LMFDB - Embedded newform 690.2.x.a.77.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(77,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 11, 12]))

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

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

chi := DirichletCharacter("690.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.x (of order $44$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$48$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			77.20
Character	$\chi$	$=$	690.77
Dual form			690.2.x.a.233.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.599278 - 0.800541i) q^{2} +(1.05792 - 1.37142i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-2.22480 + 0.224149i) q^{5} +(-1.73187 - 0.0250473i) q^{6} +(-0.0551290 - 0.253424i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-0.761601 - 2.90172i) q^{9} +O(q^{10})$	\(q+(-0.599278 - 0.800541i) q^{2} +(1.05792 - 1.37142i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-2.22480 + 0.224149i) q^{5} +(-1.73187 - 0.0250473i) q^{6} +(-0.0551290 - 0.253424i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-0.761601 - 2.90172i) q^{9} +(1.51272 + 1.64672i) q^{10} +(-5.03730 + 0.724255i) q^{11} +(1.01782 + 1.40144i) q^{12} +(-1.15593 + 5.31373i) q^{13} +(-0.169839 + 0.196004i) q^{14} +(-2.04627 + 3.28828i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(0.159315 - 0.291764i) q^{17} +(-1.86653 + 2.34863i) q^{18} +(-0.992451 + 3.37998i) q^{19} +(0.411731 - 2.19783i) q^{20} +(-0.405874 - 0.192498i) q^{21} +(3.59854 + 3.59854i) q^{22} +(4.69253 - 0.990013i) q^{23} +(0.511957 - 1.65466i) q^{24} +(4.89951 - 0.997376i) q^{25} +(4.94658 - 2.25903i) q^{26} +(-4.78520 - 2.02531i) q^{27} +(0.258690 + 0.0185019i) q^{28} +(-5.27914 + 1.55009i) q^{29} +(3.85869 - 0.332472i) q^{30} +(-0.922817 + 2.02069i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(-4.33582 + 7.67448i) q^{33} +(-0.329044 + 0.0473093i) q^{34} +(0.179456 + 0.551462i) q^{35} +(2.99875 + 0.0867572i) q^{36} +(-6.45466 + 0.461646i) q^{37} +(3.30057 - 1.23105i) q^{38} +(6.06448 + 7.20678i) q^{39} +(-2.00620 + 0.987506i) q^{40} +(-1.72187 + 1.49201i) q^{41} +(0.0891287 + 0.440278i) q^{42} +(-7.32343 - 2.73150i) q^{43} +(0.724255 - 5.03730i) q^{44} +(2.34483 + 6.28504i) q^{45} +(-3.60468 - 3.16327i) q^{46} +(-8.34623 + 8.34623i) q^{47} +(-1.63143 + 0.581758i) q^{48} +(6.30624 - 2.87996i) q^{49} +(-3.73461 - 3.32456i) q^{50} +(-0.231589 - 0.527153i) q^{51} +(-4.77282 - 2.60616i) q^{52} +(1.00334 + 4.61229i) q^{53} +(1.24631 + 5.04447i) q^{54} +(11.0447 - 2.74043i) q^{55} +(-0.140216 - 0.218180i) q^{56} +(3.58544 + 4.93682i) q^{57} +(4.40458 + 3.29723i) q^{58} +(6.54699 - 4.20749i) q^{59} +(-2.57858 - 2.88979i) q^{60} +(4.17041 - 9.13192i) q^{61} +(2.17067 - 0.472200i) q^{62} +(-0.693379 + 0.352977i) q^{63} +(0.755750 - 0.654861i) q^{64} +(1.38065 - 12.0811i) q^{65} +(8.74209 - 1.12814i) q^{66} +(-11.4133 + 8.54388i) q^{67} +(0.235062 + 0.235062i) q^{68} +(3.60661 - 7.48281i) q^{69} +(0.333924 - 0.474141i) q^{70} +(-1.75742 - 0.252679i) q^{71} +(-1.72763 - 2.45261i) q^{72} +(9.12981 - 4.98525i) q^{73} +(4.23770 + 4.89057i) q^{74} +(3.81548 - 7.77445i) q^{75} +(-2.96346 - 1.90450i) q^{76} +(0.461245 + 1.23665i) q^{77} +(2.13502 - 9.17373i) q^{78} +(4.43696 + 6.90405i) q^{79} +(1.99281 + 1.01425i) q^{80} +(-7.83993 + 4.41990i) q^{81} +(2.22630 + 0.484301i) q^{82} +(-2.10266 + 0.150385i) q^{83} +(0.299048 - 0.335200i) q^{84} +(-0.289047 + 0.684830i) q^{85} +(2.20209 + 7.49963i) q^{86} +(-3.45908 + 8.87981i) q^{87} +(-4.46660 + 2.43895i) q^{88} +(-0.351729 - 0.770179i) q^{89} +(3.62623 - 5.64362i) q^{90} +1.41035 q^{91} +(-0.372129 + 4.78137i) q^{92} +(1.79495 + 3.40330i) q^{93} +(11.6832 + 1.67979i) q^{94} +(1.45039 - 7.74225i) q^{95} +(1.44340 + 0.957391i) q^{96} +(0.122787 - 1.71678i) q^{97} +(-6.08472 - 3.32251i) q^{98} +(5.93800 + 14.0652i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) $ 960 * q + 8 * q^3 + 8 * q^6	$ 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) $ 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	−0.599278	−	0.800541i	−0.423753	−	0.566068i
$2$	−0.599278	−	0.800541i	−0.423753	−	0.566068i
$3$	1.05792	−	1.37142i	0.610792	−	0.791791i
$3$	1.05792	−	1.37142i	0.610792	−	0.791791i
$4$	−0.281733	+	0.959493i	−0.140866	+	0.479746i
$5$	−2.22480	+	0.224149i	−0.994963	+	0.100243i
$5$	−2.22480	+	0.224149i	−0.994963	+	0.100243i
$6$	−1.73187	−	0.0250473i	−0.707033	−	0.0102255i
$7$	−0.0551290	−	0.253424i	−0.0208368	−	0.0957853i	0.965554	−	0.260202i	$-0.0837893\pi$
$7$	−0.0551290	−	0.253424i	−0.0208368	−	0.0957853i	−0.986391	+	0.164417i	$0.947426\pi$
$8$	0.936950	−	0.349464i	0.331262	−	0.123554i
$9$	−0.761601	−	2.90172i	−0.253867	−	0.967239i
$10$	1.51272	+	1.64672i	0.478363	+	0.520739i
$11$	−5.03730	+	0.724255i	−1.51880	+	0.218371i	−0.850682	−	0.525680i	$-0.823811\pi$
$11$	−5.03730	+	0.724255i	−1.51880	+	0.218371i	−0.668122	+	0.744052i	$0.732902\pi$
$12$	1.01782	+	1.40144i	0.293819	+	0.404562i
$13$	−1.15593	+	5.31373i	−0.320597	+	1.47376i	0.481435	+	0.876482i	$0.340116\pi$
$13$	−1.15593	+	5.31373i	−0.320597	+	1.47376i	−0.802032	+	0.597281i	$0.796248\pi$
$14$	−0.169839	+	0.196004i	−0.0453913	+	0.0523844i
$15$	−2.04627	+	3.28828i	−0.528344	+	0.849030i
$16$	−0.841254	−	0.540641i	−0.210313	−	0.135160i
$17$	0.159315	−	0.291764i	0.0386397	−	0.0707633i	−0.857646	−	0.514241i	$-0.828074\pi$
$17$	0.159315	−	0.291764i	0.0386397	−	0.0707633i	0.896285	+	0.443478i	$0.146255\pi$
$18$	−1.86653	+	2.34863i	−0.439946	+	0.553577i
$19$	−0.992451	+	3.37998i	−0.227684	+	0.775420i	0.763830	+	0.645418i	$0.223317\pi$
$19$	−0.992451	+	3.37998i	−0.227684	+	0.775420i	−0.991514	+	0.130002i	$0.958501\pi$
$20$	0.411731	−	2.19783i	0.0920657	−	0.491451i
$21$	−0.405874	−	0.192498i	−0.0885689	−	0.0420065i
$22$	3.59854	+	3.59854i	0.767211	+	0.767211i
$23$	4.69253	−	0.990013i	0.978461	−	0.206432i
$23$	4.69253	−	0.990013i	0.978461	−	0.206432i
$24$	0.511957	−	1.65466i	0.104503	−	0.337756i
$25$	4.89951	−	0.997376i	0.979903	−	0.199475i
$26$	4.94658	−	2.25903i	0.970104	−	0.443032i
$27$	−4.78520	−	2.02531i	−0.920911	−	0.389772i
$28$	0.258690	+	0.0185019i	0.0488879	+	0.00349653i
$29$	−5.27914	+	1.55009i	−0.980311	+	0.287845i	−0.732353	−	0.680925i	$-0.761578\pi$
$29$	−5.27914	+	1.55009i	−0.980311	+	0.287845i	−0.247958	+	0.968771i	$0.579760\pi$
$30$	3.85869	−	0.332472i	0.704497	−	0.0607008i
$31$	−0.922817	+	2.02069i	−0.165743	+	0.362926i	−0.974220	−	0.225602i	$-0.927565\pi$
$31$	−0.922817	+	2.02069i	−0.165743	+	0.362926i	0.808477	+	0.588528i	$0.200292\pi$
$32$	0.0713392	+	0.997452i	0.0126111	+	0.176326i
$33$	−4.33582	+	7.67448i	−0.754769	+	1.33596i
$34$	−0.329044	+	0.0473093i	−0.0564305	+	0.00811349i
$35$	0.179456	+	0.551462i	0.0303336	+	0.0932141i
$36$	2.99875	+	0.0867572i	0.499791	+	0.0144595i
$37$	−6.45466	+	0.461646i	−1.06114	+	0.0758942i	−0.590979	−	0.806687i	$-0.701258\pi$
$37$	−6.45466	+	0.461646i	−1.06114	+	0.0758942i	−0.470160	+	0.882581i	$0.655804\pi$
$38$	3.30057	−	1.23105i	0.535422	−	0.199702i
$39$	6.06448	+	7.20678i	0.971094	+	1.15401i
$40$	−2.00620	+	0.987506i	−0.317208	+	0.156138i
$41$	−1.72187	+	1.49201i	−0.268911	+	0.233013i	−0.778869	−	0.627186i	$-0.784206\pi$
$41$	−1.72187	+	1.49201i	−0.268911	+	0.233013i	0.509958	+	0.860199i	$0.329661\pi$
$42$	0.0891287	+	0.440278i	0.0137529	+	0.0679364i
$43$	−7.32343	−	2.73150i	−1.11681	−	0.416549i	−0.277787	−	0.960643i	$-0.589601\pi$
$43$	−7.32343	−	2.73150i	−1.11681	−	0.416549i	−0.839025	+	0.544093i	$0.816874\pi$
$44$	0.724255	−	5.03730i	0.109186	−	0.759402i
$45$	2.34483	+	6.28504i	0.349547	+	0.936919i
$46$	−3.60468	−	3.16327i	−0.531481	−	0.466399i
$47$	−8.34623	+	8.34623i	−1.21742	+	1.21742i	−0.248892	+	0.968531i	$0.580066\pi$
$47$	−8.34623	+	8.34623i	−1.21742	+	1.21742i	−0.968531	+	0.248892i	$0.919934\pi$
$48$	−1.63143	+	0.581758i	−0.235476	+	0.0839696i
$49$	6.30624	−	2.87996i	0.900891	−	0.411423i
$50$	−3.73461	−	3.32456i	−0.528154	−	0.470164i
$51$	−0.231589	−	0.527153i	−0.0324290	−	0.0738162i
$52$	−4.77282	−	2.60616i	−0.661871	−	0.361409i
$53$	1.00334	+	4.61229i	0.137820	+	0.633547i	0.993286	+	0.115688i	$0.0369071\pi$
$53$	1.00334	+	4.61229i	0.137820	+	0.633547i	−0.855466	+	0.517859i	$0.826729\pi$
$54$	1.24631	+	5.04447i	0.169602	+	0.686466i
$55$	11.0447	−	2.74043i	1.48926	−	0.369520i
$56$	−0.140216	−	0.218180i	−0.0187371	−	0.0291555i
$57$	3.58544	+	4.93682i	0.474904	+	0.653898i
$58$	4.40458	+	3.29723i	0.578350	+	0.432947i
$59$	6.54699	−	4.20749i	0.852345	−	0.547769i	−0.0399604	−	0.999201i	$-0.512723\pi$
$59$	6.54699	−	4.20749i	0.852345	−	0.547769i	0.892305	+	0.451432i	$0.149087\pi$
$60$	−2.57858	−	2.88979i	−0.332894	−	0.373071i
$61$	4.17041	−	9.13192i	0.533966	−	1.16922i	−0.429910	−	0.902872i	$-0.641455\pi$
$61$	4.17041	−	9.13192i	0.533966	−	1.16922i	0.963876	−	0.266351i	$-0.0858179\pi$
$62$	2.17067	−	0.472200i	0.275675	−	0.0599694i
$63$	−0.693379	+	0.352977i	−0.0873575	+	0.0444709i
$64$	0.755750	−	0.654861i	0.0944687	−	0.0818576i
$65$	1.38065	−	12.0811i	0.171249	−	1.49848i
$66$	8.74209	−	1.12814i	1.07608	−	0.138865i
$67$	−11.4133	+	8.54388i	−1.39435	+	1.04380i	−0.402637	+	0.915360i	$0.631906\pi$
$67$	−11.4133	+	8.54388i	−1.39435	+	1.04380i	−0.991717	+	0.128441i	$0.959003\pi$
$68$	0.235062	+	0.235062i	0.0285054	+	0.0285054i
$69$	3.60661	−	7.48281i	0.434185	−	0.900824i
$70$	0.333924	−	0.474141i	0.0399116	−	0.0566707i
$71$	−1.75742	−	0.252679i	−0.208568	−	0.0299875i	0.0372389	−	0.999306i	$-0.488144\pi$
$71$	−1.75742	−	0.252679i	−0.208568	−	0.0299875i	−0.245807	+	0.969319i	$0.579053\pi$
