LMFDB - Embedded newform 966.2.be.b.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(19,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 45]))

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

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

chi := DirichletCharacter("966.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.be (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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	966.19
Dual form			966.2.be.b.661.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.995472 - 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-2.88028 + 1.48489i) q^{5} +(0.755750 - 0.654861i) q^{6} +(-2.06769 + 1.65065i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})$	\(q+(-0.995472 - 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-2.88028 + 1.48489i) q^{5} +(0.755750 - 0.654861i) q^{6} +(-2.06769 + 1.65065i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(3.00838 - 1.20438i) q^{10} +(0.551774 + 5.77843i) q^{11} +(-0.814576 + 0.580057i) q^{12} +(6.26183 + 0.900315i) q^{13} +(2.21523 - 1.44663i) q^{14} +(0.912957 - 3.10924i) q^{15} +(0.928368 + 0.371662i) q^{16} +(0.363922 - 1.05148i) q^{17} +(-0.0475819 + 0.998867i) q^{18} +(2.19426 + 6.33991i) q^{19} +(-3.10924 + 0.912957i) q^{20} +(0.232241 - 2.63554i) q^{21} -5.80472i q^{22} +(-1.12525 + 4.66195i) q^{23} +(0.866025 - 0.500000i) q^{24} +(3.19083 - 4.48090i) q^{25} +(-6.14790 - 1.49146i) q^{26} +(0.755750 + 0.654861i) q^{27} +(-2.34272 + 1.22951i) q^{28} +(-5.45523 - 6.29567i) q^{29} +(-1.20438 + 3.00838i) q^{30} +(-8.64491 + 2.09723i) q^{31} +(-0.888835 - 0.458227i) q^{32} +(-4.56282 - 3.58824i) q^{33} +(-0.462224 + 1.01213i) q^{34} +(3.50451 - 7.82462i) q^{35} +(0.142315 - 0.989821i) q^{36} +(-0.666684 + 0.0317581i) q^{37} +(-1.58168 - 6.51978i) q^{38} +(-4.97275 + 3.91061i) q^{39} +(3.18195 - 0.613270i) q^{40} +(-2.75630 + 4.28889i) q^{41} +(-0.481713 + 2.60153i) q^{42} +(-2.56484 - 8.73506i) q^{43} +(-0.551774 + 5.77843i) q^{44} +(1.62025 + 2.80636i) q^{45} +(1.56330 - 4.53388i) q^{46} +(-2.12752 - 1.22832i) q^{47} +(-0.909632 + 0.415415i) q^{48} +(1.55071 - 6.82607i) q^{49} +(-3.60232 + 4.15730i) q^{50} +(0.509860 + 0.988990i) q^{51} +(5.97829 + 2.06910i) q^{52} +(2.21562 + 2.81739i) q^{53} +(-0.690079 - 0.723734i) q^{54} +(-10.1696 - 15.8242i) q^{55} +(2.44898 - 1.00125i) q^{56} +(-6.10263 - 2.78698i) q^{57} +(4.83209 + 6.78572i) q^{58} +(1.01118 + 2.52581i) q^{59} +(1.48489 - 2.88028i) q^{60} +(5.13212 - 4.89346i) q^{61} +(8.80512 - 1.26598i) q^{62} +(1.74716 + 1.98681i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-19.3727 + 6.70495i) q^{65} +(4.20107 + 4.00571i) q^{66} +(3.75096 + 2.67105i) q^{67} +(0.556340 - 0.963609i) q^{68} +(-2.59750 - 4.03150i) q^{69} +(-4.23241 + 7.45607i) q^{70} +(-1.30278 - 2.85269i) q^{71} +(-0.235759 + 0.971812i) q^{72} +(-0.870434 + 4.51624i) q^{73} +(0.666684 + 0.0317581i) q^{74} +(1.04105 + 5.40149i) q^{75} +(0.954775 + 6.64061i) q^{76} +(-10.6791 - 11.0372i) q^{77} +(5.32196 - 3.42021i) q^{78} +(9.19904 - 11.6975i) q^{79} +(-3.22584 + 0.308030i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(3.15151 - 4.00747i) q^{82} +(6.29934 - 4.04834i) q^{83} +(0.726823 - 2.54396i) q^{84} +(0.513137 + 3.56895i) q^{85} +(1.72291 + 8.93931i) q^{86} +(8.32093 + 0.396375i) q^{87} +(1.09855 - 5.69982i) q^{88} +(-0.579394 + 2.38829i) q^{89} +(-1.34616 - 2.94767i) q^{90} +(-14.4337 + 8.47451i) q^{91} +(-1.98720 + 4.36475i) q^{92} +(4.44783 - 7.70387i) q^{93} +(2.00113 + 1.42499i) q^{94} +(-15.7341 - 15.0025i) q^{95} +(0.945001 - 0.327068i) q^{96} +(3.01030 + 1.93460i) q^{97} +(-2.19255 + 6.64776i) q^{98} +(5.74563 - 0.826098i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9}+O(q^{10}) $ 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9	$ 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9} + 22 q^{14} + 16 q^{16} - 66 q^{17} - 16 q^{18} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+O(q^{100}) $ 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9 + 22 * q^14 + 16 * q^16 - 66 * q^17 - 16 * q^18 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{15}{22}\right)$

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 $

$2$	−0.995472	−	0.0950560i	−0.703905	−	0.0672148i
$2$	−0.995472	−	0.0950560i	−0.703905	−	0.0672148i
$3$	−0.690079	+	0.723734i	−0.398417	+	0.417848i
$3$	−0.690079	+	0.723734i	−0.398417	+	0.417848i
$4$	0.981929	+	0.189251i	0.490964	+	0.0946256i
$5$	−2.88028	+	1.48489i	−1.28810	+	0.664062i	−0.959846	−	0.280528i	$-0.909490\pi$
$5$	−2.88028	+	1.48489i	−1.28810	+	0.664062i	−0.328254	+	0.944590i	$0.606460\pi$
$6$	0.755750	−	0.654861i	0.308533	−	0.267346i
$7$	−2.06769	+	1.65065i	−0.781515	+	0.623887i
$7$	−2.06769	+	1.65065i	−0.781515	+	0.623887i
$8$	−0.959493	−	0.281733i	−0.339232	−	0.0996075i
$9$	−0.0475819	−	0.998867i	−0.0158606	−	0.332956i
$10$	3.00838	−	1.20438i	0.951335	−	0.380857i
$11$	0.551774	+	5.77843i	0.166366	+	1.74226i	0.564944	+	0.825129i	$0.308898\pi$
$11$	0.551774	+	5.77843i	0.166366	+	1.74226i	−0.398578	+	0.917134i	$0.630496\pi$
$12$	−0.814576	+	0.580057i	−0.235148	+	0.167448i
$13$	6.26183	+	0.900315i	1.73672	+	0.249703i	0.936665	−	0.350225i	$-0.113895\pi$
$13$	6.26183	+	0.900315i	1.73672	+	0.249703i	0.800054	+	0.599928i	$0.204804\pi$
$14$	2.21523	−	1.44663i	0.592046	−	0.386628i
$15$	0.912957	−	3.10924i	0.235724	−	0.802804i
$16$	0.928368	+	0.371662i	0.232092	+	0.0929156i
$17$	0.363922	−	1.05148i	0.0882641	−	0.255022i	−0.892227	−	0.451588i	$-0.850858\pi$
$17$	0.363922	−	1.05148i	0.0882641	−	0.255022i	0.980491	+	0.196566i	$0.0629789\pi$
$18$	−0.0475819	+	0.998867i	−0.0112152	+	0.235435i
$19$	2.19426	+	6.33991i	0.503399	+	1.45448i	0.855149	+	0.518382i	$0.173465\pi$
$19$	2.19426	+	6.33991i	0.503399	+	1.45448i	−0.351751	+	0.936094i	$0.614413\pi$
$20$	−3.10924	+	0.912957i	−0.695248	+	0.204143i
$21$	0.232241	−	2.63554i	0.0506791	−	0.575122i
$22$		−	5.80472i		−	1.23757i
$23$	−1.12525	+	4.66195i	−0.234631	+	0.972084i
$23$	−1.12525	+	4.66195i	−0.234631	+	0.972084i
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	3.19083	−	4.48090i	0.638166	−	0.896179i
$26$	−6.14790	−	1.49146i	−1.20570	−	0.292500i
$27$	0.755750	+	0.654861i	0.145444	+	0.126028i
$28$	−2.34272	+	1.22951i	−0.442732	+	0.232355i
$29$	−5.45523	−	6.29567i	−1.01301	−	1.16908i	−0.985538	−	0.169454i	$-0.945800\pi$
$29$	−5.45523	−	6.29567i	−1.01301	−	1.16908i	−0.0274725	−	0.999623i	$-0.508746\pi$
$30$	−1.20438	+	3.00838i	−0.219888	+	0.549253i
$31$	−8.64491	+	2.09723i	−1.55267	+	0.376674i	−0.918151	−	0.396232i	$-0.870318\pi$
$31$	−8.64491	+	2.09723i	−1.55267	+	0.376674i	−0.634521	+	0.772906i	$0.718803\pi$
$32$	−0.888835	−	0.458227i	−0.157125	−	0.0810038i
$33$	−4.56282	−	3.58824i	−0.794284	−	0.624632i
$34$	−0.462224	+	1.01213i	−0.0792708	+	0.173579i
$35$	3.50451	−	7.82462i	0.592370	−	1.32260i
$36$	0.142315	−	0.989821i	0.0237191	−	0.164970i
$37$	−0.666684	+	0.0317581i	−0.109602	+	0.00522100i	−0.102311	−	0.994752i	$-0.532624\pi$
$37$	−0.666684	+	0.0317581i	−0.109602	+	0.00522100i	−0.00729084	+	0.999973i	$0.502321\pi$
$38$	−1.58168	−	6.51978i	−0.256583	−	1.05765i
$39$	−4.97275	+	3.91061i	−0.796277	+	0.626199i
$40$	3.18195	−	0.613270i	0.503110	−	0.0969665i
$41$	−2.75630	+	4.28889i	−0.430462	+	0.669812i	−0.986947	−	0.161046i	$-0.948513\pi$
$41$	−2.75630	+	4.28889i	−0.430462	+	0.669812i	0.556485	+	0.830858i	$0.312150\pi$
$42$	−0.481713	+	2.60153i	−0.0743299	+	0.401425i
$43$	−2.56484	−	8.73506i	−0.391135	−	1.33208i	−0.886230	−	0.463245i	$-0.846685\pi$
$43$	−2.56484	−	8.73506i	−0.391135	−	1.33208i	0.495095	−	0.868839i	$-0.335133\pi$
$44$	−0.551774	+	5.77843i	−0.0831830	+	0.871132i
$45$	1.62025	+	2.80636i	0.241533	+	0.418348i
$46$	1.56330	−	4.53388i	0.230497	−	0.668484i
$47$	−2.12752	−	1.22832i	−0.310330	−	0.179169i	0.336744	−	0.941596i	$-0.390674\pi$
$47$	−2.12752	−	1.22832i	−0.310330	−	0.179169i	−0.647074	+	0.762427i	$0.724008\pi$
$48$	−0.909632	+	0.415415i	−0.131294	+	0.0599600i
$49$	1.55071	−	6.82607i	0.221530	−	0.975153i
$50$	−3.60232	+	4.15730i	−0.509445	+	0.587931i
$51$	0.509860	+	0.988990i	0.0713946	+	0.138486i
$52$	5.97829	+	2.06910i	0.829039	+	0.286933i
$53$	2.21562	+	2.81739i	0.304338	+	0.386998i	0.914034	−	0.405638i	$-0.132951\pi$
$53$	2.21562	+	2.81739i	0.304338	+	0.386998i	−0.609695	+	0.792636i	$0.708708\pi$
$54$	−0.690079	−	0.723734i	−0.0939079	−	0.0984877i
$55$	−10.1696	−	15.8242i	−1.37127	−	2.13373i
$56$	2.44898	−	1.00125i	0.327259	−	0.133798i
$57$	−6.10263	−	2.78698i	−0.808312	−	0.369144i
$58$	4.83209	+	6.78572i	0.634484	+	0.891008i
$59$	1.01118	+	2.52581i	0.131645	+	0.328833i	0.979515	−	0.201371i	$-0.0645396\pi$
$59$	1.01118	+	2.52581i	0.131645	+	0.328833i	−0.847870	+	0.530204i	$0.822115\pi$
$60$	1.48489	−	2.88028i	0.191698	−	0.371842i
$61$	5.13212	−	4.89346i	0.657100	−	0.626544i	−0.286324	−	0.958133i	$-0.592433\pi$
$61$	5.13212	−	4.89346i	0.657100	−	0.626544i	0.943424	+	0.331589i	$0.107585\pi$
$62$	8.80512	−	1.26598i	1.11825	−	0.160780i
$63$	1.74716	+	1.98681i	0.220122	+	0.250315i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	−19.3727	+	6.70495i	−2.40289	+	0.831647i
$66$	4.20107	+	4.00571i	0.517116	+	0.493069i
$67$	3.75096	+	2.67105i	0.458253	+	0.326320i	0.785763	−	0.618527i	$-0.212270\pi$
$67$	3.75096	+	2.67105i	0.458253	+	0.326320i	−0.327511	+	0.944847i	$0.606210\pi$
$68$	0.556340	−	0.963609i	0.0674661	−	0.116855i
$69$	−2.59750	−	4.03150i	−0.312702	−	0.485335i
$70$	−4.23241	+	7.45607i	−0.505870	+	0.891170i
