LMFDB - Embedded newform 78.2.k.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,2,Mod(11,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 7]))

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

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

chi := DirichletCharacter("78.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	78.k (of order $12$, degree $4$, 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:	$0.622833135766$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + 9297 x^{8} - 11276 x^{7} + 11224 x^{6} - 9024 x^{5} + 5736 x^{4} - 2780 x^{3} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.3
Root			$0.500000 - 0.331082i$ of defining polynomial
Character	$\chi$	$=$	78.11
Dual form			78.2.k.a.71.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(-0.933998 + 1.45865i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.313444 - 0.313444i) q^{5} +(-1.27970 + 1.16721i) q^{6} +(-0.0745867 - 0.278362i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.25529 - 2.72474i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(-0.933998 + 1.45865i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.313444 - 0.313444i) q^{5} +(-1.27970 + 1.16721i) q^{6} +(-0.0745867 - 0.278362i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.25529 - 2.72474i) q^{9} +(0.383889 - 0.221638i) q^{10} +(0.150860 - 0.563016i) q^{11} +(-1.53819 + 0.796225i) q^{12} +(-1.79144 - 3.12902i) q^{13} -0.288181i q^{14} +(0.164448 + 0.749960i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.79907 - 4.84812i) q^{17} +(-0.507306 - 2.95680i) q^{18} +(-6.79127 + 1.81971i) q^{19} +(0.428173 - 0.114729i) q^{20} +(0.475695 + 0.151194i) q^{21} +(0.291439 - 0.504787i) q^{22} +(3.32595 + 5.76071i) q^{23} +(-1.69185 + 0.370982i) q^{24} +4.80351i q^{25} +(-0.920548 - 3.48606i) q^{26} +(5.14688 + 0.713876i) q^{27} +(0.0745867 - 0.278362i) q^{28} +(-3.57681 + 2.06507i) q^{29} +(-0.0352597 + 0.766968i) q^{30} +(-1.03573 - 1.03573i) q^{31} +(0.258819 + 0.965926i) q^{32} +(0.680339 + 0.745907i) q^{33} +(3.95848 - 3.95848i) q^{34} +(-0.110630 - 0.0638720i) q^{35} +(0.275255 - 2.98735i) q^{36} +(6.72147 + 1.80101i) q^{37} -7.03084 q^{38} +(6.23733 + 0.309422i) q^{39} +0.443277 q^{40} +(-7.36988 - 1.97475i) q^{41} +(0.420354 + 0.269161i) q^{42} +(-3.26299 - 1.88389i) q^{43} +(0.412157 - 0.412157i) q^{44} +(-1.24752 - 0.460590i) q^{45} +(1.72164 + 6.42524i) q^{46} +(3.71799 + 3.71799i) q^{47} +(-1.73022 - 0.0795432i) q^{48} +(5.99026 - 3.45848i) q^{49} +(-1.24324 + 4.63983i) q^{50} +(4.45737 + 8.61098i) q^{51} +(0.0130771 - 3.60553i) q^{52} +3.64778i q^{53} +(4.78674 + 2.02166i) q^{54} +(-0.129188 - 0.223760i) q^{55} +(0.144091 - 0.249572i) q^{56} +(3.68871 - 11.6057i) q^{57} +(-3.98942 + 1.06896i) q^{58} +(-3.29111 + 0.881850i) q^{59} +(-0.232564 + 0.731708i) q^{60} +(-5.25554 + 9.10286i) q^{61} +(-0.732370 - 1.26850i) q^{62} +(-0.664836 + 0.552656i) q^{63} +1.00000i q^{64} +(-1.54229 - 0.419256i) q^{65} +(0.464102 + 0.896575i) q^{66} +(2.29144 - 8.55177i) q^{67} +(4.84812 - 2.79907i) q^{68} +(-11.5093 - 0.529114i) q^{69} +(-0.0903287 - 0.0903287i) q^{70} +(-3.98229 - 14.8621i) q^{71} +(1.03906 - 2.81431i) q^{72} +(3.52053 - 3.52053i) q^{73} +(6.02630 + 3.47929i) q^{74} +(-7.00661 - 4.48647i) q^{75} +(-6.79127 - 1.81971i) q^{76} -0.167974 q^{77} +(5.94471 + 1.91322i) q^{78} +1.10886 q^{79} +(0.428173 + 0.114729i) q^{80} +(-5.84847 + 6.84072i) q^{81} +(-6.60765 - 3.81493i) q^{82} +(-8.23032 + 8.23032i) q^{83} +(0.336367 + 0.368785i) q^{84} +(-0.642265 - 2.39697i) q^{85} +(-2.66422 - 2.66422i) q^{86} +(0.328525 - 7.14608i) q^{87} +(0.504787 - 0.291439i) q^{88} +(3.64478 - 13.6025i) q^{89} +(-1.08580 - 0.767778i) q^{90} +(-0.737380 + 0.732051i) q^{91} +6.65190i q^{92} +(2.47813 - 0.543392i) q^{93} +(2.62902 + 4.55359i) q^{94} +(-1.55830 + 2.69906i) q^{95} +(-1.65068 - 0.524648i) q^{96} +(2.59245 - 0.694645i) q^{97} +(6.68126 - 1.79024i) q^{98} +(-1.72345 + 0.295697i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} - 24 q^{10} - 24 q^{13} + 8 q^{16} - 16 q^{19} - 24 q^{21} - 8 q^{28} + 24 q^{30} + 16 q^{31} - 24 q^{33} + 24 q^{34} + 24 q^{36} + 16 q^{37} + 48 q^{39} + 24 q^{45} + 24 q^{46} + 24 q^{49} - 8 q^{52} - 24 q^{55} - 24 q^{57} - 24 q^{60} - 24 q^{61} - 24 q^{63} - 48 q^{66} + 32 q^{67} - 48 q^{69} - 24 q^{72} + 56 q^{73} - 16 q^{76} - 96 q^{79} + 24 q^{81} - 48 q^{82} - 24 q^{85} + 48 q^{87} - 16 q^{91} - 24 q^{93} - 24 q^{94} + 16 q^{97}+O(q^{100}) $ 16 * q + 8 * q^7 - 24 * q^10 - 24 * q^13 + 8 * q^16 - 16 * q^19 - 24 * q^21 - 8 * q^28 + 24 * q^30 + 16 * q^31 - 24 * q^33 + 24 * q^34 + 24 * q^36 + 16 * q^37 + 48 * q^39 + 24 * q^45 + 24 * q^46 + 24 * q^49 - 8 * q^52 - 24 * q^55 - 24 * q^57 - 24 * q^60 - 24 * q^61 - 24 * q^63 - 48 * q^66 + 32 * q^67 - 48 * q^69 - 24 * q^72 + 56 * q^73 - 16 * q^76 - 96 * q^79 + 24 * q^81 - 48 * q^82 - 24 * q^85 + 48 * q^87 - 16 * q^91 - 24 * q^93 - 24 * q^94 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	−0.933998	+	1.45865i	−0.539244	+	0.842150i
$3$	−0.933998	+	1.45865i	−0.539244	+	0.842150i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	0.313444	−	0.313444i	0.140176	−	0.140176i	−0.633536	−	0.773713i	$-0.718397\pi$
$5$	0.313444	−	0.313444i	0.140176	−	0.140176i	0.773713	+	0.633536i	$0.218397\pi$
$6$	−1.27970	+	1.16721i	−0.522435	+	0.476510i
$7$	−0.0745867	−	0.278362i	−0.0281911	−	0.105211i	0.950397	−	0.311040i	$-0.100677\pi$
$7$	−0.0745867	−	0.278362i	−0.0281911	−	0.105211i	−0.978588	+	0.205830i	$0.934011\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.25529	−	2.72474i	−0.418432	−	0.908248i
$10$	0.383889	−	0.221638i	0.121396	−	0.0700882i
$11$	0.150860	−	0.563016i	0.0454859	−	0.169756i	−0.939446	−	0.342696i	$-0.888660\pi$
$11$	0.150860	−	0.563016i	0.0454859	−	0.169756i	0.984932	+	0.172940i	$0.0553267\pi$
$12$	−1.53819	+	0.796225i	−0.444037	+	0.229850i
$13$	−1.79144	−	3.12902i	−0.496856	−	0.867833i
$13$	−1.79144	−	3.12902i	−0.496856	−	0.867833i
$14$		−	0.288181i		−	0.0770196i
$15$	0.164448	+	0.749960i	0.0424602	+	0.193639i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.79907	−	4.84812i	0.678873	−	1.17584i	−0.296448	−	0.955049i	$-0.595802\pi$
$17$	2.79907	−	4.84812i	0.678873	−	1.17584i	0.975321	−	0.220793i	$-0.0708647\pi$
$18$	−0.507306	−	2.95680i	−0.119573	−	0.696923i
$19$	−6.79127	+	1.81971i	−1.55802	+	0.417471i	−0.932037	−	0.362363i	$-0.881970\pi$
$19$	−6.79127	+	1.81971i	−1.55802	+	0.417471i	−0.625986	+	0.779834i	$0.715304\pi$
$20$	0.428173	−	0.114729i	0.0957423	−	0.0256541i
$21$	0.475695	+	0.151194i	0.103805	+	0.0329931i
$22$	0.291439	−	0.504787i	0.0621349	−	0.107621i
$23$	3.32595	+	5.76071i	0.693509	+	1.20119i	0.970681	+	0.240372i	$0.0772694\pi$
$23$	3.32595	+	5.76071i	0.693509	+	1.20119i	−0.277172	+	0.960820i	$0.589397\pi$
$24$	−1.69185	+	0.370982i	−0.345348	+	0.0757264i
$25$			4.80351i			0.960701i
$26$	−0.920548	−	3.48606i	−0.180534	−	0.683672i
$27$	5.14688	+	0.713876i	0.990518	+	0.137386i
$28$	0.0745867	−	0.278362i	0.0140956	−	0.0526054i
$29$	−3.57681	+	2.06507i	−0.664198	+	0.383475i	−0.793874	−	0.608082i	$-0.791939\pi$
$29$	−3.57681	+	2.06507i	−0.664198	+	0.383475i	0.129677	+	0.991556i	$0.458606\pi$
$30$	−0.0352597	+	0.766968i	−0.00643751	+	0.140029i
$31$	−1.03573	−	1.03573i	−0.186022	−	0.186022i	0.607952	−	0.793974i	$-0.291991\pi$
$31$	−1.03573	−	1.03573i	−0.186022	−	0.186022i	−0.793974	+	0.607952i	$0.791991\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	0.680339	+	0.745907i	0.118432	+	0.129846i
$34$	3.95848	−	3.95848i	0.678873	−	0.678873i
$35$	−0.110630	−	0.0638720i	−0.0186998	−	0.0107963i
