LMFDB - Embedded newform 560.2.q.d.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(81,560)]

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([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("560.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.q (of order $3$, degree $2$, not 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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	560.81
Dual form			560.2.q.d.401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{11} +5.00000 q^{13} -2.00000 q^{15} +(-3.00000 + 5.19615i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(-5.00000 + 1.73205i) q^{21} +(1.50000 + 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.00000 q^{27} -6.00000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(3.00000 + 5.19615i) q^{33} +(-0.500000 + 2.59808i) q^{35} +(-5.50000 - 9.52628i) q^{37} +(-5.00000 + 8.66025i) q^{39} +3.00000 q^{41} +10.0000 q^{43} +(0.500000 - 0.866025i) q^{45} +(1.50000 + 2.59808i) q^{47} +(1.00000 + 6.92820i) q^{49} +(-6.00000 - 10.3923i) q^{51} +(-1.50000 + 2.59808i) q^{53} +3.00000 q^{55} +2.00000 q^{57} +(2.00000 + 3.46410i) q^{61} +(0.500000 - 2.59808i) q^{63} +(2.50000 + 4.33013i) q^{65} +(-2.00000 + 3.46410i) q^{67} -6.00000 q^{69} -12.0000 q^{71} +(2.00000 - 3.46410i) q^{73} +(-1.00000 - 1.73205i) q^{75} +(7.50000 - 2.59808i) q^{77} +(-5.00000 - 8.66025i) q^{79} +(5.50000 - 9.52628i) q^{81} +12.0000 q^{83} -6.00000 q^{85} +(6.00000 - 10.3923i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(10.0000 + 8.66025i) q^{91} +(-4.00000 - 6.92820i) q^{93} +(0.500000 - 0.866025i) q^{95} +14.0000 q^{97} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + q^{5} + 4 q^{7} - q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 + q^5 + 4 * q^7 - q^9	$ 2 q - 2 q^{3} + q^{5} + 4 q^{7} - q^{9} + 3 q^{11} + 10 q^{13} - 4 q^{15} - 6 q^{17} - q^{19} - 10 q^{21} + 3 q^{23} - q^{25} - 8 q^{27} - 12 q^{29} - 4 q^{31} + 6 q^{33} - q^{35} - 11 q^{37} - 10 q^{39} + 6 q^{41} + 20 q^{43} + q^{45} + 3 q^{47} + 2 q^{49} - 12 q^{51} - 3 q^{53} + 6 q^{55} + 4 q^{57} + 4 q^{61} + q^{63} + 5 q^{65} - 4 q^{67} - 12 q^{69} - 24 q^{71} + 4 q^{73} - 2 q^{75} + 15 q^{77} - 10 q^{79} + 11 q^{81} + 24 q^{83} - 12 q^{85} + 12 q^{87} - 6 q^{89} + 20 q^{91} - 8 q^{93} + q^{95} + 28 q^{97} - 6 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 + q^5 + 4 * q^7 - q^9 + 3 * q^11 + 10 * q^13 - 4 * q^15 - 6 * q^17 - q^19 - 10 * q^21 + 3 * q^23 - q^25 - 8 * q^27 - 12 * q^29 - 4 * q^31 + 6 * q^33 - q^35 - 11 * q^37 - 10 * q^39 + 6 * q^41 + 20 * q^43 + q^45 + 3 * q^47 + 2 * q^49 - 12 * q^51 - 3 * q^53 + 6 * q^55 + 4 * q^57 + 4 * q^61 + q^63 + 5 * q^65 - 4 * q^67 - 12 * q^69 - 24 * q^71 + 4 * q^73 - 2 * q^75 + 15 * q^77 - 10 * q^79 + 11 * q^81 + 24 * q^83 - 12 * q^85 + 12 * q^87 - 6 * q^89 + 20 * q^91 - 8 * q^93 + q^95 + 28 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	0.418432	+	0.908248i	$0.362580\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	−0.995782	+	0.0917517i	$0.970753\pi$
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		0			0
$13$	5.00000			1.38675			0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000			1.38675			0.693375	+	0.720577i	$0.256123\pi$
$14$		0			0
$15$	−2.00000			−0.516398
$16$		0			0
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	0.230285	+	0.973123i	$0.426034\pi$
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	−0.957892	+	0.287129i	$0.907299\pi$
$18$		0			0
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$	−5.00000	+	1.73205i	−1.09109	+	0.377964i
$22$		0			0
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−4.00000			−0.769800
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$		0			0
$33$	3.00000	+	5.19615i	0.522233	+	0.904534i
$34$		0			0
$35$	−0.500000	+	2.59808i	−0.0845154	+	0.439155i
$36$		0			0
$37$	−5.50000	−	9.52628i	−0.904194	−	1.56611i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−5.50000	−	9.52628i	−0.904194	−	1.56611i	−0.0821995	−	0.996616i	$-0.526194\pi$
$38$		0			0
$39$	−5.00000	+	8.66025i	−0.800641	+	1.38675i
$40$		0			0
$41$	3.00000			0.468521			0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000			0.468521			0.234261	+	0.972174i	$0.424733\pi$
$42$		0			0
$43$	10.0000			1.52499			0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000			1.52499			0.762493	+	0.646997i	$0.223975\pi$
$44$		0			0
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$		0			0
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	0.954441	−	0.298401i	$-0.0964533\pi$
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	−0.735643	+	0.677369i	$0.763120\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$		0			0
$51$	−6.00000	−	10.3923i	−0.840168	−	1.45521i
$52$		0			0
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$		0			0
$55$	3.00000			0.404520
$56$		0			0
$57$	2.00000			0.264906
$58$		0			0
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	0.965187	−	0.261562i	$-0.0842377\pi$
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	−0.709113	+	0.705095i	$0.750904\pi$
$62$		0			0
$63$	0.500000	−	2.59808i	0.0629941	−	0.327327i
$64$		0			0
$65$	2.50000	+	4.33013i	0.310087	+	0.537086i
$66$		0			0
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$		0			0
$69$	−6.00000			−0.722315
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$		0			0
$73$	2.00000	−	3.46410i	0.234082	−	0.405442i	−0.724923	−	0.688830i	$-0.758125\pi$
$73$	2.00000	−	3.46410i	0.234082	−	0.405442i	0.959006	+	0.283387i	$0.0914581\pi$
$74$		0			0
$75$	−1.00000	−	1.73205i	−0.115470	−	0.200000i
$76$		0			0
$77$	7.50000	−	2.59808i	0.854704	−	0.296078i
$78$		0			0
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	−0.997274	−	0.0737937i	$-0.976489\pi$
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	0.434730	−	0.900561i	$-0.356844\pi$
$80$		0			0
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	−6.00000			−0.650791
$86$		0			0
$87$	6.00000	−	10.3923i	0.643268	−	1.11417i
$88$		0			0
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		0			0
$91$	10.0000	+	8.66025i	1.04828	+	0.907841i
$92$		0			0
$93$	−4.00000	−	6.92820i	−0.414781	−	0.718421i
$94$		0			0
$95$	0.500000	−	0.866025i	0.0512989	−	0.0888523i
