LMFDB - Embedded newform 990.2.ba.i.829.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(289,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.ba (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,8,2,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 330)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			829.1
Character	$\chi$	$=$	990.829
Dual form			990.2.ba.i.289.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(-2.23339 - 0.109316i) q^{5} +(1.51700 - 0.492904i) q^{7} +(0.951057 + 0.309017i) q^{8} +(1.40119 - 1.74260i) q^{10} +(-3.31152 + 0.183948i) q^{11} +(-1.81548 + 2.49879i) q^{13} +(-0.492904 + 1.51700i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(4.22144 + 5.81031i) q^{17} +(2.42920 - 7.47630i) q^{19} +(0.586191 + 2.15786i) q^{20} +(1.79765 - 2.78720i) q^{22} -3.38697i q^{23} +(4.97610 + 0.488292i) q^{25} +(-0.954454 - 2.93751i) q^{26} +(-0.937558 - 1.29044i) q^{28} +(-2.17853 - 6.70484i) q^{29} +(-3.10073 - 2.25281i) q^{31} -1.00000i q^{32} -7.18194 q^{34} +(-3.44194 + 0.935015i) q^{35} +(-0.108362 + 0.0352088i) q^{37} +(4.62061 + 6.35972i) q^{38} +(-2.09030 - 0.794123i) q^{40} +(3.35707 - 10.3320i) q^{41} -5.27497i q^{43} +(1.19826 + 3.09260i) q^{44} +(2.74012 + 1.99081i) q^{46} +(-7.49596 - 2.43559i) q^{47} +(-3.60478 + 2.61903i) q^{49} +(-3.31991 + 3.73874i) q^{50} +(2.93751 + 0.954454i) q^{52} +(7.69164 - 10.5866i) q^{53} +(7.41604 - 0.0488253i) q^{55} +1.59507 q^{56} +(6.70484 + 2.17853i) q^{58} +(0.837725 + 2.57825i) q^{59} +(-2.80239 + 2.03606i) q^{61} +(3.64513 - 1.18437i) q^{62} +(0.809017 + 0.587785i) q^{64} +(4.32784 - 5.38233i) q^{65} +0.846682i q^{67} +(4.22144 - 5.81031i) q^{68} +(1.26668 - 3.33418i) q^{70} +(11.9759 - 8.70102i) q^{71} +(11.9832 - 3.89357i) q^{73} +(0.0352088 - 0.108362i) q^{74} -7.86105 q^{76} +(-4.93291 + 1.91131i) q^{77} +(2.85840 + 2.07675i) q^{79} +(1.87111 - 1.22432i) q^{80} +(6.38552 + 8.78891i) q^{82} +(-4.04681 - 5.56995i) q^{83} +(-8.79298 - 13.4382i) q^{85} +(4.26754 + 3.10055i) q^{86} +(-3.20629 - 0.848371i) q^{88} -11.0410 q^{89} +(-1.52242 + 4.68553i) q^{91} +(-3.22120 + 1.04663i) q^{92} +(6.37645 - 4.63276i) q^{94} +(-6.24263 + 16.4320i) q^{95} +(-0.957769 + 1.31826i) q^{97} -4.45575i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} + 2 q^{5} + 4 q^{10} - 10 q^{14} - 8 q^{16} + 20 q^{19} - 2 q^{20} + 4 q^{25} + 2 q^{26} - 2 q^{29} - 24 q^{31} - 28 q^{34} - 44 q^{35} - 4 q^{40} + 34 q^{41} + 20 q^{44} - 38 q^{46} + 14 q^{49}+ \cdots + 60 q^{95}+O(q^{100}) $ 32 * q + 8 * q^4 + 2 * q^5 + 4 * q^10 - 10 * q^14 - 8 * q^16 + 20 * q^19 - 2 * q^20 + 4 * q^25 + 2 * q^26 - 2 * q^29 - 24 * q^31 - 28 * q^34 - 44 * q^35 - 4 * q^40 + 34 * q^41 + 20 * q^44 - 38 * q^46 + 14 * q^49 + 24 * q^50 + 28 * q^55 - 20 * q^56 + 4 * q^59 - 8 * q^61 + 8 * q^64 + 44 * q^65 - 10 * q^70 - 8 * q^71 - 20 * q^74 + 20 * q^76 + 2 * q^79 + 2 * q^80 - 20 * q^85 - 34 * q^86 + 132 * q^89 + 78 * q^91 + 22 * q^94 + 60 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$-1$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$		0			0
$3$		0			0
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	−2.23339	−	0.109316i	−0.998804	−	0.0488877i
$5$	−2.23339	−	0.109316i	−0.998804	−	0.0488877i
$6$		0			0
$7$	1.51700	−	0.492904i	0.573373	−	0.186300i	−0.00795682	−	0.999968i	$-0.502533\pi$
$7$	1.51700	−	0.492904i	0.573373	−	0.186300i	0.581329	+	0.813668i	$0.302533\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$		0			0
$10$	1.40119	−	1.74260i	0.443097	−	0.551058i
$11$	−3.31152	+	0.183948i	−0.998461	+	0.0554623i
$11$	−3.31152	+	0.183948i	−0.998461	+	0.0554623i
$12$		0			0
$13$	−1.81548	+	2.49879i	−0.503523	+	0.693040i	−0.982810	−	0.184618i	$-0.940895\pi$
$13$	−1.81548	+	2.49879i	−0.503523	+	0.693040i	0.479287	+	0.877658i	$0.340895\pi$
$14$	−0.492904	+	1.51700i	−0.131734	+	0.405436i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	4.22144	+	5.81031i	1.02385	+	1.40921i	0.909469	+	0.415771i	$0.136488\pi$
$17$	4.22144	+	5.81031i	1.02385	+	1.40921i	0.114380	+	0.993437i	$0.463512\pi$
$18$		0			0
$19$	2.42920	−	7.47630i	0.557296	−	1.71518i	−0.132506	−	0.991182i	$-0.542302\pi$
$19$	2.42920	−	7.47630i	0.557296	−	1.71518i	0.689802	−	0.723998i	$-0.257698\pi$
$20$	0.586191	+	2.15786i	0.131076	+	0.482513i
$21$		0			0
$22$	1.79765	−	2.78720i	0.383259	−	0.594233i
$23$		−	3.38697i		−	0.706232i	−0.935579	−	0.353116i	$-0.885122\pi$
$23$		−	3.38697i		−	0.706232i	0.935579	−	0.353116i	$-0.114878\pi$
$24$		0			0
$25$	4.97610	+	0.488292i	0.995220	+	0.0976584i
$26$	−0.954454	−	2.93751i	−0.187184	−	0.576093i
$27$		0			0
$28$	−0.937558	−	1.29044i	−0.177182	−	0.243870i
$29$	−2.17853	−	6.70484i	−0.404544	−	1.24506i	−0.921276	−	0.388910i	$-0.872852\pi$
$29$	−2.17853	−	6.70484i	−0.404544	−	1.24506i	0.516732	−	0.856147i	$-0.327148\pi$
$30$		0			0
$31$	−3.10073	−	2.25281i	−0.556908	−	0.404617i	0.273418	−	0.961895i	$-0.411846\pi$
$31$	−3.10073	−	2.25281i	−0.556908	−	0.404617i	−0.830326	+	0.557278i	$0.811846\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−7.18194			−1.23169
$35$	−3.44194	+	0.935015i	−0.581795	+	0.158046i
$36$		0			0
$37$	−0.108362	+	0.0352088i	−0.0178145	+	0.00578829i	−0.317911	−	0.948121i	$-0.602981\pi$
$37$	−0.108362	+	0.0352088i	−0.0178145	+	0.00578829i	0.300096	+	0.953909i	$0.402981\pi$
$38$	4.62061	+	6.35972i	0.749561	+	1.03168i
$39$		0			0
$40$	−2.09030	−	0.794123i	−0.330506	−	0.125562i
$41$	3.35707	−	10.3320i	0.524286	−	1.61359i	−0.241439	−	0.970416i	$-0.577619\pi$
$41$	3.35707	−	10.3320i	0.524286	−	1.61359i	0.765724	−	0.643169i	$-0.222381\pi$
$42$		0			0
$43$		−	5.27497i		−	0.804426i	−0.915546	−	0.402213i	$-0.868241\pi$
$43$		−	5.27497i		−	0.804426i	0.915546	−	0.402213i	$-0.131759\pi$
$44$	1.19826	+	3.09260i	0.180645	+	0.466227i
$45$		0			0
$46$	2.74012	+	1.99081i	0.404008	+	0.293529i
$47$	−7.49596	−	2.43559i	−1.09340	−	0.355267i	−0.293840	−	0.955855i	$-0.594933\pi$
$47$	−7.49596	−	2.43559i	−1.09340	−	0.355267i	−0.799559	+	0.600588i	$0.794933\pi$
$48$		0			0
$49$	−3.60478	+	2.61903i	−0.514969	+	0.374147i
$50$	−3.31991	+	3.73874i	−0.469507	+	0.528737i
$51$		0			0
$52$	2.93751	+	0.954454i	0.407359	+	0.132359i
$53$	7.69164	−	10.5866i	1.05653	−	1.45419i	0.173518	−	0.984831i	$-0.444487\pi$
$53$	7.69164	−	10.5866i	1.05653	−	1.45419i	0.883010	−	0.469354i	$-0.155513\pi$
$54$		0			0
$55$	7.41604	−	0.0488253i	0.999978	−	0.00658360i
$56$	1.59507			0.213150
$57$		0			0
$58$	6.70484	+	2.17853i	0.880388	+	0.286056i
$59$	0.837725	+	2.57825i	0.109063	+	0.335660i	0.990662	−	0.136338i	$-0.0435332\pi$
$59$	0.837725	+	2.57825i	0.109063	+	0.335660i	−0.881600	+	0.471997i	$0.843533\pi$
$60$		0			0
$61$	−2.80239	+	2.03606i	−0.358809	+	0.260690i	−0.752555	−	0.658529i	$-0.771179\pi$
$61$	−2.80239	+	2.03606i	−0.358809	+	0.260690i	0.393746	+	0.919219i	$0.371179\pi$
$62$	3.64513	−	1.18437i	0.462932	−	0.150416i
$63$		0			0
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	4.32784	−	5.38233i	0.536802	−	0.667596i
$66$		0			0
$67$			0.846682i			0.103439i	0.998662	+	0.0517193i	$0.0164701\pi$
$67$			0.846682i			0.103439i	−0.998662	+	0.0517193i	$0.983530\pi$
$68$	4.22144	−	5.81031i	0.511925	−	0.704604i
$69$		0			0
$70$	1.26668	−	3.33418i	0.151397	−	0.398511i
$71$	11.9759	−	8.70102i	1.42128	−	1.03262i	0.429722	−	0.902961i	$-0.358612\pi$
$71$	11.9759	−	8.70102i	1.42128	−	1.03262i	0.991559	−	0.129659i	$-0.0413884\pi$
$72$		0			0
$73$	11.9832	−	3.89357i	1.40252	−	0.455708i	0.492518	−	0.870302i	$-0.336077\pi$
$73$	11.9832	−	3.89357i	1.40252	−	0.455708i	0.910006	+	0.414595i	$0.136077\pi$
