LMFDB - Embedded newform 507.2.s.a.5.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(5,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(52))

chi = DirichletCharacter(H, H._module([26, 3]))

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

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

chi := DirichletCharacter("507.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.s (of order $52$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$1392$
Relative dimension:	$58$ over $\Q(\zeta_{52})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{52}]$

Embedding invariants

Embedding label			5.16
Character	$\chi$	$=$	507.5
Dual form			507.2.s.a.203.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.287822 + 1.57060i) q^{2} +(1.61828 - 0.617401i) q^{3} +(-0.513895 - 0.194895i) q^{4} +(-0.563686 - 0.0340967i) q^{5} +(0.503912 + 2.71936i) q^{6} +(2.05136 + 1.24009i) q^{7} +(-1.19811 + 1.98191i) q^{8} +(2.23763 - 1.99825i) q^{9} +(0.215793 - 0.875508i) q^{10} +(-0.235347 - 1.28425i) q^{11} +(-0.951952 + 0.00188616i) q^{12} +(1.58427 + 3.23884i) q^{13} +(-2.53810 + 2.86493i) q^{14} +(-0.933250 + 0.292842i) q^{15} +(-3.59072 - 3.18110i) q^{16} +(2.94651 - 0.726251i) q^{17} +(2.49440 + 4.08955i) q^{18} +(0.734211 - 0.734211i) q^{19} +(0.283030 + 0.127382i) q^{20} +(4.08529 + 0.740295i) q^{21} +2.08477 q^{22} -2.68577 q^{23} +(-0.715233 + 3.94699i) q^{24} +(-4.64697 - 0.564244i) q^{25} +(-5.54289 + 1.55604i) q^{26} +(2.38738 - 4.61524i) q^{27} +(-0.812496 - 1.03707i) q^{28} +(-3.25401 + 2.24608i) q^{29} +(-0.191327 - 1.55004i) q^{30} +(6.78244 + 5.31370i) q^{31} +(2.38362 - 1.86744i) q^{32} +(-1.17375 - 1.93296i) q^{33} +(0.292573 + 4.83681i) q^{34} +(-1.11404 - 0.768965i) q^{35} +(-1.53936 + 0.590789i) q^{36} +(4.81493 - 6.14580i) q^{37} +(0.941826 + 1.36447i) q^{38} +(4.56345 + 4.26320i) q^{39} +(0.742933 - 1.07632i) q^{40} +(3.47479 + 11.1510i) q^{41} +(-2.33854 + 6.20327i) q^{42} +(-1.84364 - 0.223858i) q^{43} +(-0.129349 + 0.705837i) q^{44} +(-1.32945 + 1.05009i) q^{45} +(0.773026 - 4.21827i) q^{46} +(-5.07004 - 2.28184i) q^{47} +(-7.77479 - 2.93098i) q^{48} +(-0.582815 - 1.11046i) q^{49} +(2.22370 - 7.13610i) q^{50} +(4.31988 - 2.99446i) q^{51} +(-0.182917 - 1.97319i) q^{52} +(-1.85851 - 7.54028i) q^{53} +(6.56153 + 5.07798i) q^{54} +(0.0888732 + 0.731936i) q^{55} +(-4.91549 + 2.57985i) q^{56} +(0.734853 - 1.64146i) q^{57} +(-2.59111 - 5.75721i) q^{58} +(0.601112 - 9.93757i) q^{59} +(0.536666 + 0.0313952i) q^{60} +(0.662969 + 0.163407i) q^{61} +(-10.2978 + 9.12306i) q^{62} +(7.06819 - 1.32426i) q^{63} +(-2.21175 - 4.21414i) q^{64} +(-0.782598 - 1.87971i) q^{65} +(3.37373 - 1.28714i) q^{66} +(-14.5555 - 6.55088i) q^{67} +(-1.65574 - 0.201044i) q^{68} +(-4.34632 + 1.65820i) q^{69} +(1.52838 - 1.52838i) q^{70} +(4.61187 + 14.8000i) q^{71} +(1.27943 + 6.82891i) q^{72} +(-10.8971 + 1.99697i) q^{73} +(8.26672 + 9.33120i) q^{74} +(-7.86844 + 1.95594i) q^{75} +(-0.520401 + 0.234214i) q^{76} +(1.10980 - 2.92630i) q^{77} +(-8.00923 + 5.94029i) q^{78} +(-3.59624 - 9.48251i) q^{79} +(1.91557 + 1.91557i) q^{80} +(1.01399 - 8.94270i) q^{81} +(-18.5138 + 2.24798i) q^{82} +(1.31195 + 0.408822i) q^{83} +(-1.95513 - 1.17664i) q^{84} +(-1.68567 + 0.308911i) q^{85} +(0.882230 - 2.83117i) q^{86} +(-3.87915 + 5.64381i) q^{87} +(2.82724 + 1.07223i) q^{88} +(10.0723 - 10.0723i) q^{89} +(-1.26662 - 2.39027i) q^{90} +(-0.766541 + 8.60866i) q^{91} +(1.38021 + 0.523444i) q^{92} +(14.2565 + 4.41155i) q^{93} +(5.04311 - 7.30621i) q^{94} +(-0.438898 + 0.388830i) q^{95} +(2.70439 - 4.49369i) q^{96} +(-6.00056 + 0.362967i) q^{97} +(1.91183 - 0.595751i) q^{98} +(-3.09287 - 2.40339i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9} - 52 q^{10} - 26 q^{12} - 44 q^{13} - 34 q^{15} + 48 q^{16} - 34 q^{18} - 56 q^{19} - 22 q^{21} - 96 q^{22} - 194 q^{24} - 52 q^{25} - 34 q^{27}+ \cdots - 58 q^{99}+O(q^{100}) $ 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9 - 52 * q^10 - 26 * q^12 - 44 * q^13 - 34 * q^15 + 48 * q^16 - 34 * q^18 - 56 * q^19 - 22 * q^21 - 96 * q^22 - 194 * q^24 - 52 * q^25 - 34 * q^27 - 56 * q^28 + 78 * q^30 - 32 * q^31 - 10 * q^33 - 52 * q^34 - 26 * q^36 - 56 * q^37 + 70 * q^39 - 36 * q^40 - 10 * q^42 - 52 * q^43 - 140 * q^45 - 180 * q^46 - 2 * q^48 - 52 * q^49 - 26 * q^51 - 64 * q^52 - 22 * q^54 + 132 * q^55 - 22 * q^57 - 60 * q^58 - 18 * q^60 - 92 * q^61 + 108 * q^63 - 52 * q^64 - 124 * q^66 - 240 * q^67 - 104 * q^69 - 268 * q^70 - 2 * q^72 - 56 * q^73 + 104 * q^75 - 48 * q^76 - 22 * q^78 - 12 * q^79 + 2 * q^81 + 208 * q^82 - 22 * q^84 - 52 * q^85 - 26 * q^87 - 260 * q^88 - 26 * q^90 - 32 * q^91 - 176 * q^93 - 240 * q^94 + 292 * q^96 - 80 * q^97 - 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{3}{52}\right)$

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 $

$2$	−0.287822	+	1.57060i	−0.203521	+	1.11058i	0.710127	+	0.704073i	$0.248637\pi$
$2$	−0.287822	+	1.57060i	−0.203521	+	1.11058i	−0.913648	+	0.406505i	$0.866747\pi$
$3$	1.61828	−	0.617401i	0.934312	−	0.356457i
$3$	1.61828	−	0.617401i	0.934312	−	0.356457i
$4$	−0.513895	−	0.194895i	−0.256948	−	0.0974474i
$5$	−0.563686	−	0.0340967i	−0.252088	−	0.0152485i	−0.0661488	−	0.997810i	$-0.521071\pi$
$5$	−0.563686	−	0.0340967i	−0.252088	−	0.0152485i	−0.185939	+	0.982561i	$0.559533\pi$
$6$	0.503912	+	2.71936i	0.205721	+	1.11017i
$7$	2.05136	+	1.24009i	0.775340	+	0.468709i	0.848882	−	0.528583i	$-0.177276\pi$
$7$	2.05136	+	1.24009i	0.775340	+	0.468709i	−0.0735416	+	0.997292i	$0.523430\pi$
$8$	−1.19811	+	1.98191i	−0.423595	+	0.700711i
$9$	2.23763	−	1.99825i	0.745877	−	0.666084i
$10$	0.215793	−	0.875508i	0.0682399	−	0.276860i
$11$	−0.235347	−	1.28425i	−0.0709598	−	0.387215i	−0.999858	−	0.0168788i	$-0.994627\pi$
$11$	−0.235347	−	1.28425i	−0.0709598	−	0.387215i	0.928898	−	0.370336i	$-0.120758\pi$
$12$	−0.951952	+	0.00188616i	−0.274805	+	0.000544487i
$13$	1.58427	+	3.23884i	0.439398	+	0.898293i
$13$	1.58427	+	3.23884i	0.439398	+	0.898293i
$14$	−2.53810	+	2.86493i	−0.678337	+	0.765684i
$15$	−0.933250	+	0.292842i	−0.240964	+	0.0756116i
$16$	−3.59072	−	3.18110i	−0.897680	−	0.795275i
$17$	2.94651	−	0.726251i	0.714635	−	0.176142i	0.134797	−	0.990873i	$-0.456962\pi$
$17$	2.94651	−	0.726251i	0.714635	−	0.176142i	0.579838	+	0.814732i	$0.303116\pi$
$18$	2.49440	+	4.08955i	0.587936	+	0.963917i
$19$	0.734211	−	0.734211i	0.168439	−	0.168439i	−0.617854	−	0.786293i	$-0.711998\pi$
$19$	0.734211	−	0.734211i	0.168439	−	0.168439i	0.786293	+	0.617854i	$0.211998\pi$
$20$	0.283030	+	0.127382i	0.0632875	+	0.0284834i
$21$	4.08529	+	0.740295i	0.891484	+	0.161546i
$22$	2.08477			0.444475
$23$	−2.68577			−0.560023			−0.280011	−	0.959997i	$-0.590338\pi$
$23$	−2.68577			−0.560023			−0.280011	+	0.959997i	$0.590338\pi$
$24$	−0.715233	+	3.94699i	−0.145996	+	0.805676i
$25$	−4.64697	−	0.564244i	−0.929393	−	0.112849i
$26$	−5.54289	+	1.55604i	−1.08705	+	0.305164i
$27$	2.38738	−	4.61524i	0.459452	−	0.888203i
$28$	−0.812496	−	1.03707i	−0.153547	−	0.195989i
$29$	−3.25401	+	2.24608i	−0.604255	+	0.417087i	−0.830528	−	0.556977i	$-0.811961\pi$
$29$	−3.25401	+	2.24608i	−0.604255	+	0.417087i	0.226273	+	0.974064i	$0.427346\pi$
$30$	−0.191327	−	1.55004i	−0.0349313	−	0.282998i
$31$	6.78244	+	5.31370i	1.21816	+	0.954369i	0.999769	−	0.0214924i	$-0.00684176\pi$
$31$	6.78244	+	5.31370i	1.21816	+	0.954369i	0.218393	+	0.975861i	$0.429919\pi$
$32$	2.38362	−	1.86744i	0.421368	−	0.330121i
$33$	−1.17375	−	1.93296i	−0.204324	−	0.336486i
$34$	0.292573	+	4.83681i	0.0501759	+	0.829506i
$35$	−1.11404	−	0.768965i	−0.188307	−	0.129979i
$36$	−1.53936	+	0.590789i	−0.256559	+	0.0984648i
$37$	4.81493	−	6.14580i	0.791569	−	1.01036i	−0.207912	−	0.978148i	$-0.566667\pi$