$36$	0.275255	−	2.98735i	0.0458759	−	0.497891i
$37$	6.72147	+	1.80101i	1.10500	+	0.296085i	0.764800	−	0.644268i	$-0.222838\pi$
$37$	6.72147	+	1.80101i	1.10500	+	0.296085i	0.340202	+	0.940352i	$0.389504\pi$
$38$	−7.03084			−1.14055
$39$	6.23733	+	0.309422i	0.998772	+	0.0495471i
$40$	0.443277			0.0700882
$41$	−7.36988	−	1.97475i	−1.15098	−	0.308404i	−0.367623	−	0.929975i	$-0.619828\pi$
$41$	−7.36988	−	1.97475i	−1.15098	−	0.308404i	−0.783358	+	0.621570i	$0.786495\pi$
$42$	0.420354	+	0.269161i	0.0648620	+	0.0415324i
$43$	−3.26299	−	1.88389i	−0.497602	−	0.287290i	0.230121	−	0.973162i	$-0.426088\pi$
$43$	−3.26299	−	1.88389i	−0.497602	−	0.287290i	−0.727723	+	0.685872i	$0.759421\pi$
$44$	0.412157	−	0.412157i	0.0621349	−	0.0621349i
$45$	−1.24752	−	0.460590i	−0.185969	−	0.0686608i
$46$	1.72164	+	6.42524i	0.253842	+	0.947350i
$47$	3.71799	+	3.71799i	0.542325	+	0.542325i	0.924210	−	0.381885i	$-0.124725\pi$
$47$	3.71799	+	3.71799i	0.542325	+	0.542325i	−0.381885	+	0.924210i	$0.624725\pi$
$48$	−1.73022	−	0.0795432i	−0.249736	−	0.0114811i
$49$	5.99026	−	3.45848i	0.855751	−	0.494068i
$50$	−1.24324	+	4.63983i	−0.175821	+	0.656171i
$51$	4.45737	+	8.61098i	0.624157	+	1.20578i
$52$	0.0130771	−	3.60553i	0.00181347	−	0.499997i
$53$			3.64778i			0.501062i	0.968109	+	0.250531i	$0.0806052\pi$
$53$			3.64778i			0.501062i	−0.968109	+	0.250531i	$0.919395\pi$
$54$	4.78674	+	2.02166i	0.651393	+	0.275113i
$55$	−0.129188	−	0.223760i	−0.0174197	−	0.0301718i
$56$	0.144091	−	0.249572i	0.0192549	−	0.0333505i
$57$	3.68871	−	11.6057i	0.488582	−	1.53721i
$58$	−3.98942	+	1.06896i	−0.523836	+	0.140361i
$59$	−3.29111	+	0.881850i	−0.428466	+	0.114807i	−0.466606	−	0.884465i	$-0.654523\pi$
$59$	−3.29111	+	0.881850i	−0.428466	+	0.114807i	0.0381400	+	0.999272i	$0.487857\pi$
$60$	−0.232564	+	0.731708i	−0.0300239	+	0.0944632i
$61$	−5.25554	+	9.10286i	−0.672903	+	1.16550i	0.304174	+	0.952616i	$0.401620\pi$
$61$	−5.25554	+	9.10286i	−0.672903	+	1.16550i	−0.977077	+	0.212886i	$0.931714\pi$
$62$	−0.732370	−	1.26850i	−0.0930111	−	0.161100i
$63$	−0.664836	+	0.552656i	−0.0837614	+	0.0696281i
$64$			1.00000i			0.125000i
$65$	−1.54229	−	0.419256i	−0.191297	−	0.0520023i
$66$	0.464102	+	0.896575i	0.0571270	+	0.110361i
$67$	2.29144	−	8.55177i	0.279944	−	1.04476i	−0.672512	−	0.740087i	$-0.734785\pi$
$67$	2.29144	−	8.55177i	0.279944	−	1.04476i	0.952455	−	0.304678i	$-0.0985488\pi$
$68$	4.84812	−	2.79907i	0.587921	−	0.339437i
$69$	−11.5093	−	0.529114i	−1.38555	−	0.0636978i
$70$	−0.0903287	−	0.0903287i	−0.0107963	−	0.0107963i
$71$	−3.98229	−	14.8621i	−0.472611	−	1.76381i	−0.630334	−	0.776324i	$-0.717082\pi$
$71$	−3.98229	−	14.8621i	−0.472611	−	1.76381i	0.157723	−	0.987483i	$-0.449585\pi$
$72$	1.03906	−	2.81431i	0.122454	−	0.331670i
$73$	3.52053	−	3.52053i	0.412047	−	0.412047i	−0.470404	−	0.882451i	$-0.655892\pi$
$73$	3.52053	−	3.52053i	0.412047	−	0.412047i	0.882451	+	0.470404i	$0.155892\pi$
$74$	6.02630	+	3.47929i	0.700543	+	0.404459i
$75$	−7.00661	−	4.48647i	−0.809054	−	0.518052i
$76$	−6.79127	−	1.81971i	−0.779012	−	0.208736i
$77$	−0.167974			−0.0191424
$78$	5.94471	+	1.91322i	0.673106	+	0.216629i
$79$	1.10886			0.124757			0.0623783	−	0.998053i	$-0.480131\pi$
$79$	1.10886			0.124757			0.0623783	+	0.998053i	$0.480131\pi$
$80$	0.428173	+	0.114729i	0.0478712	+	0.0128270i
$81$	−5.84847	+	6.84072i	−0.649830	+	0.760080i
$82$	−6.60765	−	3.81493i	−0.729693	−	0.421288i
$83$	−8.23032	+	8.23032i	−0.903395	+	0.903395i	−0.995728	−	0.0923332i	$-0.970567\pi$
$83$	−8.23032	+	8.23032i	−0.903395	+	0.903395i	0.0923332	+	0.995728i	$0.470567\pi$
$84$	0.336367	+	0.368785i	0.0367006	+	0.0402377i
$85$	−0.642265	−	2.39697i	−0.0696634	−	0.259987i
$86$	−2.66422	−	2.66422i	−0.287290	−	0.287290i
$87$	0.328525	−	7.14608i	0.0352216	−	0.766140i
$88$	0.504787	−	0.291439i	0.0538104	−	0.0310675i
$89$	3.64478	−	13.6025i	0.386346	−	1.44186i	−0.449687	−	0.893186i	$-0.648465\pi$
$89$	3.64478	−	13.6025i	0.386346	−	1.44186i	0.836034	−	0.548678i	$-0.184869\pi$
$90$	−1.08580	−	0.767778i	−0.114454	−	0.0809309i
$91$	−0.737380	+	0.732051i	−0.0772985	+	0.0767398i
$92$			6.65190i			0.693509i
$93$	2.47813	−	0.543392i	0.256970	−	0.0563471i
$94$	2.62902	+	4.55359i	0.271162	+	0.469667i
$95$	−1.55830	+	2.69906i	−0.159879	+	0.276918i
$96$	−1.65068	−	0.524648i	−0.168472	−	0.0535466i
$97$	2.59245	−	0.694645i	0.263223	−	0.0705305i	−0.124794	−	0.992183i	$-0.539827\pi$
$97$	2.59245	−	0.694645i	0.263223	−	0.0705305i	0.388017	+	0.921652i	$0.373160\pi$
$98$	6.68126	−	1.79024i	0.674909	−	0.180841i
$99$	−1.72345	+	0.295697i	−0.173213	+	0.0297187i
$100$	−2.40175	+	4.15996i	−0.240175	+	0.415996i
$101$	7.12030	+	12.3327i	0.708497	+	1.22715i	0.965415	+	0.260719i	$0.0839596\pi$
$101$	7.12030	+	12.3327i	0.708497	+	1.22715i	−0.256918	+	0.966433i	$0.582707\pi$
$102$	2.07680	+	9.47122i	0.205634	+	0.937791i
$103$			4.60903i			0.454141i	0.973878	+	0.227071i	$0.0729148\pi$
$103$			4.60903i			0.454141i	−0.973878	+	0.227071i	$0.927085\pi$
$104$	0.945811	−	3.47929i	0.0927444	−	0.341172i
$105$	0.196494	−	0.101713i	0.0191759	−	0.00992617i
$106$	−0.944116	+	3.52349i	−0.0917007	+	0.342232i
$107$	11.7017	−	6.75600i	1.13125	−	0.653127i	0.187001	−	0.982360i	$-0.440123\pi$
$107$	11.7017	−	6.75600i	1.13125	−	0.653127i	0.944249	+	0.329232i	$0.106790\pi$
$108$	4.10039	+	3.19168i	0.394560	+	0.307119i
$109$	2.06188	+	2.06188i	0.197492	+	0.197492i	0.798924	−	0.601432i	$-0.205403\pi$
$109$	2.06188	+	2.06188i	0.197492	+	0.197492i	−0.601432	+	0.798924i	$0.705403\pi$
$110$	−0.0668726	−	0.249572i	−0.00637606	−	0.0237958i
$111$	−8.90488	+	8.12210i	−0.845213	+	0.770915i
$112$	0.203775	−	0.203775i	0.0192549	−	0.0192549i
$113$	9.02108	+	5.20832i	0.848632	+	0.489958i	0.860189	−	0.509975i	$-0.170345\pi$
$113$	9.02108	+	5.20832i	0.848632	+	0.489958i	−0.0115570	+	0.999933i	$0.503679\pi$
$114$	6.56679	−	10.2555i	0.615036	−	0.960516i
$115$	2.84816	+	0.763163i	0.265592	+	0.0711653i
$116$	−4.13015			−0.383475
$117$	−6.27699	+	8.80905i	−0.580308	+	0.814397i
$118$	−3.40721			−0.313659
$119$	−1.55830	−	0.417546i	−0.142850	−	0.0382764i
$120$	−0.414020	+	0.646584i	−0.0377947	+	0.0590248i
$121$	9.23205	+	5.33013i	0.839277	+	0.484557i
$122$	−7.43246	+	7.43246i	−0.672903	+	0.672903i
$123$	9.76391	−	8.90562i	0.880382	−	0.802993i
$124$	−0.379103	−	1.41483i	−0.0340444	−	0.127055i
$125$	3.07285	+	3.07285i	0.274844	+	0.274844i
$126$	−0.785220	+	0.361752i	−0.0699529	+	0.0322274i
$127$	−0.209104	+	0.120726i	−0.0185550	+	0.0107127i	−0.509249	−	0.860619i	$-0.670077\pi$
$127$	−0.209104	+	0.120726i	−0.0185550	+	0.0107127i	0.490694	+	0.871332i	$0.336743\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	5.79555	−	3.00000i	0.510270	−	0.264135i
$130$	−1.38122	−	0.804144i	−0.121141	−	0.0705281i
$131$		−	8.09043i		−	0.706864i	−0.935460	−	0.353432i	$-0.885015\pi$
$131$		−	8.09043i		−	0.706864i	0.935460	−	0.353432i	$-0.114985\pi$
$132$	0.216237	+	0.986144i	0.0188210	+	0.0858328i
$133$	1.01308	+	1.75470i	0.0878449	+	0.152152i
$134$	4.42672	−	7.66730i	0.382410	−	0.662354i
$135$	1.83702	−	1.38950i	0.158105	−	0.119589i
$136$	5.40738	−	1.44890i	0.463679	−	0.124242i
$137$	−0.0798882	+	0.0214060i	−0.00682531	+	0.00182884i	−0.262230	−	0.965005i	$-0.584458\pi$
$137$	−0.0798882	+	0.0214060i	−0.00682531	+	0.00182884i	0.255405	+	0.966834i	$0.417791\pi$
$138$	−10.9802	−	3.48990i	−0.934693	−	0.297080i
$139$	3.12073	−	5.40526i	0.264697	−	0.458468i	−0.702788	−	0.711400i	$-0.748062\pi$
$139$	3.12073	−	5.40526i	0.264697	−	0.458468i	0.967484	+	0.252932i	$0.0813949\pi$
$140$	−0.0638720	−	0.110630i	−0.00539817	−	0.00934990i
