LMFDB - Embedded newform 966.2.bf.a.389.57

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(11,966)]

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([33, 44, 27]))

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

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

chi := DirichletCharacter("966.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.bf (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:	$1280$
Relative dimension:	$64$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			389.57
Character	$\chi$	$=$	966.389
Dual form			966.2.bf.a.149.57

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.998867 + 0.0475819i) q^{2} +(1.34995 + 1.08519i) q^{3} +(0.995472 + 0.0950560i) q^{4} +(-0.449881 - 1.85443i) q^{5} +(1.29679 + 1.14819i) q^{6} +(-0.772606 + 2.53043i) q^{7} +(0.989821 + 0.142315i) q^{8} +(0.644746 + 2.92990i) q^{9} +O(q^{10})$	\(q+(0.998867 + 0.0475819i) q^{2} +(1.34995 + 1.08519i) q^{3} +(0.995472 + 0.0950560i) q^{4} +(-0.449881 - 1.85443i) q^{5} +(1.29679 + 1.14819i) q^{6} +(-0.772606 + 2.53043i) q^{7} +(0.989821 + 0.142315i) q^{8} +(0.644746 + 2.92990i) q^{9} +(-0.361134 - 1.87374i) q^{10} +(-0.0300548 - 0.630929i) q^{11} +(1.24069 + 1.20859i) q^{12} +(0.227800 + 0.262896i) q^{13} +(-0.892133 + 2.49080i) q^{14} +(1.40509 - 2.99160i) q^{15} +(0.981929 + 0.189251i) q^{16} +(3.14747 + 4.42000i) q^{17} +(0.504605 + 2.95726i) q^{18} +(4.63151 + 3.29809i) q^{19} +(-0.271569 - 1.88880i) q^{20} +(-3.78897 + 2.57754i) q^{21} -0.631644i q^{22} +(-1.27903 - 4.62213i) q^{23} +(1.18177 + 1.26626i) q^{24} +(1.20765 - 0.622585i) q^{25} +(0.215033 + 0.273437i) q^{26} +(-2.30911 + 4.65489i) q^{27} +(-1.00964 + 2.44553i) q^{28} +(4.30240 + 1.96484i) q^{29} +(1.54584 - 2.92136i) q^{30} +(-1.92293 - 1.51221i) q^{31} +(0.971812 + 0.235759i) q^{32} +(0.644102 - 0.884339i) q^{33} +(2.93359 + 4.56475i) q^{34} +(5.04010 + 0.294354i) q^{35} +(0.363322 + 2.97792i) q^{36} +(-7.10684 + 7.45344i) q^{37} +(4.46934 + 3.51473i) q^{38} +(0.0222293 + 0.602103i) q^{39} +(-0.181388 - 1.89958i) q^{40} +(2.72236 - 9.27152i) q^{41} +(-3.90732 + 2.39434i) q^{42} +(3.70601 - 0.532844i) q^{43} +(0.0300548 - 0.630929i) q^{44} +(5.14324 - 2.51374i) q^{45} +(-1.05765 - 4.67775i) q^{46} +(-3.60549 + 2.08163i) q^{47} +(1.12018 + 1.32105i) q^{48} +(-5.80616 - 3.91005i) q^{49} +(1.23590 - 0.564417i) q^{50} +(-0.547586 + 9.38237i) q^{51} +(0.201779 + 0.283359i) q^{52} +(-2.82502 - 8.16237i) q^{53} +(-2.52798 + 4.53975i) q^{54} +(-1.15649 + 0.339577i) q^{55} +(-1.12486 + 2.39472i) q^{56} +(2.67329 + 9.47831i) q^{57} +(4.20403 + 2.16733i) q^{58} +(-1.20197 - 6.23640i) q^{59} +(1.68309 - 2.84449i) q^{60} +(-4.44520 - 11.1036i) q^{61} +(-1.84880 - 1.60199i) q^{62} +(-7.91204 - 0.632172i) q^{63} +(0.959493 + 0.281733i) q^{64} +(0.385040 - 0.540713i) q^{65} +(0.685451 - 0.852690i) q^{66} +(-5.12924 - 9.94934i) q^{67} +(2.71307 + 4.69917i) q^{68} +(3.28924 - 7.62764i) q^{69} +(5.02038 + 0.533838i) q^{70} +(-5.70308 + 8.87416i) q^{71} +(0.221215 + 2.99183i) q^{72} +(16.4385 + 1.56969i) q^{73} +(-7.45344 + 7.10684i) q^{74} +(2.30588 + 0.470059i) q^{75} +(4.29704 + 3.72340i) q^{76} +(1.61974 + 0.411408i) q^{77} +(-0.00644508 + 0.602478i) q^{78} +(-11.8188 - 4.09053i) q^{79} +(-0.0907969 - 1.90606i) q^{80} +(-8.16861 + 3.77808i) q^{81} +(3.16044 - 9.13148i) q^{82} +(2.90370 - 0.852603i) q^{83} +(-4.01682 + 2.20571i) q^{84} +(6.78061 - 7.82524i) q^{85} +(3.72717 - 0.355901i) q^{86} +(3.67582 + 7.32134i) q^{87} +(0.0600416 - 0.628784i) q^{88} +(-0.199393 + 0.156804i) q^{89} +(5.25703 - 2.26617i) q^{90} +(-0.841240 + 0.373319i) q^{91} +(-0.833878 - 4.72278i) q^{92} +(-0.954838 - 4.12814i) q^{93} +(-3.70045 + 1.90772i) q^{94} +(4.03245 - 10.0726i) q^{95} +(1.05606 + 1.37286i) q^{96} +(-0.162509 + 0.553456i) q^{97} +(-5.61354 - 4.18189i) q^{98} +(1.82918 - 0.494846i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) $ 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9	$ 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9} + 64 q^{16} + 44 q^{18} - 132 q^{21} - 4 q^{24} + 72 q^{25} + 108 q^{27} + 44 q^{30} + 8 q^{36} + 44 q^{37} - 4 q^{39} - 88 q^{43} - 12 q^{46} + 60 q^{49} - 48 q^{54} + 96 q^{55} + 44 q^{58} - 176 q^{61} - 110 q^{63} + 128 q^{64} + 56 q^{69} - 120 q^{70} + 44 q^{72} + 40 q^{73} - 268 q^{75} + 16 q^{78} + 88 q^{79} + 8 q^{81} - 56 q^{82} - 22 q^{84} + 64 q^{85} - 42 q^{87} - 32 q^{93} + 8 q^{94} + 4 q^{96} + 132 q^{99}+O(q^{100}) $ 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9 + 64 * q^16 + 44 * q^18 - 132 * q^21 - 4 * q^24 + 72 * q^25 + 108 * q^27 + 44 * q^30 + 8 * q^36 + 44 * q^37 - 4 * q^39 - 88 * q^43 - 12 * q^46 + 60 * q^49 - 48 * q^54 + 96 * q^55 + 44 * q^58 - 176 * q^61 - 110 * q^63 + 128 * q^64 + 56 * q^69 - 120 * q^70 + 44 * q^72 + 40 * q^73 - 268 * q^75 + 16 * q^78 + 88 * q^79 + 8 * q^81 - 56 * q^82 - 22 * q^84 + 64 * q^85 - 42 * q^87 - 32 * q^93 + 8 * q^94 + 4 * q^96 + 132 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{22}\right)$

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 $

$2$	0.998867	+	0.0475819i	0.706306	+	0.0336455i
$2$	0.998867	+	0.0475819i	0.706306	+	0.0336455i
$3$	1.34995	+	1.08519i	0.779396	+	0.626532i
$3$	1.34995	+	1.08519i	0.779396	+	0.626532i
$4$	0.995472	+	0.0950560i	0.497736	+	0.0475280i
$5$	−0.449881	−	1.85443i	−0.201193	−	0.829328i	−0.979500	−	0.201444i	$-0.935437\pi$
$5$	−0.449881	−	1.85443i	−0.201193	−	0.829328i	0.778307	−	0.627884i	$-0.216079\pi$
$6$	1.29679	+	1.14819i	0.529412	+	0.468746i
$7$	−0.772606	+	2.53043i	−0.292018	+	0.956413i
$7$	−0.772606	+	2.53043i	−0.292018	+	0.956413i
$8$	0.989821	+	0.142315i	0.349955	+	0.0503159i
$9$	0.644746	+	2.92990i	0.214915	+	0.976633i
$10$	−0.361134	−	1.87374i	−0.114200	−	0.592528i
$11$	−0.0300548	−	0.630929i	−0.00906188	−	0.190232i	−0.998859	−	0.0477504i	$-0.984795\pi$
$11$	−0.0300548	−	0.630929i	−0.00906188	−	0.190232i	0.989797	−	0.142482i	$-0.0455082\pi$
$12$	1.24069	+	1.20859i	0.358155	+	0.348891i
$13$	0.227800	+	0.262896i	0.0631805	+	0.0729142i	0.786460	−	0.617641i	$-0.211912\pi$
$13$	0.227800	+	0.262896i	0.0631805	+	0.0729142i	−0.723279	+	0.690555i	$0.757366\pi$
$14$	−0.892133	+	2.49080i	−0.238433	+	0.665695i
$15$	1.40509	−	2.99160i	0.362792	−	0.772428i
$16$	0.981929	+	0.189251i	0.245482	+	0.0473128i
$17$	3.14747	+	4.42000i	0.763373	+	1.07201i	0.995066	+	0.0992182i	$0.0316342\pi$
$17$	3.14747	+	4.42000i	0.763373	+	1.07201i	−0.231693	+	0.972789i	$0.574426\pi$
$18$	0.504605	+	2.95726i	0.118937	+	0.697032i
$19$	4.63151	+	3.29809i	1.06254	+	0.756633i	0.970979	−	0.239167i	$-0.0768742\pi$
$19$	4.63151	+	3.29809i	1.06254	+	0.756633i	0.0915634	+	0.995799i	$0.470814\pi$
$20$	−0.271569	−	1.88880i	−0.0607246	−	0.422349i
$21$	−3.78897	+	2.57754i	−0.826821	+	0.562466i
$22$		−	0.631644i		−	0.134667i
$23$	−1.27903	−	4.62213i	−0.266696	−	0.963781i
$23$	−1.27903	−	4.62213i	−0.266696	−	0.963781i
$24$	1.18177	+	1.26626i	0.241229	+	0.258474i
$25$	1.20765	−	0.622585i	0.241529	−	0.124517i
$26$	0.215033	+	0.273437i	0.0421715	+	0.0536254i
$27$	−2.30911	+	4.65489i	−0.444388	+	0.895835i
$28$	−1.00964	+	2.44553i	−0.190804	+	0.462162i
$29$	4.30240	+	1.96484i	0.798935	+	0.364861i	0.772681	−	0.634794i	$-0.218915\pi$
$29$	4.30240	+	1.96484i	0.798935	+	0.364861i	0.0262535	+	0.999655i	$0.491642\pi$
$30$	1.54584	−	2.92136i	0.282231	−	0.533364i
$31$	−1.92293	−	1.51221i	−0.345368	−	0.271601i	0.430374	−	0.902651i	$-0.358382\pi$
$31$	−1.92293	−	1.51221i	−0.345368	−	0.271601i	−0.775742	+	0.631050i	$0.782624\pi$
$32$	0.971812	+	0.235759i	0.171794	+	0.0416767i
$33$	0.644102	−	0.884339i	0.112124	−	0.153944i
$34$	2.93359	+	4.56475i	0.503107	+	0.782849i
$35$	5.04010	+	0.294354i	0.851932	+	0.0497549i
$36$	0.363322	+	2.97792i	0.0605536	+	0.496320i
$37$	−7.10684	+	7.45344i	−1.16836	+	1.22534i	−0.198916	+	0.980017i	$0.563742\pi$
$37$	−7.10684	+	7.45344i	−1.16836	+	1.22534i	−0.969442	+	0.245322i	$0.921106\pi$
$38$	4.46934	+	3.51473i	0.725022	+	0.570164i
$39$	0.0222293	+	0.602103i	0.00355954	+	0.0964136i
$40$	−0.181388	−	1.89958i	−0.0286800	−	0.300350i
$41$	2.72236	−	9.27152i	0.425162	−	1.44797i	−0.417081	−	0.908869i	$-0.636947\pi$
$41$	2.72236	−	9.27152i	0.425162	−	1.44797i	0.842243	−	0.539098i	$-0.181235\pi$
$42$	−3.90732	+	2.39434i	−0.602913	+	0.369454i
$43$	3.70601	−	0.532844i	0.565162	−	0.0812580i	0.146189	−	0.989257i	$-0.453299\pi$
$43$	3.70601	−	0.532844i	0.565162	−	0.0812580i	0.418973	+	0.907999i	$0.362390\pi$
$44$	0.0300548	−	0.630929i	0.00453094	−	0.0951161i
$45$	5.14324	−	2.51374i	0.766709	−	0.374727i
$46$	−1.05765	−	4.67775i	−0.155942	−	0.689697i
$47$	−3.60549	+	2.08163i	−0.525914	+	0.303637i	−0.739351	−	0.673320i	$-0.764868\pi$
$47$	−3.60549	+	2.08163i	−0.525914	+	0.303637i	0.213437	+	0.976957i	$0.431534\pi$
$48$	1.12018	+	1.32105i	0.161685	+	0.190678i
$49$	−5.80616	−	3.91005i	−0.829452	−	0.558579i
$50$	1.23590	−	0.564417i	0.174783	−	0.0798207i
$51$	−0.547586	+	9.38237i	−0.0766773	+	1.31380i
$52$	0.201779	+	0.283359i	0.0279817	+	0.0392948i
$53$	−2.82502	−	8.16237i	−0.388047	−	1.12119i	−0.954787	−	0.297291i	$-0.903917\pi$
$53$	−2.82502	−	8.16237i	−0.388047	−	1.12119i	0.566740	−	0.823897i	$-0.308204\pi$
$54$	−2.52798	+	4.53975i	−0.344014	+	0.617782i
$55$	−1.15649	+	0.339577i	−0.155942	+	0.0457886i
$56$	−1.12486	+	2.39472i	−0.150316	+	0.320008i
$57$	2.67329	+	9.47831i	0.354086	+	1.25543i
$58$	4.20403	+	2.16733i	0.552017	+	0.284584i
$59$	−1.20197	−	6.23640i	−0.156483	−	0.811910i	−0.972324	−	0.233635i	$-0.924938\pi$
$59$	−1.20197	−	6.23640i	−0.156483	−	0.811910i	0.815842	−	0.578275i	$-0.196274\pi$
$60$	1.68309	−	2.84449i	0.217286	−	0.367223i
$61$	−4.44520	−	11.1036i	−0.569150	−	1.42167i	−0.881720	−	0.471773i	$-0.843614\pi$
$61$	−4.44520	−	11.1036i	−0.569150	−	1.42167i	0.312570	−	0.949895i	$-0.398810\pi$
