LMFDB - Embedded newform 1950.2.bc.j.901.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(751,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1950.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.bc (of order $6$, degree $2$, 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:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + \cdots + 2197 $ x^12 - 2x^11 - 8x^10 + 34x^9 + 8x^8 - 134x^7 + 98x^6 + 154x^5 + 104x^4 + 190x^3 - 1196x^2 - 338*x + 2197
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.2
Root			$-1.44229 + 0.433312i$ of defining polynomial
Character	$\chi$	$=$	1950.901
Dual form			1950.2.bc.j.751.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(-0.749482 + 0.432713i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(-0.749482 + 0.432713i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.151430 + 0.0874279i) q^{11} +1.00000 q^{12} +(3.34131 - 1.35486i) q^{13} +0.865427 q^{14} +(-0.500000 + 0.866025i) q^{16} +(4.08960 + 7.08339i) q^{17} +1.00000i q^{18} +(-5.20843 + 3.00709i) q^{19} +0.865427i q^{21} +(-0.0874279 - 0.151430i) q^{22} +(1.45614 - 2.52211i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-3.57109 - 0.497314i) q^{26} -1.00000 q^{27} +(-0.749482 - 0.432713i) q^{28} +(-3.24491 + 5.62035i) q^{29} +6.95057i q^{31} +(0.866025 - 0.500000i) q^{32} +(0.151430 - 0.0874279i) q^{33} -8.17919i q^{34} +(0.500000 - 0.866025i) q^{36} +(-1.52347 - 0.879573i) q^{37} +6.01418 q^{38} +(0.497314 - 3.57109i) q^{39} +(-7.08339 - 4.08960i) q^{41} +(0.432713 - 0.749482i) q^{42} +(4.58691 + 7.94476i) q^{43} +0.174856i q^{44} +(-2.52211 + 1.45614i) q^{46} -11.9021i q^{47} +(0.500000 + 0.866025i) q^{48} +(-3.12552 + 5.41356i) q^{49} +8.17919 q^{51} +(2.84400 + 2.21623i) q^{52} +2.48735 q^{53} +(0.866025 + 0.500000i) q^{54} +(0.432713 + 0.749482i) q^{56} +6.01418i q^{57} +(5.62035 - 3.24491i) q^{58} +(6.09393 - 3.51833i) q^{59} +(3.98695 + 6.90559i) q^{61} +(3.47529 - 6.01937i) q^{62} +(0.749482 + 0.432713i) q^{63} -1.00000 q^{64} -0.174856 q^{66} +(2.36886 + 1.36766i) q^{67} +(-4.08960 + 7.08339i) q^{68} +(-1.45614 - 2.52211i) q^{69} +(12.2677 - 7.08275i) q^{71} +(-0.866025 + 0.500000i) q^{72} +12.8706i q^{73} +(0.879573 + 1.52347i) q^{74} +(-5.20843 - 3.00709i) q^{76} -0.151325 q^{77} +(-2.21623 + 2.84400i) q^{78} -9.48961 q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.08960 + 7.08339i) q^{82} -0.139544i q^{83} +(-0.749482 + 0.432713i) q^{84} -9.17382i q^{86} +(3.24491 + 5.62035i) q^{87} +(0.0874279 - 0.151430i) q^{88} +(11.3790 + 6.56966i) q^{89} +(-1.91799 + 2.46127i) q^{91} +2.91228 q^{92} +(6.01937 + 3.47529i) q^{93} +(-5.95105 + 10.3075i) q^{94} -1.00000i q^{96} +(7.48957 - 4.32411i) q^{97} +(5.41356 - 3.12552i) q^{98} -0.174856i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + 6 q^{4} - 12 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 + 6 * q^4 - 12 * q^7 - 6 * q^9	$ 12 q + 6 q^{3} + 6 q^{4} - 12 q^{7} - 6 q^{9} + 6 q^{11} + 12 q^{12} + 4 q^{13} - 4 q^{14} - 6 q^{16} + 8 q^{17} + 6 q^{19} - 6 q^{22} + 16 q^{23} - 2 q^{26} - 12 q^{27} - 12 q^{28} - 14 q^{29} + 6 q^{33} + 6 q^{36} - 6 q^{37} - 8 q^{38} + 2 q^{39} - 18 q^{41} - 2 q^{42} + 10 q^{43} - 6 q^{46} + 6 q^{48} - 8 q^{49} + 16 q^{51} + 2 q^{52} - 2 q^{56} + 6 q^{58} + 36 q^{59} + 10 q^{61} + 16 q^{62} + 12 q^{63} - 12 q^{64} - 12 q^{66} + 24 q^{67} - 8 q^{68} - 16 q^{69} - 12 q^{71} + 12 q^{74} + 6 q^{76} + 24 q^{77} - 10 q^{78} - 4 q^{79} - 6 q^{81} + 8 q^{82} - 12 q^{84} + 14 q^{87} + 6 q^{88} - 18 q^{89} + 2 q^{91} + 32 q^{92} - 6 q^{93} + 8 q^{94} - 24 q^{97} + 24 q^{98}+O(q^{100}) $ 12 * q + 6 * q^3 + 6 * q^4 - 12 * q^7 - 6 * q^9 + 6 * q^11 + 12 * q^12 + 4 * q^13 - 4 * q^14 - 6 * q^16 + 8 * q^17 + 6 * q^19 - 6 * q^22 + 16 * q^23 - 2 * q^26 - 12 * q^27 - 12 * q^28 - 14 * q^29 + 6 * q^33 + 6 * q^36 - 6 * q^37 - 8 * q^38 + 2 * q^39 - 18 * q^41 - 2 * q^42 + 10 * q^43 - 6 * q^46 + 6 * q^48 - 8 * q^49 + 16 * q^51 + 2 * q^52 - 2 * q^56 + 6 * q^58 + 36 * q^59 + 10 * q^61 + 16 * q^62 + 12 * q^63 - 12 * q^64 - 12 * q^66 + 24 * q^67 - 8 * q^68 - 16 * q^69 - 12 * q^71 + 12 * q^74 + 6 * q^76 + 24 * q^77 - 10 * q^78 - 4 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^84 + 14 * q^87 + 6 * q^88 - 18 * q^89 + 2 * q^91 + 32 * q^92 - 6 * q^93 + 8 * q^94 - 24 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	−0.749482	+	0.432713i	−0.283277	+	0.163550i	−0.634906	−	0.772589i	$-0.718961\pi$
$7$	−0.749482	+	0.432713i	−0.283277	+	0.163550i	0.351629	+	0.936140i	$0.385628\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	0.151430	+	0.0874279i	0.0456577	+	0.0263605i	0.522655	−	0.852544i	$-0.324942\pi$
$11$	0.151430	+	0.0874279i	0.0456577	+	0.0263605i	−0.476997	+	0.878905i	$0.658275\pi$
$12$	1.00000			0.288675
$13$	3.34131	−	1.35486i	0.926713	−	0.375770i
$13$	3.34131	−	1.35486i	0.926713	−	0.375770i
$14$	0.865427			0.231295
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.08960	+	7.08339i	0.991873	+	1.71797i	0.606125	+	0.795370i	$0.292723\pi$
$17$	4.08960	+	7.08339i	0.991873	+	1.71797i	0.385748	+	0.922604i	$0.373943\pi$
$18$			1.00000i			0.235702i
$19$	−5.20843	+	3.00709i	−1.19490	+	0.689873i	−0.959413	−	0.282005i	$-0.909000\pi$
$19$	−5.20843	+	3.00709i	−1.19490	+	0.689873i	−0.235483	+	0.971879i	$0.575667\pi$
$20$		0			0
$21$			0.865427i			0.188852i
$22$	−0.0874279	−	0.151430i	−0.0186397	−	0.0322849i
$23$	1.45614	−	2.52211i	0.303626	−	0.525896i	−0.673328	−	0.739344i	$-0.735136\pi$
$23$	1.45614	−	2.52211i	0.303626	−	0.525896i	0.976954	+	0.213448i	$0.0684693\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$		0			0
$26$	−3.57109	−	0.497314i	−0.700348	−	0.0975312i
$27$	−1.00000			−0.192450
$28$	−0.749482	−	0.432713i	−0.141639	−	0.0817752i
$29$	−3.24491	+	5.62035i	−0.602564	+	1.04367i	0.389867	+	0.920871i	$0.372521\pi$
$29$	−3.24491	+	5.62035i	−0.602564	+	1.04367i	−0.992431	+	0.122801i	$0.960812\pi$
$30$		0			0
$31$			6.95057i			1.24836i	0.781281	+	0.624180i	$0.214567\pi$
$31$			6.95057i			1.24836i	−0.781281	+	0.624180i	$0.785433\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	0.151430	−	0.0874279i	0.0263605	−	0.0152192i
$34$		−	8.17919i		−	1.40272i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−1.52347	−	0.879573i	−0.250456	−	0.144601i	0.369517	−	0.929224i	$-0.379523\pi$
$37$	−1.52347	−	0.879573i	−0.250456	−	0.144601i	−0.619973	+	0.784623i	$0.712856\pi$
$38$	6.01418			0.975628
$39$	0.497314	−	3.57109i	0.0796339	−	0.571832i
$40$		0			0
$41$	−7.08339	−	4.08960i	−1.10624	−	0.638688i	−0.168387	−	0.985721i	$-0.553856\pi$
$41$	−7.08339	−	4.08960i	−1.10624	−	0.638688i	−0.937853	+	0.347034i	$0.887189\pi$
$42$	0.432713	−	0.749482i	0.0667691	−	0.115648i
$43$	4.58691	+	7.94476i	0.699497	+	1.21156i	0.968641	+	0.248465i	$0.0799259\pi$
$43$	4.58691	+	7.94476i	0.699497	+	1.21156i	−0.269144	+	0.963100i	$0.586741\pi$
$44$			0.174856i			0.0263605i
$45$		0			0
$46$	−2.52211	+	1.45614i	−0.371865	+	0.214696i
$47$		−	11.9021i		−	1.73610i	−0.496478	−	0.868050i	$-0.665373\pi$
$47$		−	11.9021i		−	1.73610i	0.496478	−	0.868050i	$-0.334627\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−3.12552	+	5.41356i	−0.446503	+	0.773365i
$50$		0			0
$51$	8.17919			1.14532
$52$	2.84400	+	2.21623i	0.394391	+	0.307336i
$53$	2.48735			0.341663			0.170832	−	0.985300i	$-0.445355\pi$
$53$	2.48735			0.341663			0.170832	+	0.985300i	$0.445355\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$		0			0
$56$	0.432713	+	0.749482i	0.0578238	+	0.100154i
$57$			6.01418i			0.796597i
$58$	5.62035	−	3.24491i	0.737988	−	0.426077i
$59$	6.09393	−	3.51833i	0.793363	−	0.458048i	−0.0477824	−	0.998858i	$-0.515215\pi$
$59$	6.09393	−	3.51833i	0.793363	−	0.458048i	0.841145	+	0.540810i	$0.181882\pi$
$60$		0			0
$61$	3.98695	+	6.90559i	0.510476	+	0.884171i	0.999926	+	0.0121394i	$0.00386418\pi$
$61$	3.98695	+	6.90559i	0.510476	+	0.884171i	−0.489450	+	0.872031i	$0.662802\pi$
$62$	3.47529	−	6.01937i	0.441362	−	0.764461i
$63$	0.749482	+	0.432713i	0.0944258	+	0.0545168i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−0.174856			−0.0215233
