LMFDB - Embedded newform 100.9.f.c.57.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,9,Mod(57,100)] 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("100.57"); S:= CuspForms(chi, 9); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 9, names="a")

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
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} - 4 x^{11} + 8 x^{10} + 1412 x^{9} + 550393 x^{8} - 1456736 x^{7} + 2420672 x^{6} + \cdots + 547748010000 $ x^12 - 4x^11 + 8x^10 + 1412x^9 + 550393x^8 - 1456736x^7 + 2420672x^6 + 375321568x^5 + 69558134536x^4 - 89027503680x^3 + 58317955200x^2 + 252758952000*x + 547748010000
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{6}\cdot 5^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			57.1
Root			$-16.9725 + 16.9725i$ of defining polynomial
Character	$\chi$	$=$	100.57
Dual form			100.9.f.c.93.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-90.6200 + 90.6200i) q^{3} +(2970.95 + 2970.95i) q^{7} -9862.98i q^{9} -6646.99 q^{11} +(29865.6 - 29865.6i) q^{13} +(-70342.7 - 70342.7i) q^{17} -41039.9i q^{19} -538454. q^{21} +(351512. - 351512. i) q^{23} +(299225. + 299225. i) q^{27} -659291. i q^{29} +1.00223e6 q^{31} +(602350. - 602350. i) q^{33} +(-13566.3 - 13566.3i) q^{37} +5.41284e6i q^{39} +1.01834e6 q^{41} +(-2.43704e6 + 2.43704e6i) q^{43} +(4.91560e6 + 4.91560e6i) q^{47} +1.18882e7i q^{49} +1.27489e7 q^{51} +(8.64186e6 - 8.64186e6i) q^{53} +(3.71903e6 + 3.71903e6i) q^{57} -1.29676e7i q^{59} -1.00542e7 q^{61} +(2.93024e7 - 2.93024e7i) q^{63} +(1.52513e7 + 1.52513e7i) q^{67} +6.37081e7i q^{69} -4.11270e7 q^{71} +(1.73470e7 - 1.73470e7i) q^{73} +(-1.97478e7 - 1.97478e7i) q^{77} -2.57526e7i q^{79} +1.04794e7 q^{81} +(5.97228e7 - 5.97228e7i) q^{83} +(5.97449e7 + 5.97449e7i) q^{87} +3.34415e7i q^{89} +1.77458e8 q^{91} +(-9.08221e7 + 9.08221e7i) q^{93} +(1.14246e7 + 1.14246e7i) q^{97} +6.55590e7i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 420 q^{11} - 921168 q^{21} + 3833112 q^{31} + 3587532 q^{41} + 46092564 q^{51} + 31354704 q^{61} - 29589384 q^{71} + 104018868 q^{81} + 433229088 q^{91}+O(q^{100}) $ 12 * q - 420 * q^11 - 921168 * q^21 + 3833112 * q^31 + 3587532 * q^41 + 46092564 * q^51 + 31354704 * q^61 - 29589384 * q^71 + 104018868 * q^81 + 433229088 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−90.6200	+	90.6200i	−1.11877	+	1.11877i	−0.126843	+	0.991923i	$0.540484\pi$
$3$	−90.6200	+	90.6200i	−1.11877	+	1.11877i	−0.991923	+	0.126843i	$0.959516\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2970.95	+	2970.95i	1.23738	+	1.23738i	0.961069	+	0.276310i	$0.0891116\pi$
$7$	2970.95	+	2970.95i	1.23738	+	1.23738i	0.276310	+	0.961069i	$0.410888\pi$
$8$		0			0
$9$		−	9862.98i		−	1.50327i
$10$		0			0
$11$	−6646.99			−0.453998			−0.226999	−	0.973895i	$-0.572891\pi$
$11$	−6646.99			−0.453998			−0.226999	+	0.973895i	$0.572891\pi$
$12$		0			0
$13$	29865.6	−	29865.6i	1.04568	−	1.04568i	0.0467719	−	0.998906i	$-0.485107\pi$
$13$	29865.6	−	29865.6i	1.04568	−	1.04568i	0.998906	−	0.0467719i	$-0.0148934\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−70342.7	−	70342.7i	−0.842216	−	0.842216i	0.146931	−	0.989147i	$-0.453060\pi$
$17$	−70342.7	−	70342.7i	−0.842216	−	0.842216i	−0.989147	+	0.146931i	$0.953060\pi$
$18$		0			0
$19$		−	41039.9i		−	0.314914i	−0.987526	−	0.157457i	$-0.949670\pi$
$19$		−	41039.9i		−	0.314914i	0.987526	−	0.157457i	$-0.0503295\pi$
$20$		0			0
$21$	−538454.			−2.76867
$22$		0			0
$23$	351512.	−	351512.i	1.25611	−	1.25611i	0.303181	−	0.952933i	$-0.401951\pi$
$23$	351512.	−	351512.i	1.25611	−	1.25611i	0.952933	−	0.303181i	$-0.0980486\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	299225.	+	299225.i	0.563045	+	0.563045i
$28$		0			0
$29$		−	659291.i		−	0.932148i	−0.884746	−	0.466074i	$-0.845668\pi$
$29$		−	659291.i		−	0.932148i	0.884746	−	0.466074i	$-0.154332\pi$
$30$		0			0
$31$	1.00223e6			1.08523			0.542613	−	0.839983i	$-0.317435\pi$
$31$	1.00223e6			1.08523			0.542613	+	0.839983i	$0.317435\pi$
$32$		0			0
$33$	602350.	−	602350.i	0.507917	−	0.507917i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−13566.3	−	13566.3i	−0.00723862	−	0.00723862i	0.703478	−	0.710717i	$-0.251629\pi$
$37$	−13566.3	−	13566.3i	−0.00723862	−	0.00723862i	−0.710717	+	0.703478i	$0.751629\pi$
$38$		0			0
$39$			5.41284e6i			2.33974i
$40$		0			0
$41$	1.01834e6			0.360376			0.180188	−	0.983632i	$-0.442329\pi$
$41$	1.01834e6			0.360376			0.180188	+	0.983632i	$0.442329\pi$
$42$		0			0
$43$	−2.43704e6	+	2.43704e6i	−0.712836	+	0.712836i	−0.967128	−	0.254292i	$-0.918158\pi$
$43$	−2.43704e6	+	2.43704e6i	−0.712836	+	0.712836i	0.254292	+	0.967128i	$0.418158\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.91560e6	+	4.91560e6i	1.00736	+	1.00736i	0.999973	+	0.00738753i	$0.00235155\pi$
$47$	4.91560e6	+	4.91560e6i	1.00736	+	1.00736i	0.00738753	+	0.999973i	$0.497648\pi$
$48$		0			0
$49$			1.18882e7i			2.06221i
$50$		0			0
$51$	1.27489e7			1.88448
$52$		0			0
$53$	8.64186e6	−	8.64186e6i	1.09523	−	1.09523i	0.100265	−	0.994961i	$-0.468031\pi$
$53$	8.64186e6	−	8.64186e6i	1.09523	−	1.09523i	0.994961	−	0.100265i	$-0.0319691\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.71903e6	+	3.71903e6i	0.352315	+	0.352315i
$58$		0			0
$59$		−	1.29676e7i		−	1.07017i	−0.844799	−	0.535084i	$-0.820280\pi$
$59$		−	1.29676e7i		−	1.07017i	0.844799	−	0.535084i	$-0.179720\pi$
$60$		0			0
$61$	−1.00542e7			−0.726150			−0.363075	−	0.931760i	$-0.618273\pi$
$61$	−1.00542e7			−0.726150			−0.363075	+	0.931760i	$0.618273\pi$
$62$		0			0
$63$	2.93024e7	−	2.93024e7i	1.86012	−	1.86012i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.52513e7	+	1.52513e7i	0.756849	+	0.756849i	0.975748	−	0.218899i	$-0.0702465\pi$
$67$	1.52513e7	+	1.52513e7i	0.756849	+	0.756849i	−0.218899	+	0.975748i	$0.570246\pi$
$68$		0			0
$69$			6.37081e7i			2.81059i
$70$		0			0
$71$	−4.11270e7			−1.61843			−0.809215	−	0.587513i	$-0.800107\pi$
$71$	−4.11270e7			−1.61843			−0.809215	+	0.587513i	$0.800107\pi$
$72$		0			0