$62$	−1.84880	−	1.60199i	−0.234797	−	0.203453i
$63$	−7.91204	−	0.632172i	−0.996823	−	0.0796461i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	0.385040	−	0.540713i	0.0477583	−	0.0670671i
$66$	0.685451	−	0.852690i	0.0843732	−	0.104959i
$67$	−5.12924	−	9.94934i	−0.626637	−	1.21551i	−0.961905	−	0.273383i	$-0.911857\pi$
$67$	−5.12924	−	9.94934i	−0.626637	−	1.21551i	0.335269	−	0.942123i	$-0.391173\pi$
$68$	2.71307	+	4.69917i	0.329008	+	0.569858i
$69$	3.28924	−	7.62764i	0.395977	−	0.918260i
$70$	5.02038	+	0.533838i	0.600050	+	0.0638059i
$71$	−5.70308	+	8.87416i	−0.676831	+	1.05317i	0.317645	+	0.948210i	$0.397108\pi$
$71$	−5.70308	+	8.87416i	−0.676831	+	1.05317i	−0.994476	+	0.104960i	$0.966529\pi$
$72$	0.221215	+	2.99183i	0.0260705	+	0.352591i
$73$	16.4385	+	1.56969i	1.92398	+	0.183718i	0.986437	−	0.164141i	$-0.0524854\pi$
$73$	16.4385	+	1.56969i	1.92398	+	0.183718i	0.937547	+	0.347860i	$0.113091\pi$
$74$	−7.45344	+	7.10684i	−0.866445	+	0.826154i
$75$	2.30588	+	0.470059i	0.266261	+	0.0542778i
$76$	4.29704	+	3.72340i	0.492904	+	0.427104i
$77$	1.61974	+	0.411408i	0.184587	+	0.0468842i
$78$	−0.00644508	+	0.602478i	−0.000729761	+	0.0682172i
$79$	−11.8188	−	4.09053i	−1.32972	−	0.460220i	−0.432432	−	0.901667i	$-0.642344\pi$
$79$	−11.8188	−	4.09053i	−1.32972	−	0.460220i	−0.897288	+	0.441446i	$0.854466\pi$
$80$	−0.0907969	−	1.90606i	−0.0101514	−	0.213104i
$81$	−8.16861	+	3.77808i	−0.907623	+	0.419787i
$82$	3.16044	−	9.13148i	0.349012	−	1.00840i
$83$	2.90370	−	0.852603i	0.318723	−	0.0935854i	−0.118458	−	0.992959i	$-0.537795\pi$
$83$	2.90370	−	0.852603i	0.318723	−	0.0935854i	0.437181	+	0.899374i	$0.355977\pi$
$84$	−4.01682	+	2.20571i	−0.438271	+	0.240662i
$85$	6.78061	−	7.82524i	0.735460	−	0.848767i
$86$	3.72717	−	0.355901i	0.401911	−	0.0383778i
$87$	3.67582	+	7.32134i	0.394089	+	0.784930i
$88$	0.0600416	−	0.628784i	0.00640046	−	0.0670286i
$89$	−0.199393	+	0.156804i	−0.0211356	+	0.0166212i	−0.628671	−	0.777671i	$-0.716401\pi$
$89$	−0.199393	+	0.156804i	−0.0211356	+	0.0166212i	0.607535	+	0.794293i	$0.292158\pi$
$90$	5.25703	−	2.26617i	0.554139	−	0.238875i
$91$	−0.841240	+	0.373319i	−0.0881859	+	0.0391344i
$92$	−0.833878	−	4.72278i	−0.0869378	−	0.492384i
$93$	−0.954838	−	4.12814i	−0.0990121	−	0.428069i
$94$	−3.70045	+	1.90772i	−0.381672	+	0.196766i
$95$	4.03245	−	10.0726i	0.413721	−	1.03342i
$96$	1.05606	+	1.37286i	0.107783	+	0.140117i
$97$	−0.162509	+	0.553456i	−0.0165003	+	0.0561949i	−0.967332	−	0.253514i	$-0.918414\pi$
$97$	−0.162509	+	0.553456i	−0.0165003	+	0.0561949i	0.950831	+	0.309709i	$0.100232\pi$
$98$	−5.61354	−	4.18189i	−0.567053	−	0.422435i
$99$	1.82918	−	0.494846i	0.183839	−	0.0497339i
$100$	1.26136	−	0.504971i	0.126136	−	0.0504971i
$101$	6.68692	+	1.62223i	0.665374	+	0.161418i	0.554201	−	0.832383i	$-0.313024\pi$
$101$	6.68692	+	1.62223i	0.665374	+	0.161418i	0.111173	+	0.993801i	$0.464539\pi$
$102$	−0.993397	+	9.34569i	−0.0983609	+	0.925361i
$103$	−5.91300	+	11.4696i	−0.582625	+	1.13013i	0.394783	+	0.918774i	$0.370820\pi$
$103$	−5.91300	+	11.4696i	−0.582625	+	1.13013i	−0.977408	+	0.211360i	$0.932211\pi$
$104$	0.188068	+	0.292639i	0.0184416	+	0.0286956i
$105$	6.48446	+	5.86680i	0.632819	+	0.572541i
$106$	−2.43344	−	8.28755i	−0.236357	−	0.804958i
$107$	−17.6041	+	7.04760i	−1.70185	+	0.681318i	−0.999533	−	0.0305482i	$-0.990275\pi$
$107$	−17.6041	+	7.04760i	−1.70185	+	0.681318i	−0.702316	+	0.711866i	$0.747850\pi$
$108$	−2.74113	+	4.41432i	−0.263765	+	0.424768i
$109$	−3.33760	+	2.37669i	−0.319684	+	0.227646i	−0.728622	−	0.684916i	$-0.759839\pi$
$109$	−3.33760	+	2.37669i	−0.319684	+	0.227646i	0.408938	+	0.912562i	$0.365899\pi$
$110$	−1.17134	+	0.284165i	−0.111683	+	0.0270940i
$111$	−17.6823	+	2.34955i	−1.67833	+	0.223010i
$112$	−1.23753	+	2.33849i	−0.116936	+	0.220966i
$113$	−15.0173	−	9.65103i	−1.41271	−	0.907893i	−0.412713	−	0.910861i	$-0.635419\pi$
$113$	−15.0173	−	9.65103i	−1.41271	−	0.907893i	−0.999996	+	0.00296834i	$0.999055\pi$
$114$	2.21927	+	9.59477i	0.207853	+	0.898633i
$115$	−7.99602	+	4.45128i	−0.745633	+	0.415084i
$116$	4.09615	+	2.36491i	0.380318	+	0.219576i
$117$	−0.623384	+	0.836933i	−0.0576319	+	0.0773745i
$118$	−0.903866	−	6.28653i	−0.0832076	−	0.578722i
$119$	−13.6163	+	4.54953i	−1.24820	+	0.417055i
$120$	1.81653	−	2.76119i	0.165826	−	0.252061i
$121$	10.5530	−	1.00769i	0.959366	−	0.0916083i
$122$	−3.91184	−	11.3025i	−0.354161	−	1.02328i
$123$	13.7364	−	9.56184i	1.23857	−	0.862162i
$124$	−1.77048	−	1.68815i	−0.158994	−	0.151600i
$125$	−7.94594	−	9.17011i	−0.710707	−	0.820199i
$126$	−7.87300	−	1.00793i	−0.701382	−	0.0897931i
$127$	9.31702	−	5.98768i	0.826752	−	0.531321i	−0.0574926	−	0.998346i	$-0.518311\pi$
$127$	9.31702	−	5.98768i	0.826752	−	0.531321i	0.884244	+	0.467025i	$0.154674\pi$
$128$	0.945001	+	0.327068i	0.0835271	+	0.0289090i
$129$	5.58118	+	3.30240i	0.491395	+	0.290760i
$130$	0.410332	−	0.521779i	0.0359885	−	0.0457631i
$131$	−2.38263	+	12.3623i	−0.208171	+	1.08010i	0.715995	+	0.698106i	$0.245973\pi$
$131$	−2.38263	+	12.3623i	−0.208171	+	1.08010i	−0.924166	+	0.381990i	$0.875239\pi$
$132$	0.725247	−	0.819109i	0.0631247	−	0.0712943i
$133$	−11.9239	+	9.17160i	−1.03393	+	0.795279i
$134$	−4.65002	−	10.1821i	−0.401701	−	0.879602i
$135$	9.67101	+	2.18794i	0.832348	+	0.188308i
$136$	2.48640	+	4.82294i	0.213207	+	0.413564i
$137$	5.40254	−	9.35747i	0.461570	−	0.799463i	−0.537469	−	0.843283i	$-0.680620\pi$
$137$	5.40254	−	9.35747i	0.461570	−	0.799463i	0.999039	+	0.0438205i	$0.0139530\pi$
$138$	3.64845	−	7.46249i	0.310577	−	0.635250i
$139$	8.22880			0.697957			0.348979	−	0.937131i	$-0.386529\pi$
$139$	8.22880			0.697957			0.348979	+	0.937131i	$0.386529\pi$
$140$	4.98929	+	0.772113i	0.421672	+	0.0652554i
$141$	−7.12619	−	1.10252i	−0.600134	−	0.0928490i
$142$	−6.11887	+	8.59275i	−0.513484	+	0.721088i
$143$	0.159022	−	0.151627i	0.0132981	−	0.0126797i
$144$	0.0786075	+	2.99897i	0.00655062	+	0.249914i
$145$	1.70810	−	8.86245i	0.141850	−	0.735987i
$146$	16.3452	+	2.35009i	1.35274	+	0.194495i
$147$	−3.59491	−	11.5791i	−0.296503	−	0.955032i
$148$	−7.78316	+	6.74414i	−0.639772	+	0.554365i
$149$	−0.902224	−	0.465129i	−0.0739131	−	0.0381049i	0.420874	−	0.907119i	$-0.361724\pi$
$149$	−0.902224	−	0.465129i	−0.0739131	−	0.0381049i	−0.494787	+	0.869014i	$0.664754\pi$
$150$	2.28091	+	0.579245i	0.186235	+	0.0472952i
$151$	2.10499	−	0.405704i	0.171302	−	0.0330158i	−0.102879	−	0.994694i	$-0.532805\pi$
$151$	2.10499	−	0.405704i	0.171302	−	0.0330158i	0.274181	+	0.961678i	$0.411593\pi$
$152$	4.11500	+	3.92365i	0.333771	+	0.318250i
$153$	−10.9208	+	12.0715i	−0.882897	+	0.975926i
$154$	1.59833	+	0.488012i	0.128797	+	0.0393251i
$155$	−1.93920	+	4.24626i	−0.155760	+	0.341068i
$156$	−0.0351049	+	0.601489i	−0.00281064	+	0.0481577i
$157$	−0.424785	+	4.44854i	−0.0339015	+	0.355033i	0.962566	+	0.271049i	$0.0873705\pi$
$157$	−0.424785	+	4.44854i	−0.0339015	+	0.355033i	−0.996467	+	0.0839838i	$0.973236\pi$
$158$	−11.6108	−	4.64826i	−0.923704	−	0.369795i
$159$	5.04404	−	14.0845i	0.400018	−	1.11697i
$160$		−	1.90822i		−	0.150858i
$161$	12.6842	+	0.334585i	0.999652	+	0.0263690i
$162$	−8.33912	+	3.38512i	−0.655183	+	0.265960i
$163$	0.295030	−	6.19345i	0.0231086	−	0.485109i	−0.957416	−	0.288712i	$-0.906773\pi$
$163$	0.295030	−	6.19345i	0.0231086	−	0.485109i	0.980525	−	0.196397i	$-0.0629240\pi$
$164$	3.59135	−	8.97076i	0.280437	−	0.700499i
$165$	−1.92972	−	0.796597i	−0.150228	−	0.0620150i
$166$	2.94098	−	0.713474i	0.228264	−	0.0553763i
$167$	13.5673	+	6.19598i	1.04987	+	0.479460i	0.864198	−	0.503152i	$-0.167826\pi$
$167$	13.5673	+	6.19598i	1.04987	+	0.479460i	0.185672	+	0.982612i	$0.440554\pi$
$168$	−4.11722	+	2.01208i	−0.317651	+	0.155235i
$169$	1.83287	−	12.7479i	0.140990	−	0.980608i
$170$	7.14527	−	7.49374i	0.548017	−	0.574744i
$171$	−6.67691	+	15.6963i	−0.510596	+	1.20033i
$172$	3.73988	−	0.178152i	0.285163	−	0.0135840i
$173$	−2.36323	+	4.58402i	−0.179673	+	0.348516i	−0.961423	−	0.275076i	$-0.911297\pi$
$173$	−2.36323	+	4.58402i	−0.179673	+	0.348516i	0.781750	+	0.623592i	$0.214327\pi$
$174$	3.32329	+	7.48795i	0.251938	+	0.567660i
$175$	0.642373	+	3.53688i	0.0485589	+	0.267363i
$176$	0.0898924	−	0.625215i	0.00677589	−	0.0471274i
$177$	5.14505	−	9.72320i	0.386726	−	0.730841i
$178$	−0.206628	+	0.147139i	−0.0154874	+	0.0110285i
$179$	5.03294	+	5.27840i	0.376180	+	0.394526i	0.884422	−	0.466688i	$-0.154553\pi$
$179$	5.03294	+	5.27840i	0.376180	+	0.394526i	−0.508242	+	0.861214i	$0.669704\pi$
$180$	5.35890	−	2.01346i	0.399429	−	0.150075i
$181$	10.4603	−	1.50396i	0.777505	−	0.111788i	0.257873	−	0.966179i	$-0.416978\pi$
$181$	10.4603	−	1.50396i	0.777505	−	0.111788i	0.519632	+	0.854390i	$0.326069\pi$
$182$	−0.858050	+	0.332868i	−0.0636029	+	0.0246738i
$183$	6.04863	−	19.8132i	0.447127	−	1.46463i
$184$	−0.608214	−	4.75711i	−0.0448382	−	0.350699i
$185$	17.0191	+	9.82601i	1.25127	+	0.722422i
$186$	−0.757331	−	4.16890i	−0.0555302	−	0.305679i
$187$	2.69411	−	2.11867i	0.197013	−	0.154932i
$188$	−3.78703	+	1.72948i	−0.276198	+	0.126135i
$189$	−9.99486	−	9.43943i	−0.727019	−	0.686618i
$190$	4.50716	−	9.86930i	0.326984	−	0.715994i
$191$	0.964589	+	0.185909i	0.0697952	+	0.0134519i	0.224029	−	0.974582i	$-0.428079\pi$
$191$	0.964589	+	0.185909i	0.0697952	+	0.0134519i	−0.154234	+	0.988034i	$0.549291\pi$
$192$	0.989538	+	1.42155i	0.0714138	+	0.102592i
$193$	3.22277	−	13.2844i	0.231980	−	0.956235i	−0.730072	−	0.683370i	$-0.760514\pi$
$193$	3.22277	−	13.2844i	0.231980	−	0.956235i	0.962052	−	0.272865i	$-0.0879712\pi$
$194$	−0.188660	+	0.545096i	−0.0135450	+	0.0391356i
$195$	1.10656	−	0.312097i	0.0792423	−	0.0223497i
$196$	−5.40820	−	4.44426i	−0.386300	−	0.317447i
$197$	−3.01039	+	2.60851i	−0.214481	+	0.185849i	−0.755475	−	0.655178i	$-0.772594\pi$
$197$	−3.01039	+	2.60851i	−0.214481	+	0.185849i	0.540994	+	0.841027i	$0.318048\pi$
