LMFDB - Embedded newform 820.2.x.a.273.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(273,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 6, 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("820.273"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.x (of order $8$, 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:	$84$
Relative dimension:	$21$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			273.19
Character	$\chi$	$=$	820.273
Dual form			820.2.x.a.817.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.42535 + 1.00461i) q^{3} +(-1.21756 + 1.87551i) q^{5} +(1.20713 - 2.91427i) q^{7} +(2.75177 + 2.75177i) q^{9} +(0.413305 + 0.997808i) q^{11} +(5.08419 + 2.10594i) q^{13} +(-4.83719 + 3.32559i) q^{15} +(-0.984862 + 0.407943i) q^{17} +(-1.93434 + 4.66992i) q^{19} +(5.85543 - 5.85543i) q^{21} +(0.936242 - 0.936242i) q^{23} +(-2.03507 - 4.56711i) q^{25} +(0.895703 + 2.16242i) q^{27} +(1.58912 + 3.83648i) q^{29} +2.33421i q^{31} +2.83525i q^{33} +(3.99598 + 5.81229i) q^{35} +(8.08219 - 8.08219i) q^{37} +(10.2153 + 10.2153i) q^{39} +(-5.07254 - 3.90760i) q^{41} +0.648637i q^{43} +(-8.51143 + 1.81051i) q^{45} +(-4.54681 + 1.88335i) q^{47} +(-2.08604 - 2.08604i) q^{49} -2.79846 q^{51} +(-3.06923 + 7.40978i) q^{53} +(-2.37462 - 0.439737i) q^{55} +(-9.38293 + 9.38293i) q^{57} -2.33725i q^{59} +(0.848427 + 0.848427i) q^{61} +(11.3411 - 4.69765i) q^{63} +(-10.1400 + 6.97133i) q^{65} +(1.32747 - 0.549855i) q^{67} +(3.21128 - 1.33016i) q^{69} +(-2.87573 + 1.19117i) q^{71} -14.5992i q^{73} +(-0.347590 - 13.1213i) q^{75} +3.40679 q^{77} +(-3.00671 + 1.24542i) q^{79} -5.53030i q^{81} +(-12.4559 - 12.4559i) q^{83} +(0.434032 - 2.34382i) q^{85} +10.9013i q^{87} +(-1.68705 - 4.07290i) q^{89} +(12.2745 - 12.2745i) q^{91} +(-2.34498 + 5.66129i) q^{93} +(-6.40329 - 9.31381i) q^{95} +(3.12641 + 7.54783i) q^{97} +(-1.60842 + 3.88306i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) $ 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.42535	+	1.00461i	1.40028	+	0.580014i	0.949824	−	0.312785i	$-0.101262\pi$
$3$	2.42535	+	1.00461i	1.40028	+	0.580014i	0.450455	+	0.892799i	$0.351262\pi$
$4$		0			0
$5$	−1.21756	+	1.87551i	−0.544511	+	0.838753i
$5$	−1.21756	+	1.87551i	−0.544511	+	0.838753i
$6$		0			0
$7$	1.20713	−	2.91427i	0.456252	−	1.10149i	−0.513652	−	0.857999i	$-0.671708\pi$
$7$	1.20713	−	2.91427i	0.456252	−	1.10149i	0.969903	−	0.243490i	$-0.0782923\pi$
$8$		0			0
$9$	2.75177	+	2.75177i	0.917256	+	0.917256i
$10$		0			0
$11$	0.413305	+	0.997808i	0.124616	+	0.300850i	0.973859	−	0.227152i	$-0.0729413\pi$
$11$	0.413305	+	0.997808i	0.124616	+	0.300850i	−0.849243	+	0.528002i	$0.822941\pi$
$12$		0			0
$13$	5.08419	+	2.10594i	1.41010	+	0.584083i	0.952353	−	0.304999i	$-0.0986561\pi$
$13$	5.08419	+	2.10594i	1.41010	+	0.584083i	0.457748	+	0.889082i	$0.348656\pi$
$14$		0			0
$15$	−4.83719	+	3.32559i	−1.24896	+	0.858664i
$16$		0			0
$17$	−0.984862	+	0.407943i	−0.238864	+	0.0989408i	−0.498904	−	0.866657i	$-0.666264\pi$
$17$	−0.984862	+	0.407943i	−0.238864	+	0.0989408i	0.260040	+	0.965598i	$0.416264\pi$
$18$		0			0
$19$	−1.93434	+	4.66992i	−0.443769	+	1.07135i	0.530847	+	0.847468i	$0.321874\pi$
$19$	−1.93434	+	4.66992i	−0.443769	+	1.07135i	−0.974616	+	0.223885i	$0.928126\pi$
$20$		0			0
$21$	5.85543	−	5.85543i	1.27776	−	1.27776i
$22$		0			0
$23$	0.936242	−	0.936242i	0.195220	−	0.195220i	−0.602727	−	0.797947i	$-0.705919\pi$
$23$	0.936242	−	0.936242i	0.195220	−	0.195220i	0.797947	+	0.602727i	$0.205919\pi$
$24$		0			0
$25$	−2.03507	−	4.56711i	−0.407015	−	0.913422i
$26$		0			0
$27$	0.895703	+	2.16242i	0.172378	+	0.416158i
$28$		0			0
$29$	1.58912	+	3.83648i	0.295092	+	0.712416i	0.999995	+	0.00311206i	$0.000990601\pi$
$29$	1.58912	+	3.83648i	0.295092	+	0.712416i	−0.704903	+	0.709304i	$0.749009\pi$
$30$		0			0
$31$			2.33421i			0.419237i	0.977783	+	0.209618i	$0.0672221\pi$
$31$			2.33421i			0.419237i	−0.977783	+	0.209618i	$0.932778\pi$
$32$		0			0
$33$			2.83525i			0.493553i
$34$		0			0
$35$	3.99598	+	5.81229i	0.675443	+	0.982456i
$36$		0			0
$37$	8.08219	−	8.08219i	1.32870	−	1.32870i	0.422202	−	0.906502i	$-0.361257\pi$
$37$	8.08219	−	8.08219i	1.32870	−	1.32870i	0.906502	−	0.422202i	$-0.138743\pi$
$38$		0			0
$39$	10.2153	+	10.2153i	1.63576	+	1.63576i
$40$		0			0
$41$	−5.07254	−	3.90760i	−0.792198	−	0.610265i
$41$	−5.07254	−	3.90760i	−0.792198	−	0.610265i
$42$		0			0
$43$			0.648637i			0.0989162i	0.998776	+	0.0494581i	$0.0157494\pi$
$43$			0.648637i			0.0989162i	−0.998776	+	0.0494581i	$0.984251\pi$
$44$		0			0
$45$	−8.51143	+	1.81051i	−1.26881	+	0.269895i
$46$		0			0
$47$	−4.54681	+	1.88335i	−0.663221	+	0.274715i	−0.688793	−	0.724958i	$-0.741859\pi$
$47$	−4.54681	+	1.88335i	−0.663221	+	0.274715i	0.0255724	+	0.999673i	$0.491859\pi$
$48$		0			0
$49$	−2.08604	−	2.08604i	−0.298005	−	0.298005i
$50$		0			0
$51$	−2.79846			−0.391863
$52$		0			0
$53$	−3.06923	+	7.40978i	−0.421591	+	1.01781i	0.560287	+	0.828298i	$0.310691\pi$
$53$	−3.06923	+	7.40978i	−0.421591	+	1.01781i	−0.981878	+	0.189513i	$0.939309\pi$
$54$		0			0
$55$	−2.37462	−	0.439737i	−0.320194	−	0.0592941i
$56$		0			0
$57$	−9.38293	+	9.38293i	−1.24280	+	1.24280i
$58$		0			0
$59$		−	2.33725i		−	0.304283i	−0.988359	−	0.152142i	$-0.951383\pi$
$59$		−	2.33725i		−	0.304283i	0.988359	−	0.152142i	$-0.0486170\pi$
$60$		0			0
$61$	0.848427	+	0.848427i	0.108630	+	0.108630i	0.759333	−	0.650703i	$-0.225526\pi$
$61$	0.848427	+	0.848427i	0.108630	+	0.108630i	−0.650703	+	0.759333i	$0.725526\pi$
$62$		0			0
$63$	11.3411	−	4.69765i	1.42885	−	0.591848i
$64$		0			0
$65$	−10.1400	+	6.97133i	−1.25772	+	0.864687i
$66$		0			0
$67$	1.32747	−	0.549855i	0.162176	−	0.0671755i	−0.300119	−	0.953902i	$-0.597026\pi$
$67$	1.32747	−	0.549855i	0.162176	−	0.0671755i	0.462295	+	0.886726i	$0.347026\pi$
$68$		0			0
$69$	3.21128	−	1.33016i	0.386593	−	0.160132i
$70$		0			0
$71$	−2.87573	+	1.19117i	−0.341287	+	0.141366i	−0.546742	−	0.837301i	$-0.684132\pi$
$71$	−2.87573	+	1.19117i	−0.341287	+	0.141366i	0.205456	+	0.978666i	$0.434132\pi$
$72$		0			0
$73$		−	14.5992i		−	1.70871i	−0.519692	−	0.854354i	$-0.673953\pi$
$73$		−	14.5992i		−	1.70871i	0.519692	−	0.854354i	$-0.326047\pi$
$74$		0			0
$75$	−0.347590	−	13.1213i	−0.0401363	−	1.51512i
$76$		0			0
$77$	3.40679			0.388240
$78$		0			0
$79$	−3.00671	+	1.24542i	−0.338281	+	0.140121i	−0.545356	−	0.838204i	$-0.683606\pi$
$79$	−3.00671	+	1.24542i	−0.338281	+	0.140121i	0.207075	+	0.978325i	$0.433606\pi$
$80$		0			0
