LMFDB - Embedded newform 1100.2.n.f.201.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1100,2,Mod(201,1100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1100, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("1100.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1100.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.78354422234$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 220)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.2
Character	$\chi$	$=$	1100.201
Dual form			1100.2.n.f.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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
$3$	−0.616907	−	1.89864i	−0.356171	−	1.09618i	−0.955327	−	0.295550i	$-0.904497\pi$
$3$	−0.616907	−	1.89864i	−0.356171	−	1.09618i	0.599156	−	0.800633i	$-0.295503\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.139922	+	0.430637i	−0.0528857	+	0.162765i	−0.974011	−	0.226501i	$-0.927271\pi$
$7$	−0.139922	+	0.430637i	−0.0528857	+	0.162765i	0.921125	+	0.389266i	$0.127271\pi$
$8$		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
$13$	−5.32793	+	3.87097i	−1.47770	+	1.07361i	−0.499413	+	0.866364i	$0.666451\pi$
$13$	−5.32793	+	3.87097i	−1.47770	+	1.07361i	−0.978288	+	0.207248i	$0.933549\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.959042	+	0.696785i	0.232602	+	0.168995i	0.697981	−	0.716116i	$-0.254082\pi$
$17$	0.959042	+	0.696785i	0.232602	+	0.168995i	−0.465379	+	0.885111i	$0.654082\pi$
$18$		0			0
$19$	0.575851	+	1.77229i	0.132109	+	0.406590i	0.995129	−	0.0985795i	$-0.0314299\pi$
$19$	0.575851	+	1.77229i	0.132109	+	0.406590i	−0.863020	+	0.505170i	$0.831430\pi$
$20$		0			0
$21$	0.903946			0.197257
$22$		0			0
$23$	−5.37034			−1.11979			−0.559897	−	0.828562i	$-0.689159\pi$
$23$	−5.37034			−1.11979			−0.559897	+	0.828562i	$0.689159\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.25371	−	2.36396i	−0.626176	−	0.454943i
$28$		0			0
$29$	−2.35601	+	7.25106i	−0.437501	+	1.34649i	0.453001	+	0.891510i	$0.350353\pi$
$29$	−2.35601	+	7.25106i	−0.437501	+	1.34649i	−0.890502	+	0.454979i	$0.849647\pi$
$30$		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
$33$	5.36666	−	3.87797i	0.934216	−	0.675068i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.78842	+	5.50419i	−0.294014	+	0.904883i	0.689536	+	0.724251i	$0.257814\pi$
$37$	−1.78842	+	5.50419i	−0.294014	+	0.904883i	−0.983551	+	0.180632i	$0.942186\pi$
$38$		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
$43$	10.9423			1.66868			0.834342	−	0.551247i	$-0.185848\pi$
$43$	10.9423			1.66868			0.834342	+	0.551247i	$0.185848\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.98164	−	6.09886i	−0.289052	−	0.889611i	−0.985155	−	0.171669i	$-0.945084\pi$
$47$	−1.98164	−	6.09886i	−0.289052	−	0.889611i	0.696103	−	0.717942i	$-0.254916\pi$
$48$		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
$53$	−1.85581	+	1.34833i	−0.254915	+	0.185207i	−0.707902	−	0.706310i	$-0.750358\pi$
$53$	−1.85581	+	1.34833i	−0.254915	+	0.185207i	0.452987	+	0.891517i	$0.350358\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.00970	−	2.18667i	0.398644	−	0.289632i
$58$		0			0
$59$	0.449071	−	1.38210i	0.0584641	−	0.179934i	−0.917560	−	0.397598i	$-0.869844\pi$
$59$	0.449071	−	1.38210i	0.0584641	−	0.179934i	0.976024	+	0.217664i	$0.0698438\pi$
$60$		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
$63$	−0.137883	−	0.424361i	−0.0173716	−	0.0534644i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	4.37584			0.534593			0.267297	−	0.963614i	$-0.413870\pi$
$67$	4.37584			0.534593			0.267297	+	0.963614i	$0.413870\pi$
$68$		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
$73$	−1.09278	+	3.36324i	−0.127901	+	0.393638i	−0.994418	−	0.105508i	$-0.966353\pi$
$73$	−1.09278	+	3.36324i	−0.127901	+	0.393638i	0.866518	+	0.499146i	$0.166353\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.50176	−	0.00387889i	−0.171141	−	0.000442040i
$78$		0			0
$79$	2.46562	−	1.79138i	0.277404	−	0.201546i	−0.440380	−	0.897811i	$-0.645156\pi$
$79$	2.46562	−	1.79138i	0.277404	−	0.201546i	0.717784	+	0.696265i	$0.245156\pi$
$80$		0			0
$81$	−3.39462	+	10.4476i	−0.377180	+	1.16084i
$82$		0			0
$83$	7.95714	+	5.78120i	0.873409	+	0.634569i	0.931500	−	0.363743i	$-0.118501\pi$
$83$	7.95714	+	5.78120i	0.873409	+	0.634569i	−0.0580905	+	0.998311i	$0.518501\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	15.2206			1.63182
$88$		0			0
$89$	−12.7892			−1.35566			−0.677828	−	0.735220i	$-0.737079\pi$
$89$	−12.7892			−1.35566			−0.677828	+	0.735220i	$0.737079\pi$
$90$		0			0
$91$	−0.921484	−	2.83604i	−0.0965978	−	0.297297i
$92$		0			0
$93$	5.65021	+	4.10511i	0.585899	+	0.425681i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−11.2098	+	8.14443i	−1.13819	+	0.826941i	−0.986866	−	0.161543i	$-0.948353\pi$
$97$	−11.2098	+	8.14443i	−1.13819	+	0.826941i	−0.151321	+	0.988485i	$0.548353\pi$
