LMFDB - Embedded newform 574.2.u.a.197.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [574,2,Mod(43,574)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(574, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 13]))

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

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

chi := DirichletCharacter("574.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 574 = 2 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	574.u (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.58341307602$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			197.2
Character	$\chi$	$=$	574.197
Dual form			574.2.u.a.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(-1.38661 + 1.38661i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.51658 - 0.492765i) q^{5} +(-0.306761 - 1.93682i) q^{6} +(0.156434 - 0.987688i) q^{7} +(0.951057 + 0.309017i) q^{8} -0.845358i q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(-1.38661 + 1.38661i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.51658 - 0.492765i) q^{5} +(-0.306761 - 1.93682i) q^{6} +(0.156434 - 0.987688i) q^{7} +(0.951057 + 0.309017i) q^{8} -0.845358i q^{9} +(-0.492765 + 1.51658i) q^{10} +(-1.27582 - 2.50394i) q^{11} +(1.74723 + 0.890256i) q^{12} +(-5.14839 + 0.815424i) q^{13} +(0.707107 + 0.707107i) q^{14} +(-1.41962 + 2.78617i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-5.11559 + 2.60652i) q^{17} +(0.683909 + 0.496889i) q^{18} +(-1.87485 - 0.296947i) q^{19} +(-0.937295 - 1.29008i) q^{20} +(1.15262 + 1.58645i) q^{21} +(2.77564 + 0.439618i) q^{22} +(0.969791 + 0.704595i) q^{23} +(-1.74723 + 0.890256i) q^{24} +(-1.98790 + 1.44430i) q^{25} +(2.36645 - 4.64443i) q^{26} +(-2.98764 - 2.98764i) q^{27} +(-0.987688 + 0.156434i) q^{28} +(-1.95086 - 0.994011i) q^{29} +(-1.41962 - 2.78617i) q^{30} +(1.60902 - 4.95206i) q^{31} -1.00000i q^{32} +(5.24105 + 1.70292i) q^{33} +(0.898147 - 5.67068i) q^{34} +(-0.249454 - 1.57499i) q^{35} +(-0.803983 + 0.261230i) q^{36} +(0.437468 + 1.34639i) q^{37} +(1.34224 - 1.34224i) q^{38} +(6.00811 - 8.26946i) q^{39} +1.59462 q^{40} +(-5.55050 - 3.19248i) q^{41} -1.96096 q^{42} +(-1.05360 + 1.45015i) q^{43} +(-1.98714 + 1.98714i) q^{44} +(-0.416563 - 1.28205i) q^{45} +(-1.14006 + 0.370427i) q^{46} +(-0.915936 - 5.78299i) q^{47} +(0.306761 - 1.93682i) q^{48} +(-0.951057 - 0.309017i) q^{49} -2.45718i q^{50} +(3.47909 - 10.7075i) q^{51} +(2.36645 + 4.64443i) q^{52} +(0.828181 + 0.421979i) q^{53} +(4.17315 - 0.660961i) q^{54} +(-3.16874 - 3.16874i) q^{55} +(0.453990 - 0.891007i) q^{56} +(3.01142 - 2.18793i) q^{57} +(1.95086 - 0.994011i) q^{58} +(6.29541 + 4.57388i) q^{59} +(3.08849 + 0.489169i) q^{60} +(3.77924 + 5.20167i) q^{61} +(3.06054 + 4.21247i) q^{62} +(-0.834950 - 0.132243i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-7.40610 + 3.77360i) q^{65} +(-4.45830 + 3.23915i) q^{66} +(-1.15389 + 2.26463i) q^{67} +(4.05976 + 4.05976i) q^{68} +(-2.32171 + 0.367724i) q^{69} +(1.42082 + 0.723943i) q^{70} +(-6.26660 - 12.2989i) q^{71} +(0.261230 - 0.803983i) q^{72} -5.70230i q^{73} +(-1.34639 - 0.437468i) q^{74} +(0.753769 - 4.75911i) q^{75} +(0.296947 + 1.87485i) q^{76} +(-2.67270 + 0.868412i) q^{77} +(3.15865 + 9.72133i) q^{78} +(6.80085 - 6.80085i) q^{79} +(-0.937295 + 1.29008i) q^{80} +10.8214 q^{81} +(5.84527 - 2.61396i) q^{82} -15.3729 q^{83} +(1.15262 - 1.58645i) q^{84} +(-6.47378 + 6.47378i) q^{85} +(-0.553909 - 1.70476i) q^{86} +(4.08337 - 1.32677i) q^{87} +(-0.439618 - 2.77564i) q^{88} +(-2.63706 + 16.6498i) q^{89} +(1.28205 + 0.416563i) q^{90} +5.21256i q^{91} +(0.370427 - 1.14006i) q^{92} +(4.63548 + 9.09763i) q^{93} +(5.21691 + 2.65815i) q^{94} +(-2.98967 + 0.473517i) q^{95} +(1.38661 + 1.38661i) q^{96} +(-4.73263 + 9.28831i) q^{97} +(0.809017 - 0.587785i) q^{98} +(-2.11673 + 1.07853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 20 q^{4} + 16 q^{6}+O(q^{10}) $ 80 * q + 4 * q^3 + 20 * q^4 + 16 * q^6	$ 80 q + 4 q^{3} + 20 q^{4} + 16 q^{6} - 16 q^{11} - 4 q^{12} + 20 q^{13} + 36 q^{15} - 20 q^{16} + 4 q^{17} + 20 q^{18} + 28 q^{19} - 20 q^{20} + 16 q^{22} - 8 q^{23} + 4 q^{24} + 20 q^{25} + 16 q^{27} - 12 q^{29} + 36 q^{30} - 12 q^{31} + 4 q^{34} - 20 q^{36} + 12 q^{37} - 32 q^{38} - 80 q^{39} - 8 q^{41} + 16 q^{44} - 108 q^{45} - 20 q^{46} + 8 q^{47} - 16 q^{48} - 20 q^{51} - 40 q^{53} + 16 q^{54} + 60 q^{55} + 52 q^{57} + 12 q^{58} - 12 q^{59} + 24 q^{60} + 100 q^{61} - 16 q^{63} + 20 q^{64} - 20 q^{65} - 36 q^{67} + 36 q^{68} - 32 q^{69} - 12 q^{71} - 20 q^{72} + 20 q^{74} + 40 q^{75} + 12 q^{76} + 40 q^{77} + 16 q^{78} + 16 q^{79} - 20 q^{80} - 104 q^{81} - 12 q^{82} - 16 q^{85} + 12 q^{86} + 140 q^{87} + 24 q^{88} - 32 q^{89} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} + 4 q^{97} + 20 q^{98} - 72 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 + 20 * q^4 + 16 * q^6 - 16 * q^11 - 4 * q^12 + 20 * q^13 + 36 * q^15 - 20 * q^16 + 4 * q^17 + 20 * q^18 + 28 * q^19 - 20 * q^20 + 16 * q^22 - 8 * q^23 + 4 * q^24 + 20 * q^25 + 16 * q^27 - 12 * q^29 + 36 * q^30 - 12 * q^31 + 4 * q^34 - 20 * q^36 + 12 * q^37 - 32 * q^38 - 80 * q^39 - 8 * q^41 + 16 * q^44 - 108 * q^45 - 20 * q^46 + 8 * q^47 - 16 * q^48 - 20 * q^51 - 40 * q^53 + 16 * q^54 + 60 * q^55 + 52 * q^57 + 12 * q^58 - 12 * q^59 + 24 * q^60 + 100 * q^61 - 16 * q^63 + 20 * q^64 - 20 * q^65 - 36 * q^67 + 36 * q^68 - 32 * q^69 - 12 * q^71 - 20 * q^72 + 20 * q^74 + 40 * q^75 + 12 * q^76 + 40 * q^77 + 16 * q^78 + 16 * q^79 - 20 * q^80 - 104 * q^81 - 12 * q^82 - 16 * q^85 + 12 * q^86 + 140 * q^87 + 24 * q^88 - 32 * q^89 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 + 4 * q^97 + 20 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/574\mathbb{Z}\right)^\times$.

$n$	$211$	$493$
$\chi(n)$	$e\left(\frac{9}{20}\right)$	$1$

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	−1.38661	+	1.38661i	−0.800558	+	0.800558i	−0.983183	−	0.182625i	$-0.941541\pi$
$3$	−1.38661	+	1.38661i	−0.800558	+	0.800558i	0.182625	+	0.983183i	$0.441541\pi$
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	1.51658	−	0.492765i	0.678233	−	0.220371i	0.0504115	−	0.998729i	$-0.483947\pi$
$5$	1.51658	−	0.492765i	0.678233	−	0.220371i	0.627822	+	0.778357i	$0.283947\pi$
$6$	−0.306761	−	1.93682i	−0.125235	−	0.790702i
$7$	0.156434	−	0.987688i	0.0591267	−	0.373311i
$7$	0.156434	−	0.987688i	0.0591267	−	0.373311i
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$		−	0.845358i		−	0.281786i
$10$	−0.492765	+	1.51658i	−0.155826	+	0.479583i
$11$	−1.27582	−	2.50394i	−0.384675	−	0.754967i	0.614755	−	0.788718i	$-0.289255\pi$
$11$	−1.27582	−	2.50394i	−0.384675	−	0.754967i	−0.999430	+	0.0337508i	$0.989255\pi$
$12$	1.74723	+	0.890256i	0.504381	+	0.256995i
$13$	−5.14839	+	0.815424i	−1.42791	+	0.226158i	−0.822049	−	0.569416i	$-0.807169\pi$
$13$	−5.14839	+	0.815424i	−1.42791	+	0.226158i	−0.605856	+	0.795574i	$0.707169\pi$
$14$	0.707107	+	0.707107i	0.188982	+	0.188982i
$15$	−1.41962	+	2.78617i	−0.366545	+	0.719385i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−5.11559	+	2.60652i	−1.24071	+	0.632175i	−0.946234	−	0.323483i	$-0.895146\pi$
$17$	−5.11559	+	2.60652i	−1.24071	+	0.632175i	−0.294479	+	0.955658i	$0.595146\pi$
$18$	0.683909	+	0.496889i	0.161199	+	0.117118i
$19$	−1.87485	−	0.296947i	−0.430119	−	0.0681242i	−0.0623786	−	0.998053i	$-0.519869\pi$
$19$	−1.87485	−	0.296947i	−0.430119	−	0.0681242i	−0.367741	+	0.929928i	$0.619869\pi$
$20$	−0.937295	−	1.29008i	−0.209586	−	0.288470i
$21$	1.15262	+	1.58645i	0.251523	+	0.346191i
$22$	2.77564	+	0.439618i	0.591769	+	0.0937270i
$23$	0.969791	+	0.704595i	0.202215	+	0.146918i	0.684285	−	0.729215i	$-0.260115\pi$
$23$	0.969791	+	0.704595i	0.202215	+	0.146918i	−0.482069	+	0.876133i	$0.660115\pi$
$24$	−1.74723	+	0.890256i	−0.356651	+	0.181723i
$25$	−1.98790	+	1.44430i	−0.397580	+	0.288859i
$26$	2.36645	−	4.64443i	0.464100	−	0.910847i
$27$	−2.98764	−	2.98764i	−0.574972	−	0.574972i
$28$	−0.987688	+	0.156434i	−0.186656	+	0.0295633i
$29$	−1.95086	−	0.994011i	−0.362265	−	0.184583i	0.263378	−	0.964693i	$-0.415163\pi$
$29$	−1.95086	−	0.994011i	−0.362265	−	0.184583i	−0.625643	+	0.780109i	$0.715163\pi$
$30$	−1.41962	−	2.78617i	−0.259186	−	0.508682i
$31$	1.60902	−	4.95206i	0.288989	−	0.889416i	−0.696186	−	0.717861i	$-0.745121\pi$
$31$	1.60902	−	4.95206i	0.288989	−	0.889416i	0.985175	−	0.171554i	$-0.0548789\pi$
$32$		−	1.00000i		−	0.176777i
$33$	5.24105	+	1.70292i	0.912349	+	0.296440i
$34$	0.898147	−	5.67068i	0.154031	−	0.972513i
$35$	−0.249454	−	1.57499i	−0.0421654	−	0.266222i
$36$	−0.803983	+	0.261230i	−0.133997	+	0.0435383i
$37$	0.437468	+	1.34639i	0.0719192	+	0.221345i	0.980555	−	0.196245i	$-0.0628749\pi$
$37$	0.437468	+	1.34639i	0.0719192	+	0.221345i	−0.908636	+	0.417590i	$0.862875\pi$
$38$	1.34224	−	1.34224i	0.217740	−	0.217740i
$39$	6.00811	−	8.26946i	0.962068	−	1.32417i
$40$	1.59462			0.252132
$41$	−5.55050	−	3.19248i	−0.866843	−	0.498582i
$41$	−5.55050	−	3.19248i	−0.866843	−	0.498582i
$42$	−1.96096			−0.302582
$43$	−1.05360	+	1.45015i	−0.160672	+	0.221146i	−0.881761	−	0.471696i	$-0.843642\pi$
$43$	−1.05360	+	1.45015i	−0.160672	+	0.221146i	0.721089	+	0.692842i	$0.243642\pi$
$44$	−1.98714	+	1.98714i	−0.299573	+	0.299573i
$45$	−0.416563	−	1.28205i	−0.0620975	−	0.191117i
$46$	−1.14006	+	0.370427i	−0.168092	+	0.0546165i
$47$	−0.915936	−	5.78299i	−0.133603	−	0.843536i	−0.959908	−	0.280314i	$-0.909561\pi$
$47$	−0.915936	−	5.78299i	−0.133603	−	0.843536i	0.826305	−	0.563222i	$-0.190439\pi$
$48$	0.306761	−	1.93682i	0.0442772	−	0.279555i
$49$	−0.951057	−	0.309017i	−0.135865	−	0.0441453i
$50$		−	2.45718i		−	0.347498i
$51$	3.47909	−	10.7075i	0.487170	−	1.49936i