$73$	1.73470e7	−	1.73470e7i	0.610847	−	0.610847i	−0.332320	−	0.943167i	$-0.607831\pi$
$73$	1.73470e7	−	1.73470e7i	0.610847	−	0.610847i	0.943167	+	0.332320i	$0.107831\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.97478e7	−	1.97478e7i	−0.561767	−	0.561767i
$78$		0			0
$79$		−	2.57526e7i		−	0.661170i	−0.943776	−	0.330585i	$-0.892754\pi$
$79$		−	2.57526e7i		−	0.661170i	0.943776	−	0.330585i	$-0.107246\pi$
$80$		0			0
$81$	1.04794e7			0.243443
$82$		0			0
$83$	5.97228e7	−	5.97228e7i	1.25843	−	1.25843i	0.306583	−	0.951844i	$-0.400814\pi$
$83$	5.97228e7	−	5.97228e7i	1.25843	−	1.25843i	0.951844	−	0.306583i	$-0.0991856\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	5.97449e7	+	5.97449e7i	1.04286	+	1.04286i
$88$		0			0
$89$			3.34415e7i			0.532999i	0.963835	+	0.266499i	$0.0858670\pi$
$89$			3.34415e7i			0.532999i	−0.963835	+	0.266499i	$0.914133\pi$
$90$		0			0
$91$	1.77458e8			2.58780
$92$		0			0
$93$	−9.08221e7	+	9.08221e7i	−1.21411	+	1.21411i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	1.14246e7	+	1.14246e7i	0.129048	+	0.129048i	0.768681	−	0.639633i	$-0.220913\pi$
$97$	1.14246e7	+	1.14246e7i	0.129048	+	0.129048i	−0.639633	+	0.768681i	$0.720913\pi$
$98$		0			0
$99$			6.55590e7i			0.682483i
$100$		0			0
$101$	−7.74199e7			−0.743990			−0.371995	−	0.928235i	$-0.621326\pi$
$101$	−7.74199e7			−0.743990			−0.371995	+	0.928235i	$0.621326\pi$
$102$		0			0
$103$	−1.14727e8	+	1.14727e8i	−1.01933	+	1.01933i	−0.0195251	+	0.999809i	$0.506215\pi$
$103$	−1.14727e8	+	1.14727e8i	−1.01933	+	1.01933i	−0.999809	+	0.0195251i	$0.993785\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.49269e7	−	1.49269e7i	−0.113877	−	0.113877i	0.647872	−	0.761749i	$-0.275659\pi$
$107$	−1.49269e7	−	1.49269e7i	−0.113877	−	0.113877i	−0.761749	+	0.647872i	$0.775659\pi$
$108$		0			0
$109$			6.68163e7i			0.473344i	0.971590	+	0.236672i	$0.0760567\pi$
$109$			6.68163e7i			0.473344i	−0.971590	+	0.236672i	$0.923943\pi$
$110$		0			0
$111$	2.45876e6			0.0161966
$112$		0			0
$113$	766402.	−	766402.i	0.00470048	−	0.00470048i	−0.704753	−	0.709453i	$-0.748942\pi$
$113$	766402.	−	766402.i	0.00470048	−	0.00470048i	0.709453	+	0.704753i	$0.248942\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.94564e8	−	2.94564e8i	−1.57194	−	1.57194i
$118$		0			0
$119$		−	4.17969e8i		−	2.08428i
$120$		0			0
$121$	−1.70176e8			−0.793886
$122$		0			0
$123$	−9.22817e7	+	9.22817e7i	−0.403176	+	0.403176i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	1.69873e7	+	1.69873e7i	0.0652995	+	0.0652995i	0.739002	−	0.673703i	$-0.235297\pi$
$127$	1.69873e7	+	1.69873e7i	0.0652995	+	0.0652995i	−0.673703	+	0.739002i	$0.735297\pi$
$128$		0			0
$129$		−	4.41690e8i		−	1.59499i
$130$		0			0
$131$	−5.31061e6			−0.0180326			−0.00901631	−	0.999959i	$-0.502870\pi$
$131$	−5.31061e6			−0.0180326			−0.00901631	+	0.999959i	$0.502870\pi$
$132$		0			0
$133$	1.21927e8	−	1.21927e8i	0.389668	−	0.389668i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.84377e8	+	3.84377e8i	1.09113	+	1.09113i	0.995408	+	0.0957180i	$0.0305147\pi$
$137$	3.84377e8	+	3.84377e8i	1.09113	+	1.09113i	0.0957180	+	0.995408i	$0.469485\pi$
$138$		0			0
$139$		−	5.67954e8i		−	1.52144i	−0.649082	−	0.760719i	$-0.724847\pi$
$139$		−	5.67954e8i		−	1.52144i	0.649082	−	0.760719i	$-0.275153\pi$
$140$		0			0
$141$	−8.90903e8			−2.25400
$142$		0			0
$143$	−1.98516e8	+	1.98516e8i	−0.474736	+	0.474736i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.07731e9	−	1.07731e9i	−2.30713	−	2.30713i
$148$		0			0
$149$		−	9.53258e7i		−	0.193404i	−0.995313	−	0.0967020i	$-0.969171\pi$
$149$		−	9.53258e7i		−	0.193404i	0.995313	−	0.0967020i	$-0.0308294\pi$
$150$		0			0
$151$	−4.08318e7			−0.0785400			−0.0392700	−	0.999229i	$-0.512503\pi$
$151$	−4.08318e7			−0.0785400			−0.0392700	+	0.999229i	$0.512503\pi$
$152$		0			0
$153$	−6.93788e8	+	6.93788e8i	−1.26608	+	1.26608i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	2.50691e8	+	2.50691e8i	0.412610	+	0.412610i	0.882647	−	0.470037i	$-0.155759\pi$
$157$	2.50691e8	+	2.50691e8i	0.412610	+	0.412610i	−0.470037	+	0.882647i	$0.655759\pi$
$158$		0			0
$159$			1.56625e9i			2.45060i
$160$		0			0
$161$	2.08865e9			3.10858
$162$		0			0
$163$	2.05019e8	−	2.05019e8i	0.290431	−	0.290431i	−0.546819	−	0.837251i	$-0.684162\pi$
$163$	2.05019e8	−	2.05019e8i	0.290431	−	0.290431i	0.837251	+	0.546819i	$0.184162\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.22941e7	+	2.22941e7i	0.0286632	+	0.0286632i	0.721293	−	0.692630i	$-0.243548\pi$
$167$	2.22941e7	+	2.22941e7i	0.0286632	+	0.0286632i	−0.692630	+	0.721293i	$0.743548\pi$
$168$		0			0
$169$		−	9.68177e8i		−	1.18688i
$170$		0			0
$171$	−4.04775e8			−0.473401
$172$		0			0
$173$	−7.67051e8	+	7.67051e8i	−0.856327	+	0.856327i	−0.990903	−	0.134576i	$-0.957033\pi$
$173$	−7.67051e8	+	7.67051e8i	−0.856327	+	0.856327i	0.134576	+	0.990903i	$0.457033\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.17513e9	+	1.17513e9i	1.19727	+	1.19727i
$178$		0			0
$179$			1.91640e8i			0.186670i	0.995635	+	0.0933348i	$0.0297527\pi$
$179$			1.91640e8i			0.186670i	−0.995635	+	0.0933348i	$0.970247\pi$
$180$		0			0
$181$	1.05009e8			0.0978388			0.0489194	−	0.998803i	$-0.484422\pi$
$181$	1.05009e8			0.0978388			0.0489194	+	0.998803i	$0.484422\pi$
$182$		0			0
$183$	9.11108e8	−	9.11108e8i	0.812391	−	0.812391i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	4.67567e8	+	4.67567e8i	0.382364	+	0.382364i
$188$		0			0
$189$			1.77796e9i			1.39340i
$190$		0			0
$191$	1.09356e9			0.821689			0.410845	−	0.911705i	$-0.365234\pi$
$191$	1.09356e9			0.821689			0.410845	+	0.911705i	$0.365234\pi$
$192$		0			0
$193$	6.30439e8	−	6.30439e8i	0.454374	−	0.454374i	−0.442429	−	0.896804i	$-0.645883\pi$
$193$	6.30439e8	−	6.30439e8i	0.454374	−	0.454374i	0.896804	+	0.442429i	$0.145883\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.16879e8	+	5.16879e8i	0.343182	+	0.343182i	0.857562	−	0.514380i	$-0.171978\pi$
$197$	5.16879e8	+	5.16879e8i	0.343182	+	0.343182i	−0.514380	+	0.857562i	$0.671978\pi$
$198$		0			0
$199$			5.34647e8i			0.340922i	0.985364	+	0.170461i	$0.0545257\pi$