$71$	−1.30278	−	2.85269i	−0.154612	−	0.338553i	0.816437	−	0.577435i	$-0.195946\pi$
$71$	−1.30278	−	2.85269i	−0.154612	−	0.338553i	−0.971049	+	0.238882i	$0.923219\pi$
$72$	−0.235759	+	0.971812i	−0.0277845	+	0.114529i
$73$	−0.870434	+	4.51624i	−0.101877	+	0.528586i	0.894754	+	0.446560i	$0.147351\pi$
$73$	−0.870434	+	4.51624i	−0.101877	+	0.528586i	−0.996630	+	0.0820259i	$0.973861\pi$
$74$	0.666684	+	0.0317581i	0.0775004	+	0.00369180i
$75$	1.04105	+	5.40149i	0.120210	+	0.623710i
$76$	0.954775	+	6.64061i	0.109520	+	0.761730i
$77$	−10.6791	−	11.0372i	−1.21699	−	1.25781i
$78$	5.32196	−	3.42021i	0.602593	−	0.387263i
$79$	9.19904	−	11.6975i	1.03497	−	1.31607i	0.0875258	−	0.996162i	$-0.472104\pi$
$79$	9.19904	−	11.6975i	1.03497	−	1.31607i	0.947447	−	0.319913i	$-0.103654\pi$
$80$	−3.22584	+	0.308030i	−0.360659	+	0.0344388i
$81$	−0.995472	+	0.0950560i	−0.110608	+	0.0105618i
$82$	3.15151	−	4.00747i	0.348026	−	0.442551i
$83$	6.29934	−	4.04834i	0.691442	−	0.444363i	−0.147156	−	0.989113i	$-0.547012\pi$
$83$	6.29934	−	4.04834i	0.691442	−	0.444363i	0.838598	+	0.544750i	$0.183376\pi$
$84$	0.726823	−	2.54396i	0.0793029	−	0.277569i
$85$	0.513137	+	3.56895i	0.0556576	+	0.387107i
$86$	1.72291	+	8.93931i	0.185786	+	0.963951i
$87$	8.32093	+	0.396375i	0.892097	+	0.0424958i
$88$	1.09855	−	5.69982i	0.117106	−	0.607603i
$89$	−0.579394	+	2.38829i	−0.0614156	+	0.253159i	−0.994241	−	0.107171i	$-0.965821\pi$
$89$	−0.579394	+	2.38829i	−0.0614156	+	0.253159i	0.932825	+	0.360330i	$0.117336\pi$
$90$	−1.34616	−	2.94767i	−0.141897	−	0.310712i
$91$	−14.4337	+	8.47451i	−1.51306	+	0.888370i
$92$	−1.98720	+	4.36475i	−0.207180	+	0.455057i
$93$	4.44783	−	7.70387i	0.461219	−	0.798854i
$94$	2.00113	+	1.42499i	0.206400	+	0.146977i
$95$	−15.7341	−	15.0025i	−1.61429	−	1.53922i
$96$	0.945001	−	0.327068i	0.0964487	−	0.0333812i
$97$	3.01030	+	1.93460i	0.305650	+	0.196429i	0.684470	−	0.729041i	$-0.260034\pi$
$97$	3.01030	+	1.93460i	0.305650	+	0.196429i	−0.378820	+	0.925470i	$0.623670\pi$
$98$	−2.19255	+	6.64776i	−0.221481	+	0.671525i
$99$	5.74563	−	0.826098i	0.577458	−	0.0830259i
$100$	3.98118	−	3.79605i	0.398118	−	0.379605i
$101$	−2.10570	+	4.08448i	−0.209524	+	0.406421i	−0.970056	−	0.242880i	$-0.921908\pi$
$101$	−2.10570	+	4.08448i	−0.209524	+	0.406421i	0.760532	+	0.649301i	$0.224938\pi$
$102$	−0.413541	−	1.03298i	−0.0409467	−	0.102280i
$103$	8.97824	+	12.6082i	0.884653	+	1.24232i	0.969293	+	0.245909i	$0.0790865\pi$
$103$	8.97824	+	12.6082i	0.884653	+	1.24232i	−0.0846402	+	0.996412i	$0.526974\pi$
$104$	−5.75454	−	2.62801i	−0.564279	−	0.257697i
$105$	3.24456	+	7.93594i	0.316637	+	0.774468i
$106$	−1.93777	−	3.01524i	−0.188213	−	0.292866i
$107$	−3.48822	−	3.65834i	−0.337219	−	0.353665i	0.533189	−	0.845996i	$-0.320993\pi$
$107$	−3.48822	−	3.65834i	−0.337219	−	0.353665i	−0.870408	+	0.492331i	$0.836145\pi$
$108$	0.618159	+	0.786053i	0.0594824	+	0.0756380i
$109$	−14.5493	−	5.03556i	−1.39357	−	0.482319i	−0.475843	−	0.879530i	$-0.657857\pi$
$109$	−14.5493	−	5.03556i	−1.39357	−	0.482319i	−0.917727	+	0.397211i	$0.869978\pi$
$110$	8.61935	+	16.7192i	0.821823	+	1.59411i
$111$	0.437080	−	0.504418i	0.0414858	−	0.0478772i
$112$	−2.53306	+	0.763926i	−0.239352	+	0.0721842i
$113$	−2.17535	+	0.993449i	−0.204640	+	0.0934558i	−0.515098	−	0.857131i	$-0.672245\pi$
$113$	−2.17535	+	0.993449i	−0.204640	+	0.0934558i	0.310459	+	0.950587i	$0.399517\pi$
$114$	5.81007	+	3.35445i	0.544163	+	0.314173i
$115$	−3.68143	−	15.0986i	−0.343296	−	1.40795i
$116$	−4.16518	−	7.21431i	−0.386727	−	0.669832i
$117$	0.601346	−	6.29758i	0.0555944	−	0.582211i
$118$	−0.766511	−	2.61050i	−0.0705630	−	0.240316i
$119$	0.983152	+	2.77485i	0.0901254	+	0.254370i
$120$	−1.75195	+	2.72609i	−0.159931	+	0.248857i
$121$	−22.2846	+	4.29501i	−2.02588	+	0.390456i
$122$	−5.57403	+	4.38347i	−0.504649	+	0.396860i
$123$	−1.20195	−	4.95450i	−0.108376	−	0.446733i
$124$	−8.88559	+	0.423273i	−0.797949	+	0.0380110i
$125$	−0.230998	+	1.60663i	−0.0206611	+	0.143701i
$126$	−1.55040	−	2.14389i	−0.138120	−	0.190993i
$127$	2.17353	−	4.75936i	0.192869	−	0.422325i	−0.788348	−	0.615229i	$-0.789063\pi$
$127$	2.17353	−	4.75936i	0.192869	−	0.422325i	0.981218	+	0.192904i	$0.0617907\pi$
$128$	−0.786053	−	0.618159i	−0.0694779	−	0.0546381i
$129$	8.09181	+	4.17162i	0.712444	+	0.367290i
$130$	19.9223	−	4.83310i	1.74730	−	0.423891i
$131$	−2.99022	+	7.46920i	−0.261256	+	0.652587i	−0.999765	−	0.0216566i	$-0.993106\pi$
$131$	−2.99022	+	7.46920i	−0.261256	+	0.652587i	0.738509	+	0.674244i	$0.235530\pi$
$132$	−3.80128	−	4.38691i	−0.330859	−	0.381832i
$133$	−15.0020	−	9.48703i	−1.30084	−	0.822630i
$134$	−3.48008	−	3.01550i	−0.300633	−	0.260500i
$135$	−3.14916	−	0.763979i	−0.271037	−	0.0657528i
$136$	−0.645418	+	0.906362i	−0.0553441	+	0.0777199i
$137$	11.7491	−	6.78333i	1.00379	−	0.579539i	0.0944235	−	0.995532i	$-0.469899\pi$
$137$	11.7491	−	6.78333i	1.00379	−	0.579539i	0.909368	+	0.415993i	$0.136566\pi$
$138$	2.20252	+	4.26015i	0.187491	+	0.362648i
$139$			7.68169i			0.651553i	0.945447	+	0.325776i	$0.105626\pi$
$139$			7.68169i			0.651553i	−0.945447	+	0.325776i	$0.894374\pi$
$140$	4.92199	−	7.01999i	0.415984	−	0.593297i
$141$	2.35714	−	0.692117i	0.198507	−	0.0582868i
$142$	1.02572	+	2.96361i	0.0860763	+	0.248701i
$143$	−1.74730	+	36.6804i	−0.146117	+	3.06737i
$144$	0.327068	−	0.945001i	0.0272557	−	0.0787501i
$145$	25.0609	+	10.0329i	2.08120	+	0.833186i
$146$	1.29579	−	4.41305i	0.107240	−	0.365227i
$147$	3.87015	+	5.83283i	0.319204	+	0.481084i
$148$	−0.660646	−	0.0949866i	−0.0543048	−	0.00780785i
$149$	−12.9243	+	9.20336i	−1.05880	+	0.753969i	−0.970251	−	0.242103i	$-0.922163\pi$
$149$	−12.9243	+	9.20336i	−1.05880	+	0.753969i	−0.0885502	+	0.996072i	$0.528223\pi$
$150$	−0.522893	−	5.47599i	−0.0426941	−	0.447112i
$151$	−20.6085	+	8.25042i	−1.67710	+	0.671409i	−0.998034	−	0.0626687i	$-0.980039\pi$
$151$	−20.6085	+	8.25042i	−1.67710	+	0.671409i	−0.679065	+	0.734078i	$0.737615\pi$
$152$	−0.319222	−	6.70130i	−0.0258923	−	0.543547i
$153$	−1.06761	−	0.313478i	−0.0863111	−	0.0253432i
$154$	9.58156	+	12.0024i	0.772104	+	0.967179i
$155$	21.7856	−	18.8773i	1.74986	−	1.51626i
$156$	−5.62297	+	2.89884i	−0.450198	+	0.232093i
$157$	6.37561	+	1.22880i	0.508829	+	0.0980688i	0.437203	−	0.899363i	$-0.355969\pi$
$157$	6.37561	+	1.22880i	0.508829	+	0.0980688i	0.0716260	+	0.997432i	$0.477181\pi$
$158$	−10.2693	+	10.7701i	−0.816982	+	0.856826i
$159$	−3.56799	−	0.340702i	−0.282960	−	0.0270194i
$160$	3.24051			0.256185
$161$	−5.36857	−	11.4969i	−0.423103	−	0.906082i
$162$	1.00000			0.0785674
$163$	−6.07621	−	0.580208i	−0.475926	−	0.0454454i	−0.145663	−	0.989334i	$-0.546531\pi$
$163$	−6.07621	−	0.580208i	−0.475926	−	0.0454454i	−0.330263	+	0.943889i	$0.607137\pi$
$164$	−3.51817	+	3.68975i	−0.274723	+	0.288121i
$165$	18.4703	+	3.55986i	1.43791	+	0.277135i
$166$	−6.65563	+	3.43122i	−0.516577	+	0.266314i
$167$	−0.839517	+	0.727445i	−0.0649637	+	0.0562914i	−0.686737	−	0.726906i	$-0.740958\pi$
$167$	−0.839517	+	0.727445i	−0.0649637	+	0.0562914i	0.621774	+	0.783197i	$0.286412\pi$
$168$	−0.965350	+	2.46335i	−0.0744784	+	0.190052i
$169$	25.9266	+	7.61272i	1.99435	+	0.585594i
$170$	−0.171564	−	3.60157i	−0.0131583	−	0.276227i
$171$	6.22832	−	2.49344i	0.476292	−	0.190678i
$172$	−0.865374	−	9.06261i	−0.0659841	−	0.691017i
$173$	11.8177	−	8.41536i	0.898485	−	0.639808i	−0.0346246	−	0.999400i	$-0.511024\pi$
$173$	11.8177	−	8.41536i	0.898485	−	0.639808i	0.933110	+	0.359592i	$0.117084\pi$
$174$	−8.24557	−	1.18553i	−0.625095	−	0.0898751i
$175$	0.798727	+	14.5321i	0.0603781	+	1.09852i
$176$	−1.63538	+	5.56959i	−0.123271	+	0.419823i
$177$	−2.52581	−	1.01118i	−0.189852	−	0.0760052i
$178$	0.803792	−	2.32241i	0.0602468	−	0.174072i
$179$	1.19170	−	25.0168i	0.0890717	−	1.86985i	−0.307111	−	0.951674i	$-0.599362\pi$
$179$	1.19170	−	25.0168i	0.0890717	−	1.86985i	0.396183	−	0.918172i	$-0.370335\pi$
$180$	1.05987	+	3.06228i	0.0789978	+	0.228249i
$181$	11.4661	−	3.36675i	0.852269	−	0.250249i	0.173712	−	0.984796i	$-0.444424\pi$
$181$	11.4661	−	3.36675i	0.852269	−	0.250249i	0.678557	+	0.734548i	$0.262606\pi$
$182$	15.1739	−	7.06413i	1.12476	−	0.523628i
$183$			7.09116i			0.524194i
$184$	2.39310	−	4.15609i	0.176421	−	0.306391i
$185$	1.87308	−	1.08142i	0.137711	−	0.0795078i
$186$	−5.15999	+	7.24619i	−0.378349	+	0.531317i
$187$	6.27673	+	1.52272i	0.459000	+	0.111352i
$188$	−1.85661	−	1.60876i	−0.135407	−	0.117331i
$189$	−2.64360	−	0.106574i	−0.192294	−	0.00775209i
$190$	14.2368	+	16.4302i	1.03285	+	1.19197i
$191$	−1.61435	+	4.03245i	−0.116810	+	0.291778i	−0.975239	−	0.221156i	$-0.929017\pi$
$191$	−1.61435	+	4.03245i	−0.116810	+	0.291778i	0.858428	+	0.512934i	$0.171441\pi$
$192$	−0.971812	+	0.235759i	−0.0701345	+	0.0170144i
$193$	2.10350	+	1.08443i	0.151414	+	0.0780591i	0.532268	−	0.846576i	$-0.321340\pi$
$193$	2.10350	+	1.08443i	0.151414	+	0.0780591i	−0.380855	+	0.924635i	$0.624370\pi$
$194$	−2.81278	−	2.21199i	−0.201946	−	0.158812i
$195$	8.51608	−	18.6476i	0.609849	−	1.33538i
$196$	2.81453	−	6.40924i	0.201038	−	0.457803i
$197$	1.58171	−	11.0010i	0.112692	−	0.783791i	−0.852590	−	0.522581i	$-0.824969\pi$
$197$	1.58171	−	11.0010i	0.112692	−	0.783791i	0.965282	−	0.261210i	$-0.0841216\pi$
$198$	−5.79814	+	0.276200i	−0.412056	+	0.0196287i
$199$	−1.36600	−	5.63072i	−0.0968330	−	0.399151i	0.902681	−	0.430309i	$-0.141596\pi$
$199$	−1.36600	−	5.63072i	−0.0968330	−	0.399151i	−0.999514	+	0.0311584i	$0.990080\pi$
$200$	−4.32399	+	3.40043i	−0.305753	+	0.240446i
$201$	−4.52159	+	0.871464i	−0.318928	+	0.0614683i
