LMFDB - Embedded newform 1560.2.bg.g.601.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1560.601");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1560.bg (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.4566627153$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			601.2
Root			$-1.63746 - 1.52274i$ of defining polynomial
Character	$\chi$	$=$	1560.601
Dual form			1560.2.bg.g.841.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(2.13746 + 3.70219i) q^{11} +(2.50000 + 2.59808i) q^{13} +(0.500000 + 0.866025i) q^{15} +(1.13746 - 1.97014i) q^{19} -1.00000 q^{21} +(-3.27492 - 5.67232i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(5.27492 + 9.13642i) q^{29} -7.27492 q^{31} +(-2.13746 + 3.70219i) q^{33} +(-0.500000 + 0.866025i) q^{35} +(-0.137459 - 0.238085i) q^{37} +(-1.00000 + 3.46410i) q^{39} +(-4.27492 - 7.40437i) q^{41} +(-3.63746 + 6.30026i) q^{43} +(-0.500000 + 0.866025i) q^{45} +4.27492 q^{47} +(3.00000 + 5.19615i) q^{49} +1.72508 q^{53} +(2.13746 + 3.70219i) q^{55} +2.27492 q^{57} +(-7.27492 + 12.6005i) q^{59} +(1.63746 - 2.83616i) q^{61} +(-0.500000 - 0.866025i) q^{63} +(2.50000 + 2.59808i) q^{65} +(2.63746 + 4.56821i) q^{67} +(3.27492 - 5.67232i) q^{69} +(1.00000 - 1.73205i) q^{71} +11.8248 q^{73} +(0.500000 + 0.866025i) q^{75} -4.27492 q^{77} -0.725083 q^{79} +(-0.500000 - 0.866025i) q^{81} +17.0997 q^{83} +(-5.27492 + 9.13642i) q^{87} +(2.86254 + 4.95807i) q^{89} +(-3.50000 + 0.866025i) q^{91} +(-3.63746 - 6.30026i) q^{93} +(1.13746 - 1.97014i) q^{95} +(-3.91238 + 6.77643i) q^{97} -4.27492 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 4 q^{5} - 2 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 4 * q^5 - 2 * q^7 - 2 * q^9	$ 4 q + 2 q^{3} + 4 q^{5} - 2 q^{7} - 2 q^{9} + q^{11} + 10 q^{13} + 2 q^{15} - 3 q^{19} - 4 q^{21} + 2 q^{23} + 4 q^{25} - 4 q^{27} + 6 q^{29} - 14 q^{31} - q^{33} - 2 q^{35} + 7 q^{37} - 4 q^{39} - 2 q^{41} - 7 q^{43} - 2 q^{45} + 2 q^{47} + 12 q^{49} + 22 q^{53} + q^{55} - 6 q^{57} - 14 q^{59} - q^{61} - 2 q^{63} + 10 q^{65} + 3 q^{67} - 2 q^{69} + 4 q^{71} + 2 q^{73} + 2 q^{75} - 2 q^{77} - 18 q^{79} - 2 q^{81} + 8 q^{83} - 6 q^{87} + 19 q^{89} - 14 q^{91} - 7 q^{93} - 3 q^{95} + 7 q^{97} - 2 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 4 * q^5 - 2 * q^7 - 2 * q^9 + q^11 + 10 * q^13 + 2 * q^15 - 3 * q^19 - 4 * q^21 + 2 * q^23 + 4 * q^25 - 4 * q^27 + 6 * q^29 - 14 * q^31 - q^33 - 2 * q^35 + 7 * q^37 - 4 * q^39 - 2 * q^41 - 7 * q^43 - 2 * q^45 + 2 * q^47 + 12 * q^49 + 22 * q^53 + q^55 - 6 * q^57 - 14 * q^59 - q^61 - 2 * q^63 + 10 * q^65 + 3 * q^67 - 2 * q^69 + 4 * q^71 + 2 * q^73 + 2 * q^75 - 2 * q^77 - 18 * q^79 - 2 * q^81 + 8 * q^83 - 6 * q^87 + 19 * q^89 - 14 * q^91 - 7 * q^93 - 3 * q^95 + 7 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i	0.755929	+	0.654654i	$0.227186\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	2.13746	+	3.70219i	0.644468	+	1.11625i	0.984424	+	0.175810i	$0.0562545\pi$
$11$	2.13746	+	3.70219i	0.644468	+	1.11625i	−0.339956	+	0.940441i	$0.610412\pi$
$12$		0			0
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$14$		0			0
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$		0			0
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	1.13746	−	1.97014i	0.260951	−	0.451980i	−0.705544	−	0.708666i	$-0.749297\pi$
$19$	1.13746	−	1.97014i	0.260951	−	0.451980i	0.966495	+	0.256686i	$0.0826306\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$		0			0
$23$	−3.27492	−	5.67232i	−0.682867	−	1.18276i	−0.974102	−	0.226109i	$-0.927399\pi$
$23$	−3.27492	−	5.67232i	−0.682867	−	1.18276i	0.291234	−	0.956652i	$-0.405934\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	5.27492	+	9.13642i	0.979528	+	1.69659i	0.664104	+	0.747641i	$0.268813\pi$
$29$	5.27492	+	9.13642i	0.979528	+	1.69659i	0.315424	+	0.948951i	$0.397853\pi$
$30$		0			0
$31$	−7.27492			−1.30661			−0.653307	−	0.757093i	$-0.726619\pi$
$31$	−7.27492			−1.30661			−0.653307	+	0.757093i	$0.726619\pi$
$32$		0			0
$33$	−2.13746	+	3.70219i	−0.372084	+	0.644468i
$34$		0			0
$35$	−0.500000	+	0.866025i	−0.0845154	+	0.146385i
$36$		0			0
$37$	−0.137459	−	0.238085i	−0.0225981	−	0.0391410i	0.854505	−	0.519443i	$-0.173860\pi$
$37$	−0.137459	−	0.238085i	−0.0225981	−	0.0391410i	−0.877103	+	0.480302i	$0.840527\pi$
$38$		0			0
$39$	−1.00000	+	3.46410i	−0.160128	+	0.554700i
$40$		0			0
$41$	−4.27492	−	7.40437i	−0.667630	−	1.15637i	−0.978565	−	0.205938i	$-0.933976\pi$
$41$	−4.27492	−	7.40437i	−0.667630	−	1.15637i	0.310935	−	0.950431i	$-0.399358\pi$
$42$		0			0
$43$	−3.63746	+	6.30026i	−0.554707	+	0.960781i	0.443219	+	0.896413i	$0.353836\pi$
$43$	−3.63746	+	6.30026i	−0.554707	+	0.960781i	−0.997926	+	0.0643678i	$0.979497\pi$
$44$		0			0
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$		0			0
$47$	4.27492			0.623561			0.311780	−	0.950154i	$-0.399075\pi$
$47$	4.27492			0.623561			0.311780	+	0.950154i	$0.399075\pi$
$48$		0			0
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.72508			0.236958			0.118479	−	0.992957i	$-0.462198\pi$
$53$	1.72508			0.236958			0.118479	+	0.992957i	$0.462198\pi$
$54$		0			0
$55$	2.13746	+	3.70219i	0.288215	+	0.499203i
$56$		0			0
$57$	2.27492			0.301320
$58$		0			0
$59$	−7.27492	+	12.6005i	−0.947114	+	1.64045i	−0.195650	+	0.980674i	$0.562682\pi$
$59$	−7.27492	+	12.6005i	−0.947114	+	1.64045i	−0.751463	+	0.659775i	$0.770652\pi$
$60$		0			0
$61$	1.63746	−	2.83616i	0.209655	−	0.363133i	−0.741951	−	0.670454i	$-0.766099\pi$
$61$	1.63746	−	2.83616i	0.209655	−	0.363133i	0.951606	+	0.307321i	$0.0994326\pi$
$62$		0			0
$63$	−0.500000	−	0.866025i	−0.0629941	−	0.109109i
$64$		0			0
$65$	2.50000	+	2.59808i	0.310087	+	0.322252i
$66$		0			0
$67$	2.63746	+	4.56821i	0.322217	+	0.558096i	0.980945	−	0.194285i	$-0.0622386\pi$
$67$	2.63746	+	4.56821i	0.322217	+	0.558096i	−0.658728	+	0.752381i	$0.728905\pi$
$68$		0			0
$69$	3.27492	−	5.67232i	0.394254	−	0.682867i
$70$		0			0
$71$	1.00000	−	1.73205i	0.118678	−	0.205557i	−0.800566	−	0.599245i	$-0.795468\pi$
$71$	1.00000	−	1.73205i	0.118678	−	0.205557i	0.919244	+	0.393688i	$0.128801\pi$
$72$		0			0
$73$	11.8248			1.38398			0.691991	−	0.721906i	$-0.256734\pi$
$73$	11.8248			1.38398			0.691991	+	0.721906i	$0.256734\pi$
$74$		0			0
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$		0			0