$199$			5.34647e8i			0.340922i	−0.985364	+	0.170461i	$0.945474\pi$
$200$		0			0
$201$	−2.76416e9			−1.69347
$202$		0			0
$203$	1.95872e9	−	1.95872e9i	1.15342	−	1.15342i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−3.46696e9	−	3.46696e9i	−1.88828	−	1.88828i
$208$		0			0
$209$			2.72791e8i			0.142970i
$210$		0			0
$211$	4.52826e8			0.228456			0.114228	−	0.993455i	$-0.463561\pi$
$211$	4.52826e8			0.228456			0.114228	+	0.993455i	$0.463561\pi$
$212$		0			0
$213$	3.72693e9	−	3.72693e9i	1.81064	−	1.81064i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	2.97757e9	+	2.97757e9i	1.34284	+	1.34284i
$218$		0			0
$219$			3.14397e9i			1.36679i
$220$		0			0
$221$	−4.20165e9			−1.76137
$222$		0			0
$223$	3.39101e8	−	3.39101e8i	0.137123	−	0.137123i	−0.635214	−	0.772336i	$-0.719088\pi$
$223$	3.39101e8	−	3.39101e8i	0.137123	−	0.137123i	0.772336	+	0.635214i	$0.219088\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.03987e9	+	2.03987e9i	0.768243	+	0.768243i	0.977797	−	0.209554i	$-0.0672013\pi$
$227$	2.03987e9	+	2.03987e9i	0.768243	+	0.768243i	−0.209554	+	0.977797i	$0.567201\pi$
$228$		0			0
$229$		−	2.53791e9i		−	0.922856i	−0.887178	−	0.461428i	$-0.847337\pi$
$229$		−	2.53791e9i		−	0.922856i	0.887178	−	0.461428i	$-0.152663\pi$
$230$		0			0
$231$	3.57910e9			1.25697
$232$		0			0
$233$	−8.40808e8	+	8.40808e8i	−0.285281	+	0.285281i	−0.835211	−	0.549930i	$-0.814655\pi$
$233$	−8.40808e8	+	8.40808e8i	−0.285281	+	0.285281i	0.549930	+	0.835211i	$0.314655\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	2.33370e9	+	2.33370e9i	0.739695	+	0.739695i
$238$		0			0
$239$		−	4.00576e9i		−	1.22770i	−0.789421	−	0.613852i	$-0.789619\pi$
$239$		−	4.00576e9i		−	1.22770i	0.789421	−	0.613852i	$-0.210381\pi$
$240$		0			0
$241$	3.32963e9			0.987026			0.493513	−	0.869739i	$-0.335713\pi$
$241$	3.32963e9			0.987026			0.493513	+	0.869739i	$0.335713\pi$
$242$		0			0
$243$	−2.91286e9	+	2.91286e9i	−0.835400	+	0.835400i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.22568e9	−	1.22568e9i	−0.329298	−	0.329298i
$248$		0			0
$249$			1.08242e10i			2.81577i
$250$		0			0
$251$	6.75867e9			1.70281			0.851405	−	0.524508i	$-0.175751\pi$
$251$	6.75867e9			1.70281			0.851405	+	0.524508i	$0.175751\pi$
$252$		0			0
$253$	−2.33650e9	+	2.33650e9i	−0.570273	+	0.570273i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.27842e9	−	4.27842e9i	−0.980733	−	0.980733i	0.0190845	−	0.999818i	$-0.493925\pi$
$257$	−4.27842e9	−	4.27842e9i	−0.980733	−	0.980733i	−0.999818	+	0.0190845i	$0.993925\pi$
$258$		0			0
$259$		−	8.06097e7i		−	0.0179138i
$260$		0			0
$261$	−6.50257e9			−1.40127
$262$		0			0
$263$	4.95060e9	−	4.95060e9i	1.03475	−	1.03475i	0.0353742	−	0.999374i	$-0.488738\pi$
$263$	4.95060e9	−	4.95060e9i	1.03475	−	1.03475i	0.999374	−	0.0353742i	$-0.0112623\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−3.03047e9	−	3.03047e9i	−0.596301	−	0.596301i
$268$		0			0
$269$		−	2.68957e9i		−	0.513658i	−0.966457	−	0.256829i	$-0.917322\pi$
$269$		−	2.68957e9i		−	0.513658i	0.966457	−	0.256829i	$-0.0826778\pi$
$270$		0			0
$271$	3.72670e9			0.690951			0.345476	−	0.938428i	$-0.387718\pi$
$271$	3.72670e9			0.690951			0.345476	+	0.938428i	$0.387718\pi$
$272$		0			0
$273$	−1.60813e10	+	1.60813e10i	−2.89514	+	2.89514i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	1.02673e9	+	1.02673e9i	0.174396	+	0.174396i	0.788908	−	0.614512i	$-0.210647\pi$
$277$	1.02673e9	+	1.02673e9i	0.174396	+	0.174396i	−0.614512	+	0.788908i	$0.710647\pi$
$278$		0			0
$279$		−	9.88497e9i		−	1.63139i
$280$		0			0
$281$	−3.84428e9			−0.616580			−0.308290	−	0.951292i	$-0.599757\pi$
$281$	−3.84428e9			−0.616580			−0.308290	+	0.951292i	$0.599757\pi$
$282$		0			0
$283$	−3.44897e7	+	3.44897e7i	−0.00537704	+	0.00537704i	−0.709790	−	0.704413i	$-0.751210\pi$
$283$	−3.44897e7	+	3.44897e7i	−0.00537704	+	0.00537704i	0.704413	+	0.709790i	$0.251210\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.02542e9	+	3.02542e9i	0.445922	+	0.445922i
$288$		0			0
$289$			2.92043e9i			0.418655i
$290$		0			0
$291$	−2.07059e9			−0.288750
$292$		0			0
$293$	3.52777e9	−	3.52777e9i	0.478663	−	0.478663i	−0.426041	−	0.904704i	$-0.640092\pi$
$293$	3.52777e9	−	3.52777e9i	0.478663	−	0.478663i	0.904704	+	0.426041i	$0.140092\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.98894e9	−	1.98894e9i	−0.255621	−	0.255621i
$298$		0			0
$299$		−	2.09962e10i		−	2.62698i
$300$		0			0
$301$	−1.44807e10			−1.76410
$302$		0			0
$303$	7.01579e9	−	7.01579e9i	0.832350	−	0.832350i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−6.32942e9	−	6.32942e9i	−0.712541	−	0.712541i	0.254525	−	0.967066i	$-0.418081\pi$
$307$	−6.32942e9	−	6.32942e9i	−0.712541	−	0.712541i	−0.967066	+	0.254525i	$0.918081\pi$
$308$		0			0
$309$		−	2.07931e10i		−	2.28079i
$310$		0			0
$311$	−1.39821e7			−0.00149462			−0.000747308	−	1.00000i	$-0.500238\pi$
$311$	−1.39821e7			−0.00149462			−0.000747308		1.00000i	$0.500238\pi$
$312$		0			0
$313$	−3.09559e9	+	3.09559e9i	−0.322527	+	0.322527i	−0.849736	−	0.527209i	$-0.823239\pi$
$313$	−3.09559e9	+	3.09559e9i	−0.322527	+	0.322527i	0.527209	+	0.849736i	$0.323239\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.00493e9	−	8.00493e9i	−0.792721	−	0.792721i	0.189214	−	0.981936i	$-0.439406\pi$
$317$	−8.00493e9	−	8.00493e9i	−0.792721	−	0.792721i	−0.981936	+	0.189214i	$0.939406\pi$
$318$		0			0
$319$			4.38229e9i			0.423193i
$320$		0			0
$321$	2.70535e9			0.254803
$322$		0			0
$323$	−2.88686e9	+	2.88686e9i	−0.265225	+	0.265225i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−6.05490e9	−	6.05490e9i	−0.529561	−	0.529561i
$328$		0			0
$329$			2.92079e10i			2.49297i
$330$		0			0
$331$	−4.90966e9			−0.409015			−0.204507	−	0.978865i	$-0.565559\pi$
$331$	−4.90966e9			−0.409015			−0.204507	+	0.978865i	$0.565559\pi$
$332$		0			0
$333$	−1.33804e8	+	1.33804e8i	−0.0108816	+	0.0108816i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.36565e10	+	1.36565e10i	1.05882	+	1.05882i	0.998159	+	0.0606590i	$0.0193202\pi$
$337$	1.36565e10	+	1.36565e10i	1.05882	+	1.05882i	0.0606590	+	0.998159i	$0.480680\pi$
$338$		0			0
