LMFDB - Embedded newform 1560.2.bg.h.841.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1560,2,Mod(601,1560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1560, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2]))

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

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

chi := DirichletCharacter("1560.601");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1560.bg (of order $3$ , degree $2$ , 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:	$12.4566627153$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.591408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{6} - x^{5} + 4x^{4} + x^{3} + 10x^{2} - 3x + 1$ x^6 - x^5 + 4x^4 + x^3 + 10x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.1
Root			$-0.740597 - 1.28275i$ of defining polynomial
Character	$\chi$	$=$	1560.841
Dual form			1560.2.bg.h.601.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} -1.00000 q^{5} +(-0.740597 - 1.28275i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.67513 - 2.90141i) q^{11} +(-3.01270 + 1.98082i) q^{13} +(0.500000 - 0.866025i) q^{15} +(1.24060 + 2.14878i) q^{17} +(1.07816 + 1.86743i) q^{19} +1.48119 q^{21} +(-2.96239 + 5.13101i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(3.31876 - 5.74826i) q^{29} +3.54420 q^{31} +(1.67513 + 2.90141i) q^{33} +(0.740597 + 1.28275i) q^{35} +(-0.193937 + 0.335908i) q^{37} +(-0.209095 - 3.59948i) q^{39} +(-5.12482 + 8.87645i) q^{41} +(5.01270 + 8.68224i) q^{43} +(0.500000 + 0.866025i) q^{45} +12.5320 q^{47} +(2.40303 - 4.16217i) q^{49} -2.48119 q^{51} +1.73813 q^{53} +(-1.67513 + 2.90141i) q^{55} -2.15633 q^{57} +(4.93089 + 8.54055i) q^{59} +(-3.05936 - 5.29896i) q^{61} +(-0.740597 + 1.28275i) q^{63} +(3.01270 - 1.98082i) q^{65} +(-5.62482 + 9.74248i) q^{67} +(-2.96239 - 5.13101i) q^{69} +(7.76234 + 13.4448i) q^{71} -11.6678 q^{73} +(-0.500000 + 0.866025i) q^{75} -4.96239 q^{77} -10.7685 q^{79} +(-0.500000 + 0.866025i) q^{81} +6.77575 q^{83} +(-1.24060 - 2.14878i) q^{85} +(3.31876 + 5.74826i) q^{87} +(-9.15022 + 15.8486i) q^{89} +(4.77210 + 2.39755i) q^{91} +(-1.77210 + 3.06937i) q^{93} +(-1.07816 - 1.86743i) q^{95} +(0.531502 + 0.920588i) q^{97} -3.35026 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$6 q - 3 q^{3} - 6 q^{5} + q^{7} - 3 q^{9} - 3 q^{13} + 3 q^{15} + 2 q^{17} - 4 q^{19} - 2 q^{21} + 4 q^{23} + 6 q^{25} + 6 q^{27} + 4 q^{29} + 2 q^{31} - q^{35} - 2 q^{37} - 14 q^{41} + 15 q^{43} + 3 q^{45}+ \cdots - q^{97}+O(q^{100})$ 6 * q - 3 * q^3 - 6 * q^5 + q^7 - 3 * q^9 - 3 * q^13 + 3 * q^15 + 2 * q^17 - 4 * q^19 - 2 * q^21 + 4 * q^23 + 6 * q^25 + 6 * q^27 + 4 * q^29 + 2 * q^31 - q^35 - 2 * q^37 - 14 * q^41 + 15 * q^43 + 3 * q^45 + 4 * q^47 + 14 * q^49 - 4 * q^51 - 8 * q^53 + 8 * q^57 + 12 * q^59 + 3 * q^61 + q^63 + 3 * q^65 - 17 * q^67 + 4 * q^69 - 2 * q^71 - 34 * q^73 - 3 * q^75 - 8 * q^77 - 42 * q^79 - 3 * q^81 + 44 * q^83 - 2 * q^85 + 4 * q^87 - 8 * q^89 + 19 * q^91 - q^93 + 4 * q^95 - q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times$ .

$n$	$391$	$521$	$781$	$937$	$1081$
$\chi(n)$	$1$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−0.740597	−	1.28275i	−0.279919	−	0.484835i	0.691445	−	0.722429i	$-0.256974\pi$
$7$	−0.740597	−	1.28275i	−0.279919	−	0.484835i	−0.971364	+	0.237594i	$0.923641\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.67513	−	2.90141i	0.505071	−	0.874809i	−0.494912	−	0.868943i	$-0.664800\pi$
$11$	1.67513	−	2.90141i	0.505071	−	0.874809i	0.999983	−	0.00586537i	$-0.00186702\pi$
$12$		0			0
$13$	−3.01270	+	1.98082i	−0.835572	+	0.549382i
$13$	−3.01270	+	1.98082i	−0.835572	+	0.549382i
$14$		0			0
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$		0			0
$17$	1.24060	+	2.14878i	0.300889	+	0.521155i	0.976338	−	0.216252i	$-0.0693833\pi$
$17$	1.24060	+	2.14878i	0.300889	+	0.521155i	−0.675449	+	0.737407i	$0.736050\pi$
$18$		0			0
$19$	1.07816	+	1.86743i	0.247347	+	0.428418i	0.962789	−	0.270254i	$-0.0871078\pi$
$19$	1.07816	+	1.86743i	0.247347	+	0.428418i	−0.715442	+	0.698673i	$0.753774\pi$
$20$		0			0
$21$	1.48119			0.323223
$22$		0			0
$23$	−2.96239	+	5.13101i	−0.617701	+	1.06989i	0.372203	+	0.928151i	$0.378602\pi$
$23$	−2.96239	+	5.13101i	−0.617701	+	1.06989i	−0.989904	+	0.141738i	$0.954731\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	3.31876	−	5.74826i	0.616278	−	1.06743i	−0.373881	−	0.927477i	$-0.621973\pi$
$29$	3.31876	−	5.74826i	0.616278	−	1.06743i	0.990159	−	0.139948i	$-0.0446936\pi$
$30$		0			0
$31$	3.54420			0.636557			0.318278	−	0.947997i	$-0.396895\pi$
$31$	3.54420			0.636557			0.318278	+	0.947997i	$0.396895\pi$
$32$		0			0
$33$	1.67513	+	2.90141i	0.291603	+	0.505071i
$34$		0			0
$35$	0.740597	+	1.28275i	0.125184	+	0.216825i
$36$		0			0
$37$	−0.193937	+	0.335908i	−0.0318830	+	0.0552229i	−0.881527	−	0.472134i	$-0.843484\pi$
$37$	−0.193937	+	0.335908i	−0.0318830	+	0.0552229i	0.849644	+	0.527357i	$0.176817\pi$
$38$		0			0
$39$	−0.209095	−	3.59948i	−0.0334820	−	0.576379i
$40$		0			0
$41$	−5.12482	+	8.87645i	−0.800363	+	1.38627i	0.119014	+	0.992893i	$0.462027\pi$
$41$	−5.12482	+	8.87645i	−0.800363	+	1.38627i	−0.919377	+	0.393377i	$0.871307\pi$
$42$		0			0
$43$	5.01270	+	8.68224i	0.764429	+	1.32403i	0.940548	+	0.339661i	$0.110312\pi$
$43$	5.01270	+	8.68224i	0.764429	+	1.32403i	−0.176119	+	0.984369i	$0.556354\pi$
$44$		0			0
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$		0			0
$47$	12.5320			1.82798			0.913989	−	0.405740i	$-0.132986\pi$
$47$	12.5320			1.82798			0.913989	+	0.405740i	$0.132986\pi$
$48$		0			0
$49$	2.40303	−	4.16217i	0.343290	−	0.594596i
$50$		0			0
$51$	−2.48119			−0.347437
$52$		0			0
$53$	1.73813			0.238751			0.119376	−	0.992849i	$-0.461911\pi$
$53$	1.73813			0.238751			0.119376	+	0.992849i	$0.461911\pi$
$54$		0			0
$55$	−1.67513	+	2.90141i	−0.225875	+	0.391226i
$56$		0			0
$57$	−2.15633			−0.285612
$58$		0			0
$59$	4.93089	+	8.54055i	0.641947	+	1.11188i	0.984998	+	0.172568i	$0.0552063\pi$
$59$	4.93089	+	8.54055i	0.641947	+	1.11188i	−0.343051	+	0.939317i	$0.611460\pi$
$60$		0			0
$61$	−3.05936	−	5.29896i	−0.391711	−	0.678463i	0.600965	−	0.799276i	$-0.294783\pi$
$61$	−3.05936	−	5.29896i	−0.391711	−	0.678463i	−0.992675	+	0.120813i	$0.961450\pi$
