LMFDB - Embedded newform 210.2.u.b.157.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(73,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("210.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.u (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:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.3
Root			$-1.09227 + 0.838128i$ of defining polynomial
Character	$\chi$	$=$	210.157
Dual form			210.2.u.b.103.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.21628 - 0.296818i) q^{5} +1.00000i q^{6} +(-1.87796 - 1.86367i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.21628 - 0.296818i) q^{5} +1.00000i q^{6} +(-1.87796 - 1.86367i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-0.860320 + 2.06394i) q^{10} +(-2.74315 + 4.75127i) q^{11} +(0.965926 + 0.258819i) q^{12} +(-2.41668 - 2.41668i) q^{13} +(-2.28622 + 1.33161i) q^{14} +(2.21758 - 0.286912i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.548242 - 2.04607i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-3.49797 - 6.05866i) q^{19} +(1.77095 + 1.36519i) q^{20} +(2.29632 + 1.31412i) q^{21} +(3.87940 + 3.87940i) q^{22} +(1.69461 + 0.454069i) q^{23} +(0.500000 - 0.866025i) q^{24} +(4.82380 + 1.31566i) q^{25} +(-2.95981 + 1.70885i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.694523 + 2.55297i) q^{28} +0.684610i q^{29} +(0.296818 - 2.21628i) q^{30} +(4.82932 + 2.78821i) q^{31} +(0.965926 - 0.258819i) q^{32} +(1.41996 - 5.29936i) q^{33} -2.11825 q^{34} +(3.60891 + 4.68783i) q^{35} -1.00000 q^{36} +(2.53646 - 9.46620i) q^{37} +(-6.75755 + 1.81068i) q^{38} +(2.95981 + 1.70885i) q^{39} +(1.77703 - 1.35727i) q^{40} -2.50597i q^{41} +(1.86367 - 1.87796i) q^{42} +(-1.95305 + 1.95305i) q^{43} +(4.75127 - 2.74315i) q^{44} +(-2.06776 + 0.851088i) q^{45} +(0.877194 - 1.51935i) q^{46} +(-3.40506 - 0.912383i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(0.0534500 + 6.99980i) q^{49} +(2.51932 - 4.31891i) q^{50} +(1.05912 + 1.83445i) q^{51} +(0.884566 + 3.30124i) q^{52} +(-2.43353 - 9.08204i) q^{53} +(0.500000 + 0.866025i) q^{54} +(7.48985 - 9.71594i) q^{55} +(2.64573 - 0.0101012i) q^{56} +(4.94687 + 4.94687i) q^{57} +(0.661282 + 0.177190i) q^{58} +(-5.08015 + 8.79907i) q^{59} +(-2.06394 - 0.860320i) q^{60} +(1.01469 - 0.585830i) q^{61} +(3.94312 - 3.94312i) q^{62} +(-2.55820 - 0.675009i) q^{63} -1.00000i q^{64} +(4.63872 + 6.07335i) q^{65} +(-4.75127 - 2.74315i) q^{66} +(-9.61398 + 2.57606i) q^{67} +(-0.548242 + 2.04607i) q^{68} -1.75439 q^{69} +(5.46215 - 2.27264i) q^{70} -11.9716 q^{71} +(-0.258819 + 0.965926i) q^{72} +(4.70482 - 1.26065i) q^{73} +(-8.48716 - 4.90007i) q^{74} +(-4.99995 - 0.0223420i) q^{75} +6.99593i q^{76} +(14.0063 - 3.81036i) q^{77} +(2.41668 - 2.41668i) q^{78} +(7.21474 - 4.16543i) q^{79} +(-0.851088 - 2.06776i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-2.42058 - 0.648592i) q^{82} +(-4.05281 - 4.05281i) q^{83} +(-1.33161 - 2.28622i) q^{84} +(0.607749 + 4.69739i) q^{85} +(1.38101 + 2.39198i) q^{86} +(-0.177190 - 0.661282i) q^{87} +(-1.41996 - 5.29936i) q^{88} +(-3.59178 - 6.22115i) q^{89} +(0.286912 + 2.21758i) q^{90} +(0.0345228 + 9.04232i) q^{91} +(-1.24054 - 1.24054i) q^{92} +(-5.38640 - 1.44328i) q^{93} +(-1.76259 + 3.05289i) q^{94} +(5.95416 + 14.4659i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-13.1212 + 13.1212i) q^{97} +(6.77512 + 1.76005i) q^{98} +5.48630i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5} - 4 q^{7}+O(q^{10}) $ 16 * q + 12 * q^5 - 4 * q^7	$ 16 q + 12 q^{5} - 4 q^{7} + 4 q^{10} + 4 q^{11} + 16 q^{13} - 16 q^{14} + 4 q^{15} + 8 q^{16} + 12 q^{17} + 8 q^{19} + 8 q^{20} + 8 q^{21} + 4 q^{22} - 40 q^{23} + 8 q^{24} + 16 q^{25} - 12 q^{26} - 4 q^{28} - 4 q^{30} - 24 q^{31} + 4 q^{33} - 16 q^{34} - 44 q^{35} - 16 q^{36} - 8 q^{37} - 20 q^{38} + 12 q^{39} + 8 q^{42} - 24 q^{43} - 4 q^{45} - 4 q^{46} - 52 q^{49} + 8 q^{51} + 8 q^{52} - 28 q^{53} + 8 q^{54} + 56 q^{55} + 8 q^{56} - 8 q^{57} - 12 q^{58} - 8 q^{59} + 24 q^{61} - 8 q^{62} - 4 q^{63} + 16 q^{65} - 84 q^{67} + 12 q^{68} + 8 q^{69} + 4 q^{70} - 32 q^{71} + 16 q^{73} + 24 q^{74} - 24 q^{75} + 44 q^{77} - 16 q^{78} - 12 q^{79} + 12 q^{80} + 8 q^{81} + 36 q^{82} + 16 q^{83} - 4 q^{84} + 8 q^{85} - 8 q^{86} + 48 q^{87} - 4 q^{88} + 16 q^{89} + 8 q^{91} + 8 q^{92} - 32 q^{93} - 8 q^{94} + 72 q^{95} - 44 q^{97} + 24 q^{98}+O(q^{100}) $ 16 * q + 12 * q^5 - 4 * q^7 + 4 * q^10 + 4 * q^11 + 16 * q^13 - 16 * q^14 + 4 * q^15 + 8 * q^16 + 12 * q^17 + 8 * q^19 + 8 * q^20 + 8 * q^21 + 4 * q^22 - 40 * q^23 + 8 * q^24 + 16 * q^25 - 12 * q^26 - 4 * q^28 - 4 * q^30 - 24 * q^31 + 4 * q^33 - 16 * q^34 - 44 * q^35 - 16 * q^36 - 8 * q^37 - 20 * q^38 + 12 * q^39 + 8 * q^42 - 24 * q^43 - 4 * q^45 - 4 * q^46 - 52 * q^49 + 8 * q^51 + 8 * q^52 - 28 * q^53 + 8 * q^54 + 56 * q^55 + 8 * q^56 - 8 * q^57 - 12 * q^58 - 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 + 16 * q^65 - 84 * q^67 + 12 * q^68 + 8 * q^69 + 4 * q^70 - 32 * q^71 + 16 * q^73 + 24 * q^74 - 24 * q^75 + 44 * q^77 - 16 * q^78 - 12 * q^79 + 12 * q^80 + 8 * q^81 + 36 * q^82 + 16 * q^83 - 4 * q^84 + 8 * q^85 - 8 * q^86 + 48 * q^87 - 4 * q^88 + 16 * q^89 + 8 * q^91 + 8 * q^92 - 32 * q^93 - 8 * q^94 + 72 * q^95 - 44 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−2.21628	−	0.296818i	−0.991151	−	0.132741i
$5$	−2.21628	−	0.296818i	−0.991151	−	0.132741i
$6$			1.00000i			0.408248i
$7$	−1.87796	−	1.86367i	−0.709801	−	0.704402i
$7$	−1.87796	−	1.86367i	−0.709801	−	0.704402i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	−0.860320	+	2.06394i	−0.272057	+	0.652675i
$11$	−2.74315	+	4.75127i	−0.827091	+	1.43256i	0.0732202	+	0.997316i	$0.476672\pi$
$11$	−2.74315	+	4.75127i	−0.827091	+	1.43256i	−0.900311	+	0.435247i	$0.856661\pi$
$12$	0.965926	+	0.258819i	0.278839	+	0.0747146i
$13$	−2.41668	−	2.41668i	−0.670266	−	0.670266i	0.287511	−	0.957777i	$-0.407172\pi$
$13$	−2.41668	−	2.41668i	−0.670266	−	0.670266i	−0.957777	+	0.287511i	$0.907172\pi$
$14$	−2.28622	+	1.33161i	−0.611018	+	0.355889i
$15$	2.21758	−	0.286912i	0.572578	−	0.0740803i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.548242	−	2.04607i	−0.132968	−	0.496244i	0.867030	−	0.498256i	$-0.166026\pi$
$17$	−0.548242	−	2.04607i	−0.132968	−	0.496244i	−0.999998	+	0.00201209i	$0.999360\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	−3.49797	−	6.05866i	−0.802489	−	1.38995i	−0.917974	−	0.396642i	$-0.870176\pi$
$19$	−3.49797	−	6.05866i	−0.802489	−	1.38995i	0.115485	−	0.993309i	$-0.463158\pi$
$20$	1.77095	+	1.36519i	0.395996	+	0.305266i
$21$	2.29632	+	1.31412i	0.501098	+	0.286764i
$22$	3.87940	+	3.87940i	0.827091	+	0.827091i
$23$	1.69461	+	0.454069i	0.353350	+	0.0946800i	0.431128	−	0.902291i	$-0.358116\pi$
$23$	1.69461	+	0.454069i	0.353350	+	0.0946800i	−0.0777776	+	0.996971i	$0.524782\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	4.82380	+	1.31566i	0.964760	+	0.263133i
$26$	−2.95981	+	1.70885i	−0.580467	+	0.335133i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	0.694523	+	2.55297i	0.131252	+	0.482465i
$29$			0.684610i			0.127129i	0.997978	+	0.0635644i	$0.0202468\pi$
$29$			0.684610i			0.127129i	−0.997978	+	0.0635644i	$0.979753\pi$
$30$	0.296818	−	2.21628i	0.0541913	−	0.404636i
$31$	4.82932	+	2.78821i	0.867371	+	0.500777i	0.866474	−	0.499223i	$-0.166381\pi$
$31$	4.82932	+	2.78821i	0.867371	+	0.500777i	0.000897301		1.00000i	$0.499714\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	1.41996	−	5.29936i	0.247183	−	0.922500i
$34$	−2.11825			−0.363276
$35$	3.60891	+	4.68783i	0.610017	+	0.792388i
$36$	−1.00000			−0.166667
$37$	2.53646	−	9.46620i	0.416992	−	1.55623i	−0.363821	−	0.931469i	$-0.618528\pi$
$37$	2.53646	−	9.46620i	0.416992	−	1.55623i	0.780813	−	0.624765i	$-0.214805\pi$
$38$	−6.75755	+	1.81068i	−1.09622	+	0.293731i
$39$	2.95981	+	1.70885i	0.473950	+	0.273635i
$40$	1.77703	−	1.35727i	0.280973	−	0.214602i
$41$		−	2.50597i		−	0.391366i	−0.980667	−	0.195683i	$-0.937308\pi$
$41$		−	2.50597i		−	0.391366i	0.980667	−	0.195683i	$-0.0626924\pi$
$42$	1.86367	−	1.87796i	0.287571	−	0.289775i
$43$	−1.95305	+	1.95305i	−0.297837	+	0.297837i	−0.840166	−	0.542329i	$-0.817543\pi$
$43$	−1.95305	+	1.95305i	−0.297837	+	0.297837i	0.542329	+	0.840166i	$0.317543\pi$
$44$	4.75127	−	2.74315i	0.716282	−	0.413545i
$45$	−2.06776	+	0.851088i	−0.308244	+	0.126873i
$46$	0.877194	−	1.51935i	0.129335	−	0.224015i
$47$	−3.40506	−	0.912383i	−0.496679	−	0.133085i	0.00177938	−	0.999998i	$-0.499434\pi$
$47$	−3.40506	−	0.912383i	−0.496679	−	0.133085i	−0.498458	+	0.866914i	$0.666100\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$	0.0534500	+	6.99980i	0.00763571	+	0.999971i
$50$	2.51932	−	4.31891i	0.356286	−	0.610787i
$51$	1.05912	+	1.83445i	0.148307	+	0.256875i
$52$	0.884566	+	3.30124i	0.122667	+	0.457800i
$53$	−2.43353	−	9.08204i	−0.334270	−	1.24751i	−0.904658	−	0.426138i	$-0.859874\pi$
$53$	−2.43353	−	9.08204i	−0.334270	−	1.24751i	0.570388	−	0.821376i	$-0.306793\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	7.48985	−	9.71594i	1.00993	−	1.31010i
$56$	2.64573	−	0.0101012i	0.353551	−	0.00134983i
$57$	4.94687	+	4.94687i	0.655229	+	0.655229i
$58$	0.661282	+	0.177190i	0.0868306	+	0.0232662i
$59$	−5.08015	+	8.79907i	−0.661379	+	1.14554i	0.318875	+	0.947797i	$0.396695\pi$
$59$	−5.08015	+	8.79907i	−0.661379	+	1.14554i	−0.980253	+	0.197745i	$0.936638\pi$
$60$	−2.06394	−	0.860320i	−0.266454	−	0.111067i
$61$	1.01469	−	0.585830i	0.129917	−	0.0750079i	−0.433633	−	0.901090i	$-0.642768\pi$
$61$	1.01469	−	0.585830i	0.129917	−	0.0750079i	0.563550	+	0.826082i	$0.309435\pi$