$198$	1.85065	−	0.407250i	0.131520	−	0.0289420i
$199$	3.54567	−	4.50869i	0.251346	−	0.319613i	−0.643964	−	0.765056i	$-0.722711\pi$
$199$	3.54567	−	4.50869i	0.251346	−	0.319613i	0.895310	+	0.445443i	$0.146954\pi$
$200$	1.28396	−	0.444382i	0.0907894	−	0.0314225i
$201$	3.87264	−	18.9973i	0.273155	−	1.33997i
$202$	6.60216	+	1.93857i	0.464526	+	0.136397i
$203$	−8.29594	+	9.36887i	−0.582261	+	0.657566i
$204$	−1.43696	+	9.28784i	−0.100607	+	0.650279i
$205$	−18.4182	−	0.877365i	−1.28638	−	0.0612778i
$206$	−6.45204	+	11.1753i	−0.449535	+	0.778618i
$207$	12.7177	−	6.72753i	0.883943	−	0.467596i
$208$	0.173930	+	0.301256i	0.0120599	+	0.0208884i
$209$	1.94166	−	3.02128i	0.134307	−	0.208986i
$210$	6.19797	+	6.16870i	0.427700	+	0.425681i
$211$	−11.9332	−	26.1300i	−0.821514	−	1.79887i	−0.546593	−	0.837398i	$-0.684076\pi$
$211$	−11.9332	−	26.1300i	−0.821514	−	1.79887i	−0.274921	−	0.961467i	$-0.588652\pi$
$212$	−2.03635	−	8.39395i	−0.139857	−	0.576499i
$213$	−17.3290	+	5.79081i	−1.18736	+	0.396780i
$214$	−17.9195	+	6.20199i	−1.22495	+	0.423959i
$215$	−2.65539	−	6.63284i	−0.181096	−	0.452356i
$216$	−2.94806	+	4.27889i	−0.200590	+	0.291142i
$217$	5.31220	−	3.69750i	0.360616	−	0.251003i
$218$	−3.44690	+	2.21519i	−0.233454	+	0.150032i
$219$	20.4878	+	19.9578i	1.38444	+	1.34863i
$220$	−1.18354	+	0.228108i	−0.0797940	+	0.0153790i
$221$	−0.445004	+	1.83433i	−0.0299342	+	0.123391i
$222$	−17.7740	+	1.50554i	−1.19292	+	0.101045i
$223$	−1.13345	+	1.30807i	−0.0759014	+	0.0875949i	−0.792430	−	0.609963i	$-0.791184\pi$
$223$	−1.13345	+	1.30807i	−0.0759014	+	0.0875949i	0.716529	+	0.697558i	$0.245730\pi$
$224$	−1.34740	+	2.27695i	−0.0900269	+	0.152135i
$225$	2.60273	+	3.13687i	0.173516	+	0.209125i
$226$	−14.5411	−	10.3547i	−0.967258	−	0.688781i
$227$	−0.00136845		0.000547845i	−9.08273e−5		3.63618e-5i	0.371617	−	0.928386i	$-0.378803\pi$
$227$	−0.00136845		0.000547845i	−9.08273e−5		3.63618e-5i	−0.371708	+	0.928350i	$0.621228\pi$
$228$	1.76022	+	9.68950i	0.116573	+	0.641703i
$229$	8.79353	−	5.07695i	0.581093	−	0.335494i	−0.180475	−	0.983580i	$-0.557763\pi$
$229$	8.79353	−	5.07695i	0.581093	−	0.335494i	0.761567	+	0.648086i	$0.224430\pi$
$230$	−8.19877	+	4.06578i	−0.540611	+	0.268089i
$231$	1.74012	+	2.31310i	0.114492	+	0.152191i
$232$	3.97898	+	2.55713i	0.261233	+	0.167884i
$233$	4.59732	+	5.84596i	0.301180	+	0.382982i	0.912962	−	0.408045i	$-0.133789\pi$
$233$	4.59732	+	5.84596i	0.301180	+	0.382982i	−0.611782	+	0.791027i	$0.709547\pi$
$234$	−0.662501	+	0.806323i	−0.0433091	+	0.0527110i
$235$	5.48228	+	5.74965i	0.357625	+	0.375066i
$236$	−0.603717	−	6.32241i	−0.0392986	−	0.411554i
$237$	−11.5158	−	18.3476i	−0.748035	−	1.19181i
$238$	−13.8173	+	3.89649i	−0.895643	+	0.252572i
$239$	−0.985158	−	3.35514i	−0.0637246	−	0.217026i	0.921475	−	0.388438i	$-0.126985\pi$
$239$	−0.985158	−	3.35514i	−0.0637246	−	0.217026i	−0.985199	+	0.171412i	$0.945167\pi$
$240$	1.94586	−	2.67163i	0.125605	−	0.172453i
$241$	21.0428	−	1.00239i	1.35549	−	0.0645698i	0.642790	−	0.766043i	$-0.277777\pi$
$241$	21.0428	−	1.00239i	1.35549	−	0.0645698i	0.712696	+	0.701473i	$0.247474\pi$
$242$	10.5890	−	0.504417i	0.680688	−	0.0324252i
$243$	−15.1271	−	3.76422i	−0.970407	−	0.241475i
$244$	−3.36961	−	11.4758i	−0.215717	−	0.734666i
$245$	−4.63885	+	12.5262i	−0.296365	+	0.800269i
$246$	14.1758	−	8.89741i	0.903815	−	0.567278i
$247$	0.188008	+	1.96891i	0.0119627	+	0.125279i
$248$	−1.68815	−	1.77048i	−0.107197	−	0.112425i
$249$	4.84509	+	2.00008i	0.307045	+	0.126750i
$250$	−7.50061	−	9.53780i	−0.474380	−	0.603224i
$251$	13.5074	+	8.68070i	0.852582	+	0.547921i	0.892379	−	0.451287i	$-0.149035\pi$
$251$	13.5074	+	8.68070i	0.852582	+	0.547921i	−0.0397971	+	0.999208i	$0.512671\pi$
$252$	−7.81612	−	1.38140i	−0.492369	−	0.0870198i
$253$	−2.87779	+	0.945895i	−0.180925	+	0.0594679i
$254$	9.59137	−	5.53758i	0.601816	−	0.347459i
$255$	17.6453	−	3.20549i	1.10499	−	0.200735i
$256$	0.928368	+	0.371662i	0.0580230	+	0.0232289i
$257$	14.6945	+	10.4639i	0.916615	+	0.652718i	0.937844	−	0.347056i	$-0.112819\pi$
$257$	14.6945	+	10.4639i	0.916615	+	0.652718i	−0.0212296	+	0.999775i	$0.506758\pi$
$258$	5.41772	+	3.56422i	0.337293	+	0.221899i
$259$	−13.3696	−	23.7419i	−0.830748	−	1.47525i
$260$	0.434694	−	0.501664i	0.0269586	−	0.0311119i
$261$	−2.98283	+	13.8724i	−0.184632	+	0.858680i
$262$	−2.96815	+	12.2349i	−0.183373	+	0.755874i
$263$	−14.0377	+	2.70554i	−0.865599	+	0.166831i	−0.602676	−	0.797986i	$-0.705899\pi$
$263$	−14.0377	+	2.70554i	−0.865599	+	0.166831i	−0.262923	+	0.964817i	$0.584687\pi$
$264$	0.763401	−	0.783673i	0.0469841	−	0.0482317i
$265$	−13.8657	+	8.91091i	−0.851760	+	0.547393i
$266$	−12.3468	+	8.59385i	−0.757031	+	0.526923i
$267$	−0.439332	−	0.00469980i	−0.0268867	−	0.000287623i
$268$	−4.16027	−	10.3919i	−0.254129	−	0.634783i
$269$	−24.9378	+	8.63104i	−1.52048	+	0.526244i	−0.954510	−	0.298180i	$-0.903620\pi$
$269$	−24.9378	+	8.63104i	−1.52048	+	0.526244i	−0.565973	+	0.824424i	$0.691499\pi$
$270$	9.55595	+	2.64562i	0.581557	+	0.161008i
$271$	−5.32630	−	21.9553i	−0.323550	−	1.33369i	−0.868695	−	0.495348i	$-0.835041\pi$
$271$	−5.32630	−	21.9553i	−0.323550	−	1.33369i	0.545145	−	0.838342i	$-0.316474\pi$
$272$	2.25410	+	4.93579i	0.136675	+	0.299276i
$273$	−1.54075	−	0.408938i	−0.0932506	−	0.0247501i
$274$	5.84167	−	9.08981i	0.352908	−	0.549135i
$275$	−0.429102	−	0.743227i	−0.0258758	−	0.0448183i
$276$	3.99940	−	7.28044i	0.240735	−	0.438231i
$277$	1.33932	−	2.31977i	0.0804718	−	0.139381i	−0.822981	−	0.568069i	$-0.807691\pi$
$277$	1.33932	−	2.31977i	0.0804718	−	0.139381i	0.903453	+	0.428688i	$0.141024\pi$
$278$	8.21947	+	0.391542i	0.492971	+	0.0234831i
$279$	3.19082	−	6.60898i	0.191029	−	0.395669i
$280$	4.94690	+	1.00864i	0.295634	+	0.0602777i
$281$	−22.4394	−	6.58880i	−1.33862	−	0.393055i	−0.467444	−	0.884023i	$-0.654825\pi$
$281$	−22.4394	−	6.58880i	−1.33862	−	0.393055i	−0.871178	+	0.490968i	$0.836643\pi$
$282$	−7.06566	−	1.44035i	−0.420754	−	0.0857716i
$283$	−14.8116	+	5.12636i	−0.880460	+	0.304730i	−0.729640	−	0.683831i	$-0.760313\pi$
$283$	−14.8116	+	5.12636i	−0.880460	+	0.304730i	−0.150820	+	0.988561i	$0.548191\pi$
$284$	−6.52080	+	8.29187i	−0.386938	+	0.492032i
$285$	16.3742	−	9.22155i	0.969926	−	0.546237i
$286$	0.166057	−	0.143889i	0.00981913	−	0.00850833i
$287$	21.3576	+	14.0520i	1.26070	+	0.829462i
$288$	−0.0641783	+	2.99931i	−0.00378174	+	0.176736i
$289$	−4.06969	+	11.7586i	−0.239393	+	0.691681i
$290$	2.12786	−	8.77114i	0.124952	−	0.515059i
$291$	−0.819982	+	0.570787i	−0.0480682	+	0.0334601i
$292$	16.2149	+	3.12516i	0.948904	+	0.182886i
$293$	0.982919	−	2.15229i	0.0574227	−	0.125738i	−0.878745	−	0.477291i	$-0.841619\pi$
$293$	0.982919	−	2.15229i	0.0574227	−	0.125738i	0.936168	+	0.351553i	$0.114346\pi$
$294$	−3.03988	−	11.7371i	−0.177290	−	0.684521i
$295$	−11.0242	+	5.03460i	−0.641856	+	0.293126i
$296$	−8.09524	+	6.36617i	−0.470526	+	0.370026i
$297$	3.00631	+	1.31698i	0.174444	+	0.0764189i
$298$	−0.879071	−	0.507532i	−0.0509232	−	0.0294005i
$299$	0.923774	−	1.38918i	0.0534233	−	0.0803381i
$300$	2.25076	+	0.687119i	0.129948	+	0.0396708i
$301$	−1.51496	+	9.78949i	−0.0873209	+	0.564257i
$302$	2.12191	−	0.305085i	0.122102	−	0.0175557i
$303$	7.26661	+	9.44649i	0.417456	+	0.542686i
$304$	3.92365	+	4.11500i	0.225037	+	0.236012i
$305$	−18.5910	+	13.2386i	−1.06452	+	0.758041i
$306$	−11.4828	+	11.5382i	−0.656431	+	0.659596i
$307$	−3.34037	+	23.2328i	−0.190645	+	1.32596i	0.639661	+	0.768657i	$0.279075\pi$
$307$	−3.34037	+	23.2328i	−0.190645	+	1.32596i	−0.830306	+	0.557308i	$0.811834\pi$
$308$	1.57330	+	0.563511i	0.0896472	+	0.0321090i
$309$	−20.4289	+	9.06674i	−1.16216	+	0.515789i
$310$	−2.13905	+	4.14918i	−0.121490	+	0.235657i
$311$	0.732051	−	0.0348719i	0.0415108	−	0.00197740i	−0.0268162	−	0.999640i	$-0.508537\pi$
$311$	0.732051	−	0.0348719i	0.0415108	−	0.00197740i	0.0683271	+	0.997663i	$0.478234\pi$
$312$	−0.0636851	+	0.599138i	−0.00360546	+	0.0339195i
$313$	1.33469	−	1.39978i	0.0754409	−	0.0791201i	−0.684932	−	0.728607i	$-0.740168\pi$
$313$	1.33469	−	1.39978i	0.0754409	−	0.0791201i	0.760372	+	0.649487i	$0.225016\pi$
$314$	−0.635974	+	4.42329i	−0.0358901	+	0.249621i
$315$	2.38715	+	14.9568i	0.134501	+	0.842718i
$316$	−11.3765	−	5.19545i	−0.639976	−	0.292267i
$317$	−5.48823	+	1.33143i	−0.308250	+	0.0747805i	−0.386900	−	0.922122i	$-0.626454\pi$
$317$	−5.48823	+	1.33143i	−0.308250	+	0.0747805i	0.0786503	+	0.996902i	$0.474939\pi$
$318$	5.70849	−	13.8285i	0.320116	−	0.775466i
$319$	1.11037	−	2.77356i	0.0621685	−	0.155289i
$320$	0.0907969	−	1.90606i	0.00507570	−	0.106552i
$321$	−31.4126	−	9.58974i	−1.75328	−	0.535247i
$322$	12.6539	+	0.937743i	0.705173	+	0.0522584i
$323$			30.8519i			1.71665i
$324$	−8.49075	+	2.98450i	−0.471708	+	0.165805i
$325$	0.438777	+	0.175660i	0.0243390	+	0.00974386i
$326$	0.589393	−	6.17240i	0.0326434	−	0.341858i
$327$	−7.08475	−	0.413489i	−0.391788	−	0.0228660i
$328$	4.01413	−	8.78971i	0.221643	−	0.485331i
$329$	−2.48180	−	10.7317i	−0.136826	−	0.591659i
$330$	−1.88963	−	0.887515i	−0.104021	−	0.0488561i
$331$	−10.1734	−	9.70035i	−0.559182	−	0.533179i	0.356914	−	0.934137i	$-0.383829\pi$
$331$	−10.1734	−	9.70035i	−0.559182	−	0.533179i	−0.916096	+	0.400958i	$0.868677\pi$
$332$	2.97160	−	0.572728i	0.163088	−	0.0314326i
$333$	−26.4199	−	16.0167i	−1.44780	−	0.877712i
$334$	13.2571	+	6.83452i	0.725398	+	0.373969i
$335$	−16.1428	+	13.9879i	−0.881978	+	0.764238i
$336$	−4.20830	+	1.81390i	−0.229582	+	0.0989561i
$337$	−25.9099	−	3.72528i	−1.41140	−	0.202929i	−0.605909	−	0.795534i	$-0.707190\pi$
$337$	−25.9099	−	3.72528i	−1.41140	−	0.202929i	−0.805493	+	0.592605i	$0.798099\pi$
$338$	2.43737	−	12.6463i	0.132575	−	0.687865i
$339$	−9.79949	−	29.3250i	−0.532235	−	1.59271i
$340$	7.49374	−	7.14527i	0.406405	−	0.387507i
$341$	−0.896302	+	1.25868i	−0.0485375	+	0.0681614i
$342$	−7.41620	+	15.3608i	−0.401022	+	0.830617i
