LMFDB - Embedded newform 310.2.s.a.263.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,2,Mod(23,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([15, 18]))

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

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

chi := DirichletCharacter("310.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	310.s (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:	$2.47536246266$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			263.13
Character	$\chi$	$=$	310.263
Dual form			310.2.s.a.277.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.156434 - 0.987688i) q^{2} +(-0.0340912 + 0.00539952i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(0.0723287 + 2.23490i) q^{5} +0.0345162i q^{6} +(0.886641 + 1.74013i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-2.85204 + 0.926683i) q^{9} +O(q^{10})$	\(q+(0.156434 - 0.987688i) q^{2} +(-0.0340912 + 0.00539952i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(0.0723287 + 2.23490i) q^{5} +0.0345162i q^{6} +(0.886641 + 1.74013i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-2.85204 + 0.926683i) q^{9} +(2.21870 + 0.278177i) q^{10} +(5.39525 + 1.75302i) q^{11} +(0.0340912 + 0.00539952i) q^{12} +(2.98257 - 0.472393i) q^{13} +(1.85741 - 0.603509i) q^{14} +(-0.0145332 - 0.0757999i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-1.26546 + 2.48361i) q^{17} +(0.469117 + 2.96189i) q^{18} +(-1.11652 - 1.53676i) q^{19} +(0.621833 - 2.14786i) q^{20} +(-0.0396226 - 0.0545358i) q^{21} +(2.57544 - 5.05459i) q^{22} +(-0.0394199 - 0.0200854i) q^{23} +(0.0106661 - 0.0328268i) q^{24} +(-4.98954 + 0.323295i) q^{25} -3.01975i q^{26} +(0.184488 - 0.0940015i) q^{27} +(-0.305516 - 1.92895i) q^{28} +(7.51695 - 5.46138i) q^{29} +(-0.0771401 + 0.00249651i) q^{30} +(-5.31865 + 1.64679i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.193396 - 0.0306310i) q^{33} +(2.25507 + 1.63840i) q^{34} +(-3.82489 + 2.10741i) q^{35} +2.99881 q^{36} +(2.60361 + 2.60361i) q^{37} +(-1.69250 + 0.862373i) q^{38} +(-0.0991289 + 0.0322089i) q^{39} +(-2.02415 - 0.950177i) q^{40} +(4.10410 - 2.98180i) q^{41} +(-0.0600627 + 0.0306035i) q^{42} +(-0.816679 + 5.15631i) q^{43} +(-4.58948 - 3.33445i) q^{44} +(-2.27733 - 6.30698i) q^{45} +(-0.0260048 + 0.0357925i) q^{46} +(-2.48892 + 0.394206i) q^{47} +(-0.0307541 - 0.0156700i) q^{48} +(1.87257 - 2.57738i) q^{49} +(-0.461221 + 4.97868i) q^{50} +(0.0297309 - 0.0915022i) q^{51} +(-2.98257 - 0.472393i) q^{52} +(-10.9843 - 5.59680i) q^{53} +(-0.0639838 - 0.196922i) q^{54} +(-3.52760 + 12.1846i) q^{55} -1.95299 q^{56} +(0.0463614 + 0.0463614i) q^{57} +(-4.21824 - 8.27875i) q^{58} +(1.64659 - 2.26634i) q^{59} +(-0.00960160 + 0.0765810i) q^{60} -6.54992i q^{61} +(0.794496 + 5.51079i) q^{62} +(-4.14128 - 4.14128i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(1.27148 + 6.63158i) q^{65} +(-0.0605077 + 0.186224i) q^{66} +(-7.51327 + 7.51327i) q^{67} +(1.97100 - 1.97100i) q^{68} +(0.00145232 + 0.000471889i) q^{69} +(1.48312 + 4.10747i) q^{70} +(0.478046 + 1.47128i) q^{71} +(0.469117 - 2.96189i) q^{72} +(3.59187 + 7.04944i) q^{73} +(2.97885 - 2.16426i) q^{74} +(0.168354 - 0.0379626i) q^{75} +(0.586990 + 1.80657i) q^{76} +(1.73316 + 10.9428i) q^{77} +(0.0163052 + 0.102947i) q^{78} +(-0.636609 - 1.95928i) q^{79} +(-1.25512 + 1.85058i) q^{80} +(7.27248 - 5.28377i) q^{81} +(-2.30307 - 4.52003i) q^{82} +(0.509938 - 3.21962i) q^{83} +(0.0208308 + 0.0641107i) q^{84} +(-5.64214 - 2.64854i) q^{85} +(4.96507 + 1.61325i) q^{86} +(-0.226773 + 0.226773i) q^{87} +(-4.01135 + 4.01135i) q^{88} +(4.49739 - 13.8415i) q^{89} +(-6.58559 + 1.26266i) q^{90} +(3.46650 + 4.77122i) q^{91} +(0.0312838 + 0.0312838i) q^{92} +(0.172428 - 0.0848593i) q^{93} +2.51994i q^{94} +(3.35375 - 2.60646i) q^{95} +(-0.0202881 + 0.0279242i) q^{96} +(-5.47988 - 10.7549i) q^{97} +(-2.25271 - 2.25271i) q^{98} -17.0120 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 12 q^{7}+O(q^{10}) $ 128 * q + 12 * q^7	$ 128 q + 12 q^{7} + 8 q^{10} + 32 q^{16} + 8 q^{20} - 80 q^{21} - 20 q^{22} - 20 q^{23} + 40 q^{25} + 8 q^{28} - 32 q^{31} + 20 q^{33} - 48 q^{35} - 128 q^{36} + 52 q^{38} + 8 q^{41} - 20 q^{42} + 64 q^{45} - 40 q^{46} - 20 q^{47} - 20 q^{48} + 24 q^{50} - 16 q^{51} - 40 q^{53} - 40 q^{55} + 20 q^{60} - 8 q^{62} + 256 q^{63} - 160 q^{65} + 56 q^{66} + 8 q^{67} - 32 q^{70} + 56 q^{71} - 80 q^{73} - 160 q^{75} + 48 q^{76} - 20 q^{77} + 4 q^{78} - 96 q^{81} + 16 q^{82} - 240 q^{83} + 120 q^{85} + 40 q^{87} - 64 q^{90} + 80 q^{91} - 160 q^{93} + 32 q^{95} - 56 q^{97} - 176 q^{98}+O(q^{100}) $ 128 * q + 12 * q^7 + 8 * q^10 + 32 * q^16 + 8 * q^20 - 80 * q^21 - 20 * q^22 - 20 * q^23 + 40 * q^25 + 8 * q^28 - 32 * q^31 + 20 * q^33 - 48 * q^35 - 128 * q^36 + 52 * q^38 + 8 * q^41 - 20 * q^42 + 64 * q^45 - 40 * q^46 - 20 * q^47 - 20 * q^48 + 24 * q^50 - 16 * q^51 - 40 * q^53 - 40 * q^55 + 20 * q^60 - 8 * q^62 + 256 * q^63 - 160 * q^65 + 56 * q^66 + 8 * q^67 - 32 * q^70 + 56 * q^71 - 80 * q^73 - 160 * q^75 + 48 * q^76 - 20 * q^77 + 4 * q^78 - 96 * q^81 + 16 * q^82 - 240 * q^83 + 120 * q^85 + 40 * q^87 - 64 * q^90 + 80 * q^91 - 160 * q^93 + 32 * q^95 - 56 * q^97 - 176 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

$n$	$187$	$251$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{10}\right)$

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
$3$	−0.0340912	+	0.00539952i	−0.0196826	+	0.00311741i	−0.166268	−	0.986081i	$-0.553172\pi$
$3$	−0.0340912	+	0.00539952i	−0.0196826	+	0.00311741i	0.146585	+	0.989198i	$0.453172\pi$
$4$	−0.951057	−	0.309017i	−0.475528	−	0.154508i
$5$	0.0723287	+	2.23490i	0.0323464	+	0.999477i
$5$	0.0723287	+	2.23490i	0.0323464	+	0.999477i
$6$			0.0345162i			0.0140912i
$7$	0.886641	+	1.74013i	0.335119	+	0.657708i	0.995658	−	0.0930836i	$-0.0296724\pi$
$7$	0.886641	+	1.74013i	0.335119	+	0.657708i	−0.660539	+	0.750791i	$0.729672\pi$
$8$	−0.453990	+	0.891007i	−0.160510	+	0.315018i
$9$	−2.85204	+	0.926683i	−0.950679	+	0.308894i
$10$	2.21870	+	0.278177i	0.701614	+	0.0879672i
$11$	5.39525	+	1.75302i	1.62673	+	0.528557i	0.973516	−	0.228617i	$-0.0734204\pi$
$11$	5.39525	+	1.75302i	1.62673	+	0.528557i	0.653213	+	0.757174i	$0.273420\pi$
$12$	0.0340912	+	0.00539952i	0.00984129	+	0.00155871i
$13$	2.98257	−	0.472393i	0.827217	−	0.131018i	0.271551	−	0.962424i	$-0.412463\pi$
$13$	2.98257	−	0.472393i	0.827217	−	0.131018i	0.555666	+	0.831406i	$0.312463\pi$
$14$	1.85741	−	0.603509i	0.496413	−	0.161294i
$15$	−0.0145332	−	0.0757999i	−0.00375244	−	0.0195714i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−1.26546	+	2.48361i	−0.306920	+	0.602364i	−0.992019	−	0.126086i	$-0.959759\pi$
$17$	−1.26546	+	2.48361i	−0.306920	+	0.602364i	0.685100	+	0.728449i	$0.259759\pi$
$18$	0.469117	+	2.96189i	0.110572	+	0.698124i
$19$	−1.11652	−	1.53676i	−0.256148	−	0.352557i	0.661505	−	0.749941i	$-0.269918\pi$
$19$	−1.11652	−	1.53676i	−0.256148	−	0.352557i	−0.917652	+	0.397384i	$0.869918\pi$
$20$	0.621833	−	2.14786i	0.139046	−	0.480277i
$21$	−0.0396226	−	0.0545358i	−0.00864635	−	0.0119007i
$22$	2.57544	−	5.05459i	0.549087	−	1.07764i
$23$	−0.0394199	−	0.0200854i	−0.00821962	−	0.00418810i	0.449876	−	0.893091i	$-0.351468\pi$
$23$	−0.0394199	−	0.0200854i	−0.00821962	−	0.00418810i	−0.458095	+	0.888903i	$0.651468\pi$
$24$	0.0106661	−	0.0328268i	0.00217721	−	0.00670075i
$25$	−4.98954	+	0.323295i	−0.997907	+	0.0646589i
$26$		−	3.01975i		−	0.592222i
$27$	0.184488	−	0.0940015i	0.0355048	−	0.0180906i
$28$	−0.305516	−	1.92895i	−0.0577370	−	0.364537i
$29$	7.51695	−	5.46138i	1.39586	−	1.01415i	0.400670	−	0.916223i	$-0.368778\pi$
$29$	7.51695	−	5.46138i	1.39586	−	1.01415i	0.995193	−	0.0979310i	$-0.0312224\pi$
$30$	−0.0771401	+	0.00249651i	−0.0140838	+	0.000455799i
$31$	−5.31865	+	1.64679i	−0.955258	+	0.295772i
$31$	−5.31865	+	1.64679i	−0.955258	+	0.295772i
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.193396	−	0.0306310i	−0.0336660	−	0.00533217i
$34$	2.25507	+	1.63840i	0.386741	+	0.280984i
$35$	−3.82489	+	2.10741i	−0.646524	+	0.356218i
$36$	2.99881			0.499801
$37$	2.60361	+	2.60361i	0.428031	+	0.428031i	0.887957	−	0.459926i	$-0.152124\pi$
$37$	2.60361	+	2.60361i	0.428031	+	0.428031i	−0.459926	+	0.887957i	$0.652124\pi$
$38$	−1.69250	+	0.862373i	−0.274560	+	0.139895i
$39$	−0.0991289	+	0.0322089i	−0.0158733	+	0.00515756i
$40$	−2.02415	−	0.950177i	−0.320045	−	0.150236i
$41$	4.10410	−	2.98180i	0.640953	−	0.465680i	−0.219224	−	0.975674i	$-0.570353\pi$
$41$	4.10410	−	2.98180i	0.640953	−	0.465680i	0.860177	+	0.509995i	$0.170353\pi$
$42$	−0.0600627	+	0.0306035i	−0.00926787	+	0.00472222i
$43$	−0.816679	+	5.15631i	−0.124542	+	0.786329i	0.843792	+	0.536671i	$0.180318\pi$
$43$	−0.816679	+	5.15631i	−0.124542	+	0.786329i	−0.968334	+	0.249658i	$0.919682\pi$
$44$	−4.58948	−	3.33445i	−0.691890	−	0.502687i
$45$	−2.27733	−	6.30698i	−0.339484	−	0.940190i
$46$	−0.0260048	+	0.0357925i	−0.00383420	+	0.00527732i
$47$	−2.48892	+	0.394206i	−0.363046	+	0.0575008i	−0.335293	−	0.942114i	$-0.608835\pi$
$47$	−2.48892	+	0.394206i	−0.363046	+	0.0575008i	−0.0277531	+	0.999615i	$0.508835\pi$
$48$	−0.0307541	−	0.0156700i	−0.00443898	−	0.00226177i
$49$	1.87257	−	2.57738i	0.267510	−	0.368196i
$50$	−0.461221	+	4.97868i	−0.0652265	+	0.704092i
$51$	0.0297309	−	0.0915022i	0.00416315	−	0.0128129i
$52$	−2.98257	−	0.472393i	−0.413608	−	0.0655091i
$53$	−10.9843	−	5.59680i	−1.50882	−	0.768780i	−0.512847	−	0.858480i	$-0.671409\pi$
$53$	−10.9843	−	5.59680i	−1.50882	−	0.768780i	−0.995969	+	0.0897000i	$0.971409\pi$
$54$	−0.0639838	−	0.196922i	−0.00870709	−	0.0267977i
$55$	−3.52760	+	12.1846i	−0.475661	+	1.64298i
$56$	−1.95299			−0.260980
$57$	0.0463614	+	0.0463614i	0.00614072	+	0.00614072i
$58$	−4.21824	−	8.27875i	−0.553881	−	1.08705i
$59$	1.64659	−	2.26634i	0.214368	−	0.295053i	−0.688268	−	0.725456i	$-0.741629\pi$
