LMFDB - Embedded newform 220.2.t.a.69.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(9,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.9"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.t (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:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			69.5
Character	$\chi$	$=$	220.69
Dual form			220.2.t.a.169.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.89864 - 0.616907i) q^{3} +(0.978101 + 2.01080i) q^{5} +(0.430637 + 0.139922i) q^{7} +(0.797226 - 0.579219i) q^{9} +(1.01674 + 3.15693i) q^{11} +(-3.87097 - 5.32793i) q^{13} +(3.09754 + 3.21440i) q^{15} +(0.696785 - 0.959042i) q^{17} +(-0.575851 - 1.77229i) q^{19} +0.903946 q^{21} -5.37034i q^{23} +(-3.08664 + 3.93353i) q^{25} +(-2.36396 + 3.25371i) q^{27} +(2.35601 - 7.25106i) q^{29} +(-2.83026 + 2.05631i) q^{31} +(3.87797 + 5.36666i) q^{33} +(0.139850 + 1.00278i) q^{35} +(5.50419 + 1.78842i) q^{37} +(-10.6364 - 7.72781i) q^{39} +(0.103203 + 0.317626i) q^{41} +10.9423i q^{43} +(1.94446 + 1.03653i) q^{45} +(-6.09886 + 1.98164i) q^{47} +(-5.49725 - 3.99399i) q^{49} +(0.731307 - 2.25073i) q^{51} +(-1.34833 - 1.85581i) q^{53} +(-5.35349 + 5.13227i) q^{55} +(-2.18667 - 3.00970i) q^{57} +(-0.449071 + 1.38210i) q^{59} +(-7.22608 - 5.25006i) q^{61} +(0.424361 - 0.137883i) q^{63} +(6.92720 - 12.9950i) q^{65} -4.37584i q^{67} +(-3.31300 - 10.1964i) q^{69} +(8.91732 + 6.47881i) q^{71} +(-3.36324 - 1.09278i) q^{73} +(-3.43380 + 9.37255i) q^{75} +(-0.00387889 + 1.50176i) q^{77} +(-2.46562 + 1.79138i) q^{79} +(-3.39462 + 10.4476i) q^{81} +(-5.78120 + 7.95714i) q^{83} +(2.60997 + 0.463055i) q^{85} -15.2206i q^{87} +12.7892 q^{89} +(-0.921484 - 2.83604i) q^{91} +(-4.10511 + 5.65021i) q^{93} +(3.00047 - 2.89140i) q^{95} +(8.14443 + 11.2098i) q^{97} +(2.63913 + 1.92787i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{5} + 14 q^{9} - 2 q^{11} - q^{15} + 8 q^{19} - 28 q^{21} + 27 q^{25} - 16 q^{29} - 26 q^{31} + 17 q^{35} + 12 q^{39} + 10 q^{41} - 40 q^{45} - 46 q^{49} - 12 q^{51} - 33 q^{55} - 48 q^{59} - 10 q^{61}+ \cdots + 156 q^{99}+O(q^{100}) $ 24 * q + q^5 + 14 * q^9 - 2 * q^11 - q^15 + 8 * q^19 - 28 * q^21 + 27 * q^25 - 16 * q^29 - 26 * q^31 + 17 * q^35 + 12 * q^39 + 10 * q^41 - 40 * q^45 - 46 * q^49 - 12 * q^51 - 33 * q^55 - 48 * q^59 - 10 * q^61 - 22 * q^65 - 58 * q^69 + 42 * q^71 - 17 * q^75 - 64 * q^79 + 36 * q^81 - 17 * q^85 + 72 * q^89 + 10 * q^91 + 67 * q^95 + 156 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.89864	−	0.616907i	1.09618	−	0.356171i	0.295550	−	0.955327i	$-0.404497\pi$
$3$	1.89864	−	0.616907i	1.09618	−	0.356171i	0.800633	+	0.599156i	$0.204497\pi$
$4$		0			0
$5$	0.978101	+	2.01080i	0.437420	+	0.899257i
$5$	0.978101	+	2.01080i	0.437420	+	0.899257i
$6$		0			0
$7$	0.430637	+	0.139922i	0.162765	+	0.0528857i	0.389266	−	0.921125i	$-0.372729\pi$
$7$	0.430637	+	0.139922i	0.162765	+	0.0528857i	−0.226501	+	0.974011i	$0.572729\pi$
$8$		0			0
$9$	0.797226	−	0.579219i	0.265742	−	0.193073i
$10$		0			0
$11$	1.01674	+	3.15693i	0.306559	+	0.951852i
$11$	1.01674	+	3.15693i	0.306559	+	0.951852i
$12$		0			0
$13$	−3.87097	−	5.32793i	−1.07361	−	1.47770i	−0.866364	−	0.499413i	$-0.833549\pi$
$13$	−3.87097	−	5.32793i	−1.07361	−	1.47770i	−0.207248	−	0.978288i	$-0.566451\pi$
$14$		0			0
$15$	3.09754	+	3.21440i	0.799782	+	0.829954i
$16$		0			0
$17$	0.696785	−	0.959042i	0.168995	−	0.232602i	−0.716116	−	0.697981i	$-0.754082\pi$
$17$	0.696785	−	0.959042i	0.168995	−	0.232602i	0.885111	+	0.465379i	$0.154082\pi$
$18$		0			0
$19$	−0.575851	−	1.77229i	−0.132109	−	0.406590i	0.863020	−	0.505170i	$-0.168570\pi$
$19$	−0.575851	−	1.77229i	−0.132109	−	0.406590i	−0.995129	+	0.0985795i	$0.968570\pi$
$20$		0			0
$21$	0.903946			0.197257
$22$		0			0
$23$		−	5.37034i		−	1.11979i	−0.828562	−	0.559897i	$-0.810841\pi$
$23$		−	5.37034i		−	1.11979i	0.828562	−	0.559897i	$-0.189159\pi$
$24$		0			0
$25$	−3.08664	+	3.93353i	−0.617327	+	0.786706i
$26$		0			0
$27$	−2.36396	+	3.25371i	−0.454943	+	0.626176i
$28$		0			0
$29$	2.35601	−	7.25106i	0.437501	−	1.34649i	−0.453001	−	0.891510i	$-0.649647\pi$
$29$	2.35601	−	7.25106i	0.437501	−	1.34649i	0.890502	−	0.454979i	$-0.150353\pi$
$30$		0			0
$31$	−2.83026	+	2.05631i	−0.508330	+	0.369324i	−0.812190	−	0.583393i	$-0.801725\pi$
$31$	−2.83026	+	2.05631i	−0.508330	+	0.369324i	0.303859	+	0.952717i	$0.401725\pi$
$32$		0			0
$33$	3.87797	+	5.36666i	0.675068	+	0.934216i
$34$		0			0
$35$	0.139850	+	1.00278i	0.0236390	+	0.169501i
$36$		0			0
$37$	5.50419	+	1.78842i	0.904883	+	0.294014i	0.724251	−	0.689536i	$-0.242186\pi$
$37$	5.50419	+	1.78842i	0.904883	+	0.294014i	0.180632	+	0.983551i	$0.442186\pi$
$38$		0			0
$39$	−10.6364	−	7.72781i	−1.70319	−	1.23744i
$40$		0			0
$41$	0.103203	+	0.317626i	0.0161176	+	0.0496048i	0.958792	−	0.284110i	$-0.0916979\pi$
$41$	0.103203	+	0.317626i	0.0161176	+	0.0496048i	−0.942674	+	0.333714i	$0.891698\pi$
$42$		0			0
$43$			10.9423i			1.66868i	0.551247	+	0.834342i	$0.314152\pi$
$43$			10.9423i			1.66868i	−0.551247	+	0.834342i	$0.685848\pi$
$44$		0			0
$45$	1.94446	+	1.03653i	0.289863	+	0.154517i
$46$		0			0
$47$	−6.09886	+	1.98164i	−0.889611	+	0.289052i	−0.717942	−	0.696103i	$-0.754916\pi$
$47$	−6.09886	+	1.98164i	−0.889611	+	0.289052i	−0.171669	+	0.985155i	$0.554916\pi$
$48$		0			0
$49$	−5.49725	−	3.99399i	−0.785321	−	0.570569i
$50$		0			0
$51$	0.731307	−	2.25073i	0.102404	−	0.315166i
$52$		0			0
$53$	−1.34833	−	1.85581i	−0.185207	−	0.254915i	0.706310	−	0.707902i	$-0.250358\pi$
$53$	−1.34833	−	1.85581i	−0.185207	−	0.254915i	−0.891517	+	0.452987i	$0.850358\pi$
$54$		0			0
$55$	−5.35349	+	5.13227i	−0.721864	+	0.692035i
$56$		0			0
$57$	−2.18667	−	3.00970i	−0.289632	−	0.398644i
$58$		0			0
$59$	−0.449071	+	1.38210i	−0.0584641	+	0.179934i	−0.976024	−	0.217664i	$-0.930156\pi$
$59$	−0.449071	+	1.38210i	−0.0584641	+	0.179934i	0.917560	+	0.397598i	$0.130156\pi$
$60$		0			0
$61$	−7.22608	−	5.25006i	−0.925205	−	0.672201i	0.0196090	−	0.999808i	$-0.493758\pi$
$61$	−7.22608	−	5.25006i	−0.925205	−	0.672201i	−0.944814	+	0.327607i	$0.893758\pi$
$62$		0			0
$63$	0.424361	−	0.137883i	0.0534644	−	0.0173716i
$64$		0			0
$65$	6.92720	−	12.9950i	0.859214	−	1.61183i
$66$		0			0
$67$		−	4.37584i		−	0.534593i	−0.963614	−	0.267297i	$-0.913870\pi$
$67$		−	4.37584i		−	0.534593i	0.963614	−	0.267297i	$-0.0861304\pi$
$68$		0			0
$69$	−3.31300	−	10.1964i	−0.398839	−	1.22750i
$70$		0			0
$71$	8.91732	+	6.47881i	1.05829	+	0.768894i	0.973772	−	0.227528i	$-0.0730643\pi$
$71$	8.91732	+	6.47881i	1.05829	+	0.768894i	0.0845200	+	0.996422i	$0.473064\pi$
$72$		0			0
$73$	−3.36324	−	1.09278i	−0.393638	−	0.127901i	0.105508	−	0.994418i	$-0.466353\pi$
$73$	−3.36324	−	1.09278i	−0.393638	−	0.127901i	−0.499146	+	0.866518i	$0.666353\pi$
$74$		0			0
$75$	−3.43380	+	9.37255i	−0.396501	+	1.08225i