$74$	0.0352088	−	0.108362i	0.00409294	−	0.0125968i
$75$		0			0
$76$	−7.86105			−0.901724
$77$	−4.93291	+	1.91131i	−0.562157	+	0.217814i
$78$		0			0
$79$	2.85840	+	2.07675i	0.321595	+	0.233652i	0.736856	−	0.676050i	$-0.236310\pi$
$79$	2.85840	+	2.07675i	0.321595	+	0.233652i	−0.415261	+	0.909702i	$0.636310\pi$
$80$	1.87111	−	1.22432i	0.209196	−	0.136883i
$81$		0			0
$82$	6.38552	+	8.78891i	0.705163	+	0.970573i
$83$	−4.04681	−	5.56995i	−0.444195	−	0.611382i	0.526943	−	0.849901i	$-0.323338\pi$
$83$	−4.04681	−	5.56995i	−0.444195	−	0.611382i	−0.971138	+	0.238519i	$0.923338\pi$
$84$		0			0
$85$	−8.79298	−	13.4382i	−0.953732	−	1.45758i
$86$	4.26754	+	3.10055i	0.460181	+	0.334341i
$87$		0			0
$88$	−3.20629	−	0.848371i	−0.341791	−	0.0904367i
$89$	−11.0410			−1.17035			−0.585174	−	0.810907i	$-0.698974\pi$
$89$	−11.0410			−1.17035			−0.585174	+	0.810907i	$0.698974\pi$
$90$		0			0
$91$	−1.52242	+	4.68553i	−0.159593	+	0.491177i
$92$	−3.22120	+	1.04663i	−0.335833	+	0.109119i
$93$		0			0
$94$	6.37645	−	4.63276i	0.657680	−	0.477833i
$95$	−6.24263	+	16.4320i	−0.640481	+	1.68588i
$96$		0			0
$97$	−0.957769	+	1.31826i	−0.0972467	+	0.133849i	−0.854867	−	0.518846i	$-0.826362\pi$
$97$	−0.957769	+	1.31826i	−0.0972467	+	0.133849i	0.757621	+	0.652695i	$0.226362\pi$
$98$		−	4.45575i		−	0.450099i
$99$		0			0
$100$	−1.07331	−	4.88344i	−0.107331	−	0.488344i
$101$	3.24534	+	2.35788i	0.322923	+	0.234618i	0.737422	−	0.675432i	$-0.236043\pi$
$101$	3.24534	+	2.35788i	0.322923	+	0.234618i	−0.414498	+	0.910050i	$0.636043\pi$
$102$		0			0
$103$	2.70073	−	0.877521i	0.266111	−	0.0864647i	−0.172922	−	0.984935i	$-0.555321\pi$
$103$	2.70073	−	0.877521i	0.266111	−	0.0864647i	0.439033	+	0.898471i	$0.355321\pi$
$104$	−2.49879	+	1.81548i	−0.245027	+	0.178022i
$105$		0			0
$106$	4.04373	+	12.4453i	0.392762	+	1.20880i
$107$	9.64652	+	3.13435i	0.932565	+	0.303009i	0.735611	−	0.677404i	$-0.236895\pi$
$107$	9.64652	+	3.13435i	0.932565	+	0.303009i	0.196954	+	0.980413i	$0.436895\pi$
$108$		0			0
$109$	−16.6127			−1.59121			−0.795606	−	0.605815i	$-0.792847\pi$
$109$	−16.6127			−1.59121			−0.795606	+	0.605815i	$0.792847\pi$
$110$	−4.31954	+	6.02840i	−0.411852	+	0.574785i
$111$		0			0
$112$	−0.937558	+	1.29044i	−0.0885909	+	0.121935i
$113$	3.87304	+	1.25843i	0.364345	+	0.118383i	0.485468	−	0.874255i	$-0.338649\pi$
$113$	3.87304	+	1.25843i	0.364345	+	0.118383i	−0.121123	+	0.992638i	$0.538649\pi$
$114$		0			0
$115$	−0.370251	+	7.56444i	−0.0345261	+	0.705388i
$116$	−5.70348	+	4.14382i	−0.529554	+	0.384744i
$117$		0			0
$118$	−2.57825	−	0.837725i	−0.237347	−	0.0771188i
$119$	9.26785	+	6.73349i	0.849583	+	0.617258i
$120$		0			0
$121$	10.9323	−	1.21829i	0.993848	−	0.110754i
$122$		−	3.46394i		−	0.313611i
$123$		0			0
$124$	−1.18437	+	3.64513i	−0.106360	+	0.327342i
$125$	−11.0602	−	1.63452i	−0.989256	−	0.146196i
$126$		0			0
$127$	−4.05022	−	5.57465i	−0.359399	−	0.494670i	0.590582	−	0.806978i	$-0.298898\pi$
$127$	−4.05022	−	5.57465i	−0.359399	−	0.494670i	−0.949981	+	0.312307i	$0.898898\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$		0			0
$130$	1.81056	+	6.66495i	0.158796	+	0.584555i
$131$	1.65497			0.144596			0.0722979	−	0.997383i	$-0.476967\pi$
$131$	1.65497			0.144596			0.0722979	+	0.997383i	$0.476967\pi$
$132$		0			0
$133$		−	12.5389i		−	1.08726i
$134$	−0.684980	−	0.497667i	−0.0591733	−	0.0429919i
$135$		0			0
$136$	2.21934	+	6.83043i	0.190307	+	0.585705i
$137$	5.44871	+	7.49951i	0.465515	+	0.640726i	0.975641	−	0.219373i	$-0.0704012\pi$
$137$	5.44871	+	7.49951i	0.465515	+	0.640726i	−0.510126	+	0.860100i	$0.670401\pi$
$138$		0			0
$139$	−1.43113	−	4.40457i	−0.121387	−	0.373591i	0.871839	−	0.489793i	$-0.162928\pi$
$139$	−1.43113	−	4.40457i	−0.121387	−	0.373591i	−0.993226	+	0.116203i	$0.962928\pi$
$140$	1.95287	+	2.98455i	0.165048	+	0.252240i
$141$		0			0
$142$			14.8031i			1.24224i
$143$	5.55235	−	8.60876i	0.464311	−	0.719900i
$144$		0			0
$145$	4.13258	+	15.2127i	0.343192	+	1.26335i
$146$	−3.89357	+	11.9832i	−0.322234	+	0.991734i
$147$		0			0
$148$	0.0669711	+	0.0921778i	0.00550499	+	0.00757697i
$149$	−4.57146	+	3.32136i	−0.374508	+	0.272096i	−0.759078	−	0.651000i	$-0.774350\pi$
$149$	−4.57146	+	3.32136i	−0.374508	+	0.272096i	0.384570	+	0.923096i	$0.374350\pi$
$150$		0			0
$151$	0.453563	−	1.39592i	0.0369104	−	0.113599i	−0.930904	−	0.365265i	$-0.880978\pi$
$151$	0.453563	−	1.39592i	0.0369104	−	0.113599i	0.967814	+	0.251666i	$0.0809785\pi$
$152$	4.62061	−	6.35972i	0.374781	−	0.515841i
$153$		0			0
$154$	1.35321	−	5.11425i	0.109045	−	0.412118i
$155$	6.67888	+	5.37038i	0.536461	+	0.431359i
$156$		0			0
$157$	−10.6849	−	3.47175i	−0.852752	−	0.277076i	−0.150154	−	0.988663i	$-0.547977\pi$
$157$	−10.6849	−	3.47175i	−0.852752	−	0.277076i	−0.702598	+	0.711587i	$0.747977\pi$
$158$	−3.36024	+	1.09181i	−0.267327	+	0.0868597i
$159$		0			0
$160$	−0.109316	+	2.23339i	−0.00864220	+	0.176565i
$161$	−1.66945	−	5.13804i	−0.131571	−	0.404934i
$162$		0			0
$163$	−4.47958	+	6.16561i	−0.350868	+	0.482928i	−0.947576	−	0.319530i	$-0.896475\pi$
$163$	−4.47958	+	6.16561i	−0.350868	+	0.482928i	0.596708	+	0.802458i	$0.296475\pi$
$164$	−10.8637			−0.848312
$165$		0			0
$166$	6.88484			0.534367
$167$	−4.88691	+	6.72626i	−0.378161	+	0.520494i	−0.955096	−	0.296296i	$-0.904248\pi$
$167$	−4.88691	+	6.72626i	−0.378161	+	0.520494i	0.576935	+	0.816790i	$0.304248\pi$
$168$		0			0
$169$	1.06922	+	3.29072i	0.0822477	+	0.253132i
$170$	16.0401	+	0.785102i	1.23022	+	0.0602146i
$171$		0			0
$172$	−5.01680	+	1.63006i	−0.382527	+	0.124291i
$173$	7.44270	+	2.41828i	0.565858	+	0.183858i	0.577955	−	0.816069i	$-0.303851\pi$
$173$	7.44270	+	2.41828i	0.565858	+	0.183858i	−0.0120975	+	0.999927i	$0.503851\pi$
$174$		0			0
$175$	7.78943	−	1.71200i	0.588826	−	0.129415i
$176$	2.57095	−	2.09528i	0.193793	−	0.157938i
$177$		0			0
$178$	6.48977	−	8.93240i	0.486429	−	0.669511i
$179$	5.78044	−	17.7904i	0.432050	−	1.32971i	−0.464029	−	0.885820i	$-0.653597\pi$
$179$	5.78044	−	17.7904i	0.432050	−	1.32971i	0.896079	−	0.443894i	$-0.146403\pi$
$180$		0			0
$181$	3.59193	−	2.60969i	0.266986	−	0.193977i	−0.446235	−	0.894916i	$-0.647235\pi$
$181$	3.59193	−	2.60969i	0.266986	−	0.193977i	0.713221	+	0.700939i	$0.247235\pi$
$182$	−2.89582	−	3.98575i	−0.214652	−	0.295443i
$183$		0			0
$184$	1.04663	−	3.22120i	0.0771587	−	0.237470i
$185$	0.245863	−	0.0667895i	0.0180762	−	0.00491046i
$186$		0			0
$187$	−15.0482	−	18.4644i	−1.10043	−	1.35025i
$188$			7.88172i			0.574834i
$189$		0			0
$190$	−9.62442	−	14.7089i	−0.698229	−	1.06709i
$191$	−3.19243	−	9.82529i	−0.230996	−	0.710933i	−0.997627	−	0.0688452i	$-0.978069\pi$
$191$	−3.19243	−	9.82529i	−0.230996	−	0.710933i	0.766631	−	0.642088i	$-0.221931\pi$
$192$		0			0
$193$	−1.89861	−	2.61321i	−0.136665	−	0.188103i	0.735199	−	0.677851i	$-0.237089\pi$
$193$	−1.89861	−	2.61321i	−0.136665	−	0.188103i	−0.871864	+	0.489748i	$0.837089\pi$
$194$	−0.503529	−	1.54970i	−0.0361513	−	0.111262i
$195$		0			0
$196$	3.60478	+	2.61903i	0.257484	+	0.187073i
$197$			3.05335i			0.217542i	0.994067	+	0.108771i	$0.0346915\pi$
$197$			3.05335i			0.217542i	−0.994067	+	0.108771i	$0.965308\pi$
$198$		0			0
$199$	3.42982			0.243133			0.121567	−	0.992583i	$-0.461208\pi$
$199$	3.42982			0.243133			0.121567	+	0.992583i	$0.461208\pi$
$200$	4.58166	+	2.00209i	0.323972	+	0.141569i
$201$		0			0
$202$	−3.81513	+	1.23961i	−0.268431	+	0.0872186i
$203$	−6.60968	−	9.09744i	−0.463908	−	0.638515i
$204$		0			0
$205$	−8.62710	+	22.7084i	−0.602543	+	1.58602i
