LMFDB - Embedded newform 966.2.bf.a.11.4

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			11.4
Character	$\chi$	$=$	966.11
Dual form			966.2.bf.a.527.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.458227 + 0.888835i) q^{2} +(-1.61477 - 0.626501i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(-1.38105 - 1.31683i) q^{5} +(1.29679 - 1.14819i) q^{6} +(2.39472 + 1.12486i) q^{7} +(0.989821 - 0.142315i) q^{8} +(2.21499 + 2.02332i) q^{9} +O(q^{10})$	\(q+(-0.458227 + 0.888835i) q^{2} +(-1.61477 - 0.626501i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(-1.38105 - 1.31683i) q^{5} +(1.29679 - 1.14819i) q^{6} +(2.39472 + 1.12486i) q^{7} +(0.989821 - 0.142315i) q^{8} +(2.21499 + 2.02332i) q^{9} +(1.80327 - 0.624119i) q^{10} +(0.561428 - 0.289436i) q^{11} +(0.426329 + 1.67876i) q^{12} +(0.227800 - 0.262896i) q^{13} +(-2.09714 + 1.61307i) q^{14} +(1.40509 + 2.99160i) q^{15} +(-0.327068 + 0.945001i) q^{16} +(-5.40156 - 0.515787i) q^{17} +(-2.81336 + 1.04163i) q^{18} +(0.540469 + 5.66005i) q^{19} +(-0.271569 + 1.88880i) q^{20} +(-3.16221 - 3.31669i) q^{21} +0.631644i q^{22} +(-3.36337 - 3.41874i) q^{23} +(-1.68750 - 0.390318i) q^{24} +(-0.0646487 - 1.35714i) q^{25} +(0.129287 + 0.322943i) q^{26} +(-2.30911 - 4.65489i) q^{27} +(-0.472791 - 2.60317i) q^{28} +(4.30240 - 1.96484i) q^{29} +(-3.30289 - 0.121941i) q^{30} +(2.27108 + 0.909201i) q^{31} +(-0.690079 - 0.723734i) q^{32} +(-1.08791 + 0.115639i) q^{33} +(2.93359 - 4.56475i) q^{34} +(-1.82598 - 4.70691i) q^{35} +(0.363322 - 2.97792i) q^{36} +(10.0083 - 2.42799i) q^{37} +(-5.27851 - 2.11320i) q^{38} +(-0.532551 + 0.281800i) q^{39} +(-1.55439 - 1.10688i) q^{40} +(2.72236 + 9.27152i) q^{41} +(4.39700 - 1.29089i) q^{42} +(3.70601 + 0.532844i) q^{43} +(-0.561428 - 0.289436i) q^{44} +(-0.394656 - 5.71105i) q^{45} +(4.57988 - 1.42292i) q^{46} +(3.60549 - 2.08163i) q^{47} +(1.12018 - 1.32105i) q^{48} +(4.46938 + 5.38745i) q^{49} +(1.23590 + 0.564417i) q^{50} +(8.39917 + 4.21696i) q^{51} +(-0.346286 - 0.0330663i) q^{52} +(8.48133 - 1.63464i) q^{53} +(5.19553 + 0.0805802i) q^{54} +(-1.15649 - 0.339577i) q^{55} +(2.53043 + 0.772606i) q^{56} +(2.67329 - 9.47831i) q^{57} +(-0.225054 + 4.72446i) q^{58} +(6.00186 - 2.07726i) q^{59} +(1.62186 - 2.87985i) q^{60} +(-7.39338 - 9.40145i) q^{61} +(-1.84880 + 1.60199i) q^{62} +(3.02835 + 7.33683i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-0.660791 + 0.0630979i) q^{65} +(0.395726 - 1.01996i) q^{66} +(11.1810 - 0.532617i) 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} +(2.48040 + 1.68749i) q^{72} +(-9.57865 - 13.4513i) q^{73} +(-2.42799 + 10.0083i) q^{74} +(-0.745859 + 2.23198i) q^{75} +(4.29704 - 3.72340i) q^{76} +(1.67004 - 0.0615915i) q^{77} +(-0.00644508 - 0.602478i) q^{78} +(2.36690 - 12.2806i) q^{79} +(1.69610 - 0.874399i) q^{80} +(0.812391 + 8.96326i) q^{81} +(-9.48831 - 1.82872i) q^{82} +(2.90370 + 0.852603i) q^{83} +(-0.867434 + 4.49973i) q^{84} +(6.78061 + 7.82524i) q^{85} +(-2.17180 + 3.04987i) q^{86} +(-8.17837 + 0.477316i) q^{87} +(0.514522 - 0.366390i) q^{88} +(0.235493 - 0.0942770i) q^{89} +(5.25703 + 2.26617i) q^{90} +(0.841240 - 0.373319i) q^{91} +(-0.833878 + 4.72278i) q^{92} +(-3.09766 - 2.89099i) q^{93} +(0.198096 + 4.15854i) q^{94} +(6.70688 - 8.52850i) q^{95} +(0.660902 + 1.60100i) q^{96} +(-0.162509 - 0.553456i) q^{97} +(-6.83655 + 1.50387i) 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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−0.458227	+	0.888835i	−0.324015	+	0.628502i
$2$	−0.458227	+	0.888835i	−0.324015	+	0.628502i
$3$	−1.61477	−	0.626501i	−0.932290	−	0.361710i
$3$	−1.61477	−	0.626501i	−0.932290	−	0.361710i
$4$	−0.580057	−	0.814576i	−0.290028	−	0.407288i
$5$	−1.38105	−	1.31683i	−0.617623	−	0.588902i	0.315294	−	0.948994i	$-0.397897\pi$
$5$	−1.38105	−	1.31683i	−0.617623	−	0.588902i	−0.932917	+	0.360092i	$0.882745\pi$
$6$	1.29679	−	1.14819i	0.529412	−	0.468746i
$7$	2.39472	+	1.12486i	0.905120	+	0.425157i
$7$	2.39472	+	1.12486i	0.905120	+	0.425157i
$8$	0.989821	−	0.142315i	0.349955	−	0.0503159i
$9$	2.21499	+	2.02332i	0.738331	+	0.674438i
$10$	1.80327	−	0.624119i	0.570245	−	0.197364i
$11$	0.561428	−	0.289436i	0.169277	−	0.0872683i	−0.371506	−	0.928431i	$-0.621158\pi$
$11$	0.561428	−	0.289436i	0.169277	−	0.0872683i	0.540783	+	0.841162i	$0.318128\pi$
$12$	0.426329	+	1.67876i	0.123070	+	0.484617i
$13$	0.227800	−	0.262896i	0.0631805	−	0.0729142i	−0.723279	−	0.690555i	$-0.757366\pi$
$13$	0.227800	−	0.262896i	0.0631805	−	0.0729142i	0.786460	+	0.617641i	$0.211912\pi$
$14$	−2.09714	+	1.61307i	−0.560484	+	0.431112i
$15$	1.40509	+	2.99160i	0.362792	+	0.772428i
$16$	−0.327068	+	0.945001i	−0.0817670	+	0.236250i
$17$	−5.40156	−	0.515787i	−1.31007	−	0.125097i	−0.583458	−	0.812143i	$-0.698301\pi$
$17$	−5.40156	−	0.515787i	−1.31007	−	0.125097i	−0.726614	+	0.687046i	$0.758907\pi$
$18$	−2.81336	+	1.04163i	−0.663116	+	0.245514i
$19$	0.540469	+	5.66005i	0.123992	+	1.29850i	0.816606	+	0.577196i	$0.195853\pi$
$19$	0.540469	+	5.66005i	0.123992	+	1.29850i	−0.692614	+	0.721309i	$0.743541\pi$
$20$	−0.271569	+	1.88880i	−0.0607246	+	0.422349i
$21$	−3.16221	−	3.31669i	−0.690051	−	0.723761i
$22$			0.631644i			0.134667i
$23$	−3.36337	−	3.41874i	−0.701310	−	0.712856i
$23$	−3.36337	−	3.41874i	−0.701310	−	0.712856i
$24$	−1.68750	−	0.390318i	−0.344459	−	0.0796732i
$25$	−0.0646487	−	1.35714i	−0.0129297	−	0.271429i
$26$	0.129287	+	0.322943i	0.0253552	+	0.0633343i
$27$	−2.30911	−	4.65489i	−0.444388	−	0.895835i
$28$	−0.472791	−	2.60317i	−0.0893491	−	0.491952i
$29$	4.30240	−	1.96484i	0.798935	−	0.364861i	0.0262535	−	0.999655i	$-0.491642\pi$
$29$	4.30240	−	1.96484i	0.798935	−	0.364861i	0.772681	+	0.634794i	$0.218915\pi$
$30$	−3.30289	−	0.121941i	−0.603022	−	0.0222633i
$31$	2.27108	+	0.909201i	0.407897	+	0.163297i	0.566532	−	0.824040i	$-0.308285\pi$
$31$	2.27108	+	0.909201i	0.407897	+	0.163297i	−0.158634	+	0.987337i	$0.550709\pi$
$32$	−0.690079	−	0.723734i	−0.121990	−	0.127939i
$33$	−1.08791	+	0.115639i	−0.189381	+	0.0201302i
$34$	2.93359	−	4.56475i	0.503107	−	0.782849i
$35$	−1.82598	−	4.70691i	−0.308647	−	0.795613i
$36$	0.363322	−	2.97792i	0.0605536	−	0.496320i
$37$	10.0083	−	2.42799i	1.64535	−	0.399158i	0.697176	−	0.716900i	$-0.254440\pi$
$37$	10.0083	−	2.42799i	1.64535	−	0.399158i	0.948177	+	0.317742i	$0.102925\pi$
$38$	−5.27851	−	2.11320i	−0.856288	−	0.342806i
$39$	−0.532551	+	0.281800i	−0.0852764	+	0.0451241i
$40$	−1.55439	−	1.10688i	−0.245771	−	0.175013i
$41$	2.72236	+	9.27152i	0.425162	+	1.44797i	0.842243	+	0.539098i	$0.181235\pi$
$41$	2.72236	+	9.27152i	0.425162	+	1.44797i	−0.417081	+	0.908869i	$0.636947\pi$
$42$	4.39700	−	1.29089i	0.678472	−	0.199188i
$43$	3.70601	+	0.532844i	0.565162	+	0.0812580i	0.418973	−	0.907999i	$-0.362390\pi$
$43$	3.70601	+	0.532844i	0.565162	+	0.0812580i	0.146189	+	0.989257i	$0.453299\pi$
$44$	−0.561428	−	0.289436i	−0.0846384	−	0.0436341i
$45$	−0.394656	−	5.71105i	−0.0588319	−	0.851353i
$46$	4.57988	−	1.42292i	0.675266	−	0.209799i
$47$	3.60549	−	2.08163i	0.525914	−	0.303637i	−0.213437	−	0.976957i	$-0.568466\pi$
$47$	3.60549	−	2.08163i	0.525914	−	0.303637i	0.739351	+	0.673320i	$0.235132\pi$
$48$	1.12018	−	1.32105i	0.161685	−	0.190678i
$49$	4.46938	+	5.38745i	0.638483	+	0.769636i
$50$	1.23590	+	0.564417i	0.174783	+	0.0798207i
$51$	8.39917	+	4.21696i	1.17612	+	0.590493i
$52$	−0.346286	−	0.0330663i	−0.0480212	−	0.00458547i
$53$	8.48133	−	1.63464i	1.16500	−	0.224535i	0.430145	−	0.902760i	$-0.358462\pi$
$53$	8.48133	−	1.63464i	1.16500	−	0.224535i	0.734855	+	0.678224i	$0.237250\pi$
$54$	5.19553	+	0.0805802i	0.707022	+	0.0109656i
$55$	−1.15649	−	0.339577i	−0.155942	−	0.0457886i
$56$	2.53043	+	0.772606i	0.338143	+	0.103244i
$57$	2.67329	−	9.47831i	0.354086	−	1.25543i
$58$	−0.225054	+	4.72446i	−0.0295510	+	0.620352i
$59$	6.00186	−	2.07726i	0.781376	−	0.270437i	0.0928803	−	0.995677i	$-0.470393\pi$
$59$	6.00186	−	2.07726i	0.781376	−	0.270437i	0.688496	+	0.725240i	$0.258271\pi$
$60$	1.62186	−	2.87985i	0.209381	−	0.371787i
$61$	−7.39338	−	9.40145i	−0.946625	−	1.20373i	−0.978918	−	0.204254i	$-0.934523\pi$
$61$	−7.39338	−	9.40145i	−0.946625	−	1.20373i	0.0322926	−	0.999478i	$-0.489719\pi$
$62$	−1.84880	+	1.60199i	−0.234797	+	0.203453i
$63$	3.02835	+	7.33683i	0.381536	+	0.924354i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	−0.660791	+	0.0630979i	−0.0819610	+	0.00782633i
$66$	0.395726	−	1.01996i	0.0487105	−	0.125549i
$67$	11.1810	−	0.532617i	1.36598	−	0.0650695i	0.648268	−	0.761413i	$-0.275494\pi$
$67$	11.1810	−	0.532617i	1.36598	−	0.0650695i	0.717709	+	0.696343i	$0.245191\pi$
$68$	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	−0.994476	−	0.104960i	$-0.966529\pi$
$71$	−5.70308	−	8.87416i	−0.676831	−	1.05317i	0.317645	−	0.948210i	$-0.397108\pi$
$72$	2.48040	+	1.68749i	0.292317	+	0.198873i
$73$	−9.57865	−	13.4513i	−1.12110	−	1.57436i	−0.770029	−	0.638009i	$-0.779758\pi$
$73$	−9.57865	−	13.4513i	−1.12110	−	1.57436i	−0.351068	−	0.936350i	$-0.614181\pi$
$74$	−2.42799	+	10.0083i	−0.282248	+	1.16344i
$75$	−0.745859	+	2.23198i	−0.0861244	+	0.257727i
$76$	4.29704	−	3.72340i	0.492904	−	0.427104i
$77$	1.67004	−	0.0615915i	0.190319	−	0.00701900i
$78$	−0.00644508	−	0.602478i	−0.000729761	−	0.0682172i
