LMFDB - Embedded newform 1260.2.c.c.811.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,2,Mod(811,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))

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

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

chi := DirichletCharacter("1260.811");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.c (of order $2$, degree $1$, 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:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.342102016.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 $ x^8 + x^6 + 4x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			811.4
Root			$-0.599676 - 1.28078i$ of defining polynomial
Character	$\chi$	$=$	1260.811
Dual form			1260.2.c.c.811.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28078 + 0.599676i) q^{2} +(1.28078 - 1.53610i) q^{4} +1.00000i q^{5} +(2.60399 + 0.468213i) q^{7} +(-0.719224 + 2.73546i) q^{8} +O(q^{10})$	\(q+(-1.28078 + 0.599676i) q^{2} +(1.28078 - 1.53610i) q^{4} +1.00000i q^{5} +(2.60399 + 0.468213i) q^{7} +(-0.719224 + 2.73546i) q^{8} +(-0.599676 - 1.28078i) q^{10} -2.39871i q^{11} -2.00000i q^{13} +(-3.61591 + 0.961876i) q^{14} +(-0.719224 - 3.93481i) q^{16} -7.12311i q^{17} -2.39871 q^{19} +(1.53610 + 1.28078i) q^{20} +(1.43845 + 3.07221i) q^{22} -5.73384i q^{23} -1.00000 q^{25} +(1.19935 + 2.56155i) q^{26} +(4.05436 - 3.40032i) q^{28} +2.00000 q^{29} -6.67026 q^{31} +(3.28078 + 4.60831i) q^{32} +(4.27156 + 9.12311i) q^{34} +(-0.468213 + 2.60399i) q^{35} +2.00000 q^{37} +(3.07221 - 1.43845i) q^{38} +(-2.73546 - 0.719224i) q^{40} +7.12311i q^{41} -7.60669i q^{43} +(-3.68466 - 3.07221i) q^{44} +(3.43845 + 7.34376i) q^{46} -10.0054 q^{47} +(6.56155 + 2.43845i) q^{49} +(1.28078 - 0.599676i) q^{50} +(-3.07221 - 2.56155i) q^{52} -2.00000 q^{53} +2.39871 q^{55} +(-3.15363 + 6.78636i) q^{56} +(-2.56155 + 1.19935i) q^{58} +10.9418 q^{59} -2.00000i q^{61} +(8.54312 - 4.00000i) q^{62} +(-6.96543 - 3.93481i) q^{64} +2.00000 q^{65} -14.2770i q^{67} +(-10.9418 - 9.12311i) q^{68} +(-0.961876 - 3.61591i) q^{70} -6.14441i q^{71} +9.36932i q^{73} +(-2.56155 + 1.19935i) q^{74} +(-3.07221 + 3.68466i) q^{76} +(1.12311 - 6.24621i) q^{77} -4.27156i q^{79} +(3.93481 - 0.719224i) q^{80} +(-4.27156 - 9.12311i) q^{82} +0.936426 q^{83} +7.12311 q^{85} +(4.56155 + 9.74247i) q^{86} +(6.56155 + 1.72521i) q^{88} +12.0000i q^{89} +(0.936426 - 5.20798i) q^{91} +(-8.80776 - 7.34376i) q^{92} +(12.8147 - 6.00000i) q^{94} -2.39871i q^{95} -7.12311i q^{97} +(-9.86616 + 0.811703i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{4} - 14 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 + 2 * q^4 - 14 * q^8	$ 8 q - 2 q^{2} + 2 q^{4} - 14 q^{8} + 6 q^{14} - 14 q^{16} + 28 q^{22} - 8 q^{25} + 14 q^{28} + 16 q^{29} + 18 q^{32} + 16 q^{37} + 20 q^{44} + 44 q^{46} + 36 q^{49} + 2 q^{50} - 16 q^{53} - 2 q^{56} - 4 q^{58} + 2 q^{64} + 16 q^{65} + 4 q^{70} - 4 q^{74} - 24 q^{77} + 24 q^{85} + 20 q^{86} + 36 q^{88} + 12 q^{92} - 26 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 2 * q^4 - 14 * q^8 + 6 * q^14 - 14 * q^16 + 28 * q^22 - 8 * q^25 + 14 * q^28 + 16 * q^29 + 18 * q^32 + 16 * q^37 + 20 * q^44 + 44 * q^46 + 36 * q^49 + 2 * q^50 - 16 * q^53 - 2 * q^56 - 4 * q^58 + 2 * q^64 + 16 * q^65 + 4 * q^70 - 4 * q^74 - 24 * q^77 + 24 * q^85 + 20 * q^86 + 36 * q^88 + 12 * q^92 - 26 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$1$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.28078	+	0.599676i	−0.905646	+	0.424035i
$2$	−1.28078	+	0.599676i	−0.905646	+	0.424035i
$3$		0			0
$3$		0			0
$4$	1.28078	−	1.53610i	0.640388	−	0.768051i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	2.60399	+	0.468213i	0.984217	+	0.176968i
$7$	2.60399	+	0.468213i	0.984217	+	0.176968i
$8$	−0.719224	+	2.73546i	−0.254284	+	0.967130i
$9$		0			0
$10$	−0.599676	−	1.28078i	−0.189634	−	0.405017i
$11$		−	2.39871i		−	0.723237i	−0.932326	−	0.361618i	$-0.882224\pi$
$11$		−	2.39871i		−	0.723237i	0.932326	−	0.361618i	$-0.117776\pi$
$12$		0			0
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$	−3.61591	+	0.961876i	−0.966392	+	0.257072i
$15$		0			0
$16$	−0.719224	−	3.93481i	−0.179806	−	0.983702i
$17$		−	7.12311i		−	1.72761i	−0.503829	−	0.863803i	$-0.668076\pi$
$17$		−	7.12311i		−	1.72761i	0.503829	−	0.863803i	$-0.331924\pi$
$18$		0			0
$19$	−2.39871			−0.550301			−0.275150	−	0.961401i	$-0.588728\pi$
$19$	−2.39871			−0.550301			−0.275150	+	0.961401i	$0.588728\pi$
$20$	1.53610	+	1.28078i	0.343483	+	0.286390i
$21$		0			0
$22$	1.43845	+	3.07221i	0.306678	+	0.654996i
$23$		−	5.73384i		−	1.19559i	−0.801650	−	0.597794i	$-0.796044\pi$
$23$		−	5.73384i		−	1.19559i	0.801650	−	0.597794i	$-0.203956\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	1.19935	+	2.56155i	0.235212	+	0.502362i
$27$		0			0
$28$	4.05436	−	3.40032i	0.766201	−	0.642601i
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$		0			0
$31$	−6.67026			−1.19801			−0.599007	−	0.800743i	$-0.704438\pi$
$31$	−6.67026			−1.19801			−0.599007	+	0.800743i	$0.704438\pi$
$32$	3.28078	+	4.60831i	0.579965	+	0.814642i
$33$		0			0
$34$	4.27156	+	9.12311i	0.732566	+	1.56460i
$35$	−0.468213	+	2.60399i	−0.0791425	+	0.440155i
$36$		0			0
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	3.07221	−	1.43845i	0.498378	−	0.233347i
$39$		0			0
$40$	−2.73546	−	0.719224i	−0.432514	−	0.113719i
$41$			7.12311i			1.11244i	0.831034	+	0.556221i	$0.187749\pi$
$41$			7.12311i			1.11244i	−0.831034	+	0.556221i	$0.812251\pi$
$42$		0			0
$43$		−	7.60669i		−	1.16001i	−0.814613	−	0.580005i	$-0.803051\pi$
$43$		−	7.60669i		−	1.16001i	0.814613	−	0.580005i	$-0.196949\pi$
$44$	−3.68466	−	3.07221i	−0.555483	−	0.463152i
$45$		0			0
$46$	3.43845	+	7.34376i	0.506971	+	1.08278i
$47$	−10.0054			−1.45944			−0.729719	−	0.683748i	$-0.760349\pi$
$47$	−10.0054			−1.45944			−0.729719	+	0.683748i	$0.760349\pi$
$48$		0			0
$49$	6.56155	+	2.43845i	0.937365	+	0.348350i
$50$	1.28078	−	0.599676i	0.181129	−	0.0848071i
$51$		0			0
$52$	−3.07221	−	2.56155i	−0.426038	−	0.355223i
$53$	−2.00000			−0.274721			−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000			−0.274721			−0.137361	+	0.990521i	$0.543862\pi$
$54$		0			0
$55$	2.39871			0.323441
$56$	−3.15363	+	6.78636i	−0.421421	+	0.906865i
$57$		0			0
$58$	−2.56155	+	1.19935i	−0.336348	+	0.157483i
$59$	10.9418			1.42450			0.712252	−	0.701924i	$-0.247675\pi$
$59$	10.9418			1.42450			0.712252	+	0.701924i	$0.247675\pi$
$60$		0			0
$61$		−	2.00000i		−	0.256074i	−0.991769	−	0.128037i	$-0.959132\pi$
$61$		−	2.00000i		−	0.256074i	0.991769	−	0.128037i	$-0.0408676\pi$
$62$	8.54312	−	4.00000i	1.08498	−	0.508001i
$63$		0			0
$64$	−6.96543	−	3.93481i	−0.870679	−	0.491851i
$65$	2.00000			0.248069
$66$		0			0
$67$		−	14.2770i		−	1.74421i	−0.489321	−	0.872104i	$-0.662755\pi$
$67$		−	14.2770i		−	1.74421i	0.489321	−	0.872104i	$-0.337245\pi$
$68$	−10.9418	−	9.12311i	−1.32689	−	1.10634i
$69$		0			0
$70$	−0.961876	−	3.61591i	−0.114966	−	0.432184i