$81$		−	5.53030i		−	0.614478i
$82$		0			0
$83$	−12.4559	−	12.4559i	−1.36721	−	1.36721i	−0.864387	−	0.502828i	$-0.832293\pi$
$83$	−12.4559	−	12.4559i	−1.36721	−	1.36721i	−0.502828	−	0.864387i	$-0.667707\pi$
$84$		0			0
$85$	0.434032	−	2.34382i	0.0470773	−	0.254222i
$86$		0			0
$87$			10.9013i			1.16874i
$88$		0			0
$89$	−1.68705	−	4.07290i	−0.178827	−	0.431727i	0.808894	−	0.587955i	$-0.200067\pi$
$89$	−1.68705	−	4.07290i	−0.178827	−	0.431727i	−0.987721	+	0.156228i	$0.950067\pi$
$90$		0			0
$91$	12.2745	−	12.2745i	1.28672	−	1.28672i
$92$		0			0
$93$	−2.34498	+	5.66129i	−0.243163	+	0.587048i
$94$		0			0
$95$	−6.40329	−	9.31381i	−0.656964	−	0.955576i
$96$		0			0
$97$	3.12641	+	7.54783i	0.317439	+	0.766366i	0.999388	+	0.0349665i	$0.0111325\pi$
$97$	3.12641	+	7.54783i	0.317439	+	0.766366i	−0.681949	+	0.731399i	$0.738868\pi$
$98$		0			0
$99$	−1.60842	+	3.88306i	−0.161652	+	0.390262i
$100$		0			0
$101$	5.29059	+	2.19144i	0.526434	+	0.218056i	0.630040	−	0.776562i	$-0.283038\pi$
$101$	5.29059	+	2.19144i	0.526434	+	0.218056i	−0.103607	+	0.994618i	$0.533038\pi$
$102$		0			0
$103$	4.51685			0.445059			0.222529	−	0.974926i	$-0.428569\pi$
$103$	4.51685			0.445059			0.222529	+	0.974926i	$0.428569\pi$
$104$		0			0
$105$	3.85255	+	18.1113i	0.375970	+	1.76748i
$106$		0			0
$107$	−2.52187	−	2.52187i	−0.243798	−	0.243798i	0.574621	−	0.818419i	$-0.305149\pi$
$107$	−2.52187	−	2.52187i	−0.243798	−	0.243798i	−0.818419	+	0.574621i	$0.805149\pi$
$108$		0			0
$109$	−9.75628	−	4.04118i	−0.934482	−	0.387075i	−0.137105	−	0.990557i	$-0.543780\pi$
$109$	−9.75628	−	4.04118i	−0.934482	−	0.387075i	−0.797377	+	0.603481i	$0.793780\pi$
$110$		0			0
$111$	27.7217	−	11.4827i	2.63122	−	1.08989i
$112$		0			0
$113$	−10.3650	+	10.3650i	−0.975059	+	0.975059i	−0.999696	−	0.0246374i	$-0.992157\pi$
$113$	−10.3650	+	10.3650i	−0.975059	+	0.975059i	0.0246374	+	0.999696i	$0.492157\pi$
$114$		0			0
$115$	0.615996	+	2.89587i	0.0574419	+	0.270041i
$116$		0			0
$117$	8.19546	+	19.7856i	0.757670	+	1.82918i
$118$		0			0
$119$			3.36259i			0.308248i
$120$		0			0
$121$	6.95338	−	6.95338i	0.632125	−	0.632125i
$122$		0			0
$123$	−8.37707	−	14.5733i	−0.755335	−	1.31403i
$124$		0			0
$125$	11.0435	+	1.74395i	0.987760	+	0.155983i
$126$		0			0
$127$	−11.2518	−	11.2518i	−0.998439	−	0.998439i	0.00156012	−	0.999999i	$-0.499503\pi$
$127$	−11.2518	−	11.2518i	−0.998439	−	0.998439i	−0.999999	+	0.00156012i	$0.999503\pi$
$128$		0			0
$129$	−0.651630	+	1.57317i	−0.0573728	+	0.138510i
$130$		0			0
$131$	6.50361	−	6.50361i	0.568223	−	0.568223i	−0.363407	−	0.931630i	$-0.618387\pi$
$131$	6.50361	−	6.50361i	0.568223	−	0.568223i	0.931630	+	0.363407i	$0.118387\pi$
$132$		0			0
$133$	11.2744	+	11.2744i	0.977613	+	0.977613i
$134$		0			0
$135$	−5.14621	−	0.952984i	−0.442916	−	0.0820198i
$136$		0			0
$137$	11.4381	−	4.73781i	0.977221	−	0.404778i	0.163826	−	0.986489i	$-0.447617\pi$
$137$	11.4381	−	4.73781i	0.977221	−	0.404778i	0.813395	+	0.581711i	$0.197617\pi$
$138$		0			0
$139$		−	18.0108i		−	1.52766i	−0.645420	−	0.763828i	$-0.723317\pi$
$139$		−	18.0108i		−	1.52766i	0.645420	−	0.763828i	$-0.276683\pi$
$140$		0			0
$141$	−12.9197			−1.08803
$142$		0			0
$143$			5.94344i			0.497016i
$144$		0			0
$145$	−9.13021	−	1.69075i	−0.758223	−	0.140409i
$146$		0			0
$147$	−2.96372	−	7.15504i	−0.244443	−	0.590138i
$148$		0			0
$149$	3.69121	−	8.91136i	0.302395	−	0.730047i	−0.697514	−	0.716571i	$-0.745710\pi$
$149$	3.69121	−	8.91136i	0.302395	−	0.730047i	0.999909	−	0.0134756i	$-0.00428955\pi$
$150$		0			0
$151$	7.35706	+	17.7615i	0.598709	+	1.44541i	0.874898	+	0.484308i	$0.160929\pi$
$151$	7.35706	+	17.7615i	0.598709	+	1.44541i	−0.276189	+	0.961103i	$0.589071\pi$
$152$		0			0
$153$	−3.83268	−	1.58755i	−0.309854	−	0.128346i
$154$		0			0
$155$	−4.37784	−	2.84205i	−0.351636	−	0.228279i
$156$		0			0
$157$	10.4512	+	4.32903i	0.834096	+	0.345494i	0.758523	−	0.651646i	$-0.225921\pi$
$157$	10.4512	+	4.32903i	0.834096	+	0.345494i	0.0755733	+	0.997140i	$0.475921\pi$
$158$		0			0
$159$	−14.8879	+	14.8879i	−1.18069	+	1.18069i
$160$		0			0
$161$	−1.59829	−	3.85862i	−0.125963	−	0.304102i
$162$		0			0
$163$	2.38920	−	2.38920i	0.187136	−	0.187136i	−0.607321	−	0.794457i	$-0.707756\pi$
$163$	2.38920	−	2.38920i	0.187136	−	0.187136i	0.794457	+	0.607321i	$0.207756\pi$
$164$		0			0
$165$	−5.31754	−	3.45210i	−0.413970	−	0.268745i
$166$		0			0
$167$	−3.00900	+	7.26437i	−0.232843	+	0.562134i	−0.996510	−	0.0834775i	$-0.973397\pi$
$167$	−3.00900	+	7.26437i	−0.232843	+	0.562134i	0.763666	+	0.645611i	$0.223397\pi$
$168$		0			0
$169$	12.2216	+	12.2216i	0.940125	+	0.940125i
$170$		0			0
$171$	−18.1734	+	7.52767i	−1.38975	+	0.575655i
$172$		0			0
$173$	20.7089			1.57446			0.787232	−	0.616656i	$-0.211513\pi$
$173$	20.7089			1.57446			0.787232	+	0.616656i	$0.211513\pi$
$174$		0			0
$175$	−15.7664	+	0.417659i	−1.19182	+	0.0315721i
$176$		0			0
$177$	2.34803	−	5.66865i	0.176489	−	0.426081i
$178$		0			0
$179$	−21.2629	−	8.80738i	−1.58926	−	0.658294i	−0.599417	−	0.800437i	$-0.704601\pi$
$179$	−21.2629	−	8.80738i	−1.58926	−	0.658294i	−0.989846	+	0.142143i	$0.954601\pi$
$180$		0			0
$181$	−6.37442	−	2.64037i	−0.473807	−	0.196257i	0.132985	−	0.991118i	$-0.457544\pi$
$181$	−6.37442	−	2.64037i	−0.473807	−	0.196257i	−0.606792	+	0.794861i	$0.707544\pi$
$182$		0			0
$183$	1.20539	+	2.91008i	0.0891053	+	0.215119i
$184$		0			0
$185$	5.31764	+	24.9988i	0.390961	+	1.83795i
$186$		0			0
$187$	−0.814098	−	0.814098i	−0.0595327	−	0.0595327i
$188$		0			0
$189$	7.38309			0.537041
$190$		0			0
$191$	8.26712	−	19.9586i	0.598188	−	1.44415i	−0.277239	−	0.960801i	$-0.589419\pi$
$191$	8.26712	−	19.9586i	0.598188	−	1.44415i	0.875426	−	0.483352i	$-0.160581\pi$
$192$		0			0
$193$	−19.2549	−	7.97565i	−1.38600	−	0.574100i	−0.439921	−	0.898037i	$-0.644993\pi$
$193$	−19.2549	−	7.97565i	−1.38600	−	0.574100i	−0.946079	+	0.323937i	$0.894993\pi$
$194$		0			0
$195$	−31.5967	+	6.72111i	−2.26269	+	0.481309i
$196$		0			0
$197$	6.92491			0.493380			0.246690	−	0.969094i	$-0.420657\pi$
$197$	6.92491			0.493380			0.246690	+	0.969094i	$0.420657\pi$
$198$		0			0
$199$	−2.59974	−	1.07685i	−0.184291	−	0.0763357i	0.288630	−	0.957441i	$-0.406800\pi$
$199$	−2.59974	−	1.07685i	−0.184291	−	0.0763357i	−0.472921	+	0.881105i	$0.656800\pi$
$200$		0			0
$201$	3.77197			0.266054
$202$		0			0
$203$	13.0988			0.919355
$204$		0			0
$205$	13.5049	−	4.75584i	0.943222	−	0.332163i
$206$		0			0
$207$	5.15265			0.358134
$208$		0			0
$209$	−5.45915			−0.377618
$210$		0			0