$62$	3.94312	−	3.94312i	0.500777	−	0.500777i
$63$	−2.55820	−	0.675009i	−0.322302	−	0.0850431i
$64$		−	1.00000i		−	0.125000i
$65$	4.63872	+	6.07335i	0.575363	+	0.753306i
$66$	−4.75127	−	2.74315i	−0.584841	−	0.337658i
$67$	−9.61398	+	2.57606i	−1.17454	+	0.314716i	−0.792757	−	0.609538i	$-0.791355\pi$
$67$	−9.61398	+	2.57606i	−1.17454	+	0.314716i	−0.381778	+	0.924254i	$0.624688\pi$
$68$	−0.548242	+	2.04607i	−0.0664841	+	0.248122i
$69$	−1.75439			−0.211204
$70$	5.46215	−	2.27264i	0.652852	−	0.271632i
$71$	−11.9716			−1.42077			−0.710383	−	0.703816i	$-0.751478\pi$
$71$	−11.9716			−1.42077			−0.710383	+	0.703816i	$0.751478\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	4.70482	−	1.26065i	0.550657	−	0.147548i	0.0272467	−	0.999629i	$-0.491326\pi$
$73$	4.70482	−	1.26065i	0.550657	−	0.147548i	0.523411	+	0.852081i	$0.324659\pi$
$74$	−8.48716	−	4.90007i	−0.986613	−	0.569621i
$75$	−4.99995	−	0.0223420i	−0.577345	−	0.00257983i
$76$			6.99593i			0.802489i
$77$	14.0063	−	3.81036i	1.59617	−	0.434231i
$78$	2.41668	−	2.41668i	0.273635	−	0.273635i
$79$	7.21474	−	4.16543i	0.811722	−	0.468648i	−0.0358316	−	0.999358i	$-0.511408\pi$
$79$	7.21474	−	4.16543i	0.811722	−	0.468648i	0.847553	+	0.530710i	$0.178075\pi$
$80$	−0.851088	−	2.06776i	−0.0951546	−	0.231183i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−2.42058	−	0.648592i	−0.267308	−	0.0716250i
$83$	−4.05281	−	4.05281i	−0.444854	−	0.444854i	0.448786	−	0.893639i	$-0.351857\pi$
$83$	−4.05281	−	4.05281i	−0.444854	−	0.444854i	−0.893639	+	0.448786i	$0.851857\pi$
$84$	−1.33161	−	2.28622i	−0.145291	−	0.249447i
$85$	0.607749	+	4.69739i	0.0659197	+	0.509503i
$86$	1.38101	+	2.39198i	0.148918	+	0.257934i
$87$	−0.177190	−	0.661282i	−0.0189968	−	0.0708969i
$88$	−1.41996	−	5.29936i	−0.151368	−	0.564913i
$89$	−3.59178	−	6.22115i	−0.380728	−	0.659440i	0.610439	−	0.792064i	$-0.290993\pi$
$89$	−3.59178	−	6.22115i	−0.380728	−	0.659440i	−0.991166	+	0.132623i	$0.957660\pi$
$90$	0.286912	+	2.21758i	0.0302431	+	0.233754i
$91$	0.0345228	+	9.04232i	0.00361897	+	0.947892i
$92$	−1.24054	−	1.24054i	−0.129335	−	0.129335i
$93$	−5.38640	−	1.44328i	−0.558544	−	0.149661i
$94$	−1.76259	+	3.05289i	−0.181797	+	0.314882i
$95$	5.95416	+	14.4659i	0.610884	+	1.48417i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−13.1212	+	13.1212i	−1.33226	+	1.33226i	−0.428909	+	0.903348i	$0.641102\pi$
$97$	−13.1212	+	13.1212i	−1.33226	+	1.33226i	−0.903348	+	0.428909i	$0.858898\pi$
$98$	6.77512	+	1.76005i	0.684390	+	0.177792i
$99$			5.48630i			0.551394i
$100$	−3.51970	−	3.55130i	−0.351970	−	0.355130i
$101$	7.16001	+	4.13383i	0.712447	+	0.411332i	0.811967	−	0.583704i	$-0.198397\pi$
$101$	7.16001	+	4.13383i	0.712447	+	0.411332i	−0.0995192	+	0.995036i	$0.531730\pi$
$102$	2.04607	−	0.548242i	0.202591	−	0.0542841i
$103$	−2.40862	+	8.98910i	−0.237329	+	0.885722i	0.739757	+	0.672874i	$0.234941\pi$
$103$	−2.40862	+	8.98910i	−0.237329	+	0.885722i	−0.977085	+	0.212848i	$0.931726\pi$
$104$	3.41770			0.335133
$105$	−4.69924	−	3.59404i	−0.458599	−	0.350743i
$106$	−9.40242			−0.913244
$107$	−3.17510	+	11.8496i	−0.306949	+	1.14555i	0.624306	+	0.781180i	$0.285382\pi$
$107$	−3.17510	+	11.8496i	−0.306949	+	1.14555i	−0.931255	+	0.364369i	$0.881285\pi$
$108$	0.965926	−	0.258819i	0.0929463	−	0.0249049i
$109$	−0.291523	−	0.168311i	−0.0279228	−	0.0161213i	0.485974	−	0.873973i	$-0.338465\pi$
$109$	−0.291523	−	0.168311i	−0.0279228	−	0.0161213i	−0.513896	+	0.857852i	$0.671798\pi$
$110$	−7.44636	−	9.74931i	−0.709983	−	0.929560i
$111$			9.80013i			0.930188i
$112$	0.675009	−	2.55820i	0.0637823	−	0.241727i
$113$	10.1896	−	10.1896i	0.958555	−	0.958555i	−0.0406198	−	0.999175i	$-0.512933\pi$
$113$	10.1896	−	10.1896i	0.958555	−	0.958555i	0.999175	+	0.0406198i	$0.0129332\pi$
$114$	6.05866	−	3.49797i	0.567445	−	0.327615i
$115$	−3.62095	−	1.50933i	−0.337656	−	0.140746i
$116$	0.342305	−	0.592889i	0.0317822	−	0.0550484i
$117$	−3.30124	−	0.884566i	−0.305200	−	0.0817781i
$118$	7.18441	+	7.18441i	0.661379	+	0.661379i
$119$	−2.78362	+	4.86417i	−0.255174	+	0.445898i
$120$	−1.36519	+	1.77095i	−0.124624	+	0.161665i
$121$	−9.54974	−	16.5406i	−0.868158	−	1.50369i
$122$	−0.303248	−	1.13174i	−0.0274548	−	0.102463i
$123$	0.648592	+	2.42058i	0.0584816	+	0.218256i
$124$	−2.78821	−	4.82932i	−0.250388	−	0.433686i
$125$	−10.3004	−	4.34767i	−0.921294	−	0.388867i
$126$	−1.31412	+	2.29632i	−0.117071	+	0.204573i
$127$	−4.77054	−	4.77054i	−0.423317	−	0.423317i	0.463027	−	0.886344i	$-0.346763\pi$
$127$	−4.77054	−	4.77054i	−0.423317	−	0.423317i	−0.886344	+	0.463027i	$0.846763\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	1.38101	−	2.39198i	0.121591	−	0.210602i
$130$	7.06700	−	2.90876i	0.619817	−	0.255116i
$131$	15.7695	−	9.10455i	1.37779	−	0.795468i	0.385898	−	0.922542i	$-0.373892\pi$
$131$	15.7695	−	9.10455i	1.37779	−	0.795468i	0.991893	+	0.127074i	$0.0405585\pi$
$132$	−3.87940	+	3.87940i	−0.337658	+	0.337658i
$133$	−4.72232	+	17.8970i	−0.409477	+	1.55186i
$134$			9.95313i			0.859819i
$135$	1.77703	−	1.35727i	0.152942	−	0.116815i
$136$	1.83445	+	1.05912i	0.157303	+	0.0908190i
$137$	−2.11024	+	0.565438i	−0.180290	+	0.0483086i	−0.347835	−	0.937556i	$-0.613083\pi$
$137$	−2.11024	+	0.565438i	−0.180290	+	0.0483086i	0.167544	+	0.985865i	$0.446416\pi$
$138$	−0.454069	+	1.69461i	−0.0386529	+	0.144255i
$139$	−18.1446			−1.53900			−0.769501	−	0.638645i	$-0.779495\pi$
$139$	−18.1446			−1.53900			−0.769501	+	0.638645i	$0.779495\pi$
$140$	−0.781491	−	5.86424i	−0.0660481	−	0.495618i
$141$	3.52518			0.296873
$142$	−3.09847	+	11.5637i	−0.260018	+	0.970401i
$143$	18.1116	−	4.85299i	1.51457	−	0.405828i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	0.203204	−	1.51729i	0.0168752	−	0.126004i
$146$		−	4.87079i		−	0.403109i
$147$	−1.86331	−	6.74745i	−0.153683	−	0.556520i
$148$	−6.92974	+	6.92974i	−0.569621	+	0.569621i
$149$	−0.167711	+	0.0968279i	−0.0137394	+	0.00793245i	−0.506854	−	0.862032i	$-0.669192\pi$
$149$	−0.167711	+	0.0968279i	−0.0137394	+	0.00793245i	0.493115	+	0.869964i	$0.335858\pi$
$150$	−1.31566	+	4.82380i	−0.107423	+	0.393861i
$151$	10.6614	−	18.4660i	0.867610	−	1.50274i	0.00317777	−	0.999995i	$-0.498988\pi$
$151$	10.6614	−	18.4660i	0.867610	−	1.50274i	0.864432	−	0.502750i	$-0.167678\pi$
$152$	6.75755	+	1.81068i	0.548110	+	0.146866i
$153$	−1.49783	−	1.49783i	−0.121092	−	0.121092i
$154$	−0.0554181	−	14.5153i	−0.00446571	−	1.16967i
$155$	−9.87553	−	7.61288i	−0.793222	−	0.611481i
$156$	−1.70885	−	2.95981i	−0.136817	−	0.236975i
$157$	−0.952462	−	3.55464i	−0.0760147	−	0.283691i	0.917447	−	0.397859i	$-0.130247\pi$
$157$	−0.952462	−	3.55464i	−0.0760147	−	0.283691i	−0.993461	+	0.114168i	$0.963580\pi$
$158$	−2.15619	−	8.04700i	−0.171537	−	0.640185i
$159$	4.70121	+	8.14273i	0.372830	+	0.645761i
$160$	−2.21758	+	0.286912i	−0.175315	+	0.0226824i
$161$	−2.33617	−	4.01092i	−0.184116	−	0.316105i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	13.6012	+	3.64443i	1.06533	+	0.285454i	0.748572	−	0.663054i	$-0.230740\pi$
$163$	13.6012	+	3.64443i	1.06533	+	0.285454i	0.316756	+	0.948507i	$0.397406\pi$
$164$	−1.25298	+	2.17023i	−0.0978416	+	0.169467i
$165$	−4.71997	+	11.3234i	−0.367449	+	0.881525i
$166$	−4.96366	+	2.86577i	−0.385255	+	0.222427i
$167$	6.07259	−	6.07259i	0.469911	−	0.469911i	−0.431974	−	0.901886i	$-0.642183\pi$
$167$	6.07259	−	6.07259i	0.469911	−	0.469911i	0.901886	+	0.431974i	$0.142183\pi$
$168$	−2.55297	+	0.694523i	−0.196966	+	0.0535836i
$169$		−	1.31933i		−	0.101487i
$170$	4.69463	+	0.628733i	0.360061	+	0.0482216i
$171$	−6.05866	−	3.49797i	−0.463317	−	0.267496i
$172$	2.66791	−	0.714864i	0.203426	−	0.0545079i
$173$	−1.04797	+	3.91108i	−0.0796757	+	0.297354i	−0.994253	−	0.107058i	$-0.965857\pi$
$173$	−1.04797	+	3.91108i	−0.0796757	+	0.297354i	0.914577	+	0.404412i	$0.132524\pi$
$174$	−0.684610			−0.0519001
$175$	−6.60692	−	11.4607i	−0.499437	−	0.866350i
$176$	−5.48630			−0.413545
$177$	2.62968	−	9.81409i	0.197659	−	0.737672i
$178$	−6.93879	+	1.85924i	−0.520084	+	0.139356i
$179$	3.17428	+	1.83267i	0.237256	+	0.136980i	0.613915	−	0.789372i	$-0.289594\pi$
$179$	3.17428	+	1.83267i	0.237256	+	0.136980i	−0.376659	+	0.926352i	$0.622927\pi$
$180$	2.21628	+	0.296818i	0.165192	+	0.0221235i
$181$			2.39985i			0.178379i	0.996015	+	0.0891896i	$0.0284277\pi$
$181$			2.39985i			0.178379i	−0.996015	+	0.0891896i	$0.971572\pi$
$182$	8.74314	+	2.30698i	0.648085	+	0.171005i
$183$	−0.828489	+	0.828489i	−0.0612437	+	0.0612437i
$184$	−1.51935	+	0.877194i	−0.112008	+	0.0646676i
$185$	−8.43125	+	20.2269i	−0.619878	+	1.48711i
$186$	−2.78821	+	4.82932i	−0.204441	+	0.354103i
$187$	11.2253	+	3.00782i	0.820878	+	0.219954i
$188$	2.49268	+	2.49268i	0.181797	+	0.181797i
$189$	2.64573	−	0.0101012i	0.192449	−	0.000734752i
$190$	15.5141	−	2.00721i	1.12551	−	0.145619i
$191$	−4.03766	−	6.99344i	−0.292155	−	0.506027i	0.682164	−	0.731199i	$-0.261039\pi$
$191$	−4.03766	−	6.99344i	−0.292155	−	0.506027i	−0.974319	+	0.225172i	$0.927706\pi$
$192$	0.258819	+	0.965926i	0.0186787	+	0.0697097i
$193$	−0.445821	−	1.66383i	−0.0320909	−	0.119765i	0.948022	−	0.318204i	$-0.103080\pi$
$193$	−0.445821	−	1.66383i	−0.0320909	−	0.119765i	−0.980113	+	0.198439i	$0.936413\pi$
$194$	9.27809	+	16.0701i	0.666128	+	1.15377i
$195$	−6.05256	−	4.66582i	−0.433433	−	0.334126i
$196$	3.45361	−	6.08873i	0.246686	−	0.434909i
$197$	6.01174	+	6.01174i	0.428319	+	0.428319i	0.888055	−	0.459737i	$-0.152056\pi$
$197$	6.01174	+	6.01174i	0.428319	+	0.428319i	−0.459737	+	0.888055i	$0.652056\pi$
$198$	5.29936	+	1.41996i	0.376609	+	0.100912i
$199$	5.50897	−	9.54181i	0.390520	−	0.676401i	−0.601998	−	0.798498i	$-0.705628\pi$
