LMFDB - Embedded newform 980.2.bd.a.169.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(29,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 7, 6]))

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

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

chi := DirichletCharacter("980.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.bd (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$28$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			169.14
Character	$\chi$	$=$	980.169
Dual form			980.2.bd.a.29.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.332725 - 0.0759423i) q^{3} +(-2.22696 - 0.201644i) q^{5} +(2.62035 - 0.365762i) q^{7} +(-2.59797 - 1.25112i) q^{9} +(-2.15292 + 1.03679i) q^{11} +(2.62135 + 5.44329i) q^{13} +(0.725651 + 0.236212i) q^{15} +(4.75577 - 3.79260i) q^{17} -5.33478 q^{19} +(-0.899631 - 0.0772969i) q^{21} +(5.09974 + 4.06691i) q^{23} +(4.91868 + 0.898104i) q^{25} +(1.56987 + 1.25193i) q^{27} +(1.23433 + 1.54780i) q^{29} +7.15404 q^{31} +(0.795064 - 0.181468i) q^{33} +(-5.90915 + 0.286160i) q^{35} +(-4.79848 + 3.82666i) q^{37} +(-0.458813 - 2.01019i) q^{39} +(0.899666 - 3.94169i) q^{41} +(6.77863 - 1.54718i) q^{43} +(5.53328 + 3.31005i) q^{45} +(-0.788580 - 1.63750i) q^{47} +(6.73244 - 1.91685i) q^{49} +(-1.87038 + 0.900727i) q^{51} +(3.31926 + 2.64702i) q^{53} +(5.00351 - 1.87476i) q^{55} +(1.77501 + 0.405135i) q^{57} +(2.13782 + 9.36639i) q^{59} +(8.60315 + 10.7880i) q^{61} +(-7.26519 - 2.32812i) q^{63} +(-4.74003 - 12.6506i) q^{65} +8.80941i q^{67} +(-1.38796 - 1.74045i) q^{69} +(-4.00099 + 5.01708i) q^{71} +(-0.989387 + 2.05448i) q^{73} +(-1.56836 - 0.672357i) q^{75} +(-5.26217 + 3.50420i) q^{77} +2.15058 q^{79} +(4.96629 + 6.22753i) q^{81} +(7.68593 - 15.9600i) q^{83} +(-11.3556 + 7.48698i) q^{85} +(-0.293148 - 0.608728i) q^{87} +(-15.5807 - 7.50326i) q^{89} +(8.85980 + 13.3045i) q^{91} +(-2.38033 - 0.543294i) q^{93} +(11.8803 + 1.07572i) q^{95} +9.31644i q^{97} +6.89035 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 2 q^{5} + 18 q^{9} + 6 q^{11} + 16 q^{15} + 20 q^{19} - 6 q^{21} + 6 q^{25} - 14 q^{29} + 20 q^{31} + 2 q^{35} + 40 q^{39} - 14 q^{41} + 96 q^{45} + 32 q^{49} + 4 q^{51} - 30 q^{55} - 28 q^{59}+ \cdots + 136 q^{99}+O(q^{100}) $ 168 * q + 2 * q^5 + 18 * q^9 + 6 * q^11 + 16 * q^15 + 20 * q^19 - 6 * q^21 + 6 * q^25 - 14 * q^29 + 20 * q^31 + 2 * q^35 + 40 * q^39 - 14 * q^41 + 96 * q^45 + 32 * q^49 + 4 * q^51 - 30 * q^55 - 28 * q^59 - 16 * q^61 - 20 * q^65 + 12 * q^69 + 34 * q^71 - 24 * q^75 - 24 * q^79 - 62 * q^81 - 42 * q^85 - 74 * q^89 + 60 * q^91 - 10 * q^95 + 136 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{4}{7}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.332725	−	0.0759423i	−0.192099	−	0.0438453i	0.125389	−	0.992108i	$-0.459982\pi$
$3$	−0.332725	−	0.0759423i	−0.192099	−	0.0438453i	−0.317488	+	0.948262i	$0.602839\pi$
$4$		0			0
$5$	−2.22696	−	0.201644i	−0.995926	−	0.0901779i
$5$	−2.22696	−	0.201644i	−0.995926	−	0.0901779i
$6$		0			0
$7$	2.62035	−	0.365762i	0.990398	−	0.138245i
$7$	2.62035	−	0.365762i	0.990398	−	0.138245i
$8$		0			0
$9$	−2.59797	−	1.25112i	−0.865989	−	0.417038i
$10$		0			0
$11$	−2.15292	+	1.03679i	−0.649128	+	0.312604i	−0.729317	−	0.684176i	$-0.760162\pi$
$11$	−2.15292	+	1.03679i	−0.649128	+	0.312604i	0.0801886	+	0.996780i	$0.474448\pi$
$12$		0			0
$13$	2.62135	+	5.44329i	0.727032	+	1.50970i	0.855398	+	0.517971i	$0.173312\pi$
$13$	2.62135	+	5.44329i	0.727032	+	1.50970i	−0.128366	+	0.991727i	$0.540973\pi$
$14$		0			0
$15$	0.725651	+	0.236212i	0.187362	+	0.0609897i
$16$		0			0
$17$	4.75577	−	3.79260i	1.15344	−	0.919840i	0.155754	−	0.987796i	$-0.450219\pi$
$17$	4.75577	−	3.79260i	1.15344	−	0.919840i	0.997688	+	0.0679561i	$0.0216478\pi$
$18$		0			0
$19$	−5.33478			−1.22388			−0.611941	−	0.790904i	$-0.709611\pi$
$19$	−5.33478			−1.22388			−0.611941	+	0.790904i	$0.709611\pi$
$20$		0			0
$21$	−0.899631	−	0.0772969i	−0.196316	−	0.0168676i
$22$		0			0
$23$	5.09974	+	4.06691i	1.06337	+	0.848009i	0.988806	−	0.149207i	$-0.0476721\pi$
$23$	5.09974	+	4.06691i	1.06337	+	0.848009i	0.0745638	+	0.997216i	$0.476244\pi$
$24$		0			0
$25$	4.91868	+	0.898104i	0.983736	+	0.179621i
$26$		0			0
$27$	1.56987	+	1.25193i	0.302121	+	0.240934i
$28$		0			0
$29$	1.23433	+	1.54780i	0.229209	+	0.287419i	0.883115	−	0.469157i	$-0.155442\pi$
$29$	1.23433	+	1.54780i	0.229209	+	0.287419i	−0.653906	+	0.756576i	$0.726871\pi$
$30$		0			0
$31$	7.15404			1.28490			0.642452	−	0.766326i	$-0.277917\pi$
$31$	7.15404			1.28490			0.642452	+	0.766326i	$0.277917\pi$
$32$		0			0
$33$	0.795064	−	0.181468i	0.138403	−	0.0315896i
$34$		0			0
$35$	−5.90915	+	0.286160i	−0.998829	+	0.0483699i
$36$		0			0
$37$	−4.79848	+	3.82666i	−0.788865	+	0.629099i	−0.932761	−	0.360494i	$-0.882608\pi$
$37$	−4.79848	+	3.82666i	−0.788865	+	0.629099i	0.143897	+	0.989593i	$0.454037\pi$
$38$		0			0
$39$	−0.458813	−	2.01019i	−0.0734688	−	0.321888i
$40$		0			0
$41$	0.899666	−	3.94169i	0.140504	−	0.615589i	−0.854814	−	0.518935i	$-0.826329\pi$
$41$	0.899666	−	3.94169i	0.140504	−	0.615589i	0.995318	−	0.0966544i	$-0.0308142\pi$
$42$		0			0
$43$	6.77863	−	1.54718i	1.03373	−	0.235943i	0.328191	−	0.944611i	$-0.393561\pi$
$43$	6.77863	−	1.54718i	1.03373	−	0.235943i	0.705541	+	0.708669i	$0.250704\pi$
$44$		0			0
$45$	5.53328	+	3.31005i	0.824853	+	0.493432i
$46$		0			0
$47$	−0.788580	−	1.63750i	−0.115026	−	0.238854i	0.835505	−	0.549482i	$-0.185175\pi$
$47$	−0.788580	−	1.63750i	−0.115026	−	0.238854i	−0.950532	+	0.310628i	$0.899461\pi$
$48$		0			0
$49$	6.73244	−	1.91685i	0.961777	−	0.273835i
$50$		0			0
$51$	−1.87038	+	0.900727i	−0.261905	+	0.126127i
$52$		0			0
$53$	3.31926	+	2.64702i	0.455935	+	0.363596i	0.824364	−	0.566060i	$-0.191533\pi$
$53$	3.31926	+	2.64702i	0.455935	+	0.363596i	−0.368429	+	0.929656i	$0.620104\pi$
$54$		0			0
$55$	5.00351	−	1.87476i	0.674674	−	0.252793i
$56$		0			0
$57$	1.77501	+	0.405135i	0.235106	+	0.0536614i
$58$		0			0
$59$	2.13782	+	9.36639i	0.278320	+	1.21940i	0.899917	+	0.436062i	$0.143627\pi$
$59$	2.13782	+	9.36639i	0.278320	+	1.21940i	−0.621597	+	0.783338i	$0.713516\pi$
$60$		0			0
$61$	8.60315	+	10.7880i	1.10152	+	1.38126i	0.917215	+	0.398394i	$0.130432\pi$
$61$	8.60315	+	10.7880i	1.10152	+	1.38126i	0.184306	+	0.982869i	$0.440996\pi$
$62$		0			0
$63$	−7.26519	−	2.32812i	−0.915328	−	0.293315i
$64$		0			0
$65$	−4.74003	−	12.6506i	−0.587929	−	1.56911i
$66$		0			0
$67$			8.80941i			1.07624i	0.842868	+	0.538121i	$0.180865\pi$
$67$			8.80941i			1.07624i	−0.842868	+	0.538121i	$0.819135\pi$
$68$		0			0
$69$	−1.38796	−	1.74045i	−0.167091	−	0.209525i
$70$		0			0
$71$	−4.00099	+	5.01708i	−0.474830	+	0.595418i	−0.960346	−	0.278810i	$-0.910060\pi$
$71$	−4.00099	+	5.01708i	−0.474830	+	0.595418i	0.485516	+	0.874228i	$0.338632\pi$
$72$		0			0