$98$		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
$103$	3.44568	−	10.6047i	0.339513	−	1.04491i	−0.624943	−	0.780671i	$-0.714878\pi$
$103$	3.44568	−	10.6047i	0.339513	−	1.04491i	0.964456	−	0.264244i	$-0.0851223\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.22972	+	6.86236i	0.215555	+	0.663409i	0.999114	+	0.0420918i	$0.0134022\pi$
$107$	2.22972	+	6.86236i	0.215555	+	0.663409i	−0.783559	+	0.621317i	$0.786598\pi$
$108$		0			0
$109$	−5.14652			−0.492947			−0.246473	−	0.969150i	$-0.579272\pi$
$109$	−5.14652			−0.492947			−0.246473	+	0.969150i	$0.579272\pi$
$110$		0			0
$111$	11.5538			1.09664
$112$		0			0
$113$	−3.10809	−	9.56572i	−0.292385	−	0.899868i	−0.984087	−	0.177685i	$-0.943139\pi$
$113$	−3.10809	−	9.56572i	−0.292385	−	0.899868i	0.691703	−	0.722182i	$-0.256861\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	2.00543	−	6.17207i	0.185402	−	0.570608i
$118$		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
$123$	0.539392	−	0.391891i	0.0486353	−	0.0353356i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−10.7675	−	7.82306i	−0.955463	−	0.694184i	−0.00337009	−	0.999994i	$-0.501073\pi$
$127$	−10.7675	−	7.82306i	−0.955463	−	0.694184i	−0.952093	+	0.305810i	$0.901073\pi$
$128$		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
$133$	−0.843786			−0.0731655
$134$		0			0
$135$		0			0
$136$		0			0
$137$	15.2558	+	11.0840i	1.30339	+	0.946971i	0.999983	−	0.00588916i	$-0.00187459\pi$
$137$	15.2558	+	11.0840i	1.30339	+	0.946971i	0.303411	+	0.952860i	$0.401875\pi$
$138$		0			0
$139$	−1.86346	+	5.73515i	−0.158057	+	0.486449i	−0.998458	−	0.0555163i	$-0.982320\pi$
$139$	−1.86346	+	5.73515i	−0.158057	+	0.486449i	0.840401	+	0.541965i	$0.182320\pi$
$140$		0			0
$141$	−10.3571	+	7.52487i	−0.872224	+	0.633708i
$142$		0			0
$143$	−17.6375	−	12.8841i	−1.47492	−	1.07743i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	4.19187	−	12.9012i	0.345739	−	1.06408i
$148$		0			0
$149$	9.26073	+	6.72832i	0.758669	+	0.551205i	0.898502	−	0.438970i	$-0.144657\pi$
$149$	9.26073	+	6.72832i	0.758669	+	0.551205i	−0.139833	+	0.990175i	$0.544657\pi$
$150$		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
$153$	−1.16816			−0.0944405
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−1.59685	−	4.91461i	−0.127443	−	0.392229i	0.866895	−	0.498490i	$-0.166112\pi$
$157$	−1.59685	−	4.91461i	−0.127443	−	0.392229i	−0.994338	+	0.106261i	$0.966112\pi$
$158$		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
$163$	−13.4916	+	9.80223i	−1.05674	+	0.767770i	−0.973483	−	0.228758i	$-0.926534\pi$
$163$	−13.4916	+	9.80223i	−1.05674	+	0.767770i	−0.0832613	+	0.996528i	$0.526534\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−16.9713	+	12.3304i	−1.31328	+	0.954153i	−0.313289	+	0.949658i	$0.601431\pi$
$167$	−16.9713	+	12.3304i	−1.31328	+	0.954153i	−0.999990	+	0.00449557i	$0.998569\pi$
$168$		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
$173$	7.69389	+	23.6794i	0.584956	+	1.80031i	0.599449	+	0.800413i	$0.295387\pi$
$173$	7.69389	+	23.6794i	0.584956	+	1.80031i	−0.0144929	+	0.999895i	$0.504613\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−2.90115			−0.218064
$178$		0			0
$179$	−1.71334	−	5.27311i	−0.128061	−	0.394131i	0.866385	−	0.499376i	$-0.166437\pi$
$179$	−1.71334	−	5.27311i	−0.128061	−	0.394131i	−0.994446	+	0.105245i	$0.966437\pi$
$180$		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
$183$	−5.51017	+	16.9586i	−0.407323	+	1.25361i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.22461	+	3.73609i	−0.0895520	+	0.273210i
$188$		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
$193$	−5.72807	−	4.16169i	−0.412316	−	0.299565i	0.362223	−	0.932091i	$-0.382018\pi$
$193$	−5.72807	−	4.16169i	−0.412316	−	0.299565i	−0.774539	+	0.632527i	$0.782018\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−12.5739			−0.895856			−0.447928	−	0.894070i	$-0.647838\pi$
$197$	−12.5739			−0.895856			−0.447928	+	0.894070i	$0.647838\pi$
$198$		0			0
$199$	−11.9790			−0.849171			−0.424585	−	0.905388i	$-0.639580\pi$
$199$	−11.9790			−0.849171			−0.424585	+	0.905388i	$0.639580\pi$
$200$		0			0
$201$	−2.69948	−	8.30816i	−0.190407	−	0.586012i
$202$		0			0
$203$	−2.79292	−	2.02917i	−0.196024	−	0.142420i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	4.28138	−	3.11060i	0.297576	−	0.216202i
$208$		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
$213$	6.79981	−	20.9277i	0.465915	−	1.43394i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−0.489504	−	1.50654i	−0.0332297	−	0.102271i
$218$		0			0
$219$	7.05975			0.477054
$220$		0			0
$221$	−7.80694			−0.525152
$222$		0			0
$223$	−1.81034	−	5.57166i	−0.121229	−	0.373106i	0.871966	−	0.489567i	$-0.162845\pi$
$223$	−1.81034	−	5.57166i	−0.121229	−	0.373106i	−0.993195	+	0.116461i	$0.962845\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.32412	−	4.07522i	0.0878848	−	0.270482i	−0.897449	−	0.441118i	$-0.854582\pi$