$339$			1.38903e8i			0.0105175i
$340$		0			0
$341$	−6.66181e9			−0.492691
$342$		0			0
$343$	−1.81924e10	+	1.81924e10i	−1.31436	+	1.31436i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.54109e10	−	1.54109e10i	−1.06294	−	1.06294i	−0.997881	−	0.0650602i	$-0.979276\pi$
$347$	−1.54109e10	−	1.54109e10i	−1.06294	−	1.06294i	−0.0650602	−	0.997881i	$-0.520724\pi$
$348$		0			0
$349$		−	1.18288e10i		−	0.797333i	−0.917096	−	0.398666i	$-0.869473\pi$
$349$		−	1.18288e10i		−	0.797333i	0.917096	−	0.398666i	$-0.130527\pi$
$350$		0			0
$351$	1.78731e10			1.17753
$352$		0			0
$353$	−3.49848e9	+	3.49848e9i	−0.225310	+	0.225310i	−0.810730	−	0.585420i	$-0.800930\pi$
$353$	−3.49848e9	+	3.49848e9i	−0.225310	+	0.225310i	0.585420	+	0.810730i	$0.300930\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	3.78763e10	+	3.78763e10i	2.33182	+	2.33182i
$358$		0			0
$359$			2.51731e10i			1.51551i	0.652541	+	0.757754i	$0.273703\pi$
$359$			2.51731e10i			1.51551i	−0.652541	+	0.757754i	$0.726297\pi$
$360$		0			0
$361$	1.52993e10			0.900829
$362$		0			0
$363$	1.54214e10	−	1.54214e10i	0.888172	−	0.888172i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	5.63577e9	+	5.63577e9i	0.310662	+	0.310662i	0.845166	−	0.534504i	$-0.179501\pi$
$367$	5.63577e9	+	5.63577e9i	0.310662	+	0.310662i	−0.534504	+	0.845166i	$0.679501\pi$
$368$		0			0
$369$		−	1.00438e10i		−	0.541744i
$370$		0			0
$371$	5.13490e10			2.71042
$372$		0			0
$373$	2.56465e10	−	2.56465e10i	1.32493	−	1.32493i	0.415199	−	0.909731i	$-0.363712\pi$
$373$	2.56465e10	−	2.56465e10i	1.32493	−	1.32493i	0.909731	−	0.415199i	$-0.136288\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.96901e10	−	1.96901e10i	−0.974726	−	0.974726i
$378$		0			0
$379$			3.39594e10i			1.64590i	0.568113	+	0.822950i	$0.307673\pi$
$379$			3.39594e10i			1.64590i	−0.568113	+	0.822950i	$0.692327\pi$
$380$		0			0
$381$	−3.07878e9			−0.146110
$382$		0			0
$383$	−1.53625e10	+	1.53625e10i	−0.713946	+	0.713946i	−0.967358	−	0.253412i	$-0.918447\pi$
$383$	−1.53625e10	+	1.53625e10i	−0.713946	+	0.713946i	0.253412	+	0.967358i	$0.418447\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.40365e10	+	2.40365e10i	1.07159	+	1.07159i
$388$		0			0
$389$			8.40830e9i			0.367206i	0.983000	+	0.183603i	$0.0587761\pi$
$389$			8.40830e9i			0.367206i	−0.983000	+	0.183603i	$0.941224\pi$
$390$		0			0
$391$	−4.94526e10			−2.11584
$392$		0			0
$393$	4.81247e8	−	4.81247e8i	0.0201743	−	0.0201743i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−2.21861e10	−	2.21861e10i	−0.893138	−	0.893138i	0.101679	−	0.994817i	$-0.467578\pi$
$397$	−2.21861e10	−	2.21861e10i	−0.893138	−	0.893138i	−0.994817	+	0.101679i	$0.967578\pi$
$398$		0			0
$399$			2.20981e10i			0.871893i
$400$		0			0
$401$	1.96181e10			0.758717			0.379358	−	0.925250i	$-0.376145\pi$
$401$	1.96181e10			0.758717			0.379358	+	0.925250i	$0.376145\pi$
$402$		0			0
$403$	2.99322e10	−	2.99322e10i	1.13480	−	1.13480i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	9.01752e7	+	9.01752e7i	0.00328632	+	0.00328632i
$408$		0			0
$409$			3.43621e9i			0.122797i	0.998113	+	0.0613984i	$0.0195560\pi$
$409$			3.43621e9i			0.122797i	−0.998113	+	0.0613984i	$0.980444\pi$
$410$		0			0
$411$	−6.96645e10			−2.44143
$412$		0			0
$413$	3.85261e10	−	3.85261e10i	1.32420	−	1.32420i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	5.14680e10	+	5.14680e10i	1.70213	+	1.70213i
$418$		0			0
$419$			7.44102e9i			0.241422i	0.992688	+	0.120711i	$0.0385174\pi$
$419$			7.44102e9i			0.241422i	−0.992688	+	0.120711i	$0.961483\pi$
$420$		0			0
$421$	−3.89651e10			−1.24036			−0.620180	−	0.784460i	$-0.712940\pi$
$421$	−3.89651e10			−1.24036			−0.620180	+	0.784460i	$0.712940\pi$
$422$		0			0
$423$	4.84824e10	−	4.84824e10i	1.51434	−	1.51434i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−2.98703e10	−	2.98703e10i	−0.898522	−	0.898522i
$428$		0			0
$429$		−	3.59791e10i		−	1.06224i
$430$		0			0
$431$	1.07978e10			0.312914			0.156457	−	0.987685i	$-0.449993\pi$
$431$	1.07978e10			0.312914			0.156457	+	0.987685i	$0.449993\pi$
$432$		0			0
$433$	−4.40971e10	+	4.40971e10i	−1.25446	+	1.25446i	−0.300766	+	0.953698i	$0.597242\pi$
$433$	−4.40971e10	+	4.40971e10i	−1.25446	+	1.25446i	−0.953698	+	0.300766i	$0.902758\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.44260e10	−	1.44260e10i	−0.395568	−	0.395568i
$438$		0			0
$439$			1.45300e9i			0.0391207i	0.999809	+	0.0195604i	$0.00622665\pi$
$439$			1.45300e9i			0.0391207i	−0.999809	+	0.0195604i	$0.993773\pi$
$440$		0			0
$441$	1.17253e11			3.10007
$442$		0			0
$443$	−2.28542e9	+	2.28542e9i	−0.0593404	+	0.0593404i	−0.736154	−	0.676814i	$-0.763360\pi$
$443$	−2.28542e9	+	2.28542e9i	−0.0593404	+	0.0593404i	0.676814	+	0.736154i	$0.263360\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	8.63843e9	+	8.63843e9i	0.216374	+	0.216374i
$448$		0			0
$449$		−	3.16339e10i		−	0.778336i	−0.921167	−	0.389168i	$-0.872763\pi$
$449$		−	3.16339e10i		−	0.778336i	0.921167	−	0.389168i	$-0.127237\pi$
$450$		0			0
$451$	−6.76887e9			−0.163610
$452$		0			0
$453$	3.70018e9	−	3.70018e9i	0.0878679	−	0.0878679i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.76578e10	+	3.76578e10i	0.863356	+	0.863356i	0.991726	−	0.128371i	$-0.0409747\pi$
$457$	3.76578e10	+	3.76578e10i	0.863356	+	0.863356i	−0.128371	+	0.991726i	$0.540975\pi$
$458$		0			0
$459$		−	4.20966e10i		−	0.948410i
$460$		0			0
$461$	−2.10491e9			−0.0466048			−0.0233024	−	0.999728i	$-0.507418\pi$
$461$	−2.10491e9			−0.0466048			−0.0233024	+	0.999728i	$0.507418\pi$
$462$		0			0
$463$	−3.32456e10	+	3.32456e10i	−0.723453	+	0.723453i	−0.969307	−	0.245854i	$-0.920932\pi$
$463$	−3.32456e10	+	3.32456e10i	−0.723453	+	0.723453i	0.245854	+	0.969307i	$0.420932\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−1.58121e10	−	1.58121e10i	−0.332446	−	0.332446i	0.521069	−	0.853515i	$-0.325533\pi$
$467$	−1.58121e10	−	1.58121e10i	−0.332446	−	0.332446i	−0.853515	+	0.521069i	$0.825533\pi$
$468$		0			0
$469$			9.06219e10i			1.87302i
$470$		0			0
$471$	−4.54352e10			−0.923228
$472$		0			0
