LMFDB - Embedded newform 1950.2.bc.i.751.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1950,2,Mod(751,1950)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [12,0,-6,6,0,0,12,0,-6,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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			751.5
Root			$-1.44229 - 0.433312i$ of defining polynomial
Character	$\chi$	$=$	1950.751
Dual form			1950.2.bc.i.901.5

$q$-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} +(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} + 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}+ \cdots - 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

Character values

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

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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	$-0.281039\pi$
$7$	0.749482	+	0.432713i	0.283277	+	0.163550i	−0.351629	+	0.936140i	$0.614372\pi$
$8$		−	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	−0.476997	−	0.878905i	$-0.658275\pi$
$11$	0.151430	−	0.0874279i	0.0456577	−	0.0263605i	0.522655	+	0.852544i	$0.324942\pi$
$12$	−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	−0.385748	+	0.922604i	$0.626057\pi$
$17$	−4.08960	+	7.08339i	−0.991873	+	1.71797i	−0.606125	+	0.795370i	$0.707277\pi$
$18$			1.00000i			0.235702i
$19$	−5.20843	−	3.00709i	−1.19490	−	0.689873i	−0.235483	−	0.971879i	$-0.575667\pi$
$19$	−5.20843	−	3.00709i	−1.19490	−	0.689873i	−0.959413	+	0.282005i	$0.909000\pi$
$20$		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	$-0.264864\pi$
$23$	−1.45614	−	2.52211i	−0.303626	−	0.525896i	−0.976954	+	0.213448i	$0.931531\pi$
$24$	−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	−0.992431	−	0.122801i	$-0.960812\pi$
$29$	−3.24491	−	5.62035i	−0.602564	−	1.04367i	0.389867	−	0.920871i	$-0.372521\pi$
$30$		0			0
$31$		−	6.95057i		−	1.24836i	−0.781281	−	0.624180i	$-0.785433\pi$
$31$		−	6.95057i		−	1.24836i	0.781281	−	0.624180i	$-0.214567\pi$
$32$	−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	$-0.620477\pi$
$37$	1.52347	−	0.879573i	0.250456	−	0.144601i	0.619973	+	0.784623i	$0.287144\pi$
$38$	−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	−0.937853	−	0.347034i	$-0.887189\pi$
$41$	−7.08339	+	4.08960i	−1.10624	+	0.638688i	−0.168387	+	0.985721i	$0.553856\pi$
$42$	−0.432713	−	0.749482i	−0.0667691	−	0.115648i
$43$	−4.58691	+	7.94476i	−0.699497	+	1.21156i	0.269144	+	0.963100i	$0.413259\pi$
$43$	−4.58691	+	7.94476i	−0.699497	+	1.21156i	−0.968641	+	0.248465i	$0.920074\pi$
$44$		−	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	$-0.554645\pi$
$53$	−2.48735			−0.341663			−0.170832	+	0.985300i	$0.554645\pi$
$54$	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	0.841145	−	0.540810i	$-0.181882\pi$
$59$	6.09393	+	3.51833i	0.793363	+	0.458048i	−0.0477824	+	0.998858i	$0.515215\pi$
$60$		0			0
$61$	3.98695	−	6.90559i	0.510476	−	0.884171i	−0.489450	−	0.872031i	$-0.662802\pi$
$61$	3.98695	−	6.90559i	0.510476	−	0.884171i	0.999926	−	0.0121394i	$-0.00386418\pi$
$62$	−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	$-0.720103\pi$
$67$	−2.36886	+	1.36766i	−0.289402	+	0.167086i	0.348270	+	0.937394i	$0.386769\pi$
$68$	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	0.998806	−	0.0488476i	$-0.0155549\pi$
