LMFDB - Embedded newform 820.2.bi.a.189.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(189,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.189"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bi (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			189.13
Character	$\chi$	$=$	820.189
Dual form			820.2.bi.a.269.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.660390 q^{3} +(0.00764381 - 2.23605i) q^{5} +(-0.328706 - 1.01165i) q^{7} -2.56389 q^{9} +(-1.85813 - 2.55750i) q^{11} +(0.103580 - 0.318787i) q^{13} +(0.00504790 - 1.47667i) q^{15} +(-4.74676 + 3.44872i) q^{17} +(5.69881 - 1.85166i) q^{19} +(-0.217074 - 0.668085i) q^{21} +(-7.08290 - 2.30138i) q^{23} +(-4.99988 - 0.0341840i) q^{25} -3.67433 q^{27} +(2.91444 - 4.01139i) q^{29} +(-7.53890 + 5.47733i) q^{31} +(-1.22709 - 1.68895i) q^{33} +(-2.26462 + 0.727271i) q^{35} +(3.51520 - 4.83826i) q^{37} +(0.0684032 - 0.210523i) q^{39} +(6.18424 - 1.65986i) q^{41} +(7.57529 + 2.46136i) q^{43} +(-0.0195979 + 5.73299i) q^{45} +(-2.46228 + 7.57812i) q^{47} +(4.74773 - 3.44943i) q^{49} +(-3.13471 + 2.27750i) q^{51} +(-8.99438 - 6.53480i) q^{53} +(-5.73292 + 4.13534i) q^{55} +(3.76343 - 1.22281i) q^{57} +(3.16987 - 9.75587i) q^{59} +(-2.19027 - 6.74094i) q^{61} +(0.842764 + 2.59376i) q^{63} +(-0.712032 - 0.234047i) q^{65} +(0.514472 + 0.373785i) q^{67} +(-4.67748 - 1.51980i) q^{69} +(3.09514 + 4.26010i) q^{71} -4.81973i q^{73} +(-3.30187 - 0.0225747i) q^{75} +(-1.97652 + 2.72045i) q^{77} -11.1861i q^{79} +5.26517 q^{81} +8.67639i q^{83} +(7.67525 + 10.6404i) q^{85} +(1.92467 - 2.64908i) q^{87} +(-1.49719 + 0.486466i) q^{89} -0.356548 q^{91} +(-4.97861 + 3.61717i) q^{93} +(-4.09684 - 12.7570i) q^{95} +(-9.61413 - 6.98507i) q^{97} +(4.76404 + 6.55714i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 68 q^{9} + 10 q^{15} - 26 q^{21} + 10 q^{25} - 20 q^{29} + 4 q^{31} + 15 q^{35} - 8 q^{39} + 4 q^{41} - 4 q^{45} + 18 q^{49} + 52 q^{51} - 36 q^{59} - 42 q^{61} - 15 q^{65} + 30 q^{69} - 20 q^{75}+ \cdots + 80 q^{99}+O(q^{100}) $ 80 * q + 68 * q^9 + 10 * q^15 - 26 * q^21 + 10 * q^25 - 20 * q^29 + 4 * q^31 + 15 * q^35 - 8 * q^39 + 4 * q^41 - 4 * q^45 + 18 * q^49 + 52 * q^51 - 36 * q^59 - 42 * q^61 - 15 * q^65 + 30 * q^69 - 20 * q^75 + 32 * q^81 + 10 * q^89 - 132 * q^91 + 50 * q^95 + 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$	$-1$

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			0
$2$		0			0
$3$	0.660390			0.381276			0.190638	−	0.981660i	$-0.438944\pi$
$3$	0.660390			0.381276			0.190638	+	0.981660i	$0.438944\pi$
$4$		0			0
$5$	0.00764381	−	2.23605i	0.00341842	−	0.999994i
$5$	0.00764381	−	2.23605i	0.00341842	−	0.999994i
$6$		0			0
$7$	−0.328706	−	1.01165i	−0.124239	−	0.382369i	0.869523	−	0.493893i	$-0.164427\pi$
$7$	−0.328706	−	1.01165i	−0.124239	−	0.382369i	−0.993762	+	0.111525i	$0.964427\pi$
$8$		0			0
$9$	−2.56389			−0.854629
$10$		0			0
$11$	−1.85813	−	2.55750i	−0.560248	−	0.771116i	0.431110	−	0.902300i	$-0.358122\pi$
$11$	−1.85813	−	2.55750i	−0.560248	−	0.771116i	−0.991358	+	0.131184i	$0.958122\pi$
$12$		0			0
$13$	0.103580	−	0.318787i	0.0287279	−	0.0884155i	−0.935665	−	0.352891i	$-0.885199\pi$
$13$	0.103580	−	0.318787i	0.0287279	−	0.0884155i	0.964392	+	0.264475i	$0.0851987\pi$
$14$		0			0
$15$	0.00504790	−	1.47667i	0.00130336	−	0.381274i
$16$		0			0
$17$	−4.74676	+	3.44872i	−1.15126	+	0.836438i	−0.988648	−	0.150252i	$-0.951992\pi$
$17$	−4.74676	+	3.44872i	−1.15126	+	0.836438i	−0.162611	+	0.986690i	$0.551992\pi$
$18$		0			0
$19$	5.69881	−	1.85166i	1.30740	−	0.424799i	0.429248	−	0.903187i	$-0.358779\pi$
$19$	5.69881	−	1.85166i	1.30740	−	0.424799i	0.878149	+	0.478388i	$0.158779\pi$
$20$		0			0
$21$	−0.217074	−	0.668085i	−0.0473694	−	0.145788i
$22$		0			0
$23$	−7.08290	−	2.30138i	−1.47689	−	0.479870i	−0.543706	−	0.839276i	$-0.682979\pi$
$23$	−7.08290	−	2.30138i	−1.47689	−	0.479870i	−0.933181	+	0.359406i	$0.882979\pi$
$24$		0			0
$25$	−4.99988	−	0.0341840i	−0.999977	−	0.00683679i
$26$		0			0
$27$	−3.67433			−0.707126
$28$		0			0
$29$	2.91444	−	4.01139i	0.541198	−	0.744896i	−0.447587	−	0.894241i	$-0.647716\pi$
$29$	2.91444	−	4.01139i	0.541198	−	0.744896i	0.988785	+	0.149345i	$0.0477164\pi$
$30$		0			0
$31$	−7.53890	+	5.47733i	−1.35403	+	0.983757i	−0.355226	+	0.934781i	$0.615596\pi$
$31$	−7.53890	+	5.47733i	−1.35403	+	0.983757i	−0.998800	+	0.0489767i	$0.984404\pi$
$32$		0			0
$33$	−1.22709	−	1.68895i	−0.213609	−	0.294008i
$34$		0			0
$35$	−2.26462	+	0.727271i	−0.382791	+	0.122931i
$36$		0			0
$37$	3.51520	−	4.83826i	0.577895	−	0.795404i	−0.415567	−	0.909562i	$-0.636417\pi$
$37$	3.51520	−	4.83826i	0.577895	−	0.795404i	0.993463	+	0.114158i	$0.0364170\pi$
$38$		0			0
$39$	0.0684032	−	0.210523i	0.0109533	−	0.0337107i
$40$		0			0
$41$	6.18424	−	1.65986i	0.965817	−	0.259226i
$41$	6.18424	−	1.65986i	0.965817	−	0.259226i
$42$		0			0
$43$	7.57529	+	2.46136i	1.15522	+	0.375354i	0.823108	−	0.567885i	$-0.192238\pi$
$43$	7.57529	+	2.46136i	1.15522	+	0.375354i	0.332113	+	0.943239i	$0.392238\pi$
$44$		0			0
$45$	−0.0195979	+	5.73299i	−0.00292148	+	0.854624i
$46$		0			0
$47$	−2.46228	+	7.57812i	−0.359161	+	1.10538i	0.594397	+	0.804172i	$0.297391\pi$
$47$	−2.46228	+	7.57812i	−0.359161	+	1.10538i	−0.953558	+	0.301211i	$0.902609\pi$
$48$		0			0
$49$	4.74773	−	3.44943i	0.678247	−	0.492775i
$50$		0			0
$51$	−3.13471	+	2.27750i	−0.438947	+	0.318914i
$52$		0			0
$53$	−8.99438	−	6.53480i	−1.23547	−	0.897624i	−0.238186	−	0.971220i	$-0.576553\pi$
$53$	−8.99438	−	6.53480i	−1.23547	−	0.897624i	−0.997288	+	0.0735954i	$0.976553\pi$
$54$		0			0
$55$	−5.73292	+	4.13534i	−0.773027	+	0.557609i
$56$		0			0
$57$	3.76343	−	1.22281i	0.498479	−	0.161966i
$58$		0			0
$59$	3.16987	−	9.75587i	0.412682	−	1.27011i	−0.501625	−	0.865085i	$-0.667264\pi$
$59$	3.16987	−	9.75587i	0.412682	−	1.27011i	0.914307	−	0.405021i	$-0.132736\pi$
$60$		0			0
$61$	−2.19027	−	6.74094i	−0.280435	−	0.863089i	−0.987730	−	0.156171i	$-0.950085\pi$
$61$	−2.19027	−	6.74094i	−0.280435	−	0.863089i	0.707295	−	0.706918i	$-0.249915\pi$
$62$		0			0
$63$	0.842764	+	2.59376i	0.106178	+	0.326783i
$64$		0			0
$65$	−0.712032	−	0.234047i	−0.0883168	−	0.0290300i
$66$		0			0
$67$	0.514472	+	0.373785i	0.0628527	+	0.0456652i	0.618768	−	0.785574i	$-0.287632\pi$
$67$	0.514472	+	0.373785i	0.0628527	+	0.0456652i	−0.555915	+	0.831239i	$0.687632\pi$
$68$		0			0
$69$	−4.67748	−	1.51980i	−0.563102	−	0.182963i
$70$		0			0
$71$	3.09514	+	4.26010i	0.367326	+	0.505581i	0.952172	−	0.305564i	$-0.0988449\pi$
$71$	3.09514	+	4.26010i	0.367326	+	0.505581i	−0.584846	+	0.811145i	$0.698845\pi$
$72$		0			0
$73$		−	4.81973i		−	0.564107i	−0.959399	−	0.282053i	$-0.908984\pi$
