LMFDB - Embedded newform 78.2.k.a.71.2

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} + \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			71.2
Root			$0.500000 - 1.33108i$ of defining polynomial
Character	$\chi$	$=$	78.71
Dual form			78.2.k.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(1.73022 + 0.0795432i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.313444 - 0.313444i) q^{5} +(-1.69185 + 0.370982i) q^{6} +(-0.0745867 + 0.278362i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.98735 + 0.275255i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(1.73022 + 0.0795432i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.313444 - 0.313444i) q^{5} +(-1.69185 + 0.370982i) q^{6} +(-0.0745867 + 0.278362i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.98735 + 0.275255i) 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} +(-0.517396 - 0.567261i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.79907 - 4.84812i) q^{17} +(-2.95680 + 0.507306i) q^{18} +(-6.79127 - 1.81971i) q^{19} +(-0.428173 - 0.114729i) q^{20} +(-0.151194 + 0.475695i) q^{21} +(0.291439 + 0.504787i) q^{22} +(-3.32595 + 5.76071i) q^{23} +(-1.27970 + 1.16721i) 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} +(0.646584 + 0.414020i) q^{30} +(-1.03573 + 1.03573i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-0.216237 - 0.986144i) q^{33} +(3.95848 + 3.95848i) q^{34} +(0.110630 - 0.0638720i) q^{35} +(2.72474 - 1.25529i) q^{36} +(6.72147 - 1.80101i) q^{37} +7.03084 q^{38} +(-3.34848 + 5.27140i) q^{39} +0.443277 q^{40} +(7.36988 - 1.97475i) q^{41} +(0.0229229 - 0.498618i) q^{42} +(-3.26299 + 1.88389i) q^{43} +(-0.412157 - 0.412157i) q^{44} +(-0.850089 - 1.02264i) q^{45} +(1.72164 - 6.42524i) q^{46} +(-3.71799 + 3.71799i) q^{47} +(0.933998 - 1.45865i) 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} +(-5.15627 + 0.642559i) q^{54} +(-0.129188 + 0.223760i) q^{55} +(-0.144091 - 0.249572i) q^{56} +(-11.6057 - 3.68871i) q^{57} +(-3.98942 - 1.06896i) q^{58} +(3.29111 + 0.881850i) q^{59} +(-0.731708 - 0.232564i) q^{60} +(-5.25554 - 9.10286i) q^{61} +(0.732370 - 1.26850i) q^{62} +(-0.299437 + 0.811032i) 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} +(-6.21286 + 9.70277i) q^{69} +(-0.0903287 + 0.0903287i) q^{70} +(3.98229 - 14.8621i) q^{71} +(-2.30701 + 1.91774i) q^{72} +(3.52053 + 3.52053i) q^{73} +(-6.02630 + 3.47929i) q^{74} +(0.382086 - 8.31114i) q^{75} +(-6.79127 + 1.81971i) q^{76} +0.167974 q^{77} +(1.87005 - 5.95843i) q^{78} +1.10886 q^{79} +(-0.428173 + 0.114729i) q^{80} +(8.84847 + 1.64456i) q^{81} +(-6.60765 + 3.81493i) q^{82} +(8.23032 + 8.23032i) q^{83} +(0.106910 + 0.487560i) q^{84} +(-0.642265 + 2.39697i) q^{85} +(2.66422 - 2.66422i) q^{86} +(6.02442 + 3.85755i) 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} +(-1.87442 + 1.70965i) q^{93} +(2.62902 - 4.55359i) q^{94} +(1.55830 + 2.69906i) q^{95} +(-0.524648 + 1.65068i) q^{96} +(2.59245 + 0.694645i) q^{97} +(-6.68126 - 1.79024i) q^{98} +(-0.295697 - 1.72345i) 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 $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$-1$	$e\left(\frac{5}{12}\right)$

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
$3$	1.73022	+	0.0795432i	0.998945	+	0.0459243i
$3$	1.73022	+	0.0795432i	0.998945	+	0.0459243i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−0.313444	−	0.313444i	−0.140176	−	0.140176i	0.633536	−	0.773713i	$-0.281603\pi$
$5$	−0.313444	−	0.313444i	−0.140176	−	0.140176i	−0.773713	+	0.633536i	$0.781603\pi$
$6$	−1.69185	+	0.370982i	−0.690697	+	0.151453i
$7$	−0.0745867	+	0.278362i	−0.0281911	+	0.105211i	−0.978588	−	0.205830i	$-0.934011\pi$
$7$	−0.0745867	+	0.278362i	−0.0281911	+	0.105211i	0.950397	+	0.311040i	$0.100677\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.98735	+	0.275255i	0.995782	+	0.0917517i
$10$	0.383889	+	0.221638i	0.121396	+	0.0700882i
$11$	−0.150860	−	0.563016i	−0.0454859	−	0.169756i	0.939446	−	0.342696i	$-0.111340\pi$
$11$	−0.150860	−	0.563016i	−0.0454859	−	0.169756i	−0.984932	+	0.172940i	$0.944673\pi$
$12$	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
$15$	−0.517396	−	0.567261i	−0.133591	−	0.146466i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−2.79907	−	4.84812i	−0.678873	−	1.17584i	−0.975321	−	0.220793i	$-0.929135\pi$
$17$	−2.79907	−	4.84812i	−0.678873	−	1.17584i	0.296448	−	0.955049i	$-0.404198\pi$
$18$	−2.95680	+	0.507306i	−0.696923	+	0.119573i
$19$	−6.79127	−	1.81971i	−1.55802	−	0.417471i	−0.625986	−	0.779834i	$-0.715304\pi$
$19$	−6.79127	−	1.81971i	−1.55802	−	0.417471i	−0.932037	+	0.362363i	$0.881970\pi$
$20$	−0.428173	−	0.114729i	−0.0957423	−	0.0256541i
$21$	−0.151194	+	0.475695i	−0.0329931	+	0.103805i
$22$	0.291439	+	0.504787i	0.0621349	+	0.107621i
$23$	−3.32595	+	5.76071i	−0.693509	+	1.20119i	0.277172	+	0.960820i	$0.410603\pi$
$23$	−3.32595	+	5.76071i	−0.693509	+	1.20119i	−0.970681	+	0.240372i	$0.922731\pi$
$24$	−1.27970	+	1.16721i	−0.261217	+	0.238255i
$25$		−	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	$-0.208061\pi$
$29$	3.57681	+	2.06507i	0.664198	+	0.383475i	−0.129677	+	0.991556i	$0.541394\pi$
$30$	0.646584	+	0.414020i	0.118050	+	0.0755893i
$31$	−1.03573	+	1.03573i	−0.186022	+	0.186022i	−0.793974	−	0.607952i	$-0.791991\pi$
$31$	−1.03573	+	1.03573i	−0.186022	+	0.186022i	0.607952	+	0.793974i	$0.291991\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−0.216237	−	0.986144i	−0.0376420	−	0.171666i
$34$	3.95848	+	3.95848i	0.678873	+	0.678873i
$35$	0.110630	−	0.0638720i	0.0186998	−	0.0107963i
$36$	2.72474	−	1.25529i	0.454124	−	0.209216i
$37$	6.72147	−	1.80101i	1.10500	−	0.296085i	0.340202	−	0.940352i	$-0.389504\pi$
$37$	6.72147	−	1.80101i	1.10500	−	0.296085i	0.764800	+	0.644268i	$0.222838\pi$
$38$	7.03084			1.14055
$39$	−3.34848	+	5.27140i	−0.536186	+	0.844100i
$40$	0.443277			0.0700882
$41$	7.36988	−	1.97475i	1.15098	−	0.308404i	0.367623	−	0.929975i	$-0.380172\pi$
$41$	7.36988	−	1.97475i	1.15098	−	0.308404i	0.783358	+	0.621570i	$0.213505\pi$
$42$	0.0229229	−	0.498618i	0.00353707	−	0.0769384i
$43$	−3.26299	+	1.88389i	−0.497602	+	0.287290i	−0.727723	−	0.685872i	$-0.759421\pi$
$43$	−3.26299	+	1.88389i	−0.497602	+	0.287290i	0.230121	+	0.973162i	$0.426088\pi$
$44$	−0.412157	−	0.412157i	−0.0621349	−	0.0621349i
$45$	−0.850089	−	1.02264i	−0.126724	−	0.152447i
$46$	1.72164	−	6.42524i	0.253842	−	0.947350i
$47$	−3.71799	+	3.71799i	−0.542325	+	0.542325i	−0.924210	−	0.381885i	$-0.875275\pi$
$47$	−3.71799	+	3.71799i	−0.542325	+	0.542325i	0.381885	+	0.924210i	$0.375275\pi$
$48$	0.933998	−	1.45865i	0.134811	−	0.210537i
$49$	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	$0.919395\pi$
$54$	−5.15627	+	0.642559i	−0.701679	+	0.0874413i
$55$	−0.129188	+	0.223760i	−0.0174197	+	0.0301718i
$56$	−0.144091	−	0.249572i	−0.0192549	−	0.0333505i
$57$	−11.6057	−	3.68871i	−1.53721	−	0.488582i
$58$	−3.98942	−	1.06896i	−0.523836	−	0.140361i
$59$	3.29111	+	0.881850i	0.428466	+	0.114807i	0.466606	−	0.884465i	$-0.345477\pi$
$59$	3.29111	+	0.881850i	0.428466	+	0.114807i	−0.0381400	+	0.999272i	$0.512143\pi$
$60$	−0.731708	−	0.232564i	−0.0944632	−	0.0300239i
$61$	−5.25554	−	9.10286i	−0.672903	−	1.16550i	−0.977077	−	0.212886i	$-0.931714\pi$
$61$	−5.25554	−	9.10286i	−0.672903	−	1.16550i	0.304174	−	0.952616i	$-0.401620\pi$
$62$	0.732370	−	1.26850i	0.0930111	−	0.161100i
$63$	−0.299437	+	0.811032i	−0.0377255	+	0.102180i
$64$		−	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	0.952455	+	0.304678i	$0.0985488\pi$
$67$	2.29144	+	8.55177i	0.279944	+	1.04476i	−0.672512	+	0.740087i	$0.734785\pi$
$68$	−4.84812	−	2.79907i	−0.587921	−	0.339437i
$69$	−6.21286	+	9.70277i	−0.747941	+	1.16808i
$70$	−0.0903287	+	0.0903287i	−0.0107963	+	0.0107963i
$71$	3.98229	−	14.8621i	0.472611	−	1.76381i	−0.157723	−	0.987483i	$-0.550415\pi$
$71$	3.98229	−	14.8621i	0.472611	−	1.76381i	0.630334	−	0.776324i	$-0.282918\pi$
$72$	−2.30701	+	1.91774i	−0.271883	+	0.226008i
$73$	3.52053	+	3.52053i	0.412047	+	0.412047i	0.882451	−	0.470404i	$-0.155892\pi$
$73$	3.52053	+	3.52053i	0.412047	+	0.412047i	−0.470404	+	0.882451i	$0.655892\pi$
$74$	−6.02630	+	3.47929i	−0.700543	+	0.404459i
$75$	0.382086	−	8.31114i	0.0441195	−	0.959687i
$76$	−6.79127	+	1.81971i	−0.779012	+	0.208736i
$77$	0.167974			0.0191424
$78$	1.87005	−	5.95843i	0.211741	−	0.674660i
$79$	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
$81$	8.84847	+	1.64456i	0.983163	+	0.182729i