$62$		0			0
$63$	−0.740597	+	1.28275i	−0.0933065	+	0.161612i
$64$		0			0
$65$	3.01270	−	1.98082i	0.373679	−	0.245691i
$66$		0			0
$67$	−5.62482	+	9.74248i	−0.687182	+	1.19023i	0.285564	+	0.958360i	$0.407819\pi$
$67$	−5.62482	+	9.74248i	−0.687182	+	1.19023i	−0.972746	+	0.231874i	$0.925514\pi$
$68$		0			0
$69$	−2.96239	−	5.13101i	−0.356630	−	0.617701i
$70$		0			0
$71$	7.76234	+	13.4448i	0.921221	+	1.59560i	0.797529	+	0.603280i	$0.206140\pi$
$71$	7.76234	+	13.4448i	0.921221	+	1.59560i	0.123691	+	0.992321i	$0.460527\pi$
$72$		0			0
$73$	−11.6678			−1.36562			−0.682808	−	0.730597i	$-0.739242\pi$
$73$	−11.6678			−1.36562			−0.682808	+	0.730597i	$0.739242\pi$
$74$		0			0
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$		0			0
$77$	−4.96239			−0.565517
$78$		0			0
$79$	−10.7685			−1.21155			−0.605773	−	0.795638i	$-0.707136\pi$
$79$	−10.7685			−1.21155			−0.605773	+	0.795638i	$0.707136\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	6.77575			0.743735			0.371867	−	0.928286i	$-0.378718\pi$
$83$	6.77575			0.743735			0.371867	+	0.928286i	$0.378718\pi$
$84$		0			0
$85$	−1.24060	−	2.14878i	−0.134562	−	0.233068i
$86$		0			0
$87$	3.31876	+	5.74826i	0.355808	+	0.616278i
$88$		0			0
$89$	−9.15022	+	15.8486i	−0.969921	+	1.67995i	−0.274152	+	0.961686i	$0.588397\pi$
$89$	−9.15022	+	15.8486i	−0.969921	+	1.67995i	−0.695769	+	0.718266i	$0.744936\pi$
$90$		0			0
$91$	4.77210	+	2.39755i	0.500252	+	0.251332i
$92$		0			0
$93$	−1.77210	+	3.06937i	−0.183758	+	0.318278i
$94$		0			0
$95$	−1.07816	−	1.86743i	−0.110617	−	0.191595i
$96$		0			0
$97$	0.531502	+	0.920588i	0.0539659	+	0.0934716i	0.891746	−	0.452536i	$-0.149480\pi$
$97$	0.531502	+	0.920588i	0.0539659	+	0.0934716i	−0.837780	+	0.546007i	$0.816147\pi$
$98$		0			0
$99$	−3.35026			−0.336714
$100$		0			0
$101$	−0.156325	+	0.270763i	−0.0155549	+	0.0269419i	−0.873698	−	0.486469i	$-0.838285\pi$
$101$	−0.156325	+	0.270763i	−0.0155549	+	0.0269419i	0.858143	+	0.513410i	$0.171618\pi$
$102$		0			0
$103$	−6.86177			−0.676111			−0.338055	−	0.941126i	$-0.609769\pi$
$103$	−6.86177			−0.676111			−0.338055	+	0.941126i	$0.609769\pi$
$104$		0			0
$105$	−1.48119			−0.144550
$106$		0			0
$107$	4.97873	−	8.62342i	0.481312	−	0.833657i	−0.518458	−	0.855103i	$-0.673494\pi$
$107$	4.97873	−	8.62342i	0.481312	−	0.833657i	0.999770	+	0.0214460i	$0.00682701\pi$
$108$		0			0
$109$	8.53690			0.817687			0.408844	−	0.912604i	$-0.365932\pi$
$109$	8.53690			0.817687			0.408844	+	0.912604i	$0.365932\pi$
$110$		0			0
$111$	−0.193937	−	0.335908i	−0.0184076	−	0.0318830i
$112$		0			0
$113$	6.83146	+	11.8324i	0.642649	+	1.11310i	0.984839	+	0.173470i	$0.0554981\pi$
$113$	6.83146	+	11.8324i	0.642649	+	1.11310i	−0.342190	+	0.939631i	$0.611169\pi$
$114$		0			0
$115$	2.96239	−	5.13101i	0.276244	−	0.478469i
$116$		0			0
$117$	3.22179	+	1.61866i	0.297855	+	0.149645i
$118$		0			0
$119$	1.83757	−	3.18276i	0.168449	−	0.291763i
$120$		0			0
$121$	−0.112127	−	0.194209i	−0.0101934	−	0.0176554i
$122$		0			0
$123$	−5.12482	−	8.87645i	−0.462090	−	0.800363i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−2.57205	+	4.45493i	−0.228233	+	0.395311i	−0.957284	−	0.289148i	$-0.906628\pi$
$127$	−2.57205	+	4.45493i	−0.228233	+	0.395311i	0.729052	+	0.684459i	$0.239961\pi$
$128$		0			0
$129$	−10.0254			−0.882687
$130$		0			0
$131$	17.6507			1.54215			0.771074	−	0.636745i	$-0.219720\pi$
$131$	17.6507			1.54215			0.771074	+	0.636745i	$0.219720\pi$
$132$		0			0
$133$	1.59697	−	2.76603i	0.138475	−	0.239845i
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	1.91573	+	3.31814i	0.163672	+	0.283488i	0.936183	−	0.351514i	$-0.114333\pi$
$137$	1.91573	+	3.31814i	0.163672	+	0.283488i	−0.772511	+	0.635001i	$0.781000\pi$
$138$		0			0
$139$	−3.88787	−	6.73399i	−0.329765	−	0.571170i	0.652700	−	0.757616i	$-0.273636\pi$
$139$	−3.88787	−	6.73399i	−0.329765	−	0.571170i	−0.982465	+	0.186447i	$0.940303\pi$
$140$		0			0
$141$	−6.26599	+	10.8530i	−0.527692	+	0.913989i
$142$		0			0
$143$	0.700523	+	12.0592i	0.0585807	+	1.00844i
$144$		0			0
$145$	−3.31876	+	5.74826i	−0.275608	+	0.477367i
$146$		0			0
$147$	2.40303	+	4.16217i	0.198199	+	0.343290i
$148$		0			0
$149$	−10.7562	−	18.6303i	−0.881185	−	1.52626i	−0.850025	−	0.526743i	$-0.823413\pi$
$149$	−10.7562	−	18.6303i	−0.881185	−	1.52626i	−0.0311602	−	0.999514i	$-0.509920\pi$
$150$		0			0
$151$	−2.15633			−0.175479			−0.0877396	−	0.996143i	$-0.527964\pi$
$151$	−2.15633			−0.175479			−0.0877396	+	0.996143i	$0.527964\pi$
$152$		0			0
$153$	1.24060	−	2.14878i	0.100296	−	0.173718i
$154$		0			0
$155$	−3.54420			−0.284677
$156$		0			0
$157$	−11.5017			−0.917933			−0.458966	−	0.888454i	$-0.651780\pi$
$157$	−11.5017			−0.917933			−0.458966	+	0.888454i	$0.651780\pi$
$158$		0			0
$159$	−0.869067	+	1.50527i	−0.0689215	+	0.119376i
$160$		0			0
$161$	8.77575			0.691626
$162$		0			0
$163$	5.95993	+	10.3229i	0.466817	+	0.808552i	0.999281	−	0.0379011i	$-0.0120672\pi$
$163$	5.95993	+	10.3229i	0.466817	+	0.808552i	−0.532464	+	0.846453i	$0.678734\pi$
$164$		0			0
$165$	−1.67513	−	2.90141i	−0.130409	−	0.225875i
$166$		0			0
$167$	−0.418190	+	0.724327i	−0.0323605	+	0.0560501i	−0.881752	−	0.471713i	$-0.843636\pi$
$167$	−0.418190	+	0.724327i	−0.0323605	+	0.0560501i	0.849392	+	0.527763i	$0.176969\pi$
$168$		0			0
$169$	5.15268	−	11.9352i	0.396360	−	0.918095i
$170$		0			0
$171$	1.07816	−	1.86743i	0.0824492	−	0.142806i
$172$		0			0
$173$	9.03444	+	15.6481i	0.686876	+	1.18970i	0.972843	+	0.231465i	$0.0743517\pi$
$173$	9.03444	+	15.6481i	0.686876	+	1.18970i	−0.285967	+	0.958239i	$0.592315\pi$
$174$		0			0
$175$	−0.740597	−	1.28275i	−0.0559839	−	0.0969669i
$176$		0			0
$177$	−9.86177			−0.741256
$178$		0			0
$179$	10.8253	−	18.7501i	0.809124	−	1.40144i	−0.104347	−	0.994541i	$-0.533275\pi$
$179$	10.8253	−	18.7501i	0.809124	−	1.40144i	0.913471	−	0.406904i	$-0.133392\pi$
$180$		0			0
$181$	−7.19394			−0.534721			−0.267361	−	0.963597i	$-0.586151\pi$
$181$	−7.19394			−0.534721			−0.267361	+	0.963597i	$0.586151\pi$
$182$		0			0
$183$	6.11871			0.452308
$184$		0			0
$185$	0.193937	−	0.335908i	0.0142585	−	0.0246964i
$186$		0			0
$187$	8.31265			0.607881
$188$		0			0
$189$	−0.740597	−	1.28275i	−0.0538705	−	0.0933065i
$190$		0			0