$59$	1.64659	−	2.26634i	0.214368	−	0.295053i	0.902636	+	0.430404i	$0.141629\pi$
$60$	−0.00960160	+	0.0765810i	−0.00123956	+	0.00988656i
$61$		−	6.54992i		−	0.838631i	−0.907841	−	0.419316i	$-0.862270\pi$
$61$		−	6.54992i		−	0.838631i	0.907841	−	0.419316i	$-0.137730\pi$
$62$	0.794496	+	5.51079i	0.100901	+	0.699871i
$63$	−4.14128	−	4.14128i	−0.521753	−	0.521753i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	1.27148	+	6.63158i	0.157707	+	0.822546i
$66$	−0.0605077	+	0.186224i	−0.00744798	+	0.0229225i
$67$	−7.51327	+	7.51327i	−0.917891	+	0.917891i	−0.996876	−	0.0789844i	$-0.974832\pi$
$67$	−7.51327	+	7.51327i	−0.917891	+	0.917891i	0.0789844	+	0.996876i	$0.474832\pi$
$68$	1.97100	−	1.97100i	0.239019	−	0.239019i
$69$	0.00145232		0.000471889i	0.000174839		5.68088e-5i
$70$	1.48312	+	4.10747i	0.177267	+	0.490936i
$71$	0.478046	+	1.47128i	0.0567337	+	0.174608i	0.975408	−	0.220408i	$-0.0707389\pi$
$71$	0.478046	+	1.47128i	0.0567337	+	0.174608i	−0.918674	+	0.395016i	$0.870739\pi$
$72$	0.469117	−	2.96189i	0.0552860	−	0.349062i
$73$	3.59187	+	7.04944i	0.420396	+	0.825074i	0.999949	+	0.0101392i	$0.00322746\pi$
$73$	3.59187	+	7.04944i	0.420396	+	0.825074i	−0.579552	+	0.814935i	$0.696773\pi$
$74$	2.97885	−	2.16426i	0.346284	−	0.251590i
$75$	0.168354	−	0.0379626i	0.0194398	−	0.00438355i
$76$	0.586990	+	1.80657i	0.0673324	+	0.207228i
$77$	1.73316	+	10.9428i	0.197512	+	1.24704i
$78$	0.0163052	+	0.102947i	0.00184620	+	0.0116565i
$79$	−0.636609	−	1.95928i	−0.0716242	−	0.220437i	0.908836	−	0.417153i	$-0.136972\pi$
$79$	−0.636609	−	1.95928i	−0.0716242	−	0.220437i	−0.980460	+	0.196717i	$0.936972\pi$
$80$	−1.25512	+	1.85058i	−0.140327	+	0.206902i
$81$	7.27248	−	5.28377i	0.808053	−	0.587085i
$82$	−2.30307	−	4.52003i	−0.254332	−	0.499154i
$83$	0.509938	−	3.21962i	0.0559730	−	0.353400i	−0.943767	−	0.330610i	$-0.892745\pi$
$83$	0.509938	−	3.21962i	0.0559730	−	0.353400i	0.999740	−	0.0227891i	$-0.00725464\pi$
$84$	0.0208308	+	0.0641107i	0.00227283	+	0.00699505i
$85$	−5.64214	−	2.64854i	−0.611976	−	0.287275i
$86$	4.96507	+	1.61325i	0.535397	+	0.173961i
$87$	−0.226773	+	0.226773i	−0.0243126	+	0.0243126i
$88$	−4.01135	+	4.01135i	−0.427611	+	0.427611i
$89$	4.49739	−	13.8415i	0.476722	−	1.46720i	−0.366899	−	0.930261i	$-0.619580\pi$
$89$	4.49739	−	13.8415i	0.476722	−	1.46720i	0.843621	−	0.536939i	$-0.180420\pi$
$90$	−6.58559	+	1.26266i	−0.694182	+	0.133096i
$91$	3.46650	+	4.77122i	0.363388	+	0.500160i
$92$	0.0312838	+	0.0312838i	0.00326156	+	0.00326156i
$93$	0.172428	−	0.0848593i	0.0178799	−	0.00879950i
$94$			2.51994i			0.259912i
$95$	3.35375	−	2.60646i	0.344087	−	0.267418i
$96$	−0.0202881	+	0.0279242i	−0.00207065	+	0.00285000i
$97$	−5.47988	−	10.7549i	−0.556398	−	1.09199i	−0.982316	−	0.187231i	$-0.940049\pi$
$97$	−5.47988	−	10.7549i	−0.556398	−	1.09199i	0.425918	−	0.904762i	$-0.359951\pi$
$98$	−2.25271	−	2.25271i	−0.227558	−	0.227558i
$99$	−17.0120			−1.70977
$100$	4.84524	+	1.23438i	0.484524	+	0.123438i
$101$	−0.227738	−	0.700904i	−0.0226607	−	0.0697426i	0.939087	−	0.343680i	$-0.111674\pi$
$101$	−0.227738	−	0.700904i	−0.0226607	−	0.0697426i	−0.961747	+	0.273938i	$0.911674\pi$
$102$	−0.0857247	−	0.0436789i	−0.00848801	−	0.00432486i
$103$	−8.59175	−	1.36080i	−0.846570	−	0.134084i	−0.281945	−	0.959431i	$-0.590979\pi$
$103$	−8.59175	−	1.36080i	−0.846570	−	0.134084i	−0.564626	+	0.825347i	$0.690979\pi$
$104$	−0.933154	+	2.87195i	−0.0915033	+	0.281618i
$105$	0.119016	−	0.0924969i	0.0116148	−	0.00902677i
$106$	−7.24623	+	9.97358i	−0.703816	+	0.968719i
$107$	5.76634	+	2.93810i	0.557453	+	0.284037i	0.709932	−	0.704270i	$-0.248726\pi$
$107$	5.76634	+	2.93810i	0.557453	+	0.284037i	−0.152479	+	0.988307i	$0.548726\pi$
$108$	−0.204507	+	0.0323907i	−0.0196787	+	0.00311680i
$109$	−0.929272	+	1.27903i	−0.0890081	+	0.122509i	−0.851199	−	0.524843i	$-0.824124\pi$
$109$	−0.929272	+	1.27903i	−0.0890081	+	0.122509i	0.762191	+	0.647353i	$0.224124\pi$
$110$	11.4828	+	5.39026i	1.09484	+	0.513941i
$111$	−0.102819	−	0.0747020i	−0.00975910	−	0.00709040i
$112$	−0.305516	+	1.92895i	−0.0288685	+	0.182269i
$113$	14.9555	−	7.62020i	1.40689	−	0.716848i	0.424808	−	0.905284i	$-0.360342\pi$
$113$	14.9555	−	7.62020i	1.40689	−	0.716848i	0.982086	+	0.188436i	$0.0603417\pi$
$114$	0.0530431	−	0.0385381i	0.00496794	−	0.00360942i
$115$	0.0420377	−	0.0895522i	0.00392004	−	0.00835079i
$116$	−8.83671	+	2.87122i	−0.820468	+	0.266586i
$117$	−8.06865	+	4.11118i	−0.745947	+	0.380079i
$118$	−1.98086	−	1.98086i	−0.182352	−	0.182352i
$119$	−5.44382			−0.499034
$120$	0.0741361	+	0.0214633i	0.00676767	+	0.00195932i
$121$	17.1365	+	12.4504i	1.55786	+	1.13185i
$122$	−6.46928	−	1.02463i	−0.585701	−	0.0927659i
$123$	−0.123814	+	0.123814i	−0.0111639	+	0.0111639i
$124$	5.56723	+	0.0773630i	0.499952	+	0.00694740i
$125$	−1.08342	−	11.1277i	−0.0969038	−	0.995294i
$126$	−4.73814	+	3.44246i	−0.422107	+	0.306678i
$127$	−2.19161	−	13.8373i	−0.194474	−	1.22786i	−0.870941	−	0.491388i	$-0.836490\pi$
$127$	−2.19161	−	13.8373i	−0.194474	−	1.22786i	0.676467	−	0.736473i	$-0.263510\pi$
$128$	−0.891007	+	0.453990i	−0.0787546	+	0.0401275i
$129$		−	0.180195i		−	0.0158652i
$130$	6.74883	−	0.218415i	0.591912	−	0.0191562i
$131$	6.69245	−	20.5973i	0.584722	−	1.79959i	−0.0156598	−	0.999877i	$-0.504985\pi$
$131$	6.69245	−	20.5973i	0.584722	−	1.79959i	0.600382	−	0.799713i	$-0.295015\pi$
$132$	0.174465	+	0.0888945i	0.0151853	+	0.00773728i
$133$	1.68421	−	3.30545i	0.146040	−	0.286619i
$134$	6.24543	+	8.59610i	0.539523	+	0.742590i
$135$	0.223427	+	0.405513i	0.0192296	+	0.0349010i
$136$	−1.63840	−	2.25507i	−0.140492	−	0.193371i
$137$	0.987694	+	6.23606i	0.0843844	+	0.532782i	0.993278	+	0.115754i	$0.0369284\pi$
$137$	0.987694	+	6.23606i	0.0843844	+	0.532782i	−0.908893	+	0.417028i	$0.863072\pi$
$138$	0.000693273	−	0.00136062i	5.90153e−5	−	0.000115824i
$139$	4.12745	+	2.99877i	0.350086	+	0.254352i	0.748905	−	0.662677i	$-0.230580\pi$
$139$	4.12745	+	2.99877i	0.350086	+	0.254352i	−0.398819	+	0.917030i	$0.630580\pi$
$140$	4.28891	−	0.822315i	0.362479	−	0.0694983i
$141$	0.0827217	−	0.0268779i	0.00696643	−	0.00226353i
$142$	1.52794	−	0.242003i	0.128222	−	0.0203084i
$143$	16.9198	+	2.67984i	1.41491	+	0.224100i
$144$	−2.85204	−	0.926683i	−0.237670	−	0.0772236i
$145$	12.7493	+	16.4046i	1.05877	+	1.36233i
$146$	7.52454	−	2.44487i	0.622735	−	0.202339i
$147$	−0.0499217	+	0.0979769i	−0.00411747	+	0.00808100i
$148$	−1.67162	−	3.28074i	−0.137406	−	0.269675i
$149$			18.0009i			1.47469i	0.675514	+	0.737347i	$0.263922\pi$
$149$			18.0009i			1.47469i	−0.675514	+	0.737347i	$0.736078\pi$
$150$	−0.0111589	−	0.172220i	−0.000911120	−	0.0140617i
$151$	1.48691	+	0.483127i	0.121003	+	0.0393163i	0.368893	−	0.929472i	$-0.379737\pi$
$151$	1.48691	+	0.483127i	0.121003	+	0.0393163i	−0.247890	+	0.968788i	$0.579737\pi$
$152$	1.87615	−	0.297154i	0.152176	−	0.0241023i
$153$	1.30763	−	8.25602i	0.105715	−	0.667460i
$154$	11.0792			0.892784
$155$	−4.06510	−	11.7675i	−0.326517	−	0.945191i
$156$	0.104230			0.00834510
$157$	0.485647	−	3.06625i	0.0387588	−	0.244714i	−0.960701	−	0.277586i	$-0.910466\pi$
$157$	0.485647	−	3.06625i	0.0387588	−	0.244714i	0.999460	+	0.0328726i	$0.0104656\pi$
$158$	−2.03475	+	0.322272i	−0.161876	+	0.0256386i
$159$	0.404690	+	0.131492i	0.0320940	+	0.0104280i
$160$	1.63146	+	1.52917i	0.128978	+	0.120891i
$161$		−	0.0864044i		−	0.00680962i
$162$	−4.08105	−	8.00951i	−0.320637	−	0.629286i
$163$	−10.7815	+	21.1600i	−0.844475	+	1.65738i	−0.0948703	+	0.995490i	$0.530244\pi$
$163$	−10.7815	+	21.1600i	−0.844475	+	1.65738i	−0.749605	+	0.661886i	$0.769756\pi$
$164$	−4.82466	+	1.56763i	−0.376743	+	0.122411i
$165$	0.0544690	−	0.434436i	0.00424040	−	0.0338208i
$166$	−3.10021	−	1.00732i	−0.240623	−	0.0781832i
$167$	19.4122	+	3.07460i	1.50216	+	0.237920i	0.852671	−	0.522448i	$-0.174981\pi$
$167$	19.4122	+	3.07460i	1.50216	+	0.237920i	0.649493	+	0.760367i	$0.274981\pi$
$168$	0.0665800	−	0.0105452i	0.00513676	−	0.000813583i
$169$	−3.69115	+	1.19933i	−0.283935	+	0.0922559i
$170$	−3.49856	+	5.15835i	−0.268327	+	0.395628i
$171$	4.60845	+	3.34824i	0.352417	+	0.256046i
$172$	2.37009	−	4.65157i	0.180718	−	0.354679i
$173$	−2.75716	−	17.4080i	−0.209623	−	1.32351i	−0.838031	−	0.545622i	$-0.816293\pi$
$173$	−2.75716	−	17.4080i	−0.209623	−	1.32351i	0.628409	−	0.777883i	$-0.283707\pi$
$174$	0.188506	+	0.259456i	0.0142906	+	0.0196693i
$175$	−4.98650	−	8.39580i	−0.376944	−	0.634663i
$176$	3.33445	+	4.58948i	0.251344	+	0.345945i
$177$	−0.0438972	+	0.0861532i	−0.00329952	+	0.00647567i
$178$	−12.9676	−	6.60731i	−0.971961	−	0.495239i
$179$	4.12127	−	12.6840i	0.308038	−	0.948043i	−0.670488	−	0.741920i	$-0.733915\pi$
$179$	4.12127	−	12.6840i	0.308038	−	0.948043i	0.978526	−	0.206123i	$-0.0660847\pi$
$180$	0.216900	+	6.70203i	0.0161668	+	0.499540i
$181$		−	13.5096i		−	1.00416i	−0.864820	−	0.502082i	$-0.832568\pi$
$181$		−	13.5096i		−	1.00416i	0.864820	−	0.502082i	$-0.167432\pi$
$182$	5.25476	−	2.67744i	0.389509	−	0.198465i
$183$	0.0353664	+	0.223295i	0.00261436	+	0.0165064i
$184$	0.0357925	−	0.0260048i	0.00263866	−	0.00191710i
$185$	−5.63049	+	6.00712i	−0.413962	+	0.441652i
$186$	−0.0568409	−	0.183580i	−0.00416778	−	0.0134607i
$187$	−11.1813	+	11.1813i	−0.817658	+	0.817658i
$188$	2.48892	+	0.394206i	0.181523	+	0.0287504i
$189$	0.327150	+	0.237688i	0.0237966	+	0.0172893i
$190$	−2.04973	−	3.72020i	−0.148703	−	0.269891i
$191$	23.6172			1.70888			0.854441	−	0.519548i	$-0.173900\pi$
$191$	23.6172			1.70888			0.854441	+	0.519548i	$0.173900\pi$
$192$	0.0244066	+	0.0244066i	0.00176140	+	0.00176140i
$193$	23.1802	−	11.8109i	1.66855	−	0.850169i	0.674869	−	0.737938i	$-0.264200\pi$
$193$	23.1802	−	11.8109i	1.66855	−	0.850169i	0.993682	−	0.112231i	$-0.0357998\pi$
$194$	−11.4797	+	3.72998i	−0.824195	+	0.267797i
