LMFDB - Embedded newform 930.2.bk.a.47.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(47,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 5, 4]))

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

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

chi := DirichletCharacter("930.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bk (of order $20$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$64$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			47.8
Character	$\chi$	$=$	930.47
Dual form			930.2.bk.a.653.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156434 + 0.987688i) q^{2} +(-1.20093 - 1.24811i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-1.74392 + 1.39955i) q^{5} +(1.42061 - 0.990898i) q^{6} +(-2.75830 + 1.40542i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-0.115534 + 2.99777i) q^{9} +O(q^{10})$	\(q+(-0.156434 + 0.987688i) q^{2} +(-1.20093 - 1.24811i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-1.74392 + 1.39955i) q^{5} +(1.42061 - 0.990898i) q^{6} +(-2.75830 + 1.40542i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-0.115534 + 2.99777i) q^{9} +(-1.10951 - 1.94139i) q^{10} +(-1.51970 - 0.493780i) q^{11} +(0.756467 + 1.55813i) q^{12} +(-1.80652 + 0.286124i) q^{13} +(-0.956627 - 2.94419i) q^{14} +(3.84111 + 0.495828i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-1.05875 - 0.539458i) q^{17} +(-2.94279 - 0.583067i) q^{18} +(3.67068 + 5.05225i) q^{19} +(2.09105 - 0.792154i) q^{20} +(5.06664 + 1.75483i) q^{21} +(0.725434 - 1.42375i) q^{22} +(3.83937 - 7.53519i) q^{23} +(-1.65728 + 0.503409i) q^{24} +(1.08250 - 4.88141i) q^{25} -1.82904i q^{26} +(3.88029 - 3.45592i) q^{27} +(3.05760 - 0.484276i) q^{28} +(0.328688 - 0.238806i) q^{29} +(-1.09061 + 3.71626i) q^{30} +(-1.42241 + 5.38300i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.20876 + 2.48974i) q^{33} +(0.698441 - 0.961322i) q^{34} +(2.84328 - 6.31133i) q^{35} +(1.03624 - 2.81535i) q^{36} +(-4.48906 - 4.48906i) q^{37} +(-5.56427 + 2.83514i) q^{38} +(2.52661 + 1.91111i) q^{39} +(0.455289 + 2.18923i) q^{40} +(-7.42247 - 10.2162i) q^{41} +(-2.52582 + 4.72974i) q^{42} +(-0.180965 + 1.14257i) q^{43} +(1.29273 + 0.939226i) q^{44} +(-3.99406 - 5.38957i) q^{45} +(6.84181 + 4.97087i) q^{46} +(8.95593 - 1.41848i) q^{47} +(-0.237955 - 1.71563i) q^{48} +(1.51849 - 2.09003i) q^{49} +(4.65197 + 1.83280i) q^{50} +(0.598180 + 1.96928i) q^{51} +(1.80652 + 0.286124i) q^{52} +(4.94962 - 9.71417i) q^{53} +(2.80636 + 4.37314i) q^{54} +(3.34130 - 1.26579i) q^{55} +3.09571i q^{56} +(1.89752 - 10.6488i) q^{57} +(0.184448 + 0.361999i) q^{58} +(5.19354 + 3.77333i) q^{59} +(-3.49990 - 1.65853i) q^{60} +5.65997 q^{61} +(-5.09422 - 2.24699i) q^{62} +(-3.89446 - 8.43113i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(2.74997 - 3.02729i) q^{65} +(-2.64818 + 0.804400i) q^{66} +(-0.547307 - 0.547307i) q^{67} +(0.840226 + 0.840226i) q^{68} +(-14.0155 + 4.25730i) q^{69} +(5.78884 + 3.79558i) q^{70} +(1.81059 - 0.588296i) q^{71} +(2.61859 + 1.46390i) q^{72} +(2.88043 + 5.65315i) q^{73} +(5.13604 - 3.73155i) q^{74} +(-7.39253 + 4.51116i) q^{75} +(-1.92979 - 5.93928i) q^{76} +(4.88575 - 0.773827i) q^{77} +(-2.28283 + 2.19654i) q^{78} +(10.8657 - 3.53048i) q^{79} +(-2.23350 + 0.107213i) q^{80} +(-8.97330 - 0.692690i) q^{81} +(11.2515 - 5.73293i) q^{82} +(-11.9325 - 1.88992i) q^{83} +(-4.27639 - 3.23462i) q^{84} +(2.60137 - 0.541001i) q^{85} +(-1.10019 - 0.357475i) q^{86} +(-0.692787 - 0.123448i) q^{87} +(-1.12989 + 1.12989i) q^{88} +(0.934106 - 2.87488i) q^{89} +(5.94802 - 3.10178i) q^{90} +(4.58078 - 3.32814i) q^{91} +(-5.97996 + 5.97996i) q^{92} +(8.42678 - 4.68929i) q^{93} +9.06757i q^{94} +(-13.4723 - 3.67341i) q^{95} +(1.73173 + 0.0333580i) q^{96} +(3.60448 - 1.83657i) q^{97} +(1.82675 + 1.82675i) q^{98} +(1.65582 - 4.49867i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q + 8 q^{3} - 12 q^{7}+O(q^{10}) $ 512 * q + 8 * q^3 - 12 * q^7	$ 512 q + 8 q^{3} - 12 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} + 128 q^{16} + 28 q^{22} + 32 q^{25} + 44 q^{27} + 8 q^{28} + 24 q^{30} + 8 q^{31} + 28 q^{33} + 176 q^{37} + 24 q^{42} - 40 q^{45} - 24 q^{46} + 12 q^{48} - 16 q^{51} - 40 q^{55} + 40 q^{57} + 56 q^{58} + 12 q^{60} - 32 q^{61} - 224 q^{63} + 32 q^{66} + 48 q^{67} + 24 q^{70} + 40 q^{73} - 32 q^{75} + 48 q^{76} - 76 q^{78} - 96 q^{81} + 24 q^{85} - 80 q^{87} - 72 q^{88} + 16 q^{90} + 80 q^{91} - 168 q^{93} - 112 q^{97}+O(q^{100}) $ 512 * q + 8 * q^3 - 12 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 + 128 * q^16 + 28 * q^22 + 32 * q^25 + 44 * q^27 + 8 * q^28 + 24 * q^30 + 8 * q^31 + 28 * q^33 + 176 * q^37 + 24 * q^42 - 40 * q^45 - 24 * q^46 + 12 * q^48 - 16 * q^51 - 40 * q^55 + 40 * q^57 + 56 * q^58 + 12 * q^60 - 32 * q^61 - 224 * q^63 + 32 * q^66 + 48 * q^67 + 24 * q^70 + 40 * q^73 - 32 * q^75 + 48 * q^76 - 76 * q^78 - 96 * q^81 + 24 * q^85 - 80 * q^87 - 72 * q^88 + 16 * q^90 + 80 * q^91 - 168 * q^93 - 112 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.156434	+	0.987688i	−0.110616	+	0.698401i
$2$	−0.156434	+	0.987688i	−0.110616	+	0.698401i
$3$	−1.20093	−	1.24811i	−0.693357	−	0.720594i
$3$	−1.20093	−	1.24811i	−0.693357	−	0.720594i
$4$	−0.951057	−	0.309017i	−0.475528	−	0.154508i
$5$	−1.74392	+	1.39955i	−0.779904	+	0.625899i
$5$	−1.74392	+	1.39955i	−0.779904	+	0.625899i
$6$	1.42061	−	0.990898i	0.579960	−	0.404532i
$7$	−2.75830	+	1.40542i	−1.04254	+	0.531200i	−0.889459	−	0.457014i	$-0.848919\pi$
$7$	−2.75830	+	1.40542i	−1.04254	+	0.531200i	−0.153079	+	0.988214i	$0.548919\pi$
$8$	0.453990	−	0.891007i	0.160510	−	0.315018i
$9$	−0.115534	+	2.99777i	−0.0385113	+	0.999258i
$10$	−1.10951	−	1.94139i	−0.350859	−	0.613920i
$11$	−1.51970	−	0.493780i	−0.458207	−	0.148880i	0.0708136	−	0.997490i	$-0.477440\pi$
$11$	−1.51970	−	0.493780i	−0.458207	−	0.148880i	−0.529020	+	0.848609i	$0.677440\pi$
$12$	0.756467	+	1.55813i	0.218373	+	0.449792i
$13$	−1.80652	+	0.286124i	−0.501038	+	0.0793566i	−0.401838	−	0.915711i	$-0.631628\pi$
$13$	−1.80652	+	0.286124i	−0.501038	+	0.0793566i	−0.0992000	+	0.995068i	$0.531628\pi$
$14$	−0.956627	−	2.94419i	−0.255669	−	0.786869i
$15$	3.84111	+	0.495828i	0.991771	+	0.128022i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−1.05875	−	0.539458i	−0.256784	−	0.130838i	0.320861	−	0.947126i	$-0.396028\pi$
$17$	−1.05875	−	0.539458i	−0.256784	−	0.130838i	−0.577644	+	0.816289i	$0.696028\pi$
$18$	−2.94279	−	0.583067i	−0.693623	−	0.137430i
$19$	3.67068	+	5.05225i	0.842111	+	1.15907i	0.985546	+	0.169407i	$0.0541851\pi$
$19$	3.67068	+	5.05225i	0.842111	+	1.15907i	−0.143435	+	0.989660i	$0.545815\pi$
$20$	2.09105	−	0.792154i	0.467573	−	0.177131i
$21$	5.06664	+	1.75483i	1.10563	+	0.382936i
$22$	0.725434	−	1.42375i	0.154663	−	0.303544i
$23$	3.83937	−	7.53519i	0.800564	−	1.57120i	−0.0201088	−	0.999798i	$-0.506401\pi$
$23$	3.83937	−	7.53519i	0.800564	−	1.57120i	0.820673	−	0.571398i	$-0.193599\pi$
$24$	−1.65728	+	0.503409i	−0.338291	+	0.102758i
$25$	1.08250	−	4.88141i	0.216500	−	0.976283i
$26$		−	1.82904i		−	0.358703i
$27$	3.88029	−	3.45592i	0.746762	−	0.665092i
$28$	3.05760	−	0.484276i	0.577831	−	0.0915195i
$29$	0.328688	−	0.238806i	0.0610359	−	0.0443452i	−0.556849	−	0.830614i	$-0.687990\pi$
$29$	0.328688	−	0.238806i	0.0610359	−	0.0443452i	0.617885	+	0.786269i	$0.287990\pi$
$30$	−1.09061	+	3.71626i	−0.199117	+	0.678493i
$31$	−1.42241	+	5.38300i	−0.255473	+	0.966816i
$31$	−1.42241	+	5.38300i	−0.255473	+	0.966816i
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	1.20876	+	2.48974i	0.210419	+	0.433408i
$34$	0.698441	−	0.961322i	0.119782	−	0.164865i
$35$	2.84328	−	6.31133i	0.480602	−	1.06681i
$36$	1.03624	−	2.81535i	0.172707	−	0.469225i
$37$	−4.48906	−	4.48906i	−0.737997	−	0.737997i	0.234193	−	0.972190i	$-0.424755\pi$
$37$	−4.48906	−	4.48906i	−0.737997	−	0.737997i	−0.972190	+	0.234193i	$0.924755\pi$
$38$	−5.56427	+	2.83514i	−0.902644	+	0.459920i
$39$	2.52661	+	1.91111i	0.404582	+	0.306022i
$40$	0.455289	+	2.18923i	0.0719875	+	0.346147i
$41$	−7.42247	−	10.2162i	−1.15920	−	1.59550i	−0.714159	−	0.699984i	$-0.753191\pi$
$41$	−7.42247	−	10.2162i	−1.15920	−	1.59550i	−0.445037	−	0.895512i	$-0.646809\pi$
$42$	−2.52582	+	4.72974i	−0.389743	+	0.729815i
$43$	−0.180965	+	1.14257i	−0.0275970	+	0.174240i	−0.997637	−	0.0687045i	$-0.978113\pi$
$43$	−0.180965	+	1.14257i	−0.0275970	+	0.174240i	0.970040	+	0.242945i	$0.0781134\pi$
$44$	1.29273	+	0.939226i	0.194887	+	0.141594i
$45$	−3.99406	−	5.38957i	−0.595400	−	0.803430i
$46$	6.84181	+	4.97087i	1.00877	+	0.732914i
$47$	8.95593	−	1.41848i	1.30636	−	0.206907i	0.535836	−	0.844322i	$-0.319996\pi$
$47$	8.95593	−	1.41848i	1.30636	−	0.206907i	0.770521	+	0.637415i	$0.219996\pi$
$48$	−0.237955	−	1.71563i	−0.0343458	−	0.247629i
$49$	1.51849	−	2.09003i	0.216928	−	0.298575i
$50$	4.65197	+	1.83280i	0.657888	+	0.259196i
$51$	0.598180	+	1.96928i	0.0837619	+	0.275754i
$52$	1.80652	+	0.286124i	0.250519	+	0.0396783i
$53$	4.94962	−	9.71417i	0.679882	−	1.33434i	−0.250630	−	0.968083i	$-0.580638\pi$
$53$	4.94962	−	9.71417i	0.679882	−	1.33434i	0.930512	−	0.366261i	$-0.119362\pi$
$54$	2.80636	+	4.37314i	0.381897	+	0.595109i
$55$	3.34130	−	1.26579i	0.450541	−	0.170679i
$56$			3.09571i			0.413682i
$57$	1.89752	−	10.6488i	0.251332	−	1.41047i
$58$	0.184448	+	0.361999i	0.0242192	+	0.0475328i
$59$	5.19354	+	3.77333i	0.676142	+	0.491246i	0.872075	−	0.489371i	$-0.162774\pi$
$59$	5.19354	+	3.77333i	0.676142	+	0.491246i	−0.195934	+	0.980617i	$0.562774\pi$
$60$	−3.49990	−	1.65853i	−0.451835	−	0.214115i
$61$	5.65997			0.724684			0.362342	−	0.932045i	$-0.381977\pi$
$61$	5.65997			0.724684			0.362342	+	0.932045i	$0.381977\pi$
