LMFDB - Embedded newform 552.2.t.a.235.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("552.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			235.2
Character	$\chi$	$=$	552.235
Dual form			552.2.t.a.451.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38539 + 0.284082i) q^{2} +(0.654861 - 0.755750i) q^{3} +(1.83859 - 0.787128i) q^{4} +(0.131847 - 0.917018i) q^{5} +(-0.692540 + 1.23304i) q^{6} +(-0.0841231 - 0.184204i) q^{7} +(-2.32356 + 1.61279i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-1.38539 + 0.284082i) q^{2} +(0.654861 - 0.755750i) q^{3} +(1.83859 - 0.787128i) q^{4} +(0.131847 - 0.917018i) q^{5} +(-0.692540 + 1.23304i) q^{6} +(-0.0841231 - 0.184204i) q^{7} +(-2.32356 + 1.61279i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.0778492 + 1.30788i) q^{10} +(1.60270 + 5.45831i) q^{11} +(0.609151 - 1.90498i) q^{12} +(2.77492 + 1.26726i) q^{13} +(0.168872 + 0.231296i) q^{14} +(-0.606695 - 0.700163i) q^{15} +(2.76086 - 2.89442i) q^{16} +(2.86746 + 4.46186i) q^{17} +(0.478352 + 1.33086i) q^{18} +(2.36103 - 3.67383i) q^{19} +(-0.479397 - 1.78981i) q^{20} +(-0.194301 - 0.0570519i) q^{21} +(-3.77098 - 7.10657i) q^{22} +(1.13343 - 4.65997i) q^{23} +(-0.302740 + 2.81218i) q^{24} +(3.97393 + 1.16685i) q^{25} +(-4.20434 - 0.967343i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(-0.299660 - 0.272461i) q^{28} +(-2.14129 - 3.33191i) q^{29} +(1.03941 + 0.797645i) q^{30} +(-1.22207 + 1.05893i) q^{31} +(-3.00260 + 4.79420i) q^{32} +(5.17466 + 2.36319i) q^{33} +(-5.24008 - 5.36680i) q^{34} +(-0.180010 + 0.0528556i) q^{35} +(-1.04078 - 1.70786i) q^{36} +(-1.42570 - 9.91599i) q^{37} +(-2.22727 + 5.76041i) q^{38} +(2.77492 - 1.26726i) q^{39} +(1.17260 + 2.34338i) q^{40} +(0.414389 - 2.88214i) q^{41} +(0.285389 + 0.0238415i) q^{42} +(-1.13709 - 0.985294i) q^{43} +(7.24311 + 8.77408i) q^{44} -0.926448 q^{45} +(-0.246420 + 6.77785i) q^{46} +12.0701i q^{47} +(-0.379478 - 3.98196i) q^{48} +(4.55717 - 5.25926i) q^{49} +(-5.83691 - 0.487616i) q^{50} +(5.24983 + 0.754812i) q^{51} +(6.09944 + 0.145765i) q^{52} +(-5.69226 - 12.4643i) q^{53} +(1.31905 + 0.510011i) q^{54} +(5.21668 - 0.750046i) q^{55} +(0.492547 + 0.292335i) q^{56} +(-1.23035 - 4.19020i) q^{57} +(3.91305 + 4.00768i) q^{58} +(2.40581 - 5.26800i) q^{59} +(-1.66658 - 0.809769i) q^{60} +(9.48472 + 10.9460i) q^{61} +(1.39221 - 1.81419i) q^{62} +(-0.170357 + 0.109482i) q^{63} +(2.79782 - 7.49481i) q^{64} +(1.52797 - 2.37756i) q^{65} +(-7.84025 - 1.80390i) q^{66} +(-1.82054 + 6.20017i) q^{67} +(8.78415 + 5.94648i) q^{68} +(-2.77953 - 3.90822i) q^{69} +(0.234368 - 0.124363i) q^{70} +(-1.62908 + 5.54815i) q^{71} +(1.92705 + 2.07038i) q^{72} +(7.53405 + 4.84184i) q^{73} +(4.79211 + 13.3325i) q^{74} +(3.48421 - 2.23917i) q^{75} +(1.44920 - 8.61313i) q^{76} +(0.870617 - 0.754394i) q^{77} +(-3.48433 + 2.54395i) q^{78} +(-1.72521 + 3.77767i) q^{79} +(-2.29022 - 2.91338i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(0.244676 + 4.11060i) q^{82} +(-6.47236 + 0.930585i) q^{83} +(-0.402148 + 0.0480444i) q^{84} +(4.46967 - 2.04123i) q^{85} +(1.85521 + 1.04199i) q^{86} +(-3.92033 - 0.563659i) q^{87} +(-12.5271 - 10.0979i) q^{88} +(8.71852 + 7.55464i) q^{89} +(1.28349 - 0.263188i) q^{90} -0.617756i q^{91} +(-1.58408 - 9.45995i) q^{92} +1.61703i q^{93} +(-3.42891 - 16.7218i) q^{94} +(-3.05768 - 2.64949i) q^{95} +(1.65693 + 5.40875i) q^{96} +(-12.3742 - 1.77914i) q^{97} +(-4.81938 + 8.58072i) q^{98} +(5.17466 - 2.36319i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.38539	+	0.284082i	−0.979617	+	0.200877i
$2$	−1.38539	+	0.284082i	−0.979617	+	0.200877i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$4$	1.83859	−	0.787128i	0.919297	−	0.393564i
$5$	0.131847	−	0.917018i	0.0589639	−	0.410103i	−0.938867	−	0.344279i	$-0.888123\pi$
$5$	0.131847	−	0.917018i	0.0589639	−	0.410103i	0.997831	−	0.0658239i	$-0.0209676\pi$
$6$	−0.692540	+	1.23304i	−0.282728	+	0.503387i
$7$	−0.0841231	−	0.184204i	−0.0317955	−	0.0696225i	0.893068	−	0.449922i	$-0.148548\pi$
$7$	−0.0841231	−	0.184204i	−0.0317955	−	0.0696225i	−0.924863	+	0.380299i	$0.875821\pi$
$8$	−2.32356	+	1.61279i	−0.821501	+	0.570207i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	0.0778492	+	1.30788i	0.0246181	+	0.413588i
$11$	1.60270	+	5.45831i	0.483233	+	1.64574i	0.735084	+	0.677976i	$0.237143\pi$
$11$	1.60270	+	5.45831i	0.483233	+	1.64574i	−0.251851	+	0.967766i	$0.581039\pi$
$12$	0.609151	−	1.90498i	0.175847	−	0.549919i
$13$	2.77492	+	1.26726i	0.769623	+	0.351475i	0.761223	−	0.648490i	$-0.224599\pi$
$13$	2.77492	+	1.26726i	0.769623	+	0.351475i	0.00839962	+	0.999965i	$0.497326\pi$
$14$	0.168872	+	0.231296i	0.0451330	+	0.0618164i
$15$	−0.606695	−	0.700163i	−0.156648	−	0.180781i
$16$	2.76086	−	2.89442i	0.690215	−	0.723605i
$17$	2.86746	+	4.46186i	0.695461	+	1.08216i	0.991889	+	0.127104i	$0.0405681\pi$
$17$	2.86746	+	4.46186i	0.695461	+	1.08216i	−0.296428	+	0.955055i	$0.595795\pi$
$18$	0.478352	+	1.33086i	0.112749	+	0.313686i
$19$	2.36103	−	3.67383i	0.541658	−	0.842836i	−0.457261	−	0.889333i	$-0.651169\pi$
$19$	2.36103	−	3.67383i	0.541658	−	0.842836i	0.998918	+	0.0464970i	$0.0148058\pi$
$20$	−0.479397	−	1.78981i	−0.107196	−	0.400213i
$21$	−0.194301	−	0.0570519i	−0.0423999	−	0.0124497i
$22$	−3.77098	−	7.10657i	−0.803975	−	1.51513i
$23$	1.13343	−	4.65997i	0.236336	−	0.971671i
$23$	1.13343	−	4.65997i	0.236336	−	0.971671i
$24$	−0.302740	+	2.81218i	−0.0617966	+	0.574034i
$25$	3.97393	+	1.16685i	0.794785	+	0.233370i
$26$	−4.20434	−	0.967343i	−0.824539	−	0.189712i
$27$	−0.841254	−	0.540641i	−0.161899	−	0.104046i
$28$	−0.299660	−	0.272461i	−0.0566305	−	0.0514902i
$29$	−2.14129	−	3.33191i	−0.397627	−	0.618720i	0.583493	−	0.812118i	$-0.301685\pi$
$29$	−2.14129	−	3.33191i	−0.397627	−	0.618720i	−0.981120	+	0.193398i	$0.938049\pi$
$30$	1.03941	+	0.797645i	0.189770	+	0.145629i
$31$	−1.22207	+	1.05893i	−0.219490	+	0.190189i	−0.757664	−	0.652645i	$-0.773660\pi$
$31$	−1.22207	+	1.05893i	−0.219490	+	0.190189i	0.538175	+	0.842833i	$0.319114\pi$
$32$	−3.00260	+	4.79420i	−0.530790	+	0.847503i
$33$	5.17466	+	2.36319i	0.900793	+	0.411378i
$34$	−5.24008	−	5.36680i	−0.898666	−	0.920399i
$35$	−0.180010	+	0.0528556i	−0.0304272	+	0.00893423i
$36$	−1.04078	−	1.70786i	−0.173463	−	0.284643i
$37$	−1.42570	−	9.91599i	−0.234384	−	1.63018i	−0.678776	−	0.734345i	$-0.737489\pi$
$37$	−1.42570	−	9.91599i	−0.234384	−	1.63018i	0.444392	−	0.895833i	$-0.353420\pi$
$38$	−2.22727	+	5.76041i	−0.361311	+	0.934462i
$39$	2.77492	−	1.26726i	0.444342	−	0.202924i
$40$	1.17260	+	2.34338i	0.185405	+	0.370522i
$41$	0.414389	−	2.88214i	0.0647166	−	0.450114i	−0.931538	−	0.363644i	$-0.881532\pi$
$41$	0.414389	−	2.88214i	0.0647166	−	0.450114i	0.996254	−	0.0864697i	$-0.0275586\pi$
$42$	0.285389	+	0.0238415i	0.0440365	+	0.00367882i
$43$	−1.13709	−	0.985294i	−0.173405	−	0.150256i	0.563835	−	0.825888i	$-0.309325\pi$
$43$	−1.13709	−	0.985294i	−0.173405	−	0.150256i	−0.737239	+	0.675632i	$0.763871\pi$
$44$	7.24311	+	8.77408i	1.09194	+	1.32274i
$45$	−0.926448			−0.138107
$46$	−0.246420	+	6.77785i	−0.0363326	+	0.999340i
$47$			12.0701i			1.76061i	0.474410	+	0.880304i	$0.342662\pi$
$47$			12.0701i			1.76061i	−0.474410	+	0.880304i	$0.657338\pi$
$48$	−0.379478	−	3.98196i	−0.0547730	−	0.574746i
$49$	4.55717	−	5.25926i	0.651024	−	0.751322i
$50$	−5.83691	−	0.487616i	−0.825463	−	0.0689593i
$51$	5.24983	+	0.754812i	0.735124	+	0.105695i
$52$	6.09944	+	0.145765i	0.845840	+	0.0202140i
$53$	−5.69226	−	12.4643i	−0.781892	−	1.71210i	−0.698525	−	0.715586i	$-0.746160\pi$
$53$	−5.69226	−	12.4643i	−0.781892	−	1.71210i	−0.0833675	−	0.996519i	$-0.526568\pi$
$54$	1.31905	+	0.510011i	0.179500	+	0.0694038i
$55$	5.21668	−	0.750046i	0.703417	−	0.101136i
$56$	0.492547	+	0.292335i	0.0658193	+	0.0390649i
$57$	−1.23035	−	4.19020i	−0.162964	−	0.555005i
$58$	3.91305	+	4.00768i	0.513809	+	0.526234i
$59$	2.40581	−	5.26800i	0.313210	−	0.685835i	−0.685914	−	0.727683i	$-0.740597\pi$
$59$	2.40581	−	5.26800i	0.313210	−	0.685835i	0.999124	+	0.0418481i	$0.0133245\pi$
$60$	−1.66658	−	0.809769i	−0.215155	−	0.104541i
$61$	9.48472	+	10.9460i	1.21439	+	1.40149i	0.890247	+	0.455479i	$0.150532\pi$
$61$	9.48472	+	10.9460i	1.21439	+	1.40149i	0.324148	+	0.946007i	$0.394923\pi$
$62$	1.39221	−	1.81419i	0.176811	−	0.230402i
$63$	−0.170357	+	0.109482i	−0.0214630	+	0.0137934i
$64$	2.79782	−	7.49481i	0.349727	−	0.936852i
$65$	1.52797	−	2.37756i	0.189521	−	0.294900i
$66$	−7.84025	−	1.80390i	−0.965068	−	0.222045i
$67$	−1.82054	+	6.20017i	−0.222414	+	0.757472i	0.770375	+	0.637592i	$0.220069\pi$
$67$	−1.82054	+	6.20017i	−0.222414	+	0.757472i	−0.992788	+	0.119880i	$0.961749\pi$
$68$	8.78415	+	5.94648i	1.06523	+	0.721117i
$69$	−2.77953	−	3.90822i	−0.334617	−	0.470494i
$70$	0.234368	−	0.124363i	0.0280123	−	0.0148642i
$71$	−1.62908	+	5.54815i	−0.193337	+	0.658444i	0.804575	+	0.593851i	$0.202393\pi$
$71$	−1.62908	+	5.54815i	−0.193337	+	0.658444i	−0.997912	+	0.0645931i	$0.979425\pi$
$72$	1.92705	+	2.07038i	0.227105	+	0.243997i
$73$	7.53405	+	4.84184i	0.881794	+	0.566694i	0.901339	−	0.433115i	$-0.142585\pi$
$73$	7.53405	+	4.84184i	0.881794	+	0.566694i	−0.0195451	+	0.999809i	$0.506222\pi$
$74$	4.79211	+	13.3325i	0.557071	+	1.54987i
$75$	3.48421	−	2.23917i	0.402322	−	0.258557i
$76$	1.44920	−	8.61313i	0.166234	−	0.987993i
$77$	0.870617	−	0.754394i	0.0992160	−	0.0859712i