$195$	−0.0791535	−	0.219213i	−0.00566830	−	0.0156982i
$196$	−2.57738	+	1.87257i	−0.184098	+	0.133755i
$197$	4.50514	−	2.29549i	0.320978	−	0.163547i	−0.286076	−	0.958207i	$-0.592351\pi$
$197$	4.50514	−	2.29549i	0.320978	−	0.163547i	0.607054	+	0.794660i	$0.292351\pi$
$198$	−2.66126	+	16.8025i	−0.189127	+	1.19410i
$199$	−2.78740	−	2.02517i	−0.197594	−	0.143560i	0.484589	−	0.874742i	$-0.338969\pi$
$199$	−2.78740	−	2.02517i	−0.197594	−	0.143560i	−0.682183	+	0.731182i	$0.738969\pi$
$200$	1.97714	−	4.59248i	0.139805	−	0.324738i
$201$	0.215568	−	0.296705i	0.0152050	−	0.0209279i
$202$	−0.727901	+	0.115288i	−0.0512149	+	0.00811165i
$203$	16.1684	+	8.23819i	1.13480	+	0.578208i
$204$	−0.0565515	+	0.0778364i	−0.00395939	+	0.00544964i
$205$	6.96087	+	8.95658i	0.486169	+	0.625555i
$206$	−2.68809	+	8.27309i	−0.187288	+	0.576414i
$207$	0.131040	+	0.0207547i	0.00910790	+	0.00144255i
$208$	2.69062	+	1.37094i	0.186561	+	0.0950575i
$209$	−3.32994	−	10.2485i	−0.230337	−	0.708904i
$210$	−0.0727399	−	0.132020i	−0.00501953	−	0.00911028i
$211$	−5.48313			−0.377474			−0.188737	−	0.982028i	$-0.560439\pi$
$211$	−5.48313			−0.377474			−0.188737	+	0.982028i	$0.560439\pi$
$212$	8.71723	+	8.71723i	0.598701	+	0.598701i
$213$	−0.0242414	−	0.0475764i	−0.00166099	−	0.00325988i
$214$	3.80398	−	5.23573i	0.260035	−	0.357907i
$215$	−11.5829	−	1.45224i	−0.789946	−	0.0990422i
$216$			0.207056i			0.0140884i
$217$	−7.58137	−	7.79504i	−0.514657	−	0.529162i
$218$	1.11792	+	1.11792i	0.0757148	+	0.0757148i
$219$	−0.160515	−	0.220930i	−0.0108466	−	0.0149290i
$220$	7.12020	−	10.4982i	0.480044	−	0.707788i
$221$	−2.60109	+	8.00534i	−0.174968	+	0.538497i
$222$	−0.0898667	+	0.0898667i	−0.00603146	+	0.00603146i
$223$	−18.7462	+	18.7462i	−1.25534	+	1.25534i	−0.302040	+	0.953295i	$0.597668\pi$
$223$	−18.7462	+	18.7462i	−1.25534	+	1.25534i	−0.953295	+	0.302040i	$0.902332\pi$
$224$	1.85741	+	0.603509i	0.124103	+	0.0403236i
$225$	13.9308	−	5.54577i	0.928717	−	0.369718i
$226$	−5.18683	−	15.9634i	−0.345023	−	1.06187i
$227$	−3.36987	+	21.2765i	−0.223666	+	1.41217i	0.578799	+	0.815471i	$0.303522\pi$
$227$	−3.36987	+	21.2765i	−0.223666	+	1.41217i	−0.802464	+	0.596700i	$0.796478\pi$
$228$	−0.0297658	−	0.0584188i	−0.00197129	−	0.00386888i
$229$	−17.5781	+	12.7713i	−1.16160	+	0.843948i	−0.989979	−	0.141215i	$-0.954899\pi$
$229$	−17.5781	+	12.7713i	−1.16160	+	0.843948i	−0.171617	+	0.985164i	$0.554899\pi$
$230$	−0.0818735	−	0.0555292i	−0.00539858	−	0.00366149i
$231$	−0.118171	−	0.363694i	−0.00777510	−	0.0239293i
$232$	1.45350	+	9.17707i	0.0954273	+	0.602504i
$233$	−1.21710	−	7.68445i	−0.0797346	−	0.503425i	−0.994943	−	0.100443i	$-0.967974\pi$
$233$	−1.21710	−	7.68445i	−0.0797346	−	0.503425i	0.915208	−	0.402981i	$-0.132026\pi$
$234$	2.79835	+	8.61244i	0.182934	+	0.563013i
$235$	−1.06103	−	5.53396i	−0.0692139	−	0.360996i
$236$	−2.26634	+	1.64659i	−0.147526	+	0.107184i
$237$	0.0322820	+	0.0633570i	0.00209694	+	0.00411548i
$238$	−0.851600	+	5.37679i	−0.0552011	+	0.348526i
$239$	3.53760	+	10.8876i	0.228828	+	0.704261i	0.997880	+	0.0650748i	$0.0207286\pi$
$239$	3.53760	+	10.8876i	0.228828	+	0.704261i	−0.769052	+	0.639186i	$0.779271\pi$
$240$	0.0327965	−	0.0698658i	0.00211700	−	0.00450982i
$241$	−11.5827	−	3.76345i	−0.746108	−	0.242425i	−0.0888026	−	0.996049i	$-0.528304\pi$
$241$	−11.5827	−	3.76345i	−0.746108	−	0.242425i	−0.657306	+	0.753624i	$0.728304\pi$
$242$	14.9778	−	14.9778i	0.962811	−	0.962811i
$243$	−0.658630	+	0.658630i	−0.0422511	+	0.0422511i
$244$	−2.02404	+	6.22934i	−0.129576	+	0.398793i
$245$	5.89561	+	3.99859i	0.376657	+	0.255461i
$246$	0.102921	+	0.141658i	0.00656197	+	0.00903178i
$247$	−4.05606	−	4.05606i	−0.258081	−	0.258081i
$248$	0.947317	−	5.48658i	0.0601547	−	0.348398i
$249$			0.112514i			0.00713031i
$250$	−11.1602	−	0.670681i	−0.705833	−	0.0424176i
$251$	−8.24981	+	11.3549i	−0.520724	+	0.716714i	−0.985681	−	0.168618i	$-0.946069\pi$
$251$	−8.24981	+	11.3549i	−0.520724	+	0.716714i	0.464958	+	0.885333i	$0.346069\pi$
$252$	2.65887	+	5.21832i	0.167493	+	0.328723i
$253$	−0.177470	−	0.177470i	−0.0111574	−	0.0111574i
$254$	−14.0098			−0.879051
$255$	0.206648	+	0.0598272i	0.0129408	+	0.00374652i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−4.96749	−	2.53106i	−0.309864	−	0.157883i	0.292143	−	0.956375i	$-0.405632\pi$
$257$	−4.96749	−	2.53106i	−0.309864	−	0.157883i	−0.602006	+	0.798491i	$0.705632\pi$
$258$	−0.177976	−	0.0281886i	−0.0110803	−	0.00175495i
$259$	−2.22216	+	6.83909i	−0.138078	+	0.424961i
$260$	0.840025	−	6.69991i	0.0520961	−	0.415511i
$261$	−16.3776	+	22.5419i	−1.01375	+	1.39531i
$262$	−19.2967	−	9.83218i	−1.19216	−	0.607434i
$263$	−20.0708	+	3.17891i	−1.23762	+	0.196020i	−0.740736	−	0.671797i	$-0.765523\pi$
$263$	−20.0708	+	3.17891i	−1.23762	+	0.196020i	−0.496885	+	0.867816i	$0.665523\pi$
$264$	0.115092	−	0.158411i	0.00708345	−	0.00974954i
$265$	11.7138	−	24.9537i	0.719573	−	1.53289i
$266$	−3.00129	−	2.18056i	−0.184021	−	0.133699i
$267$	−0.0785838	+	0.496159i	−0.00480925	+	0.0303644i
$268$	9.46727	−	4.82381i	0.578305	−	0.294661i
$269$	−12.5847	+	9.14330i	−0.767301	+	0.557477i	−0.901141	−	0.433526i	$-0.857269\pi$
$269$	−12.5847	+	9.14330i	−0.767301	+	0.557477i	0.133840	+	0.991003i	$0.457269\pi$
$270$	0.435473	−	0.157240i	0.0265020	−	0.00956935i
$271$	−14.7283	+	4.78550i	−0.894678	+	0.290699i	−0.720039	−	0.693934i	$-0.755876\pi$
$271$	−14.7283	+	4.78550i	−0.894678	+	0.290699i	−0.174640	+	0.984632i	$0.555876\pi$
$272$	−2.48361	+	1.26546i	−0.150591	+	0.0767299i
$273$	−0.143940	−	0.143940i	−0.00871162	−	0.00871162i
$274$	6.31379			0.381430
$275$	−27.4866	−	7.00252i	−1.65750	−	0.422268i
$276$	−0.00123542		0.000897586i	−7.43636e−5		5.40283e-5i
$277$	−8.95144	−	1.41777i	−0.537840	−	0.0851855i	−0.118396	−	0.992967i	$-0.537775\pi$
$277$	−8.95144	−	1.41777i	−0.537840	−	0.0851855i	−0.419444	+	0.907781i	$0.637775\pi$
$278$	3.60752	−	3.60752i	0.216365	−	0.216365i
$279$	13.6429	−	9.62541i	0.816782	−	0.576258i
$280$	−0.141258	−	4.36474i	−0.00844176	−	0.260843i
$281$	−3.88307	+	2.82122i	−0.231645	+	0.168300i	−0.697553	−	0.716533i	$-0.745728\pi$
$281$	−3.88307	+	2.82122i	−0.231645	+	0.168300i	0.465908	+	0.884833i	$0.345728\pi$
$282$	−0.0136065	−	0.0859079i	−0.000810254	−	0.00511574i
$283$	3.81399	−	1.94332i	0.226718	−	0.115519i	−0.336942	−	0.941525i	$-0.609393\pi$
$283$	3.81399	−	1.94332i	0.226718	−	0.115519i	0.563660	+	0.826007i	$0.309393\pi$
$284$		−	1.54699i		−	0.0917970i
$285$	−0.100260	+	0.106966i	−0.00593887	+	0.00633613i
$286$	5.29370	−	16.2923i	0.313023	−	0.963385i
$287$	8.82760	+	4.49789i	0.521077	+	0.265502i
$288$	−1.36143	+	2.67196i	−0.0802231	+	0.157447i
$289$	5.42543	+	7.46747i	0.319143	+	0.439263i
$290$	18.1971	−	10.0261i	1.06857	−	0.588754i
$291$	0.244887	+	0.337058i	0.0143555	+	0.0197587i
$292$	−1.23767	−	7.81436i	−0.0724294	−	0.457301i
$293$	1.68306	−	3.30319i	0.0983254	−	0.192974i	−0.836604	−	0.547808i	$-0.815462\pi$
$293$	1.68306	−	3.30319i	0.0983254	−	0.192974i	0.934930	+	0.354833i	$0.115462\pi$
$294$	0.0889612	+	0.0646341i	0.00518832	+	0.00376953i
$295$	5.18414	+	3.51605i	0.301832	+	0.204712i
$296$	−3.50185	+	1.13782i	−0.203541	+	0.0661344i
$297$	1.16015	−	0.183749i	0.0673186	−	0.0106622i
$298$	17.7793	+	2.81597i	1.02993	+	0.163125i
$299$	−0.127061	−	0.0412846i	−0.00734812	−	0.00238755i
$300$	−0.171845	−	0.0159196i	−0.00992148	−	0.000919118i
$301$	−9.69675	+	3.15067i	−0.558911	+	0.181601i
$302$	0.709783	−	1.39303i	0.0408434	−	0.0801597i
$303$	0.0115484	+	0.0226650i	0.000663438	+	0.00130207i
$304$		−	1.89954i		−	0.108946i
$305$	14.6384	−	0.473747i	0.838192	−	0.0271267i
$306$	−7.94982	−	2.58305i	−0.454461	−	0.147663i
$307$	16.5781	−	2.62571i	0.946160	−	0.149857i	0.335758	−	0.941948i	$-0.391008\pi$
$307$	16.5781	−	2.62571i	0.946160	−	0.149857i	0.610403	+	0.792091i	$0.291008\pi$
$308$	1.73316	−	10.9428i	0.0987560	−	0.623521i
$309$	0.300251			0.0170807
$310$	−12.2586	+	2.17420i	−0.696241	+	0.123487i
$311$	−28.5542			−1.61916			−0.809581	−	0.587009i	$-0.800305\pi$
$311$	−28.5542			−1.61916			−0.809581	+	0.587009i	$0.800305\pi$
$312$	0.0163052	−	0.102947i	0.000923101	−	0.00582823i
$313$	−5.74111	+	0.909303i	−0.324507	+	0.0513968i	−0.316563	−	0.948572i	$-0.602529\pi$
$313$	−5.74111	+	0.909303i	−0.324507	+	0.0513968i	−0.00794419	+	0.999968i	$0.502529\pi$
$314$	−2.95253	−	0.959336i	−0.166621	−	0.0541384i
$315$	8.95581	−	9.55488i	0.504603	−	0.538356i
$316$			2.06011i			0.115890i
$317$	−3.49396	−	6.85728i	−0.196240	−	0.385143i	0.771827	−	0.635832i	$-0.219343\pi$
$317$	−3.49396	−	6.85728i	−0.196240	−	0.385143i	−0.968068	+	0.250689i	$0.919343\pi$
$318$	0.193180	−	0.379138i	0.0108330	−	0.0212610i
$319$	50.1298	−	16.2882i	2.80673	−	0.911962i
$320$	1.76556	−	1.37216i	0.0986976	−	0.0767058i
$321$	−0.212446	−	0.0690279i	−0.0118576	−	0.00385276i
$322$	−0.0853406	−	0.0135166i	−0.00475585	−	0.000753252i
$323$	5.22963	−	0.828292i	0.290984	−	0.0460874i
$324$	−8.54931	+	2.77784i	−0.474962	+	0.154324i
$325$	−14.7289	+	3.32127i	−0.817014	+	0.184231i
$326$	19.2128	+	13.9589i	1.06410	+	0.773114i
$327$	0.0247739	−	0.0486214i	0.00137000	−	0.00268877i
$328$	0.793584	+	5.01049i	0.0438184	+	0.276658i
$329$	−2.89275	−	3.98152i	−0.159482	−	0.219508i
$330$	−0.420567	−	0.121759i	−0.0231515	−	0.00670262i
$331$	−20.7682	−	28.5850i	−1.14153	−	1.57118i	−0.764051	−	0.645156i	$-0.776792\pi$
$331$	−20.7682	−	28.5850i	−1.14153	−	1.57118i	−0.377475	−	0.926020i	$-0.623208\pi$
$332$	−1.47990	+	2.90446i	−0.0812200	+	0.159403i
$333$	−9.83831	−	5.01287i	−0.539136	−	0.274704i
$334$	6.07349	−	18.6923i	0.332327	−	1.02280i
$335$	−17.3348	−	16.2480i	−0.947102	−	0.887721i
$336$		−	0.0674099i		−	0.00367751i
$337$	4.05823	−	2.06777i	0.221066	−	0.112639i	−0.339951	−	0.940443i	$-0.610410\pi$
$337$	4.05823	−	2.06777i	0.221066	−	0.112639i	0.561017	+	0.827804i	$0.310410\pi$
$338$	0.607139	+	3.83332i	0.0330240	+	0.208505i