$227$	1.32412	−	4.07522i	0.0878848	−	0.270482i	0.985334	+	0.170636i	$0.0545822\pi$
$228$		0			0
$229$	−15.3127	+	11.1254i	−1.01189	+	0.735184i	−0.964606	−	0.263697i	$-0.915058\pi$
$229$	−15.3127	+	11.1254i	−1.01189	+	0.735184i	−0.0472890	+	0.998881i	$0.515058\pi$
$230$		0			0
$231$	0.919080	+	2.85370i	0.0604710	+	0.187759i
$232$		0			0
$233$	−4.69672	+	3.41237i	−0.307692	+	0.223552i	−0.730906	−	0.682478i	$-0.760902\pi$
$233$	−4.69672	+	3.41237i	−0.307692	+	0.223552i	0.423213	+	0.906030i	$0.360902\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−4.92225	−	3.57623i	−0.319735	−	0.232301i
$238$		0			0
$239$	−8.71209	−	26.8131i	−0.563538	−	1.73439i	−0.672255	−	0.740320i	$-0.734674\pi$
$239$	−8.71209	−	26.8131i	−0.563538	−	1.73439i	0.108717	−	0.994073i	$-0.465326\pi$
$240$		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
$243$	9.86496			0.632838
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−9.92855	−	7.21351i	−0.631738	−	0.458985i
$248$		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
$253$	−5.46026	−	16.9538i	−0.343283	−	1.06588i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	0.879772	−	2.70766i	0.0548786	−	0.168899i	−0.919860	−	0.392246i	$-0.871698\pi$
$257$	0.879772	−	2.70766i	0.0548786	−	0.168899i	0.974739	+	0.223347i	$0.0716982\pi$
$258$		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
$263$	12.6105			0.777594			0.388797	−	0.921323i	$-0.372891\pi$
$263$	12.6105			0.777594			0.388797	+	0.921323i	$0.372891\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	7.88977	+	24.2822i	0.482846	+	1.48605i
$268$		0			0
$269$	11.1045	+	8.06788i	0.677053	+	0.491907i	0.872379	−	0.488831i	$-0.162576\pi$
$269$	11.1045	+	8.06788i	0.677053	+	0.491907i	−0.195326	+	0.980738i	$0.562576\pi$
$270$		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
$273$	−4.81616	+	3.49914i	−0.291487	+	0.211778i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	18.0332	−	13.1019i	1.08351	−	0.787216i	0.105218	−	0.994449i	$-0.466446\pi$
$277$	18.0332	−	13.1019i	1.08351	−	0.787216i	0.978291	+	0.207234i	$0.0664460\pi$
$278$		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
$283$	6.98457	+	21.4963i	0.415189	+	1.27782i	0.912081	+	0.410009i	$0.134474\pi$
$283$	6.98457	+	21.4963i	0.415189	+	1.27782i	−0.496892	+	0.867812i	$0.665526\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.151222			−0.00892633
$288$		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
$293$	1.06476	−	3.27699i	0.0622039	−	0.191444i	−0.915125	−	0.403170i	$-0.867908\pi$
$293$	1.06476	−	3.27699i	0.0622039	−	0.191444i	0.977329	+	0.211726i	$0.0679084\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	4.15467	−	12.6753i	0.241078	−	0.735494i
$298$		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
$303$	−9.00125	−	6.53979i	−0.517109	−	0.375701i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	9.58110			0.546822			0.273411	−	0.961897i	$-0.411848\pi$
$307$	9.58110			0.546822			0.273411	+	0.961897i	$0.411848\pi$
$308$		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
$313$	10.0307	+	7.28776i	0.566971	+	0.411928i	0.834004	−	0.551759i	$-0.186043\pi$
$313$	10.0307	+	7.28776i	0.566971	+	0.411928i	−0.267033	+	0.963687i	$0.586043\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.32110	−	1.68638i	0.130366	−	0.0947165i	−0.520691	−	0.853745i	$-0.674326\pi$
$317$	2.32110	−	1.68638i	0.130366	−	0.0947165i	0.651057	+	0.759029i	$0.274326\pi$
$318$		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
$323$	−0.682637	+	2.10094i	−0.0379830	+	0.116900i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	3.17492	+	9.77141i	0.175574	+	0.540360i
$328$		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
$333$	−1.76235	−	5.42397i	−0.0965764	−	0.297232i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−9.59399	+	29.5273i	−0.522618	+	1.60845i	0.246361	+	0.969178i	$0.420765\pi$
$337$	−9.59399	+	29.5273i	−0.522618	+	1.60845i	−0.768979	+	0.639274i	$0.779235\pi$
$338$		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
$343$	−5.05340	+	3.67151i	−0.272858	+	0.198243i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	19.0758	+	13.8594i	1.02404	+	0.744012i	0.967108	−	0.254366i	$-0.0818669\pi$
$347$	19.0758	+	13.8594i	1.02404	+	0.744012i	0.0569361	+	0.998378i	$0.481867\pi$
$348$		0			0
$349$	−7.42097	−	22.8394i	−0.397236	−	1.22257i	−0.927207	−	0.374550i	$-0.877797\pi$
$349$	−7.42097	−	22.8394i	−0.397236	−	1.22257i	0.529971	−	0.848016i	$-0.322203\pi$
$350$		0			0
$351$	26.4863			1.41373
$352$		0			0
$353$	4.85808			0.258570			0.129285	−	0.991608i	$-0.458732\pi$
$353$	4.85808			0.258570			0.129285	+	0.991608i	$0.458732\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	0.866922	+	0.629856i	0.0458824	+	0.0333355i
$358$		0			0
$359$	−1.24032	+	3.81733i	−0.0654618	+	0.201471i	−0.978437	−	0.206543i	$-0.933779\pi$