$343$	14.3800	−	11.6712i	0.776446	−	0.630183i
$344$	3.74412			0.201870
$345$	−15.6247	−	2.66814i	−0.841207	−	0.143648i
$346$	−2.57866	+	4.46638i	−0.138630	+	0.240114i
$347$	3.06830	+	5.95168i	0.164715	+	0.319503i	0.956719	−	0.291013i	$-0.0939924\pi$
$347$	3.06830	+	5.95168i	0.164715	+	0.319503i	−0.792004	+	0.610516i	$0.790962\pi$
$348$	2.96324	+	7.63759i	0.158846	+	0.409418i
$349$	0.930448	+	2.03740i	0.0498057	+	0.109059i	0.932899	−	0.360138i	$-0.117270\pi$
$349$	0.930448	+	2.03740i	0.0498057	+	0.109059i	−0.883093	+	0.469198i	$0.844543\pi$
$350$	0.473354	+	3.56344i	0.0253019	+	0.190474i
$351$	−1.74977	+	0.453333i	−0.0933957	+	0.0241971i
$352$	0.119539	−	0.620230i	0.00637147	−	0.0330584i
$353$	15.3904	−	19.5705i	0.819148	−	1.04163i	−0.179179	−	0.983816i	$-0.557344\pi$
$353$	15.3904	−	19.5705i	0.819148	−	1.04163i	0.998327	−	0.0578149i	$-0.0184133\pi$
$354$	5.60187	−	9.46738i	0.297736	−	0.503185i
$355$	19.0223	+	6.58367i	1.00960	+	0.349425i
$356$	−0.213395	+	0.137141i	−0.0113099	+	0.00726844i
$357$	−23.3184	−	8.63450i	−1.23414	−	0.456986i
$358$	4.77609	+	5.51190i	0.252424	+	0.291313i
$359$	19.0830	+	18.1956i	1.00716	+	0.960329i	0.999214	−	0.0396393i	$-0.0126209\pi$
$359$	19.0830	+	18.1956i	1.00716	+	0.960329i	0.00795012	+	0.999968i	$0.497469\pi$
$360$	5.44864	−	1.75620i	0.287168	−	0.0925597i
$361$	4.35925	+	12.5952i	0.229434	+	0.662907i
$362$	10.5200	−	1.00454i	0.552917	−	0.0527972i
$363$	15.3396	+	10.0916i	0.805121	+	0.529674i
$364$	−0.872917	+	0.291663i	−0.0457533	+	0.0152873i
$365$	−4.48449	−	31.1903i	−0.234729	−	1.63258i
$366$	6.98452	−	19.5029i	0.365087	−	1.01943i
$367$	27.9848	+	16.1571i	1.46080	+	0.843391i	0.999048	−	0.0436197i	$-0.0138890\pi$
$367$	27.9848	+	16.1571i	1.46080	+	0.843391i	0.461748	+	0.887011i	$0.347222\pi$
$368$	−0.381173	−	4.78066i	−0.0198700	−	0.249209i
$369$	28.9198	+	1.99848i	1.50551	+	0.104036i
$370$	16.5323	+	10.6247i	0.859475	+	0.552351i
$371$	22.8369	−	0.842233i	1.18564	−	0.0437266i
$372$	−0.558109	−	4.20021i	−0.0289366	−	0.217771i
$373$	−8.95094	+	2.17147i	−0.463462	+	0.112435i	−0.460689	−	0.887562i	$-0.652398\pi$
$373$	−8.95094	+	2.17147i	−0.463462	+	0.112435i	−0.00277265	+	0.999996i	$0.500883\pi$
$374$	2.79187	−	1.98808i	0.144364	−	0.102801i
$375$	−0.775383	−	21.0020i	−0.0400406	−	1.08454i
$376$	−3.86504	+	1.54733i	−0.199324	+	0.0797973i
$377$	0.463540	+	1.57867i	0.0238735	+	0.0813058i
$378$	−9.53439	−	9.90431i	−0.490396	−	0.509423i
$379$	4.34297	+	6.75779i	0.223083	+	0.347124i	0.934696	−	0.355447i	$-0.115671\pi$
$379$	4.34297	+	6.75779i	0.223083	+	0.347124i	−0.711613	+	0.702571i	$0.752035\pi$
$380$	4.97165	−	9.64366i	0.255040	−	0.494709i
$381$	19.0753	+	2.02760i	0.977256	+	0.103877i
$382$	0.954651	+	0.231596i	0.0488442	+	0.0118495i
$383$	0.869233	−	0.347988i	0.0444157	−	0.0177814i	−0.349348	−	0.936993i	$-0.613597\pi$
$383$	0.869233	−	0.347988i	0.0444157	−	0.0177814i	0.393764	+	0.919212i	$0.371173\pi$
$384$	0.920777	+	1.46703i	0.0469882	+	0.0748639i
$385$	0.0342371	−	3.18879i	0.00174488	−	0.162516i
$386$	3.85122	−	13.1160i	0.196022	−	0.667589i
$387$	3.95061	+	10.5147i	0.200821	+	0.534492i
$388$	−0.214383	+	0.535502i	−0.0108836	+	0.0271860i
$389$	16.6264	−	8.57152i	0.842994	−	0.434594i	0.0180696	−	0.999837i	$-0.494248\pi$
$389$	16.6264	−	8.57152i	0.842994	−	0.434594i	0.824924	+	0.565243i	$0.191218\pi$
$390$	1.12016	−	0.259091i	0.0567213	−	0.0131196i
$391$	16.4041	−	20.2013i	0.829591	−	1.02162i
$392$	−5.19060	−	4.69655i	−0.262165	−	0.237212i
$393$	−16.6318	+	14.1029i	−0.838963	+	0.711396i
$394$	−3.13109	+	2.46232i	−0.157742	+	0.124050i
$395$	−2.26856	+	23.7574i	−0.114144	+	1.19537i
$396$	1.86793	−	0.318731i	0.0938673	−	0.0160168i
$397$	6.30501	−	0.602056i	0.316440	−	0.0302163i	0.0643721	−	0.997926i	$-0.479496\pi$
$397$	6.30501	−	0.602056i	0.316440	−	0.0302163i	0.252068	+	0.967710i	$0.418889\pi$
$398$	3.75619	−	4.33487i	0.188281	−	0.217288i
$399$	−26.0496	−	0.558420i	−1.30411	−	0.0279560i
$400$	1.30365	−	0.382785i	0.0651823	−	0.0191393i
$401$	−8.35931	+	24.1526i	−0.417444	+	1.20612i	0.518837	+	0.854873i	$0.326365\pi$
$401$	−8.35931	+	24.1526i	−0.417444	+	1.20612i	−0.936281	+	0.351252i	$0.885756\pi$
$402$	4.77219	−	18.7915i	0.238015	−	0.937236i
$403$	−0.0404910	−	0.850012i	−0.00201700	−	0.0423421i
$404$	6.50244	+	2.25052i	0.323509	+	0.111967i
$405$	10.6811	+	13.4485i	0.530748	+	0.668259i
$406$	−8.73234	+	8.96352i	−0.433379	+	0.444852i
$407$	4.91619	+	4.25990i	0.243686	+	0.211155i
$408$	−1.87726	+	9.20895i	−0.0929384	+	0.455911i
$409$	−18.0125	+	17.1749i	−0.890662	+	0.849245i	−0.989303	−	0.145878i	$-0.953399\pi$
$409$	−18.0125	+	17.1749i	−0.890662	+	0.849245i	0.0986401	+	0.995123i	$0.468551\pi$
$410$	−18.3555	−	1.75274i	−0.906516	−	0.0865618i
$411$	17.4478	−	6.76939i	0.860635	−	0.333909i
$412$	−6.97648	+	10.8556i	−0.343706	+	0.534818i
$413$	16.7094	+	1.77678i	0.822217	+	0.0874297i
$414$	13.0234	−	6.11477i	0.640066	−	0.300525i
$415$	−2.88742	−	5.00115i	−0.141738	−	0.245497i
$416$	0.159399	+	0.309191i	0.00781518	+	0.0151593i
$417$	11.1085	+	8.92977i	0.543985	+	0.437293i
$418$	2.08322	−	2.92547i	0.101893	−	0.143089i
$419$	9.83246	+	2.88707i	0.480347	+	0.141043i	0.512937	−	0.858426i	$-0.328557\pi$
$419$	9.83246	+	2.88707i	0.480347	+	0.141043i	−0.0325901	+	0.999469i	$0.510376\pi$
$420$	5.89743	+	6.45663i	0.287765	+	0.315051i
$421$	2.30902	+	2.00077i	0.112535	+	0.0975117i	0.709310	−	0.704896i	$-0.249006\pi$
$421$	2.30902	+	2.00077i	0.112535	+	0.0975117i	−0.596776	+	0.802408i	$0.703552\pi$
$422$	−10.6763	−	26.6682i	−0.519717	−	1.29819i
$423$	−8.42358	−	9.22159i	−0.409569	−	0.448369i
$424$	−1.63464	−	8.48133i	−0.0793853	−	0.411890i
$425$	6.55285	+	3.37823i	0.317860	+	0.163868i
$426$	−17.5849	+	4.95970i	−0.851992	+	0.240298i
$427$	31.5312	−	2.66959i	1.52590	−	0.129190i
$428$	−18.1943	+	5.34232i	−0.879453	+	0.258231i
$429$	0.379216	−	0.0321212i	0.0183087	−	0.00155083i
$430$	−2.33678	−	6.75167i	−0.112689	−	0.325595i
$431$	21.7431	+	30.5339i	1.04733	+	1.47077i	0.874015	+	0.485899i	$0.161508\pi$
$431$	21.7431	+	30.5339i	1.04733	+	1.47077i	0.173313	+	0.984867i	$0.444553\pi$
$432$	−3.14832	+	4.13377i	−0.151474	+	0.198886i
$433$	−16.5508	+	7.55851i	−0.795382	+	0.363239i	−0.771300	−	0.636471i	$-0.780393\pi$
$433$	−16.5508	+	7.55851i	−0.795382	+	0.363239i	−0.0240816	+	0.999710i	$0.507666\pi$
$434$	5.48212	−	3.44055i	0.263150	−	0.165151i
$435$	11.9233	−	10.1103i	0.571676	−	0.484751i
$436$	−3.54840	+	2.04867i	−0.169938	+	0.0981136i
$437$	9.32033	−	25.6258i	0.445852	−	1.22585i
$438$	19.5150	+	20.9101i	0.932462	+	0.999123i
$439$	−0.844318	+	17.7244i	−0.0402971	+	0.845940i	0.884745	+	0.466075i	$0.154332\pi$
$439$	−0.844318	+	17.7244i	−0.0402971	+	0.845940i	−0.925042	+	0.379865i	$0.875971\pi$
$440$	−1.19305	+	0.171535i	−0.0568764	+	0.00817760i
$441$	7.71255	−	19.5324i	0.367264	−	0.930117i
$442$	−0.531782	+	1.81108i	−0.0252943	+	0.0861444i
$443$	3.49283	+	36.5786i	0.165949	+	1.73790i	0.568660	+	0.822573i	$0.307462\pi$
$443$	3.49283	+	36.5786i	0.165949	+	1.73790i	−0.402710	+	0.915328i	$0.631932\pi$
$444$	−17.8255	+	0.658109i	−0.845963	+	0.0312325i
$445$	0.380486	+	0.299217i	0.0180367	+	0.0141843i
$446$	−1.19441	+	1.25266i	−0.0565568	+	0.0593151i
$447$	−0.713209	−	1.60698i	−0.0337336	−	0.0760077i
$448$	−1.45421	+	2.21026i	−0.0687052	+	0.104425i
$449$	−15.1452	−	23.5664i	−0.714747	−	1.11217i	−0.988625	−	0.150404i	$-0.951943\pi$
$449$	−15.1452	−	23.5664i	−0.714747	−	1.11217i	0.273877	−	0.961765i	$-0.411694\pi$
$450$	2.45053	+	3.25716i	0.115519	+	0.153544i
$451$	−5.93149	−	1.43896i	−0.279303	−	0.0677581i
$452$	−14.0319	−	11.0348i	−0.660006	−	0.519034i
$453$	3.28191	+	1.73663i	0.154197	+	0.0815939i
$454$	−0.00134083		0.000612338i	−6.29284e−5		2.87385e-5i
$455$	1.07075	+	1.39207i	0.0501976	+	0.0652614i
$456$	1.29718	+	9.76228i	0.0607458	+	0.457161i
$457$	16.9037	+	21.4948i	0.790723	+	1.00549i	0.999620	+	0.0275488i	$0.00877016\pi$
$457$	16.9037	+	21.4948i	0.790723	+	1.00549i	−0.208897	+	0.977938i	$0.566987\pi$
$458$	9.02514	−	4.65278i	0.421717	−	0.217410i
$459$	−27.8425	+	4.44488i	−1.29957	+	0.207469i
$460$	−8.38294	+	3.67106i	−0.390856	+	0.171164i
$461$		−	33.8300i		−	1.57562i	−0.615917	−	0.787811i	$-0.711214\pi$
$461$		−	33.8300i		−	1.57562i	0.615917	−	0.787811i	$-0.288786\pi$
$462$	1.62809	+	2.39328i	0.0757456	+	0.111345i
$463$	1.34286	+	9.33979i	0.0624080	+	0.434057i	0.996940	+	0.0781766i	$0.0249098\pi$
$463$	1.34286	+	9.33979i	0.0624080	+	0.434057i	−0.934532	+	0.355880i	$0.884181\pi$
$464$	3.85280	+	2.74357i	0.178862	+	0.127367i
$465$	−7.22581	+	3.62786i	−0.335089	+	0.168238i
$466$	4.31395	+	6.05809i	0.199840	+	0.280636i
$467$	−37.9482	−	7.31392i	−1.75603	−	0.338448i	−0.793286	−	0.608850i	$-0.791631\pi$
$467$	−37.9482	−	7.31392i	−1.75603	−	0.338448i	−0.962747	+	0.270402i	$0.912843\pi$
$468$	−0.700117	+	0.773887i	−0.0323629	+	0.0357729i
$469$	29.1390	−	5.29227i	1.34551	−	0.244374i
$470$	5.20249	+	6.00400i	0.239973	+	0.276944i
$471$	−5.40093	+	5.54436i	−0.248862	+	0.255470i
$472$	−0.302201	−	6.34398i	−0.0139099	−	0.292005i
$473$	−0.447570	−	2.32222i	−0.0205793	−	0.106776i
$474$	−10.6298	−	18.8748i	−0.488242	−	0.866947i
$475$	7.64656	+	1.09941i	0.350848	+	0.0504444i
$476$	−13.9871	+	3.23462i	−0.641096	+	0.148259i
$477$	22.0935	−	13.5397i	1.01159	−	0.619940i
$478$	−0.824398	−	3.39822i	−0.0377071	−	0.155431i
$479$	−14.8991	−	1.42269i	−0.680756	−	0.0650043i	−0.251051	−	0.967974i	$-0.580776\pi$
$479$	−14.8991	−	1.42269i	−0.680756	−	0.0650043i	−0.429705	+	0.902970i	$0.641382\pi$
$480$	2.07078	−	2.57601i	0.0945176	−	0.117578i
$481$	−3.57842	−	0.170461i	−0.163162	−	0.00777236i
$482$	21.0667			0.959560
$483$	16.7599	+	14.2163i	0.762604	+	0.646866i
$484$	10.6010			0.481865
$485$	1.09946	+	0.0523736i	0.0499238	+	0.00237816i
$486$	−14.9309	−	4.47974i	−0.677280	−	0.203205i
