LMFDB - Embedded newform 560.2.cc.d.159.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(159,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 3, 5]))

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

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

chi := DirichletCharacter("560.159");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.cc (of order $6$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			159.2
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	560.159
Dual form			560.2.cc.d.479.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.18614 - 1.26217i) q^{3} +(0.686141 - 2.12819i) q^{5} +(2.00000 - 1.73205i) q^{7} +(1.68614 - 2.92048i) q^{9} +(-1.50000 + 0.866025i) q^{11} -1.37228 q^{13} +(-1.18614 - 5.51856i) q^{15} +(0.813859 + 1.40965i) q^{17} +(-2.87228 + 4.97494i) q^{19} +(2.18614 - 6.31084i) q^{21} +(-2.87228 + 4.97494i) q^{23} +(-4.05842 - 2.92048i) q^{25} -0.939764i q^{27} +8.74456 q^{29} +(-3.55842 - 6.16337i) q^{31} +(-2.18614 + 3.78651i) q^{33} +(-2.31386 - 5.44482i) q^{35} +(7.50000 + 4.33013i) q^{37} +(-3.00000 + 1.73205i) q^{39} +4.25639i q^{41} -4.00000 q^{43} +(-5.05842 - 5.59230i) q^{45} +(-1.24456 - 0.718549i) q^{47} +(1.00000 - 6.92820i) q^{49} +(3.55842 + 2.05446i) q^{51} +(11.6168 - 6.70699i) q^{53} +(0.813859 + 3.78651i) q^{55} +14.5012i q^{57} +(5.18614 + 8.98266i) q^{59} +(-9.55842 - 5.51856i) q^{61} +(-1.68614 - 8.76144i) q^{63} +(-0.941578 + 2.92048i) q^{65} +(4.55842 + 7.89542i) q^{67} +14.5012i q^{69} -10.3923i q^{71} +(-5.18614 - 8.98266i) q^{73} +(-12.5584 - 1.26217i) q^{75} +(-1.50000 + 4.33013i) q^{77} +(0.558422 + 0.322405i) q^{79} +(3.87228 + 6.70699i) q^{81} +1.87953i q^{83} +(3.55842 - 0.764836i) q^{85} +(19.1168 - 11.0371i) q^{87} +(-0.813859 - 0.469882i) q^{89} +(-2.74456 + 2.37686i) q^{91} +(-15.5584 - 8.98266i) q^{93} +(8.61684 + 9.52628i) q^{95} +6.00000 q^{97} +5.84096i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{3} - 3 q^{5} + 8 q^{7} + q^{9} - 6 q^{11} + 6 q^{13} + q^{15} + 9 q^{17} + 3 q^{21} + q^{25} + 12 q^{29} + 3 q^{31} - 3 q^{33} - 15 q^{35} + 30 q^{37} - 12 q^{39} - 16 q^{43} - 3 q^{45} + 18 q^{47}+ \cdots + 24 q^{97}+O(q^{100}) $ 4 * q + 3 * q^3 - 3 * q^5 + 8 * q^7 + q^9 - 6 * q^11 + 6 * q^13 + q^15 + 9 * q^17 + 3 * q^21 + q^25 + 12 * q^29 + 3 * q^31 - 3 * q^33 - 15 * q^35 + 30 * q^37 - 12 * q^39 - 16 * q^43 - 3 * q^45 + 18 * q^47 + 4 * q^49 - 3 * q^51 + 12 * q^53 + 9 * q^55 + 15 * q^59 - 21 * q^61 - q^63 - 21 * q^65 + q^67 - 15 * q^73 - 33 * q^75 - 6 * q^77 - 15 * q^79 + 4 * q^81 - 3 * q^85 + 42 * q^87 - 9 * q^89 + 12 * q^91 - 45 * q^93 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	2.18614	−	1.26217i	1.26217	−	0.728714i	0.288675	−	0.957427i	$-0.406785\pi$
$3$	2.18614	−	1.26217i	1.26217	−	0.728714i	0.973494	+	0.228714i	$0.0734519\pi$
$4$		0			0
$5$	0.686141	−	2.12819i	0.306851	−	0.951757i
$5$	0.686141	−	2.12819i	0.306851	−	0.951757i
$6$		0			0
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$8$		0			0
$9$	1.68614	−	2.92048i	0.562047	−	0.973494i
$10$		0			0
$11$	−1.50000	+	0.866025i	−0.452267	+	0.261116i	−0.708787	−	0.705422i	$-0.750757\pi$
$11$	−1.50000	+	0.866025i	−0.452267	+	0.261116i	0.256520	+	0.966539i	$0.417424\pi$
$12$		0			0
$13$	−1.37228			−0.380602			−0.190301	−	0.981726i	$-0.560946\pi$
$13$	−1.37228			−0.380602			−0.190301	+	0.981726i	$0.560946\pi$
$14$		0			0
$15$	−1.18614	−	5.51856i	−0.306260	−	1.42489i
$16$		0			0
$17$	0.813859	+	1.40965i	0.197390	+	0.341889i	0.947681	−	0.319218i	$-0.103420\pi$
$17$	0.813859	+	1.40965i	0.197390	+	0.341889i	−0.750291	+	0.661107i	$0.770087\pi$
$18$		0			0
$19$	−2.87228	+	4.97494i	−0.658947	+	1.14133i	0.321942	+	0.946759i	$0.395664\pi$
$19$	−2.87228	+	4.97494i	−0.658947	+	1.14133i	−0.980889	+	0.194570i	$0.937669\pi$
$20$		0			0
$21$	2.18614	−	6.31084i	0.477055	−	1.37714i
$22$		0			0
$23$	−2.87228	+	4.97494i	−0.598912	+	1.03735i	0.394070	+	0.919080i	$0.371067\pi$
$23$	−2.87228	+	4.97494i	−0.598912	+	1.03735i	−0.992982	+	0.118266i	$0.962267\pi$
$24$		0			0
$25$	−4.05842	−	2.92048i	−0.811684	−	0.584096i
$26$		0			0
$27$		−	0.939764i		−	0.180858i
$28$		0			0
$29$	8.74456			1.62382			0.811912	−	0.583779i	$-0.198427\pi$
$29$	8.74456			1.62382			0.811912	+	0.583779i	$0.198427\pi$
$30$		0			0
$31$	−3.55842	−	6.16337i	−0.639111	−	1.10697i	−0.985628	−	0.168930i	$-0.945969\pi$
$31$	−3.55842	−	6.16337i	−0.639111	−	1.10697i	0.346517	−	0.938044i	$-0.387364\pi$
$32$		0			0
$33$	−2.18614	+	3.78651i	−0.380558	+	0.659146i
$34$		0			0
$35$	−2.31386	−	5.44482i	−0.391114	−	0.920342i
$36$		0			0
$37$	7.50000	+	4.33013i	1.23299	+	0.711868i	0.967653	−	0.252286i	$-0.0811825\pi$
$37$	7.50000	+	4.33013i	1.23299	+	0.711868i	0.265340	+	0.964155i	$0.414516\pi$
$38$		0			0
$39$	−3.00000	+	1.73205i	−0.480384	+	0.277350i
$40$		0			0
$41$			4.25639i			0.664736i	0.943150	+	0.332368i	$0.107848\pi$
$41$			4.25639i			0.664736i	−0.943150	+	0.332368i	$0.892152\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$	−5.05842	−	5.59230i	−0.754065	−	0.833650i
$46$		0			0
$47$	−1.24456	−	0.718549i	−0.181538	−	0.104811i	0.406477	−	0.913661i	$-0.366757\pi$
$47$	−1.24456	−	0.718549i	−0.181538	−	0.104811i	−0.588015	+	0.808850i	$0.700090\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$	3.55842	+	2.05446i	0.498279	+	0.287681i
$52$		0			0
$53$	11.6168	−	6.70699i	1.59570	−	0.921276i	0.603393	−	0.797444i	$-0.293815\pi$
$53$	11.6168	−	6.70699i	1.59570	−	0.921276i	0.992303	−	0.123832i	$-0.0395183\pi$
$54$		0			0
$55$	0.813859	+	3.78651i	0.109741	+	0.510572i
$56$		0			0
$57$			14.5012i			1.92073i
$58$		0			0
$59$	5.18614	+	8.98266i	0.675178	+	1.16944i	0.976417	+	0.215894i	$0.0692665\pi$
$59$	5.18614	+	8.98266i	0.675178	+	1.16944i	−0.301239	+	0.953549i	$0.597400\pi$
$60$		0			0
$61$	−9.55842	−	5.51856i	−1.22383	−	0.706579i	−0.258098	−	0.966119i	$-0.583096\pi$
$61$	−9.55842	−	5.51856i	−1.22383	−	0.706579i	−0.965732	+	0.259540i	$0.916429\pi$
$62$		0			0
$63$	−1.68614	−	8.76144i	−0.212434	−	1.10384i
$64$		0			0
$65$	−0.941578	+	2.92048i	−0.116788	+	0.362241i
$66$		0			0
$67$	4.55842	+	7.89542i	0.556900	+	0.964579i	0.997753	+	0.0669996i	$0.0213426\pi$
$67$	4.55842	+	7.89542i	0.556900	+	0.964579i	−0.440853	+	0.897579i	$0.645324\pi$
$68$		0			0
$69$			14.5012i			1.74574i
$70$		0			0
$71$		−	10.3923i		−	1.23334i	−0.787222	−	0.616670i	$-0.788481\pi$
$71$		−	10.3923i		−	1.23334i	0.787222	−	0.616670i	$-0.211519\pi$
$72$		0			0
$73$	−5.18614	−	8.98266i	−0.606992	−	1.05134i	−0.991733	−	0.128316i	$-0.959043\pi$