$82$	−6.60765	+	3.81493i	−0.729693	+	0.421288i
$83$	8.23032	+	8.23032i	0.903395	+	0.903395i	0.995728	−	0.0923332i	$-0.0294325\pi$
$83$	8.23032	+	8.23032i	0.903395	+	0.903395i	−0.0923332	+	0.995728i	$0.529433\pi$
$84$	0.106910	+	0.487560i	0.0116648	+	0.0531972i
$85$	−0.642265	+	2.39697i	−0.0696634	+	0.259987i
$86$	2.66422	−	2.66422i	0.287290	−	0.287290i
$87$	6.02442	+	3.85755i	0.645886	+	0.413573i
$88$	0.504787	+	0.291439i	0.0538104	+	0.0310675i
$89$	−3.64478	−	13.6025i	−0.386346	−	1.44186i	−0.836034	−	0.548678i	$-0.815131\pi$
$89$	−3.64478	−	13.6025i	−0.386346	−	1.44186i	0.449687	−	0.893186i	$-0.351535\pi$
$90$	1.08580	+	0.767778i	0.114454	+	0.0809309i
$91$	−0.737380	−	0.732051i	−0.0772985	−	0.0767398i
$92$			6.65190i			0.693509i
$93$	−1.87442	+	1.70965i	−0.194369	+	0.177283i
$94$	2.62902	−	4.55359i	0.271162	−	0.469667i
$95$	1.55830	+	2.69906i	0.159879	+	0.276918i
$96$	−0.524648	+	1.65068i	−0.0535466	+	0.168472i
$97$	2.59245	+	0.694645i	0.263223	+	0.0705305i	0.388017	−	0.921652i	$-0.373160\pi$
$97$	2.59245	+	0.694645i	0.263223	+	0.0705305i	−0.124794	+	0.992183i	$0.539827\pi$
$98$	−6.68126	−	1.79024i	−0.674909	−	0.180841i
$99$	−0.295697	−	1.72345i	−0.0297187	−	0.173213i
$100$	−2.40175	−	4.15996i	−0.240175	−	0.415996i
$101$	−7.12030	+	12.3327i	−0.708497	+	1.22715i	0.256918	+	0.966433i	$0.417293\pi$
$101$	−7.12030	+	12.3327i	−0.708497	+	1.22715i	−0.965415	+	0.260719i	$0.916040\pi$
$102$	6.53418	+	7.16392i	0.646980	+	0.709334i
$103$		−	4.60903i		−	0.454141i	−0.973878	−	0.227071i	$-0.927085\pi$
$103$		−	4.60903i		−	0.454141i	0.973878	−	0.227071i	$-0.0729148\pi$
$104$	−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	$-0.559877\pi$
$107$	−11.7017	−	6.75600i	−1.13125	−	0.653127i	−0.944249	+	0.329232i	$0.893210\pi$
$108$	4.81427	−	1.95521i	0.463253	−	0.188140i
$109$	2.06188	−	2.06188i	0.197492	−	0.197492i	−0.601432	−	0.798924i	$-0.705403\pi$
$109$	2.06188	−	2.06188i	0.197492	−	0.197492i	0.798924	+	0.601432i	$0.205403\pi$
$110$	0.0668726	−	0.249572i	0.00637606	−	0.0237958i
$111$	11.7729	−	2.58151i	1.11743	−	0.245026i
$112$	0.203775	+	0.203775i	0.0192549	+	0.0192549i
$113$	−9.02108	+	5.20832i	−0.848632	+	0.489958i	−0.860189	−	0.509975i	$-0.829655\pi$
$113$	−9.02108	+	5.20832i	−0.848632	+	0.489958i	0.0115570	+	0.999933i	$0.496321\pi$
$114$	12.1649	+	0.559256i	1.13935	+	0.0523791i
$115$	2.84816	−	0.763163i	0.265592	−	0.0711653i
$116$	4.13015			0.383475
$117$	−6.21292	+	8.85435i	−0.574385	+	0.818585i
$118$	−3.40721			−0.313659
$119$	1.55830	−	0.417546i	0.142850	−	0.0382764i
$120$	0.766968	+	0.0352597i	0.0700143	+	0.00321875i
$121$	9.23205	−	5.33013i	0.839277	−	0.484557i
$122$	7.43246	+	7.43246i	0.672903	+	0.672903i
$123$	12.9086	−	2.83054i	1.16393	−	0.255221i
$124$	−0.379103	+	1.41483i	−0.0340444	+	0.127055i
$125$	−3.07285	+	3.07285i	−0.274844	+	0.274844i
$126$	0.0793233	−	0.860896i	0.00706668	−	0.0766948i
$127$	−0.209104	−	0.120726i	−0.0185550	−	0.0107127i	0.490694	−	0.871332i	$-0.336743\pi$
$127$	−0.209104	−	0.120726i	−0.0185550	−	0.0107127i	−0.509249	+	0.860619i	$0.670077\pi$
$128$	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	$-0.114985\pi$
$132$	−0.680339	−	0.745907i	−0.0592159	−	0.0649229i
$133$	1.01308	−	1.75470i	0.0878449	−	0.152152i
$134$	−4.42672	−	7.66730i	−0.382410	−	0.662354i
$135$	−1.38950	−	1.83702i	−0.119589	−	0.158105i
$136$	5.40738	+	1.44890i	0.463679	+	0.124242i
$137$	0.0798882	+	0.0214060i	0.00682531	+	0.00182884i	0.262230	−	0.965005i	$-0.415542\pi$
$137$	0.0798882	+	0.0214060i	0.00682531	+	0.00182884i	−0.255405	+	0.966834i	$0.582209\pi$
$138$	3.48990	−	10.9802i	0.297080	−	0.934693i
$139$	3.12073	+	5.40526i	0.264697	+	0.458468i	0.967484	−	0.252932i	$-0.0813949\pi$
$139$	3.12073	+	5.40526i	0.264697	+	0.458468i	−0.702788	+	0.711400i	$0.748062\pi$
$140$	0.0638720	−	0.110630i	0.00539817	−	0.00934990i
$141$	−6.72870	+	6.13721i	−0.566658	+	0.516847i
$142$			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
$147$	10.0894	+	6.46042i	0.832158	+	0.532846i
$148$	4.92046	−	4.92046i	0.404459	−	0.404459i
$149$	−3.76251	+	14.0419i	−0.308237	+	1.15036i	0.621886	+	0.783108i	$0.286367\pi$
$149$	−3.76251	+	14.0419i	−0.308237	+	1.15036i	−0.930123	+	0.367249i	$0.880300\pi$
$150$	1.78201	+	8.12683i	0.145501	+	0.663553i
$151$	−6.40358	−	6.40358i	−0.521116	−	0.521116i	0.396793	−	0.917908i	$-0.370123\pi$
$151$	−6.40358	−	6.40358i	−0.521116	−	0.521116i	−0.917908	+	0.396793i	$0.870123\pi$
$152$	6.08888	−	3.51542i	0.493874	−	0.285138i
$153$	−7.02730	−	15.2535i	−0.568124	−	1.23317i
$154$	−0.162251	+	0.0434749i	−0.0130745	+	0.00350331i
$155$	0.649285			0.0521519
$156$	−0.264169	+	6.23941i	−0.0211504	+	0.499552i
$157$	−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
$159$	−0.290157	+	6.31148i	−0.0230109	+	0.500533i
$160$	0.383889	−	0.221638i	0.0303491	−	0.0175221i
$161$	−1.35549	−	1.35549i	−0.106828	−	0.106828i
$162$	−8.97261	+	0.701625i	−0.704955	+	0.0551249i
$163$	−3.59245	+	13.4072i	−0.281382	+	1.05013i	0.670060	+	0.742307i	$0.266268\pi$
$163$	−3.59245	+	13.4072i	−0.281382	+	1.05013i	−0.951442	+	0.307827i	$0.900398\pi$
$164$	5.39512	−	5.39512i	0.421288	−	0.421288i
$165$	−0.241323	+	0.376879i	−0.0187870	+	0.0293400i
$166$	−10.0800	−	5.81971i	−0.782363	−	0.451697i
$167$	−3.47123	−	12.9548i	−0.268612	−	1.00247i	−0.960003	−	0.279991i	$-0.909668\pi$
$167$	−3.47123	−	12.9548i	−0.268612	−	1.00247i	0.691391	−	0.722481i	$-0.256998\pi$
$168$	−0.229457	−	0.443277i	−0.0177030	−	0.0341996i
$169$	−6.58150	−	11.2109i	−0.506269	−	0.862376i
$170$		−	2.48152i		−	0.190324i
$171$	−19.7870	−	7.30545i	−1.51315	−	0.558662i
$172$	−1.88389	+	3.26299i	−0.143645	+	0.248801i
$173$	−0.551099	−	0.954532i	−0.0418993	−	0.0725717i	0.844315	−	0.535847i	$-0.180008\pi$
$173$	−0.551099	−	0.954532i	−0.0418993	−	0.0725717i	−0.886215	+	0.463275i	$0.846674\pi$
$174$	−6.81755	−	2.16687i	−0.516837	−	0.164270i
$175$	1.33711	+	0.358278i	0.101076	+	0.0270833i
$176$	−0.563016	−	0.150860i	−0.0424389	−	0.0113715i
$177$	5.62421	+	1.78758i	0.422741	+	0.134363i
$178$	7.04118	+	12.1957i	0.527759	+	0.914105i
$179$	−2.79777	+	4.84589i	−0.209115	+	0.362199i	−0.951436	−	0.307846i	$-0.900392\pi$
$179$	−2.79777	+	4.84589i	−0.209115	+	0.362199i	0.742321	+	0.670045i	$0.233725\pi$
$180$	−1.24752	−	0.460590i	−0.0929847	−	0.0343304i
$181$			14.4687i			1.07545i	0.843119	+	0.537727i	$0.180717\pi$
$181$			14.4687i			1.07545i	−0.843119	+	0.537727i	$0.819283\pi$
$182$	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
$186$	1.36806	−	2.13654i	0.100311	−	0.156658i
$187$	−2.30731	+	2.30731i	−0.168727	+	0.168727i
$188$	−1.36088	+	5.07887i	−0.0992523	+	0.370415i
$189$	−0.582605	+	1.37945i	−0.0423783	+	0.100340i
$190$	−2.20377	−	2.20377i	−0.159879	−	0.159879i
$191$	5.78136	−	3.33787i	0.418324	−	0.241520i	−0.276036	−	0.961147i	$-0.589021\pi$
$191$	5.78136	−	3.33787i	0.418324	−	0.241520i	0.694360	+	0.719628i	$0.255688\pi$
$192$	0.0795432	−	1.73022i	0.00574054	−	0.124868i
$193$	5.88685	−	1.57738i	0.423745	−	0.113542i	−0.0406437	−	0.999174i	$-0.512941\pi$
$193$	5.88685	−	1.57738i	0.423745	−	0.113542i	0.464388	+	0.885632i	$0.346274\pi$
$194$	−2.68390			−0.192693
$195$	2.70185	−	0.602728i	0.193484	−	0.0431623i
$196$	6.91695			0.494068
$197$	14.2844	−	3.82748i	1.01772	−	0.272697i	0.288868	−	0.957369i	$-0.406721\pi$
$197$	14.2844	−	3.82748i	1.01772	−	0.272697i	0.728851	+	0.684672i	$0.240055\pi$
$198$	0.731683	+	1.58819i	0.0519984	+	0.112868i
$199$	13.4064	−	7.74017i	0.950352	−	0.548686i	0.0571619	−	0.998365i	$-0.481795\pi$
$199$	13.4064	−	7.74017i	0.950352	−	0.548686i	0.893190	+	0.449679i	$0.148462\pi$
$200$	3.39659	+	3.39659i	0.240175	+	0.240175i
$201$	3.28447	+	14.9787i	0.231668	+	1.05652i
$202$	3.68574	−	13.7554i	0.259328	−	0.967824i
$203$	−0.841620	+	0.841620i	−0.0590701	+	0.0590701i
$204$	−8.16569	−	5.22864i	−0.571713	−	0.366078i
$205$	−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
$210$	−0.163474	+	0.149104i	−0.0112808	+	0.0102891i
$211$	−9.40721	+	16.2938i	−0.647619	+	1.12171i	0.336071	+	0.941837i	$0.390902\pi$
$211$	−9.40721	+	16.2938i	−0.647619	+	1.12171i	−0.983690	+	0.179872i	$0.942432\pi$
$212$	1.82389	+	3.15907i	0.125265	+	0.216966i
$213$	8.07243	−	25.3980i	0.553114	−	1.74024i
$214$	13.0516	+	3.49716i	0.892189	+	0.239061i
$215$	1.61326	+	0.432272i	0.110023	+	0.0294807i
$216$	−4.14418	+	3.13461i	−0.281976	+	0.213283i
$217$	−0.211055	−	0.365558i	−0.0143274	−	0.0248157i
$218$	−1.45797	+	2.52528i	−0.0987462	+	0.171033i
$219$	5.81127	+	6.37133i	0.392689	+	0.430535i