$71$		−	6.14441i		−	0.729207i	−0.931163	−	0.364604i	$-0.881204\pi$
$71$		−	6.14441i		−	0.729207i	0.931163	−	0.364604i	$-0.118796\pi$
$72$		0			0
$73$			9.36932i			1.09660i	0.836283	+	0.548298i	$0.184724\pi$
$73$			9.36932i			1.09660i	−0.836283	+	0.548298i	$0.815276\pi$
$74$	−2.56155	+	1.19935i	−0.297774	+	0.139422i
$75$		0			0
$76$	−3.07221	+	3.68466i	−0.352406	+	0.422659i
$77$	1.12311	−	6.24621i	0.127990	−	0.711822i
$78$		0			0
$79$		−	4.27156i		−	0.480588i	−0.970700	−	0.240294i	$-0.922756\pi$
$79$		−	4.27156i		−	0.480588i	0.970700	−	0.240294i	$-0.0772438\pi$
$80$	3.93481	−	0.719224i	0.439925	−	0.0804116i
$81$		0			0
$82$	−4.27156	−	9.12311i	−0.471715	−	1.00748i
$83$	0.936426			0.102786			0.0513931	−	0.998679i	$-0.483634\pi$
$83$	0.936426			0.102786			0.0513931	+	0.998679i	$0.483634\pi$
$84$		0			0
$85$	7.12311			0.772609
$86$	4.56155	+	9.74247i	0.491885	+	1.05056i
$87$		0			0
$88$	6.56155	+	1.72521i	0.699464	+	0.183908i
$89$			12.0000i			1.27200i	0.771690	+	0.635999i	$0.219412\pi$
$89$			12.0000i			1.27200i	−0.771690	+	0.635999i	$0.780588\pi$
$90$		0			0
$91$	0.936426	−	5.20798i	0.0981642	−	0.545945i
$92$	−8.80776	−	7.34376i	−0.918273	−	0.765640i
$93$		0			0
$94$	12.8147	−	6.00000i	1.32173	−	0.618853i
$95$		−	2.39871i		−	0.246102i
$96$		0			0
$97$		−	7.12311i		−	0.723242i	−0.932325	−	0.361621i	$-0.882223\pi$
$97$		−	7.12311i		−	0.723242i	0.932325	−	0.361621i	$-0.117777\pi$
$98$	−9.86616	+	0.811703i	−0.996633	+	0.0819944i
$99$		0			0
$100$	−1.28078	+	1.53610i	−0.128078	+	0.153610i
$101$		−	6.87689i		−	0.684277i	−0.939650	−	0.342138i	$-0.888849\pi$
$101$		−	6.87689i		−	0.684277i	0.939650	−	0.342138i	$-0.111151\pi$
$102$		0			0
$103$	−1.46228			−0.144083			−0.0720413	−	0.997402i	$-0.522951\pi$
$103$	−1.46228			−0.144083			−0.0720413	+	0.997402i	$0.522951\pi$
$104$	5.47091	+	1.43845i	0.536467	+	0.141051i
$105$		0			0
$106$	2.56155	−	1.19935i	0.248800	−	0.116491i
$107$		−	9.47954i		−	0.916422i	−0.888843	−	0.458211i	$-0.848490\pi$
$107$		−	9.47954i		−	0.916422i	0.888843	−	0.458211i	$-0.151510\pi$
$108$		0			0
$109$	1.12311			0.107574			0.0537870	−	0.998552i	$-0.482871\pi$
$109$	1.12311			0.107574			0.0537870	+	0.998552i	$0.482871\pi$
$110$	−3.07221	+	1.43845i	−0.292923	+	0.137151i
$111$		0			0
$112$	−0.0305236	−	10.5830i	−0.00288420	−	0.999996i
$113$	14.4924			1.36333			0.681666	−	0.731663i	$-0.261256\pi$
$113$	14.4924			1.36333			0.681666	+	0.731663i	$0.261256\pi$
$114$		0			0
$115$	5.73384			0.534683
$116$	2.56155	−	3.07221i	0.237834	−	0.285247i
$117$		0			0
$118$	−14.0140	+	6.56155i	−1.29010	+	0.604040i
$119$	3.33513	−	18.5485i	0.305731	−	1.70034i
$120$		0			0
$121$	5.24621			0.476928
$122$	1.19935	+	2.56155i	0.108584	+	0.231912i
$123$		0			0
$124$	−8.54312	+	10.2462i	−0.767195	+	0.920137i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$			13.2252i			1.17355i	0.809750	+	0.586776i	$0.199603\pi$
$127$			13.2252i			1.17355i	−0.809750	+	0.586776i	$0.800397\pi$
$128$	11.2808	+	0.862603i	0.997089	+	0.0762440i
$129$		0			0
$130$	−2.56155	+	1.19935i	−0.224663	+	0.105190i
$131$	−13.8664			−1.21151			−0.605756	−	0.795651i	$-0.707129\pi$
$131$	−13.8664			−1.21151			−0.605756	+	0.795651i	$0.707129\pi$
$132$		0			0
$133$	−6.24621	−	1.12311i	−0.541615	−	0.0973856i
$134$	8.56155	+	18.2856i	0.739606	+	1.57963i
$135$		0			0
$136$	19.4849	+	5.12311i	1.67082	+	0.439303i
$137$	14.0000			1.19610			0.598050	−	0.801459i	$-0.295942\pi$
$137$	14.0000			1.19610			0.598050	+	0.801459i	$0.295942\pi$
$138$		0			0
$139$	−1.34700			−0.114251			−0.0571255	−	0.998367i	$-0.518194\pi$
$139$	−1.34700			−0.114251			−0.0571255	+	0.998367i	$0.518194\pi$
$140$	3.40032	+	4.05436i	0.287380	+	0.342656i
$141$		0			0
$142$	3.68466	+	7.86962i	0.309210	+	0.660404i
$143$	−4.79741			−0.401180
$144$		0			0
$145$			2.00000i			0.166091i
$146$	−5.61856	−	12.0000i	−0.464995	−	0.993127i
$147$		0			0
$148$	2.56155	−	3.07221i	0.210558	−	0.252534i
$149$	19.3693			1.58680			0.793398	−	0.608703i	$-0.208310\pi$
$149$	19.3693			1.58680			0.793398	+	0.608703i	$0.208310\pi$
$150$		0			0
$151$			14.6875i			1.19525i	0.801774	+	0.597627i	$0.203890\pi$
$151$			14.6875i			1.19525i	−0.801774	+	0.597627i	$0.796110\pi$
$152$	1.72521	−	6.56155i	0.139933	−	0.532212i
$153$		0			0
$154$	2.30726	+	8.67350i	0.185924	+	0.698931i
$155$		−	6.67026i		−	0.535769i
$156$		0			0
$157$		−	16.2462i		−	1.29659i	−0.761390	−	0.648294i	$-0.775483\pi$
$157$		−	16.2462i		−	1.29659i	0.761390	−	0.648294i	$-0.224517\pi$
$158$	2.56155	+	5.47091i	0.203786	+	0.435242i
$159$		0			0
$160$	−4.60831	+	3.28078i	−0.364319	+	0.259368i
$161$	2.68466	−	14.9309i	0.211581	−	1.17672i
$162$		0			0
$163$		−	0.936426i		−	0.0733466i	−0.999327	−	0.0366733i	$-0.988324\pi$
$163$		−	0.936426i		−	0.0733466i	0.999327	−	0.0366733i	$-0.0116761\pi$
$164$	10.9418	+	9.12311i	0.854413	+	0.712395i
$165$		0			0
$166$	−1.19935	+	0.561553i	−0.0930878	+	0.0435850i
$167$	−2.28343			−0.176697			−0.0883484	−	0.996090i	$-0.528159\pi$
$167$	−2.28343			−0.176697			−0.0883484	+	0.996090i	$0.528159\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$	−9.12311	+	4.27156i	−0.699710	+	0.327614i
$171$		0			0
$172$	−11.6847	−	9.74247i	−0.890947	−	0.742856i
$173$			0.246211i			0.0187191i	0.999956	+	0.00935955i	$0.00297928\pi$
$173$			0.246211i			0.0187191i	−0.999956	+	0.00935955i	$0.997021\pi$
$174$		0			0
$175$	−2.60399	−	0.468213i	−0.196843	−	0.0353936i
$176$	−9.43845	+	1.72521i	−0.711450	+	0.130042i
$177$		0			0
$178$	−7.19612	−	15.3693i	−0.539372	−	1.15198i
$179$			0.525853i			0.0393041i	0.999807	+	0.0196520i	$0.00625584\pi$
$179$			0.525853i			0.0393041i	−0.999807	+	0.0196520i	$0.993744\pi$
$180$		0			0
$181$			6.87689i			0.511156i	0.966789	+	0.255578i	$0.0822657\pi$
$181$			6.87689i			0.511156i	−0.966789	+	0.255578i	$0.917734\pi$
$182$	1.92375	+	7.23182i	0.142598	+	0.536058i
$183$		0			0
$184$	15.6847	+	4.12391i	1.15629	+	0.304019i
$185$			2.00000i			0.147043i
$186$		0			0
$187$	−17.0862			−1.24947
$188$	−12.8147	+	15.3693i	−0.934606	+	1.12092i
$189$		0			0
$190$	1.43845	+	3.07221i	0.104356	+	0.222881i
$191$			1.34700i			0.0974655i	0.998812	+	0.0487327i	$0.0155183\pi$
$191$			1.34700i			0.0974655i	−0.998812	+	0.0487327i	$0.984482\pi$
$192$		0			0
$193$	10.4924			0.755261			0.377631	−	0.925956i	$-0.376739\pi$
$193$	10.4924			0.755261			0.377631	+	0.925956i	$0.376739\pi$
$194$	4.27156	+	9.12311i	0.306680	+	0.655001i
$195$		0			0
$196$	12.1496	−	6.95611i	0.867828	−	0.496865i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	16.0345			1.13666			0.568329	−	0.822802i	$-0.307590\pi$
$199$	16.0345			1.13666			0.568329	+	0.822802i	$0.307590\pi$
$200$	0.719224	−	2.73546i	0.0508568	−	0.193426i
$201$		0			0
$202$	4.12391	+	8.80776i	0.290157	+	0.619712i
$203$	5.20798	+	0.936426i	0.365529	+	0.0657242i
$204$		0			0
$205$	−7.12311			−0.497499
$206$	1.87285	−	0.876894i	0.130488	−	0.0610961i
$207$		0			0
$208$	−7.86962	+	1.43845i	−0.545660	+	0.0997384i
