LMFDB - Embedded newform 1120.2.bi.a.463.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1120,2,Mod(463,1120)] 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("1120.463"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1120, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.bi (of order $4$, degree $2$, not 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:	$8.94324502638$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			463.20
Character	$\chi$	$=$	1120.463
Dual form			1120.2.bi.a.687.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.161197 + 0.161197i) q^{3} +(-0.0283969 - 2.23589i) q^{5} +(0.707107 + 0.707107i) q^{7} -2.94803i q^{9} -4.93386 q^{11} +(-4.05315 + 4.05315i) q^{13} +(0.355840 - 0.364995i) q^{15} +(-0.793172 + 0.793172i) q^{17} -5.81519i q^{19} +0.227966i q^{21} +(-0.565908 + 0.565908i) q^{23} +(-4.99839 + 0.126984i) q^{25} +(0.958802 - 0.958802i) q^{27} -8.34882 q^{29} +6.01380i q^{31} +(-0.795321 - 0.795321i) q^{33} +(1.56093 - 1.60109i) q^{35} +(3.79589 + 3.79589i) q^{37} -1.30671 q^{39} +1.53295 q^{41} +(3.41409 + 3.41409i) q^{43} +(-6.59147 + 0.0837149i) q^{45} +(-3.43120 - 3.43120i) q^{47} +1.00000i q^{49} -0.255713 q^{51} +(-3.22442 + 3.22442i) q^{53} +(0.140106 + 11.0316i) q^{55} +(0.937389 - 0.937389i) q^{57} +1.96633i q^{59} -5.27850i q^{61} +(2.08457 - 2.08457i) q^{63} +(9.17749 + 8.94730i) q^{65} +(5.02471 - 5.02471i) q^{67} -0.182445 q^{69} -6.02581i q^{71} +(-10.7665 - 10.7665i) q^{73} +(-0.826192 - 0.785253i) q^{75} +(-3.48876 - 3.48876i) q^{77} -8.60880 q^{79} -8.53498 q^{81} +(-10.2290 - 10.2290i) q^{83} +(1.79597 + 1.75092i) q^{85} +(-1.34580 - 1.34580i) q^{87} -0.308629i q^{89} -5.73203 q^{91} +(-0.969404 + 0.969404i) q^{93} +(-13.0021 + 0.165133i) q^{95} +(3.04108 - 3.04108i) q^{97} +14.5452i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 8 q^{17} - 8 q^{25} + 64 q^{43} + 32 q^{51} - 8 q^{65} - 40 q^{73} - 112 q^{75} - 72 q^{81} - 80 q^{83} - 8 q^{97}+O(q^{100}) $ 72 * q + 8 * q^17 - 8 * q^25 + 64 * q^43 + 32 * q^51 - 8 * q^65 - 40 * q^73 - 112 * q^75 - 72 * q^81 - 80 * q^83 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.161197	+	0.161197i	0.0930669	+	0.0930669i	0.752107	−	0.659041i	$-0.229037\pi$
$3$	0.161197	+	0.161197i	0.0930669	+	0.0930669i	−0.659041	+	0.752107i	$0.729037\pi$
$4$		0			0
$5$	−0.0283969	−	2.23589i	−0.0126995	−	0.999919i
$5$	−0.0283969	−	2.23589i	−0.0126995	−	0.999919i
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$		0			0
$9$		−	2.94803i		−	0.982677i
$10$		0			0
$11$	−4.93386			−1.48761			−0.743807	−	0.668394i	$-0.766982\pi$
$11$	−4.93386			−1.48761			−0.743807	+	0.668394i	$0.766982\pi$
$12$		0			0
$13$	−4.05315	+	4.05315i	−1.12414	+	1.12414i	−0.133031	+	0.991112i	$0.542471\pi$
$13$	−4.05315	+	4.05315i	−1.12414	+	1.12414i	−0.991112	+	0.133031i	$0.957529\pi$
$14$		0			0
$15$	0.355840	−	0.364995i	0.0918775	−	0.0942413i
$16$		0			0
$17$	−0.793172	+	0.793172i	−0.192372	+	0.192372i	−0.796720	−	0.604348i	$-0.793434\pi$
$17$	−0.793172	+	0.793172i	−0.192372	+	0.192372i	0.604348	+	0.796720i	$0.293434\pi$
$18$		0			0
$19$		−	5.81519i		−	1.33410i	−0.745015	−	0.667048i	$-0.767558\pi$
$19$		−	5.81519i		−	1.33410i	0.745015	−	0.667048i	$-0.232442\pi$
$20$		0			0
$21$			0.227966i			0.0497463i
$22$		0			0
$23$	−0.565908	+	0.565908i	−0.118000	+	0.118000i	−0.763641	−	0.645641i	$-0.776590\pi$
$23$	−0.565908	+	0.565908i	−0.118000	+	0.118000i	0.645641	+	0.763641i	$0.276590\pi$
$24$		0			0
$25$	−4.99839	+	0.126984i	−0.999677	+	0.0253969i
$26$		0			0
$27$	0.958802	−	0.958802i	0.184522	−	0.184522i
$28$		0			0
$29$	−8.34882			−1.55034			−0.775169	−	0.631754i	$-0.782335\pi$
$29$	−8.34882			−1.55034			−0.775169	+	0.631754i	$0.782335\pi$
$30$		0			0
$31$			6.01380i			1.08011i	0.841629	+	0.540055i	$0.181597\pi$
$31$			6.01380i			1.08011i	−0.841629	+	0.540055i	$0.818403\pi$
$32$		0			0
$33$	−0.795321	−	0.795321i	−0.138448	−	0.138448i
$34$		0			0
$35$	1.56093	−	1.60109i	0.263846	−	0.270634i
$36$		0			0
$37$	3.79589	+	3.79589i	0.624040	+	0.624040i	0.946562	−	0.322522i	$-0.104531\pi$
$37$	3.79589	+	3.79589i	0.624040	+	0.624040i	−0.322522	+	0.946562i	$0.604531\pi$
$38$		0			0
$39$	−1.30671			−0.209241
$40$		0			0
$41$	1.53295			0.239406			0.119703	−	0.992810i	$-0.461806\pi$
$41$	1.53295			0.239406			0.119703	+	0.992810i	$0.461806\pi$
$42$		0			0
$43$	3.41409	+	3.41409i	0.520643	+	0.520643i	0.917766	−	0.397122i	$-0.129991\pi$
$43$	3.41409	+	3.41409i	0.520643	+	0.520643i	−0.397122	+	0.917766i	$0.629991\pi$
$44$		0			0
$45$	−6.59147	+	0.0837149i	−0.982598	+	0.0124795i
$46$		0			0
$47$	−3.43120	−	3.43120i	−0.500492	−	0.500492i	0.411099	−	0.911591i	$-0.365145\pi$
$47$	−3.43120	−	3.43120i	−0.500492	−	0.500492i	−0.911591	+	0.411099i	$0.865145\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	−0.255713			−0.0358070
$52$		0			0
$53$	−3.22442	+	3.22442i	−0.442909	+	0.442909i	−0.892988	−	0.450080i	$-0.851396\pi$
$53$	−3.22442	+	3.22442i	−0.442909	+	0.442909i	0.450080	+	0.892988i	$0.351396\pi$
$54$		0			0
$55$	0.140106	+	11.0316i	0.0188919	+	1.48749i
$56$		0			0
$57$	0.937389	−	0.937389i	0.124160	−	0.124160i
$58$		0			0
$59$			1.96633i			0.255994i	0.991775	+	0.127997i	$0.0408548\pi$
$59$			1.96633i			0.255994i	−0.991775	+	0.127997i	$0.959145\pi$
$60$		0			0
$61$		−	5.27850i		−	0.675843i	−0.941174	−	0.337922i	$-0.890276\pi$
$61$		−	5.27850i		−	0.675843i	0.941174	−	0.337922i	$-0.109724\pi$
$62$		0			0
$63$	2.08457	−	2.08457i	0.262632	−	0.262632i
$64$		0			0
$65$	9.17749	+	8.94730i	1.13833	+	1.10978i
$66$		0			0
$67$	5.02471	−	5.02471i	0.613866	−	0.613866i	−0.330085	−	0.943951i	$-0.607077\pi$
$67$	5.02471	−	5.02471i	0.613866	−	0.613866i	0.943951	+	0.330085i	$0.107077\pi$
$68$		0			0
$69$	−0.182445			−0.0219638
$70$		0			0
$71$		−	6.02581i		−	0.715132i	−0.933888	−	0.357566i	$-0.883607\pi$
$71$		−	6.02581i		−	0.715132i	0.933888	−	0.357566i	$-0.116393\pi$
$72$		0			0
$73$	−10.7665	−	10.7665i	−1.26013	−	1.26013i	−0.951030	−	0.309098i	$-0.899973\pi$
$73$	−10.7665	−	10.7665i	−1.26013	−	1.26013i	−0.309098	−	0.951030i	$-0.600027\pi$
$74$		0			0
$75$	−0.826192	−	0.785253i	−0.0954005	−	0.0906733i
$76$		0			0
$77$	−3.48876	−	3.48876i	−0.397582	−	0.397582i
$78$		0			0