$37$	4.81493	−	6.14580i	0.791569	−	1.01036i	0.999481	−	0.0322158i	$-0.0102564\pi$
$38$	0.941826	+	1.36447i	0.152784	+	0.221346i
$39$	4.56345	+	4.26320i	0.730737	+	0.682659i
$40$	0.742933	−	1.07632i	0.117468	−	0.170182i
$41$	3.47479	+	11.1510i	0.542671	+	1.74149i	0.662862	+	0.748741i	$0.269341\pi$
$41$	3.47479	+	11.1510i	0.542671	+	1.74149i	−0.120192	+	0.992751i	$0.538351\pi$
$42$	−2.33854	+	6.20327i	−0.360845	+	0.957185i
$43$	−1.84364	−	0.223858i	−0.281152	−	0.0341380i	−0.0212539	−	0.999774i	$-0.506766\pi$
$43$	−1.84364	−	0.223858i	−0.281152	−	0.0341380i	−0.259898	+	0.965636i	$0.583689\pi$
$44$	−0.129349	+	0.705837i	−0.0195001	+	0.106409i
$45$	−1.32945	+	1.05009i	−0.198183	+	0.156538i
$46$	0.773026	−	4.21827i	0.113976	−	0.621949i
$47$	−5.07004	−	2.28184i	−0.739541	−	0.332840i	0.00538688	−	0.999985i	$-0.498285\pi$
$47$	−5.07004	−	2.28184i	−0.739541	−	0.332840i	−0.744928	+	0.667145i	$0.767516\pi$
$48$	−7.77479	−	2.93098i	−1.12219	−	0.423051i
$49$	−0.582815	−	1.11046i	−0.0832593	−	0.158637i
$50$	2.22370	−	7.13610i	0.314478	−	1.00920i
$51$	4.31988	−	2.99446i	0.604905	−	0.419308i
$52$	−0.182917	−	1.97319i	−0.0253660	−	0.273632i
$53$	−1.85851	−	7.54028i	−0.255286	−	1.03574i	−0.948947	−	0.315435i	$-0.897849\pi$
$53$	−1.85851	−	7.54028i	−0.255286	−	1.03574i	0.693661	−	0.720302i	$-0.255997\pi$
$54$	6.56153	+	5.07798i	0.892911	+	0.691025i
$55$	0.0888732	+	0.731936i	0.0119837	+	0.0986943i
$56$	−4.91549	+	2.57985i	−0.656860	+	0.344747i
$57$	0.734853	−	1.64146i	0.0973336	−	0.217416i
$58$	−2.59111	−	5.75721i	−0.340229	−	0.755958i
$59$	0.601112	−	9.93757i	0.0782582	−	1.29376i	−0.721068	−	0.692864i	$-0.756349\pi$
$59$	0.601112	−	9.93757i	0.0782582	−	1.29376i	0.799326	−	0.600897i	$-0.205190\pi$
$60$	0.536666	+	0.0313952i	0.0692833	+	0.00405311i
$61$	0.662969	+	0.163407i	0.0848845	+	0.0209222i	0.281529	−	0.959553i	$-0.409158\pi$
$61$	0.662969	+	0.163407i	0.0848845	+	0.0209222i	−0.196645	+	0.980475i	$0.563005\pi$
$62$	−10.2978	+	9.12306i	−1.30782	+	1.15863i
$63$	7.06819	−	1.32426i	0.890508	−	0.166842i
$64$	−2.21175	−	4.21414i	−0.276469	−	0.526768i
$65$	−0.782598	−	1.87971i	−0.0970693	−	0.233149i
$66$	3.37373	−	1.28714i	0.415278	−	0.158436i
$67$	−14.5555	−	6.55088i	−1.77823	−	0.800318i	−0.980284	−	0.197592i	$-0.936688\pi$
$67$	−14.5555	−	6.55088i	−1.77823	−	0.800318i	−0.797948	−	0.602726i	$-0.794081\pi$
$68$	−1.65574	−	0.201044i	−0.200788	−	0.0243801i
$69$	−4.34632	+	1.65820i	−0.523236	+	0.199624i
$70$	1.52838	−	1.52838i	0.182676	−	0.182676i
$71$	4.61187	+	14.8000i	0.547329	+	1.75644i	0.648127	+	0.761532i	$0.275553\pi$
$71$	4.61187	+	14.8000i	0.547329	+	1.75644i	−0.100799	+	0.994907i	$0.532140\pi$
$72$	1.27943	+	6.82891i	0.150783	+	0.804794i
$73$	−10.8971	+	1.99697i	−1.27541	+	0.233728i	−0.774946	−	0.632027i	$-0.782223\pi$
$73$	−10.8971	+	1.99697i	−1.27541	+	0.233728i	−0.500467	+	0.865755i	$0.666838\pi$
$74$	8.26672	+	9.33120i	0.960987	+	1.08473i
$75$	−7.86844	+	1.95594i	−0.908569	+	0.225853i
$76$	−0.520401	+	0.234214i	−0.0596941	+	0.0268661i
$77$	1.10980	−	2.92630i	0.126473	−	0.333483i
$78$	−8.00923	+	5.94029i	−0.906867	+	0.672606i
$79$	−3.59624	−	9.48251i	−0.404609	−	1.06687i	−0.970227	−	0.242199i	$-0.922131\pi$
$79$	−3.59624	−	9.48251i	−0.404609	−	1.06687i	0.565618	−	0.824668i	$-0.308638\pi$
$80$	1.91557	+	1.91557i	0.214167	+	0.214167i
$81$	1.01399	−	8.94270i	0.112665	−	0.993633i
$82$	−18.5138	+	2.24798i	−2.04451	+	0.248248i
$83$	1.31195	+	0.408822i	0.144006	+	0.0448740i	0.368659	−	0.929565i	$-0.379817\pi$
$83$	1.31195	+	0.408822i	0.144006	+	0.0448740i	−0.224653	+	0.974439i	$0.572125\pi$
$84$	−1.95513	−	1.17664i	−0.213323	−	0.128382i
$85$	−1.68567	+	0.308911i	−0.182837	+	0.0335061i
$86$	0.882230	−	2.83117i	0.0951333	−	0.305293i
$87$	−3.87915	+	5.64381i	−0.415889	+	0.605080i
$88$	2.82724	+	1.07223i	0.301384	+	0.114300i
$89$	10.0723	−	10.0723i	1.06767	−	1.06767i	0.0701279	−	0.997538i	$-0.477659\pi$
$89$	10.0723	−	10.0723i	1.06767	−	1.06767i	0.997538	−	0.0701279i	$-0.0223407\pi$
$90$	−1.26662	−	2.39027i	−0.133513	−	0.251957i
$91$	−0.766541	+	8.60866i	−0.0803553	+	0.902432i
$92$	1.38021	+	0.523444i	0.143897	+	0.0545728i
$93$	14.2565	+	4.41155i	1.47833	+	0.457456i
$94$	5.04311	−	7.30621i	0.520157	−	0.753578i
$95$	−0.438898	+	0.388830i	−0.0450300	+	0.0398931i
$96$	2.70439	−	4.49369i	0.276015	−	0.458635i
$97$	−6.00056	+	0.362967i	−0.609264	+	0.0368537i	−0.362130	−	0.932128i	$-0.617950\pi$
$97$	−6.00056	+	0.362967i	−0.609264	+	0.0368537i	−0.247134	+	0.968981i	$0.579489\pi$
$98$	1.91183	−	0.595751i	0.193124	−	0.0601800i
$99$	−3.09287	−	2.40339i	−0.310845	−	0.241550i
$100$	2.27809	+	1.19563i	0.227809	+	0.119563i
$101$	0.804625	−	6.62669i	0.0800632	−	0.659380i	−0.896331	−	0.443385i	$-0.853777\pi$
$101$	0.804625	−	6.62669i	0.0800632	−	0.659380i	0.976394	−	0.215995i	$-0.0692995\pi$
$102$	3.45972	+	7.64666i	0.342563	+	0.757132i
$103$	6.55403	−	12.4877i	0.645787	−	1.23044i	−0.313922	−	0.949449i	$-0.601643\pi$
$103$	6.55403	−	12.4877i	0.645787	−	1.23044i	0.959709	−	0.280996i	$-0.0906648\pi$
$104$	−8.31722	−	0.740591i	−0.815571	−	0.0726209i
$105$	−2.27758	−	0.556589i	−0.222269	−	0.0543175i
$106$	12.3777	−	0.748710i	1.20222	−	0.0727211i
$107$	2.09457	+	2.36428i	0.202490	+	0.228564i	0.840980	−	0.541066i	$-0.181979\pi$
$107$	2.09457	+	2.36428i	0.202490	+	0.228564i	−0.638490	+	0.769630i	$0.720441\pi$
$108$	−2.12635	+	1.90646i	−0.204608	+	0.183449i
$109$	2.64345	+	3.37412i	0.253197	+	0.323182i	0.897018	−	0.441994i	$-0.145729\pi$
$109$	2.64345	+	3.37412i	0.253197	+	0.323182i	−0.643821	+	0.765176i	$0.722652\pi$
$110$	−1.17516	−	0.0710838i	−0.112047	−	0.00677758i
$111$	3.99745	−	12.9183i	0.379422	−	1.22615i
$112$	−3.42100	−	10.9784i	−0.323254	−	1.03736i
$113$	−4.38929	−	8.36309i	−0.412909	−	0.786733i	0.586826	−	0.809713i	$-0.300377\pi$
$113$	−4.38929	−	8.36309i	−0.412909	−	0.786733i	−0.999736	+	0.0229794i	$0.992685\pi$
$114$	2.36656	+	1.62660i	0.221649	+	0.152345i
$115$	1.51393	+	0.0915761i	0.141175	+	0.00853951i
$116$	2.10997	−	0.520061i	0.195906	−	0.0482865i
$117$	10.0170	+	4.08156i	0.926075	+	0.377340i
$118$	15.4349	+	3.80436i	1.42090	+	0.350220i
$119$	6.94497	+	2.16414i	0.636644	+	0.198386i
$120$	0.537746	−	2.20048i	0.0490893	−	0.200875i
$121$	8.69128	−	3.29617i	0.790116	−	0.299651i
$122$	−0.447464	+	0.994224i	−0.0405115	+	0.0900128i
$123$	12.5078	+	15.9000i	1.12779	+	1.43366i
$124$	−2.44985	−	4.05255i	−0.220003	−	0.363929i
$125$	5.37752	+	0.985467i	0.480980	+	0.0881428i
$126$	0.0455017	+	11.4824i	0.00405362	+	1.02294i
$127$	−4.09727	+	1.55389i	−0.363574	+	0.137885i	−0.529625	−	0.848232i	$-0.677667\pi$
$127$	−4.09727	+	1.55389i	−0.363574	+	0.137885i	0.166052	+	0.986117i	$0.446898\pi$
$128$	13.0372	−	4.06254i	1.15233	−	0.359081i
$129$	−3.12172	+	0.775999i	−0.274852	+	0.0683229i
$130$	3.17751	−	0.688123i	0.278686	−	0.0603524i
$131$	−6.37731	+	4.40194i	−0.557188	+	0.384599i	−0.813120	−	0.582095i	$-0.802233\pi$
$131$	−6.37731	+	4.40194i	−0.557188	+	0.384599i	0.255932	+	0.966695i	$0.417618\pi$
$132$	0.226461	+	1.22210i	0.0197109	+	0.106370i
$133$	2.41662	−	0.595642i	0.209547	−	0.0516487i
$134$	14.4782	−	20.9752i	1.25072	−	1.81199i
$135$	−1.50310	+	2.52014i	−0.129366	+	0.216899i
$136$	−2.09088	+	6.70986i	−0.179291	+	0.575365i
$137$	−5.75646	−	7.34758i	−0.491807	−	0.627746i	0.475998	−	0.879446i	$-0.342087\pi$
$137$	−5.75646	−	7.34758i	−0.491807	−	0.627746i	−0.967805	+	0.251701i	$0.919010\pi$
$138$	−1.35339	−	7.30358i	−0.115209	−	0.621722i
$139$	−2.02288	−	1.79211i	−0.171578	−	0.152005i	0.572964	−	0.819581i	$-0.305794\pi$
$139$	−2.02288	−	1.79211i	−0.171578	−	0.152005i	−0.744542	+	0.667576i	$0.767332\pi$
$140$	0.422632	+	0.612288i	0.0357189	+	0.0517478i
$141$	−9.61353	−	0.562396i	−0.809605	−	0.0473623i
$142$	−24.5722	+	2.98361i	−2.06206	+	0.250379i