$359$	−1.24032	+	3.81733i	−0.0654618	+	0.201471i	0.912976	+	0.408014i	$0.133779\pi$
$360$		0			0
$361$	12.5619	−	9.12678i	0.661154	−	0.480357i
$362$		0			0
$363$	17.6990	+	12.9993i	0.928957	+	0.682286i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−4.17659	+	12.8542i	−0.218016	+	0.670985i	0.780910	+	0.624644i	$0.214756\pi$
$367$	−4.17659	+	12.8542i	−0.218016	+	0.670985i	−0.998926	+	0.0463406i	$0.985244\pi$
$368$		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
$373$	25.5794			1.32445			0.662225	−	0.749305i	$-0.269612\pi$
$373$	25.5794			1.32445			0.662225	+	0.749305i	$0.269612\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−15.5160	−	47.7532i	−0.799112	−	2.45941i
$378$		0			0
$379$	5.21257	+	3.78715i	0.267752	+	0.194533i	0.713557	−	0.700597i	$-0.247083\pi$
$379$	5.21257	+	3.78715i	0.267752	+	0.194533i	−0.445806	+	0.895130i	$0.647083\pi$
$380$		0			0
$381$	−8.21065	+	25.2698i	−0.420644	+	1.29461i
$382$		0			0
$383$	10.9681	−	7.96880i	0.560444	−	0.407187i	−0.271177	−	0.962529i	$-0.587413\pi$
$383$	10.9681	−	7.96880i	0.560444	−	0.407187i	0.831622	+	0.555343i	$0.187413\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−8.72349	+	6.33798i	−0.443440	+	0.322178i
$388$		0			0
$389$	−4.16176	+	12.8086i	−0.211010	+	0.649421i	0.788403	+	0.615159i	$0.210908\pi$
$389$	−4.16176	+	12.8086i	−0.211010	+	0.649421i	−0.999413	+	0.0342621i	$0.989092\pi$
$390$		0			0
$391$	−5.15039	−	3.74197i	−0.260466	−	0.189240i
$392$		0			0
$393$	−10.4245	−	32.0834i	−0.525847	−	1.61839i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	19.3608			0.971689			0.485844	−	0.874045i	$-0.338512\pi$
$397$	19.3608			0.971689			0.485844	+	0.874045i	$0.338512\pi$
$398$		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
$403$	7.11954	−	21.9117i	0.354650	−	1.09150i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−19.1947	−	0.0495780i	−0.951447	−	0.00245749i
$408$		0			0
$409$	1.95665	−	1.42159i	0.0967500	−	0.0702930i	−0.538359	−	0.842716i	$-0.680955\pi$
$409$	1.95665	−	1.42159i	0.0967500	−	0.0702930i	0.635109	+	0.772423i	$0.280955\pi$
$410$		0			0
$411$	11.6332	−	35.8032i	0.573822	−	1.76604i
$412$		0			0
$413$	0.532348	+	0.386773i	0.0261951	+	0.0190319i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	12.0386			0.589532
$418$		0			0
$419$	22.0047			1.07500			0.537499	−	0.843264i	$-0.319369\pi$
$419$	22.0047			1.07500			0.537499	+	0.843264i	$0.319369\pi$
$420$		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
$423$	5.11239	+	3.71437i	0.248573	+	0.180599i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	3.27196	−	2.37722i	0.158341	−	0.115042i
$428$		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
$433$	−7.77254	+	23.9214i	−0.373524	+	1.14959i	0.570944	+	0.820989i	$0.306577\pi$
$433$	−7.77254	+	23.9214i	−0.373524	+	1.14959i	−0.944469	+	0.328601i	$0.893423\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.09252	−	9.51778i	−0.147935	−	0.455297i
$438$		0			0
$439$	34.6857			1.65546			0.827729	−	0.561129i	$-0.189633\pi$
$439$	34.6857			1.65546			0.827729	+	0.561129i	$0.189633\pi$
$440$		0			0
$441$	−6.69594			−0.318854
$442$		0			0
$443$	−0.0711411	−	0.218950i	−0.00338002	−	0.0104026i	0.949352	−	0.314214i	$-0.101741\pi$
$443$	−0.0711411	−	0.218950i	−0.00338002	−	0.0104026i	−0.952732	+	0.303811i	$0.901741\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	7.06167	−	21.7336i	0.334006	−	1.02796i
$448$		0			0
$449$	−6.09776	+	4.43028i	−0.287771	+	0.209078i	−0.722300	−	0.691580i	$-0.756915\pi$
$449$	−6.09776	+	4.43028i	−0.287771	+	0.209078i	0.434529	+	0.900658i	$0.356915\pi$
$450$		0			0
$451$	−0.897792	+	0.648748i	−0.0422754	+	0.0305484i
$452$		0			0
$453$	−15.2449	+	11.0761i	−0.716269	+	0.520400i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	8.80561	+	6.39765i	0.411909	+	0.299269i	0.774374	−	0.632728i	$-0.218065\pi$
$457$	8.80561	+	6.39765i	0.411909	+	0.299269i	−0.362465	+	0.931997i	$0.618065\pi$
$458$		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
$463$	−21.9889			−1.02191			−0.510956	−	0.859607i	$-0.670709\pi$
$463$	−21.9889			−1.02191			−0.510956	+	0.859607i	$0.670709\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.29656	−	2.39509i	−0.152547	−	0.110832i	0.508894	−	0.860829i	$-0.330055\pi$
$467$	−3.29656	−	2.39509i	−0.152547	−	0.110832i	−0.661440	+	0.749998i	$0.730055\pi$
$468$		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
$473$	11.1255	+	34.5441i	0.511551	+	1.58834i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.698526	−	2.14984i	0.0319833	−	0.0984345i
$478$		0			0
$479$	18.1820	+	13.2100i	0.830758	+	0.603581i	0.919774	−	0.392449i	$-0.128372\pi$
$479$	18.1820	+	13.2100i	0.830758	+	0.603581i	−0.0890157	+	0.996030i	$0.528372\pi$
$480$		0			0
$481$	−11.7780	−	36.2488i	−0.537029	−	1.65280i
$482$		0			0
$483$	−4.85450			−0.220887
$484$		0			0
$485$		0			0
$486$		0			0