$96$		0			0
$97$	14.0000			1.42148			0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000			1.42148			0.710742	+	0.703452i	$0.248359\pi$
$98$		0			0
$99$	−3.00000			−0.301511
$100$		0			0
$101$	6.00000	−	10.3923i	0.597022	−	1.03407i	−0.396236	−	0.918149i	$-0.629684\pi$
$101$	6.00000	−	10.3923i	0.597022	−	1.03407i	0.993258	−	0.115924i	$-0.0369830\pi$
$102$		0			0
$103$	−2.00000	−	3.46410i	−0.197066	−	0.341328i	0.750510	−	0.660859i	$-0.229808\pi$
$103$	−2.00000	−	3.46410i	−0.197066	−	0.341328i	−0.947576	+	0.319531i	$0.896475\pi$
$104$		0			0
$105$	−4.00000	−	3.46410i	−0.390360	−	0.338062i
$106$		0			0
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$		0			0
$109$	2.00000	−	3.46410i	0.191565	−	0.331801i	−0.754204	−	0.656640i	$-0.771977\pi$
$109$	2.00000	−	3.46410i	0.191565	−	0.331801i	0.945769	+	0.324840i	$0.105310\pi$
$110$		0			0
$111$	22.0000			2.08815
$112$		0			0
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$		0			0
$115$	−1.50000	+	2.59808i	−0.139876	+	0.242272i
$116$		0			0
$117$	−2.50000	−	4.33013i	−0.231125	−	0.400320i
$118$		0			0
$119$	−15.0000	+	5.19615i	−1.37505	+	0.476331i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$	−3.00000	+	5.19615i	−0.270501	+	0.468521i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	19.0000			1.68598			0.842989	−	0.537931i	$-0.180794\pi$
$127$	19.0000			1.68598			0.842989	+	0.537931i	$0.180794\pi$
$128$		0			0
$129$	−10.0000	+	17.3205i	−0.880451	+	1.52499i
$130$		0			0
$131$	1.50000	+	2.59808i	0.131056	+	0.226995i	0.924084	−	0.382190i	$-0.124830\pi$
$131$	1.50000	+	2.59808i	0.131056	+	0.226995i	−0.793028	+	0.609185i	$0.791497\pi$
$132$		0			0
$133$	0.500000	−	2.59808i	0.0433555	−	0.225282i
$134$		0			0
$135$	−2.00000	−	3.46410i	−0.172133	−	0.298142i
$136$		0			0
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$		0			0
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$		0			0
$143$	7.50000	−	12.9904i	0.627182	−	1.08631i
$144$		0			0
$145$	−3.00000	−	5.19615i	−0.249136	−	0.431517i
$146$		0			0
$147$	−13.0000	−	5.19615i	−1.07222	−	0.428571i
$148$		0			0
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$		0			0
$151$	7.00000	−	12.1244i	0.569652	−	0.986666i	−0.426948	−	0.904276i	$-0.640411\pi$
$151$	7.00000	−	12.1244i	0.569652	−	0.986666i	0.996600	−	0.0823900i	$-0.0262553\pi$
$152$		0			0
$153$	6.00000			0.485071
$154$		0			0
$155$	−4.00000			−0.321288
$156$		0			0
$157$	−2.50000	+	4.33013i	−0.199522	+	0.345582i	−0.948373	−	0.317156i	$-0.897272\pi$
$157$	−2.50000	+	4.33013i	−0.199522	+	0.345582i	0.748852	+	0.662738i	$0.230606\pi$
$158$		0			0
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$		0			0
$161$	−1.50000	+	7.79423i	−0.118217	+	0.614271i
$162$		0			0
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	0.777007	−	0.629492i	$-0.216737\pi$
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	−0.933659	+	0.358162i	$0.883403\pi$
$164$		0			0
$165$	−3.00000	+	5.19615i	−0.233550	+	0.404520i
$166$		0			0
$167$	−9.00000			−0.696441			−0.348220	−	0.937413i	$-0.613214\pi$
$167$	−9.00000			−0.696441			−0.348220	+	0.937413i	$0.613214\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$		0			0
$171$	−0.500000	+	0.866025i	−0.0382360	+	0.0662266i
$172$		0			0
$173$	−1.50000	−	2.59808i	−0.114043	−	0.197528i	0.803354	−	0.595502i	$-0.203047\pi$
$173$	−1.50000	−	2.59808i	−0.114043	−	0.197528i	−0.917397	+	0.397974i	$0.869713\pi$
$174$		0			0
$175$	−2.50000	+	0.866025i	−0.188982	+	0.0654654i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.50000	+	2.59808i	−0.112115	+	0.194189i	−0.916623	−	0.399753i	$-0.869096\pi$
$179$	−1.50000	+	2.59808i	−0.112115	+	0.194189i	0.804508	+	0.593942i	$0.202429\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$	−8.00000			−0.591377
$184$		0			0
$185$	5.50000	−	9.52628i	0.404368	−	0.700386i
$186$		0			0
$187$	9.00000	+	15.5885i	0.658145	+	1.13994i
$188$		0			0
$189$	−8.00000	−	6.92820i	−0.581914	−	0.503953i
$190$		0			0
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	0.997225	−	0.0744412i	$-0.0237173\pi$
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	−0.563081	+	0.826402i	$0.690384\pi$
$192$		0			0
$193$	2.00000	−	3.46410i	0.143963	−	0.249351i	−0.785022	−	0.619467i	$-0.787349\pi$
$193$	2.00000	−	3.46410i	0.143963	−	0.249351i	0.928986	+	0.370116i	$0.120682\pi$
$194$		0			0
$195$	−10.0000			−0.716115
$196$		0			0
$197$	−3.00000			−0.213741			−0.106871	−	0.994273i	$-0.534083\pi$
$197$	−3.00000			−0.213741			−0.106871	+	0.994273i	$0.534083\pi$
$198$		0			0
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	−0.928166	−	0.372168i	$-0.878615\pi$
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	0.786389	+	0.617731i	$0.211948\pi$
$200$		0			0
$201$	−4.00000	−	6.92820i	−0.282138	−	0.488678i
$202$		0			0
$203$	−12.0000	−	10.3923i	−0.842235	−	0.729397i
$204$		0			0
$205$	1.50000	+	2.59808i	0.104765	+	0.181458i
$206$		0			0
$207$	1.50000	−	2.59808i	0.104257	−	0.180579i
$208$		0			0
$209$	−3.00000			−0.207514
$210$		0			0
$211$	1.00000			0.0688428			0.0344214	−	0.999407i	$-0.489041\pi$
$211$	1.00000			0.0688428			0.0344214	+	0.999407i	$0.489041\pi$
$212$		0			0
$213$	12.0000	−	20.7846i	0.822226	−	1.42414i
$214$		0			0
$215$	5.00000	+	8.66025i	0.340997	+	0.590624i
$216$		0			0
$217$	−10.0000	+	3.46410i	−0.678844	+	0.235159i
$218$		0			0
$219$	4.00000	+	6.92820i	0.270295	+	0.468165i
$220$		0			0
$221$	−15.0000	+	25.9808i	−1.00901	+	1.74766i
$222$		0			0
$223$	−8.00000			−0.535720			−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000			−0.535720			−0.267860	+	0.963458i	$0.586316\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−12.0000	+	20.7846i	−0.796468	+	1.37952i	0.125435	+	0.992102i	$0.459967\pi$
$227$	−12.0000	+	20.7846i	−0.796468	+	1.37952i	−0.921903	+	0.387421i	$0.873366\pi$
$228$		0			0
$229$	14.0000	+	24.2487i	0.925146	+	1.60240i	0.791326	+	0.611394i	$0.209391\pi$
$229$	14.0000	+	24.2487i	0.925146	+	1.60240i	0.133820	+	0.991006i	$0.457276\pi$
$230$		0			0
$231$	−3.00000	+	15.5885i	−0.197386	+	1.02565i
$232$		0			0
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$		0			0
$235$	−1.50000	+	2.59808i	−0.0978492	+	0.169480i
$236$		0			0
$237$	20.0000			1.29914
$238$		0			0