$487$	7.55355	+	0.721276i	0.342284	+	0.0326842i	0.264783	−	0.964308i	$-0.414700\pi$
$487$	7.55355	+	0.721276i	0.342284	+	0.0326842i	0.0775012	+	0.996992i	$0.475306\pi$
$488$	−2.81975	−	11.6232i	−0.127644	−	0.526157i
$489$	7.11932	−	8.04071i	0.321947	−	0.363613i
$490$	−5.22962	+	12.2913i	−0.236250	+	0.555264i
$491$	29.1153	+	4.18615i	1.31396	+	0.188918i	0.763425	−	0.645897i	$-0.223516\pi$
$491$	29.1153	+	4.18615i	1.31396	+	0.188918i	0.550530	+	0.834815i	$0.314426\pi$
$492$	14.5831	−	8.21282i	0.657456	−	0.370263i
$493$	4.85707	+	25.2009i	0.218751	+	1.13499i
$494$	0.0941107	+	1.97563i	0.00423424	+	0.0888876i
$495$	−1.74057	−	3.16947i	−0.0782329	−	0.142457i
$496$	−1.60199	−	1.84880i	−0.0719316	−	0.0830134i
$497$	−18.0492	−	21.2875i	−0.809619	−	0.954874i
$498$	4.74444	+	2.22835i	0.212603	+	0.0998548i
$499$	11.8212	+	2.27835i	0.529190	+	0.101993i	0.446846	−	0.894611i	$-0.352547\pi$
$499$	11.8212	+	2.27835i	0.529190	+	0.101993i	0.0823441	+	0.996604i	$0.473759\pi$
$500$	−7.03829	−	9.88389i	−0.314762	−	0.442021i
$501$	11.5914	+	23.0873i	0.517867	+	1.03147i
$502$	13.0791	+	9.31358i	0.583749	+	0.415685i
$503$	−0.789341	−	5.48999i	−0.0351950	−	0.244787i	0.964628	−	0.263616i	$-0.0849152\pi$
$503$	−0.789341	−	5.48999i	−0.0351950	−	0.244787i	−0.999823	+	0.0188294i	$0.994006\pi$
$504$	−7.74154	−	1.75174i	−0.344836	−	0.0780286i
$505$		−	13.1303i		−	0.584289i
$506$	−2.91954	+	0.807892i	−0.129789	+	0.0359152i
$507$	16.3081	−	15.2201i	0.724269	−	0.675947i
$508$	9.84399	−	5.07493i	0.436757	−	0.225164i
$509$	−14.4565	−	18.3829i	−0.640772	−	0.814807i	0.351851	−	0.936056i	$-0.385553\pi$
$509$	−14.4565	−	18.3829i	−0.640772	−	0.814807i	−0.992622	+	0.121249i	$0.961310\pi$
$510$	17.7779	−	2.36226i	0.787218	−	0.104603i
$511$	−16.6725	+	40.3838i	−0.737547	+	1.78647i
$512$	0.909632	+	0.415415i	0.0402004	+	0.0183589i
$513$	−26.0469	+	13.9436i	−1.15000	+	0.615624i
$514$	14.1799	+	11.1512i	0.625449	+	0.491859i
$515$	23.9298	+	5.80530i	1.05447	+	0.255812i
$516$	5.24199	+	3.81797i	0.230766	+	0.168077i
$517$	1.42172	+	2.21224i	0.0625273	+	0.0972943i
$518$	−12.2248	−	24.3512i	−0.537127	−	1.06993i
$519$	−8.16475	+	3.62367i	−0.358393	+	0.159061i
$520$	0.458072	−	0.480412i	0.0200878	−	0.0210675i
$521$	−2.62522	−	2.06449i	−0.115013	−	0.0904470i	0.558996	−	0.829170i	$-0.311187\pi$
$521$	−2.62522	−	2.06449i	−0.115013	−	0.0904470i	−0.674009	+	0.738723i	$0.735429\pi$
$522$	−3.63952	+	13.7148i	−0.159298	+	0.600279i
$523$	1.14480	+	11.9889i	0.0500585	+	0.524237i	0.985372	+	0.170417i	$0.0545114\pi$
$523$	1.14480	+	11.9889i	0.0500585	+	0.524237i	−0.935314	+	0.353820i	$0.884883\pi$
$524$	−3.54695	+	12.0798i	−0.154949	+	0.527709i
$525$	−2.97099	+	5.47171i	−0.129665	+	0.238805i
$526$	−14.1505	+	2.03453i	−0.616991	+	0.0887099i
$527$	0.631603	−	13.2590i	0.0275130	−	0.577570i
$528$	0.799825	−	0.746461i	0.0348079	−	0.0324855i
$529$	−19.7282	+	11.8237i	−0.857746	+	0.514074i
$530$	−14.2739	+	8.24107i	−0.620021	+	0.357969i
$531$	17.4970	−	7.54253i	0.759307	−	0.327318i
$532$	−12.7417	+	7.99663i	−0.552424	+	0.346698i
$533$	3.05760	−	1.39636i	0.132439	−	0.0604830i
$534$	−0.438611	−	0.0255987i	−0.0189805	−	0.00110777i
$535$	20.9890	+	29.4750i	0.907435	+	1.27431i
$536$	−3.66109	−	10.5780i	−0.158135	−	0.456902i
$537$	1.06620	+	12.5873i	0.0460097	+	0.543181i
$538$	−25.3202	+	7.43468i	−1.09163	+	0.320532i
$539$	−2.29246	+	3.78079i	−0.0987433	+	0.162850i
$540$	9.41925	+	3.09732i	0.405340	+	0.133287i
$541$	−13.6560	−	7.04015i	−0.587117	−	0.302680i	0.138955	−	0.990299i	$-0.455626\pi$
$541$	−13.6560	−	7.04015i	−0.587117	−	0.302680i	−0.726072	+	0.687619i	$0.758656\pi$
$542$	−4.27559	−	22.1839i	−0.183652	−	0.952879i
$543$	15.7529	+	9.32104i	0.676023	+	0.400004i
$544$	2.01669	+	5.03745i	0.0864649	+	0.215979i
$545$	5.90894	+	5.12013i	0.253111	+	0.219322i
$546$	−1.51955	−	0.481787i	−0.0650308	−	0.0206186i
$547$	−28.4044	−	8.34029i	−1.21448	−	0.356605i	−0.389111	−	0.921191i	$-0.627218\pi$
$547$	−28.4044	−	8.34029i	−1.21448	−	0.356605i	−0.825374	+	0.564586i	$0.809036\pi$
$548$	6.26756	−	8.80156i	0.267737	−	0.375984i
$549$	29.6663	−	20.1830i	1.26613	−	0.861388i
$550$	−0.393252	−	0.762802i	−0.0167683	−	0.0325260i
$551$	13.4464	+	23.2898i	0.572836	+	0.992181i
$552$	4.34128	−	7.08190i	0.184777	−	0.301426i
$553$	19.4821	−	26.7463i	0.828462	−	1.13737i
$554$	1.44818	−	2.25341i	0.0615273	−	0.0957383i
$555$	12.3120	+	31.7336i	0.522615	+	1.34702i
$556$	8.19153	+	0.782197i	0.347398	+	0.0331725i
$557$	0.467515	−	0.445775i	0.0198093	−	0.0188881i	−0.680110	−	0.733110i	$-0.738068\pi$
$557$	0.467515	−	0.445775i	0.0198093	−	0.0188881i	0.699919	+	0.714222i	$0.253219\pi$
$558$	3.50167	−	6.44967i	0.148237	−	0.273036i
$559$	0.984314	+	0.852913i	0.0416320	+	0.0360744i
$560$	4.89331	+	1.24288i	0.206780	+	0.0525212i
$561$	5.93607	+	0.0635017i	0.250621	+	0.00268105i
$562$	−22.1005	−	7.64905i	−0.932252	−	0.322656i
$563$	1.10285	+	23.1516i	0.0464795	+	0.975724i	0.894863	+	0.446342i	$0.147273\pi$
$563$	1.10285	+	23.1516i	0.0464795	+	0.975724i	−0.848383	+	0.529383i	$0.822424\pi$
$564$	−6.98912	−	1.77492i	−0.294295	−	0.0747374i
$565$	−11.1412	+	32.1904i	−0.468714	+	1.35426i
$566$	−15.0388	+	4.41578i	−0.632127	+	0.185609i
$567$	−3.24905	−	23.5891i	−0.136447	−	0.990647i
$568$	−6.90796	+	7.97221i	−0.289851	+	0.334506i
$569$	24.6546	−	2.35423i	1.03358	−	0.0986945i	0.435544	−	0.900167i	$-0.356556\pi$
$569$	24.6546	−	2.35423i	1.03358	−	0.0986945i	0.598031	+	0.801473i	$0.295950\pi$
$570$	16.7945	−	8.43199i	0.703443	−	0.353177i
$571$	−0.0762504	+	0.798530i	−0.00319098	+	0.0334175i	−0.996927	−	0.0783339i	$-0.975040\pi$
$571$	−0.0762504	+	0.798530i	−0.00319098	+	0.0334175i	0.993736	+	0.111751i	$0.0356460\pi$
$572$	0.172715	−	0.135825i	0.00722158	−	0.00567911i
$573$	1.10040	+	1.29773i	0.0459700	+	0.0542133i
$574$	20.6648	+	15.0523i	0.862533	+	0.628271i
$575$	−4.42228	−	4.78559i	−0.184422	−	0.199573i
$576$	−0.206819	+	2.99286i	−0.00861745	+	0.124703i
$577$	6.27484	−	3.23490i	0.261225	−	0.134671i	−0.322640	−	0.946522i	$-0.604570\pi$
$577$	6.27484	−	3.23490i	0.261225	−	0.134671i	0.583865	+	0.811851i	$0.301540\pi$
$578$	−4.62457	+	11.5516i	−0.192357	+	0.480484i
$579$	18.7667	−	14.4361i	0.779916	−	0.599942i
$580$	2.54279	−	8.65996i	0.105584	−	0.359585i
$581$	−0.0859617	+	8.00634i	−0.00356629	+	0.332159i
$582$	−0.846212	+	0.531124i	−0.0350766	+	0.0220158i
$583$	−5.06497	+	2.02771i	−0.209770	+	0.0839791i
$584$	16.0478	+	3.89316i	0.664063	+	0.161100i
$585$	1.83249	+	0.779505i	0.0757640	+	0.0322286i
$586$	1.08422	−	2.10308i	0.0447885	−	0.0868776i
$587$	−24.6002	−	38.2787i	−1.01536	−	1.57993i	−0.796925	−	0.604078i	$-0.793542\pi$
$587$	−24.6002	−	38.2787i	−1.01536	−	1.57993i	−0.218434	−	0.975852i	$-0.570095\pi$
$588$	−2.47797	−	11.8684i	−0.102190	−	0.489446i
$589$	−3.91868	−	13.3458i	−0.161466	−	0.549904i
$590$	−11.2513	+	4.50435i	−0.463209	+	0.185441i
$591$	−6.89460	+	0.254545i	−0.283606	+	0.0104706i
$592$	−8.38899	+	5.97377i	−0.344785	+	0.245520i
$593$	1.78783	−	0.433723i	0.0734174	−	0.0178109i	−0.198882	−	0.980023i	$-0.563731\pi$
$593$	1.78783	−	0.433723i	0.0734174	−	0.0178109i	0.272299	+	0.962213i	$0.412216\pi$
$594$	2.94024	+	1.45853i	0.120639	+	0.0598444i
$595$	14.5625	+	23.2037i	0.597004	+	0.951259i
$596$	−0.853926	−	0.548785i	−0.0349782	−	0.0224791i
$597$	9.67925	−	2.23881i	0.396146	−	0.0916283i
$598$	0.988828	−	1.34365i	0.0404362	−	0.0549458i
$599$	−16.0580	−	9.27109i	−0.656112	−	0.378806i	0.134682	−	0.990889i	$-0.456999\pi$
$599$	−16.0580	−	9.27109i	−0.656112	−	0.378806i	−0.790794	+	0.612082i	$0.790332\pi$
$600$	2.21552	+	0.793436i	0.0904481	+	0.0323919i
$601$	5.53282	+	38.4816i	0.225688	+	1.56970i	0.715968	+	0.698133i	$0.245986\pi$
$601$	5.53282	+	38.4816i	0.225688	+	1.56970i	−0.490280	+	0.871565i	$0.663105\pi$
$602$	−1.97905	+	9.70631i	−0.0806600	+	0.395600i
$603$	25.8435	−	21.4429i	1.05243	−	0.873224i
$604$	2.13403	−	0.203775i	0.0868324	−	0.00829148i
$605$	−6.61630	−	19.1165i	−0.268991	−	0.777198i
$606$	6.80890	+	9.78155i	0.276593	+	0.397348i
$607$	0.336088	+	0.320460i	0.0136414	+	0.0130071i	0.696869	−	0.717198i	$-0.254576\pi$
$607$	0.336088	+	0.320460i	0.0136414	+	0.0130071i	−0.683228	+	0.730205i	$0.739424\pi$
$608$	3.72340	+	4.29704i	0.151004	+	0.174268i
$609$	−21.3661	+	3.64490i	−0.865798	+	0.147699i
$610$	−19.1999	+	12.3390i	−0.777381	+	0.499593i
$611$	−1.36858	−	0.473671i	−0.0553670	−	0.0191627i
$612$	−12.0189	+	10.9788i	−0.485833	+	0.443791i
$613$	1.44322	−	1.83521i	0.0582912	−	0.0741233i	−0.756033	−	0.654533i	$-0.772865\pi$
$613$	1.44322	−	1.83521i	0.0582912	−	0.0741233i	0.814325	+	0.580410i	$0.197108\pi$
$614$	−4.44205	+	23.0475i	−0.179266	+	0.930122i
$615$	−23.9115	−	21.1715i	−0.964206	−	0.853718i
$616$	1.54471	+	0.637733i	0.0622380	+	0.0256950i
$617$	16.0329	+	35.1073i	0.645462	+	1.41336i	0.895470	+	0.445121i	$0.146839\pi$
$617$	16.0329	+	35.1073i	0.645462	+	1.41336i	−0.250008	+	0.968244i	$0.580433\pi$
$618$	−20.8372	+	8.08442i	−0.838195	+	0.325203i
$619$	0.205369	+	0.398360i	0.00825448	+	0.0160115i	0.892927	−	0.450202i	$-0.148648\pi$
$619$	0.205369	+	0.398360i	0.00825448	+	0.0160115i	−0.884672	+	0.466214i	$0.845618\pi$
$620$	−2.33405	+	4.04270i	−0.0937378	+	0.162359i
$621$	24.4689	+	4.71924i	0.981905	+	0.189376i
$622$	0.732881			0.0293859
$623$	−0.242730	−	0.625697i	−0.00972477	−	0.0250680i
$624$	−0.0921211	+	0.595429i	−0.00368779	+	0.0238362i
$625$	−9.49006	+	13.3269i	−0.379602	+	0.533077i
$626$	1.39978	−	1.33469i	0.0559464	−	0.0533448i
$627$	5.89979	−	1.97153i	0.235615	−	0.0787351i
$628$	−0.845722	+	4.38802i	−0.0337480	+	0.175101i
$629$	−55.3128	−	7.95277i	−2.20546	−	0.317098i
$630$	1.67278	+	15.0534i	0.0666451	+	0.599742i
$631$	34.4698	−	29.8682i	1.37222	−	1.18904i	0.411535	−	0.911394i	$-0.364993\pi$
$631$	34.4698	−	29.8682i	1.37222	−	1.18904i	0.960685	−	0.277642i	$-0.0895527\pi$
