LMFDB - Embedded newform 1560.2.bg.g.601.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1560.601");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.4566627153$
Analytic rank:	$0$
Dimension:	$4$
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			601.1
Root			$2.13746 + 0.656712i$ of defining polynomial
Character	$\chi$	$=$	1560.601
Dual form			1560.2.bg.g.841.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-1.63746 - 2.83616i) q^{11} +(2.50000 + 2.59808i) q^{13} +(0.500000 + 0.866025i) q^{15} +(-2.63746 + 4.56821i) q^{19} -1.00000 q^{21} +(4.27492 + 7.40437i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-2.27492 - 3.94027i) q^{29} +0.274917 q^{31} +(1.63746 - 2.83616i) q^{33} +(-0.500000 + 0.866025i) q^{35} +(3.63746 + 6.30026i) q^{37} +(-1.00000 + 3.46410i) q^{39} +(3.27492 + 5.67232i) q^{41} +(0.137459 - 0.238085i) q^{43} +(-0.500000 + 0.866025i) q^{45} -3.27492 q^{47} +(3.00000 + 5.19615i) q^{49} +9.27492 q^{53} +(-1.63746 - 2.83616i) q^{55} -5.27492 q^{57} +(0.274917 - 0.476171i) q^{59} +(-2.13746 + 3.70219i) q^{61} +(-0.500000 - 0.866025i) q^{63} +(2.50000 + 2.59808i) q^{65} +(-1.13746 - 1.97014i) q^{67} +(-4.27492 + 7.40437i) q^{69} +(1.00000 - 1.73205i) q^{71} -10.8248 q^{73} +(0.500000 + 0.866025i) q^{75} +3.27492 q^{77} -8.27492 q^{79} +(-0.500000 - 0.866025i) q^{81} -13.0997 q^{83} +(2.27492 - 3.94027i) q^{87} +(6.63746 + 11.4964i) q^{89} +(-3.50000 + 0.866025i) q^{91} +(0.137459 + 0.238085i) q^{93} +(-2.63746 + 4.56821i) q^{95} +(7.41238 - 12.8386i) q^{97} +3.27492 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$11$	−1.63746	−	2.83616i	−0.493712	−	0.855135i	0.506261	−	0.862380i	$-0.331027\pi$
$11$	−1.63746	−	2.83616i	−0.493712	−	0.855135i	−0.999974	+	0.00724520i	$0.997694\pi$
$12$		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
$19$	−2.63746	+	4.56821i	−0.605075	+	1.04802i	0.386965	+	0.922094i	$0.373523\pi$
$19$	−2.63746	+	4.56821i	−0.605075	+	1.04802i	−0.992040	+	0.125925i	$0.959810\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$		0			0
$23$	4.27492	+	7.40437i	0.891382	+	1.54392i	0.838220	+	0.545333i	$0.183597\pi$
$23$	4.27492	+	7.40437i	0.891382	+	1.54392i	0.0531622	+	0.998586i	$0.483070\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−2.27492	−	3.94027i	−0.422442	−	0.731690i	0.573736	−	0.819040i	$-0.305493\pi$
$29$	−2.27492	−	3.94027i	−0.422442	−	0.731690i	−0.996178	+	0.0873500i	$0.972160\pi$
$30$		0			0
$31$	0.274917			0.0493766			0.0246883	−	0.999695i	$-0.492141\pi$
$31$	0.274917			0.0493766			0.0246883	+	0.999695i	$0.492141\pi$
$32$		0			0
$33$	1.63746	−	2.83616i	0.285045	−	0.493712i
$34$		0			0
$35$	−0.500000	+	0.866025i	−0.0845154	+	0.146385i
$36$		0			0
$37$	3.63746	+	6.30026i	0.597995	+	1.03576i	0.993117	+	0.117128i	$0.0373689\pi$
$37$	3.63746	+	6.30026i	0.597995	+	1.03576i	−0.395122	+	0.918629i	$0.629298\pi$
$38$		0			0
$39$	−1.00000	+	3.46410i	−0.160128	+	0.554700i
$40$		0			0
$41$	3.27492	+	5.67232i	0.511456	+	0.885868i	0.999912	+	0.0132793i	$0.00422706\pi$
$41$	3.27492	+	5.67232i	0.511456	+	0.885868i	−0.488456	+	0.872589i	$0.662440\pi$
$42$		0			0
$43$	0.137459	−	0.238085i	0.0209622	−	0.0363077i	−0.855354	−	0.518044i	$-0.826660\pi$
$43$	0.137459	−	0.238085i	0.0209622	−	0.0363077i	0.876316	+	0.481736i	$0.159994\pi$
$44$		0			0
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$		0			0
$47$	−3.27492			−0.477696			−0.238848	−	0.971057i	$-0.576770\pi$
$47$	−3.27492			−0.477696			−0.238848	+	0.971057i	$0.576770\pi$
$48$		0			0
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	9.27492			1.27401			0.637004	−	0.770861i	$-0.280173\pi$
$53$	9.27492			1.27401			0.637004	+	0.770861i	$0.280173\pi$
$54$		0			0
$55$	−1.63746	−	2.83616i	−0.220795	−	0.382428i
$56$		0			0
$57$	−5.27492			−0.698680
$58$		0			0
$59$	0.274917	−	0.476171i	0.0357912	−	0.0619921i	−0.847575	−	0.530676i	$-0.821938\pi$
$59$	0.274917	−	0.476171i	0.0357912	−	0.0619921i	0.883366	+	0.468684i	$0.155272\pi$
$60$		0			0
$61$	−2.13746	+	3.70219i	−0.273674	+	0.474016i	−0.969800	−	0.243903i	$-0.921572\pi$
$61$	−2.13746	+	3.70219i	−0.273674	+	0.474016i	0.696126	+	0.717920i	$0.254905\pi$
$62$		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
$67$	−1.13746	−	1.97014i	−0.138963	−	0.240690i	0.788142	−	0.615494i	$-0.211043\pi$
$67$	−1.13746	−	1.97014i	−0.138963	−	0.240690i	−0.927104	+	0.374804i	$0.877710\pi$
$68$		0			0
$69$	−4.27492	+	7.40437i	−0.514640	+	0.891382i
$70$		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
$73$	−10.8248			−1.26694			−0.633471	−	0.773767i	$-0.718370\pi$
$73$	−10.8248			−1.26694			−0.633471	+	0.773767i	$0.718370\pi$
$74$		0			0
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$		0			0
$77$	3.27492			0.373211
$78$		0			0
$79$	−8.27492			−0.931001			−0.465500	−	0.885048i	$-0.654126\pi$
$79$	−8.27492			−0.931001			−0.465500	+	0.885048i	$0.654126\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−13.0997			−1.43788			−0.718938	−	0.695074i	$-0.755371\pi$
$83$	−13.0997			−1.43788			−0.718938	+	0.695074i	$0.755371\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	2.27492	−	3.94027i	0.243897	−	0.422442i
$88$		0			0
$89$	6.63746	+	11.4964i	0.703569	+	1.21862i	0.967205	+	0.253995i	$0.0817448\pi$
$89$	6.63746	+	11.4964i	0.703569	+	1.21862i	−0.263636	+	0.964622i	$0.584922\pi$
$90$		0			0
$91$	−3.50000	+	0.866025i	−0.366900	+	0.0907841i
$92$		0			0
$93$	0.137459	+	0.238085i	0.0142538	+	0.0246883i
$94$		0			0
$95$	−2.63746	+	4.56821i	−0.270598	+	0.468689i
$96$		0			0
