.96755	−	4.25870i	−0.165892	−	0.178065i
$573$	−15.2503	+	23.2666i	−0.637091	+	0.971976i
$574$	−8.25312	−	1.41514i	−0.344479	−	0.0590668i
$575$	17.3722	−	6.69678i	0.724470	−	0.279275i
$576$	7.34207	−	2.13532i	0.305919	−	0.0889717i
$577$	2.86288	+	28.8061i	0.119183	+	1.19921i	0.853753	+	0.520678i	$0.174321\pi$
$577$	2.86288	+	28.8061i	0.119183	+	1.19921i	−0.734570	+	0.678533i	$0.762616\pi$
$578$	−7.59689	+	15.0675i	−0.315989	+	0.626727i
$579$	−11.5772	+	21.4308i	−0.481130	+	0.890635i
$580$	−7.72721	+	1.78013i	−0.320855	+	0.0739158i
$581$	9.36185	+	4.88751i	0.388395	+	0.202768i
$582$	1.54339	+	36.3325i	0.0639754	+	1.50603i
$583$	5.28606	+	14.3129i	0.218926	+	0.592780i
$584$	−12.4439	+	1.41483i	−0.514933	+	0.0585462i
$585$	−10.0225	+	9.07575i	−0.414377	+	0.375236i
$586$	1.82849	+	25.7988i	0.0755342	+	1.06574i
$587$	−16.1978	−	40.3098i	−0.668555	−	1.66376i	−0.745314	−	0.666714i	$-0.767700\pi$
$587$	−16.1978	−	40.3098i	−0.668555	−	1.66376i	0.0767586	−	0.997050i	$-0.475543\pi$
$588$	3.68360	+	19.7968i	0.151909	+	0.816405i
$589$	0.136938	−	1.37787i	0.00564245	−	0.0567740i
$590$	15.0958	+	9.59206i	0.621483	+	0.394899i
$591$	49.3874	+	35.4567i	2.03153	+	1.45849i
$592$	2.08458	+	1.88767i	0.0856756	+	0.0775828i
$593$	−15.7044	+	20.0227i	−0.644901	+	0.822234i	−0.993355	−	0.115093i	$-0.963284\pi$
$593$	−15.7044	+	20.0227i	−0.644901	+	0.822234i	0.348453	+	0.937326i	$0.386707\pi$
$594$	−1.01892	+	71.9970i	−0.0418068	+	2.95407i
$595$	0.197768	−	0.421516i	0.00810770	−	0.0172805i
$596$	−9.27593	−	21.3194i	−0.379957	−	0.873277i
$597$	−27.6697	−	42.2141i	−1.13244	−	1.72771i
$598$	−1.86307	+	7.59434i	−0.0761865	+	0.310555i
$599$	−10.7205	+	29.0275i	−0.438027	+	1.18603i	0.507833	+	0.861455i	$0.330447\pi$
$599$	−10.7205	+	29.0275i	−0.438027	+	1.18603i	−0.945860	+	0.324575i	$0.894779\pi$
$600$	−9.06287	−	2.91637i	−0.369990	−	0.119060i
$601$	0.0319590	−	0.0795330i	0.00130363	−	0.00324422i	−0.927236	−	0.374478i	$-0.877822\pi$
$601$	0.0319590	−	0.0795330i	0.00130363	−	0.00324422i	0.928539	+	0.371234i	$0.121065\pi$
$602$	−0.620717	−	0.124610i	−0.0252985	−	0.00507873i
$603$	−80.3248	+	64.8578i	−3.27108	+	2.64121i
$604$	18.0186	+	2.56703i	0.733168	+	0.104451i
$605$	−13.8182	−	9.33946i	−0.561789	−	0.379703i
$606$	6.61222	+	19.5928i	0.268603	+	0.795901i
$607$	2.15724	+	7.82894i	0.0875598	+	0.317767i	0.994668	−	0.103131i	$-0.0328862\pi$
$607$	2.15724	+	7.82894i	0.0875598	+	0.317767i	−0.907108	+	0.420898i	$0.861715\pi$
$608$	1.43920	+	2.06575i	0.0583673	+	0.0837770i
$609$	−14.2488	−	7.95987i	−0.577391	−	0.322550i
$610$	−6.00263	−	5.75305i	−0.243039	−	0.232934i
$611$	12.8962	−	0.365094i	0.521724	−	0.0147701i
$612$	1.28828	+	2.38477i	0.0520756	+	0.0963988i
$613$	−21.7507	−	24.7136i	−0.878502	−	0.998172i	−0.999984	−	0.00557811i	$-0.998224\pi$
$613$	−21.7507	−	24.7136i	−0.878502	−	0.998172i	0.121483	−	0.992594i	$-0.461235\pi$
$614$	2.26757	−	5.21169i	0.0915116	−	0.210327i
$615$	42.6884	−	7.31967i	1.72136	−	0.295157i
$616$	−3.71314	+	2.21442i	−0.149606	+	0.0892216i
$617$	18.0451	−	24.3986i	0.726470	−	0.982252i	−0.273324	−	0.961922i	$-0.588123\pi$
$617$	18.0451	−	24.3986i	0.726470	−	0.982252i	0.999793	−	0.0203296i	$-0.00647155\pi$
$618$	5.46318	+	5.54105i	0.219761	+	0.222894i
$619$	−15.4105	−	0.436276i	−0.619402	−	0.0175354i	−0.282795	−	0.959180i	$-0.591262\pi$
$619$	−15.4105	−	0.436276i	−0.619402	−	0.0175354i	−0.336608	+	0.941645i	$0.609280\pi$
$620$	0.357280	+	0.708623i	0.0143487	+	0.0284590i
$621$	81.6460	−	51.8789i	3.27634	−	2.08183i
$622$	16.5348	+	0.936960i	0.662987	+	0.0375687i
$623$	−0.00156134	+	0.00462642i	−6.25536e−5	+	0.000185353i
$624$	3.18086	−	2.42293i	0.127336	−	0.0969948i
$625$	−1.17065	−	1.49255i	−0.0468260	−	0.0597021i
$626$	−0.541509	+	7.64036i	−0.0216431	+	0.305370i
$627$	−37.1410	+	11.9517i	−1.48327	+	0.477306i
$628$	−0.495789	+	11.6713i	−0.0197841	+	0.465734i
$629$	−0.498453	+	0.863345i	−0.0198746	+	0.0344238i
$630$	5.02156	+	8.69759i	0.200064	+	0.346520i
$631$	−28.1837	+	14.7138i	−1.12197	+	0.585746i	−0.919322	−	0.393505i	$-0.871262\pi$
$631$	−28.1837	+	14.7138i	−1.12197	+	0.585746i	−0.202652	+	0.979251i	$0.564956\pi$