$76$		0			0
$77$	−0.00387889	+	1.50176i	−0.000442040	+	0.171141i
$78$		0			0
$79$	−2.46562	+	1.79138i	−0.277404	+	0.201546i	−0.717784	−	0.696265i	$-0.754844\pi$
$79$	−2.46562	+	1.79138i	−0.277404	+	0.201546i	0.440380	+	0.897811i	$0.354844\pi$
$80$		0			0
$81$	−3.39462	+	10.4476i	−0.377180	+	1.16084i
$82$		0			0
$83$	−5.78120	+	7.95714i	−0.634569	+	0.873409i	−0.998311	−	0.0580905i	$-0.981499\pi$
$83$	−5.78120	+	7.95714i	−0.634569	+	0.873409i	0.363743	+	0.931500i	$0.381499\pi$
$84$		0			0
$85$	2.60997	+	0.463055i	0.283091	+	0.0502254i
$86$		0			0
$87$		−	15.2206i		−	1.63182i
$88$		0			0
$89$	12.7892			1.35566			0.677828	−	0.735220i	$-0.262921\pi$
$89$	12.7892			1.35566			0.677828	+	0.735220i	$0.262921\pi$
$90$		0			0
$91$	−0.921484	−	2.83604i	−0.0965978	−	0.297297i
$92$		0			0
$93$	−4.10511	+	5.65021i	−0.425681	+	0.585899i
$94$		0			0
$95$	3.00047	−	2.89140i	0.307842	−	0.296651i
$96$		0			0
$97$	8.14443	+	11.2098i	0.826941	+	1.13819i	0.988485	+	0.151321i	$0.0483528\pi$
$97$	8.14443	+	11.2098i	0.826941	+	1.13819i	−0.161543	+	0.986866i	$0.551647\pi$
$98$		0			0
$99$	2.63913	+	1.92787i	0.265243	+	0.193759i
$100$		0			0
$101$	4.50885	−	3.27587i	0.448647	−	0.325961i	−0.340414	−	0.940276i	$-0.610567\pi$
$101$	4.50885	−	3.27587i	0.448647	−	0.325961i	0.789061	+	0.614314i	$0.210567\pi$
$102$		0			0
$103$	10.6047	+	3.44568i	1.04491	+	0.339513i	0.780671	−	0.624943i	$-0.214878\pi$
$103$	10.6047	+	3.44568i	1.04491	+	0.339513i	0.264244	+	0.964456i	$0.414878\pi$
$104$		0			0
$105$	0.884150	+	1.81765i	0.0862842	+	0.177385i
$106$		0			0
$107$	6.86236	−	2.22972i	0.663409	−	0.215555i	0.0420918	−	0.999114i	$-0.486598\pi$
$107$	6.86236	−	2.22972i	0.663409	−	0.215555i	0.621317	+	0.783559i	$0.286598\pi$
$108$		0			0
$109$	5.14652			0.492947			0.246473	−	0.969150i	$-0.420728\pi$
$109$	5.14652			0.492947			0.246473	+	0.969150i	$0.420728\pi$
$110$		0			0
$111$	11.5538			1.09664
$112$		0			0
$113$	9.56572	−	3.10809i	0.899868	−	0.292385i	0.177685	−	0.984087i	$-0.443139\pi$
$113$	9.56572	−	3.10809i	0.899868	−	0.292385i	0.722182	+	0.691703i	$0.243139\pi$
$114$		0			0
$115$	10.7987	−	5.25274i	1.00698	−	0.489820i
$116$		0			0
$117$	−6.17207	−	2.00543i	−0.570608	−	0.185402i
$118$		0			0
$119$	0.434253	−	0.315503i	0.0398079	−	0.0289221i
$120$		0			0
$121$	−8.93247	+	6.41958i	−0.812043	+	0.583598i
$122$		0			0
$123$	0.391891	+	0.539392i	0.0353356	+	0.0486353i
$124$		0			0
$125$	−10.9286	−	2.35922i	−0.977483	−	0.211015i
$126$		0			0
$127$	−7.82306	+	10.7675i	−0.694184	+	0.955463i	0.305810	+	0.952093i	$0.401073\pi$
$127$	−7.82306	+	10.7675i	−0.694184	+	0.955463i	−0.999994	+	0.00337009i	$0.998927\pi$
$128$		0			0
$129$	6.75038	+	20.7755i	0.594338	+	1.82918i
$130$		0			0
$131$	16.8980			1.47639			0.738194	−	0.674588i	$-0.235679\pi$
$131$	16.8980			1.47639			0.738194	+	0.674588i	$0.235679\pi$
$132$		0			0
$133$		−	0.843786i		−	0.0731655i
$134$		0			0
$135$	−8.85474	−	1.57099i	−0.762095	−	0.135209i
$136$		0			0
$137$	11.0840	−	15.2558i	0.946971	−	1.30339i	−0.00588916	−	0.999983i	$-0.501875\pi$
$137$	11.0840	−	15.2558i	0.946971	−	1.30339i	0.952860	−	0.303411i	$-0.0981254\pi$
$138$		0			0
$139$	1.86346	−	5.73515i	0.158057	−	0.486449i	−0.840401	−	0.541965i	$-0.817680\pi$
$139$	1.86346	−	5.73515i	0.158057	−	0.486449i	0.998458	+	0.0555163i	$0.0176805\pi$
$140$		0			0
$141$	−10.3571	+	7.52487i	−0.872224	+	0.633708i
$142$		0			0
$143$	12.8841	−	17.6375i	1.07743	−	1.47492i
$144$		0			0
$145$	16.8849	−	2.35480i	1.40221	−	0.195556i
$146$		0			0
$147$	−12.9012	−	4.19187i	−1.06408	−	0.345739i
$148$		0			0
$149$	−9.26073	−	6.72832i	−0.758669	−	0.551205i	0.139833	−	0.990175i	$-0.455343\pi$
$149$	−9.26073	−	6.72832i	−0.758669	−	0.551205i	−0.898502	+	0.438970i	$0.855343\pi$
$150$		0			0
$151$	−2.91684	−	8.97712i	−0.237369	−	0.730547i	−0.996798	−	0.0799572i	$-0.974522\pi$
$151$	−2.91684	−	8.97712i	−0.237369	−	0.730547i	0.759429	−	0.650590i	$-0.225478\pi$
$152$		0			0
$153$		−	1.16816i		−	0.0944405i
$154$		0			0
$155$	−6.90311	−	3.67982i	−0.554471	−	0.295570i
$156$		0			0
$157$	−4.91461	+	1.59685i	−0.392229	+	0.127443i	−0.498490	−	0.866895i	$-0.666112\pi$
$157$	−4.91461	+	1.59685i	−0.392229	+	0.127443i	0.106261	+	0.994338i	$0.466112\pi$
$158$		0			0
$159$	−3.70486	−	2.69174i	−0.293814	−	0.213469i
$160$		0			0
$161$	0.751431	−	2.31267i	0.0592211	−	0.182264i
$162$		0			0
$163$	−9.80223	−	13.4916i	−0.767770	−	1.05674i	−0.996528	−	0.0832613i	$-0.973466\pi$
$163$	−9.80223	−	13.4916i	−0.767770	−	1.05674i	0.228758	−	0.973483i	$-0.426534\pi$
$164$		0			0
$165$	−6.99824	+	13.0470i	−0.544812	+	1.01570i
$166$		0			0
$167$	12.3304	+	16.9713i	0.954153	+	1.31328i	0.949658	+	0.313289i	$0.101431\pi$
$167$	12.3304	+	16.9713i	0.954153	+	1.31328i	0.00449557	+	0.999990i	$0.498569\pi$
$168$		0			0
$169$	−9.38521	+	28.8847i	−0.721939	+	2.22190i
$170$		0			0
$171$	−1.48562	−	1.07937i	−0.113609	−	0.0825415i
$172$		0			0
$173$	−23.6794	+	7.69389i	−1.80031	+	0.584956i	−0.999895	−	0.0144929i	$-0.995387\pi$
$173$	−23.6794	+	7.69389i	−1.80031	+	0.584956i	−0.800413	+	0.599449i	$0.795387\pi$
$174$		0			0
$175$	−1.87961	+	1.26203i	−0.142085	+	0.0954008i
$176$		0			0
$177$			2.90115i			0.218064i
$178$		0			0
$179$	1.71334	+	5.27311i	0.128061	+	0.394131i	0.994446	−	0.105245i	$-0.0335627\pi$
$179$	1.71334	+	5.27311i	0.128061	+	0.394131i	−0.866385	+	0.499376i	$0.833563\pi$
$180$		0			0
$181$	−16.5782	−	12.0448i	−1.23225	−	0.895283i	−0.235194	−	0.971948i	$-0.575573\pi$
$181$	−16.5782	−	12.0448i	−1.23225	−	0.895283i	−0.997057	+	0.0766655i	$0.975573\pi$
$182$		0			0
$183$	−16.9586	−	5.51017i	−1.25361	−	0.407323i
$184$		0			0
$185$	1.78750	+	12.8171i	0.131420	+	0.942330i
$186$		0			0
$187$	3.73609	+	1.22461i	0.273210	+	0.0895520i
$188$		0			0
$189$	−1.47327	+	1.07040i	−0.107165	+	0.0778598i
$190$		0			0
$191$	2.63516	−	8.11018i	0.190673	−	0.586832i	−0.809327	−	0.587359i	$-0.800168\pi$
$191$	2.63516	−	8.11018i	0.190673	−	0.586832i	1.00000		0.000526942i	$0.000167731\pi$
$192$		0			0
$193$	4.16169	−	5.72807i	0.299565	−	0.412316i	−0.632527	−	0.774539i	$-0.717982\pi$
$193$	4.16169	−	5.72807i	0.299565	−	0.412316i	0.932091	+	0.362223i	$0.117982\pi$
$194$		0			0
$195$	5.13559	−	28.9463i	0.367768	−	2.07289i
$196$		0			0
$197$			12.5739i			0.895856i	0.894070	+	0.447928i	$0.147838\pi$
$197$			12.5739i			0.895856i	−0.894070	+	0.447928i	$0.852162\pi$
$198$		0			0
$199$	11.9790			0.849171			0.424585	−	0.905388i	$-0.360420\pi$
$199$	11.9790			0.849171			0.424585	+	0.905388i	$0.360420\pi$
$200$		0			0
$201$	−2.69948	−	8.30816i	−0.190407	−	0.586012i
$202$		0			0
$203$	2.02917	−	2.79292i	0.142420	−	0.196024i
$204$		0			0
$205$	−0.537739	+	0.518190i	−0.0375573	+	0.0361920i
$206$		0			0
$207$	−3.11060	−	4.28138i	−0.216202	−	0.297576i
$208$		0			0
$209$	5.00950	−	3.61988i	0.346514	−	0.250392i