$143$	3.78662	−	2.79685i	0.316653	−	0.233884i
$144$	−14.3913	+	0.0570290i	−1.19928	+	0.00475242i
$145$	1.91082	−	1.15513i	0.158685	−	0.0959286i
$146$		−	17.6898i		−	1.46402i
$147$	−1.62876	−	1.43720i	−0.134338	−	0.118538i
$148$	−3.67215	+	2.21989i	−0.301849	+	0.182474i
$149$	0.465725	−	1.03480i	0.0381536	−	0.0847739i	−0.891837	−	0.452356i	$-0.850584\pi$
$149$	0.465725	−	1.03480i	0.0381536	−	0.0847739i	0.929991	+	0.367582i	$0.119814\pi$
$150$	−0.807280	−	12.9211i	−0.0659141	−	1.05500i
$151$	−5.95149	+	2.67855i	−0.484326	+	0.217977i	−0.637840	−	0.770169i	$-0.720172\pi$
$151$	−5.95149	+	2.67855i	−0.484326	+	0.217977i	0.153514	+	0.988146i	$0.450941\pi$
$152$	0.575477	+	2.33480i	0.0466774	+	0.189378i
$153$	5.14198	−	7.51296i	0.415705	−	0.607386i
$154$	4.27661	+	2.58530i	0.344619	+	0.208329i
$155$	−3.64198	−	3.22652i	−0.292531	−	0.259160i
$156$	−1.51426	−	3.08023i	−0.121238	−	0.246616i
$157$	8.11084	−	7.18557i	0.647315	−	0.573471i	−0.274267	−	0.961653i	$-0.588435\pi$
$157$	8.11084	−	7.18557i	0.647315	−	0.573471i	0.921583	+	0.388182i	$0.126897\pi$
$158$	15.9283	−	2.91896i	1.26718	−	0.232220i
$159$	−7.66296	−	11.0548i	−0.607713	−	0.876703i
$160$	−1.40728	+	0.971379i	−0.111256	+	0.0767942i
$161$	−5.50948	−	3.33060i	−0.434208	−	0.262488i
$162$	13.7535	+	4.16647i	1.08058	+	0.327349i
$163$	1.57598	−	2.01159i	0.123441	−	0.157560i	−0.721511	−	0.692403i	$-0.756552\pi$
$163$	1.57598	−	2.01159i	0.123441	−	0.157560i	0.844952	+	0.534843i	$0.179629\pi$
$164$	0.387592	−	6.40766i	0.0302658	−	0.500354i
$165$	0.595720	+	1.12960i	0.0463767	+	0.0879396i
$166$	−1.01970	+	1.94288i	−0.0791443	+	0.150797i
$167$	5.90398	+	1.08194i	0.456864	+	0.0837234i	0.403759	−	0.914866i	$-0.367704\pi$
$167$	5.90398	+	1.08194i	0.456864	+	0.0837234i	0.0531051	+	0.998589i	$0.483088\pi$
$168$	−6.36182	+	7.20974i	−0.490825	+	0.556243i
$169$	−7.98017	+	10.2624i	−0.613859	+	0.789416i
$170$		−	2.73642i		−	0.209874i
$171$	0.175756	−	3.11003i	0.0134404	−	0.237830i
$172$	0.903807	+	0.474354i	0.0689146	+	0.0361692i
$173$	−2.96154	+	7.80894i	−0.225162	+	0.593703i	−0.999223	−	0.0394076i	$-0.987453\pi$
$173$	−2.96154	+	7.80894i	−0.225162	+	0.593703i	0.774061	+	0.633111i	$0.218222\pi$
$174$	−7.74763	−	7.71699i	−0.587347	−	0.585024i
$175$	−8.83287	−	6.92011i	−0.667703	−	0.523112i
$176$	−3.24025	+	5.36003i	−0.244243	+	0.404028i
$177$	−5.16270	−	16.4529i	−0.388053	−	1.23667i
$178$	12.9205	+	18.7186i	0.968434	+	1.40302i
$179$	19.6973	+	4.85494i	1.47224	+	0.362875i	0.892173	−	0.451693i	$-0.149180\pi$
$179$	19.6973	+	4.85494i	1.47224	+	0.362875i	0.580068	+	0.814568i	$0.303026\pi$
$180$	0.887858	−	0.280532i	0.0661770	−	0.0209096i
$181$	7.90179	+	8.91928i	0.587336	+	0.662965i	0.964777	−	0.263068i	$-0.0847345\pi$
$181$	7.90179	+	8.91928i	0.587336	+	0.662965i	−0.377441	+	0.926033i	$0.623196\pi$
$182$	−13.3001	−	3.68169i	−0.985868	−	0.272905i
$183$	1.17375	−	0.144880i	0.0867665	−	0.0107098i
$184$	3.21785	−	5.32297i	0.237223	−	0.392414i
$185$	−2.92366	+	3.30013i	−0.214952	+	0.242630i
$186$	−11.0321	+	21.1215i	−0.808913	+	1.54870i
$187$	−1.62614	−	3.61313i	−0.118915	−	0.264218i
$188$	2.16075	+	2.16075i	0.157589	+	0.157589i
$189$	10.6207	−	6.50693i	0.772540	−	0.473310i
$190$	−0.484370	−	0.801246i	−0.0351399	−	0.0581285i
$191$			4.58013i			0.331406i	0.986176	+	0.165703i	$0.0529894\pi$
$191$			4.58013i			0.331406i	−0.986176	+	0.165703i	$0.947011\pi$
$192$	−6.18104	−	5.45410i	−0.446078	−	0.393616i
$193$	5.14930	+	8.51799i	0.370655	+	0.613138i	0.984312	−	0.176434i	$-0.0564563\pi$
$193$	5.14930	+	8.51799i	0.370655	+	0.613138i	−0.613658	+	0.789572i	$0.710302\pi$
$194$	1.15702	−	9.52892i	0.0830692	−	0.684136i
$195$	−2.42699	−	2.55871i	−0.173800	−	0.183233i
$196$	0.0830829	+	0.684249i	0.00593449	+	0.0488749i
$197$	−4.69215	+	3.67606i	−0.334302	+	0.261909i	−0.769806	−	0.638278i	$-0.779647\pi$
$197$	−4.69215	+	3.67606i	−0.334302	+	0.261909i	0.435504	+	0.900187i	$0.356570\pi$
$198$	4.66495	−	4.16589i	0.331523	−	0.296057i
$199$	−4.27335	+	4.82361i	−0.302930	+	0.341937i	−0.880188	−	0.474624i	$-0.842584\pi$
$199$	−4.27335	+	4.82361i	−0.302930	+	0.341937i	0.577259	+	0.816561i	$0.304122\pi$
$200$	6.68584	−	8.53385i	0.472761	−	0.603434i
$201$	−27.5993	−	1.61457i	−1.94670	−	0.113883i
$202$	10.1763	+	3.17105i	0.715999	+	0.223114i
$203$	−9.46048	+	0.572254i	−0.663995	+	0.0401643i
$204$	−2.80357	+	0.696914i	−0.196289	+	0.0487937i
$205$	−1.57848	−	6.40413i	−0.110246	−	0.447284i
$206$	17.7267	+	13.8879i	1.23507	+	0.967619i
$207$	−6.00977	+	5.36685i	−0.417708	+	0.373022i
$208$	4.61440	−	16.6695i	0.319951	−	1.15582i
$209$	−1.11570	−	0.770114i	−0.0771747	−	0.0532699i
$210$	1.52971	−	3.41696i	0.105560	−	0.235793i
$211$	−6.10842	−	16.1066i	−0.420521	−	1.10882i	−0.963177	−	0.268868i	$-0.913350\pi$
$211$	−6.10842	−	16.1066i	−0.420521	−	1.10882i	0.542656	−	0.839955i	$-0.317419\pi$
$212$	−0.514481	+	4.23713i	−0.0353347	+	0.291007i
$213$	16.6008	+	21.1031i	1.13747	+	1.44596i
$214$	−4.31620	+	2.60923i	−0.295049	+	0.178363i
$215$	1.03160	+	0.189047i	0.0703544	+	0.0128929i
$216$	6.28665	+	10.2611i	0.427752	+	0.698181i
$217$	7.32374	+	19.3111i	0.497168	+	1.31092i
$218$	−6.06021	+	3.18065i	−0.410449	+	0.215420i
$219$	−16.4016	+	9.95956i	−1.10832	+	0.673005i
$220$	0.0969791	−	0.393460i	0.00653833	−	0.0265270i
$221$	7.02029	+	8.39271i	0.472236	+	0.564555i
$222$	19.1389	+	9.99657i	1.28452	+	0.670926i
$223$	−0.204783	+	3.38546i	−0.0137133	+	0.226707i	0.984862	+	0.173342i	$0.0554564\pi$
$223$	−0.204783	+	3.38546i	−0.0137133	+	0.226707i	−0.998575	+	0.0533657i	$0.983005\pi$
$224$	7.20545	−	0.874900i	0.481434	−	0.0584567i
$225$	−11.5257	+	8.02323i	−0.768380	+	0.534882i
$226$	14.3984	−	4.48671i	0.957765	−	0.298452i
$227$	−14.7152	+	6.62279i	−0.976685	+	0.439570i	−0.834945	−	0.550334i	$-0.814501\pi$
$227$	−14.7152	+	6.62279i	−0.976685	+	0.439570i	−0.141740	+	0.989904i	$0.545270\pi$
$228$	−0.697549	+	0.700319i	−0.0461963	+	0.0463797i
$229$	−15.7876	+	12.3688i	−1.04328	+	0.817354i	−0.983509	−	0.180858i	$-0.942113\pi$
$229$	−15.7876	+	12.3688i	−1.04328	+	0.817354i	−0.0597666	+	0.998212i	$0.519036\pi$
$230$	−0.579573	+	2.35142i	−0.0382159	+	0.155048i
$231$	−0.0107405	−	5.42075i	−0.000706670	−	0.356659i
$232$	−0.552881	−	9.14021i	−0.0362984	−	0.600084i
$233$	−3.48895	+	1.83114i	−0.228568	+	0.119962i	−0.575120	−	0.818069i	$-0.695045\pi$
$233$	−3.48895	+	1.83114i	−0.228568	+	0.119962i	0.346552	+	0.938031i	$0.387352\pi$
$234$	−9.29360	+	14.5579i	−0.607542	+	0.951682i
$235$	2.78010	+	1.45911i	0.181354	+	0.0951819i
$236$	−2.24569	+	4.98972i	−0.146182	+	0.324803i
$237$	−11.6742	−	13.1250i	−0.758323	−	0.852560i
$238$	−5.39790	+	10.2848i	−0.349894	+	0.666668i
$239$	−12.9356	−	12.9356i	−0.836738	−	0.836738i	0.151690	−	0.988428i	$-0.451528\pi$
$239$	−12.9356	−	12.9356i	−0.836738	−	0.836738i	−0.988428	+	0.151690i	$0.951528\pi$
$240$	4.28260	+	1.91725i	0.276441	+	0.123758i
$241$	0.292345	+	4.83304i	0.0188316	+	0.311323i	0.995379	+	0.0960219i	$0.0306119\pi$
$241$	0.292345	+	4.83304i	0.0188316	+	0.311323i	−0.976548	+	0.215301i	$0.930927\pi$
$242$	2.67540	+	14.5992i	0.171981	+	0.938471i
$243$	−3.88032	−	15.0978i	−0.248923	−	0.968523i
$244$	−0.308850	−	0.213183i	−0.0197721	−	0.0136477i
$245$	0.290662	+	0.645824i	0.0185697	+	0.0412602i
$246$	−28.5725	+	15.0683i	−1.82172	+	0.960720i
$247$	3.54118	+	1.21480i	0.225320	+	0.0772960i
$248$	−18.6574	+	7.07581i	−1.18474	+	0.449314i
$249$	2.37551	−	0.148416i	0.150542	−	0.00940551i
$250$	−3.09554	+	8.16227i	−0.195779	+	0.516227i
$251$	−0.470054	−	3.87124i	−0.0296696	−	0.244351i	−0.999997	−	0.00255506i	$-0.999187\pi$
$251$	−0.470054	−	3.87124i	−0.0296696	−	0.244351i	0.970327	−	0.241796i	$-0.0777364\pi$
$252$	−3.89040	−	0.697020i	−0.245072	−	0.0439081i
$253$	0.632089	+	3.44920i	0.0397391	+	0.216849i