$78$	−3.48433	+	2.54395i	−0.394522	+	0.288046i
$79$	−1.72521	+	3.77767i	−0.194101	+	0.425021i	−0.981510	−	0.191409i	$-0.938694\pi$
$79$	−1.72521	+	3.77767i	−0.194101	+	0.425021i	0.787410	+	0.616430i	$0.211422\pi$
$80$	−2.29022	−	2.91338i	−0.256055	−	0.325726i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	0.244676	+	4.11060i	0.0270199	+	0.453939i
$83$	−6.47236	+	0.930585i	−0.710434	+	0.102145i	−0.488052	−	0.872815i	$-0.662292\pi$
$83$	−6.47236	+	0.930585i	−0.710434	+	0.102145i	−0.222382	+	0.974960i	$0.571383\pi$
$84$	−0.402148	+	0.0480444i	−0.0438779	+	0.00524208i
$85$	4.46967	−	2.04123i	0.484804	−	0.221403i
$86$	1.85521	+	1.04199i	0.200053	+	0.112360i
$87$	−3.92033	−	0.563659i	−0.420304	−	0.0604306i
$88$	−12.5271	−	10.0979i	−1.33539	−	1.07644i
$89$	8.71852	+	7.55464i	0.924162	+	0.800791i	0.980276	−	0.197634i	$-0.0633256\pi$
$89$	8.71852	+	7.55464i	0.924162	+	0.800791i	−0.0561142	+	0.998424i	$0.517871\pi$
$90$	1.28349	−	0.263188i	0.135292	−	0.0277424i
$91$		−	0.617756i		−	0.0647584i
$92$	−1.58408	−	9.45995i	−0.165152	−	0.986268i
$93$			1.61703i			0.167678i
$94$	−3.42891	−	16.7218i	−0.353665	−	1.72472i
$95$	−3.05768	−	2.64949i	−0.313711	−	0.271832i
$96$	1.65693	+	5.40875i	0.169110	+	0.552028i
$97$	−12.3742	−	1.77914i	−1.25641	−	0.180644i	−0.518224	−	0.855245i	$-0.673407\pi$
$97$	−12.3742	−	1.77914i	−1.25641	−	0.180644i	−0.738182	+	0.674601i	$0.764316\pi$
$98$	−4.81938	+	8.58072i	−0.486831	+	0.866783i
$99$	5.17466	−	2.36319i	0.520073	−	0.237509i
$100$	8.22490	−	0.982626i	0.822490	−	0.0982626i
$101$	14.8941	−	2.14145i	1.48202	−	0.213083i	0.646658	−	0.762780i	$-0.276166\pi$
$101$	14.8941	−	2.14145i	1.48202	−	0.213083i	0.835364	+	0.549698i	$0.185257\pi$
$102$	−7.48748	+	0.445679i	−0.741371	+	0.0441288i
$103$	−13.6803	+	4.01689i	−1.34796	+	0.395796i	−0.874502	−	0.485022i	$-0.838811\pi$
$103$	−13.6803	+	4.01689i	−1.34796	+	0.395796i	−0.473455	+	0.880818i	$0.656993\pi$
$104$	−8.49150	+	1.53080i	−0.832660	+	0.150108i
$105$	−0.0779357	+	0.170655i	−0.00760574	+	0.0166543i
$106$	11.4269	+	15.6508i	1.10988	+	1.52014i
$107$	−9.32118	+	8.07685i	−0.901113	+	0.780818i	−0.976316	−	0.216350i	$-0.930585\pi$
$107$	−9.32118	+	8.07685i	−0.901113	+	0.780818i	0.0752034	+	0.997168i	$0.476039\pi$
$108$	−1.97228	−	0.331845i	−0.189783	−	0.0319318i
$109$	−1.13664	+	0.730474i	−0.108870	+	0.0699667i	−0.593943	−	0.804507i	$-0.702430\pi$
$109$	−1.13664	+	0.730474i	−0.108870	+	0.0699667i	0.485073	+	0.874474i	$0.338793\pi$
$110$	−7.01405	+	2.52107i	−0.668763	+	0.240375i
$111$	−8.42764	−	5.41611i	−0.799916	−	0.514075i
$112$	−0.765415	−	0.265073i	−0.0723249	−	0.0250471i
$113$	−1.11414	+	3.79442i	−0.104810	+	0.356949i	−0.995153	−	0.0983413i	$-0.968646\pi$
$113$	−1.11414	+	3.79442i	−0.104810	+	0.356949i	0.890343	+	0.455290i	$0.150465\pi$
$114$	2.89488	+	5.45552i	0.271130	+	0.510957i
$115$	−4.12384	−	1.65378i	−0.384550	−	0.154216i
$116$	−6.55960	−	4.44056i	−0.609044	−	0.412296i
$117$	0.859451	−	2.92702i	0.0794563	−	0.270603i
$118$	−1.83644	+	7.98166i	−0.169058	+	0.734772i
$119$	0.580671	−	0.903542i	0.0532301	−	0.0828276i
$120$	2.53890	+	0.648396i	0.231769	+	0.0591902i
$121$	−17.9707	+	11.5491i	−1.63370	+	1.04991i
$122$	−16.2496	−	12.4699i	−1.47117	−	1.12898i
$123$	−1.90681	−	2.20057i	−0.171931	−	0.198419i
$124$	−1.41337	+	2.90886i	−0.126925	+	0.261223i
$125$	3.51828	−	7.70395i	0.314684	−	0.689062i
$126$	0.204908	−	0.200070i	0.0182547	−	0.0178237i
$127$	−0.662112	−	2.25495i	−0.0587530	−	0.200094i	0.924886	−	0.380244i	$-0.124160\pi$
$127$	−0.662112	−	2.25495i	−0.0587530	−	0.200094i	−0.983639	+	0.180150i	$0.942342\pi$
$128$	−1.74692	+	11.1780i	−0.154407	+	0.988007i
$129$	−1.48927	+	0.214125i	−0.131123	+	0.0188526i
$130$	−1.44140	+	3.72791i	−0.126419	+	0.326960i
$131$	−6.92425	−	15.1620i	−0.604974	−	1.32471i	−0.925959	−	0.377625i	$-0.876741\pi$
$131$	−6.92425	−	15.1620i	−0.604974	−	1.32471i	0.320984	−	0.947085i	$-0.395986\pi$
$132$	11.3742	+	0.271823i	0.990000	+	0.0236592i
$133$	−0.875352	−	0.125857i	−0.0759026	−	0.0109131i
$134$	0.760785	−	9.10682i	0.0657218	−	0.786710i
$135$	−0.606695	+	0.700163i	−0.0522160	+	0.0602604i
$136$	−13.8587	−	5.74276i	−1.18838	−	0.492437i
$137$		−	3.60894i		−	0.308332i	−0.988045	−	0.154166i	$-0.950731\pi$
$137$		−	3.60894i		−	0.308332i	0.988045	−	0.154166i	$-0.0492691\pi$
$138$	4.96099	+	4.62478i	0.422307	+	0.393687i
$139$	−7.40138			−0.627777			−0.313888	−	0.949460i	$-0.601632\pi$
$139$	−7.40138			−0.627777			−0.313888	+	0.949460i	$0.601632\pi$
$140$	−0.289361	+	0.238871i	−0.0244554	+	0.0201883i
$141$	9.12199	+	7.90425i	0.768210	+	0.665658i
$142$	0.680779	−	8.14913i	0.0571297	−	0.683859i
$143$	−2.46974	+	17.1774i	−0.206530	+	1.43645i
$144$	−3.25787	−	2.32084i	−0.271489	−	0.193403i
$145$	−3.33775	+	1.52430i	−0.277185	+	0.126586i
$146$	−11.8131	−	4.56753i	−0.977655	−	0.378011i
$147$	−0.990368	−	6.88816i	−0.0816842	−	0.568126i
$148$	−10.4264	−	17.1093i	−0.857048	−	1.40637i
$149$	−3.51005	+	1.03064i	−0.287555	+	0.0844337i	−0.422329	−	0.906443i	$-0.638787\pi$
$149$	−3.51005	+	1.03064i	−0.287555	+	0.0844337i	0.134774	+	0.990876i	$0.456969\pi$
$150$	−4.19088	+	4.09192i	−0.342184	+	0.334104i
$151$	9.33698	+	4.26406i	0.759833	+	0.347004i	0.757364	−	0.652993i	$-0.226487\pi$
$151$	9.33698	+	4.26406i	0.759833	+	0.347004i	0.00246886	+	0.999997i	$0.499214\pi$
$152$	0.439138	+	12.3442i	0.0356188	+	1.00125i
$153$	4.00836	−	3.47326i	0.324057	−	0.280797i
$154$	−0.991832	+	1.29245i	−0.0799241	+	0.104149i
$155$	0.809929	+	1.26027i	0.0650550	+	0.101228i
$156$	4.10445	−	4.51419i	0.328619	−	0.361425i
$157$	−2.74069	−	1.76134i	−0.218731	−	0.140570i	0.426687	−	0.904399i	$-0.359681\pi$
$157$	−2.74069	−	1.76134i	−0.218731	−	0.140570i	−0.645418	+	0.763829i	$0.723317\pi$
$158$	1.31691	−	5.72364i	0.104767	−	0.455348i
$159$	−13.1475	−	3.86046i	−1.04267	−	0.306155i
$160$	4.00049	+	3.38555i	0.316266	+	0.267651i
$161$	−0.953732	+	0.183229i	−0.0751646	+	0.0144405i
$162$	1.24923	−	0.662884i	0.0981491	−	0.0520811i
$163$	0.225888	+	0.0663267i	0.0176929	+	0.00519510i	0.290567	−	0.956855i	$-0.406156\pi$
$163$	0.225888	+	0.0663267i	0.0176929	+	0.00519510i	−0.272874	+	0.962050i	$0.587974\pi$
$164$	−1.50672	−	5.62526i	−0.117655	−	0.439259i
$165$	2.84935	−	4.43368i	0.221822	−	0.345162i
$166$	8.70236	−	3.12791i	0.675434	−	0.242773i
$167$	1.18789	+	1.84840i	0.0919218	+	0.143033i	0.884169	−	0.467167i	$-0.154725\pi$
$167$	1.18789	+	1.84840i	0.0919218	+	0.143033i	−0.792247	+	0.610200i	$0.791089\pi$
$168$	0.543482	−	0.180803i	0.0419305	−	0.0139493i
$169$	−2.41898	−	2.79166i	−0.186076	−	0.214743i
$170$	−5.61235	+	4.09765i	−0.430447	+	0.314275i
$171$	−3.97245	−	1.81416i	−0.303781	−	0.138732i
$172$	−2.86620	−	0.916520i	−0.218546	−	0.0698840i
$173$	−6.57650	−	22.3975i	−0.500002	−	1.70285i	−0.692382	−	0.721531i	$-0.743439\pi$
$173$	−6.57650	−	22.3975i	−0.500002	−	1.70285i	0.192380	−	0.981321i	$-0.438380\pi$
$174$	5.59131	−	0.332812i	0.423876	−	0.0252304i
$175$	−0.119361	−	0.830172i	−0.00902282	−	0.0627551i
$176$	20.2235	+	10.4307i	1.52440	+	0.786245i
$177$	−2.40581	−	5.26800i	−0.180832	−	0.395967i
$178$	−14.2247	−	7.98933i	−1.06618	−	0.598825i
$179$	−0.695910	+	4.84016i	−0.0520148	+	0.361771i	0.947146	+	0.320804i	$0.103953\pi$
$179$	−0.695910	+	4.84016i	−0.0520148	+	0.361771i	−0.999161	+	0.0409670i	$0.986956\pi$
$180$	−1.70336	+	0.729234i	−0.126961	+	0.0543539i
$181$	−6.96415	+	8.03706i	−0.517641	+	0.597390i	−0.953039	−	0.302848i	$-0.902062\pi$
$181$	−6.96415	+	8.03706i	−0.517641	+	0.597390i	0.435397	+	0.900238i	$0.356608\pi$
$182$	0.175494	+	0.855831i	0.0130085	+	0.0634384i
$183$	14.4836			1.07066
$184$	4.88197	+	12.6557i	0.359904	+	0.932989i
$185$	−9.28112			−0.682361
$186$	−0.459368	−	2.24021i	−0.0336825	−	0.164260i
$187$	−19.7585	+	22.8025i	−1.44488	+	1.66749i
$188$	9.50073	+	22.1921i	0.692912	+	1.61852i
$189$	−0.0288193	+	0.200443i	−0.00209629	+	0.0145800i
$190$	4.98874	+	2.80194i	0.361921	+	0.203274i
$191$	5.13936	+	11.2536i	0.371871	+	0.814284i	0.999364	+	0.0356618i	$0.0113539\pi$
$191$	5.13936	+	11.2536i	0.371871	+	0.814284i	−0.627493	+	0.778622i	$0.715919\pi$
$192$	−3.83202	−	7.02251i	−0.276552	−	0.506806i
$193$	1.75833	+	12.2295i	0.126568	+	0.880297i	0.949859	+	0.312678i	$0.101226\pi$
$193$	1.75833	+	12.2295i	0.126568	+	0.880297i	−0.823291	+	0.567619i	$0.807865\pi$
$194$	17.6484	−	1.05049i	1.26708	−	0.0754209i
$195$	−0.796237	−	2.71173i	−0.0570197	−	0.194191i
$196$	4.23908	−	13.2567i	0.302791	−	0.946908i
$197$	−3.41496	−	1.55956i	−0.243306	−	0.111114i	0.290030	−	0.957017i	$-0.406335\pi$
$197$	−3.41496	−	1.55956i	−0.243306	−	0.111114i	−0.533336	+	0.845903i	$0.679062\pi$
$198$	−6.49757	+	4.74396i	−0.461762	+	0.337139i
$199$	9.72722	+	11.2258i	0.689545	+	0.795777i	0.987300	−	0.158865i	$-0.0507835\pi$
$199$	9.72722	+	11.2258i	0.689545	+	0.795777i	−0.297756	+	0.954642i	$0.596238\pi$
$200$	−11.1155	+	3.69787i	−0.785986	+	0.261479i
$201$	3.49358	+	5.43612i	0.246418	+	0.383434i
$202$	−20.0258	+	7.19790i	−1.40901	+	0.506443i
$203$	−0.433619	+	0.674724i	−0.0304341	+	0.0473563i
$204$	10.2464	−	2.74450i	0.717395	−	0.192153i
$205$	−2.58834	−	0.760004i	−0.180777	−	0.0530810i
$206$	17.8113	−	9.45127i	1.24097	−	0.658501i
$207$	−4.77384	−	0.458708i	−0.331805	−	0.0318824i
$208$	11.3291	−	4.53304i	0.785534	−	0.314310i
$209$	23.8370	+	6.99916i	1.64884	+	0.484142i
