LMFDB - Embedded newform 525.2.r.a.499.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [525,2,Mod(424,525)] 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("525.424"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(525, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-6,0,4,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	525.499
Dual form			525.2.r.a.424.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.36603 - 1.36603i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.73205 + 4.73205i) q^{4} +2.73205 q^{6} +(2.50000 - 0.866025i) q^{7} -9.46410i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.366025 - 0.633975i) q^{11} +(-4.73205 - 2.73205i) q^{12} +2.26795i q^{13} +(-7.09808 - 1.36603i) q^{14} +(-7.46410 + 12.9282i) q^{16} +(-2.83013 + 1.63397i) q^{17} +(-2.36603 + 1.36603i) q^{18} +(2.23205 - 3.86603i) q^{19} +(-1.73205 + 2.00000i) q^{21} +2.00000i q^{22} +(4.09808 + 2.36603i) q^{23} +(4.73205 + 8.19615i) q^{24} +(3.09808 - 5.36603i) q^{26} +1.00000i q^{27} +(10.9282 + 9.46410i) q^{28} +4.19615 q^{29} +(0.232051 + 0.401924i) q^{31} +(18.9282 - 10.9282i) q^{32} +(0.633975 + 0.366025i) q^{33} +8.92820 q^{34} +5.46410 q^{36} +(-2.76795 - 1.59808i) q^{37} +(-10.5622 + 6.09808i) q^{38} +(-1.13397 - 1.96410i) q^{39} -0.732051 q^{41} +(6.83013 - 2.36603i) q^{42} +3.19615i q^{43} +(2.00000 - 3.46410i) q^{44} +(-6.46410 - 11.1962i) q^{46} +(1.73205 + 1.00000i) q^{47} -14.9282i q^{48} +(5.50000 - 4.33013i) q^{49} +(1.63397 - 2.83013i) q^{51} +(-10.7321 + 6.19615i) q^{52} +(10.7321 - 6.19615i) q^{53} +(1.36603 - 2.36603i) q^{54} +(-8.19615 - 23.6603i) q^{56} +4.46410i q^{57} +(-9.92820 - 5.73205i) q^{58} +(-0.0980762 - 0.169873i) q^{59} +(-2.00000 + 3.46410i) q^{61} -1.26795i q^{62} +(0.500000 - 2.59808i) q^{63} -29.8564 q^{64} +(-1.00000 - 1.73205i) q^{66} +(12.6962 - 7.33013i) q^{67} +(-15.4641 - 8.92820i) q^{68} -4.73205 q^{69} +6.19615 q^{71} +(-8.19615 - 4.73205i) q^{72} +(10.9641 - 6.33013i) q^{73} +(4.36603 + 7.56218i) q^{74} +24.3923 q^{76} +(-1.46410 - 1.26795i) q^{77} +6.19615i q^{78} +(-3.69615 + 6.40192i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.73205 + 1.00000i) q^{82} +15.1244i q^{83} +(-14.1962 - 2.73205i) q^{84} +(4.36603 - 7.56218i) q^{86} +(-3.63397 + 2.09808i) q^{87} +(-6.00000 + 3.46410i) q^{88} +(7.56218 - 13.0981i) q^{89} +(1.96410 + 5.66987i) q^{91} +25.8564i q^{92} +(-0.401924 - 0.232051i) q^{93} +(-2.73205 - 4.73205i) q^{94} +(-10.9282 + 18.9282i) q^{96} -14.9282i q^{97} +(-18.9282 + 2.73205i) q^{98} -0.732051 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{2} + 4 q^{4} + 4 q^{6} + 10 q^{7} + 2 q^{9} + 2 q^{11} - 12 q^{12} - 18 q^{14} - 16 q^{16} + 6 q^{17} - 6 q^{18} + 2 q^{19} + 6 q^{23} + 12 q^{24} + 2 q^{26} + 16 q^{28} - 4 q^{29} - 6 q^{31}+ \cdots + 4 q^{99}+O(q^{100}) $ 4 * q - 6 * q^2 + 4 * q^4 + 4 * q^6 + 10 * q^7 + 2 * q^9 + 2 * q^11 - 12 * q^12 - 18 * q^14 - 16 * q^16 + 6 * q^17 - 6 * q^18 + 2 * q^19 + 6 * q^23 + 12 * q^24 + 2 * q^26 + 16 * q^28 - 4 * q^29 - 6 * q^31 + 48 * q^32 + 6 * q^33 + 8 * q^34 + 8 * q^36 - 18 * q^37 - 18 * q^38 - 8 * q^39 + 4 * q^41 + 10 * q^42 + 8 * q^44 - 12 * q^46 + 22 * q^49 + 10 * q^51 - 36 * q^52 + 36 * q^53 + 2 * q^54 - 12 * q^56 - 12 * q^58 + 10 * q^59 - 8 * q^61 + 2 * q^63 - 64 * q^64 - 4 * q^66 + 30 * q^67 - 48 * q^68 - 12 * q^69 + 4 * q^71 - 12 * q^72 + 30 * q^73 + 14 * q^74 + 56 * q^76 + 8 * q^77 + 6 * q^79 - 2 * q^81 - 36 * q^84 + 14 * q^86 - 18 * q^87 - 24 * q^88 + 6 * q^89 - 6 * q^91 - 12 * q^93 - 4 * q^94 - 16 * q^96 - 48 * q^98 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.36603	−	1.36603i	−1.67303	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$2$	−2.36603	−	1.36603i	−1.67303	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	2.73205	+	4.73205i	1.36603	+	2.36603i
$5$		0			0
$5$		0			0
$6$	2.73205			1.11536
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$		−	9.46410i		−	3.34607i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−0.366025	−	0.633975i	−0.110361	−	0.191151i	0.805555	−	0.592521i	$-0.201867\pi$
$11$	−0.366025	−	0.633975i	−0.110361	−	0.191151i	−0.915916	+	0.401371i	$0.868534\pi$
$12$	−4.73205	−	2.73205i	−1.36603	−	0.788675i
$13$			2.26795i			0.629016i	0.949255	+	0.314508i	$0.101840\pi$
$13$			2.26795i			0.629016i	−0.949255	+	0.314508i	$0.898160\pi$
$14$	−7.09808	−	1.36603i	−1.89704	−	0.365086i
$15$		0			0
$16$	−7.46410	+	12.9282i	−1.86603	+	3.23205i
$17$	−2.83013	+	1.63397i	−0.686407	+	0.396297i	−0.802264	−	0.596969i	$-0.796372\pi$
$17$	−2.83013	+	1.63397i	−0.686407	+	0.396297i	0.115858	+	0.993266i	$0.463038\pi$
$18$	−2.36603	+	1.36603i	−0.557678	+	0.321975i
$19$	2.23205	−	3.86603i	0.512068	−	0.886927i	−0.487835	−	0.872936i	$-0.662213\pi$
$19$	2.23205	−	3.86603i	0.512068	−	0.886927i	0.999902	−	0.0139909i	$-0.00445360\pi$
$20$		0			0
$21$	−1.73205	+	2.00000i	−0.377964	+	0.436436i
$22$			2.00000i			0.426401i
$23$	4.09808	+	2.36603i	0.854508	+	0.493350i	0.862169	−	0.506620i	$-0.169105\pi$
$23$	4.09808	+	2.36603i	0.854508	+	0.493350i	−0.00766135	+	0.999971i	$0.502439\pi$
$24$	4.73205	+	8.19615i	0.965926	+	1.67303i
$25$		0			0
$26$	3.09808	−	5.36603i	0.607583	−	1.05236i
$27$			1.00000i			0.192450i
$28$	10.9282	+	9.46410i	2.06524	+	1.78855i
$29$	4.19615			0.779206			0.389603	−	0.920983i	$-0.372612\pi$
$29$	4.19615			0.779206			0.389603	+	0.920983i	$0.372612\pi$
$30$		0			0
$31$	0.232051	+	0.401924i	0.0416776	+	0.0721876i	0.886112	−	0.463472i	$-0.153396\pi$
$31$	0.232051	+	0.401924i	0.0416776	+	0.0721876i	−0.844434	+	0.535659i	$0.820063\pi$
$32$	18.9282	−	10.9282i	3.34607	−	1.93185i
$33$	0.633975	+	0.366025i	0.110361	+	0.0637168i
$34$	8.92820			1.53117
$35$		0			0
$36$	5.46410			0.910684
$37$	−2.76795	−	1.59808i	−0.455048	−	0.262722i	0.254912	−	0.966964i	$-0.417954\pi$
$37$	−2.76795	−	1.59808i	−0.455048	−	0.262722i	−0.709960	+	0.704242i	$0.751287\pi$
$38$	−10.5622	+	6.09808i	−1.71341	+	0.989239i
$39$	−1.13397	−	1.96410i	−0.181581	−	0.314508i
$40$		0			0
$41$	−0.732051			−0.114327			−0.0571636	−	0.998365i	$-0.518206\pi$
$41$	−0.732051			−0.114327			−0.0571636	+	0.998365i	$0.518206\pi$
$42$	6.83013	−	2.36603i	1.05391	−	0.365086i
$43$			3.19615i			0.487409i	0.969850	+	0.243704i	$0.0783627\pi$
$43$			3.19615i			0.487409i	−0.969850	+	0.243704i	$0.921637\pi$
$44$	2.00000	−	3.46410i	0.301511	−	0.522233i
$45$		0			0
$46$	−6.46410	−	11.1962i	−0.953080	−	1.65078i
$47$	1.73205	+	1.00000i	0.252646	+	0.145865i	0.620975	−	0.783830i	$-0.286737\pi$
$47$	1.73205	+	1.00000i	0.252646	+	0.145865i	−0.368329	+	0.929695i	$0.620070\pi$
$48$		−	14.9282i		−	2.15470i
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$		0			0
$51$	1.63397	−	2.83013i	0.228802	−	0.396297i
$52$	−10.7321	+	6.19615i	−1.48827	+	0.859252i
$53$	10.7321	−	6.19615i	1.47416	−	0.851107i	0.474584	−	0.880210i	$-0.342598\pi$
$53$	10.7321	−	6.19615i	1.47416	−	0.851107i	0.999576	+	0.0291032i	$0.00926513\pi$
$54$	1.36603	−	2.36603i	0.185893	−	0.321975i
$55$		0			0
$56$	−8.19615	−	23.6603i	−1.09526	−	3.16173i
$57$			4.46410i			0.591285i
$58$	−9.92820	−	5.73205i	−1.30364	−	0.752655i
$59$	−0.0980762	−	0.169873i	−0.0127684	−	0.0221156i	0.859571	−	0.511017i	$-0.170731\pi$
$59$	−0.0980762	−	0.169873i	−0.0127684	−	0.0221156i	−0.872339	+	0.488901i	$0.837398\pi$
$60$		0			0
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	−0.965187	−	0.261562i	$-0.915762\pi$
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	0.709113	+	0.705095i	$0.249096\pi$
$62$		−	1.26795i		−	0.161030i
$63$	0.500000	−	2.59808i	0.0629941	−	0.327327i
$64$	−29.8564			−3.73205
$65$		0			0
$66$	−1.00000	−	1.73205i	−0.123091	−	0.213201i
$67$	12.6962	−	7.33013i	1.55108	−	0.895518i	0.553028	−	0.833163i	$-0.313472\pi$
$67$	12.6962	−	7.33013i	1.55108	−	0.895518i	0.998054	−	0.0623548i	$-0.0198610\pi$
$68$	−15.4641	−	8.92820i	−1.87530	−	1.08270i
$69$	−4.73205			−0.569672
$70$		0			0
$71$	6.19615			0.735348			0.367674	−	0.929955i	$-0.380154\pi$