$254$	−1.26125	−	6.88239i	−0.0791376	−	0.431840i
$255$	−2.53716	+	1.54064i	−0.158883	+	0.0964785i
$256$	1.48089	+	12.1962i	0.0925554	+	0.762263i
$257$	−10.4080	+	27.4436i	−0.649232	+	1.71188i	0.0517082	+	0.998662i	$0.483533\pi$
$257$	−10.4080	+	27.4436i	−0.649232	+	1.71188i	−0.700940	+	0.713221i	$0.747236\pi$
$258$	−0.320280	−	5.12631i	−0.0199398	−	0.319150i
$259$	17.4985	−	6.63630i	1.08730	−	0.412359i
$260$	0.0358283	+	1.11850i	0.00222198	+	0.0693662i
$261$	−2.79304	+	11.5282i	−0.172885	+	0.713580i
$262$	−5.07813	−	11.2832i	−0.313728	−	0.697075i
$263$	13.1560	+	9.08093i	0.811234	+	0.559954i	0.899895	−	0.436108i	$-0.143643\pi$
$263$	13.1560	+	9.08093i	0.811234	+	0.559954i	−0.0886607	+	0.996062i	$0.528259\pi$
$264$	5.23724	−	0.0103768i	0.322330	−	0.000638651i
$265$	0.790518	+	4.31372i	0.0485612	+	0.264990i
$266$	0.239957	+	3.96696i	0.0147127	+	0.243230i
$267$	10.0811	−	22.5185i	0.616956	−	1.37811i
$268$	6.20325	+	6.20325i	0.378924	+	0.378924i
$269$	−3.25983	+	6.21108i	−0.198755	+	0.378696i	−0.964351	−	0.264625i	$-0.914752\pi$
$269$	−3.25983	+	6.21108i	−0.198755	+	0.378696i	0.765596	+	0.643321i	$0.222444\pi$
$270$	−3.52550	−	3.08611i	−0.214555	−	0.187815i
$271$	1.18051	−	2.62299i	0.0717109	−	0.159335i	−0.872558	−	0.488511i	$-0.837540\pi$
$271$	1.18051	−	2.62299i	0.0717109	−	0.159335i	0.944269	+	0.329176i	$0.106771\pi$
$272$	−12.8904	−	6.76539i	−0.781594	−	0.410212i
$273$	4.07452	+	14.4044i	0.246601	+	0.871796i
$274$	13.1969	−	6.92627i	0.797254	−	0.418431i
$275$	0.369021	+	6.10065i	0.0222528	+	0.367883i
$276$	2.55673	−	0.00506580i	0.153897	−	0.000304925i
$277$	−4.94483	+	20.0620i	−0.297106	+	1.20541i	0.612681	+	0.790330i	$0.290091\pi$
$277$	−4.94483	+	20.0620i	−0.297106	+	1.20541i	−0.909787	+	0.415076i	$0.863755\pi$
$278$	3.39692	−	2.66131i	0.203733	−	0.159615i
$279$	25.7947	−	1.66291i	1.54429	−	0.0995557i
$280$	2.85876	−	1.28662i	0.170843	−	0.0768904i
$281$	−25.2499	+	7.86819i	−1.50628	+	0.469377i	−0.935979	−	0.352056i	$-0.885482\pi$
$281$	−25.2499	+	7.86819i	−1.50628	+	0.469377i	−0.570305	+	0.821433i	$0.693175\pi$
$282$	3.65028	−	14.9371i	0.217371	−	0.889491i
$283$	22.2044	−	2.69610i	1.31991	−	0.160266i	0.569913	−	0.821705i	$-0.306977\pi$
$283$	22.2044	−	2.69610i	1.31991	−	0.160266i	0.749999	+	0.661438i	$0.230054\pi$
$284$	0.514427	−	8.50449i	0.0305256	−	0.504649i
$285$	−0.470194	+	0.900210i	−0.0278519	+	0.0533239i
$286$	3.30284	+	6.75224i	0.195301	+	0.399268i
$287$	−6.70018	+	27.1837i	−0.395499	+	1.60460i
$288$	1.60203	−	8.94172i	0.0944007	−	0.526896i
$289$	−6.89825	+	3.62048i	−0.405779	+	0.212969i
$290$	1.26427	+	3.33360i	0.0742404	+	0.195756i
$291$	−9.48646	+	4.29213i	−0.556106	+	0.251609i
$292$	5.98919	+	1.09756i	0.350491	+	0.0642298i
$293$	−4.93587	+	2.98384i	−0.288357	+	0.174318i	−0.654121	−	0.756390i	$-0.726961\pi$
$293$	−4.93587	+	2.98384i	−0.288357	+	0.174318i	0.365764	+	0.930707i	$0.380808\pi$
$294$	2.72606	−	2.14446i	0.158987	−	0.125067i
$295$	−0.677677	+	5.58117i	−0.0394559	+	0.324948i
$296$	6.41163	+	16.9061i	0.372669	+	0.982646i
$297$	−6.48897	−	1.97981i	−0.376528	−	0.114880i
$298$	1.49120	+	1.02930i	0.0863830	+	0.0596259i
$299$	−4.25500	−	8.69879i	−0.246073	−	0.503064i
$300$	4.42475	+	0.528368i	0.255463	+	0.0305054i
$301$	−3.50435	−	2.74548i	−0.201987	−	0.158247i
$302$	−2.49395	−	10.1183i	−0.143510	−	0.582245i
$303$	−2.78922	−	11.2206i	−0.160236	−	0.644605i
$304$	−4.97194	+	0.300747i	−0.285160	+	0.0172490i
$305$	−0.368135	−	0.114715i	−0.0210793	−	0.00656859i
$306$	10.3198	+	10.2384i	0.589946	+	0.585289i
$307$	4.09726	−	5.22977i	0.233843	−	0.298479i	−0.655986	−	0.754773i	$-0.727747\pi$
$307$	4.09726	−	5.22977i	0.233843	−	0.298479i	0.889829	+	0.456295i	$0.150824\pi$
$308$	−1.14064	+	1.28752i	−0.0649941	+	0.0733632i
$309$	2.89633	−	24.2549i	0.164766	−	1.37981i
$310$	6.11579	−	4.79142i	0.347354	−	0.272134i
$311$	−3.00983	−	24.7882i	−0.170672	−	1.40561i	−0.786433	−	0.617675i	$-0.788075\pi$
$311$	−3.00983	−	24.7882i	−0.170672	−	1.40561i	0.615762	−	0.787932i	$-0.288848\pi$
$312$	−13.9168	+	3.93658i	−0.787883	+	0.222865i
$313$	−3.84711	+	31.6838i	−0.217451	+	1.79087i	0.319836	+	0.947473i	$0.396372\pi$
$313$	−3.84711	+	31.6838i	−0.217451	+	1.79087i	−0.537287	+	0.843399i	$0.680551\pi$
$314$	8.95115	+	14.8070i	0.505143	+	0.835608i
$315$	−4.02939	+	0.505467i	−0.227030	+	0.0284799i
$316$			5.57391i			0.313557i
$317$	3.69963	+	6.11994i	0.207792	+	0.343730i	0.942242	−	0.334933i	$-0.108714\pi$
$317$	3.69963	+	6.11994i	0.207792	+	0.343730i	−0.734450	+	0.678663i	$0.762560\pi$
$318$	19.5682	−	8.85360i	1.09733	−	0.496485i
$319$	3.65035	+	3.65035i	0.204380	+	0.204380i
$320$	1.10304	+	2.45086i	0.0616621	+	0.137007i
$321$	4.84931	+	2.53287i	0.270662	+	0.141371i
$322$	6.81678	−	7.69455i	0.379884	−	0.428800i
$323$	1.63014	−	2.69658i	0.0907035	−	0.150042i
$324$	−2.26397	+	4.39799i	−0.125776	+	0.244333i
$325$	−5.53456	−	15.9447i	−0.307002	−	0.884452i
$326$	2.70580	+	3.05421i	0.149860	+	0.169157i
$327$	6.36101	+	3.82818i	0.351765	+	0.211699i
$328$	−26.2634	−	6.47336i	−1.45016	−	0.357431i
$329$	−7.57077	−	10.9682i	−0.417390	−	0.604694i
$330$	−1.94561	+	0.610509i	−0.107102	+	0.0336074i
$331$	−10.9484	+	18.1109i	−0.601779	+	0.995465i	0.395260	+	0.918569i	$0.370655\pi$
$331$	−10.9484	+	18.1109i	−0.601779	+	0.995465i	−0.997039	+	0.0768953i	$0.975499\pi$
$332$	−0.594530	−	0.465785i	−0.0326291	−	0.0255632i
$333$	−1.50682	−	23.3735i	−0.0825731	−	1.28086i
$334$	−3.39859	+	8.96136i	−0.185963	+	0.490344i
$335$	7.98134	+	4.18893i	0.436067	+	0.228866i
$336$	−12.3142	−	15.6539i	−0.671794	−	0.853991i
$337$			10.0858i			0.549407i	0.961529	+	0.274704i	$0.0885797\pi$
$337$			10.0858i			0.549407i	−0.961529	+	0.274704i	$0.911420\pi$
$338$	−13.8212	−	15.4874i	−0.751775	−	0.842401i
$339$	−12.2665	−	10.8238i	−0.666223	−	0.587870i
$340$	0.926463	+	0.169781i	0.0502445	+	0.00920765i
$341$	5.22788	−	9.96089i	0.283105	−	0.539412i
$342$	4.83401	+	1.17118i	0.261393	+	0.0633300i
$343$	1.19462	−	19.7495i	0.0645036	−	1.06637i
$344$	2.65254	−	3.38572i	0.143015	−	0.182546i
$345$	2.50650	−	0.786509i	0.134945	−	0.0423442i
$346$	−11.4123	−	6.89897i	−0.613528	−	0.370891i
$347$	−3.95350	+	2.72890i	−0.212235	+	0.146495i	−0.669440	−	0.742866i	$-0.733466\pi$
$347$	−3.95350	+	2.72890i	−0.212235	+	0.146495i	0.457205	+	0.889361i	$0.348851\pi$
$348$	3.09343	−	2.14430i	0.165825	−	0.114947i
$349$	9.88702	−	1.81186i	0.529240	−	0.0969868i	0.0910104	−	0.995850i	$-0.470990\pi$
$349$	9.88702	−	1.81186i	0.529240	−	0.0969868i	0.438229	+	0.898863i	$0.355606\pi$
$350$	13.4110	−	11.8811i	0.716848	−	0.635072i
$351$	18.7303	+	0.420557i	0.999748	+	0.0224476i
$352$	−2.95924	−	2.62166i	−0.157728	−	0.139735i
$353$	−14.3889	−	8.69842i	−0.765846	−	0.462970i	0.0797354	−	0.996816i	$-0.474592\pi$
$353$	−14.3889	−	8.69842i	−0.765846	−	0.462970i	−0.845582	+	0.533846i	$0.820746\pi$
$354$	27.3267	−	3.37302i	1.45240	−	0.179274i
$355$	−2.09501	−	8.49981i	−0.111192	−	0.451123i
$356$	−7.13917	+	3.21308i	−0.378376	+	0.170293i
$357$	12.5750	−	0.785658i	0.665540	−	0.0415814i
$358$	−13.2944	+	29.5391i	−0.702633	+	1.56119i
$359$	11.2811	−	6.81967i	0.595394	−	0.359928i	−0.187330	−	0.982297i	$-0.559983\pi$
$359$	11.2811	−	6.81967i	0.595394	−	0.359928i	0.782724	+	0.622369i	$0.213830\pi$
$360$	−0.488355	−	3.89298i	−0.0257386	−	0.205178i
$361$			17.9219i			0.943256i
$362$	−16.2829	+	9.84335i	−0.855810	+	0.517355i
$363$	12.0298	−	10.7001i	0.631402	−	0.561610i
$364$	2.07170	−	4.27455i	0.108587	−	0.224047i
$365$	6.21065	−	0.754110i	0.325080	−	0.0394719i
$366$	−0.110285	+	1.88519i	−0.00576468	+	0.0985406i
$367$	3.24629	+	4.70306i	0.169455	+	0.245498i	0.898506	−	0.438962i	$-0.144654\pi$
$367$	3.24629	+	4.70306i	0.169455	+	0.245498i	−0.729051	+	0.684459i	$0.760038\pi$