$211$	−17.2196	−	7.13257i	−1.18544	−	0.491027i	−0.299175	−	0.954198i	$-0.596711\pi$
$211$	−17.2196	−	7.13257i	−1.18544	−	0.491027i	−0.886269	+	0.463172i	$0.846711\pi$
$212$		0			0
$213$	−8.17133			−0.559890
$214$		0			0
$215$	−1.21652	−	0.789757i	−0.0829663	−	0.0538610i
$216$		0			0
$217$	6.80251	+	2.81769i	0.461784	+	0.191277i
$218$		0			0
$219$	14.6666	−	35.4082i	0.991075	−	2.39267i
$220$		0			0
$221$	−5.86633			−0.394612
$222$		0			0
$223$	−12.8175	−	12.8175i	−0.858326	−	0.858326i	0.132815	−	0.991141i	$-0.457598\pi$
$223$	−12.8175	−	12.8175i	−0.858326	−	0.858326i	−0.991141	+	0.132815i	$0.957598\pi$
$224$		0			0
$225$	6.96757	−	18.1677i	0.464505	−	1.21118i
$226$		0			0
$227$	9.58650	+	23.1438i	0.636278	+	1.53611i	0.831602	+	0.555372i	$0.187424\pi$
$227$	9.58650	+	23.1438i	0.636278	+	1.53611i	−0.195324	+	0.980739i	$0.562576\pi$
$228$		0			0
$229$	−15.2243	−	6.30609i	−1.00605	−	0.416718i	−0.182036	−	0.983292i	$-0.558269\pi$
$229$	−15.2243	−	6.30609i	−1.00605	−	0.416718i	−0.824011	+	0.566573i	$0.808269\pi$
$230$		0			0
$231$	8.26267	+	3.42251i	0.543644	+	0.225185i
$232$		0			0
$233$	−3.66880	+	8.85726i	−0.240351	+	0.580258i	−0.997318	−	0.0731950i	$-0.976680\pi$
$233$	−3.66880	+	8.85726i	−0.240351	+	0.580258i	0.756967	+	0.653453i	$0.226680\pi$
$234$		0			0
$235$	2.00379	−	10.8207i	0.130713	−	0.705864i
$236$		0			0
$237$	−8.54350			−0.554960
$238$		0			0
$239$	5.67023	−	2.34869i	0.366777	−	0.151924i	−0.191680	−	0.981457i	$-0.561394\pi$
$239$	5.67023	−	2.34869i	0.366777	−	0.151924i	0.558457	+	0.829534i	$0.311394\pi$
$240$		0			0
$241$	−17.0474	−	17.0474i	−1.09812	−	1.09812i	−0.994631	−	0.103487i	$-0.967000\pi$
$241$	−17.0474	−	17.0474i	−1.09812	−	1.09812i	−0.103487	−	0.994631i	$-0.533000\pi$
$242$		0			0
$243$	8.24293	−	19.9002i	0.528784	−	1.27660i
$244$		0			0
$245$	6.45227	−	1.37250i	0.412220	−	0.0876857i
$246$		0			0
$247$	−19.6691	+	19.6691i	−1.25152	+	1.25152i
$248$		0			0
$249$	−17.6966	−	42.7234i	−1.12148	−	2.70748i
$250$		0			0
$251$	−14.9325	+	14.9325i	−0.942528	+	0.942528i	−0.998436	−	0.0559078i	$-0.982195\pi$
$251$	−14.9325	+	14.9325i	−0.942528	+	0.942528i	0.0559078	+	0.998436i	$0.482195\pi$
$252$		0			0
$253$	1.32114	+	0.547236i	0.0830596	+	0.0344044i
$254$		0			0
$255$	3.40731	−	5.24855i	0.213374	−	0.328677i
$256$		0			0
$257$	19.1474	+	7.93109i	1.19438	+	0.494728i	0.889179	−	0.457560i	$-0.151276\pi$
$257$	19.1474	+	7.93109i	1.19438	+	0.494728i	0.305201	+	0.952288i	$0.401276\pi$
$258$		0			0
$259$	−13.7974	−	33.3099i	−0.857329	−	2.06978i
$260$		0			0
$261$	−6.18421	+	14.9300i	−0.382793	+	0.924143i
$262$		0			0
$263$	−9.59106	−	23.1549i	−0.591410	−	1.42779i	−0.882141	−	0.470985i	$-0.843899\pi$
$263$	−9.59106	−	23.1549i	−0.591410	−	1.42779i	0.290731	−	0.956805i	$-0.406101\pi$
$264$		0			0
$265$	−10.1601	−	14.7783i	−0.624131	−	0.907821i
$266$		0			0
$267$		−	11.5731i		−	0.708260i
$268$		0			0
$269$	1.29173			0.0787579			0.0393789	−	0.999224i	$-0.487462\pi$
$269$	1.29173			0.0787579			0.0393789	+	0.999224i	$0.487462\pi$
$270$		0			0
$271$		−	8.96242i		−	0.544428i	−0.962237	−	0.272214i	$-0.912244\pi$
$271$		−	8.96242i		−	0.544428i	0.962237	−	0.272214i	$-0.0877559\pi$
$272$		0			0
$273$	42.1013	−	17.4389i	2.54809	−	1.05545i
$274$		0			0
$275$	3.71599	−	3.91822i	0.224083	−	0.236278i
$276$		0			0
$277$	16.8202	+	16.8202i	1.01063	+	1.01063i	0.999943	+	0.0106849i	$0.00340118\pi$
$277$	16.8202	+	16.8202i	1.01063	+	1.01063i	0.0106849	+	0.999943i	$0.496599\pi$
$278$		0			0
$279$	−6.42321	+	6.42321i	−0.384547	+	0.384547i
$280$		0			0
$281$	−8.10684	+	19.5716i	−0.483613	+	1.16755i	0.474268	+	0.880381i	$0.342713\pi$
$281$	−8.10684	+	19.5716i	−0.483613	+	1.16755i	−0.957881	+	0.287165i	$0.907287\pi$
$282$		0			0
$283$	16.2782	+	16.2782i	0.967636	+	0.967636i	0.999492	−	0.0318563i	$-0.0101419\pi$
$283$	16.2782	+	16.2782i	0.967636	+	0.967636i	−0.0318563	+	0.999492i	$0.510142\pi$
$284$		0			0
$285$	−6.17346	−	29.0221i	−0.365684	−	1.71912i
$286$		0			0
$287$	−17.5110	+	10.0658i	−1.03364	+	0.594163i
$288$		0			0
$289$	−11.2173	+	11.2173i	−0.659840	+	0.659840i
$290$		0			0
$291$			21.4470i			1.25725i
$292$		0			0
$293$	10.8524	+	26.2001i	0.634007	+	1.53063i	0.834544	+	0.550942i	$0.185731\pi$
$293$	10.8524	+	26.2001i	0.634007	+	1.53063i	−0.200537	+	0.979686i	$0.564269\pi$
$294$		0			0
$295$	4.38353	+	2.84575i	0.255219	+	0.165686i
$296$		0			0
$297$	−1.78748	+	1.78748i	−0.103720	+	0.103720i
$298$		0			0
$299$	6.73171	−	2.78836i	0.389305	−	0.161255i
$300$		0			0
$301$	1.89030	+	0.782988i	0.108955	+	0.0451307i
$302$		0			0
$303$	10.6300	+	10.6300i	0.610678	+	0.610678i
$304$		0			0
$305$	−2.62425	+	0.558219i	−0.150264	+	0.0319635i
$306$		0			0
$307$	7.70729			0.439878			0.219939	−	0.975514i	$-0.429414\pi$
$307$	7.70729			0.439878			0.219939	+	0.975514i	$0.429414\pi$
$308$		0			0
$309$	10.9550	+	4.53769i	0.623206	+	0.258140i
$310$		0			0
$311$	−1.36919	+	3.30551i	−0.0776395	+	0.187438i	−0.957934	−	0.286990i	$-0.907345\pi$
$311$	−1.36919	+	3.30551i	−0.0776395	+	0.187438i	0.880294	+	0.474429i	$0.157345\pi$
$312$		0			0
$313$	6.63323	+	16.0140i	0.374932	+	0.905167i	0.992899	+	0.118962i	$0.0379568\pi$
$313$	6.63323	+	16.0140i	0.374932	+	0.905167i	−0.617966	+	0.786205i	$0.712043\pi$
$314$		0			0
$315$	−4.99807	+	26.9901i	−0.281609	+	1.52072i
$316$		0			0
$317$	−0.893597	+	2.15733i	−0.0501894	+	0.121168i	−0.946986	−	0.321276i	$-0.895888\pi$
$317$	−0.893597	+	2.15733i	−0.0501894	+	0.121168i	0.896796	+	0.442444i	$0.145888\pi$
$318$		0			0
$319$	−3.17127	+	3.17127i	−0.177557	+	0.177557i
$320$		0			0
$321$	−3.58292	−	8.64992i	−0.199979	−	0.482792i
$322$		0			0
$323$		−	5.38833i		−	0.299814i
$324$		0			0
$325$	−0.728643	−	27.5058i	−0.0404178	−	1.52575i
$326$		0			0
$327$	−19.6026	−	19.6026i	−1.08403	−	1.08403i
$328$		0			0
$329$			15.5241i			0.855869i
$330$		0			0
$331$	−0.290948	+	0.120514i	−0.0159919	+	0.00662407i	−0.390665	−	0.920533i	$-0.627755\pi$
$331$	−0.290948	+	0.120514i	−0.0159919	+	0.00662407i	0.374673	+	0.927157i	$0.377755\pi$
$332$		0			0
$333$	44.4806			2.43752
$334$		0			0
$335$	−0.585019	+	3.15916i	−0.0319630	+	0.172604i
$336$		0			0
$337$			12.4727i			0.679431i	0.940528	+	0.339715i	$0.110331\pi$
$337$			12.4727i			0.679431i	−0.940528	+	0.339715i	$0.889669\pi$
$338$		0			0
$339$	−35.5517	+	14.7260i	−1.93090	+	0.799806i
$340$		0			0
$341$	−2.32909	+	0.964742i	−0.126127	+	0.0522437i
$342$		0			0
$343$	11.8025	−	4.88875i	0.637274	−	0.263967i
$344$		0			0