$191$	−11.5005	−	19.9194i	−0.832145	−	1.44132i	−0.896334	−	0.443380i	$-0.853779\pi$
$191$	−11.5005	−	19.9194i	−0.832145	−	1.44132i	0.0641883	−	0.997938i	$-0.479554\pi$
$192$		0			0
$193$	3.28480	−	5.68943i	0.236445	−	0.409534i	−0.723247	−	0.690590i	$-0.757351\pi$
$193$	3.28480	−	5.68943i	0.236445	−	0.409534i	0.959692	+	0.281055i	$0.0906844\pi$
$194$		0			0
$195$	0.209095	+	3.59948i	0.0149736	+	0.257764i
$196$		0			0
$197$	7.40597	−	12.8275i	0.527654	−	0.913923i	−0.471827	−	0.881691i	$-0.656405\pi$
$197$	7.40597	−	12.8275i	0.527654	−	0.913923i	0.999480	−	0.0322316i	$-0.0102614\pi$
$198$		0			0
$199$	10.0188	+	17.3531i	0.710214	+	1.23013i	0.964777	+	0.263071i	$0.0847353\pi$
$199$	10.0188	+	17.3531i	0.710214	+	1.23013i	−0.254562	+	0.967056i	$0.581931\pi$
$200$		0			0
$201$	−5.62482	−	9.74248i	−0.396744	−	0.687182i
$202$		0			0
$203$	−9.83146			−0.690033
$204$		0			0
$205$	5.12482	−	8.87645i	0.357933	−	0.619958i
$206$		0			0
$207$	5.92478			0.411800
$208$		0			0
$209$	7.22425			0.499712
$210$		0			0
$211$	1.50000	−	2.59808i	0.103264	−	0.178859i	−0.809763	−	0.586756i	$-0.800405\pi$
$211$	1.50000	−	2.59808i	0.103264	−	0.178859i	0.913028	+	0.407898i	$0.133738\pi$
$212$		0			0
$213$	−15.5247			−1.06373
$214$		0			0
$215$	−5.01270	−	8.68224i	−0.341863	−	0.592124i
$216$		0			0
$217$	−2.62482	−	4.54633i	−0.178185	−	0.308625i
$218$		0			0
$219$	5.83392	−	10.1046i	0.394220	−	0.682808i
$220$		0			0
$221$	−7.99389	−	4.01621i	−0.537727	−	0.270159i
$222$		0			0
$223$	−2.86907	+	4.96937i	−0.192127	+	0.332774i	−0.945955	−	0.324298i	$-0.894872\pi$
$223$	−2.86907	+	4.96937i	−0.192127	+	0.332774i	0.753828	+	0.657072i	$0.228205\pi$
$224$		0			0
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$		0			0
$227$	6.16537	+	10.6787i	0.409210	+	0.708773i	0.994801	−	0.101834i	$-0.0324709\pi$
$227$	6.16537	+	10.6787i	0.409210	+	0.708773i	−0.585591	+	0.810607i	$0.699138\pi$
$228$		0			0
$229$	−16.4083			−1.08429			−0.542147	−	0.840284i	$-0.682388\pi$
$229$	−16.4083			−1.08429			−0.542147	+	0.840284i	$0.682388\pi$
$230$		0			0
$231$	2.48119	−	4.29755i	0.163251	−	0.282758i
$232$		0			0
$233$	9.73813			0.637966			0.318983	−	0.947760i	$-0.396659\pi$
$233$	9.73813			0.637966			0.318983	+	0.947760i	$0.396659\pi$
$234$		0			0
$235$	−12.5320			−0.817496
$236$		0			0
$237$	5.38423	−	9.32575i	0.349743	−	0.605773i
$238$		0			0
$239$	15.7988			1.02194			0.510969	−	0.859599i	$-0.329287\pi$
$239$	15.7988			1.02194			0.510969	+	0.859599i	$0.329287\pi$
$240$		0			0
$241$	13.1969	+	22.8577i	0.850086	+	1.47239i	0.881130	+	0.472873i	$0.156783\pi$
$241$	13.1969	+	22.8577i	0.850086	+	1.47239i	−0.0310449	+	0.999518i	$0.509883\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−2.40303	+	4.16217i	−0.153524	+	0.265911i
$246$		0			0
$247$	−6.94723	−	3.49036i	−0.442042	−	0.222086i
$248$		0			0
$249$	−3.38787	+	5.86797i	−0.214698	+	0.371867i
$250$		0			0
$251$	10.3806	+	17.9797i	0.655216	+	1.13487i	0.981840	+	0.189713i	$0.0607559\pi$
$251$	10.3806	+	17.9797i	0.655216	+	1.13487i	−0.326623	+	0.945155i	$0.605911\pi$
$252$		0			0
$253$	9.92478	+	17.1902i	0.623965	+	1.08074i
$254$		0			0
$255$	2.48119			0.155378
$256$		0			0
$257$	−1.13998	+	1.97451i	−0.0711101	+	0.123166i	−0.899388	−	0.437151i	$-0.855988\pi$
$257$	−1.13998	+	1.97451i	−0.0711101	+	0.123166i	0.828278	+	0.560317i	$0.189321\pi$
$258$		0			0
$259$	0.574515			0.0356987
$260$		0			0
$261$	−6.63752			−0.410852
$262$		0			0
$263$	−1.62847	+	2.82059i	−0.100416	+	0.173925i	−0.911856	−	0.410510i	$-0.865351\pi$
$263$	−1.62847	+	2.82059i	−0.100416	+	0.173925i	0.811440	+	0.584435i	$0.198684\pi$
$264$		0			0
$265$	−1.73813			−0.106773
$266$		0			0
$267$	−9.15022	−	15.8486i	−0.559984	−	0.969921i
$268$		0			0
$269$	−5.64363	−	9.77505i	−0.344098	−	0.595995i	0.641091	−	0.767465i	$-0.278482\pi$
$269$	−5.64363	−	9.77505i	−0.344098	−	0.595995i	−0.985189	+	0.171469i	$0.945149\pi$
$270$		0			0
$271$	0.887873	−	1.53784i	0.0539345	−	0.0934172i	−0.837798	−	0.545981i	$-0.816157\pi$
$271$	0.887873	−	1.53784i	0.0539345	−	0.0934172i	0.891732	+	0.452564i	$0.149490\pi$
$272$		0			0
$273$	−4.46239	+	2.93398i	−0.270076	+	0.177573i
$274$		0			0
$275$	1.67513	−	2.90141i	0.101014	−	0.174962i
$276$		0			0
$277$	−12.6629	−	21.9328i	−0.760841	−	1.31781i	−0.942418	−	0.334438i	$-0.891454\pi$
$277$	−12.6629	−	21.9328i	−0.760841	−	1.31781i	0.181577	−	0.983377i	$-0.441880\pi$
$278$		0			0
$279$	−1.77210	−	3.06937i	−0.106093	−	0.183758i
$280$		0			0
$281$	−14.0122			−0.835899			−0.417949	−	0.908470i	$-0.637251\pi$
$281$	−14.0122			−0.835899			−0.417949	+	0.908470i	$0.637251\pi$
$282$		0			0
$283$	9.74060	−	16.8712i	0.579018	−	1.00289i	−0.416574	−	0.909102i	$-0.636769\pi$
$283$	9.74060	−	16.8712i	0.579018	−	1.00289i	0.995592	−	0.0937874i	$-0.0298974\pi$
$284$		0			0
$285$	2.15633			0.127730
$286$		0			0
$287$	15.1817			0.896148
$288$		0			0
$289$	5.42184	−	9.39090i	0.318932	−	0.552406i
$290$		0			0
$291$	−1.06300			−0.0623144
$292$		0			0
$293$	1.17759	+	2.03965i	0.0687957	+	0.119158i	0.898371	−	0.439237i	$-0.144751\pi$
$293$	1.17759	+	2.03965i	0.0687957	+	0.119158i	−0.829576	+	0.558394i	$0.811418\pi$
$294$		0			0
$295$	−4.93089	−	8.54055i	−0.287087	−	0.497250i
$296$		0			0
$297$	1.67513	−	2.90141i	0.0972010	−	0.168357i
$298$		0			0
$299$	−1.23884	−	21.3261i	−0.0716441	−	1.23332i
$300$		0			0
$301$	7.42478	−	12.8601i	0.427957	−	0.741243i
$302$		0			0
$303$	−0.156325	−	0.270763i	−0.00898065	−	0.0155549i
$304$		0			0
$305$	3.05936	+	5.29896i	0.175178	+	0.303418i
$306$		0			0
$307$	−17.5623			−1.00233			−0.501167	−	0.865351i	$-0.667096\pi$
$307$	−17.5623			−1.00233			−0.501167	+	0.865351i	$0.667096\pi$
$308$		0			0
$309$	3.43089	−	5.94247i	0.195176	−	0.338055i
$310$		0			0
$311$	15.0762			0.854892			0.427446	−	0.904041i	$-0.359413\pi$
$311$	15.0762			0.854892			0.427446	+	0.904041i	$0.359413\pi$
$312$		0			0
$313$	17.6883			0.999802			0.499901	−	0.866083i	$-0.333370\pi$
$313$	17.6883			0.999802			0.499901	+	0.866083i	$0.333370\pi$
$314$		0			0
$315$	0.740597	−	1.28275i	0.0417279	−	0.0722749i
$316$		0			0
$317$	3.48612			0.195800			0.0979000	−	0.995196i	$-0.468787\pi$
$317$	3.48612			0.195800			0.0979000	+	0.995196i	$0.468787\pi$
$318$		0			0
$319$	−11.1187	−	19.2582i	−0.622528	−	1.07825i