$73$	−5.18614	−	8.98266i	−0.606992	−	1.05134i	0.384741	−	0.923024i	$-0.374291\pi$
$74$		0			0
$75$	−12.5584	−	1.26217i	−1.45012	−	0.145743i
$76$		0			0
$77$	−1.50000	+	4.33013i	−0.170941	+	0.493464i
$78$		0			0
$79$	0.558422	+	0.322405i	0.0628274	+	0.0362734i	0.531085	−	0.847319i	$-0.321785\pi$
$79$	0.558422	+	0.322405i	0.0628274	+	0.0362734i	−0.468257	+	0.883592i	$0.655118\pi$
$80$		0			0
$81$	3.87228	+	6.70699i	0.430253	+	0.745221i
$82$		0			0
$83$			1.87953i			0.206305i	0.994666	+	0.103152i	$0.0328930\pi$
$83$			1.87953i			0.206305i	−0.994666	+	0.103152i	$0.967107\pi$
$84$		0			0
$85$	3.55842	−	0.764836i	0.385965	−	0.0829581i
$86$		0			0
$87$	19.1168	−	11.0371i	2.04954	−	1.18330i
$88$		0			0
$89$	−0.813859	−	0.469882i	−0.0862689	−	0.0498074i	0.456245	−	0.889854i	$-0.349194\pi$
$89$	−0.813859	−	0.469882i	−0.0862689	−	0.0498074i	−0.542514	+	0.840047i	$0.682527\pi$
$90$		0			0
$91$	−2.74456	+	2.37686i	−0.287708	+	0.249163i
$92$		0			0
$93$	−15.5584	−	8.98266i	−1.61333	−	0.931458i
$94$		0			0
$95$	8.61684	+	9.52628i	0.884070	+	0.977376i
$96$		0			0
$97$	6.00000			0.609208			0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000			0.609208			0.304604	+	0.952479i	$0.401476\pi$
$98$		0			0
$99$			5.84096i			0.587039i
$100$		0			0
$101$	−4.93070	+	2.84674i	−0.490623	+	0.283262i	−0.724833	−	0.688925i	$-0.758083\pi$
$101$	−4.93070	+	2.84674i	−0.490623	+	0.283262i	0.234210	+	0.972186i	$0.424750\pi$
$102$		0			0
$103$	0.558422	+	0.322405i	0.0550230	+	0.0317675i	0.527259	−	0.849705i	$-0.323220\pi$
$103$	0.558422	+	0.322405i	0.0550230	+	0.0317675i	−0.472236	+	0.881472i	$0.656553\pi$
$104$		0			0
$105$	−11.9307	−	8.98266i	−1.16432	−	0.876618i
$106$		0			0
$107$	2.18614	−	3.78651i	0.211342	−	0.366055i	−0.740793	−	0.671734i	$-0.765550\pi$
$107$	2.18614	−	3.78651i	0.211342	−	0.366055i	0.952135	+	0.305678i	$0.0988832\pi$
$108$		0			0
$109$	−2.55842	−	4.43132i	−0.245052	−	0.424443i	0.717094	−	0.696977i	$-0.245472\pi$
$109$	−2.55842	−	4.43132i	−0.245052	−	0.424443i	−0.962146	+	0.272533i	$0.912138\pi$
$110$		0			0
$111$	21.8614			2.07499
$112$		0			0
$113$		−	6.92820i		−	0.651751i	−0.945413	−	0.325875i	$-0.894341\pi$
$113$		−	6.92820i		−	0.651751i	0.945413	−	0.325875i	$-0.105659\pi$
$114$		0			0
$115$	8.61684	+	9.52628i	0.803525	+	0.888330i
$116$		0			0
$117$	−2.31386	+	4.00772i	−0.213916	+	0.370514i
$118$		0			0
$119$	4.06930	+	1.40965i	0.373032	+	0.129222i
$120$		0			0
$121$	−4.00000	+	6.92820i	−0.363636	+	0.629837i
$122$		0			0
$123$	5.37228	+	9.30506i	0.484402	+	0.839009i
$124$		0			0
$125$	−9.00000	+	6.63325i	−0.804984	+	0.593296i
$126$		0			0
$127$	−2.11684			−0.187840			−0.0939198	−	0.995580i	$-0.529940\pi$
$127$	−2.11684			−0.187840			−0.0939198	+	0.995580i	$0.529940\pi$
$128$		0			0
$129$	−8.74456	+	5.04868i	−0.769916	+	0.444511i
$130$		0			0
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	−0.924084	−	0.382190i	$-0.875170\pi$
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	0.793028	+	0.609185i	$0.208503\pi$
$132$		0			0
$133$	2.87228	+	14.9248i	0.249058	+	1.29415i
$134$		0			0
$135$	−2.00000	−	0.644810i	−0.172133	−	0.0554964i
$136$		0			0
$137$	0.558422	−	0.322405i	0.0477092	−	0.0275449i	−0.475956	−	0.879469i	$-0.657898\pi$
$137$	0.558422	−	0.322405i	0.0477092	−	0.0275449i	0.523665	+	0.851924i	$0.324564\pi$
$138$		0			0
$139$	−12.0000			−1.01783			−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000			−1.01783			−0.508913	+	0.860818i	$0.669953\pi$
$140$		0			0
$141$	−3.62772			−0.305509
$142$		0			0
$143$	2.05842	−	1.18843i	0.172134	−	0.0993815i
$144$		0			0
$145$	6.00000	−	18.6101i	0.498273	−	1.54549i
$146$		0			0
$147$	−6.55842	−	16.4082i	−0.540930	−	1.35333i
$148$		0			0
$149$	−7.93070	+	13.7364i	−0.649709	+	1.12533i	0.333484	+	0.942756i	$0.391776\pi$
$149$	−7.93070	+	13.7364i	−0.649709	+	1.12533i	−0.983192	+	0.182572i	$0.941558\pi$
$150$		0			0
$151$	−18.5584	+	10.7147i	−1.51026	+	0.871951i	−0.510335	+	0.859976i	$0.670478\pi$
$151$	−18.5584	+	10.7147i	−1.51026	+	0.871951i	−0.999928	+	0.0119748i	$0.996188\pi$
$152$		0			0
$153$	5.48913			0.443769
$154$		0			0
$155$	−15.5584	+	3.34408i	−1.24968	+	0.268603i
$156$		0			0
$157$	4.50000	+	7.79423i	0.359139	+	0.622047i	0.987817	−	0.155618i	$-0.0497370\pi$
$157$	4.50000	+	7.79423i	0.359139	+	0.622047i	−0.628678	+	0.777666i	$0.716404\pi$
$158$		0			0
$159$	16.9307	−	29.3248i	1.34269	−	2.32561i
$160$		0			0
$161$	2.87228	+	14.9248i	0.226367	+	1.17624i
$162$		0			0
$163$	−10.5584	+	18.2877i	−0.826999	+	1.43241i	0.0733821	+	0.997304i	$0.476621\pi$
$163$	−10.5584	+	18.2877i	−0.826999	+	1.43241i	−0.900382	+	0.435101i	$0.856713\pi$
$164$		0			0
$165$	6.55842	+	7.25061i	0.510572	+	0.564459i
$166$		0			0
$167$			10.8896i			0.842666i	0.906906	+	0.421333i	$0.138438\pi$
$167$			10.8896i			0.842666i	−0.906906	+	0.421333i	$0.861562\pi$
$168$		0			0
$169$	−11.1168			−0.855142
$170$		0			0
$171$	9.68614	+	16.7769i	0.740718	+	1.28296i
$172$		0			0
$173$	−11.6168	+	20.1210i	−0.883212	+	1.52977i	−0.0354633	+	0.999371i	$0.511291\pi$
$173$	−11.6168	+	20.1210i	−0.883212	+	1.52977i	−0.847749	+	0.530398i	$0.822043\pi$
$174$		0			0
$175$	−13.1753	+	1.18843i	−0.995956	+	0.0898369i
$176$		0			0
$177$	22.6753	+	13.0916i	1.70438	+	0.984023i
$178$		0			0
$179$	18.7337	−	10.8159i	1.40022	−	0.808418i	0.405807	−	0.913959i	$-0.366991\pi$
$179$	18.7337	−	10.8159i	1.40022	−	0.808418i	0.994415	+	0.105541i	$0.0336573\pi$
$180$		0			0
$181$		−	18.6101i		−	1.38328i	−0.722242	−	0.691640i	$-0.756889\pi$
$181$		−	18.6101i		−	1.38328i	0.722242	−	0.691640i	$-0.243111\pi$
$182$		0			0
$183$	−27.8614			−2.05957
$184$		0			0
$185$	14.3614	−	12.9904i	1.05587	−	0.955072i
$186$		0			0
$187$	−2.44158	−	1.40965i	−0.178546	−	0.103084i
$188$		0			0
$189$	−1.62772	−	1.87953i	−0.118399	−	0.136716i
$190$		0			0
$191$	−3.55842	−	2.05446i	−0.257478	−	0.148655i	0.365705	−	0.930731i	$-0.380828\pi$
$191$	−3.55842	−	2.05446i	−0.257478	−	0.148655i	−0.623184	+	0.782075i	$0.714161\pi$
$192$		0			0
$193$	12.5584	−	7.25061i	0.903975	−	0.521910i	0.0254873	−	0.999675i	$-0.491886\pi$
$193$	12.5584	−	7.25061i	0.903975	−	0.521910i	0.878488	+	0.477765i	$0.158553\pi$
$194$		0			0
$195$	1.62772	+	7.57301i	0.116563	+	0.542315i
$196$		0			0
$197$			19.6974i			1.40338i	0.712483	+	0.701690i	$0.247571\pi$
$197$			19.6974i			1.40338i	−0.712483	+	0.701690i	$0.752429\pi$
$198$		0			0
$199$	−10.9307	−	18.9325i	−0.774857	−	1.34209i	−0.934875	−	0.354978i	$-0.884488\pi$
$199$	−10.9307	−	18.9325i	−0.774857	−	1.34209i	0.160018	−	0.987114i	$-0.448845\pi$
$200$		0			0
$201$	19.9307	+	11.5070i	1.40580	+	0.811641i