$141$	−8.89583	+	1.95064i	−0.749164	+	0.164273i
$142$		−	15.3864i		−	1.29120i
$143$	−2.03194	+	0.536566i	−0.169920	+	0.0448699i
$144$	1.73205	−	2.44949i	0.144338	−	0.204124i
$145$	−0.473846	+	1.76842i	−0.0393507	+	0.146859i
$146$	4.31175	−	2.48939i	0.356843	−	0.206023i
$147$	−0.550197	+	11.9679i	−0.0453795	+	0.987093i
$148$	4.92046	+	4.92046i	0.404459	+	0.404459i
$149$	3.76251	+	14.0419i	0.308237	+	1.15036i	0.930123	+	0.367249i	$0.119700\pi$
$149$	3.76251	+	14.0419i	0.308237	+	1.15036i	−0.621886	+	0.783108i	$0.713633\pi$
$150$	−5.60669	−	6.14704i	−0.457784	−	0.501904i
$151$	−6.40358	+	6.40358i	−0.521116	+	0.521116i	−0.917908	−	0.396793i	$-0.870123\pi$
$151$	−6.40358	+	6.40358i	−0.521116	+	0.521116i	0.396793	+	0.917908i	$0.370123\pi$
$152$	−6.08888	−	3.51542i	−0.493874	−	0.285138i
$153$	−16.7236	−	1.54091i	−1.35202	−	0.124576i
$154$	−0.162251	−	0.0434749i	−0.0130745	−	0.00350331i
$155$	−0.649285			−0.0521519
$156$	5.24697	+	3.38663i	0.420094	+	0.271147i
$157$	−10.2127			−0.815065			−0.407532	−	0.913191i	$-0.633611\pi$
$157$	−10.2127			−0.815065			−0.407532	+	0.913191i	$0.633611\pi$
$158$	1.07108	+	0.286994i	0.0852103	+	0.0228320i
$159$	−5.32083	−	3.40702i	−0.421969	−	0.270195i
$160$	0.383889	+	0.221638i	0.0303491	+	0.0175221i
$161$	1.35549	−	1.35549i	0.106828	−	0.106828i
$162$	−7.41970	+	5.09393i	−0.582946	+	0.400217i
$163$	−3.59245	−	13.4072i	−0.281382	−	1.05013i	−0.951442	−	0.307827i	$-0.900398\pi$
$163$	−3.59245	−	13.4072i	−0.281382	−	1.05013i	0.670060	−	0.742307i	$-0.266268\pi$
$164$	−5.39512	−	5.39512i	−0.421288	−	0.421288i
$165$	0.447048	+	0.0205521i	0.0348027	+	0.00159998i
$166$	−10.0800	+	5.81971i	−0.782363	+	0.451697i
$167$	3.47123	−	12.9548i	0.268612	−	1.00247i	−0.691391	−	0.722481i	$-0.743002\pi$
$167$	3.47123	−	12.9548i	0.268612	−	1.00247i	0.960003	−	0.279991i	$-0.0903316\pi$
$168$	0.229457	+	0.443277i	0.0177030	+	0.0341996i
$169$	−6.58150	+	11.2109i	−0.506269	+	0.862376i
$170$		−	2.48152i		−	0.190324i
$171$	13.4833	+	16.2202i	1.03109	+	1.24039i
$172$	−1.88389	−	3.26299i	−0.143645	−	0.248801i
$173$	0.551099	−	0.954532i	0.0418993	−	0.0725717i	−0.844315	−	0.535847i	$-0.819992\pi$
$173$	0.551099	−	0.954532i	0.0418993	−	0.0725717i	0.886215	+	0.463275i	$0.153326\pi$
$174$	2.16687	−	6.81755i	0.164270	−	0.516837i
$175$	1.33711	−	0.358278i	0.101076	−	0.0270833i
$176$	0.563016	−	0.150860i	0.0424389	−	0.0113715i
$177$	1.78758	−	5.62421i	0.134363	−	0.422741i
$178$	7.04118	−	12.1957i	0.527759	−	0.914105i
$179$	2.79777	+	4.84589i	0.209115	+	0.362199i	0.951436	−	0.307846i	$-0.0996082\pi$
$179$	2.79777	+	4.84589i	0.209115	+	0.362199i	−0.742321	+	0.670045i	$0.766275\pi$
$180$	−0.850089	−	1.02264i	−0.0633619	−	0.0762233i
$181$		−	14.4687i		−	1.07545i	−0.843119	−	0.537727i	$-0.819283\pi$
$181$		−	14.4687i		−	1.07545i	0.843119	−	0.537727i	$-0.180717\pi$
$182$	−0.901723	+	0.516259i	−0.0668402	+	0.0382676i
$183$	−8.36919	−	16.1680i	−0.618668	−	1.19518i
$184$	−1.72164	+	6.42524i	−0.126921	+	0.473675i
$185$	2.67132	−	1.54229i	0.196399	−	0.113391i
$186$	2.53433	+	0.116510i	0.185826	+	0.00854294i
$187$	−2.30731	−	2.30731i	−0.168727	−	0.168727i
$188$	1.36088	+	5.07887i	0.0992523	+	0.370415i
$189$	−0.185173	−	1.48594i	−0.0134694	−	0.108086i
$190$	−2.20377	+	2.20377i	−0.159879	+	0.159879i
$191$	−5.78136	−	3.33787i	−0.418324	−	0.241520i	0.276036	−	0.961147i	$-0.410979\pi$
$191$	−5.78136	−	3.33787i	−0.418324	−	0.241520i	−0.694360	+	0.719628i	$0.744312\pi$
$192$	−1.45865	−	0.933998i	−0.105269	−	0.0674055i
$193$	5.88685	+	1.57738i	0.423745	+	0.113542i	0.464388	−	0.885632i	$-0.346274\pi$
$193$	5.88685	+	1.57738i	0.423745	+	0.113542i	−0.0406437	+	0.999174i	$0.512941\pi$
$194$	2.68390			0.192693
$195$	2.05204	−	1.85807i	0.146950	−	0.133059i
$196$	6.91695			0.494068
$197$	−14.2844	−	3.82748i	−1.01772	−	0.272697i	−0.288868	−	0.957369i	$-0.593279\pi$
$197$	−14.2844	−	3.82748i	−1.01772	−	0.272697i	−0.728851	+	0.684672i	$0.759945\pi$
$198$	−1.74126	−	0.160440i	−0.123746	−	0.0114020i
$199$	13.4064	+	7.74017i	0.950352	+	0.548686i	0.893190	−	0.449679i	$-0.148462\pi$
$199$	13.4064	+	7.74017i	0.950352	+	0.548686i	0.0571619	+	0.998365i	$0.481795\pi$
$200$	−3.39659	+	3.39659i	−0.240175	+	0.240175i
$201$	10.3338	+	11.3297i	0.728890	+	0.799138i
$202$	3.68574	+	13.7554i	0.259328	+	0.967824i
$203$	0.841620	+	0.841620i	0.0590701	+	0.0590701i
$204$	−0.445293	+	9.68602i	−0.0311768	+	0.678157i
$205$	−2.92902	+	1.69107i	−0.204572	+	0.118109i
$206$	−1.19291	+	4.45198i	−0.0831136	+	0.310184i
$207$	11.5214	−	16.2938i	0.800795	−	1.13249i
$208$	1.81409	−	3.11594i	0.125784	−	0.216052i
$209$			4.09812i			0.283473i
$210$	0.216124	−	0.0473907i	0.0149140	−	0.00327027i
$211$	−9.40721	−	16.2938i	−0.647619	−	1.12171i	−0.983690	−	0.179872i	$-0.942432\pi$
$211$	−9.40721	−	16.2938i	−0.647619	−	1.12171i	0.336071	−	0.941837i	$-0.390902\pi$
$212$	−1.82389	+	3.15907i	−0.125265	+	0.216966i
$213$	25.3980	+	8.07243i	1.74024	+	0.553114i
$214$	13.0516	−	3.49716i	0.892189	−	0.239061i
$215$	−1.61326	+	0.432272i	−0.110023	+	0.0294807i
$216$	3.13461	+	4.14418i	0.213283	+	0.281976i
$217$	−0.211055	+	0.365558i	−0.0143274	+	0.0248157i
$218$	1.45797	+	2.52528i	0.0987462	+	0.171033i
$219$	1.84704	+	8.42337i	0.124811	+	0.569199i
$220$		−	0.258376i		−	0.0174197i
$221$	−20.1842	−	0.0732075i	−1.35774	−	0.00492447i
$222$	−10.7036	+	5.54059i	−0.718379	+	0.371860i
$223$	−1.86235	+	6.95039i	−0.124712	+	0.465432i	−0.999829	−	0.0184790i	$-0.994118\pi$
$223$	−1.86235	+	6.95039i	−0.124712	+	0.465432i	0.875117	+	0.483911i	$0.160784\pi$
$224$	0.249572	−	0.144091i	0.0166752	−	0.00962745i
$225$	13.0883	−	6.02982i	0.872555	−	0.401988i
$226$	7.36568	+	7.36568i	0.489958	+	0.489958i
$227$	1.38733	+	5.17758i	0.0920803	+	0.343648i	0.996561	−	0.0828671i	$-0.0264077\pi$
$227$	1.38733	+	5.17758i	0.0920803	+	0.343648i	−0.904480	+	0.426515i	$0.859741\pi$
$228$	8.99735	−	8.20644i	0.595864	−	0.543485i
$229$	−8.24846	+	8.24846i	−0.545074	+	0.545074i	−0.925012	−	0.379938i	$-0.875945\pi$
$229$	−8.24846	+	8.24846i	−0.545074	+	0.545074i	0.379938	+	0.925012i	$0.375945\pi$
$230$	2.55359	+	1.47432i	0.168379	+	0.0972136i
$231$	0.156888	−	0.245015i	0.0103224	−	0.0161208i
$232$	−3.98942	−	1.06896i	−0.261918	−	0.0701807i
$233$	−9.54763			−0.625486			−0.312743	−	0.949838i	$-0.601248\pi$
$233$	−9.54763			−0.625486			−0.312743	+	0.949838i	$0.601248\pi$
$234$	−8.34306	+	6.88429i	−0.545403	+	0.450040i
$235$	2.33077			0.152042
$236$	−3.29111	−	0.881850i	−0.214233	−	0.0574036i
$237$	−1.03567	+	1.61743i	−0.0672742	+	0.105064i
$238$	−1.39714	−	0.806638i	−0.0905630	−	0.0522865i
$239$	−20.6375	+	20.6375i	−1.33493	+	1.33493i	−0.434036	+	0.900895i	$0.642911\pi$
$239$	−20.6375	+	20.6375i	−1.33493	+	1.33493i	−0.900895	+	0.434036i	$0.857089\pi$
$240$	−0.567261	+	0.517396i	−0.0366165	+	0.0333978i
$241$	−2.88685	−	10.7739i	−0.185958	−	0.694006i	−0.994423	−	0.105462i	$-0.966368\pi$
$241$	−2.88685	−	10.7739i	−0.185958	−	0.694006i	0.808465	−	0.588544i	$-0.200299\pi$
$242$	7.53794	+	7.53794i	0.484557	+	0.484557i
$243$	−4.51572	−	14.9201i	−0.289684	−	0.957122i
$244$	−9.10286	+	5.25554i	−0.582751	+	0.336451i
$245$	0.793572	−	2.96165i	0.0506994	−	0.189213i
$246$	11.7362	−	6.07508i	0.748270	−	0.387333i
$247$	17.8601	+	17.9901i	1.13641	+	1.14468i
$248$		−	1.46474i		−	0.0930111i
$249$	−4.31802	−	19.6922i	−0.273643	−	1.24794i
$250$	2.17283	+	3.76346i	0.137422	+	0.238022i
$251$	2.23476	−	3.87071i	0.141057	−	0.244317i	−0.786838	−	0.617159i	$-0.788283\pi$
$251$	2.23476	−	3.87071i	0.141057	−	0.244317i	0.927895	+	0.372842i	$0.121617\pi$
$252$	−0.852093	+	0.146196i	−0.0536768	+	0.00920948i
$253$	3.74513	−	1.00350i	0.235454	−	0.0630898i