$79$	−8.60880			−0.968565			−0.484283	−	0.874912i	$-0.660919\pi$
$79$	−8.60880			−0.968565			−0.484283	+	0.874912i	$0.660919\pi$
$80$		0			0
$81$	−8.53498			−0.948331
$82$		0			0
$83$	−10.2290	−	10.2290i	−1.12277	−	1.12277i	−0.991323	−	0.131451i	$-0.958036\pi$
$83$	−10.2290	−	10.2290i	−1.12277	−	1.12277i	−0.131451	−	0.991323i	$-0.541964\pi$
$84$		0			0
$85$	1.79597	+	1.75092i	0.194800	+	0.189914i
$86$		0			0
$87$	−1.34580	−	1.34580i	−0.144285	−	0.144285i
$88$		0			0
$89$		−	0.308629i		−	0.0327146i	−0.999866	−	0.0163573i	$-0.994793\pi$
$89$		−	0.308629i		−	0.0327146i	0.999866	−	0.0163573i	$-0.00520692\pi$
$90$		0			0
$91$	−5.73203			−0.600880
$92$		0			0
$93$	−0.969404	+	0.969404i	−0.100523	+	0.100523i
$94$		0			0
$95$	−13.0021	+	0.165133i	−1.33399	+	0.0169423i
$96$		0			0
$97$	3.04108	−	3.04108i	0.308775	−	0.308775i	−0.535659	−	0.844434i	$-0.679937\pi$
$97$	3.04108	−	3.04108i	0.308775	−	0.308775i	0.844434	+	0.535659i	$0.179937\pi$
$98$		0			0
$99$			14.5452i			1.46184i
$100$		0			0
$101$		−	3.91032i		−	0.389091i	−0.980893	−	0.194546i	$-0.937677\pi$
$101$		−	3.91032i		−	0.389091i	0.980893	−	0.194546i	$-0.0623232\pi$
$102$		0			0
$103$	−4.13590	+	4.13590i	−0.407522	+	0.407522i	−0.880874	−	0.473352i	$-0.843044\pi$
$103$	−4.13590	+	4.13590i	−0.407522	+	0.407522i	0.473352	+	0.880874i	$0.343044\pi$
$104$		0			0
$105$	0.509707	−	0.00647353i	0.0497423	−	0.000631752i
$106$		0			0
$107$	9.50203	−	9.50203i	0.918596	−	0.918596i	−0.0783311	−	0.996927i	$-0.524959\pi$
$107$	9.50203	−	9.50203i	0.918596	−	0.918596i	0.996927	+	0.0783311i	$0.0249591\pi$
$108$		0			0
$109$	16.9042			1.61913			0.809563	−	0.587032i	$-0.199704\pi$
$109$	16.9042			1.61913			0.809563	+	0.587032i	$0.199704\pi$
$110$		0			0
$111$			1.22377i			0.116155i
$112$		0			0
$113$	−10.7566	−	10.7566i	−1.01190	−	1.01190i	−0.999928	−	0.0119714i	$-0.996189\pi$
$113$	−10.7566	−	10.7566i	−1.01190	−	1.01190i	−0.0119714	−	0.999928i	$-0.503811\pi$
$114$		0			0
$115$	1.28138	+	1.24924i	0.119489	+	0.116492i
$116$		0			0
$117$	11.9488	+	11.9488i	1.10467	+	1.10467i
$118$		0			0
$119$	−1.12171			−0.102827
$120$		0			0
$121$	13.3429			1.21300
$122$		0			0
$123$	0.247106	+	0.247106i	0.0222808	+	0.0222808i
$124$		0			0
$125$	0.425862	+	11.1722i	0.0380902	+	0.999274i
$126$		0			0
$127$	7.44595	+	7.44595i	0.660722	+	0.660722i	0.955550	−	0.294829i	$-0.0952626\pi$
$127$	7.44595	+	7.44595i	0.660722	+	0.660722i	−0.294829	+	0.955550i	$0.595263\pi$
$128$		0			0
$129$			1.10068i			0.0969093i
$130$		0			0
$131$	−19.2815			−1.68464			−0.842318	−	0.538981i	$-0.818809\pi$
$131$	−19.2815			−1.68464			−0.842318	+	0.538981i	$0.818809\pi$
$132$		0			0
$133$	4.11196	−	4.11196i	0.356552	−	0.356552i
$134$		0			0
$135$	−2.17100	−	2.11655i	−0.186850	−	0.182163i
$136$		0			0
$137$	8.17817	−	8.17817i	0.698708	−	0.698708i	−0.265424	−	0.964132i	$-0.585512\pi$
$137$	8.17817	−	8.17817i	0.698708	−	0.698708i	0.964132	+	0.265424i	$0.0855118\pi$
$138$		0			0
$139$			9.23438i			0.783250i	0.920125	+	0.391625i	$0.128087\pi$
$139$			9.23438i			0.783250i	−0.920125	+	0.391625i	$0.871913\pi$
$140$		0			0
$141$		−	1.10620i		−	0.0931585i
$142$		0			0
$143$	19.9977	−	19.9977i	1.67229	−	1.67229i
$144$		0			0
$145$	0.237080	+	18.6670i	0.0196885	+	1.55021i
$146$		0			0
$147$	−0.161197	+	0.161197i	−0.0132953	+	0.0132953i
$148$		0			0
$149$	−4.94060			−0.404750			−0.202375	−	0.979308i	$-0.564866\pi$
$149$	−4.94060			−0.404750			−0.202375	+	0.979308i	$0.564866\pi$
$150$		0			0
$151$		−	8.15959i		−	0.664018i	−0.943276	−	0.332009i	$-0.892274\pi$
$151$		−	8.15959i		−	0.664018i	0.943276	−	0.332009i	$-0.107726\pi$
$152$		0			0
$153$	2.33829	+	2.33829i	0.189040	+	0.189040i
$154$		0			0
$155$	13.4462	−	0.170773i	1.08002	−	0.0137168i
$156$		0			0
$157$	0.893861	+	0.893861i	0.0713379	+	0.0713379i	0.741876	−	0.670538i	$-0.233937\pi$
$157$	0.893861	+	0.893861i	0.0713379	+	0.0713379i	−0.670538	+	0.741876i	$0.733937\pi$
$158$		0			0
$159$	−1.03953			−0.0824403
$160$		0			0
$161$	−0.800315			−0.0630737
$162$		0			0
$163$	14.3530	+	14.3530i	1.12422	+	1.12422i	0.991101	+	0.133114i	$0.0424978\pi$
$163$	14.3530	+	14.3530i	1.12422	+	1.12422i	0.133114	+	0.991101i	$0.457502\pi$
$164$		0			0
$165$	−1.75566	+	1.80083i	−0.136678	+	0.140195i
$166$		0			0
$167$	−4.02024	−	4.02024i	−0.311095	−	0.311095i	0.534239	−	0.845334i	$-0.320598\pi$
$167$	−4.02024	−	4.02024i	−0.311095	−	0.311095i	−0.845334	+	0.534239i	$0.820598\pi$
$168$		0			0
$169$		−	19.8561i		−	1.52739i
$170$		0			0
$171$	−17.1434			−1.31099
$172$		0			0
$173$	11.2339	−	11.2339i	0.854097	−	0.854097i	−0.136538	−	0.990635i	$-0.543598\pi$
$173$	11.2339	−	11.2339i	0.854097	−	0.854097i	0.990635	+	0.136538i	$0.0435975\pi$
$174$		0			0
$175$	−3.62419	−	3.44460i	−0.273963	−	0.260387i
$176$		0			0
$177$	−0.316965	+	0.316965i	−0.0238246	+	0.0238246i
$178$		0			0
$179$			9.06992i			0.677917i	0.940801	+	0.338959i	$0.110075\pi$
$179$			9.06992i			0.677917i	−0.940801	+	0.338959i	$0.889925\pi$
$180$		0			0
$181$		−	15.8706i		−	1.17965i	−0.807531	−	0.589826i	$-0.799196\pi$
$181$		−	15.8706i		−	1.17965i	0.807531	−	0.589826i	$-0.200804\pi$
$182$		0			0
$183$	0.850877	−	0.850877i	0.0628986	−	0.0628986i
$184$		0			0
$185$	8.37939	−	8.59497i	0.616065	−	0.631915i
$186$		0			0
$187$	3.91340	−	3.91340i	0.286176	−	0.286176i
$188$		0			0
$189$	1.35595			0.0986309
$190$		0			0
$191$			15.0376i			1.08809i	0.839057	+	0.544043i	$0.183107\pi$
$191$			15.0376i			1.08809i	−0.839057	+	0.544043i	$0.816893\pi$
$192$		0			0
$193$	5.19746	+	5.19746i	0.374121	+	0.374121i	0.868976	−	0.494854i	$-0.164779\pi$
$193$	5.19746	+	5.19746i	0.374121	+	0.374121i	−0.494854	+	0.868976i	$0.664779\pi$
$194$		0			0
$195$	0.0371065	+	2.92165i	0.00265725	+	0.209224i
$196$		0			0
$197$	4.61388	+	4.61388i	0.328725	+	0.328725i	0.852102	−	0.523376i	$-0.175328\pi$
$197$	4.61388	+	4.61388i	0.328725	+	0.328725i	−0.523376	+	0.852102i	$0.675328\pi$
$198$		0			0
$199$	−4.66360			−0.330594			−0.165297	−	0.986244i	$-0.552858\pi$
$199$	−4.66360			−0.330594			−0.165297	+	0.986244i	$0.552858\pi$
$200$		0			0
$201$	1.61993			0.114261
$202$		0			0
$203$	−5.90351	−	5.90351i	−0.414345	−	0.414345i
$204$		0			0
$205$	−0.0435309	−	3.42750i	−0.00304033	−	0.239387i
$206$		0			0
$207$	1.66832	+	1.66832i	0.115956	+	0.115956i