$339$	−0.468705	+	0.340534i	−0.0254566	+	0.0184953i
$340$	4.54755	+	4.26243i	0.246626	+	0.231163i
$341$	−31.5823	−	0.438873i	−1.71028	−	0.0237663i
$342$	4.02793	−	4.02793i	0.217806	−	0.217806i
$343$	19.6479	+	3.11193i	1.06089	+	0.168028i
$344$	−4.22354	−	3.06858i	−0.227718	−	0.165447i
$345$	−0.000949579		0.00327993i	−5.11236e−5		0.000176585i
$346$	−17.6250			−0.947525
$347$	17.0082	+	17.0082i	0.913049	+	0.913049i	0.996511	−	0.0834619i	$-0.0265977\pi$
$347$	17.0082	+	17.0082i	0.913049	+	0.913049i	−0.0834619	+	0.996511i	$0.526598\pi$
$348$	0.285751	−	0.145597i	0.0153179	−	0.00780484i
$349$	3.52713	−	1.14603i	0.188803	−	0.0613458i	−0.213089	−	0.977033i	$-0.568353\pi$
$349$	3.52713	−	1.14603i	0.188803	−	0.0613458i	0.401892	+	0.915687i	$0.368353\pi$
$350$	−9.07250	+	3.61172i	−0.484945	+	0.193054i
$351$	0.505844	−	0.367517i	0.0270000	−	0.0196166i
$352$	5.05459	−	2.57544i	0.269411	−	0.137272i
$353$	−2.59476	+	16.3827i	−0.138105	+	0.871963i	0.817203	+	0.576350i	$0.195524\pi$
$353$	−2.59476	+	16.3827i	−0.138105	+	0.871963i	−0.955308	+	0.295612i	$0.904476\pi$
$354$	0.0782255	+	0.0568341i	0.00415764	+	0.00302070i
$355$	−3.25357	+	1.17480i	−0.172682	+	0.0623519i
$356$	−8.55454	+	11.7743i	−0.453390	+	0.624037i
$357$	0.185586	−	0.0293940i	0.00982227	−	0.00155570i
$358$	−11.8831	−	6.05473i	−0.628041	−	0.320003i
$359$	−16.9015	+	23.2629i	−0.892026	+	1.22777i	0.0809164	+	0.996721i	$0.474215\pi$
$359$	−16.9015	+	23.2629i	−0.892026	+	1.22777i	−0.972942	+	0.231048i	$0.925785\pi$
$360$	6.65345	+	0.834199i	0.350668	+	0.0439662i
$361$	4.75631	−	14.6384i	0.250332	−	0.770443i
$362$	−13.3433	−	2.11337i	−0.701309	−	0.111076i
$363$	−0.651430	−	0.331920i	−0.0341912	−	0.0174213i
$364$	−1.82245	−	5.60891i	−0.0955221	−	0.293987i
$365$	−15.4950	+	8.53733i	−0.811044	+	0.446865i
$366$	0.226078			0.0118173
$367$	−11.6599	−	11.6599i	−0.608644	−	0.608644i	0.333948	−	0.942592i	$-0.391619\pi$
$367$	−11.6599	−	11.6599i	−0.608644	−	0.608644i	−0.942592	+	0.333948i	$0.891619\pi$
$368$	−0.0200854	−	0.0394199i	−0.00104703	−	0.00205490i
$369$	−8.94186	+	12.3074i	−0.465495	+	0.640699i
$370$	5.05236	+	6.50089i	0.262660	+	0.337965i
$371$		−	24.0766i		−	1.24999i
$372$	−0.190211	+	0.0274230i	−0.00986200	+	0.00142181i
$373$	16.9373	+	16.9373i	0.876980	+	0.876980i	0.993221	−	0.116241i	$-0.0370845\pi$
$373$	16.9373	+	16.9373i	0.876980	+	0.876980i	−0.116241	+	0.993221i	$0.537084\pi$
$374$	9.29451	+	12.7928i	0.480608	+	0.661500i
$375$	0.0970194	+	0.373508i	0.00501006	+	0.0192879i
$376$	0.778705	−	2.39661i	0.0401586	−	0.123596i
$377$	19.8399	−	19.8399i	1.02181	−	1.02181i
$378$	0.285939	−	0.285939i	0.0147071	−	0.0147071i
$379$	16.5201	+	5.36769i	0.848579	+	0.275720i	0.700851	−	0.713308i	$-0.252804\pi$
$379$	16.5201	+	5.36769i	0.848579	+	0.275720i	0.147728	+	0.989028i	$0.452804\pi$
$380$	−3.99504	+	1.44253i	−0.204941	+	0.0740003i
$381$	0.149429	+	0.459896i	0.00765550	+	0.0235612i
$382$	3.69455	−	23.3265i	0.189030	−	1.19349i
$383$	12.2890	+	24.1185i	0.627937	+	1.23240i	0.957547	+	0.288279i	$0.0930829\pi$
$383$	12.2890	+	24.1185i	0.627937	+	1.23240i	−0.329609	+	0.944117i	$0.606917\pi$
$384$	0.0279242	−	0.0202881i	0.00142500	−	0.00103532i
$385$	−24.3306	+	4.66491i	−1.24000	+	0.237746i
$386$	−8.03932	−	24.7425i	−0.409191	−	1.25936i
$387$	−2.44906	−	15.4628i	−0.124493	−	0.786017i
$388$	1.88824	+	11.9219i	0.0958608	+	0.605241i
$389$	3.29079	+	10.1280i	0.166850	+	0.513510i	0.999168	−	0.0407877i	$-0.0129867\pi$
$389$	3.29079	+	10.1280i	0.166850	+	0.513510i	−0.832318	+	0.554298i	$0.812987\pi$
$390$	−0.228897	+	0.0438865i	−0.0115906	+	0.00222228i
$391$	0.0997688	−	0.0724862i	0.00504552	−	0.00366579i
$392$	1.44633	+	2.83858i	0.0730506	+	0.143370i
$393$	−0.116939	+	0.738322i	−0.00589878	+	0.0372434i
$394$	−1.56246	−	4.80877i	−0.0787158	−	0.242262i
$395$	4.33275	−	1.56447i	0.218004	−	0.0787170i
$396$	16.1793	+	5.25698i	0.813042	+	0.264173i
$397$	−22.1373	+	22.1373i	−1.11104	+	1.11104i	−0.118027	+	0.993010i	$0.537657\pi$
$397$	−22.1373	+	22.1373i	−1.11104	+	1.11104i	−0.993010	+	0.118027i	$0.962343\pi$
$398$	−2.43628	+	2.43628i	−0.122120	+	0.122120i
$399$	−0.0395690	+	0.121781i	−0.00198093	+	0.00609667i
$400$	−4.22665	−	2.67123i	−0.211332	−	0.133561i
$401$	15.2827	+	21.0348i	0.763181	+	1.05043i	0.996943	+	0.0781347i	$0.0248964\pi$
$401$	15.2827	+	21.0348i	0.763181	+	1.05043i	−0.233762	+	0.972294i	$0.575104\pi$
$402$	−0.259329	−	0.259329i	−0.0129342	−	0.0129342i
$403$	−15.0853	+	7.42417i	−0.751454	+	0.369824i
$404$			0.736974i			0.0366658i
$405$	12.3347	+	15.8711i	0.612915	+	0.788640i
$406$	10.6661	−	14.6806i	0.529347	−	0.728584i
$407$	9.48295	+	18.6113i	0.470052	+	0.922529i
$408$	0.0680315	+	0.0680315i	0.00336806	+	0.00336806i
$409$	0.627954			0.0310503			0.0155252	−	0.999879i	$-0.495058\pi$
$409$	0.627954			0.0310503			0.0155252	+	0.999879i	$0.495058\pi$
$410$	9.93523	−	5.47406i	0.490666	−	0.270344i
$411$	−0.0673434	−	0.207262i	−0.00332181	−	0.0102235i
$412$	7.75073	+	3.94919i	0.381851	+	0.194563i
$413$	5.40367	+	0.855857i	0.265897	+	0.0421140i
$414$	0.0409983	−	0.126180i	0.00201496	−	0.00620140i
$415$	7.23241	+	0.906789i	0.355025	+	0.0445125i
$416$	1.77497	−	2.44303i	0.0870248	−	0.119779i
$417$	−0.156902	−	0.0799455i	−0.00768351	−	0.00391495i
$418$	−10.6432	+	1.68572i	−0.520578	+	0.0824515i
$419$	7.71708	−	10.6216i	0.377004	−	0.518902i	−0.577784	−	0.816190i	$-0.696082\pi$
$419$	7.71708	−	10.6216i	0.377004	−	0.518902i	0.954788	+	0.297288i	$0.0960823\pi$
$420$	−0.141774	+	0.0511918i	−0.00691787	+	0.00249790i
$421$	21.0200	+	15.2719i	1.02445	+	0.744307i	0.967191	−	0.254052i	$-0.0817634\pi$
$421$	21.0200	+	15.2719i	1.02445	+	0.744307i	0.0572606	+	0.998359i	$0.481763\pi$
$422$	−0.857751	+	5.41563i	−0.0417547	+	0.263629i
$423$	6.73318	−	3.43073i	0.327378	−	0.166808i
$424$	9.97358	−	7.24623i	0.484360	−	0.351908i
$425$	5.51113	−	12.8012i	0.267329	−	0.620948i
$426$	−0.0507828	+	0.0165003i	−0.00246044	+	0.000799444i
$427$	11.3977	−	5.80743i	0.551574	−	0.281041i
$428$	−4.57619	−	4.57619i	−0.221199	−	0.221199i
$429$	−0.591288			−0.0285477
$430$	−3.24633	+	11.2131i	−0.156552	+	0.540744i
$431$	2.40686	+	1.74869i	0.115934	+	0.0842313i	0.644242	−	0.764822i	$-0.277173\pi$
$431$	2.40686	+	1.74869i	0.115934	+	0.0842313i	−0.528307	+	0.849053i	$0.677173\pi$
$432$	0.204507	+	0.0323907i	0.00983934	+	0.00155840i
$433$	8.08981	−	8.08981i	0.388771	−	0.388771i	−0.485478	−	0.874249i	$-0.661354\pi$
$433$	8.08981	−	8.08981i	0.388771	−	0.388771i	0.874249	+	0.485478i	$0.161354\pi$
$434$	−8.88506	+	6.26862i	−0.426497	+	0.300903i
$435$	−0.523217	−	0.490413i	−0.0250864	−	0.0235135i
$436$	1.27903	−	0.929272i	0.0612546	−	0.0445040i
$437$	0.0131467	+	0.0830048i	0.000628890	+	0.00397066i
$438$	−0.243320	+	0.123978i	−0.0116263	+	0.00592388i
$439$			12.1121i			0.578079i	0.957317	+	0.289039i	$0.0933358\pi$
$439$			12.1121i			0.578079i	−0.957317	+	0.289039i	$0.906664\pi$
$440$	−9.25509	−	8.67482i	−0.441219	−	0.413556i
$441$	−2.95224	+	9.08605i	−0.140583	+	0.432669i
$442$	7.49988	+	3.82138i	0.356733	+	0.181764i
$443$	−4.92630	+	9.66840i	−0.234055	+	0.459360i	−0.977922	−	0.208968i	$-0.932990\pi$
$443$	−4.92630	+	9.66840i	−0.234055	+	0.459360i	0.743867	+	0.668328i	$0.232990\pi$
$444$	0.0747020	+	0.102819i	0.00354520	+	0.00487955i
$445$	31.2597	+	9.05006i	1.48185	+	0.429014i
$446$	15.5828	+	21.4479i	0.737868	+	1.01559i
$447$	−0.0971964	−	0.613674i	−0.00459723	−	0.0290258i
$448$	0.886641	−	1.74013i	0.0418899	−	0.0822135i
$449$	−27.4106	−	19.9150i	−1.29359	−	0.939845i	−0.293715	−	0.955893i	$-0.594892\pi$
$449$	−27.4106	−	19.9150i	−1.29359	−	0.939845i	−0.999871	+	0.0160475i	$0.994892\pi$
$450$	−3.29824	−	14.6268i	−0.155480	−	0.689513i
$451$	27.3698	−	8.89300i	1.28880	−	0.418755i
$452$	−16.5783	+	2.62574i	−0.779777	+	0.123504i
$453$	−0.0532993	−	0.00844178i	−0.00250422	−	0.000396629i
$454$	20.4874	+	6.65675i	0.961521	+	0.312417i
$455$	−10.4125	+	8.09237i	−0.488144	+	0.379376i
$456$	−0.0623559	+	0.0202607i	−0.00292008	+	0.000948793i
$457$	−4.23532	+	8.31228i	−0.198120	+	0.388832i	−0.968597	−	0.248635i	$-0.920018\pi$
$457$	−4.23532	+	8.31228i	−0.198120	+	0.388832i	0.770477	+	0.637467i	$0.220018\pi$
$458$	9.86420	+	19.3596i	0.460924	+	0.904614i
$459$			0.577152i			0.0269391i
$460$	−0.0676534	+	0.0721788i	−0.00315436	+	0.00336536i
$461$	−29.8079	−	9.68517i	−1.38829	−	0.451084i	−0.482906	−	0.875672i	$-0.660419\pi$
$461$	−29.8079	−	9.68517i	−1.38829	−	0.451084i	−0.905386	+	0.424589i	$0.860419\pi$
$462$	−0.377702	+	0.0598221i	−0.0175723	+	0.00278318i
$463$	2.63249	−	16.6209i	0.122342	−	0.772439i	−0.847874	−	0.530198i	$-0.822118\pi$
$463$	2.63249	−	16.6209i	0.122342	−	0.772439i	0.970216	−	0.242241i	$-0.0778824\pi$
$464$	9.29146			0.431345
$465$	0.202123	+	0.379220i	0.00937325	+	0.0175859i
$466$	−7.78023			−0.360412
$467$	6.41863	−	40.5256i	0.297019	−	1.87530i	−0.161876	−	0.986811i	$-0.551754\pi$
$467$	6.41863	−	40.5256i	0.297019	−	1.87530i	0.458895	−	0.888491i	$-0.348246\pi$
$468$	8.94416	−	1.41662i	0.413444	−	0.0654831i
$469$	−19.7356	−	6.41250i	−0.911307	−	0.296102i
$470$	−5.63181	+	0.182264i	−0.259776	+	0.00840722i
$471$			0.107155i			0.00493743i
$472$	1.27179	+	2.49602i	0.0585388	+	0.114889i
$473$	−13.4453	+	26.3879i	−0.618216	+	1.21332i
$474$	0.0676270	−	0.0219733i	0.00310621	−	0.00100927i
$475$	6.06775	+	7.30676i	0.278408	+	0.335257i
$476$	5.17738	+	1.68223i	0.237305	+	0.0771050i
$477$	36.5142	+	5.78328i	1.67187	+	0.264798i
$478$	11.3070	−	1.79085i	0.517169	−	0.0819114i
$479$	0.656294	−	0.213243i	0.0299868	−	0.00974332i	−0.293985	−	0.955810i	$-0.594982\pi$
$479$	0.656294	−	0.213243i	0.0299868	−	0.00974332i	0.323972	+	0.946067i	$0.394982\pi$
$480$	−0.0638751	−	0.0433221i	−0.00291549	−	0.00197738i
$481$	8.99539	+	6.53553i	0.410154	+	0.297995i
$482$	−5.52906	+	10.8514i	−0.251842	+	0.494267i