$632$	−11.1164	−	5.73088i	−0.442185	−	0.227962i
$633$	12.2467	−	48.2240i	0.486762	−	1.91673i
$634$	−5.54536	+	1.06878i	−0.220235	+	0.0424467i
$635$	−15.2953	−	14.5840i	−0.606976	−	0.578750i
$636$	6.36001	−	13.5412i	0.252191	−	0.536945i
$637$	−0.294710	−	2.41713i	−0.0116769	−	0.0957700i
$638$	1.24108	−	2.71758i	0.0491348	−	0.107590i
$639$	−29.6774	−	10.9879i	−1.17402	−	0.434673i
$640$	0.181388	−	1.89958i	0.00717000	−	0.0750876i
$641$	18.2739	+	7.31578i	0.721777	+	0.288956i	0.703320	−	0.710874i	$-0.251700\pi$
$641$	18.2739	+	7.31578i	0.721777	+	0.288956i	0.0184573	+	0.999830i	$0.494125\pi$
$642$	−30.9207	−	11.0735i	−1.22034	−	0.437038i
$643$			13.4825i			0.531699i	0.964015	+	0.265850i	$0.0856525\pi$
$643$			13.4825i			0.531699i	−0.964015	+	0.265850i	$0.914348\pi$
$644$	12.5949	+	1.53878i	0.496310	+	0.0606363i
$645$	3.61321	−	11.8356i	0.142270	−	0.466027i
$646$	−1.46799	+	30.8170i	−0.0577574	+	1.21248i
$647$	−5.17891	+	12.9363i	−0.203604	+	0.508578i	−0.994665	−	0.103159i	$-0.967105\pi$
$647$	−5.17891	+	12.9363i	−0.203604	+	0.508578i	0.791061	+	0.611737i	$0.209529\pi$
$648$	−8.62314	+	2.57711i	−0.338749	+	0.101238i
$649$	−3.89860	+	0.945790i	−0.153033	+	0.0371255i
$650$	0.429922	+	0.196339i	0.0168629	+	0.00770104i
$651$	11.1837	+	0.773277i	0.438324	+	0.0303071i
$652$	0.882420	−	6.13736i	0.0345582	−	0.240358i
$653$	4.78342	−	5.01670i	0.187189	−	0.196319i	−0.623452	−	0.781862i	$-0.714270\pi$
$653$	4.78342	−	5.01670i	0.187189	−	0.196319i	0.810641	+	0.585543i	$0.199119\pi$
$654$	−7.05705	−	0.750127i	−0.275953	−	0.0293323i
$655$	23.9969	−	1.14311i	0.937636	−	0.0446651i
$656$	4.42781	−	8.58876i	0.172877	−	0.335335i
$657$	5.99964	+	49.1752i	0.234068	+	1.91851i
$658$	−1.96835	−	10.8376i	−0.0767343	−	0.422496i
$659$	−2.62082	+	18.2282i	−0.102093	+	0.710070i	0.872911	+	0.487880i	$0.162230\pi$
$659$	−2.62082	+	18.2282i	−0.102093	+	0.710070i	−0.975003	+	0.222190i	$0.928679\pi$
$660$	−1.84526	−	0.976422i	−0.0718266	−	0.0380072i
$661$	−12.6623	+	9.01679i	−0.492507	+	0.350712i	−0.799169	−	0.601106i	$-0.794727\pi$
$661$	−12.6623	+	9.01679i	−0.492507	+	0.350712i	0.306663	+	0.951818i	$0.400788\pi$
$662$	−9.70035	−	10.1734i	−0.377015	−	0.395402i
$663$	−2.59133	+	1.99335i	−0.100639	+	0.0774154i
$664$	2.99548	−	0.430685i	0.116247	−	0.0167138i
$665$	22.3725	+	17.9860i	0.867567	+	0.697466i
$666$	−25.6279	−	17.2557i	−0.993061	−	0.668646i
$667$	3.57884	−	22.3993i	0.138573	−	0.867305i
$668$	12.9169	+	7.45758i	0.499770	+	0.288543i
$669$	−2.94960	+	0.535831i	−0.114038	+	0.0207164i
$670$	−16.7901	+	13.2039i	−0.648659	+	0.510111i
$671$	−6.87197	+	3.13832i	−0.265289	+	0.121154i
$672$	−4.28984	+	1.61160i	−0.165484	+	0.0621689i
$673$	−17.3841	+	38.0659i	−0.670108	+	1.46733i	0.202686	+	0.979244i	$0.435033\pi$
$673$	−17.3841	+	38.0659i	−0.670108	+	1.46733i	−0.872794	+	0.488089i	$0.837694\pi$
$674$	−25.7033	−	4.95390i	−0.990053	−	0.190817i
$675$	0.109483	+	7.05907i	0.00421400	+	0.271704i
$676$	3.03634	−	12.5160i	0.116782	−	0.481383i
$677$	−4.14730	+	11.9828i	−0.159394	+	0.460538i	−0.996213	−	0.0869406i	$-0.972291\pi$
$677$	−4.14730	+	11.9828i	−0.159394	+	0.460538i	0.836820	+	0.547478i	$0.184412\pi$
$678$	−8.39305	−	29.7581i	−0.322333	−	1.14285i
$679$	−1.27493	−	0.838822i	−0.0489272	−	0.0321910i
$680$	7.82524	−	6.78061i	0.300084	−	0.260025i
$681$	−0.00125283	−	0.00222459i	−4.80086e−5	−	8.52464e-5i
$682$	−0.955178	+	1.21461i	−0.0365756	+	0.0465097i
$683$	−1.08886	+	0.376859i	−0.0416642	+	0.0144201i	−0.347821	−	0.937561i	$-0.613078\pi$
$683$	−1.08886	+	0.376859i	−0.0416642	+	0.0144201i	0.306156	+	0.951981i	$0.400957\pi$
$684$	−8.13870	+	14.9905i	−0.311191	+	0.573177i
$685$	−19.7833	−	5.80890i	−0.755881	−	0.221947i
$686$	14.9190	−	10.9737i	0.569611	−	0.418978i
$687$	17.3803	+	2.68897i	0.663099	+	0.102591i
$688$	3.73988	+	0.178152i	0.142582	+	0.00679200i
$689$	1.50231	−	2.60208i	0.0572335	−	0.0991313i
$690$	−15.4801	−	3.40857i	−0.589316	−	0.129762i
$691$	−12.3927	−	21.4648i	−0.471441	−	0.816560i	0.528025	−	0.849229i	$-0.322933\pi$
$691$	−12.3927	−	21.4648i	−0.471441	−	0.816560i	−0.999466	+	0.0326690i	$0.989599\pi$
$692$	−2.78826	+	4.33862i	−0.105994	+	0.164930i
$693$	−0.161060	+	5.01093i	−0.00611817	+	0.190350i
$694$	2.78163	+	6.09093i	0.105589	+	0.231209i
$695$	−3.70198	−	15.2598i	−0.140424	−	0.578836i
$696$	2.59647	+	7.76994i	0.0984189	+	0.294519i
$697$	49.5486	−	17.1490i	1.87679	−	0.649563i
$698$	0.832451	+	2.07936i	0.0315087	+	0.0787050i
$699$	−0.137793	+	12.8807i	−0.00521180	+	0.487193i
$700$	0.303263	+	3.58192i	0.0114623	+	0.135384i
$701$	21.2430	−	13.6520i	0.802336	−	0.515630i	−0.0740413	−	0.997255i	$-0.523590\pi$
$701$	21.2430	−	13.6520i	0.802336	−	0.515630i	0.876377	+	0.481625i	$0.159953\pi$
$702$	−1.76936	+	0.369562i	−0.0667800	+	0.0139482i
$703$	−57.4975	+	11.0817i	−2.16856	+	0.417956i
$704$	0.148916	−	0.613839i	0.00561247	−	0.0231349i
$705$	1.16138	+	13.7111i	0.0437403	+	0.516388i
$706$	16.3042	−	18.8160i	0.613615	−	0.708150i
$707$	−9.27130	+	15.6675i	−0.348683	+	0.589235i
$708$	6.04600	−	9.19011i	0.227223	−	0.345385i
$709$	−35.4259	−	25.2267i	−1.33045	−	0.947408i	−0.999994	−	0.00358612i	$-0.998858\pi$
$709$	−35.4259	−	25.2267i	−1.33045	−	0.947408i	−0.330455	−	0.943822i	$-0.607202\pi$
$710$	18.6874	+	7.48132i	0.701327	+	0.280769i
$711$	4.36471	−	37.2652i	0.163689	−	1.39756i
$712$	−0.219679	+	0.126832i	−0.00823280	+	0.00475321i
$713$	−4.53014	+	10.8222i	−0.169655	+	0.405294i
$714$	−22.8811	−	9.73426i	−0.856305	−	0.364295i
$715$	−0.352723	−	0.226682i	−0.0131911	−	0.00847741i
$716$	4.50841	+	5.73291i	0.168487	+	0.214249i
$717$	2.31103	−	5.59836i	0.0863071	−	0.209075i
$718$	18.1956	+	19.0830i	0.679055	+	0.712173i
$719$	2.05985	+	21.5717i	0.0768195	+	0.804490i	0.948994	+	0.315295i	$0.102103\pi$
$719$	2.05985	+	21.5717i	0.0768195	+	0.804490i	−0.872174	+	0.489195i	$0.837291\pi$
$720$	5.52603	−	1.49495i	0.205943	−	0.0557135i
$721$	−24.4546	−	23.8239i	−0.910739	−	0.887249i
$722$	3.75501	+	12.7884i	0.139747	+	0.475935i
$723$	29.4946	+	21.4822i	1.09691	+	0.798930i
$724$	10.5559	−	0.502837i	0.392305	−	0.0186878i
$725$	6.41905	−	0.305777i	0.238397	−	0.0113563i
$726$	14.8421	+	10.8101i	0.550841	+	0.401201i
$727$	8.79165	+	29.9416i	0.326064	+	1.11047i	0.945553	+	0.325467i	$0.105522\pi$
$727$	8.79165	+	29.9416i	0.326064	+	1.11047i	−0.619489	+	0.785005i	$0.712660\pi$
$728$	−0.885806	+	0.249798i	−0.0328301	+	0.00925813i
$729$	−16.3361	−	21.4973i	−0.605039	−	0.796196i
$730$	−2.99532	−	31.3684i	−0.110862	−	1.16100i
$731$	14.0197	+	14.7035i	0.518538	+	0.543827i
$732$	7.90460	−	19.1485i	0.292162	−	0.707749i
$733$	−19.5874	−	24.9075i	−0.723478	−	0.919978i	0.275669	−	0.961253i	$-0.411101\pi$
$733$	−19.5874	−	24.9075i	−0.723478	−	0.919978i	−0.999148	+	0.0412748i	$0.986858\pi$
$734$	27.1844	+	17.4703i	1.00339	+	0.644841i
$735$	−19.8555	+	11.8758i	−0.732380	+	0.438044i
$736$	−0.153269	−	4.79338i	−0.00564955	−	0.176686i
$737$	−6.12317	+	3.53521i	−0.225550	+	0.130221i
$738$	28.7920	+	3.37227i	1.05985	+	0.124135i
$739$	−20.0347	−	8.02068i	−0.736988	−	0.295045i	−0.0273633	−	0.999626i	$-0.508711\pi$
$739$	−20.0347	−	8.02068i	−0.736988	−	0.295045i	−0.709624	+	0.704580i	$0.751135\pi$
$740$	16.0081	+	11.3993i	0.588468	+	0.419046i
$741$	−1.88283	+	2.86196i	−0.0691675	+	0.105137i
$742$	22.8512	+	0.245346i	0.838892	+	0.00900694i
$743$	−14.6371	+	16.8921i	−0.536984	+	0.619712i	−0.957801	−	0.287433i	$-0.907198\pi$
$743$	−14.6371	+	16.8921i	−0.536984	+	0.619712i	0.420817	+	0.907146i	$0.361743\pi$
$744$	−0.357623	−	4.22201i	−0.0131111	−	0.154787i
$745$	−0.456658	+	1.88237i	−0.0167306	+	0.0689646i
$746$	−9.04412	+	1.74311i	−0.331129	+	0.0638198i
$747$	4.37019	+	7.95783i	0.159897	+	0.291162i
$748$	2.88330	−	1.85299i	0.105424	−	0.0677518i
$749$	−4.23247	−	49.9909i	−0.154651	−	1.82663i
$750$	0.224812	−	21.0151i	0.00820896	−	0.767364i
$751$	8.23247	+	20.5637i	0.300407	+	0.750380i	0.999379	+	0.0352315i	$0.0112169\pi$
$751$	8.23247	+	20.5637i	0.300407	+	0.750380i	−0.698972	+	0.715149i	$0.746359\pi$
$752$	−3.93428	+	1.36167i	−0.143469	+	0.0496549i
$753$	8.81423	+	26.3766i	0.321209	+	0.961217i
$754$	0.387899	+	1.59894i	0.0141264	+	0.0582300i
$755$	−1.69935	−	3.72105i	−0.0618456	−	0.135423i
$756$	−9.05232	−	10.3468i	−0.329230	−	0.376308i
$757$	−18.4037	+	28.6368i	−0.668895	+	1.04082i	0.326521	+	0.945190i	$0.394124\pi$
$757$	−18.4037	+	28.6368i	−0.668895	+	1.04082i	−0.995417	+	0.0956318i	$0.969513\pi$
$758$	4.01650	+	6.95678i	0.145886	+	0.252682i
$759$	−4.91136	−	1.84603i	−0.178271	−	0.0670065i
$760$	5.42489	−	9.39618i	0.196781	−	0.340835i
$761$	−5.01717	−	0.238997i	−0.181872	−	0.00866364i	−0.0435518	−	0.999051i	$-0.513867\pi$
$761$	−5.01717	−	0.238997i	−0.181872	−	0.00866364i	−0.138320	+	0.990388i	$0.544170\pi$
$762$	18.9572	+	2.93294i	0.686747	+	0.106249i
$763$	−3.43541	−	10.2818i	−0.124370	−	0.372226i
$764$	0.942550	+	0.276758i	0.0341003	+	0.0100127i
$765$	27.2989	+	14.8212i	0.986995	+	0.535862i
$766$	0.884806	−	0.306234i	0.0319693	−	0.0110647i
$767$	1.36571	−	1.73665i	0.0493131	−	0.0627067i
$768$	0.849930	+	1.50918i	0.0306692	+	0.0544578i
$769$	33.6628	−	29.1690i	1.21391	−	1.05186i	0.216777	−	0.976221i	$-0.430446\pi$
$769$	33.6628	−	29.1690i	1.21391	−	1.05186i	0.997135	−	0.0756397i	$-0.0240999\pi$
$770$	0.185927	−	3.18355i	0.00670034	−	0.114727i
$771$	8.48158	+	30.0719i	0.305457	+	1.08301i
$772$	4.47094	−	12.9179i	0.160913	−	0.464927i
$773$	9.85310	−	40.6150i	0.354391	−	1.46082i	−0.463834	−	0.885922i	$-0.653526\pi$
$773$	9.85310	−	40.6150i	0.354391	−	1.46082i	0.818225	−	0.574898i	$-0.194958\pi$
$774$	3.44583	+	10.6908i	0.123858	+	0.384271i
$775$	−3.26369	−	0.629026i	−0.117235	−	0.0225953i
$776$	−0.239620	+	0.524695i	−0.00860186	+	0.0188354i
$777$	7.71604	−	46.5590i	0.276811	−	1.67030i
$778$	17.0155	−	7.77070i	0.610034	−	0.278593i
$779$	43.1869	−	33.9626i	1.54733	−	1.21684i