$209$			5.75379i			0.397998i
$210$		0			0
$211$		−	18.4332i		−	1.26900i	−0.772924	−	0.634498i	$-0.781207\pi$
$211$		−	18.4332i		−	1.26900i	0.772924	−	0.634498i	$-0.218793\pi$
$212$	−2.56155	+	3.07221i	−0.175928	+	0.211000i
$213$		0			0
$214$	5.68466	+	12.1412i	0.388595	+	0.829954i
$215$	7.60669			0.518772
$216$		0			0
$217$	−17.3693	−	3.12311i	−1.17911	−	0.212010i
$218$	−1.43845	+	0.673500i	−0.0974239	+	0.0456152i
$219$		0			0
$220$	3.07221	−	3.68466i	0.207128	−	0.248420i
$221$	−14.2462			−0.958304
$222$		0			0
$223$	12.9300			0.865854			0.432927	−	0.901429i	$-0.357481\pi$
$223$	12.9300			0.865854			0.432927	+	0.901429i	$0.357481\pi$
$224$	6.38545	+	13.5361i	0.426646	+	0.904419i
$225$		0			0
$226$	−18.5616	+	8.69076i	−1.23470	+	0.578101i
$227$	14.2770			0.947595			0.473797	−	0.880634i	$-0.342883\pi$
$227$	14.2770			0.947595			0.473797	+	0.880634i	$0.342883\pi$
$228$		0			0
$229$			21.1231i			1.39585i	0.716169	+	0.697927i	$0.245894\pi$
$229$			21.1231i			1.39585i	−0.716169	+	0.697927i	$0.754106\pi$
$230$	−7.34376	+	3.43845i	−0.484233	+	0.226724i
$231$		0			0
$232$	−1.43845	+	5.47091i	−0.0944387	+	0.359183i
$233$	−24.2462			−1.58842			−0.794211	−	0.607642i	$-0.792116\pi$
$233$	−24.2462			−1.58842			−0.794211	+	0.607642i	$0.792116\pi$
$234$		0			0
$235$		−	10.0054i		−	0.652680i
$236$	14.0140	−	16.8078i	0.912236	−	1.09409i
$237$		0			0
$238$	6.85155	+	25.7565i	0.444120	+	1.66955i
$239$			12.8147i			0.828912i	0.910069	+	0.414456i	$0.136028\pi$
$239$			12.8147i			0.828912i	−0.910069	+	0.414456i	$0.863972\pi$
$240$		0			0
$241$		−	15.6155i		−	1.00588i	−0.864320	−	0.502942i	$-0.832251\pi$
$241$		−	15.6155i		−	1.00588i	0.864320	−	0.502942i	$-0.167749\pi$
$242$	−6.71922	+	3.14603i	−0.431928	+	0.202234i
$243$		0			0
$244$	−3.07221	−	2.56155i	−0.196678	−	0.163987i
$245$	−2.43845	+	6.56155i	−0.155787	+	0.419202i
$246$		0			0
$247$			4.79741i			0.305252i
$248$	4.79741	−	18.2462i	0.304636	−	1.15864i
$249$		0			0
$250$	0.599676	+	1.28078i	0.0379269	+	0.0810034i
$251$	−16.5604			−1.04528			−0.522641	−	0.852553i	$-0.675053\pi$
$251$	−16.5604			−1.04528			−0.522641	+	0.852553i	$0.675053\pi$
$252$		0			0
$253$	−13.7538			−0.864693
$254$	−7.93087	−	16.9386i	−0.497627	−	1.06282i
$255$		0			0
$256$	−14.9654	+	5.66001i	−0.935340	+	0.353751i
$257$			13.3693i			0.833955i	0.908917	+	0.416978i	$0.136911\pi$
$257$			13.3693i			0.833955i	−0.908917	+	0.416978i	$0.863089\pi$
$258$		0			0
$259$	5.20798	+	0.936426i	0.323608	+	0.0581867i
$260$	2.56155	−	3.07221i	0.158861	−	0.190530i
$261$		0			0
$262$	17.7597	−	8.31534i	1.09720	−	0.513724i
$263$			1.98813i			0.122593i	0.998120	+	0.0612967i	$0.0195236\pi$
$263$			1.98813i			0.122593i	−0.998120	+	0.0612967i	$0.980476\pi$
$264$		0			0
$265$		−	2.00000i		−	0.122859i
$266$	8.67350	−	2.30726i	0.531806	−	0.141467i
$267$		0			0
$268$	−21.9309	−	18.2856i	−1.33964	−	1.11697i
$269$			16.2462i			0.990549i	0.868737	+	0.495274i	$0.164933\pi$
$269$			16.2462i			0.990549i	−0.868737	+	0.495274i	$0.835067\pi$
$270$		0			0
$271$	−23.7565			−1.44310			−0.721552	−	0.692360i	$-0.756571\pi$
$271$	−23.7565			−1.44310			−0.721552	+	0.692360i	$0.756571\pi$
$272$	−28.0281	+	5.12311i	−1.69945	+	0.310634i
$273$		0			0
$274$	−17.9309	+	8.39547i	−1.08324	+	0.507189i
$275$			2.39871i			0.144647i
$276$		0			0
$277$	−4.24621			−0.255130			−0.127565	−	0.991830i	$-0.540716\pi$
$277$	−4.24621			−0.255130			−0.127565	+	0.991830i	$0.540716\pi$
$278$	1.72521	−	0.807764i	0.103471	−	0.0484465i
$279$		0			0
$280$	−6.78636	−	3.15363i	−0.405562	−	0.188465i
$281$	4.63068			0.276243			0.138122	−	0.990415i	$-0.455893\pi$
$281$	4.63068			0.276243			0.138122	+	0.990415i	$0.455893\pi$
$282$		0			0
$283$	24.6929			1.46784			0.733921	−	0.679235i	$-0.237688\pi$
$283$	24.6929			1.46784			0.733921	+	0.679235i	$0.237688\pi$
$284$	−9.43845	−	7.86962i	−0.560069	−	0.466976i
$285$		0			0
$286$	6.14441	−	2.87689i	0.363327	−	0.170114i
$287$	−3.33513	+	18.5485i	−0.196867	+	1.09488i
$288$		0			0
$289$	−33.7386			−1.98463
$290$	−1.19935	−	2.56155i	−0.0704284	−	0.150420i
$291$		0			0
$292$	14.3922	+	12.0000i	0.842242	+	0.702247i
$293$		−	32.2462i		−	1.88384i	−0.335832	−	0.941922i	$-0.609017\pi$
$293$		−	32.2462i		−	1.88384i	0.335832	−	0.941922i	$-0.390983\pi$
$294$		0			0
$295$			10.9418i			0.637058i
$296$	−1.43845	+	5.47091i	−0.0836080	+	0.317990i
$297$		0			0
$298$	−24.8078	+	11.6153i	−1.43708	+	0.672858i
$299$	−11.4677			−0.663193
$300$		0			0
$301$	3.56155	−	19.8078i	0.205284	−	1.14170i
$302$	−8.80776	−	18.8114i	−0.506830	−	1.08248i
$303$		0			0
$304$	1.72521	+	9.43845i	0.0989473	+	0.541332i
$305$	2.00000			0.114520
$306$		0			0
$307$	−31.3632			−1.78999			−0.894996	−	0.446074i	$-0.852822\pi$
$307$	−31.3632			−1.78999			−0.894996	+	0.446074i	$0.852822\pi$
$308$	−8.15638	−	9.72521i	−0.464753	−	0.554145i
$309$		0			0
$310$	4.00000	+	8.54312i	0.227185	+	0.485216i
$311$	9.36426			0.530999			0.265499	−	0.964111i	$-0.414463\pi$
$311$	9.36426			0.530999			0.265499	+	0.964111i	$0.414463\pi$
$312$		0			0
$313$			7.61553i			0.430455i	0.976564	+	0.215228i	$0.0690493\pi$
$313$			7.61553i			0.430455i	−0.976564	+	0.215228i	$0.930951\pi$
$314$	9.74247	+	20.8078i	0.549799	+	1.17425i
$315$		0			0
$316$	−6.56155	−	5.47091i	−0.369116	−	0.307763i
$317$	4.24621			0.238491			0.119245	−	0.992865i	$-0.461952\pi$
$317$	4.24621			0.238491			0.119245	+	0.992865i	$0.461952\pi$
$318$		0			0
$319$		−	4.79741i		−	0.268603i
$320$	3.93481	−	6.96543i	0.219962	−	0.389380i
$321$		0			0
$322$	5.51524	+	20.7330i	0.307352	+	1.15541i
$323$			17.0862i			0.950703i
$324$		0			0
$325$			2.00000i			0.110940i
$326$	0.561553	+	1.19935i	0.0311015	+	0.0664260i
$327$		0			0
$328$	−19.4849	−	5.12311i	−1.07588	−	0.282876i
$329$	−26.0540	−	4.68466i	−1.43640	−	0.258274i
$330$		0			0
$331$			29.0798i			1.59837i	0.601086	+	0.799184i	$0.294735\pi$
$331$			29.0798i			1.59837i	−0.601086	+	0.799184i	$0.705265\pi$
$332$	1.19935	−	1.43845i	0.0658230	−	0.0789450i
$333$		0			0
$334$	2.92456	−	1.36932i	0.160025	−	0.0749257i
$335$	14.2770			0.780033
$336$		0			0
$337$	4.24621			0.231306			0.115653	−	0.993290i	$-0.463104\pi$
$337$	4.24621			0.231306			0.115653	+	0.993290i	$0.463104\pi$
$338$	−11.5270	+	5.39709i	−0.626985	+	0.293563i
$339$		0			0
$340$	9.12311	−	10.9418i	0.494770	−	0.593404i
$341$			16.0000i			0.866449i
$342$		0			0
$343$	15.9445	+	9.42190i	0.860923	+	0.508735i
$344$	20.8078	+	5.47091i	1.12188	+	0.294972i
$345$		0			0
$346$	−0.147647	−	0.315342i	−0.00793756	−	0.0169529i
$347$		−	9.47954i		−	0.508889i	−0.967087	−	0.254444i	$-0.918107\pi$
$347$		−	9.47954i		−	0.508889i	0.967087	−	0.254444i	$-0.0818925\pi$
$348$		0			0
$349$			27.8617i			1.49140i	0.666279	+	0.745702i	$0.267886\pi$
$349$			27.8617i			1.49140i	−0.666279	+	0.745702i	$0.732114\pi$
$350$	3.61591	−	0.961876i	0.193278	−	0.0514145i
$351$		0			0
$352$	11.0540	−	7.86962i	0.589179	−	0.419452i
$353$			5.36932i			0.285780i	0.989739	+	0.142890i	$0.0456395\pi$
