LMFDB - Embedded newform 630.2.bv.b.577.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(73,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.73"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bv (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,-12,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.03057532734$
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:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			577.2
Root			$0.277956 + 0.213283i$ of defining polynomial
Character	$\chi$	$=$	630.577
Dual form			630.2.bv.b.523.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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			0
$3$		0			0
$4$	−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
$6$		0			0
$7$	−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			0
$10$	−0.860320	+	2.06394i	−0.272057	+	0.652675i
$11$	2.74315	−	4.75127i	0.827091	−	1.43256i	−0.0732202	−	0.997316i	$-0.523328\pi$
$11$	2.74315	−	4.75127i	0.827091	−	1.43256i	0.900311	−	0.435247i	$-0.143339\pi$
$12$		0			0
$13$	−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
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.548242	+	2.04607i	0.132968	+	0.496244i	0.999998	−	0.00201209i	$-0.000640467\pi$
$17$	0.548242	+	2.04607i	0.132968	+	0.496244i	−0.867030	+	0.498256i	$0.833974\pi$
$18$		0			0
$19$	−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
$21$		0			0
$22$	3.87940	+	3.87940i	0.827091	+	0.827091i
$23$	−1.69461	−	0.454069i	−0.353350	−	0.0946800i	0.0777776	−	0.996971i	$-0.475218\pi$
$23$	−1.69461	−	0.454069i	−0.353350	−	0.0946800i	−0.431128	+	0.902291i	$0.641884\pi$
$24$		0			0
$25$	4.82380	+	1.31566i	0.964760	+	0.263133i
$26$	2.95981	−	1.70885i	0.580467	−	0.335133i
$27$		0			0
$28$	0.694523	+	2.55297i	0.131252	+	0.482465i
$29$		−	0.684610i		−	0.127129i	−0.997978	−	0.0635644i	$-0.979753\pi$
$29$		−	0.684610i		−	0.127129i	0.997978	−	0.0635644i	$-0.0202468\pi$
$30$		0			0
$31$	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
$33$		0			0
$34$	−2.11825			−0.363276
$35$	−3.60891	−	4.68783i	−0.610017	−	0.792388i
$36$		0			0
$37$	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
$39$		0			0
$40$	1.77703	−	1.35727i	0.280973	−	0.214602i
$41$			2.50597i			0.391366i	0.980667	+	0.195683i	$0.0626924\pi$
$41$			2.50597i			0.391366i	−0.980667	+	0.195683i	$0.937308\pi$
$42$		0			0
$43$	−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
$45$		0			0
$46$	0.877194	−	1.51935i	0.129335	−	0.224015i
$47$	3.40506	+	0.912383i	0.496679	+	0.133085i	0.498458	−	0.866914i	$-0.333900\pi$
$47$	3.40506	+	0.912383i	0.496679	+	0.133085i	−0.00177938	+	0.999998i	$0.500566\pi$
$48$		0			0
$49$	0.0534500	+	6.99980i	0.00763571	+	0.999971i
$50$	−2.51932	+	4.31891i	−0.356286	+	0.610787i
$51$		0			0
$52$	0.884566	+	3.30124i	0.122667	+	0.457800i
$53$	2.43353	+	9.08204i	0.334270	+	1.24751i	0.904658	+	0.426138i	$0.140126\pi$
$53$	2.43353	+	9.08204i	0.334270	+	1.24751i	−0.570388	+	0.821376i	$0.693207\pi$
$54$		0			0
$55$	7.48985	−	9.71594i	1.00993	−	1.31010i
$56$	−2.64573	+	0.0101012i	−0.353551	+	0.00134983i
$57$		0			0
$58$	0.661282	+	0.177190i	0.0868306	+	0.0232662i
$59$	5.08015	−	8.79907i	0.661379	−	1.14554i	−0.318875	−	0.947797i	$-0.603305\pi$
$59$	5.08015	−	8.79907i	0.661379	−	1.14554i	0.980253	−	0.197745i	$-0.0633618\pi$
$60$		0			0
$61$	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
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−4.63872	−	6.07335i	−0.575363	−	0.753306i
$66$		0			0
$67$	−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
$69$		0			0
$70$	5.46215	−	2.27264i	0.652852	−	0.271632i
$71$	11.9716			1.42077			0.710383	−	0.703816i	$-0.248522\pi$
$71$	11.9716			1.42077			0.710383	+	0.703816i	$0.248522\pi$
$72$		0			0
$73$	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
$75$		0			0
$76$			6.99593i			0.802489i
$77$	−14.0063	+	3.81036i	−1.59617	+	0.434231i
$78$		0			0
$79$	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			0
$82$	−2.42058	−	0.648592i	−0.267308	−	0.0716250i
$83$	4.05281	+	4.05281i	0.444854	+	0.444854i	0.893639	−	0.448786i	$-0.148143\pi$
$83$	4.05281	+	4.05281i	0.444854	+	0.444854i	−0.448786	+	0.893639i	$0.648143\pi$
$84$		0			0
$85$	0.607749	+	4.69739i	0.0659197	+	0.509503i
$86$	−1.38101	−	2.39198i	−0.148918	−	0.257934i
$87$		0			0
$88$	−1.41996	−	5.29936i	−0.151368	−	0.564913i
$89$	3.59178	+	6.22115i	0.380728	+	0.659440i	0.991166	−	0.132623i	$-0.0423401\pi$
$89$	3.59178	+	6.22115i	0.380728	+	0.659440i	−0.610439	+	0.792064i	$0.709007\pi$
$90$		0			0
$91$	0.0345228	+	9.04232i	0.00361897	+	0.947892i
$92$	1.24054	+	1.24054i	0.129335	+	0.129335i
$93$		0			0
$94$	−1.76259	+	3.05289i	−0.181797	+	0.314882i
$95$	−5.95416	−	14.4659i	−0.610884	−	1.48417i
$96$		0			0
$97$	−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
$99$		0			0
$100$	−3.51970	−	3.55130i	−0.351970	−	0.355130i
$101$	−7.16001	−	4.13383i	−0.712447	−	0.411332i	0.0995192	−	0.995036i	$-0.468270\pi$
$101$	−7.16001	−	4.13383i	−0.712447	−	0.411332i	−0.811967	+	0.583704i	$0.801603\pi$
$102$		0			0
$103$	−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
$105$		0			0
$106$	−9.40242			−0.913244
$107$	3.17510	−	11.8496i	0.306949	−	1.14555i	−0.624306	−	0.781180i	$-0.714618\pi$
$107$	3.17510	−	11.8496i	0.306949	−	1.14555i	0.931255	−	0.364369i	$-0.118715\pi$
$108$		0			0
$109$	−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
$111$		0			0
$112$	0.675009	−	2.55820i	0.0637823	−	0.241727i
$113$	−10.1896	+	10.1896i	−0.958555	+	0.958555i	−0.999175	−	0.0406198i	$-0.987067\pi$