$202$		0			0
$203$	17.4891	−	15.1460i	1.22750	−	1.06304i
$204$		0			0
$205$	9.05842	+	2.92048i	0.632668	+	0.203975i
$206$		0			0
$207$	9.68614	+	16.7769i	0.673233	+	1.16607i
$208$		0			0
$209$		−	9.94987i		−	0.688247i
$210$		0			0
$211$			2.37686i			0.163630i	0.996648	+	0.0818149i	$0.0260716\pi$
$211$			2.37686i			0.163630i	−0.996648	+	0.0818149i	$0.973928\pi$
$212$		0			0
$213$	−13.1168	−	22.7190i	−0.898751	−	1.55668i
$214$		0			0
$215$	−2.74456	+	8.51278i	−0.187178	+	0.580567i
$216$		0			0
$217$	−17.7921	−	6.16337i	−1.20781	−	0.418397i
$218$		0			0
$219$	−22.6753	−	13.0916i	−1.53225	−	0.884646i
$220$		0			0
$221$	−1.11684	−	1.93443i	−0.0751271	−	0.130124i
$222$		0			0
$223$		−	10.3923i		−	0.695920i	−0.937509	−	0.347960i	$-0.886874\pi$
$223$		−	10.3923i		−	0.695920i	0.937509	−	0.347960i	$-0.113126\pi$
$224$		0			0
$225$	−15.3723	+	6.92820i	−1.02482	+	0.461880i
$226$		0			0
$227$	8.18614	−	4.72627i	0.543333	−	0.313694i	−0.203096	−	0.979159i	$-0.565100\pi$
$227$	8.18614	−	4.72627i	0.543333	−	0.313694i	0.746429	+	0.665465i	$0.231767\pi$
$228$		0			0
$229$	−15.5584	−	8.98266i	−1.02813	−	0.593591i	−0.111681	−	0.993744i	$-0.535624\pi$
$229$	−15.5584	−	8.98266i	−1.02813	−	0.593591i	−0.916448	+	0.400153i	$0.868957\pi$
$230$		0			0
$231$	2.18614	+	11.3595i	0.143837	+	0.747402i
$232$		0			0
$233$	−7.67527	−	4.43132i	−0.502823	−	0.290305i	0.227055	−	0.973882i	$-0.427090\pi$
$233$	−7.67527	−	4.43132i	−0.502823	−	0.290305i	−0.729879	+	0.683577i	$0.760423\pi$
$234$		0			0
$235$	−2.38316	+	2.15565i	−0.155460	+	0.140619i
$236$		0			0
$237$	1.62772			0.105732
$238$		0			0
$239$			10.3923i			0.672222i	0.941822	+	0.336111i	$0.109112\pi$
$239$			10.3923i			0.672222i	−0.941822	+	0.336111i	$0.890888\pi$
$240$		0			0
$241$	13.5000	−	7.79423i	0.869611	−	0.502070i	0.00239235	−	0.999997i	$-0.499238\pi$
$241$	13.5000	−	7.79423i	0.869611	−	0.502070i	0.867219	+	0.497927i	$0.165905\pi$
$242$		0			0
$243$	19.3723	+	11.1846i	1.24273	+	0.717492i
$244$		0			0
$245$	−14.0584	−	6.88192i	−0.898160	−	0.439670i
$246$		0			0
$247$	3.94158	−	6.82701i	0.250797	−	0.434392i
$248$		0			0
$249$	2.37228	+	4.10891i	0.150337	+	0.260392i
$250$		0			0
$251$	−24.8614			−1.56924			−0.784619	−	0.619978i	$-0.787141\pi$
$251$	−24.8614			−1.56924			−0.784619	+	0.619978i	$0.787141\pi$
$252$		0			0
$253$		−	9.94987i		−	0.625543i
$254$		0			0
$255$	6.81386	−	6.16337i	0.426700	−	0.385965i
$256$		0			0
$257$	3.55842	−	6.16337i	0.221968	−	0.384460i	−0.733437	−	0.679757i	$-0.762085\pi$
$257$	3.55842	−	6.16337i	0.221968	−	0.384460i	0.955406	+	0.295297i	$0.0954185\pi$
$258$		0			0
$259$	22.5000	−	4.33013i	1.39808	−	0.269061i
$260$		0			0
$261$	14.7446	−	25.5383i	0.912666	−	1.58078i
$262$		0			0
$263$	−6.81386	−	11.8020i	−0.420161	−	0.727739i	0.575794	−	0.817595i	$-0.304693\pi$
$263$	−6.81386	−	11.8020i	−0.420161	−	0.727739i	−0.995955	+	0.0898552i	$0.971360\pi$
$264$		0			0
$265$	−6.30298	−	29.3248i	−0.387189	−	1.80141i
$266$		0			0
$267$	−2.37228			−0.145181
$268$		0			0
$269$	21.3030	−	12.2993i	1.29887	−	0.749901i	0.318658	−	0.947870i	$-0.396768\pi$
$269$	21.3030	−	12.2993i	1.29887	−	0.749901i	0.980208	+	0.197969i	$0.0634346\pi$
$270$		0			0
$271$	2.18614	−	3.78651i	0.132799	−	0.230014i	−0.791956	−	0.610578i	$-0.790937\pi$
$271$	2.18614	−	3.78651i	0.132799	−	0.230014i	0.924754	+	0.380565i	$0.124270\pi$
$272$		0			0
$273$	−3.00000	+	8.66025i	−0.181568	+	0.524142i
$274$		0			0
$275$	8.61684	+	0.866025i	0.519615	+	0.0522233i
$276$		0			0
$277$	8.44158	−	4.87375i	0.507205	−	0.292835i	−0.224479	−	0.974479i	$-0.572068\pi$
$277$	8.44158	−	4.87375i	0.507205	−	0.292835i	0.731684	+	0.681644i	$0.238735\pi$
$278$		0			0
$279$	−24.0000			−1.43684
$280$		0			0
$281$	−7.88316			−0.470270			−0.235135	−	0.971963i	$-0.575553\pi$
$281$	−7.88316			−0.470270			−0.235135	+	0.971963i	$0.575553\pi$
$282$		0			0
$283$	15.5584	−	8.98266i	0.924852	−	0.533964i	0.0396724	−	0.999213i	$-0.487369\pi$
$283$	15.5584	−	8.98266i	0.924852	−	0.533964i	0.885180	+	0.465249i	$0.154035\pi$
$284$		0			0
$285$	30.8614	+	9.94987i	1.82807	+	0.589380i
$286$		0			0
$287$	7.37228	+	8.51278i	0.435172	+	0.502493i
$288$		0			0
$289$	7.17527	−	12.4279i	0.422074	−	0.731054i
$290$		0			0
$291$	13.1168	−	7.57301i	0.768923	−	0.443938i
$292$		0			0
$293$	30.8614			1.80294			0.901471	−	0.432839i	$-0.142488\pi$
$293$	30.8614			1.80294			0.901471	+	0.432839i	$0.142488\pi$
$294$		0			0
$295$	22.6753	−	4.87375i	1.32021	−	0.283761i
$296$		0			0
$297$	0.813859	+	1.40965i	0.0472249	+	0.0817959i
$298$		0			0
$299$	3.94158	−	6.82701i	0.227947	−	0.394816i
$300$		0			0
$301$	−8.00000	+	6.92820i	−0.461112	+	0.399335i
$302$		0			0
$303$	−7.18614	+	12.4468i	−0.412833	+	0.715048i
$304$		0			0
$305$	−18.3030	+	16.5557i	−1.04803	+	0.947975i
$306$		0			0
$307$		−	26.8280i		−	1.53115i	−0.643345	−	0.765576i	$-0.722454\pi$
$307$		−	26.8280i		−	1.53115i	0.643345	−	0.765576i	$-0.277546\pi$
$308$		0			0
$309$	1.62772			0.0925977
$310$		0			0
$311$	−2.18614	−	3.78651i	−0.123965	−	0.214713i	0.797363	−	0.603500i	$-0.206228\pi$
$311$	−2.18614	−	3.78651i	−0.123965	−	0.214713i	−0.921328	+	0.388787i	$0.872894\pi$
$312$		0			0
$313$	−7.93070	+	13.7364i	−0.448270	+	0.776426i	−0.998274	−	0.0587361i	$-0.981293\pi$
$313$	−7.93070	+	13.7364i	−0.448270	+	0.776426i	0.550004	+	0.835162i	$0.314626\pi$
$314$		0			0
$315$	−19.8030	−	2.42315i	−1.11577	−	0.136529i
$316$		0			0
$317$	−9.55842	−	5.51856i	−0.536854	−	0.309953i	0.206949	−	0.978352i	$-0.433647\pi$
$317$	−9.55842	−	5.51856i	−0.536854	−	0.309953i	−0.743803	+	0.668399i	$0.766980\pi$
$318$		0			0
$319$	−13.1168	+	7.57301i	−0.734402	+	0.424007i
$320$		0			0
$321$		−	11.0371i		−	0.616032i
$322$		0			0
$323$	−9.35053			−0.520278
$324$		0			0
$325$	5.56930	+	4.00772i	0.308929	+	0.222308i
$326$		0			0
$327$	−11.1861	−	6.45832i	−0.618595	−	0.357146i
$328$		0			0
$329$	−3.73369	+	0.718549i	−0.205845	+	0.0396149i
$330$		0			0
$331$	−10.5000	−	6.06218i	−0.577132	−	0.333207i	0.182861	−	0.983139i	$-0.441464\pi$
$331$	−10.5000	−	6.06218i	−0.577132	−	0.333207i	−0.759993	+	0.649931i	$0.774798\pi$
$332$		0			0
$333$	25.2921	−	14.6024i	1.38600	−	0.800207i
$334$		0			0
$335$	19.9307	−	4.28384i	1.08893	−	0.234051i
$336$		0			0
$337$		−	6.92820i		−	0.377403i	−0.982034	−	0.188702i	$-0.939572\pi$
$337$		−	6.92820i		−	0.377403i	0.982034	−	0.188702i	$-0.0604279\pi$
$338$		0			0
$339$	−8.74456	−	15.1460i	−0.474939	−	0.822619i
$340$		0			0
$341$	10.6753	+	6.16337i	0.578098	+	0.333765i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$	30.8614	+	9.94987i	1.66152	+	0.535683i