$52$	2.36645	+	4.64443i	0.328168	+	0.644066i
$53$	0.828181	+	0.421979i	0.113759	+	0.0579633i	0.509944	−	0.860207i	$-0.329666\pi$
$53$	0.828181	+	0.421979i	0.113759	+	0.0579633i	−0.396185	+	0.918171i	$0.629666\pi$
$54$	4.17315	−	0.660961i	0.567893	−	0.0899454i
$55$	−3.16874	−	3.16874i	−0.427272	−	0.427272i
$56$	0.453990	−	0.891007i	0.0606670	−	0.119066i
$57$	3.01142	−	2.18793i	0.398873	−	0.289798i
$58$	1.95086	−	0.994011i	0.256160	−	0.130520i
$59$	6.29541	+	4.57388i	0.819592	+	0.595469i	0.916596	−	0.399815i	$-0.130926\pi$
$59$	6.29541	+	4.57388i	0.819592	+	0.595469i	−0.0970034	+	0.995284i	$0.530926\pi$
$60$	3.08849	+	0.489169i	0.398722	+	0.0631514i
$61$	3.77924	+	5.20167i	0.483881	+	0.666006i	0.979245	−	0.202680i	$-0.0649651\pi$
$61$	3.77924	+	5.20167i	0.483881	+	0.666006i	−0.495364	+	0.868686i	$0.664965\pi$
$62$	3.06054	+	4.21247i	0.388689	+	0.534984i
$63$	−0.834950	−	0.132243i	−0.105194	−	0.0166611i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−7.40610	+	3.77360i	−0.918614	+	0.468057i
$66$	−4.45830	+	3.23915i	−0.548779	+	0.398711i
$67$	−1.15389	+	2.26463i	−0.140970	+	0.276668i	−0.950687	−	0.310151i	$-0.899620\pi$
$67$	−1.15389	+	2.26463i	−0.140970	+	0.276668i	0.809718	+	0.586820i	$0.199620\pi$
$68$	4.05976	+	4.05976i	0.492318	+	0.492318i
$69$	−2.32171	+	0.367724i	−0.279502	+	0.0442687i
$70$	1.42082	+	0.723943i	0.169820	+	0.0865278i
$71$	−6.26660	−	12.2989i	−0.743709	−	1.45961i	−0.883007	−	0.469361i	$-0.844484\pi$
$71$	−6.26660	−	12.2989i	−0.743709	−	1.45961i	0.139298	−	0.990251i	$-0.455516\pi$
$72$	0.261230	−	0.803983i	0.0307862	−	0.0947503i
$73$		−	5.70230i		−	0.667404i	−0.942679	−	0.333702i	$-0.891702\pi$
$73$		−	5.70230i		−	0.667404i	0.942679	−	0.333702i	$-0.108298\pi$
$74$	−1.34639	−	0.437468i	−0.156514	−	0.0508546i
$75$	0.753769	−	4.75911i	0.0870377	−	0.549534i
$76$	0.296947	+	1.87485i	0.0340621	+	0.215060i
$77$	−2.67270	+	0.868412i	−0.304582	+	0.0989647i
$78$	3.15865	+	9.72133i	0.357647	+	1.10072i
$79$	6.80085	−	6.80085i	0.765156	−	0.765156i	−0.212094	−	0.977249i	$-0.568028\pi$
$79$	6.80085	−	6.80085i	0.765156	−	0.765156i	0.977249	+	0.212094i	$0.0680282\pi$
$80$	−0.937295	+	1.29008i	−0.104793	+	0.144235i
$81$	10.8214			1.20238
$82$	5.84527	−	2.61396i	0.645503	−	0.288663i
$83$	−15.3729			−1.68740			−0.843698	−	0.536818i	$-0.819626\pi$
$83$	−15.3729			−1.68740			−0.843698	+	0.536818i	$0.819626\pi$
$84$	1.15262	−	1.58645i	0.125761	−	0.173096i
$85$	−6.47378	+	6.47378i	−0.702180	+	0.702180i
$86$	−0.553909	−	1.70476i	−0.0597295	−	0.183829i
$87$	4.08337	−	1.32677i	0.437784	−	0.142245i
$88$	−0.439618	−	2.77564i	−0.0468635	−	0.295884i
$89$	−2.63706	+	16.6498i	−0.279528	+	1.76487i	0.303898	+	0.952704i	$0.401712\pi$
$89$	−2.63706	+	16.6498i	−0.279528	+	1.76487i	−0.583426	+	0.812166i	$0.698288\pi$
$90$	1.28205	+	0.416563i	0.135140	+	0.0439096i
$91$			5.21256i			0.546425i
$92$	0.370427	−	1.14006i	0.0386197	−	0.118859i
$93$	4.63548	+	9.09763i	0.480677	+	0.943381i
$94$	5.21691	+	2.65815i	0.538084	+	0.274167i
$95$	−2.98967	+	0.473517i	−0.306734	+	0.0485819i
$96$	1.38661	+	1.38661i	0.141520	+	0.141520i
$97$	−4.73263	+	9.28831i	−0.480526	+	0.943085i	0.515740	+	0.856745i	$0.327517\pi$
$97$	−4.73263	+	9.28831i	−0.480526	+	0.943085i	−0.996266	+	0.0863398i	$0.972483\pi$
$98$	0.809017	−	0.587785i	0.0817231	−	0.0593753i
$99$	−2.11673	+	1.07853i	−0.212739	+	0.108396i
$100$	1.98790	+	1.44430i	0.198790	+	0.144430i
$101$	−13.4030	−	2.12282i	−1.33365	−	0.211229i	−0.551422	−	0.834226i	$-0.685915\pi$
$101$	−13.4030	−	2.12282i	−1.33365	−	0.211229i	−0.782224	+	0.622998i	$0.785915\pi$
$102$	6.61762	+	9.10838i	0.655242	+	0.901864i
$103$	5.94159	+	8.17789i	0.585442	+	0.805792i	0.994279	−	0.106816i	$-0.0340655\pi$
$103$	5.94159	+	8.17789i	0.585442	+	0.805792i	−0.408837	+	0.912608i	$0.634065\pi$
$104$	−5.14839	−	0.815424i	−0.504841	−	0.0799589i
$105$	2.52979	+	1.83800i	0.246882	+	0.179370i
$106$	−0.828181	+	0.421979i	−0.0804401	+	0.0409863i
$107$	−0.231562	+	0.168240i	−0.0223859	+	0.0162643i	−0.598922	−	0.800807i	$-0.704404\pi$
$107$	−0.231562	+	0.168240i	−0.0223859	+	0.0162643i	0.576536	+	0.817072i	$0.304404\pi$
$108$	−1.91818	+	3.76465i	−0.184577	+	0.362253i
$109$	1.82502	+	1.82502i	0.174805	+	0.174805i	0.789087	−	0.614282i	$-0.210554\pi$
$109$	1.82502	+	1.82502i	0.174805	+	0.174805i	−0.614282	+	0.789087i	$0.710554\pi$
$110$	4.42610	−	0.701025i	0.422012	−	0.0668401i
$111$	−2.47351	−	1.26031i	−0.234775	−	0.119624i
$112$	0.453990	+	0.891007i	0.0428981	+	0.0841922i
$113$	−0.353531	+	1.08806i	−0.0332574	+	0.102356i	−0.966307	−	0.257391i	$-0.917137\pi$
$113$	−0.353531	+	1.08806i	−0.0332574	+	0.102356i	0.933050	+	0.359747i	$0.117137\pi$
$114$			3.72232i			0.348628i
$115$	1.81796	+	0.590691i	0.169526	+	0.0550823i
$116$	−0.342513	+	2.16254i	−0.0318015	+	0.200787i
$117$	0.689325	+	4.35223i	0.0637281	+	0.402363i
$118$	−7.40070	+	2.40463i	−0.681289	+	0.221364i
$119$	1.77418	+	5.46036i	0.162639	+	0.500551i
$120$	−2.21111	+	2.21111i	−0.201846	+	0.201846i
$121$	1.82363	−	2.51002i	0.165785	−	0.228183i
$122$	−6.42962			−0.582110
$123$	12.1231	−	3.26965i	1.09310	−	0.294814i
$124$	−5.20690			−0.467593
$125$	−6.98958	+	9.62033i	−0.625167	+	0.860469i
$126$	0.597758	−	0.597758i	0.0532525	−	0.0532525i
$127$	4.60589	+	14.1755i	0.408707	+	1.25787i	0.917760	+	0.397135i	$0.129996\pi$
$127$	4.60589	+	14.1755i	0.408707	+	1.25787i	−0.509054	+	0.860735i	$0.670004\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	−0.549866	−	3.47172i	−0.0484130	−	0.305668i
$130$	1.30029	−	8.20973i	0.114043	−	0.720041i
$131$	−9.94063	−	3.22991i	−0.868517	−	0.282198i	−0.159335	−	0.987225i	$-0.550935\pi$
$131$	−9.94063	−	3.22991i	−0.868517	−	0.282198i	−0.709181	+	0.705026i	$0.750935\pi$
$132$		−	5.51076i		−	0.479650i
$133$	−0.586581	+	1.80531i	−0.0508630	+	0.156540i
$134$	−1.15389	−	2.26463i	−0.0996805	−	0.195634i
$135$	−6.00319	−	3.05878i	−0.516672	−	0.263258i
$136$	−5.67068	+	0.898147i	−0.486257	+	0.0770155i
$137$	3.12810	+	3.12810i	0.267252	+	0.267252i	0.827992	−	0.560740i	$-0.189483\pi$
$137$	3.12810	+	3.12810i	0.267252	+	0.267252i	−0.560740	+	0.827992i	$0.689483\pi$
$138$	1.06718	−	2.09445i	0.0908440	−	0.178291i
$139$	5.07936	−	3.69037i	0.430825	−	0.313013i	−0.351153	−	0.936318i	$-0.614210\pi$
$139$	5.07936	−	3.69037i	0.430825	−	0.313013i	0.781979	+	0.623305i	$0.214210\pi$
$140$	−1.42082	+	0.723943i	−0.120081	+	0.0611844i
$141$	9.28878	+	6.74869i	0.782257	+	0.568343i
$142$	13.6334	+	2.15932i	1.14409	+	0.181206i
$143$	8.61020	+	11.8509i	0.720021	+	0.991024i
$144$	0.496889	+	0.683909i	0.0414074	+	0.0569924i
$145$	−3.44843	−	0.546178i	−0.286377	−	0.0453576i
$146$	4.61326	+	3.35173i	0.381796	+	0.277391i
$147$	1.74723	−	0.890256i	0.144109	−	0.0734271i
$148$	1.14531	−	0.832113i	0.0941435	−	0.0683993i
$149$	3.58859	−	7.04301i	0.293989	−	0.576986i	−0.696015	−	0.718027i	$-0.745045\pi$
$149$	3.58859	−	7.04301i	0.293989	−	0.576986i	0.990004	+	0.141042i	$0.0450452\pi$
$150$	3.40714	+	3.40714i	0.278192	+	0.278192i
$151$	11.2927	−	1.78858i	0.918983	−	0.145553i	0.321016	−	0.947074i	$-0.395976\pi$
$151$	11.2927	−	1.78858i	0.918983	−	0.145553i	0.597967	+	0.801521i	$0.295976\pi$
$152$	−1.69132	−	0.861772i	−0.137184	−	0.0698990i
$153$	2.20345	+	4.32451i	0.178138	+	0.349616i
$154$	0.868412	−	2.67270i	0.0699786	−	0.215372i
$155$		−	8.30304i		−	0.666916i
$156$	−9.72133	−	3.15865i	−0.778330	−	0.252895i
$157$	0.105036	−	0.663174i	0.00838282	−	0.0529271i	−0.983142	−	0.182842i	$-0.941470\pi$
$157$	0.105036	−	0.663174i	0.00838282	−	0.0529271i	0.991525	+	0.129915i	$0.0414704\pi$
$158$	1.50456	+	9.49945i	0.119697	+	0.755735i
$159$	−1.73348	+	0.563242i	−0.137474	+	0.0446680i
$160$	−0.492765	−	1.51658i	−0.0389565	−	0.119896i
$161$	0.847629	−	0.847629i	0.0668025	−	0.0668025i
$162$	−6.36068	+	8.75473i	−0.499743	+	0.687837i
$163$	−10.5489			−0.826255			−0.413127	−	0.910673i	$-0.635564\pi$
$163$	−10.5489			−0.826255			−0.413127	+	0.910673i	$0.635564\pi$
$164$	−1.32103	+	6.26537i	−0.103155	+	0.489243i
$165$	8.78758			0.684112
$166$	9.03597	−	12.4369i	0.701327	−	0.965294i
$167$	−7.12293	+	7.12293i	−0.551189	+	0.551189i	−0.926784	−	0.375595i	$-0.877438\pi$
$167$	−7.12293	+	7.12293i	−0.551189	+	0.551189i	0.375595	+	0.926784i	$0.377438\pi$
$168$	0.605969	+	1.86498i	0.0467516	+	0.143887i
$169$	13.4772	−	4.37901i	1.03671	−	0.336847i
$170$	−1.43221	−	9.04259i	−0.109845	−	0.693535i
$171$	−0.251026	+	1.58492i	−0.0191964	+	0.121202i
$172$	1.70476	+	0.553909i	0.129986	+	0.0422352i
$173$		−	12.0211i		−	0.913949i	−0.889480	−	0.456975i	$-0.848933\pi$
$173$		−	12.0211i		−	0.913949i	0.889480	−	0.456975i	$-0.151067\pi$
$174$	−1.32677	+	4.08337i	−0.100582	+	0.309560i
$175$	1.11554	+	2.18936i	0.0843267	+	0.165500i
$176$	2.50394	+	1.27582i	0.188742	+	0.0961687i
$177$	−15.0714	+	2.38708i	−1.13284	+	0.179424i
$178$	−11.9199	−	11.9199i	−0.893435	−	0.893435i
$179$	−0.124335	+	0.244021i	−0.00929324	+	0.0182390i	−0.895606	−	0.444847i	$-0.853258\pi$
$179$	−0.124335	+	0.244021i	−0.00929324	+	0.0182390i	0.886313	+	0.463086i	$0.153258\pi$
$180$	−1.09058	+	0.792350i	−0.0812867	+	0.0590583i
$181$	3.41087	−	1.73793i	0.253528	−	0.129179i	−0.322608	−	0.946533i	$-0.604560\pi$
$181$	3.41087	−	1.73793i	0.253528	−	0.129179i	0.576137	+	0.817353i	$0.304560\pi$
$182$	−4.21705	−	3.06387i	−0.312589	−	0.227109i
$183$	−12.4530	−	1.97236i	−0.920551	−	0.145801i
$184$	0.704595	+	0.969791i	0.0519434	+	0.0714940i
$185$	1.32691	+	1.82633i	0.0975560	+	0.134274i
$186$	−10.0848	−	1.59728i	−0.739454	−	0.117118i
$187$	13.0532	+	9.48369i	0.954543	+	0.693516i
$188$	−5.21691	+	2.65815i	−0.380482	+	0.193866i
$189$	−3.41823	+	2.48349i	−0.248640	+	0.180647i
$190$	1.37420	−	2.69702i	0.0996950	−	0.195662i