$320$		0			0
$321$	4.97873	+	8.62342i	0.277886	+	0.481312i
$322$		0			0
$323$	−2.67513	+	4.63346i	−0.148848	+	0.257813i
$324$		0			0
$325$	−3.01270	+	1.98082i	−0.167114	+	0.109876i
$326$		0			0
$327$	−4.26845	+	7.39318i	−0.236046	+	0.408844i
$328$		0			0
$329$	−9.28115	−	16.0754i	−0.511686	−	0.886267i
$330$		0			0
$331$	−3.81265	−	6.60370i	−0.209562	−	0.362972i	0.742014	−	0.670384i	$-0.233871\pi$
$331$	−3.81265	−	6.60370i	−0.209562	−	0.362972i	−0.951577	+	0.307411i	$0.900537\pi$
$332$		0			0
$333$	0.387873			0.0212553
$334$		0			0
$335$	5.62482	−	9.74248i	0.307317	−	0.532289i
$336$		0			0
$337$	−18.0254			−0.981906			−0.490953	−	0.871186i	$-0.663351\pi$
$337$	−18.0254			−0.981906			−0.490953	+	0.871186i	$0.663351\pi$
$338$		0			0
$339$	−13.6629			−0.742068
$340$		0			0
$341$	5.93700	−	10.2832i	0.321506	−	0.556865i
$342$		0			0
$343$	−17.4871			−0.944213
$344$		0			0
$345$	2.96239	+	5.13101i	0.159490	+	0.276244i
$346$		0			0
$347$	10.4060	+	18.0237i	0.558622	+	0.967561i	0.997612	+	0.0690694i	$0.0220030\pi$
$347$	10.4060	+	18.0237i	0.558622	+	0.967561i	−0.438990	+	0.898492i	$0.644664\pi$
$348$		0			0
$349$	15.3344	−	26.5600i	0.820831	−	1.42172i	−0.0842325	−	0.996446i	$-0.526844\pi$
$349$	15.3344	−	26.5600i	0.820831	−	1.42172i	0.905064	−	0.425276i	$-0.139823\pi$
$350$		0			0
$351$	−3.01270	+	1.98082i	−0.160806	+	0.105729i
$352$		0			0
$353$	−1.16125	+	2.01134i	−0.0618071	+	0.107053i	−0.895273	−	0.445518i	$-0.853020\pi$
$353$	−1.16125	+	2.01134i	−0.0618071	+	0.107053i	0.833466	+	0.552571i	$0.186353\pi$
$354$		0			0
$355$	−7.76234	−	13.4448i	−0.411982	−	0.713574i
$356$		0			0
$357$	1.83757	+	3.18276i	0.0972543	+	0.168449i
$358$		0			0
$359$	−9.87636			−0.521254			−0.260627	−	0.965440i	$-0.583929\pi$
$359$	−9.87636			−0.521254			−0.260627	+	0.965440i	$0.583929\pi$
$360$		0			0
$361$	7.17513	−	12.4277i	0.377638	−	0.654089i
$362$		0			0
$363$	0.224254			0.0117703
$364$		0			0
$365$	11.6678			0.610722
$366$		0			0
$367$	2.52421	−	4.37206i	0.131763	−	0.228219i	−0.792594	−	0.609750i	$-0.791270\pi$
$367$	2.52421	−	4.37206i	0.131763	−	0.228219i	0.924356	+	0.381531i	$0.124603\pi$
$368$		0			0
$369$	10.2496			0.533575
$370$		0			0
$371$	−1.28726	−	2.22960i	−0.0668311	−	0.115755i
$372$		0			0
$373$	9.70299	+	16.8061i	0.502402	+	0.870185i	0.999996	+	0.00277530i	$0.000883408\pi$
$373$	9.70299	+	16.8061i	0.502402	+	0.870185i	−0.497595	+	0.867410i	$0.665783\pi$
$374$		0			0
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$		0			0
$377$	1.38787	+	23.8916i	0.0714791	+	1.23048i
$378$		0			0
$379$	14.7223	−	25.4997i	0.756232	−	1.30983i	−0.188527	−	0.982068i	$-0.560371\pi$
$379$	14.7223	−	25.4997i	0.756232	−	1.30983i	0.944759	−	0.327765i	$-0.106295\pi$
$380$		0			0
$381$	−2.57205	−	4.45493i	−0.131770	−	0.228233i
$382$		0			0
$383$	−2.39692	−	4.15159i	−0.122477	−	0.212136i	0.798267	−	0.602304i	$-0.205750\pi$
$383$	−2.39692	−	4.15159i	−0.122477	−	0.212136i	−0.920744	+	0.390167i	$0.872417\pi$
$384$		0			0
$385$	4.96239			0.252907
$386$		0			0
$387$	5.01270	−	8.68224i	0.254810	−	0.441343i
$388$		0			0
$389$	−0.850969			−0.0431458			−0.0215729	−	0.999767i	$-0.506867\pi$
$389$	−0.850969			−0.0431458			−0.0215729	+	0.999767i	$0.506867\pi$
$390$		0			0
$391$	−14.7005			−0.743437
$392$		0			0
$393$	−8.82535	+	15.2859i	−0.445180	+	0.771074i
$394$		0			0
$395$	10.7685			0.541820
$396$		0			0
$397$	−15.0938	−	26.1432i	−0.757536	−	1.31209i	−0.944104	−	0.329649i	$-0.893070\pi$
$397$	−15.0938	−	26.1432i	−0.757536	−	1.31209i	0.186568	−	0.982442i	$-0.440264\pi$
$398$		0			0
$399$	1.59697	+	2.76603i	0.0799484	+	0.138475i
$400$		0			0
$401$	−5.67513	+	9.82962i	−0.283403	+	0.490868i	−0.972221	−	0.234067i	$-0.924797\pi$
$401$	−5.67513	+	9.82962i	−0.283403	+	0.490868i	0.688818	+	0.724934i	$0.258130\pi$
$402$		0			0
$403$	−10.6776	+	7.02043i	−0.531889	+	0.349713i
$404$		0			0
$405$	0.500000	−	0.866025i	0.0248452	−	0.0430331i
$406$		0			0
$407$	0.649738	+	1.12538i	0.0322063	+	0.0557830i
$408$		0			0
$409$	−2.18536	−	3.78516i	−0.108059	−	0.187164i	0.806925	−	0.590654i	$-0.201130\pi$
$409$	−2.18536	−	3.78516i	−0.108059	−	0.187164i	−0.914984	+	0.403490i	$0.867797\pi$
$410$		0			0
$411$	−3.83146			−0.188992
$412$		0			0
$413$	7.30360	−	12.6502i	0.359387	−	0.622476i
$414$		0			0
$415$	−6.77575			−0.332608
$416$		0			0
$417$	7.77575			0.380780
$418$		0			0
$419$	2.38669	−	4.13387i	0.116597	−	0.201953i	−0.801820	−	0.597566i	$-0.796135\pi$
$419$	2.38669	−	4.13387i	0.116597	−	0.201953i	0.918417	+	0.395613i	$0.129468\pi$
$420$		0			0
$421$	−33.4445			−1.62999			−0.814994	−	0.579470i	$-0.803260\pi$
$421$	−33.4445			−1.62999			−0.814994	+	0.579470i	$0.803260\pi$
$422$		0			0
$423$	−6.26599	−	10.8530i	−0.304663	−	0.527692i
$424$		0			0
$425$	1.24060	+	2.14878i	0.0601778	+	0.104231i
$426$		0			0
$427$	−4.53150	+	7.84879i	−0.219295	+	0.379830i
$428$		0			0
$429$	−10.7938	−	5.42293i	−0.521132	−	0.261822i
$430$		0			0
$431$	−11.5623	+	20.0265i	−0.556936	+	0.964642i	0.440814	+	0.897599i	$0.354690\pi$
$431$	−11.5623	+	20.0265i	−0.556936	+	0.964642i	−0.997750	+	0.0670433i	$0.978643\pi$
$432$		0			0
$433$	13.1466	+	22.7705i	0.631784	+	1.09428i	0.987187	+	0.159568i	$0.0510103\pi$
$433$	13.1466	+	22.7705i	0.631784	+	1.09428i	−0.355403	+	0.934713i	$0.615656\pi$
$434$		0			0
$435$	−3.31876	−	5.74826i	−0.159122	−	0.275608i
$436$		0			0
$437$	−12.7757			−0.611147
$438$		0			0
$439$	−7.47262	+	12.9430i	−0.356649	+	0.617734i	−0.987399	−	0.158252i	$-0.949414\pi$
$439$	−7.47262	+	12.9430i	−0.356649	+	0.617734i	0.630750	+	0.775986i	$0.282747\pi$
$440$		0			0
$441$	−4.80606			−0.228860
$442$		0			0
$443$	−41.3439			−1.96431			−0.982155	−	0.188076i	$-0.939775\pi$
$443$	−41.3439			−1.96431			−0.982155	+	0.188076i	$0.939775\pi$
$444$		0			0
$445$	9.15022	−	15.8486i	0.433762	−	0.751298i
$446$		0			0
$447$	21.5125			1.01750
$448$		0			0
$449$	−15.1744	−	26.2829i	−0.716125	−	1.24037i	−0.962524	−	0.271197i	$-0.912581\pi$
$449$	−15.1744	−	26.2829i	−0.716125	−	1.24037i	0.246399	−	0.969169i	$-0.420753\pi$
$450$		0			0
$451$	17.1695	+	29.7384i	0.808480	+	1.40033i
$452$		0			0
$453$	1.07816	−	1.86743i	0.0506565	−	0.0877396i
$454$		0			0
$455$	−4.77210	−	2.39755i	−0.223719	−	0.112399i
$456$		0			0