$220$			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	0.875117	−	0.483911i	$-0.160784\pi$
$223$	−1.86235	−	6.95039i	−0.124712	−	0.465432i	−0.999829	+	0.0184790i	$0.994118\pi$
$224$	−0.249572	−	0.144091i	−0.0166752	−	0.00962745i
$225$	1.32219	−	14.3497i	0.0881460	−	0.956649i
$226$	7.36568	−	7.36568i	0.489958	−	0.489958i
$227$	−1.38733	+	5.17758i	−0.0920803	+	0.343648i	−0.996561	−	0.0828671i	$-0.973592\pi$
$227$	−1.38733	+	5.17758i	−0.0920803	+	0.343648i	0.904480	+	0.426515i	$0.140259\pi$
$228$	−11.8952	+	2.60831i	−0.787776	+	0.172740i
$229$	−8.24846	−	8.24846i	−0.545074	−	0.545074i	0.379938	−	0.925012i	$-0.375945\pi$
$229$	−8.24846	−	8.24846i	−0.545074	−	0.545074i	−0.925012	+	0.379938i	$0.875945\pi$
$230$	−2.55359	+	1.47432i	−0.168379	+	0.0972136i
$231$	0.290633	+	0.0133612i	0.0191222	+	0.000879103i
$232$	−3.98942	+	1.06896i	−0.261918	+	0.0701807i
$233$	9.54763			0.625486			0.312743	−	0.949838i	$-0.398752\pi$
$233$	9.54763			0.625486			0.312743	+	0.949838i	$0.398752\pi$
$234$	3.70955	−	10.1607i	0.242501	−	0.664224i
$235$	2.33077			0.152042
$236$	3.29111	−	0.881850i	0.214233	−	0.0574036i
$237$	1.91858	+	0.0882024i	0.124625	+	0.00572936i
$238$	−1.39714	+	0.806638i	−0.0905630	+	0.0522865i
$239$	20.6375	+	20.6375i	1.33493	+	1.33493i	0.900895	+	0.434036i	$0.142911\pi$
$239$	20.6375	+	20.6375i	1.33493	+	1.33493i	0.434036	+	0.900895i	$0.357089\pi$
$240$	−0.749960	+	0.164448i	−0.0484097	+	0.0106151i
$241$	−2.88685	+	10.7739i	−0.185958	+	0.694006i	0.808465	+	0.588544i	$0.200299\pi$
$241$	−2.88685	+	10.7739i	−0.185958	+	0.694006i	−0.994423	+	0.105462i	$0.966368\pi$
$242$	−7.53794	+	7.53794i	−0.484557	+	0.484557i
$243$	15.1790	+	3.54930i	0.973734	+	0.227688i
$244$	−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
$249$	13.5856	+	14.8950i	0.860954	+	0.943930i
$250$	2.17283	−	3.76346i	0.137422	−	0.238022i
$251$	−2.23476	−	3.87071i	−0.141057	−	0.244317i	0.786838	−	0.617159i	$-0.211717\pi$
$251$	−2.23476	−	3.87071i	−0.141057	−	0.244317i	−0.927895	+	0.372842i	$0.878383\pi$
$252$	0.146196	+	0.852093i	0.00920948	+	0.0536768i
$253$	3.74513	+	1.00350i	0.235454	+	0.0630898i
$254$	0.233226	+	0.0624926i	0.0146339	+	0.00392114i
$255$	−1.30192	+	4.09620i	−0.0815297	+	0.256514i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.97416	−	10.3475i	0.372658	−	0.645462i	−0.617316	−	0.786715i	$-0.711780\pi$
$257$	5.97416	−	10.3475i	0.372658	−	0.645462i	0.989973	+	0.141254i	$0.0451133\pi$
$258$	4.82162	−	4.39778i	0.300181	−	0.273794i
$259$			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	$-0.306301\pi$
$263$	2.38262	+	1.37560i	0.146918	+	0.0848234i	−0.424739	+	0.905316i	$0.639634\pi$
$264$	0.850212	+	0.544406i	0.0523269	+	0.0335059i
$265$	1.14338	−	1.14338i	0.0702371	−	0.0702371i
$266$	−0.524407	+	1.95711i	−0.0321535	+	0.119998i
$267$	−5.22430	−	23.8253i	−0.319722	−	1.45809i
$268$	6.26033	+	6.26033i	0.382410	+	0.382410i
$269$	−5.40423	+	3.12013i	−0.329502	+	0.190238i	−0.655620	−	0.755091i	$-0.727593\pi$
$269$	−5.40423	+	3.12013i	−0.329502	+	0.190238i	0.326118	+	0.945329i	$0.394259\pi$
$270$	1.81761	+	1.41480i	0.110616	+	0.0861017i
$271$	−21.6057	+	5.78922i	−1.31245	+	0.351670i	−0.846144	−	0.532954i	$-0.821082\pi$
$271$	−21.6057	+	5.78922i	−1.31245	+	0.351670i	−0.466306	+	0.884624i	$0.654415\pi$
$272$	−5.59813			−0.339437
$273$	−1.21760	−	1.32527i	−0.0736927	−	0.0802087i
$274$	−0.0827063			−0.00499647
$275$	−2.70445	+	0.724656i	−0.163085	+	0.0436984i
$276$	−0.529114	+	11.5093i	−0.0318489	+	0.692777i
$277$	−4.84833	+	2.79919i	−0.291308	+	0.168187i	−0.638532	−	0.769596i	$-0.720458\pi$
$277$	−4.84833	+	2.79919i	−0.291308	+	0.168187i	0.347224	+	0.937782i	$0.387125\pi$
$278$	−4.41337	−	4.41337i	−0.264697	−	0.264697i
$279$	−3.37917	+	2.80899i	−0.202305	+	0.168170i
$280$	−0.0330626	+	0.123391i	−0.00197587	+	0.00737404i
$281$	8.82870	−	8.82870i	0.526676	−	0.526676i	−0.392903	−	0.919580i	$-0.628529\pi$
$281$	8.82870	−	8.82870i	0.526676	−	0.526676i	0.919580	+	0.392903i	$0.128529\pi$
$282$	4.91099	−	7.66961i	0.292445	−	0.456719i
$283$	−5.93983	−	3.42936i	−0.353086	−	0.203854i	0.312958	−	0.949767i	$-0.398680\pi$
$283$	−5.93983	−	3.42936i	−0.353086	−	0.203854i	−0.666044	+	0.745913i	$0.732014\pi$
$284$	−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
$288$	−1.03906	+	2.81431i	−0.0612271	+	0.165835i
$289$	−7.16953	+	12.4180i	−0.421737	+	0.730470i
$290$	0.915400	+	1.58552i	0.0537541	+	0.0931049i
$291$	4.43026	+	1.40810i	0.259707	+	0.0825445i
$292$	4.80913	+	1.28860i	0.281433	+	0.0754098i
$293$	−26.4232	−	7.08007i	−1.54366	−	0.413622i	−0.616213	−	0.787579i	$-0.711334\pi$
$293$	−26.4232	−	7.08007i	−1.54366	−	0.413622i	−0.927446	+	0.373957i	$0.878001\pi$
$294$	−11.4177	−	3.62896i	−0.665892	−	0.211645i
$295$	−0.755168	−	1.30799i	−0.0439676	−	0.0761541i
$296$	−3.47929	+	6.02630i	−0.202229	+	0.350272i
$297$	−0.374533	−	3.00547i	−0.0217326	−	0.174395i
$298$		−	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
$303$	−13.3007	+	20.7720i	−0.764105	+	1.19332i
$304$	−4.97155	+	4.97155i	−0.285138	+	0.285138i
$305$	−1.20592	+	4.50056i	−0.0690508	+	0.257701i
$306$	10.7357	+	12.9149i	0.613722	+	0.738297i
$307$	−15.4869	−	15.4869i	−0.883883	−	0.883883i	0.110044	−	0.993927i	$-0.464901\pi$
$307$	−15.4869	−	15.4869i	−0.883883	−	0.883883i	−0.993927	+	0.110044i	$0.964901\pi$
$308$	0.145470	−	0.0839871i	0.00828892	−	0.00478561i
$309$	0.366617	−	7.97465i	0.0208561	−	0.453662i
$310$	−0.627161	+	0.168047i	−0.0356204	+	0.00954445i
$311$	−31.8012			−1.80328			−0.901642	−	0.432484i	$-0.857637\pi$
$311$	−31.8012			−1.80328			−0.901642	+	0.432484i	$0.857637\pi$
$312$	−1.35971	−	6.09518i	−0.0769784	−	0.345071i
$313$	−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
$315$	0.348070	−	0.160356i	0.0196115	−	0.00903506i
$316$	0.960301	−	0.554430i	0.0540212	−	0.0311891i
$317$	−16.8936	−	16.8936i	−0.948841	−	0.948841i	0.0499128	−	0.998754i	$-0.484106\pi$
$317$	−16.8936	−	16.8936i	−0.948841	−	0.948841i	−0.998754	+	0.0499128i	$0.984106\pi$
$318$	−1.35326	−	6.17152i	−0.0758872	−	0.346082i
$319$	0.623073	−	2.32534i	0.0348854	−	0.130194i
$320$	−0.313444	+	0.313444i	−0.0175221	+	0.0175221i
$321$	−19.7092	−	12.6202i	−1.10006	−	0.704390i
$322$	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
$327$	3.73152	−	3.40351i	0.206354	−	0.188214i
$328$	−3.81493	+	6.60765i	−0.210644	+	0.364846i
$329$	−0.757633	−	1.31226i	−0.0417697	−	0.0723472i
$330$	0.135556	−	0.426496i	0.00746213	−	0.0234778i
$331$	15.9259	+	4.26733i	0.875367	+	0.234554i	0.668407	−	0.743795i	$-0.266976\pi$
$331$	15.9259	+	4.26733i	0.875367	+	0.234554i	0.206960	+	0.978349i	$0.433643\pi$
$332$	11.2428	+	3.01251i	0.617030	+	0.165333i
$333$	20.5751	−	3.53013i	1.12751	−	0.193450i
$334$	6.70590	+	11.6150i	0.366930	+	0.635542i
$335$	1.96226	−	3.39874i	0.107210	−	0.185693i
$336$	0.336367	+	0.368785i	0.0183503	+	0.0201189i
$337$			3.24846i			0.176955i	0.996078	+	0.0884775i	$0.0282001\pi$
$337$			3.24846i			0.176955i	−0.996078	+	0.0884775i	$0.971800\pi$
$338$	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
$342$	21.0035	+	1.93527i	1.13574	+	0.104648i
$343$	−2.83592	+	2.83592i	−0.153125	+	0.153125i
$344$	0.975173	−	3.63939i	0.0525778	−	0.196223i
$345$	4.98866	−	1.09389i	0.268580	−	0.0588930i
$346$	0.779372	+	0.779372i	0.0418993	+	0.0418993i
$347$	7.11715	−	4.10909i	0.382069	−	0.220587i	−0.296649	−	0.954986i	$-0.595869\pi$
$347$	7.11715	−	4.10909i	0.382069	−	0.220587i	0.678718	+	0.734399i	$0.262536\pi$
$348$	7.14608	+	0.328525i	0.383070	+	0.0176108i
$349$	7.73980	−	2.07387i	0.414302	−	0.111012i	−0.0456462	−	0.998958i	$-0.514535\pi$
$349$	7.73980	−	2.07387i	0.414302	−	0.111012i	0.459948	+	0.887946i	$0.347868\pi$
$350$	−1.38428			−0.0739928
$351$	−11.4541	+	14.8258i	−0.611372	+	0.791343i
$352$	0.582877			0.0310675
$353$	−2.70035	+	0.723557i	−0.143725	+	0.0385111i	−0.329964	−	0.943993i	$-0.607037\pi$
$353$	−2.70035	+	0.723557i	−0.143725	+	0.0385111i	0.186239	+	0.982504i	$0.440370\pi$
$354$	−5.89523	−	0.271020i	−0.313328	−	0.0144046i
$355$	−5.90666	+	3.41021i	−0.313493	+	0.180995i
$356$	−9.95774	−	9.95774i	−0.527759	−	0.527759i
$357$	2.72943	−	0.598496i	0.144457	−	0.0316758i
$358$	1.44823	−	5.40488i	0.0765416	−	0.285657i
$359$	−11.6531	+	11.6531i	−0.615028	+	0.615028i	−0.944252	−	0.329224i	$-0.893213\pi$
$359$	−11.6531	+	11.6531i	−0.615028	+	0.615028i	0.329224	+	0.944252i	$0.393213\pi$
$360$	1.32422	+	0.122014i	0.0697926	+	0.00643072i
$361$	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