$72$	−1.72763	−	2.45261i	−0.203603	−	0.289043i
$73$	9.12981	−	4.98525i	1.06856	−	0.583480i	0.154062	−	0.988061i	$-0.450765\pi$
$73$	9.12981	−	4.98525i	1.06856	−	0.583480i	0.914502	+	0.404581i	$0.132583\pi$
$74$	4.23770	+	4.89057i	0.492623	+	0.568517i
$75$	3.81548	−	7.77445i	0.440574	−	0.897716i
$76$	−2.96346	−	1.90450i	−0.339932	−	0.218461i
$77$	0.461245	+	1.23665i	0.0525638	+	0.140929i
$78$	2.13502	−	9.17373i	0.241743	−	1.03872i
$79$	4.43696	+	6.90405i	0.499198	+	0.776767i	0.995833	−	0.0911925i	$-0.0290679\pi$
$79$	4.43696	+	6.90405i	0.499198	+	0.776767i	−0.496636	+	0.867959i	$0.665432\pi$
$80$	1.99281	+	1.01425i	0.222803	+	0.113397i
$81$	−7.83993	+	4.41990i	−0.871103	+	0.491100i
$82$	2.22630	+	0.484301i	0.245853	+	0.0534821i
$83$	−2.10266	+	0.150385i	−0.230797	+	0.0165069i	−0.186259	−	0.982501i	$-0.559636\pi$
$83$	−2.10266	+	0.150385i	−0.230797	+	0.0165069i	−0.0445384	+	0.999008i	$0.514182\pi$
$84$	0.299048	−	0.335200i	0.0326288	−	0.0365733i
$85$	−0.289047	+	0.684830i	−0.0313516	+	0.0742802i
$86$	2.20209	+	7.49963i	0.237457	+	0.808706i
$87$	−3.45908	+	8.87981i	−0.370852	+	0.952015i
$88$	−4.46660	+	2.43895i	−0.476141	+	0.259993i
$89$	−0.351729	−	0.770179i	−0.0372832	−	0.0816388i	0.890074	−	0.455816i	$-0.150652\pi$
$89$	−0.351729	−	0.770179i	−0.0372832	−	0.0816388i	−0.927357	+	0.374177i	$0.877925\pi$
$90$	3.62623	−	5.64362i	0.382238	−	0.594890i
$91$	1.41035			0.147845
$92$	−0.372129	+	4.78137i	−0.0387971	+	0.498493i
$93$	1.79495	+	3.40330i	0.186127	+	0.352906i
$94$	11.6832	+	1.67979i	1.20503	+	0.173257i
$95$	1.45039	−	7.74225i	0.148807	−	0.794338i
$96$	1.44340	+	0.957391i	0.147316	+	0.0977133i
$97$	0.122787	−	1.71678i	0.0124671	−	0.174313i	−0.987403	−	0.158223i	$-0.949424\pi$
$97$	0.122787	−	1.71678i	0.0124671	−	0.174313i	0.999871	−	0.0160901i	$-0.00512185\pi$
$98$	−6.08472	−	3.32251i	−0.614649	−	0.335624i
$99$	5.93800	+	14.0652i	0.596791	+	1.41361i
$100$	−0.423377	+	4.98204i	−0.0423377	+	0.498204i
$101$	−4.06703	−	3.52410i	−0.404684	−	0.350661i	0.428611	−	0.903489i	$-0.359003\pi$
$101$	−4.06703	−	3.52410i	−0.404684	−	0.350661i	−0.833295	+	0.552828i	$0.813549\pi$
$102$	−0.283222	+	0.501308i	−0.0280431	+	0.0496369i
$103$	−0.765066	−	0.572721i	−0.0753842	−	0.0564319i	0.560921	−	0.827869i	$-0.310447\pi$
$103$	−0.765066	−	0.572721i	−0.0753842	−	0.0564319i	−0.636305	+	0.771437i	$0.719538\pi$
$104$	0.773908	+	5.38265i	0.0758880	+	0.527812i
$105$	0.946138	+	0.337294i	0.0923337	+	0.0329165i
$106$	3.09105	−	3.56726i	0.300229	−	0.346483i
$107$	−7.03161	−	18.8525i	−0.679772	−	1.82254i	−0.557746	−	0.830012i	$-0.688334\pi$
$107$	−7.03161	−	18.8525i	−0.679772	−	1.82254i	−0.122026	−	0.992527i	$-0.538939\pi$
$108$	3.29142	−	4.02077i	0.316717	−	0.386898i
$109$	−3.85182	−	13.1181i	−0.368938	−	1.25649i	−0.909684	−	0.415301i	$-0.863676\pi$
$109$	−3.85182	−	13.1181i	−0.368938	−	1.25649i	0.540746	−	0.841186i	$-0.318142\pi$
$110$	−8.81266	−	7.19944i	−0.840254	−	0.686440i
$111$	−6.19542	+	9.34046i	−0.588043	+	0.886557i
$112$	−0.0906339	+	0.242999i	−0.00856410	+	0.0229612i
$113$	−9.82588	+	7.35556i	−0.924341	+	0.691953i	−0.951490	−	0.307678i	$-0.900448\pi$
$113$	−9.82588	+	7.35556i	−0.924341	+	0.691953i	0.0271492	+	0.999631i	$0.491357\pi$
$114$	1.80346	−	5.82882i	0.168909	−	0.545919i
$115$	−10.2181	+	3.25441i	−0.952839	+	0.303476i
$116$		−	5.50201i		−	0.510849i
$117$	16.2993	−	0.692757i	1.50687	−	0.0640454i
$118$	−7.29173	−	2.71968i	−0.671258	−	0.250366i
$119$	−0.0827231	−	0.0242897i	−0.00758321	−	0.00222663i
$120$	−0.768113	+	3.79605i	−0.0701188	+	0.346530i
$121$	14.2955	−	4.19753i	1.29959	−	0.381593i
$122$	−9.80971	+	2.13397i	−0.888129	+	0.193201i
$123$	0.224571	+	3.93985i	0.0202489	+	0.355244i
$124$	−1.67885	−	1.45473i	−0.150765	−	0.130639i
$125$	−10.6769	+	3.31719i	−0.954971	+	0.296698i
$126$	0.698099	+	0.343547i	0.0621916	+	0.0306056i
$127$	−6.36685	+	8.50511i	−0.564966	+	0.754707i	−0.988508	−	0.151170i	$-0.951696\pi$
$127$	−6.36685	+	8.50511i	−0.564966	+	0.754707i	0.423541	+	0.905877i	$0.360787\pi$
$128$	−0.977147	−	0.212565i	−0.0863684	−	0.0187883i
$129$	−11.4937	+	7.15380i	−1.01196	+	0.629857i
$130$	−10.4988	+	6.13467i	−0.920807	+	0.538046i
$131$	−6.84702	+	10.6542i	−0.598227	+	0.930860i	0.401659	+	0.915789i	$0.368434\pi$
$131$	−6.84702	+	10.6542i	−0.598227	+	0.930860i	−0.999886	+	0.0150705i	$0.995203\pi$
$132$	−6.14207	−	6.32234i	−0.534598	−	0.550289i
$133$	0.911281	+	0.0651761i	0.0790181	+	0.00565148i
$134$	13.6795	+	4.01665i	1.18172	+	0.346986i
$135$	11.1001	+	3.43333i	0.955345	+	0.295494i
$136$	0.0473093	−	0.329044i	0.00405674	−	0.0282153i
$137$	−10.0920	+	10.0920i	−0.862220	+	0.862220i	−0.991596	−	0.129376i	$-0.958703\pi$
$137$	−10.0920	+	10.0920i	−0.862220	+	0.862220i	0.129376	+	0.991596i	$0.458703\pi$
$138$	−8.15165	+	1.59704i	−0.693915	+	0.135949i
$139$		−	21.5445i		−	1.82738i	−0.406409	−	0.913691i	$-0.633219\pi$
$139$		−	21.5445i		−	1.82738i	0.406409	−	0.913691i	$-0.366781\pi$
$140$	−0.579683	+	0.0168221i	−0.0489921	+	0.00142173i
$141$	2.61655	+	20.2759i	0.220353	+	1.70754i
$142$	0.850904	+	1.55831i	0.0714063	+	0.130771i
$143$	1.97428	−	27.6040i	0.165098	−	2.30837i
$144$	−0.928087	+	2.85283i	−0.0773406	+	0.237736i
$145$	11.3976	−	4.63197i	0.946519	−	0.384664i
$146$	−9.46219	−	4.32124i	−0.783097	−	0.357628i
$147$	2.72186	−	11.6953i	0.224496	−	0.964612i
$148$	1.37554	−	6.32326i	0.113069	−	0.519769i
$149$	1.28735	+	8.95369i	0.105464	+	0.733515i	0.972099	+	0.234572i	$0.0753690\pi$
$149$	1.28735	+	8.95369i	0.105464	+	0.733515i	−0.866635	+	0.498942i	$0.833722\pi$
$150$	−8.51030	+	1.60461i	−0.694863	+	0.131016i
$151$	4.50111	−	2.89269i	0.366295	−	0.235404i	−0.344525	−	0.938777i	$-0.611960\pi$
$151$	4.50111	−	2.89269i	0.366295	−	0.235404i	0.710821	+	0.703373i	$0.248324\pi$
$152$	0.251304	+	3.51370i	0.0203835	+	0.284998i
$153$	−0.967953	−	0.240080i	−0.0782544	−	0.0194093i
$154$	0.713573	−	1.11034i	0.0575013	−	0.0894738i
$155$	1.60015	−	4.70248i	0.128527	−	0.377712i
$156$	−8.62342	+	3.78844i	−0.690426	+	0.303318i
$157$	7.03052	+	12.8754i	0.561097	+	1.02757i	0.992127	+	0.125234i	$0.0399683\pi$
$157$	7.03052	+	12.8754i	0.561097	+	1.02757i	−0.431031	+	0.902337i	$0.641850\pi$
$158$	2.86800	−	7.68942i	0.228166	−	0.611737i
$159$	7.38686	+	3.50344i	0.585816	+	0.277841i
$160$	−0.382294	−	2.20315i	−0.0302230	−	0.174174i
$161$	−0.509588	−	1.13462i	−0.0401612	−	0.0894208i
$162$	8.23661	+	3.62744i	0.647129	+	0.284998i
$163$	−9.38955	−	12.5430i	−0.735446	−	0.982441i	−0.999838	−	0.0180259i	$-0.994262\pi$
$163$	−9.38955	−	12.5430i	−0.735446	−	0.982441i	0.264391	−	0.964416i	$-0.414829\pi$
$164$	−0.946467	−	2.07247i	−0.0739067	−	0.161833i
$165$	7.92612	−	18.0461i	0.617047	−	1.40489i
$166$	1.38047	+	1.59315i	0.107145	+	0.123652i
$167$	−4.70832	+	8.62264i	−0.364340	+	0.667240i	−0.993970	−	0.109656i	$-0.965025\pi$
$167$	−4.70832	+	8.62264i	−0.364340	+	0.667240i	0.629629	+	0.776896i	$0.283207\pi$
$168$	−0.447554	−	0.0385224i	−0.0345296	−	0.00297206i
$169$	−15.0743	−	6.88420i	−1.15956	−	0.529554i
$170$	0.721454	−	0.179009i	0.0553330	−	0.0137294i
$171$	10.5636	+	0.305617i	0.807818	+	0.0233711i
$172$	4.68410	−	6.25722i	0.357159	−	0.477109i
$173$	12.8196	−	17.1250i	0.974659	−	1.30199i	0.0214213	−	0.999771i	$-0.493181\pi$
$173$	12.8196	−	17.1250i	0.974659	−	1.30199i	0.953238	−	0.302221i	$-0.0977282\pi$
$174$	9.18160	−	2.55233i	0.696056	−	0.193492i
$175$	−0.522865	−	1.18667i	−0.0395249	−	0.0897039i
$176$	4.62921	+	2.11409i	0.348940	+	0.159356i
$177$	1.15595	−	13.4299i	0.0868866	−	1.00945i
$178$	−0.405777	+	0.743125i	−0.0304143	+	0.0556996i
$179$	−4.05457	−	4.67923i	−0.303053	−	0.349742i	0.583713	−	0.811960i	$-0.301599\pi$
$179$	−4.05457	−	4.67923i	−0.303053	−	0.349742i	−0.886766	+	0.462218i	$0.847054\pi$
$180$	−6.69107	+	0.479148i	−0.498723	+	0.0357136i
$181$	−2.38725	−	5.22734i	−0.177443	−	0.388545i	0.799923	−	0.600103i	$-0.204874\pi$
$181$	−2.38725	−	5.22734i	−0.177443	−	0.388545i	−0.977366	+	0.211558i	$0.932146\pi$
$182$	−0.845192	−	1.12904i	−0.0626498	−	0.0836904i
$183$	−8.11175	−	15.3803i	−0.599638	−	1.13694i
$184$	4.05069	−	2.56747i	0.298621	−	0.189276i
$185$	14.2569	−	2.47388i	1.04819	−	0.181883i
$186$	1.64881	−	3.47645i	0.120897	−	0.254906i
$187$	−0.591209	+	1.58509i	−0.0432335	+	0.115913i
$188$	−5.65675	−	10.3596i	−0.412561	−	0.755549i
$189$	−0.249460	+	1.32434i	−0.0181456	+	0.0963314i
$190$	−7.06718	+	3.47866i	−0.512707	+	0.252368i
$191$	4.62673	−	7.19934i	0.334779	−	0.520926i	−0.632527	−	0.774538i	$-0.717982\pi$
$191$	4.62673	−	7.19934i	0.334779	−	0.520926i	0.967306	+	0.253612i	$0.0816187\pi$
$192$	−0.0985667	−	1.72924i	−0.00711344	−	0.124797i
$193$	0.0362284	+	0.506539i	0.00260777	+	0.0364614i	0.998589	−	0.0530965i	$-0.0169091\pi$
$193$	0.0362284	+	0.506539i	0.00260777	+	0.0364614i	−0.995982	+	0.0895580i	$0.971455\pi$
$194$	−1.44794	+	0.930533i	−0.103956	+	0.0668084i
$195$	−15.1077	−	14.6743i	−1.08188	−	1.05085i
$196$	0.986631	+	6.86217i	0.0704737	+	0.490155i
$197$	−1.15992	+	5.33207i	−0.0826409	+	0.379894i	−0.999828	−	0.0185634i	$-0.994091\pi$
$197$	−1.15992	+	5.33207i	−0.0826409	+	0.379894i	0.917187	+	0.398458i	$0.130454\pi$
$198$	7.70129	−	13.1826i	0.547307	−	0.936846i
$199$	−19.3496	−	8.83666i	−1.37166	−	0.626414i	−0.412934	−	0.910761i	$-0.635496\pi$
$199$	−19.3496	−	8.83666i	−1.37166	−	0.626414i	−0.958722	+	0.284346i	$0.908223\pi$
$200$	4.24205	−	2.64670i	0.299958	−	0.187150i
$201$	−0.357098	+	24.6912i	−0.0251877	+	1.74158i
$202$	−0.383908	+	5.36774i	−0.0270117	+	0.377673i
$203$	0.683865	+	1.25241i	0.0479979	+	0.0879016i