$457$	−7.98238	+	13.8259i	−0.373400	+	0.646748i	−0.990086	−	0.140461i	$-0.955141\pi$
$457$	−7.98238	+	13.8259i	−0.373400	+	0.646748i	0.616686	+	0.787209i	$0.288475\pi$
$458$		0			0
$459$	1.24060	+	2.14878i	0.0579061	+	0.100296i
$460$		0			0
$461$	14.9939	+	25.9702i	0.698335	+	1.20955i	0.969043	+	0.246890i	$0.0794088\pi$
$461$	14.9939	+	25.9702i	0.698335	+	1.20955i	−0.270708	+	0.962661i	$0.587258\pi$
$462$		0			0
$463$	2.39868			0.111476			0.0557380	−	0.998445i	$-0.482249\pi$
$463$	2.39868			0.111476			0.0557380	+	0.998445i	$0.482249\pi$
$464$		0			0
$465$	1.77210	−	3.06937i	0.0821791	−	0.142338i
$466$		0			0
$467$	−18.6434			−0.862714			−0.431357	−	0.902181i	$-0.641965\pi$
$467$	−18.6434			−0.862714			−0.431357	+	0.902181i	$0.641965\pi$
$468$		0			0
$469$	16.6629			0.769422
$470$		0			0
$471$	5.75083	−	9.96073i	0.264984	−	0.458966i
$472$		0			0
$473$	33.5877			1.54436
$474$		0			0
$475$	1.07816	+	1.86743i	0.0494695	+	0.0856837i
$476$		0			0
$477$	−0.869067	−	1.50527i	−0.0397919	−	0.0689215i
$478$		0			0
$479$	−0.356371	+	0.617253i	−0.0162830	+	0.0282030i	−0.874052	−	0.485832i	$-0.838517\pi$
$479$	−0.356371	+	0.617253i	−0.0162830	+	0.0282030i	0.857769	+	0.514035i	$0.171850\pi$
$480$		0			0
$481$	−0.0811024	−	1.39614i	−0.00369795	−	0.0636586i
$482$		0			0
$483$	−4.38787	+	7.60002i	−0.199655	+	0.345813i
$484$		0			0
$485$	−0.531502	−	0.920588i	−0.0241343	−	0.0418018i
$486$		0			0
$487$	1.62966	+	2.82265i	0.0738467	+	0.127906i	0.900584	−	0.434682i	$-0.143139\pi$
$487$	1.62966	+	2.82265i	0.0738467	+	0.127906i	−0.826737	+	0.562588i	$0.809806\pi$
$488$		0			0
$489$	−11.9199			−0.539034
$490$		0			0
$491$	16.3442	−	28.3089i	0.737601	−	1.27756i	−0.215971	−	0.976400i	$-0.569292\pi$
$491$	16.3442	−	28.3089i	0.737601	−	1.27756i	0.953573	−	0.301163i	$-0.0973749\pi$
$492$		0			0
$493$	16.4690			0.741725
$494$		0			0
$495$	3.35026			0.150583
$496$		0			0
$497$	11.4975	−	19.9143i	0.515735	−	0.893279i
$498$		0			0
$499$	7.26916			0.325412			0.162706	−	0.986675i	$-0.447978\pi$
$499$	7.26916			0.325412			0.162706	+	0.986675i	$0.447978\pi$
$500$		0			0
$501$	−0.418190	−	0.724327i	−0.0186834	−	0.0323605i
$502$		0			0
$503$	−6.38058	−	11.0515i	−0.284496	−	0.492761i	0.687991	−	0.725719i	$-0.258493\pi$
$503$	−6.38058	−	11.0515i	−0.284496	−	0.492761i	−0.972487	+	0.232958i	$0.925160\pi$
$504$		0			0
$505$	0.156325	−	0.270763i	0.00695638	−	0.0120488i
$506$		0			0
$507$	7.75988	+	10.4300i	0.344628	+	0.463211i
$508$		0			0
$509$	−11.1817	+	19.3673i	−0.495621	+	0.858441i	−0.999987	−	0.00504916i	$-0.998393\pi$
$509$	−11.1817	+	19.3673i	−0.495621	+	0.858441i	0.504366	+	0.863490i	$0.331726\pi$
$510$		0			0
$511$	8.64117	+	14.9669i	0.382263	+	0.662098i
$512$		0			0
$513$	1.07816	+	1.86743i	0.0476020	+	0.0824492i
$514$		0			0
$515$	6.86177			0.302366
$516$		0			0
$517$	20.9927	−	36.3604i	0.923258	−	1.59913i
$518$		0			0
$519$	−18.0689			−0.793136
$520$		0			0
$521$	2.78797			0.122143			0.0610715	−	0.998133i	$-0.480548\pi$
$521$	2.78797			0.122143			0.0610715	+	0.998133i	$0.480548\pi$
$522$		0			0
$523$	−14.8994	+	25.8065i	−0.651505	+	1.12844i	0.331253	+	0.943542i	$0.392529\pi$
$523$	−14.8994	+	25.8065i	−0.651505	+	1.12844i	−0.982758	+	0.184897i	$0.940805\pi$
$524$		0			0
$525$	1.48119			0.0646446
$526$		0			0
$527$	4.39692	+	7.61569i	0.191533	+	0.331745i
$528$		0			0
$529$	−6.05149	−	10.4815i	−0.263108	−	0.455717i
$530$		0			0
$531$	4.93089	−	8.54055i	0.213982	−	0.370628i
$532$		0			0
$533$	−2.14315	−	36.8934i	−0.0928302	−	1.59803i
$534$		0			0
$535$	−4.97873	+	8.62342i	−0.215249	+	0.372823i
$536$		0			0
$537$	10.8253	+	18.7501i	0.467148	+	0.809124i
$538$		0			0
$539$	−8.05079	−	13.9444i	−0.346772	−	0.600626i
$540$		0			0
$541$	−23.3371			−1.00334			−0.501670	−	0.865059i	$-0.667281\pi$
$541$	−23.3371			−1.00334			−0.501670	+	0.865059i	$0.667281\pi$
$542$		0			0
$543$	3.59697	−	6.23013i	0.154361	−	0.267361i
$544$		0			0
$545$	−8.53690			−0.365681
$546$		0			0
$547$	−42.7377			−1.82733			−0.913666	−	0.406467i	$-0.866761\pi$
$547$	−42.7377			−1.82733			−0.913666	+	0.406467i	$0.866761\pi$
$548$		0			0
$549$	−3.05936	+	5.29896i	−0.130570	+	0.226154i
$550$		0			0
$551$	14.3127			0.609739
$552$		0			0
$553$	7.97508	+	13.8133i	0.339135	+	0.587399i
$554$		0			0
$555$	0.193937	+	0.335908i	0.00823215	+	0.0142585i
$556$		0			0
$557$	−5.01222	+	8.68142i	−0.212375	+	0.367843i	−0.952457	−	0.304672i	$-0.901453\pi$
$557$	−5.01222	+	8.68142i	−0.212375	+	0.367843i	0.740083	+	0.672516i	$0.234786\pi$
$558$		0			0
$559$	−32.2997	−	16.2277i	−1.36613	−	0.686359i
$560$		0			0
$561$	−4.15633	+	7.19897i	−0.175480	+	0.303941i
$562$		0			0
$563$	−0.224254	−	0.388419i	−0.00945117	−	0.0163699i	0.861261	−	0.508163i	$-0.169675\pi$
$563$	−0.224254	−	0.388419i	−0.00945117	−	0.0163699i	−0.870712	+	0.491793i	$0.836342\pi$
$564$		0			0
$565$	−6.83146	−	11.8324i	−0.287402	−	0.497794i
$566$		0			0
$567$	1.48119			0.0622043
$568$		0			0
$569$	−15.4072	+	26.6860i	−0.645902	+	1.11873i	0.338191	+	0.941078i	$0.390185\pi$
$569$	−15.4072	+	26.6860i	−0.645902	+	1.11873i	−0.984092	+	0.177657i	$0.943148\pi$
$570$		0			0
$571$	11.4314			0.478388			0.239194	−	0.970972i	$-0.423117\pi$
$571$	11.4314			0.478388			0.239194	+	0.970972i	$0.423117\pi$
$572$		0			0
$573$	23.0010			0.960879
$574$		0			0
$575$	−2.96239	+	5.13101i	−0.123540	+	0.213978i
$576$		0			0
$577$	21.9149			0.912330			0.456165	−	0.889895i	$-0.349223\pi$
$577$	21.9149			0.912330			0.456165	+	0.889895i	$0.349223\pi$
$578$		0			0
$579$	3.28480	+	5.68943i	0.136511	+	0.236445i
$580$		0			0
$581$	−5.01810	−	8.69160i	−0.208186	−	0.360588i
$582$		0			0
$583$	2.91160	−	5.04304i	0.120586	−	0.208862i
$584$		0			0
$585$	−3.22179	−	1.61866i	−0.133205	−	0.0669233i
$586$		0			0
$587$	1.65879	−	2.87310i	0.0684655	−	0.118586i	−0.829761	−	0.558120i	$-0.811523\pi$
$587$	1.65879	−	2.87310i	0.0684655	−	0.118586i	0.898226	+	0.439534i	$0.144856\pi$
$588$		0			0
$589$	3.82122	+	6.61855i	0.157451	+	0.272713i
$590$		0			0
$591$	7.40597	+	12.8275i	0.304641	+	0.527654i
$592$		0			0
$593$	−12.7250			−0.522552			−0.261276	−	0.965264i	$-0.584143\pi$
$593$	−12.7250			−0.522552			−0.261276	+	0.965264i	$0.584143\pi$
$594$		0			0
$595$	−1.83757	+	3.18276i	−0.0753328	+	0.130480i