$199$	5.50897	−	9.54181i	0.390520	−	0.676401i	0.992518	+	0.122097i	$0.0389618\pi$
$200$	−4.34125	+	2.48063i	−0.306973	+	0.175407i
$201$	8.61966	−	4.97656i	0.607984	−	0.351020i
$202$	5.84612	−	5.84612i	0.411332	−	0.411332i
$203$	1.27589	−	1.28567i	0.0895498	−	0.0902362i
$204$		−	2.11825i		−	0.148307i
$205$	−0.743816	+	5.55393i	−0.0519503	+	0.387903i
$206$	8.05941	+	4.65310i	0.561526	+	0.324197i
$207$	1.69461	−	0.454069i	0.117783	−	0.0315600i
$208$	0.884566	−	3.30124i	0.0613336	−	0.228900i
$209$	38.3818			2.65492
$210$	−4.68783	+	3.60891i	−0.323491	+	0.249038i
$211$	10.3323			0.711302			0.355651	−	0.934619i	$-0.384259\pi$
$211$	10.3323			0.711302			0.355651	+	0.934619i	$0.384259\pi$
$212$	−2.43353	+	9.08204i	−0.167135	+	0.623757i
$213$	11.5637	−	3.09847i	0.792329	−	0.212304i
$214$	10.6241	+	6.13383i	0.726249	+	0.419300i
$215$	4.90820	−	3.74880i	0.334736	−	0.255666i
$216$		−	1.00000i		−	0.0680414i
$217$	−3.87295	−	14.2364i	−0.262913	−	0.966430i
$218$	−0.238027	+	0.238027i	−0.0161213	+	0.0161213i
$219$	−4.21822	+	2.43539i	−0.285041	+	0.164569i
$220$	−11.3444	+	4.66933i	−0.764837	+	0.314806i
$221$	−3.61976	+	6.26961i	−0.243492	+	0.421740i
$222$	9.46620	+	2.53646i	0.635330	+	0.170236i
$223$	3.41183	+	3.41183i	0.228473	+	0.228473i	0.812054	−	0.583582i	$-0.198349\pi$
$223$	3.41183	+	3.41183i	0.228473	+	0.228473i	−0.583582	+	0.812054i	$0.698349\pi$
$224$	−2.29632	−	1.31412i	−0.153429	−	0.0878032i
$225$	4.83536	−	1.27250i	0.322358	−	0.0848334i
$226$	−7.20512	−	12.4796i	−0.479277	−	0.830133i
$227$	−4.68301	−	17.4772i	−0.310822	−	1.16000i	−0.927816	−	0.373037i	$-0.878316\pi$
$227$	−4.68301	−	17.4772i	−0.310822	−	1.16000i	0.616994	−	0.786968i	$-0.288350\pi$
$228$	−1.81068	−	6.75755i	−0.119915	−	0.447530i
$229$	4.82375	+	8.35497i	0.318762	+	0.552112i	0.980230	−	0.197861i	$-0.0633996\pi$
$229$	4.82375	+	8.35497i	0.318762	+	0.552112i	−0.661468	+	0.749973i	$0.730066\pi$
$230$	−2.39508	+	3.10693i	−0.157927	+	0.204865i
$231$	−12.5429	+	7.30563i	−0.825262	+	0.480675i
$232$	−0.484092	−	0.484092i	−0.0317822	−	0.0317822i
$233$	−13.9801	−	3.74597i	−0.915870	−	0.245407i	−0.230051	−	0.973179i	$-0.573889\pi$
$233$	−13.9801	−	3.74597i	−0.915870	−	0.245407i	−0.685819	+	0.727772i	$0.740556\pi$
$234$	−1.70885	+	2.95981i	−0.111711	+	0.193489i
$235$	7.27575	+	3.03278i	0.474618	+	0.197837i
$236$	8.79907	−	5.08015i	0.572771	−	0.330689i
$237$	−5.89081	+	5.89081i	−0.382649	+	0.382649i
$238$	3.97798	+	3.94772i	0.257854	+	0.255892i
$239$		−	29.9736i		−	1.93883i	−0.245427	−	0.969415i	$-0.578928\pi$
$239$		−	29.9736i		−	1.93883i	0.245427	−	0.969415i	$-0.421072\pi$
$240$	1.35727	+	1.77703i	0.0876111	+	0.114707i
$241$	14.3934	+	8.31003i	0.927161	+	0.535296i	0.885912	−	0.463853i	$-0.153533\pi$
$241$	14.3934	+	8.31003i	0.927161	+	0.535296i	0.0412481	+	0.999149i	$0.486867\pi$
$242$	−18.4487	+	4.94331i	−1.18593	+	0.317768i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	−1.17166			−0.0750079
$245$	1.95920	−	15.5294i	0.125169	−	0.992135i
$246$	2.50597			0.159775
$247$	−6.18836	+	23.0953i	−0.393756	+	1.46952i
$248$	−5.38640	+	1.44328i	−0.342037	+	0.0916485i
$249$	4.96366	+	2.86577i	0.314559	+	0.181611i
$250$	−6.86546	+	8.82414i	−0.434210	+	0.558088i
$251$		−	10.7660i		−	0.679546i	−0.940508	−	0.339773i	$-0.889650\pi$
$251$		−	10.7660i		−	0.679546i	0.940508	−	0.339773i	$-0.110350\pi$
$252$	1.87796	+	1.86367i	0.118300	+	0.117400i
$253$	−6.80597	+	6.80597i	−0.427888	+	0.427888i
$254$	−5.84270	+	3.37328i	−0.366604	+	0.211659i
$255$	−1.80281	−	4.38003i	−0.112897	−	0.274288i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−14.5299	−	3.89328i	−0.906352	−	0.242856i	−0.224610	−	0.974449i	$-0.572111\pi$
$257$	−14.5299	−	3.89328i	−0.906352	−	0.242856i	−0.681742	+	0.731593i	$0.738777\pi$
$258$	−1.95305	−	1.95305i	−0.121591	−	0.121591i
$259$	−22.4053	+	13.0500i	−1.39220	+	0.810887i
$260$	−0.980578	−	7.57904i	−0.0608128	−	0.470032i
$261$	0.342305	+	0.592889i	0.0211881	+	0.0366989i
$262$	−4.71286	−	17.5886i	−0.291161	−	1.08663i
$263$	5.83157	+	21.7637i	0.359590	+	1.34201i	0.874609	+	0.484829i	$0.161118\pi$
$263$	5.83157	+	21.7637i	0.359590	+	1.34201i	−0.515019	+	0.857179i	$0.672215\pi$
$264$	2.74315	+	4.75127i	0.168829	+	0.292421i
$265$	2.69766	+	20.8507i	0.165716	+	1.28085i
$266$	16.0649	+	9.19348i	0.985003	+	0.563689i
$267$	5.07954	+	5.07954i	0.310863	+	0.310863i
$268$	9.61398	+	2.57606i	0.587268	+	0.157358i
$269$	5.52122	−	9.56304i	0.336635	−	0.583069i	−0.647163	−	0.762352i	$-0.724045\pi$
$269$	5.52122	−	9.56304i	0.336635	−	0.583069i	0.983797	+	0.179283i	$0.0573779\pi$
$270$	−0.851088	−	2.06776i	−0.0517956	−	0.125840i
$271$	4.34433	−	2.50820i	0.263899	−	0.152362i	−0.362213	−	0.932095i	$-0.617979\pi$
$271$	4.34433	−	2.50820i	0.263899	−	0.152362i	0.626112	+	0.779733i	$0.284645\pi$
$272$	1.49783	−	1.49783i	0.0908190	−	0.0908190i
$273$	−2.37367	−	8.72527i	−0.143661	−	0.528077i
$274$			2.18468i			0.131982i
$275$	−19.4835	+	19.3101i	−1.17490	+	1.16444i
$276$	1.51935	+	0.877194i	0.0914538	+	0.0528009i
$277$	−6.11920	+	1.63963i	−0.367667	+	0.0985161i	−0.437922	−	0.899013i	$-0.644285\pi$
$277$	−6.11920	+	1.63963i	−0.367667	+	0.0985161i	0.0702549	+	0.997529i	$0.477619\pi$
$278$	−4.69616	+	17.5263i	−0.281657	+	1.05116i
$279$	5.57642			0.333851
$280$	−5.86668	−	0.762913i	−0.350601	−	0.0455928i
$281$	−29.4723			−1.75817			−0.879085	−	0.476665i	$-0.841846\pi$
$281$	−29.4723			−1.75817			−0.879085	+	0.476665i	$0.841846\pi$
$282$	0.912383	−	3.40506i	0.0543316	−	0.202768i
$283$	−0.0944925	+	0.0253192i	−0.00561700	+	0.00150507i	−0.261626	−	0.965169i	$-0.584259\pi$
$283$	−0.0944925	+	0.0253192i	−0.00561700	+	0.00150507i	0.256009	+	0.966674i	$0.417592\pi$
$284$	10.3677	+	5.98579i	0.615210	+	0.355191i
$285$	−9.49534	−	12.4320i	−0.562455	−	0.736407i
$286$		−	18.7505i		−	1.10874i
$287$	−4.67030	+	4.70610i	−0.275679	+	0.277792i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$	10.8366	−	6.25652i	0.637447	−	0.368030i
$290$	−1.41299	−	0.588983i	−0.0829738	−	0.0345863i
$291$	9.27809	−	16.0701i	0.543891	−	0.942048i
$292$	−4.70482	−	1.26065i	−0.275329	−	0.0737741i
$293$	−14.0076	−	14.0076i	−0.818330	−	0.818330i	0.167536	−	0.985866i	$-0.446419\pi$
$293$	−14.0076	−	14.0076i	−0.818330	−	0.818330i	−0.985866	+	0.167536i	$0.946419\pi$
$294$	−6.99980	+	0.0534500i	−0.408236	+	0.00311727i
$295$	13.8708	−	17.9933i	0.807587	−	1.04761i
$296$	4.90007	+	8.48716i	0.284811	+	0.493306i
$297$	−1.41996	−	5.29936i	−0.0823944	−	0.307500i
$298$	0.0501218	+	0.187057i	0.00290348	+	0.0108359i
$299$	−2.99799	−	5.19266i	−0.173378	−	0.300300i
$300$	4.31891	+	2.51932i	0.249353	+	0.145453i
$301$	7.30758	−	0.0278997i	0.421202	−	0.00160811i
$302$	−15.0775	−	15.0775i	−0.867610	−	0.867610i
$303$	−7.98595	−	2.13983i	−0.458781	−	0.122930i
$304$	3.49797	−	6.05866i	0.200622	−	0.347488i
$305$	−2.42272	+	0.997187i	−0.138724	+	0.0570987i
$306$	−1.83445	+	1.05912i	−0.104869	+	0.0605460i
$307$	−3.05320	+	3.05320i	−0.174255	+	0.174255i	−0.788846	−	0.614591i	$-0.789321\pi$
$307$	−3.05320	+	3.05320i	−0.174255	+	0.174255i	0.614591	+	0.788846i	$0.289321\pi$
$308$	−14.0350	−	3.70330i	−0.799720	−	0.211015i
$309$		−	9.30620i		−	0.529411i
$310$	−9.90945	+	7.56867i	−0.562819	+	0.429872i
$311$	−7.31386	−	4.22266i	−0.414731	−	0.239445i	0.278089	−	0.960555i	$-0.410299\pi$
$311$	−7.31386	−	4.22266i	−0.414731	−	0.239445i	−0.692820	+	0.721110i	$0.743632\pi$
$312$	−3.30124	+	0.884566i	−0.186896	+	0.0500787i
$313$	−5.02358	+	18.7482i	−0.283949	+	1.05971i	0.665654	+	0.746260i	$0.268153\pi$
$313$	−5.02358	+	18.7482i	−0.283949	+	1.05971i	−0.949604	+	0.313453i	$0.898514\pi$
$314$	−3.68003			−0.207676
$315$	5.46932	+	2.25533i	0.308161	+	0.127073i
$316$	−8.33087			−0.468648
$317$	−4.02471	+	15.0204i	−0.226050	+	0.843632i	0.755931	+	0.654652i	$0.227185\pi$
$317$	−4.02471	+	15.0204i	−0.226050	+	0.843632i	−0.981981	+	0.188980i	$0.939482\pi$
$318$	9.08204	−	2.43353i	0.509296	−	0.136465i
$319$	−3.25277	−	1.87799i	−0.182120	−	0.105147i
$320$	−0.296818	+	2.21628i	−0.0165926	+	0.123894i
$321$		−	12.2677i		−	0.684714i
$322$	−4.47890	+	1.21846i	−0.249599	+	0.0679023i
$323$	−10.4787	+	10.4787i	−0.583050	+	0.583050i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	−8.47803	−	14.8371i	−0.470277	−	0.823014i
$326$	7.04050	−	12.1945i	0.389937	−	0.675391i
$327$	0.325151	+	0.0871241i	0.0179809	+	0.00481797i
$328$	1.77199	+	1.77199i	0.0978416	+	0.0978416i
$329$	4.69417	+	8.05933i	0.258798	+	0.444325i
$330$	9.71594	+	7.48985i	0.534845	+	0.412303i
$331$	−8.09296	−	14.0174i	−0.444830	−	0.770467i	0.553211	−	0.833041i	$-0.313402\pi$
$331$	−8.09296	−	14.0174i	−0.444830	−	0.770467i	−0.998040	+	0.0625739i	$0.980069\pi$
$332$	1.48343	+	5.53624i	0.0814139	+	0.303841i
$333$	−2.53646	−	9.46620i	−0.138997	−	0.518745i
$334$	−4.29397	−	7.43738i	−0.234956	−	0.406955i
$335$	22.0719	−	2.85567i	1.20592	−	0.156022i
$336$	0.0101012	+	2.64573i	0.000551064	+	0.144337i
$337$	19.2055	+	19.2055i	1.04619	+	1.04619i	0.998880	+	0.0473073i	$0.0150640\pi$
$337$	19.2055	+	19.2055i	1.04619	+	1.04619i	0.0473073	+	0.998880i	$0.484936\pi$
$338$	−1.27438	−	0.341468i	−0.0693169	−	0.0185734i
$339$	−7.20512	+	12.4796i	−0.391328	+	0.677801i
$340$	1.82237	−	4.37193i	0.0988318	−	0.237101i
$341$	−26.4951	+	15.2969i	−1.43479	+	0.828376i
$342$	−4.94687	+	4.94687i	−0.267496	+	0.267496i
$343$	12.9450	−	13.2449i	0.698962	−	0.715159i
$344$		−	2.76202i		−	0.148918i
$345$	3.88822	+	0.520734i	0.209335	+	0.0280354i
$346$	3.50658	+	2.02452i	0.188515	+	0.108839i
$347$	−9.91592	+	2.65696i	−0.532315	+	0.142633i	−0.514957	−	0.857216i	$-0.672192\pi$