$204$	0.571046	−	0.0736920i	0.0399812	−	0.00515947i
$205$	3.49640	−	3.70539i	0.244199	−	0.258796i
$206$			0.955686i			0.0665858i
$207$	−6.44658	−	12.8624i	−0.448068	−	0.893999i
$208$	3.84525	−	3.84525i	0.266620	−	0.266620i
$209$	2.55131	−	17.7448i	0.176478	−	1.22743i
$210$	−0.296982	−	0.959555i	−0.0204937	−	0.0662156i
$211$	−7.02800	−	2.06361i	−0.483827	−	0.142065i	0.0307173	−	0.999528i	$-0.490221\pi$
$211$	−7.02800	−	2.06361i	−0.483827	−	0.142065i	−0.514545	+	0.857464i	$0.672039\pi$
$212$	−4.70813	−	0.336732i	−0.323356	−	0.0231269i
$213$	−2.20575	+	2.14285i	−0.151135	+	0.146826i
$214$	−10.8783	+	16.9270i	−0.743625	+	1.15710i
$215$	16.9055	+	4.43551i	1.15294	+	0.302499i
$216$	−5.19126	−	0.225363i	−0.353221	−	0.0153340i
$217$	0.562965	+	0.122465i	0.0382165	+	0.00831350i
$218$	−8.19327	+	10.9449i	−0.554918	+	0.741284i
$219$	2.82174	−	17.7948i	0.190675	−	1.20246i
$220$	−0.482219	+	11.3694i	−0.0325112	+	0.766522i
$221$	1.36620	+	1.18382i	0.0919005	+	0.0796322i
$222$	11.1902	−	0.637840i	0.751037	−	0.0428090i
$223$	20.5335	−	4.46679i	1.37503	−	0.299119i	0.536463	−	0.843924i	$-0.319760\pi$
$223$	20.5335	−	4.46679i	1.37503	−	0.299119i	0.838563	+	0.544805i	$0.183396\pi$
$224$	0.248846	−	0.0730677i	0.0166267	−	0.00488204i
$225$	−6.62558	−	13.4574i	−0.441705	−	0.897160i
$226$	11.7769	+	3.45800i	0.783385	+	0.230023i
$227$	3.05145	+	1.13813i	0.202532	+	0.0755405i	0.448683	−	0.893691i	$-0.351893\pi$
$227$	3.05145	+	1.13813i	0.202532	+	0.0755405i	−0.246151	+	0.969231i	$0.579166\pi$
$228$	−5.74698	+	2.04934i	−0.380603	+	0.135721i
$229$			23.1478i			1.52965i	0.644237	+	0.764826i	$0.277175\pi$
$229$			23.1478i			1.52965i	−0.644237	+	0.764826i	$0.722825\pi$
$230$	8.72875	+	6.22968i	0.575557	+	0.410773i
$231$	2.18393	+	0.675714i	0.143692	+	0.0444587i
$232$	−4.40458	+	3.29723i	−0.289175	+	0.216474i
$233$	−5.07401	+	13.6040i	−0.332410	+	0.891224i	0.657995	+	0.753023i	$0.271405\pi$
$233$	−5.07401	+	13.6040i	−0.332410	+	0.891224i	−0.990404	+	0.138202i	$0.955868\pi$
$234$	−10.3224	−	12.6331i	−0.674795	−	0.825852i
$235$	16.6979	−	20.4395i	1.08925	−	1.33333i
$236$	2.19256	+	7.46717i	0.142724	+	0.486072i
$237$	14.1623	+	1.21900i	0.919943	+	0.0791822i
$238$	0.0301292	+	0.0807795i	0.00195299	+	0.00523616i
$239$	4.91761	−	5.67523i	0.318094	−	0.367100i	−0.574074	−	0.818803i	$-0.694638\pi$
$239$	4.91761	−	5.67523i	0.318094	−	0.367100i	0.892168	+	0.451703i	$0.149183\pi$
$240$	3.49921	−	1.65998i	0.225873	−	0.107151i
$241$	−1.13798	−	7.91485i	−0.0733040	−	0.509840i	−0.993084	−	0.117406i	$-0.962542\pi$
$241$	−1.13798	−	7.91485i	−0.0733040	−	0.509840i	0.919780	−	0.392434i	$-0.128367\pi$
$242$	−11.9272	−	8.92862i	−0.766712	−	0.573954i
$243$	−2.23248	+	15.4278i	−0.143213	+	0.989692i
$244$	7.58707	+	6.57424i	0.485713	+	0.420872i
$245$	−13.3846	+	7.82089i	−0.855111	+	0.499659i
$246$	3.01943	−	2.54084i	0.192512	−	0.161998i
$247$	−16.8131	−	9.18063i	−1.06979	−	0.584150i
$248$	−0.158475	+	2.21577i	−0.0100632	+	0.140702i
$249$	−2.01821	+	3.04273i	−0.127899	+	0.192825i
$250$	9.05398	+	6.55938i	0.572624	+	0.414852i
$251$	−15.1782	−	2.18230i	−0.958041	−	0.137745i	−0.354481	−	0.935063i	$-0.615342\pi$
$251$	−15.1782	−	2.18230i	−0.958041	−	0.137745i	−0.603560	+	0.797318i	$0.706251\pi$
$252$	−0.143332	−	0.764737i	−0.00902904	−	0.0481739i
$253$	−22.9207	+	8.38559i	−1.44101	+	0.527197i
$254$	10.6242			0.666622
$255$	0.633401	+	1.12090i	0.0396651	+	0.0701936i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−7.82583	+	4.27323i	−0.488162	+	0.266556i	−0.704425	−	0.709779i	$-0.748795\pi$
$257$	−7.82583	+	4.27323i	−0.488162	+	0.266556i	0.216263	+	0.976335i	$0.430613\pi$
$258$	12.6148	+	4.91403i	0.785363	+	0.305934i
$259$	0.472832	+	1.61032i	0.0293803	+	0.100060i
$260$	11.2028	+	4.72837i	0.694766	+	0.293241i
$261$	8.51853	+	14.1380i	0.527284	+	0.875121i
$262$	12.6324	−	0.903485i	0.780431	−	0.0558175i
$263$	15.4854	+	3.36864i	0.954871	+	0.207719i	0.662900	−	0.748708i	$-0.269325\pi$
$263$	15.4854	+	3.36864i	0.954871	+	0.207719i	0.291971	+	0.956427i	$0.405689\pi$
$264$	−1.38049	+	8.70581i	−0.0849630	+	0.535806i
$265$	−3.26608	−	10.0365i	−0.200634	−	0.616540i
$266$	−0.493934	−	0.768577i	−0.0302850	−	0.0471244i
$267$	−1.42834	−	0.332420i	−0.0874132	−	0.0203438i
$268$	−4.98230	−	13.3581i	−0.304342	−	0.815973i
$269$	26.4756	+	17.0149i	1.61425	+	1.03741i	0.959556	+	0.281517i	$0.0908377\pi$
$269$	26.4756	+	17.0149i	1.61425	+	1.03741i	0.654691	+	0.755896i	$0.272799\pi$
$270$	−3.90352	−	10.9436i	−0.237561	−	0.666007i
$271$	−0.396548	−	0.457640i	−0.0240885	−	0.0277997i	0.743577	−	0.668650i	$-0.233127\pi$
$271$	−0.396548	−	0.457640i	−0.0240885	−	0.0277997i	−0.767666	+	0.640850i	$0.778582\pi$
$272$	−0.291764	+	0.159315i	−0.0176908	+	0.00965992i
$273$	1.49204	−	1.93419i	0.0903025	−	0.117062i
$274$	14.1270	+	2.03116i	0.853444	+	0.122707i
$275$	−23.9580	+	8.57258i	−1.44472	+	0.516946i
$276$	6.16360	+	5.56867i	0.371005	+	0.335194i
$277$	10.0798	+	10.0798i	0.605636	+	0.605636i	0.941802	−	0.336167i	$-0.109131\pi$
$277$	10.0798	+	10.0798i	0.605636	+	0.605636i	−0.336167	+	0.941802i	$0.609131\pi$
$278$	−17.2473	+	12.9112i	−1.03442	+	0.774359i
$279$	6.56628	+	1.13880i	0.393113	+	0.0681779i
$280$	0.360858	+	0.453979i	0.0215654	+	0.0271304i
$281$	11.7943	−	10.2198i	0.703588	−	0.609662i	−0.227793	−	0.973710i	$-0.573151\pi$
$281$	11.7943	−	10.2198i	0.703588	−	0.609662i	0.931380	+	0.364048i	$0.118605\pi$
$282$	14.6636	−	14.2455i	0.873207	−	0.848310i
$283$	−2.62498	+	0.571029i	−0.156039	+	0.0339441i	−0.289906	−	0.957055i	$-0.593624\pi$
$283$	−2.62498	+	0.571029i	−0.156039	+	0.0339441i	0.133867	+	0.990999i	$0.457260\pi$
$284$	0.737567	−	1.61505i	0.0437666	−	0.0958354i
$285$	−9.08350	−	10.1798i	−0.538060	−	0.602999i
$286$	−23.2813	+	14.9620i	−1.37665	+	0.884721i
$287$	0.473037	+	0.354111i	0.0279225	+	0.0209025i
$288$	2.83999	−	0.966667i	0.167348	−	0.0569614i
$289$	9.13115	+	14.2083i	0.537126	+	0.835785i
$290$	−10.5384	−	6.34841i	−0.618837	−	0.372791i
$291$	−2.22453	−	1.98461i	−0.130405	−	0.116340i
$292$	2.21115	+	10.1645i	0.129398	+	0.594832i
$293$	0.701528	+	0.383063i	0.0409837	+	0.0223788i	0.499610	−	0.866250i	$-0.333477\pi$
$293$	0.701528	+	0.383063i	0.0409837	+	0.0223788i	−0.458627	+	0.888629i	$0.651658\pi$
$294$	−10.9937	+	4.82977i	−0.641167	+	0.281678i
$295$	−13.6227	+	10.8284i	−0.793142	+	0.630451i
$296$	−5.88636	+	2.68821i	−0.342138	+	0.156249i
$297$	25.5713	+	6.73642i	1.48380	+	0.390887i
$298$	6.39632	−	6.39632i	0.370529	−	0.370529i
$299$	−0.163583	+	26.0792i	−0.00946027	+	1.50820i
$300$	6.38459	+	5.85124i	0.368614	+	0.337822i
$301$	−0.288494	+	2.00652i	−0.0166285	+	0.115654i
$302$	−5.01313	−	1.86980i	−0.288473	−	0.107595i
$303$	−9.13563	+	1.84939i	−0.524828	+	0.106245i
$304$	2.66226	−	2.30686i	0.152691	−	0.132307i
$305$	−7.23143	+	21.2515i	−0.414071	+	1.21686i
$306$	0.387878	+	0.918761i	0.0221735	+	0.0525221i
$307$	−6.28126	+	2.34279i	−0.358491	+	0.133710i	−0.522255	−	0.852789i	$-0.674909\pi$
$307$	−6.28126	+	2.34279i	−0.358491	+	0.133710i	0.163764	+	0.986499i	$0.447636\pi$
$308$	−1.31650	+	0.0941581i	−0.0750147	+	0.00536515i
$309$	−1.59482	+	0.443335i	−0.0907264	+	0.0252204i
$310$	−4.72347	+	1.53710i	−0.268275	+	0.0873017i
$311$	19.0489	−	2.73882i	1.08016	−	0.155304i	0.420819	−	0.907144i	$-0.361743\pi$
$311$	19.0489	−	2.73882i	1.08016	−	0.155304i	0.659345	+	0.751840i	$0.270834\pi$
$312$	8.20063	+	4.63307i	0.464269	+	0.262296i
$313$	1.20231	+	16.8106i	0.0679589	+	0.950189i	0.911018	+	0.412367i	$0.135298\pi$
$313$	1.20231	+	16.8106i	0.0679589	+	0.950189i	−0.843059	+	0.537821i	$0.819247\pi$
$314$	6.09408	−	13.3442i	0.343909	−	0.753056i
$315$	1.46351	−	0.940725i	0.0824596	−	0.0530039i
$316$	−7.87443	+	2.31214i	−0.442971	+	0.130068i
$317$	24.4147	+	1.74617i	1.37127	+	0.0980749i	0.737446	−	0.675406i	$-0.236031\pi$
$317$	24.4147	+	1.74617i	1.37127	+	0.0980749i	0.633820	+	0.773481i	$0.281486\pi$
$318$	−1.62213	−	8.01301i	−0.0909647	−	0.449347i
$319$	25.4700	−	11.6317i	1.42604	−	0.651252i
$320$	−1.53461	+	1.62634i	−0.0857872	+	0.0909151i
$321$	−33.2936	−	10.3011i	−1.85827	−	0.574954i
$322$	−0.602928	+	1.08790i	−0.0335998	+	0.0606263i
$323$	0.828045	+	0.828045i	0.0460736	+	0.0460736i
$324$	−2.03210	−	8.76759i	−0.112895	−	0.487088i
$325$	−0.363714	+	27.1876i	−0.0201752	+	1.50810i
$326$	−4.41422	+	15.0334i	−0.244481	+	0.832626i
$327$	−22.0654	−	8.59546i	−1.22022	−	0.475330i
$328$	−1.09190	+	1.99967i	−0.0602903	+	0.110413i
$329$	2.57526	+	1.65502i	0.141979	+	0.0912441i
$330$	−19.1966	+	4.46943i	−1.05674	+	0.246034i
$331$	−1.88246	+	2.17247i	−0.103469	+	0.119410i	−0.805122	−	0.593109i	$-0.797900\pi$
$331$	−1.88246	+	2.17247i	−0.103469	+	0.119410i	0.701653	+	0.712519i	$0.252446\pi$
$332$	0.448095	−	2.05986i	0.0245924	−	0.113049i
$333$	6.25544	+	18.3780i	0.342796	+	1.00711i
$334$	9.72437	−	1.39815i	0.532094	−	0.0765035i
$335$	23.4772	−	21.5667i	1.28270	−	1.17832i
$336$	0.237371	+	0.381371i	0.0129496	+	0.0208055i
$337$	−4.82060	+	1.79799i	−0.262595	+	0.0979427i	−0.477313	−	0.878733i	$-0.658389\pi$
$337$	−4.82060	+	1.79799i	−0.262595	+	0.0979427i	0.214719	+	0.976676i	$0.431117\pi$
$338$	3.52260	+	16.1931i	0.191604	+	0.880791i
$339$	−0.307432	+	21.2571i	−0.0166974	+	1.15452i
$340$	−0.575655	−	0.470277i	−0.0312193	−	0.0255044i
$341$	3.18502	−	10.8472i	0.172478	−	0.587407i
$342$	−6.08587	−	8.63974i	−0.329086	−	0.467184i
$343$	−2.16547	−	2.89273i	−0.116925	−	0.156193i
$344$	−7.81624			−0.421424
$345$	−6.34674	+	17.4562i	−0.341697	+	0.939810i
$346$	−21.3918			−1.15003
$347$	6.43592	+	8.59739i	0.345498	+	0.461532i	0.939309	−	0.343073i	$-0.111468\pi$