$67$	2.36886	+	1.36766i	0.289402	+	0.167086i	0.637672	−	0.770308i	$-0.279897\pi$
$67$	2.36886	+	1.36766i	0.289402	+	0.167086i	−0.348270	+	0.937394i	$0.613231\pi$
$68$	−4.08960	+	7.08339i	−0.495936	+	0.858987i
$69$	−1.45614	−	2.52211i	−0.175299	−	0.303626i
$70$		0			0
$71$	12.2677	−	7.08275i	1.45591	−	0.840568i	0.457100	−	0.889415i	$-0.348888\pi$
$71$	12.2677	−	7.08275i	1.45591	−	0.840568i	0.998806	+	0.0488476i	$0.0155549\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$			12.8706i			1.50639i	0.657800	+	0.753193i	$0.271487\pi$
$73$			12.8706i			1.50639i	−0.657800	+	0.753193i	$0.728513\pi$
$74$	0.879573	+	1.52347i	0.102248	+	0.177099i
$75$		0			0
$76$	−5.20843	−	3.00709i	−0.597448	−	0.344937i
$77$	−0.151325			−0.0172451
$78$	−2.21623	+	2.84400i	−0.250939	+	0.322019i
$79$	−9.48961			−1.06766			−0.533832	−	0.845590i	$-0.679249\pi$
$79$	−9.48961			−1.06766			−0.533832	+	0.845590i	$0.679249\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.08960	+	7.08339i	0.451620	+	0.782229i
$83$		−	0.139544i		−	0.0153169i	−0.999971	−	0.00765845i	$-0.997562\pi$
$83$		−	0.139544i		−	0.0153169i	0.999971	−	0.00765845i	$-0.00243778\pi$
$84$	−0.749482	+	0.432713i	−0.0817752	+	0.0472129i
$85$		0			0
$86$		−	9.17382i		−	0.989238i
$87$	3.24491	+	5.62035i	0.347891	+	0.602564i
$88$	0.0874279	−	0.151430i	0.00931985	−	0.0161424i
$89$	11.3790	+	6.56966i	1.20617	+	0.696382i	0.961920	−	0.273330i	$-0.0881253\pi$
$89$	11.3790	+	6.56966i	1.20617	+	0.696382i	0.244249	+	0.969713i	$0.421459\pi$
$90$		0			0
$91$	−1.91799	+	2.46127i	−0.201060	+	0.258011i
$92$	2.91228			0.303626
$93$	6.01937	+	3.47529i	0.624180	+	0.360370i
$94$	−5.95105	+	10.3075i	−0.613804	+	1.06314i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	7.48957	−	4.32411i	0.760451	−	0.439047i	−0.0690066	−	0.997616i	$-0.521983\pi$
$97$	7.48957	−	4.32411i	0.760451	−	0.439047i	0.829458	+	0.558570i	$0.188650\pi$
$98$	5.41356	−	3.12552i	0.546852	−	0.315725i
$99$		−	0.174856i		−	0.0175737i
$100$		0			0
$101$	−5.28276	+	9.15001i	−0.525654	+	0.910460i	0.473899	+	0.880579i	$0.342846\pi$
$101$	−5.28276	+	9.15001i	−0.525654	+	0.910460i	−0.999553	+	0.0298810i	$0.990487\pi$
$102$	−7.08339	−	4.08960i	−0.701360	−	0.404930i
$103$	8.93568			0.880459			0.440230	−	0.897885i	$-0.354897\pi$
$103$	8.93568			0.880459			0.440230	+	0.897885i	$0.354897\pi$
$104$	−1.35486	−	3.34131i	−0.132855	−	0.327642i
$105$		0			0
$106$	−2.15410	−	1.24367i	−0.209225	−	0.120796i
$107$	0.430389	−	0.745455i	0.0416072	−	0.0720658i	−0.844472	−	0.535600i	$-0.820086\pi$
$107$	0.430389	−	0.745455i	0.0416072	−	0.0720658i	0.886079	+	0.463534i	$0.153419\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$			5.45336i			0.522337i	0.965293	+	0.261168i	$0.0841078\pi$
$109$			5.45336i			0.522337i	−0.965293	+	0.261168i	$0.915892\pi$
$110$		0			0
$111$	−1.52347	+	0.879573i	−0.144601	+	0.0834854i
$112$		−	0.865427i		−	0.0817752i
$113$	5.89106	+	10.2036i	0.554184	+	0.959876i	0.997966	+	0.0637409i	$0.0203031\pi$
$113$	5.89106	+	10.2036i	0.554184	+	0.959876i	−0.443782	+	0.896135i	$0.646364\pi$
$114$	3.00709	−	5.20843i	0.281640	−	0.487814i
$115$		0			0
$116$	−6.48982			−0.602564
$117$	−2.84400	−	2.21623i	−0.262928	−	0.204891i
$118$	−7.03667			−0.647778
$119$	−6.13015	−	3.53925i	−0.561950	−	0.324442i
$120$		0			0
$121$	−5.48471	−	9.49980i	−0.498610	−	0.863618i
$122$		−	7.97389i		−	0.721922i
$123$	−7.08339	+	4.08960i	−0.638688	+	0.368746i
$124$	−6.01937	+	3.47529i	−0.540555	+	0.312090i
$125$		0			0
$126$	−0.432713	−	0.749482i	−0.0385492	−	0.0667691i
$127$	−3.47119	+	6.01228i	−0.308018	+	0.533503i	−0.977929	−	0.208939i	$-0.932999\pi$
$127$	−3.47119	+	6.01228i	−0.308018	+	0.533503i	0.669911	+	0.742442i	$0.266332\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	9.17382			0.807710
$130$		0			0
$131$	2.27133			0.198447			0.0992235	−	0.995065i	$-0.468364\pi$
$131$	2.27133			0.198447			0.0992235	+	0.995065i	$0.468364\pi$
$132$	0.151430	+	0.0874279i	0.0131803	+	0.00760962i
$133$	2.60241	−	4.50751i	0.225658	−	0.390851i
$134$	−1.36766	−	2.36886i	−0.118148	−	0.204638i
$135$		0			0
$136$	7.08339	−	4.08960i	0.607395	−	0.350680i
$137$	−6.38795	+	3.68809i	−0.545760	+	0.315094i	−0.747410	−	0.664363i	$-0.768703\pi$
$137$	−6.38795	+	3.68809i	−0.545760	+	0.315094i	0.201650	+	0.979458i	$0.435370\pi$
$138$			2.91228i			0.247910i
$139$	−0.410380	−	0.710798i	−0.0348079	−	0.0602891i	0.848097	−	0.529842i	$-0.177749\pi$
$139$	−0.410380	−	0.710798i	−0.0348079	−	0.0602891i	−0.882905	+	0.469552i	$0.844415\pi$
$140$		0			0
$141$	−10.3075	−	5.95105i	−0.868050	−	0.501169i
$142$	−14.1655			−1.18874
$143$	0.624426	+	0.0869582i	0.0522171	+	0.00727181i
$144$	1.00000			0.0833333
$145$		0			0
$146$	6.43528	−	11.1462i	0.532588	−	0.922469i
$147$	3.12552	+	5.41356i	0.257788	+	0.446503i
$148$		−	1.75915i		−	0.144601i
$149$	8.90766	−	5.14284i	0.729744	−	0.421318i	−0.0885845	−	0.996069i	$-0.528234\pi$
$149$	8.90766	−	5.14284i	0.729744	−	0.421318i	0.818329	+	0.574751i	$0.194901\pi$
$150$		0			0
$151$			11.7419i			0.955544i	0.878484	+	0.477772i	$0.158555\pi$
$151$			11.7419i			0.955544i	−0.878484	+	0.477772i	$0.841445\pi$
$152$	3.00709	+	5.20843i	0.243907	+	0.422459i
$153$	4.08960	−	7.08339i	0.330624	−	0.572658i
$154$	0.131051	+	0.0756625i	0.0105604	+	0.00609706i
$155$		0			0
$156$	3.34131	−	1.35486i	0.267519	−	0.108475i
$157$	6.76034			0.539534			0.269767	−	0.962926i	$-0.413053\pi$
$157$	6.76034			0.539534			0.269767	+	0.962926i	$0.413053\pi$
$158$	8.21824	+	4.74480i	0.653808	+	0.377476i
$159$	1.24367	−	2.15410i	0.0986297	−	0.170832i
$160$		0			0
$161$			2.52036i			0.198633i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	−1.23624	+	0.713746i	−0.0968301	+	0.0559049i	−0.547633	−	0.836719i	$-0.684471\pi$
$163$	−1.23624	+	0.713746i	−0.0968301	+	0.0559049i	0.450803	+	0.892623i	$0.351138\pi$
$164$		−	8.17919i		−	0.638688i
$165$		0			0
$166$	−0.0697718	+	0.120848i	−0.00541534	+	0.00937964i
$167$	5.08406	+	2.93528i	0.393416	+	0.227139i	0.683639	−	0.729820i	$-0.260396\pi$
$167$	5.08406	+	2.93528i	0.393416	+	0.227139i	−0.290223	+	0.956959i	$0.593729\pi$
$168$	0.865427			0.0667691
$169$	9.32872	−	9.05401i	0.717594	−	0.696462i
$170$		0			0
$171$	5.20843	+	3.00709i	0.398298	+	0.229958i
$172$	−4.58691	+	7.94476i	−0.349749	+	0.605782i
$173$	−6.85138	−	11.8669i	−0.520901	−	0.902226i	−0.999705	−	0.0243045i	$-0.992263\pi$
$173$	−6.85138	−	11.8669i	−0.520901	−	0.902226i	0.478804	−	0.877922i	$-0.341070\pi$
$174$		−	6.48982i		−	0.491992i
$175$		0			0
$176$	−0.151430	+	0.0874279i	−0.0114144	+	0.00659013i
$177$		−	7.03667i		−	0.528908i
$178$	−6.56966	−	11.3790i	−0.492416	−	0.852890i
$179$	7.09191	−	12.2835i	0.530074	−	0.918115i	−0.469310	−	0.883033i	$-0.655497\pi$
$179$	7.09191	−	12.2835i	0.530074	−	0.918115i	0.999384	−	0.0350821i	$-0.0111693\pi$
$180$		0			0
$181$	13.7728			1.02373			0.511863	−	0.859067i	$-0.328956\pi$
$181$	13.7728			1.02373			0.511863	+	0.859067i	$0.328956\pi$
$182$	2.89166	−	1.17253i	0.214344	−	0.0869138i
$183$	7.97389			0.589447
$184$	−2.52211	−	1.45614i	−0.185932	−	0.107348i
$185$		0			0
$186$	−3.47529	−	6.01937i	−0.254820	−	0.441362i
$187$			1.43018i			0.104585i
$188$	10.3075	−	5.95105i	0.751753	−	0.434025i
$189$	0.749482	−	0.432713i	0.0545168	−	0.0314753i
$190$		0			0
$191$	2.78821	+	4.82932i	0.201748	+	0.349437i	0.949092	−	0.315000i	$-0.102005\pi$
$191$	2.78821	+	4.82932i	0.201748	+	0.349437i	−0.747344	+	0.664437i	$0.768671\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	0.191227	+	0.110405i	0.0137648	+	0.00794712i	0.506867	−	0.862024i	$-0.330804\pi$
$193$	0.191227	+	0.110405i	0.0137648	+	0.00794712i	−0.493102	+	0.869972i	$0.664137\pi$
$194$	−8.64822			−0.620906
$195$		0			0
$196$	−6.25104			−0.446503
$197$	1.49286	+	0.861905i	0.106362	+	0.0614082i	0.552237	−	0.833687i	$-0.313774\pi$
$197$	1.49286	+	0.861905i	0.106362	+	0.0614082i	−0.445875	+	0.895095i	$0.647108\pi$
$198$	−0.0874279	+	0.151430i	−0.00621323	+	0.0107616i
$199$	3.97927	+	6.89229i	0.282083	+	0.488581i	0.971898	−	0.235404i	$-0.0756414\pi$