$210$		0			0
$211$	7.65767	−	5.56363i	0.527176	−	0.383016i	−0.292124	−	0.956380i	$-0.594362\pi$
$211$	7.65767	−	5.56363i	0.527176	−	0.383016i	0.819300	+	0.573365i	$0.194362\pi$
$212$		0			0
$213$	20.9277	+	6.79981i	1.43394	+	0.465915i
$214$		0			0
$215$	−22.0028	+	10.7027i	−1.50058	+	0.729916i
$216$		0			0
$217$	−1.50654	+	0.489504i	−0.102271	+	0.0332297i
$218$		0			0
$219$	−7.05975			−0.477054
$220$		0			0
$221$	−7.80694			−0.525152
$222$		0			0
$223$	5.57166	−	1.81034i	0.373106	−	0.121229i	−0.116461	−	0.993195i	$-0.537155\pi$
$223$	5.57166	−	1.81034i	0.373106	−	0.121229i	0.489567	+	0.871966i	$0.337155\pi$
$224$		0			0
$225$	−0.182372	+	4.92375i	−0.0121581	+	0.328250i
$226$		0			0
$227$	−4.07522	−	1.32412i	−0.270482	−	0.0878848i	0.170636	−	0.985334i	$-0.445418\pi$
$227$	−4.07522	−	1.32412i	−0.270482	−	0.0878848i	−0.441118	+	0.897449i	$0.645418\pi$
$228$		0			0
$229$	15.3127	−	11.1254i	1.01189	−	0.735184i	0.0472890	−	0.998881i	$-0.484942\pi$
$229$	15.3127	−	11.1254i	1.01189	−	0.735184i	0.964606	+	0.263697i	$0.0849418\pi$
$230$		0			0
$231$	0.919080	+	2.85370i	0.0604710	+	0.187759i
$232$		0			0
$233$	−3.41237	−	4.69672i	−0.223552	−	0.307692i	0.682478	−	0.730906i	$-0.260902\pi$
$233$	−3.41237	−	4.69672i	−0.223552	−	0.307692i	−0.906030	+	0.423213i	$0.860902\pi$
$234$		0			0
$235$	−9.94999	−	10.3254i	−0.649066	−	0.673552i
$236$		0			0
$237$	−3.57623	+	4.92225i	−0.232301	+	0.319735i
$238$		0			0
$239$	8.71209	+	26.8131i	0.563538	+	1.73439i	0.672255	+	0.740320i	$0.265326\pi$
$239$	8.71209	+	26.8131i	0.563538	+	1.73439i	−0.108717	+	0.994073i	$0.534674\pi$
$240$		0			0
$241$	−25.1660			−1.62109			−0.810544	−	0.585678i	$-0.800828\pi$
$241$	−25.1660			−1.62109			−0.810544	+	0.585678i	$0.800828\pi$
$242$		0			0
$243$			9.86496i			0.632838i
$244$		0			0
$245$	2.65424	−	14.9604i	0.169573	−	0.955784i
$246$		0			0
$247$	−7.21351	+	9.92855i	−0.458985	+	0.631738i
$248$		0			0
$249$	−6.06763	+	18.6742i	−0.384520	+	1.18343i
$250$		0			0
$251$	−2.05932	+	1.49618i	−0.129983	+	0.0944381i	−0.650877	−	0.759183i	$-0.725599\pi$
$251$	−2.05932	+	1.49618i	−0.129983	+	0.0944381i	0.520894	+	0.853621i	$0.325599\pi$
$252$		0			0
$253$	16.9538	−	5.46026i	1.06588	−	0.343283i
$254$		0			0
$255$	5.24107	−	0.730931i	0.328208	−	0.0457727i
$256$		0			0
$257$	−2.70766	−	0.879772i	−0.168899	−	0.0548786i	0.223347	−	0.974739i	$-0.428302\pi$
$257$	−2.70766	−	0.879772i	−0.168899	−	0.0548786i	−0.392246	+	0.919860i	$0.628302\pi$
$258$		0			0
$259$	2.12007	+	1.54032i	0.131735	+	0.0957107i
$260$		0			0
$261$	−2.32168	−	7.14539i	−0.143708	−	0.442288i
$262$		0			0
$263$			12.6105i			0.777594i	0.921323	+	0.388797i	$0.127109\pi$
$263$			12.6105i			0.777594i	−0.921323	+	0.388797i	$0.872891\pi$
$264$		0			0
$265$	2.41287	−	4.52639i	0.148221	−	0.278054i
$266$		0			0
$267$	24.2822	−	7.88977i	1.48605	−	0.482846i
$268$		0			0
$269$	−11.1045	−	8.06788i	−0.677053	−	0.491907i	0.195326	−	0.980738i	$-0.437424\pi$
$269$	−11.1045	−	8.06788i	−0.677053	−	0.491907i	−0.872379	+	0.488831i	$0.837424\pi$
$270$		0			0
$271$	5.81483	−	17.8962i	0.353226	−	1.08712i	−0.603805	−	0.797132i	$-0.706350\pi$
$271$	5.81483	−	17.8962i	0.353226	−	1.08712i	0.957031	−	0.289985i	$-0.0936504\pi$
$272$		0			0
$273$	−3.49914	−	4.81616i	−0.211778	−	0.291487i
$274$		0			0
$275$	−15.5562	−	5.74492i	−0.938075	−	0.346432i
$276$		0			0
$277$	−13.1019	−	18.0332i	−0.787216	−	1.08351i	−0.994449	−	0.105218i	$-0.966446\pi$
$277$	−13.1019	−	18.0332i	−0.787216	−	1.08351i	0.207234	−	0.978291i	$-0.433554\pi$
$278$		0			0
$279$	−1.06531	+	3.27868i	−0.0637784	+	0.196290i
$280$		0			0
$281$	13.6094	+	9.88778i	0.811867	+	0.589856i	0.914371	−	0.404877i	$-0.132686\pi$
$281$	13.6094	+	9.88778i	0.811867	+	0.589856i	−0.102505	+	0.994733i	$0.532686\pi$
$282$		0			0
$283$	−21.4963	+	6.98457i	−1.27782	+	0.415189i	−0.867812	−	0.496892i	$-0.834474\pi$
$283$	−21.4963	+	6.98457i	−1.27782	+	0.415189i	−0.410009	+	0.912081i	$0.634474\pi$
$284$		0			0
$285$	3.91311	−	7.34075i	0.231793	−	0.434828i
$286$		0			0
$287$			0.151222i			0.00892633i
$288$		0			0
$289$	4.81904	+	14.8315i	0.283473	+	0.872439i
$290$		0			0
$291$	22.3788	+	16.2592i	1.31187	+	0.953128i
$292$		0			0
$293$	3.27699	+	1.06476i	0.191444	+	0.0622039i	0.403170	−	0.915125i	$-0.367908\pi$
$293$	3.27699	+	1.06476i	0.191444	+	0.0622039i	−0.211726	+	0.977329i	$0.567908\pi$
$294$		0			0
$295$	−3.21836	+	0.448840i	−0.187380	+	0.0261325i
$296$		0			0
$297$	−12.6753	−	4.15467i	−0.735494	−	0.241078i
$298$		0			0
$299$	−28.6128	+	20.7884i	−1.65472	+	1.20222i
$300$		0			0
$301$	−1.53107	+	4.71216i	−0.0882496	+	0.271604i
$302$		0			0
$303$	6.53979	−	9.00125i	0.375701	−	0.517109i
$304$		0			0
$305$	3.48898	−	19.6653i	0.199778	−	1.12603i
$306$		0			0
$307$		−	9.58110i		−	0.546822i	−0.961897	−	0.273411i	$-0.911848\pi$
$307$		−	9.58110i		−	0.546822i	0.961897	−	0.273411i	$-0.0881520\pi$
$308$		0			0
$309$	22.2603			1.26634
$310$		0			0
$311$	3.38071	+	10.4048i	0.191703	+	0.590000i	0.999999	+	0.00122469i	$0.000389831\pi$
$311$	3.38071	+	10.4048i	0.191703	+	0.590000i	−0.808297	+	0.588776i	$0.799610\pi$
$312$		0			0
$313$	−7.28776	+	10.0307i	−0.411928	+	0.566971i	−0.963687	−	0.267033i	$-0.913957\pi$
$313$	−7.28776	+	10.0307i	−0.411928	+	0.566971i	0.551759	+	0.834004i	$0.313957\pi$
$314$		0			0
$315$	0.692323	+	0.718441i	0.0390080	+	0.0404796i
$316$		0			0
$317$	−1.68638	−	2.32110i	−0.0947165	−	0.130366i	0.759029	−	0.651057i	$-0.225674\pi$
$317$	−1.68638	−	2.32110i	−0.0947165	−	0.130366i	−0.853745	+	0.520691i	$0.825674\pi$
$318$		0			0
$319$	25.2866	+	0.0653127i	1.41578	+	0.00365681i
$320$		0			0
$321$	11.6537	−	8.46687i	0.650443	−	0.472575i
$322$		0			0
$323$	−2.10094	−	0.682637i	−0.116900	−	0.0379830i
$324$		0			0
$325$	32.9058	+	1.21881i	1.82529	+	0.0676072i
$326$		0			0
$327$	9.77141	−	3.17492i	0.540360	−	0.175574i
$328$		0			0
$329$	−2.90367			−0.160085
$330$		0			0
$331$	−27.2623			−1.49847			−0.749237	−	0.662302i	$-0.769579\pi$
$331$	−27.2623			−1.49847			−0.749237	+	0.662302i	$0.769579\pi$
$332$		0			0
$333$	5.42397	−	1.76235i	0.297232	−	0.0965764i
$334$		0			0
$335$	8.79893	−	4.28001i	0.480737	−	0.233842i
$336$		0			0
$337$	29.5273	+	9.59399i	1.60845	+	0.522618i	0.969178	−	0.246361i	$-0.0792348\pi$
$337$	29.5273	+	9.59399i	1.60845	+	0.522618i	0.639274	+	0.768979i	$0.279235\pi$
$338$		0			0
$339$	16.2445	−	11.8023i	0.882280	−	0.641014i
$340$		0			0
$341$	−9.36928	−	6.84422i	−0.507375	−	0.370635i
$342$		0			0
$343$	−3.67151	−	5.05340i	−0.198243	−	0.272858i
$344$		0			0
$345$	17.2624	−	16.6349i	0.929377	−	0.895591i
$346$		0			0
$347$	13.8594	−	19.0758i	0.744012	−	1.02404i	−0.254366	−	0.967108i	$-0.581867\pi$
$347$	13.8594	−	19.0758i	0.744012	−	1.02404i	0.998378	−	0.0569361i	$-0.0181331\pi$
$348$		0			0
$349$	7.42097	+	22.8394i	0.397236	+	1.22257i	0.927207	+	0.374550i	$0.122203\pi$