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	−0.110963	−	0.993825i	$-0.535394\pi$
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	0.916159	−	0.400815i	$-0.131273\pi$
$242$		0			0
$243$	5.00000	+	8.66025i	0.320750	+	0.555556i
$244$		0			0
$245$	−5.50000	+	4.33013i	−0.351382	+	0.276642i
$246$		0			0
$247$	−2.50000	−	4.33013i	−0.159071	−	0.275519i
$248$		0			0
$249$	−12.0000	+	20.7846i	−0.760469	+	1.31717i
$250$		0			0
$251$	15.0000			0.946792			0.473396	−	0.880850i	$-0.343028\pi$
$251$	15.0000			0.946792			0.473396	+	0.880850i	$0.343028\pi$
$252$		0			0
$253$	9.00000			0.565825
$254$		0			0
$255$	6.00000	−	10.3923i	0.375735	−	0.650791i
$256$		0			0
$257$	6.00000	+	10.3923i	0.374270	+	0.648254i	0.990217	−	0.139533i	$-0.0445601\pi$
$257$	6.00000	+	10.3923i	0.374270	+	0.648254i	−0.615948	+	0.787787i	$0.711227\pi$
$258$		0			0
$259$	5.50000	−	28.5788i	0.341753	−	1.77580i
$260$		0			0
$261$	3.00000	+	5.19615i	0.185695	+	0.321634i
$262$		0			0
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$	−3.00000			−0.184289
$266$		0			0
$267$	12.0000			0.734388
$268$		0			0
$269$	6.00000	−	10.3923i	0.365826	−	0.633630i	−0.623082	−	0.782157i	$-0.714120\pi$
$269$	6.00000	−	10.3923i	0.365826	−	0.633630i	0.988908	+	0.148527i	$0.0474530\pi$
$270$		0			0
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	0.513905	−	0.857847i	$-0.328199\pi$
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	−0.999870	+	0.0161307i	$0.994865\pi$
$272$		0			0
$273$	−25.0000	+	8.66025i	−1.51307	+	0.524142i
$274$		0			0
$275$	1.50000	+	2.59808i	0.0904534	+	0.156670i
$276$		0			0
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	−0.894503	−	0.447062i	$-0.852470\pi$
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	0.834419	+	0.551131i	$0.185804\pi$
$278$		0			0
$279$	4.00000			0.239474
$280$		0			0
$281$	−3.00000			−0.178965			−0.0894825	−	0.995988i	$-0.528521\pi$
$281$	−3.00000			−0.178965			−0.0894825	+	0.995988i	$0.528521\pi$
$282$		0			0
$283$	13.0000	−	22.5167i	0.772770	−	1.33848i	−0.163270	−	0.986581i	$-0.552204\pi$
$283$	13.0000	−	22.5167i	0.772770	−	1.33848i	0.936039	−	0.351895i	$-0.114463\pi$
$284$		0			0
$285$	1.00000	+	1.73205i	0.0592349	+	0.102598i
$286$		0			0
$287$	6.00000	+	5.19615i	0.354169	+	0.306719i
$288$		0			0
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$		0			0
$291$	−14.0000	+	24.2487i	−0.820695	+	1.42148i
$292$		0			0
$293$	−27.0000			−1.57736			−0.788678	−	0.614806i	$-0.789234\pi$
$293$	−27.0000			−1.57736			−0.788678	+	0.614806i	$0.789234\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−6.00000	+	10.3923i	−0.348155	+	0.603023i
$298$		0			0
$299$	7.50000	+	12.9904i	0.433736	+	0.751253i
$300$		0			0
$301$	20.0000	+	17.3205i	1.15278	+	0.998337i
$302$		0			0
$303$	12.0000	+	20.7846i	0.689382	+	1.19404i
$304$		0			0
$305$	−2.00000	+	3.46410i	−0.114520	+	0.198354i
$306$		0			0
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$		0			0
$309$	8.00000			0.455104
$310$		0			0
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	−0.644246	−	0.764818i	$-0.722829\pi$
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	0.984475	+	0.175525i	$0.0561621\pi$
$312$		0			0
$313$	−4.00000	−	6.92820i	−0.226093	−	0.391605i	0.730554	−	0.682855i	$-0.239262\pi$
$313$	−4.00000	−	6.92820i	−0.226093	−	0.391605i	−0.956647	+	0.291250i	$0.905929\pi$
$314$		0			0
$315$	2.50000	−	0.866025i	0.140859	−	0.0487950i
$316$		0			0
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	−0.999980	−	0.00635137i	$-0.997978\pi$
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	0.494489	−	0.869184i	$-0.335355\pi$
$318$		0			0
$319$	−9.00000	+	15.5885i	−0.503903	+	0.872786i
$320$		0			0
$321$	24.0000			1.33955
$322$		0			0
$323$	6.00000			0.333849
$324$		0			0
$325$	−2.50000	+	4.33013i	−0.138675	+	0.240192i
$326$		0			0
$327$	4.00000	+	6.92820i	0.221201	+	0.383131i
$328$		0			0
$329$	−1.50000	+	7.79423i	−0.0826977	+	0.429710i
$330$		0			0
$331$	−3.50000	−	6.06218i	−0.192377	−	0.333207i	0.753660	−	0.657264i	$-0.228286\pi$
$331$	−3.50000	−	6.06218i	−0.192377	−	0.333207i	−0.946038	+	0.324057i	$0.894953\pi$
$332$		0			0
$333$	−5.50000	+	9.52628i	−0.301398	+	0.522037i
$334$		0			0
$335$	−4.00000			−0.218543
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$		0			0
$339$	−12.0000	+	20.7846i	−0.651751	+	1.12887i
$340$		0			0
$341$	6.00000	+	10.3923i	0.324918	+	0.562775i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$	−3.00000	−	5.19615i	−0.161515	−	0.279751i
$346$		0			0
$347$	12.0000	−	20.7846i	0.644194	−	1.11578i	−0.340293	−	0.940319i	$-0.610526\pi$
$347$	12.0000	−	20.7846i	0.644194	−	1.11578i	0.984487	−	0.175457i	$-0.0561403\pi$
$348$		0			0
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$		0			0
$351$	−20.0000			−1.06752
$352$		0			0
$353$	−6.00000	+	10.3923i	−0.319348	+	0.553127i	−0.980352	−	0.197256i	$-0.936797\pi$
$353$	−6.00000	+	10.3923i	−0.319348	+	0.553127i	0.661004	+	0.750382i	$0.270130\pi$
$354$		0			0
$355$	−6.00000	−	10.3923i	−0.318447	−	0.551566i
$356$		0			0
$357$	6.00000	−	31.1769i	0.317554	−	1.65006i
$358$		0			0
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	0.934268	−	0.356572i	$-0.116054\pi$
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	−0.775934	+	0.630814i	$0.782721\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$		0			0
$363$	−4.00000			−0.209946
$364$		0			0
$365$	4.00000			0.209370
$366$		0			0
$367$	−0.500000	+	0.866025i	−0.0260998	+	0.0452062i	−0.878780	−	0.477227i	$-0.841642\pi$
$367$	−0.500000	+	0.866025i	−0.0260998	+	0.0452062i	0.852680	+	0.522433i	$0.174975\pi$
$368$		0			0
$369$	−1.50000	−	2.59808i	−0.0780869	−	0.135250i
$370$		0			0
$371$	−7.50000	+	2.59808i	−0.389381	+	0.134885i
$372$		0			0
$373$	17.0000	+	29.4449i	0.880227	+	1.52460i	0.851089	+	0.525022i	$0.175943\pi$
$373$	17.0000	+	29.4449i	0.880227	+	1.52460i	0.0291379	+	0.999575i	$0.490724\pi$
$374$		0			0
$375$	1.00000	−	1.73205i	0.0516398	−	0.0894427i
$376$		0			0
$377$	−30.0000			−1.54508
$378$		0			0
$379$	25.0000			1.28416			0.642082	−	0.766636i	$-0.278071\pi$
$379$	25.0000			1.28416			0.642082	+	0.766636i	$0.278071\pi$
$380$		0			0
$381$	−19.0000	+	32.9090i	−0.973399	+	1.68598i
$382$		0			0