$71$	12.2677	+	7.08275i	1.45591	+	0.840568i	0.457100	+	0.889415i	$0.348888\pi$
$72$	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	0.244249	−	0.969713i	$-0.421459\pi$
$89$	11.3790	−	6.56966i	1.20617	−	0.696382i	0.961920	+	0.273330i	$0.0881253\pi$
$90$		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	$-0.478017\pi$
$97$	−7.48957	−	4.32411i	−0.760451	−	0.439047i	−0.829458	+	0.558570i	$0.811350\pi$
$98$	−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	−0.999553	−	0.0298810i	$-0.990487\pi$
$101$	−5.28276	−	9.15001i	−0.525654	−	0.910460i	0.473899	−	0.880579i	$-0.342846\pi$
$102$	7.08339	−	4.08960i	0.701360	−	0.404930i
$103$	−8.93568			−0.880459			−0.440230	−	0.897885i	$-0.645103\pi$
$103$	−8.93568			−0.880459			−0.440230	+	0.897885i	$0.645103\pi$
$104$	−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	$-0.179914\pi$
$107$	−0.430389	−	0.745455i	−0.0416072	−	0.0720658i	−0.886079	+	0.463534i	$0.846581\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$		−	5.45336i		−	0.522337i	−0.965293	−	0.261168i	$-0.915892\pi$
$109$		−	5.45336i		−	0.522337i	0.965293	−	0.261168i	$-0.0841078\pi$
$110$		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	0.443782	+	0.896135i	$0.353636\pi$
$113$	−5.89106	+	10.2036i	−0.554184	+	0.959876i	−0.997966	+	0.0637409i	$0.979697\pi$
$114$	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	$-0.0670009\pi$
$127$	3.47119	+	6.01228i	0.308018	+	0.533503i	−0.669911	+	0.742442i	$0.733668\pi$
$128$	−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	$-0.231297\pi$
$137$	6.38795	+	3.68809i	0.545760	+	0.315094i	−0.201650	+	0.979458i	$0.564630\pi$
$138$			2.91228i			0.247910i
$139$	−0.410380	+	0.710798i	−0.0348079	+	0.0602891i	−0.882905	−	0.469552i	$-0.844415\pi$
$139$	−0.410380	+	0.710798i	−0.0348079	+	0.0602891i	0.848097	+	0.529842i	$0.177749\pi$
$140$		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	0.818329	−	0.574751i	$-0.194901\pi$
$149$	8.90766	+	5.14284i	0.729744	+	0.421318i	−0.0885845	+	0.996069i	$0.528234\pi$
$150$		0			0
$151$		−	11.7419i		−	0.955544i	−0.878484	−	0.477772i	$-0.841445\pi$
$151$		−	11.7419i		−	0.955544i	0.878484	−	0.477772i	$-0.158555\pi$
$152$	−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	$-0.586947\pi$
$157$	−6.76034			−0.539534			−0.269767	+	0.962926i	$0.586947\pi$
$158$	−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	$-0.315529\pi$
$163$	1.23624	+	0.713746i	0.0968301	+	0.0559049i	−0.450803	+	0.892623i	$0.648862\pi$
$164$			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	$-0.739604\pi$
$167$	−5.08406	+	2.93528i	−0.393416	+	0.227139i	0.290223	+	0.956959i	$0.406271\pi$
$168$	−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	−0.478804	−	0.877922i	$-0.658930\pi$
$173$	6.85138	−	11.8669i	0.520901	−	0.902226i	0.999705	−	0.0243045i	$-0.00773712\pi$
$174$			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	0.999384	+	0.0350821i	$0.0111693\pi$
$179$	7.09191	+	12.2835i	0.530074	+	0.918115i	−0.469310	+	0.883033i	$0.655497\pi$
$180$		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	−0.747344	−	0.664437i	$-0.768671\pi$
$191$	2.78821	−	4.82932i	0.201748	−	0.349437i	0.949092	+	0.315000i	$0.102005\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−0.191227	+	0.110405i	−0.0137648	+	0.00794712i	−0.506867	−	0.862024i	$-0.669196\pi$