$202$	2.48441	−	3.86582i	0.174803	−	0.271998i
$203$	21.6717	+	4.01284i	1.52105	+	0.281646i
$204$	0.313478	+	1.06761i	0.0219479	+	0.0747476i
$205$	1.57040	−	16.4460i	0.109682	−	1.14864i
$206$	−7.73911	−	13.4045i	−0.539209	−	0.933938i
$207$	4.71021	+	0.902153i	0.327383	+	0.0627039i
$208$	5.47867	+	3.16311i	0.379877	+	0.219322i
$209$	−35.4240	+	16.1776i	−2.45033	+	1.11903i
$210$	−2.47551	−	8.20842i	−0.170826	−	0.566435i
$211$	−10.4404	+	12.0489i	−0.718747	+	0.829479i	−0.991156	−	0.132703i	$-0.957634\pi$
$211$	−10.4404	+	12.0489i	−0.718747	+	0.829479i	0.272408	+	0.962182i	$0.412180\pi$
$212$	1.64238	+	3.18578i	0.112799	+	0.218800i
$213$	2.96361	+	1.02572i	0.203064	+	0.0702810i
$214$	3.12468	+	3.97335i	0.213598	+	0.271613i
$215$	20.3580	+	21.3509i	1.38841	+	1.45612i
$216$	−0.540641	−	0.841254i	−0.0367859	−	0.0572401i
$217$	14.4132	−	18.6061i	0.978434	−	1.26307i
$218$	14.0048	+	6.39576i	0.948522	+	0.433175i
$219$	−2.66789	−	3.74653i	−0.180279	−	0.253167i
$220$	−6.99106	−	17.4628i	−0.471337	−	1.17734i
$221$	3.22549	−	6.25657i	0.216970	−	0.420862i
$222$	−0.483049	+	0.460586i	−0.0324201	+	0.0309125i
$223$	0.179647	−	0.0258294i	0.0120301	−	0.00172966i	−0.136297	−	0.990668i	$-0.543520\pi$
$223$	0.179647	−	0.0258294i	0.0120301	−	0.00172966i	0.148327	+	0.988938i	$0.452611\pi$
$224$	2.59421	−	0.519684i	0.173333	−	0.0347228i
$225$	−4.62765	−	2.97401i	−0.308510	−	0.198267i
$226$	2.25993	−	0.782171i	0.150329	−	0.0520292i
$227$	12.9659	+	12.3629i	0.860575	+	0.820556i	0.985158	−	0.171653i	$-0.0549107\pi$
$227$	12.9659	+	12.3629i	0.860575	+	0.820556i	−0.124583	+	0.992209i	$0.539759\pi$
$228$	−5.46490	−	3.89154i	−0.361922	−	0.257724i
$229$	−12.0979	+	20.9542i	−0.799454	+	1.38470i	0.120518	+	0.992711i	$0.461545\pi$
$229$	−12.0979	+	20.9542i	−0.799454	+	1.38470i	−0.919972	+	0.391984i	$0.871789\pi$
$230$	2.22955	+	15.3802i	0.147012	+	1.01414i
$231$	15.3574	−	0.112233i	1.01044	−	0.00738441i
$232$	3.46056	+	7.57757i	0.227197	+	0.497492i
$233$	−0.119648	+	0.493197i	−0.00783842	+	0.0323104i	−0.975596	−	0.219571i	$-0.929534\pi$
$233$	−0.119648	+	0.493197i	−0.00783842	+	0.0323104i	0.967758	+	0.251882i	$0.0810493\pi$
$234$	−1.19725	+	6.21190i	−0.0782664	+	0.406085i
$235$	7.95177	+	0.378789i	0.518716	+	0.0247095i
$236$	0.514897	+	2.67154i	0.0335169	+	0.173902i
$237$	2.11784	+	14.7299i	0.137568	+	0.956808i
$238$	−0.714933	−	2.85574i	−0.0463422	−	0.185110i
$239$	3.37163	−	2.16682i	0.218093	−	0.140160i	−0.427033	−	0.904236i	$-0.640441\pi$
$239$	3.37163	−	2.16682i	0.218093	−	0.140160i	0.645126	+	0.764076i	$0.276805\pi$
$240$	2.00315	−	2.54721i	0.129303	−	0.164422i
$241$	−18.3801	+	1.75509i	−1.18397	+	0.113055i	−0.668406	−	0.743796i	$-0.733023\pi$
$241$	−18.3801	+	1.75509i	−1.18397	+	0.113055i	−0.515563	+	0.856852i	$0.672417\pi$
$242$	22.5920	−	2.15727i	1.45227	−	0.138675i
$243$	0.618159	−	0.786053i	0.0396549	−	0.0504253i
$244$	5.96547	−	3.83377i	0.381900	−	0.245432i
$245$	5.66946	+	21.9636i	0.362209	+	1.40320i
$246$	0.725552	+	5.04632i	0.0462595	+	0.321742i
$247$	8.03219	+	41.6750i	0.511076	+	2.65172i
$248$	8.88559	+	0.423273i	0.564235	+	0.0268778i
$249$	−1.41712	+	7.35272i	−0.0898063	+	0.465960i
$250$	0.382672	−	1.57740i	0.0242023	−	0.0997633i
$251$	7.95825	+	17.4261i	0.502320	+	1.09993i	0.975708	+	0.219074i	$0.0703037\pi$
$251$	7.95825	+	17.4261i	0.502320	+	1.09993i	−0.473388	+	0.880854i	$0.656969\pi$
$252$	1.33958	+	2.28156i	0.0843859	+	0.143725i
$253$	−27.5597	−	3.92985i	−1.73266	−	0.247068i
$254$	−2.61609	+	4.53120i	−0.164148	+	0.284313i
$255$	−2.93708	−	2.09148i	−0.183927	−	0.130974i
$256$	0.723734	+	0.690079i	0.0452334	+	0.0431299i
$257$	10.8090	−	3.74103i	0.674246	−	0.233359i	0.0315755	−	0.999501i	$-0.489948\pi$
$257$	10.8090	−	3.74103i	0.674246	−	0.233359i	0.642671	+	0.766142i	$0.277826\pi$
$258$	−7.65863	−	4.92190i	−0.476805	−	0.306424i
$259$	1.32608	−	1.16613i	0.0823984	−	0.0724596i
$260$	−20.2915	+	2.91748i	−1.25843	+	0.180934i
$261$	−6.02897	+	5.74861i	−0.373184	+	0.355830i
$262$	3.68667	−	7.15114i	0.227763	−	0.441799i
$263$	3.16029	+	7.89402i	0.194872	+	0.486766i	0.993333	−	0.115280i	$-0.0367766\pi$
$263$	3.16029	+	7.89402i	0.194872	+	0.486766i	−0.798461	+	0.602046i	$0.794352\pi$
$264$	3.36707	+	4.72838i	0.207229	+	0.291012i
$265$	−10.5651	−	4.82492i	−0.649008	−	0.296392i
$266$	14.0323	+	10.8701i	0.860376	+	0.666489i
$267$	−1.32866	−	2.06744i	−0.0813128	−	0.126525i
$268$	3.17768	+	3.33265i	0.194107	+	0.203574i
$269$	−4.41924	−	5.61952i	−0.269446	−	0.342628i	0.632435	−	0.774614i	$-0.282056\pi$
$269$	−4.41924	−	5.61952i	−0.269446	−	0.342628i	−0.901881	+	0.431985i	$0.857813\pi$
$270$	3.06228	+	1.05987i	0.186365	+	0.0645014i
$271$	−6.64933	−	12.8979i	−0.403918	−	0.783491i	0.595891	−	0.803066i	$-0.296799\pi$
$271$	−6.64933	−	12.8979i	−0.403918	−	0.783491i	−0.999808	+	0.0195744i	$0.993769\pi$
$272$	0.728651	−	0.840908i	0.0441809	−	0.0509875i
$273$	3.82707	−	16.2942i	0.231625	−	0.986170i
$274$	−12.3407	+	5.63580i	−0.745527	+	0.340471i
$275$	27.6532	+	15.9656i	1.66755	+	0.962760i
$276$	−1.78760	−	4.45023i	−0.107601	−	0.267872i
$277$	−8.07124	−	13.9798i	−0.484954	−	0.839965i	0.514897	−	0.857252i	$-0.327830\pi$
$277$	−8.07124	−	13.9798i	−0.484954	−	0.839965i	−0.999851	+	0.0172875i	$0.994497\pi$
$278$	0.730191	−	7.64691i	0.0437940	−	0.458631i
$279$	2.50620	+	8.53533i	0.150042	+	0.510997i
$280$	−5.56700	+	6.52034i	−0.332692	+	0.389665i
$281$	1.40552	−	2.18703i	0.0838461	−	0.130467i	−0.796797	−	0.604246i	$-0.793474\pi$
$281$	1.40552	−	2.18703i	0.0838461	−	0.130467i	0.880644	+	0.473779i	$0.157111\pi$
$282$	−2.41225	+	0.464923i	−0.143648	+	0.0276858i
$283$	14.3992	−	11.3237i	0.855944	−	0.673122i	−0.0905329	−	0.995893i	$-0.528857\pi$
$283$	14.3992	−	11.3237i	0.855944	−	0.673122i	0.946477	+	0.322772i	$0.104615\pi$
$284$	−0.739363	−	3.04770i	−0.0438731	−	0.180847i
$285$	21.7156	−	1.03444i	1.28632	−	0.0612750i
$286$	5.22608	−	36.3482i	0.309024	−	2.14931i
$287$	−1.38027	−	13.4178i	−0.0814745	−	0.792028i
$288$	−0.415415	+	0.909632i	−0.0244786	+	0.0536006i
$289$	12.3897	+	9.74339i	0.728807	+	0.573140i
$290$	−23.9938	−	12.3696i	−1.40896	−	0.726371i
$291$	−3.47749	+	0.843629i	−0.203854	+	0.0494544i
$292$	−1.70941	+	4.26990i	−0.100036	+	0.249877i
$293$	−7.56884	−	8.73491i	−0.442176	−	0.510299i	0.490288	−	0.871560i	$-0.336892\pi$
$293$	−7.56884	−	8.73491i	−0.442176	−	0.510299i	−0.932465	+	0.361262i	$0.882346\pi$
$294$	−3.29818	−	6.17430i	−0.192354	−	0.360093i
$295$	−6.66304	−	5.77356i	−0.387937	−	0.336149i
$296$	0.648626	+	0.157355i	0.0377006	+	0.00914607i
$297$	−3.36707	+	4.72838i	−0.195377	+	0.274369i
$298$	13.7406	−	7.93315i	0.795973	−	0.459555i
$299$	−11.2434	+	28.1793i	−0.650221	+	1.62965i
$300$			5.50089i			0.317594i
$301$	19.7218	+	13.8278i	1.13675	+	0.797019i
$302$	21.2995	−	6.25409i	1.22565	−	0.359883i
$303$	−1.50298	−	4.34258i	−0.0863440	−	0.249474i
$304$	−0.319222	+	6.70130i	−0.0183086	+	0.384346i
$305$	−7.51569	+	21.7151i	−0.430347	+	1.24341i
$306$	1.03298	+	0.413541i	0.0590513	+	0.0236406i
$307$	0.383180	−	1.30499i	0.0218692	−	0.0744797i	−0.947835	−	0.318760i	$-0.896734\pi$
$307$	0.383180	−	1.30499i	0.0218692	−	0.0744797i	0.969705	+	0.244280i	$0.0785517\pi$
$308$	−8.39727	−	12.8588i	−0.478479	−	0.732699i
$309$	−15.3207	−	2.20278i	−0.871562	−	0.125312i
$310$	−23.4814	+	16.7210i	−1.33365	+	0.949689i
$311$	−2.31505	−	24.2443i	−0.131274	−	1.37477i	−0.785684	−	0.618628i	$-0.787689\pi$
$311$	−2.31505	−	24.2443i	−0.131274	−	1.37477i	0.654410	−	0.756140i	$-0.272917\pi$
$312$	5.87306	−	2.35122i	0.332497	−	0.133112i
$313$	0.149771	+	3.14407i	0.00846554	+	0.177714i	0.999140	+	0.0414635i	$0.0132020\pi$
$313$	0.149771	+	3.14407i	0.00846554	+	0.177714i	−0.990674	+	0.136250i	$0.956495\pi$
$314$	−6.22994	−	1.82927i	−0.351576	−	0.103232i
$315$	−7.98251	−	3.12823i	−0.449763	−	0.176256i
$316$	11.2466	−	9.74521i	0.632669	−	0.548211i
$317$	9.67485	−	4.98773i	0.543394	−	0.280139i	−0.164597	−	0.986361i	$-0.552632\pi$
$317$	9.67485	−	4.98773i	0.543394	−	0.280139i	0.707990	+	0.706222i	$0.249602\pi$
$318$	3.51945	+	0.678318i	0.197361	+	0.0380382i
$319$	33.3691	−	34.9965i	1.86831	−	1.95943i
$320$	−3.22584	−	0.308030i	−0.180330	−	0.0172194i
$321$	5.05481			0.282132
$322$	4.25142	+	11.9551i	0.236922	+	0.666234i
$323$	7.46485			0.415356
$324$	−0.995472	−	0.0950560i	−0.0553040	−	0.00528089i
$325$	24.0147	−	25.1859i	1.33209	−	1.39706i
$326$	5.99355	+	1.15516i	0.331952	+	0.0639785i
$327$	13.6846	−	7.05489i	0.756759	−	0.390136i
$328$	3.85297	−	3.33862i	0.212745	−	0.184344i
$329$	6.42659	−	0.971991i	0.354309	−	0.0535876i
$330$	−18.0483	−	5.29946i	−0.993526	−	0.291725i
$331$	0.565085	+	11.8626i	0.0310599	+	0.652027i	0.959697	+	0.281037i	$0.0906785\pi$
$331$	0.565085	+	11.8626i	0.0310599	+	0.652027i	−0.928637	+	0.370990i	$0.879018\pi$
$332$	6.95165	−	2.78302i	0.381521	−	0.152738i
$333$	0.0634442	+	0.664418i	0.00347672	+	0.0364099i
$334$	0.904863	−	0.644350i	0.0495119	−	0.0352573i
$335$	−14.7700	−	2.12361i	−0.806972	−	0.116025i
$336$	1.19514	−	2.36043i	0.0652000	−	0.128772i
$337$	−8.41174	+	28.6478i	−0.458217	+	1.56054i	0.329285	+	0.944231i	$0.393192\pi$
$337$	−8.41174	+	28.6478i	−0.458217	+	1.56054i	−0.787502	+	0.616313i	$0.788626\pi$
$338$	−25.0855	−	10.0427i	−1.36447	−	0.546252i
$339$	0.782171	−	2.25993i	0.0424817	−	0.122743i
$340$	−0.171564	+	3.60157i	−0.00930435	+	0.195322i
$341$	−16.8888	−	48.7968i	−0.914577	−	2.64250i
$342$	−6.43714	+	1.89011i	−0.348081	+	0.102206i
$343$	8.06106	+	16.6739i	0.435256	+	0.900307i
$344$			9.10383i			0.490846i
$345$	13.4678	+	7.75484i	0.725085	+	0.417507i