$77$	−4.27492			−0.487172
$78$		0			0
$79$	−0.725083			−0.0815782			−0.0407891	−	0.999168i	$-0.512987\pi$
$79$	−0.725083			−0.0815782			−0.0407891	+	0.999168i	$0.512987\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	17.0997			1.87693			0.938466	−	0.345371i	$-0.112247\pi$
$83$	17.0997			1.87693			0.938466	+	0.345371i	$0.112247\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−5.27492	+	9.13642i	−0.565530	+	0.979528i
$88$		0			0
$89$	2.86254	+	4.95807i	0.303429	+	0.525554i	0.976910	−	0.213650i	$-0.0685352\pi$
$89$	2.86254	+	4.95807i	0.303429	+	0.525554i	−0.673481	+	0.739204i	$0.735202\pi$
$90$		0			0
$91$	−3.50000	+	0.866025i	−0.366900	+	0.0907841i
$92$		0			0
$93$	−3.63746	−	6.30026i	−0.377187	−	0.653307i
$94$		0			0
$95$	1.13746	−	1.97014i	0.116701	−	0.202132i
$96$		0			0
$97$	−3.91238	+	6.77643i	−0.397242	+	0.688043i	−0.993384	−	0.114836i	$-0.963366\pi$
$97$	−3.91238	+	6.77643i	−0.397242	+	0.688043i	0.596143	+	0.802878i	$0.296699\pi$
$98$		0			0
$99$	−4.27492			−0.429645
$100$		0			0
$101$	3.27492	+	5.67232i	0.325866	+	0.564417i	0.981687	−	0.190499i	$-0.0610107\pi$
$101$	3.27492	+	5.67232i	0.325866	+	0.564417i	−0.655821	+	0.754917i	$0.727677\pi$
$102$		0			0
$103$	−15.5498			−1.53217			−0.766085	−	0.642739i	$-0.777798\pi$
$103$	−15.5498			−1.53217			−0.766085	+	0.642739i	$0.777798\pi$
$104$		0			0
$105$	−1.00000			−0.0975900
$106$		0			0
$107$	−7.54983	−	13.0767i	−0.729870	−	1.26417i	−0.956938	−	0.290293i	$-0.906247\pi$
$107$	−7.54983	−	13.0767i	−0.729870	−	1.26417i	0.227068	−	0.973879i	$-0.427086\pi$
$108$		0			0
$109$	−13.8248			−1.32417			−0.662086	−	0.749428i	$-0.730328\pi$
$109$	−13.8248			−1.32417			−0.662086	+	0.749428i	$0.730328\pi$
$110$		0			0
$111$	0.137459	−	0.238085i	0.0130470	−	0.0225981i
$112$		0			0
$113$	2.72508	−	4.71998i	0.256354	−	0.444019i	−0.708908	−	0.705301i	$-0.750812\pi$
$113$	2.72508	−	4.71998i	0.256354	−	0.444019i	0.965262	+	0.261282i	$0.0841453\pi$
$114$		0			0
$115$	−3.27492	−	5.67232i	−0.305388	−	0.528947i
$116$		0			0
$117$	−3.50000	+	0.866025i	−0.323575	+	0.0800641i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−3.63746	+	6.30026i	−0.330678	+	0.572751i
$122$		0			0
$123$	4.27492	−	7.40437i	0.385456	−	0.667630i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−0.500000	−	0.866025i	−0.0443678	−	0.0768473i	0.842989	−	0.537931i	$-0.180794\pi$
$127$	−0.500000	−	0.866025i	−0.0443678	−	0.0768473i	−0.887357	+	0.461084i	$0.847461\pi$
$128$		0			0
$129$	−7.27492			−0.640521
$130$		0			0
$131$	3.72508			0.325462			0.162731	−	0.986670i	$-0.447970\pi$
$131$	3.72508			0.325462			0.162731	+	0.986670i	$0.447970\pi$
$132$		0			0
$133$	1.13746	+	1.97014i	0.0986302	+	0.170832i
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	10.5498	−	18.2728i	0.901333	−	1.56115i	0.0755681	−	0.997141i	$-0.475923\pi$
$137$	10.5498	−	18.2728i	0.901333	−	1.56115i	0.825765	−	0.564014i	$-0.190744\pi$
$138$		0			0
$139$	−5.50000	+	9.52628i	−0.466504	+	0.808008i	−0.999268	−	0.0382553i	$-0.987820\pi$
$139$	−5.50000	+	9.52628i	−0.466504	+	0.808008i	0.532764	+	0.846264i	$0.321153\pi$
$140$		0			0
$141$	2.13746	+	3.70219i	0.180006	+	0.311780i
$142$		0			0
$143$	−4.27492	+	14.8087i	−0.357487	+	1.23837i
$144$		0			0
$145$	5.27492	+	9.13642i	0.438058	+	0.758739i
$146$		0			0
$147$	−3.00000	+	5.19615i	−0.247436	+	0.428571i
$148$		0			0
$149$	8.27492	−	14.3326i	0.677908	−	1.17417i	−0.297702	−	0.954659i	$-0.596220\pi$
$149$	8.27492	−	14.3326i	0.677908	−	1.17417i	0.975610	−	0.219512i	$-0.0704464\pi$
$150$		0			0
$151$	−3.45017			−0.280770			−0.140385	−	0.990097i	$-0.544834\pi$
$151$	−3.45017			−0.280770			−0.140385	+	0.990097i	$0.544834\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−7.27492			−0.584335
$156$		0			0
$157$	11.5498			0.921777			0.460889	−	0.887458i	$-0.347531\pi$
$157$	11.5498			0.921777			0.460889	+	0.887458i	$0.347531\pi$
$158$		0			0
$159$	0.862541	+	1.49397i	0.0684040	+	0.118479i
$160$		0			0
$161$	6.54983			0.516199
$162$		0			0
$163$	−1.36254	+	2.35999i	−0.106722	+	0.184849i	−0.914441	−	0.404720i	$-0.867369\pi$
$163$	−1.36254	+	2.35999i	−0.106722	+	0.184849i	0.807718	+	0.589569i	$0.200702\pi$
$164$		0			0
$165$	−2.13746	+	3.70219i	−0.166401	+	0.288215i
$166$		0			0
$167$	5.13746	+	8.89834i	0.397548	+	0.688574i	0.993423	−	0.114503i	$-0.0365277\pi$
$167$	5.13746	+	8.89834i	0.397548	+	0.688574i	−0.595874	+	0.803078i	$0.703194\pi$
$168$		0			0
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$		0			0
$171$	1.13746	+	1.97014i	0.0869836	+	0.150660i
$172$		0			0
$173$	7.86254	−	13.6183i	0.597778	−	1.03538i	−0.395370	−	0.918522i	$-0.629384\pi$
$173$	7.86254	−	13.6183i	0.597778	−	1.03538i	0.993148	−	0.116860i	$-0.0372829\pi$
$174$		0			0
$175$	−0.500000	+	0.866025i	−0.0377964	+	0.0654654i
$176$		0			0
$177$	−14.5498			−1.09363
$178$		0			0
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	0.998286	−	0.0585225i	$-0.0186389\pi$
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	−0.549825	+	0.835280i	$0.685306\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$	3.27492			0.242089
$184$		0			0
$185$	−0.137459	−	0.238085i	−0.0101062	−	0.0175044i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	0.500000	−	0.866025i	0.0363696	−	0.0629941i
$190$		0			0
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	−0.331611	−	0.943416i	$-0.607592\pi$
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	0.982828	−	0.184525i	$-0.0590746\pi$
$192$		0			0
$193$	−7.18729	−	12.4488i	−0.517353	−	0.896081i	−0.999797	−	0.0201544i	$-0.993584\pi$
$193$	−7.18729	−	12.4488i	−0.517353	−	0.896081i	0.482444	−	0.875927i	$-0.339749\pi$
$194$		0			0
$195$	−1.00000	+	3.46410i	−0.0716115	+	0.248069i
$196$		0			0
$197$	1.41238	+	2.44631i	0.100628	+	0.174292i	0.911943	−	0.410316i	$-0.134582\pi$
$197$	1.41238	+	2.44631i	0.100628	+	0.174292i	−0.811316	+	0.584608i	$0.801248\pi$
$198$		0			0
$199$	−2.36254	+	4.09204i	−0.167476	+	0.290077i	−0.937532	−	0.347899i	$-0.886895\pi$
$199$	−2.36254	+	4.09204i	−0.167476	+	0.290077i	0.770056	+	0.637977i	$0.220228\pi$
$200$		0			0
$201$	−2.63746	+	4.56821i	−0.186032	+	0.322217i
$202$		0			0
$203$	−10.5498			−0.740453
$204$		0			0
$205$	−4.27492	−	7.40437i	−0.298573	−	0.517144i
$206$		0			0
$207$	6.54983			0.455245
