LMFDB - Embedded newform 770.2.bv.a.537.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(3,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 10, 48]))

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

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

chi := DirichletCharacter("770.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bv (of order $60$, degree $16$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$48$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			537.20
Character	$\chi$	$=$	770.537
Dual form			770.2.bv.a.423.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0523360 + 0.998630i) q^{2} +(0.752251 + 1.95968i) q^{3} +(-0.994522 - 0.104528i) q^{4} +(0.432112 + 2.19392i) q^{5} +(-1.99636 + 0.648658i) q^{6} +(2.50628 - 0.847671i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-1.04503 + 0.940951i) q^{9} +O(q^{10})$	\(q+(-0.0523360 + 0.998630i) q^{2} +(0.752251 + 1.95968i) q^{3} +(-0.994522 - 0.104528i) q^{4} +(0.432112 + 2.19392i) q^{5} +(-1.99636 + 0.648658i) q^{6} +(2.50628 - 0.847671i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-1.04503 + 0.940951i) q^{9} +(-2.21353 + 0.316699i) q^{10} +(0.421151 + 3.28978i) q^{11} +(-0.543288 - 2.02758i) q^{12} +(-3.67653 + 1.87329i) q^{13} +(0.715341 + 2.54721i) q^{14} +(-3.97432 + 2.49718i) q^{15} +(0.978148 + 0.207912i) q^{16} +(-0.220531 - 4.20798i) q^{17} +(-0.884969 - 1.09285i) q^{18} +(0.441745 + 4.20292i) q^{19} +(-0.200418 - 2.22707i) q^{20} +(3.54652 + 4.27385i) q^{21} +(-3.30731 + 0.248400i) q^{22} +(0.0879899 + 0.328383i) q^{23} +(2.05323 - 0.436428i) q^{24} +(-4.62656 + 1.89604i) q^{25} +(-1.67830 - 3.76953i) q^{26} +(2.98085 + 1.51882i) q^{27} +(-2.58116 + 0.581050i) q^{28} +(1.61696 - 2.22556i) q^{29} +(-2.28576 - 4.09957i) q^{30} +(-0.111571 - 0.524901i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-6.13010 + 3.30006i) q^{33} +4.21375 q^{34} +(2.94272 + 5.13229i) q^{35} +(1.13766 - 0.826561i) q^{36} +(10.2083 + 3.91858i) q^{37} +(-4.22028 + 0.221176i) q^{38} +(-6.43672 - 5.79565i) q^{39} +(2.23451 - 0.0835871i) q^{40} +(-6.66075 - 9.16774i) q^{41} +(-4.45361 + 3.31798i) q^{42} +(-1.34185 + 1.34185i) q^{43} +(-0.0749684 - 3.31578i) q^{44} +(-2.51594 - 1.88612i) q^{45} +(-0.332538 + 0.0706831i) q^{46} +(-7.98761 - 6.46824i) q^{47} +(0.328372 + 2.07326i) q^{48} +(5.56291 - 4.24901i) q^{49} +(-1.65130 - 4.71945i) q^{50} +(8.08040 - 3.59762i) q^{51} +(3.85220 - 1.47872i) q^{52} +(-4.58705 + 7.06344i) q^{53} +(-1.67274 + 2.89728i) q^{54} +(-7.03552 + 2.34552i) q^{55} +(-0.445166 - 2.60803i) q^{56} +(-7.90408 + 4.02733i) q^{57} +(2.13788 + 1.73122i) q^{58} +(0.712147 - 6.77562i) q^{59} +(4.21358 - 2.06807i) q^{60} +(1.70159 - 8.00534i) q^{61} +(0.530020 - 0.0839470i) q^{62} +(-1.82153 + 3.24413i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(-5.69851 - 7.25654i) q^{65} +(-2.97471 - 6.29441i) q^{66} +(-1.55099 + 5.78837i) q^{67} +(-0.220531 + 4.20798i) q^{68} +(-0.577335 + 0.419458i) q^{69} +(-5.27927 + 2.67008i) q^{70} +(1.64543 + 5.06410i) q^{71} +(0.765887 + 1.17936i) q^{72} +(5.65049 - 4.57568i) q^{73} +(-4.44747 + 9.98919i) q^{74} +(-7.19596 - 7.64028i) q^{75} -4.22607i q^{76} +(3.84417 + 7.88811i) q^{77} +(6.12458 - 6.12458i) q^{78} +(9.43552 - 8.49578i) q^{79} +(-0.0334724 + 2.23582i) q^{80} +(-1.17503 + 11.1796i) q^{81} +(9.50377 - 6.17182i) q^{82} +(0.105502 - 0.207060i) q^{83} +(-3.08035 - 4.62115i) q^{84} +(9.13667 - 2.30214i) q^{85} +(-1.26978 - 1.41023i) q^{86} +(5.57775 + 1.49455i) q^{87} +(3.31516 + 0.0986687i) q^{88} +(5.17427 - 8.96210i) q^{89} +(2.01521 - 2.41378i) q^{90} +(-7.62650 + 7.81148i) q^{91} +(-0.0531825 - 0.335781i) q^{92} +(0.944708 - 0.613501i) q^{93} +(6.87741 - 7.63814i) q^{94} +(-9.02999 + 2.78528i) q^{95} +(-2.08760 + 0.219416i) q^{96} +(4.60392 + 9.03571i) q^{97} +(3.95205 + 5.77766i) q^{98} +(-3.53563 - 3.04164i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) $ 768 * q + 24 * q^5 + 4 * q^7	$ 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) $ 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.0523360	+	0.998630i	−0.0370071	+	0.706138i
$2$	−0.0523360	+	0.998630i	−0.0370071	+	0.706138i
$3$	0.752251	+	1.95968i	0.434312	+	1.13142i	0.959816	+	0.280631i	$0.0905436\pi$
$3$	0.752251	+	1.95968i	0.434312	+	1.13142i	−0.525504	+	0.850791i	$0.676123\pi$
$4$	−0.994522	−	0.104528i	−0.497261	−	0.0522642i
$5$	0.432112	+	2.19392i	0.193246	+	0.981150i
$5$	0.432112	+	2.19392i	0.193246	+	0.981150i
$6$	−1.99636	+	0.648658i	−0.815012	+	0.264814i
$7$	2.50628	−	0.847671i	0.947286	−	0.320390i
$7$	2.50628	−	0.847671i	0.947286	−	0.320390i
$8$	0.156434	−	0.987688i	0.0553079	−	0.349201i
$9$	−1.04503	+	0.940951i	−0.348344	+	0.313650i
$10$	−2.21353	+	0.316699i	−0.699979	+	0.100149i
$11$	0.421151	+	3.28978i	0.126982	+	0.991905i
$11$	0.421151	+	3.28978i	0.126982	+	0.991905i
$12$	−0.543288	−	2.02758i	−0.156834	−	0.585311i
$13$	−3.67653	+	1.87329i	−1.01969	+	0.519556i	−0.882164	−	0.470942i	$-0.843914\pi$
$13$	−3.67653	+	1.87329i	−1.01969	+	0.519556i	−0.137523	+	0.990499i	$0.543914\pi$
$14$	0.715341	+	2.54721i	0.191183	+	0.680771i
$15$	−3.97432	+	2.49718i	−1.02617	+	0.644769i
$16$	0.978148	+	0.207912i	0.244537	+	0.0519779i
$17$	−0.220531	−	4.20798i	−0.0534866	−	1.02058i	−0.885150	−	0.465305i	$-0.845945\pi$
$17$	−0.220531	−	4.20798i	−0.0534866	−	1.02058i	0.831664	−	0.555279i	$-0.187389\pi$
$18$	−0.884969	−	1.09285i	−0.208589	−	0.257586i
$19$	0.441745	+	4.20292i	0.101343	+	0.964216i	0.920525	+	0.390683i	$0.127761\pi$
$19$	0.441745	+	4.20292i	0.101343	+	0.964216i	−0.819182	+	0.573534i	$0.805572\pi$
$20$	−0.200418	−	2.22707i	−0.0448147	−	0.497988i
$21$	3.54652	+	4.27385i	0.773914	+	0.932631i
$22$	−3.30731	+	0.248400i	−0.705121	+	0.0529591i
$23$	0.0879899	+	0.328383i	0.0183472	+	0.0684725i	0.974492	−	0.224420i	$-0.0720488\pi$
$23$	0.0879899	+	0.328383i	0.0183472	+	0.0684725i	−0.956145	+	0.292893i	$0.905382\pi$
$24$	2.05323	−	0.436428i	0.419114	−	0.0890855i
$25$	−4.62656	+	1.89604i	−0.925312	+	0.379207i
$26$	−1.67830	−	3.76953i	−0.329143	−	0.739266i
$27$	2.98085	+	1.51882i	0.573665	+	0.292297i
$28$	−2.58116	+	0.581050i	−0.487793	+	0.109808i
$29$	1.61696	−	2.22556i	0.300263	−	0.413276i	−0.632051	−	0.774927i	$-0.717787\pi$
$29$	1.61696	−	2.22556i	0.300263	−	0.413276i	0.932314	+	0.361651i	$0.117787\pi$
$30$	−2.28576	−	4.09957i	−0.417320	−	0.748475i
$31$	−0.111571	−	0.524901i	−0.0200388	−	0.0942749i	0.966992	−	0.254808i	$-0.0820121\pi$
$31$	−0.111571	−	0.524901i	−0.0200388	−	0.0942749i	−0.987031	+	0.160533i	$0.948679\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−6.13010	+	3.30006i	−1.06711	+	0.574466i
$34$	4.21375			0.722653
$35$	2.94272	+	5.13229i	0.497410	+	0.867516i
$36$	1.13766	−	0.826561i	0.189611	−	0.137760i
$37$	10.2083	+	3.91858i	1.67823	+	0.644211i	0.996198	−	0.0871138i	$-0.0277644\pi$
$37$	10.2083	+	3.91858i	1.67823	+	0.644211i	0.682029	+	0.731325i	$0.261098\pi$
$38$	−4.22028	+	0.221176i	−0.684620	+	0.0358794i
$39$	−6.43672	−	5.79565i	−1.03070	−	0.928046i
$40$	2.23451	−	0.0835871i	0.353306	−	0.0132163i
$41$	−6.66075	−	9.16774i	−1.04024	−	1.43176i	−0.896978	−	0.442075i	$-0.854242\pi$
$41$	−6.66075	−	9.16774i	−1.04024	−	1.43176i	−0.143257	−	0.989686i	$-0.545758\pi$
$42$	−4.45361	+	3.31798i	−0.687206	+	0.511976i
$43$	−1.34185	+	1.34185i	−0.204629	+	0.204629i	−0.801980	−	0.597351i	$-0.796220\pi$
$43$	−1.34185	+	1.34185i	−0.204629	+	0.204629i	0.597351	+	0.801980i	$0.296220\pi$
$44$	−0.0749684	−	3.31578i	−0.0113019	−	0.499872i
$45$	−2.51594	−	1.88612i	−0.375054	−	0.281166i
$46$	−0.332538	+	0.0706831i	−0.0490300	+	0.0104216i
$47$	−7.98761	−	6.46824i	−1.16511	−	0.943490i	−0.166022	−	0.986122i	$-0.553092\pi$
$47$	−7.98761	−	6.46824i	−1.16511	−	0.943490i	−0.999091	+	0.0426324i	$0.986426\pi$
$48$	0.328372	+	2.07326i	0.0473964	+	0.299249i
$49$	5.56291	−	4.24901i	0.794701	−	0.607001i
$50$	−1.65130	−	4.71945i	−0.233529	−	0.667431i
$51$	8.08040	−	3.59762i	1.13148	−	0.503768i
$52$	3.85220	−	1.47872i	0.534205	−	0.205062i
$53$	−4.58705	+	7.06344i	−0.630080	+	0.970238i	0.369086	+	0.929395i	$0.379671\pi$
$53$	−4.58705	+	7.06344i	−0.630080	+	0.970238i	−0.999166	+	0.0408424i	$0.986996\pi$
$54$	−1.67274	+	2.89728i	−0.227632	+	0.394270i
$55$	−7.03552	+	2.34552i	−0.948669	+	0.316270i
$56$	−0.445166	−	2.60803i	−0.0594878	−	0.348513i
$57$	−7.90408	+	4.02733i	−1.04692	+	0.533433i
$58$	2.13788	+	1.73122i	0.280718	+	0.227321i
$59$	0.712147	−	6.77562i	0.0927136	−	0.882111i	−0.845015	−	0.534742i	$-0.820409\pi$
$59$	0.712147	−	6.77562i	0.0927136	−	0.882111i	0.937729	−	0.347368i	$-0.112925\pi$
$60$	4.21358	−	2.06807i	0.543971	−	0.266986i
$61$	1.70159	−	8.00534i	0.217866	−	1.02498i	−0.724210	−	0.689579i	$-0.757795\pi$
$61$	1.70159	−	8.00534i	0.217866	−	1.02498i	0.942076	−	0.335399i	$-0.108871\pi$
$62$	0.530020	−	0.0839470i	0.0673127	−	0.0106613i
$63$	−1.82153	+	3.24413i	−0.229491	+	0.408722i
$64$	−0.951057	−	0.309017i	−0.118882	−	0.0386271i
$65$	−5.69851	−	7.25654i	−0.706813	−	0.900063i
$66$	−2.97471	−	6.29441i	−0.366162	−	0.774788i
$67$	−1.55099	+	5.78837i	−0.189483	+	0.707162i	0.804143	+	0.594436i	$0.202625\pi$
$67$	−1.55099	+	5.78837i	−0.189483	+	0.707162i	−0.993626	+	0.112726i	$0.964042\pi$
$68$	−0.220531	+	4.20798i	−0.0267433	+	0.510292i
$69$	−0.577335	+	0.419458i	−0.0695029	+	0.0504968i
$70$	−5.27927	+	2.67008i	−0.630993	+	0.319136i
$71$	1.64543	+	5.06410i	0.195276	+	0.600998i	0.999973	+	0.00731266i	$0.00232771\pi$
$71$	1.64543	+	5.06410i	0.195276	+	0.600998i	−0.804697	+	0.593686i	$0.797672\pi$