$73$	−0.989387	+	2.05448i	−0.115799	+	0.240459i	−0.950810	−	0.309774i	$-0.899747\pi$
$73$	−0.989387	+	2.05448i	−0.115799	+	0.240459i	0.835011	+	0.550233i	$0.185461\pi$
$74$		0			0
$75$	−1.56836	−	0.672357i	−0.181099	−	0.0776371i
$76$		0			0
$77$	−5.26217	+	3.50420i	−0.599680	+	0.399341i
$78$		0			0
$79$	2.15058			0.241959			0.120979	−	0.992655i	$-0.461396\pi$
$79$	2.15058			0.241959			0.120979	+	0.992655i	$0.461396\pi$
$80$		0			0
$81$	4.96629	+	6.22753i	0.551810	+	0.691948i
$82$		0			0
$83$	7.68593	−	15.9600i	0.843640	−	1.75184i	0.210842	−	0.977520i	$-0.432379\pi$
$83$	7.68593	−	15.9600i	0.843640	−	1.75184i	0.632798	−	0.774317i	$-0.281906\pi$
$84$		0			0
$85$	−11.3556	+	7.48698i	−1.23169	+	0.812077i
$86$		0			0
$87$	−0.293148	−	0.608728i	−0.0314288	−	0.0652625i
$88$		0			0
$89$	−15.5807	−	7.50326i	−1.65155	−	0.795344i	−0.999303	−	0.0373359i	$-0.988113\pi$
$89$	−15.5807	−	7.50326i	−1.65155	−	0.795344i	−0.652245	−	0.758008i	$-0.726173\pi$
$90$		0			0
$91$	8.85980	+	13.3045i	0.928759	+	1.39469i
$92$		0			0
$93$	−2.38033	−	0.543294i	−0.246828	−	0.0563370i
$94$		0			0
$95$	11.8803	+	1.07572i	1.21890	+	0.110367i
$96$		0			0
$97$			9.31644i			0.945941i	0.881078	+	0.472971i	$0.156818\pi$
$97$			9.31644i			0.945941i	−0.881078	+	0.472971i	$0.843182\pi$
$98$		0			0
$99$	6.89035			0.692506
$100$		0			0
$101$	2.96073	−	12.9718i	0.294604	−	1.29074i	−0.583438	−	0.812158i	$-0.698293\pi$
$101$	2.96073	−	12.9718i	0.294604	−	1.29074i	0.878041	−	0.478585i	$-0.158850\pi$
$102$		0			0
$103$	14.4513	+	3.29841i	1.42393	+	0.325002i	0.863980	−	0.503527i	$-0.167965\pi$
$103$	14.4513	+	3.29841i	1.42393	+	0.325002i	0.559946	+	0.828529i	$0.310822\pi$
$104$		0			0
$105$	1.98785	+	0.353542i	0.193995	+	0.0345022i
$106$		0			0
$107$	2.03295	−	4.22146i	0.196533	−	0.408104i	−0.779292	−	0.626662i	$-0.784421\pi$
$107$	2.03295	−	4.22146i	0.196533	−	0.408104i	0.975824	+	0.218558i	$0.0701351\pi$
$108$		0			0
$109$	−7.72178	+	3.71861i	−0.739613	+	0.356179i	−0.765457	−	0.643487i	$-0.777487\pi$
$109$	−7.72178	+	3.71861i	−0.739613	+	0.356179i	0.0258441	+	0.999666i	$0.491773\pi$
$110$		0			0
$111$	1.88718	−	0.908817i	0.179123	−	0.0862610i
$112$		0			0
$113$	−4.04829	+	8.40636i	−0.380831	+	0.790803i	0.619154	+	0.785270i	$0.287476\pi$
$113$	−4.04829	+	8.40636i	−0.380831	+	0.790803i	−0.999985	+	0.00553370i	$0.998239\pi$
$114$		0			0
$115$	−10.5368	−	10.0852i	−0.982566	−	0.940446i
$116$		0			0
$117$		−	17.4211i		−	1.61058i
$118$		0			0
$119$	11.0746	−	11.6774i	1.01520	−	1.07047i
$120$		0			0
$121$	−3.29828	+	4.13591i	−0.299843	+	0.375991i
$122$		0			0
$123$	−0.598682	+	1.24318i	−0.0539814	+	0.112093i
$124$		0			0
$125$	−10.7726	−	2.99186i	−0.963530	−	0.267600i
$126$		0			0
$127$	7.02620	−	5.60320i	0.623474	−	0.497204i	−0.260047	−	0.965596i	$-0.583738\pi$
$127$	7.02620	−	5.60320i	0.623474	−	0.497204i	0.883521	+	0.468392i	$0.155167\pi$
$128$		0			0
$129$	−2.37292			−0.208924
$130$		0			0
$131$	−1.38302	−	6.05939i	−0.120835	−	0.529412i	−0.998722	−	0.0505439i	$-0.983905\pi$
$131$	−1.38302	−	6.05939i	−0.120835	−	0.529412i	0.877887	−	0.478868i	$-0.158953\pi$
$132$		0			0
$133$	−13.9790	+	1.95126i	−1.21213	+	0.169196i
$134$		0			0
$135$	−3.24359	−	3.10455i	−0.279164	−	0.267197i
$136$		0			0
$137$	−8.24497	+	1.88186i	−0.704415	+	0.160778i	−0.559700	−	0.828695i	$-0.689084\pi$
$137$	−8.24497	+	1.88186i	−0.704415	+	0.160778i	−0.144715	+	0.989473i	$0.546227\pi$
$138$		0			0
$139$	4.54794	−	19.9258i	0.385751	−	1.69009i	−0.293319	−	0.956014i	$-0.594760\pi$
$139$	4.54794	−	19.9258i	0.385751	−	1.69009i	0.679071	−	0.734073i	$-0.262383\pi$
$140$		0			0
$141$	0.138024	+	0.604724i	0.0116237	+	0.0509270i
$142$		0			0
$143$	−11.2871	−	9.00116i	−0.943874	−	0.752715i
$144$		0			0
$145$	−2.43669	−	3.69578i	−0.202356	−	0.306917i
$146$		0			0
$147$	−2.38562	+	0.126506i	−0.196762	+	0.0104341i
$148$		0			0
$149$	−13.3617	+	6.43464i	−1.09463	+	0.527146i	−0.891966	−	0.452103i	$-0.850674\pi$
$149$	−13.3617	+	6.43464i	−1.09463	+	0.527146i	−0.202664	+	0.979248i	$0.564960\pi$
$150$		0			0
$151$	−7.77462	+	9.74907i	−0.632690	+	0.793368i	−0.990068	−	0.140592i	$-0.955099\pi$
$151$	−7.77462	+	9.74907i	−0.632690	+	0.793368i	0.357378	+	0.933960i	$0.383671\pi$
$152$		0			0
$153$	−17.1003	+	3.90303i	−1.38248	+	0.315541i
$154$		0			0
$155$	−15.9317	−	1.44257i	−1.27967	−	0.115870i
$156$		0			0
$157$	0.425653	−	0.0971525i	0.0339708	−	0.00775361i	−0.205502	−	0.978657i	$-0.565883\pi$
$157$	0.425653	−	0.0971525i	0.0339708	−	0.00775361i	0.239473	+	0.970903i	$0.423025\pi$
$158$		0			0
$159$	−0.903379	−	1.13280i	−0.0716426	−	0.0898370i
$160$		0			0
$161$	14.8506	+	8.79142i	1.17039	+	0.692861i
$162$		0			0
$163$	5.00396	−	1.14212i	0.391940	−	0.0894578i	−0.0220090	−	0.999758i	$-0.507006\pi$
$163$	5.00396	−	1.14212i	0.391940	−	0.0894578i	0.413949	+	0.910300i	$0.364149\pi$
$164$		0			0
$165$	−1.80717	+	0.243802i	−0.140688	+	0.0189800i
$166$		0			0
$167$	−0.445777	+	0.355495i	−0.0344953	+	0.0275091i	−0.640586	−	0.767887i	$-0.721308\pi$
$167$	−0.445777	+	0.355495i	−0.0344953	+	0.0275091i	0.606090	+	0.795396i	$0.292737\pi$
$168$		0			0
$169$	−14.6526	+	18.3738i	−1.12712	+	1.41337i
$170$		0			0
$171$	13.8596	+	6.67442i	1.05987	+	0.510406i
$172$		0			0
$173$	−4.31139	−	3.43821i	−0.327789	−	0.261403i	0.445742	−	0.895161i	$-0.352940\pi$
$173$	−4.31139	−	3.43821i	−0.327789	−	0.261403i	−0.773531	+	0.633759i	$0.781511\pi$
$174$		0			0
$175$	13.2171	+	0.554279i	0.999122	+	0.0418995i
$176$		0			0
$177$		−	3.27878i		−	0.246448i
$178$		0			0
$179$	9.26293	+	11.6153i	0.692344	+	0.868171i	0.996426	−	0.0844744i	$-0.0269211\pi$
$179$	9.26293	+	11.6153i	0.692344	+	0.868171i	−0.304082	+	0.952646i	$0.598350\pi$
$180$		0			0
$181$	−3.48283	−	1.67724i	−0.258877	−	0.124669i	0.299944	−	0.953957i	$-0.403032\pi$
$181$	−3.48283	−	1.67724i	−0.258877	−	0.124669i	−0.558821	+	0.829288i	$0.688746\pi$
$182$		0			0
$183$	−2.04321	−	4.24278i	−0.151039	−	0.313635i
$184$		0			0
$185$	11.4576	−	7.55422i	0.842381	−	0.555397i
$186$		0			0
$187$	−6.30664	+	13.0959i	−0.461187	+	0.957665i
$188$		0			0
$189$	4.57151	+	2.70629i	0.332528	+	0.196854i
$190$		0			0
$191$	1.16153	−	5.08900i	0.0840454	−	0.368227i	−0.915363	−	0.402630i	$-0.868096\pi$
$191$	1.16153	−	5.08900i	0.0840454	−	0.368227i	0.999408	+	0.0344034i	$0.0109531\pi$
$192$		0			0
$193$	−19.8795	−	4.53736i	−1.43096	−	0.326606i	−0.564324	−	0.825553i	$-0.690863\pi$
$193$	−19.8795	−	4.53736i	−1.43096	−	0.326606i	−0.866633	+	0.498947i	$0.833720\pi$
$194$		0			0
$195$	0.616414	+	4.56912i	0.0441423	+	0.327202i
$196$		0			0
$197$			0.970401i			0.0691382i	0.999402	+	0.0345691i	$0.0110059\pi$
$197$			0.970401i			0.0691382i	−0.999402	+	0.0345691i	$0.988994\pi$
$198$		0			0
$199$	3.63743	−	15.9366i	0.257851	−	1.12972i	−0.665693	−	0.746226i	$-0.731864\pi$
$199$	3.63743	−	15.9366i	0.257851	−	1.12972i	0.923544	−	0.383493i	$-0.125279\pi$