$483$	0.000466542		0.00294563i	2.12284e−5		0.000134031i
$484$	−12.4504	−	17.1365i	−0.565926	−	0.778931i
$485$	23.6397	−	13.0249i	1.07342	−	0.591429i
$486$	0.547489	+	0.753554i	0.0248346	+	0.0341819i
$487$	2.62873	−	5.15917i	0.119119	−	0.233784i	−0.823746	−	0.566959i	$-0.808120\pi$
$487$	2.62873	−	5.15917i	0.119119	−	0.233784i	0.942865	+	0.333175i	$0.108120\pi$
$488$	5.83602	+	2.97360i	0.264184	+	0.134609i
$489$	0.253302	−	0.779584i	0.0114547	−	0.0352540i
$490$	4.87164	−	5.19751i	0.220078	−	0.234800i
$491$		−	17.7599i		−	0.801493i	−0.916189	−	0.400746i	$-0.868751\pi$
$491$		−	17.7599i		−	0.801493i	0.916189	−	0.400746i	$-0.131249\pi$
$492$	0.156014	−	0.0794932i	0.00703366	−	0.00358383i
$493$	4.05153	+	25.5803i	0.182472	+	1.15208i
$494$	−4.64063	+	3.37162i	−0.208792	+	0.151696i
$495$	−1.23045	−	38.0200i	−0.0553047	−	1.70887i
$496$	−5.27084	−	1.79394i	−0.236668	−	0.0805505i
$497$	−2.13636	+	2.13636i	−0.0958287	+	0.0958287i
$498$	0.111129	+	0.0176011i	0.00497982	+	0.000788725i
$499$	15.8163	+	11.4912i	0.708035	+	0.514417i	0.882539	−	0.470239i	$-0.155832\pi$
$499$	15.8163	+	11.4912i	0.708035	+	0.514417i	−0.174504	+	0.984656i	$0.555832\pi$
$500$	−2.40826	+	10.9179i	−0.107701	+	0.488263i
$501$	−0.678389			−0.0303082
$502$	9.92454	+	9.92454i	0.442954	+	0.442954i
$503$	3.68478	−	1.87749i	0.164296	−	0.0837130i	−0.369909	−	0.929068i	$-0.620611\pi$
$503$	3.68478	−	1.87749i	0.164296	−	0.0837130i	0.534205	+	0.845355i	$0.320611\pi$
$504$	5.57001	−	1.80981i	0.248108	−	0.0806152i
$505$	1.54998	−	0.559666i	0.0689731	−	0.0249048i
$506$	−0.203048	+	0.147523i	−0.00902656	+	0.00655818i
$507$	0.119360	−	0.0608170i	0.00530097	−	0.00270098i
$508$	−2.19161	+	13.8373i	−0.0972370	+	0.613930i
$509$	4.51246	+	3.27849i	0.200011	+	0.145317i	0.683283	−	0.730154i	$-0.260552\pi$
$509$	4.51246	+	3.27849i	0.200011	+	0.145317i	−0.483272	+	0.875471i	$0.660552\pi$
$510$	0.0914176	−	0.194745i	0.00404804	−	0.00862346i
$511$	−9.08225	+	12.5006i	−0.401775	+	0.552996i
$512$	0.987688	−	0.156434i	0.0436501	−	0.00691349i
$513$	−0.350443	−	0.178560i	−0.0154724	−	0.00788360i
$514$	−3.27699	+	4.51039i	−0.144542	+	0.198945i
$515$	2.41982	−	19.3001i	0.106630	−	0.850464i
$516$	−0.0556832	+	0.171375i	−0.00245131	+	0.00754437i
$517$	−14.1194	−	2.23629i	−0.620970	−	0.0983520i
$518$	6.40727	+	3.26467i	0.281519	+	0.143441i
$519$	0.187990	+	0.578573i	0.00825183	+	0.0253965i
$520$	−6.48602	−	1.87778i	−0.284431	−	0.0823461i
$521$	18.6021			0.814972			0.407486	−	0.913212i	$-0.366406\pi$
$521$	18.6021			0.814972			0.407486	+	0.913212i	$0.366406\pi$
$522$	19.7023	+	19.7023i	0.862348	+	0.862348i
$523$	13.6136	+	26.7183i	0.595283	+	1.16831i	0.970439	+	0.241346i	$0.0775890\pi$
$523$	13.6136	+	26.7183i	0.595283	+	1.16831i	−0.375156	+	0.926962i	$0.622411\pi$
$524$	−12.7298	+	17.5211i	−0.556104	+	0.765412i
$525$	0.215329	+	0.259299i	0.00939774	+	0.0113167i
$526$			20.3210i			0.886039i
$527$	2.64057	−	15.2934i	0.115025	−	0.666191i
$528$	−0.138456	−	0.138456i	−0.00602554	−	0.00602554i
$529$	−13.5179	−	18.6058i	−0.587735	−	0.808948i
$530$	−22.8140	−	15.4732i	−0.990978	−	0.672113i
$531$	−2.59596	+	7.98956i	−0.112655	+	0.346717i
$532$	−2.62322	+	2.62322i	−0.113731	+	0.113731i
$533$	10.8322	−	10.8322i	0.469195	−	0.469195i
$534$	0.477757	+	0.155233i	0.0206746	+	0.00671758i
$535$	−6.14928	+	13.0997i	−0.265856	+	0.566349i
$536$	−3.28342	−	10.1053i	−0.141822	−	0.436483i
$537$	−0.0720118	+	0.454665i	−0.00310754	+	0.0196202i
$538$	7.06206	+	13.8601i	0.304467	+	0.597550i
$539$	14.6212	−	10.6229i	0.629780	−	0.457562i
$540$	−0.0871816	−	0.454709i	−0.00375170	−	0.0195676i
$541$	−3.23443	−	9.95456i	−0.139059	−	0.427980i	0.857140	−	0.515083i	$-0.172239\pi$
$541$	−3.23443	−	9.95456i	−0.139059	−	0.427980i	−0.996199	+	0.0871034i	$0.972239\pi$
$542$	2.42258	+	15.2956i	0.104059	+	0.657000i
$543$	0.0729455	+	0.460560i	0.00313039	+	0.0197645i
$544$	0.861360	+	2.65099i	0.0369305	+	0.113660i
$545$	−2.92572	−	1.98432i	−0.125324	−	0.0849988i
$546$	−0.164684	+	0.119650i	−0.00704785	+	0.00512056i
$547$	−2.92976	−	5.74997i	−0.125267	−	0.245851i	0.819853	−	0.572575i	$-0.194055\pi$
$547$	−2.92976	−	5.74997i	−0.125267	−	0.245851i	−0.945120	+	0.326724i	$0.894055\pi$
$548$	0.987694	−	6.23606i	0.0421922	−	0.266391i
$549$	6.06970	+	18.6806i	0.259048	+	0.797269i
$550$	−11.2162	+	26.0527i	−0.478258	+	1.11089i
$551$	−16.7857	−	5.45400i	−0.715094	−	0.232348i
$552$	−0.00107980	+	0.00107980i	−4.59592e−5	+	4.59592e-5i
$553$	2.84496	−	2.84496i	0.120980	−	0.120980i
$554$	−2.80063	+	8.61945i	−0.118987	+	0.366205i
$555$	0.159515	−	0.235192i	0.00677102	−	0.00998335i
$556$	−2.99877	−	4.12745i	−0.127176	−	0.175043i
$557$	−19.1191	−	19.1191i	−0.810104	−	0.810104i	0.174545	−	0.984649i	$-0.444155\pi$
$557$	−19.1191	−	19.1191i	−0.810104	−	0.810104i	−0.984649	+	0.174545i	$0.944155\pi$
$558$	−7.37268	−	14.9807i	−0.312111	−	0.634184i
$559$			15.7649i			0.666782i
$560$	−4.33310	−	0.543278i	−0.183107	−	0.0229577i
$561$	0.320811	−	0.441558i	0.0135446	−	0.0186426i
$562$	2.17904	+	4.27660i	0.0919171	+	0.180397i
$563$	−4.58638	−	4.58638i	−0.193293	−	0.193293i	0.603824	−	0.797117i	$-0.293643\pi$
$563$	−4.58638	−	4.58638i	−0.193293	−	0.193293i	−0.797117	+	0.603824i	$0.793643\pi$
$564$	−0.0869788			−0.00366247
$565$	18.1121	+	32.8728i	0.761981	+	1.38297i
$566$	−1.32276	−	4.07104i	−0.0555997	−	0.171118i
$567$	15.6425	+	7.97026i	0.656924	+	0.334720i
$568$	−1.52794	−	0.242003i	−0.0641111	−	0.0101542i
$569$	−1.71123	+	5.26663i	−0.0717386	+	0.220789i	−0.980497	−	0.196534i	$-0.937031\pi$
$569$	−1.71123	+	5.26663i	−0.0717386	+	0.220789i	0.908758	+	0.417322i	$0.137031\pi$
$570$	0.0899652	+	0.115759i	0.00376823	+	0.00484859i
$571$	−18.1616	+	24.9974i	−0.760041	+	1.04611i	0.237170	+	0.971468i	$0.423780\pi$
$571$	−18.1616	+	24.9974i	−0.760041	+	1.04611i	−0.997211	+	0.0746385i	$0.976220\pi$
$572$	−15.2636	−	7.77720i	−0.638204	−	0.325181i
$573$	−0.805141	+	0.127522i	−0.0336352	+	0.00532730i
$574$	5.82345	−	8.01529i	0.243066	−	0.334552i
$575$	0.203181	+	0.0874728i	0.00847322	+	0.00364787i
$576$	2.42609	+	1.76266i	0.101087	+	0.0734440i
$577$	4.34118	−	27.4091i	0.180726	−	1.14106i	−0.715879	−	0.698224i	$-0.753974\pi$
$577$	4.34118	−	27.4091i	0.180726	−	1.14106i	0.896605	−	0.442832i	$-0.146026\pi$
$578$	8.22425	−	4.19047i	0.342084	−	0.174300i
$579$	−0.726470	+	0.527811i	−0.0301911	+	0.0219351i
$580$	−7.05603	−	19.5415i	−0.292986	−	0.811415i
$581$	6.05470	−	1.96729i	0.251191	−	0.0816170i
$582$	0.371217	−	0.189145i	0.0153875	−	0.00784030i
$583$	−49.4520	−	49.4520i	−2.04809	−	2.04809i
$584$	−7.91177			−0.327391
$585$	−9.77167	−	17.7352i	−0.404009	−	0.733262i
$586$	−2.99923	−	2.17907i	−0.123897	−	0.0900166i
$587$	3.23281	+	0.512027i	0.133432	+	0.0211336i	0.222793	−	0.974866i	$-0.428482\pi$
$587$	3.23281	+	0.512027i	0.133432	+	0.0211336i	−0.0893610	+	0.995999i	$0.528482\pi$
$588$	0.0777549	−	0.0777549i	0.00320656	−	0.00320656i
$589$	8.46912	+	6.33482i	0.348964	+	0.261022i
$590$	4.28374	−	4.57028i	0.176359	−	0.188156i
$591$	−0.141191	+	0.102582i	−0.00580784	+	0.00421964i
$592$	0.576001	+	3.63673i	0.0236735	+	0.149469i
$593$	−3.39823	+	1.73148i	−0.139549	+	0.0711036i	−0.522371	−	0.852719i	$-0.674952\pi$
$593$	−3.39823	+	1.73148i	−0.139549	+	0.0711036i	0.382822	+	0.923822i	$0.374952\pi$
$594$		−	1.17461i		−	0.0481948i
$595$	−0.393744	−	12.1664i	−0.0161419	−	0.498773i
$596$	5.56259	−	17.1199i	0.227853	−	0.701259i
$597$	0.105961	+	0.0539898i	0.00433669	+	0.00220965i
$598$	−0.0606530	+	0.119038i	−0.00248029	+	0.00486784i
$599$	−19.1192	−	26.3153i	−0.781190	−	1.07522i	−0.995150	−	0.0983730i	$-0.968636\pi$
$599$	−19.1192	−	26.3153i	−0.781190	−	1.07522i	0.213960	−	0.976842i	$-0.431364\pi$
$600$	−0.0426061	+	0.167239i	−0.00173939	+	0.00682751i
$601$	−0.678554	−	0.933950i	−0.0276788	−	0.0380966i	0.794953	−	0.606671i	$-0.207495\pi$
$601$	−0.678554	−	0.933950i	−0.0276788	−	0.0380966i	−0.822632	+	0.568574i	$0.807495\pi$
$602$	1.59497	+	10.0702i	0.0650061	+	0.410432i
$603$	14.4657	−	28.3905i	0.589089	−	1.15615i
$604$	−1.26484	−	0.918962i	−0.0514657	−	0.0373920i
$605$	−26.5859	+	39.1988i	−1.08087	+	1.59366i
$606$	0.0241925	−	0.00786063i	0.000982755	−	0.000319316i
$607$	−35.8154	+	5.67260i	−1.45370	+	0.230244i	−0.832769	−	0.553620i	$-0.813246\pi$
$607$	−35.8154	+	5.67260i	−1.45370	+	0.230244i	−0.620933	+	0.783864i	$0.713246\pi$
$608$	−1.87615	−	0.297154i	−0.0760881	−	0.0120512i
$609$	−0.595682	−	0.193549i	−0.0241382	−	0.00784299i
$610$	1.82204	−	14.5323i	0.0737721	−	0.588395i
$611$	−7.23716	+	2.35149i	−0.292784	+	0.0951313i
$612$	−3.79488	+	7.44787i	−0.153399	+	0.301062i
$613$	−15.7653	−	30.9411i	−0.636753	−	1.24970i	−0.953558	−	0.301208i	$-0.902610\pi$
$613$	−15.7653	−	30.9411i	−0.636753	−	1.24970i	0.316805	−	0.948491i	$-0.397390\pi$
$614$		−	16.7847i		−	0.677376i
$615$	−0.285666	−	0.267755i	−0.0115192	−	0.0107969i
$616$	−10.5369	−	3.42365i	−0.424544	−	0.137943i
$617$	22.6571	−	3.58854i	0.912141	−	0.144469i	0.317312	−	0.948321i	$-0.397220\pi$
$617$	22.6571	−	3.58854i	0.912141	−	0.144469i	0.594829	+	0.803852i	$0.297220\pi$
$618$	0.0469696	−	0.296554i	0.00188939	−	0.0119292i
$619$	5.60182			0.225156			0.112578	−	0.993643i	$-0.464089\pi$
$619$	5.60182			0.225156			0.112578	+	0.993643i	$0.464089\pi$
$620$	0.229772	+	12.4478i	0.00922786	+	0.499915i
$621$	−0.00916057			−0.000367601
$622$	−4.46686	+	28.2027i	−0.179105	+	1.13082i
$623$	28.0737	−	4.44643i	1.12475	−	0.178143i
$624$	−0.0991289	−	0.0322089i	−0.00396833	−	0.00128939i
$625$	24.7910	−	3.22618i	0.991638	−	0.129047i
$626$			5.81268i			0.232321i
$627$	0.168859	+	0.331404i	0.00674357	+	0.0132350i
$628$	−1.40940	+	2.76611i	−0.0562413	+	0.110380i
$629$	−9.76112	+	3.17158i	−0.389201	+	0.126459i
$630$	−8.03624	−	10.3403i	−0.320172	−	0.411966i
$631$	25.9756	+	8.43999i	1.03407	+	0.335991i	0.776399	−	0.630241i	$-0.217044\pi$