$72$	0.765887	+	1.17936i	0.0902607	+	0.138989i
$73$	5.65049	−	4.57568i	0.661340	−	0.535543i	−0.238841	−	0.971059i	$-0.576767\pi$
$73$	5.65049	−	4.57568i	0.661340	−	0.535543i	0.900181	+	0.435516i	$0.143434\pi$
$74$	−4.44747	+	9.98919i	−0.517008	+	1.16122i
$75$	−7.19596	−	7.64028i	−0.830918	−	0.882224i
$76$		−	4.22607i		−	0.484764i
$77$	3.84417	+	7.88811i	0.438084	+	0.898934i
$78$	6.12458	−	6.12458i	0.693472	−	0.693472i
$79$	9.43552	−	8.49578i	1.06158	−	0.955850i	0.0624700	−	0.998047i	$-0.480102\pi$
$79$	9.43552	−	8.49578i	1.06158	−	0.955850i	0.999109	+	0.0421965i	$0.0134356\pi$
$80$	−0.0334724	+	2.23582i	−0.00374233	+	0.249972i
$81$	−1.17503	+	11.1796i	−0.130558	+	1.24218i
$82$	9.50377	−	6.17182i	1.04952	−	0.681564i
$83$	0.105502	−	0.207060i	0.0115804	−	0.0227278i	−0.885144	−	0.465317i	$-0.845940\pi$
$83$	0.105502	−	0.207060i	0.0115804	−	0.0227278i	0.896724	+	0.442590i	$0.145940\pi$
$84$	−3.08035	−	4.62115i	−0.336094	−	0.504209i
$85$	9.13667	−	2.30214i	0.991011	−	0.249702i
$86$	−1.26978	−	1.41023i	−0.136924	−	0.152069i
$87$	5.57775	+	1.49455i	0.597997	+	0.160233i
$88$	3.31516	+	0.0986687i	0.353397	+	0.0105181i
$89$	5.17427	−	8.96210i	0.548472	−	0.949981i	−0.449908	−	0.893075i	$-0.648543\pi$
$89$	5.17427	−	8.96210i	0.548472	−	0.949981i	0.998380	−	0.0569059i	$-0.0181235\pi$
$90$	2.01521	−	2.41378i	0.212422	−	0.254435i
$91$	−7.62650	+	7.81148i	−0.799474	+	0.818865i
$92$	−0.0531825	−	0.335781i	−0.00554466	−	0.0350076i
$93$	0.944708	−	0.613501i	0.0979617	−	0.0636170i
$94$	6.87741	−	7.63814i	0.709351	−	0.787814i
$95$	−9.02999	+	2.78528i	−0.926457	+	0.285764i
$96$	−2.08760	+	0.219416i	−0.213065	+	0.0223940i
$97$	4.60392	+	9.03571i	0.467458	+	0.917437i	0.997581	+	0.0695165i	$0.0221457\pi$
$97$	4.60392	+	9.03571i	0.467458	+	0.917437i	−0.530123	+	0.847921i	$0.677854\pi$
$98$	3.95205	+	5.77766i	0.399217	+	0.583632i
$99$	−3.53563	−	3.04164i	−0.355345	−	0.305696i
$100$	4.79940	−	1.40204i	0.479940	−	0.140204i
$101$	1.62180	+	7.62997i	0.161375	+	0.759210i	0.982171	+	0.187989i	$0.0601968\pi$
$101$	1.62180	+	7.62997i	0.161375	+	0.759210i	−0.820796	+	0.571221i	$0.806470\pi$
$102$	3.16980	+	8.25761i	0.313857	+	0.817625i
$103$	7.39820	+	2.83990i	0.728966	+	0.279824i	0.694411	−	0.719579i	$-0.255665\pi$
$103$	7.39820	+	2.83990i	0.728966	+	0.279824i	0.0345553	+	0.999403i	$0.488999\pi$
$104$	1.27509	+	3.92431i	0.125033	+	0.384811i
$105$	−7.84399	+	9.62755i	−0.765495	+	0.939553i
$106$	−6.81369	−	4.95043i	−0.661804	−	0.480829i
$107$	6.79031	−	8.38534i	0.656445	−	0.810641i	−0.334855	−	0.942270i	$-0.608687\pi$
$107$	6.79031	−	8.38534i	0.656445	−	0.810641i	0.991299	+	0.131628i	$0.0420205\pi$
$108$	−2.80576	−	1.82208i	−0.269985	−	0.175330i
$109$	−1.89080	+	1.09166i	−0.181106	+	0.104562i	−0.587812	−	0.808997i	$-0.700011\pi$
$109$	−1.89080	+	1.09166i	−0.181106	+	0.104562i	0.406706	+	0.913559i	$0.366677\pi$
$110$	−1.97410	−	7.14863i	−0.188223	−	0.681595i
$111$			22.9527i			2.17857i
$112$	2.62776	−	0.308062i	0.248300	−	0.0291091i
$113$	−2.87667	+	18.1626i	−0.270614	+	1.70859i	0.360381	+	0.932805i	$0.382647\pi$
$113$	−2.87667	+	18.1626i	−0.270614	+	1.70859i	−0.630995	+	0.775787i	$0.717353\pi$
$114$	−3.60814	−	8.10402i	−0.337934	−	0.759011i
$115$	−0.682423	+	0.334941i	−0.0636363	+	0.0312334i
$116$	−1.84074	+	2.04435i	−0.170908	+	0.189813i
$117$	2.07942	−	5.41708i	0.192243	−	0.500809i
$118$	6.72907	+	1.06578i	0.619461	+	0.0981129i
$119$	−4.11969	−	10.3594i	−0.377652	−	0.949649i
$120$	1.84471	+	4.31604i	0.168398	+	0.393999i
$121$	−10.6453	+	2.77098i	−0.967751	+	0.251908i
$122$	7.90531	+	2.11822i	0.715713	+	0.191775i
$123$	12.9553	−	19.9494i	1.16814	−	1.79878i
$124$	0.0560928	+	0.533688i	0.00503728	+	0.0479266i
$125$	−6.15894	−	9.33100i	−0.550872	−	0.834590i
$126$	−3.14436	−	1.98882i	−0.280121	−	0.177178i
$127$	3.24473	−	6.36815i	0.287924	−	0.565082i	−0.701061	−	0.713101i	$-0.747290\pi$
$127$	3.24473	−	6.36815i	0.287924	−	0.565082i	0.988984	+	0.148020i	$0.0472899\pi$
$128$	0.358368	−	0.933580i	0.0316756	−	0.0825176i
$129$	−3.63899	−	1.62018i	−0.320395	−	0.142649i
$130$	7.54484	−	5.31092i	0.661726	−	0.465799i
$131$	−0.720018	−	0.415702i	−0.0629082	−	0.0363201i	0.468216	−	0.883614i	$-0.344897\pi$
$131$	−0.720018	−	0.415702i	−0.0629082	−	0.0363201i	−0.531124	+	0.847294i	$0.678230\pi$
$132$	6.44147	−	2.64121i	0.560658	−	0.229888i
$133$	4.66983	+	10.1593i	0.404926	+	0.880919i
$134$	−5.69927	−	1.85180i	−0.492342	−	0.159971i
$135$	−2.04411	+	7.19605i	−0.175929	+	0.619337i
$136$	−4.19067	−	0.440457i	−0.359347	−	0.0377689i
$137$	−1.97532	+	0.103522i	−0.168763	+	0.00884451i	−0.136530	−	0.990636i	$-0.543595\pi$
$137$	−1.97532	+	0.103522i	−0.168763	+	0.00884451i	−0.0322328	+	0.999480i	$0.510262\pi$
$138$	−0.388668	−	0.598496i	−0.0330856	−	0.0509474i
$139$	4.80445	+	3.49064i	0.407508	+	0.296072i	0.772592	−	0.634903i	$-0.218960\pi$
$139$	4.80445	+	3.49064i	0.407508	+	0.296072i	−0.365084	+	0.930974i	$0.618960\pi$
$140$	−2.39013	−	5.41177i	−0.202002	−	0.457378i
$141$	6.66700	−	20.5189i	0.561462	−	1.72800i
$142$	−5.14328	+	1.37814i	−0.431614	+	0.115651i
$143$	−7.71107	−	11.3060i	−0.644832	−	0.945458i
$144$	−1.21783	+	0.703115i	−0.101486	+	0.0585929i
$145$	5.58141	+	2.58580i	0.463511	+	0.214739i
$146$	4.27368	+	5.88222i	0.353693	+	0.486816i
$147$	12.5114	+	7.70520i	1.03192	+	0.635514i
$148$	−9.74273	−	4.96417i	−0.800848	−	0.408052i
$149$	−2.57683	+	12.1230i	−0.211102	+	0.993157i	0.737172	+	0.675705i	$0.236161\pi$
$149$	−2.57683	+	12.1230i	−0.211102	+	0.993157i	−0.948274	+	0.317452i	$0.897173\pi$
$150$	8.00642	−	6.78623i	0.653721	−	0.554094i
$151$	15.2181	+	6.77553i	1.23843	+	0.551385i	0.918261	−	0.395975i	$-0.129593\pi$
$151$	15.2181	+	6.77553i	1.23843	+	0.551385i	0.320170	+	0.947360i	$0.396260\pi$
$152$	4.22028	+	0.221176i	0.342310	+	0.0179397i
$153$	4.18996	+	4.18996i	0.338738	+	0.338738i
$154$	−8.07849	+	3.42607i	−0.650983	+	0.276081i
$155$	1.10338	−	0.471594i	0.0886255	−	0.0378793i
$156$	5.79565	+	6.43672i	0.464023	+	0.515350i
$157$	−6.61573	+	2.53954i	−0.527993	+	0.202677i	−0.607738	−	0.794138i	$-0.707923\pi$
$157$	−6.61573	+	2.53954i	−0.527993	+	0.202677i	0.0797449	+	0.996815i	$0.474589\pi$
$158$	7.99032	+	9.86723i	0.635676	+	0.784994i
$159$	−17.2927	−	3.67568i	−1.37140	−	0.291500i
$160$	−2.23100	−	0.150440i	−0.176376	−	0.0118933i
$161$	0.498888	+	0.748433i	0.0393179	+	0.0589848i
$162$	−11.1028	−	1.75851i	−0.872319	−	0.138162i
$163$	−7.74958	−	0.406138i	−0.606994	−	0.0318112i	−0.253636	−	0.967300i	$-0.581627\pi$
$163$	−7.74958	−	0.406138i	−0.606994	−	0.0318112i	−0.353357	+	0.935488i	$0.614960\pi$
$164$	5.66598	+	9.81376i	0.442438	+	0.766326i
$165$	−9.88895	−	12.0229i	−0.769854	−	0.935985i
$166$	0.201255	+	0.116194i	0.0156204	+	0.00901843i
$167$	3.38135	+	6.63627i	0.261656	+	0.513530i	0.984037	−	0.177966i	$-0.0569519\pi$
$167$	3.38135	+	6.63627i	0.261656	+	0.513530i	−0.722380	+	0.691496i	$0.756952\pi$
$168$	4.77603	−	2.83428i	0.368479	−	0.218669i
$169$	2.36648	−	3.25718i	0.182037	−	0.250552i
$170$	1.82081	+	9.24463i	0.139650	+	0.709031i
$171$	−4.41638	−	3.97653i	−0.337729	−	0.304093i
$172$	1.47476	−	1.19423i	0.112449	−	0.0910594i
$173$	0.315778	−	0.389954i	0.0240082	−	0.0296476i	−0.765000	−	0.644030i	$-0.777261\pi$
$173$	0.315778	−	0.389954i	0.0240082	−	0.0296476i	0.789009	+	0.614382i	$0.210595\pi$
$174$	−1.78442	+	5.49189i	−0.135277	+	0.416339i
$175$	−9.98825	+	8.67380i	−0.755041	+	0.655678i
$176$	−0.272035	+	3.30545i	−0.0205054	+	0.249158i
$177$	13.8138	−	3.70139i	1.03831	−	0.278213i
$178$	8.67902	+	5.63622i	0.650520	+	0.422453i
$179$	9.97066	−	22.3945i	0.745242	−	1.67384i	0.00638535	−	0.999980i	$-0.497967\pi$
$179$	9.97066	−	22.3945i	0.745242	−	1.67384i	0.738857	−	0.673862i	$-0.235366\pi$
$180$	2.30500	+	2.13877i	0.171805	+	0.159415i
$181$	−14.6100	+	4.74707i	−1.08595	+	0.352847i	−0.796681	−	0.604400i	$-0.793413\pi$
$181$	−14.6100	+	4.74707i	−1.08595	+	0.352847i	−0.289271	+	0.957247i	$0.593413\pi$
$182$	−7.40163	−	8.02487i	−0.548645	−	0.594843i
$183$	16.9679	−	2.68746i	1.25431	−	0.198662i
$184$	0.338104	−	0.0355362i	0.0249254	−	0.00261976i
$185$	−4.18595	+	24.0894i	−0.307757	+	1.77108i
$186$	0.563218	+	0.975522i	0.0412971	+	0.0715287i
$187$	13.7504	−	2.49769i	1.00553	−	0.182649i
$188$	7.26774	+	7.26774i	0.530054	+	0.530054i
$189$	8.75832	+	1.27981i	0.637074	+	0.0930924i
$190$	−2.30887	−	9.16338i	−0.167503	−	0.664782i
$191$	22.8202	−	10.1602i	1.65121	−	0.735167i	0.651489	−	0.758658i	$-0.274145\pi$
$191$	22.8202	−	10.1602i	1.65121	−	0.735167i	0.999724	+	0.0234913i	$0.00747819\pi$
$192$	−0.109859	−	2.09623i	−0.00792835	−	0.151282i
$193$	1.14116	+	21.7747i	0.0821428	+	1.56738i	0.660016	+	0.751251i	$0.270549\pi$
$193$	1.14116	+	21.7747i	0.0821428	+	1.56738i	−0.577873	+	0.816127i	$0.696117\pi$
$194$	−9.26428	+	4.12472i	−0.665136	+	0.296138i
$195$	9.93380	−	16.6260i	0.711374	−	1.19061i
$196$	−5.97657	+	3.64425i	−0.426898	+	0.260304i
$197$	13.5807	+	13.5807i	0.967585	+	0.967585i	0.999491	−	0.0319055i	$-0.0101575\pi$
$197$	13.5807	+	13.5807i	0.967585	+	0.967585i	−0.0319055	+	0.999491i	$0.510158\pi$
$198$	3.22251	−	3.37160i	0.229014	−	0.239609i
$199$	−4.07584	−	7.05957i	−0.288929	−	0.500440i	0.684625	−	0.728895i	$-0.259966\pi$
$199$	−4.07584	−	7.05957i	−0.288929	−	0.500440i	−0.973554	+	0.228456i	$0.926632\pi$
$200$	1.14894	+	4.86620i	0.0812423	+	0.344093i
$201$	−12.5101	+	1.31486i	−0.882394	+	0.0927433i
$202$	−7.70439	+	1.22026i	−0.542079	+	0.0858569i
$203$	2.16603	−	6.94854i	0.152025	−	0.487692i
$204$	−8.41219	+	2.73328i	−0.588971	+	0.191368i
$205$	17.2351	−	18.5746i	1.20375	−	1.29731i