$206$	−0.877521	+	2.70073i	−0.0611398	+	0.188169i
$207$		0			0
$208$		−	3.08868i		−	0.214161i
$209$	−6.66908	+	25.2048i	−0.461310	+	1.74345i
$210$		0			0
$211$	−16.9759	−	12.3337i	−1.16867	−	0.849089i	−0.177821	−	0.984063i	$-0.556905\pi$
$211$	−16.9759	−	12.3337i	−1.16867	−	0.849089i	−0.990849	+	0.134974i	$0.956905\pi$
$212$	−12.4453	−	4.04373i	−0.854749	−	0.277725i
$213$		0			0
$214$	−8.20582	+	5.96188i	−0.560939	+	0.407546i
$215$	−0.576640	+	11.7811i	−0.0393265	+	0.803464i
$216$		0			0
$217$	−5.81423	−	1.88916i	−0.394696	−	0.128244i
$218$	9.76472	−	13.4400i	0.661350	−	0.910271i
$219$		0			0
$220$	−2.33812	−	7.03798i	−0.157636	−	0.474501i
$221$	−22.1827			−1.49217
$222$		0			0
$223$	11.7590	+	3.82072i	0.787439	+	0.255854i	0.675013	−	0.737806i	$-0.264138\pi$
$223$	11.7590	+	3.82072i	0.787439	+	0.255854i	0.112426	+	0.993660i	$0.464138\pi$
$224$	−0.492904	−	1.51700i	−0.0329335	−	0.101359i
$225$		0			0
$226$	−3.29461	+	2.39367i	−0.219154	+	0.159225i
$227$	−21.0624	+	6.84360i	−1.39796	+	0.454226i	−0.908532	−	0.417816i	$-0.862796\pi$
$227$	−21.0624	+	6.84360i	−1.39796	+	0.454226i	−0.489432	+	0.872042i	$0.662796\pi$
$228$		0			0
$229$	1.99941	+	1.45266i	0.132125	+	0.0959944i	0.651885	−	0.758318i	$-0.273979\pi$
$229$	1.99941	+	1.45266i	0.132125	+	0.0959944i	−0.519760	+	0.854312i	$0.673979\pi$
$230$	−5.90213	−	4.74581i	−0.389175	−	0.312929i
$231$		0			0
$232$		−	7.04988i		−	0.462848i
$233$	−16.6677	+	22.9411i	−1.09193	+	1.50292i	−0.246273	+	0.969200i	$0.579206\pi$
$233$	−16.6677	+	22.9411i	−1.09193	+	1.50292i	−0.845662	+	0.533719i	$0.820794\pi$
$234$		0			0
$235$	16.4752	+	6.25905i	1.07472	+	0.408296i
$236$	2.19319	−	1.59345i	0.142765	−	0.103725i
$237$		0			0
$238$	−10.8950	+	3.54000i	−0.706219	+	0.229464i
$239$	−2.51287	+	7.73381i	−0.162544	+	0.500259i	−0.998847	−	0.0480089i	$-0.984712\pi$
$239$	−2.51287	+	7.73381i	−0.162544	+	0.500259i	0.836303	+	0.548268i	$0.184712\pi$
$240$		0			0
$241$	3.13125			0.201702			0.100851	−	0.994902i	$-0.467843\pi$
$241$	3.13125			0.201702			0.100851	+	0.994902i	$0.467843\pi$
$242$	−5.44024	+	9.56053i	−0.349712	+	0.614574i
$243$		0			0
$244$	2.80239	+	2.03606i	0.179405	+	0.130345i
$245$	8.33720	−	5.45526i	0.532644	−	0.348524i
$246$		0			0
$247$	14.2716	+	19.6431i	0.908078	+	1.24986i
$248$	−2.25281	−	3.10073i	−0.143054	−	0.196897i
$249$		0			0
$250$	7.82338	−	7.98716i	0.494794	−	0.505152i
$251$	10.1301	+	7.35992i	0.639404	+	0.464554i	0.859645	−	0.510891i	$-0.170684\pi$
$251$	10.1301	+	7.35992i	0.639404	+	0.464554i	−0.220241	+	0.975445i	$0.570684\pi$
$252$		0			0
$253$	0.623026	+	11.2160i	0.0391693	+	0.705145i
$254$	6.89065			0.432358
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	3.49308	−	1.13497i	0.217892	−	0.0707974i	−0.198037	−	0.980195i	$-0.563457\pi$
$257$	3.49308	−	1.13497i	0.217892	−	0.0707974i	0.415929	+	0.909397i	$0.363457\pi$
$258$		0			0
$259$	−0.147030	+	0.106824i	−0.00913600	+	0.00663770i
$260$	−6.45627	−	2.45279i	−0.400401	−	0.152116i
$261$		0			0
$262$	−0.972769	+	1.33890i	−0.0600979	+	0.0827176i
$263$		−	18.0696i		−	1.11422i	−0.830438	−	0.557111i	$-0.811910\pi$
$263$		−	18.0696i		−	1.11422i	0.830438	−	0.557111i	$-0.188090\pi$
$264$		0			0
$265$	−18.3357	+	22.8033i	−1.12636	+	1.40080i
$266$	10.1442	+	7.37019i	0.621981	+	0.451895i
$267$		0			0
$268$	0.805243	−	0.261639i	0.0491880	−	0.0159822i
$269$	16.6144	−	12.0711i	1.01300	−	0.735985i	0.0481615	−	0.998840i	$-0.484664\pi$
$269$	16.6144	−	12.0711i	1.01300	−	0.735985i	0.964836	+	0.262854i	$0.0846638\pi$
$270$		0			0
$271$	−2.48430	−	7.64590i	−0.150911	−	0.464455i	0.846813	−	0.531891i	$-0.178518\pi$
$271$	−2.48430	−	7.64590i	−0.150911	−	0.464455i	−0.997724	+	0.0674356i	$0.978518\pi$
$272$	−6.83043	−	2.21934i	−0.414156	−	0.134567i
$273$		0			0
$274$	−9.26991			−0.560015
$275$	−16.5683	−	0.701647i	−0.999104	−	0.0423109i
$276$		0			0
$277$	−13.5594	+	18.6629i	−0.814707	+	1.12135i	0.175873	+	0.984413i	$0.443725\pi$
$277$	−13.5594	+	18.6629i	−0.814707	+	1.12135i	−0.990580	+	0.136935i	$0.956275\pi$
$278$	4.40457	+	1.43113i	0.264168	+	0.0858335i
$279$		0			0
$280$	−3.56242	−	0.174367i	−0.212895	−	0.0104204i
$281$	−12.6377	+	9.18182i	−0.753902	+	0.547742i	−0.897034	−	0.441962i	$-0.854283\pi$
$281$	−12.6377	+	9.18182i	−0.753902	+	0.547742i	0.143132	+	0.989704i	$0.454283\pi$
$282$		0			0
$283$	−11.1248	−	3.61468i	−0.661303	−	0.214870i	−0.0409115	−	0.999163i	$-0.513026\pi$
$283$	−11.1248	−	3.61468i	−0.661303	−	0.214870i	−0.620391	+	0.784293i	$0.713026\pi$
$284$	−11.9759	−	8.70102i	−0.710640	−	0.516310i
$285$		0			0
$286$	3.70104	+	9.55204i	0.218847	+	0.564824i
$287$		−	17.3283i		−	1.02286i
$288$		0			0
$289$	−10.6859	+	32.8878i	−0.628582	+	1.93458i
$290$	−14.7364	−	5.59847i	−0.865351	−	0.328754i
$291$		0			0
$292$	−7.40601	−	10.1935i	−0.433404	−	0.596529i
$293$	−15.4572	+	5.02234i	−0.903018	+	0.293408i	−0.723482	−	0.690343i	$-0.757460\pi$
$293$	−15.4572	+	5.02234i	−0.903018	+	0.293408i	−0.179536	+	0.983751i	$0.557460\pi$
$294$		0			0
$295$	−1.58913	−	5.84983i	−0.0925225	−	0.340590i
$296$	−0.113938			−0.00662252
$297$		0			0
$298$		−	5.65063i		−	0.327332i
$299$	8.46334	+	6.14898i	0.489448	+	0.355605i
$300$		0			0
$301$	−2.60005	−	8.00214i	−0.149865	−	0.461236i
$302$	0.862727	+	1.18744i	0.0496444	+	0.0683296i
$303$		0			0
$304$	2.42920	+	7.47630i	0.139324	+	0.428795i
$305$	6.48141	−	4.24097i	0.371125	−	0.242837i
$306$		0			0
$307$		−	21.8451i		−	1.24676i	−0.781917	−	0.623382i	$-0.785758\pi$
$307$		−	21.8451i		−	1.24676i	0.781917	−	0.623382i	$-0.214242\pi$
$308$	3.34212	+	4.10085i	0.190435	+	0.233668i
$309$		0			0
$310$	−8.27048	+	2.24670i	−0.469732	+	0.127604i
$311$	−6.79652	+	20.9175i	−0.385395	+	1.18613i	0.550797	+	0.834639i	$0.314324\pi$
$311$	−6.79652	+	20.9175i	−0.385395	+	1.18613i	−0.936193	+	0.351486i	$0.885676\pi$
$312$		0			0
$313$	4.45719	+	6.13479i	0.251935	+	0.346759i	0.916188	−	0.400749i	$-0.131250\pi$
$313$	4.45719	+	6.13479i	0.251935	+	0.346759i	−0.664253	+	0.747508i	$0.731250\pi$
$314$	9.08916	−	6.60366i	0.512931	−	0.372666i
$315$		0			0
$316$	1.09181	−	3.36024i	0.0614191	−	0.189029i
$317$	−5.67596	+	7.81229i	−0.318794	+	0.438782i	−0.938098	−	0.346369i	$-0.887415\pi$
$317$	−5.67596	+	7.81229i	−0.318794	+	0.438782i	0.619305	+	0.785151i	$0.287415\pi$
$318$		0			0
$319$	8.44760	+	21.8025i	0.472975	+	1.22070i
$320$	−1.74260	−	1.40119i	−0.0974143	−	0.0783292i
$321$		0			0
$322$	5.13804	+	1.66945i	0.286332	+	0.0930348i
$323$	53.6943	−	17.4463i	2.98763	−	0.970741i
$324$		0			0
$325$	−10.2541	+	11.5478i	−0.568798	+	0.640554i
$326$	−2.35505	−	7.24811i	−0.130434	−	0.401436i
$327$		0			0
$328$	6.38552	−	8.78891i	0.352581	−	0.485287i
$329$	−12.5719			−0.693111
$330$		0			0
$331$	31.5303			1.73306			0.866531	−	0.499123i	$-0.166345\pi$
$331$	31.5303			1.73306			0.866531	+	0.499123i	$0.166345\pi$
$332$	−4.04681	+	5.56995i	−0.222097	+	0.305691i
$333$		0			0
$334$	−2.56920	−	7.90719i	−0.140581	−	0.432662i
$335$	0.0925560	−	1.89097i	0.00505688	−	0.103315i
$336$		0			0
$337$	14.0752	−	4.57330i	0.766723	−	0.249123i	0.100561	−	0.994931i	$-0.467936\pi$
$337$	14.0752	−	4.57330i	0.766723	−	0.249123i	0.666161	+	0.745808i	$0.267936\pi$
$338$	−3.29072	−	1.06922i	−0.178992	−	0.0581579i
$339$		0			0
$340$	−10.0633	+	12.5152i	−0.545759	+	0.678735i
$341$	10.6825	+	6.88986i	0.578491	+	0.373107i
$342$		0			0
$343$	−10.7404	+	14.7829i	−0.579929	+	0.798204i
$344$	1.63006	−	5.01680i	0.0878867	−	0.270488i
$345$		0			0
$346$	−6.33114	+	4.59984i	−0.340364	+	0.247289i
$347$	1.72561	+	2.37509i	0.0926354	+	0.127502i	0.852819	−	0.522207i	$-0.174891\pi$