$780$	1.13122	−	0.205499i	0.0405040	−	0.00735804i
$781$	5.77037	+	3.33153i	0.206480	+	0.119211i
$782$	17.3467	−	19.3979i	0.620318	−	0.693667i
$783$	−19.0808	+	15.4902i	−0.681892	+	0.553574i
$784$	−4.96125	−	4.93821i	−0.177188	−	0.176365i
$785$	8.44063	−	1.21358i	0.301259	−	0.0433145i
$786$	−17.2840	+	13.2955i	−0.616500	+	0.474236i
$787$	21.1059	+	22.1353i	0.752346	+	0.789037i	0.982923	−	0.184017i	$-0.0589100\pi$
$787$	21.1059	+	22.1353i	0.752346	+	0.789037i	−0.230577	+	0.973054i	$0.574062\pi$
$788$	−3.24471	+	2.31055i	−0.115588	+	0.0823099i
$789$	−21.8862	−	11.5811i	−0.779169	−	0.412298i
$790$	−3.39641	+	23.6226i	−0.120839	+	0.840454i
$791$	36.0237	−	30.5438i	1.28086	−	1.08601i
$792$	1.88099	−	0.229490i	0.0668379	−	0.00815458i
$793$	1.90646	−	3.69803i	0.0677005	−	0.131321i
$794$	6.32652	−	0.301369i	0.224520	−	0.0106952i
$795$	−28.3880	−	3.01749i	−1.00682	−	0.107019i
$796$	3.95820	−	4.15124i	0.140295	−	0.147137i
$797$	0.887580	−	6.17325i	0.0314397	−	0.218668i	−0.968045	−	0.250778i	$-0.919314\pi$
$797$	0.887580	−	6.17325i	0.0314397	−	0.218668i	0.999484	+	0.0321100i	$0.0102227\pi$
$798$	−25.9935	−	1.79728i	−0.920161	−	0.0636229i
$799$	−20.5490	−	9.38439i	−0.726970	−	0.331996i
$800$	1.32038	−	0.320322i	0.0466826	−	0.0113251i
$801$	−0.587977	−	0.483101i	−0.0207752	−	0.0170695i
$802$	−9.49907	+	23.7275i	−0.335424	+	0.837848i
$803$	0.496305	−	10.4187i	0.0175142	−	0.367668i
$804$	5.66092	−	18.5432i	0.199645	−	0.653967i
$805$	−5.08590	−	23.6725i	−0.179254	−	0.834345i
$806$		−	0.850976i		−	0.0299743i
$807$	−43.0311	−	15.4106i	−1.51477	−	0.542478i
$808$	6.38799	+	2.55737i	0.224729	+	0.0899678i
$809$	−1.85352	+	19.4110i	−0.0651664	+	0.682453i	0.902579	+	0.430524i	$0.141671\pi$
$809$	−1.85352	+	19.4110i	−0.0651664	+	0.682453i	−0.967746	+	0.251930i	$0.918935\pi$
$810$	10.0291	+	13.9414i	0.352386	+	0.489853i
$811$	5.54719	−	12.1467i	0.194788	−	0.426527i	−0.786885	−	0.617100i	$-0.788307\pi$
$811$	5.54719	−	12.1467i	0.194788	−	0.426527i	0.981673	+	0.190573i	$0.0610347\pi$
$812$	−9.14895	+	8.53787i	−0.321065	+	0.299620i
$813$	16.6353	−	35.4186i	0.583426	−	1.24219i
$814$	4.70792	+	4.48900i	0.165013	+	0.157339i
$815$	−11.6181	+	2.23920i	−0.406963	+	0.0784358i
$816$	−2.31332	+	9.10919i	−0.0809823	+	0.318885i
$817$	18.9218	+	9.75487i	0.661990	+	0.341280i
$818$	−18.8093	+	16.2984i	−0.657653	+	0.569860i
$819$	−1.63617	−	2.22405i	−0.0571724	−	0.0777146i
$820$	−18.2514	−	2.62415i	−0.637365	−	0.0916393i
$821$	−6.37160	+	33.0590i	−0.222370	+	1.15377i	0.683415	+	0.730030i	$0.260494\pi$
$821$	−6.37160	+	33.0590i	−0.222370	+	1.15377i	−0.905785	+	0.423737i	$0.860718\pi$
$822$	17.7501	−	5.93153i	0.619106	−	0.206886i
$823$	−26.2258	+	25.0063i	−0.914175	+	0.871664i	−0.992120	−	0.125294i	$-0.960013\pi$
$823$	−26.2258	+	25.0063i	−0.914175	+	0.871664i	0.0779451	+	0.996958i	$0.475164\pi$
$824$	−7.48511	+	10.5114i	−0.260756	+	0.366181i
$825$	0.227271	−	1.46898i	0.00791256	−	0.0511432i
$826$	16.6060	+	2.56984i	0.577795	+	0.0894160i
$827$	−28.5004			−0.991054			−0.495527	−	0.868592i	$-0.665025\pi$
$827$	−28.5004			−0.991054			−0.495527	+	0.868592i	$0.665025\pi$
$828$	13.2996	−	5.48817i	0.462194	−	0.190727i
$829$	−6.09825	+	10.5625i	−0.211801	+	0.366850i	−0.952278	−	0.305231i	$-0.901266\pi$
$829$	−6.09825	+	10.5625i	−0.211801	+	0.366850i	0.740477	+	0.672081i	$0.234600\pi$
$830$	−2.64618	−	5.13287i	−0.0918503	−	0.178165i
$831$	4.32539	−	1.67817i	0.150046	−	0.0582150i
$832$	0.144507	+	0.316425i	0.00500987	+	0.0109701i
$833$	−0.992279	−	37.9700i	−0.0343804	−	1.31558i
$834$	10.6710	+	9.44822i	0.369507	+	0.327165i
$835$	5.38637	−	27.9471i	0.186403	−	0.967150i
$836$	2.22006	−	2.82303i	0.0767823	−	0.0976366i
$837$	11.4794	−	5.45918i	0.396787	−	0.188697i
$838$	9.68395	+	3.35165i	0.334526	+	0.115781i
$839$	2.55988	−	1.64513i	0.0883769	−	0.0567964i	−0.495706	−	0.868490i	$-0.665091\pi$
$839$	2.55988	−	1.64513i	0.0883769	−	0.0567964i	0.584083	+	0.811694i	$0.301454\pi$
$840$	5.58353	+	6.72992i	0.192650	+	0.232204i
$841$	−4.34094	−	5.00971i	−0.149687	−	0.172749i
$842$	2.21120	+	2.10837i	0.0762030	+	0.0726594i
$843$	−23.1421	−	33.2455i	−0.797055	−	1.14503i
$844$	−9.39533	−	27.1460i	−0.323401	−	0.934405i
$845$	−24.4647	+	2.33610i	−0.841612	+	0.0803642i
$846$	−7.97526	−	9.61195i	−0.274195	−	0.330466i
$847$	−5.60343	+	27.4822i	−0.192536	+	0.944301i
$848$	−1.22923	−	8.54950i	−0.0422120	−	0.293591i
$849$	−25.5581	−	9.15303i	−0.877150	−	0.314131i
$850$	6.38468	+	3.68620i	0.218993	+	0.126436i
$851$	43.5406	+	23.3156i	1.49255	+	0.799247i
$852$	−17.8010	+	4.11736i	−0.609852	+	0.141058i
$853$	−35.8284	−	23.0255i	−1.22674	−	0.788380i	−0.243362	−	0.969936i	$-0.578250\pi$
$853$	−35.8284	−	23.0255i	−1.22674	−	0.788380i	−0.983381	+	0.181556i	$0.941887\pi$
$854$	31.6225	−	1.16625i	1.08210	−	0.0399082i
$855$	32.1115	+	5.32042i	1.09819	+	0.181955i
$856$	−18.4279	+	4.47055i	−0.629851	+	0.152800i
$857$	1.01027	−	0.719409i	0.0345101	−	0.0245745i	−0.562672	−	0.826680i	$-0.690226\pi$
$857$	1.01027	−	0.719409i	0.0345101	−	0.0245745i	0.597182	+	0.802106i	$0.296287\pi$
$858$	0.380315	−	0.0140410i	0.0129837	−	0.000479352i
$859$	−16.1157	+	6.45177i	−0.549862	+	0.220132i	−0.629922	−	0.776658i	$-0.716913\pi$
$859$	−16.1157	+	6.45177i	−0.549862	+	0.220132i	0.0800597	+	0.996790i	$0.474489\pi$
$860$	−2.01287	−	6.85521i	−0.0686384	−	0.233761i
$861$	13.5828	+	42.1465i	0.462900	+	1.43635i
$862$	20.2656	+	31.5339i	0.690249	+	1.07405i
$863$	−16.2678	+	31.5552i	−0.553763	+	1.07415i	0.431341	+	0.902189i	$0.358041\pi$
$863$	−16.2678	+	31.5552i	−0.553763	+	1.07415i	−0.985104	+	0.171961i	$0.944990\pi$
$864$	−3.34145	+	3.97929i	−0.113678	+	0.135378i
$865$	9.56393	+	2.32018i	0.325183	+	0.0788886i
$866$	−16.8917	+	6.76243i	−0.574004	+	0.229797i
$867$	−18.2541	+	11.4572i	−0.619943	+	0.389106i
$868$	5.63962	−	3.17580i	0.191421	−	0.107794i
$869$	−2.22562	+	7.57976i	−0.0754990	+	0.257126i
$870$	12.3908	−	9.53151i	0.420088	−	0.323148i
$871$	1.44720	−	3.61492i	0.0490364	−	0.122487i
$872$	−3.64186	+	1.87751i	−0.123329	+	0.0635806i
$873$	−1.72635	−	0.119297i	−0.0584280	−	0.00403760i
$874$	10.5291	−	25.1533i	0.356152	−	0.850823i
$875$	29.3434	−	13.0218i	0.991988	−	0.440217i
$876$	18.4979	+	21.8150i	0.624988	+	0.737059i
$877$	30.6112	−	24.0729i	1.03367	−	0.812884i	0.0510810	−	0.998695i	$-0.483733\pi$
$877$	30.6112	−	24.0729i	1.03367	−	0.812884i	0.982586	+	0.185810i	$0.0594909\pi$
$878$	−1.68672	+	17.6642i	−0.0569241	+	0.596137i
$879$	3.66253	−	1.83884i	0.123534	−	0.0620226i
$880$	−1.19986	+	0.114573i	−0.0404473	+	0.00386225i
$881$	−10.6442	+	12.2840i	−0.358612	+	0.413860i	−0.906174	−	0.422905i	$-0.861010\pi$
$881$	−10.6442	+	12.2840i	−0.358612	+	0.413860i	0.547562	+	0.836765i	$0.315556\pi$
$882$	8.63321	−	19.1433i	0.290695	−	0.644590i
$883$	16.5236	−	4.85178i	0.556064	−	0.163275i	0.00838704	−	0.999965i	$-0.497330\pi$
$883$	16.5236	−	4.85178i	0.556064	−	0.163275i	0.547677	+	0.836690i	$0.315512\pi$
$884$	−0.617354	+	1.78373i	−0.0207639	+	0.0599932i
$885$	−20.3457	−	5.16687i	−0.683913	−	0.173682i
$886$	1.74840	+	36.7033i	0.0587385	+	1.23307i
$887$	−34.4618	−	11.9273i	−1.15711	−	0.400481i	−0.319950	−	0.947434i	$-0.603666\pi$
$887$	−34.4618	−	11.9273i	−1.15711	−	0.400481i	−0.837163	+	0.546954i	$0.815787\pi$
$888$	−17.8367	−	0.190810i	−0.598559	−	0.00640315i
$889$	7.95304	+	28.2022i	0.266736	+	0.945871i
$890$	0.365817	+	0.316983i	0.0122622	+	0.0106253i
$891$	2.62920	+	5.04026i	0.0880817	+	0.168855i
$892$	−1.25266	+	1.19441i	−0.0419421	+	0.0399917i
$893$	−23.5643	−	2.25011i	−0.788548	−	0.0752972i
$894$	−0.635938	−	1.63910i	−0.0212690	−	0.0548197i
$895$	7.52422	−	11.7079i	0.251507	−	0.391352i
$896$	−1.55774	+	2.13856i	−0.0520403	+	0.0714444i
$897$	2.75456	−	0.872854i	0.0919722	−	0.0291438i
$898$	−14.0067	−	24.2604i	−0.467411	−	0.809579i
$899$	−5.30196	−	10.2844i	−0.176830	−	0.343003i
$900$	2.29277	+	3.37007i	0.0764257	+	0.112336i
$901$	27.1860	−	38.1774i	0.905697	−	1.27187i
$902$	−5.85630	−	1.71957i	−0.194993	−	0.0572553i
$903$	−12.6685	+	11.5713i	−0.421582	+	0.385070i
$904$	−13.4910	−	11.6900i	−0.448703	−	0.388803i
$905$	−7.49486	−	18.7213i	−0.249138	−	0.622315i
$906$	3.19556	+	1.89082i	0.106165	+	0.0628183i
$907$	5.31368	+	27.5700i	0.176438	+	0.915446i	0.956938	+	0.290291i	$0.0937522\pi$
$907$	5.31368	+	27.5700i	0.176438	+	0.915446i	−0.780501	+	0.625155i	$0.785036\pi$
$908$	−0.00131018		0.000675444i	−4.34798e−5		2.24154e-5i
$909$	−0.441604	+	20.6379i	−0.0146471	+	0.684517i
$910$	1.00330	+	1.44145i	0.0332591	+	0.0477835i
$911$	−24.4007	+	7.16470i	−0.808432	+	0.237377i	−0.659728	−	0.751505i	$-0.729328\pi$
$911$	−24.4007	+	7.16470i	−0.808432	+	0.237377i	−0.148704	+	0.988882i	$0.547510\pi$
$912$	0.831199	+	9.81295i	0.0275237	+	0.324939i
$913$	−0.625202	−	1.80640i	−0.0206912	−	0.0597832i
$914$	15.8618	+	22.2748i	0.524662	+	0.736785i
$915$	−39.4634	−	2.30321i	−1.30462	−	0.0761418i
$916$	9.23630	−	4.21808i	0.305176	−	0.139369i
$917$	−29.4410	−	15.5802i	−0.972228	−	0.514505i
$918$	−28.0224	+	3.11504i	−0.924878	+	0.102812i
$919$	28.8742	−	16.6705i	0.952471	−	0.549909i	0.0586230	−	0.998280i	$-0.481329\pi$
$919$	28.8742	−	16.6705i	0.952471	−	0.549909i	0.893848	+	0.448371i	$0.147996\pi$
$920$	−8.54812	+	3.26802i	−0.281823	+	0.107744i
$921$	−29.7212	+	27.7382i	−0.979347	+	0.914006i
$922$	1.60970	−	33.7917i	0.0530126	−	1.11287i
$923$	−3.63214	+	0.522224i	−0.119553	+	0.0171892i
$924$	1.51237	+	2.46804i	0.0497533	+	0.0811924i
$925$	−3.94215	+	13.4257i	−0.129617	+	0.441435i
$926$	0.896933	+	9.39311i	0.0294750	+	0.308677i
$927$	−37.4172	−	9.92949i	−1.22894	−	0.326127i
$928$	3.71789	+	2.92378i	0.122046	+	0.0959778i
$929$	16.7935	−	17.6125i	0.550977	−	0.577848i	−0.388073	−	0.921629i	$-0.626859\pi$
$929$	16.7935	−	17.6125i	0.550977	−	0.577848i	0.939050	+	0.343781i	$0.111708\pi$
$930$	−7.39024	+	3.27993i	−0.242336	+	0.107553i