$254$	−0.233226	+	0.0624926i	−0.0146339	+	0.00392114i
$255$	4.09620	+	1.30192i	0.256514	+	0.0815297i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.97416	−	10.3475i	−0.372658	−	0.645462i	0.617316	−	0.786715i	$-0.288220\pi$
$257$	−5.97416	−	10.3475i	−0.372658	−	0.645462i	−0.989973	+	0.141254i	$0.954887\pi$
$258$	6.37453	−	1.39778i	0.396861	−	0.0870218i
$259$		−	2.00533i		−	0.124605i
$260$	−1.12603	−	1.13423i	−0.0698336	−	0.0703420i
$261$	10.1168	+	7.15363i	0.626211	+	0.442798i
$262$	2.09396	−	7.81476i	0.129365	−	0.482797i
$263$	−2.38262	+	1.37560i	−0.146918	+	0.0848234i	−0.571657	−	0.820493i	$-0.693699\pi$
$263$	−2.38262	+	1.37560i	−0.146918	+	0.0848234i	0.424739	+	0.905316i	$0.360366\pi$
$264$	−0.0463639	+	1.00851i	−0.00285350	+	0.0620694i
$265$	1.14338	+	1.14338i	0.0702371	+	0.0702371i
$266$	0.524407	+	1.95711i	0.0321535	+	0.119998i
$267$	16.4370	+	18.0212i	1.00593	+	1.10288i
$268$	6.26033	−	6.26033i	0.382410	−	0.382410i
$269$	5.40423	+	3.12013i	0.329502	+	0.190238i	0.655620	−	0.755091i	$-0.272407\pi$
$269$	5.40423	+	3.12013i	0.329502	+	0.190238i	−0.326118	+	0.945329i	$0.605741\pi$
$270$	2.13405	−	0.866698i	0.129874	−	0.0527455i
$271$	−21.6057	−	5.78922i	−1.31245	−	0.351670i	−0.466306	−	0.884624i	$-0.654415\pi$
$271$	−21.6057	−	5.78922i	−1.31245	−	0.351670i	−0.846144	+	0.532954i	$0.821082\pi$
$272$	5.59813			0.339437
$273$	−0.379091	−	1.75931i	−0.0229436	−	0.106478i
$274$	−0.0827063			−0.00499647
$275$	2.70445	+	0.724656i	0.163085	+	0.0436984i
$276$	−9.70277	−	6.21286i	−0.584038	−	0.373970i
$277$	−4.84833	−	2.79919i	−0.291308	−	0.168187i	0.347224	−	0.937782i	$-0.387125\pi$
$277$	−4.84833	−	2.79919i	−0.291308	−	0.168187i	−0.638532	+	0.769596i	$0.720458\pi$
$278$	4.41337	−	4.41337i	0.264697	−	0.264697i
$279$	−1.52195	+	4.12224i	−0.0911167	+	0.246792i
$280$	−0.0330626	−	0.123391i	−0.00197587	−	0.00737404i
$281$	−8.82870	−	8.82870i	−0.526676	−	0.526676i	0.392903	−	0.919580i	$-0.371471\pi$
$281$	−8.82870	−	8.82870i	−0.526676	−	0.526676i	−0.919580	+	0.392903i	$0.871471\pi$
$282$	−9.09757	−	0.418241i	−0.541753	−	0.0249059i
$283$	−5.93983	+	3.42936i	−0.353086	+	0.203854i	−0.666044	−	0.745913i	$-0.732014\pi$
$283$	−5.93983	+	3.42936i	−0.353086	+	0.203854i	0.312958	+	0.949767i	$0.398680\pi$
$284$	3.98229	−	14.8621i	0.236305	−	0.881904i
$285$	−2.48152	−	4.79393i	−0.146993	−	0.283968i
$286$	−2.10158	−	0.00762236i	−0.124269	−	0.000450720i
$287$			2.19878i			0.129790i
$288$	2.30701	−	1.91774i	0.135942	−	0.113004i
$289$	−7.16953	−	12.4180i	−0.421737	−	0.730470i
$290$	−0.915400	+	1.58552i	−0.0537541	+	0.0931049i
$291$	−1.40810	+	4.43026i	−0.0825445	+	0.259707i
$292$	4.80913	−	1.28860i	0.281433	−	0.0754098i
$293$	26.4232	−	7.08007i	1.54366	−	0.413622i	0.616213	−	0.787579i	$-0.288666\pi$
$293$	26.4232	−	7.08007i	1.54366	−	0.413622i	0.927446	+	0.373957i	$0.121999\pi$
$294$	−3.62896	+	11.4177i	−0.211645	+	0.665892i
$295$	−0.755168	+	1.30799i	−0.0439676	+	0.0761541i
$296$	3.47929	+	6.02630i	0.202229	+	0.350272i
$297$	1.17838	−	2.79008i	0.0683766	−	0.161897i
$298$			14.5372i			0.842119i
$299$	12.0671	−	20.7269i	0.697861	−	1.19867i
$300$	−3.82467	−	7.38870i	−0.220818	−	0.426587i
$301$	−0.281026	+	1.04880i	−0.0161981	+	0.0604521i
$302$	−7.84275	+	4.52801i	−0.451300	+	0.260558i
$303$	−24.6394	−	1.13274i	−1.41550	−	0.0650744i
$304$	−4.97155	−	4.97155i	−0.285138	−	0.285138i
$305$	1.20592	+	4.50056i	0.0690508	+	0.257701i
$306$	−15.7549	−	5.81678i	−0.900647	−	0.332523i
$307$	−15.4869	+	15.4869i	−0.883883	+	0.883883i	−0.993927	−	0.110044i	$-0.964901\pi$
$307$	−15.4869	+	15.4869i	−0.883883	+	0.883883i	0.110044	+	0.993927i	$0.464901\pi$
$308$	−0.145470	−	0.0839871i	−0.00828892	−	0.00478561i
$309$	−6.72294	−	4.30483i	−0.382455	−	0.244893i
$310$	−0.627161	−	0.168047i	−0.0356204	−	0.00954445i
$311$	31.8012			1.80328			0.901642	−	0.432484i	$-0.142363\pi$
$311$	31.8012			1.80328			0.901642	+	0.432484i	$0.142363\pi$
$312$	4.19166	+	4.62925i	0.237306	+	0.262080i
$313$	−23.7424			−1.34200			−0.670999	−	0.741458i	$-0.734135\pi$
$313$	−23.7424			−1.34200			−0.670999	+	0.741458i	$0.734135\pi$
$314$	−9.86474	−	2.64325i	−0.556700	−	0.149167i
$315$	−0.0351622	+	0.381616i	−0.00198117	+	0.0215016i
$316$	0.960301	+	0.554430i	0.0540212	+	0.0311891i
$317$	16.8936	−	16.8936i	0.948841	−	0.948841i	−0.0499128	−	0.998754i	$-0.515894\pi$
$317$	16.8936	−	16.8936i	0.948841	−	0.948841i	0.998754	+	0.0499128i	$0.0158944\pi$
$318$	−4.25772	−	4.66806i	−0.238761	−	0.261772i
$319$	0.623073	+	2.32534i	0.0348854	+	0.130194i
$320$	0.313444	+	0.313444i	0.0175221	+	0.0175221i
$321$	−1.07479	+	23.3788i	−0.0599888	+	1.30488i
$322$	1.66013	−	0.958476i	0.0925154	−	0.0534138i
$323$	−10.1870	+	38.0184i	−0.566820	+	2.11540i
$324$	−8.48528	+	3.00000i	−0.471405	+	0.166667i
$325$	15.0303	−	8.60519i	0.833728	−	0.477330i
$326$		−	13.8802i		−	0.768751i
$327$	−4.93335	+	1.08176i	−0.272815	+	0.0598215i
$328$	−3.81493	−	6.60765i	−0.210644	−	0.364846i
$329$	0.757633	−	1.31226i	0.0417697	−	0.0723472i
$330$	0.426496	+	0.135556i	0.0234778	+	0.00746213i
$331$	15.9259	−	4.26733i	0.875367	−	0.234554i	0.206960	−	0.978349i	$-0.433643\pi$
$331$	15.9259	−	4.26733i	0.875367	−	0.234554i	0.668407	+	0.743795i	$0.266976\pi$
$332$	−11.2428	+	3.01251i	−0.617030	+	0.165333i
$333$	−3.53013	−	20.5751i	−0.193450	−	1.12751i
$334$	6.70590	−	11.6150i	0.366930	−	0.635542i
$335$	−1.96226	−	3.39874i	−0.107210	−	0.185693i
$336$	0.106910	+	0.487560i	0.00583242	+	0.0265986i
$337$		−	3.24846i		−	0.176955i	−0.996078	−	0.0884775i	$-0.971800\pi$
$337$		−	3.24846i		−	0.176955i	0.996078	−	0.0884775i	$-0.0282001\pi$
$338$	−9.25883	+	9.12547i	−0.503614	+	0.496360i
$339$	−16.0228	+	8.29400i	−0.870238	+	0.450468i
$340$	0.642265	−	2.39697i	0.0348317	−	0.129994i
$341$	−0.739381	+	0.426882i	−0.0400397	+	0.0231169i
$342$	8.82577	+	19.1572i	0.477243	+	1.03590i
$343$	−2.83592	−	2.83592i	−0.153125	−	0.153125i
$344$	−0.975173	−	3.63939i	−0.0525778	−	0.196223i
$345$	−3.77336	+	3.44167i	−0.203151	+	0.185293i
$346$	0.779372	−	0.779372i	0.0418993	−	0.0418993i
$347$	−7.11715	−	4.10909i	−0.382069	−	0.220587i	0.296649	−	0.954986i	$-0.404131\pi$
$347$	−7.11715	−	4.10909i	−0.382069	−	0.220587i	−0.678718	+	0.734399i	$0.737464\pi$
$348$	3.85755	−	6.02442i	0.206786	−	0.322943i
$349$	7.73980	+	2.07387i	0.414302	+	0.111012i	0.459948	−	0.887946i	$-0.347868\pi$
$349$	7.73980	+	2.07387i	0.414302	+	0.111012i	−0.0456462	+	0.998958i	$0.514535\pi$
$350$	1.38428			0.0739928
$351$	−6.98659	−	17.3835i	−0.372917	−	0.927865i
$352$	0.582877			0.0310675
$353$	2.70035	+	0.723557i	0.143725	+	0.0385111i	0.329964	−	0.943993i	$-0.392963\pi$
$353$	2.70035	+	0.723557i	0.143725	+	0.0385111i	−0.186239	+	0.982504i	$0.559630\pi$
$354$	3.18233	−	4.96991i	0.169139	−	0.264148i
$355$	−5.90666	−	3.41021i	−0.313493	−	0.180995i
$356$	9.95774	−	9.95774i	0.527759	−	0.527759i
$357$	2.06451	−	1.88303i	0.109265	−	0.0996603i
$358$	1.44823	+	5.40488i	0.0765416	+	0.285657i
$359$	11.6531	+	11.6531i	0.615028	+	0.615028i	0.944252	−	0.329224i	$-0.106787\pi$
$359$	11.6531	+	11.6531i	0.615028	+	0.615028i	−0.329224	+	0.944252i	$0.606787\pi$
$360$	−0.556443	−	1.20782i	−0.0293271	−	0.0636575i
$361$	26.3555	−	15.2163i	1.38713	−	0.800860i
$362$	3.74479	−	13.9757i	0.196822	−	0.734548i
$363$	−16.3975	+	8.48796i	−0.860645	+	0.445503i
$364$	−1.00462	+	0.265284i	−0.0526562	+	0.0139047i
$365$		−	2.20698i		−	0.115519i
$366$	−3.89942	−	17.7832i	−0.203826	−	0.929544i
$367$	18.5929	+	32.2039i	0.970544	+	1.68103i	0.693918	+	0.720054i	$0.255883\pi$
$367$	18.5929	+	32.2039i	0.970544	+	1.68103i	0.276626	+	0.960978i	$0.410784\pi$