$191$	12.5634	+	12.5634i	0.909056	+	0.909056i	0.996196	−	0.0871400i	$-0.0277728\pi$
$191$	12.5634	+	12.5634i	0.909056	+	0.909056i	−0.0871400	+	0.996196i	$0.527773\pi$
$192$	−1.93682	+	0.306761i	−0.139778	+	0.0221386i
$193$	21.5759	+	10.9935i	1.55307	+	0.791326i	0.999149	−	0.0412456i	$-0.0131326\pi$
$193$	21.5759	+	10.9935i	1.55307	+	0.791326i	0.553917	+	0.832572i	$0.313133\pi$
$194$	−4.73263	−	9.28831i	−0.339783	−	0.666862i
$195$	5.03686	−	15.5018i	0.360697	−	1.11011i
$196$			1.00000i			0.0714286i
$197$	−20.2846	−	6.59087i	−1.44522	−	0.469580i	−0.521699	−	0.853130i	$-0.674702\pi$
$197$	−20.2846	−	6.59087i	−1.44522	−	0.469580i	−0.923520	+	0.383549i	$0.874702\pi$
$198$	0.371635	−	2.34641i	0.0264109	−	0.166752i
$199$	−3.07463	−	19.4125i	−0.217955	−	1.37611i	−0.817572	−	0.575827i	$-0.804680\pi$
$199$	−3.07463	−	19.4125i	−0.217955	−	1.37611i	0.599617	−	0.800287i	$-0.295320\pi$
$200$	−2.33692	+	0.759311i	−0.165245	+	0.0536914i
$201$	−1.54016	−	4.74014i	−0.108635	−	0.334343i
$202$	9.59547	−	9.59547i	0.675135	−	0.675135i
$203$	−1.28695	+	1.77134i	−0.0903265	+	0.124324i
$204$	−11.2586			−0.788258
$205$	−9.99090	−	2.10655i	−0.697795	−	0.147128i
$206$	−10.1084			−0.704288
$207$	0.595634	−	0.819820i	0.0413995	−	0.0569815i
$208$	3.68584	−	3.68584i	0.255567	−	0.255567i
$209$	1.64843	+	5.07336i	0.114025	+	0.350932i
$210$	−2.97394	+	0.966292i	−0.205221	+	0.0666805i
$211$	−1.70401	−	10.7587i	−0.117309	−	0.740659i	−0.974288	−	0.225307i	$-0.927661\pi$
$211$	−1.70401	−	10.7587i	−0.117309	−	0.740659i	0.856979	−	0.515352i	$-0.172339\pi$
$212$	0.145404	−	0.918046i	0.00998640	−	0.0630517i
$213$	25.7431	+	8.36443i	1.76389	+	0.573121i
$214$		−	0.286226i		−	0.0195660i
$215$	−0.883275	+	2.71844i	−0.0602389	+	0.185396i
$216$	−1.91818	−	3.76465i	−0.130516	−	0.256152i
$217$	−4.63938	−	2.36388i	−0.314942	−	0.160471i
$218$	−2.54919	+	0.403753i	−0.172653	+	0.0273456i
$219$	7.90685	+	7.90685i	0.534296	+	0.534296i
$220$	−2.03445	+	3.99284i	−0.137163	+	0.269197i
$221$	24.2116	−	17.5908i	1.62865	−	1.18328i
$222$	2.47351	−	1.26031i	0.166011	−	0.0845867i
$223$	19.6518	+	14.2779i	1.31598	+	0.956117i	0.999973	+	0.00736017i	$0.00234284\pi$
$223$	19.6518	+	14.2779i	1.31598	+	0.956117i	0.316009	+	0.948756i	$0.397657\pi$
$224$	−0.987688	−	0.156434i	−0.0659927	−	0.0104522i
$225$	1.22095	+	1.68049i	0.0813964	+	0.112033i
$226$	−0.672456	−	0.925556i	−0.0447311	−	0.0615671i
$227$	−18.9839	−	3.00676i	−1.26001	−	0.199565i	−0.509524	−	0.860456i	$-0.670179\pi$
$227$	−18.9839	−	3.00676i	−1.26001	−	0.199565i	−0.750482	+	0.660891i	$0.770179\pi$
$228$	−3.01142	−	2.18793i	−0.199436	−	0.144899i
$229$	−7.24080	+	3.68937i	−0.478486	+	0.243801i	−0.676562	−	0.736386i	$-0.736531\pi$
$229$	−7.24080	+	3.68937i	−0.478486	+	0.243801i	0.198076	+	0.980187i	$0.436531\pi$
$230$	−1.54645	+	1.12356i	−0.101970	+	0.0740855i
$231$	2.50183	−	4.91013i	0.164609	−	0.323063i
$232$	−1.54821	−	1.54821i	−0.101645	−	0.101645i
$233$	17.2148	−	2.72655i	1.12778	−	0.178622i	0.435454	−	0.900211i	$-0.356588\pi$
$233$	17.2148	−	2.72655i	1.12778	−	0.178622i	0.692322	+	0.721589i	$0.256588\pi$
$234$	−3.92620	−	2.00050i	−0.256664	−	0.130777i
$235$	−4.23874	−	8.31900i	−0.276505	−	0.542672i
$236$	2.40463	−	7.40070i	0.156528	−	0.481744i
$237$			18.8602i			1.22510i
$238$	−5.46036	−	1.77418i	−0.353943	−	0.115003i
$239$	−1.77418	+	11.2018i	−0.114762	+	0.724582i	0.861462	+	0.507821i	$0.169549\pi$
$239$	−1.77418	+	11.2018i	−0.114762	+	0.724582i	−0.976225	+	0.216760i	$0.930451\pi$
$240$	−0.489169	−	3.08849i	−0.0315757	−	0.199361i
$241$	−16.9873	+	5.51949i	−1.09425	+	0.355542i	−0.799885	−	0.600153i	$-0.795106\pi$
$241$	−16.9873	+	5.51949i	−1.09425	+	0.355542i	−0.294360	+	0.955695i	$0.595106\pi$
$242$	0.958741	+	2.95070i	0.0616302	+	0.189678i
$243$	−6.04216	+	6.04216i	−0.387605	+	0.387605i
$244$	3.77924	−	5.20167i	0.241941	−	0.333003i
$245$	−1.59462			−0.101877
$246$	−4.48057	+	11.7296i	−0.285671	+	0.747854i
$247$	9.89457			0.629576
$248$	3.06054	−	4.21247i	0.194344	−	0.267492i
$249$	21.3162	−	21.3162i	1.35086	−	1.35086i
$250$	−3.67464	−	11.3094i	−0.232405	−	0.715268i
$251$	−11.7192	+	3.80780i	−0.739709	+	0.240346i	−0.654547	−	0.756021i	$-0.727141\pi$
$251$	−11.7192	+	3.80780i	−0.739709	+	0.240346i	−0.0851616	+	0.996367i	$0.527141\pi$
$252$	0.132243	+	0.834950i	0.00833053	+	0.0525969i
$253$	0.526983	−	3.32724i	0.0331311	−	0.209182i
$254$	−14.1755	−	4.60589i	−0.889448	−	0.288999i
$255$		−	17.9532i		−	1.12427i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	10.9265	+	21.4445i	0.681577	+	1.33767i	0.929476	+	0.368884i	$0.120260\pi$
$257$	10.9265	+	21.4445i	0.681577	+	1.33767i	−0.247899	+	0.968786i	$0.579740\pi$
$258$	3.13188	+	1.59577i	0.194982	+	0.0993485i
$259$	1.39825	−	0.221460i	0.0868828	−	0.0137609i
$260$	5.87752	+	5.87752i	0.364508	+	0.364508i
$261$	−0.840295	+	1.64917i	−0.0520129	+	0.102081i
$262$	8.45600	−	6.14364i	0.522414	−	0.379556i
$263$	4.17085	−	2.12515i	0.257185	−	0.131043i	−0.320645	−	0.947200i	$-0.603900\pi$
$263$	4.17085	−	2.12515i	0.257185	−	0.131043i	0.577830	+	0.816157i	$0.303900\pi$
$264$	4.45830	+	3.23915i	0.274390	+	0.199356i
$265$	1.46394	+	0.231865i	0.0899289	+	0.0142433i
$266$	−1.11574	−	1.53569i	−0.0684106	−	0.0941592i
$267$	−19.4301	−	26.7432i	−1.18910	−	1.63666i
$268$	2.51036	+	0.397602i	0.153345	+	0.0242874i
$269$	1.67881	+	1.21972i	0.102359	+	0.0743678i	0.637787	−	0.770213i	$-0.279850\pi$
$269$	1.67881	+	1.21972i	0.102359	+	0.0743678i	−0.535429	+	0.844580i	$0.679850\pi$
$270$	6.00319	−	3.05878i	0.365343	−	0.186151i
$271$	−5.33236	+	3.87419i	−0.323918	+	0.235340i	−0.737845	−	0.674970i	$-0.764157\pi$
$271$	−5.33236	+	3.87419i	−0.323918	+	0.235340i	0.413928	+	0.910310i	$0.364157\pi$
$272$	2.60652	−	5.11559i	0.158044	−	0.310178i
$273$	−7.22777	−	7.22777i	−0.437445	−	0.437445i
$274$	−4.36934	+	0.692036i	−0.263962	+	0.0418074i
$275$	6.15264	+	3.13493i	0.371018	+	0.189043i
$276$	1.06718	+	2.09445i	0.0642364	+	0.126071i
$277$	−4.08875	+	12.5839i	−0.245669	+	0.756091i	0.749857	+	0.661600i	$0.230122\pi$
$277$	−4.08875	+	12.5839i	−0.245669	+	0.756091i	−0.995526	+	0.0944911i	$0.969878\pi$
$278$			6.27843i			0.376555i
$279$	−4.18626	−	1.36020i	−0.250625	−	0.0814329i
$280$	0.249454	−	1.57499i	0.0149077	−	0.0941236i
$281$	−4.00195	−	25.2673i	−0.238736	−	1.50732i	−0.757744	−	0.652552i	$-0.773699\pi$
$281$	−4.00195	−	25.2673i	−0.238736	−	1.50732i	0.519008	−	0.854769i	$-0.326301\pi$
$282$	−10.9196	+	3.54800i	−0.650254	+	0.211280i
$283$	4.18696	+	12.8861i	0.248889	+	0.766001i	0.994972	+	0.100149i	$0.0319319\pi$
$283$	4.18696	+	12.8861i	0.248889	+	0.766001i	−0.746084	+	0.665852i	$0.768068\pi$
$284$	−9.76046	+	9.76046i	−0.579177	+	0.579177i
$285$	3.48892	−	4.80208i	0.206666	−	0.284451i
$286$	−14.6485			−0.866187
$287$	−4.02147	+	4.98275i	−0.237380	+	0.294122i
$288$	−0.845358			−0.0498132
$289$	9.38297	−	12.9145i	0.551939	−	0.759679i
$290$	2.46881	−	2.46881i	0.144973	−	0.144973i
$291$	−6.31694	−	19.4415i	−0.370305	−	1.13968i
$292$	−5.42321	+	1.76211i	−0.317369	+	0.103120i
$293$	3.64840	+	23.0351i	0.213142	+	1.34573i	0.829609	+	0.558345i	$0.188563\pi$
$293$	3.64840	+	23.0351i	0.213142	+	1.34573i	−0.616467	+	0.787381i	$0.711437\pi$
$294$	−0.306761	+	1.93682i	−0.0178907	+	0.112957i
$295$	11.8013	+	3.83448i	0.687099	+	0.223252i
$296$			1.41568i			0.0822845i
$297$	−3.66918	+	11.2926i	−0.212908	+	0.655262i
$298$	3.58859	+	7.04301i	0.207881	+	0.407990i
$299$	−5.56740	−	2.83673i	−0.321971	−	0.164053i
$300$	−4.75911	+	0.753769i	−0.274767	+	0.0435189i
$301$	1.26748	+	1.26748i	0.0730563	+	0.0730563i
$302$	−5.19066	+	10.1872i	−0.298689	+	0.586210i
$303$	21.5282	−	15.6411i	1.23676	−	0.898560i
$304$	1.69132	−	0.861772i	0.0970041	−	0.0494260i
$305$	8.29470	+	6.02645i	0.474953	+	0.345074i
$306$	−4.79375	−	0.759256i	−0.274041	−	0.0434038i
$307$	−17.3871	−	23.9313i	−0.992337	−	1.36583i	−0.929911	−	0.367785i	$-0.880116\pi$
$307$	−17.3871	−	23.9313i	−0.992337	−	1.36583i	−0.0624257	−	0.998050i	$-0.519884\pi$
$308$	1.65182	+	2.27353i	0.0941211	+	0.129547i
$309$	−19.5782	−	3.10088i	−1.11376	−	0.176403i
$310$	6.71730	+	4.88040i	0.381517	+	0.277188i
$311$	1.05596	−	0.538037i	0.0598778	−	0.0305093i	−0.423795	−	0.905758i	$-0.639302\pi$
$311$	1.05596	−	0.538037i	0.0598778	−	0.0305093i	0.483673	+	0.875249i	$0.339302\pi$
$312$	8.26946	−	6.00811i	0.468166	−	0.340142i
$313$	9.65018	−	18.9395i	0.545460	−	1.07053i	−0.439580	−	0.898203i	$-0.644873\pi$
$313$	9.65018	−	18.9395i	0.545460	−	1.07053i	0.985041	−	0.172323i	$-0.0551273\pi$
$314$	0.474780	+	0.474780i	0.0267934	+	0.0267934i
$315$	−1.33143	+	0.210878i	−0.0750175	+	0.0118816i
$316$	−8.56957	−	4.36642i	−0.482076	−	0.245630i
$317$	−8.35680	−	16.4011i	−0.469365	−	0.921180i	−0.997407	−	0.0719620i	$-0.977074\pi$
$317$	−8.35680	−	16.4011i	−0.469365	−	0.921180i	0.528043	−	0.849218i	$-0.322926\pi$
$318$	0.563242	−	1.73348i	0.0315851	−	0.0972088i
$319$			6.15301i			0.344503i
$320$	1.51658	+	0.492765i	0.0847791	+	0.0275464i
$321$	0.0878032	−	0.554368i	0.00490070	−	0.0309418i
$322$	0.187522	+	1.18397i	0.0104502	+	0.0659800i
$323$	10.3650	−	3.36778i	0.576721	−	0.187388i
$324$	−3.34401	−	10.2918i	−0.185778	−	0.571767i
$325$	9.05677	−	9.05677i	0.502379	−	0.502379i
$326$	6.20050	−	8.53425i	0.343414	−	0.472668i
$327$	−5.06117			−0.279884
$328$	−4.29231	−	4.75143i	−0.237003	−	0.262354i
$329$	−5.85508			−0.322801
$330$	−5.16521	+	7.10930i	−0.284336	+	0.391354i
$331$	−25.1860	+	25.1860i	−1.38435	+	1.38435i	−0.547620	+	0.836727i	$0.684466\pi$
$331$	−25.1860	+	25.1860i	−1.38435	+	1.38435i	−0.836727	+	0.547620i	$0.815534\pi$
$332$	4.75049	+	14.6205i	0.260717	+	0.802404i
$333$	1.13818	−	0.369817i	0.0623718	−	0.0202658i