$210$	0.0594909	−	0.258564i	0.00410526	−	0.0178426i
$211$	−8.36095	−	5.37326i	−0.575592	−	0.369910i	0.220224	−	0.975449i	$-0.429321\pi$
$211$	−8.36095	−	5.37326i	−0.575592	−	0.369910i	−0.795816	+	0.605539i	$0.792958\pi$
$212$	−20.2768	−	18.4363i	−1.39261	−	1.26621i
$213$	3.12619	+	4.86444i	0.214203	+	0.333306i
$214$	10.6190	−	13.8375i	0.725897	−	0.945915i
$215$	−1.05345	+	0.912824i	−0.0718450	+	0.0622541i
$216$	2.82664	−	0.100556i	0.192328	−	0.00684198i
$217$	0.297862	+	0.136029i	0.0202202	+	0.00923426i
$218$	1.36717	−	1.33489i	0.0925965	−	0.0904101i
$219$	8.59297	−	2.52312i	0.580659	−	0.170497i
$220$	9.00098	−	5.48523i	0.606846	−	0.369814i
$221$	2.30262	+	16.0151i	0.154891	+	1.07729i
$222$	13.2142	+	5.10927i	0.886877	+	0.342912i
$223$	−7.86015	+	3.58961i	−0.526354	+	0.240378i	−0.660826	−	0.750540i	$-0.729794\pi$
$223$	−7.86015	+	3.58961i	−0.526354	+	0.240378i	0.134471	+	0.990918i	$0.457066\pi$
$224$	1.13570	+	0.149788i	0.0758821	+	0.0100081i
$225$	0.589424	−	4.09954i	0.0392950	−	0.273302i
$226$	0.465590	−	5.57325i	0.0309706	−	0.370727i
$227$	−8.55473	−	7.41271i	−0.567797	−	0.491999i	0.323001	−	0.946399i	$-0.395308\pi$
$227$	−8.55473	−	7.41271i	−0.567797	−	0.491999i	−0.890798	+	0.454400i	$0.849854\pi$
$228$	−5.56034	−	6.73563i	−0.368243	−	0.446078i
$229$	1.17566			0.0776901			0.0388450	−	0.999245i	$-0.487632\pi$
$229$	1.17566			0.0776901			0.0388450	+	0.999245i	$0.487632\pi$
$230$	6.18292	+	1.11961i	0.407690	+	0.0738251i
$231$		−	1.15199i		−	0.0757955i
$232$	10.3491	+	4.28843i	0.679450	+	0.281549i
$233$	19.1153	−	22.0602i	1.25229	−	1.44521i	0.404792	−	0.914409i	$-0.367344\pi$
$233$	19.1153	−	22.0602i	1.25229	−	1.44521i	0.847493	−	0.530806i	$-0.178111\pi$
$234$	−0.359157	+	4.29921i	−0.0234788	+	0.281048i
$235$	11.0685	+	1.59141i	0.722031	+	0.103812i
$236$	0.276726	−	11.5794i	0.0180133	−	0.753754i
$237$	1.72521	+	3.77767i	0.112064	+	0.245386i
$238$	−0.547774	+	1.41671i	−0.0355069	+	0.0918320i
$239$	−1.17241	+	0.168567i	−0.0758369	+	0.0109037i	−0.180129	−	0.983643i	$-0.557651\pi$
$239$	−1.17241	+	0.168567i	−0.0758369	+	0.0109037i	0.104292	+	0.994547i	$0.466742\pi$
$240$	−3.70156	−	0.177022i	−0.238935	−	0.0114267i
$241$	−0.232358	−	0.791338i	−0.0149675	−	0.0509746i	0.951671	−	0.307120i	$-0.0993654\pi$
$241$	−0.232358	−	0.791338i	−0.0149675	−	0.0509746i	−0.966638	+	0.256146i	$0.917547\pi$
$242$	21.6155	−	21.1051i	1.38949	−	1.35669i
$243$	−0.415415	+	0.909632i	−0.0266489	+	0.0583529i
$244$	26.0544	+	12.6595i	1.66796	+	0.810440i
$245$	−4.22198	−	4.87243i	−0.269733	−	0.311288i
$246$	3.26681	+	2.50695i	0.208284	+	0.159838i
$247$	11.2074	−	7.20254i	0.713108	−	0.458287i
$248$	1.13171	−	4.43141i	0.0718638	−	0.281395i
$249$	−3.53521	+	5.50089i	−0.224035	+	0.348605i
$250$	−2.68562	+	11.6724i	−0.169853	+	0.738230i
$251$	3.63523	−	12.3805i	0.229454	−	0.781448i	−0.761607	−	0.648039i	$-0.775589\pi$
$251$	3.63523	−	12.3805i	0.229454	−	0.781448i	0.991061	−	0.133409i	$-0.0425923\pi$
$252$	−0.227041	+	0.335385i	−0.0143022	+	0.0211273i
$253$	27.2521	−	1.28196i	1.71333	−	0.0805960i
$254$	1.55787	+	2.93588i	0.0977496	+	0.184213i
$255$	1.38435	−	4.71467i	0.0866915	−	0.295244i
$256$	−0.755325	−	15.9822i	−0.0472078	−	0.998885i
$257$	−23.8145	−	15.3047i	−1.48551	−	0.954679i	−0.996604	−	0.0823423i	$-0.973760\pi$
$257$	−23.8145	−	15.3047i	−1.48551	−	0.954679i	−0.488906	−	0.872337i	$-0.662604\pi$
$258$	2.00239	−	0.719721i	0.124663	−	0.0448079i
$259$	−1.70663	+	1.09678i	−0.106045	+	0.0681508i
$260$	0.937864	−	5.57408i	0.0581639	−	0.345690i
$261$	−2.99326	+	2.59367i	−0.185278	+	0.160544i
$262$	13.9000	+	19.0382i	0.858746	+	1.17618i
$263$	−3.77248	+	8.26057i	−0.232621	+	0.509368i	−0.989561	−	0.144116i	$-0.953966\pi$
$263$	−3.77248	+	8.26057i	−0.232621	+	0.509368i	0.756940	+	0.653484i	$0.226693\pi$
$264$	−15.8349	+	2.85464i	−0.974573	+	0.175691i
$265$	−12.1805	+	3.57652i	−0.748243	+	0.219704i
$266$	1.24845	−	0.0743120i	0.0765477	−	0.00455636i
$267$	11.4188	−	1.64178i	0.698822	−	0.100475i
$268$	1.53311	+	12.8326i	0.0936494	+	0.783876i
$269$	3.94407	−	1.80120i	0.240474	−	0.109821i	−0.291533	−	0.956561i	$-0.594165\pi$
$269$	3.94407	−	1.80120i	0.240474	−	0.109821i	0.532007	+	0.846740i	$0.321438\pi$
$270$	0.641603	−	1.14235i	0.0390467	−	0.0695211i
$271$	−25.2208	−	3.62621i	−1.53206	−	0.220277i	−0.675901	−	0.736993i	$-0.736245\pi$
$271$	−25.2208	−	3.62621i	−1.53206	−	0.220277i	−0.856157	+	0.516716i	$0.827154\pi$
$272$	20.8311	+	4.01892i	1.26307	+	0.243683i
$273$	−0.466869	−	0.404544i	−0.0282562	−	0.0244841i
$274$	1.02524	+	4.99977i	0.0619367	+	0.302047i
$275$			23.5610i			1.42078i
$276$	−8.18671	−	4.99778i	−0.492782	−	0.300831i
$277$			22.2355i			1.33600i	0.744161	+	0.668001i	$0.232850\pi$
$277$			22.2355i			1.33600i	−0.744161	+	0.668001i	$0.767150\pi$
$278$	10.2538	−	2.10260i	0.614980	−	0.126106i
$279$	1.22207	+	1.05893i	0.0731632	+	0.0633963i
$280$	0.333018	−	0.413131i	0.0199016	−	0.0246893i
$281$	11.8734	+	1.70714i	0.708307	+	0.101839i	0.487047	−	0.873376i	$-0.338074\pi$
$281$	11.8734	+	1.70714i	0.708307	+	0.101839i	0.221260	+	0.975215i	$0.428983\pi$
$282$	−14.8829	−	8.35905i	−0.886266	−	0.497774i
$283$	25.7931	−	11.7793i	1.53324	−	0.700208i	0.543021	−	0.839719i	$-0.317280\pi$
$283$	25.7931	−	11.7793i	1.53324	−	0.700208i	0.990221	+	0.139511i	$0.0445530\pi$
$284$	1.37188	+	11.4831i	0.0814062	+	0.681396i
$285$	−4.00471	+	0.575790i	−0.237218	+	0.0341069i
$286$	−1.45826	−	24.4989i	−0.0862284	−	1.44865i
$287$	−0.565760	+	0.166122i	−0.0333958	+	0.00980589i
$288$	5.17272	+	2.28976i	0.304805	+	0.134925i
$289$	−4.62377	+	10.1246i	−0.271987	+	0.595568i
$290$	4.19104	−	3.05994i	0.246106	−	0.179686i
$291$	−9.44794	+	8.18668i	−0.553848	+	0.479912i
$292$	17.6632	+	2.97192i	1.03366	+	0.173918i
$293$	−9.15954	+	5.88648i	−0.535106	+	0.343892i	−0.780122	−	0.625627i	$-0.784843\pi$
$293$	−9.15954	+	5.88648i	−0.535106	+	0.343892i	0.245016	+	0.969519i	$0.421207\pi$
$294$	3.32885	+	9.26142i	0.194142	+	0.540137i
$295$	−4.51365	−	2.90075i	−0.262795	−	0.168888i
$296$	19.3051	+	20.7410i	1.12209	+	1.20555i
$297$	1.60270	−	5.45831i	0.0929983	−	0.316723i
$298$	4.56999	−	2.42499i	0.264733	−	0.140476i
$299$	9.05057	−	11.4947i	0.523408	−	0.664755i
$300$	4.64354	−	6.85945i	0.268095	−	0.396030i
$301$	−0.0858394	+	0.292342i	−0.00494770	+	0.0168503i
$302$	−14.1467	−	3.25490i	−0.814050	−	0.187298i
$303$	8.13518	−	12.6586i	0.467354	−	0.727217i
$304$	−4.11515	−	16.9767i	−0.236020	−	0.973683i
$305$	11.2882	−	7.25447i	0.646359	−	0.415390i
$306$	−4.56643	+	5.95052i	−0.261046	+	0.340168i
$307$	−5.47474	−	6.31818i	−0.312460	−	0.360598i	0.577698	−	0.816251i	$-0.303951\pi$
$307$	−5.47474	−	6.31818i	−0.312460	−	0.360598i	−0.890157	+	0.455653i	$0.849406\pi$
$308$	1.00691	−	2.07231i	0.0573738	−	0.118081i
$309$	−5.92291	+	12.9694i	−0.336942	+	0.737801i
$310$	−1.48009	−	1.51588i	−0.0840633	−	0.0860962i
$311$	−6.16337	−	20.9905i	−0.349493	−	1.19026i	−0.927372	−	0.374141i	$-0.877938\pi$
$311$	−6.16337	−	20.9905i	−0.349493	−	1.19026i	0.577879	−	0.816122i	$-0.303881\pi$
$312$	−4.40384	+	7.41991i	−0.249319	+	0.420070i
$313$	−13.1874	+	1.89606i	−0.745395	+	0.107172i	−0.504539	−	0.863389i	$-0.668337\pi$
$313$	−13.1874	+	1.89606i	−0.745395	+	0.107172i	−0.240857	+	0.970561i	$0.577428\pi$
$314$	4.29728	+	1.66155i	0.242510	+	0.0937666i
$315$	0.0779357	+	0.170655i	0.00439118	+	0.00961534i
$316$	−0.198440	+	8.30357i	−0.0111631	+	0.467112i
$317$	−22.9026	−	3.29290i	−1.28634	−	0.184948i	−0.534994	−	0.844856i	$-0.679686\pi$
$317$	−22.9026	−	3.29290i	−1.28634	−	0.184948i	−0.751347	+	0.659908i	$0.770595\pi$
$318$	19.3111	+	1.61325i	1.08291	+	0.0904668i
$319$	14.7547	−	17.0279i	0.826107	−	0.953378i
$320$	−6.50400	−	3.55382i	−0.363584	−	0.198665i
$321$			12.3337i			0.688399i
$322$	1.26924	−	0.524782i	0.0707318	−	0.0292450i
$323$	23.1623			1.28878
$324$	−1.54236	+	1.27324i	−0.0856866	+	0.0707353i
$325$	9.54861	+	8.27391i	0.529661	+	0.458954i
$326$	−0.331784	−	0.0277173i	−0.0183758	−	0.00153512i
$327$	−0.192285	+	1.33737i	−0.0106334	+	0.0739569i
$328$	3.68543	+	7.36513i	0.203494	+	0.406671i
$329$	2.22336	−	1.01538i	0.122578	−	0.0559795i
$330$	−2.68793	+	6.95181i	−0.147965	+	0.382685i
$331$	−2.51020	−	17.4588i	−0.137973	−	0.959625i	−0.934739	−	0.355336i	$-0.884366\pi$
$331$	−2.51020	−	17.4588i	−0.137973	−	0.959625i	0.796765	−	0.604289i	$-0.206543\pi$
$332$	−11.1676	+	6.80555i	−0.612899	+	0.373503i
$333$	−9.61216	+	2.82238i	−0.526743	+	0.154666i
$334$	−2.17079	−	2.22328i	−0.118780	−	0.121653i
$335$	5.44564	+	2.48694i	0.297527	+	0.135876i
$336$	−0.701569	+	0.404876i	−0.0382737	+	0.0220878i
$337$	10.0810	−	8.73524i	0.549148	−	0.475839i	−0.335538	−	0.942027i	$-0.608918\pi$
$337$	10.0810	−	8.73524i	0.549148	−	0.475839i	0.884686	+	0.466187i	$0.154373\pi$
$338$	4.14429	+	3.18033i	0.225420	+	0.172987i
$339$	2.13802	+	3.32683i	0.116121	+	0.180689i
$340$	6.61120	−	7.27120i	0.358543	−	0.394336i
$341$	−7.73856	−	4.97327i	−0.419066	−	0.269318i
$342$	6.01875	+	1.38481i	0.325457	+	0.0748818i
$343$	−2.71224	−	0.796387i	−0.146447	−	0.0430009i
$344$	4.23116	+	0.455498i	0.228129	+	0.0245588i
$345$	−3.95038	+	2.03360i	−0.212682	+	0.109485i
$346$	15.4737	+	29.1610i	0.831874	+	1.56770i
$347$	−20.4584	−	6.00714i	−1.09827	−	0.322480i	−0.318103	−	0.948056i	$-0.603046\pi$
$347$	−20.4584	−	6.00714i	−1.09827	−	0.322480i	−0.780163	+	0.625576i	$0.784864\pi$