$368$	−3.32595	+	5.76071i	−0.173377	+	0.300298i
$369$	3.87067	+	22.5599i	0.201499	+	1.17442i
$370$	2.97947	−	0.798347i	0.154895	−	0.0415041i
$371$	1.01540	−	0.272076i	0.0527171	−	0.0141255i
$372$	2.41782	+	0.768472i	0.125358	+	0.0398434i
$373$	3.94412	−	6.83141i	0.204219	−	0.353717i	−0.745665	−	0.666321i	$-0.767868\pi$
$373$	3.94412	−	6.83141i	0.204219	−	0.353717i	0.949883	+	0.312604i	$0.101201\pi$
$374$	−1.63151	−	2.82586i	−0.0843635	−	0.146122i
$375$	−7.35224	+	1.61216i	−0.379668	+	0.0832518i
$376$			5.25803i			0.271162i
$377$	12.8693	+	7.49246i	0.662802	+	0.385881i
$378$	0.205726	−	1.48323i	0.0105814	−	0.0762893i
$379$	0.481911	−	1.79852i	0.0247541	−	0.0923837i	−0.952444	−	0.304715i	$-0.901439\pi$
$379$	0.481911	−	1.79852i	0.0247541	−	0.0923837i	0.977198	+	0.212331i	$0.0681055\pi$
$380$	−2.69906	+	1.55830i	−0.138459	+	0.0799393i
$381$	0.0192059	−	0.417767i	0.000983950	−	0.0214029i
$382$	−4.72046	−	4.72046i	−0.241520	−	0.241520i
$383$	0.745523	+	2.78233i	0.0380945	+	0.142170i	0.982354	−	0.187032i	$-0.0598868\pi$
$383$	0.745523	+	2.78233i	0.0380945	+	0.142170i	−0.944259	+	0.329202i	$0.893220\pi$
$384$	−1.16721	−	1.27970i	−0.0595638	−	0.0653043i
$385$	−0.0526505	+	0.0526505i	−0.00268332	+	0.00268332i
$386$	5.27801	+	3.04726i	0.268643	+	0.155101i
$387$	−1.03710	+	11.2557i	−0.0527188	+	0.572157i
$388$	2.59245	+	0.694645i	0.131612	+	0.0352653i
$389$	−23.4187			−1.18738			−0.593688	−	0.804695i	$-0.702329\pi$
$389$	−23.4187			−1.18738			−0.593688	+	0.804695i	$0.702329\pi$
$390$	2.46302	−	1.26365i	0.124720	−	0.0639873i
$391$	37.2382			1.88322
$392$	6.68126	+	1.79024i	0.337455	+	0.0904207i
$393$	11.8011	+	7.55645i	0.595285	+	0.381172i
$394$	−12.8070	−	7.39413i	−0.645208	−	0.372511i
$395$	0.347566	−	0.347566i	0.0174879	−	0.0174879i
$396$	−1.64040	−	0.605643i	−0.0824332	−	0.0304347i
$397$	4.76427	+	17.7805i	0.239112	+	0.892378i	0.976252	+	0.216638i	$0.0695092\pi$
$397$	4.76427	+	17.7805i	0.239112	+	0.892378i	−0.737140	+	0.675740i	$0.763824\pi$
$398$	10.9463	+	10.9463i	0.548686	+	0.548686i
$399$	−3.50570	−	0.161167i	−0.175504	−	0.00806844i
$400$	−4.15996	+	2.40175i	−0.207998	+	0.120088i
$401$	−1.75607	+	6.55376i	−0.0876942	+	0.327279i	−0.995811	−	0.0914383i	$-0.970854\pi$
$401$	−1.75607	+	6.55376i	−0.0876942	+	0.327279i	0.908117	+	0.418717i	$0.137520\pi$
$402$	7.04933	+	13.6183i	0.351589	+	0.679217i
$403$	−1.38537	+	5.09625i	−0.0690100	+	0.253862i
$404$			14.2406i			0.708497i
$405$	0.311014	+	3.97735i	0.0154544	+	0.197636i
$406$	0.595115	+	1.03077i	0.0295351	+	0.0511562i
$407$	2.02800	−	3.51260i	0.100524	−	0.174113i
$408$	−2.93705	+	9.24072i	−0.145405	+	0.457484i
$409$	−28.2895	+	7.58014i	−1.39882	+	0.374814i	−0.877923	−	0.478803i	$-0.841071\pi$
$409$	−28.2895	+	7.58014i	−1.39882	+	0.374814i	−0.520902	+	0.853617i	$0.674404\pi$
$410$	−3.26690	+	0.875362i	−0.161340	+	0.0432311i
$411$	0.0433917	−	0.136522i	0.00214035	−	0.00673412i
$412$	−2.30452	+	3.99154i	−0.113535	+	0.196649i
$413$	0.490946	+	0.850344i	0.0241579	+	0.0418427i
$414$	15.3460	−	12.7566i	0.754214	−	0.626953i
$415$			5.15949i			0.253269i
$416$	2.55874	−	2.54025i	0.125453	−	0.124546i
$417$	4.96960	+	9.60053i	0.243362	+	0.470140i
$418$	−1.06067	+	3.95848i	−0.0518791	+	0.193615i
$419$	8.00397	−	4.62109i	0.391020	−	0.225755i	−0.291582	−	0.956546i	$-0.594182\pi$
$419$	8.00397	−	4.62109i	0.391020	−	0.225755i	0.682602	+	0.730791i	$0.260848\pi$
$420$	0.221026	+	0.0101612i	0.0107849	+	0.000495814i
$421$	−18.4490	−	18.4490i	−0.899149	−	0.899149i	0.0962115	−	0.995361i	$-0.469327\pi$
$421$	−18.4490	−	18.4490i	−0.899149	−	0.899149i	−0.995361	+	0.0962115i	$0.969327\pi$
$422$	−4.86953	−	18.1733i	−0.237045	−	0.884664i
$423$	5.46340	−	14.7978i	0.265640	−	0.719491i
$424$	−2.57937	+	2.57937i	−0.125265	+	0.125265i
$425$	23.2880	+	13.4453i	1.12963	+	0.652194i
$426$	22.4433	+	14.3709i	1.08738	+	0.696270i
$427$	2.92588	+	0.783987i	0.141593	+	0.0379398i
$428$	13.5120			0.653127
$429$	1.11517	−	3.46504i	0.0538410	−	0.167294i
$430$	−1.67017			−0.0805427
$431$	21.6015	+	5.78811i	1.04051	+	0.278803i	0.738324	−	0.674446i	$-0.235617\pi$
$431$	21.6015	+	5.78811i	1.04051	+	0.278803i	0.302184	+	0.953249i	$0.402284\pi$
$432$	1.95521	+	4.81427i	0.0940699	+	0.231627i
$433$	3.41910	+	1.97402i	0.164311	+	0.0948652i	0.579901	−	0.814687i	$-0.303091\pi$
$433$	3.41910	+	1.97402i	0.164311	+	0.0948652i	−0.415589	+	0.909552i	$0.636425\pi$
$434$	−0.298477	+	0.298477i	−0.0143274	+	0.0143274i
$435$	−2.13692	−	2.34287i	−0.102458	−	0.112332i
$436$	0.754701	+	2.81658i	0.0361436	+	0.134890i
$437$	−33.0703	−	33.0703i	−1.58197	−	1.58197i
$438$	−0.396028	+	8.61440i	−0.0189230	+	0.411612i
$439$	15.8569	−	9.15500i	0.756810	−	0.436944i	−0.0713394	−	0.997452i	$-0.522727\pi$
$439$	15.8569	−	9.15500i	0.756810	−	0.436944i	0.828149	+	0.560508i	$0.189394\pi$
$440$	0.0668726	−	0.249572i	0.00318803	−	0.0118979i
$441$	−16.9430	−	11.9805i	−0.806810	−	0.570501i
$442$	−19.4775	−	5.29477i	−0.926450	−	0.251847i
$443$		−	5.86371i		−	0.278593i	−0.990251	−	0.139297i	$-0.955516\pi$
$443$		−	5.86371i		−	0.278593i	0.990251	−	0.139297i	$-0.0444841\pi$
$444$	−11.7729	+	2.58151i	−0.558717	+	0.122513i
$445$	−3.12119	−	5.40607i	−0.147959	−	0.256272i
$446$	−3.59778	+	6.23155i	−0.170360	+	0.295072i
$447$	−23.9963	−	7.62693i	−1.13499	−	0.360741i
$448$	0.278362	−	0.0745867i	0.0131513	−	0.00352389i
$449$	−27.5332	+	7.37750i	−1.29937	+	0.348166i	−0.841213	−	0.540704i	$-0.818158\pi$
$449$	−27.5332	+	7.37750i	−1.29937	+	0.348166i	−0.458160	+	0.888870i	$0.651491\pi$
$450$	14.2030	−	2.43685i	0.669535	−	0.114874i
$451$	−2.22364	+	3.85145i	−0.104707	+	0.181358i
$452$	5.20832	+	9.02108i	0.244979	+	0.424316i
$453$	−3.35962	−	15.3215i	−0.157849	−	0.719866i
$454$			5.36023i			0.251568i
$455$	−0.00167052	+	0.460585i	−7.83154e−5	+	0.0215925i
$456$	10.8148	−	5.59813i	0.506447	−	0.262156i
$457$	−4.96154	+	18.5167i	−0.232091	+	0.866175i	0.747348	+	0.664433i	$0.231327\pi$
$457$	−4.96154	+	18.5167i	−0.232091	+	0.866175i	−0.979439	+	0.201742i	$0.935340\pi$
$458$	−10.1023	+	5.83254i	−0.472048	+	0.272537i
$459$	17.8674	−	22.9545i	0.833979	−	1.07143i
$460$	2.08500	+	2.08500i	0.0972136	+	0.0972136i
$461$	−7.67398	−	28.6397i	−0.357413	−	1.33388i	−0.877421	−	0.479722i	$-0.840738\pi$
$461$	−7.67398	−	28.6397i	−0.357413	−	1.33388i	0.520007	−	0.854162i	$-0.325929\pi$
$462$	0.214956	−	0.196061i	0.0100007	−	0.00912157i
$463$	18.2554	−	18.2554i	0.848400	−	0.848400i	−0.141533	−	0.989934i	$-0.545203\pi$
$463$	18.2554	−	18.2554i	0.848400	−	0.848400i	0.989934	+	0.141533i	$0.0452032\pi$
$464$	−3.57681	−	2.06507i	−0.166049	−	0.0958687i
$465$	0.606431	−	0.947077i	0.0281226	−	0.0439197i
$466$	−9.22231	−	2.47111i	−0.427215	−	0.114472i
$467$	−32.4456			−1.50140			−0.750701	−	0.660642i	$-0.770284\pi$
$467$	−32.4456			−1.50140			−0.750701	+	0.660642i	$0.770284\pi$
$468$	−9.84056	+	4.49037i	−0.454880	+	0.207567i
$469$	−2.55139			−0.117812
$470$	2.25135	+	0.603246i	0.103847	+	0.0278257i
$471$	9.53867	−	14.8968i	0.439519	−	0.686406i
$472$	−2.95073	−	1.70360i	−0.135818	−	0.0784147i
$473$	−1.55291	+	1.55291i	−0.0714031	+	0.0714031i
$474$	−1.41901	+	1.29427i	−0.0651771	+	0.0594478i
$475$	−8.74101	−	32.6219i	−0.401065	−	1.49680i
$476$	−1.14076	−	1.14076i	−0.0522865	−	0.0522865i
$477$	9.93928	−	4.57905i	0.455088	−	0.209660i
$478$	−25.2757	+	14.5929i	−1.15608	+	0.667466i
$479$	−2.14571	+	8.00792i	−0.0980402	+	0.365891i	−0.997463	−	0.0711890i	$-0.977321\pi$
$479$	−2.14571	+	8.00792i	−0.0980402	+	0.365891i	0.899423	+	0.437080i	$0.143987\pi$
$480$	−0.681844	+	0.352948i	−0.0311218	+	0.0161098i
$481$	−6.40570	−	24.2580i	−0.292075	−	1.10607i