$200$		0			0
$201$	0.669007	−	2.93111i	0.0471881	−	0.206745i
$202$		0			0
$203$	3.80049	+	3.60430i	0.266742	+	0.252972i
$204$		0			0
$205$	−2.79834	+	8.59657i	−0.195444	+	0.600411i
$206$		0			0
$207$	−8.16079	−	16.9461i	−0.567214	−	1.17783i
$208$		0			0
$209$	11.4853	−	5.53104i	0.794456	−	0.382590i
$210$		0			0
$211$	8.28130	+	3.98807i	0.570108	+	0.274550i	0.696650	−	0.717412i	$-0.254673\pi$
$211$	8.28130	+	3.98807i	0.570108	+	0.274550i	−0.126541	+	0.991961i	$0.540388\pi$
$212$		0			0
$213$	1.71224	−	1.36546i	0.117320	−	0.0935600i
$214$		0			0
$215$	−15.4077	+	2.07863i	−1.05080	+	0.141762i
$216$		0			0
$217$	18.7461	−	2.61668i	1.27257	−	0.177632i
$218$		0			0
$219$	0.485215	−	0.608441i	0.0327878	−	0.0411146i
$220$		0			0
$221$	33.1107	+	15.9453i	2.22727	+	1.07260i
$222$		0			0
$223$	1.74204	+	1.38923i	0.116655	+	0.0930295i	0.680080	−	0.733138i	$-0.261945\pi$
$223$	1.74204	+	1.38923i	0.116655	+	0.0930295i	−0.563425	+	0.826167i	$0.690516\pi$
$224$		0			0
$225$	−11.6549	−	8.48708i	−0.776996	−	0.565806i
$226$		0			0
$227$			5.15626i			0.342233i	0.985251	+	0.171117i	$0.0547375\pi$
$227$			5.15626i			0.342233i	−0.985251	+	0.171117i	$0.945263\pi$
$228$		0			0
$229$	−4.69852	−	20.5856i	−0.310487	−	1.36033i	−0.853712	−	0.520746i	$-0.825654\pi$
$229$	−4.69852	−	20.5856i	−0.310487	−	1.36033i	0.543225	−	0.839587i	$-0.317203\pi$
$230$		0			0
$231$	2.01697	−	0.766314i	0.132707	−	0.0504198i
$232$		0			0
$233$	9.58805	−	7.64621i	0.628134	−	0.500920i	−0.256905	−	0.966437i	$-0.582703\pi$
$233$	9.58805	−	7.64621i	0.628134	−	0.500920i	0.885039	+	0.465516i	$0.154131\pi$
$234$		0			0
$235$	1.42594	+	3.80566i	0.0930182	+	0.248254i
$236$		0			0
$237$	−0.715550	−	0.163320i	−0.0464800	−	0.0106088i
$238$		0			0
$239$	1.02671	+	4.49832i	0.0664126	+	0.290972i	0.997218	−	0.0745431i	$-0.0237498\pi$
$239$	1.02671	+	4.49832i	0.0664126	+	0.290972i	−0.930805	+	0.365516i	$0.880893\pi$
$240$		0			0
$241$	7.48771	−	9.38930i	0.482326	−	0.604818i	−0.479815	−	0.877370i	$-0.659296\pi$
$241$	7.48771	−	9.38930i	0.482326	−	0.604818i	0.962141	+	0.272552i	$0.0878676\pi$
$242$		0			0
$243$	−3.79311	−	7.87647i	−0.243328	−	0.505276i
$244$		0			0
$245$	−15.3794	+	2.91118i	−0.982552	+	0.185989i
$246$		0			0
$247$	−13.9843	−	29.0387i	−0.889801	−	1.84769i
$248$		0			0
$249$	−3.76934	+	4.72660i	−0.238872	+	0.299536i
$250$		0			0
$251$	−0.306205	−	1.34157i	−0.0193275	−	0.0846794i	0.964344	−	0.264651i	$-0.0852567\pi$
$251$	−0.306205	−	1.34157i	−0.0193275	−	0.0846794i	−0.983672	+	0.179971i	$0.942400\pi$
$252$		0			0
$253$	−15.1958	−	3.46835i	−0.955354	−	0.218053i
$254$		0			0
$255$	4.34688	−	1.62873i	0.272212	−	0.101995i
$256$		0			0
$257$	−22.4685	+	17.9180i	−1.40155	+	1.11770i	−0.424317	+	0.905514i	$0.639486\pi$
$257$	−22.4685	+	17.9180i	−1.40155	+	1.11770i	−0.977230	+	0.212183i	$0.931943\pi$
$258$		0			0
$259$	−11.1740	+	11.7823i	−0.694320	+	0.732115i
$260$		0			0
$261$	−1.27027	−	5.56542i	−0.0786278	−	0.344491i
$262$		0			0
$263$		−	6.02698i		−	0.371640i	−0.982584	−	0.185820i	$-0.940506\pi$
$263$		−	6.02698i		−	0.371640i	0.982584	−	0.185820i	$-0.0594941\pi$
$264$		0			0
$265$	−6.85810	−	6.56411i	−0.421289	−	0.403230i
$266$		0			0
$267$	4.61426	+	3.67975i	0.282388	+	0.225197i
$268$		0			0
$269$	−3.04962	−	1.46862i	−0.185938	−	0.0895432i	0.338598	−	0.940931i	$-0.390047\pi$
$269$	−3.04962	−	1.46862i	−0.185938	−	0.0895432i	−0.524537	+	0.851388i	$0.675761\pi$
$270$		0			0
$271$	−12.1366	+	15.2188i	−0.737247	+	0.924479i	−0.999175	−	0.0406086i	$-0.987070\pi$
$271$	−12.1366	+	15.2188i	−0.737247	+	0.924479i	0.261928	+	0.965087i	$0.415642\pi$
$272$		0			0
$273$	−1.93750	−	5.09958i	−0.117263	−	0.308640i
$274$		0			0
$275$	−11.5206	+	3.16609i	−0.694721	+	0.190923i
$276$		0			0
$277$	3.19881	−	2.55097i	0.192198	−	0.153273i	−0.522663	−	0.852539i	$-0.675061\pi$
$277$	3.19881	−	2.55097i	0.192198	−	0.153273i	0.714861	+	0.699267i	$0.246490\pi$
$278$		0			0
$279$	−18.5860	−	8.95053i	−1.11271	−	0.535854i
$280$		0			0
$281$	−14.0884	+	6.78464i	−0.840446	+	0.404737i	−0.804022	−	0.594599i	$-0.797311\pi$
$281$	−14.0884	+	6.78464i	−0.840446	+	0.404737i	−0.0364236	+	0.999336i	$0.511597\pi$
$282$		0			0
$283$	6.77162	+	14.0614i	0.402531	+	0.835865i	0.999437	+	0.0335533i	$0.0106824\pi$
$283$	6.77162	+	14.0614i	0.402531	+	0.835865i	−0.596906	+	0.802311i	$0.703603\pi$
$284$		0			0
$285$	−3.87118	−	1.26014i	−0.229309	−	0.0746442i
$286$		0			0
$287$	0.915715	−	10.6577i	0.0540529	−	0.629102i
$288$		0			0
$289$	4.45066	−	19.4996i	0.261804	−	1.14704i
$290$		0			0
$291$	0.707512	−	3.09981i	0.0414751	−	0.181714i
$292$		0			0
$293$		−	26.2811i		−	1.53536i	−0.640833	−	0.767680i	$-0.721411\pi$
$293$		−	26.2811i		−	1.53536i	0.640833	−	0.767680i	$-0.278589\pi$
$294$		0			0
$295$	−2.87215	−	21.2896i	−0.167223	−	1.23953i
$296$		0			0
$297$	−4.67778	−	1.06767i	−0.271432	−	0.0619527i
$298$		0			0
$299$	−8.76916	+	38.4202i	−0.507133	+	2.22190i
$300$		0			0
$301$	17.1965	−	6.53351i	0.991188	−	0.376585i
$302$		0			0
$303$	−1.97022	+	4.09120i	−0.113186	+	0.235033i
$304$		0			0
$305$	−16.9835	−	25.7592i	−0.972473	−	1.47497i
$306$		0			0
$307$	6.89782	+	14.3235i	0.393680	+	0.817484i	0.999756	+	0.0220779i	$0.00702819\pi$
$307$	6.89782	+	14.3235i	0.393680	+	0.817484i	−0.606077	+	0.795406i	$0.707258\pi$
$308$		0			0
$309$	−4.55781	−	2.19492i	−0.259285	−	0.124865i
$310$		0			0
$311$	9.97538	+	12.5087i	0.565652	+	0.709305i	0.979591	−	0.201000i	$-0.0644190\pi$
$311$	9.97538	+	12.5087i	0.565652	+	0.709305i	−0.413940	+	0.910304i	$0.635848\pi$
$312$		0			0
$313$			21.1368i			1.19472i	0.801972	+	0.597361i	$0.203784\pi$
$313$			21.1368i			1.19472i	−0.801972	+	0.597361i	$0.796216\pi$
$314$		0			0
$315$	15.7098	+	6.64960i	0.885148	+	0.374663i
$316$		0			0
$317$	18.6795	+	14.8964i	1.04914	+	0.836663i	0.986890	−	0.161397i	$-0.0516000\pi$
$317$	18.6795	+	14.8964i	1.04914	+	0.836663i	0.0622531	+	0.998060i	$0.480171\pi$
$318$		0			0
$319$	−4.26214	−	2.05254i	−0.238634	−	0.114920i
$320$		0			0
$321$	−0.996999	+	1.25020i	−0.0556471	+	0.0697792i
$322$		0			0
$323$	−25.3709	+	20.2327i	−1.41168	+	1.12577i
$324$		0			0
$325$	8.00494	+	29.1281i	0.444034	+	1.61573i
$326$		0			0
$327$	2.85163	−	0.650866i	0.157695	−	0.0359929i
$328$		0			0
$329$	−2.66529	−	4.00239i	−0.146942	−	0.220659i
$330$		0			0
$331$	−19.6703	−	24.6658i	−1.08118	−	1.35575i	−0.930131	−	0.367228i	$-0.880307\pi$
$331$	−19.6703	−	24.6658i	−1.08118	−	1.35575i	−0.151048	−	0.988526i	$-0.548265\pi$
$332$		0			0
$333$	17.2539	−	3.93809i	0.945507	−	0.215806i
$334$		0			0
$335$	1.77636	−	19.6182i	0.0970531	−	1.07186i
$336$		0			0
$337$	−3.64126	+	0.831095i	−0.198352	+	0.0452726i	−0.320543	−	0.947234i	$-0.603865\pi$
$337$	−3.64126	+	0.831095i	−0.198352	+	0.0452726i	0.122190	+	0.992507i	$0.461008\pi$
$338$		0			0