$473$	1.61990e10	−	1.61990e10i	0.323626	−	0.323626i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−8.52344e10	−	8.52344e10i	−1.64642	−	1.64642i
$478$		0			0
$479$		−	8.68402e9i		−	0.164960i	−0.996593	−	0.0824800i	$-0.973716\pi$
$479$		−	8.68402e9i		−	0.164960i	0.996593	−	0.0824800i	$-0.0262841\pi$
$480$		0			0
$481$	−8.10333e8			−0.0151385
$482$		0			0
$483$	−1.89273e11	+	1.89273e11i	−3.47777	+	3.47777i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	7.63087e10	+	7.63087e10i	1.35662	+	1.35662i	0.878050	+	0.478570i	$0.158845\pi$
$487$	7.63087e10	+	7.63087e10i	1.35662	+	1.35662i	0.478570	+	0.878050i	$0.341155\pi$
$488$		0			0
$489$			3.71576e10i			0.649849i
$490$		0			0
$491$	3.56179e10			0.612834			0.306417	−	0.951897i	$-0.400870\pi$
$491$	3.56179e10			0.612834			0.306417	+	0.951897i	$0.400870\pi$
$492$		0			0
$493$	−4.63763e10	+	4.63763e10i	−0.785070	+	0.785070i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.22186e11	−	1.22186e11i	−2.00261	−	2.00261i
$498$		0			0
$499$		−	2.89181e10i		−	0.466410i	−0.972428	−	0.233205i	$-0.925079\pi$
$499$		−	2.89181e10i		−	0.466410i	0.972428	−	0.233205i	$-0.0749213\pi$
$500$		0			0
$501$	−4.04059e9			−0.0641348
$502$		0			0
$503$	7.36803e10	−	7.36803e10i	1.15101	−	1.15101i	0.164660	−	0.986350i	$-0.447347\pi$
$503$	7.36803e10	−	7.36803e10i	1.15101	−	1.15101i	0.986350	−	0.164660i	$-0.0526528\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	8.77362e10	+	8.77362e10i	1.32784	+	1.32784i
$508$		0			0
$509$		−	5.71815e10i		−	0.851892i	−0.904749	−	0.425946i	$-0.859941\pi$
$509$		−	5.71815e10i		−	0.851892i	0.904749	−	0.425946i	$-0.140059\pi$
$510$		0			0
$511$	1.03074e11			1.51170
$512$		0			0
$513$	1.22802e10	−	1.22802e10i	0.177311	−	0.177311i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−3.26739e10	−	3.26739e10i	−0.457340	−	0.457340i
$518$		0			0
$519$		−	1.39020e11i		−	1.91606i
$520$		0			0
$521$	−2.35052e10			−0.319016			−0.159508	−	0.987197i	$-0.550991\pi$
$521$	−2.35052e10			−0.319016			−0.159508	+	0.987197i	$0.550991\pi$
$522$		0			0
$523$	−3.78984e10	+	3.78984e10i	−0.506540	+	0.506540i	−0.913463	−	0.406923i	$-0.866602\pi$
$523$	−3.78984e10	+	3.78984e10i	−0.506540	+	0.506540i	0.406923	+	0.913463i	$0.366602\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−7.04995e10	−	7.04995e10i	−0.913995	−	0.913995i
$528$		0			0
$529$		−	1.68811e11i		−	2.15564i
$530$		0			0
$531$	−1.27899e11			−1.60875
$532$		0			0
$533$	3.04132e10	−	3.04132e10i	0.376837	−	0.376837i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−1.73664e10	−	1.73664e10i	−0.208839	−	0.208839i
$538$		0			0
$539$		−	7.90209e10i		−	0.936240i
$540$		0			0
$541$	−1.19351e11			−1.39327			−0.696637	−	0.717423i	$-0.745321\pi$
$541$	−1.19351e11			−1.39327			−0.696637	+	0.717423i	$0.745321\pi$
$542$		0			0
$543$	−9.51589e9	+	9.51589e9i	−0.109459	+	0.109459i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	9.33612e10	+	9.33612e10i	1.04284	+	1.04284i	0.999040	+	0.0437983i	$0.0139459\pi$
$547$	9.33612e10	+	9.33612e10i	1.04284	+	1.04284i	0.0437983	+	0.999040i	$0.486054\pi$
$548$		0			0
$549$			9.91639e10i			1.09160i
$550$		0			0
$551$	−2.70572e10			−0.293546
$552$		0			0
$553$	7.65097e10	−	7.65097e10i	0.818118	−	0.818118i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.81494e10	−	4.81494e10i	−0.500231	−	0.500231i	0.411279	−	0.911510i	$-0.365082\pi$
$557$	−4.81494e10	−	4.81494e10i	−0.500231	−	0.500231i	−0.911510	+	0.411279i	$0.865082\pi$
$558$		0			0
$559$			1.45568e11i			1.49079i
$560$		0			0
$561$	−8.47418e10			−0.855552
$562$		0			0
$563$	7.09654e10	−	7.09654e10i	0.706339	−	0.706339i	−0.259424	−	0.965763i	$-0.583533\pi$
$563$	7.09654e10	−	7.09654e10i	0.706339	−	0.706339i	0.965763	+	0.259424i	$0.0835328\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	3.11338e10	+	3.11338e10i	0.301231	+	0.301231i
$568$		0			0
$569$		−	3.39381e10i		−	0.323772i	−0.986810	−	0.161886i	$-0.948242\pi$
$569$		−	3.39381e10i		−	0.323772i	0.986810	−	0.161886i	$-0.0517576\pi$
$570$		0			0
$571$	−1.14297e11			−1.07520			−0.537602	−	0.843198i	$-0.680670\pi$
$571$	−1.14297e11			−1.07520			−0.537602	+	0.843198i	$0.680670\pi$
$572$		0			0
$573$	−9.90981e10	+	9.90981e10i	−0.919277	+	0.919277i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−8.05524e10	−	8.05524e10i	−0.726734	−	0.726734i	0.243234	−	0.969968i	$-0.421792\pi$
$577$	−8.05524e10	−	8.05524e10i	−0.726734	−	0.726734i	−0.969968	+	0.243234i	$0.921792\pi$
$578$		0			0
$579$			1.14261e11i			1.01668i
$580$		0			0
$581$	3.54867e11			3.11430
$582$		0			0
$583$	−5.74423e10	+	5.74423e10i	−0.497230	+	0.497230i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	5.91168e9	+	5.91168e9i	0.0497919	+	0.0497919i	0.731564	−	0.681772i	$-0.238791\pi$
$587$	5.91168e9	+	5.91168e9i	0.0497919	+	0.0497919i	−0.681772	+	0.731564i	$0.738791\pi$
$588$		0			0
$589$		−	4.11314e10i		−	0.341753i
$590$		0			0
$591$	−9.36792e10			−0.767880
$592$		0			0
$593$	5.91467e10	−	5.91467e10i	0.478312	−	0.478312i	−0.426279	−	0.904592i	$-0.640176\pi$
$593$	5.91467e10	−	5.91467e10i	0.478312	−	0.478312i	0.904592	+	0.426279i	$0.140176\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−4.84498e10	−	4.84498e10i	−0.381412	−	0.381412i
$598$		0			0
$599$			1.36683e10i			0.106171i	0.998590	+	0.0530857i	$0.0169057\pi$
$599$			1.36683e10i			0.106171i	−0.998590	+	0.0530857i	$0.983094\pi$
$600$		0			0
$601$	1.11154e10			0.0851972			0.0425986	−	0.999092i	$-0.486436\pi$
$601$	1.11154e10			0.0851972			0.0425986	+	0.999092i	$0.486436\pi$
$602$		0			0
$603$	1.50424e11	−	1.50424e11i	1.13775	−	1.13775i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	1.63338e11	+	1.63338e11i	1.20319	+	1.20319i	0.973191	+	0.229997i	$0.0738717\pi$
$607$	1.63338e11	+	1.63338e11i	1.20319	+	1.20319i	0.229997	+	0.973191i	$0.426128\pi$
$608$		0			0
$609$			3.54998e11i			2.58081i
$610$		0			0
$611$	2.93614e11			2.10675
$612$		0			0
$613$	6.60222e10	−	6.60222e10i	0.467571	−	0.467571i	−0.433555	−	0.901127i	$-0.642741\pi$
$613$	6.60222e10	−	6.60222e10i	0.467571	−	0.467571i	0.901127	+	0.433555i	$0.142741\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.82679e11	+	1.82679e11i	1.26052	+	1.26052i	0.950843	+	0.309673i	$0.100220\pi$