$199$	3.97927	+	6.89229i	0.282083	+	0.488581i	−0.689815	+	0.723986i	$0.742308\pi$
$200$		0			0
$201$	2.36886	−	1.36766i	0.167086	−	0.0964673i
$202$	9.15001	−	5.28276i	0.643793	−	0.371694i
$203$		−	5.61646i		−	0.394198i
$204$	4.08960	+	7.08339i	0.286329	+	0.495936i
$205$		0			0
$206$	−7.73853	−	4.46784i	−0.539169	−	0.311289i
$207$	−2.91228			−0.202417
$208$	−0.497314	+	3.57109i	−0.0344825	+	0.247610i
$209$	−1.05161			−0.0727416
$210$		0			0
$211$	2.10991	−	3.65448i	0.145252	−	0.251585i	−0.784215	−	0.620490i	$-0.786934\pi$
$211$	2.10991	−	3.65448i	0.145252	−	0.251585i	0.929467	+	0.368905i	$0.120267\pi$
$212$	1.24367	+	2.15410i	0.0854158	+	0.147945i
$213$		−	14.1655i		−	0.970604i
$214$	−0.745455	+	0.430389i	−0.0509582	+	0.0294208i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	−3.00761	−	5.20933i	−0.204170	−	0.353632i
$218$	2.72668	−	4.72274i	0.184674	−	0.319865i
$219$	11.1462	+	6.43528i	0.753193	+	0.434856i
$220$		0			0
$221$	23.2616	+	18.1270i	1.56474	+	1.21935i
$222$	1.75915			0.118066
$223$	−6.02126	−	3.47638i	−0.403214	−	0.232795i	0.284656	−	0.958630i	$-0.408121\pi$
$223$	−6.02126	−	3.47638i	−0.403214	−	0.232795i	−0.687870	+	0.725834i	$0.741454\pi$
$224$	−0.432713	+	0.749482i	−0.0289119	+	0.0500769i
$225$		0			0
$226$		−	11.7821i		−	0.783735i
$227$	−2.50840	+	1.44823i	−0.166488	+	0.0961221i	−0.580929	−	0.813954i	$-0.697311\pi$
$227$	−2.50840	+	1.44823i	−0.166488	+	0.0961221i	0.414441	+	0.910076i	$0.363977\pi$
$228$	−5.20843	+	3.00709i	−0.344937	+	0.199149i
$229$			7.88800i			0.521254i	0.965440	+	0.260627i	$0.0839293\pi$
$229$			7.88800i			0.521254i	−0.965440	+	0.260627i	$0.916071\pi$
$230$		0			0
$231$	−0.0756625	+	0.131051i	−0.00497823	+	0.00862254i
$232$	5.62035	+	3.24491i	0.368994	+	0.213039i
$233$	−1.42749			−0.0935181			−0.0467590	−	0.998906i	$-0.514889\pi$
$233$	−1.42749			−0.0935181			−0.0467590	+	0.998906i	$0.514889\pi$
$234$	1.35486	+	3.34131i	0.0885699	+	0.218428i
$235$		0			0
$236$	6.09393	+	3.51833i	0.396681	+	0.229024i
$237$	−4.74480	+	8.21824i	−0.308208	+	0.533832i
$238$	3.53925	+	6.13015i	0.229415	+	0.397359i
$239$		−	10.9084i		−	0.705604i	−0.935698	−	0.352802i	$-0.885229\pi$
$239$		−	10.9084i		−	0.705604i	0.935698	−	0.352802i	$-0.114771\pi$
$240$		0			0
$241$	−25.4317	+	14.6830i	−1.63820	+	0.945816i	−0.656749	+	0.754109i	$0.728069\pi$
$241$	−25.4317	+	14.6830i	−1.63820	+	0.945816i	−0.981452	+	0.191707i	$0.938598\pi$
$242$			10.9694i			0.705141i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−3.98695	+	6.90559i	−0.255238	+	0.442085i
$245$		0			0
$246$	8.17919			0.521486
$247$	−13.3288	+	17.1043i	−0.848091	+	1.08832i
$248$	6.95057			0.441362
$249$	−0.120848	−	0.0697718i	−0.00765845	−	0.00442161i
$250$		0			0
$251$	8.94708	+	15.4968i	0.564735	+	0.978150i	0.997074	+	0.0764387i	$0.0243549\pi$
$251$	8.94708	+	15.4968i	0.564735	+	0.978150i	−0.432339	+	0.901711i	$0.642312\pi$
$252$			0.865427i			0.0545168i
$253$	0.441005	−	0.254615i	0.0277258	−	0.0160075i
$254$	6.01228	−	3.47119i	0.377244	−	0.217802i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.08945	−	10.5472i	0.379849	−	0.657918i	−0.611191	−	0.791483i	$-0.709309\pi$
$257$	6.08945	−	10.5472i	0.379849	−	0.657918i	0.991040	+	0.133565i	$0.0426425\pi$
$258$	−7.94476	−	4.58691i	−0.494619	−	0.285568i
$259$	1.52241			0.0945981
$260$		0			0
$261$	6.48982			0.401710
$262$	−1.96703	−	1.13567i	−0.121524	−	0.0701616i
$263$	−10.5834	+	18.3309i	−0.652598	+	1.13033i	0.329892	+	0.944019i	$0.392988\pi$
$263$	−10.5834	+	18.3309i	−0.652598	+	1.13033i	−0.982490	+	0.186314i	$0.940346\pi$
$264$	−0.0874279	−	0.151430i	−0.00538082	−	0.00931985i
$265$		0			0
$266$	−4.50751	+	2.60241i	−0.276373	+	0.159564i
$267$	11.3790	−	6.56966i	0.696382	−	0.402056i
$268$			2.73532i			0.167086i
$269$	6.04371	+	10.4680i	0.368492	+	0.638246i	0.989330	−	0.145692i	$-0.0465410\pi$
$269$	6.04371	+	10.4680i	0.368492	+	0.638246i	−0.620838	+	0.783939i	$0.713208\pi$
$270$		0			0
$271$	−12.7275	−	7.34824i	−0.773142	−	0.446374i	0.0608525	−	0.998147i	$-0.480618\pi$
$271$	−12.7275	−	7.34824i	−0.773142	−	0.446374i	−0.833994	+	0.551773i	$0.813951\pi$
$272$	−8.17919			−0.495936
$273$	1.17253	+	2.89166i	0.0709648	+	0.175011i
$274$	7.37617			0.445611
$275$		0			0
$276$	1.45614	−	2.52211i	0.0876493	−	0.151813i
$277$	−9.85638	−	17.0717i	−0.592212	−	1.02574i	−0.993934	−	0.109980i	$-0.964921\pi$
$277$	−9.85638	−	17.0717i	−0.592212	−	1.02574i	0.401722	−	0.915762i	$-0.368412\pi$
$278$			0.820759i			0.0492259i
$279$	6.01937	−	3.47529i	0.360370	−	0.208060i
$280$		0			0
$281$		−	9.93073i		−	0.592418i	−0.955123	−	0.296209i	$-0.904278\pi$
$281$		−	9.93073i		−	0.592418i	0.955123	−	0.296209i	$-0.0957225\pi$
$282$	5.95105	+	10.3075i	0.354380	+	0.613804i
$283$	5.81912	−	10.0790i	0.345911	−	0.599135i	−0.639608	−	0.768701i	$-0.720903\pi$
$283$	5.81912	−	10.0790i	0.345911	−	0.599135i	0.985519	+	0.169566i	$0.0542366\pi$
$284$	12.2677	+	7.08275i	0.727953	+	0.420284i
$285$		0			0
$286$	−0.497290	−	0.387521i	−0.0294053	−	0.0229146i
$287$	7.07849			0.417830
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	−24.9496	+	43.2139i	−1.46762	+	2.54200i
$290$		0			0
$291$		−	8.64822i		−	0.506967i
$292$	−11.1462	+	6.43528i	−0.652284	+	0.376596i
$293$	11.3906	−	6.57636i	0.665445	−	0.384195i	−0.128903	−	0.991657i	$-0.541146\pi$
$293$	11.3906	−	6.57636i	0.665445	−	0.384195i	0.794349	+	0.607462i	$0.207812\pi$
$294$		−	6.25104i		−	0.364568i
$295$		0			0
$296$	−0.879573	+	1.52347i	−0.0511241	+	0.0885496i
$297$	−0.151430	−	0.0874279i	−0.00878684	−	0.00507308i
$298$	−10.2857			−0.595834
$299$	1.44832	−	10.4000i	0.0837583	−	0.601448i
$300$		0			0
$301$	−6.87561	−	3.96963i	−0.396304	−	0.228806i
$302$	5.87096	−	10.1688i	0.337836	−	0.585149i
$303$	5.28276	+	9.15001i	0.303487	+	0.525654i
$304$		−	6.01418i		−	0.344937i
$305$		0			0
$306$	−7.08339	+	4.08960i	−0.404930	+	0.233787i
$307$		−	14.8609i		−	0.848155i	−0.905626	−	0.424077i	$-0.860598\pi$
$307$		−	14.8609i		−	0.848155i	0.905626	−	0.424077i	$-0.139402\pi$
$308$	−0.0756625	−	0.131051i	−0.00431127	−	0.00746734i
$309$	4.46784	−	7.73853i	0.254167	−	0.440230i
$310$		0			0
$311$	9.17666			0.520361			0.260180	−	0.965560i	$-0.416218\pi$
$311$	9.17666			0.520361			0.260180	+	0.965560i	$0.416218\pi$
$312$	−3.57109	−	0.497314i	−0.202173	−	0.0281548i
$313$	−7.43905			−0.420480			−0.210240	−	0.977650i	$-0.567424\pi$
$313$	−7.43905			−0.420480			−0.210240	+	0.977650i	$0.567424\pi$
$314$	−5.85463	−	3.38017i	−0.330396	−	0.190754i
$315$		0			0
$316$	−4.74480	−	8.21824i	−0.266916	−	0.462312i
$317$		−	25.7510i		−	1.44632i	−0.690679	−	0.723161i	$-0.742688\pi$
$317$		−	25.7510i		−	1.44632i	0.690679	−	0.723161i	$-0.257312\pi$
$318$	−2.15410	+	1.24367i	−0.120796	+	0.0697417i
$319$	−0.982750	+	0.567391i	−0.0550235	+	0.0317678i
$320$		0			0
$321$	−0.430389	−	0.745455i	−0.0240219	−	0.0416072i
$322$	1.26018	−	2.18270i	0.0702272	−	0.121637i
$323$	−42.6007	−	24.5955i	−2.37037	−	1.36853i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	1.42749			0.0790614
$327$	4.72274	+	2.72668i	0.261168	+	0.150786i
$328$	−4.08960	+	7.08339i	−0.225810	+	0.391115i
$329$	5.15020	+	8.92040i	0.283940	+	0.491798i
$330$		0			0
$331$	5.63295	−	3.25219i	0.309615	−	0.178756i	−0.337139	−	0.941455i	$-0.609459\pi$
$331$	5.63295	−	3.25219i	0.309615	−	0.178756i	0.646754	+	0.762699i	$0.276126\pi$
$332$	0.120848	−	0.0697718i	0.00663241	−	0.00382922i
$333$			1.75915i			0.0964006i
$334$	−2.93528	−	5.08406i	−0.160612	−	0.278187i
$335$		0			0
$336$	−0.749482	−	0.432713i	−0.0408876	−	0.0236065i
$337$	18.6696			1.01700			0.508498	−	0.861063i	$-0.330201\pi$
$337$	18.6696			1.01700			0.508498	+	0.861063i	$0.330201\pi$
$338$	−12.6059	+	3.17664i	−0.685671	+	0.172786i
$339$	11.7821			0.639917
$340$		0			0
$341$	−0.607674	+	1.05252i	−0.0329074	+	0.0569973i
$342$	−3.00709	−	5.20843i	−0.162605	−	0.281640i
$343$		−	11.4678i		−	0.619203i
$344$	7.94476	−	4.58691i	0.428353	−	0.247310i
$345$		0			0
$346$			13.7028i			0.736665i
$347$	−14.2033	−	24.6009i	−0.762474	−	1.32064i	−0.941572	−	0.336813i	$-0.890651\pi$
