LMFDB - Embedded newform 804.2.bd.a.35.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(23,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 33, 28]))

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

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

chi := DirichletCharacter("804.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.bd (of order $66$, degree $20$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$2640$
Relative dimension:	$132$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			35.17
Character	$\chi$	$=$	804.35
Dual form			804.2.bd.a.23.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30218 - 0.551664i) q^{2} +(-0.881313 + 1.49107i) q^{3} +(1.39133 + 1.43673i) q^{4} +(-1.21127 - 0.553168i) q^{5} +(1.97020 - 1.45545i) q^{6} +(1.08361 - 1.13646i) q^{7} +(-1.01917 - 2.63843i) q^{8} +(-1.44658 - 2.62820i) q^{9} +O(q^{10})$	\(q+(-1.30218 - 0.551664i) q^{2} +(-0.881313 + 1.49107i) q^{3} +(1.39133 + 1.43673i) q^{4} +(-1.21127 - 0.553168i) q^{5} +(1.97020 - 1.45545i) q^{6} +(1.08361 - 1.13646i) q^{7} +(-1.01917 - 2.63843i) q^{8} +(-1.44658 - 2.62820i) q^{9} +(1.27212 + 1.38854i) q^{10} +(-1.25029 + 0.119389i) q^{11} +(-3.36846 + 0.808366i) q^{12} +(-0.394523 + 0.0760380i) q^{13} +(-2.03800 + 0.882082i) q^{14} +(1.89232 - 1.31857i) q^{15} +(-0.128386 + 3.99794i) q^{16} +(0.992017 + 1.92424i) q^{17} +(0.433817 + 4.22040i) q^{18} +(5.54672 + 5.81724i) q^{19} +(-0.890526 - 2.50991i) q^{20} +(0.739539 + 2.61732i) q^{21} +(1.69397 + 0.534278i) q^{22} +(1.10694 + 0.443150i) q^{23} +(4.83228 + 0.805626i) q^{24} +(-2.11312 - 2.43868i) q^{25} +(0.555686 + 0.118629i) q^{26} +(5.19371 + 0.159317i) q^{27} +(3.14045 - 0.0243355i) q^{28} +(-6.34401 + 3.66271i) q^{29} +(-3.19155 + 0.673091i) q^{30} +(0.0714776 - 0.370861i) q^{31} +(2.37270 - 5.13520i) q^{32} +(0.923883 - 1.96949i) q^{33} +(-0.230245 - 3.05297i) q^{34} +(-1.94120 + 0.777139i) q^{35} +(1.76334 - 5.73504i) q^{36} +(-0.164311 + 0.284595i) q^{37} +(-4.01366 - 10.6350i) q^{38} +(0.234320 - 0.655274i) q^{39} +(-0.225005 + 3.75962i) q^{40} +(-10.5865 - 0.504295i) q^{41} +(0.480869 - 3.81619i) q^{42} +(-4.52097 + 7.03477i) q^{43} +(-1.91110 - 1.63023i) q^{44} +(0.298359 + 3.98366i) q^{45} +(-1.19696 - 1.18772i) q^{46} +(0.246085 - 0.193523i) q^{47} +(-5.84806 - 3.71487i) q^{48} +(0.215748 + 4.52911i) q^{49} +(1.40633 + 4.34132i) q^{50} +(-3.74346 - 0.216695i) q^{51} +(-0.658159 - 0.461029i) q^{52} +(3.76196 + 5.85372i) q^{53} +(-6.67524 - 3.07264i) q^{54} +(1.58049 + 0.547011i) q^{55} +(-4.10285 - 1.70079i) q^{56} +(-13.5623 + 3.14375i) q^{57} +(10.2816 - 1.26974i) q^{58} +(-2.90403 + 3.35143i) q^{59} +(4.52728 + 0.884179i) q^{60} +(-7.52455 - 0.718507i) q^{61} +(-0.297667 + 0.443495i) q^{62} +(-4.55437 - 1.20397i) q^{63} +(-5.92259 + 5.37801i) q^{64} +(0.519935 + 0.126135i) q^{65} +(-2.28956 + 2.05496i) q^{66} +(-2.25814 - 7.86770i) q^{67} +(-1.38439 + 4.10252i) q^{68} +(-1.63632 + 1.25996i) q^{69} +(2.95651 + 0.0589177i) q^{70} +(-1.69621 - 0.874459i) q^{71} +(-5.46000 + 6.49526i) q^{72} +(-0.924416 - 0.0882711i) q^{73} +(0.370964 - 0.279949i) q^{74} +(5.49856 - 1.00158i) q^{75} +(-0.640460 + 16.0629i) q^{76} +(-1.21915 + 1.55028i) q^{77} +(-0.666618 + 0.724017i) q^{78} +(0.351000 + 0.121482i) q^{79} +(2.36704 - 4.77156i) q^{80} +(-4.81483 + 7.60377i) q^{81} +(13.5072 + 6.49685i) q^{82} +(4.69899 + 6.59880i) q^{83} +(-2.73143 + 4.70408i) q^{84} +(-0.137169 - 2.87953i) q^{85} +(9.76793 - 6.66646i) q^{86} +(0.129692 - 12.6873i) q^{87} +(1.58926 + 3.17713i) q^{88} +(-3.01184 - 0.433038i) q^{89} +(1.80912 - 5.35202i) q^{90} +(-0.341096 + 0.530755i) q^{91} +(0.903429 + 2.20694i) q^{92} +(0.489985 + 0.433422i) q^{93} +(-0.427206 + 0.116245i) q^{94} +(-3.50067 - 10.1145i) q^{95} +(5.56585 + 8.06358i) q^{96} +(-4.97724 + 8.62084i) q^{97} +(2.21761 - 6.01672i) q^{98} +(2.12242 + 3.11331i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9}+O(q^{10}) $ 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9	$ 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9} - 46 q^{10} - 24 q^{12} - 88 q^{13} - 26 q^{16} - 23 q^{18} - 128 q^{22} - 22 q^{24} + 160 q^{25} + 44 q^{28} - 18 q^{30} - 44 q^{33} - 6 q^{34} - 35 q^{36} - 48 q^{37} - 92 q^{40} - 10 q^{42} + 40 q^{45} + 46 q^{46} - 11 q^{48} - 216 q^{49} - 76 q^{52} + 129 q^{54} - 42 q^{57} - 56 q^{58} - 90 q^{60} - 80 q^{61} - 48 q^{64} - 74 q^{66} - 4 q^{69} + 96 q^{70} - 20 q^{72} - 216 q^{73} + 76 q^{76} - 66 q^{78} - 16 q^{81} + 20 q^{82} - 55 q^{84} - 104 q^{85} - 30 q^{88} - 64 q^{90} - 192 q^{93} - 32 q^{94} - 205 q^{96} - 64 q^{97}+O(q^{100}) $ 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9 - 46 * q^10 - 24 * q^12 - 88 * q^13 - 26 * q^16 - 23 * q^18 - 128 * q^22 - 22 * q^24 + 160 * q^25 + 44 * q^28 - 18 * q^30 - 44 * q^33 - 6 * q^34 - 35 * q^36 - 48 * q^37 - 92 * q^40 - 10 * q^42 + 40 * q^45 + 46 * q^46 - 11 * q^48 - 216 * q^49 - 76 * q^52 + 129 * q^54 - 42 * q^57 - 56 * q^58 - 90 * q^60 - 80 * q^61 - 48 * q^64 - 74 * q^66 - 4 * q^69 + 96 * q^70 - 20 * q^72 - 216 * q^73 + 76 * q^76 - 66 * q^78 - 16 * q^81 + 20 * q^82 - 55 * q^84 - 104 * q^85 - 30 * q^88 - 64 * q^90 - 192 * q^93 - 32 * q^94 - 205 * q^96 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{19}{33}\right)$	$-1$

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 $

$2$	−1.30218	−	0.551664i	−0.920779	−	0.390086i
$2$	−1.30218	−	0.551664i	−0.920779	−	0.390086i
$3$	−0.881313	+	1.49107i	−0.508826	+	0.860869i
$3$	−0.881313	+	1.49107i	−0.508826	+	0.860869i
$4$	1.39133	+	1.43673i	0.695666	+	0.718365i
$5$	−1.21127	−	0.553168i	−0.541696	−	0.247384i	0.125725	−	0.992065i	$-0.459874\pi$
$5$	−1.21127	−	0.553168i	−0.541696	−	0.247384i	−0.667421	+	0.744681i	$0.732602\pi$
$6$	1.97020	−	1.45545i	0.804329	−	0.594184i
$7$	1.08361	−	1.13646i	0.409567	−	0.429541i	−0.486349	−	0.873764i	$-0.661672\pi$
$7$	1.08361	−	1.13646i	0.409567	−	0.429541i	0.895916	+	0.444223i	$0.146520\pi$
$8$	−1.01917	−	2.63843i	−0.360331	−	0.932825i
$9$	−1.44658	−	2.62820i	−0.482192	−	0.876065i
$10$	1.27212	+	1.38854i	0.402281	+	0.439094i
$11$	−1.25029	+	0.119389i	−0.376978	+	0.0359970i	−0.281825	−	0.959466i	$-0.590940\pi$
$11$	−1.25029	+	0.119389i	−0.376978	+	0.0359970i	−0.0951524	+	0.995463i	$0.530334\pi$
$12$	−3.36846	+	0.808366i	−0.972392	+	0.233355i
$13$	−0.394523	+	0.0760380i	−0.109421	+	0.0210892i	−0.243668	−	0.969859i	$-0.578351\pi$
$13$	−0.394523	+	0.0760380i	−0.109421	+	0.0210892i	0.134247	+	0.990948i	$0.457139\pi$
$14$	−2.03800	+	0.882082i	−0.544678	+	0.235746i
$15$	1.89232	−	1.31857i	0.488595	−	0.340454i
$16$	−0.128386	+	3.99794i	−0.0320966	+	0.999485i
$17$	0.992017	+	1.92424i	0.240599	+	0.466698i	0.977957	−	0.208804i	$-0.0669572\pi$
$17$	0.992017	+	1.92424i	0.240599	+	0.466698i	−0.737358	+	0.675502i	$0.763927\pi$
$18$	0.433817	+	4.22040i	0.102252	+	0.994759i
$19$	5.54672	+	5.81724i	1.27251	+	1.33457i	0.916475	+	0.400091i	$0.131022\pi$
$19$	5.54672	+	5.81724i	1.27251	+	1.33457i	0.356030	+	0.934474i	$0.384130\pi$
$20$	−0.890526	−	2.50991i	−0.199128	−	0.561233i
$21$	0.739539	+	2.61732i	0.161381	+	0.571145i
$22$	1.69397	+	0.534278i	0.361155	+	0.113908i
$23$	1.10694	+	0.443150i	0.230812	+	0.0924032i	0.484186	−	0.874965i	$-0.339116\pi$
$23$	1.10694	+	0.443150i	0.230812	+	0.0924032i	−0.253374	+	0.967369i	$0.581540\pi$
$24$	4.83228	+	0.805626i	0.986386	+	0.164448i
$25$	−2.11312	−	2.43868i	−0.422625	−	0.487735i
$26$	0.555686	+	0.118629i	0.108979	+	0.0232651i
$27$	5.19371	+	0.159317i	0.999530	+	0.0306605i
$28$	3.14045	−	0.0243355i	0.593489	−	0.00459898i
$29$	−6.34401	+	3.66271i	−1.17805	+	0.680149i	−0.955563	−	0.294786i	$-0.904751\pi$
$29$	−6.34401	+	3.66271i	−1.17805	+	0.680149i	−0.222489	+	0.974935i	$0.571418\pi$
$30$	−3.19155	+	0.673091i	−0.582694	+	0.122889i
$31$	0.0714776	−	0.370861i	0.0128378	−	0.0666086i	−0.974945	−	0.222447i	$-0.928596\pi$
$31$	0.0714776	−	0.370861i	0.0128378	−	0.0666086i	0.987783	+	0.155838i	$0.0498078\pi$
$32$	2.37270	−	5.13520i	0.419439	−	0.907784i
$33$	0.923883	−	1.96949i	0.160827	−	0.342845i
$34$	−0.230245	−	3.05297i	−0.0394867	−	0.523580i
$35$	−1.94120	+	0.777139i	−0.328123	+	0.131360i
$36$	1.76334	−	5.73504i	0.293890	−	0.955839i
$37$	−0.164311	+	0.284595i	−0.0270126	+	0.0467872i	−0.879216	−	0.476424i	$-0.841933\pi$
$37$	−0.164311	+	0.284595i	−0.0270126	+	0.0467872i	0.852203	+	0.523211i	$0.175266\pi$
$38$	−4.01366	−	10.6350i	−0.651101	−	1.72523i
$39$	0.234320	−	0.655274i	0.0375212	−	0.104928i
$40$	−0.225005	+	3.75962i	−0.0355764	+	0.594448i
$41$	−10.5865	−	0.504295i	−1.65333	−	0.0787576i	−0.799954	−	0.600061i	$-0.795143\pi$
$41$	−10.5865	−	0.504295i	−1.65333	−	0.0787576i	−0.853371	+	0.521303i	$0.825446\pi$
$42$	0.480869	−	3.81619i	0.0741997	−	0.588851i
$43$	−4.52097	+	7.03477i	−0.689441	+	1.07279i	0.303343	+	0.952881i	$0.401897\pi$
$43$	−4.52097	+	7.03477i	−0.689441	+	1.07279i	−0.992785	+	0.119910i	$0.961739\pi$
$44$	−1.91110	−	1.63023i	−0.288110	−	0.245766i
$45$	0.298359	+	3.98366i	0.0444767	+	0.593848i
$46$	−1.19696	−	1.18772i	−0.176482	−	0.175119i
$47$	0.246085	−	0.193523i	0.0358952	−	0.0282283i	−0.600050	−	0.799962i	$-0.704853\pi$
$47$	0.246085	−	0.193523i	0.0358952	−	0.0282283i	0.635945	+	0.771734i	$0.280610\pi$
$48$	−5.84806	−	3.71487i	−0.844094	−	0.536195i
$49$	0.215748	+	4.52911i	0.0308211	+	0.647016i
$50$	1.40633	+	4.34132i	0.198885	+	0.613956i
$51$	−3.74346	−	0.216695i	−0.524189	−	0.0303433i
$52$	−0.658159	−	0.461029i	−0.0912702	−	0.0639332i
$53$	3.76196	+	5.85372i	0.516745	+	0.804070i	0.997341	−	0.0728713i	$-0.0232162\pi$
$53$	3.76196	+	5.85372i	0.516745	+	0.804070i	−0.480597	+	0.876942i	$0.659580\pi$
$54$	−6.67524	−	3.07264i	−0.908385	−	0.418134i
$55$	1.58049	+	0.547011i	0.213113	+	0.0737590i
$56$	−4.10285	−	1.70079i	−0.548266	−	0.227277i
$57$	−13.5623	+	3.14375i	−1.79637	+	0.416399i
$58$	10.2816	−	1.26974i	1.35004	−	0.166725i