$346$		0			0
$347$	7.93070	+	13.7364i	0.425742	+	0.737408i	0.996489	−	0.0837184i	$-0.0266796\pi$
$347$	7.93070	+	13.7364i	0.425742	+	0.737408i	−0.570747	+	0.821126i	$0.693346\pi$
$348$		0			0
$349$		−	11.6819i		−	0.625319i	−0.949865	−	0.312660i	$-0.898780\pi$
$349$		−	11.6819i		−	0.625319i	0.949865	−	0.312660i	$-0.101220\pi$
$350$		0			0
$351$			1.28962i			0.0688348i
$352$		0			0
$353$	8.18614	+	14.1788i	0.435704	+	0.754662i	0.997353	−	0.0727139i	$-0.0231660\pi$
$353$	8.18614	+	14.1788i	0.435704	+	0.754662i	−0.561649	+	0.827376i	$0.689833\pi$
$354$		0			0
$355$	−22.1168	−	7.13058i	−1.17384	−	0.378452i
$356$		0			0
$357$	10.6753	−	2.05446i	0.564995	−	0.108733i
$358$		0			0
$359$	16.6753	+	9.62747i	0.880087	+	0.508118i	0.870687	−	0.491837i	$-0.163675\pi$
$359$	16.6753	+	9.62747i	0.880087	+	0.508118i	0.00939982	+	0.999956i	$0.497008\pi$
$360$		0			0
$361$	−7.00000	−	12.1244i	−0.368421	−	0.638124i
$362$		0			0
$363$			20.1947i			1.05995i
$364$		0			0
$365$	−22.6753	+	4.87375i	−1.18688	+	0.255104i
$366$		0			0
$367$	2.61684	−	1.51084i	0.136598	−	0.0788650i	−0.430144	−	0.902760i	$-0.641537\pi$
$367$	2.61684	−	1.51084i	0.136598	−	0.0788650i	0.566742	+	0.823896i	$0.308204\pi$
$368$		0			0
$369$	12.4307	+	7.17687i	0.647117	+	0.373613i
$370$		0			0
$371$	11.6168	−	33.5349i	0.603116	−	1.74105i
$372$		0			0
$373$	−29.7921	−	17.2005i	−1.54258	−	0.890607i	−0.998675	−	0.0514584i	$-0.983613\pi$
$373$	−29.7921	−	17.2005i	−1.54258	−	0.890607i	−0.543902	−	0.839149i	$-0.683054\pi$
$374$		0			0
$375$	−11.3030	+	25.8607i	−0.583684	+	1.33544i
$376$		0			0
$377$	−12.0000			−0.618031
$378$		0			0
$379$			25.3360i			1.30142i	0.759326	+	0.650710i	$0.225529\pi$
$379$			25.3360i			1.30142i	−0.759326	+	0.650710i	$0.774471\pi$
$380$		0			0
$381$	−4.62772	+	2.67181i	−0.237085	+	0.136881i
$382$		0			0
$383$	−7.75544	−	4.47760i	−0.396284	−	0.228795i	0.288595	−	0.957451i	$-0.406812\pi$
$383$	−7.75544	−	4.47760i	−0.396284	−	0.228795i	−0.684879	+	0.728656i	$0.740145\pi$
$384$		0			0
$385$	8.18614	+	6.16337i	0.417204	+	0.314114i
$386$		0			0
$387$	−6.74456	+	11.6819i	−0.342845	+	0.593826i
$388$		0			0
$389$	3.55842	+	6.16337i	0.180419	+	0.312495i	0.942023	−	0.335547i	$-0.108921\pi$
$389$	3.55842	+	6.16337i	0.180419	+	0.312495i	−0.761604	+	0.648042i	$0.775588\pi$
$390$		0			0
$391$	−9.35053			−0.472877
$392$		0			0
$393$			7.57301i			0.382008i
$394$		0			0
$395$	1.06930	−	0.967215i	0.0538022	−	0.0486659i
$396$		0			0
$397$	−0.558422	+	0.967215i	−0.0280264	+	0.0485431i	−0.879698	−	0.475532i	$-0.842256\pi$
$397$	−0.558422	+	0.967215i	−0.0280264	+	0.0485431i	0.851672	+	0.524075i	$0.175589\pi$
$398$		0			0
$399$	25.1168	+	29.0024i	1.25741	+	1.45194i
$400$		0			0
$401$	−8.87228	+	15.3672i	−0.443061	+	0.767403i	−0.997915	−	0.0645441i	$-0.979441\pi$
$401$	−8.87228	+	15.3672i	−0.443061	+	0.767403i	0.554854	+	0.831948i	$0.312774\pi$
$402$		0			0
$403$	4.88316	+	8.45787i	0.243247	+	0.421317i
$404$		0			0
$405$	16.9307	−	3.63903i	0.841293	−	0.180825i
$406$		0			0
$407$	−15.0000			−0.743522
$408$		0			0
$409$	−9.55842	+	5.51856i	−0.472634	+	0.272875i	−0.717342	−	0.696722i	$-0.754641\pi$
$409$	−9.55842	+	5.51856i	−0.472634	+	0.272875i	0.244708	+	0.969597i	$0.421308\pi$
$410$		0			0
$411$	0.813859	−	1.40965i	0.0401447	−	0.0695327i
$412$		0			0
$413$	25.9307	+	8.98266i	1.27597	+	0.442008i
$414$		0			0
$415$	4.00000	+	1.28962i	0.196352	+	0.0633050i
$416$		0			0
$417$	−26.2337	+	15.1460i	−1.28467	+	0.741704i
$418$		0			0
$419$	−31.3723			−1.53264			−0.766318	−	0.642461i	$-0.777913\pi$
$419$	−31.3723			−1.53264			−0.766318	+	0.642461i	$0.777913\pi$
$420$		0			0
$421$	−18.2337			−0.888656			−0.444328	−	0.895864i	$-0.646557\pi$
$421$	−18.2337			−0.888656			−0.444328	+	0.895864i	$0.646557\pi$
$422$		0			0
$423$	−4.19702	+	2.42315i	−0.204066	+	0.117817i
$424$		0			0
$425$	0.813859	−	8.09780i	0.0394780	−	0.392801i
$426$		0			0
$427$	−28.6753	+	5.51856i	−1.38769	+	0.267062i
$428$		0			0
$429$	3.00000	−	5.19615i	0.144841	−	0.250873i
$430$		0			0
$431$	13.6753	−	7.89542i	0.658714	−	0.380309i	−0.133073	−	0.991106i	$-0.542484\pi$
$431$	13.6753	−	7.89542i	0.658714	−	0.380309i	0.791787	+	0.610797i	$0.209151\pi$
$432$		0			0
$433$	−23.4891			−1.12882			−0.564408	−	0.825496i	$-0.690895\pi$
$433$	−23.4891			−1.12882			−0.564408	+	0.825496i	$0.690895\pi$
$434$		0			0
$435$	−10.3723	−	48.2574i	−0.497313	−	2.31376i
$436$		0			0
$437$	−16.5000	−	28.5788i	−0.789302	−	1.36711i
$438$		0			0
$439$	−9.30298	+	16.1132i	−0.444007	+	0.769043i	−0.997982	−	0.0634901i	$-0.979777\pi$
$439$	−9.30298	+	16.1132i	−0.444007	+	0.769043i	0.553975	+	0.832533i	$0.313110\pi$
$440$		0			0
$441$	−18.5475	−	14.6024i	−0.883217	−	0.695353i
$442$		0			0
$443$	6.81386	−	11.8020i	0.323736	−	0.560728i	−0.657520	−	0.753437i	$-0.728394\pi$
$443$	6.81386	−	11.8020i	0.323736	−	0.560728i	0.981256	+	0.192710i	$0.0617276\pi$
$444$		0			0
$445$	−1.55842	+	1.40965i	−0.0738763	+	0.0668236i
$446$		0			0
$447$			40.0395i			1.89381i
$448$		0			0
$449$	30.8614			1.45644			0.728220	−	0.685344i	$-0.240348\pi$
$449$	30.8614			1.45644			0.728220	+	0.685344i	$0.240348\pi$
$450$		0			0
$451$	−3.68614	−	6.38458i	−0.173574	−	0.300638i
$452$		0			0
$453$	−27.0475	+	46.8477i	−1.27080	+	2.20110i
$454$		0			0
$455$	3.17527	+	7.47182i	0.148859	+	0.350284i
$456$		0			0
$457$	14.7921	+	8.54023i	0.691946	+	0.399495i	0.804341	−	0.594169i	$-0.202519\pi$
$457$	14.7921	+	8.54023i	0.691946	+	0.399495i	−0.112395	+	0.993664i	$0.535852\pi$
$458$		0			0
$459$	1.32473	−	0.764836i	0.0618333	−	0.0356995i
$460$		0			0
$461$			18.0202i			0.839285i	0.907689	+	0.419643i	$0.137845\pi$
$461$			18.0202i			0.839285i	−0.907689	+	0.419643i	$0.862155\pi$
$462$		0			0
$463$	14.3505			0.666926			0.333463	−	0.942763i	$-0.391783\pi$
$463$	14.3505			0.666926			0.333463	+	0.942763i	$0.391783\pi$
$464$		0			0
$465$	−29.7921	+	26.9480i	−1.38158	+	1.24968i
$466$		0			0
$467$	−16.4198	−	9.47999i	−0.759819	−	0.438682i	0.0694117	−	0.997588i	$-0.477888\pi$
$467$	−16.4198	−	9.47999i	−0.759819	−	0.438682i	−0.829231	+	0.558906i	$0.811221\pi$
$468$		0			0
$469$	22.7921	+	7.89542i	1.05244	+	0.364577i
$470$		0			0
$471$	19.6753	+	11.3595i	0.906588	+	0.523419i
$472$		0			0
$473$	6.00000	−	3.46410i	0.275880	−	0.159280i
$474$		0			0
$475$	26.1861	−	11.8020i	1.20150	−	0.541511i
$476$		0			0
$477$		−	45.2357i		−	2.07120i
$478$		0			0
$479$	3.30298	+	5.72094i	0.150917	+	0.261396i	0.931565	−	0.363575i	$-0.118444\pi$
$479$	3.30298	+	5.72094i	0.150917	+	0.261396i	−0.780648	+	0.624971i	$0.785111\pi$
$480$		0			0