$632$	−1.94359	+	1.66236i	−0.0773118	+	0.0661252i
$633$	1.56422	+	9.96738i	0.0621722	+	0.396168i
$634$	−11.7135	+	11.8804i	−0.465202	+	0.471833i
$635$	−14.2384	+	13.6464i	−0.565033	+	0.541540i
$636$	−10.1436	+	2.64119i	−0.402221	+	0.104730i
$637$	3.96531	+	6.44007i	0.157111	+	0.255165i
$638$	−4.04654	+	25.7850i	−0.160204	+	1.02084i
$639$	53.4530	+	72.2732i	2.11457	+	2.85908i
$640$	−1.33116	−	0.556912i	−0.0526189	−	0.0220139i
$641$	6.21215	+	20.2848i	0.245365	+	0.801201i	0.990884	+	0.134717i	$0.0430125\pi$
$641$	6.21215	+	20.2848i	0.245365	+	0.801201i	−0.745519	+	0.666484i	$0.767798\pi$
$642$	−32.3020	−	8.41079i	−1.27486	−	0.331947i
$643$	5.41568	−	3.02538i	0.213573	−	0.119309i	−0.377246	−	0.926113i	$-0.623129\pi$
$643$	5.41568	−	3.02538i	0.213573	−	0.119309i	0.590819	+	0.806804i	$0.298805\pi$
$644$	5.22274	+	2.54120i	0.205805	+	0.100137i
$645$	3.24192	−	0.461862i	0.127650	−	0.0181858i
$646$	−0.608359	+	0.653002i	−0.0239356	+	0.0256920i
$647$	−6.63121	−	27.0305i	−0.260700	−	1.06268i	−0.943315	−	0.331900i	$-0.892310\pi$
$647$	−6.63121	−	27.0305i	−0.260700	−	1.06268i	0.682615	−	0.730778i	$-0.260843\pi$
$648$	−26.3569	−	2.99669i	−1.03540	−	0.117721i
$649$	47.8225	−	34.3332i	1.87720	−	1.34769i
$650$	−3.57003	+	0.202299i	−0.140028	+	0.00793480i
$651$	−0.433921	+	1.57476i	−0.0170067	+	0.0617197i
$652$	2.37925	−	0.840643i	0.0931787	−	0.0329221i
$653$	−6.28793	−	49.1034i	−0.246066	−	1.92156i	−0.369540	−	0.929215i	$-0.620485\pi$
$653$	−6.28793	−	49.1034i	−0.246066	−	1.92156i	0.123474	−	0.992348i	$-0.460597\pi$
$654$	−11.6942	−	54.2612i	−0.457279	−	2.12178i
$655$	1.74322	−	13.6130i	0.0681132	−	0.531906i
$656$	−9.16601	+	0.780143i	−0.357873	+	0.0304595i
$657$	91.9527	+	26.7429i	3.58742	+	1.04334i
$658$	1.75300	−	9.42112i	0.0683390	−	0.367274i
$659$	−15.0679	+	3.02492i	−0.586964	+	0.117834i	−0.481282	−	0.876566i	$-0.659829\pi$
$659$	−15.0679	+	3.02492i	−0.586964	+	0.117834i	−0.105682	+	0.994400i	$0.533702\pi$
$660$	14.2930	−	17.1978i	0.556354	−	0.669424i
$661$	7.80589	−	25.4889i	0.303614	−	0.991404i	−0.665832	−	0.746101i	$-0.731923\pi$
$661$	7.80589	−	25.4889i	0.303614	−	0.991404i	0.969447	−	0.245303i	$-0.0788874\pi$
$662$	18.4199	−	29.9159i	0.715912	−	1.16271i
$663$	1.07717	+	0.921312i	0.0418340	+	0.0357808i
$664$	11.3060	+	2.60457i	0.438757	+	0.101077i
$665$	−2.18476	+	2.48237i	−0.0847212	+	0.0962620i
$666$	−9.13361	−	19.4671i	−0.353920	−	0.754334i
$667$	31.9521	−	14.4432i	1.23719	−	0.559245i
$668$	−6.95778			−0.269205
$669$	−1.46550	−	48.7029i	−0.0566594	−	1.88296i
$670$	19.4830			0.752694
$671$	−24.9377	+	11.2725i	−0.962709	+	0.435172i
$672$	−1.26154	−	2.68880i	−0.0486648	−	0.103723i
$673$	−14.6668	+	16.6647i	−0.565363	+	0.642377i	−0.961170	−	0.275957i	$-0.911005\pi$
$673$	−14.6668	+	16.6647i	−0.565363	+	0.642377i	0.395807	+	0.918334i	$0.370465\pi$
$674$	3.34095	+	0.769658i	0.128688	+	0.0296461i
$675$	33.6163	+	28.7522i	1.29389	+	1.10667i
$676$	−6.02860	+	9.79106i	−0.231869	+	0.376579i
$677$	0.280521	−	0.915998i	0.0107813	−	0.0352047i	−0.950614	−	0.310375i	$-0.899545\pi$
$677$	0.280521	−	0.915998i	0.0107813	−	0.0352047i	0.961395	+	0.275171i	$0.0887344\pi$
$678$	−23.0572	+	27.7432i	−0.885505	+	1.06547i
$679$	9.94652	−	1.99678i	0.381713	−	0.0766295i
$680$	0.0935714	−	0.502880i	0.00358830	−	0.0192846i
$681$	47.7732	+	13.8941i	1.83067	+	0.532421i
$682$	2.60274	−	0.221526i	0.0996641	−	0.00848266i
$683$	4.59586	−	35.8897i	0.175856	−	1.37328i	−0.627887	−	0.778304i	$-0.716080\pi$
$683$	4.59586	−	35.8897i	0.175856	−	1.37328i	0.803743	−	0.594977i	$-0.202839\pi$
$684$	−4.05573	−	18.8186i	−0.155075	−	0.719549i
$685$	1.21590	+	9.49517i	0.0464573	+	0.362792i
$686$	11.3045	−	3.99413i	0.431608	−	0.152497i
$687$	−0.279938	+	1.01594i	−0.0106803	+	0.0387604i
$688$	−0.694408	+	0.0393492i	−0.0264741	+	0.00150017i
$689$	−3.19799	+	2.29593i	−0.121834	+	0.0874679i
$690$	−29.8498	−	3.39382i	−1.13636	−	0.129201i
$691$	4.60881	+	18.7867i	0.175328	+	0.714679i	0.990737	+	0.135794i	$0.0433587\pi$
$691$	4.60881	+	18.7867i	0.175328	+	0.714679i	−0.815409	+	0.578885i	$0.803488\pi$
$692$	7.39742	−	7.94027i	0.281208	−	0.301844i
$693$	32.7268	−	4.66244i	1.24319	−	0.177111i