$73$		−	4.81973i		−	0.564107i	0.959399	−	0.282053i	$-0.0910155\pi$
$74$		0			0
$75$	−3.30187	−	0.0225747i	−0.381267	−	0.00260671i
$76$		0			0
$77$	−1.97652	+	2.72045i	−0.225246	+	0.310024i
$78$		0			0
$79$		−	11.1861i		−	1.25854i	−0.777189	−	0.629268i	$-0.783355\pi$
$79$		−	11.1861i		−	1.25854i	0.777189	−	0.629268i	$-0.216645\pi$
$80$		0			0
$81$	5.26517			0.585018
$82$		0			0
$83$			8.67639i			0.952358i	0.879348	+	0.476179i	$0.157979\pi$
$83$			8.67639i			0.952358i	−0.879348	+	0.476179i	$0.842021\pi$
$84$		0			0
$85$	7.67525	+	10.6404i	0.832498	+	1.15411i
$86$		0			0
$87$	1.92467	−	2.64908i	0.206346	−	0.284011i
$88$		0			0
$89$	−1.49719	+	0.486466i	−0.158702	+	0.0515653i	−0.387290	−	0.921958i	$-0.626589\pi$
$89$	−1.49719	+	0.486466i	−0.158702	+	0.0515653i	0.228589	+	0.973523i	$0.426589\pi$
$90$		0			0
$91$	−0.356548			−0.0373764
$92$		0			0
$93$	−4.97861	+	3.61717i	−0.516258	+	0.375083i
$94$		0			0
$95$	−4.09684	−	12.7570i	−0.420327	−	1.30884i
$96$		0			0
$97$	−9.61413	−	6.98507i	−0.976167	−	0.709227i	−0.0193183	−	0.999813i	$-0.506150\pi$
$97$	−9.61413	−	6.98507i	−0.976167	−	0.709227i	−0.956849	+	0.290586i	$0.906150\pi$
$98$		0			0
$99$	4.76404	+	6.55714i	0.478804	+	0.659018i
$100$		0			0
$101$	3.72916	−	1.21168i	0.371065	−	0.120566i	−0.117547	−	0.993067i	$-0.537503\pi$
$101$	3.72916	−	1.21168i	0.371065	−	0.120566i	0.488613	+	0.872501i	$0.337503\pi$
$102$		0			0
$103$	16.2366	−	5.27558i	1.59984	−	0.519819i	0.632770	−	0.774340i	$-0.281918\pi$
$103$	16.2366	−	5.27558i	1.59984	−	0.519819i	0.967067	+	0.254521i	$0.0819179\pi$
$104$		0			0
$105$	−1.49553	+	0.480282i	−0.145949	+	0.0468708i
$106$		0			0
$107$	9.51588	−	3.09190i	0.919934	−	0.298905i	0.189495	−	0.981882i	$-0.439315\pi$
$107$	9.51588	−	3.09190i	0.919934	−	0.298905i	0.730440	+	0.682977i	$0.239315\pi$
$108$		0			0
$109$		−	9.17559i		−	0.878863i	−0.898276	−	0.439431i	$-0.855180\pi$
$109$		−	9.17559i		−	0.878863i	0.898276	−	0.439431i	$-0.144820\pi$
$110$		0			0
$111$	2.32140	−	3.19513i	0.220338	−	0.303269i
$112$		0			0
$113$	2.97609	+	4.09624i	0.279967	+	0.385342i	0.925723	−	0.378202i	$-0.123458\pi$
$113$	2.97609	+	4.09624i	0.279967	+	0.385342i	−0.645756	+	0.763544i	$0.723458\pi$
$114$		0			0
$115$	−5.20014	+	15.8202i	−0.484916	+	1.47524i
$116$		0			0
$117$	−0.265567	+	0.817332i	−0.0245517	+	0.0755624i
$118$		0			0
$119$	5.04920	+	3.66846i	0.462859	+	0.336287i
$120$		0			0
$121$	0.311032	−	0.957258i	0.0282756	−	0.0870235i
$122$		0			0
$123$	4.08401	−	1.09615i	0.368243	−	0.0988368i
$124$		0			0
$125$	−0.114655	+	11.1798i	−0.0102551	+	0.999947i
$126$		0			0
$127$	1.28835	−	1.77326i	0.114323	−	0.157352i	−0.748021	−	0.663675i	$-0.768996\pi$
$127$	1.28835	−	1.77326i	0.114323	−	0.157352i	0.862344	+	0.506323i	$0.168996\pi$
$128$		0			0
$129$	5.00264	+	1.62546i	0.440458	+	0.143114i
$130$		0			0
$131$	−14.6455	+	10.6406i	−1.27958	+	0.929670i	−0.999540	−	0.0303183i	$-0.990348\pi$
$131$	−14.6455	+	10.6406i	−1.27958	+	0.929670i	−0.280041	+	0.959988i	$0.590348\pi$
$132$		0			0
$133$	−3.74646	−	5.15656i	−0.324860	−	0.447131i
$134$		0			0
$135$	−0.0280859	+	8.21601i	−0.00241725	+	0.707121i
$136$		0			0
$137$	−20.0857			−1.71604			−0.858018	−	0.513620i	$-0.828304\pi$
$137$	−20.0857			−1.71604			−0.858018	+	0.513620i	$0.828304\pi$
$138$		0			0
$139$	2.89359	+	8.90555i	0.245431	+	0.755359i	0.995565	+	0.0940735i	$0.0299889\pi$
$139$	2.89359	+	8.90555i	0.245431	+	0.755359i	−0.750134	+	0.661286i	$0.770011\pi$
$140$		0			0
$141$	−1.62606	+	5.00451i	−0.136939	+	0.421456i
$142$		0			0
$143$	−1.00776	+	0.327442i	−0.0842734	+	0.0273821i
$144$		0			0
$145$	−8.94740	−	6.54752i	−0.743041	−	0.543742i
$146$		0			0
$147$	3.13535	−	2.27796i	0.258599	−	0.187883i
$148$		0			0
$149$	11.8683	−	16.3354i	0.972292	−	1.33824i	0.0314107	−	0.999507i	$-0.490000\pi$
$149$	11.8683	−	16.3354i	0.972292	−	1.33824i	0.940881	−	0.338738i	$-0.110000\pi$
$150$		0			0
$151$	4.11680	+	1.33763i	0.335021	+	0.108855i	0.471696	−	0.881761i	$-0.343642\pi$
$151$	4.11680	+	1.33763i	0.335021	+	0.108855i	−0.136676	+	0.990616i	$0.543642\pi$
$152$		0			0
$153$	12.1702	−	8.84213i	0.983899	−	0.714844i
$154$		0			0
$155$	12.1900	+	16.8993i	0.979123	+	1.35738i
$156$		0			0
$157$	6.52474	+	20.0811i	0.520731	+	1.60264i	0.772607	+	0.634885i	$0.218952\pi$
$157$	6.52474	+	20.0811i	0.520731	+	1.60264i	−0.251876	+	0.967759i	$0.581048\pi$
$158$		0			0
$159$	−5.93980	−	4.31552i	−0.471057	−	0.342243i
$160$		0			0
$161$			7.92191i			0.624334i
$162$		0			0
$163$			16.0461i			1.25683i	0.777880	+	0.628413i	$0.216295\pi$
$163$			16.0461i			1.25683i	−0.777880	+	0.628413i	$0.783705\pi$
$164$		0			0
$165$	−3.78596	+	2.73094i	−0.294737	+	0.212603i
$166$		0			0
$167$	11.7231			0.907163			0.453582	−	0.891215i	$-0.350146\pi$
$167$	11.7231			0.907163			0.453582	+	0.891215i	$0.350146\pi$
$168$		0			0
$169$	10.4263	+	7.57517i	0.802025	+	0.582705i
$170$		0			0
$171$	−14.6111	+	4.74743i	−1.11734	+	0.363045i
$172$		0			0
$173$		−	11.3943i		−	0.866293i	−0.901324	−	0.433146i	$-0.857403\pi$
$173$		−	11.3943i		−	0.866293i	0.901324	−	0.433146i	$-0.142597\pi$
$174$		0			0
$175$	1.60891	+	5.06938i	0.121622	+	0.383209i
$176$		0			0
$177$	2.09335	−	6.44267i	0.157346	−	0.484261i
$178$		0			0
$179$	2.68993	−	3.70237i	0.201055	−	0.276728i	−0.696570	−	0.717489i	$-0.745291\pi$
$179$	2.68993	−	3.70237i	0.201055	−	0.276728i	0.897624	+	0.440761i	$0.145291\pi$
$180$		0			0
$181$	−5.34204	−	7.35268i	−0.397071	−	0.546521i	0.562935	−	0.826501i	$-0.309672\pi$
$181$	−5.34204	−	7.35268i	−0.397071	−	0.546521i	−0.960006	+	0.279980i	$0.909672\pi$
$182$		0			0
$183$	−1.44643	−	4.45165i	−0.106923	−	0.329075i
$184$		0			0
$185$	−10.7917	−	7.89716i	−0.793424	−	0.580611i
$186$		0			0
$187$	17.6402	+	5.73166i	1.28998	+	0.419141i
$188$		0			0
$189$	1.20777	+	3.71715i	0.0878526	+	0.270383i
$190$		0			0
$191$			18.2622i			1.32141i	0.750647	+	0.660704i	$0.229742\pi$
$191$			18.2622i			1.32141i	−0.750647	+	0.660704i	$0.770258\pi$
$192$		0			0
$193$	14.6747	+	10.6618i	1.05631	+	0.767451i	0.973401	−	0.229107i	$-0.0735806\pi$
$193$	14.6747	+	10.6618i	1.05631	+	0.767451i	0.0829039	+	0.996558i	$0.473581\pi$
$194$		0			0
$195$	−0.470219	−	0.154562i	−0.0336731	−	0.0110684i
$196$		0			0
$197$	−15.1221	−	20.8138i	−1.07741	−	1.48292i	−0.862346	−	0.506320i	$-0.831006\pi$
$197$	−15.1221	−	20.8138i	−1.07741	−	1.48292i	−0.215059	−	0.976601i	$-0.568994\pi$
$198$		0			0
$199$	2.15374	+	0.699791i	0.152674	+	0.0496069i	0.384357	−	0.923184i	$-0.374423\pi$
$199$	2.15374	+	0.699791i	0.152674	+	0.0496069i	−0.231683	+	0.972791i	$0.574423\pi$
$200$		0			0
$201$	0.339752	+	0.246844i	0.0239642	+	0.0174110i
$202$		0			0
$203$	−5.01612	−	1.62984i	−0.352063	−	0.114392i
$204$		0			0