$208$		0			0
$209$			28.6913i			1.98462i
$210$		0			0
$211$	5.48822			0.377824			0.188912	−	0.981994i	$-0.439504\pi$
$211$	5.48822			0.377824			0.188912	+	0.981994i	$0.439504\pi$
$212$		0			0
$213$	0.971340	−	0.971340i	0.0665551	−	0.0665551i
$214$		0			0
$215$	7.53656	−	7.73046i	0.513989	−	0.527213i
$216$		0			0
$217$	−4.25240	+	4.25240i	−0.288672	+	0.288672i
$218$		0			0
$219$		−	3.47106i		−	0.234552i
$220$		0			0
$221$		−	6.42969i		−	0.432508i
$222$		0			0
$223$	−5.41097	+	5.41097i	−0.362346	+	0.362346i	−0.864676	−	0.502330i	$-0.832476\pi$
$223$	−5.41097	+	5.41097i	−0.362346	+	0.362346i	0.502330	+	0.864676i	$0.332476\pi$
$224$		0			0
$225$	0.374354	+	14.7354i	0.0249569	+	0.982360i
$226$		0			0
$227$	0.614111	−	0.614111i	0.0407600	−	0.0407600i	−0.686433	−	0.727193i	$-0.740825\pi$
$227$	0.614111	−	0.614111i	0.0407600	−	0.0407600i	0.727193	+	0.686433i	$0.240825\pi$
$228$		0			0
$229$	−18.2039			−1.20295			−0.601475	−	0.798892i	$-0.705420\pi$
$229$	−18.2039			−1.20295			−0.601475	+	0.798892i	$0.705420\pi$
$230$		0			0
$231$		−	1.12475i		−	0.0740034i
$232$		0			0
$233$	11.7656	+	11.7656i	0.770789	+	0.770789i	0.978245	−	0.207455i	$-0.0665181\pi$
$233$	11.7656	+	11.7656i	0.770789	+	0.770789i	−0.207455	+	0.978245i	$0.566518\pi$
$234$		0			0
$235$	−7.57435	+	7.76922i	−0.494096	+	0.506808i
$236$		0			0
$237$	−1.38771	−	1.38771i	−0.0901413	−	0.0901413i
$238$		0			0
$239$	8.80908			0.569812			0.284906	−	0.958555i	$-0.408038\pi$
$239$	8.80908			0.569812			0.284906	+	0.958555i	$0.408038\pi$
$240$		0			0
$241$	−21.3908			−1.37791			−0.688953	−	0.724806i	$-0.741929\pi$
$241$	−21.3908			−1.37791			−0.688953	+	0.724806i	$0.741929\pi$
$242$		0			0
$243$	−4.25222	−	4.25222i	−0.272780	−	0.272780i
$244$		0			0
$245$	2.23589	−	0.0283969i	0.142846	−	0.00181421i
$246$		0			0
$247$	23.5699	+	23.5699i	1.49971	+	1.49971i
$248$		0			0
$249$		−	3.29774i		−	0.208986i
$250$		0			0
$251$	31.3913			1.98140			0.990701	−	0.136057i	$-0.0434431\pi$
$251$	31.3913			1.98140			0.990701	+	0.136057i	$0.0434431\pi$
$252$		0			0
$253$	2.79211	−	2.79211i	0.175538	−	0.175538i
$254$		0			0
$255$	0.00726145	+	0.571746i	0.000454730	+	0.0358041i
$256$		0			0
$257$	−2.22517	+	2.22517i	−0.138802	+	0.138802i	−0.773094	−	0.634292i	$-0.781292\pi$
$257$	−2.22517	+	2.22517i	−0.138802	+	0.138802i	0.634292	+	0.773094i	$0.281292\pi$
$258$		0			0
$259$			5.36820i			0.333563i
$260$		0			0
$261$			24.6126i			1.52348i
$262$		0			0
$263$	5.98405	−	5.98405i	0.368993	−	0.368993i	−0.498117	−	0.867110i	$-0.665975\pi$
$263$	5.98405	−	5.98405i	0.368993	−	0.368993i	0.867110	+	0.498117i	$0.165975\pi$
$264$		0			0
$265$	7.30101	+	7.11789i	0.448498	+	0.437248i
$266$		0			0
$267$	0.0497499	−	0.0497499i	0.00304465	−	0.00304465i
$268$		0			0
$269$	0.590188			0.0359844			0.0179922	−	0.999838i	$-0.494273\pi$
$269$	0.590188			0.0359844			0.0179922	+	0.999838i	$0.494273\pi$
$270$		0			0
$271$		−	16.0576i		−	0.975431i	−0.873003	−	0.487715i	$-0.837830\pi$
$271$		−	16.0576i		−	0.975431i	0.873003	−	0.487715i	$-0.162170\pi$
$272$		0			0
$273$	−0.923983	−	0.923983i	−0.0559220	−	0.0559220i
$274$		0			0
$275$	24.6613	−	0.626523i	1.48713	−	0.0377808i
$276$		0			0
$277$	−10.0221	−	10.0221i	−0.602172	−	0.602172i	0.338716	−	0.940889i	$-0.390007\pi$
$277$	−10.0221	−	10.0221i	−0.602172	−	0.602172i	−0.940889	+	0.338716i	$0.890007\pi$
$278$		0			0
$279$	17.7289			1.06140
$280$		0			0
$281$	3.54046			0.211206			0.105603	−	0.994408i	$-0.466323\pi$
$281$	3.54046			0.211206			0.105603	+	0.994408i	$0.466323\pi$
$282$		0			0
$283$	1.18755	+	1.18755i	0.0705928	+	0.0705928i	0.741522	−	0.670929i	$-0.234104\pi$
$283$	1.18755	+	1.18755i	0.0705928	+	0.0705928i	−0.670929	+	0.741522i	$0.734104\pi$
$284$		0			0
$285$	−2.12251	−	2.06928i	−0.125727	−	0.122573i
$286$		0			0
$287$	1.08396	+	1.08396i	0.0639840	+	0.0639840i
$288$		0			0
$289$			15.7418i			0.925986i
$290$		0			0
$291$	0.980423			0.0574734
$292$		0			0
$293$	10.7306	−	10.7306i	0.626889	−	0.626889i	−0.320395	−	0.947284i	$-0.603816\pi$
$293$	10.7306	−	10.7306i	0.626889	−	0.626889i	0.947284	+	0.320395i	$0.103816\pi$
$294$		0			0
$295$	4.39649	−	0.0558376i	0.255973	−	0.00325099i
$296$		0			0
$297$	−4.73059	+	4.73059i	−0.274497	+	0.274497i
$298$		0			0
$299$		−	4.58743i		−	0.265298i
$300$		0			0
$301$			4.82825i			0.278296i
$302$		0			0
$303$	0.630330	−	0.630330i	0.0362115	−	0.0362115i
$304$		0			0
$305$	−11.8021	+	0.149893i	−0.675789	+	0.00858285i
$306$		0			0
$307$	6.20070	−	6.20070i	0.353893	−	0.353893i	−0.507663	−	0.861556i	$-0.669491\pi$
$307$	6.20070	−	6.20070i	0.353893	−	0.353893i	0.861556	+	0.507663i	$0.169491\pi$
$308$		0			0
$309$	−1.33339			−0.0758536
$310$		0			0
$311$		−	22.9744i		−	1.30276i	−0.758752	−	0.651380i	$-0.774191\pi$
$311$		−	22.9744i		−	1.30276i	0.758752	−	0.651380i	$-0.225809\pi$
$312$		0			0
$313$	−15.3383	−	15.3383i	−0.866974	−	0.866974i	0.125162	−	0.992136i	$-0.460055\pi$
$313$	−15.3383	−	15.3383i	−0.866974	−	0.866974i	−0.992136	+	0.125162i	$0.960055\pi$
$314$		0			0
$315$	−4.72007	−	4.60168i	−0.265946	−	0.259275i
$316$		0			0
$317$	1.54114	+	1.54114i	0.0865589	+	0.0865589i	0.749060	−	0.662502i	$-0.230505\pi$
$317$	1.54114	+	1.54114i	0.0865589	+	0.0865589i	−0.662502	+	0.749060i	$0.730505\pi$
$318$		0			0
$319$	41.1919			2.30630
$320$		0			0
$321$	3.06339			0.170982
$322$		0			0
$323$	4.61244	+	4.61244i	0.256643	+	0.256643i
$324$		0			0
$325$	19.7445	−	20.7739i	1.09523	−	1.15233i
$326$		0			0
$327$	2.72490	+	2.72490i	0.150687	+	0.150687i
$328$		0			0
$329$		−	4.85245i		−	0.267524i
$330$		0			0
$331$	−23.1716			−1.27363			−0.636814	−	0.771017i	$-0.719748\pi$
$331$	−23.1716			−1.27363			−0.636814	+	0.771017i	$0.719748\pi$
$332$		0			0
$333$	11.1904	−	11.1904i	0.613230	−	0.613230i
$334$		0			0
$335$	−11.3774	−	11.0920i	−0.621613	−	0.606021i
$336$		0			0
$337$	8.31200	−	8.31200i	0.452783	−	0.452783i	−0.443494	−	0.896277i	$-0.646261\pi$
$337$	8.31200	−	8.31200i	0.452783	−	0.452783i	0.896277	+	0.443494i	$0.146261\pi$
$338$		0			0
$339$		−	3.46787i		−	0.188349i
$340$		0			0
$341$		−	29.6712i		−	1.60679i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$		0			0
$345$	0.00518087	+	0.407926i	0.000278928	+	0.0219620i
$346$		0			0