$208$		0			0
$209$	9.72508			0.672698
$210$		0			0
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	0.767049	−	0.641588i	$-0.221724\pi$
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	−0.939156	+	0.343490i	$0.888391\pi$
$212$		0			0
$213$	2.00000			0.137038
$214$		0			0
$215$	−3.63746	+	6.30026i	−0.248073	+	0.429674i
$216$		0			0
$217$	3.63746	−	6.30026i	0.246927	−	0.427690i
$218$		0			0
$219$	5.91238	+	10.2405i	0.399521	+	0.691991i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−13.4124	−	23.2309i	−0.898159	−	1.55566i	−0.829845	−	0.557993i	$-0.811571\pi$
$223$	−13.4124	−	23.2309i	−0.898159	−	1.55566i	−0.0683137	−	0.997664i	$-0.521762\pi$
$224$		0			0
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$		0			0
$227$	−4.54983	+	7.88054i	−0.301983	+	0.523050i	−0.976585	−	0.215132i	$-0.930982\pi$
$227$	−4.54983	+	7.88054i	−0.301983	+	0.523050i	0.674602	+	0.738182i	$0.264315\pi$
$228$		0			0
$229$	−10.0000			−0.660819			−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000			−0.660819			−0.330409	+	0.943838i	$0.607187\pi$
$230$		0			0
$231$	−2.13746	−	3.70219i	−0.140634	−	0.243586i
$232$		0			0
$233$	23.0997			1.51331			0.756655	−	0.653815i	$-0.226832\pi$
$233$	23.0997			1.51331			0.756655	+	0.653815i	$0.226832\pi$
$234$		0			0
$235$	4.27492			0.278865
$236$		0			0
$237$	−0.362541	−	0.627940i	−0.0235496	−	0.0407891i
$238$		0			0
$239$	−4.54983			−0.294304			−0.147152	−	0.989114i	$-0.547011\pi$
$239$	−4.54983			−0.294304			−0.147152	+	0.989114i	$0.547011\pi$
$240$		0			0
$241$	−4.13746	+	7.16629i	−0.266517	+	0.461621i	−0.967960	−	0.251104i	$-0.919206\pi$
$241$	−4.13746	+	7.16629i	−0.266517	+	0.461621i	0.701443	+	0.712726i	$0.252540\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	3.00000	+	5.19615i	0.191663	+	0.331970i
$246$		0			0
$247$	7.96221	−	1.97014i	0.506623	−	0.125357i
$248$		0			0
$249$	8.54983	+	14.8087i	0.541824	+	0.938466i
$250$		0			0
$251$	13.1375	−	22.7547i	0.829229	−	1.43627i	−0.0694148	−	0.997588i	$-0.522113\pi$
$251$	13.1375	−	22.7547i	0.829229	−	1.43627i	0.898644	−	0.438679i	$-0.144553\pi$
$252$		0			0
$253$	14.0000	−	24.2487i	0.880172	−	1.52450i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.00000	−	6.92820i	−0.249513	−	0.432169i	0.713878	−	0.700270i	$-0.246937\pi$
$257$	−4.00000	−	6.92820i	−0.249513	−	0.432169i	−0.963391	+	0.268101i	$0.913604\pi$
$258$		0			0
$259$	0.274917			0.0170825
$260$		0			0
$261$	−10.5498			−0.653018
$262$		0			0
$263$	1.13746	+	1.97014i	0.0701387	+	0.121484i	0.898962	−	0.438027i	$-0.144322\pi$
$263$	1.13746	+	1.97014i	0.0701387	+	0.121484i	−0.828823	+	0.559511i	$0.810989\pi$
$264$		0			0
$265$	1.72508			0.105971
$266$		0			0
$267$	−2.86254	+	4.95807i	−0.175185	+	0.303429i
$268$		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
$271$	−12.6375	−	21.8887i	−0.767671	−	1.32965i	−0.938823	−	0.344400i	$-0.888082\pi$
$271$	−12.6375	−	21.8887i	−0.767671	−	1.32965i	0.171152	−	0.985245i	$-0.445251\pi$
$272$		0			0
$273$	−2.50000	−	2.59808i	−0.151307	−	0.157243i
$274$		0			0
$275$	2.13746	+	3.70219i	0.128894	+	0.223250i
$276$		0			0
$277$	14.4124	−	24.9630i	0.865956	−	1.49988i	−0.000139316	−	1.00000i	$-0.500044\pi$
$277$	14.4124	−	24.9630i	0.865956	−	1.49988i	0.866095	−	0.499879i	$-0.166622\pi$
$278$		0			0
$279$	3.63746	−	6.30026i	0.217769	−	0.377187i
$280$		0			0
$281$	−27.0997			−1.61663			−0.808315	−	0.588750i	$-0.799620\pi$
$281$	−27.0997			−1.61663			−0.808315	+	0.588750i	$0.799620\pi$
$282$		0			0
$283$	11.4622	+	19.8531i	0.681358	+	1.18015i	0.974567	+	0.224098i	$0.0719435\pi$
$283$	11.4622	+	19.8531i	0.681358	+	1.18015i	−0.293209	+	0.956048i	$0.594723\pi$
$284$		0			0
$285$	2.27492			0.134754
$286$		0			0
$287$	8.54983			0.504681
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$	−7.82475			−0.458695
$292$		0			0
$293$	14.1375	−	24.4868i	0.825919	−	1.43053i	−0.0752957	−	0.997161i	$-0.523990\pi$
$293$	14.1375	−	24.4868i	0.825919	−	1.43053i	0.901215	−	0.433373i	$-0.142677\pi$
$294$		0			0
$295$	−7.27492	+	12.6005i	−0.423562	+	0.733631i
$296$		0			0
$297$	−2.13746	−	3.70219i	−0.124028	−	0.214823i
$298$		0			0
$299$	6.54983	−	22.6893i	0.378787	−	1.31216i
$300$		0			0
$301$	−3.63746	−	6.30026i	−0.209660	−	0.363141i
$302$		0			0
$303$	−3.27492	+	5.67232i	−0.188139	+	0.325866i
$304$		0			0
$305$	1.63746	−	2.83616i	0.0937606	−	0.162398i
$306$		0			0
$307$	−22.9244			−1.30837			−0.654183	−	0.756336i	$-0.726987\pi$
$307$	−22.9244			−1.30837			−0.654183	+	0.756336i	$0.726987\pi$
$308$		0			0
$309$	−7.77492	−	13.4666i	−0.442300	−	0.766085i
$310$		0			0
$311$	12.0000			0.680458			0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000			0.680458			0.340229	+	0.940343i	$0.389495\pi$
$312$		0			0
$313$	4.72508			0.267077			0.133539	−	0.991044i	$-0.457366\pi$
$313$	4.72508			0.267077			0.133539	+	0.991044i	$0.457366\pi$
$314$		0			0
$315$	−0.500000	−	0.866025i	−0.0281718	−	0.0487950i
$316$		0			0
$317$	−19.3746			−1.08819			−0.544093	−	0.839025i	$-0.683126\pi$
$317$	−19.3746			−1.08819			−0.544093	+	0.839025i	$0.683126\pi$
$318$		0			0
$319$	−22.5498	+	39.0575i	−1.26255	+	2.18680i
$320$		0			0
$321$	7.54983	−	13.0767i	0.421391	−	0.729870i
$322$		0			0
$323$		0			0
$324$		0			0
$325$	2.50000	+	2.59808i	0.138675	+	0.144115i
$326$		0			0
$327$	−6.91238	−	11.9726i	−0.382255	−	0.662086i
$328$		0			0
$329$	−2.13746	+	3.70219i	−0.117842	+	0.204108i
$330$		0			0
$331$	9.36254	−	16.2164i	0.514612	−	0.891334i	−0.485244	−	0.874379i	$-0.661269\pi$
$331$	9.36254	−	16.2164i	0.514612	−	0.891334i	0.999856	−	0.0169553i	$-0.00539729\pi$
$332$		0			0
$333$	0.274917			0.0150654
$334$		0			0
$335$	2.63746	+	4.56821i	0.144100	+	0.249588i
$336$		0			0
$337$	19.2749			1.04997			0.524986	−	0.851111i	$-0.324071\pi$
$337$	19.2749			1.04997			0.524986	+	0.851111i	$0.324071\pi$
$338$		0			0
$339$	5.45017			0.296012
$340$		0			0
$341$	−15.5498	−	26.9331i	−0.842071	−	1.45851i
$342$		0			0
$343$	−13.0000			−0.701934
$344$		0			0
$345$	3.27492	−	5.67232i	0.176316	−	0.305388i
$346$		0			0
$347$	8.54983	−	14.8087i	0.458979	−	0.794975i	−0.539928	−	0.841711i	$-0.681549\pi$
$347$	8.54983	−	14.8087i	0.458979	−	0.794975i	0.998907	+	0.0467359i	$0.0148819\pi$
$348$		0			0
$349$	10.4622	+	18.1211i	0.560029	+	0.969999i	0.997493	+	0.0707632i	$0.0225435\pi$