$334$	−1.57582	−	9.94933i	−0.0862250	−	0.544403i
$335$	−0.634025	+	4.00307i	−0.0346405	+	0.218711i
$336$	−1.86498	−	0.605969i	−0.101743	−	0.0330583i
$337$		−	28.4126i		−	1.54773i	−0.633350	−	0.773866i	$-0.718321\pi$
$337$		−	28.4126i		−	1.54773i	0.633350	−	0.773866i	$-0.281679\pi$
$338$	−4.37901	+	13.4772i	−0.238187	+	0.733064i
$339$	−1.01850	−	1.99892i	−0.0553172	−	0.108566i
$340$	8.15744	+	4.15642i	0.442399	+	0.225414i
$341$	−14.4525	+	2.28905i	−0.782646	+	0.123959i
$342$	−1.13467	−	1.13467i	−0.0613562	−	0.0613562i
$343$	−0.453990	+	0.891007i	−0.0245132	+	0.0481098i
$344$	−1.45015	+	1.05360i	−0.0781870	+	0.0568062i
$345$	−3.33985	+	1.70174i	−0.179812	+	0.0916186i
$346$	9.72530	+	7.06584i	0.522835	+	0.379862i
$347$	−23.2936	−	3.68934i	−1.25047	−	0.198054i	−0.504132	−	0.863627i	$-0.668187\pi$
$347$	−23.2936	−	3.68934i	−1.25047	−	0.198054i	−0.746333	+	0.665572i	$0.768187\pi$
$348$	−2.52366	−	3.47353i	−0.135283	−	0.186200i
$349$	11.3078	+	15.5639i	0.605293	+	0.833114i	0.996180	−	0.0873244i	$-0.0278317\pi$
$349$	11.3078	+	15.5639i	0.605293	+	0.833114i	−0.390887	+	0.920439i	$0.627832\pi$
$350$	−2.42693	−	0.384388i	−0.129725	−	0.0205464i
$351$	17.8177	+	12.9453i	0.951040	+	0.690971i
$352$	−2.50394	+	1.27582i	−0.133461	+	0.0680016i
$353$	−12.7991	+	9.29906i	−0.681225	+	0.494939i	−0.873764	−	0.486350i	$-0.838328\pi$
$353$	−12.7991	+	9.29906i	−0.681225	+	0.494939i	0.192539	+	0.981289i	$0.438328\pi$
$354$	6.92758	−	13.5961i	0.368197	−	0.722626i
$355$	−15.5642	−	15.5642i	−0.826064	−	0.826064i
$356$	16.6498	−	2.63706i	0.882435	−	0.139764i
$357$	−10.0315	−	5.11129i	−0.530921	−	0.270518i
$358$	−0.124335	−	0.244021i	−0.00657131	−	0.0128969i
$359$	−1.03993	+	3.20058i	−0.0548855	+	0.168920i	−0.974742	−	0.223336i	$-0.928305\pi$
$359$	−1.03993	+	3.20058i	−0.0548855	+	0.168920i	0.919856	+	0.392256i	$0.128305\pi$
$360$		−	1.34803i		−	0.0710472i
$361$	−14.6432	−	4.75786i	−0.770695	−	0.250414i
$362$	−0.598849	+	3.78098i	−0.0314748	+	0.198724i
$363$	0.951743	+	6.00907i	0.0499535	+	0.315394i
$364$	4.95744	−	1.61077i	0.259840	−	0.0844273i
$365$	−2.80990	−	8.64797i	−0.147077	−	0.452656i
$366$	8.91535	−	8.91535i	0.466013	−	0.466013i
$367$	7.66467	−	10.5495i	0.400092	−	0.550680i	−0.560675	−	0.828036i	$-0.689458\pi$
$367$	7.66467	−	10.5495i	0.400092	−	0.550680i	0.960767	+	0.277356i	$0.0894582\pi$
$368$	−1.19873			−0.0624880
$369$	−2.69879	+	4.69216i	−0.140493	+	0.244264i
$370$	−2.25747			−0.117360
$371$	0.546340	−	0.751973i	0.0283646	−	0.0390405i
$372$	7.21992	−	7.21992i	0.374336	−	0.374336i
$373$	6.50860	+	20.0314i	0.337002	+	1.03719i	0.965727	+	0.259559i	$0.0835771\pi$
$373$	6.50860	+	20.0314i	0.337002	+	1.03719i	−0.628725	+	0.777628i	$0.716423\pi$
$374$	−15.3449	+	4.98587i	−0.793467	+	0.257813i
$375$	−3.64782	−	23.0314i	−0.188373	−	1.18934i
$376$	0.915936	−	5.78299i	0.0472358	−	0.298235i
$377$	10.8543	+	3.52678i	0.559025	+	0.181638i
$378$		−	4.22516i		−	0.217319i
$379$	5.37379	−	16.5388i	0.276033	−	0.849543i	−0.712911	−	0.701255i	$-0.752624\pi$
$379$	5.37379	−	16.5388i	0.276033	−	0.849543i	0.988944	−	0.148288i	$-0.0473764\pi$
$380$	1.37420	+	2.69702i	0.0704950	+	0.138354i
$381$	−26.0424	−	13.2692i	−1.33419	−	0.679804i
$382$	−17.5486	+	2.77942i	−0.897864	+	0.142208i
$383$	−4.79766	−	4.79766i	−0.245149	−	0.245149i	0.573827	−	0.818976i	$-0.305458\pi$
$383$	−4.79766	−	4.79766i	−0.245149	−	0.245149i	−0.818976	+	0.573827i	$0.805458\pi$
$384$	0.890256	−	1.74723i	0.0454307	−	0.0891628i
$385$	−3.62542	+	2.63402i	−0.184769	+	0.134242i
$386$	−21.5759	+	10.9935i	−1.09818	+	0.559552i
$387$	1.22590	+	0.890667i	0.0623159	+	0.0452751i
$388$	10.2962	+	1.63075i	0.522709	+	0.0827890i
$389$	−8.60303	−	11.8411i	−0.436191	−	0.600365i	0.533169	−	0.846009i	$-0.321001\pi$
$389$	−8.60303	−	11.8411i	−0.436191	−	0.600365i	−0.969360	+	0.245643i	$0.921001\pi$
$390$	9.58067	+	13.1867i	0.485136	+	0.667732i
$391$	−6.79760	−	1.07663i	−0.343769	−	0.0544477i
$392$	−0.809017	−	0.587785i	−0.0408615	−	0.0296876i
$393$	18.2623	−	9.30513i	0.921214	−	0.469382i
$394$	17.2551	−	12.5366i	0.869301	−	0.631584i
$395$	6.96278	−	13.6652i	0.350336	−	0.687572i
$396$	1.67984	+	1.67984i	0.0844153	+	0.0844153i
$397$	35.4027	−	5.60723i	1.77681	−	0.281419i	0.820048	−	0.572295i	$-0.193947\pi$
$397$	35.4027	−	5.60723i	1.77681	−	0.281419i	0.956761	+	0.290877i	$0.0939469\pi$
$398$	17.5123	+	8.92294i	0.877810	+	0.447266i
$399$	−1.68990	−	3.31662i	−0.0846008	−	0.166038i
$400$	0.759311	−	2.33692i	0.0379655	−	0.116846i
$401$			8.50575i			0.424757i	0.977188	+	0.212378i	$0.0681209\pi$
$401$			8.50575i			0.424757i	−0.977188	+	0.212378i	$0.931879\pi$
$402$	4.74014	+	1.54016i	0.236416	+	0.0768164i
$403$	−4.24583	+	26.8071i	−0.211500	+	1.33536i
$404$	2.12282	+	13.4030i	0.105614	+	0.666823i
$405$	16.4115	−	5.33243i	0.815496	−	0.264971i
$406$	−0.676592	−	2.08234i	−0.0335787	−	0.103345i
$407$	2.81314	−	2.81314i	0.139442	−	0.139442i
$408$	6.61762	−	9.10838i	0.327621	−	0.450932i
$409$	−12.5365			−0.619890			−0.309945	−	0.950755i	$-0.600311\pi$
$409$	−12.5365			−0.619890			−0.309945	+	0.950755i	$0.600311\pi$
$410$	7.57673	−	6.84461i	0.374188	−	0.338031i
$411$	−8.67490			−0.427901
$412$	5.94159	−	8.17789i	0.292721	−	0.402896i
$413$	5.50239	−	5.50239i	0.270755	−	0.270755i
$414$	0.313144	+	0.963757i	0.0153902	+	0.0473661i
$415$	−23.3142	+	7.57523i	−1.14445	+	0.371854i
$416$	0.815424	+	5.14839i	0.0399795	+	0.252420i
$417$	−1.92598	+	12.1602i	−0.0943157	+	0.595486i
$418$	−5.07336	−	1.64843i	−0.248146	−	0.0806276i
$419$			9.40573i			0.459500i	0.973250	+	0.229750i	$0.0737908\pi$
$419$			9.40573i			0.459500i	−0.973250	+	0.229750i	$0.926209\pi$
$420$	0.966292	−	2.97394i	0.0471502	−	0.145113i
$421$	5.63664	+	11.0625i	0.274713	+	0.539154i	0.986604	−	0.163136i	$-0.0521609\pi$
$421$	5.63664	+	11.0625i	0.274713	+	0.539154i	−0.711891	+	0.702290i	$0.752161\pi$
$422$	9.70556	+	4.94523i	0.472459	+	0.240730i
$423$	−4.88870	+	0.774294i	−0.237697	+	0.0376474i
$424$	0.657248	+	0.657248i	0.0319188	+	0.0319188i
$425$	6.40470	−	12.5699i	0.310674	−	0.609732i
$426$	−21.8984	+	15.9101i	−1.06098	+	0.770846i
$427$	5.72883	−	2.91899i	0.277238	−	0.141260i
$428$	0.231562	+	0.168240i	0.0111930	+	0.00813217i
$429$	−28.3715	−	4.49361i	−1.36979	−	0.216954i
$430$	−1.68009	−	2.31244i	−0.0810211	−	0.111516i
$431$	−12.7126	−	17.4975i	−0.612346	−	0.842823i	0.384421	−	0.923158i	$-0.374401\pi$
$431$	−12.7126	−	17.4975i	−0.612346	−	0.842823i	−0.996768	+	0.0803351i	$0.974401\pi$
$432$	4.17315	+	0.660961i	0.200781	+	0.0318005i
$433$	24.3330	+	17.6790i	1.16937	+	0.849596i	0.990933	−	0.134355i	$-0.0428963\pi$
$433$	24.3330	+	17.6790i	1.16937	+	0.849596i	0.178436	+	0.983952i	$0.442896\pi$
$434$	4.63938	−	2.36388i	0.222697	−	0.113470i
$435$	5.53896	−	4.02429i	0.265573	−	0.192950i
$436$	1.17174	−	2.29966i	0.0561160	−	0.110134i
$437$	−1.60898	−	1.60898i	−0.0769681	−	0.0769681i
$438$	−11.0443	+	1.74925i	−0.527717	+	0.0835822i
$439$	29.1685	+	14.8621i	1.39214	+	0.709329i	0.979477	−	0.201556i	$-0.0645997\pi$
$439$	29.1685	+	14.8621i	1.39214	+	0.709329i	0.412660	+	0.910885i	$0.364600\pi$
$440$	−2.03445	−	3.99284i	−0.0969888	−	0.190351i
$441$	−0.261230	+	0.803983i	−0.0124395	+	0.0382849i
$442$			29.9272i			1.42349i
$443$	5.93584	+	1.92867i	0.282020	+	0.0916339i	0.446612	−	0.894728i	$-0.352631\pi$
$443$	5.93584	+	1.92867i	0.282020	+	0.0916339i	−0.164592	+	0.986362i	$0.552631\pi$
$444$	−0.434275	+	2.74190i	−0.0206098	+	0.130125i
$445$	4.20512	+	26.5501i	0.199342	+	1.25859i
$446$	−23.1021	+	7.50632i	−1.09391	+	0.355434i
$447$	4.78992	+	14.7418i	0.226555	+	0.697265i
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$	−2.42187	+	3.33342i	−0.114295	+	0.157314i	−0.862332	−	0.506344i	$-0.830997\pi$
$449$	−2.42187	+	3.33342i	−0.114295	+	0.157314i	0.748037	+	0.663657i	$0.230997\pi$
$450$	−2.07720			−0.0979200
$451$	−0.912338	+	17.9712i	−0.0429603	+	0.846230i
$452$	1.14405			0.0538116
$453$	−13.1784	+	18.1385i	−0.619176	+	0.852222i
$454$	13.5910	−	13.5910i	0.637856	−	0.637856i
$455$	2.56857	+	7.90524i	0.120416	+	0.370603i
$456$	3.54014	−	1.15026i	0.165782	−	0.0538659i
$457$	−0.154455	−	0.975188i	−0.00722508	−	0.0456174i	0.983812	−	0.179201i	$-0.0573514\pi$
$457$	−0.154455	−	0.975188i	−0.00722508	−	0.0456174i	−0.991037	+	0.133584i	$0.957351\pi$
$458$	1.27127	−	8.02649i	0.0594026	−	0.375053i
$459$	23.0709	+	7.49620i	1.07686	+	0.349893i
$460$		−	1.91152i		−	0.0891250i
$461$	3.93457	−	12.1094i	0.183251	−	0.563990i	−0.816663	−	0.577116i	$-0.804178\pi$
$461$	3.93457	−	12.1094i	0.183251	−	0.563990i	0.999914	+	0.0131259i	$0.00417823\pi$
$462$	2.50183	+	4.91013i	0.116396	+	0.228440i
$463$	10.9463	+	5.57744i	0.508719	+	0.259205i	0.689458	−	0.724326i	$-0.257849\pi$
$463$	10.9463	+	5.57744i	0.508719	+	0.259205i	−0.180739	+	0.983531i	$0.557849\pi$
$464$	2.16254	−	0.342513i	0.100393	−	0.0159008i
$465$	11.5130	+	11.5130i	0.533905	+	0.533905i
$466$	−7.91275	+	15.5297i	−0.366551	+	0.719397i
$467$	23.9441	−	17.3964i	1.10800	−	0.805011i	0.125654	−	0.992074i	$-0.459897\pi$
$467$	23.9441	−	17.3964i	1.10800	−	0.805011i	0.982348	+	0.187063i	$0.0598969\pi$
$468$	3.92620	−	2.00050i	0.181489	−	0.0924731i
$469$	2.05624	+	1.49395i	0.0949483	+	0.0689840i
$470$	9.22169	+	1.46057i	0.425365	+	0.0673711i
$471$	0.773918	+	1.06521i	0.0356602	+	0.0490821i
$472$	4.57388	+	6.29541i	0.210530	+	0.289770i
$473$	4.97530	+	0.788010i	0.228765	+	0.0362328i
$474$	−15.2582	−	11.0858i	−0.700834	−	0.509186i
$475$	4.15589	−	2.11753i	0.190685	−	0.0971590i
$476$	4.64486	−	3.37469i	0.212897	−	0.154679i
$477$	0.356724	−	0.700109i	0.0163332	−	0.0320558i
$478$	−8.01958	−	8.01958i	−0.366807	−	0.366807i
$479$	−41.0388	+	6.49991i	−1.87511	+	0.296988i	−0.986761	−	0.162180i	$-0.948147\pi$