$347$	6.43592	+	8.59739i	0.345498	+	0.461532i	−0.593810	+	0.804605i	$0.702377\pi$
$348$	−7.54558	−	5.82070i	−0.404485	−	0.312022i
$349$	−1.16820	+	3.97851i	−0.0625321	+	0.212965i	−0.984832	−	0.173510i	$-0.944489\pi$
$349$	−1.16820	+	3.97851i	−0.0625321	+	0.212965i	0.922300	+	0.386475i	$0.126307\pi$
$350$	−0.636638	+	1.12972i	−0.0340297	+	0.0603861i
$351$	16.2933	−	23.0861i	0.869673	−	1.23225i
$352$	−1.08177	−	4.97280i	−0.0576584	−	0.265051i
$353$	−19.5016	+	7.27374i	−1.03797	+	0.387142i	−0.809940	−	0.586513i	$-0.800500\pi$
$353$	−19.5016	+	7.27374i	−1.03797	+	0.387142i	−0.228028	+	0.973655i	$0.573228\pi$
$354$	−11.4439	+	7.12284i	−0.608237	+	0.378575i
$355$	3.96656	+	0.168237i	0.210523	+	0.00892911i
$356$	0.838075	−	0.120497i	0.0444179	−	0.00638633i
$357$	−0.120826	+	0.0877517i	−0.00639479	+	0.00464431i
$358$	−1.31610	+	6.05001i	−0.0695580	+	0.319753i
$359$	14.5768	−	16.8226i	0.769336	−	0.887861i	−0.226956	−	0.973905i	$-0.572877\pi$
$359$	14.5768	−	16.8226i	0.769336	−	0.887861i	0.996291	+	0.0860445i	$0.0274227\pi$
$360$	4.39339	+	5.06933i	0.231552	+	0.267177i
$361$	5.54452	+	3.56325i	0.291817	+	0.187539i
$362$	−2.75408	+	5.04372i	−0.144751	+	0.265092i
$363$	9.36690	−	24.0458i	0.491635	−	1.26208i
$364$	−0.397342	+	1.35322i	−0.0208264	+	0.0709281i
$365$	−19.1946	+	13.1377i	−1.00469	+	0.687656i
$366$	−7.45133	+	15.7108i	−0.389487	+	0.821219i
$367$	−16.7336	−	16.7336i	−0.873484	−	0.873484i	0.119366	−	0.992850i	$-0.461914\pi$
$367$	−16.7336	−	16.7336i	−0.873484	−	0.873484i	−0.992850	+	0.119366i	$0.961914\pi$
$368$	−4.48285	−	1.70412i	−0.233685	−	0.0888336i
$369$	5.64078	+	3.86007i	0.293647	+	0.200947i
$370$	−10.5243	−	9.93068i	−0.547131	−	0.516272i
$371$	1.11355	−	0.508542i	0.0578127	−	0.0264022i
$372$	−3.77114	+	0.763419i	−0.195524	+	0.0395814i
$373$	19.3077	+	1.38092i	0.999717	+	0.0715012i	0.561593	−	0.827414i	$-0.310189\pi$
$373$	19.3077	+	1.38092i	0.999717	+	0.0715012i	0.438124	+	0.898915i	$0.355643\pi$
$374$	1.62323	−	0.476623i	0.0839352	−	0.0246456i
$375$	−6.74606	+	18.1519i	−0.348365	+	0.937359i
$376$	−4.90329	+	10.7367i	−0.252868	+	0.553704i
$377$	−2.13446	−	29.8437i	−0.109930	−	1.53703i
$378$	1.20968	−	0.593943i	0.0622194	−	0.0305491i
$379$	−7.39403	+	1.06310i	−0.379806	+	0.0546078i	−0.329574	−	0.944130i	$-0.606905\pi$
$379$	−7.39403	+	1.06310i	−0.379806	+	0.0546078i	−0.0502318	+	0.998738i	$0.515996\pi$
$380$	7.02001	+	3.57288i	0.360119	+	0.183285i
$381$	4.92848	+	17.7294i	0.252493	+	0.908304i
$382$	−8.53606	+	0.610511i	−0.436743	+	0.0312365i
$383$	11.6889	−	4.35973i	0.597274	−	0.222772i	−0.0326008	−	0.999468i	$-0.510379\pi$
$383$	11.6889	−	4.35973i	0.597274	−	0.222772i	0.629875	+	0.776697i	$0.283106\pi$
$384$	−1.32526	+	1.11520i	−0.0676295	+	0.0569100i
$385$	−1.30337	−	2.64791i	−0.0664261	−	0.134950i
$386$	0.383794	−	0.332560i	0.0195346	−	0.0169268i
$387$	−2.34850	+	23.3308i	−0.119381	+	1.18597i
$388$	1.61265	+	0.601486i	0.0818697	+	0.0305358i
$389$	−3.97084	+	27.6178i	−0.201330	+	1.40028i	0.599015	+	0.800738i	$0.295559\pi$
$389$	−3.97084	+	27.6178i	−0.201330	+	1.40028i	−0.800345	+	0.599540i	$0.795350\pi$
$390$	−2.69371	+	20.8883i	−0.136401	+	1.05772i
$391$	0.458743	−	1.52684i	0.0231996	−	0.0772156i
$392$	4.90219	−	4.90219i	0.247598	−	0.247598i
$393$	7.36776	+	20.6615i	0.371654	+	1.04223i
$394$	4.96366	−	2.26683i	0.250065	−	0.114201i
$395$	−11.4189	−	14.3656i	−0.574548	−	0.722813i
$396$	−15.1684	+	1.73483i	−0.762242	+	0.0871787i
$397$	0.539889	+	0.294802i	0.0270963	+	0.0147957i	0.492740	−	0.870177i	$-0.335995\pi$
$397$	0.539889	+	0.294802i	0.0270963	+	0.0147957i	−0.465644	+	0.884972i	$0.654177\pi$
$398$	4.52167	+	20.7858i	0.226651	+	1.04190i
$399$	1.05345	−	1.18080i	0.0527384	−	0.0591139i
$400$	−4.66096	−	1.80983i	−0.233048	−	0.0904916i
$401$	11.4363	+	17.7952i	0.571102	+	0.888652i	0.999891	−	0.0147527i	$-0.00469609\pi$
$401$	11.4363	+	17.7952i	0.571102	+	0.888652i	−0.428789	+	0.903405i	$0.641060\pi$
$402$	19.9803	−	14.5110i	0.996528	−	0.723743i
$403$	−9.67066	−	7.23937i	−0.481730	−	0.360619i
$404$	4.52716	−	2.90943i	0.225235	−	0.144750i
$405$	16.4516	−	11.5907i	0.817486	−	0.575948i
$406$	0.592777	−	1.29800i	0.0294190	−	0.0644187i
$407$	32.1797	−	7.00027i	1.59509	−	0.346991i
$408$	−0.401208	−	0.412984i	−0.0198628	−	0.0204457i
$409$	12.6645	−	10.9738i	0.626218	−	0.542621i	−0.282905	−	0.959148i	$-0.591298\pi$
$409$	12.6645	−	10.9738i	0.626218	−	0.542621i	0.909123	+	0.416527i	$0.136753\pi$
$410$	−5.06163	−	0.578453i	−0.249976	−	0.0285678i
$411$	3.16386	+	24.5170i	0.156062	+	1.20934i
$412$	0.765066	−	0.572721i	0.0376921	−	0.0282160i
$413$	−1.42721	−	1.42721i	−0.0702284	−	0.0702284i
$414$	−6.43360	+	12.8689i	−0.316194	+	0.632472i
$415$	4.64430	−	0.805888i	0.227980	−	0.0395595i
$416$	−5.38265	−	0.773908i	−0.263906	−	0.0379440i
$417$	−29.5467	−	22.7924i	−1.44691	−	1.11615i
$418$	−15.7344	+	8.59161i	−0.769593	+	0.420229i
$419$	3.62971	+	4.18891i	0.177323	+	0.204642i	0.837452	−	0.546510i	$-0.184044\pi$
$419$	3.62971	+	4.18891i	0.177323	+	0.204642i	−0.660129	+	0.751152i	$0.729499\pi$
$420$	−0.590189	+	0.812787i	−0.0287983	+	0.0396599i
$421$	−19.9890	−	12.8461i	−0.974202	−	0.626082i	−0.0463085	−	0.998927i	$-0.514746\pi$
$421$	−19.9890	−	12.8461i	−0.974202	−	0.626082i	−0.927893	+	0.372846i	$0.878382\pi$
$422$	2.55972	+	6.86288i	0.124605	+	0.334080i
$423$	30.5749	+	17.8619i	1.48660	+	0.868476i
$424$	2.55191	+	3.97085i	0.123932	+	0.192842i
$425$	0.489569	−	1.58840i	0.0237476	−	0.0770488i
$426$	3.03730	+	0.481626i	0.147158	+	0.0233349i
$427$	−2.54416	−	0.553448i	−0.123120	−	0.0267832i
$428$	20.0699	−	1.43542i	0.970113	−	0.0693839i
$429$	−35.7682	−	31.9105i	−1.72690	−	1.54065i
$430$	−6.58026	−	16.1916i	−0.317328	−	0.780829i
$431$	2.09576	+	7.13752i	0.100949	+	0.343802i	0.994443	−	0.105273i	$-0.0335717\pi$
$431$	2.09576	+	7.13752i	0.100949	+	0.343802i	−0.893494	+	0.449075i	$0.851754\pi$
$432$	2.93060	+	4.29087i	0.140998	+	0.206445i
$433$	−27.3379	+	14.9276i	−1.31377	+	0.717375i	−0.974728	−	0.223395i	$-0.928286\pi$
$433$	−27.3379	+	14.9276i	−1.31377	+	0.717375i	−0.339046	+	0.940770i	$0.610104\pi$
$434$	−0.239334	−	0.524067i	−0.0114884	−	0.0251560i
$435$	5.70538	−	20.5312i	0.273552	−	0.984395i
$436$	13.6719			0.654766
$437$	−1.31089	+	16.8432i	−0.0627083	+	0.805720i
$438$	−15.9365	+	8.40513i	−0.761476	+	0.401613i
$439$	−24.2154	−	3.48165i	−1.15574	−	0.166170i	−0.462325	−	0.886711i	$-0.652985\pi$
$439$	−24.2154	−	3.48165i	−1.15574	−	0.166170i	−0.693413	+	0.720541i	$0.743894\pi$
$440$	9.39062	−	6.42737i	0.447680	−	0.306413i
$441$	−13.1597	−	16.1055i	−0.626651	−	0.766931i
$442$	0.128963	−	1.80313i	0.00613413	−	0.0857664i
$443$	11.8469	+	6.46891i	0.562864	+	0.307347i	0.735375	−	0.677660i	$-0.237006\pi$
$443$	11.8469	+	6.46891i	0.562864	+	0.307347i	−0.172510	+	0.985008i	$0.555188\pi$
$444$	−7.21665	−	8.57597i	−0.342487	−	0.406997i
$445$	0.955164	+	1.63466i	0.0452791	+	0.0774903i
$446$	−15.8811	−	13.7611i	−0.751993	−	0.651606i
$447$	13.6412	+	7.70681i	0.645207	+	0.364520i
$448$	−0.207621	−	0.155423i	−0.00980918	−	0.00734306i
$449$	−0.587605	−	4.08689i	−0.0277308	−	0.192872i	0.971247	−	0.238074i	$-0.0765160\pi$
$449$	−0.587605	−	4.08689i	−0.0277308	−	0.192872i	−0.998978	+	0.0452018i	$0.985607\pi$
$450$	−6.80264	+	13.3688i	−0.320680	+	0.630210i
$451$	7.59300	−	8.76279i	0.357541	−	0.412624i
$452$	−4.28934	−	11.5002i	−0.201754	−	0.540922i
$453$	0.794727	−	9.23317i	0.0373395	−	0.433812i
$454$	−0.917545	−	3.12487i	−0.0430625	−	0.146657i
$455$	−3.13776	+	0.316129i	−0.147100	+	0.0148204i
$456$	5.08462	+	3.37257i	0.238109	+	0.157935i
$457$	−5.39146	+	14.4551i	−0.252202	+	0.676179i	0.747724	+	0.664009i	$0.231147\pi$
$457$	−5.39146	+	14.4551i	−0.252202	+	0.676179i	−0.999926	+	0.0121696i	$0.996126\pi$
$458$	18.5308	−	13.8720i	0.865887	−	0.648195i
$459$	−1.35327	+	1.07349i	−0.0631653	+	0.0501061i
$460$	−0.243826	−	10.7210i	−0.0113685	−	0.499871i
$461$		−	29.7294i		−	1.38464i	−0.721592	−	0.692319i	$-0.756589\pi$
$461$		−	29.7294i		−	1.38464i	0.721592	−	0.692319i	$-0.243411\pi$
$462$	−0.767842	−	2.15326i	−0.0357233	−	0.100179i
$463$	17.2191	+	6.42241i	0.800241	+	0.298475i	0.716117	−	0.697981i	$-0.245918\pi$
$463$	17.2191	+	6.42241i	0.800241	+	0.298475i	0.0841247	+	0.996455i	$0.473191\pi$
$464$	5.27914	+	1.55009i	0.245078	+	0.0719613i
$465$	−4.75625	−	7.16935i	−0.220566	−	0.332470i
$466$	13.9313	−	4.09059i	0.645353	−	0.189493i
$467$	25.2076	−	5.48357i	1.16647	−	0.253750i	0.412686	−	0.910874i	$-0.364591\pi$
$467$	25.2076	−	5.48357i	1.16647	−	0.253750i	0.753783	+	0.657124i	$0.228227\pi$
$468$	−3.92735	+	15.8342i	−0.181542	+	0.731937i
$469$	2.79443	+	2.42139i	0.129035	+	0.111809i
$470$	−26.3694	−	1.11843i	−1.21633	−	0.0515893i
$471$	25.0954	+	3.97939i	1.15634	+	0.183361i
$472$	4.66383	−	6.23015i	0.214670	−	0.286766i
$473$	38.8686	+	8.45535i	1.78718	+	0.388777i
$474$	−7.51132	−	12.0681i	−0.345006	−	0.554304i
$475$	−1.49142	+	17.5501i	−0.0684310	+	0.805254i
$476$	0.0466116	−	0.0725290i	0.00213644	−	0.00332436i
$477$	12.6194	−	6.42414i	0.577803	−	0.294141i
$478$	−7.49027	−	0.535715i	−0.342597	−	0.0245030i
$479$	−13.4236	−	3.94153i	−0.613340	−	0.180093i	−0.0397152	−	0.999211i	$-0.512645\pi$
$479$	−13.4236	−	3.94153i	−0.613340	−	0.180093i	−0.573625	+	0.819118i	$0.694463\pi$
$480$	−3.42588	−	1.80647i	−0.156369	−	0.0824537i
$481$	5.00808	−	34.8319i	0.228349	−	1.58820i
$482$	−5.65420	+	5.65420i	−0.257542	+	0.257542i
$483$	−2.09515	−	0.501482i	−0.0953327	−	0.0228182i
$484$			14.8990i			0.677226i
$485$	0.111639	+	3.84703i	0.00506925	+	0.174684i