$113$	−10.1896	+	10.1896i	−0.958555	+	0.958555i	0.0406198	+	0.999175i	$0.487067\pi$
$114$		0			0
$115$	−3.62095	−	1.50933i	−0.337656	−	0.140746i
$116$	−0.342305	+	0.592889i	−0.0317822	+	0.0550484i
$117$		0			0
$118$	7.18441	+	7.18441i	0.661379	+	0.661379i
$119$	2.78362	−	4.86417i	0.255174	−	0.445898i
$120$		0			0
$121$	−9.54974	−	16.5406i	−0.868158	−	1.50369i
$122$	0.303248	+	1.13174i	0.0274548	+	0.102463i
$123$		0			0
$124$	−2.78821	−	4.82932i	−0.250388	−	0.433686i
$125$	10.3004	+	4.34767i	0.921294	+	0.388867i
$126$		0			0
$127$	−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
$129$		0			0
$130$	7.06700	−	2.90876i	0.619817	−	0.255116i
$131$	−15.7695	+	9.10455i	−1.37779	+	0.795468i	−0.991893	−	0.127074i	$-0.959442\pi$
$131$	−15.7695	+	9.10455i	−1.37779	+	0.795468i	−0.385898	+	0.922542i	$0.626108\pi$
$132$		0			0
$133$	−4.72232	+	17.8970i	−0.409477	+	1.55186i
$134$		−	9.95313i		−	0.859819i
$135$		0			0
$136$	1.83445	+	1.05912i	0.157303	+	0.0908190i
$137$	2.11024	−	0.565438i	0.180290	−	0.0483086i	−0.167544	−	0.985865i	$-0.553584\pi$
$137$	2.11024	−	0.565438i	0.180290	−	0.0483086i	0.347835	+	0.937556i	$0.386917\pi$
$138$		0			0
$139$	−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
$141$		0			0
$142$	−3.09847	+	11.5637i	−0.260018	+	0.970401i
$143$	−18.1116	+	4.85299i	−1.51457	+	0.405828i
$144$		0			0
$145$	0.203204	−	1.51729i	0.0168752	−	0.126004i
$146$			4.87079i			0.403109i
$147$		0			0
$148$	−6.92974	+	6.92974i	−0.569621	+	0.569621i
$149$	0.167711	−	0.0968279i	0.0137394	−	0.00793245i	−0.493115	−	0.869964i	$-0.664142\pi$
$149$	0.167711	−	0.0968279i	0.0137394	−	0.00793245i	0.506854	+	0.862032i	$0.330808\pi$
$150$		0			0
$151$	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
$153$		0			0
$154$	−0.0554181	−	14.5153i	−0.00446571	−	1.16967i
$155$	9.87553	+	7.61288i	0.793222	+	0.611481i
$156$		0			0
$157$	−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
$159$		0			0
$160$	−2.21758	+	0.286912i	−0.175315	+	0.0226824i
$161$	2.33617	+	4.01092i	0.184116	+	0.316105i
$162$		0			0
$163$	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
$165$		0			0
$166$	−4.96366	+	2.86577i	−0.385255	+	0.222427i
$167$	−6.07259	+	6.07259i	−0.469911	+	0.469911i	−0.901886	−	0.431974i	$-0.857817\pi$
$167$	−6.07259	+	6.07259i	−0.469911	+	0.469911i	0.431974	+	0.901886i	$0.357817\pi$
$168$		0			0
$169$		−	1.31933i		−	0.101487i
$170$	−4.69463	−	0.628733i	−0.360061	−	0.0482216i
$171$		0			0
$172$	2.66791	−	0.714864i	0.203426	−	0.0545079i
$173$	1.04797	−	3.91108i	0.0796757	−	0.297354i	−0.914577	−	0.404412i	$-0.867476\pi$
$173$	1.04797	−	3.91108i	0.0796757	−	0.297354i	0.994253	+	0.107058i	$0.0341430\pi$
$174$		0			0
$175$	−6.60692	−	11.4607i	−0.499437	−	0.866350i
$176$	5.48630			0.413545
$177$		0			0
$178$	−6.93879	+	1.85924i	−0.520084	+	0.139356i
$179$	−3.17428	−	1.83267i	−0.237256	−	0.136980i	0.376659	−	0.926352i	$-0.377073\pi$
$179$	−3.17428	−	1.83267i	−0.237256	−	0.136980i	−0.613915	+	0.789372i	$0.710406\pi$
$180$		0			0
$181$			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			0
$184$	−1.51935	+	0.877194i	−0.112008	+	0.0646676i
$185$	8.43125	−	20.2269i	0.619878	−	1.48711i
$186$		0			0
$187$	11.2253	+	3.00782i	0.820878	+	0.219954i
$188$	−2.49268	−	2.49268i	−0.181797	−	0.181797i
$189$		0			0
$190$	15.5141	−	2.00721i	1.12551	−	0.145619i
$191$	4.03766	+	6.99344i	0.292155	+	0.506027i	0.974319	−	0.225172i	$-0.0722944\pi$
$191$	4.03766	+	6.99344i	0.292155	+	0.506027i	−0.682164	+	0.731199i	$0.738961\pi$
$192$		0			0
$193$	−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
$195$		0			0
$196$	3.45361	−	6.08873i	0.246686	−	0.434909i
$197$	−6.01174	−	6.01174i	−0.428319	−	0.428319i	0.459737	−	0.888055i	$-0.347944\pi$
$197$	−6.01174	−	6.01174i	−0.428319	−	0.428319i	−0.888055	+	0.459737i	$0.847944\pi$
$198$		0			0
$199$	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
$201$		0			0
$202$	5.84612	−	5.84612i	0.411332	−	0.411332i
$203$	−1.27589	+	1.28567i	−0.0895498	+	0.0902362i
$204$		0			0
$205$	−0.743816	+	5.55393i	−0.0519503	+	0.387903i
$206$	−8.05941	−	4.65310i	−0.561526	−	0.324197i
$207$		0			0
$208$	0.884566	−	3.30124i	0.0613336	−	0.228900i
$209$	−38.3818			−2.65492
$210$		0			0
$211$	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
$213$		0			0
$214$	10.6241	+	6.13383i	0.726249	+	0.419300i
$215$	−4.90820	+	3.74880i	−0.334736	+	0.255666i
$216$		0			0
$217$	−3.87295	−	14.2364i	−0.262913	−	0.966430i
$218$	0.238027	−	0.238027i	0.0161213	−	0.0161213i
$219$		0			0
$220$	−11.3444	+	4.66933i	−0.764837	+	0.314806i
$221$	3.61976	−	6.26961i	0.243492	−	0.421740i
$222$		0			0
$223$	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
$225$		0			0
$226$	−7.20512	−	12.4796i	−0.479277	−	0.830133i
$227$	4.68301	+	17.4772i	0.310822	+	1.16000i	0.927816	+	0.373037i	$0.121684\pi$
$227$	4.68301	+	17.4772i	0.310822	+	1.16000i	−0.616994	+	0.786968i	$0.711650\pi$
$228$		0			0
$229$	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
$231$		0			0
$232$	−0.484092	−	0.484092i	−0.0317822	−	0.0317822i
$233$	13.9801	+	3.74597i	0.915870	+	0.245407i	0.685819	−	0.727772i	$-0.259444\pi$
$233$	13.9801	+	3.74597i	0.915870	+	0.245407i	0.230051	+	0.973179i	$0.426111\pi$
$234$		0			0
$235$	7.27575	+	3.03278i	0.474618	+	0.197837i
$236$	−8.79907	+	5.08015i	−0.572771	+	0.330689i
$237$		0			0
$238$	3.97798	+	3.94772i	0.257854	+	0.255892i
$239$			29.9736i			1.93883i	0.245427	+	0.969415i	$0.421072\pi$
$239$			29.9736i			1.93883i	−0.245427	+	0.969415i	$0.578928\pi$