$481$	−10.2921	−	5.94215i	−0.469280	−	0.270939i
$482$		0			0
$483$	25.1168	+	29.0024i	1.14286	+	1.31966i
$484$		0			0
$485$	4.11684	−	12.7692i	0.186936	−	0.579818i
$486$		0			0
$487$	−13.5584	−	23.4839i	−0.614391	−	1.06416i	−0.990491	−	0.137577i	$-0.956069\pi$
$487$	−13.5584	−	23.4839i	−0.614391	−	1.06416i	0.376100	−	0.926579i	$-0.377265\pi$
$488$		0			0
$489$			53.3060i			2.41058i
$490$		0			0
$491$		−	10.3923i		−	0.468998i	−0.972116	−	0.234499i	$-0.924655\pi$
$491$		−	10.3923i		−	0.468998i	0.972116	−	0.234499i	$-0.0753450\pi$
$492$		0			0
$493$	7.11684	+	12.3267i	0.320527	+	0.555168i
$494$		0			0
$495$	12.4307	+	4.00772i	0.558719	+	0.180134i
$496$		0			0
$497$	−18.0000	−	20.7846i	−0.807410	−	0.932317i
$498$		0			0
$499$	26.7921	+	15.4684i	1.19938	+	0.692462i	0.960417	−	0.278567i	$-0.0898593\pi$
$499$	26.7921	+	15.4684i	1.19938	+	0.692462i	0.238963	+	0.971029i	$0.423193\pi$
$500$		0			0
$501$	13.7446	+	23.8063i	0.614062	+	1.06359i
$502$		0			0
$503$		−	27.4179i		−	1.22250i	−0.791437	−	0.611251i	$-0.790667\pi$
$503$		−	27.4179i		−	1.22250i	0.791437	−	0.611251i	$-0.209333\pi$
$504$		0			0
$505$	2.67527	+	12.4468i	0.119048	+	0.553874i
$506$		0			0
$507$	−24.3030	+	14.0313i	−1.07933	+	0.623153i
$508$		0			0
$509$	−22.0693	−	12.7417i	−0.978204	−	0.564767i	−0.0764768	−	0.997071i	$-0.524367\pi$
$509$	−22.0693	−	12.7417i	−0.978204	−	0.564767i	−0.901728	+	0.432305i	$0.857700\pi$
$510$		0			0
$511$	−25.9307	−	8.98266i	−1.14711	−	0.397369i
$512$		0			0
$513$	4.67527	+	2.69927i	0.206418	+	0.119176i
$514$		0			0
$515$	1.06930	−	0.967215i	0.0471188	−	0.0426206i
$516$		0			0
$517$	2.48913			0.109472
$518$		0			0
$519$			58.6497i			2.57444i
$520$		0			0
$521$	14.3614	−	8.29156i	0.629185	−	0.363260i	−0.151252	−	0.988495i	$-0.548330\pi$
$521$	14.3614	−	8.29156i	0.629185	−	0.363260i	0.780436	+	0.625235i	$0.214997\pi$
$522$		0			0
$523$	24.5584	+	14.1788i	1.07386	+	0.619996i	0.929235	−	0.369490i	$-0.120467\pi$
$523$	24.5584	+	14.1788i	1.07386	+	0.619996i	0.144630	+	0.989486i	$0.453801\pi$
$524$		0			0
$525$	−27.3030	+	19.2275i	−1.19160	+	0.839156i
$526$		0			0
$527$	5.79211	−	10.0322i	0.252308	−	0.437011i
$528$		0			0
$529$	−5.00000	−	8.66025i	−0.217391	−	0.376533i
$530$		0			0
$531$	34.9783			1.51793
$532$		0			0
$533$		−	5.84096i		−	0.253000i
$534$		0			0
$535$	−6.55842	−	7.25061i	−0.283545	−	0.313471i
$536$		0			0
$537$	27.3030	−	47.2902i	1.17821	−	2.04072i
$538$		0			0
$539$	4.50000	+	11.2583i	0.193829	+	0.484931i
$540$		0			0
$541$	−14.6753	+	25.4183i	−0.630939	+	1.09282i	0.356421	+	0.934325i	$0.383997\pi$
$541$	−14.6753	+	25.4183i	−0.630939	+	1.09282i	−0.987360	+	0.158493i	$0.949336\pi$
$542$		0			0
$543$	−23.4891	−	40.6844i	−1.00801	−	1.74593i
$544$		0			0
$545$	−11.1861	+	2.40431i	−0.479162	+	0.102989i
$546$		0			0
$547$	32.4674			1.38820			0.694102	−	0.719876i	$-0.255801\pi$
$547$	32.4674			1.38820			0.694102	+	0.719876i	$0.255801\pi$
$548$		0			0
$549$	−32.2337	+	18.6101i	−1.37570	+	0.794261i
$550$		0			0
$551$	−25.1168	+	43.5036i	−1.07001	+	1.85332i
$552$		0			0
$553$	1.67527	−	0.322405i	0.0712396	−	0.0137101i
$554$		0			0
$555$	15.0000	−	46.5253i	0.636715	−	1.97489i
$556$		0			0
$557$	3.73369	−	2.15565i	0.158201	−	0.0913376i	−0.418809	−	0.908074i	$-0.637552\pi$
$557$	3.73369	−	2.15565i	0.158201	−	0.0913376i	0.577011	+	0.816737i	$0.304219\pi$
$558$		0			0
$559$	5.48913			0.232165
$560$		0			0
$561$	−7.11684			−0.300473
$562$		0			0
$563$	−3.30298	+	1.90698i	−0.139204	+	0.0803696i	−0.567985	−	0.823039i	$-0.692277\pi$
$563$	−3.30298	+	1.90698i	−0.139204	+	0.0803696i	0.428780	+	0.903409i	$0.358943\pi$
$564$		0			0
$565$	−14.7446	−	4.75372i	−0.620308	−	0.199991i
$566$		0			0
$567$	19.3614	+	6.70699i	0.813103	+	0.281667i
$568$		0			0
$569$	−17.6168	+	30.5133i	−0.738537	+	1.27918i	0.214618	+	0.976698i	$0.431149\pi$
$569$	−17.6168	+	30.5133i	−0.738537	+	1.27918i	−0.953154	+	0.302485i	$0.902184\pi$
$570$		0			0
$571$	13.6753	−	7.89542i	0.572292	−	0.330413i	−0.185772	−	0.982593i	$-0.559479\pi$
$571$	13.6753	−	7.89542i	0.572292	−	0.330413i	0.758064	+	0.652180i	$0.226145\pi$
$572$		0			0
$573$	−10.3723			−0.433308
$574$		0			0
$575$	26.1861	−	11.8020i	1.09204	−	0.492175i
$576$		0			0
$577$	−9.81386	−	16.9981i	−0.408556	−	0.707640i	0.586172	−	0.810187i	$-0.300634\pi$
$577$	−9.81386	−	16.9981i	−0.408556	−	0.707640i	−0.994728	+	0.102546i	$0.967301\pi$
$578$		0			0
$579$	18.3030	−	31.7017i	0.760646	−	1.31748i
$580$		0			0
$581$	3.25544	+	3.75906i	0.135058	+	0.155952i
$582$		0			0
$583$	−11.6168	+	20.1210i	−0.481121	+	0.833325i
$584$		0			0
$585$	6.94158	+	7.67420i	0.286999	+	0.317289i
$586$		0			0
$587$		−	6.63325i		−	0.273784i	−0.990586	−	0.136892i	$-0.956289\pi$
$587$		−	6.63325i		−	0.273784i	0.990586	−	0.136892i	$-0.0437113\pi$
$588$		0			0
$589$	40.8832			1.68456
$590$		0			0
$591$	24.8614	+	43.0612i	1.02266	+	1.77130i
$592$		0			0
$593$	21.0475	−	36.4554i	0.864319	−	1.49704i	−0.00340244	−	0.999994i	$-0.501083\pi$
$593$	21.0475	−	36.4554i	0.864319	−	1.49704i	0.867722	−	0.497051i	$-0.165584\pi$
$594$		0			0
$595$	5.79211	−	7.69304i	0.237453	−	0.315384i
$596$		0			0
$597$	−47.7921	−	27.5928i	−1.95600	−	1.12930i
$598$		0			0
$599$	1.32473	−	0.764836i	0.0541272	−	0.0312503i	−0.472692	−	0.881228i	$-0.656718\pi$
$599$	1.32473	−	0.764836i	0.0541272	−	0.0312503i	0.526819	+	0.849977i	$0.323384\pi$
$600$		0			0
$601$			30.2921i			1.23564i	0.786320	+	0.617819i	$0.211984\pi$
$601$			30.2921i			1.23564i	−0.786320	+	0.617819i	$0.788016\pi$
$602$		0			0
$603$	30.7446			1.25202
$604$		0			0
$605$	12.0000	+	13.2665i	0.487869	+	0.539360i
$606$		0			0
$607$	23.6168	+	13.6352i	0.958578	+	0.553435i	0.895735	−	0.444588i	$-0.146650\pi$
$607$	23.6168	+	13.6352i	0.958578	+	0.553435i	0.0628430	+	0.998023i	$0.479983\pi$
$608$		0			0
$609$	19.1168	−	55.1856i	0.774654	−	2.23623i
$610$		0			0
$611$	1.70789	+	0.986051i	0.0690938	+	0.0398913i
$612$		0			0
$613$	−4.50000	+	2.59808i	−0.181753	+	0.104935i	−0.588116	−	0.808776i	$-0.700130\pi$
$613$	−4.50000	+	2.59808i	−0.181753	+	0.104935i	0.406363	+	0.913712i	$0.366797\pi$
$614$		0			0
$615$	23.4891	−	5.04868i	0.947173	−	0.203582i
$616$		0			0
$617$			14.2612i			0.574133i	0.957911	+	0.287066i	$0.0926801\pi$
$617$			14.2612i			0.574133i	−0.957911	+	0.287066i	$0.907320\pi$
$618$		0			0
$619$	0.989125	+	1.71322i	0.0397563	+	0.0688599i	0.885219	−	0.465175i	$-0.154009\pi$
$619$	0.989125	+	1.71322i	0.0397563	+	0.0688599i	−0.845463	+	0.534035i	$0.820675\pi$
$620$		0			0
$621$	4.67527	+	2.69927i	0.187612	+	0.108318i
$622$		0			0
$623$	−2.44158	+	0.469882i	−0.0978198	+	0.0188254i