$59$	−2.90403	+	3.35143i	−0.378073	+	0.436320i	−0.912614	−	0.408823i	$-0.865939\pi$
$59$	−2.90403	+	3.35143i	−0.378073	+	0.436320i	0.534540	+	0.845143i	$0.320485\pi$
$60$	4.52728	+	0.884179i	0.584469	+	0.114147i
$61$	−7.52455	−	0.718507i	−0.963419	−	0.0919954i	−0.398524	−	0.917158i	$-0.630477\pi$
$61$	−7.52455	−	0.718507i	−0.963419	−	0.0919954i	−0.564895	+	0.825163i	$0.691083\pi$
$62$	−0.297667	+	0.443495i	−0.0378038	+	0.0563239i
$63$	−4.55437	−	1.20397i	−0.573796	−	0.151686i
$64$	−5.92259	+	5.37801i	−0.740323	+	0.672251i
$65$	0.519935	+	0.126135i	0.0644900	+	0.0156451i
$66$	−2.28956	+	2.05496i	−0.281825	+	0.252948i
$67$	−2.25814	−	7.86770i	−0.275876	−	0.961193i
$67$	−2.25814	−	7.86770i	−0.275876	−	0.961193i
$68$	−1.38439	+	4.10252i	−0.167882	+	0.497504i
$69$	−1.63632	+	1.25996i	−0.196990	+	0.151682i
$70$	2.95651	+	0.0589177i	0.353370	+	0.00704201i
$71$	−1.69621	−	0.874459i	−0.201303	−	0.103779i	0.354627	−	0.935008i	$-0.384608\pi$
$71$	−1.69621	−	0.874459i	−0.201303	−	0.103779i	−0.555931	+	0.831229i	$0.687638\pi$
$72$	−5.46000	+	6.49526i	−0.643467	+	0.765474i
$73$	−0.924416	−	0.0882711i	−0.108195	−	0.0103313i	0.0408182	−	0.999167i	$-0.487004\pi$
$73$	−0.924416	−	0.0882711i	−0.108195	−	0.0103313i	−0.149013	+	0.988835i	$0.547610\pi$
$74$	0.370964	−	0.279949i	0.0431236	−	0.0325434i
$75$	5.49856	−	1.00158i	0.634919	−	0.115652i
$76$	−0.640460	+	16.0629i	−0.0734658	+	1.84254i
$77$	−1.21915	+	1.55028i	−0.138935	+	0.176671i
$78$	−0.666618	+	0.724017i	−0.0754796	+	0.0819788i
$79$	0.351000	+	0.121482i	0.0394906	+	0.0136678i	0.346742	−	0.937961i	$-0.387288\pi$
$79$	0.351000	+	0.121482i	0.0394906	+	0.0136678i	−0.307251	+	0.951628i	$0.599409\pi$
$80$	2.36704	−	4.77156i	0.264644	−	0.533477i
$81$	−4.81483	+	7.60377i	−0.534982	+	0.844864i
$82$	13.5072	+	6.49685i	1.49162	+	0.717457i
$83$	4.69899	+	6.59880i	0.515781	+	0.724313i	0.987532	−	0.157419i	$-0.0503174\pi$
$83$	4.69899	+	6.59880i	0.515781	+	0.724313i	−0.471751	+	0.881732i	$0.656378\pi$
$84$	−2.73143	+	4.70408i	−0.298024	+	0.513257i
$85$	−0.137169	−	2.87953i	−0.0148781	−	0.312329i
$86$	9.76793	−	6.66646i	1.05330	−	0.718862i
$87$	0.129692	−	12.6873i	0.0139044	−	1.36023i
$88$	1.58926	+	3.17713i	0.169416	+	0.338683i
$89$	−3.01184	−	0.433038i	−0.319255	−	0.0459019i	−0.0191754	−	0.999816i	$-0.506104\pi$
$89$	−3.01184	−	0.433038i	−0.319255	−	0.0459019i	−0.300079	+	0.953914i	$0.597013\pi$
$90$	1.80912	−	5.35202i	0.190698	−	0.564152i
$91$	−0.341096	+	0.530755i	−0.0357565	+	0.0556382i
$92$	0.903429	+	2.20694i	0.0941890	+	0.230089i
$93$	0.489985	+	0.433422i	0.0508091	+	0.0449438i
$94$	−0.427206	+	0.116245i	−0.0440629	+	0.0119898i
$95$	−3.50067	−	10.1145i	−0.359161	−	1.03773i
$96$	5.56585	+	8.06358i	0.568062	+	0.822986i
$97$	−4.97724	+	8.62084i	−0.505362	+	0.875313i	0.494618	+	0.869110i	$0.335308\pi$
$97$	−4.97724	+	8.62084i	−0.505362	+	0.875313i	−0.999981	+	0.00620311i	$0.998025\pi$
$98$	2.21761	−	6.01672i	0.224012	−	0.607781i
$99$	2.12242	+	3.11331i	0.213311	+	0.312900i
$100$	0.563659	−	6.42900i	0.0563659	−	0.642900i
$101$	3.10299	−	0.752777i	0.308759	−	0.0749041i	−0.0783858	−	0.996923i	$-0.524977\pi$
$101$	3.10299	−	0.752777i	0.308759	−	0.0749041i	0.387145	+	0.922019i	$0.373461\pi$
$102$	4.75510	+	2.34731i	0.470826	+	0.232418i
$103$	−1.67198	+	8.67503i	−0.164745	+	0.854776i	0.801666	+	0.597772i	$0.203947\pi$
$103$	−1.67198	+	8.67503i	−0.164745	+	0.854776i	−0.966410	+	0.257004i	$0.917265\pi$
$104$	0.602706	+	0.963424i	0.0591002	+	0.0944715i
$105$	0.552035	−	3.57937i	0.0538731	−	0.349310i
$106$	−1.66945	−	9.69792i	−0.162151	−	0.941945i
$107$	6.32274	+	13.8449i	0.611242	+	1.33843i	0.921721	+	0.387854i	$0.126783\pi$
$107$	6.32274	+	13.8449i	0.611242	+	1.33843i	−0.310479	+	0.950580i	$0.600489\pi$
$108$	6.99728	+	7.68362i	0.673314	+	0.739357i
$109$	−9.63599	−	11.1205i	−0.922961	−	1.06515i	−0.997689	−	0.0679496i	$-0.978354\pi$
$109$	−9.63599	−	11.1205i	−0.922961	−	1.06515i	0.0747280	−	0.997204i	$-0.476191\pi$
$110$	−1.75631	−	1.58420i	−0.167457	−	0.151048i
$111$	−0.279542	−	0.495817i	−0.0265330	−	0.0470609i
$112$	4.40438	+	4.47812i	0.416174	+	0.423143i
$113$	2.12920	+	1.51620i	0.200298	+	0.142632i	0.675805	−	0.737080i	$-0.263796\pi$
$113$	2.12920	+	1.51620i	0.200298	+	0.142632i	−0.475507	+	0.879712i	$0.657735\pi$
$114$	19.3948	+	3.38812i	1.81649	+	0.317327i
$115$	−1.09566	−	1.14910i	−0.102171	−	0.107154i
$116$	−14.0890	−	4.01857i	−1.30813	−	0.373115i
$117$	0.770550	+	0.926889i	0.0712374	+	0.0856909i
$118$	5.63044	−	2.76211i	0.518324	−	0.254273i
$119$	3.26179	+	0.957747i	0.299008	+	0.0877965i
$120$	−5.40755	−	3.64890i	−0.493640	−	0.333097i
$121$	−9.25223	+	1.78322i	−0.841112	+	0.162111i
$122$	9.40192	+	5.08665i	0.851210	+	0.460523i
$123$	10.0819	−	15.3407i	0.909055	−	1.38322i
$124$	0.632276	−	0.413297i	0.0567801	−	0.0371152i
$125$	3.08635	+	10.5111i	0.276051	+	0.940144i
$126$	5.26641	+	4.08026i	0.469169	+	0.363499i
$127$	−9.12403	+	9.56901i	−0.809627	+	0.849112i	−0.990939	−	0.134314i	$-0.957117\pi$
$127$	−9.12403	+	9.56901i	−0.809627	+	0.849112i	0.181312	+	0.983426i	$0.441966\pi$
$128$	10.6791	−	3.73584i	0.943909	−	0.330205i
$129$	−6.50494	−	12.9409i	−0.572728	−	1.13938i
$130$	−0.607464	−	0.451080i	−0.0532781	−	0.0395623i
$131$	1.13221	+	7.87466i	0.0989213	+	0.688012i	0.977580	+	0.210563i	$0.0675296\pi$
$131$	1.13221	+	7.87466i	0.0989213	+	0.688012i	−0.878659	+	0.477450i	$0.841561\pi$
$132$	4.11506	−	1.41285i	0.358170	−	0.122973i
$133$	12.6216			1.09443
$134$	−1.39983	+	11.4909i	−0.120927	+	0.992661i
$135$	−6.20285	−	3.06597i	−0.533857	−	0.263877i
$136$	4.06594	−	4.57849i	0.348652	−	0.392603i
$137$	14.4822	−	2.08222i	1.23729	−	0.177896i	0.507554	−	0.861620i	$-0.330550\pi$
$137$	14.4822	−	2.08222i	1.23729	−	0.177896i	0.729741	+	0.683724i	$0.239641\pi$
$138$	2.82586	−	0.737996i	0.240553	−	0.0628224i
$139$	2.03419	+	0.928982i	0.172538	+	0.0787952i	0.499811	−	0.866134i	$-0.333403\pi$
$139$	2.03419	+	0.928982i	0.172538	+	0.0787952i	−0.327274	+	0.944930i	$0.606130\pi$
$140$	−3.81739	−	1.70772i	−0.322629	−	0.144329i
$141$	0.0716789	+	0.537484i	0.00603646	+	0.0452643i
$142$	1.72636	+	2.07444i	0.144873	+	0.174083i
$143$	0.484191	−	0.142171i	0.0404901	−	0.0118890i
$144$	10.6931	−	5.44590i	0.891091	−	0.453825i
$145$	9.71040	−	0.927231i	0.806405	−	0.0770023i
$146$	1.15506	+	0.624912i	0.0955933	+	0.0517181i
$147$	−6.94336	−	3.66987i	−0.572678	−	0.302685i
$148$	−0.637499	+	0.159896i	−0.0524021	+	0.0131434i
$149$	−3.68264	+	12.5419i	−0.301694	+	1.02748i	0.659524	+	0.751684i	$0.270758\pi$
$149$	−3.68264	+	12.5419i	−0.301694	+	1.02748i	−0.961218	+	0.275791i	$0.911060\pi$
$150$	−7.71264	−	1.72912i	−0.629734	−	0.141182i
$151$	−4.48884	−	8.70713i	−0.365296	−	0.708576i	0.632526	−	0.774539i	$-0.282018\pi$
$151$	−4.48884	−	8.70713i	−0.365296	−	0.708576i	−0.997822	+	0.0659632i	$0.978988\pi$
$152$	9.69530	−	20.5634i	0.786393	−	1.66791i
$153$	3.62226	−	5.39078i	0.292843	−	0.435819i
$154$	2.44279	−	1.34618i	0.196845	−	0.108478i
$155$	−0.291727	+	0.409673i	−0.0234321	+	0.0329058i
$156$	1.26747	−	0.575050i	0.101479	−	0.0460408i
$157$	−8.75452	−	3.50478i	−0.698687	−	0.279712i	−0.00499875	−	0.999988i	$-0.501591\pi$
$157$	−8.75452	−	3.50478i	−0.698687	−	0.279712i	−0.693688	+	0.720275i	$0.744015\pi$
$158$	−0.390047	−	0.351826i	−0.0310304	−	0.0279897i
$159$	−12.0438	+	0.450383i	−0.955133	+	0.0357177i
$160$	−5.71461	+	4.90761i	−0.451780	+	0.387981i
$161$	1.70311	−	0.777785i	0.134224	−	0.0612980i
$162$	10.4645	−	7.24529i	0.822169	−	0.569244i
$163$	−6.81989	+	3.93747i	−0.534175	+	0.308406i	−0.742715	−	0.669608i	$-0.766462\pi$
$163$	−6.81989	+	3.93747i	−0.534175	+	0.308406i	0.208540	+	0.978014i	$0.433129\pi$
$164$	−14.0047	−	15.9115i	−1.09359	−	1.24248i
$165$	−2.20853	+	1.87453i	−0.171934	+	0.145932i
$166$	−2.47859	−	11.1851i	−0.192376	−	0.868130i
$167$	−1.72287	−	7.10176i	−0.133320	−	0.549551i	−0.998817	−	0.0486365i	$-0.984512\pi$
$167$	−1.72287	−	7.10176i	−0.133320	−	0.549551i	0.865497	−	0.500914i	$-0.167003\pi$
$168$	6.15188	−	4.61871i	0.474628	−	0.356341i
$169$	−11.9189	+	4.77161i	−0.916840	+	0.367047i
$170$	−1.40992	+	3.82533i	−0.108136	+	0.293390i
$171$	7.26508	−	22.9930i	0.555575	−	1.75832i
$172$	−16.3972	+	3.29229i	−1.25028	+	0.251035i
$173$	22.6596	−	7.84256i	1.72278	−	0.596259i	0.726881	−	0.686763i	$-0.240969\pi$
$173$	22.6596	−	7.84256i	1.72278	−	0.596259i	0.995896	+	0.0905042i	$0.0288478\pi$
$174$	−7.16804	+	16.4496i	−0.543408	+	1.24704i
$175$	−5.06126	−	0.241098i	−0.382596	−	0.0182253i
$176$	−0.316788	−	5.01393i	−0.0238788	−	0.377939i
$177$	−2.43786	−	7.28378i	−0.183241	−	0.547482i
$178$	3.68306	+	2.22542i	0.276057	+	0.166802i
$179$	−2.10379	+	14.6322i	−0.157245	+	1.09366i	0.746437	+	0.665456i	$0.231763\pi$
$179$	−2.10379	+	14.6322i	−0.157245	+	1.09366i	−0.903682	+	0.428205i	$0.859146\pi$
$180$	−5.30832	+	5.97125i	−0.395659	+	0.445071i
$181$	15.6206	−	12.2842i	1.16107	−	0.913074i	0.163767	−	0.986499i	$-0.447635\pi$
$181$	15.6206	−	12.2842i	1.16107	−	0.913074i	0.997301	+	0.0734251i	$0.0233930\pi$
$182$	0.736966	−	0.502967i	0.0546275	−	0.0372824i
$183$	7.70282	−	10.5864i	0.569409	−	0.782568i
$184$	0.0410642	−	3.37221i	0.00302729	−	0.248603i
$185$	0.356454	−	0.253830i	0.0262071	−	0.0186620i
$186$	−0.398944	−	0.834700i	−0.0292520	−	0.0612032i
$187$	−1.47005	−	2.28744i	−0.107500	−	0.167274i
$188$	0.620426	+	0.0843022i	0.0452492	+	0.00614837i
$189$	5.80902	−	5.72980i	0.422544	−	0.416782i
$190$	−1.02133	+	15.1021i	−0.0740948	+	1.09562i
$191$	−14.7266	−	11.5811i	−1.06558	−	0.837981i	−0.0782927	−	0.996930i	$-0.524947\pi$
$191$	−14.7266	−	11.5811i	−1.06558	−	0.837981i	−0.987287	+	0.158949i	$0.949189\pi$
$192$	−2.79933	−	13.5707i	−0.202024	−	0.979380i
$193$	10.8629	−	12.5364i	0.781927	−	0.902392i	−0.215320	−	0.976544i	$-0.569079\pi$
$193$	10.8629	−	12.5364i	0.781927	−	0.902392i	0.997247	+	0.0741516i	$0.0236249\pi$
$194$	11.2371	−	8.48009i	0.806774	−	0.608835i
$195$	−0.646302	+	0.664095i	−0.0462826	+	0.0475569i