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	0.991522	−	0.129937i	$-0.0414776\pi$
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	−0.608290	+	0.793715i	$0.708144\pi$
$384$		0			0
$385$	6.00000	+	5.19615i	0.305788	+	0.264820i
$386$		0			0
$387$	−5.00000	−	8.66025i	−0.254164	−	0.440225i
$388$		0			0
$389$	12.0000	−	20.7846i	0.608424	−	1.05382i	−0.383076	−	0.923717i	$-0.625135\pi$
$389$	12.0000	−	20.7846i	0.608424	−	1.05382i	0.991500	−	0.130105i	$-0.0415314\pi$
$390$		0			0
$391$	−18.0000			−0.910299
$392$		0			0
$393$	−6.00000			−0.302660
$394$		0			0
$395$	5.00000	−	8.66025i	0.251577	−	0.435745i
$396$		0			0
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	0.839840	−	0.542834i	$-0.182649\pi$
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	−0.890028	+	0.455905i	$0.849316\pi$
$398$		0			0
$399$	4.00000	+	3.46410i	0.200250	+	0.173422i
$400$		0			0
$401$	−10.5000	−	18.1865i	−0.524345	−	0.908192i	−0.999598	−	0.0283431i	$-0.990977\pi$
$401$	−10.5000	−	18.1865i	−0.524345	−	0.908192i	0.475253	−	0.879849i	$-0.342356\pi$
$402$		0			0
$403$	−10.0000	+	17.3205i	−0.498135	+	0.862796i
$404$		0			0
$405$	11.0000			0.546594
$406$		0			0
$407$	−33.0000			−1.63575
$408$		0			0
$409$	11.0000	−	19.0526i	0.543915	−	0.942088i	−0.454759	−	0.890614i	$-0.650275\pi$
$409$	11.0000	−	19.0526i	0.543915	−	0.942088i	0.998674	−	0.0514740i	$-0.0163919\pi$
$410$		0			0
$411$	−12.0000	−	20.7846i	−0.591916	−	1.02523i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	6.00000	+	10.3923i	0.294528	+	0.510138i
$416$		0			0
$417$	−4.00000	+	6.92820i	−0.195881	+	0.339276i
$418$		0			0
$419$	−15.0000			−0.732798			−0.366399	−	0.930458i	$-0.619409\pi$
$419$	−15.0000			−0.732798			−0.366399	+	0.930458i	$0.619409\pi$
$420$		0			0
$421$	−34.0000			−1.65706			−0.828529	−	0.559946i	$-0.810822\pi$
$421$	−34.0000			−1.65706			−0.828529	+	0.559946i	$0.810822\pi$
$422$		0			0
$423$	1.50000	−	2.59808i	0.0729325	−	0.126323i
$424$		0			0
$425$	−3.00000	−	5.19615i	−0.145521	−	0.252050i
$426$		0			0
$427$	−2.00000	+	10.3923i	−0.0967868	+	0.502919i
$428$		0			0
$429$	15.0000	+	25.9808i	0.724207	+	1.25436i
$430$		0			0
$431$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$431$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$432$		0			0
$433$	−16.0000			−0.768911			−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000			−0.768911			−0.384455	+	0.923144i	$0.625611\pi$
$434$		0			0
$435$	12.0000			0.575356
$436$		0			0
$437$	1.50000	−	2.59808i	0.0717547	−	0.124283i
$438$		0			0
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	0.721686	−	0.692220i	$-0.243367\pi$
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	−0.960323	+	0.278889i	$0.910034\pi$
$440$		0			0
$441$	5.50000	−	4.33013i	0.261905	−	0.206197i
$442$		0			0
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	−0.996551	−	0.0829786i	$-0.973557\pi$
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	0.426414	−	0.904528i	$-0.359777\pi$
$444$		0			0
$445$	3.00000	−	5.19615i	0.142214	−	0.246321i
$446$		0			0
$447$	36.0000			1.70274
$448$		0			0
$449$	−3.00000			−0.141579			−0.0707894	−	0.997491i	$-0.522552\pi$
$449$	−3.00000			−0.141579			−0.0707894	+	0.997491i	$0.522552\pi$
$450$		0			0
$451$	4.50000	−	7.79423i	0.211897	−	0.367016i
$452$		0			0
$453$	14.0000	+	24.2487i	0.657777	+	1.13930i
$454$		0			0
$455$	−2.50000	+	12.9904i	−0.117202	+	0.608998i
$456$		0			0
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	0.999857	+	0.0168929i	$0.00537742\pi$
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	−0.485299	+	0.874348i	$0.661289\pi$
$458$		0			0
$459$	12.0000	−	20.7846i	0.560112	−	0.970143i
$460$		0			0
$461$	6.00000			0.279448			0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000			0.279448			0.139724	+	0.990190i	$0.455378\pi$
$462$		0			0
$463$	19.0000			0.883005			0.441502	−	0.897260i	$-0.354446\pi$
$463$	19.0000			0.883005			0.441502	+	0.897260i	$0.354446\pi$
$464$		0			0
$465$	4.00000	−	6.92820i	0.185496	−	0.321288i
$466$		0			0
$467$	−9.00000	−	15.5885i	−0.416470	−	0.721348i	0.579111	−	0.815249i	$-0.303400\pi$
$467$	−9.00000	−	15.5885i	−0.416470	−	0.721348i	−0.995582	+	0.0939008i	$0.970066\pi$
$468$		0			0
$469$	−10.0000	+	3.46410i	−0.461757	+	0.159957i
$470$		0			0
$471$	−5.00000	−	8.66025i	−0.230388	−	0.399043i
$472$		0			0
$473$	15.0000	−	25.9808i	0.689701	−	1.19460i
$474$		0			0
$475$	1.00000			0.0458831
$476$		0			0
$477$	3.00000			0.137361
$478$		0			0
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	−0.450098	−	0.892979i	$-0.648611\pi$
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	0.998392	−	0.0566937i	$-0.0180558\pi$
$480$		0			0
$481$	−27.5000	−	47.6314i	−1.25389	−	2.17180i
$482$		0			0
$483$	−12.0000	−	10.3923i	−0.546019	−	0.472866i
$484$		0			0
$485$	7.00000	+	12.1244i	0.317854	+	0.550539i
$486$		0			0
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	−0.988374	−	0.152042i	$-0.951415\pi$
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	0.625859	+	0.779936i	$0.284748\pi$
$488$		0			0
$489$	8.00000			0.361773
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$		0			0
$493$	18.0000	−	31.1769i	0.810679	−	1.40414i
$494$		0			0
$495$	−1.50000	−	2.59808i	−0.0674200	−	0.116775i
$496$		0			0
$497$	−24.0000	−	20.7846i	−1.07655	−	0.932317i
$498$		0			0
$499$	−14.0000	−	24.2487i	−0.626726	−	1.08552i	−0.988204	−	0.153141i	$-0.951061\pi$
$499$	−14.0000	−	24.2487i	−0.626726	−	1.08552i	0.361478	−	0.932381i	$-0.382272\pi$
$500$		0			0
$501$	9.00000	−	15.5885i	0.402090	−	0.696441i
$502$		0			0
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$	12.0000			0.533993
$506$		0			0
$507$	−12.0000	+	20.7846i	−0.532939	+	0.923077i
$508$		0			0
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	0.791849	−	0.610718i	$-0.209119\pi$
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	−0.924821	+	0.380402i	$0.875786\pi$
$510$		0			0
$511$	10.0000	−	3.46410i	0.442374	−	0.153243i
$512$		0			0
$513$	2.00000	+	3.46410i	0.0883022	+	0.152944i
$514$		0			0
$515$	2.00000	−	3.46410i	0.0881305	−	0.152647i
$516$		0			0
$517$	9.00000			0.395820
$518$		0			0
$519$	6.00000			0.263371
$520$		0			0
$521$	−16.5000	+	28.5788i	−0.722878	+	1.25206i	0.236963	+	0.971519i	$0.423848\pi$