$694$	24.2224	+	11.7858i	0.919468	+	0.447381i
$695$	−11.3531	+	6.34222i	−0.430647	+	0.240574i
$696$	−17.3520	−	4.51812i	−0.657727	−	0.171259i
$697$	−0.954887	−	3.11803i	−0.0361689	−	0.118104i
$698$	−5.28303	−	2.21023i	−0.199966	−	0.0836586i
$699$	26.7976	+	36.2328i	1.01358	+	1.37045i
$700$	−0.411775	+	2.62387i	−0.0155636	+	0.0991731i
$701$	9.18999	+	14.9255i	0.347101	+	0.563728i	0.977077	−	0.212887i	$-0.0682865\pi$
$701$	9.18999	+	14.9255i	0.347101	+	0.563728i	−0.629976	+	0.776615i	$0.716935\pi$
$702$	−17.9789	+	4.68135i	−0.678571	+	0.176686i
$703$	5.11166	−	4.89913i	0.192790	−	0.184774i
$704$	−3.33460	+	3.38213i	−0.125678	+	0.127469i
$705$	7.68457	+	48.9669i	0.289418	+	1.84420i
$706$	7.89628	−	6.75373i	0.297180	−	0.254180i
$707$	5.11379	−	2.66974i	0.192324	−	0.100406i
$708$	20.2215	+	35.0247i	0.759971	+	1.31631i
$709$	0.735575	−	1.27405i	0.0276251	−	0.0478481i	−0.851882	−	0.523733i	$-0.824539\pi$
$709$	0.735575	−	1.27405i	0.0276251	−	0.0478481i	0.879507	+	0.475885i	$0.157872\pi$
$710$	0.719973	−	16.9487i	0.0270201	−	0.636074i
$711$	18.6155	−	5.99035i	0.698136	−	0.224656i
$712$	−0.000379235		0.00535077i	−1.42124e−5		0.000200528i
$713$	−2.16575	−	2.76128i	−0.0811080	−	0.103411i
$714$	0.837534	−	0.637967i	0.0313439	−	0.0238753i
$715$	2.68562	−	7.95779i	0.100436	−	0.297604i
$716$	14.0203	+	0.794471i	0.523963	+	0.0296908i
$717$	−65.5787	+	41.6696i	−2.44908	+	1.55618i
$718$	−0.848161	−	1.68223i	−0.0316531	−	0.0627801i
$719$	8.74871	+	0.247678i	0.326272	+	0.00923682i	0.191055	−	0.981579i	$-0.438809\pi$
$719$	8.74871	+	0.247678i	0.326272	+	0.00923682i	0.135217	+	0.990816i	$0.456827\pi$
$720$	7.74633	+	7.85673i	0.288689	+	0.292803i
$721$	1.29083	−	1.74532i	0.0480730	−	0.0649989i
$722$	−10.8744	+	6.48523i	−0.404703	+	0.241355i
$723$	57.0539	−	9.78287i	2.12186	−	0.363829i
$724$	−8.54096	+	19.6302i	−0.317422	+	0.729550i
$725$	10.5937	+	12.0368i	0.393440	+	0.447034i
$726$	−17.9249	−	33.1814i	−0.665256	−	1.23148i
$727$	23.6545	−	0.669662i	0.877295	−	0.0248364i	0.413219	−	0.910632i	$-0.364404\pi$
$727$	23.6545	−	0.669662i	0.877295	−	0.0248364i	0.464076	+	0.885795i	$0.346386\pi$
$728$	−0.805338	−	0.771854i	−0.0298478	−	0.0286068i
$729$	47.5216	+	26.5472i	1.76006	+	0.983228i
$730$	−10.3306	−	14.8280i	−0.382353	−	0.548808i
$731$	−0.0654961	−	0.237694i	−0.00242246	−	0.00879145i
$732$	−6.01178	−	17.8136i	−0.222202	−	0.658410i
$733$	−14.7639	−	9.97866i	−0.545317	−	0.368570i	0.256124	−	0.966644i	$-0.417555\pi$
$733$	−14.7639	−	9.97866i	−0.545317	−	0.368570i	−0.801441	+	0.598074i	$0.795933\pi$
$734$	−15.5954	−	2.22181i	−0.575637	−	0.0820084i
$735$	−22.6069	+	18.2538i	−0.833867	+	0.673301i
$736$	6.25599	+	1.25590i	0.230599	+	0.0462932i
$737$	23.9109	−	59.5046i	0.880769	−	2.19188i
$738$	66.9579	+	21.5466i	2.46475	+	0.793142i
$739$	−1.46057	+	3.95473i	−0.0537278	+	0.145477i	−0.962108	−	0.272667i	$-0.912094\pi$
$739$	−1.46057	+	3.95473i	−0.0537278	+	0.145477i	0.908381	+	0.418144i	$0.137319\pi$
$740$	−0.966849	+	3.94112i	−0.0355421	+	0.144878i
$741$	−5.51868	−	8.41955i	−0.202734	−	0.309300i
$742$	1.16664	+	2.68136i	0.0428287	+	0.0984357i
$743$	−17.4106	+	37.1085i	−0.638735	+	1.36138i	0.277496	+	0.960727i	$0.410496\pi$
$743$	−17.4106	+	37.1085i	−0.638735	+	1.36138i	−0.916230	+	0.400652i	$0.868784\pi$
$744$	−0.0253937	+	1.79432i	−0.000930977	+	0.0657829i
$745$	20.7046	−	26.3978i	0.758557	−	0.967142i
$746$	−18.2986	−	16.5701i	−0.669959	−	0.606676i
$747$	−72.0643	−	51.7371i	−2.63670	−	1.89296i
$748$	−1.42105	−	0.902953i	−0.0519586	−	0.0330152i
$749$	−0.920921	+	9.26624i	−0.0336497	+	0.338581i
$750$	−6.81946	−	36.6498i	−0.249011	−	1.33826i
$751$	−12.6221	−	31.4113i	−0.460586	−	1.14621i	−0.960038	−	0.279871i	$-0.909708\pi$
$751$	−12.6221	−	31.4113i	−0.460586	−	1.14621i	0.499451	−	0.866342i	$-0.333535\pi$
$752$	−0.744278	−	10.5013i	−0.0271410	−	0.382943i
$753$	−14.2751	+	12.9267i	−0.520213	+	0.471075i
$754$	−6.69132	+	0.760781i	−0.243683	+	0.0277060i
$755$	9.09871	+	24.6363i	0.331136	+	0.896607i
$756$	0.585672	+	13.7872i	0.0213007	+	0.501434i
$757$	−0.797424	−	0.416309i	−0.0289829	−	0.0151310i	0.448241	−	0.893913i	$-0.352051\pi$