$347$	1.72561	+	2.37509i	0.0926354	+	0.127502i	−0.760184	+	0.649708i	$0.774891\pi$
$348$		0			0
$349$	4.44198	−	13.6710i	0.237774	−	0.731792i	−0.758968	−	0.651128i	$-0.774296\pi$
$349$	4.44198	−	13.6710i	0.237774	−	0.731792i	0.996741	−	0.0806635i	$-0.0257039\pi$
$350$	−3.19348	+	7.30807i	−0.170699	+	0.390633i
$351$		0			0
$352$	0.183948	+	3.31152i	0.00980445	+	0.176505i
$353$		−	27.8075i		−	1.48005i	−0.672582	−	0.740023i	$-0.734815\pi$
$353$		−	27.8075i		−	1.48005i	0.672582	−	0.740023i	$-0.265185\pi$
$354$		0			0
$355$	−27.6981	+	18.1236i	−1.47006	+	0.961903i
$356$	3.41187	+	10.5007i	0.180829	+	0.556534i
$357$		0			0
$358$	10.9950	+	15.1334i	0.581106	+	0.799824i
$359$	−0.318387	−	0.979893i	−0.0168038	−	0.0517168i	0.942303	−	0.334761i	$-0.108656\pi$
$359$	−0.318387	−	0.979893i	−0.0168038	−	0.0517168i	−0.959107	+	0.283044i	$0.908656\pi$
$360$		0			0
$361$	−34.6227	−	25.1549i	−1.82225	−	1.32394i
$362$			4.43987i			0.233355i
$363$		0			0
$364$	4.92666			0.258227
$365$	−27.1888	+	7.38592i	−1.42313	+	0.386597i
$366$		0			0
$367$	1.44410	−	0.469215i	0.0753812	−	0.0244928i	−0.271084	−	0.962556i	$-0.587382\pi$
$367$	1.44410	−	0.469215i	0.0753812	−	0.0244928i	0.346465	+	0.938063i	$0.387382\pi$
$368$	1.99081	+	2.74012i	0.103778	+	0.142839i
$369$		0			0
$370$	−0.0904808	+	0.238165i	−0.00470387	+	0.0123816i
$371$	6.45003	−	19.8512i	0.334869	−	1.03062i
$372$		0			0
$373$		−	3.44516i		−	0.178384i	−0.996014	−	0.0891918i	$-0.971572\pi$
$373$		−	3.44516i		−	0.178384i	0.996014	−	0.0891918i	$-0.0284284\pi$
$374$	23.7831	−	1.32110i	1.22980	−	0.0683126i
$375$		0			0
$376$	−6.37645	−	4.63276i	−0.328840	−	0.238916i
$377$	20.7091	+	6.72879i	1.06657	+	0.346550i
$378$		0			0
$379$	12.5810	−	9.14067i	0.646245	−	0.469524i	−0.215745	−	0.976450i	$-0.569218\pi$
$379$	12.5810	−	9.14067i	0.646245	−	0.469524i	0.861990	+	0.506925i	$0.169218\pi$
$380$	17.5568	+	0.859339i	0.900646	+	0.0440832i
$381$		0			0
$382$	9.82529	+	3.19243i	0.502705	+	0.163339i
$383$	9.21991	−	12.6901i	0.471115	−	0.648435i	−0.505652	−	0.862738i	$-0.668748\pi$
$383$	9.21991	−	12.6901i	0.471115	−	0.648435i	0.976767	+	0.214303i	$0.0687480\pi$
$384$		0			0
$385$	11.2261	−	3.72946i	0.572134	−	0.190071i
$386$	3.23010			0.164408
$387$		0			0
$388$	1.54970	+	0.503529i	0.0786742	+	0.0255628i
$389$	−8.79657	−	27.0731i	−0.446004	−	1.37266i	−0.881379	−	0.472410i	$-0.843384\pi$
$389$	−8.79657	−	27.0731i	−0.446004	−	1.37266i	0.435375	−	0.900249i	$-0.356616\pi$
$390$		0			0
$391$	19.6794	−	14.2979i	0.995228	−	0.723076i
$392$	−4.23767	+	1.37690i	−0.214035	+	0.0695441i
$393$		0			0
$394$	−2.47021	−	1.79471i	−0.124447	−	0.0904163i
$395$	−6.15690	−	4.95066i	−0.309787	−	0.249095i
$396$		0			0
$397$			13.8905i			0.697143i	0.937282	+	0.348572i	$0.113333\pi$
$397$			13.8905i			0.697143i	−0.937282	+	0.348572i	$0.886667\pi$
$398$	−2.01600	+	2.77478i	−0.101053	+	0.139087i
$399$		0			0
$400$	−4.31276	+	2.52984i	−0.215638	+	0.126492i
$401$	−13.4104	+	9.74323i	−0.669684	+	0.486554i	−0.869919	−	0.493194i	$-0.835829\pi$
$401$	−13.4104	+	9.74323i	−0.669684	+	0.486554i	0.200236	+	0.979748i	$0.435829\pi$
$402$		0			0
$403$	11.2586	−	3.65815i	0.560832	−	0.182225i
$404$	1.23961	−	3.81513i	0.0616729	−	0.189810i
$405$		0			0
$406$	11.2451			0.558083
$407$	0.352365	−	0.136528i	0.0174661	−	0.00676742i
$408$		0			0
$409$	−4.31694	−	3.13644i	−0.213459	−	0.155087i	0.475918	−	0.879489i	$-0.342116\pi$
$409$	−4.31694	−	3.13644i	−0.213459	−	0.155087i	−0.689377	+	0.724403i	$0.742116\pi$
$410$	−13.3006	−	20.3271i	−0.656870	−	1.00389i
$411$		0			0
$412$	−1.66914	−	2.29738i	−0.0822328	−	0.113184i
$413$	2.54166	+	3.49829i	0.125067	+	0.172140i
$414$		0			0
$415$	8.42923	+	12.8823i	0.413775	+	0.632366i
$416$	2.49879	+	1.81548i	0.122513	+	0.0890112i
$417$		0			0
$418$	−16.4711	−	20.2104i	−0.805627	−	0.988522i
$419$	36.5583			1.78599			0.892994	−	0.450068i	$-0.148600\pi$
$419$	36.5583			1.78599			0.892994	+	0.450068i	$0.148600\pi$
$420$		0			0
$421$	11.3452	−	34.9170i	0.552933	−	1.70175i	−0.148409	−	0.988926i	$-0.547415\pi$
$421$	11.3452	−	34.9170i	0.552933	−	1.70175i	0.701341	−	0.712826i	$-0.252585\pi$
$422$	19.9564	−	6.48423i	0.971462	−	0.315647i
$423$		0			0
$424$	10.5866	−	7.69164i	0.514132	−	0.373539i
$425$	18.1692	+	30.9740i	0.881334	+	1.50246i
$426$		0			0
$427$	−3.24765	+	4.47001i	−0.157165	+	0.216319i
$428$		−	10.1430i		−	0.490278i
$429$		0			0
$430$	−9.19216	−	7.39126i	−0.443285	−	0.356438i
$431$	−1.48092	−	1.07595i	−0.0713332	−	0.0518266i	0.551547	−	0.834144i	$-0.314038\pi$
$431$	−1.48092	−	1.07595i	−0.0713332	−	0.0518266i	−0.622880	+	0.782317i	$0.714038\pi$
$432$		0			0
$433$	1.96304	−	0.637830i	0.0943377	−	0.0306522i	−0.261468	−	0.965212i	$-0.584207\pi$
$433$	1.96304	−	0.637830i	0.0943377	−	0.0306522i	0.355806	+	0.934560i	$0.384207\pi$
$434$	4.94588	−	3.59339i	0.237410	−	0.172488i
$435$		0			0
$436$	5.13362	+	15.7996i	0.245856	+	0.756666i
$437$	−25.3220	−	8.22762i	−1.21132	−	0.393580i
$438$		0			0
$439$	20.5451			0.980562			0.490281	−	0.871564i	$-0.336894\pi$
$439$	20.5451			0.980562			0.490281	+	0.871564i	$0.336894\pi$
$440$	7.06816	+	2.24525i	0.336961	+	0.107038i
$441$		0			0
$442$	13.0387	−	17.9462i	0.620186	−	0.853613i
$443$	8.10708	+	2.63415i	0.385179	+	0.125152i	0.495204	−	0.868777i	$-0.335093\pi$
$443$	8.10708	+	2.63415i	0.385179	+	0.125152i	−0.110025	+	0.993929i	$0.535093\pi$
$444$		0			0
$445$	24.6590	+	1.20696i	1.16895	+	0.0572156i
$446$	−10.0028	+	7.26744i	−0.473645	+	0.344123i
$447$		0			0
$448$	1.51700	+	0.492904i	0.0716716	+	0.0232875i
$449$	−13.9587	−	10.1416i	−0.658751	−	0.478610i	0.207490	−	0.978237i	$-0.433471\pi$
$449$	−13.9587	−	10.1416i	−0.658751	−	0.478610i	−0.866241	+	0.499627i	$0.833471\pi$
$450$		0			0
$451$	−9.21644	+	34.8321i	−0.433985	+	1.64018i
$452$		−	4.07236i		−	0.191548i
$453$		0			0
$454$	6.84360	−	21.0624i	0.321186	−	0.988509i
$455$	3.91237	−	10.2982i	0.183415	−	0.482787i
$456$		0			0
$457$	2.85897	+	3.93503i	0.133737	+	0.184073i	0.870633	−	0.491933i	$-0.163709\pi$
$457$	2.85897	+	3.93503i	0.133737	+	0.184073i	−0.736896	+	0.676006i	$0.763709\pi$
$458$	−2.35045	+	0.763708i	−0.109829	+	0.0356857i
$459$		0			0
$460$	7.30863	−	1.98541i	0.340766	−	0.0925703i
$461$	−7.98212			−0.371765			−0.185882	−	0.982572i	$-0.559514\pi$
$461$	−7.98212			−0.371765			−0.185882	+	0.982572i	$0.559514\pi$
$462$		0			0
$463$		−	35.8094i		−	1.66420i	−0.554623	−	0.832102i	$-0.687137\pi$
$463$		−	35.8094i		−	1.66420i	0.554623	−	0.832102i	$-0.312863\pi$
$464$	5.70348	+	4.14382i	0.264777	+	0.192372i
$465$		0			0
$466$	−8.76271	−	26.9688i	−0.405925	−	1.24931i
$467$	19.3266	+	26.6008i	0.894330	+	1.23094i	0.972241	+	0.233980i	$0.0751750\pi$
$467$	19.3266	+	26.6008i	0.894330	+	1.23094i	−0.0779110	+	0.996960i	$0.524825\pi$
$468$		0			0
$469$	0.417333	+	1.28442i	0.0192706	+	0.0593089i
$470$	−14.7476	+	9.64973i	−0.680254	+	0.445109i
$471$		0			0
$472$			2.71094i			0.124781i
$473$	0.970319	+	17.4682i	0.0446153	+	0.803187i
$474$		0			0
$475$	15.7385	−	36.0167i	0.722134	−	1.65256i
$476$	3.54000	−	10.8950i	0.162256	−	0.499372i
$477$		0			0
$478$	−4.77976	−	6.57877i	−0.218621	−	0.300906i
$479$	−11.6452	+	8.46071i	−0.532081	+	0.386580i	−0.821136	−	0.570733i	$-0.806659\pi$
$479$	−11.6452	+	8.46071i	−0.532081	+	0.386580i	0.289054	+	0.957313i	$0.406659\pi$
$480$		0			0
$481$	0.108749	−	0.334694i	0.00495851	−	0.0152607i
$482$	−1.84051	+	2.53324i	−0.0838327	+	0.115386i
$483$		0			0
$484$	−4.53694	−	10.0208i	−0.206225	−	0.455490i
$485$	2.28318	−	2.83948i	0.103674	−	0.128934i