$521$	−16.5000	+	28.5788i	−0.722878	+	1.25206i	−0.959841	+	0.280543i	$0.909485\pi$
$522$		0			0
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	0.997478	−	0.0709788i	$-0.0226123\pi$
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	−0.560208	+	0.828352i	$0.689279\pi$
$524$		0			0
$525$	1.00000	−	5.19615i	0.0436436	−	0.226779i
$526$		0			0
$527$	−12.0000	−	20.7846i	−0.522728	−	0.905392i
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	15.0000			0.649722
$534$		0			0
$535$	6.00000	−	10.3923i	0.259403	−	0.449299i
$536$		0			0
$537$	−3.00000	−	5.19615i	−0.129460	−	0.224231i
$538$		0			0
$539$	19.5000	+	7.79423i	0.839924	+	0.335721i
$540$		0			0
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	0.767136	−	0.641484i	$-0.221681\pi$
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	−0.939110	+	0.343617i	$0.888348\pi$
$542$		0			0
$543$	−2.00000	+	3.46410i	−0.0858282	+	0.148659i
$544$		0			0
$545$	4.00000			0.171341
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$		0			0
$549$	2.00000	−	3.46410i	0.0853579	−	0.147844i
$550$		0			0
$551$	3.00000	+	5.19615i	0.127804	+	0.221364i
$552$		0			0
$553$	5.00000	−	25.9808i	0.212622	−	1.10481i
$554$		0			0
$555$	11.0000	+	19.0526i	0.466924	+	0.808736i
$556$		0			0
$557$	13.5000	−	23.3827i	0.572013	−	0.990756i	−0.424346	−	0.905500i	$-0.639496\pi$
$557$	13.5000	−	23.3827i	0.572013	−	0.990756i	0.996359	−	0.0852559i	$-0.0271708\pi$
$558$		0			0
$559$	50.0000			2.11477
$560$		0			0
$561$	−36.0000			−1.51992
$562$		0			0
$563$	−9.00000	+	15.5885i	−0.379305	+	0.656975i	−0.990961	−	0.134148i	$-0.957170\pi$
$563$	−9.00000	+	15.5885i	−0.379305	+	0.656975i	0.611656	+	0.791123i	$0.290503\pi$
$564$		0			0
$565$	6.00000	+	10.3923i	0.252422	+	0.437208i
$566$		0			0
$567$	27.5000	−	9.52628i	1.15489	−	0.400066i
$568$		0			0
$569$	1.50000	+	2.59808i	0.0628833	+	0.108917i	0.895753	−	0.444552i	$-0.146637\pi$
$569$	1.50000	+	2.59808i	0.0628833	+	0.108917i	−0.832870	+	0.553469i	$0.813304\pi$
$570$		0			0
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	−0.577301	−	0.816532i	$-0.695894\pi$
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	0.995788	+	0.0916910i	$0.0292272\pi$
$572$		0			0
$573$	−24.0000			−1.00261
$574$		0			0
$575$	−3.00000			−0.125109
$576$		0			0
$577$	−10.0000	+	17.3205i	−0.416305	+	0.721062i	−0.995565	−	0.0940813i	$-0.970009\pi$
$577$	−10.0000	+	17.3205i	−0.416305	+	0.721062i	0.579259	+	0.815144i	$0.303342\pi$
$578$		0			0
$579$	4.00000	+	6.92820i	0.166234	+	0.287926i
$580$		0			0
$581$	24.0000	+	20.7846i	0.995688	+	0.862291i
$582$		0			0
$583$	4.50000	+	7.79423i	0.186371	+	0.322804i
$584$		0			0
$585$	2.50000	−	4.33013i	0.103362	−	0.179029i
$586$		0			0
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	4.00000			0.164817
$590$		0			0
$591$	3.00000	−	5.19615i	0.123404	−	0.213741i
$592$		0			0
$593$	18.0000	+	31.1769i	0.739171	+	1.28028i	0.952869	+	0.303383i	$0.0981160\pi$
$593$	18.0000	+	31.1769i	0.739171	+	1.28028i	−0.213697	+	0.976900i	$0.568551\pi$
$594$		0			0
$595$	−12.0000	−	10.3923i	−0.491952	−	0.426043i
$596$		0			0
$597$	−4.00000	−	6.92820i	−0.163709	−	0.283552i
$598$		0			0
$599$	21.0000	−	36.3731i	0.858037	−	1.48616i	−0.0157622	−	0.999876i	$-0.505017\pi$
$599$	21.0000	−	36.3731i	0.858037	−	1.48616i	0.873799	−	0.486287i	$-0.161649\pi$
$600$		0			0
$601$	2.00000			0.0815817			0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000			0.0815817			0.0407909	+	0.999168i	$0.487012\pi$
$602$		0			0
$603$	4.00000			0.162893
$604$		0			0
$605$	−1.00000	+	1.73205i	−0.0406558	+	0.0704179i
$606$		0			0
$607$	−9.50000	−	16.4545i	−0.385593	−	0.667867i	0.606258	−	0.795268i	$-0.292670\pi$
$607$	−9.50000	−	16.4545i	−0.385593	−	0.667867i	−0.991851	+	0.127401i	$0.959336\pi$
$608$		0			0
$609$	30.0000	−	10.3923i	1.21566	−	0.421117i
$610$		0			0
$611$	7.50000	+	12.9904i	0.303418	+	0.525535i
$612$		0			0
$613$	−23.5000	+	40.7032i	−0.949156	+	1.64399i	−0.201948	+	0.979396i	$0.564727\pi$
$613$	−23.5000	+	40.7032i	−0.949156	+	1.64399i	−0.747208	+	0.664590i	$0.768606\pi$
$614$		0			0
$615$	−6.00000			−0.241943
$616$		0			0
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$		0			0
$619$	−0.500000	+	0.866025i	−0.0200967	+	0.0348085i	−0.875899	−	0.482495i	$-0.839731\pi$
$619$	−0.500000	+	0.866025i	−0.0200967	+	0.0348085i	0.855802	+	0.517303i	$0.173064\pi$
$620$		0			0
$621$	−6.00000	−	10.3923i	−0.240772	−	0.417029i
$622$		0			0
$623$	3.00000	−	15.5885i	0.120192	−	0.624538i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	3.00000	−	5.19615i	0.119808	−	0.207514i
$628$		0			0
$629$	66.0000			2.63159
$630$		0			0
$631$	−32.0000			−1.27390			−0.636950	−	0.770905i	$-0.719804\pi$
$631$	−32.0000			−1.27390			−0.636950	+	0.770905i	$0.719804\pi$
$632$		0			0
$633$	−1.00000	+	1.73205i	−0.0397464	+	0.0688428i
$634$		0			0
$635$	9.50000	+	16.4545i	0.376996	+	0.652976i
$636$		0			0
$637$	5.00000	+	34.6410i	0.198107	+	1.37253i
$638$		0			0
$639$	6.00000	+	10.3923i	0.237356	+	0.411113i
$640$		0			0
$641$	22.5000	−	38.9711i	0.888697	−	1.53927i	0.0472793	−	0.998882i	$-0.484945\pi$
$641$	22.5000	−	38.9711i	0.888697	−	1.53927i	0.841417	−	0.540386i	$-0.181722\pi$
$642$		0			0
$643$	−38.0000			−1.49857			−0.749287	−	0.662246i	$-0.769604\pi$
$643$	−38.0000			−1.49857			−0.749287	+	0.662246i	$0.769604\pi$
$644$		0			0
$645$	−20.0000			−0.787499
$646$		0			0
$647$	−10.5000	+	18.1865i	−0.412798	+	0.714986i	−0.995194	−	0.0979182i	$-0.968782\pi$
$647$	−10.5000	+	18.1865i	−0.412798	+	0.714986i	0.582397	+	0.812905i	$0.302115\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	4.00000	−	20.7846i	0.156772	−	0.814613i
$652$		0			0
$653$	−10.5000	−	18.1865i	−0.410897	−	0.711694i	0.584091	−	0.811688i	$-0.301451\pi$
$653$	−10.5000	−	18.1865i	−0.410897	−	0.711694i	−0.994988	+	0.0999939i	$0.968118\pi$
$654$		0			0
$655$	−1.50000	+	2.59808i	−0.0586098	+	0.101515i
$656$		0			0
$657$	−4.00000			−0.156055
$658$		0			0
$659$	−24.0000			−0.934907			−0.467454	−	0.884018i	$-0.654829\pi$
$659$	−24.0000			−0.934907			−0.467454	+	0.884018i	$0.654829\pi$
$660$		0			0
$661$	−22.0000	+	38.1051i	−0.855701	+	1.48212i	0.0202925	+	0.999794i	$0.493540\pi$