$486$	13.6884	−	7.45833i	0.620920	−	0.338317i
$487$	9.33750	+	17.1004i	0.423123	+	0.774891i	0.999093	−	0.0425792i	$-0.0135575\pi$
$487$	9.33750	+	17.1004i	0.423123	+	0.774891i	−0.575970	+	0.817471i	$0.695376\pi$
$488$	0.716184	−	10.0136i	0.0324201	−	0.453292i
$489$	−27.1351	−	0.392444i	−1.22709	−	0.0177469i
$490$	14.2820	+	6.02805i	0.645197	+	0.272319i
$491$	−5.52979	−	2.52537i	−0.249556	−	0.113968i	0.286710	−	0.958017i	$-0.407438\pi$
$491$	−5.52979	−	2.52537i	−0.249556	−	0.113968i	−0.536266	+	0.844049i	$0.680166\pi$
$492$	−3.84353	−	0.894509i	−0.173280	−	0.0403276i
$493$	−0.388786	+	1.78722i	−0.0175100	+	0.0804923i
$494$	2.72622	+	18.9613i	0.122659	+	0.853110i
$495$	−16.3636	−	29.9614i	−0.735489	−	1.34667i
$496$	1.86879	−	1.20100i	0.0839111	−	0.0539264i
$497$	0.0328500	+	0.459303i	0.00147352	+	0.0206026i
$498$	3.64530	−	0.207782i	0.163350	−	0.00931093i
$499$	−12.4908	+	19.4361i	−0.559167	+	0.870081i	−0.999616	−	0.0276965i	$-0.991183\pi$
$499$	−12.4908	+	19.4361i	−0.559167	+	0.870081i	0.440449	+	0.897778i	$0.354819\pi$
$500$	−0.174788	−	11.1790i	−0.00781677	−	0.499939i
$501$	6.84425	+	15.5792i	0.305779	+	0.696026i
$502$	7.34895	+	13.4586i	0.328000	+	0.600686i
$503$	−7.11578	+	19.0782i	−0.317277	+	0.850653i	0.676210	+	0.736709i	$0.263621\pi$
$503$	−7.11578	+	19.0782i	−0.317277	+	0.850653i	−0.993487	+	0.113944i	$0.963652\pi$
$504$	−0.526308	+	0.573033i	−0.0234436	+	0.0255249i
$505$	9.83827	+	6.92882i	0.437797	+	0.308328i
$506$	20.4489	+	13.3237i	0.909063	+	0.592309i
$507$	−25.3886	+	13.3903i	−1.12755	+	0.594684i
$508$	−6.36685	−	8.50511i	−0.282483	−	0.377353i
$509$	−1.71876	−	3.76356i	−0.0761827	−	0.166817i	0.867709	−	0.497073i	$-0.165592\pi$
$509$	−1.71876	−	3.76356i	−0.0761827	−	0.166817i	−0.943891	+	0.330257i	$0.892865\pi$
$510$	0.517745	−	1.17880i	0.0229261	−	0.0521979i
$511$	−1.76670	−	2.03888i	−0.0781543	−	0.0901948i
$512$	0.479249	−	0.877679i	0.0211800	−	0.0387883i
$513$	11.5946	−	14.1638i	0.511914	−	0.625349i
$514$	8.11074	+	3.70405i	0.357749	+	0.163379i
$515$	1.83050	+	1.10270i	0.0806614	+	0.0485910i
$516$	−3.62589	−	13.0435i	−0.159621	−	0.574210i
$517$	35.9977	−	48.0873i	1.58318	−	2.11488i
$518$	1.00577	−	1.34355i	0.0441909	−	0.0590321i
$519$	−9.92348	−	35.6981i	−0.435592	−	1.56697i
$520$	−2.92831	−	11.8019i	−0.128415	−	0.517547i
$521$	7.93016	+	3.62158i	0.347426	+	0.158664i	0.581483	−	0.813559i	$-0.302473\pi$
$521$	7.93016	+	3.62158i	0.347426	+	0.158664i	−0.234056	+	0.972223i	$0.575200\pi$
$522$	6.21309	−	15.2920i	0.271940	−	0.669314i
$523$	−2.17186	+	3.97746i	−0.0949687	+	0.173922i	−0.920845	−	0.389930i	$-0.872499\pi$
$523$	−2.17186	+	3.97746i	−0.0949687	+	0.173922i	0.825876	+	0.563852i	$0.190681\pi$
$524$	−8.29358	−	9.57130i	−0.362307	−	0.418124i
$525$	−2.18058	−	0.538337i	−0.0951682	−	0.0234949i
$526$	−6.58332	−	14.4155i	−0.287046	−	0.628544i
$527$	0.442546	+	0.591172i	0.0192776	+	0.0257518i
$528$	7.79666	−	4.11206i	0.339306	−	0.178955i
$529$	21.0397	−	9.29134i	0.914772	−	0.403971i
$530$	−6.07738	+	8.62931i	−0.263984	+	0.374833i
$531$	−17.1951	−	15.7931i	−0.746206	−	0.685361i
$532$	−0.319274	+	0.856005i	−0.0138423	+	0.0371125i
$533$	−5.93778	−	10.8742i	−0.257194	−	0.471015i
$534$	0.589858	+	1.34266i	0.0255257	+	0.0581026i
$535$	19.8697	+	40.3670i	0.859044	+	1.74522i
$536$	−7.70789	+	11.9937i	−0.332930	+	0.518050i
$537$	−10.7066	+	0.610276i	−0.462025	+	0.0263354i
$538$	−2.24516	−	31.3914i	−0.0967958	−	1.35338i
$539$	−29.6806	+	19.0746i	−1.27843	+	0.821600i
$540$	−6.42152	+	9.68319i	−0.276338	+	0.416698i
$541$	4.60088	+	31.9998i	0.197807	+	1.37578i	0.810629	+	0.585560i	$0.199125\pi$
$541$	4.60088	+	31.9998i	0.197807	+	1.37578i	−0.612822	+	0.790221i	$0.709966\pi$
$542$	−0.128718	+	0.591706i	−0.00552890	+	0.0254160i
$543$	−9.69441	−	2.25620i	−0.416027	−	0.0968226i
$544$	0.302387	+	0.138095i	0.0129647	+	0.00592079i
$545$	11.5100	+	28.3218i	0.493033	+	1.21317i
$546$	−2.44255	−	0.0353255i	−0.104531	−	0.00151179i
$547$	−1.49237	+	20.8661i	−0.0638093	+	0.892170i	0.860238	+	0.509892i	$0.170315\pi$
$547$	−1.49237	+	20.8661i	−0.0638093	+	0.892170i	−0.924048	+	0.382278i	$0.875140\pi$
$548$	−6.83998	−	12.5265i	−0.292189	−	0.535105i
$549$	−29.6744	−	5.14646i	−1.26647	−	0.219646i
$550$	21.2202	+	14.0420i	0.904832	+	0.598753i
$551$		−	19.3818i		−	0.825691i
$552$	0.764239	−	8.27139i	0.0325282	−	0.352054i
$553$	1.50505	−	1.50505i	0.0640011	−	0.0640011i
$554$	2.02869	−	14.1099i	0.0861909	−	0.599471i
$555$	11.6899	−	22.1694i	0.496210	−	0.941038i
$556$	20.6718	+	6.06979i	0.876680	+	0.257417i
$557$	30.3347	+	2.16958i	1.28532	+	0.0919280i	0.697219	−	0.716858i	$-0.254421\pi$
$557$	30.3347	+	2.16958i	1.28532	+	0.0919280i	0.588103	+	0.808786i	$0.299875\pi$
$558$	−3.02337	−	5.93903i	−0.127990	−	0.251419i
$559$	22.9798	−	35.7573i	0.971942	−	1.51237i
$560$	0.147175	−	0.560941i	0.00621927	−	0.0237041i
$561$	1.54838	+	2.48770i	0.0653726	+	0.105031i
$562$	−15.2494	−	3.31731i	−0.643258	−	0.139932i
$563$	−26.7218	+	35.6961i	−1.12619	+	1.50441i	−0.289137	+	0.957288i	$0.593368\pi$
$563$	−26.7218	+	35.6961i	−1.12619	+	1.50441i	−0.837051	+	0.547124i	$0.815723\pi$
$564$	−20.1917	−	3.20182i	−0.850225	−	0.134821i
$565$	20.2119	−	18.5672i	0.850322	−	0.781126i
$566$	2.03022	+	1.75920i	0.0853366	+	0.0739446i
$567$	1.55232	+	1.74316i	0.0651912	+	0.0732059i
$568$	−1.73492	+	0.377409i	−0.0727956	+	0.0158357i
$569$	−11.4512	+	3.36238i	−0.480060	+	0.140958i	−0.512804	−	0.858506i	$-0.671393\pi$
$569$	−11.4512	+	3.36238i	−0.480060	+	0.140958i	0.0327447	+	0.999464i	$0.489575\pi$
$570$	−2.70581	+	13.3722i	−0.113334	+	0.560101i
$571$	12.8967	+	3.78680i	0.539708	+	0.158473i	0.540215	−	0.841527i	$-0.318343\pi$
$571$	12.8967	+	3.78680i	0.539708	+	0.158473i	−0.000506545		1.00000i	$0.500161\pi$
$572$	25.9297	+	9.67127i	1.08417	+	0.404376i
$573$	−4.97861	−	13.9615i	−0.207985	−	0.583252i
$574$		−	0.590896i		−	0.0246635i
$575$	22.0037	−	9.53080i	0.917619	−	0.397462i
$576$	−2.47580	−	1.69423i	−0.103158	−	0.0705929i
$577$	4.49871	−	3.36770i	0.187284	−	0.140199i	−0.501522	−	0.865145i	$-0.667226\pi$
$577$	4.49871	−	3.36770i	0.187284	−	0.140199i	0.688806	+	0.724946i	$0.258135\pi$
$578$	5.90227	−	15.8246i	0.245502	−	0.658217i
$579$	0.733005	+	0.486194i	0.0304627	+	0.0202055i
$580$	1.23327	+	12.2409i	0.0512087	+	0.508275i
$581$	0.154029	+	0.524575i	0.00639020	+	0.0217630i
$582$	−0.255651	+	2.97017i	−0.0105971	+	0.123117i
$583$	−8.39461	−	22.5068i	−0.347669	−	0.932137i
$584$	6.81201	−	7.86148i	0.281883	−	0.325310i
$585$	−36.1075	+	5.19472i	−1.49286	+	0.214775i
$586$	−0.113752	−	0.791163i	−0.00469906	−	0.0326826i
$587$	−32.9178	−	24.6420i	−1.35866	−	1.01708i	−0.996380	−	0.0850151i	$-0.972906\pi$
$587$	−32.9178	−	24.6420i	−1.35866	−	1.01708i	−0.362284	−	0.932068i	$-0.618003\pi$
$588$	10.4547	+	5.90656i	0.431145	+	0.243582i
$589$	−5.91403	−	5.12453i	−0.243683	−	0.211153i
$590$	16.8323	+	4.41631i	0.692975	+	0.181817i
$591$	6.08542	+	7.23166i	0.250321	+	0.297471i
$592$	5.67959	+	3.10129i	0.233430	+	0.127462i
$593$	−2.41446	+	33.7586i	−0.0991500	+	1.38630i	0.667680	+	0.744448i	$0.267287\pi$
$593$	−2.41446	+	33.7586i	−0.0991500	+	1.38630i	−0.766830	+	0.641850i	$0.778167\pi$
$594$	−9.93155	−	24.5079i	−0.407496	−	1.00557i
$595$	0.189487	+	0.0354975i	0.00776822	+	0.00145526i
$596$	−8.95369	−	1.28735i	−0.366757	−	0.0527318i
$597$	−32.5892	+	17.1880i	−1.33379	+	0.703457i
$598$	20.9755	−	15.4977i	0.857753	−	0.633750i
$599$	−29.0230			−1.18585			−0.592924	−	0.805259i	$-0.702026\pi$
$599$	−29.0230			−1.18585			−0.592924	+	0.805259i	$0.702026\pi$
$600$	0.858021	−	8.61764i	0.0350286	−	0.351814i
$601$	−16.8624	−	36.9235i	−0.687832	−	1.50614i	−0.854126	−	0.520066i	$-0.825907\pi$
$601$	−16.8624	−	36.9235i	−0.687832	−	1.50614i	0.166294	−	0.986076i	$-0.446820\pi$
$602$	1.77919	−	0.971510i	0.0725143	−	0.0395958i
$603$	33.4843	+	26.6111i	1.36359	+	1.08369i
$604$	1.50741	+	5.13375i	0.0613355	+	0.208889i
$605$	−30.8637	+	12.5430i	−1.25479	+	0.509945i
$606$	6.95529	+	6.20515i	0.282540	+	0.252067i
$607$	−34.1448	+	2.44208i	−1.38589	+	0.0991210i	−0.744260	−	0.667890i	$-0.767198\pi$
$607$	−34.1448	+	2.44208i	−1.38589	+	0.0991210i	−0.641634	+	0.767011i	$0.721743\pi$
$608$	−3.44217	−	0.748798i	−0.139598	−	0.0303678i
$609$	2.44105	+	0.387079i	0.0989165	+	0.0156852i
$610$	21.3464	−	6.94651i	0.864289	−	0.281256i
$611$	−34.7019	−	53.9973i	−1.40389	−	2.18450i
$612$	0.503059	−	0.861106i	0.0203350	−	0.0348081i
$613$	7.79807	+	20.9074i	0.314961	+	0.844443i	0.993904	+	0.110252i	$0.0351657\pi$
$613$	7.79807	+	20.9074i	0.314961	+	0.844443i	−0.678943	+	0.734191i	$0.737562\pi$
$614$	5.63972	+	3.62443i	0.227601	+	0.146270i
$615$	−1.38274	−	8.71506i	−0.0557575	−	0.351425i
$616$	0.864328	+	0.997487i	0.0348248	+	0.0401899i
$617$	−30.4952	+	16.6516i	−1.22769	+	0.670370i	−0.956381	−	0.292122i	$-0.905639\pi$
$617$	−30.4952	+	16.6516i	−1.22769	+	0.670370i	−0.271310	+	0.962492i	$0.587457\pi$
$618$	1.31065	+	1.01104i	0.0527221	+	0.0406701i
$619$	0.716458	+	0.103011i	0.0287969	+	0.00414037i	0.156698	−	0.987647i	$-0.449915\pi$
$619$	0.716458	+	0.103011i	0.0287969	+	0.00414037i	−0.127901	+	0.991787i	$0.540824\pi$
$620$	4.06118	+	2.86018i	0.163101	+	0.114867i
$621$	−24.4598	−	4.76645i	−0.981537	−	0.191271i
$622$	−13.6081	−	13.6081i	−0.545636	−	0.545636i
$623$	−0.175792	+	0.131596i	−0.00704294	+	0.00527228i
$624$	−1.20549	−	9.34143i	−0.0482581	−	0.373957i
$625$	23.0105	−	9.77332i	0.920419	−	0.390933i
$626$	12.7370	−	11.0367i	0.509074	−	0.441115i
$627$	−21.6365	−	22.2715i	−0.864078	−	0.889438i
$628$	−14.3346	+	3.11831i	−0.572013	+	0.124434i
$629$	−0.893635	+	1.95679i	−0.0356316	+	0.0780223i