$193$	−0.191227	+	0.110405i	−0.0137648	+	0.00794712i	0.493102	+	0.869972i	$0.335863\pi$
$194$	−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	$-0.686226\pi$
$197$	−1.49286	+	0.861905i	−0.106362	+	0.0614082i	0.445875	+	0.895095i	$0.352892\pi$
$198$	0.0874279	+	0.151430i	0.00621323	+	0.0107616i
$199$	3.97927	−	6.89229i	0.282083	−	0.488581i	−0.689815	−	0.723986i	$-0.742308\pi$
$199$	3.97927	−	6.89229i	0.282083	−	0.488581i	0.971898	+	0.235404i	$0.0756414\pi$
$200$		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	0.929467	−	0.368905i	$-0.120267\pi$
$211$	2.10991	+	3.65448i	0.145252	+	0.251585i	−0.784215	+	0.620490i	$0.786934\pi$
$212$	−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	$-0.591879\pi$
$223$	6.02126	−	3.47638i	0.403214	−	0.232795i	0.687870	+	0.725834i	$0.258546\pi$
$224$	−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	$-0.302689\pi$
$227$	2.50840	+	1.44823i	0.166488	+	0.0961221i	−0.414441	+	0.910076i	$0.636023\pi$
$228$	5.20843	+	3.00709i	0.344937	+	0.199149i
$229$		−	7.88800i		−	0.521254i	−0.965440	−	0.260627i	$-0.916071\pi$
$229$		−	7.88800i		−	0.521254i	0.965440	−	0.260627i	$-0.0839293\pi$
$230$		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	$-0.485111\pi$
$233$	1.42749			0.0935181			0.0467590	+	0.998906i	$0.485111\pi$
$234$	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	$0.114771\pi$
$239$			10.9084i			0.705604i	−0.935698	+	0.352802i	$0.885229\pi$
$240$		0			0
$241$	−25.4317	−	14.6830i	−1.63820	−	0.945816i	−0.981452	−	0.191707i	$-0.938598\pi$
$241$	−25.4317	−	14.6830i	−1.63820	−	0.945816i	−0.656749	−	0.754109i	$-0.728069\pi$
$242$			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	−0.432339	−	0.901711i	$-0.642312\pi$
$251$	8.94708	−	15.4968i	0.564735	−	0.978150i	0.997074	−	0.0764387i	$-0.0243549\pi$
$252$			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	$-0.290691\pi$
$257$	−6.08945	−	10.5472i	−0.379849	−	0.657918i	−0.991040	+	0.133565i	$0.957358\pi$
$258$	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	0.982490	+	0.186314i	$0.0596542\pi$
$263$	10.5834	+	18.3309i	0.652598	+	1.13033i	−0.329892	+	0.944019i	$0.607012\pi$
$264$	−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	−0.620838	−	0.783939i	$-0.713208\pi$
$269$	6.04371	−	10.4680i	0.368492	−	0.638246i	0.989330	+	0.145692i	$0.0465410\pi$
$270$		0			0
$271$	−12.7275	+	7.34824i	−0.773142	+	0.446374i	−0.833994	−	0.551773i	$-0.813951\pi$
$271$	−12.7275	+	7.34824i	−0.773142	+	0.446374i	0.0608525	+	0.998147i	$0.480618\pi$
$272$	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	−0.401722	−	0.915762i	$-0.631588\pi$
$277$	9.85638	−	17.0717i	0.592212	−	1.02574i	0.993934	−	0.109980i	$-0.0350786\pi$
$278$			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	$0.0957225\pi$
$281$			9.93073i			0.592418i	−0.955123	+	0.296209i	$0.904278\pi$
$282$	−5.95105	+	10.3075i	−0.354380	+	0.613804i
$283$	−5.81912	−	10.0790i	−0.345911	−	0.599135i	0.639608	−	0.768701i	$-0.279097\pi$
$283$	−5.81912	−	10.0790i	−0.345911	−	0.599135i	−0.985519	+	0.169566i	$0.945763\pi$
$284$	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	$-0.458854\pi$
$293$	−11.3906	−	6.57636i	−0.665445	−	0.384195i	−0.794349	+	0.607462i	$0.792188\pi$