$349$	7.42097	+	22.8394i	0.397236	+	1.22257i	−0.529971	+	0.848016i	$0.677797\pi$
$350$		0			0
$351$	26.4863			1.41373
$352$		0			0
$353$			4.85808i			0.258570i	0.991608	+	0.129285i	$0.0412681\pi$
$353$			4.85808i			0.258570i	−0.991608	+	0.129285i	$0.958732\pi$
$354$		0			0
$355$	−4.30556	+	24.2679i	−0.228515	+	1.28801i
$356$		0			0
$357$	0.629856	−	0.866922i	0.0333355	−	0.0458824i
$358$		0			0
$359$	1.24032	−	3.81733i	0.0654618	−	0.201471i	−0.912976	−	0.408014i	$-0.866221\pi$
$359$	1.24032	−	3.81733i	0.0654618	−	0.201471i	0.978437	+	0.206543i	$0.0662214\pi$
$360$		0			0
$361$	12.5619	−	9.12678i	0.661154	−	0.480357i
$362$		0			0
$363$	−12.9993	+	17.6990i	−0.682286	+	0.928957i
$364$		0			0
$365$	−1.09222	−	7.83167i	−0.0571695	−	0.409928i
$366$		0			0
$367$	12.8542	+	4.17659i	0.670985	+	0.218016i	0.624644	−	0.780910i	$-0.285244\pi$
$367$	12.8542	+	4.17659i	0.670985	+	0.218016i	0.0463406	+	0.998926i	$0.485244\pi$
$368$		0			0
$369$	0.266251	+	0.193442i	0.0138605	+	0.0100702i
$370$		0			0
$371$	−0.320969	−	0.987842i	−0.0166639	−	0.0512862i
$372$		0			0
$373$			25.5794i			1.32445i	0.749305	+	0.662225i	$0.230388\pi$
$373$			25.5794i			1.32445i	−0.749305	+	0.662225i	$0.769612\pi$
$374$		0			0
$375$	−22.2049	+	2.26261i	−1.14666	+	0.116841i
$376$		0			0
$377$	−47.7532	+	15.5160i	−2.45941	+	0.799112i
$378$		0			0
$379$	−5.21257	−	3.78715i	−0.267752	−	0.194533i	0.445806	−	0.895130i	$-0.352917\pi$
$379$	−5.21257	−	3.78715i	−0.267752	−	0.194533i	−0.713557	+	0.700597i	$0.752917\pi$
$380$		0			0
$381$	−8.21065	+	25.2698i	−0.420644	+	1.29461i
$382$		0			0
$383$	7.96880	+	10.9681i	0.407187	+	0.560444i	0.962529	−	0.271177i	$-0.0874129\pi$
$383$	7.96880	+	10.9681i	0.407187	+	0.560444i	−0.555343	+	0.831622i	$0.687413\pi$
$384$		0			0
$385$	−3.02353	+	1.46107i	−0.154093	+	0.0744631i
$386$		0			0
$387$	6.33798	+	8.72349i	0.322178	+	0.443440i
$388$		0			0
$389$	4.16176	−	12.8086i	0.211010	−	0.649421i	−0.788403	−	0.615159i	$-0.789092\pi$
$389$	4.16176	−	12.8086i	0.211010	−	0.649421i	0.999413	−	0.0342621i	$-0.0109081\pi$
$390$		0			0
$391$	−5.15039	−	3.74197i	−0.260466	−	0.189240i
$392$		0			0
$393$	32.0834	−	10.4245i	1.61839	−	0.525847i
$394$		0			0
$395$	−6.01373	−	3.20572i	−0.302584	−	0.161297i
$396$		0			0
$397$		−	19.3608i		−	0.971689i	−0.874045	−	0.485844i	$-0.838512\pi$
$397$		−	19.3608i		−	0.971689i	0.874045	−	0.485844i	$-0.161488\pi$
$398$		0			0
$399$	−0.520538	−	1.60205i	−0.0260595	−	0.0802028i
$400$		0			0
$401$	2.19624	+	1.59567i	0.109675	+	0.0796837i	0.641271	−	0.767314i	$-0.278407\pi$
$401$	2.19624	+	1.59567i	0.109675	+	0.0796837i	−0.531596	+	0.846998i	$0.678407\pi$
$402$		0			0
$403$	21.9117	+	7.11954i	1.09150	+	0.354650i
$404$		0			0
$405$	−24.3282	+	3.39287i	−1.20888	+	0.168593i
$406$		0			0
$407$	−0.0495780	+	19.1947i	−0.00245749	+	0.951447i
$408$		0			0
$409$	−1.95665	+	1.42159i	−0.0967500	+	0.0702930i	−0.635109	−	0.772423i	$-0.719045\pi$
$409$	−1.95665	+	1.42159i	−0.0967500	+	0.0702930i	0.538359	+	0.842716i	$0.319045\pi$
$410$		0			0
$411$	11.6332	−	35.8032i	0.573822	−	1.76604i
$412$		0			0
$413$	−0.386773	+	0.532348i	−0.0190319	+	0.0261951i
$414$		0			0
$415$	−21.6548	−	3.84195i	−1.06299	−	0.188594i
$416$		0			0
$417$		−	12.0386i		−	0.589532i
$418$		0			0
$419$	−22.0047			−1.07500			−0.537499	−	0.843264i	$-0.680631\pi$
$419$	−22.0047			−1.07500			−0.537499	+	0.843264i	$0.680631\pi$
$420$		0			0
$421$	4.24460	+	13.0635i	0.206869	+	0.636678i	0.999631	+	0.0271469i	$0.00864218\pi$
$421$	4.24460	+	13.0635i	0.206869	+	0.636678i	−0.792762	+	0.609531i	$0.791358\pi$
$422$		0			0
$423$	−3.71437	+	5.11239i	−0.180599	+	0.248573i
$424$		0			0
$425$	1.62170	+	5.70104i	0.0786641	+	0.276541i
$426$		0			0
$427$	−2.37722	−	3.27196i	−0.115042	−	0.158341i
$428$		0			0
$429$	13.5817	−	41.4357i	0.655730	−	2.00053i
$430$		0			0
$431$	−30.8402	+	22.4067i	−1.48552	+	1.07929i	−0.509796	+	0.860296i	$0.670279\pi$
$431$	−30.8402	+	22.4067i	−1.48552	+	1.07929i	−0.975725	+	0.218998i	$0.929721\pi$
$432$		0			0
$433$	−23.9214	−	7.77254i	−1.14959	−	0.373524i	−0.328601	−	0.944469i	$-0.606577\pi$
$433$	−23.9214	−	7.77254i	−1.14959	−	0.373524i	−0.820989	+	0.570944i	$0.806577\pi$
$434$		0			0
$435$	30.6057	−	14.8873i	1.46743	−	0.713792i
$436$		0			0
$437$	−9.51778	+	3.09252i	−0.455297	+	0.147935i
$438$		0			0
$439$	−34.6857			−1.65546			−0.827729	−	0.561129i	$-0.810367\pi$
$439$	−34.6857			−1.65546			−0.827729	+	0.561129i	$0.810367\pi$
$440$		0			0
$441$	−6.69594			−0.318854
$442$		0			0
$443$	0.218950	−	0.0711411i	0.0104026	−	0.00338002i	−0.303811	−	0.952732i	$-0.598259\pi$
$443$	0.218950	−	0.0711411i	0.0104026	−	0.00338002i	0.314214	+	0.949352i	$0.398259\pi$
$444$		0			0
$445$	12.5092	+	25.7166i	0.592991	+	1.21908i
$446$		0			0
$447$	−21.7336	−	7.06167i	−1.02796	−	0.334006i
$448$		0			0
$449$	6.09776	−	4.43028i	0.287771	−	0.209078i	−0.434529	−	0.900658i	$-0.643085\pi$
$449$	6.09776	−	4.43028i	0.287771	−	0.209078i	0.722300	+	0.691580i	$0.243085\pi$
$450$		0			0
$451$	−0.897792	+	0.648748i	−0.0422754	+	0.0305484i
$452$		0			0
$453$	−11.0761	−	15.2449i	−0.520400	−	0.716269i
$454$		0			0
$455$	4.80140	−	4.62685i	0.225093	−	0.216910i
$456$		0			0
$457$	6.39765	−	8.80561i	0.299269	−	0.411909i	−0.632728	−	0.774374i	$-0.718065\pi$
$457$	6.39765	−	8.80561i	0.299269	−	0.411909i	0.931997	+	0.362465i	$0.118065\pi$
$458$		0			0
$459$	1.47327	+	4.53427i	0.0687665	+	0.211641i
$460$		0			0
$461$	−4.57537			−0.213096			−0.106548	−	0.994308i	$-0.533980\pi$
$461$	−4.57537			−0.213096			−0.106548	+	0.994308i	$0.533980\pi$
$462$		0			0
$463$		−	21.9889i		−	1.02191i	−0.859607	−	0.510956i	$-0.829291\pi$
$463$		−	21.9889i		−	1.02191i	0.859607	−	0.510956i	$-0.170709\pi$
$464$		0			0
$465$	−15.3767	−	2.72809i	−0.713075	−	0.126512i
$466$		0			0
$467$	−2.39509	+	3.29656i	−0.110832	+	0.152547i	−0.860829	−	0.508894i	$-0.830055\pi$
$467$	−2.39509	+	3.29656i	−0.110832	+	0.152547i	0.749998	+	0.661440i	$0.230055\pi$
$468$		0			0
$469$	0.612278	−	1.88440i	0.0282723	−	0.0870133i
$470$		0			0
$471$	−8.34599	+	6.06372i	−0.384563	+	0.279401i
$472$		0			0
$473$	−34.5441	+	11.1255i	−1.58834	+	0.511551i
$474$		0			0
$475$	8.74879	+	3.20528i	0.401422	+	0.147068i
$476$		0			0
$477$	−2.14984	−	0.698526i	−0.0984345	−	0.0319833i
$478$		0			0
$479$	−18.1820	−	13.2100i	−0.830758	−	0.603581i	0.0890157	−	0.996030i	$-0.471628\pi$
$479$	−18.1820	−	13.2100i	−0.830758	−	0.603581i	−0.919774	+	0.392449i	$0.871628\pi$
$480$		0			0
$481$	−11.7780	−	36.2488i	−0.537029	−	1.65280i
$482$		0			0
$483$		−	4.85450i		−	0.220887i
$484$		0			0
$485$	−14.5747	+	27.3412i	−0.661802	+	1.24150i
$486$		0			0
$487$	21.7952	−	7.08168i	0.987634	−	0.320902i	0.229720	−	0.973257i	$-0.426219\pi$
$487$	21.7952	−	7.08168i	0.987634	−	0.320902i	0.757914	+	0.652355i	$0.226219\pi$