$347$	−9.91592	+	2.65696i	−0.532315	+	0.142633i	−0.0173577	+	0.999849i	$0.505525\pi$
$348$	−0.177190	+	0.661282i	−0.00949838	+	0.0354484i
$349$	6.61441			0.354061			0.177031	−	0.984205i	$-0.443351\pi$
$349$	6.61441			0.354061			0.177031	+	0.984205i	$0.443351\pi$
$350$	−12.7802	+	3.41554i	−0.683132	+	0.182568i
$351$	3.41770			0.182423
$352$	−1.41996	+	5.29936i	−0.0756841	+	0.282457i
$353$	13.1604	−	3.52633i	0.700460	−	0.187688i	0.109023	−	0.994039i	$-0.465228\pi$
$353$	13.1604	−	3.52633i	0.700460	−	0.187688i	0.591436	+	0.806352i	$0.298561\pi$
$354$	−8.79907	−	5.08015i	−0.467666	−	0.270007i
$355$	26.5324	+	3.55338i	1.40819	+	0.188594i
$356$			7.18356i			0.380728i
$357$	1.42983	−	5.41889i	0.0756749	−	0.286798i
$358$	2.59178	−	2.59178i	0.136980	−	0.136980i
$359$	−14.9791	+	8.64822i	−0.790569	+	0.456435i	−0.840163	−	0.542334i	$-0.817541\pi$
$359$	−14.9791	+	8.64822i	−0.790569	+	0.456435i	0.0495937	+	0.998769i	$0.484207\pi$
$360$	0.860320	−	2.06394i	0.0453428	−	0.108779i
$361$	−14.9715	+	25.9315i	−0.787976	+	1.36481i
$362$	2.31807	+	0.621126i	0.121835	+	0.0326457i
$363$	13.5054	+	13.5054i	0.708848	+	0.708848i
$364$	4.49126	−	7.84814i	0.235406	−	0.411354i
$365$	−10.8014	+	1.39749i	−0.565370	+	0.0731477i
$366$	0.585830	+	1.01469i	0.0306218	+	0.0530386i
$367$	−6.69852	−	24.9992i	−0.349660	−	1.30495i	−0.887073	−	0.461629i	$-0.847265\pi$
$367$	−6.69852	−	24.9992i	−0.349660	−	1.30495i	0.537413	−	0.843319i	$-0.319402\pi$
$368$	0.454069	+	1.69461i	0.0236700	+	0.0883376i
$369$	−1.25298	−	2.17023i	−0.0652277	−	0.112978i
$370$	17.3555	+	13.3791i	0.902270	+	0.695544i
$371$	−12.3559	+	21.5910i	−0.641486	+	1.12095i
$372$	3.94312	+	3.94312i	0.204441	+	0.204441i
$373$	−8.85404	−	2.37243i	−0.458445	−	0.122840i	0.0222033	−	0.999753i	$-0.492932\pi$
$373$	−8.85404	−	2.37243i	−0.458445	−	0.122840i	−0.480648	+	0.876914i	$0.659599\pi$
$374$	5.81066	−	10.0644i	0.300462	−	0.520416i
$375$	11.0747	+	1.53359i	0.571893	+	0.0791943i
$376$	3.05289	−	1.76259i	0.157441	−	0.0908985i
$377$	1.65448	−	1.65448i	0.0852101	−	0.0852101i
$378$	0.675009	−	2.55820i	0.0347187	−	0.131579i
$379$		−	18.6871i		−	0.959891i	−0.877298	−	0.479946i	$-0.840656\pi$
$379$		−	18.6871i		−	0.959891i	0.877298	−	0.479946i	$-0.159344\pi$
$380$	2.07652	−	15.5049i	0.106523	−	0.795387i
$381$	5.84270	+	3.37328i	0.299331	+	0.172819i
$382$	−7.80016	+	2.09005i	−0.399091	+	0.106936i
$383$	−5.13534	+	19.1654i	−0.262404	+	0.979304i	0.701417	+	0.712752i	$0.252551\pi$
$383$	−5.13534	+	19.1654i	−0.262404	+	0.979304i	−0.963820	+	0.266553i	$0.914115\pi$
$384$	1.00000			0.0510310
$385$	−32.1730	+	4.28750i	−1.63969	+	0.218511i
$386$	−1.72252			−0.0876740
$387$	−0.714864	+	2.66791i	−0.0363386	+	0.135618i
$388$	17.9239	−	4.80269i	0.909948	−	0.243820i
$389$	−4.44026	−	2.56359i	−0.225130	−	0.129979i	0.383193	−	0.923668i	$-0.374824\pi$
$389$	−4.44026	−	2.56359i	−0.225130	−	0.129979i	−0.608323	+	0.793689i	$0.708158\pi$
$390$	−6.07335	+	4.63872i	−0.307536	+	0.234891i
$391$		−	3.71623i		−	0.187938i
$392$	−4.98740	−	4.91181i	−0.251902	−	0.248084i
$393$	−12.8758	+	12.8758i	−0.649497	+	0.649497i
$394$	7.36285	−	4.25094i	0.370935	−	0.214159i
$395$	−17.2263	+	7.09030i	−0.866747	+	0.356752i
$396$	2.74315	−	4.75127i	0.137848	−	0.238761i
$397$	25.4941	+	6.83113i	1.27951	+	0.342844i	0.833668	−	0.552266i	$-0.186237\pi$
$397$	25.4941	+	6.83113i	1.27951	+	0.342844i	0.445845	+	0.895110i	$0.352903\pi$
$398$	−7.79086	−	7.79086i	−0.390520	−	0.390520i
$399$	−0.0706671	−	18.5094i	−0.00353778	−	0.926627i
$400$	1.27250	+	4.83536i	0.0636251	+	0.241768i
$401$	8.61471	+	14.9211i	0.430198	+	0.745125i	0.996890	−	0.0788050i	$-0.0251104\pi$
$401$	8.61471	+	14.9211i	0.430198	+	0.745125i	−0.566692	+	0.823930i	$0.691777\pi$
$402$	−2.57606	−	9.61398i	−0.128482	−	0.479502i
$403$	−4.93271	−	18.4091i	−0.245716	−	0.917023i
$404$	−4.13383	−	7.16001i	−0.205666	−	0.356224i
$405$	−1.36519	+	1.77095i	−0.0678369	+	0.0879990i
$406$	−0.911636	−	1.56517i	−0.0452437	−	0.0776780i
$407$	38.0186	+	38.0186i	1.88451	+	1.88451i
$408$	−2.04607	−	0.548242i	−0.101295	−	0.0271420i
$409$	−17.8569	+	30.9290i	−0.882967	+	1.52934i	−0.0349400	+	0.999389i	$0.511124\pi$
$409$	−17.8569	+	30.9290i	−0.882967	+	1.52934i	−0.848027	+	0.529954i	$0.822209\pi$
$410$	5.17217	+	2.15593i	0.255435	+	0.106474i
$411$	1.89199	−	1.09234i	0.0933251	−	0.0538813i
$412$	6.58048	−	6.58048i	0.324197	−	0.324197i
$413$	25.9389	−	7.05656i	1.27637	−	0.347230i
$414$		−	1.75439i		−	0.0862235i
$415$	7.77922	+	10.1851i	0.381867	+	0.499967i
$416$	−2.95981	−	1.70885i	−0.145117	−	0.0837832i
$417$	17.5263	−	4.69616i	0.858267	−	0.229972i
$418$	9.93394	−	37.0740i	0.485885	−	1.81335i
$419$	14.0414			0.685966			0.342983	−	0.939342i	$-0.388563\pi$
$419$	14.0414			0.685966			0.342983	+	0.939342i	$0.388563\pi$
$420$	2.27264	+	5.46215i	0.110893	+	0.266526i
$421$	24.4332			1.19080			0.595401	−	0.803429i	$-0.296993\pi$
$421$	24.4332			1.19080			0.595401	+	0.803429i	$0.296993\pi$
$422$	2.67419	−	9.98020i	0.130177	−	0.485829i
$423$	−3.40506	+	0.912383i	−0.165560	+	0.0443616i
$424$	8.14273	+	4.70121i	0.395446	+	0.228311i
$425$	0.0473258	−	10.5911i	0.00229564	−	0.513745i
$426$		−	11.9716i		−	0.580025i
$427$	−2.99734	−	0.790881i	−0.145051	−	0.0382734i
$428$	8.67454	−	8.67454i	0.419300	−	0.419300i
$429$	−16.2384	+	9.37526i	−0.783999	+	0.452642i
$430$	−2.35073	−	5.71121i	−0.113362	−	0.275419i
$431$	19.3886	−	33.5820i	0.933914	−	1.61759i	0.157354	−	0.987542i	$-0.449704\pi$
$431$	19.3886	−	33.5820i	0.933914	−	1.61759i	0.776559	−	0.630044i	$-0.216963\pi$
$432$	−0.965926	−	0.258819i	−0.0464731	−	0.0124524i
$433$	−7.85700	−	7.85700i	−0.377583	−	0.377583i	0.492646	−	0.870230i	$-0.336030\pi$
$433$	−7.85700	−	7.85700i	−0.377583	−	0.377583i	−0.870230	+	0.492646i	$0.836030\pi$
$434$	−14.7537	+	0.0563283i	−0.708200	+	0.00270385i
$435$	0.196422	+	1.51818i	0.00941774	+	0.0727911i
$436$	0.168311	+	0.291523i	0.00806063	+	0.0139614i
$437$	−3.17664	−	11.8554i	−0.151959	−	0.567119i
$438$	1.26065	+	4.70482i	0.0602363	+	0.224805i
$439$	10.5640	+	18.2973i	0.504190	+	0.873283i	0.999988	+	0.00484487i	$0.00154217\pi$
$439$	10.5640	+	18.2973i	0.504190	+	0.873283i	−0.495798	+	0.868438i	$0.665124\pi$
$440$	1.57408	+	12.1663i	0.0750415	+	0.580007i
$441$	3.54619	+	6.03528i	0.168866	+	0.287394i
$442$	5.11912	+	5.11912i	0.243492	+	0.243492i
$443$	−6.48289	−	1.73709i	−0.308011	−	0.0825314i	0.101503	−	0.994835i	$-0.467635\pi$
$443$	−6.48289	−	1.73709i	−0.308011	−	0.0825314i	−0.409514	+	0.912304i	$0.634302\pi$
$444$	4.90007	−	8.48716i	0.232547	−	0.402783i
$445$	6.11385	+	14.8539i	0.289824	+	0.704143i
$446$	4.17862	−	2.41253i	0.197863	−	0.114236i
$447$	0.136935	−	0.136935i	0.00647682	−	0.00647682i
$448$	−1.86367	+	1.87796i	−0.0880502	+	0.0887252i
$449$			8.28979i			0.391219i	0.980682	+	0.195610i	$0.0626685\pi$
$449$			8.28979i			0.391219i	−0.980682	+	0.195610i	$0.937331\pi$
$450$	0.0223420	−	4.99995i	0.00105321	−	0.235700i
$451$	11.9065	+	6.87424i	0.560657	+	0.323695i
$452$	−13.9192	+	3.72964i	−0.654705	+	0.175428i
$453$	−5.51873	+	20.5962i	−0.259293	+	0.967693i
$454$	−18.0938			−0.849182
$455$	2.60741	−	20.0506i	0.122237	−	0.939985i
$456$	−6.99593			−0.327615
$457$	5.71524	−	21.3296i	0.267348	−	0.997755i	−0.693450	−	0.720505i	$-0.743910\pi$
$457$	5.71524	−	21.3296i	0.267348	−	0.997755i	0.960798	−	0.277250i	$-0.0894231\pi$
$458$	9.31876	−	2.49695i	0.435437	−	0.116675i
$459$	1.83445	+	1.05912i	0.0856250	+	0.0494356i
$460$	2.38117	+	3.11760i	0.111023	+	0.145359i
$461$			19.0130i			0.885524i	0.896639	+	0.442762i	$0.146001\pi$
$461$			19.0130i			0.885524i	−0.896639	+	0.442762i	$0.853999\pi$
$462$	3.81036	+	14.0063i	0.177274	+	0.651634i
$463$	−16.6091	+	16.6091i	−0.771891	+	0.771891i	−0.978437	−	0.206546i	$-0.933778\pi$
$463$	−16.6091	+	16.6091i	−0.771891	+	0.771891i	0.206546	+	0.978437i	$0.433778\pi$
$464$	−0.592889	+	0.342305i	−0.0275242	+	0.0158911i
$465$	11.5094	+	4.79750i	0.533735	+	0.222479i
$466$	−7.23665	+	12.5343i	−0.335232	+	0.580638i
$467$	15.4446	+	4.13837i	0.714691	+	0.191501i	0.597802	−	0.801644i	$-0.296041\pi$
$467$	15.4446	+	4.13837i	0.714691	+	0.191501i	0.116889	+	0.993145i	$0.462708\pi$
$468$	2.41668	+	2.41668i	0.111711	+	0.111711i
$469$	22.8556	+	13.0796i	1.05537	+	0.603959i
$470$	4.81254	−	6.24290i	0.221986	−	0.287963i
$471$	1.84001	+	3.18700i	0.0847834	+	0.146849i
$472$	−2.62968	−	9.81409i	−0.121041	−	0.451730i
$473$	−3.92196	−	14.6370i	−0.180332	−	0.673008i
$474$	4.16543	+	7.21474i	0.191325	+	0.331384i
$475$	−8.90234	−	33.8279i	−0.408467	−	1.55213i
$476$	4.84278	−	2.82069i	0.221968	−	0.129286i
$477$	−6.64852	−	6.64852i	−0.304415	−	0.304415i
$478$	−28.9523	−	7.75773i	−1.32425	−	0.354831i
$479$	4.50526	−	7.80333i	0.205850	−	0.356543i	−0.744553	−	0.667563i	$-0.767337\pi$
$479$	4.50526	−	7.80333i	0.205850	−	0.356543i	0.950403	+	0.311020i	$0.100671\pi$
$480$	2.06776	−	0.851088i	0.0943801	−	0.0388467i
$481$	−29.0066	+	16.7470i	−1.32259	+	0.763595i
$482$	11.7522	−	11.7522i	0.535296	−	0.535296i
$483$	3.29467	+	3.26961i	0.149913	+	0.148772i
$484$			19.0995i			0.868158i
$485$	32.9749	−	25.1857i	1.49731	−	1.14362i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	−9.02186	+	2.41740i	−0.408820	+	0.109543i	−0.457367	−	0.889278i	$-0.651207\pi$
$487$	−9.02186	+	2.41740i	−0.408820	+	0.109543i	0.0485475	+	0.998821i	$0.484541\pi$
$488$	−0.303248	+	1.13174i	−0.0137274	+	0.0512313i
$489$	−14.0810			−0.636764
$490$	−14.4931	−	5.91174i	−0.654734	−	0.267065i
$491$	2.08535			0.0941107			0.0470554	−	0.998892i	$-0.485016\pi$
$491$	2.08535			0.0941107			0.0470554	+	0.998892i	$0.485016\pi$