$347$	−14.2033	−	24.6009i	−0.762474	−	1.32064i	0.179098	−	0.983831i	$-0.442682\pi$
$348$	−3.24491	+	5.62035i	−0.173945	+	0.301282i
$349$	−1.93797	−	1.11889i	−0.103737	−	0.0598926i	0.447234	−	0.894417i	$-0.352409\pi$
$349$	−1.93797	−	1.11889i	−0.103737	−	0.0598926i	−0.550971	+	0.834524i	$0.685742\pi$
$350$		0			0
$351$	−3.34131	+	1.35486i	−0.178346	+	0.0723170i
$352$	0.174856			0.00931985
$353$	−1.40866	−	0.813287i	−0.0749751	−	0.0432869i	0.462044	−	0.886857i	$-0.347116\pi$
$353$	−1.40866	−	0.813287i	−0.0749751	−	0.0432869i	−0.537019	+	0.843570i	$0.680450\pi$
$354$	−3.51833	+	6.09393i	−0.186997	+	0.323889i
$355$		0			0
$356$			13.1393i			0.696382i
$357$	−6.13015	+	3.53925i	−0.324442	+	0.187317i
$358$	−12.2835	+	7.09191i	−0.649206	+	0.374819i
$359$		−	34.4613i		−	1.81880i	−0.415923	−	0.909400i	$-0.636541\pi$
$359$		−	34.4613i		−	1.81880i	0.415923	−	0.909400i	$-0.363459\pi$
$360$		0			0
$361$	8.58515	−	14.8699i	0.451850	−	0.782627i
$362$	−11.9276	−	6.88641i	−0.626901	−	0.361942i
$363$	−10.9694			−0.575746
$364$	−3.09052	−	0.430389i	−0.161987	−	0.0225585i
$365$		0			0
$366$	−6.90559	−	3.98695i	−0.360961	−	0.208401i
$367$	−7.31703	+	12.6735i	−0.381946	+	0.661550i	−0.991340	−	0.131317i	$-0.958079\pi$
$367$	−7.31703	+	12.6735i	−0.381946	+	0.661550i	0.609394	+	0.792867i	$0.291413\pi$
$368$	1.45614	+	2.52211i	0.0759065	+	0.131474i
$369$			8.17919i			0.425792i
$370$		0			0
$371$	−1.86422	+	1.07631i	−0.0967855	+	0.0558791i
$372$			6.95057i			0.360370i
$373$	11.0370	+	19.1166i	0.571472	+	0.989819i	0.996415	+	0.0845988i	$0.0269609\pi$
$373$	11.0370	+	19.1166i	0.571472	+	0.989819i	−0.424943	+	0.905220i	$0.639706\pi$
$374$	0.715090	−	1.23857i	0.0369764	−	0.0640450i
$375$		0			0
$376$	−11.9021			−0.613804
$377$	−3.22747	+	23.1757i	−0.166223	+	1.19361i
$378$	−0.865427			−0.0445128
$379$	−12.0573	−	6.96127i	−0.619341	−	0.357577i	0.157272	−	0.987555i	$-0.449730\pi$
$379$	−12.0573	−	6.96127i	−0.619341	−	0.357577i	−0.776612	+	0.629979i	$0.783064\pi$
$380$		0			0
$381$	3.47119	+	6.01228i	0.177834	+	0.308018i
$382$		−	5.57642i		−	0.285314i
$383$	−21.3119	+	12.3044i	−1.08899	+	0.628728i	−0.933307	−	0.359080i	$-0.883091\pi$
$383$	−21.3119	+	12.3044i	−1.08899	+	0.628728i	−0.155681	+	0.987807i	$0.549757\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$		0			0
$386$	−0.110405	−	0.191227i	−0.00561946	−	0.00973319i
$387$	4.58691	−	7.94476i	0.233166	−	0.403855i
$388$	7.48957	+	4.32411i	0.380226	+	0.219523i
$389$	−5.60980			−0.284428			−0.142214	−	0.989836i	$-0.545422\pi$
$389$	−5.60980			−0.284428			−0.142214	+	0.989836i	$0.545422\pi$
$390$		0			0
$391$	23.8201			1.20463
$392$	5.41356	+	3.12552i	0.273426	+	0.157863i
$393$	1.13567	−	1.96703i	0.0572867	−	0.0992235i
$394$	−0.861905	−	1.49286i	−0.0434222	−	0.0752094i
$395$		0			0
$396$	0.151430	−	0.0874279i	0.00760962	−	0.00439342i
$397$	2.05141	−	1.18438i	0.102957	−	0.0594424i	−0.447637	−	0.894215i	$-0.647734\pi$
$397$	2.05141	−	1.18438i	0.102957	−	0.0594424i	0.550595	+	0.834773i	$0.314401\pi$
$398$		−	7.95853i		−	0.398925i
$399$	−2.60241	−	4.50751i	−0.130284	−	0.225658i
$400$		0			0
$401$	14.2942	+	8.25276i	0.713818	+	0.412123i	0.812473	−	0.582998i	$-0.198121\pi$
$401$	14.2942	+	8.25276i	0.713818	+	0.412123i	−0.0986548	+	0.995122i	$0.531454\pi$
$402$	−2.73532			−0.136425
$403$	9.41704	+	23.2240i	0.469096	+	1.15687i
$404$	−10.5655			−0.525654
$405$		0			0
$406$	−2.80823	+	4.86400i	−0.139370	+	0.241396i
$407$	−0.153798	−	0.266387i	−0.00762351	−	0.0132043i
$408$		−	8.17919i		−	0.404930i
$409$	−28.8448	+	16.6535i	−1.42628	+	0.823464i	−0.996825	−	0.0796230i	$-0.974628\pi$
$409$	−28.8448	+	16.6535i	−1.42628	+	0.823464i	−0.429457	+	0.903087i	$0.641295\pi$
$410$		0			0
$411$			7.37617i			0.363840i
$412$	4.46784	+	7.73853i	0.220115	+	0.381250i
$413$	−3.04486	+	5.27385i	−0.149828	+	0.259509i
$414$	2.52211	+	1.45614i	0.123955	+	0.0715654i
$415$		0			0
$416$	2.21623	−	2.84400i	0.108660	−	0.139438i
$417$	−0.820759			−0.0401927
$418$	0.910724	+	0.525807i	0.0445450	+	0.0257181i
$419$	−15.1303	+	26.2065i	−0.739164	+	1.28027i	0.213708	+	0.976898i	$0.431446\pi$
$419$	−15.1303	+	26.2065i	−0.739164	+	1.28027i	−0.952872	+	0.303372i	$0.901887\pi$
$420$		0			0
$421$			40.2235i			1.96038i	0.198070	+	0.980188i	$0.436533\pi$
$421$			40.2235i			1.96038i	−0.198070	+	0.980188i	$0.563467\pi$
$422$	−3.65448	+	2.10991i	−0.177897	+	0.102709i
$423$	−10.3075	+	5.95105i	−0.501169	+	0.289350i
$424$		−	2.48735i		−	0.120796i
$425$		0			0
$426$	−7.08275	+	12.2677i	−0.343160	+	0.594371i
$427$	−5.97629	−	3.45041i	−0.289213	−	0.166977i
$428$	0.860777			0.0416072
$429$	0.387521	−	0.497290i	0.0187097	−	0.0240094i
$430$		0			0
$431$	−28.1980	−	16.2801i	−1.35825	−	0.784185i	−0.368860	−	0.929485i	$-0.620252\pi$
$431$	−28.1980	−	16.2801i	−1.35825	−	0.784185i	−0.989388	+	0.145300i	$0.953585\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−15.3663	−	26.6153i	−0.738460	−	1.27905i	−0.953189	−	0.302376i	$-0.902220\pi$
$433$	−15.3663	−	26.6153i	−0.738460	−	1.27905i	0.214729	−	0.976674i	$-0.431113\pi$
$434$			6.01521i			0.288739i
$435$		0			0
$436$	−4.72274	+	2.72668i	−0.226178	+	0.130584i
$437$			17.5150i			0.837854i
$438$	−6.43528	−	11.1462i	−0.307490	−	0.532588i
$439$	−3.26422	+	5.65380i	−0.155793	+	0.269841i	−0.933347	−	0.358974i	$-0.883127\pi$
$439$	−3.26422	+	5.65380i	−0.155793	+	0.269841i	0.777555	+	0.628815i	$0.216460\pi$
$440$		0			0
$441$	6.25104			0.297668
$442$	−11.0816	−	27.3292i	−0.527100	−	1.29992i
$443$	−30.3111			−1.44012			−0.720061	−	0.693911i	$-0.755886\pi$
$443$	−30.3111			−1.44012			−0.720061	+	0.693911i	$0.755886\pi$
$444$	−1.52347	−	0.879573i	−0.0723005	−	0.0417427i
$445$		0			0
$446$	3.47638	+	6.02126i	0.164611	+	0.285115i
$447$		−	10.2857i		−	0.486496i
$448$	0.749482	−	0.432713i	0.0354097	−	0.0204438i
$449$	−13.8034	+	7.96938i	−0.651421	+	0.376098i	−0.789001	−	0.614392i	$-0.789401\pi$
$449$	−13.8034	+	7.96938i	−0.651421	+	0.376098i	0.137579	+	0.990491i	$0.456068\pi$
$450$		0			0
$451$	−0.715090	−	1.23857i	−0.0336723	−	0.0583221i
$452$	−5.89106	+	10.2036i	−0.277092	+	0.479938i
$453$	10.1688	+	5.87096i	0.477772	+	0.275842i
$454$	2.89645			0.135937
$455$		0			0
$456$	6.01418			0.281640
$457$	17.1548	+	9.90436i	0.802470	+	0.463306i	0.844334	−	0.535817i	$-0.179996\pi$
$457$	17.1548	+	9.90436i	0.802470	+	0.463306i	−0.0418642	+	0.999123i	$0.513330\pi$
$458$	3.94400	−	6.83121i	0.184291	−	0.319202i
$459$	−4.08960	−	7.08339i	−0.190886	−	0.330624i
$460$		0			0
$461$	−11.5898	+	6.69139i	−0.539792	+	0.311649i	−0.744995	−	0.667070i	$-0.767548\pi$
$461$	−11.5898	+	6.69139i	−0.539792	+	0.311649i	0.205202	+	0.978720i	$0.434215\pi$
$462$	0.131051	−	0.0756625i	0.00609706	−	0.00352014i
$463$		−	42.3599i		−	1.96863i	−0.176412	−	0.984316i	$-0.556449\pi$
$463$		−	42.3599i		−	1.96863i	0.176412	−	0.984316i	$-0.443551\pi$
$464$	−3.24491	−	5.62035i	−0.150641	−	0.260918i
$465$		0			0
$466$	1.23624	+	0.713746i	0.0572679	+	0.0330636i
$467$	−33.4593			−1.54831			−0.774155	−	0.632996i	$-0.781825\pi$
$467$	−33.4593			−1.54831			−0.774155	+	0.632996i	$0.781825\pi$
$468$	0.497314	−	3.57109i	0.0229883	−	0.165074i
$469$	−2.36722			−0.109308
$470$		0			0
$471$	3.38017	−	5.85463i	0.155750	−	0.269767i
$472$	−3.51833	−	6.09393i	−0.161944	−	0.280496i
$473$			1.60410i			0.0737564i
$474$	8.21824	−	4.74480i	0.377476	−	0.217936i
$475$		0			0
$476$		−	7.07849i		−	0.324442i
$477$	−1.24367	−	2.15410i	−0.0569439	−	0.0986297i
$478$	−5.45418	+	9.44692i	−0.249469	+	0.432092i
$479$	19.3387	+	11.1652i	0.883606	+	0.510150i	0.871846	−	0.489781i	$-0.162923\pi$
$479$	19.3387	+	11.1652i	0.883606	+	0.510150i	0.0117600	+	0.999931i	$0.496257\pi$
$480$		0			0
$481$	−6.28207	−	0.874847i	−0.286438	−	0.0398896i
$482$	29.3660			1.33759
$483$	2.18270	+	1.26018i	0.0993163	+	0.0573403i
$484$	5.48471	−	9.49980i	0.249305	−	0.431809i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	24.8982	−	14.3750i	1.12824	−	0.651392i	0.184751	−	0.982785i	$-0.440852\pi$