$479$	−41.0388	+	6.49991i	−1.87511	+	0.296988i	−0.888349	+	0.459168i	$0.848147\pi$
$480$	2.78617	+	1.41962i	0.127170	+	0.0647966i
$481$	−3.35013	−	6.57500i	−0.152753	−	0.299794i
$482$	5.51949	−	16.9873i	0.251406	−	0.773748i
$483$			2.35066i			0.106959i
$484$	−2.95070	−	0.958741i	−0.134123	−	0.0435791i
$485$	−2.60043	+	16.4185i	−0.118080	+	0.745526i
$486$	−1.33672	−	8.43971i	−0.0606348	−	0.382833i
$487$	−24.2038	+	7.86428i	−1.09678	+	0.356365i	−0.800862	−	0.598849i	$-0.795625\pi$
$487$	−24.2038	+	7.86428i	−1.09678	+	0.356365i	−0.295916	+	0.955214i	$0.595625\pi$
$488$	1.98686	+	6.11493i	0.0899410	+	0.276810i
$489$	14.6272	−	14.6272i	0.661465	−	0.661465i
$490$	0.937295	−	1.29008i	0.0423427	−	0.0582797i
$491$	29.0134			1.30936			0.654679	−	0.755907i	$-0.272804\pi$
$491$	29.0134			1.30936			0.654679	+	0.755907i	$0.272804\pi$
$492$	−6.85586	−	10.5194i	−0.309086	−	0.474249i
$493$	12.5707			0.566156
$494$	−5.81588	+	8.00488i	−0.261669	+	0.360156i
$495$	−2.67872	+	2.67872i	−0.120399	+	0.120399i
$496$	1.60902	+	4.95206i	0.0722472	+	0.222354i
$497$	−13.1278	+	4.26548i	−0.588862	+	0.191333i
$498$	4.71581	+	29.7745i	0.211321	+	1.33423i
$499$	−0.0732329	+	0.462374i	−0.00327835	+	0.0206987i	−0.989273	−	0.146077i	$-0.953335\pi$
$499$	−0.0732329	+	0.462374i	−0.00327835	+	0.0206987i	0.985995	+	0.166775i	$0.0533354\pi$
$500$	11.3094	+	3.67464i	0.505771	+	0.164335i
$501$		−	19.7534i		−	0.882518i
$502$	3.80780	−	11.7192i	0.169950	−	0.523053i
$503$	−13.8531	−	27.1882i	−0.617678	−	1.21226i	−0.961907	−	0.273376i	$-0.911860\pi$
$503$	−13.8531	−	27.1882i	−0.617678	−	1.21226i	0.344229	−	0.938886i	$-0.388140\pi$
$504$	−0.753219	−	0.383784i	−0.0335510	−	0.0170951i
$505$	−21.3727	+	3.38510i	−0.951071	+	0.150635i
$506$	2.38204	+	2.38204i	0.105895	+	0.105895i
$507$	−12.6156	+	24.7596i	−0.560280	+	1.09961i
$508$	12.0584	−	8.76092i	0.535004	−	0.388703i
$509$	−2.27859	+	1.16100i	−0.100997	+	0.0514603i	−0.503759	−	0.863844i	$-0.668050\pi$
$509$	−2.27859	+	1.16100i	−0.100997	+	0.0514603i	0.402762	+	0.915305i	$0.368050\pi$
$510$	14.5244	+	10.5526i	0.643152	+	0.467277i
$511$	−5.63210	−	0.892037i	−0.249149	−	0.0394614i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	4.71420	+	6.48854i	0.208137	+	0.286476i
$514$	−23.7714	−	3.76502i	−1.04851	−	0.166068i
$515$	13.0406	+	9.47459i	0.574640	+	0.417500i
$516$	−3.13188	+	1.59577i	−0.137873	+	0.0702500i
$517$	−13.3117	+	9.67152i	−0.585448	+	0.425353i
$518$	−0.642703	+	1.26138i	−0.0282388	+	0.0554217i
$519$	16.6686	+	16.6686i	0.731669	+	0.731669i
$520$	−8.20973	+	1.30029i	−0.360020	+	0.0570216i
$521$	5.26153	+	2.68088i	0.230512	+	0.117452i	0.565432	−	0.824795i	$-0.308709\pi$
$521$	5.26153	+	2.68088i	0.230512	+	0.117452i	−0.334920	+	0.942246i	$0.608709\pi$
$522$	−0.840295	−	1.64917i	−0.0367787	−	0.0721823i
$523$	−0.0152453	+	0.0469204i	−0.000666632	+	0.00205168i	−0.951389	−	0.307991i	$-0.900343\pi$
$523$	−0.0152453	+	0.0469204i	−0.000666632	+	0.00205168i	0.950723	+	0.310043i	$0.100343\pi$
$524$			10.4522i			0.456606i
$525$	−4.58260	−	1.48898i	−0.200001	−	0.0649843i
$526$	−0.732278	+	4.62342i	−0.0319288	+	0.201591i
$527$	4.67656	+	29.5267i	0.203714	+	1.28620i
$528$	−5.24105	+	1.70292i	−0.228087	+	0.0741101i
$529$	−6.66335	−	20.5077i	−0.289711	−	0.891638i
$530$	−1.04806	+	1.04806i	−0.0455249	+	0.0455249i
$531$	3.86657	−	5.32187i	0.167795	−	0.230950i
$532$	1.89822			0.0822981
$533$	31.1793	+	11.9101i	1.35053	+	0.515884i
$534$	33.0565			1.43049
$535$	−0.268279	+	0.369254i	−0.0115987	+	0.0159642i
$536$	−1.79722	+	1.79722i	−0.0776280	+	0.0776280i
$537$	−0.165958	−	0.510766i	−0.00716161	−	0.0220412i
$538$	−1.97355	+	0.641247i	−0.0850859	+	0.0276461i
$539$	0.439618	+	2.77564i	0.0189357	+	0.119555i
$540$	−1.05398	+	6.65459i	−0.0453562	+	0.286368i
$541$	−24.2987	−	7.89512i	−1.04468	−	0.339438i	−0.264103	−	0.964495i	$-0.585076\pi$
$541$	−24.2987	−	7.89512i	−1.04468	−	0.339438i	−0.780579	+	0.625057i	$0.785076\pi$
$542$		−	6.59116i		−	0.283115i
$543$	−2.31972	+	7.13936i	−0.0995487	+	0.306379i
$544$	2.60652	+	5.11559i	0.111754	+	0.219329i
$545$	3.66709	+	1.86848i	0.157081	+	0.0800367i
$546$	10.0958	−	1.59901i	0.432059	−	0.0684314i
$547$	14.1269	+	14.1269i	0.604022	+	0.604022i	0.941377	−	0.337355i	$-0.109532\pi$
$547$	14.1269	+	14.1269i	0.604022	+	0.604022i	−0.337355	+	0.941377i	$0.609532\pi$
$548$	2.00837	−	3.94164i	0.0857932	−	0.168379i
$549$	4.39727	−	3.19481i	0.187671	−	0.136351i
$550$	−6.15264	+	3.13493i	−0.262349	+	0.133674i
$551$	3.36239	+	2.44292i	0.143243	+	0.104072i
$552$	−2.32171	−	0.367724i	−0.0988187	−	0.0156514i
$553$	−5.65324	−	7.78101i	−0.240400	−	0.330882i
$554$	−7.77726	−	10.7045i	−0.330424	−	0.454790i
$555$	−4.37230	−	0.692504i	−0.185594	−	0.0293951i
$556$	−5.07936	−	3.69037i	−0.215413	−	0.156507i
$557$	−23.7847	+	12.1189i	−1.00779	+	0.513495i	−0.878312	−	0.478087i	$-0.841330\pi$
$557$	−23.7847	+	12.1189i	−1.00779	+	0.513495i	−0.129478	+	0.991582i	$0.541330\pi$
$558$	3.56104	−	2.58725i	0.150751	−	0.109527i
$559$	4.24184	−	8.32507i	0.179411	−	0.352113i
$560$	1.12757	+	1.12757i	0.0476484	+	0.0476484i
$561$	−31.2498	+	4.94948i	−1.31937	+	0.208967i
$562$	22.7940	+	11.6141i	0.961505	+	0.489911i
$563$	−11.1975	−	21.9763i	−0.471918	−	0.926192i	−0.997165	−	0.0752419i	$-0.976027\pi$
$563$	−11.1975	−	21.9763i	−0.471918	−	0.926192i	0.525247	−	0.850950i	$-0.323973\pi$
$564$	3.54800	−	10.9196i	0.149398	−	0.459799i
$565$			1.82433i			0.0767500i
$566$	−12.8861	−	4.18696i	−0.541644	−	0.175991i
$567$	1.69285	−	10.6882i	0.0710929	−	0.448863i
$568$	−2.15932	−	13.6334i	−0.0906032	−	0.572046i
$569$	25.9885	−	8.44416i	1.08949	−	0.353998i	0.291443	−	0.956588i	$-0.405865\pi$
$569$	25.9885	−	8.44416i	1.08949	−	0.353998i	0.798050	+	0.602591i	$0.205865\pi$
$570$	1.83423	+	5.64519i	0.0768275	+	0.236451i
$571$	−29.1124	+	29.1124i	−1.21832	+	1.21832i	−0.250096	+	0.968221i	$0.580462\pi$
$571$	−29.1124	+	29.1124i	−1.21832	+	1.21832i	−0.968221	+	0.250096i	$0.919538\pi$
$572$	8.61020	−	11.8509i	0.360011	−	0.495512i
$573$	−34.8410			−1.45550
$574$	−1.66737	−	6.18222i	−0.0695947	−	0.258041i
$575$	−2.94549			−0.122836
$576$	0.496889	−	0.683909i	0.0207037	−	0.0284962i
$577$	−7.66363	+	7.66363i	−0.319041	+	0.319041i	−0.848399	−	0.529358i	$-0.822433\pi$
$577$	−7.66363	+	7.66363i	−0.319041	+	0.319041i	0.529358	+	0.848399i	$0.322433\pi$
$578$	4.93292	+	15.1820i	0.205182	+	0.631486i
$579$	−45.1609	+	14.6737i	−1.87682	+	0.609816i
$580$	0.546178	+	3.44843i	0.0226788	+	0.143188i
$581$	−2.40485	+	15.1836i	−0.0997701	+	0.629923i
$582$	19.4415	+	6.31694i	0.805877	+	0.261845i
$583$		−	2.61209i		−	0.108182i
$584$	1.76211	−	5.42321i	0.0729166	−	0.224414i
$585$	3.19004	+	6.26080i	0.131892	+	0.258852i
$586$	−20.7803	−	10.5881i	−0.858425	−	0.437389i
$587$	24.1330	−	3.82230i	0.996077	−	0.157763i	0.362948	−	0.931809i	$-0.381770\pi$
$587$	24.1330	−	3.82230i	0.996077	−	0.157763i	0.633129	+	0.774046i	$0.281770\pi$
$588$	−1.38661	−	1.38661i	−0.0571827	−	0.0571827i
$589$	−4.48716	+	8.80655i	−0.184890	+	0.362868i
$590$	−10.0388	+	7.29361i	−0.413291	+	0.300273i
$591$	37.2657	−	18.9878i	1.53291	−	0.781056i
$592$	−1.14531	−	0.832113i	−0.0470718	−	0.0341996i
$593$	22.0817	+	3.49739i	0.906786	+	0.143621i	0.592371	−	0.805665i	$-0.298192\pi$
$593$	22.0817	+	3.49739i	0.906786	+	0.143621i	0.314414	+	0.949286i	$0.398192\pi$
$594$	−6.97920	−	9.60605i	−0.286360	−	0.394141i
$595$	5.38135	+	7.40680i	0.220614	+	0.303649i
$596$	−7.80723	−	1.23654i	−0.319797	−	0.0506508i
$597$	31.1808	+	22.6542i	1.27614	+	0.927173i
$598$	5.56740	−	2.83673i	0.227668	−	0.116003i
$599$	2.57877	−	1.87359i	0.105366	−	0.0765527i	−0.533855	−	0.845576i	$-0.679257\pi$
$599$	2.57877	−	1.87359i	0.105366	−	0.0765527i	0.639221	+	0.769024i	$0.279257\pi$
$600$	2.18752	−	4.29325i	0.0893052	−	0.175271i
$601$	−5.48424	−	5.48424i	−0.223707	−	0.223707i	0.586351	−	0.810057i	$-0.300564\pi$
$601$	−5.48424	−	5.48424i	−0.223707	−	0.223707i	−0.810057	+	0.586351i	$0.800564\pi$
$602$	−1.77042	+	0.280407i	−0.0721569	+	0.0114285i
$603$	1.91442	+	0.975446i	0.0779612	+	0.0397232i
$604$	−5.19066	−	10.1872i	−0.211205	−	0.414513i
$605$	1.52883	−	4.70525i	0.0621557	−	0.191296i
$606$			26.6103i			1.08097i
$607$	−20.6722	−	6.71682i	−0.839061	−	0.272627i	−0.142204	−	0.989837i	$-0.545419\pi$
$607$	−20.6722	−	6.71682i	−0.839061	−	0.272627i	−0.696857	+	0.717210i	$0.745419\pi$
$608$	−0.296947	+	1.87485i	−0.0120428	+	0.0760351i
$609$	−0.671653	−	4.24065i	−0.0272168	−	0.171840i
$610$	−9.75100	+	3.16829i	−0.394807	+	0.128280i
$611$	9.43118	+	29.0262i	0.381545	+	1.17427i
$612$	3.43195	−	3.43195i	0.138728	−	0.138728i
$613$	−17.1427	+	23.5949i	−0.692386	+	0.952988i	0.307613	+	0.951512i	$0.400470\pi$
$613$	−17.1427	+	23.5949i	−0.692386	+	0.952988i	−0.999999	+	0.00147605i	$0.999530\pi$
$614$	29.5808			1.19378
$615$	16.7744	−	10.9325i	0.676409	−	0.440841i
$616$	−2.81024			−0.113228
$617$	−19.2010	+	26.4280i	−0.773005	+	1.06395i	0.223014	+	0.974815i	$0.428410\pi$
$617$	−19.2010	+	26.4280i	−0.773005	+	1.06395i	−0.996020	+	0.0891351i	$0.971590\pi$
$618$	14.0164	−	14.0164i	0.563823	−	0.563823i
$619$	−2.60664	−	8.02243i	−0.104770	−	0.322449i	0.884906	−	0.465769i	$-0.154222\pi$
$619$	−2.60664	−	8.02243i	−0.104770	−	0.322449i	−0.989676	+	0.143320i	$0.954222\pi$
$620$	−7.89666	+	2.56578i	−0.317137	+	0.103044i
$621$	−0.792313	−	5.00247i	−0.0317944	−	0.200742i
$622$	−0.185395	+	1.17054i	−0.00743366	+	0.0469343i
$623$	16.0322	+	5.20919i	0.642318	+	0.208702i
$624$			10.2216i			0.409192i
$625$	−2.06311	+	6.34959i	−0.0825242	+	0.253983i
$626$	9.65018	+	18.9395i	0.385699	+	0.756976i
$627$	−9.32049	−	4.74902i	−0.372224	−	0.189658i
$628$	−0.663174	+	0.105036i	−0.0264635	+	0.00419141i