$368$	9.64386	+	8.54372i	0.502721	+	0.445372i
$369$	30.0578	+	18.0083i	1.56474	+	0.937475i
$370$	−4.34167	−	5.54173i	−0.225713	−	0.288101i
$371$	5.53814	−	17.7725i	0.287526	−	0.922704i
$372$	−6.46658	−	5.04560i	−0.335277	−	0.261602i
$373$	13.8624	−	20.0831i	0.717766	−	1.03986i	−0.279062	−	0.960273i	$-0.590023\pi$
$373$	13.8624	−	20.0831i	0.717766	−	1.03986i	0.996828	−	0.0795900i	$-0.0253611\pi$
$374$	6.14281	−	1.51407i	0.317637	−	0.0782905i
$375$	9.31074	−	1.72533i	0.480804	−	0.0890957i
$376$	10.5968	−	7.31448i	0.546491	−	0.377215i
$377$	−12.4299	−	6.98082i	−0.640174	−	0.359530i
$378$	7.16289	+	18.5536i	0.368420	+	0.954295i
$379$	17.6289	−	5.49339i	0.905536	−	0.282176i	0.190848	−	0.981620i	$-0.438876\pi$
$379$	17.6289	−	5.49339i	0.905536	−	0.282176i	0.714688	+	0.699443i	$0.246569\pi$
$380$	0.301329	−	0.114279i	0.0154578	−	0.00586238i
$381$	−5.67113	+	5.04428i	−0.290541	+	0.258426i
$382$	−7.19353	−	1.31826i	−0.368053	−	0.0674482i
$383$	−5.24623	−	8.67833i	−0.268070	−	0.443442i	0.692525	−	0.721394i	$-0.256498\pi$
$383$	−5.24623	−	8.67833i	−0.268070	−	0.443442i	−0.960595	+	0.277952i	$0.910344\pi$
$384$	18.5895	−	14.6235i	0.948641	−	0.746251i
$385$	−0.725355	+	1.61167i	−0.0369675	+	0.0821385i
$386$	−14.8604	+	5.63580i	−0.756374	+	0.286855i
$387$	−4.57270	+	3.18313i	−0.232443	+	0.161808i
$388$	3.15440	+	0.982950i	0.160140	+	0.0499017i
$389$	−9.85969	−	2.43020i	−0.499906	−	0.123216i	−0.0187034	−	0.999825i	$-0.505954\pi$
$389$	−9.85969	−	2.43020i	−0.499906	−	0.123216i	−0.481203	+	0.876609i	$0.659800\pi$
$390$	4.71723	−	3.07537i	0.238866	−	0.155727i
$391$	−7.91367	+	1.95055i	−0.400212	+	0.0986433i
$392$	2.89911	+	0.175364i	0.146427	+	0.00885722i
$393$	−7.60248	+	11.0609i	−0.383495	+	0.557949i
$394$	−4.42310	−	8.42752i	−0.222833	−	0.424572i
$395$	1.70383	+	5.46778i	0.0857289	+	0.275114i
$396$	1.12100	+	1.83787i	0.0563325	+	0.0923567i
$397$	10.3063	+	0.623419i	0.517261	+	0.0312885i	0.316947	−	0.948443i	$-0.397342\pi$
$397$	10.3063	+	0.623419i	0.517261	+	0.0312885i	0.200314	+	0.979732i	$0.435804\pi$
$398$	−6.34598	−	8.10004i	−0.318095	−	0.406018i
$399$	3.54300	−	2.45593i	0.177372	−	0.122950i
$400$	14.8910	+	16.8085i	0.744551	+	0.840425i
$401$	25.4113	−	1.53710i	1.26898	−	0.0767590i	0.587878	−	0.808949i	$-0.299963\pi$
$401$	25.4113	−	1.53710i	1.26898	−	0.0767590i	0.681100	+	0.732190i	$0.261502\pi$
$402$	10.4795	−	42.8826i	0.522671	−	2.13879i
$403$	−6.46500	+	30.3856i	−0.322045	+	1.51361i
$404$	−1.70500	+	3.24861i	−0.0848269	+	0.161624i
$405$	−0.876487	+	5.00630i	−0.0435530	+	0.248765i
$406$	1.82416	−	15.0233i	0.0905314	−	0.745593i
$407$	−9.02591	−	4.73716i	−0.447398	−	0.234812i
$408$	0.759061	+	12.1493i	0.0375791	+	0.601480i
$409$	23.5899	−	7.35092i	1.16645	−	0.363480i	0.347685	−	0.937612i	$-0.386968\pi$
$409$	23.5899	−	7.35092i	1.16645	−	0.363480i	0.818763	+	0.574132i	$0.194660\pi$
$410$	10.5126	−	0.635896i	0.519181	−	0.0314047i
$411$	−13.8519	−	8.33636i	−0.683266	−	0.411202i
$412$	−5.80186	+	5.14000i	−0.285837	+	0.253230i
$413$	13.5566	−	19.6401i	0.667075	−	0.966425i
$414$	−6.69940	−	10.9836i	−0.329258	−	0.539816i
$415$	−0.725591	−	0.275180i	−0.0356178	−	0.0135081i
$416$	9.82465	+	4.76161i	0.481693	+	0.233457i
$417$	−4.38003	−	1.65121i	−0.214491	−	0.0808599i
$418$	1.53066	−	1.53066i	0.0748671	−	0.0748671i
$419$	35.0993	+	13.3114i	1.71471	+	0.650304i	0.998850	−	0.0479376i	$-0.0152649\pi$
$419$	35.0993	+	13.3114i	1.71471	+	0.650304i	0.715862	+	0.698242i	$0.246034\pi$
$420$	1.06196	+	0.729917i	0.0518184	+	0.0356163i
$421$	−9.24386	+	29.6646i	−0.450518	+	1.44576i	0.398387	+	0.917218i	$0.369570\pi$
$421$	−9.24386	+	29.6646i	−0.450518	+	1.44576i	−0.848905	+	0.528546i	$0.822737\pi$
$422$	27.0551	−	4.95802i	1.31702	−	0.241353i
$423$	−15.9046	+	5.02529i	−0.773306	+	0.244338i
$424$	17.1709	+	5.35066i	0.833891	+	0.259851i
$425$	−14.1021	+	1.71231i	−0.684054	+	0.0830592i
$426$	−37.9226	+	19.9992i	−1.83735	+	0.968966i
$427$	1.15735	+	1.15735i	0.0560080	+	0.0560080i
$428$	−0.615604	−	1.62322i	−0.0297564	−	0.0784611i
$429$	4.40101	−	6.86393i	0.212483	−	0.331394i
$430$	−0.593834	+	1.56581i	−0.0286372	+	0.0755101i
$431$	17.0685	−	7.68193i	0.822163	−	0.370025i	0.0447359	−	0.998999i	$-0.485755\pi$
$431$	17.0685	−	7.68193i	0.822163	−	0.370025i	0.777427	+	0.628973i	$0.216525\pi$
$432$	−23.2539	+	8.97752i	−1.11881	+	0.431931i
$433$	−18.8697	−	21.2995i	−0.906819	−	1.02359i	−0.999611	−	0.0279014i	$-0.991118\pi$
$433$	−18.8697	−	21.2995i	−0.906819	−	1.02359i	0.0927918	−	0.995686i	$-0.470421\pi$
$434$	−32.4379	+	5.94446i	−1.55707	+	0.285343i
$435$	2.37906	−	3.04907i	0.114067	−	0.146192i
$436$	−0.700859	−	2.24914i	−0.0335651	−	0.107714i
$437$	−1.97192	+	1.97192i	−0.0943300	+	0.0943300i
$438$	−10.9217	−	28.6269i	−0.521858	−	1.36785i
$439$	19.9670	+	2.42443i	0.952973	+	0.115712i	0.582230	−	0.813024i	$-0.302180\pi$
$439$	19.9670	+	2.42443i	0.952973	+	0.115712i	0.370742	+	0.928736i	$0.379103\pi$
$440$	−1.55711	−	0.700800i	−0.0742324	−	0.0334093i
$441$	−3.52311	−	1.32019i	−0.167767	−	0.0628663i
$442$	−15.2021	+	8.61042i	−0.723092	+	0.409556i
$443$	1.18670	+	2.26108i	0.0563820	+	0.107427i	0.912016	−	0.410154i	$-0.134525\pi$
$443$	1.18670	+	2.26108i	0.0563820	+	0.107427i	−0.855634	+	0.517581i	$0.826833\pi$
$444$	−4.57199	+	5.85959i	−0.216977	+	0.278084i
$445$	−6.02107	+	5.33420i	−0.285426	+	0.252865i
$446$	−5.25825	−	1.29604i	−0.248985	−	0.0613694i
$447$	0.114785	−	1.96213i	0.00542916	−	0.0928054i
$448$	0.688815	−	11.3875i	0.0325435	−	0.538008i
$449$	1.08262	+	2.40549i	0.0510922	+	0.113522i	0.935678	−	0.352856i	$-0.114789\pi$
$449$	1.08262	+	2.40549i	0.0510922	+	0.113522i	−0.884585	+	0.466378i	$0.845559\pi$
$450$	−9.28390	−	20.4115i	−0.437647	−	0.962206i
$451$	13.5028	−	7.08684i	0.635824	−	0.333706i
$452$	0.625712	+	5.15320i	0.0294310	+	0.242386i
$453$	−7.97742	+	8.00909i	−0.374812	+	0.376300i
$454$	−6.16635	−	25.0179i	−0.289401	−	1.17415i
$455$	0.725615	−	4.82644i	0.0340174	−	0.226267i
$456$	2.37279	+	3.42306i	0.111116	+	0.160299i
$457$	−7.76772	+	24.9275i	−0.363359	+	1.16606i	0.574342	+	0.818616i	$0.305258\pi$
$457$	−7.76772	+	24.9275i	−0.363359	+	1.16606i	−0.937701	+	0.347444i	$0.887050\pi$
$458$	−14.8824	−	28.3560i	−0.695408	−	1.32499i
$459$	3.68264	−	15.3327i	0.171891	−	0.715669i
$460$	−0.760155	−	0.342118i	−0.0354424	−	0.0159513i
$461$	4.01511	−	21.9098i	0.187002	−	1.02044i	−0.747441	−	0.664328i	$-0.768718\pi$
$461$	4.01511	−	21.9098i	0.187002	−	1.02044i	0.934444	−	0.356111i	$-0.115898\pi$
$462$	8.51690	+	1.54334i	0.396242	+	0.0718029i
$463$	−3.47038	+	18.9373i	−0.161282	+	0.880090i	0.799057	+	0.601255i	$0.205333\pi$
$463$	−3.47038	+	18.9373i	−0.161282	+	0.880090i	−0.960339	+	0.278834i	$0.910052\pi$
$464$	18.8292	+	2.28628i	0.874126	+	0.106138i
$465$	−7.88579	−	2.97283i	−0.365695	−	0.137862i
$466$	−1.87178	−	6.00677i	−0.0867087	−	0.278258i
$467$	−0.650338	+	0.942177i	−0.0300941	+	0.0435988i	−0.837742	−	0.546066i	$-0.816125\pi$
$467$	−0.650338	+	0.942177i	−0.0300941	+	0.0435988i	0.807648	+	0.589665i	$0.200740\pi$
$468$	−4.35223	−	4.04976i	−0.201182	−	0.187200i
$469$	−21.7348	−	31.4883i	−1.00362	−	1.45399i
$470$	−3.09185	+	3.94645i	−0.142616	+	0.182036i
$471$	8.68919	−	16.6359i	0.400377	−	0.766541i
$472$	18.9752	+	13.0976i	0.873404	+	0.602867i
$473$	0.146405	+	2.42037i	0.00673172	+	0.111289i
$474$	23.9742	−	14.5578i	1.10117	−	0.668663i
$475$	−3.82613	+	2.99758i	−0.175555	+	0.137538i
$476$	−3.14721	−	2.46568i	−0.144252	−	0.113014i
$477$	−19.2260	−	13.1586i	−0.880300	−	0.602491i
$478$	24.0398	−	16.5935i	1.09956	−	0.758969i
$479$	−14.5616	−	18.5865i	−0.665335	−	0.849237i	0.330173	−	0.943921i	$-0.392893\pi$
$479$	−14.5616	−	18.5865i	−0.665335	−	0.849237i	−0.995507	+	0.0946836i	$0.969816\pi$
$480$	−1.67764	+	2.44082i	−0.0765736	+	0.111408i