$757$	−0.797424	−	0.416309i	−0.0289829	−	0.0151310i	−0.477224	+	0.878782i	$0.658357\pi$
$758$	−1.82642	+	0.420754i	−0.0663384	+	0.0152825i
$759$	−46.9991	+	87.0014i	−1.70596	+	3.15795i
$760$	−1.63554	+	3.24390i	−0.0593273	+	0.117669i
$761$	−2.55268	−	25.6848i	−0.0925344	−	0.931075i	−0.925752	−	0.378130i	$-0.876567\pi$
$761$	−2.55268	−	25.6848i	−0.0925344	−	0.931075i	0.833218	−	0.552945i	$-0.186496\pi$
$762$	−42.8214	+	12.4539i	−1.55126	+	0.451158i
$763$	−14.4487	+	5.56979i	−0.523077	+	0.201640i
$764$	8.40336	+	1.44090i	0.304023	+	0.0521300i
$765$	−2.14408	+	3.27110i	−0.0775192	+	0.118267i
$766$	−10.7985	−	11.5909i	−0.390165	−	0.418797i
$767$	11.8181	+	9.54248i	0.426728	+	0.344559i
$768$	−2.08551	−	2.50936i	−0.0752545	−	0.0905489i
$769$	28.3589	−	11.8643i	1.02265	−	0.427839i	0.190083	−	0.981768i	$-0.439124\pi$
$769$	28.3589	−	11.8643i	1.02265	−	0.427839i	0.832564	+	0.553929i	$0.186872\pi$
$770$	−5.35792	−	3.19533i	−0.193086	−	0.115152i
$771$	69.0880	+	26.6326i	2.48814	+	0.959151i
$772$	7.43832	+	0.633094i	0.267711	+	0.0227856i
$773$	4.28515	−	19.8832i	0.154126	−	0.715148i	−0.832747	−	0.553653i	$-0.813233\pi$
$773$	4.28515	−	19.8832i	0.154126	−	0.715148i	0.986874	−	0.161495i	$-0.0516315\pi$
$774$	5.01437	+	1.77169i	0.180238	+	0.0636820i
$775$	0.917344	−	1.31670i	0.0329520	−	0.0472973i
$776$	10.0219	−	4.87629i	0.359764	−	0.175048i
$777$	−6.92012	+	4.67718i	−0.248258	+	0.167793i
$778$	−7.51564	−	5.72482i	−0.269449	−	0.205245i
$779$	0.327738	+	23.1580i	0.0117424	+	0.829722i
$780$	5.25759	+	2.37658i	0.188252	+	0.0850952i
$781$	−50.8808	−	22.9996i	−1.82066	−	0.822990i
$782$	0.0320079	+	2.26168i	0.00114460	+	0.0808776i
$783$	66.2737	+	50.4821i	2.36843	+	1.80408i
$784$	5.11310	−	3.45585i	0.182611	−	0.123423i
$785$	−15.1574	+	7.37507i	−0.540991	+	0.263227i
$786$	17.7401	−	25.4630i	0.632767	−	0.908236i
$787$	32.5468	+	11.4995i	1.16017	+	0.409914i	0.842715	−	0.538360i	$-0.180956\pi$
$787$	32.5468	+	11.4995i	1.16017	+	0.409914i	0.317454	+	0.948274i	$0.397172\pi$
$788$	3.92560	−	18.2148i	0.139844	−	0.648877i
$789$	94.2172	+	8.01907i	3.35422	+	0.285486i
$790$	−3.44344	−	1.32741i	−0.122512	−	0.0472270i
$791$	8.64329	+	5.15465i	0.307320	+	0.183278i
$792$	33.5027	−	14.0163i	1.19047	−	0.498049i
$793$	−4.51330	−	5.43056i	−0.160272	−	0.192845i
$794$	3.70669	+	2.99294i	0.131546	+	0.106216i
$795$	−10.3100	−	11.0665i	−0.365657	−	0.392490i
$796$	−8.48018	+	12.9377i	−0.300572	+	0.458566i
$797$	−1.12074	−	0.192171i	−0.0396987	−	0.00680703i	0.149117	−	0.988820i	$-0.452357\pi$
$797$	−1.12074	−	0.192171i	−0.0396987	−	0.00680703i	−0.188816	+	0.982013i	$0.560465\pi$
$798$	−6.97708	+	2.68958i	−0.246986	+	0.0952103i
$799$	3.58343	−	1.04218i	0.126773	−	0.0368697i
$800$	0.288568	+	2.90355i	0.0102024	+	0.102656i
$801$	0.0184656	−	0.0366243i	0.000652450	−	0.00129406i
$802$	6.58870	−	12.1965i	0.232655	−	0.430675i
$803$	−57.9657	+	13.3536i	−2.04557	+	0.471240i
$804$	39.0536	+	20.3886i	1.37731	+	0.719050i
$805$	0.355698	+	8.37342i	0.0125367	+	0.295124i
$806$	0.233501	+	0.632242i	0.00822471	+	0.0222698i
$807$	16.8776	−	1.91892i	0.594119	−	0.0675494i
$808$	4.69767	−	4.25394i	0.165263	−	0.149653i
$809$	0.0610289	+	0.861079i	0.00214566	+	0.0302739i	0.998456	−	0.0555525i	$-0.0176920\pi$
$809$	0.0610289	+	0.861079i	0.00214566	+	0.0302739i	−0.996310	+	0.0858264i	$0.972647\pi$
$810$	−14.2719	−	35.5169i	−0.501462	−	1.24794i
$811$	2.66836	+	14.3405i	0.0936986	+	0.503564i	0.997187	+	0.0749516i	$0.0238802\pi$
$811$	2.66836	+	14.3405i	0.0936986	+	0.503564i	−0.903489	+	0.428612i	$0.859003\pi$
$812$	−0.494701	+	4.97765i	−0.0173606	+	0.174681i
$813$	−47.0734	−	29.9111i	−1.65093	−	1.04903i
$814$	10.8503	+	7.78975i	0.380303	+	0.273030i
$815$	2.69901	+	2.44407i	0.0945422	+	0.0856119i
$816$	0.713817	−	0.910100i	0.0249886	−	0.0318599i
$817$	−0.0247794	+	1.75091i	−0.000866920	+	0.0612566i
$818$	−8.07059	+	17.2014i	−0.282182	+	0.601433i
$819$	3.40293	+	7.82115i	0.118908	+	0.273293i
$820$	−7.27677	−	11.1018i	−0.254116	−	0.387690i
$821$	−2.88316	+	11.7525i	−0.100623	+	0.410165i	−0.999613	−	0.0278037i	$-0.991149\pi$
$821$	−2.88316	+	11.7525i	−0.100623	+	0.410165i	0.898990	+	0.437968i	$0.144302\pi$