$661$	−22.0000	+	38.1051i	−0.855701	+	1.48212i	−0.875993	+	0.482323i	$0.839793\pi$
$662$		0			0
$663$	−30.0000	−	51.9615i	−1.16510	−	2.01802i
$664$		0			0
$665$	2.50000	−	0.866025i	0.0969458	−	0.0335830i
$666$		0			0
$667$	−9.00000	−	15.5885i	−0.348481	−	0.603587i
$668$		0			0
$669$	8.00000	−	13.8564i	0.309298	−	0.535720i
$670$		0			0
$671$	12.0000			0.463255
$672$		0			0
$673$	−34.0000			−1.31060			−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000			−1.31060			−0.655302	+	0.755367i	$0.727459\pi$
$674$		0			0
$675$	2.00000	−	3.46410i	0.0769800	−	0.133333i
$676$		0			0
$677$	1.50000	+	2.59808i	0.0576497	+	0.0998522i	0.893410	−	0.449242i	$-0.148306\pi$
$677$	1.50000	+	2.59808i	0.0576497	+	0.0998522i	−0.835760	+	0.549095i	$0.814973\pi$
$678$		0			0
$679$	28.0000	+	24.2487i	1.07454	+	0.930580i
$680$		0			0
$681$	−24.0000	−	41.5692i	−0.919682	−	1.59294i
$682$		0			0
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$		0			0
$687$	−56.0000			−2.13653
$688$		0			0
$689$	−7.50000	+	12.9904i	−0.285727	+	0.494894i
$690$		0			0
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	0.991460	+	0.130410i	$0.0416295\pi$
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	−0.382791	+	0.923835i	$0.625037\pi$
$692$		0			0
$693$	−6.00000	−	5.19615i	−0.227921	−	0.197386i
$694$		0			0
$695$	2.00000	+	3.46410i	0.0758643	+	0.131401i
$696$		0			0
$697$	−9.00000	+	15.5885i	−0.340899	+	0.590455i
$698$		0			0
$699$	−12.0000			−0.453882
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$		0			0
$703$	−5.50000	+	9.52628i	−0.207436	+	0.359290i
$704$		0			0
$705$	−3.00000	−	5.19615i	−0.112987	−	0.195698i
$706$		0			0
$707$	30.0000	−	10.3923i	1.12827	−	0.390843i
$708$		0			0
$709$	−7.00000	−	12.1244i	−0.262891	−	0.455340i	0.704118	−	0.710083i	$-0.251342\pi$
$709$	−7.00000	−	12.1244i	−0.262891	−	0.455340i	−0.967009	+	0.254743i	$0.918009\pi$
$710$		0			0
$711$	−5.00000	+	8.66025i	−0.187515	+	0.324785i
$712$		0			0
$713$	−12.0000			−0.449404
$714$		0			0
$715$	15.0000			0.560968
$716$		0			0
$717$	6.00000	−	10.3923i	0.224074	−	0.388108i
$718$		0			0
$719$	−18.0000	−	31.1769i	−0.671287	−	1.16270i	−0.977539	−	0.210752i	$-0.932409\pi$
$719$	−18.0000	−	31.1769i	−0.671287	−	1.16270i	0.306253	−	0.951950i	$-0.400925\pi$
$720$		0			0
$721$	2.00000	−	10.3923i	0.0744839	−	0.387030i
$722$		0			0
$723$	25.0000	+	43.3013i	0.929760	+	1.61039i
$724$		0			0
$725$	3.00000	−	5.19615i	0.111417	−	0.192980i
$726$		0			0
$727$	−29.0000			−1.07555			−0.537775	−	0.843088i	$-0.680735\pi$
$727$	−29.0000			−1.07555			−0.537775	+	0.843088i	$0.680735\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−30.0000	+	51.9615i	−1.10959	+	1.92187i
$732$		0			0
$733$	−23.5000	−	40.7032i	−0.867992	−	1.50341i	−0.864045	−	0.503415i	$-0.832077\pi$
$733$	−23.5000	−	40.7032i	−0.867992	−	1.50341i	−0.00394730	−	0.999992i	$-0.501256\pi$
$734$		0			0
$735$	−2.00000	−	13.8564i	−0.0737711	−	0.511101i
$736$		0			0
$737$	6.00000	+	10.3923i	0.221013	+	0.382805i
$738$		0			0
$739$	−18.5000	+	32.0429i	−0.680534	+	1.17872i	0.294285	+	0.955718i	$0.404919\pi$
$739$	−18.5000	+	32.0429i	−0.680534	+	1.17872i	−0.974818	+	0.223001i	$0.928415\pi$
$740$		0			0
$741$	10.0000			0.367359
$742$		0			0
$743$	−9.00000			−0.330178			−0.165089	−	0.986279i	$-0.552791\pi$
$743$	−9.00000			−0.330178			−0.165089	+	0.986279i	$0.552791\pi$
$744$		0			0
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$		0			0
$747$	−6.00000	−	10.3923i	−0.219529	−	0.380235i
$748$		0			0
$749$	6.00000	−	31.1769i	0.219235	−	1.13918i
$750$		0			0
$751$	13.0000	+	22.5167i	0.474377	+	0.821645i	0.999570	−	0.0293387i	$-0.00934013\pi$
$751$	13.0000	+	22.5167i	0.474377	+	0.821645i	−0.525193	+	0.850983i	$0.676007\pi$
$752$		0			0
$753$	−15.0000	+	25.9808i	−0.546630	+	0.946792i
$754$		0			0
$755$	14.0000			0.509512
$756$		0			0
$757$	26.0000			0.944986			0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000			0.944986			0.472493	+	0.881334i	$0.343354\pi$
$758$		0			0
$759$	−9.00000	+	15.5885i	−0.326679	+	0.565825i
$760$		0			0
$761$	25.5000	+	44.1673i	0.924374	+	1.60106i	0.792564	+	0.609788i	$0.208745\pi$
$761$	25.5000	+	44.1673i	0.924374	+	1.60106i	0.131810	+	0.991275i	$0.457921\pi$
$762$		0			0
$763$	10.0000	−	3.46410i	0.362024	−	0.125409i
$764$		0			0
$765$	3.00000	+	5.19615i	0.108465	+	0.187867i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−49.0000			−1.76699			−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−49.0000			−1.76699			−0.883493	+	0.468445i	$0.844814\pi$
$770$		0			0
$771$	−24.0000			−0.864339
$772$		0			0
$773$	−19.5000	+	33.7750i	−0.701366	+	1.21480i	0.266621	+	0.963802i	$0.414093\pi$
$773$	−19.5000	+	33.7750i	−0.701366	+	1.21480i	−0.967987	+	0.251000i	$0.919240\pi$
$774$		0			0
$775$	−2.00000	−	3.46410i	−0.0718421	−	0.124434i
$776$		0			0
$777$	44.0000	+	38.1051i	1.57849	+	1.36701i
$778$		0			0
$779$	−1.50000	−	2.59808i	−0.0537431	−	0.0930857i
$780$		0			0
$781$	−18.0000	+	31.1769i	−0.644091	+	1.11560i
$782$		0			0
$783$	24.0000			0.857690
$784$		0			0
$785$	−5.00000			−0.178458
$786$		0			0
$787$	−17.0000	+	29.4449i	−0.605985	+	1.04960i	0.385911	+	0.922536i	$0.373887\pi$
$787$	−17.0000	+	29.4449i	−0.605985	+	1.04960i	−0.991895	+	0.127060i	$0.959446\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	24.0000	+	20.7846i	0.853342	+	0.739016i
$792$		0			0
$793$	10.0000	+	17.3205i	0.355110	+	0.615069i
$794$		0			0
$795$	3.00000	−	5.19615i	0.106399	−	0.184289i
$796$		0			0
$797$	−30.0000			−1.06265			−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000			−1.06265			−0.531327	+	0.847167i	$0.678307\pi$
$798$		0			0
$799$	−18.0000			−0.636794
$800$		0			0
$801$	−3.00000	+	5.19615i	−0.106000	+	0.183597i
$802$		0			0
$803$	−6.00000	−	10.3923i	−0.211735	−	0.366736i
$804$		0			0
$805$	−7.50000	+	2.59808i	−0.264340	+	0.0915702i
$806$		0			0
$807$	12.0000	+	20.7846i	0.422420	+	0.731653i
$808$		0			0
$809$	−19.5000	+	33.7750i	−0.685583	+	1.18747i	0.287670	+	0.957730i	$0.407120\pi$
$809$	−19.5000	+	33.7750i	−0.685583	+	1.18747i	−0.973253	+	0.229736i	$0.926214\pi$
$810$		0			0
$811$	−47.0000			−1.65039			−0.825197	−	0.564846i	$-0.808936\pi$
$811$	−47.0000			−1.65039			−0.825197	+	0.564846i	$0.808936\pi$
$812$		0			0
$813$	32.0000			1.12229