$205$	−3.66426	−	13.8410i	−0.255923	−	0.966697i
$206$		0			0
$207$	18.1598	+	5.90046i	1.26219	+	0.410111i
$208$		0			0
$209$	−15.3248	−	11.1341i	−1.06004	−	0.770161i
$210$		0			0
$211$	−4.55685	−	1.48061i	−0.313707	−	0.101930i	0.147932	−	0.988998i	$-0.452738\pi$
$211$	−4.55685	−	1.48061i	−0.313707	−	0.101930i	−0.461639	+	0.887068i	$0.652738\pi$
$212$		0			0
$213$	2.04400	+	2.81333i	0.140053	+	0.192766i
$214$		0			0
$215$	5.56164	−	16.9200i	0.379301	−	1.15393i
$216$		0			0
$217$	8.01923	+	5.82631i	0.544381	+	0.395516i
$218$		0			0
$219$		−	3.18290i		−	0.215080i
$220$		0			0
$221$	0.607737	+	1.87042i	0.0408808	+	0.125818i
$222$		0			0
$223$	−19.6670	−	6.39020i	−1.31700	−	0.427920i	−0.435537	−	0.900171i	$-0.643441\pi$
$223$	−19.6670	−	6.39020i	−1.31700	−	0.427920i	−0.881464	+	0.472251i	$0.843441\pi$
$224$		0			0
$225$	12.8191	+	0.0876438i	0.854609	+	0.00584292i
$226$		0			0
$227$	0.629511	+	1.93743i	0.0417821	+	0.128592i	0.969772	−	0.244014i	$-0.0784643\pi$
$227$	0.629511	+	1.93743i	0.0417821	+	0.128592i	−0.927990	+	0.372606i	$0.878464\pi$
$228$		0			0
$229$	14.1206	+	19.4353i	0.933113	+	1.28432i	0.958633	+	0.284646i	$0.0918760\pi$
$229$	14.1206	+	19.4353i	0.933113	+	1.28432i	−0.0255195	+	0.999674i	$0.508124\pi$
$230$		0			0
$231$	−1.30528	+	1.79656i	−0.0858808	+	0.118205i
$232$		0			0
$233$	−3.46641	+	10.6685i	−0.227092	+	0.698918i	0.770980	+	0.636859i	$0.219767\pi$
$233$	−3.46641	+	10.6685i	−0.227092	+	0.698918i	−0.998072	+	0.0620589i	$0.980233\pi$
$234$		0			0
$235$	16.9263	+	5.56372i	1.10415	+	0.362937i
$236$		0			0
$237$		−	7.38719i		−	0.479850i
$238$		0			0
$239$	13.2472	−	4.30427i	0.856889	−	0.278420i	0.152561	−	0.988294i	$-0.451248\pi$
$239$	13.2472	−	4.30427i	0.856889	−	0.278420i	0.704329	+	0.709874i	$0.251248\pi$
$240$		0			0
$241$	20.1436	+	14.6352i	1.29756	+	0.942734i	0.999929	−	0.0119467i	$-0.00380285\pi$
$241$	20.1436	+	14.6352i	1.29756	+	0.942734i	0.297633	+	0.954680i	$0.403803\pi$
$242$		0			0
$243$	14.5001			0.930179
$244$		0			0
$245$	−7.67681	−	10.6425i	−0.490454	−	0.679927i
$246$		0			0
$247$		−	2.00850i		−	0.127798i
$248$		0			0
$249$			5.72980i			0.363111i
$250$		0			0
$251$	−13.0061	−	9.44947i	−0.820936	−	0.596445i	0.0960444	−	0.995377i	$-0.469381\pi$
$251$	−13.0061	−	9.44947i	−0.820936	−	0.596445i	−0.916980	+	0.398932i	$0.869381\pi$
$252$		0			0
$253$	7.27521	+	22.3908i	0.457389	+	1.40770i
$254$		0			0
$255$	5.06866	+	7.02680i	0.317412	+	0.440035i
$256$		0			0
$257$	8.99268	−	6.53357i	0.560948	−	0.407553i	−0.270858	−	0.962619i	$-0.587307\pi$
$257$	8.99268	−	6.53357i	0.560948	−	0.407553i	0.831806	+	0.555067i	$0.187307\pi$
$258$		0			0
$259$	−6.05010	−	1.96580i	−0.375935	−	0.122149i
$260$		0			0
$261$	−7.47230	+	10.2847i	−0.462524	+	0.636609i
$262$		0			0
$263$	−5.52230	+	4.01218i	−0.340519	+	0.247402i	−0.744881	−	0.667197i	$-0.767494\pi$
$263$	−5.52230	+	4.01218i	−0.340519	+	0.247402i	0.404362	+	0.914599i	$0.367494\pi$
$264$		0			0
$265$	−14.6809	+	20.0620i	−0.901842	+	1.23240i
$266$		0			0
$267$	−0.988728	+	0.321257i	−0.0605092	+	0.0196606i
$268$		0			0
$269$	6.89711	−	21.2271i	0.420524	−	1.29424i	−0.486691	−	0.873574i	$-0.661796\pi$
$269$	6.89711	−	21.2271i	0.420524	−	1.29424i	0.907215	−	0.420667i	$-0.138204\pi$
$270$		0			0
$271$	7.58522	+	23.3449i	0.460769	+	1.41810i	0.864226	+	0.503104i	$0.167809\pi$
$271$	7.58522	+	23.3449i	0.460769	+	1.41810i	−0.403456	+	0.914999i	$0.632191\pi$
$272$		0			0
$273$	−0.235461			−0.0142507
$274$		0			0
$275$	9.20303	+	12.8507i	0.554963	+	0.774928i
$276$		0			0
$277$	6.37482	+	8.77418i	0.383026	+	0.527189i	0.956383	−	0.292116i	$-0.0943593\pi$
$277$	6.37482	+	8.77418i	0.383026	+	0.527189i	−0.573357	+	0.819305i	$0.694359\pi$
$278$		0			0
$279$	19.3289	−	14.0432i	1.15719	−	0.840747i
$280$		0			0
$281$	−14.4808	−	4.70509i	−0.863851	−	0.280682i	−0.156615	−	0.987660i	$-0.550058\pi$
$281$	−14.4808	−	4.70509i	−0.863851	−	0.280682i	−0.707236	+	0.706978i	$0.750058\pi$
$282$		0			0
$283$	0.896420	−	1.23382i	0.0532866	−	0.0733427i	−0.781542	−	0.623852i	$-0.785567\pi$
$283$	0.896420	−	1.23382i	0.0532866	−	0.0733427i	0.834829	+	0.550510i	$0.185567\pi$
$284$		0			0
$285$	−2.70551	−	8.42459i	−0.160261	−	0.499030i
$286$		0			0
$287$	−3.71200	−	5.71070i	−0.219112	−	0.337092i
$288$		0			0
$289$	5.38476	−	16.5726i	0.316750	−	0.974858i
$290$		0			0
$291$	−6.34907	−	4.61287i	−0.372189	−	0.270411i
$292$		0			0
$293$	9.55648	−	29.4118i	0.558296	−	1.71826i	−0.128782	−	0.991673i	$-0.541107\pi$
$293$	9.55648	−	29.4118i	0.558296	−	1.71826i	0.687077	−	0.726584i	$-0.258893\pi$
$294$		0			0
$295$	−21.7904	−	7.16258i	−1.26869	−	0.417022i
$296$		0			0
$297$	6.82740	+	9.39711i	0.396166	+	0.545276i
$298$		0			0
$299$	−1.46729	+	2.01956i	−0.0848559	+	0.116794i
$300$		0			0
$301$		−	8.47262i		−	0.488354i
$302$		0			0
$303$	2.46270	−	0.800179i	0.141478	−	0.0459691i
$304$		0			0
$305$	−15.0899	+	4.84603i	−0.864043	+	0.277483i
$306$		0			0
$307$	−22.8885	+	7.43693i	−1.30632	+	0.424448i	−0.877774	−	0.479074i	$-0.840973\pi$
$307$	−22.8885	+	7.43693i	−1.30632	+	0.424448i	−0.428542	+	0.903522i	$0.640973\pi$
$308$		0			0
$309$	10.7225	−	3.48394i	0.609980	−	0.198194i
$310$		0			0
$311$	−17.3351	−	23.8598i	−0.982986	−	1.35296i	−0.935205	−	0.354106i	$-0.884785\pi$
$311$	−17.3351	−	23.8598i	−0.982986	−	1.35296i	−0.0477809	−	0.998858i	$-0.515215\pi$
$312$		0			0
$313$	−18.4353	−	13.3940i	−1.04203	−	0.757076i	−0.0713463	−	0.997452i	$-0.522730\pi$
$313$	−18.4353	−	13.3940i	−1.04203	−	0.757076i	−0.970680	+	0.240375i	$0.922730\pi$
$314$		0			0
$315$	5.80623	−	1.86464i	0.327144	−	0.105061i
$316$		0			0
$317$	−6.81817	+	4.95369i	−0.382947	+	0.278227i	−0.762559	−	0.646919i	$-0.776057\pi$
$317$	−6.81817	+	4.95369i	−0.382947	+	0.278227i	0.379612	+	0.925146i	$0.376057\pi$
$318$		0			0
$319$	−15.6746			−0.877607
$320$		0			0
$321$	6.28419	−	2.04186i	0.350749	−	0.113965i
$322$		0			0
$323$	−20.6650	+	28.4430i	−1.14983	+	1.58261i
$324$		0			0
$325$	−0.528785	+	1.59035i	−0.0293317	+	0.0882170i
$326$		0			0
$327$		−	6.05947i		−	0.335089i
$328$		0			0
$329$	8.47579			0.467285
$330$		0			0
$331$		−	4.22204i		−	0.232064i	−0.993245	−	0.116032i	$-0.962982\pi$
$331$		−	4.22204i		−	0.232064i	0.993245	−	0.116032i	$-0.0370175\pi$
$332$		0			0
$333$	−9.01257	+	12.4047i	−0.493886	+	0.679775i
$334$		0			0
$335$	0.839737	−	1.14753i	0.0458797	−	0.0626962i
$336$		0			0
$337$		−	17.2136i		−	0.937683i	−0.883282	−	0.468842i	$-0.844671\pi$
$337$		−	17.2136i		−	0.937683i	0.883282	−	0.468842i	$-0.155329\pi$
$338$		0			0
$339$	1.96538	+	2.70512i	0.106745	+	0.146922i
$340$		0			0
$341$	28.0166	+	9.10313i	1.51718	+	0.492962i
$342$		0			0
$343$	−11.0742	−	8.04585i	−0.597949	−	0.434435i
$344$		0			0