$294$			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	$-0.432576\pi$
$313$	7.43905			0.420480			0.210240	+	0.977650i	$0.432576\pi$
$314$	−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	0.646754	−	0.762699i	$-0.276126\pi$
$331$	5.63295	+	3.25219i	0.309615	+	0.178756i	−0.337139	+	0.941455i	$0.609459\pi$
$332$	−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	$-0.669799\pi$
$337$	−18.6696			−1.01700			−0.508498	+	0.861063i	$0.669799\pi$
$338$	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	−0.179098	−	0.983831i	$-0.557318\pi$
$347$	14.2033	−	24.6009i	0.762474	−	1.32064i	0.941572	−	0.336813i	$-0.109349\pi$
$348$	3.24491	+	5.62035i	0.173945	+	0.301282i
$349$	−1.93797	+	1.11889i	−0.103737	+	0.0598926i	−0.550971	−	0.834524i	$-0.685742\pi$
$349$	−1.93797	+	1.11889i	−0.103737	+	0.0598926i	0.447234	+	0.894417i	$0.352409\pi$
$350$		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	$-0.652884\pi$
$353$	1.40866	−	0.813287i	0.0749751	−	0.0432869i	0.537019	+	0.843570i	$0.319550\pi$
$354$	−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	$0.363459\pi$
$359$			34.4613i			1.81880i	−0.415923	+	0.909400i	$0.636541\pi$
$360$		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	$-0.0419207\pi$
$367$	7.31703	+	12.6735i	0.381946	+	0.661550i	−0.609394	+	0.792867i	$0.708587\pi$
$368$	−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	0.424943	+	0.905220i	$0.360294\pi$
$373$	−11.0370	+	19.1166i	−0.571472	+	0.989819i	−0.996415	+	0.0845988i	$0.973039\pi$
$374$	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	−0.776612	−	0.629979i	$-0.783064\pi$
$379$	−12.0573	+	6.96127i	−0.619341	+	0.357577i	0.157272	+	0.987555i	$0.449730\pi$
$380$		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	$-0.116909\pi$
$383$	21.3119	+	12.3044i	1.08899	+	0.628728i	0.155681	+	0.987807i	$0.450243\pi$
$384$	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	$-0.352266\pi$
$397$	−2.05141	−	1.18438i	−0.102957	−	0.0594424i	−0.550595	+	0.834773i	$0.685599\pi$
$398$		−	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	−0.0986548	−	0.995122i	$-0.531454\pi$
$401$	14.2942	−	8.25276i	0.713818	−	0.412123i	0.812473	+	0.582998i	$0.198121\pi$
$402$	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	−0.429457	−	0.903087i	$-0.641295\pi$
$409$	−28.8448	−	16.6535i	−1.42628	−	0.823464i	−0.996825	+	0.0796230i	$0.974628\pi$
$410$		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	−0.952872	−	0.303372i	$-0.901887\pi$
$419$	−15.1303	−	26.2065i	−0.739164	−	1.28027i	0.213708	−	0.976898i	$-0.431446\pi$
$420$		0			0
$421$		−	40.2235i		−	1.96038i	−0.198070	−	0.980188i	$-0.563467\pi$
$421$		−	40.2235i		−	1.96038i	0.198070	−	0.980188i	$-0.436533\pi$
$422$	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	−0.989388	−	0.145300i	$-0.953585\pi$
$431$	−28.1980	+	16.2801i	−1.35825	+	0.784185i	−0.368860	+	0.929485i	$0.620252\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	15.3663	−	26.6153i	0.738460	−	1.27905i	−0.214729	−	0.976674i	$-0.568887\pi$
$433$	15.3663	−	26.6153i	0.738460	−	1.27905i	0.953189	−	0.302376i	$-0.0977798\pi$
$434$		−	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	0.777555	−	0.628815i	$-0.216460\pi$