$366$	12.2686	+	13.4510i	0.641290	+	0.703096i
$367$	18.5929	−	32.2039i	0.970544	−	1.68103i	0.276626	−	0.960978i	$-0.410784\pi$
$367$	18.5929	−	32.2039i	0.970544	−	1.68103i	0.693918	−	0.720054i	$-0.255883\pi$
$368$	3.32595	+	5.76071i	0.173377	+	0.300298i
$369$	22.5599	−	3.87067i	1.17442	−	0.201499i
$370$	2.97947	+	0.798347i	0.154895	+	0.0415041i
$371$	−1.01540	−	0.272076i	−0.0527171	−	0.0141255i
$372$	−0.768472	+	2.41782i	−0.0398434	+	0.125358i
$373$	3.94412	+	6.83141i	0.204219	+	0.353717i	0.949883	−	0.312604i	$-0.101201\pi$
$373$	3.94412	+	6.83141i	0.204219	+	0.353717i	−0.745665	+	0.666321i	$0.767868\pi$
$374$	1.63151	−	2.82586i	0.0843635	−	0.146122i
$375$	−5.56114	+	5.07229i	−0.287176	+	0.261932i
$376$		−	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	0.977198	−	0.212331i	$-0.0681055\pi$
$379$	0.481911	+	1.79852i	0.0247541	+	0.0923837i	−0.952444	+	0.304715i	$0.901439\pi$
$380$	2.69906	+	1.55830i	0.138459	+	0.0799393i
$381$	−0.352194	−	0.225517i	−0.0180435	−	0.0115536i
$382$	−4.72046	+	4.72046i	−0.241520	+	0.241520i
$383$	−0.745523	+	2.78233i	−0.0380945	+	0.142170i	−0.982354	−	0.187032i	$-0.940113\pi$
$383$	−0.745523	+	2.78233i	−0.0380945	+	0.142170i	0.944259	+	0.329202i	$0.106780\pi$
$384$	0.370982	+	1.69185i	0.0189316	+	0.0863371i
$385$	−0.0526505	−	0.0526505i	−0.00268332	−	0.00268332i
$386$	−5.27801	+	3.04726i	−0.268643	+	0.155101i
$387$	−10.2662	+	4.72967i	−0.521862	+	0.240423i
$388$	2.59245	−	0.694645i	0.131612	−	0.0352653i
$389$	23.4187			1.18738			0.593688	−	0.804695i	$-0.297671\pi$
$389$	23.4187			1.18738			0.593688	+	0.804695i	$0.297671\pi$
$390$	−2.45379	+	1.28148i	−0.124253	+	0.0648903i
$391$	37.2382			1.88322
$392$	−6.68126	+	1.79024i	−0.337455	+	0.0904207i
$393$	0.643539	−	13.9983i	0.0324623	−	0.706119i
$394$	−12.8070	+	7.39413i	−0.645208	+	0.372511i
$395$	−0.347566	−	0.347566i	−0.0174879	−	0.0174879i
$396$	−1.11781	−	1.34470i	−0.0561719	−	0.0675738i
$397$	4.76427	−	17.7805i	0.239112	−	0.892378i	−0.737140	−	0.675740i	$-0.763824\pi$
$397$	4.76427	−	17.7805i	0.239112	−	0.892378i	0.976252	−	0.216638i	$-0.0695092\pi$
$398$	−10.9463	+	10.9463i	−0.548686	+	0.548686i
$399$	1.89242	−	2.95544i	0.0947397	−	0.147957i
$400$	−4.15996	−	2.40175i	−0.207998	−	0.120088i
$401$	1.75607	+	6.55376i	0.0876942	+	0.327279i	0.995811	−	0.0914383i	$-0.0291464\pi$
$401$	1.75607	+	6.55376i	0.0876942	+	0.327279i	−0.908117	+	0.418717i	$0.862480\pi$
$402$	−7.04933	−	13.6183i	−0.351589	−	0.679217i
$403$	−1.38537	−	5.09625i	−0.0690100	−	0.253862i
$404$			14.2406i			0.708497i
$405$	−2.25802	−	3.28898i	−0.112202	−	0.163431i
$406$	0.595115	−	1.03077i	0.0295351	−	0.0511562i
$407$	−2.02800	−	3.51260i	−0.100524	−	0.174113i
$408$	9.24072	+	2.93705i	0.457484	+	0.145405i
$409$	−28.2895	−	7.58014i	−1.39882	−	0.374814i	−0.520902	−	0.853617i	$-0.674404\pi$
$409$	−28.2895	−	7.58014i	−1.39882	−	0.374814i	−0.877923	+	0.478803i	$0.841071\pi$
$410$	3.26690	+	0.875362i	0.161340	+	0.0432311i
$411$	0.136522	+	0.0433917i	0.00673412	+	0.00214035i
$412$	−2.30452	−	3.99154i	−0.113535	−	0.196649i
$413$	−0.490946	+	0.850344i	−0.0241579	+	0.0418427i
$414$	6.91171	−	18.7205i	0.339692	−	0.920064i
$415$		−	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	$-0.405818\pi$
$419$	−8.00397	−	4.62109i	−0.391020	−	0.225755i	−0.682602	+	0.730791i	$0.739152\pi$
$420$	0.119313	−	0.186333i	0.00582186	−	0.00909213i
$421$	−18.4490	+	18.4490i	−0.899149	+	0.899149i	−0.995361	−	0.0962115i	$-0.969327\pi$
$421$	−18.4490	+	18.4490i	−0.899149	+	0.899149i	0.0962115	+	0.995361i	$0.469327\pi$
$422$	4.86953	−	18.1733i	0.237045	−	0.884664i
$423$	−12.1303	+	10.0835i	−0.589796	+	0.490278i
$424$	−2.57937	−	2.57937i	−0.125265	−	0.125265i
$425$	−23.2880	+	13.4453i	−1.12963	+	0.652194i
$426$	−1.22388	+	26.6219i	−0.0592973	+	1.28983i
$427$	2.92588	−	0.783987i	0.141593	−	0.0379398i
$428$	−13.5120			−0.653127
$429$	3.47304	+	1.09001i	0.167680	+	0.0526260i
$430$	−1.67017			−0.0805427
$431$	−21.6015	+	5.78811i	−1.04051	+	0.278803i	−0.738324	−	0.674446i	$-0.764383\pi$
$431$	−21.6015	+	5.78811i	−1.04051	+	0.278803i	−0.302184	+	0.953249i	$0.597716\pi$
$432$	3.19168	−	4.10039i	0.153560	−	0.197280i
$433$	3.41910	−	1.97402i	0.164311	−	0.0948652i	−0.415589	−	0.909552i	$-0.636425\pi$
$433$	3.41910	−	1.97402i	0.164311	−	0.0948652i	0.579901	+	0.814687i	$0.303091\pi$
$434$	0.298477	+	0.298477i	0.0143274	+	0.0143274i
$435$	−0.679193	−	3.09745i	−0.0325648	−	0.148511i
$436$	0.754701	−	2.81658i	0.0361436	−	0.134890i
$437$	33.0703	−	33.0703i	1.58197	−	1.58197i
$438$	−7.26228	−	4.65017i	−0.347005	−	0.222194i
$439$	15.8569	+	9.15500i	0.756810	+	0.436944i	0.828149	−	0.560508i	$-0.189394\pi$
$439$	15.8569	+	9.15500i	0.756810	+	0.436944i	−0.0713394	+	0.997452i	$0.522727\pi$
$440$	−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	$-0.0444841\pi$
$444$	8.90488	−	8.12210i	0.422607	−	0.385458i
$445$	−3.12119	+	5.40607i	−0.147959	+	0.256272i
$446$	3.59778	+	6.23155i	0.170360	+	0.295072i
$447$	−7.62693	+	23.9963i	−0.360741	+	1.13499i
$448$	0.278362	+	0.0745867i	0.0131513	+	0.00352389i
$449$	27.5332	+	7.37750i	1.29937	+	0.348166i	0.841213	−	0.540704i	$-0.181842\pi$
$449$	27.5332	+	7.37750i	1.29937	+	0.348166i	0.458160	+	0.888870i	$0.348509\pi$
$450$	2.43685	+	14.2030i	0.114874	+	0.669535i
$451$	−2.22364	−	3.85145i	−0.104707	−	0.181358i
$452$	−5.20832	+	9.02108i	−0.244979	+	0.424316i
$453$	−10.5703	−	11.5890i	−0.496634	−	0.544498i
$454$		−	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	−0.979439	−	0.201742i	$-0.935340\pi$
$457$	−4.96154	−	18.5167i	−0.232091	−	0.866175i	0.747348	−	0.664433i	$-0.231327\pi$
$458$	10.1023	+	5.83254i	0.472048	+	0.272537i
$459$	−10.9455	−	26.9509i	−0.510892	−	1.25796i
$460$	2.08500	−	2.08500i	0.0972136	−	0.0972136i
$461$	7.67398	−	28.6397i	0.357413	−	1.33388i	−0.520007	−	0.854162i	$-0.674071\pi$
$461$	7.67398	−	28.6397i	0.357413	−	1.33388i	0.877421	−	0.479722i	$-0.159262\pi$
$462$	−0.284188	+	0.0623154i	−0.0132216	+	0.00289917i
$463$	18.2554	+	18.2554i	0.848400	+	0.848400i	0.989934	−	0.141533i	$-0.0452032\pi$
$463$	18.2554	+	18.2554i	0.848400	+	0.848400i	−0.141533	+	0.989934i	$0.545203\pi$
$464$	3.57681	−	2.06507i	0.166049	−	0.0958687i
$465$	1.12341	+	0.0516463i	0.0520968	+	0.00239504i
$466$	−9.22231	+	2.47111i	−0.427215	+	0.114472i
$467$	32.4456			1.50140			0.750701	−	0.660642i	$-0.229716\pi$
$467$	32.4456			1.50140			0.750701	+	0.660642i	$0.229716\pi$
$468$	−0.953374	+	10.7746i	−0.0440697	+	0.498054i
$469$	−2.55139			−0.117812
$470$	−2.25135	+	0.603246i	−0.103847	+	0.0278257i
$471$	−17.6703	−	0.812354i	−0.814205	−	0.0374313i
$472$	−2.95073	+	1.70360i	−0.135818	+	0.0784147i
$473$	1.55291	+	1.55291i	0.0714031	+	0.0714031i
$474$	−1.87603	+	0.411367i	−0.0861690	+	0.0188947i
$475$	−8.74101	+	32.6219i	−0.401065	+	1.49680i
$476$	1.14076	−	1.14076i	0.0522865	−	0.0522865i
$477$	−1.00407	+	10.8972i	−0.0459733	+	0.498948i
$478$	−25.2757	−	14.5929i	−1.15608	−	0.667466i
$479$	2.14571	+	8.00792i	0.0980402	+	0.365891i	0.997463	−	0.0711890i	$-0.0226793\pi$
$479$	2.14571	+	8.00792i	0.0980402	+	0.365891i	−0.899423	+	0.437080i	$0.856013\pi$
$480$	0.681844	−	0.352948i	0.0311218	−	0.0161098i
$481$	−6.40570	+	24.2580i	−0.292075	+	1.10607i
$482$		−	11.1539i		−	0.508048i
$483$	−2.23748	−	2.45312i	−0.101809	−	0.111621i
$484$	5.33013	−	9.23205i	0.242279	−	0.419639i
$485$	−0.594856	−	1.03032i	−0.0270110	−	0.0467845i
$486$	−15.5804	+	0.500258i	−0.706743	+	0.0226921i
$487$	−31.0359	−	8.31604i	−1.40637	−	0.376836i	−0.525742	−	0.850644i	$-0.676212\pi$
$487$	−31.0359	−	8.31604i	−1.40637	−	0.376836i	−0.880628	+	0.473808i	$0.842879\pi$
$488$	10.1529	+	2.72047i	0.459601	+	0.123150i
$489$	−7.28219	+	22.9117i	−0.329312	+	1.03610i
$490$	1.53306	+	2.65534i	0.0692567	+	0.119956i
$491$	13.2100	−	22.8803i	0.596157	−	1.03257i	−0.397226	−	0.917721i	$-0.630027\pi$
$491$	13.2100	−	22.8803i	0.596157	−	1.03257i	0.993383	−	0.114853i	$-0.0366397\pi$
$492$	9.76391	−	8.90562i	0.440191	−	0.401496i
$493$		−	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
$498$	−16.9778	−	10.8712i	−0.760794	−	0.487150i
$499$	−9.27427	+	9.27427i	−0.415173	+	0.415173i	−0.883536	−	0.468363i	$-0.844844\pi$
$499$	−9.27427	+	9.27427i	−0.415173	+	0.415173i	0.468363	+	0.883536i	$0.344844\pi$
$500$	−1.12474	+	4.19759i	−0.0503000	+	0.187722i
$501$	−4.97553	−	22.6908i	−0.222290	−	1.01375i
$502$	3.16043	+	3.16043i	0.141057	+	0.141057i
$503$	26.4513	−	15.2717i	1.17941	−	0.680931i	0.223529	−	0.974697i	$-0.428242\pi$