$71$	6.19615			0.735348			0.367674	+	0.929955i	$0.380154\pi$
$72$	−8.19615	−	4.73205i	−0.965926	−	0.557678i
$73$	10.9641	−	6.33013i	1.28325	−	0.740885i	0.305810	−	0.952093i	$-0.401073\pi$
$73$	10.9641	−	6.33013i	1.28325	−	0.740885i	0.977441	+	0.211207i	$0.0677395\pi$
$74$	4.36603	+	7.56218i	0.507540	+	0.879085i
$75$		0			0
$76$	24.3923			2.79799
$77$	−1.46410	−	1.26795i	−0.166850	−	0.144496i
$78$			6.19615i			0.701576i
$79$	−3.69615	+	6.40192i	−0.415850	+	0.720273i	−0.995517	−	0.0945803i	$-0.969849\pi$
$79$	−3.69615	+	6.40192i	−0.415850	+	0.720273i	0.579668	+	0.814853i	$0.303182\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.73205	+	1.00000i	0.191273	+	0.110432i
$83$			15.1244i			1.66011i	0.557679	+	0.830057i	$0.311692\pi$
$83$			15.1244i			1.66011i	−0.557679	+	0.830057i	$0.688308\pi$
$84$	−14.1962	−	2.73205i	−1.54893	−	0.298091i
$85$		0			0
$86$	4.36603	−	7.56218i	0.470801	−	0.815451i
$87$	−3.63397	+	2.09808i	−0.389603	+	0.224937i
$88$	−6.00000	+	3.46410i	−0.639602	+	0.369274i
$89$	7.56218	−	13.0981i	0.801589	−	1.38839i	−0.116980	−	0.993134i	$-0.537321\pi$
$89$	7.56218	−	13.0981i	0.801589	−	1.38839i	0.918570	−	0.395259i	$-0.129345\pi$
$90$		0			0
$91$	1.96410	+	5.66987i	0.205894	+	0.594364i
$92$			25.8564i			2.69572i
$93$	−0.401924	−	0.232051i	−0.0416776	−	0.0240625i
$94$	−2.73205	−	4.73205i	−0.281790	−	0.488074i
$95$		0			0
$96$	−10.9282	+	18.9282i	−1.11536	+	1.93185i
$97$		−	14.9282i		−	1.51573i	−0.652412	−	0.757865i	$-0.726243\pi$
$97$		−	14.9282i		−	1.51573i	0.652412	−	0.757865i	$-0.273757\pi$
$98$	−18.9282	+	2.73205i	−1.91204	+	0.275979i
$99$	−0.732051			−0.0735739
$100$		0			0
$101$	3.63397	+	6.29423i	0.361594	+	0.626299i	0.988223	−	0.153018i	$-0.0488993\pi$
$101$	3.63397	+	6.29423i	0.361594	+	0.626299i	−0.626629	+	0.779317i	$0.715566\pi$
$102$	−7.73205	+	4.46410i	−0.765587	+	0.442012i
$103$	7.96410	+	4.59808i	0.784726	+	0.453062i	0.838103	−	0.545513i	$-0.183665\pi$
$103$	7.96410	+	4.59808i	0.784726	+	0.453062i	−0.0533764	+	0.998574i	$0.516998\pi$
$104$	21.4641			2.10473
$105$		0			0
$106$	−33.8564			−3.28842
$107$	1.90192	+	1.09808i	0.183866	+	0.106155i	0.589108	−	0.808054i	$-0.299479\pi$
$107$	1.90192	+	1.09808i	0.183866	+	0.106155i	−0.405242	+	0.914210i	$0.632813\pi$
$108$	−4.73205	+	2.73205i	−0.455342	+	0.262892i
$109$	5.50000	+	9.52628i	0.526804	+	0.912452i	0.999512	+	0.0312328i	$0.00994332\pi$
$109$	5.50000	+	9.52628i	0.526804	+	0.912452i	−0.472708	+	0.881219i	$0.656723\pi$
$110$		0			0
$111$	3.19615			0.303365
$112$	−7.46410	+	38.7846i	−0.705291	+	3.66480i
$113$			8.92820i			0.839895i	0.907548	+	0.419947i	$0.137951\pi$
$113$			8.92820i			0.839895i	−0.907548	+	0.419947i	$0.862049\pi$
$114$	6.09808	−	10.5622i	0.571137	−	0.989239i
$115$		0			0
$116$	11.4641	+	19.8564i	1.06442	+	1.84362i
$117$	1.96410	+	1.13397i	0.181581	+	0.104836i
$118$			0.535898i			0.0493334i
$119$	−5.66025	+	6.53590i	−0.518875	+	0.599145i
$120$		0			0
$121$	5.23205	−	9.06218i	0.475641	−	0.823834i
$122$	9.46410	−	5.46410i	0.856840	−	0.494697i
$123$	0.633975	−	0.366025i	0.0571636	−	0.0330034i
$124$	−1.26795	+	2.19615i	−0.113865	+	0.197220i
$125$		0			0
$126$	−4.73205	+	5.46410i	−0.421565	+	0.486781i
$127$		−	4.80385i		−	0.426273i	−0.977022	−	0.213136i	$-0.931632\pi$
$127$		−	4.80385i		−	0.426273i	0.977022	−	0.213136i	$-0.0683678\pi$
$128$	32.7846	+	18.9282i	2.89778	+	1.67303i
$129$	−1.59808	−	2.76795i	−0.140703	−	0.243704i
$130$		0			0
$131$	−7.73205	+	13.3923i	−0.675552	+	1.17009i	0.300755	+	0.953702i	$0.402761\pi$
$131$	−7.73205	+	13.3923i	−0.675552	+	1.17009i	−0.976307	+	0.216390i	$0.930572\pi$
$132$			4.00000i			0.348155i
$133$	2.23205	−	11.5981i	0.193543	−	1.00568i
$134$	−40.0526			−3.46001
$135$		0			0
$136$	15.4641	+	26.7846i	1.32604	+	2.29676i
$137$	−1.90192	+	1.09808i	−0.162492	+	0.0938150i	−0.579041	−	0.815298i	$-0.696573\pi$
$137$	−1.90192	+	1.09808i	−0.162492	+	0.0938150i	0.416549	+	0.909113i	$0.363240\pi$
$138$	11.1962	+	6.46410i	0.953080	+	0.550261i
$139$	−5.92820			−0.502824			−0.251412	−	0.967880i	$-0.580895\pi$
$139$	−5.92820			−0.502824			−0.251412	+	0.967880i	$0.580895\pi$
$140$		0			0
$141$	−2.00000			−0.168430
$142$	−14.6603	−	8.46410i	−1.23026	−	0.710292i
$143$	1.43782	−	0.830127i	0.120237	−	0.0694187i
$144$	7.46410	+	12.9282i	0.622008	+	1.07735i
$145$		0			0
$146$	−34.5885			−2.86256
$147$	−2.59808	+	6.50000i	−0.214286	+	0.536111i
$148$		−	17.4641i		−	1.43554i
$149$	2.92820	−	5.07180i	0.239888	−	0.415498i	−0.720794	−	0.693149i	$-0.756223\pi$
$149$	2.92820	−	5.07180i	0.239888	−	0.415498i	0.960682	+	0.277651i	$0.0895560\pi$
$150$		0			0
$151$	4.46410	+	7.73205i	0.363283	+	0.629225i	0.988499	−	0.151227i	$-0.0483223\pi$
$151$	4.46410	+	7.73205i	0.363283	+	0.629225i	−0.625216	+	0.780452i	$0.714989\pi$
$152$	−36.5885	−	21.1244i	−2.96772	−	1.71341i
$153$			3.26795i			0.264198i
$154$	1.73205	+	5.00000i	0.139573	+	0.402911i
$155$		0			0
$156$	6.19615	−	10.7321i	0.496089	−	0.859252i
$157$	−5.53590	+	3.19615i	−0.441813	+	0.255081i	−0.704366	−	0.709837i	$-0.748769\pi$
$157$	−5.53590	+	3.19615i	−0.441813	+	0.255081i	0.262553	+	0.964917i	$0.415435\pi$
$158$	17.4904	−	10.0981i	1.39146	−	0.803360i
$159$	−6.19615	+	10.7321i	−0.491387	+	0.851107i
$160$		0			0
$161$	12.2942	+	2.36603i	0.968921	+	0.186469i
$162$			2.73205i			0.214650i
$163$	−18.9282	−	10.9282i	−1.48257	−	0.855963i	−0.482767	−	0.875749i	$-0.660368\pi$
$163$	−18.9282	−	10.9282i	−1.48257	−	0.855963i	−0.999804	+	0.0197859i	$0.993702\pi$
$164$	−2.00000	−	3.46410i	−0.156174	−	0.270501i
$165$		0			0
$166$	20.6603	−	35.7846i	1.60355	−	2.77742i
$167$			17.6603i			1.36659i	0.730142	+	0.683296i	$0.239454\pi$
$167$			17.6603i			1.36659i	−0.730142	+	0.683296i	$0.760546\pi$
$168$	18.9282	+	16.3923i	1.46034	+	1.26469i
$169$	7.85641			0.604339
$170$		0			0
$171$	−2.23205	−	3.86603i	−0.170689	−	0.295642i
$172$	−15.1244	+	8.73205i	−1.15322	+	0.665813i
$173$	−12.5885	−	7.26795i	−0.957083	−	0.552572i	−0.0618087	−	0.998088i	$-0.519687\pi$
$173$	−12.5885	−	7.26795i	−0.957083	−	0.552572i	−0.895274	+	0.445516i	$0.853020\pi$
$174$	11.4641			0.869091
$175$		0			0
$176$	10.9282			0.823744
$177$	0.169873	+	0.0980762i	0.0127684	+	0.00737186i
$178$	−35.7846	+	20.6603i	−2.68217	+	1.54855i
$179$	−5.00000	−	8.66025i	−0.373718	−	0.647298i	0.616417	−	0.787420i	$-0.288584\pi$
$179$	−5.00000	−	8.66025i	−0.373718	−	0.647298i	−0.990134	+	0.140122i	$0.955250\pi$
$180$		0			0
$181$	−24.3205			−1.80773			−0.903865	−	0.427819i	$-0.859282\pi$
$181$	−24.3205			−1.80773			−0.903865	+	0.427819i	$0.859282\pi$
$182$	3.09808	−	16.0981i	0.229645	−	1.19327i
$183$		−	4.00000i		−	0.295689i
$184$	22.3923	−	38.7846i	1.65078	−	2.85924i
$185$		0			0
$186$	0.633975	+	1.09808i	0.0464853	+	0.0805149i
$187$	2.07180	+	1.19615i	0.151505	+	0.0874713i
$188$			10.9282i			0.797021i
$189$	0.866025	+	2.50000i	0.0629941	+	0.181848i
$190$		0			0
$191$	4.46410	−	7.73205i	0.323011	−	0.559472i	−0.658097	−	0.752933i	$-0.728638\pi$
$191$	4.46410	−	7.73205i	0.323011	−	0.559472i	0.981108	+	0.193462i	$0.0619716\pi$
$192$	25.8564	−	14.9282i	1.86603	−	1.07735i
$193$	1.03590	−	0.598076i	0.0745656	−	0.0430505i	−0.462254	−	0.886748i	$-0.652959\pi$
$193$	1.03590	−	0.598076i	0.0745656	−	0.0430505i	0.536819	+	0.843697i	$0.319626\pi$
$194$	−20.3923	+	35.3205i	−1.46408	+	2.53586i
$195$		0			0
$196$	35.5167	+	14.1962i	2.53690	+	1.01401i
$197$			0.339746i			0.0242059i	0.999927	+	0.0121029i	$0.00385258\pi$
$197$			0.339746i			0.0242059i	−0.999927	+	0.0121029i	$0.996147\pi$
$198$	1.73205	+	1.00000i	0.123091	+	0.0710669i
$199$	11.0000	+	19.0526i	0.779769	+	1.35060i	0.932075	+	0.362267i	$0.117997\pi$
$199$	11.0000	+	19.0526i	0.779769	+	1.35060i	−0.152305	+	0.988334i	$0.548670\pi$
$200$		0			0
$201$	−7.33013	+	12.6962i	−0.517027	+	0.895518i
$202$		−	19.8564i		−	1.39709i
$203$	10.4904	−	3.63397i	0.736280	−	0.255055i
$204$	17.8564			1.25020
$205$		0			0
$206$	−12.5622	−	21.7583i	−0.875248	−	1.51597i