$481$	27.5334	+	5.85816i	1.25542	+	0.267109i
$482$	−7.67489	−	0.931900i	−0.349582	−	0.0424469i
$483$	−10.9722	−	1.98826i	−0.499251	−	0.0904692i
$484$	−5.10881			−0.232219
$485$	3.39480			0.154150
$486$	24.8294	−	1.74893i	1.12628	−	0.0793333i
$487$	18.8656	+	8.49073i	0.854883	+	0.384752i	0.789974	−	0.613140i	$-0.210094\pi$
$487$	18.8656	+	8.49073i	0.854883	+	0.384752i	0.0649083	+	0.997891i	$0.479325\pi$
$488$	−1.11817	+	1.11817i	−0.0506170	+	0.0506170i
$489$	1.30841	−	4.22833i	0.0591685	−	0.191212i
$490$	−1.09799	+	0.270629i	−0.0496020	+	0.0122258i
$491$	16.1537	+	14.3109i	0.729005	+	0.645842i	0.943686	−	0.330842i	$-0.107333\pi$
$491$	16.1537	+	14.3109i	0.729005	+	0.645842i	−0.214681	+	0.976684i	$0.568871\pi$
$492$	−3.32887	−	10.6087i	−0.150077	−	0.478275i
$493$	−7.95677	+	8.98134i	−0.358355	+	0.404499i
$494$	−2.92719	+	5.21211i	−0.131701	+	0.234504i
$495$	1.66146	+	1.46021i	0.0746770	+	0.0656317i
$496$	−7.45041	−	40.6556i	−0.334534	−	1.82549i
$497$	−8.89274	+	36.0793i	−0.398894	+	1.61838i
$498$	−0.450623	+	3.77368i	−0.0201929	+	0.169103i
$499$	−10.3308	+	17.0892i	−0.462468	+	0.765016i	−0.996773	−	0.0802765i	$-0.974420\pi$
$499$	−10.3308	+	17.0892i	−0.462468	+	0.765016i	0.534305	+	0.845292i	$0.320574\pi$
$500$	−2.57142	−	1.55448i	−0.114997	−	0.0695183i
$501$	10.2223	−	1.89424i	0.456697	−	0.0846284i
$502$	6.21545	+	0.375965i	0.277409	+	0.0167802i
$503$	−15.2048	−	5.76643i	−0.677949	−	0.257112i	−0.00849324	−	0.999964i	$-0.502704\pi$
$503$	−15.2048	−	5.76643i	−0.677949	−	0.257112i	−0.669456	+	0.742852i	$0.733473\pi$
$504$	−5.84387	+	15.5951i	−0.260307	+	0.694663i
$505$	−0.679504	+	3.70793i	−0.0302375	+	0.165001i
$506$	−5.59922			−0.248916
$507$	−6.57808	+	21.5344i	−0.292143	+	0.956375i
$508$	2.40841			0.106856
$509$	−0.387334	+	2.11361i	−0.0171683	+	0.0936843i	−0.991088	−	0.133208i	$-0.957472\pi$
$509$	−0.387334	+	2.11361i	−0.0171683	+	0.0936843i	0.973920	+	0.226893i	$0.0728567\pi$
$510$	−1.68947	−	4.42828i	−0.0748109	−	0.196087i
$511$	−24.8303	−	9.41691i	−1.09843	−	0.416580i
$512$	7.67956	+	0.464528i	0.339392	+	0.0205294i
$513$	−1.63572	−	5.14140i	−0.0722186	−	0.226998i
$514$	−40.1071	−	24.2456i	−1.76905	−	1.06943i
$515$	−4.12020	+	6.81564i	−0.181558	+	0.300333i
$516$	1.75548	+	0.209625i	0.0772805	+	0.00922821i
$517$	−1.73723	+	7.04820i	−0.0764031	+	0.309980i
$518$	5.38648	+	29.3931i	0.236669	+	1.29146i
$519$	0.0286613	+	14.4655i	0.00125809	+	0.634964i
$520$	4.66305	+	0.701050i	0.204488	+	0.0307431i
$521$	−26.3089	+	29.6966i	−1.15261	+	1.30103i	−0.206040	+	0.978544i	$0.566058\pi$
$521$	−26.3089	+	29.6966i	−1.15261	+	1.30103i	−0.946574	+	0.322488i	$0.895481\pi$
$522$	−17.3023	−	7.70482i	−0.757301	−	0.337231i
$523$	1.30132	+	1.15287i	0.0569028	+	0.0504114i	0.691095	−	0.722764i	$-0.257129\pi$
$523$	1.30132	+	1.15287i	0.0569028	+	0.0504114i	−0.634192	+	0.773176i	$0.718667\pi$
$524$	4.13519	−	1.01923i	0.180646	−	0.0445253i
$525$	−18.5665	−	5.74522i	−0.810309	−	0.250742i
$526$	−18.0491	+	18.0491i	−0.786976	+	0.786976i
$527$	23.8436	+	10.7311i	1.03864	+	0.467456i
$528$	−1.93433	+	10.6745i	−0.0841809	+	0.464550i
$529$	−15.7866			−0.686374
$530$	−7.00263			−0.304175
$531$	−18.5127	−	23.4378i	−0.803382	−	1.01711i
$532$	−1.35797	−	0.164888i	−0.0588757	−	0.00714880i
$533$	−30.6113	+	28.9205i	−1.32592	+	1.25269i
$534$	32.4659	+	22.3147i	1.40494	+	0.965653i
$535$	−1.10007	−	1.40413i	−0.0475600	−	0.0607059i
$536$	30.4223	−	20.9990i	1.31404	−	0.907018i
$537$	34.8730	−	4.30448i	1.50488	−	0.185752i
$538$	−8.81684	−	6.90755i	−0.380121	−	0.297806i
$539$	−1.28894	+	1.00982i	−0.0555187	+	0.0434962i
$540$	1.26360	−	1.00214i	0.0543766	−	0.0431254i
$541$	2.15340	+	35.5999i	0.0925817	+	1.53056i	0.687152	+	0.726514i	$0.258861\pi$
$541$	2.15340	+	35.5999i	0.0925817	+	1.53056i	−0.594570	+	0.804044i	$0.702678\pi$
$542$	3.77988	+	2.60906i	0.162360	+	0.112069i
$543$	18.2941	+	9.55528i	0.785073	+	0.410056i
$544$	5.66713	−	7.23356i	0.242976	−	0.310136i
$545$	−1.37503	−	1.99207i	−0.0588998	−	0.0853311i
$546$	−23.7963	+	2.25350i	−1.01839	+	0.0964411i
$547$	23.7824	−	34.4547i	1.01686	−	1.47318i	0.141362	−	0.989958i	$-0.454852\pi$
$547$	23.7824	−	34.4547i	1.01686	−	1.47318i	0.875499	−	0.483220i	$-0.160533\pi$
$548$	1.52621	+	4.89779i	0.0651966	+	0.209223i
$549$	1.81001	−	0.959134i	0.0772493	−	0.0409348i
$550$	−9.68786	−	1.17632i	−0.413092	−	0.0501584i
$551$	−0.740033	+	4.03823i	−0.0315264	+	0.172034i
$552$	1.92095	−	10.6007i	0.0817613	−	0.451197i
$553$	4.38198	−	23.9117i	0.186341	−	1.01683i
$554$	−30.0860	−	13.5406i	−1.27823	−	0.575285i
$555$	−2.69378	+	7.14558i	−0.114345	+	0.303313i
$556$	0.690274	+	1.31521i	0.0292741	+	0.0557772i
$557$	−2.85337	+	9.15680i	−0.120901	+	0.387986i	−0.995255	−	0.0973038i	$-0.968978\pi$
$557$	−2.85337	+	9.15680i	−0.120901	+	0.387986i	0.874353	+	0.485290i	$0.161286\pi$
$558$	−4.81253	+	40.9917i	−0.203731	+	1.73531i
$559$	−2.19578	−	6.32589i	−0.0928716	−	0.267557i
$560$	1.55404	+	6.30500i	0.0656703	+	0.266435i
$561$	−4.86229	−	4.84306i	−0.205286	−	0.204474i
$562$	−5.09026	−	41.9220i	−0.214719	−	1.76837i
$563$	−7.32497	+	3.84444i	−0.308711	+	0.162024i	−0.611963	−	0.790887i	$-0.709620\pi$
$563$	−7.32497	+	3.84444i	−0.308711	+	0.162024i	0.303252	+	0.952910i	$0.401928\pi$
$564$	4.83074	+	2.16264i	0.203411	+	0.0910635i
$565$	2.18903	+	4.86382i	0.0920930	+	0.204622i
$566$	−2.15643	+	35.6501i	−0.0906416	+	1.49848i
$567$	13.1698	−	17.0872i	0.553079	−	0.717596i
$568$	−34.8578	−	8.59169i	−1.46260	−	0.360499i
$569$	30.3579	−	26.8948i	1.27267	−	1.12749i	0.287158	−	0.957883i	$-0.407290\pi$
$569$	30.3579	−	26.8948i	1.27267	−	1.12749i	0.985512	−	0.169604i	$-0.0542489\pi$
$570$	−1.27853	−	0.997586i	−0.0535519	−	0.0417843i
$571$	2.58408	+	4.92356i	0.108141	+	0.206045i	0.933513	−	0.358545i	$-0.116727\pi$
$571$	2.58408	+	4.92356i	0.108141	+	0.206045i	−0.825372	+	0.564589i	$0.809035\pi$
$572$	−2.49102	+	0.699295i	−0.104155	+	0.0292390i
$573$	2.82778	+	7.41191i	0.118132	+	0.309637i
$574$	−40.7661	−	18.3474i	−1.70155	−	0.765804i
$575$	12.4807	+	1.51543i	0.520481	+	0.0631979i
$576$	−13.3700	−	5.01006i	−0.557083	−	0.208752i
$577$	−19.1611	+	19.1611i	−0.797686	+	0.797686i	−0.982730	−	0.185044i	$-0.940757\pi$
$577$	−19.1611	+	19.1611i	−0.797686	+	0.797686i	0.185044	+	0.982730i	$0.440757\pi$
$578$	−3.70084	−	11.8764i	−0.153935	−	0.493993i
$579$	13.5920	+	10.6053i	0.564864	+	0.440740i
$580$	−1.20709	+	0.221208i	−0.0501218	+	0.00918516i
$581$	2.18431	+	2.46558i	0.0906205	+	0.102289i
$582$	−4.01079	−	16.1348i	−0.166253	−	0.668807i
$583$	−9.24619	+	4.16137i	−0.382938	+	0.172346i
$584$	9.09811	−	23.9897i	0.376483	−	0.992703i
$585$	−5.50729	−	2.64226i	−0.227698	−	0.109244i
$586$	−3.26575	−	8.61108i	−0.134907	−	0.355720i
$587$	0.453717	+	0.453717i	0.0187269	+	0.0187269i	0.716408	−	0.697681i	$-0.245785\pi$
$587$	0.453717	+	0.453717i	0.0187269	+	0.0187269i	−0.697681	+	0.716408i	$0.745785\pi$
$588$	0.556907	+	1.05601i	0.0229665	+	0.0435490i
$589$	8.88111	−	1.07836i	0.365940	−	0.0444331i
$590$	−8.57071	−	2.67074i	−0.352851	−	0.109953i
$591$	−5.32358	+	8.84582i	−0.218983	+	0.363868i
$592$	−36.8394	+	6.75108i	−1.51409	+	0.277468i
$593$	−7.26468	+	23.3132i	−0.298325	+	0.957357i	0.676888	+	0.736086i	$0.263328\pi$
$593$	−7.26468	+	23.3132i	−0.298325	+	0.957357i	−0.975212	+	0.221271i	$0.928979\pi$
$594$	4.97714	−	9.62171i	0.204215	−	0.394784i
$595$	−3.84099	−	1.45670i	−0.157465	−	0.0597187i
$596$	−0.441010	+	0.441010i	−0.0180645	+	0.0180645i
$597$	−3.93735	+	10.4443i	−0.161145	+	0.427457i
$598$	14.8870	−	4.17917i	0.608773	−	0.170899i
$599$	26.9370	+	10.2159i	1.10062	+	0.417409i	0.836992	−	0.547216i	$-0.184312\pi$
$599$	26.9370	+	10.2159i	1.10062	+	0.417409i	0.263626	+	0.964625i	$0.415081\pi$
$600$	5.55073	−	17.9380i	0.226608	−	0.732314i