$62$	−5.09422	−	2.24699i	−0.646966	−	0.285368i
$63$	−3.89446	−	8.43113i	−0.490656	−	1.06222i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	2.74997	−	3.02729i	0.341092	−	0.375490i
$66$	−2.64818	+	0.804400i	−0.325968	+	0.0990148i
$67$	−0.547307	−	0.547307i	−0.0668642	−	0.0668642i	0.672884	−	0.739748i	$-0.265055\pi$
$67$	−0.547307	−	0.547307i	−0.0668642	−	0.0668642i	−0.739748	+	0.672884i	$0.765055\pi$
$68$	0.840226	+	0.840226i	0.101892	+	0.101892i
$69$	−14.0155	+	4.25730i	−1.68727	+	0.512518i
$70$	5.78884	+	3.79558i	0.691898	+	0.453659i
$71$	1.81059	−	0.588296i	0.214877	−	0.0698179i	−0.199600	−	0.979877i	$-0.563964\pi$
$71$	1.81059	−	0.588296i	0.214877	−	0.0698179i	0.414478	+	0.910060i	$0.363964\pi$
$72$	2.61859	+	1.46390i	0.308603	+	0.172523i
$73$	2.88043	+	5.65315i	0.337128	+	0.661651i	0.995877	−	0.0907113i	$-0.0289141\pi$
$73$	2.88043	+	5.65315i	0.337128	+	0.661651i	−0.658749	+	0.752363i	$0.728914\pi$
$74$	5.13604	−	3.73155i	0.597052	−	0.433784i
$75$	−7.39253	+	4.51116i	−0.853615	+	0.520904i
$76$	−1.92979	−	5.93928i	−0.221362	−	0.681282i
$77$	4.88575	−	0.773827i	0.556783	−	0.0881858i
$78$	−2.28283	+	2.19654i	−0.258479	+	0.248710i
$79$	10.8657	−	3.53048i	1.22249	−	0.397210i	0.374499	−	0.927227i	$-0.377815\pi$
$79$	10.8657	−	3.53048i	1.22249	−	0.397210i	0.847987	+	0.530017i	$0.177815\pi$
$80$	−2.23350	+	0.107213i	−0.249712	+	0.0119868i
$81$	−8.97330	−	0.692690i	−0.997034	−	0.0769655i
$82$	11.2515	−	5.73293i	1.24252	−	0.633096i
$83$	−11.9325	−	1.88992i	−1.30976	−	0.207445i	−0.537775	−	0.843088i	$-0.680735\pi$
$83$	−11.9325	−	1.88992i	−1.30976	−	0.207445i	−0.771983	+	0.635643i	$0.780735\pi$
$84$	−4.27639	−	3.23462i	−0.466592	−	0.352926i
$85$	2.60137	−	0.541001i	0.282158	−	0.0586798i
$86$	−1.10019	−	0.357475i	−0.118637	−	0.0385475i
$87$	−0.692787	−	0.123448i	−0.0742746	−	0.0132350i
$88$	−1.12989	+	1.12989i	−0.120447	+	0.120447i
$89$	0.934106	−	2.87488i	0.0990151	−	0.304737i	−0.889264	−	0.457394i	$-0.848783\pi$
$89$	0.934106	−	2.87488i	0.0990151	−	0.304737i	0.988279	+	0.152657i	$0.0487829\pi$
$90$	5.94802	−	3.10178i	0.626977	−	0.326956i
$91$	4.58078	−	3.32814i	0.480197	−	0.348883i
$92$	−5.97996	+	5.97996i	−0.623454	+	0.623454i
$93$	8.42678	−	4.68929i	0.873816	−	0.486257i
$94$			9.06757i			0.935248i
$95$	−13.4723	−	3.67341i	−1.38222	−	0.376884i
$96$	1.73173	+	0.0333580i	0.176744	+	0.00340458i
$97$	3.60448	−	1.83657i	0.365980	−	0.186476i	−0.261323	−	0.965251i	$-0.584159\pi$
$97$	3.60448	−	1.83657i	0.365980	−	0.186476i	0.627303	+	0.778775i	$0.284159\pi$
$98$	1.82675	+	1.82675i	0.184530	+	0.184530i
$99$	1.65582	−	4.49867i	0.166416	−	0.452133i
$100$	−2.53796	+	4.30799i	−0.253796	+	0.430799i
$101$	8.63047	−	2.80421i	0.858764	−	0.279029i	0.153652	−	0.988125i	$-0.450897\pi$
$101$	8.63047	−	2.80421i	0.858764	−	0.279029i	0.705112	+	0.709096i	$0.250897\pi$
$102$	−2.03861	+	0.282752i	−0.201852	+	0.0279966i
$103$	−1.13240	+	7.14968i	−0.111578	+	0.704479i	0.866954	+	0.498388i	$0.166074\pi$
$103$	−1.13240	+	7.14968i	−0.111578	+	0.704479i	−0.978533	+	0.206091i	$0.933926\pi$
$104$	−0.565203	+	1.73952i	−0.0554227	+	0.170574i
$105$	−11.2918	+	4.03075i	−1.10196	+	0.393361i
$106$	8.82028	+	6.40831i	0.856701	+	0.622430i
$107$	2.39916	+	1.22243i	0.231936	+	0.118177i	0.566097	−	0.824339i	$-0.308453\pi$
$107$	2.39916	+	1.22243i	0.231936	+	0.118177i	−0.334161	+	0.942516i	$0.608453\pi$
$108$	−4.75831	+	2.08770i	−0.457869	+	0.200889i
$109$	−2.25655	+	3.10587i	−0.216138	+	0.297488i	−0.903295	−	0.429021i	$-0.858859\pi$
$109$	−2.25655	+	3.10587i	−0.216138	+	0.297488i	0.687157	+	0.726509i	$0.258859\pi$
$110$	0.727509	+	3.49818i	0.0693653	+	0.333538i
$111$	−0.211773	+	10.9939i	−0.0201006	+	1.04349i
$112$	−3.05760	−	0.484276i	−0.288916	−	0.0457597i
$113$	−8.14307	+	4.14910i	−0.766035	+	0.390314i	−0.792921	−	0.609324i	$-0.791441\pi$
$113$	−8.14307	+	4.14910i	−0.766035	+	0.390314i	0.0268860	+	0.999639i	$0.491441\pi$
$114$	10.2209	+	3.53999i	0.957270	+	0.331551i
$115$	3.85035	+	18.5142i	0.359047	+	1.72645i
$116$	−0.386396	+	0.125548i	−0.0358760	+	0.0116568i
$117$	−0.649022	−	5.44859i	−0.0600021	−	0.503722i
$118$	−4.53932	+	4.53932i	−0.417878	+	0.417878i
$119$	3.67850			0.337208
$120$	2.18562	−	3.19736i	0.199518	−	0.291877i
$121$	−6.83352	−	4.96484i	−0.621229	−	0.451349i
$122$	−0.885414	+	5.59028i	−0.0801616	+	0.506120i
$123$	−3.83697	+	21.5329i	−0.345968	+	1.94156i
$124$	3.01624	−	4.67999i	0.270866	−	0.420276i
$125$	4.94400	+	10.0278i	0.442205	+	0.896914i
$126$	8.93655	−	2.52760i	0.796131	−	0.225176i
$127$	−2.32943	−	14.7074i	−0.206703	−	1.30507i	−0.844785	−	0.535105i	$-0.820272\pi$
$127$	−2.32943	−	14.7074i	−0.206703	−	1.30507i	0.638082	−	0.769968i	$-0.279728\pi$
$128$	0.891007	−	0.453990i	0.0787546	−	0.0401275i
$129$	1.64338	−	1.14628i	0.144691	−	0.100925i
$130$	2.55983	+	3.18969i	0.224512	+	0.279754i
$131$	11.9388	+	3.87917i	1.04310	+	0.338924i	0.779958	−	0.625832i	$-0.215240\pi$
$131$	11.9388	+	3.87917i	1.04310	+	0.338924i	0.263144	+	0.964756i	$0.415240\pi$
$132$	−0.380230	−	2.74141i	−0.0330948	−	0.238609i
$133$	−17.2254	−	8.77676i	−1.49363	−	0.761042i
$134$	0.626186	−	0.454951i	0.0540943	−	0.0393018i
$135$	−1.93016	+	11.4575i	−0.166122	+	0.986105i
$136$	−0.961322	+	0.698441i	−0.0824327	+	0.0598908i
$137$	−7.30471	+	1.15695i	−0.624083	+	0.0988451i	−0.460464	−	0.887678i	$-0.652317\pi$
$137$	−7.30471	+	1.15695i	−0.624083	+	0.0988451i	−0.163620	+	0.986524i	$0.552317\pi$
$138$	−2.01237	−	14.5090i	−0.171304	−	1.23508i
$139$	10.6990	−	14.7259i	0.907480	−	1.24904i	−0.0605405	−	0.998166i	$-0.519282\pi$
$139$	10.6990	−	14.7259i	0.907480	−	1.24904i	0.968020	−	0.250873i	$-0.0807176\pi$
$140$	−4.65443	+	5.12381i	−0.393371	+	0.433041i
$141$	−12.5259	−	9.47445i	−1.05487	−	0.797893i
$142$	0.297814	+	1.88033i	0.0249920	+	0.157794i
$143$	2.88665	+	0.457200i	0.241393	+	0.0382330i
$144$	−1.85552	+	2.35734i	−0.154626	+	0.196445i
$145$	−0.238984	+	0.876475i	−0.0198465	+	0.0727873i
$146$	−6.03415	+	1.96061i	−0.499390	+	0.162262i
$147$	−4.43218	+	0.614736i	−0.365560	+	0.0507026i
$148$	2.88215	+	5.65655i	0.236912	+	0.464965i
$149$	−9.04242			−0.740784			−0.370392	−	0.928876i	$-0.620777\pi$
$149$	−9.04242			−0.740784			−0.370392	+	0.928876i	$0.620777\pi$
$150$	−3.29917	−	8.00721i	−0.269376	−	0.653786i
$151$	−3.22951	+	9.93940i	−0.262813	+	0.808857i	0.729376	+	0.684113i	$0.239811\pi$
$151$	−3.22951	+	9.93940i	−0.262813	+	0.808857i	−0.992189	+	0.124743i	$0.960189\pi$
$152$	6.16804	−	0.976922i	0.500294	−	0.0792388i
$153$	1.73950	−	3.11156i	0.140630	−	0.251555i
$154$			4.94665i			0.398613i
$155$	−5.05323	−	11.3783i	−0.405885	−	0.913924i
$156$	−1.81239	−	2.59834i	−0.145107	−	0.208034i
$157$	−11.4735	−	1.81722i	−0.915683	−	0.145030i	−0.319229	−	0.947678i	$-0.603424\pi$
$157$	−11.4735	−	1.81722i	−0.915683	−	0.145030i	−0.596453	+	0.802648i	$0.703424\pi$
$158$	1.78724	+	11.2842i	0.142185	+	0.897723i
$159$	−18.0685	+	5.48840i	−1.43292	+	0.435258i
$160$	0.243503	−	2.22277i	0.0192506	−	0.175725i
$161$			26.1802i			2.06329i
$162$	2.08790	−	8.75447i	0.164041	−	0.687816i
$163$	11.8888	+	6.05767i	0.931206	+	0.474473i	0.852677	−	0.522438i	$-0.174978\pi$
$163$	11.8888	+	6.05767i	0.931206	+	0.474473i	0.0785294	+	0.996912i	$0.474978\pi$
$164$	3.90223	+	12.0098i	0.304713	+	0.937809i
$165$	−5.59251	−	2.65018i	−0.435376	−	0.206316i
$166$	3.73330	−	11.4899i	0.289760	−	0.891790i
$167$	3.15880	−	19.9439i	0.244435	−	1.54330i	−0.494289	−	0.869297i	$-0.664572\pi$
$167$	3.15880	−	19.9439i	0.244435	−	1.54330i	0.738725	−	0.674007i	$-0.235428\pi$
$168$	3.86377	−	3.71773i	0.298096	−	0.286829i
$169$	−9.18210	+	2.98344i	−0.706315	+	0.229496i
$170$	0.127397	+	2.65397i	0.00977088	+	0.203550i
$171$	−15.5696	+	10.4202i	−1.19064	+	0.796849i
$172$	0.525182	−	1.03073i	0.0400448	−	0.0785923i
$173$	0.894940	+	5.65043i	0.0680410	+	0.429594i	0.998070	+	0.0621067i	$0.0197819\pi$
$173$	0.894940	+	5.65043i	0.0680410	+	0.429594i	−0.930028	+	0.367487i	$0.880218\pi$
$174$	0.230304	−	0.664946i	0.0174593	−	0.0504094i
$175$	3.87459	+	14.9858i	0.292891	+	1.13282i
$176$	−0.939226	−	1.29273i	−0.0707968	−	0.0974435i
$177$	−1.52757	−	11.0136i	−0.114819	−	0.827832i
$178$	2.69336	+	1.37234i	0.201876	+	0.102861i
$179$	−6.30339	+	19.3998i	−0.471137	+	1.45001i	0.379960	+	0.925003i	$0.375938\pi$
$179$	−6.30339	+	19.3998i	−0.471137	+	1.45001i	−0.851097	+	0.525008i	$0.824062\pi$
$180$	2.13311	+	6.36002i	0.158993	+	0.474048i
$181$	18.9075			1.40538			0.702690	−	0.711496i	$-0.251982\pi$
$181$	18.9075			1.40538			0.702690	+	0.711496i	$0.251982\pi$
$182$	2.57057	+	5.04502i	0.190543	+	0.373962i
$183$	−6.79722	−	7.06423i	−0.502465	−	0.522203i
$184$	−4.97087	−	6.84181i	−0.366457	−	0.504385i
$185$	14.1112	+	1.54588i	1.03748	+	0.113655i
$186$	3.31332	+	9.05660i	0.242944	+	0.664062i
$187$	1.34260	+	1.34260i	0.0981809	+	0.0981809i
$188$	−8.95593	−	1.41848i	−0.653179	−	0.103453i
$189$	−5.84596	+	14.9859i	−0.425231	+	1.09006i
$190$	5.73571	−	12.7317i	0.416112	−	0.923658i
$191$			18.8501i			1.36395i	0.731377	+	0.681974i	$0.238878\pi$
$191$			18.8501i			1.36395i	−0.731377	+	0.681974i	$0.761122\pi$
$192$	−0.303849	+	1.70519i	−0.0219284	+	0.123062i
$193$	−10.8839	−	21.3608i	−0.783438	−	1.53758i	−0.842110	−	0.539306i	$-0.818687\pi$
$193$	−10.8839	−	21.3608i	−0.783438	−	1.53758i	0.0586718	−	0.998277i	$-0.481313\pi$
$194$	1.25010	+	3.84741i	0.0897518	+	0.276228i
$195$	−7.08091	+	0.203313i	−0.507074	+	0.0145596i
$196$	−2.09003	+	1.51849i	−0.149288	+	0.108464i
$197$	6.47278	+	12.7035i	0.461166	+	0.905090i	0.998109	+	0.0614710i	$0.0195792\pi$
$197$	6.47278	+	12.7035i	0.461166	+	0.905090i	−0.536943	+	0.843619i	$0.680421\pi$
$198$	4.18426	+	2.33918i	0.297362	+	0.166238i