$617$	1.82679e11	+	1.82679e11i	1.26052	+	1.26052i	0.309673	+	0.950843i	$0.399780\pi$
$618$		0			0
$619$		−	1.49534e11i		−	1.01854i	−0.860607	−	0.509270i	$-0.829915\pi$
$619$		−	1.49534e11i		−	1.01854i	0.860607	−	0.509270i	$-0.170085\pi$
$620$		0			0
$621$	2.10362e11			1.41450
$622$		0			0
$623$	−9.93530e10	+	9.93530e10i	−0.659521	+	0.659521i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−2.47204e10	−	2.47204e10i	−0.159950	−	0.159950i
$628$		0			0
$629$			1.90859e9i			0.0121930i
$630$		0			0
$631$	3.42950e10			0.216329			0.108164	−	0.994133i	$-0.465503\pi$
$631$	3.42950e10			0.216329			0.108164	+	0.994133i	$0.465503\pi$
$632$		0			0
$633$	−4.10351e10	+	4.10351e10i	−0.255588	+	0.255588i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	3.55049e11	+	3.55049e11i	2.15641	+	2.15641i
$638$		0			0
$639$			4.05635e11i			2.43294i
$640$		0			0
$641$	1.61952e11			0.959301			0.479651	−	0.877460i	$-0.340763\pi$
$641$	1.61952e11			0.959301			0.479651	+	0.877460i	$0.340763\pi$
$642$		0			0
$643$	−1.41082e11	+	1.41082e11i	−0.825328	+	0.825328i	−0.986866	−	0.161538i	$-0.948355\pi$
$643$	−1.41082e11	+	1.41082e11i	−0.825328	+	0.825328i	0.161538	+	0.986866i	$0.448355\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.34609e11	−	1.34609e11i	−0.768171	−	0.768171i	0.209614	−	0.977784i	$-0.432779\pi$
$647$	−1.34609e11	−	1.34609e11i	−0.768171	−	0.768171i	−0.977784	+	0.209614i	$0.932779\pi$
$648$		0			0
$649$			8.61955e10i			0.485854i
$650$		0			0
$651$	−5.39655e11			−3.00464
$652$		0			0
$653$	9.46722e10	−	9.46722e10i	0.520678	−	0.520678i	−0.397098	−	0.917776i	$-0.629983\pi$
$653$	9.46722e10	−	9.46722e10i	0.520678	−	0.520678i	0.917776	+	0.397098i	$0.129983\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−1.71093e11	−	1.71093e11i	−0.918269	−	0.918269i
$658$		0			0
$659$		−	3.61317e9i		−	0.0191579i	−0.999954	−	0.00957893i	$-0.996951\pi$
$659$		−	3.61317e9i		−	0.0191579i	0.999954	−	0.00957893i	$-0.00304911\pi$
$660$		0			0
$661$	−4.66817e10			−0.244535			−0.122267	−	0.992497i	$-0.539017\pi$
$661$	−4.66817e10			−0.244535			−0.122267	+	0.992497i	$0.539017\pi$
$662$		0			0
$663$	3.80754e11	−	3.80754e11i	1.97056	−	1.97056i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−2.31749e11	−	2.31749e11i	−1.17088	−	1.17088i
$668$		0			0
$669$			6.14586e10i			0.306816i
$670$		0			0
$671$	6.68298e10			0.329671
$672$		0			0
$673$	2.73169e11	−	2.73169e11i	1.33159	−	1.33159i	0.427647	−	0.903946i	$-0.359343\pi$
$673$	2.73169e11	−	2.73169e11i	1.33159	−	1.33159i	0.903946	−	0.427647i	$-0.140657\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−3.25095e10	−	3.25095e10i	−0.154759	−	0.154759i	0.625481	−	0.780240i	$-0.284903\pi$
$677$	−3.25095e10	−	3.25095e10i	−0.154759	−	0.154759i	−0.780240	+	0.625481i	$0.784903\pi$
$678$		0			0
$679$			6.78835e10i			0.319363i
$680$		0			0
$681$	−3.69706e11			−1.71897
$682$		0			0
$683$	−6.40148e10	+	6.40148e10i	−0.294169	+	0.294169i	−0.838725	−	0.544556i	$-0.816698\pi$
$683$	−6.40148e10	+	6.40148e10i	−0.294169	+	0.294169i	0.544556	+	0.838725i	$0.316698\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	2.29985e11	+	2.29985e11i	1.03246	+	1.03246i
$688$		0			0
$689$		−	5.16189e11i		−	2.29051i
$690$		0			0
$691$	1.11602e11			0.489509			0.244754	−	0.969585i	$-0.421293\pi$
$691$	1.11602e11			0.489509			0.244754	+	0.969585i	$0.421293\pi$
$692$		0			0
$693$	−1.94772e11	+	1.94772e11i	−0.844490	+	0.844490i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−7.16325e10	−	7.16325e10i	−0.303514	−	0.303514i
$698$		0			0
$699$		−	1.52388e11i		−	0.638326i
$700$		0			0
$701$	3.83506e11			1.58818			0.794090	−	0.607800i	$-0.207948\pi$
$701$	3.83506e11			1.58818			0.794090	+	0.607800i	$0.207948\pi$
$702$		0			0
$703$	−5.56761e8	+	5.56761e8i	−0.00227954	+	0.00227954i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.30010e11	−	2.30010e11i	−0.920597	−	0.920597i
$708$		0			0
$709$		−	3.77851e11i		−	1.49532i	−0.664079	−	0.747662i	$-0.731176\pi$
$709$		−	3.77851e11i		−	1.49532i	0.664079	−	0.747662i	$-0.268824\pi$
$710$		0			0
$711$	−2.53998e11			−0.993920
$712$		0			0
$713$	3.52296e11	−	3.52296e11i	1.36317	−	1.36317i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	3.63002e11	+	3.63002e11i	1.37351	+	1.37351i
$718$		0			0
$719$			5.07005e11i			1.89713i	0.316583	+	0.948565i	$0.397465\pi$
$719$			5.07005e11i			1.89713i	−0.316583	+	0.948565i	$0.602535\pi$
$720$		0			0
$721$	−6.81695e11			−2.52261
$722$		0			0
$723$	−3.01732e11	+	3.01732e11i	−1.10425	+	1.10425i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	2.65494e11	+	2.65494e11i	0.950424	+	0.950424i	0.998828	−	0.0484043i	$-0.0154136\pi$
$727$	2.65494e11	+	2.65494e11i	0.950424	+	0.950424i	−0.0484043	+	0.998828i	$0.515414\pi$
$728$		0			0
$729$		−	4.59172e11i		−	1.62579i
$730$		0			0
$731$	3.42856e11			1.20072
$732$		0			0
$733$	−2.64181e11	+	2.64181e11i	−0.915136	+	0.915136i	−0.996670	−	0.0815349i	$-0.974018\pi$
$733$	−2.64181e11	+	2.64181e11i	−0.915136	+	0.915136i	0.0815349	+	0.996670i	$0.474018\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.01375e11	−	1.01375e11i	−0.343608	−	0.343608i
$738$		0			0
$739$		−	8.68176e9i		−	0.0291092i	−0.999894	−	0.0145546i	$-0.995367\pi$
$739$		−	8.68176e9i		−	0.0291092i	0.999894	−	0.0145546i	$-0.00463304\pi$
$740$		0			0
$741$	2.22142e11			0.736815
$742$		0			0
$743$	3.15796e9	−	3.15796e9i	0.0103622	−	0.0103622i	−0.701907	−	0.712269i	$-0.747668\pi$
$743$	3.15796e9	−	3.15796e9i	0.0103622	−	0.0103622i	0.712269	+	0.701907i	$0.247668\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−5.89045e11	−	5.89045e11i	−1.89176	−	1.89176i
$748$		0			0
$749$		−	8.86941e10i		−	0.281817i
$750$		0			0
$751$	2.93351e11			0.922204			0.461102	−	0.887347i	$-0.347454\pi$
$751$	2.93351e11			0.922204			0.461102	+	0.887347i	$0.347454\pi$
$752$		0			0
$753$	−6.12471e11	+	6.12471e11i	−1.90505	+	1.90505i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−5.15795e10	−	5.15795e10i	−0.157070	−	0.157070i	0.624197	−	0.781267i	$-0.285426\pi$