$345$	−3.43412	+	10.4475i	−0.184887	+	0.562473i
$346$		0			0
$347$	9.45217	+	29.0908i	0.507419	+	1.56168i	0.796665	+	0.604421i	$0.206595\pi$
$347$	9.45217	+	29.0908i	0.507419	+	1.56168i	−0.289246	+	0.957255i	$0.593405\pi$
$348$		0			0
$349$	−3.26408	−	10.0458i	−0.174722	−	0.537740i	0.824898	−	0.565281i	$-0.191232\pi$
$349$	−3.26408	−	10.0458i	−0.174722	−	0.537740i	−0.999621	+	0.0275411i	$0.991232\pi$
$350$		0			0
$351$	−0.380587	+	1.17133i	−0.0203143	+	0.0625208i
$352$		0			0
$353$	−19.1523	+	6.22297i	−1.01938	+	0.331215i	−0.770582	−	0.637341i	$-0.780034\pi$
$353$	−19.1523	+	6.22297i	−1.01938	+	0.331215i	−0.248794	+	0.968556i	$0.580034\pi$
$354$		0			0
$355$	9.54948	−	6.88835i	0.506834	−	0.365596i
$356$		0			0
$357$	3.33444	+	2.42261i	0.176477	+	0.128218i
$358$		0			0
$359$	3.87063	−	2.81218i	0.204284	−	0.148421i	−0.480940	−	0.876754i	$-0.659704\pi$
$359$	3.87063	−	2.81218i	0.204284	−	0.148421i	0.685224	+	0.728333i	$0.259704\pi$
$360$		0			0
$361$	13.6765	−	9.93655i	0.719815	−	0.522976i
$362$		0			0
$363$	0.205402	−	0.632164i	0.0107808	−	0.0331800i
$364$		0			0
$365$	−10.7772	−	0.0368411i	−0.564104	−	0.00192835i
$366$		0			0
$367$	−27.2466	−	8.85297i	−1.42226	−	0.462121i	−0.505942	−	0.862567i	$-0.668855\pi$
$367$	−27.2466	−	8.85297i	−1.42226	−	0.462121i	−0.916320	+	0.400446i	$0.868855\pi$
$368$		0			0
$369$	−15.8557	+	4.25569i	−0.825414	+	0.221542i
$370$		0			0
$371$	−3.65444	+	11.2472i	−0.189729	+	0.583926i
$372$		0			0
$373$	7.66205	−	10.5459i	0.396726	−	0.546046i	−0.563193	−	0.826326i	$-0.690427\pi$
$373$	7.66205	−	10.5459i	0.396726	−	0.546046i	0.959919	+	0.280279i	$0.0904271\pi$
$374$		0			0
$375$	−0.0757172	+	7.38299i	−0.00391002	+	0.381256i
$376$		0			0
$377$	−0.976898	−	1.34458i	−0.0503128	−	0.0692496i
$378$		0			0
$379$	−1.23886	+	0.900083i	−0.0636359	+	0.0462342i	−0.619148	−	0.785274i	$-0.712522\pi$
$379$	−1.23886	+	0.900083i	−0.0636359	+	0.0462342i	0.555513	+	0.831508i	$0.312522\pi$
$380$		0			0
$381$	0.850813	−	1.17104i	0.0435885	−	0.0599944i
$382$		0			0
$383$	19.5767			1.00032			0.500161	−	0.865933i	$-0.333274\pi$
$383$	19.5767			1.00032			0.500161	+	0.865933i	$0.333274\pi$
$384$		0			0
$385$	6.06797	+	4.44041i	0.309252	+	0.226304i
$386$		0			0
$387$	−19.4222	−	6.31065i	−0.987285	−	0.320788i
$388$		0			0
$389$	−7.00663	−	21.5642i	−0.355250	−	1.09335i	−0.955864	−	0.293808i	$-0.905077\pi$
$389$	−7.00663	−	21.5642i	−0.355250	−	1.09335i	0.600614	−	0.799539i	$-0.294923\pi$
$390$		0			0
$391$	41.5577	−	13.5029i	2.10166	−	0.682871i
$392$		0			0
$393$	−9.67172	+	7.02691i	−0.487874	+	0.354461i
$394$		0			0
$395$	−25.0128	−	0.0855045i	−1.25853	−	0.00430220i
$396$		0			0
$397$	2.74461	−	8.44703i	0.137748	−	0.423944i	−0.858259	−	0.513216i	$-0.828454\pi$
$397$	2.74461	−	8.44703i	0.137748	−	0.423944i	0.996007	+	0.0892717i	$0.0284539\pi$
$398$		0			0
$399$	−2.47413	−	3.40534i	−0.123861	−	0.170480i
$400$		0			0
$401$	2.64667			0.132168			0.0660842	−	0.997814i	$-0.478949\pi$
$401$	2.64667			0.132168			0.0660842	+	0.997814i	$0.478949\pi$
$402$		0			0
$403$	0.965220	+	2.97064i	0.0480810	+	0.147978i
$404$		0			0
$405$	0.0402459	−	11.7732i	0.00199984	−	0.585015i
$406$		0			0
$407$	−18.9056			−0.937114
$408$		0			0
$409$	−32.3548			−1.59984			−0.799921	−	0.600105i	$-0.795125\pi$
$409$	−32.3548			−1.59984			−0.799921	+	0.600105i	$0.795125\pi$
$410$		0			0
$411$	−13.2644			−0.654284
$412$		0			0
$413$	−10.9115			−0.536920
$414$		0			0
$415$	19.4009	+	0.0663207i	0.952352	+	0.00325556i
$416$		0			0
$417$	1.91090	+	5.88114i	0.0935770	+	0.288000i
$418$		0			0
$419$	−5.25518			−0.256732			−0.128366	−	0.991727i	$-0.540973\pi$
$419$	−5.25518			−0.256732			−0.128366	+	0.991727i	$0.540973\pi$
$420$		0			0
$421$	−13.6424	−	18.7772i	−0.664890	−	0.915143i	0.334741	−	0.942310i	$-0.391351\pi$
$421$	−13.6424	−	18.7772i	−0.664890	−	0.915143i	−0.999631	+	0.0271674i	$0.991351\pi$
$422$		0			0
$423$	6.31301	−	19.4294i	0.306949	−	0.944691i
$424$		0			0
$425$	23.8511	−	17.0810i	1.15695	−	0.828548i
$426$		0			0
$427$	−6.09954	+	4.43157i	−0.295177	+	0.214459i
$428$		0			0
$429$	−0.665516	+	0.216239i	−0.0321314	+	0.0104401i
$430$		0			0
$431$	−4.08733	−	12.5795i	−0.196880	−	0.605934i	−0.999950	−	0.0100487i	$-0.996801\pi$
$431$	−4.08733	−	12.5795i	−0.196880	−	0.605934i	0.803070	−	0.595885i	$-0.203199\pi$
$432$		0			0
$433$	25.0827	+	8.14986i	1.20540	+	0.391657i	0.841744	−	0.539877i	$-0.181529\pi$
$433$	25.0827	+	8.14986i	1.20540	+	0.391657i	0.363653	+	0.931534i	$0.381529\pi$
$434$		0			0
$435$	−5.90877	−	4.32391i	−0.283304	−	0.207316i
$436$		0			0
$437$	−44.6255			−2.13473
$438$		0			0
$439$	−11.6245	+	15.9997i	−0.554807	+	0.763626i	−0.990655	−	0.136395i	$-0.956449\pi$
$439$	−11.6245	+	15.9997i	−0.554807	+	0.763626i	0.435848	+	0.900020i	$0.356449\pi$
$440$		0			0
$441$	−12.1726	+	8.84393i	−0.579649	+	0.421140i
$442$		0			0
$443$	−11.6748	−	16.0689i	−0.554685	−	0.763458i	0.435954	−	0.899969i	$-0.356411\pi$
$443$	−11.6748	−	16.0689i	−0.554685	−	0.763458i	−0.990639	+	0.136511i	$0.956411\pi$
$444$		0			0
$445$	1.07632	+	3.35151i	0.0510225	+	0.158877i
$446$		0			0
$447$	7.83772	−	10.7877i	0.370712	−	0.510241i
$448$		0			0
$449$	3.30193	−	10.1623i	0.155828	−	0.479589i	−0.842416	−	0.538828i	$-0.818867\pi$
$449$	3.30193	−	10.1623i	0.155828	−	0.479589i	0.998244	+	0.0592389i	$0.0188674\pi$
$450$		0			0
$451$	−15.7362	−	12.7320i	−0.740991	−	0.599525i
$452$		0			0
$453$	2.71870	+	0.883358i	0.127735	+	0.0415038i
$454$		0			0
$455$	−0.00272539	+	0.797262i	−0.000127768	+	0.0373762i
$456$		0			0
$457$	0.501380	−	1.54309i	0.0234536	−	0.0721827i	−0.938645	−	0.344886i	$-0.887918\pi$
$457$	0.501380	−	1.54309i	0.0234536	−	0.0721827i	0.962098	+	0.272703i	$0.0879177\pi$
$458$		0			0
$459$	17.4412	−	12.6718i	0.814085	−	0.591467i
$460$		0			0
$461$	5.81401	−	4.22412i	0.270785	−	0.196737i	−0.444103	−	0.895976i	$-0.646478\pi$
$461$	5.81401	−	4.22412i	0.270785	−	0.196737i	0.714888	+	0.699239i	$0.246478\pi$
$462$		0			0
$463$	−14.7455	−	10.7133i	−0.685283	−	0.497887i	0.189823	−	0.981818i	$-0.439209\pi$
$463$	−14.7455	−	10.7133i	−0.685283	−	0.497887i	−0.875106	+	0.483931i	$0.839209\pi$
$464$		0			0
$465$	8.05014	+	11.1601i	0.373316	+	0.517537i
$466$		0			0
$467$	10.1947	−	3.31247i	0.471756	−	0.153283i	−0.0634839	−	0.997983i	$-0.520221\pi$
$467$	10.1947	−	3.31247i	0.471756	−	0.153283i	0.535240	+	0.844700i	$0.320221\pi$
$468$		0			0
$469$	0.209031	−	0.643332i	0.00965216	−	0.0297063i
$470$		0			0
$471$	4.30887	+	13.2613i	0.198542	+	0.611050i
$472$		0			0
$473$	−7.78097	−	23.9474i	−0.357769	−	1.10110i
$474$		0			0
$475$	−28.5567	+	9.06325i	−1.31027	+	0.415851i
$476$		0			0
$477$	23.0606	+	16.7545i	1.05587	+	0.767135i
$478$		0			0