$349$	10.4622	+	18.1211i	0.560029	+	0.969999i	−0.437464	+	0.899236i	$0.644123\pi$
$350$		0			0
$351$	−2.50000	−	2.59808i	−0.133440	−	0.138675i
$352$		0			0
$353$	−15.2749	−	26.4569i	−0.813002	−	1.40816i	−0.910754	−	0.412950i	$-0.864499\pi$
$353$	−15.2749	−	26.4569i	−0.813002	−	1.40816i	0.0977520	−	0.995211i	$-0.468835\pi$
$354$		0			0
$355$	1.00000	−	1.73205i	0.0530745	−	0.0919277i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	28.5498			1.50680			0.753401	−	0.657561i	$-0.228412\pi$
$359$	28.5498			1.50680			0.753401	+	0.657561i	$0.228412\pi$
$360$		0			0
$361$	6.91238	+	11.9726i	0.363809	+	0.630136i
$362$		0			0
$363$	−7.27492			−0.381834
$364$		0			0
$365$	11.8248			0.618936
$366$		0			0
$367$	−8.63746	−	14.9605i	−0.450872	−	0.780933i	0.547569	−	0.836761i	$-0.315553\pi$
$367$	−8.63746	−	14.9605i	−0.450872	−	0.780933i	−0.998440	+	0.0558281i	$0.982220\pi$
$368$		0			0
$369$	8.54983			0.445087
$370$		0			0
$371$	−0.862541	+	1.49397i	−0.0447809	+	0.0775628i
$372$		0			0
$373$	7.63746	−	13.2285i	0.395453	−	0.684944i	−0.597706	−	0.801715i	$-0.703921\pi$
$373$	7.63746	−	13.2285i	0.395453	−	0.684944i	0.993159	+	0.116771i	$0.0372544\pi$
$374$		0			0
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$		0			0
$377$	−10.5498	+	36.5457i	−0.543344	+	1.88220i
$378$		0			0
$379$	−10.7749	−	18.6627i	−0.553470	−	0.958639i	−0.998021	−	0.0628849i	$-0.979970\pi$
$379$	−10.7749	−	18.6627i	−0.553470	−	0.958639i	0.444550	−	0.895754i	$-0.353363\pi$
$380$		0			0
$381$	0.500000	−	0.866025i	0.0256158	−	0.0443678i
$382$		0			0
$383$	12.5498	−	21.7370i	0.641267	−	1.11071i	−0.343884	−	0.939012i	$-0.611743\pi$
$383$	12.5498	−	21.7370i	0.641267	−	1.11071i	0.985150	−	0.171694i	$-0.0549241\pi$
$384$		0			0
$385$	−4.27492			−0.217870
$386$		0			0
$387$	−3.63746	−	6.30026i	−0.184902	−	0.320260i
$388$		0			0
$389$	−8.00000			−0.405616			−0.202808	−	0.979219i	$-0.565007\pi$
$389$	−8.00000			−0.405616			−0.202808	+	0.979219i	$0.565007\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	1.86254	+	3.22602i	0.0939528	+	0.162731i
$394$		0			0
$395$	−0.725083			−0.0364829
$396$		0			0
$397$	−2.04983	+	3.55042i	−0.102878	+	0.178190i	−0.912869	−	0.408252i	$-0.866139\pi$
$397$	−2.04983	+	3.55042i	−0.102878	+	0.178190i	0.809991	+	0.586442i	$0.199472\pi$
$398$		0			0
$399$	−1.13746	+	1.97014i	−0.0569442	+	0.0986302i
$400$		0			0
$401$	19.9622	+	34.5756i	0.996865	+	1.72662i	0.566951	+	0.823751i	$0.308123\pi$
$401$	19.9622	+	34.5756i	0.996865	+	1.72662i	0.429914	+	0.902870i	$0.358544\pi$
$402$		0			0
$403$	−18.1873	−	18.9008i	−0.905974	−	0.941515i
$404$		0			0
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$		0			0
$407$	0.587624	−	1.01779i	0.0291274	−	0.0504502i
$408$		0			0
$409$	−1.95017	+	3.37779i	−0.0964295	+	0.167021i	−0.910204	−	0.414160i	$-0.864076\pi$
$409$	−1.95017	+	3.37779i	−0.0964295	+	0.167021i	0.813775	+	0.581180i	$0.197409\pi$
$410$		0			0
$411$	21.0997			1.04077
$412$		0			0
$413$	−7.27492	−	12.6005i	−0.357975	−	0.620031i
$414$		0			0
$415$	17.0997			0.839390
$416$		0			0
$417$	−11.0000			−0.538672
$418$		0			0
$419$	15.0997	+	26.1534i	0.737667	+	1.27768i	0.953543	+	0.301256i	$0.0974059\pi$
$419$	15.0997	+	26.1534i	0.737667	+	1.27768i	−0.215876	+	0.976421i	$0.569261\pi$
$420$		0			0
$421$	15.8248			0.771251			0.385626	−	0.922655i	$-0.373986\pi$
$421$	15.8248			0.771251			0.385626	+	0.922655i	$0.373986\pi$
$422$		0			0
$423$	−2.13746	+	3.70219i	−0.103927	+	0.180006i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.63746	+	2.83616i	0.0792422	+	0.137251i
$428$		0			0
$429$	−14.9622	+	3.70219i	−0.722382	+	0.178743i
$430$		0			0
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$		0			0
$433$	−7.18729	+	12.4488i	−0.345399	+	0.598249i	−0.985426	−	0.170103i	$-0.945590\pi$
$433$	−7.18729	+	12.4488i	−0.345399	+	0.598249i	0.640027	+	0.768352i	$0.278923\pi$
$434$		0			0
$435$	−5.27492	+	9.13642i	−0.252913	+	0.438058i
$436$		0			0
$437$	−14.9003			−0.712780
$438$		0			0
$439$	12.3625	+	21.4125i	0.590032	+	1.02197i	0.994227	+	0.107293i	$0.0342182\pi$
$439$	12.3625	+	21.4125i	0.590032	+	1.02197i	−0.404196	+	0.914673i	$0.632448\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$		0			0
$443$	−17.6495			−0.838553			−0.419277	−	0.907859i	$-0.637716\pi$
$443$	−17.6495			−0.838553			−0.419277	+	0.907859i	$0.637716\pi$
$444$		0			0
$445$	2.86254	+	4.95807i	0.135697	+	0.235035i
$446$		0			0
$447$	16.5498			0.782780
$448$		0			0
$449$	−7.86254	+	13.6183i	−0.371056	+	0.642688i	−0.989728	−	0.142961i	$-0.954338\pi$
$449$	−7.86254	+	13.6183i	−0.371056	+	0.642688i	0.618672	+	0.785649i	$0.287671\pi$
$450$		0			0
$451$	18.2749	−	31.6531i	0.860532	−	1.49049i
$452$		0			0
$453$	−1.72508	−	2.98793i	−0.0810515	−	0.140385i
$454$		0			0
$455$	−3.50000	+	0.866025i	−0.164083	+	0.0405999i
$456$		0			0
$457$	−14.1873	−	24.5731i	−0.663654	−	1.14948i	−0.979648	−	0.200721i	$-0.935672\pi$
$457$	−14.1873	−	24.5731i	−0.663654	−	1.14948i	0.315995	−	0.948761i	$-0.397662\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	6.00000	−	10.3923i	0.279448	−	0.484018i	−0.691800	−	0.722089i	$-0.743182\pi$
$461$	6.00000	−	10.3923i	0.279448	−	0.484018i	0.971248	+	0.238071i	$0.0765153\pi$
$462$		0			0
$463$	−30.7251			−1.42792			−0.713958	−	0.700189i	$-0.753099\pi$
$463$	−30.7251			−1.42792			−0.713958	+	0.700189i	$0.753099\pi$
$464$		0			0
$465$	−3.63746	−	6.30026i	−0.168683	−	0.292168i
$466$		0			0
$467$	14.5498			0.673286			0.336643	−	0.941632i	$-0.390708\pi$
$467$	14.5498			0.673286			0.336643	+	0.941632i	$0.390708\pi$
$468$		0			0
$469$	−5.27492			−0.243573
$470$		0			0
$471$	5.77492	+	10.0025i	0.266094	+	0.460889i
$472$		0			0
$473$	−31.0997			−1.42996
$474$		0			0
$475$	1.13746	−	1.97014i	0.0521902	−	0.0903960i
$476$		0			0
$477$	−0.862541	+	1.49397i	−0.0394931	+	0.0684040i
$478$		0			0
$479$	−14.5498	−	25.2011i	−0.664799	−	1.15147i	−0.979340	−	0.202222i	$-0.935184\pi$
$479$	−14.5498	−	25.2011i	−0.664799	−	1.15147i	0.314541	−	0.949244i	$-0.398149\pi$
$480$		0			0
$481$	0.274917	−	0.952341i	0.0125351	−	0.0434230i
$482$		0			0
$483$	3.27492	+	5.67232i	0.149014	+	0.258100i
$484$		0			0
$485$	−3.91238	+	6.77643i	−0.177652	+	0.307702i
$486$		0			0
$487$	17.1375	−	29.6829i	0.776572	−	1.34506i	−0.157334	−	0.987545i	$-0.550290\pi$