$346$	−12.5641	+	7.25391i	−0.675453	+	0.389973i
$347$	−6.88752	+	9.67216i	−0.369741	+	0.519229i	−0.956968	−	0.290194i	$-0.906280\pi$
$347$	−6.88752	+	9.67216i	−0.369741	+	0.519229i	0.587227	+	0.809423i	$0.300220\pi$
$348$	8.09555	+	1.96396i	0.433967	+	0.105279i
$349$	−4.50786	−	3.90608i	−0.241300	−	0.209088i	0.525812	−	0.850601i	$-0.323762\pi$
$349$	−4.50786	−	3.90608i	−0.241300	−	0.209088i	−0.767112	+	0.641513i	$0.778307\pi$
$350$	0.586250	−	14.5422i	0.0313364	−	0.777312i
$351$	4.14280	+	4.78104i	0.221126	+	0.255193i
$352$	2.15740	−	5.38891i	0.114990	−	0.287230i
$353$	−6.00779	+	1.45747i	−0.319763	+	0.0775736i	−0.392428	−	0.919783i	$-0.628365\pi$
$353$	−6.00779	+	1.45747i	−0.319763	+	0.0775736i	0.0726652	+	0.997356i	$0.476850\pi$
$354$	2.41826	+	1.24670i	0.128529	+	0.0662613i
$355$	7.98830	+	6.28207i	0.423975	+	0.333418i
$356$	−1.02091	+	2.23548i	−0.0541082	+	0.118480i
$357$	−2.68671	−	1.20333i	−0.142196	−	0.0636869i
$358$	−3.56430	+	24.7903i	−0.188379	+	1.31021i
$359$	5.45699	−	0.259948i	0.288009	−	0.0137196i	0.0969196	−	0.995292i	$-0.469101\pi$
$359$	5.45699	−	0.259948i	0.288009	−	0.0137196i	0.191089	+	0.981573i	$0.438798\pi$
$360$	−0.763979	−	3.14916i	−0.0402652	−	0.165975i
$361$	−20.4447	+	16.0779i	−1.07603	+	0.846203i
$362$	−11.7342	+	2.26159i	−0.616737	+	0.118866i
$363$	12.2697	−	19.0920i	0.643993	−	1.00207i
$364$	−15.7766	+	5.58978i	−0.826920	+	0.292984i
$365$	−4.19902	−	14.3005i	−0.219786	−	0.748524i
$366$	0.674058	−	7.05905i	0.0352336	−	0.368983i
$367$	6.86988	+	11.8990i	0.358605	+	0.621121i	0.987728	−	0.156184i	$-0.0499193\pi$
$367$	6.86988	+	11.8990i	0.358605	+	0.621121i	−0.629123	+	0.777305i	$0.716586\pi$
$368$	−2.77732	+	3.90979i	−0.144778	+	0.203812i
$369$	4.41518	+	2.54911i	0.229845	+	0.132701i
$370$	−1.96739	+	0.898478i	−0.102280	+	0.0467097i
$371$	−9.23173	−	2.16828i	−0.479288	−	0.112572i
$372$	5.82542	−	6.72289i	0.302034	−	0.348566i
$373$	−9.49533	−	18.4184i	−0.491649	−	0.953667i	−0.995930	−	0.0901271i	$-0.971273\pi$
$373$	−9.49533	−	18.4184i	−0.491649	−	0.953667i	0.504281	−	0.863540i	$-0.331758\pi$
$374$	−6.10357	−	2.11246i	−0.315608	−	0.109233i
$375$	−1.00337	−	1.27588i	−0.0518136	−	0.0658863i
$376$	1.69528	+	1.77796i	0.0874274	+	0.0916912i
$377$	−28.4916	−	44.3339i	−1.46739	−	2.28331i
$378$	2.62150	+	0.357382i	0.134836	+	0.0183817i
$379$	−24.9840	−	11.4098i	−1.28334	−	0.586083i	−0.347229	−	0.937780i	$-0.612877\pi$
$379$	−24.9840	−	11.4098i	−1.28334	−	0.586083i	−0.936114	+	0.351697i	$0.885605\pi$
$380$	−12.6106	−	17.7091i	−0.646909	−	0.908456i
$381$	1.94461	+	4.85739i	0.0996252	+	0.248852i
$382$	1.99035	−	3.86074i	0.101835	−	0.197533i
$383$	−2.93920	+	2.80252i	−0.150186	+	0.143202i	−0.761447	−	0.648227i	$-0.775511\pi$
$383$	−2.93920	+	2.80252i	−0.150186	+	0.143202i	0.611261	+	0.791429i	$0.290662\pi$
$384$	0.989821	−	0.142315i	0.0505116	−	0.00726247i
$385$	47.1478	+	15.9331i	2.40287	+	0.812028i
$386$	−1.99090	−	1.27947i	−0.101334	−	0.0651234i
$387$	−8.60313	+	2.97757i	−0.437321	+	0.151358i
$388$	2.58978	+	2.46935i	0.131476	+	0.125362i
$389$	0.678740	+	0.483328i	0.0344135	+	0.0245057i	0.597134	−	0.802141i	$-0.296306\pi$
$389$	0.678740	+	0.483328i	0.0344135	+	0.0245057i	−0.562721	+	0.826647i	$0.690245\pi$
$390$	−10.2501	+	17.7537i	−0.519033	+	0.898992i
$391$	4.49246	+	2.87977i	0.227194	+	0.145636i
$392$	−3.41103	+	6.11268i	−0.172283	+	0.308737i
$393$	−3.34223	−	7.31846i	−0.168593	−	0.369167i
$394$	−2.62026	+	10.8009i	−0.132007	+	0.544140i
$395$	−9.12629	+	47.3517i	−0.459193	+	2.38252i
$396$	5.79814	+	0.276200i	0.291368	+	0.0138796i
$397$	−3.71255	−	19.2625i	−0.186328	−	0.966759i	−0.947873	−	0.318648i	$-0.896771\pi$
$397$	−3.71255	−	19.2625i	−0.186328	−	0.966759i	0.761546	−	0.648111i	$-0.224441\pi$
$398$	0.824578	+	5.73507i	0.0413324	+	0.287473i
$399$	17.2187	−	4.31068i	0.862012	−	0.215804i
$400$	4.62765	−	2.97401i	0.231382	−	0.148700i
$401$	0.00127759	−	0.00162459i	6.37999e−5	−	8.11281e-5i	−0.786021	−	0.618200i	$-0.787862\pi$
$401$	0.00127759	−	0.00162459i	6.37999e−5	−	8.11281e-5i	0.786085	+	0.618118i	$0.212105\pi$
$402$	4.58395	−	0.437714i	0.228627	−	0.0218312i
$403$	−56.0211	+	5.34937i	−2.79061	+	0.266471i
$404$	−2.84064	+	3.61216i	−0.141327	+	0.179712i
$405$	2.72609	−	1.75195i	0.135460	−	0.0870551i
$406$	−21.1921	−	6.05470i	−1.05175	−	0.300490i
$407$	−0.551371	−	3.83487i	−0.0273304	−	0.190087i
$408$	−0.210576	−	1.09257i	−0.0104251	−	0.0540904i
$409$	−11.3014	−	0.538354i	−0.558821	−	0.0266199i	−0.233728	−	0.972302i	$-0.575092\pi$
$409$	−11.3014	−	0.538354i	−0.558821	−	0.0266199i	−0.325093	+	0.945682i	$0.605396\pi$
$410$	−3.12658	+	16.2223i	−0.154411	+	0.801160i
$411$	−3.19846	+	13.1842i	−0.157769	+	0.650331i
$412$	6.42988	+	14.0795i	0.316778	+	0.693646i
$413$	−6.26005	−	3.55350i	−0.308037	−	0.174856i
$414$	−4.60313	−	1.34580i	−0.226232	−	0.0661426i
$415$	−12.1325	+	21.0141i	−0.595562	+	1.03154i
$416$	−5.15319	−	3.66957i	−0.252656	−	0.179915i
$417$	−5.55950	−	5.30098i	−0.272250	−	0.259590i
$418$	36.8014	−	12.7371i	1.80002	−	0.622991i
$419$	18.1066	+	11.6364i	0.884565	+	0.568475i	0.902175	−	0.431370i	$-0.141970\pi$
$419$	18.1066	+	11.6364i	0.884565	+	0.568475i	−0.0176106	+	0.999845i	$0.505606\pi$
$420$	1.68404	+	8.40656i	0.0821727	+	0.410198i
$421$	−3.74743	+	0.538799i	−0.182639	+	0.0262595i	−0.233027	−	0.972470i	$-0.574863\pi$
$421$	−3.74743	+	0.538799i	−0.182639	+	0.0262595i	0.0503886	+	0.998730i	$0.483954\pi$
$422$	11.5385	−	11.0019i	0.561683	−	0.535564i
$423$	−1.12570	+	2.18355i	−0.0547334	+	0.106168i
$424$	−1.33212	−	3.32747i	−0.0646934	−	0.161596i
$425$	−3.55037	−	4.98580i	−0.172218	−	0.241847i
$426$	−2.85269	−	1.30278i	−0.138213	−	0.0631200i
$427$	−2.53425	+	18.5895i	−0.122641	+	0.899609i
$428$	−2.73284	−	4.25238i	−0.132097	−	0.205546i
$429$	−25.3410	−	26.5769i	−1.22348	−	1.28315i
$430$	−18.2363	−	23.1894i	−0.879434	−	1.11829i
$431$	33.2156	+	11.4960i	1.59994	+	0.553744i	0.974082	−	0.226196i	$-0.0726288\pi$
$431$	33.2156	+	11.4960i	1.59994	+	0.553744i	0.625855	+	0.779939i	$0.284750\pi$
$432$	0.458227	+	0.888835i	0.0220464	+	0.0427641i
$433$	−8.38972	+	9.68225i	−0.403184	+	0.465299i	−0.920641	−	0.390410i	$-0.872333\pi$
$433$	−8.38972	+	9.68225i	−0.403184	+	0.465299i	0.517457	+	0.855709i	$0.326879\pi$
$434$	−16.1166	+	17.1518i	−0.773621	+	0.823314i
$435$	−24.5552	+	11.2140i	−1.17733	+	0.537669i
$436$	−13.3334	−	7.69804i	−0.638554	−	0.368669i
$437$	−32.0255	+	3.09556i	−1.53199	+	0.148081i
$438$	2.29968	+	3.98316i	0.109883	+	0.190323i
$439$	−2.81751	+	29.5063i	−0.134473	+	1.40826i	0.636443	+	0.771324i	$0.280405\pi$
$439$	−2.81751	+	29.5063i	−0.134473	+	1.40826i	−0.770916	+	0.636937i	$0.780201\pi$
$440$	5.29946	+	18.0483i	0.252642	+	0.860419i
$441$	−6.89213	−	1.22416i	−0.328197	−	0.0582933i
$442$	−3.80560	+	5.92164i	−0.181014	+	0.281664i
$443$	2.09028	−	0.402869i	0.0993124	−	0.0191409i	−0.139353	−	0.990243i	$-0.544502\pi$
$443$	2.09028	−	0.402869i	0.0993124	−	0.0191409i	0.238665	+	0.971102i	$0.423290\pi$
$444$	0.524643	−	0.412584i	0.0248985	−	0.0195804i
$445$	−1.87753	−	7.73929i	−0.0890035	−	0.366877i
$446$	−0.181289	+	0.00863586i	−0.00858429	+	0.000408920i
$447$	2.25801	−	15.7048i	0.106800	−	0.742812i
$448$	−2.63186	+	0.270735i	−0.124344	+	0.0127910i
$449$	4.13978	−	9.06486i	0.195368	−	0.427797i	−0.786441	−	0.617665i	$-0.788079\pi$
$449$	4.13978	−	9.06486i	0.195368	−	0.427797i	0.981810	+	0.189868i	$0.0608060\pi$
$450$	4.32399	+	3.40043i	0.203835	+	0.160298i
$451$	−26.3039	−	13.5606i	−1.23860	−	0.638545i
$452$	−2.32405	+	0.563809i	−0.109314	+	0.0265193i
$453$	8.25042	−	20.6085i	0.387638	−	0.968274i
$454$	−11.7320	−	13.5394i	−0.550609	−	0.635437i
$455$	28.9893	−	45.8413i	1.35904	−	2.14907i
$456$	5.07024	+	4.39339i	0.237436	+	0.205739i
$457$	8.14030	+	1.97481i	0.380787	+	0.0923779i	0.421584	−	0.906790i	$-0.361474\pi$
$457$	8.14030	+	1.97481i	0.380787	+	0.0923779i	−0.0407966	+	0.999167i	$0.512990\pi$
$458$	14.0350	−	19.7094i	0.655812	−	0.920959i
$459$	0.963609	−	0.556340i	0.0449774	−	0.0259677i
$460$	−0.757478	−	15.5225i	−0.0353176	−	0.723738i
$461$			13.5678i			0.631918i	0.948773	+	0.315959i	$0.102326\pi$
$461$			13.5678i			0.631918i	−0.948773	+	0.315959i	$0.897674\pi$
$462$	−15.2986	−	1.34809i	−0.711753	−	0.0627189i
$463$	29.3292	−	8.61184i	1.36305	−	0.400226i	0.483210	−	0.875504i	$-0.339471\pi$
$463$	29.3292	−	8.61184i	1.36305	−	0.400226i	0.879836	+	0.475278i	$0.157653\pi$
$464$	−2.72460	−	7.87220i	−0.126486	−	0.365458i
$465$	−1.37162	+	28.7938i	−0.0636073	+	1.33528i
$466$	0.165988	−	0.479590i	0.00768924	−	0.0222166i
$467$	−10.4527	−	4.18463i	−0.483693	−	0.193642i	0.116983	−	0.993134i	$-0.462678\pi$
$467$	−10.4527	−	4.18463i	−0.483693	−	0.193642i	−0.600676	+	0.799492i	$0.705102\pi$
$468$	1.78230	−	6.06997i	0.0823870	−	0.280584i
$469$	−12.1648	+	0.668615i	−0.561718	+	0.0308738i
$470$	−7.87975	−	1.13294i	−0.363466	−	0.0522585i
$471$	−5.28900	+	3.76628i	−0.243704	+	0.173541i
$472$	−0.258619	−	2.70838i	−0.0119039	−	0.124663i
$473$	49.0598	−	19.6406i	2.25577	−	0.903074i
$474$	−0.708083	−	14.8645i	−0.0325233	−	0.682749i
$475$	35.4100	+	10.3973i	1.62472	+	0.477062i
$476$	0.440240	+	2.91077i	0.0201784	+	0.133415i
$477$	2.70877	−	2.34716i	0.124026	−	0.107469i
$478$	−3.56233	+	1.83651i	−0.162937	+	0.0840000i
$479$	−22.6622	−	4.36778i	−1.03546	−	0.199569i	−0.356923	−	0.934134i	$-0.616174\pi$
$479$	−22.6622	−	4.36778i	−1.03546	−	0.199569i	−0.678538	+	0.734565i	$0.737386\pi$
$480$	−2.23621	+	2.34527i	−0.102068	+	0.107046i
$481$	−4.20326	−	0.401362i	−0.191652	−	0.0183005i