$97$	7.41238	−	12.8386i	0.752613	−	1.30356i	−0.193940	−	0.981013i	$-0.562127\pi$
$97$	7.41238	−	12.8386i	0.752613	−	1.30356i	0.946552	−	0.322550i	$-0.104540\pi$
$98$		0			0
$99$	3.27492			0.329142
$100$		0			0
$101$	−4.27492	−	7.40437i	−0.425370	−	0.736763i	0.571085	−	0.820891i	$-0.306523\pi$
$101$	−4.27492	−	7.40437i	−0.425370	−	0.736763i	−0.996455	+	0.0841284i	$0.973189\pi$
$102$		0			0
$103$	−0.450166			−0.0443561			−0.0221781	−	0.999754i	$-0.507060\pi$
$103$	−0.450166			−0.0443561			−0.0221781	+	0.999754i	$0.507060\pi$
$104$		0			0
$105$	−1.00000			−0.0975900
$106$		0			0
$107$	7.54983	+	13.0767i	0.729870	+	1.26417i	0.956938	+	0.290293i	$0.0937528\pi$
$107$	7.54983	+	13.0767i	0.729870	+	1.26417i	−0.227068	+	0.973879i	$0.572914\pi$
$108$		0			0
$109$	8.82475			0.845258			0.422629	−	0.906303i	$-0.361107\pi$
$109$	8.82475			0.845258			0.422629	+	0.906303i	$0.361107\pi$
$110$		0			0
$111$	−3.63746	+	6.30026i	−0.345252	+	0.597995i
$112$		0			0
$113$	10.2749	−	17.7967i	0.966583	−	1.67417i	0.261282	−	0.965262i	$-0.415855\pi$
$113$	10.2749	−	17.7967i	0.966583	−	1.67417i	0.705301	−	0.708908i	$-0.250812\pi$
$114$		0			0
$115$	4.27492	+	7.40437i	0.398638	+	0.690461i
$116$		0			0
$117$	−3.50000	+	0.866025i	−0.323575	+	0.0800641i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.137459	−	0.238085i	0.0124962	−	0.0216441i
$122$		0			0
$123$	−3.27492	+	5.67232i	−0.295289	+	0.511456i
$124$		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
$129$	0.274917			0.0242051
$130$		0			0
$131$	11.2749			0.985094			0.492547	−	0.870286i	$-0.336066\pi$
$131$	11.2749			0.985094			0.492547	+	0.870286i	$0.336066\pi$
$132$		0			0
$133$	−2.63746	−	4.56821i	−0.228697	−	0.396114i
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	−4.54983	+	7.88054i	−0.388719	+	0.673280i	−0.992277	−	0.124038i	$-0.960415\pi$
$137$	−4.54983	+	7.88054i	−0.388719	+	0.673280i	0.603559	+	0.797318i	$0.293749\pi$
$138$		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
$141$	−1.63746	−	2.83616i	−0.137899	−	0.238848i
$142$		0			0
$143$	3.27492	−	11.3446i	0.273862	−	0.948687i
$144$		0			0
$145$	−2.27492	−	3.94027i	−0.188922	−	0.327222i
$146$		0			0
$147$	−3.00000	+	5.19615i	−0.247436	+	0.428571i
$148$		0			0
$149$	0.725083	−	1.25588i	0.0594011	−	0.102886i	−0.834796	−	0.550560i	$-0.814414\pi$
$149$	0.725083	−	1.25588i	0.0594011	−	0.102886i	0.894197	+	0.447674i	$0.147748\pi$
$150$		0			0
$151$	−18.5498			−1.50956			−0.754782	−	0.655976i	$-0.772257\pi$
$151$	−18.5498			−1.50956			−0.754782	+	0.655976i	$0.772257\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.274917			0.0220819
$156$		0			0
$157$	−3.54983			−0.283308			−0.141654	−	0.989916i	$-0.545242\pi$
$157$	−3.54983			−0.283308			−0.141654	+	0.989916i	$0.545242\pi$
$158$		0			0
$159$	4.63746	+	8.03231i	0.367774	+	0.637004i
$160$		0			0
$161$	−8.54983			−0.673821
$162$		0			0
$163$	−5.13746	+	8.89834i	−0.402397	+	0.696972i	−0.994015	−	0.109247i	$-0.965156\pi$
$163$	−5.13746	+	8.89834i	−0.402397	+	0.696972i	0.591618	+	0.806219i	$0.298489\pi$
$164$		0			0
$165$	1.63746	−	2.83616i	0.127476	−	0.220795i
$166$		0			0
$167$	1.36254	+	2.35999i	0.105437	+	0.182622i	0.913917	−	0.405902i	$-0.133043\pi$
$167$	1.36254	+	2.35999i	0.105437	+	0.182622i	−0.808480	+	0.588524i	$0.799709\pi$
$168$		0			0
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$		0			0
$171$	−2.63746	−	4.56821i	−0.201692	−	0.349340i
$172$		0			0
$173$	11.6375	−	20.1567i	0.884780	−	1.53248i	0.0388135	−	0.999246i	$-0.487642\pi$
$173$	11.6375	−	20.1567i	0.884780	−	1.53248i	0.845966	−	0.533237i	$-0.179025\pi$
$174$		0			0
$175$	−0.500000	+	0.866025i	−0.0377964	+	0.0654654i
$176$		0			0
$177$	0.549834			0.0413281
$178$		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
$183$	−4.27492			−0.316011
$184$		0			0
$185$	3.63746	+	6.30026i	0.267431	+	0.463205i
$186$		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
$193$	11.6873	+	20.2430i	0.841270	+	1.45712i	0.888822	+	0.458253i	$0.151525\pi$
$193$	11.6873	+	20.2430i	0.841270	+	1.45712i	−0.0475519	+	0.998869i	$0.515142\pi$
$194$		0			0
$195$	−1.00000	+	3.46410i	−0.0716115	+	0.248069i
$196$		0			0
$197$	−9.91238	−	17.1687i	−0.706228	−	1.22322i	−0.966247	−	0.257619i	$-0.917062\pi$
$197$	−9.91238	−	17.1687i	−0.706228	−	1.22322i	0.260019	−	0.965603i	$-0.416271\pi$
$198$		0			0
$199$	−6.13746	+	10.6304i	−0.435073	+	0.753568i	−0.997302	−	0.0734134i	$-0.976611\pi$
$199$	−6.13746	+	10.6304i	−0.435073	+	0.753568i	0.562229	+	0.826982i	$0.309944\pi$
$200$		0			0
$201$	1.13746	−	1.97014i	0.0802301	−	0.138963i
$202$		0			0
$203$	4.54983			0.319336
$204$		0			0
$205$	3.27492	+	5.67232i	0.228730	+	0.396172i
$206$		0			0
$207$	−8.54983			−0.594255
$208$		0			0
$209$	17.2749			1.19493
$210$		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
$215$	0.137459	−	0.238085i	0.00937460	−	0.0162373i
$216$		0			0
$217$	−0.137459	+	0.238085i	−0.00933130	+	0.0161623i
$218$		0			0
$219$	−5.41238	−	9.37451i	−0.365734	−	0.633471i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−2.08762	−	3.61587i	−0.139798	−	0.242137i	0.787622	−	0.616158i	$-0.211312\pi$
$223$	−2.08762	−	3.61587i	−0.139798	−	0.242137i	−0.927420	+	0.374022i	$0.877979\pi$
$224$		0			0
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$		0			0
$227$	10.5498	−	18.2728i	0.700217	−	1.21281i	−0.268173	−	0.963371i	$-0.586420\pi$
$227$	10.5498	−	18.2728i	0.700217	−	1.21281i	0.968390	−	0.249441i	$-0.0802468\pi$
$228$		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