$601$	−17.8903	+	25.9186i	−0.729763	+	1.05724i	0.265881	+	0.964006i	$0.414337\pi$
$601$	−17.8903	+	25.9186i	−0.729763	+	1.05724i	−0.995644	+	0.0932378i	$0.970278\pi$
$602$	5.32068	−	4.71371i	0.216855	−	0.192116i
$603$	−45.6601	+	14.4270i	−1.85942	+	0.587513i
$604$	3.58048	−	0.216579i	0.145688	−	0.00881248i
$605$	−5.01154	+	1.56166i	−0.203748	+	0.0634904i
$606$	18.4258	−	1.15120i	0.748496	−	0.0467643i
$607$	1.57404	+	0.826119i	0.0638883	+	0.0335311i	0.496365	−	0.868114i	$-0.334668\pi$
$607$	1.57404	+	0.826119i	0.0638883	+	0.0335311i	−0.432477	+	0.901645i	$0.642360\pi$
$608$	0.378979	−	3.12118i	0.0153696	−	0.126580i
$609$	−14.9564	+	6.76698i	−0.606062	+	0.274212i
$610$	0.286129	−	0.545173i	0.0115850	−	0.0220734i
$611$	−0.641808	−	20.0361i	−0.0259648	−	0.810573i
$612$	−4.10668	+	2.85873i	−0.166003	+	0.115557i
$613$	39.2497	−	2.37417i	1.58528	−	0.0958917i	0.755941	−	0.654639i	$-0.227179\pi$
$613$	39.2497	−	2.37417i	1.58528	−	0.0958917i	0.829338	+	0.558748i	$0.188718\pi$
$614$	7.03457	+	7.94039i	0.283892	+	0.320448i
$615$	−6.50833	−	9.38910i	−0.262441	−	0.378605i
$616$	4.47001	+	5.70555i	0.180102	+	0.229883i
$617$	−41.0653	−	2.48399i	−1.65323	−	0.100002i	−0.792769	−	0.609522i	$-0.791361\pi$
$617$	−41.0653	−	2.48399i	−1.65323	−	0.100002i	−0.860459	+	0.509520i	$0.829823\pi$
$618$	37.2610	+	11.5301i	1.49886	+	0.463807i
$619$	5.24153	+	16.8207i	0.210675	+	0.676080i	0.998210	+	0.0598096i	$0.0190494\pi$
$619$	5.24153	+	16.8207i	0.210675	+	0.676080i	−0.787535	+	0.616270i	$0.788643\pi$
$620$	1.24277	+	2.36789i	0.0499107	+	0.0950969i
$621$	−6.41197	+	12.3955i	−0.257303	+	0.497414i
$622$	39.7985	+	2.40736i	1.59577	+	0.0965265i
$623$	33.1526	−	8.17137i	1.32823	−	0.327379i
$624$	−2.82440	−	29.8248i	−0.113066	−	1.19395i
$625$	19.7277	+	4.86245i	0.789109	+	0.194498i
$626$	−48.6551	−	15.1615i	−1.94465	−	0.605977i
$627$	−2.28098	−	0.557420i	−0.0910937	−	0.0222612i
$628$	−5.56855	+	2.11187i	−0.222209	+	0.0842729i
$629$	9.72386	−	21.6055i	0.387716	−	0.861469i
$630$	0.365864	−	6.47403i	0.0145764	−	0.257931i
$631$	0.628165	+	1.03911i	0.0250069	+	0.0413664i	0.868035	−	0.496504i	$-0.165383\pi$
$631$	0.628165	+	1.03911i	0.0250069	+	0.0413664i	−0.843028	+	0.537870i	$0.819229\pi$
$632$	23.1022	+	4.23363i	0.918956	+	0.168405i
$633$	−19.8293	−	22.2935i	−0.788145	−	0.886089i
$634$	−10.6768	+	4.04917i	−0.424029	+	0.160813i
$635$	2.36255	−	0.736202i	0.0937551	−	0.0292153i
$636$	1.78344	+	7.17448i	0.0707179	+	0.284487i
$637$	2.67327	−	3.64692i	0.105919	−	0.144496i
$638$	−6.78387	+	4.68256i	−0.268576	+	0.185385i
$639$	39.8938	+	23.9013i	1.57818	+	0.945521i
$640$	−7.48738	+	1.84547i	−0.295965	+	0.0729487i
$641$	20.1644	−	29.2132i	0.796446	−	1.15385i	−0.188684	−	0.982038i	$-0.560422\pi$
$641$	20.1644	−	29.2132i	0.796446	−	1.15385i	0.985130	−	0.171813i	$-0.0549625\pi$
$642$	−5.37385	+	6.88728i	−0.212089	+	0.271819i
$643$	13.3430	−	42.8193i	0.526198	−	1.68863i	−0.182576	−	0.983192i	$-0.558444\pi$
$643$	13.3430	−	42.8193i	0.526198	−	1.68863i	0.708774	−	0.705436i	$-0.249249\pi$
$644$	2.18218	+	2.78535i	0.0859900	+	0.109758i
$645$	1.78613	−	0.330979i	0.0703287	−	0.0130323i
$646$	3.76605	+	3.33643i	0.148173	+	0.131270i
$647$	−0.563243	−	0.815998i	−0.0221433	−	0.0320802i	0.811756	−	0.583997i	$-0.198512\pi$
$647$	−0.563243	−	0.815998i	−0.0221433	−	0.0320802i	−0.833899	+	0.551917i	$0.813897\pi$
$648$	16.5088	+	12.7239i	0.648526	+	0.499844i
$649$	−12.9038	+	1.56680i	−0.506517	+	0.0615023i
$650$	26.6356	−	4.10332i	1.04474	−	0.160945i
$651$	23.7745	+	26.7290i	0.931798	+	1.04759i
$652$	−1.20194	+	0.726598i	−0.0470716	+	0.0284558i
$653$			25.7213i			1.00655i	0.864126	+	0.503276i	$0.167872\pi$
$653$			25.7213i			1.00655i	−0.864126	+	0.503276i	$0.832128\pi$
$654$	−7.84336	+	8.88874i	−0.306700	+	0.347577i
$655$	3.74489	−	2.26387i	0.146325	−	0.0884566i
$656$	22.9954	−	51.0937i	0.897820	−	1.99487i
$657$	−20.3933	+	26.2437i	−0.795619	+	1.02386i
$658$	19.4056	−	8.73374i	0.756508	−	0.340477i
$659$	−0.592177	−	2.40256i	−0.0230680	−	0.0935904i	0.958280	−	0.285833i	$-0.0922702\pi$
$659$	−0.592177	−	2.40256i	−0.0230680	−	0.0935904i	−0.981347	+	0.192242i	$0.938424\pi$
$660$	−0.0859836	−	0.696601i	−0.00334691	−	0.0271152i
$661$	−27.9889	−	16.9199i	−1.08864	−	0.658108i	−0.145120	−	0.989414i	$-0.546357\pi$
$661$	−27.9889	−	16.9199i	−1.08864	−	0.658108i	−0.943523	+	0.331306i	$0.892511\pi$
$662$	−25.2937	−	22.4082i	−0.983067	−	0.870921i
$663$	16.5424	+	9.24738i	0.642455	+	0.359139i
$664$	−2.38211	+	2.11037i	−0.0924438	+	0.0818981i
$665$	−1.38252	+	0.253356i	−0.0536119	+	0.00982474i
$666$	37.1440	+	4.36080i	1.43930	+	0.168978i
$667$	8.73954	−	6.03247i	0.338396	−	0.233578i
$668$	−2.82316	−	1.70666i	−0.109231	−	0.0660327i
$669$	1.75879	+	5.60504i	0.0679989	+	0.216703i
$670$	−8.87632	+	11.3298i	−0.342922	+	0.437708i
$671$	0.0538275	−	0.889874i	0.00207799	−	0.0343532i
$672$	11.1202	−	5.86448i	0.428972	−	0.226227i
$673$	−7.61637	+	14.5118i	−0.293590	+	0.559388i	−0.986916	−	0.161235i	$-0.948452\pi$
$673$	−7.61637	+	14.5118i	−0.293590	+	0.559388i	0.693326	+	0.720624i	$0.256144\pi$
$674$	−15.8407	−	2.90291i	−0.610160	−	0.111816i
$675$	−13.6982	+	20.0998i	−0.527244	+	0.773641i
$676$	6.10106	−	3.71851i	0.234656	−	0.143020i
$677$		−	30.9148i		−	1.18815i	−0.804409	−	0.594076i	$-0.797518\pi$
$677$		−	30.9148i		−	1.18815i	0.804409	−	0.594076i	$-0.202482\pi$
$678$	20.5304	−	16.1503i	0.788466	−	0.620249i
$679$	−12.7594	−	6.69665i	−0.489661	−	0.256994i
$680$	1.40738	−	3.71096i	0.0539706	−	0.142309i
$681$	−19.7244	+	19.8027i	−0.755841	+	0.758842i
$682$	14.1398	+	11.0778i	0.541442	+	0.424193i
$683$	4.74784	−	7.85389i	0.181671	−	0.300521i	−0.751651	−	0.659561i	$-0.770742\pi$
$683$	4.74784	−	7.85389i	0.181671	−	0.300521i	0.933322	+	0.359040i	$0.116896\pi$
$684$	−0.696449	+	1.56398i	−0.0266294	+	0.0598001i
$685$	2.99431	+	4.33800i	0.114407	+	0.165746i
$686$	30.6746	+	7.56061i	1.17116	+	0.288666i
$687$	−17.9122	+	29.7635i	−0.683393	+	1.13555i
$688$	5.90786	+	6.66860i	0.225235	+	0.254238i
$689$	21.4774	−	17.9653i	0.818223	−	0.684423i
$690$	0.513861	+	4.16307i	0.0195623	+	0.158485i
$691$	25.6245	−	42.3881i	0.974803	−	1.61252i	0.200511	−	0.979691i	$-0.435740\pi$
$691$	25.6245	−	42.3881i	0.974803	−	1.61252i	0.774292	−	0.632829i	$-0.218106\pi$
$692$	3.04384	−	3.43579i	0.115710	−	0.130609i
$693$	−3.36416	−	8.76564i	−0.127794	−	0.332979i
$694$	−3.14810	−	6.99478i	−0.119500	−	0.265518i
$695$	1.07916	+	1.07916i	0.0409350	+	0.0409350i
$696$	−6.53789	−	14.4500i	−0.247818	−	0.547727i
$697$	18.3369	+	30.3330i	0.694561	+	1.14894i
$698$			16.0500i			0.607501i
$699$	−4.51553	+	5.11737i	−0.170793	+	0.193557i
$700$	3.19048	+	5.27770i	0.120589	+	0.199478i
$701$	1.24075	−	10.2185i	0.0468624	−	0.385947i	−0.950341	−	0.311211i	$-0.899266\pi$
$701$	1.24075	−	10.2185i	0.0468624	−	0.385947i	0.997203	−	0.0747360i	$-0.0238114\pi$
$702$	−6.05151	+	29.2966i	−0.228400	+	1.10573i
$703$	−0.977141	−	8.04748i	−0.0368536	−	0.303517i
$704$	−4.89147	+	3.83222i	−0.184354	+	0.144432i
$705$	5.39983	+	0.644804i	0.203369	+	0.0242847i
$706$	17.8032	−	20.0956i	0.670031	−	0.756308i
$707$	9.86825	−	12.5959i	0.371134	−	0.473717i
$708$	−0.553487	+	9.46123i	−0.0208013	+	0.355575i
$709$	−25.0586	−	7.80859i	−0.941097	−	0.293258i	−0.211689	−	0.977337i	$-0.567896\pi$
$709$	−25.0586	−	7.80859i	−0.941097	−	0.293258i	−0.729408	+	0.684079i	$0.760204\pi$
$710$	13.9528	−	0.843986i	0.523637	−	0.0316742i
$711$	−26.9955	−	14.0322i	−1.01241	−	0.526248i
$712$	7.89474	+	32.0302i	0.295868	+	1.20038i
$713$	−18.2161	−	14.2714i	−0.682198	−	0.534468i
$714$	−2.38542	+	19.9764i	−0.0892720	+	0.747598i
$715$	−2.22983	+	1.44743i	−0.0833907	+	0.0541309i
$716$	−9.17612	−	6.33382i	−0.342928	−	0.236706i
$717$	−28.9199	−	12.9470i	−1.08003	−	0.483513i