$207$	4.09808	−	2.36603i	0.284836	−	0.164450i
$208$	−29.3205	−	16.9282i	−2.03301	−	1.17376i
$209$	−3.26795			−0.226049
$210$		0			0
$211$	7.07180			0.486843			0.243421	−	0.969921i	$-0.421730\pi$
$211$	7.07180			0.486843			0.243421	+	0.969921i	$0.421730\pi$
$212$	58.6410	+	33.8564i	4.02748	+	2.32527i
$213$	−5.36603	+	3.09808i	−0.367674	+	0.212277i
$214$	−3.00000	−	5.19615i	−0.205076	−	0.355202i
$215$		0			0
$216$	9.46410			0.643951
$217$	0.928203	+	0.803848i	0.0630105	+	0.0545687i
$218$		−	30.0526i		−	2.03542i
$219$	−6.33013	+	10.9641i	−0.427750	+	0.740885i
$220$		0			0
$221$	−3.70577	−	6.41858i	−0.249277	−	0.431761i
$222$	−7.56218	−	4.36603i	−0.507540	−	0.293028i
$223$		−	20.3923i		−	1.36557i	−0.730619	−	0.682785i	$-0.760769\pi$
$223$		−	20.3923i		−	1.36557i	0.730619	−	0.682785i	$-0.239231\pi$
$224$	37.8564	−	43.7128i	2.52939	−	2.92069i
$225$		0			0
$226$	12.1962	−	21.1244i	0.811276	−	1.40517i
$227$	1.43782	−	0.830127i	0.0954316	−	0.0550975i	−0.451525	−	0.892259i	$-0.649120\pi$
$227$	1.43782	−	0.830127i	0.0954316	−	0.0550975i	0.546956	+	0.837161i	$0.315786\pi$
$228$	−21.1244	+	12.1962i	−1.39899	+	0.807710i
$229$	−1.50000	+	2.59808i	−0.0991228	+	0.171686i	−0.911322	−	0.411695i	$-0.864937\pi$
$229$	−1.50000	+	2.59808i	−0.0991228	+	0.171686i	0.812199	+	0.583380i	$0.198270\pi$
$230$		0			0
$231$	1.90192	+	0.366025i	0.125137	+	0.0240827i
$232$		−	39.7128i		−	2.60727i
$233$	−15.0000	−	8.66025i	−0.982683	−	0.567352i	−0.0796037	−	0.996827i	$-0.525365\pi$
$233$	−15.0000	−	8.66025i	−0.982683	−	0.567352i	−0.903079	+	0.429474i	$0.858699\pi$
$234$	−3.09808	−	5.36603i	−0.202528	−	0.350788i
$235$		0			0
$236$	0.535898	−	0.928203i	0.0348840	−	0.0604209i
$237$		−	7.39230i		−	0.480182i
$238$	22.3205	−	7.73205i	1.44682	−	0.501194i
$239$	−7.07180			−0.457437			−0.228718	−	0.973493i	$-0.573453\pi$
$239$	−7.07180			−0.457437			−0.228718	+	0.973493i	$0.573453\pi$
$240$		0			0
$241$	−6.73205	−	11.6603i	−0.433650	−	0.751103i	0.563535	−	0.826092i	$-0.309441\pi$
$241$	−6.73205	−	11.6603i	−0.433650	−	0.751103i	−0.997184	+	0.0749893i	$0.976108\pi$
$242$	−24.7583	+	14.2942i	−1.59153	+	0.918868i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−21.8564			−1.39921
$245$		0			0
$246$	−2.00000			−0.127515
$247$	8.76795	+	5.06218i	0.557891	+	0.322099i
$248$	3.80385	−	2.19615i	0.241545	−	0.139456i
$249$	−7.56218	−	13.0981i	−0.479234	−	0.830057i
$250$		0			0
$251$	−24.5885			−1.55201			−0.776005	−	0.630727i	$-0.782757\pi$
$251$	−24.5885			−1.55201			−0.776005	+	0.630727i	$0.782757\pi$
$252$	13.6603	−	4.73205i	0.860515	−	0.298091i
$253$		−	3.46410i		−	0.217786i
$254$	−6.56218	+	11.3660i	−0.411748	+	0.713168i
$255$		0			0
$256$	−21.8564	−	37.8564i	−1.36603	−	2.36603i
$257$	−4.90192	−	2.83013i	−0.305774	−	0.176538i	0.339260	−	0.940693i	$-0.389823\pi$
$257$	−4.90192	−	2.83013i	−0.305774	−	0.176538i	−0.645034	+	0.764154i	$0.723157\pi$
$258$			8.73205i			0.543634i
$259$	−8.30385	−	1.59808i	−0.515976	−	0.0992996i
$260$		0			0
$261$	2.09808	−	3.63397i	0.129868	−	0.224937i
$262$	36.5885	−	21.1244i	2.26044	−	1.30507i
$263$	7.26795	−	4.19615i	0.448161	−	0.258746i	−0.258892	−	0.965906i	$-0.583357\pi$
$263$	7.26795	−	4.19615i	0.448161	−	0.258746i	0.707053	+	0.707160i	$0.250024\pi$
$264$	3.46410	−	6.00000i	0.213201	−	0.369274i
$265$		0			0
$266$	−21.1244	+	24.3923i	−1.29522	+	1.49559i
$267$			15.1244i			0.925596i
$268$	69.3731	+	40.0526i	4.23763	+	2.44660i
$269$	−6.26795	−	10.8564i	−0.382164	−	0.661927i	0.609208	−	0.793011i	$-0.291488\pi$
$269$	−6.26795	−	10.8564i	−0.382164	−	0.661927i	−0.991371	+	0.131084i	$0.958154\pi$
$270$		0			0
$271$	−1.53590	+	2.66025i	−0.0932992	+	0.161599i	−0.908897	−	0.417020i	$-0.863075\pi$
$271$	−1.53590	+	2.66025i	−0.0932992	+	0.161599i	0.815598	+	0.578619i	$0.196408\pi$
$272$		−	48.7846i		−	2.95800i
$273$	−4.53590	−	3.92820i	−0.274525	−	0.237746i
$274$	6.00000			0.362473
$275$		0			0
$276$	−12.9282	−	22.3923i	−0.778186	−	1.34786i
$277$	12.6962	−	7.33013i	0.762838	−	0.440425i	−0.0674759	−	0.997721i	$-0.521495\pi$
$277$	12.6962	−	7.33013i	0.762838	−	0.440425i	0.830314	+	0.557296i	$0.188161\pi$
$278$	14.0263	+	8.09808i	0.841240	+	0.485690i
$279$	0.464102			0.0277850
$280$		0			0
$281$	13.8564			0.826604			0.413302	−	0.910594i	$-0.364375\pi$
$281$	13.8564			0.826604			0.413302	+	0.910594i	$0.364375\pi$
$282$	4.73205	+	2.73205i	0.281790	+	0.162691i
$283$	−20.8923	+	12.0622i	−1.24192	+	0.717022i	−0.969485	−	0.245152i	$-0.921162\pi$
$283$	−20.8923	+	12.0622i	−1.24192	+	0.717022i	−0.272434	+	0.962174i	$0.587829\pi$
$284$	16.9282	+	29.3205i	1.00450	+	1.73985i
$285$		0			0
$286$	−4.53590			−0.268213
$287$	−1.83013	+	0.633975i	−0.108029	+	0.0374223i
$288$		−	21.8564i		−	1.28790i
$289$	−3.16025	+	5.47372i	−0.185897	+	0.321984i
$290$		0			0
$291$	7.46410	+	12.9282i	0.437553	+	0.757865i
$292$	59.9090	+	34.5885i	3.50591	+	2.02414i
$293$			18.9282i			1.10580i	0.833248	+	0.552899i	$0.186478\pi$
$293$			18.9282i			1.10580i	−0.833248	+	0.552899i	$0.813522\pi$
$294$	15.0263	−	11.8301i	0.876350	−	0.689947i
$295$		0			0
$296$	−15.1244	+	26.1962i	−0.879085	+	1.52262i
$297$	0.633975	−	0.366025i	0.0367869	−	0.0212389i
$298$	−13.8564	+	8.00000i	−0.802680	+	0.463428i
$299$	−5.36603	+	9.29423i	−0.310325	+	0.537499i
$300$		0			0
$301$	2.76795	+	7.99038i	0.159542	+	0.460558i
$302$		−	24.3923i		−	1.40362i
$303$	−6.29423	−	3.63397i	−0.361594	−	0.208766i
$304$	33.3205	+	57.7128i	1.91106	+	3.31006i
$305$		0			0
$306$	4.46410	−	7.73205i	0.255196	−	0.442012i
$307$			32.1244i			1.83343i	0.399537	+	0.916717i	$0.369171\pi$
$307$			32.1244i			1.83343i	−0.399537	+	0.916717i	$0.630829\pi$
$308$	2.00000	−	10.3923i	0.113961	−	0.592157i
$309$	−9.19615			−0.523151
$310$		0			0
$311$	−4.56218	−	7.90192i	−0.258697	−	0.448077i	0.707196	−	0.707018i	$-0.249960\pi$
$311$	−4.56218	−	7.90192i	−0.258697	−	0.448077i	−0.965893	+	0.258941i	$0.916627\pi$
$312$	−18.5885	+	10.7321i	−1.05236	+	0.607583i
$313$	10.9641	+	6.33013i	0.619728	+	0.357800i	0.776763	−	0.629793i	$-0.216860\pi$
$313$	10.9641	+	6.33013i	0.619728	+	0.357800i	−0.157035	+	0.987593i	$0.550194\pi$
$314$	17.4641			0.985556
$315$		0			0
$316$	−40.3923			−2.27224
$317$	−24.6340	−	14.2224i	−1.38358	−	0.798811i	−0.391000	−	0.920391i	$-0.627871\pi$
$317$	−24.6340	−	14.2224i	−1.38358	−	0.798811i	−0.992582	+	0.121579i	$0.961204\pi$
$318$	29.3205	−	16.9282i	1.64421	−	0.949286i
$319$	−1.53590	−	2.66025i	−0.0859938	−	0.148946i
$320$		0			0
$321$	−2.19615			−0.122577
$322$	−25.8564	−	22.3923i	−1.44092	−	1.24787i
$323$			14.5885i			0.811723i
$324$	2.73205	−	4.73205i	0.151781	−	0.262892i
$325$		0			0
$326$	29.8564	+	51.7128i	1.65359	+	2.86411i
$327$	−9.52628	−	5.50000i	−0.526804	−	0.304151i
$328$			6.92820i			0.382546i
$329$	5.19615	+	1.00000i	0.286473	+	0.0551318i
$330$		0			0
$331$	−4.03590	+	6.99038i	−0.221833	+	0.384226i	−0.955365	−	0.295429i	$-0.904537\pi$
$331$	−4.03590	+	6.99038i	−0.221833	+	0.384226i	0.733532	+	0.679655i	$0.237871\pi$
$332$	−71.5692	+	41.3205i	−3.92787	+	2.26776i
$333$	−2.76795	+	1.59808i	−0.151683	+	0.0875740i
$334$	24.1244	−	41.7846i	1.32003	−	2.28635i
$335$		0			0
$336$	−12.9282	−	37.3205i	−0.705291	−	2.03600i
$337$		−	17.9808i		−	0.979475i	−0.871870	−	0.489737i	$-0.837093\pi$
$337$		−	17.9808i		−	0.979475i	0.871870	−	0.489737i	$-0.162907\pi$
$338$	−18.5885	−	10.7321i	−1.01108	−	0.583747i
$339$	−4.46410	−	7.73205i	−0.242457	−	0.419947i
$340$		0			0
$341$	0.169873	−	0.294229i	0.00919914	−	0.0159334i
$342$			12.1962i			0.659492i
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	30.2487			1.63090
$345$		0			0
$346$	19.8564	+	34.3923i	1.06749	+	1.84894i
$347$	18.2487	−	10.5359i	0.979642	−	0.565597i	0.0774801	−	0.996994i	$-0.475313\pi$
$347$	18.2487	−	10.5359i	0.979642	−	0.565597i	0.902162	+	0.431397i	$0.141979\pi$
$348$	−19.8564	−	11.4641i	−1.06442	−	0.614540i
$349$	−22.0000			−1.17763			−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000			−1.17763			−0.588817	+	0.808267i	$0.700406\pi$