$231$	1.63746	+	2.83616i	0.107737	+	0.186606i
$232$		0			0
$233$	−7.09967			−0.465115			−0.232557	−	0.972583i	$-0.574709\pi$
$233$	−7.09967			−0.465115			−0.232557	+	0.972583i	$0.574709\pi$
$234$		0			0
$235$	−3.27492			−0.213632
$236$		0			0
$237$	−4.13746	−	7.16629i	−0.268757	−	0.465500i
$238$		0			0
$239$	10.5498			0.682412			0.341206	−	0.939989i	$-0.389165\pi$
$239$	10.5498			0.682412			0.341206	+	0.939989i	$0.389165\pi$
$240$		0			0
$241$	−0.362541	+	0.627940i	−0.0233533	+	0.0404492i	−0.877466	−	0.479639i	$-0.840768\pi$
$241$	−0.362541	+	0.627940i	−0.0233533	+	0.0404492i	0.854113	+	0.520088i	$0.174101\pi$
$242$		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
$247$	−18.4622	+	4.56821i	−1.17472	+	0.290668i
$248$		0			0
$249$	−6.54983	−	11.3446i	−0.415079	−	0.718938i
$250$		0			0
$251$	9.36254	−	16.2164i	0.590958	−	1.02357i	−0.403145	−	0.915136i	$-0.632083\pi$
$251$	9.36254	−	16.2164i	0.590958	−	1.02357i	0.994104	−	0.108434i	$-0.0345836\pi$
$252$		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
$259$	−7.27492			−0.452041
$260$		0			0
$261$	4.54983			0.281628
$262$		0			0
$263$	−2.63746	−	4.56821i	−0.162633	−	0.281688i	0.773179	−	0.634187i	$-0.218665\pi$
$263$	−2.63746	−	4.56821i	−0.162633	−	0.281688i	−0.935812	+	0.352499i	$0.885332\pi$
$264$		0			0
$265$	9.27492			0.569754
$266$		0			0
$267$	−6.63746	+	11.4964i	−0.406206	+	0.703569i
$268$		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
$271$	−8.86254	−	15.3504i	−0.538361	−	0.932469i	−0.998993	−	0.0448772i	$-0.985710\pi$
$271$	−8.86254	−	15.3504i	−0.538361	−	0.932469i	0.460631	−	0.887591i	$-0.347623\pi$
$272$		0			0
$273$	−2.50000	−	2.59808i	−0.151307	−	0.157243i
$274$		0			0
$275$	−1.63746	−	2.83616i	−0.0987425	−	0.171027i
$276$		0			0
$277$	3.08762	−	5.34792i	0.185517	−	0.321325i	−0.758233	−	0.651983i	$-0.773937\pi$
$277$	3.08762	−	5.34792i	0.185517	−	0.321325i	0.943751	+	0.330658i	$0.107271\pi$
$278$		0			0
$279$	−0.137459	+	0.238085i	−0.00822943	+	0.0142538i
$280$		0			0
$281$	3.09967			0.184911			0.0924554	−	0.995717i	$-0.470528\pi$
$281$	3.09967			0.184911			0.0924554	+	0.995717i	$0.470528\pi$
$282$		0			0
$283$	−14.9622	−	25.9153i	−0.889411	−	1.54051i	−0.840573	−	0.541698i	$-0.817781\pi$
$283$	−14.9622	−	25.9153i	−0.889411	−	1.54051i	−0.0488382	−	0.998807i	$-0.515552\pi$
$284$		0			0
$285$	−5.27492			−0.312459
$286$		0			0
$287$	−6.54983			−0.386625
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$	14.8248			0.869042
$292$		0			0
$293$	10.3625	−	17.9484i	0.605386	−	1.04856i	−0.386604	−	0.922246i	$-0.626352\pi$
$293$	10.3625	−	17.9484i	0.605386	−	1.04856i	0.991990	−	0.126314i	$-0.0403146\pi$
$294$		0			0
$295$	0.274917	−	0.476171i	0.0160063	−	0.0277237i
$296$		0			0
$297$	1.63746	+	2.83616i	0.0950150	+	0.164571i
$298$		0			0
$299$	−8.54983	+	29.6175i	−0.494450	+	1.71282i
$300$		0			0
$301$	0.137459	+	0.238085i	0.00792298	+	0.0137230i
$302$		0			0
$303$	4.27492	−	7.40437i	0.245588	−	0.425370i
$304$		0			0
$305$	−2.13746	+	3.70219i	−0.122391	+	0.211987i
$306$		0			0
$307$	29.9244			1.70788			0.853938	−	0.520374i	$-0.174207\pi$
$307$	29.9244			1.70788			0.853938	+	0.520374i	$0.174207\pi$
$308$		0			0
$309$	−0.225083	−	0.389855i	−0.0128045	−	0.0221781i
$310$		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
$313$	12.2749			0.693819			0.346910	−	0.937899i	$-0.387231\pi$
$313$	12.2749			0.693819			0.346910	+	0.937899i	$0.387231\pi$
$314$		0			0
$315$	−0.500000	−	0.866025i	−0.0281718	−	0.0487950i
$316$		0			0
$317$	18.3746			1.03202			0.516010	−	0.856583i	$-0.327417\pi$
$317$	18.3746			1.03202			0.516010	+	0.856583i	$0.327417\pi$
$318$		0			0
$319$	−7.45017	+	12.9041i	−0.417129	+	0.722489i
$320$		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
$327$	4.41238	+	7.64246i	0.244005	+	0.422629i
$328$		0			0
$329$	1.63746	−	2.83616i	0.0902760	−	0.156363i
$330$		0			0
$331$	13.1375	−	22.7547i	0.722100	−	1.25071i	−0.238057	−	0.971251i	$-0.576510\pi$
$331$	13.1375	−	22.7547i	0.722100	−	1.25071i	0.960157	−	0.279463i	$-0.0901563\pi$
$332$		0			0
$333$	−7.27492			−0.398663
$334$		0			0
$335$	−1.13746	−	1.97014i	−0.0621460	−	0.107640i
$336$		0			0
$337$	11.7251			0.638706			0.319353	−	0.947636i	$-0.396534\pi$
$337$	11.7251			0.638706			0.319353	+	0.947636i	$0.396534\pi$
$338$		0			0
$339$	20.5498			1.11611
$340$		0			0
$341$	−0.450166	−	0.779710i	−0.0243778	−	0.0422236i
$342$		0			0
$343$	−13.0000			−0.701934
$344$		0			0
$345$	−4.27492	+	7.40437i	−0.230154	+	0.398638i
$346$		0			0
$347$	−6.54983	+	11.3446i	−0.351614	+	0.609013i	−0.986532	−	0.163566i	$-0.947700\pi$
$347$	−6.54983	+	11.3446i	−0.351614	+	0.609013i	0.634919	+	0.772579i	$0.281034\pi$
$348$		0			0
$349$	−15.9622	−	27.6474i	−0.854438	−	1.47993i	−0.877166	−	0.480188i	$-0.840569\pi$
$349$	−15.9622	−	27.6474i	−0.854438	−	1.47993i	0.0227283	−	0.999742i	$-0.492765\pi$
$350$		0			0
$351$	−2.50000	−	2.59808i	−0.133440	−	0.138675i
$352$		0			0
$353$	−7.72508	−	13.3802i	−0.411165	−	0.712158i	0.583853	−	0.811860i	$-0.301545\pi$
$353$	−7.72508	−	13.3802i	−0.411165	−	0.712158i	−0.995017	+	0.0997015i	$0.968211\pi$
$354$		0			0
$355$	1.00000	−	1.73205i	0.0530745	−	0.0919277i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	13.4502			0.709873			0.354936	−	0.934890i	$-0.384503\pi$
$359$	13.4502			0.709873			0.354936	+	0.934890i	$0.384503\pi$
$360$		0			0
$361$	−4.41238	−	7.64246i	−0.232230	−	0.402235i
$362$		0			0
$363$	0.274917			0.0144294
$364$		0			0
$365$	−10.8248			−0.566593
$366$		0			0
$367$	−4.86254	−	8.42217i	−0.253823	−	0.439634i	0.710752	−	0.703442i	$-0.248355\pi$