$718$	7.46398	+	19.6809i	0.278553	+	0.734485i
$719$	0.706671	−	5.81996i	0.0263544	−	0.217048i	−0.973582	−	0.228338i	$-0.926671\pi$
$719$	0.706671	−	5.81996i	0.0263544	−	0.217048i	0.999936	+	0.0112904i	$0.00359392\pi$
$720$	8.11414	+	0.458551i	0.302396	+	0.0170892i
$721$	28.9304	−	17.4891i	1.07743	−	0.651327i
$722$	−28.1480	−	5.15831i	−1.04756	−	0.191973i
$723$	3.45702	+	7.64069i	0.128568	+	0.284160i
$724$	−2.32237	−	6.12360i	−0.0863103	−	0.227582i
$725$	16.3886	−	8.60141i	0.608658	−	0.319448i
$726$	13.3431	+	21.9737i	0.495209	+	0.815521i
$727$	2.57911	−	10.4638i	0.0956538	−	0.388083i	−0.903528	−	0.428529i	$-0.859032\pi$
$727$	2.57911	−	10.4638i	0.0956538	−	0.388083i	0.999182	+	0.0404466i	$0.0128781\pi$
$728$	−16.1432	−	11.8333i	−0.598307	−	0.438572i
$729$	−15.6008	−	22.0367i	−0.577808	−	0.816173i
$730$	−0.603163	+	9.97147i	−0.0223241	+	0.369061i
$731$	−5.59488	+	0.679341i	−0.206934	+	0.0251263i
$732$	−0.631424	−	0.154305i	−0.0233381	−	0.00570329i
$733$	−21.7021	+	6.76263i	−0.801584	+	0.249784i	−0.670811	−	0.741629i	$-0.734054\pi$
$733$	−21.7021	+	6.76263i	−0.801584	+	0.249784i	−0.130773	+	0.991412i	$0.541746\pi$
$734$	−8.32096	+	3.74496i	−0.307132	+	0.138229i
$735$	0.869103	+	0.865666i	0.0320573	+	0.0319306i
$736$	−6.40186	+	5.01554i	−0.235976	+	0.184875i
$737$	−4.98737	+	20.2345i	−0.183712	+	0.745349i
$738$	−36.9351	+	42.0254i	−1.35960	+	1.54698i
$739$	−0.543726	−	8.98885i	−0.0200013	−	0.330660i	−0.994389	−	0.105786i	$-0.966264\pi$
$739$	−0.543726	−	8.98885i	−0.0200013	−	0.330660i	0.974388	−	0.224875i	$-0.0721973\pi$
$740$	2.14563	−	1.12611i	0.0788750	−	0.0413968i
$741$	6.48063	−	0.220446i	0.238072	−	0.00809827i
$742$	26.3195	+	13.8135i	0.966218	+	0.507110i
$743$	−17.5664	+	39.0310i	−0.644449	+	1.43191i	0.242551	+	0.970139i	$0.422016\pi$
$743$	−17.5664	+	39.0310i	−0.644449	+	1.43191i	−0.887000	+	0.461769i	$0.847215\pi$
$744$	−25.8241	+	22.9697i	−0.946759	+	0.842110i
$745$	−0.297805	+	0.567421i	−0.0109107	+	0.0207887i
$746$	27.5525	+	27.5525i	1.00877	+	1.00877i
$747$	3.75260	−	1.70682i	0.137300	−	0.0624494i
$748$	0.131484	+	2.17370i	0.00480755	+	0.0794782i
$749$	1.36480	+	7.44745i	0.0498685	+	0.272124i
$750$	0.0299581	+	15.1200i	0.00109392	+	0.552104i
$751$	35.7228	+	24.6576i	1.30354	+	0.899770i	0.998615	−	0.0526055i	$-0.0167526\pi$
$751$	35.7228	+	24.6576i	1.30354	+	0.899770i	0.304927	+	0.952376i	$0.401368\pi$
$752$	10.9463	+	24.3217i	0.399171	+	0.886922i
$753$	−3.15079	−	5.97453i	−0.114821	−	0.217724i
$754$	14.5416	−	17.5132i	0.529576	−	0.637792i
$755$	3.44610	−	1.30693i	0.125416	−	0.0475642i
$756$	−6.72608	+	1.27397i	−0.244625	+	0.0463338i
$757$	9.40636	−	24.8025i	0.341880	−	0.901464i	−0.648265	−	0.761415i	$-0.724505\pi$
$757$	9.40636	−	24.8025i	0.341880	−	0.901464i	0.990145	−	0.140048i	$-0.0447258\pi$
$758$	3.55390	+	29.2690i	0.129083	+	1.06310i
$759$	3.15243	+	5.19150i	0.114426	+	0.188440i
$760$	−0.244779	−	1.33572i	−0.00887908	−	0.0484516i
$761$	−4.13363	−	22.5565i	−0.149844	−	0.817673i	−0.969551	−	0.244890i	$-0.921248\pi$
$761$	−4.13363	−	22.5565i	−0.149844	−	0.817673i	0.819707	−	0.572783i	$-0.194136\pi$
$762$	−6.29024	−	10.3589i	−0.227871	−	0.375264i
$763$	1.23846	+	10.1996i	0.0448352	+	0.369251i
$764$	0.892643	−	2.35371i	0.0322947	−	0.0851541i
$765$	−3.15463	+	4.05962i	−0.114056	+	0.146776i
$766$	15.1401	−	5.74189i	0.547035	−	0.207463i
$767$	33.1385	−	13.7969i	1.19656	−	0.498177i
$768$	9.92643	+	18.8225i	0.358189	+	0.679199i
$769$	−3.75129	−	8.33502i	−0.135275	−	0.300569i	0.831793	−

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.s (of order \(52\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.287822 + 1.57060i) q^{2} +(1.61828 - 0.617401i) q^{3} +(-0.513895 - 0.194895i) q^{4} +(-0.563686 - 0.0340967i) q^{5} +(0.503912 + 2.71936i) q^{6} +(2.05136 + 1.24009i) q^{7} +(-1.19811 + 1.98191i) q^{8} +(2.23763 - 1.99825i) q^{9} +(0.215793 - 0.875508i) q^{10} +(-0.235347 - 1.28425i) q^{11} +(-0.951952 + 0.00188616i) q^{12} +(1.58427 + 3.23884i) q^{13} +(-2.53810 + 2.86493i) q^{14} +(-0.933250 + 0.292842i) q^{15} +(-3.59072 - 3.18110i) q^{16} +(2.94651 - 0.726251i) q^{17} +(2.49440 + 4.08955i) q^{18} +(0.734211 - 0.734211i) q^{19} +(0.283030 + 0.127382i) q^{20} +(4.08529 + 0.740295i) q^{21} +2.08477 q^{22} -2.68577 q^{23} +(-0.715233 + 3.94699i) q^{24} +(-4.64697 - 0.564244i) q^{25} +(-5.54289 + 1.55604i) q^{26} +(2.38738 - 4.61524i) q^{27} +(-0.812496 - 1.03707i) q^{28} +(-3.25401 + 2.24608i) q^{29} +(-0.191327 - 1.55004i) q^{30} +(6.78244 + 5.31370i) q^{31} +(2.38362 - 1.86744i) q^{32} +(-1.17375 - 1.93296i) q^{33} +(0.292573 + 4.83681i) q^{34} +(-1.11404 - 0.768965i) q^{35} +(-1.53936 + 0.590789i) q^{36} +(4.81493 - 6.14580i) q^{37} +(0.941826 + 1.36447i) q^{38} +(4.56345 + 4.26320i) q^{39} +(0.742933 - 1.07632i) q^{40} +(3.47479 + 11.1510i) q^{41} +(-2.33854 + 6.20327i) q^{42} +(-1.84364 - 0.223858i) q^{43} +(-0.129349 + 0.705837i) q^{44} +(-1.32945 + 1.05009i) q^{45} +(0.773026 - 4.21827i) q^{46} +(-5.07004 - 2.28184i) q^{47} +(-7.77479 - 2.93098i) q^{48} +(-0.582815 - 1.11046i) q^{49} +(2.22370 - 7.13610i) q^{50} +(4.31988 - 2.99446i) q^{51} +(-0.182917 - 1.97319i) q^{52} +(-1.85851 - 7.54028i) q^{53} +(6.56153 + 5.07798i) q^{54} +(0.0888732 + 0.731936i) q^{55} +(-4.91549 + 2.57985i) q^{56} +(0.734853 - 1.64146i) q^{57} +(-2.59111 - 5.75721i) q^{58} +(0.601112 - 9.93757i) q^{59} +(0.536666 + 0.0313952i) q^{60} +(0.662969 + 0.163407i) q^{61} +(-10.2978 + 9.12306i) q^{62} +(7.06819 - 1.32426i) q^{63} +(-2.21175 - 4.21414i) q^{64} +(-0.782598 - 1.87971i) q^{65} +(3.37373 - 1.28714i) q^{66} +(-14.5555 - 6.55088i) q^{67} +(-1.65574 - 0.201044i) q^{68} +(-4.34632 + 1.65820i) q^{69} +(1.52838 - 1.52838i) q^{70} +(4.61187 + 14.8000i) q^{71} +(1.27943 + 6.82891i) q^{72} +(-10.8971 + 1.99697i) q^{73} +(8.26672 + 9.33120i) q^{74} +(-7.86844 + 1.95594i) q^{75} +(-0.520401 + 0.234214i) q^{76} +(1.10980 - 2.92630i) q^{77} +(-8.00923 + 5.94029i) q^{78} +(-3.59624 - 9.48251i) q^{79} +(1.91557 + 1.91557i) q^{80} +(1.01399 - 8.94270i) q^{81} +(-18.5138 + 2.24798i) q^{82} +(1.31195 + 0.408822i) q^{83} +(-1.95513 - 1.17664i) q^{84} +(-1.68567 + 0.308911i) q^{85} +(0.882230 - 2.83117i) q^{86} +(-3.87915 + 5.64381i) q^{87} +(2.82724 + 1.07223i) q^{88} +(10.0723 - 10.0723i) q^{89} +(-1.26662 - 2.39027i) q^{90} +(-0.766541 + 8.60866i) q^{91} +(1.38021 + 0.523444i) q^{92} +(14.2565 + 4.41155i) q^{93} +(5.04311 - 7.30621i) q^{94} +(-0.438898 + 0.388830i) q^{95} +(2.70439 - 4.49369i) q^{96} +(-6.00056 + 0.362967i) q^{97} +(1.91183 - 0.595751i) q^{98} +(-3.09287 - 2.40339i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1392 q - 22 q^{3} - 52 q^{4} - 22 q^{6} - 56 q^{7} - 22 q^{9} - 52 q^{10} - 26 q^{12} - 44 q^{13} - 34 q^{15} + 48 q^{16} - 34 q^{18} - 56 q^{19} - 22 q^{21} - 96 q^{22} - 194 q^{24} - 52 q^{25} - 34 q^{27}+ \cdots - 58 q^{99}+O(q^{100}) \) 1392 * q - 22 * q^3 - 52 * q^4 - 22 * q^6 - 56 * q^7 - 22 * q^9 - 52 * q^10 - 26 * q^12 - 44 * q^13 - 34 * q^15 + 48 * q^16 - 34 * q^18 - 56 * q^19 - 22 * q^21 - 96 * q^22 - 194 * q^24 - 52 * q^25 - 34 * q^27 - 56 * q^28 + 78 * q^30 - 32 * q^31 - 10 * q^33 - 52 * q^34 - 26 * q^36 - 56 * q^37 + 70 * q^39 - 36 * q^40 - 10 * q^42 - 52 * q^43 - 140 * q^45 - 180 * q^46 - 2 * q^48 - 52 * q^49 - 26 * q^51 - 64 * q^52 - 22 * q^54 + 132 * q^55 - 22 * q^57 - 60 * q^58 - 18 * q^60 - 92 * q^61 + 108 * q^63 - 52 * q^64 - 124 * q^66 - 240 * q^67 - 104 * q^69 - 268 * q^70 - 2 * q^72 - 56 * q^73 + 104 * q^75 - 48 * q^76 - 22 * q^78 - 12 * q^79 + 2 * q^81 + 208 * q^82 - 22 * q^84 - 52 * q^85 - 26 * q^87 - 260 * q^88 - 26 * q^90 - 32 * q^91 - 176 * q^93 - 240 * q^94 + 292 * q^96 - 80 * q^97 - 58 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more