$339$	1.98536	−	2.48957i	0.107830	−	0.135215i
$340$		0			0
$341$	−15.4020	+	7.41723i	−0.834068	+	0.401666i
$342$		0			0
$343$	16.9402	−	7.48528i	0.914685	−	0.404167i
$344$		0			0
$345$	2.73998	+	4.15578i	0.147515	+	0.223739i
$346$		0			0
$347$	−9.91010	−	7.90304i	−0.532002	−	0.424257i	0.320293	−	0.947318i	$-0.396219\pi$
$347$	−9.91010	−	7.90304i	−0.532002	−	0.424257i	−0.852295	+	0.523061i	$0.824790\pi$
$348$		0			0
$349$	−4.07420	−	17.8502i	−0.218087	−	0.955501i	−0.958890	−	0.283778i	$-0.908412\pi$
$349$	−4.07420	−	17.8502i	−0.218087	−	0.955501i	0.740803	−	0.671722i	$-0.234445\pi$
$350$		0			0
$351$	−2.69944	+	11.8270i	−0.144085	+	0.631279i
$352$		0			0
$353$	13.3927	−	3.05679i	0.712820	−	0.162696i	0.149291	−	0.988793i	$-0.452301\pi$
$353$	13.3927	−	3.05679i	0.712820	−	0.162696i	0.563528	+	0.826097i	$0.309444\pi$
$354$		0			0
$355$	9.92169	−	10.3661i	0.526589	−	0.550173i
$356$		0			0
$357$	−4.57159	+	3.04433i	−0.241954	+	0.161123i
$358$		0			0
$359$	−6.02335	−	26.3900i	−0.317900	−	1.39281i	−0.841228	−	0.540681i	$-0.818167\pi$
$359$	−6.02335	−	26.3900i	−0.317900	−	1.39281i	0.523327	−	0.852132i	$-0.324690\pi$
$360$		0			0
$361$	9.45983			0.497886
$362$		0			0
$363$	1.41151	−	1.12564i	0.0740849	−	0.0590808i
$364$		0			0
$365$	2.61760	−	4.37574i	0.137011	−	0.229037i
$366$		0			0
$367$	−3.42527	+	7.11265i	−0.178798	+	0.371277i	−0.971035	−	0.238935i	$-0.923202\pi$
$367$	−3.42527	+	7.11265i	−0.178798	+	0.371277i	0.792238	+	0.610212i	$0.208916\pi$
$368$		0			0
$369$	−7.26882	+	9.11481i	−0.378400	+	0.474498i
$370$		0			0
$371$	9.66579	+	5.72206i	0.501823	+	0.297074i
$372$		0			0
$373$			0.578508i			0.0299540i	0.999888	+	0.0149770i	$0.00476750\pi$
$373$			0.578508i			0.0299540i	−0.999888	+	0.0149770i	$0.995232\pi$
$374$		0			0
$375$	3.35710	+	1.81356i	0.173360	+	0.0936519i
$376$		0			0
$377$	−5.18951	+	10.7761i	−0.267273	+	0.554999i
$378$		0			0
$379$	8.44698	−	4.06785i	0.433892	−	0.208952i	−0.204171	−	0.978935i	$-0.565450\pi$
$379$	8.44698	−	4.06785i	0.433892	−	0.208952i	0.638064	+	0.769984i	$0.279736\pi$
$380$		0			0
$381$	−2.76331	+	1.33074i	−0.141569	+	0.0681758i
$382$		0			0
$383$	8.53738	−	17.7281i	0.436240	−	0.905861i	−0.560725	−	0.828002i	$-0.689477\pi$
$383$	8.53738	−	17.7281i	0.436240	−	0.905861i	0.996964	−	0.0778589i	$-0.0248084\pi$
$384$		0			0
$385$	12.4252	−	6.74263i	0.633248	−	0.343636i
$386$		0			0
$387$	−19.5464	−	4.46133i	−0.993598	−	0.226782i
$388$		0			0
$389$	−1.38407	+	6.06402i	−0.0701752	+	0.307458i	−0.997819	−	0.0660083i	$-0.978974\pi$
$389$	−1.38407	+	6.06402i	−0.0701752	+	0.307458i	0.927644	+	0.373466i	$0.121831\pi$
$390$		0			0
$391$	39.6773			2.00657
$392$		0			0
$393$			2.12114i			0.106997i
$394$		0			0
$395$	−4.78924	−	0.433651i	−0.240973	−	0.0218193i
$396$		0			0
$397$	3.76363	+	0.859023i	0.188891	+	0.0431131i	0.315920	−	0.948786i	$-0.397687\pi$
$397$	3.76363	+	0.859023i	0.188891	+	0.0431131i	−0.127029	+	0.991899i	$0.540544\pi$
$398$		0			0
$399$	4.79933	+	0.412362i	0.240267	+	0.0206439i
$400$		0			0
$401$	35.3912	+	17.0435i	1.76735	+	0.851112i	0.968276	+	0.249883i	$0.0803923\pi$
$401$	35.3912	+	17.0435i	1.76735	+	0.851112i	0.799077	+	0.601229i	$0.205322\pi$
$402$		0			0
$403$	18.7533	+	38.9415i	0.934166	+	1.93982i
$404$		0			0
$405$	−9.80397	−	14.8699i	−0.487163	−	0.738890i
$406$		0			0
$407$	6.36328	−	13.2135i	0.315416	−	0.654968i
$408$		0			0
$409$	3.43815	+	4.31131i	0.170006	+	0.213180i	0.859534	−	0.511078i	$-0.170754\pi$
$409$	3.43815	+	4.31131i	0.170006	+	0.213180i	−0.689529	+	0.724258i	$0.742182\pi$
$410$		0			0
$411$	2.88622			0.142367
$412$		0			0
$413$	9.02769	+	23.7612i	0.444224	+	1.16921i
$414$		0			0
$415$	−20.3345	+	33.9924i	−0.998180	+	1.66862i
$416$		0			0
$417$	−3.02643	+	6.28444i	−0.148205	+	0.307750i
$418$		0			0
$419$	5.75577	−	7.21751i	0.281188	−	0.352598i	−0.621101	−	0.783731i	$-0.713314\pi$
$419$	5.75577	−	7.21751i	0.281188	−	0.352598i	0.902289	+	0.431132i	$0.141886\pi$
$420$		0			0
$421$	18.5080	+	23.2083i	0.902024	+	1.13110i	0.990838	+	0.135054i	$0.0431209\pi$
$421$	18.5080	+	23.2083i	0.902024	+	1.13110i	−0.0888140	+	0.996048i	$0.528308\pi$
$422$		0			0
$423$			5.24079i			0.254816i
$424$		0			0
$425$	26.7982	−	14.3834i	1.29991	−	0.697697i
$426$		0			0
$427$	26.4891	+	25.1216i	1.28190	+	1.21572i
$428$		0			0
$429$	3.07193	+	3.85208i	0.148314	+	0.185980i
$430$		0			0
$431$	2.83499	+	12.4209i	0.136556	+	0.598293i	0.996177	+	0.0873596i	$0.0278429\pi$
$431$	2.83499	+	12.4209i	0.136556	+	0.598293i	−0.859620	+	0.510933i	$0.829300\pi$
$432$		0			0
$433$	17.0802	+	3.89845i	0.820824	+	0.187348i	0.612255	−	0.790660i	$-0.290262\pi$
$433$	17.0802	+	3.89845i	0.820824	+	0.187348i	0.208569	+	0.978008i	$0.433120\pi$
$434$		0			0
$435$	0.530082	+	1.41472i	0.0254155	+	0.0678308i
$436$		0			0
$437$	−27.2060	−	21.6960i	−1.30144	−	1.03786i
$438$		0			0
$439$	−5.91260	+	2.84736i	−0.282193	+	0.135897i	−0.569627	−	0.821904i	$-0.692912\pi$
$439$	−5.91260	+	2.84736i	−0.282193	+	0.135897i	0.287434	+	0.957801i	$0.407198\pi$
$440$		0			0
$441$	−19.8889	−	3.44315i	−0.947088	−	0.163959i
$442$		0			0
$443$	−0.625654	−	1.29918i	−0.0297257	−	0.0617261i	0.885577	−	0.464492i	$-0.153763\pi$
$443$	−0.625654	−	1.29918i	−0.0297257	−	0.0617261i	−0.915303	+	0.402766i	$0.868049\pi$
$444$		0			0
$445$	33.1845	+	19.8512i	1.57310	+	0.941036i
$446$		0			0
$447$	4.93441	−	1.12625i	0.233390	−	0.0532697i
$448$		0			0
$449$	−3.97284	+	17.4062i	−0.187490	+	0.821448i	0.790444	+	0.612534i	$0.209850\pi$
$449$	−3.97284	+	17.4062i	−0.187490	+	0.821448i	−0.977934	+	0.208913i	$0.933007\pi$
$450$		0			0
$451$	2.14980	+	9.41890i	0.101230	+	0.443519i
$452$		0			0
$453$	3.32718	−	2.65333i	0.156324	−	0.124664i
$454$		0			0
$455$	−17.0476	−	31.4151i	−0.799205	−	1.47276i
$456$		0			0
$457$	34.3722	−	7.84523i	1.60786	−	0.366984i	0.678050	−	0.735016i	$-0.262825\pi$
$457$	34.3722	−	7.84523i	1.60786	−	0.366984i	0.929813	+	0.368032i	$0.119968\pi$
$458$		0			0
$459$	12.2140			0.570100
$460$		0			0
$461$	0.0303831	+	0.0380992i	0.00141508	+	0.00177445i	0.782539	−	0.622602i	$-0.213924\pi$
$461$	0.0303831	+	0.0380992i	0.00141508	+	0.00177445i	−0.781123	+	0.624377i	$0.785353\pi$
$462$		0			0
$463$	18.2160	+	14.5268i	0.846569	+	0.675116i	0.947493	−	0.319778i	$-0.103608\pi$
$463$	18.2160	+	14.5268i	0.846569	+	0.675116i	−0.100923	+	0.994894i	$0.532180\pi$
$464$		0			0
$465$	5.19133	+	1.68987i	0.240742	+	0.0783659i
$466$		0			0
$467$	24.3802	+	19.4425i	1.12818	+	0.899693i	0.995804	−	0.0915069i	$-0.0291683\pi$
$467$	24.3802	+	19.4425i	1.12818	+	0.899693i	0.132375	+	0.991200i	$0.457740\pi$
$468$		0			0
$469$	3.22215	+	23.0837i	0.148785	+	1.06591i
$470$		0			0
$471$	−0.149003			−0.00686570
$472$		0			0
$473$	−12.9897	+	10.3590i	−0.597268	+	0.476306i
$474$		0			0
$475$	−26.2401	−	4.79119i	−1.20398	−	0.219835i
$476$		0			0
$477$	−5.31160	−	11.0297i	−0.243202	−	0.505013i