$479$	16.4705	+	5.35157i	0.752554	+	0.244520i	0.660080	−	0.751195i	$-0.270522\pi$
$479$	16.4705	+	5.35157i	0.752554	+	0.244520i	0.0924743	+	0.995715i	$0.470522\pi$
$480$		0			0
$481$	−1.17827	−	1.62174i	−0.0537243	−	0.0739452i
$482$		0			0
$483$			5.23155i			0.238044i
$484$		0			0
$485$	−15.6925	+	21.4443i	−0.712560	+	0.973737i
$486$		0			0
$487$	−6.32367	+	8.70379i	−0.286553	+	0.394406i	−0.927891	−	0.372852i	$-0.878380\pi$
$487$	−6.32367	+	8.70379i	−0.286553	+	0.394406i	0.641338	+	0.767259i	$0.278380\pi$
$488$		0			0
$489$			10.5967i			0.479198i
$490$		0			0
$491$	−19.2401			−0.868295			−0.434148	−	0.900842i	$-0.642950\pi$
$491$	−19.2401			−0.868295			−0.434148	+	0.900842i	$0.642950\pi$
$492$		0			0
$493$			29.0922i			1.31025i
$494$		0			0
$495$	14.6985	−	10.6025i	0.660651	−	0.476549i
$496$		0			0
$497$	3.29235	−	4.53153i	0.147682	−	0.203267i
$498$		0			0
$499$	10.9742	−	3.56575i	0.491274	−	0.159625i	−0.0528950	−	0.998600i	$-0.516845\pi$
$499$	10.9742	−	3.56575i	0.491274	−	0.159625i	0.544169	+	0.838975i	$0.316845\pi$
$500$		0			0
$501$	7.74184			0.345880
$502$		0			0
$503$	3.65664	−	2.65671i	0.163042	−	0.118457i	−0.503273	−	0.864128i	$-0.667871\pi$
$503$	3.65664	−	2.65671i	0.163042	−	0.118457i	0.666314	+	0.745671i	$0.267871\pi$
$504$		0			0
$505$	−2.68087	−	8.34787i	−0.119297	−	0.371475i
$506$		0			0
$507$	6.88544	+	5.00256i	0.305793	+	0.222172i
$508$		0			0
$509$	12.5008	+	17.2059i	0.554090	+	0.762639i	0.990560	−	0.137080i	$-0.0437716\pi$
$509$	12.5008	+	17.2059i	0.554090	+	0.762639i	−0.436470	+	0.899719i	$0.643772\pi$
$510$		0			0
$511$	−4.87589	+	1.58427i	−0.215697	+	0.0700841i
$512$		0			0
$513$	−20.9393	+	6.80360i	−0.924494	+	0.300386i
$514$		0			0
$515$	−11.6724	−	36.3462i	−0.514347	−	1.60160i
$516$		0			0
$517$	23.9563	−	7.78388i	1.05360	−	0.342335i
$518$		0			0
$519$		−	7.52468i		−	0.330297i
$520$		0			0
$521$	17.0563	−	23.4760i	0.747250	−	1.02850i	−0.250919	−	0.968008i	$-0.580733\pi$
$521$	17.0563	−	23.4760i	0.747250	−	1.02850i	0.998169	−	0.0604927i	$-0.0192672\pi$
$522$		0			0
$523$	3.18174	+	4.37928i	0.139128	+	0.191493i	0.872895	−	0.487908i	$-0.162240\pi$
$523$	3.18174	+	4.37928i	0.139128	+	0.191493i	−0.733767	+	0.679401i	$0.762240\pi$
$524$		0			0
$525$	1.06251	+	3.34777i	0.0463716	+	0.146108i
$526$		0			0
$527$	16.8955	−	51.9991i	0.735982	−	2.26512i
$528$		0			0
$529$	26.2638	+	19.0818i	1.14191	+	0.829643i
$530$		0			0
$531$	−8.12719	+	25.0129i	−0.352690	+	1.08547i
$532$		0			0
$533$	0.111423	−	2.14338i	0.00482629	−	0.0928402i
$534$		0			0
$535$	−6.84091	−	21.3017i	−0.295758	−	0.920951i
$536$		0			0
$537$	1.77640	−	2.44501i	0.0766573	−	0.105510i
$538$		0			0
$539$	−17.6438	−	5.73283i	−0.759973	−	0.246930i
$540$		0			0
$541$	−12.3217	+	8.95227i	−0.529753	+	0.384888i	−0.820265	−	0.571983i	$-0.806174\pi$
$541$	−12.3217	+	8.95227i	−0.529753	+	0.384888i	0.290512	+	0.956871i	$0.406174\pi$
$542$		0			0
$543$	−3.52783	−	4.85564i	−0.151394	−	0.208375i
$544$		0			0
$545$	−20.5171	−	0.0701365i	−0.878857	−	0.00300432i
$546$		0			0
$547$	20.6548			0.883135			0.441568	−	0.897228i	$-0.354423\pi$
$547$	20.6548			0.883135			0.441568	+	0.897228i	$0.354423\pi$
$548$		0			0
$549$	5.61559	+	17.2830i	0.239668	+	0.737621i
$550$		0			0
$551$	9.18115	−	28.2567i	0.391130	−	1.20377i
$552$		0			0
$553$	−11.3165	+	3.67694i	−0.481224	+	0.156359i
$554$		0			0
$555$	−7.12675	−	5.21520i	−0.302514	−	0.221373i
$556$		0			0
$557$	−32.5963	+	23.6826i	−1.38115	+	1.00346i	−0.384377	+	0.923176i	$0.625584\pi$
$557$	−32.5963	+	23.6826i	−1.38115	+	1.00346i	−0.996772	+	0.0802870i	$0.974416\pi$
$558$		0			0
$559$	1.56930	−	2.15995i	0.0663742	−	0.0913563i
$560$		0			0
$561$	11.6494	+	3.78513i	0.491839	+	0.159808i
$562$		0			0
$563$	11.5129	−	8.36462i	0.485211	−	0.352527i	−0.318129	−	0.948048i	$-0.603054\pi$
$563$	11.5129	−	8.36462i	0.485211	−	0.352527i	0.803340	+	0.595521i	$0.203054\pi$
$564$		0			0
$565$	9.18217	−	6.62340i	0.386297	−	0.278649i
$566$		0			0
$567$	−1.73069	−	5.32652i	−0.0726821	−	0.223693i
$568$		0			0
$569$	−28.0793	−	20.4008i	−1.17714	−	0.855245i	−0.185298	−	0.982682i	$-0.559325\pi$
$569$	−28.0793	−	20.4008i	−1.17714	−	0.855245i	−0.991847	+	0.127437i	$0.959325\pi$
$570$		0			0
$571$		−	13.0777i		−	0.547285i	−0.961832	−	0.273642i	$-0.911772\pi$
$571$		−	13.0777i		−	0.547285i	0.961832	−	0.273642i	$-0.0882284\pi$
$572$		0			0
$573$			12.0602i			0.503821i
$574$		0			0
$575$	35.3350	+	11.7487i	1.47357	+	0.489956i
$576$		0			0
$577$	19.9728			0.831477			0.415738	−	0.909484i	$-0.363523\pi$
$577$	19.9728			0.831477			0.415738	+	0.909484i	$0.363523\pi$
$578$		0			0
$579$	9.69099	+	7.04092i	0.402744	+	0.292611i
$580$		0			0
$581$	8.77749	−	2.85198i	0.364152	−	0.118320i
$582$		0			0
$583$			35.1457i			1.45559i
$584$		0			0
$585$	1.82557	+	0.600071i	0.0754780	+	0.0248099i
$586$		0			0
$587$	−0.0725942	+	0.223422i	−0.00299628	+	0.00922161i	−0.952543	−	0.304403i	$-0.901543\pi$
$587$	−0.0725942	+	0.223422i	−0.00299628	+	0.00922161i	0.949547	+	0.313624i	$0.101543\pi$
$588$		0			0
$589$	−32.8206	+	45.1737i	−1.35235	+	1.86135i
$590$		0			0
$591$	−9.98648	−	13.7452i	−0.410789	−	0.565402i
$592$		0			0
$593$	7.28724	+	22.4278i	0.299251	+	0.921000i	0.981760	+	0.190123i	$0.0608886\pi$
$593$	7.28724	+	22.4278i	0.299251	+	0.921000i	−0.682509	+	0.730877i	$0.739111\pi$
$594$		0			0
$595$	8.24146	−	11.2622i	0.337867	−	0.461707i
$596$		0			0
$597$	1.42231	+	0.462135i	0.0582111	+	0.0189139i
$598$		0			0
$599$	−4.29555	−	13.2203i	−0.175511	−	0.540168i	0.824145	−	0.566379i	$-0.191656\pi$
$599$	−4.29555	−	13.2203i	−0.175511	−	0.540168i	−0.999656	+	0.0262105i	$0.991656\pi$
$600$		0			0
$601$			5.81938i			0.237377i	0.992932	+	0.118689i	$0.0378690\pi$
$601$			5.81938i			0.237377i	−0.992932	+	0.118689i	$0.962131\pi$
$602$		0			0
$603$	−1.31905	−	0.958343i	−0.0537157	−	0.0390267i
$604$		0			0
$605$	−2.13811	−	0.702802i	−0.0869263	−	0.0285730i
$606$		0			0
$607$	−16.0074	−	22.0323i	−0.649722	−	0.894265i	0.349366	−	0.936987i	$-0.386397\pi$
$607$	−16.0074	−	22.0323i	−0.649722	−	0.894265i	−0.999087	+	0.0427216i	$0.986397\pi$
$608$		0			0
$609$	−3.31260	−	1.07633i	−0.134233	−	0.0436150i
$610$		0			0
$611$	2.16076	+	1.56988i	0.0874150	+	0.0635107i
$612$		0			0
$613$	4.31509	+	1.40206i	0.174285	+	0.0566286i	0.394860	−	0.918741i	$-0.370793\pi$
$613$	4.31509	+	1.40206i	0.174285	+	0.0566286i	−0.220575	+	0.975370i	$0.570793\pi$
$614$		0			0
$615$	−2.41984	−	9.14045i	−0.0975775	−	0.368579i
$616$		0			0
$617$	−9.87253	−	3.20778i	−0.397453	−	0.129140i	0.103469	−	0.994633i	$-0.467006\pi$
$617$	−9.87253	−	3.20778i	−0.397453	−	0.129140i	−0.500922	+	0.865492i	$0.667006\pi$
$618$		0			0
$619$	9.90738	+	7.19813i	0.398211	+	0.289317i	0.768812	−	0.639475i	$-0.220848\pi$