$488$		0			0
$489$	−26.9340	−	19.5687i	−1.21800	−	0.884928i
$490$		0			0
$491$	−8.39244	+	25.8293i	−0.378746	+	1.16566i	0.562171	+	0.827021i	$0.309966\pi$
$491$	−8.39244	+	25.8293i	−0.378746	+	1.16566i	−0.940917	+	0.338638i	$0.890034\pi$
$492$		0			0
$493$	−5.31244	−	7.31195i	−0.239260	−	0.329314i
$494$		0			0
$495$	−1.29523	+	7.19242i	−0.0582165	+	0.323275i
$496$		0			0
$497$	2.93360	+	4.03775i	0.131590	+	0.181118i
$498$		0			0
$499$	6.23790	−	19.1983i	0.279247	−	0.859433i	−0.708818	−	0.705392i	$-0.750771\pi$
$499$	6.23790	−	19.1983i	0.279247	−	0.859433i	0.988064	−	0.154041i	$-0.0492288\pi$
$500$		0			0
$501$	33.8807	+	24.6158i	1.51368	+	1.09975i
$502$		0			0
$503$	34.3741	−	11.1688i	1.53267	−	0.497994i	0.583325	−	0.812239i	$-0.301751\pi$
$503$	34.3741	−	11.1688i	1.53267	−	0.497994i	0.949342	+	0.314245i	$0.101751\pi$
$504$		0			0
$505$	10.9972	+	5.86226i	0.489370	+	0.260867i
$506$		0			0
$507$			60.6316i			2.69274i
$508$		0			0
$509$	−12.2057	−	37.5652i	−0.541007	−	1.66505i	−0.730299	−	0.683127i	$-0.760619\pi$
$509$	−12.2057	−	37.5652i	−0.541007	−	1.66505i	0.189292	−	0.981921i	$-0.439381\pi$
$510$		0			0
$511$	−1.29543	−	0.941186i	−0.0573065	−	0.0416356i
$512$		0			0
$513$	7.12778	+	2.31596i	0.314699	+	0.102252i
$514$		0			0
$515$	3.44391	+	24.6942i	0.151757	+	1.08816i
$516$		0			0
$517$	−12.4569	−	17.2389i	−0.547853	−	0.758166i
$518$		0			0
$519$	−40.2123	+	29.2159i	−1.76512	+	1.28244i
$520$		0			0
$521$	3.89376	−	11.9838i	0.170589	−	0.525018i	−0.828816	−	0.559521i	$-0.810985\pi$
$521$	3.89376	−	11.9838i	0.170589	−	0.525018i	0.999405	+	0.0345036i	$0.0109850\pi$
$522$		0			0
$523$	−1.62625	+	2.23834i	−0.0711109	+	0.0978757i	−0.843091	−	0.537771i	$-0.819266\pi$
$523$	−1.62625	+	2.23834i	−0.0711109	+	0.0978757i	0.771980	+	0.635647i	$0.219266\pi$
$524$		0			0
$525$	−2.79015	+	3.55570i	−0.121772	+	0.155183i
$526$		0			0
$527$			4.14715i			0.180653i
$528$		0			0
$529$	−5.84058			−0.253938
$530$		0			0
$531$	0.442526	+	1.36196i	0.0192040	+	0.0591038i
$532$		0			0
$533$	1.29279	−	1.77937i	0.0559970	−	0.0770733i
$534$		0			0
$535$	11.1956	+	11.6179i	0.484028	+	0.502288i
$536$		0			0
$537$	6.50604	+	8.95479i	0.280756	+	0.386428i
$538$		0			0
$539$	7.01946	−	21.4153i	0.302350	−	0.922423i
$540$		0			0
$541$	16.0757	−	11.6797i	0.691150	−	0.502150i	−0.185888	−	0.982571i	$-0.559516\pi$
$541$	16.0757	−	11.6797i	0.691150	−	0.502150i	0.877038	+	0.480421i	$0.159516\pi$
$542$		0			0
$543$	−38.9067	−	12.6416i	−1.66965	−	0.542501i
$544$		0			0
$545$	5.03381	+	10.3486i	0.215625	+	0.443286i
$546$		0			0
$547$	−14.7398	+	4.78926i	−0.630229	+	0.204774i	−0.606677	−	0.794949i	$-0.707498\pi$
$547$	−14.7398	+	4.78926i	−0.630229	+	0.204774i	−0.0235526	+	0.999723i	$0.507498\pi$
$548$		0			0
$549$	−8.80175			−0.375650
$550$		0			0
$551$	−14.2077			−0.605267
$552$		0			0
$553$	−1.31244	+	0.426438i	−0.0558107	+	0.0181340i
$554$		0			0
$555$	11.3008	+	23.2324i	0.479691	+	0.986159i
$556$		0			0
$557$	40.7773	+	13.2493i	1.72779	+	0.561393i	0.993127	−	0.117041i	$-0.0373410\pi$
$557$	40.7773	+	13.2493i	1.72779	+	0.561393i	0.734662	+	0.678434i	$0.237341\pi$
$558$		0			0
$559$	58.2998	−	42.3573i	2.46582	−	1.79152i
$560$		0			0
$561$	7.84897	+	0.0202731i	0.331384	+	0.000855931i
$562$		0			0
$563$	10.3901	+	14.3007i	0.437890	+	0.602704i	0.969742	−	0.244134i	$-0.0785035\pi$
$563$	10.3901	+	14.3007i	0.437890	+	0.602704i	−0.531851	+	0.846838i	$0.678504\pi$
$564$		0			0
$565$	15.6060	+	16.1947i	0.656549	+	0.681318i
$566$		0			0
$567$	−2.92370	+	4.02412i	−0.122784	+	0.168997i
$568$		0			0
$569$	6.53602	+	20.1158i	0.274004	+	0.843298i	0.989481	+	0.144662i	$0.0462095\pi$
$569$	6.53602	+	20.1158i	0.274004	+	0.843298i	−0.715477	+	0.698636i	$0.753791\pi$
$570$		0			0
$571$	−24.5047			−1.02549			−0.512745	−	0.858541i	$-0.671371\pi$
$571$	−24.5047			−1.02549			−0.512745	+	0.858541i	$0.671371\pi$
$572$		0			0
$573$		−	17.0240i		−	0.711188i
$574$		0			0
$575$	21.1244	+	16.5763i	0.880949	+	0.691279i
$576$		0			0
$577$	−11.2053	+	15.4228i	−0.466485	+	0.642061i	−0.975838	−	0.218496i	$-0.929885\pi$
$577$	−11.2053	+	15.4228i	−0.466485	+	0.642061i	0.509353	+	0.860558i	$0.329885\pi$
$578$		0			0
$579$	4.36788	−	13.4430i	0.181523	−	0.558670i
$580$		0			0
$581$	−3.60298	+	2.61772i	−0.149477	+	0.108601i
$582$		0			0
$583$	4.48778	−	6.14346i	0.185865	−	0.254436i
$584$		0			0
$585$	−2.00439	−	14.3723i	−0.0828715	−	0.594222i
$586$		0			0
$587$	−3.32326	−	1.07979i	−0.137165	−	0.0445677i	0.239630	−	0.970864i	$-0.422974\pi$
$587$	−3.32326	−	1.07979i	−0.137165	−	0.0445677i	−0.376795	+	0.926297i	$0.622974\pi$
$588$		0			0
$589$	5.27417	+	3.83191i	0.217319	+	0.157891i
$590$		0			0
$591$	7.75695	+	23.8734i	0.319078	+	0.982022i
$592$		0			0
$593$		−	21.3791i		−	0.877933i	−0.898503	−	0.438967i	$-0.855345\pi$
$593$		−	21.3791i		−	0.877933i	0.898503	−	0.438967i	$-0.144655\pi$
$594$		0			0
$595$	1.05916	+	0.564602i	0.0434212	+	0.0231464i
$596$		0			0
$597$	22.7439	−	7.38995i	0.930847	−	0.302450i
$598$		0			0
$599$	−25.3976	−	18.4524i	−1.03772	−	0.753946i	−0.0678787	−	0.997694i	$-0.521623\pi$
$599$	−25.3976	−	18.4524i	−1.03772	−	0.753946i	−0.969839	+	0.243748i	$0.921623\pi$
$600$		0			0
$601$	2.63123	−	8.09811i	0.107330	−	0.330329i	−0.882940	−	0.469486i	$-0.844439\pi$
$601$	2.63123	−	8.09811i	0.107330	−	0.330329i	0.990270	+	0.139157i	$0.0444393\pi$
$602$		0			0
$603$	−2.53457	−	3.48853i	−0.103216	−	0.142064i
$604$		0			0
$605$	−21.6454	−	11.6824i	−0.880009	−	0.474958i
$606$		0			0
$607$	−18.4093	−	25.3383i	−0.747211	−	1.02845i	−0.998171	−	0.0604508i	$-0.980746\pi$
$607$	−18.4093	−	25.3383i	−0.747211	−	1.02845i	0.250960	−	0.967998i	$-0.419254\pi$
$608$		0			0
$609$	2.12971	−	6.55457i	0.0863001	−	0.265604i
$610$		0			0
$611$	34.1665	+	24.8234i	1.38223	+	1.00425i
$612$		0			0
$613$	15.4136	−	5.00820i	0.622551	−	0.202279i	0.0192784	−	0.999814i	$-0.493863\pi$
$613$	15.4136	−	5.00820i	0.622551	−	0.202279i	0.603273	+	0.797535i	$0.293863\pi$
$614$		0			0
$615$	−0.701300	+	1.31559i	−0.0282791	+	0.0530499i
$616$		0			0
$617$		−	36.1862i		−	1.45680i	−0.685151	−	0.728401i	$-0.740264\pi$
$617$		−	36.1862i		−	1.45680i	0.685151	−	0.728401i	$-0.259736\pi$
$618$		0			0
$619$	9.73725	+	29.9682i	0.391373	+	1.20452i	0.931750	+	0.363099i	$0.118281\pi$
$619$	9.73725	+	29.9682i	0.391373	+	1.20452i	−0.540378	+	0.841423i	$0.681719\pi$
$620$		0			0
$621$	17.4735	+	12.6953i	0.701188	+	0.509443i
$622$		0			0
$623$	5.50752	+	1.78950i	0.220654	+	0.0716948i
$624$		0			0
$625$	−5.94535	−	24.2828i	−0.237814	−	0.971311i
$626$		0			0
$627$	7.27813	−	9.96327i	0.290660	−	0.397894i
$628$		0			0
$629$	5.55041	−	4.03261i	0.221309	−	0.160791i
$630$		0			0
$631$	−0.596734	+	1.83656i	−0.0237556	+	0.0731123i	−0.962232	−	0.272232i	$-0.912238\pi$
$631$	−0.596734	+	1.83656i	−0.0237556	+	0.0731123i	0.938476	+	0.345345i	$0.112238\pi$