$199$	8.51693	−	11.7225i	0.603749	−	0.830989i	−0.392296	−	0.919839i	$-0.628319\pi$
$199$	8.51693	−	11.7225i	0.603749	−	0.830989i	0.996045	+	0.0888500i	$0.0283192\pi$
$200$	−3.85793	−	3.18063i	−0.272797	−	0.224905i
$201$	−0.0258194	+	1.34037i	−0.00182116	+	0.0945427i
$202$	1.41958	+	8.96289i	0.0998815	+	0.630627i
$203$	−0.570997	+	1.12064i	−0.0400761	+	0.0786538i
$204$	0.0396379	−	2.05774i	0.00277521	−	0.144071i
$205$	27.2422	+	7.42800i	1.90268	+	0.518794i
$206$	−6.88451	−	2.23691i	−0.479666	−	0.155853i
$207$	22.1452	+	12.3801i	1.53920	+	0.860479i
$208$	−1.62968	−	0.830365i	−0.112998	−	0.0575754i
$209$	−3.08362	−	9.49041i	−0.213299	−	0.656466i
$210$	−2.21470	−	11.7833i	−0.152829	−	0.813125i
$211$	−23.9958			−1.65194			−0.825969	−	0.563715i	$-0.809372\pi$
$211$	−23.9958			−1.65194			−0.825969	+	0.563715i	$0.809372\pi$
$212$	−7.70921	+	7.70921i	−0.529471	+	0.529471i
$213$	−2.90865	−	1.55330i	−0.199297	−	0.106431i
$214$	−1.58269	+	2.17839i	−0.108191	+	0.148912i
$215$	−1.28350	−	2.24582i	−0.0875340	−	0.153164i
$216$	−1.31763	−	5.02632i	−0.0896536	−	0.341997i
$217$	−3.64195	−	16.8470i	−0.247232	−	1.14365i
$218$	−2.71463	−	2.71463i	−0.183858	−	0.183858i
$219$	3.59654	−	10.3841i	0.243032	−	0.701693i
$220$	−3.56892	+	0.171316i	−0.240616	+	0.0115501i
$221$	2.06700	+	0.671608i	0.139041	+	0.0451772i
$222$	−10.8254	−	1.92899i	−0.726552	−	0.129465i
$223$	−0.431903	+	0.431903i	−0.0289224	+	0.0289224i	−0.721420	−	0.692498i	$-0.756510\pi$
$223$	−0.431903	+	0.431903i	−0.0289224	+	0.0289224i	0.692498	+	0.721420i	$0.256510\pi$
$224$	0.956627	−	2.94419i	0.0639173	−	0.196717i
$225$	14.5083	+	3.80906i	0.967221	+	0.253938i
$226$	−2.82416	−	8.69187i	−0.187860	−	0.578175i
$227$	0.850633	−	5.37069i	0.0564585	−	0.356465i	−0.943245	−	0.332099i	$-0.892243\pi$
$227$	0.850633	−	5.37069i	0.0564585	−	0.356465i	0.999703	−	0.0243662i	$-0.00775677\pi$
$228$	−5.09530	+	9.54124i	−0.337445	+	0.631884i
$229$	−3.41839	−	4.70501i	−0.225894	−	0.310916i	0.680993	−	0.732289i	$-0.261548\pi$
$229$	−3.41839	−	4.70501i	−0.225894	−	0.310916i	−0.906887	+	0.421373i	$0.861548\pi$
$230$	−18.8885	+	0.906693i	−1.24547	+	0.0597856i
$231$	−6.83327	−	5.16862i	−0.449596	−	0.340070i
$232$	−0.0635564	−	0.401279i	−0.00417268	−	0.0263453i
$233$	−2.58509	−	16.3216i	−0.169355	−	1.06926i	−0.915158	−	0.403096i	$-0.867934\pi$
$233$	−2.58509	−	16.3216i	−0.169355	−	1.06926i	0.745803	−	0.666167i	$-0.232066\pi$
$234$	5.48304	+	0.211316i	0.358437	+	0.0138141i
$235$	−13.6332	+	15.0080i	−0.889330	+	0.979015i
$236$	−3.77333	−	5.19354i	−0.245623	−	0.338071i
$237$	−17.4553	−	9.32167i	−1.13385	−	0.605508i
$238$	−0.575445	+	3.63322i	−0.0373006	+	0.235506i
$239$	−8.40296	−	25.8616i	−0.543542	−	1.67285i	−0.724431	−	0.689347i	$-0.757897\pi$
$239$	−8.40296	−	25.8616i	−0.543542	−	1.67285i	0.180889	−	0.983504i	$-0.442103\pi$
$240$	2.81609	+	2.65888i	0.181778	+	0.171630i
$241$	4.38615	−	13.4992i	0.282537	−	0.869559i	−0.704589	−	0.709615i	$-0.748869\pi$
$241$	4.38615	−	13.4992i	0.282537	−	0.869559i	0.987126	−	0.159943i	$-0.0511312\pi$
$242$	5.97271	−	5.97271i	0.383941	−	0.383941i
$243$	9.91176	+	12.0315i	0.635840	+	0.771821i
$244$	−5.38295	−	1.74903i	−0.344608	−	0.111970i
$245$	0.276975	+	5.77005i	0.0176953	+	0.368635i
$246$	−20.6676	−	7.15822i	−1.31772	−	0.456392i
$247$	−8.07671	−	8.07671i	−0.513909	−	0.513909i
$248$	4.15053	+	3.71121i	0.263559	+	0.235662i
$249$	11.9712	+	17.1626i	0.758646	+	1.08764i
$250$	−10.6778	+	3.31444i	−0.675321	+	0.209624i
$251$	−4.72521	+	6.50369i	−0.298253	+	0.410509i	−0.931673	−	0.363299i	$-0.881650\pi$
$251$	−4.72521	+	6.50369i	−0.298253	+	0.410509i	0.633420	+	0.773808i	$0.281650\pi$
$252$	1.09849	+	9.22193i	0.0691985	+	0.580927i
$253$	−9.55542	+	9.55542i	−0.600744	+	0.600744i
$254$	14.8908			0.934330
$255$	−3.79929	−	2.59708i	−0.237921	−	0.162635i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−7.28346	−	3.71111i	−0.454330	−	0.231493i	0.211823	−	0.977308i	$-0.432060\pi$
$257$	−7.28346	−	3.71111i	−0.454330	−	0.231493i	−0.666153	+	0.745816i	$0.732060\pi$
$258$	0.875091	+	1.80246i	0.0544808	+	0.112216i
$259$	18.6912	+	6.07313i	1.16141	+	0.377366i
$260$	−3.55086	+	2.02934i	−0.220215	+	0.125854i
$261$	0.677912	+	1.01292i	0.0419617	+	0.0626984i
$262$	−5.69906	+	11.1850i	−0.352089	+	0.691013i
$263$	−2.08887	−	13.1886i	−0.128805	−	0.813242i	−0.964507	−	0.264059i	$-0.914939\pi$
$263$	−2.08887	−	13.1886i	−0.128805	−	0.813242i	0.835702	−	0.549184i	$-0.185061\pi$
$264$	2.76714	+	0.0533029i	0.170306	+	0.00328057i
$265$	4.96377	+	23.8680i	0.304922	+	1.46620i
$266$	11.3633	−	15.6403i	0.696731	−	0.958969i
$267$	−4.70995	+	2.28667i	−0.288244	+	0.139942i
$268$	0.351393	+	0.689647i	0.0214647	+	0.0421269i
$269$	13.1086	−	9.52397i	0.799246	−	0.580687i	−0.111446	−	0.993770i	$-0.535548\pi$
$269$	13.1086	−	9.52397i	0.799246	−	0.580687i	0.910693	+	0.413084i	$0.135548\pi$
$270$	−11.0145	−	3.69875i	−0.670321	−	0.225099i
$271$	−1.76287	−	5.42556i	−0.107087	−	0.329579i	0.883128	−	0.469133i	$-0.155433\pi$
$271$	−1.76287	−	5.42556i	−0.107087	−	0.329579i	−0.990215	+	0.139553i	$0.955433\pi$
$272$	−0.539458	−	1.05875i	−0.0327095	−	0.0641959i
$273$	−9.65507	−	1.72044i	−0.584351	−	0.104126i
$274$		−	7.39576i		−	0.446794i
$275$	−4.05542	+	6.88376i	−0.244551	+	0.415107i
$276$	14.6451	+	0.282106i	0.881534	+	0.0169808i
$277$	6.96284	+	1.10281i	0.418356	+	0.0662611i	0.362064	−	0.932153i	$-0.382072\pi$
$277$	6.96284	+	1.10281i	0.418356	+	0.0662611i	0.0562923	+	0.998414i	$0.482072\pi$
$278$	12.8709	+	12.8709i	0.771948	+	0.771948i
$279$	−15.9727	−	4.88600i	−0.956260	−	0.292517i
$280$	−4.33261	−	5.39866i	−0.258923	−	0.322632i
$281$	−1.90927	−	2.62788i	−0.113897	−	0.156766i	0.748262	−	0.663403i	$-0.230888\pi$
$281$	−1.90927	−	2.62788i	−0.113897	−	0.156766i	−0.862160	+	0.506637i	$0.830888\pi$
$282$	11.3173	−	10.8895i	0.673934	−	0.648461i
$283$	−8.93184	−	17.5297i	−0.530943	−	1.04203i	−0.988267	−	0.152734i	$-0.951192\pi$
$283$	−8.93184	−	17.5297i	−0.530943	−	1.04203i	0.457324	−	0.889300i	$-0.348808\pi$
$284$	−1.90377			−0.112968
$285$	11.5944	+	21.2263i	0.686795	+	1.25734i
$286$	−0.903142	+	2.77958i	−0.0534039	+	0.164360i
$287$	34.8314	+	17.7475i	2.05603	+	1.04760i
$288$	−2.03805	−	2.20144i	−0.120093	−	0.129721i
$289$	−9.16242	−	12.6110i	−0.538966	−	0.741823i
$290$	−0.828299	−	0.373152i	−0.0486394	−	0.0219123i
$291$	−6.62097	−	2.29317i	−0.388128	−	0.134428i
$292$	−0.992527	−	6.26657i	−0.0580832	−	0.366723i
$293$	3.84086	−	7.53811i	0.224385	−	0.440381i	−0.751178	−	0.660100i	$-0.770514\pi$
$293$	3.84086	−	7.53811i	0.224385	−	0.440381i	0.975563	+	0.219719i	$0.0705140\pi$
$294$	0.0861775	−	4.47378i	0.00502597	−	0.260916i
$295$	−14.3381	+	0.688261i	−0.834796	+	0.0400721i
$296$	−6.03777	+	1.96179i	−0.350938	+	0.114027i
$297$	−7.60334	+	3.33595i	−0.441190	+	0.193571i
$298$	1.41455	−	8.93110i	0.0819425	−	0.517365i
$299$	−4.77989	+	14.7110i	−0.276428	+	0.850758i
$300$	8.42474	−	2.00595i	0.486402	−	0.115814i
$301$	−1.10664	−	3.40588i	−0.0637856	−	0.196312i
$302$	−9.31182	−	4.74461i	−0.535835	−	0.273022i
$303$	−13.8645	−	7.40408i	−0.796497	−	0.425353i
$304$			6.24493i			0.358171i
$305$	−9.87052	+	7.92142i	−0.565184	+	0.453579i
$306$	2.80113	+	2.20483i	0.160130	+	0.126042i
$307$	4.05471	+	25.6004i	0.231415	+	1.46109i	0.780409	+	0.625269i	$0.215011\pi$
$307$	4.05471	+	25.6004i	0.231415	+	1.46109i	−0.548995	+	0.835826i	$0.684989\pi$
$308$	−4.88575	−	0.773827i	−0.278392	−	0.0440929i
$309$	10.2835	−	7.17291i	0.585007	−	0.408053i
$310$	12.0287	−	3.21106i	0.683183	−	0.182376i
$311$		−	27.5344i		−	1.56133i	−0.624947	−	0.780667i	$-0.714879\pi$
$311$		−	27.5344i		−	1.56133i	0.624947	−	0.780667i	$-0.285121\pi$
$312$	2.84987	−	1.38360i	0.161342	−	0.0783312i
$313$	0.250359	−	0.0396529i	0.0141511	−	0.00224132i	−0.149355	−	0.988784i	$-0.547720\pi$
$313$	0.250359	−	0.0396529i	0.0141511	−	0.00224132i	0.163506	+	0.986542i	$0.447720\pi$
$314$	3.58969	−	11.0479i	0.202578	−	0.623471i
$315$	18.5914	+	9.25269i	1.04751	+	0.521330i
$316$	−11.4249			−0.642699
$317$	−5.61948	−	11.0289i	−0.315622	−	0.619442i	0.677633	−	0.735401i	$-0.263006\pi$
$317$	−5.61948	−	11.0289i	−0.315622	−	0.619442i	−0.993254	+	0.115959i	$0.963006\pi$
$318$	−2.59430	−	18.7046i	−0.145481	−	1.04890i
$319$	−0.617425	+	0.200614i	−0.0345692	+	0.0112322i
$320$	2.15731	+	0.588223i	0.120597	+	0.0328827i
$321$	−1.35550	−	4.46246i	−0.0756565	−	0.249070i
$322$	−25.8579	−	4.09549i	−1.44100	−	0.228233i
$323$	−1.16084	−	7.32923i	−0.0645907	−	0.407809i
$324$	8.32007	+	3.43169i	0.462226	+	0.190649i
$325$	−0.558867	+	9.12808i	−0.0310004	+	0.506335i
$326$	−7.84292	+	10.7948i	−0.434379	+	0.597871i
$327$	6.58641	−	0.913525i	0.364229	−	0.0505180i
$328$	−12.4724	+	1.97543i	−0.688673	+	0.109075i
$329$	−22.7096	+	16.4995i	−1.25202	+	0.909645i
$330$	3.49241	−	5.10908i	0.192251	−	0.281245i
$331$	−0.222684	+	0.161789i	−0.0122398	+	0.00889273i	−0.593888	−	0.804547i	$-0.702408\pi$
$331$	−0.222684	+	0.161789i	−0.0122398	+	0.00889273i	0.581649	+	0.813440i	$0.302408\pi$
$332$	10.7644	+	5.48475i	0.590775	+	0.301015i
$333$	13.9758	−	12.9386i	0.765871	−	0.709028i
$334$	19.2042	+	6.23982i	1.05081	+	0.341428i
$335$	1.72044	+	0.188473i	0.0939979	+	0.0102974i
$336$	3.06753	+	4.39778i	0.167348	+	0.239919i
$337$	−1.32523	+	0.675241i	−0.0721901	+	0.0367827i	−0.489713	−	0.871884i	$-0.662898\pi$
$337$	−1.32523	+	0.675241i	−0.0721901	+	0.0367827i	0.417523	+	0.908666i	$0.362898\pi$
$338$	−1.51032	−	9.53577i	−0.0821504	−	0.518677i
$339$	14.9578	+	5.18063i	0.812394	+	0.281373i
$340$	−2.64123	−	0.289344i	−0.143241	−	0.0156919i
$341$	4.81966	−	7.47819i	0.260999	−	0.404967i
$342$	−7.85624	−	17.0080i	−0.424817	−	0.919687i