$367$	−4.86254	−	8.42217i	−0.253823	−	0.439634i	−0.964575	+	0.263809i	$0.915021\pi$
$368$		0			0
$369$	−6.54983			−0.340971
$370$		0			0
$371$	−4.63746	+	8.03231i	−0.240765	+	0.417017i
$372$		0			0
$373$	3.86254	−	6.69012i	0.199995	−	0.346401i	−0.748532	−	0.663099i	$-0.769241\pi$
$373$	3.86254	−	6.69012i	0.199995	−	0.346401i	0.948526	+	0.316698i	$0.102574\pi$
$374$		0			0
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$		0			0
$377$	4.54983	−	15.7611i	0.234328	−	0.811737i
$378$		0			0
$379$	−3.22508	−	5.58601i	−0.165661	−	0.286934i	0.771229	−	0.636558i	$-0.219643\pi$
$379$	−3.22508	−	5.58601i	−0.165661	−	0.286934i	−0.936890	+	0.349624i	$0.886309\pi$
$380$		0			0
$381$	0.500000	−	0.866025i	0.0256158	−	0.0443678i
$382$		0			0
$383$	−2.54983	+	4.41644i	−0.130290	+	0.225670i	−0.923789	−	0.382903i	$-0.874924\pi$
$383$	−2.54983	+	4.41644i	−0.130290	+	0.225670i	0.793498	+	0.608573i	$0.208258\pi$
$384$		0			0
$385$	3.27492			0.166905
$386$		0			0
$387$	0.137459	+	0.238085i	0.00698741	+	0.0121026i
$388$		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
$393$	5.63746	+	9.76436i	0.284372	+	0.492547i
$394$		0			0
$395$	−8.27492			−0.416356
$396$		0			0
$397$	13.0498	−	22.6030i	0.654952	−	1.13441i	−0.326953	−	0.945040i	$-0.606022\pi$
$397$	13.0498	−	22.6030i	0.654952	−	1.13441i	0.981906	−	0.189370i	$-0.0606447\pi$
$398$		0			0
$399$	2.63746	−	4.56821i	0.132038	−	0.228697i
$400$		0			0
$401$	−6.46221	−	11.1929i	−0.322707	−	0.558946i	0.658338	−	0.752722i	$-0.271260\pi$
$401$	−6.46221	−	11.1929i	−0.322707	−	0.558946i	−0.981046	+	0.193777i	$0.937926\pi$
$402$		0			0
$403$	0.687293	+	0.714256i	0.0342365	+	0.0355796i
$404$		0			0
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$		0			0
$407$	11.9124	−	20.6328i	0.590475	−	1.02273i
$408$		0			0
$409$	−17.0498	+	29.5312i	−0.843060	+	1.46022i	0.0442353	+	0.999021i	$0.485915\pi$
$409$	−17.0498	+	29.5312i	−0.843060	+	1.46022i	−0.887295	+	0.461202i	$0.847418\pi$
$410$		0			0
$411$	−9.09967			−0.448854
$412$		0			0
$413$	0.274917	+	0.476171i	0.0135278	+	0.0234308i
$414$		0			0
$415$	−13.0997			−0.643037
$416$		0			0
$417$	−11.0000			−0.538672
$418$		0			0
$419$	−15.0997	−	26.1534i	−0.737667	−	1.27768i	−0.953543	−	0.301256i	$-0.902594\pi$
$419$	−15.0997	−	26.1534i	−0.737667	−	1.27768i	0.215876	−	0.976421i	$-0.430739\pi$
$420$		0			0
$421$	−6.82475			−0.332618			−0.166309	−	0.986074i	$-0.553185\pi$
$421$	−6.82475			−0.332618			−0.166309	+	0.986074i	$0.553185\pi$
$422$		0			0
$423$	1.63746	−	2.83616i	0.0796160	−	0.137899i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−2.13746	−	3.70219i	−0.103439	−	0.179161i
$428$		0			0
$429$	11.4622	−	2.83616i	0.553401	−	0.136931i
$430$		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
$433$	11.6873	−	20.2430i	0.561655	−	0.972816i	−0.435697	−	0.900094i	$-0.643498\pi$
$433$	11.6873	−	20.2430i	0.561655	−	0.972816i	0.997352	−	0.0727223i	$-0.0231687\pi$
$434$		0			0
$435$	2.27492	−	3.94027i	0.109074	−	0.188922i
$436$		0			0
$437$	−45.0997			−2.15741
$438$		0			0
$439$	16.1375	+	27.9509i	0.770199	+	1.33402i	0.937454	+	0.348110i	$0.113176\pi$
$439$	16.1375	+	27.9509i	0.770199	+	1.33402i	−0.167255	+	0.985914i	$0.553490\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$		0			0
$443$	27.6495			1.31367			0.656834	−	0.754035i	$-0.271895\pi$
$443$	27.6495			1.31367			0.656834	+	0.754035i	$0.271895\pi$
$444$		0			0
$445$	6.63746	+	11.4964i	0.314646	+	0.544982i
$446$		0			0
$447$	1.45017			0.0685905
$448$		0			0
$449$	−11.6375	+	20.1567i	−0.549206	+	0.951252i	0.449124	+	0.893470i	$0.351736\pi$
$449$	−11.6375	+	20.1567i	−0.549206	+	0.951252i	−0.998329	+	0.0577824i	$0.981597\pi$
$450$		0			0
$451$	10.7251	−	18.5764i	0.505024	−	0.874728i
$452$		0			0
$453$	−9.27492	−	16.0646i	−0.435774	−	0.754782i
$454$		0			0
$455$	−3.50000	+	0.866025i	−0.164083	+	0.0405999i
$456$		0			0
$457$	4.68729	+	8.11863i	0.219262	+	0.379773i	0.954583	−	0.297946i	$-0.0963016\pi$
$457$	4.68729	+	8.11863i	0.219262	+	0.379773i	−0.735320	+	0.677720i	$0.762968\pi$
$458$		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
$463$	−38.2749			−1.77879			−0.889393	−	0.457143i	$-0.848873\pi$
$463$	−38.2749			−1.77879			−0.889393	+	0.457143i	$0.848873\pi$
$464$		0			0
$465$	0.137459	+	0.238085i	0.00637449	+	0.0110409i
$466$		0			0
$467$	−0.549834			−0.0254433			−0.0127217	−	0.999919i	$-0.504050\pi$
$467$	−0.549834			−0.0254433			−0.0127217	+	0.999919i	$0.504050\pi$
$468$		0			0
$469$	2.27492			0.105046
$470$		0			0
$471$	−1.77492	−	3.07425i	−0.0817839	−	0.141654i
$472$		0			0
$473$	−0.900331			−0.0413973
$474$		0			0
$475$	−2.63746	+	4.56821i	−0.121015	+	0.209604i
$476$		0			0
$477$	−4.63746	+	8.03231i	−0.212335	+	0.367774i
$478$		0			0
$479$	0.549834	+	0.952341i	0.0251226	+	0.0435136i	0.878313	−	0.478085i	$-0.158669\pi$
$479$	0.549834	+	0.952341i	0.0251226	+	0.0435136i	−0.853191	+	0.521599i	$0.825336\pi$
$480$		0			0
$481$	−7.27492	+	25.2011i	−0.331708	+	1.14907i
$482$		0			0
$483$	−4.27492	−	7.40437i	−0.194515	−	0.336911i
$484$		0			0
$485$	7.41238	−	12.8386i	0.336579	−	0.582971i
$486$		0			0
$487$	13.3625	−	23.1446i	0.605515	−	1.04878i	−0.386455	−	0.922308i	$-0.626301\pi$
$487$	13.3625	−	23.1446i	0.605515	−	1.04878i	0.991970	−	0.126474i	$-0.0403660\pi$
$488$		0			0
$489$	−10.2749			−0.464648
$490$		0			0
$491$	14.9124	+	25.8290i	0.672986	+	1.16565i	0.977053	+	0.212995i	$0.0683220\pi$