$624$		0			0
$625$	7.94158	+	23.7051i	0.317663	+	0.948204i
$626$		0			0
$627$	−12.5584	−	21.7518i	−0.501535	−	0.868684i
$628$		0			0
$629$			14.0965i			0.562063i
$630$		0			0
$631$		−	31.5817i		−	1.25725i	−0.777710	−	0.628623i	$-0.783619\pi$
$631$		−	31.5817i		−	1.25725i	0.777710	−	0.628623i	$-0.216381\pi$
$632$		0			0
$633$	3.00000	+	5.19615i	0.119239	+	0.206529i
$634$		0			0
$635$	−1.45245	+	4.50506i	−0.0576388	+	0.178778i
$636$		0			0
$637$	−1.37228	+	9.50744i	−0.0543718	+	0.376699i
$638$		0			0
$639$	−30.3505	−	17.5229i	−1.20065	−	0.693195i
$640$		0			0
$641$	−12.1277	−	21.0058i	−0.479016	−	0.829680i	0.520694	−	0.853743i	$-0.325673\pi$
$641$	−12.1277	−	21.0058i	−0.479016	−	0.829680i	−0.999710	+	0.0240630i	$0.992340\pi$
$642$		0			0
$643$			0.884861i			0.0348955i	0.999848	+	0.0174478i	$0.00555407\pi$
$643$			0.884861i			0.0348955i	−0.999848	+	0.0174478i	$0.994446\pi$
$644$		0			0
$645$	4.74456	+	22.0742i	0.186817	+	0.869172i
$646$		0			0
$647$	−32.3614	+	18.6839i	−1.27226	+	0.734539i	−0.975413	−	0.220387i	$-0.929268\pi$
$647$	−32.3614	+	18.6839i	−1.27226	+	0.734539i	−0.296846	+	0.954925i	$0.595935\pi$
$648$		0			0
$649$	−15.5584	−	8.98266i	−0.610721	−	0.352600i
$650$		0			0
$651$	−46.6753	+	8.98266i	−1.82935	+	0.352058i
$652$		0			0
$653$	9.38316	+	5.41737i	0.367191	+	0.211998i	0.672231	−	0.740342i	$-0.265336\pi$
$653$	9.38316	+	5.41737i	0.367191	+	0.211998i	−0.305039	+	0.952340i	$0.598670\pi$
$654$		0			0
$655$	4.50000	+	4.97494i	0.175830	+	0.194387i
$656$		0			0
$657$	−34.9783			−1.36463
$658$		0			0
$659$			0.884861i			0.0344693i	0.999851	+	0.0172346i	$0.00548623\pi$
$659$			0.884861i			0.0344693i	−0.999851	+	0.0172346i	$0.994514\pi$
$660$		0			0
$661$	4.67527	−	2.69927i	0.181847	−	0.104989i	−0.406313	−	0.913734i	$-0.633186\pi$
$661$	4.67527	−	2.69927i	0.181847	−	0.104989i	0.588160	+	0.808745i	$0.299853\pi$
$662$		0			0
$663$	−4.88316	−	2.81929i	−0.189646	−	0.109492i
$664$		0			0
$665$	33.7337	+	4.12775i	1.30814	+	0.160067i
$666$		0			0
$667$	−25.1168	+	43.5036i	−0.972528	+	1.68447i
$668$		0			0
$669$	−13.1168	−	22.7190i	−0.507126	−	0.878369i
$670$		0			0
$671$	19.1168			0.737998
$672$		0			0
$673$		−	4.75372i		−	0.183243i	−0.995794	−	0.0916213i	$-0.970795\pi$
$673$		−	4.75372i		−	0.183243i	0.995794	−	0.0916213i	$-0.0292049\pi$
$674$		0			0
$675$	−2.74456	+	3.81396i	−0.105638	+	0.146799i
$676$		0			0
$677$	−5.61684	+	9.72866i	−0.215873	+	0.373903i	−0.953542	−	0.301259i	$-0.902593\pi$
$677$	−5.61684	+	9.72866i	−0.215873	+	0.373903i	0.737669	+	0.675162i	$0.235926\pi$
$678$		0			0
$679$	12.0000	−	10.3923i	0.460518	−	0.398820i
$680$		0			0
$681$	11.9307	−	20.6646i	0.457186	−	0.791869i
$682$		0			0
$683$	−8.18614	−	14.1788i	−0.313234	−	0.542537i	0.665827	−	0.746107i	$-0.268079\pi$
$683$	−8.18614	−	14.1788i	−0.313234	−	0.542537i	−0.979061	+	0.203569i	$0.934746\pi$
$684$		0			0
$685$	−0.302985	−	1.40965i	−0.0115764	−	0.0538598i
$686$		0			0
$687$	−45.3505			−1.73023
$688$		0			0
$689$	−15.9416	+	9.20387i	−0.607326	+	0.350640i
$690$		0			0
$691$	−11.1861	+	19.3750i	−0.425541	+	0.737058i	−0.996471	−	0.0839404i	$-0.973249\pi$
$691$	−11.1861	+	19.3750i	−0.425541	+	0.737058i	0.570930	+	0.820999i	$0.306583\pi$
$692$		0			0
$693$	10.1168	+	11.6819i	0.384307	+	0.443760i
$694$		0			0
$695$	−8.23369	+	25.5383i	−0.312322	+	0.968724i
$696$		0			0
$697$	−6.00000	+	3.46410i	−0.227266	+	0.131212i
$698$		0			0
$699$	−22.3723			−0.846197
$700$		0			0
$701$	20.7446			0.783511			0.391756	−	0.920069i	$-0.371868\pi$
$701$	20.7446			0.783511			0.391756	+	0.920069i	$0.371868\pi$
$702$		0			0
$703$	−43.0842	+	24.8747i	−1.62495	+	0.938167i
$704$		0			0
$705$	−2.48913	+	7.72049i	−0.0937459	+	0.290770i
$706$		0			0
$707$	−4.93070	+	14.2337i	−0.185438	+	0.535314i
$708$		0			0
$709$	−8.67527	+	15.0260i	−0.325806	+	0.564313i	−0.981675	−	0.190562i	$-0.938969\pi$
$709$	−8.67527	+	15.0260i	−0.325806	+	0.564313i	0.655869	+	0.754875i	$0.272302\pi$
$710$		0			0
$711$	1.88316	−	1.08724i	0.0706239	−	0.0407747i
$712$		0			0
$713$	40.8832			1.53109
$714$		0			0
$715$	−1.11684	−	5.19615i	−0.0417676	−	0.194325i
$716$		0			0
$717$	13.1168	+	22.7190i	0.489858	+	0.848458i
$718$		0			0
$719$	14.1861	−	24.5711i	0.529054	−	0.916348i	−0.470372	−	0.882468i	$-0.655880\pi$
$719$	14.1861	−	24.5711i	0.529054	−	0.916348i	0.999426	−	0.0338799i	$-0.0107864\pi$
$720$		0			0
$721$	1.67527	−	0.322405i	0.0623902	−	0.0120070i
$722$		0			0
$723$	19.6753	−	34.0786i	0.731731	−	1.26740i
$724$		0			0
$725$	−35.4891	−	25.5383i	−1.31803	−	0.948470i
$726$		0			0
$727$		−	6.72582i		−	0.249447i	−0.992192	−	0.124723i	$-0.960196\pi$
$727$		−	6.72582i		−	0.249447i	0.992192	−	0.124723i	$-0.0398044\pi$
$728$		0			0
$729$	33.2337			1.23088
$730$		0			0
$731$	−3.25544	−	5.63858i	−0.120407	−	0.208551i
$732$		0			0
$733$	3.98913	−	6.90937i	0.147342	−	0.255203i	−0.782902	−	0.622144i	$-0.786262\pi$
$733$	3.98913	−	6.90937i	0.147342	−	0.255203i	0.930244	+	0.366941i	$0.119595\pi$
$734$		0			0
$735$	−39.4198	+	2.69927i	−1.45402	+	0.0995639i
$736$		0			0
$737$	−13.6753	−	7.89542i	−0.503735	−	0.290831i
$738$		0			0
$739$	0.383156	−	0.221215i	0.0140946	−	0.00813753i	−0.492936	−	0.870065i	$-0.664076\pi$
$739$	0.383156	−	0.221215i	0.0140946	−	0.00813753i	0.507031	+	0.861928i	$0.330743\pi$
$740$		0			0
$741$		−	19.8997i		−	0.731036i
$742$		0			0
$743$	0.861407			0.0316019			0.0158010	−	0.999875i	$-0.494970\pi$
$743$	0.861407			0.0316019			0.0158010	+	0.999875i	$0.494970\pi$
$744$		0			0
$745$	23.7921	+	26.3032i	0.871675	+	0.963673i
$746$		0			0
$747$	5.48913	+	3.16915i	0.200837	+	0.115953i
$748$		0			0
$749$	−2.18614	−	11.3595i	−0.0798798	−	0.415068i
$750$		0			0
$751$	−15.5584	−	8.98266i	−0.567735	−	0.327782i	0.188509	−	0.982071i	$-0.439634\pi$
$751$	−15.5584	−	8.98266i	−0.567735	−	0.327782i	−0.756244	+	0.654290i	$0.772968\pi$
$752$		0			0
$753$	−54.3505	+	31.3793i	−1.98064	+	1.14353i
$754$		0			0
$755$	10.0693	+	46.8477i	0.366459	+	1.70496i
$756$		0			0
$757$		−	23.3639i		−	0.849174i	−0.905387	−	0.424587i	$-0.860419\pi$
$757$		−	23.3639i		−	0.849174i	0.905387	−	0.424587i	$-0.139581\pi$
$758$		0			0
$759$	−12.5584	−	21.7518i	−0.455842	−	0.789541i
$760$		0			0
$761$	−28.3397	−	16.3619i	−1.02731	−	0.593119i	−0.111098	−	0.993809i	$-0.535437\pi$
$761$	−28.3397	−	16.3619i	−1.02731	−	0.593119i	−0.916213	+	0.400691i	$0.868770\pi$
$762$		0			0
$763$	−12.7921	−	4.43132i	−0.463105	−	0.160424i
$764$		0			0
$765$	3.76631	−	11.6819i	0.136171	−	0.422361i
$766$		0			0
$767$	−7.11684	−	12.3267i	−0.256974	−	0.445093i
$768$		0			0