$822$	−7.49924	+	20.3055i	−0.261566	+	0.708234i
$823$	34.9835	+	11.2574i	1.21945	+	0.392410i	0.844964	−	0.534824i	$-0.179622\pi$
$823$	34.9835	+	11.2574i	1.21945	+	0.392410i	0.374483	+	0.927234i	$0.377820\pi$
$824$	0.889198	−	2.21285i	0.0309767	−	0.0770884i
$825$	−44.3340	−	8.90013i	−1.54351	−	0.309863i
$826$	8.77823	−	7.08793i	0.305434	−	0.246620i
$827$	18.5281	+	2.63962i	0.644286	+	0.0917886i	0.455509	−	0.890231i	$-0.349457\pi$
$827$	18.5281	+	2.63962i	0.644286	+	0.0917886i	0.188778	+	0.982020i	$0.439547\pi$
$828$	−40.4225	−	27.3208i	−1.40478	−	0.949465i
$829$	14.4482	+	42.8116i	0.501806	+	1.48691i	0.838292	+	0.545221i	$0.183554\pi$
$829$	14.4482	+	42.8116i	0.501806	+	1.48691i	−0.336486	+	0.941688i	$0.609238\pi$
$830$	4.44731	+	16.1399i	0.154369	+	0.560225i
$831$	−34.6340	−	49.7116i	−1.20144	−	1.72448i
$832$	−1.06986	−	0.597658i	−0.0370906	−	0.0207201i
$833$	1.57942	+	1.51375i	0.0547235	+	0.0524483i
$834$	−29.3942	+	0.832156i	−1.01784	+	0.0288152i
$835$	−4.77185	−	8.83333i	−0.165137	−	0.305690i
$836$	7.90021	+	8.97638i	0.273235	+	0.310455i
$837$	3.32647	−	7.64542i	0.114980	−	0.264264i
$838$	21.6322	−	3.70921i	0.747271	−	0.128132i
$839$	18.9370	−	11.2936i	0.653777	−	0.389897i	−0.146766	−	0.989171i	$-0.546887\pi$
$839$	18.9370	−	11.2936i	0.653777	−	0.389897i	0.800544	+	0.599274i	$0.204544\pi$
$840$	2.54839	−	3.44565i	0.0879279	−	0.118886i
$841$	0.841775	+	0.853773i	0.0290267	+	0.0294404i
$842$	19.7170	+	0.558193i	0.679494	+	0.0192366i
$843$	−42.6698	−	84.6306i	−1.46963	−	2.91483i
$844$	2.60988	−	1.65835i	0.0898357	−	0.0570828i
$845$	−16.5649	−	0.938666i	−0.569851	−	0.0322911i
$846$	−25.7401	+	76.2709i	−0.884963	+	2.62225i
$847$	−8.36954	+	6.37526i	−0.287581	+	0.219056i
$848$	1.98257	+	2.52772i	0.0680816	+	0.0868024i
$849$	0.130571	−	1.84228i	0.00448120	−	0.0632269i
$850$	−0.984615	+	0.316843i	−0.0337720	+	0.0108676i
$851$	0.761584	−	17.9283i	0.0261068	−	0.614573i
$852$	19.1797	−	33.2202i	0.657086	−	1.13811i
$853$	−8.73290	−	15.1258i	−0.299009	−	0.517898i	0.676901	−	0.736074i	$-0.263323\pi$
$853$	−8.73290	−	15.1258i	−0.299009	−	0.517898i	−0.975909	+	0.218176i	$0.929989\pi$
$854$	−4.64943	+	2.42731i	−0.159100	+	0.0830609i
$855$	21.1099	−	18.0554i	0.721942	−	0.617481i
$856$	1.58602	+	10.1063i	0.0542091	+	0.345426i
$857$	23.6802	−	24.0177i	0.808899	−	0.820428i	−0.177616	−	0.984100i	$-0.556838\pi$
$857$	23.6802	−	24.0177i	0.808899	−	0.820428i	0.986515	+	0.163672i	$0.0523339\pi$
$858$	13.7110	−	13.1409i	0.468085	−	0.448623i
$859$	20.4459	−	5.32370i	0.697606	−	0.181642i	0.113761	−	0.993508i	$-0.463710\pi$
$859$	20.4459	−	5.32370i	0.697606	−	0.181642i	0.583844	+	0.811866i	$0.301548\pi$
$860$	−0.526202	−	0.854606i	−0.0179433	−	0.0291418i
$861$	4.23588	−	26.9914i	0.144358	−	0.919866i
$862$	−22.3710	−	30.2476i	−0.761958	−	1.03024i
$863$	−0.977141	−	0.408801i	−0.0332623	−	0.0139158i	0.369256	−	0.929328i	$-0.379613\pi$
$863$	−0.977141	−	0.408801i	−0.0332623	−	0.0139158i	−0.402518	+	0.915412i	$0.631865\pi$
$864$	4.43924	+	14.4956i	0.151026	+	0.493152i
$865$	15.1540	+	3.94580i	0.515253	+	0.134161i
$866$	−7.78229	+	4.34745i	−0.264453	+	0.147732i
$867$	−49.5091	−	24.0894i	−1.68142	−	0.818120i
$868$	0.495614	−	0.0706079i	0.0168222	−	0.00239659i
$869$	−8.28016	+	8.88779i	−0.280885	+	0.301498i
$870$	−6.16452	−	25.1281i	−0.208997	−	0.851923i
$871$	16.4405	+	1.86923i	0.557066	+	0.0633366i
$872$	−13.8192	+	9.92121i	−0.467977	+	0.335974i
$873$	−85.0829	+	4.82129i	−2.87962	+	0.163176i
$874$	4.26754	−	15.4875i	0.144352	−	0.523872i
$875$	−9.80576	+	3.46459i	−0.331495	+	0.117125i
$876$	−5.19050	−	40.5334i	−0.175371	−	1.36950i
$877$	−0.829593	−	3.84932i	−0.0280134	−	0.129982i	0.961386	−	0.275204i	$-0.0887455\pi$
$877$	−0.829593	−	3.84932i	−0.0280134	−	0.129982i	−0.989399	+	0.145222i	$0.953610\pi$
$878$	1.50314	−	11.7383i	0.0507287	−	0.396147i
$879$	−84.0851	+	7.15670i	−2.83612	+	0.241390i
$880$	−6.58079	−	1.91392i	−0.221838	−	0.0645181i
$881$	3.60717	−	19.3860i	0.121529	−	0.653131i	−0.866539	−	0.499110i	$-0.833660\pi$
$881$	3.60717	−	19.3860i	0.121529	−	0.653131i	0.988068	−	0.154021i	$-0.0492224\pi$
$882$	−46.2654	+	9.28788i	−1.55784	+	0.312739i