$206$	−3.22320	+	7.23943i	−0.224571	+	0.504395i
$207$	−0.400944	−	0.260376i	−0.0278675	−	0.0180974i
$208$	−3.98567	+	1.06796i	−0.276356	+	0.0740495i
$209$	−13.6406	+	3.22331i	−0.943542	+	0.222961i
$210$	−9.20384	−	8.33711i	−0.635125	−	0.575315i
$211$	3.17431	−	9.76953i	0.218529	−	0.672562i	−0.780356	−	0.625336i	$-0.784962\pi$
$211$	3.17431	−	9.76953i	0.218529	−	0.672562i	0.998884	−	0.0472259i	$-0.0150381\pi$
$212$	5.30025	−	6.54527i	0.364023	−	0.449531i
$213$	−8.68625	+	7.03398i	−0.595172	+	0.481961i
$214$	8.01847	+	7.21986i	0.548131	+	0.493540i
$215$	−3.52373	−	2.36407i	−0.240316	−	0.161228i
$216$	1.96643	−	2.70656i	0.133799	−	0.184158i
$217$	−0.724572	−	1.22097i	−0.0491871	−	0.0828851i
$218$	−0.991203	−	1.94535i	−0.0671328	−	0.131755i
$219$	13.2175	+	7.63110i	0.893153	+	0.515662i
$220$	7.24215	−	1.59726i	0.488266	−	0.107687i
$221$	8.69354	+	15.0576i	0.584791	+	1.01289i
$222$	−22.9212	−	1.20125i	−1.53837	−	0.0806227i
$223$	22.7582	+	3.60455i	1.52400	+	0.241378i	0.861529	−	0.507708i	$-0.169507\pi$
$223$	22.7582	+	3.60455i	1.52400	+	0.241378i	0.662473	+	0.749086i	$0.269507\pi$
$224$	0.170114	+	2.64028i	0.0113662	+	0.176411i
$225$	3.05082	−	6.33478i	0.203388	−	0.422319i
$226$	−17.9871	−	3.82328i	−1.19649	−	0.254321i
$227$	−5.11458	−	6.31598i	−0.339466	−	0.419206i	0.578613	−	0.815602i	$-0.303594\pi$
$227$	−5.11458	−	6.31598i	−0.339466	−	0.419206i	−0.918080	+	0.396396i	$0.870261\pi$
$228$	8.28175	−	3.17907i	0.548472	−	0.210539i
$229$	−5.59773	−	6.21691i	−0.369909	−	0.410825i	0.529237	−	0.848474i	$-0.322478\pi$
$229$	−5.59773	−	6.21691i	−0.369909	−	0.410825i	−0.899146	+	0.437649i	$0.855811\pi$
$230$	−0.298766	−	0.699018i	−0.0197001	−	0.0460919i
$231$	−12.5664	+	13.4672i	−0.826808	+	0.886076i
$232$	−1.94521	−	1.94521i	−0.127709	−	0.127709i
$233$	−2.76472	−	0.144893i	−0.181123	−	0.00949224i	−0.0384411	−	0.999261i	$-0.512239\pi$
$233$	−2.76472	−	0.144893i	−0.181123	−	0.00949224i	−0.142682	+	0.989769i	$0.545573\pi$
$234$	5.30083	+	2.36008i	0.346526	+	0.154283i
$235$	10.7393	−	20.3192i	0.700552	−	1.32548i
$236$	−1.41649	+	6.66406i	−0.0922057	+	0.433794i
$237$	23.7469	+	12.0997i	1.54253	+	0.785957i
$238$	10.5609	−	3.57188i	0.684558	−	0.231530i
$239$	9.41058	+	12.9526i	0.608720	+	0.837831i	0.996471	−	0.0839328i	$-0.0267481\pi$
$239$	9.41058	+	12.9526i	0.608720	+	0.837831i	−0.387751	+	0.921764i	$0.626748\pi$
$240$	−4.40667	+	1.61630i	−0.284449	+	0.104332i
$241$	10.4295	−	6.02145i	0.671821	−	0.387876i	−0.124945	−	0.992164i	$-0.539876\pi$
$241$	10.4295	−	6.02145i	0.671821	−	0.387876i	0.796766	+	0.604288i	$0.206542\pi$
$242$	−2.21006	−	10.7757i	−0.142068	−	0.692688i
$243$	−13.0979	+	3.50958i	−0.840233	+	0.225140i
$244$	−2.52905	+	7.78362i	−0.161906	+	0.498295i
$245$	11.7258	+	10.3685i	0.749132	+	0.662420i
$246$	19.2440	+	13.9816i	1.22695	+	0.891434i
$247$	−9.49737	−	14.6247i	−0.604303	−	0.930545i
$248$	−0.535892	+	0.0280849i	−0.0340292	+	0.00178339i
$249$	0.485135	+	0.0509898i	0.0307442	+	0.00323135i
$250$	9.64054	−	5.66215i	0.609721	−	0.358106i
$251$	−13.9202	−	4.52296i	−0.878638	−	0.285487i	−0.165246	−	0.986252i	$-0.552842\pi$
$251$	−13.9202	−	4.52296i	−0.878638	−	0.285487i	−0.713392	+	0.700766i	$0.752842\pi$
$252$	2.15065	−	3.03596i	0.135478	−	0.191247i
$253$	−1.04325	+	0.427766i	−0.0655885	+	0.0268934i
$254$	6.18960	+	3.57357i	0.388370	+	0.224226i
$255$	11.3845	+	16.1732i	0.712927	+	1.01280i
$256$	0.913545	+	0.406737i	0.0570966	+	0.0254210i
$257$	6.03232	−	15.7147i	0.376286	−	0.980258i	−0.606430	−	0.795137i	$-0.707399\pi$
$257$	6.03232	−	15.7147i	0.376286	−	0.980258i	0.982716	−	0.185121i	$-0.0592678\pi$
$258$	1.80841	−	3.54921i	0.112587	−	0.220964i
$259$	28.9065	+	1.16783i	1.79616	+	0.0725654i
$260$	4.90878	+	7.81245i	0.304430	+	0.484507i
$261$	0.404364	+	3.84726i	0.0250295	+	0.238140i
$262$	0.452816	−	0.697275i	0.0279750	−	0.0430778i
$263$	−11.3312	−	3.03619i	−0.698712	−	0.187219i	−0.108058	−	0.994145i	$-0.534463\pi$
$263$	−11.3312	−	3.03619i	−0.698712	−	0.187219i	−0.590653	+	0.806925i	$0.701130\pi$
$264$	2.30047	+	6.57087i	0.141584	+	0.404409i
$265$	−17.4787	−	7.01142i	−1.07371	−	0.430708i
$266$	−10.3897	+	4.13174i	−0.637035	+	0.253333i
$267$	21.4552	+	3.39817i	1.31304	+	0.207965i
$268$	2.14754	−	5.59454i	0.131182	−	0.341741i
$269$	−18.7168	+	20.7872i	−1.14119	+	1.26742i	−0.182420	+	0.983221i	$0.558393\pi$
$269$	−18.7168	+	20.7872i	−1.14119	+	1.26742i	−0.958767	+	0.284195i	$0.908274\pi$
$270$	−7.07920	−	2.41792i	−0.430827	−	0.147150i
$271$	−6.02609	−	13.5348i	−0.366059	−	0.822182i	−0.998854	−	0.0478626i	$-0.984759\pi$
$271$	−6.02609	−	13.5348i	−0.366059	−	0.822182i	0.632795	−	0.774319i	$-0.281908\pi$
$272$	0.659176	−	4.16187i	0.0399684	−	0.252351i
$273$	−21.0450	−	9.06931i	−1.27370	−	0.548899i
$274$		−	1.97803i		−	0.119497i
$275$	−8.18601	−	14.4218i	−0.493635	−	0.869669i
$276$	0.618017	−	0.356812i	0.0372003	−	0.0214776i
$277$	−5.31070	−	3.44881i	−0.319089	−	0.207219i	0.375149	−	0.926965i	$-0.377592\pi$
$277$	−5.31070	−	3.44881i	−0.319089	−	0.207219i	−0.694238	+	0.719746i	$0.744258\pi$
$278$	−3.73730	+	4.61518i	−0.224148	+	0.276800i
$279$	0.610501	+	0.443555i	0.0365497	+	0.0265549i
$280$	5.52945	−	2.10362i	0.330448	−	0.125715i
$281$	−9.60412	−	29.5584i	−0.572934	−	1.76331i	−0.643110	−	0.765774i	$-0.722356\pi$
$281$	−9.60412	−	29.5584i	−0.572934	−	1.76331i	0.0701768	−	0.997535i	$-0.477644\pi$
$282$	20.1419	+	7.73174i	1.19943	+	0.460418i
$283$	−2.53195	−	6.59596i	−0.150509	−	0.392089i	0.837510	−	0.546422i	$-0.184011\pi$
$283$	−2.53195	−	6.59596i	−0.150509	−	0.392089i	−0.988019	+	0.154333i	$0.950677\pi$
$284$	−1.10707	−	5.20835i	−0.0656925	−	0.309059i
$285$	−12.2511	−	15.6007i	−0.725692	−	0.924103i
$286$	11.6941	−	7.10879i	0.691487	−	0.420352i
$287$	−24.4650	−	17.3308i	−1.44412	−	1.02301i
$288$	−0.638415	−	1.25296i	−0.0376189	−	0.0738313i
$289$	−0.751567	+	0.0789928i	−0.0442098	+	0.00464664i
$290$	−2.87436	+	5.43843i	−0.168788	+	0.319355i
$291$	−14.2438	+	15.8193i	−0.834986	+	0.927346i
$292$	−6.09783	+	3.95998i	−0.356848	+	0.231740i
$293$	1.29565	+	8.18044i	0.0756929	+	0.477906i	0.996194	+	0.0871657i	$0.0277810\pi$
$293$	1.29565	+	8.18044i	0.0756929	+	0.477906i	−0.920501	+	0.390740i	$0.872219\pi$
$294$	−8.34944	+	12.0910i	−0.486949	+	0.705161i
$295$	15.1729	−	1.36543i	0.883400	−	0.0794986i
$296$	5.46726	−	9.46958i	0.317778	−	0.550408i
$297$	−3.74119	+	10.4460i	−0.217086	+	0.606138i
$298$	−11.9715	−	3.20777i	−0.693493	−	0.185821i
$299$	−0.938652	−	1.04248i	−0.0542837	−	0.0602881i
$300$	6.35791	+	8.35061i	0.367074	+	0.482123i
$301$	−2.22560	+	4.50049i	−0.128281	+	0.259404i
$302$	−7.56270	+	14.8426i	−0.435184	+	0.854098i
$303$	−13.7323	+	8.91786i	−0.788900	+	0.512317i
$304$	−0.441745	+	4.20292i	−0.0253358	+	0.241054i
$305$	18.2983	+	0.273944i	1.04776	+	0.0156860i
$306$	−4.40350	+	3.96493i	−0.251732	+	0.226660i
$307$	−14.4650	+	14.4650i	−0.825558	+	0.825558i	−0.986899	−	0.161340i	$-0.948418\pi$
$307$	−14.4650	+	14.4650i	−0.825558	+	0.825558i	0.161340	+	0.986899i	$0.448418\pi$
$308$	−2.99858	−	8.24673i	−0.170860	−	0.469901i
$309$			16.6344i			0.946299i
$310$	0.413201	+	1.12655i	0.0234682	+	0.0639836i
$311$	8.35560	−	18.7670i	0.473802	−	1.06418i	−0.505693	−	0.862713i	$-0.668763\pi$
$311$	8.35560	−	18.7670i	0.473802	−	1.06418i	0.979496	−	0.201464i	$-0.0645700\pi$
$312$	−6.73122	+	5.45083i	−0.381080	+	0.308593i
$313$	−7.65071	−	11.7811i	−0.432444	−	0.665905i	0.553526	−	0.832832i	$-0.313282\pi$
$313$	−7.65071	−	11.7811i	−0.432444	−	0.665905i	−0.985969	+	0.166927i	$0.946615\pi$
$314$	−2.18982	−	6.73957i	−0.123579	−	0.380336i
$315$	−7.90447	−	2.59446i	−0.445366	−	0.146181i
$316$	−10.2719	+	7.46296i	−0.577839	+	0.419824i
$317$	1.59090	−	30.3561i	0.0893536	−	1.70497i	−0.475450	−	0.879743i	$-0.657715\pi$
$317$	1.59090	−	30.3561i	0.0893536	−	1.70497i	0.564804	−	0.825225i	$-0.308952\pi$
$318$	4.57567	−	17.0766i	0.256591	−	0.957609i
$319$	8.00258	+	4.38215i	0.448059	+	0.245354i
$320$	0.266996	−	2.22007i	0.0149255	−	0.124106i
$321$	21.5406	+	6.99897i	1.20228	+	0.390644i
$322$	−0.773517	+	0.459034i	−0.0431064	+	0.0255810i
$323$	17.5884	−	2.78573i	0.978644	−	0.155002i
$324$	2.33718	−	10.9956i	0.129843	−	0.610864i
$325$	13.4579	−	15.6377i	0.746509	−	0.867424i
$326$	0.811163	−	7.71770i	0.0449262	−	0.427444i
$327$	−3.56166	−	2.88417i	−0.196960	−	0.159495i
$328$	−10.0968	+	5.14460i	−0.557505	+	0.284063i
$329$	−25.5022	−	9.44037i	−1.40598	−	0.520464i
$330$	12.5240	−	9.24616i	0.689425	−	0.508985i
$331$	−1.39876	+	2.42273i	−0.0768830	+	0.133165i	−0.901904	−	0.431937i	$-0.857830\pi$
$331$	−1.39876	+	2.42273i	−0.0768830	+	0.133165i	0.825021	+	0.565103i	$0.191163\pi$
$332$	−0.126568	+	0.194898i	−0.00694632	+	0.0106964i
$333$	−14.3552	+	5.51043i	−0.786657	+	0.301969i
$334$	−6.80414	+	3.02940i	−0.372306	+	0.165761i
$335$	−13.3694	−	0.901522i	−0.730449	−	0.0492554i
$336$	2.58043	+	4.91782i	0.140774	+	0.268289i
$337$	−4.18549	−	26.4261i	−0.227998	−	1.43952i	−0.790365	−	0.612636i	$-0.790109\pi$
$337$	−4.18549	−	26.4261i	−0.227998	−	1.43952i	0.562367	−	0.826888i	$-0.309891\pi$
$338$	3.12886	+	2.53370i	0.170188	+	0.137815i
$339$	−37.7568	+	8.02546i	−2.05067	+	0.435883i
$340$	−9.32725	+	1.33449i	−0.505841	+	0.0723729i
$341$	1.67982	−	0.588106i	0.0909672	−	0.0318477i
$342$	4.20221	−	4.20221i	0.227230	−	0.227230i
$343$	10.3405	−	15.3647i	0.558332	−	0.829618i
$344$	1.11541	+	1.53524i	0.0601391	+	0.0827744i
$345$	−1.16973	−	1.08537i	−0.0629762	−	0.0584345i
$346$	0.372893	+	0.335754i	0.0200468	+	0.0180503i
$347$	−10.3231	+	0.541009i	−0.554171	+	0.0290429i	−0.327366	−	0.944897i	$-0.606161\pi$