$347$	−2.43072	+	2.43072i	−0.130488	+	0.130488i	−0.769334	−	0.638846i	$-0.779412\pi$
$347$	−2.43072	+	2.43072i	−0.130488	+	0.130488i	0.638846	+	0.769334i	$0.279412\pi$
$348$		0			0
$349$	4.27164			0.228656			0.114328	−	0.993443i	$-0.463529\pi$
$349$	4.27164			0.228656			0.114328	+	0.993443i	$0.463529\pi$
$350$		0			0
$351$			7.77235i			0.414857i
$352$		0			0
$353$	1.56759	+	1.56759i	0.0834343	+	0.0834343i	0.747592	−	0.664158i	$-0.231210\pi$
$353$	1.56759	+	1.56759i	0.0834343	+	0.0834343i	−0.664158	+	0.747592i	$0.731210\pi$
$354$		0			0
$355$	−13.4730	+	0.171114i	−0.715075	+	0.00908180i
$356$		0			0
$357$	−0.180816	−	0.180816i	−0.00956982	−	0.00956982i
$358$		0			0
$359$	−14.1532			−0.746975			−0.373488	−	0.927635i	$-0.621838\pi$
$359$	−14.1532			−0.746975			−0.373488	+	0.927635i	$0.621838\pi$
$360$		0			0
$361$	−14.8164			−0.779813
$362$		0			0
$363$	2.15084	+	2.15084i	0.112890	+	0.112890i
$364$		0			0
$365$	−23.7670	+	24.3785i	−1.24402	+	1.27603i
$366$		0			0
$367$	13.0374	+	13.0374i	0.680544	+	0.680544i	0.960123	−	0.279578i	$-0.0901947\pi$
$367$	13.0374	+	13.0374i	0.680544	+	0.680544i	−0.279578	+	0.960123i	$0.590195\pi$
$368$		0			0
$369$		−	4.51918i		−	0.235259i
$370$		0			0
$371$	−4.56002			−0.236745
$372$		0			0
$373$	−8.98073	+	8.98073i	−0.465004	+	0.465004i	−0.900292	−	0.435287i	$-0.856647\pi$
$373$	−8.98073	+	8.98073i	−0.465004	+	0.465004i	0.435287	+	0.900292i	$0.356647\pi$
$374$		0			0
$375$	−1.73228	+	1.86957i	−0.0894544	+	0.0965443i
$376$		0			0
$377$	33.8391	−	33.8391i	1.74280	−	1.74280i
$378$		0			0
$379$			10.9173i			0.560785i	0.959885	+	0.280392i	$0.0904646\pi$
$379$			10.9173i			0.560785i	−0.959885	+	0.280392i	$0.909535\pi$
$380$		0			0
$381$			2.40052i			0.122983i
$382$		0			0
$383$	3.00460	−	3.00460i	0.153528	−	0.153528i	−0.626164	−	0.779692i	$-0.715376\pi$
$383$	3.00460	−	3.00460i	0.153528	−	0.153528i	0.779692	+	0.626164i	$0.215376\pi$
$384$		0			0
$385$	−7.70141	+	7.89955i	−0.392500	+	0.402599i
$386$		0			0
$387$	10.0648	−	10.0648i	0.511624	−	0.511624i
$388$		0			0
$389$	−25.6455			−1.30028			−0.650140	−	0.759814i	$-0.725290\pi$
$389$	−25.6455			−1.30028			−0.650140	+	0.759814i	$0.725290\pi$
$390$		0			0
$391$		−	0.897725i		−	0.0453999i
$392$		0			0
$393$	−3.10812	−	3.10812i	−0.156784	−	0.156784i
$394$		0			0
$395$	0.244463	+	19.2483i	0.0123003	+	0.968487i
$396$		0			0
$397$	6.63522	+	6.63522i	0.333012	+	0.333012i	0.853729	−	0.520717i	$-0.174335\pi$
$397$	6.63522	+	6.63522i	0.333012	+	0.333012i	−0.520717	+	0.853729i	$0.674335\pi$
$398$		0			0
$399$	1.32567			0.0663664
$400$		0			0
$401$	19.7675			0.987141			0.493570	−	0.869706i	$-0.335692\pi$
$401$	19.7675			0.987141			0.493570	+	0.869706i	$0.335692\pi$
$402$		0			0
$403$	−24.3749	−	24.3749i	−1.21420	−	1.21420i
$404$		0			0
$405$	0.242367	+	19.0833i	0.0120433	+	0.948255i
$406$		0			0
$407$	−18.7284	−	18.7284i	−0.928331	−	0.928331i
$408$		0			0
$409$		−	7.16001i		−	0.354040i	−0.984207	−	0.177020i	$-0.943354\pi$
$409$		−	7.16001i		−	0.354040i	0.984207	−	0.177020i	$-0.0566457\pi$
$410$		0			0
$411$	2.63659			0.130053
$412$		0			0
$413$	−1.39040	+	1.39040i	−0.0684173	+	0.0684173i
$414$		0			0
$415$	−22.5803	+	23.1613i	−1.10842	+	1.13694i
$416$		0			0
$417$	−1.48855	+	1.48855i	−0.0728946	+	0.0728946i
$418$		0			0
$419$		−	27.2101i		−	1.32930i	−0.747156	−	0.664649i	$-0.768581\pi$
$419$		−	27.2101i		−	1.32930i	0.747156	−	0.664649i	$-0.231419\pi$
$420$		0			0
$421$		−	7.10155i		−	0.346108i	−0.984912	−	0.173054i	$-0.944636\pi$
$421$		−	7.10155i		−	0.346108i	0.984912	−	0.173054i	$-0.0553636\pi$
$422$		0			0
$423$	−10.1153	+	10.1153i	−0.491822	+	0.491822i
$424$		0			0
$425$	3.86386	−	4.06530i	0.187425	−	0.197196i
$426$		0			0
$427$	3.73247	−	3.73247i	0.180627	−	0.180627i
$428$		0			0
$429$	6.44712			0.311270
$430$		0			0
$431$		−	30.0783i		−	1.44882i	−0.689369	−	0.724410i	$-0.742112\pi$
$431$		−	30.0783i		−	1.44882i	0.689369	−	0.724410i	$-0.257888\pi$
$432$		0			0
$433$	23.6663	+	23.6663i	1.13733	+	1.13733i	0.988927	+	0.148403i	$0.0474133\pi$
$433$	23.6663	+	23.6663i	1.13733	+	1.13733i	0.148403	+	0.988927i	$0.452587\pi$
$434$		0			0
$435$	−2.97084	+	3.04728i	−0.142441	+	0.146106i
$436$		0			0
$437$	3.29086	+	3.29086i	0.157423	+	0.157423i
$438$		0			0
$439$	−11.9778			−0.571670			−0.285835	−	0.958279i	$-0.592271\pi$
$439$	−11.9778			−0.571670			−0.285835	+	0.958279i	$0.592271\pi$
$440$		0			0
$441$	2.94803			0.140382
$442$		0			0
$443$	7.85823	+	7.85823i	0.373356	+	0.373356i	0.868698	−	0.495342i	$-0.164957\pi$
$443$	7.85823	+	7.85823i	0.373356	+	0.373356i	−0.495342	+	0.868698i	$0.664957\pi$
$444$		0			0
$445$	−0.690059	+	0.00876410i	−0.0327120	+	0.000415458i
$446$		0			0
$447$	−0.796408	−	0.796408i	−0.0376688	−	0.0376688i
$448$		0			0
$449$			30.5279i			1.44070i	0.693609	+	0.720351i	$0.256019\pi$
$449$			30.5279i			1.44070i	−0.693609	+	0.720351i	$0.743981\pi$
$450$		0			0
$451$	−7.56335			−0.356144
$452$		0			0
$453$	1.31530	−	1.31530i	0.0617981	−	0.0617981i
$454$		0			0
$455$	0.162772	+	12.8162i	0.00763085	+	0.600831i
$456$		0			0
$457$	15.9007	−	15.9007i	0.743805	−	0.743805i	−0.229503	−	0.973308i	$-0.573710\pi$
$457$	15.9007	−	15.9007i	0.743805	−	0.743805i	0.973308	+	0.229503i	$0.0737100\pi$
$458$		0			0
$459$			1.52099i			0.0709937i
$460$		0			0
$461$			10.3015i			0.479789i	0.970799	+	0.239895i	$0.0771129\pi$
$461$			10.3015i			0.479789i	−0.970799	+	0.239895i	$0.922887\pi$
$462$		0			0
$463$	−29.5149	+	29.5149i	−1.37167	+	1.37167i	−0.513708	+	0.857965i	$0.671729\pi$
$463$	−29.5149	+	29.5149i	−1.37167	+	1.37167i	−0.857965	+	0.513708i	$0.828271\pi$
$464$		0			0
$465$	2.19501	+	2.13995i	0.101791	+	0.0992379i
$466$		0			0
$467$	−12.4119	+	12.4119i	−0.574357	+	0.574357i	−0.933343	−	0.358986i	$-0.883122\pi$
$467$	−12.4119	+	12.4119i	−0.574357	+	0.574357i	0.358986	+	0.933343i	$0.383122\pi$
$468$		0			0
$469$	7.10602			0.328125
$470$		0			0
$471$			0.288175i			0.0132784i
$472$		0			0
$473$	−16.8446	−	16.8446i	−0.774516	−	0.774516i
$474$		0			0
$475$	0.738439	+	29.0666i	0.0338819	+	1.33367i
$476$		0			0
$477$	9.50570	+	9.50570i	0.435236	+	0.435236i
$478$		0			0
$479$	−38.2100			−1.74586			−0.872929	−	0.487848i	$-0.837782\pi$
$479$	−38.2100			−1.74586			−0.872929	+	0.487848i	$0.837782\pi$
$480$		0			0
$481$	−30.7706			−1.40302