$482$	18.4638			0.841001
$483$	12.0254	+	4.04834i	0.547176	+	0.184206i
$484$	−22.6948			−1.03158
$485$	−11.5432	−	1.10224i	−0.524149	−	0.0500501i
$486$	−0.690079	+	0.723734i	−0.0313026	+	0.0328292i
$487$	−1.50491	−	0.290047i	−0.0681939	−	0.0131433i	0.155040	−	0.987908i	$-0.450449\pi$
$487$	−1.50491	−	0.290047i	−0.0681939	−	0.0131433i	−0.223234	+	0.974765i	$0.571661\pi$
$488$	−6.30288	+	3.24936i	−0.285318	+	0.147092i
$489$	4.61298	−	3.99717i	0.208606	−	0.180758i
$490$	−3.55602	−	22.4031i	−0.160644	−	1.01207i
$491$	30.5157	+	8.96023i	1.37716	+	0.404369i	0.884778	−	0.466012i	$-0.154310\pi$
$491$	30.5157	+	8.96023i	1.37716	+	0.404369i	0.492377	+	0.870382i	$0.336128\pi$
$492$	−0.242583	−	5.09244i	−0.0109365	−	0.229585i
$493$	−8.60507	+	3.44495i	−0.387553	+	0.155153i
$494$	−4.03437	−	42.2498i	−0.181515	−	1.90091i
$495$	−15.3224	+	10.9110i	−0.688689	+	0.490413i
$496$	−8.80512	−	1.26598i	−0.395361	−	0.0568444i
$497$	7.40255	+	3.74806i	0.332050	+	0.168124i
$498$	2.10962	−	7.18472i	0.0945345	−	0.321955i
$499$	−35.7719	−	14.3209i	−1.60137	−	0.641092i	−0.612582	−	0.790407i	$-0.709869\pi$
$499$	−35.7719	−	14.3209i	−1.60137	−	0.641092i	−0.988790	+	0.149315i	$0.952293\pi$
$500$	−0.530881	+	1.53388i	−0.0237417	+	0.0685971i
$501$	0.0528559	−	1.10958i	0.00236143	−	0.0495724i
$502$	−6.26576	−	18.1037i	−0.279654	−	0.808008i
$503$	−35.6719	+	10.4742i	−1.59053	+	0.467022i	−0.952891	−	0.303312i	$-0.901908\pi$
$503$	−35.6719	+	10.4742i	−1.59053	+	0.467022i	−0.637640	+	0.770334i	$0.720089\pi$
$504$	−1.11664	−	2.39856i	−0.0497392	−	0.106841i
$505$		−	14.8912i		−	0.662648i
$506$	27.0613	+	6.53177i	1.20302	+	0.290373i
$507$	−23.4010	+	13.5106i	−1.03927	+	0.600025i
$508$	3.03496	−	4.26201i	0.134655	−	0.189096i
$509$	−15.0601	−	3.65355i	−0.667528	−	0.161941i	−0.112346	−	0.993669i	$-0.535836\pi$
$509$	−15.0601	−	3.65355i	−0.667528	−	0.161941i	−0.555183	+	0.831729i	$0.687352\pi$
$510$	2.72497	+	2.36120i	0.120664	+	0.104556i
$511$	−5.65494	−	10.7750i	−0.250160	−	0.476657i
$512$	−0.654861	−	0.755750i	−0.0289410	−	0.0333997i
$513$	−2.49344	+	6.22832i	−0.110088	+	0.274987i
$514$	−11.1157	+	2.69663i	−0.490290	+	0.118943i
$515$	−44.5816	−	22.9834i	−1.96450	−	1.01277i
$516$	7.15609	+	5.62761i	0.315029	+	0.247742i
$517$	5.92388	−	12.9715i	0.260532	−	0.570485i
$518$	−1.43092	+	1.03480i	−0.0628710	+	0.0454663i
$519$	−2.06468	+	14.3602i	−0.0906293	+	0.630341i
$520$	20.4770	−	0.975438i	0.897974	−	0.0427758i
$521$	5.77426	+	23.8018i	0.252975	+	1.04278i	0.946592	+	0.322433i	$0.104501\pi$
$521$	5.77426	+	23.8018i	0.252975	+	1.04278i	−0.693618	+	0.720343i	$0.743984\pi$
$522$	6.54811	−	5.14949i	0.286603	−	0.225387i
$523$	−26.6168	+	5.12996i	−1.16387	+	0.224318i	−0.734370	−	0.678749i	$-0.762522\pi$
$523$	−26.6168	+	5.12996i	−1.16387	+	0.224318i	−0.429500	+	0.903067i	$0.641310\pi$
$524$	−4.34973	+	6.76832i	−0.190019	+	0.295675i
$525$	−11.0685	−	9.45021i	−0.483070	−	0.412441i
$526$	−2.39560	−	8.15868i	−0.104453	−	0.355735i
$527$	−0.940867	+	9.85321i	−0.0409848	+	0.429213i
$528$	−2.90236	−	5.02703i	−0.126309	−	0.218774i
$529$	−20.4676	−	10.4917i	−0.889896	−	0.456163i
$530$	10.0586	+	5.80734i	0.436918	+	0.252255i
$531$	2.47484	−	1.13022i	0.107399	−	0.0490474i
$532$	−12.9355	−	12.1547i	−0.560825	−	0.526975i
$533$	−21.1209	+	24.3748i	−0.914846	+	1.05579i
$534$	1.12612	+	2.18437i	0.0487321	+	0.0945271i
$535$	15.4793	+	5.35742i	0.669227	+	0.231622i
$536$	−2.84650	−	3.61962i	−0.122950	−	0.156344i
$537$	17.2832	+	18.1261i	0.745824	+	0.782197i
$538$	3.86506	+	6.01415i	0.166634	+	0.259288i
$539$	40.2997	+	5.19424i	1.73583	+	0.223732i
$540$	−2.94767	−	1.34616i	−0.126848	−	0.0579293i
$541$	−1.29280	−	1.81548i	−0.0555816	−	0.0780535i	0.785850	−	0.618418i	$-0.212226\pi$
$541$	−1.29280	−	1.81548i	−0.0555816	−	0.0780535i	−0.841431	+	0.540364i	$0.818287\pi$
$542$	5.39320	+	13.4716i	0.231658	+	0.578653i
$543$	−5.47589	+	10.6217i	−0.234993	+	0.455822i
$544$	−0.805284	+	0.767837i	−0.0345263	+	0.0329207i
$545$	49.3833	−	7.10024i	2.11535	−	0.304141i
$546$	−5.35860	+	15.8566i	−0.229327	+	0.678602i
$547$	−0.468552	−	0.301120i	−0.0200338	−	0.0128750i	0.530586	−	0.847631i	$-0.321972\pi$
$547$	−0.468552	−	0.301120i	−0.0200338	−	0.0128750i	−0.550619	+	0.834756i	$0.685608\pi$
$548$	12.8205	−	4.43722i	0.547665	−	0.189549i
$549$	−5.13212	−	4.89346i	−0.219033	−	0.208848i
$550$	−26.0103	−	18.5219i	−1.10908	−	0.789776i
$551$	27.9438	−	48.4000i	1.19044	−	2.06191i
$552$	1.35648	+	4.60000i	0.0577356	+	0.195789i
$553$	0.287729	+	39.3713i	0.0122355	+	1.67424i
$554$	6.70583	+	14.6837i	0.284903	+	0.623851i
$555$	−0.509910	+	2.10188i	−0.0216445	+	0.0892197i
$556$	−1.45377	+	7.54288i	−0.0616536	+	0.319889i
$557$	16.2798	+	0.775504i	0.689799	+	0.0328592i	0.389555	−	0.921003i	$-0.372629\pi$
$557$	16.2798	+	0.775504i	0.689799	+	0.0328592i	0.300244	+	0.953862i	$0.402932\pi$
$558$	−1.68352	−	8.73491i	−0.0712689	−	0.369778i
$559$	−8.19632	−	57.0066i	−0.346667	−	2.41112i
$560$	6.16159	−	5.96163i	0.260375	−	0.251925i
$561$	−5.43348	+	3.49189i	−0.229402	+	0.147428i
$562$	−1.60704	+	2.04352i	−0.0677890	+	0.0862007i
$563$	4.04136	−	0.385903i	0.170323	−	0.0162639i	−0.00954601	−	0.999954i	$-0.503039\pi$
$563$	4.04136	−	0.385903i	0.170323	−	0.0162639i	0.179869	+	0.983691i	$0.442433\pi$
$564$	2.44552	−	0.233519i	0.102975	−	0.00983293i
$565$	4.79046	−	6.09156i	0.201536	−	0.256274i
$566$	−15.4104	+	9.90365i	−0.647747	+	0.416282i
$567$	1.90143	−	1.83972i	0.0798524	−	0.0772611i
$568$	0.446313	+	3.10418i	0.0187269	+	0.130248i
$569$	−3.37480	−	17.5101i	−0.141479	−	0.734062i	−0.981493	−	0.191498i	$-0.938666\pi$
$569$	−3.37480	−	17.5101i	−0.141479	−	0.734062i	0.840014	−	0.542564i	$-0.182547\pi$
$570$	−21.7156	−	1.03444i	−0.909567	−	0.0433280i
$571$	−6.59364	+	34.2110i	−0.275935	+	1.43169i	0.534157	+	0.845385i	$0.320629\pi$
$571$	−6.59364	+	34.2110i	−0.275935	+	1.43169i	−0.810093	+	0.586302i	$0.800583\pi$
$572$	−8.65753	+	35.6868i	−0.361989	+	1.49214i
$573$	−1.80439	−	3.95107i	−0.0753797	−	0.165058i
$574$	0.0985732	+	13.4882i	0.00411437	+	0.562989i
$575$	17.2992	+	19.9176i	0.721428	+	0.830623i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	0.674463	+	0.480283i	0.0280783	+	0.0199944i	0.594010	−	0.804458i	$-0.297544\pi$
$577$	0.674463	+	0.480283i	0.0280783	+	0.0199944i	−0.565932	+	0.824452i	$0.691483\pi$
$578$	−11.4075	−	10.8770i	−0.474488	−	0.452423i
$579$	−2.23642	+	0.774034i	−0.0929426	+	0.0321677i
$580$	22.7093	+	14.5944i	0.942953	+	0.605999i
$581$	−6.34271	+	18.7687i	−0.263140	+	0.778658i
$582$	3.54193	−	0.509253i	0.146818	−	0.0211092i
$583$	−15.0576	+	14.3574i	−0.623620	+	0.594621i
$584$	2.10755	−	4.08807i	0.0872110	−	0.169166i
$585$	7.61915	+	19.0317i	0.315013	+	0.786864i
$586$	6.70426	+	9.41482i	0.276951	+	0.388923i
$587$	25.7104	+	11.7415i	1.06118	+	0.484626i	0.868014	−	0.496540i	$-0.165396\pi$
$587$	25.7104	+	11.7415i	1.06118	+	0.484626i	0.193168	+	0.981166i	$0.438124\pi$
$588$	2.69634	+	6.45986i	0.111195	+	0.266400i
$589$	−32.2655	−	50.2061i	−1.32948	−	2.06871i
$590$	6.08406	+	6.38077i	0.250477	+	0.262692i
$591$	6.87032	+	8.73632i	0.282607	+	0.359364i
$592$	−0.630731	−	0.218298i	−0.0259229	−	0.00897200i
$593$	−4.46829	−	8.66728i	−0.183491	−	0.355922i	0.779092	−	0.626909i	$-0.215680\pi$
$593$	−4.46829	−	8.66728i	−0.183491	−	0.355922i	−0.962583	+	0.270987i	$0.912650\pi$
$594$	3.80128	−	4.38691i	0.155969	−	0.179997i
$595$	−6.95209	−	6.53248i	−0.285008	−	0.267806i
$596$	−14.4325	+	6.59110i	−0.591178	+	0.269982i
$597$	5.01779	+	2.89702i	0.205364	+	0.118567i
$598$	13.8711	−	26.9829i	0.567230	−	1.10341i
$599$	−0.150654	−	0.260940i	−0.00615554	−	0.0106617i	0.862931	−	0.505321i	$-0.168626\pi$
$599$	−0.150654	−	0.260940i	−0.00615554	−	0.0106617i	−0.869087	+	0.494660i	$0.835293\pi$
$600$	0.522893	−	5.47599i	0.0213470	−	0.223556i
$601$	12.3389	+	42.0223i	0.503313	+	1.71413i	0.683014	+	0.730405i	$0.260669\pi$
$601$	12.3389	+	42.0223i	0.503313	+	1.71413i	−0.179701	+	0.983721i	$0.557513\pi$
$602$	−18.3181	−	15.6398i	−0.746591	−	0.637432i
$603$	2.48954	−	3.87380i	0.101382	−	0.157754i
$604$	−21.7975	+	4.20113i	−0.886929	+	0.170941i
$605$	57.8083	−	45.4610i	2.35024	−	1.84825i
$606$	1.08339	+	4.46578i	0.0440096	+	0.181410i
$607$	−0.940362	+	0.0447950i	−0.0381681	+	0.00181817i	−0.0666573	−	0.997776i	$-0.521233\pi$
$607$	−0.940362	+	0.0447950i	−0.0381681	+	0.00181817i	0.0284892	+	0.999594i	$0.490930\pi$
$608$	0.954775	−	6.64061i	0.0387212	−	0.269312i
$609$	−17.8594	+	12.9154i	−0.723700	+	0.523357i
$610$	9.54581	−	20.9024i	0.386499	−	0.846314i
$611$	−12.2163	−	9.60699i	−0.494218	−	0.388657i
$612$	−0.988990	−	0.509860i	−0.0399775	−	0.0206098i
$613$	−23.0236	+	5.58548i	−0.929916	+	0.225595i	−0.671982	−	0.740567i	$-0.734557\pi$
$613$	−23.0236	+	5.58548i	−0.929916	+	0.225595i	−0.257934	+	0.966163i	$0.583042\pi$
$614$	−0.505492	+	1.26266i	−0.0204000	+	0.0509567i
$615$	10.8188	+	12.4856i	0.436257	+	0.503468i
$616$	7.13694	+	13.5988i	0.287555	+	0.547911i
$617$	32.7030	+	28.3373i	1.31657	+	1.14082i	0.979964	+	0.199173i	$0.0638256\pi$
$617$	32.7030	+	28.3373i	1.31657	+	1.14082i	0.336609	+	0.941644i	$0.390720\pi$
$618$	15.0419	+	3.64913i	0.605074	+	0.146789i
$619$	−4.41874	+	6.20525i	−0.177604	+	0.249410i	−0.893776	−	0.448514i	$-0.851953\pi$
$619$	−4.41874	+	6.20525i	−0.177604	+	0.249410i	0.716172	+	0.697924i	$0.245893\pi$
$620$	24.9645	−	14.4132i	1.00260	−	0.578849i
$621$	−3.90334	+	2.78639i	−0.156636	+	0.111814i
$622$			24.3546i			0.976529i
$623$	−2.74423	−	5.89464i	−0.109945	−	0.236164i