$79$	2.36690	−	12.2806i	0.266297	−	1.38168i	−0.564650	−	0.825330i	$-0.690989\pi$
$79$	2.36690	−	12.2806i	0.266297	−	1.38168i	0.830948	−	0.556351i	$-0.187799\pi$
$80$	1.69610	−	0.874399i	0.189629	−	0.0977607i
$81$	0.812391	+	8.96326i	0.0902657	+	0.995918i
$82$	−9.48831	−	1.82872i	−1.04781	−	0.201949i
$83$	2.90370	+	0.852603i	0.318723	+	0.0935854i	0.437181	−	0.899374i	$-0.355977\pi$
$83$	2.90370	+	0.852603i	0.318723	+	0.0935854i	−0.118458	+	0.992959i	$0.537795\pi$
$84$	−0.867434	+	4.49973i	−0.0946448	+	0.490961i
$85$	6.78061	+	7.82524i	0.735460	+	0.848767i
$86$	−2.17180	+	3.04987i	−0.234192	+	0.328876i
$87$	−8.17837	+	0.477316i	−0.876814	+	0.0511737i
$88$	0.514522	−	0.366390i	0.0548483	−	0.0390573i
$89$	0.235493	−	0.0942770i	0.0249622	−	0.00999334i	−0.359148	−	0.933281i	$-0.616933\pi$
$89$	0.235493	−	0.0942770i	0.0249622	−	0.00999334i	0.384110	+	0.923287i	$0.374508\pi$
$90$	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
$93$	−3.09766	−	2.89099i	−0.321212	−	0.299781i
$94$	0.198096	+	4.15854i	0.0204320	+	0.428921i
$95$	6.70688	−	8.52850i	0.688112	−	0.875005i
$96$	0.660902	+	1.60100i	0.0674530	+	0.163402i
$97$	−0.162509	−	0.553456i	−0.0165003	−	0.0561949i	0.950831	−	0.309709i	$-0.100232\pi$
$97$	−0.162509	−	0.553456i	−0.0165003	−	0.0561949i	−0.967332	+	0.253514i	$0.918414\pi$
$98$	−6.83655	+	1.50387i	−0.690595	+	0.151914i
$99$	1.82918	+	0.494846i	0.183839	+	0.0497339i
$100$	−1.06800	+	0.839882i	−0.106800	+	0.0839882i
$101$	−4.74835	−	4.97993i	−0.472479	−	0.495522i	0.443765	−	0.896143i	$-0.353643\pi$
$101$	−4.74835	−	4.97993i	−0.472479	−	0.495522i	−0.916244	+	0.400622i	$0.868794\pi$
$102$	−7.59691	+	5.53315i	−0.752206	+	0.547864i
$103$	12.8895	+	0.614001i	1.27004	+	0.0604993i	0.671747	−	0.740780i	$-0.265544\pi$
$103$	12.8895	+	0.614001i	1.27004	+	0.0604993i	0.598290	+	0.801280i	$0.295847\pi$
$104$	0.188068	−	0.292639i	0.0184416	−	0.0286956i
$105$	−0.000341857		8.74458i	−3.33618e−5		0.853384i
$106$	−2.43344	+	8.28755i	−0.236357	+	0.804958i
$107$	14.9054	−	11.7218i	1.44096	−	1.13319i	0.473311	−	0.880895i	$-0.343059\pi$
$107$	14.9054	−	11.7218i	1.44096	−	1.13319i	0.967652	−	0.252290i	$-0.0811838\pi$
$108$	−2.45235	+	4.58105i	−0.235978	+	0.440811i
$109$	−0.389477	+	4.07879i	−0.0373052	+	0.390677i	0.957466	+	0.288547i	$0.0931720\pi$
$109$	−0.389477	+	4.07879i	−0.0373052	+	0.390677i	−0.994771	+	0.102131i	$0.967434\pi$
$110$	0.831765	−	0.872330i	0.0793057	−	0.0831734i
$111$	−17.6823	−	2.34955i	−1.67833	−	0.223010i
$112$	−1.84623	+	1.89511i	−0.174452	+	0.179071i
$113$	−15.0173	+	9.65103i	−1.41271	+	0.907893i	−0.999996	−	0.00296834i	$-0.999055\pi$
$113$	−15.0173	+	9.65103i	−1.41271	+	0.907893i	−0.412713	+	0.910861i	$0.635419\pi$
$114$	7.19969	+	6.71933i	0.674312	+	0.629323i
$115$	0.143085	+	9.15040i	0.0133427	+	0.853279i
$116$	−4.09615	−	2.36491i	−0.380318	−	0.219576i
$117$	1.03650	−	0.121400i	0.0958242	−	0.0112235i
$118$	−0.903866	+	6.28653i	−0.0832076	+	0.578722i
$119$	−12.3551	−	7.31117i	−1.13259	−	0.670214i
$120$	1.81653	+	2.76119i	0.165826	+	0.252061i
$121$	−6.14920	+	8.63534i	−0.559018	+	0.785031i
$122$	11.7442	−	2.26351i	1.06327	−	0.204928i
$123$	1.41261	−	16.6770i	0.127371	−	1.50371i
$124$	−0.576739	−	2.37735i	−0.0517927	−	0.213492i
$125$	−7.94594	+	9.17011i	−0.710707	+	0.820199i
$126$	−7.90891	−	0.670230i	−0.704581	−	0.0597088i
$127$	9.31702	+	5.98768i	0.826752	+	0.531321i	0.884244	−	0.467025i	$-0.154674\pi$
$127$	9.31702	+	5.98768i	0.826752	+	0.531321i	−0.0574926	+	0.998346i	$0.518311\pi$
$128$	−0.189251	+	0.981929i	−0.0167276	+	0.0867911i
$129$	−5.65055	−	3.18224i	−0.497503	−	0.280181i
$130$	0.246708	−	0.616247i	0.0216377	−	0.0540485i
$131$	11.8974	+	4.11771i	1.03948	+	0.359766i	0.792897	−	0.609356i	$-0.208572\pi$
$131$	11.8974	+	4.11771i	1.03948	+	0.359766i	0.246580	+	0.969122i	$0.420693\pi$
$132$	0.725247	+	0.819109i	0.0631247	+	0.0712943i
$133$	−5.07249	+	14.1622i	−0.439841	+	1.22802i
$134$	−4.65002	+	10.1821i	−0.401701	+	0.879602i
$135$	−2.94070	+	9.46931i	−0.253095	+	0.814989i
$136$	−5.41999	+	0.258186i	−0.464760	+	0.0221393i
$137$	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	$0.0139530\pi$
$138$	−8.28693	−	0.571599i	−0.705431	−	0.0486577i
$139$	8.22880			0.697957			0.348979	−	0.937131i	$-0.386529\pi$
$139$	8.22880			0.697957			0.348979	+	0.937131i	$0.386529\pi$
$140$	−2.77497	+	4.21767i	−0.234527	+	0.356459i
$141$	−7.12619	+	1.10252i	−0.600134	+	0.0928490i
$142$	10.5010	−	1.00272i	0.881222	−	0.0841465i
$143$	0.0518020	−	0.213531i	0.00433190	−	0.0178563i
$144$	−2.63649	+	1.43141i	−0.219707	+	0.119284i
$145$	−8.52916	−	2.95197i	−0.708308	−	0.245148i
$146$	16.3452	−	2.35009i	1.35274	−	0.194495i
$147$	−3.84180	−	11.4996i	−0.316866	−	0.948470i
$148$	−7.78316	−	6.74414i	−0.639772	−	0.554365i
$149$	0.0482987	−	1.01391i	0.00395678	−	0.0830631i	−0.996025	−	0.0890723i	$-0.971610\pi$
$149$	0.0482987	−	1.01391i	0.00395678	−	0.0830631i	0.999982	+	0.00600924i	$0.00191281\pi$
$150$	−1.64209	−	1.68570i	−0.134076	−	0.137637i
$151$	−0.701147	−	2.02583i	−0.0570585	−	0.164860i	0.912870	−	0.408251i	$-0.133861\pi$
$151$	−0.701147	−	2.02583i	−0.0570585	−	0.164860i	−0.969928	+	0.243391i	$0.921740\pi$
$152$	1.34048	+	5.52552i	0.108727	+	0.448179i
$153$	−10.9208	−	12.0715i	−0.882897	−	0.975926i
$154$	−0.710511	+	1.51261i	−0.0572546	+	0.121890i
$155$	−1.93920	−	4.24626i	−0.155760	−	0.341068i
$156$	0.538457	+	0.270343i	0.0431111	+	0.0216448i
$157$	−3.64016	+	2.59215i	−0.290516	+	0.206876i	−0.716018	−	0.698082i	$-0.754037\pi$
$157$	−3.64016	+	2.59215i	−0.290516	+	0.206876i	0.425501	+	0.904958i	$0.360098\pi$
$158$	9.83090	+	7.73110i	0.782104	+	0.615054i
$159$	−14.7195	−	2.67398i	−1.16734	−	0.212061i
$160$			1.90822i			0.150858i
$161$	−4.20873	−	11.9702i	−0.331694	−	0.943387i
$162$	−8.33912	−	3.38512i	−0.655183	−	0.265960i
$163$	−5.51120	−	2.84122i	−0.431671	−	0.222542i	0.228676	−	0.973503i	$-0.426560\pi$
$163$	−5.51120	−	2.84122i	−0.431671	−	0.222542i	−0.660347	+	0.750961i	$0.729591\pi$
$164$	5.97323	−	7.59558i	0.466431	−	0.593115i
$165$	1.65473	+	1.27289i	0.128821	+	0.0990940i
$166$	−2.08838	+	2.19023i	−0.162089	+	0.169995i
$167$	13.5673	−	6.19598i	1.04987	−	0.479460i	0.185672	−	0.982612i	$-0.440554\pi$
$167$	13.5673	−	6.19598i	1.04987	−	0.479460i	0.864198	+	0.503152i	$0.167826\pi$
$168$	−3.60204	−	2.83290i	−0.277903	−	0.218563i
$169$	1.83287	+	12.7479i	0.140990	+	0.980608i
$170$	−10.0624	+	2.44111i	−0.771751	+	0.187225i
$171$	−10.2549	+	13.6305i	−0.784214	+	1.04235i
$172$	−1.71566	−	3.32791i	−0.130818	−	0.253751i
$173$	5.15149	+	0.245396i	0.391660	+	0.0186571i	0.242489	−	0.970154i	$-0.422036\pi$
$173$	5.15149	+	0.245396i	0.391660	+	0.0186571i	0.149172	+	0.988811i	$0.452339\pi$
$174$	3.32329	−	7.48795i	0.251938	−	0.567660i
$175$	1.37178	−	3.32270i	0.103697	−	0.251173i
$176$	0.0898924	+	0.625215i	0.00677589	+	0.0471274i
$177$	−10.9931	−	0.405858i	−0.826289	−	0.0305061i
$178$	−0.0241122	+	0.252514i	−0.00180729	+	0.0189268i
$179$	−7.08770	−	1.71946i	−0.529759	−	0.128518i	−0.0380471	−	0.999276i	$-0.512114\pi$
$179$	−7.08770	−	1.71946i	−0.529759	−	0.128518i	−0.491712	+	0.870758i	$0.663629\pi$
$180$	−4.42316	+	3.63421i	−0.329683	+	0.270878i
$181$	10.4603	+	1.50396i	0.777505	+	0.111788i	0.519632	−	0.854390i	$-0.326069\pi$
$181$	10.4603	+	1.50396i	0.777505	+	0.111788i	0.257873	+	0.966179i	$0.416978\pi$
$182$	−0.0536595	+	0.918788i	−0.00397750	+	0.0681051i
$183$	6.04863	+	19.8132i	0.447127	+	1.46463i
$184$	−3.81567	−	2.90528i	−0.281295	−	0.214180i
$185$	−17.0191	−	9.82601i	−1.25127	−	0.722422i
$186$	3.98904	−	1.42858i	0.292491	−	0.104749i
$187$	−3.18188	+	1.27383i	−0.232682	+	0.0931517i
$188$	−3.78703	−	1.72948i	−0.276198	−	0.126135i
$189$	−0.293565	−	13.7446i	−0.0213537	−	0.999772i
$190$	4.50716	+	9.86930i	0.326984	+	0.715994i
$191$	−0.321292	+	0.928314i	−0.0232479	+	0.0671704i	−0.956028	−	0.293276i	$-0.905254\pi$
$191$	−0.321292	+	0.928314i	−0.0232479	+	0.0671704i	0.932780	+	0.360447i	$0.117376\pi$
$192$	−1.72587	−	0.146189i	−0.124554	−	0.0105503i
$193$	9.89327	−	9.43322i	0.712133	−	0.679018i	−0.244718	−	0.969594i	$-0.578696\pi$
$193$	9.89327	−	9.43322i	0.712133	−	0.679018i	0.956852	+	0.290576i	$0.0938470\pi$
$194$	0.566397	+	0.109164i	0.0406649	+	0.00783753i
$195$	1.10656	+	0.312097i	0.0792423	+	0.0223497i
$196$	1.79599	−	6.76568i	0.128285	−	0.483263i
$197$	−3.01039	−	2.60851i	−0.214481	−	0.185849i	0.540994	−	0.841027i	$-0.318048\pi$
$197$	−3.01039	−	2.60851i	−0.214481	−	0.185849i	−0.755475	+	0.655178i	$0.772594\pi$
$198$	−1.27802	+	1.39909i	−0.0908246	+	0.0994288i
$199$	2.13180	−	5.32499i	0.151120	−	0.377478i	−0.833420	−	0.552640i	$-0.813621\pi$
$199$	2.13180	−	5.32499i	0.151120	−	0.377478i	0.984540	+	0.175162i	$0.0560448\pi$
$200$	−0.257132	−	1.33413i	−0.0181820	−	0.0943372i
$201$	−18.3885	−	6.14485i	−1.29702	−	0.433424i
$202$	6.60216	−	1.93857i	0.464526	−	0.136397i
$203$	12.5132	+	0.134351i	0.878255	+	0.00942957i
$204$	−1.43696	−	9.28784i	−0.100607	−	0.650279i
$205$	8.44926	−	16.3893i	0.590122	−	1.14468i
$206$	−6.45204	+	11.1753i	−0.449535	+	0.778618i
$207$	−0.532649	−	14.3776i	−0.0370217	−	0.999314i
$208$	0.173930	+	0.301256i	0.0120599	+	0.0208884i
$209$	1.94166	+	3.02128i	0.134307	+	0.208986i
$210$	−7.77233	−	4.00730i	−0.536342	−	0.276530i