$240$		0			0
$241$	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			0
$244$	−1.17166			−0.0750079
$245$	−1.95920	+	15.5294i	−0.125169	+	0.992135i
$246$		0			0
$247$	−6.18836	+	23.0953i	−0.393756	+	1.46952i
$248$	5.38640	−	1.44328i	0.342037	−	0.0916485i
$249$		0			0
$250$	−6.86546	+	8.82414i	−0.434210	+	0.558088i
$251$			10.7660i			0.679546i	0.940508	+	0.339773i	$0.110350\pi$
$251$			10.7660i			0.679546i	−0.940508	+	0.339773i	$0.889650\pi$
$252$		0			0
$253$	−6.80597	+	6.80597i	−0.427888	+	0.427888i
$254$	5.84270	−	3.37328i	0.366604	−	0.211659i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	14.5299	+	3.89328i	0.906352	+	0.242856i	0.681742	−	0.731593i	$-0.261223\pi$
$257$	14.5299	+	3.89328i	0.906352	+	0.242856i	0.224610	+	0.974449i	$0.427889\pi$
$258$		0			0
$259$	−22.4053	+	13.0500i	−1.39220	+	0.810887i
$260$	0.980578	+	7.57904i	0.0608128	+	0.470032i
$261$		0			0
$262$	−4.71286	−	17.5886i	−0.291161	−	1.08663i
$263$	−5.83157	−	21.7637i	−0.359590	−	1.34201i	−0.874609	−	0.484829i	$-0.838882\pi$
$263$	−5.83157	−	21.7637i	−0.359590	−	1.34201i	0.515019	−	0.857179i	$-0.327785\pi$
$264$		0			0
$265$	2.69766	+	20.8507i	0.165716	+	1.28085i
$266$	−16.0649	−	9.19348i	−0.985003	−	0.563689i
$267$		0			0
$268$	9.61398	+	2.57606i	0.587268	+	0.157358i
$269$	−5.52122	+	9.56304i	−0.336635	+	0.583069i	−0.983797	−	0.179283i	$-0.942622\pi$
$269$	−5.52122	+	9.56304i	−0.336635	+	0.583069i	0.647163	+	0.762352i	$0.275955\pi$
$270$		0			0
$271$	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
$273$		0			0
$274$			2.18468i			0.131982i
$275$	19.4835	−	19.3101i	1.17490	−	1.16444i
$276$		0			0
$277$	−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
$279$		0			0
$280$	−5.86668	−	0.762913i	−0.350601	−	0.0455928i
$281$	29.4723			1.75817			0.879085	−	0.476665i	$-0.158154\pi$
$281$	29.4723			1.75817			0.879085	+	0.476665i	$0.158154\pi$
$282$		0			0
$283$	−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
$285$		0			0
$286$		−	18.7505i		−	1.10874i
$287$	4.67030	−	4.70610i	0.275679	−	0.277792i
$288$		0			0
$289$	10.8366	−	6.25652i	0.637447	−	0.368030i
$290$	1.41299	+	0.588983i	0.0829738	+	0.0345863i
$291$		0			0
$292$	−4.70482	−	1.26065i	−0.275329	−	0.0737741i
$293$	14.0076	+	14.0076i	0.818330	+	0.818330i	0.985866	−	0.167536i	$-0.0535810\pi$
$293$	14.0076	+	14.0076i	0.818330	+	0.818330i	−0.167536	+	0.985866i	$0.553581\pi$
$294$		0			0
$295$	13.8708	−	17.9933i	0.807587	−	1.04761i
$296$	−4.90007	−	8.48716i	−0.284811	−	0.493306i
$297$		0			0
$298$	0.0501218	+	0.187057i	0.00290348	+	0.0108359i
$299$	2.99799	+	5.19266i	0.173378	+	0.300300i
$300$		0			0
$301$	7.30758	−	0.0278997i	0.421202	−	0.00160811i
$302$	15.0775	+	15.0775i	0.867610	+	0.867610i
$303$		0			0
$304$	3.49797	−	6.05866i	0.200622	−	0.347488i
$305$	2.42272	−	0.997187i	0.138724	−	0.0570987i
$306$		0			0
$307$	−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
$309$		0			0
$310$	−9.90945	+	7.56867i	−0.562819	+	0.429872i
$311$	7.31386	+	4.22266i	0.414731	+	0.239445i	0.692820	−	0.721110i	$-0.256368\pi$
$311$	7.31386	+	4.22266i	0.414731	+	0.239445i	−0.278089	+	0.960555i	$0.589701\pi$
$312$		0			0
$313$	−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
$315$		0			0
$316$	−8.33087			−0.468648
$317$	4.02471	−	15.0204i	0.226050	−	0.843632i	−0.755931	−	0.654652i	$-0.772815\pi$
$317$	4.02471	−	15.0204i	0.226050	−	0.843632i	0.981981	−	0.188980i	$-0.0605181\pi$
$318$		0			0
$319$	−3.25277	−	1.87799i	−0.182120	−	0.105147i
$320$	0.296818	−	2.21628i	0.0165926	−	0.123894i
$321$		0			0
$322$	−4.47890	+	1.21846i	−0.249599	+	0.0679023i
$323$	10.4787	−	10.4787i	0.583050	−	0.583050i
$324$		0			0
$325$	−8.47803	−	14.8371i	−0.470277	−	0.823014i
$326$	−7.04050	+	12.1945i	−0.389937	+	0.675391i
$327$		0			0
$328$	1.77199	+	1.77199i	0.0978416	+	0.0978416i
$329$	−4.69417	−	8.05933i	−0.258798	−	0.444325i
$330$		0			0
$331$	−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
$333$		0			0
$334$	−4.29397	−	7.43738i	−0.234956	−	0.406955i
$335$	−22.0719	+	2.85567i	−1.20592	+	0.156022i
$336$		0			0
$337$	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
$339$		0			0
$340$	1.82237	−	4.37193i	0.0988318	−	0.237101i
$341$	26.4951	−	15.2969i	1.43479	−	0.828376i
$342$		0			0
$343$	12.9450	−	13.2449i	0.698962	−	0.715159i
$344$			2.76202i			0.148918i
$345$		0			0
$346$	3.50658	+	2.02452i	0.188515	+	0.108839i
$347$	9.91592	−	2.65696i	0.532315	−	0.142633i	0.0173577	−	0.999849i	$-0.494475\pi$
$347$	9.91592	−	2.65696i	0.532315	−	0.142633i	0.514957	+	0.857216i	$0.327808\pi$
$348$		0			0
$349$	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
$351$		0			0
$352$	−1.41996	+	5.29936i	−0.0756841	+	0.282457i
$353$	−13.1604	+	3.52633i	−0.700460	+	0.187688i	−0.591436	−	0.806352i	$-0.701439\pi$
$353$	−13.1604	+	3.52633i	−0.700460	+	0.187688i	−0.109023	+	0.994039i	$0.534772\pi$
$354$		0			0
$355$	26.5324	+	3.55338i	1.40819	+	0.188594i
$356$		−	7.18356i		−	0.380728i
$357$		0			0
$358$	2.59178	−	2.59178i	0.136980	−	0.136980i
$359$	14.9791	−	8.64822i	0.790569	−	0.456435i	−0.0495937	−	0.998769i	$-0.515793\pi$
$359$	14.9791	−	8.64822i	0.790569	−	0.456435i	0.840163	+	0.542334i	$0.182459\pi$
$360$		0			0
$361$	−14.9715	+	25.9315i	−0.787976	+	1.36481i
$362$	−2.31807	−	0.621126i	−0.121835	−	0.0326457i
$363$		0			0
$364$	4.49126	−	7.84814i	0.235406	−	0.411354i
$365$	10.8014	−	1.39749i	0.565370	−	0.0731477i
$366$		0			0
$367$	−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
$369$		0			0
$370$	17.3555	+	13.3791i	0.902270	+	0.695544i