$491$	14.9124	+	25.8290i	0.672986	+	1.16565i	−0.304067	+	0.952651i	$0.598345\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	3.27492			0.147197
$496$		0			0
$497$	1.00000	+	1.73205i	0.0448561	+	0.0776931i
$498$		0			0
$499$	−13.0997			−0.586422			−0.293211	−	0.956048i	$-0.594724\pi$
$499$	−13.0997			−0.586422			−0.293211	+	0.956048i	$0.594724\pi$
$500$		0			0
$501$	−1.36254	+	2.35999i	−0.0608739	+	0.105437i
$502$		0			0
$503$	1.08762	−	1.88382i	0.0484948	−	0.0839954i	−0.840759	−	0.541409i	$-0.817891\pi$
$503$	1.08762	−	1.88382i	0.0484948	−	0.0839954i	0.889254	+	0.457414i	$0.151224\pi$
$504$		0			0
$505$	−4.27492	−	7.40437i	−0.190231	−	0.329490i
$506$		0			0
$507$	−11.5000	+	6.06218i	−0.510733	+	0.269231i
$508$		0			0
$509$	3.54983	+	6.14849i	0.157344	+	0.272527i	0.933910	−	0.357508i	$-0.116374\pi$
$509$	3.54983	+	6.14849i	0.157344	+	0.272527i	−0.776566	+	0.630036i	$0.783040\pi$
$510$		0			0
$511$	5.41238	−	9.37451i	0.239429	−	0.414704i
$512$		0			0
$513$	2.63746	−	4.56821i	0.116447	−	0.201692i
$514$		0			0
$515$	−0.450166			−0.0198367
$516$		0			0
$517$	5.36254	+	9.28819i	0.235844	+	0.408494i
$518$		0			0
$519$	23.2749			1.02166
$520$		0			0
$521$	−21.2749			−0.932071			−0.466036	−	0.884766i	$-0.654318\pi$
$521$	−21.2749			−0.932071			−0.466036	+	0.884766i	$0.654318\pi$
$522$		0			0
$523$	−8.72508	−	15.1123i	−0.381521	−	0.660814i	0.609759	−	0.792587i	$-0.291266\pi$
$523$	−8.72508	−	15.1123i	−0.381521	−	0.660814i	−0.991280	+	0.131773i	$0.957933\pi$
$524$		0			0
$525$	−1.00000			−0.0436436
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−25.0498	+	43.3876i	−1.08912	+	1.88642i
$530$		0			0
$531$	0.274917	+	0.476171i	0.0119304	+	0.0206640i
$532$		0			0
$533$	−6.54983	+	22.6893i	−0.283705	+	0.982782i
$534$		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
$539$	9.82475	−	17.0170i	0.423182	−	0.732973i
$540$		0			0
$541$	−7.17525			−0.308488			−0.154244	−	0.988033i	$-0.549294\pi$
$541$	−7.17525			−0.308488			−0.154244	+	0.988033i	$0.549294\pi$
$542$		0			0
$543$	−1.00000	−	1.73205i	−0.0429141	−	0.0743294i
$544$		0			0
$545$	8.82475			0.378011
$546$		0			0
$547$	7.17525			0.306791			0.153396	−	0.988165i	$-0.450979\pi$
$547$	7.17525			0.306791			0.153396	+	0.988165i	$0.450979\pi$
$548$		0			0
$549$	−2.13746	−	3.70219i	−0.0912245	−	0.158005i
$550$		0			0
$551$	24.0000			1.02243
$552$		0			0
$553$	4.13746	−	7.16629i	0.175943	−	0.304742i
$554$		0			0
$555$	−3.63746	+	6.30026i	−0.154402	+	0.267431i
$556$		0			0
$557$	21.1873	+	36.6975i	0.897734	+	1.55492i	0.830384	+	0.557192i	$0.188121\pi$
$557$	21.1873	+	36.6975i	0.897734	+	1.55492i	0.0673509	+	0.997729i	$0.478545\pi$
$558$		0			0
$559$	0.962210	−	0.238085i	0.0406972	−	0.0100699i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.72508	−	2.98793i	0.0727036	−	0.125926i	−0.827382	−	0.561640i	$-0.810171\pi$
$563$	1.72508	−	2.98793i	0.0727036	−	0.125926i	0.900085	+	0.435714i	$0.143504\pi$
$564$		0			0
$565$	10.2749	−	17.7967i	0.432269	−	0.748712i
$566$		0			0
$567$	1.00000			0.0419961
$568$		0			0
$569$	1.81271	+	3.13970i	0.0759926	+	0.131623i	0.901518	−	0.432743i	$-0.142454\pi$
$569$	1.81271	+	3.13970i	0.0759926	+	0.131623i	−0.825525	+	0.564366i	$0.809121\pi$
$570$		0			0
$571$	42.3746			1.77332			0.886661	−	0.462421i	$-0.153019\pi$
$571$	42.3746			1.77332			0.886661	+	0.462421i	$0.153019\pi$
$572$		0			0
$573$	18.0000			0.751961
$574$		0			0
$575$	4.27492	+	7.40437i	0.178276	+	0.308784i
$576$		0			0
$577$	0.900331			0.0374813			0.0187406	−	0.999824i	$-0.494034\pi$
$577$	0.900331			0.0374813			0.0187406	+	0.999824i	$0.494034\pi$
$578$		0			0
$579$	−11.6873	+	20.2430i	−0.485707	+	0.841270i
$580$		0			0
$581$	6.54983	−	11.3446i	0.271733	−	0.470655i
$582$		0			0
$583$	−15.1873	−	26.3052i	−0.628993	−	1.08945i
$584$		0			0
$585$	−3.50000	+	0.866025i	−0.144707	+	0.0358057i
$586$		0			0
$587$	−20.0997	−	34.8136i	−0.829602	−	1.43691i	−0.898351	−	0.439279i	$-0.855234\pi$
$587$	−20.0997	−	34.8136i	−0.829602	−	1.43691i	0.0687486	−	0.997634i	$-0.478099\pi$
$588$		0			0
$589$	−0.725083	+	1.25588i	−0.0298765	+	0.0517476i
$590$		0			0
$591$	9.91238	−	17.1687i	0.407741	−	0.706228i
$592$		0			0
$593$	−32.5498			−1.33666			−0.668331	−	0.743864i	$-0.732991\pi$
$593$	−32.5498			−1.33666			−0.668331	+	0.743864i	$0.732991\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−12.2749			−0.502379
$598$		0			0
$599$	35.0997			1.43413			0.717067	−	0.697004i	$-0.245484\pi$
$599$	35.0997			1.43413			0.717067	+	0.697004i	$0.245484\pi$
$600$		0			0
$601$	14.3625	+	24.8767i	0.585860	+	1.01474i	0.994768	+	0.102164i	$0.0325766\pi$
$601$	14.3625	+	24.8767i	0.585860	+	1.01474i	−0.408907	+	0.912576i	$0.634090\pi$
$602$		0			0
$603$	2.27492			0.0926418
$604$		0			0
$605$	0.137459	−	0.238085i	0.00558849	−	0.00967954i
$606$		0			0
$607$	11.1873	−	19.3770i	0.454078	−	0.786487i	−0.544556	−	0.838724i	$-0.683302\pi$
$607$	11.1873	−	19.3770i	0.454078	−	0.786487i	0.998635	+	0.0522376i	$0.0166353\pi$
$608$		0			0
$609$	2.27492	+	3.94027i	0.0921843	+	0.159668i
$610$		0			0
$611$	−8.18729	−	8.50848i	−0.331222	−	0.344216i
$612$		0			0
$613$	−20.5997	−	35.6797i	−0.832013	−	1.44109i	−0.896440	−	0.443166i	$-0.853855\pi$
$613$	−20.5997	−	35.6797i	−0.832013	−	1.44109i	0.0644268	−	0.997922i	$-0.479478\pi$
$614$		0			0
$615$	−3.27492	+	5.67232i	−0.132057	+	0.228730i
$616$		0			0
$617$	−17.5498	+	30.3972i	−0.706530	+	1.22375i	0.259607	+	0.965714i	$0.416407\pi$
$617$	−17.5498	+	30.3972i	−0.706530	+	1.22375i	−0.966137	+	0.258031i	$0.916926\pi$
$618$		0			0
$619$	−7.54983			−0.303453			−0.151727	−	0.988422i	$-0.548483\pi$