$629$	−5.74730	−	5.74730i	−0.229160	−	0.229160i
$630$	0.611991	−	1.20110i	0.0243823	−	0.0478530i
$631$	−12.3357	+	8.96239i	−0.491075	+	0.356787i	−0.805598	−	0.592463i	$-0.798156\pi$
$631$	−12.3357	+	8.96239i	−0.491075	+	0.356787i	0.314522	+	0.949250i	$0.398156\pi$
$632$	8.56957	−	4.36642i	0.340879	−	0.173687i
$633$	17.2809	+	12.5553i	0.686853	+	0.499028i
$634$	18.1808	+	2.87956i	0.722052	+	0.114362i
$635$	13.9704	+	19.2286i	0.554397	+	0.763062i
$636$	1.07135	+	1.47459i	0.0424818	+	0.0584712i
$637$	5.14839	+	0.815424i	0.203986	+	0.0323083i
$638$	−4.97789	−	3.61665i	−0.197077	−	0.143185i
$639$	−10.3970	+	5.29752i	−0.411298	+	0.209567i
$640$	−1.29008	+	0.937295i	−0.0509947	+	0.0370498i
$641$	7.63945	−	14.9933i	0.301740	−	0.592198i	−0.689498	−	0.724288i	$-0.742169\pi$
$641$	7.63945	−	14.9933i	0.301740	−	0.592198i	0.991238	+	0.132090i	$0.0421686\pi$
$642$	0.396883	+	0.396883i	0.0156637	+	0.0156637i
$643$	−38.0159	+	6.02113i	−1.49920	+	0.237450i	−0.851464	−	0.524413i	$-0.824285\pi$
$643$	−38.0159	+	6.02113i	−1.49920	+	0.237450i	−0.647738	+	0.761863i	$0.724285\pi$
$644$	−1.06807	−	0.544211i	−0.0420880	−	0.0214449i
$645$	−2.54465	−	4.99417i	−0.100196	−	0.196645i
$646$	−3.36778	+	10.3650i	−0.132503	+	0.407804i
$647$		−	42.2338i		−	1.66038i	−0.557479	−	0.830191i	$-0.688231\pi$
$647$		−	42.2338i		−	1.66038i	0.557479	−	0.830191i	$-0.311769\pi$
$648$	10.2918	+	3.34401i	0.404300	+	0.131365i
$649$	3.42091	−	21.5988i	0.134283	−	0.847827i
$650$	2.00365	+	12.6505i	0.0785894	+	0.496194i
$651$	9.71078	−	3.15522i	0.380595	−	0.123663i
$652$	3.25979	+	10.0326i	0.127663	+	0.392908i
$653$	−2.12400	+	2.12400i	−0.0831184	+	0.0831184i	−0.747444	−	0.664325i	$-0.768719\pi$
$653$	−2.12400	+	2.12400i	−0.0831184	+	0.0831184i	0.664325	+	0.747444i	$0.268719\pi$
$654$	2.97488	−	4.09458i	0.116327	−	0.160111i
$655$	−16.6673			−0.651245
$656$	6.36694	−	0.679730i	0.248587	−	0.0265390i
$657$	−4.82048			−0.188065
$658$	3.44153	−	4.73686i	0.134165	−	0.184662i
$659$	30.5077	−	30.5077i	1.18841	−	1.18841i	0.210903	−	0.977507i	$-0.432360\pi$
$659$	30.5077	−	30.5077i	1.18841	−	1.18841i	0.977507	−	0.210903i	$-0.0676403\pi$
$660$	−2.71551	−	8.35749i	−0.105701	−	0.325315i
$661$	27.7069	−	9.00250i	1.07767	−	0.350157i	0.284201	−	0.958765i	$-0.408272\pi$
$661$	27.7069	−	9.00250i	1.07767	−	0.350157i	0.793471	+	0.608608i	$0.208272\pi$
$662$	−5.57194	−	35.1798i	−0.216560	−	1.36730i
$663$	−9.18051	+	57.9635i	−0.356542	+	2.25112i
$664$	−14.6205	−	4.75049i	−0.567386	−	0.184355i
$665$			3.02694i			0.117380i
$666$	−0.369817	+	1.13818i	−0.0143301	+	0.0441035i
$667$	−1.19155	−	2.33855i	−0.0461369	−	0.0905489i
$668$	8.97542	+	4.57320i	0.347269	+	0.176943i
$669$	−47.0471	+	7.45153i	−1.81895	+	0.288093i
$670$	−2.86588	−	2.86588i	−0.110719	−	0.110719i
$671$	8.20305	−	16.0994i	0.316675	−	0.621510i
$672$	1.58645	−	1.15262i	0.0611986	−	0.0444634i
$673$	27.6798	−	14.1035i	1.06698	−	0.543652i	0.169870	−	0.985466i	$-0.445665\pi$
$673$	27.6798	−	14.1035i	1.06698	−	0.543652i	0.897106	+	0.441815i	$0.145665\pi$
$674$	22.9862	+	16.7005i	0.885397	+	0.643279i
$675$	10.2542	+	1.62410i	0.394683	+	0.0625117i
$676$	−8.32938	−	11.4644i	−0.320361	−	0.440939i
$677$	−11.1030	−	15.2820i	−0.426723	−	0.587334i	0.540474	−	0.841361i	$-0.318245\pi$
$677$	−11.1030	−	15.2820i	−0.426723	−	0.587334i	−0.967197	+	0.254027i	$0.918245\pi$
$678$	2.21581	+	0.350951i	0.0850979	+	0.0134782i
$679$	8.43361	+	6.12738i	0.323652	+	0.235147i
$680$	−8.15744	+	4.15642i	−0.312823	+	0.159391i
$681$	30.4924	−	22.1540i	1.16847	−	0.848944i
$682$	6.64308	−	13.0378i	0.254377	−	0.499242i
$683$	−19.9186	−	19.9186i	−0.762166	−	0.762166i	0.214548	−	0.976713i	$-0.431172\pi$
$683$	−19.9186	−	19.9186i	−0.762166	−	0.762166i	−0.976713	+	0.214548i	$0.931172\pi$
$684$	1.58492	−	0.251026i	0.0606008	−	0.00959822i
$685$	6.28543	+	3.20258i	0.240154	+	0.122364i
$686$	−0.453990	−	0.891007i	−0.0173334	−	0.0340188i
$687$	4.92443	−	15.1559i	0.187879	−	0.578232i
$688$		−	1.79249i		−	0.0683379i
$689$	−4.60789	−	1.49719i	−0.175547	−	0.0570385i
$690$	0.586380	−	3.70226i	0.0223231	−	0.140943i
$691$	−7.35682	−	46.4491i	−0.279866	−	1.76701i	−0.581464	−	0.813572i	$-0.697520\pi$
$691$	−7.35682	−	46.4491i	−0.279866	−	1.76701i	0.301597	−	0.953435i	$-0.402480\pi$
$692$	−11.4328	+	3.71473i	−0.434609	+	0.141213i
$693$	0.734119	+	2.25939i	0.0278869	+	0.0858269i
$694$	16.6764	−	16.6764i	0.633026	−	0.633026i
$695$	5.88474	−	8.09965i	0.223221	−	0.307237i
$696$	4.29351			0.162745
$697$	36.7154	+	1.86392i	1.39069	+	0.0706010i
$698$	−19.2380			−0.728169
$699$	−20.0894	+	27.6507i	−0.759852	+	1.04585i
$700$	1.73749	−	1.73749i	0.0656709	−	0.0656709i
$701$	2.75404	+	8.47606i	0.104019	+	0.320136i	0.989499	−	0.144541i	$-0.0461705\pi$
$701$	2.75404	+	8.47606i	0.104019	+	0.320136i	−0.885480	+	0.464677i	$0.846170\pi$
$702$	−20.9460	+	6.80577i	−0.790556	+	0.256867i
$703$	−0.420380	−	2.65417i	−0.0158549	−	0.100104i
$704$	0.439618	−	2.77564i	0.0165687	−	0.104611i
$705$	17.4127	+	5.65772i	0.655799	+	0.213082i
$706$		−	15.8205i		−	0.595413i
$707$	−4.19337	+	12.9059i	−0.157708	+	0.485376i
$708$	6.92758	+	13.5961i	0.260354	+	0.510974i
$709$	−38.9182	−	19.8298i	−1.46160	−	0.744725i	−0.471084	−	0.882088i	$-0.656137\pi$
$709$	−38.9182	−	19.8298i	−1.46160	−	0.744725i	−0.990521	+	0.137364i	$0.956137\pi$
$710$	21.7402	−	3.44331i	0.815894	−	0.129225i
$711$	−5.74915	−	5.74915i	−0.215610	−	0.215610i
$712$	−7.65305	+	15.0200i	−0.286810	+	0.562897i
$713$	5.04961	−	3.66875i	0.189109	−	0.137396i
$714$	10.0315	−	5.11129i	0.375418	−	0.191285i
$715$	18.8977	+	13.7300i	0.706735	+	0.513473i
$716$	0.270500	+	0.0428429i	0.0101090	+	0.00160112i
$717$	−13.0723	−	17.9925i	−0.488196	−	0.671944i
$718$	−1.97807	−	2.72258i	−0.0738208	−	0.101606i
$719$	8.55548	+	1.35505i	0.319065	+	0.0505350i	0.313913	−	0.949452i	$-0.398360\pi$
$719$	8.55548	+	1.35505i	0.319065	+	0.0505350i	0.00515237	+	0.999987i	$0.498360\pi$
$720$	1.09058	+	0.792350i	0.0406434	+	0.0295291i
$721$	9.00668	−	4.58913i	0.335426	−	0.170908i
$722$	12.4563	−	9.05000i	0.463574	−	0.336806i
$723$	15.9013	−	31.2080i	0.591375	−	1.16064i
$724$	−2.70688	−	2.70688i	−0.100601	−	0.100601i
$725$	5.31376	−	0.841616i	0.197348	−	0.0312568i
$726$	−5.42086	−	2.76206i	−0.201187	−	0.102510i
$727$	−16.7126	−	32.8002i	−0.619834	−	1.21649i	−0.961015	−	0.276496i	$-0.910827\pi$
$727$	−16.7126	−	32.8002i	−0.619834	−	1.21649i	0.341181	−	0.939998i	$-0.389173\pi$
$728$	−1.61077	+	4.95744i	−0.0596991	+	0.183735i
$729$			15.7081i			0.581782i
$730$	8.64797	+	2.80990i	0.320076	+	0.103999i
$731$	1.60992	−	10.1646i	0.0595449	−	0.375952i
$732$	1.97236	+	12.4530i	0.0729005	+	0.460276i
$733$	−30.1878	+	9.80862i	−1.11501	+	0.362290i	−0.807862	−	0.589371i	$-0.799376\pi$
$733$	−30.1878	+	9.80862i	−1.11501	+	0.362290i	−0.307151	+	0.951661i	$0.599376\pi$
$734$	4.02955	+	12.4017i	0.148734	+	0.457755i
$735$	2.21111	−	2.21111i	0.0815582	−	0.0815582i
$736$	0.704595	−	0.969791i	0.0259717	−	0.0357470i
$737$	7.14265			0.263103
$738$	−2.20973	−	4.94135i	−0.0813412	−	0.181894i
$739$	5.55669			0.204406			0.102203	−	0.994764i	$-0.467411\pi$
$739$	5.55669			0.204406			0.102203	+	0.994764i	$0.467411\pi$
$740$	1.32691	−	1.82633i	0.0487780	−	0.0671372i
$741$	−13.7199	+	13.7199i	−0.504012	+	0.504012i
$742$	0.287228	+	0.883997i	0.0105445	+	0.0324526i
$743$	16.9047	−	5.49267i	0.620173	−	0.201506i	0.0179559	−	0.999839i	$-0.494284\pi$
$743$	16.9047	−	5.49267i	0.620173	−	0.201506i	0.602217	+	0.798332i	$0.294284\pi$
$744$	1.59728	+	10.0848i	0.0585590	+	0.369727i
$745$	1.97182	−	12.4496i	0.0722419	−	0.456117i
$746$	−20.0314	−	6.50860i	−0.733402	−	0.238297i
$747$			12.9956i			0.475484i
$748$	4.98587	−	15.3449i	0.182301	−	0.561066i
$749$	0.129944	+	0.255029i	0.00474805	+	0.00931857i
$750$	20.7769	+	10.5864i	0.758667	+	0.386560i
$751$	5.11600	−	0.810295i	0.186685	−	0.0295681i	−0.0623916	−	0.998052i	$-0.519873\pi$
$751$	5.11600	−	0.810295i	0.186685	−	0.0295681i	0.249077	+	0.968484i	$0.419873\pi$
$752$	4.14017	+	4.14017i	0.150976	+	0.150976i
$753$	10.9700	−	21.5298i	0.399769	−	0.784590i
$754$	−9.23322	+	6.70833i	−0.336254	+	0.244303i
$755$	16.2448	−	8.27714i	0.591209	−	0.301236i
$756$	3.41823	+	2.48349i	0.124320	+	0.0903236i
$757$	−31.1069	−	4.92685i	−1.13060	−	0.179069i	−0.437021	−	0.899451i	$-0.643967\pi$
$757$	−31.1069	−	4.92685i	−1.13060	−	0.179069i	−0.693578	+	0.720382i	$0.743967\pi$
$758$	10.2216	+	14.0688i	0.371264	+	0.511001i
$759$	3.88285	+	5.34429i	0.140939	+	0.193985i
$760$	−2.98967	−	0.473517i	−0.108447	−	0.0171763i
$761$	11.4462	+	8.31612i	0.414923	+	0.301459i	0.775592	−	0.631235i	$-0.217452\pi$
$761$	11.4462	+	8.31612i	0.414923	+	0.301459i	−0.360669	+	0.932694i	$0.617452\pi$
$762$	26.0424	−	13.2692i	0.943415	−	0.480694i
$763$	2.08805	−	1.51706i	0.0755924	−	0.0549211i
$764$	8.06620	−	15.8308i	0.291825	−	0.572739i
$765$	5.47266	+	5.47266i	0.197864	+	0.197864i
$766$	6.70138	−	1.06139i	0.242131	−	0.0383497i
$767$	−36.1408	−	18.4147i	−1.30497	−	0.664915i
$768$	0.890256	+	1.74723i	0.0321244	+	0.0630476i
$769$	2.47729	−	7.62431i	0.0893334	−	0.274940i	−0.896402	−	0.443242i	$-0.853828\pi$
$769$	2.47729	−	7.62431i	0.0893334	−	0.274940i	0.985735	+	0.168302i	$0.0538283\pi$
$770$		−	4.48127i		−	0.161494i
$771$	−44.8858	−	14.5843i	−1.61652	−	0.525240i
$772$	3.78809	−	23.9170i	0.136336	−	0.860793i
$773$	−3.37116	−	21.2846i	−0.121252	−	0.765555i	−0.971126	−	0.238569i	$-0.923322\pi$
$773$	−3.37116	−	21.2846i	−0.121252	−	0.765555i	0.849874	−	0.526987i	$-0.176678\pi$
$774$	−1.44113	+	0.468251i	−0.0518003	+	0.0168309i
$775$	3.95366	+	12.1681i	0.142020	+	0.437091i
$776$	−7.37124	+	7.37124i	−0.264612	+	0.264612i
$777$	−1.63174	+	2.24590i	−0.0585383	+	0.0805711i