$343$	2.13884	−	13.5041i	0.115487	−	0.729155i
$344$	0.935881	+	0.679958i	0.0504593	+	0.0366609i
$345$	18.4836	−	27.0399i	0.995125	−	1.45578i
$346$	−5.72086			−0.307555
$347$	4.42563	−	4.42563i	0.237581	−	0.237581i	−0.578267	−	0.815848i	$-0.696271\pi$
$347$	4.42563	−	4.42563i	0.237581	−	0.237581i	0.815848	+	0.578267i	$0.196271\pi$
$348$	0.620732	+	0.331489i	0.0332747	+	0.0177697i
$349$	26.6417	−	8.65642i	1.42610	−	0.463367i	0.508564	−	0.861024i	$-0.330176\pi$
$349$	26.6417	−	8.65642i	1.42610	−	0.463367i	0.917534	+	0.397657i	$0.130176\pi$
$350$	−15.4074	+	1.48259i	−0.823559	+	0.0792480i
$351$	−6.02098	+	7.35342i	−0.321376	+	0.392497i
$352$	1.42375	−	0.725434i	0.0758859	−	0.0386658i
$353$	−12.9136	−	2.04532i	−0.687322	−	0.108861i	−0.197002	−	0.980403i	$-0.563120\pi$
$353$	−12.9136	−	2.04532i	−0.687322	−	0.108861i	−0.490321	+	0.871542i	$0.663120\pi$
$354$	11.1170	+	0.214144i	0.590860	+	0.0113816i
$355$	−2.33417	+	3.55995i	−0.123885	+	0.188943i
$356$	−1.77678	+	2.44552i	−0.0941689	+	0.129612i
$357$	−4.41763	−	4.59116i	−0.233806	−	0.242990i
$358$	−18.1749	−	9.26058i	−0.960574	−	0.489437i
$359$	17.1042	+	12.4270i	0.902727	+	0.655869i	0.939165	−	0.343467i	$-0.111601\pi$
$359$	17.1042	+	12.4270i	0.902727	+	0.655869i	−0.0364381	+	0.999336i	$0.511601\pi$
$360$	−6.61541	+	1.11192i	−0.348663	+	0.0586035i
$361$	−6.18007	+	19.0203i	−0.325267	+	1.00107i
$362$	−2.95778	+	18.6747i	−0.155457	+	0.981519i
$363$	2.00993	+	14.4914i	0.105494	+	0.760600i
$364$	−5.38504	+	1.74970i	−0.282253	+	0.0917094i
$365$	−12.9351	−	5.82733i	−0.677055	−	0.305016i
$366$	8.04058	−	5.60845i	0.420288	−	0.293158i
$367$	13.4015	+	13.4015i	0.699554	+	0.699554i	0.964314	−	0.264760i	$-0.0852927\pi$
$367$	13.4015	+	13.4015i	0.699554	+	0.699554i	−0.264760	+	0.964314i	$0.585293\pi$
$368$	7.53519	−	3.83937i	0.392799	−	0.200141i
$369$	31.4833	−	21.0706i	1.63895	−	1.09689i
$370$	−3.73433	+	13.6957i	−0.194138	+	0.712004i
$371$			33.7509i			1.75226i
$372$	−9.46341	+	1.85576i	−0.490655	+	0.0962167i
$373$	4.22849	−	4.22849i	0.218943	−	0.218943i	−0.589110	−	0.808053i	$-0.700521\pi$
$373$	4.22849	−	4.22849i	0.218943	−	0.218943i	0.808053	+	0.589110i	$0.200521\pi$
$374$	−1.53610	+	1.11604i	−0.0794300	+	0.0577093i
$375$	6.57835	−	18.2133i	0.339705	−	0.940532i
$376$	2.80203	−	8.62377i	0.144504	−	0.444737i
$377$	−0.525453	+	0.525453i	−0.0270622	+	0.0270622i
$378$	−13.8869	−	8.11829i	−0.714264	−	0.417560i
$379$	30.7045	+	9.97649i	1.57718	+	0.512458i	0.961329	−	0.275403i	$-0.0888111\pi$
$379$	30.7045	+	9.97649i	1.57718	+	0.512458i	0.615854	+	0.787860i	$0.288811\pi$
$380$	11.6777	+	7.65678i	0.599055	+	0.392784i
$381$	−15.5589	+	20.5700i	−0.797109	+	1.05383i
$382$	−18.6181	−	2.94881i	−0.952583	−	0.150874i
$383$	−2.14578	+	1.09333i	−0.109644	+	0.0558665i	−0.507952	−	0.861385i	$-0.669597\pi$
$383$	−2.14578	+	1.09333i	−0.109644	+	0.0558665i	0.398308	+	0.917252i	$0.369597\pi$
$384$	−1.63666	−	0.566859i	−0.0835207	−	0.0289274i
$385$	−7.43734	+	8.18736i	−0.379042	+	0.417267i
$386$	22.8004	−	7.40830i	1.16051	−	0.377073i
$387$	−3.40426	−	0.674499i	−0.173048	−	0.0342867i
$388$	−3.99560	+	0.632841i	−0.202846	+	0.0321276i
$389$	−7.63207	−	23.4891i	−0.386961	−	1.19094i	−0.935048	−	0.354522i	$-0.884644\pi$
$389$	−7.63207	−	23.4891i	−0.386961	−	1.19094i	0.548086	−	0.836422i	$-0.315356\pi$
$390$	0.906887	−	7.02553i	0.0459220	−	0.355752i
$391$	−8.12984	+	5.90668i	−0.411144	+	0.298713i
$392$	−1.17285	−	2.30184i	−0.0592377	−	0.116260i
$393$	−9.49611	−	19.5596i	−0.479016	−	0.986649i
$394$	−13.5597	+	4.40582i	−0.683128	+	0.221962i
$395$	−14.0078	+	21.3640i	−0.704808	+	1.07494i
$396$	−2.96494	+	3.76681i	−0.148994	+	0.189289i
$397$	18.8573	+	18.8573i	0.946420	+	0.946420i	0.998636	−	0.0522162i	$-0.0166285\pi$
$397$	18.8573	+	18.8573i	0.946420	+	0.946420i	−0.0522162	+	0.998636i	$0.516628\pi$
$398$	10.2459	+	10.2459i	0.513579	+	0.513579i
$399$	9.73214	+	32.0393i	0.487216	+	1.60397i
$400$	3.74498	−	3.31287i	0.187249	−	0.165643i
$401$	12.0837	+	16.6317i	0.603430	+	0.830550i	0.996017	−	0.0891651i	$-0.0284199\pi$
$401$	12.0837	+	16.6317i	0.603430	+	0.830550i	−0.392587	+	0.919715i	$0.628420\pi$
$402$	−1.31983	−	0.235182i	−0.0658273	−	0.0117298i
$403$	1.02941	−	10.1315i	0.0512785	−	0.504685i
$404$	−9.07462			−0.451479
$405$	16.6182	−	11.3506i	0.825763	−	0.564017i
$406$	−1.01752	−	0.739274i	−0.0504988	−	0.0366896i
$407$	4.60541	+	9.03863i	0.228282	+	0.448028i
$408$	2.02621	+	0.361052i	0.100312	+	0.0178747i
$409$		−	9.54427i		−	0.471934i	−0.971761	−	0.235967i	$-0.924174\pi$
$409$		−	9.54427i		−	0.471934i	0.971761	−	0.235967i	$-0.0758257\pi$
$410$	−11.5982	+	25.7449i	−0.572793	+	1.27145i
$411$	10.2164	+	7.72763i	0.503940	+	0.381176i
$412$	3.28635	−	6.44982i	0.161907	−	0.317760i
$413$	−19.6285	−	3.10884i	−0.965853	−	0.152976i
$414$	−15.6920	+	19.9359i	−0.771220	+	0.979796i
$415$	23.4543	−	13.4043i	1.15133	−	0.657989i
$416$	1.07508	−	1.47972i	0.0527101	−	0.0725493i
$417$	−31.2283	+	4.33132i	−1.52926	+	0.212106i
$418$	9.85596	−	1.56103i	0.482071	−	0.0763525i
$419$	−19.2888	−	14.0141i	−0.942319	−	0.684635i	0.00665860	−	0.999978i	$-0.497880\pi$
$419$	−19.2888	−	14.0141i	−0.942319	−	0.684635i	−0.948978	+	0.315343i	$0.897880\pi$
$420$	11.9847	−	0.344115i	0.584793	−	0.0167911i
$421$	20.3989	+	14.8207i	0.994183	+	0.722316i	0.960833	−	0.277127i	$-0.0893824\pi$
$421$	20.3989	+	14.8207i	0.994183	+	0.722316i	0.0333500	+	0.999444i	$0.489382\pi$
$422$	3.75377	−	23.7004i	0.182731	−	1.15372i
$423$	3.21757	+	27.0117i	0.156444	+	1.31336i
$424$	−6.40831	−	8.82028i	−0.311215	−	0.428351i
$425$	−3.77941	+	4.58421i	−0.183329	+	0.222367i
$426$	1.98919	−	2.62984i	0.0963766	−	0.127416i
$427$	−15.6119	+	7.95464i	−0.755511	+	0.384952i
$428$	−1.90398	−	1.90398i	−0.0920325	−	0.0920325i
$429$	−2.89603	−	4.15190i	−0.139821	−	0.200456i
$430$	2.41895	−	0.916374i	0.116652	−	0.0441915i
$431$	10.1759	−	14.0059i	0.490155	−	0.674640i	−0.490262	−	0.871575i	$-0.663099\pi$
$431$	10.1759	−	14.0059i	0.490155	−	0.674640i	0.980417	+	0.196935i	$0.0630988\pi$
$432$	5.17056	−	0.515122i	0.248768	−	0.0247838i
$433$	12.4386	−	12.4386i	0.597760	−	0.597760i	−0.341956	−	0.939716i	$-0.611089\pi$
$433$	12.4386	−	12.4386i	0.597760	−	0.597760i	0.939716	+	0.341956i	$0.111089\pi$
$434$	17.2093	−	0.961661i	0.826074	−	0.0461612i
$435$	1.38094	−	0.754308i	0.0662108	−	0.0361663i
$436$	3.10587	−	2.25655i	0.148744	−	0.108069i
$437$	52.1628	−	8.26177i	2.49528	−	0.395214i
$438$	9.69365	+	5.17670i	0.463180	+	0.247352i
$439$		−	10.9260i		−	0.521469i	−0.965411	−	0.260734i	$-0.916035\pi$
$439$		−	10.9260i		−	0.521469i	0.965411	−	0.260734i	$-0.0839647\pi$
$440$	0.389095	−	3.55178i	0.0185494	−	0.169324i
$441$	6.08999	+	4.79357i	0.290000	+	0.228265i
$442$	−0.986688	+	1.93649i	−0.0469320	+	0.0921092i
$443$	−5.56102	+	10.9141i	−0.264212	+	0.518546i	−0.984556	−	0.175072i	$-0.943984\pi$
$443$	−5.56102	+	10.9141i	−0.264212	+	0.518546i	0.720343	+	0.693618i	$0.243984\pi$
$444$	3.59870	−	10.3903i	0.170787	−	0.493104i
$445$	2.39455	+	6.32089i	0.113512	+	0.299639i
$446$	−0.359021	−	0.494150i	−0.0170001	−	0.0233987i
$447$	10.8593	+	11.2859i	0.513628	+	0.533805i
$448$	2.75830	+	1.40542i	0.130317	+	0.0664000i
$449$	−22.9123	−	16.6468i	−1.08130	−	0.785610i	−0.103390	−	0.994641i	$-0.532969\pi$
$449$	−22.9123	−	16.6468i	−1.08130	−	0.785610i	−0.977909	+	0.209031i	$0.932969\pi$
$450$	−6.03177	+	13.7338i	−0.284340	+	0.647418i
$451$	6.23539	+	19.1906i	0.293613	+	0.903648i
$452$	9.02666	−	1.42968i	0.424578	−	0.0672466i
$453$	16.2838	−	7.90576i	0.765081	−	0.371445i
$454$	5.17150	+	1.68032i	0.242710	+	0.0788614i
$455$	−3.33061	+	12.2150i	−0.156142	+	0.572650i
$456$	−8.62669	−	6.52515i	−0.403982	−	0.305568i
$457$	8.05296	−	15.8048i	0.376702	−	0.739318i	−0.622356	−	0.782735i	$-0.713824\pi$
$457$	8.05296	−	15.8048i	0.376702	−	0.739318i	0.999057	+	0.0434163i	$0.0138242\pi$
$458$	5.18184	−	2.64028i	0.242132	−	0.123372i
$459$	−5.97256	+	1.56569i	−0.278775	+	0.0730801i
$460$	2.05929	−	18.7978i	0.0960149	−	0.876454i
$461$	34.2850	+	11.1399i	1.59681	+	0.518836i	0.966316	−	0.257357i	$-0.0828518\pi$
$461$	34.2850	+	11.1399i	1.59681	+	0.518836i	0.630495	+	0.776193i	$0.282852\pi$
$462$	6.17395	−	5.94059i	0.287238	−	0.276381i
$463$	−5.32293	+	33.6077i	−0.247378	+	1.56188i	0.481010	+	0.876715i	$0.340270\pi$
$463$	−5.32293	+	33.6077i	−0.247378	+	1.56188i	−0.728388	+	0.685165i	$0.759730\pi$
$464$	0.406281			0.0188611
$465$	−8.13270	+	19.9715i	−0.377145	+	0.926154i
$466$	16.5250			0.765508
$467$	0.947228	−	5.98056i	0.0438325	−	0.276747i	−0.956031	−	0.293265i	$-0.905258\pi$
$467$	0.947228	−	5.98056i	0.0438325	−	0.276747i	0.999864	+	0.0165180i	$0.00525808\pi$
$468$	−1.06645	+	5.38247i	−0.0492967	+	0.248805i
$469$	2.27883	+	0.740438i	0.105227	+	0.0341902i
$470$	−12.6905	−	15.8131i	−0.585371	−	0.729404i
$471$	11.5108	+	16.5025i	0.530388	+	0.760393i
$472$	5.71988	−	2.91442i	0.263279	−	0.134147i
$473$	0.839192	−	1.64701i	0.0385861	−	0.0757295i
$474$	11.9375	−	15.7822i	0.548309	−	0.724901i
$475$	28.6356	−	12.4490i	1.31389	−	0.571200i
$476$	−3.49847	−	1.13672i	−0.160352	−	0.0521015i
$477$	28.5490	+	15.9602i	1.30717	+	0.730765i
$478$	26.8578	−	4.25385i	1.22845	−	0.194567i
$479$	−1.39248	−	4.28563i	−0.0636243	−	0.195815i	0.914191	−	0.405283i	$-0.132827\pi$
$479$	−1.39248	−	4.28563i	−0.0636243	−	0.195815i	−0.977816	+	0.209468i	$0.932827\pi$
$480$	−3.06668	+	2.36547i	−0.139974	+	0.107969i
$481$	9.39399	+	6.82513i	0.428329	+	0.311199i
$482$	12.6468	+	6.44389i	0.576048	+	0.293511i
$483$	32.6757	−	31.4406i	1.48680	−	1.43060i
$484$	4.96484	+	6.83352i	0.225675	+	0.310614i
$485$	−3.71554	+	8.24750i	−0.168714	+	0.374500i
$486$	−13.4339	+	7.90759i	−0.609375	+	0.358696i