$757$	−5.15795e10	−	5.15795e10i	−0.157070	−	0.157070i	−0.781267	+	0.624197i	$0.785426\pi$
$758$		0			0
$759$		−	4.23467e11i		−	1.27600i
$760$		0			0
$761$	−5.97828e11			−1.78253			−0.891266	−	0.453480i	$-0.850182\pi$
$761$	−5.97828e11			−1.78253			−0.891266	+	0.453480i	$0.850182\pi$
$762$		0			0
$763$	−1.98508e11	+	1.98508e11i	−0.585706	+	0.585706i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−3.87285e11	−	3.87285e11i	−1.11905	−	1.11905i
$768$		0			0
$769$			5.99304e11i			1.71373i	0.515543	+	0.856864i	$0.327590\pi$
$769$			5.99304e11i			1.71373i	−0.515543	+	0.856864i	$0.672410\pi$
$770$		0			0
$771$	7.75421e11			2.19442
$772$		0			0
$773$	−2.84108e11	+	2.84108e11i	−0.795730	+	0.795730i	−0.982419	−	0.186689i	$-0.940224\pi$
$773$	−2.84108e11	+	2.84108e11i	−0.795730	+	0.795730i	0.186689	+	0.982419i	$0.440224\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	7.30485e9	+	7.30485e9i	0.0200414	+	0.0200414i
$778$		0			0
$779$		−	4.17924e10i		−	0.113487i
$780$		0			0
$781$	2.73371e11			0.734764
$782$		0			0
$783$	1.97276e11	−	1.97276e11i	0.524841	−	0.524841i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	2.28710e11	+	2.28710e11i	0.596192	+	0.596192i	0.939297	−	0.343105i	$-0.111479\pi$
$787$	2.28710e11	+	2.28710e11i	0.596192	+	0.596192i	−0.343105	+	0.939297i	$0.611479\pi$
$788$		0			0
$789$			8.97247e11i			2.31528i
$790$		0			0
$791$	4.55387e9			0.0116326
$792$		0			0
$793$	−3.00273e11	+	3.00273e11i	−0.759318	+	0.759318i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.96930e11	−	1.96930e11i	−0.488065	−	0.488065i	0.419630	−	0.907695i	$-0.362160\pi$
$797$	−1.96930e11	−	1.96930e11i	−0.488065	−	0.488065i	−0.907695	+	0.419630i	$0.862160\pi$
$798$		0			0
$799$		−	6.91553e11i		−	1.69683i
$800$		0			0
$801$	3.29833e11			0.801243
$802$		0			0
$803$	−1.15305e11	+	1.15305e11i	−0.277323	+	0.277323i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2.43729e11	+	2.43729e11i	0.574663	+	0.574663i
$808$		0			0
$809$		−	3.96404e11i		−	0.925432i	−0.886507	−	0.462716i	$-0.846875\pi$
$809$		−	3.96404e11i		−	0.925432i	0.886507	−	0.462716i	$-0.153125\pi$
$810$		0			0
$811$	−5.68736e11			−1.31470			−0.657351	−	0.753585i	$-0.728323\pi$
$811$	−5.68736e11			−1.31470			−0.657351	+	0.753585i	$0.728323\pi$
$812$		0			0
$813$	−3.37714e11	+	3.37714e11i	−0.773013	+	0.773013i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	1.00016e11	+	1.00016e11i	0.224482	+	0.224482i
$818$		0			0
$819$		−	1.75027e12i		−	3.89017i
$820$		0			0
$821$	−7.39178e11			−1.62696			−0.813479	−	0.581595i	$-0.802429\pi$
$821$	−7.39178e11			−1.62696			−0.813479	+	0.581595i	$0.802429\pi$
$822$		0			0
$823$	2.44251e11	−	2.44251e11i	0.532399	−	0.532399i	−0.388887	−	0.921286i	$-0.627140\pi$
$823$	2.44251e11	−	2.44251e11i	0.532399	−	0.532399i	0.921286	+	0.388887i	$0.127140\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	2.78370e11	+	2.78370e11i	0.595115	+	0.595115i	0.939009	−	0.343893i	$-0.111746\pi$
$827$	2.78370e11	+	2.78370e11i	0.595115	+	0.595115i	−0.343893	+	0.939009i	$0.611746\pi$
$828$		0			0
$829$			4.66722e11i			0.988190i	0.869408	+	0.494095i	$0.164500\pi$
$829$			4.66722e11i			0.988190i	−0.869408	+	0.494095i	$0.835500\pi$
$830$		0			0
$831$	−1.86084e11			−0.390216
$832$		0			0
$833$	8.36251e11	−	8.36251e11i	1.73683	−	1.73683i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	2.99892e11	+	2.99892e11i	0.611031	+	0.611031i
$838$		0			0
$839$			2.02414e11i			0.408501i	0.978919	+	0.204250i	$0.0654757\pi$
$839$			2.02414e11i			0.408501i	−0.978919	+	0.204250i	$0.934524\pi$
$840$		0			0
$841$	6.55823e10			0.131100
$842$		0			0
$843$	3.48369e11	−	3.48369e11i	0.689809	−	0.689809i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−5.05585e11	−	5.05585e11i	−0.982337	−	0.982337i
$848$		0			0
$849$		−	6.25091e9i		−	0.0120313i
$850$		0			0
$851$	−9.53746e9			−0.0181851
$852$		0			0
$853$	−8.15896e10	+	8.15896e10i	−0.154113	+	0.154113i	−0.779952	−	0.625839i	$-0.784757\pi$
$853$	−8.15896e10	+	8.15896e10i	−0.154113	+	0.154113i	0.625839	+	0.779952i	$0.284757\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.44457e11	−	1.44457e11i	−0.267803	−	0.267803i	0.560411	−	0.828215i	$-0.310643\pi$
$857$	−1.44457e11	−	1.44457e11i	−0.267803	−	0.267803i	−0.828215	+	0.560411i	$0.810643\pi$
$858$		0			0
$859$			8.76933e11i			1.61062i	0.592852	+	0.805312i	$0.298002\pi$
$859$			8.76933e11i			1.61062i	−0.592852	+	0.805312i	$0.701998\pi$
$860$		0			0
$861$	−5.48328e11			−0.997763
$862$		0			0
$863$	3.51189e11	−	3.51189e11i	0.633138	−	0.633138i	−0.315716	−	0.948854i	$-0.602245\pi$
$863$	3.51189e11	−	3.51189e11i	0.633138	−	0.633138i	0.948854	+	0.315716i	$0.102245\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−2.64650e11	−	2.64650e11i	−0.468376	−	0.468376i
$868$		0			0
$869$			1.71177e11i			0.300170i
$870$		0			0
$871$	9.10981e11			1.58284
$872$		0			0
$873$	1.12680e11	−	1.12680e11i	0.193995	−	0.193995i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−6.46416e11	−	6.46416e11i	−1.09273	−	1.09273i	−0.995236	−	0.0974969i	$-0.968916\pi$
$877$	−6.46416e11	−	6.46416e11i	−1.09273	−	1.09273i	−0.0974969	−	0.995236i	$-0.531084\pi$
$878$		0			0
$879$			6.39374e11i			1.07102i
$880$		0			0
$881$	−5.80336e11			−0.963332			−0.481666	−	0.876355i	$-0.659968\pi$
$881$	−5.80336e11			−0.963332			−0.481666	+	0.876355i	$0.659968\pi$
$882$		0			0
$883$	1.18221e11	−	1.18221e11i	0.194470	−	0.194470i	−0.603155	−	0.797624i	$-0.706090\pi$
$883$	1.18221e11	−	1.18221e11i	0.194470	−	0.194470i	0.797624	+	0.603155i	$0.206090\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.34202e11	−	2.34202e11i	−0.378352	−	0.378352i	0.492156	−	0.870507i	$-0.336209\pi$
$887$	−2.34202e11	−	2.34202e11i	−0.378352	−	0.378352i	−0.870507	+	0.492156i	$0.836209\pi$
$888$		0			0
$889$			1.00937e11i			0.161600i
$890$		0			0
$891$	−6.96566e10			−0.110523
$892$		0			0
$893$	2.01735e11	−	2.01735e11i	0.317232	−	0.317232i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1.90268e12	+	1.90268e12i	2.93897	+	2.93897i
$898$		0			0
$899$		−	6.60761e11i		−	1.01159i