$353$			5.36932i			0.285780i	−0.989739	+	0.142890i	$0.954361\pi$
$354$		0			0
$355$	6.14441			0.326111
$356$	18.4332	+	15.3693i	0.976959	+	0.814572i
$357$		0			0
$358$	−0.315342	−	0.673500i	−0.0166663	−	0.0355956i
$359$			16.5604i			0.874023i	0.899456	+	0.437012i	$0.143963\pi$
$359$			16.5604i			0.874023i	−0.899456	+	0.437012i	$0.856037\pi$
$360$		0			0
$361$	−13.2462			−0.697169
$362$	−4.12391	−	8.80776i	−0.216748	−	0.462926i
$363$		0			0
$364$	−6.80065	−	8.10871i	−0.356451	−	0.425012i
$365$	−9.36932			−0.490412
$366$		0			0
$367$	7.08084			0.369617			0.184808	−	0.982775i	$-0.440834\pi$
$367$	7.08084			0.369617			0.184808	+	0.982775i	$0.440834\pi$
$368$	−22.5616	+	4.12391i	−1.17610	+	0.214974i
$369$		0			0
$370$	−1.19935	−	2.56155i	−0.0623514	−	0.133169i
$371$	−5.20798	−	0.936426i	−0.270385	−	0.0486168i
$372$		0			0
$373$	22.4924			1.16461			0.582307	−	0.812969i	$-0.302150\pi$
$373$	22.4924			1.16461			0.582307	+	0.812969i	$0.302150\pi$
$374$	21.8836	−	10.2462i	1.13158	−	0.529819i
$375$		0			0
$376$	7.19612	−	27.3693i	0.371111	−	1.41146i
$377$		−	4.00000i		−	0.206010i
$378$		0			0
$379$			22.4095i			1.15110i	0.817767	+	0.575549i	$0.195212\pi$
$379$			22.4095i			1.15110i	−0.817767	+	0.575549i	$0.804788\pi$
$380$	−3.68466	−	3.07221i	−0.189019	−	0.157601i
$381$		0			0
$382$	−0.807764	−	1.72521i	−0.0413288	−	0.0882692i
$383$	−17.4968			−0.894045			−0.447023	−	0.894523i	$-0.647516\pi$
$383$	−17.4968			−0.894045			−0.447023	+	0.894523i	$0.647516\pi$
$384$		0			0
$385$	6.24621	+	1.12311i	0.318336	+	0.0572388i
$386$	−13.4384	+	6.29206i	−0.683999	+	0.320257i
$387$		0			0
$388$	−10.9418	−	9.12311i	−0.555487	−	0.463156i
$389$	−1.12311			−0.0569437			−0.0284719	−	0.999595i	$-0.509064\pi$
$389$	−1.12311			−0.0569437			−0.0284719	+	0.999595i	$0.509064\pi$
$390$		0			0
$391$	−40.8427			−2.06551
$392$	−11.3895	+	16.1950i	−0.575256	+	0.817973i
$393$		0			0
$394$	23.0540	−	10.7942i	1.16144	−	0.543803i
$395$	4.27156			0.214925
$396$		0			0
$397$			14.0000i			0.702640i	0.936255	+	0.351320i	$0.114267\pi$
$397$			14.0000i			0.702640i	−0.936255	+	0.351320i	$0.885733\pi$
$398$	−20.5366	+	9.61553i	−1.02941	+	0.481983i
$399$		0			0
$400$	0.719224	+	3.93481i	0.0359612	+	0.196740i
$401$	−6.00000			−0.299626			−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000			−0.299626			−0.149813	+	0.988714i	$0.547867\pi$
$402$		0			0
$403$			13.3405i			0.664539i
$404$	−10.5636	−	8.80776i	−0.525560	−	0.438203i
$405$		0			0
$406$	−7.23182	+	1.92375i	−0.358909	+	0.0954742i
$407$		−	4.79741i		−	0.237799i
$408$		0			0
$409$			8.87689i			0.438934i	0.975620	+	0.219467i	$0.0704319\pi$
$409$			8.87689i			0.438934i	−0.975620	+	0.219467i	$0.929568\pi$
$410$	9.12311	−	4.27156i	0.450558	−	0.210957i
$411$		0			0
$412$	−1.87285	+	2.24621i	−0.0922688	+	0.110663i
$413$	28.4924	+	5.12311i	1.40202	+	0.252092i
$414$		0			0
$415$			0.936426i			0.0459674i
$416$	9.21662	−	6.56155i	0.451882	−	0.321707i
$417$		0			0
$418$	−3.45041	−	7.36932i	−0.168765	−	0.360445i
$419$	11.9935			0.585922			0.292961	−	0.956124i	$-0.405359\pi$
$419$	11.9935			0.585922			0.292961	+	0.956124i	$0.405359\pi$
$420$		0			0
$421$	−17.6155			−0.858528			−0.429264	−	0.903179i	$-0.641227\pi$
$421$	−17.6155			−0.858528			−0.429264	+	0.903179i	$0.641227\pi$
$422$	11.0540	+	23.6089i	0.538099	+	1.14926i
$423$		0			0
$424$	1.43845	−	5.47091i	0.0698572	−	0.265691i
$425$			7.12311i			0.345521i
$426$		0			0
$427$	0.936426	−	5.20798i	0.0453168	−	0.252032i
$428$	−14.5616	−	12.1412i	−0.703859	−	0.586866i
$429$		0			0
$430$	−9.74247	+	4.56155i	−0.469824	+	0.219978i
$431$			36.5712i			1.76157i	0.473515	+	0.880786i	$0.342985\pi$
$431$			36.5712i			1.76157i	−0.473515	+	0.880786i	$0.657015\pi$
$432$		0			0
$433$			11.6155i			0.558207i	0.960261	+	0.279103i	$0.0900372\pi$
$433$			11.6155i			0.558207i	−0.960261	+	0.279103i	$0.909963\pi$
$434$	24.1191	−	6.41597i	1.15775	−	0.307976i
$435$		0			0
$436$	1.43845	−	1.72521i	0.0688891	−	0.0826224i
$437$			13.7538i			0.657933i
$438$		0			0
$439$	18.1379			0.865677			0.432838	−	0.901472i	$-0.357512\pi$
$439$	18.1379			0.865677			0.432838	+	0.901472i	$0.357512\pi$
$440$	−1.72521	+	6.56155i	−0.0822460	+	0.312810i
$441$		0			0
$442$	18.2462	−	8.54312i	0.867884	−	0.406355i
$443$		−	30.3115i		−	1.44014i	−0.693900	−	0.720071i	$-0.744109\pi$
$443$		−	30.3115i		−	1.44014i	0.693900	−	0.720071i	$-0.255891\pi$
$444$		0			0
$445$	−12.0000			−0.568855
$446$	−16.5604	+	7.75379i	−0.784157	+	0.367153i
$447$		0			0
$448$	−16.2956	−	13.5075i	−0.769895	−	0.638170i
$449$	−25.6155			−1.20887			−0.604436	−	0.796654i	$-0.706601\pi$
$449$	−25.6155			−1.20887			−0.604436	+	0.796654i	$0.706601\pi$
$450$		0			0
$451$	17.0862			0.804559
$452$	18.5616	−	22.2619i	0.873062	−	1.04711i
$453$		0			0
$454$	−18.2856	+	8.56155i	−0.858185	+	0.401814i
$455$	5.20798	+	0.936426i	0.244154	+	0.0439003i
$456$		0			0
$457$	6.00000			0.280668			0.140334	−	0.990104i	$-0.455182\pi$
$457$	6.00000			0.280668			0.140334	+	0.990104i	$0.455182\pi$
$458$	−12.6670	−	27.0540i	−0.591891	−	1.26415i
$459$		0			0
$460$	7.34376	−	8.80776i	0.342405	−	0.410664i
$461$		−	37.6155i		−	1.75193i	−0.482375	−	0.875965i	$-0.660226\pi$
$461$		−	37.6155i		−	1.75193i	0.482375	−	0.875965i	$-0.339774\pi$
$462$		0			0
$463$		−	21.9989i		−	1.02238i	−0.859469	−	0.511188i	$-0.829205\pi$
$463$		−	21.9989i		−	1.02238i	0.859469	−	0.511188i	$-0.170795\pi$
$464$	−1.43845	−	7.86962i	−0.0667782	−	0.365338i
$465$		0			0
$466$	31.0540	−	14.5399i	1.43855	−	0.673547i
$467$	−1.98813			−0.0919998			−0.0459999	−	0.998941i	$-0.514647\pi$
$467$	−1.98813			−0.0919998			−0.0459999	+	0.998941i	$0.514647\pi$
$468$		0			0
$469$	6.68466	−	37.1771i	0.308669	−	1.71668i
$470$	6.00000	+	12.8147i	0.276759	+	0.591097i
$471$		0			0
$472$	−7.86962	+	29.9309i	−0.362228	+	1.37768i
$473$	−18.2462			−0.838962
$474$		0			0
$475$	2.39871			0.110060
$476$	−24.2209	−	28.8796i	−1.11016	−	1.32369i
$477$		0			0
$478$	−7.68466	−	16.4127i	−0.351488	−	0.750701i
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$		0			0
$481$		−	4.00000i		−	0.182384i
$482$	9.36426	+	20.0000i	0.426531	+	0.910975i
$483$		0			0
$484$	6.71922	−	8.05872i	0.305419	−	0.366305i
$485$	7.12311			0.323444
$486$		0			0
$487$			19.0744i			0.864342i	0.901792	+	0.432171i	$0.142252\pi$
$487$			19.0744i			0.864342i	−0.901792	+	0.432171i	$0.857748\pi$
$488$	5.47091	+	1.43845i	0.247657	+	0.0651154i
$489$		0			0
$490$	−0.811703	−	9.86616i	−0.0366690	−	0.445708i
$491$		−	13.6358i		−	0.615376i	−0.951487	−	0.307688i	$-0.900445\pi$
$491$		−	13.6358i		−	0.615376i	0.951487	−	0.307688i	$-0.0995553\pi$
$492$		0			0
$493$		−	14.2462i		−	0.641617i
$494$	−2.87689	−	6.14441i	−0.129438	−	0.276450i
$495$		0			0
$496$	4.79741	+	26.2462i	0.215410	+	1.17849i
$497$	2.87689	−	16.0000i	0.129046	−	0.717698i
$498$		0			0
$499$		−	27.2069i		−	1.21795i	−0.793190	−	0.608974i	$-0.791581\pi$
$499$		−	27.2069i		−	1.21795i	0.793190	−	0.608974i	$-0.208419\pi$
$500$	−1.53610	−	1.28078i	−0.0686966	−	0.0572781i