$487$	7.08168	+	21.7952i	0.320902	+	0.987634i	0.973257	+	0.229720i	$0.0737811\pi$
$487$	7.08168	+	21.7952i	0.320902	+	0.987634i	−0.652355	+	0.757914i	$0.726219\pi$
$488$		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
$493$	−7.31195	+	5.31244i	−0.329314	+	0.239260i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.03775	+	2.93360i	−0.181118	+	0.131590i
$498$		0			0
$499$	−6.23790	+	19.1983i	−0.279247	+	0.859433i	0.708818	+	0.705392i	$0.249229\pi$
$499$	−6.23790	+	19.1983i	−0.279247	+	0.859433i	−0.988064	+	0.154041i	$0.950771\pi$
$500$		0			0
$501$	33.8807	+	24.6158i	1.51368	+	1.09975i
$502$		0			0
$503$	−11.1688	−	34.3741i	−0.497994	−	1.53267i	−0.812239	−	0.583325i	$-0.801751\pi$
$503$	−11.1688	−	34.3741i	−0.497994	−	1.53267i	0.314245	−	0.949342i	$-0.398249\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−60.6316			−2.69274
$508$		0			0
$509$	12.2057	+	37.5652i	0.541007	+	1.66505i	0.730299	+	0.683127i	$0.239381\pi$
$509$	12.2057	+	37.5652i	0.541007	+	1.66505i	−0.189292	+	0.981921i	$0.560619\pi$
$510$		0			0
$511$	−1.29543	−	0.941186i	−0.0573065	−	0.0416356i
$512$		0			0
$513$	2.31596	−	7.12778i	0.102252	−	0.314699i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	17.2389	−	12.4569i	0.758166	−	0.547853i
$518$		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
$523$	2.23834	+	1.62625i	0.0978757	+	0.0711109i	0.635647	−	0.771980i	$-0.280734\pi$
$523$	2.23834	+	1.62625i	0.0978757	+	0.0711109i	−0.537771	+	0.843091i	$0.680734\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.14715			−0.180653
$528$		0			0
$529$	5.84058			0.253938
$530$		0			0
$531$	0.442526	+	1.36196i	0.0192040	+	0.0591038i
$532$		0			0
$533$	−1.77937	−	1.29279i	−0.0770733	−	0.0559970i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−8.95479	+	6.50604i	−0.386428	+	0.280756i
$538$		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
$543$	−12.6416	+	38.9067i	−0.542501	+	1.66965i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−4.78926	−	14.7398i	−0.204774	−	0.630229i	−0.999723	−	0.0235526i	$-0.992502\pi$
$547$	−4.78926	−	14.7398i	−0.204774	−	0.630229i	0.794949	−	0.606677i	$-0.207498\pi$
$548$		0			0
$549$	8.80175			0.375650
$550$		0			0
$551$	−14.2077			−0.605267
$552$		0			0
$553$	0.426438	+	1.31244i	0.0181340	+	0.0558107i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−13.2493	+	40.7773i	−0.561393	+	1.72779i	0.117041	+	0.993127i	$0.462659\pi$
$557$	−13.2493	+	40.7773i	−0.561393	+	1.72779i	−0.678434	+	0.734662i	$0.737341\pi$
$558$		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
$563$	14.3007	−	10.3901i	0.602704	−	0.437890i	−0.244134	−	0.969742i	$-0.578504\pi$
$563$	14.3007	−	10.3901i	0.602704	−	0.437890i	0.846838	+	0.531851i	$0.178504\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−4.02412	−	2.92370i	−0.168997	−	0.122784i
$568$		0			0
$569$	−6.53602	−	20.1158i	−0.274004	−	0.843298i	−0.989481	−	0.144662i	$-0.953791\pi$
$569$	−6.53602	−	20.1158i	−0.274004	−	0.843298i	0.715477	−	0.698636i	$-0.246209\pi$
$570$		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
$573$	−17.0240			−0.711188
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−15.4228	−	11.2053i	−0.642061	−	0.466485i	0.218496	−	0.975838i	$-0.429885\pi$
$577$	−15.4228	−	11.2053i	−0.642061	−	0.466485i	−0.860558	+	0.509353i	$0.829885\pi$
$578$		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
$583$	−6.14346	−	4.48778i	−0.254436	−	0.185865i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.07979	−	3.32326i	0.0445677	−	0.137165i	−0.926297	−	0.376795i	$-0.877026\pi$
$587$	1.07979	−	3.32326i	0.0445677	−	0.137165i	0.970864	+	0.239630i	$0.0770261\pi$
$588$		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
$593$	−21.3791			−0.877933			−0.438967	−	0.898503i	$-0.644655\pi$
$593$	−21.3791			−0.877933			−0.438967	+	0.898503i	$0.644655\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	7.38995	+	22.7439i	0.302450	+	0.930847i
$598$		0			0
$599$	25.3976	+	18.4524i	1.03772	+	0.753946i	0.969839	−	0.243748i	$-0.0783769\pi$
$599$	25.3976	+	18.4524i	1.03772	+	0.753946i	0.0678787	+	0.997694i	$0.478377\pi$
$600$		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
$603$	−3.48853	+	2.53457i	−0.142064	+	0.103216i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	25.3383	−	18.4093i	1.02845	−	0.747211i	0.0604508	−	0.998171i	$-0.480746\pi$
$607$	25.3383	−	18.4093i	1.02845	−	0.747211i	0.967998	+	0.250960i	$0.0807462\pi$
$608$		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
$613$	−5.00820	−	15.4136i	−0.202279	−	0.622551i	−0.999814	−	0.0192784i	$-0.993863\pi$
$613$	−5.00820	−	15.4136i	−0.202279	−	0.622551i	0.797535	−	0.603273i	$-0.206137\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	36.1862			1.45680			0.728401	−	0.685151i	$-0.240264\pi$
$617$	36.1862			1.45680			0.728401	+	0.685151i	$0.240264\pi$
$618$		0			0
$619$	−9.73725	−	29.9682i	−0.391373	−	1.20452i	−0.931750	−	0.363099i	$-0.881719\pi$
