LMFDB - Embedded newform 1560.2.bg.e.841.2

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:	$\Q(\sqrt{-3}, \sqrt{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 10x^{2} + 100 $ x^4 + 10*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.2
Root			$1.58114 + 2.73861i$ of defining polynomial
Character	$\chi$	$=$	1560.841
Dual form			1560.2.bg.e.601.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} -1.00000 q^{5} +(1.08114 + 1.87259i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} -1.00000 q^{5} +(1.08114 + 1.87259i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} +(-0.0811388 - 3.60464i) q^{13} +(-0.500000 + 0.866025i) q^{15} +(3.58114 + 6.20271i) q^{17} +(-1.00000 - 1.73205i) q^{19} +2.16228 q^{21} +(1.00000 - 1.73205i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(0.418861 - 0.725489i) q^{29} +3.32456 q^{31} +(-1.00000 - 1.73205i) q^{33} +(-1.08114 - 1.87259i) q^{35} +(2.16228 - 3.74517i) q^{37} +(-3.16228 - 1.73205i) q^{39} +(0.581139 - 1.00656i) q^{41} +(-1.91886 - 3.32357i) q^{43} +(0.500000 + 0.866025i) q^{45} +11.4868 q^{47} +(1.16228 - 2.01312i) q^{49} +7.16228 q^{51} +6.32456 q^{53} +(-1.00000 + 1.73205i) q^{55} -2.00000 q^{57} +(0.418861 + 0.725489i) q^{59} +(-6.50000 - 11.2583i) q^{61} +(1.08114 - 1.87259i) q^{63} +(0.0811388 + 3.60464i) q^{65} +(-1.91886 + 3.32357i) q^{67} +(-1.00000 - 1.73205i) q^{69} +(6.74342 + 11.6799i) q^{71} +0.162278 q^{73} +(0.500000 - 0.866025i) q^{75} +4.32456 q^{77} +11.0000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-3.58114 - 6.20271i) q^{85} +(-0.418861 - 0.725489i) q^{87} +(-1.74342 + 3.01969i) q^{89} +(6.66228 - 4.04905i) q^{91} +(1.66228 - 2.87915i) q^{93} +(1.00000 + 1.73205i) q^{95} +(-9.40569 - 16.2911i) q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 4 q^{11} + 6 q^{13} - 2 q^{15} + 8 q^{17} - 4 q^{19} - 4 q^{21} + 4 q^{23} + 4 q^{25} - 4 q^{27} + 8 q^{29} - 12 q^{31} - 4 q^{33} + 2 q^{35} - 4 q^{37} - 4 q^{41} - 14 q^{43} + 2 q^{45} + 8 q^{47} - 8 q^{49} + 16 q^{51} - 4 q^{55} - 8 q^{57} + 8 q^{59} - 26 q^{61} - 2 q^{63} - 6 q^{65} - 14 q^{67} - 4 q^{69} + 8 q^{71} - 12 q^{73} + 2 q^{75} - 8 q^{77} + 44 q^{79} - 2 q^{81} - 8 q^{85} - 8 q^{87} + 12 q^{89} + 14 q^{91} - 6 q^{93} + 4 q^{95} - 6 q^{97} - 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 - 2 * q^9 + 4 * q^11 + 6 * q^13 - 2 * q^15 + 8 * q^17 - 4 * q^19 - 4 * q^21 + 4 * q^23 + 4 * q^25 - 4 * q^27 + 8 * q^29 - 12 * q^31 - 4 * q^33 + 2 * q^35 - 4 * q^37 - 4 * q^41 - 14 * q^43 + 2 * q^45 + 8 * q^47 - 8 * q^49 + 16 * q^51 - 4 * q^55 - 8 * q^57 + 8 * q^59 - 26 * q^61 - 2 * q^63 - 6 * q^65 - 14 * q^67 - 4 * q^69 + 8 * q^71 - 12 * q^73 + 2 * q^75 - 8 * q^77 + 44 * q^79 - 2 * q^81 - 8 * q^85 - 8 * q^87 + 12 * q^89 + 14 * q^91 - 6 * q^93 + 4 * q^95 - 6 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$391$	$521$	$781$	$937$	$1081$
$\chi(n)$	$1$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$7$	1.08114	+	1.87259i	0.408632	+	0.707772i	0.994737	−	0.102464i	$-0.0326726\pi$
$7$	1.08114	+	1.87259i	0.408632	+	0.707772i	−0.586105	+	0.810235i	$0.699339\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$		0			0
$13$	−0.0811388	−	3.60464i	−0.0225039	−	0.999747i
$13$	−0.0811388	−	3.60464i	−0.0225039	−	0.999747i
$14$		0			0
$15$	−0.500000	+	0.866025i	−0.129099	+	0.223607i
$16$		0			0
$17$	3.58114	+	6.20271i	0.868554	+	1.50438i	0.863475	+	0.504392i	$0.168283\pi$
$17$	3.58114	+	6.20271i	0.868554	+	1.50438i	0.00507902	+	0.999987i	$0.498383\pi$
$18$		0			0
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$		0			0
$21$	2.16228			0.471848
$22$		0			0
$23$	1.00000	−	1.73205i	0.208514	−	0.361158i	−0.742732	−	0.669588i	$-0.766471\pi$
$23$	1.00000	−	1.73205i	0.208514	−	0.361158i	0.951247	+	0.308431i	$0.0998038\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	0.418861	−	0.725489i	0.0777806	−	0.134720i	−0.824511	−	0.565845i	$-0.808550\pi$
$29$	0.418861	−	0.725489i	0.0777806	−	0.134720i	0.902292	+	0.431125i	$0.141883\pi$
$30$		0			0
$31$	3.32456			0.597108			0.298554	−	0.954393i	$-0.403496\pi$
$31$	3.32456			0.597108			0.298554	+	0.954393i	$0.403496\pi$
$32$		0			0
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$		0			0
$35$	−1.08114	−	1.87259i	−0.182746	−	0.316525i
$36$		0			0
$37$	2.16228	−	3.74517i	0.355476	−	0.615703i	−0.631723	−	0.775194i	$-0.717652\pi$
$37$	2.16228	−	3.74517i	0.355476	−	0.615703i	0.987199	+	0.159491i	$0.0509854\pi$
$38$		0			0
$39$	−3.16228	−	1.73205i	−0.506370	−	0.277350i
$40$		0			0
$41$	0.581139	−	1.00656i	0.0907586	−	0.157199i	−0.817072	−	0.576536i	$-0.804404\pi$
$41$	0.581139	−	1.00656i	0.0907586	−	0.157199i	0.907831	+	0.419337i	$0.137737\pi$
$42$		0			0
$43$	−1.91886	−	3.32357i	−0.292624	−	0.506839i	0.681806	−	0.731533i	$-0.261195\pi$
$43$	−1.91886	−	3.32357i	−0.292624	−	0.506839i	−0.974429	+	0.224694i	$0.927862\pi$
$44$		0			0
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$		0			0