$814$		0			0
$815$	2.00000	−	3.46410i	0.0700569	−	0.121342i
$816$		0			0
$817$	−5.00000	−	8.66025i	−0.174928	−	0.302984i
$818$		0			0
$819$	2.50000	−	12.9904i	0.0873571	−	0.453921i
$820$		0			0
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	0.979246	−	0.202674i	$-0.0649632\pi$
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	−0.665144	+	0.746715i	$0.731630\pi$
$822$		0			0
$823$	22.0000	−	38.1051i	0.766872	−	1.32826i	−0.172379	−	0.985031i	$-0.555146\pi$
$823$	22.0000	−	38.1051i	0.766872	−	1.32826i	0.939251	−	0.343230i	$-0.111521\pi$
$824$		0			0
$825$	−6.00000			−0.208893
$826$		0			0
$827$	54.0000			1.87776			0.938882	−	0.344239i	$-0.111863\pi$
$827$	54.0000			1.87776			0.938882	+	0.344239i	$0.111863\pi$
$828$		0			0
$829$	−7.00000	+	12.1244i	−0.243120	+	0.421096i	−0.961601	−	0.274450i	$-0.911504\pi$
$829$	−7.00000	+	12.1244i	−0.243120	+	0.421096i	0.718481	+	0.695546i	$0.244838\pi$
$830$		0			0
$831$	−2.00000	−	3.46410i	−0.0693792	−	0.120168i
$832$		0			0
$833$	−39.0000	−	15.5885i	−1.35127	−	0.540108i
$834$		0			0
$835$	−4.50000	−	7.79423i	−0.155729	−	0.269730i
$836$		0			0
$837$	8.00000	−	13.8564i	0.276520	−	0.478947i
$838$		0			0
$839$	6.00000			0.207143			0.103572	−	0.994622i	$-0.466973\pi$
$839$	6.00000			0.207143			0.103572	+	0.994622i	$0.466973\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	3.00000	−	5.19615i	0.103325	−	0.178965i
$844$		0			0
$845$	6.00000	+	10.3923i	0.206406	+	0.357506i
$846$		0			0
$847$	−1.00000	+	5.19615i	−0.0343604	+	0.178542i
$848$		0			0
$849$	26.0000	+	45.0333i	0.892318	+	1.54554i
$850$		0			0
$851$	16.5000	−	28.5788i	0.565613	−	0.979670i
$852$		0			0
$853$	−1.00000			−0.0342393			−0.0171197	−	0.999853i	$-0.505450\pi$
$853$	−1.00000			−0.0342393			−0.0171197	+	0.999853i	$0.505450\pi$
$854$		0			0
$855$	−1.00000			−0.0341993
$856$		0			0
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	−0.670366	−	0.742030i	$-0.733863\pi$
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	0.977800	+	0.209539i	$0.0671963\pi$
$858$		0			0
$859$	16.0000	+	27.7128i	0.545913	+	0.945549i	0.998549	+	0.0538535i	$0.0171504\pi$
$859$	16.0000	+	27.7128i	0.545913	+	0.945549i	−0.452636	+	0.891695i	$0.649516\pi$
$860$		0			0
$861$	−15.0000	+	5.19615i	−0.511199	+	0.177084i
$862$		0			0
$863$	19.5000	+	33.7750i	0.663788	+	1.14971i	0.979612	+	0.200897i	$0.0643855\pi$
$863$	19.5000	+	33.7750i	0.663788	+	1.14971i	−0.315825	+	0.948818i	$0.602281\pi$
$864$		0			0
$865$	1.50000	−	2.59808i	0.0510015	−	0.0883372i
$866$		0			0
$867$	38.0000			1.29055
$868$		0			0
$869$	−30.0000			−1.01768
$870$		0			0
$871$	−10.0000	+	17.3205i	−0.338837	+	0.586883i
$872$		0			0
$873$	−7.00000	−	12.1244i	−0.236914	−	0.410347i
$874$		0			0
$875$	−2.00000	−	1.73205i	−0.0676123	−	0.0585540i
$876$		0			0
$877$	3.50000	+	6.06218i	0.118187	+	0.204705i	0.919049	−	0.394143i	$-0.128959\pi$
$877$	3.50000	+	6.06218i	0.118187	+	0.204705i	−0.800862	+	0.598848i	$0.795625\pi$
$878$		0			0
$879$	27.0000	−	46.7654i	0.910687	−	1.57736i
$880$		0			0
$881$	33.0000			1.11180			0.555899	−	0.831250i	$-0.312374\pi$
$881$	33.0000			1.11180			0.555899	+	0.831250i	$0.312374\pi$
$882$		0			0
$883$	−8.00000			−0.269221			−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000			−0.269221			−0.134611	+	0.990899i	$0.542978\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	0.994077	−	0.108678i	$-0.0346618\pi$
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	−0.591156	+	0.806557i	$0.701328\pi$
$888$		0			0
$889$	38.0000	+	32.9090i	1.27448	+	1.10373i
$890$		0			0
$891$	−16.5000	−	28.5788i	−0.552771	−	0.957427i
$892$		0			0
$893$	1.50000	−	2.59808i	0.0501956	−	0.0869413i
$894$		0			0
$895$	−3.00000			−0.100279
$896$		0			0
$897$	−30.0000			−1.00167
$898$		0			0
$899$	12.0000	−	20.7846i	0.400222	−	0.693206i
$900$		0			0
$901$	−9.00000	−	15.5885i	−0.299833	−	0.519327i
$902$		0			0
$903$	−50.0000	+	17.3205i	−1.66390	+	0.576390i
$904$		0			0
$905$	1.00000	+	1.73205i	0.0332411	+	0.0575753i
$906$		0			0
$907$	−5.00000	+	8.66025i	−0.166022	+	0.287559i	−0.937018	−	0.349281i	$-0.886426\pi$
$907$	−5.00000	+	8.66025i	−0.166022	+	0.287559i	0.770996	+	0.636841i	$0.219759\pi$
$908$		0			0
$909$	−12.0000			−0.398015
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$		0			0
$913$	18.0000	−	31.1769i	0.595713	−	1.03181i
$914$		0			0
$915$	−4.00000	−	6.92820i	−0.132236	−	0.229039i
$916$		0			0
$917$	−1.50000	+	7.79423i	−0.0495344	+	0.257388i
$918$		0			0
$919$	19.0000	+	32.9090i	0.626752	+	1.08557i	0.988199	+	0.153174i	$0.0489495\pi$
$919$	19.0000	+	32.9090i	0.626752	+	1.08557i	−0.361447	+	0.932393i	$0.617717\pi$
$920$		0			0
$921$	2.00000	−	3.46410i	0.0659022	−	0.114146i
$922$		0			0
$923$	−60.0000			−1.97492
$924$		0			0
$925$	11.0000			0.361678
$926$		0			0
$927$	−2.00000	+	3.46410i	−0.0656886	+	0.113776i
$928$		0			0
$929$	−16.5000	−	28.5788i	−0.541347	−	0.937641i	−0.998827	−	0.0484211i	$-0.984581\pi$
$929$	−16.5000	−	28.5788i	−0.541347	−	0.937641i	0.457480	−	0.889220i	$-0.348752\pi$
$930$		0			0
$931$	5.50000	−	4.33013i	0.180255	−	0.141914i
$932$		0			0
$933$	12.0000	+	20.7846i	0.392862	+	0.680458i
$934$		0			0
$935$	−9.00000	+	15.5885i	−0.294331	+	0.509797i
$936$		0			0
$937$	2.00000			0.0653372			0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000			0.0653372			0.0326686	+	0.999466i	$0.489599\pi$
$938$		0			0
$939$	16.0000			0.522140
$940$		0			0
$941$	−12.0000	+	20.7846i	−0.391189	+	0.677559i	−0.992607	−	0.121376i	$-0.961269\pi$
$941$	−12.0000	+	20.7846i	−0.391189	+	0.677559i	0.601418	+	0.798935i	$0.294603\pi$
$942$		0			0
$943$	4.50000	+	7.79423i	0.146540	+	0.253815i
$944$		0			0
$945$	2.00000	−	10.3923i	0.0650600	−	0.338062i
$946$		0			0
$947$	15.0000	+	25.9808i	0.487435	+	0.844261i	0.999896	−	0.0144491i	$-0.00459946\pi$
$947$	15.0000	+	25.9808i	0.487435	+	0.844261i	−0.512461	+	0.858710i	$0.671266\pi$
$948$		0			0
$949$	10.0000	−	17.3205i	0.324614	−	0.562247i
$950$		0			0
$951$	36.0000			1.16738
$952$		0			0
$953$	−12.0000			−0.388718			−0.194359	−	0.980930i	$-0.562263\pi$
$953$	−12.0000			−0.388718			−0.194359	+	0.980930i	$0.562263\pi$
$954$		0			0
$955$	−6.00000	+	10.3923i	−0.194155	+	0.336287i
$956$		0			0
$957$	−18.0000	−	31.1769i	−0.581857	−	1.00781i