$883$	21.6602	−	26.0623i	0.728924	−	0.877066i	−0.267325	−	0.963606i	$-0.586140\pi$
$883$	21.6602	−	26.0623i	0.728924	−	0.877066i	0.996248	+	0.0865402i	$0.0275811\pi$
$884$	0.127206	−	0.415373i	0.00427841	−	0.0139705i
$885$	−30.5975	+	49.6934i	−1.02852	+	1.67043i
$886$	26.2910	+	22.4868i	0.883262	+	0.755458i
$887$	16.7407	+	3.85657i	0.562097	+	0.129491i	0.496000	−	0.868322i	$-0.334801\pi$
$887$	16.7407	+	3.85657i	0.562097	+	0.129491i	0.0660962	+	0.997813i	$0.478946\pi$
$888$	−6.06235	+	6.88817i	−0.203439	+	0.231152i
$889$	5.28439	+	11.2630i	0.177233	+	0.377748i
$890$	−0.00705322	+	0.00318825i	−0.000236424	+	0.000106871i
$891$	−125.990			−4.22084
$892$	−13.5078	+	6.36698i	−0.452276	+	0.213182i
$893$	−26.5050			−0.886956
$894$	69.1271	−	31.2474i	2.31196	−	1.04507i
$895$	8.60690	+	18.3445i	0.287697	+	0.613188i
$896$	−0.601382	+	0.683303i	−0.0200908	+	0.0228275i
$897$	−24.8628	−	5.72768i	−0.830145	−	0.191242i
$898$	−29.1555	−	24.9369i	−0.972933	−	0.832154i
$899$	1.58462	−	2.57359i	0.0528502	−	0.0858341i
$900$	6.53308	−	21.3328i	0.217769	−	0.711092i
$901$	−0.727868	+	0.875796i	−0.0242488	+	0.0291770i
$902$	−42.8373	+	8.59968i	−1.42633	+	0.286338i
$903$	0.377885	−	2.03087i	0.0125752	−	0.0675830i
$904$	10.6160	+	3.08749i	0.353083	+	0.102688i
$905$	−30.7794	+	2.61971i	−1.02314	+	0.0870821i
$906$	−7.54308	+	58.9050i	−0.250602	+	1.95699i
$907$	−4.45073	−	20.6514i	−0.147784	−	0.685720i	−0.989349	−	0.145564i	$-0.953500\pi$
$907$	−4.45073	−	20.6514i	−0.147784	−	0.685720i	0.841565	−	0.540156i	$-0.181635\pi$
$908$	−1.93679	−	15.1246i	−0.0642745	−	0.501929i
$909$	−45.6903	+	16.1434i	−1.51545	+	0.535443i
$910$	0.427591	−	1.55179i	0.0141745	−	0.0514412i
$911$	−3.28232	+	0.185995i	−0.108748	+	0.00616231i	−0.110865	−	0.993835i	$-0.535362\pi$
$911$	−3.28232	+	0.185995i	−0.108748	+	0.00616231i	0.00211698	+	0.999998i	$0.499326\pi$
$912$	−6.67312	+	4.79083i	−0.220969	+	0.158640i
$913$	54.7523	+	6.22515i	1.81204	+	0.206022i
$914$	0.493541	+	2.01180i	0.0163249	+	0.0665444i
$915$	18.4924	−	19.8494i	0.611340	−	0.656202i
$916$	0.319739	−	0.0455518i	0.0105645	−	0.00150507i
$917$	−7.78491	−	3.78787i	−0.257080	−	0.125086i
$918$	−4.69164	+	2.62091i	−0.154847	+	0.0865028i
$919$	−33.2800	−	8.66544i	−1.09781	−	0.285846i	−0.341380	−	0.939926i	$-0.610894\pi$
$919$	−33.2800	−	8.66544i	−1.09781	−	0.285846i	−0.756426	+	0.654079i	$0.773056\pi$
$920$	2.69610	+	8.80370i	0.0888878	+	0.290249i
$921$	17.1080	+	7.15739i	0.563729	+	0.235844i
$922$	13.1664	+	17.8021i	0.433612	+	0.586282i
$923$	2.23363	−	14.2329i	0.0735209	−	0.468483i
$924$	−7.39608	−	12.0120i	−0.243313	−	0.395166i
$925$	7.94096	−	2.06767i	0.261097	−	0.0679844i
$926$	−9.30119	+	8.91447i	−0.305656	+	0.292948i
$927$	−12.8026	+	12.9850i	−0.420491	+	0.426484i
$928$	0.851982	+	5.42891i	0.0279677	+	0.178213i
$929$	25.4246	−	21.7458i	0.834153	−	0.713455i	−0.126272	−	0.991996i	$-0.540301\pi$
$929$	25.4246	−	21.7458i	0.834153	−	0.713455i	0.960424	+	0.278540i	$0.0898506\pi$
$930$	−2.29541	+	1.19836i	−0.0752695	+	0.0392957i
$931$	−7.76879	−	13.4559i	−0.254612	−	0.441000i
$932$	6.90587	−	11.9613i	0.226209	−	0.391806i
$933$	−2.29342	+	53.9888i	−0.0750830	+	1.76751i
$934$	16.6534	−	5.35896i	0.544916	−	0.175351i
$935$	0.171757	−	2.42338i	0.00561705	−	0.0792530i
$936$	5.78287	+	7.37302i	0.189019	+	0.240995i
$937$	7.10306	−	5.41055i	0.232047	−	0.176755i	−0.483448	−	0.875373i	$-0.660616\pi$
$937$	7.10306	−	5.41055i	0.232047	−	0.176755i	0.715495	+	0.698618i	$0.246201\pi$
$938$	3.93000	−	11.6450i	0.128319	−	0.380224i
$939$	−24.9519	−	1.41392i	−0.814276	−	0.0461416i
$940$	12.8216	−	8.14701i	0.418194	−	0.265726i
$941$	−7.06967	−	14.0218i	−0.230465	−	0.457099i	0.747949	−	0.663756i	$-0.231039\pi$
$941$	−7.06967	−	14.0218i	−0.230465	−	0.457099i	−0.978413	+	0.206657i	$0.933742\pi$
$942$	−38.1008	−	1.07864i	−1.24139	−	0.0351440i
$943$	41.2111	+	41.7984i	1.34202	+	1.36114i
$944$	7.37045	−	9.96550i	0.239888	−	0.324350i
$945$	−17.1020	+	10.1992i	−0.556327	+	0.331780i
$946$	−3.25591	+	0.558282i	−0.105859	+	0.0181513i
$947$	−6.87995	+	15.8126i	−0.223568	+	0.513840i	−0.992022	−	0.126065i	$-0.959765\pi$
$947$	−6.87995	+	15.8126i	−0.223568	+	0.513840i	0.768454	+	0.639905i	$0.221026\pi$