$487$	17.1375	−	29.6829i	0.776572	−	1.34506i	0.933906	−	0.357517i	$-0.116377\pi$
$488$		0			0
$489$	−2.72508			−0.123233
$490$		0			0
$491$	3.58762	+	6.21395i	0.161907	+	0.280432i	0.935553	−	0.353187i	$-0.114902\pi$
$491$	3.58762	+	6.21395i	0.161907	+	0.280432i	−0.773645	+	0.633619i	$0.781569\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−4.27492			−0.192143
$496$		0			0
$497$	1.00000	+	1.73205i	0.0448561	+	0.0776931i
$498$		0			0
$499$	17.0997			0.765486			0.382743	−	0.923855i	$-0.374979\pi$
$499$	17.0997			0.765486			0.382743	+	0.923855i	$0.374979\pi$
$500$		0			0
$501$	−5.13746	+	8.89834i	−0.229525	+	0.397548i
$502$		0			0
$503$	12.4124	−	21.4989i	0.553440	−	0.958587i	−0.444583	−	0.895738i	$-0.646648\pi$
$503$	12.4124	−	21.4989i	0.553440	−	0.958587i	0.998023	−	0.0628492i	$-0.0200187\pi$
$504$		0			0
$505$	3.27492	+	5.67232i	0.145732	+	0.252415i
$506$		0			0
$507$	−11.5000	+	6.06218i	−0.510733	+	0.269231i
$508$		0			0
$509$	−11.5498	−	20.0049i	−0.511937	−	0.886702i	−0.999904	−	0.0138394i	$-0.995595\pi$
$509$	−11.5498	−	20.0049i	−0.511937	−	0.886702i	0.487967	−	0.872862i	$-0.337739\pi$
$510$		0			0
$511$	−5.91238	+	10.2405i	−0.261548	+	0.453015i
$512$		0			0
$513$	−1.13746	+	1.97014i	−0.0502200	+	0.0869836i
$514$		0			0
$515$	−15.5498			−0.685208
$516$		0			0
$517$	9.13746	+	15.8265i	0.401865	+	0.696051i
$518$		0			0
$519$	15.7251			0.690255
$520$		0			0
$521$	−13.7251			−0.601307			−0.300653	−	0.953733i	$-0.597205\pi$
$521$	−13.7251			−0.601307			−0.300653	+	0.953733i	$0.597205\pi$
$522$		0			0
$523$	−16.2749	−	28.1890i	−0.711652	−	1.23262i	−0.964237	−	0.265043i	$-0.914614\pi$
$523$	−16.2749	−	28.1890i	−0.711652	−	1.23262i	0.252584	−	0.967575i	$-0.418720\pi$
$524$		0			0
$525$	−1.00000			−0.0436436
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−9.95017	+	17.2342i	−0.432616	+	0.749313i
$530$		0			0
$531$	−7.27492	−	12.6005i	−0.315705	−	0.546816i
$532$		0			0
$533$	8.54983	−	29.6175i	0.370334	−	1.28288i
$534$		0			0
$535$	−7.54983	−	13.0767i	−0.326408	−	0.565355i
$536$		0			0
$537$	−6.00000	+	10.3923i	−0.258919	+	0.448461i
$538$		0			0
$539$	−12.8248	+	22.2131i	−0.552401	+	0.956787i
$540$		0			0
$541$	−29.8248			−1.28227			−0.641133	−	0.767430i	$-0.721535\pi$
$541$	−29.8248			−1.28227			−0.641133	+	0.767430i	$0.721535\pi$
$542$		0			0
$543$	−1.00000	−	1.73205i	−0.0429141	−	0.0743294i
$544$		0			0
$545$	−13.8248			−0.592187
$546$		0			0
$547$	29.8248			1.27521			0.637607	−	0.770362i	$-0.279924\pi$
$547$	29.8248			1.27521			0.637607	+	0.770362i	$0.279924\pi$
$548$		0			0
$549$	1.63746	+	2.83616i	0.0698850	+	0.121044i
$550$		0			0
$551$	24.0000			1.02243
$552$		0			0
$553$	0.362541	−	0.627940i	0.0154168	−	0.0267027i
$554$		0			0
$555$	0.137459	−	0.238085i	0.00583479	−	0.0101062i
$556$		0			0
$557$	2.31271	+	4.00573i	0.0979925	+	0.169728i	0.910854	−	0.412730i	$-0.135425\pi$
$557$	2.31271	+	4.00573i	0.0979925	+	0.169728i	−0.812861	+	0.582458i	$0.802091\pi$
$558$		0			0
$559$	−25.4622	+	6.30026i	−1.07694	+	0.266473i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	9.27492	−	16.0646i	0.390891	−	0.677043i	−0.601676	−	0.798740i	$-0.705500\pi$
$563$	9.27492	−	16.0646i	0.390891	−	0.677043i	0.992567	+	0.121697i	$0.0388335\pi$
$564$		0			0
$565$	2.72508	−	4.71998i	0.114645	−	0.198571i
$566$		0			0
$567$	1.00000			0.0419961
$568$		0			0
$569$	20.6873	+	35.8314i	0.867256	+	1.50213i	0.864789	+	0.502135i	$0.167452\pi$
$569$	20.6873	+	35.8314i	0.867256	+	1.50213i	0.00246734	+	0.999997i	$0.499215\pi$
$570$		0			0
$571$	4.62541			0.193568			0.0967838	−	0.995305i	$-0.469144\pi$
$571$	4.62541			0.193568			0.0967838	+	0.995305i	$0.469144\pi$
$572$		0			0
$573$	18.0000			0.751961
$574$		0			0
$575$	−3.27492	−	5.67232i	−0.136573	−	0.236552i
$576$		0			0
$577$	31.0997			1.29470			0.647348	−	0.762195i	$-0.275878\pi$
$577$	31.0997			1.29470			0.647348	+	0.762195i	$0.275878\pi$
$578$		0			0
$579$	7.18729	−	12.4488i	0.298694	−	0.517353i
$580$		0			0
$581$	−8.54983	+	14.8087i	−0.354707	+	0.614370i
$582$		0			0
$583$	3.68729	+	6.38658i	0.152712	+	0.264505i
$584$		0			0
$585$	−3.50000	+	0.866025i	−0.144707	+	0.0358057i
$586$		0			0
$587$	10.0997	+	17.4931i	0.416858	+	0.722019i	0.995622	−	0.0934763i	$-0.0297979\pi$
$587$	10.0997	+	17.4931i	0.416858	+	0.722019i	−0.578764	+	0.815495i	$0.696465\pi$
$588$		0			0
$589$	−8.27492	+	14.3326i	−0.340962	+	0.590564i
$590$		0			0
$591$	−1.41238	+	2.44631i	−0.0580974	+	0.100628i
$592$		0			0
$593$	−17.4502			−0.716592			−0.358296	−	0.933608i	$-0.616642\pi$
$593$	−17.4502			−0.716592			−0.358296	+	0.933608i	$0.616642\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−4.72508			−0.193385
$598$		0			0
$599$	4.90033			0.200222			0.100111	−	0.994976i	$-0.468080\pi$
$599$	4.90033			0.200222			0.100111	+	0.994976i	$0.468080\pi$
$600$		0			0
$601$	18.1375	+	31.4150i	0.739842	+	1.28144i	0.952566	+	0.304332i	$0.0984333\pi$
$601$	18.1375	+	31.4150i	0.739842	+	1.28144i	−0.212724	+	0.977112i	$0.568233\pi$
$602$		0			0
$603$	−5.27492			−0.214811
$604$		0			0
$605$	−3.63746	+	6.30026i	−0.147884	+	0.256142i
$606$		0			0
$607$	−7.68729	+	13.3148i	−0.312018	+	0.540430i	−0.978799	−	0.204823i	$-0.934338\pi$
$607$	−7.68729	+	13.3148i	−0.312018	+	0.540430i	0.666781	+	0.745253i	$0.267671\pi$
$608$		0			0
$609$	−5.27492	−	9.13642i	−0.213750	−	0.370227i
$610$		0			0
$611$	10.6873	+	11.1066i	0.432362	+	0.449323i
$612$		0			0
$613$	9.59967	+	16.6271i	0.387727	+	0.671563i	0.992143	−	0.125106i	$-0.0399270\pi$
$613$	9.59967	+	16.6271i	0.387727	+	0.671563i	−0.604416	+	0.796669i	$0.706594\pi$
$614$		0			0
$615$	4.27492	−	7.40437i	0.172381	−	0.298573i
$616$		0			0
$617$	−2.45017	+	4.24381i	−0.0986400	+	0.170849i	−0.911122	−	0.412137i	$-0.864783\pi$
$617$	−2.45017	+	4.24381i	−0.0986400	+	0.170849i	0.812482	+	0.582986i	$0.198116\pi$
$618$		0			0
$619$	7.54983			0.303453			0.151727	−	0.988422i	$-0.451517\pi$
$619$	7.54983			0.303453			0.151727	+	0.988422i	$0.451517\pi$
$620$		0			0
$621$	3.27492	+	5.67232i	0.131418	+	0.227622i
$622$		0			0
$623$	−5.72508			−0.229371
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	4.86254	+	8.42217i	0.194191	+	0.336349i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−1.36254	+	2.35999i	−0.0542419	+	0.0939498i	−0.891871	−	0.452289i	$-0.850608\pi$