$486$		0			0
$487$	20.6203	+	6.69995i	0.934396	+	0.303604i	0.736359	−	0.676591i	$-0.236543\pi$
$487$	20.6203	+	6.69995i	0.934396	+	0.303604i	0.198037	+	0.980195i	$0.436543\pi$
$488$	−3.29441	+	1.07042i	−0.149131	+	0.0484555i
$489$		0			0
$490$	−0.487086	+	9.95145i	−0.0220043	+	0.449561i
$491$	8.87015	+	27.2995i	0.400304	+	1.23201i	0.924753	+	0.380568i	$0.124271\pi$
$491$	8.87015	+	27.2995i	0.400304	+	1.23201i	−0.524449	+	0.851442i	$0.675729\pi$
$492$		0			0
$493$	29.7607	−	40.9620i	1.34035	−	1.84484i
$494$	−24.2802			−1.09242
$495$		0			0
$496$	3.83271			0.172094
$497$	13.8787	−	19.1024i	0.622546	−	0.856861i
$498$		0			0
$499$	−4.01880	−	12.3686i	−0.179906	−	0.553694i	0.819917	−	0.572482i	$-0.194019\pi$
$499$	−4.01880	−	12.3686i	−0.179906	−	0.553694i	−0.999823	+	0.0187879i	$0.994019\pi$
$500$	1.86328	+	11.0240i	0.0833283	+	0.493008i
$501$		0			0
$502$	−11.9086	+	3.86934i	−0.531507	+	0.172697i
$503$	20.2810	+	6.58970i	0.904285	+	0.293820i	0.724004	−	0.689795i	$-0.242299\pi$
$503$	20.2810	+	6.58970i	0.904285	+	0.293820i	0.180280	+	0.983615i	$0.442299\pi$
$504$		0			0
$505$	−6.99037	−	5.62084i	−0.311067	−	0.250124i
$506$	−9.44016	−	6.08857i	−0.419666	−	0.270670i
$507$		0			0
$508$	−4.05022	+	5.57465i	−0.179700	+	0.247335i
$509$	−13.1764	+	40.5528i	−0.584034	+	1.79747i	0.0190823	+	0.999818i	$0.493926\pi$
$509$	−13.1764	+	40.5528i	−0.584034	+	1.79747i	−0.603116	+	0.797653i	$0.706074\pi$
$510$		0			0
$511$	16.2593	−	11.8131i	0.719271	−	0.522581i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$		0			0
$514$	−1.13497	+	3.49308i	−0.0500613	+	0.154073i
$515$	−6.12773	+	1.66462i	−0.270020	+	0.0733518i
$516$		0			0
$517$	25.2710	+	6.68662i	1.11142	+	0.294077i
$518$		−	0.181739i		−	0.00798516i
$519$		0			0
$520$	5.77925	−	3.78152i	0.253437	−	0.165831i
$521$	6.85194	+	21.0881i	0.300189	+	0.923886i	0.981429	+	0.191826i	$0.0614409\pi$
$521$	6.85194	+	21.0881i	0.300189	+	0.923886i	−0.681240	+	0.732060i	$0.738559\pi$
$522$		0			0
$523$	9.87255	+	13.5884i	0.431697	+	0.594179i	0.968342	−	0.249629i	$-0.0803085\pi$
$523$	9.87255	+	13.5884i	0.431697	+	0.594179i	−0.536645	+	0.843808i	$0.680309\pi$
$524$	−0.511415	−	1.57397i	−0.0223413	−	0.0687594i
$525$		0			0
$526$	14.6186	+	10.6211i	0.637403	+	0.463100i
$527$		−	27.5263i		−	1.19907i
$528$		0			0
$529$	11.5284			0.501236
$530$	−7.67077	−	28.2374i	−0.333197	−	1.22655i
$531$		0			0
$532$	−11.9252	+	3.87474i	−0.517024	+	0.167991i
$533$	19.7228	+	27.1461i	0.854290	+	1.17583i
$534$		0			0
$535$	−21.2019	−	8.05475i	−0.916636	−	0.348237i
$536$	−0.261639	+	0.805243i	−0.0113011	+	0.0347812i
$537$		0			0
$538$			20.5365i			0.885392i
$539$	11.4555	−	9.33605i	0.493425	−	0.402132i
$540$		0			0
$541$	−29.7967	−	21.6486i	−1.28106	−	0.930745i	−0.281476	−	0.959568i	$-0.590824\pi$
$541$	−29.7967	−	21.6486i	−1.28106	−	0.930745i	−0.999585	+	0.0288233i	$0.990824\pi$
$542$	7.64590	+	2.48430i	0.328419	+	0.106710i
$543$		0			0
$544$	5.81031	−	4.22144i	0.249115	−	0.180993i
$545$	37.1028	+	1.81604i	1.58931	+	0.0777906i
$546$		0			0
$547$	−12.0381	−	3.91143i	−0.514714	−	0.167241i	0.0401310	−	0.999194i	$-0.487222\pi$
$547$	−12.0381	−	3.91143i	−0.514714	−	0.167241i	−0.554845	+	0.831954i	$0.687222\pi$
$548$	5.44871	−	7.49951i	0.232758	−	0.320363i
$549$		0			0
$550$	10.3062	−	12.9916i	0.439459	−	0.553964i
$551$	−55.4195			−2.36095
$552$		0			0
$553$	5.35982	+	1.74151i	0.227923	+	0.0740566i
$554$	−7.12861	−	21.9396i	−0.302866	−	0.932125i
$555$		0			0
$556$	−3.74675	+	2.72217i	−0.158898	+	0.115446i
$557$	−16.5671	+	5.38297i	−0.701969	+	0.228084i	−0.638188	−	0.769880i	$-0.720316\pi$
$557$	−16.5671	+	5.38297i	−0.701969	+	0.228084i	−0.0637811	+	0.997964i	$0.520316\pi$
$558$		0			0
$559$	13.1811	+	9.57660i	0.557499	+	0.405047i
$560$	2.23500	−	2.77957i	0.0944461	−	0.117458i
$561$		0			0
$562$		−	15.6210i		−	0.658934i
$563$	13.4907	−	18.5684i	0.568566	−	0.782564i	−0.423818	−	0.905747i	$-0.639310\pi$
$563$	13.4907	−	18.5684i	0.568566	−	0.782564i	0.992384	+	0.123183i	$0.0393103\pi$
$564$		0			0
$565$	−8.51246	−	3.23395i	−0.358122	−	0.136053i
$566$	9.46335	−	6.87552i	0.397774	−	0.289000i
$567$		0			0
$568$	14.0785	−	4.57440i	0.590722	−	0.191937i
$569$	−3.37831	+	10.3974i	−0.141626	+	0.435880i	−0.996562	−	0.0828538i	$-0.973597\pi$
$569$	−3.37831	+	10.3974i	−0.141626	+	0.435880i	0.854936	+	0.518734i	$0.173597\pi$
$570$		0			0
$571$	−40.1311			−1.67944			−0.839718	−	0.543023i	$-0.817280\pi$
$571$	−40.1311			−1.67944			−0.839718	+	0.543023i	$0.817280\pi$
$572$	−9.90318	−	2.62035i	−0.414073	−	0.109562i
$573$		0			0
$574$	14.0189	+	10.1853i	0.585139	+	0.425128i
$575$	1.65383	−	16.8539i	0.0689695	−	0.702857i
$576$		0			0
$577$	2.82996	+	3.89510i	0.117813	+	0.162155i	0.863850	−	0.503748i	$-0.168046\pi$
$577$	2.82996	+	3.89510i	0.117813	+	0.162155i	−0.746038	+	0.665904i	$0.768046\pi$
$578$	−20.3258	−	27.9760i	−0.845441	−	1.16365i
$579$		0			0
$580$	13.1911	−	8.63130i	0.547731	−	0.358395i
$581$	−8.88446	−	6.45494i	−0.368590	−	0.267796i
$582$		0			0
$583$	−23.5236	+	36.4727i	−0.974249	+	1.51054i
$584$	12.5999			0.521386
$585$		0			0
$586$	5.02234	−	15.4572i	0.207471	−	0.638530i
$587$	12.2061	−	3.96601i	0.503800	−	0.163695i	−0.0460806	−	0.998938i	$-0.514673\pi$
$587$	12.2061	−	3.96601i	0.503800	−	0.163695i	0.549881	+	0.835243i	$0.314673\pi$
$588$		0			0
$589$	−24.3750	+	17.7095i	−1.00435	+	0.729706i
$590$	5.66668	+	2.15281i	0.233293	+	0.0886300i
$591$		0			0
$592$	0.0669711	−	0.0921778i	0.00275250	−	0.00378849i
$593$			22.0348i			0.904862i	0.891799	+	0.452431i	$0.149443\pi$
$593$			22.0348i			0.904862i	−0.891799	+	0.452431i	$0.850557\pi$
$594$		0			0
$595$	−19.9627	−	16.0517i	−0.818391	−	0.658054i
$596$	4.57146	+	3.32136i	0.187254	+	0.136048i
$597$		0			0
$598$	−9.94925	+	3.23271i	−0.406855	+	0.132195i
$599$	12.1174	−	8.80382i	0.495104	−	0.359714i	−0.312040	−	0.950069i	$-0.601012\pi$
$599$	12.1174	−	8.80382i	0.495104	−	0.359714i	0.807144	+	0.590355i	$0.201012\pi$
$600$		0			0
$601$	3.26421	+	10.0462i	0.133150	+	0.409793i	0.995298	−	0.0968639i	$-0.0308812\pi$
$601$	3.26421	+	10.0462i	0.133150	+	0.409793i	−0.862148	+	0.506657i	$0.830881\pi$
$602$	8.00214	+	2.60005i	0.326143	+	0.105970i
$603$		0			0
$604$	−1.46776			−0.0597223
$605$	−24.5494	+	1.52585i	−0.998074	+	0.0620346i
$606$		0			0
$607$	3.11488	−	4.28726i	0.126429	−	0.174015i	−0.741110	−	0.671383i	$-0.765700\pi$
$607$	3.11488	−	4.28726i	0.126429	−	0.174015i	0.867539	+	0.497369i	$0.165700\pi$
$608$	−7.47630	−	2.42920i	−0.303204	−	0.0985169i
$609$		0			0
$610$	−0.378665	+	7.73635i	−0.0153317	+	0.313236i
$611$	19.6948	−	14.3091i	0.796766	−	0.578884i
$612$		0			0
$613$	14.1110	+	4.58495i	0.569939	+	0.185184i	0.579788	−	0.814767i	$-0.303135\pi$
$613$	14.1110	+	4.58495i	0.569939	+	0.185184i	−0.00984944	+	0.999951i	$0.503135\pi$
$614$	17.6730	+	12.8402i	0.713226	+	0.518189i
$615$		0			0
$616$	−5.28210	+	0.293409i	−0.212822	+	0.0118218i
$617$		−	30.2576i		−	1.21812i	−0.793123	−	0.609062i	$-0.791546\pi$
$617$		−	30.2576i		−	1.21812i	0.793123	−	0.609062i	$-0.208454\pi$
$618$		0			0
$619$	−2.37812	+	7.31911i	−0.0955848	+	0.294180i	−0.987406	−	0.158209i	$-0.949428\pi$
$619$	−2.37812	+	7.31911i	−0.0955848	+	0.294180i	0.891821	+	0.452389i	$0.149428\pi$
$620$	3.04364	−	8.01153i	0.122236	−	0.321751i
$621$		0			0
$622$	−12.9278	−	17.7935i	−0.518356	−	0.713456i
$623$	−16.7493	+	5.44217i	−0.671046	+	0.218036i
$624$		0			0
$625$	24.5231	+	4.85958i	0.980926	+	0.194383i
$626$	−7.58302			−0.303078
$627$		0			0
$628$			11.2348i			0.448318i