$478$		0			0
$479$	33.9787	−	16.3633i	1.55252	−	0.747656i	0.556018	−	0.831170i	$-0.312329\pi$
$479$	33.9787	−	16.3633i	1.55252	−	0.747656i	0.996507	+	0.0835140i	$0.0266143\pi$
$480$		0			0
$481$	−33.4081	−	16.0885i	−1.52328	−	0.733572i
$482$		0			0
$483$	−4.27353	−	4.05291i	−0.194452	−	0.184414i
$484$		0			0
$485$	1.87860	−	20.7473i	0.0853030	−	0.942087i
$486$		0			0
$487$	−16.9456	−	3.86772i	−0.767877	−	0.175263i	−0.179399	−	0.983776i	$-0.557415\pi$
$487$	−16.9456	−	3.86772i	−0.767877	−	0.175263i	−0.588478	+	0.808513i	$0.700273\pi$
$488$		0			0
$489$	−1.75168			−0.0792135
$490$		0			0
$491$	−20.6589			−0.932325			−0.466162	−	0.884699i	$-0.654364\pi$
$491$	−20.6589			−0.932325			−0.466162	+	0.884699i	$0.654364\pi$
$492$		0			0
$493$	11.7403	+	2.67966i	0.528759	+	0.120686i
$494$		0			0
$495$	−15.3445	−	1.38940i	−0.689685	−	0.0624487i
$496$		0			0
$497$	−8.64892	+	14.6099i	−0.387957	+	0.655344i
$498$		0			0
$499$	−34.4876	−	16.6084i	−1.54388	−	0.743493i	−0.548199	−	0.836348i	$-0.684686\pi$
$499$	−34.4876	−	16.6084i	−1.54388	−	0.743493i	−0.995680	+	0.0928551i	$0.970401\pi$
$500$		0			0
$501$	0.175318	−	0.0844288i	0.00783264	−	0.00377200i
$502$		0			0
$503$	−2.60388	−	5.40700i	−0.116101	−	0.241086i	0.834818	−	0.550526i	$-0.185573\pi$
$503$	−2.60388	−	5.40700i	−0.116101	−	0.241086i	−0.950919	+	0.309440i	$0.899859\pi$
$504$		0			0
$505$	−9.20910	+	28.2906i	−0.409800	+	1.25892i
$506$		0			0
$507$	6.27062	−	5.00065i	0.278488	−	0.222087i
$508$		0			0
$509$	28.2839			1.25366			0.626831	−	0.779155i	$-0.284352\pi$
$509$	28.2839			1.25366			0.626831	+	0.779155i	$0.284352\pi$
$510$		0			0
$511$	−1.84108	+	5.74534i	−0.0814448	+	0.254159i
$512$		0			0
$513$	−8.37490	−	6.67876i	−0.369761	−	0.294874i
$514$		0			0
$515$	−31.5173	−	10.2594i	−1.38882	−	0.452084i
$516$		0			0
$517$	3.39549	+	2.70781i	0.149334	+	0.119090i
$518$		0			0
$519$	1.17340	+	1.47140i	0.0515065	+	0.0645871i
$520$		0			0
$521$	−9.14950			−0.400847			−0.200423	−	0.979709i	$-0.564232\pi$
$521$	−9.14950			−0.400847			−0.200423	+	0.979709i	$0.564232\pi$
$522$		0			0
$523$	−10.2822	+	2.34685i	−0.449610	+	0.102620i	−0.441329	−	0.897345i	$-0.645493\pi$
$523$	−10.2822	+	2.34685i	−0.449610	+	0.102620i	−0.00828042	+	0.999966i	$0.502636\pi$
$524$		0			0
$525$	−4.35558	−	1.18816i	−0.190093	−	0.0518556i
$526$		0			0
$527$	34.0229	−	27.1324i	1.48206	−	1.18191i
$528$		0			0
$529$	4.34964	+	19.0570i	0.189115	+	0.828566i
$530$		0			0
$531$	6.16445	−	27.0082i	0.267514	−	1.17206i
$532$		0			0
$533$	23.8141	−	5.43542i	1.03150	−	0.235434i
$534$		0			0
$535$	−5.37852	+	8.99108i	−0.232534	+	0.388718i
$536$		0			0
$537$	−2.19991	−	4.56816i	−0.0949331	−	0.197131i
$538$		0			0
$539$	−12.5070	+	11.1069i	−0.538715	+	0.478409i
$540$		0			0
$541$	−25.5246	+	12.2920i	−1.09739	+	0.528474i	−0.892836	−	0.450382i	$-0.851288\pi$
$541$	−25.5246	+	12.2920i	−1.09739	+	0.528474i	−0.204552	+	0.978856i	$0.565574\pi$
$542$		0			0
$543$	1.03145	+	0.822555i	0.0442638	+	0.0352992i
$544$		0			0
$545$	17.9459	−	6.72415i	0.768719	−	0.288031i
$546$		0			0
$547$	33.0539	+	7.54433i	1.41328	+	0.322572i	0.859945	−	0.510386i	$-0.170498\pi$
$547$	33.0539	+	7.54433i	1.41328	+	0.322572i	0.553336	+	0.832958i	$0.313355\pi$
$548$		0			0
$549$	−8.85366	−	38.7904i	−0.377865	−	1.65554i
$550$		0			0
$551$	−6.58486	−	8.25716i	−0.280525	−	0.351767i
$552$		0			0
$553$	5.63526	−	0.786600i	0.239636	−	0.0334496i
$554$		0			0
$555$	−4.38592	+	1.64336i	−0.186172	+	0.0697567i
$556$		0			0
$557$			19.7210i			0.835606i	0.908538	+	0.417803i	$0.137200\pi$
$557$			19.7210i			0.835606i	−0.908538	+	0.417803i	$0.862800\pi$
$558$		0			0
$559$	26.1909	+	32.8424i	1.10776	+	1.38909i
$560$		0			0
$561$	3.09290	−	3.87838i	0.130583	−	0.163745i
$562$		0			0
$563$	−8.03066	+	16.6758i	−0.338452	+	0.702802i	−0.998842	−	0.0481206i	$-0.984677\pi$
$563$	−8.03066	+	16.6758i	−0.338452	+	0.702802i	0.660390	+	0.750923i	$0.270391\pi$
$564$		0			0
$565$	10.7105	−	17.9043i	0.450592	−	0.753239i
$566$		0			0
$567$	15.2912	+	14.5018i	0.642170	+	0.609019i
$568$		0			0
$569$	−14.1897			−0.594864			−0.297432	−	0.954743i	$-0.596130\pi$
$569$	−14.1897			−0.594864			−0.297432	+	0.954743i	$0.596130\pi$
$570$		0			0
$571$	−10.8365	−	13.5885i	−0.453493	−	0.568662i	0.501551	−	0.865128i	$-0.332763\pi$
$571$	−10.8365	−	13.5885i	−0.453493	−	0.568662i	−0.955043	+	0.296466i	$0.904192\pi$
$572$		0			0
$573$	−0.772940	+	1.60503i	−0.0322900	+	0.0670510i
$574$		0			0
$575$	21.4315	+	24.5839i	0.893755	+	1.02522i
$576$		0			0
$577$	−12.9319	−	26.8534i	−0.538362	−	1.11792i	−0.975798	−	0.218672i	$-0.929828\pi$
$577$	−12.9319	−	26.8534i	−0.538362	−	1.11792i	0.437436	−	0.899250i	$-0.355887\pi$
$578$		0			0
$579$	6.26982	+	3.01939i	0.260565	+	0.125481i
$580$		0			0
$581$	14.3022	−	44.6319i	0.593357	−	1.85165i
$582$		0			0
$583$	−9.89049	−	2.25744i	−0.409622	−	0.0934936i
$584$		0			0
$585$	−3.51286	+	38.7961i	−0.145239	+	1.60402i
$586$		0			0
$587$			31.9910i			1.32041i	0.751085	+	0.660206i	$0.229531\pi$
$587$			31.9910i			1.32041i	−0.751085	+	0.660206i	$0.770469\pi$
$588$		0			0
$589$	−38.1652			−1.57257
$590$		0			0
$591$	0.0736944	−	0.322876i	0.00303138	−	0.0132814i
$592$		0			0
$593$	−3.08913	−	0.705074i	−0.126855	−	0.0289539i	0.158622	−	0.987339i	$-0.449295\pi$
$593$	−3.08913	−	0.705074i	−0.126855	−	0.0289539i	−0.285477	+	0.958385i	$0.592152\pi$
$594$		0			0
$595$	−27.0173	+	23.7719i	−1.10760	+	0.974555i
$596$		0			0
$597$	−2.42053	+	5.02628i	−0.0990656	+	0.205712i
$598$		0			0
$599$	31.4348	−	15.1382i	1.28439	−	0.618530i	0.337876	−	0.941191i	$-0.390291\pi$
$599$	31.4348	−	15.1382i	1.28439	−	0.618530i	0.946515	+	0.322660i	$0.104577\pi$
$600$		0			0
$601$	−10.8354	+	5.21808i	−0.441987	+	0.212850i	−0.641623	−	0.767020i	$-0.721738\pi$
$601$	−10.8354	+	5.21808i	−0.441987	+	0.212850i	0.199636	+	0.979870i	$0.436024\pi$
$602$		0			0
$603$	11.0216	−	22.8866i	0.448834	−	0.932013i
$604$		0			0
$605$	8.17910	−	8.54541i	0.332528	−	0.347420i
$606$		0			0
$607$		−	4.64403i		−	0.188495i	−0.995549	−	0.0942477i	$-0.969955\pi$
$607$		−	4.64403i		−	0.188495i	0.995549	−	0.0942477i	$-0.0300446\pi$
$608$		0			0
$609$	−0.990800	−	1.48786i	−0.0401492	−	0.0602910i
$610$		0			0
$611$	6.84626	−	8.58494i	0.276970	−	0.347310i
$612$		0			0
$613$	17.2688	−	35.8590i	0.697480	−	1.44833i	−0.187290	−	0.982305i	$-0.559971\pi$
$613$	17.2688	−	35.8590i	0.697480	−	1.44833i	0.884770	−	0.466027i	$-0.154315\pi$
$614$		0			0
$615$	1.58392	−	2.64778i	0.0638698	−	0.106769i
$616$		0			0
$617$	32.9123	−	26.2467i	1.32500	−	1.05665i	0.331425	−	0.943482i	$-0.392471\pi$
$617$	32.9123	−	26.2467i	1.32500	−	1.05665i	0.993576	−	0.113171i	$-0.0361007\pi$
$618$		0			0
$619$	23.8857			0.960049			0.480024	−	0.877255i	$-0.340628\pi$
$619$	23.8857			0.960049			0.480024	+	0.877255i	$0.340628\pi$
$620$		0			0