$350$		0			0
$351$	−2.26795			−0.121054
$352$	−13.8564	−	8.00000i	−0.738549	−	0.426401i
$353$	−2.70577	+	1.56218i	−0.144014	+	0.0831463i	−0.570276	−	0.821453i	$-0.693164\pi$
$353$	−2.70577	+	1.56218i	−0.144014	+	0.0831463i	0.426262	+	0.904600i	$0.359830\pi$
$354$	−0.267949	−	0.464102i	−0.0142413	−	0.0246667i
$355$		0			0
$356$	82.6410			4.37997
$357$	1.63397	−	8.49038i	0.0864791	−	0.449359i
$358$			27.3205i			1.44393i
$359$	−0.633975	+	1.09808i	−0.0334599	+	0.0579542i	−0.882270	−	0.470743i	$-0.843986\pi$
$359$	−0.633975	+	1.09808i	−0.0334599	+	0.0579542i	0.848811	+	0.528697i	$0.177319\pi$
$360$		0			0
$361$	−0.464102	−	0.803848i	−0.0244264	−	0.0423078i
$362$	57.5429	+	33.2224i	3.02439	+	1.74613i
$363$			10.4641i			0.549223i
$364$	−21.4641	+	24.7846i	−1.12502	+	1.29907i
$365$		0			0
$366$	−5.46410	+	9.46410i	−0.285613	+	0.494697i
$367$	−9.69615	+	5.59808i	−0.506135	+	0.292217i	−0.731244	−	0.682117i	$-0.761060\pi$
$367$	−9.69615	+	5.59808i	−0.506135	+	0.292217i	0.225108	+	0.974334i	$0.427726\pi$
$368$	−61.1769	+	35.3205i	−3.18907	+	1.84121i
$369$	−0.366025	+	0.633975i	−0.0190545	+	0.0330034i
$370$		0			0
$371$	21.4641	−	24.7846i	1.11436	−	1.28675i
$372$		−	2.53590i		−	0.131480i
$373$	−22.9641	−	13.2583i	−1.18904	−	0.686490i	−0.230949	−	0.972966i	$-0.574183\pi$
$373$	−22.9641	−	13.2583i	−1.18904	−	0.686490i	−0.958088	+	0.286476i	$0.907516\pi$
$374$	−3.26795	−	5.66025i	−0.168982	−	0.292685i
$375$		0			0
$376$	9.46410	−	16.3923i	0.488074	−	0.845369i
$377$			9.51666i			0.490133i
$378$	1.36603	−	7.09808i	0.0702608	−	0.365086i
$379$	−6.32051			−0.324663			−0.162331	−	0.986736i	$-0.551901\pi$
$379$	−6.32051			−0.324663			−0.162331	+	0.986736i	$0.551901\pi$
$380$		0			0
$381$	2.40192	+	4.16025i	0.123054	+	0.213136i
$382$	−21.1244	+	12.1962i	−1.08082	+	0.624009i
$383$	20.1962	+	11.6603i	1.03198	+	0.595811i	0.917550	−	0.397621i	$-0.130164\pi$
$383$	20.1962	+	11.6603i	1.03198	+	0.595811i	0.114425	+	0.993432i	$0.463497\pi$
$384$	−37.8564			−1.93185
$385$		0			0
$386$	−3.26795			−0.166334
$387$	2.76795	+	1.59808i	0.140703	+	0.0812348i
$388$	70.6410	−	40.7846i	3.58625	−	2.07052i
$389$	2.70577	+	4.68653i	0.137188	+	0.237617i	0.926431	−	0.376464i	$-0.122860\pi$
$389$	2.70577	+	4.68653i	0.137188	+	0.237617i	−0.789243	+	0.614081i	$0.789527\pi$
$390$		0			0
$391$	−15.4641			−0.782053
$392$	−40.9808	−	52.0526i	−2.06984	−	2.62905i
$393$		−	15.4641i		−	0.780061i
$394$	0.464102	−	0.803848i	0.0233811	−	0.0404973i
$395$		0			0
$396$	−2.00000	−	3.46410i	−0.100504	−	0.174078i
$397$	−27.0167	−	15.5981i	−1.35593	−	0.782845i	−0.366855	−	0.930278i	$-0.619566\pi$
$397$	−27.0167	−	15.5981i	−1.35593	−	0.782845i	−0.989072	+	0.147433i	$0.952899\pi$
$398$		−	60.1051i		−	3.01280i
$399$	3.86603	+	11.1603i	0.193543	+	0.558712i
$400$		0			0
$401$	8.19615	−	14.1962i	0.409296	−	0.708922i	−0.585515	−	0.810662i	$-0.699108\pi$
$401$	8.19615	−	14.1962i	0.409296	−	0.708922i	0.994811	+	0.101740i	$0.0324409\pi$
$402$	34.6865	−	20.0263i	1.73001	−	0.998820i
$403$	−0.911543	+	0.526279i	−0.0454072	+	0.0262158i
$404$	−19.8564	+	34.3923i	−0.987893	+	1.71108i
$405$		0			0
$406$	−29.7846	−	5.73205i	−1.47819	−	0.284477i
$407$			2.33975i			0.115977i
$408$	−26.7846	−	15.4641i	−1.32604	−	0.765587i
$409$	1.57180	+	2.72243i	0.0777203	+	0.134616i	0.902266	−	0.431180i	$-0.141903\pi$
$409$	1.57180	+	2.72243i	0.0777203	+	0.134616i	−0.824546	+	0.565795i	$0.808569\pi$
$410$		0			0
$411$	1.09808	−	1.90192i	0.0541641	−	0.0938150i
$412$			50.2487i			2.47558i
$413$	−0.392305	−	0.339746i	−0.0193041	−	0.0167178i
$414$	−12.9282			−0.635387
$415$		0			0
$416$	24.7846	+	42.9282i	1.21517	+	2.10473i
$417$	5.13397	−	2.96410i	0.251412	−	0.145153i
$418$	7.73205	+	4.46410i	0.378187	+	0.218346i
$419$	35.4641			1.73253			0.866267	−	0.499581i	$-0.166513\pi$
$419$	35.4641			1.73253			0.866267	+	0.499581i	$0.166513\pi$
$420$		0			0
$421$	0.0717968			0.00349916			0.00174958	−	0.999998i	$-0.499443\pi$
$421$	0.0717968			0.00349916			0.00174958	+	0.999998i	$0.499443\pi$
$422$	−16.7321	−	9.66025i	−0.814503	−	0.470254i
$423$	1.73205	−	1.00000i	0.0842152	−	0.0486217i
$424$	−58.6410	−	101.569i	−2.84786	−	4.93264i
$425$		0			0
$426$	16.9282			0.820174
$427$	−2.00000	+	10.3923i	−0.0967868	+	0.502919i
$428$			12.0000i			0.580042i
$429$	−0.830127	+	1.43782i	−0.0400789	+	0.0694187i
$430$		0			0
$431$	−8.66025	−	15.0000i	−0.417150	−	0.722525i	0.578502	−	0.815681i	$-0.303638\pi$
$431$	−8.66025	−	15.0000i	−0.417150	−	0.722525i	−0.995651	+	0.0931566i	$0.970304\pi$
$432$	−12.9282	−	7.46410i	−0.622008	−	0.359117i
$433$			15.1962i			0.730280i	0.930953	+	0.365140i	$0.118979\pi$
$433$			15.1962i			0.730280i	−0.930953	+	0.365140i	$0.881021\pi$
$434$	−1.09808	−	3.16987i	−0.0527093	−	0.152159i
$435$		0			0
$436$	−30.0526	+	52.0526i	−1.43926	+	2.49287i
$437$	18.2942	−	10.5622i	0.875132	−	0.505257i
$438$	29.9545	−	17.2942i	1.43128	−	0.826350i
$439$	0.267949	−	0.464102i	0.0127885	−	0.0221504i	−0.859560	−	0.511034i	$-0.829263\pi$
$439$	0.267949	−	0.464102i	0.0127885	−	0.0221504i	0.872349	+	0.488884i	$0.162596\pi$
$440$		0			0
$441$	−1.00000	−	6.92820i	−0.0476190	−	0.329914i
$442$			20.2487i			0.963133i
$443$	−8.19615	−	4.73205i	−0.389411	−	0.224827i	0.292494	−	0.956267i	$-0.405515\pi$
$443$	−8.19615	−	4.73205i	−0.389411	−	0.224827i	−0.681905	+	0.731441i	$0.738848\pi$
$444$	8.73205	+	15.1244i	0.414405	+	0.717770i
$445$		0			0
$446$	−27.8564	+	48.2487i	−1.31904	+	2.28464i
$447$			5.85641i			0.276999i
$448$	−74.6410	+	25.8564i	−3.52646	+	1.22160i
$449$	35.8564			1.69217			0.846084	−	0.533049i	$-0.178954\pi$
$449$	35.8564			1.69217			0.846084	+	0.533049i	$0.178954\pi$
$450$		0			0
$451$	0.267949	+	0.464102i	0.0126172	+	0.0218537i
$452$	−42.2487	+	24.3923i	−1.98721	+	1.14732i
$453$	−7.73205	−	4.46410i	−0.363283	−	0.209742i
$454$	−4.53590			−0.212880
$455$		0			0
$456$	42.2487			1.97848
$457$	−14.4282	−	8.33013i	−0.674923	−	0.389667i	0.123016	−	0.992405i	$-0.460743\pi$
$457$	−14.4282	−	8.33013i	−0.674923	−	0.389667i	−0.797939	+	0.602738i	$0.794077\pi$
$458$	7.09808	−	4.09808i	0.331671	−	0.191491i
$459$	−1.63397	−	2.83013i	−0.0762674	−	0.132099i
$460$		0			0
$461$	16.9808			0.790873			0.395436	−	0.918493i	$-0.370593\pi$
$461$	16.9808			0.790873			0.395436	+	0.918493i	$0.370593\pi$
$462$	−4.00000	−	3.46410i	−0.186097	−	0.161165i
$463$			25.7321i			1.19587i	0.801545	+	0.597935i	$0.204012\pi$
$463$			25.7321i			1.19587i	−0.801545	+	0.597935i	$0.795988\pi$
$464$	−31.3205	+	54.2487i	−1.45402	+	2.51843i
$465$		0			0
$466$	23.6603	+	40.9808i	1.09604	+	1.89840i
$467$	−0.124356	−	0.0717968i	−0.00575449	−	0.00332236i	0.497120	−	0.867682i	$-0.334391\pi$
$467$	−0.124356	−	0.0717968i	−0.00575449	−	0.00332236i	−0.502874	+	0.864359i	$0.667724\pi$
$468$			12.3923i			0.572834i
$469$	25.3923	−	29.3205i	1.17251	−	1.35390i
$470$		0			0
$471$	3.19615	−	5.53590i	0.147271	−	0.255081i
$472$	−1.60770	+	0.928203i	−0.0740002	+	0.0427240i
$473$	2.02628	−	1.16987i	0.0931684	−	0.0537908i
$474$	−10.0981	+	17.4904i	−0.463820	+	0.803360i
$475$		0			0
$476$	−46.3923	−	8.92820i	−2.12639	−	0.409224i
$477$		−	12.3923i		−	0.567405i
$478$	16.7321	+	9.66025i	0.765306	+	0.441850i
$479$	4.39230	+	7.60770i	0.200690	+	0.347604i	0.948751	−	0.316025i	$-0.102348\pi$
$479$	4.39230	+	7.60770i	0.200690	+	0.347604i	−0.748061	+	0.663630i	$0.769015\pi$
$480$		0			0
$481$	3.62436	−	6.27757i	0.165256	−	0.286232i
$482$			36.7846i			1.67549i
$483$	−11.8301	+	4.09808i	−0.538289	+	0.186469i
$484$	57.1769			2.59895
$485$		0			0
$486$	−1.36603	−	2.36603i	−0.0619642	−	0.107325i
$487$	0.356406	−	0.205771i	0.0161503	−	0.00932439i	−0.491903	−	0.870650i	$-0.663699\pi$
$487$	0.356406	−	0.205771i	0.0161503	−	0.00932439i	0.508053	+	0.861326i	$0.330365\pi$
$488$	32.7846	+	18.9282i	1.48409	+	0.856840i
$489$	21.8564			0.988381
$490$		0			0
$491$	−38.2487			−1.72614			−0.863070	−	0.505084i	$-0.831461\pi$
$491$	−38.2487			−1.72614			−0.863070	+	0.505084i	$0.831461\pi$