$211$	−11.9332	+	26.1300i	−0.821514	+	1.79887i	−0.274921	+	0.961467i	$0.588652\pi$
$211$	−11.9332	+	26.1300i	−0.821514	+	1.79887i	−0.546593	+	0.837398i	$0.684076\pi$
$212$	−6.25120	−	5.96050i	−0.429334	−	0.409369i
$213$	3.64952	+	17.9028i	0.250061	+	1.22668i
$214$	3.58865	+	18.6197i	0.245315	+	1.27282i
$215$	−4.41651	−	5.61605i	−0.301204	−	0.383012i
$216$	−2.94806	−	4.27889i	−0.200590	−	0.291142i
$217$	4.41587	+	4.73192i	0.299769	+	0.321224i
$218$	−3.44690	−	2.21519i	−0.233454	−	0.150032i
$219$	7.04009	+	27.7219i	0.475725	+	1.87327i
$220$	0.394221	+	1.13903i	0.0265784	+	0.0767932i
$221$	−1.36608	+	1.30255i	−0.0918923	+	0.0876191i
$222$	10.1909	−	14.6400i	0.683965	−	0.982572i
$223$	−1.13345	−	1.30807i	−0.0759014	−	0.0875949i	0.716529	−	0.697558i	$-0.245730\pi$
$223$	−1.13345	−	1.30807i	−0.0759014	−	0.0875949i	−0.792430	+	0.609963i	$0.791184\pi$
$224$	−0.838448	−	2.50938i	−0.0560212	−	0.167665i
$225$	2.60273	−	3.13687i	0.173516	−	0.209125i
$226$	−1.69685	−	17.7703i	−0.112873	−	1.18206i
$227$	0.00115867		0.000911191i	7.69039e−5		6.04779e-5i	0.618197	−	0.786023i	$-0.287863\pi$
$227$	0.00115867		0.000911191i	7.69039e−5		6.04779e-5i	−0.618121	+	0.786083i	$0.712106\pi$
$228$	−9.27146	+	3.32036i	−0.614018	+	0.219896i
$229$	−8.79353	+	5.07695i	−0.581093	+	0.335494i	−0.761567	−	0.648086i	$-0.775570\pi$
$229$	−8.79353	+	5.07695i	−0.581093	+	0.335494i	0.180475	+	0.983580i	$0.442237\pi$
$230$	−8.19877	−	4.06578i	−0.540611	−	0.268089i
$231$	−2.73532	−	0.946824i	−0.179971	−	0.0622964i
$232$	3.97898	−	2.55713i	0.261233	−	0.167884i
$233$	2.76409	+	6.90437i	0.181082	+	0.452321i	0.990940	−	0.134305i	$-0.0428802\pi$
$233$	2.76409	+	6.90437i	0.181082	+	0.452321i	−0.809858	+	0.586626i	$0.800456\pi$
$234$	−0.367046	+	0.976905i	−0.0239945	+	0.0638622i
$235$	−7.72049	−	1.87297i	−0.503629	−	0.122179i
$236$	−5.17351	−	3.68404i	−0.336767	−	0.239811i
$237$	−11.5158	+	18.3476i	−0.748035	+	1.19181i
$238$	12.1598	−	7.63144i	0.788205	−	0.494673i
$239$	−0.985158	+	3.35514i	−0.0637246	+	0.217026i	−0.985199	−	0.171412i	$-0.945167\pi$
$239$	−0.985158	+	3.35514i	−0.0637246	+	0.217026i	0.921475	+	0.388438i	$0.126985\pi$
$240$	−3.28663	+	0.349351i	−0.212151	+	0.0225505i
$241$	−9.65330	−	18.7248i	−0.621824	−	1.20617i	−0.963841	−	0.266477i	$-0.914141\pi$
$241$	−9.65330	−	18.7248i	−0.621824	−	1.20617i	0.342018	−	0.939694i	$-0.388890\pi$
$242$	−4.85767	−	9.42257i	−0.312263	−	0.605706i
$243$	4.30366	−	14.9826i	0.276080	−	0.961135i
$244$	−3.36961	+	11.4758i	−0.215717	+	0.734666i
$245$	0.921907	−	13.3257i	0.0588985	−	0.851349i
$246$	14.1758	+	8.89741i	0.903815	+	0.567278i
$247$	1.61112	+	1.14728i	0.102513	+	0.0729994i
$248$	2.37735	+	0.576739i	0.150962	+	0.0366230i
$249$	−4.15466	−	3.19593i	−0.263291	−	0.202534i
$250$	−4.50967	−	11.2646i	−0.285217	−	0.712437i
$251$	13.5074	−	8.68070i	0.852582	−	0.547921i	−0.0397971	−	0.999208i	$-0.512671\pi$
$251$	13.5074	−	8.68070i	0.852582	−	0.547921i	0.892379	+	0.451287i	$0.149035\pi$
$252$	4.21979	−	6.72260i	0.265822	−	0.423484i
$253$	−2.87779	−	0.945895i	−0.180925	−	0.0594679i
$254$	−9.59137	+	5.53758i	−0.601816	+	0.347459i
$255$	−6.04664	−	16.8841i	−0.378655	−	1.05732i
$256$	−0.786053	−	0.618159i	−0.0491283	−	0.0386349i
$257$	1.71475	+	17.9577i	0.106963	+	1.12017i	0.876445	+	0.481502i	$0.159909\pi$
$257$	1.71475	+	17.9577i	0.106963	+	1.12017i	−0.769482	+	0.638669i	$0.779485\pi$
$258$	5.41772	−	3.56422i	0.337293	−	0.221899i
$259$	26.6982	+	5.44357i	1.65895	+	0.338247i
$260$	0.434694	+	0.501664i	0.0269586	+	0.0311119i
$261$	13.5053	+	4.35300i	0.835955	+	0.269444i
$262$	−9.11165	+	8.68794i	−0.562920	+	0.536743i
$263$	4.67576	+	13.5097i	0.288320	+	0.833046i	0.992414	+	0.122939i	$0.0392321\pi$
$263$	4.67576	+	13.5097i	0.288320	+	0.833046i	−0.704094	+	0.710107i	$0.748647\pi$
$264$	−1.06038	+	0.269288i	−0.0652619	+	0.0165735i
$265$	−13.8657	−	8.91091i	−0.851760	−	0.547393i
$266$	−10.2635	−	10.9981i	−0.629296	−	0.674337i
$267$	−0.439332	+	0.00469980i	−0.0268867	+	0.000287623i
$268$	−6.91947	−	8.79883i	−0.422674	−	0.537474i
$269$	4.99418	+	25.9123i	0.304500	+	1.57990i	0.735486	+	0.677540i	$0.236954\pi$
$269$	4.99418	+	25.9123i	0.304500	+	1.57990i	−0.430986	+	0.902359i	$0.641834\pi$
$270$	−7.06915	−	6.95289i	−0.430215	−	0.423139i
$271$	−16.3507	−	15.5904i	−0.993234	−	0.947047i	0.00536376	−	0.999986i	$-0.498293\pi$
$271$	−16.3507	−	15.5904i	−0.993234	−	0.947047i	−0.998598	+	0.0529389i	$0.983141\pi$
$272$	2.25410	−	4.93579i	0.136675	−	0.299276i
$273$	−1.59230	+	0.0757880i	−0.0963702	+	0.00458690i
$274$	5.84167	+	9.08981i	0.352908	+	0.549135i
$275$	−0.429102	−	0.743227i	−0.0258758	−	0.0448183i
$276$	4.30535	−	7.10380i	0.259152	−	0.427598i
$277$	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	$0.141024\pi$
$278$	−3.77065	+	7.31404i	−0.226149	+	0.438667i
$279$	3.19082	+	6.60898i	0.191029	+	0.395669i
$280$	−2.47726	−	4.39914i	−0.148044	−	0.262899i
$281$	−22.4394	+	6.58880i	−1.33862	+	0.393055i	−0.871178	−	0.490968i	$-0.836643\pi$
$281$	−22.4394	+	6.58880i	−1.33862	+	0.393055i	−0.467444	+	0.884023i	$0.654825\pi$
$282$	2.28545	−	6.83922i	0.136097	−	0.407269i
$283$	2.96626	+	15.3904i	0.176326	+	0.914866i	0.957035	+	0.289972i	$0.0936458\pi$
$283$	2.96626	+	15.3904i	0.176326	+	0.914866i	−0.780709	+	0.624894i	$0.785142\pi$
$284$	−3.92057	+	9.79311i	−0.232643	+	0.581114i
$285$	−16.1732	+	9.56973i	−0.958018	+	0.566862i
$286$	0.166057	+	0.143889i	0.00981913	+	0.00850833i
$287$	−3.90985	+	25.2650i	−0.230791	+	1.49134i
$288$	−0.0641783	−	2.99931i	−0.00378174	−	0.176736i
$289$	12.2181	+	2.35484i	0.718710	+	0.138520i
$290$	6.53210	−	6.22835i	0.383578	−	0.365741i
$291$	−0.0843247	+	0.995518i	−0.00494320	+	0.0583583i
$292$	−5.40097	+	15.6051i	−0.316068	+	0.913218i
$293$	0.982919	+	2.15229i	0.0574227	+	0.125738i	0.936168	−	0.351553i	$-0.114346\pi$
$293$	0.982919	+	2.15229i	0.0574227	+	0.125738i	−0.878745	+	0.477291i	$0.841619\pi$
$294$	11.9817	+	1.85469i	0.698784	+	0.108168i
$295$	−11.0242	−	5.03460i	−0.641856	−	0.293126i
$296$	9.56088	−	3.82760i	0.555715	−	0.222475i
$297$	−2.64369	−	1.94505i	−0.153402	−	0.112863i
$298$	0.879071	+	0.507532i	0.0509232	+	0.0294005i
$299$	−1.66495	+	0.105425i	−0.0962864	+	0.00609686i
$300$	2.25076	−	0.687119i	0.129948	−	0.0396708i
$301$	8.27549	+	5.44476i	0.476991	+	0.313831i
$302$	2.12191	+	0.305085i	0.122102	+	0.0175557i
$303$	4.54759	+	11.0163i	0.261252	+	0.632871i
$304$	−5.52552	−	1.34048i	−0.316910	−	0.0768816i
$305$	−2.16946	+	22.7196i	−0.124223	+	1.30092i
$306$	15.7338	−	4.17532i	0.899443	−	0.238687i
$307$	−3.34037	−	23.2328i	−0.190645	−	1.32596i	−0.830306	−	0.557308i	$-0.811834\pi$
$307$	−3.34037	−	23.2328i	−0.190645	−	1.32596i	0.639661	−	0.768657i	$-0.279075\pi$
$308$	−1.01889	−	1.32465i	−0.0580565	−	0.0754787i
$309$	−20.4289	−	9.06674i	−1.16216	−	0.515789i
$310$	4.66282	+	0.222117i	0.264830	+	0.0126154i
$311$	−0.335826	−	0.651411i	−0.0190429	−	0.0369381i	0.879122	−	0.476597i	$-0.158130\pi$
$311$	−0.335826	−	0.651411i	−0.0190429	−	0.0369381i	−0.898165	+	0.439659i	$0.855099\pi$
$312$	−0.487026	+	0.354722i	−0.0275724	+	0.0200822i
$313$	−1.87959	+	0.455983i	−0.106240	+	0.0257737i	−0.288527	−	0.957472i	$-0.593165\pi$
$313$	−1.87959	+	0.455983i	−0.106240	+	0.0257737i	0.182286	+	0.983246i	$0.441650\pi$
$314$	−0.635974	−	4.42329i	−0.0358901	−	0.249621i
$315$	5.47904	−	14.1203i	0.308709	−	0.795589i
$316$	−11.3765	+	5.19545i	−0.639976	+	0.292267i
$317$	3.89717	−	4.08723i	0.218887	−	0.229562i	−0.605131	−	0.796126i	$-0.706879\pi$
$317$	3.89717	−	4.08723i	0.218887	−	0.229562i	0.824018	+	0.566564i	$0.191728\pi$
$318$	9.12162	−	11.8580i	0.511515	−	0.664962i
$319$	1.84679	−	2.34838i	0.103400	−	0.131484i
$320$	−1.69610	−	0.874399i	−0.0948147	−	0.0488804i
$321$	−31.4126	+	9.58974i	−1.75328	+	0.535247i
$322$	12.5681	+	1.74422i	0.700394	+	0.0972014i
$323$		−	30.8519i		−	1.71665i
$324$	6.83002	−	5.86095i	0.379446	−	0.325609i
$325$	−0.371514	−	0.292162i	−0.0206079	−	0.0162062i
$326$	5.05076	−	3.59663i	0.279736	−	0.199199i
$327$	3.18428	−	6.34232i	0.176091	−	0.350731i
$328$	4.01413	+	8.78971i	0.221643	+	0.485331i
$329$	10.9757	−	0.929255i	0.605109	−	0.0512315i
$330$	−1.88963	+	0.887515i	−0.104021	+	0.0488561i
$331$	−3.31403	−	13.6606i	−0.182156	−	0.750856i	−0.987444	−	0.157972i	$-0.949504\pi$
$331$	−3.31403	−	13.6606i	−0.182156	−	0.750856i	0.805288	−	0.592884i	$-0.202011\pi$
$332$	−0.989801	−	2.85984i	−0.0543224	−	0.156954i
$333$	27.0809	+	14.8720i	1.48402	+	0.814978i
$334$	−0.709692	+	14.8983i	−0.0388326	+	0.815197i
$335$	−16.1428	−	13.9879i	−0.881978	−	0.764238i
$336$	4.16853	−	1.90351i	0.227412	−	0.103845i
$337$	−25.9099	+	3.72528i	−1.41140	+	0.202929i	−0.805493	−	0.592605i	$-0.798099\pi$
$337$	−25.9099	+	3.72528i	−1.41140	+	0.202929i	−0.605909	+	0.795534i	$0.707190\pi$
$338$	−12.1707	−	4.21231i	−0.661997	−	0.229119i
$339$	30.2959	−	6.17589i	1.64545	−	0.335428i
$340$	2.44111	−	10.0624i	0.132388	−	0.545711i
$341$	1.53820	−	0.146880i	0.0832982	−	0.00795402i
$342$	−7.41620	−	15.3608i	−0.401022	−	0.830617i
$343$	4.64280	+	17.9289i	0.250688	+	0.968068i
$344$	3.74412			0.201870
$345$	5.50168	−	14.8655i	0.296201	−	0.800330i
$346$	−2.57866	+	4.46638i	−0.138630	+	0.240114i
$347$	−6.68845	+	0.318610i	−0.359055	+	0.0171039i	−0.226335	−	0.974050i	$-0.572674\pi$