$487$	−0.345159	+	0.677413i	−0.0156407	+	0.0306965i	−0.898695	−	0.438575i	$-0.855483\pi$
$487$	−0.345159	+	0.677413i	−0.0156407	+	0.0306965i	0.883054	+	0.469271i	$0.155483\pi$
$488$	2.56957	−	5.04307i	0.116319	−	0.228289i
$489$	−6.71706	−	22.1134i	−0.303756	−	1.00000i
$490$	−5.74234	−	0.629069i	−0.259412	−	0.0284184i
$491$		−	20.5622i		−	0.927961i	−0.885845	−	0.463981i	$-0.846421\pi$
$491$		−	20.5622i		−	0.927961i	0.885845	−	0.463981i	$-0.153579\pi$
$492$	10.3032	−	19.2933i	0.464505	−	0.869811i
$493$	−0.476824	+	0.0755214i	−0.0214751	+	0.00340132i
$494$	9.24075	−	6.71380i	0.415761	−	0.302068i
$495$	3.40851	+	10.1627i	0.153201	+	0.456780i
$496$	−4.31481	+	3.51887i	−0.193741	+	0.158002i
$497$	−4.16734	+	4.16734i	−0.186931	+	0.186931i
$498$	−18.8240	+	9.13903i	−0.843525	+	0.409530i
$499$	−15.2010	+	20.9223i	−0.680489	+	0.936613i	−0.999940	−	0.0109903i	$-0.996502\pi$
$499$	−15.2010	+	20.9223i	−0.680489	+	0.936613i	0.319451	+	0.947603i	$0.396502\pi$
$500$	−1.60326	−	11.0648i	−0.0717002	−	0.494832i
$501$	−28.6856	+	20.0087i	−1.28158	+	0.893923i
$502$	−5.68444	−	5.68444i	−0.253709	−	0.253709i
$503$	12.0572	−	6.14343i	0.537602	−	0.273922i	−0.164037	−	0.986454i	$-0.552452\pi$
$503$	12.0572	−	6.14343i	0.537602	−	0.273922i	0.701639	+	0.712532i	$0.252452\pi$
$504$	−9.28024	−	0.357660i	−0.413375	−	0.0159314i
$505$	−11.1262	+	16.9691i	−0.495109	+	0.755116i
$506$	−7.94298	−	10.9326i	−0.353109	−	0.486012i
$507$	14.7507	+	7.87732i	0.655102	+	0.349844i
$508$	−2.32943	+	14.7074i	−0.103352	+	0.652537i
$509$	−15.9445	−	11.5844i	−0.706728	−	0.513468i	0.175388	−	0.984499i	$-0.443882\pi$
$509$	−15.9445	−	11.5844i	−0.706728	−	0.513468i	−0.882117	+	0.471031i	$0.843882\pi$
$510$	3.15944	−	3.34624i	0.139902	−	0.148174i
$511$	−15.8901	−	11.5449i	−0.702938	−	0.510715i
$512$	−0.987688	+	0.156434i	−0.0436501	+	0.00691349i
$513$	31.7035	+	6.91863i	1.39974	+	0.305465i
$514$	4.80480	−	6.61324i	0.211931	−	0.291698i
$515$	−8.03154	−	14.0533i	−0.353912	−	0.619263i
$516$	−1.91716	+	0.582350i	−0.0843985	+	0.0256365i
$517$	−14.3107	−	2.26660i	−0.629386	−	0.0996849i
$518$	−8.92231	+	17.5110i	−0.392024	+	0.769390i
$519$	5.97757	−	7.90275i	0.262386	−	0.346892i
$520$	−1.44888	−	3.82461i	−0.0635375	−	0.167720i
$521$			22.8916i			1.00290i	0.865187	+	0.501450i	$0.167200\pi$
$521$			22.8916i			1.00290i	−0.865187	+	0.501450i	$0.832800\pi$
$522$	−1.10650	+	0.511110i	−0.0484303	+	0.0223707i
$523$	−10.4128	−	20.4363i	−0.455321	−	0.893618i	−0.998540	−	0.0540263i	$-0.982795\pi$
$523$	−10.4128	−	20.4363i	−0.455321	−	0.893618i	0.543219	−	0.839591i	$-0.317205\pi$
$524$	−10.1558	−	7.37861i	−0.443658	−	0.322336i
$525$	14.0507	−	22.8327i	0.613223	−	0.996502i
$526$	13.3530			0.582217
$527$	4.40988	−	4.93190i	0.192098	−	0.214837i
$528$	−0.485523	+	2.72474i	−0.0211297	+	0.118579i
$529$	−28.5193	−	39.2534i	−1.23997	−	1.70667i
$530$	−24.3506	+	1.16889i	−1.05772	+	0.0507731i
$531$	−11.9116	+	15.1331i	−0.516920	+	0.656722i
$532$	13.6701	+	13.6701i	0.592675	+	0.592675i
$533$	16.3319	+	16.3319i	0.707414	+	0.707414i
$534$	−1.52172	−	5.00968i	−0.0658512	−	0.216790i
$535$	−5.89480	+	1.22593i	−0.254854	+	0.0530015i
$536$	−0.736126	+	0.239182i	−0.0317958	+	0.0103311i
$537$	31.7830	−	15.4305i	1.37154	−	0.665877i
$538$	7.35607	+	14.4371i	0.317143	+	0.622428i
$539$	−3.33967	+	2.42641i	−0.143850	+	0.104513i
$540$	5.37626	−	10.3003i	0.231357	−	0.443254i
$541$	−6.88651	−	21.1945i	−0.296074	−	0.911223i	−0.982858	−	0.184362i	$-0.940978\pi$
$541$	−6.88651	−	21.1945i	−0.296074	−	0.911223i	0.686784	−	0.726862i	$-0.259022\pi$
$542$	5.63454	−	0.892423i	0.242024	−	0.0383328i
$543$	−22.7065	−	23.5985i	−0.974431	−	1.01271i
$544$	1.13010	−	0.367192i	0.0484527	−	0.0157432i
$545$	−0.411597	−	8.57454i	−0.0176309	−	0.367293i
$546$	3.20965	−	9.26706i	0.137360	−	0.396593i
$547$	−21.2156	+	10.8099i	−0.907114	+	0.462198i	−0.844326	−	0.535829i	$-0.819999\pi$
$547$	−21.2156	+	10.8099i	−0.907114	+	0.462198i	−0.0627875	+	0.998027i	$0.519999\pi$
$548$	7.30471	+	1.15695i	0.312042	+	0.0494226i
$549$	−0.653918	+	16.9673i	−0.0279086	+	0.724147i
$550$	−6.16460	−	5.08235i	−0.262860	−	0.216712i
$551$	2.41302	+	0.784037i	0.102798	+	0.0334011i
$552$	−2.56964	+	14.4207i	−0.109371	+	0.613786i
$553$	−25.0090	+	25.0090i	−1.06349	+	1.06349i
$554$	−2.17846	+	6.70460i	−0.0925537	+	0.284851i
$555$	−15.0172	−	19.4688i	−0.637444	−	0.826404i
$556$	−14.7259	+	10.6990i	−0.624519	+	0.453740i
$557$	−20.8448	+	20.8448i	−0.883221	+	0.883221i	−0.993861	−	0.110639i	$-0.964710\pi$
$557$	−20.8448	+	20.8448i	−0.883221	+	0.883221i	0.110639	+	0.993861i	$0.464710\pi$
$558$	7.32452	−	15.0117i	0.310072	−	0.635496i
$559$		−	2.11585i		−	0.0894910i
$560$	6.00997	−	3.43473i	0.253967	−	0.145144i
$561$	0.0633377	−	3.28808i	0.00267412	−	0.138823i
$562$	2.89420	−	1.47467i	0.122084	−	0.0622051i
$563$	10.2353	+	10.2353i	0.431367	+	0.431367i	0.889093	−	0.457726i	$-0.151336\pi$
$563$	10.2353	+	10.2353i	0.431367	+	0.431367i	−0.457726	+	0.889093i	$0.651336\pi$
$564$	8.98504	+	12.8814i	0.378338	+	0.542407i
$565$	8.39396	−	18.6323i	0.353136	−	0.783869i
$566$	18.7112	−	6.07962i	0.786489	−	0.255546i
$567$	25.7246	−	10.7006i	1.08033	−	0.449385i
$568$	0.297814	−	1.88033i	0.0124960	−	0.0788968i
$569$	7.00652	−	21.5638i	0.293729	−	0.904004i	−0.689917	−	0.723888i	$-0.742353\pi$
$569$	7.00652	−	21.5638i	0.293729	−	0.904004i	0.983646	−	0.180115i	$-0.0576470\pi$
$570$	−22.7787	+	8.13116i	−0.954096	+	0.340577i
$571$	13.8772	+	10.0823i	0.580741	+	0.421933i	0.838991	−	0.544145i	$-0.183146\pi$
$571$	13.8772	+	10.0823i	0.580741	+	0.421933i	−0.258250	+	0.966078i	$0.583146\pi$
$572$	−2.60408	−	1.32685i	−0.108882	−	0.0554782i
$573$	23.5270	−	22.6377i	0.982852	−	0.945703i
$574$	−22.9778	+	31.6263i	−0.959076	+	1.32005i
$575$	−32.6262	−	26.8984i	−1.36061	−	1.12174i
$576$	2.49316	−	1.66858i	0.103882	−	0.0695241i
$577$	−10.4308	−	1.65207i	−0.434239	−	0.0687766i	−0.0645114	−	0.997917i	$-0.520549\pi$
$577$	−10.4308	−	1.65207i	−0.434239	−	0.0687766i	−0.369727	+	0.929140i	$0.620549\pi$
$578$	13.8890	−	7.07682i	0.577708	−	0.294357i
$579$	−13.5898	+	39.2370i	−0.564771	+	1.63064i
$580$	0.498133	−	0.759727i	0.0206838	−	0.0315460i
$581$	35.5694	−	11.5572i	1.47567	−	0.479473i
$582$	3.30069	−	6.18072i	0.136818	−	0.256199i
$583$	−12.3186	+	12.3186i	−0.510184	+	0.510184i
$584$	6.34468			0.262545
$585$	8.75743	+	8.59355i	0.362075	+	0.355300i
$586$	6.84446	+	4.97279i	0.282742	+	0.205424i
$587$	−5.54948	+	35.0381i	−0.229052	+	1.44618i	0.558283	+	0.829650i	$0.311460\pi$
$587$	−5.54948	+	35.0381i	−0.229052	+	1.44618i	−0.787335	+	0.616525i	$0.788540\pi$
$588$	4.40522	+	0.784969i	0.181668	+	0.0323716i
$589$	−32.4175	+	12.5729i	−1.33574	+	0.518056i
$590$	1.56318	−	14.2692i	0.0643553	−	0.587455i
$591$	8.08200	−	23.3348i	0.332449	−	0.959864i
$592$	−0.993123	−	6.27033i	−0.0408171	−	0.257709i
$593$	−19.5860	+	9.97958i	−0.804302	+	0.409812i	−0.807269	−	0.590183i	$-0.799055\pi$
$593$	−19.5860	+	9.97958i	−0.804302	+	0.409812i	0.00296728	+	0.999996i	$0.499055\pi$
$594$	−2.10545	−	8.03158i	−0.0863879	−	0.329540i
$595$	−6.41501	+	5.14826i	−0.262990	+	0.211058i
$596$	8.59986	+	2.79426i	0.352264	+	0.114457i
$597$	−24.8592	+	3.44793i	−1.01742	+	0.141115i
$598$	−13.7821	−	7.02235i	−0.563593	−	0.287165i
$599$	33.0435	−	24.0075i	1.35012	−	0.980920i	0.351115	−	0.936332i	$-0.385803\pi$
$599$	33.0435	−	24.0075i	1.35012	−	0.980920i	0.999005	−	0.0445873i	$-0.0141973\pi$
$600$	0.663336	+	8.63481i	0.0270806	+	0.352515i
$601$	11.6825	−	8.48786i	0.476541	−	0.346227i	−0.323444	−	0.946247i	$-0.604841\pi$
$601$	11.6825	−	8.48786i	0.476541	−	0.346227i	0.799985	+	0.600020i	$0.204841\pi$
$602$	3.53707	−	0.560216i	0.144160	−	0.0228327i
$603$	1.70394	−	1.57747i	0.0693896	−	0.0642396i
$604$	6.14289	−	8.45496i	0.249950	−	0.344027i
$605$	18.8657	−	0.905595i	0.766998	−	0.0368177i
$606$	9.48181	−	12.5356i	0.385172	−	0.509224i
$607$	−0.443953	−	2.80301i	−0.0180195	−	0.113771i	0.977039	−	0.213060i	$-0.0683430\pi$
$607$	−0.443953	−	2.80301i	−0.0180195	−	0.113771i	−0.995059	+	0.0992894i	$0.968343\pi$
$608$	−6.16804	−	0.976922i	−0.250147	−	0.0396194i
$609$	2.08441	−	0.633151i	0.0844645	−	0.0256566i
$610$	−6.27981	−	10.9882i	−0.254262	−	0.444898i
$611$	−15.7732	+	5.12502i	−0.638115	+	0.207336i
$612$	−2.61588	+	2.42173i	−0.105741	+	0.0978928i
$613$	−6.54915	−	12.8534i	−0.264518	−	0.519145i	0.720099	−	0.693871i	$-0.244096\pi$
$613$	−6.54915	−	12.8534i	−0.264518	−	0.519145i	−0.984617	+	0.174726i	$0.944096\pi$
$614$	−25.9196			−1.04603
$615$	−23.4451	−	42.9217i	−0.945398	−	1.73077i
$616$	1.52860	−	4.70455i	0.0615891	−	0.189552i
$617$	41.7791	−	6.61715i	1.68196	−	0.266397i	0.758945	−	0.651155i	$-0.225715\pi$
$617$	41.7791	−	6.61715i	1.68196	−	0.266397i	0.923017	+	0.384758i	$0.125715\pi$
$618$	5.47591	+	11.2790i	0.220273	+	0.453706i
$619$		−	2.29824i		−	0.0923740i	−0.998933	−	0.0461870i	$-0.985293\pi$
$619$		−	2.29824i		−	0.0923740i	0.998933	−	0.0461870i	$-0.0147070\pi$
$620$	1.28983	+	12.3829i	0.0518007	+	0.497309i
$621$	−11.1431	−	42.5073i	−0.447159	−	1.70576i
$622$	27.1954	+	4.30734i	1.09044	+	0.172708i
$623$	1.46388	+	9.24260i	0.0586492	+	0.370297i
$624$	0.920752	+	3.03123i	0.0368596	+	0.121346i
$625$	−22.6564	−	10.5683i	−0.906255	−	0.422731i
$626$			0.253479i			0.0101311i
$627$	−8.14182	+	15.2460i	−0.325153	+	0.608867i
$628$	10.3504	+	5.27377i	0.413025	+	0.210447i
$629$	2.33112	+	7.17444i	0.0929477	+	0.286064i
$630$	−12.0471	+	16.9151i	−0.479968	+	0.673914i
$631$	8.39285	−	25.8305i	0.334114	−	1.02830i	−0.633043	−	0.774117i	$-0.718194\pi$
$631$	8.39285	−	25.8305i	0.334114	−	1.02830i	0.967157	−	0.254181i	$-0.0818058\pi$
$632$	1.78724	−	11.2842i	0.0710927	−	0.448862i
$633$	28.8173	+	29.9493i	1.14538	+	1.19038i