$347$	−10.3231	+	0.541009i	−0.554171	+	0.0290429i	−0.226804	+	0.973940i	$0.572828\pi$
$348$	−5.39097	−	2.06940i	−0.288986	−	0.110931i
$349$	4.88261	−	3.54742i	0.261360	−	0.189889i	−0.449386	−	0.893338i	$-0.648357\pi$
$349$	4.88261	−	3.54742i	0.261360	−	0.189889i	0.710746	+	0.703448i	$0.248357\pi$
$350$	−8.13917	−	10.4285i	−0.435057	−	0.557427i
$351$	−13.8044			−0.736823
$352$	−3.28668	−	0.444656i	−0.175181	−	0.0237003i
$353$	−8.09560	+	30.2132i	−0.430885	+	1.60809i	0.319840	+	0.947471i	$0.396371\pi$
$353$	−8.09560	+	30.2132i	−0.430885	+	1.60809i	−0.750726	+	0.660614i	$0.770296\pi$
$354$	2.97336	+	13.9886i	0.158032	+	0.743483i
$355$	−10.3992	+	5.79819i	−0.551933	+	0.307736i
$356$	−6.08272	+	8.37215i	−0.322384	+	0.443723i
$357$	17.2022	−	15.8662i	0.910435	−	0.839728i
$358$	21.8420	+	11.1290i	1.15438	+	0.588188i
$359$	−7.40698	−	16.6363i	−0.390925	−	0.878033i	−0.996606	−	0.0823247i	$-0.973766\pi$
$359$	−7.40698	−	16.6363i	−0.390925	−	0.878033i	0.605680	−	0.795708i	$-0.292901\pi$
$360$	−2.25648	+	2.18991i	−0.118927	+	0.115418i
$361$	1.11539	−	0.237083i	0.0587046	−	0.0124780i
$362$	−3.97594	−	14.8384i	−0.208971	−	0.779890i
$363$	−13.4382	−	18.7768i	−0.705320	−	0.985529i
$364$	8.40124	−	6.97150i	0.440345	−	0.365406i
$365$	12.4803	+	10.4195i	0.653249	+	0.545383i
$366$	1.79574	+	17.0853i	0.0938648	+	0.893064i
$367$	−1.11844	−	1.38116i	−0.0583820	−	0.0720958i	0.747118	−	0.664691i	$-0.231437\pi$
$367$	−1.11844	−	1.38116i	−0.0583820	−	0.0720958i	−0.805500	+	0.592595i	$0.798103\pi$
$368$	0.0177925	+	0.339501i	0.000927497	+	0.0176977i
$369$	15.5871	+	3.31314i	0.811432	+	0.172475i
$370$	−23.8373	−	5.44095i	−1.23924	−	0.282861i
$371$	−5.50897	+	21.5913i	−0.286011	+	1.12096i
$372$	−1.00366	+	0.511391i	−0.0520374	+	0.0265144i
$373$	−0.976011	−	3.64252i	−0.0505360	−	0.188603i	0.936044	−	0.351884i	$-0.114459\pi$
$373$	−0.976011	−	3.64252i	−0.0505360	−	0.188603i	−0.986580	+	0.163281i	$0.947792\pi$
$374$	1.77463	+	13.8623i	0.0917637	+	0.716803i
$375$	13.6527	−	19.0888i	0.705023	−	0.985741i
$376$	−7.63814	+	6.87741i	−0.393907	+	0.354676i
$377$	−1.77571	+	11.2114i	−0.0914536	+	0.577415i
$378$	−1.73643	+	8.67933i	−0.0893123	+	0.446417i
$379$	−22.9956	+	7.47173i	−1.18121	+	0.383797i	−0.832815	−	0.553552i	$-0.813272\pi$
$379$	−22.9956	+	7.47173i	−1.18121	+	0.383797i	−0.348391	+	0.937349i	$0.613272\pi$
$380$	9.27166	−	1.82614i	0.475626	−	0.0936788i
$381$	14.9204	+	1.56820i	0.764395	+	0.0803411i
$382$	8.95197	+	23.3207i	0.458023	+	1.19319i
$383$	−1.11367	+	21.2501i	−0.0569059	+	1.08583i	0.809703	+	0.586840i	$0.199628\pi$
$383$	−1.11367	+	21.2501i	−0.0569059	+	1.08583i	−0.866609	+	0.498988i	$0.833705\pi$
$384$	2.09910			0.107119
$385$	−15.6448	+	11.8423i	−0.797331	+	0.603542i
$386$	−21.8046			−1.10982
$387$	0.139661	−	2.66488i	0.00709934	−	0.135464i
$388$	−3.63421	−	9.46745i	−0.184499	−	0.480637i
$389$	12.2214	+	1.28452i	0.619650	+	0.0651279i	0.409152	−	0.912466i	$-0.365825\pi$
$389$	12.2214	+	1.28452i	0.619650	+	0.0651279i	0.210498	+	0.977594i	$0.432491\pi$
$390$	16.0833	+	10.7903i	0.814411	+	0.546389i
$391$	1.36242	−	0.442678i	0.0689007	−	0.0223872i
$392$	−3.32647	−	6.15911i	−0.168012	−	0.311082i
$393$	0.273010	−	1.72372i	0.0137715	−	0.0869500i
$394$	−14.2729	+	12.8513i	−0.719056	+	0.647441i
$395$	22.7163	+	17.0296i	1.14298	+	0.856854i
$396$	3.19833	+	3.39455i	0.160722	+	0.170583i
$397$	9.33618	+	34.8431i	0.468569	+	1.74872i	0.644777	+	0.764371i	$0.276950\pi$
$397$	9.33618	+	34.8431i	0.468569	+	1.74872i	−0.176207	+	0.984353i	$0.556383\pi$
$398$	7.26321	−	3.70079i	0.364072	−	0.185504i
$399$	−16.3960	+	16.7937i	−0.820827	+	0.840736i
$400$	−4.91967	+	0.892687i	−0.245983	+	0.0446344i
$401$	−3.14257	−	0.667974i	−0.156933	−	0.0333570i	0.128775	−	0.991674i	$-0.458895\pi$
$401$	−3.14257	−	0.667974i	−0.156933	−	0.0333570i	−0.285708	+	0.958317i	$0.592229\pi$
$402$	−0.658334	−	12.5618i	−0.0328347	−	0.626524i
$403$	1.39348	+	1.72081i	0.0694144	+	0.0857196i
$404$	−0.815366	−	7.75769i	−0.0405660	−	0.385960i
$405$	−25.0349	+	2.25294i	−1.24400	+	0.111949i
$406$	6.82565	+	2.52672i	0.338751	+	0.125399i
$407$	−8.59205	+	35.2332i	−0.425892	+	1.74645i
$408$	−2.28928	−	8.54371i	−0.113336	−	0.422976i
$409$	14.4021	−	3.06126i	0.712137	−	0.151369i	0.162422	−	0.986721i	$-0.448069\pi$
$409$	14.4021	−	3.06126i	0.712137	−	0.151369i	0.549716	+	0.835352i	$0.314736\pi$
$410$	17.6472	+	18.1836i	0.871532	+	0.898024i
$411$	−1.68881	−	3.79313i	−0.0833028	−	0.187101i
$412$	−7.06082	−	3.59767i	−0.347862	−	0.177244i
$413$	−3.95866	−	17.5853i	−0.194793	−	0.865316i
$414$	0.281003	−	0.386768i	0.0138106	−	0.0190086i
$415$	0.499861	+	0.141990i	0.0245372	+	0.00697004i
$416$	−0.857899	−	4.03610i	−0.0420620	−	0.197886i
$417$	−3.22638	+	12.0410i	−0.157997	+	0.589651i
$418$	−2.50499	−	13.7906i	−0.122523	−	0.674522i
$419$	−31.6365			−1.54554			−0.772771	−	0.634685i	$-0.781130\pi$
$419$	−31.6365			−1.54554			−0.772771	+	0.634685i	$0.781130\pi$
$420$	8.80738	−	8.75489i	0.429756	−	0.427195i
$421$	0.211831	−	0.153905i	0.0103240	−	0.00750085i	−0.582611	−	0.812751i	$-0.697969\pi$
$421$	0.211831	−	0.153905i	0.0103240	−	0.00750085i	0.592935	+	0.805250i	$0.297969\pi$
$422$	9.59001	+	3.68126i	0.466834	+	0.179201i
$423$	14.4336	−	0.756433i	0.701786	−	0.0367790i
$424$	6.25890	+	5.63554i	0.303959	+	0.273686i
$425$	8.99877	+	19.0503i	0.436505	+	0.924076i
$426$	−6.56974	−	9.04247i	−0.318305	−	0.438109i
$427$	−2.52124	−	21.5060i	−0.122011	−	1.04075i
$428$	−7.62962	+	7.62962i	−0.368792	+	0.368792i
$429$	16.3556	−	23.6162i	0.789654	−	1.14020i
$430$	2.54525	−	3.39517i	0.122743	−	0.163730i
$431$	6.00748	−	1.27693i	0.289370	−	0.0615076i	−0.0609394	−	0.998141i	$-0.519410\pi$
$431$	6.00748	−	1.27693i	0.289370	−	0.0615076i	0.350310	+	0.936634i	$0.386076\pi$
$432$	2.59993	+	2.10538i	0.125089	+	0.101295i
$433$	−0.246620	−	1.55709i	−0.0118518	−	0.0748292i	0.981054	−	0.193737i	$-0.0620608\pi$
$433$	−0.246620	−	1.55709i	−0.0118518	−	0.0748292i	−0.992905	+	0.118908i	$0.962061\pi$
$434$	1.25722	−	0.659678i	0.0603486	−	0.0316656i
$435$	−0.868718	+	12.8829i	−0.0416519	+	0.617690i
$436$	1.99456	−	0.888033i	0.0955219	−	0.0425291i
$437$	−1.34130	+	0.514876i	−0.0641630	+	0.0246299i
$438$	−8.31239	+	12.8000i	−0.397182	+	0.611606i
$439$	14.9168	−	25.8367i	0.711942	−	1.23312i	−0.252186	−	0.967679i	$-0.581149\pi$
$439$	14.9168	−	25.8367i	0.711942	−	1.23312i	0.964127	−	0.265440i	$-0.0855173\pi$
$440$	1.21605	+	7.31582i	0.0579728	+	0.348768i
$441$	−1.81531	+	9.67477i	−0.0864431	+	0.460703i
$442$	−15.4920	+	7.89357i	−0.736879	+	0.375459i
$443$	−12.0349	−	9.74563i	−0.571793	−	0.463029i	0.299292	−	0.954162i	$-0.403250\pi$
$443$	−12.0349	−	9.74563i	−0.571793	−	0.463029i	−0.871085	+	0.491133i	$0.836583\pi$
$444$	2.39921	−	22.8269i	0.113861	−	1.08332i
$445$	21.8980	+	7.47930i	1.03806	+	0.354553i
$446$	−4.79068	+	22.5384i	−0.226845	+	1.06722i
$447$	−25.6957	+	4.06980i	−1.21536	+	0.192495i
$448$	−2.64556	+	0.0316995i	−0.124991	+	0.00149766i
$449$	−25.6794	−	8.34374i	−1.21189	−	0.393766i	−0.367765	−	0.929919i	$-0.619877\pi$
$449$	−25.6794	−	8.34374i	−1.21189	−	0.393766i	−0.844121	+	0.536153i	$0.819877\pi$
$450$	6.16643	+	3.37818i	0.290688	+	0.159249i
$451$	27.3546	−	25.7734i	1.28808	−	1.21362i
$452$	4.75942	−	17.7624i	0.223864	−	0.835473i
$453$	−1.83005	+	34.9195i	−0.0859834	+	1.64066i
$454$	6.57500	−	4.77701i	0.308580	−	0.224196i
$455$	−20.4332	−	13.3565i	−0.957925	−	0.626162i
$456$	2.74128	+	8.43678i	0.128372	+	0.395089i
$457$	10.8056	+	16.6392i	0.505466	+	0.778349i	0.995640	−	0.0932751i	$-0.0297336\pi$
$457$	10.8056	+	16.6392i	0.505466	+	0.778349i	−0.490174	+	0.871624i	$0.663067\pi$
$458$	6.50136	−	5.26469i	0.303788	−	0.246003i
$459$	5.73379	−	12.8783i	0.267630	−	0.601108i
$460$	0.713696	−	0.261773i	0.0332762	−	0.0122052i
$461$		−	34.5849i		−	1.61078i	−0.592745	−	0.805390i	$-0.701956\pi$
$461$		−	34.5849i		−	1.61078i	0.592745	−	0.805390i	$-0.298044\pi$
$462$	−12.7911	−	13.2540i	−0.595094	−	0.616632i
$463$	−1.59816	+	1.59816i	−0.0742728	+	0.0742728i	−0.743267	−	0.668995i	$-0.766725\pi$
$463$	−1.59816	+	1.59816i	−0.0742728	+	0.0742728i	0.668995	+	0.743267i	$0.266725\pi$
$464$	2.04435	−	1.84074i	0.0949065	−	0.0854542i
$465$	1.75419	+	1.80751i	0.0813486	+	0.0838214i
$466$	0.289388	−	2.75335i	0.0134057	−	0.127546i
$467$	8.17304	−	5.30764i	0.378203	−	0.245608i	−0.341512	−	0.939877i	$-0.610939\pi$
$467$	8.17304	−	5.30764i	0.378203	−	0.245608i	0.719715	+	0.694269i	$0.244272\pi$
$468$	−2.63427	+	5.17005i	−0.121769	+	0.238985i
$469$	1.01942	+	15.8220i	0.0470724	+	0.730593i
$470$	19.7293	+	11.7880i	0.910044	+	0.543738i
$471$	−9.95338	−	11.0543i	−0.458627	−	0.509357i
$472$	−6.58080	−	1.76332i	−0.302906	−	0.0811634i
$473$	−4.97949	−	3.84925i	−0.228957	−	0.176989i
$474$	−13.3259	+	23.0811i	−0.612078	+	1.06015i
$475$	−10.0126	−	18.6075i	−0.459412	−	0.853771i
$476$	3.01427	+	10.7333i	0.138159	+	0.491961i
$477$	−1.85273	−	11.6977i	−0.0848309	−	0.535601i
$478$	−13.4273	+	8.71980i	−0.614151	+	0.398834i
$479$	−28.1144	+	31.2242i	−1.28458	+	1.42667i	−0.433918	+	0.900952i	$0.642869\pi$
$479$	−28.1144	+	31.2242i	−1.28458	+	1.42667i	−0.850660	+	0.525716i	$0.823797\pi$
$480$	−1.38346	−	4.48522i	−0.0631459	−	0.204721i
$481$	−44.8716	+	4.71620i	−2.04597	+	0.215040i
$482$	5.46736	+	10.7303i	0.249032	+	0.488752i
$483$	−1.09140	+	1.54067i	−0.0496605	+	0.0701030i
$484$	10.8766	−	1.64307i	0.494391	−	0.0746851i
$485$	−17.8342	+	14.0051i	−0.809809	+	0.635937i
$486$	−2.81928	−	13.2637i	−0.127885	−	0.601652i