$347$	−6.68845	+	0.318610i	−0.359055	+	0.0171039i	−0.132720	+	0.991154i	$0.542371\pi$
$348$	5.13273	+	6.38504i	0.275143	+	0.342274i
$349$	0.930448	−	2.03740i	0.0498057	−	0.109059i	−0.883093	−	0.469198i	$-0.844543\pi$
$349$	0.930448	−	2.03740i	0.0498057	−	0.109059i	0.932899	+	0.360138i	$0.117270\pi$
$350$	2.32475	+	2.74184i	0.124263	+	0.146557i
$351$	−1.74977	−	0.453333i	−0.0933957	−	0.0241971i
$352$	−0.596904	−	0.206591i	−0.0318151	−	0.0110113i
$353$	9.25333	−	23.1137i	0.492505	−	1.23022i	−0.449094	−	0.893484i	$-0.648253\pi$
$353$	9.25333	−	23.1137i	0.492505	−	1.23022i	0.941600	−	0.336734i	$-0.109322\pi$
$354$	5.39805	−	9.58505i	0.286903	−	0.509440i
$355$	−3.80951	+	19.7656i	−0.202188	+	1.04905i
$356$	−0.213395	−	0.137141i	−0.0113099	−	0.00726844i
$357$	15.3702	+	19.5463i	0.813476	+	1.03450i
$358$	4.77609	−	5.51190i	0.252424	−	0.291313i
$359$	6.21637	+	25.6242i	0.328087	+	1.35239i	0.862023	+	0.506869i	$0.169197\pi$
$359$	6.21637	+	25.6242i	0.328087	+	1.35239i	−0.533936	+	0.845525i	$0.679288\pi$
$360$	−1.20341	−	5.59675i	−0.0634251	−	0.294975i
$361$	−13.0874	+	2.52239i	−0.688812	+	0.132758i
$362$	−6.12994	+	8.60829i	−0.322182	+	0.452442i
$363$	15.3396	−	10.0916i	0.805121	−	0.529674i
$364$	−0.792063	−	0.468707i	−0.0415154	−	0.0245669i
$365$	−4.48449	+	31.1903i	−0.234729	+	1.63258i
$366$	−20.3823	−	3.70269i	−1.06540	−	0.193543i
$367$	−27.9848	−	16.1571i	−1.46080	−	0.843391i	−0.461748	−	0.887011i	$-0.652778\pi$
$367$	−27.9848	−	16.1571i	−1.46080	−	0.843391i	−0.999048	+	0.0436197i	$0.986111\pi$
$368$	4.33076	−	2.06022i	0.225756	−	0.107397i
$369$	−12.7292	+	26.0445i	−0.662655	+	1.35583i
$370$	16.5323	−	10.6247i	0.859475	−	0.552351i
$371$	22.1492	+	5.62579i	1.14993	+	0.292077i
$372$	−0.558109	+	4.20021i	−0.0289366	+	0.217771i
$373$	6.35602	−	6.66600i	0.329102	−	0.345152i	−0.538306	−	0.842749i	$-0.680936\pi$
$373$	6.35602	−	6.66600i	0.329102	−	0.345152i	0.867408	+	0.497597i	$0.165784\pi$
$374$	0.325794	−	3.41187i	0.0168464	−	0.176423i
$375$	18.5760	−	9.82951i	0.959260	−	0.507594i
$376$	3.27254	−	2.57356i	0.168768	−	0.132721i
$377$	0.463540	−	1.57867i	0.0238735	−	0.0813058i
$378$	12.3512	+	6.03721i	0.635277	+	0.310520i
$379$	4.34297	−	6.75779i	0.223083	−	0.347124i	−0.711613	−	0.702571i	$-0.752035\pi$
$379$	4.34297	−	6.75779i	0.223083	−	0.347124i	0.934696	+	0.355447i	$0.115671\pi$
$380$	−10.8375	−	0.516253i	−0.555951	−	0.0264832i
$381$	−11.2936	−	15.5059i	−0.578588	−	0.794390i
$382$	−0.677893	−	0.710954i	−0.0346840	−	0.0363756i
$383$	−0.735983	+	0.578783i	−0.0376070	+	0.0295745i	−0.636786	−	0.771041i	$-0.719736\pi$
$383$	−0.735983	+	0.578783i	−0.0376070	+	0.0295745i	0.599179	+	0.800615i	$0.295494\pi$
$384$	0.920777	−	1.46703i	0.0469882	−	0.0748639i
$385$	−2.38751	−	2.11409i	−0.121679	−	0.107744i
$386$	3.85122	+	13.1160i	0.196022	+	0.667589i
$387$	7.13068	+	8.67868i	0.362473	+	0.441162i
$388$	−0.356567	+	0.453412i	−0.0181020	+	0.0230185i
$389$	−0.890061	−	18.6847i	−0.0451279	−	0.947351i	−0.901977	−	0.431784i	$-0.857884\pi$
$389$	−0.890061	−	18.6847i	−0.0451279	−	0.947351i	0.856849	−	0.515567i	$-0.172419\pi$
$390$	−0.784458	+	0.840538i	−0.0397226	+	0.0425623i
$391$	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
$394$	3.69798	−	1.48045i	0.186301	−	0.0745839i
$395$	−19.4403	+	13.8433i	−0.978146	+	0.696534i
$396$	−0.657938	−	1.77704i	−0.0330626	−	0.0892999i
$397$	−3.67390	+	5.15928i	−0.184388	+	0.258937i	−0.896415	−	0.443215i	$-0.853838\pi$
$397$	−3.67390	+	5.15928i	−0.184388	+	0.258937i	0.712027	+	0.702152i	$0.247777\pi$
$398$	3.75619	+	4.33487i	0.188281	+	0.217288i
$399$	17.0636	−	19.6908i	0.854246	−	0.985775i
$400$	1.30365	+	0.382785i	0.0651823	+	0.0191393i
$401$	25.0964	+	4.83694i	1.25326	+	0.241545i	0.772334	−	0.635217i	$-0.219089\pi$
$401$	25.0964	+	4.83694i	1.25326	+	0.241545i	0.480923	+	0.876763i	$0.340302\pi$
$402$	13.8879	−	13.5286i	0.692663	−	0.674745i
$403$	0.756377	−	0.389940i	0.0376778	−	0.0194243i
$404$	−1.30222	+	6.75654i	−0.0647877	+	0.336150i
$405$	10.6811	−	13.4485i	0.530748	−	0.668259i
$406$	−5.85330	+	11.0606i	−0.290494	+	0.548929i
$407$	4.91619	−	4.25990i	0.243686	−	0.211155i
$408$	8.91381	+	2.97872i	0.441299	+	0.147468i
$409$	−5.86765	+	24.1868i	−0.290136	+	1.19596i	0.620986	+	0.783822i	$0.286733\pi$
$409$	−5.86765	+	24.1868i	−0.290136	+	1.19596i	−0.911122	+	0.412137i	$0.864783\pi$
$410$	10.6957	+	15.0200i	0.528223	+	0.741785i
$411$	−14.5863	+	11.7255i	−0.719491	+	0.578377i
$412$	−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
$416$	−0.347467	+	0.0165519i	−0.0170360	+	0.000811523i
$417$	−13.2876	−	5.15535i	−0.650699	−	0.252458i
$418$	−3.57514	+	0.341384i	−0.174866	+	0.0166977i
$419$	9.83246	−	2.88707i	0.480347	−	0.141043i	−0.0325901	−	0.999469i	$-0.510376\pi$
$419$	9.83246	−	2.88707i	0.480347	−	0.141043i	0.512937	+	0.858426i	$0.328557\pi$
$420$	7.12332	−	5.07207i	0.347583	−	0.247492i
$421$	2.30902	−	2.00077i	0.112535	−	0.0975117i	−0.596776	−	0.802408i	$-0.703552\pi$
$421$	2.30902	−	2.00077i	0.112535	−	0.0975117i	0.709310	+	0.704896i	$0.249006\pi$
$422$	−17.7572	−	22.5801i	−0.864407	−	1.09918i
$423$	12.1979	+	2.68424i	0.593083	+	0.130512i
$424$	8.16237	−	2.82502i	0.396400	−	0.137195i
$425$	−0.350793	+	7.36405i	−0.0170159	+	0.357209i
$426$	−17.5849	−	4.95970i	−0.851992	−	0.240298i
$427$	−7.12978	−	30.8304i	−0.345034	−	1.49199i
$428$	−18.1943	−	5.34232i	−0.879453	−	0.258231i
$429$	−0.217426	+	0.312350i	−0.0104974	+	0.0150804i
$430$	7.01551	−	1.35213i	0.338318	−	0.0652054i
$431$	−37.3147	−	3.56312i	−1.79738	−	0.171629i	−0.857808	−	0.513970i	$-0.828174\pi$
$431$	−37.3147	−	3.56312i	−1.79738	−	0.171629i	−0.939576	+	0.342340i	$0.888780\pi$
$432$	5.15411	−	0.659641i	0.247977	−	0.0317370i
$433$	−16.5508	−	7.55851i	−0.795382	−	0.363239i	−0.0240816	−	0.999710i	$-0.507666\pi$
$433$	−16.5508	−	7.55851i	−0.795382	−	0.363239i	−0.771300	+	0.636471i	$0.780393\pi$
$434$	−6.22937	+	1.75669i	−0.299019	+	0.0843237i
$435$	11.9233	+	10.1103i	0.571676	+	0.484751i
$436$	3.54840	−	2.04867i	0.169938	−	0.0981136i
$437$	17.5324	−	20.8845i	0.838690	−	0.999043i
$438$	−27.8662	−	6.44543i	−1.33150	−	0.307975i
$439$	15.7720	+	8.13101i	0.752754	+	0.388072i	0.791493	−	0.611178i	$-0.209304\pi$
$439$	15.7720	+	8.13101i	0.752754	+	0.388072i	−0.0387393	+	0.999249i	$0.512334\pi$
$440$	−1.19305	−	0.171535i	−0.0568764	−	0.00817760i
$441$	−1.00086	+	20.9761i	−0.0476600	+	0.998864i
$442$	−0.531782	−	1.81108i	−0.0252943	−	0.0861444i
$443$	29.9316	+	21.3142i	1.42209	+	1.01267i	0.994052	+	0.108907i	$0.0347349\pi$
$443$	29.9316	+	21.3142i	1.42209	+	1.01267i	0.428039	+	0.903760i	$0.359204\pi$
$444$	8.34283	+	15.7664i	0.395933	+	0.748241i
$445$	−0.449373	−	0.179902i	−0.0213023	−	0.00852815i
$446$	1.68204	−	0.408058i	0.0796468	−	0.0193221i
$447$	−0.713209	+	1.60698i	−0.0337336	+	0.0760077i
$448$	2.61463	+	0.404624i	0.123530	+	0.0191167i
$449$	−15.1452	+	23.5664i	−0.714747	+	1.11217i	0.273877	+	0.961765i	$0.411694\pi$
$449$	−15.1452	+	23.5664i	−0.714747	+	1.11217i	−0.988625	+	0.150404i	$0.951943\pi$
$450$	1.59552	+	3.75080i	0.0752135	+	0.176814i
$451$	4.21192	+	4.41734i	0.198332	+	0.208004i
$452$	16.5724	+	6.63458i	0.779500	+	0.312065i
$453$	−0.136991	+	3.71053i	−0.00643638	+	0.174336i
$454$	−0.00134083		0.000612338i	−6.29284e−5		2.87385e-5i
$455$	−1.65339	−	0.592195i	−0.0775119	−	0.0277625i
$456$	1.29718	−	9.76228i	0.0607458	−	0.457161i
$457$	10.1632	+	25.3865i	0.475415	+	1.18753i	0.951367	+	0.308058i	$0.0996793\pi$
$457$	10.1632	+	25.3865i	0.475415	+	1.18753i	−0.475952	+	0.879471i	$0.657897\pi$
$458$	−0.483142	−	10.1424i	−0.0225757	−	0.473923i
$459$	10.0719	+	26.3347i	0.470114	+	1.22920i
$460$	7.37070	−	5.42431i	0.343661	−	0.252910i
$461$			33.8300i			1.57562i	0.615917	+	0.787811i	$0.288786\pi$
$461$			33.8300i			1.57562i	−0.615917	+	0.787811i	$0.711214\pi$
$462$	2.09497	−	1.99739i	0.0974667	−	0.0929271i
$463$	1.34286	−	9.33979i	0.0624080	−	0.434057i	−0.934532	−	0.355880i	$-0.884181\pi$
$463$	1.34286	−	9.33979i	0.0624080	−	0.434057i	0.996940	−	0.0781766i	$-0.0249098\pi$
$464$	0.449598	+	4.70840i	0.0208721	+	0.218582i
$465$	0.471088	+	8.07166i	0.0218462	+	0.374314i
$466$	−7.40343	−	0.706942i	−0.342957	−	0.0327485i
$467$	12.6401	−	36.5211i	0.584912	−	1.68999i	−0.130637	−	0.991430i	$-0.541702\pi$
$467$	12.6401	−	36.5211i	0.584912	−	1.68999i	0.715549	−	0.698563i	$-0.246177\pi$
$468$	−0.700117	−	0.773887i	−0.0323629	−	0.0357729i
$469$	27.3745	+	11.3016i	1.26404	+	0.521859i
$470$	5.20249	−	6.00400i	0.239973	−	0.276944i
$471$	7.50202	−	1.90517i	0.345675	−	0.0877855i
$472$	5.64515	−	2.91028i	0.259839	−	0.133956i
$473$	2.23488	−	0.773500i	0.102760	−	0.0355656i
$474$	−11.0311	−	18.6431i	−0.506677	−	0.856304i
$475$	7.64656	−	1.09941i	0.350848	−	0.0504444i
$476$	1.21113	+	14.3050i	0.0555122	+	0.655670i
$477$	22.0935	+	13.5397i	1.01159	+	0.619940i
$478$	−2.53074	−	2.41306i	−0.115753	−	0.110371i
$479$	8.68162	+	12.1916i	0.396673	+	0.557050i	0.963816	−	0.266570i	$-0.0858904\pi$
$479$	8.68162	+	12.1916i	0.396673	+	0.557050i	−0.567142	+	0.823620i	$0.691951\pi$
$480$	1.19550	−	3.08135i	0.0545670	−	0.140644i
$481$	1.64159	−	3.18423i	0.0748499	−	0.145189i
$482$	21.0667			0.959560
$483$	−0.703223	+	21.9660i	−0.0319978	+	0.999488i
$484$	10.6010			0.481865
$485$	−0.504372	+	0.978344i	−0.0229023	+	0.0444243i