$501$		0			0
$502$	21.2101	−	9.93087i	0.946655	−	0.443236i
$503$	21.4731			0.957437			0.478718	−	0.877968i	$-0.341101\pi$
$503$	21.4731			0.957437			0.478718	+	0.877968i	$0.341101\pi$
$504$		0			0
$505$	6.87689			0.306018
$506$	17.6155	−	8.24782i	0.783106	−	0.366660i
$507$		0			0
$508$	20.3153	+	16.9386i	0.901348	+	0.751528i
$509$			17.6155i			0.780795i	0.920646	+	0.390397i	$0.127662\pi$
$509$			17.6155i			0.780795i	−0.920646	+	0.390397i	$0.872338\pi$
$510$		0			0
$511$	−4.38684	+	24.3976i	−0.194062	+	1.07929i
$512$	15.7732	−	16.2236i	0.697083	−	0.716990i
$513$		0			0
$514$	−8.01726	−	17.1231i	−0.353626	−	0.755268i
$515$		−	1.46228i		−	0.0644357i
$516$		0			0
$517$			24.0000i			1.05552i
$518$	−7.23182	+	1.92375i	−0.317748	+	0.0845248i
$519$		0			0
$520$	−1.43845	+	5.47091i	−0.0630801	+	0.239915i
$521$		−	26.2462i		−	1.14987i	−0.818200	−	0.574934i	$-0.805028\pi$
$521$		−	26.2462i		−	1.14987i	0.818200	−	0.574934i	$-0.194972\pi$
$522$		0			0
$523$	17.2015			0.752170			0.376085	−	0.926585i	$-0.377270\pi$
$523$	17.2015			0.752170			0.376085	+	0.926585i	$0.377270\pi$
$524$	−17.7597	+	21.3002i	−0.775838	+	0.930503i
$525$		0			0
$526$	−1.19224	−	2.54635i	−0.0519840	−	0.111026i
$527$			47.5130i			2.06970i
$528$		0			0
$529$	−9.87689			−0.429430
$530$	1.19935	+	2.56155i	0.0520966	+	0.111267i
$531$		0			0
$532$	−9.72521	+	8.15638i	−0.421641	+	0.353624i
$533$	14.2462			0.617072
$534$		0			0
$535$	9.47954			0.409836
$536$	39.0540	+	10.2683i	1.68687	+	0.443524i
$537$		0			0
$538$	−9.74247	−	20.8078i	−0.420028	−	0.897086i
$539$	5.84912	−	15.7392i	0.251939	−	0.677937i
$540$		0			0
$541$	30.0000			1.28980			0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000			1.28980			0.644900	+	0.764267i	$0.276899\pi$
$542$	30.4268	−	14.2462i	1.30694	−	0.611927i
$543$		0			0
$544$	32.8255	−	23.3693i	1.40738	−	1.00195i
$545$			1.12311i			0.0481086i
$546$		0			0
$547$		−	1.75757i		−	0.0751484i	−0.999294	−	0.0375742i	$-0.988037\pi$
$547$		−	1.75757i		−	0.0751484i	0.999294	−	0.0375742i	$-0.0119631\pi$
$548$	17.9309	−	21.5054i	0.765969	−	0.918667i
$549$		0			0
$550$	−1.43845	−	3.07221i	−0.0613356	−	0.130999i
$551$	−4.79741			−0.204377
$552$		0			0
$553$	2.00000	−	11.1231i	0.0850487	−	0.473003i
$554$	5.43845	−	2.54635i	0.231057	−	0.108184i
$555$		0			0
$556$	−1.72521	+	2.06913i	−0.0731650	+	0.0877507i
$557$	−6.49242			−0.275093			−0.137546	−	0.990495i	$-0.543922\pi$
$557$	−6.49242			−0.275093			−0.137546	+	0.990495i	$0.543922\pi$
$558$		0			0
$559$	−15.2134			−0.643457
$560$	10.5830	−	0.0305236i	0.447212	−	0.00128986i
$561$		0			0
$562$	−5.93087	+	2.77691i	−0.250179	+	0.117137i
$563$	26.7963			1.12933			0.564665	−	0.825320i	$-0.309005\pi$
$563$	26.7963			1.12933			0.564665	+	0.825320i	$0.309005\pi$
$564$		0			0
$565$			14.4924i			0.609701i
$566$	−31.6261	+	14.8078i	−1.32934	+	0.622417i
$567$		0			0
$568$	16.8078	+	4.41921i	0.705238	+	0.185426i
$569$	37.1231			1.55628			0.778141	−	0.628090i	$-0.216163\pi$
$569$	37.1231			1.55628			0.778141	+	0.628090i	$0.216163\pi$
$570$		0			0
$571$		−	28.0281i		−	1.17294i	−0.809972	−	0.586469i	$-0.800518\pi$
$571$		−	28.0281i		−	1.17294i	0.809972	−	0.586469i	$-0.199482\pi$
$572$	−6.14441	+	7.36932i	−0.256911	+	0.308127i
$573$		0			0
$574$	−6.85155	−	25.7565i	−0.285978	−	1.07506i
$575$			5.73384i			0.239118i
$576$		0			0
$577$		−	4.38447i		−	0.182528i	−0.995827	−	0.0912640i	$-0.970909\pi$
$577$		−	4.38447i		−	0.182528i	0.995827	−	0.0912640i	$-0.0290907\pi$
$578$	43.2116	−	20.2323i	1.79737	−	0.841551i
$579$		0			0
$580$	3.07221	+	2.56155i	0.127566	+	0.106363i
$581$	2.43845	+	0.438447i	0.101164	+	0.0181899i
$582$		0			0
$583$			4.79741i			0.198688i
$584$	−25.6294	−	6.73863i	−1.06055	−	0.278847i
$585$		0			0
$586$	19.3373	+	41.3002i	0.798816	+	1.70609i
$587$	8.65840			0.357370			0.178685	−	0.983906i	$-0.442816\pi$
$587$	8.65840			0.357370			0.178685	+	0.983906i	$0.442816\pi$
$588$		0			0
$589$	16.0000			0.659269
$590$	−6.56155	−	14.0140i	−0.270135	−	0.576948i
$591$		0			0
$592$	−1.43845	−	7.86962i	−0.0591198	−	0.323439i
$593$			13.3693i			0.549012i	0.961585	+	0.274506i	$0.0885143\pi$
$593$			13.3693i			0.549012i	−0.961585	+	0.274506i	$0.911486\pi$
$594$		0			0
$595$	18.5485	+	3.33513i	0.760415	+	0.136727i
$596$	24.8078	−	29.7533i	1.01617	−	1.21874i
$597$		0			0
$598$	14.6875	−	6.87689i	0.600618	−	0.281217i
$599$			10.1207i			0.413520i	0.978392	+	0.206760i	$0.0662919\pi$
$599$			10.1207i			0.413520i	−0.978392	+	0.206760i	$0.933708\pi$
$600$		0			0
$601$		−	8.87689i		−	0.362096i	−0.983474	−	0.181048i	$-0.942051\pi$
$601$		−	8.87689i		−	0.362096i	0.983474	−	0.181048i	$-0.0579489\pi$
$602$	7.31670	+	27.5051i	0.298206	+	1.12102i
$603$		0			0
$604$	22.5616	+	18.8114i	0.918017	+	0.765427i
$605$			5.24621i			0.213289i
$606$		0			0
$607$	7.90198			0.320732			0.160366	−	0.987058i	$-0.448733\pi$
$607$	7.90198			0.320732			0.160366	+	0.987058i	$0.448733\pi$
$608$	−7.86962	−	11.0540i	−0.319155	−	0.448298i
$609$		0			0
$610$	−2.56155	+	1.19935i	−0.103714	+	0.0485604i
$611$			20.0108i			0.809550i
$612$		0			0
$613$	11.7538			0.474731			0.237366	−	0.971420i	$-0.423716\pi$
$613$	11.7538			0.474731			0.237366	+	0.971420i	$0.423716\pi$
$614$	40.1692	−	18.8078i	1.62110	−	0.759020i
$615$		0			0
$616$	16.2785	+	7.56463i	0.655878	+	0.304788i
$617$	26.0000			1.04672			0.523360	−	0.852111i	$-0.324678\pi$
$617$	26.0000			1.04672			0.523360	+	0.852111i	$0.324678\pi$
$618$		0			0
$619$	−48.8600			−1.96385			−0.981925	−	0.189273i	$-0.939387\pi$
$619$	−48.8600			−1.96385			−0.981925	+	0.189273i	$0.939387\pi$
$620$	−10.2462	−	8.54312i	−0.411498	−	0.343100i
$621$		0			0
$622$	−11.9935	+	5.61553i	−0.480897	+	0.225162i
$623$	−5.61856	+	31.2479i	−0.225103	+	1.25192i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−4.56685	−	9.75379i	−0.182528	−	0.389840i
$627$		0			0
$628$	−24.9559	−	20.8078i	−0.995847	−	0.830320i
$629$		−	14.2462i		−	0.568034i
$630$		0			0
$631$		−	7.19612i		−	0.286473i	−0.989688	−	0.143236i	$-0.954249\pi$
$631$		−	7.19612i		−	0.286473i	0.989688	−	0.143236i	$-0.0457509\pi$
$632$	11.6847	+	3.07221i	0.464791	+	0.122206i
$633$		0			0
$634$	−5.43845	+	2.54635i	−0.215988	+	0.101129i
$635$	−13.2252			−0.524828
$636$		0			0
$637$	4.87689	−	13.1231i	0.193230	−	0.519956i
$638$	2.87689	+	6.14441i	0.113897	+	0.243260i
$639$		0			0
$640$	−0.862603	+	11.2808i	−0.0340974	+	0.445912i
$641$	−1.12311			−0.0443600			−0.0221800	−	0.999754i	$-0.507061\pi$
$641$	−1.12311			−0.0443600			−0.0221800	+	0.999754i	$0.507061\pi$
$642$		0			0
$643$	4.91269			0.193738			0.0968688	−	0.995297i	$-0.469117\pi$
$643$	4.91269			0.193738			0.0968688	+	0.995297i	$0.469117\pi$
$644$	−19.4969	−	23.2470i	−0.768286	−	0.916061i
$645$		0			0
$646$	−10.2462	−	21.8836i	−0.403132	−	0.861000i
$647$	−37.7382			−1.48364			−0.741820	−	0.670599i	$-0.766037\pi$
$647$	−37.7382			−1.48364			−0.741820	+	0.670599i	$0.766037\pi$
$648$		0			0
$649$		−	26.2462i		−	1.03025i
$650$	−1.19935	−	2.56155i	−0.0470425	−	0.100472i