$482$		−	11.1539i		−	0.508048i
$483$	0.711154	+	3.24320i	0.0323586	+	0.147571i
$484$	5.33013	+	9.23205i	0.242279	+	0.419639i
$485$	0.594856	−	1.03032i	0.0270110	−	0.0467845i
$486$	−0.500258	−	15.5804i	−0.0226921	−	0.706743i
$487$	−31.0359	+	8.31604i	−1.40637	+	0.376836i	−0.880628	−	0.473808i	$-0.842879\pi$
$487$	−31.0359	+	8.31604i	−1.40637	+	0.376836i	−0.525742	+	0.850644i	$0.676212\pi$
$488$	−10.1529	+	2.72047i	−0.459601	+	0.123150i
$489$	22.9117	+	7.28219i	1.03610	+	0.329312i
$490$	1.53306	−	2.65534i	0.0692567	−	0.119956i
$491$	−13.2100	−	22.8803i	−0.596157	−	1.03257i	−0.993383	−	0.114853i	$-0.963360\pi$
$491$	−13.2100	−	22.8803i	−0.596157	−	1.03257i	0.397226	−	0.917721i	$-0.369973\pi$
$492$	12.9086	−	2.83054i	0.581965	−	0.127611i
$493$			23.1211i			1.04132i
$494$	12.5953	+	21.9996i	0.566690	+	0.989809i
$495$	−0.447520	+	0.632890i	−0.0201145	+	0.0284463i
$496$	0.379103	−	1.41483i	0.0170222	−	0.0635277i
$497$	−3.84001	+	2.21703i	−0.172248	+	0.0994475i
$498$	0.925838	−	20.1388i	0.0414878	−	0.902442i
$499$	−9.27427	−	9.27427i	−0.415173	−	0.415173i	0.468363	−	0.883536i	$-0.344844\pi$
$499$	−9.27427	−	9.27427i	−0.415173	−	0.415173i	−0.883536	+	0.468363i	$0.844844\pi$
$500$	1.12474	+	4.19759i	0.0503000	+	0.187722i
$501$	15.6543	+	17.1630i	0.699384	+	0.766788i
$502$	3.16043	−	3.16043i	0.141057	−	0.141057i
$503$	−26.4513	−	15.2717i	−1.17941	−	0.680931i	−0.223529	−	0.974697i	$-0.571758\pi$
$503$	−26.4513	−	15.2717i	−1.17941	−	0.680931i	−0.955877	+	0.293767i	$0.905091\pi$
$504$	−0.860896	−	0.0793233i	−0.0383474	−	0.00353334i
$505$	6.09744	+	1.63380i	0.271332	+	0.0727033i
$506$	3.87724			0.172364
$507$	−10.2056	−	20.0710i	−0.453247	−	0.891385i
$508$	−0.241453			−0.0107127
$509$	23.0380	+	6.17302i	1.02114	+	0.273614i	0.730278	−	0.683150i	$-0.239390\pi$
$509$	23.0380	+	6.17302i	1.02114	+	0.273614i	0.290865	+	0.956764i	$0.406057\pi$
$510$	3.61966	+	2.31774i	0.160281	+	0.102631i
$511$	−1.24256	−	0.717395i	−0.0549678	−	0.0317357i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−36.2529	+	4.51773i	−1.60060	+	0.199463i
$514$	−3.09245	−	11.5412i	−0.136402	−	0.509060i
$515$	1.44467	+	1.44467i	0.0636599	+	0.0636599i
$516$	6.51910	+	0.299701i	0.286987	+	0.0131936i
$517$	2.65418	−	1.53239i	0.116731	−	0.0673946i
$518$	0.519017	−	1.93700i	0.0228043	−	0.0851069i
$519$	0.877598	+	1.69539i	0.0385223	+	0.0744193i
$520$	−0.794103	−	1.38702i	−0.0348237	−	0.0608249i
$521$			42.5422i			1.86381i	0.362704	+	0.931904i	$0.381854\pi$
$521$			42.5422i			1.86381i	−0.362704	+	0.931904i	$0.618146\pi$
$522$	7.92054	+	9.52828i	0.346673	+	0.417042i
$523$	17.0400	+	29.5141i	0.745107	+	1.29056i	0.950145	+	0.311809i	$0.100935\pi$
$523$	17.0400	+	29.5141i	0.745107	+	1.29056i	−0.205037	+	0.978754i	$0.565732\pi$
$524$	4.04522	−	7.00652i	0.176716	−	0.306081i
$525$	−0.726259	+	2.28500i	−0.0316965	+	0.0997257i
$526$	−2.65746	+	0.712065i	−0.115871	+	0.0310475i
$527$	−7.92040	+	2.12227i	−0.345018	+	0.0924473i
$528$	−0.305805	+	0.962144i	−0.0133085	+	0.0418719i
$529$	−10.6239	+	18.4011i	−0.461908	+	0.800048i
$530$	0.808489	+	1.40034i	0.0351185	+	0.0608271i
$531$	6.53413	+	7.86045i	0.283557	+	0.341115i
$532$			2.02615i			0.0878449i
$533$	7.02365	+	26.5981i	0.304228	+	1.15209i
$534$	11.2127	+	21.6613i	0.485222	+	0.937378i
$535$	1.55021	−	5.78547i	0.0670215	−	0.250128i
$536$	7.66730	−	4.42672i	0.331177	−	0.191205i
$537$	−9.68155	−	0.445088i	−0.417790	−	0.0192070i
$538$	4.41254	+	4.41254i	0.190238	+	0.190238i
$539$	−1.04349	−	3.89436i	−0.0449463	−	0.167742i
$540$	2.28566	−	0.284832i	0.0983590	−	0.0122572i
$541$	18.5013	−	18.5013i	0.795434	−	0.795434i	−0.186938	−	0.982372i	$-0.559856\pi$
$541$	18.5013	−	18.5013i	0.795434	−	0.795434i	0.982372	+	0.186938i	$0.0598564\pi$
$542$	−19.3711	−	11.1839i	−0.832060	−	0.480390i
$543$	21.1048	+	13.5138i	0.905693	+	0.579932i
$544$	5.40738	+	1.44890i	0.231839	+	0.0621212i
$545$	1.29257			0.0553676
$546$	0.0891695	−	1.79748i	0.00381610	−	0.0769250i
$547$	39.5058			1.68915			0.844573	−	0.535440i	$-0.179854\pi$
$547$	39.5058			1.68915			0.844573	+	0.535440i	$0.179854\pi$
$548$	−0.0798882	−	0.0214060i	−0.00341265	−	0.000914418i
$549$	31.4002	+	2.89323i	1.34013	+	0.123480i
$550$	2.42475	+	1.39993i	0.103391	+	0.0596931i
$551$	20.5332	−	20.5332i	0.874746	−	0.874746i
$552$	−7.76415	−	8.51242i	−0.330464	−	0.362313i
$553$	−0.0827063	−	0.308664i	−0.00351703	−	0.0131257i
$554$	−3.95865	−	3.95865i	−0.168187	−	0.168187i
$555$	−0.245357	+	5.33701i	−0.0104148	+	0.226543i
$556$	5.40526	−	3.12073i	0.229234	−	0.132348i
$557$	−4.08768	+	15.2554i	−0.173201	+	0.646394i	0.823650	+	0.567098i	$0.191934\pi$
$557$	−4.08768	+	15.2554i	−0.173201	+	0.646394i	−0.996851	+	0.0792958i	$0.974733\pi$
$558$	−2.53700	+	3.58786i	−0.107400	+	0.151886i
$559$	−0.0492717	+	13.5848i	−0.00208397	+	0.574577i
$560$		−	0.127744i		−	0.00539817i
$561$	5.52056	−	1.21052i	0.233078	−	0.0511083i
$562$	−6.24284	−	10.8129i	−0.263338	−	0.456115i
$563$	−10.6906	+	18.5166i	−0.450555	+	0.780383i	−0.998421	−	0.0561827i	$-0.982107\pi$
$563$	−10.6906	+	18.5166i	−0.450555	+	0.780383i	0.547866	+	0.836566i	$0.315440\pi$
$564$	−8.67933	−	2.75862i	−0.365466	−	0.116159i
$565$	4.46012	−	1.19509i	0.187639	−	0.0502777i
$566$	−6.62502	+	1.77517i	−0.278470	+	0.0746159i
$567$	2.34041	+	1.11776i	0.0982880	+	0.0469416i
$568$	7.69319	−	13.3250i	0.322799	−	0.559105i
$569$	−14.5203	−	25.1500i	−0.608725	−	1.05434i	−0.991451	−	0.130480i	$-0.958348\pi$
$569$	−14.5203	−	25.1500i	−0.608725	−	1.05434i	0.382726	−	0.923862i	$-0.374985\pi$
$570$	−1.15621	−	5.27285i	−0.0484281	−	0.220855i
$571$			9.91137i			0.414778i	0.978259	+	0.207389i	$0.0664966\pi$
$571$			9.91137i			0.414778i	−0.978259	+	0.207389i	$0.933503\pi$
$572$	−2.02800	−	0.551292i	−0.0847948	−	0.0230507i
$573$	10.2685	−	5.31539i	0.428974	−	0.222054i
$574$	−0.569086	+	2.12386i	−0.0237532	+	0.0886481i
$575$	−27.6716	+	15.9762i	−1.15399	+	0.666254i
$576$	2.72474	−	1.25529i	0.113531	−	0.0523040i
$577$	−4.91283	−	4.91283i	−0.204524	−	0.204524i	0.597411	−	0.801935i	$-0.296196\pi$
$577$	−4.91283	−	4.91283i	−0.204524	−	0.204524i	−0.801935	+	0.597411i	$0.796196\pi$
$578$	−3.71122	−	13.8505i	−0.154366	−	0.576104i
$579$	−7.79914	+	7.11356i	−0.324121	+	0.295630i
$580$	−1.29457	+	1.29457i	−0.0537541	+	0.0537541i
$581$	2.90488	+	1.67713i	0.120515	+	0.0695791i
$582$	−2.50676	+	3.91486i	−0.103909	+	0.162276i
$583$	2.05376	+	0.550304i	0.0850581	+	0.0227913i
$584$	4.97878			0.206023
$585$	0.793660	+	4.72863i	0.0328138	+	0.195505i
$586$	27.3553			1.13004
$587$	23.2001	+	6.21644i	0.957569	+	0.256580i	0.703571	−	0.710625i	$-0.251588\pi$
$587$	23.2001	+	6.21644i	0.957569	+	0.256580i	0.253998	+	0.967205i	$0.418254\pi$
$588$	−6.46042	+	10.0894i	−0.266423	+	0.416079i
$589$	8.91863	+	5.14917i	0.367486	+	0.212168i
$590$	−1.06797	+	1.06797i	−0.0439676	+	0.0439676i
$591$	18.9245	−	17.2610i	0.778450	−	0.710021i
$592$	1.80101	+	6.72147i	0.0740211	+	0.276251i
$593$	22.0744	+	22.0744i	0.906489	+	0.906489i	0.995987	−	0.0894984i	$-0.0285264\pi$
$593$	22.0744	+	22.0744i	0.906489	+	0.906489i	−0.0894984	+	0.995987i	$0.528526\pi$
$594$	1.86036	−	2.39003i	0.0763313	−	0.0980639i
$595$	−0.619319	+	0.357564i	−0.0253896	+	0.0146587i
$596$	−3.76251	+	14.0419i	−0.154119	+	0.575178i
$597$	−23.8117	+	12.3258i	−0.974548	+	0.504463i
$598$	17.0205	−	16.8975i	0.696019	−	0.690989i
$599$		−	35.2538i		−	1.44043i	−0.693750	−	0.720216i	$-0.744043\pi$
$599$		−	35.2538i		−	1.44043i	0.693750	−	0.720216i	$-0.255957\pi$
$600$	−1.78201	−	8.12683i	−0.0727504	−	0.331777i
$601$	−10.0883	−	17.4735i	−0.411512	−	0.712759i	0.583544	−	0.812082i	$-0.301666\pi$