$492$	3.46410	+	2.00000i	0.156174	+	0.0901670i
$493$	−11.8756	+	6.85641i	−0.534852	+	0.308797i
$494$	−13.8301	−	23.9545i	−0.622247	−	1.07776i
$495$		0			0
$496$	−6.92820			−0.311086
$497$	15.4904	−	5.36603i	0.694839	−	0.240699i
$498$			41.3205i			1.85162i
$499$	−6.76795	+	11.7224i	−0.302975	+	0.524768i	−0.976808	−	0.214115i	$-0.931313\pi$
$499$	−6.76795	+	11.7224i	−0.302975	+	0.524768i	0.673833	+	0.738883i	$0.264647\pi$
$500$		0			0
$501$	−8.83013	−	15.2942i	−0.394501	−	0.683296i
$502$	58.1769	+	33.5885i	2.59656	+	1.49913i
$503$			14.3923i			0.641721i	0.947126	+	0.320861i	$0.103972\pi$
$503$			14.3923i			0.641721i	−0.947126	+	0.320861i	$0.896028\pi$
$504$	−24.5885	−	4.73205i	−1.09526	−	0.210782i
$505$		0			0
$506$	−4.73205	+	8.19615i	−0.210365	+	0.364363i
$507$	−6.80385	+	3.92820i	−0.302169	+	0.174458i
$508$	22.7321	−	13.1244i	1.00857	−	0.582299i
$509$	2.26795	−	3.92820i	0.100525	−	0.174115i	−0.811376	−	0.584525i	$-0.801281\pi$
$509$	2.26795	−	3.92820i	0.100525	−	0.174115i	0.911901	+	0.410410i	$0.134614\pi$
$510$		0			0
$511$	21.9282	−	25.3205i	0.970047	−	1.12011i
$512$			43.7128i			1.93185i
$513$	3.86603	+	2.23205i	0.170689	+	0.0985475i
$514$	7.73205	+	13.3923i	0.341046	+	0.590709i
$515$		0			0
$516$	8.73205	−	15.1244i	0.384407	−	0.665813i
$517$		−	1.46410i		−	0.0643911i
$518$	17.4641	+	15.1244i	0.767329	+	0.664526i
$519$	14.5359			0.638055
$520$		0			0
$521$	2.73205	+	4.73205i	0.119693	+	0.207315i	0.919646	−	0.392748i	$-0.128476\pi$
$521$	2.73205	+	4.73205i	0.119693	+	0.207315i	−0.799953	+	0.600063i	$0.795142\pi$
$522$	−9.92820	+	5.73205i	−0.434546	+	0.250885i
$523$	24.0167	+	13.8660i	1.05018	+	0.606319i	0.922698	−	0.385523i	$-0.125979\pi$
$523$	24.0167	+	13.8660i	1.05018	+	0.606319i	0.127477	+	0.991842i	$0.459312\pi$
$524$	−84.4974			−3.69129
$525$		0			0
$526$	−22.9282			−0.999717
$527$	−1.31347	−	0.758330i	−0.0572155	−	0.0330334i
$528$	−9.46410	+	5.46410i	−0.411872	+	0.237795i
$529$	−0.303848	−	0.526279i	−0.0132108	−	0.0228817i
$530$		0			0
$531$	−0.196152			−0.00851229
$532$	60.9808	−	21.1244i	2.64385	−	0.915857i
$533$		−	1.66025i		−	0.0719136i
$534$	20.6603	−	35.7846i	0.894057	−	1.54855i
$535$		0			0
$536$	−69.3731	−	120.158i	−2.99646	−	5.19002i
$537$	8.66025	+	5.00000i	0.373718	+	0.215766i
$538$			34.2487i			1.47657i
$539$	−4.75833	−	1.90192i	−0.204956	−	0.0819217i
$540$		0			0
$541$	−2.89230	+	5.00962i	−0.124350	+	0.215380i	−0.921479	−	0.388429i	$-0.873018\pi$
$541$	−2.89230	+	5.00962i	−0.124350	+	0.215380i	0.797129	+	0.603809i	$0.206351\pi$
$542$	7.26795	−	4.19615i	0.312185	−	0.180240i
$543$	21.0622	−	12.1603i	0.903865	−	0.521846i
$544$	−35.7128	+	61.8564i	−1.53117	+	2.65207i
$545$		0			0
$546$	5.36603	+	15.4904i	0.229645	+	0.662927i
$547$			26.2487i			1.12231i	0.827709	+	0.561157i	$0.189644\pi$
$547$			26.2487i			1.12231i	−0.827709	+	0.561157i	$0.810356\pi$
$548$	−10.3923	−	6.00000i	−0.443937	−	0.256307i
$549$	2.00000	+	3.46410i	0.0853579	+	0.147844i
$550$		0			0
$551$	9.36603	−	16.2224i	0.399006	−	0.691099i
$552$			44.7846i			1.90616i
$553$	−3.69615	+	19.2058i	−0.157176	+	0.816712i
$554$	−40.0526			−1.70167
$555$		0			0
$556$	−16.1962	−	28.0526i	−0.686870	−	1.18969i
$557$	−12.8038	+	7.39230i	−0.542516	+	0.313222i	−0.746098	−	0.665836i	$-0.768075\pi$
$557$	−12.8038	+	7.39230i	−0.542516	+	0.313222i	0.203582	+	0.979058i	$0.434742\pi$
$558$	−1.09808	−	0.633975i	−0.0464853	−	0.0268383i
$559$	−7.24871			−0.306588
$560$		0			0
$561$	−2.39230			−0.101003
$562$	−32.7846	−	18.9282i	−1.38294	−	0.798438i
$563$	−15.5885	+	9.00000i	−0.656975	+	0.379305i	−0.791123	−	0.611656i	$-0.790503\pi$
$563$	−15.5885	+	9.00000i	−0.656975	+	0.379305i	0.134148	+	0.990961i	$0.457170\pi$
$564$	−5.46410	−	9.46410i	−0.230080	−	0.398511i
$565$		0			0
$566$	65.9090			2.77036
$567$	−2.00000	−	1.73205i	−0.0839921	−	0.0727393i
$568$		−	58.6410i		−	2.46052i
$569$	16.2224	−	28.0981i	0.680080	−	1.17793i	−0.294876	−	0.955535i	$-0.595278\pi$
$569$	16.2224	−	28.0981i	0.680080	−	1.17793i	0.974956	−	0.222397i	$-0.0713882\pi$
$570$		0			0
$571$	−9.30385	−	16.1147i	−0.389354	−	0.674381i	0.603009	−	0.797734i	$-0.293968\pi$
$571$	−9.30385	−	16.1147i	−0.389354	−	0.674381i	−0.992363	+	0.123354i	$0.960635\pi$
$572$	7.85641	+	4.53590i	0.328493	+	0.189655i
$573$			8.92820i			0.372981i
$574$	5.19615	+	1.00000i	0.216883	+	0.0417392i
$575$		0			0
$576$	−14.9282	+	25.8564i	−0.622008	+	1.07735i
$577$	−24.8205	+	14.3301i	−1.03329	+	0.596571i	−0.917926	−	0.396752i	$-0.870137\pi$
$577$	−24.8205	+	14.3301i	−1.03329	+	0.596571i	−0.115365	+	0.993323i	$0.536804\pi$
$578$	14.9545	−	8.63397i	0.622024	−	0.359126i
$579$	−0.598076	+	1.03590i	−0.0248552	+	0.0430505i
$580$		0			0
$581$	13.0981	+	37.8109i	0.543400	+	1.56866i
$582$		−	40.7846i		−	1.69058i
$583$	−7.85641	−	4.53590i	−0.325379	−	0.187858i
$584$	−59.9090	−	103.765i	−2.47905	−	4.29384i
$585$		0			0
$586$	25.8564	−	44.7846i	1.06812	−	1.85004i
$587$		−	40.7321i		−	1.68119i	−0.541663	−	0.840596i	$-0.682205\pi$
$587$		−	40.7321i		−	1.68119i	0.541663	−	0.840596i	$-0.317795\pi$
$588$	−37.8564	+	5.46410i	−1.56117	+	0.225336i
$589$	2.07180			0.0853669
$590$		0			0
$591$	−0.169873	−	0.294229i	−0.00698764	−	0.0121029i
$592$	41.3205	−	23.8564i	1.69826	−	0.980492i
$593$	−24.1699	−	13.9545i	−0.992538	−	0.573042i	−0.0865058	−	0.996251i	$-0.527570\pi$
$593$	−24.1699	−	13.9545i	−0.992538	−	0.573042i	−0.906032	+	0.423209i	$0.860903\pi$
$594$	−2.00000			−0.0820610
$595$		0			0
$596$	32.0000			1.31077
$597$	−19.0526	−	11.0000i	−0.779769	−	0.450200i
$598$	25.3923	−	14.6603i	1.03837	−	0.599502i
$599$	−19.1244	−	33.1244i	−0.781400	−	1.35342i	−0.931126	−	0.364697i	$-0.881173\pi$
$599$	−19.1244	−	33.1244i	−0.781400	−	1.35342i	0.149726	−	0.988727i	$-0.452161\pi$
$600$		0			0
$601$	−0.0717968			−0.00292865			−0.00146433	−	0.999999i	$-0.500466\pi$
$601$	−0.0717968			−0.00292865			−0.00146433	+	0.999999i	$0.500466\pi$
$602$	4.36603	−	22.6865i	0.177946	−	0.924634i
$603$		−	14.6603i		−	0.597012i
$604$	−24.3923	+	42.2487i	−0.992509	+	1.71908i
$605$		0			0
$606$	9.92820	+	17.1962i	0.403306	+	0.698546i
$607$	2.76795	+	1.59808i	0.112348	+	0.0648639i	0.555121	−	0.831770i	$-0.312672\pi$
$607$	2.76795	+	1.59808i	0.112348	+	0.0648639i	−0.442773	+	0.896634i	$0.646005\pi$
$608$		−	97.5692i		−	3.95695i
$609$	−7.26795	+	8.39230i	−0.294512	+	0.340073i
$610$		0			0
$611$	−2.26795	+	3.92820i	−0.0917514	+	0.158918i
$612$	−15.4641	+	8.92820i	−0.625099	+	0.360901i
$613$	−23.3205	+	13.4641i	−0.941906	+	0.543810i	−0.890557	−	0.454871i	$-0.849685\pi$
$613$	−23.3205	+	13.4641i	−0.941906	+	0.543810i	−0.0513490	+	0.998681i	$0.516352\pi$
$614$	43.8827	−	76.0070i	1.77096	−	3.06739i
$615$		0			0
$616$	−12.0000	+	13.8564i	−0.483494	+	0.558291i
$617$			36.2487i			1.45932i	0.683811	+	0.729659i	$0.260321\pi$
$617$			36.2487i			1.45932i	−0.683811	+	0.729659i	$0.739679\pi$
$618$	21.7583	+	12.5622i	0.875248	+	0.505325i
$619$	−15.0359	−	26.0429i	−0.604344	−	1.04675i	−0.992155	−	0.125015i	$-0.960102\pi$
$619$	−15.0359	−	26.0429i	−0.604344	−	1.04675i	0.387811	−	0.921739i	$-0.373231\pi$
$620$		0			0
$621$	−2.36603	+	4.09808i	−0.0949453	+	0.164450i
$622$			24.9282i			0.999530i
$623$	7.56218	−	39.2942i	0.302972	−	1.57429i
$624$	33.8564			1.35534
$625$		0			0
$626$	−17.2942	−	29.9545i	−0.691216	−	1.19722i
$627$	2.83013	−	1.63397i	0.113024	−	0.0652547i
$628$	−30.2487	−	17.4641i	−1.20705	−	0.696894i
$629$	10.4449			0.416464
$630$		0			0
$631$	48.7846			1.94208			0.971042	−	0.238908i	$-0.0767893\pi$
$631$	48.7846			1.94208			0.971042	+	0.238908i	$0.0767893\pi$
$632$	60.5885	+	34.9808i	2.41008	+	1.39146i
$633$	−6.12436	+	3.53590i	−0.243421	+	0.140539i
$634$	38.8564	+	67.3013i	1.54319	+	2.67287i
$635$		0			0
$636$	−67.7128			−2.68499
$637$	9.82051	+	12.4737i	0.389103	+	0.494227i
$638$			8.39230i			0.332255i
$639$	3.09808	−	5.36603i	0.122558	−	0.212277i
$640$		0			0
$641$	−1.90192	−	3.29423i	−0.0751215	−	0.130114i	0.826018	−	0.563644i	$-0.190601\pi$