$196$	−6.20693	+	6.61147i	−0.443352	+	0.472248i
$197$	8.31078	−	16.1207i	0.592118	−	1.14855i	−0.382348	−	0.924018i	$-0.624885\pi$
$197$	8.31078	−	16.1207i	0.592118	−	1.14855i	0.974467	−	0.224531i	$-0.0720851\pi$
$198$	−1.04627	−	5.22495i	−0.0743549	−	0.371321i
$199$	18.6679	+	4.52879i	1.32333	+	0.321037i	0.834340	−	0.551250i	$-0.185849\pi$
$199$	18.6679	+	4.52879i	1.32333	+	0.321037i	0.488993	+	0.872288i	$0.337364\pi$
$200$	−4.28063	+	8.06075i	−0.302687	+	0.569981i
$201$	13.7214	+	3.56686i	0.967835	+	0.251587i
$202$	−4.45592	−	0.731559i	−0.313517	−	0.0514723i
$203$	−2.71191	+	11.1787i	−0.190339	+	0.784588i
$204$	−4.89706	−	5.67983i	−0.342863	−	0.397668i
$205$	12.5441	+	6.46693i	0.876117	+	0.451670i
$206$	6.96291	−	10.3741i	0.485129	−	0.722795i
$207$	−0.436581	−	3.55030i	−0.0303445	−	0.246763i
$208$	−0.253344	−	1.58704i	−0.0175663	−	0.110041i
$209$	−7.62955	−	6.61104i	−0.527747	−	0.457295i
$210$	−2.69346	+	4.35643i	−0.185866	+	0.300622i
$211$	−6.09443	+	7.74970i	−0.419558	+	0.533511i	−0.949185	−	0.314719i	$-0.898090\pi$
$211$	−6.09443	+	7.74970i	−0.419558	+	0.533511i	0.529627	+	0.848231i	$0.322332\pi$
$212$	−3.17608	+	13.5494i	−0.218134	+	0.930576i
$213$	2.79877	−	1.75850i	0.191769	−	0.120490i
$214$	−0.595608	−	21.5165i	−0.0407149	−	1.47084i
$215$	9.36752	−	6.02014i	0.638860	−	0.410570i
$216$	−4.87292	−	13.8656i	−0.331561	−	0.943434i
$217$	−0.344014	−	0.483101i	−0.0233532	−	0.0327950i
$218$	6.41297	+	19.7967i	0.434341	+	1.34080i
$219$	0.946318	−	1.30057i	0.0639463	−	0.0878847i
$220$	1.41307	+	3.03181i	0.0952694	+	0.204404i
$221$	−0.537689	−	0.683727i	−0.0361689	−	0.0459925i
$222$	0.0904887	+	0.799855i	0.00607321	+	0.0536828i
$223$	10.8903	+	1.56580i	0.729271	+	0.104853i	0.496942	−	0.867784i	$-0.334456\pi$
$223$	10.8903	+	1.56580i	0.729271	+	0.104853i	0.232329	+	0.972637i	$0.425365\pi$
$224$	−3.26486	−	8.26105i	−0.218143	−	0.551964i
$225$	−3.35252	+	9.08144i	−0.223502	+	0.605429i
$226$	−1.93617	−	3.14896i	−0.128792	−	0.209466i
$227$	−0.0803747	+	1.68727i	−0.00533466	+	0.111988i	0.994629	+	0.103501i	$0.0330046\pi$
$227$	−0.0803747	+	1.68727i	−0.00533466	+	0.111988i	−0.999964	+	0.00848702i	$0.997298\pi$
$228$	−23.3864	−	15.1114i	−1.54880	−	1.00077i
$229$	4.88369	+	14.1105i	0.322723	+	0.932447i	0.983348	+	0.181731i	$0.0581701\pi$
$229$	4.88369	+	14.1105i	0.322723	+	0.932447i	−0.660625	+	0.750716i	$0.729709\pi$
$230$	0.792830	+	2.10076i	0.0522777	+	0.138520i
$231$	−1.23712	−	3.18412i	−0.0813965	−	0.209500i
$232$	16.1294	+	13.0053i	1.05895	+	0.853837i
$233$	−0.501584	−	1.25290i	−0.0328599	−	0.0820800i	0.911030	−	0.412339i	$-0.135288\pi$
$233$	−0.501584	−	1.25290i	−0.0328599	−	0.0820800i	−0.943890	+	0.330259i	$0.892864\pi$
$234$	−0.492062	−	1.63206i	−0.0321671	−	0.106691i
$235$	−0.405126	+	0.0982825i	−0.0264275	+	0.00641124i
$236$	−8.85558	+	0.490647i	−0.576449	+	0.0319384i
$237$	−0.490479	+	0.416301i	−0.0318600	+	0.0270417i
$238$	−3.71907	−	3.04657i	−0.241072	−	0.197480i
$239$	8.76847	+	15.1874i	0.567185	+	0.982394i	0.996843	+	0.0794018i	$0.0253010\pi$
$239$	8.76847	+	15.1874i	0.567185	+	0.982394i	−0.429657	+	0.902992i	$0.641366\pi$
$240$	5.02863	+	7.73467i	0.324596	+	0.499270i
$241$	−3.94821	−	8.64537i	−0.254326	−	0.556897i	0.738803	−	0.673922i	$-0.235392\pi$
$241$	−3.94821	−	8.64537i	−0.254326	−	0.556897i	−0.993129	+	0.117025i	$0.962664\pi$
$242$	13.0318	+	2.78206i	0.837715	+	0.178837i
$243$	−7.09438	−	13.8806i	−0.455105	−	0.890438i
$244$	−9.43685	−	11.8104i	−0.604132	−	0.756085i
$245$	2.24403	−	5.60532i	0.143366	−	0.358111i
$246$	−21.5914	+	14.4145i	−1.37661	+	0.919033i
$247$	−2.63064	−	1.87327i	−0.167384	−	0.119193i
$248$	−1.05134	+	0.189382i	−0.0667600	+	0.0120258i
$249$	−13.9805	+	1.19091i	−0.885981	+	0.0754707i
$250$	1.77965	−	15.3900i	0.112555	−	0.973348i
$251$	−3.35589	+	1.73008i	−0.211822	+	0.109202i	−0.560873	−	0.827902i	$-0.689534\pi$
$251$	−3.35589	+	1.73008i	−0.211822	+	0.109202i	0.349051	+	0.937104i	$0.386504\pi$
$252$	−4.60686	−	8.21852i	−0.290205	−	0.517718i
$253$	−1.43690	−	0.421913i	−0.0903373	−	0.0265254i
$254$	17.1600	−	7.42714i	1.07671	−	0.466020i
$255$	4.41447	+	2.33324i	0.276445	+	0.146113i
$256$	−15.9670	−	1.02656i	−0.997940	−	0.0641601i
$257$	−1.43549	−	15.0331i	−0.0895431	−	0.937738i	−0.922909	−	0.385017i	$-0.874196\pi$
$257$	−1.43549	−	15.0331i	−0.0895431	−	0.937738i	0.833366	−	0.552721i	$-0.186410\pi$
$258$	1.33155	+	20.4399i	0.0828984	+	1.27253i
$259$	0.145382	+	0.495124i	0.00903357	+	0.0307655i
$260$	0.542181	+	0.922502i	0.0336247	+	0.0572112i
$261$	18.8034	+	11.3749i	1.16390	+	0.704088i
$262$	2.86984	−	10.8788i	0.177299	−	0.672095i
$263$	−8.81204	+	19.2957i	−0.543374	+	1.18982i	0.416435	+	0.909166i	$0.363279\pi$
$263$	−8.81204	+	19.2957i	−0.543374	+	1.18982i	−0.959808	+	0.280657i	$0.909448\pi$
$264$	−6.13796	−	0.430350i	−0.377765	−	0.0264862i
$265$	−1.31865	−	9.17143i	−0.0810042	−	0.563397i
$266$	−16.4355	−	6.96286i	−1.00773	−	0.426920i
$267$	3.30006	−	4.10923i	0.201961	−	0.251481i
$268$	8.16194	−	14.1909i	0.498570	−	0.866850i
$269$			4.39856i			0.268185i	0.990969	+	0.134092i	$0.0428119\pi$
$269$			4.39856i			0.268185i	−0.990969	+	0.134092i	$0.957188\pi$
$270$	6.38583	+	7.41433i	0.388629	+	0.451222i
$271$	21.4555	−	3.08484i	1.30333	−	0.187391i	0.544546	−	0.838731i	$-0.316702\pi$
$271$	21.4555	−	3.08484i	1.30333	−	0.187391i	0.758786	+	0.651340i	$0.225793\pi$
$272$	−7.82037	+	3.71898i	−0.474180	+	0.225496i
$273$	−0.490781	−	0.976358i	−0.0297034	−	0.0590919i
$274$	−20.0070	−	5.27787i	−1.20867	−	0.318848i
$275$	2.93318	+	2.79678i	0.176877	+	0.168652i
$276$	−4.08690	−	0.597927i	−0.246003	−	0.0359910i
$277$	26.0949	−	7.66217i	1.56789	−	0.460375i	0.621506	−	0.783409i	$-0.286521\pi$
$277$	26.0949	−	7.66217i	1.56789	−	0.460375i	0.946387	+	0.323034i	$0.104703\pi$
$278$	−2.13639	−	2.33189i	−0.128132	−	0.139857i
$279$	−1.07809	+	0.348621i	−0.0645437	+	0.0208714i
$280$	4.02884	+	4.32968i	0.240769	+	0.258748i
$281$	−1.89960	−	9.85607i	−0.113321	−	0.587964i	−0.993548	−	0.113411i	$-0.963822\pi$
$281$	−1.89960	−	9.85607i	−0.113321	−	0.587964i	0.880227	−	0.474552i	$-0.157390\pi$
$282$	0.203172	−	0.739442i	0.0120987	−	0.0440331i
$283$	−2.94129	+	10.0171i	−0.174841	+	0.595455i	0.824712	+	0.565554i	$0.191337\pi$
$283$	−2.94129	+	10.0171i	−0.174841	+	0.595455i	−0.999553	+	0.0299012i	$0.990481\pi$
$284$	−1.10364	−	3.65366i	−0.0654887	−	0.216805i
$285$	18.1666	+	3.69431i	1.07610	+	0.218832i
$286$	−0.708934	−	0.0819787i	−0.0419202	−	0.00484750i
$287$	−12.0447	+	11.4846i	−0.710977	+	0.677915i
$288$	−16.9286	+	1.19253i	−0.997528	+	0.0702706i
$289$	7.14235	−	10.0300i	0.420138	−	0.590002i
$290$	−13.1562	−	4.14946i	−0.772558	−	0.243665i
$291$	−8.46776	−	15.0191i	−0.496389	−	0.880433i
$292$	−1.15935	−	1.45095i	−0.0678458	−	0.0849105i
$293$	4.72490	−	4.09415i	0.276032	−	0.239183i	−0.505832	−	0.862632i	$-0.668815\pi$
$293$	4.72490	−	4.09415i	0.276032	−	0.239183i	0.781864	+	0.623449i	$0.214269\pi$
$294$	7.01695	+	8.60922i	0.409237	+	0.502100i
$295$	5.37148	−	2.45307i	0.312739	−	0.142823i
$296$	0.918345	+	0.143472i	0.0533777	+	0.00833915i
$297$	−6.51268	+	0.420877i	−0.377904	+	0.0244218i
$298$	11.7144	−	14.3002i	0.678597	−	0.828391i
$299$	−0.470408	−	0.0906637i	−0.0272044	−	0.00524322i
$300$	9.08932	+	6.50641i	0.524772	+	0.375648i
$301$	3.09575	+	12.7609i	0.178436	+	0.735523i
$302$	1.04185	+	13.8146i	0.0599517	+	0.794939i
$303$	−1.61226	+	5.29020i	−0.0926219	+	0.303914i
$304$	−23.9691	+	21.4286i	−1.37472	+	1.22902i
$305$	8.71680	+	5.03265i	0.499122	+	0.288168i
$306$	−7.69073	+	5.02148i	−0.439650	+	0.287059i
$307$	−2.74094	+	0.948648i	−0.156434	+	0.0541422i	−0.404163	−	0.914687i	$-0.632437\pi$
$307$	−2.74094	+	0.948648i	−0.156434	+	0.0541422i	0.247729	+	0.968829i	$0.420316\pi$
$308$	−3.92358	+	0.405361i	−0.223567	+	0.0230976i
$309$	−11.4615	−	10.1384i	−0.652024	−	0.576756i
$310$	0.605883	−	0.372532i	0.0344118	−	0.0211584i
$311$	−20.0123	−	12.8611i	−1.13479	−	0.729288i	−0.168239	−	0.985746i	$-0.553808\pi$
$311$	−20.0123	−	12.8611i	−1.13479	−	0.729288i	−0.966555	+	0.256459i	$0.917444\pi$
$312$	−1.96770	+	0.0495996i	−0.111399	+	0.00280803i
$313$	−2.19338	+	15.2553i	−0.123977	+	0.862281i	0.829002	+	0.559246i	$0.188909\pi$
$313$	−2.19338	+	15.2553i	−0.123977	+	0.862281i	−0.952979	+	0.303035i	$0.902000\pi$
$314$	9.46648	+	9.39341i	0.534224	+	0.530101i
$315$	4.85057	+	3.97766i	0.273299	+	0.224116i
$316$	0.313820	+	0.673314i	0.0176538	+	0.0378769i
$317$	−16.9683	+	0.808302i	−0.953037	+	0.0453988i	−0.518337	−	0.855176i	$-0.673449\pi$
$317$	−16.9683	+	0.808302i	−0.953037	+	0.0453988i	−0.434700	+	0.900575i	$0.643146\pi$
$318$	15.9316	+	6.05764i	0.893399	+	0.339695i
$319$	7.49459	−	5.33687i	0.419616	−	0.298807i
$320$	10.1488	−	3.23803i	0.567335	−	0.181011i
$321$	−26.2160	−	2.77401i	−1.46323	−	0.154830i
$322$	−2.64683	+	0.0732681i	−0.147502	+	0.00408307i
$323$	−5.69134	+	16.4440i	−0.316675	+	0.914971i
$324$	−17.6236	+	3.66176i	−0.979089	+	0.203431i
$325$	1.01911	+	0.801435i	0.0565299	+	0.0444556i
$326$	11.0529	−	1.36499i	0.612162	−	0.0755997i
$327$	25.0738	−	4.56727i	1.38658	−	0.252571i
$328$	9.45884	+	28.4455i	0.522277	+	1.57064i
$329$	0.0467291	−	0.489369i	0.00257626	−	0.0269798i
$330$	3.91001	−	1.22260i	0.215239	−	0.0673017i
$331$	7.83977	−	15.2070i	0.430913	−	0.835854i	−0.568996	−	0.822340i	$-0.692668\pi$
$331$	7.83977	−	15.2070i	0.430913	−	0.835854i	0.999909	−	0.0135137i	$-0.00430166\pi$
$332$	−2.94284	+	15.9323i	−0.161510	+	0.874399i
$333$	0.985662	+	0.0201532i	0.0540139	+	0.00110439i
$334$	−1.67431	+	10.1982i	−0.0916140	+	0.558020i
$335$	−1.61694	+	10.7790i	−0.0883430	+	0.588922i
$336$	−10.5588	+	2.62061i	−0.576031	+	0.142966i
$337$	−1.09976	+	4.53329i	−0.0599080	+	0.246944i	−0.993890	−	0.110376i	$-0.964794\pi$
$337$	−1.09976	+	4.53329i	−0.0599080	+	0.246944i	0.933982	+	0.357320i	$0.116310\pi$
$338$	18.1529	+	0.361753i	0.987386	+	0.0196768i
$339$	−4.13725	+	1.83854i	−0.224704	+	0.0998560i