$958$		0			0
$959$	−30.0000	+	10.3923i	−0.968751	+	0.335585i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$	−6.00000	+	10.3923i	−0.193347	+	0.334887i
$964$		0			0
$965$	4.00000			0.128765
$966$		0			0
$967$	−32.0000			−1.02905			−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000			−1.02905			−0.514525	+	0.857475i	$0.672032\pi$
$968$		0			0
$969$	−6.00000	+	10.3923i	−0.192748	+	0.333849i
$970$		0			0
$971$	13.5000	+	23.3827i	0.433236	+	0.750386i	0.997150	−	0.0754473i	$-0.0240385\pi$
$971$	13.5000	+	23.3827i	0.433236	+	0.750386i	−0.563914	+	0.825833i	$0.690705\pi$
$972$		0			0
$973$	8.00000	+	6.92820i	0.256468	+	0.222108i
$974$		0			0
$975$	−5.00000	−	8.66025i	−0.160128	−	0.277350i
$976$		0			0
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	−0.519841	−	0.854263i	$-0.674009\pi$
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	0.999734	+	0.0230645i	$0.00734232\pi$
$978$		0			0
$979$	−18.0000			−0.575282
$980$		0			0
$981$	−4.00000			−0.127710
$982$		0			0
$983$	28.5000	−	49.3634i	0.909009	−	1.57445i	0.0935651	−	0.995613i	$-0.470174\pi$
$983$	28.5000	−	49.3634i	0.909009	−	1.57445i	0.815444	−	0.578836i	$-0.196493\pi$
$984$		0			0
$985$	−1.50000	−	2.59808i	−0.0477940	−	0.0827816i
$986$		0			0
$987$	−12.0000	−	10.3923i	−0.381964	−	0.330791i
$988$		0			0
$989$	15.0000	+	25.9808i	0.476972	+	0.826140i
$990$		0			0
$991$	10.0000	−	17.3205i	0.317660	−	0.550204i	−0.662339	−	0.749204i	$-0.730436\pi$
$991$	10.0000	−	17.3205i	0.317660	−	0.550204i	0.979999	+	0.199000i	$0.0637695\pi$
$992$		0			0
$993$	14.0000			0.444277
$994$		0			0
$995$	−4.00000			−0.126809
$996$		0			0
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	−0.955322	−	0.295567i	$-0.904491\pi$
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	0.733630	+	0.679549i	$0.237825\pi$
$998$		0			0
$999$	22.0000	+	38.1051i	0.696049	+	1.20559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.q.d.81.1		2
4.3	odd	2		70.2.e.b.11.1	✓	2
7.2	even	3	inner	560.2.q.d.401.1		2
7.3	odd	6		3920.2.a.g.1.1		1
7.4	even	3		3920.2.a.be.1.1		1
12.11	even	2		630.2.k.e.361.1		2
20.3	even	4		350.2.j.a.249.1		4
20.7	even	4		350.2.j.a.249.2		4
20.19	odd	2		350.2.e.h.151.1		2
28.3	even	6		490.2.a.j.1.1		1
28.11	odd	6		490.2.a.g.1.1		1
28.19	even	6		490.2.e.a.471.1		2
28.23	odd	6		70.2.e.b.51.1	yes	2
28.27	even	2		490.2.e.a.361.1		2
84.11	even	6		4410.2.a.m.1.1		1
84.23	even	6		630.2.k.e.541.1		2
84.59	odd	6		4410.2.a.c.1.1		1
140.3	odd	12		2450.2.c.p.99.1		2
140.23	even	12		350.2.j.a.149.2		4
140.39	odd	6		2450.2.a.p.1.1		1
140.59	even	6		2450.2.a.f.1.1		1
140.67	even	12		2450.2.c.f.99.2		2
140.79	odd	6		350.2.e.h.51.1		2
140.87	odd	12		2450.2.c.p.99.2		2
140.107	even	12		350.2.j.a.149.1		4
140.123	even	12		2450.2.c.f.99.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.e.b.11.1	✓	2	4.3	odd	2
70.2.e.b.51.1	yes	2	28.23	odd	6
350.2.e.h.51.1		2	140.79	odd	6
350.2.e.h.151.1		2	20.19	odd	2
350.2.j.a.149.1		4	140.107	even	12
350.2.j.a.149.2		4	140.23	even	12
350.2.j.a.249.1		4	20.3	even	4
350.2.j.a.249.2		4	20.7	even	4
490.2.a.g.1.1		1	28.11	odd	6
490.2.a.j.1.1		1	28.3	even	6
490.2.e.a.361.1		2	28.27	even	2
490.2.e.a.471.1		2	28.19	even	6
560.2.q.d.81.1		2	1.1	even	1	trivial
560.2.q.d.401.1		2	7.2	even	3	inner
630.2.k.e.361.1		2	12.11	even	2
630.2.k.e.541.1		2	84.23	even	6
2450.2.a.f.1.1		1	140.59	even	6
2450.2.a.p.1.1		1	140.39	odd	6
2450.2.c.f.99.1		2	140.123	even	12
2450.2.c.f.99.2		2	140.67	even	12
2450.2.c.p.99.1		2	140.3	odd	12
2450.2.c.p.99.2		2	140.87	odd	12
3920.2.a.g.1.1		1	7.3	odd	6
3920.2.a.be.1.1		1	7.4	even	3
4410.2.a.c.1.1		1	84.59	odd	6
4410.2.a.m.1.1		1	84.11	even	6

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.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{11} +5.00000 q^{13} -2.00000 q^{15} +(-3.00000 + 5.19615i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(-5.00000 + 1.73205i) q^{21} +(1.50000 + 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.00000 q^{27} -6.00000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(3.00000 + 5.19615i) q^{33} +(-0.500000 + 2.59808i) q^{35} +(-5.50000 - 9.52628i) q^{37} +(-5.00000 + 8.66025i) q^{39} +3.00000 q^{41} +10.0000 q^{43} +(0.500000 - 0.866025i) q^{45} +(1.50000 + 2.59808i) q^{47} +(1.00000 + 6.92820i) q^{49} +(-6.00000 - 10.3923i) q^{51} +(-1.50000 + 2.59808i) q^{53} +3.00000 q^{55} +2.00000 q^{57} +(2.00000 + 3.46410i) q^{61} +(0.500000 - 2.59808i) q^{63} +(2.50000 + 4.33013i) q^{65} +(-2.00000 + 3.46410i) q^{67} -6.00000 q^{69} -12.0000 q^{71} +(2.00000 - 3.46410i) q^{73} +(-1.00000 - 1.73205i) q^{75} +(7.50000 - 2.59808i) q^{77} +(-5.00000 - 8.66025i) q^{79} +(5.50000 - 9.52628i) q^{81} +12.0000 q^{83} -6.00000 q^{85} +(6.00000 - 10.3923i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(10.0000 + 8.66025i) q^{91} +(-4.00000 - 6.92820i) q^{93} +(0.500000 - 0.866025i) q^{95} +14.0000 q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + q^{5} + 4 q^{7} - q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 + q^5 + 4 * q^7 - q^9	\( 2 q - 2 q^{3} + q^{5} + 4 q^{7} - q^{9} + 3 q^{11} + 10 q^{13} - 4 q^{15} - 6 q^{17} - q^{19} - 10 q^{21} + 3 q^{23} - q^{25} - 8 q^{27} - 12 q^{29} - 4 q^{31} + 6 q^{33} - q^{35} - 11 q^{37} - 10 q^{39} + 6 q^{41} + 20 q^{43} + q^{45} + 3 q^{47} + 2 q^{49} - 12 q^{51} - 3 q^{53} + 6 q^{55} + 4 q^{57} + 4 q^{61} + q^{63} + 5 q^{65} - 4 q^{67} - 12 q^{69} - 24 q^{71} + 4 q^{73} - 2 q^{75} + 15 q^{77} - 10 q^{79} + 11 q^{81} + 24 q^{83} - 12 q^{85} + 12 q^{87} - 6 q^{89} + 20 q^{91} - 8 q^{93} + q^{95} + 28 q^{97} - 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 + q^5 + 4 * q^7 - q^9 + 3 * q^11 + 10 * q^13 - 4 * q^15 - 6 * q^17 - q^19 - 10 * q^21 + 3 * q^23 - q^25 - 8 * q^27 - 12 * q^29 - 4 * q^31 + 6 * q^33 - q^35 - 11 * q^37 - 10 * q^39 + 6 * q^41 + 20 * q^43 + q^45 + 3 * q^47 + 2 * q^49 - 12 * q^51 - 3 * q^53 + 6 * q^55 + 4 * q^57 + 4 * q^61 + q^63 + 5 * q^65 - 4 * q^67 - 12 * q^69 - 24 * q^71 + 4 * q^73 - 2 * q^75 + 15 * q^77 - 10 * q^79 + 11 * q^81 + 24 * q^83 - 12 * q^85 + 12 * q^87 - 6 * q^89 + 20 * q^91 - 8 * q^93 + q^95 + 28 * q^97 - 6 * q^99

Introduction

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