$487$	−11.3663	−	29.6103i	−0.515057	−	1.34177i	−0.906748	−	0.421672i	$-0.861443\pi$
$487$	−11.3663	−	29.6103i	−0.515057	−	1.34177i	0.391691	−	0.920097i	$-0.371890\pi$
$488$	−7.64059	−	2.93295i	−0.345873	−	0.132768i
$489$	−5.03372	−	15.4922i	−0.227633	−	0.700582i
$490$	−10.9680	+	11.1671i	−0.495483	+	0.504476i
$491$	8.62184	+	6.26414i	0.389098	+	0.282697i	0.765086	−	0.643928i	$-0.222696\pi$
$491$	8.62184	+	6.26414i	0.389098	+	0.282697i	−0.375988	+	0.926625i	$0.622696\pi$
$492$	−14.9696	+	18.4859i	−0.674882	+	0.833409i
$493$	−9.72170	−	6.31334i	−0.437843	−	0.284339i
$494$	15.1017	−	8.71896i	0.679456	−	0.392284i
$495$	5.14532	−	9.07122i	0.231265	−	0.407721i
$496$		−	0.536627i		−	0.0240953i
$497$	8.41660	+	11.2973i	0.377536	+	0.506753i
$498$	−0.0763099	+	0.481802i	−0.00341953	+	0.0215901i
$499$	−5.86801	−	13.1798i	−0.262688	−	0.590008i	0.733259	−	0.679950i	$-0.237998\pi$
$499$	−5.86801	−	13.1798i	−0.262688	−	0.590008i	−0.995947	+	0.0899421i	$0.971332\pi$
$500$	5.14984	+	9.92366i	0.230308	+	0.443800i
$501$	−10.4613	+	11.6185i	−0.467378	+	0.519076i
$502$	5.24529	−	13.6645i	0.234109	−	0.609874i
$503$	1.12970	+	0.178927i	0.0503707	+	0.00797794i	0.181569	−	0.983378i	$-0.441882\pi$
$503$	1.12970	+	0.178927i	0.0503707	+	0.00797794i	−0.131198	+	0.991356i	$0.541882\pi$
$504$	2.91924	+	2.30660i	0.130033	+	0.102744i
$505$	−16.0387	+	6.85509i	−0.713714	+	0.305048i
$506$	−0.372580	−	1.06421i	−0.0165632	−	0.0473097i
$507$	8.16321	+	2.18733i	0.362541	+	0.0971425i
$508$	−3.89261	+	5.99410i	−0.172707	+	0.265945i
$509$	−3.10077	−	29.5019i	−0.137439	−	1.30765i	−0.818111	−	0.575060i	$-0.804979\pi$
$509$	−3.10077	−	29.5019i	−0.137439	−	1.30765i	0.680672	−	0.732588i	$-0.261688\pi$
$510$	−16.7468	+	10.5225i	−0.741561	+	0.465944i
$511$	10.2831	−	16.2577i	0.454896	−	0.719199i
$512$	−0.453990	+	0.891007i	−0.0200637	+	0.0393773i
$513$	−5.06670	+	13.1992i	−0.223700	+	0.582760i
$514$	15.3775	+	6.84650i	0.678272	+	0.301986i
$515$	−3.03367	+	17.4582i	−0.133679	+	0.769300i
$516$	3.44970	+	1.99169i	0.151865	+	0.0876791i
$517$	17.9151	−	29.0016i	0.787904	−	1.27549i
$518$	−2.67908	+	28.8057i	−0.117712	+	1.26565i
$519$	1.00173	+	0.325482i	0.0439710	+	0.0142871i
$520$	−8.05865	+	4.49318i	−0.353395	+	0.197039i
$521$	−22.0527	−	2.31784i	−0.966148	−	0.101546i	−0.391705	−	0.920091i	$-0.628115\pi$
$521$	−22.0527	−	2.31784i	−0.966148	−	0.101546i	−0.574443	+	0.818544i	$0.694781\pi$
$522$	−3.86315	+	0.202459i	−0.169086	+	0.00886141i
$523$	−11.8363	−	18.2263i	−0.517565	−	0.796980i	0.479170	−	0.877722i	$-0.340938\pi$
$523$	−11.8363	−	18.2263i	−0.517565	−	0.796980i	−0.996735	+	0.0807419i	$0.974271\pi$
$524$	0.672621	+	0.488688i	0.0293836	+	0.0213484i
$525$	−24.5116	−	13.0489i	−1.06977	−	0.569501i
$526$	3.62505	−	11.1568i	0.158060	−	0.486458i
$527$	−2.18416	+	0.585245i	−0.0951437	+	0.0254937i
$528$	−6.68226	+	1.95342i	−0.290808	+	0.0850119i
$529$	19.8185	−	11.4422i	0.861674	−	0.497487i
$530$	7.91658	−	17.0878i	0.343874	−	0.742248i
$531$	5.63131	+	7.75084i	0.244378	+	0.336358i
$532$	−3.58232	−	10.5917i	−0.155313	−	0.459210i
$533$	41.6623	+	21.2280i	1.80459	+	0.919487i
$534$	−4.51639	+	21.2480i	−0.195443	+	0.919489i
$535$	21.3309	+	11.2740i	0.922217	+	0.487417i
$536$	5.47448	+	2.43739i	0.236461	+	0.105279i
$537$	51.3865	+	2.69305i	2.21749	+	0.116214i
$538$	−19.7791	−	19.7791i	−0.852738	−	0.852738i
$539$	16.3211	+	16.5112i	0.703000	+	0.711190i
$540$	2.78510	−	6.94296i	0.119852	−	0.298777i
$541$	22.6453	+	25.1501i	0.973596	+	1.08129i	0.996669	+	0.0815545i	$0.0259885\pi$
$541$	22.6453	+	25.1501i	0.973596	+	1.08129i	−0.0230725	+	0.999734i	$0.507345\pi$
$542$	13.8317	−	5.30948i	0.594121	−	0.228062i
$543$	−20.2931	−	25.0599i	−0.870861	−	1.07542i
$544$	4.12167	+	0.876088i	0.176715	+	0.0375620i
$545$	−3.21204	−	3.67655i	−0.137589	−	0.157486i
$546$	10.1583	−	20.5415i	0.434735	−	0.879097i
$547$	2.93359	+	0.464635i	0.125431	+	0.0198663i	0.218834	−	0.975762i	$-0.429775\pi$
$547$	2.93359	+	0.464635i	0.125431	+	0.0198663i	−0.0934032	+	0.995628i	$0.529775\pi$
$548$	1.97532	+	0.103522i	0.0843816	+	0.00442225i
$549$	5.75442	+	9.96694i	0.245593	+	0.425379i
$550$	14.8305	−	7.42001i	0.632374	−	0.316391i
$551$	10.0681	+	5.81284i	0.428917	+	0.247635i
$552$	0.323979	+	0.635844i	0.0137895	+	0.0270633i
$553$	16.4465	−	29.2911i	0.699374	−	1.24558i
$554$	3.72202	−	5.12293i	0.158134	−	0.217652i
$555$	−50.3563	+	9.91812i	−2.13751	+	0.421001i
$556$	−4.41326	−	3.97371i	−0.187164	−	0.168523i
$557$	−19.6552	+	15.9164i	−0.832816	+	0.674401i	−0.947765	−	0.318970i	$-0.896663\pi$
$557$	−19.6552	+	15.9164i	−0.832816	+	0.674401i	0.114949	+	0.993371i	$0.463330\pi$
$558$	−0.474898	+	0.586450i	−0.0201040	+	0.0248264i
$559$	2.41968	−	7.44700i	0.102341	−	0.314974i
$560$	1.81135	+	5.63196i	0.0765434	+	0.237994i
$561$	15.2384	+	25.0676i	0.643368	+	1.05835i
$562$	30.0206	−	8.04399i	1.26634	−	0.339315i
$563$	−20.4326	−	13.2691i	−0.861133	−	0.559227i	0.0368177	−	0.999322i	$-0.488278\pi$
$563$	−20.4326	−	13.2691i	−0.861133	−	0.559227i	−0.897951	+	0.440095i	$0.854945\pi$
$564$	−8.77528	+	19.7096i	−0.369506	+	0.829924i
$565$	−41.0903	+	1.53708i	−1.72868	+	0.0646655i
$566$	6.71943	−	2.18328i	0.282439	−	0.0917699i
$567$	6.53170	+	29.0153i	0.274306	+	1.21853i
$568$	5.25916	−	0.832968i	0.220669	−	0.0349506i
$569$	−3.30234	+	0.347090i	−0.138441	+	0.0145508i	−0.173496	−	0.984835i	$-0.555506\pi$
$569$	−3.30234	+	0.347090i	−0.138441	+	0.0145508i	0.0350543	+	0.999385i	$0.488840\pi$
$570$	16.2204	−	11.4178i	0.679400	−	0.478240i
$571$	−8.05969	−	13.9598i	−0.337288	−	0.584199i	0.646634	−	0.762800i	$-0.276176\pi$
$571$	−8.05969	−	13.9598i	−0.337288	−	0.584199i	−0.983922	+	0.178601i	$0.942843\pi$
$572$	6.48703	+	12.0501i	0.271236	+	0.503841i
$573$	37.0773	+	37.0773i	1.54893	+	1.54893i
$574$	18.5875	−	23.5244i	0.775826	−	0.981890i
$575$	−1.02972	−	1.35245i	−0.0429421	−	0.0564011i
$576$	1.28465	−	0.571965i	0.0535273	−	0.0238319i
$577$	−0.849717	−	16.2136i	−0.0353742	−	0.674979i	−0.957560	−	0.288233i	$-0.906932\pi$
$577$	−0.849717	−	16.2136i	−0.0353742	−	0.674979i	0.922186	−	0.386746i	$-0.126401\pi$
$578$	−0.0395506	−	0.754671i	−0.00164509	−	0.0313902i
$579$	−41.8130	+	18.6164i	−1.73769	+	0.773670i
$580$	−5.28054	−	3.15505i	−0.219263	−	0.131006i
$581$	0.0888998	−	0.608382i	0.00368819	−	0.0252399i
$582$	−15.0522	−	15.0522i	−0.623934	−	0.623934i
$583$	−25.1690	−	12.1156i	−1.04239	−	0.501777i
$584$	−3.63541	−	6.29672i	−0.150434	−	0.260560i
$585$	12.7832	+	2.22130i	0.528519	+	0.0918395i
$586$	−8.23703	+	0.865747i	−0.340269	+	0.0357637i
$587$	15.6417	−	2.47740i	0.645601	−	0.102253i	0.174956	−	0.984576i	$-0.444022\pi$
$587$	15.6417	−	2.47740i	0.645601	−	0.102253i	0.470644	+	0.882323i	$0.344022\pi$
$588$	−11.6374	−	8.97079i	−0.479920	−	0.369949i
$589$	2.15683	−	0.700797i	0.0888707	−	0.0288758i
$590$	0.569475	+	15.2236i	0.0234449	+	0.626744i
$591$	−16.3978	+	36.8300i	−0.674513	+	1.51498i
$592$	9.17047	+	5.95537i	0.376904	+	0.244764i
$593$	30.3766	−	8.13938i	1.24742	−	0.334244i	0.426078	−	0.904686i	$-0.359895\pi$
$593$	30.3766	−	8.13938i	1.24742	−	0.334244i	0.821338	+	0.570442i	$0.193228\pi$
$594$	−10.2359	−	4.28276i	−0.419983	−	0.175724i
$595$	20.9476	−	13.5147i	0.858768	−	0.554049i
$596$	3.82991	−	11.7873i	0.156879	−	0.482825i
$597$	10.7684	−	13.2979i	0.440723	−	0.544248i
$598$	1.09018	−	0.882807i	0.0445806	−	0.0361007i
$599$	−3.71196	−	3.34226i	−0.151667	−	0.136561i	0.589804	−	0.807546i	$-0.299205\pi$
$599$	−3.71196	−	3.34226i	−0.151667	−	0.136561i	−0.741471	+	0.670985i	$0.765872\pi$
$600$	−8.67191	+	5.91216i	−0.354029	+	0.241363i
$601$	6.70737	−	9.23190i	0.273599	−	0.376577i	−0.650001	−	0.759933i	$-0.725232\pi$
$601$	6.70737	−	9.23190i	0.273599	−	0.376577i	0.923601	+	0.383356i	$0.125232\pi$
$602$	−4.37784	−	2.45809i	−0.178427	−	0.100184i
$603$	−3.82574	−	7.50844i	−0.155796	−	0.305767i
$604$	−14.4265	−	8.32914i	−0.587006	−	0.338908i
$605$	−10.6793	−	22.1575i	−0.434174	−	0.900829i
$606$	−8.18694	−	14.1802i	−0.332572	−	0.576031i
$607$	20.9316	+	1.09698i	0.849589	+	0.0445251i	0.472160	−	0.881513i	$-0.343475\pi$
$607$	20.9316	+	1.09698i	0.849589	+	0.0445251i	0.377430	+	0.926038i	$0.376808\pi$
$608$	−4.17404	−	0.661103i	−0.169280	−	0.0268113i
$609$	15.2463	−	0.982325i	0.617812	−	0.0398058i
$610$	−1.23123	+	18.2589i	−0.0498510	+	0.739282i
$611$	41.4836	+	8.81761i	1.67825	+	0.356722i
$612$	−3.72904	−	4.60498i	−0.150737	−	0.186145i
$613$	18.2721	−	7.01400i	0.738003	−	0.283293i	0.0398149	−	0.999207i	$-0.487323\pi$
$613$	18.2721	−	7.01400i	0.738003	−	0.283293i	0.698188	+	0.715914i	$0.253990\pi$
$614$	−13.6881	−	15.2022i	−0.552406	−	0.613509i
$615$	49.3655	+	19.8025i	1.99061	+	0.798513i
$616$	8.39236	−	2.56287i	0.338138	−	0.103261i
$617$	−0.269198	−	0.269198i	−0.0108375	−	0.0108375i	0.701667	−	0.712505i	$-0.252439\pi$
$617$	−0.269198	−	0.269198i	−0.0108375	−	0.0108375i	−0.712505	+	0.701667i	$0.752439\pi$
$618$	−16.6116	−	0.870578i	−0.668217	−	0.0350198i
$619$	29.1399	+	12.9739i	1.17123	+	0.521465i	0.897790	−	0.440424i	$-0.145172\pi$
$619$	29.1399	+	12.9739i	1.17123	+	0.521465i	0.273440	+	0.961889i	$0.411838\pi$
$620$	−1.14663	+	0.353676i	−0.0460497	+	0.0142040i
$621$	−0.236469	+	1.11250i	−0.00948919	+	0.0446431i
$622$	18.3040	+	9.32633i	0.733922	+	0.373952i
$623$	5.37127	−	26.8476i	0.215195	−	1.07563i
$624$	−5.09108	−	7.00727i	−0.203806	−	0.280515i
$625$	17.8101	−	17.5442i	0.712404	−	0.701770i
$626$	12.1653	−	7.02365i	0.486224	−	0.280722i
$627$	−16.5778	−	24.3066i	−0.662055	−	0.970710i
$628$	6.84494	−	1.83410i	0.273143	−	0.0731884i
$629$	14.2381	−	43.8203i	0.567709	−	1.74723i