$651$		0			0
$652$	−1.43845	−	1.19935i	−0.0563339	−	0.0469703i
$653$	−42.9848			−1.68213			−0.841063	−	0.540936i	$-0.818070\pi$
$653$	−42.9848			−1.68213			−0.841063	+	0.540936i	$0.818070\pi$
$654$		0			0
$655$		−	13.8664i		−	0.541804i
$656$	28.0281	−	5.12311i	1.09431	−	0.200024i
$657$		0			0
$658$	36.1786	−	9.62395i	1.41039	−	0.375181i
$659$			4.27156i			0.166396i	0.996533	+	0.0831981i	$0.0265134\pi$
$659$			4.27156i			0.166396i	−0.996533	+	0.0831981i	$0.973487\pi$
$660$		0			0
$661$		−	4.24621i		−	0.165158i	−0.996585	−	0.0825792i	$-0.973684\pi$
$661$		−	4.24621i		−	0.165158i	0.996585	−	0.0825792i	$-0.0263158\pi$
$662$	−17.4384	−	37.2447i	−0.677764	−	1.44756i
$663$		0			0
$664$	−0.673500	+	2.56155i	−0.0261369	+	0.0994075i
$665$	1.12311	−	6.24621i	0.0435522	−	0.242218i
$666$		0			0
$667$		−	11.4677i		−	0.444030i
$668$	−2.92456	+	3.50758i	−0.113155	+	0.135712i
$669$		0			0
$670$	−18.2856	+	8.56155i	−0.706434	+	0.330762i
$671$	−4.79741			−0.185202
$672$		0			0
$673$	−14.0000			−0.539660			−0.269830	−	0.962908i	$-0.586968\pi$
$673$	−14.0000			−0.539660			−0.269830	+	0.962908i	$0.586968\pi$
$674$	−5.43845	+	2.54635i	−0.209481	+	0.0980818i
$675$		0			0
$676$	11.5270	−	13.8249i	0.443346	−	0.531728i
$677$			16.7386i			0.643318i	0.946856	+	0.321659i	$0.104240\pi$
$677$			16.7386i			0.643318i	−0.946856	+	0.321659i	$0.895760\pi$
$678$		0			0
$679$	3.33513	−	18.5485i	0.127991	−	0.711827i
$680$	−5.12311	+	19.4849i	−0.196462	+	0.747213i
$681$		0			0
$682$	−9.59482	−	20.4924i	−0.367405	−	0.784695i
$683$			7.60669i			0.291062i	0.989354	+	0.145531i	$0.0464890\pi$
$683$			7.60669i			0.291062i	−0.989354	+	0.145531i	$0.953511\pi$
$684$		0			0
$685$			14.0000i			0.534913i
$686$	−26.0715	−	2.50580i	−0.995413	−	0.0956718i
$687$		0			0
$688$	−29.9309	+	5.47091i	−1.14110	+	0.208577i
$689$			4.00000i			0.152388i
$690$		0			0
$691$	−22.4095			−0.852497			−0.426249	−	0.904606i	$-0.640165\pi$
$691$	−22.4095			−0.852497			−0.426249	+	0.904606i	$0.640165\pi$
$692$	0.378206	+	0.315342i	0.0143772	+	0.0119875i
$693$		0			0
$694$	5.68466	+	12.1412i	0.215787	+	0.460873i
$695$		−	1.34700i		−	0.0510946i
$696$		0			0
$697$	50.7386			1.92186
$698$	−16.7080	−	35.6847i	−0.632408	−	1.35068i
$699$		0			0
$700$	−4.05436	+	3.40032i	−0.153240	+	0.128520i
$701$	−2.87689			−0.108659			−0.0543294	−	0.998523i	$-0.517302\pi$
$701$	−2.87689			−0.108659			−0.0543294	+	0.998523i	$0.517302\pi$
$702$		0			0
$703$	−4.79741			−0.180938
$704$	−9.43845	+	16.7080i	−0.355725	+	0.629707i
$705$		0			0
$706$	−3.21985	−	6.87689i	−0.121181	−	0.258815i
$707$	3.21985	−	17.9074i	0.121095	−	0.673476i
$708$		0			0
$709$	−4.73863			−0.177963			−0.0889816	−	0.996033i	$-0.528361\pi$
$709$	−4.73863			−0.177963			−0.0889816	+	0.996033i	$0.528361\pi$
$710$	−7.86962	+	3.68466i	−0.295341	+	0.138283i
$711$		0			0
$712$	−32.8255	−	8.63068i	−1.23019	−	0.323449i
$713$			38.2462i			1.43233i
$714$		0			0
$715$		−	4.79741i		−	0.179413i
$716$	0.807764	+	0.673500i	0.0301876	+	0.0251699i
$717$		0			0
$718$	−9.93087	−	21.2101i	−0.370617	−	0.791556i
$719$	37.9182			1.41411			0.707055	−	0.707159i	$-0.250023\pi$
$719$	37.9182			1.41411			0.707055	+	0.707159i	$0.250023\pi$
$720$		0			0
$721$	−3.80776	−	0.684658i	−0.141809	−	0.0254980i
$722$	16.9654	−	7.94344i	0.631388	−	0.295624i
$723$		0			0
$724$	10.5636	+	8.80776i	0.392594	+	0.327338i
$725$	−2.00000			−0.0742781
$726$		0			0
$727$	22.2942			0.826847			0.413423	−	0.910539i	$-0.364333\pi$
$727$	22.2942			0.826847			0.413423	+	0.910539i	$0.364333\pi$
$728$	13.5727	+	6.30726i	0.503038	+	0.233763i
$729$		0			0
$730$	12.0000	−	5.61856i	0.444140	−	0.207952i
$731$	−54.1833			−2.00404
$732$		0			0
$733$			48.7386i			1.80020i	0.435681	+	0.900101i	$0.356508\pi$
$733$			48.7386i			1.80020i	−0.435681	+	0.900101i	$0.643492\pi$
$734$	−9.06897	+	4.24621i	−0.334742	+	0.156731i
$735$		0			0
$736$	26.4233	−	18.8114i	0.973975	−	0.693399i
$737$	−34.2462			−1.26148
$738$		0			0
$739$		−	15.5087i		−	0.570496i	−0.958454	−	0.285248i	$-0.907924\pi$
$739$		−	15.5087i		−	0.570496i	0.958454	−	0.285248i	$-0.0920759\pi$
$740$	3.07221	+	2.56155i	0.112937	+	0.0941646i
$741$		0			0
$742$	7.23182	−	1.92375i	0.265488	−	0.0706232i
$743$			15.0981i			0.553896i	0.960885	+	0.276948i	$0.0893229\pi$
$743$			15.0981i			0.553896i	−0.960885	+	0.276948i	$0.910677\pi$
$744$		0			0
$745$			19.3693i			0.709637i
$746$	−28.8078	+	13.4882i	−1.05473	+	0.493837i
$747$		0			0
$748$	−21.8836	+	26.2462i	−0.800145	+	0.959657i
$749$	4.43845	−	24.6847i	0.162177	−	0.901958i
$750$		0			0
$751$			5.09271i			0.185835i	0.995674	+	0.0929177i	$0.0296194\pi$
$751$			5.09271i			0.185835i	−0.995674	+	0.0929177i	$0.970381\pi$
$752$	7.19612	+	39.3693i	0.262415	+	1.43565i
$753$		0			0
$754$	2.39871	+	5.12311i	0.0873557	+	0.186573i
$755$	−14.6875			−0.534534
$756$		0			0
$757$	−12.2462			−0.445096			−0.222548	−	0.974922i	$-0.571437\pi$
$757$	−12.2462			−0.445096			−0.222548	+	0.974922i	$0.571437\pi$
$758$	−13.4384	−	28.7016i	−0.488106	−	1.04249i
$759$		0			0
$760$	6.56155	+	1.72521i	0.238013	+	0.0625798i
$761$			35.2311i			1.27712i	0.769570	+	0.638562i	$0.220471\pi$
$761$			35.2311i			1.27712i	−0.769570	+	0.638562i	$0.779529\pi$
$762$		0			0
$763$	2.92456	+	0.525853i	0.105876	+	0.0190372i
$764$	2.06913	+	1.72521i	0.0748585	+	0.0624158i
$765$		0			0
$766$	22.4095	−	10.4924i	0.809688	−	0.379107i
$767$		−	21.8836i		−	0.790173i
$768$		0			0
$769$		−	55.2311i		−	1.99168i	−0.0911037	−	0.995841i	$-0.529039\pi$
$769$		−	55.2311i		−	1.99168i	0.0911037	−	0.995841i	$-0.470961\pi$
$770$	−8.67350	+	2.30726i	−0.312571	+	0.0831478i
$771$		0			0
$772$	13.4384	−	16.1174i	0.483660	−	0.580079i
$773$			16.7386i			0.602047i	0.953617	+	0.301023i	$0.0973282\pi$
$773$			16.7386i			0.602047i	−0.953617	+	0.301023i	$0.902672\pi$
$774$		0			0
$775$	6.67026			0.239603
$776$	19.4849	+	5.12311i	0.699469	+	0.183909i
$777$		0			0
$778$	1.43845	−	0.673500i	0.0515708	−	0.0241461i
$779$		−	17.0862i		−	0.612178i
$780$		0			0
$781$	−14.7386			−0.527390
$782$	52.3104	−	24.4924i	1.87062	−	0.875847i
$783$		0			0
$784$	4.87560	−	27.5722i	0.174129	−	0.984723i
$785$	16.2462			0.579852
$786$		0			0
$787$	−0.936426			−0.0333800			−0.0166900	−	0.999861i	$-0.505313\pi$
$787$	−0.936426			−0.0333800			−0.0166900	+	0.999861i	$0.505313\pi$
$788$	−23.0540	+	27.6499i	−0.821264	+	0.984985i
$789$		0			0
$790$	−5.47091	+	2.56155i	−0.194646	+	0.0911360i
$791$	37.7382	+	6.78554i	1.34181	+	0.241266i
$792$		0			0
$793$	−4.00000			−0.142044
$794$	−8.39547	−	17.9309i	−0.297944	−	0.636343i
$795$		0			0
$796$	20.5366	−	24.6307i	0.727902	−	0.873011i
$797$		−	20.2462i		−	0.717158i	−0.933499	−	0.358579i	$-0.883261\pi$
$797$		−	20.2462i		−	0.717158i	0.933499	−	0.358579i	$-0.116739\pi$
$798$		0			0
$799$			71.2695i			2.52133i
$800$	−3.28078	−	4.60831i	−0.115993	−	0.162928i
$801$		0			0
$802$	7.68466	−	3.59806i	0.271355	−	0.127052i
$803$	22.4742			0.793098
$804$		0			0
$805$	14.9309	+	2.68466i	0.526244	+	0.0946218i