$641$	−1.90192	−	3.29423i	−0.0751215	−	0.130114i	−0.901139	+	0.433530i	$0.857268\pi$
$642$	5.19615	+	3.00000i	0.205076	+	0.118401i
$643$			4.51666i			0.178120i	0.996026	+	0.0890599i	$0.0283862\pi$
$643$			4.51666i			0.178120i	−0.996026	+	0.0890599i	$0.971614\pi$
$644$	22.3923	+	64.6410i	0.882380	+	2.54721i
$645$		0			0
$646$	19.9282	−	34.5167i	0.784065	−	1.35804i
$647$	24.1699	−	13.9545i	0.950216	−	0.548607i	0.0570678	−	0.998370i	$-0.481825\pi$
$647$	24.1699	−	13.9545i	0.950216	−	0.548607i	0.893148	+	0.449763i	$0.148492\pi$
$648$	−8.19615	+	4.73205i	−0.321975	+	0.185893i
$649$	−0.0717968	+	0.124356i	−0.00281827	+	0.00488139i
$650$		0			0
$651$	−1.20577	−	0.232051i	−0.0472579	−	0.00909479i
$652$		−	119.426i		−	4.67707i
$653$	38.6147	+	22.2942i	1.51111	+	0.872441i	0.999916	+	0.0129762i	$0.00413057\pi$
$653$	38.6147	+	22.2942i	1.51111	+	0.872441i	0.511196	+	0.859464i	$0.329203\pi$
$654$	15.0263	+	26.0263i	0.587574	+	1.01771i
$655$		0			0
$656$	5.46410	−	9.46410i	0.213337	−	0.369511i
$657$		−	12.6603i		−	0.493924i
$658$	−10.9282	−	9.46410i	−0.426026	−	0.368949i
$659$	−2.92820			−0.114067			−0.0570333	−	0.998372i	$-0.518164\pi$
$659$	−2.92820			−0.114067			−0.0570333	+	0.998372i	$0.518164\pi$
$660$		0			0
$661$	−5.23205	−	9.06218i	−0.203503	−	0.352478i	0.746152	−	0.665776i	$-0.231899\pi$
$661$	−5.23205	−	9.06218i	−0.203503	−	0.352478i	−0.949655	+	0.313298i	$0.898566\pi$
$662$	19.0981	−	11.0263i	0.742268	−	0.428549i
$663$	6.41858	+	3.70577i	0.249277	+	0.143920i
$664$	143.138			5.55485
$665$		0			0
$666$	8.73205			0.338360
$667$	17.1962	+	9.92820i	0.665838	+	0.384422i
$668$	−83.5692	+	48.2487i	−3.23339	+	1.86680i
$669$	10.1962	+	17.6603i	0.394206	+	0.682785i
$670$		0			0
$671$	2.92820			0.113042
$672$	−10.9282	+	56.7846i	−0.421565	+	2.19051i
$673$		−	27.3397i		−	1.05387i	−0.849906	−	0.526935i	$-0.823341\pi$
$673$		−	27.3397i		−	1.05387i	0.849906	−	0.526935i	$-0.176659\pi$
$674$	−24.5622	+	42.5429i	−0.946100	+	1.63869i
$675$		0			0
$676$	21.4641	+	37.1769i	0.825542	+	1.42988i
$677$	−28.6865	−	16.5622i	−1.10251	−	0.636536i	−0.165633	−	0.986187i	$-0.552967\pi$
$677$	−28.6865	−	16.5622i	−1.10251	−	0.636536i	−0.936880	+	0.349651i	$0.886300\pi$
$678$			24.3923i			0.936781i
$679$	−12.9282	−	37.3205i	−0.496139	−	1.43223i
$680$		0			0
$681$	−0.830127	+	1.43782i	−0.0318105	+	0.0550975i
$682$	−0.803848	+	0.464102i	−0.0307809	+	0.0177714i
$683$	−24.2942	+	14.0263i	−0.929593	+	0.536701i	−0.886683	−	0.462378i	$-0.846996\pi$
$683$	−24.2942	+	14.0263i	−0.929593	+	0.536701i	−0.0429101	+	0.999079i	$0.513663\pi$
$684$	12.1962	−	21.1244i	0.466332	−	0.807710i
$685$		0			0
$686$	−44.9545	+	23.2224i	−1.71637	+	0.886637i
$687$		−	3.00000i		−	0.114457i
$688$	−41.3205	−	23.8564i	−1.57533	−	0.909517i
$689$	14.0526	+	24.3397i	0.535360	+	0.927270i
$690$		0			0
$691$	−4.42820	+	7.66987i	−0.168457	+	0.291776i	−0.937877	−	0.346967i	$-0.887212\pi$
$691$	−4.42820	+	7.66987i	−0.168457	+	0.291776i	0.769421	+	0.638742i	$0.220545\pi$
$692$		−	79.4256i		−	3.01931i
$693$	−1.83013	+	0.633975i	−0.0695208	+	0.0240827i
$694$	−57.5692			−2.18530
$695$		0			0
$696$	19.8564	+	34.3923i	0.752655	+	1.30364i
$697$	2.07180	−	1.19615i	0.0784749	−	0.0453075i
$698$	52.0526	+	30.0526i	1.97022	+	1.13751i
$699$	17.3205			0.655122
$700$		0			0
$701$	−8.58846			−0.324382			−0.162191	−	0.986759i	$-0.551856\pi$
$701$	−8.58846			−0.324382			−0.162191	+	0.986759i	$0.551856\pi$
$702$	5.36603	+	3.09808i	0.202528	+	0.116929i
$703$	−12.3564	+	7.13397i	−0.466031	+	0.269063i
$704$	10.9282	+	18.9282i	0.411872	+	0.713384i
$705$		0			0
$706$	8.53590			0.321253
$707$	14.5359	+	12.5885i	0.546679	+	0.473438i
$708$			1.07180i			0.0402806i
$709$	−0.535898	+	0.928203i	−0.0201261	+	0.0348594i	−0.875913	−	0.482469i	$-0.839740\pi$
$709$	−0.535898	+	0.928203i	−0.0201261	+	0.0348594i	0.855787	+	0.517328i	$0.173073\pi$
$710$		0			0
$711$	3.69615	+	6.40192i	0.138617	+	0.240091i
$712$	−123.962	−	71.5692i	−4.64565	−	2.68217i
$713$			2.19615i			0.0822466i
$714$	−15.4641	+	17.8564i	−0.578729	+	0.668259i
$715$		0			0
$716$	27.3205	−	47.3205i	1.02102	−	1.76845i
$717$	6.12436	−	3.53590i	0.228718	−	0.132051i
$718$	3.00000	−	1.73205i	0.111959	−	0.0646396i
$719$	−10.2679	+	17.7846i	−0.382930	+	0.663254i	−0.991480	−	0.130262i	$-0.958418\pi$
$719$	−10.2679	+	17.7846i	−0.382930	+	0.663254i	0.608550	+	0.793516i	$0.291752\pi$
$720$		0			0
$721$	23.8923	+	4.59808i	0.889796	+	0.171241i
$722$			2.53590i			0.0943764i
$723$	11.6603	+	6.73205i	0.433650	+	0.250368i
$724$	−66.4449	−	115.086i	−2.46940	−	4.27713i
$725$		0			0
$726$	14.2942	−	24.7583i	0.530509	−	0.918868i
$727$			13.3397i			0.494744i	0.968921	+	0.247372i	$0.0795669\pi$
$727$			13.3397i			0.494744i	−0.968921	+	0.247372i	$0.920433\pi$
$728$	53.6603	−	18.5885i	1.98878	−	0.688934i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−5.22243	−	9.04552i	−0.193159	−	0.334561i
$732$	18.9282	−	10.9282i	0.699607	−	0.403918i
$733$	1.16025	+	0.669873i	0.0428550	+	0.0247423i	0.521274	−	0.853389i	$-0.325457\pi$
$733$	1.16025	+	0.669873i	0.0428550	+	0.0247423i	−0.478419	+	0.878131i	$0.658790\pi$
$734$	30.5885			1.12904
$735$		0			0
$736$	103.426			3.81232
$737$	−9.29423	−	5.36603i	−0.342357	−	0.197660i
$738$	1.73205	−	1.00000i	0.0637577	−	0.0368105i
$739$	13.8923	+	24.0622i	0.511037	+	0.885142i	0.999918	+	0.0127913i	$0.00407171\pi$
$739$	13.8923	+	24.0622i	0.511037	+	0.885142i	−0.488881	+	0.872350i	$0.662595\pi$
$740$		0			0
$741$	−10.1244			−0.371927
$742$	−84.6410	+	29.3205i	−3.10727	+	1.07639i
$743$		−	15.9090i		−	0.583643i	−0.956473	−	0.291822i	$-0.905739\pi$
$743$		−	15.9090i		−	0.583643i	0.956473	−	0.291822i	$-0.0942614\pi$
$744$	−2.19615	+	3.80385i	−0.0805149	+	0.139456i
$745$		0			0
$746$	36.2224	+	62.7391i	1.32620	+	2.29704i
$747$	13.0981	+	7.56218i	0.479234	+	0.276686i
$748$			13.0718i			0.477952i
$749$	5.70577	+	1.09808i	0.208484	+	0.0401228i
$750$		0			0
$751$	−9.03590	+	15.6506i	−0.329725	+	0.571100i	−0.982457	−	0.186489i	$-0.940289\pi$
$751$	−9.03590	+	15.6506i	−0.329725	+	0.571100i	0.652732	+	0.757588i	$0.273623\pi$
$752$	−25.8564	+	14.9282i	−0.942886	+	0.544376i
$753$	21.2942	−	12.2942i	0.776005	−	0.448027i
$754$	13.0000	−	22.5167i	0.473432	−	0.820008i
$755$		0			0
$756$	−9.46410	+	10.9282i	−0.344206	+	0.397455i
$757$			27.8564i			1.01246i	0.862399	+	0.506229i	$0.168961\pi$
$757$			27.8564i			1.01246i	−0.862399	+	0.506229i	$0.831039\pi$
$758$	14.9545	+	8.63397i	0.543171	+	0.313600i
$759$	1.73205	+	3.00000i	0.0628695	+	0.108893i
$760$		0			0
$761$	−23.3660	+	40.4711i	−0.847018	+	1.46708i	0.0368396	+	0.999321i	$0.488271\pi$
$761$	−23.3660	+	40.4711i	−0.847018	+	1.46708i	−0.883857	+	0.467757i	$0.845062\pi$
$762$		−	13.1244i		−	0.475445i
$763$	22.0000	+	19.0526i	0.796453	+	0.689749i
$764$	48.7846			1.76497
$765$		0			0
$766$	−31.8564	−	55.1769i	−1.15102	−	1.99362i
$767$	0.385263	−	0.222432i	0.0139111	−	0.00803155i
$768$	37.8564	+	21.8564i	1.36603	+	0.788675i
$769$	−52.3205			−1.88673			−0.943363	−	0.331763i	$-0.892357\pi$
$769$	−52.3205			−1.88673			−0.943363	+	0.331763i	$0.892357\pi$
$770$		0			0
$771$	5.66025			0.203849
$772$	5.66025	+	3.26795i	0.203717	+	0.117616i
$773$	37.6865	−	21.7583i	1.35549	−	0.782593i	0.366478	−	0.930427i	$-0.380563\pi$
$773$	37.6865	−	21.7583i	1.35549	−	0.782593i	0.989012	+	0.147834i	$0.0472301\pi$
$774$	−4.36603	−	7.56218i	−0.156934	−	0.271817i
$775$		0			0
$776$	−141.282			−5.07173
$777$	7.99038	−	2.76795i	0.286653	−	0.0992996i
$778$		−	14.7846i		−	0.530054i
$779$	−1.63397	+	2.83013i	−0.0585432	+	0.101400i
$780$		0			0
$781$	−2.26795	−	3.92820i	−0.0811536	−	0.140562i
$782$	36.5885	+	21.1244i	1.30840	+	0.755405i
$783$			4.19615i			0.149958i
$784$	14.9282	+	103.426i	0.533150	+	3.69377i
$785$		0			0
$786$	−21.1244	+	36.5885i	−0.753481	+	1.30507i
$787$	−11.6603	+	6.73205i	−0.415643	+	0.239972i	−0.693212	−	0.720734i	$-0.743805\pi$
$787$	−11.6603	+	6.73205i	−0.415643	+	0.239972i	0.277568	+	0.960706i	$0.410471\pi$