$492$	0.648592	−	2.42058i	0.0292408	−	0.109128i
$493$	1.40076	−	0.375332i	0.0630870	−	0.0169041i
$494$	20.7067	+	11.9550i	0.931637	+	0.537881i
$495$	1.62843	−	12.1592i	0.0731925	−	0.546514i
$496$			5.57642i			0.250388i
$497$	22.4821	+	22.3111i	1.00846	+	1.00079i
$498$	4.05281	−	4.05281i	0.181611	−	0.181611i
$499$	−11.6260	+	6.71229i	−0.520452	+	0.300483i	−0.737120	−	0.675762i	$-0.763815\pi$
$499$	−11.6260	+	6.71229i	−0.520452	+	0.300483i	0.216668	+	0.976245i	$0.430481\pi$
$500$	6.74656	+	8.91538i	0.301715	+	0.398708i
$501$	−4.29397	+	7.43738i	−0.191841	+	0.332278i
$502$	−10.3992	−	2.78645i	−0.464138	−	0.124366i
$503$	−7.19669	−	7.19669i	−0.320885	−	0.320885i	0.528222	−	0.849106i	$-0.322859\pi$
$503$	−7.19669	−	7.19669i	−0.320885	−	0.320885i	−0.849106	+	0.528222i	$0.822859\pi$
$504$	2.28622	−	1.33161i	0.101836	−	0.0593148i
$505$	−14.6416	−	11.2869i	−0.651542	−	0.502263i
$506$	4.81255	+	8.33558i	0.213944	+	0.370562i
$507$	0.341468	+	1.27438i	0.0151651	+	0.0565970i
$508$	1.74614	+	6.51668i	0.0774724	+	0.289131i
$509$	2.14078	+	3.70794i	0.0948884	+	0.164352i	0.909562	−	0.415568i	$-0.136417\pi$
$509$	2.14078	+	3.70794i	0.0948884	+	0.164352i	−0.814674	+	0.579920i	$0.803084\pi$
$510$	−4.69739	+	0.607749i	−0.208004	+	0.0269116i
$511$	−11.1849	−	6.40079i	−0.494791	−	0.283154i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	6.75755	+	1.81068i	0.298353	+	0.0799435i
$514$	−7.52124	+	13.0272i	−0.331748	+	0.574604i
$515$	8.00631	−	19.2074i	0.352800	−	0.846381i
$516$	−2.39198	+	1.38101i	−0.105301	+	0.0607957i
$517$	13.6756	−	13.6756i	0.601451	−	0.601451i
$518$	6.80642	+	25.0194i	0.299057	+	1.09929i
$519$		−	4.04905i		−	0.177733i
$520$	−7.57458	−	1.01443i	−0.332167	−	0.0444859i
$521$	−12.6226	−	7.28768i	−0.553007	−	0.319279i	0.197327	−	0.980338i	$-0.436774\pi$
$521$	−12.6226	−	7.28768i	−0.553007	−	0.319279i	−0.750334	+	0.661059i	$0.770107\pi$
$522$	0.661282	−	0.177190i	0.0289435	−	0.00775540i
$523$	9.85794	−	36.7904i	0.431058	−	1.60873i	−0.319270	−	0.947664i	$-0.603438\pi$
$523$	9.85794	−	36.7904i	0.431058	−	1.60873i	0.750328	−	0.661066i	$-0.229896\pi$
$524$	−18.2091			−0.795468
$525$	9.34806	+	9.36023i	0.407983	+	0.408514i
$526$	22.5315			0.982418
$527$	3.05723	−	11.4097i	0.133175	−	0.497015i
$528$	5.29936	−	1.41996i	0.230625	−	0.0617958i
$529$	−17.2531	−	9.96106i	−0.750133	−	0.433090i
$530$	20.8384	+	2.79081i	0.905162	+	0.121225i
$531$			10.1603i			0.440919i
$532$	13.0381	−	13.1381i	0.565275	−	0.569607i
$533$	−6.05612	+	6.05612i	−0.262319	+	0.262319i
$534$	6.22115	−	3.59178i	0.269215	−	0.155432i
$535$	10.5541	−	25.3197i	0.456294	−	1.09467i
$536$	4.97656	−	8.61966i	0.214955	−	0.372313i
$537$	−3.54044	−	0.948659i	−0.152781	−	0.0409377i
$538$	−7.80819	−	7.80819i	−0.336635	−	0.336635i
$539$	−33.4046	−	18.9475i	−1.43884	−	0.816128i
$540$	−2.21758	+	0.286912i	−0.0954296	+	0.0123467i
$541$	−8.43016	−	14.6015i	−0.362441	−	0.627766i	0.625921	−	0.779886i	$-0.284723\pi$
$541$	−8.43016	−	14.6015i	−0.362441	−	0.627766i	−0.988362	+	0.152121i	$0.951390\pi$
$542$	−1.29834	−	4.84547i	−0.0557684	−	0.208131i
$543$	−0.621126	−	2.31807i	−0.0266551	−	0.0994781i
$544$	−1.05912	−	1.83445i	−0.0454095	−	0.0786516i
$545$	0.596139	+	0.459553i	0.0255358	+	0.0196851i
$546$	−9.04232	+	0.0345228i	−0.386975	+	0.00147744i
$547$	−2.04444	−	2.04444i	−0.0874141	−	0.0874141i	0.662048	−	0.749462i	$-0.269688\pi$
$547$	−2.04444	−	2.04444i	−0.0874141	−	0.0874141i	−0.749462	+	0.662048i	$0.769688\pi$
$548$	2.11024	+	0.565438i	0.0901451	+	0.0241543i
$549$	0.585830	−	1.01469i	0.0250026	−	0.0433058i
$550$	13.6095	+	23.8174i	0.580309	+	1.01558i
$551$	4.14781	−	2.39474i	0.176703	−	0.102019i
$552$	1.24054	−	1.24054i	0.0528009	−	0.0528009i
$553$	−21.3120	−	5.62341i	−0.906278	−	0.239132i
$554$			6.33506i			0.269151i
$555$	2.90885	−	21.7198i	0.123474	−	0.921956i
$556$	15.7137	+	9.07229i	0.666408	+	0.384751i
$557$	−4.04187	+	1.08302i	−0.171260	+	0.0458889i	−0.343430	−	0.939178i	$-0.611589\pi$
$557$	−4.04187	+	1.08302i	−0.171260	+	0.0458889i	0.172170	+	0.985067i	$0.444922\pi$
$558$	1.44328	−	5.38640i	0.0610990	−	0.228025i
$559$	9.43977			0.399260
$560$	−2.25533	+	5.46932i	−0.0953050	+	0.231121i
$561$	−11.6213			−0.490653
$562$	−7.62799	+	28.4681i	−0.321767	+	1.20085i
$563$	24.1918	−	6.48217i	1.01956	−	0.273191i	0.289943	−	0.957044i	$-0.406364\pi$
$563$	24.1918	−	6.48217i	1.01956	−	0.273191i	0.729620	+	0.683853i	$0.239697\pi$
$564$	−3.05289	−	1.76259i	−0.128550	−	0.0742183i
$565$	−25.6074	+	19.5585i	−1.07731	+	0.822833i
$566$			0.0978259i			0.00411193i
$567$	−2.55297	+	0.694523i	−0.107215	+	0.0291672i
$568$	8.46519	−	8.46519i	0.355191	−	0.355191i
$569$	−1.99827	+	1.15370i	−0.0837720	+	0.0483658i	−0.541301	−	0.840829i	$-0.682068\pi$
$569$	−1.99827	+	1.15370i	−0.0837720	+	0.0483658i	0.457529	+	0.889195i	$0.348735\pi$
$570$	−14.4659	+	5.95416i	−0.605911	+	0.249392i
$571$	−7.94325	+	13.7581i	−0.332415	+	0.575759i	−0.982985	−	0.183687i	$-0.941197\pi$
$571$	−7.94325	+	13.7581i	−0.332415	+	0.575759i	0.650570	+	0.759446i	$0.274530\pi$
$572$	−18.1116	−	4.85299i	−0.757285	−	0.202914i
$573$	5.71012	+	5.71012i	0.238544	+	0.238544i
$574$	3.33698	+	5.72919i	0.139283	+	0.239132i
$575$	7.57705	+	4.41987i	0.315985	+	0.184321i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	1.03550	+	3.86453i	0.0431084	+	0.160883i	0.984125	−	0.177479i	$-0.0567941\pi$
$577$	1.03550	+	3.86453i	0.0431084	+	0.160883i	−0.941016	+	0.338361i	$0.890127\pi$
$578$	−3.23861	−	12.0867i	−0.134709	−	0.502739i
$579$	0.861260	+	1.49175i	0.0357928	+	0.0619949i
$580$	−0.934623	+	1.21241i	−0.0388081	+	0.0503425i
$581$	0.0578953	+	15.1641i	0.00240190	+	0.629114i
$582$	−13.1212	−	13.1212i	−0.543891	−	0.543891i
$583$	49.8268	+	13.3510i	2.06361	+	0.552944i
$584$	−2.43539	+	4.21822i	−0.100777	+	0.174551i
$585$	7.05393	+	2.94031i	0.291644	+	0.121567i
$586$	−17.1557	+	9.90484i	−0.708695	+	0.409165i
$587$	−5.31785	+	5.31785i	−0.219491	+	0.219491i	−0.808284	−	0.588793i	$-0.799603\pi$
$587$	−5.31785	+	5.31785i	−0.219491	+	0.219491i	0.588793	+	0.808284i	$0.299603\pi$
$588$	−1.76005	+	6.77512i	−0.0725833	+	0.279401i
$589$		−	39.0122i		−	1.60747i
$590$	−13.7902	−	18.0551i	−0.567734	−	0.743318i
$591$	−7.36285	−	4.25094i	−0.302867	−	0.174860i
$592$	9.46620	−	2.53646i	0.389059	−	0.104248i
$593$	4.58156	−	17.0986i	0.188142	−	0.702156i	−0.805794	−	0.592196i	$-0.798261\pi$
$593$	4.58156	−	17.0986i	0.188142	−	0.702156i	0.993936	−	0.109960i	$-0.0350722\pi$
$594$	−5.48630			−0.225106
$595$	7.61307	−	9.95414i	0.312105	−	0.408080i
$596$	0.193656			0.00793245
$597$	−2.85165	+	10.6425i	−0.116710	+	0.435569i
$598$	−5.79167	+	1.55187i	−0.236839	+	0.0634608i
$599$	−27.0972	−	15.6446i	−1.10716	−	0.639220i	−0.169069	−	0.985604i	$-0.554076\pi$
$599$	−27.0972	−	15.6446i	−1.10716	−	0.639220i	−0.938093	+	0.346384i	$0.887409\pi$
$600$	3.55130	−	3.51970i	0.144981	−	0.143691i
$601$			47.5637i			1.94016i	0.242776	+	0.970082i	$0.421942\pi$
$601$			47.5637i			1.94016i	−0.242776	+	0.970082i	$0.578058\pi$
$602$	1.86439	−	7.06580i	0.0759869	−	0.287980i
$603$	−7.03792	+	7.03792i	−0.286606	+	0.286606i
$604$	−18.4660	+	10.6614i	−0.751372	+	0.433805i
$605$	16.2553	+	39.4932i	0.660874	+	1.60563i
$606$	−4.13383	+	7.16001i	−0.167925	+	0.290855i
$607$	23.7082	+	6.35260i	0.962287	+	0.257844i	0.705568	−	0.708642i	$-0.250692\pi$
$607$	23.7082	+	6.35260i	0.962287	+	0.257844i	0.256719	+	0.966486i	$0.417359\pi$
$608$	−4.94687	−	4.94687i	−0.200622	−	0.200622i
$609$	−0.899658	+	1.57208i	−0.0364560	+	0.0637041i
$610$	0.336163	+	2.59826i	0.0136108	+	0.105200i
$611$	6.02400	+	10.4339i	0.243705	+	0.422109i
$612$	0.548242	+	2.04607i	0.0221614	+	0.0827074i
$613$	−7.20472	−	26.8884i	−0.290996	−	1.08601i	−0.944345	−	0.328955i	$-0.893303\pi$
$613$	−7.20472	−	26.8884i	−0.290996	−	1.08601i	0.653349	−	0.757056i	$-0.273363\pi$
$614$	2.15894	+	3.73939i	0.0871277	+	0.150910i
$615$	−0.718991	−	5.55719i	−0.0289925	−	0.224088i
$616$	−7.20965	+	12.5983i	−0.290485	+	0.507600i
$617$	−24.4884	−	24.4884i	−0.985865	−	0.985865i	0.0140365	−	0.999901i	$-0.495532\pi$
$617$	−24.4884	−	24.4884i	−0.985865	−	0.985865i	−0.999901	+	0.0140365i	$0.995532\pi$
$618$	−8.98910	−	2.40862i	−0.361595	−	0.0968890i
$619$	−15.9137	+	27.5634i	−0.639627	+	1.10787i	0.345888	+	0.938276i	$0.387578\pi$
$619$	−15.9137	+	27.5634i	−0.639627	+	1.10787i	−0.985515	+	0.169590i	$0.945756\pi$
$620$	4.74602	+	11.5307i	0.190605	+	0.463085i
$621$	−1.51935	+	0.877194i	−0.0609692	+	0.0352006i
$622$	−5.97174	+	5.97174i	−0.239445	+	0.239445i
$623$	−4.84897	+	18.3770i	−0.194270	+	0.736257i
$624$			3.41770i			0.136817i
$625$	21.5381	+	12.6930i	0.861522	+	0.507719i
$626$	16.8092	+	9.70480i	0.671831	+	0.387882i
$627$	−37.0740	+	9.93394i	−1.48059	+	0.396723i
$628$	−0.952462	+	3.55464i	−0.0380074	+	0.141845i
$629$	−20.7591			−0.827719
$630$	3.59404	−	4.69924i	0.143190	−	0.187222i
$631$	−34.9471			−1.39122			−0.695610	−	0.718419i	$-0.744866\pi$
$631$	−34.9471			−1.39122			−0.695610	+	0.718419i	$0.744866\pi$
$632$	−2.15619	+	8.04700i	−0.0857685	+	0.320092i
$633$	−9.98020	+	2.67419i	−0.396677	+	0.106289i
$634$	13.4670	+	7.77515i	0.534841	+	0.308791i
$635$	9.15688	+	11.9888i	0.363380	+	0.475763i
$636$		−	9.40242i		−	0.372830i
$637$	16.7871	−	17.0454i	0.665128	−	0.675364i
$638$	−2.65587	+	2.65587i	−0.105147	+	0.105147i
$639$	−10.3677	+	5.98579i	−0.410140	+	0.236794i
$640$	2.06394	+	0.860320i	0.0815844	+	0.0340071i
$641$	5.61488	−	9.72526i	0.221774	−	0.384125i	−0.733572	−	0.679611i	$-0.762148\pi$
$641$	5.61488	−	9.72526i	0.221774	−	0.384125i	0.955347	+	0.295487i	$0.0954818\pi$
$642$	−11.8496	−	3.17510i	−0.467668	−	0.125311i