$629$	−0.662016	−	0.480983i	−0.0263963	−	0.0191780i
$630$		0			0
$631$	0.599553	+	1.84523i	0.0238678	+	0.0734576i	0.962281	−	0.272058i	$-0.0877041\pi$
$631$	0.599553	+	1.84523i	0.0238678	+	0.0734576i	−0.938413	+	0.345515i	$0.887704\pi$
$632$	2.07675	+	2.85840i	0.0826085	+	0.113701i
$633$		0			0
$634$	−2.98403	−	9.18390i	−0.118511	−	0.364739i
$635$	8.43634	+	12.8931i	0.334786	+	0.511649i
$636$		0			0
$637$		−	13.7624i		−	0.545286i
$638$	−22.6039	−	5.98092i	−0.894899	−	0.236787i
$639$		0			0
$640$	2.15786	−	0.586191i	0.0852971	−	0.0231712i
$641$	9.06687	−	27.9050i	0.358120	−	1.10218i	−0.596058	−	0.802941i	$-0.703267\pi$
$641$	9.06687	−	27.9050i	0.358120	−	1.10218i	0.954178	−	0.299239i	$-0.0967327\pi$
$642$		0			0
$643$	−9.13808	−	12.5775i	−0.360371	−	0.496007i	0.589881	−	0.807490i	$-0.299174\pi$
$643$	−9.13808	−	12.5775i	−0.360371	−	0.496007i	−0.950252	+	0.311482i	$0.899174\pi$
$644$	−4.37068	+	3.17548i	−0.172229	+	0.125132i
$645$		0			0
$646$	−17.4463	+	53.6943i	−0.686417	+	2.11258i
$647$	−17.7161	+	24.3842i	−0.696493	+	0.958640i	0.303490	+	0.952835i	$0.401848\pi$
$647$	−17.7161	+	24.3842i	−0.696493	+	0.958640i	−0.999983	+	0.00580579i	$0.998152\pi$
$648$		0			0
$649$	−3.24841	−	8.38384i	−0.127511	−	0.329094i
$650$	−3.31510	−	15.0834i	−0.130029	−	0.591619i
$651$		0			0
$652$	7.24811	+	2.35505i	0.283858	+	0.0922310i
$653$	−27.5016	+	8.93580i	−1.07622	+	0.349685i	−0.792907	−	0.609343i	$-0.791433\pi$
$653$	−27.5016	+	8.93580i	−1.07622	+	0.349685i	−0.283313	+	0.959028i	$0.591433\pi$
$654$		0			0
$655$	−3.69621	−	0.180915i	−0.144423	−	0.00706895i
$656$	3.35707	+	10.3320i	0.131071	+	0.403396i
$657$		0			0
$658$	7.38957	−	10.1709i	0.288076	−	0.396502i
$659$	15.6578			0.609941			0.304970	−	0.952362i	$-0.401353\pi$
$659$	15.6578			0.609941			0.304970	+	0.952362i	$0.401353\pi$
$660$		0			0
$661$	4.58381			0.178289			0.0891447	−	0.996019i	$-0.471587\pi$
$661$	4.58381			0.178289			0.0891447	+	0.996019i	$0.471587\pi$
$662$	−18.5330	+	25.5085i	−0.720307	+	0.991418i
$663$		0			0
$664$	−2.12753	−	6.54787i	−0.0825643	−	0.254107i
$665$	−1.37071	+	28.0043i	−0.0531537	+	1.08596i
$666$		0			0
$667$	−22.7091	+	7.37863i	−0.879300	+	0.285702i
$668$	7.90719	+	2.56920i	0.305938	+	0.0994054i
$669$		0			0
$670$	1.47543	+	1.18637i	0.0570007	+	0.0458333i
$671$	8.90564	−	7.25793i	0.343798	−	0.280189i
$672$		0			0
$673$	−4.50567	+	6.20153i	−0.173681	+	0.239051i	−0.886979	−	0.461809i	$-0.847200\pi$
$673$	−4.50567	+	6.20153i	−0.173681	+	0.239051i	0.713298	+	0.700860i	$0.247200\pi$
$674$	−4.57330	+	14.0752i	−0.176157	+	0.542155i
$675$		0			0
$676$	2.79925	−	2.03378i	0.107664	−	0.0782222i
$677$	10.3141	+	14.1961i	0.396402	+	0.545601i	0.959837	−	0.280560i	$-0.0905201\pi$
$677$	10.3141	+	14.1961i	0.396402	+	0.545601i	−0.563434	+	0.826161i	$0.690520\pi$
$678$		0			0
$679$	−0.803163	+	2.47188i	−0.0308226	+	0.0948622i
$680$	−4.20999	−	15.4977i	−0.161446	−	0.594308i
$681$		0			0
$682$	−11.8530	+	4.59259i	−0.453877	+	0.175859i
$683$			26.1699i			1.00136i	0.865631	+	0.500682i	$0.166918\pi$
$683$			26.1699i			1.00136i	−0.865631	+	0.500682i	$0.833082\pi$
$684$		0			0
$685$	−11.3493	−	17.3450i	−0.433635	−	0.662718i
$686$	−5.64658	−	17.3784i	−0.215588	−	0.663510i
$687$		0			0
$688$	3.10055	+	4.26754i	0.118207	+	0.162699i
$689$	12.4898	+	38.4396i	0.475823	+	1.46443i
$690$		0			0
$691$	−14.2231	−	10.3337i	−0.541072	−	0.393112i	0.283411	−	0.958999i	$-0.408534\pi$
$691$	−14.2231	−	10.3337i	−0.541072	−	0.393112i	−0.824483	+	0.565887i	$0.808534\pi$
$692$		−	7.82571i		−	0.297489i
$693$		0			0
$694$	−2.93578			−0.111441
$695$	2.71479	+	9.99358i	0.102978	+	0.379078i
$696$		0			0
$697$	74.2037	−	24.1103i	2.81067	−	0.913241i
$698$	8.44914	+	11.6292i	0.319805	+	0.440173i
$699$		0			0
$700$	−4.03527	−	6.87915i	−0.152519	−	0.260008i
$701$	15.7781	−	48.5601i	0.595931	−	1.83409i	0.0458967	−	0.998946i	$-0.485385\pi$
$701$	15.7781	−	48.5601i	0.595931	−	1.83409i	0.550035	−	0.835142i	$-0.314615\pi$
$702$		0			0
$703$			0.895672i			0.0337809i
$704$	−2.78720	−	1.79765i	−0.105046	−	0.0677513i
$705$		0			0
$706$	22.4968	+	16.3449i	0.846677	+	0.615147i
$707$	6.08539	+	1.97726i	0.228865	+	0.0743627i
$708$		0			0
$709$	0.429513	−	0.312059i	0.0161307	−	0.0117196i	−0.579691	−	0.814837i	$-0.696827\pi$
$709$	0.429513	−	0.312059i	0.0161307	−	0.0117196i	0.595821	+	0.803117i	$0.296827\pi$
$710$	1.61821	−	33.0611i	0.0607304	−	1.24076i
$711$		0			0
$712$	−10.5007	−	3.41187i	−0.393529	−	0.127865i
$713$	−7.63021	+	10.5021i	−0.285754	+	0.393306i
$714$		0			0
$715$	−13.3417	+	18.6198i	−0.498950	+	0.696340i
$716$	−18.7059			−0.699072
$717$		0			0
$718$	0.979893	+	0.318387i	0.0365693	+	0.0118821i
$719$	−2.56495	−	7.89412i	−0.0956566	−	0.294401i	0.891768	−	0.452494i	$-0.149465\pi$
$719$	−2.56495	−	7.89412i	−0.0956566	−	0.294401i	−0.987424	+	0.158093i	$0.949465\pi$
$720$		0			0
$721$	3.66448	−	2.66240i	0.136472	−	0.0991530i
$722$	40.7015	−	13.2247i	1.51475	−	0.492172i
$723$		0			0
$724$	−3.59193	−	2.60969i	−0.133493	−	0.0969885i
$725$	−7.56668	−	34.4277i	−0.281020	−	1.27861i
$726$		0			0
$727$			37.1595i			1.37817i	0.724681	+	0.689084i	$0.241987\pi$
$727$			37.1595i			1.37817i	−0.724681	+	0.689084i	$0.758013\pi$
$728$	−2.89582	+	3.98575i	−0.107326	+	0.147722i
$729$		0			0
$730$	10.0058	−	26.3375i	0.370332	−	0.974795i
$731$	30.6492	−	22.2680i	1.13360	−	0.823611i
$732$		0			0
$733$	−17.6297	+	5.72823i	−0.651167	+	0.211577i	−0.615928	−	0.787802i	$-0.711219\pi$
$733$	−17.6297	+	5.72823i	−0.651167	+	0.211577i	−0.0352381	+	0.999379i	$0.511219\pi$
$734$	−0.469215	+	1.44410i	−0.0173191	+	0.0533026i
$735$		0			0
$736$	−3.38697			−0.124845
$737$	−0.155745	−	2.80380i	−0.00573695	−	0.103279i
$738$		0			0
$739$	34.5945	+	25.1344i	1.27258	+	0.924583i	0.999302	−	0.0373528i	$-0.0118925\pi$
$739$	34.5945	+	25.1344i	1.27258	+	0.924583i	0.273277	+	0.961935i	$0.411893\pi$
$740$	−0.139496	−	0.213190i	−0.00512799	−	0.00783704i
$741$		0			0
$742$	12.2687	+	16.8864i	0.450398	+	0.619920i
$743$	−23.7030	−	32.6244i	−0.869579	−	1.19687i	−0.979200	−	0.202899i	$-0.934964\pi$
$743$	−23.7030	−	32.6244i	−0.869579	−	1.19687i	0.109621	−	0.993973i	$-0.465036\pi$
$744$		0			0
$745$	10.5729	−	6.91817i	0.387363	−	0.253462i
$746$	2.78719	+	2.02501i	0.102046	+	0.0741411i
$747$		0			0
$748$	−12.9106	+	20.0175i	−0.472058	+	0.731912i
$749$	16.1787			0.591158
$750$		0			0
$751$	2.97952	−	9.17002i	0.108724	−	0.334619i	−0.881862	−	0.471507i	$-0.843710\pi$
$751$	2.97952	−	9.17002i	0.108724	−	0.334619i	0.990586	+	0.136888i	$0.0437101\pi$
$752$	7.49596	−	2.43559i	0.273350	−	0.0888167i
$753$		0			0
$754$	−17.6162	+	12.7989i	−0.641544	+	0.466109i
$755$	−1.16558	+	3.06806i	−0.0424198	+	0.111658i
$756$		0			0
$757$	−19.3024	+	26.5674i	−0.701557	+	0.965610i	0.298381	+	0.954447i	$0.403553\pi$
$757$	−19.3024	+	26.5674i	−0.701557	+	0.965610i	−0.999938	+	0.0111630i	$0.996447\pi$
$758$			15.5510i			0.564839i
$759$		0			0
$760$	−11.0149	+	13.6987i	−0.399551	+	0.496902i
$761$	24.6628	+	17.9186i	0.894027	+	0.649549i	0.936925	−	0.349531i	$-0.113659\pi$
$761$	24.6628	+	17.9186i	0.894027	+	0.649549i	−0.0428976	+	0.999079i	$0.513659\pi$
$762$		0			0
$763$	−25.2015	+	8.18848i	−0.912357	+	0.296443i
$764$	−8.35789	+	6.07236i	−0.302378	+	0.219690i
$765$		0			0
$766$	4.84719	+	14.9181i	0.175136	+	0.539014i
$767$	−7.96339	−	2.58746i	−0.287541	−	0.0934279i
$768$		0			0
$769$	21.5091			0.775639			0.387819	−	0.921735i	$-0.373228\pi$
$769$	21.5091			0.775639			0.387819	+	0.921735i	$0.373228\pi$
$770$	−3.58132	+	11.2742i	−0.129062	+	0.406294i