$340$	3.94626	−	4.20346i	0.214016	−	0.227965i
$341$	−0.0450914	+	0.472219i	−0.00244184	+	0.0255721i
$342$	−22.1448	+	25.9330i	−1.19745	+	1.40230i
$343$	13.6881	+	11.8608i	0.739086	+	0.640422i
$344$	23.1683	+	4.75863i	1.24915	+	0.256568i
$345$	2.67900	−	0.620994i	0.144233	−	0.0334332i
$346$	−33.8333	−	2.28808i	−1.81889	−	0.123008i
$347$	1.24180	−	3.58794i	0.0666632	−	0.192611i	−0.906749	−	0.421670i	$-0.861444\pi$
$347$	1.24180	−	3.58794i	0.0666632	−	0.192611i	0.973412	+	0.229060i	$0.0735651\pi$
$348$	18.4087	−	17.4660i	0.986812	−	0.936275i
$349$	−12.4839	+	8.02294i	−0.668250	+	0.429458i	−0.830294	−	0.557325i	$-0.811828\pi$
$349$	−12.4839	+	8.02294i	−0.668250	+	0.429458i	0.162044	+	0.986783i	$0.448191\pi$
$350$	6.45766	+	3.10607i	0.345176	+	0.166026i
$351$	−2.06115	+	0.332065i	−0.110016	+	0.0177243i
$352$	−2.35349	+	6.70378i	−0.125442	+	0.357313i
$353$	−12.2977	+	0.585813i	−0.654542	+	0.0311797i	−0.372227	−	0.928142i	$-0.621406\pi$
$353$	−12.2977	+	0.585813i	−0.654542	+	0.0311797i	−0.282316	+	0.959322i	$0.591103\pi$
$354$	−0.843675	+	10.8297i	−0.0448408	+	0.575590i
$355$	1.57085	+	1.99750i	0.0833720	+	0.106016i
$356$	−3.56832	−	4.92971i	−0.189120	−	0.261274i
$357$	−4.30272	+	4.01948i	−0.227724	+	0.212733i
$358$	10.8116	−	17.8931i	0.571409	−	0.945681i
$359$	23.8177	+	15.3067i	1.25705	+	0.807856i	0.987877	−	0.155237i	$-0.0496141\pi$
$359$	23.8177	+	15.3067i	1.25705	+	0.807856i	0.269170	+	0.963093i	$0.413251\pi$
$360$	10.2065	−	4.84722i	0.537930	−	0.255471i
$361$	−2.17004	+	45.5547i	−0.114213	+	2.39762i
$362$	−27.1175	+	7.37884i	−1.42526	+	0.387823i
$363$	5.49520	−	15.3673i	0.288423	−	0.806574i
$364$	−1.23713	+	0.248395i	−0.0648432	+	0.0130194i
$365$	1.07089	+	0.618278i	0.0560529	+	0.0323621i
$366$	−15.8706	+	9.53599i	−0.829568	+	0.498454i
$367$	−12.7677	−	31.8921i	−0.666466	−	1.66475i	−0.744350	−	0.667790i	$-0.767240\pi$
$367$	−12.7677	−	31.8921i	−0.666466	−	1.66475i	0.0778831	−	0.996962i	$-0.475184\pi$
$368$	−1.91380	+	4.36857i	−0.0997639	+	0.227727i
$369$	13.9887	+	28.5528i	0.728224	+	1.48640i
$370$	−0.604196	+	0.133889i	−0.0314107	+	0.00696054i
$371$	10.7290	+	2.06785i	0.557023	+	0.107357i
$372$	0.0590216	+	1.30701i	0.00306013	+	0.0677654i
$373$	7.82556	+	13.5543i	0.405192	+	0.701814i	0.994344	−	0.106209i	$-0.0338712\pi$
$373$	7.82556	+	13.5543i	0.405192	+	0.701814i	−0.589152	+	0.808023i	$0.700538\pi$
$374$	0.652363	+	3.78962i	0.0337329	+	0.195957i
$375$	−18.3929	−	4.66163i	−0.949803	−	0.240726i
$376$	−0.761399	−	0.452044i	−0.0392661	−	0.0233124i
$377$	2.22435	−	1.92741i	0.114560	−	0.0992666i
$378$	−10.7253	+	4.25659i	−0.551650	+	0.218935i
$379$	−12.4791	+	31.1712i	−0.641007	+	1.60116i	0.149539	+	0.988756i	$0.452221\pi$
$379$	−12.4791	+	31.1712i	−0.641007	+	1.60116i	−0.790546	+	0.612403i	$0.790203\pi$
$380$	9.66123	−	19.1022i	0.495611	−	0.979921i
$381$	−6.22693	−	22.0378i	−0.319015	−	1.12903i
$382$	12.7878	+	23.2048i	0.654278	+	1.18726i
$383$	21.4499	−	20.4524i	1.09604	−	1.04507i	0.0972793	−	0.995257i	$-0.468986\pi$
$383$	21.4499	−	20.4524i	1.09604	−	1.04507i	0.998759	−	0.0498129i	$-0.0158625\pi$
$384$	−3.84124	+	19.2157i	−0.196023	+	0.980599i
$385$	2.33429	−	1.20341i	0.118966	−	0.0613314i
$386$	−21.0613	+	10.3320i	−1.07199	+	0.525885i
$387$	25.0287	+	1.70567i	1.27228	+	0.0867041i
$388$	−19.3108	+	4.84350i	−0.980358	+	0.245891i
$389$	6.44550	+	33.4424i	0.326800	+	1.69560i	0.658800	+	0.752318i	$0.271064\pi$
$389$	6.44550	+	33.4424i	0.326800	+	1.69560i	−0.332000	+	0.943279i	$0.607723\pi$
$390$	1.20796	−	0.508229i	0.0611673	−	0.0257352i
$391$	0.245370	+	2.56963i	0.0124089	+	0.129952i
$392$	11.7298	−	5.18516i	0.592446	−	0.261890i
$393$	−12.7395	−	5.25184i	−0.642623	−	0.264920i
$394$	−19.7153	+	16.4072i	−0.993243	+	0.826583i
$395$	−0.357955	−	0.341310i	−0.0180107	−	0.0171732i
$396$	−1.52000	+	7.38100i	−0.0763826	+	0.370909i
$397$	12.4869	−	27.3425i	0.626699	−	1.37228i	−0.283846	−	0.958870i	$-0.591610\pi$
$397$	12.4869	−	27.3425i	0.626699	−	1.37228i	0.910545	−	0.413410i	$-0.135662\pi$
$398$	−21.8106	−	16.1957i	−1.09326	−	0.811817i
$399$	−11.1235	+	18.8196i	−0.556873	+	0.942159i
$400$	10.0210	−	8.13505i	0.501049	−	0.406753i
$401$			3.24464i			0.162030i	0.996713	+	0.0810148i	$0.0258161\pi$
$401$			3.24464i			0.162030i	−0.996713	+	0.0810148i	$0.974184\pi$
$402$	−15.9000	−	12.2143i	−0.793021	−	0.609194i
$403$			0.151748i			0.00755911i
$404$	5.39882	+	3.41079i	0.268602	+	0.169693i
$405$	10.0382	−	6.54681i	0.498804	−	0.325313i
$406$	9.69827	−	13.0605i	0.481317	−	0.648184i
$407$	0.171460	−	0.375445i	0.00849895	−	0.0186101i
$408$	3.24349	+	10.0977i	0.160576	+	0.499910i
$409$	−2.97971	−	2.84115i	−0.147337	−	0.140486i	0.612826	−	0.790218i	$-0.290033\pi$
$409$	−2.97971	−	2.84115i	−0.147337	−	0.140486i	−0.760163	+	0.649732i	$0.774881\pi$
$410$	−12.7671	−	15.3412i	−0.630520	−	0.757648i
$411$	−9.65858	+	23.4290i	−0.476423	+	1.15567i
$412$	−14.7900	+	9.66768i	−0.728649	+	0.476292i
$413$	0.661923	+	6.93197i	0.0325711	+	0.341100i
$414$	−1.39007	+	4.86396i	−0.0683180	+	0.239051i
$415$	−2.04149	−	10.5923i	−0.100213	−	0.519954i
$416$	−0.545615	+	2.20637i	−0.0267510	+	0.108176i
$417$	−3.17793	+	2.21439i	−0.155624	+	0.108439i
$418$	6.28795	+	12.8177i	0.307554	+	0.626934i
$419$	−8.75938	+	4.51578i	−0.427924	+	0.220610i	−0.658714	−	0.752393i	$-0.728899\pi$
$419$	−8.75938	+	4.51578i	−0.427924	+	0.220610i	0.230790	+	0.973004i	$0.425869\pi$
$420$	5.91065	−	4.18696i	0.288410	−	0.204303i
$421$	1.05138	−	1.00249i	0.0512410	−	0.0488582i	−0.664026	−	0.747709i	$-0.731154\pi$
$421$	1.05138	−	1.00249i	0.0512410	−	0.0488582i	0.715267	+	0.698851i	$0.246305\pi$
$422$	12.2113	−	6.72940i	0.594435	−	0.327582i
$423$	−0.864597	−	0.366813i	−0.0420382	−	0.0178351i
$424$	11.6105	−	15.8916i	0.563858	−	0.771763i
$425$	2.59635	−	6.48537i	0.125942	−	0.314587i
$426$	−4.61460	+	0.745896i	−0.223578	+	0.0361388i
$427$	−8.97024	+	7.77276i	−0.434100	+	0.376150i
$428$	−11.0943	+	28.3469i	−0.536263	+	1.37020i
$429$	−0.214737	+	0.847261i	−0.0103676	+	0.0409061i
$430$	−15.5193	+	2.67156i	−0.748406	+	0.128834i
$431$	14.1428	+	24.4960i	0.681235	+	1.17993i	0.974604	+	0.223934i	$0.0718900\pi$
$431$	14.1428	+	24.4960i	0.681235	+	1.17993i	−0.293370	+	0.955999i	$0.594777\pi$
$432$	−1.30374	+	20.7437i	−0.0627262	+	0.998031i
$433$	7.16645	+	1.38122i	0.344397	+	0.0663772i	0.358517	−	0.933523i	$-0.383282\pi$
$433$	7.16645	+	1.38122i	0.344397	+	0.0663772i	−0.0141197	+	0.999900i	$0.504495\pi$
$434$	0.181458	+	0.818863i	0.00871028	+	0.0393067i
$435$	−7.17533	+	15.2961i	−0.344031	+	0.733390i
$436$	2.57033	−	29.3167i	0.123096	−	1.40401i
$437$	3.56196	+	8.89734i	0.170392	+	0.425618i
$438$	−1.94976	+	1.17153i	−0.0931629	+	0.0559778i
$439$	−21.2896	−	12.2916i	−1.01610	−	0.586644i	−0.103127	−	0.994668i	$-0.532885\pi$
$439$	−21.2896	−	12.2916i	−1.01610	−	0.586644i	−0.912971	+	0.408024i	$0.866218\pi$
$440$	−0.167533	−	4.72749i	−0.00798684	−	0.225374i
$441$	11.5913	−	7.11873i	0.551966	−	0.338987i
$442$	0.322979	+	1.18696i	0.0153625	+	0.0564578i
$443$	1.27611	−	26.7888i	0.0606297	−	1.27277i	−0.739586	−	0.673062i	$-0.764979\pi$
$443$	1.27611	−	26.7888i	0.0606297	−	1.27277i	0.800216	−	0.599712i	$-0.204718\pi$
$444$	0.323419	−	1.09147i	0.0153488	−	0.0517990i
$445$	3.40861	+	2.19058i	0.161584	+	0.103844i
$446$	−13.3174	−	8.04676i	−0.630596	−	0.381025i
$447$	−15.4553	−	16.5444i	−0.731012	−	0.782525i
$448$	−0.305899	+	12.5585i	−0.0144524	+	0.593331i
$449$	−22.9121	−	29.1352i	−1.08129	−	1.37497i	−0.921751	−	0.387781i	$-0.873242\pi$
$449$	−22.9121	−	29.1352i	−1.08129	−	1.37497i	−0.159539	−	0.987192i	$-0.551001\pi$
$450$	9.37549	−	9.97618i	0.441965	−	0.470281i
$451$	13.2964	−	0.633385i	0.626102	−	0.0298249i
$452$	0.784061	+	5.16862i	0.0368791	+	0.243112i
$453$	16.9390	+	0.980534i	0.795864	+	0.0460695i
$454$	1.03547	−	2.15279i	0.0485970	−	0.101035i
$455$	0.706755	−	0.454204i	0.0331332	−	0.0212934i
$456$	22.1168	+	32.5791i	1.03572	+	1.52566i
$457$	−3.40645	+	9.84229i	−0.159347	+	0.460403i	−0.996207	−	0.0870140i	$-0.972268\pi$
$457$	−3.40645	+	9.84229i	−0.159347	+	0.460403i	0.836860	+	0.547417i	$0.184389\pi$
$458$	1.42483	−	21.0685i	0.0665777	−	0.984467i
$459$	4.84568	+	10.1520i	0.226177	+	0.473855i
$460$	0.126512	−	3.17295i	0.00589865	−	0.147939i
$461$	−15.9427	−	13.8144i	−0.742525	−	0.643401i	0.199133	−	0.979972i	$-0.436187\pi$
$461$	−15.9427	−	13.8144i	−0.742525	−	0.643401i	−0.941658	+	0.336571i	$0.890733\pi$
$462$	−0.145618	+	4.82877i	−0.00677478	+	0.224655i
$463$	1.43328	−	15.0099i	0.0666099	−	0.697571i	−0.899065	−	0.437816i	$-0.855752\pi$
$463$	1.43328	−	15.0099i	0.0666099	−	0.697571i	0.965675	−	0.259755i	$-0.0836418\pi$
$464$	−13.8288	−	25.8332i	−0.641987	−	1.19928i
$465$	−0.353749	−	0.796036i	−0.0164047	−	0.0369153i
$466$	−0.0380269	+	1.90820i	−0.00176156	+	0.0883957i
$467$	−9.70176	+	39.9912i	−0.448944	+	1.85057i	0.0726213	+	0.997360i	$0.476864\pi$
$467$	−9.70176	+	39.9912i	−0.448944	+	1.85057i	−0.521565	+	0.853212i	$0.674652\pi$
$468$	−0.259597	+	2.39668i	−0.0119999	+	0.110787i
$469$	−11.3883	−	5.95925i	−0.525862	−	0.275173i
$470$	0.581765	+	0.0955123i	0.0268348	+	0.00440565i
$471$	12.9413	−	9.96479i	0.596306	−	0.459153i
$472$	11.8022	+	4.24640i	0.543241	+	0.195456i
$473$	4.81267	−	9.33528i	0.221287	−	0.429236i
$474$	0.868349	−	0.271518i	0.0398846	−	0.0124713i
$475$	2.46544	−	25.8192i	0.113122	−	1.18467i
$476$	3.16221	+	6.01885i	0.144940	+	0.275874i
$477$	9.94277	−	18.3550i	0.455248	−	0.840419i
$478$	−3.03974	−	24.6140i	−0.139034	−	1.12582i
$479$	−1.78606	−	1.40458i	−0.0816073	−	0.0641767i	0.576522	−	0.817082i	$-0.304410\pi$
$479$	−1.78606	−	1.40458i	−0.0816073	−	0.0641767i	−0.658129	+	0.752905i	$0.728652\pi$
$480$	−2.28123	−	12.8460i	−0.104123	−	0.586338i
$481$	0.0431845	−	0.124773i	0.00196904	−	0.00568917i
$482$	0.371925	+	13.4359i	0.0169407	+	0.611988i
$483$	−0.341242	+	3.22493i	−0.0155271	+	0.146739i
$484$	−15.4349	−	10.8119i	−0.701588	−	0.491450i