$806$	−8.00000	−	17.0862i	−0.281788	−	0.601837i
$807$		0			0
$808$	18.8114	+	4.94602i	0.661784	+	0.174001i
$809$	18.9848			0.667472			0.333736	−	0.942667i	$-0.391691\pi$
$809$	18.9848			0.667472			0.333736	+	0.942667i	$0.391691\pi$
$810$		0			0
$811$	9.06897			0.318455			0.159227	−	0.987242i	$-0.449100\pi$
$811$	9.06897			0.318455			0.159227	+	0.987242i	$0.449100\pi$
$812$	8.10871	−	6.80065i	0.284560	−	0.238656i
$813$		0			0
$814$	2.87689	+	6.14441i	0.100835	+	0.215362i
$815$	0.936426			0.0328016
$816$		0			0
$817$			18.2462i			0.638354i
$818$	−5.32326	−	11.3693i	−0.186124	−	0.397519i
$819$		0			0
$820$	−9.12311	+	10.9418i	−0.318593	+	0.382105i
$821$	25.6155			0.893988			0.446994	−	0.894537i	$-0.352495\pi$
$821$	25.6155			0.893988			0.446994	+	0.894537i	$0.352495\pi$
$822$		0			0
$823$			32.1843i			1.12188i	0.827858	+	0.560938i	$0.189559\pi$
$823$			32.1843i			1.12188i	−0.827858	+	0.560938i	$0.810441\pi$
$824$	1.05171	−	4.00000i	0.0366379	−	0.139347i
$825$		0			0
$826$	−39.5646	+	10.5247i	−1.37663	+	0.366200i
$827$			0.115279i			0.00400866i	0.999998	+	0.00200433i	$0.000637998\pi$
$827$			0.115279i			0.00400866i	−0.999998	+	0.00200433i	$0.999362\pi$
$828$		0			0
$829$		−	32.2462i		−	1.11996i	−0.828507	−	0.559979i	$-0.810809\pi$
$829$		−	32.2462i		−	1.11996i	0.828507	−	0.559979i	$-0.189191\pi$
$830$	−0.561553	−	1.19935i	−0.0194918	−	0.0416301i
$831$		0			0
$832$	−7.86962	+	13.9309i	−0.272830	+	0.482966i
$833$	17.3693	−	46.7386i	0.601811	−	1.61940i
$834$		0			0
$835$		−	2.28343i		−	0.0790212i
$836$	8.83841	+	7.36932i	0.305683	+	0.254873i
$837$		0			0
$838$	−15.3610	+	7.19224i	−0.530638	+	0.248452i
$839$	−35.2242			−1.21607			−0.608037	−	0.793909i	$-0.708043\pi$
$839$	−35.2242			−1.21607			−0.608037	+	0.793909i	$0.708043\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	22.5616	−	10.5636i	0.777522	−	0.364046i
$843$		0			0
$844$	−28.3153	−	23.6089i	−0.974654	−	0.812650i
$845$			9.00000i			0.309609i
$846$		0			0
$847$	13.6611	+	2.45635i	0.469401	+	0.0844010i
$848$	1.43845	+	7.86962i	0.0493965	+	0.270244i
$849$		0			0
$850$	−4.27156	−	9.12311i	−0.146513	−	0.312920i
$851$		−	11.4677i		−	0.393107i
$852$		0			0
$853$		−	7.75379i		−	0.265485i	−0.991151	−	0.132742i	$-0.957622\pi$
$853$		−	7.75379i		−	0.265485i	0.991151	−	0.132742i	$-0.0423783\pi$
$854$	1.92375	+	7.23182i	0.0658295	+	0.247468i
$855$		0			0
$856$	25.9309	+	6.81791i	0.886299	+	0.233031i
$857$		−	15.6155i		−	0.533416i	−0.963777	−	0.266708i	$-0.914064\pi$
$857$		−	15.6155i		−	0.533416i	0.963777	−	0.266708i	$-0.0859360\pi$
$858$		0			0
$859$	−41.3686			−1.41148			−0.705739	−	0.708472i	$-0.749385\pi$
$859$	−41.3686			−1.41148			−0.705739	+	0.708472i	$0.749385\pi$
$860$	9.74247	−	11.6847i	0.332215	−	0.398444i
$861$		0			0
$862$	−21.9309	−	46.8395i	−0.746968	−	1.59536i
$863$		−	41.7792i		−	1.42218i	−0.703101	−	0.711090i	$-0.748202\pi$
$863$		−	41.7792i		−	1.42218i	0.703101	−	0.711090i	$-0.251798\pi$
$864$		0			0
$865$	−0.246211			−0.00837143
$866$	−6.96556	−	14.8769i	−0.236699	−	0.505537i
$867$		0			0
$868$	−27.0436	+	22.6811i	−0.917920	+	0.769845i
$869$	−10.2462			−0.347579
$870$		0			0
$871$	−28.5539			−0.967512
$872$	−0.807764	+	3.07221i	−0.0273543	+	0.104038i
$873$		0			0
$874$	−8.24782	−	17.6155i	−0.278987	−	0.595854i
$875$	0.468213	−	2.60399i	0.0158285	−	0.0880310i
$876$		0			0
$877$	−48.7386			−1.64579			−0.822893	−	0.568196i	$-0.807642\pi$
$877$	−48.7386			−1.64579			−0.822893	+	0.568196i	$0.807642\pi$
$878$	−23.2306	+	10.8769i	−0.783996	+	0.367077i
$879$		0			0
$880$	−1.72521	−	9.43845i	−0.0581567	−	0.318170i
$881$			6.63068i			0.223393i	0.993742	+	0.111697i	$0.0356285\pi$
$881$			6.63068i			0.223393i	−0.993742	+	0.111697i	$0.964371\pi$
$882$		0			0
$883$		−	13.4558i		−	0.452824i	−0.974032	−	0.226412i	$-0.927300\pi$
$883$		−	13.4558i		−	0.452824i	0.974032	−	0.226412i	$-0.0726996\pi$
$884$	−18.2462	+	21.8836i	−0.613686	+	0.736027i
$885$		0			0
$886$	18.1771	+	38.8222i	0.610671	+	1.30426i
$887$	−17.7274			−0.595227			−0.297613	−	0.954686i	$-0.596191\pi$
$887$	−17.7274			−0.595227			−0.297613	+	0.954686i	$0.596191\pi$
$888$		0			0
$889$	−6.19224	+	34.4384i	−0.207681	+	1.15503i
$890$	15.3693	−	7.19612i	0.515181	−	0.241214i
$891$		0			0
$892$	16.5604	−	19.8617i	0.554483	−	0.665020i
$893$	24.0000			0.803129
$894$		0			0
$895$	−0.525853			−0.0175773
$896$	28.9712	+	7.52802i	0.967859	+	0.251493i
$897$		0			0
$898$	32.8078	−	15.3610i	1.09481	−	0.512604i
$899$	−13.3405			−0.444932
$900$		0			0
$901$			14.2462i			0.474610i
$902$	−21.8836	+	10.2462i	−0.728646	+	0.341162i
$903$		0			0
$904$	−10.4233	+	39.6434i	−0.346674	+	1.31852i
$905$	−6.87689			−0.228596
$906$		0			0
$907$			14.5075i			0.481714i	0.970561	+	0.240857i	$0.0774285\pi$
$907$			14.5075i			0.481714i	−0.970561	+	0.240857i	$0.922572\pi$
$908$	18.2856	−	21.9309i	0.606829	−	0.727801i
$909$		0			0
$910$	−7.23182	+	1.92375i	−0.239732	+	0.0637718i
$911$		−	10.9418i		−	0.362519i	−0.983435	−	0.181259i	$-0.941983\pi$
$911$		−	10.9418i		−	0.362519i	0.983435	−	0.181259i	$-0.0580174\pi$
$912$		0			0
$913$		−	2.24621i		−	0.0743387i
$914$	−7.68466	+	3.59806i	−0.254186	+	0.119013i
$915$		0			0
$916$	32.4473	+	27.0540i	1.07209	+	0.893889i
$917$	−36.1080	−	6.49242i	−1.19239	−	0.214399i
$918$		0			0
$919$			29.9009i			0.986340i	0.869933	+	0.493170i	$0.164162\pi$
$919$			29.9009i			0.986340i	−0.869933	+	0.493170i	$0.835838\pi$
$920$	−4.12391	+	15.6847i	−0.135961	+	0.517108i
$921$		0			0
$922$	22.5571	+	48.1771i	0.742880	+	1.58663i
$923$	−12.2888			−0.404492
$924$		0			0
$925$	−2.00000			−0.0657596
$926$	13.1922	+	28.1757i	0.433524	+	0.925911i
$927$		0			0
$928$	6.56155	+	9.21662i	0.215394	+	0.302550i
$929$		−	12.8769i		−	0.422477i	−0.977435	−	0.211239i	$-0.932250\pi$
$929$		−	12.8769i		−	0.422477i	0.977435	−	0.211239i	$-0.0677497\pi$
$930$		0			0
$931$	−15.7392	−	5.84912i	−0.515833	−	0.191697i
$932$	−31.0540	+	37.2447i	−1.01721	+	1.21999i
$933$		0			0
$934$	2.54635	−	1.19224i	0.0833192	−	0.0390112i
$935$		−	17.0862i		−	0.558780i
$936$		0			0
$937$		−	36.1080i		−	1.17960i	−0.807551	−	0.589798i	$-0.799207\pi$
$937$		−	36.1080i		−	1.17960i	0.807551	−	0.589798i	$-0.200793\pi$
$938$	13.7327	+	51.6242i	0.448387	+	1.68559i
$939$		0			0
$940$	−15.3693	−	12.8147i	−0.501292	−	0.417969i
$941$			51.3693i			1.67459i	0.546750	+	0.837296i	$0.315865\pi$
$941$			51.3693i			1.67459i	−0.546750	+	0.837296i	$0.684135\pi$
$942$		0			0
$943$	40.8427			1.33002
$944$	−7.86962	−	43.0540i	−0.256134	−	1.40129i
$945$		0			0
$946$	23.3693	−	10.9418i	0.759802	−	0.355749i
$947$			18.8438i			0.612341i	0.951977	+	0.306171i	$0.0990478\pi$
$947$			18.8438i			0.612341i	−0.951977	+	0.306171i	$0.900952\pi$
$948$		0			0
$949$	18.7386			0.608282
$950$	−3.07221	+	1.43845i	−0.0996755	+	0.0466694i
$951$		0			0
$952$	48.3399	+	22.4636i	1.56671	+	0.728051i
$953$	−11.7538			−0.380743			−0.190371	−	0.981712i	$-0.560969\pi$
$953$	−11.7538			−0.380743			−0.190371	+	0.981712i	$0.560969\pi$