$601$	−10.0883	−	17.4735i	−0.411512	−	0.712759i	−0.995055	+	0.0993227i	$0.968332\pi$
$602$	−0.542901	+	0.940332i	−0.0221270	+	0.0383251i
$603$	−26.1778	+	4.49140i	−1.06604	+	0.182904i
$604$	−8.74745	+	2.34387i	−0.355929	+	0.0953708i
$605$	4.56443	−	1.22304i	0.185570	−	0.0497234i
$606$	−23.5067	−	7.47130i	−0.954894	−	0.303501i
$607$	2.42837	−	4.20607i	0.0985647	−	0.170719i	−0.812526	−	0.582925i	$-0.801908\pi$
$607$	2.42837	−	4.20607i	0.0985647	−	0.170719i	0.911091	+	0.412206i	$0.135242\pi$
$608$	−3.51542	−	6.08888i	−0.142569	−	0.246937i
$609$	−2.01370	+	0.441554i	−0.0815991	+	0.0178927i
$610$			4.65932i			0.188650i
$611$	4.97311	−	18.2942i	0.201190	−	0.740105i
$612$	−13.7126	−	9.69625i	−0.554297	−	0.391948i
$613$	−0.235455	+	0.878731i	−0.00950994	+	0.0354916i	−0.970518	−	0.241030i	$-0.922515\pi$
$613$	−0.235455	+	0.878731i	−0.00950994	+	0.0354916i	0.961008	+	0.276521i	$0.0891816\pi$
$614$	−18.9675	+	10.9509i	−0.765465	+	0.441941i
$615$	0.269026	−	5.85186i	0.0108482	−	0.235970i
$616$	−0.118776	−	0.118776i	−0.00478561	−	0.00478561i
$617$	11.6445	+	43.4580i	0.468792	+	1.74956i	0.644002	+	0.765024i	$0.277273\pi$
$617$	11.6445	+	43.4580i	0.468792	+	1.74956i	−0.175210	+	0.984531i	$0.556060\pi$
$618$	−5.37969	−	5.89817i	−0.216403	−	0.237259i
$619$	11.7433	−	11.7433i	0.472003	−	0.472003i	−0.430559	−	0.902562i	$-0.641684\pi$
$619$	11.7433	−	11.7433i	0.472003	−	0.472003i	0.902562	+	0.430559i	$0.141684\pi$
$620$	−0.562298	−	0.324643i	−0.0225824	−	0.0130380i
$621$	13.0058	+	32.0240i	0.521906	+	1.28508i
$622$	30.7176	+	8.23077i	1.23167	+	0.330024i
$623$	−4.05827			−0.162591
$624$	2.85070	+	5.55640i	0.114119	+	0.222434i
$625$	−22.0912			−0.883648
$626$	−22.9334	−	6.14498i	−0.916602	−	0.245603i
$627$	−5.97770	−	3.82763i	−0.238726	−	0.152861i
$628$	−8.84449	−	5.10637i	−0.352933	−	0.203766i
$629$	27.5454	−	27.5454i	1.09831	−	1.09831i
$630$	−0.132733	+	0.359512i	−0.00528823	+	0.0143233i
$631$	9.44656	+	35.2551i	0.376062	+	1.40348i	0.851787	+	0.523888i	$0.175519\pi$
$631$	9.44656	+	35.2551i	0.376062	+	1.40348i	−0.475725	+	0.879594i	$0.657814\pi$
$632$	0.784083	+	0.784083i	0.0311891	+	0.0311891i
$633$	32.5531	+	1.49656i	1.29387	+	0.0594829i
$634$	20.6904	−	11.9456i	0.821720	−	0.474420i
$635$	−0.0277015	+	0.103384i	−0.00109930	+	0.00410265i
$636$	−2.90446	−	5.61098i	−0.115169	−	0.222490i
$637$	−21.5528	−	12.5480i	−0.853953	−	0.497168i
$638$			2.40737i			0.0953087i
$639$	−35.4965	+	29.5070i	−1.40422	+	1.16728i
$640$	0.221638	+	0.383889i	0.00876103	+	0.0151745i
$641$	−0.424453	+	0.735175i	−0.0167649	+	0.0290377i	−0.874286	−	0.485411i	$-0.838670\pi$
$641$	−0.424453	+	0.735175i	−0.0167649	+	0.0290377i	0.857521	+	0.514449i	$0.172003\pi$
$642$	−7.08904	+	22.3040i	−0.279782	+	0.880269i
$643$	−16.6824	+	4.47005i	−0.657891	+	0.176281i	−0.572294	−	0.820048i	$-0.693946\pi$
$643$	−16.6824	+	4.47005i	−0.657891	+	0.176281i	−0.0855970	+	0.996330i	$0.527280\pi$
$644$	1.85163	−	0.496144i	0.0729646	−	0.0195508i
$645$	0.876250	−	2.75692i	0.0345023	−	0.108553i
$646$	−19.6798	+	34.0864i	−0.774290	+	1.34111i
$647$	7.87623	+	13.6420i	0.309646	+	0.536323i	0.978285	−	0.207264i	$-0.0664560\pi$
$647$	7.87623	+	13.6420i	0.309646	+	0.536323i	−0.668639	+	0.743588i	$0.733123\pi$
$648$	−8.97261	+	0.701625i	−0.352477	+	0.0275624i
$649$			1.98598i			0.0779567i
$650$	16.7453	−	4.42186i	0.656804	−	0.173439i
$651$	−0.336095	−	0.649285i	−0.0131726	−	0.0254475i
$652$	3.59245	−	13.4072i	0.140691	−	0.525067i
$653$	21.3400	−	12.3207i	0.835099	−	0.482145i	−0.0204964	−	0.999790i	$-0.506525\pi$
$653$	21.3400	−	12.3207i	0.835099	−	0.482145i	0.855595	+	0.517645i	$0.173191\pi$
$654$	−5.04523	−	0.231943i	−0.197284	−	0.00906970i
$655$	−2.53590	−	2.53590i	−0.0990857	−	0.0990857i
$656$	−1.97475	−	7.36988i	−0.0771011	−	0.287745i
$657$	−14.0118	−	5.17324i	−0.546654	−	0.201827i
$658$	1.07145	−	1.07145i	0.0417697	−	0.0417697i
$659$	−15.3411	−	8.85721i	−0.597606	−	0.345028i	0.170493	−	0.985359i	$-0.445464\pi$
$659$	−15.3411	−	8.85721i	−0.597606	−	0.345028i	−0.768099	+	0.640331i	$0.778797\pi$
$660$	0.376879	+	0.241323i	0.0146700	+	0.00939348i
$661$	−9.15665	−	2.45352i	−0.356153	−	0.0954308i	0.0763064	−	0.997084i	$-0.475687\pi$
$661$	−9.15665	−	2.45352i	−0.356153	−	0.0954308i	−0.432459	+	0.901654i	$0.642354\pi$
$662$	16.4877			0.640813
$663$	18.9588	−	29.3732i	0.736299	−	1.14076i
$664$	−11.6394			−0.451697
$665$	0.867544	+	0.232458i	0.0336419	+	0.00901432i
$666$	1.91538	−	20.7877i	0.0742196	−	0.805506i
$667$	−23.7926	−	13.7367i	−0.921253	−	0.531886i
$668$	9.48357	−	9.48357i	0.366930	−	0.366930i
$669$	−8.39872	−	9.20816i	−0.324713	−	0.356008i
$670$	−1.01574	−	3.79080i	−0.0392415	−	0.146451i
$671$	4.33221	+	4.33221i	0.167243	+	0.167243i
$672$	−0.0229229	+	0.498618i	−0.000884268	+	0.0192346i
$673$	−0.150089	+	0.0866536i	−0.00578549	+	0.00334025i	−0.502890	−	0.864350i	$-0.667730\pi$
$673$	−0.150089	+	0.0866536i	−0.00578549	+	0.00334025i	0.497104	+	0.867691i	$0.334397\pi$
$674$	0.840764	−	3.13777i	0.0323850	−	0.120862i
$675$	−3.42911	+	24.7231i	−0.131986	+	0.951591i
$676$	−11.3052	+	6.41816i	−0.434815	+	0.246852i
$677$			2.12205i			0.0815568i	0.999168	+	0.0407784i	$0.0129838\pi$
$677$			2.12205i			0.0815568i	−0.999168	+	0.0407784i	$0.987016\pi$
$678$	−17.6235	+	3.86439i	−0.676825	+	0.148411i
$679$	−0.386725	−	0.669827i	−0.0148411	−	0.0257056i
$680$	1.24076	−	2.14906i	0.0475810	−	0.0824127i
$681$	−8.84802	−	2.81223i	−0.339057	−	0.107765i
$682$	−0.824672	+	0.220970i	−0.0315783	+	0.00846139i
$683$	30.9953	−	8.30516i	1.18600	−	0.317788i	0.388697	−	0.921365i	$-0.372925\pi$
$683$	30.9953	−	8.30516i	1.18600	−	0.317788i	0.797305	+	0.603577i	$0.206258\pi$
$684$	3.56679	+	20.7888i	0.136379	+	0.794878i
$685$	−0.0183309	+	0.0317500i	−0.000700388	+	0.00121311i
$686$	−2.00530	−	3.47328i	−0.0765627	−	0.132611i
$687$	−4.32754	−	19.7356i	−0.165106	−	0.752961i
$688$		−	3.76778i		−	0.143645i
$689$	11.4140	−	6.53478i	0.434838	−	0.248955i
$690$	−4.53556	+	2.34778i	−0.172666	+	0.0893783i
$691$	7.89090	−	29.4492i	0.300184	−	1.12030i	−0.636829	−	0.771005i	$-0.719754\pi$
$691$	7.89090	−	29.4492i	0.300184	−	1.12030i	0.937012	−	0.349296i	$-0.113579\pi$
$692$	0.954532	−	0.551099i	0.0362858	−	0.0209496i
$693$	0.210857	+	0.457687i	0.00800980	+	0.0173861i
$694$	−5.81113	−	5.81113i	−0.220587	−	0.220587i
$695$	−0.716073	−	2.67242i	−0.0271622	−	0.101371i
$696$	5.28534	−	4.82074i	0.200340	−	0.182730i
$697$	−30.2026	+	30.2026i	−1.14401	+	1.14401i
$698$	6.93931	+	4.00641i	0.262657	+	0.151645i
$699$	8.91747	−	13.9266i	0.337290	−	0.526753i
$700$	1.33711	+	0.358278i	0.0505381	+	0.0135416i
$701$	1.23549			0.0466638			0.0233319	−	0.999728i	$-0.492573\pi$
$701$	1.23549			0.0466638			0.0233319	+	0.999728i	$0.492573\pi$
$702$	−2.24934	−	18.5995i	−0.0848957	−	0.701992i
$703$	−48.9246			−1.84523
$704$	0.563016	+	0.150860i	0.0212195	+	0.00568574i
$705$	−2.17693	+	3.39976i	−0.0819879	+	0.128042i
$706$	2.42107	+	1.39781i	0.0911182	+	0.0526071i
$707$	2.90188	−	2.90188i	0.109136	−	0.109136i
$708$	4.36020	−	3.97692i	0.163866	−	0.149462i
$709$	4.09728	+	15.2913i	0.153877	+	0.574276i	0.999199	+	0.0400188i	$0.0127418\pi$
$709$	4.09728	+	15.2913i	0.153877	+	0.574276i	−0.845322	+	0.534257i	$0.820592\pi$
$710$	−4.82277	−	4.82277i	−0.180995	−	0.180995i
$711$	−1.39195	−	3.02136i	−0.0522021	−	0.113310i
$712$	12.1957	−	7.04118i	0.457053	−	0.263879i
$713$	2.52175	−	9.41131i	0.0944404	−	0.352456i
$714$	2.48152	−	1.28453i	0.0928686	−	0.0480723i
$715$	−0.468717	+	0.805084i	−0.0175290	+	0.0301084i
$716$			5.59555i			0.209115i
$717$	−10.8274	−	49.3783i	−0.404358	−	1.84407i