$631$	−1.36254	+	2.35999i	−0.0542419	+	0.0939498i	0.837630	+	0.546239i	$0.183941\pi$
$632$		0			0
$633$	2.50000	−	4.33013i	0.0993661	−	0.172107i
$634$		0			0
$635$	−0.500000	−	0.866025i	−0.0198419	−	0.0343672i
$636$		0			0
$637$	−6.00000	+	20.7846i	−0.237729	+	0.823516i
$638$		0			0
$639$	1.00000	+	1.73205i	0.0395594	+	0.0685189i
$640$		0			0
$641$	16.9622	−	29.3794i	0.669967	−	1.16042i	−0.307946	−	0.951404i	$-0.599642\pi$
$641$	16.9622	−	29.3794i	0.669967	−	1.16042i	0.977913	−	0.209013i	$-0.0670251\pi$
$642$		0			0
$643$	−1.36254	+	2.35999i	−0.0537334	+	0.0930690i	−0.891641	−	0.452743i	$-0.850445\pi$
$643$	−1.36254	+	2.35999i	−0.0537334	+	0.0930690i	0.837908	+	0.545812i	$0.183779\pi$
$644$		0			0
$645$	−7.27492			−0.286450
$646$		0			0
$647$	7.58762	+	13.1422i	0.298300	+	0.516671i	0.975747	−	0.218900i	$-0.0702470\pi$
$647$	7.58762	+	13.1422i	0.298300	+	0.516671i	−0.677447	+	0.735572i	$0.736914\pi$
$648$		0			0
$649$	−62.1993			−2.44154
$650$		0			0
$651$	7.27492			0.285126
$652$		0			0
$653$	−2.58762	−	4.48190i	−0.101262	−	0.175390i	0.810943	−	0.585125i	$-0.198955\pi$
$653$	−2.58762	−	4.48190i	−0.101262	−	0.175390i	−0.912205	+	0.409735i	$0.865621\pi$
$654$		0			0
$655$	3.72508			0.145551
$656$		0			0
$657$	−5.91238	+	10.2405i	−0.230664	+	0.399521i
$658$		0			0
$659$	−6.00000	+	10.3923i	−0.233727	+	0.404827i	−0.958902	−	0.283738i	$-0.908425\pi$
$659$	−6.00000	+	10.3923i	−0.233727	+	0.404827i	0.725175	+	0.688565i	$0.241759\pi$
$660$		0			0
$661$	−11.4622	−	19.8531i	−0.445828	−	0.772197i	0.552281	−	0.833658i	$-0.313757\pi$
$661$	−11.4622	−	19.8531i	−0.445828	−	0.772197i	−0.998110	+	0.0614606i	$0.980424\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.13746	+	1.97014i	0.0441088	+	0.0763986i
$666$		0			0
$667$	34.5498	−	59.8421i	1.33777	−	2.31709i
$668$		0			0
$669$	13.4124	−	23.2309i	0.518552	−	0.898159i
$670$		0			0
$671$	14.0000			0.540464
$672$		0			0
$673$	4.81271	+	8.33585i	0.185516	+	0.321324i	0.943750	−	0.330659i	$-0.107271\pi$
$673$	4.81271	+	8.33585i	0.185516	+	0.321324i	−0.758234	+	0.651982i	$0.773938\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	−7.45017			−0.286333			−0.143167	−	0.989699i	$-0.545728\pi$
$677$	−7.45017			−0.286333			−0.143167	+	0.989699i	$0.545728\pi$
$678$		0			0
$679$	−3.91238	−	6.77643i	−0.150143	−	0.260056i
$680$		0			0
$681$	−9.09967			−0.348700
$682$		0			0
$683$	−15.0000	+	25.9808i	−0.573959	+	0.994126i	0.422195	+	0.906505i	$0.361260\pi$
$683$	−15.0000	+	25.9808i	−0.573959	+	0.994126i	−0.996154	+	0.0876211i	$0.972074\pi$
$684$		0			0
$685$	10.5498	−	18.2728i	0.403088	−	0.698170i
$686$		0			0
$687$	−5.00000	−	8.66025i	−0.190762	−	0.330409i
$688$		0			0
$689$	4.31271	+	4.48190i	0.164301	+	0.170747i
$690$		0			0
$691$	17.3248	+	30.0074i	0.659065	+	1.14153i	0.980858	+	0.194724i	$0.0623810\pi$
$691$	17.3248	+	30.0074i	0.659065	+	1.14153i	−0.321794	+	0.946810i	$0.604286\pi$
$692$		0			0
$693$	2.13746	−	3.70219i	0.0811953	−	0.140634i
$694$		0			0
$695$	−5.50000	+	9.52628i	−0.208627	+	0.361352i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	11.5498	+	20.0049i	0.436855	+	0.756655i
$700$		0			0
$701$	−28.0000			−1.05755			−0.528773	−	0.848763i	$-0.677348\pi$
$701$	−28.0000			−1.05755			−0.528773	+	0.848763i	$0.677348\pi$
$702$		0			0
$703$	−0.625414			−0.0235879
$704$		0			0
$705$	2.13746	+	3.70219i	0.0805013	+	0.139432i
$706$		0			0
$707$	−6.54983			−0.246332
$708$		0			0
$709$	−5.36254	+	9.28819i	−0.201394	+	0.348825i	−0.948978	−	0.315342i	$-0.897881\pi$
$709$	−5.36254	+	9.28819i	−0.201394	+	0.348825i	0.747583	+	0.664168i	$0.231214\pi$
$710$		0			0
$711$	0.362541	−	0.627940i	0.0135964	−	0.0235496i
$712$		0			0
$713$	23.8248	+	41.2657i	0.892244	+	1.54541i
$714$		0			0
$715$	−4.27492	+	14.8087i	−0.159873	+	0.553816i
$716$		0			0
$717$	−2.27492	−	3.94027i	−0.0849583	−	0.147152i
$718$		0			0
$719$	11.2749	−	19.5287i	0.420483	−	0.728299i	−0.575503	−	0.817799i	$-0.695194\pi$
$719$	11.2749	−	19.5287i	0.420483	−	0.728299i	0.995987	+	0.0895007i	$0.0285271\pi$
$720$		0			0
$721$	7.77492	−	13.4666i	0.289553	−	0.501521i
$722$		0			0
$723$	−8.27492			−0.307747
$724$		0			0
$725$	5.27492	+	9.13642i	0.195906	+	0.339318i
$726$		0			0
$727$	28.4502			1.05516			0.527579	−	0.849506i	$-0.323100\pi$
$727$	28.4502			1.05516			0.527579	+	0.849506i	$0.323100\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$		0			0
$732$		0			0
$733$	26.6495			0.984322			0.492161	−	0.870504i	$-0.336207\pi$
$733$	26.6495			0.984322			0.492161	+	0.870504i	$0.336207\pi$
$734$		0			0
$735$	−3.00000	+	5.19615i	−0.110657	+	0.191663i
$736$		0			0
$737$	−11.2749	+	19.5287i	−0.415317	+	0.719350i
$738$		0			0
$739$	−2.86254	−	4.95807i	−0.105300	−	0.182385i	0.808561	−	0.588413i	$-0.200247\pi$
$739$	−2.86254	−	4.95807i	−0.105300	−	0.182385i	−0.913861	+	0.406028i	$0.866914\pi$
$740$		0			0
$741$	5.68729	+	5.91041i	0.208928	+	0.217124i
$742$		0			0
$743$	11.8248	+	20.4811i	0.433808	+	0.751378i	0.997198	−	0.0748138i	$-0.0238363\pi$
$743$	11.8248	+	20.4811i	0.433808	+	0.751378i	−0.563389	+	0.826191i	$0.690503\pi$
$744$		0			0
$745$	8.27492	−	14.3326i	0.303170	−	0.525105i
$746$		0			0
$747$	−8.54983	+	14.8087i	−0.312822	+	0.541824i
$748$		0			0
$749$	15.0997			0.551730
$750$		0			0
$751$	3.45017	+	5.97586i	0.125898	+	0.218062i	0.922084	−	0.386990i	$-0.126485\pi$
$751$	3.45017	+	5.97586i	0.125898	+	0.218062i	−0.796185	+	0.605053i	$0.793152\pi$
$752$		0			0
$753$	26.2749			0.957511
$754$		0			0
$755$	−3.45017			−0.125564
$756$		0			0
$757$	−6.68729	−	11.5827i	−0.243054	−	0.420982i	0.718529	−	0.695497i	$-0.244816\pi$
$757$	−6.68729	−	11.5827i	−0.243054	−	0.420982i	−0.961583	+	0.274516i	$0.911482\pi$
$758$		0			0
$759$	28.0000			1.01634
$760$		0			0
$761$	−25.6873	+	44.4917i	−0.931164	+	1.61282i	−0.149828	+	0.988712i	$0.547872\pi$
$761$	−25.6873	+	44.4917i	−0.931164	+	1.61282i	−0.781336	+	0.624111i	$0.785461\pi$
$762$		0			0
$763$	6.91238	−	11.9726i	0.250245	−	0.433437i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−50.9244	+	12.6005i	−1.83877	+	0.454979i
$768$		0			0
$769$	5.00000	+	8.66025i	0.180305	+	0.312297i	0.941984	−	0.335657i	$-0.108958\pi$
$769$	5.00000	+	8.66025i	0.180305	+	0.312297i	−0.761680	+	0.647954i	$0.775625\pi$
$770$		0			0