$634$	11.7721	−	3.82500i	0.467532	−	0.151910i
$635$	24.6462	+	22.3884i	0.978054	+	0.888457i
$636$	18.8801	+	0.363684i	0.748646	+	0.0144210i
$637$	−2.14518	+	4.21015i	−0.0849950	+	0.166812i
$638$	−0.101557	−	0.641207i	−0.00402069	−	0.0253856i
$639$	1.55439	+	5.49570i	0.0614909	+	0.217407i
$640$	−0.918459	+	2.03873i	−0.0363053	+	0.0805880i
$641$	−16.0330	−	22.0676i	−0.633267	−	0.871617i	0.364967	−	0.931020i	$-0.381080\pi$
$641$	−16.0330	−	22.0676i	−0.633267	−	0.871617i	−0.998234	+	0.0594033i	$0.981080\pi$
$642$	4.61957	−	0.640727i	0.182320	−	0.0252875i
$643$	−19.4796	−	9.92533i	−0.768199	−	0.391417i	0.0255415	−	0.999674i	$-0.491869\pi$
$643$	−19.4796	−	9.92533i	−0.768199	−	0.391417i	−0.793740	+	0.608257i	$0.791869\pi$
$644$	8.09014	−	24.8989i	0.318796	−	0.981153i
$645$	−1.26163	+	4.29902i	−0.0496765	+	0.169274i
$646$	7.42059			0.291959
$647$	−1.58649	−	3.11365i	−0.0623712	−	0.122410i	0.857716	−	0.514123i	$-0.171883\pi$
$647$	−1.58649	−	3.11365i	−0.0623712	−	0.122410i	−0.920087	+	0.391713i	$0.871883\pi$
$648$	−4.69099	+	7.68080i	−0.184279	+	0.301730i
$649$	−6.02943	−	8.29880i	−0.236676	−	0.325756i
$650$	−8.92828	−	1.97993i	−0.350196	−	0.0776594i
$651$	−16.6531	+	24.7776i	−0.652687	+	0.971112i
$652$	−9.43504	−	9.43504i	−0.369505	−	0.369505i
$653$	−26.0987	−	4.13362i	−1.02132	−	0.161761i	−0.376757	−	0.926312i	$-0.622961\pi$
$653$	−26.0987	−	4.13362i	−1.02132	−	0.161761i	−0.644563	+	0.764551i	$0.722961\pi$
$654$	−0.128063	+	6.64822i	−0.00500768	+	0.259966i
$655$	−26.2495	+	9.94410i	−1.02565	+	0.388548i
$656$		−	12.6279i		−	0.493035i
$657$	−17.2797	+	7.98173i	−0.674144	+	0.311397i
$658$	−12.7438	−	25.0111i	−0.496804	−	0.975032i
$659$	−11.1717	−	34.3830i	−0.435188	−	1.33937i	−0.892894	−	0.450267i	$-0.851329\pi$
$659$	−11.1717	−	34.3830i	−0.435188	−	1.33937i	0.457707	−	0.889103i	$-0.348671\pi$
$660$	4.49984	+	4.24865i	0.175156	+	0.165378i
$661$	−10.2054	+	7.41467i	−0.396945	+	0.288397i	−0.768295	−	0.640096i	$-0.778895\pi$
$661$	−10.2054	+	7.41467i	−0.396945	+	0.288397i	0.371351	+	0.928493i	$0.378895\pi$
$662$	−0.124962	−	0.245251i	−0.00485678	−	0.00953196i
$663$	−1.64408	−	3.38638i	−0.0638508	−	0.131516i
$664$	−7.10115	+	9.77390i	−0.275578	+	0.379301i
$665$	42.3232	−	8.80186i	1.64122	−	0.341322i
$666$	10.5930	+	15.8278i	0.410469	+	0.613315i
$667$	−0.537493	−	3.39359i	−0.0208118	−	0.131401i
$668$	−9.16720	+	17.9916i	−0.354690	+	0.696118i
$669$	1.05775	+	0.0203752i	0.0408948	+	0.000787749i
$670$	−0.455290	+	1.66978i	−0.0175894	+	0.0645092i
$671$	−8.60145	−	2.79478i	−0.332055	−	0.107891i
$672$	−4.82351	+	2.34180i	−0.186071	+	0.0903369i
$673$	−9.25461	−	4.71546i	−0.356739	−	0.181768i	0.266431	−	0.963854i	$-0.414156\pi$
$673$	−9.25461	−	4.71546i	−0.356739	−	0.181768i	−0.623170	+	0.782086i	$0.714156\pi$
$674$	−0.459615	−	1.41455i	−0.0177037	−	0.0544864i
$675$	−12.6694	−	22.6823i	−0.487644	−	0.873043i
$676$	9.65463			0.371332
$677$	−15.0378	+	15.0378i	−0.577951	+	0.577951i	−0.934338	−	0.356387i	$-0.884008\pi$
$677$	−15.0378	+	15.0378i	−0.577951	+	0.577951i	0.356387	+	0.934338i	$0.384008\pi$
$678$	−7.45676	+	13.9632i	−0.286375	+	0.536253i
$679$	−7.36107	+	10.1316i	−0.282492	+	0.388817i
$680$	0.698961	−	2.56345i	0.0268039	−	0.0983036i
$681$	−7.72474	+	5.38814i	−0.296012	+	0.206474i
$682$	6.63216	+	5.93017i	0.253958	+	0.227078i
$683$	−33.5536	−	33.5536i	−1.28389	−	1.28389i	−0.938433	−	0.345460i	$-0.887723\pi$
$683$	−33.5536	−	33.5536i	−1.28389	−	1.28389i	−0.345460	−	0.938433i	$-0.612277\pi$
$684$	18.0276	−	5.09888i	0.689302	−	0.194961i
$685$	11.1196	−	12.2410i	0.424858	−	0.467703i
$686$	13.0033	+	4.22502i	0.496468	+	0.161312i
$687$	−1.76710	+	9.91691i	−0.0674192	+	0.378354i
$688$	−0.817990	+	0.817990i	−0.0311856	+	0.0311856i
$689$	−6.16211	+	18.9650i	−0.234758	+	0.722510i
$690$	23.8155	+	22.4860i	0.906640	+	0.856028i
$691$	−15.2787	−	47.0231i	−0.581230	−	1.78884i	−0.613909	−	0.789377i	$-0.710404\pi$
$691$	−15.2787	−	47.0231i	−0.581230	−	1.78884i	0.0326782	−	0.999466i	$-0.489596\pi$
$692$	0.894940	−	5.65043i	0.0340205	−	0.214797i
$693$	1.75529	+	14.7358i	0.0666779	+	0.559766i
$694$	3.67883	+	5.06347i	0.139646	+	0.192207i
$695$	1.95152	+	40.6547i	0.0740253	+	1.54212i
$696$	−0.424512	+	0.561233i	−0.0160911	+	0.0212735i
$697$	2.34733	+	14.8204i	0.0889113	+	0.561364i
$698$	4.38216	+	27.6679i	0.165867	+	1.04724i
$699$	−17.2666	+	22.8275i	−0.653081	+	0.863417i
$700$	0.945903	−	15.4496i	0.0357518	−	0.583941i
$701$	−27.9970	−	38.5346i	−1.05743	−	1.45543i	−0.882182	−	0.470908i	$-0.843926\pi$
$701$	−27.9970	−	38.5346i	−1.05743	−	1.45543i	−0.175251	−	0.984524i	$-0.556074\pi$
$702$	−6.32100	−	7.09718i	−0.238571	−	0.267866i
$703$	6.20198	−	39.1578i	0.233912	−	1.47686i
$704$	0.493780	+	1.51970i	0.0186100	+	0.0572758i
$705$	35.1041	−	1.00794i	1.32210	−	0.0379612i
$706$	4.04027	−	12.4347i	0.152058	−	0.467985i
$707$	−19.8643	+	19.8643i	−0.747074	+	0.747074i
$708$	−1.95058	+	10.9466i	−0.0733074	+	0.411398i
$709$	−15.1938	−	4.93677i	−0.570615	−	0.185404i	0.00947667	−	0.999955i	$-0.496983\pi$
$709$	−15.1938	−	4.93677i	−0.570615	−	0.185404i	−0.580092	+	0.814551i	$0.696983\pi$
$710$	−3.15098	−	2.86233i	−0.118254	−	0.107421i
$711$	9.32822	+	32.9808i	0.349836	+	1.23688i
$712$	−2.13746	−	2.13746i	−0.0801049	−	0.0801049i
$713$	35.1008	+	31.3855i	1.31453	+	1.17540i
$714$	5.22571	−	3.64502i	0.195567	−	0.136412i
$715$	−5.67395	+	3.24270i	−0.212194	+	0.121270i
$716$	11.9898	−	16.5025i	0.448078	−	0.616727i
$717$	−22.1867	+	41.5458i	−0.828577	+	1.55156i
$718$	−14.9496	+	14.9496i	−0.557916	+	0.557916i
$719$	7.49559			0.279538			0.139769	−	0.990184i	$-0.455364\pi$
$719$	7.49559			0.279538			0.139769	+	0.990184i	$0.455364\pi$
$720$	−0.0633554	−	6.70790i	−0.00236112	−	0.249989i
$721$	−6.92483	−	21.3124i	−0.257894	−	0.793716i
$722$	−17.8193	−	9.07941i	−0.663168	−	0.337901i
$723$	−22.1159	+	10.7372i	−0.822498	+	0.399321i
$724$	−17.9821	−	5.84273i	−0.668298	−	0.217143i
$725$	−0.809905	−	1.86297i	−0.0300791	−	0.0691890i
$726$	−14.6274	−	0.281765i	−0.542873	−	0.0104573i
$727$	12.2435	−	24.0292i	0.454087	−	0.891196i	−0.544536	−	0.838737i	$-0.683294\pi$
$727$	12.2435	−	24.0292i	0.454087	−	0.891196i	0.998623	−	0.0524583i	$-0.0167057\pi$
$728$	−0.885757	−	5.59245i	−0.0328283	−	0.207270i
$729$	3.11325	−	26.8199i	0.115306	−	0.993330i
$730$	7.77908	−	11.8643i	0.287917	−	0.439116i
$731$	0.807966	−	1.11207i	0.0298837	−	0.0411314i
$732$	4.28158	+	8.81894i	0.158252	+	0.325958i
$733$	15.4378	+	30.2984i	0.570208	+	1.11910i	0.978500	+	0.206245i	$0.0661243\pi$
$733$	15.4378	+	30.2984i	0.570208	+	1.11910i	−0.408293	+	0.912851i	$0.633876\pi$
$734$	−15.3330	+	11.1401i	−0.565951	+	0.411188i
$735$	6.86900	−	7.27512i	0.253367	−	0.268347i
$736$	2.61334	+	8.04303i	0.0963289	+	0.296470i
$737$	0.561493	+	1.10199i	0.0206829	+	0.0405924i
$738$	15.8861	+	34.3918i	0.584776	+	1.26598i
$739$			21.1113i			0.776591i	0.921535	+	0.388296i	$0.126936\pi$
$739$			21.1113i			0.776591i	−0.921535	+	0.388296i	$0.873064\pi$
$740$	−12.9429	−	5.83083i	−0.475790	−	0.214345i
$741$	−0.381021	+	19.7802i	−0.0139972	+	0.726642i
$742$	−33.3353	−	5.27980i	−1.22378	−	0.193828i
$743$	15.0759	+	15.0759i	0.553081	+	0.553081i	0.927329	−	0.374248i	$-0.122099\pi$
$743$	15.0759	+	15.0759i	0.553081	+	0.553081i	−0.374248	+	0.927329i	$0.622099\pi$
$744$	−0.352510	−	9.63721i	−0.0129236	−	0.353317i
$745$	15.7692	−	12.6554i	0.577741	−	0.463656i
$746$	3.51495	+	4.83791i	0.128691	+	0.177129i
$747$	7.04415	−	35.5525i	0.257732	−	1.30080i
$748$	−0.862004	−	1.69178i	−0.0315180	−	0.0618575i
$749$	−8.33563			−0.304577
$750$	16.9600	+	9.34656i	0.619292	+	0.341288i
$751$	−5.38146	+	16.5624i	−0.196372	+	0.604372i	0.803586	+	0.595189i	$0.202923\pi$
$751$	−5.38146	+	16.5624i	−0.196372	+	0.604372i	−0.999958	+	0.00918247i	$0.997077\pi$
$752$	8.07926	+	4.11659i	0.294620	+	0.150117i
$753$	13.7919	−	1.91292i	0.502606	−	0.0697107i
$754$	−0.436785	−	0.601183i	−0.0159068	−	0.0218938i
$755$	−8.27872	−	21.8534i	−0.301294	−	0.795325i
$756$	10.1907	−	12.4459i	0.370633	−	0.452654i
$757$	5.00760	+	31.6168i	0.182004	+	1.14913i	0.894372	+	0.447324i	$0.147623\pi$
$757$	5.00760	+	31.6168i	0.182004	+	1.14913i	−0.712368	+	0.701807i	$0.752377\pi$
$758$	−14.6569	+	28.7658i	−0.532363	+	1.04482i
$759$	23.4016	+	0.450780i	0.849423	+	0.0163623i
$760$	−9.38931	+	10.3362i	−0.340586	+	0.374932i
$761$	32.9618	−	10.7099i	1.19486	−	0.388234i	0.356994	−	0.934107i	$-0.383802\pi$
$761$	32.9618	−	10.7099i	1.19486	−	0.388234i	0.837868	+	0.545872i	$0.183802\pi$
$762$	−17.8828	−	18.5852i	−0.647824	−	0.673272i
$763$	1.85917	−	11.7383i	0.0673063	−	0.424955i
$764$	5.82501	−	17.9275i	0.210742	−	0.648596i
$765$	1.32125	+	7.86082i	0.0477700	+	0.284209i
$766$	−0.744195	−	2.29040i	−0.0268889	−	0.0827554i
$767$	−10.4619	−	5.33059i	−0.377756	−	0.192476i
$768$	0.815911	−	1.52784i	0.0294416	−	0.0551311i
$769$			34.2150i			1.23382i	0.787032	+	0.616912i	$0.211616\pi$
$769$			34.2150i			1.23382i	−0.787032	+	0.616912i	$0.788384\pi$
$770$	−6.92311	−	8.62656i	−0.249491	−	0.310880i
$771$	4.11507	+	13.5473i	0.148201	+	0.487894i
$772$	3.75033	+	23.6786i	0.134977	+	0.852212i
$773$	−6.54348	−	1.03639i	−0.235353	−	0.0372762i	0.0376439	−	0.999291i	$-0.488015\pi$
$773$	−6.54348	−	1.03639i	−0.235353	−	0.0372762i	−0.272996	+	0.962015i	$0.588015\pi$
$774$	1.19874	−	3.25684i	0.0430878	−	0.117065i
$775$	24.7369	+	12.7705i	0.888576	+	0.458730i
$776$		−	4.04540i		−	0.145222i
$777$	−14.8669	−	30.6220i	−0.533347	−	1.09856i
$778$	24.3938	−	3.86360i	0.874561	−	0.138517i
$779$	24.3691	−	75.0004i	0.873114	−	2.68717i
$780$	6.79717	+	1.99476i	0.243378	+	0.0714238i
$781$	−3.04204			−0.108853
$782$	−4.56217	−	8.95376i	−0.163143	−	0.320186i