$631$	25.9756	+	8.43999i	1.03407	+	0.335991i	0.257674	+	0.966232i	$0.417044\pi$
$632$	2.03475	+	0.322272i	0.0809379	+	0.0128193i
$633$	0.186927	−	0.0296063i	0.00742967	−	0.00117674i
$634$	−7.31944	+	2.37823i	−0.290692	+	0.0944515i
$635$	30.7664	−	5.89886i	1.22093	−	0.234089i
$636$	−0.344250	−	0.250112i	−0.0136504	−	0.00991759i
$637$	4.36755	−	8.57180i	0.173049	−	0.339627i
$638$	−8.24559	−	52.0606i	−0.326446	−	2.06110i
$639$	−2.72681	−	3.75313i	−0.107871	−	0.148472i
$640$	−1.07907	−	1.95847i	−0.0426539	−	0.0774154i
$641$	23.4107	+	32.2221i	0.924667	+	1.27270i	0.961904	+	0.273389i	$0.0881445\pi$
$641$	23.4107	+	32.2221i	0.924667	+	1.27270i	−0.0372366	+	0.999306i	$0.511856\pi$
$642$	−0.101412	+	0.199032i	−0.00400241	+	0.00785517i
$643$	−32.3484	−	16.4824i	−1.27570	−	0.650001i	−0.320860	−	0.947127i	$-0.603972\pi$
$643$	−32.3484	−	16.4824i	−1.27570	−	0.650001i	−0.954838	+	0.297126i	$0.903972\pi$
$644$	−0.0267004	+	0.0821755i	−0.00105214	+	0.00323817i
$645$	0.402716	−	0.0130332i	0.0158569	−	0.000513183i
$646$		−	5.29482i		−	0.208322i
$647$	−10.9972	+	5.60337i	−0.432346	+	0.220291i	−0.656599	−	0.754240i	$-0.728006\pi$
$647$	−10.9972	+	5.60337i	−0.432346	+	0.220291i	0.224253	+	0.974531i	$0.428006\pi$
$648$	1.40623	+	8.87861i	0.0552421	+	0.348785i
$649$	12.8567	−	9.34097i	0.504671	−	0.366665i
$650$	0.976269	+	15.0672i	0.0382924	+	0.590983i
$651$	0.300548	+	0.224807i	0.0117794	+	0.00881088i
$652$	16.7926	−	16.7926i	0.657650	−	0.657650i
$653$	−20.0699	−	3.17876i	−0.785396	−	0.124395i	−0.249160	−	0.968462i	$-0.580154\pi$
$653$	−20.0699	−	3.17876i	−0.785396	−	0.124395i	−0.536237	+	0.844068i	$0.680154\pi$
$654$	−0.0441473	−	0.0320749i	−0.00172630	−	0.00125423i
$655$	46.5168	+	13.4672i	1.81756	+	0.526206i
$656$	5.07295			0.198065
$657$	−16.7767	−	16.7767i	−0.654523	−	0.654523i
$658$	−4.38503	+	2.23428i	−0.170946	+	0.0871015i
$659$	−10.9403	+	3.55473i	−0.426175	+	0.138473i	−0.514248	−	0.857641i	$-0.671929\pi$
$659$	−10.9403	+	3.55473i	−0.426175	+	0.138473i	0.0880735	+	0.996114i	$0.471929\pi$
$660$	−0.186051	+	0.396342i	−0.00724204	+	0.0154276i
$661$	−4.65235	+	3.38013i	−0.180956	+	0.131472i	−0.674576	−	0.738206i	$-0.735673\pi$
$661$	−4.65235	+	3.38013i	−0.180956	+	0.131472i	0.493620	+	0.869678i	$0.335673\pi$
$662$	−31.4820	+	16.0409i	−1.22358	+	0.623446i
$663$	0.0454495	−	0.286957i	0.00176511	−	0.0111445i
$664$	2.63720	+	1.91604i	0.102343	+	0.0743567i
$665$	7.50916	+	3.52496i	0.291193	+	0.136692i
$666$	−6.49021	+	8.93300i	−0.251490	+	0.346147i
$667$	−0.406012	+	0.0643060i	−0.0157208	+	0.00248994i
$668$	−17.5120	−	8.92283i	−0.677561	−	0.345235i
$669$	0.537859	−	0.740300i	0.0207948	−	0.0286216i
$670$	−18.7597	+	14.5796i	−0.724750	+	0.563261i
$671$	11.4822	−	35.3385i	0.443264	−	1.36423i
$672$	−0.0665800	−	0.0105452i	−0.00256838	−	0.000406791i
$673$	3.30924	+	1.68614i	0.127562	+	0.0649960i	0.516607	−	0.856223i	$-0.327195\pi$
$673$	3.30924	+	1.68614i	0.127562	+	0.0649960i	−0.389045	+	0.921219i	$0.627195\pi$
$674$	−1.40747	−	4.33174i	−0.0542136	−	0.166852i
$675$	−0.890121	+	0.528668i	−0.0342608	+	0.0203484i
$676$	3.88110			0.149273
$677$	−27.2168	−	27.2168i	−1.04603	−	1.04603i	−0.998888	−	0.0471380i	$-0.984990\pi$
$677$	−27.2168	−	27.2168i	−1.04603	−	1.04603i	−0.0471380	−	0.998888i	$-0.515010\pi$
$678$	0.263020	+	0.516206i	0.0101012	+	0.0198248i
$679$	13.8562	−	19.0714i	0.531752	−	0.731894i
$680$	4.92135	−	3.82477i	0.188725	−	0.146673i
$681$		−	0.743538i		−	0.0284924i
$682$	−5.37404	+	31.1249i	−0.205783	+	1.19183i
$683$	−25.6664	−	25.6664i	−0.982096	−	0.982096i	0.0177469	−	0.999843i	$-0.494351\pi$
$683$	−25.6664	−	25.6664i	−0.982096	−	0.982096i	−0.999843	+	0.0177469i	$0.994351\pi$
$684$	−3.34824	−	4.60845i	−0.128023	−	0.176209i
$685$	−13.8655	+	2.65844i	−0.529774	+	0.101574i
$686$	6.14722	−	18.9192i	0.234702	−	0.722339i
$687$	0.530301	−	0.530301i	0.0202323	−	0.0202323i
$688$	−3.69151	+	3.69151i	−0.140737	+	0.140737i
$689$	−35.4055	−	11.5039i	−1.34884	−	0.438265i
$690$	0.00309100	+	0.00145098i	0.000117672	+	5.52379e-5i
$691$	11.7796	+	36.2539i	0.448117	+	1.37916i	0.879029	+	0.476769i	$0.158192\pi$
$691$	11.7796	+	36.2539i	0.448117	+	1.37916i	−0.430912	+	0.902394i	$0.641808\pi$
$692$	−2.75716	+	17.4080i	−0.104811	+	0.661753i
$693$	−15.0835	−	29.6030i	−0.572975	−	1.12453i
$694$	19.4595	−	14.1381i	0.738672	−	0.536677i
$695$	−6.40341	+	9.44133i	−0.242895	+	0.358130i
$696$	−0.0991036	−	0.305009i	−0.00375651	−	0.0115614i
$697$	2.21205	+	13.9663i	0.0837874	+	0.529013i
$698$	−0.580160	−	3.66299i	−0.0219594	−	0.138646i
$699$	0.0829846	+	0.255400i	0.00313877	+	0.00966013i
$700$	2.14800	+	9.52580i	0.0811868	+	0.360041i
$701$	−4.31349	+	3.13393i	−0.162918	+	0.118367i	−0.666257	−	0.745722i	$-0.732105\pi$
$701$	−4.31349	+	3.13393i	−0.162918	+	0.118367i	0.503339	+	0.864089i	$0.332105\pi$
$702$	−0.283861	−	0.557109i	−0.0107136	−	0.0210267i
$703$	1.09414	−	6.90811i	0.0412662	−	0.260544i
$704$	−1.75302	−	5.39525i	−0.0660696	−	0.203341i
$705$	0.0660526	+	0.182931i	0.00248768	+	0.00688956i
$706$	15.7751	+	5.12564i	0.593703	+	0.192906i
$707$	1.01774	−	1.01774i	0.0382762	−	0.0382762i
$708$	0.0683716	−	0.0683716i	0.00256956	−	0.00256956i
$709$	0.0256596	−	0.0789722i	0.000963667	−	0.00296586i	−0.950574	−	0.310500i	$-0.899504\pi$
$709$	0.0256596	−	0.0789722i	0.000963667	−	0.00296586i	0.951537	+	0.307534i	$0.0995037\pi$
$710$	0.651366	+	3.39730i	0.0244453	+	0.127498i
$711$	3.63127	+	4.99801i	0.136183	+	0.187440i
$712$	10.2911	+	10.2911i	0.385676	+	0.385676i
$713$	0.242737	+	0.0419112i	0.00909059	+	0.00156959i
$714$		−	0.187900i		−	0.00703197i
$715$	−4.76538	+	38.0080i	−0.178215	+	1.42142i
$716$	−7.83912	+	10.7896i	−0.292961	+	0.403227i
$717$	−0.179389	−	0.352071i	−0.00669940	−	0.0131483i
$718$	20.3325	+	20.3325i	0.758803	+	0.758803i
$719$	42.7233			1.59331			0.796655	−	0.604435i	$-0.206601\pi$
$719$	42.7233			1.59331			0.796655	+	0.604435i	$0.206601\pi$
$720$	1.86476	−	6.44104i	0.0694954	−	0.240043i
$721$	−5.24983	−	16.1573i	−0.195514	−	0.601730i
$722$	−13.7141	−	6.98771i	−0.510388	−	0.260055i
$723$	0.415190	+	0.0657596i	0.0154411	+	0.00244563i
$724$	−4.17471	+	12.8484i	−0.155152	+	0.477508i
$725$	−35.7405	+	29.6800i	−1.32737	+	1.10229i
$726$	−0.429739	+	0.591486i	−0.0159491	+	0.0219521i
$727$	26.1859	+	13.3424i	0.971180	+	0.494841i	0.866235	−	0.499637i	$-0.166533\pi$
$727$	26.1859	+	13.3424i	0.971180	+	0.494841i	0.104945	+	0.994478i	$0.466533\pi$
$728$	−5.82495	+	0.922581i	−0.215887	+	0.0341931i
$729$	−15.8324	+	21.7914i	−0.586385	+	0.807090i
$730$	6.00828	+	16.6397i	0.222376	+	0.615864i
$731$	−11.7728	−	8.55342i	−0.435432	−	0.316360i
$732$	0.0353664	−	0.223295i	0.00130718	−	0.00825321i
$733$	−25.9516	+	13.2230i	−0.958544	+	0.488403i	−0.861990	−	0.506925i	$-0.830782\pi$
$733$	−25.9516	+	13.2230i	−0.958544	+	0.488403i	−0.0965539	+	0.995328i	$0.530782\pi$
$734$	−13.3404	+	9.69237i	−0.492403	+	0.357752i
$735$	−0.222579	−	0.104483i	−0.00820995	−	0.00385393i
$736$	−0.0420766	+	0.0136715i	−0.00155097	+	0.000503939i
$737$	−53.7069	+	27.3650i	−1.97832	+	1.00800i
$738$	10.7571	+	10.7571i	0.395973	+	0.395973i
$739$	16.6028			0.610745			0.305373	−	0.952233i	$-0.401219\pi$
$739$	16.6028			0.610745			0.305373	+	0.952233i	$0.401219\pi$
$740$	7.21121	−	3.97319i	0.265089	−	0.146058i
$741$	0.160177	+	0.116375i	0.00588425	+	0.00427516i
$742$	−23.7801	−	3.76640i	−0.872996	−	0.138269i
$743$	−24.9154	+	24.9154i	−0.914056	+	0.914056i	−0.996588	−	0.0825327i	$-0.973699\pi$
$743$	−24.9154	+	24.9154i	−0.914056	+	0.914056i	0.0825327	+	0.996588i	$0.473699\pi$
$744$	−0.00267028	+	0.192159i	−9.78971e−5	+	0.00704491i
$745$	−40.2303	+	1.30198i	−1.47392	+	0.0477010i
$746$	19.3784	−	14.0792i	0.709492	−	0.515476i
$747$	1.52921	+	9.65504i	0.0559508	+	0.353259i
$748$	14.0893	−	7.17884i	0.515155	−	0.262485i
$749$			12.6392i			0.461827i
$750$	0.384087	−	0.0373954i	0.0140249	−	0.00136549i
$751$	13.1028	−	40.3263i	0.478128	−	1.47153i	−0.363564	−	0.931569i	$-0.618440\pi$
$751$	13.1028	−	40.3263i	0.478128	−	1.47153i	0.841692	−	0.539958i	$-0.181560\pi$
$752$	−2.24528	−	1.14403i	−0.0818771	−	0.0417185i
$753$	0.219935	−	0.431647i	0.00801489	−	0.0157301i
$754$	−16.4920	−	22.6993i	−0.600604	−	0.826660i
$755$	−0.972192	+	3.35804i	−0.0353817	+	0.122212i
$756$	−0.237688	−	0.327150i	−0.00864464	−	0.0118983i
$757$	−1.49414	−	9.43363i	−0.0543055	−	0.342871i	−0.999849	−	0.0173757i	$-0.994469\pi$
$757$	−1.49414	−	9.43363i	−0.0543055	−	0.342871i	0.945544	−	0.325496i	$-0.105531\pi$
$758$	7.88592	−	15.4770i	0.286429	−	0.562149i
$759$	0.00700843	+	0.00509192i	0.000254390	+	0.000184825i
$760$	0.799808	+	4.17152i	0.0290121	+	0.151317i
$761$	42.2928	−	13.7418i	1.53311	−	0.498138i	0.583646	−	0.812008i	$-0.301625\pi$
$761$	42.2928	−	13.7418i	1.53311	−	0.498138i	0.949466	+	0.313869i	$0.101625\pi$
$762$	0.477610	−	0.0756460i	0.0173020	−	0.00274037i
$763$	−3.04962	−	0.483012i	−0.110403	−	0.0174862i
$764$	−22.4613	−	7.29813i	−0.812622	−	0.264037i
$765$	18.5460	+	2.32526i	0.670530	+	0.0840700i
$766$	25.7439	−	8.36471i	0.930167	−	0.302229i
$767$	3.84048	−	7.53737i	0.138672	−	0.272159i
$768$	−0.0156700	−	0.0307541i	−0.000565443	−	0.00110974i
$769$		−	14.3245i		−	0.516554i	−0.966071	−	0.258277i	$-0.916845\pi$
$769$		−	14.3245i		−	0.516554i	0.966071	−	0.258277i	$-0.0831547\pi$
$770$	0.801341	+	24.7608i	0.0288783	+	0.892316i
$771$	0.183015	+	0.0594650i	0.00659111	+	0.00214158i
$772$	−25.6955	+	4.06977i	−0.924801	+	0.146474i
$773$	1.97695	−	12.4820i	0.0711059	−	0.448945i	−0.926289	−	0.376813i	$-0.877020\pi$
$773$	1.97695	−	12.4820i	0.0711059	−	0.448945i	0.997395	−	0.0721317i	$-0.0229802\pi$
$774$	−15.6555			−0.562726
$775$	26.0052	−	9.93622i	0.934135	−	0.356919i
$776$	12.0705			0.433305
$777$	0.0388282	−	0.245152i	0.00139295	−	0.00879477i
$778$	10.5181	−	1.66590i	0.377092	−	0.0597256i