$619$	9.90738	+	7.19813i	0.398211	+	0.289317i	−0.370601	+	0.928792i	$0.620848\pi$
$620$		0			0
$621$	26.0249	+	8.45602i	1.04435	+	0.339328i
$622$		0			0
$623$	0.984269	+	1.35473i	0.0394339	+	0.0542761i
$624$		0			0
$625$	24.9977	+	0.341832i	0.999907	+	0.0136733i
$626$		0			0
$627$	−10.1203	−	7.35284i	−0.404167	−	0.293644i
$628$		0			0
$629$			35.0890i			1.39909i
$630$		0			0
$631$	−5.16557	−	15.8980i	−0.205638	−	0.632889i	−0.999687	−	0.0250343i	$-0.992030\pi$
$631$	−5.16557	−	15.8980i	−0.205638	−	0.632889i	0.794049	−	0.607854i	$-0.207970\pi$
$632$		0			0
$633$	−3.00930	−	0.977781i	−0.119609	−	0.0388633i
$634$		0			0
$635$	−3.95526	−	2.89438i	−0.156960	−	0.114860i
$636$		0			0
$637$	−0.607861	−	1.87080i	−0.0240843	−	0.0741239i
$638$		0			0
$639$	−7.93559	−	10.9224i	−0.313927	−	0.432084i
$640$		0			0
$641$	4.49182	−	6.18246i	0.177416	−	0.244193i	−0.711042	−	0.703149i	$-0.751777\pi$
$641$	4.49182	−	6.18246i	0.177416	−	0.244193i	0.888459	+	0.458956i	$0.151777\pi$
$642$		0			0
$643$	13.3593	−	41.1157i	0.526839	−	1.62144i	−0.233812	−	0.972282i	$-0.575120\pi$
$643$	13.3593	−	41.1157i	0.526839	−	1.62144i	0.760651	−	0.649162i	$-0.224880\pi$
$644$		0			0
$645$	3.67285	−	11.1738i	0.144618	−	0.439966i
$646$		0			0
$647$			41.3690i			1.62638i	0.581996	+	0.813192i	$0.302272\pi$
$647$			41.3690i			1.62638i	−0.581996	+	0.813192i	$0.697728\pi$
$648$		0			0
$649$	−30.8407	+	10.0208i	−1.21060	+	0.393349i
$650$		0			0
$651$	5.29582	+	3.84764i	0.207559	+	0.150801i
$652$		0			0
$653$	4.42966			0.173346			0.0866731	−	0.996237i	$-0.472376\pi$
$653$	4.42966			0.173346			0.0866731	+	0.996237i	$0.472376\pi$
$654$		0			0
$655$	23.6809	+	32.8294i	0.925290	+	1.28275i
$656$		0			0
$657$			12.3572i			0.482102i
$658$		0			0
$659$			42.8788i			1.67032i	0.550007	+	0.835160i	$0.314625\pi$
$659$			42.8788i			1.67032i	−0.550007	+	0.835160i	$0.685375\pi$
$660$		0			0
$661$	21.1233	+	15.3469i	0.821599	+	0.596927i	0.917170	−	0.398496i	$-0.130468\pi$
$661$	21.1233	+	15.3469i	0.821599	+	0.596927i	−0.0955709	+	0.995423i	$0.530468\pi$
$662$		0			0
$663$	0.401343	+	1.23521i	0.0155869	+	0.0479715i
$664$		0			0
$665$	−11.5590	+	8.33788i	−0.448239	+	0.323329i
$666$		0			0
$667$	−29.8744	+	21.7050i	−1.15674	+	0.840423i
$668$		0			0
$669$	−12.9879	−	4.22002i	−0.502141	−	0.163155i
$670$		0			0
$671$	−13.1702	+	18.1272i	−0.508429	+	0.699792i
$672$		0			0
$673$	1.73504	−	1.26058i	0.0668809	−	0.0485918i	−0.553842	−	0.832621i	$-0.686839\pi$
$673$	1.73504	−	1.26058i	0.0668809	−	0.0485918i	0.620723	+	0.784030i	$0.286839\pi$
$674$		0			0
$675$	18.3712	+	0.125603i	0.707109	+	0.00483447i
$676$		0			0
$677$	7.14351	−	2.32107i	0.274547	−	0.0892059i	−0.168507	−	0.985700i	$-0.553895\pi$
$677$	7.14351	−	2.32107i	0.274547	−	0.0892059i	0.443055	+	0.896495i	$0.353895\pi$
$678$		0			0
$679$	−3.90625	+	12.0222i	−0.149908	+	0.461369i
$680$		0			0
$681$	0.415722	+	1.27946i	0.0159305	+	0.0490291i
$682$		0			0
$683$	−2.00945			−0.0768896			−0.0384448	−	0.999261i	$-0.512240\pi$
$683$	−2.00945			−0.0768896			−0.0384448	+	0.999261i	$0.512240\pi$
$684$		0			0
$685$	−0.153531	+	44.9127i	−0.00586613	+	1.71603i
$686$		0			0
$687$	9.32508	+	12.8349i	0.355774	+	0.489681i
$688$		0			0
$689$	−3.01485	+	2.19041i	−0.114856	+	0.0834481i
$690$		0			0
$691$	23.2165	+	7.54351i	0.883198	+	0.286968i	0.715285	−	0.698833i	$-0.246297\pi$
$691$	23.2165	+	7.54351i	0.883198	+	0.286968i	0.167914	+	0.985802i	$0.446297\pi$
$692$		0			0
$693$	5.06758	−	6.97492i	0.192501	−	0.264955i
$694$		0			0
$695$	19.9354	−	6.40215i	0.756194	−	0.242848i
$696$		0			0
$697$	−23.6307	+	29.2067i	−0.895078	+	1.10628i
$698$		0			0
$699$	−2.28918	+	7.04538i	−0.0865848	+	0.266481i
$700$		0			0
$701$	17.4256	+	12.6604i	0.658155	+	0.478178i	0.866039	−	0.499976i	$-0.166658\pi$
$701$	17.4256	+	12.6604i	0.658155	+	0.478178i	−0.207884	+	0.978153i	$0.566658\pi$
$702$		0			0
$703$	11.0737	−	34.0812i	0.417651	−	1.28540i
$704$		0			0
$705$	11.1779	+	3.67422i	0.420985	+	0.138379i
$706$		0			0
$707$	−2.45159	−	3.37433i	−0.0922016	−	0.126905i
$708$		0			0
$709$	−10.8949	+	14.9955i	−0.409166	+	0.563169i	−0.963015	−	0.269449i	$-0.913159\pi$
$709$	−10.8949	+	14.9955i	−0.409166	+	0.563169i	0.553849	+	0.832617i	$0.313159\pi$
$710$		0			0
$711$			28.6799i			1.07558i
$712$		0			0
$713$	66.0027	−	21.4456i	2.47182	−	0.803143i
$714$		0			0
$715$	0.724475	+	2.25592i	0.0270938	+	0.0843665i
$716$		0			0
$717$	8.74831	−	2.84250i	0.326711	−	0.106155i
$718$		0			0
$719$	0.711334	−	0.231126i	0.0265283	−	0.00861956i	−0.295723	−	0.955274i	$-0.595560\pi$
$719$	0.711334	−	0.231126i	0.0265283	−	0.00861956i	0.322251	+	0.946654i	$0.395560\pi$
$720$		0			0
$721$	−10.6741	−	14.6917i	−0.397525	−	0.547146i
$722$		0			0
$723$	13.3026	+	9.66491i	0.494729	+	0.359442i
$724$		0			0
$725$	−14.7090	+	19.9568i	−0.546279	+	0.741178i
$726$		0			0
$727$	24.2760	−	17.6376i	0.900348	−	0.654141i	−0.0382076	−	0.999270i	$-0.512165\pi$
$727$	24.2760	−	17.6376i	0.900348	−	0.654141i	0.938555	+	0.345129i	$0.112165\pi$
$728$		0			0
$729$	−6.21981			−0.230363
$730$		0			0
$731$	−44.4467	+	14.4416i	−1.64392	+	0.534142i
$732$		0			0
$733$	25.6344	−	35.2828i	0.946829	−	1.30320i	−0.00609265	−	0.999981i	$-0.501939\pi$
$733$	25.6344	−	35.2828i	0.946829	−	1.30320i	0.952922	−	0.303217i	$-0.0980606\pi$
$734$		0			0
$735$	−5.06969	−	7.02823i	−0.186998	−	0.259240i
$736$		0			0
$737$		−	2.01031i		−	0.0740506i
$738$		0			0
$739$	−14.2424			−0.523914			−0.261957	−	0.965080i	$-0.584368\pi$
$739$	−14.2424			−0.523914			−0.261957	+	0.965080i	$0.584368\pi$
$740$		0			0
$741$		−	1.32639i		−	0.0487262i
$742$		0			0
$743$	3.42570	−	4.71507i	0.125677	−	0.172979i	−0.741542	−	0.670906i	$-0.765905\pi$
$743$	3.42570	−	4.71507i	0.125677	−	0.172979i	0.867219	+	0.497927i	$0.165905\pi$
$744$		0			0
$745$	−36.4360	−	26.6631i	−1.33491	−	0.976860i
$746$		0			0
$747$		−	22.2453i		−	0.813912i
$748$		0			0
$749$	−6.25585	−	8.61043i	−0.228584	−	0.314618i
$750$		0			0
$751$	6.94331	+	2.25602i	0.253365	+	0.0823232i	0.432946	−	0.901420i	$-0.357474\pi$
$751$	6.94331	+	2.25602i	0.253365	+	0.0823232i	−0.179581	+	0.983743i	$0.557474\pi$
$752$		0			0
$753$	−8.58908	−	6.24033i	−0.313003	−	0.227410i
$754$		0			0
$755$	3.02248	−	9.19518i	0.109999	−	0.334647i
$756$		0			0
$757$	4.06255	+	12.5033i	0.147656	+	0.454439i	0.997343	−	0.0728489i	$-0.0232091\pi$
$757$	4.06255	+	12.5033i	0.147656	+	0.454439i	−0.849687	+	0.527288i	$0.823209\pi$
$758$		0			0
$759$	4.80448	+	14.7867i	0.174391	+	0.536722i
$760$		0			0
$761$	−2.32548	+	7.15709i	−0.0842986	+	0.259444i	−0.984317	−	0.176407i	$-0.943553\pi$
$761$	−2.32548	+	7.15709i	−0.0842986	+	0.259444i	0.900019	+	0.435851i	$0.143553\pi$