$439$	−3.26422	−	5.65380i	−0.155793	−	0.269841i	−0.933347	+	0.358974i	$0.883127\pi$
$440$		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	$-0.244114\pi$
$443$	30.3111			1.44012			0.720061	+	0.693911i	$0.244114\pi$
$444$	−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	0.137579	−	0.990491i	$-0.456068\pi$
$449$	−13.8034	−	7.96938i	−0.651421	−	0.376098i	−0.789001	+	0.614392i	$0.789401\pi$
$450$		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	$-0.820004\pi$
$457$	−17.1548	+	9.90436i	−0.802470	+	0.463306i	0.0418642	+	0.999123i	$0.486670\pi$
$458$	−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	0.205202	−	0.978720i	$-0.434215\pi$
$461$	−11.5898	−	6.69139i	−0.539792	−	0.311649i	−0.744995	+	0.667070i	$0.767548\pi$
$462$	−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	$-0.218175\pi$
$467$	33.4593			1.54831			0.774155	+	0.632996i	$0.218175\pi$
$468$	−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	0.0117600	−	0.999931i	$-0.496257\pi$
$479$	19.3387	−	11.1652i	0.883606	−	0.510150i	0.871846	+	0.489781i	$0.162923\pi$
$480$		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	$-0.559148\pi$
$487$	−24.8982	−	14.3750i	−1.12824	−	0.651392i	−0.943493	+	0.331393i	$0.892481\pi$
$488$	−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	0.988320	−	0.152393i	$-0.0486978\pi$
$491$	8.02546	+	13.9005i	0.362184	+	0.627321i	−0.626136	+	0.779714i	$0.715364\pi$
$492$	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	$0.267196\pi$
$499$			33.2509i			1.48851i	−0.667894	+	0.744256i	$0.732804\pi$
$500$		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	0.436938	+	0.899492i	$0.356063\pi$
$503$	−12.5710	+	21.7736i	−0.560514	+	0.970838i	−0.997452	+	0.0713466i	$0.977270\pi$
$504$	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	−0.912412	−	0.409272i	$-0.865783\pi$
$509$	−22.8809	+	13.2103i	−1.01418	+	0.585536i	−0.101766	+	0.994808i	$0.532449\pi$
$510$		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	−0.986361	−	0.164598i	$-0.947367\pi$
$523$	−14.5385	−	25.1815i	−0.635726	−	1.10111i	0.350635	−	0.936512i	$-0.385966\pi$
$524$	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	$0.0562151\pi$
$541$			8.17282i			0.351377i	−0.984446	+	0.175688i	$0.943785\pi$
$542$	−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	$-0.163509\pi$
$547$	40.7393			1.74188			0.870942	+	0.491385i	$0.163509\pi$
$548$	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	$-0.660483\pi$
$557$	0.794008	−	0.458421i	0.0336432	−	0.0194239i	0.516727	+	0.856150i	$0.327150\pi$
$558$	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	$-0.919287\pi$
$563$	−6.32961	+	10.9632i	−0.266761	+	0.462044i	0.701262	+	0.712903i	$0.252620\pi$
$564$			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	−0.999872	−	0.0160026i	$-0.994906\pi$
$569$	−12.2559	−	21.2279i	−0.513795	−	0.889918i	0.486077	−	0.873916i	$-0.338427\pi$
$570$		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	$-0.946935\pi$
$587$	−32.3566	+	18.6811i	−1.33550	+	0.771051i	−0.349362	+	0.936988i	$0.613602\pi$
$588$	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	0.858356	−	0.513055i	$-0.171486\pi$
$601$	−0.371169	−	0.642883i	−0.0151403	−	0.0262237i	−0.873496	+	0.486831i	$0.838153\pi$
$602$	−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	0.394272	+	0.918994i	$0.370997\pi$