$485$	10.7976	−	7.68891i	0.490292	−	0.349135i
$486$	1.58074	+	21.9887i	0.0717037	+	0.997426i
$487$	2.91964	−	0.139080i	0.132302	−	0.00630231i	0.0186734	−	0.999826i	$-0.494056\pi$
$487$	2.91964	−	0.139080i	0.132302	−	0.00630231i	0.113628	+	0.993523i	$0.463753\pi$
$488$	5.77306	+	20.5852i	0.261334	+	0.931850i
$489$	0.139420	−	13.6391i	0.00630480	−	0.616780i
$490$	−6.01438	+	6.06117i	−0.271702	+	0.273816i
$491$	3.92759	−	27.3170i	0.177250	−	1.23280i	−0.685841	−	0.727751i	$-0.740565\pi$
$491$	3.92759	−	27.3170i	0.177250	−	1.23280i	0.863091	−	0.505049i	$-0.168525\pi$
$492$	36.0677	−	6.85902i	1.62606	−	0.309229i
$493$	−13.3413	−	8.57394i	−0.600863	−	0.386151i
$494$	2.39214	+	3.89056i	0.107628	+	0.175045i
$495$	−0.848640	−	4.94512i	−0.0381435	−	0.222267i
$496$	1.47350	+	0.333376i	0.0661622	+	0.0149690i
$497$	−2.83182	+	0.980104i	−0.127025	+	0.0439637i
$498$	18.8621	+	6.16180i	0.845232	+	0.276117i
$499$	−9.94167	−	5.73983i	−0.445050	−	0.256950i	0.260687	−	0.965423i	$-0.416051\pi$
$499$	−9.94167	−	5.73983i	−0.445050	−	0.256950i	−0.705738	+	0.708473i	$0.749384\pi$
$500$	−10.8075	+	19.0587i	−0.483327	+	0.852332i
$501$	12.1076	+	3.68995i	0.540928	+	0.164855i
$502$	5.32440	−	0.401549i	0.237639	−	0.0179220i
$503$	−1.15909	−	4.77785i	−0.0516814	−	0.213034i	0.940116	−	0.340855i	$-0.110717\pi$
$503$	−1.15909	−	4.77785i	−0.0516814	−	0.213034i	−0.991797	+	0.127822i	$0.959201\pi$
$504$	1.46509	+	13.2434i	0.0652601	+	0.589908i
$505$	−4.17497	−	0.804659i	−0.185784	−	0.0358068i
$506$	1.63835	+	1.34209i	0.0728335	+	0.0596633i
$507$	3.38948	−	21.9772i	0.150532	−	0.976042i
$508$	−26.4426	+	0.204905i	−1.17320	+	0.00909120i
$509$	−7.74189	+	3.53560i	−0.343153	+	0.156713i	−0.579535	−	0.814948i	$-0.696766\pi$
$509$	−7.74189	+	3.53560i	−0.343153	+	0.156713i	0.236382	+	0.971660i	$0.424038\pi$
$510$	−4.46126	−	5.47360i	−0.197548	−	0.242375i
$511$	−1.10203	+	0.954910i	−0.0487507	+	0.0422427i
$512$	20.2256	+	10.1452i	0.893853	+	0.448359i
$513$	27.8813	+	31.0967i	1.23099	+	1.37295i
$514$	−6.42396	+	20.3677i	−0.283349	+	0.898379i
$515$	6.82397	−	9.58292i	0.300700	−	0.422274i
$516$	9.54206	−	27.3509i	0.420066	−	1.20406i
$517$	−0.284574	+	0.271341i	−0.0125155	+	0.0119335i
$518$	0.0838298	−	0.724941i	0.00368327	−	0.0318521i
$519$	−8.27638	+	40.6988i	−0.363293	+	1.78648i
$520$	−0.197104	−	1.50036i	−0.00864360	−	0.0657953i
$521$	11.6776	−	39.7704i	0.511607	−	1.74237i	−0.146267	−	0.989245i	$-0.546726\pi$
$521$	11.6776	−	39.7704i	0.511607	−	1.74237i	0.657874	−	0.753128i	$-0.271456\pi$
$522$	−18.2103	−	25.1853i	−0.797042	−	1.10233i
$523$	−0.500274	−	2.59567i	−0.0218755	−	0.113501i	0.969350	−	0.245685i	$-0.0790130\pi$
$523$	−0.500274	−	2.59567i	−0.0218755	−	0.113501i	−0.991225	+	0.132185i	$0.957801\pi$
$524$	−9.73849	+	12.5829i	−0.425428	+	0.549689i
$525$	4.82005	−	7.33421i	0.210364	−	0.320091i
$526$	22.1196	−	20.2651i	0.964459	−	0.883601i
$527$	0.784534	−	0.230360i	0.0341748	−	0.0100346i
$528$	7.75530	+	3.94648i	0.337506	+	0.171749i
$529$	−15.6170	−	14.8907i	−0.678998	−	0.647423i
$530$	−3.34243	+	12.6703i	−0.145186	+	0.550362i
$531$	13.0091	+	2.78427i	0.564548	+	0.120827i
$532$	17.5608	+	18.1338i	0.761356	+	0.786198i
$533$	4.21494	−	0.606017i	0.182569	−	0.0262495i
$534$	−6.56418	+	3.53041i	−0.284060	+	0.152776i
$535$		−	20.2674i		−	0.876237i
$536$	−18.4569	+	13.9765i	−0.797218	+	0.603692i
$537$	−19.9635	−	16.0324i	−0.861489	−	0.691851i
$538$	2.42653	−	5.72770i	0.104615	−	0.246939i
$539$	−0.810472	−	5.63696i	−0.0349095	−	0.242801i
$540$	−4.22526	−	13.1776i	−0.181826	−	0.567074i
$541$	−10.6960	+	23.4209i	−0.459856	+	1.00694i	0.527665	+	0.849453i	$0.323068\pi$
$541$	−10.6960	+	23.4209i	−0.459856	+	1.00694i	−0.987520	+	0.157491i	$0.949659\pi$
$542$	−29.6407	−	7.81925i	−1.27318	−	0.335866i
$543$	4.54992	+	34.1175i	0.195256	+	1.46412i
$544$	12.2351	−	0.528546i	0.524577	−	0.0226612i
$545$	5.52026	+	18.8003i	0.236462	+	0.805316i
$546$	0.100462	+	1.54214i	0.00429936	+	0.0659974i
$547$	−2.96983	−	31.1015i	−0.126981	−	1.32980i	−0.804348	−	0.594159i	$-0.797485\pi$
$547$	−2.96983	−	31.1015i	−0.126981	−	1.32980i	0.677367	−	0.735646i	$-0.263121\pi$
$548$	23.1411	+	17.9099i	0.988539	+	0.765073i
$549$	8.99645	+	20.8154i	0.383959	+	0.888378i
$550$	−2.27663	−	5.26003i	−0.0970760	−	0.224289i
$551$	−56.4953	−	16.5885i	−2.40678	−	0.706695i
$552$	4.99202	+	3.03320i	0.212474	+	0.129102i
$553$	0.518407	−	0.267258i	0.0220449	−	0.0113649i
$554$	−38.2072	−	4.41815i	−1.62327	−	0.187709i
$555$	0.0643305	+	0.755202i	0.00273068	+	0.0320565i
$556$	1.49553	+	4.21510i	0.0634248	+	0.178760i
$557$	−6.69693	−	4.76886i	−0.283758	−	0.202063i	0.429312	−	0.903156i	$-0.358756\pi$
$557$	−6.69693	−	4.76886i	−0.283758	−	0.202063i	−0.713069	+	0.701093i	$0.752696\pi$
$558$	1.59619	+	0.140779i	0.0675721	+	0.00595963i
$559$	1.24872	−	3.11914i	0.0528150	−	0.131926i
$560$	−2.85773	−	7.86057i	−0.120761	−	0.332170i
$561$	4.70629	−	0.175994i	0.198700	−	0.00743049i
$562$	−2.96362	+	13.8823i	−0.125013	+	0.585589i
$563$	−14.8135	−	32.4370i	−0.624313	−	1.36706i	−0.912340	−	0.409433i	$-0.865726\pi$
$563$	−14.8135	−	32.4370i	−0.624313	−	1.36706i	0.288027	−	0.957622i	$-0.407001\pi$
$564$	−0.672490	+	0.850802i	−0.0283169	+	0.0358252i
$565$	−1.74032	−	3.01433i	−0.0732160	−	0.126814i
$566$	9.35615	−	11.4214i	0.393269	−	0.480079i
$567$	3.42397	+	13.7114i	0.143793	+	0.575825i
$568$	−0.578466	+	5.36655i	−0.0242719	+	0.225176i
$569$	−21.6522	+	5.25277i	−0.907708	+	0.220208i	−0.662323	−	0.749218i	$-0.730429\pi$
$569$	−21.6522	+	5.25277i	−0.907708	+	0.220208i	−0.245385	+	0.969426i	$0.578914\pi$
$570$	−21.6182	−	14.8325i	−0.905485	−	0.621266i
$571$	−9.02301	−	22.5384i	−0.377601	−	0.943202i	−0.988463	−	0.151465i	$-0.951601\pi$
$571$	−9.02301	−	22.5384i	−0.377601	−	0.943202i	0.610861	−	0.791738i	$-0.290823\pi$
$572$	0.877933	+	0.497845i	0.0367082	+	0.0208159i
$573$	30.2470	−	11.7518i	1.26359	−	0.490938i
$574$	22.0200	−	8.31036i	0.919097	−	0.346868i
$575$	−1.25839	−	3.63589i	−0.0524786	−	0.151627i
$576$	22.7019	+	7.78603i	0.945914	+	0.324418i
$577$	−0.154498	+	3.24331i	−0.00643183	+	0.135021i	0.993367	+	0.114983i	$0.0366815\pi$
$577$	−0.154498	+	3.24331i	−0.00643183	+	0.135021i	−0.999799	+	0.0200372i	$0.993622\pi$
$578$	−14.8338	+	9.12070i	−0.617005	+	0.379371i
$579$	9.11910	+	27.2458i	0.378977	+	1.13230i
$580$	14.8426	+	12.6611i	0.616304	+	0.525725i
$581$	12.5911	+	1.81033i	0.522369	+	0.0751053i
$582$	2.74104	+	24.2289i	0.113620	+	1.00432i
$583$	−5.40242	−	6.86974i	−0.223745	−	0.284515i
$584$	0.709240	+	2.52897i	0.0293486	+	0.104649i
$585$	−0.420619	−	1.54896i	−0.0173904	−	0.0640415i
$586$	−8.41126	+	2.72475i	−0.347466	+	0.112558i
$587$	2.96514	+	4.16396i	0.122385	+	0.171865i	0.871223	−	0.490888i	$-0.163327\pi$
$587$	2.96514	+	4.16396i	0.122385	+	0.171865i	−0.748838	+	0.662753i	$0.769388\pi$
$588$	−4.38792	−	15.0817i	−0.180955	−	0.621960i
$589$	2.55385	−	1.64126i	0.105230	−	0.0676270i
$590$	−8.34789	+	0.231082i	−0.343677	+	0.00951348i
$591$	16.7126	+	26.5993i	0.687466	+	1.09415i
$592$	−1.11670	−	0.693445i	−0.0458961	−	0.0285004i
$593$	−12.0063	+	15.2673i	−0.493040	+	0.626951i	−0.967361	−	0.253401i	$-0.918451\pi$
$593$	−12.0063	+	15.2673i	−0.493040	+	0.626951i	0.474322	+	0.880352i	$0.342693\pi$
$594$	8.71285	+	3.04476i	0.357493	+	0.124928i
$595$	−3.42111	−	2.96441i	−0.140252	−	0.121529i
$596$	−23.1432	+	12.1590i	−0.947981	+	0.498054i
$597$	−23.2050	+	23.8439i	−0.949717	+	0.975865i
$598$	0.562539	+	0.377567i	0.0230039	+	0.0154399i
$599$	−15.4293	−	7.95438i	−0.630426	−	0.325007i	0.113231	−	0.993569i	$-0.463880\pi$
$599$	−15.4293	−	7.95438i	−0.630426	−	0.325007i	−0.743657	+	0.668561i	$0.766910\pi$
$600$	−8.24656	−	13.4868i	−0.336664	−	0.550595i
$601$	−5.24221	+	21.6087i	−0.213834	+	0.881437i	0.759215	+	0.650840i	$0.225583\pi$
$601$	−5.24221	+	21.6087i	−0.213834	+	0.881437i	−0.973049	+	0.230597i	$0.925932\pi$
$602$	3.00849	−	18.3247i	0.122617	−	0.746860i
$603$	−17.4113	+	17.3161i	−0.709043	+	0.705165i
$604$	6.26433	−	18.5638i	0.254892	−	0.755349i
$605$	12.1934	+	2.95808i	0.495731	+	0.120263i
$606$	5.01786	−	5.99935i	0.203837	−	0.243707i
$607$	2.70028	−	5.23782i	0.109601	−	0.212596i	−0.827656	−	0.561236i	$-0.810326\pi$
$607$	2.70028	−	5.23782i	0.109601	−	0.212596i	0.937257	+	0.348640i	$0.113356\pi$
$608$	43.0334	−	14.6810i	1.74523	−	0.595392i
$609$	−14.2781	−	13.8956i	−0.578579	−	0.563076i
$610$	−8.57449	−	11.3621i	−0.347171	−	0.460040i
$611$	−0.0823709	+	0.0950611i	−0.00333237	+	0.00384576i
$612$	12.7849	−	2.29616i	0.516798	−	0.0928166i
$613$	28.0984	+	22.0969i	1.13489	+	0.892484i	0.995215	−	0.0977140i	$-0.0311530\pi$
$613$	28.0984	+	22.0969i	1.13489	+	0.892484i	0.139671	+	0.990198i	$0.455395\pi$
$614$	4.09252	+	0.276770i	0.165161	+	0.0111695i
$615$	−20.6979	+	13.0047i	−0.834620	+	0.524401i
$616$	5.33282	+	1.63665i	0.214866	+	0.0659425i
$617$	−5.66757	−	8.81892i	−0.228168	−	0.355036i	0.708227	−	0.705985i	$-0.249495\pi$
$617$	−5.66757	−	8.81892i	−0.228168	−	0.355036i	−0.936395	+	0.350949i	$0.885859\pi$
$618$	9.33194	+	19.5250i	0.375386	+	0.785410i
$619$	−27.4318	+	19.5341i	−1.10258	+	0.785140i	−0.978318	−	0.207110i	$-0.933594\pi$
$619$	−27.4318	+	19.5341i	−1.10258	+	0.785140i	−0.124258	+	0.992250i	$0.539655\pi$
$620$	−0.994480	+	0.150859i	−0.0399393	+	0.00605864i
$621$	5.67850	+	2.47795i	0.227870	+	0.0994366i
$622$	18.9645	+	27.7876i	0.760409	+	1.11418i
$623$	−3.75580	+	2.95359i	−0.150473	+	0.118333i
$624$	2.58966	+	1.02092i	0.103669	+	0.0408697i
$625$	−0.220102	+	1.53085i	−0.00880410	+	0.0612338i
$626$	11.2720	−	18.6551i	0.450519	−	0.745608i
$627$	16.5815	−	5.54979i	0.662203	−	0.221637i
$628$	−7.14503	−	17.4542i	−0.285118	−	0.696498i
$629$	−0.710631	−	0.0338515i	−0.0283347	−	0.00134975i
$630$	−4.12197	−	7.85551i	−0.164223	−	0.312971i
$631$	−14.9631	+	5.17877i	−0.595670	+	0.206163i	−0.608234	−	0.793758i	$-0.708122\pi$
$631$	−14.9631	+	5.17877i	−0.595670	+	0.206163i	0.0125641	+	0.999921i	$0.496001\pi$