$596$		0			0
$597$	−20.0376			−0.820085
$598$		0			0
$599$	8.30043			0.339146			0.169573	−	0.985518i	$-0.445761\pi$
$599$	8.30043			0.339146			0.169573	+	0.985518i	$0.445761\pi$
$600$		0			0
$601$	−7.61507	+	13.1897i	−0.310625	+	0.538018i	−0.978498	−	0.206257i	$-0.933872\pi$
$601$	−7.61507	+	13.1897i	−0.310625	+	0.538018i	0.667873	+	0.744275i	$0.267205\pi$
$602$		0			0
$603$	11.2496			0.458121
$604$		0			0
$605$	0.112127	+	0.194209i	0.00455861	+	0.00789574i
$606$		0			0
$607$	−0.884226	−	1.53152i	−0.0358896	−	0.0621627i	0.847523	−	0.530759i	$-0.178093\pi$
$607$	−0.884226	−	1.53152i	−0.0358896	−	0.0621627i	−0.883412	+	0.468597i	$0.844760\pi$
$608$		0			0
$609$	4.91573	−	8.51429i	0.199195	−	0.345016i
$610$		0			0
$611$	−37.7550	+	24.8236i	−1.52741	+	1.00426i
$612$		0			0
$613$	8.20171	−	14.2058i	0.331264	−	0.573766i	−0.651496	−	0.758652i	$-0.725858\pi$
$613$	8.20171	−	14.2058i	0.331264	−	0.573766i	0.982760	+	0.184886i	$0.0591916\pi$
$614$		0			0
$615$	5.12482	+	8.87645i	0.206653	+	0.357933i
$616$		0			0
$617$	21.3380	+	36.9586i	0.859037	+	1.48790i	0.872848	+	0.487992i	$0.162270\pi$
$617$	21.3380	+	36.9586i	0.859037	+	1.48790i	−0.0138111	+	0.999905i	$0.504396\pi$
$618$		0			0
$619$	16.8641			0.677827			0.338914	−	0.940818i	$-0.389941\pi$
$619$	16.8641			0.677827			0.338914	+	0.940818i	$0.389941\pi$
$620$		0			0
$621$	−2.96239	+	5.13101i	−0.118877	+	0.205900i
$622$		0			0
$623$	27.1065			1.08600
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−3.61213	+	6.25639i	−0.144254	+	0.249856i
$628$		0			0
$629$	−0.962389			−0.0383729
$630$		0			0
$631$	13.1405	+	22.7599i	0.523113	+	0.906059i	0.999638	+	0.0268980i	$0.00856293\pi$
$631$	13.1405	+	22.7599i	0.523113	+	0.906059i	−0.476525	+	0.879161i	$0.658104\pi$
$632$		0			0
$633$	1.50000	+	2.59808i	0.0596196	+	0.103264i
$634$		0			0
$635$	2.57205	−	4.45493i	0.102069	−	0.176788i
$636$		0			0
$637$	1.00492	+	17.2993i	0.0398166	+	0.685425i
$638$		0			0
$639$	7.76234	−	13.4448i	0.307074	−	0.531867i
$640$		0			0
$641$	−10.9624	−	18.9874i	−0.432988	−	0.749958i	0.564141	−	0.825679i	$-0.309208\pi$
$641$	−10.9624	−	18.9874i	−0.432988	−	0.749958i	−0.997129	+	0.0757209i	$0.975874\pi$
$642$		0			0
$643$	−4.40351	−	7.62710i	−0.173657	−	0.300784i	0.766038	−	0.642795i	$-0.222225\pi$
$643$	−4.40351	−	7.62710i	−0.173657	−	0.300784i	−0.939696	+	0.342011i	$0.888892\pi$
$644$		0			0
$645$	10.0254			0.394749
$646$		0			0
$647$	13.7381	−	23.7951i	0.540102	−	0.935484i	−0.458796	−	0.888542i	$-0.651719\pi$
$647$	13.7381	−	23.7951i	0.540102	−	0.935484i	0.998898	−	0.0469420i	$-0.0149476\pi$
$648$		0			0
$649$	33.0395			1.29691
$650$		0			0
$651$	5.24965			0.205750
$652$		0			0
$653$	3.86002	−	6.68575i	0.151054	−	0.261634i	−0.780561	−	0.625080i	$-0.785067\pi$
$653$	3.86002	−	6.68575i	0.151054	−	0.261634i	0.931615	+	0.363446i	$0.118400\pi$
$654$		0			0
$655$	−17.6507			−0.689670
$656$		0			0
$657$	5.83392	+	10.1046i	0.227603	+	0.394220i
$658$		0			0
$659$	−13.9126	−	24.0973i	−0.541956	−	0.938696i	−0.998792	−	0.0491446i	$-0.984350\pi$
$659$	−13.9126	−	24.0973i	−0.541956	−	0.938696i	0.456835	−	0.889551i	$-0.348983\pi$
$660$		0			0
$661$	0.575223	−	0.996315i	0.0223736	−	0.0387522i	−0.854622	−	0.519251i	$-0.826211\pi$
$661$	0.575223	−	0.996315i	0.0223736	−	0.0387522i	0.876995	+	0.480499i	$0.159544\pi$
$662$		0			0
$663$	7.47508	−	4.91481i	0.290308	−	0.190875i
$664$		0			0
$665$	−1.59697	+	2.76603i	−0.0619278	+	0.107262i
$666$		0			0
$667$	19.6629	+	34.0572i	0.761351	+	1.31870i
$668$		0			0
$669$	−2.86907	−	4.96937i	−0.110925	−	0.192127i
$670$		0			0
$671$	−20.4993			−0.791366
$672$		0			0
$673$	8.77328	−	15.1958i	0.338185	−	0.585754i	−0.645906	−	0.763417i	$-0.723520\pi$
$673$	8.77328	−	15.1958i	0.338185	−	0.585754i	0.984091	+	0.177663i	$0.0568536\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$		0			0
$677$	18.9868			0.729723			0.364862	−	0.931062i	$-0.381116\pi$
$677$	18.9868			0.729723			0.364862	+	0.931062i	$0.381116\pi$
$678$		0			0
$679$	0.787258	−	1.36357i	0.0302122	−	0.0523290i
$680$		0			0
$681$	−12.3307			−0.472515
$682$		0			0
$683$	5.23567	+	9.06845i	0.200337	+	0.346995i	0.948637	−	0.316366i	$-0.102463\pi$
$683$	5.23567	+	9.06845i	0.200337	+	0.346995i	−0.748300	+	0.663361i	$0.769129\pi$
$684$		0			0
$685$	−1.91573	−	3.31814i	−0.0731962	−	0.126780i
$686$		0			0
$687$	8.20417	−	14.2100i	0.313009	−	0.542147i
$688$		0			0
$689$	−5.23647	+	3.44294i	−0.199494	+	0.131165i
$690$		0			0
$691$	−19.7272	+	34.1685i	−0.750458	+	1.29983i	0.197143	+	0.980375i	$0.436834\pi$
$691$	−19.7272	+	34.1685i	−0.750458	+	1.29983i	−0.947601	+	0.319456i	$0.896500\pi$
$692$		0			0
$693$	2.48119	+	4.29755i	0.0942528	+	0.163251i
$694$		0			0
$695$	3.88787	+	6.73399i	0.147475	+	0.255435i
$696$		0			0
$697$	−25.4314			−0.963282
$698$		0			0
$699$	−4.86907	+	8.43347i	−0.184165	+	0.318983i
$700$		0			0
$701$	−18.3634			−0.693577			−0.346789	−	0.937943i	$-0.612728\pi$
$701$	−18.3634			−0.693577			−0.346789	+	0.937943i	$0.612728\pi$
$702$		0			0
$703$	−0.836381			−0.0315447
$704$		0			0
$705$	6.26599	−	10.8530i	0.235991	−	0.408748i
$706$		0			0
$707$	0.463096			0.0174165
$708$		0			0
$709$	25.9993	+	45.0321i	0.976424	+	1.69122i	0.675154	+	0.737677i	$0.264077\pi$
$709$	25.9993	+	45.0321i	0.976424	+	1.69122i	0.301270	+	0.953539i	$0.402589\pi$
$710$		0			0
$711$	5.38423	+	9.32575i	0.201924	+	0.349743i
$712$		0			0
$713$	−10.4993	+	18.1853i	−0.393202	+	0.681045i
$714$		0			0
$715$	−0.700523	−	12.0592i	−0.0261981	−	0.450989i
$716$		0			0
$717$	−7.89938	+	13.6821i	−0.295008	+	0.510969i
$718$		0			0
$719$	10.0618	+	17.4276i	0.375243	+	0.649939i	0.990363	−	0.138494i	$-0.0442261\pi$
$719$	10.0618	+	17.4276i	0.375243	+	0.649939i	−0.615121	+	0.788433i	$0.710893\pi$
$720$		0			0
$721$	5.08181	+	8.80195i	0.189256	+	0.327802i
$722$		0			0
$723$	−26.3938			−0.981594
$724$		0			0
$725$	3.31876	−	5.74826i	0.123256	−	0.213485i
$726$		0			0
$727$	−11.3249			−0.420016			−0.210008	−	0.977700i	$-0.567349\pi$
$727$	−11.3249			−0.420016			−0.210008	+	0.977700i	$0.567349\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−12.4375	+	21.5423i	−0.460017	+	0.796772i
$732$		0			0
$733$	43.0503			1.59010			0.795050	−	0.606544i	$-0.207445\pi$