$487$	24.8982	−	14.3750i	1.12824	−	0.651392i	0.943493	+	0.331393i	$0.107519\pi$
$488$	6.90559	−	3.98695i	0.312602	−	0.180481i
$489$			1.42749i			0.0645534i
$490$		0			0
$491$	8.02546	−	13.9005i	0.362184	−	0.627321i	−0.626136	−	0.779714i	$-0.715364\pi$
$491$	8.02546	−	13.9005i	0.362184	−	0.627321i	0.988320	+	0.152393i	$0.0486978\pi$
$492$	−7.08339	−	4.08960i	−0.319344	−	0.184373i
$493$	−53.0815			−2.39067
$494$	20.0952	−	8.14836i	0.904127	−	0.366612i
$495$		0			0
$496$	−6.01937	−	3.47529i	−0.270278	−	0.156045i
$497$	−6.12960	+	10.6168i	−0.274950	+	0.476228i
$498$	0.0697718	+	0.120848i	0.00312655	+	0.00541534i
$499$		−	33.2509i		−	1.48851i	−0.667894	−	0.744256i	$-0.732804\pi$
$499$		−	33.2509i		−	1.48851i	0.667894	−	0.744256i	$-0.267196\pi$
$500$		0			0
$501$	5.08406	−	2.93528i	0.227139	−	0.131139i
$502$		−	17.8942i		−	0.798656i
$503$	12.5710	+	21.7736i	0.560514	+	0.970838i	0.997452	+	0.0713466i	$0.0227296\pi$
$503$	12.5710	+	21.7736i	0.560514	+	0.970838i	−0.436938	+	0.899492i	$0.643937\pi$
$504$	0.432713	−	0.749482i	0.0192746	−	0.0333846i
$505$		0			0
$506$	−0.509229			−0.0226380
$507$	−3.17664	−	12.6059i	−0.141080	−	0.559848i
$508$	−6.94238			−0.308018
$509$	−22.8809	−	13.2103i	−1.01418	−	0.585536i	−0.101766	−	0.994808i	$-0.532449\pi$
$509$	−22.8809	−	13.2103i	−1.01418	−	0.585536i	−0.912412	+	0.409272i	$0.865783\pi$
$510$		0			0
$511$	−5.56927	−	9.64625i	−0.246370	−	0.426725i
$512$			1.00000i			0.0441942i
$513$	5.20843	−	3.00709i	0.229958	−	0.132766i
$514$	−10.5472	+	6.08945i	−0.465219	+	0.268594i
$515$		0			0
$516$	4.58691	+	7.94476i	0.201927	+	0.349749i
$517$	1.04058	−	1.80233i	0.0457645	−	0.0792664i
$518$	−1.31845	−	0.761206i	−0.0579293	−	0.0334455i
$519$	−13.7028			−0.601484
$520$		0			0
$521$	−22.4462			−0.983384			−0.491692	−	0.870769i	$-0.663621\pi$
$521$	−22.4462			−0.983384			−0.491692	+	0.870769i	$0.663621\pi$
$522$	−5.62035	−	3.24491i	−0.245996	−	0.142026i
$523$	14.5385	−	25.1815i	0.635726	−	1.10111i	−0.350635	−	0.936512i	$-0.614034\pi$
$523$	14.5385	−	25.1815i	0.635726	−	1.10111i	0.986361	−	0.164598i	$-0.0526326\pi$
$524$	1.13567	+	1.96703i	0.0496118	+	0.0859301i
$525$		0			0
$526$	18.3309	−	10.5834i	0.799266	−	0.461456i
$527$	−49.2336	+	28.4250i	−2.14465	+	1.23821i
$528$			0.174856i			0.00760962i
$529$	7.25931	+	12.5735i	0.315622	+	0.546674i
$530$		0			0
$531$	−6.09393	−	3.51833i	−0.264454	−	0.152683i
$532$	5.20483			0.225658
$533$	−29.2086	−	4.06762i	−1.26517	−	0.176188i
$534$	−13.1393			−0.568594
$535$		0			0
$536$	1.36766	−	2.36886i	0.0590739	−	0.102319i
$537$	−7.09191	−	12.2835i	−0.306038	−	0.530074i
$538$		−	12.0874i		−	0.521126i
$539$	−0.946592	+	0.546515i	−0.0407726	+	0.0235401i
$540$		0			0
$541$		−	8.17282i		−	0.351377i	−0.984446	−	0.175688i	$-0.943785\pi$
$541$		−	8.17282i		−	0.351377i	0.984446	−	0.175688i	$-0.0562151\pi$
$542$	7.34824	+	12.7275i	0.315634	+	0.546694i
$543$	6.88641	−	11.9276i	0.295524	−	0.511863i
$544$	7.08339	+	4.08960i	0.303698	+	0.175340i
$545$		0			0
$546$	0.430389	−	3.09052i	0.0184189	−	0.132262i
$547$	−40.7393			−1.74188			−0.870942	−	0.491385i	$-0.836491\pi$
$547$	−40.7393			−1.74188			−0.870942	+	0.491385i	$0.836491\pi$
$548$	−6.38795	−	3.68809i	−0.272880	−	0.157547i
$549$	3.98695	−	6.90559i	0.170159	−	0.294724i
$550$		0			0
$551$		−	39.0309i		−	1.66277i
$552$	−2.52211	+	1.45614i	−0.107348	+	0.0619774i
$553$	7.11229	−	4.10628i	0.302445	−	0.174617i
$554$			19.7128i			0.837515i
$555$		0			0
$556$	0.410380	−	0.710798i	0.0174040	−	0.0301446i
$557$	−0.794008	−	0.458421i	−0.0336432	−	0.0194239i	0.483084	−	0.875574i	$-0.339517\pi$
$557$	−0.794008	−	0.458421i	−0.0336432	−	0.0194239i	−0.516727	+	0.856150i	$0.672850\pi$
$558$	−6.95057			−0.294241
$559$	26.0903	+	20.3313i	1.10350	+	0.859922i
$560$		0			0
$561$	1.23857	+	0.715090i	0.0522925	+	0.0301911i
$562$	−4.96537	+	8.60027i	−0.209451	+	0.362780i
$563$	6.32961	+	10.9632i	0.266761	+	0.462044i	0.968024	−	0.250859i	$-0.0807131\pi$
$563$	6.32961	+	10.9632i	0.266761	+	0.462044i	−0.701262	+	0.712903i	$0.747380\pi$
$564$		−	11.9021i		−	0.501169i
$565$		0			0
$566$	−10.0790	+	5.81912i	−0.423652	+	0.244596i
$567$		−	0.865427i		−	0.0363445i
$568$	−7.08275	−	12.2677i	−0.297186	−	0.514741i
$569$	−12.2559	+	21.2279i	−0.513795	+	0.889918i	0.486077	+	0.873916i	$0.338427\pi$
$569$	−12.2559	+	21.2279i	−0.513795	+	0.889918i	−0.999872	+	0.0160026i	$0.994906\pi$
$570$		0			0
$571$	−11.1443			−0.466376			−0.233188	−	0.972432i	$-0.574916\pi$
$571$	−11.1443			−0.466376			−0.233188	+	0.972432i	$0.574916\pi$
$572$	0.236905	+	0.584248i	0.00990549	+	0.0244286i
$573$	5.57642			0.232958
$574$	−6.13015	−	3.53925i	−0.255868	−	0.147725i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$			23.8325i			0.992161i	0.868276	+	0.496081i	$0.165228\pi$
$577$			23.8325i			0.992161i	−0.868276	+	0.496081i	$0.834772\pi$
$578$	43.2139	−	24.9496i	1.79746	−	1.03777i
$579$	0.191227	−	0.110405i	0.00794712	−	0.00458827i
$580$		0			0
$581$	0.0603824	+	0.104585i	0.00250508	+	0.00433893i
$582$	−4.32411	+	7.48957i	−0.179240	+	0.310453i
$583$	0.376658	+	0.217463i	0.0155996	+	0.00900642i
$584$	12.8706			0.532588
$585$		0			0
$586$	−13.1527			−0.543334
$587$	32.3566	+	18.6811i	1.33550	+	0.771051i	0.986136	−	0.165937i	$-0.0530649\pi$
$587$	32.3566	+	18.6811i	1.33550	+	0.771051i	0.349362	+	0.936988i	$0.386398\pi$
$588$	−3.12552	+	5.41356i	−0.128894	+	0.223251i
$589$	−20.9010	−	36.2016i	−0.861210	−	1.49166i
$590$		0			0
$591$	1.49286	−	0.861905i	0.0614082	−	0.0354540i
$592$	1.52347	−	0.879573i	0.0626140	−	0.0361502i
$593$		−	6.46136i		−	0.265336i	−0.991161	−	0.132668i	$-0.957646\pi$
$593$		−	6.46136i		−	0.265336i	0.991161	−	0.132668i	$-0.0423544\pi$
$594$	0.0874279	+	0.151430i	0.00358721	+	0.00621323i
$595$		0			0
$596$	8.90766	+	5.14284i	0.364872	+	0.210659i
$597$	7.95853			0.325721
$598$	−6.45428	+	8.28251i	−0.263935	+	0.338697i
$599$	38.5057			1.57330			0.786651	−	0.617398i	$-0.211813\pi$
$599$	38.5057			1.57330			0.786651	+	0.617398i	$0.211813\pi$
$600$		0			0
$601$	−0.371169	+	0.642883i	−0.0151403	+	0.0262237i	−0.873496	−	0.486831i	$-0.838153\pi$
$601$	−0.371169	+	0.642883i	−0.0151403	+	0.0262237i	0.858356	+	0.513055i	$0.171486\pi$
$602$	3.96963	+	6.87561i	0.161790	+	0.280229i
$603$		−	2.73532i		−	0.111391i
$604$	−10.1688	+	5.87096i	−0.413763	+	0.238886i
$605$		0			0
$606$		−	10.5655i		−	0.429195i
$607$	14.7513	+	25.5500i	0.598736	+	1.03704i	0.993008	+	0.118047i	$0.0376634\pi$
$607$	14.7513	+	25.5500i	0.598736	+	1.03704i	−0.394272	+	0.918994i	$0.629003\pi$
$608$	−3.00709	+	5.20843i	−0.121954	+	0.211230i
$609$	−4.86400	−	2.80823i	−0.197099	−	0.113795i
$610$		0			0
$611$	−16.1257	−	39.7686i	−0.652374	−	1.60887i
$612$	8.17919			0.330624
$613$	11.8943	+	6.86720i	0.480408	+	0.277364i	0.720587	−	0.693365i	$-0.243873\pi$
$613$	11.8943	+	6.86720i	0.480408	+	0.277364i	−0.240178	+	0.970729i	$0.577206\pi$
$614$	−7.43044	+	12.8699i	−0.299868	+	0.519387i
$615$		0			0
$616$			0.151325i			0.00609706i
$617$	−37.1342	+	21.4394i	−1.49497	+	0.863119i	−0.999983	−	0.00578297i	$-0.998159\pi$
$617$	−37.1342	+	21.4394i	−1.49497	+	0.863119i	−0.494983	+	0.868902i	$0.664826\pi$
$618$	−7.73853	+	4.46784i	−0.311289	+	0.179723i
$619$		−	30.0054i		−	1.20602i	−0.797734	−	0.603010i	$-0.793968\pi$
$619$		−	30.0054i		−	1.20602i	0.797734	−	0.603010i	$-0.206032\pi$
$620$		0			0
$621$	−1.45614	+	2.52211i	−0.0584329	+	0.101209i
$622$	−7.94722	−	4.58833i	−0.318655	−	0.183975i
$623$	−11.3711			−0.455574
$624$	2.84400	+	2.21623i	0.113851	+	0.0887202i
$625$		0			0
$626$	6.44240	+	3.71952i	0.257490	+	0.148662i
$627$	−0.525807	+	0.910724i	−0.0209987	+	0.0363708i
$628$	3.38017	+	5.85463i	0.134884	+	0.233625i
$629$		−	14.3884i		−	0.573703i
$630$		0			0
$631$	7.73137	−	4.46371i	0.307781	−	0.177697i	−0.338152	−	0.941091i	$-0.609802\pi$
$631$	7.73137	−	4.46371i	0.307781	−	0.177697i	0.645933	+	0.763394i	$0.276468\pi$
$632$			9.48961i			0.377476i
$633$	−2.10991	−	3.65448i	−0.0838616	−	0.145252i
$634$	−12.8755	+	22.3011i	−0.511352	+	0.885688i
$635$		0			0
$636$	2.48735			0.0986297
$637$	−3.10873	+	22.3230i	−0.123172	+	0.884470i