$762$		0			0
$763$	−9.28251	+	3.01607i	−0.336049	+	0.109189i
$764$		0			0
$765$	−19.6785	−	27.2807i	−0.711477	−	0.986336i
$766$		0			0
$767$	−2.78170	−	2.02103i	−0.100442	−	0.0729750i
$768$		0			0
$769$	3.09767	−	2.25059i	0.111705	−	0.0811582i	−0.530530	−	0.847666i	$-0.678007\pi$
$769$	3.09767	−	2.25059i	0.111705	−	0.0811582i	0.642235	+	0.766508i	$0.278007\pi$
$770$		0			0
$771$	5.93868	−	4.31470i	0.213876	−	0.155390i
$772$		0			0
$773$	3.60376	−	11.0912i	0.129618	−	0.398924i	−0.865096	−	0.501607i	$-0.832743\pi$
$773$	3.60376	−	11.0912i	0.129618	−	0.398924i	0.994714	+	0.102682i	$0.0327425\pi$
$774$		0			0
$775$	37.8808	−	27.1283i	1.36072	−	0.974477i
$776$		0			0
$777$	−3.99542	−	1.29819i	−0.143335	−	0.0465724i
$778$		0			0
$779$	32.1693	−	20.9103i	1.15259	−	0.749190i
$780$		0			0
$781$	5.14402	−	15.8317i	0.184068	−	0.566502i
$782$		0			0
$783$	−10.7086	+	14.7392i	−0.382695	+	0.526735i
$784$		0			0
$785$	44.9523	−	14.4362i	1.60441	−	0.515249i
$786$		0			0
$787$	11.5799	+	15.9384i	0.412780	+	0.568143i	0.963894	−	0.266287i	$-0.0857970\pi$
$787$	11.5799	+	15.9384i	0.412780	+	0.568143i	−0.551114	+	0.834430i	$0.685797\pi$
$788$		0			0
$789$	−3.64687	+	2.64960i	−0.129832	+	0.0943284i
$790$		0			0
$791$	3.16571	−	4.35723i	0.112560	−	0.154925i
$792$		0			0
$793$	−2.37579			−0.0843668
$794$		0			0
$795$	−9.69513	+	13.2487i	−0.343851	+	0.469884i
$796$		0			0
$797$	3.78166	+	1.22874i	0.133953	+	0.0435241i	0.375226	−	0.926933i	$-0.377565\pi$
$797$	3.78166	+	1.22874i	0.133953	+	0.0435241i	−0.241273	+	0.970457i	$0.577565\pi$
$798$		0			0
$799$	−14.4470	−	44.4633i	−0.511098	−	1.57300i
$800$		0			0
$801$	3.83862	−	1.24724i	0.135631	−	0.0440692i
$802$		0			0
$803$	−12.3265	+	8.95571i	−0.434992	+	0.316040i
$804$		0			0
$805$	17.7138	+	0.0605536i	0.624330	+	0.00213423i
$806$		0			0
$807$	4.55478	−	14.0182i	0.160336	−	0.493463i
$808$		0			0
$809$	25.8469	+	35.5752i	0.908727	+	1.25076i	0.967599	+	0.252491i	$0.0812497\pi$
$809$	25.8469	+	35.5752i	0.908727	+	1.25076i	−0.0588719	+	0.998266i	$0.518750\pi$
$810$		0			0
$811$	−26.1811			−0.919341			−0.459671	−	0.888089i	$-0.652033\pi$
$811$	−26.1811			−0.919341			−0.459671	+	0.888089i	$0.652033\pi$
$812$		0			0
$813$	5.00920	+	15.4167i	0.175680	+	0.540689i
$814$		0			0
$815$	35.8799	+	0.122653i	1.25682	+	0.00429636i
$816$		0			0
$817$	47.7277			1.66978
$818$		0			0
$819$	0.914149			0.0319430
$820$		0			0
$821$	−29.1646			−1.01785			−0.508925	−	0.860811i	$-0.669957\pi$
$821$	−29.1646			−1.01785			−0.508925	+	0.860811i	$0.669957\pi$
$822$		0			0
$823$	31.5017			1.09808			0.549040	−	0.835796i	$-0.314993\pi$
$823$	31.5017			1.09808			0.549040	+	0.835796i	$0.314993\pi$
$824$		0			0
$825$	6.07758	+	8.48649i	0.211594	+	0.295462i
$826$		0			0
$827$	8.03286	+	24.7226i	0.279330	+	0.859689i	0.988041	+	0.154190i	$0.0492768\pi$
$827$	8.03286	+	24.7226i	0.279330	+	0.859689i	−0.708711	+	0.705498i	$0.750723\pi$
$828$		0			0
$829$	−24.7547			−0.859766			−0.429883	−	0.902884i	$-0.641445\pi$
$829$	−24.7547			−0.859766			−0.429883	+	0.902884i	$0.641445\pi$
$830$		0			0
$831$	4.20986	+	5.79438i	0.146039	+	0.201005i
$832$		0			0
$833$	−10.6402	+	32.7472i	−0.368661	+	1.13462i
$834$		0			0
$835$	0.0896094	−	26.2136i	0.00310106	−	0.907158i
$836$		0			0
$837$	27.7004	−	20.1255i	0.957466	−	0.695640i
$838$		0			0
$839$	−35.1913	+	11.4343i	−1.21494	+	0.394758i	−0.845236	−	0.534393i	$-0.820540\pi$
$839$	−35.1913	+	11.4343i	−1.21494	+	0.394758i	−0.369703	+	0.929150i	$0.620540\pi$
$840$		0			0
$841$	1.36425	+	4.19872i	0.0470430	+	0.144784i
$842$		0			0
$843$	−9.56295	−	3.10719i	−0.329366	−	0.107017i
$844$		0			0
$845$	17.0182	−	23.2559i	0.585444	−	0.800028i
$846$		0			0
$847$	−1.07065			−0.0367880
$848$		0			0
$849$	0.591986	−	0.814799i	0.0203169	−	0.0279638i
$850$		0			0
$851$	−36.0325	+	26.1791i	−1.23518	+	0.897409i
$852$		0			0
$853$	2.04171	+	2.81017i	0.0699068	+	0.0962185i	0.842539	−	0.538636i	$-0.181060\pi$
$853$	2.04171	+	2.81017i	0.0699068	+	0.0962185i	−0.772632	+	0.634854i	$0.781060\pi$
$854$		0			0
$855$	10.5038	+	32.7075i	0.359224	+	1.11857i
$856$		0			0
$857$	21.8788	−	30.1136i	0.747367	−	1.02866i	−0.250794	−	0.968040i	$-0.580692\pi$
$857$	21.8788	−	30.1136i	0.747367	−	1.02866i	0.998161	−	0.0606215i	$-0.0193083\pi$
$858$		0			0
$859$	−8.79316	+	27.0626i	−0.300019	+	0.923363i	0.681470	+	0.731846i	$0.261341\pi$
$859$	−8.79316	+	27.0626i	−0.300019	+	0.923363i	−0.981489	+	0.191517i	$0.938659\pi$
$860$		0			0
$861$	−2.45136	−	3.77129i	−0.0835423	−	0.128525i
$862$		0			0
$863$	−1.31947	−	0.428723i	−0.0449154	−	0.0145939i	0.286473	−	0.958088i	$-0.407517\pi$
$863$	−1.31947	−	0.428723i	−0.0449154	−	0.0145939i	−0.331389	+	0.943494i	$0.607517\pi$
$864$		0			0
$865$	−25.4783	−	0.0870959i	−0.866288	−	0.00296135i
$866$		0			0
$867$	3.55604	−	10.9444i	0.120769	−	0.371690i
$868$		0			0
$869$	−28.6085	+	20.7853i	−0.970477	+	0.705093i
$870$		0			0
$871$	0.172447	−	0.125290i	0.00584313	−	0.00424529i
$872$		0			0
$873$	24.6495	+	17.9089i	0.834260	+	0.606126i
$874$		0			0
$875$	11.3477	−	3.55886i	0.383623	−	0.120311i
$876$		0			0
$877$	−19.2245	+	6.24642i	−0.649165	+	0.210927i	−0.615046	−	0.788491i	$-0.710863\pi$
$877$	−19.2245	+	6.24642i	−0.649165	+	0.210927i	−0.0341192	+	0.999418i	$0.510863\pi$
$878$		0			0
$879$	6.31100	−	19.4233i	0.212865	−	0.655130i
$880$		0			0
$881$	2.70122	+	8.31350i	0.0910064	+	0.280089i	0.986192	−	0.165604i	$-0.0529573\pi$
$881$	2.70122	+	8.31350i	0.0910064	+	0.280089i	−0.895186	+	0.445693i	$0.852957\pi$
$882$		0			0
$883$	−8.29249	−	25.5217i	−0.279065	−	0.858872i	−0.988115	−	0.153715i	$-0.950876\pi$
$883$	−8.29249	−	25.5217i	−0.279065	−	0.858872i	0.709051	−	0.705158i	$-0.249124\pi$
$884$		0			0
$885$	−14.3902	−	4.73010i	−0.483720	−	0.159000i
$886$		0			0
$887$	14.4004	+	10.4625i	0.483519	+	0.351297i	0.802687	−	0.596401i	$-0.203403\pi$
$887$	14.4004	+	10.4625i	0.483519	+	0.351297i	−0.319167	+	0.947698i	$0.603403\pi$
$888$		0			0
$889$	−2.21741	−	0.720481i	−0.0743696	−	0.0241642i
$890$		0			0
$891$	−9.78338	−	13.4657i	−0.327756	−	0.451117i
$892$		0			0
$893$			47.7456i			1.59774i
$894$		0			0
$895$	−8.25814	−	6.04313i	−0.276039	−	0.201999i
$896$		0			0
$897$	−0.968986	+	1.33370i	−0.0323535	+	0.0445308i
$898$		0			0
$899$			46.2048i			1.54102i
$900$		0			0
$901$	65.2309			2.17316
$902$		0			0
$903$		−	5.59523i		−	0.186198i
$904$		0			0
$905$	−16.4818	+	11.8889i	−0.547875	+	0.395200i
$906$		0			0
$907$	20.4739	−	28.1799i	0.679826	−	0.935700i	−0.320106	−	0.947382i	$-0.603719\pi$
$907$	20.4739	−	28.1799i	0.679826	−	0.935700i	0.999932	+	0.0116819i	$0.00371856\pi$
$908$		0			0
$909$	−9.56114	+	3.10660i	−0.317123	+	0.103040i
$910$		0			0