$348$	−7.65158	+	2.04947i	−0.410168	+	0.109863i
$349$	−8.77052	+	13.6472i	−0.469475	+	0.730518i	−0.992559	−	0.121764i	$-0.961145\pi$
$349$	−8.77052	+	13.6472i	−0.469475	+	0.730518i	0.523084	+	0.852281i	$0.324781\pi$
$350$	0.401198	+	1.11620i	0.0214449	+	0.0596634i
$351$	−1.64927	−	2.56632i	−0.0880317	−	0.136980i
$352$	−30.9805	−	8.70545i	−1.65127	−	0.464002i
$353$	−6.98861	−	8.06529i	−0.371966	−	0.429272i	0.538647	−	0.842532i	$-0.318936\pi$
$353$	−6.98861	−	8.06529i	−0.371966	−	0.429272i	−0.910613	+	0.413260i	$0.864390\pi$
$354$	4.82953	+	6.61477i	0.256687	+	0.351571i
$355$	4.87296	+	2.22541i	0.258630	+	0.118112i
$356$	21.9763	+	7.02733i	1.16474	+	0.372448i
$357$	−0.302593	−	1.03054i	−0.0160149	−	0.0545418i
$358$	−0.410900	−	6.90319i	−0.0217167	−	0.364845i
$359$	4.73808	+	32.9541i	0.250066	+	1.73925i	0.597790	+	0.801653i	$0.296046\pi$
$359$	4.73808	+	32.9541i	0.250066	+	1.73925i	−0.347723	+	0.937597i	$0.613045\pi$
$360$	2.15265	−	1.49417i	0.113455	−	0.0787495i
$361$	−0.0297137	−	0.0650639i	−0.00156388	−	0.00342441i
$362$	7.36486	−	13.1128i	0.387088	−	0.689195i
$363$	−3.04010	+	21.1444i	−0.159564	+	1.10979i
$364$	−0.486253	−	1.13580i	−0.0254866	−	0.0595322i
$365$	5.43340	−	6.27048i	0.284397	−	0.328212i
$366$	−20.0653	+	4.11453i	−1.04883	+	0.215070i
$367$	−12.3136			−0.642763			−0.321381	−	0.946950i	$-0.604147\pi$
$367$	−12.3136			−0.642763			−0.321381	+	0.946950i	$0.604147\pi$
$368$	−10.3587	−	16.1461i	−0.539984	−	0.841676i
$369$	−2.91177			−0.151581
$370$	12.8579	−	2.63660i	0.668452	−	0.137070i
$371$	−1.81712	+	2.09707i	−0.0943404	+	0.108875i
$372$	1.27281	+	2.97305i	0.0659919	+	0.154146i
$373$	−4.34766	+	30.2386i	−0.225113	+	1.56570i	0.493161	+	0.869938i	$0.335841\pi$
$373$	−4.34766	+	30.2386i	−0.225113	+	1.56570i	−0.718275	+	0.695760i	$0.755068\pi$
$374$	20.8954	−	37.2034i	1.08047	−	1.92374i
$375$	−3.51828	−	7.70395i	−0.181683	−	0.397830i
$376$	−19.4666	−	28.0456i	−1.00391	−	1.44634i
$377$	−1.71949	−	11.9593i	−0.0885584	−	0.615937i
$378$	−0.0170163	−	0.285878i	−0.000875226	−	0.0147040i
$379$	4.46584	+	15.2092i	0.229395	+	0.781246i	0.991076	+	0.133295i	$0.0425558\pi$
$379$	4.46584	+	15.2092i	0.229395	+	0.781246i	−0.761682	+	0.647951i	$0.775626\pi$
$380$	−7.70732	−	2.46456i	−0.395377	−	0.126429i
$381$	−2.13777	−	0.976285i	−0.109521	−	0.0500166i
$382$	−10.3170	−	14.1306i	−0.527862	−	0.722986i
$383$	8.62982	+	9.95935i	0.440963	+	0.508899i	0.932109	−	0.362179i	$-0.117967\pi$
$383$	8.62982	+	9.95935i	0.440963	+	0.508899i	−0.491145	+	0.871078i	$0.663422\pi$
$384$	7.30380	+	8.64028i	0.372721	+	0.440923i
$385$	−0.577005	−	0.897837i	−0.0294069	−	0.0457580i
$386$	−5.91015	−	16.4431i	−0.300819	−	0.836929i
$387$	−0.813440	+	1.26574i	−0.0413495	+	0.0643411i
$388$	−24.1515	+	6.46895i	−1.22611	+	0.328411i
$389$	−10.2394	−	3.00657i	−0.519160	−	0.152439i	0.0116467	−	0.999932i	$-0.496293\pi$
$389$	−10.2394	−	3.00657i	−0.519160	−	0.152439i	−0.530806	+	0.847493i	$0.678111\pi$
$390$	1.87345	+	3.53060i	0.0948659	+	0.178779i
$391$	24.0422	−	8.30510i	1.21587	−	0.420007i
$392$	−2.10677	+	19.5699i	−0.106408	+	0.988431i
$393$	−15.9931	−	4.69599i	−0.806745	−	0.236882i
$394$	5.17409	+	1.19046i	0.260667	+	0.0599747i
$395$	3.23673	+	2.08012i	0.162858	+	0.104662i
$396$	7.65397	−	8.41807i	0.384627	−	0.423024i
$397$	−6.12814	−	9.53558i	−0.307563	−	0.478577i	0.652723	−	0.757597i	$-0.273627\pi$
$397$	−6.12814	−	9.53558i	−0.307563	−	0.478577i	−0.960285	+	0.279020i	$0.909990\pi$
$398$	−16.6650	−	12.7888i	−0.835342	−	0.641043i
$399$	−0.668350	+	0.579128i	−0.0334593	+	0.0289927i
$400$	14.3488	−	8.28070i	0.717440	−	0.414035i
$401$	−23.4511	−	10.7098i	−1.17109	−	0.534820i	−0.267644	−	0.963518i	$-0.586245\pi$
$401$	−23.4511	−	10.7098i	−1.17109	−	0.534820i	−0.903448	+	0.428698i	$0.858972\pi$
$402$	−6.38427	−	6.53866i	−0.318418	−	0.326119i
$403$	−4.73307	+	1.38975i	−0.235771	+	0.0692286i
$404$	25.6987	−	15.6609i	1.27856	−	0.779157i
$405$	0.131847	+	0.917018i	0.00655155	+	0.0455670i
$406$	0.409053	−	1.05794i	0.0203009	−	0.0525046i
$407$	51.8395	−	23.6743i	2.56959	−	1.17349i
$408$	−13.4156	+	6.71303i	−0.664173	+	0.332344i
$409$	0.443640	−	3.08558i	0.0219366	−	0.152572i	−0.975909	−	0.218178i	$-0.929989\pi$
$409$	0.443640	−	3.08558i	0.0219366	−	0.152572i	0.997846	+	0.0656054i	$0.0208979\pi$
$410$	3.80175	+	0.317599i	0.187755	+	0.0156851i
$411$	−2.72745	−	2.36335i	−0.134535	−	0.116576i
$412$	−21.9906	+	18.1536i	−1.08340	+	0.894361i
$413$	−1.17277			−0.0577082
$414$	6.74393	−	0.720678i	0.331446	−	0.0354194i
$415$			6.05797i			0.297374i
$416$	−14.4075	+	9.49842i	−0.706385	+	0.465698i
$417$	−4.84687	+	5.59359i	−0.237352	+	0.273919i
$418$	−35.0118	−	2.92489i	−1.71248	−	0.143061i
$419$	−4.64869	−	0.668381i	−0.227104	−	0.0326526i	0.0278235	−	0.999613i	$-0.491142\pi$
$419$	−4.64869	−	0.668381i	−0.227104	−	0.0326526i	−0.254927	+	0.966960i	$0.582051\pi$
$420$	−0.00896446	+	0.375111i	−0.000437421	+	0.0183036i
$421$	−4.69325	−	10.2768i	−0.228735	−	0.500860i	0.760112	−	0.649792i	$-0.225144\pi$
$421$	−4.69325	−	10.2768i	−0.228735	−	0.500860i	−0.988848	+	0.148932i	$0.952417\pi$
$422$	13.1096	+	5.06884i	0.638166	+	0.246747i
$423$	11.9473	−	1.71776i	0.580896	−	0.0835202i
$424$	33.3286	+	19.7811i	1.61858	+	0.960655i
$425$	6.18876	+	21.0770i	0.300199	+	1.02238i
$426$	−5.71288	−	5.85104i	−0.276790	−	0.283484i
$427$	1.21840	−	2.66793i	0.0589626	−	0.129110i
$428$	−10.7804	+	22.1870i	−0.521088	+	1.07245i
$429$	11.3645	+	13.1153i	0.548682	+	0.633213i
$430$	1.20013	−	1.56388i	0.0578752	−	0.0754171i
$431$	−3.81303	+	2.45048i	−0.183667	+	0.118036i	−0.629243	−	0.777208i	$-0.716635\pi$
$431$	−3.81303	+	2.45048i	−0.183667	+	0.118036i	0.445576	+	0.895244i	$0.352999\pi$
$432$	−3.88742	+	0.942308i	−0.187034	+	0.0453368i
$433$	−11.8404	+	18.4240i	−0.569012	+	0.885401i	−0.999855	−	0.0170265i	$-0.994580\pi$
$433$	−11.8404	+	18.4240i	−0.569012	+	0.885401i	0.430843	+	0.902427i	$0.358216\pi$
$434$	−0.451298	−	0.103836i	−0.0216630	−	0.00498427i
$435$	−1.03377	+	3.52070i	−0.0495655	+	0.168805i
$436$	−1.51484	+	2.23773i	−0.0725478	+	0.107168i
$437$	−14.4439	−	15.1664i	−0.690946	−	0.725505i
$438$	−11.1878	+	5.93662i	−0.534574	+	0.283662i
$439$	1.53974	−	5.24387i	0.0734877	−	0.250276i	−0.914554	−	0.404464i	$-0.867458\pi$
$439$	1.53974	−	5.24387i	0.0734877	−	0.250276i	0.988042	+	0.154188i	$0.0492762\pi$
$440$	−10.9116	+	10.1562i	−0.520189	+	0.484177i
$441$	−5.85428	−	3.76232i	−0.278775	−	0.179158i
$442$	−7.73963	−	21.5330i	−0.368137	−	1.02422i
$443$	−25.8908	+	16.6390i	−1.23011	+	0.790542i	−0.983908	−	0.178677i	$-0.942818\pi$
$443$	−25.8908	+	16.6390i	−1.23011	+	0.790542i	−0.246200	+	0.969219i	$0.579182\pi$
$444$	−19.7582	−	3.32440i	−0.937682	−	0.157769i
$445$	8.07726	−	6.99899i	0.382899	−	0.331784i
$446$	9.86960	−	7.20593i	0.467339	−	0.341211i
$447$	−1.51969	+	3.32765i	−0.0718787	+	0.157392i
$448$	−1.61593	+	0.115118i	−0.0763457	+	0.00543880i
$449$	18.1997	−	5.34392i	0.858899	−	0.252195i	0.177512	−	0.984119i	$-0.443195\pi$
$449$	18.1997	−	5.34392i	0.858899	−	0.252195i	0.681387	+	0.731923i	$0.261377\pi$
$450$	0.348026	+	5.84689i	0.0164061	+	0.275625i
$451$	16.3957	−	2.35735i	0.772045	−	0.111003i
$452$	0.938240	+	7.85337i	0.0441311	+	0.369392i
$453$	9.33698	−	4.26406i	0.438690	−	0.200343i
$454$	13.9574	+	7.83923i	0.655055	+	0.367913i
$455$	−0.566494	−	0.0814495i	−0.0265576	−	0.00381841i
$456$	9.61670	+	7.75186i	0.450343	+	0.363014i
$457$	−12.8086	−	11.0987i	−0.599161	−	0.519176i	0.301632	−	0.953424i	$-0.402469\pi$
$457$	−12.8086	−	11.0987i	−0.599161	−	0.519176i	−0.900793	+	0.434248i	$0.857014\pi$
$458$	−1.62875	+	0.333985i	−0.0761065	+	0.0156061i
$459$		−	5.30382i		−	0.247561i
$460$	−8.88381	+	0.205363i	−0.414210	+	0.00957511i
$461$		−	14.7348i		−	0.686267i	−0.939287	−	0.343134i	$-0.888512\pi$
$461$		−	14.7348i		−	0.686267i	0.939287	−	0.343134i	$-0.111488\pi$
$462$	0.327261	+	1.59595i	0.0152255	+	0.0742505i
$463$	−22.4526	−	19.4553i	−1.04346	−	0.904163i	−0.0479523	−	0.998850i	$-0.515270\pi$
$463$	−22.4526	−	19.4553i	−1.04346	−	0.904163i	−0.995507	+	0.0946869i	$0.969815\pi$
$464$	−15.5557	−	3.00114i	−0.722157	−	0.139325i
$465$	1.48284	+	0.213200i	0.0687651	+	0.00988693i
$466$	−20.2152	+	35.9923i	−0.936450	+	1.66731i
$467$	10.2840	−	4.69653i	0.475885	−	0.217329i	−0.163008	−	0.986625i	$-0.552120\pi$
$467$	10.2840	−	4.69653i	0.475885	−	0.217329i	0.638893	+	0.769295i	$0.279392\pi$
$468$	−0.723759	−	6.05810i	−0.0334558	−	0.280036i
$469$	1.29524	−	0.186228i	0.0598088	−	0.00859921i
$470$	−15.7863	+	0.939650i	−0.728167	+	0.0433428i
$471$	−3.12590	+	0.917847i	−0.144034	+	0.0422922i
$472$	2.90613	+	16.1206i	0.133765	+	0.742009i
$473$	3.55562	−	7.78572i	0.163488	−	0.357988i
$474$	−3.46325	−	4.74344i	−0.159072	−	0.217873i
$475$	13.6694	−	11.8446i	0.627194	−	0.543467i
$476$	0.356415	−	2.11831i	0.0163363	−	0.0970926i
$477$	−11.5274	+	7.40818i	−0.527801	+	0.339197i
$478$	1.57635	−	0.566592i	0.0721008	−	0.0259153i
$479$	−15.6550	−	10.0608i	−0.715294	−	0.459692i	0.131703	−	0.991289i	$-0.457956\pi$
$479$	−15.6550	−	10.0608i	−0.715294	−	0.459692i	−0.846997	+	0.531597i	$0.821592\pi$
$480$	5.17839	−	0.806305i	0.236360	−	0.0368026i
$481$	8.60994	−	29.3228i	0.392579	−	1.33700i
$482$	0.546711	+	1.03030i	0.0249020	+	0.0469289i
$483$	−0.486086	+	0.840773i	−0.0221177	+	0.0382565i
$484$	−23.9502	+	35.3793i	−1.08865	+	1.60815i
$485$	−3.26300	+	11.1128i	−0.148165	+	0.504605i