$643$	9.89036	+	9.89036i	0.390038	+	0.390038i	0.874701	−	0.484663i	$-0.161058\pi$
$643$	9.89036	+	9.89036i	0.390038	+	0.390038i	−0.484663	+	0.874701i	$0.661058\pi$
$644$	0.0177214	+	4.64164i	0.000698320	+	0.182906i
$645$	−3.77069	+	4.89140i	−0.148471	+	0.192599i
$646$	7.40955	+	12.8337i	0.291525	+	0.504936i
$647$	4.06147	+	15.1576i	0.159673	+	0.595908i	0.998660	+	0.0517559i	$0.0164818\pi$
$647$	4.06147	+	15.1576i	0.159673	+	0.595908i	−0.838987	+	0.544152i	$0.816852\pi$
$648$	0.258819	+	0.965926i	0.0101674	+	0.0379452i
$649$	−27.8712	−	48.2744i	−1.09404	−	1.89493i
$650$	−16.5258	+	4.34903i	−0.648196	+	0.170583i
$651$	7.42563	+	12.7489i	0.291033	+	0.499669i
$652$	−9.95676	−	9.95676i	−0.389937	−	0.389937i
$653$	−15.4045	−	4.12761i	−0.602823	−	0.161526i	−0.0555160	−	0.998458i	$-0.517680\pi$
$653$	−15.4045	−	4.12761i	−0.602823	−	0.161526i	−0.547307	+	0.836932i	$0.684347\pi$
$654$	0.168311	−	0.291523i	0.00658147	−	0.0113994i
$655$	−37.6521	+	15.4975i	−1.47119	+	0.605539i
$656$	2.17023	−	1.25298i	0.0847333	−	0.0489208i
$657$	3.44417	−	3.44417i	0.134370	−	0.134370i
$658$	8.99966	−	2.44832i	0.350843	−	0.0954453i
$659$		−	10.4778i		−	0.408157i	−0.978955	−	0.204078i	$-0.934580\pi$
$659$		−	10.4778i		−	0.408157i	0.978955	−	0.204078i	$-0.0654198\pi$
$660$	9.74931	−	7.44636i	0.379491	−	0.289849i
$661$	−20.9764	−	12.1107i	−0.815888	−	0.471053i	0.0331084	−	0.999452i	$-0.489459\pi$
$661$	−20.9764	−	12.1107i	−0.815888	−	0.471053i	−0.848996	+	0.528399i	$0.822793\pi$
$662$	−15.6344	+	4.18923i	−0.607648	+	0.162819i
$663$	1.87373	−	6.99285i	0.0727695	−	0.271580i
$664$	5.73154			0.222427
$665$	15.7781	−	38.2630i	0.611849	−	1.48378i
$666$	−9.80013			−0.379747
$667$	−0.310860	+	1.16015i	−0.0120366	+	0.0449210i
$668$	−8.29532	+	2.22272i	−0.320955	+	0.0859998i
$669$	−4.17862	−	2.41253i	−0.161555	−	0.0932736i
$670$	2.95427	−	22.0589i	0.114133	−	0.852211i
$671$			6.42808i			0.248153i
$672$	2.55820	+	0.675009i	0.0986845	+	0.0260390i
$673$	−1.16725	+	1.16725i	−0.0449943	+	0.0449943i	−0.729246	−	0.684252i	$-0.760129\pi$
$673$	−1.16725	+	1.16725i	−0.0449943	+	0.0449943i	0.684252	+	0.729246i	$0.260129\pi$
$674$	23.5218	−	13.5803i	0.906025	−	0.523094i
$675$	−4.34125	+	2.48063i	−0.167095	+	0.0954794i
$676$	−0.659666	+	1.14257i	−0.0253718	+	0.0439452i
$677$	−12.4001	−	3.32260i	−0.476575	−	0.127698i	0.0125322	−	0.999921i	$-0.496011\pi$
$677$	−12.4001	−	3.32260i	−0.476575	−	0.127698i	−0.489108	+	0.872223i	$0.662677\pi$
$678$	10.1896	+	10.1896i	0.391328	+	0.391328i
$679$	49.0947	−	0.187439i	1.88408	−	0.00719326i
$680$	−3.75130	−	2.89181i	−0.143856	−	0.110896i
$681$	9.04688	+	15.6697i	0.346677	+	0.600463i
$682$	7.91828	+	29.5514i	0.303207	+	1.13158i
$683$	5.52974	+	20.6373i	0.211589	+	0.789663i	0.987339	+	0.158622i	$0.0507051\pi$
$683$	5.52974	+	20.6373i	0.211589	+	0.789663i	−0.775750	+	0.631040i	$0.782628\pi$
$684$	3.49797	+	6.05866i	0.133748	+	0.231658i
$685$	4.84472	−	0.626811i	0.185107	−	0.0239492i
$686$	−9.44322	−	15.9319i	−0.360544	−	0.608283i
$687$	−6.82181	−	6.82181i	−0.260268	−	0.260268i
$688$	−2.66791	−	0.714864i	−0.101713	−	0.0272540i
$689$	−16.0673	+	27.8294i	−0.612116	+	1.06022i
$690$	1.50933	−	3.62095i	0.0574594	−	0.137847i
$691$	−37.0127	+	21.3693i	−1.40803	+	0.812927i	−0.995198	−	0.0978797i	$-0.968794\pi$
$691$	−37.0127	+	21.3693i	−1.40803	+	0.812927i	−0.412833	+	0.910807i	$0.635461\pi$
$692$	2.86311	−	2.86311i	0.108839	−	0.108839i
$693$	10.2247	−	10.3030i	0.388403	−	0.391380i
$694$			10.2657i			0.389681i
$695$	40.2135	+	5.38563i	1.52538	+	0.204289i
$696$	0.592889	+	0.342305i	0.0224734	+	0.0129750i
$697$	−5.12738	+	1.37388i	−0.194213	+	0.0520393i
$698$	1.71194	−	6.38903i	0.0647977	−	0.241828i
$699$	14.4733			0.547431
$700$	−0.00860549	+	13.2288i	−0.000325257	+	0.500000i
$701$	44.5959			1.68436			0.842182	−	0.539194i	$-0.181271\pi$
$701$	44.5959			1.68436			0.842182	+	0.539194i	$0.181271\pi$
$702$	0.884566	−	3.30124i	0.0333858	−	0.124597i
$703$	−66.2249	+	17.7449i	−2.49772	+	0.669262i
$704$	4.75127	+	2.74315i	0.179070	+	0.103386i
$705$	−7.81278	−	1.04633i	−0.294246	−	0.0394073i
$706$		−	13.6247i		−	0.512772i
$707$	−5.74208	−	21.1071i	−0.215953	−	0.793813i
$708$	−7.18441	+	7.18441i	−0.270007	+	0.270007i
$709$	35.8750	−	20.7125i	1.34732	−	0.777873i	0.359447	−	0.933166i	$-0.382965\pi$
$709$	35.8750	−	20.7125i	1.34732	−	0.777873i	0.987869	+	0.155293i	$0.0496320\pi$
$710$	10.2994	−	24.7086i	0.386529	−	0.927299i
$711$	4.16543	−	7.21474i	0.156216	−	0.270574i
$712$	6.93879	+	1.85924i	0.260042	+	0.0696781i
$713$	6.91777	+	6.91777i	0.259072	+	0.259072i
$714$	−4.86417	−	2.78362i	−0.182037	−	0.104175i
$715$	−41.5809	+	5.37974i	−1.55504	+	0.201191i
$716$	−1.83267	−	3.17428i	−0.0684900	−	0.118628i
$717$	7.75773	+	28.9523i	0.289718	+	1.08124i
$718$	4.47665	+	16.7071i	0.167067	+	0.623502i
$719$	−11.7839	−	20.4103i	−0.439464	−	0.761174i	0.558184	−	0.829717i	$-0.311498\pi$
$719$	−11.7839	−	20.4103i	−0.439464	−	0.761174i	−0.997648	+	0.0685431i	$0.978165\pi$
$720$	−1.77095	−	1.36519i	−0.0659993	−	0.0508777i
$721$	21.2760	−	12.3923i	0.792361	−	0.461512i
$722$	21.1730	+	21.1730i	0.787976	+	0.787976i
$723$	−16.0538	−	4.30159i	−0.597046	−	0.159978i
$724$	1.19992	−	2.07833i	0.0445948	−	0.0772405i
$725$	−0.900715	+	3.30242i	−0.0334517	+	0.122649i
$726$	16.5406	−	9.54974i	0.613881	−	0.354424i
$727$	3.38556	−	3.38556i	0.125563	−	0.125563i	−0.641532	−	0.767096i	$-0.721701\pi$
$727$	3.38556	−	3.38556i	0.125563	−	0.125563i	0.767096	+	0.641532i	$0.221701\pi$
$728$	−6.41829	−	6.36947i	−0.237878	−	0.236068i
$729$		−	1.00000i		−	0.0370370i
$730$	−1.44574	+	10.7950i	−0.0535091	+	0.399542i
$731$	5.06681	+	2.92532i	0.187403	+	0.108197i
$732$	1.13174	−	0.303248i	0.0418302	−	0.0112084i
$733$	10.1653	−	37.9373i	0.375463	−	1.40125i	−0.477204	−	0.878792i	$-0.658350\pi$
$733$	10.1653	−	37.9373i	0.375463	−	1.40125i	0.852667	−	0.522454i	$-0.174983\pi$
$734$	−25.8811			−0.955288
$735$	2.12685	+	15.5073i	0.0784501	+	0.571996i
$736$	1.75439			0.0646676
$737$	14.1330	−	52.7452i	0.520597	−	1.94289i
$738$	−2.42058	+	0.648592i	−0.0891027	+	0.0238750i
$739$	38.6211	+	22.2979i	1.42070	+	0.820242i	0.996359	−	0.0852593i	$-0.0271719\pi$
$739$	38.6211	+	22.2979i	1.42070	+	0.820242i	0.424343	+	0.905502i	$0.360505\pi$
$740$	17.4151	−	13.3014i	0.640193	−	0.488968i
$741$		−	23.9100i		−	0.878356i
$742$	17.6573	+	17.5230i	0.648222	+	0.643291i
$743$	24.7787	−	24.7787i	0.909041	−	0.909041i	−0.0871537	−	0.996195i	$-0.527777\pi$
$743$	24.7787	−	24.7787i	0.909041	−	0.909041i	0.996195	+	0.0871537i	$0.0277771\pi$
$744$	4.82932	−	2.78821i	0.177051	−	0.102221i
$745$	0.400435	−	0.164818i	0.0146708	−	0.00603847i
$746$	−4.58319	+	7.93832i	−0.167802	+	0.290642i
$747$	−5.53624	−	1.48343i	−0.202561	−	0.0542759i
$748$	−8.21752	−	8.21752i	−0.300462	−	0.300462i
$749$	28.0466	−	16.3358i	1.02480	−	0.596897i
$750$	4.34767	−	10.3004i	0.158754	−	0.376117i
$751$	−2.54731	−	4.41207i	−0.0929526	−	0.160999i	0.815800	−	0.578335i	$-0.196297\pi$
$751$	−2.54731	−	4.41207i	−0.0929526	−	0.160999i	−0.908752	+	0.417336i	$0.862964\pi$
$752$	−0.912383	−	3.40506i	−0.0332712	−	0.124170i
$753$	2.78645	+	10.3992i	0.101544	+	0.378967i
$754$	−1.16989	−	2.02632i	−0.0426051	−	0.0737941i
$755$	−29.1096	+	37.7614i	−1.05941	+	1.37428i
$756$	−2.29632	−	1.31412i	−0.0835164	−	0.0477940i
$757$	18.2623	+	18.2623i	0.663754	+	0.663754i	0.956263	−	0.292509i	$-0.0944900\pi$
$757$	18.2623	+	18.2623i	0.663754	+	0.663754i	−0.292509	+	0.956263i	$0.594490\pi$
$758$	−18.0503	−	4.83657i	−0.655618	−	0.175672i
$759$	4.81255	−	8.33558i	0.174685	−	0.302562i
$760$	−14.4392	−	6.01874i	−0.523764	−	0.218323i
$761$	24.3626	−	14.0657i	0.883142	−	0.509882i	0.0114488	−	0.999934i	$-0.496356\pi$
$761$	24.3626	−	14.0657i	0.883142	−	0.509882i	0.871693	+	0.490052i	$0.163022\pi$
$762$	4.77054	−	4.77054i	0.172819	−	0.172819i
$763$	0.233791	+	0.859384i	0.00846382	+	0.0311118i
$764$			8.07532i			0.292155i
$765$	2.87502	+	3.76418i	0.103947	+	0.136094i
$766$	17.1832	+	9.92072i	0.620854	+	0.358450i
$767$	33.5416	−	8.98745i	1.21112	−	0.324518i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	−3.03517			−0.109451			−0.0547256	−	0.998501i	$-0.517428\pi$
$769$	−3.03517			−0.109451			−0.0547256	+	0.998501i	$0.517428\pi$
$770$	−4.18557	+	32.1864i	−0.150838	+	1.15992i
$771$	15.0425			0.541742
$772$	−0.445821	+	1.66383i	−0.0160455	+	0.0598825i
$773$	−46.8575	+	12.5554i	−1.68535	+	0.451588i	−0.969183	−	0.246342i	$-0.920771\pi$
$773$	−46.8575	+	12.5554i	−1.68535	+	0.451588i	−0.716166	+	0.697930i	$0.754105\pi$
$774$	2.39198	+	1.38101i	0.0859781	+	0.0496395i
$775$	19.6273	+	19.8035i	0.705034	+	0.711363i
$776$		−	18.5562i		−	0.666128i
$777$	18.2642	−	18.4042i	0.655226	−	0.660248i
$778$	−3.62546	+	3.62546i	−0.129979	+	0.129979i
$779$	−15.1828	+	8.76579i	−0.543980	+	0.314067i
$780$	2.90876	+	7.06700i	0.104150	+	0.253039i
$781$	32.8398	−	56.8803i	1.17510	−	2.03534i
$782$	−3.58960	−	0.961830i	−0.128364	−	0.0343950i
$783$	−0.484092	−	0.484092i	−0.0173000	−	0.0173000i
$784$	−6.03528	+	3.54619i	−0.215546	+	0.126650i
$785$	1.05584	+	8.16078i	0.0376847	+	0.291271i
$786$	9.10455	+	15.7695i	0.324748	+	0.562481i
$787$	−9.83063	−	36.6884i	−0.350424	−	1.30780i	−0.886146	−	0.463406i	$-0.846627\pi$
$787$	−9.83063	−	36.6884i	−0.350424	−	1.30780i	0.535722	−	0.844394i	$-0.320039\pi$
$788$	−2.20045	−	8.21219i	−0.0783878	−	0.292547i
$789$	−11.2657	−	19.5128i	−0.401070	−	0.694674i
$790$	2.39022	+	18.4744i	0.0850403	+	0.657290i
$791$	−38.1256	+	0.145560i	−1.35559	+	0.00517553i
$792$	−3.87940	−	3.87940i	−0.137848	−	0.137848i
$793$	−3.86794	−	1.03641i	−0.137354	−	0.0368040i