$482$		0			0
$483$	−0.129008	−	0.129008i	−0.00587007	−	0.00587007i
$484$		0			0
$485$	−6.88587	−	6.71316i	−0.312671	−	0.304829i
$486$		0			0
$487$	10.0740	+	10.0740i	0.456496	+	0.456496i	0.897503	−	0.441007i	$-0.145379\pi$
$487$	10.0740	+	10.0740i	0.456496	+	0.456496i	−0.441007	+	0.897503i	$0.645379\pi$
$488$		0			0
$489$			4.62731i			0.209254i
$490$		0			0
$491$	−1.05766			−0.0477314			−0.0238657	−	0.999715i	$-0.507597\pi$
$491$	−1.05766			−0.0477314			−0.0238657	+	0.999715i	$0.507597\pi$
$492$		0			0
$493$	6.62205	−	6.62205i	0.298242	−	0.298242i
$494$		0			0
$495$	32.5214	−	0.413037i	1.46173	−	0.0185646i
$496$		0			0
$497$	4.26089	−	4.26089i	0.191127	−	0.191127i
$498$		0			0
$499$			27.3238i			1.22318i	0.791175	+	0.611590i	$0.209470\pi$
$499$			27.3238i			1.22318i	−0.791175	+	0.611590i	$0.790530\pi$
$500$		0			0
$501$		−	1.29610i		−	0.0579053i
$502$		0			0
$503$	−4.15122	+	4.15122i	−0.185094	+	0.185094i	−0.793571	−	0.608477i	$-0.791781\pi$
$503$	−4.15122	+	4.15122i	−0.185094	+	0.185094i	0.608477	+	0.793571i	$0.291781\pi$
$504$		0			0
$505$	−8.74303	+	0.111041i	−0.389060	+	0.00494125i
$506$		0			0
$507$	3.20074	−	3.20074i	0.142150	−	0.142150i
$508$		0			0
$509$	1.69580			0.0751651			0.0375826	−	0.999294i	$-0.488034\pi$
$509$	1.69580			0.0751651			0.0375826	+	0.999294i	$0.488034\pi$
$510$		0			0
$511$		−	15.2262i		−	0.673567i
$512$		0			0
$513$	−5.57562	−	5.57562i	−0.246170	−	0.246170i
$514$		0			0
$515$	9.36485	+	9.12996i	0.412665	+	0.402314i
$516$		0			0
$517$	16.9291	+	16.9291i	0.744539	+	0.744539i
$518$		0			0
$519$	3.62173			0.158976
$520$		0			0
$521$	−17.5802			−0.770204			−0.385102	−	0.922874i	$-0.625834\pi$
$521$	−17.5802			−0.770204			−0.385102	+	0.922874i	$0.625834\pi$
$522$		0			0
$523$	−17.3356	−	17.3356i	−0.758034	−	0.758034i	0.217931	−	0.975964i	$-0.430069\pi$
$523$	−17.3356	−	17.3356i	−0.758034	−	0.758034i	−0.975964	+	0.217931i	$0.930069\pi$
$524$		0			0
$525$	−0.0289482	−	1.13946i	−0.00126340	−	0.0497303i
$526$		0			0
$527$	−4.76998	−	4.76998i	−0.207784	−	0.207784i
$528$		0			0
$529$			22.3595i			0.972152i
$530$		0			0
$531$	5.79680			0.251560
$532$		0			0
$533$	−6.21327	+	6.21327i	−0.269127	+	0.269127i
$534$		0			0
$535$	−21.5153	−	20.9757i	−0.930188	−	0.906857i
$536$		0			0
$537$	−1.46204	+	1.46204i	−0.0630917	+	0.0630917i
$538$		0			0
$539$		−	4.93386i		−	0.212516i
$540$		0			0
$541$			40.8275i			1.75531i	0.479292	+	0.877655i	$0.340893\pi$
$541$			40.8275i			1.75531i	−0.479292	+	0.877655i	$0.659107\pi$
$542$		0			0
$543$	2.55828	−	2.55828i	0.109786	−	0.109786i
$544$		0			0
$545$	−0.480026	−	37.7959i	−0.0205621	−	1.61900i
$546$		0			0
$547$	9.45318	−	9.45318i	0.404189	−	0.404189i	−0.475518	−	0.879706i	$-0.657739\pi$
$547$	9.45318	−	9.45318i	0.404189	−	0.404189i	0.879706	+	0.475518i	$0.157739\pi$
$548$		0			0
$549$	−15.5612			−0.664136
$550$		0			0
$551$			48.5500i			2.06830i
$552$		0			0
$553$	−6.08734	−	6.08734i	−0.258860	−	0.258860i
$554$		0			0
$555$	2.73621	−	0.0347512i	0.116146	−	0.00147511i
$556$		0			0
$557$	−19.2588	−	19.2588i	−0.816023	−	0.816023i	0.169507	−	0.985529i	$-0.445783\pi$
$557$	−19.2588	−	19.2588i	−0.816023	−	0.816023i	−0.985529	+	0.169507i	$0.945783\pi$
$558$		0			0
$559$	−27.6756			−1.17055
$560$		0			0
$561$	1.26165			0.0532670
$562$		0			0
$563$	−22.4254	−	22.4254i	−0.945119	−	0.945119i	0.0534519	−	0.998570i	$-0.482978\pi$
$563$	−22.4254	−	22.4254i	−0.945119	−	0.945119i	−0.998570	+	0.0534519i	$0.982978\pi$
$564$		0			0
$565$	−23.7452	+	24.3561i	−0.998968	+	1.02467i
$566$		0			0
$567$	−6.03514	−	6.03514i	−0.253452	−	0.253452i
$568$		0			0
$569$		−	31.3785i		−	1.31545i	−0.753256	−	0.657727i	$-0.771518\pi$
$569$		−	31.3785i		−	1.31545i	0.753256	−	0.657727i	$-0.228482\pi$
$570$		0			0
$571$	15.2261			0.637194			0.318597	−	0.947890i	$-0.396788\pi$
$571$	15.2261			0.637194			0.318597	+	0.947890i	$0.396788\pi$
$572$		0			0
$573$	−2.42402	+	2.42402i	−0.101265	+	0.101265i
$574$		0			0
$575$	2.75677	−	2.90049i	0.114965	−	0.120959i
$576$		0			0
$577$	−23.1621	+	23.1621i	−0.964252	+	0.964252i	−0.999383	−	0.0351312i	$-0.988815\pi$
$577$	−23.1621	+	23.1621i	−0.964252	+	0.964252i	0.0351312	+	0.999383i	$0.488815\pi$
$578$		0			0
$579$			1.67563i			0.0696366i
$580$		0			0
$581$		−	14.4659i		−	0.600148i
$582$		0			0
$583$	15.9088	−	15.9088i	0.658877	−	0.658877i
$584$		0			0
$585$	26.3769	−	27.0555i	1.09055	−	1.11861i
$586$		0			0
$587$	−6.02231	+	6.02231i	−0.248567	+	0.248567i	−0.820382	−	0.571815i	$-0.806239\pi$
$587$	−6.02231	+	6.02231i	−0.248567	+	0.248567i	0.571815	+	0.820382i	$0.306239\pi$
$588$		0			0
$589$	34.9714			1.44097
$590$		0			0
$591$			1.48748i			0.0611869i
$592$		0			0
$593$	−5.40684	−	5.40684i	−0.222032	−	0.222032i	0.587321	−	0.809354i	$-0.300182\pi$
$593$	−5.40684	−	5.40684i	−0.222032	−	0.222032i	−0.809354	+	0.587321i	$0.800182\pi$
$594$		0			0
$595$	0.0318532	+	2.50803i	0.00130585	+	0.102819i
$596$		0			0
$597$	−0.751756	−	0.751756i	−0.0307673	−	0.0307673i
$598$		0			0
$599$	−47.4665			−1.93943			−0.969715	−	0.244240i	$-0.921462\pi$
$599$	−47.4665			−1.93943			−0.969715	+	0.244240i	$0.921462\pi$
$600$		0			0
$601$	−47.1229			−1.92218			−0.961092	−	0.276227i	$-0.910916\pi$
$601$	−47.1229			−1.92218			−0.961092	+	0.276227i	$0.910916\pi$
$602$		0			0
$603$	−14.8130	−	14.8130i	−0.603232	−	0.603232i
$604$		0			0
$605$	−0.378898	−	29.8333i	−0.0154044	−	1.21290i
$606$		0			0
$607$	−20.6362	−	20.6362i	−0.837599	−	0.837599i	0.150943	−	0.988542i	$-0.451769\pi$
$607$	−20.6362	−	20.6362i	−0.837599	−	0.837599i	−0.988542	+	0.150943i	$0.951769\pi$
$608$		0			0
$609$		−	1.90325i		−	0.0771236i
$610$		0			0
$611$	27.8144			1.12525
$612$		0			0
$613$	−15.1404	+	15.1404i	−0.611514	+	0.611514i	−0.943340	−	0.331827i	$-0.892335\pi$
$613$	−15.1404	+	15.1404i	−0.611514	+	0.611514i	0.331827	+	0.943340i	$0.392335\pi$
$614$		0			0
$615$	0.545484	−	0.559518i	0.0219960	−	0.0225620i
$616$		0			0
$617$	14.1397	−	14.1397i	0.569242	−	0.569242i	−0.362674	−	0.931916i	$-0.618136\pi$
$617$	14.1397	−	14.1397i	0.569242	−	0.569242i	0.931916	+	0.362674i	$0.118136\pi$
$618$		0			0
$619$		−	41.2646i		−	1.65857i	−0.558829	−	0.829283i	$-0.688749\pi$
$619$		−	41.2646i		−	1.65857i	0.558829	−	0.829283i	$-0.311251\pi$
$620$		0			0