$486$	11.3450	+	10.6907i	0.514621	+	0.484939i
$487$	−4.40142	−	6.18093i	−0.199447	−	0.280085i	0.702724	−	0.711463i	$-0.251967\pi$
$487$	−4.40142	−	6.18093i	−0.199447	−	0.280085i	−0.902171	+	0.431378i	$0.858028\pi$
$488$	−8.65609	−	8.25357i	−0.391843	−	0.373621i
$489$	7.11932	+	8.04071i	0.321947	+	0.363613i
$490$	11.4219	+	6.92562i	0.515990	+	0.312868i
$491$	29.1153	−	4.18615i	1.31396	−	0.188918i	0.550530	−	0.834815i	$-0.314426\pi$
$491$	29.1153	−	4.18615i	1.31396	−	0.188918i	0.763425	+	0.645897i	$0.223516\pi$
$492$	−14.4041	+	8.52291i	−0.649385	+	0.384243i
$493$	−24.2531	+	8.39408i	−1.09231	+	0.378050i
$494$	−1.75800	+	0.906311i	−0.0790961	+	0.0407769i
$495$	−1.87456	−	3.09211i	−0.0842550	−	0.138980i
$496$	−1.60199	+	1.84880i	−0.0719316	+	0.0830134i
$497$	−3.67510	−	27.6663i	−0.164851	−	1.24100i
$498$	4.74444	−	2.22835i	0.212603	−	0.0998548i
$499$	−3.93749	+	11.3766i	−0.176266	+	0.509289i	−0.998179	−	0.0603256i	$-0.980786\pi$
$499$	−3.93749	+	11.3766i	−0.176266	+	0.509289i	0.821912	+	0.569614i	$0.192907\pi$
$500$	12.0788	+	1.15339i	0.540182	+	0.0515812i
$501$	−25.7899	+	1.50518i	−1.15221	+	0.0672467i
$502$	1.52625	+	15.9836i	0.0681199	+	0.713384i
$503$	−0.789341	+	5.48999i	−0.0351950	+	0.244787i	−0.999823	−	0.0188294i	$-0.994006\pi$
$503$	−0.789341	+	5.48999i	−0.0351950	+	0.244787i	0.964628	+	0.263616i	$0.0849152\pi$
$504$	4.04166	+	6.83118i	0.180030	+	0.304285i
$505$			13.1303i			0.584289i
$506$	2.15943	−	2.12445i	0.0959982	−	0.0944434i
$507$	5.02690	−	21.7333i	0.223252	−	0.965209i
$508$	−0.526977	−	11.0626i	−0.0233808	−	0.490824i
$509$	−8.69182	−	21.7111i	−0.385258	−	0.962328i	−0.986574	−	0.163317i	$-0.947781\pi$
$509$	−8.69182	−	21.7111i	−0.385258	−	0.962328i	0.601316	−	0.799012i	$-0.294643\pi$
$510$	17.7779	+	2.36226i	0.787218	+	0.104603i
$511$	−7.80734	−	42.9868i	−0.345376	−	1.90163i
$512$	0.909632	−	0.415415i	0.0402004	−	0.0183589i
$513$	25.0989	−	15.5855i	1.10814	−	0.688116i
$514$	−16.7472	−	6.70456i	−0.738687	−	0.295726i
$515$	−16.9924	−	17.8211i	−0.748776	−	0.785293i
$516$	0.685460	+	6.44868i	0.0301757	+	0.283887i
$517$	1.42172	−	2.21224i	0.0625273	−	0.0972943i
$518$	−17.0723	+	21.2359i	−0.750112	+	0.933053i
$519$	−8.16475	−	3.62367i	−0.358393	−	0.159061i
$520$	−0.645085	+	0.156496i	−0.0282889	+	0.00686280i
$521$	3.10051	+	1.24126i	0.135836	+	0.0543805i	0.438584	−	0.898690i	$-0.355480\pi$
$521$	3.10051	+	1.24126i	0.135836	+	0.0543805i	−0.302749	+	0.953070i	$0.597904\pi$
$522$	−10.0576	+	10.0093i	−0.440208	+	0.438095i
$523$	9.81027	+	6.98586i	0.428973	+	0.305470i	0.774074	−	0.633095i	$-0.218216\pi$
$523$	9.81027	+	6.98586i	0.428973	+	0.305470i	−0.345101	+	0.938566i	$0.612155\pi$
$524$	−3.54695	−	12.0798i	−0.154949	−	0.527709i
$525$	−4.29679	+	4.50599i	−0.187527	+	0.196658i
$526$	−14.1505	−	2.03453i	−0.616991	−	0.0887099i
$527$	−11.7984	−	6.08250i	−0.513947	−	0.264958i
$528$	0.246542	−	1.06590i	0.0107294	−	0.0463873i
$529$	−0.375536	+	22.9969i	−0.0163277	+	0.999867i
$530$	14.2739	−	8.24107i	0.620021	−	0.357969i
$531$	17.4970	+	7.54253i	0.759307	+	0.327318i
$532$	14.4785	−	4.08295i	0.627723	−	0.177018i
$533$	3.05760	+	1.39636i	0.132439	+	0.0604830i
$534$	0.197136	−	0.392648i	0.00853092	−	0.0169915i
$535$	−36.0206	−	3.43955i	−1.55731	−	0.148705i
$536$	10.9914	−	2.11842i	0.474756	−	0.0915017i
$537$	10.3678	+	7.21699i	0.447403	+	0.311436i
$538$	−25.3202	−	7.43468i	−1.09163	−	0.320532i
$539$	4.06856	+	1.73106i	0.175245	+	0.0745622i
$540$	9.41925	−	3.09732i	0.405340	−	0.133287i
$541$	0.731044	−	15.3465i	0.0314300	−	0.659798i	−0.927101	−	0.374811i	$-0.877708\pi$
$541$	0.731044	−	15.3465i	0.0314300	−	0.659798i	0.958531	−	0.284987i	$-0.0919893\pi$
$542$	21.3496	−	7.38916i	0.917043	−	0.317392i
$543$	−15.9487	−	8.98191i	−0.684425	−	0.385451i
$544$	3.35421	+	4.26523i	0.143811	+	0.182870i
$545$	5.90894	−	5.12013i	0.253111	−	0.219322i
$546$	0.662269	−	1.45002i	0.0283425	−	0.0620550i
$547$	−28.4044	+	8.34029i	−1.21448	+	0.356605i	−0.825374	−	0.564586i	$-0.809036\pi$
$547$	−28.4044	+	8.34029i	−1.21448	+	0.356605i	−0.389111	+	0.921191i	$0.627218\pi$
$548$	−10.7562	+	1.02709i	−0.459480	+	0.0438750i
$549$	2.64580	−	35.7833i	0.112920	−	1.52719i
$550$	0.857232	−	0.0408350i	0.0365525	−	0.00174121i
$551$	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
$555$	21.3261	+	26.5293i	0.905242	+	1.12611i
$556$	−4.77317	−	6.70298i	−0.202427	−	0.284270i
$557$	0.152295	−	0.627768i	0.00645294	−	0.0265994i	−0.968494	−	0.249037i	$-0.919886\pi$
$557$	0.152295	−	0.627768i	0.00645294	−	0.0265994i	0.974947	+	0.222437i	$0.0714012\pi$
$558$	−7.33641	−	0.192298i	−0.310575	−	0.00814063i
$559$	0.984314	−	0.852913i	0.0416320	−	0.0360744i
$560$	5.04525	−	0.186071i	0.213201	−	0.00786291i
$561$	5.93607	−	0.0635017i	0.250621	−	0.00268105i
$562$	4.42596	−	22.9641i	0.186698	−	0.968682i
$563$	−20.6013	+	10.6207i	−0.868242	+	0.447610i	−0.833975	−	0.551803i	$-0.813940\pi$
$563$	−20.6013	+	10.6207i	−0.868242	+	0.447610i	−0.0342674	+	0.999413i	$0.510910\pi$
$564$	5.03168	+	5.16530i	0.211872	+	0.217498i
$565$	33.4483	+	6.44663i	1.40718	+	0.271212i
$566$	−15.0388	−	4.41578i	−0.632127	−	0.185609i
$567$	−8.13696	+	22.3783i	−0.341720	+	0.939802i
$568$	−6.90796	−	7.97221i	−0.289851	−	0.334506i
$569$	−14.3661	+	20.1744i	−0.602260	+	0.845756i	−0.997340	−	0.0728910i	$-0.976777\pi$
$569$	−14.3661	+	20.1744i	−0.602260	+	0.845756i	0.395080	+	0.918647i	$0.370717\pi$
$570$	−1.09492	−	18.7604i	−0.0458611	−	0.785788i
$571$	−0.653422	+	0.465300i	−0.0273449	+	0.0194722i	−0.593648	−	0.804725i	$-0.702313\pi$
$571$	−0.653422	+	0.465300i	−0.0273449	+	0.0194722i	0.566303	+	0.824197i	$0.308373\pi$
$572$	−0.203985	+	0.0816633i	−0.00852904	+	0.00341451i
$573$	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
$576$	2.69530	+	1.31732i	0.112304	+	0.0548884i
$577$	−0.335910	−	7.05162i	−0.0139841	−	0.293563i	−0.995016	−	0.0997160i	$-0.968207\pi$
$577$	−0.335910	−	7.05162i	−0.0139841	−	0.293563i	0.981032	−	0.193847i	$-0.0620965\pi$
$578$	−7.69171	+	9.78081i	−0.319933	+	0.406828i
$579$	−21.8853	+	9.03437i	−0.909523	+	0.375456i
$580$	2.54279	+	8.65996i	0.105584	+	0.359585i
$581$	5.99449	+	5.30800i	0.248694	+	0.220213i
$582$	−0.846212	−	0.531124i	−0.0350766	−	0.0220158i
$583$	4.28853	−	3.37254i	0.177613	−	0.139676i
$584$	−11.3955	−	11.9512i	−0.471548	−	0.494546i
$585$	−1.59131	−	1.19723i	−0.0657927	−	0.0494992i
$586$	−2.36343	−	0.112584i	−0.0976325	−	0.00465081i
$587$	−24.6002	+	38.2787i	−1.01536	+	1.57993i	−0.218434	+	0.975852i	$0.570095\pi$
$587$	−24.6002	+	38.2787i	−1.01536	+	1.57993i	−0.796925	+	0.604078i	$0.793542\pi$
$588$	−7.13883	+	9.79986i	−0.294400	+	0.404139i
$589$	−3.91868	+	13.3458i	−0.161466	+	0.549904i
$590$	9.52654	−	7.49175i	0.392201	−	0.308431i
$591$	3.22686	+	6.09817i	0.132735	+	0.250845i
$592$	−0.978943	+	10.2520i	−0.0402343	+	0.421353i
$593$	−1.26953	+	1.33145i	−0.0521334	+	0.0546759i	−0.749284	−	0.662249i	$-0.769602\pi$
$593$	−1.26953	+	1.33145i	−0.0521334	+	0.0546759i	0.697151	+	0.716924i	$0.254451\pi$
$594$	2.94024	−	1.45853i	0.120639	−	0.0598444i
$595$	7.43537	+	26.3665i	0.304821	+	1.08092i
$596$	−0.853926	+	0.548785i	−0.0349782	+	0.0224791i
$597$	−6.77849	+	7.26308i	−0.277425	+	0.297258i
$598$	0.669218	−	1.52817i	0.0273664	−	0.0624917i
$599$	16.0580	+	9.27109i	0.656112	+	0.378806i	0.790794	−	0.612082i	$-0.209668\pi$
$599$	16.0580	+	9.27109i	0.656112	+	0.378806i	−0.134682	+	0.990889i	$0.543001\pi$
$600$	−0.420623	+	2.31541i	−0.0171718	+	0.0945263i
$601$	5.53282	−	38.4816i	0.225688	−	1.56970i	−0.490280	−	0.871565i	$-0.663105\pi$
$601$	5.53282	−	38.4816i	0.225688	−	1.56970i	0.715968	−	0.698133i	$-0.245986\pi$
$602$	−8.63154	+	4.86062i	−0.351795	+	0.198104i
$603$	25.8435	+	21.4429i	1.05243	+	0.873224i
$604$	−1.24349	+	1.74623i	−0.0505968	+	0.0710533i
$605$	19.8636	−	3.82839i	0.807569	−	0.155646i
$606$	−11.8755	−	1.00591i	−0.482410	−	0.0408622i
$607$	0.109482	+	0.451291i	0.00444374	+	0.0183173i	0.973990	−	0.226590i	$-0.0727577\pi$
$607$	0.109482	+	0.451291i	0.00444374	+	0.0183173i	−0.969547	+	0.244907i	$0.921243\pi$
$608$	3.72340	−	4.29704i	0.151004	−	0.174268i
$609$	−20.1218	−	8.05648i	−0.815378	−	0.326465i
$610$	−19.1999	−	12.3390i	−0.777381	−	0.499593i
$611$	0.274080	−	1.42206i	0.0110881	−	0.0575305i
$612$	−3.49848	+	15.8980i	−0.141418	+	0.642639i
$613$	0.867724	−	2.16747i	0.0350471	−	0.0875433i	−0.909812	−	0.415021i	$-0.863774\pi$
$613$	0.867724	−	2.16747i	0.0350471	−	0.0875433i	0.944859	+	0.327477i	$0.106199\pi$
$614$	22.1808	+	7.67684i	0.895143	+	0.309812i
$615$	−23.9115	+	21.1715i	−0.964206	+	0.853718i
$616$	1.64427	−	0.298636i	0.0662497	−	0.0120324i
$617$	16.0329	−	35.1073i	0.645462	−	1.41336i	−0.250008	−	0.968244i	$-0.580433\pi$
$617$	16.0329	−	35.1073i	0.645462	−	1.41336i	0.895470	−	0.445121i	$-0.146839\pi$
$618$	17.4199	−	14.0033i	0.700732	−	0.563296i
$619$	−0.447675	+	0.0213254i	−0.0179936	+	0.000857139i	−0.0565768	−	0.998398i	$-0.518019\pi$
$619$	−0.447675	+	0.0213254i	−0.0179936	+	0.000857139i	0.0385832	+	0.999255i	$0.487716\pi$
$620$	−2.33405	+	4.04270i	−0.0937378	+	0.162359i
$621$	−8.14749	+	23.5503i	−0.326948	+	0.945043i
$622$	0.732881			0.0293859
$623$	0.669988	+	0.0391289i	0.0268425	+	0.00156767i
$624$	−0.0921211	−	0.595429i	−0.00368779	−	0.0238362i
$625$	16.2865	−	1.55517i	0.651459	−	0.0622068i