$911$	7.64944			0.253437			0.126719	−	0.991939i	$-0.459555\pi$
$911$	7.64944			0.253437			0.126719	+	0.991939i	$0.459555\pi$
$912$		0			0
$913$	22.1899	−	16.1219i	0.734378	−	0.533557i
$914$		0			0
$915$	−9.96519	+	3.20027i	−0.329439	+	0.105798i
$916$		0			0
$917$	15.5786	+	11.3185i	0.514451	+	0.373770i
$918$		0			0
$919$	2.68553	+	3.69632i	0.0885876	+	0.121930i	0.851010	−	0.525149i	$-0.175990\pi$
$919$	2.68553	+	3.69632i	0.0885876	+	0.121930i	−0.762423	+	0.647079i	$0.775990\pi$
$920$		0			0
$921$	−15.1153	+	4.91127i	−0.498067	+	0.161832i
$922$		0			0
$923$	1.67866	−	0.545429i	0.0552537	−	0.0179530i
$924$		0			0
$925$	−17.7410	+	24.0706i	−0.583320	+	0.791435i
$926$		0			0
$927$	−41.6287	+	13.5260i	−1.36727	+	0.444252i
$928$		0			0
$929$			23.2050i			0.761330i	0.924713	+	0.380665i	$0.124305\pi$
$929$			23.2050i			0.761330i	−0.924713	+	0.380665i	$0.875695\pi$
$930$		0			0
$931$	20.6692	−	28.4488i	0.677407	−	0.932371i
$932$		0			0
$933$	−11.4480	−	15.7568i	−0.374789	−	0.515853i
$934$		0			0
$935$	12.9511	−	39.4007i	0.423548	−	1.28854i
$936$		0			0
$937$	−8.30676	+	25.5656i	−0.271370	+	0.835191i	0.718787	+	0.695230i	$0.244698\pi$
$937$	−8.30676	+	25.5656i	−0.271370	+	0.835191i	−0.990157	+	0.139961i	$0.955302\pi$
$938$		0			0
$939$	−12.1745	−	8.84529i	−0.397300	−	0.288655i
$940$		0			0
$941$	13.2076	−	40.6490i	0.430557	−	1.32512i	−0.467015	−	0.884250i	$-0.654670\pi$
$941$	13.2076	−	40.6490i	0.430557	−	1.32512i	0.897572	−	0.440869i	$-0.145330\pi$
$942$		0			0
$943$	−47.6224	−	2.47564i	−1.55080	−	0.0806180i
$944$		0			0
$945$	8.32098	−	2.67224i	0.270681	−	0.0869278i
$946$		0			0
$947$	−6.59295	+	9.07441i	−0.214242	+	0.294879i	−0.902589	−	0.430502i	$-0.858336\pi$
$947$	−6.59295	+	9.07441i	−0.214242	+	0.294879i	0.688348	+	0.725381i	$0.258336\pi$
$948$		0			0
$949$	−1.53647	−	0.499228i	−0.0498758	−	0.0162056i
$950$		0			0
$951$	−4.50265	+	3.27137i	−0.146008	+	0.106081i
$952$		0			0
$953$	−0.947106	−	1.30358i	−0.0306798	−	0.0422271i	0.793402	−	0.608699i	$-0.208308\pi$
$953$	−0.947106	−	1.30358i	−0.0306798	−	0.0422271i	−0.824081	+	0.566472i	$0.808308\pi$
$954$		0			0
$955$	40.8353	+	0.139593i	1.32140	+	0.00451712i
$956$		0			0
$957$	−10.3513			−0.334610
$958$		0			0
$959$	6.60228	+	20.3197i	0.213199	+	0.656158i
$960$		0			0
$961$	17.2543	−	53.1033i	0.556590	−	1.71301i
$962$		0			0
$963$	−24.3976	+	7.92727i	−0.786202	+	0.255453i
$964$		0			0
$965$	23.9525	−	32.7318i	0.771057	−	1.05368i
$966$		0			0
$967$	28.6428	−	20.8102i	0.921090	−	0.669211i	−0.0227051	−	0.999742i	$-0.507228\pi$
$967$	28.6428	−	20.8102i	0.921090	−	0.669211i	0.943795	+	0.330531i	$0.107228\pi$
$968$		0			0
$969$	−13.6470	+	18.7835i	−0.438404	+	0.603412i
$970$		0			0
$971$	3.99310	+	1.29744i	0.128145	+	0.0416368i	0.372387	−	0.928077i	$-0.378539\pi$
$971$	3.99310	+	1.29744i	0.128145	+	0.0416368i	−0.244243	+	0.969714i	$0.578539\pi$
$972$		0			0
$973$	8.05818	−	5.85461i	0.258333	−	0.187690i
$974$		0			0
$975$	−0.349204	+	1.05025i	−0.0111835	+	0.0336350i
$976$		0			0
$977$	11.0894	+	34.1297i	0.354781	+	1.09190i	0.956136	+	0.292922i	$0.0946278\pi$
$977$	11.0894	+	34.1297i	0.354781	+	1.09190i	−0.601355	+	0.798982i	$0.705372\pi$
$978$		0			0
$979$	4.02612	+	2.92514i	0.128675	+	0.0934880i
$980$		0			0
$981$			23.5252i			0.751101i
$982$		0			0
$983$		−	30.3353i		−	0.967547i	−0.875193	−	0.483773i	$-0.839266\pi$
$983$		−	30.3353i		−	0.967547i	0.875193	−	0.483773i	$-0.160734\pi$
$984$		0			0
$985$	−46.6564	+	33.6547i	−1.48660	+	1.07233i
$986$		0			0
$987$	5.59732			0.178165
$988$		0			0
$989$	−47.9905	−	34.8672i	−1.52601	−	1.10871i
$990$		0			0
$991$	0.911277	−	0.296092i	0.0289477	−	0.00940567i	−0.294507	−	0.955649i	$-0.595156\pi$
$991$	0.911277	−	0.296092i	0.0289477	−	0.00940567i	0.323455	+	0.946244i	$0.395156\pi$
$992$		0			0
$993$		−	2.78819i		−	0.0884805i
$994$		0			0
$995$	1.58123	−	4.81052i	0.0501285	−	0.152504i
$996$		0			0
$997$	9.30869	−	28.6492i	0.294809	−	0.907329i	−0.688476	−	0.725259i	$-0.741720\pi$
$997$	9.30869	−	28.6492i	0.294809	−	0.907329i	0.983285	−	0.182070i	$-0.0582799\pi$
$998$		0			0
$999$	−12.9160	+	17.7774i	−0.408644	+	0.562451i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bi.a.189.13	yes	80
5.4	even	2	inner	820.2.bi.a.189.8	✓	80
41.23	even	10	inner	820.2.bi.a.269.8	yes	80
205.64	even	10	inner	820.2.bi.a.269.13	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bi.a.189.8	✓	80	5.4	even	2	inner
820.2.bi.a.189.13	yes	80	1.1	even	1	trivial
820.2.bi.a.269.8	yes	80	41.23	even	10	inner
820.2.bi.a.269.13	yes	80	205.64	even	10	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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+0.660390 q^{3} +(0.00764381 - 2.23605i) q^{5} +(-0.328706 - 1.01165i) q^{7} -2.56389 q^{9} +(-1.85813 - 2.55750i) q^{11} +(0.103580 - 0.318787i) q^{13} +(0.00504790 - 1.47667i) q^{15} +(-4.74676 + 3.44872i) q^{17} +(5.69881 - 1.85166i) q^{19} +(-0.217074 - 0.668085i) q^{21} +(-7.08290 - 2.30138i) q^{23} +(-4.99988 - 0.0341840i) q^{25} -3.67433 q^{27} +(2.91444 - 4.01139i) q^{29} +(-7.53890 + 5.47733i) q^{31} +(-1.22709 - 1.68895i) q^{33} +(-2.26462 + 0.727271i) q^{35} +(3.51520 - 4.83826i) q^{37} +(0.0684032 - 0.210523i) q^{39} +(6.18424 - 1.65986i) q^{41} +(7.57529 + 2.46136i) q^{43} +(-0.0195979 + 5.73299i) q^{45} +(-2.46228 + 7.57812i) q^{47} +(4.74773 - 3.44943i) q^{49} +(-3.13471 + 2.27750i) q^{51} +(-8.99438 - 6.53480i) q^{53} +(-5.73292 + 4.13534i) q^{55} +(3.76343 - 1.22281i) q^{57} +(3.16987 - 9.75587i) q^{59} +(-2.19027 - 6.74094i) q^{61} +(0.842764 + 2.59376i) q^{63} +(-0.712032 - 0.234047i) q^{65} +(0.514472 + 0.373785i) q^{67} +(-4.67748 - 1.51980i) q^{69} +(3.09514 + 4.26010i) q^{71} -4.81973i q^{73} +(-3.30187 - 0.0225747i) q^{75} +(-1.97652 + 2.72045i) q^{77} -11.1861i q^{79} +5.26517 q^{81} +8.67639i q^{83} +(7.67525 + 10.6404i) q^{85} +(1.92467 - 2.64908i) q^{87} +(-1.49719 + 0.486466i) q^{89} -0.356548 q^{91} +(-4.97861 + 3.61717i) q^{93} +(-4.09684 - 12.7570i) q^{95} +(-9.61413 - 6.98507i) q^{97} +(4.76404 + 6.55714i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 68 q^{9} + 10 q^{15} - 26 q^{21} + 10 q^{25} - 20 q^{29} + 4 q^{31} + 15 q^{35} - 8 q^{39} + 4 q^{41} - 4 q^{45} + 18 q^{49} + 52 q^{51} - 36 q^{59} - 42 q^{61} - 15 q^{65} + 30 q^{69} - 20 q^{75}+ \cdots + 80 q^{99}+O(q^{100}) \) 80 * q + 68 * q^9 + 10 * q^15 - 26 * q^21 + 10 * q^25 - 20 * q^29 + 4 * q^31 + 15 * q^35 - 8 * q^39 + 4 * q^41 - 4 * q^45 + 18 * q^49 + 52 * q^51 - 36 * q^59 - 42 * q^61 - 15 * q^65 + 30 * q^69 - 20 * q^75 + 32 * q^81 + 10 * q^89 - 132 * q^91 + 50 * q^95 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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