$621$	2.91445	+	12.7690i	0.116953	+	0.512404i
$622$		0			0
$623$	−43.5712	−	13.9623i	−1.74564	−	0.559388i
$624$		0			0
$625$	23.3868	+	8.83498i	0.935473	+	0.353399i
$626$		0			0
$627$	−4.24149	+	0.968092i	−0.169389	+	0.0386619i
$628$		0			0
$629$	−8.30746	+	36.3974i	−0.331240	+	1.45126i
$630$		0			0
$631$	6.06139	+	26.5567i	0.241300	+	1.05721i	0.939835	+	0.341629i	$0.110979\pi$
$631$	6.06139	+	26.5567i	0.241300	+	1.05721i	−0.698534	+	0.715576i	$0.746164\pi$
$632$		0			0
$633$	−2.45253	−	1.95583i	−0.0974794	−	0.0777372i
$634$		0			0
$635$	−16.7769	+	11.0613i	−0.665771	+	0.438955i
$636$		0			0
$637$	28.0820	+	31.6219i	1.11265	+	1.25290i
$638$		0			0
$639$	16.6714	−	8.02852i	0.659510	−	0.317603i
$640$		0			0
$641$	−17.9032	+	22.4499i	−0.707134	+	0.886718i	−0.997534	−	0.0701876i	$-0.977640\pi$
$641$	−17.9032	+	22.4499i	−0.707134	+	0.886718i	0.290400	+	0.956905i	$0.406212\pi$
$642$		0			0
$643$	−7.95756	+	1.81626i	−0.313815	+	0.0716263i	−0.376528	−	0.926405i	$-0.622882\pi$
$643$	−7.95756	+	1.81626i	−0.313815	+	0.0716263i	0.0627124	+	0.998032i	$0.480025\pi$
$644$		0			0
$645$	5.28438	+	0.478484i	0.208072	+	0.0188403i
$646$		0			0
$647$	18.8792	−	4.30904i	0.742216	−	0.169406i	0.165339	−	0.986237i	$-0.447128\pi$
$647$	18.8792	−	4.30904i	0.742216	−	0.169406i	0.576877	+	0.816831i	$0.304271\pi$
$648$		0			0
$649$	−14.3135	−	17.9486i	−0.561854	−	0.704543i
$650$		0			0
$651$	−6.43600	−	0.552985i	−0.252247	−	0.0216732i
$652$		0			0
$653$	−14.6558	+	3.34510i	−0.573528	+	0.130904i	−0.499441	−	0.866348i	$-0.666461\pi$
$653$	−14.6558	+	3.34510i	−0.573528	+	0.130904i	−0.0740865	+	0.997252i	$0.523604\pi$
$654$		0			0
$655$	1.85808	+	13.7729i	0.0726012	+	0.538151i
$656$		0			0
$657$	5.14079	−	4.09964i	0.200561	−	0.159942i
$658$		0			0
$659$	3.32038	−	4.16363i	0.129344	−	0.162192i	−0.712942	−	0.701223i	$-0.752638\pi$
$659$	3.32038	−	4.16363i	0.129344	−	0.162192i	0.842286	+	0.539031i	$0.181209\pi$
$660$		0			0
$661$	−44.6623	−	21.5082i	−1.73716	−	0.836573i	−0.983869	−	0.178888i	$-0.942750\pi$
$661$	−44.6623	−	21.5082i	−1.73716	−	0.836573i	−0.753293	−	0.657685i	$-0.771536\pi$
$662$		0			0
$663$	−9.80584	−	7.81990i	−0.380827	−	0.303700i
$664$		0			0
$665$	31.5240	−	1.52660i	1.22245	−	0.0591990i
$666$		0			0
$667$			12.9133i			0.500004i
$668$		0			0
$669$	−0.474117	−	0.594524i	−0.0183304	−	0.0229856i
$670$		0			0
$671$	−29.7067	−	14.3060i	−1.14682	−	0.552277i
$672$		0			0
$673$	−8.93194	−	18.5474i	−0.344301	−	0.714948i	0.654867	−	0.755744i	$-0.272725\pi$
$673$	−8.93194	−	18.5474i	−0.344301	−	0.714948i	−0.999167	+	0.0407964i	$0.987011\pi$
$674$		0			0
$675$	6.59732	+	7.56774i	0.253931	+	0.291283i
$676$		0			0
$677$	−7.69414	+	15.9770i	−0.295710	+	0.614048i	−0.994898	−	0.100890i	$-0.967831\pi$
$677$	−7.69414	+	15.9770i	−0.295710	+	0.614048i	0.699188	+	0.714938i	$0.253545\pi$
$678$		0			0
$679$	3.40760	+	24.4123i	0.130772	+	0.936858i
$680$		0			0
$681$	0.391578	−	1.71562i	0.0150053	−	0.0657426i
$682$		0			0
$683$	−21.3258	−	4.86748i	−0.816010	−	0.186249i	−0.205908	−	0.978571i	$-0.566015\pi$
$683$	−21.3258	−	4.86748i	−0.816010	−	0.186249i	−0.610103	+	0.792322i	$0.708872\pi$
$684$		0			0
$685$	18.7407	−	2.52827i	0.716044	−	0.0966004i
$686$		0			0
$687$			7.20614i			0.274932i
$688$		0			0
$689$	−5.70757	+	25.0065i	−0.217441	+	0.952671i
$690$		0			0
$691$	2.89949	−	12.7035i	0.110302	−	0.483263i	−0.889359	−	0.457210i	$-0.848849\pi$
$691$	2.89949	−	12.7035i	0.110302	−	0.483263i	0.999661	−	0.0260535i	$-0.00829403\pi$
$692$		0			0
$693$	18.0551	−	2.52023i	0.685857	−	0.0957356i
$694$		0			0
$695$	−14.1460	+	43.4569i	−0.536588	+	1.64842i
$696$		0			0
$697$	−10.6707	−	22.1578i	−0.404180	−	0.839288i
$698$		0			0
$699$	−3.77085	+	1.81595i	−0.142627	+	0.0686854i
$700$		0			0
$701$	−7.83780	−	3.77449i	−0.296030	−	0.142560i	0.279974	−	0.960008i	$-0.409674\pi$
$701$	−7.83780	−	3.77449i	−0.296030	−	0.142560i	−0.576003	+	0.817447i	$0.695389\pi$
$702$		0			0
$703$	25.5988	−	20.4144i	0.965477	−	0.769942i
$704$		0			0
$705$	−0.185435	−	1.37453i	−0.00698390	−	0.0517677i
$706$		0			0
$707$	3.01354	−	35.0736i	0.113336	−	1.31908i
$708$		0			0
$709$	−4.96449	+	6.22528i	−0.186445	+	0.233795i	−0.866266	−	0.499584i	$-0.833486\pi$
$709$	−4.96449	+	6.22528i	−0.186445	+	0.233795i	0.679820	+	0.733379i	$0.262058\pi$
$710$		0			0
$711$	−5.58713	−	2.69062i	−0.209534	−	0.100906i
$712$		0			0
$713$	36.4838	+	29.0948i	1.36633	+	1.08961i
$714$		0			0
$715$	23.3209	+	22.3212i	0.872151	+	0.834764i
$716$		0			0
$717$		−	1.57467i		−	0.0588073i
$718$		0			0
$719$	5.69182	+	24.9375i	0.212269	+	0.930011i	0.963021	+	0.269427i	$0.0868342\pi$
$719$	5.69182	+	24.9375i	0.212269	+	0.930011i	−0.750752	+	0.660584i	$0.770309\pi$
$720$		0			0
$721$	39.0738	+	3.35725i	1.45518	+	0.125030i
$722$		0			0
$723$	−3.20439	+	2.55542i	−0.119173	+	0.0950370i
$724$		0			0
$725$	4.68118	+	8.72168i	0.173855	+	0.323915i
$726$		0			0
$727$	3.09226	+	0.705789i	0.114686	+	0.0261763i	0.279479	−	0.960152i	$-0.409838\pi$
$727$	3.09226	+	0.705789i	0.114686	+	0.0261763i	−0.164793	+	0.986328i	$0.552696\pi$
$728$		0			0
$729$	−4.65344	−	20.3881i	−0.172350	−	0.755113i
$730$		0			0
$731$	26.3698	−	33.0666i	0.975321	−	1.22301i
$732$		0			0
$733$	−8.74410	−	18.1573i	−0.322971	−	0.670655i	0.674756	−	0.738040i	$-0.264249\pi$
$733$	−8.74410	−	18.1573i	−0.322971	−	0.670655i	−0.997727	+	0.0673851i	$0.978534\pi$
$734$		0			0
$735$	5.33818	+	0.199321i	0.196902	+	0.00735207i
$736$		0			0
$737$	−9.13351	−	18.9659i	−0.336437	−	0.698619i
$738$		0			0
$739$	20.7358	−	26.0018i	0.762778	−	0.956493i	−0.237110	−	0.971483i	$-0.576200\pi$
$739$	20.7358	−	26.0018i	0.762778	−	0.956493i	0.999888	+	0.0149897i	$0.00477154\pi$
$740$		0			0
$741$	2.44766	+	10.7239i	0.0899171	+	0.393953i
$742$		0			0
$743$	−38.8528	−	8.86790i	−1.42537	−	0.325332i	−0.560846	−	0.827920i	$-0.689524\pi$
$743$	−38.8528	−	8.86790i	−1.42537	−	0.325332i	−0.864526	+	0.502589i	$0.832381\pi$
$744$		0			0
$745$	31.0533	−	11.6354i	1.13771	−	0.426287i
$746$		0			0
$747$	−39.9356	+	31.8476i	−1.46117	+	1.16524i
$748$		0			0
$749$	3.78298	−	11.8053i	0.138227	−	0.431355i
$750$		0			0
$751$	−2.77500	−	12.1581i	−0.101261	−	0.443655i	−0.999987	−	0.00514314i	$-0.998363\pi$
$751$	−2.77500	−	12.1581i	−0.101261	−	0.443655i	0.898725	−	0.438512i	$-0.144494\pi$
$752$		0			0
$753$			0.469629i			0.0171142i
$754$		0			0
$755$	19.2796	−	20.1431i	0.701656	−	0.733081i
$756$		0			0
$757$	−14.3746	−	11.4634i	−0.522454	−	0.416643i	0.326431	−	0.945221i	$-0.394154\pi$
$757$	−14.3746	−	11.4634i	−0.522454	−	0.416643i	−0.848885	+	0.528578i	$0.822725\pi$
$758$		0			0
$759$	4.79264	+	2.30801i	0.173962	+	0.0837756i
$760$		0			0
$761$	21.0902	−	26.4463i	0.764519	−	0.958676i	−0.235394	−	0.971900i	$-0.575638\pi$
$761$	21.0902	−	26.4463i	0.764519	−	0.958676i	0.999913	+	0.0132238i	$0.00420940\pi$