$345$	−1.41522	+	7.64234i	−0.0761929	+	0.411450i
$346$		0			0
$347$	−29.5407	+	12.2362i	−1.58583	+	0.656871i	−0.989323	−	0.145739i	$-0.953444\pi$
$347$	−29.5407	+	12.2362i	−1.58583	+	0.656871i	−0.596504	+	0.802610i	$0.703444\pi$
$348$		0			0
$349$	−0.582286	−	0.582286i	−0.0311691	−	0.0311691i	0.691350	−	0.722520i	$-0.257016\pi$
$349$	−0.582286	−	0.582286i	−0.0311691	−	0.0311691i	−0.722520	+	0.691350i	$0.757016\pi$
$350$		0			0
$351$			12.8804i			0.687507i
$352$		0			0
$353$	−21.7080	+	21.7080i	−1.15540	+	1.15540i	−0.169944	+	0.985454i	$0.554359\pi$
$353$	−21.7080	+	21.7080i	−1.15540	+	1.15540i	−0.985454	+	0.169944i	$0.945641\pi$
$354$		0			0
$355$	1.26734	−	6.84378i	0.0672636	−	0.363230i
$356$		0			0
$357$	−3.37811	+	8.15547i	−0.178788	+	0.431633i
$358$		0			0
$359$	11.2307			0.592733			0.296367	−	0.955074i	$-0.404225\pi$
$359$	11.2307			0.592733			0.296367	+	0.955074i	$0.404225\pi$
$360$		0			0
$361$	−4.63142	−	4.63142i	−0.243759	−	0.243759i
$362$		0			0
$363$	23.8499	−	9.87893i	1.25179	−	0.518510i
$364$		0			0
$365$	27.3810	+	17.7755i	1.43318	+	0.930411i
$366$		0			0
$367$			28.7691i			1.50174i	0.660452	+	0.750868i	$0.270365\pi$
$367$			28.7691i			1.50174i	−0.660452	+	0.750868i	$0.729635\pi$
$368$		0			0
$369$	−3.20565	−	24.7113i	−0.166879	−	1.28642i
$370$		0			0
$371$	17.8891	+	17.8891i	0.928756	+	0.928756i
$372$		0			0
$373$	−21.1337	+	21.1337i	−1.09426	+	1.09426i	−0.0991924	+	0.995068i	$0.531626\pi$
$373$	−21.1337	+	21.1337i	−1.09426	+	1.09426i	−0.995068	+	0.0991924i	$0.968374\pi$
$374$		0			0
$375$	25.0324	+	15.3241i	1.29267	+	0.791335i
$376$		0			0
$377$			22.8520i			1.17694i
$378$		0			0
$379$			16.7294i			0.859330i	0.902988	+	0.429665i	$0.141368\pi$
$379$			16.7294i			0.859330i	−0.902988	+	0.429665i	$0.858632\pi$
$380$		0			0
$381$	−15.9859	−	38.5934i	−0.818983	−	1.97720i
$382$		0			0
$383$	−6.45033	−	15.5725i	−0.329596	−	0.795716i	−0.998622	−	0.0524769i	$-0.983288\pi$
$383$	−6.45033	−	15.5725i	−0.329596	−	0.795716i	0.669026	−	0.743239i	$-0.266712\pi$
$384$		0			0
$385$	−4.14799	+	6.38947i	−0.211401	+	0.325637i
$386$		0			0
$387$	−1.78490	+	1.78490i	−0.0907315	+	0.0907315i
$388$		0			0
$389$	−17.8409	+	17.8409i	−0.904569	+	0.904569i	−0.995827	−	0.0912579i	$-0.970911\pi$
$389$	−17.8409	+	17.8409i	−0.904569	+	0.904569i	0.0912579	+	0.995827i	$0.470911\pi$
$390$		0			0
$391$	−0.540136	+	1.30400i	−0.0273158	+	0.0659463i
$392$		0			0
$393$	22.3072	−	9.23994i	1.12525	−	0.466093i
$394$		0			0
$395$	1.32507	−	7.15549i	0.0666713	−	0.360032i
$396$		0			0
$397$	−14.0586	−	5.82325i	−0.705579	−	0.292260i	0.000894877	−	1.00000i	$-0.499715\pi$
$397$	−14.0586	−	5.82325i	−0.705579	−	0.292260i	−0.706474	+	0.707739i	$0.749715\pi$
$398$		0			0
$399$	16.0180	+	38.6708i	0.801901	+	1.93596i
$400$		0			0
$401$	−14.8032	−	14.8032i	−0.739236	−	0.739236i	0.233194	−	0.972430i	$-0.425082\pi$
$401$	−14.8032	−	14.8032i	−0.739236	−	0.739236i	−0.972430	+	0.233194i	$0.925082\pi$
$402$		0			0
$403$	−4.91571	+	11.8676i	−0.244869	+	0.591166i
$404$		0			0
$405$	10.3721	+	6.73350i	0.515395	+	0.334590i
$406$		0			0
$407$	11.4049	+	4.72406i	0.565319	+	0.234163i
$408$		0			0
$409$	29.6137			1.46430			0.732151	−	0.681143i	$-0.238517\pi$
$409$	29.6137			1.46430			0.732151	+	0.681143i	$0.238517\pi$
$410$		0			0
$411$	32.5011			1.60316
$412$		0			0
$413$	−6.81135	−	2.82135i	−0.335165	−	0.138830i
$414$		0			0
$415$	38.5271	−	8.19531i	1.89122	−	0.402292i
$416$		0			0
$417$	18.0939	−	43.6826i	0.886063	−	2.13914i
$418$		0			0
$419$	23.2478	+	23.2478i	1.13573	+	1.13573i	0.989208	+	0.146520i	$0.0468073\pi$
$419$	23.2478	+	23.2478i	1.13573	+	1.13573i	0.146520	+	0.989208i	$0.453193\pi$
$420$		0			0
$421$	13.6203	+	32.8822i	0.663811	+	1.60258i	0.791783	+	0.610803i	$0.209153\pi$
$421$	13.6203	+	32.8822i	0.663811	+	1.60258i	−0.127972	+	0.991778i	$0.540847\pi$
$422$		0			0
$423$	−17.6943	−	7.32923i	−0.860327	−	0.356359i
$424$		0			0
$425$	3.86739	+	3.66778i	0.187596	+	0.177913i
$426$		0			0
$427$	3.49670	−	1.44838i	0.169217	−	0.0700921i
$428$		0			0
$429$	−5.97087	+	14.4149i	−0.288276	+	0.695960i
$430$		0			0
$431$	16.5082	−	16.5082i	0.795170	−	0.795170i	−0.187159	−	0.982330i	$-0.559928\pi$
$431$	16.5082	−	16.5082i	0.795170	−	0.795170i	0.982330	+	0.187159i	$0.0599280\pi$
$432$		0			0
$433$	−21.9194	+	21.9194i	−1.05338	+	1.05338i	−0.0548872	+	0.998493i	$0.517480\pi$
$433$	−21.9194	+	21.9194i	−1.05338	+	1.05338i	−0.998493	+	0.0548872i	$0.982520\pi$
$434$		0			0
$435$	−20.4454	−	13.2730i	−0.980283	−	0.636391i
$436$		0			0
$437$	2.56116	+	6.18319i	0.122517	+	0.295782i
$438$		0			0
$439$	1.09885	+	2.65286i	0.0524454	+	0.126614i	0.947931	−	0.318477i	$-0.103171\pi$
$439$	1.09885	+	2.65286i	0.0524454	+	0.126614i	−0.895485	+	0.445091i	$0.853171\pi$
$440$		0			0
$441$		−	11.4806i		−	0.546695i
$442$		0			0
$443$		−	27.0162i		−	1.28358i	−0.766882	−	0.641788i	$-0.778193\pi$
$443$		−	27.0162i		−	1.28358i	0.766882	−	0.641788i	$-0.221807\pi$
$444$		0			0
$445$	9.69286	+	1.79494i	0.459486	+	0.0850883i
$446$		0			0
$447$	17.9050	−	17.9050i	0.846875	−	0.846875i
$448$		0			0
$449$	−10.6090	−	10.6090i	−0.500670	−	0.500670i	0.410976	−	0.911646i	$-0.365188\pi$
$449$	−10.6090	−	10.6090i	−0.500670	−	0.500670i	−0.911646	+	0.410976i	$0.865188\pi$
$450$		0			0
$451$	1.80252	−	6.67645i	0.0848775	−	0.314382i
$452$		0			0
$453$			50.4689i			2.37124i
$454$		0			0
$455$	8.07598	+	37.9661i	0.378608	+	1.77988i
$456$		0			0
$457$	25.3967	−	10.5197i	1.18801	−	0.492089i	0.300902	−	0.953655i	$-0.402712\pi$
$457$	25.3967	−	10.5197i	1.18801	−	0.492089i	0.887106	+	0.461566i	$0.152712\pi$
$458$		0			0
$459$	−1.76429	−	1.76429i	−0.0823499	−	0.0823499i
$460$		0			0
$461$	28.3960			1.32253			0.661266	−	0.750151i	$-0.270019\pi$
$461$	28.3960			1.32253			0.661266	+	0.750151i	$0.270019\pi$
$462$		0			0
$463$	6.50003	−	15.6925i	0.302082	−	0.729291i	−0.697833	−	0.716261i	$-0.745852\pi$
$463$	6.50003	−	15.6925i	0.302082	−	0.729291i	0.999915	−	0.0130304i	$-0.00414781\pi$
$464$		0			0
$465$	−7.76263	−	11.2910i	−0.359983	−	0.523608i
$466$		0			0
$467$	21.5157	−	21.5157i	0.995629	−	0.995629i	−0.00436113	−	0.999990i	$-0.501388\pi$
$467$	21.5157	−	21.5157i	0.995629	−	0.995629i	0.999990	+	0.00436113i	$0.00138820\pi$
$468$		0			0
$469$		−	4.53234i		−	0.209284i
$470$		0			0
$471$	20.9988	+	20.9988i	0.967576	+	0.967576i
$472$		0			0
$473$	−0.647215	+	0.268085i	−0.0297590	+	0.0123266i
$474$		0			0
$475$	25.2645	−	0.669271i	1.15922	−	0.0307083i
$476$		0			0
$477$	−28.8358	+	11.9442i	−1.32030	+	0.546887i