$788$	−1.60770	+	0.928203i	−0.0572718	+	0.0330659i
$789$	−4.19615	+	7.26795i	−0.149387	+	0.258746i
$790$		0			0
$791$	7.73205	+	22.3205i	0.274920	+	0.793626i
$792$			6.92820i			0.246183i
$793$	−7.85641	−	4.53590i	−0.278989	−	0.161074i
$794$	42.6147	+	73.8109i	1.51234	+	2.61945i
$795$		0			0
$796$	−60.1051	+	104.105i	−2.13037	+	3.68991i
$797$			3.94744i			0.139826i	0.997553	+	0.0699128i	$0.0222721\pi$
$797$			3.94744i			0.139826i	−0.997553	+	0.0699128i	$0.977728\pi$
$798$	6.09808	−	31.6865i	0.215870	−	1.12169i
$799$	−6.53590			−0.231223
$800$		0			0
$801$	−7.56218	−	13.0981i	−0.267196	−	0.462798i
$802$	−38.7846	+	22.3923i	−1.36953	+	0.790700i
$803$	−8.02628	−	4.63397i	−0.283241	−	0.163529i
$804$	−80.1051			−2.82509
$805$		0			0
$806$	2.87564			0.101290
$807$	10.8564	+	6.26795i	0.382164	+	0.220642i
$808$	59.5692	−	34.3923i	2.09564	−	1.20992i
$809$	12.8564	+	22.2679i	0.452007	+	0.782899i	0.998511	−	0.0545574i	$-0.0173748\pi$
$809$	12.8564	+	22.2679i	0.452007	+	0.782899i	−0.546503	+	0.837457i	$0.684041\pi$
$810$		0			0
$811$	−3.46410			−0.121641			−0.0608205	−	0.998149i	$-0.519372\pi$
$811$	−3.46410			−0.121641			−0.0608205	+	0.998149i	$0.519372\pi$
$812$	45.8564	+	39.7128i	1.60924	+	1.39365i
$813$		−	3.07180i		−	0.107733i
$814$	3.19615	−	5.53590i	0.112025	−	0.194033i
$815$		0			0
$816$	24.3923	+	42.2487i	0.853901	+	1.47900i
$817$	12.3564	+	7.13397i	0.432296	+	0.249586i
$818$		−	8.58846i		−	0.300288i
$819$	5.89230	+	1.13397i	0.205894	+	0.0396243i
$820$		0			0
$821$	12.7583	−	22.0981i	0.445269	−	0.771228i	−0.552802	−	0.833313i	$-0.686441\pi$
$821$	12.7583	−	22.0981i	0.445269	−	0.771228i	0.998071	+	0.0620844i	$0.0197748\pi$
$822$	−5.19615	+	3.00000i	−0.181237	+	0.104637i
$823$	33.9282	−	19.5885i	1.18266	−	0.682811i	0.226034	−	0.974119i	$-0.427424\pi$
$823$	33.9282	−	19.5885i	1.18266	−	0.682811i	0.956629	+	0.291309i	$0.0940907\pi$
$824$	43.5167	−	75.3731i	1.51597	−	2.62575i
$825$		0			0
$826$	0.464102	+	1.33975i	0.0161482	+	0.0466157i
$827$			3.75129i			0.130445i	0.997871	+	0.0652225i	$0.0207757\pi$
$827$			3.75129i			0.130445i	−0.997871	+	0.0652225i	$0.979224\pi$
$828$	22.3923	+	12.9282i	0.778186	+	0.449286i
$829$	−2.30385	−	3.99038i	−0.0800159	−	0.138592i	0.823241	−	0.567693i	$-0.192164\pi$
$829$	−2.30385	−	3.99038i	−0.0800159	−	0.138592i	−0.903257	+	0.429101i	$0.858830\pi$
$830$		0			0
$831$	−7.33013	+	12.6962i	−0.254279	+	0.440425i
$832$		−	67.7128i		−	2.34752i
$833$	−8.49038	+	21.2417i	−0.294174	+	0.735980i
$834$	−16.1962			−0.560827
$835$		0			0
$836$	−8.92820	−	15.4641i	−0.308788	−	0.534837i
$837$	−0.401924	+	0.232051i	−0.0138925	+	0.00802085i
$838$	−83.9090	−	48.4449i	−2.89859	−	1.67350i
$839$	−18.4449			−0.636787			−0.318394	−	0.947959i	$-0.603143\pi$
$839$	−18.4449			−0.636787			−0.318394	+	0.947959i	$0.603143\pi$
$840$		0			0
$841$	−11.3923			−0.392838
$842$	−0.169873	−	0.0980762i	−0.00585421	−	0.00337993i
$843$	−12.0000	+	6.92820i	−0.413302	+	0.238620i
$844$	19.3205	+	33.4641i	0.665039	+	1.15188i
$845$		0			0
$846$	−5.46410			−0.187860
$847$	5.23205	−	27.1865i	0.179775	−	0.934140i
$848$			184.995i			6.35275i
$849$	12.0622	−	20.8923i	0.413973	−	0.717022i
$850$		0			0
$851$	−7.56218	−	13.0981i	−0.259228	−	0.448996i
$852$	−29.3205	−	16.9282i	−1.00450	−	0.579951i
$853$		−	31.9808i		−	1.09500i	−0.836806	−	0.547500i	$-0.815580\pi$
$853$		−	31.9808i		−	1.09500i	0.836806	−	0.547500i	$-0.184420\pi$
$854$	18.9282	−	21.8564i	0.647710	−	0.747911i
$855$		0			0
$856$	10.3923	−	18.0000i	0.355202	−	0.615227i
$857$	−25.2224	+	14.5622i	−0.861582	+	0.497435i	−0.864542	−	0.502561i	$-0.832391\pi$
$857$	−25.2224	+	14.5622i	−0.861582	+	0.497435i	0.00295983	+	0.999996i	$0.499058\pi$
$858$	3.92820	−	2.26795i	0.134107	−	0.0774265i
$859$	3.73205	−	6.46410i	0.127336	−	0.220552i	−0.795308	−	0.606206i	$-0.792691\pi$
$859$	3.73205	−	6.46410i	0.127336	−	0.220552i	0.922644	+	0.385654i	$0.126024\pi$
$860$		0			0
$861$	1.26795	−	1.46410i	0.0432116	−	0.0498964i
$862$			47.3205i			1.61174i
$863$	−12.4641	−	7.19615i	−0.424283	−	0.244960i	0.272625	−	0.962120i	$-0.412108\pi$
$863$	−12.4641	−	7.19615i	−0.424283	−	0.244960i	−0.696908	+	0.717160i	$0.745441\pi$
$864$	10.9282	+	18.9282i	0.371785	+	0.643951i
$865$		0			0
$866$	20.7583	−	35.9545i	0.705397	−	1.22178i
$867$		−	6.32051i		−	0.214656i
$868$	−1.26795	+	6.58846i	−0.0430370	+	0.223627i
$869$	5.41154			0.183574
$870$		0			0
$871$	16.6244	+	28.7942i	0.563295	+	0.975655i
$872$	90.1577	−	52.0526i	3.05312	−	1.76272i
$873$	−12.9282	−	7.46410i	−0.437553	−	0.252622i
$874$	−57.7128			−1.95217
$875$		0			0
$876$	−69.1769			−2.33727
$877$	−3.58846	−	2.07180i	−0.121174	−	0.0699596i	0.438188	−	0.898883i	$-0.355620\pi$
$877$	−3.58846	−	2.07180i	−0.121174	−	0.0699596i	−0.559362	+	0.828924i	$0.688954\pi$
$878$	−1.26795	+	0.732051i	−0.0427912	+	0.0247055i
$879$	−9.46410	−	16.3923i	−0.319216	−	0.552899i
$880$		0			0
$881$	9.85641			0.332071			0.166035	−	0.986120i	$-0.446903\pi$
$881$	9.85641			0.332071			0.166035	+	0.986120i	$0.446903\pi$
$882$	−7.09808	+	17.7583i	−0.239005	+	0.597954i
$883$			53.5885i			1.80340i	0.432367	+	0.901698i	$0.357678\pi$
$883$			53.5885i			1.80340i	−0.432367	+	0.901698i	$0.642322\pi$
$884$	20.2487	−	35.0718i	0.681038	−	1.17959i
$885$		0			0
$886$	12.9282	+	22.3923i	0.434331	+	0.752284i
$887$	−21.8827	−	12.6340i	−0.734749	−	0.424207i	0.0854082	−	0.996346i	$-0.472781\pi$
$887$	−21.8827	−	12.6340i	−0.734749	−	0.424207i	−0.820157	+	0.572139i	$0.806114\pi$
$888$		−	30.2487i		−	1.01508i
$889$	−4.16025	−	12.0096i	−0.139530	−	0.402790i
$890$		0			0
$891$	−0.366025	+	0.633975i	−0.0122623	+	0.0212389i
$892$	96.4974	−	55.7128i	3.23097	−	1.86540i
$893$	7.73205	−	4.46410i	0.258743	−	0.149385i
$894$	8.00000	−	13.8564i	0.267560	−	0.463428i
$895$		0			0
$896$	98.3538	+	18.9282i	3.28577	+	0.632347i
$897$		−	10.7321i		−	0.358333i
$898$	−84.8372	−	48.9808i	−2.83105	−	1.63451i
$899$	0.973721	+	1.68653i	0.0324754	+	0.0562490i
$900$		0			0
$901$	−20.2487	+	35.0718i	−0.674582	+	1.16841i
$902$		−	1.46410i		−	0.0487493i
$903$	−6.39230	−	5.53590i	−0.212723	−	0.184223i
$904$	84.4974			2.81034
$905$		0			0
$906$	12.1962	+	21.1244i	0.405190	+	0.701810i
$907$	−29.0885	+	16.7942i	−0.965866	+	0.557643i	−0.897974	−	0.440049i	$-0.854961\pi$
$907$	−29.0885	+	16.7942i	−0.965866	+	0.557643i	−0.0678928	+	0.997693i	$0.521628\pi$
$908$	7.85641	+	4.53590i	0.260724	+	0.150529i
$909$	7.26795			0.241063
$910$		0			0
$911$	−14.7321			−0.488095			−0.244047	−	0.969763i	$-0.578475\pi$
$911$	−14.7321			−0.488095			−0.244047	+	0.969763i	$0.578475\pi$
$912$	−57.7128	−	33.3205i	−1.91106	−	1.10335i
$913$	9.58846	−	5.53590i	0.317332	−	0.183211i
$914$	22.7583	+	39.4186i	0.752779	+	1.30385i
$915$		0			0
$916$	−16.3923			−0.541617
$917$	−7.73205	+	40.1769i	−0.255335	+	1.32676i
$918$			8.92820i			0.294675i
$919$	−15.4282	+	26.7224i	−0.508929	+	0.881492i	0.491017	+	0.871150i	$0.336625\pi$
$919$	−15.4282	+	26.7224i	−0.508929	+	0.881492i	−0.999947	+	0.0103417i	$0.996708\pi$
$920$		0			0
$921$	−16.0622	−	27.8205i	−0.529267	−	0.916717i
$922$	−40.1769	−	23.1962i	−1.32316	−	0.763925i
$923$			14.0526i			0.462546i
$924$	3.46410	+	10.0000i	0.113961	+	0.328976i
$925$		0			0
$926$	35.1506	−	60.8827i	1.15512	−	2.00073i
$927$	7.96410	−	4.59808i	0.261575	−	0.151021i
$928$	79.4256	−	45.8564i	2.60727	−	1.50531i
$929$	−26.2224	+	45.4186i	−0.860330	+	1.49014i	0.0112804	+	0.999936i	$0.496409\pi$
$929$	−26.2224	+	45.4186i	−0.860330	+	1.49014i	−0.871611	+	0.490199i	$0.836924\pi$
$930$		0			0
$931$	−4.46410	−	30.9282i	−0.146305	−	1.01363i
$932$		−	94.6410i		−	3.10007i
$933$	7.90192	+	4.56218i	0.258697	+	0.149359i
$934$	0.196152	+	0.339746i	0.00641830	+	0.0111168i
$935$		0			0
$936$	10.7321	−	18.5885i	0.350788	−	0.607583i
$937$		−	31.7321i		−	1.03664i	−0.855186	−	0.518320i	$-0.826557\pi$
$937$		−	31.7321i		−	1.03664i	0.855186	−	0.518320i	$-0.173443\pi$
$938$	−100.131	+	34.6865i	−3.26941	+	1.13256i
$939$	−12.6603			−0.413152