$762$		0			0
$763$	−18.8736	+	12.5684i	−0.683271	+	0.455006i
$764$		0			0
$765$	38.8687	−	5.24372i	1.40530	−	0.189587i
$766$		0			0
$767$	−45.3800	+	36.1893i	−1.63858	+	1.30672i
$768$		0			0
$769$	−7.88695	−	3.79815i	−0.284411	−	0.136965i	0.286240	−	0.958158i	$-0.407595\pi$
$769$	−7.88695	−	3.79815i	−0.284411	−	0.136965i	−0.570650	+	0.821193i	$0.693309\pi$
$770$		0			0
$771$	8.83656	−	4.25546i	0.318241	−	0.153257i
$772$		0			0
$773$	3.29667	+	6.84560i	0.118573	+	0.246219i	0.951805	−	0.306705i	$-0.0992264\pi$
$773$	3.29667	+	6.84560i	0.118573	+	0.246219i	−0.833232	+	0.552924i	$0.813512\pi$
$774$		0			0
$775$	35.1884	+	6.42508i	1.26401	+	0.230796i
$776$		0			0
$777$	4.61265	−	3.07167i	0.165478	−	0.110196i
$778$		0			0
$779$	−4.79952	+	21.0281i	−0.171961	+	0.753408i
$780$		0			0
$781$	3.41213	−	14.9495i	0.122096	−	0.534936i
$782$		0			0
$783$			3.97513i			0.142060i
$784$		0			0
$785$	−0.967501	+	0.130524i	−0.0345316	+	0.00465861i
$786$		0			0
$787$	−46.1123	−	10.5248i	−1.64372	−	0.375169i	−0.702164	−	0.712015i	$-0.747783\pi$
$787$	−46.1123	−	10.5248i	−1.64372	−	0.375169i	−0.941560	+	0.336845i	$0.890640\pi$
$788$		0			0
$789$	−0.457703	+	2.00533i	−0.0162946	+	0.0713915i
$790$		0			0
$791$	−7.53319	+	23.5083i	−0.267849	+	0.835858i
$792$		0			0
$793$	−36.1704	+	75.1086i	−1.28445	+	2.66718i
$794$		0			0
$795$	1.78336	+	2.70486i	0.0632494	+	0.0959316i
$796$		0			0
$797$	−1.16816	−	2.42571i	−0.0413784	−	0.0859232i	0.879255	−	0.476352i	$-0.158041\pi$
$797$	−1.16816	−	2.42571i	−0.0413784	−	0.0859232i	−0.920633	+	0.390429i	$0.872327\pi$
$798$		0			0
$799$	−9.96069	−	4.79682i	−0.352384	−	0.169699i
$800$		0			0
$801$	31.0907	+	38.9864i	1.09853	+	1.37752i
$802$		0			0
$803$		−	5.44891i		−	0.192288i
$804$		0			0
$805$	−31.2990	−	22.5727i	−1.10314	−	0.795581i
$806$		0			0
$807$	0.903153	+	0.720240i	0.0317925	+	0.0253537i
$808$		0			0
$809$	−4.00344	−	1.92796i	−0.140753	−	0.0677833i	0.362181	−	0.932108i	$-0.382032\pi$
$809$	−4.00344	−	1.92796i	−0.140753	−	0.0677833i	−0.502935	+	0.864324i	$0.667746\pi$
$810$		0			0
$811$	3.19940	−	4.01192i	0.112346	−	0.140877i	−0.722479	−	0.691393i	$-0.756997\pi$
$811$	3.19940	−	4.01192i	0.112346	−	0.140877i	0.834825	+	0.550515i	$0.185569\pi$
$812$		0			0
$813$	5.19391	−	4.14200i	0.182158	−	0.145266i
$814$		0			0
$815$	−11.3739	+	1.53444i	−0.398410	+	0.0537490i
$816$		0			0
$817$	−36.1625	+	8.25385i	−1.26517	+	0.288766i
$818$		0			0
$819$	−6.37198	−	45.6494i	−0.222655	−	1.59512i
$820$		0			0
$821$	5.54381	+	6.95172i	0.193480	+	0.242617i	0.869103	−	0.494631i	$-0.164697\pi$
$821$	5.54381	+	6.95172i	0.193480	+	0.242617i	−0.675623	+	0.737247i	$0.736125\pi$
$822$		0			0
$823$	53.5010	−	12.2113i	1.86493	−	0.425658i	0.867508	−	0.497424i	$-0.165721\pi$
$823$	53.5010	−	12.2113i	1.86493	−	0.425658i	0.997422	+	0.0717659i	$0.0228635\pi$
$824$		0			0
$825$	4.07364	−	0.178533i	0.141826	−	0.00621573i
$826$		0			0
$827$	−24.7335	+	5.64525i	−0.860067	+	0.196305i	−0.629738	−	0.776808i	$-0.716838\pi$
$827$	−24.7335	+	5.64525i	−0.860067	+	0.196305i	−0.230330	+	0.973113i	$0.573980\pi$
$828$		0			0
$829$	−21.6069	+	27.0942i	−0.750438	+	0.941020i	−0.999624	−	0.0274359i	$-0.991266\pi$
$829$	−21.6069	+	27.0942i	−0.750438	+	0.941020i	0.249185	+	0.968456i	$0.419837\pi$
$830$		0			0
$831$	−1.25805	+	0.605845i	−0.0436413	+	0.0210165i
$832$		0			0
$833$	24.7481	−	34.6495i	0.857469	−	1.20053i
$834$		0			0
$835$	1.06441	−	0.701785i	0.0368354	−	0.0242863i
$836$		0			0
$837$	11.2309	+	8.95635i	0.388197	+	0.309577i
$838$		0			0
$839$	−4.11804	−	18.0423i	−0.142171	−	0.622890i	−0.994929	−	0.100584i	$-0.967929\pi$
$839$	−4.11804	−	18.0423i	−0.142171	−	0.622890i	0.852758	−	0.522306i	$-0.174928\pi$
$840$		0			0
$841$	5.58099	−	24.4519i	0.192448	−	0.843170i
$842$		0			0
$843$	5.20281	−	1.18751i	0.179194	−	0.0409000i
$844$		0			0
$845$	36.3356	−	37.9630i	1.24998	−	1.30597i
$846$		0			0
$847$	−7.12987	+	12.0439i	−0.244985	+	0.413833i
$848$		0			0
$849$	−1.18523	−	5.19284i	−0.0406770	−	0.178218i
$850$		0			0
$851$	−40.0337			−1.37234
$852$		0			0
$853$	−30.8883	+	24.6326i	−1.05760	+	0.843405i	−0.988044	−	0.154173i	$-0.950729\pi$
$853$	−30.8883	+	24.6326i	−1.05760	+	0.843405i	−0.0695529	+	0.997578i	$0.522157\pi$
$854$		0			0
$855$	−29.5188	−	17.6583i	−1.00952	−	0.603903i
$856$		0			0
$857$	7.80132	−	16.1996i	0.266488	−	0.553368i	−0.724189	−	0.689602i	$-0.757785\pi$
$857$	7.80132	−	16.1996i	0.266488	−	0.553368i	0.990677	+	0.136234i	$0.0434998\pi$
$858$		0			0
$859$	29.9894	−	37.6055i	1.02322	−	1.28308i	0.0647497	−	0.997902i	$-0.479375\pi$
$859$	29.9894	−	37.6055i	1.02322	−	1.28308i	0.958474	−	0.285180i	$-0.0920535\pi$
$860$		0			0
$861$	−1.11405	+	3.47653i	−0.0379667	+	0.118480i
$862$		0			0
$863$		−	15.7778i		−	0.537082i	−0.963268	−	0.268541i	$-0.913459\pi$
$863$		−	15.7778i		−	0.537082i	0.963268	−	0.268541i	$-0.0865415\pi$
$864$		0			0
$865$	8.90798	+	8.52612i	0.302880	+	0.289897i
$866$		0			0
$867$	−2.96169	+	6.15001i	−0.100584	+	0.208865i
$868$		0			0
$869$	−4.63001	+	2.22970i	−0.157062	+	0.0756372i
$870$		0			0
$871$	−47.9522	+	23.0926i	−1.62480	+	0.782462i
$872$		0			0
$873$	11.6559	−	24.2038i	0.394494	−	0.819175i
$874$		0			0
$875$	−29.3222	−	3.89951i	−0.991273	−	0.131827i
$876$		0			0
$877$	−36.1563	−	8.25243i	−1.22091	−	0.278665i	−0.436956	−	0.899483i	$-0.643943\pi$
$877$	−36.1563	−	8.25243i	−1.22091	−	0.278665i	−0.783955	+	0.620818i	$0.786800\pi$
$878$		0			0
$879$	−1.99585	+	8.74439i	−0.0673183	+	0.294941i
$880$		0			0
$881$	−49.4464			−1.66589			−0.832946	−	0.553354i	$-0.813348\pi$
$881$	−49.4464			−1.66589			−0.832946	+	0.553354i	$0.813348\pi$
$882$		0			0
$883$			20.5962i			0.693118i	0.938028	+	0.346559i	$0.112650\pi$
$883$			20.5962i			0.693118i	−0.938028	+	0.346559i	$0.887350\pi$
$884$		0			0
$885$	−0.661146	+	7.30170i	−0.0222242	+	0.245444i
$886$		0			0
$887$	−30.9964	−	7.07471i	−1.04076	−	0.237546i	−0.332206	−	0.943207i	$-0.607793\pi$
$887$	−30.9964	−	7.07471i	−1.04076	−	0.237546i	−0.708549	+	0.705661i	$0.750650\pi$
$888$		0			0
$889$	16.3616	−	17.2523i	0.548751	−	0.578622i
$890$		0			0
$891$	−17.1486	−	8.25835i	−0.574501	−	0.276665i
$892$		0			0
$893$	4.20690	+	8.73571i	0.140778	+	0.292329i
$894$		0			0
$895$	−18.2860	−	27.7347i	−0.611233	−	0.927068i
$896$		0			0
$897$	5.83543	−	12.1174i	0.194839	−	0.404588i
$898$		0			0
$899$	8.83043	+	11.0730i	0.294511	+	0.369306i
$900$		0			0
$901$	25.8247			0.860346
$902$		0			0
$903$	−6.21786	+	0.867923i	−0.206918	+	0.0288827i
$904$		0			0
$905$	7.41791	+	4.43744i	0.246580	+	0.147506i
$906$		0			0
$907$	15.9020	−	33.0208i	0.528016	−	1.09644i	−0.450975	−	0.892536i	$-0.648924\pi$
$907$	15.9020	−	33.0208i	0.528016	−	1.09644i	0.978992	−	0.203901i	$-0.0653620\pi$
$908$		0			0
$909$	−23.9211	+	29.9961i	−0.793413	+	0.994909i
$910$		0			0