$478$		0			0
$479$	1.85973	−	0.770327i	0.0849734	−	0.0351971i	−0.339792	−	0.940501i	$-0.610357\pi$
$479$	1.85973	−	0.770327i	0.0849734	−	0.0351971i	0.424765	+	0.905304i	$0.360357\pi$
$480$		0			0
$481$	58.1120	−	24.0708i	2.64968	−	1.09753i
$482$		0			0
$483$		−	10.9642i		−	0.498888i
$484$		0			0
$485$	−17.9626	−	3.32635i	−0.815641	−	0.151042i
$486$		0			0
$487$	−9.44274			−0.427891			−0.213946	−	0.976846i	$-0.568632\pi$
$487$	−9.44274			−0.427891			−0.213946	+	0.976846i	$0.568632\pi$
$488$		0			0
$489$	8.19486	−	3.39442i	0.370585	−	0.153501i
$490$		0			0
$491$			6.71474i			0.303032i	0.988455	+	0.151516i	$0.0484155\pi$
$491$			6.71474i			0.303032i	−0.988455	+	0.151516i	$0.951585\pi$
$492$		0			0
$493$	−3.13013	−	3.13013i	−0.140974	−	0.140974i
$494$		0			0
$495$	−5.32436	−	7.74447i	−0.239312	−	0.348088i
$496$		0			0
$497$			9.81854i			0.440422i
$498$		0			0
$499$	−0.298130	−	0.719750i	−0.0133462	−	0.0322205i	0.917066	−	0.398735i	$-0.130551\pi$
$499$	−0.298130	−	0.719750i	−0.0133462	−	0.0322205i	−0.930412	+	0.366515i	$0.880551\pi$
$500$		0			0
$501$	−14.5958	+	14.5958i	−0.652091	+	0.652091i
$502$		0			0
$503$	−8.70608	+	21.0183i	−0.388185	+	0.937161i	0.602140	+	0.798391i	$0.294315\pi$
$503$	−8.70608	+	21.0183i	−0.388185	+	0.937161i	−0.990325	+	0.138771i	$0.955685\pi$
$504$		0			0
$505$	−10.5517	+	7.25435i	−0.469544	+	0.322814i
$506$		0			0
$507$	17.3637	+	41.9198i	0.771151	+	1.86172i
$508$		0			0
$509$	5.46749	−	13.1997i	0.242342	−	0.585066i	−0.755172	−	0.655526i	$-0.772447\pi$
$509$	5.46749	−	13.1997i	0.242342	−	0.585066i	0.997515	+	0.0704605i	$0.0224469\pi$
$510$		0			0
$511$	−42.5460	−	17.6231i	−1.88212	−	0.779601i
$512$		0			0
$513$	−11.8309			−0.522348
$514$		0			0
$515$	−5.49956	+	8.47140i	−0.242339	+	0.373294i
$516$		0			0
$517$	−3.75844	−	3.75844i	−0.165296	−	0.165296i
$518$		0			0
$519$	50.2263	+	20.8044i	2.20469	+	0.913212i
$520$		0			0
$521$	−6.59684	+	2.73250i	−0.289013	+	0.119713i	−0.522480	−	0.852652i	$-0.674993\pi$
$521$	−6.59684	+	2.73250i	−0.289013	+	0.119713i	0.233467	+	0.972365i	$0.424993\pi$
$522$		0			0
$523$	−5.95182	+	5.95182i	−0.260255	+	0.260255i	−0.825158	−	0.564903i	$-0.808914\pi$
$523$	−5.95182	+	5.95182i	−0.260255	+	0.260255i	0.564903	+	0.825158i	$0.308914\pi$
$524$		0			0
$525$	−38.6586	−	14.8261i	−1.68720	−	0.647066i
$526$		0			0
$527$	−0.952225	−	2.29888i	−0.0414796	−	0.100141i
$528$		0			0
$529$			21.2469i			0.923778i
$530$		0			0
$531$	6.43156	−	6.43156i	0.279106	−	0.279106i
$532$		0			0
$533$	−17.5606	−	30.5495i	−0.760634	−	1.32324i
$534$		0			0
$535$	7.80032	−	1.65925i	0.337237	−	0.0717357i
$536$		0			0
$537$	−42.7220	−	42.7220i	−1.84359	−	1.84359i
$538$		0			0
$539$	1.21929	−	2.94364i	0.0525187	−	0.126791i
$540$		0			0
$541$	−2.13184	+	2.13184i	−0.0916548	+	0.0916548i	−0.751448	−	0.659793i	$-0.770644\pi$
$541$	−2.13184	+	2.13184i	−0.0916548	+	0.0916548i	0.659793	+	0.751448i	$0.270644\pi$
$542$		0			0
$543$	−12.8077	−	12.8077i	−0.549630	−	0.549630i
$544$		0			0
$545$	19.4582	−	13.3776i	0.833497	−	0.573033i
$546$		0			0
$547$	4.09364	−	1.69564i	0.175031	−	0.0725003i	−0.293447	−	0.955975i	$-0.594802\pi$
$547$	4.09364	−	1.69564i	0.175031	−	0.0725003i	0.468478	+	0.883475i	$0.344802\pi$
$548$		0			0
$549$			4.66935i			0.199283i
$550$		0			0
$551$	−20.9899			−0.894201
$552$		0			0
$553$			10.2657i			0.436543i
$554$		0			0
$555$	−12.2170	+	65.9731i	−0.518583	+	2.80040i
$556$		0			0
$557$	−7.10001	−	17.1409i	−0.300837	−	0.726285i	−0.999937	−	0.0112607i	$-0.996416\pi$
$557$	−7.10001	−	17.1409i	−0.300837	−	0.726285i	0.699099	−	0.715024i	$-0.253584\pi$
$558$		0			0
$559$	−1.36599	+	3.29779i	−0.0577753	+	0.139482i
$560$		0			0
$561$	−1.15662	−	2.79233i	−0.0488326	−	0.117892i
$562$		0			0
$563$	−4.19236	−	1.73653i	−0.176687	−	0.0731860i	0.292586	−	0.956239i	$-0.405484\pi$
$563$	−4.19236	−	1.73653i	−0.176687	−	0.0731860i	−0.469273	+	0.883053i	$0.655484\pi$
$564$		0			0
$565$	−6.81962	−	32.0598i	−0.286903	−	1.34876i
$566$		0			0
$567$	−16.1168	−	6.67578i	−0.676841	−	0.280357i
$568$		0			0
$569$	−9.86128	+	9.86128i	−0.413406	+	0.413406i	−0.882923	−	0.469517i	$-0.844428\pi$
$569$	−9.86128	+	9.86128i	−0.413406	+	0.413406i	0.469517	+	0.882923i	$0.344428\pi$
$570$		0			0
$571$	−11.0185	−	26.6010i	−0.461110	−	1.11322i	−0.967942	−	0.251174i	$-0.919183\pi$
$571$	−11.0185	−	26.6010i	−0.461110	−	1.11322i	0.506832	−	0.862045i	$-0.330817\pi$
$572$		0			0
$573$	40.1014	−	40.1014i	1.67526	−	1.67526i
$574$		0			0
$575$	−6.18124	−	2.37060i	−0.257776	−	0.0988608i
$576$		0			0
$577$	−4.40714	+	10.6398i	−0.183472	+	0.442940i	−0.988678	−	0.150056i	$-0.952055\pi$
$577$	−4.40714	+	10.6398i	−0.183472	+	0.442940i	0.805206	+	0.592995i	$0.202055\pi$
$578$		0			0
$579$	−38.6875	−	38.6875i	−1.60780	−	1.60780i
$580$		0			0
$581$	−51.3357	+	21.2640i	−2.12977	+	0.882178i
$582$		0			0
$583$	−8.66206			−0.358746
$584$		0			0
$585$	−47.0865	−	8.71956i	−1.94679	−	0.360510i
$586$		0			0
$587$	−12.2649	+	29.6101i	−0.506227	+	1.22214i	0.439812	+	0.898090i	$0.355045\pi$
$587$	−12.2649	+	29.6101i	−0.506227	+	1.22214i	−0.946040	+	0.324051i	$0.894955\pi$
$588$		0			0
$589$	−10.9006	−	4.51516i	−0.449150	−	0.186044i
$590$		0			0
$591$	16.7954	+	6.95687i	0.690869	+	0.286167i
$592$		0			0
$593$	3.17733	+	7.67076i	0.130477	+	0.315000i	0.975594	−	0.219581i	$-0.0704692\pi$
$593$	3.17733	+	7.67076i	0.130477	+	0.315000i	−0.845117	+	0.534582i	$0.820469\pi$
$594$		0			0
$595$	−6.30657	−	4.09417i	−0.258544	−	0.167845i
$596$		0			0
$597$	−5.22348	−	5.22348i	−0.213783	−	0.213783i
$598$		0			0
$599$	31.8779			1.30250			0.651249	−	0.758864i	$-0.274245\pi$
$599$	31.8779			1.30250			0.651249	+	0.758864i	$0.274245\pi$
$600$		0			0
$601$	12.2611	−	29.6008i	0.500139	−	1.20744i	−0.449268	−	0.893397i	$-0.648315\pi$
$601$	12.2611	−	29.6008i	0.500139	−	1.20744i	0.949408	−	0.314046i	$-0.101685\pi$
$602$		0			0
$603$	5.16596	+	2.13981i	0.210374	+	0.0871399i
$604$		0			0
$605$	4.57494	+	21.5073i	0.185998	+	0.874396i
$606$		0			0
$607$	22.2182			0.901811			0.450905	−	0.892572i	$-0.351101\pi$
$607$	22.2182			0.901811			0.450905	+	0.892572i	$0.351101\pi$
$608$		0			0
$609$	31.7692	+	13.1592i	1.28735	+	0.533239i
$610$		0			0
$611$	−27.0831			−1.09566
$612$		0			0
$613$	−16.1325			−0.651586			−0.325793	−	0.945441i	$-0.605631\pi$
$613$	−16.1325			−0.651586			−0.325793	+	0.945441i	$0.605631\pi$
$614$		0			0
$615$	37.5319	+	2.03260i	1.51343	+	0.0819622i
$616$		0			0
$617$	−36.3321			−1.46268			−0.731338	−	0.682015i	$-0.761104\pi$