$371$	12.3559	−	21.5910i	0.641486	−	1.12095i
$372$		0			0
$373$	−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
$375$		0			0
$376$	3.05289	−	1.76259i	0.157441	−	0.0908985i
$377$	−1.65448	+	1.65448i	−0.0852101	+	0.0852101i
$378$		0			0
$379$		−	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
$381$		0			0
$382$	−7.80016	+	2.09005i	−0.399091	+	0.106936i
$383$	5.13534	−	19.1654i	0.262404	−	0.979304i	−0.701417	−	0.712752i	$-0.747449\pi$
$383$	5.13534	−	19.1654i	0.262404	−	0.979304i	0.963820	−	0.266553i	$-0.0858846\pi$
$384$		0			0
$385$	−32.1730	+	4.28750i	−1.63969	+	0.218511i
$386$	1.72252			0.0876740
$387$		0			0
$388$	17.9239	−	4.80269i	0.909948	−	0.243820i
$389$	4.44026	+	2.56359i	0.225130	+	0.129979i	0.608323	−	0.793689i	$-0.291842\pi$
$389$	4.44026	+	2.56359i	0.225130	+	0.129979i	−0.383193	+	0.923668i	$0.625176\pi$
$390$		0			0
$391$		−	3.71623i		−	0.187938i
$392$	4.98740	+	4.91181i	0.251902	+	0.248084i
$393$		0			0
$394$	7.36285	−	4.25094i	0.370935	−	0.214159i
$395$	17.2263	−	7.09030i	0.866747	−	0.356752i
$396$		0			0
$397$	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			0
$400$	1.27250	+	4.83536i	0.0636251	+	0.241768i
$401$	−8.61471	−	14.9211i	−0.430198	−	0.745125i	0.566692	−	0.823930i	$-0.308223\pi$
$401$	−8.61471	−	14.9211i	−0.430198	−	0.745125i	−0.996890	+	0.0788050i	$0.974890\pi$
$402$		0			0
$403$	−4.93271	−	18.4091i	−0.245716	−	0.917023i
$404$	4.13383	+	7.16001i	0.205666	+	0.356224i
$405$		0			0
$406$	−0.911636	−	1.56517i	−0.0452437	−	0.0776780i
$407$	−38.0186	−	38.0186i	−1.88451	−	1.88451i
$408$		0			0
$409$	−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
$411$		0			0
$412$	6.58048	−	6.58048i	0.324197	−	0.324197i
$413$	−25.9389	+	7.05656i	−1.27637	+	0.347230i
$414$		0			0
$415$	7.77922	+	10.1851i	0.381867	+	0.499967i
$416$	2.95981	+	1.70885i	0.145117	+	0.0837832i
$417$		0			0
$418$	9.93394	−	37.0740i	0.485885	−	1.81335i
$419$	−14.0414			−0.685966			−0.342983	−	0.939342i	$-0.611437\pi$
$419$	−14.0414			−0.685966			−0.342983	+	0.939342i	$0.611437\pi$
$420$		0			0
$421$	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
$423$		0			0
$424$	8.14273	+	4.70121i	0.395446	+	0.228311i
$425$	−0.0473258	+	10.5911i	−0.00229564	+	0.513745i
$426$		0			0
$427$	−2.99734	−	0.790881i	−0.145051	−	0.0382734i
$428$	−8.67454	+	8.67454i	−0.419300	+	0.419300i
$429$		0			0
$430$	−2.35073	−	5.71121i	−0.113362	−	0.275419i
$431$	−19.3886	+	33.5820i	−0.933914	+	1.61759i	−0.157354	+	0.987542i	$0.550296\pi$
$431$	−19.3886	+	33.5820i	−0.933914	+	1.61759i	−0.776559	+	0.630044i	$0.783037\pi$
$432$		0			0
$433$	−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			0
$436$	0.168311	+	0.291523i	0.00806063	+	0.0139614i
$437$	3.17664	+	11.8554i	0.151959	+	0.567119i
$438$		0			0
$439$	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
$441$		0			0
$442$	5.11912	+	5.11912i	0.243492	+	0.243492i
$443$	6.48289	+	1.73709i	0.308011	+	0.0825314i	0.409514	−	0.912304i	$-0.365698\pi$
$443$	6.48289	+	1.73709i	0.308011	+	0.0825314i	−0.101503	+	0.994835i	$0.532365\pi$
$444$		0			0
$445$	6.11385	+	14.8539i	0.289824	+	0.704143i
$446$	−4.17862	+	2.41253i	−0.197863	+	0.114236i
$447$		0			0
$448$	−1.86367	+	1.87796i	−0.0880502	+	0.0887252i
$449$		−	8.28979i		−	0.391219i	−0.980682	−	0.195610i	$-0.937331\pi$
$449$		−	8.28979i		−	0.391219i	0.980682	−	0.195610i	$-0.0626685\pi$
$450$		0			0
$451$	11.9065	+	6.87424i	0.560657	+	0.323695i
$452$	13.9192	−	3.72964i	0.654705	−	0.175428i
$453$		0			0
$454$	−18.0938			−0.849182
$455$	−2.60741	+	20.0506i	−0.122237	+	0.939985i
$456$		0			0
$457$	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
$459$		0			0
$460$	2.38117	+	3.11760i	0.111023	+	0.145359i
$461$		−	19.0130i		−	0.885524i	−0.896639	−	0.442762i	$-0.853999\pi$
$461$		−	19.0130i		−	0.885524i	0.896639	−	0.442762i	$-0.146001\pi$
$462$		0			0
$463$	−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
$465$		0			0
$466$	−7.23665	+	12.5343i	−0.335232	+	0.580638i
$467$	−15.4446	−	4.13837i	−0.714691	−	0.191501i	−0.116889	−	0.993145i	$-0.537292\pi$
$467$	−15.4446	−	4.13837i	−0.714691	−	0.191501i	−0.597802	+	0.801644i	$0.703959\pi$
$468$		0			0
$469$	22.8556	+	13.0796i	1.05537	+	0.603959i
$470$	−4.81254	+	6.24290i	−0.221986	+	0.287963i
$471$		0			0
$472$	−2.62968	−	9.81409i	−0.121041	−	0.451730i
$473$	3.92196	+	14.6370i	0.180332	+	0.673008i
$474$		0			0
$475$	−8.90234	−	33.8279i	−0.408467	−	1.55213i
$476$	−4.84278	+	2.82069i	−0.221968	+	0.129286i
$477$		0			0
$478$	−28.9523	−	7.75773i	−1.32425	−	0.354831i
$479$	−4.50526	+	7.80333i	−0.205850	+	0.356543i	−0.950403	−	0.311020i	$-0.899329\pi$
$479$	−4.50526	+	7.80333i	−0.205850	+	0.356543i	0.744553	+	0.667563i	$0.232663\pi$
$480$		0			0
$481$	−29.0066	+	16.7470i	−1.32259	+	0.763595i
$482$	−11.7522	+	11.7522i	−0.535296	+	0.535296i
$483$		0			0
$484$			19.0995i			0.868158i
$485$	−32.9749	+	25.1857i	−1.49731	+	1.14362i
$486$		0			0
$487$	−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
$489$		0			0
$490$	−14.4931	−	5.91174i	−0.654734	−	0.267065i
$491$	−2.08535			−0.0941107			−0.0470554	−	0.998892i	$-0.514984\pi$
$491$	−2.08535			−0.0941107			−0.0470554	+	0.998892i	$0.514984\pi$
$492$		0			0
$493$	1.40076	−	0.375332i	0.0630870	−	0.0169041i
$494$	−20.7067	−	11.9550i	−0.931637	−	0.537881i
$495$		0			0
$496$			5.57642i			0.250388i
$497$	−22.4821	−	22.3111i	−1.00846	−	1.00079i
$498$		0			0
$499$	−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
$501$		0			0
$502$	−10.3992	−	2.78645i	−0.464138	−	0.124366i