$503$	26.4513	−	15.2717i	1.17941	−	0.680931i	0.955877	+	0.293767i	$0.0949089\pi$
$504$	−0.361752	−	0.785220i	−0.0161137	−	0.0349765i
$505$	6.09744	−	1.63380i	0.271332	−	0.0727033i
$506$	−3.87724			−0.172364
$507$	−10.4957	−	19.9208i	−0.466131	−	0.884716i
$508$	−0.241453			−0.0107127
$509$	−23.0380	+	6.17302i	−1.02114	+	0.273614i	−0.730278	−	0.683150i	$-0.760610\pi$
$509$	−23.0380	+	6.17302i	−1.02114	+	0.273614i	−0.290865	+	0.956764i	$0.593943\pi$
$510$	0.197388	−	4.29359i	0.00874050	−	0.190123i
$511$	−1.24256	+	0.717395i	−0.0549678	+	0.0317357i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−33.6548	−	14.2140i	−1.48590	−	0.627562i
$514$	−3.09245	+	11.5412i	−0.136402	+	0.509060i
$515$	−1.44467	+	1.44467i	−0.0636599	+	0.0636599i
$516$	−3.51910	+	5.49585i	−0.154920	+	0.241941i
$517$	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	$0.618146\pi$
$522$	−11.6235	−	4.29146i	−0.508748	−	0.187832i
$523$	17.0400	−	29.5141i	0.745107	−	1.29056i	−0.205037	−	0.978754i	$-0.565732\pi$
$523$	17.0400	−	29.5141i	0.745107	−	1.29056i	0.950145	−	0.311809i	$-0.100935\pi$
$524$	−4.04522	−	7.00652i	−0.176716	−	0.306081i
$525$	2.28500	+	0.726259i	0.0997257	+	0.0316965i
$526$	−2.65746	−	0.712065i	−0.115871	−	0.0310475i
$527$	7.92040	+	2.12227i	0.345018	+	0.0924473i
$528$	−0.962144	−	0.305805i	−0.0418719	−	0.0133085i
$529$	−10.6239	−	18.4011i	−0.461908	−	0.800048i
$530$	−0.808489	+	1.40034i	−0.0351185	+	0.0608271i
$531$	9.58895	+	3.54029i	0.416125	+	0.153635i
$532$		−	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
$537$	−5.22623	+	8.16192i	−0.225529	+	0.352213i
$538$	4.41254	−	4.41254i	0.190238	−	0.190238i
$539$	1.04349	−	3.89436i	0.0449463	−	0.167742i
$540$	−2.12185	−	0.896156i	−0.0913100	−	0.0385644i
$541$	18.5013	+	18.5013i	0.795434	+	0.795434i	0.982372	−	0.186938i	$-0.0598564\pi$
$541$	18.5013	+	18.5013i	0.795434	+	0.795434i	−0.186938	+	0.982372i	$0.559856\pi$
$542$	19.3711	−	11.1839i	0.832060	−	0.480390i
$543$	−1.15089	+	25.0342i	−0.0493895	+	1.07432i
$544$	5.40738	−	1.44890i	0.231839	−	0.0621212i
$545$	−1.29257			−0.0553676
$546$	1.51912	+	0.964969i	0.0650123	+	0.0412969i
$547$	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
$549$	−13.1945	−	28.6400i	−0.563128	−	1.22233i
$550$	2.42475	−	1.39993i	0.103391	−	0.0596931i
$551$	−20.5332	−	20.5332i	−0.874746	−	0.874746i
$552$	−2.46773	−	11.2540i	−0.105034	−	0.479004i
$553$	−0.0827063	+	0.308664i	−0.00351703	+	0.0131257i
$554$	3.95865	−	3.95865i	0.168187	−	0.168187i
$555$	−4.49930	−	2.88099i	−0.190985	−	0.122291i
$556$	5.40526	+	3.12073i	0.229234	+	0.132348i
$557$	4.08768	+	15.2554i	0.173201	+	0.646394i	0.996851	+	0.0792958i	$0.0252672\pi$
$557$	4.08768	+	15.2554i	0.173201	+	0.646394i	−0.823650	+	0.567098i	$0.808066\pi$
$558$	2.53700	−	3.58786i	0.107400	−	0.151886i
$559$	−0.0492717	−	13.5848i	−0.00208397	−	0.574577i
$560$		−	0.127744i		−	0.00539817i
$561$	−4.17568	+	3.80862i	−0.176298	+	0.160800i
$562$	−6.24284	+	10.8129i	−0.263338	+	0.456115i
$563$	10.6906	+	18.5166i	0.450555	+	0.780383i	0.998421	−	0.0561827i	$-0.0178929\pi$
$563$	10.6906	+	18.5166i	0.450555	+	0.780383i	−0.547866	+	0.836566i	$0.684560\pi$
$564$	−2.75862	+	8.67933i	−0.116159	+	0.365466i
$565$	4.46012	+	1.19509i	0.187639	+	0.0502777i
$566$	6.62502	+	1.77517i	0.278470	+	0.0746159i
$567$	−1.11776	+	2.34041i	−0.0469416	+	0.0982880i
$568$	7.69319	+	13.3250i	0.322799	+	0.559105i
$569$	14.5203	−	25.1500i	0.608725	−	1.05434i	−0.382726	−	0.923862i	$-0.625015\pi$
$569$	14.5203	−	25.1500i	0.608725	−	1.05434i	0.991451	−	0.130480i	$-0.0416519\pi$
$570$	−3.63773	−	3.98832i	−0.152368	−	0.167052i
$571$		−	9.91137i		−	0.414778i	−0.978259	−	0.207389i	$-0.933503\pi$
$571$		−	9.91137i		−	0.414778i	0.978259	−	0.207389i	$-0.0664966\pi$
$572$	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
$576$	0.275255	−	2.98735i	0.0114690	−	0.124473i
$577$	−4.91283	+	4.91283i	−0.204524	+	0.204524i	−0.801935	−	0.597411i	$-0.796196\pi$
$577$	−4.91283	+	4.91283i	−0.204524	+	0.204524i	0.597411	+	0.801935i	$0.296196\pi$
$578$	3.71122	−	13.8505i	0.154366	−	0.576104i
$579$	10.3110	−	2.26095i	0.428512	−	0.0939621i
$580$	−1.29457	−	1.29457i	−0.0537541	−	0.0537541i
$581$	−2.90488	+	1.67713i	−0.120515	+	0.0695791i
$582$	−4.64375	−	0.213486i	−0.192490	−	0.00884929i
$583$	2.05376	−	0.550304i	0.0850581	−	0.0227913i
$584$	−4.97878			−0.206023
$585$	4.72275	−	0.827940i	0.195262	−	0.0342311i
$586$	27.3553			1.13004
$587$	−23.2001	+	6.21644i	−0.957569	+	0.256580i	−0.703571	−	0.710625i	$-0.748412\pi$
$587$	−23.2001	+	6.21644i	−0.957569	+	0.256580i	−0.253998	+	0.967205i	$0.581746\pi$
$588$	11.9679	+	0.550197i	0.493547	+	0.0226897i
$589$	8.91863	−	5.14917i	0.367486	−	0.212168i
$590$	1.06797	+	1.06797i	0.0439676	+	0.0439676i
$591$	25.0196	−	5.48618i	1.02917	−	0.225671i
$592$	1.80101	−	6.72147i	0.0740211	−	0.276251i
$593$	−22.0744	+	22.0744i	−0.906489	+	0.906489i	−0.995987	−	0.0894984i	$-0.971474\pi$
$593$	−22.0744	+	22.0744i	−0.906489	+	0.906489i	0.0894984	+	0.995987i	$0.471474\pi$
$594$	1.13964	+	2.80613i	0.0467602	+	0.115137i
$595$	−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	$-0.255957\pi$
$600$	5.60669	+	6.14704i	0.228892	+	0.250952i
$601$	−10.0883	+	17.4735i	−0.411512	+	0.712759i	−0.995055	−	0.0993227i	$-0.968332\pi$
$601$	−10.0883	+	17.4735i	−0.411512	+	0.712759i	0.583544	+	0.812082i	$0.301666\pi$
$602$	0.542901	+	0.940332i	0.0221270	+	0.0383251i
$603$	4.49140	+	26.1778i	0.182904	+	1.06604i
$604$	−8.74745	−	2.34387i	−0.355929	−	0.0953708i
$605$	−4.56443	−	1.22304i	−0.185570	−	0.0497234i
$606$	7.47130	−	23.5067i	0.303501	−	0.954894i
$607$	2.42837	+	4.20607i	0.0985647	+	0.170719i	0.911091	−	0.412206i	$-0.135242\pi$
$607$	2.42837	+	4.20607i	0.0985647	+	0.170719i	−0.812526	+	0.582925i	$0.801908\pi$
$608$	3.51542	−	6.08888i	0.142569	−	0.246937i
$609$	−1.52314	+	1.38925i	−0.0617206	+	0.0562951i
$610$		−	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	0.961008	−	0.276521i	$-0.0891816\pi$
$613$	−0.235455	−	0.878731i	−0.00950994	−	0.0354916i	−0.970518	+	0.241030i	$0.922515\pi$
$614$	18.9675	+	10.9509i	0.765465	+	0.441941i
$615$	−4.93334	−	3.15891i	−0.198932	−	0.127380i
$616$	−0.118776	+	0.118776i	−0.00478561	+	0.00478561i
$617$	−11.6445	+	43.4580i	−0.468792	+	1.74956i	0.175210	+	0.984531i	$0.443940\pi$
$617$	−11.6445	+	43.4580i	−0.468792	+	1.74956i	−0.644002	+	0.765024i	$0.722727\pi$
$618$	1.70987	+	7.79781i	0.0687809	+	0.313674i
$619$	11.7433	+	11.7433i	0.472003	+	0.472003i	0.902562	−	0.430559i	$-0.141684\pi$
$619$	11.7433	+	11.7433i	0.472003	+	0.472003i	−0.430559	+	0.902562i	$0.641684\pi$
$620$	0.562298	−	0.324643i	0.0225824	−	0.0130380i
$621$	−21.2307	+	27.2754i	−0.851959	+	1.09452i
$622$	30.7176	−	8.23077i	1.23167	−	0.330024i
$623$	4.05827			0.162591
$624$	2.89093	+	5.53557i	0.115730	+	0.221600i
$625$	−22.0912			−0.883648
$626$	22.9334	−	6.14498i	0.916602	−	0.245603i
$627$	−0.325977	+	7.09066i	−0.0130183	+	0.283174i
$628$	−8.84449	+	5.10637i	−0.352933	+	0.203766i
$629$	−27.5454	−	27.5454i	−1.09831	−	1.09831i
$630$	−0.294706	+	0.244980i	−0.0117414	+	0.00976022i
$631$	9.44656	−	35.2551i	0.376062	−	1.40348i	−0.475725	−	0.879594i	$-0.657814\pi$
$631$	9.44656	−	35.2551i	0.376062	−	1.40348i	0.851787	−	0.523888i	$-0.175519\pi$
$632$	−0.784083	+	0.784083i	−0.0311891	+	0.0311891i
$633$	−17.5726	+	27.4436i	−0.698449	+	1.09078i
$634$	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
$639$	15.9873	−	43.3021i	0.632450	−	1.71300i
$640$	0.221638	−	0.383889i	0.00876103	−	0.0151745i
$641$	0.424453	+	0.735175i	0.0167649	+	0.0290377i	0.874286	−	0.485411i	$-0.161330\pi$
$641$	0.424453	+	0.735175i	0.0167649	+	0.0290377i	−0.857521	+	0.514449i	$0.827997\pi$
$642$	22.3040	+	7.08904i	0.880269	+	0.279782i
$643$	−16.6824	−	4.47005i	−0.657891	−	0.176281i	−0.0855970	−	0.996330i	$-0.527280\pi$
$643$	−16.6824	−	4.47005i	−0.657891	−	0.176281i	−0.572294	+	0.820048i	$0.693946\pi$
$644$	−1.85163	−	0.496144i	−0.0729646	−	0.0195508i
$645$	2.75692	+	0.876250i	0.108553	+	0.0345023i
$646$	−19.6798	−	34.0864i	−0.774290	−	1.34111i
$647$	−7.87623	+	13.6420i	−0.309646	+	0.536323i	−0.978285	−	0.207264i	$-0.933544\pi$
$647$	−7.87623	+	13.6420i	−0.309646	+	0.536323i	0.668639	+	0.743588i	$0.266877\pi$
$648$	−7.41970	+	5.09393i	−0.291473	+	0.200108i
$649$		−	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	$-0.493475\pi$
$653$	−21.3400	−	12.3207i	−0.835099	−	0.482145i	−0.855595	+	0.517645i	$0.826809\pi$
$654$	−2.72348	+	4.25332i	−0.106497	+	0.166318i