$948$	−5.51325	−	6.26427i	−0.179062	−	0.203454i
$949$	−7.29477	−	13.5036i	−0.236798	−	0.438344i
$950$	7.34322	−	0.207888i	0.238245	−	0.00674477i
$951$	−39.3012	−	37.6672i	−1.27443	−	1.22144i
$952$	−0.281698	−	0.157366i	−0.00912988	−	0.00510026i
$953$	−24.0681	−	34.5460i	−0.779643	−	1.11905i	−0.989950	−	0.141418i	$-0.954834\pi$
$953$	−24.0681	−	34.5460i	−0.779643	−	1.11905i	0.210307	−	0.977635i	$-0.432554\pi$
$954$	−6.52520	−	23.6809i	−0.211261	−	0.766696i
$955$	3.93397	+	11.6568i	0.127300	+	0.377205i
$956$	19.7291	+	13.3345i	0.638083	+	0.431269i
$957$	−84.3113	−	12.0114i	−2.72540	−	0.388275i
$958$	−8.23042	+	6.64560i	−0.265913	+	0.214709i
$959$	5.92055	+	1.18856i	0.191185	+	0.0383807i
$960$	1.75548	−	4.36868i	0.0566579	−	0.140999i
$961$	29.2218	+	9.40339i	0.942639	+	0.303335i
$962$	−1.19398	+	3.23291i	−0.0384956	+	0.104233i
$963$	18.6369	−	75.9687i	0.600566	−	2.44806i
$964$	−9.72553	−	14.8377i	−0.313238	−	0.477891i
$965$	4.29767	+	9.87759i	0.138347	+	0.317971i
$966$	−8.04962	+	17.1567i	−0.258992	+	0.552008i
$967$	0.250918	−	17.7299i	0.00806898	−	0.570155i	−0.954366	−	0.298641i	$-0.903467\pi$
$967$	0.250918	−	17.7299i	0.00806898	−	0.570155i	0.962434	−	0.271514i	$-0.0875243\pi$
$968$	−7.13323	+	9.09470i	−0.229271	+	0.292315i
$969$	−2.15853	−	1.95464i	−0.0693421	−	0.0627922i
$970$	13.0640	+	9.37905i	0.419461	+	0.301143i
$971$	35.5135	+	22.5658i	1.13968	+	0.724169i	0.965464	−	0.260538i	$-0.0838998\pi$
$971$	35.5135	+	22.5658i	1.13968	+	0.724169i	0.174218	+	0.984707i	$0.444260\pi$
$972$	4.06196	−	40.8712i	0.130288	−	1.31094i
$973$	1.50068	+	8.06508i	0.0481095	+	0.258555i
$974$	−8.13833	−	20.2530i	−0.260769	−	0.648949i
$975$	−0.824843	−	11.6380i	−0.0264161	−	0.372715i
$976$	−4.27109	+	3.86765i	−0.136714	+	0.123800i
$977$	−56.8940	+	6.46866i	−1.82020	+	0.206951i	−0.955431	−	0.295216i	$-0.904609\pi$
$977$	−56.8940	+	6.46866i	−1.82020	+	0.206951i	−0.864771	+	0.502167i	$0.832536\pi$
$978$	2.85248	+	7.72358i	0.0912124	+	0.246973i
$979$	0.00108130	+	0.0254546i	3.45585e−5	+	0.000813533i
$980$	7.89413	+	4.12126i	0.252169	+	0.131649i
$981$	126.757	−	29.2011i	4.04703	−	0.932320i
$982$	−9.10040	+	16.8460i	−0.290405	+	0.537578i
$983$	−23.8190	+	47.2422i	−0.759709	+	1.50679i	0.0994269	+	0.995045i	$0.468299\pi$
$983$	−23.8190	+	47.2422i	−0.759709	+	1.50679i	−0.859136	+	0.511748i	$0.828998\pi$
$984$	−2.96846	−	29.8684i	−0.0946310	−	0.952171i
$985$	25.8171	−	7.50850i	0.822603	−	0.239241i
$986$	−1.81765	+	0.700684i	−0.0578858	+	0.0223143i
$987$	30.8177	+	5.28422i	0.980938	+	0.168199i
$988$	−1.69136	+	2.58042i	−0.0538094	+	0.0820940i
$989$	3.02517	+	3.24717i	0.0961949	+	0.103254i
$990$	40.7718	+	32.9209i	1.29581	+	1.04629i
$991$	−14.8987	−	17.9267i	−0.473274	−	0.569460i	0.477782	−	0.878479i	$-0.341441\pi$
$991$	−14.8987	−	17.9267i	−0.473274	−	0.569460i	−0.951056	+	0.309018i	$0.900000\pi$
$992$	0.507364	−	0.212263i	0.0161088	−	0.00673936i
$993$	98.4522	+	58.7145i	3.12429	+	1.86325i
$994$	−9.98506	−	3.84913i	−0.316707	−	0.122087i
$995$	−22.2412	−	1.89301i	−0.705094	−	0.0600123i
$996$	−7.97550	+	37.0064i	−0.252713	+	1.17259i
$997$	22.9343	+	8.10320i	0.726336	+	0.256631i	0.670605	−	0.741815i	$-0.266035\pi$
$997$	22.9343	+	8.10320i	0.726336	+	0.256631i	0.0557317	+	0.998446i	$0.482251\pi$
$998$	20.3161	−	29.1606i	0.643096	−	0.923062i
$999$	38.3370	−	18.6535i	1.21293	−	0.590169i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	446.2.g.b.53.9	✓	648
223.101	even	111	inner	446.2.g.b.101.9	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
446.2.g.b.53.9	✓	648	1.1	even	1	trivial
446.2.g.b.101.9	yes	648	223.101	even	111	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 446 = 2 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	446.g (of order \(111\), degree \(72\), minimal)