$931$	−13.9956	−	37.2587i	−0.458688	−	1.22110i
$932$	4.02080	+	6.25649i	0.131706	+	0.204938i
$933$	1.02608	+	0.747336i	0.0335923	+	0.0244667i
$934$	−37.5572	−	9.11128i	−1.22891	−	0.298130i
$935$	−5.14096	−	4.04290i	−0.168127	−	0.132217i
$936$	−0.736147	+	0.739697i	−0.0240617	+	0.0241778i
$937$	46.9313	+	21.4328i	1.53318	+	0.700179i	0.990211	−	0.139575i	$-0.0445736\pi$
$937$	46.9313	+	21.4328i	1.53318	+	0.700179i	0.542967	+	0.839754i	$0.317301\pi$
$938$	29.3578	−	3.89979i	0.958566	−	0.127333i
$939$	3.32078	−	0.441253i	0.108370	−	0.0143998i
$940$	4.91092	+	6.24474i	0.160177	+	0.203681i
$941$	−6.80338	+	3.50738i	−0.221784	+	0.114337i	−0.565538	−	0.824722i	$-0.691332\pi$
$941$	−6.80338	+	3.50738i	−0.221784	+	0.114337i	0.343754	+	0.939060i	$0.388301\pi$
$942$	−5.65863	+	5.28109i	−0.184368	+	0.172067i
$943$	−46.3361	−	0.724559i	−1.50891	−	0.0235949i
$944$		−	6.35117i		−	0.206713i
$945$	−13.0083	+	22.7814i	−0.423160	+	0.741080i
$946$	−0.336568	−	2.34088i	−0.0109428	−	0.0761086i
$947$	16.1157	+	11.4759i	0.523688	+	0.372917i	0.811116	−	0.584886i	$-0.198861\pi$
$947$	16.1157	+	11.4759i	0.523688	+	0.372917i	−0.287427	+	0.957802i	$0.592800\pi$
$948$	−9.71965	−	19.3592i	−0.315680	−	0.628757i
$949$	3.33204	+	4.67919i	0.108163	+	0.151893i
$950$	7.58559	+	1.46200i	0.246109	+	0.0474336i
$951$	−8.85370	−	4.15838i	−0.287101	−	0.134845i
$952$	−14.1251	+	2.56543i	−0.457798	+	0.0831460i
$953$	−27.5886	−	31.8389i	−0.893682	−	1.03136i	−0.999317	−	0.0369593i	$-0.988233\pi$
$953$	−27.5886	−	31.8389i	−0.893682	−	1.03136i	0.105634	−	0.994405i	$-0.466313\pi$
$954$	22.7127	−	12.4731i	0.735351	−	0.403831i
$955$	−0.0891936	−	1.87240i	−0.00288624	−	0.0605896i
$956$	−0.661771	−	3.43359i	−0.0214032	−	0.111050i
$957$	4.50877	−	2.53922i	0.145748	−	0.0820814i
$958$	−14.8145	−	2.13000i	−0.478635	−	0.0688173i
$959$	19.5044	+	20.9004i	0.629830	+	0.674909i
$960$	2.19100	−	2.47456i	0.0707143	−	0.0798662i
$961$	−5.89764	−	24.3104i	−0.190247	−	0.784207i
$962$	−3.56626	−	0.340536i	−0.114981	−	0.0109793i
$963$	−31.9989	−	47.0342i	−1.03115	−	1.51566i
$964$	21.0428	+	1.00239i	0.677743	+	0.0322849i
$965$	−26.0850			−0.839705
$966$	16.0645	+	14.9977i	0.516867	+	0.482543i
$967$	−2.81122			−0.0904027			−0.0452014	−	0.998978i	$-0.514393\pi$
$967$	−2.81122			−0.0904027			−0.0452014	+	0.998978i	$0.514393\pi$
$968$	10.5890	+	0.504417i	0.340344	+	0.0162126i
$969$	−33.4800	+	41.6486i	−1.07553	+	1.33795i
$970$	1.09572	+	0.104629i	0.0351814	+	0.00335942i
$971$	−5.96243	−	24.5775i	−0.191343	−	0.788728i	−0.983869	−	0.178890i	$-0.942749\pi$
$971$	−5.96243	−	24.5775i	−0.191343	−	0.788728i	0.792526	−	0.609839i	$-0.208766\pi$
$972$	−14.7008	−	5.18511i	−0.471530	−	0.166312i
$973$	−6.35761	+	20.8224i	−0.203816	+	0.667535i
$974$	7.51067	+	1.07987i	0.240657	+	0.0346013i
$975$	0.401705	+	0.713287i	0.0128649	+	0.0228435i
$976$	−2.26351	−	11.7442i	−0.0724531	−	0.375922i
$977$	0.312502	+	6.56022i	0.00999781	+	0.209880i	0.998339	+	0.0576214i	$0.0183516\pi$
$977$	0.312502	+	6.56022i	0.00999781	+	0.209880i	−0.988341	+	0.152259i	$0.951345\pi$
$978$	7.49385	−	7.69285i	0.239627	−	0.245990i
$979$	0.104925	+	0.121090i	0.00335342	+	0.00387005i
$980$	−5.80854	+	12.0285i	−0.185547	+	0.384237i
$981$	−9.11537	−	8.24646i	−0.291031	−	0.263289i
$982$	28.8831	+	5.56677i	0.921698	+	0.177643i
$983$	−2.37252	−	3.33173i	−0.0756716	−	0.106266i	0.775005	−	0.631955i	$-0.217747\pi$
$983$	−2.37252	−	3.33173i	−0.0756716	−	0.106266i	−0.850677	+	0.525689i	$0.823808\pi$
$984$	14.9574	−	7.50963i	0.476823	−	0.239398i
$985$	6.19163	+	4.40904i	0.197282	+	0.140484i
$986$	3.65246	+	25.4034i	0.116318	+	0.809010i
$987$	8.29559	−	17.1805i	0.264052	−	0.546862i
$988$			1.97787i			0.0629243i
$989$	−7.20298	−	16.4481i	−0.229041	−	0.523021i
$990$	−1.58779	−	3.24870i	−0.0504633	−	0.103250i
$991$	−2.65605	+	1.36929i	−0.0843722	+	0.0434969i	−0.499896	−	0.866085i	$-0.666629\pi$
$991$	−2.65605	+	1.36929i	−0.0843722	+	0.0434969i	0.415524	+	0.909582i	$0.363598\pi$
$992$	−1.51221	−	1.92293i	−0.0480127	−	0.0610531i
$993$	−3.20698	−	24.1351i	−0.101770	−	0.765903i
$994$	−17.0159	−	22.1222i	−0.539711	−	0.701673i
$995$	−9.95620	−	4.54684i	−0.315633	−	0.144145i
$996$	4.63303	+	2.45158i	0.146803	+	0.0776812i
$997$	14.4041	+	11.3275i	0.456183	+	0.358746i	0.819654	−	0.572860i	$-0.194166\pi$
$997$	14.4041	+	11.3275i	0.456183	+	0.358746i	−0.363471	+	0.931606i	$0.618408\pi$
$998$	11.6994	+	2.83825i	0.370338	+	0.0898431i
$999$	−18.2845	−	50.2924i	−0.578497	−	1.59118i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.bf.a.389.57	yes	1280
3.2	odd	2	inner	966.2.bf.a.389.32	yes	1280
7.2	even	3	inner	966.2.bf.a.527.4	yes	1280
21.2	odd	6	inner	966.2.bf.a.527.43	yes	1280
23.11	odd	22	inner	966.2.bf.a.11.43	yes	1280
69.11	even	22	inner	966.2.bf.a.11.4	✓	1280
161.149	odd	66	inner	966.2.bf.a.149.32	yes	1280
483.149	even	66	inner	966.2.bf.a.149.57	yes	1280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.bf.a.11.4	✓	1280	69.11	even	22	inner
966.2.bf.a.11.43	yes	1280	23.11	odd	22	inner
966.2.bf.a.149.32	yes	1280	161.149	odd	66	inner
966.2.bf.a.149.57	yes	1280	483.149	even	66	inner
966.2.bf.a.389.32	yes	1280	3.2	odd	2	inner
966.2.bf.a.389.57	yes	1280	1.1	even	1	trivial
966.2.bf.a.527.4	yes	1280	7.2	even	3	inner
966.2.bf.a.527.43	yes	1280	21.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.bf (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.998867 + 0.0475819i) q^{2} +(1.34995 + 1.08519i) q^{3} +(0.995472 + 0.0950560i) q^{4} +(-0.449881 - 1.85443i) q^{5} +(1.29679 + 1.14819i) q^{6} +(-0.772606 + 2.53043i) q^{7} +(0.989821 + 0.142315i) q^{8} +(0.644746 + 2.92990i) q^{9} +O(q^{10})\)	\(q+(0.998867 + 0.0475819i) q^{2} +(1.34995 + 1.08519i) q^{3} +(0.995472 + 0.0950560i) q^{4} +(-0.449881 - 1.85443i) q^{5} +(1.29679 + 1.14819i) q^{6} +(-0.772606 + 2.53043i) q^{7} +(0.989821 + 0.142315i) q^{8} +(0.644746 + 2.92990i) q^{9} +(-0.361134 - 1.87374i) q^{10} +(-0.0300548 - 0.630929i) q^{11} +(1.24069 + 1.20859i) q^{12} +(0.227800 + 0.262896i) q^{13} +(-0.892133 + 2.49080i) q^{14} +(1.40509 - 2.99160i) q^{15} +(0.981929 + 0.189251i) q^{16} +(3.14747 + 4.42000i) q^{17} +(0.504605 + 2.95726i) q^{18} +(4.63151 + 3.29809i) q^{19} +(-0.271569 - 1.88880i) q^{20} +(-3.78897 + 2.57754i) q^{21} -0.631644i q^{22} +(-1.27903 - 4.62213i) q^{23} +(1.18177 + 1.26626i) q^{24} +(1.20765 - 0.622585i) q^{25} +(0.215033 + 0.273437i) q^{26} +(-2.30911 + 4.65489i) q^{27} +(-1.00964 + 2.44553i) q^{28} +(4.30240 + 1.96484i) q^{29} +(1.54584 - 2.92136i) q^{30} +(-1.92293 - 1.51221i) q^{31} +(0.971812 + 0.235759i) q^{32} +(0.644102 - 0.884339i) q^{33} +(2.93359 + 4.56475i) q^{34} +(5.04010 + 0.294354i) q^{35} +(0.363322 + 2.97792i) q^{36} +(-7.10684 + 7.45344i) q^{37} +(4.46934 + 3.51473i) q^{38} +(0.0222293 + 0.602103i) q^{39} +(-0.181388 - 1.89958i) q^{40} +(2.72236 - 9.27152i) q^{41} +(-3.90732 + 2.39434i) q^{42} +(3.70601 - 0.532844i) q^{43} +(0.0300548 - 0.630929i) q^{44} +(5.14324 - 2.51374i) q^{45} +(-1.05765 - 4.67775i) q^{46} +(-3.60549 + 2.08163i) q^{47} +(1.12018 + 1.32105i) q^{48} +(-5.80616 - 3.91005i) q^{49} +(1.23590 - 0.564417i) q^{50} +(-0.547586 + 9.38237i) q^{51} +(0.201779 + 0.283359i) q^{52} +(-2.82502 - 8.16237i) q^{53} +(-2.52798 + 4.53975i) q^{54} +(-1.15649 + 0.339577i) q^{55} +(-1.12486 + 2.39472i) q^{56} +(2.67329 + 9.47831i) q^{57} +(4.20403 + 2.16733i) q^{58} +(-1.20197 - 6.23640i) q^{59} +(1.68309 - 2.84449i) q^{60} +(-4.44520 - 11.1036i) q^{61} +(-1.84880 - 1.60199i) q^{62} +(-7.91204 - 0.632172i) q^{63} +(0.959493 + 0.281733i) q^{64} +(0.385040 - 0.540713i) q^{65} +(0.685451 - 0.852690i) q^{66} +(-5.12924 - 9.94934i) q^{67} +(2.71307 + 4.69917i) q^{68} +(3.28924 - 7.62764i) q^{69} +(5.02038 + 0.533838i) q^{70} +(-5.70308 + 8.87416i) q^{71} +(0.221215 + 2.99183i) q^{72} +(16.4385 + 1.56969i) q^{73} +(-7.45344 + 7.10684i) q^{74} +(2.30588 + 0.470059i) q^{75} +(4.29704 + 3.72340i) q^{76} +(1.61974 + 0.411408i) q^{77} +(-0.00644508 + 0.602478i) q^{78} +(-11.8188 - 4.09053i) q^{79} +(-0.0907969 - 1.90606i) q^{80} +(-8.16861 + 3.77808i) q^{81} +(3.16044 - 9.13148i) q^{82} +(2.90370 - 0.852603i) q^{83} +(-4.01682 + 2.20571i) q^{84} +(6.78061 - 7.82524i) q^{85} +(3.72717 - 0.355901i) q^{86} +(3.67582 + 7.32134i) q^{87} +(0.0600416 - 0.628784i) q^{88} +(-0.199393 + 0.156804i) q^{89} +(5.25703 - 2.26617i) q^{90} +(-0.841240 + 0.373319i) q^{91} +(-0.833878 - 4.72278i) q^{92} +(-0.954838 - 4.12814i) q^{93} +(-3.70045 + 1.90772i) q^{94} +(4.03245 - 10.0726i) q^{95} +(1.05606 + 1.37286i) q^{96} +(-0.162509 + 0.553456i) q^{97} +(-5.61354 - 4.18189i) q^{98} +(1.82918 - 0.494846i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) \) 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9	\( 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9} + 64 q^{16} + 44 q^{18} - 132 q^{21} - 4 q^{24} + 72 q^{25} + 108 q^{27} + 44 q^{30} + 8 q^{36} + 44 q^{37} - 4 q^{39} - 88 q^{43} - 12 q^{46} + 60 q^{49} - 48 q^{54} + 96 q^{55} + 44 q^{58} - 176 q^{61} - 110 q^{63} + 128 q^{64} + 56 q^{69} - 120 q^{70} + 44 q^{72} + 40 q^{73} - 268 q^{75} + 16 q^{78} + 88 q^{79} + 8 q^{81} - 56 q^{82} - 22 q^{84} + 64 q^{85} - 42 q^{87} - 32 q^{93} + 8 q^{94} + 4 q^{96} + 132 q^{99}+O(q^{100}) \) 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9 + 64 * q^16 + 44 * q^18 - 132 * q^21 - 4 * q^24 + 72 * q^25 + 108 * q^27 + 44 * q^30 + 8 * q^36 + 44 * q^37 - 4 * q^39 - 88 * q^43 - 12 * q^46 + 60 * q^49 - 48 * q^54 + 96 * q^55 + 44 * q^58 - 176 * q^61 - 110 * q^63 + 128 * q^64 + 56 * q^69 - 120 * q^70 + 44 * q^72 + 40 * q^73 - 268 * q^75 + 16 * q^78 + 88 * q^79 + 8 * q^81 - 56 * q^82 - 22 * q^84 + 64 * q^85 - 42 * q^87 - 32 * q^93 + 8 * q^94 + 4 * q^96 + 132 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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