$655$	−2.53590	+	2.53590i	−0.0990857	+	0.0990857i
$656$	1.97475	−	7.36988i	0.0771011	−	0.287745i
$657$	9.54799	+	11.4861i	0.372503	+	0.448115i
$658$	1.07145	+	1.07145i	0.0417697	+	0.0417697i
$659$	15.3411	−	8.85721i	0.597606	−	0.345028i	−0.170493	−	0.985359i	$-0.554536\pi$
$659$	15.3411	−	8.85721i	0.597606	−	0.345028i	0.768099	+	0.640331i	$0.221203\pi$
$660$	−0.0205521	+	0.447048i	−0.000799988	+	0.0174013i
$661$	−9.15665	+	2.45352i	−0.356153	+	0.0954308i	−0.432459	−	0.901654i	$-0.642354\pi$
$661$	−9.15665	+	2.45352i	−0.356153	+	0.0954308i	0.0763064	+	0.997084i	$0.475687\pi$
$662$	−16.4877			−0.640813
$663$	34.9290	+	1.47885i	1.35653	+	0.0574339i
$664$	−11.6394			−0.451697
$665$	−0.867544	+	0.232458i	−0.0336419	+	0.00901432i
$666$	−18.9603	+	8.73506i	−0.734698	+	0.338477i
$667$	−23.7926	+	13.7367i	−0.921253	+	0.531886i
$668$	−9.48357	−	9.48357i	−0.366930	−	0.366930i
$669$	−2.66943	−	12.1739i	−0.103206	−	0.470669i
$670$	−1.01574	+	3.79080i	−0.0392415	+	0.146451i
$671$	−4.33221	+	4.33221i	−0.167243	+	0.167243i
$672$	−0.420354	−	0.269161i	−0.0162155	−	0.0103831i
$673$	−0.150089	−	0.0866536i	−0.00578549	−	0.00334025i	0.497104	−	0.867691i	$-0.334397\pi$
$673$	−0.150089	−	0.0866536i	−0.00578549	−	0.00334025i	−0.502890	+	0.864350i	$0.667730\pi$
$674$	−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	$0.987016\pi$
$678$	13.3302	−	12.1584i	0.511942	−	0.466940i
$679$	−0.386725	+	0.669827i	−0.0148411	+	0.0257056i
$680$	−1.24076	−	2.14906i	−0.0475810	−	0.0824127i
$681$	−2.81223	+	8.84802i	−0.107765	+	0.339057i
$682$	−0.824672	−	0.220970i	−0.0315783	−	0.00846139i
$683$	−30.9953	−	8.30516i	−1.18600	−	0.317788i	−0.388697	−	0.921365i	$-0.627075\pi$
$683$	−30.9953	−	8.30516i	−1.18600	−	0.317788i	−0.797305	+	0.603577i	$0.793742\pi$
$684$	−20.7888	+	3.56679i	−0.794878	+	0.136379i
$685$	−0.0183309	−	0.0317500i	−0.000700388	−	0.00121311i
$686$	2.00530	−	3.47328i	0.0765627	−	0.132611i
$687$	−13.6156	−	14.9278i	−0.519466	−	0.569531i
$688$			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	0.937012	+	0.349296i	$0.113579\pi$
$691$	7.89090	+	29.4492i	0.300184	+	1.12030i	−0.636829	+	0.771005i	$0.719754\pi$
$692$	−0.954532	−	0.551099i	−0.0362858	−	0.0209496i
$693$	0.501797	+	0.0462358i	0.0190617	+	0.00175635i
$694$	−5.81113	+	5.81113i	−0.220587	+	0.220587i
$695$	0.716073	−	2.67242i	0.0271622	−	0.101371i
$696$	−6.98761	+	1.53221i	−0.264865	+	0.0580783i
$697$	−30.2026	−	30.2026i	−1.14401	−	1.14401i
$698$	−6.93931	+	4.00641i	−0.262657	+	0.151645i
$699$	16.5195	+	0.759450i	0.624826	+	0.0287250i
$700$	1.33711	−	0.358278i	0.0505381	−	0.0135416i
$701$	−1.23549			−0.0466638			−0.0233319	−	0.999728i	$-0.507427\pi$
$701$	−1.23549			−0.0466638			−0.0233319	+	0.999728i	$0.507427\pi$
$702$	7.22656	−	17.2852i	0.272749	−	0.652386i
$703$	−48.9246			−1.84523
$704$	−0.563016	+	0.150860i	−0.0212195	+	0.00568574i
$705$	4.03274	+	0.185397i	0.151882	+	0.00698244i
$706$	2.42107	−	1.39781i	0.0911182	−	0.0526071i
$707$	−2.90188	−	2.90188i	−0.109136	−	0.109136i
$708$	5.76450	−	1.26401i	0.216643	−	0.0475045i
$709$	4.09728	−	15.2913i	0.153877	−	0.574276i	−0.845322	−	0.534257i	$-0.820592\pi$
$709$	4.09728	−	15.2913i	0.153877	−	0.574276i	0.999199	−	0.0400188i	$-0.0127418\pi$
$710$	4.82277	−	4.82277i	0.180995	−	0.180995i
$711$	3.31255	+	0.305220i	0.124230	+	0.0114466i
$712$	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
$717$	34.0660	+	37.3491i	1.27222	+	1.39483i
$718$	8.24000	−	14.2721i	0.307514	−	0.532630i
$719$	1.55033	+	2.68525i	0.0578176	+	0.100143i	0.893486	−	0.449092i	$-0.148252\pi$
$719$	1.55033	+	2.68525i	0.0578176	+	0.100143i	−0.835668	+	0.549235i	$0.814919\pi$
$720$	−1.31068	+	0.224877i	−0.0488461	+	0.00838067i
$721$	1.28298	+	0.343773i	0.0477806	+	0.0128028i
$722$	−29.3957	−	7.87656i	−1.09400	−	0.293135i
$723$	−5.85188	+	18.4116i	−0.217634	+	0.684734i
$724$	7.23437	+	12.5303i	0.268863	+	0.465685i
$725$	9.91959	−	17.1812i	0.368404	−	0.638095i
$726$	−13.6419	+	12.4427i	−0.506299	+	0.461793i
$727$			20.0877i			0.745011i	0.928030	+	0.372506i	$0.121501\pi$
$727$			20.0877i			0.745011i	−0.928030	+	0.372506i	$0.878499\pi$
$728$	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
$732$	−15.3319	−	9.81733i	−0.566685	−	0.362859i
$733$	35.4832	−	35.4832i	1.31060	−	1.31060i	0.389628	−	0.920972i	$-0.372604\pi$
$733$	35.4832	−	35.4832i	1.31060	−	1.31060i	0.920972	−	0.389628i	$-0.127396\pi$
$734$	−9.62442	+	35.9188i	−0.355244	+	1.32579i
$735$	−1.13748	−	5.18744i	−0.0419565	−	0.191342i
$736$	−4.70360	−	4.70360i	−0.173377	−	0.173377i
$737$	4.46910	−	2.58023i	0.164621	−	0.0950442i
$738$	−20.7894	+	9.57772i	−0.765269	+	0.352561i
$739$	−22.4899	+	6.02615i	−0.827305	+	0.221676i	−0.647538	−	0.762034i	$-0.724201\pi$
$739$	−22.4899	+	6.02615i	−0.827305	+	0.221676i	−0.179767	+	0.983709i	$0.557534\pi$
$740$	−3.08458			−0.113391
$741$	32.3329	−	29.7062i	1.18778	−	1.09129i
$742$	1.05122			0.0385916
$743$	25.8872	−	6.93645i	0.949709	−	0.254474i	0.249470	−	0.968382i	$-0.419743\pi$
$743$	25.8872	−	6.93645i	0.949709	−	0.254474i	0.700239	+	0.713909i	$0.253077\pi$
$744$	0.116510	−	2.53433i	0.00427147	−	0.0929129i
$745$	5.58069	−	3.22201i	0.204461	−	0.118045i
$746$	−5.57782	−	5.57782i	−0.204219	−	0.204219i
$747$	22.3214	+	26.8522i	0.816696	+	0.982472i
$748$	−0.844533	+	3.15184i	−0.0308792	+	0.115243i
$749$	2.75341	−	2.75341i	0.100607	−	0.100607i
$750$	4.05885	−	6.33879i	0.148208	−	0.231460i
$751$	−15.4295	−	8.90822i	−0.563030	−	0.325065i	0.191331	−	0.981526i	$-0.438720\pi$
$751$	−15.4295	−	8.90822i	−0.563030	−	0.325065i	−0.754361	+	0.656460i	$0.772053\pi$
$752$	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
$756$	0.185173	+	1.48594i	0.00673469	+	0.0540431i
$757$	−12.3906	+	21.4612i	−0.450345	+	0.780020i	−0.998407	−	0.0564171i	$-0.982032\pi$
$757$	−12.3906	+	21.4612i	−0.450345	+	0.780020i	0.548062	+	0.836438i	$0.315366\pi$
$758$	−0.930981	−	1.61251i	−0.0338148	−	0.0585689i
$759$	6.40009	+	2.03419i	0.232308	+	0.0738363i
$760$	−3.01041	−	0.806638i	−0.109199	−	0.0292598i
$761$	14.6883	+	3.93572i	0.532451	+	0.142670i	0.515020	−	0.857178i	$-0.327785\pi$
$761$	14.6883	+	3.93572i	0.532451	+	0.142670i	0.0174313	+	0.999848i	$0.494451\pi$
$762$	0.398562	+	0.126678i	0.0144384	+	0.00458905i
$763$	0.420159	+	0.727738i	0.0152108	+	0.0263459i
$764$	3.33787	−	5.78136i	0.120760	−	0.209162i
$765$	−2.57845	+	6.98378i	−0.0932239	+	0.252499i
$766$		−	2.88048i		−	0.104076i
$767$	−8.65515	+	8.71816i	−0.312519	+	0.314794i
$768$	−0.796225	−	1.53819i	−0.0287313	−	0.0555046i
$769$	4.74330	+	17.7022i	0.171048	+	0.638359i	0.997191	+	0.0748992i	$0.0238635\pi$
$769$	4.74330	+	17.7022i	0.171048	+	0.638359i	−0.826143	+	0.563460i	$0.809470\pi$
$770$	0.0644835	+	0.0372295i	0.00232382	+	0.00134166i
$771$	11.1597	−	17.4284i	0.401907	−	0.627667i
$772$	4.30947	−	4.30947i	0.155101	−	0.155101i
$773$	8.71254	−	32.5156i	0.313368	−	1.16951i	−0.612131	−	0.790757i	$-0.709687\pi$
$773$	8.71254	−	32.5156i	0.313368	−	1.16951i	0.925499	−	0.378750i	$-0.123646\pi$
$774$	8.69229	−	7.22561i	0.312438	−	0.259719i
$775$	4.97512	+	4.97512i	0.178712	+	0.178712i
$776$	−2.32433	+	1.34195i	−0.0834385	+	0.0481732i
$777$	−0.159510	+	3.46967i	−0.00572240	+	0.124474i
$778$	−22.6208	+	6.06121i	−0.810993	+	0.217305i
$779$	−53.6443			−1.92201
$780$	2.03851	−	1.87290i	0.0729903	−	0.0670607i
$781$	−8.96837			−0.320914
$782$	−35.9693	+	9.63796i	−1.28626	+	0.344653i
$783$	16.9352	+	13.1821i	0.605216	+	0.471089i
$784$	5.99026	−	3.45848i	0.213938	−	0.123517i
$785$	3.20112	+	3.20112i	0.114253	+	0.114253i
$786$	3.00140	+	13.6878i	0.107057	+	0.488229i
$787$	−2.43856	+	9.10084i	−0.0869253	+	0.324410i	−0.995672	−	0.0929388i	$-0.970374\pi$
$787$	−2.43856	+	9.10084i	−0.0869253	+	0.324410i	0.908746	+	0.417349i	$0.137041\pi$
$788$	10.4569	−	10.4569i	0.372511	−	0.372511i
$789$	4.01304	+	2.56962i	0.142868	+	0.0914810i
$790$	0.425679	+	0.245766i	0.0151450	+	0.00874397i
$791$	−0.776944	−	2.89959i	−0.0276249	−	0.103098i
$792$	1.42775	+	1.00957i	0.0507330	+	0.0358736i
$793$	37.8980	−	0.137455i	1.34580	−	0.00488116i
$794$			18.4077i			0.653266i
$795$	2.06924	−	1.88735i	0.0733886	−	0.0669374i
$796$	7.74017	−	13.4064i	0.274343	−	0.475176i
$797$	23.4250	+	40.5734i	0.829757	+	1.43718i	0.898228	+	0.439529i	$0.144855\pi$
$797$	23.4250	+	40.5734i	0.829757	+	1.43718i	−0.0684710	+	0.997653i	$0.521812\pi$
$798$	−1.06302	+	3.34453i	−0.0376304	+	0.118395i
$799$	28.4322	+	7.61838i	1.00586	+	0.269519i
$800$	4.63983	+	1.24324i	0.164043	+	0.0439551i