$624$	−6.06997	+	1.78230i	−0.242993	+	0.0713492i
$625$	7.27551	+	21.0212i	0.291020	+	0.840848i
$626$	0.149771	−	3.14407i	0.00598604	−	0.125662i
$627$	12.7371	−	36.8014i	0.508670	−	1.46971i
$628$	6.02784	+	2.41318i	0.240537	+	0.0962966i
$629$	−0.209228	+	0.712565i	−0.00834246	+	0.0284118i
$630$	7.64901	+	3.87285i	0.304744	+	0.154298i
$631$	17.3636	+	2.49650i	0.691232	+	0.0993842i	0.478974	−	0.877829i	$-0.341009\pi$
$631$	17.3636	+	2.49650i	0.691232	+	0.0993842i	0.212259	+	0.977214i	$0.431918\pi$
$632$	−12.1220	+	8.63203i	−0.482187	+	0.343364i
$633$	−1.51547	−	15.8708i	−0.0602347	−	0.630806i
$634$	−10.1052	+	4.04549i	−0.401327	+	0.160667i
$635$	0.806748	+	16.9357i	0.0320148	+	0.672074i
$636$	−3.43903	−	1.00979i	−0.136366	−	0.0400408i
$637$	15.8559	−	41.3476i	0.628234	−	1.63825i
$638$	−36.5446	+	31.6661i	−1.44681	+	1.25367i
$639$	−2.78747	+	1.43704i	−0.110271	+	0.0568485i
$640$	3.18195	+	0.613270i	0.125778	+	0.0242416i
$641$	5.54068	−	5.81090i	0.218844	−	0.229517i	−0.605156	−	0.796107i	$-0.706889\pi$
$641$	5.54068	−	5.81090i	0.218844	−	0.229517i	0.824000	+	0.566590i	$0.191738\pi$
$642$	−5.03192	−	0.480490i	−0.198594	−	0.0189634i
$643$	34.7539			1.37056			0.685280	−	0.728280i	$-0.259680\pi$
$643$	34.7539			1.37056			0.685280	+	0.728280i	$0.259680\pi$
$644$	−3.09576	−	12.3051i	−0.121990	−	0.484890i
$645$	−29.5010			−1.16160
$646$	−7.43105	−	0.709579i	−0.292371	−	0.0279180i
$647$	12.2673	−	12.8656i	0.482279	−	0.505800i	−0.436970	−	0.899476i	$-0.643948\pi$
$647$	12.2673	−	12.8656i	0.482279	−	0.505800i	0.919249	+	0.393676i	$0.128797\pi$
$648$	0.981929	+	0.189251i	0.0385738	+	0.00743449i
$649$	−14.0373	+	7.23674i	−0.551013	+	0.284067i
$650$	−26.3000	+	22.7891i	−1.03157	+	0.893861i
$651$	3.51964	+	23.2711i	0.137945	+	0.912065i
$652$	−5.85660	−	1.71965i	−0.229362	−	0.0673468i
$653$	1.65238	+	34.6877i	0.0646625	+	1.35743i	0.765188	+	0.643806i	$0.222646\pi$
$653$	1.65238	+	34.6877i	0.0646625	+	1.35743i	−0.700526	+	0.713627i	$0.747051\pi$
$654$	−14.2932	+	5.72214i	−0.558909	+	0.223753i
$655$	−2.47826	−	25.9535i	−0.0968336	−	1.01409i
$656$	−4.15288	+	2.95725i	−0.162143	+	0.115461i
$657$	4.55254	+	0.654557i	0.177612	+	0.0255367i
$658$	−6.48988	+	0.356704i	−0.253002	+	0.0139058i
$659$	11.7530	−	40.0269i	0.457830	−	1.55923i	−0.330397	−	0.943842i	$-0.607183\pi$
$659$	11.7530	−	40.0269i	0.457830	−	1.55923i	0.788227	−	0.615384i	$-0.210999\pi$
$660$	17.4628	+	6.99106i	0.679739	+	0.272127i
$661$	−11.2270	+	32.4382i	−0.436679	+	1.26170i	0.485262	+	0.874369i	$0.338724\pi$
$661$	−11.2270	+	32.4382i	−0.436679	+	1.26170i	−0.921941	+	0.387331i	$0.873397\pi$
$662$	0.565085	−	11.8626i	0.0219627	−	0.461053i
$663$	2.30225	+	6.65192i	0.0894121	+	0.258339i
$664$	−7.18472	+	2.10962i	−0.278821	+	0.0818693i
$665$	57.2972	+	5.04896i	2.22189	+	0.195790i
$666$		−	0.667440i		−	0.0258628i
$667$	35.4886	−	18.3478i	1.37413	−	0.710430i
$668$	−0.962015	+	0.555420i	−0.0372215	+	0.0214898i
$669$	−0.105277	+	0.147841i	−0.00407025	+	0.00571587i
$670$	14.5013	+	3.51797i	0.560233	+	0.135911i
$671$	31.1083	+	26.9555i	1.20092	+	1.04061i
$672$	−1.41410	+	2.23614i	−0.0545500	+	0.0862610i
$673$	7.54139	+	8.70323i	0.290699	+	0.335485i	0.882248	−	0.470784i	$-0.156029\pi$
$673$	7.54139	+	8.70323i	0.290699	+	0.335485i	−0.591549	+	0.806269i	$0.701483\pi$
$674$	11.0968	−	27.7185i	0.427433	−	1.06768i
$675$	5.34583	−	1.29688i	0.205761	−	0.0499171i
$676$	24.0173	+	12.3818i	0.923743	+	0.476223i
$677$	−1.29080	−	1.01510i	−0.0496096	−	0.0390134i	0.593046	−	0.805168i	$-0.297925\pi$
$677$	−1.29080	−	1.01510i	−0.0496096	−	0.0390134i	−0.642656	+	0.766155i	$0.722168\pi$
$678$	−0.993449	+	2.17535i	−0.0381532	+	0.0835438i
$679$	−9.41774	+	0.968787i	−0.361420	+	0.0371786i
$680$	0.513137	−	3.56895i	0.0196779	−	0.136863i
$681$	−17.8949	+	0.852441i	−0.685736	+	0.0326656i
$682$	12.1738	+	50.1813i	0.466161	+	1.92154i
$683$	−27.1112	+	21.3205i	−1.03738	+	0.815804i	−0.983164	−	0.182725i	$-0.941508\pi$
$683$	−27.1112	+	21.3205i	−1.03738	+	0.815804i	−0.0542155	+	0.998529i	$0.517266\pi$
$684$	6.58766	−	1.26967i	0.251885	−	0.0485469i
$685$	−23.7681	+	36.9839i	−0.908134	+	1.41308i
$686$	−6.43960	−	17.3647i	−0.245865	−	0.662986i
$687$	−6.81677	−	23.2158i	−0.260076	−	0.885737i
$688$	0.865374	−	9.06261i	0.0329921	−	0.345509i
$689$	11.3373	+	19.6367i	0.431916	+	0.748100i
$690$	−12.6697	−	8.99993i	−0.482328	−	0.342622i
$691$	−17.9272	−	10.3503i	−0.681984	−	0.393744i	0.118618	−	0.992940i	$-0.462154\pi$
$691$	−17.9272	−	10.3503i	−0.681984	−	0.393744i	−0.800602	+	0.599196i	$0.795487\pi$
$692$	13.1968	−	6.02677i	0.501666	−	0.229103i
$693$	−10.5166	+	11.1921i	−0.399493	+	0.425154i
$694$	7.77573	−	8.97367i	0.295163	−	0.340636i
$695$	−11.4064	−	22.1254i	−0.432671	−	0.839265i
$696$	−7.87220	−	2.72460i	−0.298395	−	0.103276i
$697$	3.50662	+	4.45903i	0.132823	+	0.168898i
$698$	4.11615	+	4.31689i	0.155799	+	0.163397i
$699$	−0.274377	−	0.426938i	−0.0103779	−	0.0161483i
$700$	−1.96592	+	14.4206i	−0.0743047	+	0.545048i
$701$	30.6616	+	14.0027i	1.15807	+	0.528874i	0.899415	−	0.437095i	$-0.143993\pi$
$701$	30.6616	+	14.0027i	1.15807	+	0.528874i	0.258658	+	0.965969i	$0.416720\pi$
$702$	−3.66957	−	5.15319i	−0.138499	−	0.194495i
$703$	−1.66422	−	4.15703i	−0.0627674	−	0.156785i
$704$	−2.65988	+	5.15944i	−0.100248	+	0.194454i
$705$	−5.76149	+	5.49357i	−0.216990	+	0.206900i
$706$	6.11913	−	0.879798i	0.230297	−	0.0331116i
$707$	−2.38811	−	11.9212i	−0.0898141	−	0.448343i
$708$	−2.28880	−	1.47092i	−0.0860184	−	0.0552807i
$709$	−21.3256	+	7.38086i	−0.800900	+	0.277194i	−0.696700	−	0.717362i	$-0.745349\pi$
$709$	−21.3256	+	7.38086i	−0.800900	+	0.277194i	−0.104199	+	0.994556i	$0.533228\pi$
$710$	−7.35498	−	7.01296i	−0.276028	−	0.263192i
$711$	−12.1220	−	8.63203i	−0.454610	−	0.323726i
$712$	1.22878	−	2.12832i	0.0460507	−	0.0797621i
$713$	−0.0494989	−	42.6621i	−0.00185375	−	1.59771i
$714$	2.56016	+	1.45327i	0.0958115	+	0.0543871i
$715$	−49.4335	−	108.244i	−1.84871	−	4.04810i
$716$	5.90463	−	24.3392i	0.220666	−	0.909599i
$717$	−0.758493	+	3.93544i	−0.0283265	+	0.146972i
$718$	−5.45699	−	0.259948i	−0.203653	−	0.00970119i
$719$	5.48127	+	28.4395i	0.204417	+	1.06062i	0.928621	+	0.371030i	$0.120995\pi$
$719$	5.48127	+	28.4395i	0.204417	+	1.06062i	−0.724204	+	0.689586i	$0.757793\pi$
$720$	0.461172	+	3.20752i	0.0171869	+	0.119537i
$721$	−39.3759	−	11.2499i	−1.46644	−	0.418969i
$722$	21.8804	−	14.0617i	0.814304	−	0.523321i
$723$	11.4135	−	14.5135i	0.424474	−	0.539762i
$724$	11.8961	−	1.13594i	0.442114	−	0.0422167i
$725$	−45.6170	+	4.35589i	−1.69417	+	0.161774i
$726$	−14.0290	+	17.8393i	−0.520664	+	0.662078i
$727$	−42.1082	+	27.0613i	−1.56171	+	1.00365i	−0.579692	+	0.814836i	$0.696827\pi$
$727$	−42.1082	+	27.0613i	−1.56171	+	1.00365i	−0.982013	+	0.188811i	$0.939537\pi$
$728$	16.2365	−	4.06481i	0.601766	−	0.150652i
$729$	0.142315	+	0.989821i	0.00527092	+	0.0366601i
$730$	2.82065	+	14.6349i	0.104397	+	0.541663i
$731$	−10.1182	−	0.481988i	−0.374234	−	0.0178270i
$732$	−1.34201	+	6.96302i	−0.0496022	+	0.257361i
$733$	−1.44101	+	5.93993i	−0.0532250	+	0.219396i	−0.992213	−	0.124554i	$-0.960250\pi$
$733$	−1.44101	+	5.93993i	−0.0532250	+	0.219396i	0.938988	+	0.343950i	$0.111765\pi$
$734$	−5.70770	−	12.4981i	−0.210675	−	0.461314i
$735$	−19.8082	−	11.0535i	−0.730637	−	0.407713i
$736$	3.13639	−	3.62809i	0.115609	−	0.133733i
$737$	−13.3648	+	23.1485i	−0.492298	+	0.852685i
$738$	−4.15288	−	2.95725i	−0.152870	−	0.108858i
$739$	24.4063	+	23.2714i	0.897801	+	0.856051i	0.990198	−	0.139671i	$-0.0446045\pi$
$739$	24.4063	+	23.2714i	0.897801	+	0.856051i	−0.0923972	+	0.995722i	$0.529453\pi$
$740$	2.04389	−	0.707397i	0.0751349	−	0.0260044i
$741$	−35.7045	−	22.9459i	−1.31164	−	0.842937i
$742$	8.98382	+	3.03600i	0.329806	+	0.111455i
$743$	−19.9932	+	2.87459i	−0.733481	+	0.105459i	−0.498926	−	0.866644i	$-0.666272\pi$
$743$	−19.9932	+	2.87459i	−0.733481	+	0.105459i	−0.234554	+	0.972103i	$0.575363\pi$
$744$	−6.43809	+	6.13871i	−0.236032	+	0.225056i
$745$	23.5597	−	45.6994i	0.863159	−	1.67430i
$746$	7.70155	+	19.2376i	0.281974	+	0.704337i
$747$	−4.34349	−	6.09957i	−0.158920	−	0.223172i
$748$	5.87513	+	2.68308i	0.214816	+	0.0981031i
$749$	13.2512	+	1.80650i	0.484188	+	0.0660079i
$750$	0.877542	+	1.36548i	0.0320433	+	0.0498603i
$751$	−16.0227	−	16.8041i	−0.584677	−	0.613192i	0.363245	−	0.931694i	$-0.381669\pi$
$751$	−16.0227	−	16.8041i	−0.584677	−	0.613192i	−0.947922	+	0.318502i	$0.896820\pi$
$752$	−1.51860	−	1.93105i	−0.0553776	−	0.0704183i
$753$	−18.1037	−	6.26576i	−0.659736	−	0.228337i
$754$	24.1484	+	46.8414i	0.879434	+	1.70586i
$755$	47.1074	−	54.3649i	1.71441	−	1.97854i
$756$	−2.57566	−	0.604953i	−0.0936759	−	0.0220019i
$757$	14.5966	−	6.66603i	0.530521	−	0.242281i	−0.132099	−	0.991237i	$-0.542172\pi$
$757$	14.5966	−	6.66603i	0.530521	−	0.242281i	0.662620	+	0.748956i	$0.269444\pi$
$758$	23.7863	+	13.7330i	0.863958	+	0.498806i
$759$	21.8625	−	17.2340i	0.793559	−	0.625553i
$760$	10.8701	+	18.8276i	0.394300	+	0.682948i
$761$	−1.23640	+	12.9482i	−0.0448196	+	0.469372i	0.945003	+	0.327063i	$0.106059\pi$
$761$	−1.23640	+	12.9482i	−0.0448196	+	0.469372i	−0.989822	+	0.142309i	$0.954547\pi$
$762$	−1.47408	−	5.02024i	−0.0534002	−	0.181864i
$763$	38.3954	−	13.6038i	1.39001	−	0.492491i
$764$	−2.34832	+	3.65406i	−0.0849594	+	0.132199i
$765$	3.54049	−	0.682374i	0.128007	−	0.0246713i
$766$	3.19229	−	2.51044i	0.115342	−	0.0907059i
$767$	4.05783	+	16.7266i	0.146520	+	0.603963i
$768$	−0.998867	+	0.0475819i	−0.0360435	+	0.00171696i
$769$	5.37152	−	37.3597i	0.193702	−	1.34723i	−0.628402	−	0.777889i	$-0.716291\pi$