$630$	−1.63014	−	0.607847i	−0.0649463	−	0.0242172i
$631$	−11.1538	+	7.16810i	−0.444025	+	0.285358i	−0.743487	−	0.668751i	$-0.766829\pi$
$631$	−11.1538	+	7.16810i	−0.444025	+	0.285358i	0.299461	+	0.954108i	$0.403193\pi$
$632$	6.56993	+	4.91819i	0.261338	+	0.195635i
$633$	−10.2652	+	7.45522i	−0.408003	+	0.296319i
$634$	−13.2333	−	20.5914i	−0.525562	−	0.817790i
$635$	12.2586	−	20.3493i	0.486467	−	0.807539i
$636$	−5.44264	+	6.10060i	−0.215815	+	0.241905i
$637$	8.01376	+	36.8387i	0.317517	+	1.45960i
$638$	−24.5753	−	13.4191i	−0.972944	−	0.531268i
$639$	0.605252	+	5.29199i	0.0239434	+	0.209348i
$640$	2.22161	+	0.253890i	0.0878167	+	0.0100359i
$641$	35.7555	−	16.3290i	1.41226	−	0.644957i	0.444257	−	0.895900i	$-0.353468\pi$
$641$	35.7555	−	16.3290i	1.41226	−	0.644957i	0.968002	+	0.250943i	$0.0807406\pi$
$642$	11.7056	+	32.8262i	0.461985	+	1.29555i
$643$	−15.1100	+	15.1100i	−0.595880	+	0.595880i	−0.939213	−	0.343334i	$-0.888444\pi$
$643$	−15.1100	+	15.1100i	−0.595880	+	0.595880i	0.343334	+	0.939213i	$0.388444\pi$
$644$	1.23223	−	0.169286i	0.0485567	−	0.00667081i
$645$	23.9676	−	18.4921i	0.943724	−	0.728126i
$646$	0.166655	−	1.15911i	0.00655696	−	0.0456047i
$647$	−20.7927	−	7.75528i	−0.817446	−	0.304892i	−0.0942625	−	0.995547i	$-0.530049\pi$
$647$	−20.7927	−	7.75528i	−0.817446	−	0.304892i	−0.723184	+	0.690656i	$0.757322\pi$
$648$	−5.80102	+	6.88100i	−0.227886	+	0.270311i
$649$	−29.9319	+	25.9361i	−1.17493	+	1.01808i
$650$	21.9827	−	16.0017i	0.862234	−	0.627640i
$651$	0.763525	−	0.642504i	0.0299249	−	0.0251817i
$652$	14.6802	−	5.47545i	0.574922	−	0.214435i
$653$	44.5741	−	3.18800i	1.74432	−	0.124756i	0.837544	−	0.546370i	$-0.183991\pi$
$653$	44.5741	−	3.18800i	1.74432	−	0.124756i	0.906775	+	0.421614i	$0.138536\pi$
$654$	6.34228	+	22.8153i	0.248003	+	0.892150i
$655$	12.8452	−	25.2382i	0.501902	−	0.986139i
$656$	2.25517	−	0.324245i	0.0880498	−	0.0126596i
$657$	−21.4191	−	22.6954i	−0.835638	−	0.885430i
$658$	−0.218385	−	3.05341i	−0.00851351	−	0.119034i
$659$	17.7244	−	38.8109i	0.690443	−	1.51186i	−0.160744	−	0.986996i	$-0.551389\pi$
$659$	17.7244	−	38.8109i	0.690443	−	1.51186i	0.851187	−	0.524863i	$-0.175883\pi$
$660$	15.0821	+	12.6892i	0.587068	+	0.493927i
$661$	5.04596	−	1.48163i	0.196265	−	0.0576286i	−0.182123	−	0.983276i	$-0.558297\pi$
$661$	5.04596	−	1.48163i	0.196265	−	0.0576286i	0.378388	+	0.925647i	$0.376479\pi$
$662$	2.86726	+	0.205071i	0.111439	+	0.00797030i
$663$	3.06885	−	0.621249i	0.119184	−	0.0241273i
$664$	−1.91753	+	0.875709i	−0.0744148	+	0.0339841i
$665$	−2.04203	+	0.0592587i	−0.0791866	+	0.00229795i
$666$	10.9636	−	16.0213i	0.424831	−	0.620812i
$667$	−23.2379	+	12.5003i	−0.899776	+	0.484013i
$668$	−6.94687	−	6.94687i	−0.268783	−	0.268783i
$669$	15.5970	−	32.8856i	0.603015	−	1.27143i
$670$	−31.3344	−	5.87002i	−1.21055	−	0.226779i
$671$	−14.3938	+	49.0207i	−0.555665	+	1.89242i
$672$	0.163053	−	0.418572i	0.00628989	−	0.0161468i
$673$	14.3303	−	26.2439i	0.552391	−	1.01163i	−0.441071	−	0.897472i	$-0.645401\pi$
$673$	14.3303	−	26.2439i	0.552391	−	1.01163i	0.993463	−	0.114157i	$-0.0364167\pi$
$674$	4.32824	+	2.78159i	0.166718	+	0.107143i
$675$	−25.4651	−	5.15041i	−0.980154	−	0.198240i
$676$	10.8523	−	12.5242i	0.417395	−	0.481699i
$677$	3.11910	−	14.3383i	0.119877	−	0.551064i	−0.877557	−	0.479472i	$-0.840828\pi$
$677$	3.11910	−	14.3383i	0.119877	−	0.551064i	0.997434	−	0.0715924i	$-0.0228081\pi$
$678$	17.2014	−	12.4928i	0.660615	−	0.479782i
$679$	−0.441843	+	0.0635274i	−0.0169564	+	0.00243796i
$680$	−0.0314992	+	0.742662i	−0.00120794	+	0.0284798i
$681$	4.78906	−	2.98078i	0.183517	−	0.114224i
$682$	−10.5923	+	3.95073i	−0.405601	+	0.151281i
$683$	−0.575664	−	2.64629i	−0.0220272	−	0.101257i	0.964821	−	0.262908i	$-0.0846817\pi$
$683$	−0.575664	−	2.64629i	−0.0220272	−	0.101257i	−0.986848	+	0.161651i	$0.948318\pi$
$684$	−3.26935	+	10.0496i	−0.125007	+	0.384256i
$685$	20.1907	−	24.7149i	0.771446	−	0.944308i
$686$	−1.01803	+	3.46710i	−0.0388687	+	0.132374i
$687$	31.7455	+	24.4886i	1.21117	+	0.934299i
$688$	4.68410	+	6.25722i	0.178580	+	0.238554i
$689$	−25.6682			−0.977882
$690$	17.7779	−	5.38029i	0.676792	−	0.204824i
$691$	24.8095			0.943797			0.471898	−	0.881653i	$-0.343569\pi$
$691$	24.8095			0.943797			0.471898	+	0.881653i	$0.343569\pi$
$692$	12.8196	+	17.1250i	0.487330	+	0.650996i
$693$	3.23711	−	2.28024i	0.122968	−	0.0866190i
$694$	3.02566	−	10.3044i	0.114852	−	0.391151i
$695$	4.82919	+	47.9324i	0.183181	+	1.81818i
$696$	−0.137810	+	9.52876i	−0.00522369	+	0.361187i
$697$	0.160995	+	0.740082i	0.00609812	+	0.0280326i
$698$	3.88503	−	1.44904i	0.147051	−	0.0548471i
$699$	13.2889	+	21.3505i	0.502631	+	0.807551i
$700$	1.28591	−	0.167361i	0.0486028	−	0.00632566i
$701$	−7.37368	+	1.06017i	−0.278500	+	0.0400422i	−0.280149	−	0.959956i	$-0.590384\pi$
$701$	−7.37368	+	1.06017i	−0.278500	+	0.0400422i	0.00164953	+	0.999999i	$0.499475\pi$
$702$	−28.2456	+	0.791512i	−1.06606	+	0.0298737i
$703$	4.84558	−	22.2748i	0.182755	−	0.840109i
$704$	−3.33265	+	3.84609i	−0.125604	+	0.144955i
$705$	−10.3661	−	44.5234i	−0.390411	−	1.67685i
$706$	17.5098	+	11.2529i	0.658991	+	0.423508i
$707$	−0.668881	+	1.22496i	−0.0251558	+	0.0460695i
$708$	12.5602	+	4.89276i	0.472042	+	0.183881i
$709$	−2.22498	+	7.57758i	−0.0835608	+	0.284582i	−0.990664	−	0.136326i	$-0.956470\pi$
$709$	−2.22498	+	7.57758i	−0.0835608	+	0.284582i	0.907103	+	0.420908i	$0.138289\pi$
$710$	−2.24239	−	3.27622i	−0.0841554	−	0.122954i
$711$	16.6544	−	18.1330i	0.624589	−	0.680039i
$712$	−0.598703	−	0.598703i	−0.0224373	−	0.0224373i
$713$	−2.32984	+	10.3957i	−0.0872533	+	0.389324i
$714$	0.142657	+	0.0441386i	0.00533881	+	0.00165184i
$715$	1.79503	+	61.8562i	0.0671304	+	2.31329i
$716$	5.63199	−	2.57204i	0.210477	−	0.0961218i
$717$	−2.58068	−	12.7481i	−0.0963774	−	0.476086i
$718$	−22.2027	−	1.58797i	−0.828598	−	0.0592625i
$719$	−49.7272	+	14.6012i	−1.85451	+	0.544533i	−0.854839	+	0.518893i	$0.826344\pi$
$719$	−49.7272	+	14.6012i	−1.85451	+	0.544533i	−0.999671	+	0.0256402i	$0.991838\pi$
$720$	1.42535	−	6.55503i	0.0531198	−	0.244291i
$721$	−0.102964	+	0.225460i	−0.00383458	+	0.00839656i
$722$	−0.470181	−	6.57400i	−0.0174983	−	0.244659i
$723$	−12.0585	−	6.81264i	−0.448461	−	0.253365i
$724$	5.68816	−	0.817834i	0.211399	−	0.0303946i
$725$	−24.3192	+	12.8600i	−0.903192	+	0.477608i
$726$	−24.8630	+	6.91151i	−0.922753	+	0.256510i
$727$	−43.0743	+	3.08073i	−1.59754	+	0.114258i	−0.841495	−	0.540265i	$-0.818324\pi$
$727$	−43.0743	+	3.08073i	−1.59754	+	0.114258i	−0.756042	+	0.654523i	$0.772869\pi$
$728$	1.32143	−	0.492867i	0.0489754	−	0.0182669i
$729$	18.7962	+	19.3830i	0.696156	+	0.717891i
$730$	22.0201	+	7.49297i	0.815002	+	0.277327i
$731$	−1.96369	+	1.70155i	−0.0726297	+	0.0629340i
$732$	17.0426	−	3.45005i	0.629912	−	0.127518i
$733$	−11.2192	−	4.18456i	−0.414392	−	0.154560i	0.133616	−	0.991033i	$-0.457341\pi$
$733$	−11.2192	−	4.18456i	−0.414392	−	0.154560i	−0.548008	+	0.836473i	$0.684614\pi$
$734$	−3.36785	+	23.4239i	−0.124310	+	0.864593i
$735$	−3.43413	+	26.6299i	−0.126670	+	0.982257i
$736$	1.32225	+	4.60995i	0.0487389	+	0.169925i
$737$	51.3042	−	51.3042i	1.88982	−	1.88982i
$738$	−0.290245	−	6.82893i	−0.0106841	−	0.251376i
$739$	30.4957	−	13.9269i	1.12180	−	0.512311i	0.233864	−	0.972269i	$-0.424863\pi$
$739$	30.4957	−	13.9269i	1.12180	−	0.512311i	0.887940	+	0.459959i	$0.152136\pi$
$740$	−1.64296	+	14.3764i	−0.0603963	+	0.528485i
$741$	−30.3775	+	13.3454i	−1.11594	+	0.490257i
$742$	−1.07444	−	0.586686i	−0.0394438	−	0.0215379i
$743$	2.76747	+	12.7219i	0.101529	+	0.466720i	0.999637	+	0.0269453i	$0.00857799\pi$
$743$	2.76747	+	12.7219i	0.101529	+	0.466720i	−0.898108	+	0.439774i	$0.855058\pi$
$744$	2.87111	+	2.56145i	0.105260	+	0.0939074i
$745$	−4.87106	−	19.6317i	−0.178462	−	0.719248i
$746$	−10.4652	−	16.2842i	−0.383159	−	0.596207i
$747$	2.03777	+	5.98680i	0.0745580	+	0.219045i
$748$	−1.35432	−	1.01383i	−0.0495189	−	0.0370694i
$749$	−4.39003	+	2.82130i	−0.160408	+	0.103088i
$750$	18.5741	−	5.47751i	0.678230	−	0.200010i
$751$	6.48418	−	14.1984i	0.236611	−	0.518106i	−0.753659	−	0.657266i	$-0.771713\pi$
$751$	6.48418	−	14.1984i	0.236611	−	0.518106i	0.990270	+	0.139160i	$0.0444401\pi$
$752$	11.5336	−	2.50898i	0.420588	−	0.0914932i
$753$	−19.0502	+	18.5071i	−0.694229	+	0.674434i
$754$	−22.6120	+	19.5934i	−0.823479	+	0.713549i
$755$	−9.36570	+	7.44459i	−0.340853	+	0.270936i
$756$	−1.20041	−	0.612464i	−0.0436586	−	0.0222751i
$757$	−17.5089	+	13.1070i	−0.636373	+	0.476383i	−0.868094	−	0.496400i	$-0.834655\pi$
$757$	−17.5089	+	13.1070i	−0.636373	+	0.476383i	0.231722	+	0.972782i	$0.425564\pi$
$758$	5.28213	+	5.28213i	0.191856	+	0.191856i
$759$	−12.7481	+	40.3053i	−0.462728	+	1.46299i
$760$	−1.34670	−	7.76096i	−0.0488498	−	0.281520i
$761$	−1.42493	−	0.204874i	−0.0516538	−	0.00742669i	0.116439	−	0.993198i	$-0.462852\pi$
$761$	−1.42493	−	0.204874i	−0.0516538	−	0.00742669i	−0.168093	+	0.985771i	$0.553761\pi$
$762$	11.2396	−	14.5703i	0.407167	−	0.527825i
$763$	−3.11210	+	1.69933i	−0.112665	+	0.0615200i
$764$	5.60421	+	6.46761i	0.202753	+	0.233990i
$765$	2.20732	+	0.317166i	0.0798058	+	0.0114672i
$766$	−10.4950	−	6.74474i	−0.379201	−	0.243697i
$767$	14.7896	+	39.6525i	0.534022	+	1.43177i
$768$	1.68697	+	0.392610i	0.0608732	+	0.0141671i
$769$	−16.7545	−	26.0706i	−0.604184	−	0.940128i	−0.999765	−	0.0216971i	$-0.993093\pi$
$769$	−16.7545	−	26.0706i	−0.604184	−	0.940128i	0.395581	−	0.918431i	$-0.370543\pi$
$770$	−1.33868	+	2.63024i	−0.0482426	+	0.0947872i
$771$	−2.41872	+	15.2533i	−0.0871080	+	0.549333i