$503$	7.19669	+	7.19669i	0.320885	+	0.320885i	0.849106	−	0.528222i	$-0.177141\pi$
$503$	7.19669	+	7.19669i	0.320885	+	0.320885i	−0.528222	+	0.849106i	$0.677141\pi$
$504$		0			0
$505$	−14.6416	−	11.2869i	−0.651542	−	0.502263i
$506$	−4.81255	−	8.33558i	−0.213944	−	0.370562i
$507$		0			0
$508$	1.74614	+	6.51668i	0.0774724	+	0.289131i
$509$	−2.14078	−	3.70794i	−0.0948884	−	0.164352i	0.814674	−	0.579920i	$-0.196916\pi$
$509$	−2.14078	−	3.70794i	−0.0948884	−	0.164352i	−0.909562	+	0.415568i	$0.863583\pi$
$510$		0			0
$511$	−11.1849	−	6.40079i	−0.494791	−	0.283154i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	−7.52124	+	13.0272i	−0.331748	+	0.574604i
$515$	−8.00631	+	19.2074i	−0.352800	+	0.846381i
$516$		0			0
$517$	13.6756	−	13.6756i	0.601451	−	0.601451i
$518$	−6.80642	−	25.0194i	−0.299057	−	1.09929i
$519$		0			0
$520$	−7.57458	−	1.01443i	−0.332167	−	0.0444859i
$521$	12.6226	+	7.28768i	0.553007	+	0.319279i	0.750334	−	0.661059i	$-0.229893\pi$
$521$	12.6226	+	7.28768i	0.553007	+	0.319279i	−0.197327	+	0.980338i	$0.563226\pi$
$522$		0			0
$523$	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
$525$		0			0
$526$	22.5315			0.982418
$527$	−3.05723	+	11.4097i	−0.133175	+	0.497015i
$528$		0			0
$529$	−17.2531	−	9.96106i	−0.750133	−	0.433090i
$530$	−20.8384	−	2.79081i	−0.905162	−	0.121225i
$531$		0			0
$532$	13.0381	−	13.1381i	0.565275	−	0.569607i
$533$	6.05612	−	6.05612i	0.262319	−	0.262319i
$534$		0			0
$535$	10.5541	−	25.3197i	0.456294	−	1.09467i
$536$	−4.97656	+	8.61966i	−0.214955	+	0.372313i
$537$		0			0
$538$	−7.80819	−	7.80819i	−0.336635	−	0.336635i
$539$	33.4046	+	18.9475i	1.43884	+	0.816128i
$540$		0			0
$541$	−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			0
$544$	−1.05912	−	1.83445i	−0.0454095	−	0.0786516i
$545$	−0.596139	−	0.459553i	−0.0255358	−	0.0196851i
$546$		0			0
$547$	−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			0
$550$	13.6095	+	23.8174i	0.580309	+	1.01558i
$551$	−4.14781	+	2.39474i	−0.176703	+	0.102019i
$552$		0			0
$553$	−21.3120	−	5.62341i	−0.906278	−	0.239132i
$554$		−	6.33506i		−	0.269151i
$555$		0			0
$556$	15.7137	+	9.07229i	0.666408	+	0.384751i
$557$	4.04187	−	1.08302i	0.171260	−	0.0458889i	−0.172170	−	0.985067i	$-0.555078\pi$
$557$	4.04187	−	1.08302i	0.171260	−	0.0458889i	0.343430	+	0.939178i	$0.388411\pi$
$558$		0			0
$559$	9.43977			0.399260
$560$	2.25533	−	5.46932i	0.0953050	−	0.231121i
$561$		0			0
$562$	−7.62799	+	28.4681i	−0.321767	+	1.20085i
$563$	−24.1918	+	6.48217i	−1.01956	+	0.273191i	−0.729620	−	0.683853i	$-0.760303\pi$
$563$	−24.1918	+	6.48217i	−1.01956	+	0.273191i	−0.289943	+	0.957044i	$0.593636\pi$
$564$		0			0
$565$	−25.6074	+	19.5585i	−1.07731	+	0.822833i
$566$		−	0.0978259i		−	0.00411193i
$567$		0			0
$568$	8.46519	−	8.46519i	0.355191	−	0.355191i
$569$	1.99827	−	1.15370i	0.0837720	−	0.0483658i	−0.457529	−	0.889195i	$-0.651265\pi$
$569$	1.99827	−	1.15370i	0.0837720	−	0.0483658i	0.541301	+	0.840829i	$0.317932\pi$
$570$		0			0
$571$	−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
$573$		0			0
$574$	3.33698	+	5.72919i	0.139283	+	0.239132i
$575$	−7.57705	−	4.41987i	−0.315985	−	0.184321i
$576$		0			0
$577$	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			0
$580$	−0.934623	+	1.21241i	−0.0388081	+	0.0503425i
$581$	−0.0578953	−	15.1641i	−0.00240190	−	0.629114i
$582$		0			0
$583$	49.8268	+	13.3510i	2.06361	+	0.552944i
$584$	2.43539	−	4.21822i	0.100777	−	0.174551i
$585$		0			0
$586$	−17.1557	+	9.90484i	−0.708695	+	0.409165i
$587$	5.31785	−	5.31785i	0.219491	−	0.219491i	−0.588793	−	0.808284i	$-0.700397\pi$
$587$	5.31785	−	5.31785i	0.219491	−	0.219491i	0.808284	+	0.588793i	$0.200397\pi$
$588$		0			0
$589$		−	39.0122i		−	1.60747i
$590$	13.7902	+	18.0551i	0.567734	+	0.743318i
$591$		0			0
$592$	9.46620	−	2.53646i	0.389059	−	0.104248i
$593$	−4.58156	+	17.0986i	−0.188142	+	0.702156i	0.805794	+	0.592196i	$0.201739\pi$
$593$	−4.58156	+	17.0986i	−0.188142	+	0.702156i	−0.993936	+	0.109960i	$0.964928\pi$
$594$		0			0
$595$	7.61307	−	9.95414i	0.312105	−	0.408080i
$596$	−0.193656			−0.00793245
$597$		0			0
$598$	−5.79167	+	1.55187i	−0.236839	+	0.0634608i
$599$	27.0972	+	15.6446i	1.10716	+	0.639220i	0.938093	−	0.346384i	$-0.112591\pi$
$599$	27.0972	+	15.6446i	1.10716	+	0.639220i	0.169069	+	0.985604i	$0.445924\pi$
$600$		0			0
$601$			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
$603$		0			0
$604$	−18.4660	+	10.6614i	−0.751372	+	0.433805i
$605$	−16.2553	−	39.4932i	−0.660874	−	1.60563i
$606$		0			0
$607$	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			0
$610$	0.336163	+	2.59826i	0.0136108	+	0.105200i
$611$	−6.02400	−	10.4339i	−0.243705	−	0.422109i
$612$		0			0
$613$	−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			0
$616$	−7.20965	+	12.5983i	−0.290485	+	0.507600i
$617$	24.4884	+	24.4884i	0.985865	+	0.985865i	0.999901	−	0.0140365i	$-0.00446811\pi$
$617$	24.4884	+	24.4884i	0.985865	+	0.985865i	−0.0140365	+	0.999901i	$0.504468\pi$
$618$		0			0
$619$	−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
$621$		0			0
$622$	−5.97174	+	5.97174i	−0.239445	+	0.239445i
$623$	4.84897	−	18.3770i	0.194270	−	0.736257i
$624$		0			0
$625$	21.5381	+	12.6930i	0.861522	+	0.507719i
$626$	−16.8092	−	9.70480i	−0.671831	−	0.387882i
$627$		0			0
$628$	−0.952462	+	3.55464i	−0.0380074	+	0.141845i
$629$	20.7591			0.827719
$630$		0			0
$631$	−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
$633$		0			0
$634$	13.4670	+	7.77515i	0.534841	+	0.308791i
$635$	−9.15688	−	11.9888i	−0.363380	−	0.475763i
$636$		0			0