$626$	0.455983	−	1.87959i	0.0182247	−	0.0751234i
$627$	−1.24251	−	6.09513i	−0.0496209	−	0.243416i
$628$	4.22300	+	1.46159i	0.168516	+	0.0583240i
$629$	−55.3128	+	7.95277i	−2.20546	+	0.317098i
$630$	10.0400	+	11.3403i	0.400003	+	0.451807i
$631$	34.4698	+	29.8682i	1.37222	+	1.18904i	0.960685	+	0.277642i	$0.0895527\pi$
$631$	34.4698	+	29.8682i	1.37222	+	1.18904i	0.411535	+	0.911394i	$0.364993\pi$
$632$	0.595091	−	12.4925i	0.0236714	−	0.496925i
$633$	35.6399	−	34.7179i	1.41656	−	1.37991i
$634$	1.84709	+	5.33682i	0.0733573	+	0.211952i
$635$	−4.98250	−	20.5381i	−0.197725	−	0.815032i
$636$	6.36001	+	13.5412i	0.252191	+	0.536945i
$637$	2.43447	+	0.0522823i	0.0964570	+	0.00207150i
$638$	1.24108	+	2.71758i	0.0491348	+	0.107590i
$639$	5.32295	−	31.1953i	0.210573	−	1.23407i
$640$	1.55439	−	1.10688i	0.0614428	−	0.0437532i
$641$	−15.4726	−	12.1678i	−0.611132	−	0.480599i	0.263975	−	0.964530i	$-0.414966\pi$
$641$	−15.4726	−	12.1678i	−0.611132	−	0.480599i	−0.875107	+	0.483930i	$0.839209\pi$
$642$	5.87039	−	32.3149i	0.231686	−	1.27537i
$643$		−	13.4825i		−	0.531699i	−0.964015	−	0.265850i	$-0.914348\pi$
$643$		−	13.4825i		−	0.531699i	0.964015	−	0.265850i	$-0.0856525\pi$
$644$	−7.30937	+	10.3717i	−0.288029	+	0.408704i
$645$	3.61321	+	11.8356i	0.142270	+	0.466027i
$646$	27.4223	+	14.1372i	1.07891	+	0.556219i
$647$	−8.61370	+	10.9532i	−0.338640	+	0.430615i	−0.925311	−	0.379210i	$-0.876196\pi$
$647$	−8.61370	+	10.9532i	−0.338640	+	0.430615i	0.586671	+	0.809825i	$0.300438\pi$
$648$	2.07973	+	8.75641i	0.0816994	+	0.343984i
$649$	2.76838	−	2.90339i	0.108668	−	0.113968i
$650$	0.429922	−	0.196339i	0.0168629	−	0.00770104i
$651$	−4.16608	−	10.4075i	−0.163281	−	0.407904i
$652$	0.882420	+	6.13736i	0.0345582	+	0.240358i
$653$	−6.73630	+	1.63421i	−0.263612	+	0.0639515i	−0.365386	−	0.930856i	$-0.619063\pi$
$653$	−6.73630	+	1.63421i	−0.263612	+	0.0639515i	0.101775	+	0.994807i	$0.467548\pi$
$654$	4.17815	+	5.73652i	0.163379	+	0.224316i
$655$	−11.0085	−	21.3535i	−0.430137	−	0.834350i
$656$	−9.65199	−	0.459781i	−0.376847	−	0.0179514i
$657$	5.99964	−	49.1752i	0.234068	−	1.91851i
$658$	−4.20339	+	10.1814i	−0.163865	+	0.396912i
$659$	−2.62082	−	18.2282i	−0.102093	−	0.710070i	−0.975003	−	0.222190i	$-0.928679\pi$
$659$	−2.62082	−	18.2282i	−0.102093	−	0.710070i	0.872911	−	0.487880i	$-0.162230\pi$
$660$	0.0770233	−	2.08625i	0.00299813	−	0.0812072i
$661$	−1.47761	+	15.4743i	−0.0574725	+	0.601879i	0.920158	+	0.391548i	$0.128060\pi$
$661$	−1.47761	+	15.4743i	−0.0574725	+	0.601879i	−0.977630	+	0.210331i	$0.932546\pi$
$662$	13.6606	+	3.31403i	0.530935	+	0.128803i
$663$	3.02196	−	1.24748i	0.117363	−	0.0484481i
$664$	2.99548	+	0.430685i	0.116247	+	0.0167138i
$665$	25.6545	−	12.8791i	0.994838	−	0.499429i
$666$	−25.6279	+	17.2557i	−0.993061	+	0.668646i
$667$	−21.1878	−	8.10029i	−0.820395	−	0.313645i
$668$	−12.9169	−	7.45758i	−0.499770	−	0.288543i
$669$	1.01076	+	2.82235i	0.0390782	+	0.109118i
$670$	19.8300	−	7.93873i	0.766099	−	0.306700i
$671$	−6.87197	−	3.13832i	−0.265289	−	0.121154i
$672$	−0.218227	+	4.57738i	−0.00841828	+	0.176576i
$673$	−17.3841	−	38.0659i	−0.670108	−	1.46733i	−0.872794	−	0.488089i	$-0.837694\pi$
$673$	−17.3841	−	38.0659i	−0.670108	−	1.46733i	0.202686	−	0.979244i	$-0.435033\pi$
$674$	8.56144	−	24.7366i	0.329774	−	0.952820i
$675$	−6.16808	+	3.43472i	−0.237409	+	0.132203i
$676$	9.32097	−	8.88752i	0.358499	−	0.341828i
$677$	12.4511	+	2.39975i	0.478534	+	0.0922299i	0.422814	−	0.906217i	$-0.361042\pi$
$677$	12.4511	+	2.39975i	0.478534	+	0.0922299i	0.0557203	+	0.998446i	$0.482254\pi$
$678$	−8.39305	+	29.7581i	−0.322333	+	1.14285i
$679$	0.233396	−	1.50817i	0.00895690	−	0.0578783i
$680$	7.82524	+	6.78061i	0.300084	+	0.260025i
$681$	−0.00130013	−	0.00219728i	−4.98213e−5	−	8.41999e-5i
$682$	−0.574292	+	1.43451i	−0.0219908	+	0.0549303i
$683$	0.218062	+	1.13141i	0.00834391	+	0.0432923i	0.985862	−	0.167559i	$-0.0535885\pi$
$683$	0.218062	+	1.13141i	0.00834391	+	0.0432923i	−0.977518	+	0.210851i	$0.932376\pi$
$684$	17.0515	+	0.446946i	0.651982	+	0.0170894i
$685$	−19.7833	+	5.80890i	−0.755881	+	0.221947i
$686$	−18.0633	−	4.08880i	−0.689659	−	0.156111i
$687$	17.3803	−	2.68897i	0.663099	−	0.102591i
$688$	−1.71566	+	3.32791i	−0.0654088	+	0.126875i
$689$	1.50231	−	2.60208i	0.0572335	−	0.0991313i
$690$	10.6919	+	11.7018i	0.407035	+	0.445482i
$691$	−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
$693$	3.82374	+	3.24259i	0.145252	+	0.123176i
$694$	2.78163	−	6.09093i	0.105589	−	0.231209i
$695$	−11.3643	−	10.8359i	−0.431074	−	0.411028i
$696$	−8.02720	+	1.63636i	−0.304270	+	0.0620261i
$697$	−9.92289	−	51.4849i	−0.375856	−	1.95013i
$698$	1.38455	+	1.76060i	0.0524062	+	0.0666399i
$699$	−0.137793	−	12.8807i	−0.00521180	−	0.487193i
$700$	−3.50230	+	0.809937i	−0.132375	+	0.0306127i
$701$	21.2430	+	13.6520i	0.802336	+	0.515630i	0.876377	−	0.481625i	$-0.159953\pi$
$701$	21.2430	+	13.6520i	0.802336	+	0.515630i	−0.0740413	+	0.997255i	$0.523590\pi$
$702$	1.20473	−	1.34753i	0.0454695	−	0.0508591i
$703$	19.1517	+	55.3352i	0.722320	+	2.08701i
$704$	0.457142	−	0.435884i	0.0172292	−	0.0164280i
$705$	11.2934	+	7.86132i	0.425335	+	0.296074i
$706$	16.3042	+	18.8160i	0.613615	+	0.708150i
$707$	−5.76926	−	17.2668i	−0.216975	−	0.649384i
$708$	6.04600	+	9.19011i	0.227223	+	0.345385i
$709$	−4.13399	−	43.2931i	−0.155255	−	1.62591i	−0.652146	−	0.758093i	$-0.726131\pi$
$709$	−4.13399	−	43.2931i	−0.155255	−	1.62591i	0.496891	−	0.867813i	$-0.334475\pi$
$710$	−15.8227	−	12.4431i	−0.593817	−	0.466983i
$711$	30.0903	−	22.4126i	1.12847	−	0.840537i
$712$	0.219679	−	0.126832i	0.00823280	−	0.00475321i
$713$	−4.53014	−	10.8222i	−0.169655	−	0.405294i
$714$	−24.4165	+	4.70490i	−0.913765	+	0.176077i
$715$	−0.352723	+	0.226682i	−0.0131911	+	0.00847741i
$716$	2.71064	+	6.77085i	0.101301	+	0.253039i
$717$	3.69281	−	4.80059i	0.137910	−	0.179281i
$718$	−25.6242	−	6.21637i	−0.956287	−	0.231993i
$719$	17.6517	+	12.5698i	0.658299	+	0.468773i	0.859743	−	0.510727i	$-0.170624\pi$
$719$	17.6517	+	12.5698i	0.658299	+	0.468773i	−0.201444	+	0.979500i	$0.564563\pi$
$720$	5.52603	+	1.49495i	0.205943	+	0.0557135i
$721$	30.1760	+	15.9692i	1.12381	+	0.594724i
$722$	3.75501	−	12.7884i	0.139747	−	0.475935i
$723$	3.85681	+	36.2841i	0.143436	+	1.34942i
$724$	−4.84246	−	9.39306i	−0.179968	−	0.349090i
$725$	−2.94471	−	5.71195i	−0.109364	−	0.212136i
$726$	1.94080	+	18.2587i	0.0720297	+	0.677642i
$727$	8.79165	−	29.9416i	0.326064	−	1.11047i	−0.619489	−	0.785005i	$-0.712660\pi$
$727$	8.79165	−	29.9416i	0.326064	−	1.11047i	0.945553	−	0.325467i	$-0.105522\pi$
$728$	0.779548	−	0.489240i	0.0288920	−	0.0181324i
$729$	−16.3361	+	21.4973i	−0.605039	+	0.796196i
$730$	−25.6682	−	18.2782i	−0.950021	−	0.676507i
$731$	−19.7434	−	4.78970i	−0.730237	−	0.177154i
$732$	12.6308	−	16.4198i	0.466847	−	0.606895i
$733$	−11.7768	−	29.4169i	−0.434985	−	1.08654i	−0.970304	−	0.241890i	$-0.922233\pi$
$733$	−11.7768	−	29.4169i	−0.434985	−	1.08654i	0.535319	−	0.844650i	$-0.320191\pi$
$734$	27.1844	−	17.4703i	1.00339	−	0.644841i
$735$	−9.83724	+	20.9404i	−0.362852	+	0.772400i
$736$	−0.153269	+	4.79338i	−0.00564955	+	0.176686i
$737$	6.12317	−	3.53521i	0.225550	−	0.130221i
$738$	−17.3165	−	23.2485i	−0.637428	−	0.855787i
$739$	16.9634	+	13.3402i	0.624011	+	0.490727i	0.879383	−	0.476115i	$-0.157956\pi$
$739$	16.9634	+	13.3402i	0.624011	+	0.490727i	−0.255372	+	0.966843i	$0.582198\pi$
$740$	1.86804	+	19.5630i	0.0686706	+	0.719151i
$741$	−1.88283	−	2.86196i	−0.0691675	−	0.105137i
$742$	−15.1497	+	17.1091i	−0.556165	+	0.628094i
$743$	−14.6371	−	16.8921i	−0.536984	−	0.619712i	0.420817	−	0.907146i	$-0.361743\pi$
$743$	−14.6371	−	16.8921i	−0.536984	−	0.619712i	−0.957801	+	0.287433i	$0.907198\pi$
$744$	−3.47756	−	2.42072i	−0.127494	−	0.0887478i
$745$	−1.40185	+	1.33666i	−0.0513598	+	0.0489715i
$746$	3.01248	+	8.70399i	0.110295	+	0.318676i
$747$	4.70659	+	7.76361i	0.172205	+	0.284056i
$748$	2.88330	+	1.85299i	0.105424	+	0.0677518i
$749$	48.8797	−	11.3038i	1.78603	−	0.413033i
$750$	0.224812	+	21.0151i	0.00820896	+	0.767364i
$751$	13.6925	+	17.4114i	0.499645	+	0.635350i	0.968823	−	0.247753i	$-0.0796922\pi$
$751$	13.6925	+	17.4114i	0.499645	+	0.635350i	−0.469178	+	0.883104i	$0.655450\pi$
$752$	0.787902	+	4.08802i	0.0287318	+	0.149075i
$753$	−27.2499	+	5.55496i	−0.993043	+	0.202434i
$754$	1.19077	+	1.13540i	0.0433654	+	0.0413489i
$755$	−1.69935	+	3.72105i	−0.0618456	+	0.135423i
$756$	−11.0257	+	8.21178i	−0.401002	+	0.298659i
$757$	−18.4037	−	28.6368i	−0.668895	−	1.04082i	−0.995417	−	0.0956318i	$-0.969513\pi$
$757$	−18.4037	−	28.6368i	−0.668895	−	1.04082i	0.326521	−	0.945190i	$-0.394124\pi$
$758$	4.01650	+	6.95678i	0.145886	+	0.252682i
$759$	4.05438	+	3.33035i	0.147165	+	0.120884i
$760$	5.42489	−	9.39618i	0.196781	−	0.340835i
$761$	2.30161	−	4.46449i	0.0834332	−	0.161838i	−0.843428	−	0.537243i	$-0.819466\pi$
$761$	2.30161	−	4.46449i	0.0834332	−	0.161838i	0.926861	+	0.375405i	$0.122496\pi$
$762$	18.9572	−	2.93294i	0.686747	−	0.106249i
$763$	−5.52076	+	9.32946i	−0.199865	+	0.337749i
$764$	0.942550	−	0.276758i	0.0341003	−	0.0100127i
$765$	−0.813923	+	31.0522i	−0.0294275	+	1.12269i
$766$	−0.177196	−	0.919382i	−0.00640236	−	0.0332186i
$767$	0.821123	−	2.05107i	0.0296490	−	0.0740597i