$783$	0.450111	−	2.06256i	0.0160856	−	0.0737098i
$784$	2.45697	−	0.798319i	0.0877491	−	0.0285114i
$785$	22.5521	−	12.8886i	0.804918	−	0.460016i
$786$	20.8043	−	6.31941i	0.742063	−	0.225406i
$787$	−2.24413	−	0.355436i	−0.0799947	−	0.0126699i	0.116309	−	0.993213i	$-0.462894\pi$
$787$	−2.24413	−	0.355436i	−0.0799947	−	0.0126699i	−0.196303	+	0.980543i	$0.562894\pi$
$788$	−2.23037	−	14.0820i	−0.0794535	−	0.501650i
$789$	−13.9522	+	18.4457i	−0.496710	+	0.656684i
$790$	−18.9097	−	17.1774i	−0.672775	−	0.611144i
$791$	16.6298	−	22.8889i	0.591286	−	0.813836i
$792$	−3.25662	−	3.51770i	−0.115719	−	0.124996i
$793$	−10.2248	+	1.61945i	−0.363094	+	0.0575085i
$794$	−21.5750	+	15.6752i	−0.765670	+	0.556291i
$795$	23.8286	−	34.8591i	0.845113	−	1.23632i
$796$	−11.7225	+	8.51693i	−0.415494	+	0.301874i
$797$	−22.6059	−	11.5183i	−0.800743	−	0.407999i	0.00520417	−	0.999986i	$-0.498343\pi$
$797$	−22.6059	−	11.5183i	−0.800743	−	0.407999i	−0.805947	+	0.591988i	$0.798343\pi$
$798$	−33.1673	+	4.60026i	−1.17411	+	0.162847i
$799$	−10.2473	−	3.32954i	−0.362523	−	0.117791i
$800$	2.68624	+	4.21712i	0.0949728	+	0.149098i
$801$	8.51033	+	3.13239i	0.300698	+	0.110677i
$802$	−18.3173	+	9.33312i	−0.646806	+	0.329564i
$803$	−1.58597	−	10.0134i	−0.0559675	−	0.353365i
$804$	0.438754	−	1.26679i	0.0154737	−	0.0446763i
$805$	−36.6406	−	45.6562i	−1.29141	−	1.60917i
$806$	9.84571	+	2.60165i	0.346800	+	0.0916391i
$807$	−27.6294	−	4.92332i	−0.972603	−	0.173309i
$808$	1.41958	−	8.96289i	0.0499407	−	0.315313i
$809$	18.8880	+	13.7229i	0.664067	+	0.482473i	0.868034	−	0.496505i	$-0.165384\pi$
$809$	18.8880	+	13.7229i	0.664067	+	0.482473i	−0.203967	+	0.978978i	$0.565384\pi$
$810$	8.61122	+	18.1892i	0.302568	+	0.639103i
$811$	2.30649			0.0809918			0.0404959	−	0.999180i	$-0.487106\pi$
$811$	2.30649			0.0809918			0.0404959	+	0.999180i	$0.487106\pi$
$812$	0.889348	−	0.889348i	0.0312100	−	0.0312100i
$813$	−4.65458	+	8.71597i	−0.163243	+	0.305682i
$814$	−9.64780	+	3.13476i	−0.338155	+	0.109873i
$815$	−29.2112	+	6.07499i	−1.02322	+	0.212798i
$816$	−0.673576	+	1.94478i	−0.0235799	+	0.0680810i
$817$	−6.43682	+	3.27972i	−0.225196	+	0.114743i
$818$	9.42676	+	1.49305i	0.329599	+	0.0522034i
$819$	9.44776	+	14.1167i	0.330132	+	0.493276i
$820$	−23.6135	−	15.4828i	−0.824620	−	0.540682i
$821$	−3.47058	+	4.77684i	−0.121124	+	0.166713i	−0.865273	−	0.501301i	$-0.832855\pi$
$821$	−3.47058	+	4.77684i	−0.121124	+	0.166713i	0.744149	+	0.668013i	$0.232855\pi$
$822$	−9.23069	+	8.88179i	−0.321957	+	0.309788i
$823$	25.1425	+	12.8107i	0.876412	+	0.446554i	0.833497	−	0.552525i	$-0.186335\pi$
$823$	25.1425	+	12.8107i	0.876412	+	0.446554i	0.0429151	+	0.999079i	$0.486335\pi$
$824$	5.85631	+	4.25486i	0.204014	+	0.148225i
$825$	13.4619	−	3.20532i	0.468685	−	0.111595i
$826$	6.14113	−	18.9005i	0.213677	−	0.657631i
$827$	1.21308	−	7.65909i	0.0421829	−	0.266332i	−0.957579	−	0.288172i	$-0.906952\pi$
$827$	1.21308	−	7.65909i	0.0421829	−	0.266332i	0.999761	+	0.0218399i	$0.00695240\pi$
$828$	−17.2357	−	18.6175i	−0.598981	−	0.647002i
$829$	−22.4367	+	7.29013i	−0.779259	+	0.253197i	−0.671524	−	0.740983i	$-0.734360\pi$
$829$	−22.4367	+	7.29013i	−0.779259	+	0.253197i	−0.107735	+	0.994180i	$0.534360\pi$
$830$	9.57017	+	25.2624i	0.332185	+	0.876871i
$831$	−6.98547	−	10.0147i	−0.242323	−	0.347408i
$832$	1.29332	+	1.29332i	0.0448379	+	0.0448379i
$833$	−2.73518	+	1.39364i	−0.0947684	+	0.0482869i
$834$	0.607191	−	31.5214i	0.0210253	−	1.09150i
$835$	22.4038	+	39.2014i	0.775317	+	1.35662i
$836$			9.97881i			0.345124i
$837$	13.0839	+	25.8033i	0.452244	+	0.891894i
$838$	16.8590	−	16.8590i	0.582385	−	0.582385i
$839$	19.4760	−	14.1502i	0.672387	−	0.488518i	−0.198436	−	0.980114i	$-0.563586\pi$
$839$	19.4760	−	14.1502i	0.672387	−	0.488518i	0.870823	+	0.491596i	$0.163586\pi$
$840$	−1.53494	+	11.8910i	−0.0529605	+	0.410277i
$841$	−8.91049	+	27.4237i	−0.307258	+	0.945643i
$842$	−17.8293	+	17.8293i	−0.614439	+	0.614439i
$843$	−0.986975	+	5.53886i	−0.0339932	+	0.190769i
$844$	22.8214	+	7.41511i	0.785543	+	0.255239i
$845$	11.8373	−	18.0537i	0.407217	−	0.621067i
$846$	−27.1825	−	1.04761i	−0.934555	−	0.0360177i
$847$	25.8266	+	4.09053i	0.887412	+	0.140552i
$848$	9.71417	−	4.94962i	0.333586	−	0.169971i
$849$	−11.1524	+	32.1999i	−0.382750	+	1.10510i
$850$	−3.93655	−	4.45001i	−0.135022	−	0.152634i
$851$	−51.0611	+	16.5908i	−1.75035	+	0.568724i
$852$	2.28629	+	2.37610i	0.0783270	+	0.0814038i
$853$	16.8549	−	2.66956i	0.577101	−	0.0914038i	0.138941	−	0.990301i	$-0.455630\pi$
$853$	16.8549	−	2.66956i	0.577101	−	0.0914038i	0.438160	+	0.898897i	$0.355630\pi$
$854$	−5.41448	−	16.6640i	−0.185280	−	0.570232i
$855$	12.5686	−	39.9624i	0.429835	−	1.36668i
$856$	2.17839	−	1.58269i	0.0744559	−	0.0540954i
$857$	−6.24452	−	12.2556i	−0.213309	−	0.418642i	0.759416	−	0.650606i	$-0.225485\pi$
$857$	−6.24452	−	12.2556i	−0.213309	−	0.418642i	−0.972724	+	0.231964i	$0.925485\pi$
$858$	4.55382	−	2.21087i	0.155465	−	0.0754779i
$859$	−18.2589	+	5.93266i	−0.622984	+	0.202420i	−0.603465	−	0.797390i	$-0.706214\pi$
$859$	−18.2589	+	5.93266i	−0.622984	+	0.202420i	−0.0195195	+	0.999809i	$0.506214\pi$
$860$	0.526684	+	2.53253i	0.0179598	+	0.0863584i
$861$	−19.6793	−	64.7868i	−0.670670	−	2.20793i
$862$	12.2416	+	12.2416i	0.416951	+	0.416951i
$863$	−1.61601	−	1.61601i	−0.0550097	−	0.0550097i	0.679067	−	0.734076i	$-0.262385\pi$
$863$	−1.61601	−	1.61601i	−0.0550097	−	0.0550097i	−0.734076	+	0.679067i	$0.762385\pi$
$864$	−0.300073	+	5.18748i	−0.0102087	+	0.176482i
$865$	−9.46878	−	8.60137i	−0.321948	−	0.292455i
$866$	10.3396	+	14.2313i	0.351355	+	0.483598i
$867$	−4.73642	+	26.5806i	−0.160857	+	0.902724i
$868$	−1.74231	+	17.1479i	−0.0591379	+	0.582037i
$869$	−18.2559			−0.619288
$870$	0.528996	+	1.48193i	0.0179346	+	0.0502423i
$871$	1.14532	+	0.832122i	0.0388076	+	0.0281954i
$872$	1.74290	+	3.42063i	0.0590220	+	0.115837i
$873$	5.08920	+	11.0176i	0.172243	+	0.372890i
$874$			52.8130i			1.78643i
$875$	−27.7303	−	20.7112i	−0.937456	−	0.700168i
$876$	−6.62938	+	8.76449i	−0.223986	+	0.296125i
$877$	7.83366	−	15.3744i	0.264524	−	0.519158i	−0.720094	−	0.693876i	$-0.755902\pi$
$877$	7.83366	−	15.3744i	0.264524	−	0.519158i	0.984618	+	0.174718i	$0.0559015\pi$
$878$	10.7915	+	1.70920i	0.364194	+	0.0576827i
$879$	−14.0210	+	4.25894i	−0.472915	+	0.143651i
$880$	3.44718	+	0.939925i	0.116205	+	0.0316849i
$881$	−11.6575	+	16.0452i	−0.392753	+	0.540578i	−0.958907	−	0.283722i	$-0.908431\pi$
$881$	−11.6575	+	16.0452i	−0.392753	+	0.540578i	0.566154	+	0.824300i	$0.308431\pi$
$882$	−5.68724	+	5.26513i	−0.191499	+	0.177286i
$883$	54.1044	−	8.56929i	1.82076	−	0.288379i	0.849707	−	0.527256i	$-0.176779\pi$
$883$	54.1044	−	8.56929i	1.82076	−	0.288379i	0.971050	+	0.238876i	$0.0767791\pi$
$884$	−1.75829	−	1.27747i	−0.0591377	−	0.0429661i
$885$	18.0781	+	17.0689i	0.607687	+	0.573765i
$886$	−9.90982	−	7.19990i	−0.332927	−	0.241886i
$887$	−6.94892	+	43.8738i	−0.233322	+	1.47314i	0.541363	+	0.840789i	$0.317909\pi$
$887$	−6.94892	+	43.8738i	−0.233322	+	1.47314i	−0.774685	+	0.632348i	$0.782091\pi$
$888$	9.69946	+	5.17980i	0.325493	+	0.173823i
$889$	27.0954	+	37.2936i	0.908751	+	1.25079i
$890$	−6.61766	+	1.37626i	−0.221825	+	0.0461324i
$891$	13.2947	+	5.48352i	0.445389	+	0.183705i
$892$	0.544230	−	0.277299i	0.0182222	−	0.00928465i
$893$	40.0409	+	40.0409i	1.33992	+	1.33992i
$894$	−12.8457	+	8.96012i	−0.429625	+	0.299671i
$895$	−16.1585	−	42.6536i	−0.540119	−	1.42575i
$896$	−1.81961	+	2.50448i	−0.0607890	+	0.0836688i
$897$	24.1012	−	11.7011i	0.804715	−	0.390687i
$898$	20.0261	−	20.0261i	0.668280	−	0.668280i
$899$	0.817963	+	2.10901i	0.0272806	+	0.0703395i
$900$	−12.6212	−	8.10595i	−0.420705	−	0.270198i
$901$	−10.4808	+	7.61473i	−0.349165	+	0.253684i
$902$	−19.9297	+	3.15656i	−0.663587	+	0.105102i
$903$	−2.92191	+	5.47143i	−0.0972349	+	0.182078i
$904$			9.13918i			0.303965i
$905$	−32.9731	+	26.4620i	−1.09606	+	0.879626i
$906$	5.26107	+	17.3201i	0.174787	+	0.575421i
$907$	4.66303	−	9.15172i	0.154833	−	0.303878i	−0.800540	−	0.599280i	$-0.795454\pi$
$907$	4.66303	−	9.15172i	0.154833	−	0.303878i	0.955373	+	0.295402i	$0.0954536\pi$
$908$	−2.46863	+	4.84497i	−0.0819245	+	0.160786i
$909$	7.40928	+	26.1962i	0.245750	+	0.868873i
$910$	−11.5436	−	5.20046i	−0.382668	−	0.172394i
$911$	3.08724	+	4.24922i	0.102285	+	0.140783i	0.857091	−	0.515165i	$-0.172269\pi$
$911$	3.08724	+	4.24922i	0.102285	+	0.140783i	−0.754806	+	0.655948i	$0.772269\pi$
$912$	7.79433	−	7.49972i	0.258096	−	0.248341i
$913$	17.2006	+	8.76412i	0.569255	+	0.290050i
$914$	14.3505	+	10.4262i	0.474672	+	0.344869i
$915$	21.7406	+	2.80637i	0.718721	+	0.0927758i
$916$	1.79716	+	5.53108i	0.0593797	+	0.182752i
$917$	−38.3828	+	6.07923i	−1.26751	+	0.200754i
$918$	−0.612098	−	6.14396i	−0.0202023	−	0.202781i
$919$	29.1007	+	9.45540i	0.959945	+	0.311905i	0.746750	−	0.665105i	$-0.231613\pi$
$919$	29.1007	+	9.45540i	0.959945	+	0.311905i	0.213195	+	0.977010i	$0.431613\pi$
$920$	18.2443	+	4.97457i	0.601495	+	0.164007i
$921$	27.0826	−	35.8051i	0.892403	−	1.17982i
$922$	−16.3661	+	32.1202i	−0.538988	+	1.05782i
$923$	−3.10253	+	1.58082i	−0.102121	+	0.0520333i
$924$	4.90163	+	7.02725i	0.161252	+	0.231179i
$925$	−26.7724	+	17.0535i	−0.880270	+	0.560717i
$926$	−32.3612	−	10.5148i	−1.06346	−	0.345538i
$927$	−21.3023	−	4.22070i	−0.699659	−	0.138626i
$928$	−0.0635564	+	0.401279i	−0.00208634	+	0.0131726i
$929$	−5.07146			−0.166389			−0.0831946	−	0.996533i	$-0.526512\pi$
$929$	−5.07146			−0.166389			−0.0831946	+	0.996533i	$0.526512\pi$
$930$	−18.4533	−	11.1568i	−0.605109	−	0.365846i
$931$	16.1332			0.528746
$932$	−2.58509	+	16.3216i	−0.0846773	+	0.534631i
$933$	−34.3659	+	33.0669i	−1.12509	+	1.08256i