$617$	−36.3321			−1.46268			−0.731338	+	0.682015i	$0.761104\pi$
$618$		0			0
$619$	−9.70603			−0.390118			−0.195059	−	0.980791i	$-0.562490\pi$
$619$	−9.70603			−0.390118			−0.195059	+	0.980791i	$0.562490\pi$
$620$		0			0
$621$	2.86314	+	1.18595i	0.114894	+	0.0475906i
$622$		0			0
$623$	−13.9060			−0.557132
$624$		0			0
$625$	−16.7170	+	18.5888i	−0.668678	+	0.743552i
$626$		0			0
$627$	−13.2404	−	5.48434i	−0.528770	−	0.219024i
$628$		0			0
$629$	−4.66277	+	11.2569i	−0.185917	+	0.448843i
$630$		0			0
$631$	7.91017			0.314899			0.157449	−	0.987527i	$-0.449673\pi$
$631$	7.91017			0.314899			0.157449	+	0.987527i	$0.449673\pi$
$632$		0			0
$633$	−34.5980	−	34.5980i	−1.37515	−	1.37515i
$634$		0			0
$635$	34.8028	−	7.40309i	1.38111	−	0.293783i
$636$		0			0
$637$	−6.21274	−	14.9989i	−0.246158	−	0.594278i
$638$		0			0
$639$	−11.1912	−	4.63553i	−0.442716	−	0.183379i
$640$		0			0
$641$	19.6921	+	8.15672i	0.777790	+	0.322171i	0.736023	−	0.676956i	$-0.236701\pi$
$641$	19.6921	+	8.15672i	0.777790	+	0.322171i	0.0417665	+	0.999127i	$0.486701\pi$
$642$		0			0
$643$	−18.5428	+	44.7664i	−0.731258	+	1.76541i	−0.0928991	+	0.995676i	$0.529613\pi$
$643$	−18.5428	+	44.7664i	−0.731258	+	1.76541i	−0.638359	+	0.769739i	$0.720387\pi$
$644$		0			0
$645$	−2.15710	−	3.13758i	−0.0849358	−	0.123542i
$646$		0			0
$647$	34.5446			1.35809			0.679044	−	0.734098i	$-0.262395\pi$
$647$	34.5446			1.35809			0.679044	+	0.734098i	$0.262395\pi$
$648$		0			0
$649$	2.33212	−	0.965996i	0.0915438	−	0.0379187i
$650$		0			0
$651$	13.6678	+	13.6678i	0.535683	+	0.535683i
$652$		0			0
$653$	−6.73311	+	16.2552i	−0.263487	+	0.636113i	−0.999149	−	0.0412346i	$-0.986871\pi$
$653$	−6.73311	+	16.2552i	−0.263487	+	0.636113i	0.735663	+	0.677348i	$0.236871\pi$
$654$		0			0
$655$	4.27902	+	20.1162i	0.167195	+	0.786003i
$656$		0			0
$657$	40.1736	−	40.1736i	1.56732	−	1.56732i
$658$		0			0
$659$	−1.95543	−	4.72083i	−0.0761728	−	0.183897i	0.881206	−	0.472732i	$-0.156732\pi$
$659$	−1.95543	−	4.72083i	−0.0761728	−	0.183897i	−0.957379	+	0.288835i	$0.906732\pi$
$660$		0			0
$661$	20.1997	−	20.1997i	0.785679	−	0.785679i	−0.195104	−	0.980783i	$-0.562504\pi$
$661$	20.1997	−	20.1997i	0.785679	−	0.785679i	0.980783	+	0.195104i	$0.0625045\pi$
$662$		0			0
$663$	−14.2279	−	5.89340i	−0.552567	−	0.228881i
$664$		0			0
$665$	−34.8725	+	7.41792i	−1.35230	+	0.287655i
$666$		0			0
$667$	5.07967	+	2.10407i	0.196686	+	0.0814699i
$668$		0			0
$669$	−18.2104	−	43.9637i	−0.704054	−	1.69974i
$670$		0			0
$671$	−0.495907	+	1.19723i	−0.0191443	+	0.0462184i
$672$		0			0
$673$	1.36122	+	3.28626i	0.0524710	+	0.126676i	0.947941	−	0.318445i	$-0.103161\pi$
$673$	1.36122	+	3.28626i	0.0524710	+	0.126676i	−0.895470	+	0.445121i	$0.853161\pi$
$674$		0			0
$675$	8.05318	−	8.49145i	0.309967	−	0.326836i
$676$		0			0
$677$		−	19.9324i		−	0.766065i	−0.923735	−	0.383033i	$-0.874880\pi$
$677$		−	19.9324i		−	0.766065i	0.923735	−	0.383033i	$-0.125120\pi$
$678$		0			0
$679$	25.7704			0.988976
$680$		0			0
$681$			65.7627i			2.52003i
$682$		0			0
$683$	8.07906	−	3.34646i	0.309137	−	0.128049i	−0.222721	−	0.974882i	$-0.571494\pi$
$683$	8.07906	−	3.34646i	0.309137	−	0.128049i	0.531858	+	0.846834i	$0.321494\pi$
$684$		0			0
$685$	−5.04079	+	27.2208i	−0.192599	+	1.04005i
$686$		0			0
$687$	−30.5890	−	30.5890i	−1.16704	−	1.16704i
$688$		0			0
$689$	−31.2091	+	31.2091i	−1.18897	+	1.18897i
$690$		0			0
$691$	6.14263	−	14.8296i	0.233677	−	0.564146i	−0.762928	−	0.646484i	$-0.776239\pi$
$691$	6.14263	−	14.8296i	0.233677	−	0.564146i	0.996604	+	0.0823381i	$0.0262387\pi$
$692$		0			0
$693$	9.37470	+	9.37470i	0.356115	+	0.356115i
$694$		0			0
$695$	33.7794	+	21.9293i	1.28133	+	0.831826i
$696$		0			0
$697$	6.58983	+	1.77914i	0.249608	+	0.0673897i
$698$		0			0
$699$	−17.7963	+	17.7963i	−0.673116	+	0.673116i
$700$		0			0
$701$			3.67898i			0.138953i	0.997584	+	0.0694765i	$0.0221329\pi$
$701$			3.67898i			0.138953i	−0.997584	+	0.0694765i	$0.977867\pi$
$702$		0			0
$703$	22.1094	+	53.3769i	0.833873	+	2.01315i
$704$		0			0
$705$	15.7305	−	24.2310i	0.592446	−	0.912591i
$706$		0			0
$707$	12.7729	−	12.7729i	0.480373	−	0.480373i
$708$		0			0
$709$	14.2608	−	5.90701i	0.535575	−	0.221842i	−0.0984682	−	0.995140i	$-0.531394\pi$
$709$	14.2608	−	5.90701i	0.535575	−	0.221842i	0.634043	+	0.773298i	$0.281394\pi$
$710$		0			0
$711$	−11.7009	−	4.84666i	−0.438817	−	0.181764i
$712$		0			0
$713$	2.18539	+	2.18539i	0.0818434	+	0.0818434i
$714$		0			0
$715$	−11.1470	−	7.23652i	−0.416874	−	0.270631i
$716$		0			0
$717$	16.1118			0.601707
$718$		0			0
$719$	−27.0695	−	11.2125i	−1.00952	−	0.418157i	−0.184241	−	0.982881i	$-0.558983\pi$
$719$	−27.0695	−	11.2125i	−1.00952	−	0.418157i	−0.825280	+	0.564724i	$0.808983\pi$
$720$		0			0
$721$	5.45242	−	13.1633i	0.203059	−	0.490227i
$722$		0			0
$723$	−24.2199	−	58.4719i	−0.900747	−	2.17459i
$724$		0			0
$725$	14.2876	−	15.0652i	0.530629	−	0.559508i
$726$		0			0
$727$	3.53627	−	8.53730i	0.131153	−	0.316631i	−0.844638	−	0.535339i	$-0.820184\pi$
$727$	3.53627	−	8.53730i	0.131153	−	0.316631i	0.975790	+	0.218707i	$0.0701840\pi$
$728$		0			0
$729$	28.2525	−	28.2525i	1.04639	−	1.04639i
$730$		0			0
$731$	−0.264607	−	0.638818i	−0.00978684	−	0.0236275i
$732$		0			0
$733$		−	46.9842i		−	1.73540i	−0.497086	−	0.867701i	$-0.665597\pi$
$733$		−	46.9842i		−	1.73540i	0.497086	−	0.867701i	$-0.334403\pi$
$734$		0			0
$735$	17.0279	+	3.15325i	0.628082	+	0.116309i
$736$		0			0
$737$	1.09730	+	1.09730i	0.0404196	+	0.0404196i
$738$		0			0
$739$		−	6.68838i		−	0.246036i	−0.992404	−	0.123018i	$-0.960743\pi$
$739$		−	6.68838i		−	0.246036i	0.992404	−	0.123018i	$-0.0392573\pi$
$740$		0			0
$741$	−67.4645	+	27.9447i	−2.47837	+	1.02657i
$742$		0			0
$743$	−7.11427			−0.260997			−0.130499	−	0.991448i	$-0.541658\pi$
$743$	−7.11427			−0.260997			−0.130499	+	0.991448i	$0.541658\pi$
$744$		0			0
$745$	12.2191	+	17.7730i	0.447672	+	0.651154i
$746$		0			0
$747$		−	68.5516i		−	2.50817i
$748$		0			0
$749$	−10.3936	+	4.30517i	−0.379774	+	0.157308i
$750$		0			0
$751$	−39.3848	+	16.3137i	−1.43717	+	0.595296i	−0.959111	−	0.283030i	$-0.908660\pi$
$751$	−39.3848	+	16.3137i	−1.43717	+	0.595296i	−0.478062	+	0.878326i	$0.658660\pi$
$752$		0			0
$753$	−51.2178	+	21.2151i	−1.86648	+	0.773122i
$754$		0			0
$755$	−42.2696	−	7.82755i	−1.53835	−	0.284874i
$756$		0			0
$757$	17.2746	−	7.15536i	0.627855	−	0.260066i	−0.0459865	−	0.998942i	$-0.514643\pi$
$757$	17.2746	−	7.15536i	0.627855	−	0.260066i	0.673841	+	0.738876i	$0.264643\pi$