$718$	8.24000	+	14.2721i	0.307514	+	0.532630i
$719$	−1.55033	+	2.68525i	−0.0578176	+	0.100143i	−0.893486	−	0.449092i	$-0.851748\pi$
$719$	−1.55033	+	2.68525i	−0.0578176	+	0.100143i	0.835668	+	0.549235i	$0.185081\pi$
$720$	−0.224877	−	1.31068i	−0.00838067	−	0.0488461i
$721$	1.28298	−	0.343773i	0.0477806	−	0.0128028i
$722$	29.3957	−	7.87656i	1.09400	−	0.293135i
$723$	18.4116	+	5.85188i	0.684734	+	0.217634i
$724$	7.23437	−	12.5303i	0.268863	−	0.465685i
$725$	−9.91959	−	17.1812i	−0.368404	−	0.638095i
$726$	−18.0356	+	3.95476i	−0.669364	+	0.146775i
$727$		−	20.0877i		−	0.745011i	−0.928030	−	0.372506i	$-0.878499\pi$
$727$		−	20.0877i		−	0.745011i	0.928030	−	0.372506i	$-0.121501\pi$
$728$	−1.03904	−	0.00376858i	−0.0385096	−	0.000139673i
$729$	25.9808	+	7.34847i	0.962250	+	0.272166i
$730$	0.571208	−	2.13178i	0.0211414	−	0.0789006i
$731$	−18.2667	+	10.5463i	−0.675617	+	0.390067i
$732$	0.836085	−	18.1865i	0.0309026	−	0.672193i
$733$	35.4832	+	35.4832i	1.31060	+	1.31060i	0.920972	+	0.389628i	$0.127396\pi$
$733$	35.4832	+	35.4832i	1.31060	+	1.31060i	0.389628	+	0.920972i	$0.372604\pi$
$734$	9.62442	+	35.9188i	0.355244	+	1.32579i
$735$	3.57880	+	3.92371i	0.132006	+	0.144728i
$736$	−4.70360	+	4.70360i	−0.173377	+	0.173377i
$737$	−4.46910	−	2.58023i	−0.164621	−	0.0950442i
$738$	−2.10016	+	22.7930i	−0.0773078	+	0.839023i
$739$	−22.4899	−	6.02615i	−0.827305	−	0.221676i	−0.179767	−	0.983709i	$-0.557534\pi$
$739$	−22.4899	−	6.02615i	−0.827305	−	0.221676i	−0.647538	+	0.762034i	$0.724201\pi$
$740$	3.08458			0.113391
$741$	−42.9224	+	9.24879i	−1.57679	+	0.339763i
$742$	1.05122			0.0385916
$743$	−25.8872	−	6.93645i	−0.949709	−	0.254474i	−0.249470	−	0.968382i	$-0.580257\pi$
$743$	−25.8872	−	6.93645i	−0.949709	−	0.254474i	−0.700239	+	0.713909i	$0.746923\pi$
$744$	2.13654	+	1.36806i	0.0783292	+	0.0501557i
$745$	5.58069	+	3.22201i	0.204461	+	0.118045i
$746$	5.57782	−	5.57782i	0.204219	−	0.204219i
$747$	32.7570	+	12.0940i	1.19852	+	0.442498i
$748$	−0.844533	−	3.15184i	−0.0308792	−	0.115243i
$749$	−2.75341	−	2.75341i	−0.100607	−	0.100607i
$750$	−7.51898	−	0.345668i	−0.274554	−	0.0126220i
$751$	−15.4295	+	8.90822i	−0.563030	+	0.325065i	−0.754361	−	0.656460i	$-0.772053\pi$
$751$	−15.4295	+	8.90822i	−0.563030	+	0.325065i	0.191331	+	0.981526i	$0.438720\pi$
$752$	−1.36088	+	5.07887i	−0.0496262	+	0.185207i
$753$	3.55874	+	6.87496i	0.129688	+	0.250537i
$754$	10.4916	+	10.5680i	0.382081	+	0.384863i
$755$			4.01433i			0.146096i
$756$	0.582605	−	1.37945i	0.0211891	−	0.0501700i
$757$	−12.3906	−	21.4612i	−0.450345	−	0.780020i	0.548062	−	0.836438i	$-0.315366\pi$
$757$	−12.3906	−	21.4612i	−0.450345	−	0.780020i	−0.998407	+	0.0564171i	$0.982032\pi$
$758$	0.930981	−	1.61251i	0.0338148	−	0.0585689i
$759$	−2.03419	+	6.40009i	−0.0738363	+	0.232308i
$760$	−3.01041	+	0.806638i	−0.109199	+	0.0292598i
$761$	−14.6883	+	3.93572i	−0.532451	+	0.142670i	−0.515020	−	0.857178i	$-0.672215\pi$
$761$	−14.6883	+	3.93572i	−0.532451	+	0.142670i	−0.0174313	+	0.999848i	$0.505549\pi$
$762$	0.126678	−	0.398562i	0.00458905	−	0.0144384i
$763$	0.420159	−	0.727738i	0.0152108	−	0.0263459i
$764$	−3.33787	−	5.78136i	−0.120760	−	0.209162i
$765$	−5.72489	+	4.75891i	−0.206984	+	0.172059i
$766$			2.88048i			0.104076i

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:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	78.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.933998 + 1.45865i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.313444 - 0.313444i) q^{5} +(-1.27970 + 1.16721i) q^{6} +(-0.0745867 - 0.278362i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.25529 - 2.72474i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.933998 + 1.45865i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.313444 - 0.313444i) q^{5} +(-1.27970 + 1.16721i) q^{6} +(-0.0745867 - 0.278362i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.25529 - 2.72474i) q^{9} +(0.383889 - 0.221638i) q^{10} +(0.150860 - 0.563016i) q^{11} +(-1.53819 + 0.796225i) q^{12} +(-1.79144 - 3.12902i) q^{13} -0.288181i q^{14} +(0.164448 + 0.749960i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.79907 - 4.84812i) q^{17} +(-0.507306 - 2.95680i) q^{18} +(-6.79127 + 1.81971i) q^{19} +(0.428173 - 0.114729i) q^{20} +(0.475695 + 0.151194i) q^{21} +(0.291439 - 0.504787i) q^{22} +(3.32595 + 5.76071i) q^{23} +(-1.69185 + 0.370982i) q^{24} +4.80351i q^{25} +(-0.920548 - 3.48606i) q^{26} +(5.14688 + 0.713876i) q^{27} +(0.0745867 - 0.278362i) q^{28} +(-3.57681 + 2.06507i) q^{29} +(-0.0352597 + 0.766968i) q^{30} +(-1.03573 - 1.03573i) q^{31} +(0.258819 + 0.965926i) q^{32} +(0.680339 + 0.745907i) q^{33} +(3.95848 - 3.95848i) q^{34} +(-0.110630 - 0.0638720i) q^{35} +(0.275255 - 2.98735i) q^{36} +(6.72147 + 1.80101i) q^{37} -7.03084 q^{38} +(6.23733 + 0.309422i) q^{39} +0.443277 q^{40} +(-7.36988 - 1.97475i) q^{41} +(0.420354 + 0.269161i) q^{42} +(-3.26299 - 1.88389i) q^{43} +(0.412157 - 0.412157i) q^{44} +(-1.24752 - 0.460590i) q^{45} +(1.72164 + 6.42524i) q^{46} +(3.71799 + 3.71799i) q^{47} +(-1.73022 - 0.0795432i) q^{48} +(5.99026 - 3.45848i) q^{49} +(-1.24324 + 4.63983i) q^{50} +(4.45737 + 8.61098i) q^{51} +(0.0130771 - 3.60553i) q^{52} +3.64778i q^{53} +(4.78674 + 2.02166i) q^{54} +(-0.129188 - 0.223760i) q^{55} +(0.144091 - 0.249572i) q^{56} +(3.68871 - 11.6057i) q^{57} +(-3.98942 + 1.06896i) q^{58} +(-3.29111 + 0.881850i) q^{59} +(-0.232564 + 0.731708i) q^{60} +(-5.25554 + 9.10286i) q^{61} +(-0.732370 - 1.26850i) q^{62} +(-0.664836 + 0.552656i) q^{63} +1.00000i q^{64} +(-1.54229 - 0.419256i) q^{65} +(0.464102 + 0.896575i) q^{66} +(2.29144 - 8.55177i) q^{67} +(4.84812 - 2.79907i) q^{68} +(-11.5093 - 0.529114i) q^{69} +(-0.0903287 - 0.0903287i) q^{70} +(-3.98229 - 14.8621i) q^{71} +(1.03906 - 2.81431i) q^{72} +(3.52053 - 3.52053i) q^{73} +(6.02630 + 3.47929i) q^{74} +(-7.00661 - 4.48647i) q^{75} +(-6.79127 - 1.81971i) q^{76} -0.167974 q^{77} +(5.94471 + 1.91322i) q^{78} +1.10886 q^{79} +(0.428173 + 0.114729i) q^{80} +(-5.84847 + 6.84072i) q^{81} +(-6.60765 - 3.81493i) q^{82} +(-8.23032 + 8.23032i) q^{83} +(0.336367 + 0.368785i) q^{84} +(-0.642265 - 2.39697i) q^{85} +(-2.66422 - 2.66422i) q^{86} +(0.328525 - 7.14608i) q^{87} +(0.504787 - 0.291439i) q^{88} +(3.64478 - 13.6025i) q^{89} +(-1.08580 - 0.767778i) q^{90} +(-0.737380 + 0.732051i) q^{91} +6.65190i q^{92} +(2.47813 - 0.543392i) q^{93} +(2.62902 + 4.55359i) q^{94} +(-1.55830 + 2.69906i) q^{95} +(-1.65068 - 0.524648i) q^{96} +(2.59245 - 0.694645i) q^{97} +(6.68126 - 1.79024i) q^{98} +(-1.72345 + 0.295697i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} - 24 q^{10} - 24 q^{13} + 8 q^{16} - 16 q^{19} - 24 q^{21} - 8 q^{28} + 24 q^{30} + 16 q^{31} - 24 q^{33} + 24 q^{34} + 24 q^{36} + 16 q^{37} + 48 q^{39} + 24 q^{45} + 24 q^{46} + 24 q^{49} - 8 q^{52} - 24 q^{55} - 24 q^{57} - 24 q^{60} - 24 q^{61} - 24 q^{63} - 48 q^{66} + 32 q^{67} - 48 q^{69} - 24 q^{72} + 56 q^{73} - 16 q^{76} - 96 q^{79} + 24 q^{81} - 48 q^{82} - 24 q^{85} + 48 q^{87} - 16 q^{91} - 24 q^{93} - 24 q^{94} + 16 q^{97}+O(q^{100}) \) 16 * q + 8 * q^7 - 24 * q^10 - 24 * q^13 + 8 * q^16 - 16 * q^19 - 24 * q^21 - 8 * q^28 + 24 * q^30 + 16 * q^31 - 24 * q^33 + 24 * q^34 + 24 * q^36 + 16 * q^37 + 48 * q^39 + 24 * q^45 + 24 * q^46 + 24 * q^49 - 8 * q^52 - 24 * q^55 - 24 * q^57 - 24 * q^60 - 24 * q^61 - 24 * q^63 - 48 * q^66 + 32 * q^67 - 48 * q^69 - 24 * q^72 + 56 * q^73 - 16 * q^76 - 96 * q^79 + 24 * q^81 - 48 * q^82 - 24 * q^85 + 48 * q^87 - 16 * q^91 - 24 * q^93 - 24 * q^94 + 16 * q^97

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