$486$	0.317100	−	1.37820i	0.0143840	−	0.0625166i
$487$	6.59926	−	10.2686i	0.299041	−	0.465317i	−0.658921	−	0.752212i	$-0.728987\pi$
$487$	6.59926	−	10.2686i	0.299041	−	0.465317i	0.957962	+	0.286895i	$0.0926232\pi$
$488$	−39.6918	−	10.1367i	−1.79676	−	0.458865i
$489$	0.198051	−	0.127280i	0.00895620	−	0.00575580i
$490$	7.23325	+	5.55081i	0.326765	+	0.250760i
$491$	5.64089	+	6.50994i	0.254570	+	0.293789i	0.868621	−	0.495477i	$-0.165007\pi$
$491$	5.64089	+	6.50994i	0.254570	+	0.293789i	−0.614051	+	0.789266i	$0.710461\pi$
$492$	−5.23798	−	2.54506i	−0.236146	−	0.114740i
$493$	8.72644	−	19.1082i	0.393019	−	0.860592i
$494$	−13.4804	+	13.1621i	−0.606513	+	0.592192i
$495$	−1.48482	−	5.05684i	−0.0667378	−	0.227288i
$496$	−0.308975	+	6.46072i	−0.0138734	+	0.290095i
$497$	1.15903	−	0.166644i	0.0519898	−	0.00747500i
$498$	3.33492	−	8.62515i	0.149441	−	0.386502i
$499$	17.3321	+	37.9519i	0.775889	+	1.69896i	0.713235	+	0.700925i	$0.247229\pi$
$499$	17.3321	+	37.9519i	0.775889	+	1.69896i	0.0626546	+	0.998035i	$0.480043\pi$
$500$	0.404686	−	16.9338i	0.0180981	−	0.757302i
$501$	2.17483	+	0.312693i	0.0971642	+	0.0139701i
$502$	−1.51913	+	18.1844i	−0.0678021	+	0.811611i
$503$	20.3881	−	23.5291i	0.909060	−	1.04911i	−0.0895274	−	0.995984i	$-0.528536\pi$
$503$	20.3881	−	23.5291i	0.909060	−	1.04911i	0.998588	−	0.0531272i	$-0.0169189\pi$
$504$	0.219263	−	0.529137i	0.00976674	−	0.0235696i
$505$		−	13.9405i		−	0.620346i
$506$	−37.3905	+	9.51786i	−1.66221	+	0.423120i
$507$	−3.69389			−0.164051
$508$	−2.99229	−	3.62477i	−0.132761	−	0.160823i
$509$	25.3473	+	21.9636i	1.12350	+	0.973519i	0.999823	−	0.0188034i	$-0.00598567\pi$
$509$	25.3473	+	21.9636i	1.12350	+	0.973519i	0.123678	+	0.992322i	$0.460531\pi$
$510$	−0.578509	+	6.92492i	−0.0256168	+	0.306641i
$511$	0.258098	−	1.79511i	0.0114176	−	0.0794111i
$512$	5.58667	+	21.9269i	0.246898	+	0.969041i
$513$	−3.97245	+	1.81416i	−0.175388	+	0.0800970i
$514$	37.3401	+	14.4376i	1.64700	+	0.636815i
$515$	1.87985	+	13.0747i	0.0828362	+	0.576139i
$516$	−2.56962	+	1.56594i	−0.113121	+	0.0689365i
$517$	−65.8825	+	19.3448i	−2.89751	+	0.850785i
$518$	2.05276	−	2.00429i	0.0901933	−	0.0880636i
$519$	−21.2336	−	9.69706i	−0.932052	−	0.425654i
$520$	0.284193	+	7.98869i	0.0124627	+	0.350327i
$521$	−11.2719	+	9.76715i	−0.493831	+	0.427907i	−0.865839	−	0.500323i	$-0.833215\pi$
$521$	−11.2719	+	9.76715i	−0.493831	+	0.427907i	0.372008	+	0.928229i	$0.378669\pi$
$522$	3.41000	−	4.44357i	0.149252	−	0.194490i
$523$	5.46842	+	8.50903i	0.239117	+	0.372074i	0.939984	−	0.341218i	$-0.110840\pi$
$523$	5.46842	+	8.50903i	0.239117	+	0.372074i	−0.700867	+	0.713292i	$0.747203\pi$
$524$	−24.6653	−	22.4265i	−1.07751	−	0.979705i
$525$	−0.705566	−	0.453440i	−0.0307934	−	0.0197897i
$526$	2.87966	−	12.5158i	0.125559	−	0.545714i
$527$	−8.22900	−	2.41625i	−0.358461	−	0.105254i
$528$	21.1266	−	8.45321i	0.919416	−	0.367879i
$529$	−20.4307	−	10.5635i	−0.888291	−	0.459282i
$530$	15.8587	−	8.41514i	0.688858	−	0.365530i
$531$	−5.55676	−	1.63161i	−0.241143	−	0.0708059i
$532$	−1.70848	+	0.457615i	−0.0740721	+	0.0198401i
$533$	4.80231	−	7.47255i	0.208011	−	0.323672i
$534$	−15.3531	+	5.51839i	−0.664394	+	0.238804i
$535$	6.17765	+	9.61260i	0.267083	+	0.415589i
$536$	−5.76946	−	17.3426i	−0.249203	−	0.749086i
$537$	3.20223	+	3.69556i	0.138186	+	0.159475i
$538$	−4.95237	+	3.61579i	−0.213512	+	0.155888i
$539$	36.0104	+	16.4454i	1.55108	+	0.708354i
$540$	−0.564347	+	1.76486i	−0.0242856	+	0.0759476i
$541$	−5.20899	−	17.7402i	−0.223952	−	0.762711i	−0.992428	−	0.122832i	$-0.960803\pi$
$541$	−5.20899	−	17.7402i	−0.223952	−	0.762711i	0.768475	−	0.639879i	$-0.221016\pi$
$542$	35.9708	−	2.14110i	1.54508	−	0.0919679i
$543$	1.51346	+	10.5263i	0.0649486	+	0.451727i
$544$	−30.0009	+	0.350003i	−1.28628	+	0.0150062i
$545$	0.519995	+	1.13863i	0.0222741	+	0.0487736i
$546$	0.761718	+	0.427821i	0.0325985	+	0.0183091i
$547$	4.24770	−	29.5434i	0.181619	−	1.26318i	−0.671318	−	0.741170i	$-0.734271\pi$
$547$	4.24770	−	29.5434i	0.181619	−	1.26318i	0.852936	−	0.522015i	$-0.174820\pi$
$548$	−2.84070	−	6.63537i	−0.121349	−	0.283449i
$549$	9.48472	−	10.9460i	0.404798	−	0.467162i
$550$	−6.69328	−	32.6411i	−0.285402	−	1.39182i
$551$	−17.2965			−0.736857
$552$	12.7615	+	4.59816i	0.543167	+	0.195711i
$553$	0.840992			0.0357626
$554$	−6.31671	−	30.8048i	−0.268371	−	1.30877i
$555$	−6.07784	+	7.01420i	−0.257990	+	0.297736i
$556$	−13.6081	+	5.82583i	−0.577113	+	0.247070i
$557$	−6.32433	+	43.9867i	−0.267971	+	1.86378i	0.199677	+	0.979862i	$0.436011\pi$
$557$	−6.32433	+	43.9867i	−0.267971	+	1.86378i	−0.467647	+	0.883915i	$0.654898\pi$
$558$	−1.99386	−	1.11986i	−0.0844067	−	0.0474073i
$559$	−1.90670	−	4.17510i	−0.0806449	−	0.176588i
$560$	−0.343995	+	0.666950i	−0.0145364	+	0.0281838i
$561$	4.29393	+	29.8650i	0.181290	+	1.26090i
$562$	−16.9342	+	1.00798i	−0.714327	+	0.0425190i
$563$	−8.01378	−	27.2924i	−0.337741	−	1.15024i	−0.936897	−	0.349607i	$-0.886315\pi$
$563$	−8.01378	−	27.2924i	−0.337741	−	1.15024i	0.599156	−	0.800632i	$-0.295503\pi$
$564$	22.9933	+	7.35253i	0.968192	+	0.309597i
$565$	3.33266	+	1.52197i	0.140206	+	0.0640299i
$566$	−32.3872	+	23.6463i	−1.36133	+	0.993928i
$567$	0.132612	+	0.153042i	0.00556917	+	0.00642716i
$568$	−5.16273	−	15.5188i	−0.216623	−	0.651154i
$569$	13.7727	+	21.4307i	0.577380	+	0.898421i	0.999969	−	0.00790039i	$-0.00251480\pi$
$569$	13.7727	+	21.4307i	0.577380	+	0.898421i	−0.422588	+	0.906322i	$0.638878\pi$
$570$	5.38450	−	1.93536i	0.225532	−	0.0810633i
$571$	−3.36774	+	5.24030i	−0.140936	+	0.219300i	−0.904545	−	0.426379i	$-0.859789\pi$
$571$	−3.36774	+	5.24030i	−0.140936	+	0.219300i	0.763609	+	0.645679i	$0.223425\pi$
$572$	8.97997	+	33.5263i	0.375471	+	1.40180i
$573$	11.8705	+	3.48549i	0.495897	+	0.145608i
$574$	0.736605	−	0.390866i	0.0307453	−	0.0163144i
$575$	9.94165	−	17.1958i	0.414595	−	0.717116i
$576$	−7.81670	−	1.70272i	−0.325696	−	0.0709466i
$577$	28.2697	+	8.30075i	1.17689	+	0.345565i	0.810972	−	0.585085i	$-0.198939\pi$
$577$	28.2697	+	8.30075i	1.17689	+	0.345565i	0.365913	+	0.930649i	$0.380757\pi$
$578$	3.52948	−	15.3401i	0.146807	−	0.638064i
$579$	10.3939	+	6.67975i	0.431955	+	0.277601i
$580$	−4.93694	+	5.42980i	−0.204995	+	0.225460i
$581$	0.715893	+	1.11395i	0.0297002	+	0.0462145i
$582$	10.7634	−	14.0257i	0.446155	−	0.581385i
$583$	58.9111	−	51.0467i	2.43985	−	2.11414i
$584$	−25.3146	+	0.900555i	−1.04753	+	0.0372652i
$585$	−2.57082	−	1.17405i	−0.106290	−	0.0485411i
$586$	11.0173	−	10.7571i	0.455119	−	0.444373i
$587$	−3.94078	+	1.15712i	−0.162653	+	0.0477594i	−0.362045	−	0.932160i	$-0.617921\pi$
$587$	−3.94078	+	1.15712i	−0.162653	+	0.0477594i	0.199392	+	0.979920i	$0.436103\pi$
$588$	−7.24275	−	11.8850i	−0.298686	−	0.490129i
$589$	1.00499	+	6.98983i	0.0414097	+	0.288011i
$590$	7.07720	+	2.73641i	0.291364	+	0.112656i
$591$	−3.41496	+	1.55956i	−0.140473	+	0.0641517i
$592$	−32.6372	−	23.2500i	−1.34138	−	0.955571i
$593$	−5.45699	+	37.9542i	−0.224092	+	1.55859i	0.498237	+	0.867041i	$0.333981\pi$
$593$	−5.45699	+	37.9542i	−0.224092	+	1.55859i	−0.722329	+	0.691550i	$0.756928\pi$
$594$	−0.669756	+	8.01717i	−0.0274804	+	0.328948i
$595$	−0.752005	−	0.651616i	−0.0308292	−	0.0267137i
$596$	−5.64231	+	4.65780i	−0.231118	+	0.190791i
$597$	14.8539			0.607929
$598$	−9.27310	+	18.4957i	−0.379205	+	0.756345i
$599$		−	9.20302i		−	0.376025i	−0.982167	−	0.188013i	$-0.939795\pi$
$599$		−	9.20302i		−	0.376025i	0.982167	−	0.188013i	$-0.0602046\pi$
$600$	−4.48446	+	10.8221i	−0.183077	+	0.441812i
$601$	13.0357	−	15.0440i	0.531739	−	0.613659i	−0.424792	−	0.905291i	$-0.639653\pi$
$601$	13.0357	−	15.0440i	0.531739	−	0.613659i	0.956531	+	0.291632i	$0.0941981\pi$
$602$	0.0358715	−	0.429393i	0.00146201	−	0.0175007i
$603$	6.39615	+	0.919628i	0.260471	+	0.0374501i
$604$	20.5233	+	0.490468i	0.835081	+	0.0199569i
$605$	8.22131	+	18.0022i	0.334244	+	0.731892i
$606$	−7.67429	+	19.8481i	−0.311747	+	0.806274i
$607$	7.59528	−	1.09204i	0.308283	−	0.0443244i	0.0135629	−	0.999908i	$-0.495683\pi$
$607$	7.59528	−	1.09204i	0.308283	−	0.0443244i	0.294720	+	0.955584i	$0.404774\pi$
$608$	10.5239	+	22.3503i	0.426799	+	0.906425i
$609$	0.225962	+	0.769558i	0.00915646	+	0.0311840i
$610$	−13.5776	+	13.2570i	−0.549742	+	0.536761i
$611$	−15.2960	+	33.4936i	−0.618810	+	1.35500i
$612$	4.63584	−	9.54101i	0.187393	−	0.385673i
$613$	15.3094	+	17.6680i	0.618341	+	0.713604i	0.975391	−	0.220482i	$-0.0707629\pi$
$613$	15.3094	+	17.6680i	0.618341	+	0.713604i	−0.357050	+	0.934085i	$0.616217\pi$
$614$	9.37951	+	7.19785i	0.378526	+	0.290482i
$615$	−2.26937	+	1.45844i	−0.0915099	+	0.0588099i
$616$	−0.806248	+	3.15700i	−0.0324847	+	0.127199i
$617$	−5.26780	+	8.19686i	−0.212074	+	0.329993i	−0.930951	−	0.365144i	$-0.881020\pi$
$617$	−5.26780	+	8.19686i	−0.212074	+	0.329993i	0.718877	+	0.695137i	$0.244656\pi$
$618$	4.52115	−	19.6502i	0.181867	−	0.790446i
$619$	4.76989	−	16.2448i	0.191718	−	0.652932i	−0.806386	−	0.591389i	$-0.798580\pi$
$619$	4.76989	−	16.2448i	0.191718	−	0.652932i	0.998104	−	0.0615428i	$-0.0196021\pi$
$620$	2.48113	+	1.67961i	0.0996445	+	0.0674549i
$621$	−3.47287	+	3.30744i	−0.139362	+	0.132723i
$622$	14.5017	+	27.3291i	0.581465	+	1.09580i
$623$	0.658166	−	2.24151i	0.0263688	−	0.0898040i
$624$	3.99316	−	11.5305i	0.159854	−	0.461589i
$625$	10.8203	+	6.95377i	0.432811	+	0.278151i
$626$	17.7310	−	6.37308i	0.708673	−	0.254720i