$632$		0			0
$633$	11.1070	−	15.2874i	0.441462	−	0.607620i
$634$		0			0
$635$	−29.3031	−	5.19889i	−1.16286	−	0.206312i
$636$		0			0
$637$			44.7495i			1.77304i
$638$		0			0
$639$	10.8618			0.429685
$640$		0			0
$641$	5.81266	+	17.8895i	0.229586	+	0.706594i	0.997794	+	0.0663928i	$0.0211490\pi$
$641$	5.81266	+	17.8895i	0.229586	+	0.706594i	−0.768207	+	0.640201i	$0.778851\pi$
$642$		0			0
$643$	25.8302	−	35.5522i	1.01864	−	1.40204i	0.105490	−	0.994420i	$-0.466359\pi$
$643$	25.8302	−	35.5522i	1.01864	−	1.40204i	0.913152	−	0.407620i	$-0.133641\pi$
$644$		0			0
$645$	−35.1729	+	33.8942i	−1.38493	+	1.33458i
$646$		0			0
$647$	−16.6889	−	22.9703i	−0.656108	−	0.903055i	0.343237	−	0.939249i	$-0.388477\pi$
$647$	−16.6889	−	22.9703i	−0.656108	−	0.903055i	−0.999345	+	0.0361942i	$0.988477\pi$
$648$		0			0
$649$	−4.81978	−	0.0124490i	−0.189193	−	0.000488667i
$650$		0			0
$651$	−2.55840	+	1.85879i	−0.100272	+	0.0728517i
$652$		0			0
$653$	0.0226164	+	0.00734853i	0.000885050	+	0.000287570i	0.309459	−	0.950913i	$-0.399852\pi$
$653$	0.0226164	+	0.00734853i	0.000885050	+	0.000287570i	−0.308574	+	0.951200i	$0.599852\pi$
$654$		0			0
$655$	16.5280	+	33.9786i	0.645802	+	1.32765i
$656$		0			0
$657$	−3.31423	+	1.07686i	−0.129300	+	0.0420122i
$658$		0			0
$659$	10.0841			0.392821			0.196410	−	0.980522i	$-0.437072\pi$
$659$	10.0841			0.392821			0.196410	+	0.980522i	$0.437072\pi$
$660$		0			0
$661$	7.89227			0.306974			0.153487	−	0.988151i	$-0.450950\pi$
$661$	7.89227			0.306974			0.153487	+	0.988151i	$0.450950\pi$
$662$		0			0
$663$	−14.8226	+	4.81616i	−0.575662	+	0.187044i
$664$		0			0
$665$	1.69669	−	0.825308i	0.0657947	−	0.0320041i
$666$		0			0
$667$	−38.9407	−	12.6526i	−1.50779	−	0.489911i
$668$		0			0
$669$	9.46179	−	6.87439i	0.365814	−	0.265779i
$670$		0			0
$671$	9.22702	−	28.1502i	0.356205	−	1.08673i
$672$		0			0
$673$	20.5307	+	28.2580i	0.791399	+	1.08927i	0.993933	+	0.109992i	$0.0350824\pi$
$673$	20.5307	+	28.2580i	0.791399	+	1.08927i	−0.202534	+	0.979275i	$0.564918\pi$
$674$		0			0
$675$	−5.50188	−	19.3417i	−0.211768	−	0.744462i
$676$		0			0
$677$	11.0939	−	15.2694i	0.426372	−	0.586851i	−0.540744	−	0.841187i	$-0.681857\pi$
$677$	11.0939	−	15.2694i	0.426372	−	0.586851i	0.967116	+	0.254337i	$0.0818572\pi$
$678$		0			0
$679$	1.93878	+	5.96696i	0.0744036	+	0.228991i
$680$		0			0
$681$	−8.55425			−0.327799
$682$		0			0
$683$			30.1188i			1.15246i	0.817286	+	0.576232i	$0.195478\pi$
$683$			30.1188i			1.15246i	−0.817286	+	0.576232i	$0.804522\pi$
$684$		0			0
$685$	41.5177	+	7.36599i	1.58631	+	0.281440i
$686$		0			0
$687$	22.2101	−	30.5696i	0.847370	−	1.16630i
$688$		0			0
$689$	−4.66831	+	14.3676i	−0.177848	+	0.547361i
$690$		0			0
$691$	−22.1409	+	16.0863i	−0.842279	+	0.611951i	−0.923006	−	0.384785i	$-0.874276\pi$
$691$	−22.1409	+	16.0863i	−0.842279	+	0.611951i	0.0807277	+	0.996736i	$0.474276\pi$
$692$		0			0
$693$	0.866754	+	1.19949i	0.0329253	+	0.0455647i
$694$		0			0
$695$	13.3549	−	1.86250i	0.506580	−	0.0706488i
$696$		0			0
$697$	0.376527	+	0.122341i	0.0142620	+	0.00463399i
$698$		0			0
$699$	−9.37631	−	6.81229i	−0.354645	−	0.257664i
$700$		0			0
$701$	0.281166	+	0.865341i	0.0106195	+	0.0326835i	0.956226	−	0.292630i	$-0.0945303\pi$
$701$	0.281166	+	0.865341i	0.0106195	+	0.0326835i	−0.945606	+	0.325313i	$0.894530\pi$
$702$		0			0
$703$		−	10.7849i		−	0.406759i
$704$		0			0
$705$	−25.2613	−	13.4660i	−0.951395	−	0.507157i
$706$		0			0
$707$	2.40004	−	0.779822i	0.0902629	−	0.0293282i
$708$		0			0
$709$	−26.7984	−	19.4701i	−1.00643	−	0.731217i	−0.0429754	−	0.999076i	$-0.513684\pi$
$709$	−26.7984	−	19.4701i	−1.00643	−	0.731217i	−0.963458	+	0.267859i	$0.913684\pi$
$710$		0			0
$711$	−0.928058	+	2.85627i	−0.0348049	+	0.107118i
$712$		0			0
$713$	11.0431	+	15.1995i	0.413566	+	0.569225i
$714$		0			0
$715$	48.0675	+	8.65616i	1.79762	+	0.323722i
$716$		0			0
$717$	33.0823	+	45.5339i	1.23548	+	1.70050i
$718$		0			0
$719$	−6.87209	+	21.1501i	−0.256286	+	0.788766i	0.737288	+	0.675578i	$0.236106\pi$
$719$	−6.87209	+	21.1501i	−0.256286	+	0.788766i	−0.993574	+	0.113187i	$0.963894\pi$
$720$		0			0
$721$	4.08466	+	2.96768i	0.152121	+	0.110522i
$722$		0			0
$723$	−47.7814	+	15.5251i	−1.77701	+	0.577385i
$724$		0			0
$725$	21.2501	+	31.6489i	0.789210	+	1.17541i
$726$		0			0
$727$			25.2768i			0.937466i	0.883340	+	0.468733i	$0.155289\pi$
$727$			25.2768i			0.937466i	−0.883340	+	0.468733i	$0.844711\pi$
$728$		0			0
$729$	−4.09809	−	12.6126i	−0.151781	−	0.467134i
$730$		0			0
$731$	10.4941	+	7.62443i	0.388139	+	0.282000i
$732$		0			0
$733$	−25.8940	−	8.41348i	−0.956417	−	0.310759i	−0.211097	−	0.977465i	$-0.567704\pi$
$733$	−25.8940	−	8.41348i	−0.956417	−	0.310759i	−0.745321	+	0.666706i	$0.767704\pi$
$734$		0			0
$735$	−4.18971	−	30.0419i	−0.154540	−	1.10811i
$736$		0			0
$737$	13.8142	−	4.44910i	0.508854	−	0.163885i
$738$		0			0
$739$	20.9752	−	15.2394i	0.771587	−	0.560591i	−0.130855	−	0.991401i	$-0.541772\pi$
$739$	20.9752	−	15.2394i	0.771587	−	0.560591i	0.902442	+	0.430811i	$0.141772\pi$
$740$		0			0
$741$	−7.57091	+	23.3009i	−0.278124	+	0.855978i
$742$		0			0
$743$	−4.85699	+	6.68508i	−0.178186	+	0.245252i	−0.888762	−	0.458368i	$-0.848434\pi$
$743$	−4.85699	+	6.68508i	−0.178186	+	0.245252i	0.710577	+	0.703620i	$0.248434\pi$
$744$		0			0
$745$	4.47137	−	25.2025i	0.163818	−	0.923347i
$746$		0			0
$747$			9.69221i			0.354620i
$748$		0			0
$749$	3.26717			0.119380
$750$		0			0
$751$	−4.78129	−	14.7153i	−0.174472	−	0.536969i	0.825137	−	0.564933i	$-0.191098\pi$
$751$	−4.78129	−	14.7153i	−0.174472	−	0.536969i	−0.999609	+	0.0279634i	$0.991098\pi$
$752$		0			0
$753$	−2.98691	+	4.11112i	−0.108849	+	0.149818i
$754$		0			0
$755$	15.1982	−	14.6457i	0.553120	−	0.533012i
$756$		0			0
$757$	−19.6231	−	27.0088i	−0.713212	−	0.981653i	−0.999722	−	0.0235752i	$-0.992495\pi$
$757$	−19.6231	−	27.0088i	−0.713212	−	0.981653i	0.286510	−	0.958077i	$-0.407505\pi$
$758$		0			0
$759$	28.8208	−	20.8260i	1.04613	−	0.755937i
$760$		0			0
$761$	42.5921	−	30.9449i	1.54396	−	1.12175i	0.596171	−	0.802857i	$-0.296688\pi$
$761$	42.5921	−	30.9449i	1.54396	−	1.12175i	0.947790	−	0.318896i	$-0.103312\pi$
$762$		0			0
$763$	2.21628	+	0.720113i	0.0802347	+	0.0260698i
$764$		0			0
$765$	2.34895	−	1.14258i	0.0849263	−	0.0413102i
$766$		0			0
$767$	9.10206	−	2.95744i	0.328656	−	0.106787i
$768$		0			0
$769$	−50.2205			−1.81100			−0.905499	−	0.424349i	$-0.860503\pi$
$769$	−50.2205			−1.81100			−0.905499	+	0.424349i	$0.860503\pi$
$770$		0			0
$771$	−5.68362			−0.204691
$772$		0			0
$773$	−14.7823	+	4.80308i	−0.531684	+	0.172755i	−0.562541	−	0.826769i	$-0.690176\pi$
$773$	−14.7823	+	4.80308i	−0.531684	+	0.172755i	0.0308572	+	0.999524i	$0.490176\pi$
$774$		0			0
$775$	0.647446	−	17.4800i	0.0232569	−	0.627900i
$776$		0			0
$777$	4.97549	+	1.61663i	0.178495	+	0.0579964i