$638$	1.13478			0.0449265
$639$	−12.2677	−	7.08275i	−0.485302	−	0.280189i
$640$		0			0
$641$	−11.9079	−	20.6250i	−0.470332	−	0.814639i	0.529092	−	0.848564i	$-0.322532\pi$
$641$	−11.9079	−	20.6250i	−0.470332	−	0.814639i	−0.999424	+	0.0339254i	$0.989199\pi$
$642$			0.860777i			0.0339722i
$643$	−8.30300	+	4.79374i	−0.327439	+	0.189047i	−0.654703	−	0.755886i	$-0.727206\pi$
$643$	−8.30300	+	4.79374i	−0.327439	+	0.189047i	0.327265	+	0.944933i	$0.393873\pi$
$644$	−2.18270	+	1.26018i	−0.0860104	+	0.0496581i
$645$		0			0
$646$	24.5955	+	42.6007i	0.967699	+	1.67610i
$647$	22.6448	−	39.2219i	0.890259	−	1.54197i	0.0506940	−	0.998714i	$-0.483857\pi$
$647$	22.6448	−	39.2219i	0.890259	−	1.54197i	0.839565	−	0.543259i	$-0.182810\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	1.23040			0.0482975
$650$		0			0
$651$	−6.01521			−0.235755
$652$	−1.23624	−	0.713746i	−0.0484150	−	0.0279524i
$653$	4.62451	−	8.00988i	0.180971	−	0.313451i	−0.761241	−	0.648470i	$-0.775409\pi$
$653$	4.62451	−	8.00988i	0.180971	−	0.313451i	0.942211	+	0.335019i	$0.108743\pi$
$654$	−2.72668	−	4.72274i	−0.106622	−	0.184674i
$655$		0			0
$656$	7.08339	−	4.08960i	0.276560	−	0.159672i
$657$	11.1462	−	6.43528i	0.434856	−	0.251064i
$658$		−	10.3004i		−	0.401551i
$659$	11.0666	+	19.1679i	0.431093	+	0.746676i	0.996968	−	0.0778159i	$-0.0247946\pi$
$659$	11.0666	+	19.1679i	0.431093	+	0.746676i	−0.565874	+	0.824491i	$0.691461\pi$
$660$		0			0
$661$	8.75083	+	5.05229i	0.340368	+	0.196511i	0.660435	−	0.750884i	$-0.270372\pi$
$661$	8.75083	+	5.05229i	0.340368	+	0.196511i	−0.320067	+	0.947395i	$0.603705\pi$
$662$	−6.50437			−0.252800
$663$	27.3292	−	11.0816i	1.06138	−	0.430375i
$664$	−0.139544			−0.00541534
$665$		0			0
$666$	0.879573	−	1.52347i	0.0340828	−	0.0590331i
$667$	9.45008	+	16.3680i	0.365909	+	0.633772i
$668$			5.87057i			0.227139i
$669$	−6.02126	+	3.47638i	−0.232795	+	0.134405i
$670$		0			0
$671$			1.39428i			0.0538256i
$672$	0.432713	+	0.749482i	0.0166923	+	0.0289119i
$673$	6.73157	−	11.6594i	0.259483	−	0.449437i	−0.706621	−	0.707593i	$-0.749781\pi$
$673$	6.73157	−	11.6594i	0.259483	−	0.449437i	0.966103	+	0.258155i	$0.0831146\pi$
$674$	−16.1683	−	9.33479i	−0.622781	−	0.359562i
$675$		0			0
$676$	12.5054	+	3.55190i	0.480975	+	0.136612i
$677$	7.86444			0.302255			0.151127	−	0.988514i	$-0.451710\pi$
$677$	7.86444			0.302255			0.151127	+	0.988514i	$0.451710\pi$
$678$	−10.2036	−	5.89106i	−0.391868	−	0.226245i
$679$	−3.74220	+	6.48168i	−0.143612	+	0.248744i
$680$		0			0
$681$			2.89645i			0.110992i
$682$	1.05252	−	0.607674i	0.0403032	−	0.0232690i
$683$	15.9565	−	9.21246i	0.610557	−	0.352505i	−0.162627	−	0.986688i	$-0.551997\pi$
$683$	15.9565	−	9.21246i	0.610557	−	0.352505i	0.773183	+	0.634183i	$0.218663\pi$
$684$			6.01418i			0.229958i
$685$		0			0
$686$	−5.73390	+	9.93141i	−0.218921	+	0.379183i
$687$	6.83121	+	3.94400i	0.260627	+	0.150473i
$688$	−9.17382			−0.349749
$689$	8.31100	−	3.37000i	0.316624	−	0.128387i
$690$		0			0
$691$	−20.5618	−	11.8714i	−0.782208	−	0.451608i	0.0550042	−	0.998486i	$-0.482483\pi$
$691$	−20.5618	−	11.8714i	−0.782208	−	0.451608i	−0.837212	+	0.546878i	$0.815816\pi$
$692$	6.85138	−	11.8669i	0.260450	−	0.451113i
$693$	0.0756625	+	0.131051i	0.00287418	+	0.00497823i
$694$			28.4066i			1.07830i
$695$		0			0
$696$	5.62035	−	3.24491i	0.213039	−	0.122998i
$697$		−	66.8992i		−	2.53399i
$698$	1.11889	+	1.93797i	0.0423505	+	0.0733532i
$699$	−0.713746	+	1.23624i	−0.0269963	+	0.0467590i
$700$		0			0
$701$	−6.52189			−0.246328			−0.123164	−	0.992386i	$-0.539304\pi$
$701$	−6.52189			−0.246328			−0.123164	+	0.992386i	$0.539304\pi$
$702$	3.57109	+	0.497314i	0.134782	+	0.0187699i
$703$	10.5798			0.399025
$704$	−0.151430	−	0.0874279i	−0.00570722	−	0.00329506i
$705$		0			0
$706$	0.813287	+	1.40866i	0.0306085	+	0.0530154i
$707$		−	9.14369i		−	0.343884i
$708$	6.09393	−	3.51833i	0.229024	−	0.132227i
$709$	−27.5565	+	15.9098i	−1.03491	+	0.597504i	−0.918387	−	0.395684i	$-0.870507\pi$
$709$	−27.5565	+	15.9098i	−1.03491	+	0.597504i	−0.116521	+	0.993188i	$0.537174\pi$
$710$		0			0
$711$	4.74480	+	8.21824i	0.177944	+	0.308208i
$712$	6.56966	−	11.3790i	0.246208	−	0.426445i
$713$	17.5301	+	10.1210i	0.656507	+	0.379035i
$714$	7.07849			0.264906
$715$		0			0
$716$	14.1838			0.530074
$717$	−9.44692	−	5.45418i	−0.352802	−	0.203690i
$718$	−17.2307	+	29.8444i	−0.643043	+	1.11378i
$719$	−11.6970	−	20.2597i	−0.436223	−	0.755560i	0.561172	−	0.827699i	$-0.310351\pi$
$719$	−11.6970	−	20.2597i	−0.436223	−	0.755560i	−0.997395	+	0.0721392i	$0.977017\pi$
$720$		0			0
$721$	−6.69713	+	3.86659i	−0.249414	+	0.143999i
$722$	−14.8699	+	8.58515i	−0.553401	+	0.319506i
$723$			29.3660i			1.09213i
$724$	6.88641	+	11.9276i	0.255931	+	0.443286i
$725$		0			0
$726$	9.49980	+	5.48471i	0.352571	+	0.203557i
$727$	36.0471			1.33691			0.668457	−	0.743750i	$-0.266955\pi$
$727$	36.0471			1.33691			0.668457	+	0.743750i	$0.266955\pi$
$728$	2.46127	+	1.91799i	0.0912208	+	0.0710853i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−37.5172	+	64.9817i	−1.38762	+	2.40344i
$732$	3.98695	+	6.90559i	0.147362	+	0.255238i
$733$			17.0888i			0.631189i	0.948894	+	0.315594i	$0.102204\pi$
$733$			17.0888i			0.631189i	−0.948894	+	0.315594i	$0.897796\pi$
$734$	12.6735	−	7.31703i	0.467787	−	0.270077i
$735$		0			0
$736$		−	2.91228i		−	0.107348i
$737$	0.239143	+	0.414209i	0.00880896	+	0.0152576i
$738$	4.08960	−	7.08339i	0.150540	−	0.260743i
$739$	−33.4931	−	19.3373i	−1.23206	−	0.711333i	−0.264604	−	0.964357i	$-0.585241\pi$
$739$	−33.4931	−	19.3373i	−1.23206	−	0.711333i	−0.967460	+	0.253024i	$0.918575\pi$
$740$		0			0
$741$	8.14836	+	20.0952i	0.299337	+	0.738217i
$742$	2.15262			0.0790250
$743$	−0.390632	−	0.225532i	−0.0143309	−	0.00827395i	0.492817	−	0.870133i	$-0.335967\pi$
$743$	−0.390632	−	0.225532i	−0.0143309	−	0.00827395i	−0.507148	+	0.861859i	$0.669300\pi$
$744$	3.47529	−	6.01937i	0.127410	−	0.220681i
$745$		0			0
$746$		−	22.0739i		−	0.808184i
$747$	−0.120848	+	0.0697718i	−0.00442161	+	0.00255282i
$748$	−1.23857	+	0.715090i	−0.0452867	+	0.0261463i
$749$			0.744940i			0.0272195i
$750$		0			0
$751$	−11.1206	+	19.2614i	−0.405795	+	0.702858i	−0.994414	−	0.105553i	$-0.966339\pi$
$751$	−11.1206	+	19.2614i	−0.405795	+	0.702858i	0.588618	+	0.808411i	$0.299672\pi$
$752$	10.3075	+	5.95105i	0.375876	+	0.217012i
$753$	17.8942			0.652100
$754$	14.3829	−	18.4570i	0.523796	−	0.672165i
$755$		0			0
$756$	0.749482	+	0.432713i	0.0272584	+	0.0157376i
$757$	−4.21654	+	7.30326i	−0.153253	+	0.265442i	−0.932421	−	0.361373i	$-0.882308\pi$
$757$	−4.21654	+	7.30326i	−0.153253	+	0.265442i	0.779169	+	0.626814i	$0.215642\pi$
$758$	6.96127	+	12.0573i	0.252845	+	0.437940i
$759$		−	0.509229i		−	0.0184838i
$760$		0			0
$761$	18.3585	−	10.5993i	0.665496	−	0.384224i	−0.128872	−	0.991661i	$-0.541136\pi$
$761$	18.3585	−	10.5993i	0.665496	−	0.384224i	0.794368	+	0.607437i	$0.207802\pi$
$762$		−	6.94238i		−	0.251496i
$763$	−2.35974	−	4.08719i	−0.0854283	−	0.147966i
$764$	−2.78821	+	4.82932i	−0.100874	+	0.174719i
$765$		0			0
$766$	24.6089			0.889155
$767$	15.5949	−	20.0123i	0.563099	−	0.722601i
$768$	−1.00000			−0.0360844
$769$	−3.34820	−	1.93308i	−0.120739	−	0.0697088i	0.438414	−	0.898773i	$-0.355540\pi$
$769$	−3.34820	−	1.93308i	−0.120739	−	0.0697088i	−0.559153	+	0.829064i	$0.688874\pi$
$770$		0			0
$771$	−6.08945	−	10.5472i	−0.219306	−	0.379849i
$772$			0.220810i			0.00794712i
$773$	−28.7898	+	16.6218i	−1.03550	+	0.597845i	−0.918555	−	0.395293i	$-0.870643\pi$
$773$	−28.7898	+	16.6218i	−1.03550	+	0.597845i	−0.116944	+	0.993139i	$0.537310\pi$
$774$	−7.94476	+	4.58691i	−0.285568	+	0.164873i
$775$		0			0
$776$	−4.32411	−	7.48957i	−0.155226	−	0.268860i
$777$	0.761206	−	1.31845i	0.0273081	−	0.0472990i
$778$	4.85823	+	2.80490i	0.174176	+	0.100561i
$779$	49.1911			1.76245
$780$		0			0
$781$	2.47692			0.0886312
$782$	−20.6288	−	11.9100i	−0.737684	−	0.425902i
$783$	3.24491	−	5.62035i	0.115964	−	0.200855i
$784$	−3.12552	−	5.41356i	−0.111626	−	0.193341i
$785$		0			0