$733$	43.0503			1.59010			0.795050	+	0.606544i	$0.207445\pi$
$734$		0			0
$735$	−2.40303	−	4.16217i	−0.0886372	−	0.153524i
$736$		0			0
$737$	18.8446	+	32.6399i	0.694151	+	1.20230i
$738$		0			0
$739$	−15.9429	+	27.6139i	−0.586468	+	1.01579i	0.408222	+	0.912882i	$0.366149\pi$
$739$	−15.9429	+	27.6139i	−0.586468	+	1.01579i	−0.994691	+	0.102910i	$0.967185\pi$
$740$		0			0
$741$	6.49635	−	4.27130i	0.238649	−	0.156910i
$742$		0			0
$743$	−0.754478	+	1.30679i	−0.0276791	+	0.0479416i	−0.879533	−	0.475838i	$-0.842145\pi$
$743$	−0.754478	+	1.30679i	−0.0276791	+	0.0479416i	0.851854	+	0.523779i	$0.175478\pi$
$744$		0			0
$745$	10.7562	+	18.6303i	0.394078	+	0.682563i
$746$		0			0
$747$	−3.38787	−	5.86797i	−0.123956	−	0.214698i
$748$		0			0
$749$	−14.7489			−0.538915
$750$		0			0
$751$	8.75329	−	15.1611i	0.319412	−	0.553238i	−0.660953	−	0.750427i	$-0.729848\pi$
$751$	8.75329	−	15.1611i	0.319412	−	0.553238i	0.980366	+	0.197189i	$0.0631812\pi$
$752$		0			0
$753$	−20.7612			−0.756579
$754$		0			0
$755$	2.15633			0.0784767
$756$		0			0
$757$	−13.4538	+	23.3027i	−0.488987	+	0.846951i	−0.999920	−	0.0126700i	$-0.995967\pi$
$757$	−13.4538	+	23.3027i	−0.488987	+	0.846951i	0.510932	+	0.859621i	$0.329300\pi$
$758$		0			0
$759$	−19.8496			−0.720493
$760$		0			0
$761$	−2.90668	−	5.03452i	−0.105367	−	0.182501i	0.808521	−	0.588467i	$-0.200268\pi$
$761$	−2.90668	−	5.03452i	−0.105367	−	0.182501i	−0.913888	+	0.405966i	$0.866935\pi$
$762$		0			0
$763$	−6.32241	−	10.9507i	−0.228886	−	0.396443i
$764$		0			0
$765$	−1.24060	+	2.14878i	−0.0448539	+	0.0776892i
$766$		0			0
$767$	−31.7726	−	15.9629i	−1.14724	−	0.576385i
$768$		0			0
$769$	−12.8212	+	22.2070i	−0.462345	+	0.800805i	−0.999077	−	0.0429474i	$-0.986325\pi$
$769$	−12.8212	+	22.2070i	−0.462345	+	0.800805i	0.536732	+	0.843753i	$0.319659\pi$
$770$		0			0
$771$	−1.13998	−	1.97451i	−0.0410554	−	0.0711101i
$772$		0			0
$773$	17.8315	+	30.8850i	0.641353	+	1.11086i	0.985131	+	0.171805i	$0.0549599\pi$
$773$	17.8315	+	30.8850i	0.641353	+	1.11086i	−0.343778	+	0.939051i	$0.611707\pi$
$774$		0			0
$775$	3.54420			0.127311
$776$		0			0
$777$	−0.287258	+	0.497545i	−0.0103053	+	0.0178493i
$778$		0			0
$779$	−22.1016			−0.791871
$780$		0			0
$781$	52.0118			1.86113
$782$		0			0
$783$	3.31876	−	5.74826i	0.118603	−	0.205426i
$784$		0			0
$785$	11.5017			0.410512
$786$		0			0
$787$	−15.2218	−	26.3649i	−0.542598	−	0.939808i	−0.998754	−	0.0499077i	$-0.984107\pi$
$787$	−15.2218	−	26.3649i	−0.542598	−	0.939808i	0.456156	−	0.889900i	$-0.349226\pi$
$788$		0			0
$789$	−1.62847	−	2.82059i	−0.0579751	−	0.100416i
$790$		0			0
$791$	10.1187	−	17.5261i	0.359780	−	0.623157i
$792$		0			0
$793$	19.7132	+	9.90412i	0.700037	+	0.351705i
$794$		0			0
$795$	0.869067	−	1.50527i	0.0308226	−	0.0533864i
$796$		0			0
$797$	−9.77162	−	16.9249i	−0.346129	−	0.599512i	0.639430	−	0.768850i	$-0.279171\pi$
$797$	−9.77162	−	16.9249i	−0.346129	−	0.599512i	−0.985558	+	0.169337i	$0.945837\pi$
$798$		0			0
$799$	15.5471	+	26.9284i	0.550018	+	0.952659i
$800$		0			0
$801$	18.3004			0.646614
$802$		0			0
$803$	−19.5452	+	33.8532i	−0.689733	+	1.19465i
$804$		0			0
$805$	−8.77575			−0.309304
$806$		0			0
$807$	11.2873			0.397330
$808$		0			0
$809$	15.8618	−	27.4734i	0.557670	−	0.965913i	−0.440020	−	0.897988i	$-0.645029\pi$
$809$	15.8618	−	27.4734i	0.557670	−	0.965913i	0.997690	−	0.0679253i	$-0.0216380\pi$
$810$		0			0
$811$	7.12601			0.250228			0.125114	−	0.992142i	$-0.460070\pi$
$811$	7.12601			0.250228			0.125114	+	0.992142i	$0.460070\pi$
$812$		0			0
$813$	0.887873	+	1.53784i	0.0311391	+	0.0539345i
$814$		0			0
$815$	−5.95993	−	10.3229i	−0.208767	−	0.361595i
$816$		0			0
$817$	−10.8090	+	18.7217i	−0.378159	+	0.654991i
$818$		0			0
$819$	−0.309711	−	5.33153i	−0.0108222	−	0.186299i
$820$		0			0
$821$	6.38058	−	11.0515i	0.222684	−	0.385700i	−0.732938	−	0.680295i	$-0.761852\pi$
$821$	6.38058	−	11.0515i	0.222684	−	0.385700i	0.955622	+	0.294596i	$0.0951849\pi$
$822$		0			0
$823$	15.0376	+	26.0459i	0.524178	+	0.907903i	0.999604	+	0.0281473i	$0.00896075\pi$
$823$	15.0376	+	26.0459i	0.524178	+	0.907903i	−0.475426	+	0.879756i	$0.657706\pi$
$824$		0			0
$825$	1.67513	+	2.90141i	0.0583206	+	0.101014i
$826$		0			0
$827$	34.6697			1.20559			0.602793	−	0.797898i	$-0.294055\pi$
$827$	34.6697			1.20559			0.602793	+	0.797898i	$0.294055\pi$
$828$		0			0
$829$	9.47992	−	16.4197i	0.329251	−	0.570280i	−0.653112	−	0.757261i	$-0.726537\pi$
$829$	9.47992	−	16.4197i	0.329251	−	0.570280i	0.982363	+	0.186981i	$0.0598704\pi$
$830$		0			0
$831$	25.3258			0.878543
$832$		0			0
$833$	11.9248			0.413169
$834$		0			0
$835$	0.418190	−	0.724327i	0.0144721	−	0.0250664i
$836$		0			0
$837$	3.54420			0.122505
$838$		0			0
$839$	−19.3054	−	33.4379i	−0.666495	−	1.15440i	−0.978878	−	0.204447i	$-0.934460\pi$
$839$	−19.3054	−	33.4379i	−0.666495	−	1.15440i	0.312383	−	0.949956i	$-0.398873\pi$
$840$		0			0
$841$	−7.52833	−	13.0395i	−0.259598	−	0.449636i
$842$		0			0
$843$	7.00611	−	12.1349i	0.241303	−	0.417949i
$844$		0			0
$845$	−5.15268	+	11.9352i	−0.177258	+	0.410585i
$846$		0			0
$847$	−0.166082	+	0.287662i	−0.00570663	+	0.00988418i
$848$		0			0
$849$	9.74060	+	16.8712i	0.334296	+	0.579018i
$850$		0			0
$851$	−1.14903	−	1.99018i	−0.0393883	−	0.0682225i
$852$		0			0
$853$	10.9330			0.374340			0.187170	−	0.982328i	$-0.440069\pi$
$853$	10.9330			0.374340			0.187170	+	0.982328i	$0.440069\pi$
$854$		0			0
$855$	−1.07816	+	1.86743i	−0.0368724	+	0.0638648i
$856$		0			0
$857$	−9.57944			−0.327227			−0.163614	−	0.986524i	$-0.552315\pi$
$857$	−9.57944			−0.327227			−0.163614	+	0.986524i	$0.552315\pi$
$858$		0			0
$859$	49.1944			1.67849			0.839246	−	0.543752i	$-0.182997\pi$
$859$	49.1944			1.67849			0.839246	+	0.543752i	$0.182997\pi$
$860$		0			0
$861$	−7.59086	+	13.1478i	−0.258696	+	0.448074i
$862$		0			0
$863$	4.32250			0.147140			0.0735698	−	0.997290i	$-0.476561\pi$
$863$	4.32250			0.147140			0.0735698	+	0.997290i	$0.476561\pi$
$864$		0			0
$865$	−9.03444	−	15.6481i	−0.307180	−	0.532052i
$866$		0			0
$867$	5.42184	+	9.39090i	0.184135	+	0.318932i
$868$		0			0
$869$	−18.0386	+	31.2437i	−0.611916	+	1.05987i
$870$		0			0
$871$	−2.35225	−	40.4929i	−0.0797028	−	1.37205i
$872$		0			0
$873$	0.531502	−	0.920588i	0.0179886	−	0.0311572i