$47$	11.4868			1.67553			0.837763	−	0.546033i	$-0.183863\pi$
$47$	11.4868			1.67553			0.837763	+	0.546033i	$0.183863\pi$
$48$		0			0
$49$	1.16228	−	2.01312i	0.166040	−	0.287589i
$50$		0			0
$51$	7.16228			1.00292
$52$		0			0
$53$	6.32456			0.868744			0.434372	−	0.900733i	$-0.356970\pi$
$53$	6.32456			0.868744			0.434372	+	0.900733i	$0.356970\pi$
$54$		0			0
$55$	−1.00000	+	1.73205i	−0.134840	+	0.233550i
$56$		0			0
$57$	−2.00000			−0.264906
$58$		0			0
$59$	0.418861	+	0.725489i	0.0545311	+	0.0944506i	0.892002	−	0.452031i	$-0.149300\pi$
$59$	0.418861	+	0.725489i	0.0545311	+	0.0944506i	−0.837471	+	0.546481i	$0.815967\pi$
$60$		0			0
$61$	−6.50000	−	11.2583i	−0.832240	−	1.44148i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−6.50000	−	11.2583i	−0.832240	−	1.44148i	0.0640184	−	0.997949i	$-0.479608\pi$
$62$		0			0
$63$	1.08114	−	1.87259i	0.136211	−	0.235924i
$64$		0			0
$65$	0.0811388	+	3.60464i	0.0100640	+	0.447100i
$66$		0			0
$67$	−1.91886	+	3.32357i	−0.234426	+	0.406038i	−0.959106	−	0.283048i	$-0.908654\pi$
$67$	−1.91886	+	3.32357i	−0.234426	+	0.406038i	0.724680	+	0.689086i	$0.241988\pi$
$68$		0			0
$69$	−1.00000	−	1.73205i	−0.120386	−	0.208514i
$70$		0			0
$71$	6.74342	+	11.6799i	0.800296	+	1.38615i	0.919421	+	0.393275i	$0.128658\pi$
$71$	6.74342	+	11.6799i	0.800296	+	1.38615i	−0.119125	+	0.992879i	$0.538009\pi$
$72$		0			0
$73$	0.162278			0.0189932			0.00949658	−	0.999955i	$-0.496977\pi$
$73$	0.162278			0.0189932			0.00949658	+	0.999955i	$0.496977\pi$
$74$		0			0
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$		0			0
$77$	4.32456			0.492829
$78$		0			0
$79$	11.0000			1.23760			0.618798	−	0.785550i	$-0.287620\pi$
$79$	11.0000			1.23760			0.618798	+	0.785550i	$0.287620\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	−3.58114	−	6.20271i	−0.388429	−	0.672779i
$86$		0			0
$87$	−0.418861	−	0.725489i	−0.0449066	−	0.0777806i
$88$		0			0
$89$	−1.74342	+	3.01969i	−0.184802	+	0.320086i	−0.943510	−	0.331345i	$-0.892498\pi$
$89$	−1.74342	+	3.01969i	−0.184802	+	0.320086i	0.758708	+	0.651431i	$0.225831\pi$
$90$		0			0
$91$	6.66228	−	4.04905i	0.698396	−	0.424456i
$92$		0			0
$93$	1.66228	−	2.87915i	0.172370	−	0.298554i
$94$		0			0
$95$	1.00000	+	1.73205i	0.102598	+	0.177705i
$96$		0			0
$97$	−9.40569	−	16.2911i	−0.955004	−	1.65411i	−0.734360	−	0.678760i	$-0.762518\pi$
$97$	−9.40569	−	16.2911i	−0.955004	−	1.65411i	−0.220644	−	0.975355i	$-0.570816\pi$
$98$		0			0
$99$	−2.00000			−0.201008
$100$		0			0
$101$	6.16228	−	10.6734i	0.613170	−	1.06204i	−0.377533	−	0.925996i	$-0.623228\pi$
$101$	6.16228	−	10.6734i	0.613170	−	1.06204i	0.990703	−	0.136045i	$-0.0434391\pi$
$102$		0			0
$103$	8.48683			0.836233			0.418116	−	0.908394i	$-0.362690\pi$
$103$	8.48683			0.836233			0.418116	+	0.908394i	$0.362690\pi$
$104$		0			0
$105$	−2.16228			−0.211017
$106$		0			0
$107$	0.256584	−	0.444416i	0.0248049	−	0.0429633i	−0.853357	−	0.521328i	$-0.825437\pi$
$107$	0.256584	−	0.444416i	0.0248049	−	0.0429633i	0.878161	+	0.478365i	$0.158770\pi$
$108$		0			0
$109$	−5.32456			−0.510000			−0.255000	−	0.966941i	$-0.582075\pi$
$109$	−5.32456			−0.510000			−0.255000	+	0.966941i	$0.582075\pi$
$110$		0			0
$111$	−2.16228	−	3.74517i	−0.205234	−	0.355476i
$112$		0			0
$113$	−4.16228	−	7.20928i	−0.391554	−	0.678192i	0.601101	−	0.799173i	$-0.294729\pi$
$113$	−4.16228	−	7.20928i	−0.391554	−	0.678192i	−0.992655	+	0.120982i	$0.961396\pi$
$114$		0			0
$115$	−1.00000	+	1.73205i	−0.0932505	+	0.161515i
$116$		0			0
$117$	−3.08114	+	1.87259i	−0.284851	+	0.173121i
$118$		0			0
$119$	−7.74342	+	13.4120i	−0.709838	+	1.22948i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$	−0.581139	−	1.00656i	−0.0523995	−	0.0907586i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	3.08114	−	5.33669i	0.273407	−	0.473555i	−0.696325	−	0.717727i	$-0.745183\pi$
$127$	3.08114	−	5.33669i	0.273407	−	0.473555i	0.969732	+	0.244172i	$0.0785161\pi$
$128$		0			0
$129$	−3.83772			−0.337893
$130$		0			0
$131$	−15.8114			−1.38145			−0.690724	−	0.723119i	$-0.742708\pi$
$131$	−15.8114			−1.38145			−0.690724	+	0.723119i	$0.742708\pi$
$132$		0			0
$133$	2.16228	−	3.74517i	0.187493	−	0.324748i
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	−9.58114	−	16.5950i	−0.818572	−	1.41781i	−0.906734	−	0.421702i	$-0.861433\pi$
$137$	−9.58114	−	16.5950i	−0.818572	−	1.41781i	0.0881625	−	0.996106i	$-0.471901\pi$
$138$		0			0
$139$	5.66228	+	9.80735i	0.480268	+	0.831849i	0.999744	−	0.0226365i	$-0.00720603\pi$
$139$	5.66228	+	9.80735i	0.480268	+	0.831849i	−0.519476	+	0.854485i	$0.673873\pi$
$140$		0			0
$141$	5.74342	−	9.94789i	0.483683	−	0.837763i
$142$		0			0
$143$	−6.32456	−	3.46410i	−0.528886	−	0.289683i
$144$		0			0
$145$	−0.418861	+	0.725489i	−0.0347845	+	0.0602486i
$146$		0			0
$147$	−1.16228	−	2.01312i	−0.0958630	−	0.166040i
$148$		0			0
$149$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$149$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$150$		0			0