$786$	−1.96703	+	1.13567i	−0.0701616	+	0.0405078i
$787$	−27.6908	+	15.9873i	−0.987071	+	0.569886i	−0.904398	−	0.426691i	$-0.859679\pi$
$787$	−27.6908	+	15.9873i	−0.987071	+	0.569886i	−0.0826737	+	0.996577i	$0.526346\pi$
$788$			1.72381i			0.0614082i
$789$	10.5834	+	18.3309i	0.376778	+	0.652598i
$790$		0			0
$791$	−8.83049	−	5.09828i	−0.313976	−	0.181274i
$792$	−0.174856			−0.00621323
$793$	22.6777	+	17.6720i	0.805310	+	0.627551i
$794$	−2.36876			−0.0840643
$795$		0			0
$796$	−3.97927	+	6.89229i	−0.141041	+	0.244291i
$797$	18.0401	+	31.2464i	0.639014	+	1.10680i	0.985649	+	0.168805i	$0.0539908\pi$
$797$	18.0401	+	31.2464i	0.639014	+	1.10680i	−0.346635	+	0.938000i	$0.612676\pi$
$798$			5.20483i			0.184249i
$799$	84.3072	−	48.6748i	2.98257	−	1.72199i
$800$		0			0
$801$		−	13.1393i		−	0.464255i
$802$	−8.25276	−	14.2942i	−0.291415	−	0.504746i
$803$	−1.12525	+	1.94898i	−0.0397091	+	0.0687782i
$804$	2.36886	+	1.36766i	0.0835432	+	0.0482337i
$805$		0			0
$806$	3.45661	−	24.8211i	0.121754	−	0.874286i
$807$	12.0874			0.425498
$808$	9.15001	+	5.28276i	0.321896	+	0.185847i
$809$	−12.4162	+	21.5054i	−0.436529	+	0.756090i	−0.997419	−	0.0718003i	$-0.977126\pi$
$809$	−12.4162	+	21.5054i	−0.436529	+	0.756090i	0.560890	+	0.827890i	$0.310459\pi$
$810$		0			0
$811$		−	21.3899i		−	0.751102i	−0.926802	−	0.375551i	$-0.877453\pi$
$811$		−	21.3899i		−	0.751102i	0.926802	−	0.375551i	$-0.122547\pi$
$812$	4.86400	−	2.80823i	0.170693	−	0.0985496i
$813$	−12.7275	+	7.34824i	−0.446374	+	0.257714i
$814$			0.307597i			0.0107813i
$815$		0			0
$816$	−4.08960	+	7.08339i	−0.143164	+	0.247968i
$817$	−47.7812	−	27.5865i	−1.67165	−	0.965129i
$818$	33.3071			1.16455
$819$	3.09052	+	0.430389i	0.107991	+	0.0150390i
$820$		0			0
$821$	28.4938	+	16.4509i	0.994441	+	0.574141i	0.906599	−	0.421994i	$-0.138670\pi$
$821$	28.4938	+	16.4509i	0.994441	+	0.574141i	0.0878420	+	0.996134i	$0.472003\pi$
$822$	3.68809	−	6.38795i	0.128637	−	0.222805i
$823$	15.9221	+	27.5779i	0.555010	+	0.961306i	0.997903	+	0.0647309i	$0.0206189\pi$
$823$	15.9221	+	27.5779i	0.555010	+	0.961306i	−0.442893	+	0.896575i	$0.646048\pi$
$824$		−	8.93568i		−	0.311289i
$825$		0			0
$826$	5.27385	−	3.04486i	0.183501	−	0.105944i
$827$		−	1.91814i		−	0.0667004i	−0.999444	−	0.0333502i	$-0.989382\pi$
$827$		−	1.91814i		−	0.0667004i	0.999444	−	0.0333502i	$-0.0106177\pi$
$828$	−1.45614	−	2.52211i	−0.0506044	−	0.0876493i
$829$	13.2223	−	22.9016i	0.459228	−	0.795407i	−0.539692	−	0.841863i	$-0.681459\pi$
$829$	13.2223	−	22.9016i	0.459228	−	0.795407i	0.998920	+	0.0464558i	$0.0147927\pi$
$830$		0			0
$831$	−19.7128			−0.683828
$832$	−3.34131	+	1.35486i	−0.115839	+	0.0469713i
$833$	−51.1284			−1.77149
$834$	0.710798	+	0.410380i	0.0246129	+	0.0142103i
$835$		0			0
$836$	−0.525807	−	0.910724i	−0.0181854	−	0.0314981i
$837$		−	6.95057i		−	0.240247i
$838$	26.2065	−	15.1303i	0.905288	−	0.522668i
$839$	−25.9126	+	14.9607i	−0.894604	+	0.516500i	−0.875446	−	0.483317i	$-0.839432\pi$
$839$	−25.9126	+	14.9607i	−0.894604	+	0.516500i	−0.0191582	+	0.999816i	$0.506099\pi$
$840$		0			0
$841$	−6.55886	−	11.3603i	−0.226168	−	0.391734i
$842$	20.1118	−	34.8346i	0.693098	−	1.20048i
$843$	−8.60027	−	4.96537i	−0.296209	−	0.171016i
$844$	4.21983			0.145252
$845$		0			0
$846$	11.9021			0.409202
$847$	8.22138	+	4.74662i	0.282490	+	0.163096i
$848$	−1.24367	+	2.15410i	−0.0427079	+	0.0739723i
$849$	−5.81912	−	10.0790i	−0.199712	−	0.345911i
$850$		0			0
$851$	−4.43676	+	2.56156i	−0.152090	+	0.0878092i
$852$	12.2677	−	7.08275i	0.420284	−	0.242651i
$853$		−	9.19805i		−	0.314935i	−0.987524	−	0.157468i	$-0.949667\pi$
$853$		−	9.19805i		−	0.314935i	0.987524	−	0.157468i	$-0.0503330\pi$
$854$	3.45041	+	5.97629i	0.118071	+	0.204504i
$855$		0			0
$856$	−0.745455	−	0.430389i	−0.0254791	−	0.0147104i
$857$	13.1946			0.450720			0.225360	−	0.974276i	$-0.427644\pi$
$857$	13.1946			0.450720			0.225360	+	0.974276i	$0.427644\pi$
$858$	−0.584248	+	0.236905i	−0.0199459	+	0.00808780i
$859$	52.7575			1.80006			0.900032	−	0.435824i	$-0.143543\pi$
$859$	52.7575			1.80006			0.900032	+	0.435824i	$0.143543\pi$
$860$		0			0
$861$	3.53925	−	6.13015i	0.120617	−	0.208915i
$862$	16.2801	+	28.1980i	0.554502	+	0.960426i
$863$			18.6411i			0.634551i	0.948333	+	0.317276i	$0.102768\pi$
$863$			18.6411i			0.634551i	−0.948333	+	0.317276i	$0.897232\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$		0			0
$866$			30.7327i			1.04434i
$867$	24.9496	+	43.2139i	0.847332	+	1.46762i
$868$	3.00761	−	5.20933i	0.102085	−	0.176816i
$869$	−1.43701	−	0.829657i	−0.0487471	−	0.0281442i
$870$		0			0
$871$	9.76808	+	1.36031i	0.330979	+	0.0460924i
$872$	5.45336			0.184674
$873$	−7.48957	−	4.32411i	−0.253484	−	0.146349i
$874$	8.75748	−	15.1684i	0.296226	−	0.513079i
$875$		0			0
$876$			12.8706i			0.434856i
$877$	39.3640	−	22.7268i	1.32923	−	0.767429i	0.344047	−	0.938953i	$-0.388202\pi$
$877$	39.3640	−	22.7268i	1.32923	−	0.767429i	0.985180	+	0.171523i	$0.0548688\pi$
$878$	5.65380	−	3.26422i	0.190807	−	0.110162i
$879$		−	13.1527i		−	0.443630i
$880$		0			0
$881$	10.0027	−	17.3252i	0.337000	−	0.583701i	−0.646867	−	0.762603i	$-0.723921\pi$
$881$	10.0027	−	17.3252i	0.337000	−	0.583701i	0.983867	+	0.178902i	$0.0572545\pi$
$882$	−5.41356	−	3.12552i	−0.182284	−	0.105242i
$883$	29.0388			0.977233			0.488617	−	0.872499i	$-0.337502\pi$
$883$	29.0388			0.977233			0.488617	+	0.872499i	$0.337502\pi$
$884$	−4.06762	+	29.2086i	−0.136809	+	0.982392i
$885$		0			0
$886$	26.2501	+	15.1555i	0.881891	+	0.509160i
$887$	−1.43623	+	2.48763i	−0.0482240	+	0.0835264i	−0.889130	−	0.457655i	$-0.848689\pi$
$887$	−1.43623	+	2.48763i	−0.0482240	+	0.0835264i	0.840906	+	0.541181i	$0.182023\pi$
$888$	0.879573	+	1.52347i	0.0295165	+	0.0511241i
$889$		−	6.00812i		−	0.201506i
$890$		0			0
$891$	−0.151430	+	0.0874279i	−0.00507308	+	0.00292895i
$892$		−	6.95276i		−	0.232795i
$893$	35.7906	+	61.9912i	1.19769	+	2.07446i
$894$	−5.14284	+	8.90766i	−0.172002	+	0.297917i
$895$		0			0
$896$	−0.865427			−0.0289119
$897$	−8.28251	−	6.45428i	−0.276545	−	0.215502i
$898$	15.9388			0.531883
$899$	−39.0646	−	22.5540i	−1.30288	−	0.752217i
$900$		0			0
$901$	10.1722	+	17.6188i	0.338886	+	0.586968i
$902$			1.43018i			0.0476198i
$903$	−6.87561	+	3.96963i	−0.228806	+	0.132101i
$904$	10.2036	−	5.89106i	0.339367	−	0.195934i
$905$		0			0
$906$	−5.87096	−	10.1688i	−0.195050	−	0.337836i
$907$	16.7351	−	28.9860i	0.555679	−	0.962464i	−0.442171	−	0.896931i	$-0.645792\pi$
$907$	16.7351	−	28.9860i	0.555679	−	0.962464i	0.997850	−	0.0655336i	$-0.0208750\pi$
$908$	−2.50840	−	1.44823i	−0.0832442	−	0.0480611i
$909$	10.5655			0.350436
$910$		0			0
$911$	20.7528			0.687570			0.343785	−	0.939048i	$-0.388291\pi$
$911$	20.7528			0.687570			0.343785	+	0.939048i	$0.388291\pi$
$912$	−5.20843	−	3.00709i	−0.172468	−	0.0995746i
$913$	0.0122000	−	0.0211310i	0.000403761	−	0.000699335i
$914$	−9.90436	−	17.1548i	−0.327607	−	0.567432i
$915$		0			0
$916$	−6.83121	+	3.94400i	−0.225710	+	0.130313i
$917$	−1.70232	+	0.982835i	−0.0562156	+	0.0324561i
$918$			8.17919i			0.269954i
$919$	13.7419	+	23.8017i	0.453304	+	0.785146i	0.998589	−	0.0531051i	$-0.0169118\pi$
$919$	13.7419	+	23.8017i	0.453304	+	0.785146i	−0.545285	+	0.838251i	$0.683579\pi$
$920$		0			0
$921$	−12.8699	−	7.43044i	−0.424077	−	0.244841i
$922$	13.3828			0.440739
$923$	31.3940	−	40.2866i	1.03335	−	1.32605i
$924$	−0.151325			−0.00497823
$925$		0			0
$926$	−21.1800	+	36.6848i	−0.696017	+	1.20554i
$927$	−4.46784	−	7.73853i	−0.146743	−	0.254167i
$928$			6.48982i			0.213039i
$929$	−8.03305	+	4.63788i	−0.263556	+	0.152164i	−0.625956	−	0.779859i	$-0.715291\pi$
$929$	−8.03305	+	4.63788i	−0.263556	+	0.152164i	0.362400	+	0.932023i	$0.381958\pi$
$930$		0			0
$931$		−	37.5948i		−	1.23212i
$932$	−0.713746	−	1.23624i	−0.0233795	−	0.0404945i
$933$	4.58833	−	7.94722i	0.150215	−	0.260180i
$934$	28.9766	+	16.7296i	0.948143	+	0.547410i
$935$		0			0
$936$	−2.21623	+	2.84400i	−0.0724398	+	0.0929590i
$937$	15.0600			0.491989			0.245995	−	0.969271i	$-0.420885\pi$
$937$	15.0600			0.491989			0.245995	+	0.969271i	$0.420885\pi$