$771$		0			0
$772$	−1.89861	+	2.61321i	−0.0683324	+	0.0940515i
$773$	−22.1692	−	7.20320i	−0.797369	−	0.259081i	−0.118130	−	0.992998i	$-0.537690\pi$
$773$	−22.1692	−	7.20320i	−0.797369	−	0.259081i	−0.679239	+	0.733917i	$0.737690\pi$
$774$		0			0
$775$	−14.3295	−	12.7243i	−0.514731	−	0.457070i
$776$	−1.31826	+	0.957769i	−0.0473226	+	0.0343819i
$777$		0			0
$778$	27.0731	+	8.79657i	0.970616	+	0.315372i
$779$	−69.0900	−	50.1969i	−2.47541	−	1.79849i
$780$		0			0
$781$	−38.0580	+	31.0165i	−1.36182	+	1.10986i
$782$			24.3250i			0.869861i
$783$		0			0
$784$	1.37690	−	4.23767i	0.0491751	−	0.151345i
$785$	23.4842	+	8.92183i	0.838187	+	0.318434i
$786$		0			0
$787$	21.8340	+	30.0520i	0.778299	+	1.07124i	0.995467	+	0.0951025i	$0.0303179\pi$
$787$	21.8340	+	30.0520i	0.778299	+	1.07124i	−0.217169	+	0.976134i	$0.569682\pi$
$788$	2.90391	−	0.943537i	0.103447	−	0.0336121i
$789$		0			0
$790$	7.62410	−	2.07111i	0.271253	−	0.0736869i
$791$	6.49569			0.230960
$792$		0			0
$793$		−	10.6990i		−	0.379933i
$794$	−11.2376	−	8.16462i	−0.398809	−	0.289751i
$795$		0			0
$796$	−1.05987	−	3.26195i	−0.0375662	−	0.115617i
$797$	6.96155	+	9.58176i	0.246591	+	0.339403i	0.914314	−	0.405007i	$-0.132731\pi$
$797$	6.96155	+	9.58176i	0.246591	+	0.339403i	−0.667723	+	0.744410i	$0.732731\pi$
$798$		0			0
$799$	−17.4922	−	53.8356i	−0.618831	−	1.90457i
$800$	0.488292	−	4.97610i	0.0172637	−	0.175932i
$801$		0			0
$802$		−	16.5762i		−	0.585325i
$803$	−38.9663	+	15.0979i	−1.37509	+	0.532794i
$804$		0			0
$805$	3.16687	+	11.6578i	0.111618	+	0.410882i
$806$	−3.65815	+	11.2586i	−0.128853	+	0.396568i
$807$		0			0
$808$	2.35788	+	3.24534i	0.0829499	+	0.114171i
$809$	27.3999	−	19.9072i	0.963330	−	0.699900i	0.00940804	−	0.999956i	$-0.497005\pi$
$809$	27.3999	−	19.9072i	0.963330	−	0.699900i	0.953922	+	0.300056i	$0.0970053\pi$
$810$		0			0
$811$	−5.10014	+	15.6966i	−0.179090	+	0.551182i	−0.999797	−	0.0201674i	$-0.993580\pi$
$811$	−5.10014	+	15.6966i	−0.179090	+	0.551182i	0.820707	+	0.571350i	$0.193580\pi$
$812$	−6.60968	+	9.09744i	−0.231954	+	0.319258i
$813$		0			0
$814$	−0.0966618	+	0.365318i	−0.00338799	+	0.0128044i
$815$	10.6787	−	13.2805i	0.374057	−	0.465197i
$816$		0			0
$817$	−39.4373	−	12.8139i	−1.37974	−	0.448303i
$818$	5.07486	−	1.64892i	0.177438	−	0.0576533i
$819$		0			0
$820$	24.2629	+	1.18758i	0.847298	+	0.0414720i
$821$	−10.2401	−	31.5158i	−0.357382	−	1.09991i	−0.954615	−	0.297842i	$-0.903733\pi$
$821$	−10.2401	−	31.5158i	−0.357382	−	1.09991i	0.597233	−	0.802068i	$-0.296267\pi$
$822$		0			0
$823$	−9.70984	+	13.3644i	−0.338464	+	0.465855i	−0.943992	−	0.329968i	$-0.892962\pi$
$823$	−9.70984	+	13.3644i	−0.338464	+	0.465855i	0.605528	+	0.795824i	$0.292962\pi$
$824$	2.83972			0.0989263
$825$		0			0
$826$	−4.32413			−0.150456
$827$	13.3414	−	18.3628i	0.463924	−	0.638537i	−0.511393	−	0.859347i	$-0.670870\pi$
$827$	13.3414	−	18.3628i	0.463924	−	0.638537i	0.975317	+	0.220810i	$0.0708702\pi$
$828$		0			0
$829$	−4.48511	−	13.8038i	−0.155774	−	0.479424i	0.842464	−	0.538752i	$-0.181104\pi$
$829$	−4.48511	−	13.8038i	−0.155774	−	0.479424i	−0.998239	+	0.0593282i	$0.981104\pi$
$830$	−15.3766	−	0.752624i	−0.533728	−	0.0261240i
$831$		0			0
$832$	−2.93751	+	0.954454i	−0.101840	+	0.0330897i
$833$	−30.4347	−	9.88884i	−1.05450	−	0.342628i
$834$		0			0
$835$	11.6497	−	14.4882i	0.403154	−	0.501384i
$836$	26.0320	−	1.44602i	0.900336	−	0.0500117i
$837$		0			0
$838$	−21.4884	+	29.5763i	−0.742305	+	1.02170i
$839$	−7.55580	+	23.2544i	−0.260855	+	0.802830i	0.731764	+	0.681558i	$0.238697\pi$
$839$	−7.55580	+	23.2544i	−0.260855	+	0.802830i	−0.992619	+	0.121272i	$0.961303\pi$
$840$		0			0
$841$	−16.7474	+	12.1677i	−0.577495	+	0.419575i
$842$	21.5799	+	29.7022i	0.743693	+	1.02361i
$843$		0			0
$844$	−6.48423	+	19.9564i	−0.223196	+	0.686927i
$845$	−2.02826	−	7.46636i	−0.0697743	−	0.256851i
$846$		0			0
$847$	15.9839	−	7.23674i	0.549212	−	0.248657i
$848$			13.0858i			0.449368i
$849$		0			0
$850$	−35.7381	−	3.50689i	−1.22581	−	0.120285i
$851$	0.119251	+	0.367017i	0.00408788	+	0.0125812i
$852$		0			0
$853$	−27.3396	−	37.6297i	−0.936089	−	1.28842i	−0.957437	−	0.288643i	$-0.906796\pi$
$853$	−27.3396	−	37.6297i	−0.936089	−	1.28842i	0.0213482	−	0.999772i	$-0.493204\pi$
$854$	−1.70739	−	5.25481i	−0.0584257	−	0.179816i
$855$		0			0
$856$	8.20582	+	5.96188i	0.280469	+	0.203773i
$857$		−	29.5687i		−	1.01005i	−0.863105	−	0.505025i	$-0.831483\pi$
$857$		−	29.5687i		−	1.01005i	0.863105	−	0.505025i	$-0.168517\pi$
$858$		0			0
$859$	4.06703			0.138765			0.0693827	−	0.997590i	$-0.477897\pi$
$859$	4.06703			0.138765			0.0693827	+	0.997590i	$0.477897\pi$
$860$	11.3827	−	3.09214i	0.388146	−	0.105441i
$861$		0			0
$862$	1.74092	−	0.565659i	0.0592960	−	0.0192664i
$863$	−17.9725	−	24.7370i	−0.611792	−	0.842059i	0.384932	−	0.922945i	$-0.374225\pi$
$863$	−17.9725	−	24.7370i	−0.611792	−	0.842059i	−0.996723	+	0.0808861i	$0.974225\pi$
$864$		0			0
$865$	−16.3581	−	6.21458i	−0.556193	−	0.211302i
$866$	−0.637830	+	1.96304i	−0.0216744	+	0.0667068i
$867$		0			0
$868$			6.11344i			0.207504i
$869$	−9.84764	−	6.35139i	−0.334058	−	0.215456i
$870$		0			0
$871$	−2.11568	−	1.53713i	−0.0716872	−	0.0520838i
$872$	−15.7996	−	5.13362i	−0.535044	−	0.173846i
$873$		0			0
$874$	21.5402	−	15.6499i	0.728608	−	0.529365i
$875$	−17.5840	+	2.97206i	−0.594448	+	0.100474i
$876$		0			0
$877$	−9.86823	−	3.20638i	−0.333226	−	0.108272i	0.137625	−	0.990484i	$-0.456053\pi$
$877$	−9.86823	−	3.20638i	−0.333226	−	0.108272i	−0.470851	+	0.882213i	$0.656053\pi$
$878$	−12.0761	+	16.6213i	−0.407548	+	0.560942i
$879$		0			0
$880$	−5.97100	+	4.39854i	−0.201282	+	0.148275i
$881$	−53.8606			−1.81461			−0.907305	−	0.420472i	$-0.861864\pi$
$881$	−53.8606			−1.81461			−0.907305	+	0.420472i	$0.861864\pi$
$882$		0			0
$883$	43.3238	+	14.0768i	1.45796	+	0.473721i	0.927447	−	0.373954i	$-0.121998\pi$
$883$	43.3238	+	14.0768i	1.45796	+	0.473721i	0.530516	+	0.847675i	$0.321998\pi$
$884$	6.85483	+	21.0970i	0.230553	+	0.709569i
$885$		0			0
$886$	−6.89630	+	5.01045i	−0.231686	+	0.168329i
$887$	0.816383	−	0.265259i	0.0274115	−	0.00890653i	−0.295279	−	0.955411i	$-0.595413\pi$
$887$	0.816383	−	0.265259i	0.0274115	−	0.00890653i	0.322691	+	0.946504i	$0.395413\pi$
$888$		0			0
$889$	−8.89196	−	6.46038i	−0.298227	−	0.216674i
$890$	−15.4707	+	19.2401i	−0.518578	+	0.644931i
$891$		0			0
$892$		−	12.3641i		−	0.413981i
$893$	−36.4183	+	50.1255i	−1.21869	+	1.67739i
$894$		0			0
$895$	−14.8548	+	39.1010i	−0.496540	+	1.30700i
$896$	−1.29044	+	0.937558i	−0.0431105	+	0.0313216i
$897$		0			0
$898$	16.4094	−	5.33174i	0.547589	−	0.177923i
$899$	−8.34970	+	25.6977i	−0.278478	+	0.857067i
$900$		0			0
$901$	93.9814			3.13097
$902$	−22.7625	−	27.9301i	−0.757907	−	0.929969i
$903$		0			0
$904$	3.29461	+	2.39367i	0.109577	+	0.0796123i
$905$	−8.30749	+	5.43582i	−0.276150	+	0.180693i
$906$		0			0
$907$	−26.5459	−	36.5372i	−0.881441	−	1.21320i	−0.976020	−	0.217682i	$-0.930150\pi$
$907$	−26.5459	−	36.5372i	−0.881441	−	1.21320i	0.0945788	−	0.995517i	$-0.469850\pi$
$908$	13.0173	+	17.9168i	0.431994	+	0.594589i
$909$		0			0
$910$	6.03179	+	9.21831i	0.199952	+	0.305584i
$911$	−2.57442	−	1.87043i	−0.0852944	−	0.0619700i	0.544321	−	0.838877i	$-0.316787\pi$
$911$	−2.57442	−	1.87043i	−0.0852944	−	0.0619700i	−0.629615	+	0.776907i	$0.716787\pi$
$912$		0			0
$913$	14.4257	+	17.7006i	0.477420	+	0.585804i
$914$	−4.86397			−0.160886
$915$		0			0
$916$	0.763708	−	2.35045i	0.0252336	−	0.0776611i
$917$	2.51060	−	0.815743i	0.0829072	−	0.0269382i
$918$		0			0