$627$	20.8995	−	13.4313i	0.834646	−	0.536394i
$628$	−6.42542	−	1.08111i	−0.256402	−	0.0431408i
$629$	40.1556	−	34.7950i	1.60111	−	1.38737i
$630$	−0.156451	−	0.214284i	−0.00623317	−	0.00853726i
$631$	2.82529	−	6.18653i	0.112473	−	0.246282i	−0.845022	−	0.534732i	$-0.820413\pi$
$631$	2.82529	−	6.18653i	0.112473	−	0.246282i	0.957495	+	0.288450i	$0.0931399\pi$
$632$	−2.08398	−	11.5600i	−0.0828964	−	0.459833i
$633$	−9.53610	+	2.80005i	−0.379026	+	0.111292i
$634$	32.6645	−	1.94429i	1.29727	−	0.0772178i
$635$	−2.15513	+	0.309860i	−0.0855236	+	0.0122964i
$636$	−27.2117	+	3.25097i	−1.07901	+	0.128909i
$637$	19.3106	−	8.81886i	0.765114	−	0.349416i
$638$	−15.6037	+	27.7818i	−0.617756	+	1.09989i
$639$	5.72352	+	0.822918i	0.226419	+	0.0325541i
$640$	10.0201	+	3.07575i	0.396080	+	0.121580i
$641$	−2.91391	−	2.52492i	−0.115093	−	0.0997283i	0.595413	−	0.803420i	$-0.296988\pi$
$641$	−2.91391	−	2.52492i	−0.115093	−	0.0997283i	−0.710506	+	0.703691i	$0.751534\pi$
$642$	−3.50378	−	17.0869i	−0.138283	−	0.674367i
$643$			21.8728i			0.862580i	0.902213	+	0.431290i	$0.141941\pi$
$643$			21.8728i			0.862580i	−0.902213	+	0.431290i	$0.858059\pi$
$644$	−1.60930	+	1.08759i	−0.0634154	+	0.0428572i
$645$			1.39392i			0.0548856i
$646$	−32.0887	+	6.58000i	−1.26251	+	0.258887i
$647$	18.4655	+	16.0005i	0.725955	+	0.629044i	0.937363	−	0.348354i	$-0.113259\pi$
$647$	18.4655	+	16.0005i	0.725955	+	0.629044i	−0.211408	+	0.977398i	$0.567805\pi$
$648$	1.77506	−	2.20208i	0.0697309	−	0.0865059i
$649$	32.6102	+	4.68863i	1.28006	+	0.184045i
$650$	−15.5790	−	8.74998i	−0.611058	−	0.343202i
$651$	0.297862	−	0.136029i	0.0116741	−	0.00533140i
$652$	0.467524	−	0.0558549i	0.0183096	−	0.00218745i
$653$	−41.5415	+	5.97276i	−1.62564	+	0.233732i	−0.894037	−	0.447994i	$-0.852139\pi$
$653$	−41.5415	+	5.97276i	−1.62564	+	0.233732i	−0.731607	+	0.681726i	$0.761230\pi$
$654$	−0.113535	−	1.90741i	−0.00443956	−	0.0745854i
$655$	−14.8168	+	4.35060i	−0.578939	+	0.169992i
$656$	−7.19804	−	9.15659i	−0.281036	−	0.357505i
$657$	3.72035	−	8.14643i	0.145145	−	0.317822i
$658$	−2.79177	+	2.03831i	−0.108834	+	0.0794615i
$659$	34.1982	−	29.6329i	1.33217	−	1.15434i	0.356700	−	0.934219i	$-0.383902\pi$
$659$	34.1982	−	29.6329i	1.33217	−	1.15434i	0.975474	−	0.220116i	$-0.0706436\pi$
$660$	1.74893	−	10.3945i	0.0680770	−	0.404607i
$661$	−7.90976	+	5.08329i	−0.307654	+	0.197717i	−0.685353	−	0.728211i	$-0.740352\pi$
$661$	−7.90976	+	5.08329i	−0.307654	+	0.197717i	0.377699	+	0.925929i	$0.376716\pi$
$662$	8.43736	+	23.4742i	0.327927	+	0.912349i
$663$	13.6113	+	8.74745i	0.528619	+	0.339723i
$664$	13.5381	−	12.6008i	0.525378	−	0.489007i
$665$	−0.230826	+	0.786120i	−0.00895103	+	0.0304844i
$666$	12.5148	−	6.64074i	0.484937	−	0.257323i
$667$	−17.9536	+	6.20187i	−0.695166	+	0.240137i
$668$	3.63898	+	2.46343i	0.140796	+	0.0953128i
$669$	−2.43446	+	8.29100i	−0.0941215	+	0.320548i
$670$	−8.25081	−	1.89836i	−0.318757	−	0.0733402i
$671$	−44.5452	+	69.3137i	−1.71965	+	2.67582i
$672$	0.856927	−	0.760214i	0.0330567	−	0.0293259i
$673$	18.1780	−	11.6823i	0.700711	−	0.450320i	−0.141168	−	0.989986i	$-0.545086\pi$
$673$	18.1780	−	11.6823i	0.700711	−	0.450320i	0.841879	+	0.539666i	$0.181450\pi$
$674$	−11.4846	+	14.9655i	−0.442369	+	0.576451i
$675$	−2.71223	−	3.13008i	−0.104394	−	0.120477i
$676$	−6.64492	−	3.22867i	−0.255574	−	0.124180i
$677$	4.25282	−	9.31238i	0.163449	−	0.357904i	−0.810131	−	0.586249i	$-0.800604\pi$
$677$	4.25282	−	9.31238i	0.163449	−	0.357904i	0.973580	+	0.228345i	$0.0733314\pi$
$678$	−3.90708	−	4.00157i	−0.150051	−	0.153679i
$679$	0.713229	+	2.42904i	0.0273712	+	0.0932178i
$680$	−7.09345	+	11.9516i	−0.272021	+	0.458321i
$681$	−11.2043	+	1.61094i	−0.429350	+	0.0617312i
$682$	12.1337	+	4.69151i	0.464624	+	0.179647i
$683$	−9.28447	−	20.3301i	−0.355260	−	0.777911i	−0.999910	−	0.0134332i	$-0.995724\pi$
$683$	−9.28447	−	20.3301i	−0.355260	−	0.777911i	0.644649	−	0.764478i	$-0.277003\pi$
$684$	−8.73170	−	0.208671i	−0.333865	−	0.00797875i
$685$	−3.30946	−	0.475829i	−0.126448	−	0.0181805i
$686$	3.98375	+	0.332803i	0.152100	+	0.0127065i
$687$	0.769896	−	0.888507i	0.0293734	−	0.0338987i
$688$	−5.99120	+	0.570958i	−0.228412	+	0.0217676i
$689$		−	41.8010i		−	1.59249i
$690$	4.89510	−	3.93955i	0.186353	−	0.149976i
$691$	−0.568566			−0.0216293			−0.0108146	−	0.999942i	$-0.503442\pi$
$691$	−0.568566			−0.0216293			−0.0108146	+	0.999942i	$0.503442\pi$
$692$	−29.7212	−	36.0034i	−1.12983	−	1.36864i
$693$	−0.870617	−	0.754394i	−0.0330720	−	0.0286571i
$694$	30.0494	+	2.51033i	1.14066	+	0.0952908i
$695$	−0.975852	+	6.78720i	−0.0370162	+	0.257453i
$696$	10.0182	−	5.01298i	0.379738	−	0.190017i
$697$	14.0479	−	6.41547i	0.532103	−	0.243003i
$698$	8.27363	−	21.3982i	0.313162	−	0.809934i
$699$	−4.15415	−	28.8928i	−0.157125	−	1.09283i
$700$	−0.872907	−	1.43240i	−0.0329928	−	0.0541395i
$701$	3.62813	−	1.06532i	0.137033	−	0.0402364i	−0.212497	−	0.977162i	$-0.568160\pi$
$701$	3.62813	−	1.06532i	0.137033	−	0.0402364i	0.349530	+	0.936925i	$0.386341\pi$
$702$	3.01393	+	3.08682i	0.113753	+	0.116504i
$703$	−39.7958	−	18.1741i	−1.50093	−	0.685451i
$704$	45.3931	+	3.25939i	1.71082	+	0.122843i
$705$	8.45105	−	7.32288i	0.318285	−	0.275796i
$706$	11.9731	+	9.18820i	0.450615	+	0.345802i
$707$	−1.64740	−	2.56341i	−0.0619570	−	0.0964070i
$708$	−8.56990	−	7.79203i	−0.322077	−	0.292842i
$709$	−25.6884	−	16.5090i	−0.964750	−	0.620007i	−0.0394411	−	0.999222i	$-0.512558\pi$
$709$	−25.6884	−	16.5090i	−0.964750	−	0.620007i	−0.925309	+	0.379215i	$0.876194\pi$
$710$	−7.38314	−	1.69873i	−0.277084	−	0.0637521i
$711$	3.98474	+	1.17003i	0.149440	+	0.0438794i
$712$	−32.4420	−	3.49249i	−1.21582	−	0.130887i
$713$	3.54944	+	6.89501i	0.132928	+	0.258220i
$714$	0.711966	+	1.34173i	0.0266446	+	0.0502130i
$715$	15.4264	+	4.52959i	0.576913	+	0.169397i
$716$	2.53033	+	9.44686i	0.0945629	+	0.353046i
$717$	−0.640371	+	0.996436i	−0.0239151	+	0.0372126i
$718$	−15.9258	−	44.3082i	−0.594344	−	1.65357i
$719$	−23.4540	−	36.4952i	−0.874688	−	1.36104i	−0.931914	−	0.362680i	$-0.881862\pi$
$719$	−23.4540	−	36.4952i	−0.874688	−	1.36104i	0.0572253	−	0.998361i	$-0.481775\pi$
$720$	−2.55779	+	2.68153i	−0.0953233	+	0.0999347i
$721$	1.89075	+	2.18204i	0.0704153	+	0.0812636i
$722$	0.0596484	+	0.0816975i	0.00221988	+	0.00304047i
$723$	−0.750216	−	0.342612i	−0.0279008	−	0.0127419i
$724$	−6.47805	+	20.2586i	−0.240755	+	0.752904i
$725$	−4.62148	−	15.7393i	−0.171638	−	0.584544i
$726$	−1.79503	−	30.1568i	−0.0666197	−	1.11922i
$727$	−3.92252	−	27.2817i	−0.145478	−	1.01182i	−0.923503	−	0.383590i	$-0.874687\pi$
$727$	−3.92252	−	27.2817i	−0.145478	−	1.01182i	0.778025	−	0.628233i	$-0.216222\pi$
$728$	0.996311	+	1.43539i	0.0369257	+	0.0531991i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	−5.74603	+	10.2306i	−0.212670	+	0.378650i
$731$	1.13568	−	7.89882i	0.0420046	−	0.292148i
$732$	26.6294	−	11.4004i	0.984251	−	0.421372i
$733$	13.7356	−	15.8517i	0.507334	−	0.585495i	−0.443080	−	0.896482i	$-0.646114\pi$
$733$	13.7356	−	15.8517i	0.507334	−	0.585495i	0.950414	+	0.310987i	$0.100660\pi$
$734$	17.0590	−	3.49807i	0.629661	−	0.129116i
$735$	−6.44715			−0.237807
$736$	18.9376	+	19.4259i	0.698050	+	0.716049i
$737$	−36.7602			−1.35408
$738$	4.03393	−	0.827184i	0.148491	−	0.0304491i
$739$	26.7580	−	30.8803i	0.984308	−	1.13595i	−0.00640517	−	0.999979i	$-0.502039\pi$
$739$	26.7580	−	30.8803i	0.984308	−	1.13595i	0.990713	−	0.135972i	$-0.0434157\pi$
$740$	−17.0642	+	7.30543i	−0.627293	+	0.268553i
$741$	1.89595	−	13.1866i	0.0696495	−	0.484423i
$742$	1.92168	−	3.42147i	0.0705470	−	0.125606i
$743$	6.21396	+	13.6067i	0.227968	+	0.499180i	0.988704	−	0.149881i	$-0.0478891\pi$
$743$	6.21396	+	13.6067i	0.227968	+	0.499180i	−0.760736	+	0.649061i	$0.775162\pi$
$744$	−2.60792	−	3.75725i	−0.0956110	−	0.137747i
$745$	0.482329	+	3.35467i	0.0176712	+	0.122906i
$746$	−2.56708	−	43.1273i	−0.0939873	−	1.57900i
$747$	1.84223	+	6.27405i	0.0674035	+	0.229555i
$748$	−18.3794	+	57.4771i	−0.672016	+	2.10157i
$749$	2.27191	+	1.03755i	0.0830139	+	0.0379112i
$750$	7.06273	+	9.67347i	0.257895	+	0.353225i
$751$	12.3102	+	14.2067i	0.449204	+	0.518409i	0.934511	−	0.355935i	$-0.115837\pi$
$751$	12.3102	+	14.2067i	0.449204	+	0.518409i	−0.485307	+	0.874344i	$0.661292\pi$
$752$	34.9360	+	33.3239i	1.27398	+	1.21520i
$753$	−6.97596	−	10.8548i	−0.254218	−	0.395571i
$754$	5.77960	+	16.0798i	0.210481	+	0.585593i
$755$	5.14127	−	7.99998i	0.187110	−	0.291149i
$756$	0.104787	+	0.391217i	0.00381107	+	0.0142284i
$757$	30.1973	+	8.86672i	1.09754	+	0.322267i	0.779874	−	0.625936i	$-0.215283\pi$
$757$	30.1973	+	8.86672i	1.09754	+	0.322267i	0.317665	+	0.948203i	$0.397101\pi$
$758$	−10.5076	−	19.8020i	−0.381653	−	0.719242i
$759$	16.8775	−	21.4353i	0.612614	−	0.778051i
$760$	11.3778	+	1.22485i	0.412715	+	0.0444301i
$761$	−7.20792	−	2.11644i	−0.261287	−	0.0767208i	0.148465	−	0.988918i	$-0.452567\pi$
$761$	−7.20792	−	2.11644i	−0.261287	−	0.0767208i	−0.409752	+	0.912197i	$0.634385\pi$
$762$	3.23898	+	0.745231i	0.117336	+	0.0269969i
$763$	0.230174	+	0.147924i	0.00833285	+	0.00535520i
$764$	18.3072	+	16.6455i	0.662333	+	0.602214i
$765$	−2.65655	−	4.13368i	−0.0960479	−	0.149453i
$766$	−14.7849	−	11.3460i	−0.534201	−	0.409946i
$767$	13.3519	−	11.5695i	0.482108	−	0.417749i
$768$	−12.5731	−	9.89525i	−0.453694	−	0.357064i
$769$	3.85070	+	1.75856i	0.138860	+	0.0634152i	0.483633	−	0.875271i	$-0.339317\pi$