$630$	3.00459	−	7.75785i	0.119706	−	0.309080i
$631$	6.36752	+	4.62627i	0.253487	+	0.184169i	0.707271	−	0.706943i	$-0.249926\pi$
$631$	6.36752	+	4.62627i	0.253487	+	0.184169i	−0.453784	+	0.891112i	$0.649926\pi$
$632$	−6.91515	−	10.6484i	−0.275070	−	0.423570i
$633$	21.5330	−	1.12850i	0.855861	−	0.0448538i
$634$	30.2312	+	3.17743i	1.20064	+	0.126192i
$635$	15.3733	+	4.36693i	0.610070	+	0.173296i
$636$	16.8137	+	5.46312i	0.666708	+	0.216627i
$637$	−12.4926	+	26.0425i	−0.494975	+	1.03184i
$638$	−4.79497	+	7.76227i	−0.189835	+	0.307311i
$639$	−6.48459	−	3.74388i	−0.256527	−	0.148106i
$640$	2.20305	+	0.382819i	0.0870834	+	0.0151323i
$641$	−11.5848	−	5.15789i	−0.457573	−	0.203724i	0.164989	−	0.986295i	$-0.447241\pi$
$641$	−11.5848	−	5.15789i	−0.457573	−	0.203724i	−0.622561	+	0.782571i	$0.713908\pi$
$642$	−8.11672	+	21.1448i	−0.320342	+	0.834518i
$643$	5.22931	−	10.2631i	0.206224	−	0.404737i	−0.764609	−	0.644495i	$-0.777068\pi$
$643$	5.22931	−	10.2631i	0.206224	−	0.404737i	0.970833	+	0.239757i	$0.0770678\pi$
$644$	−0.417923	−	0.796481i	−0.0164685	−	0.0313858i
$645$	1.98210	−	8.68375i	0.0780451	−	0.341922i
$646$	1.86140	+	17.7101i	0.0732359	+	0.696793i
$647$	−7.59196	+	11.6906i	−0.298471	+	0.459604i	−0.955808	−	0.293992i	$-0.905016\pi$
$647$	−7.59196	+	11.6906i	−0.298471	+	0.459604i	0.657337	+	0.753597i	$0.271683\pi$
$648$	10.8582	+	2.90944i	0.426549	+	0.114294i
$649$	22.5902	−	0.510756i	0.886743	−	0.0200489i
$650$	14.9119	+	14.2578i	0.584895	+	0.559239i
$651$	1.84766	−	2.33841i	0.0724154	−	0.0916494i
$652$	7.66467	+	1.21396i	0.300172	+	0.0475425i
$653$	−11.6253	+	30.2850i	−0.454934	+	1.18514i	0.493941	+	0.869495i	$0.335556\pi$
$653$	−11.6253	+	30.2850i	−0.454934	+	1.18514i	−0.948876	+	0.315650i	$0.897778\pi$
$654$	3.06662	−	3.40583i	0.119914	−	0.133178i
$655$	0.600889	−	1.75929i	0.0234787	−	0.0687412i
$656$	−4.60912	−	10.3523i	−0.179956	−	0.404188i
$657$	−1.59946	+	10.0986i	−0.0624007	+	0.393983i
$658$	10.7621	−	24.9731i	0.419551	−	0.973554i
$659$		−	46.1565i		−	1.79800i	−0.437946	−	0.899001i	$-0.644294\pi$
$659$		−	46.1565i		−	1.79800i	0.437946	−	0.899001i	$-0.355706\pi$
$660$	8.57804	+	12.9908i	0.333900	+	0.505665i
$661$	−24.4425	+	14.1119i	−0.950703	+	0.548889i	−0.893299	−	0.449462i	$-0.851616\pi$
$661$	−24.4425	+	14.1119i	−0.950703	+	0.548889i	−0.0574038	+	0.998351i	$0.518282\pi$
$662$	−2.34620	−	1.52364i	−0.0911878	−	0.0592180i
$663$	−22.9685	+	28.3637i	−0.892021	+	1.10155i
$664$	−0.188006	−	0.136595i	−0.00729607	−	0.00530090i
$665$	−20.2707	+	14.6352i	−0.786064	+	0.567528i
$666$	−4.75158	−	14.6239i	−0.184120	−	0.566664i
$667$	0.873112	+	0.335156i	0.0338070	+	0.0129773i
$668$	−2.66914	−	6.95336i	−0.103272	−	0.269034i
$669$	10.0561	+	47.3103i	0.388792	+	1.82912i
$670$	1.59999	−	13.3039i	0.0618129	−	0.513975i
$671$	27.0524	+	2.22639i	1.04435	+	0.0859487i
$672$	−5.04613	+	2.31952i	−0.194659	+	0.0894774i
$673$	−7.26447	−	14.2573i	−0.280025	−	0.549579i	0.707563	−	0.706651i	$-0.249795\pi$
$673$	−7.26447	−	14.2573i	−0.280025	−	0.549579i	−0.987587	+	0.157071i	$0.949795\pi$
$674$	26.6090	−	2.79672i	1.02494	−	0.107726i
$675$	−16.6708	−	1.37511i	−0.641660	−	0.0529279i
$676$	−2.69398	+	2.99197i	−0.103615	+	0.115076i
$677$	−40.2451	+	26.1355i	−1.54675	+	1.00447i	−0.562677	+	0.826677i	$0.690229\pi$
$677$	−40.2451	+	26.1355i	−1.54675	+	1.00447i	−0.984068	+	0.177792i	$0.943105\pi$
$678$	−6.03843	−	38.1251i	−0.231904	−	1.46419i
$679$	19.1980	+	18.7434i	0.736753	+	0.719307i
$680$	−0.844510	−	9.38431i	−0.0323855	−	0.359872i
$681$	8.52985	−	14.7741i	0.326865	−	0.566146i
$682$	0.499385	+	1.70829i	0.0191225	+	0.0654140i
$683$	−15.3813	−	4.12139i	−0.588547	−	0.157701i	−0.0477580	−	0.998859i	$-0.515208\pi$
$683$	−15.3813	−	4.12139i	−0.588547	−	0.157701i	−0.540789	+	0.841158i	$0.681874\pi$
$684$	3.97653	+	4.41638i	0.152046	+	0.168865i
$685$	−1.08068	−	4.28897i	−0.0412907	−	0.163873i
$686$	14.8025	+	11.1304i	0.565162	+	0.424961i
$687$	7.97226	−	15.6464i	0.304161	−	0.596949i
$688$	−1.59151	+	1.03354i	−0.0606757	+	0.0394032i
$689$	3.63259	−	34.5618i	0.138391	−	1.31670i
$690$	1.14510	−	1.11132i	0.0435934	−	0.0423073i
$691$	12.7204	−	11.4535i	0.483906	−	0.435711i	−0.390719	−	0.920510i	$-0.627774\pi$
$691$	12.7204	−	11.4535i	0.483906	−	0.435711i	0.874626	+	0.484799i	$0.161107\pi$
$692$	−0.354810	+	0.354810i	−0.0134878	+	0.0134878i
$693$	−11.4396	−	4.62615i	−0.434555	−	0.175733i
$694$		−	10.3372i		−	0.392396i
$695$	−5.58211	+	12.0489i	−0.211742	+	0.457041i
$696$	2.34871	−	5.27528i	0.0890274	−	0.199959i
$697$	−37.1087	+	30.0501i	−1.40559	+	1.13823i
$698$	3.28703	+	5.06158i	0.124416	+	0.191583i
$699$	−1.79582	−	5.52696i	−0.0679241	−	0.209049i
$700$	10.8402	−	7.58223i	0.409721	−	0.286581i
$701$	−8.31280	+	6.03961i	−0.313970	+	0.228113i	−0.733598	−	0.679583i	$-0.762161\pi$
$701$	−8.31280	+	6.03961i	−0.313970	+	0.228113i	0.419628	+	0.907696i	$0.362161\pi$
$702$	0.722465	−	13.7855i	0.0272677	−	0.520299i
$703$	−11.9601	+	44.6355i	−0.451082	+	1.68346i
$704$	0.616059	−	3.25891i	0.0232186	−	0.122825i
$705$	47.8977	+	5.76039i	1.80393	+	0.216949i
$706$	−29.7481	−	9.66574i	−1.11958	−	0.363775i
$707$	10.5324	+	17.7481i	0.396111	+	0.667486i
$708$	−14.1250	+	2.23718i	−0.530850	+	0.0840783i
$709$	−6.81423	+	32.0584i	−0.255914	+	1.20398i	0.643004	+	0.765863i	$0.277688\pi$
$709$	−6.81423	+	32.0584i	−0.255914	+	1.20398i	−0.898918	+	0.438117i	$0.855646\pi$
$710$	−5.24599	−	10.6884i	−0.196878	−	0.401129i
$711$	−1.86631	+	17.7567i	−0.0699920	+	0.665929i
$712$	−8.04233	−	6.51255i	−0.301399	−	0.244068i
$713$	0.162551	−	0.0828239i	0.00608759	−	0.00310178i
$714$	14.9441	+	18.0090i	0.559271	+	0.673968i
$715$	21.4725	−	21.8029i	0.803025	−	0.815383i
$716$	−12.2569	+	21.2296i	−0.458062	+	0.793387i
$717$	−18.3038	+	28.1853i	−0.683566	+	1.05260i
$718$	17.0012	−	6.52615i	0.634479	−	0.243554i
$719$	17.4917	−	7.78783i	0.652332	−	0.290437i	−0.0537632	−	0.998554i	$-0.517122\pi$
$719$	17.4917	−	7.78783i	0.652332	−	0.290437i	0.706095	+	0.708117i	$0.250455\pi$
$720$	−2.06881	−	2.36800i	−0.0771002	−	0.0882500i
$721$	20.9493	+	0.846357i	0.780192	+	0.0315200i
$722$	0.178383	+	1.12627i	0.00663873	+	0.0419153i
$723$	19.6457	+	15.9088i	0.730631	+	0.591654i
$724$	15.0262	−	3.19391i	0.558443	−	0.118701i
$725$	−3.26124	+	13.3625i	−0.121119	+	0.496271i
$726$	19.4544	−	12.4370i	0.722021	−	0.461582i
$727$	−35.6687	+	35.6687i	−1.32288	+	1.32288i	−0.411441	+	0.911436i	$0.634974\pi$
$727$	−35.6687	+	35.6687i	−1.32288	+	1.32288i	−0.911436	+	0.411441i	$0.865026\pi$
$728$	6.52226	+	8.75459i	0.241731	+	0.324467i
$729$	3.09166	+	4.25531i	0.114506	+	0.157604i
$730$	−11.0584	+	11.9179i	−0.409290	+	0.441101i
$731$	5.94237	+	5.35054i	0.219787	+	0.197897i
$732$	−17.1559	+	0.899102i	−0.634100	+	0.0332318i
$733$	40.9027	+	15.7011i	1.51077	+	0.579932i	0.965975	−	0.258635i	$-0.0832725\pi$
$733$	40.9027	+	15.7011i	1.51077	+	0.579932i	0.544799	+	0.838567i	$0.316606\pi$
$734$	1.43780	−	1.04462i	0.0530701	−	0.0385577i
$735$	−11.4983	+	30.7785i	−0.424120	+	1.13528i
$736$	−0.339967			−0.0125313
$737$	−19.6956	−	2.66463i	−0.725499	−	0.0981530i
$738$	−4.12436	+	15.3923i	−0.151820	+	0.566600i
$739$	2.33063	+	10.9648i	0.0857337	+	0.403345i	0.999998	−	0.00177192i	$-0.000564021\pi$
$739$	2.33063	+	10.9648i	0.0857337	+	0.403345i	−0.914265	+	0.405117i	$0.867231\pi$
$740$	6.68104	−	23.5198i	0.245600	−	0.864607i
$741$	21.5153	−	29.6132i	0.790383	−	1.08787i
$742$	−21.2734	−	6.63142i	−0.780970	−	0.243447i
$743$	−2.05087	−	1.04497i	−0.0752392	−	0.0383363i	0.415966	−	0.909380i	$-0.363444\pi$
$743$	−2.05087	−	1.04497i	−0.0752392	−	0.0383363i	−0.491205	+	0.871044i	$0.663444\pi$
$744$	−0.458162	−	1.02905i	−0.0167971	−	0.0377268i
$745$	−27.7104	−	0.414852i	−1.01523	−	0.0151990i
$746$	3.68861	−	0.784039i	0.135050	−	0.0287057i
$747$	0.0845800	+	0.315657i	0.00309462	+	0.0115493i
$748$	−13.9362	+	1.04670i	−0.509557	+	0.0382710i
$749$	9.91044	−	26.7720i	0.362119	−	0.978227i
$750$	18.3481	+	14.6330i	0.669978	+	0.534322i
$751$	1.73151	+	16.4742i	0.0631835	+	0.601151i	0.979604	+	0.200935i	$0.0643981\pi$
$751$	1.73151	+	16.4742i	0.0631835	+	0.601151i	−0.916421	+	0.400216i	$0.868935\pi$
$752$	−6.46824	−	7.98761i	−0.235872	−	0.291278i
$753$	−1.60796	−	30.6816i	−0.0585972	−	1.11810i
$754$	−11.1031	−	2.36003i	−0.404350	−	0.0859473i
$755$	−8.28905	+	36.3150i	−0.301669	+	1.32164i
$756$	−8.57656	−	2.18829i	−0.311927	−	0.0795874i
$757$	−6.52509	+	3.32470i	−0.237158	+	0.120838i	−0.568531	−	0.822662i	$-0.692488\pi$
$757$	−6.52509	+	3.32470i	−0.237158	+	0.120838i	0.331373	+	0.943500i	$0.392488\pi$
$758$	−6.25799	−	23.3552i	−0.227301	−	0.848297i
$759$	−1.62307	−	1.72265i	−0.0589137	−	0.0625281i
$760$	1.33839	+	9.35453i	0.0485486	+	0.339324i
$761$	38.2479	−	34.4385i	1.38648	−	1.24840i	0.452177	−	0.891928i	$-0.350647\pi$
$761$	38.2479	−	34.4385i	1.38648	−	1.24840i	0.934307	−	0.356468i	$-0.116019\pi$
$762$	−2.34692	+	14.8179i	−0.0850199	+	0.536795i
$763$	−3.81352	+	4.33878i	−0.138059	+	0.157074i
$764$	−23.7572	+	7.71919i	−0.859506	+	0.279271i
$765$	−7.38190	+	11.0030i	−0.266893	+	0.397813i
$766$	−21.1627	−	2.22429i	−0.764638	−	0.0803667i
$767$	10.0745	+	26.2448i	0.363767	+	0.947646i
$768$	−0.109859	+	2.09623i	−0.00396418	+	0.0756410i
$769$	−13.5287			−0.487858			−0.243929	−	0.969793i	$-0.578436\pi$
$769$	−13.5287			−0.487858			−0.243929	+	0.969793i	$0.578436\pi$
$770$	−11.0073	−	16.2431i	−0.396677	−	0.585361i
$771$	35.3337			1.27251
$772$	1.14116	−	21.7747i	0.0410714	−	0.783689i
$773$	3.34087	+	8.70325i	0.120163	+	0.313034i	0.980448	−	0.196779i	$-0.0630480\pi$