$637$	16.7871	−	17.0454i	0.665128	−	0.675364i
$638$	2.65587	−	2.65587i	0.105147	−	0.105147i
$639$		0			0
$640$	2.06394	+	0.860320i	0.0815844	+	0.0340071i
$641$	−5.61488	+	9.72526i	−0.221774	+	0.384125i	−0.955347	−	0.295487i	$-0.904518\pi$
$641$	−5.61488	+	9.72526i	−0.221774	+	0.384125i	0.733572	+	0.679611i	$0.237852\pi$
$642$		0			0
$643$	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
$645$		0			0
$646$	7.40955	+	12.8337i	0.291525	+	0.504936i
$647$	−4.06147	−	15.1576i	−0.159673	−	0.595908i	−0.998660	−	0.0517559i	$-0.983518\pi$
$647$	−4.06147	−	15.1576i	−0.159673	−	0.595908i	0.838987	−	0.544152i	$-0.183148\pi$
$648$		0			0
$649$	−27.8712	−	48.2744i	−1.09404	−	1.89493i
$650$	16.5258	−	4.34903i	0.648196	−	0.170583i
$651$		0			0
$652$	−9.95676	−	9.95676i	−0.389937	−	0.389937i
$653$	15.4045	+	4.12761i	0.602823	+	0.161526i	0.547307	−	0.836932i	$-0.315653\pi$
$653$	15.4045	+	4.12761i	0.602823	+	0.161526i	0.0555160	+	0.998458i	$0.482320\pi$
$654$		0			0
$655$	−37.6521	+	15.4975i	−1.47119	+	0.605539i
$656$	−2.17023	+	1.25298i	−0.0847333	+	0.0489208i
$657$		0			0
$658$	8.99966	−	2.44832i	0.350843	−	0.0954453i
$659$			10.4778i			0.408157i	0.978955	+	0.204078i	$0.0654198\pi$
$659$			10.4778i			0.408157i	−0.978955	+	0.204078i	$0.934580\pi$
$660$		0			0
$661$	−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
$663$		0			0
$664$	5.73154			0.222427
$665$	−15.7781	+	38.2630i	−0.611849	+	1.48378i
$666$		0			0
$667$	−0.310860	+	1.16015i	−0.0120366	+	0.0449210i
$668$	8.29532	−	2.22272i	0.320955	−	0.0859998i
$669$		0			0
$670$	2.95427	−	22.0589i	0.114133	−	0.852211i
$671$		−	6.42808i		−	0.248153i
$672$		0			0
$673$	−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
$675$		0			0
$676$	−0.659666	+	1.14257i	−0.0253718	+	0.0439452i
$677$	12.4001	+	3.32260i	0.476575	+	0.127698i	0.489108	−	0.872223i	$-0.337323\pi$
$677$	12.4001	+	3.32260i	0.476575	+	0.127698i	−0.0125322	+	0.999921i	$0.503989\pi$
$678$		0			0
$679$	49.0947	−	0.187439i	1.88408	−	0.00719326i
$680$	3.75130	+	2.89181i	0.143856	+	0.110896i
$681$		0			0
$682$	7.91828	+	29.5514i	0.303207	+	1.13158i
$683$	−5.52974	−	20.6373i	−0.211589	−	0.789663i	−0.987339	−	0.158622i	$-0.949295\pi$
$683$	−5.52974	−	20.6373i	−0.211589	−	0.789663i	0.775750	−	0.631040i	$-0.217372\pi$
$684$		0			0
$685$	4.84472	−	0.626811i	0.185107	−	0.0239492i
$686$	9.44322	+	15.9319i	0.360544	+	0.608283i
$687$		0			0
$688$	−2.66791	−	0.714864i	−0.101713	−	0.0272540i
$689$	16.0673	−	27.8294i	0.612116	−	1.06022i
$690$		0			0
$691$	−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
$693$		0			0
$694$			10.2657i			0.389681i
$695$	−40.2135	−	5.38563i	−1.52538	−	0.204289i
$696$		0			0
$697$	−5.12738	+	1.37388i	−0.194213	+	0.0520393i
$698$	−1.71194	+	6.38903i	−0.0647977	+	0.241828i
$699$		0			0
$700$	−0.00860549	+	13.2288i	−0.000325257	+	0.500000i
$701$	−44.5959			−1.68436			−0.842182	−	0.539194i	$-0.818729\pi$
$701$	−44.5959			−1.68436			−0.842182	+	0.539194i	$0.818729\pi$
$702$		0			0
$703$	−66.2249	+	17.7449i	−2.49772	+	0.669262i
$704$	−4.75127	−	2.74315i	−0.179070	−	0.103386i
$705$		0			0
$706$		−	13.6247i		−	0.512772i
$707$	5.74208	+	21.1071i	0.215953	+	0.793813i
$708$		0			0
$709$	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
$711$		0			0
$712$	6.93879	+	1.85924i	0.260042	+	0.0696781i
$713$	−6.91777	−	6.91777i	−0.259072	−	0.259072i
$714$		0			0
$715$	−41.5809	+	5.37974i	−1.55504	+	0.201191i
$716$	1.83267	+	3.17428i	0.0684900	+	0.118628i
$717$		0			0
$718$	4.47665	+	16.7071i	0.167067	+	0.623502i
$719$	11.7839	+	20.4103i	0.439464	+	0.761174i	0.997648	−	0.0685431i	$-0.0218351\pi$
$719$	11.7839	+	20.4103i	0.439464	+	0.761174i	−0.558184	+	0.829717i	$0.688502\pi$
$720$		0			0
$721$	21.2760	−	12.3923i	0.792361	−	0.461512i
$722$	−21.1730	−	21.1730i	−0.787976	−	0.787976i
$723$		0			0
$724$	1.19992	−	2.07833i	0.0445948	−	0.0772405i
$725$	0.900715	−	3.30242i	0.0334517	−	0.122649i
$726$		0			0
$727$	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
$729$		0			0
$730$	−1.44574	+	10.7950i	−0.0535091	+	0.399542i
$731$	−5.06681	−	2.92532i	−0.187403	−	0.108197i
$732$		0			0
$733$	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
$735$		0			0
$736$	1.75439			0.0646676
$737$	−14.1330	+	52.7452i	−0.520597	+	1.94289i
$738$		0			0
$739$	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
$741$		0			0
$742$	17.6573	+	17.5230i	0.648222	+	0.643291i
$743$	−24.7787	+	24.7787i	−0.909041	+	0.909041i	−0.996195	−	0.0871537i	$-0.972223\pi$
$743$	−24.7787	+	24.7787i	−0.909041	+	0.909041i	0.0871537	+	0.996195i	$0.472223\pi$
$744$		0			0
$745$	0.400435	−	0.164818i	0.0146708	−	0.00603847i
$746$	4.58319	−	7.93832i	0.167802	−	0.290642i
$747$		0			0
$748$	−8.21752	−	8.21752i	−0.300462	−	0.300462i
$749$	−28.0466	+	16.3358i	−1.02480	+	0.596897i
$750$		0			0
$751$	−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
$753$		0			0
$754$	−1.16989	−	2.02632i	−0.0426051	−	0.0737941i
$755$	29.1096	−	37.7614i	1.05941	−	1.37428i
$756$		0			0
$757$	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
$759$		0			0
$760$	−14.4392	−	6.01874i	−0.523764	−	0.218323i
$761$	−24.3626	+	14.0657i	−0.883142	+	0.509882i	−0.871693	−	0.490052i	$-0.836978\pi$
$761$	−24.3626	+	14.0657i	−0.883142	+	0.509882i	−0.0114488	+	0.999934i	$0.503644\pi$
$762$		0			0
$763$	0.233791	+	0.859384i	0.00846382	+	0.0311118i
$764$		−	8.07532i		−	0.292155i
$765$		0			0
$766$	17.1832	+	9.92072i	0.620854	+	0.358450i
$767$	−33.5416	+	8.98745i	−1.21112	+	0.324518i
$768$		0			0