$940$		0			0
$941$	15.0263	+	26.0263i	0.489843	+	0.848432i	0.999932	−	0.0116892i	$-0.00372087\pi$
$941$	15.0263	+	26.0263i	0.489843	+	0.848432i	−0.510089	+	0.860122i	$0.670388\pi$
$942$	−15.1244	+	8.73205i	−0.492778	+	0.284506i
$943$	−3.00000	−	1.73205i	−0.0976934	−	0.0564033i
$944$	2.92820			0.0953049
$945$		0			0
$946$	−6.39230			−0.207832
$947$	−4.90192	−	2.83013i	−0.159291	−	0.0919668i	0.418235	−	0.908339i	$-0.362649\pi$
$947$	−4.90192	−	2.83013i	−0.159291	−	0.0919668i	−0.577527	+	0.816372i	$0.695982\pi$
$948$	34.9808	−	20.1962i	1.13612	−	0.655941i
$949$	14.3564	+	24.8660i	0.466029	+	0.807185i
$950$		0			0
$951$	28.4449			0.922388
$952$	61.8564	+	53.5692i	2.00478	+	1.73619i
$953$		−	36.1051i		−	1.16956i	−0.811192	−	0.584780i	$-0.801181\pi$
$953$		−	36.1051i		−	1.16956i	0.811192	−	0.584780i	$-0.198819\pi$
$954$	−16.9282	+	29.3205i	−0.548071	+	0.949286i
$955$		0			0
$956$	−19.3205	−	33.4641i	−0.624870	−	1.08231i
$957$	2.66025	+	1.53590i	0.0859938	+	0.0496485i
$958$		−	24.0000i		−	0.775405i
$959$	−3.80385	+	4.39230i	−0.122833	+	0.141835i
$960$		0			0
$961$	15.3923	−	26.6603i	0.496526	−	0.860008i
$962$	−17.1506	+	9.90192i	−0.552959	+	0.319251i
$963$	1.90192	−	1.09808i	0.0612886	−	0.0353850i
$964$	36.7846	−	63.7128i	1.18475	−	2.05205i
$965$		0			0
$966$	33.5885	+	6.46410i	1.08069	+	0.207979i
$967$			10.1244i			0.325577i	0.986661	+	0.162789i	$0.0520489\pi$
$967$			10.1244i			0.325577i	−0.986661	+	0.162789i	$0.947951\pi$
$968$	−85.7654	−	49.5167i	−2.75660	−	1.59153i
$969$	−7.29423	−	12.6340i	−0.234324	−	0.405862i
$970$		0			0
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	−0.606685	−	0.794943i	$-0.707501\pi$
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	0.991783	+	0.127933i	$0.0408342\pi$
$972$			5.46410i			0.175261i
$973$	−14.8205	+	5.13397i	−0.475124	+	0.164588i
$974$	−1.12436			−0.0360267
$975$		0			0
$976$	−29.8564	−	51.7128i	−0.955680	−	1.65529i
$977$	14.3660	−	8.29423i	0.459610	−	0.265356i	−0.252270	−	0.967657i	$-0.581177\pi$
$977$	14.3660	−	8.29423i	0.459610	−	0.265356i	0.711880	+	0.702301i	$0.247844\pi$
$978$	−51.7128	−	29.8564i	−1.65359	−	0.954703i
$979$	−11.0718			−0.353856
$980$		0			0
$981$	11.0000			0.351203
$982$	90.4974	+	52.2487i	2.88789	+	1.66732i
$983$	8.49038	−	4.90192i	0.270801	−	0.156347i	−0.358451	−	0.933549i	$-0.616695\pi$
$983$	8.49038	−	4.90192i	0.270801	−	0.156347i	0.629252	+	0.777202i	$0.283361\pi$
$984$	−3.46410	−	6.00000i	−0.110432	−	0.191273i
$985$		0			0
$986$	37.4641			1.19310
$987$	−5.00000	+	1.73205i	−0.159152	+	0.0551318i
$988$			55.3205i			1.75998i
$989$	−7.56218	+	13.0981i	−0.240463	+	0.416495i
$990$		0			0
$991$	10.5526	+	18.2776i	0.335213	+	0.580606i	0.983526	−	0.180768i	$-0.0578584\pi$
$991$	10.5526	+	18.2776i	0.335213	+	0.580606i	−0.648313	+	0.761374i	$0.724525\pi$
$992$	8.78461	+	5.07180i	0.278912	+	0.161030i
$993$		−	8.07180i		−	0.256151i
$994$	−43.9808	−	8.46410i	−1.39499	−	0.268465i
$995$		0			0
$996$	41.3205	−	71.5692i	1.30929	−	2.26776i
$997$	48.4808	−	27.9904i	1.53540	−	0.886464i	0.536302	−	0.844026i	$-0.319821\pi$
$997$	48.4808	−	27.9904i	1.53540	−	0.886464i	0.999099	−	0.0424381i	$-0.0135125\pi$
$998$	32.0263	−	18.4904i	1.01377	−	0.585303i
$999$	1.59808	−	2.76795i	0.0505609	−	0.0875740i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.r.a.499.1		4
5.2	odd	4		105.2.i.d.16.2	✓	4
5.3	odd	4		525.2.i.f.226.1		4
5.4	even	2		525.2.r.f.499.2		4
7.4	even	3		525.2.r.f.424.2		4
15.2	even	4		315.2.j.c.226.1		4
20.7	even	4		1680.2.bg.o.961.1		4
35.2	odd	12		735.2.a.g.1.1		2
35.4	even	6	inner	525.2.r.a.424.1		4
35.12	even	12		735.2.a.h.1.1		2
35.17	even	12		735.2.i.l.361.2		4
35.18	odd	12		525.2.i.f.151.1		4
35.23	odd	12		3675.2.a.bg.1.2		2
35.27	even	4		735.2.i.l.226.2		4
35.32	odd	12		105.2.i.d.46.2	yes	4
35.33	even	12		3675.2.a.be.1.2		2
105.2	even	12		2205.2.a.z.1.2		2
105.32	even	12		315.2.j.c.46.1		4
105.47	odd	12		2205.2.a.ba.1.2		2
140.67	even	12		1680.2.bg.o.1201.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.i.d.16.2	✓	4	5.2	odd	4
105.2.i.d.46.2	yes	4	35.32	odd	12
315.2.j.c.46.1		4	105.32	even	12
315.2.j.c.226.1		4	15.2	even	4
525.2.i.f.151.1		4	35.18	odd	12
525.2.i.f.226.1		4	5.3	odd	4
525.2.r.a.424.1		4	35.4	even	6	inner
525.2.r.a.499.1		4	1.1	even	1	trivial
525.2.r.f.424.2		4	7.4	even	3
525.2.r.f.499.2		4	5.4	even	2
735.2.a.g.1.1		2	35.2	odd	12
735.2.a.h.1.1		2	35.12	even	12
735.2.i.l.226.2		4	35.27	even	4
735.2.i.l.361.2		4	35.17	even	12
1680.2.bg.o.961.1		4	20.7	even	4
1680.2.bg.o.1201.1		4	140.67	even	12
2205.2.a.z.1.2		2	105.2	even	12
2205.2.a.ba.1.2		2	105.47	odd	12
3675.2.a.be.1.2		2	35.33	even	12
3675.2.a.bg.1.2		2	35.23	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.36603 - 1.36603i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.73205 + 4.73205i) q^{4} +2.73205 q^{6} +(2.50000 - 0.866025i) q^{7} -9.46410i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.366025 - 0.633975i) q^{11} +(-4.73205 - 2.73205i) q^{12} +2.26795i q^{13} +(-7.09808 - 1.36603i) q^{14} +(-7.46410 + 12.9282i) q^{16} +(-2.83013 + 1.63397i) q^{17} +(-2.36603 + 1.36603i) q^{18} +(2.23205 - 3.86603i) q^{19} +(-1.73205 + 2.00000i) q^{21} +2.00000i q^{22} +(4.09808 + 2.36603i) q^{23} +(4.73205 + 8.19615i) q^{24} +(3.09808 - 5.36603i) q^{26} +1.00000i q^{27} +(10.9282 + 9.46410i) q^{28} +4.19615 q^{29} +(0.232051 + 0.401924i) q^{31} +(18.9282 - 10.9282i) q^{32} +(0.633975 + 0.366025i) q^{33} +8.92820 q^{34} +5.46410 q^{36} +(-2.76795 - 1.59808i) q^{37} +(-10.5622 + 6.09808i) q^{38} +(-1.13397 - 1.96410i) q^{39} -0.732051 q^{41} +(6.83013 - 2.36603i) q^{42} +3.19615i q^{43} +(2.00000 - 3.46410i) q^{44} +(-6.46410 - 11.1962i) q^{46} +(1.73205 + 1.00000i) q^{47} -14.9282i q^{48} +(5.50000 - 4.33013i) q^{49} +(1.63397 - 2.83013i) q^{51} +(-10.7321 + 6.19615i) q^{52} +(10.7321 - 6.19615i) q^{53} +(1.36603 - 2.36603i) q^{54} +(-8.19615 - 23.6603i) q^{56} +4.46410i q^{57} +(-9.92820 - 5.73205i) q^{58} +(-0.0980762 - 0.169873i) q^{59} +(-2.00000 + 3.46410i) q^{61} -1.26795i q^{62} +(0.500000 - 2.59808i) q^{63} -29.8564 q^{64} +(-1.00000 - 1.73205i) q^{66} +(12.6962 - 7.33013i) q^{67} +(-15.4641 - 8.92820i) q^{68} -4.73205 q^{69} +6.19615 q^{71} +(-8.19615 - 4.73205i) q^{72} +(10.9641 - 6.33013i) q^{73} +(4.36603 + 7.56218i) q^{74} +24.3923 q^{76} +(-1.46410 - 1.26795i) q^{77} +6.19615i q^{78} +(-3.69615 + 6.40192i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.73205 + 1.00000i) q^{82} +15.1244i q^{83} +(-14.1962 - 2.73205i) q^{84} +(4.36603 - 7.56218i) q^{86} +(-3.63397 + 2.09808i) q^{87} +(-6.00000 + 3.46410i) q^{88} +(7.56218 - 13.0981i) q^{89} +(1.96410 + 5.66987i) q^{91} +25.8564i q^{92} +(-0.401924 - 0.232051i) q^{93} +(-2.73205 - 4.73205i) q^{94} +(-10.9282 + 18.9282i) q^{96} -14.9282i q^{97} +(-18.9282 + 2.73205i) q^{98} -0.732051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{2} + 4 q^{4} + 4 q^{6} + 10 q^{7} + 2 q^{9} + 2 q^{11} - 12 q^{12} - 18 q^{14} - 16 q^{16} + 6 q^{17} - 6 q^{18} + 2 q^{19} + 6 q^{23} + 12 q^{24} + 2 q^{26} + 16 q^{28} - 4 q^{29} - 6 q^{31}+ \cdots + 4 q^{99}+O(q^{100}) \) 4 * q - 6 * q^2 + 4 * q^4 + 4 * q^6 + 10 * q^7 + 2 * q^9 + 2 * q^11 - 12 * q^12 - 18 * q^14 - 16 * q^16 + 6 * q^17 - 6 * q^18 + 2 * q^19 + 6 * q^23 + 12 * q^24 + 2 * q^26 + 16 * q^28 - 4 * q^29 - 6 * q^31 + 48 * q^32 + 6 * q^33 + 8 * q^34 + 8 * q^36 - 18 * q^37 - 18 * q^38 - 8 * q^39 + 4 * q^41 + 10 * q^42 + 8 * q^44 - 12 * q^46 + 22 * q^49 + 10 * q^51 - 36 * q^52 + 36 * q^53 + 2 * q^54 - 12 * q^56 - 12 * q^58 + 10 * q^59 - 8 * q^61 + 2 * q^63 - 64 * q^64 - 4 * q^66 + 30 * q^67 - 48 * q^68 - 12 * q^69 + 4 * q^71 - 12 * q^72 + 30 * q^73 + 14 * q^74 + 56 * q^76 + 8 * q^77 + 6 * q^79 - 2 * q^81 - 36 * q^84 + 14 * q^86 - 18 * q^87 - 24 * q^88 + 6 * q^89 - 6 * q^91 - 12 * q^93 - 4 * q^94 - 16 * q^96 - 48 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

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