$632$	−0.0372064	−	1.04990i	−0.00147999	−	0.0417627i
$633$	−6.18424	−	15.9171i	−0.245802	−	0.632649i
$634$	22.5417	+	8.30828i	0.895246	+	0.329964i
$635$	16.3449	−	6.54352i	0.648629	−	0.259672i
$636$	−17.4040	−	16.6770i	−0.690112	−	0.661286i
$637$	−0.429502	−	1.77043i	−0.0170175	−	0.0701471i
$638$	−12.7034	+	2.81506i	−0.502934	+	0.111449i
$639$	0.155453	+	5.72295i	0.00614961	+	0.226396i
$640$	−15.0018	−	1.38224i	−0.593000	−	0.0546378i
$641$	−3.03653	+	1.75314i	−0.119936	+	0.0692449i	−0.558768	−	0.829324i	$-0.688726\pi$
$641$	−3.03653	+	1.75314i	−0.119936	+	0.0692449i	0.438832	+	0.898569i	$0.355392\pi$
$642$	32.6075	+	18.0747i	1.28692	+	0.713351i
$643$	13.1414	−	6.00147i	0.518246	−	0.236675i	−0.139081	−	0.990281i	$-0.544415\pi$
$643$	13.1414	−	6.00147i	0.518246	−	0.236675i	0.657326	+	0.753606i	$0.271687\pi$
$644$	3.48706	+	1.36475i	0.137409	+	0.0537788i
$645$	0.720734	+	19.2733i	0.0283789	+	0.758884i
$646$	16.4827	−	18.2734i	0.648504	−	0.718956i
$647$	18.8067	+	7.52906i	0.739367	+	0.295998i	0.710608	−	0.703589i	$-0.248420\pi$
$647$	18.8067	+	7.52906i	0.739367	+	0.295998i	0.0287592	+	0.999586i	$0.490844\pi$
$648$	24.9691	+	4.95405i	0.980880	+	0.194613i
$649$	3.23077	−	4.53699i	0.126819	−	0.178092i
$650$	−0.884936	−	1.60582i	−0.0347101	−	0.0629853i
$651$	1.02352	−	0.0871867i	0.0401149	−	0.00341712i
$652$	−15.1458	−	4.32002i	−0.593156	−	0.169185i
$653$	9.67162	+	18.7603i	0.378480	+	0.734148i	0.998737	−	0.0502505i	$-0.0160020\pi$
$653$	9.67162	+	18.7603i	0.378480	+	0.734148i	−0.620257	+	0.784399i	$0.712972\pi$
$654$	−35.1701	−	7.88492i	−1.37526	−	0.308325i
$655$	2.98461	−	10.1646i	0.116618	−	0.397165i
$656$	3.37530	−	42.2592i	0.131783	−	1.64995i
$657$	1.10525	+	2.55724i	0.0431197	+	0.0997674i
$658$	−0.330817	+	0.611467i	−0.0128966	+	0.0238375i
$659$	−4.75584	+	0.454128i	−0.185261	+	0.0176903i	−0.187274	−	0.982308i	$-0.559965\pi$
$659$	−4.75584	+	0.454128i	−0.185261	+	0.0176903i	0.00201302	+	0.999998i	$0.499359\pi$
$660$	−5.76599	−	0.564977i	−0.224441	−	0.0219917i
$661$	−3.15566	+	0.926587i	−0.122741	+	0.0360400i	−0.342526	−	0.939508i	$-0.611283\pi$
$661$	−3.15566	+	0.926587i	−0.122741	+	0.0360400i	0.219785	+	0.975548i	$0.429464\pi$
$662$	−18.5979	+	15.4773i	−0.722830	+	0.601544i
$663$	1.49336	−	0.199154i	0.0579972	−	0.00773451i
$664$	12.6214	−	19.1232i	0.489805	−	0.742125i
$665$	−15.2881	−	6.98184i	−0.592847	−	0.270744i
$666$	−1.27239	−	0.569998i	−0.0493041	−	0.0220870i
$667$	−8.64554	+	1.24304i	−0.334757	+	0.0481307i
$668$	7.80623	−	12.3562i	0.302032	−	0.478076i
$669$	−11.9325	+	14.8583i	−0.461337	+	0.574455i
$670$	8.05196	−	13.1442i	0.311074	−	0.507806i
$671$	9.49367			0.366499
$672$	15.1952	+	2.41243i	0.586166	+	0.0930616i
$673$	−3.68981	−	25.6632i	−0.142232	−	0.989242i	−0.928493	−	0.371349i	$-0.878895\pi$
$673$	−3.68981	−	25.6632i	−0.142232	−	0.989242i	0.786262	−	0.617894i	$-0.212014\pi$
$674$	3.93294	−	5.29645i	0.151491	−	0.204012i
$675$	−10.5864	−	13.0024i	−0.407472	−	0.500464i
$676$	−23.4387	−	10.4854i	−0.901488	−	0.403283i
$677$	−18.8629	+	19.7828i	−0.724959	+	0.760315i	−0.978329	−	0.207055i	$-0.933612\pi$
$677$	−18.8629	+	19.7828i	−0.724959	+	0.760315i	0.253371	+	0.967369i	$0.418461\pi$
$678$	6.40169	−	0.111738i	0.245855	−	0.00429126i
$679$	4.40383	+	14.9981i	0.169004	+	0.575573i
$680$	−7.45763	+	3.29664i	−0.285987	+	0.126420i
$681$	−2.44501	−	1.60686i	−0.0936928	−	0.0615750i
$682$	0.319223	−	0.590037i	0.0122237	−	0.0225937i
$683$	33.7153	−	6.49810i	1.29008	−	0.248643i	0.502352	−	0.864663i	$-0.332468\pi$
$683$	33.7153	−	6.49810i	1.29008	−	0.248643i	0.787730	+	0.616021i	$0.211256\pi$
$684$	43.1428	−	21.5529i	1.64961	−	0.824095i
$685$	−18.6936	−	5.48894i	−0.714247	−	0.209722i
$686$	−11.2811	−	22.9961i	−0.430715	−	0.877993i
$687$	−25.3438	−	5.15383i	−0.966925	−	0.196631i
$688$	−27.5441	−	18.9777i	−1.05011	−	0.723519i
$689$	−1.92928	−	2.02337i	−0.0734999	−	0.0770844i
$690$	−3.83112	−	0.669266i	−0.145848	−	0.0254785i
$691$	3.27757	+	2.33395i	0.124685	+	0.0887877i	0.640698	−	0.767793i	$-0.278645\pi$
$691$	3.27757	+	2.33395i	0.124685	+	0.0887877i	−0.516013	+	0.856581i	$0.672584\pi$
$692$	42.7947	+	21.6441i	1.62681	+	0.822786i
$693$	5.83804	+	0.961577i	0.221769	+	0.0365273i
$694$	−3.59638	+	3.98708i	−0.136517	+	0.151347i
$695$	−1.95007	−	2.25050i	−0.0739702	−	0.0853662i
$696$	−33.6068	+	12.5884i	−1.27386	+	0.477161i
$697$	−9.53155	−	20.8712i	−0.361033	−	0.790552i
$698$	20.6823	−	3.56035i	0.782836	−	0.134761i
$699$	2.31021	+	0.356297i	0.0873802	+	0.0134764i
$700$	−6.69551	−	7.60712i	−0.253066	−	0.287522i
$701$	1.94582	−	10.0959i	0.0734928	−	0.381317i	−0.926495	−	0.376308i	$-0.877194\pi$
$701$	1.94582	−	10.0959i	0.0734928	−	0.381317i	0.999987	−	0.00500886i	$-0.00159438\pi$
$702$	2.86717	+	0.704656i	0.108214	+	0.0265955i
$703$	−2.56695	+	0.622735i	−0.0968143	+	0.0234869i
$704$	6.76290	−	7.43118i	0.254886	−	0.280073i
$705$	0.210497	−	0.690688i	0.00792776	−	0.0260128i
$706$	16.3370	+	6.02139i	0.614851	+	0.226618i
$707$	2.50693	−	4.34214i	0.0942830	−	0.163303i
$708$	7.07295	−	13.6367i	0.265818	−	0.512499i
$709$	−14.2973	−	41.3093i	−0.536946	−	1.55140i	−0.808207	−	0.588898i	$-0.799562\pi$
$709$	−14.2973	−	41.3093i	−0.536946	−	1.55140i	0.271261	−	0.962506i	$-0.412559\pi$
$710$	−0.943576	−	3.46768i	−0.0354118	−	0.130140i
$711$	−0.188469	−	1.09823i	−0.00706814	−	0.0411868i
$712$	1.92704	+	8.38787i	0.0722189	+	0.314349i
$713$	0.243468	−	0.378844i	0.00911796	−	0.0141878i
$714$	7.82031	−	2.86041i	0.292668	−	0.107048i
$715$	−0.665131	−	0.0956314i	−0.0248745	−	0.00357641i
$716$	−23.9496	+	17.3357i	−0.895038	+	0.647864i
$717$	−30.3733	−	0.310480i	−1.13431	−	0.0115951i
$718$	−22.5707	−	33.0714i	−0.842330	−	1.23421i
$719$	−0.423487	−	8.89009i	−0.0157934	−	0.331544i	−0.992912	−	0.118850i	$-0.962079\pi$
$719$	−0.423487	−	8.89009i	−0.0157934	−	0.331544i	0.977119	−	0.212694i	$-0.0682238\pi$
$720$	−15.9647	+	0.681374i	−0.594970	+	0.0253933i
$721$	8.04705	+	11.3005i	0.299688	+	0.420853i
$722$	27.9567	−	58.1232i	1.04044	−	2.16312i
$723$	16.3705	+	1.73222i	0.608824	+	0.0644220i
$724$	39.3824	+	5.35120i	1.46364	+	0.198876i
$725$	22.3378	+	7.73120i	0.829607	+	0.287130i
$726$	−15.6333	+	16.9794i	−0.580207	+	0.630166i
$727$	18.0993	−	23.0151i	0.671266	−	0.853584i	−0.324464	−	0.945898i	$-0.605184\pi$
$727$	18.0993	−	23.0151i	0.671266	−	0.853584i	0.995730	+	0.0923141i	$0.0294264\pi$
$728$	1.74799	+	0.359026i	0.0647849	+	0.0133064i
$729$	26.9492	+	1.65489i	0.998120	+	0.0612922i
$730$	−1.05341	−	1.39588i	−0.0389883	−	0.0516638i
$731$	−18.0215	−	1.72084i	−0.666549	−	0.0636477i
$732$	25.9270	−	3.66232i	0.958288	−	0.135363i
$733$	−15.9478	−	8.22164i	−0.589044	−	0.303673i	0.137817	−	0.990458i	$-0.455991\pi$
$733$	−15.9478	−	8.22164i	−0.589044	−	0.303673i	−0.726861	+	0.686784i	$0.759022\pi$
$734$	−0.967961	+	48.5726i	−0.0357281	+	1.79285i
$735$	6.38023	+	8.28604i	0.235338	+	0.305635i
$736$	4.90210	−	4.63287i	0.180694	−	0.170770i
$737$	3.76266	+	9.56735i	0.138599	+	0.352418i
$738$	−2.46425	−	44.8979i	−0.0907104	−	1.65271i
$739$	−1.78939	−	0.434102i	−0.0658238	−	0.0159687i	0.202712	−	0.979238i	$-0.435025\pi$
$739$	−1.78939	−	0.434102i	−0.0658238	−	0.0159687i	−0.268536	+	0.963270i	$0.586540\pi$
$740$	0.860632	+	0.158967i	0.0316375	+	0.00584373i
$741$	5.11159	−	2.27153i	0.187779	−	0.0834468i
$742$	−12.8303	−	8.61153i	−0.471016	−	0.316139i
$743$	31.9976	+	3.05540i	1.17388	+	0.112092i	0.663715	−	0.747985i	$-0.268979\pi$
$743$	31.9976	+	3.05540i	1.17388	+	0.112092i	0.510164	+	0.860077i	$0.329585\pi$
$744$	0.644175	−	1.73452i	0.0236166	−	0.0635906i
$745$	11.3985	−	13.1545i	0.417608	−	0.481945i
$746$	−2.71286	−	21.9672i	−0.0993250	−	0.804275i
$747$	10.5455	−	21.8955i	0.385840	−	0.801115i
$748$	1.24110	−	5.29464i	0.0453793	−	0.193591i
$749$	22.5855	+	7.81693i	0.825257	+	0.285624i
$750$	21.3791	+	16.2170i	0.780655	+	0.592160i
$751$	26.4194	+	41.1093i	0.964056	+	1.50010i	0.862990	+	0.505221i	$0.168589\pi$
$751$	26.4194	+	41.1093i	0.964056	+	1.50010i	0.101067	+	0.994880i	$0.467775\pi$
$752$	0.742100	+	1.00868i	0.0270616	+	0.0367827i
$753$	0.377917	−	6.52862i	0.0137721	−	0.237916i
$754$	−3.95978	+	1.28274i	−0.144207	+	0.0467145i
$755$	0.620684	+	13.0298i	0.0225890	+	0.474202i
$756$	16.3145	+	0.373935i	0.593351	+	0.0135999i
$757$	8.90886	−	7.00600i	0.323798	−	0.254638i	−0.443006	−	0.896518i	$-0.646088\pi$
$757$	8.90886	−	7.00600i	0.323798	−	0.254638i	0.766804	+	0.641881i	$0.221846\pi$
$758$	33.4460	−	33.7062i	1.21481	−	1.22426i
$759$	1.89546	−	1.77068i	0.0688009	−	0.0642718i
$760$	−23.1186	+	19.5447i	−0.838601	+	0.708959i
$761$	5.60040	−	8.71440i	0.203014	−	0.315897i	−0.724786	−	0.688974i	$-0.758061\pi$
$761$	5.60040	−	8.71440i	0.203014	−	0.315897i	0.927800	+	0.373078i	$0.121698\pi$
$762$	−4.04892	+	32.1324i	−0.146677	+	1.16403i
$763$	−23.0797	−	1.09942i	−0.835542	−	0.0398018i
$764$	−3.85065	−	37.2714i	−0.139312	−	1.34843i
$765$	−7.36955	+	4.52597i	−0.266447	+	0.163637i
$766$	−39.2144	+	14.7995i	−1.41687	+	0.534729i
$767$	0.890871	−	1.54303i	0.0321675	−	0.0557157i
$768$	15.6026	−	22.9032i	0.563011	−	0.826449i
$769$	18.7902	−	7.52247i	0.677593	−	0.271267i	−0.00723306	−	0.999974i	$-0.502302\pi$
$769$	18.7902	−	7.52247i	0.677593	−	0.271267i	0.684826	+	0.728706i	$0.259878\pi$
$770$	−3.70354	+	0.279309i	−0.133466	+	0.0100656i
$771$	23.6805	+	11.1084i	0.852832	+	0.400061i
$772$	33.1253	−	1.83532i	1.19221	−	0.0660547i
$773$	−4.65094	+	24.1314i	−0.167283	+	0.867945i	0.797183	+	0.603738i	$0.206323\pi$
$773$	−4.65094	+	24.1314i	−0.167283	+	0.867945i	−0.964466	+	0.264208i	$0.914890\pi$
$774$	−31.6508	−	16.0285i	−1.13767	−	0.576133i
$775$	−1.05545	+	0.609365i	−0.0379129	+	0.0218890i
$776$	27.8181	+	4.34599i	0.998612	+	0.156012i
$777$	−0.866391	−	0.219585i	−0.0310816	−	0.00787757i
$778$	10.0558	−	47.1037i	0.360518	−	1.68875i
$779$	−55.7865	−	64.3811i	−1.99876	−	2.30669i
$780$	−1.85335	−	0.00458311i	−0.0663604	−	0.000164102i