$773$	3.34087	+	8.70325i	0.120163	+	0.313034i	−0.860285	+	0.509813i	$0.829715\pi$
$774$	2.65392	+	0.278938i	0.0953932	+	0.0100262i
$775$	1.51142	+	2.21694i	0.0542918	+	0.0796349i
$776$	9.64468	−	3.13375i	0.346224	−	0.112495i
$777$	19.4563	+	57.5259i	0.697992	+	2.06373i
$778$	−1.92238	+	12.1374i	−0.0689207	+	0.435148i
$779$	35.5890	−	32.0444i	1.27511	−	1.14811i
$780$	−11.6173	+	15.4966i	−0.415965	+	0.554866i
$781$	−15.9668	+	7.54584i	−0.571337	+	0.270011i
$782$	0.370767	+	1.38372i	0.0132586	+	0.0494818i
$783$	8.20015	−	4.17819i	0.293050	−	0.149316i
$784$	6.32476	−	2.99956i	0.225884	−	0.107127i
$785$	−8.43028	−	13.4170i	−0.300890	−	0.478874i
$786$	1.70707	+	0.362848i	0.0608891	+	0.0129424i
$787$	−2.14358	−	40.9020i	−0.0764105	−	1.45800i	−0.720716	−	0.693230i	$-0.756187\pi$
$787$	−2.14358	−	40.9020i	−0.0764105	−	1.45800i	0.644306	−	0.764768i	$-0.277146\pi$
$788$	−12.0867	−	14.9259i	−0.430572	−	0.531713i
$789$	−2.57395	−	24.4895i	−0.0916351	−	0.871849i
$790$	−18.1952	+	21.7939i	−0.647356	+	0.775391i
$791$	8.18615	+	47.9590i	0.291066	+	1.70523i
$792$	−3.55729	+	3.01629i	−0.126403	+	0.107179i
$793$	8.74035	+	32.6194i	0.310379	+	1.15835i
$794$	−35.2839	+	7.49983i	−1.25218	+	0.266159i
$795$	0.591759	−	39.5271i	0.0209875	−	1.40188i
$796$	3.31559	+	7.44694i	0.117518	+	0.263950i
$797$	40.3200	+	20.5441i	1.42821	+	0.727708i	0.985614	−	0.169015i	$-0.0540586\pi$
$797$	40.3200	+	20.5441i	1.42821	+	0.727708i	0.442593	+	0.896723i	$0.354059\pi$
$798$	−15.9126	−	17.2525i	−0.563299	−	0.610730i
$799$	−25.4567	+	35.0381i	−0.900593	+	1.23956i
$800$	−0.633988	−	4.95964i	−0.0224149	−	0.175350i
$801$	3.02562	+	14.2344i	0.106905	+	0.502948i
$802$	0.831528	−	3.10331i	0.0293623	−	0.109582i
$803$	17.4327	+	16.6618i	0.615186	+	0.587983i
$804$	12.5790			0.443627
$805$	−1.42643	+	1.41793i	−0.0502749	+	0.0499753i
$806$	−1.79138	+	1.30151i	−0.0630987	+	0.0458439i
$807$	−54.8160	−	21.0419i	−1.92961	−	0.740709i
$808$	7.78973	−	0.408243i	0.274042	−	0.0143619i
$809$	−16.1091	−	14.5047i	−0.566365	−	0.509957i	0.335463	−	0.942053i	$-0.391107\pi$
$809$	−16.1091	−	14.5047i	−0.566365	−	0.509957i	−0.901827	+	0.432096i	$0.857774\pi$
$810$	−0.939620	−	25.1185i	−0.0330149	−	0.882575i
$811$	−18.3057	−	25.1957i	−0.642801	−	0.884740i	0.355960	−	0.934501i	$-0.384154\pi$
$811$	−18.3057	−	25.1957i	−0.642801	−	0.884740i	−0.998761	+	0.0497612i	$0.984154\pi$
$812$	−2.88048	+	6.68406i	−0.101085	+	0.234565i
$813$	21.9908	−	21.9908i	0.771251	−	0.771251i
$814$	−34.7353	−	10.4242i	−1.21747	−	0.365369i
$815$	−2.45765	−	17.1774i	−0.0860877	−	0.601699i
$816$	8.65181	−	1.83900i	0.302874	−	0.0643778i
$817$	−6.23242	−	5.04692i	−0.218045	−	0.176569i
$818$	2.30332	+	14.5426i	0.0805336	+	0.508469i
$819$	0.619716	−	15.3394i	0.0216546	−	0.536002i
$820$	−19.0823	+	16.6713i	−0.666381	+	0.582188i
$821$	13.2135	−	5.88302i	0.461153	−	0.205319i	−0.162991	−	0.986627i	$-0.552114\pi$
$821$	13.2135	−	5.88302i	0.461153	−	0.205319i	0.624145	+	0.781309i	$0.285448\pi$
$822$	3.87632	−	1.48798i	0.135202	−	0.0518992i
$823$	−10.7970	+	16.6259i	−0.376359	+	0.579543i	−0.975200	−	0.221326i	$-0.928962\pi$
$823$	−10.7970	+	16.6259i	−0.376359	+	0.579543i	0.598841	+	0.800868i	$0.295628\pi$
$824$	3.96227	−	6.86285i	0.138032	−	0.239079i
$825$	22.1042	−	26.8908i	0.769571	−	0.936218i
$826$	17.7684	−	3.03289i	0.618241	−	0.105528i
$827$	−11.1440	+	5.67814i	−0.387514	+	0.197448i	−0.636883	−	0.770960i	$-0.719777\pi$
$827$	−11.1440	+	5.67814i	−0.387514	+	0.197448i	0.249369	+	0.968408i	$0.419777\pi$
$828$	0.371531	+	0.300860i	0.0129116	+	0.0104556i
$829$	−3.22748	+	30.7075i	−0.112095	+	1.06651i	0.783423	+	0.621489i	$0.213472\pi$
$829$	−3.22748	+	30.7075i	−0.112095	+	1.06651i	−0.895518	+	0.445025i	$0.853195\pi$
$830$	−0.167957	+	0.491745i	−0.00582986	+	0.0170687i
$831$	2.76359	−	13.0016i	0.0958677	−	0.451022i
$832$	4.07547	−	0.645491i	0.141291	−	0.0223784i
$833$	−19.1065	−	22.4715i	−0.662002	−	0.778593i
$834$	−11.8557	−	3.85214i	−0.410528	−	0.133389i
$835$	−13.0983	+	10.2860i	−0.453286	+	0.355962i
$836$	13.9028	−	1.77981i	0.480840	−	0.0615562i
$837$	0.464653	−	1.73411i	0.0160607	−	0.0599395i
$838$	1.65572	−	31.5931i	0.0571961	−	1.09137i
$839$	0.217962	−	0.158358i	0.00752487	−	0.00546714i	−0.584016	−	0.811742i	$-0.698520\pi$
$839$	0.217962	−	0.158358i	0.00752487	−	0.00546714i	0.591541	+	0.806275i	$0.298520\pi$
$840$	8.28195	+	9.25350i	0.285755	+	0.319276i
$841$	6.62295	+	20.3833i	0.228378	+	0.702874i
$842$	0.142607	+	0.219596i	0.00491457	+	0.00756777i
$843$	50.7004	−	41.0564i	1.74621	−	1.41406i
$844$	−4.17812	+	9.38420i	−0.143817	+	0.323018i
$845$	8.16856	+	3.78439i	0.281007	+	0.130187i
$846$			14.4534i			0.496918i
$847$	−24.3312	+	15.9686i	−0.836028	+	0.548686i
$848$	−5.95538	+	5.95538i	−0.204509	+	0.204509i
$849$	11.0213	−	9.92363i	0.378250	−	0.340578i
$850$	−19.4952	+	7.98942i	−0.668679	+	0.274035i
$851$	−0.388572	+	3.69701i	−0.0133201	+	0.126732i
$852$	9.37391	−	6.08749i	0.321145	−	0.208554i
$853$	10.3847	−	20.3812i	0.355567	−	0.697839i	−0.642063	−	0.766652i	$-0.721921\pi$
$853$	10.3847	−	20.3812i	0.355567	−	0.697839i	0.997630	+	0.0688129i	$0.0219211\pi$
$854$	21.6085	−	1.39224i	0.739428	−	0.0476416i
$855$	6.81581	−	11.4075i	0.233096	−	0.390128i
$856$	−7.21986	−	8.01847i	−0.246770	−	0.274066i
$857$	−33.0115	−	8.84541i	−1.12765	−	0.302154i	−0.353676	−	0.935368i	$-0.615068\pi$
$857$	−33.0115	−	8.84541i	−1.12765	−	0.302154i	−0.773976	+	0.633214i	$0.781735\pi$
$858$	22.7279	+	17.5691i	0.775916	+	0.599800i
$859$	−12.4435	+	21.5528i	−0.424567	+	0.735372i	−0.996380	−	0.0850124i	$-0.972907\pi$
$859$	−12.4435	+	21.5528i	−0.424567	+	0.735372i	0.571813	+	0.820384i	$0.306240\pi$
$860$	3.25731	+	2.71945i	0.111073	+	0.0927325i
$861$	15.5591	−	60.9806i	0.530252	−	2.07821i
$862$	0.960773	+	6.06608i	0.0327241	+	0.206612i
$863$	9.31383	−	6.04847i	0.317047	−	0.205892i	−0.376298	−	0.926499i	$-0.622803\pi$
$863$	9.31383	−	6.04847i	0.317047	−	0.205892i	0.693344	+	0.720606i	$0.256136\pi$
$864$	−2.23857	+	2.48618i	−0.0761576	+	0.0845816i
$865$	0.991979	+	0.524289i	0.0337283	+	0.0178263i
$866$	1.56787	−	0.164790i	0.0532783	−	0.00559978i
$867$	−0.720167	−	1.41341i	−0.0244582	−	0.0480019i
$868$	0.592976	+	1.29002i	0.0201269	+	0.0437863i
$869$	31.9230	+	27.4628i	1.08291	+	0.931610i
$870$	−12.8198	−	1.54177i	−0.434633	−	0.0522709i
$871$	−5.14102	−	24.1866i	−0.174197	−	0.819531i
$872$	0.782429	+	2.03830i	0.0264964	+	0.0690255i
$873$	−13.3134	−	5.11054i	−0.450590	−	0.172965i
$874$	−0.443972	−	1.36641i	−0.0150176	−	0.0462194i
$875$	−23.3457	−	18.1654i	−0.789227	−	0.614101i
$876$	−12.3474	−	8.97090i	−0.417179	−	0.303099i
$877$	−6.72157	+	8.30045i	−0.226971	+	0.280286i	−0.877891	−	0.478860i	$-0.841050\pi$
$877$	−6.72157	+	8.30045i	−0.226971	+	0.280286i	0.650920	+	0.759147i	$0.274383\pi$
$878$	25.0206	+	16.2486i	0.844405	+	0.548363i
$879$	−15.0564	+	8.69281i	−0.507839	+	0.293201i
$880$	−7.36944	+	0.831500i	−0.248424	+	0.0280299i
$881$		−	26.3183i		−	0.886686i	−0.896352	−	0.443343i	$-0.853792\pi$
$881$		−	26.3183i		−	0.886686i	0.896352	−	0.443343i	$-0.146208\pi$
$882$	−9.56651	−	2.31916i	−0.322121	−	0.0780901i
$883$	0.728280	−	4.59818i	0.0245086	−	0.154741i	−0.972399	−	0.233324i	$-0.925040\pi$
$883$	0.728280	−	4.59818i	0.0245086	−	0.154741i	0.996908	+	0.0785833i	$0.0250396\pi$
$884$	−7.07196	−	15.8839i	−0.237856	−	0.534233i
$885$	14.0896	+	28.7069i	0.473618	+	0.964971i
$886$	10.3621	−	11.5083i	0.348123	−	0.386629i
$887$	7.45445	−	19.4195i	0.250296	−	0.652044i	−0.749656	−	0.661828i	$-0.769781\pi$
$887$	7.45445	−	19.4195i	0.250296	−	0.652044i	0.999952	+	0.00978402i	$0.00311440\pi$
$888$	22.6701	+	3.59059i	0.760759	+	0.120492i
$889$	2.73412	−	18.7108i	0.0916995	−	0.627542i
$890$	−8.61511	+	21.4765i	−0.288779	+	0.719895i
$891$	−37.2733	+	0.842736i	−1.24870	+	0.0282327i
$892$	−22.2568	−	5.96368i	−0.745211	−	0.199679i
$893$	23.6570	−	36.4286i	0.791652	−	1.21904i
$894$	−2.71941	−	25.8735i	−0.0909507	−	0.865338i
$895$	53.4401	+	12.1979i	1.78631	+	0.407731i
$896$	0.106802	−	2.64359i	0.00356800	−	0.0883163i
$897$	1.33682	−	2.62366i	0.0446353	−	0.0876016i
$898$	9.67626	−	25.2075i	0.322901	−	0.841186i
$899$	−1.34860	−	0.600437i	−0.0449785	−	0.0200257i
$900$	−3.69628	+	5.98118i	−0.123209	+	0.199373i
$901$	30.7344	+	17.7445i	1.02391	+	0.591155i
$902$	24.3064	+	28.6660i	0.809316	+	0.954474i
$903$	−10.4937	−	0.975969i	−0.349209	−	0.0324782i
$904$	17.4890	+	5.68251i	0.581674	+	0.188997i
$905$	−16.7278	−	30.0019i	−0.556052	−	0.997296i
$906$	−34.7759	−	3.65509i	−1.15535	−	0.121432i
$907$	25.5528	−	1.33917i	0.848467	−	0.0444663i	0.376855	−	0.926272i	$-0.377006\pi$
$907$	25.5528	−	1.33917i	0.848467	−	0.0444663i	0.471612	+	0.881806i	$0.343672\pi$
$908$	4.42636	+	6.81600i	0.146894	+	0.226197i
$909$	−8.87425	−	6.44752i	−0.294340	−	0.213851i
$910$	14.4076	−	19.7062i	0.477606	−	0.653255i
$911$	5.00556	−	15.4055i	0.165842	−	0.510408i	−0.833256	−	0.552888i	$-0.813526\pi$
$911$	5.00556	−	15.4055i	0.165842	−	0.510408i	0.999097	+	0.0424797i	$0.0135258\pi$
$912$	−8.56869	+	2.29597i	−0.283738	+	0.0760273i
$913$	0.725613	+	0.259876i	0.0240143	+	0.00860063i
$914$	−17.1819	+	9.91999i	−0.568328	+	0.328124i
$915$	13.2281	+	36.0650i	0.437307	+	1.19227i
$916$	4.91722	+	6.76798i	0.162470	+	0.223620i
$917$	−2.15695	−	0.431529i	−0.0712287	−	0.0142504i
$918$	12.5606	+	6.39993i	0.414561	+	0.211229i
$919$	−5.89998	+	27.7572i	−0.194622	+	0.915627i	0.767084	+	0.641546i	$0.221707\pi$
$919$	−5.89998	+	27.7572i	−0.194622	+	0.915627i	−0.961707	+	0.274080i	$0.911627\pi$
$920$	0.224062	+	0.726418i	0.00738712	+	0.0239493i