$900$		0			0
$901$	−1.21578e12			−1.84483
$902$		0			0
$903$	1.31224e12	−	1.31224e12i	1.97361	−	1.97361i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1.81328e11	+	1.81328e11i	0.267939	+	0.267939i	0.828269	−	0.560330i	$-0.189326\pi$
$907$	1.81328e11	+	1.81328e11i	0.267939	+	0.267939i	−0.560330	+	0.828269i	$0.689326\pi$
$908$		0			0
$909$			7.63590e11i			1.11842i
$910$		0			0
$911$	1.27141e12			1.84592			0.922959	−	0.384899i	$-0.125764\pi$
$911$	1.27141e12			1.84592			0.922959	+	0.384899i	$0.125764\pi$
$912$		0			0
$913$	−3.96977e11	+	3.96977e11i	−0.571323	+	0.571323i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.57775e10	−	1.57775e10i	−0.0223132	−	0.0223132i
$918$		0			0
$919$			1.32316e12i			1.85503i	0.373788	+	0.927514i	$0.378059\pi$
$919$			1.32316e12i			1.85503i	−0.373788	+	0.927514i	$0.621941\pi$
$920$		0			0
$921$	1.14714e12			1.59433
$922$		0			0
$923$	−1.22828e12	+	1.22828e12i	−1.69236	+	1.69236i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	1.13155e12	+	1.13155e12i	1.53234	+	1.53234i
$928$		0			0
$929$			7.15235e11i			0.960254i	0.877199	+	0.480127i	$0.159409\pi$
$929$			7.15235e11i			0.960254i	−0.877199	+	0.480127i	$0.840591\pi$
$930$		0			0
$931$	4.87892e11			0.649419
$932$		0			0
$933$	1.26705e9	−	1.26705e9i	0.00167213	−	0.00167213i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−6.49769e11	−	6.49769e11i	−0.842948	−	0.842948i	0.146294	−	0.989241i	$-0.453266\pi$
$937$	−6.49769e11	−	6.49769e11i	−0.842948	−	0.842948i	−0.989241	+	0.146294i	$0.953266\pi$
$938$		0			0
$939$		−	5.61046e11i		−	0.721665i
$940$		0			0
$941$	5.55246e11			0.708153			0.354077	−	0.935216i	$-0.384795\pi$
$941$	5.55246e11			0.708153			0.354077	+	0.935216i	$0.384795\pi$
$942$		0			0
$943$	3.57958e11	−	3.57958e11i	0.452673	−	0.452673i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	6.35027e11	+	6.35027e11i	0.789573	+	0.789573i	0.981424	−	0.191851i	$-0.0614491\pi$
$947$	6.35027e11	+	6.35027e11i	0.789573	+	0.789573i	−0.191851	+	0.981424i	$0.561449\pi$
$948$		0			0
$949$		−	1.03616e12i		−	1.27750i
$950$		0			0
$951$	1.45081e12			1.77374
$952$		0			0
$953$	−5.80327e11	+	5.80327e11i	−0.703560	+	0.703560i	−0.965173	−	0.261613i	$-0.915746\pi$
$953$	−5.80327e11	+	5.80327e11i	−0.703560	+	0.703560i	0.261613	+	0.965173i	$0.415746\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−3.97124e11	−	3.97124e11i	−0.473454	−	0.473454i
$958$		0			0
$959$			2.28393e12i			2.70027i
$960$		0			0
$961$	1.51573e11			0.177717
$962$		0			0
$963$	−1.47224e11	+	1.47224e11i	−0.171188	+	0.171188i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	2.57587e11	+	2.57587e11i	0.294590	+	0.294590i	0.838890	−	0.544300i	$-0.183205\pi$
$967$	2.57587e11	+	2.57587e11i	0.294590	+	0.294590i	−0.544300	+	0.838890i	$0.683205\pi$
$968$		0			0
$969$		−	5.23214e11i		−	0.593450i
$970$		0			0
$971$	−9.36458e11			−1.05344			−0.526722	−	0.850038i	$-0.676579\pi$
$971$	−9.36458e11			−1.05344			−0.526722	+	0.850038i	$0.676579\pi$
$972$		0			0
$973$	1.68736e12	−	1.68736e12i	1.88259	−	1.88259i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	3.59705e11	+	3.59705e11i	0.394791	+	0.394791i	0.876391	−	0.481600i	$-0.159944\pi$
$977$	3.59705e11	+	3.59705e11i	0.394791	+	0.394791i	−0.481600	+	0.876391i	$0.659944\pi$
$978$		0			0
$979$		−	2.22285e11i		−	0.241980i
$980$		0			0
$981$	6.59008e11			0.711565
$982$		0			0
$983$	−8.01741e10	+	8.01741e10i	−0.0858657	+	0.0858657i	−0.748735	−	0.662869i	$-0.769338\pi$
$983$	−8.01741e10	+	8.01741e10i	−0.0858657	+	0.0858657i	0.662869	+	0.748735i	$0.269338\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−2.64682e12	−	2.64682e12i	−2.78905	−	2.78905i
$988$		0			0
$989$			1.71330e12i			1.79081i
$990$		0			0
$991$	−7.86576e11			−0.815541			−0.407771	−	0.913084i	$-0.633694\pi$
$991$	−7.86576e11			−0.815541			−0.407771	+	0.913084i	$0.633694\pi$
$992$		0			0
$993$	4.44913e11	−	4.44913e11i	0.457592	−	0.457592i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	1.16753e12	+	1.16753e12i	1.18164	+	1.18164i	0.979319	+	0.202324i	$0.0648493\pi$
$997$	1.16753e12	+	1.16753e12i	1.18164	+	1.18164i	0.202324	+	0.979319i	$0.435151\pi$
$998$		0			0
$999$		−	8.11877e9i		−	0.00815133i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.f.c.57.1	✓	12
5.2	odd	4	inner	100.9.f.c.93.6	yes	12
5.3	odd	4	inner	100.9.f.c.93.1	yes	12
5.4	even	2	inner	100.9.f.c.57.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.f.c.57.1	✓	12	1.1	even	1	trivial
100.9.f.c.57.6	yes	12	5.4	even	2	inner
100.9.f.c.93.1	yes	12	5.3	odd	4	inner
100.9.f.c.93.6	yes	12	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-90.6200 + 90.6200i) q^{3} +(2970.95 + 2970.95i) q^{7} -9862.98i q^{9} -6646.99 q^{11} +(29865.6 - 29865.6i) q^{13} +(-70342.7 - 70342.7i) q^{17} -41039.9i q^{19} -538454. q^{21} +(351512. - 351512. i) q^{23} +(299225. + 299225. i) q^{27} -659291. i q^{29} +1.00223e6 q^{31} +(602350. - 602350. i) q^{33} +(-13566.3 - 13566.3i) q^{37} +5.41284e6i q^{39} +1.01834e6 q^{41} +(-2.43704e6 + 2.43704e6i) q^{43} +(4.91560e6 + 4.91560e6i) q^{47} +1.18882e7i q^{49} +1.27489e7 q^{51} +(8.64186e6 - 8.64186e6i) q^{53} +(3.71903e6 + 3.71903e6i) q^{57} -1.29676e7i q^{59} -1.00542e7 q^{61} +(2.93024e7 - 2.93024e7i) q^{63} +(1.52513e7 + 1.52513e7i) q^{67} +6.37081e7i q^{69} -4.11270e7 q^{71} +(1.73470e7 - 1.73470e7i) q^{73} +(-1.97478e7 - 1.97478e7i) q^{77} -2.57526e7i q^{79} +1.04794e7 q^{81} +(5.97228e7 - 5.97228e7i) q^{83} +(5.97449e7 + 5.97449e7i) q^{87} +3.34415e7i q^{89} +1.77458e8 q^{91} +(-9.08221e7 + 9.08221e7i) q^{93} +(1.14246e7 + 1.14246e7i) q^{97} +6.55590e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 420 q^{11} - 921168 q^{21} + 3833112 q^{31} + 3587532 q^{41} + 46092564 q^{51} + 31354704 q^{61} - 29589384 q^{71} + 104018868 q^{81} + 433229088 q^{91}+O(q^{100}) \) 12 * q - 420 * q^11 - 921168 * q^21 + 3833112 * q^31 + 3587532 * q^41 + 46092564 * q^51 + 31354704 * q^61 - 29589384 * q^71 + 104018868 * q^81 + 433229088 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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