$619$	−7.54983			−0.303453			−0.151727	+	0.988422i	$0.548483\pi$
$620$		0			0
$621$	−4.27492	−	7.40437i	−0.171547	−	0.297127i
$622$		0			0
$623$	−13.2749			−0.531848
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	8.63746	+	14.9605i	0.344947	+	0.597466i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−5.13746	+	8.89834i	−0.204519	+	0.354237i	−0.949979	−	0.312313i	$-0.898896\pi$
$631$	−5.13746	+	8.89834i	−0.204519	+	0.354237i	0.745460	+	0.666550i	$0.232230\pi$
$632$		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
$641$	−9.46221	+	16.3890i	−0.373735	+	0.647328i	−0.990137	−	0.140104i	$-0.955256\pi$
$641$	−9.46221	+	16.3890i	−0.373735	+	0.647328i	0.616402	+	0.787432i	$0.288590\pi$
$642$		0			0
$643$	−5.13746	+	8.89834i	−0.202602	+	0.350916i	−0.949366	−	0.314173i	$-0.898273\pi$
$643$	−5.13746	+	8.89834i	−0.202602	+	0.350916i	0.746764	+	0.665089i	$0.231606\pi$
$644$		0			0
$645$	0.274917			0.0108249
$646$		0			0
$647$	18.9124	+	32.7572i	0.743522	+	1.28782i	0.950882	+	0.309554i	$0.100180\pi$
$647$	18.9124	+	32.7572i	0.743522	+	1.28782i	−0.207360	+	0.978265i	$0.566487\pi$
$648$		0			0
$649$	−1.80066			−0.0706822
$650$		0			0
$651$	−0.274917			−0.0107749
$652$		0			0
$653$	−13.9124	−	24.0969i	−0.544433	−	0.942986i	−0.998642	−	0.0520910i	$-0.983411\pi$
$653$	−13.9124	−	24.0969i	−0.544433	−	0.942986i	0.454209	−	0.890895i	$-0.349922\pi$
$654$		0			0
$655$	11.2749			0.440547
$656$		0			0
$657$	5.41238	−	9.37451i	0.211157	−	0.365734i
$658$		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
$661$	14.9622	+	25.9153i	0.581963	+	1.00799i	0.995247	+	0.0973865i	$0.0310483\pi$
$661$	14.9622	+	25.9153i	0.581963	+	1.00799i	−0.413284	+	0.910602i	$0.635618\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−2.63746	−	4.56821i	−0.102276	−	0.177148i
$666$		0			0
$667$	19.4502	−	33.6887i	0.753113	−	1.30443i
$668$		0			0
$669$	2.08762	−	3.61587i	0.0807122	−	0.139798i
$670$		0			0
$671$	14.0000			0.540464
$672$		0			0
$673$	23.6873	+	41.0276i	0.913078	+	1.58150i	0.809691	+	0.586856i	$0.199635\pi$
$673$	23.6873	+	41.0276i	0.913078	+	1.58150i	0.103387	+	0.994641i	$0.467032\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	−22.5498			−0.866661			−0.433330	−	0.901235i	$-0.642662\pi$
$677$	−22.5498			−0.866661			−0.433330	+	0.901235i	$0.642662\pi$
$678$		0			0
$679$	7.41238	+	12.8386i	0.284461	+	0.492701i
$680$		0			0
$681$	21.0997			0.808541
$682$		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
$685$	−4.54983	+	7.88054i	−0.173840	+	0.301100i
$686$		0			0
$687$	−5.00000	−	8.66025i	−0.190762	−	0.330409i
$688$		0			0
$689$	23.1873	+	24.0969i	0.883366	+	0.918020i
$690$		0			0
$691$	−5.32475	−	9.22274i	−0.202563	−	0.350850i	0.746790	−	0.665059i	$-0.231594\pi$
$691$	−5.32475	−	9.22274i	−0.202563	−	0.350850i	−0.949354	+	0.314210i	$0.898260\pi$
$692$		0			0
$693$	−1.63746	+	2.83616i	−0.0622019	+	0.107737i
$694$		0			0
$695$	−5.50000	+	9.52628i	−0.208627	+	0.361352i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	−3.54983	−	6.14849i	−0.134267	−	0.232557i
$700$		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
$703$	−38.3746			−1.44732
$704$		0			0
$705$	−1.63746	−	2.83616i	−0.0616703	−	0.106816i
$706$		0			0
$707$	8.54983			0.321550
$708$		0			0
$709$	−9.13746	+	15.8265i	−0.343164	+	0.594378i	−0.985019	−	0.172449i	$-0.944832\pi$
$709$	−9.13746	+	15.8265i	−0.343164	+	0.594378i	0.641854	+	0.766827i	$0.278165\pi$
$710$		0			0
$711$	4.13746	−	7.16629i	0.155167	−	0.268757i
$712$		0			0
$713$	1.17525	+	2.03559i	0.0440134	+	0.0762334i
$714$		0			0
$715$	3.27492	−	11.3446i	0.122475	−	0.424266i
$716$		0			0
$717$	5.27492	+	9.13642i	0.196995	+	0.341206i
$718$		0			0
$719$	3.72508	−	6.45203i	0.138922	−	0.240620i	−0.788167	−	0.615462i	$-0.788970\pi$
$719$	3.72508	−	6.45203i	0.138922	−	0.240620i	0.927089	+	0.374842i	$0.122303\pi$
$720$		0			0
$721$	0.225083	−	0.389855i	0.00838252	−	0.0145190i
$722$		0			0
$723$	−0.725083			−0.0269661
$724$		0			0
$725$	−2.27492	−	3.94027i	−0.0844883	−	0.146338i
$726$		0			0
$727$	43.5498			1.61517			0.807587	−	0.589748i	$-0.200773\pi$
$727$	43.5498			1.61517			0.807587	+	0.589748i	$0.200773\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−18.6495			−0.688835			−0.344418	−	0.938817i	$-0.611924\pi$
$733$	−18.6495			−0.688835			−0.344418	+	0.938817i	$0.611924\pi$
$734$		0			0
$735$	−3.00000	+	5.19615i	−0.110657	+	0.191663i
$736$		0			0
$737$	−3.72508	+	6.45203i	−0.137215	+	0.237664i
$738$		0			0
$739$	−6.63746	−	11.4964i	−0.244163	−	0.422902i	0.717733	−	0.696318i	$-0.245180\pi$
$739$	−6.63746	−	11.4964i	−0.244163	−	0.422902i	−0.961896	+	0.273416i	$0.911846\pi$
$740$		0			0
$741$	−13.1873	−	13.7046i	−0.484447	−	0.503452i
$742$		0			0
$743$	−10.8248	−	18.7490i	−0.397122	−	0.687835i	0.596248	−	0.802800i	$-0.296658\pi$
$743$	−10.8248	−	18.7490i	−0.397122	−	0.687835i	−0.993369	+	0.114966i	$0.963324\pi$
$744$		0			0
$745$	0.725083	−	1.25588i	0.0265650	−	0.0460119i
$746$		0			0
$747$	6.54983	−	11.3446i	0.239646	−	0.415079i
$748$		0			0
$749$	−15.0997			−0.551730
$750$		0			0
$751$	18.5498	+	32.1293i	0.676893	+	1.17241i	0.975912	+	0.218166i	$0.0700074\pi$
$751$	18.5498	+	32.1293i	0.676893	+	1.17241i	−0.299019	+	0.954247i	$0.596659\pi$
$752$		0			0
$753$	18.7251			0.682380
$754$		0			0
$755$	−18.5498			−0.675098
$756$		0			0
$757$	12.1873	+	21.1090i	0.442955	+	0.767220i	0.997907	−	0.0646620i	$-0.0205969\pi$
$757$	12.1873	+	21.1090i	0.442955	+	0.767220i	−0.554953	+	0.831882i	$0.687264\pi$
$758$		0			0
$759$	28.0000			1.01634