$781$	2.22517	+	0.890822i	0.0796227	+	0.0318761i
$782$	1.09806	−	3.48147i	0.0392664	−	0.124497i
$783$	−33.5325	+	18.0124i	−1.19835	+	0.643709i
$784$	−18.1348	+	0.281072i	−0.647671	+	0.0100383i
$785$	8.66535	+	9.08796i	0.309280	+	0.324363i
$786$	13.6918	+	13.8668i	0.488371	+	0.494611i
$787$	23.4750	+	45.5351i	0.836792	+	1.62315i	0.780852	+	0.624717i	$0.214785\pi$
$787$	23.4750	+	45.5351i	0.836792	+	1.62315i	0.0559407	+	0.998434i	$0.482184\pi$
$788$	34.7241	−	10.4889i	1.23699	−	0.373650i
$789$	−21.0050	−	30.1449i	−0.747799	−	1.07319i
$790$	0.277833	+	0.641917i	0.00988485	+	0.0228384i
$791$	4.03033	−	0.776781i	0.143302	−	0.0276192i
$792$	6.05114	−	8.77285i	0.215018	−	0.311730i
$793$	3.02324	−	0.288684i	0.107358	−	0.0102515i
$794$	−31.3440	+	28.7162i	−1.11236	+	1.01910i
$795$	14.8374	+	6.11669i	0.526228	+	0.216937i
$796$	19.4666	+	33.1218i	0.689976	+	1.17397i
$797$	−20.7456	+	21.7574i	−0.734847	+	0.770686i	−0.980043	−	0.198788i	$-0.936299\pi$
$797$	−20.7456	+	21.7574i	−0.734847	+	0.770686i	0.245195	+	0.969474i	$0.421148\pi$
$798$	24.8669	−	18.3700i	0.880279	−	0.650291i
$799$	0.616506	+	0.281549i	0.0218104	+	0.00996048i
$800$	−17.5369	+	5.06507i	−0.620023	+	0.179077i
$801$	3.21875	+	8.54214i	0.113729	+	0.301822i
$802$	1.78995	−	4.22510i	0.0632054	−	0.149193i
$803$	1.16633			0.0411589
$804$	13.9665	+	24.6767i	0.492559	+	0.870279i
$805$	−2.49317			−0.0878728
$806$	0.0837140	−	0.197603i	0.00294870	−	0.00696027i
$807$	−6.55855	−	3.87650i	−0.230872	−	0.136459i
$808$	−5.14861	−	7.41980i	−0.181128	−	0.261028i
$809$	33.0928	+	15.1130i	1.16348	+	0.531344i	0.901096	−	0.433620i	$-0.142764\pi$
$809$	33.0928	+	15.1130i	1.16348	+	0.531344i	0.262384	+	0.964963i	$0.415491\pi$
$810$	−16.6832	+	2.98737i	−0.586188	+	0.104966i
$811$	21.7316	−	22.7915i	0.763101	−	0.800317i	−0.221495	−	0.975161i	$-0.571094\pi$
$811$	21.7316	−	22.7915i	0.763101	−	0.800317i	0.984596	+	0.174844i	$0.0559423\pi$
$812$	−19.8339	+	11.6570i	−0.696033	+	0.409079i
$813$	−14.3093	+	34.7104i	−0.501850	+	1.21735i
$814$	−0.430391	+	0.394308i	−0.0150852	+	0.0138205i
$815$	10.4388	−	0.996785i	0.365656	−	0.0349159i
$816$	1.34694	−	14.9383i	0.0471524	−	0.522945i
$817$	−65.9995	+	12.7204i	−2.30903	+	0.445029i
$818$	2.31275	+	5.34347i	0.0808634	+	0.186830i
$819$	1.88835	+	0.128688i	0.0659843	+	0.00449674i
$820$	8.16177	+	27.0201i	0.285021	+	0.943583i
$821$	17.8897	+	34.7012i	0.624355	+	1.21108i	0.962831	+	0.270105i	$0.0870584\pi$
$821$	17.8897	+	34.7012i	0.624355	+	1.21108i	−0.338476	+	0.940975i	$0.609911\pi$
$822$	25.5021	−	25.1804i	0.889489	−	0.878268i
$823$	24.1071	+	25.2828i	0.840321	+	0.881303i	0.994283	−	0.106774i	$-0.0340520\pi$
$823$	24.1071	+	25.2828i	0.840321	+	0.881303i	−0.153963	+	0.988077i	$0.549204\pi$
$824$	24.5925	−	4.42994i	0.856719	−	0.154324i
$825$	−6.75524	+	1.90873i	−0.235187	+	0.0664536i
$826$	2.96218	−	9.39182i	0.103067	−	0.326783i
$827$	−6.86677	−	2.74904i	−0.238781	−	0.0955935i	0.249186	−	0.968456i	$-0.419837\pi$
$827$	−6.86677	−	2.74904i	−0.238781	−	0.0955935i	−0.487967	+	0.872862i	$0.662261\pi$
$828$	4.49339	−	5.56689i	0.156156	−	0.193463i
$829$	−30.2719	−	34.9356i	−1.05139	−	1.21336i	−0.976353	−	0.216183i	$-0.930639\pi$
$829$	−30.2719	−	34.9356i	−1.05139	−	1.21336i	−0.0750329	−	0.997181i	$-0.523906\pi$
$830$	−3.18499	+	14.9192i	−0.110553	+	0.517854i
$831$	−11.5730	+	45.6621i	−0.401462	+	1.58400i
$832$	1.92766	−	2.57209i	0.0668297	−	0.0891711i
$833$	−8.50109	+	4.90810i	−0.294545	+	0.170056i
$834$	5.35983	−	1.13038i	0.185596	−	0.0391418i
$835$	−1.84161	+	9.55518i	−0.0637315	+	0.330671i
$836$	−1.11696	−	20.1598i	−0.0386308	−	0.697240i
$837$	0.430318	−	1.91476i	0.0148740	−	0.0661836i
$838$	13.8975	−	1.04810i	0.480080	−	0.0362061i
$839$	43.6784	−	17.4862i	1.50795	−	0.603691i	0.537127	−	0.843501i	$-0.319510\pi$
$839$	43.6784	−	17.4862i	1.50795	−	0.603691i	0.970820	+	0.239811i	$0.0770853\pi$
$840$	−10.0065	+	2.19148i	−0.345257	+	0.0756131i
$841$	12.3309	−	21.3578i	0.425205	−	0.736476i
$842$	−1.92212	+	0.725407i	−0.0662405	+	0.0249992i
$843$	16.3702	+	5.85384i	0.563820	+	0.201617i
$844$	−19.6136	+	2.02636i	−0.675128	+	0.0697501i
$845$	17.0765	+	0.813455i	0.587450	+	0.0279837i
$846$	0.923502	+	0.954623i	0.0317506	+	0.0328206i
$847$	−7.99927	+	12.4471i	−0.274858	+	0.427688i
$848$	−23.8858	+	14.2885i	−0.820242	+	0.490671i
$849$	−12.3440	−	13.2139i	−0.423645	−	0.453498i
$850$	−6.95866	+	7.01279i	−0.238680	+	0.240537i
$851$	−0.308001	+	0.242214i	−0.0105581	+	0.00830300i
$852$	6.42051	+	1.57442i	0.219963	+	0.0539388i
$853$	−0.836479	−	17.5599i	−0.0286405	−	0.601238i	−0.966877	−	0.255243i	$-0.917845\pi$
$853$	−0.836479	−	17.5599i	−0.0286405	−	0.601238i	0.938236	−	0.345995i	$-0.112459\pi$
$854$	15.9688	−	5.17295i	0.546441	−	0.177015i
$855$	−21.5189	+	23.8319i	−0.735932	+	0.815032i
$856$	30.0847	−	30.7924i	1.02827	−	1.05246i
$857$	−27.4453	−	42.7058i	−0.937515	−	1.45880i	−0.887901	−	0.460034i	$-0.847837\pi$
$857$	−27.4453	−	42.7058i	−0.937515	−	1.45880i	−0.0496139	−	0.998768i	$-0.515799\pi$
$858$	0.747029	−	0.984821i	0.0255031	−	0.0336212i
$859$	35.1564	+	12.1678i	1.19952	+	0.415158i	0.852514	−	0.522704i	$-0.175077\pi$
$859$	35.1564	+	12.1678i	1.19952	+	0.415158i	0.347007	+	0.937863i	$0.387198\pi$
$860$	21.6827	+	5.08258i	0.739373	+	0.173315i
$861$	−6.50920	−	28.0810i	−0.221833	−	0.956999i
$862$	−4.90284	−	39.7003i	−0.166991	−	1.35220i
$863$	18.4755	−	21.3219i	0.628915	−	0.725807i	−0.348459	−	0.937324i	$-0.613295\pi$
$863$	18.4755	−	21.3219i	0.628915	−	0.725807i	0.977374	+	0.211517i	$0.0678405\pi$
$864$	13.1413	−	26.2927i	0.447074	−	0.894497i
$865$	−31.7851	−	3.03511i	−1.08073	−	0.103197i
$866$	−8.57002	−	5.75207i	−0.291221	−	0.195463i
$867$	8.66082	+	19.4893i	0.294137	+	0.661892i
$868$	0.215447	−	1.16641i	0.00731274	−	0.0395905i
$869$	−0.453357	−	0.109983i	−0.0153791	−	0.00373092i
$870$	17.7818	−	15.9598i	0.602861	−	0.541088i
$871$	1.48913	+	2.93228i	0.0504574	+	0.0993567i
$872$	−19.5200	+	36.7576i	−0.661030	+	1.24477i
$873$	29.8572	+	0.610472i	1.01051	+	0.0206614i
$874$	0.270045	−	13.5509i	0.00913440	−	0.458367i
$875$	15.2899	+	7.88248i	0.516892	+	0.266476i
$876$	3.18522	−	0.449929i	0.107619	−	0.0152017i
$877$	36.4443	+	3.48001i	1.23064	+	0.117512i	0.690041	−	0.723771i	$-0.257593\pi$
$877$	36.4443	+	3.48001i	1.23064	+	0.117512i	0.540596	+	0.841282i	$0.318199\pi$
$878$	20.9420	+	27.7505i	0.706760	+	0.936535i
$879$	1.94055	+	10.6534i	0.0654531	+	0.359330i
$880$	−2.38983	+	6.24845i	−0.0805612	+	0.210635i
$881$	27.6077	−	35.1060i	0.930127	−	1.18275i	−0.0527723	−	0.998607i	$-0.516806\pi$
$881$	27.6077	−	35.1060i	0.930127	−	1.18275i	0.982899	−	0.184146i	$-0.0589518\pi$
$882$	−19.0211	+	2.87535i	−0.640473	+	0.0968180i
$883$	−30.9077	−	10.6973i	−1.04013	−	0.359992i	−0.246980	−	0.969021i	$-0.579438\pi$
$883$	−30.9077	−	10.6973i	−1.04013	−	0.359992i	−0.793148	+	0.609029i	$0.791559\pi$
$884$	0.234227	−	1.72381i	0.00787791	−	0.0579779i
$885$	−1.07625	+	10.1712i	−0.0361778	+	0.341900i
$886$	−16.4401	+	34.1798i	−0.552317	+	1.14829i
$887$	−23.1530	−	32.5138i	−0.777400	−	1.09171i	−0.993331	−	0.115297i	$-0.963218\pi$
$887$	−23.1530	−	32.5138i	−0.777400	−	1.09171i	0.215931	−	0.976409i	$-0.430721\pi$
$888$	−1.02328	+	1.24287i	−0.0343389	+	0.0417081i
$889$	0.987881	+	20.7382i	0.0331325	+	0.695536i
$890$	−3.23015	−	4.73294i	−0.108275	−	0.158648i
$891$	5.11215	−	10.0818i	0.171264	−	0.337753i
$892$	12.9025	+	17.8250i	0.432007	+	0.596826i
$893$	2.49073	+	0.358114i	0.0833492	+	0.0119838i
$894$	10.9986	+	30.0700i	0.367849	+	1.00569i
$895$	10.6423	−	16.5598i	0.355734	−	0.553532i
$896$	7.32639	−	16.1846i	0.244757	−	0.540689i
$897$	0.549762	−	0.621508i	0.0183560	−	0.0207515i
$898$	13.7628	+	50.5790i	0.459272	+	1.68784i
$899$	0.904903	+	2.61455i	0.0301802	+	0.0872000i
$900$	−17.7120	+	7.81863i	−0.590402	+	0.260621i
$901$	−7.53206	+	13.0459i	−0.250929	+	0.434622i
$902$	−17.6637	−	6.51036i	−0.588136	−	0.216771i
$903$	−21.7556	−	6.63032i	−0.723983	−	0.220643i
$904$	1.83036	−	7.16300i	0.0608768	−	0.238238i
$905$	−25.7159	+	6.23862i	−0.854826	+	0.207379i
$906$	−21.5167	−	10.6215i	−0.714843	−	0.352875i
$907$	−5.55063	+	28.7994i	−0.184305	+	0.956268i	0.765502	+	0.643433i	$0.222491\pi$
$907$	−5.55063	+	28.7994i	−0.184305	+	0.956268i	−0.949808	+	0.312834i	$0.898722\pi$
$908$	−2.53598	+	2.23208i	−0.0841596	+	0.0740742i
$909$	−6.46715	−	7.06631i	−0.214502	−	0.234375i
$910$	−1.17089	+	0.201563i	−0.0388146	+	0.00668174i
$911$	18.7747	+	41.1108i	0.622032	+	1.36206i	0.914032	+	0.405642i	$0.132952\pi$
$911$	18.7747	+	41.1108i	0.622032	+	1.36206i	−0.292000	+	0.956418i	$0.594321\pi$
$912$	−10.8273	−	54.6249i	−0.358528	−	1.80881i
$913$	−6.66293	−	7.68944i	−0.220511	−	0.254483i
$914$	9.86544	−	10.9372i	0.326320	−	0.361770i
$915$	−15.1862	+	8.56202i	−0.502042	+	0.283052i
$916$	−13.4781	+	26.6489i	−0.445330	+	0.880505i
$917$	10.1761	+	7.24637i	0.336045	+	0.239296i
$918$	−0.709437	−	15.8929i	−0.0234149	−	0.524544i
$919$	28.9336	+	30.3447i	0.954431	+	1.00098i	0.999998	+	0.00201684i	$0.000641982\pi$
$919$	28.9336	+	30.3447i	0.954431	+	1.00098i	−0.0455673	+	0.998961i	$0.514510\pi$
$920$	−1.91514	+	4.06195i	−0.0631404	+	0.133918i
$921$	1.00112	−	4.92298i	0.0329881	−	0.162218i
$922$	13.1393	+	26.7838i	0.432719	+	0.882079i
$923$	0.735687	+	0.216017i	0.0242154	+	0.00711029i
$924$	2.85348	−	6.20758i	0.0938726	−	0.204214i
$925$	1.04125	−	0.200684i	0.0342360	−	0.00659844i
$926$	−10.1468	+	18.7549i	−0.333445	+	0.616325i
$927$	25.2183	−	8.15482i	0.828278	−	0.267839i
$928$	3.75633	+	41.2683i	0.123308	+	1.35470i
$929$	4.76592	+	16.2312i	0.156365	+	0.532529i	0.999990	−	0.00440250i	$-0.00140137\pi$
$929$	4.76592	+	16.2312i	0.156365	+	0.532529i	−0.843626	+	0.536932i	$0.819583\pi$
$930$	0.0214991	+	1.23173i	0.000704983	+	0.0403900i
$931$	−25.1502	+	26.3768i	−0.824265	+	0.864464i
$932$	1.10220	−	2.46384i	0.0361039	−	0.0807057i
$933$	36.8139	−	18.5051i	1.20523	−	0.605829i
$934$	34.6951	−	46.7235i	1.13526	−	1.52884i