$778$		0			0
$779$	0.503494	−	0.365810i	0.0180395	−	0.0131065i
$780$		0			0
$781$	−11.3866	+	34.7387i	−0.407443	+	1.24305i
$782$		0			0
$783$	18.0233	+	24.8070i	0.644101	+	0.886529i
$784$		0			0
$785$	−8.01794	−	8.32042i	−0.286173	−	0.296969i
$786$		0			0
$787$	7.50169	−	10.3252i	0.267406	−	0.368053i	−0.654106	−	0.756403i	$-0.726955\pi$
$787$	7.50169	−	10.3252i	0.267406	−	0.368053i	0.921512	+	0.388350i	$0.126955\pi$
$788$		0			0
$789$	7.77948	+	23.9428i	0.276957	+	0.852385i
$790$		0			0
$791$	4.55425			0.161930
$792$		0			0
$793$			58.8228i			2.08886i
$794$		0			0
$795$	1.78882	−	10.0825i	0.0634429	−	0.357590i
$796$		0			0
$797$	−14.5203	+	19.9855i	−0.514336	+	0.707923i	−0.984643	−	0.174580i	$-0.944143\pi$
$797$	−14.5203	+	19.9855i	−0.514336	+	0.707923i	0.470307	+	0.882503i	$0.344143\pi$
$798$		0			0
$799$	−2.34912	+	7.22985i	−0.0831059	+	0.255774i
$800$		0			0
$801$	10.1959	−	7.40777i	0.360255	−	0.261741i
$802$		0			0
$803$	0.0302939	−	11.7286i	0.00106905	−	0.413894i
$804$		0			0
$805$	5.38529	−	0.751044i	0.189806	−	0.0264708i
$806$		0			0
$807$	−26.0606	−	8.46760i	−0.917377	−	0.298074i
$808$		0			0
$809$	7.44932	+	5.41225i	0.261904	+	0.190285i	0.710986	−	0.703206i	$-0.248249\pi$
$809$	7.44932	+	5.41225i	0.261904	+	0.190285i	−0.449082	+	0.893491i	$0.648249\pi$
$810$		0			0
$811$	−14.8169	−	45.6016i	−0.520291	−	1.60129i	−0.773445	−	0.633864i	$-0.781468\pi$
$811$	−14.8169	−	45.6016i	−0.520291	−	1.60129i	0.253154	−	0.967426i	$-0.418532\pi$
$812$		0			0
$813$		−	37.5657i		−	1.31749i
$814$		0			0
$815$	17.5414	−	32.9065i	0.614447	−	1.15266i
$816$		0			0
$817$	19.3929	−	6.30113i	0.678471	−	0.220449i
$818$		0			0
$819$	−2.37732	−	1.72722i	−0.0830702	−	0.0603540i
$820$		0			0
$821$	−5.81350	+	17.8921i	−0.202892	+	0.624439i	0.796901	+	0.604110i	$0.206471\pi$
$821$	−5.81350	+	17.8921i	−0.202892	+	0.624439i	−0.999793	+	0.0203286i	$0.993529\pi$
$822$		0			0
$823$	26.1803	+	36.0340i	0.912586	+	1.25607i	0.966276	+	0.257509i	$0.0829018\pi$
$823$	26.1803	+	36.0340i	0.912586	+	1.25607i	−0.0536896	+	0.998558i	$0.517098\pi$
$824$		0			0
$825$	−33.0798	−	1.31082i	−1.15169	−	0.0456368i
$826$		0			0
$827$	−21.2181	−	29.2042i	−0.737825	−	1.01553i	−0.998741	−	0.0501675i	$-0.984024\pi$
$827$	−21.2181	−	29.2042i	−0.737825	−	1.01553i	0.260916	−	0.965362i	$-0.415976\pi$
$828$		0			0
$829$	−3.34254	+	10.2873i	−0.116091	+	0.357292i	−0.992173	−	0.124870i	$-0.960148\pi$
$829$	−3.34254	+	10.2873i	−0.116091	+	0.357292i	0.876082	+	0.482162i	$0.160148\pi$
$830$		0			0
$831$	−36.0006	−	26.1560i	−1.24885	−	0.907341i
$832$		0			0
$833$	−7.66080	+	2.48915i	−0.265431	+	0.0862438i
$834$		0			0
$835$	−22.0656	+	41.3936i	−0.763610	+	1.43248i
$836$		0			0
$837$		−	14.0699i		−	0.486326i
$838$		0			0
$839$	−3.28493	−	10.1100i	−0.113408	−	0.349035i	0.878203	−	0.478287i	$-0.158742\pi$
$839$	−3.28493	−	10.1100i	−0.113408	−	0.349035i	−0.991612	+	0.129252i	$0.958742\pi$
$840$		0			0
$841$	−23.5656	−	17.1214i	−0.812608	−	0.590394i
$842$		0			0
$843$	31.9392	+	10.3777i	1.10004	+	0.357426i
$844$		0			0
$845$	−67.2611	+	9.38038i	−2.31385	+	0.322695i
$846$		0			0
$847$	−4.74489	+	1.51466i	−0.163036	+	0.0520442i
$848$		0			0
$849$	−36.5050	+	26.5224i	−1.25285	+	0.910247i
$850$		0			0
$851$	9.60442	−	29.5594i	0.329235	−	1.01328i
$852$		0			0
$853$	−15.8546	+	21.8219i	−0.542850	+	0.747169i	−0.989020	−	0.147779i	$-0.952787\pi$
$853$	−15.8546	+	21.8219i	−0.542850	+	0.747169i	0.446171	+	0.894948i	$0.352787\pi$
$854$		0			0
$855$	0.717306	−	4.04303i	0.0245313	−	0.138269i
$856$		0			0
$857$		−	3.11130i		−	0.106280i	−0.998587	−	0.0531400i	$-0.983077\pi$
$857$		−	3.11130i		−	0.106280i	0.998587	−	0.0531400i	$-0.0169230\pi$
$858$		0			0
$859$	31.5630			1.07692			0.538458	−	0.842652i	$-0.319007\pi$
$859$	31.5630			1.07692			0.538458	+	0.842652i	$0.319007\pi$
$860$		0			0
$861$	0.0932897	+	0.287116i	0.00317931	+	0.00978490i
$862$		0			0
$863$	−2.97188	+	4.09044i	−0.101164	+	0.139240i	−0.856598	−	0.515985i	$-0.827426\pi$
$863$	−2.97188	+	4.09044i	−0.101164	+	0.139240i	0.755434	+	0.655225i	$0.227426\pi$
$864$		0			0
$865$	−38.6317	−	40.0891i	−1.31352	−	1.36307i
$866$		0			0
$867$	18.2993	+	25.1868i	0.621476	+	0.855388i
$868$		0			0
$869$	−8.16217	−	5.96244i	−0.276883	−	0.202262i
$870$		0			0
$871$	−23.3141	+	16.9387i	−0.789969	+	0.573946i
$872$		0			0
$873$	12.9859	+	4.21937i	0.439506	+	0.142804i
$874$		0			0
$875$	−4.37615	−	2.54512i	−0.147941	−	0.0860408i
$876$		0			0
$877$	−8.71216	+	2.83075i	−0.294189	+	0.0955877i	−0.452393	−	0.891819i	$-0.649430\pi$
$877$	−8.71216	+	2.83075i	−0.294189	+	0.0955877i	0.158204	+	0.987406i	$0.449430\pi$
$878$		0			0
$879$	6.87871			0.232013
$880$		0			0
$881$	2.47296			0.0833160			0.0416580	−	0.999132i	$-0.486736\pi$
$881$	2.47296			0.0833160			0.0416580	+	0.999132i	$0.486736\pi$
$882$		0			0
$883$	−7.76566	+	2.52321i	−0.261335	+	0.0849129i	−0.436754	−	0.899581i	$-0.643872\pi$
$883$	−7.76566	+	2.52321i	−0.261335	+	0.0849129i	0.175419	+	0.984494i	$0.443872\pi$
$884$		0			0
$885$	−5.83363	+	2.83762i	−0.196095	+	0.0953855i
$886$		0			0
$887$	−32.1992	−	10.4622i	−1.08114	−	0.351285i	−0.286325	−	0.958132i	$-0.592434\pi$
$887$	−32.1992	−	10.4622i	−1.08114	−	0.351285i	−0.794818	+	0.606848i	$0.792434\pi$
$888$		0			0
$889$	−4.87551	+	3.54227i	−0.163520	+	0.118804i
$890$		0			0
$891$	−36.4337	−	0.0941046i	−1.22058	−	0.00315262i
$892$		0			0
$893$	7.02407	+	9.66780i	0.235052	+	0.323521i
$894$		0			0
$895$	−8.92736	+	8.60282i	−0.298409	+	0.287560i
$896$		0			0
$897$	−41.5010	+	57.1212i	−1.38568	+	1.90722i
$898$		0			0
$899$	8.24227	+	25.3671i	0.274895	+	0.846040i
$900$		0			0
$901$	−2.71930			−0.0905929
$902$		0			0
$903$			9.89124i			0.329160i
$904$		0			0
$905$	8.00449	−	45.1166i	0.266078	−	1.49973i
$906$		0			0
$907$	6.08974	−	8.38181i	0.202207	−	0.278314i	−0.695856	−	0.718182i	$-0.744975\pi$
$907$	6.08974	−	8.38181i	0.202207	−	0.278314i	0.898062	+	0.439868i	$0.144975\pi$
$908$		0			0
$909$	1.69713	−	5.22322i	0.0562901	−	0.173243i
$910$		0			0
$911$	12.7866	−	9.28999i	0.423638	−	0.307791i	−0.355462	−	0.934691i	$-0.615676\pi$
$911$	12.7866	−	9.28999i	0.423638	−	0.307791i	0.779100	+	0.626900i	$0.215676\pi$
$912$		0			0
$913$	−30.9981	−	10.1605i	−1.02589	−	0.336263i
$914$		0			0
$915$	−5.50733	−	39.4898i	−0.182067	−	1.30549i
$916$		0			0
$917$	7.27692	+	2.36441i	0.240305	+	0.0780798i
$918$		0			0
$919$	−13.2348	−	9.61568i	−0.436577	−	0.317192i	0.347696	−	0.937607i	$-0.386964\pi$
$919$	−13.2348	−	9.61568i	−0.436577	−	0.317192i	−0.784273	+	0.620415i	$0.786964\pi$
$920$		0			0
$921$	−5.91065	−	18.1911i	−0.194763	−	0.599417i
$922$		0			0
$923$		−	72.5901i		−	2.38933i
$924$		0			0
$925$	−24.0242	+	16.1307i	−0.789912	+	0.530374i
$926$		0			0
$927$	10.4502	−	3.39546i	0.343228	−	0.111522i
$928$		0			0