$621$			1.08519i			0.0435471i
$622$		0			0
$623$	0.218234	−	0.218234i	0.00874334	−	0.00874334i
$624$		0			0
$625$	24.9677	−	1.26944i	0.998710	−	0.0507774i
$626$		0			0
$627$	−4.62494	+	4.62494i	−0.184702	+	0.184702i
$628$		0			0
$629$	−6.02158			−0.240096
$630$		0			0
$631$		−	0.491483i		−	0.0195656i	−0.999952	−	0.00978281i	$-0.996886\pi$
$631$		−	0.491483i		−	0.0195656i	0.999952	−	0.00978281i	$-0.00311401\pi$
$632$		0			0
$633$	0.884682	+	0.884682i	0.0351629	+	0.0351629i
$634$		0			0
$635$	16.4369	−	16.8598i	0.652277	−	0.669059i
$636$		0			0
$637$	−4.05315	−	4.05315i	−0.160592	−	0.160592i
$638$		0			0
$639$	−17.7643			−0.702744
$640$		0			0
$641$	18.4768			0.729791			0.364896	−	0.931048i	$-0.381105\pi$
$641$	18.4768			0.729791			0.364896	+	0.931048i	$0.381105\pi$
$642$		0			0
$643$	0.743869	+	0.743869i	0.0293353	+	0.0293353i	0.721622	−	0.692287i	$-0.243397\pi$
$643$	0.743869	+	0.743869i	0.0293353	+	0.0293353i	−0.692287	+	0.721622i	$0.743397\pi$
$644$		0			0
$645$	2.46099	−	0.0312558i	0.0969015	−	0.00123070i
$646$		0			0
$647$	17.5707	+	17.5707i	0.690777	+	0.690777i	0.962403	−	0.271626i	$-0.0875614\pi$
$647$	17.5707	+	17.5707i	0.690777	+	0.690777i	−0.271626	+	0.962403i	$0.587561\pi$
$648$		0			0
$649$		−	9.70158i		−	0.380820i
$650$		0			0
$651$	−1.37094			−0.0537316
$652$		0			0
$653$	−5.81323	+	5.81323i	−0.227489	+	0.227489i	−0.811643	−	0.584154i	$-0.801426\pi$
$653$	−5.81323	+	5.81323i	−0.227489	+	0.227489i	0.584154	+	0.811643i	$0.301426\pi$
$654$		0			0
$655$	0.547535	+	43.1113i	0.0213940	+	1.68450i
$656$		0			0
$657$	−31.7401	+	31.7401i	−1.23830	+	1.23830i
$658$		0			0
$659$		−	9.18508i		−	0.357800i	−0.983867	−	0.178900i	$-0.942746\pi$
$659$		−	9.18508i		−	0.357800i	0.983867	−	0.178900i	$-0.0572539\pi$
$660$		0			0
$661$			17.3173i			0.673563i	0.941583	+	0.336782i	$0.109338\pi$
$661$			17.3173i			0.673563i	−0.941583	+	0.336782i	$0.890662\pi$
$662$		0			0
$663$	1.03644	−	1.03644i	0.0402522	−	0.0402522i
$664$		0			0
$665$	−9.31065	−	9.07712i	−0.361051	−	0.351995i
$666$		0			0
$667$	4.72467	−	4.72467i	0.182940	−	0.182940i
$668$		0			0
$669$	−1.74446			−0.0674448
$670$		0			0
$671$			26.0434i			1.00539i
$672$		0			0
$673$	14.5702	+	14.5702i	0.561639	+	0.561639i	0.929773	−	0.368134i	$-0.120003\pi$
$673$	14.5702	+	14.5702i	0.561639	+	0.561639i	−0.368134	+	0.929773i	$0.620003\pi$
$674$		0			0
$675$	−4.67071	+	4.91422i	−0.179776	+	0.189148i
$676$		0			0
$677$	0.273066	+	0.273066i	0.0104948	+	0.0104948i	0.712335	−	0.701840i	$-0.247638\pi$
$677$	0.273066	+	0.273066i	0.0104948	+	0.0104948i	−0.701840	+	0.712335i	$0.747638\pi$
$678$		0			0
$679$	4.30074			0.165047
$680$		0			0
$681$	0.197985			0.00758681
$682$		0			0
$683$	−4.61975	−	4.61975i	−0.176770	−	0.176770i	0.613176	−	0.789946i	$-0.289892\pi$
$683$	−4.61975	−	4.61975i	−0.176770	−	0.176770i	−0.789946	+	0.613176i	$0.789892\pi$
$684$		0			0
$685$	−18.5177	−	18.0532i	−0.707525	−	0.689779i
$686$		0			0
$687$	−2.93441	−	2.93441i	−0.111955	−	0.111955i
$688$		0			0
$689$		−	26.1382i		−	0.995785i
$690$		0			0
$691$	21.8634			0.831722			0.415861	−	0.909428i	$-0.363480\pi$
$691$	21.8634			0.831722			0.415861	+	0.909428i	$0.363480\pi$
$692$		0			0
$693$	−10.2850	+	10.2850i	−0.390694	+	0.390694i
$694$		0			0
$695$	20.6470	−	0.262228i	0.783187	−	0.00994686i
$696$		0			0
$697$	−1.21589	+	1.21589i	−0.0460552	+	0.0460552i
$698$		0			0
$699$			3.79314i			0.143470i
$700$		0			0
$701$		−	13.2692i		−	0.501170i	−0.968095	−	0.250585i	$-0.919377\pi$
$701$		−	13.2692i		−	0.501170i	0.968095	−	0.250585i	$-0.0806229\pi$
$702$		0			0
$703$	22.0738	−	22.0738i	0.832529	−	0.832529i
$704$		0			0
$705$	−2.47333	+	0.0314125i	−0.0931510	+	0.00118306i
$706$		0			0
$707$	2.76501	−	2.76501i	0.103989	−	0.103989i
$708$		0			0
$709$	−15.1247			−0.568020			−0.284010	−	0.958821i	$-0.591665\pi$
$709$	−15.1247			−0.568020			−0.284010	+	0.958821i	$0.591665\pi$
$710$		0			0
$711$			25.3790i			0.951787i
$712$		0			0
$713$	−3.40326	−	3.40326i	−0.127453	−	0.127453i
$714$		0			0
$715$	−45.2804	−	44.1447i	−1.69339	−	1.65092i
$716$		0			0
$717$	1.41999	+	1.41999i	0.0530306	+	0.0530306i
$718$		0			0
$719$	22.8933			0.853776			0.426888	−	0.904304i	$-0.359610\pi$
$719$	22.8933			0.853776			0.426888	+	0.904304i	$0.359610\pi$
$720$		0			0
$721$	−5.84904			−0.217830
$722$		0			0
$723$	−3.44813	−	3.44813i	−0.128237	−	0.128237i
$724$		0			0
$725$	41.7306	−	1.06017i	1.54984	−	0.0393737i
$726$		0			0
$727$	−0.712383	−	0.712383i	−0.0264208	−	0.0264208i	0.693773	−	0.720194i	$-0.255947\pi$
$727$	−0.712383	−	0.712383i	−0.0264208	−	0.0264208i	−0.720194	+	0.693773i	$0.755947\pi$
$728$		0			0
$729$			24.2341i			0.897558i
$730$		0			0
$731$	−5.41591			−0.200315
$732$		0			0
$733$	13.0673	−	13.0673i	0.482653	−	0.482653i	−0.423325	−	0.905978i	$-0.639137\pi$
$733$	13.0673	−	13.0673i	0.482653	−	0.482653i	0.905978	+	0.423325i	$0.139137\pi$
$734$		0			0
$735$	0.364995	+	0.355840i	0.0134630	+	0.0131254i
$736$		0			0
$737$	−24.7912	+	24.7912i	−0.913196	+	0.913196i
$738$		0			0
$739$		−	13.0130i		−	0.478692i	−0.970934	−	0.239346i	$-0.923067\pi$
$739$		−	13.0130i		−	0.478692i	0.970934	−	0.239346i	$-0.0769330\pi$
$740$		0			0
$741$			7.59876i			0.279147i
$742$		0			0
$743$	3.95133	−	3.95133i	0.144960	−	0.144960i	−0.630902	−	0.775862i	$-0.717315\pi$
$743$	3.95133	−	3.95133i	0.144960	−	0.144960i	0.775862	+	0.630902i	$0.217315\pi$
$744$		0			0
$745$	0.140298	+	11.0466i	0.00514011	+	0.404717i
$746$		0			0
$747$	−30.1553	+	30.1553i	−1.10332	+	1.10332i
$748$		0			0
$749$	13.4379			0.491010
$750$		0			0
$751$		−	10.6694i		−	0.389333i	−0.980869	−	0.194666i	$-0.937638\pi$
$751$		−	10.6694i		−	0.389333i	0.980869	−	0.194666i	$-0.0623625\pi$
$752$		0			0
$753$	5.06017	+	5.06017i	0.184403	+	0.184403i
$754$		0			0
$755$	−18.2439	+	0.231707i	−0.663965	+	0.00843268i
$756$		0			0
$757$	−19.7518	−	19.7518i	−0.717890	−	0.717890i	0.250283	−	0.968173i	$-0.419476\pi$
$757$	−19.7518	−	19.7518i	−0.717890	−	0.717890i	−0.968173	+	0.250283i	$0.919476\pi$
$758$		0			0
$759$	0.900157			0.0326736
$760$		0			0
$761$	5.08452			0.184314			0.0921568	−	0.995745i	$-0.470624\pi$
$761$	5.08452			0.184314			0.0921568	+	0.995745i	$0.470624\pi$
$762$		0			0
$763$	11.9531	+	11.9531i	0.432730	+	0.432730i
$764$		0			0