$794$	13.1967	−	22.8574i	0.468334	−	0.811179i
$795$	−8.00229	−	19.4420i	−0.283812	−	0.689536i
$796$	−9.54181	+	5.50897i	−0.338200	+	0.195260i
$797$	−34.4058	+	34.4058i	−1.21871	+	1.21871i	−0.250632	+	0.968082i	$0.580638\pi$
$797$	−34.4058	+	34.4058i	−1.21871	+	1.21871i	−0.968082	+	0.250632i	$0.919362\pi$
$798$	−17.8970	−	4.72232i	−0.633546	−	0.167168i
$799$			7.46719i			0.264170i
$800$	4.99995	+	0.0223420i	0.176775	+	0.000789908i
$801$	−6.22115	−	3.59178i	−0.219813	−	0.126909i
$802$	16.6423	−	4.45930i	0.587661	−	0.157463i
$803$	−6.91632	+	25.8120i	−0.244071	+	0.910887i
$804$	−9.95313			−0.351020
$805$	3.98709	+	9.58274i	0.140527	+	0.337747i
$806$	−19.0585			−0.671307
$807$	−2.85799	+	10.6662i	−0.100606	+	0.375467i
$808$	−7.98595	+	2.13983i	−0.280945	+	0.0752789i
$809$	33.6569	+	19.4318i	1.18331	+	0.683186i	0.956779	−	0.290817i	$-0.0939271\pi$
$809$	33.6569	+	19.4318i	1.18331	+	0.683186i	0.226534	+	0.974003i	$0.427260\pi$
$810$	1.35727	+	1.77703i	0.0476894	+	0.0624384i
$811$			15.3545i			0.539168i	0.962977	+	0.269584i	$0.0868862\pi$
$811$			15.3545i			0.539168i	−0.962977	+	0.269584i	$0.913114\pi$
$812$	−1.74779	+	0.475477i	−0.0613352	+	0.0166860i
$813$	−3.54713	+	3.54713i	−0.124403	+	0.124403i
$814$	46.5631	−	26.8832i	1.63204	−	0.942257i
$815$	−29.0623	−	12.1142i	−1.01801	−	0.424340i
$816$	−1.05912	+	1.83445i	−0.0370767	+	0.0642187i
$817$	18.6645	+	5.00114i	0.652989	+	0.174968i
$818$	25.2535	+	25.2535i	0.882967	+	0.882967i
$819$	4.55106	+	7.81361i	0.159027	+	0.273030i
$820$	3.42113	−	4.43793i	0.119471	−	0.154979i
$821$	−11.9561	−	20.7086i	−0.417271	−	0.722735i	0.578393	−	0.815758i	$-0.303680\pi$
$821$	−11.9561	−	20.7086i	−0.417271	−	0.722735i	−0.995664	+	0.0930235i	$0.970347\pi$
$822$	−0.565438	−	2.11024i	−0.0197219	−	0.0736032i
$823$	−7.32768	−	27.3473i	−0.255427	−	0.953267i	−0.967852	−	0.251519i	$-0.919070\pi$
$823$	−7.32768	−	27.3473i	−0.255427	−	0.953267i	0.712425	−	0.701748i	$-0.247597\pi$
$824$	−4.65310	−	8.05941i	−0.162098	−	0.280763i
$825$	13.8218	−	23.6948i	0.481212	−	0.824949i
$826$	−0.102631	−	26.8814i	−0.00357099	−	0.935324i
$827$	20.7600	+	20.7600i	0.721898	+	0.721898i	0.968992	−	0.247094i	$-0.0794757\pi$
$827$	20.7600	+	20.7600i	0.721898	+	0.721898i	−0.247094	+	0.968992i	$0.579476\pi$
$828$	−1.69461	−	0.454069i	−0.0588917	−	0.0157800i
$829$	−4.14106	+	7.17253i	−0.143825	+	0.249112i	−0.928934	−	0.370246i	$-0.879274\pi$
$829$	−4.14106	+	7.17253i	−0.143825	+	0.249112i	0.785109	+	0.619358i	$0.212607\pi$
$830$	11.8515	−	4.87805i	0.411371	−	0.169320i
$831$	5.48632	−	3.16753i	0.190318	−	0.109880i
$832$	−2.41668	+	2.41668i	−0.0837832	+	0.0837832i
$833$	14.2928	−	3.94695i	0.495215	−	0.136754i
$834$		−	18.1446i		−	0.628295i
$835$	−15.2610	+	11.6561i	−0.528130	+	0.403377i
$836$	−33.2396	−	19.1909i	−1.14962	−	0.663731i
$837$	−5.38640	+	1.44328i	−0.186181	+	0.0498871i
$838$	3.63417	−	13.5629i	0.125540	−	0.468523i
$839$	−8.03334			−0.277342			−0.138671	−	0.990339i	$-0.544283\pi$
$839$	−8.03334			−0.277342			−0.138671	+	0.990339i	$0.544283\pi$
$840$	5.86424	−	0.781491i	0.202335	−	0.0269640i
$841$	28.5313			0.983838
$842$	6.32378	−	23.6007i	0.217932	−	0.813333i
$843$	28.4681	−	7.62799i	0.980492	−	0.262722i
$844$	−8.94800	−	5.16613i	−0.308003	−	0.177826i
$845$	−0.391601	+	2.92401i	−0.0134715	+	0.100589i
$846$			3.52518i			0.121198i
$847$	−12.8923	+	48.8602i	−0.442985	+	1.67886i
$848$	6.64852	−	6.64852i	0.228311	−	0.228311i
$849$	0.0847197	−	0.0489129i	0.00290757	−	0.00167869i
$850$	−10.2180	−	2.78690i	−0.350474	−	0.0955898i
$851$	8.59662	−	14.8898i	0.294688	−	0.510415i
$852$	−11.5637	−	3.09847i	−0.396165	−	0.106152i
$853$	−23.8654	−	23.8654i	−0.817136	−	0.817136i	0.168556	−	0.985692i	$-0.446089\pi$
$853$	−23.8654	−	23.8654i	−0.817136	−	0.817136i	−0.985692	+	0.168556i	$0.946089\pi$
$854$	−1.53970	+	2.69051i	−0.0526875	+	0.0920673i
$855$	12.3894	+	9.55079i	0.423709	+	0.326630i
$856$	−6.13383	−	10.6241i	−0.209650	−	0.363124i
$857$	6.21598	+	23.1984i	0.212334	+	0.792441i	0.987088	+	0.160178i	$0.0512069\pi$
$857$	6.21598	+	23.1984i	0.212334	+	0.792441i	−0.774754	+	0.632263i	$0.782126\pi$
$858$	4.85299	+	18.1116i	0.165678	+	0.618320i
$859$	3.26421	+	5.65377i	0.111373	+	0.192904i	0.916324	−	0.400437i	$-0.131142\pi$
$859$	3.26421	+	5.65377i	0.111373	+	0.192904i	−0.804951	+	0.593341i	$0.797808\pi$
$860$	−6.12502	+	0.792457i	−0.208862	+	0.0270226i
$861$	3.29314	−	5.75451i	0.112230	−	0.196113i
$862$	−27.4196	−	27.4196i	−0.933914	−	0.933914i
$863$	15.9949	+	4.28582i	0.544473	+	0.145891i	0.520563	−	0.853823i	$-0.325722\pi$
$863$	15.9949	+	4.28582i	0.544473	+	0.145891i	0.0239095	+	0.999714i	$0.492389\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	3.48347	−	8.35699i	0.118442	−	0.284146i
$866$	−9.62282	+	5.55574i	−0.326997	+	0.188792i
$867$	−8.84805	+	8.84805i	−0.300496	+	0.300496i
$868$	−3.76413	+	14.2656i	−0.127763	+	0.484205i
$869$			45.7056i			1.55046i
$870$	1.51729	+	0.203204i	0.0514408	+	0.00688927i
$871$	29.4594	+	17.0084i	0.998194	+	0.576308i
$872$	0.325151	−	0.0871241i	0.0110110	−	0.00295039i
$873$	−4.80269	+	17.9239i	−0.162547	+	0.606632i
$874$	−12.2736			−0.415160
$875$	11.2410	+	27.3613i	0.380017	+	0.924980i
$876$	4.87079			0.164569
$877$	9.56712	−	35.7050i	0.323059	−	1.20567i	−0.593190	−	0.805062i	$-0.702132\pi$
$877$	9.56712	−	35.7050i	0.323059	−	1.20567i	0.916249	−	0.400609i	$-0.131202\pi$
$878$	20.4080	−	5.46830i	0.688736	−	0.184546i
$879$	17.1557	+	9.90484i	0.578647	+	0.334082i
$880$	12.1592	+	1.62843i	0.409886	+	0.0548944i
$881$		−	17.4940i		−	0.589386i	−0.955592	−	0.294693i	$-0.904783\pi$
$881$		−	17.4940i		−	0.589386i	0.955592	−	0.294693i	$-0.0952174\pi$
$882$	6.74745	−	1.86331i	0.227198	−	0.0627409i
$883$	−14.0857	+	14.0857i	−0.474022	+	0.474022i	−0.903214	−	0.429191i	$-0.858799\pi$
$883$	−14.0857	+	14.0857i	−0.474022	+	0.474022i	0.429191	+	0.903214i	$0.358799\pi$
$884$	6.26961	−	3.61976i	0.210870	−	0.121746i
$885$	−8.74110	+	20.9702i	−0.293829	+	0.704907i
$886$	−3.35579	+	5.81240i	−0.112740	+	0.195271i
$887$	−39.6163	−	10.6152i	−1.33018	−	0.356422i	−0.477401	−	0.878686i	$-0.658421\pi$
$887$	−39.6163	−	10.6152i	−1.33018	−	0.356422i	−0.852784	+	0.522264i	$0.825088\pi$
$888$	−6.92974	−	6.92974i	−0.232547	−	0.232547i
$889$	0.0681482	+	17.8496i	0.00228562	+	0.598657i
$890$	15.9302	−	2.06105i	0.533980	−	0.0690865i
$891$	2.74315	+	4.75127i	0.0918990	+	0.159174i
$892$	−1.24882	−	4.66064i	−0.0418134	−	0.156050i
$893$	6.38297	+	23.8216i	0.213598	+	0.797158i
$894$	−0.0968279	−	0.167711i	−0.00323841	−	0.00560909i
$895$	−6.49112	−	5.00389i	−0.216974	−	0.167262i
$896$	1.33161	+	2.28622i	0.0444861	+	0.0763773i
$897$	4.23979	+	4.23979i	0.141563	+	0.141563i
$898$	8.00732	+	2.14555i	0.267208	+	0.0715981i
$899$	−1.90883	+	3.30620i	−0.0636632	+	0.110268i
$900$	−4.82380	−	1.31566i	−0.160793	−	0.0438554i
$901$	−17.2483	+	9.95832i	−0.574625	+	0.331760i
$902$	9.72165	−	9.72165i	0.323695	−	0.323695i
$903$	−7.05136	+	1.91829i	−0.234654	+	0.0638367i
$904$			14.4102i			0.479277i
$905$	0.712317	−	5.31873i	0.0236782	−	0.176801i
$906$	18.4660	+	10.6614i	0.613493	+	0.354200i
$907$	−19.3010	+	5.17169i	−0.640879	+	0.171723i	−0.564602	−	0.825364i	$-0.690970\pi$
$907$	−19.3010	+	5.17169i	−0.640879	+	0.171723i	−0.0762776	+	0.997087i	$0.524304\pi$
$908$	−4.68301	+	17.4772i	−0.155411	+	0.580002i
$909$	8.26766			0.274221
$910$	−18.6925	−	7.70803i	−0.619650	−	0.255519i
$911$	−21.3131			−0.706136			−0.353068	−	0.935598i	$-0.614862\pi$
$911$	−21.3131			−0.706136			−0.353068	+	0.935598i	$0.614862\pi$
$912$	−1.81068	+	6.75755i	−0.0599576	+	0.223765i
$913$	30.3735	−	8.13855i	1.00522	−	0.269347i
$914$	−19.1236	−	11.0410i	−0.632551	−	0.365204i
$915$	2.08207	−	1.59025i	0.0688313	−	0.0525722i
$916$		−	9.64749i		−	0.318762i
$917$	−46.5824	−	12.2913i	−1.53829	−	0.405894i
$918$	1.49783	−	1.49783i	0.0494356	−	0.0494356i
$919$	−11.4010	+	6.58238i	−0.376085	+	0.217133i	−0.676114	−	0.736797i	$-0.736337\pi$
$919$	−11.4010	+	6.58238i	−0.376085	+	0.217133i	0.300029	+	0.953930i	$0.403004\pi$
$920$	3.62766	−	1.49314i	0.119600	−	0.0492274i
$921$	2.15894	−	3.73939i	0.0711394	−	0.123217i
$922$	18.3652	+	4.92093i	0.604824	+	0.162062i
$923$	28.9315	+	28.9315i	0.952291	+	0.952291i
$924$	14.5153	−	0.0554181i	0.477518	−	0.00182312i
$925$	24.6897	−	42.3259i	0.811793	−	1.39167i
$926$	11.7444	+	20.3419i	0.385946	+	0.668478i
$927$	2.40862	+	8.98910i	0.0791095	+	0.295241i
$928$	0.177190	+	0.661282i	0.00581655	+	0.0217076i
$929$	2.59922	+	4.50199i	0.0852777	+	0.147705i	0.905510	−	0.424326i	$-0.139489\pi$
$929$	2.59922	+	4.50199i	0.0852777	+	0.147705i	−0.820232	+	0.572031i	$0.806156\pi$
$930$	7.61288	−	9.87553i	0.249636	−	0.323831i
$931$	42.2224	−	24.8089i	1.38378	−	0.813078i
$932$	10.2342	+	10.2342i	0.335232	+	0.335232i
$933$	8.15755	+	2.18581i	0.267066	+	0.0715602i
$934$	7.99472	−	13.8473i	0.261595	−	0.453096i
$935$	−23.9857	−	9.99806i	−0.784417	−	0.326971i
$936$	2.95981	−	1.70885i	0.0967446	−	0.0558555i
$937$	−3.54515	+	3.54515i	−0.115815	+	0.115815i	−0.762639	−	0.646824i	$-0.776097\pi$
$937$	−3.54515	+	3.54515i	−0.115815	+	0.115815i	0.646824	+	0.762639i	$0.276097\pi$
$938$	18.5494	−	18.6916i	0.605658	−	0.610301i
$939$		−	19.4096i		−	0.633409i
$940$	−4.78460	−	6.26434i	−0.156056	−	0.204320i
$941$	8.88464	+	5.12955i	0.289631	+	0.167219i	0.637775	−	0.770222i	$-0.279855\pi$
$941$	8.88464	+	5.12955i	0.289631	+	0.167219i	−0.348144	+	0.937441i	$0.613188\pi$
$942$	3.55464	−	0.952462i	0.115816	−	0.0310329i
$943$	1.13788	−	4.24663i	0.0370545	−	0.138289i
$944$	−10.1603			−0.330689