$769$	5.37152	−	37.3597i	0.193702	−	1.34723i	0.822104	−	0.569338i	$-0.192800\pi$
$770$	−45.4197	−	20.3427i	−1.63681	−	0.733099i
$771$	−4.75155	+	10.4044i	−0.171123	+	0.374707i
$772$	1.86026	+	1.46293i	0.0669522	+	0.0526518i
$773$	−40.4051	−	20.8303i	−1.45327	−	0.749213i	−0.462739	−	0.886495i	$-0.653133\pi$
$773$	−40.4051	−	20.8303i	−1.45327	−	0.749213i	−0.990532	+	0.137281i	$0.956164\pi$
$774$	8.84721	−	2.14631i	0.318006	−	0.0771475i
$775$	−18.1870	+	45.4289i	−0.653295	+	1.63185i
$776$	−2.34332	−	2.70434i	−0.0841204	−	0.0970801i
$777$	−0.0711315	+	1.76445i	−0.00255183	+	0.0632992i
$778$	−0.629723	−	0.545658i	−0.0225767	−	0.0195628i
$779$	−33.2392	−	8.06375i	−1.19092	−	0.288914i
$780$	11.8913	−	16.6990i	0.425776	−	0.597918i
$781$	15.7653	−	9.10208i	0.564126	−	0.325698i
$782$	−4.19838	−	3.29377i	−0.150134	−	0.117785i
$783$		−	8.33037i		−	0.297703i
$784$	3.97663	−	5.76077i	0.142022	−	0.205742i
$785$	−20.1882	+	5.92778i	−0.720546	+	0.211572i
$786$	2.63143	+	7.60302i	0.0938600	+	0.271191i
$787$	0.723475	−	15.1876i	0.0257891	−	0.541380i	−0.948595	−	0.316491i	$-0.897495\pi$
$787$	0.723475	−	15.1876i	0.0257891	−	0.541380i	0.974384	−	0.224889i	$-0.0722018\pi$
$788$	3.63508	−	10.5029i	0.129495	−	0.374150i
$789$	−7.89402	−	3.16029i	−0.281034	−	0.112509i
$790$	13.5860	−	46.2698i	0.483369	−	1.64620i
$791$	2.85812	−	5.64489i	0.101623	−	0.200709i
$792$	−5.74563	−	0.826098i	−0.204162	−	0.0293541i
$793$	36.5421	−	26.0215i	1.29765	−	0.924051i
$794$	1.86472	+	19.5282i	0.0661764	+	0.693030i
$795$	10.7827	−	4.31674i	0.382423	−	0.153099i
$796$	−0.275692	−	5.78748i	−0.00977163	−	0.205132i
$797$	12.6307	+	3.70871i	0.447403	+	0.131369i	0.497670	−	0.867367i	$-0.334189\pi$
$797$	12.6307	+	3.70871i	0.447403	+	0.131369i	−0.0502672	+	0.998736i	$0.516007\pi$
$798$	−17.5505	+	2.65443i	−0.621280	+	0.0939656i
$799$	−2.06581	+	1.79004i	−0.0730832	+	0.0633269i
$800$	−4.88939	+	2.52066i	−0.172866	+	0.0891186i
$801$	2.41316	+	0.465098i	0.0852647	+	0.0164334i
$802$	−0.00142623	+	0.00149579i	−5.03621e−5	+	5.28182e-5i
$803$	−26.5771	−	2.53780i	−0.937885	−	0.0895572i
$804$	−4.60480			−0.162399
$805$	32.5346	+	25.1425i	1.14669	+	0.886157i
$806$	56.2760			1.98224
$807$	7.11666	+	0.679559i	0.250518	+	0.0239216i
$808$	3.17113	−	3.32579i	0.111560	−	0.117001i
$809$	−39.4631	−	7.60588i	−1.38745	−	0.267409i	−0.559786	−	0.828637i	$-0.689117\pi$
$809$	−39.4631	−	7.60588i	−1.38745	−	0.267409i	−0.827661	+	0.561228i	$0.810329\pi$
$810$	−2.88028	+	1.48489i	−0.101203	+	0.0521736i
$811$	24.9947	−	21.6580i	0.877682	−	0.760516i	−0.0943064	−	0.995543i	$-0.530063\pi$
$811$	24.9947	−	21.6580i	0.877682	−	0.760516i	0.971989	+	0.235027i	$0.0755179\pi$
$812$	20.5206	+	8.04172i	0.720132	+	0.282209i
$813$	13.9232	+	4.08822i	0.488308	+	0.143380i
$814$	0.184347	+	3.86991i	0.00646135	+	0.135640i
$815$	18.3627	−	7.35133i	0.643218	−	0.257506i
$816$	0.105767	+	1.10764i	0.00370258	+	0.0387752i
$817$	49.7515	−	35.4279i	1.74059	−	1.23947i
$818$	11.1991	+	1.61019i	0.391567	+	0.0562989i
$819$	9.15169	+	14.0141i	0.319786	+	0.489691i
$820$	4.65445	−	15.8516i	0.162540	−	0.553562i
$821$	43.3319	+	17.3475i	1.51230	+	0.605432i	0.971777	−	0.235900i	$-0.0758039\pi$
$821$	43.3319	+	17.3475i	1.51230	+	0.605432i	0.540518	+	0.841332i	$0.318228\pi$
$822$	4.43722	−	12.8205i	0.154766	−	0.447167i
$823$	−2.10470	+	44.1831i	−0.0733652	+	1.54012i	0.599509	+	0.800368i	$0.295363\pi$
$823$	−2.10470	+	44.1831i	−0.0733652	+	1.54012i	−0.672874	+	0.739757i	$0.734941\pi$
$824$	−5.06243	−	14.6269i	−0.176358	−	0.509553i
$825$	−30.6377	+	8.99604i	−1.06667	+	0.313202i
$826$	5.89392	+	4.13247i	0.205076	+	0.143787i
$827$			1.84054i			0.0640017i	0.999488	+	0.0320009i	$0.0101879\pi$
$827$			1.84054i			0.0640017i	−0.999488	+	0.0320009i	$0.989812\pi$
$828$	4.45436	+	1.77726i	0.154800	+	0.0617642i
$829$	16.6664	−	9.62237i	0.578849	−	0.334199i	−0.181827	−	0.983331i	$-0.558201\pi$
$829$	16.6664	−	9.62237i	0.578849	−	0.334199i	0.760676	+	0.649132i	$0.224868\pi$
$830$	14.0751	−	19.7657i	0.488554	−	0.686078i
$831$	15.6875	+	3.80573i	0.544192	+	0.132019i
$832$	4.78104	+	4.14280i	0.165753	+	0.143626i
$833$	−6.61317	−	4.11471i	−0.229133	−	0.142566i
$834$	5.03044	+	5.80544i	0.174190	+	0.201026i
$835$	1.33787	−	3.34183i	0.0462988	−	0.115649i
$836$	−37.8455	+	9.18122i	−1.30891	+	0.317539i
$837$	−7.90678	−	4.07623i	−0.273298	−	0.140895i
$838$	−16.9185	−	13.3048i	−0.584439	−	0.459608i
$839$	−7.67556	+	16.8071i	−0.264990	+	0.580246i	−0.994619	−	0.103596i	$-0.966965\pi$
$839$	−7.67556	+	16.8071i	−0.264990	+	0.580246i	0.729630	+	0.683842i	$0.239692\pi$
$840$	−0.877320	−	8.52857i	−0.0302704	−	0.294264i
$841$	−5.74881	+	39.9838i	−0.198235	+	1.37875i
$842$	3.78168	−	0.180143i	0.130325	−	0.00620815i
$843$	0.612908	+	2.52644i	0.0211097	+	0.0870153i
$844$	−12.5320	+	9.85527i	−0.431369	+	0.339233i
$845$	−85.9797	+	16.5712i	−2.95779	+	0.570068i
$846$	1.32816	−	2.06666i	0.0456632	−	0.0710533i
$847$	38.9882	−	45.6649i	1.33965	−	1.56906i
$848$	1.00979	+	3.43903i	0.0346764	+	0.118097i
$849$	−1.74127	+	18.2354i	−0.0597603	+	0.625838i
$850$	3.06037	+	5.30071i	0.104970	+	0.181813i
$851$	0.602133	−	3.14379i	0.0206408	−	0.107768i
$852$	2.71594	+	1.56805i	0.0930466	+	0.0537205i
$853$	−20.5714	+	9.39465i	−0.704352	+	0.321667i	−0.735193	−	0.677858i	$-0.762909\pi$
$853$	−20.5714	+	9.39465i	−0.704352	+	0.321667i	0.0308415	+	0.999524i	$0.490181\pi$
$854$	4.28982	−	18.2644i	0.146795	−	0.624996i
$855$	−14.2368	+	16.4302i	−0.486889	+	0.561900i
$856$	2.31625	+	4.49289i	0.0791677	+	0.153564i
$857$	−5.23000	−	1.81012i	−0.178653	−	0.0618325i	0.236277	−	0.971686i	$-0.424073\pi$
$857$	−5.23000	−	1.81012i	−0.178653	−	0.0618325i	−0.414930	+	0.909853i	$0.636194\pi$
$858$	22.7000	+	28.8654i	0.774965	+	0.985448i
$859$	39.5452	+	41.4738i	1.34927	+	1.41507i	0.826902	+	0.562346i	$0.190101\pi$
$859$	39.5452	+	41.4738i	1.34927	+	1.41507i	0.522364	+	0.852723i	$0.325050\pi$
$860$	15.9495	+	24.8178i	0.543872	+	0.846282i
$861$	10.6634	+	8.26040i	0.363408	+	0.281514i
$862$	−31.9724	−	14.6013i	−1.08898	−	0.497322i
$863$	−29.5827	−	41.5431i	−1.00701	−	1.41414i	−0.907958	−	0.419062i	$-0.862359\pi$
$863$	−29.5827	−	41.5431i	−1.00701	−	1.41414i	−0.0990500	−	0.995082i	$-0.531580\pi$
$864$	−0.371662	−	0.928368i	−0.0126442	−	0.0315837i
$865$	−21.5425	+	41.7866i	−0.732466	+	1.42079i
$866$	9.27209	−	8.84092i	0.315078	−	0.300427i
$867$	−15.6015	+	2.24316i	−0.529855	+	0.0761817i
$868$	17.6740	−	15.5422i	0.599895	−	0.527536i
$869$	72.6692	+	46.7017i	2.46513	+	1.58425i
$870$	25.5099	−	8.82907i	0.864868	−	0.299334i
$871$	21.0831	+	20.1027i	0.714373	+	0.681154i
$872$	12.5413	+	8.93060i	0.424701	+	0.302428i
$873$	1.78918	−	3.09895i	0.0605545	−	0.104883i
$874$	32.1747	−	0.0373309i	1.08833	−	0.00126274i
$875$	−2.17435	−	3.70331i	−0.0735064	−	0.125195i
$876$	−1.91064	−	4.18372i	−0.0645546	−	0.141355i
$877$	2.34065	−	9.64827i	0.0790380	−	0.325799i	−0.918542	−	0.395323i	$-0.870633\pi$
$877$	2.34065	−	9.64827i	0.0790380	−	0.325799i	0.997580	+	0.0695236i	$0.0221479\pi$
$878$	5.60951	−	29.1049i	0.189312	−	0.982243i
$879$	11.5449	+	0.549949i	0.389398	+	0.0185493i
$880$	−3.55986	−	18.4703i	−0.120003	−	0.622634i
$881$	7.72481	+	53.7272i	0.260255	+	1.81012i	0.530898	+	0.847436i	$0.321855\pi$
$881$	7.72481	+	53.7272i	0.260255	+	1.81012i	−0.270643	+	0.962680i	$0.587236\pi$
$882$	6.74456	+	1.87375i	0.227101	+	0.0630926i
$883$	−43.3307	+	27.8470i	−1.45819	+	0.937125i	−0.459390	+	0.888235i	$0.651932\pi$
$883$	−43.3307	+	27.8470i	−1.45819	+	0.937125i	−0.998804	+	0.0488902i	$0.984432\pi$
$884$	4.35126	−	5.53308i	0.146349	−	0.186098i
$885$	8.77654	−	0.838058i	0.295020	−	0.0281710i
$886$	−2.11911	+	0.202351i	−0.0711930	+	0.00679811i
$887$	24.6476	−	31.3420i	0.827585	−	1.05236i	−0.170171	−	0.985415i	$-0.554432\pi$
$887$	24.6476	−	31.3420i	0.827585	−	1.05236i	0.997757	−	0.0669460i	$-0.0213255\pi$
$888$	−0.561486	+	0.360845i	−0.0188422	+	0.0121092i
$889$	3.36185	+	13.4286i	0.112753	+	0.450382i
$890$	1.13336	+	7.88271i	0.0379904	+	0.264229i
$891$	−1.09855	−	5.69982i	−0.0368028	−	0.190951i
$892$	0.181289	+	0.00863586i	0.00607001	+	0.000289150i
$893$	3.11912	−	16.1835i	0.104377	−	0.541562i
$894$	−3.74062	+	15.4191i	−0.125105	+	0.515690i
$895$	33.7147	+	73.8250i	1.12696	+	2.46770i
$896$	2.64568	−	0.0193348i	0.0883860	−	0.000645932i
$897$	−12.6355	−	27.5831i	−0.421887	−	0.920974i
$898$	−4.98271	+	8.63030i	−0.166275	+	0.287997i
$899$	60.3634	+	42.9846i	2.01323	+	1.43362i
$900$	−3.98118	−	3.79605i	−0.132706	−	0.126535i
$901$	3.76875	−	1.30438i	0.125555	−	0.0434551i
$902$	24.8958	+	15.9996i	0.828940	+	0.532727i
$903$	−23.6172	+	4.73111i	−0.785933	+	0.157442i
$904$	2.36712	−	0.340341i	0.0787293	−	0.0113196i
$905$	−28.0263	+	26.7231i	−0.931627	+	0.888305i
$906$	−10.1720	+	19.7310i	−0.337943	+	0.655518i
$907$	14.6218	+	36.5236i	0.485510	+	1.21274i	0.945734	+	0.324942i	$0.105345\pi$
$907$	14.6218	+	36.5236i	0.485510	+	1.21274i	−0.460224	+	0.887803i	$0.652231\pi$
$908$	10.3919	+	14.5933i	0.344866	+	0.484296i
$909$	4.18005	+	1.90896i	0.138643	+	0.0633163i
$910$	−33.2155	+	42.8781i	−1.10108	+	1.42140i
$911$	−29.7448	−	46.2839i	−0.985490	−	1.53345i	−0.838922	−	0.544252i	$-0.816814\pi$
$911$	−29.7448	−	46.2839i	−0.985490	−	1.53345i	−0.146568	−	0.989201i	$-0.546823\pi$
$912$	−4.62967	−	4.85546i	−0.153304	−	0.160780i
$913$	26.8689	+	34.1665i	0.889230	+	1.13075i
$914$	−7.91572	−	2.73966i	−0.261829	−	0.0906198i
$915$	−10.5296	−	20.4245i	−0.348097	−	0.675214i
$916$	−15.8449	+	18.2860i	−0.523531	+	0.604187i