$874$		0			0
$875$	0.740597	+	1.28275i	0.0250368	+	0.0433649i
$876$		0			0
$877$	−18.0313	−	31.2311i	−0.608873	−	1.05460i	−0.991427	−	0.130665i	$-0.958289\pi$
$877$	−18.0313	−	31.2311i	−0.608873	−	1.05460i	0.382554	−	0.923933i	$-0.375045\pi$
$878$		0			0
$879$	−2.35519			−0.0794385
$880$		0			0
$881$	−12.9951	+	22.5081i	−0.437815	+	0.758318i	−0.997521	−	0.0703734i	$-0.977581\pi$
$881$	−12.9951	+	22.5081i	−0.437815	+	0.758318i	0.559706	+	0.828692i	$0.310914\pi$
$882$		0			0
$883$	−9.67372			−0.325546			−0.162773	−	0.986664i	$-0.552044\pi$
$883$	−9.67372			−0.325546			−0.162773	+	0.986664i	$0.552044\pi$
$884$		0			0
$885$	9.86177			0.331500
$886$		0			0
$887$	−5.32662	+	9.22598i	−0.178851	+	0.309778i	−0.941487	−	0.337049i	$-0.890571\pi$
$887$	−5.32662	+	9.22598i	−0.178851	+	0.309778i	0.762637	+	0.646827i	$0.223905\pi$
$888$		0			0
$889$	7.61942			0.255547
$890$		0			0
$891$	1.67513	+	2.90141i	0.0561190	+	0.0972010i
$892$		0			0
$893$	13.5115	+	23.4026i	0.452145	+	0.783139i
$894$		0			0
$895$	−10.8253	+	18.7501i	−0.361851	+	0.626745i
$896$		0			0
$897$	19.0884	+	9.59020i	0.637343	+	0.320207i
$898$		0			0
$899$	11.7623	−	20.3730i	0.392296	−	0.679477i
$900$		0			0
$901$	2.15633	+	3.73486i	0.0718376	+	0.124426i
$902$		0			0
$903$	7.42478	+	12.8601i	0.247081	+	0.427957i
$904$		0			0
$905$	7.19394			0.239135
$906$		0			0
$907$	29.5095	−	51.1120i	0.979848	−	1.69715i	0.316939	−	0.948446i	$-0.397345\pi$
$907$	29.5095	−	51.1120i	0.979848	−	1.69715i	0.662909	−	0.748700i	$-0.269322\pi$
$908$		0			0
$909$	0.312650			0.0103700
$910$		0			0
$911$	−8.12601			−0.269227			−0.134613	−	0.990898i	$-0.542979\pi$
$911$	−8.12601			−0.269227			−0.134613	+	0.990898i	$0.542979\pi$
$912$		0			0
$913$	11.3503	−	19.6592i	0.375639	−	0.650626i
$914$		0			0
$915$	−6.11871			−0.202278
$916$		0			0
$917$	−13.0721	−	22.6415i	−0.431677	−	0.747687i
$918$		0			0
$919$	12.0610	+	20.8903i	0.397856	+	0.689107i	0.993461	−	0.114170i	$-0.0364209\pi$
$919$	12.0610	+	20.8903i	0.397856	+	0.689107i	−0.595605	+	0.803278i	$0.703088\pi$
$920$		0			0
$921$	8.78115	−	15.2094i	0.289349	−	0.501167i
$922$		0			0
$923$	−50.0173	−	25.1292i	−1.64634	−	0.827137i
$924$		0			0
$925$	−0.193937	+	0.335908i	−0.00637660	+	0.0110446i
$926$		0			0
$927$	3.43089	+	5.94247i	0.112685	+	0.195176i
$928$		0			0
$929$	21.1939	+	36.7090i	0.695351	+	1.20438i	0.970062	+	0.242856i	$0.0780842\pi$
$929$	21.1939	+	36.7090i	0.695351	+	1.20438i	−0.274712	+	0.961527i	$0.588582\pi$
$930$		0			0
$931$	10.3634			0.339648
$932$		0			0
$933$	−7.53809	+	13.0564i	−0.246786	+	0.427446i
$934$		0			0
$935$	−8.31265			−0.271853
$936$		0			0
$937$	36.4288			1.19008			0.595039	−	0.803697i	$-0.297137\pi$
$937$	36.4288			1.19008			0.595039	+	0.803697i	$0.297137\pi$
$938$		0			0
$939$	−8.84415	+	15.3185i	−0.288618	+	0.499901i
$940$		0			0
$941$	24.1646			0.787743			0.393871	−	0.919166i	$-0.371136\pi$
$941$	24.1646			0.787743			0.393871	+	0.919166i	$0.371136\pi$
$942$		0			0
$943$	−30.3634	−	52.5910i	−0.988770	−	1.71260i
$944$		0			0
$945$	0.740597	+	1.28275i	0.0240916	+	0.0417279i
$946$		0			0
$947$	−20.4550	+	35.4291i	−0.664698	+	1.15129i	0.314669	+	0.949202i	$0.398107\pi$
$947$	−20.4550	+	35.4291i	−0.664698	+	1.15129i	−0.979367	+	0.202090i	$0.935227\pi$
$948$		0			0
$949$	35.1516	−	23.1119i	1.14107	−	0.750245i
$950$		0			0
$951$	−1.74306	+	3.01907i	−0.0565226	+	0.0979000i
$952$		0			0
$953$	−11.4944	−	19.9088i	−0.372339	−	0.644910i	0.617586	−	0.786504i	$-0.288111\pi$
$953$	−11.4944	−	19.9088i	−0.372339	−	0.644910i	−0.989925	+	0.141593i	$0.954777\pi$
$954$		0			0
$955$	11.5005	+	19.9194i	0.372147	+	0.644577i
$956$		0			0
$957$	22.2374			0.718834
$958$		0			0
$959$	2.83757	−	4.91481i	0.0916298	−	0.158707i
$960$		0			0
$961$	−18.4387			−0.594795
$962$		0			0
$963$	−9.95746			−0.320875
$964$		0			0
$965$	−3.28480	+	5.68943i	−0.105741	+	0.183149i
$966$		0			0
$967$	−51.2408			−1.64779			−0.823896	−	0.566741i	$-0.808204\pi$
$967$	−51.2408			−1.64779			−0.823896	+	0.566741i	$0.808204\pi$
$968$		0			0
$969$	−2.67513	−	4.63346i	−0.0859376	−	0.148848i
$970$		0			0
$971$	9.15633	+	15.8592i	0.293840	+	0.508947i	0.974714	−	0.223454i	$-0.0717332\pi$
$971$	9.15633	+	15.8592i	0.293840	+	0.508947i	−0.680874	+	0.732401i	$0.738400\pi$
$972$		0			0
$973$	−5.75870	+	9.97435i	−0.184615	+	0.319763i
$974$		0			0
$975$	−0.209095	−	3.59948i	−0.00669640	−	0.115276i
$976$		0			0
$977$	−10.1989	+	17.6649i	−0.326290	+	0.565152i	−0.981773	−	0.190059i	$-0.939132\pi$
$977$	−10.1989	+	17.6649i	−0.326290	+	0.565152i	0.655482	+	0.755211i	$0.272465\pi$
$978$		0			0
$979$	30.6556	+	53.0971i	0.979758	+	1.69699i
$980$		0			0
$981$	−4.26845	−	7.39318i	−0.136281	−	0.236046i
$982$		0			0
$983$	−45.6483			−1.45596			−0.727978	−	0.685601i	$-0.759540\pi$
$983$	−45.6483			−1.45596			−0.727978	+	0.685601i	$0.759540\pi$
$984$		0			0
$985$	−7.40597	+	12.8275i	−0.235974	+	0.408719i
$986$		0			0
$987$	18.5623			0.590844
$988$		0			0
$989$	−59.3982			−1.88875
$990$		0			0
$991$	1.12307	−	1.94521i	0.0356754	−	0.0617917i	−0.847636	−	0.530578i	$-0.821975\pi$
$991$	1.12307	−	1.94521i	0.0356754	−	0.0617917i	0.883312	+	0.468786i	$0.155308\pi$
$992$		0			0
$993$	7.62530			0.241982
$994$		0			0
$995$	−10.0188	−	17.3531i	−0.317617	−	0.550130i
$996$		0			0
$997$	14.2594	+	24.6980i	0.451600	+	0.782194i	0.998486	−	0.0550134i	$-0.0175201\pi$
$997$	14.2594	+	24.6980i	0.451600	+	0.782194i	−0.546886	+	0.837207i	$0.684187\pi$
$998$		0			0
$999$	−0.193937	+	0.335908i	−0.00613588	+	0.0106277i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1560.2.bg.h.841.1	yes	6
13.3	even	3	inner	1560.2.bg.h.601.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1560.2.bg.h.601.1	✓	6	13.3	even	3	inner
1560.2.bg.h.841.1	yes	6	1.1	even	1	trivial

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Hilbert	Bianchi

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

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Newspace parameters

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Embedding invariants

$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1560.2.bg.h.841.1

Level	$1560$
Weight	$2$
Character	1560.841
Analytic conductor	$12.457$
Analytic rank	$0$
Dimension	$6$
Inner twists	$2$