$151$	−8.32456			−0.677443			−0.338721	−	0.940887i	$-0.609994\pi$
$151$	−8.32456			−0.677443			−0.338721	+	0.940887i	$0.609994\pi$
$152$		0			0
$153$	3.58114	−	6.20271i	0.289518	−	0.501460i
$154$		0			0
$155$	−3.32456			−0.267035
$156$		0			0
$157$	16.8114			1.34169			0.670847	−	0.741595i	$-0.265931\pi$
$157$	16.8114			1.34169			0.670847	+	0.741595i	$0.265931\pi$
$158$		0			0
$159$	3.16228	−	5.47723i	0.250785	−	0.434372i
$160$		0			0
$161$	4.32456			0.340823
$162$		0			0
$163$	−5.24342	−	9.08186i	−0.410696	−	0.711346i	0.584270	−	0.811559i	$-0.301381\pi$
$163$	−5.24342	−	9.08186i	−0.410696	−	0.711346i	−0.994966	+	0.100213i	$0.968048\pi$
$164$		0			0
$165$	1.00000	+	1.73205i	0.0778499	+	0.134840i
$166$		0			0
$167$	−2.32456	+	4.02625i	−0.179879	+	0.311560i	−0.941839	−	0.336064i	$-0.890904\pi$
$167$	−2.32456	+	4.02625i	−0.179879	+	0.311560i	0.761960	+	0.647625i	$0.224237\pi$
$168$		0			0
$169$	−12.9868	+	0.584952i	−0.998987	+	0.0449963i
$170$		0			0
$171$	−1.00000	+	1.73205i	−0.0764719	+	0.132453i
$172$		0			0
$173$	9.74342	+	16.8761i	0.740778	+	1.28307i	0.952141	+	0.305658i	$0.0988764\pi$
$173$	9.74342	+	16.8761i	0.740778	+	1.28307i	−0.211363	+	0.977408i	$0.567790\pi$
$174$		0			0
$175$	1.08114	+	1.87259i	0.0817264	+	0.141554i
$176$		0			0
$177$	0.837722			0.0629671
$178$		0			0
$179$	−9.74342	+	16.8761i	−0.728257	+	1.26138i	0.229362	+	0.973341i	$0.426336\pi$
$179$	−9.74342	+	16.8761i	−0.728257	+	1.26138i	−0.957619	+	0.288037i	$0.906997\pi$
$180$		0			0
$181$	0.649111			0.0482480			0.0241240	−	0.999709i	$-0.492320\pi$
$181$	0.649111			0.0482480			0.0241240	+	0.999709i	$0.492320\pi$
$182$		0			0
$183$	−13.0000			−0.960988
$184$		0			0
$185$	−2.16228	+	3.74517i	−0.158974	+	0.275351i
$186$		0			0
$187$	14.3246			1.04752
$188$		0			0
$189$	−1.08114	−	1.87259i	−0.0786413	−	0.136211i
$190$		0			0
$191$	9.90569	+	17.1572i	0.716751	+	1.24145i	0.962280	+	0.272060i	$0.0877049\pi$
$191$	9.90569	+	17.1572i	0.716751	+	1.24145i	−0.245529	+	0.969389i	$0.578962\pi$
$192$		0			0
$193$	−3.08114	+	5.33669i	−0.221785	+	0.384143i	−0.955350	−	0.295476i	$-0.904522\pi$
$193$	−3.08114	+	5.33669i	−0.221785	+	0.384143i	0.733565	+	0.679619i	$0.237855\pi$
$194$		0			0
$195$	3.16228	+	1.73205i	0.226455	+	0.124035i
$196$		0			0
$197$	−9.16228	+	15.8695i	−0.652785	+	1.13066i	0.329659	+	0.944100i	$0.393066\pi$
$197$	−9.16228	+	15.8695i	−0.652785	+	1.13066i	−0.982444	+	0.186557i	$0.940267\pi$
$198$		0			0
$199$	9.66228	+	16.7356i	0.684941	+	1.18635i	0.973455	+	0.228877i	$0.0735052\pi$
$199$	9.66228	+	16.7356i	0.684941	+	1.18635i	−0.288515	+	0.957475i	$0.593161\pi$
$200$		0			0
$201$	1.91886	+	3.32357i	0.135346	+	0.234426i
$202$		0			0
$203$	1.81139			0.127135
$204$		0			0
$205$	−0.581139	+	1.00656i	−0.0405885	+	0.0703013i
$206$		0			0
$207$	−2.00000			−0.139010
$208$		0			0
$209$	−4.00000			−0.276686
$210$		0			0
$211$	−0.824555	+	1.42817i	−0.0567647	+	0.0983194i	−0.893011	−	0.450034i	$-0.851412\pi$
$211$	−0.824555	+	1.42817i	−0.0567647	+	0.0983194i	0.836247	+	0.548353i	$0.184745\pi$
$212$		0			0
$213$	13.4868			0.924103
$214$		0			0
$215$	1.91886	+	3.32357i	0.130865	+	0.226665i
$216$		0			0
$217$	3.59431	+	6.22552i	0.243997	+	0.422616i
$218$		0			0
$219$	0.0811388	−	0.140537i	0.00548285	−	0.00949658i
$220$		0			0
$221$	22.0680	−	13.4120i	1.48445	−	0.902188i
$222$		0			0
$223$	2.00000	−	3.46410i	0.133930	−	0.231973i	−0.791258	−	0.611482i	$-0.790574\pi$
$223$	2.00000	−	3.46410i	0.133930	−	0.231973i	0.925188	+	0.379509i	$0.123907\pi$
$224$		0			0
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$		0			0
$227$	5.58114	+	9.66682i	0.370433	+	0.641609i	0.989632	−	0.143625i	$-0.0458759\pi$
$227$	5.58114	+	9.66682i	0.370433	+	0.641609i	−0.619199	+	0.785234i	$0.712543\pi$
$228$		0			0
$229$	−18.3246			−1.21092			−0.605460	−	0.795875i	$-0.707011\pi$
$229$	−18.3246			−1.21092			−0.605460	+	0.795875i	$0.707011\pi$
$230$		0			0
$231$	2.16228	−	3.74517i	0.142267	−	0.246414i
$232$		0			0
$233$	7.67544			0.502835			0.251418	−	0.967879i	$-0.419103\pi$
$233$	7.67544			0.502835			0.251418	+	0.967879i	$0.419103\pi$
$234$		0			0
$235$	−11.4868			−0.749318
$236$		0			0
$237$	5.50000	−	9.52628i	0.357263	−	0.618798i
$238$		0			0
$239$	−8.64911			−0.559464			−0.279732	−	0.960078i	$-0.590246\pi$
$239$	−8.64911			−0.559464			−0.279732	+	0.960078i	$0.590246\pi$
$240$		0			0
$241$	−9.16228	−	15.8695i	−0.590194	−	1.02225i	−0.994206	−	0.107493i	$-0.965718\pi$
$241$	−9.16228	−	15.8695i	−0.590194	−	1.02225i	0.404012	−	0.914754i	$-0.367615\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	−1.16228	+	2.01312i	−0.0742552	+	0.128614i
$246$		0			0
$247$	−6.16228	+	3.74517i	−0.392096	+	0.238300i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	9.48683	+	16.4317i	0.598804	+	1.03716i	0.992998	+	0.118131i	$0.0376903\pi$
$251$	9.48683	+	16.4317i	0.598804	+	1.03716i	−0.394194	+	0.919027i	$0.628976\pi$
$252$		0			0
$253$	−2.00000	−	3.46410i	−0.125739	−	0.217786i