$768$	0.882021	+	1.49065i	0.0318272	+	0.0537892i
$769$	33.6628	+	29.1690i	1.21391	+	1.05186i	0.997135	+	0.0756397i	$0.0240999\pi$
$769$	33.6628	+	29.1690i	1.21391	+	1.05186i	0.216777	+	0.976221i	$0.430446\pi$
$770$	2.97309	−	1.15337i	0.107143	−	0.0415645i
$771$	8.48158	−	30.0719i	0.305457	−	1.08301i
$772$	−13.4227	−	2.58702i	−0.483095	−	0.0931089i
$773$	30.2471	−	28.8405i	1.08791	−	1.03732i	0.0887642	−	0.996053i	$-0.471708\pi$
$773$	30.2471	−	28.8405i	1.08791	−	1.03732i	0.999148	−	0.0412696i	$-0.0131403\pi$
$774$	−10.9814	+	2.36120i	−0.394718	+	0.0848716i
$775$	1.08710	−	3.14095i	0.0390496	−	0.112826i
$776$	−0.239620	−	0.524695i	−0.00860186	−	0.0188354i
$777$	−39.7012	−	25.5166i	−1.42427	−	0.915403i
$778$	17.0155	+	7.77070i	0.610034	+	0.278593i
$779$	−51.0059	+	20.4197i	−1.82748	+	0.731611i
$780$	−0.387640	−	1.08241i	−0.0138797	−	0.0387565i
$781$	−5.77037	−	3.33153i	−0.206480	−	0.119211i
$782$	−25.4724	+	5.32377i	−0.910892	+	0.190378i
$783$	−19.0808	−	15.4902i	−0.681892	−	0.553574i
$784$	−6.55294	+	2.46151i	−0.234033	+	0.0879110i
$785$	8.44063	+	1.21358i	0.301259	+	0.0433145i
$786$	20.1563	−	8.32061i	0.718950	−	0.296786i
$787$	−29.7227	−	7.21065i	−1.05950	−	0.257032i	−0.332099	−	0.943245i	$-0.607757\pi$
$787$	−29.7227	−	7.21065i	−1.05950	−	0.257032i	−0.727401	+	0.686213i	$0.759272\pi$
$788$	−0.378638	+	3.96528i	−0.0134884	+	0.141257i
$789$	0.913555	−	24.7445i	0.0325234	−	0.880929i
$790$	−3.39641	−	23.6226i	−0.120839	−	0.840454i
$791$	−46.8183	+	6.21918i	−1.66467	+	0.221129i
$792$	1.88099	+	0.229490i	0.0668379	+	0.00815458i
$793$	−4.15582	−	0.197966i	−0.147577	−	0.00702998i
$794$	−2.90227	−	5.62961i	−0.102998	−	0.199787i
$795$	16.8072	+	23.0760i	0.596090	+	0.818420i
$796$	−5.57417	+	1.35228i	−0.197571	+	0.0479303i
$797$	0.887580	+	6.17325i	0.0314397	+	0.218668i	0.999484	−	0.0321100i	$-0.0102227\pi$
$797$	0.887580	+	6.17325i	0.0314397	+	0.218668i	−0.968045	+	0.250778i	$0.919314\pi$
$798$	9.68294	+	24.1896i	0.342772	+	0.856301i
$799$	−20.5490	+	9.38439i	−0.726970	+	0.331996i
$800$	−0.937599	+	0.983325i	−0.0331491	+	0.0347658i
$801$	0.712367	+	0.267653i	0.0251702	+	0.00945705i
$802$	−15.7991	+	20.0902i	−0.557886	+	0.709409i
$803$	−9.27102	−	4.77954i	−0.327167	−	0.168666i
$804$	5.66092	+	18.5432i	0.199645	+	0.653967i
$805$	−9.95027	+	22.0736i	−0.350701	+	0.777993i
$806$			0.850976i			0.0299743i
$807$	8.16958	−	44.9713i	0.287583	−	1.58307i
$808$	−5.40874	−	4.25348i	−0.190279	−	0.149637i
$809$	−15.8836	+	11.3107i	−0.558439	+	0.397662i	−0.824134	−	0.566395i	$-0.808338\pi$
$809$	−15.8836	+	11.3107i	−0.558439	+	0.397662i	0.265695	+	0.964057i	$0.414398\pi$
$810$	7.05910	+	15.6562i	0.248032	+	0.550102i
$811$	5.54719	+	12.1467i	0.194788	+	0.426527i	0.981673	−	0.190573i	$-0.0610347\pi$
$811$	5.54719	+	12.1467i	0.194788	+	0.426527i	−0.786885	+	0.617100i	$0.788307\pi$
$812$	−7.14893	−	10.2709i	−0.250878	−	0.360438i
$813$	16.6353	+	35.4186i	0.583426	+	1.24219i
$814$	1.53362	+	6.32168i	0.0537535	+	0.221575i
$815$	3.86983	+	11.1811i	0.135554	+	0.391659i
$816$	−6.73213	+	6.55799i	−0.235672	+	0.229575i
$817$	−1.01294	+	21.2642i	−0.0354382	+	0.743940i
$818$	−18.8093	−	16.2984i	−0.657653	−	0.569860i
$819$	2.61868	+	0.875195i	0.0915041	+	0.0305818i
$820$	−18.2514	+	2.62415i	−0.637365	+	0.0916393i
$821$	31.8157	+	11.0115i	1.11038	+	0.384305i	0.819859	−	0.572565i	$-0.194052\pi$
$821$	31.8157	+	11.0115i	1.11038	+	0.384305i	0.290517	+	0.956870i	$0.406173\pi$
$822$	−3.73820	−	18.3378i	−0.130385	−	0.639604i
$823$	−8.54315	+	35.2154i	−0.297796	+	1.22753i	0.604568	+	0.796554i	$0.293346\pi$
$823$	−8.54315	+	35.2154i	−0.297796	+	1.22753i	−0.902363	+	0.430976i	$0.858169\pi$
$824$	12.8457	−	1.22661i	0.447500	−	0.0427310i
$825$	0.227271	+	1.46898i	0.00791256	+	0.0511432i
$826$	−9.23597	+	14.0378i	−0.321360	+	0.488436i
$827$	−28.5004			−0.991054			−0.495527	−	0.868592i	$-0.665025\pi$
$827$	−28.5004			−0.991054			−0.495527	+	0.868592i	$0.665025\pi$
$828$	−11.4027	+	8.77373i	−0.396271	+	0.304908i
$829$	−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	$0.234600\pi$
$830$	5.76829	−	0.274778i	0.200220	−	0.00953767i
$831$	−3.61603	+	2.90682i	−0.125439	+	0.100836i
$832$	0.144507	−	0.316425i	0.00500987	−	0.0109701i
$833$	−21.3629	−	31.4059i	−0.740180	−	1.08815i
$834$	10.6710	−	9.44822i	0.369507	−	0.327165i
$835$	−26.8961	−	9.30883i	−0.930778	−	0.322146i
$836$	1.33479	−	3.33414i	0.0461646	−	0.115314i
$837$	−1.01192	−	12.6711i	−0.0349770	−	0.437976i
$838$	−1.93936	+	10.0624i	−0.0669942	+	0.347599i
$839$	2.55988	+	1.64513i	0.0883769	+	0.0567964i	0.584083	−	0.811694i	$-0.301454\pi$
$839$	2.55988	+	1.64513i	0.0883769	+	0.0567964i	−0.495706	+	0.868490i	$0.665091\pi$
$840$	1.24414	+	8.65562i	0.0429271	+	0.298647i
$841$	−4.34094	+	5.00971i	−0.149687	+	0.172749i
$842$	0.720306	+	2.96914i	0.0248234	+	0.102323i
$843$	40.3624	+	3.41887i	1.39016	+	0.117752i
$844$	28.2068	−	5.43642i	0.970919	−	0.187129i
$845$	14.2555	−	20.0190i	0.490403	−	0.688675i
$846$	−7.97526	+	9.61195i	−0.274195	+	0.330466i
$847$	−24.4392	+	13.7623i	−0.839740	+	0.472877i
$848$	−1.22923	+	8.54950i	−0.0422120	+	0.293591i
$849$	4.85227	−	26.7104i	0.166530	−	0.916700i
$850$	−6.38468	−	3.68620i	−0.218993	−	0.126436i
$851$	−41.9622	−	26.0495i	−1.43845	−	0.892966i
$852$	12.4662	−	13.3574i	0.427086	−	0.457618i
$853$	−35.8284	+	23.0255i	−1.22674	+	0.788380i	−0.983381	−	0.181556i	$-0.941887\pi$
$853$	−35.8284	+	23.0255i	−1.22674	+	0.788380i	−0.243362	+	0.969936i	$0.578250\pi$
$854$	30.6702	+	7.79009i	1.04951	+	0.266571i
$855$	32.1115	−	5.32042i	1.09819	−	0.181955i
$856$	13.0855	−	13.7237i	0.447254	−	0.469067i
$857$	0.117892	−	1.23462i	0.00402712	−	0.0421739i	−0.993235	−	0.116122i	$-0.962954\pi$
$857$	0.117892	−	1.23462i	0.00402712	−	0.0421739i	0.997262	+	0.0739478i	$0.0235598\pi$
$858$	−0.177997	−	0.336383i	−0.00607673	−	0.0114839i
$859$	13.6453	−	10.7308i	0.465571	−	0.366129i	−0.357645	−	0.933858i	$-0.616420\pi$
$859$	13.6453	−	10.7308i	0.465571	−	0.366129i	0.823216	+	0.567729i	$0.192178\pi$
$860$	−2.01287	+	6.85521i	−0.0686384	+	0.233761i
$861$	22.1421	−	38.3477i	0.754599	−	1.30689i
$862$	20.2656	−	31.5339i	0.690249	−	1.07405i
$863$	35.4615	+	1.68924i	1.20712	+	0.0575024i	0.641475	−	0.767144i	$-0.278323\pi$
$863$	35.4615	+	1.68924i	1.20712	+	0.0575024i	0.565648	+	0.824647i	$0.308626\pi$
$864$	−1.77544	+	4.88342i	−0.0604017	+	0.166137i
$865$	−6.79130	−	7.12251i	−0.230911	−	0.242173i
$866$	14.3023	−	11.2475i	0.486012	−	0.382204i
$867$	−18.2541	−	11.4572i	−0.619943	−	0.389106i
$868$	1.29306	−	6.34185i	0.0438892	−	0.215256i
$869$	−2.22562	−	7.57976i	−0.0754990	−	0.257126i
$870$	−14.4499	+	5.96501i	−0.489899	+	0.202233i
$871$	2.40701	−	3.06077i	0.0815586	−	0.103710i
$872$	0.194959	+	4.09270i	0.00660216	+	0.138596i
$873$	0.759859	−	1.55471i	0.0257173	−	0.0526189i
$874$	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
$877$	−36.1534	+	14.4736i	−1.22081	+	0.488739i	−0.890435	−	0.455110i	$-0.849600\pi$
$877$	−36.1534	+	14.4736i	−1.22081	+	0.488739i	−0.330377	+	0.943849i	$0.607176\pi$
$878$	−14.4543	+	10.2928i	−0.487807	+	0.347366i
$879$	−0.238779	−	4.09126i	−0.00805383	−	0.137995i
$880$	0.699153	−	0.981823i	0.0235685	−	0.0330973i
$881$	−10.6442	−	12.2840i	−0.358612	−	0.413860i	0.547562	−	0.836765i	$-0.315556\pi$
$881$	−10.6442	−	12.2840i	−0.358612	−	0.413860i	−0.906174	+	0.422905i	$0.861010\pi$
$882$	−18.1857	−	10.5014i	−0.612345	−	0.353601i
$883$	16.5236	+	4.85178i	0.556064	+	0.163275i	0.547677	−	0.836690i	$-0.315512\pi$
$883$	16.5236	+	4.85178i	0.556064	+	0.163275i	0.00838704	+	0.999965i	$0.497330\pi$
$884$	1.85343	+	0.357219i	0.0623376	+	0.0120146i
$885$	14.6475	+	15.0364i	0.492370	+	0.505445i
$886$	−32.6602	+	16.8375i	−1.09724	+	0.565667i
$887$	6.90151	−	35.8084i	0.231730	−	1.20233i	−0.660527	−	0.750802i	$-0.729667\pi$
$887$	6.90151	−	35.8084i	0.231730	−	1.20233i	0.892257	−	0.451527i	$-0.149121\pi$
$888$	−17.8367	+	0.190810i	−0.598559	+	0.00640315i
$889$	15.5764	+	24.8192i	0.522414	+	0.832408i
$890$	0.365817	−	0.316983i	0.0122622	−	0.0106253i
$891$	3.05039	+	4.79709i	0.102192	+	0.160708i
$892$	−0.408058	+	1.68204i	−0.0136628	+	0.0563188i
$893$	13.7308	+	19.2822i	0.459483	+	0.645254i
$894$	−1.10153	−	1.37029i	−0.0368407	−	0.0458293i
$895$	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
$899$	11.5575	−	0.550552i	0.385464	−	0.0183619i
$900$	−4.06495	−	0.300561i	−0.135498	−	0.0100187i
$901$	−46.6556	+	4.45507i	−1.55432	+	0.148420i
$902$	−5.85630	+	1.71957i	−0.194993	+	0.0572553i
$903$	−9.95191	−	13.9767i	−0.331179	−	0.465114i
$904$	−13.4910	+	11.6900i	−0.448703	+	0.388803i
$905$	−12.4657	−	15.8514i	−0.414372	−	0.526917i
$906$	−3.23528	−	1.82203i	−0.107485	−	0.0605327i
$907$	−26.5331	+	9.18321i	−0.881019	+	0.304924i	−0.729869	−	0.683587i	$-0.760419\pi$
$907$	−26.5331	+	9.18321i	−0.881019	+	0.304924i	−0.151150	+	0.988511i	$0.548298\pi$
$908$	7.01376e−5	−	0.00147237i	2.32760e−6	−	4.88623e-5i
$909$	−0.441604	−	20.6379i	−0.0146471	−	0.684517i
$910$	1.28399	−	1.19823i	0.0425638	−	0.0397209i
$911$	−24.4007	−	7.16470i	−0.808432	−	0.237377i	−0.148704	−	0.988882i	$-0.547510\pi$
$911$	−24.4007	−	7.16470i	−0.808432	−	0.237377i	−0.659728	+	0.751505i	$0.729328\pi$
$912$	8.08266	+	5.62631i	0.267644	+	0.186306i
$913$	1.87699	−	0.361761i	0.0621194	−	0.0119725i