$921$	−39.2280	−	17.4654i	−1.29261	−	0.575505i
$922$	34.5375	+	1.81003i	1.13743	+	0.0596103i
$923$	−15.5360	−	15.5360i	−0.511373	−	0.511373i
$924$	13.9053	−	12.0799i	0.457450	−	0.397399i
$925$	−54.6589	+	1.22567i	−1.79717	+	0.0402997i
$926$	−1.51233	−	1.67961i	−0.0496982	−	0.0551954i
$927$	−10.4036	+	3.99355i	−0.341698	+	0.131165i
$928$	1.73122	+	2.13788i	0.0568302	+	0.0701795i
$929$	−2.39732	−	0.509566i	−0.0786536	−	0.0167183i	0.168417	−	0.985716i	$-0.446135\pi$
$929$	−2.39732	−	0.509566i	−0.0786536	−	0.0167183i	−0.247070	+	0.968998i	$0.579468\pi$
$930$	−1.89684	+	1.65719i	−0.0621999	+	0.0543413i
$931$	20.3156	+	21.5035i	0.665818	+	0.704748i
$932$	2.73443	+	0.433091i	0.0895692	+	0.0141864i
$933$	43.0628	+	2.25683i	1.40981	+	0.0738851i
$934$	4.87262	+	8.43962i	0.159437	+	0.276153i
$935$	11.4215	+	29.0880i	0.373521	+	0.951281i
$936$	−5.02509	−	2.90124i	−0.164250	−	0.0948300i
$937$	6.79100	+	13.3281i	0.221852	+	0.435410i	0.974927	−	0.222525i	$-0.0714301\pi$
$937$	6.79100	+	13.3281i	0.221852	+	0.435410i	−0.753075	+	0.657935i	$0.771430\pi$
$938$	−15.8537	+	0.189961i	−0.517641	+	0.00620245i
$939$	17.3319	−	23.8553i	0.565604	−	0.778487i
$940$	−12.8044	+	19.0853i	−0.417632	+	0.622494i
$941$	−28.9960	−	26.1082i	−0.945244	−	0.851101i	0.0437523	−	0.999042i	$-0.486069\pi$
$941$	−28.9960	−	26.1082i	−0.945244	−	0.851101i	−0.988996	+	0.147941i	$0.952735\pi$
$942$	11.5601	−	9.36120i	0.376649	−	0.305004i
$943$	2.42445	−	2.99394i	0.0789509	−	0.0974963i
$944$	2.10532	−	6.47949i	0.0685222	−	0.210890i
$945$	0.976774	+	19.7681i	0.0317745	+	0.643055i
$946$	4.10458	−	4.77121i	0.133452	−	0.155125i
$947$	45.7731	−	12.2649i	1.48743	−	0.398554i	0.578558	−	0.815641i	$-0.303616\pi$
$947$	45.7731	−	12.2649i	1.48743	−	0.398554i	0.908867	+	0.417087i	$0.136949\pi$
$948$	−22.3521	−	14.5156i	−0.725961	−	0.471445i
$949$	−12.2027	+	27.4076i	−0.396115	+	0.889689i
$950$	19.1060	−	9.02509i	0.619881	−	0.292812i
$951$	60.6850	−	19.7178i	1.96785	−	0.639392i
$952$	−10.8764	+	2.44840i	−0.352505	+	0.0793531i
$953$	−56.1251	+	8.88935i	−1.81807	+	0.287954i	−0.970210	−	0.242264i	$-0.922110\pi$
$953$	−56.1251	+	8.88935i	−1.81807	+	0.287954i	−0.847861	+	0.530218i	$0.822110\pi$
$954$	11.7786	−	1.23798i	0.381347	−	0.0400812i
$955$	32.1516	+	45.6753i	1.04040	+	1.47802i
$956$	−8.00512	−	13.8653i	−0.258904	−	0.448435i
$957$	−2.56767	+	18.9790i	−0.0830011	+	0.613503i
$958$	−29.7100	−	29.7100i	−0.959886	−	0.959886i
$959$	−4.86297	+	1.93388i	−0.157033	+	0.0624483i
$960$	4.55148	−	1.14682i	0.146898	−	0.0370136i
$961$	28.0568	−	12.4917i	0.905059	−	0.402958i
$962$	−2.36134	−	45.0570i	−0.0761325	−	1.45269i
$963$	0.794098	+	15.1523i	0.0255895	+	0.488276i
$964$	−11.0017	+	4.89829i	−0.354342	+	0.157763i
$965$	−47.2788	+	11.9127i	−1.52196	+	0.383484i
$966$	−1.48144	−	1.17054i	−0.0476645	−	0.0376614i
$967$	−21.2577	−	21.2577i	−0.683602	−	0.683602i	0.277208	−	0.960810i	$-0.410591\pi$
$967$	−21.2577	−	21.2577i	−0.683602	−	0.683602i	−0.960810	+	0.277208i	$0.910591\pi$
$968$	1.07158	+	10.9477i	0.0344420	+	0.351872i
$969$	18.6900	+	32.3720i	0.600410	+	1.03994i
$970$	−13.0525	−	18.5427i	−0.419091	−	0.595371i
$971$	−2.97793	+	0.312993i	−0.0955662	+	0.0100444i	−0.152191	−	0.988351i	$-0.548633\pi$
$971$	−2.97793	+	0.312993i	−0.0955662	+	0.0100444i	0.0566246	+	0.998396i	$0.481966\pi$
$972$	13.3930	−	2.12125i	0.429582	−	0.0680390i
$973$	15.0002	+	4.67593i	0.480885	+	0.149903i
$974$	30.1645	−	9.80106i	0.966534	−	0.314046i
$975$	40.7686	+	14.6097i	1.30564	+	0.467883i
$976$	3.32881	−	7.47662i	0.106553	−	0.239321i
$977$	−34.4610	−	22.3792i	−1.10250	−	0.715974i	−0.140792	−	0.990039i	$-0.544965\pi$
$977$	−34.4610	−	22.3792i	−1.10250	−	0.715974i	−0.961711	+	0.274065i	$0.911632\pi$
$978$	15.7344	−	4.21603i	0.503131	−	0.134814i
$979$	31.6625	+	13.2478i	1.01194	+	0.423402i
$980$	−10.5777	−	11.5374i	−0.337893	−	0.368549i
$981$	0.948756	−	2.91997i	0.0302914	−	0.0932275i
$982$	−6.70678	+	8.28219i	−0.214022	+	0.264295i
$983$	37.6553	−	30.4927i	1.20102	−	0.972565i	0.201043	−	0.979582i	$-0.435567\pi$
$983$	37.6553	−	30.4927i	1.20102	−	0.972565i	0.999975	+	0.00701711i	$0.00223364\pi$
$984$	−17.6771	−	15.9166i	−0.563526	−	0.507401i
$985$	−23.9266	+	35.6634i	−0.762365	+	1.13633i
$986$	6.81349	−	9.37796i	0.216986	−	0.298655i
$987$	−0.683911	−	57.0776i	−0.0217691	−	1.81680i
$988$	7.91665	+	15.5373i	0.251862	+	0.494307i
$989$	−0.558707	−	0.322570i	−0.0177659	−	0.0102571i
$990$	8.78951	+	5.61302i	0.279349	+	0.178393i
$991$	−0.0829972	−	0.143755i	−0.00263649	−	0.00456654i	0.864704	−	0.502282i	$-0.167506\pi$
$991$	−0.0829972	−	0.143755i	−0.00263649	−	0.00456654i	−0.867341	+	0.497715i	$0.834173\pi$
$992$	0.535892	+	0.0280849i	0.0170146	+	0.000891696i
$993$	−5.79999	−	0.918629i	−0.184057	−	0.0291518i
$994$	−11.7223	+	7.81381i	−0.371809	+	0.247839i
$995$	13.7269	−	11.9926i	0.435172	−	0.380191i
$996$	−0.477148	−	0.101421i	−0.0151190	−	0.00321365i
$997$	−22.4323	−	27.7015i	−0.710437	−	0.877316i	0.286291	−	0.958143i	$-0.407577\pi$
$997$	−22.4323	−	27.7015i	−0.710437	−	0.877316i	−0.996728	+	0.0808263i	$0.974244\pi$
$998$	13.4688	−	5.17020i	0.426348	−	0.163660i
$999$	24.4777	+	27.1852i	0.774440	+	0.860102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.537.20	yes	768
5.3	odd	4	inner	770.2.bv.a.383.29	yes	768
7.3	odd	6	inner	770.2.bv.a.647.5	yes	768
11.5	even	5	inner	770.2.bv.a.467.5	yes	768
35.3	even	12	inner	770.2.bv.a.493.5	yes	768
55.38	odd	20	inner	770.2.bv.a.313.5	✓	768
77.38	odd	30	inner	770.2.bv.a.577.29	yes	768
385.38	even	60	inner	770.2.bv.a.423.20	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.313.5	✓	768	55.38	odd	20	inner
770.2.bv.a.383.29	yes	768	5.3	odd	4	inner
770.2.bv.a.423.20	yes	768	385.38	even	60	inner
770.2.bv.a.467.5	yes	768	11.5	even	5	inner
770.2.bv.a.493.5	yes	768	35.3	even	12	inner
770.2.bv.a.537.20	yes	768	1.1	even	1	trivial
770.2.bv.a.577.29	yes	768	77.38	odd	30	inner
770.2.bv.a.647.5	yes	768	7.3	odd	6	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0523360 + 0.998630i) q^{2} +(0.752251 + 1.95968i) q^{3} +(-0.994522 - 0.104528i) q^{4} +(0.432112 + 2.19392i) q^{5} +(-1.99636 + 0.648658i) q^{6} +(2.50628 - 0.847671i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-1.04503 + 0.940951i) q^{9} +O(q^{10})\)	\(q+(-0.0523360 + 0.998630i) q^{2} +(0.752251 + 1.95968i) q^{3} +(-0.994522 - 0.104528i) q^{4} +(0.432112 + 2.19392i) q^{5} +(-1.99636 + 0.648658i) q^{6} +(2.50628 - 0.847671i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-1.04503 + 0.940951i) q^{9} +(-2.21353 + 0.316699i) q^{10} +(0.421151 + 3.28978i) q^{11} +(-0.543288 - 2.02758i) q^{12} +(-3.67653 + 1.87329i) q^{13} +(0.715341 + 2.54721i) q^{14} +(-3.97432 + 2.49718i) q^{15} +(0.978148 + 0.207912i) q^{16} +(-0.220531 - 4.20798i) q^{17} +(-0.884969 - 1.09285i) q^{18} +(0.441745 + 4.20292i) q^{19} +(-0.200418 - 2.22707i) q^{20} +(3.54652 + 4.27385i) q^{21} +(-3.30731 + 0.248400i) q^{22} +(0.0879899 + 0.328383i) q^{23} +(2.05323 - 0.436428i) q^{24} +(-4.62656 + 1.89604i) q^{25} +(-1.67830 - 3.76953i) q^{26} +(2.98085 + 1.51882i) q^{27} +(-2.58116 + 0.581050i) q^{28} +(1.61696 - 2.22556i) q^{29} +(-2.28576 - 4.09957i) q^{30} +(-0.111571 - 0.524901i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-6.13010 + 3.30006i) q^{33} +4.21375 q^{34} +(2.94272 + 5.13229i) q^{35} +(1.13766 - 0.826561i) q^{36} +(10.2083 + 3.91858i) q^{37} +(-4.22028 + 0.221176i) q^{38} +(-6.43672 - 5.79565i) q^{39} +(2.23451 - 0.0835871i) q^{40} +(-6.66075 - 9.16774i) q^{41} +(-4.45361 + 3.31798i) q^{42} +(-1.34185 + 1.34185i) q^{43} +(-0.0749684 - 3.31578i) q^{44} +(-2.51594 - 1.88612i) q^{45} +(-0.332538 + 0.0706831i) q^{46} +(-7.98761 - 6.46824i) q^{47} +(0.328372 + 2.07326i) q^{48} +(5.56291 - 4.24901i) q^{49} +(-1.65130 - 4.71945i) q^{50} +(8.08040 - 3.59762i) q^{51} +(3.85220 - 1.47872i) q^{52} +(-4.58705 + 7.06344i) q^{53} +(-1.67274 + 2.89728i) q^{54} +(-7.03552 + 2.34552i) q^{55} +(-0.445166 - 2.60803i) q^{56} +(-7.90408 + 4.02733i) q^{57} +(2.13788 + 1.73122i) q^{58} +(0.712147 - 6.77562i) q^{59} +(4.21358 - 2.06807i) q^{60} +(1.70159 - 8.00534i) q^{61} +(0.530020 - 0.0839470i) q^{62} +(-1.82153 + 3.24413i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(-5.69851 - 7.25654i) q^{65} +(-2.97471 - 6.29441i) q^{66} +(-1.55099 + 5.78837i) q^{67} +(-0.220531 + 4.20798i) q^{68} +(-0.577335 + 0.419458i) q^{69} +(-5.27927 + 2.67008i) q^{70} +(1.64543 + 5.06410i) q^{71} +(0.765887 + 1.17936i) q^{72} +(5.65049 - 4.57568i) q^{73} +(-4.44747 + 9.98919i) q^{74} +(-7.19596 - 7.64028i) q^{75} -4.22607i q^{76} +(3.84417 + 7.88811i) q^{77} +(6.12458 - 6.12458i) q^{78} +(9.43552 - 8.49578i) q^{79} +(-0.0334724 + 2.23582i) q^{80} +(-1.17503 + 11.1796i) q^{81} +(9.50377 - 6.17182i) q^{82} +(0.105502 - 0.207060i) q^{83} +(-3.08035 - 4.62115i) q^{84} +(9.13667 - 2.30214i) q^{85} +(-1.26978 - 1.41023i) q^{86} +(5.57775 + 1.49455i) q^{87} +(3.31516 + 0.0986687i) q^{88} +(5.17427 - 8.96210i) q^{89} +(2.01521 - 2.41378i) q^{90} +(-7.62650 + 7.81148i) q^{91} +(-0.0531825 - 0.335781i) q^{92} +(0.944708 - 0.613501i) q^{93} +(6.87741 - 7.63814i) q^{94} +(-9.02999 + 2.78528i) q^{95} +(-2.08760 + 0.219416i) q^{96} +(4.60392 + 9.03571i) q^{97} +(3.95205 + 5.77766i) q^{98} +(-3.53563 - 3.04164i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) \) 768 * q + 24 * q^5 + 4 * q^7	\( 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) \) 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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