$254$		0			0
$255$	−7.16228			−0.448519
$256$		0			0
$257$	−9.06797	+	15.7062i	−0.565645	+	0.979725i	0.431345	+	0.902187i	$0.358039\pi$
$257$	−9.06797	+	15.7062i	−0.565645	+	0.979725i	−0.996989	+	0.0775380i	$0.975294\pi$
$258$		0			0
$259$	9.35089			0.581036
$260$		0			0
$261$	−0.837722			−0.0518537
$262$		0			0
$263$	4.74342	−	8.21584i	0.292492	−	0.506610i	−0.681907	−	0.731439i	$-0.738849\pi$
$263$	4.74342	−	8.21584i	0.292492	−	0.506610i	0.974398	+	0.224829i	$0.0721823\pi$
$264$		0			0
$265$	−6.32456			−0.388514
$266$		0			0
$267$	1.74342	+	3.01969i	0.106695	+	0.184802i
$268$		0			0
$269$	2.25658	+	3.90852i	0.137586	+	0.238307i	0.926582	−	0.376092i	$-0.122732\pi$
$269$	2.25658	+	3.90852i	0.137586	+	0.238307i	−0.788996	+	0.614398i	$0.789399\pi$
$270$		0			0
$271$	−7.82456	+	13.5525i	−0.475308	+	0.823257i	−0.999600	−	0.0282811i	$-0.990997\pi$
$271$	−7.82456	+	13.5525i	−0.475308	+	0.823257i	0.524292	+	0.851538i	$0.324330\pi$
$272$		0			0
$273$	−0.175445	−	7.79423i	−0.0106184	−	0.471728i
$274$		0			0
$275$	1.00000	−	1.73205i	0.0603023	−	0.104447i
$276$		0			0
$277$	−12.1623	−	21.0657i	−0.730760	−	1.26571i	−0.956559	−	0.291540i	$-0.905832\pi$
$277$	−12.1623	−	21.0657i	−0.730760	−	1.26571i	0.225798	−	0.974174i	$-0.427501\pi$
$278$		0			0
$279$	−1.66228	−	2.87915i	−0.0995180	−	0.172370i
$280$		0			0
$281$	3.16228			0.188646			0.0943228	−	0.995542i	$-0.469931\pi$
$281$	3.16228			0.188646			0.0943228	+	0.995542i	$0.469931\pi$
$282$		0			0
$283$	3.40569	−	5.89884i	0.202448	−	0.350649i	−0.746869	−	0.664971i	$-0.768444\pi$
$283$	3.40569	−	5.89884i	0.202448	−	0.350649i	0.949316	+	0.314322i	$0.101777\pi$
$284$		0			0
$285$	2.00000			0.118470
$286$		0			0
$287$	2.51317			0.148348
$288$		0			0
$289$	−17.1491	+	29.7031i	−1.00877	+	1.74724i
$290$		0			0
$291$	−18.8114			−1.10274
$292$		0			0
$293$	−4.25658	−	7.37262i	−0.248672	−	0.430713i	0.714485	−	0.699650i	$-0.246661\pi$
$293$	−4.25658	−	7.37262i	−0.248672	−	0.430713i	−0.963158	+	0.268937i	$0.913328\pi$
$294$		0			0
$295$	−0.418861	−	0.725489i	−0.0243870	−	0.0422396i
$296$		0			0
$297$	−1.00000	+	1.73205i	−0.0580259	+	0.100504i
$298$		0			0
$299$	−6.32456	−	3.46410i	−0.365758	−	0.200334i
$300$		0			0
$301$	4.14911	−	7.18647i	0.239151	−	0.414221i
$302$		0			0
$303$	−6.16228	−	10.6734i	−0.354014	−	0.613170i
$304$		0			0
$305$	6.50000	+	11.2583i	0.372189	+	0.644650i
$306$		0			0
$307$	−17.8377			−1.01805			−0.509026	−	0.860751i	$-0.669994\pi$
$307$	−17.8377			−1.01805			−0.509026	+	0.860751i	$0.669994\pi$
$308$		0			0
$309$	4.24342	−	7.34981i	0.241400	−	0.418116i
$310$		0			0
$311$	−5.81139			−0.329534			−0.164767	−	0.986333i	$-0.552687\pi$
$311$	−5.81139			−0.329534			−0.164767	+	0.986333i	$0.552687\pi$
$312$		0			0
$313$	−0.486833			−0.0275174			−0.0137587	−	0.999905i	$-0.504380\pi$
$313$	−0.486833			−0.0275174			−0.0137587	+	0.999905i	$0.504380\pi$
$314$		0			0
$315$	−1.08114	+	1.87259i	−0.0609153	+	0.105508i
$316$		0			0
$317$	10.3246			0.579885			0.289942	−	0.957044i	$-0.406364\pi$
$317$	10.3246			0.579885			0.289942	+	0.957044i	$0.406364\pi$
$318$		0			0
$319$	−0.837722	−	1.45098i	−0.0469034	−	0.0812392i
$320$		0			0
$321$	−0.256584	−	0.444416i	−0.0143211	−	0.0248049i
$322$		0			0
$323$	7.16228	−	12.4054i	0.398520	−	0.690257i
$324$		0			0
$325$	−0.0811388	−	3.60464i	−0.00450077	−	0.199949i
$326$		0			0
$327$	−2.66228	+	4.61120i	−0.147224	+	0.255000i
$328$		0			0
$329$	12.4189	+	21.5101i	0.684674	+	1.18589i
$330$		0			0
$331$	7.66228	+	13.2715i	0.421157	+	0.729465i	0.996053	−	0.0887614i	$-0.0282908\pi$
$331$	7.66228	+	13.2715i	0.421157	+	0.729465i	−0.574896	+	0.818226i	$0.694958\pi$
$332$		0			0
$333$	−4.32456			−0.236984
$334$		0			0
$335$	1.91886	−	3.32357i	0.104839	−	0.181586i
$336$		0			0
$337$	−8.16228			−0.444628			−0.222314	−	0.974975i	$-0.571361\pi$
$337$	−8.16228			−0.444628			−0.222314	+	0.974975i	$0.571361\pi$
$338$		0			0
$339$	−8.32456			−0.452128
$340$		0			0
$341$	3.32456	−	5.75830i	0.180035	−	0.311829i
$342$		0			0
$343$	20.1623			1.08866
$344$		0			0
$345$	1.00000	+	1.73205i	0.0538382	+	0.0932505i
$346$		0			0
$347$	6.83772	+	11.8433i	0.367068	+	0.635781i	0.989106	−	0.147207i	$-0.0470282\pi$
$347$	6.83772	+	11.8433i	0.367068	+	0.635781i	−0.622038	+	0.782987i	$0.713695\pi$
$348$		0			0
$349$	−5.66228	+	9.80735i	−0.303095	+	0.524976i	−0.976835	−	0.213992i	$-0.931353\pi$
$349$	−5.66228	+	9.80735i	−0.303095	+	0.524976i	0.673741	+	0.738968i	$0.264687\pi$
$350$		0			0
$351$	0.0811388	+	3.60464i	0.00433087	+	0.192401i
$352$		0			0
$353$	−8.16228	+	14.1375i	−0.434434	+	0.752462i	−0.997249	−	0.0741207i	$-0.976385\pi$
$353$	−8.16228	+	14.1375i	−0.434434	+	0.752462i	0.562815	+	0.826583i	$0.309718\pi$
$354$		0			0
$355$	−6.74342	−	11.6799i	−0.357903	−	0.619907i
$356$		0			0
$357$	7.74342	+	13.4120i	0.409825	+	0.709838i
$358$		0			0
$359$	−31.4868			−1.66181			−0.830906	−	0.556413i	$-0.812177\pi$