$778$	14.6364			0.524739
$779$	9.45834	+	7.63362i	0.338880	+	0.273503i
$780$	−16.2996			−0.583620
$781$	−22.8007	+	31.3824i	−0.815872	+	1.12295i
$782$	4.86654	−	4.86654i	0.174027	−	0.174027i
$783$	2.85871	+	8.79821i	0.102162	+	0.314422i
$784$	0.951057	−	0.309017i	0.0339663	−	0.0110363i
$785$	−0.167493	−	1.05751i	−0.00597810	−	0.0377442i
$786$	−3.20633	+	20.2440i	−0.114366	+	0.722079i
$787$	23.9237	+	7.77327i	0.852786	+	0.277087i	0.702613	−	0.711573i	$-0.252017\pi$
$787$	23.9237	+	7.77327i	0.852786	+	0.277087i	0.150174	+	0.988660i	$0.452017\pi$
$788$			21.3285i			0.759797i
$789$	−2.83657	+	8.73008i	−0.100985	+	0.310799i
$790$	6.96278	+	13.6652i	0.247725	+	0.486187i
$791$	1.01936	+	0.519388i	0.0362441	+	0.0184673i
$792$	−2.34641	+	0.371635i	−0.0833760	+	0.0132055i
$793$	−23.6985	−	23.6985i	−0.841559	−	0.841559i
$794$	−16.2728	+	31.9372i	−0.577501	+	1.13341i
$795$	−2.35141	+	1.70840i	−0.0833959	+	0.0605907i
$796$	−17.5123	+	8.92294i	−0.620705	+	0.316265i
$797$	−42.7358	−	31.0494i	−1.51378	−	1.09983i	−0.964465	−	0.264209i	$-0.914889\pi$
$797$	−42.7358	−	31.0494i	−1.51378	−	1.09983i	−0.549314	−	0.835616i	$-0.685111\pi$
$798$	3.67650	+	0.582300i	0.130147	+	0.0206132i
$799$	19.7591	+	27.1960i	0.699026	+	0.962126i
$800$	1.44430	+	1.98790i	0.0510635	+	0.0702829i
$801$	14.0750	+	2.22926i	0.497316	+	0.0787670i
$802$	−6.88129	−	4.99955i	−0.242987	−	0.176540i
$803$	−14.2782	+	7.27513i	−0.503868	+	0.256734i
$804$	−4.03220	+	2.92956i	−0.142205	+	0.103318i
$805$	0.867811	−	1.70317i	0.0305863	−	0.0600290i
$806$	−19.1918	−	19.1918i	−0.676002	−	0.676002i
$807$	−4.01912	+	0.636566i	−0.141480	+	0.0224082i
$808$	−12.0910	−	6.16067i	−0.425360	−	0.216732i
$809$	−11.1090	−	21.8026i	−0.390571	−	0.766539i	0.609076	−	0.793112i	$-0.291540\pi$
$809$	−11.1090	−	21.8026i	−0.390571	−	0.766539i	−0.999647	+	0.0265732i	$0.991540\pi$
$810$	−5.33243	+	16.4115i	−0.187363	+	0.576643i
$811$		−	21.3417i		−	0.749410i	−0.927144	−	0.374705i	$-0.877744\pi$
$811$		−	21.3417i		−	0.749410i	0.927144	−	0.374705i	$-0.122256\pi$
$812$	2.08234	+	0.676592i	0.0730757	+	0.0237437i
$813$	2.02191	−	12.7659i	0.0709116	−	0.447718i
$814$	0.622357	+	3.92941i	0.0218136	+	0.137726i
$815$	−15.9982	+	5.19814i	−0.560393	+	0.182083i
$816$	3.47909	+	10.7075i	0.121793	+	0.374839i
$817$	2.40595	−	2.40595i	0.0841736	−	0.0841736i
$818$	7.36877	−	10.1422i	0.257643	−	0.354615i
$819$	4.40648			0.153975
$820$	1.08391	+	10.1529i	0.0378519	+	0.354553i
$821$	−29.7498			−1.03827			−0.519137	−	0.854691i	$-0.673747\pi$
$821$	−29.7498			−1.03827			−0.519137	+	0.854691i	$0.673747\pi$
$822$	5.09898	−	7.01814i	0.177847	−	0.244786i
$823$	−7.95191	+	7.95191i	−0.277186	+	0.277186i	−0.831985	−	0.554799i	$-0.812795\pi$
$823$	−7.95191	+	7.95191i	−0.277186	+	0.277186i	0.554799	+	0.831985i	$0.312795\pi$
$824$	3.12368	+	9.61369i	0.108818	+	0.334909i
$825$	−12.8782	+	4.18438i	−0.448362	+	0.145682i
$826$	1.21730	+	7.68575i	0.0423554	+	0.267421i
$827$	6.91323	−	43.6484i	0.240397	−	1.51780i	−0.511937	−	0.859023i	$-0.671072\pi$
$827$	6.91323	−	43.6484i	0.240397	−	1.51780i	0.752334	−	0.658782i	$-0.228928\pi$
$828$	−0.963757	−	0.313144i	−0.0334929	−	0.0108825i
$829$		−	2.66311i		−	0.0924935i	−0.998930	−	0.0462468i	$-0.985274\pi$
$829$		−	2.66311i		−	0.0924935i	0.998930	−	0.0462468i	$-0.0147261\pi$
$830$	7.57523	−	23.3142i	0.262940	−	0.809247i
$831$	−11.7794	−	23.1184i	−0.408623	−	0.801967i
$832$	−4.64443	−	2.36645i	−0.161016	−	0.0820420i
$833$	5.67068	−	0.898147i	0.196477	−	0.0311190i
$834$	−8.70572	−	8.70572i	−0.301454	−	0.301454i
$835$	−7.29253	+	14.3124i	−0.252368	+	0.495301i
$836$	4.31566	−	3.13551i	0.149260	−	0.108444i
$837$	−19.6021	+	9.98779i	−0.677549	+	0.345229i
$838$	−7.60939	−	5.52855i	−0.262862	−	0.190981i
$839$	34.2982	+	5.43230i	1.18410	+	0.187544i	0.717266	−	0.696799i	$-0.245393\pi$
$839$	34.2982	+	5.43230i	1.18410	+	0.187544i	0.466838	+	0.884343i	$0.345393\pi$
$840$	1.83800	+	2.52979i	0.0634169	+	0.0872859i
$841$	−14.2280	−	19.5831i	−0.490620	−	0.675281i
$842$	−12.2629	−	1.94225i	−0.422607	−	0.0669344i
$843$	40.5849	+	29.4867i	1.39782	+	1.01558i
$844$	−9.70556	+	4.94523i	−0.334079	+	0.170222i
$845$	18.2814	−	13.2822i	0.628899	−	0.456922i
$846$	2.24709	−	4.41016i	0.0772565	−	0.151624i
$847$	−2.19383	−	2.19383i	−0.0753810	−	0.0753810i
$848$	−0.918046	+	0.145404i	−0.0315258	+	0.00499320i
$849$	−23.6737	−	12.0623i	−0.812478	−	0.413978i
$850$	6.40470	+	12.5699i	0.219680	+	0.431145i
$851$	−0.524405	+	1.61395i	−0.0179764	+	0.0553256i
$852$		−	27.0679i		−	0.927329i
$853$	−28.1564	−	9.14857i	−0.964057	−	0.313241i	−0.215642	−	0.976472i	$-0.569185\pi$
$853$	−28.1564	−	9.14857i	−0.964057	−	0.313241i	−0.748414	+	0.663231i	$0.769185\pi$
$854$	−1.00581	+	6.35046i	−0.0344182	+	0.217308i
$855$	0.400292	+	2.52734i	0.0136897	+	0.0864332i
$856$	−0.272217	+	0.0884488i	−0.00930420	+	0.00302312i
$857$	−15.7564	−	48.4933i	−0.538229	−	1.65650i	−0.736566	−	0.676366i	$-0.763554\pi$
$857$	−15.7564	−	48.4933i	−0.538229	−	1.65650i	0.198337	−	0.980134i	$-0.436446\pi$
$858$	20.3118	−	20.3118i	0.693433	−	0.693433i
$859$	0.621635	−	0.855607i	0.0212099	−	0.0291929i	−0.798280	−	0.602286i	$-0.794257\pi$
$859$	0.621635	−	0.855607i	0.0212099	−	0.0291929i	0.819490	+	0.573093i	$0.194257\pi$
$860$	2.85834			0.0974686
$861$	−1.33292	−	12.4853i	−0.0454259	−	0.425498i
$862$	21.6280			0.736654
$863$	−21.9103	+	30.1569i	−0.745834	+	1.02655i	0.252428	+	0.967616i	$0.418771\pi$
$863$	−21.9103	+	30.1569i	−0.745834	+	1.02655i	−0.998262	+	0.0589364i	$0.981229\pi$
$864$	−2.98764	+	2.98764i	−0.101642	+	0.101642i
$865$	−5.92359	−	18.2309i	−0.201408	−	0.619871i
$866$	−28.6051	+	9.29438i	−0.972043	+	0.315836i
$867$	4.89691	+	30.9179i	0.166308	+	1.05003i
$868$	−0.814539	+	5.14279i	−0.0276472	+	0.174558i
$869$	−25.7056	−	8.35226i	−0.872004	−	0.283331i
$870$			6.84653i			0.232119i
$871$	4.09402	−	12.6001i	0.138720	−	0.426938i
$872$	1.17174	+	2.29966i	0.0396800	+	0.0778764i
$873$	7.85194	+	4.00077i	0.265748	+	0.135405i
$874$	2.24743	−	0.355958i	0.0760205	−	0.0120405i
$875$	8.40848	+	8.40848i	0.284258	+	0.284258i
$876$	5.07651	−	9.96321i	0.171519	−	0.336626i
$877$	41.7537	−	30.3359i	1.40992	−	1.02437i	0.416590	−	0.909094i	$-0.363225\pi$
$877$	41.7537	−	30.3359i	1.40992	−	1.02437i	0.993334	−	0.115275i	$-0.0367750\pi$
$878$	−29.1685	+	14.8621i	−0.984390	+	0.501572i
$879$	−36.9995	−	26.8817i	−1.24796	−	0.906699i
$880$	4.42610	+	0.701025i	0.149204	+	0.0236316i
$881$	10.1794	+	14.0108i	0.342954	+	0.472035i	0.945301	−	0.326199i	$-0.105768\pi$
$881$	10.1794	+	14.0108i	0.342954	+	0.472035i	−0.602347	+	0.798234i	$0.705768\pi$
$882$	−0.496889	−	0.683909i	−0.0167311	−	0.0230284i
$883$	22.8221	+	3.61466i	0.768024	+	0.121643i	0.528138	−	0.849158i	$-0.322890\pi$
$883$	22.8221	+	3.61466i	0.768024	+	0.121643i	0.239885	+	0.970801i	$0.422890\pi$
$884$	−24.2116	−	17.5908i	−0.814325	−	0.591642i
$885$	−21.6807	+	11.0469i	−0.728788	+	0.371336i
$886$	−5.04932	+	3.66855i	−0.169635	+	0.123247i
$887$	−1.59912	+	3.13844i	−0.0536930	+	0.105379i	−0.916294	−	0.400507i	$-0.868834\pi$
$887$	−1.59912	+	3.13844i	−0.0536930	+	0.105379i	0.862601	+	0.505885i	$0.168834\pi$
$888$	−1.96299	−	1.96299i	−0.0658735	−	0.0658735i
$889$	14.7215	−	2.33165i	0.493742	−	0.0782011i
$890$	−23.9512	−	12.2037i	−0.802845	−	0.409070i
$891$	−13.8062	−	27.0963i	−0.462526	−	0.907759i
$892$	7.50632	−	23.1021i	0.251330	−	0.773515i
$893$			11.1142i			0.371923i
$894$	−14.7418	−	4.78992i	−0.493041	−	0.160199i
$895$	−0.0683183	+	0.431345i	−0.00228363	+	0.0144183i
$896$	0.156434	+	0.987688i	0.00522611	+	0.0329964i
$897$	11.6532	−	3.78636i	0.389090	−	0.126423i
$898$	−1.27325	−	3.91867i	−0.0424890	−	0.130768i
$899$	−8.06137	+	8.06137i	−0.268862	+	0.268862i
$900$	1.22095	−	1.68049i	0.0406982	−	0.0560163i
$901$	−5.33654			−0.177786
$902$	−14.0027	−	11.3013i	−0.466240	−	0.376292i
$903$	−3.51499			−0.116972
$904$	−0.672456	+	0.925556i	−0.0223656	+	0.0307835i
$905$	4.31646	−	4.31646i	0.143484	−	0.143484i
$906$	−6.92830	−	21.3231i	−0.230177	−	0.708413i
$907$	−46.0328	+	14.9570i	−1.52850	+	0.496638i	−0.948175	−	0.317750i	$-0.897073\pi$
$907$	−46.0328	+	14.9570i	−1.52850	+	0.496638i	−0.580321	+	0.814388i	$0.697073\pi$
$908$	3.00676	+	18.9839i	0.0997827	+	0.630003i
$909$	−1.79454	+	11.3303i	−0.0595213	+	0.375803i
$910$	−7.90524	−	2.56857i	−0.262056	−	0.0851472i
$911$		−	24.7234i		−	0.819123i	−0.912283	−	0.409561i	$-0.865682\pi$
$911$		−	24.7234i		−	0.819123i	0.912283	−	0.409561i	$-0.134318\pi$
$912$	−1.15026	+	3.54014i	−0.0380890	+	0.117226i
$913$	19.6131	+	38.4929i	0.649099	+	1.27393i
$914$	0.879730	+	0.448245i	0.0290989	+	0.0148266i
$915$	−19.8578	+	3.14517i	−0.656479	+	0.103976i
$916$	5.74633	+	5.74633i	0.189864	+	0.189864i
$917$	−4.74520	+	9.31297i	−0.156700	+	0.307541i
$918$	−19.6253	+	14.2586i	−0.647731	+	0.470604i
$919$	−24.8092	+	12.6409i	−0.818380	+	0.416986i	−0.812474	−	0.582997i	$-0.801880\pi$
$919$	−24.8092	+	12.6409i	−0.818380	+	0.416986i	−0.00590607	+	0.999983i	$0.501880\pi$
$920$	1.54645	+	1.12356i	0.0509850	+	0.0370427i
$921$	57.2925	+	9.07424i	1.88785	+	0.299006i
$922$	7.48400	+	10.3008i	0.246472	+	0.339240i
$923$	42.2917	+	58.2095i	1.39205	+	1.91599i
$924$	−5.44292	−	0.862073i	−0.179059	−	0.0283601i
$925$	−2.81422	−	2.04465i	−0.0925311	−	0.0672278i
$926$	−10.9463	+	5.57744i	−0.359719	+	0.183286i
$927$	6.91325	−	5.02277i	0.227061	−	0.164969i
$928$	−0.994011	+	1.95086i	−0.0326300	+	0.0640400i
$929$	5.31690	+	5.31690i	0.174442	+	0.174442i	0.788928	−	0.614486i	$-0.210637\pi$
$929$	5.31690	+	5.31690i	0.174442	+	0.174442i	−0.614486	+	0.788928i	$0.710637\pi$
$930$	−16.0815	+	2.54705i	−0.527332	+	0.0835211i
$931$	1.69132	+	0.861772i	0.0554309	+	0.0282435i