$758$		0			0
$759$	2.65448	+	2.65448i	0.0963515	+	0.0963515i
$760$		0			0
$761$		−	44.2571i		−	1.60432i	−0.597110	−	0.802159i	$-0.703684\pi$
$761$		−	44.2571i		−	1.60432i	0.597110	−	0.802159i	$-0.296316\pi$
$762$		0			0
$763$	−23.5542	+	23.5542i	−0.852718	+	0.852718i
$764$		0			0
$765$	7.64399	−	5.25528i	0.276369	−	0.190005i
$766$		0			0
$767$	4.92210	−	11.8830i	0.177727	−	0.429070i
$768$		0			0
$769$	47.0847			1.69792			0.848959	−	0.528459i	$-0.177230\pi$
$769$	47.0847			1.69792			0.848959	+	0.528459i	$0.177230\pi$
$770$		0			0
$771$	38.4714	+	38.4714i	1.38551	+	1.38551i
$772$		0			0
$773$	29.6236	−	12.2705i	1.06549	−	0.441338i	0.220090	−	0.975480i	$-0.429365\pi$
$773$	29.6236	−	12.2705i	1.06549	−	0.441338i	0.845395	+	0.534141i	$0.179365\pi$
$774$		0			0
$775$	10.6606	−	4.75029i	0.382940	−	0.170635i
$776$		0			0
$777$		−	94.6493i		−	3.39553i
$778$		0			0
$779$	28.0602	−	16.1297i	1.00536	−	0.577907i
$780$		0			0
$781$	−2.37711	−	2.37711i	−0.0850597	−	0.0850597i
$782$		0			0
$783$	−6.87269	+	6.87269i	−0.245610	+	0.245610i
$784$		0			0
$785$	−20.8441	+	14.3305i	−0.743959	+	0.511476i
$786$		0			0
$787$		−	5.15357i		−	0.183705i	−0.995773	−	0.0918524i	$-0.970721\pi$
$787$		−	5.15357i		−	0.183705i	0.995773	−	0.0918524i	$-0.0292788\pi$
$788$		0			0
$789$		−	65.7940i		−	2.34233i
$790$		0			0
$791$	17.6945	+	42.7183i	0.629144	+	1.51889i
$792$		0			0
$793$	2.52683	+	6.10030i	0.0897303	+	0.216628i
$794$		0			0
$795$	−9.79545	−	46.0495i	−0.347409	−	1.63321i
$796$		0			0
$797$	−8.69925	+	8.69925i	−0.308143	+	0.308143i	−0.844189	−	0.536046i	$-0.819917\pi$
$797$	−8.69925	+	8.69925i	−0.308143	+	0.308143i	0.536046	+	0.844189i	$0.319917\pi$
$798$		0			0
$799$	3.70968	−	3.70968i	0.131239	−	0.131239i
$800$		0			0
$801$	6.56531	−	15.8501i	0.231974	−	0.560034i
$802$		0			0
$803$	14.5672	−	6.03393i	0.514065	−	0.212933i
$804$		0			0
$805$	9.18291	+	1.70051i	0.323655	+	0.0599350i
$806$		0			0
$807$	3.13289	+	1.29769i	0.110283	+	0.0456807i
$808$		0			0
$809$	16.4043	+	39.6035i	0.576745	+	1.39238i	0.895719	+	0.444621i	$0.146662\pi$
$809$	16.4043	+	39.6035i	0.576745	+	1.39238i	−0.318974	+	0.947763i	$0.603338\pi$
$810$		0			0
$811$	−29.7033	−	29.7033i	−1.04302	−	1.04302i	−0.999032	−	0.0439921i	$-0.985992\pi$
$811$	−29.7033	−	29.7033i	−1.04302	−	1.04302i	−0.0439921	−	0.999032i	$-0.514008\pi$
$812$		0			0
$813$	9.00377	−	21.7370i	0.315776	−	0.762351i
$814$		0			0
$815$	1.57196	+	7.38996i	0.0550634	+	0.258859i
$816$		0			0
$817$	−3.02908	−	1.25469i	−0.105974	−	0.0438959i
$818$		0			0
$819$	67.5534			2.36051
$820$		0			0
$821$	−12.2996			−0.429257			−0.214629	−	0.976696i	$-0.568854\pi$
$821$	−12.2996			−0.429257			−0.214629	+	0.976696i	$0.568854\pi$
$822$		0			0
$823$	2.80571	+	1.16216i	0.0978009	+	0.0405105i	0.431047	−	0.902329i	$-0.358144\pi$
$823$	2.80571	+	1.16216i	0.0978009	+	0.0405105i	−0.333247	+	0.942840i	$0.608144\pi$
$824$		0			0
$825$	12.9489	−	5.76994i	0.450822	−	0.200884i
$826$		0			0
$827$	−10.5196	+	25.3965i	−0.365801	+	0.883123i	0.628627	+	0.777707i	$0.283617\pi$
$827$	−10.5196	+	25.3965i	−0.365801	+	0.883123i	−0.994428	+	0.105416i	$0.966383\pi$
$828$		0			0
$829$	−16.1616	−	16.1616i	−0.561316	−	0.561316i	0.368365	−	0.929681i	$-0.379918\pi$
$829$	−16.1616	−	16.1616i	−0.561316	−	0.561316i	−0.929681	+	0.368365i	$0.879918\pi$
$830$		0			0
$831$	23.8971	+	57.6927i	0.828982	+	2.00134i
$832$		0			0
$833$	2.90544	+	1.20347i	0.100668	+	0.0416979i
$834$		0			0
$835$	−9.96074	−	14.4882i	−0.344706	−	0.501387i
$836$		0			0
$837$	−5.04754	+	2.09076i	−0.174469	+	0.0722672i
$838$		0			0
$839$	−15.7888	+	38.1175i	−0.545089	+	1.31596i	0.376004	+	0.926618i	$0.377298\pi$
$839$	−15.7888	+	38.1175i	−0.545089	+	1.31596i	−0.921093	+	0.389343i	$0.872702\pi$
$840$		0			0
$841$	8.31284	−	8.31284i	0.286650	−	0.286650i
$842$		0			0
$843$	−39.3239	+	39.3239i	−1.35439	+	1.35439i
$844$		0			0
$845$	−37.8024	+	8.04116i	−1.30044	+	0.276624i
$846$		0			0
$847$	−11.8704	−	28.6576i	−0.407871	−	0.984687i
$848$		0			0
$849$	23.1270	+	55.8336i	0.793717	+	1.91620i
$850$		0			0
$851$		−	15.1338i		−	0.518779i
$852$		0			0
$853$			27.3739i			0.937265i	0.883393	+	0.468633i	$0.155253\pi$
$853$			27.3739i			0.937265i	−0.883393	+	0.468633i	$0.844747\pi$
$854$		0			0
$855$	8.00907	−	43.2498i	0.273904	−	1.47911i
$856$		0			0
$857$	−18.1051	+	18.1051i	−0.618458	+	0.618458i	−0.945136	−	0.326678i	$-0.894071\pi$
$857$	−18.1051	+	18.1051i	−0.618458	+	0.618458i	0.326678	+	0.945136i	$0.394071\pi$
$858$		0			0
$859$	26.1459	+	26.1459i	0.892085	+	0.892085i	0.994719	−	0.102634i	$-0.0327270\pi$
$859$	26.1459	+	26.1459i	0.892085	+	0.892085i	−0.102634	+	0.994719i	$0.532727\pi$
$860$		0			0
$861$	−52.5825	+	6.82123i	−1.79201	+	0.232467i
$862$		0			0
$863$		−	4.77830i		−	0.162655i	−0.996687	−	0.0813276i	$-0.974084\pi$
$863$		−	4.77830i		−	0.162655i	0.996687	−	0.0813276i	$-0.0259160\pi$
$864$		0			0
$865$	−25.2144	+	38.8397i	−0.857314	+	1.32059i
$866$		0			0
$867$	−38.4749	+	15.9368i	−1.30668	+	0.541243i
$868$		0			0
$869$	−2.48538	−	2.48538i	−0.0843107	−	0.0843107i
$870$		0			0
$871$	7.90707			0.267921
$872$		0			0
$873$	−12.1667	+	29.3731i	−0.411781	+	0.994127i
$874$		0			0
$875$	18.4132	−	30.0785i	0.622481	−	1.01684i
$876$		0			0
$877$	33.8137	−	33.8137i	1.14181	−	1.14181i	0.153686	−	0.988120i	$-0.450886\pi$
$877$	33.8137	−	33.8137i	1.14181	−	1.14181i	0.988120	−	0.153686i	$-0.0491145\pi$
$878$		0			0
$879$			74.4471i			2.51104i
$880$		0			0
$881$	41.3081	+	41.3081i	1.39171	+	1.39171i	0.821504	+	0.570202i	$0.193135\pi$
$881$	41.3081	+	41.3081i	1.39171	+	1.39171i	0.570202	+	0.821504i	$0.306865\pi$
$882$		0			0
$883$	−25.9846	+	10.7632i	−0.874451	+	0.362210i	−0.774342	−	0.632767i	$-0.781919\pi$
$883$	−25.9846	+	10.7632i	−0.874451	+	0.362210i	−0.100109	+	0.994976i	$0.531919\pi$
$884$		0			0
$885$	7.77272	+	11.3057i	0.261277	+	0.380037i
$886$		0			0
$887$	30.9513	−	12.8204i	1.03924	−	0.430469i	0.203203	−	0.979137i	$-0.434865\pi$
$887$	30.9513	−	12.8204i	1.03924	−	0.430469i	0.836040	+	0.548668i	$0.184865\pi$
$888$		0			0
$889$	−46.3732	+	19.2084i	−1.55531	+	0.644230i
$890$		0			0
$891$	5.51818	−	2.28570i	0.184866	−	0.0765740i
$892$		0			0
$893$		−	24.8763i		−	0.832453i
$894$		0			0
$895$	42.4073	−	29.1552i	1.41752	−	0.974551i
$896$		0			0
$897$	19.1280			0.638665
$898$		0			0
$899$	−8.95515	+	3.70934i	−0.298671	+	0.123714i
$900$		0			0
$901$		−	8.54968i		−	0.284831i
$902$		0			0
$903$	3.79805	+	3.79805i	0.126391	+	0.126391i
$904$		0			0