$607$	−14.7513	+	25.5500i	−0.598736	+	1.03704i	−0.993008	+	0.118047i	$0.962337\pi$
$608$	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	$-0.756127\pi$
$613$	−11.8943	+	6.86720i	−0.480408	+	0.277364i	0.240178	+	0.970729i	$0.422794\pi$
$614$	−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	$-0.00184079\pi$
$617$	37.1342	+	21.4394i	1.49497	+	0.863119i	0.494983	+	0.868902i	$0.335174\pi$
$618$	7.73853	+	4.46784i	0.311289	+	0.179723i
$619$			30.0054i			1.20602i	0.797734	+	0.603010i	$0.206032\pi$
$619$			30.0054i			1.20602i	−0.797734	+	0.603010i	$0.793968\pi$
$620$		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	0.645933	−	0.763394i	$-0.276468\pi$
$631$	7.73137	+	4.46371i	0.307781	+	0.177697i	−0.338152	+	0.941091i	$0.609802\pi$
$632$			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	−0.999424	−	0.0339254i	$-0.989199\pi$
$641$	−11.9079	+	20.6250i	−0.470332	+	0.814639i	0.529092	+	0.848564i	$0.322532\pi$
$642$			0.860777i			0.0339722i
$643$	8.30300	+	4.79374i	0.327439	+	0.189047i	0.654703	−	0.755886i	$-0.272794\pi$
$643$	8.30300	+	4.79374i	0.327439	+	0.189047i	−0.327265	+	0.944933i	$0.606127\pi$
$644$	−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	−0.839565	−	0.543259i	$-0.817190\pi$
$647$	−22.6448	−	39.2219i	−0.890259	−	1.54197i	−0.0506940	−	0.998714i	$-0.516143\pi$
$648$	−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	$-0.224591\pi$
$653$	−4.62451	−	8.00988i	−0.180971	−	0.313451i	−0.942211	+	0.335019i	$0.891257\pi$
$654$	−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	−0.565874	−	0.824491i	$-0.691461\pi$
$659$	11.0666	−	19.1679i	0.431093	−	0.746676i	0.996968	+	0.0778159i	$0.0247946\pi$
$660$		0			0
$661$	8.75083	−	5.05229i	0.340368	−	0.196511i	−0.320067	−	0.947395i	$-0.603705\pi$
$661$	8.75083	−	5.05229i	0.340368	−	0.196511i	0.660435	+	0.750884i	$0.270372\pi$
$662$	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	$-0.250219\pi$
$673$	−6.73157	−	11.6594i	−0.259483	−	0.449437i	−0.966103	+	0.258155i	$0.916885\pi$
$674$	−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	$-0.548290\pi$
$677$	−7.86444			−0.302255			−0.151127	+	0.988514i	$0.548290\pi$
$678$	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	$-0.448003\pi$
$683$	−15.9565	−	9.21246i	−0.610557	−	0.352505i	−0.773183	+	0.634183i	$0.781337\pi$
$684$		−	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	−0.837212	−	0.546878i	$-0.815816\pi$
$691$	−20.5618	+	11.8714i	−0.782208	+	0.451608i	0.0550042	+	0.998486i	$0.482483\pi$
$692$	−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	−0.116521	−	0.993188i	$-0.537174\pi$
$709$	−27.5565	−	15.9098i	−1.03491	−	0.597504i	−0.918387	+	0.395684i	$0.870507\pi$
$710$		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	−0.997395	−	0.0721392i	$-0.977017\pi$
$719$	−11.6970	+	20.2597i	−0.436223	+	0.755560i	0.561172	+	0.827699i	$0.310351\pi$
$720$		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	$-0.733045\pi$
$727$	−36.0471			−1.33691			−0.668457	+	0.743750i	$0.733045\pi$
$728$	−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	−0.967460	−	0.253024i	$-0.918575\pi$
$739$	−33.4931	+	19.3373i	−1.23206	+	0.711333i	−0.264604	+	0.964357i	$0.585241\pi$
$740$		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	$-0.664033\pi$