$765$	5.16176	−	5.29456i	0.186624	−	0.191425i
$766$		0			0
$767$	−7.96983	−	7.96983i	−0.287774	−	0.287774i
$768$		0			0
$769$		−	41.2578i		−	1.48780i	−0.668293	−	0.743898i	$-0.732975\pi$
$769$		−	41.2578i		−	1.48780i	0.668293	−	0.743898i	$-0.267025\pi$
$770$		0			0
$771$	−0.717380			−0.0258358
$772$		0			0
$773$	−5.76976	+	5.76976i	−0.207524	+	0.207524i	−0.803214	−	0.595690i	$-0.796879\pi$
$773$	−5.76976	+	5.76976i	−0.207524	+	0.207524i	0.595690	+	0.803214i	$0.296879\pi$
$774$		0			0
$775$	−0.763660	−	30.0593i	−0.0274315	−	1.07976i
$776$		0			0
$777$	−0.865335	+	0.865335i	−0.0310437	+	0.0310437i
$778$		0			0
$779$		−	8.91439i		−	0.319391i
$780$		0			0
$781$			29.7305i			1.06384i
$782$		0			0
$783$	−8.00487	+	8.00487i	−0.286071	+	0.286071i
$784$		0			0
$785$	1.97319	−	2.02396i	0.0704261	−	0.0722381i
$786$		0			0
$787$	−35.7523	+	35.7523i	−1.27443	+	1.27443i	−0.330692	+	0.943739i	$0.607282\pi$
$787$	−35.7523	+	35.7523i	−1.27443	+	1.27443i	−0.943739	+	0.330692i	$0.892718\pi$
$788$		0			0
$789$	1.92922			0.0686820
$790$		0			0
$791$		−	15.2122i		−	0.540883i
$792$		0			0
$793$	21.3946	+	21.3946i	0.759744	+	0.759744i
$794$		0			0
$795$	0.0295195	+	2.32428i	0.00104695	+	0.0824336i
$796$		0			0
$797$	−5.97318	−	5.97318i	−0.211581	−	0.211581i	0.593358	−	0.804939i	$-0.297802\pi$
$797$	−5.97318	−	5.97318i	−0.211581	−	0.211581i	−0.804939	+	0.593358i	$0.797802\pi$
$798$		0			0
$799$	5.44306			0.192562
$800$		0			0
$801$	−0.909848			−0.0321479
$802$		0			0
$803$	53.1206	+	53.1206i	1.87458	+	1.87458i
$804$		0			0
$805$	0.0227264	+	1.78941i	0.000801002	+	0.0630686i
$806$		0			0
$807$	0.0951363	+	0.0951363i	0.00334896	+	0.00334896i
$808$		0			0
$809$			36.5735i			1.28586i	0.765927	+	0.642928i	$0.222281\pi$
$809$			36.5735i			1.28586i	−0.765927	+	0.642928i	$0.777719\pi$
$810$		0			0
$811$	0.603322			0.0211855			0.0105928	−	0.999944i	$-0.496628\pi$
$811$	0.603322			0.0211855			0.0105928	+	0.999944i	$0.496628\pi$
$812$		0			0
$813$	2.58843	−	2.58843i	0.0907803	−	0.0907803i
$814$		0			0
$815$	31.6842	−	32.4993i	1.10985	−	1.13840i
$816$		0			0
$817$	19.8536	−	19.8536i	0.694588	−	0.694588i
$818$		0			0
$819$			16.8982i			0.590471i
$820$		0			0
$821$		−	33.2259i		−	1.15959i	−0.814762	−	0.579796i	$-0.803132\pi$
$821$		−	33.2259i		−	1.15959i	0.814762	−	0.579796i	$-0.196868\pi$
$822$		0			0
$823$	9.06126	−	9.06126i	0.315856	−	0.315856i	−0.531317	−	0.847173i	$-0.678303\pi$
$823$	9.06126	−	9.06126i	0.315856	−	0.315856i	0.847173	+	0.531317i	$0.178303\pi$
$824$		0			0
$825$	4.07632	+	3.87433i	0.141919	+	0.134887i
$826$		0			0
$827$	21.4284	−	21.4284i	0.745140	−	0.745140i	−0.228422	−	0.973562i	$-0.573357\pi$
$827$	21.4284	−	21.4284i	0.745140	−	0.745140i	0.973562	+	0.228422i	$0.0733567\pi$
$828$		0			0
$829$	−24.1876			−0.840071			−0.420036	−	0.907508i	$-0.637982\pi$
$829$	−24.1876			−0.840071			−0.420036	+	0.907508i	$0.637982\pi$
$830$		0			0
$831$		−	3.23107i		−	0.112085i
$832$		0			0
$833$	−0.793172	−	0.793172i	−0.0274818	−	0.0274818i
$834$		0			0
$835$	−8.87463	+	9.10296i	−0.307119	+	0.315021i
$836$		0			0
$837$	5.76605	+	5.76605i	0.199304	+	0.199304i
$838$		0			0
$839$	34.0386			1.17514			0.587571	−	0.809172i	$-0.300084\pi$
$839$	34.0386			1.17514			0.587571	+	0.809172i	$0.300084\pi$
$840$		0			0
$841$	40.7028			1.40355
$842$		0			0
$843$	0.570711	+	0.570711i	0.0196563	+	0.0196563i
$844$		0			0
$845$	−44.3960	+	0.563852i	−1.52727	+	0.0193971i
$846$		0			0
$847$	9.43489	+	9.43489i	0.324187	+	0.324187i
$848$		0			0
$849$			0.382859i			0.0131397i
$850$		0			0
$851$	−4.29625			−0.147273
$852$		0			0
$853$	−36.0811	+	36.0811i	−1.23539	+	1.23539i	−0.273530	+	0.961863i	$0.588191\pi$
$853$	−36.0811	+	36.0811i	−1.23539	+	1.23539i	−0.961863	+	0.273530i	$0.911809\pi$
$854$		0			0
$855$	0.486818	+	38.3306i	0.0166488	+	1.31088i
$856$		0			0
$857$	20.0497	−	20.0497i	0.684885	−	0.684885i	−0.276212	−	0.961097i	$-0.589079\pi$
$857$	20.0497	−	20.0497i	0.684885	−	0.684885i	0.961097	+	0.276212i	$0.0890792\pi$
$858$		0			0
$859$			11.0584i			0.377306i	0.982044	+	0.188653i	$0.0604122\pi$
$859$			11.0584i			0.377306i	−0.982044	+	0.188653i	$0.939588\pi$
$860$		0			0
$861$			0.349461i			0.0119096i
$862$		0			0
$863$	−24.9568	+	24.9568i	−0.849539	+	0.849539i	−0.990076	−	0.140536i	$-0.955117\pi$
$863$	−24.9568	+	24.9568i	−0.849539	+	0.849539i	0.140536	+	0.990076i	$0.455117\pi$
$864$		0			0
$865$	−25.4367	−	24.7987i	−0.864875	−	0.843182i
$866$		0			0
$867$	−2.53752	+	2.53752i	−0.0861786	+	0.0861786i
$868$		0			0
$869$	42.4746			1.44085
$870$		0			0
$871$			40.7319i			1.38015i
$872$		0			0
$873$	−8.96520	−	8.96520i	−0.303426	−	0.303426i
$874$		0			0
$875$	−7.59883	+	8.20109i	−0.256887	+	0.277247i
$876$		0			0
$877$	−23.6400	−	23.6400i	−0.798265	−	0.798265i	0.184557	−	0.982822i	$-0.440915\pi$
$877$	−23.6400	−	23.6400i	−0.798265	−	0.798265i	−0.982822	+	0.184557i	$0.940915\pi$
$878$		0			0
$879$	3.45947			0.116685
$880$		0			0
$881$	−2.61767			−0.0881914			−0.0440957	−	0.999027i	$-0.514041\pi$
$881$	−2.61767			−0.0881914			−0.0440957	+	0.999027i	$0.514041\pi$
$882$		0			0
$883$	14.2779	+	14.2779i	0.480488	+	0.480488i	0.905288	−	0.424799i	$-0.139655\pi$
$883$	14.2779	+	14.2779i	0.480488	+	0.480488i	−0.424799	+	0.905288i	$0.639655\pi$
$884$		0			0
$885$	0.717700	+	0.699698i	0.0241252	+	0.0235201i
$886$		0			0
$887$	−36.9666	−	36.9666i	−1.24122	−	1.24122i	−0.959496	−	0.281723i	$-0.909094\pi$
$887$	−36.9666	−	36.9666i	−1.24122	−	1.24122i	−0.281723	−	0.959496i	$-0.590906\pi$
$888$		0			0
$889$			10.5302i			0.353171i
$890$		0			0
$891$	42.1104			1.41075
$892$		0			0
$893$	−19.9531	+	19.9531i	−0.667705	+	0.667705i
$894$		0			0
$895$	20.2793	−	0.257557i	0.677863	−	0.00860919i
$896$		0			0
$897$	0.739477	−	0.739477i	0.0246904	−	0.0246904i
$898$		0			0
$899$		−	50.2082i		−	1.67454i
$900$		0			0
$901$		−	5.11504i		−	0.170407i
$902$		0			0
$903$	−0.778297	+	0.778297i	−0.0259001	+	0.0259001i
$904$		0			0
$905$	−35.4848	+	0.450675i	−1.17956	+	0.0149809i
$906$		0			0
$907$	7.40975	−	7.40975i	0.246037	−	0.246037i	−0.573305	−	0.819342i	$-0.694339\pi$
$907$	7.40975	−	7.40975i	0.246037	−	0.246037i	0.819342	+	0.573305i	$0.194339\pi$
$908$		0			0
$909$	−11.5277			−0.382351
$910$		0			0
$911$		−	12.4164i		−	0.411374i	−0.978618	−	0.205687i	$-0.934057\pi$