$769$			22.2766i			0.803315i	0.915790	+	0.401658i	$0.131566\pi$
$769$			22.2766i			0.803315i	−0.915790	+	0.401658i	$0.868434\pi$
$770$		0			0
$771$		−	17.9653i		−	0.647005i
$772$		0			0
$773$	15.1277	+	26.2020i	0.544106	+	0.942420i	0.998663	+	0.0517016i	$0.0164645\pi$
$773$	15.1277	+	26.2020i	0.544106	+	0.942420i	−0.454556	+	0.890718i	$0.650202\pi$
$774$		0			0
$775$	−3.55842	+	35.4059i	−0.127822	+	1.27182i
$776$		0			0
$777$	43.7228	−	37.8651i	1.56855	−	1.35840i
$778$		0			0
$779$	−21.1753	−	12.2255i	−0.758683	−	0.438026i
$780$		0			0
$781$	9.00000	+	15.5885i	0.322045	+	0.557799i
$782$		0			0
$783$		−	8.21782i		−	0.293681i
$784$		0			0
$785$	19.6753	−	4.22894i	0.702240	−	0.150937i
$786$		0			0
$787$	−34.6753	+	20.0198i	−1.23604	+	0.713628i	−0.968282	−	0.249858i	$-0.919616\pi$
$787$	−34.6753	+	20.0198i	−1.23604	+	0.713628i	−0.267757	+	0.963486i	$0.586283\pi$
$788$		0			0
$789$	−29.7921	−	17.2005i	−1.06063	−	0.612353i
$790$		0			0
$791$	−12.0000	−	13.8564i	−0.426671	−	0.492677i
$792$		0			0
$793$	13.1168	+	7.57301i	0.465793	+	0.268926i
$794$		0			0
$795$	−50.7921	−	56.1528i	−1.80141	−	1.99153i
$796$		0			0
$797$	−6.00000			−0.212531			−0.106265	−	0.994338i	$-0.533889\pi$
$797$	−6.00000			−0.212531			−0.106265	+	0.994338i	$0.533889\pi$
$798$		0			0
$799$		−	2.33919i		−	0.0827546i
$800$		0			0
$801$	−2.74456	+	1.58457i	−0.0969744	+	0.0559882i
$802$		0			0
$803$	15.5584	+	8.98266i	0.549045	+	0.316991i
$804$		0			0
$805$	33.7337	+	4.12775i	1.18896	+	0.145484i
$806$		0			0
$807$	31.0475	−	53.7759i	1.09293	−	1.89300i
$808$		0			0
$809$	−12.1277	−	21.0058i	−0.426388	−	0.738525i	0.570161	−	0.821533i	$-0.306881\pi$
$809$	−12.1277	−	21.0058i	−0.426388	−	0.738525i	−0.996549	+	0.0830075i	$0.973547\pi$
$810$		0			0
$811$	40.6277			1.42663			0.713316	−	0.700842i	$-0.247192\pi$
$811$	40.6277			1.42663			0.713316	+	0.700842i	$0.247192\pi$
$812$		0			0
$813$		−	11.0371i		−	0.387089i
$814$		0			0
$815$	31.6753	+	35.0183i	1.10954	+	1.22664i
$816$		0			0
$817$	11.4891	−	19.8997i	0.401954	−	0.696204i
$818$		0			0
$819$	2.31386	+	12.0232i	0.0808528	+	0.420123i
$820$		0			0
$821$	11.4416	−	19.8174i	0.399314	−	0.691632i	−0.594328	−	0.804223i	$-0.702582\pi$
$821$	11.4416	−	19.8174i	0.399314	−	0.691632i	0.993641	+	0.112591i	$0.0359151\pi$
$822$		0			0
$823$	18.6753	+	32.3465i	0.650979	+	1.12753i	0.982886	+	0.184216i	$0.0589747\pi$
$823$	18.6753	+	32.3465i	0.650979	+	1.12753i	−0.331907	+	0.943312i	$0.607692\pi$
$824$		0			0
$825$	19.9307	−	8.98266i	0.693898	−	0.312736i
$826$		0			0
$827$	37.7228			1.31175			0.655875	−	0.754869i	$-0.272300\pi$
$827$	37.7228			1.31175			0.655875	+	0.754869i	$0.272300\pi$
$828$		0			0
$829$	18.9090	−	10.9171i	0.656735	−	0.379166i	−0.134297	−	0.990941i	$-0.542878\pi$
$829$	18.9090	−	10.9171i	0.656735	−	0.379166i	0.791032	+	0.611775i	$0.209544\pi$
$830$		0			0
$831$	12.3030	−	21.3094i	0.426786	−	0.739215i
$832$		0			0
$833$	10.5802	−	4.22894i	0.366581	−	0.146524i
$834$		0			0
$835$	23.1753	+	7.47182i	0.802013	+	0.258573i
$836$		0			0
$837$	−5.79211	+	3.34408i	−0.200205	+	0.115588i
$838$		0			0
$839$	−33.2554			−1.14811			−0.574053	−	0.818818i	$-0.694630\pi$
$839$	−33.2554			−1.14811			−0.574053	+	0.818818i	$0.694630\pi$
$840$		0			0
$841$	47.4674			1.63681
$842$		0			0
$843$	−17.2337	+	9.94987i	−0.593560	+	0.342692i
$844$		0			0
$845$	−7.62772	+	23.6588i	−0.262401	+	0.813888i
$846$		0			0
$847$	4.00000	+	20.7846i	0.137442	+	0.714168i
$848$		0			0
$849$	22.6753	−	39.2747i	0.778213	−	1.34790i
$850$		0			0
$851$	−43.0842	+	24.8747i	−1.47691	+	0.852693i
$852$		0			0
$853$	−19.8832			−0.680786			−0.340393	−	0.940283i	$-0.610560\pi$
$853$	−19.8832			−0.680786			−0.340393	+	0.940283i	$0.610560\pi$
$854$		0			0
$855$	42.3505	−	9.10268i	1.44836	−	0.311305i
$856$		0			0
$857$	2.18614	+	3.78651i	0.0746771	+	0.129345i	0.900946	−	0.433932i	$-0.142874\pi$
$857$	2.18614	+	3.78651i	0.0746771	+	0.129345i	−0.826269	+	0.563276i	$0.809541\pi$
$858$		0			0
$859$	27.0475	−	46.8477i	0.922850	−	1.59842i	0.127868	−	0.991791i	$-0.459187\pi$
$859$	27.0475	−	46.8477i	0.922850	−	1.59842i	0.794982	−	0.606633i	$-0.207480\pi$
$860$		0			0
$861$	26.8614	+	9.30506i	0.915434	+	0.317116i
$862$		0			0
$863$	23.8723	−	41.3480i	0.812622	−	1.40750i	−0.0984011	−	0.995147i	$-0.531373\pi$
$863$	23.8723	−	41.3480i	0.812622	−	1.40750i	0.911023	−	0.412356i	$-0.135294\pi$
$864$		0			0
$865$	34.8505	+	38.5287i	1.18495	+	1.31002i
$866$		0			0
$867$		−	36.2256i		−	1.23029i
$868$		0			0
$869$	−1.11684			−0.0378863
$870$		0			0
$871$	−6.25544	−	10.8347i	−0.211957	−	0.367121i
$872$		0			0
$873$	10.1168	−	17.5229i	0.342403	−	0.593060i
$874$		0			0
$875$	−6.51087	+	28.8550i	−0.220108	+	0.975476i
$876$		0			0
$877$	1.50000	+	0.866025i	0.0506514	+	0.0292436i	0.525112	−	0.851033i	$-0.324023\pi$
$877$	1.50000	+	0.866025i	0.0506514	+	0.0292436i	−0.474460	+	0.880277i	$0.657357\pi$
$878$		0			0
$879$	67.4674	−	38.9523i	2.27562	−	1.31383i
$880$		0			0
$881$		−	34.5484i		−	1.16397i	−0.813201	−	0.581983i	$-0.802277\pi$
$881$		−	34.5484i		−	1.16397i	0.813201	−	0.581983i	$-0.197723\pi$
$882$		0			0
$883$	44.4674			1.49645			0.748223	−	0.663447i	$-0.230907\pi$
$883$	44.4674			1.49645			0.748223	+	0.663447i	$0.230907\pi$
$884$		0			0
$885$	43.4198	−	39.2747i	1.45954	−	1.32021i
$886$		0			0
$887$	−8.18614	−	4.72627i	−0.274864	−	0.158693i	0.356232	−	0.934397i	$-0.384061\pi$
$887$	−8.18614	−	4.72627i	−0.274864	−	0.158693i	−0.631096	+	0.775705i	$0.717395\pi$
$888$		0			0
$889$	−4.23369	+	3.66648i	−0.141993	+	0.122970i
$890$		0			0
$891$	−11.6168	−	6.70699i	−0.389179	−	0.224693i
$892$		0			0
$893$	7.14947	−	4.12775i	0.239248	−	0.138130i
$894$		0			0
$895$	−10.1644	−	47.2902i	−0.339758	−	1.58074i
$896$		0			0
$897$		−	19.8997i		−	0.664433i
$898$		0			0
$899$	−31.1168	−	53.8960i	−1.03780	−	1.79753i
$900$		0			0
$901$	18.9090	+	10.9171i	0.629949	+	0.363701i
$902$		0			0
$903$	−8.74456	+	25.2434i	−0.291001	+	0.840047i
$904$		0			0
$905$	−39.6060	−	12.7692i	−1.31655	−	0.424461i
$906$		0			0
$907$	−3.67527	−	6.36575i	−0.122035	−	0.211371i	0.798535	−	0.601948i	$-0.205609\pi$
$907$	−3.67527	−	6.36575i	−0.122035	−	0.211371i	−0.920570	+	0.390577i	$0.872275\pi$
$908$		0			0
$909$			19.2000i			0.636825i
$910$		0			0
$911$			12.9715i			0.429766i	0.976640	+	0.214883i	$0.0689371\pi$
$911$			12.9715i			0.429766i	−0.976640	+	0.214883i	$0.931063\pi$
$912$		0			0
$913$	−1.62772	−	2.81929i	−0.0538696	−	0.0933049i
$914$		0			0
$915$	−19.1168	+	59.2945i	−0.631983	+	1.96022i
$916$		0			0
$917$	1.50000	+	7.79423i	0.0495344	+	0.257388i