$743$	0.390632	−	0.225532i	0.0143309	−	0.00827395i	0.507148	+	0.861859i	$0.330700\pi$
$744$	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	0.588618	−	0.808411i	$-0.299672\pi$
$751$	−11.1206	−	19.2614i	−0.405795	−	0.702858i	−0.994414	+	0.105553i	$0.966339\pi$
$752$	−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	$-0.117692\pi$
$757$	4.21654	+	7.30326i	0.153253	+	0.265442i	−0.779169	+	0.626814i	$0.784358\pi$
$758$	−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	0.794368	−	0.607437i	$-0.207802\pi$
$761$	18.3585	+	10.5993i	0.665496	+	0.384224i	−0.128872	+	0.991661i	$0.541136\pi$
$762$		−	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	−0.559153	−	0.829064i	$-0.688874\pi$
$769$	−3.34820	+	1.93308i	−0.120739	+	0.0697088i	0.438414	+	0.898773i	$0.355540\pi$
$770$		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	$-0.129357\pi$
$773$	28.7898	+	16.6218i	1.03550	+	0.597845i	0.116944	+	0.993139i	$0.462690\pi$
$774$	−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	$-0.140321\pi$
$787$	27.6908	+	15.9873i	0.987071	+	0.569886i	0.0826737	+	0.996577i	$0.473654\pi$
$788$			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	0.346635	+	0.938000i	$0.387324\pi$
$797$	−18.0401	+	31.2464i	−0.639014	+	1.10680i	−0.985649	+	0.168805i	$0.946009\pi$
$798$			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	0.560890	−	0.827890i	$-0.310459\pi$
$809$	−12.4162	−	21.5054i	−0.436529	−	0.756090i	−0.997419	+	0.0718003i	$0.977126\pi$
$810$		0			0
$811$			21.3899i			0.751102i	0.926802	+	0.375551i	$0.122547\pi$
$811$			21.3899i			0.751102i	−0.926802	+	0.375551i	$0.877453\pi$
$812$	−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	0.0878420	−	0.996134i	$-0.472003\pi$
$821$	28.4938	−	16.4509i	0.994441	−	0.574141i	0.906599	+	0.421994i	$0.138670\pi$
$822$	−3.68809	−	6.38795i	−0.128637	−	0.222805i
$823$	−15.9221	+	27.5779i	−0.555010	+	0.961306i	0.442893	+	0.896575i	$0.353952\pi$
$823$	−15.9221	+	27.5779i	−0.555010	+	0.961306i	−0.997903	+	0.0647309i	$0.979381\pi$
$824$			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	0.998920	−	0.0464558i	$-0.0147927\pi$
$829$	13.2223	+	22.9016i	0.459228	+	0.795407i	−0.539692	+	0.841863i	$0.681459\pi$
$830$		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	−0.0191582	−	0.999816i	$-0.506099\pi$
$839$	−25.9126	−	14.9607i	−0.894604	−	0.516500i	−0.875446	+	0.483317i	$0.839432\pi$
$840$		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	$-0.572356\pi$
$857$	−13.1946			−0.450720			−0.225360	+	0.974276i	$0.572356\pi$
$858$	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	$-0.611798\pi$
$877$	−39.3640	−	22.7268i	−1.32923	−	0.767429i	−0.985180	+	0.171523i	$0.945131\pi$
$878$	−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	0.983867	−	0.178902i	$-0.0572545\pi$
$881$	10.0027	+	17.3252i	0.337000	+	0.583701i	−0.646867	+	0.762603i	$0.723921\pi$
$882$	5.41356	−	3.12552i	0.182284	−	0.105242i
$883$	−29.0388			−0.977233			−0.488617	−	0.872499i	$-0.662498\pi$
$883$	−29.0388			−0.977233			−0.488617	+	0.872499i	$0.662498\pi$
$884$	−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	$-0.151311\pi$
$887$	1.43623	+	2.48763i	0.0482240	+	0.0835264i	−0.840906	+	0.541181i	$0.817977\pi$