$760$		0			0
$761$	−6.81271	+	11.8000i	−0.246960	+	0.427748i	−0.962681	−	0.270639i	$-0.912765\pi$
$761$	−6.81271	+	11.8000i	−0.246960	+	0.427748i	0.715721	+	0.698387i	$0.246098\pi$
$762$		0			0
$763$	−4.41238	+	7.64246i	−0.159739	+	0.276676i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.92442	−	0.476171i	0.0694868	−	0.0171935i
$768$		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
$773$	14.7371	−	25.5255i	0.530058	−	0.918087i	−0.469327	−	0.883024i	$-0.655504\pi$
$773$	14.7371	−	25.5255i	0.530058	−	0.918087i	0.999385	−	0.0350626i	$-0.0111630\pi$
$774$		0			0
$775$	0.274917			0.00987532
$776$		0			0
$777$	−3.63746	−	6.30026i	−0.130493	−	0.226021i
$778$		0			0
$779$	−34.5498			−1.23788
$780$		0			0
$781$	−6.54983			−0.234372
$782$		0			0
$783$	2.27492	+	3.94027i	0.0812989	+	0.140814i
$784$		0			0
$785$	−3.54983			−0.126699
$786$		0			0
$787$	−7.68729	+	13.3148i	−0.274022	+	0.474621i	−0.969888	−	0.243551i	$-0.921688\pi$
$787$	−7.68729	+	13.3148i	−0.274022	+	0.474621i	0.695866	+	0.718172i	$0.255021\pi$
$788$		0			0
$789$	2.63746	−	4.56821i	0.0938960	−	0.162633i
$790$		0			0
$791$	10.2749	+	17.7967i	0.365334	+	0.632777i
$792$		0			0
$793$	−14.9622	+	3.70219i	−0.531324	+	0.131469i
$794$		0			0
$795$	4.63746	+	8.03231i	0.164474	+	0.284877i
$796$		0			0
$797$	−7.27492	+	12.6005i	−0.257691	+	0.446334i	−0.965623	−	0.259947i	$-0.916295\pi$
$797$	−7.27492	+	12.6005i	−0.257691	+	0.446334i	0.707932	+	0.706280i	$0.249628\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−13.2749			−0.469046
$802$		0			0
$803$	17.7251	+	30.7007i	0.625505	+	1.08341i
$804$		0			0
$805$	−8.54983			−0.301342
$806$		0			0
$807$	12.0000			0.422420
$808$		0			0
$809$	23.2749	+	40.3133i	0.818303	+	1.41734i	0.906932	+	0.421277i	$0.138418\pi$
$809$	23.2749	+	40.3133i	0.818303	+	1.41734i	−0.0886296	+	0.996065i	$0.528249\pi$
$810$		0			0
$811$	0.450166			0.0158075			0.00790373	−	0.999969i	$-0.497484\pi$
$811$	0.450166			0.0158075			0.00790373	+	0.999969i	$0.497484\pi$
$812$		0			0
$813$	8.86254	−	15.3504i	0.310823	−	0.538361i
$814$		0			0
$815$	−5.13746	+	8.89834i	−0.179957	+	0.311695i
$816$		0			0
$817$	0.725083	+	1.25588i	0.0253674	+	0.0439377i
$818$		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
$823$	−23.1873	+	40.1616i	−0.808258	+	1.39994i	0.105811	+	0.994386i	$0.466256\pi$
$823$	−23.1873	+	40.1616i	−0.808258	+	1.39994i	−0.914069	+	0.405558i	$0.867077\pi$
$824$		0			0
$825$	1.63746	−	2.83616i	0.0570090	−	0.0987425i
$826$		0			0
$827$	−1.45017			−0.0504272			−0.0252136	−	0.999682i	$-0.508027\pi$
$827$	−1.45017			−0.0504272			−0.0252136	+	0.999682i	$0.508027\pi$
$828$		0			0
$829$	−0.587624	−	1.01779i	−0.0204090	−	0.0353495i	0.855641	−	0.517571i	$-0.173164\pi$
$829$	−0.587624	−	1.01779i	−0.0204090	−	0.0353495i	−0.876050	+	0.482221i	$0.839830\pi$
$830$		0			0
$831$	6.17525			0.214217
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.36254	+	2.35999i	0.0471527	+	0.0816709i
$836$		0			0
$837$	−0.274917			−0.00950253
$838$		0			0
$839$	−13.5498	+	23.4690i	−0.467792	+	0.810240i	−0.999323	−	0.0367993i	$-0.988284\pi$
$839$	−13.5498	+	23.4690i	−0.467792	+	0.810240i	0.531530	+	0.847039i	$0.321617\pi$
$840$		0			0
$841$	4.14950	−	7.18715i	0.143086	−	0.247833i
$842$		0			0
$843$	1.54983	+	2.68439i	0.0533791	+	0.0924554i
$844$		0			0
$845$	−0.500000	+	12.9904i	−0.0172005	+	0.446883i
$846$		0			0
$847$	0.137459	+	0.238085i	0.00472313	+	0.00818071i
$848$		0			0
$849$	14.9622	−	25.9153i	0.513502	−	0.889411i
$850$		0			0
$851$	−31.0997	+	53.8662i	−1.06608	+	1.84651i
$852$		0			0
$853$	43.5739			1.49194			0.745971	−	0.665978i	$-0.231986\pi$
$853$	43.5739			1.49194			0.745971	+	0.665978i	$0.231986\pi$
$854$		0			0
$855$	−2.63746	−	4.56821i	−0.0901992	−	0.156230i
$856$		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
$859$	28.6495			0.977508			0.488754	−	0.872422i	$-0.337451\pi$
$859$	28.6495			0.977508			0.488754	+	0.872422i	$0.337451\pi$
$860$		0			0
$861$	−3.27492	−	5.67232i	−0.111609	−	0.193312i
$862$		0			0
$863$	45.6495			1.55393			0.776964	−	0.629546i	$-0.216759\pi$
$863$	45.6495			1.55393			0.776964	+	0.629546i	$0.216759\pi$
$864$		0			0
$865$	11.6375	−	20.1567i	0.395685	−	0.685347i
$866$		0			0
$867$	−8.50000	+	14.7224i	−0.288675	+	0.500000i
$868$		0			0
$869$	13.5498	+	23.4690i	0.459647	+	0.796131i
$870$		0			0
$871$	2.27492	−	7.88054i	0.0770826	−	0.267022i
$872$		0			0
$873$	7.41238	+	12.8386i	0.250871	+	0.434521i
$874$		0			0
$875$	−0.500000	+	0.866025i	−0.0169031	+	0.0292770i
$876$		0			0
$877$	17.5498	−	30.3972i	0.592616	−	1.02644i	−0.401263	−	0.915963i	$-0.631429\pi$
$877$	17.5498	−	30.3972i	0.592616	−	1.02644i	0.993879	−	0.110478i	$-0.0352381\pi$
$878$		0			0
$879$	20.7251			0.699040
$880$		0			0
$881$	21.7371	+	37.6498i	0.732342	+	1.26845i	0.955880	+	0.293759i	$0.0949063\pi$
$881$	21.7371	+	37.6498i	0.732342	+	1.26845i	−0.223537	+	0.974695i	$0.571760\pi$
$882$		0			0
$883$	33.3746			1.12314			0.561572	−	0.827428i	$-0.310197\pi$
$883$	33.3746			1.12314			0.561572	+	0.827428i	$0.310197\pi$
$884$		0			0
$885$	0.549834			0.0184825
$886$		0			0
$887$	−9.46221	−	16.3890i	−0.317710	−	0.550290i	0.662300	−	0.749239i	$-0.269580\pi$
$887$	−9.46221	−	16.3890i	−0.317710	−	0.550290i	−0.980010	+	0.198949i	$0.936247\pi$
$888$		0			0
$889$	1.00000			0.0335389
$890$		0			0
$891$	−1.63746	+	2.83616i	−0.0548569	+	0.0950150i
$892$		0			0
$893$	8.63746	−	14.9605i	0.289042	−	0.500635i
$894$		0			0
$895$	6.00000	+	10.3923i	0.200558	+	0.347376i
$896$		0			0