$945$	−5.86668	−	0.762913i	−0.190843	−	0.0248176i
$946$	−15.1533			−0.492676
$947$	7.26545	−	27.1150i	0.236096	−	0.881120i	−0.741556	−	0.670890i	$-0.765912\pi$
$947$	7.26545	−	27.1150i	0.236096	−	0.881120i	0.977652	−	0.210230i	$-0.0674213\pi$
$948$	8.04700	−	2.15619i	0.261354	−	0.0700297i
$949$	−14.4166	−	8.32344i	−0.467983	−	0.270190i
$950$	−34.9793	−	0.156303i	−1.13488	−	0.00507113i
$951$		−	15.5503i		−	0.504253i
$952$	−1.47117	−	5.40781i	−0.0476809	−	0.175268i
$953$	−29.6648	+	29.6648i	−0.960937	+	0.960937i	−0.999265	−	0.0383279i	$-0.987797\pi$
$953$	−29.6648	+	29.6648i	−0.960937	+	0.960937i	0.0383279	+	0.999265i	$0.487797\pi$
$954$	−8.14273	+	4.70121i	−0.263631	+	0.152207i
$955$	6.87282	+	16.6979i	0.222399	+	0.540330i
$956$	−14.9868	+	25.9579i	−0.484708	+	0.839538i
$957$	3.62799	+	0.972117i	0.117276	+	0.0314241i
$958$	−6.37140	−	6.37140i	−0.205850	−	0.205850i
$959$	5.01674	+	2.87093i	0.161999	+	0.0927073i
$960$	−0.286912	−	2.21758i	−0.00926003	−	0.0715722i
$961$	0.0482042	+	0.0834922i	0.00155498	+	0.00269330i
$962$	8.66886	+	32.3526i	0.279495	+	1.04309i
$963$	3.17510	+	11.8496i	0.102316	+	0.381850i
$964$	−8.31003	−	14.3934i	−0.267648	−	0.463580i
$965$	0.494211	+	3.81984i	0.0159092	+	0.122965i
$966$	4.01092	−	2.33617i	0.129049	−	0.0751650i
$967$	−3.20889	−	3.20889i	−0.103191	−	0.103191i	0.653626	−	0.756817i	$-0.273247\pi$
$967$	−3.20889	−	3.20889i	−0.103191	−	0.103191i	−0.756817	+	0.653626i	$0.773247\pi$
$968$	18.4487	+	4.94331i	0.592963	+	0.158884i
$969$	7.40955	−	12.8337i	0.238029	−	0.412278i
$970$	−15.7930	−	38.3698i	−0.507081	−	1.23198i
$971$	51.1699	−	29.5430i	1.64212	−	0.948079i	0.662042	−	0.749467i	$-0.269690\pi$
$971$	51.1699	−	29.5430i	1.64212	−	0.948079i	0.980078	−	0.198612i	$-0.0636433\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	34.0747	+	33.8155i	1.09239	+	1.08408i
$974$			9.34012i			0.299277i
$975$	12.0293	+	12.1373i	0.385245	+	0.388704i
$976$	1.01469	+	0.585830i	0.0324794	+	0.0187520i
$977$	11.4234	−	3.06089i	0.365467	−	0.0979266i	−0.0714120	−	0.997447i	$-0.522751\pi$
$977$	11.4234	−	3.06089i	0.365467	−	0.0979266i	0.436879	+	0.899520i	$0.356084\pi$
$978$	−3.64443	+	13.6012i	−0.116536	+	0.434918i
$979$	39.4112			1.25959
$980$	−9.46141	+	12.4692i	−0.302234	+	0.398315i
$981$	−0.336622			−0.0107475
$982$	0.539730	−	2.01430i	0.0172235	−	0.0642788i
$983$	−36.7070	+	9.83561i	−1.17077	+	0.313707i	−0.791260	−	0.611480i	$-0.790575\pi$
$983$	−36.7070	+	9.83561i	−1.17077	+	0.313707i	−0.379511	+	0.925187i	$0.623908\pi$
$984$	−2.17023	−	1.25298i	−0.0691844	−	0.0399437i
$985$	−11.5393	−	15.1081i	−0.367673	−	0.481384i
$986$		−	1.45017i		−	0.0461829i
$987$	−6.62013	−	6.56977i	−0.210721	−	0.209118i
$988$	16.9069	−	16.9069i	0.537881	−	0.537881i
$989$	−4.19647	+	2.42283i	−0.133440	+	0.0770416i
$990$	−11.3234	−	4.71997i	−0.359881	−	0.150011i
$991$	−4.00630	+	6.93911i	−0.127264	+	0.220428i	−0.922616	−	0.385720i	$-0.873953\pi$
$991$	−4.00630	+	6.93911i	−0.127264	+	0.220428i	0.795352	+	0.606148i	$0.207286\pi$
$992$	5.38640	+	1.44328i	0.171018	+	0.0458243i
$993$	11.4452	+	11.4452i	0.363202	+	0.363202i
$994$	27.3697	−	15.9415i	0.868114	−	0.505635i
$995$	−15.0416	+	19.5122i	−0.476851	+	0.618577i
$996$	−2.86577	−	4.96366i	−0.0908054	−	0.157280i
$997$	11.0150	+	41.1086i	0.348849	+	1.30192i	0.888051	+	0.459745i	$0.152059\pi$
$997$	11.0150	+	41.1086i	0.348849	+	1.30192i	−0.539202	+	0.842176i	$0.681274\pi$
$998$	3.47453	+	12.9671i	0.109984	+	0.410468i
$999$	4.90007	+	8.48716i	0.155031	+	0.268522i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.u.b.157.3	yes	16
3.2	odd	2		630.2.bv.b.577.2		16
5.2	odd	4		1050.2.bc.h.493.3		16
5.3	odd	4		210.2.u.a.73.1	✓	16
5.4	even	2		1050.2.bc.g.157.2		16
7.3	odd	6		1470.2.m.d.97.6		16
7.4	even	3		1470.2.m.e.97.7		16
7.5	odd	6		210.2.u.a.187.1	yes	16
15.8	even	4		630.2.bv.a.73.4		16
21.5	even	6		630.2.bv.a.397.4		16
35.3	even	12		1470.2.m.e.1273.7		16
35.12	even	12		1050.2.bc.g.943.2		16
35.18	odd	12		1470.2.m.d.1273.6		16
35.19	odd	6		1050.2.bc.h.607.3		16
35.33	even	12	inner	210.2.u.b.103.3	yes	16
105.68	odd	12		630.2.bv.b.523.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.1	✓	16	5.3	odd	4
210.2.u.a.187.1	yes	16	7.5	odd	6
210.2.u.b.103.3	yes	16	35.33	even	12	inner
210.2.u.b.157.3	yes	16	1.1	even	1	trivial
630.2.bv.a.73.4		16	15.8	even	4
630.2.bv.a.397.4		16	21.5	even	6
630.2.bv.b.523.2		16	105.68	odd	12
630.2.bv.b.577.2		16	3.2	odd	2
1050.2.bc.g.157.2		16	5.4	even	2
1050.2.bc.g.943.2		16	35.12	even	12
1050.2.bc.h.493.3		16	5.2	odd	4
1050.2.bc.h.607.3		16	35.19	odd	6
1470.2.m.d.97.6		16	7.3	odd	6
1470.2.m.d.1273.6		16	35.18	odd	12
1470.2.m.e.97.7		16	7.4	even	3
1470.2.m.e.1273.7		16	35.3	even	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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.21628 - 0.296818i) q^{5} +1.00000i q^{6} +(-1.87796 - 1.86367i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.21628 - 0.296818i) q^{5} +1.00000i q^{6} +(-1.87796 - 1.86367i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-0.860320 + 2.06394i) q^{10} +(-2.74315 + 4.75127i) q^{11} +(0.965926 + 0.258819i) q^{12} +(-2.41668 - 2.41668i) q^{13} +(-2.28622 + 1.33161i) q^{14} +(2.21758 - 0.286912i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.548242 - 2.04607i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-3.49797 - 6.05866i) q^{19} +(1.77095 + 1.36519i) q^{20} +(2.29632 + 1.31412i) q^{21} +(3.87940 + 3.87940i) q^{22} +(1.69461 + 0.454069i) q^{23} +(0.500000 - 0.866025i) q^{24} +(4.82380 + 1.31566i) q^{25} +(-2.95981 + 1.70885i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.694523 + 2.55297i) q^{28} +0.684610i q^{29} +(0.296818 - 2.21628i) q^{30} +(4.82932 + 2.78821i) q^{31} +(0.965926 - 0.258819i) q^{32} +(1.41996 - 5.29936i) q^{33} -2.11825 q^{34} +(3.60891 + 4.68783i) q^{35} -1.00000 q^{36} +(2.53646 - 9.46620i) q^{37} +(-6.75755 + 1.81068i) q^{38} +(2.95981 + 1.70885i) q^{39} +(1.77703 - 1.35727i) q^{40} -2.50597i q^{41} +(1.86367 - 1.87796i) q^{42} +(-1.95305 + 1.95305i) q^{43} +(4.75127 - 2.74315i) q^{44} +(-2.06776 + 0.851088i) q^{45} +(0.877194 - 1.51935i) q^{46} +(-3.40506 - 0.912383i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(0.0534500 + 6.99980i) q^{49} +(2.51932 - 4.31891i) q^{50} +(1.05912 + 1.83445i) q^{51} +(0.884566 + 3.30124i) q^{52} +(-2.43353 - 9.08204i) q^{53} +(0.500000 + 0.866025i) q^{54} +(7.48985 - 9.71594i) q^{55} +(2.64573 - 0.0101012i) q^{56} +(4.94687 + 4.94687i) q^{57} +(0.661282 + 0.177190i) q^{58} +(-5.08015 + 8.79907i) q^{59} +(-2.06394 - 0.860320i) q^{60} +(1.01469 - 0.585830i) q^{61} +(3.94312 - 3.94312i) q^{62} +(-2.55820 - 0.675009i) q^{63} -1.00000i q^{64} +(4.63872 + 6.07335i) q^{65} +(-4.75127 - 2.74315i) q^{66} +(-9.61398 + 2.57606i) q^{67} +(-0.548242 + 2.04607i) q^{68} -1.75439 q^{69} +(5.46215 - 2.27264i) q^{70} -11.9716 q^{71} +(-0.258819 + 0.965926i) q^{72} +(4.70482 - 1.26065i) q^{73} +(-8.48716 - 4.90007i) q^{74} +(-4.99995 - 0.0223420i) q^{75} +6.99593i q^{76} +(14.0063 - 3.81036i) q^{77} +(2.41668 - 2.41668i) q^{78} +(7.21474 - 4.16543i) q^{79} +(-0.851088 - 2.06776i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-2.42058 - 0.648592i) q^{82} +(-4.05281 - 4.05281i) q^{83} +(-1.33161 - 2.28622i) q^{84} +(0.607749 + 4.69739i) q^{85} +(1.38101 + 2.39198i) q^{86} +(-0.177190 - 0.661282i) q^{87} +(-1.41996 - 5.29936i) q^{88} +(-3.59178 - 6.22115i) q^{89} +(0.286912 + 2.21758i) q^{90} +(0.0345228 + 9.04232i) q^{91} +(-1.24054 - 1.24054i) q^{92} +(-5.38640 - 1.44328i) q^{93} +(-1.76259 + 3.05289i) q^{94} +(5.95416 + 14.4659i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-13.1212 + 13.1212i) q^{97} +(6.77512 + 1.76005i) q^{98} +5.48630i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} - 4 q^{7}+O(q^{10}) \) 16 * q + 12 * q^5 - 4 * q^7	\( 16 q + 12 q^{5} - 4 q^{7} + 4 q^{10} + 4 q^{11} + 16 q^{13} - 16 q^{14} + 4 q^{15} + 8 q^{16} + 12 q^{17} + 8 q^{19} + 8 q^{20} + 8 q^{21} + 4 q^{22} - 40 q^{23} + 8 q^{24} + 16 q^{25} - 12 q^{26} - 4 q^{28} - 4 q^{30} - 24 q^{31} + 4 q^{33} - 16 q^{34} - 44 q^{35} - 16 q^{36} - 8 q^{37} - 20 q^{38} + 12 q^{39} + 8 q^{42} - 24 q^{43} - 4 q^{45} - 4 q^{46} - 52 q^{49} + 8 q^{51} + 8 q^{52} - 28 q^{53} + 8 q^{54} + 56 q^{55} + 8 q^{56} - 8 q^{57} - 12 q^{58} - 8 q^{59} + 24 q^{61} - 8 q^{62} - 4 q^{63} + 16 q^{65} - 84 q^{67} + 12 q^{68} + 8 q^{69} + 4 q^{70} - 32 q^{71} + 16 q^{73} + 24 q^{74} - 24 q^{75} + 44 q^{77} - 16 q^{78} - 12 q^{79} + 12 q^{80} + 8 q^{81} + 36 q^{82} + 16 q^{83} - 4 q^{84} + 8 q^{85} - 8 q^{86} + 48 q^{87} - 4 q^{88} + 16 q^{89} + 8 q^{91} + 8 q^{92} - 32 q^{93} - 8 q^{94} + 72 q^{95} - 44 q^{97} + 24 q^{98}+O(q^{100}) \) 16 * q + 12 * q^5 - 4 * q^7 + 4 * q^10 + 4 * q^11 + 16 * q^13 - 16 * q^14 + 4 * q^15 + 8 * q^16 + 12 * q^17 + 8 * q^19 + 8 * q^20 + 8 * q^21 + 4 * q^22 - 40 * q^23 + 8 * q^24 + 16 * q^25 - 12 * q^26 - 4 * q^28 - 4 * q^30 - 24 * q^31 + 4 * q^33 - 16 * q^34 - 44 * q^35 - 16 * q^36 - 8 * q^37 - 20 * q^38 + 12 * q^39 + 8 * q^42 - 24 * q^43 - 4 * q^45 - 4 * q^46 - 52 * q^49 + 8 * q^51 + 8 * q^52 - 28 * q^53 + 8 * q^54 + 56 * q^55 + 8 * q^56 - 8 * q^57 - 12 * q^58 - 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 + 16 * q^65 - 84 * q^67 + 12 * q^68 + 8 * q^69 + 4 * q^70 - 32 * q^71 + 16 * q^73 + 24 * q^74 - 24 * q^75 + 44 * q^77 - 16 * q^78 - 12 * q^79 + 12 * q^80 + 8 * q^81 + 36 * q^82 + 16 * q^83 - 4 * q^84 + 8 * q^85 - 8 * q^86 + 48 * q^87 - 4 * q^88 + 16 * q^89 + 8 * q^91 + 8 * q^92 - 32 * q^93 - 8 * q^94 + 72 * q^95 - 44 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more