$769$	3.85070	+	1.75856i	0.138860	+	0.0634152i	−0.344773	+	0.938686i	$0.612044\pi$
$770$	1.05443	+	1.07993i	0.0379992	+	0.0389181i
$771$	−27.1617	+	7.97539i	−0.978205	+	0.287227i
$772$	12.8590	+	21.1010i	0.462807	+	0.759442i
$773$	1.99233	+	13.8569i	0.0716590	+	0.498399i	0.993768	+	0.111469i	$0.0355555\pi$
$773$	1.99233	+	13.8569i	0.0716590	+	0.498399i	−0.922109	+	0.386930i	$0.873535\pi$
$774$	0.767356	−	1.98462i	0.0275820	−	0.0713357i
$775$	−6.09201	+	2.78213i	−0.218831	+	0.0999370i
$776$	31.6214	−	15.8230i	1.13514	−	0.568013i
$777$	−0.288710	+	2.00802i	−0.0103574	+	0.0720375i
$778$	15.0397	+	1.25642i	0.539199	+	0.0450448i
$779$	−9.61011	−	8.32721i	−0.344318	−	0.298353i
$780$	−3.59844	−	4.35904i	−0.128845	−	0.156079i
$781$	−32.8944			−1.17706
$782$	−30.9484	+	18.3357i	−1.10671	+	0.655685i
$783$			3.96065i			0.141542i
$784$	−2.64079	−	27.7104i	−0.0943138	−	0.989658i
$785$	−1.97653	+	2.28104i	−0.0705454	+	0.0814137i
$786$	23.4907	+	1.96241i	0.837884	+	0.0699970i
$787$	19.4314	+	2.79381i	0.692654	+	0.0995886i	0.479646	−	0.877462i	$-0.340765\pi$
$787$	19.4314	+	2.79381i	0.692654	+	0.0995886i	0.213008	+	0.977051i	$0.431674\pi$
$788$	−7.50630	−	0.179387i	−0.267401	−	0.00639038i
$789$	3.77248	+	8.26057i	0.134304	+	0.294084i
$790$	−5.07505	−	1.96227i	−0.180562	−	0.0698146i
$791$	0.792672	−	0.113969i	0.0281842	−	0.00405227i
$792$	−8.21229	+	13.8366i	−0.291811	+	0.491664i
$793$	12.4479	+	42.3937i	0.442039	+	1.50544i
$794$	11.1987	+	11.4696i	0.397428	+	0.407040i
$795$	−5.27358	+	11.5475i	−0.187035	+	0.409549i
$796$	26.7206	+	12.9831i	0.947086	+	0.460175i
$797$	−7.00294	−	8.08183i	−0.248057	−	0.286273i	0.618043	−	0.786145i	$-0.287926\pi$
$797$	−7.00294	−	8.08183i	−0.248057	−	0.286273i	−0.866099	+	0.499872i	$0.833381\pi$
$798$	0.761403	−	0.992183i	0.0269534	−	0.0351229i
$799$	−53.8551	+	34.6106i	−1.90526	+	1.22444i
$800$	−17.5262	+	15.5482i	−0.619646	+	0.549712i
$801$	6.23697	−	9.70492i	0.220373	−	0.342907i
$802$	35.5313	+	8.17511i	1.25465	+	0.288673i
$803$	−14.3534	+	48.8832i	−0.506521	+	1.72505i
$804$	10.7022	+	7.24492i	0.377438	+	0.255509i
$805$	0.0422777	+	0.898748i	0.00149009	+	0.0316767i
$806$	6.16232	−	3.26993i	0.217059	−	0.115178i
$807$	1.22156	−	4.16026i	0.0430010	−	0.146448i
$808$	−31.1536	+	28.9969i	−1.09598	+	1.02011i
$809$	−15.3301	−	9.85208i	−0.538979	−	0.346381i	0.242661	−	0.970111i	$-0.421980\pi$
$809$	−15.3301	−	9.85208i	−0.538979	−	0.346381i	−0.781639	+	0.623731i	$0.785616\pi$
$810$	−0.443168	−	1.23297i	−0.0155714	−	0.0433221i
$811$	−7.99571	+	5.13853i	−0.280767	+	0.180438i	−0.673444	−	0.739238i	$-0.735186\pi$
$811$	−7.99571	+	5.13853i	−0.280767	+	0.180438i	0.392676	+	0.919677i	$0.371549\pi$
$812$	−0.266155	+	1.58186i	−0.00934020	+	0.0555123i
$813$	−19.2567	+	16.6860i	−0.675360	+	0.585203i
$814$	−65.0924	+	47.5248i	−2.28149	+	1.66574i
$815$	0.0906055	−	0.198398i	0.00317377	−	0.00694959i
$816$	16.6788	−	13.1113i	0.583874	−	0.458987i
$817$	−6.30451	+	1.85117i	−0.220567	+	0.0647643i
$818$	0.261947	+	4.40075i	0.00915876	+	0.153869i
$819$	−0.611468	+	0.0879159i	−0.0213664	+	0.00307203i
$820$	−5.35712	+	0.640013i	−0.187079	+	0.0223502i
$821$	24.6672	−	11.2651i	0.860891	−	0.393156i	0.0644855	−	0.997919i	$-0.479459\pi$
$821$	24.6672	−	11.2651i	0.860891	−	0.393156i	0.796406	+	0.604763i	$0.206732\pi$
$822$	4.44996	+	2.49933i	0.155210	+	0.0871743i
$823$	−14.1562	−	2.03536i	−0.493455	−	0.0709481i	−0.108905	−	0.994052i	$-0.534734\pi$
$823$	−14.1562	−	2.03536i	−0.493455	−	0.0709481i	−0.384550	+	0.923104i	$0.625643\pi$
$824$	25.3085	−	31.3969i	0.881662	−	1.09376i
$825$	17.8062	+	15.4292i	0.619934	+	0.537176i
$826$	1.62474	−	0.333163i	0.0565319	−	0.0115922i
$827$			44.6603i			1.55299i	0.630123	+	0.776495i	$0.283004\pi$
$827$			44.6603i			1.55299i	−0.630123	+	0.776495i	$0.716996\pi$
$828$	−9.13822	+	2.91425i	−0.317575	+	0.101277i
$829$			12.9797i			0.450805i	0.974266	+	0.225402i	$0.0723697\pi$
$829$			12.9797i			0.450805i	−0.974266	+	0.225402i	$0.927630\pi$
$830$	−1.72096	−	8.39263i	−0.0597355	−	0.291313i
$831$	16.8045	+	14.5612i	0.582940	+	0.505121i
$832$	17.2616	−	17.2519i	0.598438	−	0.598102i
$833$	36.5335	+	5.25273i	1.26581	+	0.181996i
$834$	5.12575	−	9.12620i	0.177490	−	0.316014i
$835$	1.85163	−	0.845613i	0.0640784	−	0.0292636i
$836$	49.3357	−	5.89412i	1.70631	−	0.203853i
$837$	1.60057	−	0.230127i	0.0553237	−	0.00795434i
$838$	6.63011	−	0.394646i	0.229033	−	0.0136328i
$839$	32.9246	−	9.66753i	1.13668	−	0.333760i	0.341352	−	0.939936i	$-0.389115\pi$
$839$	32.9246	−	9.66753i	1.13668	−	0.333760i	0.795331	+	0.606175i	$0.207297\pi$
$840$	−0.0941433	−	0.522221i	−0.00324825	−	0.0180183i
$841$	5.53053	−	12.1102i	0.190708	−	0.417592i
$842$	9.42143	+	12.9041i	0.324684	+	0.444703i
$843$	9.06559	−	7.85538i	0.312235	−	0.270554i
$844$	−19.6018	−	3.29810i	−0.674723	−	0.113525i
$845$	−2.87894	+	1.85018i	−0.0990385	+	0.0636482i
$846$	−16.0636	+	5.77377i	−0.552278	+	0.198506i
$847$	3.63913	+	2.33873i	0.125042	+	0.0803596i
$848$	−51.7925	−	17.9364i	−1.77856	−	0.615939i
$849$	7.98868	−	27.2070i	0.274171	−	0.933740i
$850$	−14.5614	−	27.4417i	−0.499453	−	0.941241i
$851$	−47.8242	−	4.59531i	−1.63939	−	0.157525i
$852$	9.57673	+	6.48303i	0.328093	+	0.222105i
$853$	−2.99724	+	10.2077i	−0.102623	+	0.349504i	−0.994757	−	0.102269i	$-0.967390\pi$
$853$	−2.99724	+	10.2077i	−0.102623	+	0.349504i	0.892133	+	0.451772i	$0.149208\pi$
$854$	−0.930047	+	4.04224i	−0.0318256	+	0.138323i
$855$	−2.18737	+	3.40362i	−0.0748066	+	0.116401i
$856$	8.63202	−	33.8001i	0.295036	−	1.15526i
$857$	−3.72477	+	2.39376i	−0.127236	+	0.0817694i	−0.602711	−	0.797960i	$-0.705913\pi$
$857$	−3.72477	+	2.39376i	−0.127236	+	0.0817694i	0.475475	+	0.879729i	$0.342276\pi$
$858$	−19.4700	−	14.9413i	−0.664696	−	0.510088i
$859$	−14.7732	−	17.0492i	−0.504056	−	0.581712i	0.445511	−	0.895277i	$-0.353022\pi$
$859$	−14.7732	−	17.0492i	−0.504056	−	0.581712i	−0.949567	+	0.313565i	$0.898477\pi$
$860$	−1.21837	+	2.50752i	−0.0415459	+	0.0855056i
$861$	−0.244947	+	0.536360i	−0.00834779	+	0.0182791i
$862$	4.58638	−	4.47808i	0.156213	−	0.152524i
$863$	0.182807	+	0.622585i	0.00622283	+	0.0211930i	0.962546	−	0.271119i	$-0.0873936\pi$
$863$	0.182807	+	0.622585i	0.00622283	+	0.0211930i	−0.956323	+	0.292312i	$0.905575\pi$
$864$	5.11789	−	2.40981i	0.174114	−	0.0819834i
$865$	−21.4060	+	3.07772i	−0.727827	+	0.104646i
$866$	11.1696	−	28.8880i	0.379558	−	0.981654i
$867$	4.62377	+	10.1246i	0.157032	+	0.343851i
$868$	0.654720	+	0.0156466i	0.0222227	+	0.000531080i
$869$	−23.3847	−	3.36221i	−0.793272	−	0.114055i
$870$	0.432004	−	5.17121i	0.0146463	−	0.175320i
$871$	−12.9091	+	14.8979i	−0.437407	+	0.504795i
$872$	1.46294	−	3.53046i	0.0495415	−	0.119556i
$873$			12.5014i			0.423109i
$874$	24.3189	+	16.9080i	0.822599	+	0.571922i
$875$	−1.71507			−0.0579798
$876$	13.8130	−	11.4028i	0.466697	−	0.385264i
$877$	−24.6662	−	21.3734i	−0.832920	−	0.721729i	0.130001	−	0.991514i	$-0.458502\pi$
$877$	−24.6662	−	21.3734i	−0.832920	−	0.721729i	−0.962921	+	0.269785i	$0.913047\pi$
$878$	−0.643443	+	7.70220i	−0.0217152	+	0.259937i
$879$	−1.54952	+	10.7771i	−0.0522640	+	0.363504i
$880$	12.2316	−	17.1700i	0.412326	−	0.578802i
$881$	−12.5823	+	5.74615i	−0.423909	+	0.193593i	−0.615935	−	0.787797i	$-0.711222\pi$
$881$	−12.5823	+	5.74615i	−0.423909	+	0.193593i	0.192026	+	0.981390i	$0.438494\pi$
$882$	9.17925	+	3.54917i	0.309081	+	0.119507i
$883$	−6.37121	−	44.3128i	−0.214408	−	1.49124i	−0.758200	−	0.652022i	$-0.773921\pi$
$883$	−6.37121	−	44.3128i	−0.214408	−	1.49124i	0.543791	−	0.839220i	$-0.316988\pi$
$884$	16.8395	+	27.6328i	0.566375	+	0.929392i
$885$	−5.14805	+	1.51160i	−0.173050	+	0.0508120i
$886$	31.1419	−	30.4066i	1.04623	−	1.02153i
$887$	28.3153	+	12.9312i	0.950735	+	0.434186i	0.829543	−	0.558443i	$-0.188601\pi$
$887$	28.3153	+	12.9312i	0.950735	+	0.434186i	0.121192	+	0.992629i	$0.461328\pi$
$888$	28.3171	−	1.00737i	0.950261	−	0.0338050i
$889$	−0.359671	+	0.311657i	−0.0120630	+	0.0104526i
$890$	−9.20184	+	11.9909i	−0.308447	+	0.401936i
$891$	−3.07557	−	4.78567i	−0.103035	−	0.160326i
$892$	−11.6261	+	12.7868i	−0.389272	+	0.428133i
$893$	44.3436	+	28.4979i	1.48390	+	0.953647i
$894$	1.16003	−	5.04180i	0.0387971	−	0.168623i
$895$	4.34676	+	1.27632i	0.145296	+	0.0426628i
$896$	2.20599	−	0.618541i	0.0736970	−	0.0206640i
$897$	−2.76024	−	14.3674i	−0.0921616	−	0.479713i
$898$	−23.6956	+	12.5736i	−0.790731	+	0.419587i
$899$	6.14504	+	1.80435i	0.204949	+	0.0601783i
$900$	−2.14315	−	8.00134i	−0.0714383	−	0.266711i
$901$	39.2916	−	61.1390i	1.30899	−	2.03683i
$902$	−22.0448	+	7.92358i	−0.734010	+	0.263826i
$903$	0.164725	+	0.256317i	0.00548169	+	0.00852968i
$904$	−3.53083	−	10.6134i	−0.117434	−	0.352997i
$905$	6.45193	+	7.44592i	0.214469	+	0.247511i
$906$	−11.7240	+	8.55984i	−0.389504	+	0.284382i
$907$	−3.69688	−	1.68831i	−0.122753	−	0.0560593i	0.353092	−	0.935589i	$-0.385130\pi$
$907$	−3.69688	−	1.68831i	−0.122753	−	0.0560593i	−0.475845	+	0.879529i	$0.657858\pi$
$908$	−21.5634	−	6.89531i	−0.715608	−	0.228829i
$909$	−4.23931	−	14.4378i	−0.140609	−	0.478871i
$910$	0.807951	−	0.0480918i	0.0267833	−	0.00159423i
$911$	−3.32306	−	23.1124i	−0.110098	−	0.765748i	−0.967822	−	0.251637i	$-0.919031\pi$
$911$	−3.32306	−	23.1124i	−0.110098	−	0.765748i	0.857724	−	0.514111i	$-0.171878\pi$
$912$	−15.5250	−	8.00738i	−0.514085	−	0.265151i