$801$	−7.14407	−	41.6387i	−0.252423	−	1.47123i
$802$	−3.39248	−	5.87594i	−0.119792	−	0.207487i
$803$	1.45101	−	2.51322i	0.0512050	−	0.0886896i
$804$	10.3338	+	11.3297i	0.364445	+	0.399569i
$805$			0.849740i			0.0299494i
$806$	2.65717	+	4.56404i	0.0935948	+	0.160761i
$807$	−9.59871	+	4.96866i	−0.337891	+	0.174905i
$808$	−3.68574	−	13.7554i	−0.129664	−	0.483912i
$809$	35.1892	+	20.3165i	1.23719	+	0.714289i	0.968518	−	0.248944i	$-0.0800835\pi$
$809$	35.1892	+	20.3165i	1.23719	+	0.714289i	0.268667	+	0.963233i	$0.413417\pi$
$810$	3.03233	+	2.59249i	0.106545	+	0.0910909i
$811$	16.5531	−	16.5531i	0.581257	−	0.581257i	−0.353992	−	0.935249i	$-0.615176\pi$
$811$	16.5531	−	16.5531i	0.581257	−	0.581257i	0.935249	+	0.353992i	$0.115176\pi$
$812$	−0.308054	+	1.14967i	−0.0108106	+	0.0403457i
$813$	−37.8431	+	8.29806i	−1.32722	+	0.291026i
$814$	2.86802	+	2.86802i	0.100524	+	0.100524i
$815$	5.32844	−	3.07638i	0.186647	−	0.107761i
$816$	−9.68602	−	0.445293i	−0.339078	−	0.0155884i
$817$	25.5880	−	6.85628i	0.895210	−	0.239871i
$818$	29.2874			1.02401
$819$	−2.00131	−	2.38986i	−0.0699314	−	0.0835083i
$820$	−3.38214			−0.118109
$821$	−3.40155	+	0.911442i	−0.118715	+	0.0318095i	−0.317687	−	0.948196i	$-0.602906\pi$
$821$	−3.40155	+	0.911442i	−0.118715	+	0.0318095i	0.198972	+	0.980005i	$0.436240\pi$
$822$	−0.143100	−	0.00657873i	−0.00499120	−	0.000229459i
$823$	8.97945	−	5.18429i	0.313004	−	0.180713i	−0.335266	−	0.942124i	$-0.608826\pi$
$823$	8.97945	−	5.18429i	0.313004	−	0.180713i	0.648270	+	0.761411i	$0.275493\pi$
$824$	3.25908	+	3.25908i	0.113535	+	0.113535i
$825$	−4.73695	+	1.03870i	−0.164919	+	0.0361627i
$826$	0.254133	−	0.948436i	0.00884240	−	0.0330003i
$827$	5.61338	−	5.61338i	0.195196	−	0.195196i	−0.602741	−	0.797937i	$-0.705925\pi$
$827$	5.61338	−	5.61338i	0.195196	−	0.195196i	0.797937	+	0.602741i	$0.205925\pi$
$828$	−1.83097	+	19.8715i	−0.0636306	+	0.690583i
$829$	−1.76277	−	1.01774i	−0.0612237	−	0.0353475i	0.469076	−	0.883158i	$-0.344587\pi$
$829$	−1.76277	−	1.01774i	−0.0612237	−	0.0353475i	−0.530299	+	0.847810i	$0.677920\pi$
$830$	1.33537	+	4.98369i	0.0463515	+	0.172986i
$831$	−8.61135	+	4.45757i	−0.298725	+	0.154631i
$832$	3.12902	+	1.79144i	0.108479	+	0.0621070i
$833$		−	38.7220i		−	1.34164i
$834$	−7.28507	−	7.98718i	−0.252261	−	0.276573i
$835$	−2.97257	+	5.14864i	−0.102870	+	0.178176i
$836$	2.04906	+	3.54907i	0.0708681	+	0.122747i
$837$	−6.07015	+	4.59138i	−0.209815	+	0.158701i
$838$	8.92727	+	2.39205i	0.308387	+	0.0826322i
$839$	15.0893	+	4.04316i	0.520940	+	0.139585i	0.509701	−	0.860351i	$-0.329756\pi$
$839$	15.0893	+	4.04316i	0.520940	+	0.139585i	0.0112385	+	0.999937i	$0.496423\pi$
$840$	−0.0670206	+	0.210865i	−0.00231243	+	0.00727552i
$841$	−5.97094	−	10.3420i	−0.205894	−	0.356620i
$842$	13.0454	−	22.5953i	0.449575	−	0.778686i
$843$	15.9779	−	14.5734i	0.550308	−	0.501933i
$844$			18.8144i			0.647619i
$845$	−1.45105	+	5.57692i	−0.0499178	+	0.191852i
$846$	9.10718	−	12.8795i	0.313111	−	0.442806i
$847$	0.795114	+	2.96740i	0.0273204	+	0.101961i
$848$	3.15907	+	1.82389i	0.108483	+	0.0626327i
$849$	−10.0044	−	6.40603i	−0.343352	−	0.219854i
$850$	19.0146	−	19.0146i	0.652194	−	0.652194i
$851$	−11.9802	+	44.7105i	−0.410674	+	1.53266i
$852$	−5.70807	−	26.0315i	−0.195555	−	0.891825i
$853$	21.4461	+	21.4461i	0.734300	+	0.734300i	0.971469	−	0.237168i	$-0.0762193\pi$
$853$	21.4461	+	21.4461i	0.734300	+	0.734300i	−0.237168	+	0.971469i	$0.576219\pi$
$854$	−2.62327	+	1.51455i	−0.0897665	+	0.0518267i
$855$	3.91226	+	8.49196i	0.133797	+	0.290419i
$856$	13.0516	−	3.49716i	0.446094	−	0.119531i
$857$	−17.8872			−0.611017			−0.305508	−	0.952189i	$-0.598826\pi$
$857$	−17.8872			−0.611017			−0.305508	+	0.952189i	$0.598826\pi$
$858$	−3.63681	−	0.153978i	−0.124159	−	0.00525673i
$859$	−1.29875			−0.0443127			−0.0221564	−	0.999755i	$-0.507053\pi$
$859$	−1.29875			−0.0443127			−0.0221564	+	0.999755i	$0.507053\pi$
$860$	1.61326	−	0.432272i	0.0550117	−	0.0147403i
$861$	−0.174898	+	3.80438i	−0.00596051	+	0.129653i
$862$	19.3674	−	11.1818i	0.659656	−	0.380853i
$863$	−15.1285	−	15.1285i	−0.514979	−	0.514979i	0.401069	−	0.916048i	$-0.368639\pi$
$863$	−15.1285	−	15.1285i	−0.514979	−	0.514979i	−0.916048	+	0.401069i	$0.868639\pi$
$864$	−2.02166	+	4.78674i	−0.0687783	+	0.162848i
$865$	−0.126454	+	0.471931i	−0.00429955	+	0.0160461i
$866$	−2.79168	+	2.79168i	−0.0948652	+	0.0948652i
$867$	−13.3927	+	20.9156i	−0.454838	+	0.710331i
$868$	−0.365558	−	0.211055i	−0.0124079	−	0.00716368i
$869$	−0.167282	−	0.624307i	−0.00567467	−	0.0211781i
$870$	1.45773	+	2.81612i	0.0494216	+	0.0954753i
$871$	−30.8636	−	8.15001i	−1.04577	−	0.276153i
$872$			2.91594i			0.0987462i
$873$	7.55334	+	2.78873i	0.255642	+	0.0943842i
$874$	−23.3842	+	40.5026i	−0.790983	+	1.37002i
$875$	−0.626170	−	1.08456i	−0.0211684	−	0.0366647i
$876$	8.21837	+	2.61210i	0.277673	+	0.0882548i
$877$	21.4896	+	5.75813i	0.725654	+	0.194438i	0.602693	−	0.797973i	$-0.294094\pi$
$877$	21.4896	+	5.75813i	0.725654	+	0.194438i	0.122961	+	0.992412i	$0.460761\pi$
$878$	−17.6861	−	4.73898i	−0.596877	−	0.159933i
$879$	−45.1549	−	14.3519i	−1.52304	−	0.484077i
$880$	0.129188	+	0.223760i	0.00435493	+	0.00754296i
$881$	10.2514	−	17.7560i	0.345379	−	0.598214i	−0.640044	−	0.768338i	$-0.721084\pi$
$881$	10.2514	−	17.7560i	0.345379	−	0.598214i	0.985423	+	0.170125i	$0.0544171\pi$
$882$	−19.4665	−	7.18711i	−0.655470	−	0.242003i
$883$			27.7709i			0.934566i	0.884108	+	0.467283i	$0.154767\pi$
$883$			27.7709i			0.934566i	−0.884108	+	0.467283i	$0.845233\pi$
$884$	17.4434	−	10.1555i	0.586686	−	0.341567i
$885$	−1.20257	−	2.32318i	−0.0404239	−	0.0780929i
$886$	1.51764	+	5.66391i	0.0509861	+	0.190283i
$887$	−11.4360	−	6.60256i	−0.383982	−	0.221692i	0.295567	−	0.955322i	$-0.404491\pi$
$887$	−11.4360	−	6.60256i	−0.383982	−	0.221692i	−0.679549	+	0.733630i	$0.737825\pi$
$888$	−6.49930	+	10.1501i	−0.218102	+	0.340615i
$889$	0.0492020	−	0.0492020i	0.00165018	−	0.00165018i
$890$	1.61565	−	6.02968i	0.0541567	−	0.202115i
$891$	−0.408961	−	5.22993i	−0.0137007	−	0.175209i
$892$	−5.08804	−	5.08804i	−0.170360	−	0.170360i
$893$	32.0156	−	18.4842i	1.07136	−	0.618550i
$894$	1.15634	−	25.1527i	0.0386738	−	0.841231i
$895$	2.39586	−	0.641969i	0.0800848	−	0.0214587i
$896$	−0.288181			−0.00962745
$897$	−19.2302	−	36.8221i	−0.642076	−	1.22945i
$898$	−28.5045			−0.951207
$899$	−5.84346	+	1.56575i	−0.194890	+	0.0522207i
$900$	−6.02982	−	13.0883i	−0.200994	−	0.436278i
$901$	17.6849	−	10.2104i	0.589170	−	0.340157i
$902$	3.14469	+	3.14469i	0.104707	+	0.104707i
$903$	−0.402813	−	1.83702i	−0.0134048	−	0.0611322i
$904$	2.69603	−	10.0617i	0.0896685	−	0.334648i
$905$	4.53514	−	4.53514i	0.150753	−	0.150753i
$906$	13.2095	+	8.45831i	0.438857	+	0.281009i
$907$	−24.2160	−	13.9811i	−0.804079	−	0.464235i	0.0408168	−	0.999167i	$-0.487004\pi$
$907$	−24.2160	−	13.9811i	−0.804079	−	0.464235i	−0.844895	+	0.534932i	$0.820337\pi$
$908$	1.38733	+	5.17758i	0.0460401	+	0.171824i
$909$	−24.6655	+	34.8822i	−0.818101	+	1.15697i
$910$	−0.120822	−	0.444458i	−0.00400520	−	0.0147336i
$911$			33.2713i			1.10233i	0.834397	+	0.551164i	$0.185816\pi$
$911$			33.2713i			1.10233i	−0.834397	+	0.551164i	$0.814184\pi$
$912$	−8.99735	+	8.20644i	−0.297932	+	0.271743i
$913$	3.39218	−	5.87543i	0.112265	−	0.194448i
$914$	9.58495	+	16.6016i	0.317042	+	0.549133i
$915$	−2.44450	+	7.69105i	−0.0808127	+	0.254258i
$916$	−11.2676	−	3.01915i	−0.372292	−	0.0997554i
$917$	2.25207	+	0.603439i	0.0743697	+	0.0199273i
$918$	17.5479	+	23.1997i	0.579168	+	0.765703i
$919$	−7.21868	−	12.5031i	−0.238122	−	0.412440i	0.722053	−	0.691837i	$-0.243199\pi$
$919$	−7.21868	−	12.5031i	−0.238122	−	0.412440i	−0.960175	+	0.279398i	$0.909865\pi$
$920$	−1.47432	+	2.55359i	−0.0486068	+	0.0841894i
$921$	−25.5639	−	28.0276i	−0.842358	−	0.923542i
$922$			29.6500i			0.976471i
$923$	39.3698	+	39.0852i	1.29587	+	1.28650i
$924$	0.258376	−	0.133745i	0.00849995	−	0.00439990i
$925$	−8.65117	−	32.2866i	−0.284449	−	1.06158i
$926$	−22.3582	−	12.9085i	−0.734736	−	0.424200i
$927$	1.26866	−	13.7688i	0.0416682	−	0.452226i
$928$	−2.92046	+	2.92046i	−0.0958687	+	0.0958687i
$929$	−3.64463	+	13.6019i	−0.119576	+	0.446265i	−0.999588	−	0.0286860i	$-0.990868\pi$
$929$	−3.64463	+	13.6019i	−0.119576	+	0.446265i	0.880012	+	0.474951i	$0.157534\pi$
$930$	−1.09850	+	0.240873i	−0.0360211	+	0.00789854i
$931$	−34.3880	−	34.3880i	−1.12702	−	1.12702i
$932$	8.26849	−	4.77382i	0.270844	−	0.156372i
$933$	−55.0233	−	2.52957i	−1.80138	−	0.0828145i