$619$	−9.73725	−	29.9682i	−0.391373	−	1.20452i	0.540378	−	0.841423i	$-0.318281\pi$
$620$		0			0
$621$	17.4735	+	12.6953i	0.701188	+	0.509443i
$622$		0			0
$623$	1.78950	−	5.50752i	0.0716948	−	0.220654i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	9.96327	+	7.27813i	0.397894	+	0.290660i
$628$		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
$633$	−15.2874	−	11.1070i	−0.607620	−	0.441462i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−44.7495			−1.77304
$638$		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
$643$	−35.5522	−	25.8302i	−1.40204	−	1.01864i	−0.994420	−	0.105490i	$-0.966359\pi$
$643$	−35.5522	−	25.8302i	−1.40204	−	1.01864i	−0.407620	−	0.913152i	$-0.633641\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	22.9703	−	16.6889i	0.903055	−	0.656108i	−0.0361942	−	0.999345i	$-0.511523\pi$
$647$	22.9703	−	16.6889i	0.903055	−	0.656108i	0.939249	+	0.343237i	$0.111523\pi$
$648$		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
$653$	0.00734853	−	0.0226164i	0.000287570	−	0.000885050i	−0.950913	−	0.309459i	$-0.899852\pi$
$653$	0.00734853	−	0.0226164i	0.000287570	−	0.000885050i	0.951200	+	0.308574i	$0.0998519\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−1.07686	−	3.31423i	−0.0420122	−	0.129300i
$658$		0			0
$659$	−10.0841			−0.392821			−0.196410	−	0.980522i	$-0.562928\pi$
$659$	−10.0841			−0.392821			−0.196410	+	0.980522i	$0.562928\pi$
$660$		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
$663$	4.81616	+	14.8226i	0.187044	+	0.575662i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	12.6526	−	38.9407i	0.489911	−	1.50779i
$668$		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
$673$	28.2580	−	20.5307i	1.08927	−	0.791399i	0.109992	−	0.993933i	$-0.464918\pi$
$673$	28.2580	−	20.5307i	1.08927	−	0.791399i	0.979275	+	0.202534i	$0.0649176\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	15.2694	+	11.0939i	0.586851	+	0.426372i	0.841187	−	0.540744i	$-0.181857\pi$
$677$	15.2694	+	11.0939i	0.586851	+	0.426372i	−0.254337	+	0.967116i	$0.581857\pi$
$678$		0			0
$679$	−1.93878	−	5.96696i	−0.0744036	−	0.228991i
$680$		0			0
$681$	−8.55425			−0.327799
$682$		0			0
$683$	30.1188			1.15246			0.576232	−	0.817286i	$-0.304522\pi$
$683$	30.1188			1.15246			0.576232	+	0.817286i	$0.304522\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	30.5696	+	22.2101i	1.16630	+	0.847370i
$688$		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
$693$	1.19949	−	0.866754i	0.0455647	−	0.0329253i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−0.122341	+	0.376527i	−0.00463399	+	0.0142620i
$698$		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
$703$	−10.7849			−0.406759
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.779822	+	2.40004i	0.0293282	+	0.0902629i
$708$		0			0
$709$	26.7984	+	19.4701i	1.00643	+	0.731217i	0.963458	−	0.267859i	$-0.0863163\pi$
$709$	26.7984	+	19.4701i	1.00643	+	0.731217i	0.0429754	+	0.999076i	$0.486316\pi$
$710$		0			0
$711$	−0.928058	+	2.85627i	−0.0348049	+	0.107118i
$712$		0			0
$713$	15.1995	−	11.0431i	0.569225	−	0.413566i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−45.5339	+	33.0823i	−1.70050	+	1.23548i
$718$		0			0
$719$	6.87209	−	21.1501i	0.256286	−	0.788766i	−0.737288	−	0.675578i	$-0.763894\pi$
$719$	6.87209	−	21.1501i	0.256286	−	0.788766i	0.993574	−	0.113187i	$-0.0361060\pi$
$720$		0			0
$721$	4.08466	+	2.96768i	0.152121	+	0.110522i
$722$		0			0
$723$	15.5251	+	47.7814i	0.577385	+	1.77701i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−25.2768			−0.937466			−0.468733	−	0.883340i	$-0.655289\pi$
$727$	−25.2768			−0.937466			−0.468733	+	0.883340i	$0.655289\pi$
$728$		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
$733$	−8.41348	+	25.8940i	−0.310759	+	0.956417i	0.666706	+	0.745321i	$0.267704\pi$
$733$	−8.41348	+	25.8940i	−0.310759	+	0.956417i	−0.977465	+	0.211097i	$0.932296\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.44910	+	13.8142i	0.163885	+	0.508854i
$738$		0			0
$739$	−20.9752	+	15.2394i	−0.771587	+	0.560591i	−0.902442	−	0.430811i	$-0.858228\pi$
$739$	−20.9752	+	15.2394i	−0.771587	+	0.560591i	0.130855	+	0.991401i	$0.458228\pi$
$740$		0			0
$741$	−7.57091	+	23.3009i	−0.278124	+	0.855978i
$742$		0			0
$743$	6.68508	+	4.85699i	0.245252	+	0.178186i	0.703620	−	0.710577i	$-0.251566\pi$
$743$	6.68508	+	4.85699i	0.245252	+	0.178186i	−0.458368	+	0.888762i	$0.651566\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−9.69221			−0.354620
$748$		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
$753$	4.11112	+	2.98691i	0.149818	+	0.108849i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	27.0088	−	19.6231i	0.981653	−	0.713212i	0.0235752	−	0.999722i	$-0.492495\pi$
$757$	27.0088	−	19.6231i	0.981653	−	0.713212i	0.958077	+	0.286510i	$0.0924951\pi$
$758$		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