$919$	−9.65072	+	7.01166i	−0.318348	+	0.231293i	−0.735470	−	0.677557i	$-0.763039\pi$
$919$	−9.65072	+	7.01166i	−0.318348	+	0.231293i	0.417122	+	0.908850i	$0.363039\pi$
$920$	−2.68967	+	7.07980i	−0.0886758	+	0.233414i
$921$		0			0
$922$	4.69177	−	6.45767i	0.154515	−	0.212672i
$923$			45.7219i			1.50495i
$924$		0			0
$925$	−0.556410	+	0.122290i	−0.0182947	+	0.00402088i
$926$	28.9704	+	21.0482i	0.952027	+	0.691688i
$927$		0			0
$928$	−6.70484	+	2.17853i	−0.220097	+	0.0715139i
$929$	5.38253	−	3.91064i	0.176595	−	0.128304i	−0.495976	−	0.868336i	$-0.665190\pi$
$929$	5.38253	−	3.91064i	0.176595	−	0.128304i	0.672571	+	0.740032i	$0.265190\pi$
$930$		0			0
$931$	10.8239	+	33.3125i	0.354739	+	1.09177i
$932$	26.9688	+	8.76271i	0.883394	+	0.287032i
$933$		0			0
$934$	−32.8805			−1.07588
$935$	31.5900	+	42.8834i	1.03310	+	1.40244i
$936$		0			0
$937$	−16.3583	+	22.5152i	−0.534401	+	0.735540i	−0.987793	−	0.155771i	$-0.950214\pi$
$937$	−16.3583	+	22.5152i	−0.534401	+	0.735540i	0.453392	+	0.891311i	$0.350214\pi$
$938$	−1.28442	−	0.417333i	−0.0419377	−	0.0136264i
$939$		0			0
$940$	0.861599	−	17.6030i	0.0281023	−	0.574146i
$941$	27.7448	−	20.1578i	0.904455	−	0.657125i	−0.0351517	−	0.999382i	$-0.511191\pi$
$941$	27.7448	−	20.1578i	0.904455	−	0.657125i	0.939606	+	0.342257i	$0.111191\pi$
$942$		0			0
$943$	−34.9941	−	11.3703i	−1.13957	−	0.370267i
$944$	−2.19319	−	1.59345i	−0.0713823	−	0.0518623i
$945$		0			0
$946$	−14.7024	−	9.48253i	−0.478016	−	0.308304i
$947$			27.0026i			0.877466i	0.898617	+	0.438733i	$0.144573\pi$
$947$			27.0026i			0.877466i	−0.898617	+	0.438733i	$0.855427\pi$
$948$		0			0
$949$	−12.0260	+	37.0122i	−0.390380	+	1.20147i
$950$	19.8872	+	33.9028i	0.645226	+	1.09995i
$951$		0			0
$952$	6.73349	+	9.26785i	0.218234	+	0.300373i
$953$	15.5840	−	5.06354i	0.504814	−	0.164024i	−0.0455284	−	0.998963i	$-0.514497\pi$
$953$	15.5840	−	5.06354i	0.504814	−	0.164024i	0.550342	+	0.834939i	$0.314497\pi$
$954$		0			0
$955$	6.05589	+	22.2927i	0.195964	+	0.721376i
$956$	8.13181			0.263002
$957$		0			0
$958$		−	14.3942i		−	0.465056i
$959$	11.9622	+	8.69108i	0.386281	+	0.280650i
$960$		0			0
$961$	−5.04016	−	15.5120i	−0.162586	−	0.500388i
$962$	0.206852	+	0.284708i	0.00666918	+	0.00917934i
$963$		0			0
$964$	−0.967611	−	2.97800i	−0.0311646	−	0.0959149i
$965$	3.95467	+	6.04388i	0.127305	+	0.194559i
$966$		0			0
$967$		−	47.3726i		−	1.52340i	−0.647930	−	0.761700i	$-0.724365\pi$
$967$		−	47.3726i		−	1.52340i	0.647930	−	0.761700i	$-0.275635\pi$
$968$	10.7737	+	2.21961i	0.346281	+	0.0713409i
$969$		0			0
$970$	0.955171	+	3.51614i	0.0306687	+	0.112896i
$971$	−17.1803	+	52.8754i	−0.551341	+	1.69685i	0.154076	+	0.988059i	$0.450760\pi$
$971$	−17.1803	+	52.8754i	−0.551341	+	1.69685i	−0.705416	+	0.708793i	$0.749240\pi$
$972$		0			0
$973$	−4.34206	−	5.97633i	−0.139200	−	0.191592i
$974$	−17.5407	+	12.7441i	−0.562040	+	0.408346i
$975$		0			0
$976$	1.07042	−	3.29441i	0.0342632	−	0.105451i
$977$	−5.92739	+	8.15835i	−0.189634	+	0.261009i	−0.893239	−	0.449583i	$-0.851573\pi$
$977$	−5.92739	+	8.15835i	−0.189634	+	0.261009i	0.703605	+	0.710592i	$0.251573\pi$
$978$		0			0
$979$	36.5627	−	2.03098i	1.16855	−	0.0649103i
$980$	−7.76459	−	6.24338i	−0.248031	−	0.199437i
$981$		0			0
$982$	−27.2995	−	8.87015i	−0.871162	−	0.283058i
$983$	23.3479	−	7.58618i	0.744681	−	0.241962i	0.0879902	−	0.996121i	$-0.471956\pi$
$983$	23.3479	−	7.58618i	0.744681	−	0.241962i	0.656691	+	0.754160i	$0.271956\pi$
$984$		0			0
$985$	0.333780	−	6.81933i	0.0106351	−	0.217282i
$986$	15.6461	+	48.1538i	0.498273	+	1.53353i
$987$		0			0
$988$	14.2716	−	19.6431i	0.454039	−	0.624931i
$989$	−17.8662			−0.568111
$990$		0			0
$991$	−46.5618			−1.47908			−0.739541	−	0.673111i	$-0.764958\pi$
$991$	−46.5618			−1.47908			−0.739541	+	0.673111i	$0.764958\pi$
$992$	−2.25281	+	3.10073i	−0.0715269	+	0.0984483i
$993$		0			0
$994$	7.29648	+	22.4563i	0.231430	+	0.712269i
$995$	−7.66013	−	0.374934i	−0.242843	−	0.0118862i
$996$		0			0
$997$	−26.1266	+	8.48904i	−0.827437	+	0.268851i	−0.691965	−	0.721931i	$-0.743255\pi$
$997$	−26.1266	+	8.48904i	−0.827437	+	0.268851i	−0.135472	+	0.990781i	$0.543255\pi$
$998$	12.3686	+	4.01880i	0.391521	+	0.127213i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.ba.i.829.1		32
3.2	odd	2		330.2.s.c.169.8	yes	32
5.4	even	2	inner	990.2.ba.i.829.6		32
11.3	even	5	inner	990.2.ba.i.289.6		32
15.14	odd	2		330.2.s.c.169.3	✓	32
33.14	odd	10		330.2.s.c.289.3	yes	32
55.14	even	10	inner	990.2.ba.i.289.1		32
165.14	odd	10		330.2.s.c.289.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.s.c.169.3	✓	32	15.14	odd	2
330.2.s.c.169.8	yes	32	3.2	odd	2
330.2.s.c.289.3	yes	32	33.14	odd	10
330.2.s.c.289.8	yes	32	165.14	odd	10
990.2.ba.i.289.1		32	55.14	even	10	inner
990.2.ba.i.289.6		32	11.3	even	5	inner
990.2.ba.i.829.1		32	1.1	even	1	trivial
990.2.ba.i.829.6		32	5.4	even	2	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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(-2.23339 - 0.109316i) q^{5} +(1.51700 - 0.492904i) q^{7} +(0.951057 + 0.309017i) q^{8} +(1.40119 - 1.74260i) q^{10} +(-3.31152 + 0.183948i) q^{11} +(-1.81548 + 2.49879i) q^{13} +(-0.492904 + 1.51700i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(4.22144 + 5.81031i) q^{17} +(2.42920 - 7.47630i) q^{19} +(0.586191 + 2.15786i) q^{20} +(1.79765 - 2.78720i) q^{22} -3.38697i q^{23} +(4.97610 + 0.488292i) q^{25} +(-0.954454 - 2.93751i) q^{26} +(-0.937558 - 1.29044i) q^{28} +(-2.17853 - 6.70484i) q^{29} +(-3.10073 - 2.25281i) q^{31} -1.00000i q^{32} -7.18194 q^{34} +(-3.44194 + 0.935015i) q^{35} +(-0.108362 + 0.0352088i) q^{37} +(4.62061 + 6.35972i) q^{38} +(-2.09030 - 0.794123i) q^{40} +(3.35707 - 10.3320i) q^{41} -5.27497i q^{43} +(1.19826 + 3.09260i) q^{44} +(2.74012 + 1.99081i) q^{46} +(-7.49596 - 2.43559i) q^{47} +(-3.60478 + 2.61903i) q^{49} +(-3.31991 + 3.73874i) q^{50} +(2.93751 + 0.954454i) q^{52} +(7.69164 - 10.5866i) q^{53} +(7.41604 - 0.0488253i) q^{55} +1.59507 q^{56} +(6.70484 + 2.17853i) q^{58} +(0.837725 + 2.57825i) q^{59} +(-2.80239 + 2.03606i) q^{61} +(3.64513 - 1.18437i) q^{62} +(0.809017 + 0.587785i) q^{64} +(4.32784 - 5.38233i) q^{65} +0.846682i q^{67} +(4.22144 - 5.81031i) q^{68} +(1.26668 - 3.33418i) q^{70} +(11.9759 - 8.70102i) q^{71} +(11.9832 - 3.89357i) q^{73} +(0.0352088 - 0.108362i) q^{74} -7.86105 q^{76} +(-4.93291 + 1.91131i) q^{77} +(2.85840 + 2.07675i) q^{79} +(1.87111 - 1.22432i) q^{80} +(6.38552 + 8.78891i) q^{82} +(-4.04681 - 5.56995i) q^{83} +(-8.79298 - 13.4382i) q^{85} +(4.26754 + 3.10055i) q^{86} +(-3.20629 - 0.848371i) q^{88} -11.0410 q^{89} +(-1.52242 + 4.68553i) q^{91} +(-3.22120 + 1.04663i) q^{92} +(6.37645 - 4.63276i) q^{94} +(-6.24263 + 16.4320i) q^{95} +(-0.957769 + 1.31826i) q^{97} -4.45575i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} + 2 q^{5} + 4 q^{10} - 10 q^{14} - 8 q^{16} + 20 q^{19} - 2 q^{20} + 4 q^{25} + 2 q^{26} - 2 q^{29} - 24 q^{31} - 28 q^{34} - 44 q^{35} - 4 q^{40} + 34 q^{41} + 20 q^{44} - 38 q^{46} + 14 q^{49}+ \cdots + 60 q^{95}+O(q^{100}) \) 32 * q + 8 * q^4 + 2 * q^5 + 4 * q^10 - 10 * q^14 - 8 * q^16 + 20 * q^19 - 2 * q^20 + 4 * q^25 + 2 * q^26 - 2 * q^29 - 24 * q^31 - 28 * q^34 - 44 * q^35 - 4 * q^40 + 34 * q^41 + 20 * q^44 - 38 * q^46 + 14 * q^49 + 24 * q^50 + 28 * q^55 - 20 * q^56 + 4 * q^59 - 8 * q^61 + 8 * q^64 + 44 * q^65 - 10 * q^70 - 8 * q^71 - 20 * q^74 + 20 * q^76 + 2 * q^79 + 2 * q^80 - 20 * q^85 - 34 * q^86 + 132 * q^89 + 78 * q^91 + 22 * q^94 + 60 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more