$359$	−31.4868			−1.66181			−0.830906	+	0.556413i	$0.812177\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$		0			0
$363$	7.00000			0.367405
$364$		0			0
$365$	−0.162278			−0.00849400
$366$		0			0
$367$	11.9189	−	20.6441i	0.622159	−	1.07761i	−0.366923	−	0.930251i	$-0.619589\pi$
$367$	11.9189	−	20.6441i	0.622159	−	1.07761i	0.989083	−	0.147361i	$-0.0470778\pi$
$368$		0			0
$369$	−1.16228			−0.0605058
$370$		0			0
$371$	6.83772	+	11.8433i	0.354997	+	0.614873i
$372$		0			0
$373$	12.7302	+	22.0494i	0.659147	+	1.14168i	0.980837	+	0.194831i	$0.0624160\pi$
$373$	12.7302	+	22.0494i	0.659147	+	1.14168i	−0.321689	+	0.946845i	$0.604251\pi$
$374$		0			0
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$		0			0
$377$	−2.64911	−	1.45098i	−0.136436	−	0.0747292i
$378$		0			0
$379$	−16.9868	+	29.4221i	−0.872555	+	1.51131i	−0.0132103	+	0.999913i	$0.504205\pi$
$379$	−16.9868	+	29.4221i	−0.872555	+	1.51131i	−0.859345	+	0.511397i	$0.829128\pi$
$380$		0			0
$381$	−3.08114	−	5.33669i	−0.157852	−	0.273407i
$382$		0			0
$383$	4.74342	+	8.21584i	0.242377	+	0.419810i	0.961391	−	0.275186i	$-0.0887395\pi$
$383$	4.74342	+	8.21584i	0.242377	+	0.419810i	−0.719014	+	0.694996i	$0.755406\pi$
$384$		0			0
$385$	−4.32456			−0.220400
$386$		0			0
$387$	−1.91886	+	3.32357i	−0.0975412	+	0.168946i
$388$		0			0
$389$	−6.97367			−0.353579			−0.176789	−	0.984249i	$-0.556571\pi$
$389$	−6.97367			−0.353579			−0.176789	+	0.984249i	$0.556571\pi$
$390$		0			0
$391$	14.3246			0.724424
$392$		0			0
$393$	−7.90569	+	13.6931i	−0.398790	+	0.690724i
$394$		0			0
$395$	−11.0000			−0.553470
$396$		0			0
$397$	−15.2434	−	26.4024i	−0.765045	−	1.32510i	−0.940223	−	0.340560i	$-0.889383\pi$
$397$	−15.2434	−	26.4024i	−0.765045	−	1.32510i	0.175178	−	0.984537i	$-0.443950\pi$
$398$		0			0
$399$	−2.16228	−	3.74517i	−0.108249	−	0.187493i
$400$		0			0
$401$	−11.4868	+	19.8958i	−0.573625	+	0.993548i	0.422564	+	0.906333i	$0.361130\pi$
$401$	−11.4868	+	19.8958i	−0.573625	+	0.993548i	−0.996190	+	0.0872149i	$0.972203\pi$
$402$		0			0
$403$	−0.269751	−	11.9838i	−0.0134372	−	0.596957i
$404$		0			0
$405$	0.500000	−	0.866025i	0.0248452	−	0.0430331i
$406$		0			0
$407$	−4.32456	−	7.49035i	−0.214360	−	0.371283i
$408$		0			0
$409$	−1.82456	−	3.16022i	−0.0902185	−	0.156263i	0.817385	−	0.576092i	$-0.195423\pi$
$409$	−1.82456	−	3.16022i	−0.0902185	−	0.156263i	−0.907603	+	0.419830i	$0.862090\pi$
$410$		0			0
$411$	−19.1623			−0.945205
$412$		0			0
$413$	−0.905694	+	1.56871i	−0.0445663	+	0.0771911i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	11.3246			0.554566
$418$		0			0
$419$	−3.09431	+	5.35949i	−0.151167	+	0.261828i	−0.931657	−	0.363340i	$-0.881636\pi$
$419$	−3.09431	+	5.35949i	−0.151167	+	0.261828i	0.780490	+	0.625168i	$0.214970\pi$
$420$		0			0
$421$	−3.32456			−0.162029			−0.0810145	−	0.996713i	$-0.525816\pi$
$421$	−3.32456			−0.162029			−0.0810145	+	0.996713i	$0.525816\pi$
$422$		0			0
$423$	−5.74342	−	9.94789i	−0.279254	−	0.483683i
$424$		0			0
$425$	3.58114	+	6.20271i	0.173711	+	0.300876i
$426$		0			0
$427$	14.0548	−	24.3436i	0.680160	−	1.17807i
$428$		0			0
$429$	−6.16228	+	3.74517i	−0.297518	+	0.180819i
$430$		0			0
$431$	−1.67544	+	2.90196i	−0.0807033	+	0.139782i	−0.903552	−	0.428478i	$-0.859050\pi$
$431$	−1.67544	+	2.90196i	−0.0807033	+	0.139782i	0.822849	+	0.568260i	$0.192383\pi$
$432$		0			0
$433$	3.75658	+	6.50659i	0.180530	+	0.312687i	0.942061	−	0.335441i	$-0.108885\pi$
$433$	3.75658	+	6.50659i	0.180530	+	0.312687i	−0.761531	+	0.648128i	$0.775552\pi$
$434$		0			0
$435$	0.418861	+	0.725489i	0.0200829	+	0.0347845i
$436$		0			0
$437$	−4.00000			−0.191346
$438$		0			0
$439$	−15.3114	+	26.5201i	−0.730773	+	1.26574i	0.225781	+	0.974178i	$0.427507\pi$
$439$	−15.3114	+	26.5201i	−0.730773	+	1.26574i	−0.956553	+	0.291557i	$0.905827\pi$
$440$		0			0
$441$	−2.32456			−0.110693
$442$		0			0
$443$	38.1359			1.81189			0.905947	−	0.423392i	$-0.139161\pi$
$443$	38.1359			1.81189			0.905947	+	0.423392i	$0.139161\pi$
$444$		0			0
$445$	1.74342	−	3.01969i	0.0826459	−	0.143147i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	4.16228	+	7.20928i	0.196430	+	0.340227i	0.947368	−	0.320146i	$-0.103732\pi$
$449$	4.16228	+	7.20928i	0.196430	+	0.340227i	−0.750938	+	0.660372i	$0.770398\pi$
$450$		0			0
$451$	−1.16228	−	2.01312i	−0.0547295	−	0.0947943i
$452$		0			0
$453$	−4.16228	+	7.20928i	−0.195561	+	0.338721i
$454$		0			0
$455$	−6.66228	+	4.04905i	−0.312332	+	0.189823i
$456$		0			0
$457$	−11.0811	+	19.1931i	−0.518354	+	0.897815i	0.481419	+	0.876491i	$0.340122\pi$
$457$	−11.0811	+	19.1931i	−0.518354	+	0.897815i	−0.999773	+	0.0213244i	$0.993212\pi$
$458$		0			0
$459$	−3.58114	−	6.20271i	−0.167153	−	0.289518i
$460$		0			0
$461$	−8.58114	−	14.8630i	−0.399663	−	0.692237i	0.594021	−	0.804450i	$-0.297540\pi$
$461$	−8.58114	−	14.8630i	−0.399663	−	0.692237i	−0.993684	+	0.112212i	$0.964206\pi$
$462$		0			0
$463$	2.48683			0.115573			0.0577865	−	0.998329i	$-0.481596\pi$
$463$	2.48683			0.115573			0.0577865	+	0.998329i	$0.481596\pi$