$771$	4.00000	−	6.92820i	0.144056	−	0.249513i
$772$		0			0
$773$	−19.2371	+	33.3197i	−0.691911	+	1.19843i	0.279299	+	0.960204i	$0.409898\pi$
$773$	−19.2371	+	33.3197i	−0.691911	+	1.19843i	−0.971211	+	0.238222i	$0.923436\pi$
$774$		0			0
$775$	−7.27492			−0.261323
$776$		0			0
$777$	0.137459	+	0.238085i	0.00493130	+	0.00854126i
$778$		0			0
$779$	−19.4502			−0.696875
$780$		0			0
$781$	8.54983			0.305937
$782$		0			0
$783$	−5.27492	−	9.13642i	−0.188510	−	0.326509i
$784$		0			0
$785$	11.5498			0.412231
$786$		0			0
$787$	11.1873	−	19.3770i	0.398784	−	0.690714i	−0.594792	−	0.803879i	$-0.702766\pi$
$787$	11.1873	−	19.3770i	0.398784	−	0.690714i	0.993576	+	0.113165i	$0.0360990\pi$
$788$		0			0
$789$	−1.13746	+	1.97014i	−0.0404946	+	0.0701387i
$790$		0			0
$791$	2.72508	+	4.71998i	0.0968928	+	0.167823i
$792$		0			0
$793$	11.4622	−	2.83616i	0.407035	−	0.100715i
$794$		0			0
$795$	0.862541	+	1.49397i	0.0305912	+	0.0529855i
$796$		0			0
$797$	0.274917	−	0.476171i	0.00973807	−	0.0168668i	−0.861115	−	0.508410i	$-0.830234\pi$
$797$	0.274917	−	0.476171i	0.00973807	−	0.0168668i	0.870853	+	0.491543i	$0.163567\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−5.72508			−0.202286
$802$		0			0
$803$	25.2749	+	43.7774i	0.891932	+	1.54487i
$804$		0			0
$805$	6.54983			0.230851
$806$		0			0
$807$	12.0000			0.422420
$808$		0			0
$809$	15.7251	+	27.2366i	0.552864	+	0.957589i	0.998066	+	0.0621591i	$0.0197986\pi$
$809$	15.7251	+	27.2366i	0.552864	+	0.957589i	−0.445202	+	0.895430i	$0.646868\pi$
$810$		0			0
$811$	15.5498			0.546029			0.273014	−	0.962010i	$-0.411979\pi$
$811$	15.5498			0.546029			0.273014	+	0.962010i	$0.411979\pi$
$812$		0			0
$813$	12.6375	−	21.8887i	0.443215	−	0.767671i
$814$		0			0
$815$	−1.36254	+	2.35999i	−0.0477277	+	0.0826669i
$816$		0			0
$817$	8.27492	+	14.3326i	0.289503	+	0.501433i
$818$		0			0
$819$	1.00000	−	3.46410i	0.0349428	−	0.121046i
$820$		0			0
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	0.665144	−	0.746715i	$-0.268370\pi$
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	−0.979246	+	0.202674i	$0.935037\pi$
$822$		0			0
$823$	−4.31271	+	7.46983i	−0.150332	+	0.260382i	−0.931349	−	0.364127i	$-0.881367\pi$
$823$	−4.31271	+	7.46983i	−0.150332	+	0.260382i	0.781018	+	0.624509i	$0.214701\pi$
$824$		0			0
$825$	−2.13746	+	3.70219i	−0.0744168	+	0.128894i
$826$		0			0
$827$	−16.5498			−0.575494			−0.287747	−	0.957706i	$-0.592906\pi$
$827$	−16.5498			−0.575494			−0.287747	+	0.957706i	$0.592906\pi$
$828$		0			0
$829$	−11.9124	−	20.6328i	−0.413734	−	0.716608i	0.581561	−	0.813503i	$-0.302442\pi$
$829$	−11.9124	−	20.6328i	−0.413734	−	0.716608i	−0.995295	+	0.0968948i	$0.969109\pi$
$830$		0			0
$831$	28.8248			0.999920
$832$		0			0
$833$		0			0
$834$		0			0
$835$	5.13746	+	8.89834i	0.177789	+	0.307940i
$836$		0			0
$837$	7.27492			0.251458
$838$		0			0
$839$	1.54983	−	2.68439i	0.0535062	−	0.0926755i	−0.838032	−	0.545622i	$-0.816294\pi$
$839$	1.54983	−	2.68439i	0.0535062	−	0.0926755i	0.891538	+	0.452946i	$0.149627\pi$
$840$		0			0
$841$	−41.1495	+	71.2730i	−1.41895	+	2.45769i
$842$		0			0
$843$	−13.5498	−	23.4690i	−0.466681	−	0.808315i
$844$		0			0
$845$	−0.500000	+	12.9904i	−0.0172005	+	0.446883i
$846$		0			0
$847$	−3.63746	−	6.30026i	−0.124985	−	0.216480i
$848$		0			0
$849$	−11.4622	+	19.8531i	−0.393382	+	0.681358i
$850$		0			0
$851$	−0.900331	+	1.55942i	−0.0308630	+	0.0534562i
$852$		0			0
$853$	−54.5739			−1.86858			−0.934288	−	0.356520i	$-0.883963\pi$
$853$	−54.5739			−1.86858			−0.934288	+	0.356520i	$0.883963\pi$
$854$		0			0
$855$	1.13746	+	1.97014i	0.0389003	+	0.0673772i
$856$		0			0
$857$	−18.0000			−0.614868			−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000			−0.614868			−0.307434	+	0.951569i	$0.599470\pi$
$858$		0			0
$859$	−16.6495			−0.568074			−0.284037	−	0.958813i	$-0.591674\pi$
$859$	−16.6495			−0.568074			−0.284037	+	0.958813i	$0.591674\pi$
$860$		0			0
$861$	4.27492	+	7.40437i	0.145689	+	0.252340i
$862$		0			0
$863$	0.350497			0.0119310			0.00596552	−	0.999982i	$-0.498101\pi$
$863$	0.350497			0.0119310			0.00596552	+	0.999982i	$0.498101\pi$
$864$		0			0
$865$	7.86254	−	13.6183i	0.267334	−	0.463037i
$866$		0			0
$867$	−8.50000	+	14.7224i	−0.288675	+	0.500000i
$868$		0			0
$869$	−1.54983	−	2.68439i	−0.0525745	−	0.0910618i
$870$		0			0
$871$	−5.27492	+	18.2728i	−0.178734	+	0.619152i
$872$		0			0
$873$	−3.91238	−	6.77643i	−0.132414	−	0.229348i
$874$		0			0
$875$	−0.500000	+	0.866025i	−0.0169031	+	0.0292770i
$876$		0			0
$877$	2.45017	−	4.24381i	0.0827362	−	0.143303i	−0.821688	−	0.569937i	$-0.806967\pi$
$877$	2.45017	−	4.24381i	0.0827362	−	0.143303i	0.904424	+	0.426634i	$0.140301\pi$
$878$		0			0
$879$	28.2749			0.953689
$880$		0			0
$881$	−12.2371	−	21.1953i	−0.412279	−	0.714089i	0.582859	−	0.812573i	$-0.301934\pi$
$881$	−12.2371	−	21.1953i	−0.412279	−	0.714089i	−0.995139	+	0.0984844i	$0.968601\pi$
$882$		0			0
$883$	−4.37459			−0.147217			−0.0736083	−	0.997287i	$-0.523451\pi$
$883$	−4.37459			−0.147217			−0.0736083	+	0.997287i	$0.523451\pi$
$884$		0			0
$885$	−14.5498			−0.489087
$886$		0			0
$887$	16.9622	+	29.3794i	0.569535	+	0.986464i	0.996612	+	0.0822486i	$0.0262101\pi$
$887$	16.9622	+	29.3794i	0.569535	+	0.986464i	−0.427077	+	0.904215i	$0.640457\pi$
$888$		0			0
$889$	1.00000			0.0335389
$890$		0			0
$891$	2.13746	−	3.70219i	0.0716076	−	0.124028i
$892$		0			0
$893$	4.86254	−	8.42217i	0.162719	−	0.281837i
$894$		0			0
$895$	6.00000	+	10.3923i	0.200558	+	0.347376i
$896$		0			0
$897$	22.9244	−	5.67232i	0.765424	−	0.189393i
$898$		0			0
$899$	−38.3746	−	66.4667i	−1.27986	−	2.21679i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	3.63746	−	6.30026i	0.121047	−	0.209660i
$904$		0			0
$905$	−2.00000			−0.0664822
$906$		0			0
$907$	12.2749	+	21.2608i	0.407582	+	0.705953i	0.994618	−	0.103608i	$-0.0330387\pi$
$907$	12.2749	+	21.2608i	0.407582	+	0.705953i	−0.587036	+	0.809561i	$0.699705\pi$
$908$		0			0
$909$	−6.54983			−0.217244
$910$		0			0
$911$	9.09967			0.301485			0.150743	−	0.988573i	$-0.451833\pi$
$911$	9.09967			0.301485			0.150743	+	0.988573i	$0.451833\pi$
$912$		0			0
$913$	36.5498	+	63.3062i	1.20962	+	2.09513i
$914$		0			0
$915$	3.27492			0.108265
$916$		0			0
$917$	−1.86254	+	3.22602i	−0.0615065	+	0.106532i
$918$		0			0