$934$	−31.3400	+	8.39753i	−1.02548	+	0.274776i
$935$	1.44642			0.0473031
$936$	−1.86777	−	10.6542i	−0.0610500	−	0.348243i
$937$	25.6098			0.836635			0.418317	−	0.908301i	$-0.362620\pi$
$937$	25.6098			0.836635			0.418317	+	0.908301i	$0.362620\pi$
$938$	2.46446	−	0.660349i	0.0804674	−	0.0215612i
$939$	−41.0796	−	1.88854i	−1.34058	−	0.0616303i
$940$	2.01850	−	1.16538i	0.0658363	−	0.0380106i
$941$	24.7798	+	24.7798i	0.807800	+	0.807800i	0.984300	−	0.176501i	$-0.0564779\pi$
$941$	24.7798	+	24.7798i	0.807800	+	0.807800i	−0.176501	+	0.984300i	$0.556478\pi$
$942$	17.2785	−	3.78874i	0.562963	−	0.123444i
$943$	−13.1359	+	49.0237i	−0.427762	+	1.59643i
$944$	2.40926	−	2.40926i	0.0784147	−	0.0784147i
$945$	0.614994	−	0.249766i	0.0200058	−	0.00812488i
$946$	−1.90192	−	1.09808i	−0.0618369	−	0.0357015i
$947$	2.97658	+	11.1087i	0.0967258	+	0.360986i	0.997275	−	0.0737675i	$-0.0235023\pi$
$947$	2.97658	+	11.1087i	0.0967258	+	0.360986i	−0.900550	+	0.434753i	$0.856836\pi$
$948$	1.70564	−	0.882903i	0.0553965	−	0.0286753i
$949$	−17.3226	+	4.70898i	−0.562316	+	0.152860i
$950$		−	33.7727i		−	1.09573i
$951$	−27.8860	−	30.5735i	−0.904265	−	0.991414i
$952$	−0.806638	+	1.39714i	−0.0261433	+	0.0452815i
$953$	−24.2758	−	42.0469i	−0.786370	−	1.36203i	−0.928177	−	0.372139i	$-0.878624\pi$
$953$	−24.2758	−	42.0469i	−0.786370	−	1.36203i	0.141807	−	0.989894i	$-0.454709\pi$
$954$	−1.85054	−	10.7858i	−0.0599135	−	0.349202i
$955$	−2.85837	−	0.765897i	−0.0924946	−	0.0247838i
$956$	28.1914	+	7.55387i	0.911775	+	0.244309i
$957$	1.26302	−	3.97380i	0.0408277	−	0.128455i
$958$	−4.14520	−	7.17970i	−0.133925	−	0.231966i
$959$	−0.0119172	+	0.0206412i	−0.000384826	+	0.000666539i
$960$	−0.567261	+	0.517396i	−0.0183083	+	0.0166989i
$961$			28.8545i			0.930792i
$962$	−0.0909982	−	25.0893i	−0.00293390	−	0.808913i
$963$	−33.0975	−	23.4035i	−1.06655	−	0.754167i
$964$	2.88685	+	10.7739i	0.0929792	+	0.347003i
$965$	−2.33962	−	1.35078i	−0.0753150	−	0.0434831i
$966$	2.79615	+	1.79043i	0.0899648	+	0.0576061i
$967$	15.4257	−	15.4257i	0.496058	−	0.496058i	−0.414150	−	0.910209i	$-0.635921\pi$
$967$	15.4257	−	15.4257i	0.496058	−	0.496058i	0.910209	+	0.414150i	$0.135921\pi$
$968$	−2.75908	+	10.2970i	−0.0886801	+	0.330959i
$969$	14.6017	+	66.5906i	0.469073	+	2.13920i
$970$	0.841253	+	0.841253i	0.0270110	+	0.0270110i
$971$	−6.63550	+	3.83101i	−0.212943	+	0.122943i	−0.602679	−	0.797984i	$-0.705900\pi$
$971$	−6.63550	+	3.83101i	−0.212943	+	0.122943i	0.389735	+	0.920927i	$0.372567\pi$
$972$	14.9201	−	4.51572i	0.478561	−	0.144842i
$973$	−1.73738	+	0.465530i	−0.0556979	+	0.0149242i
$974$	32.1307			1.02953
$975$	25.3212	+	16.0844i	0.810928	+	0.515115i
$976$	−10.5111			−0.336451
$977$	19.4850	−	5.22099i	0.623381	−	0.167034i	0.0667166	−	0.997772i	$-0.478748\pi$
$977$	19.4850	−	5.22099i	0.623381	−	0.167034i	0.556664	+	0.830738i	$0.312081\pi$
$978$	1.10407	−	24.0158i	0.0353044	−	0.767940i
$979$	−7.10859	+	4.10415i	−0.227191	+	0.131169i
$980$	−2.16808	−	2.16808i	−0.0692567	−	0.0692567i
$981$	6.72710	−	5.59201i	0.214780	−	0.178539i
$982$	−6.83797	+	25.5197i	−0.218209	+	0.814365i
$983$	0.922992	−	0.922992i	0.0294389	−	0.0294389i	−0.692234	−	0.721673i	$-0.743373\pi$
$983$	0.922992	−	0.922992i	0.0294389	−	0.0294389i	0.721673	+	0.692234i	$0.243373\pi$
$984$	−7.12627	+	11.1293i	−0.227177	+	0.354788i
$985$	−5.67705	−	3.27765i	−0.180886	−	0.104435i
$986$	5.98418	+	22.3333i	0.190575	+	0.711236i
$987$	−1.20649	−	2.33077i	−0.0384031	−	0.0741891i
$988$	6.47222	−	24.5099i	0.205909	−	0.779764i
$989$		−	25.0629i		−	0.796953i
$990$	0.268468	−	0.727151i	0.00853246	−	0.0231104i
$991$	−10.2983	+	17.8371i	−0.327135	+	0.566614i	−0.981942	−	0.189182i	$-0.939416\pi$
$991$	−10.2983	+	17.8371i	−0.327135	+	0.566614i	0.654807	+	0.755796i	$0.272750\pi$
$992$	−0.732370	−	1.26850i	−0.0232528	−	0.0402750i
$993$	27.2159	+	8.65024i	0.863672	+	0.274507i
$994$	−4.28298	−	1.14762i	−0.135848	−	0.0364003i
$995$	−6.62826	−	1.77604i	−0.210130	−	0.0563041i
$996$	19.2130	+	6.10660i	0.608786	+	0.193495i
$997$	16.0894	+	27.8677i	0.509558	+	0.882580i	0.999939	+	0.0110718i	$0.00352433\pi$
$997$	16.0894	+	27.8677i	0.509558	+	0.882580i	−0.490381	+	0.871508i	$0.663142\pi$
$998$	6.55790	−	11.3586i	0.207587	−	0.359551i
$999$	35.8803	−	4.47130i	1.13520	−	0.141466i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.2.k.a.71.2	yes	16
3.2	odd	2	inner	78.2.k.a.71.3	yes	16
4.3	odd	2		624.2.cn.d.305.1		16
12.11	even	2		624.2.cn.d.305.3		16
13.4	even	6		1014.2.g.d.239.2		16
13.6	odd	12		1014.2.g.d.437.6		16
13.7	odd	12		1014.2.g.c.437.2		16
13.9	even	3		1014.2.g.c.239.6		16
13.11	odd	12	inner	78.2.k.a.11.3	yes	16
39.11	even	12	inner	78.2.k.a.11.2	✓	16
39.17	odd	6		1014.2.g.d.239.6		16
39.20	even	12		1014.2.g.c.437.6		16
39.32	even	12		1014.2.g.d.437.2		16
39.35	odd	6		1014.2.g.c.239.2		16
52.11	even	12		624.2.cn.d.401.3		16
156.11	odd	12		624.2.cn.d.401.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.k.a.11.2	✓	16	39.11	even	12	inner
78.2.k.a.11.3	yes	16	13.11	odd	12	inner
78.2.k.a.71.2	yes	16	1.1	even	1	trivial
78.2.k.a.71.3	yes	16	3.2	odd	2	inner
624.2.cn.d.305.1		16	4.3	odd	2
624.2.cn.d.305.3		16	12.11	even	2
624.2.cn.d.401.1		16	156.11	odd	12
624.2.cn.d.401.3		16	52.11	even	12
1014.2.g.c.239.2		16	39.35	odd	6
1014.2.g.c.239.6		16	13.9	even	3
1014.2.g.c.437.2		16	13.7	odd	12
1014.2.g.c.437.6		16	39.20	even	12
1014.2.g.d.239.2		16	13.4	even	6
1014.2.g.d.239.6		16	39.17	odd	6
1014.2.g.d.437.2		16	39.32	even	12
1014.2.g.d.437.6		16	13.6	odd	12

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)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(1.73022 + 0.0795432i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.313444 - 0.313444i) q^{5} +(-1.69185 + 0.370982i) q^{6} +(-0.0745867 + 0.278362i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.98735 + 0.275255i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(1.73022 + 0.0795432i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.313444 - 0.313444i) q^{5} +(-1.69185 + 0.370982i) q^{6} +(-0.0745867 + 0.278362i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.98735 + 0.275255i) 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} +(-0.517396 - 0.567261i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.79907 - 4.84812i) q^{17} +(-2.95680 + 0.507306i) q^{18} +(-6.79127 - 1.81971i) q^{19} +(-0.428173 - 0.114729i) q^{20} +(-0.151194 + 0.475695i) q^{21} +(0.291439 + 0.504787i) q^{22} +(-3.32595 + 5.76071i) q^{23} +(-1.27970 + 1.16721i) 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} +(0.646584 + 0.414020i) q^{30} +(-1.03573 + 1.03573i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-0.216237 - 0.986144i) q^{33} +(3.95848 + 3.95848i) q^{34} +(0.110630 - 0.0638720i) q^{35} +(2.72474 - 1.25529i) q^{36} +(6.72147 - 1.80101i) q^{37} +7.03084 q^{38} +(-3.34848 + 5.27140i) q^{39} +0.443277 q^{40} +(7.36988 - 1.97475i) q^{41} +(0.0229229 - 0.498618i) q^{42} +(-3.26299 + 1.88389i) q^{43} +(-0.412157 - 0.412157i) q^{44} +(-0.850089 - 1.02264i) q^{45} +(1.72164 - 6.42524i) q^{46} +(-3.71799 + 3.71799i) q^{47} +(0.933998 - 1.45865i) 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} +(-5.15627 + 0.642559i) q^{54} +(-0.129188 + 0.223760i) q^{55} +(-0.144091 - 0.249572i) q^{56} +(-11.6057 - 3.68871i) q^{57} +(-3.98942 - 1.06896i) q^{58} +(3.29111 + 0.881850i) q^{59} +(-0.731708 - 0.232564i) q^{60} +(-5.25554 - 9.10286i) q^{61} +(0.732370 - 1.26850i) q^{62} +(-0.299437 + 0.811032i) 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} +(-6.21286 + 9.70277i) q^{69} +(-0.0903287 + 0.0903287i) q^{70} +(3.98229 - 14.8621i) q^{71} +(-2.30701 + 1.91774i) q^{72} +(3.52053 + 3.52053i) q^{73} +(-6.02630 + 3.47929i) q^{74} +(0.382086 - 8.31114i) q^{75} +(-6.79127 + 1.81971i) q^{76} +0.167974 q^{77} +(1.87005 - 5.95843i) q^{78} +1.10886 q^{79} +(-0.428173 + 0.114729i) q^{80} +(8.84847 + 1.64456i) q^{81} +(-6.60765 + 3.81493i) q^{82} +(8.23032 + 8.23032i) q^{83} +(0.106910 + 0.487560i) q^{84} +(-0.642265 + 2.39697i) q^{85} +(2.66422 - 2.66422i) q^{86} +(6.02442 + 3.85755i) 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} +(-1.87442 + 1.70965i) q^{93} +(2.62902 - 4.55359i) q^{94} +(1.55830 + 2.69906i) q^{95} +(-0.524648 + 1.65068i) q^{96} +(2.59245 + 0.694645i) q^{97} +(-6.68126 - 1.79024i) q^{98} +(-0.295697 - 1.72345i) 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

Introduction

L-functions

Modular forms

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