$938$	2.05007	+	1.18361i	0.0669373	+	0.0386462i
$939$	−3.71952	+	6.44240i	−0.121382	+	0.210240i
$940$		0			0
$941$		−	19.4194i		−	0.633055i	−0.948583	−	0.316528i	$-0.897483\pi$
$941$		−	19.4194i		−	0.633055i	0.948583	−	0.316528i	$-0.102517\pi$
$942$	−5.85463	+	3.38017i	−0.190754	+	0.110132i
$943$	−20.6288	+	11.9100i	−0.671766	+	0.387844i
$944$			7.03667i			0.229024i
$945$		0			0
$946$	0.802048	−	1.38919i	0.0260768	−	0.0451664i
$947$	−4.71506	−	2.72224i	−0.153219	−	0.0884610i	0.421430	−	0.906861i	$-0.361528\pi$
$947$	−4.71506	−	2.72224i	−0.153219	−	0.0884610i	−0.574649	+	0.818400i	$0.694862\pi$
$948$	−9.48961			−0.308208
$949$	17.4378	+	43.0046i	0.566055	+	1.39599i
$950$		0			0
$951$	−22.3011	−	12.8755i	−0.723161	−	0.417517i
$952$	−3.53925	+	6.13015i	−0.114708	+	0.198679i
$953$	−11.6768	−	20.2248i	−0.378249	−	0.655146i	0.612559	−	0.790425i	$-0.290140\pi$
$953$	−11.6768	−	20.2248i	−0.378249	−	0.655146i	−0.990808	+	0.135279i	$0.956807\pi$
$954$			2.48735i			0.0805308i
$955$		0			0
$956$	9.44692	−	5.45418i	0.305535	−	0.176401i
$957$			1.13478i			0.0366823i
$958$	−11.1652	−	19.3387i	−0.360730	−	0.624803i
$959$	3.19177	−	5.52831i	0.103068	−	0.178518i
$960$		0			0
$961$	−17.3104			−0.558401
$962$	5.00301	+	3.89867i	0.161303	+	0.125698i
$963$	−0.860777			−0.0277382
$964$	−25.4317	−	14.6830i	−0.819101	−	0.472908i
$965$		0			0
$966$	−1.26018	−	2.18270i	−0.0405457	−	0.0702272i
$967$			32.2070i			1.03571i	0.855469	+	0.517854i	$0.173269\pi$
$967$			32.2070i			1.03571i	−0.855469	+	0.517854i	$0.826731\pi$
$968$	−9.49980	+	5.48471i	−0.305335	+	0.176285i
$969$	−42.6007	+	24.5955i	−1.36853	+	0.790123i
$970$		0			0
$971$	−15.4181	−	26.7049i	−0.494789	−	0.857000i	0.505193	−	0.863007i	$-0.331421\pi$
$971$	−15.4181	−	26.7049i	−0.494789	−	0.857000i	−0.999982	+	0.00600636i	$0.998088\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	0.615144	+	0.355154i	0.0197206	+	0.0113857i
$974$	−28.7499			−0.921207
$975$		0			0
$976$	−7.97389			−0.255238
$977$	18.4521	+	10.6533i	0.590334	+	0.340829i	0.765230	−	0.643758i	$-0.222625\pi$
$977$	18.4521	+	10.6533i	0.590334	+	0.340829i	−0.174896	+	0.984587i	$0.555959\pi$
$978$	0.713746	−	1.23624i	0.0228231	−	0.0395307i
$979$	1.14874	+	1.98968i	0.0367140	+	0.0635905i
$980$		0			0
$981$	4.72274	−	2.72668i	0.150786	−	0.0870561i
$982$	−13.9005	+	8.02546i	−0.443583	+	0.256103i
$983$		−	6.15826i		−	0.196418i	−0.995166	−	0.0982090i	$-0.968689\pi$
$983$		−	6.15826i		−	0.196418i	0.995166	−	0.0982090i	$-0.0313114\pi$
$984$	4.08960	+	7.08339i	0.130372	+	0.225810i
$985$		0			0
$986$	45.9699	+	26.5407i	1.46398	+	0.845229i
$987$	10.3004			0.327865
$988$	−21.4772	−	2.99093i	−0.683279	−	0.0951542i
$989$	26.7167			0.849542
$990$		0			0
$991$	−2.46451	+	4.26866i	−0.0782877	+	0.135598i	−0.902511	−	0.430666i	$-0.858279\pi$
$991$	−2.46451	+	4.26866i	−0.0782877	+	0.135598i	0.824224	+	0.566265i	$0.191612\pi$
$992$	3.47529	+	6.01937i	0.110340	+	0.191115i
$993$		−	6.50437i		−	0.206410i
$994$	10.6168	−	6.12960i	0.336744	−	0.194419i
$995$		0			0
$996$		−	0.139544i		−	0.00442161i
$997$	−11.6988	−	20.2628i	−0.370503	−	0.641730i	0.619140	−	0.785281i	$-0.287481\pi$
$997$	−11.6988	−	20.2628i	−0.370503	−	0.641730i	−0.989643	+	0.143550i	$0.954148\pi$
$998$	−16.6254	+	28.7961i	−0.526269	+	0.911524i
$999$	1.52347	+	0.879573i	0.0482003	+	0.0278285i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.j.901.2		12
5.2	odd	4		390.2.x.b.199.2	yes	12
5.3	odd	4		390.2.x.a.199.5	yes	12
5.4	even	2		1950.2.bc.i.901.5		12
13.10	even	6	inner	1950.2.bc.j.751.2		12
15.2	even	4		1170.2.bj.c.199.4		12
15.8	even	4		1170.2.bj.d.199.3		12
65.23	odd	12		390.2.x.b.49.2	yes	12
65.49	even	6		1950.2.bc.i.751.5		12
65.62	odd	12		390.2.x.a.49.5	✓	12
195.23	even	12		1170.2.bj.c.829.4		12
195.62	even	12		1170.2.bj.d.829.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.5	✓	12	65.62	odd	12
390.2.x.a.199.5	yes	12	5.3	odd	4
390.2.x.b.49.2	yes	12	65.23	odd	12
390.2.x.b.199.2	yes	12	5.2	odd	4
1170.2.bj.c.199.4		12	15.2	even	4
1170.2.bj.c.829.4		12	195.23	even	12
1170.2.bj.d.199.3		12	15.8	even	4
1170.2.bj.d.829.3		12	195.62	even	12
1950.2.bc.i.751.5		12	65.49	even	6
1950.2.bc.i.901.5		12	5.4	even	2
1950.2.bc.j.751.2		12	13.10	even	6	inner
1950.2.bc.j.901.2		12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(-0.749482 + 0.432713i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(-0.749482 + 0.432713i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.151430 + 0.0874279i) q^{11} +1.00000 q^{12} +(3.34131 - 1.35486i) q^{13} +0.865427 q^{14} +(-0.500000 + 0.866025i) q^{16} +(4.08960 + 7.08339i) q^{17} +1.00000i q^{18} +(-5.20843 + 3.00709i) q^{19} +0.865427i q^{21} +(-0.0874279 - 0.151430i) q^{22} +(1.45614 - 2.52211i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-3.57109 - 0.497314i) q^{26} -1.00000 q^{27} +(-0.749482 - 0.432713i) q^{28} +(-3.24491 + 5.62035i) q^{29} +6.95057i q^{31} +(0.866025 - 0.500000i) q^{32} +(0.151430 - 0.0874279i) q^{33} -8.17919i q^{34} +(0.500000 - 0.866025i) q^{36} +(-1.52347 - 0.879573i) q^{37} +6.01418 q^{38} +(0.497314 - 3.57109i) q^{39} +(-7.08339 - 4.08960i) q^{41} +(0.432713 - 0.749482i) q^{42} +(4.58691 + 7.94476i) q^{43} +0.174856i q^{44} +(-2.52211 + 1.45614i) q^{46} -11.9021i q^{47} +(0.500000 + 0.866025i) q^{48} +(-3.12552 + 5.41356i) q^{49} +8.17919 q^{51} +(2.84400 + 2.21623i) q^{52} +2.48735 q^{53} +(0.866025 + 0.500000i) q^{54} +(0.432713 + 0.749482i) q^{56} +6.01418i q^{57} +(5.62035 - 3.24491i) q^{58} +(6.09393 - 3.51833i) q^{59} +(3.98695 + 6.90559i) q^{61} +(3.47529 - 6.01937i) q^{62} +(0.749482 + 0.432713i) q^{63} -1.00000 q^{64} -0.174856 q^{66} +(2.36886 + 1.36766i) q^{67} +(-4.08960 + 7.08339i) q^{68} +(-1.45614 - 2.52211i) q^{69} +(12.2677 - 7.08275i) q^{71} +(-0.866025 + 0.500000i) q^{72} +12.8706i q^{73} +(0.879573 + 1.52347i) q^{74} +(-5.20843 - 3.00709i) q^{76} -0.151325 q^{77} +(-2.21623 + 2.84400i) q^{78} -9.48961 q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.08960 + 7.08339i) q^{82} -0.139544i q^{83} +(-0.749482 + 0.432713i) q^{84} -9.17382i q^{86} +(3.24491 + 5.62035i) q^{87} +(0.0874279 - 0.151430i) q^{88} +(11.3790 + 6.56966i) q^{89} +(-1.91799 + 2.46127i) q^{91} +2.91228 q^{92} +(6.01937 + 3.47529i) q^{93} +(-5.95105 + 10.3075i) q^{94} -1.00000i q^{96} +(7.48957 - 4.32411i) q^{97} +(5.41356 - 3.12552i) q^{98} -0.174856i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 6 q^{4} - 12 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 + 6 * q^4 - 12 * q^7 - 6 * q^9	\( 12 q + 6 q^{3} + 6 q^{4} - 12 q^{7} - 6 q^{9} + 6 q^{11} + 12 q^{12} + 4 q^{13} - 4 q^{14} - 6 q^{16} + 8 q^{17} + 6 q^{19} - 6 q^{22} + 16 q^{23} - 2 q^{26} - 12 q^{27} - 12 q^{28} - 14 q^{29} + 6 q^{33} + 6 q^{36} - 6 q^{37} - 8 q^{38} + 2 q^{39} - 18 q^{41} - 2 q^{42} + 10 q^{43} - 6 q^{46} + 6 q^{48} - 8 q^{49} + 16 q^{51} + 2 q^{52} - 2 q^{56} + 6 q^{58} + 36 q^{59} + 10 q^{61} + 16 q^{62} + 12 q^{63} - 12 q^{64} - 12 q^{66} + 24 q^{67} - 8 q^{68} - 16 q^{69} - 12 q^{71} + 12 q^{74} + 6 q^{76} + 24 q^{77} - 10 q^{78} - 4 q^{79} - 6 q^{81} + 8 q^{82} - 12 q^{84} + 14 q^{87} + 6 q^{88} - 18 q^{89} + 2 q^{91} + 32 q^{92} - 6 q^{93} + 8 q^{94} - 24 q^{97} + 24 q^{98}+O(q^{100}) \) 12 * q + 6 * q^3 + 6 * q^4 - 12 * q^7 - 6 * q^9 + 6 * q^11 + 12 * q^12 + 4 * q^13 - 4 * q^14 - 6 * q^16 + 8 * q^17 + 6 * q^19 - 6 * q^22 + 16 * q^23 - 2 * q^26 - 12 * q^27 - 12 * q^28 - 14 * q^29 + 6 * q^33 + 6 * q^36 - 6 * q^37 - 8 * q^38 + 2 * q^39 - 18 * q^41 - 2 * q^42 + 10 * q^43 - 6 * q^46 + 6 * q^48 - 8 * q^49 + 16 * q^51 + 2 * q^52 - 2 * q^56 + 6 * q^58 + 36 * q^59 + 10 * q^61 + 16 * q^62 + 12 * q^63 - 12 * q^64 - 12 * q^66 + 24 * q^67 - 8 * q^68 - 16 * q^69 - 12 * q^71 + 12 * q^74 + 6 * q^76 + 24 * q^77 - 10 * q^78 - 4 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^84 + 14 * q^87 + 6 * q^88 - 18 * q^89 + 2 * q^91 + 32 * q^92 - 6 * q^93 + 8 * q^94 - 24 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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