$464$		0			0
$465$	−1.66228	+	2.87915i	−0.0770863	+	0.133517i
$466$		0			0
$467$	−37.8114			−1.74970			−0.874851	−	0.484392i	$-0.839041\pi$
$467$	−37.8114			−1.74970			−0.874851	+	0.484392i	$0.839041\pi$
$468$		0			0
$469$	−8.29822			−0.383176
$470$		0			0
$471$	8.40569	−	14.5591i	0.387314	−	0.670847i
$472$		0			0
$473$	−7.67544			−0.352917
$474$		0			0
$475$	−1.00000	−	1.73205i	−0.0458831	−	0.0794719i
$476$		0			0
$477$	−3.16228	−	5.47723i	−0.144791	−	0.250785i
$478$		0			0
$479$	11.4189	−	19.7780i	0.521741	−	0.903682i	−0.477939	−	0.878393i	$-0.658616\pi$
$479$	11.4189	−	19.7780i	0.521741	−	0.903682i	0.999680	−	0.0252891i	$-0.00805063\pi$
$480$		0			0
$481$	−13.6754	−	7.49035i	−0.623547	−	0.341531i
$482$		0			0
$483$	2.16228	−	3.74517i	0.0983870	−	0.170411i
$484$		0			0
$485$	9.40569	+	16.2911i	0.427091	+	0.739743i
$486$		0			0
$487$	7.00000	+	12.1244i	0.317200	+	0.549407i	0.979903	−	0.199476i	$-0.0639239\pi$
$487$	7.00000	+	12.1244i	0.317200	+	0.549407i	−0.662702	+	0.748883i	$0.730591\pi$
$488$		0			0
$489$	−10.4868			−0.474231
$490$		0			0
$491$	7.25658	−	12.5688i	0.327485	−	0.567221i	−0.654527	−	0.756039i	$-0.727132\pi$
$491$	7.25658	−	12.5688i	0.327485	−	0.567221i	0.982012	+	0.188818i	$0.0604656\pi$
$492$		0			0
$493$	6.00000			0.270226
$494$		0			0
$495$	2.00000			0.0898933
$496$		0			0
$497$	−14.5811	+	25.2553i	−0.654053	+	1.13285i
$498$		0			0
$499$	−10.6491			−0.476720			−0.238360	−	0.971177i	$-0.576610\pi$
$499$	−10.6491			−0.476720			−0.238360	+	0.971177i	$0.576610\pi$
$500$		0			0
$501$	2.32456	+	4.02625i	0.103853	+	0.179879i
$502$		0			0
$503$	−19.6491	−	34.0333i	−0.876111	−	1.51747i	−0.855575	−	0.517679i	$-0.826796\pi$
$503$	−19.6491	−	34.0333i	−0.876111	−	1.51747i	−0.0205355	−	0.999789i	$-0.506537\pi$
$504$		0			0
$505$	−6.16228	+	10.6734i	−0.274218	+	0.474959i
$506$		0			0
$507$	−5.98683	+	11.5394i	−0.265885	+	0.512483i
$508$		0			0
$509$	−7.32456	+	12.6865i	−0.324655	+	0.562319i	−0.981443	−	0.191757i	$-0.938582\pi$
$509$	−7.32456	+	12.6865i	−0.324655	+	0.562319i	0.656787	+	0.754076i	$0.271915\pi$
$510$		0			0
$511$	0.175445	+	0.303879i	0.00776122	+	0.0134428i
$512$		0			0
$513$	1.00000	+	1.73205i	0.0441511	+	0.0764719i
$514$		0			0
$515$	−8.48683			−0.373975
$516$		0			0
$517$	11.4868	−	19.8958i	0.505190	−	0.875015i
$518$		0			0
$519$	19.4868			0.855377
$520$		0			0
$521$	−32.1359			−1.40790			−0.703951	−	0.710249i	$-0.748582\pi$
$521$	−32.1359			−1.40790			−0.703951	+	0.710249i	$0.748582\pi$
$522$		0			0
$523$	13.4868	−	23.3599i	0.589738	−	1.02146i	−0.404528	−	0.914525i	$-0.632564\pi$
$523$	13.4868	−	23.3599i	0.589738	−	1.02146i	0.994266	−	0.106931i	$-0.0341023\pi$
$524$		0			0
$525$	2.16228			0.0943695
$526$		0			0
$527$	11.9057	+	20.6213i	0.518620	+	0.898277i
$528$		0			0
$529$	9.50000	+	16.4545i	0.413043	+	0.715412i
$530$		0			0
$531$	0.418861	−	0.725489i	0.0181770	−	0.0314835i
$532$		0			0
$533$	−3.67544	−	2.01312i	−0.159201	−	0.0871981i
$534$		0			0
$535$	−0.256584	+	0.444416i	−0.0110931	+	0.0192138i
$536$		0			0
$537$	9.74342	+	16.8761i	0.420459	+	0.728257i
$538$		0			0
$539$	−2.32456	−	4.02625i	−0.100126	−	0.173423i
$540$		0			0
$541$	−26.6228			−1.14460			−0.572301	−	0.820043i	$-0.693949\pi$
$541$	−26.6228			−1.14460			−0.572301	+	0.820043i	$0.693949\pi$
$542$		0			0
$543$	0.324555	−	0.562146i	0.0139280	−	0.0241240i
$544$		0			0
$545$	5.32456			0.228079
$546$		0			0
$547$	19.1359			0.818194			0.409097	−	0.912491i	$-0.365844\pi$
$547$	19.1359			0.818194			0.409097	+	0.912491i	$0.365844\pi$
$548$		0			0
$549$	−6.50000	+	11.2583i	−0.277413	+	0.480494i
$550$		0			0
$551$	−1.67544			−0.0713763
$552$		0			0
$553$	11.8925	+	20.5985i	0.505722	+	0.875936i
$554$		0			0
$555$	2.16228	+	3.74517i	0.0917836	+	0.158974i
$556$		0			0
$557$	11.4868	−	19.8958i	0.486713	−	0.843011i	−0.513171	−	0.858287i	$-0.671529\pi$
$557$	11.4868	−	19.8958i	0.486713	−	0.843011i	0.999883	+	0.0152755i	$0.00486252\pi$
$558$		0			0
$559$	−11.8246	+	7.18647i	−0.500125	+	0.303955i
$560$		0			0
$561$	7.16228	−	12.4054i	0.302392	−	0.523758i
$562$		0			0
$563$	9.00000	+	15.5885i	0.379305	+	0.656975i	0.990961	−	0.134148i	$-0.0428299\pi$
$563$	9.00000	+	15.5885i	0.379305	+	0.656975i	−0.611656	+	0.791123i	$0.709497\pi$
$564$		0			0
$565$	4.16228	+	7.20928i	0.175108	+	0.303297i
$566$		0			0
$567$	−2.16228			−0.0908071
$568$		0			0
$569$	16.4189	−	28.4383i	0.688314	−	1.19220i	−0.284068	−	0.958804i	$-0.591684\pi$
$569$	16.4189	−	28.4383i	0.688314	−	1.19220i	0.972383	−	0.233392i	$-0.0749824\pi$
$570$		0			0
$571$	20.9737			0.877721			0.438860	−	0.898555i	$-0.355382\pi$
$571$	20.9737			0.877721			0.438860	+	0.898555i	$0.355382\pi$
$572$		0			0
$573$	19.8114			0.827633
$574$		0			0
$575$	1.00000	−	1.73205i	0.0417029	−	0.0722315i
$576$		0			0
$577$	−41.6228			−1.73278			−0.866389	−	0.499369i	$-0.833565\pi$
$577$	−41.6228			−1.73278			−0.866389	+	0.499369i	$0.833565\pi$
$578$		0			0