$919$	−6.27492	+	10.8685i	−0.206990	+	0.358518i	−0.950765	−	0.309913i	$-0.899700\pi$
$919$	−6.27492	+	10.8685i	−0.206990	+	0.358518i	0.743775	+	0.668430i	$0.233034\pi$
$920$		0			0
$921$	−11.4622	−	19.8531i	−0.377693	−	0.654183i
$922$		0			0
$923$	7.00000	−	1.73205i	0.230408	−	0.0570111i
$924$		0			0
$925$	−0.137459	−	0.238085i	−0.00451961	−	0.00782820i
$926$		0			0
$927$	7.77492	−	13.4666i	0.255362	−	0.442300i
$928$		0			0
$929$	−20.8248	+	36.0695i	−0.683238	+	1.18340i	0.290749	+	0.956799i	$0.406095\pi$
$929$	−20.8248	+	36.0695i	−0.683238	+	1.18340i	−0.973987	+	0.226604i	$0.927238\pi$
$930$		0			0
$931$	13.6495			0.447344
$932$		0			0
$933$	6.00000	+	10.3923i	0.196431	+	0.340229i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$		0			0
$939$	2.36254	+	4.09204i	0.0770986	+	0.133539i
$940$		0			0
$941$	−0.350497			−0.0114259			−0.00571293	−	0.999984i	$-0.501818\pi$
$941$	−0.350497			−0.0114259			−0.00571293	+	0.999984i	$0.501818\pi$
$942$		0			0
$943$	−28.0000	+	48.4974i	−0.911805	+	1.57929i
$944$		0			0
$945$	0.500000	−	0.866025i	0.0162650	−	0.0281718i
$946$		0			0
$947$	3.17525	+	5.49969i	0.103182	+	0.178716i	0.912994	−	0.407973i	$-0.133764\pi$
$947$	3.17525	+	5.49969i	0.103182	+	0.178716i	−0.809812	+	0.586689i	$0.800431\pi$
$948$		0			0
$949$	29.5619	+	30.7216i	0.959619	+	0.997266i
$950$		0			0
$951$	−9.68729	−	16.7789i	−0.314132	−	0.544093i
$952$		0			0
$953$	10.0997	−	17.4931i	0.327160	−	0.566658i	−0.654787	−	0.755814i	$-0.727242\pi$
$953$	10.0997	−	17.4931i	0.327160	−	0.566658i	0.981947	+	0.189155i	$0.0605749\pi$
$954$		0			0
$955$	9.00000	−	15.5885i	0.291233	−	0.504431i
$956$		0			0
$957$	−45.0997			−1.45787
$958$		0			0
$959$	10.5498	+	18.2728i	0.340672	+	0.590061i
$960$		0			0
$961$	21.9244			0.707239
$962$		0			0
$963$	15.0997			0.486580
$964$		0			0
$965$	−7.18729	−	12.4488i	−0.231367	−	0.400740i
$966$		0			0
$967$	12.6254			0.406006			0.203003	−	0.979178i	$-0.434930\pi$
$967$	12.6254			0.406006			0.203003	+	0.979178i	$0.434930\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−18.5120	+	32.0638i	−0.594080	+	1.02898i	0.399596	+	0.916691i	$0.369150\pi$
$971$	−18.5120	+	32.0638i	−0.594080	+	1.02898i	−0.993676	+	0.112285i	$0.964183\pi$
$972$		0			0
$973$	−5.50000	−	9.52628i	−0.176322	−	0.305398i
$974$		0			0
$975$	−1.00000	+	3.46410i	−0.0320256	+	0.110940i
$976$		0			0
$977$	−16.0000	−	27.7128i	−0.511885	−	0.886611i	−0.999905	−	0.0137788i	$-0.995614\pi$
$977$	−16.0000	−	27.7128i	−0.511885	−	0.886611i	0.488020	−	0.872833i	$-0.337719\pi$
$978$		0			0
$979$	−12.2371	+	21.1953i	−0.391100	+	0.677406i
$980$		0			0
$981$	6.91238	−	11.9726i	0.220695	−	0.382255i
$982$		0			0
$983$	−37.3746			−1.19206			−0.596032	−	0.802961i	$-0.703257\pi$
$983$	−37.3746			−1.19206			−0.596032	+	0.802961i	$0.703257\pi$
$984$		0			0
$985$	1.41238	+	2.44631i	0.0450020	+	0.0779458i
$986$		0			0
$987$	−4.27492			−0.136072
$988$		0			0
$989$	47.6495			1.51517
$990$		0			0
$991$	−5.72508	−	9.91613i	−0.181863	−	0.314996i	0.760652	−	0.649160i	$-0.224879\pi$
$991$	−5.72508	−	9.91613i	−0.181863	−	0.314996i	−0.942515	+	0.334164i	$0.891546\pi$
$992$		0			0
$993$	18.7251			0.594223
$994$		0			0
$995$	−2.36254	+	4.09204i	−0.0748976	+	0.129726i
$996$		0			0
$997$	−26.8746	+	46.5481i	−0.851127	+	1.47419i	0.0290657	+	0.999578i	$0.490747\pi$
$997$	−26.8746	+	46.5481i	−0.851127	+	1.47419i	−0.880192	+	0.474617i	$0.842587\pi$
$998$		0			0
$999$	0.137459	+	0.238085i	0.00434900	+	0.00753269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1560.2.bg.g.601.2	✓	4
13.9	even	3	inner	1560.2.bg.g.841.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1560.2.bg.g.601.2	✓	4	1.1	even	1	trivial
1560.2.bg.g.841.2	yes	4	13.9	even	3	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:	\( N \)	\(=\)	\( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1560.bg (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(2.13746 + 3.70219i) q^{11} +(2.50000 + 2.59808i) q^{13} +(0.500000 + 0.866025i) q^{15} +(1.13746 - 1.97014i) q^{19} -1.00000 q^{21} +(-3.27492 - 5.67232i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(5.27492 + 9.13642i) q^{29} -7.27492 q^{31} +(-2.13746 + 3.70219i) q^{33} +(-0.500000 + 0.866025i) q^{35} +(-0.137459 - 0.238085i) q^{37} +(-1.00000 + 3.46410i) q^{39} +(-4.27492 - 7.40437i) q^{41} +(-3.63746 + 6.30026i) q^{43} +(-0.500000 + 0.866025i) q^{45} +4.27492 q^{47} +(3.00000 + 5.19615i) q^{49} +1.72508 q^{53} +(2.13746 + 3.70219i) q^{55} +2.27492 q^{57} +(-7.27492 + 12.6005i) q^{59} +(1.63746 - 2.83616i) q^{61} +(-0.500000 - 0.866025i) q^{63} +(2.50000 + 2.59808i) q^{65} +(2.63746 + 4.56821i) q^{67} +(3.27492 - 5.67232i) q^{69} +(1.00000 - 1.73205i) q^{71} +11.8248 q^{73} +(0.500000 + 0.866025i) q^{75} -4.27492 q^{77} -0.725083 q^{79} +(-0.500000 - 0.866025i) q^{81} +17.0997 q^{83} +(-5.27492 + 9.13642i) q^{87} +(2.86254 + 4.95807i) q^{89} +(-3.50000 + 0.866025i) q^{91} +(-3.63746 - 6.30026i) q^{93} +(1.13746 - 1.97014i) q^{95} +(-3.91238 + 6.77643i) q^{97} -4.27492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 4 q^{5} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 4 * q^5 - 2 * q^7 - 2 * q^9	\( 4 q + 2 q^{3} + 4 q^{5} - 2 q^{7} - 2 q^{9} + q^{11} + 10 q^{13} + 2 q^{15} - 3 q^{19} - 4 q^{21} + 2 q^{23} + 4 q^{25} - 4 q^{27} + 6 q^{29} - 14 q^{31} - q^{33} - 2 q^{35} + 7 q^{37} - 4 q^{39} - 2 q^{41} - 7 q^{43} - 2 q^{45} + 2 q^{47} + 12 q^{49} + 22 q^{53} + q^{55} - 6 q^{57} - 14 q^{59} - q^{61} - 2 q^{63} + 10 q^{65} + 3 q^{67} - 2 q^{69} + 4 q^{71} + 2 q^{73} + 2 q^{75} - 2 q^{77} - 18 q^{79} - 2 q^{81} + 8 q^{83} - 6 q^{87} + 19 q^{89} - 14 q^{91} - 7 q^{93} - 3 q^{95} + 7 q^{97} - 2 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 4 * q^5 - 2 * q^7 - 2 * q^9 + q^11 + 10 * q^13 + 2 * q^15 - 3 * q^19 - 4 * q^21 + 2 * q^23 + 4 * q^25 - 4 * q^27 + 6 * q^29 - 14 * q^31 - q^33 - 2 * q^35 + 7 * q^37 - 4 * q^39 - 2 * q^41 - 7 * q^43 - 2 * q^45 + 2 * q^47 + 12 * q^49 + 22 * q^53 + q^55 - 6 * q^57 - 14 * q^59 - q^61 - 2 * q^63 + 10 * q^65 + 3 * q^67 - 2 * q^69 + 4 * q^71 + 2 * q^73 + 2 * q^75 - 2 * q^77 - 18 * q^79 - 2 * q^81 + 8 * q^83 - 6 * q^87 + 19 * q^89 - 14 * q^91 - 7 * q^93 - 3 * q^95 + 7 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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