$772$	−0.496227	−	0.107948i	−0.0178596	−	0.00388512i
$773$	−7.01295	+	0.501576i	−0.252238	+	0.0180404i	−0.196886	−	0.980426i	$-0.563083\pi$
$773$	−7.01295	+	0.501576i	−0.252238	+	0.0180404i	−0.0553525	+	0.998467i	$0.517628\pi$
$774$	20.0847	−	12.1016i	0.721929	−	0.434982i
$775$	−2.50597	+	10.8208i	−0.0900171	+	0.388694i
$776$	−0.484909	−	1.65145i	−0.0174072	−	0.0592835i
$777$	2.70864	+	1.05514i	0.0971721	+	0.0378529i
$778$	24.4888	−	13.3719i	0.877967	−	0.479406i
$779$	−3.33409	−	7.30064i	−0.119456	−	0.261573i
$780$	18.3362	−	10.3615i	0.656543	−	0.371000i
$781$	9.03568			0.323322
$782$	−1.49721	+	0.547758i	−0.0535402	+	0.0195878i
$783$	28.4011	+	3.27440i	1.01497	+	0.117018i
$784$	−6.86217	−	0.986631i	−0.245078	−	0.0352368i
$785$	−18.5276	−	27.0694i	−0.661277	−	0.966150i
$786$	12.1250	−	18.2801i	0.432485	−	0.652031i
$787$	3.00930	−	42.0754i	0.107270	−	1.49983i	−0.604043	−	0.796952i	$-0.706444\pi$
$787$	3.00930	−	42.0754i	0.107270	−	1.49983i	0.711313	−	0.702876i	$-0.248101\pi$
$788$	−4.78930	−	2.61515i	−0.170612	−	0.0931610i
$789$	21.0022	−	17.6733i	0.747698	−	0.629185i
$790$	−4.65717	+	17.7503i	−0.165695	+	0.631528i
$791$	2.40577	+	2.08461i	0.0855393	+	0.0741202i
$792$	10.4789	+	11.1033i	0.372352	+	0.394539i
$793$	43.7038	+	32.7163i	1.55197	+	1.16179i
$794$	−0.0875426	−	0.608872i	−0.00310677	−	0.0216081i
$795$	−17.2196	−	6.13871i	−0.610716	−	0.217717i
$796$	13.9301	−	16.0762i	0.493740	−	0.569807i
$797$	9.19281	+	24.6469i	0.325626	+	0.873037i	0.991864	+	0.127298i	$0.0406305\pi$
$797$	9.19281	+	24.6469i	0.325626	+	0.873037i	−0.666239	+	0.745739i	$0.732097\pi$
$798$	−1.57659	−	0.135702i	−0.0558106	−	0.00480378i
$799$	1.10545	+	3.76482i	0.0391080	+	0.133190i
$800$	1.34436	+	4.81588i	0.0475304	+	0.170267i
$801$	−1.96697	+	1.60719i	−0.0694993	+	0.0567872i
$802$	7.39230	−	19.8195i	0.261031	−	0.699852i
$803$	−42.3790	+	31.7246i	−1.49552	+	1.11954i
$804$	−23.5904	−	7.29895i	−0.831970	−	0.257414i
$805$	1.38806	+	2.41009i	0.0489226	+	0.0849445i
$806$			12.0802i			0.425505i
$807$	51.3437	−	18.3089i	1.80738	−	0.644503i
$808$	−5.04215	−	1.88062i	−0.177382	−	0.0661601i
$809$	−40.9993	−	12.0385i	−1.44146	−	0.423251i	−0.534751	−	0.845010i	$-0.679595\pi$
$809$	−40.9993	−	12.0385i	−1.44146	−	0.423251i	−0.906708	+	0.421759i	$0.861413\pi$
$810$	−19.1379	−	6.22411i	−0.672438	−	0.218693i
$811$	−18.3448	+	5.38653i	−0.644174	+	0.189147i	−0.587472	−	0.809245i	$-0.699877\pi$
$811$	−18.3448	+	5.38653i	−0.644174	+	0.189147i	−0.0567022	+	0.998391i	$0.518059\pi$
$812$	−1.39434	+	0.303320i	−0.0489318	+	0.0106445i
$813$	−1.04713	+	0.0596866i	−0.0367246	+	0.00209330i
$814$	−24.8886	−	21.5661i	−0.872345	−	0.755891i
$815$	23.7014	+	25.8010i	0.830224	+	0.903770i
$816$	−0.0901753	+	0.568676i	−0.00315677	+	0.0199076i
$817$	16.5005	−	22.0421i	0.577281	−	0.771157i
$818$	−16.3745	−	3.56206i	−0.572522	−	0.124545i
$819$	−1.07413	−	4.09244i	−0.0375330	−	0.143002i
$820$	2.57025	+	4.39870i	0.0897569	+	0.153609i
$821$	−7.32546	+	11.3986i	−0.255660	+	0.397815i	−0.945230	−	0.326404i	$-0.894163\pi$
$821$	−7.32546	+	11.3986i	−0.255660	+	0.397815i	0.689570	+	0.724219i	$0.257799\pi$
$822$	17.7309	−	17.2253i	0.618435	−	0.600801i
$823$	−27.9571	−	1.99953i	−0.974525	−	0.0696994i	−0.425015	−	0.905186i	$-0.639731\pi$
$823$	−27.9571	−	1.99953i	−0.974525	−	0.0696994i	−0.549510	+	0.835487i	$0.685186\pi$
$824$	−0.916974	−	0.269248i	−0.0319443	−	0.00937970i
$825$	−13.5891	+	41.9257i	−0.473110	+	1.45966i
$826$	−0.287245	+	1.99783i	−0.00999454	+	0.0695135i
$827$	34.2462	−	34.2462i	1.19086	−	1.19086i	0.214030	−	0.976827i	$-0.431341\pi$
$827$	34.2462	−	34.2462i	1.19086	−	1.19086i	0.976827	−	0.214030i	$-0.0686590\pi$
$828$	14.1576	−	2.56169i	0.492011	−	0.0890247i
$829$			0.819142i			0.0284500i	0.999899	+	0.0142250i	$0.00452811\pi$
$829$			0.819142i			0.0284500i	−0.999899	+	0.0142250i	$0.995472\pi$
$830$	−3.42837	−	3.23501i	−0.119001	−	0.112289i
$831$	24.4873	−	3.16002i	0.849454	−	0.109620i
$832$	2.60616	+	4.77282i	0.0903522	+	0.165468i
$833$	0.164411	−	2.29876i	0.00569649	−	0.0796473i
$834$	−0.539632	+	37.3123i	−0.0186859	+	1.29202i
$835$	8.54233	−	20.2391i	0.295619	−	0.700401i
$836$	16.3072	+	7.44724i	0.563996	+	0.257568i
$837$	8.50838	−	7.80039i	0.294093	−	0.269621i
$838$	1.17819	−	5.41606i	0.0406999	−	0.187095i
$839$	−0.583554	−	4.05871i	−0.0201465	−	0.140122i	0.977266	−	0.212019i	$-0.0680039\pi$
$839$	−0.583554	−	4.05871i	−0.0201465	−	0.140122i	−0.997412	+	0.0718968i	$0.977095\pi$
$840$	1.00436	−	0.0146142i	0.0346536	−	0.000504238i
$841$	1.07014	−	0.687737i	0.0369014	−	0.0237151i
$842$	1.69508	+	23.7004i	0.0584165	+	0.816769i
$843$	−1.53824	−	26.9867i	−0.0529797	−	0.929471i
$844$	3.96003	−	6.16193i	0.136310	−	0.212102i
$845$	35.0805	+	11.9371i	1.20680	+	0.410649i
$846$	−4.02367	−	35.1807i	−0.138337	−	1.20954i
$847$	−1.85185	−	3.39141i	−0.0636303	−	0.116530i
$848$	1.64953	−	4.42255i	0.0566450	−	0.151871i
$849$	−1.99390	+	4.20406i	−0.0684305	+	0.144283i
$850$	−1.56497	+	0.559973i	−0.0536780	+	0.0192069i
$851$	−29.8317	+	8.55649i	−1.02262	+	0.293313i
$852$	−1.43462	−	2.72011i	−0.0491494	−	0.0931895i
$853$	−6.12929	−	8.18777i	−0.209863	−	0.280344i	0.683242	−	0.730192i	$-0.260569\pi$
$853$	−6.12929	−	8.18777i	−0.209863	−	0.280344i	−0.893105	+	0.449848i	$0.851478\pi$
$854$	1.08160	+	2.36837i	0.0370116	+	0.0810441i
$855$	−23.5704	+	1.68788i	−0.806092	+	0.0577243i
$856$	−13.1765	−	15.2065i	−0.450365	−	0.519749i
$857$	4.01897	−	7.36019i	0.137285	−	0.251419i	−0.799987	−	0.600017i	$-0.795160\pi$
$857$	4.01897	−	7.36019i	0.137285	−	0.251419i	0.937272	+	0.348598i	$0.113342\pi$
$858$	−4.11060	+	47.7572i	−0.140334	+	1.63040i
$859$	33.6042	+	15.3465i	1.14656	+	0.523617i	0.895811	−	0.444435i	$-0.146595\pi$
$859$	33.6042	+	15.3465i	1.14656	+	0.523617i	0.250750	+	0.968052i	$0.419323\pi$
$860$	−9.01866	+	14.9710i	−0.307534	+	0.510508i
$861$	0.986072	−	0.274112i	0.0336053	−	0.00934170i
$862$	4.45793	−	5.95510i	0.151838	−	0.202831i
$863$	29.3972	−	39.2701i	1.00069	−	1.33677i	0.0597453	−	0.998214i	$-0.480971\pi$
$863$	29.3972	−	39.2701i	1.00069	−	1.33677i	0.940947	−	0.338554i	$-0.109938\pi$
$864$	1.67878	−	4.91749i	0.0571133	−	0.167296i
$865$	−24.6826	+	40.9734i	−0.839235	+	1.39314i
$866$	28.3331	+	12.9393i	0.962799	+	0.439696i
$867$	29.1457	+	2.50866i	0.989840	+	0.0851985i
$868$	−0.276110	+	0.505658i	−0.00937179	+	0.0171632i
$869$	−27.3506	−	31.5643i	−0.927807	−	1.07075i
$870$	−19.8552	+	7.73649i	−0.673153	+	0.262292i
$871$	−32.2069	−	70.5232i	−1.09129	−	2.38959i
$872$	−8.19327	−	10.9449i	−0.277459	−	0.370642i
$873$	−5.07513	+	0.951211i	−0.171767	+	0.0321936i
$874$	14.2693	−	9.04433i	0.482665	−	0.305929i
$875$	1.42926	+	2.52291i	0.0483179	+	0.0852900i
$876$	16.2791	+	7.72083i	0.550018	+	0.260863i
$877$	−15.8545	+	42.5074i	−0.535367	+	1.43537i	0.334645	+	0.942344i	$0.391384\pi$
$877$	−15.8545	+	42.5074i	−0.535367	+	1.43537i	−0.870012	+	0.493030i	$0.835889\pi$
$878$	11.7245	+	21.4719i	0.395684	+	0.724641i
$879$	1.26750	−	0.556840i	0.0427518	−	0.0187818i
$880$	−10.7730	−	3.66580i	−0.363157	−	0.123574i
$881$	29.7022	−	46.2175i	1.00069	−	1.55711i	0.181658	−	0.983362i	$-0.441854\pi$
$881$	29.7022	−	46.2175i	1.00069	−	1.55711i	0.819034	−	0.573745i	$-0.194510\pi$
$882$	−5.00685	+	20.1866i	−0.168589	+	0.679717i
$883$	0.587544	+	8.21493i	0.0197724	+	0.276455i	0.997714	+	0.0675764i	$0.0215266\pi$
$883$	0.587544	+	8.21493i	0.0197724	+	0.276455i	−0.977942	+	0.208878i	$0.933019\pi$
$884$	−1.52077	+	0.977338i	−0.0511490	+	0.0328714i
$885$	0.438532	+	30.1380i	0.0147411	+	1.01308i
$886$	−1.92097	−	13.3606i	−0.0645362	−	0.448859i
$887$	−1.71111	+	7.86585i	−0.0574535	+	0.264109i	−0.996909	−	0.0785605i	$-0.974968\pi$
$887$	−1.71111	+	7.86585i	−0.0574535	+	0.264109i	0.939456	+	0.342670i	$0.111331\pi$
$888$	−2.54064	+	10.9166i	−0.0852583	+	0.366338i
$889$	2.50640	+	1.14463i	0.0840619	+	0.0383898i
$890$	0.736204	−	1.74426i	0.0246776	−	0.0584678i
$891$	36.2910	−	27.9425i	1.21579	−	0.936109i
$892$	−1.49910	+	20.9602i	−0.0501937	+	0.701799i
$893$	−19.9269	−	36.4933i	−0.666827	−	1.22120i
$894$	−2.00525	−	15.5389i	−0.0670656	−	0.519698i
$895$	10.0695	+	9.50154i	0.336586	+	0.317601i
$896$			0.259351i			0.00866431i
$897$	35.5926	+	27.8141i	1.18840	+	0.928687i
$898$	−2.91958	+	2.91958i	−0.0974277	+	0.0974277i
$899$	1.73942	−	12.0979i	0.0580129	−	0.403489i
$900$	14.7789	−	2.56581i	0.492631	−	0.0855269i
$901$	1.50555	+	0.442069i	0.0501571	+	0.0147275i
$902$	−11.5653	−	0.827166i	−0.385082	−	0.0275416i
$903$	2.44658	+	2.51839i	0.0814171	+	0.0838067i
$904$	−6.63585	+	10.3256i	−0.220705	+	0.343424i
$905$	6.48286	+	11.0947i	0.215498	+	0.368801i
$906$	−7.86779	+	4.89702i	−0.261390	+	0.162693i
$907$	11.6847	+	2.54185i	0.387983	+	0.0844006i	0.402326	−	0.915497i	$-0.368202\pi$
$907$	11.6847	+	2.54185i	0.387983	+	0.0844006i	−0.0143425	+	0.999897i	$0.504566\pi$
$908$	−1.95172	+	2.60720i	−0.0647702	+	0.0865229i
$909$	−7.12849	+	14.4853i	−0.236437	+	0.480448i
$910$	2.13346	+	2.32246i	0.0707236	+	0.0769887i
$911$	−0.202506	−	0.175473i	−0.00670933	−	0.00581366i	0.651500	−	0.758649i	$-0.274140\pi$
$911$	−0.202506	−	0.175473i	−0.00670933	−	0.00581366i	−0.658209	+	0.752835i	$0.728686\pi$
$912$	−0.347218	−	6.09156i	−0.0114975	−	0.201712i
$913$	10.4828	−	2.28040i	0.346931	−	0.0754702i
$914$	14.8028	−	4.34651i	0.489635	−	0.143770i
$915$	21.4945	+	32.3998i	0.710588	+	1.07110i
$916$	−22.2102	−	6.52150i	−0.733845	−	0.215476i
$917$	3.07750	+	1.14785i	0.101628	+	0.0379052i
$918$	1.67035	+	0.440032i	0.0551299	+	0.0145232i
$919$			45.5525i			1.50264i	0.659939	+	0.751320i	$0.270582\pi$