$954$		0			0
$955$	−1.34700			−0.0435879
$956$	19.6847	+	16.4127i	0.636647	+	0.530826i
$957$		0			0
$958$		0			0
$959$	36.4559	+	6.55498i	1.17722	+	0.211671i
$960$		0			0
$961$	13.4924			0.435239
$962$	2.39871	+	5.12311i	0.0773374	+	0.165176i
$963$		0			0
$964$	−23.9871	−	20.0000i	−0.772571	−	0.644157i
$965$			10.4924i			0.337763i
$966$		0			0
$967$		−	55.1197i		−	1.77253i	−0.463179	−	0.886265i	$-0.653291\pi$
$967$		−	55.1197i		−	1.77253i	0.463179	−	0.886265i	$-0.346709\pi$
$968$	−3.77320	+	14.3508i	−0.121275	+	0.461251i
$969$		0			0
$970$	−9.12311	+	4.27156i	−0.292925	+	0.137151i
$971$	0.525853			0.0168754			0.00843771	−	0.999964i	$-0.497314\pi$
$971$	0.525853			0.0168754			0.00843771	+	0.999964i	$0.497314\pi$
$972$		0			0
$973$	−3.50758	−	0.630683i	−0.112448	−	0.0202188i
$974$	−11.4384	−	24.4300i	−0.366511	−	0.782788i
$975$		0			0
$976$	−7.86962	+	1.43845i	−0.251900	+	0.0460436i
$977$	10.4924			0.335682			0.167841	−	0.985814i	$-0.446320\pi$
$977$	10.4924			0.335682			0.167841	+	0.985814i	$0.446320\pi$
$978$		0			0
$979$	28.7845			0.919956
$980$	6.95611	+	12.1496i	0.222205	+	0.388104i
$981$		0			0
$982$	8.17708	+	17.4644i	0.260941	+	0.557313i
$983$	12.6994			0.405048			0.202524	−	0.979277i	$-0.435086\pi$
$983$	12.6994			0.405048			0.202524	+	0.979277i	$0.435086\pi$
$984$		0			0
$985$		−	18.0000i		−	0.573528i
$986$	8.54312	+	18.2462i	0.272068	+	0.581078i
$987$		0			0
$988$	7.36932	+	6.14441i	0.234449	+	0.195480i
$989$	−43.6155			−1.38689
$990$		0			0
$991$			34.4678i			1.09490i	0.836837	+	0.547452i	$0.184402\pi$
$991$			34.4678i			1.09490i	−0.836837	+	0.547452i	$0.815598\pi$
$992$	−21.8836	−	30.7386i	−0.694806	−	0.975953i
$993$		0			0
$994$	5.91016	+	22.2176i	0.187459	+	0.704700i
$995$			16.0345i			0.508329i
$996$		0			0
$997$			38.4924i			1.21907i	0.792760	+	0.609534i	$0.208643\pi$
$997$			38.4924i			1.21907i	−0.792760	+	0.609534i	$0.791357\pi$
$998$	16.3153	+	34.8460i	0.516453	+	1.10303i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.c.c.811.4		8
3.2	odd	2		140.2.g.c.111.5	✓	8
4.3	odd	2	inner	1260.2.c.c.811.2		8
7.6	odd	2	inner	1260.2.c.c.811.3		8
12.11	even	2		140.2.g.c.111.8	yes	8
15.2	even	4		700.2.c.i.699.6		8
15.8	even	4		700.2.c.j.699.3		8
15.14	odd	2		700.2.g.j.251.4		8
21.2	odd	6		980.2.o.e.31.2		16
21.5	even	6		980.2.o.e.31.1		16
21.11	odd	6		980.2.o.e.411.6		16
21.17	even	6		980.2.o.e.411.5		16
21.20	even	2		140.2.g.c.111.6	yes	8
24.5	odd	2		2240.2.k.e.1791.6		8
24.11	even	2		2240.2.k.e.1791.4		8
28.27	even	2	inner	1260.2.c.c.811.1		8
60.23	odd	4		700.2.c.j.699.5		8
60.47	odd	4		700.2.c.i.699.4		8
60.59	even	2		700.2.g.j.251.1		8
84.11	even	6		980.2.o.e.411.1		16
84.23	even	6		980.2.o.e.31.5		16
84.47	odd	6		980.2.o.e.31.6		16
84.59	odd	6		980.2.o.e.411.2		16
84.83	odd	2		140.2.g.c.111.7	yes	8
105.62	odd	4		700.2.c.j.699.6		8
105.83	odd	4		700.2.c.i.699.3		8
105.104	even	2		700.2.g.j.251.3		8
168.83	odd	2		2240.2.k.e.1791.5		8
168.125	even	2		2240.2.k.e.1791.3		8
420.83	even	4		700.2.c.i.699.5		8
420.167	even	4		700.2.c.j.699.4		8
420.419	odd	2		700.2.g.j.251.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.g.c.111.5	✓	8	3.2	odd	2
140.2.g.c.111.6	yes	8	21.20	even	2
140.2.g.c.111.7	yes	8	84.83	odd	2
140.2.g.c.111.8	yes	8	12.11	even	2
700.2.c.i.699.3		8	105.83	odd	4
700.2.c.i.699.4		8	60.47	odd	4
700.2.c.i.699.5		8	420.83	even	4
700.2.c.i.699.6		8	15.2	even	4
700.2.c.j.699.3		8	15.8	even	4
700.2.c.j.699.4		8	420.167	even	4
700.2.c.j.699.5		8	60.23	odd	4
700.2.c.j.699.6		8	105.62	odd	4
700.2.g.j.251.1		8	60.59	even	2
700.2.g.j.251.2		8	420.419	odd	2
700.2.g.j.251.3		8	105.104	even	2
700.2.g.j.251.4		8	15.14	odd	2
980.2.o.e.31.1		16	21.5	even	6
980.2.o.e.31.2		16	21.2	odd	6
980.2.o.e.31.5		16	84.23	even	6
980.2.o.e.31.6		16	84.47	odd	6
980.2.o.e.411.1		16	84.11	even	6
980.2.o.e.411.2		16	84.59	odd	6
980.2.o.e.411.5		16	21.17	even	6
980.2.o.e.411.6		16	21.11	odd	6
1260.2.c.c.811.1		8	28.27	even	2	inner
1260.2.c.c.811.2		8	4.3	odd	2	inner
1260.2.c.c.811.3		8	7.6	odd	2	inner
1260.2.c.c.811.4		8	1.1	even	1	trivial
2240.2.k.e.1791.3		8	168.125	even	2
2240.2.k.e.1791.4		8	24.11	even	2
2240.2.k.e.1791.5		8	168.83	odd	2
2240.2.k.e.1791.6		8	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28078 + 0.599676i) q^{2} +(1.28078 - 1.53610i) q^{4} +1.00000i q^{5} +(2.60399 + 0.468213i) q^{7} +(-0.719224 + 2.73546i) q^{8} +O(q^{10})\)	\(q+(-1.28078 + 0.599676i) q^{2} +(1.28078 - 1.53610i) q^{4} +1.00000i q^{5} +(2.60399 + 0.468213i) q^{7} +(-0.719224 + 2.73546i) q^{8} +(-0.599676 - 1.28078i) q^{10} -2.39871i q^{11} -2.00000i q^{13} +(-3.61591 + 0.961876i) q^{14} +(-0.719224 - 3.93481i) q^{16} -7.12311i q^{17} -2.39871 q^{19} +(1.53610 + 1.28078i) q^{20} +(1.43845 + 3.07221i) q^{22} -5.73384i q^{23} -1.00000 q^{25} +(1.19935 + 2.56155i) q^{26} +(4.05436 - 3.40032i) q^{28} +2.00000 q^{29} -6.67026 q^{31} +(3.28078 + 4.60831i) q^{32} +(4.27156 + 9.12311i) q^{34} +(-0.468213 + 2.60399i) q^{35} +2.00000 q^{37} +(3.07221 - 1.43845i) q^{38} +(-2.73546 - 0.719224i) q^{40} +7.12311i q^{41} -7.60669i q^{43} +(-3.68466 - 3.07221i) q^{44} +(3.43845 + 7.34376i) q^{46} -10.0054 q^{47} +(6.56155 + 2.43845i) q^{49} +(1.28078 - 0.599676i) q^{50} +(-3.07221 - 2.56155i) q^{52} -2.00000 q^{53} +2.39871 q^{55} +(-3.15363 + 6.78636i) q^{56} +(-2.56155 + 1.19935i) q^{58} +10.9418 q^{59} -2.00000i q^{61} +(8.54312 - 4.00000i) q^{62} +(-6.96543 - 3.93481i) q^{64} +2.00000 q^{65} -14.2770i q^{67} +(-10.9418 - 9.12311i) q^{68} +(-0.961876 - 3.61591i) q^{70} -6.14441i q^{71} +9.36932i q^{73} +(-2.56155 + 1.19935i) q^{74} +(-3.07221 + 3.68466i) q^{76} +(1.12311 - 6.24621i) q^{77} -4.27156i q^{79} +(3.93481 - 0.719224i) q^{80} +(-4.27156 - 9.12311i) q^{82} +0.936426 q^{83} +7.12311 q^{85} +(4.56155 + 9.74247i) q^{86} +(6.56155 + 1.72521i) q^{88} +12.0000i q^{89} +(0.936426 - 5.20798i) q^{91} +(-8.80776 - 7.34376i) q^{92} +(12.8147 - 6.00000i) q^{94} -2.39871i q^{95} -7.12311i q^{97} +(-9.86616 + 0.811703i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{4} - 14 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 + 2 * q^4 - 14 * q^8	\( 8 q - 2 q^{2} + 2 q^{4} - 14 q^{8} + 6 q^{14} - 14 q^{16} + 28 q^{22} - 8 q^{25} + 14 q^{28} + 16 q^{29} + 18 q^{32} + 16 q^{37} + 20 q^{44} + 44 q^{46} + 36 q^{49} + 2 q^{50} - 16 q^{53} - 2 q^{56} - 4 q^{58} + 2 q^{64} + 16 q^{65} + 4 q^{70} - 4 q^{74} - 24 q^{77} + 24 q^{85} + 20 q^{86} + 36 q^{88} + 12 q^{92} - 26 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^4 - 14 * q^8 + 6 * q^14 - 14 * q^16 + 28 * q^22 - 8 * q^25 + 14 * q^28 + 16 * q^29 + 18 * q^32 + 16 * q^37 + 20 * q^44 + 44 * q^46 + 36 * q^49 + 2 * q^50 - 16 * q^53 - 2 * q^56 - 4 * q^58 + 2 * q^64 + 16 * q^65 + 4 * q^70 - 4 * q^74 - 24 * q^77 + 24 * q^85 + 20 * q^86 + 36 * q^88 + 12 * q^92 - 26 * q^98

Introduction

L-functions

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Database

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