$897$	−29.9244	+	7.40437i	−0.999147	+	0.247225i
$898$		0			0
$899$	−0.625414	−	1.08325i	−0.0208587	−	0.0361284i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−0.137459	+	0.238085i	−0.00457434	+	0.00792298i
$904$		0			0
$905$	−2.00000			−0.0664822
$906$		0			0
$907$	4.72508	+	8.18408i	0.156894	+	0.271748i	0.933747	−	0.357934i	$-0.116519\pi$
$907$	4.72508	+	8.18408i	0.156894	+	0.271748i	−0.776853	+	0.629682i	$0.783185\pi$
$908$		0			0
$909$	8.54983			0.283580
$910$		0			0
$911$	−21.0997			−0.699063			−0.349532	−	0.936925i	$-0.613659\pi$
$911$	−21.0997			−0.699063			−0.349532	+	0.936925i	$0.613659\pi$
$912$		0			0
$913$	21.4502	+	37.1528i	0.709897	+	1.22958i
$914$		0			0
$915$	−4.27492			−0.141324
$916$		0			0
$917$	−5.63746	+	9.76436i	−0.186165	+	0.322448i
$918$		0			0
$919$	1.27492	−	2.20822i	0.0420556	−	0.0728425i	−0.844231	−	0.535979i	$-0.819943\pi$
$919$	1.27492	−	2.20822i	0.0420556	−	0.0728425i	0.886287	+	0.463136i	$0.153276\pi$
$920$		0			0
$921$	14.9622	+	25.9153i	0.493022	+	0.853938i
$922$		0			0
$923$	7.00000	−	1.73205i	0.230408	−	0.0570111i
$924$		0			0
$925$	3.63746	+	6.30026i	0.119599	+	0.207151i
$926$		0			0
$927$	0.225083	−	0.389855i	0.00739269	−	0.0128045i
$928$		0			0
$929$	1.82475	−	3.16056i	0.0598682	−	0.103695i	−0.834538	−	0.550950i	$-0.814265\pi$
$929$	1.82475	−	3.16056i	0.0598682	−	0.103695i	0.894406	+	0.447256i	$0.147599\pi$
$930$		0			0
$931$	−31.6495			−1.03727
$932$		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
$939$	6.13746	+	10.6304i	0.200288	+	0.346910i
$940$		0			0
$941$	−45.6495			−1.48813			−0.744066	−	0.668107i	$-0.767105\pi$
$941$	−45.6495			−1.48813			−0.744066	+	0.668107i	$0.767105\pi$
$942$		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
$947$	25.8248	+	44.7298i	0.839192	+	1.45352i	0.890571	+	0.454843i	$0.150305\pi$
$947$	25.8248	+	44.7298i	0.839192	+	1.45352i	−0.0513798	+	0.998679i	$0.516362\pi$
$948$		0			0
$949$	−27.0619	−	28.1235i	−0.878466	−	0.912928i
$950$		0			0
$951$	9.18729	+	15.9129i	0.297918	+	0.516010i
$952$		0			0
$953$	−20.0997	+	34.8136i	−0.651092	+	1.12772i	0.331766	+	0.943362i	$0.392356\pi$
$953$	−20.0997	+	34.8136i	−0.651092	+	1.12772i	−0.982858	+	0.184363i	$0.940978\pi$
$954$		0			0
$955$	9.00000	−	15.5885i	0.291233	−	0.504431i
$956$		0			0
$957$	−14.9003			−0.481659
$958$		0			0
$959$	−4.54983	−	7.88054i	−0.146922	−	0.254476i
$960$		0			0
$961$	−30.9244			−0.997562
$962$		0			0
$963$	−15.0997			−0.486580
$964$		0			0
$965$	11.6873	+	20.2430i	0.376227	+	0.651645i
$966$		0			0
$967$	50.3746			1.61994			0.809969	−	0.586473i	$-0.199484\pi$
$967$	50.3746			1.61994			0.809969	+	0.586473i	$0.199484\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	23.0120	−	39.8580i	0.738492	−	1.27911i	−0.214683	−	0.976684i	$-0.568872\pi$
$971$	23.0120	−	39.8580i	0.738492	−	1.27911i	0.953174	−	0.302421i	$-0.0977949\pi$
$972$		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
$979$	21.7371	−	37.6498i	0.694722	−	1.20329i
$980$		0			0
$981$	−4.41238	+	7.64246i	−0.140876	+	0.244005i
$982$		0			0
$983$	0.374586			0.0119474			0.00597372	−	0.999982i	$-0.498098\pi$
$983$	0.374586			0.0119474			0.00597372	+	0.999982i	$0.498098\pi$
$984$		0			0
$985$	−9.91238	−	17.1687i	−0.315835	−	0.547041i
$986$		0			0
$987$	3.27492			0.104242
$988$		0			0
$989$	2.35050			0.0747414
$990$		0			0
$991$	−13.2749	−	22.9928i	−0.421692	−	0.730391i	0.574413	−	0.818565i	$-0.305230\pi$
$991$	−13.2749	−	22.9928i	−0.421692	−	0.730391i	−0.996105	+	0.0881740i	$0.971897\pi$
$992$		0			0
$993$	26.2749			0.833809
$994$		0			0
$995$	−6.13746	+	10.6304i	−0.194571	+	0.337006i
$996$		0			0
$997$	10.8746	−	18.8353i	0.344402	−	0.596521i	−0.640843	−	0.767672i	$-0.721415\pi$
$997$	10.8746	−	18.8353i	0.344402	−	0.596521i	0.985245	+	0.171151i	$0.0547485\pi$
$998$		0			0
$999$	−3.63746	−	6.30026i	−0.115084	−	0.199332i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1560.2.bg.g.601.1	✓	4
13.9	even	3	inner	1560.2.bg.g.841.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1560.2.bg.g.601.1	✓	4	1.1	even	1	trivial
1560.2.bg.g.841.1	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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-1.63746 - 2.83616i) q^{11} +(2.50000 + 2.59808i) q^{13} +(0.500000 + 0.866025i) q^{15} +(-2.63746 + 4.56821i) q^{19} -1.00000 q^{21} +(4.27492 + 7.40437i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-2.27492 - 3.94027i) q^{29} +0.274917 q^{31} +(1.63746 - 2.83616i) q^{33} +(-0.500000 + 0.866025i) q^{35} +(3.63746 + 6.30026i) q^{37} +(-1.00000 + 3.46410i) q^{39} +(3.27492 + 5.67232i) q^{41} +(0.137459 - 0.238085i) q^{43} +(-0.500000 + 0.866025i) q^{45} -3.27492 q^{47} +(3.00000 + 5.19615i) q^{49} +9.27492 q^{53} +(-1.63746 - 2.83616i) q^{55} -5.27492 q^{57} +(0.274917 - 0.476171i) q^{59} +(-2.13746 + 3.70219i) q^{61} +(-0.500000 - 0.866025i) q^{63} +(2.50000 + 2.59808i) q^{65} +(-1.13746 - 1.97014i) q^{67} +(-4.27492 + 7.40437i) q^{69} +(1.00000 - 1.73205i) q^{71} -10.8248 q^{73} +(0.500000 + 0.866025i) q^{75} +3.27492 q^{77} -8.27492 q^{79} +(-0.500000 - 0.866025i) q^{81} -13.0997 q^{83} +(2.27492 - 3.94027i) q^{87} +(6.63746 + 11.4964i) q^{89} +(-3.50000 + 0.866025i) q^{91} +(0.137459 + 0.238085i) q^{93} +(-2.63746 + 4.56821i) q^{95} +(7.41238 - 12.8386i) q^{97} +3.27492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 4 q^{5} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 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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