$905$	12.7133	−	8.74047i	0.422605	−	0.290543i
$906$		0			0
$907$		−	16.7397i		−	0.555833i	−0.960605	−	0.277917i	$-0.910356\pi$
$907$		−	16.7397i		−	0.555833i	0.960605	−	0.277917i	$-0.0896439\pi$
$908$		0			0
$909$	8.52817	+	20.5888i	0.282861	+	0.682888i
$910$		0			0
$911$	−15.2683	+	15.2683i	−0.505863	+	0.505863i	−0.913254	−	0.407391i	$-0.866439\pi$
$911$	−15.2683	+	15.2683i	−0.505863	+	0.505863i	0.407391	+	0.913254i	$0.366439\pi$
$912$		0			0
$913$	7.28051	−	17.5767i	0.240950	−	0.581704i
$914$		0			0
$915$	−6.92552	−	1.28248i	−0.228951	−	0.0423975i
$916$		0			0
$917$	−11.1026	−	26.8040i	−0.366639	−	0.885145i
$918$		0			0
$919$	−2.15310	+	5.19803i	−0.0710241	+	0.171467i	−0.955405	−	0.295299i	$-0.904581\pi$
$919$	−2.15310	+	5.19803i	−0.0710241	+	0.171467i	0.884381	+	0.466766i	$0.154581\pi$
$920$		0			0
$921$	18.6929	+	7.74286i	0.615952	+	0.255136i
$922$		0			0
$923$	−17.1293			−0.563818
$924$		0			0
$925$	−53.3601	−	20.4644i	−1.75447	−	0.672865i
$926$		0			0
$927$	12.4293	+	12.4293i	0.408233	+	0.408233i
$928$		0			0
$929$	17.7404	+	7.34831i	0.582043	+	0.241090i	0.654223	−	0.756301i	$-0.272996\pi$
$929$	17.7404	+	7.34831i	0.582043	+	0.241090i	−0.0721801	+	0.997392i	$0.522996\pi$
$930$		0			0
$931$	13.7767	−	5.70651i	0.451514	−	0.187023i
$932$		0			0
$933$	−6.64153	+	6.64153i	−0.217434	+	0.217434i
$934$		0			0
$935$	2.51806	−	0.535632i	0.0823495	−	0.0175170i
$936$		0			0
$937$	4.89501	+	11.8176i	0.159913	+	0.386064i	0.983445	−	0.181205i	$-0.0579999\pi$
$937$	4.89501	+	11.8176i	0.159913	+	0.386064i	−0.823532	+	0.567269i	$0.808000\pi$
$938$		0			0
$939$			45.5035i			1.48495i
$940$		0			0
$941$	20.5071	−	20.5071i	0.668513	−	0.668513i	−0.288859	−	0.957372i	$-0.593276\pi$
$941$	20.5071	−	20.5071i	0.668513	−	0.668513i	0.957372	+	0.288859i	$0.0932759\pi$
$942$		0			0
$943$	−8.40759	+	1.09067i	−0.273789	+	0.0355170i
$944$		0			0
$945$	−8.98939	+	13.8471i	−0.292425	+	0.450445i
$946$		0			0
$947$	−23.2262	−	23.2262i	−0.754749	−	0.754749i	0.220612	−	0.975362i	$-0.429194\pi$
$947$	−23.2262	−	23.2262i	−0.754749	−	0.754749i	−0.975362	+	0.220612i	$0.929194\pi$
$948$		0			0
$949$	30.7451	−	74.2251i	0.998027	−	2.40945i
$950$		0			0
$951$	−4.33458	+	4.33458i	−0.140558	+	0.140558i
$952$		0			0
$953$	−25.5333	−	25.5333i	−0.827104	−	0.827104i	0.160012	−	0.987115i	$-0.448847\pi$
$953$	−25.5333	−	25.5333i	−0.827104	−	0.827104i	−0.987115	+	0.160012i	$0.948847\pi$
$954$		0			0
$955$	27.3668	+	39.8059i	0.885568	+	1.28809i
$956$		0			0
$957$	−10.8774	+	4.50555i	−0.351615	+	0.145644i
$958$		0			0
$959$		−	39.0527i		−	1.26108i
$960$		0			0
$961$	25.5515			0.824241
$962$		0			0
$963$		−	13.8792i		−	0.447251i
$964$		0			0
$965$	38.4025	−	26.4019i	1.23622	−	0.849908i
$966$		0			0
$967$	0.519632	+	1.25450i	0.0167102	+	0.0403421i	0.932014	−	0.362421i	$-0.118050\pi$
$967$	0.519632	+	1.25450i	0.0167102	+	0.0403421i	−0.915304	+	0.402763i	$0.868050\pi$
$968$		0			0
$969$	5.41319	−	13.0686i	0.173897	−	0.419824i
$970$		0			0
$971$	−8.05782	−	19.4533i	−0.258588	−	0.624286i	0.740258	−	0.672323i	$-0.234703\pi$
$971$	−8.05782	−	19.4533i	−0.258588	−	0.624286i	−0.998846	+	0.0480370i	$0.984703\pi$
$972$		0			0
$973$	−52.4883	−	21.7414i	−1.68270	−	0.696996i
$974$		0			0
$975$	25.8655	−	67.4433i	0.828359	−	2.15991i
$976$		0			0
$977$	22.3075	+	9.24006i	0.713680	+	0.295616i	0.709826	−	0.704377i	$-0.248773\pi$
$977$	22.3075	+	9.24006i	0.713680	+	0.295616i	0.00385348	+	0.999993i	$0.498773\pi$
$978$		0			0
$979$	3.36671	−	3.36671i	0.107600	−	0.107600i
$980$		0			0
$981$	−15.7266	−	37.9674i	−0.502112	−	1.21221i
$982$		0			0
$983$	13.5591	−	13.5591i	0.432469	−	0.432469i	−0.456999	−	0.889467i	$-0.651076\pi$
$983$	13.5591	−	13.5591i	0.432469	−	0.432469i	0.889467	+	0.456999i	$0.151076\pi$
$984$		0			0
$985$	−8.43153	+	12.9877i	−0.268651	+	0.413824i
$986$		0			0
$987$	−15.5957	+	37.6513i	−0.496417	+	1.19846i
$988$		0			0
$989$	0.607281	+	0.607281i	0.0193104	+	0.0193104i
$990$		0			0
$991$	4.51213	−	1.86899i	0.143333	−	0.0593703i	−0.309864	−	0.950781i	$-0.600284\pi$
$991$	4.51213	−	1.86899i	0.143333	−	0.0593703i	0.453197	+	0.891411i	$0.350284\pi$
$992$		0			0
$993$	−0.826721			−0.0262352
$994$		0			0
$995$	5.18499	−	3.56471i	0.164375	−	0.113009i
$996$		0			0
$997$	−20.1295	+	48.5969i	−0.637507	+	1.53908i	0.192482	+	0.981300i	$0.438346\pi$
$997$	−20.1295	+	48.5969i	−0.637507	+	1.53908i	−0.829990	+	0.557779i	$0.811654\pi$
$998$		0			0
$999$	24.7163	+	10.2378i	0.781990	+	0.323911i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.x.a.273.19	✓	84
5.2	odd	4		820.2.y.a.437.19	yes	84
41.38	odd	8		820.2.y.a.653.19	yes	84
205.202	even	8	inner	820.2.x.a.817.19	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.273.19	✓	84	1.1	even	1	trivial
820.2.x.a.817.19	yes	84	205.202	even	8	inner
820.2.y.a.437.19	yes	84	5.2	odd	4
820.2.y.a.653.19	yes	84	41.38	odd	8

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.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.42535 + 1.00461i) q^{3} +(-1.21756 + 1.87551i) q^{5} +(1.20713 - 2.91427i) q^{7} +(2.75177 + 2.75177i) q^{9} +(0.413305 + 0.997808i) q^{11} +(5.08419 + 2.10594i) q^{13} +(-4.83719 + 3.32559i) q^{15} +(-0.984862 + 0.407943i) q^{17} +(-1.93434 + 4.66992i) q^{19} +(5.85543 - 5.85543i) q^{21} +(0.936242 - 0.936242i) q^{23} +(-2.03507 - 4.56711i) q^{25} +(0.895703 + 2.16242i) q^{27} +(1.58912 + 3.83648i) q^{29} +2.33421i q^{31} +2.83525i q^{33} +(3.99598 + 5.81229i) q^{35} +(8.08219 - 8.08219i) q^{37} +(10.2153 + 10.2153i) q^{39} +(-5.07254 - 3.90760i) q^{41} +0.648637i q^{43} +(-8.51143 + 1.81051i) q^{45} +(-4.54681 + 1.88335i) q^{47} +(-2.08604 - 2.08604i) q^{49} -2.79846 q^{51} +(-3.06923 + 7.40978i) q^{53} +(-2.37462 - 0.439737i) q^{55} +(-9.38293 + 9.38293i) q^{57} -2.33725i q^{59} +(0.848427 + 0.848427i) q^{61} +(11.3411 - 4.69765i) q^{63} +(-10.1400 + 6.97133i) q^{65} +(1.32747 - 0.549855i) q^{67} +(3.21128 - 1.33016i) q^{69} +(-2.87573 + 1.19117i) q^{71} -14.5992i q^{73} +(-0.347590 - 13.1213i) q^{75} +3.40679 q^{77} +(-3.00671 + 1.24542i) q^{79} -5.53030i q^{81} +(-12.4559 - 12.4559i) q^{83} +(0.434032 - 2.34382i) q^{85} +10.9013i q^{87} +(-1.68705 - 4.07290i) q^{89} +(12.2745 - 12.2745i) q^{91} +(-2.34498 + 5.66129i) q^{93} +(-6.40329 - 9.31381i) q^{95} +(3.12641 + 7.54783i) q^{97} +(-1.60842 + 3.88306i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) \) 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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