$779$	−9.16464	−	2.97777i	−0.328357	−	0.106690i
$780$	0.00753884	+	0.232944i	0.000269934	+	0.00834073i
$781$			8.77593i			0.314027i
$782$	−0.0559866	−	0.109880i	−0.00200207	−	0.00392929i
$783$	0.873411	−	1.71417i	0.0312132	−	0.0612593i
$784$	3.02989	−	0.984470i	0.108210	−	0.0351596i
$785$	6.88789	+	0.863593i	0.245839	+	0.0308230i
$786$	0.710939	+	0.230998i	0.0253583	+	0.00823943i
$787$	−17.0852	−	2.70603i	−0.609021	−	0.0964595i	−0.155696	−	0.987805i	$-0.549762\pi$
$787$	−17.0852	−	2.70603i	−0.609021	−	0.0964595i	−0.453325	+	0.891346i	$0.649762\pi$
$788$	−4.99399	+	0.790970i	−0.177904	+	0.0281772i
$789$	0.667075	−	0.216746i	0.0237485	−	0.00771635i
$790$	−0.867417	−	4.52414i	−0.0308613	−	0.160962i
$791$	26.5203	+	19.2681i	0.942953	+	0.685095i
$792$	7.72327	−	15.1578i	0.274434	−	0.538608i
$793$	−3.09414	−	19.5356i	−0.109876	−	0.693730i
$794$	18.4017	+	25.3278i	0.653052	+	0.898848i
$795$	−0.264600	+	0.913951i	−0.00938439	+	0.0324145i
$796$	2.02517	+	2.78740i	0.0717801	+	0.0987969i
$797$	−16.1881	+	31.7709i	−0.573411	+	1.12538i	0.404143	+	0.914696i	$0.367570\pi$
$797$	−16.1881	+	31.7709i	−0.573411	+	1.12538i	−0.977554	+	0.210686i	$0.932430\pi$
$798$	0.114092	+	0.0581325i	0.00403880	+	0.00205787i
$799$	2.17058	−	6.68035i	0.0767895	−	0.236334i
$800$	−3.29953	+	3.75674i	−0.116656	+	0.132821i
$801$			43.6442i			1.54209i
$802$	23.1666	−	11.8040i	0.818040	−	0.416812i
$803$	7.02120	+	44.3301i	0.247773	+	1.56438i
$804$	−0.296705	+	0.215568i	−0.0104640	+	0.00760251i
$805$	0.193105	−	0.00624952i	0.00680606	−	0.000220267i
$806$	4.97290	+	16.0610i	0.175163	+	0.565725i
$807$	0.379658	−	0.379658i	0.0133646	−	0.0133646i
$808$	0.727901	+	0.115288i	0.0256075	+	0.00405582i
$809$	15.4769	+	11.2446i	0.544138	+	0.395339i	0.825620	−	0.564227i	$-0.190826\pi$
$809$	15.4769	+	11.2446i	0.544138	+	0.395339i	−0.281482	+	0.959567i	$0.590826\pi$
$810$	17.6053	−	9.70004i	0.618585	−	0.340825i
$811$	−39.0122			−1.36990			−0.684952	−	0.728589i	$-0.740177\pi$
$811$	−39.0122			−1.36990			−0.684952	+	0.728589i	$0.740177\pi$
$812$	−12.8313	−	12.8313i	−0.450290	−	0.450290i
$813$	0.476265	−	0.242669i	0.0167034	−	0.00851078i
$814$	19.8657	−	6.45474i	0.696291	−	0.226239i
$815$	−48.0701	−	22.5652i	−1.68382	−	0.790423i
$816$	0.0778364	−	0.0565515i	0.00272482	−	0.00197970i
$817$	8.83585	−	4.50209i	0.309127	−	0.157508i
$818$	0.0982336	−	0.620223i	0.00343466	−	0.0216856i
$819$	−14.3080	−	10.3954i	−0.499962	−	0.363243i
$820$	−3.85245	−	10.6692i	−0.134533	−	0.372586i
$821$	−12.2496	+	16.8601i	−0.427513	+	0.588421i	−0.967380	−	0.253329i	$-0.918474\pi$
$821$	−12.2496	+	16.8601i	−0.427513	+	0.588421i	0.539868	+	0.841750i	$0.318474\pi$
$822$	−0.215245	+	0.0340914i	−0.00750753	+	0.00118908i
$823$	3.71205	+	1.89138i	0.129394	+	0.0659294i	0.517489	−	0.855690i	$-0.326867\pi$
$823$	3.71205	+	1.89138i	0.129394	+	0.0659294i	−0.388095	+	0.921619i	$0.626867\pi$
$824$	5.11305	−	7.03751i	0.178122	−	0.245163i
$825$	0.974861	+	0.0903104i	0.0339403	+	0.00314420i
$826$	1.69064	−	5.20326i	0.0588249	−	0.181044i
$827$	39.2796	+	6.22128i	1.36589	+	0.216335i	0.795954	−	0.605357i	$-0.206970\pi$
$827$	39.2796	+	6.22128i	1.36589	+	0.216335i	0.569932	+	0.821692i	$0.306970\pi$
$828$	−0.118213	−	0.0602324i	−0.00410818	−	0.00209322i
$829$	−1.47597	−	4.54258i	−0.0512626	−	0.157770i	0.922148	−	0.386837i	$-0.126432\pi$
$829$	−1.47597	−	4.54258i	−0.0512626	−	0.157770i	−0.973411	+	0.229067i	$0.926432\pi$
$830$	2.02702	−	7.00152i	0.0703590	−	0.243026i
$831$	0.312821			0.0108516
$832$	−2.13529	−	2.13529i	−0.0740277	−	0.0740277i
$833$	4.03152	+	7.91231i	0.139684	+	0.274145i
$834$	−0.103506	+	0.142464i	−0.00358412	+	0.00493312i
$835$	−5.46735	+	43.6068i	−0.189205	+	1.50907i
$836$			10.7759i			0.372693i
$837$	−0.826428	+	0.803775i	−0.0285655	+	0.0277825i
$838$	−9.28366	−	9.28366i	−0.320699	−	0.320699i
$839$	−12.2154	−	16.8131i	−0.421722	−	0.580451i	0.544306	−	0.838887i	$-0.316793\pi$
$839$	−12.2154	−	16.8131i	−0.421722	−	0.580451i	−0.966028	+	0.258436i	$0.916793\pi$
$840$	0.0283832	+	0.148037i	0.000979313	+	0.00510775i
$841$	17.7163	−	54.5253i	0.610908	−	1.88018i
$842$	18.3721	−	18.3721i	0.633146	−	0.633146i
$843$	0.117145	−	0.117145i	0.00403470	−	0.00403470i
$844$	5.21477	+	1.69438i	0.179500	+	0.0583230i
$845$	−2.94735	−	8.16260i	−0.101392	−	0.280802i
$846$	−2.33519	−	7.18697i	−0.0802854	−	0.247093i
$847$	−6.47139	+	40.8587i	−0.222359	+	1.40392i
$848$	−5.59680	−	10.9843i	−0.192195	−	0.377204i
$849$	−0.119531	+	0.0868440i	−0.00410228	+	0.00298048i
$850$	−11.7814	−	7.44583i	−0.404100	−	0.255390i
$851$	−0.0503394	−	0.154929i	−0.00172561	−	0.00531089i
$852$	0.00835301	+	0.0527388i	0.000286169	+	0.00180680i
$853$	−6.04464	−	38.1643i	−0.206964	−	1.30672i	−0.844190	−	0.536044i	$-0.819918\pi$
$853$	−6.04464	−	38.1643i	−0.206964	−	1.30672i	0.637225	−	0.770677i	$-0.280082\pi$
$854$	−3.95293	−	12.1659i	−0.135267	−	0.416308i
$855$	−7.14964	+	10.5416i	−0.244513	+	0.360515i
$856$	−5.23573	+	3.80398i	−0.178953	+	0.130017i
$857$	8.59517	+	16.8690i	0.293605	+	0.576233i	0.989941	−	0.141484i	$-0.0451873\pi$
$857$	8.59517	+	16.8690i	0.293605	+	0.576233i	−0.696335	+	0.717717i	$0.745187\pi$
$858$	−0.0924979	+	0.584009i	−0.00315783	+	0.0199377i
$859$	8.68131	+	26.7183i	0.296202	+	0.911617i	0.982815	+	0.184594i	$0.0590969\pi$
$859$	8.68131	+	26.7183i	0.296202	+	0.911617i	−0.686612	+	0.727024i	$0.740903\pi$
$860$	10.5672	+	4.96048i	0.360339	+	0.169151i
$861$	−0.325230	−	0.105674i	−0.0110838	−	0.00360135i
$862$	2.10367	−	2.10367i	0.0716514	−	0.0716514i
$863$	−1.67208	+	1.67208i	−0.0569184	+	0.0569184i	−0.734993	−	0.678075i	$-0.762815\pi$
$863$	−1.67208	+	1.67208i	−0.0569184	+	0.0569184i	0.678075	+	0.734993i	$0.262815\pi$
$864$	0.0639838	−	0.196922i	0.00217677	−	0.00669942i
$865$	38.7057	−	7.42106i	1.31603	−	0.252324i
$866$	−6.72468	−	9.25573i	−0.228514	−	0.314523i
$867$	−0.225280	−	0.225280i	−0.00765092	−	0.00765092i
$868$	4.80151	+	9.75630i	0.162974	+	0.331150i
$869$		−	11.6868i		−	0.396448i
$870$	−0.566224	+	0.440058i	−0.0191968	+	0.0149194i
$871$	−18.8596	+	25.9581i	−0.639035	+	0.879556i
$872$	−0.717746	−	1.40866i	−0.0243059	−	0.0477031i
$873$	25.5952	+	25.5952i	0.866266	+	0.866266i
$874$	0.0840395			0.00284268
$875$	18.4031	−	11.7516i	0.622138	−	0.397276i
$876$	0.0843876	+	0.259718i	0.00285119	+	0.00877507i
$877$	−24.9760	−	12.7259i	−0.843378	−	0.429723i	−0.0217615	−	0.999763i	$-0.506927\pi$
$877$	−24.9760	−	12.7259i	−0.843378	−	0.429723i	−0.821616	+	0.570041i	$0.806927\pi$
$878$	11.9630	+	1.89475i	0.403731	+	0.0639447i
$879$	−0.0395419	+	0.121698i	−0.00133372	+	0.00410476i
$880$	−10.0158	+	7.78411i	−0.337634	+	0.262402i
$881$	−17.3543	+	23.8862i	−0.584683	+	0.804747i	−0.994199	−	0.107556i	$-0.965697\pi$
$881$	−17.3543	+	23.8862i	−0.584683	+	0.804747i	0.409516	+	0.912303i	$0.365697\pi$
$882$	8.51235	+	4.33726i	0.286626	+	0.146043i
$883$	−4.95696	+	0.785105i	−0.166815	+	0.0264209i	−0.239283	−	0.970950i	$-0.576912\pi$
$883$	−4.95696	+	0.785105i	−0.166815	+	0.0264209i	0.0724682	+	0.997371i	$0.476912\pi$
$884$	4.94757	−	6.80975i	0.166405	−	0.229037i
$885$	−0.195719	−	0.0918745i	−0.00657901	−	0.00308833i
$886$	8.77873	+	6.37812i	0.294927	+	0.214277i
$887$	6.33016	−	39.9671i	0.212546	−	1.34196i	−0.618512	−	0.785776i	$-0.712264\pi$
$887$	6.33016	−	39.9671i	0.212546	−	1.34196i	0.831057	−	0.556187i	$-0.187736\pi$
$888$	0.113239	−	0.0576980i	0.00380004	−	0.00193622i
$889$	22.1355	−	16.0824i	0.742402	−	0.539386i
$890$	13.8287	−	29.4591i	0.463540	−	0.987472i
$891$	48.4994	−	15.7584i	1.62479	−	0.527927i
$892$	23.6215	−	12.0358i	0.790907	−	0.402987i
$893$	3.38473	+	3.38473i	0.113266	+	0.113266i
$894$	−0.621324			−0.0207802
$895$	28.6454	+	8.29320i	0.957511	+	0.277211i
$896$	−1.58001	−	1.14794i	−0.0527843	−	0.0383500i
$897$	0.00455458		0.000721375i	0.000152073		2.40860e-5i
$898$	−23.9577	+	23.9577i	−0.799480	+	0.799480i
$899$	−30.9863	+	41.4261i	−1.03345	+	1.38164i
$900$	−14.9627	+	0.969499i	−0.498756	+	0.0323166i
$901$	27.8005	−	20.1983i	0.926170	−	0.672902i
$902$	−4.50193	−	28.4240i	−0.149898	−	0.946417i
$903$	0.313562	−	0.159768i	0.0104347	−	0.00531674i
$904$			16.7849i			0.558258i
$905$	30.1926	−	0.977134i	1.00364	−	0.0324810i
$906$	−0.0166757	+	0.0513225i	−0.000554013	+	0.00170508i
$907$	15.3588	+	7.82568i	0.509980	+	0.259848i	0.689992	−	0.723817i	$-0.257614\pi$
$907$	15.3588	+	7.82568i	0.509980	+	0.259848i	−0.180013	+	0.983664i	$0.557614\pi$
$908$	9.77973	−	19.1938i	0.324552	−	0.636969i
$909$	1.29903	+	1.78796i	0.0430862	+	0.0593030i
$910$	6.36387	+	11.5502i	0.210960	+	0.382886i
$911$	8.86607	+	12.2031i	0.293746	+	0.404307i	0.930226	−	0.366986i	$-0.119610\pi$
$911$	8.86607	+	12.2031i	0.293746	+	0.404307i	−0.636480	+	0.771293i	$0.719610\pi$
$912$	0.0102566	+	0.0647577i	0.000339630	+	0.00214434i
$913$	8.39532	−	16.4768i	0.277845	−	0.545301i
$914$	7.54739	+	5.48350i	0.249645	+	0.181378i
$915$	−0.496483	+	0.0951910i	−0.0164132	+	0.00314692i
$916$	20.6643	−	6.71425i	0.682769	−	0.221845i
$917$	41.7757	−	6.61663i	1.37956	−	0.218500i
$918$	0.570046	+	0.0902864i	0.0188143	+	0.00297990i
$919$	−12.6128	−	4.09815i	−0.416058	−	0.135185i	0.0935051	−	0.995619i	$-0.470193\pi$
$919$	−12.6128	−	4.09815i	−0.416058	−	0.135185i	−0.509563	+	0.860433i	$0.670193\pi$
$920$	0.0607069	+	0.0781117i	0.00200145	+	0.00257527i
$921$	−0.550989	+	0.179027i	−0.0181557	+	0.00589915i
$922$	−14.2289	+	27.9258i	−0.468604	+	0.919688i
$923$	2.12083	+	4.16236i	0.0698079	+	0.137006i
$924$			0.382410i			0.0125804i
$925$	−13.8325	−	12.1491i	−0.454811	−	0.399459i
$926$	−16.0045	−	5.20016i	−0.525939	−	0.170888i
$927$	25.7650	−	4.08078i	0.846234	−	0.134030i
$928$	1.45350	−	9.17707i	0.0477136	−	0.301252i
$929$	33.3045			1.09268			0.546342	−	0.837562i	$-0.316020\pi$
$929$	33.3045			1.09268			0.546342	+	0.837562i	$0.316020\pi$
$930$	0.406171	−	0.140312i	0.0133189	−	0.00460100i