$888$	−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	−0.997850	−	0.0655336i	$-0.979125\pi$
$907$	−16.7351	−	28.9860i	−0.555679	−	0.962464i	0.442171	−	0.896931i	$-0.354208\pi$
$908$	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	−0.545285	−	0.838251i	$-0.683579\pi$
$919$	13.7419	−	23.8017i	0.453304	−	0.785146i	0.998589	+	0.0531051i	$0.0169118\pi$
$920$		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	0.362400	−	0.932023i	$-0.381958\pi$
$929$	−8.03305	−	4.63788i	−0.263556	−	0.152164i	−0.625956	+	0.779859i	$0.715291\pi$
$930$		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	$-0.579115\pi$
$937$	−15.0600			−0.491989			−0.245995	+	0.969271i	$0.579115\pi$
$938$	−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	$0.102517\pi$
$941$			19.4194i			0.633055i	−0.948583	+	0.316528i	$0.897483\pi$
$942$	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	$-0.638472\pi$
$947$	4.71506	−	2.72224i	0.153219	−	0.0884610i	0.574649	+	0.818400i	$0.305138\pi$
$948$	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	$-0.709860\pi$
$953$	11.6768	−	20.2248i	0.378249	−	0.655146i	0.990808	+	0.135279i	$0.0431930\pi$
$954$		−	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	−0.999982	−	0.00600636i	$-0.998088\pi$
$971$	−15.4181	+	26.7049i	−0.494789	+	0.857000i	0.505193	+	0.863007i	$0.331421\pi$
$972$	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	$-0.777375\pi$
$977$	−18.4521	+	10.6533i	−0.590334	+	0.340829i	0.174896	+	0.984587i	$0.444041\pi$
$978$	−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	0.824224	−	0.566265i	$-0.191612\pi$
$991$	−2.46451	−	4.26866i	−0.0782877	−	0.135598i	−0.902511	+	0.430666i	$0.858279\pi$
$992$	−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	$-0.712519\pi$
$997$	11.6988	−	20.2628i	0.370503	−	0.641730i	0.989643	+	0.143550i	$0.0458519\pi$
$998$	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.i.751.5		12
5.2	odd	4		390.2.x.b.49.2	yes	12
5.3	odd	4		390.2.x.a.49.5	✓	12
5.4	even	2		1950.2.bc.j.751.2		12
13.4	even	6	inner	1950.2.bc.i.901.5		12
15.2	even	4		1170.2.bj.c.829.4		12
15.8	even	4		1170.2.bj.d.829.3		12
65.4	even	6		1950.2.bc.j.901.2		12
65.17	odd	12		390.2.x.a.199.5	yes	12
65.43	odd	12		390.2.x.b.199.2	yes	12
195.17	even	12		1170.2.bj.d.199.3		12
195.173	even	12		1170.2.bj.c.199.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.5	✓	12	5.3	odd	4
390.2.x.a.199.5	yes	12	65.17	odd	12
390.2.x.b.49.2	yes	12	5.2	odd	4
390.2.x.b.199.2	yes	12	65.43	odd	12
1170.2.bj.c.199.4		12	195.173	even	12
1170.2.bj.c.829.4		12	15.2	even	4
1170.2.bj.d.199.3		12	195.17	even	12
1170.2.bj.d.829.3		12	15.8	even	4
1950.2.bc.i.751.5		12	1.1	even	1	trivial
1950.2.bc.i.901.5		12	13.4	even	6	inner
1950.2.bc.j.751.2		12	5.4	even	2
1950.2.bc.j.901.2		12	65.4	even	6

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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 6 q^{4} + 12 q^{7} - 6 q^{9} + 6 q^{11} - 12 q^{12} - 4 q^{13} - 4 q^{14} - 6 q^{16} - 8 q^{17} + 6 q^{19} + 6 q^{22} - 16 q^{23} - 2 q^{26} + 12 q^{27} + 12 q^{28} - 14 q^{29} - 6 q^{33}+ \cdots - 24 q^{98}+O(q^{100}) \) 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

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Database

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