$929$	21.6132	+	15.7029i	0.709105	+	0.515195i	0.882885	−	0.469589i	$-0.155598\pi$
$929$	21.6132	+	15.7029i	0.709105	+	0.515195i	−0.173780	+	0.984785i	$0.555598\pi$
$930$		0			0
$931$	−3.91289	+	12.0426i	−0.128240	+	0.394682i
$932$		0			0
$933$	12.8376	+	17.6694i	0.420283	+	0.578469i
$934$		0			0
$935$	1.19183	+	8.71031i	0.0389771	+	0.284858i
$936$		0			0
$937$	−9.85708	−	13.5671i	−0.322017	−	0.443218i	0.617065	−	0.786912i	$-0.288322\pi$
$937$	−9.85708	−	13.5671i	−0.322017	−	0.443218i	−0.939082	+	0.343694i	$0.888322\pi$
$938$		0			0
$939$	−7.64883	+	23.5407i	−0.249610	+	0.768221i
$940$		0			0
$941$	13.7088	+	9.95999i	0.446893	+	0.324687i	0.788368	−	0.615204i	$-0.210926\pi$
$941$	13.7088	+	9.95999i	0.446893	+	0.324687i	−0.341475	+	0.939891i	$0.610926\pi$
$942$		0			0
$943$	1.70576	−	0.554234i	0.0555471	−	0.0180484i
$944$		0			0
$945$	−3.59336	−	1.91550i	−0.116892	−	0.0623113i
$946$		0			0
$947$		−	24.7264i		−	0.803501i	−0.915749	−	0.401750i	$-0.868402\pi$
$947$		−	24.7264i		−	0.803501i	0.915749	−	0.401750i	$-0.131598\pi$
$948$		0			0
$949$	7.19673	+	22.1492i	0.233616	+	0.718995i
$950$		0			0
$951$	−4.63374	−	3.36661i	−0.150259	−	0.109170i
$952$		0			0
$953$	7.15058	+	2.32337i	0.231630	+	0.0752612i	0.422532	−	0.906348i	$-0.361141\pi$
$953$	7.15058	+	2.32337i	0.231630	+	0.0752612i	−0.190902	+	0.981609i	$0.561141\pi$
$954$		0			0
$955$	18.8854	−	2.63380i	0.611117	−	0.0852278i
$956$		0			0
$957$	48.0505	−	15.4755i	1.55325	−	0.500251i
$958$		0			0
$959$	6.90781	−	5.01882i	0.223065	−	0.162066i
$960$		0			0
$961$	−5.79753	+	17.8430i	−0.187017	+	0.575580i
$962$		0			0
$963$	4.17936	−	5.75239i	0.134678	−	0.185368i
$964$		0			0
$965$	15.5886	+	2.76569i	0.501814	+	0.0890307i
$966$		0			0
$967$			15.0563i			0.484177i	0.970254	+	0.242089i	$0.0778325\pi$
$967$			15.0563i			0.484177i	−0.970254	+	0.242089i	$0.922168\pi$
$968$		0			0
$969$	−4.41007			−0.141672
$970$		0			0
$971$	−13.9054	−	42.7966i	−0.446247	−	1.37341i	−0.881110	−	0.472911i	$-0.843203\pi$
$971$	−13.9054	−	42.7966i	−0.446247	−	1.37341i	0.434863	−	0.900496i	$-0.356797\pi$
$972$		0			0
$973$	1.60495	−	2.20903i	0.0514524	−	0.0708181i
$974$		0			0
$975$	63.2284	−	17.9858i	2.02493	−	0.576005i
$976$		0			0
$977$	7.45912	+	10.2666i	0.238638	+	0.328458i	0.911492	−	0.411318i	$-0.134932\pi$
$977$	7.45912	+	10.2666i	0.238638	+	0.328458i	−0.672853	+	0.739776i	$0.734932\pi$
$978$		0			0
$979$	13.0034	+	40.3748i	0.415589	+	1.29038i
$980$		0			0
$981$	4.10294	−	2.98096i	0.130997	−	0.0951747i
$982$		0			0
$983$	−6.42717	−	2.08831i	−0.204995	−	0.0666069i	0.204720	−	0.978821i	$-0.434372\pi$
$983$	−6.42717	−	2.08831i	−0.204995	−	0.0666069i	−0.409715	+	0.912214i	$0.634372\pi$
$984$		0			0
$985$	−25.2837	+	12.2986i	−0.805605	+	0.391865i
$986$		0			0
$987$	−5.51304	+	1.79130i	−0.175482	+	0.0570176i
$988$		0			0
$989$	58.7639			1.86858
$990$		0			0
$991$	−8.57936			−0.272532			−0.136266	−	0.990672i	$-0.543510\pi$
$991$	−8.57936			−0.272532			−0.136266	+	0.990672i	$0.543510\pi$
$992$		0			0
$993$	−51.7615	+	16.8183i	−1.64260	+	0.533713i
$994$		0			0
$995$	11.7167	+	24.0874i	0.371444	+	0.763623i
$996$		0			0
$997$	15.8982	+	5.16564i	0.503501	+	0.163598i	0.549745	−	0.835333i	$-0.314725\pi$
$997$	15.8982	+	5.16564i	0.503501	+	0.163598i	−0.0462434	+	0.998930i	$0.514725\pi$
$998$		0			0
$999$	−18.8306	+	13.6813i	−0.595775	+	0.432856i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.t.a.69.5	yes	24
4.3	odd	2		880.2.cd.d.289.2		24
5.2	odd	4		1100.2.n.f.201.2		24
5.3	odd	4		1100.2.n.f.201.5		24
5.4	even	2	inner	220.2.t.a.69.2	✓	24
11.2	odd	10		2420.2.b.h.969.4		12
11.4	even	5	inner	220.2.t.a.169.2	yes	24
11.9	even	5		2420.2.b.i.969.4		12
20.19	odd	2		880.2.cd.d.289.5		24
44.15	odd	10		880.2.cd.d.609.5		24
55.4	even	10	inner	220.2.t.a.169.5	yes	24
55.9	even	10		2420.2.b.i.969.9		12
55.24	odd	10		2420.2.b.h.969.9		12
55.37	odd	20		1100.2.n.f.301.2		24
55.48	odd	20		1100.2.n.f.301.5		24
220.59	odd	10		880.2.cd.d.609.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.t.a.69.2	✓	24	5.4	even	2	inner
220.2.t.a.69.5	yes	24	1.1	even	1	trivial
220.2.t.a.169.2	yes	24	11.4	even	5	inner
220.2.t.a.169.5	yes	24	55.4	even	10	inner
880.2.cd.d.289.2		24	4.3	odd	2
880.2.cd.d.289.5		24	20.19	odd	2
880.2.cd.d.609.2		24	220.59	odd	10
880.2.cd.d.609.5		24	44.15	odd	10
1100.2.n.f.201.2		24	5.2	odd	4
1100.2.n.f.201.5		24	5.3	odd	4
1100.2.n.f.301.2		24	55.37	odd	20
1100.2.n.f.301.5		24	55.48	odd	20
2420.2.b.h.969.4		12	11.2	odd	10
2420.2.b.h.969.9		12	55.24	odd	10
2420.2.b.i.969.4		12	11.9	even	5
2420.2.b.i.969.9		12	55.9	even	10

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.t (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.89864 - 0.616907i) q^{3} +(0.978101 + 2.01080i) q^{5} +(0.430637 + 0.139922i) q^{7} +(0.797226 - 0.579219i) q^{9} +(1.01674 + 3.15693i) q^{11} +(-3.87097 - 5.32793i) q^{13} +(3.09754 + 3.21440i) q^{15} +(0.696785 - 0.959042i) q^{17} +(-0.575851 - 1.77229i) q^{19} +0.903946 q^{21} -5.37034i q^{23} +(-3.08664 + 3.93353i) q^{25} +(-2.36396 + 3.25371i) q^{27} +(2.35601 - 7.25106i) q^{29} +(-2.83026 + 2.05631i) q^{31} +(3.87797 + 5.36666i) q^{33} +(0.139850 + 1.00278i) q^{35} +(5.50419 + 1.78842i) q^{37} +(-10.6364 - 7.72781i) q^{39} +(0.103203 + 0.317626i) q^{41} +10.9423i q^{43} +(1.94446 + 1.03653i) q^{45} +(-6.09886 + 1.98164i) q^{47} +(-5.49725 - 3.99399i) q^{49} +(0.731307 - 2.25073i) q^{51} +(-1.34833 - 1.85581i) q^{53} +(-5.35349 + 5.13227i) q^{55} +(-2.18667 - 3.00970i) q^{57} +(-0.449071 + 1.38210i) q^{59} +(-7.22608 - 5.25006i) q^{61} +(0.424361 - 0.137883i) q^{63} +(6.92720 - 12.9950i) q^{65} -4.37584i q^{67} +(-3.31300 - 10.1964i) q^{69} +(8.91732 + 6.47881i) q^{71} +(-3.36324 - 1.09278i) q^{73} +(-3.43380 + 9.37255i) q^{75} +(-0.00387889 + 1.50176i) q^{77} +(-2.46562 + 1.79138i) q^{79} +(-3.39462 + 10.4476i) q^{81} +(-5.78120 + 7.95714i) q^{83} +(2.60997 + 0.463055i) q^{85} -15.2206i q^{87} +12.7892 q^{89} +(-0.921484 - 2.83604i) q^{91} +(-4.10511 + 5.65021i) q^{93} +(3.00047 - 2.89140i) q^{95} +(8.14443 + 11.2098i) q^{97} +(2.63913 + 1.92787i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{5} + 14 q^{9} - 2 q^{11} - q^{15} + 8 q^{19} - 28 q^{21} + 27 q^{25} - 16 q^{29} - 26 q^{31} + 17 q^{35} + 12 q^{39} + 10 q^{41} - 40 q^{45} - 46 q^{49} - 12 q^{51} - 33 q^{55} - 48 q^{59} - 10 q^{61}+ \cdots + 156 q^{99}+O(q^{100}) \) 24 * q + q^5 + 14 * q^9 - 2 * q^11 - q^15 + 8 * q^19 - 28 * q^21 + 27 * q^25 - 16 * q^29 - 26 * q^31 + 17 * q^35 + 12 * q^39 + 10 * q^41 - 40 * q^45 - 46 * q^49 - 12 * q^51 - 33 * q^55 - 48 * q^59 - 10 * q^61 - 22 * q^65 - 58 * q^69 + 42 * q^71 - 17 * q^75 - 64 * q^79 + 36 * q^81 - 17 * q^85 + 72 * q^89 + 10 * q^91 + 67 * q^95 + 156 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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