$763$	0.720113	−	2.21628i	0.0260698	−	0.0802347i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.95744	+	9.10206i	0.106787	+	0.328656i
$768$		0			0
$769$	50.2205			1.81100			0.905499	−	0.424349i	$-0.139497\pi$
$769$	50.2205			1.81100			0.905499	+	0.424349i	$0.139497\pi$
$770$		0			0
$771$	−5.68362			−0.204691
$772$		0			0
$773$	4.80308	+	14.7823i	0.172755	+	0.531684i	0.999524	−	0.0308572i	$-0.00982372\pi$
$773$	4.80308	+	14.7823i	0.172755	+	0.531684i	−0.826769	+	0.562541i	$0.809824\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1.61663	+	4.97549i	−0.0579964	+	0.178495i
$778$		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
$783$	24.8070	−	18.0233i	0.886529	−	0.644101i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	10.3252	+	7.50169i	0.368053	+	0.267406i	0.756403	−	0.654106i	$-0.226955\pi$
$787$	10.3252	+	7.50169i	0.368053	+	0.267406i	−0.388350	+	0.921512i	$0.626955\pi$
$788$		0			0
$789$	−7.77948	−	23.9428i	−0.276957	−	0.852385i
$790$		0			0
$791$	4.55425			0.161930
$792$		0			0
$793$	58.8228			2.08886
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−19.9855	−	14.5203i	−0.707923	−	0.514336i	0.174580	−	0.984643i	$-0.444143\pi$
$797$	−19.9855	−	14.5203i	−0.707923	−	0.514336i	−0.882503	+	0.470307i	$0.844143\pi$
$798$		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
$803$	−11.7286	−	0.0302939i	−0.413894	−	0.00106905i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	8.46760	−	26.0606i	0.298074	−	0.917377i
$808$		0			0
$809$	−7.44932	−	5.41225i	−0.261904	−	0.190285i	0.449082	−	0.893491i	$-0.351751\pi$
$809$	−7.44932	−	5.41225i	−0.261904	−	0.190285i	−0.710986	+	0.703206i	$0.751751\pi$
$810$		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
$813$	−37.5657			−1.31749
$814$		0			0
$815$		0			0
$816$		0			0
$817$	6.30113	+	19.3929i	0.220449	+	0.678471i
$818$		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
$823$	36.0340	−	26.1803i	1.25607	−	0.912586i	0.257509	−	0.966276i	$-0.417098\pi$
$823$	36.0340	−	26.1803i	1.25607	−	0.912586i	0.998558	+	0.0536896i	$0.0170982\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	29.2042	−	21.2181i	1.01553	−	0.737825i	0.0501675	−	0.998741i	$-0.484024\pi$
$827$	29.2042	−	21.2181i	1.01553	−	0.737825i	0.965362	+	0.260916i	$0.0840245\pi$
$828$		0			0
$829$	3.34254	−	10.2873i	0.116091	−	0.357292i	−0.876082	−	0.482162i	$-0.839852\pi$
$829$	3.34254	−	10.2873i	0.116091	−	0.357292i	0.992173	+	0.124870i	$0.0398515\pi$
$830$		0			0
$831$	−36.0006	−	26.1560i	−1.24885	−	0.907341i
$832$		0			0
$833$	2.48915	+	7.66080i	0.0862438	+	0.265431i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	14.0699			0.486326
$838$		0			0
$839$	3.28493	+	10.1100i	0.113408	+	0.349035i	0.991612	−	0.129252i	$-0.0412578\pi$
$839$	3.28493	+	10.1100i	0.113408	+	0.349035i	−0.878203	+	0.478287i	$0.841258\pi$
$840$		0			0
$841$	−23.5656	−	17.1214i	−0.812608	−	0.590394i
$842$		0			0
$843$	10.3777	−	31.9392i	0.357426	−	1.10004i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−1.51466	−	4.74489i	−0.0520442	−	0.163036i
$848$		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
$853$	21.8219	+	15.8546i	0.747169	+	0.542850i	0.894948	−	0.446171i	$-0.147213\pi$
$853$	21.8219	+	15.8546i	0.747169	+	0.542850i	−0.147779	+	0.989020i	$0.547213\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	3.11130			0.106280			0.0531400	−	0.998587i	$-0.483077\pi$
$857$	3.11130			0.106280			0.0531400	+	0.998587i	$0.483077\pi$
$858$		0			0
$859$	−31.5630			−1.07692			−0.538458	−	0.842652i	$-0.680993\pi$
$859$	−31.5630			−1.07692			−0.538458	+	0.842652i	$0.680993\pi$
$860$		0			0
$861$	0.0932897	+	0.287116i	0.00317931	+	0.00978490i
$862$		0			0
$863$	4.09044	+	2.97188i	0.139240	+	0.101164i	0.655225	−	0.755434i	$-0.272574\pi$
$863$	4.09044	+	2.97188i	0.139240	+	0.101164i	−0.515985	+	0.856598i	$0.672574\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−25.1868	+	18.2993i	−0.855388	+	0.621476i
$868$		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
$873$	4.21937	−	12.9859i	0.142804	−	0.439506i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−2.83075	−	8.71216i	−0.0955877	−	0.294189i	0.891819	−	0.452393i	$-0.149430\pi$
$877$	−2.83075	−	8.71216i	−0.0955877	−	0.294189i	−0.987406	+	0.158204i	$0.949430\pi$
$878$		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
$883$	2.52321	+	7.76566i	0.0849129	+	0.261335i	0.984494	−	0.175419i	$-0.0561280\pi$
$883$	2.52321	+	7.76566i	0.0849129	+	0.261335i	−0.899581	+	0.436754i	$0.856128\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	10.4622	−	32.1992i	0.351285	−	1.08114i	−0.606848	−	0.794818i	$-0.707566\pi$
$887$	10.4622	−	32.1992i	0.351285	−	1.08114i	0.958132	−	0.286325i	$-0.0924338\pi$
$888$		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
$893$	9.66780	−	7.02407i	0.323521	−	0.235052i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−57.1212	−	41.5010i	−1.90722	−	1.38568i