$932$	−7.91275	−	15.5297i	−0.259191	−	0.508691i
$933$	−0.718151	+	2.21024i	−0.0235112	+	0.0723601i
$934$			29.5966i			0.968430i
$935$	24.4694	+	7.95058i	0.800233	+	0.260012i
$936$	−0.689325	+	4.35223i	−0.0225313	+	0.142257i
$937$	−4.62956	−	29.2299i	−0.151241	−	0.954899i	−0.940242	−	0.340507i	$-0.889401\pi$
$937$	−4.62956	−	29.2299i	−0.151241	−	0.954899i	0.789001	−	0.614392i	$-0.210599\pi$
$938$	−2.41725	+	0.785414i	−0.0789262	+	0.0256447i
$939$	12.8807	+	39.6427i	0.420346	+	1.29369i
$940$	−6.60200	+	6.60200i	−0.215333	+	0.215333i
$941$	−14.1980	+	19.5419i	−0.462841	+	0.637046i	−0.975095	−	0.221788i	$-0.928811\pi$
$941$	−14.1980	+	19.5419i	−0.462841	+	0.637046i	0.512254	+	0.858834i	$0.328811\pi$
$942$	−1.31667			−0.0428993
$943$	−3.13342	−	7.00689i	−0.102038	−	0.228176i
$944$	−7.78155			−0.253268
$945$	−3.96023	+	5.45078i	−0.128826	+	0.177314i
$946$	−3.56192	+	3.56192i	−0.115808	+	0.115808i
$947$	−10.9041	−	33.5594i	−0.354336	−	1.09053i	−0.956394	−	0.292081i	$-0.905652\pi$
$947$	−10.9041	−	33.5594i	−0.354336	−	1.09053i	0.602058	−	0.798453i	$-0.294348\pi$
$948$	17.9371	−	5.82813i	0.582571	−	0.189289i
$949$	4.64979	+	29.3576i	0.150939	+	0.952990i
$950$	−0.729652	+	4.60684i	−0.0236730	+	0.149466i
$951$	34.3295	+	11.1543i	1.11321	+	0.361704i
$952$			5.74136i			0.186079i
$953$	14.2246	−	43.7787i	0.460779	−	1.41813i	−0.403436	−	0.915008i	$-0.632184\pi$
$953$	14.2246	−	43.7787i	0.460779	−	1.41813i	0.864215	−	0.503123i	$-0.167816\pi$
$954$	0.356724	+	0.700109i	0.0115494	+	0.0226669i
$955$	25.2442	+	12.8625i	0.816882	+	0.416222i
$956$	11.2018	−	1.77418i	0.362291	−	0.0573812i
$957$	−8.53181	−	8.53181i	−0.275794	−	0.275794i
$958$	18.8635	−	37.0216i	0.609451	−	1.19611i
$959$	3.57893	−	2.60025i	0.115570	−	0.0839664i
$960$	−2.78617	+	1.41962i	−0.0899231	+	0.0458181i
$961$	3.14561	+	2.28542i	0.101471	+	0.0737233i
$962$	7.28844	+	1.15438i	0.234989	+	0.0372186i
$963$	0.142223	+	0.195753i	0.00458306	+	0.00630804i
$964$	10.4987	+	14.4502i	0.338140	+	0.465410i
$965$	38.1386	+	6.04057i	1.22773	+	0.194453i
$966$	−1.90172	−	1.38168i	−0.0611868	−	0.0444548i
$967$	−46.1849	+	23.5324i	−1.48521	+	0.756750i	−0.993481	−	0.114000i	$-0.963634\pi$
$967$	−46.1849	+	23.5324i	−1.48521	+	0.756750i	−0.491726	+	0.870750i	$0.663634\pi$
$968$	2.51002	−	1.82363i	0.0806749	−	0.0586138i
$969$	−9.70233	+	19.0419i	−0.311684	+	0.611714i
$970$	−11.7543	−	11.7543i	−0.377409	−	0.377409i
$971$	44.2535	−	7.00907i	1.42016	−	0.224932i	0.601347	−	0.798988i	$-0.294631\pi$
$971$	44.2535	−	7.00907i	1.42016	−	0.224932i	0.818816	+	0.574056i	$0.194631\pi$
$972$	7.61357	+	3.87931i	0.244205	+	0.124429i
$973$	−2.85035	−	5.59412i	−0.0913780	−	0.179339i
$974$	7.86428	−	24.2038i	0.251988	−	0.775539i
$975$			25.1164i			0.804367i
$976$	−6.11493	−	1.98686i	−0.195734	−	0.0635979i
$977$	−5.83301	+	36.8282i	−0.186615	+	1.17824i	0.699452	+	0.714680i	$0.253427\pi$
$977$	−5.83301	+	36.8282i	−0.186615	+	1.17824i	−0.886067	+	0.463558i	$0.846573\pi$
$978$	3.23600	+	20.4313i	0.103476	+	0.653321i
$979$	45.0545	−	14.6391i	1.43995	−	0.467867i
$980$	0.492765	+	1.51658i	0.0157408	+	0.0484452i
$981$	1.54280	−	1.54280i	0.0492577	−	0.0492577i
$982$	−17.0537	+	23.4724i	−0.544205	+	0.749033i
$983$	7.32017			0.233477			0.116739	−	0.993163i	$-0.462756\pi$
$983$	7.32017			0.233477			0.116739	+	0.993163i	$0.462756\pi$
$984$	12.5401	+	0.636621i	0.399764	+	0.0202947i
$985$	−34.0109			−1.08368
$986$	−7.38887	+	10.1699i	−0.235310	+	0.323876i
$987$	8.11869	−	8.11869i	0.258421	−	0.258421i
$988$	−3.05759	−	9.41030i	−0.0972749	−	0.299381i
$989$	−2.04354	+	0.663986i	−0.0649808	+	0.0211135i
$990$	−0.592617	−	3.74164i	−0.0188346	−	0.118917i
$991$	−3.55909	+	22.4712i	−0.113058	+	0.713822i	0.864418	+	0.502775i	$0.167687\pi$
$991$	−3.55909	+	22.4712i	−0.113058	+	0.713822i	−0.977476	+	0.211047i	$0.932313\pi$
$992$	−4.95206	−	1.60902i	−0.157228	−	0.0510865i
$993$		−	69.8461i		−	2.21650i
$994$	4.26548	−	13.1278i	0.135293	−	0.416388i
$995$	−14.2287	−	27.9254i	−0.451080	−	0.885295i
$996$	−26.8599	−	13.6858i	−0.851090	−	0.433652i
$997$	2.25040	−	0.356428i	0.0712708	−	0.0112882i	−0.120697	−	0.992689i	$-0.538513\pi$
$997$	2.25040	−	0.356428i	0.0712708	−	0.0112882i	0.191968	+	0.981401i	$0.438513\pi$
$998$	−0.331023	−	0.331023i	−0.0104784	−	0.0104784i
$999$	2.71553	−	5.32952i	0.0859154	−	0.168619i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.u.a.197.2	yes	80
41.5	even	20	inner	574.2.u.a.169.2	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.u.a.169.2	✓	80	41.5	even	20	inner
574.2.u.a.197.2	yes	80	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-1.38661 + 1.38661i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.51658 - 0.492765i) q^{5} +(-0.306761 - 1.93682i) q^{6} +(0.156434 - 0.987688i) q^{7} +(0.951057 + 0.309017i) q^{8} -0.845358i q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-1.38661 + 1.38661i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.51658 - 0.492765i) q^{5} +(-0.306761 - 1.93682i) q^{6} +(0.156434 - 0.987688i) q^{7} +(0.951057 + 0.309017i) q^{8} -0.845358i q^{9} +(-0.492765 + 1.51658i) q^{10} +(-1.27582 - 2.50394i) q^{11} +(1.74723 + 0.890256i) q^{12} +(-5.14839 + 0.815424i) q^{13} +(0.707107 + 0.707107i) q^{14} +(-1.41962 + 2.78617i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-5.11559 + 2.60652i) q^{17} +(0.683909 + 0.496889i) q^{18} +(-1.87485 - 0.296947i) q^{19} +(-0.937295 - 1.29008i) q^{20} +(1.15262 + 1.58645i) q^{21} +(2.77564 + 0.439618i) q^{22} +(0.969791 + 0.704595i) q^{23} +(-1.74723 + 0.890256i) q^{24} +(-1.98790 + 1.44430i) q^{25} +(2.36645 - 4.64443i) q^{26} +(-2.98764 - 2.98764i) q^{27} +(-0.987688 + 0.156434i) q^{28} +(-1.95086 - 0.994011i) q^{29} +(-1.41962 - 2.78617i) q^{30} +(1.60902 - 4.95206i) q^{31} -1.00000i q^{32} +(5.24105 + 1.70292i) q^{33} +(0.898147 - 5.67068i) q^{34} +(-0.249454 - 1.57499i) q^{35} +(-0.803983 + 0.261230i) q^{36} +(0.437468 + 1.34639i) q^{37} +(1.34224 - 1.34224i) q^{38} +(6.00811 - 8.26946i) q^{39} +1.59462 q^{40} +(-5.55050 - 3.19248i) q^{41} -1.96096 q^{42} +(-1.05360 + 1.45015i) q^{43} +(-1.98714 + 1.98714i) q^{44} +(-0.416563 - 1.28205i) q^{45} +(-1.14006 + 0.370427i) q^{46} +(-0.915936 - 5.78299i) q^{47} +(0.306761 - 1.93682i) q^{48} +(-0.951057 - 0.309017i) q^{49} -2.45718i q^{50} +(3.47909 - 10.7075i) q^{51} +(2.36645 + 4.64443i) q^{52} +(0.828181 + 0.421979i) q^{53} +(4.17315 - 0.660961i) q^{54} +(-3.16874 - 3.16874i) q^{55} +(0.453990 - 0.891007i) q^{56} +(3.01142 - 2.18793i) q^{57} +(1.95086 - 0.994011i) q^{58} +(6.29541 + 4.57388i) q^{59} +(3.08849 + 0.489169i) q^{60} +(3.77924 + 5.20167i) q^{61} +(3.06054 + 4.21247i) q^{62} +(-0.834950 - 0.132243i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-7.40610 + 3.77360i) q^{65} +(-4.45830 + 3.23915i) q^{66} +(-1.15389 + 2.26463i) q^{67} +(4.05976 + 4.05976i) q^{68} +(-2.32171 + 0.367724i) q^{69} +(1.42082 + 0.723943i) q^{70} +(-6.26660 - 12.2989i) q^{71} +(0.261230 - 0.803983i) q^{72} -5.70230i q^{73} +(-1.34639 - 0.437468i) q^{74} +(0.753769 - 4.75911i) q^{75} +(0.296947 + 1.87485i) q^{76} +(-2.67270 + 0.868412i) q^{77} +(3.15865 + 9.72133i) q^{78} +(6.80085 - 6.80085i) q^{79} +(-0.937295 + 1.29008i) q^{80} +10.8214 q^{81} +(5.84527 - 2.61396i) q^{82} -15.3729 q^{83} +(1.15262 - 1.58645i) q^{84} +(-6.47378 + 6.47378i) q^{85} +(-0.553909 - 1.70476i) q^{86} +(4.08337 - 1.32677i) q^{87} +(-0.439618 - 2.77564i) q^{88} +(-2.63706 + 16.6498i) q^{89} +(1.28205 + 0.416563i) q^{90} +5.21256i q^{91} +(0.370427 - 1.14006i) q^{92} +(4.63548 + 9.09763i) q^{93} +(5.21691 + 2.65815i) q^{94} +(-2.98967 + 0.473517i) q^{95} +(1.38661 + 1.38661i) q^{96} +(-4.73263 + 9.28831i) q^{97} +(0.809017 - 0.587785i) q^{98} +(-2.11673 + 1.07853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 20 q^{4} + 16 q^{6}+O(q^{10}) \) 80 * q + 4 * q^3 + 20 * q^4 + 16 * q^6	\( 80 q + 4 q^{3} + 20 q^{4} + 16 q^{6} - 16 q^{11} - 4 q^{12} + 20 q^{13} + 36 q^{15} - 20 q^{16} + 4 q^{17} + 20 q^{18} + 28 q^{19} - 20 q^{20} + 16 q^{22} - 8 q^{23} + 4 q^{24} + 20 q^{25} + 16 q^{27} - 12 q^{29} + 36 q^{30} - 12 q^{31} + 4 q^{34} - 20 q^{36} + 12 q^{37} - 32 q^{38} - 80 q^{39} - 8 q^{41} + 16 q^{44} - 108 q^{45} - 20 q^{46} + 8 q^{47} - 16 q^{48} - 20 q^{51} - 40 q^{53} + 16 q^{54} + 60 q^{55} + 52 q^{57} + 12 q^{58} - 12 q^{59} + 24 q^{60} + 100 q^{61} - 16 q^{63} + 20 q^{64} - 20 q^{65} - 36 q^{67} + 36 q^{68} - 32 q^{69} - 12 q^{71} - 20 q^{72} + 20 q^{74} + 40 q^{75} + 12 q^{76} + 40 q^{77} + 16 q^{78} + 16 q^{79} - 20 q^{80} - 104 q^{81} - 12 q^{82} - 16 q^{85} + 12 q^{86} + 140 q^{87} + 24 q^{88} - 32 q^{89} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} + 4 q^{97} + 20 q^{98} - 72 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + 20 * q^4 + 16 * q^6 - 16 * q^11 - 4 * q^12 + 20 * q^13 + 36 * q^15 - 20 * q^16 + 4 * q^17 + 20 * q^18 + 28 * q^19 - 20 * q^20 + 16 * q^22 - 8 * q^23 + 4 * q^24 + 20 * q^25 + 16 * q^27 - 12 * q^29 + 36 * q^30 - 12 * q^31 + 4 * q^34 - 20 * q^36 + 12 * q^37 - 32 * q^38 - 80 * q^39 - 8 * q^41 + 16 * q^44 - 108 * q^45 - 20 * q^46 + 8 * q^47 - 16 * q^48 - 20 * q^51 - 40 * q^53 + 16 * q^54 + 60 * q^55 + 52 * q^57 + 12 * q^58 - 12 * q^59 + 24 * q^60 + 100 * q^61 - 16 * q^63 + 20 * q^64 - 20 * q^65 - 36 * q^67 + 36 * q^68 - 32 * q^69 - 12 * q^71 - 20 * q^72 + 20 * q^74 + 40 * q^75 + 12 * q^76 + 40 * q^77 + 16 * q^78 + 16 * q^79 - 20 * q^80 - 104 * q^81 - 12 * q^82 - 16 * q^85 + 12 * q^86 + 140 * q^87 + 24 * q^88 - 32 * q^89 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 + 4 * q^97 + 20 * q^98 - 72 * q^99

Introduction

L-functions

Modular forms

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