$914$	−27.2215	−	2.59933i	−0.900406	−	0.0859783i
$915$	17.7371	−	35.3279i	0.586369	−	1.16790i
$916$	9.23630	+	4.21808i	0.305176	+	0.139369i
$917$	23.8590	+	23.2436i	0.787893	+	0.767572i
$918$	−28.0224	−	3.11504i	−0.924878	−	0.102812i
$919$	−28.8742	+	16.6705i	−0.952471	+	0.549909i	−0.893848	−	0.448371i	$-0.852004\pi$
$919$	−28.8742	+	16.6705i	−0.952471	+	0.549909i	−0.0586230	+	0.998280i	$0.518671\pi$
$920$	1.44387	+	9.03690i	0.0476029	+	0.297938i
$921$	−9.16141	+	39.6084i	−0.301879	+	1.30514i
$922$	−30.0693	−	15.5018i	−0.990281	−	0.510525i
$923$	−3.63214	−	0.522224i	−0.119553	−	0.0171892i
$924$	0.815383	+	2.77734i	0.0268241	+	0.0913678i
$925$	−3.94215	−	13.4257i	−0.129617	−	0.441435i
$926$	7.68620	+	5.47332i	0.252584	+	0.179864i
$927$	27.3078	+	27.4395i	0.896905	+	0.901231i
$928$	−4.39101	−	1.75790i	−0.144142	−	0.0577058i
$929$	−23.6496	+	5.73734i	−0.775919	+	0.188236i	−0.604117	−	0.796896i	$-0.706474\pi$
$929$	−23.6496	+	5.73734i	−0.775919	+	0.188236i	−0.171802	+	0.985132i	$0.554959\pi$
$930$	−7.39024	−	3.27993i	−0.242336	−	0.107553i
$931$	−28.0777	+	28.2087i	−0.920209	+	0.924502i
$932$	4.02080	−	6.25649i	0.131706	−	0.204938i
$933$	0.134173	+	1.26228i	0.00439263	+	0.0413251i
$934$	26.6692	+	27.9699i	0.872643	+	0.915202i
$935$	6.07173	+	2.43075i	0.198567	+	0.0794942i
$936$	1.00867	−	0.267673i	0.0329694	−	0.00874918i
$937$	46.9313	−	21.4328i	1.53318	−	0.700179i	0.542967	−	0.839754i	$-0.317301\pi$
$937$	46.9313	−	21.4328i	1.53318	−	0.700179i	0.990211	+	0.139575i	$0.0445736\pi$
$938$	−22.5890	+	19.1527i	−0.737556	+	0.625359i
$939$	3.32078	+	0.441253i	0.108370	+	0.0143998i
$940$	2.95265	+	7.37535i	0.0963047	+	0.240557i
$941$	0.364204	+	7.64559i	0.0118727	+	0.249239i	0.996999	+	0.0774094i	$0.0246648\pi$
$941$	0.364204	+	7.64559i	0.0118727	+	0.249239i	−0.985127	+	0.171830i	$0.945032\pi$
$942$	−1.74424	+	7.54106i	−0.0568305	+	0.245701i
$943$	22.5406	−	40.4906i	0.734022	−	1.31855i
$944$			6.35117i			0.206713i
$945$	−17.6938	+	19.3685i	−0.575579	+	0.630057i
$946$	−0.336568	+	2.34088i	−0.0109428	+	0.0761086i
$947$	1.88060	+	19.6945i	0.0611112	+	0.639986i	0.973195	+	0.229982i	$0.0738667\pi$
$947$	1.88060	+	19.6945i	0.0611112	+	0.639986i	−0.912084	+	0.410004i	$0.865527\pi$
$948$	21.6254	−	1.26213i	0.702359	−	0.0409920i
$949$	−5.71832	−	0.546033i	−0.185625	−	0.0177250i
$950$	−2.52666	+	7.30032i	−0.0819758	+	0.236854i
$951$	−8.85370	+	4.15838i	−0.287101	+	0.134845i
$952$	−13.2698	−	5.47844i	−0.430076	−	0.177557i
$953$	−27.5886	+	31.8389i	−0.893682	+	1.03136i	0.105634	+	0.994405i	$0.466313\pi$
$953$	−27.5886	+	31.8389i	−0.893682	+	1.03136i	−0.999317	+	0.0369593i	$0.988233\pi$
$954$	−22.1584	+	13.4332i	−0.717404	+	0.434917i
$955$	1.66615	−	0.858958i	0.0539152	−	0.0277952i
$956$	3.30446	−	1.14369i	0.106874	−	0.0369895i
$957$	−4.45341	+	2.63510i	−0.143958	+	0.0851805i
$958$	−14.8145	+	2.13000i	−0.478635	+	0.0688173i
$959$	23.4634	−	16.3314i	0.757673	−	0.527370i
$960$	2.19100	+	2.47456i	0.0707143	+	0.0798662i
$961$	−18.1046	−	17.2627i	−0.584020	−	0.556862i
$962$	2.07804	+	2.91820i	0.0669987	+	0.0940866i
$963$	56.7323	+	4.19477i	1.82817	+	0.135174i
$964$	−9.65330	+	18.7248i	−0.310912	+	0.603085i
$965$	−26.0850			−0.839705
$966$	−19.2019	−	10.6905i	−0.617812	−	0.343960i
$967$	−2.81122			−0.0904027			−0.0452014	−	0.998978i	$-0.514393\pi$
$967$	−2.81122			−0.0904027			−0.0452014	+	0.998978i	$0.514393\pi$
$968$	−4.85767	+	9.42257i	−0.156131	+	0.302853i
$969$	−19.3287	+	49.8189i	−0.620929	+	1.60041i
$970$	−0.638471	−	0.896607i	−0.0205001	−	0.0287883i
$971$	−18.3035	−	17.4523i	−0.587387	−	0.560072i	0.337011	−	0.941501i	$-0.390584\pi$
$971$	−18.3035	−	17.4523i	−0.587387	−	0.560072i	−0.924398	+	0.381428i	$0.875432\pi$
$972$	−14.7008	+	5.18511i	−0.471530	+	0.166312i
$973$	19.7057	+	9.25624i	0.631735	+	0.296741i
$974$	7.51067	−	1.07987i	0.240657	−	0.0346013i
$975$	0.416872	+	0.704530i	0.0133506	+	0.0225630i
$976$	11.3025	−	3.91184i	0.361785	−	0.125215i
$977$	−5.83757	+	3.00947i	−0.186760	+	0.0962816i	−0.549071	−	0.835776i	$-0.685018\pi$
$977$	−5.83757	+	3.00947i	−0.186760	+	0.0962816i	0.362311	+	0.932057i	$0.381988\pi$
$978$	−10.4091	+	2.64344i	−0.332847	+	0.0845279i
$979$	0.104925	−	0.121090i	0.00335342	−	0.00387005i
$980$	−11.3896	+	6.97871i	−0.363826	+	0.222927i
$981$	−9.11537	+	8.24646i	−0.291031	+	0.263289i
$982$	−9.62061	+	27.7969i	−0.307006	+	0.887035i
$983$	4.07163	+	0.388793i	0.129865	+	0.0124006i	0.159786	−	0.987152i	$-0.448920\pi$
$983$	4.07163	+	0.388793i	0.129865	+	0.0124006i	−0.0299213	+	0.999552i	$0.509526\pi$
$984$	−0.975148	−	16.7083i	−0.0310866	−	0.532640i
$985$	0.722526	+	7.56663i	0.0230216	+	0.241093i
$986$	3.65246	−	25.4034i	0.116318	−	0.809010i
$987$	−18.3054	−	5.37574i	−0.582668	−	0.171112i
$988$		−	1.97787i		−	0.0629243i
$989$	−10.6430	−	14.4620i	−0.338428	−	0.459866i
$990$	3.60735	−	0.249282i	0.114649	−	0.00792271i
$991$	0.142186	+	2.98485i	0.00451668	+	0.0948169i	1.00000		0.000119859i	$-3.81522e-5\pi$
$991$	0.142186	+	2.98485i	0.00451668	+	0.0948169i	−0.995483	+	0.0949367i	$0.969735\pi$
$992$	−0.909201	−	2.27108i	−0.0288672	−	0.0721067i
$993$	−3.20698	+	24.1351i	−0.101770	+	0.765903i
$994$	26.2748	+	9.41088i	0.833387	+	0.298495i
$995$	−9.95620	+	4.54684i	−0.315633	+	0.144145i
$996$	−0.193388	+	5.23811i	−0.00612774	+	0.165976i
$997$	−17.0120	−	6.81056i	−0.538774	−	0.215693i	0.0862842	−	0.996271i	$-0.472501\pi$
$997$	−17.0120	−	6.81056i	−0.538774	−	0.215693i	−0.625059	+	0.780578i	$0.714925\pi$
$998$	−8.30770	−	8.71286i	−0.262976	−	0.275801i
$999$	−34.4122	−	40.9810i	−1.08875	−	1.29658i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.bf.a.11.4	✓	1280	1.1	even	1	trivial
966.2.bf.a.11.43	yes	1280	3.2	odd	2	inner
966.2.bf.a.149.32	yes	1280	21.2	odd	6	inner
966.2.bf.a.149.57	yes	1280	7.2	even	3	inner
966.2.bf.a.389.32	yes	1280	23.21	odd	22	inner
966.2.bf.a.389.57	yes	1280	69.44	even	22	inner
966.2.bf.a.527.4	yes	1280	483.44	even	66	inner
966.2.bf.a.527.43	yes	1280	161.44	odd	66	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.458227 + 0.888835i) q^{2} +(-1.61477 - 0.626501i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(-1.38105 - 1.31683i) q^{5} +(1.29679 - 1.14819i) q^{6} +(2.39472 + 1.12486i) q^{7} +(0.989821 - 0.142315i) q^{8} +(2.21499 + 2.02332i) q^{9} +O(q^{10})\)	\(q+(-0.458227 + 0.888835i) q^{2} +(-1.61477 - 0.626501i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(-1.38105 - 1.31683i) q^{5} +(1.29679 - 1.14819i) q^{6} +(2.39472 + 1.12486i) q^{7} +(0.989821 - 0.142315i) q^{8} +(2.21499 + 2.02332i) q^{9} +(1.80327 - 0.624119i) q^{10} +(0.561428 - 0.289436i) q^{11} +(0.426329 + 1.67876i) q^{12} +(0.227800 - 0.262896i) q^{13} +(-2.09714 + 1.61307i) q^{14} +(1.40509 + 2.99160i) q^{15} +(-0.327068 + 0.945001i) q^{16} +(-5.40156 - 0.515787i) q^{17} +(-2.81336 + 1.04163i) q^{18} +(0.540469 + 5.66005i) q^{19} +(-0.271569 + 1.88880i) q^{20} +(-3.16221 - 3.31669i) q^{21} +0.631644i q^{22} +(-3.36337 - 3.41874i) q^{23} +(-1.68750 - 0.390318i) q^{24} +(-0.0646487 - 1.35714i) q^{25} +(0.129287 + 0.322943i) q^{26} +(-2.30911 - 4.65489i) q^{27} +(-0.472791 - 2.60317i) q^{28} +(4.30240 - 1.96484i) q^{29} +(-3.30289 - 0.121941i) q^{30} +(2.27108 + 0.909201i) q^{31} +(-0.690079 - 0.723734i) q^{32} +(-1.08791 + 0.115639i) q^{33} +(2.93359 - 4.56475i) q^{34} +(-1.82598 - 4.70691i) q^{35} +(0.363322 - 2.97792i) q^{36} +(10.0083 - 2.42799i) q^{37} +(-5.27851 - 2.11320i) q^{38} +(-0.532551 + 0.281800i) q^{39} +(-1.55439 - 1.10688i) q^{40} +(2.72236 + 9.27152i) q^{41} +(4.39700 - 1.29089i) q^{42} +(3.70601 + 0.532844i) q^{43} +(-0.561428 - 0.289436i) q^{44} +(-0.394656 - 5.71105i) q^{45} +(4.57988 - 1.42292i) q^{46} +(3.60549 - 2.08163i) q^{47} +(1.12018 - 1.32105i) q^{48} +(4.46938 + 5.38745i) q^{49} +(1.23590 + 0.564417i) q^{50} +(8.39917 + 4.21696i) q^{51} +(-0.346286 - 0.0330663i) q^{52} +(8.48133 - 1.63464i) q^{53} +(5.19553 + 0.0805802i) q^{54} +(-1.15649 - 0.339577i) q^{55} +(2.53043 + 0.772606i) q^{56} +(2.67329 - 9.47831i) q^{57} +(-0.225054 + 4.72446i) q^{58} +(6.00186 - 2.07726i) q^{59} +(1.62186 - 2.87985i) q^{60} +(-7.39338 - 9.40145i) q^{61} +(-1.84880 + 1.60199i) q^{62} +(3.02835 + 7.33683i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-0.660791 + 0.0630979i) q^{65} +(0.395726 - 1.01996i) q^{66} +(11.1810 - 0.532617i) 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} +(2.48040 + 1.68749i) q^{72} +(-9.57865 - 13.4513i) q^{73} +(-2.42799 + 10.0083i) q^{74} +(-0.745859 + 2.23198i) q^{75} +(4.29704 - 3.72340i) q^{76} +(1.67004 - 0.0615915i) q^{77} +(-0.00644508 - 0.602478i) q^{78} +(2.36690 - 12.2806i) q^{79} +(1.69610 - 0.874399i) q^{80} +(0.812391 + 8.96326i) q^{81} +(-9.48831 - 1.82872i) q^{82} +(2.90370 + 0.852603i) q^{83} +(-0.867434 + 4.49973i) q^{84} +(6.78061 + 7.82524i) q^{85} +(-2.17180 + 3.04987i) q^{86} +(-8.17837 + 0.477316i) q^{87} +(0.514522 - 0.366390i) q^{88} +(0.235493 - 0.0942770i) q^{89} +(5.25703 + 2.26617i) q^{90} +(0.841240 - 0.373319i) q^{91} +(-0.833878 + 4.72278i) q^{92} +(-3.09766 - 2.89099i) q^{93} +(0.198096 + 4.15854i) q^{94} +(6.70688 - 8.52850i) q^{95} +(0.660902 + 1.60100i) q^{96} +(-0.162509 - 0.553456i) q^{97} +(-6.83655 + 1.50387i) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more