$935$	0.515285	+	3.58388i	0.0168516	+	0.117206i
$936$	1.66021	−	2.97770i	0.0542655	−	0.0973291i
$937$	−52.7537			−1.72339			−0.861695	−	0.507427i	$-0.830597\pi$
$937$	−52.7537			−1.72339			−0.861695	+	0.507427i	$0.830597\pi$
$938$	11.5421	+	14.0425i	0.376862	+	0.458504i
$939$	−20.8137	−	16.7152i	−0.679229	−	0.545479i
$940$	−0.704870	−	0.445313i	−0.0229903	−	0.0145245i
$941$	−25.5815	+	3.67807i	−0.833933	+	0.119902i	−0.546038	−	0.837760i	$-0.683865\pi$
$941$	−25.5815	+	3.67807i	−0.833933	+	0.119902i	−0.287895	+	0.957662i	$0.592956\pi$
$942$	−22.3491	+	5.83665i	−0.728175	+	0.190168i
$943$	−11.4950	−	5.24961i	−0.374330	−	0.170951i
$944$	−13.0260	−	12.0404i	−0.423960	−	0.391883i
$945$	−10.2058	+	3.72697i	−0.331996	+	0.121238i
$946$	−11.4169	+	9.50121i	−0.371195	+	0.308911i
$947$	−29.9349	+	8.78969i	−0.972754	+	0.285626i	−0.729230	−	0.684268i	$-0.760122\pi$
$947$	−29.9349	+	8.78969i	−0.972754	+	0.285626i	−0.243524	+	0.969895i	$0.578303\pi$
$948$	−1.28053	−	0.125472i	−0.0415898	−	0.00407515i
$949$	0.371415	−	0.0354659i	0.0120567	−	0.00115127i
$950$	−17.4540	+	32.2611i	−0.566282	+	1.04669i
$951$	13.7492	−	26.0134i	0.445848	−	0.843541i
$952$	−0.797368	−	9.58209i	−0.0258429	−	0.310557i
$953$	−6.26379	+	21.3325i	−0.202904	+	0.691027i	0.793672	+	0.608346i	$0.208167\pi$
$953$	−6.26379	+	21.3325i	−0.202904	+	0.691027i	−0.996576	+	0.0826815i	$0.973652\pi$
$954$	−23.0731	+	18.4164i	−0.747018	+	0.596254i
$955$	11.4316	+	22.1742i	0.369917	+	0.717539i
$956$	−9.62039	+	33.7287i	−0.311146	+	1.09086i
$957$	1.35257	+	15.8784i	0.0437224	+	0.513276i
$958$	1.55092	+	2.81431i	0.0501079	+	0.0909264i
$959$	13.3267	−	18.7147i	0.430341	−	0.604330i
$960$	−4.11613	+	17.9863i	−0.132848	+	0.580504i
$961$	28.6470	+	11.4685i	0.924096	+	0.369952i
$962$	−0.125067	+	0.138654i	−0.00403232	+	0.00447037i
$963$	27.2407	−	36.6451i	0.877820	−	1.18087i
$964$	6.92779	−	17.7011i	0.223129	−	0.570114i
$965$	−20.0926	+	9.17600i	−0.646805	+	0.295386i
$966$	2.22344	−	4.01118i	0.0715379	−	0.129058i
$967$	−30.4292	+	17.5683i	−0.978538	+	0.564959i	−0.901828	−	0.432094i	$-0.857775\pi$
$967$	−30.4292	+	17.5683i	−0.978538	+	0.564959i	−0.0767096	+	0.997053i	$0.524441\pi$
$968$	14.1345	+	22.5939i	0.454300	+	0.726197i
$969$	−19.5034	−	22.9785i	−0.626538	−	0.738177i
$970$	−18.3020	+	4.05569i	−0.587643	+	0.130220i
$971$	−2.44886	−	10.0943i	−0.0785875	−	0.323942i	0.918925	−	0.394432i	$-0.129059\pi$
$971$	−2.44886	−	10.0943i	−0.0785875	−	0.323942i	−0.997512	+	0.0704902i	$0.977544\pi$
$972$	10.0720	−	29.5052i	0.323058	−	0.946379i
$973$	3.26002	−	1.30512i	0.104511	−	0.0418401i
$974$	−3.87862	−	1.42956i	−0.124279	−	0.0458060i
$975$	−2.09315	+	0.813246i	−0.0670344	+	0.0260447i
$976$	3.83860	−	29.9904i	0.122870	−	0.959970i
$977$	−24.8445	+	8.59876i	−0.794845	+	0.275099i	−0.694161	−	0.719820i	$-0.744224\pi$
$977$	−24.8445	+	8.59876i	−0.794845	+	0.275099i	−0.100684	+	0.994918i	$0.532103\pi$
$978$	−7.70574	+	17.6836i	−0.246402	+	0.565458i
$979$	3.81739	+	0.181845i	0.122004	+	0.00581178i
$980$	11.1755	−	4.57480i	0.356989	−	0.146136i
$981$	−15.2877	+	41.4120i	−0.488100	+	1.32218i
$982$	−20.1843	+	33.4049i	−0.644105	+	1.06599i
$983$	2.67790	−	18.6252i	0.0854118	−	0.594052i	−0.901499	−	0.432782i	$-0.857532\pi$
$983$	2.67790	−	18.6252i	0.0854118	−	0.594052i	0.986910	−	0.161270i	$-0.0515589\pi$
$984$	−50.7505	−	10.9656i	−1.61787	−	0.349571i
$985$	−18.9840	+	14.9292i	−0.604882	+	0.475684i
$986$	12.6428	+	18.5247i	0.402629	+	0.589947i
$987$	0.688501	+	0.500964i	0.0219152	+	0.0159459i
$988$	−0.968712	−	6.38586i	−0.0308188	−	0.203161i
$989$	−8.12188	+	5.78357i	−0.258261	+	0.183907i
$990$	−1.62297	+	6.90759i	−0.0515813	+	0.219538i
$991$	−0.740302	−	1.15193i	−0.0235165	−	0.0365924i	0.829296	−	0.558809i	$-0.188742\pi$
$991$	−0.740302	−	1.15193i	−0.0235165	−	0.0365924i	−0.852813	+	0.522217i	$0.825105\pi$
$992$	−1.73485	−	1.24699i	−0.0550815	−	0.0395921i
$993$	15.7655	+	25.0918i	0.500301	+	0.796264i
$994$	4.22823	+	0.285947i	0.134111	+	0.00906970i
$995$	−20.1067	−	15.8121i	−0.637425	−	0.501277i
$996$	−21.1626	−	18.4293i	−0.670563	−	0.583955i
$997$	14.6521	−	16.9095i	0.464038	−	0.535529i	−0.474706	−	0.880145i	$-0.657445\pi$
$997$	14.6521	−	16.9095i	0.464038	−	0.535529i	0.938744	+	0.344616i	$0.111991\pi$
$998$	9.77936	+	12.9587i	0.309560	+	0.410202i
$999$	−0.898726	+	1.45193i	−0.0284344	+	0.0459370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.bd.a.35.17	yes	2640
3.2	odd	2	inner	804.2.bd.a.35.116	yes	2640
4.3	odd	2	inner	804.2.bd.a.35.3	yes	2640
12.11	even	2	inner	804.2.bd.a.35.130	yes	2640
67.23	even	33	inner	804.2.bd.a.23.130	yes	2640
201.23	odd	66	inner	804.2.bd.a.23.3	✓	2640
268.23	odd	66	inner	804.2.bd.a.23.116	yes	2640
804.23	even	66	inner	804.2.bd.a.23.17	yes	2640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.bd.a.23.3	✓	2640	201.23	odd	66	inner
804.2.bd.a.23.17	yes	2640	804.23	even	66	inner
804.2.bd.a.23.116	yes	2640	268.23	odd	66	inner
804.2.bd.a.23.130	yes	2640	67.23	even	33	inner
804.2.bd.a.35.3	yes	2640	4.3	odd	2	inner
804.2.bd.a.35.17	yes	2640	1.1	even	1	trivial
804.2.bd.a.35.116	yes	2640	3.2	odd	2	inner
804.2.bd.a.35.130	yes	2640	12.11	even	2	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.bd (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30218 - 0.551664i) q^{2} +(-0.881313 + 1.49107i) q^{3} +(1.39133 + 1.43673i) q^{4} +(-1.21127 - 0.553168i) q^{5} +(1.97020 - 1.45545i) q^{6} +(1.08361 - 1.13646i) q^{7} +(-1.01917 - 2.63843i) q^{8} +(-1.44658 - 2.62820i) q^{9} +O(q^{10})\)	\(q+(-1.30218 - 0.551664i) q^{2} +(-0.881313 + 1.49107i) q^{3} +(1.39133 + 1.43673i) q^{4} +(-1.21127 - 0.553168i) q^{5} +(1.97020 - 1.45545i) q^{6} +(1.08361 - 1.13646i) q^{7} +(-1.01917 - 2.63843i) q^{8} +(-1.44658 - 2.62820i) q^{9} +(1.27212 + 1.38854i) q^{10} +(-1.25029 + 0.119389i) q^{11} +(-3.36846 + 0.808366i) q^{12} +(-0.394523 + 0.0760380i) q^{13} +(-2.03800 + 0.882082i) q^{14} +(1.89232 - 1.31857i) q^{15} +(-0.128386 + 3.99794i) q^{16} +(0.992017 + 1.92424i) q^{17} +(0.433817 + 4.22040i) q^{18} +(5.54672 + 5.81724i) q^{19} +(-0.890526 - 2.50991i) q^{20} +(0.739539 + 2.61732i) q^{21} +(1.69397 + 0.534278i) q^{22} +(1.10694 + 0.443150i) q^{23} +(4.83228 + 0.805626i) q^{24} +(-2.11312 - 2.43868i) q^{25} +(0.555686 + 0.118629i) q^{26} +(5.19371 + 0.159317i) q^{27} +(3.14045 - 0.0243355i) q^{28} +(-6.34401 + 3.66271i) q^{29} +(-3.19155 + 0.673091i) q^{30} +(0.0714776 - 0.370861i) q^{31} +(2.37270 - 5.13520i) q^{32} +(0.923883 - 1.96949i) q^{33} +(-0.230245 - 3.05297i) q^{34} +(-1.94120 + 0.777139i) q^{35} +(1.76334 - 5.73504i) q^{36} +(-0.164311 + 0.284595i) q^{37} +(-4.01366 - 10.6350i) q^{38} +(0.234320 - 0.655274i) q^{39} +(-0.225005 + 3.75962i) q^{40} +(-10.5865 - 0.504295i) q^{41} +(0.480869 - 3.81619i) q^{42} +(-4.52097 + 7.03477i) q^{43} +(-1.91110 - 1.63023i) q^{44} +(0.298359 + 3.98366i) q^{45} +(-1.19696 - 1.18772i) q^{46} +(0.246085 - 0.193523i) q^{47} +(-5.84806 - 3.71487i) q^{48} +(0.215748 + 4.52911i) q^{49} +(1.40633 + 4.34132i) q^{50} +(-3.74346 - 0.216695i) q^{51} +(-0.658159 - 0.461029i) q^{52} +(3.76196 + 5.85372i) q^{53} +(-6.67524 - 3.07264i) q^{54} +(1.58049 + 0.547011i) q^{55} +(-4.10285 - 1.70079i) q^{56} +(-13.5623 + 3.14375i) q^{57} +(10.2816 - 1.26974i) q^{58} +(-2.90403 + 3.35143i) q^{59} +(4.52728 + 0.884179i) q^{60} +(-7.52455 - 0.718507i) q^{61} +(-0.297667 + 0.443495i) q^{62} +(-4.55437 - 1.20397i) q^{63} +(-5.92259 + 5.37801i) q^{64} +(0.519935 + 0.126135i) q^{65} +(-2.28956 + 2.05496i) q^{66} +(-2.25814 - 7.86770i) q^{67} +(-1.38439 + 4.10252i) q^{68} +(-1.63632 + 1.25996i) q^{69} +(2.95651 + 0.0589177i) q^{70} +(-1.69621 - 0.874459i) q^{71} +(-5.46000 + 6.49526i) q^{72} +(-0.924416 - 0.0882711i) q^{73} +(0.370964 - 0.279949i) q^{74} +(5.49856 - 1.00158i) q^{75} +(-0.640460 + 16.0629i) q^{76} +(-1.21915 + 1.55028i) q^{77} +(-0.666618 + 0.724017i) q^{78} +(0.351000 + 0.121482i) q^{79} +(2.36704 - 4.77156i) q^{80} +(-4.81483 + 7.60377i) q^{81} +(13.5072 + 6.49685i) q^{82} +(4.69899 + 6.59880i) q^{83} +(-2.73143 + 4.70408i) q^{84} +(-0.137169 - 2.87953i) q^{85} +(9.76793 - 6.66646i) q^{86} +(0.129692 - 12.6873i) q^{87} +(1.58926 + 3.17713i) q^{88} +(-3.01184 - 0.433038i) q^{89} +(1.80912 - 5.35202i) q^{90} +(-0.341096 + 0.530755i) q^{91} +(0.903429 + 2.20694i) q^{92} +(0.489985 + 0.433422i) q^{93} +(-0.427206 + 0.116245i) q^{94} +(-3.50067 - 10.1145i) q^{95} +(5.56585 + 8.06358i) q^{96} +(-4.97724 + 8.62084i) q^{97} +(2.21761 - 6.01672i) q^{98} +(2.12242 + 3.11331i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9}+O(q^{10}) \) 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9	\( 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9} - 46 q^{10} - 24 q^{12} - 88 q^{13} - 26 q^{16} - 23 q^{18} - 128 q^{22} - 22 q^{24} + 160 q^{25} + 44 q^{28} - 18 q^{30} - 44 q^{33} - 6 q^{34} - 35 q^{36} - 48 q^{37} - 92 q^{40} - 10 q^{42} + 40 q^{45} + 46 q^{46} - 11 q^{48} - 216 q^{49} - 76 q^{52} + 129 q^{54} - 42 q^{57} - 56 q^{58} - 90 q^{60} - 80 q^{61} - 48 q^{64} - 74 q^{66} - 4 q^{69} + 96 q^{70} - 20 q^{72} - 216 q^{73} + 76 q^{76} - 66 q^{78} - 16 q^{81} + 20 q^{82} - 55 q^{84} - 104 q^{85} - 30 q^{88} - 64 q^{90} - 192 q^{93} - 32 q^{94} - 205 q^{96} - 64 q^{97}+O(q^{100}) \) 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9 - 46 * q^10 - 24 * q^12 - 88 * q^13 - 26 * q^16 - 23 * q^18 - 128 * q^22 - 22 * q^24 + 160 * q^25 + 44 * q^28 - 18 * q^30 - 44 * q^33 - 6 * q^34 - 35 * q^36 - 48 * q^37 - 92 * q^40 - 10 * q^42 + 40 * q^45 + 46 * q^46 - 11 * q^48 - 216 * q^49 - 76 * q^52 + 129 * q^54 - 42 * q^57 - 56 * q^58 - 90 * q^60 - 80 * q^61 - 48 * q^64 - 74 * q^66 - 4 * q^69 + 96 * q^70 - 20 * q^72 - 216 * q^73 + 76 * q^76 - 66 * q^78 - 16 * q^81 + 20 * q^82 - 55 * q^84 - 104 * q^85 - 30 * q^88 - 64 * q^90 - 192 * q^93 - 32 * q^94 - 205 * q^96 - 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more