$917$	−6.14618	−	20.3798i	−0.202965	−	0.673001i
$918$	−1.01213	+	0.462224i	−0.0334052	+	0.0152557i
$919$	24.6597	+	14.2373i	0.813450	+	0.469645i	0.848152	−	0.529752i	$-0.177715\pi$
$919$	24.6597	+	14.2373i	0.813450	+	0.469645i	−0.0347028	+	0.999398i	$0.511048\pi$
$920$	−0.721456	+	15.5242i	−0.0237857	+	0.511817i
$921$	0.680041	+	1.17787i	0.0224081	+	0.0388120i
$922$	1.28971	−	13.5064i	0.0424742	−	0.444810i
$923$	−5.58948	−	19.0360i	−0.183980	−	0.626578i
$924$	15.1011	+	2.79621i	0.496791	+	0.0919885i
$925$	−1.98497	+	3.08868i	−0.0652655	+	0.101555i
$926$	−30.0150	+	5.78493i	−0.986356	+	0.190104i
$927$	12.1667	−	9.56800i	0.399607	−	0.314254i
$928$	1.96396	+	8.09555i	0.0644701	+	0.265749i
$929$	38.2057	−	1.81996i	1.25349	−	0.0597110i	0.589694	−	0.807627i	$-0.299248\pi$
$929$	38.2057	−	1.81996i	1.25349	−	0.0597110i	0.663794	+	0.747916i	$0.268945\pi$
$930$	4.10243	−	28.5331i	0.134524	−	0.935636i
$931$	46.6794	−	5.14683i	1.52985	−	0.168681i
$932$	−0.210824	+	0.461641i	−0.00690578	+	0.0151215i
$933$	19.1440	+	15.0550i	0.626746	+	0.492878i
$934$	10.0076	+	5.15927i	0.327458	+	0.168817i
$935$	−20.3398	+	4.93438i	−0.665183	+	0.161372i
$936$	−2.35122	+	5.87306i	−0.0768520	+	0.191967i
$937$	−17.8528	−	20.6033i	−0.583227	−	0.673079i	0.385069	−	0.922888i	$-0.374178\pi$
$937$	−17.8528	−	20.6033i	−0.583227	−	0.673079i	−0.968295	+	0.249808i	$0.919632\pi$
$938$	12.1733	+	0.490750i	0.397471	+	0.0160236i
$939$	−2.37883	−	2.06126i	−0.0776301	−	0.0672668i
$940$	7.73638	+	1.87683i	0.252333	+	0.0612153i
$941$	10.0312	−	14.0868i	0.327007	−	0.459217i	−0.618043	−	0.786145i	$-0.712074\pi$
$941$	10.0312	−	14.0868i	0.327007	−	0.459217i	0.945049	+	0.326928i	$0.106013\pi$
$942$	5.62306	−	3.24647i	0.183209	−	0.105776i
$943$	−16.8931	−	17.6758i	−0.550114	−	0.575604i
$944$			2.72070i			0.0885514i
$945$	7.77257	−	3.61849i	0.252842	−	0.117710i
$946$	−50.7046	+	14.8882i	−1.64855	+	0.484057i
$947$	−18.3675	−	53.0693i	−0.596862	−	1.72452i	−0.685128	−	0.728423i	$-0.740254\pi$
$947$	−18.3675	−	53.0693i	−0.596862	−	1.72452i	0.0882657	−	0.996097i	$-0.471868\pi$
$948$	−0.708083	+	14.8645i	−0.0229975	+	0.482776i
$949$	−9.51656	+	27.4963i	−0.308920	+	0.892567i
$950$	−34.2613	−	13.7162i	−1.11158	−	0.445011i
$951$	−3.06662	+	10.4439i	−0.0994420	+	0.338668i
$952$	−0.161561	−	2.93944i	−0.00523621	−	0.0952677i
$953$	−11.4368	−	1.64436i	−0.370473	−	0.0532660i	−0.0454359	−	0.998967i	$-0.514468\pi$
$953$	−11.4368	−	1.64436i	−0.370473	−	0.0532660i	−0.325037	+	0.945701i	$0.605377\pi$
$954$	−2.91962	+	2.07905i	−0.0945261	+	0.0673117i
$955$	−1.33796	−	14.0117i	−0.0432953	−	0.453409i
$956$	3.72077	−	1.48957i	0.120338	−	0.0481762i
$957$	2.30084	+	48.3007i	0.0743757	+	1.56134i
$958$	22.1444	+	6.50217i	0.715452	+	0.210076i
$959$	−13.0966	+	33.4195i	−0.422911	+	1.07917i
$960$	2.44901	−	2.12208i	0.0790415	−	0.0684899i
$961$	42.7822	−	22.0557i	1.38007	−	0.711476i
$962$	4.14607	+	0.799090i	0.133675	+	0.0257637i
$963$	−3.48822	+	3.65834i	−0.112406	+	0.117888i
$964$	−18.3801	−	1.75509i	−0.591985	−	0.0565277i
$965$	−7.66894			−0.246872
$966$	−11.5862	−	5.17310i	−0.372779	−	0.166442i
$967$	20.1545			0.648125			0.324062	−	0.946036i	$-0.394951\pi$
$967$	20.1545			0.648125			0.324062	+	0.946036i	$0.394951\pi$
$968$	22.5920	+	2.15727i	0.726134	+	0.0693374i
$969$	−5.15134	+	5.40257i	−0.165485	+	0.173556i
$970$	11.3861	+	2.19450i	0.365587	+	0.0704611i
$971$	−19.7764	+	10.1954i	−0.634655	+	0.327187i	−0.745356	−	0.666667i	$-0.767721\pi$
$971$	−19.7764	+	10.1954i	−0.634655	+	0.327187i	0.110702	+	0.993854i	$0.464690\pi$
$972$	0.755750	−	0.654861i	0.0242407	−	0.0210047i
$973$	−12.6798	−	15.8834i	−0.406495	−	0.509198i
$974$	1.47052	+	0.431784i	0.0471186	+	0.0138353i
$975$	1.65585	+	34.7605i	0.0530295	+	1.11323i
$976$	6.58321	−	2.63552i	0.210723	−	0.0843609i
$977$	1.17747	+	12.3310i	0.0376707	+	0.394505i	0.994569	+	0.104081i	$0.0331902\pi$
$977$	1.17747	+	12.3310i	0.0376707	+	0.394505i	−0.956898	+	0.290424i	$0.906204\pi$
$978$	−4.97205	+	3.54058i	−0.158989	+	0.113215i
$979$	−14.1203	−	2.03019i	−0.451287	−	0.0648852i
$980$	1.41037	+	22.6397i	0.0450525	+	0.723198i
$981$	−4.33757	+	14.7724i	−0.138488	+	0.471647i
$982$	−29.5258	−	11.8204i	−0.942207	−	0.377203i
$983$	−11.6325	+	33.6099i	−0.371019	+	1.07199i	0.592781	+	0.805364i	$0.298030\pi$
$983$	−11.6325	+	33.6099i	−0.371019	+	1.07199i	−0.963800	+	0.266626i	$0.914091\pi$
$984$	−0.242583	+	5.09244i	−0.00773326	+	0.162341i
$985$	11.7795	+	34.0347i	0.375327	+	1.08444i
$986$	8.89357	−	2.61139i	0.283229	−	0.0831635i
$987$	−3.73139	+	5.32189i	−0.118771	+	0.169398i
$988$			42.4420i			1.35026i
$989$	43.6085	−	2.12805i	1.38667	−	0.0676679i
$990$	16.2901	−	9.40512i	0.517735	−	0.298914i
$991$	3.67867	−	5.16597i	0.116857	−	0.164102i	−0.752005	−	0.659158i	$-0.770913\pi$
$991$	3.67867	−	5.16597i	0.116857	−	0.164102i	0.868861	+	0.495056i	$0.164852\pi$
$992$	8.64491	+	2.09723i	0.274476	+	0.0665872i
$993$	−8.97532	−	7.77716i	−0.284823	−	0.246801i
$994$	−7.01276	−	4.43475i	−0.222431	−	0.140662i
$995$	12.2954	+	14.1897i	0.389791	+	0.449843i
$996$	−2.78302	+	6.95165i	−0.0881834	+	0.220272i
$997$	46.5422	−	11.2910i	1.47400	−	0.357590i	0.583332	−	0.812234i	$-0.301749\pi$
$997$	46.5422	−	11.2910i	1.47400	−	0.357590i	0.890673	+	0.454644i	$0.150234\pi$
$998$	34.2487	+	17.6564i	1.08412	+	0.558904i
$999$	−0.524643	−	0.412584i	−0.0165990	−	0.0130536i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.b.19.1	✓	320
7.3	odd	6	inner	966.2.be.b.157.1	yes	320
23.17	odd	22	inner	966.2.be.b.523.1	yes	320
161.17	even	66	inner	966.2.be.b.661.1	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.b.19.1	✓	320	1.1	even	1	trivial
966.2.be.b.157.1	yes	320	7.3	odd	6	inner
966.2.be.b.523.1	yes	320	23.17	odd	22	inner
966.2.be.b.661.1	yes	320	161.17	even	66	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.995472 - 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-2.88028 + 1.48489i) q^{5} +(0.755750 - 0.654861i) q^{6} +(-2.06769 + 1.65065i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})\)	\(q+(-0.995472 - 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-2.88028 + 1.48489i) q^{5} +(0.755750 - 0.654861i) q^{6} +(-2.06769 + 1.65065i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(3.00838 - 1.20438i) q^{10} +(0.551774 + 5.77843i) q^{11} +(-0.814576 + 0.580057i) q^{12} +(6.26183 + 0.900315i) q^{13} +(2.21523 - 1.44663i) q^{14} +(0.912957 - 3.10924i) q^{15} +(0.928368 + 0.371662i) q^{16} +(0.363922 - 1.05148i) q^{17} +(-0.0475819 + 0.998867i) q^{18} +(2.19426 + 6.33991i) q^{19} +(-3.10924 + 0.912957i) q^{20} +(0.232241 - 2.63554i) q^{21} -5.80472i q^{22} +(-1.12525 + 4.66195i) q^{23} +(0.866025 - 0.500000i) q^{24} +(3.19083 - 4.48090i) q^{25} +(-6.14790 - 1.49146i) q^{26} +(0.755750 + 0.654861i) q^{27} +(-2.34272 + 1.22951i) q^{28} +(-5.45523 - 6.29567i) q^{29} +(-1.20438 + 3.00838i) q^{30} +(-8.64491 + 2.09723i) q^{31} +(-0.888835 - 0.458227i) q^{32} +(-4.56282 - 3.58824i) q^{33} +(-0.462224 + 1.01213i) q^{34} +(3.50451 - 7.82462i) q^{35} +(0.142315 - 0.989821i) q^{36} +(-0.666684 + 0.0317581i) q^{37} +(-1.58168 - 6.51978i) q^{38} +(-4.97275 + 3.91061i) q^{39} +(3.18195 - 0.613270i) q^{40} +(-2.75630 + 4.28889i) q^{41} +(-0.481713 + 2.60153i) q^{42} +(-2.56484 - 8.73506i) q^{43} +(-0.551774 + 5.77843i) q^{44} +(1.62025 + 2.80636i) q^{45} +(1.56330 - 4.53388i) q^{46} +(-2.12752 - 1.22832i) q^{47} +(-0.909632 + 0.415415i) q^{48} +(1.55071 - 6.82607i) q^{49} +(-3.60232 + 4.15730i) q^{50} +(0.509860 + 0.988990i) q^{51} +(5.97829 + 2.06910i) q^{52} +(2.21562 + 2.81739i) q^{53} +(-0.690079 - 0.723734i) q^{54} +(-10.1696 - 15.8242i) q^{55} +(2.44898 - 1.00125i) q^{56} +(-6.10263 - 2.78698i) q^{57} +(4.83209 + 6.78572i) q^{58} +(1.01118 + 2.52581i) q^{59} +(1.48489 - 2.88028i) q^{60} +(5.13212 - 4.89346i) q^{61} +(8.80512 - 1.26598i) q^{62} +(1.74716 + 1.98681i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-19.3727 + 6.70495i) q^{65} +(4.20107 + 4.00571i) q^{66} +(3.75096 + 2.67105i) q^{67} +(0.556340 - 0.963609i) q^{68} +(-2.59750 - 4.03150i) q^{69} +(-4.23241 + 7.45607i) q^{70} +(-1.30278 - 2.85269i) q^{71} +(-0.235759 + 0.971812i) q^{72} +(-0.870434 + 4.51624i) q^{73} +(0.666684 + 0.0317581i) q^{74} +(1.04105 + 5.40149i) q^{75} +(0.954775 + 6.64061i) q^{76} +(-10.6791 - 11.0372i) q^{77} +(5.32196 - 3.42021i) q^{78} +(9.19904 - 11.6975i) q^{79} +(-3.22584 + 0.308030i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(3.15151 - 4.00747i) q^{82} +(6.29934 - 4.04834i) q^{83} +(0.726823 - 2.54396i) q^{84} +(0.513137 + 3.56895i) q^{85} +(1.72291 + 8.93931i) q^{86} +(8.32093 + 0.396375i) q^{87} +(1.09855 - 5.69982i) q^{88} +(-0.579394 + 2.38829i) q^{89} +(-1.34616 - 2.94767i) q^{90} +(-14.4337 + 8.47451i) q^{91} +(-1.98720 + 4.36475i) q^{92} +(4.44783 - 7.70387i) q^{93} +(2.00113 + 1.42499i) q^{94} +(-15.7341 - 15.0025i) q^{95} +(0.945001 - 0.327068i) q^{96} +(3.01030 + 1.93460i) q^{97} +(-2.19255 + 6.64776i) q^{98} +(5.74563 - 0.826098i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9}+O(q^{10}) \) 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9	\( 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9} + 22 q^{14} + 16 q^{16} - 66 q^{17} - 16 q^{18} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+O(q^{100}) \) 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9 + 22 * q^14 + 16 * q^16 - 66 * q^17 - 16 * q^18 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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