$579$	3.08114	+	5.33669i	0.128048	+	0.221785i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	6.32456	−	10.9545i	0.261936	−	0.453687i
$584$		0			0
$585$	3.08114	−	1.87259i	0.127389	−	0.0774220i
$586$		0			0
$587$	−18.3925	+	31.8568i	−0.759141	+	1.31487i	0.184148	+	0.982898i	$0.441047\pi$
$587$	−18.3925	+	31.8568i	−0.759141	+	1.31487i	−0.943289	+	0.331972i	$0.892286\pi$
$588$		0			0
$589$	−3.32456	−	5.75830i	−0.136986	−	0.237267i
$590$		0			0
$591$	9.16228	+	15.8695i	0.376886	+	0.652785i
$592$		0			0
$593$	19.6754			0.807974			0.403987	−	0.914765i	$-0.367624\pi$
$593$	19.6754			0.807974			0.403987	+	0.914765i	$0.367624\pi$
$594$		0			0
$595$	7.74342	−	13.4120i	0.317449	−	0.549838i
$596$		0			0
$597$	19.3246			0.790901
$598$		0			0
$599$	−14.5132			−0.592992			−0.296496	−	0.955034i	$-0.595818\pi$
$599$	−14.5132			−0.592992			−0.296496	+	0.955034i	$0.595818\pi$
$600$		0			0
$601$	6.64911	−	11.5166i	0.271223	−	0.469772i	−0.697952	−	0.716144i	$-0.745905\pi$
$601$	6.64911	−	11.5166i	0.271223	−	0.469772i	0.969175	+	0.246372i	$0.0792386\pi$
$602$		0			0
$603$	3.83772			0.156284
$604$		0			0
$605$	−3.50000	−	6.06218i	−0.142295	−	0.246463i
$606$		0			0
$607$	−13.3246	−	23.0788i	−0.540827	−	0.936740i	−0.998857	−	0.0478030i	$-0.984778\pi$
$607$	−13.3246	−	23.0788i	−0.540827	−	0.936740i	0.458030	−	0.888937i	$-0.348555\pi$
$608$		0			0
$609$	0.905694	−	1.56871i	0.0367006	−	0.0635673i
$610$		0			0
$611$	−0.932028	−	41.4059i	−0.0377058	−	1.67510i
$612$		0			0
$613$	−14.7302	+	25.5135i	−0.594949	+	1.03048i	0.398605	+	0.917123i	$0.369494\pi$
$613$	−14.7302	+	25.5135i	−0.594949	+	1.03048i	−0.993554	+	0.113359i	$0.963839\pi$
$614$		0			0
$615$	0.581139	+	1.00656i	0.0234338	+	0.0405885i
$616$		0			0
$617$	12.4868	+	21.6278i	0.502701	+	0.870704i	0.999995	+	0.00312162i	$0.000993645\pi$
$617$	12.4868	+	21.6278i	0.502701	+	0.870704i	−0.497294	+	0.867582i	$0.665673\pi$
$618$		0			0
$619$	−31.3246			−1.25904			−0.629520	−	0.776984i	$-0.716748\pi$
$619$	−31.3246			−1.25904			−0.629520	+	0.776984i	$0.716748\pi$
$620$		0			0
$621$	−1.00000	+	1.73205i	−0.0401286	+	0.0695048i
$622$		0			0
$623$	−7.53950			−0.302064
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−2.00000	+	3.46410i	−0.0798723	+	0.138343i
$628$		0			0
$629$	30.9737			1.23500
$630$		0			0
$631$	5.66228	+	9.80735i	0.225412	+	0.390425i	0.956443	−	0.291920i	$-0.0942939\pi$
$631$	5.66228	+	9.80735i	0.225412	+	0.390425i	−0.731031	+	0.682344i	$0.760961\pi$
$632$		0			0
$633$	0.824555	+	1.42817i	0.0327731	+	0.0567647i
$634$		0			0
$635$	−3.08114	+	5.33669i	−0.122271	+	0.211780i
$636$		0			0
$637$	−7.35089	−	4.02625i	−0.291253	−	0.159526i
$638$		0			0
$639$	6.74342	−	11.6799i	0.266765	−	0.462051i
$640$		0			0
$641$	−8.16228	−	14.1375i	−0.322391	−	0.558397i	0.658590	−	0.752502i	$-0.271153\pi$
$641$	−8.16228	−	14.1375i	−0.322391	−	0.558397i	−0.980981	+	0.194105i	$0.937820\pi$
$642$		0			0
$643$	10.2434	+	17.7421i	0.403961	+	0.699681i	0.994200	−	0.107548i	$-0.0342998\pi$
$643$	10.2434	+	17.7421i	0.403961	+	0.699681i	−0.590239	+	0.807229i	$0.700967\pi$
$644$		0			0
$645$	3.83772			0.151110
$646$		0			0
$647$	19.3246	−	33.4711i	0.759727	−	1.31589i	−0.183263	−	0.983064i	$-0.558666\pi$
$647$	19.3246	−	33.4711i	0.759727	−	1.31589i	0.942990	−	0.332821i	$-0.108001\pi$
$648$		0			0
$649$	1.67544			0.0657670
$650$		0			0
$651$	7.18861			0.281744
$652$		0			0
$653$	7.25658	−	12.5688i	0.283972	−	0.491854i	−0.688387	−	0.725343i	$-0.741681\pi$
$653$	7.25658	−	12.5688i	0.283972	−	0.491854i	0.972359	+	0.233489i	$0.0750144\pi$
$654$		0			0
$655$	15.8114			0.617802
$656$		0			0
$657$	−0.0811388	−	0.140537i	−0.00316553	−	0.00548285i
$658$		0			0
$659$	−17.4868	−	30.2881i	−0.681190	−	1.17986i	−0.974618	−	0.223875i	$-0.928129\pi$
$659$	−17.4868	−	30.2881i	−0.681190	−	1.17986i	0.293428	−	0.955981i	$-0.405204\pi$
$660$		0			0
$661$	7.33772	−	12.7093i	0.285404	−	0.494335i	−0.687303	−	0.726371i	$-0.741205\pi$
$661$	7.33772	−	12.7093i	0.285404	−	0.494335i	0.972707	+	0.232036i	$0.0745388\pi$
$662$		0			0
$663$	−0.581139	−	25.8174i	−0.0225696	−	1.00267i
$664$		0			0
$665$	−2.16228	+	3.74517i	−0.0838495	+	0.145232i
$666$		0			0
$667$	−0.837722	−	1.45098i	−0.0324367	−	0.0561821i
$668$		0			0
$669$	−2.00000	−	3.46410i	−0.0773245	−	0.133930i
$670$		0			0
$671$	−26.0000			−1.00372
$672$		0			0
$673$	18.0811	−	31.3175i	0.696977	−	1.20720i	−0.272533	−	0.962146i	$-0.587861\pi$
$673$	18.0811	−	31.3175i	0.696977	−	1.20720i	0.969510	−	0.245053i	$-0.0788052\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	45.9473			1.76590			0.882950	−	0.469468i	$-0.155554\pi$
$677$	45.9473			1.76590			0.882950	+	0.469468i	$0.155554\pi$
$678$		0			0
$679$	20.3377	−	35.2260i	0.780490	−	1.35185i
$680$		0			0
$681$	11.1623			0.427739
$682$		0			0
$683$	−10.2566	−	17.7649i	−0.392457	−	0.679756i	0.600316	−	0.799763i	$-0.295042\pi$
$683$	−10.2566	−	17.7649i	−0.392457	−	0.679756i	−0.992773	+	0.120007i	$0.961708\pi$
$684$		0			0