$911$		−	12.4164i		−	0.411374i	0.978618	−	0.205687i	$-0.0659428\pi$
$912$		0			0
$913$	50.4682	+	50.4682i	1.67025	+	1.67025i
$914$		0			0
$915$	−1.92663	−	1.87830i	−0.0636923	−	0.0620948i
$916$		0			0
$917$	−13.6341	−	13.6341i	−0.450238	−	0.450238i
$918$		0			0
$919$	47.8744			1.57923			0.789616	−	0.613602i	$-0.210280\pi$
$919$	47.8744			1.57923			0.789616	+	0.613602i	$0.210280\pi$
$920$		0			0
$921$	1.99906			0.0658714
$922$		0			0
$923$	24.4235	+	24.4235i	0.803911	+	0.803911i
$924$		0			0
$925$	−19.4553	−	18.4913i	−0.639687	−	0.607990i
$926$		0			0
$927$	12.1928	+	12.1928i	0.400463	+	0.400463i
$928$		0			0
$929$			26.0603i			0.855009i	0.904013	+	0.427505i	$0.140607\pi$
$929$			26.0603i			0.855009i	−0.904013	+	0.427505i	$0.859393\pi$
$930$		0			0
$931$	5.81519			0.190585
$932$		0			0
$933$	3.70340	−	3.70340i	0.121244	−	0.121244i
$934$		0			0
$935$	−8.86104	−	8.63879i	−0.289787	−	0.282518i
$936$		0			0
$937$	19.5860	−	19.5860i	0.639848	−	0.639848i	−0.310670	−	0.950518i	$-0.600553\pi$
$937$	19.5860	−	19.5860i	0.639848	−	0.639848i	0.950518	+	0.310670i	$0.100553\pi$
$938$		0			0
$939$		−	4.94497i		−	0.161373i
$940$		0			0
$941$			36.3757i			1.18581i	0.805271	+	0.592907i	$0.202020\pi$
$941$			36.3757i			1.18581i	−0.805271	+	0.592907i	$0.797980\pi$
$942$		0			0
$943$	−0.867508	+	0.867508i	−0.0282499	+	0.0282499i
$944$		0			0
$945$	−0.0385048	−	3.03175i	−0.00125256	−	0.0986230i
$946$		0			0
$947$	−26.4642	+	26.4642i	−0.859970	+	0.859970i	−0.991334	−	0.131364i	$-0.958064\pi$
$947$	−26.4642	+	26.4642i	−0.859970	+	0.859970i	0.131364	+	0.991334i	$0.458064\pi$
$948$		0			0
$949$	87.2769			2.83313
$950$		0			0
$951$			0.496852i			0.0161115i
$952$		0			0
$953$	10.8801	+	10.8801i	0.352441	+	0.352441i	0.861017	−	0.508576i	$-0.169828\pi$
$953$	10.8801	+	10.8801i	0.352441	+	0.352441i	−0.508576	+	0.861017i	$0.669828\pi$
$954$		0			0
$955$	33.6225	−	0.427022i	1.08800	−	0.0138181i
$956$		0			0
$957$	6.63999	+	6.63999i	0.214640	+	0.214640i
$958$		0			0
$959$	11.5657			0.373475
$960$		0			0
$961$	−5.16583			−0.166640
$962$		0			0
$963$	−28.0123	−	28.0123i	−0.902684	−	0.902684i
$964$		0			0
$965$	11.4733	−	11.7685i	0.369340	−	0.378842i
$966$		0			0
$967$	−24.6020	−	24.6020i	−0.791148	−	0.791148i	0.190532	−	0.981681i	$-0.438979\pi$
$967$	−24.6020	−	24.6020i	−0.791148	−	0.791148i	−0.981681	+	0.190532i	$0.938979\pi$
$968$		0			0
$969$			1.48702i			0.0477700i
$970$		0			0
$971$	−27.2265			−0.873739			−0.436869	−	0.899525i	$-0.643913\pi$
$971$	−27.2265			−0.873739			−0.436869	+	0.899525i	$0.643913\pi$
$972$		0			0
$973$	−6.52969	+	6.52969i	−0.209332	+	0.209332i
$974$		0			0
$975$	6.53144	−	0.165932i	0.209173	−	0.00531407i
$976$		0			0
$977$	−33.1217	+	33.1217i	−1.05966	+	1.05966i	−0.0615547	+	0.998104i	$0.519606\pi$
$977$	−33.1217	+	33.1217i	−1.05966	+	1.05966i	−0.998104	+	0.0615547i	$0.980394\pi$
$978$		0			0
$979$			1.52273i			0.0486667i
$980$		0			0
$981$		−	49.8341i		−	1.59108i
$982$		0			0
$983$	−18.9409	+	18.9409i	−0.604120	+	0.604120i	−0.941403	−	0.337283i	$-0.890492\pi$
$983$	−18.9409	+	18.9409i	−0.604120	+	0.604120i	0.337283	+	0.941403i	$0.390492\pi$
$984$		0			0
$985$	10.1851	−	10.4471i	0.324524	−	0.332874i
$986$		0			0
$987$	0.782199	−	0.782199i	0.0248977	−	0.0248977i
$988$		0			0
$989$	−3.86412			−0.122872
$990$		0			0
$991$		−	47.4907i		−	1.50859i	−0.656535	−	0.754296i	$-0.727979\pi$
$991$		−	47.4907i		−	1.50859i	0.656535	−	0.754296i	$-0.272021\pi$
$992$		0			0
$993$	−3.73519	−	3.73519i	−0.118533	−	0.118533i
$994$		0			0
$995$	0.132432	+	10.4273i	0.00419837	+	0.330567i
$996$		0			0
$997$	23.6086	+	23.6086i	0.747690	+	0.747690i	0.974045	−	0.226355i	$-0.0726808\pi$
$997$	23.6086	+	23.6086i	0.747690	+	0.747690i	−0.226355	+	0.974045i	$0.572681\pi$
$998$		0			0
$999$	7.27901			0.230298

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bi.a.463.20		72
4.3	odd	2		280.2.w.a.43.33	yes	72
5.2	odd	4	inner	1120.2.bi.a.687.19		72
8.3	odd	2	inner	1120.2.bi.a.463.19		72
8.5	even	2		280.2.w.a.43.16	✓	72
20.7	even	4		280.2.w.a.267.16	yes	72
40.27	even	4	inner	1120.2.bi.a.687.20		72
40.37	odd	4		280.2.w.a.267.33	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.w.a.43.16	✓	72	8.5	even	2
280.2.w.a.43.33	yes	72	4.3	odd	2
280.2.w.a.267.16	yes	72	20.7	even	4
280.2.w.a.267.33	yes	72	40.37	odd	4
1120.2.bi.a.463.19		72	8.3	odd	2	inner
1120.2.bi.a.463.20		72	1.1	even	1	trivial
1120.2.bi.a.687.19		72	5.2	odd	4	inner
1120.2.bi.a.687.20		72	40.27	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bi (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.161197 + 0.161197i) q^{3} +(-0.0283969 - 2.23589i) q^{5} +(0.707107 + 0.707107i) q^{7} -2.94803i q^{9} -4.93386 q^{11} +(-4.05315 + 4.05315i) q^{13} +(0.355840 - 0.364995i) q^{15} +(-0.793172 + 0.793172i) q^{17} -5.81519i q^{19} +0.227966i q^{21} +(-0.565908 + 0.565908i) q^{23} +(-4.99839 + 0.126984i) q^{25} +(0.958802 - 0.958802i) q^{27} -8.34882 q^{29} +6.01380i q^{31} +(-0.795321 - 0.795321i) q^{33} +(1.56093 - 1.60109i) q^{35} +(3.79589 + 3.79589i) q^{37} -1.30671 q^{39} +1.53295 q^{41} +(3.41409 + 3.41409i) q^{43} +(-6.59147 + 0.0837149i) q^{45} +(-3.43120 - 3.43120i) q^{47} +1.00000i q^{49} -0.255713 q^{51} +(-3.22442 + 3.22442i) q^{53} +(0.140106 + 11.0316i) q^{55} +(0.937389 - 0.937389i) q^{57} +1.96633i q^{59} -5.27850i q^{61} +(2.08457 - 2.08457i) q^{63} +(9.17749 + 8.94730i) q^{65} +(5.02471 - 5.02471i) q^{67} -0.182445 q^{69} -6.02581i q^{71} +(-10.7665 - 10.7665i) q^{73} +(-0.826192 - 0.785253i) q^{75} +(-3.48876 - 3.48876i) q^{77} -8.60880 q^{79} -8.53498 q^{81} +(-10.2290 - 10.2290i) q^{83} +(1.79597 + 1.75092i) q^{85} +(-1.34580 - 1.34580i) q^{87} -0.308629i q^{89} -5.73203 q^{91} +(-0.969404 + 0.969404i) q^{93} +(-13.0021 + 0.165133i) q^{95} +(3.04108 - 3.04108i) q^{97} +14.5452i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 8 q^{17} - 8 q^{25} + 64 q^{43} + 32 q^{51} - 8 q^{65} - 40 q^{73} - 112 q^{75} - 72 q^{81} - 80 q^{83} - 8 q^{97}+O(q^{100}) \) 72 * q + 8 * q^17 - 8 * q^25 + 64 * q^43 + 32 * q^51 - 8 * q^65 - 40 * q^73 - 112 * q^75 - 72 * q^81 - 80 * q^83 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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