$769$	−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
$771$		0			0
$772$	−0.445821	+	1.66383i	−0.0160455	+	0.0598825i
$773$	46.8575	−	12.5554i	1.68535	−	0.451588i	0.716166	−	0.697930i	$-0.245895\pi$
$773$	46.8575	−	12.5554i	1.68535	−	0.451588i	0.969183	+	0.246342i	$0.0792288\pi$
$774$		0			0
$775$	19.6273	+	19.8035i	0.705034	+	0.711363i
$776$			18.5562i			0.666128i
$777$		0			0
$778$	−3.62546	+	3.62546i	−0.129979	+	0.129979i
$779$	15.1828	−	8.76579i	0.543980	−	0.314067i
$780$		0			0
$781$	32.8398	−	56.8803i	1.17510	−	2.03534i
$782$	3.58960	+	0.961830i	0.128364	+	0.0343950i
$783$		0			0
$784$	−6.03528	+	3.54619i	−0.215546	+	0.126650i
$785$	−1.05584	−	8.16078i	−0.0376847	−	0.291271i
$786$		0			0
$787$	−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
$789$		0			0
$790$	2.39022	+	18.4744i	0.0850403	+	0.657290i
$791$	38.1256	−	0.145560i	1.35559	−	0.00517553i
$792$		0			0
$793$	−3.86794	−	1.03641i	−0.137354	−	0.0368040i
$794$	−13.1967	+	22.8574i	−0.468334	+	0.811179i
$795$		0			0
$796$	−9.54181	+	5.50897i	−0.338200	+	0.195260i
$797$	34.4058	−	34.4058i	1.21871	−	1.21871i	0.250632	−	0.968082i	$-0.419362\pi$
$797$	34.4058	−	34.4058i	1.21871	−	1.21871i	0.968082	−	0.250632i	$-0.0806384\pi$
$798$		0			0
$799$			7.46719i			0.264170i
$800$	−4.99995	−	0.0223420i	−0.176775	−	0.000789908i
$801$		0			0
$802$	16.6423	−	4.45930i	0.587661	−	0.157463i
$803$	6.91632	−	25.8120i	0.244071	−	0.910887i
$804$		0			0
$805$	3.98709	+	9.58274i	0.140527	+	0.337747i
$806$	19.0585			0.671307
$807$		0			0
$808$	−7.98595	+	2.13983i	−0.280945	+	0.0752789i
$809$	−33.6569	−	19.4318i	−1.18331	−	0.683186i	−0.226534	−	0.974003i	$-0.572740\pi$
$809$	−33.6569	−	19.4318i	−1.18331	−	0.683186i	−0.956779	+	0.290817i	$0.906073\pi$
$810$		0			0
$811$			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
$813$		0			0
$814$	46.5631	−	26.8832i	1.63204	−	0.942257i
$815$	29.0623	+	12.1142i	1.01801	+	0.424340i
$816$		0			0
$817$	18.6645	+	5.00114i	0.652989	+	0.174968i
$818$	−25.2535	−	25.2535i	−0.882967	−	0.882967i
$819$		0			0
$820$	3.42113	−	4.43793i	0.119471	−	0.154979i
$821$	11.9561	+	20.7086i	0.417271	+	0.722735i	0.995664	−	0.0930235i	$-0.0296532\pi$
$821$	11.9561	+	20.7086i	0.417271	+	0.722735i	−0.578393	+	0.815758i	$0.696320\pi$
$822$		0			0
$823$	−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
$825$		0			0
$826$	−0.102631	−	26.8814i	−0.00357099	−	0.935324i
$827$	−20.7600	−	20.7600i	−0.721898	−	0.721898i	0.247094	−	0.968992i	$-0.420524\pi$
$827$	−20.7600	−	20.7600i	−0.721898	−	0.721898i	−0.968992	+	0.247094i	$0.920524\pi$
$828$		0			0
$829$	−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
$831$		0			0
$832$	−2.41668	+	2.41668i	−0.0837832	+	0.0837832i
$833$	−14.2928	+	3.94695i	−0.495215	+	0.136754i
$834$		0			0
$835$	−15.2610	+	11.6561i	−0.528130	+	0.403377i
$836$	33.2396	+	19.1909i	1.14962	+	0.663731i
$837$		0			0
$838$	3.63417	−	13.5629i	0.125540	−	0.468523i
$839$	8.03334			0.277342			0.138671	−	0.990339i	$-0.455717\pi$
$839$	8.03334			0.277342			0.138671	+	0.990339i	$0.455717\pi$
$840$		0			0
$841$	28.5313			0.983838
$842$	−6.32378	+	23.6007i	−0.217932	+	0.813333i
$843$		0			0
$844$	−8.94800	−	5.16613i	−0.308003	−	0.177826i
$845$	0.391601	−	2.92401i	0.0134715	−	0.100589i
$846$		0			0
$847$	−12.8923	+	48.8602i	−0.442985	+	1.67886i
$848$	−6.64852	+	6.64852i	−0.228311	+	0.228311i
$849$		0			0
$850$	−10.2180	−	2.78690i	−0.350474	−	0.0955898i
$851$	−8.59662	+	14.8898i	−0.294688	+	0.510415i
$852$		0			0
$853$	−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
$855$		0			0
$856$	−6.13383	−	10.6241i	−0.209650	−	0.363124i
$857$	−6.21598	−	23.1984i	−0.212334	−	0.792441i	−0.987088	−	0.160178i	$-0.948793\pi$
$857$	−6.21598	−	23.1984i	−0.212334	−	0.792441i	0.774754	−	0.632263i	$-0.217874\pi$
$858$		0			0
$859$	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
$861$		0			0
$862$	−27.4196	−	27.4196i	−0.933914	−	0.933914i
$863$	−15.9949	−	4.28582i	−0.544473	−	0.145891i	−0.0239095	−	0.999714i	$-0.507611\pi$
$863$	−15.9949	−	4.28582i	−0.544473	−	0.145891i	−0.520563	+	0.853823i	$0.674278\pi$
$864$		0			0
$865$	3.48347	−	8.35699i	0.118442	−	0.284146i
$866$	9.62282	−	5.55574i	0.326997	−	0.188792i
$867$		0			0
$868$	−3.76413	+	14.2656i	−0.127763	+	0.484205i
$869$		−	45.7056i		−	1.55046i
$870$		0			0
$871$	29.4594	+	17.0084i	0.998194	+	0.576308i
$872$	−0.325151	+	0.0871241i	−0.0110110	+	0.00295039i
$873$		0			0
$874$	−12.2736			−0.415160
$875$	−11.2410	−	27.3613i	−0.380017	−	0.924980i
$876$		0			0
$877$	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
$879$		0			0
$880$	12.1592	+	1.62843i	0.409886	+	0.0548944i
$881$			17.4940i			0.589386i	0.955592	+	0.294693i	$0.0952174\pi$
$881$			17.4940i			0.589386i	−0.955592	+	0.294693i	$0.904783\pi$
$882$		0			0
$883$	−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
$885$		0			0
$886$	−3.35579	+	5.81240i	−0.112740	+	0.195271i
$887$	39.6163	+	10.6152i	1.33018	+	0.356422i	0.852784	−	0.522264i	$-0.174912\pi$
$887$	39.6163	+	10.6152i	1.33018	+	0.356422i	0.477401	+	0.878686i	$0.341579\pi$
$888$		0			0
$889$	0.0681482	+	17.8496i	0.00228562	+	0.598657i
$890$	−15.9302	+	2.06105i	−0.533980	+	0.0690865i
$891$		0			0
$892$	−1.24882	−	4.66064i	−0.0418134	−	0.156050i
$893$	−6.38297	−	23.8216i	−0.213598	−	0.797158i
$894$		0			0
$895$	−6.49112	−	5.00389i	−0.216974	−	0.167262i
$896$	−1.33161	−	2.28622i	−0.0444861	−	0.0763773i
$897$		0			0
$898$	8.00732	+	2.14555i	0.267208	+	0.0715981i
$899$	1.90883	−	3.30620i	0.0636632	−	0.110268i
$900$		0			0