$898$		0			0
$899$	−8.24227	−	25.3671i	−0.274895	−	0.846040i
$900$		0			0
$901$	−2.71930			−0.0905929
$902$		0			0
$903$	9.89124			0.329160
$904$		0			0
$905$		0			0
$906$		0			0
$907$	8.38181	+	6.08974i	0.278314	+	0.202207i	0.718182	−	0.695856i	$-0.244975\pi$
$907$	8.38181	+	6.08974i	0.278314	+	0.202207i	−0.439868	+	0.898062i	$0.644975\pi$
$908$		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
$913$	−10.1605	+	30.9981i	−0.336263	+	1.02589i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−2.36441	+	7.27692i	−0.0780798	+	0.240305i
$918$		0			0
$919$	13.2348	+	9.61568i	0.436577	+	0.317192i	0.784273	−	0.620415i	$-0.213036\pi$
$919$	13.2348	+	9.61568i	0.436577	+	0.317192i	−0.347696	+	0.937607i	$0.613036\pi$
$920$		0			0
$921$	−5.91065	−	18.1911i	−0.194763	−	0.599417i
$922$		0			0
$923$	−72.5901			−2.38933
$924$		0			0
$925$		0			0
$926$		0			0
$927$	3.39546	+	10.4502i	0.111522	+	0.343228i
$928$		0			0
$929$	−21.6132	−	15.7029i	−0.709105	−	0.515195i	0.173780	−	0.984785i	$-0.444402\pi$
$929$	−21.6132	−	15.7029i	−0.709105	−	0.515195i	−0.882885	+	0.469589i	$0.844402\pi$
$930$		0			0
$931$	−3.91289	+	12.0426i	−0.128240	+	0.394682i
$932$		0			0
$933$	17.6694	−	12.8376i	0.578469	−	0.420283i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	13.5671	−	9.85708i	0.443218	−	0.322017i	−0.343694	−	0.939082i	$-0.611678\pi$
$937$	13.5671	−	9.85708i	0.443218	−	0.322017i	0.786912	+	0.617065i	$0.211678\pi$
$938$		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
$943$	−0.554234	−	1.70576i	−0.0180484	−	0.0555471i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	24.7264			0.803501			0.401750	−	0.915749i	$-0.368402\pi$
$947$	24.7264			0.803501			0.401750	+	0.915749i	$0.368402\pi$
$948$		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
$953$	2.32337	−	7.15058i	0.0752612	−	0.231630i	−0.906348	−	0.422532i	$-0.861141\pi$
$953$	2.32337	−	7.15058i	0.0752612	−	0.231630i	0.981609	+	0.190902i	$0.0611413\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	15.4755	+	48.0505i	0.500251	+	1.55325i
$958$		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
$963$	−5.75239	−	4.17936i	−0.185368	−	0.134678i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−15.0563			−0.484177			−0.242089	−	0.970254i	$-0.577832\pi$
$967$	−15.0563			−0.484177			−0.242089	+	0.970254i	$0.577832\pi$
$968$		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
$973$	−2.20903	−	1.60495i	−0.0708181	−	0.0514524i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−10.2666	+	7.45912i	−0.328458	+	0.238638i	−0.739776	−	0.672853i	$-0.765068\pi$
$977$	−10.2666	+	7.45912i	−0.328458	+	0.238638i	0.411318	+	0.911492i	$0.365068\pi$
$978$		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
$983$	−2.08831	+	6.42717i	−0.0666069	+	0.204995i	−0.978821	−	0.204720i	$-0.934372\pi$
$983$	−2.08831	+	6.42717i	−0.0666069	+	0.204995i	0.912214	+	0.409715i	$0.134372\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−1.79130	−	5.51304i	−0.0570176	−	0.175482i
$988$		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
$993$	16.8183	+	51.7615i	0.533713	+	1.64260i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−5.16564	+	15.8982i	−0.163598	+	0.503501i	−0.998930	−	0.0462434i	$-0.985275\pi$
$997$	−5.16564	+	15.8982i	−0.163598	+	0.503501i	0.835333	+	0.549745i	$0.185275\pi$
$998$		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	1100.2.n.f.201.2		24
5.2	odd	4		220.2.t.a.69.2	✓	24
5.3	odd	4		220.2.t.a.69.5	yes	24
5.4	even	2	inner	1100.2.n.f.201.5		24
11.4	even	5	inner	1100.2.n.f.301.2		24
20.3	even	4		880.2.cd.d.289.2		24
20.7	even	4		880.2.cd.d.289.5		24
55.2	even	20		2420.2.b.h.969.9		12
55.4	even	10	inner	1100.2.n.f.301.5		24
55.13	even	20		2420.2.b.h.969.4		12
55.37	odd	20		220.2.t.a.169.5	yes	24
55.42	odd	20		2420.2.b.i.969.9		12
55.48	odd	20		220.2.t.a.169.2	yes	24
55.53	odd	20		2420.2.b.i.969.4		12
220.103	even	20		880.2.cd.d.609.5		24
220.147	even	20		880.2.cd.d.609.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.t.a.69.2	✓	24	5.2	odd	4
220.2.t.a.69.5	yes	24	5.3	odd	4
220.2.t.a.169.2	yes	24	55.48	odd	20
220.2.t.a.169.5	yes	24	55.37	odd	20
880.2.cd.d.289.2		24	20.3	even	4
880.2.cd.d.289.5		24	20.7	even	4
880.2.cd.d.609.2		24	220.147	even	20
880.2.cd.d.609.5		24	220.103	even	20
1100.2.n.f.201.2		24	1.1	even	1	trivial
1100.2.n.f.201.5		24	5.4	even	2	inner
1100.2.n.f.301.2		24	11.4	even	5	inner
1100.2.n.f.301.5		24	55.4	even	10	inner
2420.2.b.h.969.4		12	55.13	even	20
2420.2.b.h.969.9		12	55.2	even	20
2420.2.b.i.969.4		12	55.53	odd	20
2420.2.b.i.969.9		12	55.42	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.n (of order \(5\), degree \(4\), minimal)

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

Introduction

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Database

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