$919$			45.5525i			1.50264i	−0.659939	+	0.751320i	$0.729418\pi$
$920$	−8.43651	+	6.62007i	−0.278143	+	0.218257i
$921$	−3.43213	+	11.0928i	−0.113093	+	0.365519i
$922$	−23.7996	+	17.8162i	−0.783799	+	0.586745i
$923$	3.37413	−	9.04639i	0.111061	−	0.297765i
$924$	−1.26363	+	1.90509i	−0.0415702	+	0.0626729i
$925$	−31.1643	+	8.69957i	−1.02467	+	0.286040i
$926$	−5.17764	−	17.6334i	−0.170148	−	0.579471i
$927$	−1.07920	+	2.65619i	−0.0354456	+	0.0872408i
$928$	−1.92275	−	5.15510i	−0.0631175	−	0.169225i
$929$	30.0794	−	34.7135i	0.986872	−	1.13891i	−0.00343161	−	0.999994i	$-0.501092\pi$
$929$	30.0794	−	34.7135i	0.986872	−	1.13891i	0.990304	−	0.138917i	$-0.0443622\pi$
$930$	−2.88904	+	8.10401i	−0.0947353	+	0.265741i
$931$	3.47558	+	24.1732i	0.113907	+	0.792244i
$932$	−11.6234	−	8.70115i	−0.380737	−	0.285016i
$933$	16.3962	−	29.0216i	0.536787	−	0.950124i
$934$	−19.4962	−	16.8935i	−0.637934	−	0.552773i
$935$	0.960027	−	3.65904i	0.0313962	−	0.119663i
$936$	15.0295	−	6.34510i	0.491255	−	0.207396i
$937$	9.97049	+	5.44430i	0.325722	+	0.177857i	0.633787	−	0.773508i	$-0.281500\pi$
$937$	9.97049	+	5.44430i	0.325722	+	0.177857i	−0.308065	+	0.951365i	$0.599681\pi$
$938$	0.263781	−	3.68814i	0.00861275	−	0.120422i
$939$	24.3263	+	16.1354i	0.793860	+	0.526558i
$940$	14.9072	+	21.7800i	0.486221	+	0.710387i
$941$	25.7701	+	3.70518i	0.840080	+	0.120785i	0.548905	−	0.835884i	$-0.315045\pi$
$941$	25.7701	+	3.70518i	0.840080	+	0.120785i	0.291175	+	0.956670i	$0.405954\pi$
$942$	−11.8534	−	22.4747i	−0.386206	−	0.732264i
$943$	−6.60284	+	8.70599i	−0.215018	+	0.283506i
$944$	−7.78242			−0.253296
$945$	0.258151	−	3.00231i	0.00839765	−	0.0976651i
$946$	−16.5242	−	36.1830i	−0.537249	−	1.17641i
$947$	−23.8125	+	13.0026i	−0.773803	+	0.422528i	−0.817072	−	0.576535i	$-0.804404\pi$
$947$	−23.8125	+	13.0026i	−0.773803	+	0.422528i	0.0432694	+	0.999063i	$0.486223\pi$
$948$	−5.15961	+	13.2452i	−0.167576	+	0.430185i
$949$	15.9369	+	54.2759i	0.517332	+	1.76187i
$950$	14.9434	−	9.32344i	0.484826	−	0.302492i
$951$	28.2236	−	31.6356i	0.915213	−	1.02585i
$952$	−0.0859957	+	0.00615054i	−0.00278714	+	0.000199340i
$953$	−49.3238	−	10.7297i	−1.59775	−	0.347570i	−0.676473	−	0.736468i	$-0.736492\pi$
$953$	−49.3238	−	10.7297i	−1.59775	−	0.347570i	−0.921281	+	0.388898i	$0.872856\pi$
$954$	−12.7053	−	6.25252i	−0.411350	−	0.202433i
$955$	−8.67985	+	17.0542i	−0.280873	+	0.551861i
$956$	4.05989	+	6.31731i	0.131306	+	0.204316i
$957$	10.9932	−	47.2355i	0.355360	−	1.52691i
$958$	4.88911	+	13.1082i	0.157960	+	0.423507i
$959$	3.11393	+	2.00120i	0.100554	+	0.0646221i
$960$	0.606900	+	3.82514i	0.0195876	+	0.123456i
$961$	17.0691	+	19.6988i	0.550616	+	0.635445i
$962$	−30.8856	+	16.8648i	−0.995793	+	0.543744i
$963$	−49.3493	+	34.7618i	−1.59026	+	1.12018i
$964$	7.91485	+	1.13798i	0.254920	+	0.0366520i
$965$	−0.194141	−	1.11883i	−0.00624963	−	0.0360164i
$966$	0.854121	+	1.97778i	0.0274809	+	0.0636341i
$967$	−7.54203	−	7.54203i	−0.242535	−	0.242535i	0.575363	−	0.817898i	$-0.304861\pi$
$967$	−7.54203	−	7.54203i	−0.242535	−	0.242535i	−0.817898	+	0.575363i	$0.804861\pi$
$968$	11.9272	−	8.92862i	0.383356	−	0.286977i
$969$	2.01161	−	0.259593i	0.0646221	−	0.00833931i
$970$	3.01280	−	2.39481i	0.0967352	−	0.0768927i
$971$	24.4654	−	21.1994i	0.785131	−	0.680320i	−0.167018	−	0.985954i	$-0.553414\pi$
$971$	24.4654	−	21.1994i	0.785131	−	0.680320i	0.952149	+	0.305634i	$0.0988684\pi$
$972$	−14.1739	−	6.48855i	−0.454627	−	0.208120i
$973$	−5.45990	+	1.18773i	−0.175036	+	0.0380768i
$974$	8.09379	−	17.7229i	0.259342	−	0.567879i
$975$	36.9009	+	29.2611i	1.18177	+	0.937107i
$976$	−8.44546	+	5.42757i	−0.270333	+	0.173732i
$977$	−32.5001	−	24.3292i	−1.03977	−	0.778361i	−0.0641738	−	0.997939i	$-0.520441\pi$
$977$	−32.5001	−	24.3292i	−1.03977	−	0.778361i	−0.975595	+	0.219578i	$0.929532\pi$
$978$	15.9473	+	21.9580i	0.509939	+	0.702139i
$979$	2.32957	+	3.62489i	0.0744535	+	0.115852i
$980$	−3.73321	−	15.0458i	−0.119253	−	0.480622i
$981$	−35.1315	+	21.1677i	−1.12166	+	0.675832i
$982$	1.29222	+	5.94022i	0.0412363	+	0.189560i
$983$	−3.97330	−	2.16958i	−0.126728	−	0.0691990i	0.414634	−	0.909988i	$-0.363910\pi$
$983$	−3.97330	−	2.16958i	−0.126728	−	0.0691990i	−0.541363	+	0.840789i	$0.682091\pi$
$984$	1.58725	+	3.61296i	0.0505996	+	0.115177i
$985$	1.38542	−	12.1228i	0.0441431	−	0.386265i
$986$	1.66373	−	0.759801i	0.0529840	−	0.0241970i
$987$	4.99415	−	1.78089i	0.158966	−	0.0566863i
$988$	13.5455	−	13.5455i	0.430941	−	0.430941i
$989$	−37.0696	−	5.56735i	−1.17875	−	0.177031i
$990$	−14.1790	+	31.0549i	−0.450638	+	0.986991i
$991$	−6.04542	+	42.0468i	−0.192039	+	1.33566i	0.634562	+	0.772872i	$0.281181\pi$
$991$	−6.04542	+	42.0468i	−0.192039	+	1.33566i	−0.826601	+	0.562788i	$0.809729\pi$
$992$	−2.08137	−	0.776311i	−0.0660836	−	0.0246479i
$993$	0.987883	+	4.87995i	0.0313495	+	0.154860i
$994$	0.348005	−	0.301548i	0.0110380	−	0.00956452i
$995$	45.0298	+	15.3227i	1.42754	+	0.485761i
$996$	−2.35089	−	2.79370i	−0.0744907	−	0.0885217i
$997$	41.1176	−	15.3361i	1.30221	−	0.485698i	0.399808	−	0.916599i	$-0.369077\pi$
$997$	41.1176	−	15.3361i	1.30221	−	0.485698i	0.902399	+	0.430901i	$0.141804\pi$
$998$	23.0449	−	1.64820i	0.729474	−	0.0521730i
$999$	31.8218	+	10.8636i	1.00680	+	0.343711i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.x.a.77.20	✓	960
3.2	odd	2	inner	690.2.x.a.77.37	yes	960
5.3	odd	4	inner	690.2.x.a.353.18	yes	960
15.8	even	4	inner	690.2.x.a.353.25	yes	960
23.3	even	11	inner	690.2.x.a.647.25	yes	960
69.26	odd	22	inner	690.2.x.a.647.18	yes	960
115.3	odd	44	inner	690.2.x.a.233.37	yes	960
345.233	even	44	inner	690.2.x.a.233.20	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.x.a.77.20	✓	960	1.1	even	1	trivial
690.2.x.a.77.37	yes	960	3.2	odd	2	inner
690.2.x.a.233.20	yes	960	345.233	even	44	inner
690.2.x.a.233.37	yes	960	115.3	odd	44	inner
690.2.x.a.353.18	yes	960	5.3	odd	4	inner
690.2.x.a.353.25	yes	960	15.8	even	4	inner
690.2.x.a.647.18	yes	960	69.26	odd	22	inner
690.2.x.a.647.25	yes	960	23.3	even	11	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.599278 - 0.800541i) q^{2} +(1.05792 - 1.37142i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-2.22480 + 0.224149i) q^{5} +(-1.73187 - 0.0250473i) q^{6} +(-0.0551290 - 0.253424i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-0.761601 - 2.90172i) q^{9} +O(q^{10})\)	\(q+(-0.599278 - 0.800541i) q^{2} +(1.05792 - 1.37142i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-2.22480 + 0.224149i) q^{5} +(-1.73187 - 0.0250473i) q^{6} +(-0.0551290 - 0.253424i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-0.761601 - 2.90172i) q^{9} +(1.51272 + 1.64672i) q^{10} +(-5.03730 + 0.724255i) q^{11} +(1.01782 + 1.40144i) q^{12} +(-1.15593 + 5.31373i) q^{13} +(-0.169839 + 0.196004i) q^{14} +(-2.04627 + 3.28828i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(0.159315 - 0.291764i) q^{17} +(-1.86653 + 2.34863i) q^{18} +(-0.992451 + 3.37998i) q^{19} +(0.411731 - 2.19783i) q^{20} +(-0.405874 - 0.192498i) q^{21} +(3.59854 + 3.59854i) q^{22} +(4.69253 - 0.990013i) q^{23} +(0.511957 - 1.65466i) q^{24} +(4.89951 - 0.997376i) q^{25} +(4.94658 - 2.25903i) q^{26} +(-4.78520 - 2.02531i) q^{27} +(0.258690 + 0.0185019i) q^{28} +(-5.27914 + 1.55009i) q^{29} +(3.85869 - 0.332472i) q^{30} +(-0.922817 + 2.02069i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(-4.33582 + 7.67448i) q^{33} +(-0.329044 + 0.0473093i) q^{34} +(0.179456 + 0.551462i) q^{35} +(2.99875 + 0.0867572i) q^{36} +(-6.45466 + 0.461646i) q^{37} +(3.30057 - 1.23105i) q^{38} +(6.06448 + 7.20678i) q^{39} +(-2.00620 + 0.987506i) q^{40} +(-1.72187 + 1.49201i) q^{41} +(0.0891287 + 0.440278i) q^{42} +(-7.32343 - 2.73150i) q^{43} +(0.724255 - 5.03730i) q^{44} +(2.34483 + 6.28504i) q^{45} +(-3.60468 - 3.16327i) q^{46} +(-8.34623 + 8.34623i) q^{47} +(-1.63143 + 0.581758i) q^{48} +(6.30624 - 2.87996i) q^{49} +(-3.73461 - 3.32456i) q^{50} +(-0.231589 - 0.527153i) q^{51} +(-4.77282 - 2.60616i) q^{52} +(1.00334 + 4.61229i) q^{53} +(1.24631 + 5.04447i) q^{54} +(11.0447 - 2.74043i) q^{55} +(-0.140216 - 0.218180i) q^{56} +(3.58544 + 4.93682i) q^{57} +(4.40458 + 3.29723i) q^{58} +(6.54699 - 4.20749i) q^{59} +(-2.57858 - 2.88979i) q^{60} +(4.17041 - 9.13192i) q^{61} +(2.17067 - 0.472200i) q^{62} +(-0.693379 + 0.352977i) q^{63} +(0.755750 - 0.654861i) q^{64} +(1.38065 - 12.0811i) q^{65} +(8.74209 - 1.12814i) q^{66} +(-11.4133 + 8.54388i) q^{67} +(0.235062 + 0.235062i) q^{68} +(3.60661 - 7.48281i) q^{69} +(0.333924 - 0.474141i) q^{70} +(-1.75742 - 0.252679i) q^{71} +(-1.72763 - 2.45261i) q^{72} +(9.12981 - 4.98525i) q^{73} +(4.23770 + 4.89057i) q^{74} +(3.81548 - 7.77445i) q^{75} +(-2.96346 - 1.90450i) q^{76} +(0.461245 + 1.23665i) q^{77} +(2.13502 - 9.17373i) q^{78} +(4.43696 + 6.90405i) q^{79} +(1.99281 + 1.01425i) q^{80} +(-7.83993 + 4.41990i) q^{81} +(2.22630 + 0.484301i) q^{82} +(-2.10266 + 0.150385i) q^{83} +(0.299048 - 0.335200i) q^{84} +(-0.289047 + 0.684830i) q^{85} +(2.20209 + 7.49963i) q^{86} +(-3.45908 + 8.87981i) q^{87} +(-4.46660 + 2.43895i) q^{88} +(-0.351729 - 0.770179i) q^{89} +(3.62623 - 5.64362i) q^{90} +1.41035 q^{91} +(-0.372129 + 4.78137i) q^{92} +(1.79495 + 3.40330i) q^{93} +(11.6832 + 1.67979i) q^{94} +(1.45039 - 7.74225i) q^{95} +(1.44340 + 0.957391i) q^{96} +(0.122787 - 1.71678i) q^{97} +(-6.08472 - 3.32251i) q^{98} +(5.93800 + 14.0652i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) \) 960 * q + 8 * q^3 + 8 * q^6	\( 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) \) 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more