$934$	5.75875	+	1.87113i	0.188432	+	0.0612253i
$935$	−4.22043	−	0.462346i	−0.138023	−	0.0151203i
$936$	−5.14938	−	1.89532i	−0.168313	−	0.0619506i
$937$	28.2566	−	14.3974i	0.923102	−	0.470344i	0.0732190	−	0.997316i	$-0.476673\pi$
$937$	28.2566	−	14.3974i	0.923102	−	0.470344i	0.849883	+	0.526972i	$0.176673\pi$
$938$	−1.08781	+	2.13495i	−0.0355182	+	0.0697085i
$939$	−0.350154	−	0.264854i	−0.0114269	−	0.00864317i
$940$	17.6037	−	10.0606i	0.574168	−	0.328140i
$941$	−52.2405	−	16.9740i	−1.70299	−	0.553335i	−0.713849	−	0.700300i	$-0.753050\pi$
$941$	−52.2405	−	16.9740i	−1.70299	−	0.553335i	−0.989142	+	0.146965i	$0.953050\pi$
$942$	−18.1000	+	8.78748i	−0.589728	+	0.286312i
$943$	−105.478	+	16.7061i	−3.43485	+	0.544026i
$944$	1.98376	+	6.10538i	0.0645658	+	0.198713i
$945$	−10.7787	−	34.3159i	−0.350631	−	1.11630i
$946$	1.49545	+	1.08651i	0.0486213	+	0.0353255i
$947$	−4.80550	−	2.44852i	−0.156158	−	0.0795663i	0.374165	−	0.927362i	$-0.377929\pi$
$947$	−4.80550	−	2.44852i	−0.156158	−	0.0795663i	−0.530323	+	0.847796i	$0.677929\pi$
$948$	13.7205	+	14.2594i	0.445620	+	0.463125i
$949$	−6.82104	−	9.38836i	−0.221420	−	0.304759i
$950$	7.81615	+	30.2305i	0.253589	+	0.980808i
$951$	−7.01657	+	20.2586i	−0.227528	+	0.656930i
$952$	1.67001	−	3.27757i	0.0541252	−	0.106227i
$953$	−20.5845	+	40.3994i	−0.666798	+	1.30866i	0.271367	+	0.962476i	$0.412524\pi$
$953$	−20.5845	+	40.3994i	−0.666798	+	1.30866i	−0.938165	+	0.346188i	$0.887476\pi$
$954$	−20.2297	+	25.7008i	−0.654961	+	0.832095i
$955$	−26.3818	−	32.8731i	−0.853694	−	1.06375i
$956$			27.1925i			0.879470i
$957$	0.991872	+	0.529689i	0.0320627	+	0.0171224i
$958$	4.45070	−	0.704921i	0.143795	−	0.0227750i
$959$	18.5226	−	13.4574i	0.598124	−	0.434563i
$960$	−1.85662	−	3.39897i	−0.0599220	−	0.109701i
$961$	−26.9535	−	15.3137i	−0.869467	−	0.493991i
$962$	−8.21065	+	8.21065i	−0.264722	+	0.264722i
$963$	−3.94176	+	7.05091i	−0.127022	+	0.227212i
$964$	−8.34295	+	11.4831i	−0.268708	+	0.369845i
$965$	48.8761	+	22.0189i	1.57338	+	0.708814i
$966$	25.9419	+	37.1918i	0.834668	+	1.19663i
$967$	−33.9427	−	33.9427i	−1.09152	−	1.09152i	−0.995366	−	0.0961559i	$-0.969345\pi$
$967$	−33.9427	−	33.9427i	−1.09152	−	1.09152i	−0.0961559	−	0.995366i	$-0.530655\pi$
$968$	−7.52606	+	3.83472i	−0.241897	+	0.123253i
$969$	−7.75357	+	10.2507i	−0.249081	+	0.329301i
$970$	−7.56472	−	4.95999i	−0.242889	−	0.159256i
$971$	7.49240	+	10.3124i	0.240442	+	0.330941i	0.912135	−	0.409889i	$-0.134433\pi$
$971$	7.49240	+	10.3124i	0.240442	+	0.330941i	−0.671693	+	0.740830i	$0.734433\pi$
$972$	−5.70871	−	14.5055i	−0.183107	−	0.465265i
$973$	−8.81492	+	55.6552i	−0.282593	+	1.78422i
$974$	−0.615078	−	0.446880i	−0.0197084	−	0.0143190i
$975$	12.0640	−	10.2647i	0.386356	−	0.328732i
$976$	4.57901	+	3.32684i	0.146571	+	0.106490i
$977$	−7.88541	+	1.24893i	−0.252277	+	0.0399567i	−0.281292	−	0.959622i	$-0.590763\pi$
$977$	−7.88541	+	1.24893i	−0.252277	+	0.0399567i	0.0290151	+	0.999579i	$0.490763\pi$
$978$	22.8919	−	3.17507i	0.732002	−	0.101528i
$979$	−2.83912	+	3.90772i	−0.0907387	+	0.124891i
$980$	1.51962	−	5.57323i	0.0485426	−	0.178030i
$981$	−9.04999	−	7.12345i	−0.288944	−	0.227434i
$982$	20.3091	+	3.21664i	0.648089	+	0.102647i
$983$	−24.0194	+	47.1407i	−0.766100	+	1.50356i	0.0951999	+	0.995458i	$0.469651\pi$
$983$	−24.0194	+	47.1407i	−0.766100	+	1.50356i	−0.861300	+	0.508097i	$0.830349\pi$
$984$	17.4440	+	13.1945i	0.556095	+	0.420626i
$985$	−29.0673	−	13.0949i	−0.926160	−	0.417240i
$986$		−	0.482767i		−	0.0153744i
$987$	47.8657	+	8.52922i	1.52358	+	0.271488i
$988$	5.18557	+	10.1772i	0.164975	+	0.323781i
$989$	7.91470	+	5.75036i	0.251673	+	0.182851i
$990$	−10.5708	+	1.77675i	−0.335962	+	0.0564688i
$991$	−10.6097			−0.337028			−0.168514	−	0.985699i	$-0.553897\pi$
$991$	−10.6097			−0.337028			−0.168514	+	0.985699i	$0.553897\pi$
$992$	−2.80056	−	4.81216i	−0.0889179	−	0.152786i
$993$	0.469357	+	0.0836352i	0.0148946	+	0.00265408i
$994$	−3.46411	−	4.76794i	−0.109875	−	0.151230i
$995$	1.55350	+	32.3630i	0.0492493	+	1.02598i
$996$	−6.08178	−	20.0219i	−0.192709	−	0.634420i
$997$	18.0502	+	18.0502i	0.571656	+	0.571656i	0.932591	−	0.360935i	$-0.117542\pi$
$997$	18.0502	+	18.0502i	0.571656	+	0.571656i	−0.360935	+	0.932591i	$0.617542\pi$
$998$	−18.2868	−	18.2868i	−0.578858	−	0.578858i
$999$	−32.9327	−	1.90501i	−1.04194	−	0.0602719i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bk.a.47.8	✓	512
3.2	odd	2	inner	930.2.bk.a.47.44	yes	512
5.3	odd	4	inner	930.2.bk.a.233.57	yes	512
15.8	even	4	inner	930.2.bk.a.233.5	yes	512
31.2	even	5	inner	930.2.bk.a.467.5	yes	512
93.2	odd	10	inner	930.2.bk.a.467.57	yes	512
155.33	odd	20	inner	930.2.bk.a.653.44	yes	512
465.188	even	20	inner	930.2.bk.a.653.8	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bk.a.47.8	✓	512	1.1	even	1	trivial
930.2.bk.a.47.44	yes	512	3.2	odd	2	inner
930.2.bk.a.233.5	yes	512	15.8	even	4	inner
930.2.bk.a.233.57	yes	512	5.3	odd	4	inner
930.2.bk.a.467.5	yes	512	31.2	even	5	inner
930.2.bk.a.467.57	yes	512	93.2	odd	10	inner
930.2.bk.a.653.8	yes	512	465.188	even	20	inner
930.2.bk.a.653.44	yes	512	155.33	odd	20	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.156434 + 0.987688i) q^{2} +(-1.20093 - 1.24811i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-1.74392 + 1.39955i) q^{5} +(1.42061 - 0.990898i) q^{6} +(-2.75830 + 1.40542i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-0.115534 + 2.99777i) q^{9} +O(q^{10})\)	\(q+(-0.156434 + 0.987688i) q^{2} +(-1.20093 - 1.24811i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-1.74392 + 1.39955i) q^{5} +(1.42061 - 0.990898i) q^{6} +(-2.75830 + 1.40542i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-0.115534 + 2.99777i) q^{9} +(-1.10951 - 1.94139i) q^{10} +(-1.51970 - 0.493780i) q^{11} +(0.756467 + 1.55813i) q^{12} +(-1.80652 + 0.286124i) q^{13} +(-0.956627 - 2.94419i) q^{14} +(3.84111 + 0.495828i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-1.05875 - 0.539458i) q^{17} +(-2.94279 - 0.583067i) q^{18} +(3.67068 + 5.05225i) q^{19} +(2.09105 - 0.792154i) q^{20} +(5.06664 + 1.75483i) q^{21} +(0.725434 - 1.42375i) q^{22} +(3.83937 - 7.53519i) q^{23} +(-1.65728 + 0.503409i) q^{24} +(1.08250 - 4.88141i) q^{25} -1.82904i q^{26} +(3.88029 - 3.45592i) q^{27} +(3.05760 - 0.484276i) q^{28} +(0.328688 - 0.238806i) q^{29} +(-1.09061 + 3.71626i) q^{30} +(-1.42241 + 5.38300i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.20876 + 2.48974i) q^{33} +(0.698441 - 0.961322i) q^{34} +(2.84328 - 6.31133i) q^{35} +(1.03624 - 2.81535i) q^{36} +(-4.48906 - 4.48906i) q^{37} +(-5.56427 + 2.83514i) q^{38} +(2.52661 + 1.91111i) q^{39} +(0.455289 + 2.18923i) q^{40} +(-7.42247 - 10.2162i) q^{41} +(-2.52582 + 4.72974i) q^{42} +(-0.180965 + 1.14257i) q^{43} +(1.29273 + 0.939226i) q^{44} +(-3.99406 - 5.38957i) q^{45} +(6.84181 + 4.97087i) q^{46} +(8.95593 - 1.41848i) q^{47} +(-0.237955 - 1.71563i) q^{48} +(1.51849 - 2.09003i) q^{49} +(4.65197 + 1.83280i) q^{50} +(0.598180 + 1.96928i) q^{51} +(1.80652 + 0.286124i) q^{52} +(4.94962 - 9.71417i) q^{53} +(2.80636 + 4.37314i) q^{54} +(3.34130 - 1.26579i) q^{55} +3.09571i q^{56} +(1.89752 - 10.6488i) q^{57} +(0.184448 + 0.361999i) q^{58} +(5.19354 + 3.77333i) q^{59} +(-3.49990 - 1.65853i) q^{60} +5.65997 q^{61} +(-5.09422 - 2.24699i) q^{62} +(-3.89446 - 8.43113i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(2.74997 - 3.02729i) q^{65} +(-2.64818 + 0.804400i) q^{66} +(-0.547307 - 0.547307i) q^{67} +(0.840226 + 0.840226i) q^{68} +(-14.0155 + 4.25730i) q^{69} +(5.78884 + 3.79558i) q^{70} +(1.81059 - 0.588296i) q^{71} +(2.61859 + 1.46390i) q^{72} +(2.88043 + 5.65315i) q^{73} +(5.13604 - 3.73155i) q^{74} +(-7.39253 + 4.51116i) q^{75} +(-1.92979 - 5.93928i) q^{76} +(4.88575 - 0.773827i) q^{77} +(-2.28283 + 2.19654i) q^{78} +(10.8657 - 3.53048i) q^{79} +(-2.23350 + 0.107213i) q^{80} +(-8.97330 - 0.692690i) q^{81} +(11.2515 - 5.73293i) q^{82} +(-11.9325 - 1.88992i) q^{83} +(-4.27639 - 3.23462i) q^{84} +(2.60137 - 0.541001i) q^{85} +(-1.10019 - 0.357475i) q^{86} +(-0.692787 - 0.123448i) q^{87} +(-1.12989 + 1.12989i) q^{88} +(0.934106 - 2.87488i) q^{89} +(5.94802 - 3.10178i) q^{90} +(4.58078 - 3.32814i) q^{91} +(-5.97996 + 5.97996i) q^{92} +(8.42678 - 4.68929i) q^{93} +9.06757i q^{94} +(-13.4723 - 3.67341i) q^{95} +(1.73173 + 0.0333580i) q^{96} +(3.60448 - 1.83657i) q^{97} +(1.82675 + 1.82675i) q^{98} +(1.65582 - 4.49867i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q + 8 q^{3} - 12 q^{7}+O(q^{10}) \) 512 * q + 8 * q^3 - 12 * q^7	\( 512 q + 8 q^{3} - 12 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} + 128 q^{16} + 28 q^{22} + 32 q^{25} + 44 q^{27} + 8 q^{28} + 24 q^{30} + 8 q^{31} + 28 q^{33} + 176 q^{37} + 24 q^{42} - 40 q^{45} - 24 q^{46} + 12 q^{48} - 16 q^{51} - 40 q^{55} + 40 q^{57} + 56 q^{58} + 12 q^{60} - 32 q^{61} - 224 q^{63} + 32 q^{66} + 48 q^{67} + 24 q^{70} + 40 q^{73} - 32 q^{75} + 48 q^{76} - 76 q^{78} - 96 q^{81} + 24 q^{85} - 80 q^{87} - 72 q^{88} + 16 q^{90} + 80 q^{91} - 168 q^{93} - 112 q^{97}+O(q^{100}) \) 512 * q + 8 * q^3 - 12 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 + 128 * q^16 + 28 * q^22 + 32 * q^25 + 44 * q^27 + 8 * q^28 + 24 * q^30 + 8 * q^31 + 28 * q^33 + 176 * q^37 + 24 * q^42 - 40 * q^45 - 24 * q^46 + 12 * q^48 - 16 * q^51 - 40 * q^55 + 40 * q^57 + 56 * q^58 + 12 * q^60 - 32 * q^61 - 224 * q^63 + 32 * q^66 + 48 * q^67 + 24 * q^70 + 40 * q^73 - 32 * q^75 + 48 * q^76 - 76 * q^78 - 96 * q^81 + 24 * q^85 - 80 * q^87 - 72 * q^88 + 16 * q^90 + 80 * q^91 - 168 * q^93 - 112 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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