$918$		0			0
$919$	−35.7921	−	20.6646i	−1.18067	−	0.681662i	−0.224503	−	0.974473i	$-0.572076\pi$
$919$	−35.7921	−	20.6646i	−1.18067	−	0.681662i	−0.956170	+	0.292812i	$0.905409\pi$
$920$		0			0
$921$	−33.8614	−	58.6497i	−1.11577	−	1.93257i
$922$		0			0
$923$			14.2612i			0.469412i
$924$		0			0
$925$	−17.7921	−	39.4771i	−0.585001	−	1.29800i
$926$		0			0
$927$	1.88316	−	1.08724i	0.0618510	−	0.0357097i
$928$		0			0
$929$	−24.2228	−	13.9850i	−0.794725	−	0.458835i	0.0468985	−	0.998900i	$-0.485066\pi$
$929$	−24.2228	−	13.9850i	−0.794725	−	0.458835i	−0.841623	+	0.540065i	$0.818400\pi$
$930$		0			0
$931$	31.5951	+	24.8747i	1.03549	+	0.815235i
$932$		0			0
$933$	−9.55842	−	5.51856i	−0.312929	−	0.180669i
$934$		0			0
$935$	−4.67527	+	4.22894i	−0.152898	+	0.138301i
$936$		0			0
$937$	3.25544			0.106351			0.0531753	−	0.998585i	$-0.483066\pi$
$937$	3.25544			0.106351			0.0531753	+	0.998585i	$0.483066\pi$
$938$		0			0
$939$			40.0395i			1.30664i
$940$		0			0
$941$	−30.3030	+	17.4954i	−0.987849	+	0.570335i	−0.904631	−	0.426196i	$-0.859853\pi$
$941$	−30.3030	+	17.4954i	−0.987849	+	0.570335i	−0.0832184	+	0.996531i	$0.526520\pi$
$942$		0			0
$943$	−21.1753	−	12.2255i	−0.689562	−	0.398119i
$944$		0			0
$945$	−5.11684	+	2.17448i	−0.166451	+	0.0707359i
$946$		0			0
$947$	2.69702	−	4.67137i	0.0876412	−	0.151799i	−0.818872	−	0.573976i	$-0.805400\pi$
$947$	2.69702	−	4.67137i	0.0876412	−	0.151799i	0.906514	+	0.422177i	$0.138734\pi$
$948$		0			0
$949$	7.11684	+	12.3267i	0.231023	+	0.400143i
$950$		0			0
$951$	−27.8614			−0.903468
$952$		0			0
$953$			46.3229i			1.50055i	0.661127	+	0.750274i	$0.270078\pi$
$953$			46.3229i			1.50055i	−0.661127	+	0.750274i	$0.729922\pi$
$954$		0			0
$955$	−6.81386	+	6.16337i	−0.220491	+	0.199442i
$956$		0			0
$957$	−19.1168	+	33.1113i	−0.617960	+	1.07034i
$958$		0			0
$959$	0.558422	−	1.61203i	0.0180324	−	0.0520550i
$960$		0			0
$961$	−9.82473	+	17.0169i	−0.316927	+	0.548934i
$962$		0			0
$963$	−7.37228	−	12.7692i	−0.237568	−	0.411481i
$964$		0			0
$965$	−6.81386	−	31.7017i	−0.219346	−	1.02051i
$966$		0			0
$967$	40.0000			1.28631			0.643157	−	0.765735i	$-0.277624\pi$
$967$	40.0000			1.28631			0.643157	+	0.765735i	$0.277624\pi$
$968$		0			0
$969$	−20.4416	+	11.8020i	−0.656678	+	0.379133i
$970$		0			0
$971$	3.98913	−	6.90937i	0.128017	−	0.221732i	−0.794891	−	0.606752i	$-0.792472\pi$
$971$	3.98913	−	6.90937i	0.128017	−	0.221732i	0.922908	+	0.385020i	$0.125805\pi$
$972$		0			0
$973$	−24.0000	+	20.7846i	−0.769405	+	0.666324i
$974$		0			0
$975$	17.2337	+	1.73205i	0.551920	+	0.0554700i
$976$		0			0
$977$	4.32473	−	2.49689i	0.138361	−	0.0798825i	−0.429222	−	0.903199i	$-0.641212\pi$
$977$	4.32473	−	2.49689i	0.138361	−	0.0798825i	0.567582	+	0.823317i	$0.307879\pi$
$978$		0			0
$979$	1.62772			0.0520221
$980$		0			0
$981$	−17.2554			−0.550924
$982$		0			0
$983$	23.3614	−	13.4877i	0.745113	−	0.430191i	−0.0788123	−	0.996889i	$-0.525113\pi$
$983$	23.3614	−	13.4877i	0.745113	−	0.430191i	0.823925	+	0.566698i	$0.191779\pi$
$984$		0			0
$985$	41.9198	+	13.5152i	1.33568	+	0.430629i
$986$		0			0
$987$	−7.25544	+	6.28339i	−0.230943	+	0.200003i
$988$		0			0
$989$	11.4891	−	19.8997i	0.365333	−	0.632775i
$990$		0			0
$991$	−8.79211	+	5.07613i	−0.279291	+	0.161248i	−0.633102	−	0.774068i	$-0.718219\pi$
$991$	−8.79211	+	5.07613i	−0.279291	+	0.161248i	0.353812	+	0.935317i	$0.384885\pi$
$992$		0			0
$993$	−30.6060			−0.971251
$994$		0			0
$995$	−47.7921	+	10.2723i	−1.51511	+	0.325653i
$996$		0			0
$997$	−0.558422	−	0.967215i	−0.0176854	−	0.0306320i	0.857047	−	0.515238i	$-0.172296\pi$
$997$	−0.558422	−	0.967215i	−0.0176854	−	0.0306320i	−0.874733	+	0.484606i	$0.838963\pi$
$998$		0			0
$999$	4.06930	−	7.04823i	0.128747	−	0.222996i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cc.d.159.2	yes	4
4.3	odd	2		560.2.cc.b.159.1	yes	4
5.4	even	2		560.2.cc.a.159.1	✓	4
7.3	odd	6		560.2.cc.c.479.2	yes	4
20.19	odd	2		560.2.cc.c.159.2	yes	4
28.3	even	6		560.2.cc.a.479.1	yes	4
35.24	odd	6		560.2.cc.b.479.1	yes	4
140.59	even	6	inner	560.2.cc.d.479.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cc.a.159.1	✓	4	5.4	even	2
560.2.cc.a.479.1	yes	4	28.3	even	6
560.2.cc.b.159.1	yes	4	4.3	odd	2
560.2.cc.b.479.1	yes	4	35.24	odd	6
560.2.cc.c.159.2	yes	4	20.19	odd	2
560.2.cc.c.479.2	yes	4	7.3	odd	6
560.2.cc.d.159.2	yes	4	1.1	even	1	trivial
560.2.cc.d.479.2	yes	4	140.59	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.18614 - 1.26217i) q^{3} +(0.686141 - 2.12819i) q^{5} +(2.00000 - 1.73205i) q^{7} +(1.68614 - 2.92048i) q^{9} +(-1.50000 + 0.866025i) q^{11} -1.37228 q^{13} +(-1.18614 - 5.51856i) q^{15} +(0.813859 + 1.40965i) q^{17} +(-2.87228 + 4.97494i) q^{19} +(2.18614 - 6.31084i) q^{21} +(-2.87228 + 4.97494i) q^{23} +(-4.05842 - 2.92048i) q^{25} -0.939764i q^{27} +8.74456 q^{29} +(-3.55842 - 6.16337i) q^{31} +(-2.18614 + 3.78651i) q^{33} +(-2.31386 - 5.44482i) q^{35} +(7.50000 + 4.33013i) q^{37} +(-3.00000 + 1.73205i) q^{39} +4.25639i q^{41} -4.00000 q^{43} +(-5.05842 - 5.59230i) q^{45} +(-1.24456 - 0.718549i) q^{47} +(1.00000 - 6.92820i) q^{49} +(3.55842 + 2.05446i) q^{51} +(11.6168 - 6.70699i) q^{53} +(0.813859 + 3.78651i) q^{55} +14.5012i q^{57} +(5.18614 + 8.98266i) q^{59} +(-9.55842 - 5.51856i) q^{61} +(-1.68614 - 8.76144i) q^{63} +(-0.941578 + 2.92048i) q^{65} +(4.55842 + 7.89542i) q^{67} +14.5012i q^{69} -10.3923i q^{71} +(-5.18614 - 8.98266i) q^{73} +(-12.5584 - 1.26217i) q^{75} +(-1.50000 + 4.33013i) q^{77} +(0.558422 + 0.322405i) q^{79} +(3.87228 + 6.70699i) q^{81} +1.87953i q^{83} +(3.55842 - 0.764836i) q^{85} +(19.1168 - 11.0371i) q^{87} +(-0.813859 - 0.469882i) q^{89} +(-2.74456 + 2.37686i) q^{91} +(-15.5584 - 8.98266i) q^{93} +(8.61684 + 9.52628i) q^{95} +6.00000 q^{97} +5.84096i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{3} - 3 q^{5} + 8 q^{7} + q^{9} - 6 q^{11} + 6 q^{13} + q^{15} + 9 q^{17} + 3 q^{21} + q^{25} + 12 q^{29} + 3 q^{31} - 3 q^{33} - 15 q^{35} + 30 q^{37} - 12 q^{39} - 16 q^{43} - 3 q^{45} + 18 q^{47}+ \cdots + 24 q^{97}+O(q^{100}) \) 4 * q + 3 * q^3 - 3 * q^5 + 8 * q^7 + q^9 - 6 * q^11 + 6 * q^13 + q^15 + 9 * q^17 + 3 * q^21 + q^25 + 12 * q^29 + 3 * q^31 - 3 * q^33 - 15 * q^35 + 30 * q^37 - 12 * q^39 - 16 * q^43 - 3 * q^45 + 18 * q^47 + 4 * q^49 - 3 * q^51 + 12 * q^53 + 9 * q^55 + 15 * q^59 - 21 * q^61 - q^63 - 21 * q^65 + q^67 - 15 * q^73 - 33 * q^75 - 6 * q^77 - 15 * q^79 + 4 * q^81 - 3 * q^85 + 42 * q^87 - 9 * q^89 + 12 * q^91 - 45 * q^93 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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