$913$	−15.4527	−	33.8367i	−0.511410	−	1.11983i
$914$	20.8978	+	11.7373i	0.691238	+	0.388236i
$915$	1.90962	−	13.2817i	0.0631301	−	0.439079i
$916$	2.16157	−	0.925398i	0.0714202	−	0.0305760i
$917$	−2.21041	+	2.55095i	−0.0729941	+	0.0842397i
$918$	1.50672	+	7.34784i	0.0497292	+	0.242515i
$919$	−31.8285			−1.04993			−0.524963	−	0.851125i	$-0.675921\pi$
$919$	−31.8285			−1.04993			−0.524963	+	0.851125i	$0.675921\pi$
$920$	12.2492	−	2.80824i	0.403843	−	0.0925850i
$921$	−8.36015			−0.275476
$922$	4.18589	+	20.4134i	0.137855	+	0.672279i
$923$	−11.5515	+	13.3312i	−0.380223	+	0.438801i
$924$	−0.906765	−	2.11805i	−0.0298304	−	0.0696786i
$925$	5.90483	−	41.0690i	0.194150	−	1.35034i
$926$	36.6324	+	20.5747i	1.20382	+	0.676126i
$927$	5.92291	+	12.9694i	0.194534	+	0.425970i
$928$	22.4033	−	0.261366i	0.735424	−	0.00857976i
$929$	4.58388	+	31.8816i	0.150392	+	1.04600i	0.915563	+	0.402174i	$0.131745\pi$
$929$	4.58388	+	31.8816i	0.150392	+	1.04600i	−0.765171	+	0.643827i	$0.777346\pi$
$930$	−2.11488	+	0.125884i	−0.0693495	+	0.00412790i
$931$	−8.56202	−	29.1596i	−0.280609	−	0.955666i
$932$	17.7811	−	55.6060i	0.582438	−	1.82144i
$933$	−19.8997	−	9.08790i	−0.651488	−	0.297525i
$934$	−12.9131	+	9.42800i	−0.422529	+	0.308494i
$935$	18.3052	+	21.1254i	0.598645	+	0.690873i
$936$	2.72369	+	8.18721i	0.0890265	+	0.267607i
$937$	−23.3062	−	36.2651i	−0.761380	−	1.18473i	−0.978027	−	0.208481i	$-0.933148\pi$
$937$	−23.3062	−	36.2651i	−0.761380	−	1.18473i	0.216646	−	0.976250i	$-0.430488\pi$
$938$	−1.74151	+	0.625954i	−0.0568624	+	0.0204381i
$939$	−7.20296	+	11.2080i	−0.235060	+	0.365760i
$940$	21.6032	−	5.78638i	0.704618	−	0.188731i
$941$	9.15269	+	2.68747i	0.298369	+	0.0876091i	0.427491	−	0.904020i	$-0.359398\pi$
$941$	9.15269	+	2.68747i	0.298369	+	0.0876091i	−0.129122	+	0.991629i	$0.541216\pi$
$942$	4.06984	−	2.15959i	0.132602	−	0.0703631i
$943$	−12.9610	−	5.19773i	−0.422068	−	0.169261i
$944$	−8.60568	−	21.5076i	−0.280091	−	0.700014i
$945$	0.180010	+	0.0528556i	0.00585572	+	0.00171939i
$946$	−2.71412	+	11.7963i	−0.0882437	+	0.383532i
$947$	40.7090	+	26.1621i	1.32286	+	0.850153i	0.995501	−	0.0947463i	$-0.0302040\pi$
$947$	40.7090	+	26.1621i	1.32286	+	0.850153i	0.327362	+	0.944899i	$0.393840\pi$
$948$	6.14547	+	5.58765i	0.199595	+	0.181478i
$949$	14.7705	+	22.9833i	0.479470	+	0.746070i
$950$	−15.5725	+	20.2926i	−0.505240	+	0.658377i
$951$	−17.4867	+	15.1523i	−0.567044	+	0.491346i
$952$	0.108002	+	3.03593i	0.00350035	+	0.0983951i
$953$	−20.4063	−	9.31924i	−0.661024	−	0.301880i	0.0565108	−	0.998402i	$-0.482002\pi$
$953$	−20.4063	−	9.31924i	−0.661024	−	0.301880i	−0.717535	+	0.696522i	$0.754730\pi$
$954$	13.8653	−	13.5379i	0.448906	−	0.438306i
$955$	10.9974	−	3.22913i	0.355867	−	0.104492i
$956$	−2.02290	+	1.23276i	−0.0654253	+	0.0398704i
$957$	−3.20651	−	22.3018i	−0.103652	−	0.720914i
$958$	24.5463	+	9.49086i	0.793055	+	0.306636i
$959$	−0.664780	+	0.303595i	−0.0214669	+	0.00980359i
$960$	−6.94501	+	2.58813i	−0.224149	+	0.0835316i
$961$	−4.03964	+	28.0963i	−0.130311	+	0.906333i
$962$	−3.59802	+	43.0693i	−0.116005	+	1.38861i
$963$	9.32118	+	8.07685i	0.300371	+	0.260273i
$964$	−1.05010	−	1.27205i	−0.0338213	−	0.0409701i
$965$	11.4465			0.368476
$966$	0.434569	−	1.30288i	0.0139820	−	0.0419196i
$967$			23.0585i			0.741511i	0.928731	+	0.370755i	$0.120901\pi$
$967$			23.0585i			0.741511i	−0.928731	+	0.370755i	$0.879099\pi$
$968$	23.1297	−	55.8178i	0.743416	−	1.79405i
$969$	15.1681	−	17.5049i	0.487269	−	0.562338i
$970$	1.36358	−	16.3224i	0.0437819	−	0.524082i
$971$	−40.3931	−	5.80765i	−1.29628	−	0.186376i	−0.540577	−	0.841295i	$-0.681794\pi$
$971$	−40.3931	−	5.80765i	−1.29628	−	0.186376i	−0.755700	+	0.654918i	$0.772703\pi$
$972$	−0.0477826	+	1.99943i	−0.00153263	+	0.0641317i
$973$	0.622627	+	1.36336i	0.0199605	+	0.0437074i
$974$	−6.22538	+	16.1008i	−0.199474	+	0.515902i
$975$	12.5060	−	1.79809i	0.400513	−	0.0575851i
$976$	57.8681	+	2.76746i	1.85231	+	0.0885843i
$977$	8.77866	+	29.8974i	0.280854	+	0.956502i	0.972234	+	0.234010i	$0.0751849\pi$
$977$	8.77866	+	29.8974i	0.280854	+	0.956502i	−0.691380	+	0.722491i	$0.742997\pi$
$978$	−0.238220	+	0.232595i	−0.00761743	+	0.00743756i
$979$	−27.2624	+	59.6963i	−0.871309	+	1.90790i
$980$	−11.5977	−	5.63518i	−0.370476	−	0.180009i
$981$	0.884800	+	1.02111i	0.0282495	+	0.0326016i
$982$	−9.66418	−	7.41630i	−0.308396	−	0.236664i
$983$	−4.25085	+	2.73186i	−0.135581	+	0.0871327i	−0.606673	−	0.794951i	$-0.707496\pi$
$983$	−4.25085	+	2.73186i	−0.135581	+	0.0871327i	0.471092	+	0.882084i	$0.343860\pi$
$984$	7.97963	+	2.03787i	0.254381	+	0.0649650i
$985$	−1.88040	+	2.92596i	−0.0599145	+	0.0932288i
$986$	−6.66118	+	28.9513i	−0.212135	+	0.921998i
$987$	0.688623	−	2.34524i	0.0219191	−	0.0746497i
$988$	14.9365	−	22.0642i	0.475193	−	0.701955i
$989$	−5.88025	+	4.18205i	−0.186981	+	0.132981i
$990$	3.49361	+	6.58387i	0.111034	+	0.209249i
$991$	−13.5619	+	46.1876i	−0.430808	+	1.46720i	0.403029	+	0.915187i	$0.367957\pi$
$991$	−13.5619	+	46.1876i	−0.430808	+	1.46720i	−0.833837	+	0.552010i	$0.813861\pi$
$992$	−1.40733	−	9.03837i	−0.0446827	−	0.286968i
$993$	−14.8384	−	9.53603i	−0.470881	−	0.302617i
$994$	−1.55837	+	0.560127i	−0.0494285	+	0.0177662i
$995$	11.5768	−	7.43995i	0.367009	−	0.235862i
$996$	−2.16991	+	12.8966i	−0.0687561	+	0.408643i
$997$	−17.1200	+	14.8346i	−0.542197	+	0.469816i	−0.882376	−	0.470544i	$-0.844058\pi$
$997$	−17.1200	+	14.8346i	−0.542197	+	0.469816i	0.340180	+	0.940360i	$0.389512\pi$
$998$	−34.7931	−	47.6543i	−1.10136	−	1.50847i
$999$	−4.16161	+	9.11265i	−0.131667	+	0.288312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.t.a.235.2	✓	240
8.3	odd	2	inner	552.2.t.a.235.5	yes	240
23.14	odd	22	inner	552.2.t.a.451.5	yes	240
184.83	even	22	inner	552.2.t.a.451.2	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.t.a.235.2	✓	240	1.1	even	1	trivial
552.2.t.a.235.5	yes	240	8.3	odd	2	inner
552.2.t.a.451.2	yes	240	184.83	even	22	inner
552.2.t.a.451.5	yes	240	23.14	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.38539 + 0.284082i) q^{2} +(0.654861 - 0.755750i) q^{3} +(1.83859 - 0.787128i) q^{4} +(0.131847 - 0.917018i) q^{5} +(-0.692540 + 1.23304i) q^{6} +(-0.0841231 - 0.184204i) q^{7} +(-2.32356 + 1.61279i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-1.38539 + 0.284082i) q^{2} +(0.654861 - 0.755750i) q^{3} +(1.83859 - 0.787128i) q^{4} +(0.131847 - 0.917018i) q^{5} +(-0.692540 + 1.23304i) q^{6} +(-0.0841231 - 0.184204i) q^{7} +(-2.32356 + 1.61279i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.0778492 + 1.30788i) q^{10} +(1.60270 + 5.45831i) q^{11} +(0.609151 - 1.90498i) q^{12} +(2.77492 + 1.26726i) q^{13} +(0.168872 + 0.231296i) q^{14} +(-0.606695 - 0.700163i) q^{15} +(2.76086 - 2.89442i) q^{16} +(2.86746 + 4.46186i) q^{17} +(0.478352 + 1.33086i) q^{18} +(2.36103 - 3.67383i) q^{19} +(-0.479397 - 1.78981i) q^{20} +(-0.194301 - 0.0570519i) q^{21} +(-3.77098 - 7.10657i) q^{22} +(1.13343 - 4.65997i) q^{23} +(-0.302740 + 2.81218i) q^{24} +(3.97393 + 1.16685i) q^{25} +(-4.20434 - 0.967343i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(-0.299660 - 0.272461i) q^{28} +(-2.14129 - 3.33191i) q^{29} +(1.03941 + 0.797645i) q^{30} +(-1.22207 + 1.05893i) q^{31} +(-3.00260 + 4.79420i) q^{32} +(5.17466 + 2.36319i) q^{33} +(-5.24008 - 5.36680i) q^{34} +(-0.180010 + 0.0528556i) q^{35} +(-1.04078 - 1.70786i) q^{36} +(-1.42570 - 9.91599i) q^{37} +(-2.22727 + 5.76041i) q^{38} +(2.77492 - 1.26726i) q^{39} +(1.17260 + 2.34338i) q^{40} +(0.414389 - 2.88214i) q^{41} +(0.285389 + 0.0238415i) q^{42} +(-1.13709 - 0.985294i) q^{43} +(7.24311 + 8.77408i) q^{44} -0.926448 q^{45} +(-0.246420 + 6.77785i) q^{46} +12.0701i q^{47} +(-0.379478 - 3.98196i) q^{48} +(4.55717 - 5.25926i) q^{49} +(-5.83691 - 0.487616i) q^{50} +(5.24983 + 0.754812i) q^{51} +(6.09944 + 0.145765i) q^{52} +(-5.69226 - 12.4643i) q^{53} +(1.31905 + 0.510011i) q^{54} +(5.21668 - 0.750046i) q^{55} +(0.492547 + 0.292335i) q^{56} +(-1.23035 - 4.19020i) q^{57} +(3.91305 + 4.00768i) q^{58} +(2.40581 - 5.26800i) q^{59} +(-1.66658 - 0.809769i) q^{60} +(9.48472 + 10.9460i) q^{61} +(1.39221 - 1.81419i) q^{62} +(-0.170357 + 0.109482i) q^{63} +(2.79782 - 7.49481i) q^{64} +(1.52797 - 2.37756i) q^{65} +(-7.84025 - 1.80390i) q^{66} +(-1.82054 + 6.20017i) q^{67} +(8.78415 + 5.94648i) q^{68} +(-2.77953 - 3.90822i) q^{69} +(0.234368 - 0.124363i) q^{70} +(-1.62908 + 5.54815i) q^{71} +(1.92705 + 2.07038i) q^{72} +(7.53405 + 4.84184i) q^{73} +(4.79211 + 13.3325i) q^{74} +(3.48421 - 2.23917i) q^{75} +(1.44920 - 8.61313i) q^{76} +(0.870617 - 0.754394i) q^{77} +(-3.48433 + 2.54395i) q^{78} +(-1.72521 + 3.77767i) q^{79} +(-2.29022 - 2.91338i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(0.244676 + 4.11060i) q^{82} +(-6.47236 + 0.930585i) q^{83} +(-0.402148 + 0.0480444i) q^{84} +(4.46967 - 2.04123i) q^{85} +(1.85521 + 1.04199i) q^{86} +(-3.92033 - 0.563659i) q^{87} +(-12.5271 - 10.0979i) q^{88} +(8.71852 + 7.55464i) q^{89} +(1.28349 - 0.263188i) q^{90} -0.617756i q^{91} +(-1.58408 - 9.45995i) q^{92} +1.61703i q^{93} +(-3.42891 - 16.7218i) q^{94} +(-3.05768 - 2.64949i) q^{95} +(1.65693 + 5.40875i) q^{96} +(-12.3742 - 1.77914i) q^{97} +(-4.81938 + 8.58072i) q^{98} +(5.17466 - 2.36319i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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