$901$	−17.2483	+	9.95832i	−0.574625	+	0.331760i
$902$	−9.72165	+	9.72165i	−0.323695	+	0.323695i
$903$		0			0
$904$			14.4102i			0.479277i
$905$	−0.712317	+	5.31873i	−0.0236782	+	0.176801i
$906$		0			0
$907$	−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
$909$		0			0
$910$	−18.6925	−	7.70803i	−0.619650	−	0.255519i
$911$	21.3131			0.706136			0.353068	−	0.935598i	$-0.385138\pi$
$911$	21.3131			0.706136			0.353068	+	0.935598i	$0.385138\pi$
$912$		0			0
$913$	30.3735	−	8.13855i	1.00522	−	0.269347i
$914$	19.1236	+	11.0410i	0.632551	+	0.365204i
$915$		0			0
$916$		−	9.64749i		−	0.318762i
$917$	46.5824	+	12.2913i	1.53829	+	0.405894i
$918$		0			0
$919$	−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
$921$		0			0
$922$	18.3652	+	4.92093i	0.604824	+	0.162062i
$923$	−28.9315	−	28.9315i	−0.952291	−	0.952291i
$924$		0			0
$925$	24.6897	−	42.3259i	0.811793	−	1.39167i
$926$	−11.7444	−	20.3419i	−0.385946	−	0.668478i
$927$		0			0
$928$	0.177190	+	0.661282i	0.00581655	+	0.0217076i
$929$	−2.59922	−	4.50199i	−0.0852777	−	0.147705i	0.820232	−	0.572031i	$-0.193844\pi$
$929$	−2.59922	−	4.50199i	−0.0852777	−	0.147705i	−0.905510	+	0.424326i	$0.860511\pi$
$930$		0			0
$931$	42.2224	−	24.8089i	1.38378	−	0.813078i
$932$	−10.2342	−	10.2342i	−0.335232	−	0.335232i
$933$		0			0
$934$	7.99472	−	13.8473i	0.261595	−	0.453096i
$935$	23.9857	+	9.99806i	0.784417	+	0.326971i
$936$		0			0
$937$	−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
$939$		0			0
$940$	−4.78460	−	6.26434i	−0.156056	−	0.204320i
$941$	−8.88464	−	5.12955i	−0.289631	−	0.167219i	0.348144	−	0.937441i	$-0.386812\pi$
$941$	−8.88464	−	5.12955i	−0.289631	−	0.167219i	−0.637775	+	0.770222i	$0.720145\pi$
$942$		0			0
$943$	1.13788	−	4.24663i	0.0370545	−	0.138289i
$944$	10.1603			0.330689
$945$		0			0
$946$	−15.1533			−0.492676
$947$	−7.26545	+	27.1150i	−0.236096	+	0.881120i	0.741556	+	0.670890i	$0.234088\pi$
$947$	−7.26545	+	27.1150i	−0.236096	+	0.881120i	−0.977652	+	0.210230i	$0.932579\pi$
$948$		0			0
$949$	−14.4166	−	8.32344i	−0.467983	−	0.270190i
$950$	34.9793	+	0.156303i	1.13488	+	0.00507113i
$951$		0			0
$952$	−1.47117	−	5.40781i	−0.0476809	−	0.175268i
$953$	29.6648	−	29.6648i	0.960937	−	0.960937i	−0.0383279	−	0.999265i	$-0.512203\pi$
$953$	29.6648	−	29.6648i	0.960937	−	0.960937i	0.999265	+	0.0383279i	$0.0122031\pi$
$954$		0			0
$955$	6.87282	+	16.6979i	0.222399	+	0.540330i
$956$	14.9868	−	25.9579i	0.484708	−	0.839538i
$957$		0			0
$958$	−6.37140	−	6.37140i	−0.205850	−	0.205850i
$959$	−5.01674	−	2.87093i	−0.161999	−	0.0927073i
$960$		0			0
$961$	0.0482042	+	0.0834922i	0.00155498	+	0.00269330i
$962$	−8.66886	−	32.3526i	−0.279495	−	1.04309i
$963$		0			0
$964$	−8.31003	−	14.3934i	−0.267648	−	0.463580i
$965$	−0.494211	−	3.81984i	−0.0159092	−	0.122965i
$966$		0			0
$967$	−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
$969$		0			0
$970$	−15.7930	−	38.3698i	−0.507081	−	1.23198i
$971$	−51.1699	+	29.5430i	−1.64212	+	0.948079i	−0.662042	+	0.749467i	$0.730310\pi$
$971$	−51.1699	+	29.5430i	−1.64212	+	0.948079i	−0.980078	+	0.198612i	$0.936357\pi$
$972$		0			0
$973$	34.0747	+	33.8155i	1.09239	+	1.08408i
$974$		−	9.34012i		−	0.299277i
$975$		0			0
$976$	1.01469	+	0.585830i	0.0324794	+	0.0187520i
$977$	−11.4234	+	3.06089i	−0.365467	+	0.0979266i	−0.436879	−	0.899520i	$-0.643916\pi$
$977$	−11.4234	+	3.06089i	−0.365467	+	0.0979266i	0.0714120	+	0.997447i	$0.477249\pi$
$978$		0			0
$979$	39.4112			1.25959
$980$	9.46141	−	12.4692i	0.302234	−	0.398315i
$981$		0			0
$982$	0.539730	−	2.01430i	0.0172235	−	0.0642788i
$983$	36.7070	−	9.83561i	1.17077	−	0.313707i	0.379511	−	0.925187i	$-0.376092\pi$
$983$	36.7070	−	9.83561i	1.17077	−	0.313707i	0.791260	+	0.611480i	$0.209425\pi$
$984$		0			0
$985$	−11.5393	−	15.1081i	−0.367673	−	0.481384i
$986$			1.45017i			0.0461829i
$987$		0			0
$988$	16.9069	−	16.9069i	0.537881	−	0.537881i
$989$	4.19647	−	2.42283i	0.133440	−	0.0770416i
$990$		0			0
$991$	−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
$993$		0			0
$994$	27.3697	−	15.9415i	0.868114	−	0.505635i
$995$	15.0416	−	19.5122i	0.476851	−	0.618577i
$996$		0			0
$997$	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
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bv.b.577.2		16
3.2	odd	2		210.2.u.b.157.3	yes	16
5.3	odd	4		630.2.bv.a.73.4		16
7.5	odd	6		630.2.bv.a.397.4		16
15.2	even	4		1050.2.bc.h.493.3		16
15.8	even	4		210.2.u.a.73.1	✓	16
15.14	odd	2		1050.2.bc.g.157.2		16
21.5	even	6		210.2.u.a.187.1	yes	16
21.11	odd	6		1470.2.m.e.97.7		16
21.17	even	6		1470.2.m.d.97.6		16
35.33	even	12	inner	630.2.bv.b.523.2		16
105.38	odd	12		1470.2.m.e.1273.7		16
105.47	odd	12		1050.2.bc.g.943.2		16
105.53	even	12		1470.2.m.d.1273.6		16
105.68	odd	12		210.2.u.b.103.3	yes	16
105.89	even	6		1050.2.bc.h.607.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.1	✓	16	15.8	even	4
210.2.u.a.187.1	yes	16	21.5	even	6
210.2.u.b.103.3	yes	16	105.68	odd	12
210.2.u.b.157.3	yes	16	3.2	odd	2
630.2.bv.a.73.4		16	5.3	odd	4
630.2.bv.a.397.4		16	7.5	odd	6
630.2.bv.b.523.2		16	35.33	even	12	inner
630.2.bv.b.577.2		16	1.1	even	1	trivial
1050.2.bc.g.157.2		16	15.14	odd	2
1050.2.bc.g.943.2		16	105.47	odd	12
1050.2.bc.h.493.3		16	15.2	even	4
1050.2.bc.h.607.3		16	105.89	even	6
1470.2.m.d.97.6		16	21.17	even	6
1470.2.m.d.1273.6		16	105.53	even	12
1470.2.m.e.97.7		16	21.11	odd	6
1470.2.m.e.1273.7		16	105.38	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bv (of order \(12\), degree \(4\), minimal)

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