$911$	−36.2668	−	45.4772i	−1.20157	−	1.50673i	−0.809844	−	0.586645i	$-0.800448\pi$
$911$	−36.2668	−	45.4772i	−1.20157	−	1.50673i	−0.391729	−	0.920081i	$-0.628123\pi$
$912$		0			0
$913$			42.3292i			1.40089i
$914$		0			0
$915$	3.69462	+	9.86049i	0.122140	+	0.325978i
$916$		0			0
$917$	−5.84028	−	15.3719i	−0.192863	−	0.507623i
$918$		0			0
$919$	4.93389	+	6.18691i	0.162754	+	0.204087i	0.856521	−	0.516113i	$-0.172621\pi$
$919$	4.93389	+	6.18691i	0.162754	+	0.204087i	−0.693766	+	0.720200i	$0.744050\pi$
$920$		0			0
$921$	−1.20732	−	5.28961i	−0.0397825	−	0.174299i
$922$		0			0
$923$	−37.7974	−	8.62702i	−1.24412	−	0.283962i
$924$		0			0
$925$	−27.0389	+	14.5126i	−0.889034	+	0.477170i
$926$		0			0
$927$	−33.4172	−	26.6494i	−1.09757	−	0.875280i
$928$		0			0
$929$	−42.1150	+	20.2815i	−1.38175	+	0.665415i	−0.969372	−	0.245598i	$-0.921016\pi$
$929$	−42.1150	+	20.2815i	−1.38175	+	0.665415i	−0.412377	+	0.911013i	$0.635301\pi$
$930$		0			0
$931$	−35.9160	+	10.2260i	−1.17710	+	0.335142i
$932$		0			0
$933$	−2.36911	−	4.91951i	−0.0775613	−	0.161058i
$934$		0			0
$935$	16.6853	−	27.8922i	0.545668	−	0.912174i
$936$		0			0
$937$	24.9931	−	5.70452i	0.816490	−	0.186359i	0.206173	−	0.978516i	$-0.433899\pi$
$937$	24.9931	−	5.70452i	0.816490	−	0.186359i	0.610317	+	0.792157i	$0.291042\pi$
$938$		0			0
$939$	1.60518	−	7.03273i	0.0523829	−	0.229505i
$940$		0			0
$941$	−9.24437	−	40.5022i	−0.301358	−	1.32033i	−0.868079	−	0.496425i	$-0.834646\pi$
$941$	−9.24437	−	40.5022i	−0.301358	−	1.32033i	0.566722	−	0.823909i	$-0.308212\pi$
$942$		0			0
$943$	20.6186	−	16.4428i	0.671433	−	0.535450i
$944$		0			0
$945$	−9.63485	−	6.94861i	−0.313422	−	0.226038i
$946$		0			0
$947$	5.05209	−	1.15311i	0.164171	−	0.0374709i	−0.139645	−	0.990202i	$-0.544596\pi$
$947$	5.05209	−	1.15311i	0.164171	−	0.0374709i	0.303816	+	0.952731i	$0.401739\pi$
$948$		0			0
$949$	−13.7767			−0.447210
$950$		0			0
$951$	−5.08385	−	6.37495i	−0.164855	−	0.206722i
$952$		0			0
$953$	−24.8137	−	19.7883i	−0.803795	−	0.641005i	0.132908	−	0.991128i	$-0.457568\pi$
$953$	−24.8137	−	19.7883i	−0.803795	−	0.641005i	−0.936704	+	0.350123i	$0.886140\pi$
$954$		0			0
$955$	−3.61285	+	11.0988i	−0.116909	+	0.359148i
$956$		0			0
$957$	1.26225	+	1.00661i	0.0408026	+	0.0325390i
$958$		0			0
$959$	−20.9164	+	7.94682i	−0.675424	+	0.256616i
$960$		0			0
$961$	20.1803			0.650978
$962$		0			0
$963$	−10.5631	+	8.42377i	−0.340390	+	0.271452i
$964$		0			0
$965$	43.3558	+	14.1131i	1.39567	+	0.454316i
$966$		0			0
$967$	2.32850	+	4.83518i	0.0748796	+	0.155489i	0.935048	−	0.354521i	$-0.115356\pi$
$967$	2.32850	+	4.83518i	0.0748796	+	0.155489i	−0.860169	+	0.510010i	$0.829642\pi$
$968$		0			0
$969$	9.97805	−	4.80518i	0.320541	−	0.154365i
$970$		0			0
$971$	−2.84091	−	1.36811i	−0.0911690	−	0.0439047i	0.387744	−	0.921767i	$-0.373255\pi$
$971$	−2.84091	−	1.36811i	−0.0911690	−	0.0439047i	−0.478913	+	0.877863i	$0.658969\pi$
$972$		0			0
$973$	4.62907	−	53.8761i	0.148401	−	1.72719i
$974$		0			0
$975$	−0.451392	−	10.2995i	−0.0144561	−	0.329849i
$976$		0			0
$977$	−30.5014	−	6.96175i	−0.975827	−	0.222726i	−0.295264	−	0.955416i	$-0.595408\pi$
$977$	−30.5014	−	6.96175i	−0.975827	−	0.222726i	−0.680563	+	0.732690i	$0.738265\pi$
$978$		0			0
$979$	41.3232			1.32069
$980$		0			0
$981$	24.7134			0.789037
$982$		0			0
$983$	−9.70594	−	2.21532i	−0.309571	−	0.0706576i	0.0649129	−	0.997891i	$-0.479323\pi$
$983$	−9.70594	−	2.21532i	−0.309571	−	0.0706576i	−0.374484	+	0.927233i	$0.622180\pi$
$984$		0			0
$985$	0.195675	−	2.16104i	0.00623474	−	0.0688565i
$986$		0			0
$987$	0.582857	+	1.53410i	0.0185525	+	0.0488310i
$988$		0			0
$989$	40.8615	+	19.6779i	1.29932	+	0.625720i
$990$		0			0
$991$	5.19911	−	2.50376i	0.165155	−	0.0795346i	−0.349480	−	0.936944i	$-0.613642\pi$
$991$	5.19911	−	2.50376i	0.165155	−	0.0795346i	0.514635	+	0.857409i	$0.327927\pi$
$992$		0			0
$993$	4.67162	+	9.70073i	0.148250	+	0.307843i
$994$		0			0
$995$	−11.3139	+	34.7567i	−0.358676	+	1.10186i
$996$		0			0
$997$	10.1831	−	8.12075i	0.322502	−	0.257187i	−0.448834	−	0.893615i	$-0.648160\pi$
$997$	10.1831	−	8.12075i	0.322502	−	0.257187i	0.771336	+	0.636429i	$0.219589\pi$
$998$		0			0
$999$	−12.3237			−0.389904

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.bd.a.169.14	yes	168
5.4	even	2	inner	980.2.bd.a.169.15	yes	168
49.29	even	7	inner	980.2.bd.a.29.15	yes	168
245.29	even	14	inner	980.2.bd.a.29.14	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.bd.a.29.14	✓	168	245.29	even	14	inner
980.2.bd.a.29.15	yes	168	49.29	even	7	inner
980.2.bd.a.169.14	yes	168	1.1	even	1	trivial
980.2.bd.a.169.15	yes	168	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.bd (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.332725 - 0.0759423i) q^{3} +(-2.22696 - 0.201644i) q^{5} +(2.62035 - 0.365762i) q^{7} +(-2.59797 - 1.25112i) q^{9} +(-2.15292 + 1.03679i) q^{11} +(2.62135 + 5.44329i) q^{13} +(0.725651 + 0.236212i) q^{15} +(4.75577 - 3.79260i) q^{17} -5.33478 q^{19} +(-0.899631 - 0.0772969i) q^{21} +(5.09974 + 4.06691i) q^{23} +(4.91868 + 0.898104i) q^{25} +(1.56987 + 1.25193i) q^{27} +(1.23433 + 1.54780i) q^{29} +7.15404 q^{31} +(0.795064 - 0.181468i) q^{33} +(-5.90915 + 0.286160i) q^{35} +(-4.79848 + 3.82666i) q^{37} +(-0.458813 - 2.01019i) q^{39} +(0.899666 - 3.94169i) q^{41} +(6.77863 - 1.54718i) q^{43} +(5.53328 + 3.31005i) q^{45} +(-0.788580 - 1.63750i) q^{47} +(6.73244 - 1.91685i) q^{49} +(-1.87038 + 0.900727i) q^{51} +(3.31926 + 2.64702i) q^{53} +(5.00351 - 1.87476i) q^{55} +(1.77501 + 0.405135i) q^{57} +(2.13782 + 9.36639i) q^{59} +(8.60315 + 10.7880i) q^{61} +(-7.26519 - 2.32812i) q^{63} +(-4.74003 - 12.6506i) q^{65} +8.80941i q^{67} +(-1.38796 - 1.74045i) q^{69} +(-4.00099 + 5.01708i) q^{71} +(-0.989387 + 2.05448i) q^{73} +(-1.56836 - 0.672357i) q^{75} +(-5.26217 + 3.50420i) q^{77} +2.15058 q^{79} +(4.96629 + 6.22753i) q^{81} +(7.68593 - 15.9600i) q^{83} +(-11.3556 + 7.48698i) q^{85} +(-0.293148 - 0.608728i) q^{87} +(-15.5807 - 7.50326i) q^{89} +(8.85980 + 13.3045i) q^{91} +(-2.38033 - 0.543294i) q^{93} +(11.8803 + 1.07572i) q^{95} +9.31644i q^{97} +6.89035 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 2 q^{5} + 18 q^{9} + 6 q^{11} + 16 q^{15} + 20 q^{19} - 6 q^{21} + 6 q^{25} - 14 q^{29} + 20 q^{31} + 2 q^{35} + 40 q^{39} - 14 q^{41} + 96 q^{45} + 32 q^{49} + 4 q^{51} - 30 q^{55} - 28 q^{59}+ \cdots + 136 q^{99}+O(q^{100}) \) 168 * q + 2 * q^5 + 18 * q^9 + 6 * q^11 + 16 * q^15 + 20 * q^19 - 6 * q^21 + 6 * q^25 - 14 * q^29 + 20 * q^31 + 2 * q^35 + 40 * q^39 - 14 * q^41 + 96 * q^45 + 32 * q^49 + 4 * q^51 - 30 * q^55 - 28 * q^59 - 16 * q^61 - 20 * q^65 + 12 * q^69 + 34 * q^71 - 24 * q^75 - 24 * q^79 - 62 * q^81 - 42 * q^85 - 74 * q^89 + 60 * q^91 - 10 * q^95 + 136 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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