$931$	−6.05158			−0.198332
$932$	−1.21710	+	7.68445i	−0.0398673	+	0.251712i
$933$	0.973448	−	0.154179i	0.0318693	−	0.00504760i
$934$	−39.0226	−	12.6792i	−1.27686	−	0.414876i
$935$	−25.7978	−	24.1804i	−0.843679	−	0.790782i
$936$		−	9.05566i		−	0.295993i
$937$	−16.5834	−	32.5468i	−0.541756	−	1.06326i	−0.985905	−	0.167303i	$-0.946494\pi$
$937$	−16.5834	−	32.5468i	−0.541756	−	1.06326i	0.444149	−	0.895953i	$-0.353506\pi$
$938$	−9.42088	+	18.4895i	−0.307603	+	0.603704i
$939$	0.190812	−	0.0619985i	0.00622691	−	0.00202324i
$940$	−0.700989	+	5.59099i	−0.0228638	+	0.182358i
$941$	−23.7269	−	7.70932i	−0.773473	−	0.251317i	−0.104422	−	0.994533i	$-0.533299\pi$
$941$	−23.7269	−	7.70932i	−0.773473	−	0.251317i	−0.669051	+	0.743216i	$0.733299\pi$
$942$	0.105835	+	0.0167627i	0.00344830	+	0.000546158i
$943$	−0.221674	+	0.0351097i	−0.00721870	+	0.00114333i
$944$	2.66424	−	0.865665i	0.0867138	−	0.0281750i
$945$	−0.507547	+	0.748338i	−0.0165105	+	0.0243434i
$946$	23.9597	+	17.4078i	0.778998	+	0.565975i
$947$	−21.6593	+	42.5088i	−0.703834	+	1.38135i	0.210986	+	0.977489i	$0.432332\pi$
$947$	−21.6593	+	42.5088i	−0.703834	+	1.38135i	−0.914820	+	0.403862i	$0.867668\pi$
$948$	−0.0111236	−	0.0702317i	−0.000361278	−	0.00228102i
$949$	14.0431	+	19.3287i	0.455859	+	0.627436i
$950$	8.16601	−	4.85002i	0.264940	−	0.157355i
$951$	0.156139	+	0.214908i	0.00506317	+	0.00696885i
$952$	2.47144	−	4.85048i	0.0800998	−	0.157205i
$953$	15.4046	+	7.84904i	0.499004	+	0.254255i	0.685330	−	0.728233i	$-0.259658\pi$
$953$	15.4046	+	7.84904i	0.499004	+	0.254255i	−0.186326	+	0.982488i	$0.559658\pi$
$954$	11.4242	−	35.1600i	0.369871	−	1.13835i
$955$	1.70820	+	52.7821i	0.0552762	+	1.70799i
$956$		−	11.4479i		−	0.370252i
$957$	−1.62104	+	0.825960i	−0.0524007	+	0.0266995i
$958$	−0.107950	−	0.681573i	−0.00348772	−	0.0220206i
$959$	−9.97583	+	7.24786i	−0.322136	+	0.234046i
$960$	−0.0527810	+	0.0563116i	−0.00170350	+	0.00181745i
$961$	25.5762	−	17.5174i	0.825037	−	0.565078i
$962$	7.86226	−	7.86226i	0.253489	−	0.253489i
$963$	−19.1685	−	3.03599i	−0.617696	−	0.0978335i
$964$	9.85285	+	7.15851i	0.317339	+	0.230560i
$965$	28.0728	+	50.9512i	0.903696	+	1.64018i
$966$	0.00298235			9.59555e−5
$967$	−16.8000	−	16.8000i	−0.540252	−	0.540252i	0.383351	−	0.923603i	$-0.374770\pi$
$967$	−16.8000	−	16.8000i	−0.540252	−	0.540252i	−0.923603	+	0.383351i	$0.874770\pi$
$968$	−18.8732	+	9.61636i	−0.606606	+	0.309081i
$969$	−0.173812	+	0.0564750i	−0.00558365	+	0.00181424i
$970$	−9.16644	−	25.3862i	−0.294317	−	0.815102i
$971$	−19.6694	+	14.2907i	−0.631222	+	0.458609i	−0.856823	−	0.515610i	$-0.827565\pi$
$971$	−19.6694	+	14.2907i	−0.631222	+	0.458609i	0.225602	+	0.974220i	$0.427565\pi$
$972$	0.829922	−	0.422867i	0.0266198	−	0.0135635i
$973$	−1.55868	+	9.84114i	−0.0499691	+	0.315492i
$974$	−4.68443	−	3.40344i	−0.150099	−	0.109053i
$975$	0.484194	−	0.192755i	0.0155066	−	0.00617312i
$976$	3.84995	−	5.29900i	0.123234	−	0.169617i
$977$	−2.04439	+	0.323800i	−0.0654059	+	0.0103593i	−0.189052	−	0.981967i	$-0.560541\pi$
$977$	−2.04439	+	0.323800i	−0.0654059	+	0.0103593i	0.123646	+	0.992326i	$0.460541\pi$
$978$	−0.730361	−	0.372137i	−0.0233544	−	0.0118996i
$979$	48.5291	−	66.7946i	1.55100	−	2.13476i
$980$	−4.37143	−	5.62473i	−0.139640	−	0.179675i
$981$	1.46506	−	4.50899i	0.0467757	−	0.143961i
$982$	−17.5412	−	2.77826i	−0.559764	−	0.0886578i
$983$	9.65247	+	4.91818i	0.307866	+	0.156866i	0.601097	−	0.799176i	$-0.294730\pi$
$983$	9.65247	+	4.91818i	0.307866	+	0.156866i	−0.293231	+	0.956042i	$0.594730\pi$
$984$	−0.0541085	−	0.166529i	−0.00172492	−	0.00530875i
$985$	5.45603	+	9.90251i	0.173843	+	0.315520i
$986$	25.8992			0.824799
$987$	0.120116	+	0.120116i	0.00382332	+	0.00382332i
$988$	2.60415	+	5.11094i	0.0828491	+	0.162601i
$989$	0.135760	−	0.186858i	0.00431692	−	0.00594173i
$990$	−37.7444	−	4.73233i	−1.19960	−	0.150403i
$991$		−	18.9885i		−	0.603188i	−0.953436	−	0.301594i	$-0.902481\pi$
$991$		−	18.9885i		−	0.603188i	0.953436	−	0.301594i	$-0.0975187\pi$
$992$	−2.59640	+	4.92531i	−0.0824358	+	0.156379i
$993$	0.862361	+	0.862361i	0.0273662	+	0.0273662i
$994$	1.77586	+	2.44425i	0.0563267	+	0.0775271i
$995$	4.32443	−	6.37604i	0.137094	−	0.202134i
$996$	0.0347689	−	0.107008i	0.00110169	−	0.00339066i
$997$	3.26083	−	3.26083i	0.103272	−	0.103272i	−0.653583	−	0.756855i	$-0.726735\pi$
$997$	3.26083	−	3.26083i	0.103272	−	0.103272i	0.756855	+	0.653583i	$0.226735\pi$
$998$	13.8239	−	13.8239i	0.437589	−	0.437589i
$999$	0.725079	+	0.235592i	0.0229405	+	0.00745381i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.2.s.a.263.13	yes	128
5.2	odd	4	inner	310.2.s.a.77.12	✓	128
31.29	odd	10	inner	310.2.s.a.153.12	yes	128
155.122	even	20	inner	310.2.s.a.277.13	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.s.a.77.12	✓	128	5.2	odd	4	inner
310.2.s.a.153.12	yes	128	31.29	odd	10	inner
310.2.s.a.263.13	yes	128	1.1	even	1	trivial
310.2.s.a.277.13	yes	128	155.122	even	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:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.s (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.156434 - 0.987688i) q^{2} +(-0.0340912 + 0.00539952i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(0.0723287 + 2.23490i) q^{5} +0.0345162i q^{6} +(0.886641 + 1.74013i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-2.85204 + 0.926683i) q^{9} +O(q^{10})\)	\(q+(0.156434 - 0.987688i) q^{2} +(-0.0340912 + 0.00539952i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(0.0723287 + 2.23490i) q^{5} +0.0345162i q^{6} +(0.886641 + 1.74013i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-2.85204 + 0.926683i) q^{9} +(2.21870 + 0.278177i) q^{10} +(5.39525 + 1.75302i) q^{11} +(0.0340912 + 0.00539952i) q^{12} +(2.98257 - 0.472393i) q^{13} +(1.85741 - 0.603509i) q^{14} +(-0.0145332 - 0.0757999i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-1.26546 + 2.48361i) q^{17} +(0.469117 + 2.96189i) q^{18} +(-1.11652 - 1.53676i) q^{19} +(0.621833 - 2.14786i) q^{20} +(-0.0396226 - 0.0545358i) q^{21} +(2.57544 - 5.05459i) q^{22} +(-0.0394199 - 0.0200854i) q^{23} +(0.0106661 - 0.0328268i) q^{24} +(-4.98954 + 0.323295i) q^{25} -3.01975i q^{26} +(0.184488 - 0.0940015i) q^{27} +(-0.305516 - 1.92895i) q^{28} +(7.51695 - 5.46138i) q^{29} +(-0.0771401 + 0.00249651i) q^{30} +(-5.31865 + 1.64679i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.193396 - 0.0306310i) q^{33} +(2.25507 + 1.63840i) q^{34} +(-3.82489 + 2.10741i) q^{35} +2.99881 q^{36} +(2.60361 + 2.60361i) q^{37} +(-1.69250 + 0.862373i) q^{38} +(-0.0991289 + 0.0322089i) q^{39} +(-2.02415 - 0.950177i) q^{40} +(4.10410 - 2.98180i) q^{41} +(-0.0600627 + 0.0306035i) q^{42} +(-0.816679 + 5.15631i) q^{43} +(-4.58948 - 3.33445i) q^{44} +(-2.27733 - 6.30698i) q^{45} +(-0.0260048 + 0.0357925i) q^{46} +(-2.48892 + 0.394206i) q^{47} +(-0.0307541 - 0.0156700i) q^{48} +(1.87257 - 2.57738i) q^{49} +(-0.461221 + 4.97868i) q^{50} +(0.0297309 - 0.0915022i) q^{51} +(-2.98257 - 0.472393i) q^{52} +(-10.9843 - 5.59680i) q^{53} +(-0.0639838 - 0.196922i) q^{54} +(-3.52760 + 12.1846i) q^{55} -1.95299 q^{56} +(0.0463614 + 0.0463614i) q^{57} +(-4.21824 - 8.27875i) q^{58} +(1.64659 - 2.26634i) q^{59} +(-0.00960160 + 0.0765810i) q^{60} -6.54992i q^{61} +(0.794496 + 5.51079i) q^{62} +(-4.14128 - 4.14128i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(1.27148 + 6.63158i) q^{65} +(-0.0605077 + 0.186224i) q^{66} +(-7.51327 + 7.51327i) q^{67} +(1.97100 - 1.97100i) q^{68} +(0.00145232 + 0.000471889i) q^{69} +(1.48312 + 4.10747i) q^{70} +(0.478046 + 1.47128i) q^{71} +(0.469117 - 2.96189i) q^{72} +(3.59187 + 7.04944i) q^{73} +(2.97885 - 2.16426i) q^{74} +(0.168354 - 0.0379626i) q^{75} +(0.586990 + 1.80657i) q^{76} +(1.73316 + 10.9428i) q^{77} +(0.0163052 + 0.102947i) q^{78} +(-0.636609 - 1.95928i) q^{79} +(-1.25512 + 1.85058i) q^{80} +(7.27248 - 5.28377i) q^{81} +(-2.30307 - 4.52003i) q^{82} +(0.509938 - 3.21962i) q^{83} +(0.0208308 + 0.0641107i) q^{84} +(-5.64214 - 2.64854i) q^{85} +(4.96507 + 1.61325i) q^{86} +(-0.226773 + 0.226773i) q^{87} +(-4.01135 + 4.01135i) q^{88} +(4.49739 - 13.8415i) q^{89} +(-6.58559 + 1.26266i) q^{90} +(3.46650 + 4.77122i) q^{91} +(0.0312838 + 0.0312838i) q^{92} +(0.172428 - 0.0848593i) q^{93} +2.51994i q^{94} +(3.35375 - 2.60646i) q^{95} +(-0.0202881 + 0.0279242i) q^{96} +(-5.47988 - 10.7549i) q^{97} +(-2.25271 - 2.25271i) q^{98} -17.0120 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 12 q^{7}+O(q^{10}) \) 128 * q + 12 * q^7	\( 128 q + 12 q^{7} + 8 q^{10} + 32 q^{16} + 8 q^{20} - 80 q^{21} - 20 q^{22} - 20 q^{23} + 40 q^{25} + 8 q^{28} - 32 q^{31} + 20 q^{33} - 48 q^{35} - 128 q^{36} + 52 q^{38} + 8 q^{41} - 20 q^{42} + 64 q^{45} - 40 q^{46} - 20 q^{47} - 20 q^{48} + 24 q^{50} - 16 q^{51} - 40 q^{53} - 40 q^{55} + 20 q^{60} - 8 q^{62} + 256 q^{63} - 160 q^{65} + 56 q^{66} + 8 q^{67} - 32 q^{70} + 56 q^{71} - 80 q^{73} - 160 q^{75} + 48 q^{76} - 20 q^{77} + 4 q^{78} - 96 q^{81} + 16 q^{82} - 240 q^{83} + 120 q^{85} + 40 q^{87} - 64 q^{90} + 80 q^{91} - 160 q^{93} + 32 q^{95} - 56 q^{97} - 176 q^{98}+O(q^{100}) \) 128 * q + 12 * q^7 + 8 * q^10 + 32 * q^16 + 8 * q^20 - 80 * q^21 - 20 * q^22 - 20 * q^23 + 40 * q^25 + 8 * q^28 - 32 * q^31 + 20 * q^33 - 48 * q^35 - 128 * q^36 + 52 * q^38 + 8 * q^41 - 20 * q^42 + 64 * q^45 - 40 * q^46 - 20 * q^47 - 20 * q^48 + 24 * q^50 - 16 * q^51 - 40 * q^53 - 40 * q^55 + 20 * q^60 - 8 * q^62 + 256 * q^63 - 160 * q^65 + 56 * q^66 + 8 * q^67 - 32 * q^70 + 56 * q^71 - 80 * q^73 - 160 * q^75 + 48 * q^76 - 20 * q^77 + 4 * q^78 - 96 * q^81 + 16 * q^82 - 240 * q^83 + 120 * q^85 + 40 * q^87 - 64 * q^90 + 80 * q^91 - 160 * q^93 + 32 * q^95 - 56 * q^97 - 176 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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