\(f(q)\)	\(=\)	\(q+(0.911228 - 0.411901i) q^{2} +(1.38592 + 2.95390i) q^{3} +(0.660675 - 0.750672i) q^{4} +(1.40613 + 0.323933i) q^{5} +(2.47960 + 2.12082i) q^{6} +(0.477253 - 0.775108i) q^{7} +(0.292823 - 0.956167i) q^{8} +(-4.88725 + 5.88051i) q^{9} +(1.41474 - 0.284011i) q^{10} +(0.868844 - 4.66942i) q^{11} +(3.13305 + 0.911197i) q^{12} +(1.22106 - 0.103928i) q^{13} +(0.115618 - 0.902881i) q^{14} +(0.991919 + 4.60252i) q^{15} +(-0.127018 - 0.991900i) q^{16} +(0.334237 - 0.118094i) q^{17} +(-2.03121 + 7.37155i) q^{18} +(-2.51363 + 0.142437i) q^{19} +(1.17217 - 0.841532i) q^{20} +(2.95102 + 0.335521i) q^{21} +(-1.13163 - 4.61279i) q^{22} +(-4.34950 + 4.66868i) q^{23} +(3.23025 - 0.460199i) q^{24} +(-2.62375 - 1.27663i) q^{25} +(1.06986 - 0.597658i) q^{26} +(-14.6710 - 3.82003i) q^{27} +(-0.266543 - 0.870355i) q^{28} +(-5.06958 - 2.12093i) q^{29} +(2.79965 + 3.78538i) q^{30} +(-0.0852665 + 0.543327i) q^{31} +(-0.524307 - 0.851529i) q^{32} +(14.9971 - 3.90495i) q^{33} +(0.255924 - 0.245283i) q^{34} +(0.922165 - 0.935308i) q^{35} +(1.18545 + 7.55382i) q^{36} +(-2.13716 + 1.82792i) q^{37} +(-2.23182 + 1.16516i) q^{38} +(1.99928 + 3.46285i) q^{39} +(0.721482 - 1.24964i) q^{40} +(0.390423 - 9.19086i) q^{41} +(2.82726 - 0.909793i) q^{42} +(0.0491717 - 0.693782i) q^{43} +(-2.93118 - 3.73719i) q^{44} +(-8.77702 + 6.68564i) q^{45} +(-2.04035 + 6.04580i) q^{46} +(10.5108 + 0.595602i) q^{47} +(2.75394 - 1.74989i) q^{48} +(2.77840 + 5.51064i) q^{49} +(-2.91668 - 0.0825719i) q^{50} +(0.812061 + 0.823635i) q^{51} +(0.728708 - 0.985279i) q^{52} +(-2.75907 + 1.64544i) q^{53} +(-14.9421 + 2.56208i) q^{54} +(2.73429 - 6.28439i) q^{55} +(-0.601382 - 0.683303i) q^{56} +(-3.90442 - 7.22759i) q^{57} +(-5.49316 + 0.155512i) q^{58} +(8.94861 + 8.57655i) q^{59} +(4.11032 + 2.29616i) q^{60} +(-3.29382 - 4.72775i) q^{61} +(0.146100 + 0.530216i) q^{62} +(2.22557 + 6.59463i) q^{63} +(-0.828510 - 0.559975i) q^{64} +(1.75064 + 0.249406i) q^{65} +(12.0574 - 9.73565i) q^{66} +(13.2379 + 2.65754i) q^{67} +(0.132173 - 0.328924i) q^{68} +(-19.8188 - 6.37758i) q^{69} +(0.455048 - 1.23212i) q^{70} +(2.80105 - 11.4178i) q^{71} +(4.19165 + 6.39497i) q^{72} +(-4.99668 - 11.4842i) q^{73} +(-1.19452 + 2.54596i) q^{74} +(0.134724 - 9.51960i) q^{75} +(-1.55377 + 1.98101i) q^{76} +(-3.20465 - 2.90194i) q^{77} +(3.24815 + 2.33195i) q^{78} +(-2.15862 - 1.37162i) q^{79} +(0.142705 - 1.43589i) q^{80} +(-4.85256 - 26.0791i) q^{81} +(-3.42996 - 8.53579i) q^{82} +(0.820241 + 11.5731i) q^{83} +(2.20153 - 1.99358i) q^{84} +(0.508237 - 0.0577849i) q^{85} +(-0.240963 - 0.652447i) q^{86} +(-0.760996 - 17.9144i) q^{87} +(-4.21033 - 2.19807i) q^{88} +(-0.00522727 + 0.00120421i) q^{89} +(-5.24405 + 9.70741i) q^{90} +(0.502200 - 0.996054i) q^{91} +(0.631045 + 6.34953i) q^{92} +(-1.72310 + 0.501137i) q^{93} +(9.82305 - 3.78667i) q^{94} +(-3.58064 - 0.613962i) q^{95} +(1.78868 - 2.72890i) q^{96} +(7.59717 + 8.15468i) q^{97} +(4.80160 + 3.87702i) q^{98} +(23.2123 + 27.9299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q + 18 q^{2} - 4 q^{3} - 18 q^{4} + 3 q^{5} + 4 q^{6} - 8 q^{7} + 18 q^{8} + 13 q^{9} - 3 q^{10} + 29 q^{11} - 4 q^{12} - 6 q^{13} - 66 q^{14} - 10 q^{15} - 18 q^{16} + 10 q^{17} - 13 q^{18} - 5 q^{19}+ \cdots + 301 q^{99}+O(q^{100}) \) 648 * q + 18 * q^2 - 4 * q^3 - 18 * q^4 + 3 * q^5 + 4 * q^6 - 8 * q^7 + 18 * q^8 + 13 * q^9 - 3 * q^10 + 29 * q^11 - 4 * q^12 - 6 * q^13 - 66 * q^14 - 10 * q^15 - 18 * q^16 + 10 * q^17 - 13 * q^18 - 5 * q^19 + 3 * q^20 + q^21 + 8 * q^22 + 7 * q^23 - 33 * q^24 + 14 * q^25 + 6 * q^26 + 26 * q^27 - 8 * q^28 - 328 * q^29 + 121 * q^30 + 23 * q^31 + 18 * q^32 + 14 * q^33 - 10 * q^34 + 7 * q^35 + 13 * q^36 + 47 * q^37 + 5 * q^38 + 3 * q^39 - 3 * q^40 - 55 * q^41 - q^42 + 32 * q^43 - 8 * q^44 + 13 * q^45 + 30 * q^46 - 124 * q^47 - 4 * q^48 + 18 * q^49 - 14 * q^50 - 97 * q^51 - 6 * q^52 + 12 * q^53 - 26 * q^54 + 10 * q^55 + 8 * q^56 - 105 * q^57 - 79 * q^58 - 172 * q^59 - 10 * q^60 - 23 * q^61 - 23 * q^62 + 22 * q^63 - 18 * q^64 + 3 * q^65 + 97 * q^66 + 79 * q^67 + 10 * q^68 + 241 * q^69 - 81 * q^70 - 6 * q^71 - 87 * q^72 + 5 * q^73 - 158 * q^74 - 155 * q^75 - 5 * q^76 - 27 * q^77 - 3 * q^78 - 246 * q^79 + 3 * q^80 - 189 * q^81 + 18 * q^82 + 142 * q^83 + q^84 - 63 * q^85 + 5 * q^86 - 112 * q^87 + 8 * q^88 - 162 * q^89 - 13 * q^90 + 12 * q^91 + 81 * q^92 - 64 * q^93 + 50 * q^94 + 180 * q^95 + 4 * q^96 - 48 * q^97 + 19 * q^98 + 301 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more