$685$	9.58114	+	16.5950i	0.366076	+	0.634063i
$686$		0			0
$687$	−9.16228	+	15.8695i	−0.349563	+	0.605460i
$688$		0			0
$689$	−0.513167	−	22.7977i	−0.0195501	−	0.868524i
$690$		0			0
$691$	7.82456	−	13.5525i	0.297660	−	0.515562i	−0.677940	−	0.735117i	$-0.737127\pi$
$691$	7.82456	−	13.5525i	0.297660	−	0.515562i	0.975600	+	0.219555i	$0.0704605\pi$
$692$		0			0
$693$	−2.16228	−	3.74517i	−0.0821381	−	0.142267i
$694$		0			0
$695$	−5.66228	−	9.80735i	−0.214782	−	0.372014i
$696$		0			0
$697$	8.32456			0.315315
$698$		0			0
$699$	3.83772	−	6.64713i	0.145156	−	0.251418i
$700$		0			0
$701$	−5.67544			−0.214359			−0.107179	−	0.994240i	$-0.534182\pi$
$701$	−5.67544			−0.214359			−0.107179	+	0.994240i	$0.534182\pi$
$702$		0			0
$703$	−8.64911			−0.326207
$704$		0			0
$705$	−5.74342	+	9.94789i	−0.216310	+	0.374659i
$706$		0			0
$707$	26.6491			1.00224
$708$		0			0
$709$	19.3114	+	33.4483i	0.725254	+	1.25618i	0.958869	+	0.283848i	$0.0916112\pi$
$709$	19.3114	+	33.4483i	0.725254	+	1.25618i	−0.233615	+	0.972329i	$0.575055\pi$
$710$		0			0
$711$	−5.50000	−	9.52628i	−0.206266	−	0.357263i
$712$		0			0
$713$	3.32456	−	5.75830i	0.124506	−	0.215650i
$714$		0			0
$715$	6.32456	+	3.46410i	0.236525	+	0.129550i
$716$		0			0
$717$	−4.32456	+	7.49035i	−0.161503	+	0.279732i
$718$		0			0
$719$	−9.06797	−	15.7062i	−0.338178	−	0.585742i	0.645912	−	0.763412i	$-0.276477\pi$
$719$	−9.06797	−	15.7062i	−0.338178	−	0.585742i	−0.984090	+	0.177670i	$0.943144\pi$
$720$		0			0
$721$	9.17544	+	15.8923i	0.341711	+	0.591862i
$722$		0			0
$723$	−18.3246			−0.681498
$724$		0			0
$725$	0.418861	−	0.725489i	0.0155561	−	0.0269440i
$726$		0			0
$727$	−33.8377			−1.25497			−0.627486	−	0.778628i	$-0.715916\pi$
$727$	−33.8377			−1.25497			−0.627486	+	0.778628i	$0.715916\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	13.7434	−	23.8043i	0.508319	−	0.880434i
$732$		0			0
$733$	42.1623			1.55730			0.778650	−	0.627459i	$-0.215905\pi$
$733$	42.1623			1.55730			0.778650	+	0.627459i	$0.215905\pi$
$734$		0			0
$735$	1.16228	+	2.01312i	0.0428713	+	0.0742552i
$736$		0			0
$737$	3.83772	+	6.64713i	0.141364	+	0.244850i
$738$		0			0
$739$	16.3246	−	28.2750i	0.600508	−	1.04011i	−0.392236	−	0.919865i	$-0.628298\pi$
$739$	16.3246	−	28.2750i	0.600508	−	1.04011i	0.992744	−	0.120246i	$-0.0383685\pi$
$740$		0			0
$741$	0.162278	+	7.20928i	0.00596142	+	0.264839i
$742$		0			0
$743$	22.7171	−	39.3471i	0.833409	−	1.44351i	−0.0619104	−	0.998082i	$-0.519719\pi$
$743$	22.7171	−	39.3471i	0.833409	−	1.44351i	0.895319	−	0.445425i	$-0.146947\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.10961			0.0405443
$750$		0			0
$751$	−17.6491	+	30.5692i	−0.644025	+	1.11548i	0.340501	+	0.940244i	$0.389403\pi$
$751$	−17.6491	+	30.5692i	−0.644025	+	1.11548i	−0.984526	+	0.175240i	$0.943930\pi$
$752$		0			0
$753$	18.9737			0.691439
$754$		0			0
$755$	8.32456			0.302962
$756$		0			0
$757$	17.8114	−	30.8502i	0.647366	−	1.12127i	−0.336384	−	0.941725i	$-0.609204\pi$
$757$	17.8114	−	30.8502i	0.647366	−	1.12127i	0.983750	−	0.179546i	$-0.0574628\pi$
$758$		0			0
$759$	−4.00000			−0.145191
$760$		0			0
$761$	−22.6491	−	39.2294i	−0.821030	−	1.42207i	−0.904916	−	0.425590i	$-0.860067\pi$
$761$	−22.6491	−	39.2294i	−0.821030	−	1.42207i	0.0838866	−	0.996475i	$-0.473267\pi$
$762$		0			0
$763$	−5.75658	−	9.97070i	−0.208402	−	0.360963i
$764$		0			0
$765$	−3.58114	+	6.20271i	−0.129476	+	0.224260i
$766$		0			0
$767$	2.58114	−	1.56871i	0.0931995	−	0.0566428i
$768$		0			0
$769$	6.51317	−	11.2811i	0.234871	−	0.406808i	−0.724364	−	0.689417i	$-0.757867\pi$
$769$	6.51317	−	11.2811i	0.234871	−	0.406808i	0.959235	+	0.282609i	$0.0912000\pi$
$770$		0			0
$771$	9.06797	+	15.7062i	0.326575	+	0.565645i
$772$		0			0
$773$	−2.16228	−	3.74517i	−0.0777717	−	0.134705i	0.824517	−	0.565838i	$-0.191447\pi$
$773$	−2.16228	−	3.74517i	−0.0777717	−	0.134705i	−0.902288	+	0.431133i	$0.858114\pi$
$774$		0			0
$775$	3.32456			0.119422
$776$		0			0
$777$	4.67544	−	8.09811i	0.167731	−	0.290518i
$778$		0			0
$779$	−2.32456			−0.0832858
$780$		0			0
$781$	26.9737			0.965194
$782$		0			0
$783$	−0.418861	+	0.725489i	−0.0149689	+	0.0259269i
$784$		0			0
$785$	−16.8114			−0.600024
$786$		0			0
$787$	−8.91886	−	15.4479i	−0.317923	−	0.550659i	0.662131	−	0.749388i	$-0.269652\pi$
$787$	−8.91886	−	15.4479i	−0.317923	−	0.550659i	−0.980055	+	0.198729i	$0.936319\pi$
$788$		0			0
$789$	−4.74342	−	8.21584i	−0.168870	−	0.292492i
$790$		0			0
$791$	9.00000	−	15.5885i	0.320003	−	0.554262i
$792$		0			0
$793$	−40.0548	+	24.3436i	−1.42239	+	0.864468i
$794$		0			0
$795$	−3.16228	+	5.47723i	−0.112154	+	0.194257i
$796$		0			0
$797$	8.41886	+	14.5819i	0.298211	+	0.516517i	0.975727	−	0.218991i	$-0.0702766\pi$
$797$	8.41886	+	14.5819i	0.298211	+	0.516517i	−0.677515	+	0.735509i	$0.736943\pi$
$798$		0			0
$799$	41.1359	+	71.2495i	1.45529	+	2.52063i
$800$		0			0
$801$	3.48683			0.123201
$802$		0			0
$803$	0.162278	−	0.281073i	0.00572665	−	0.00991886i
$804$		0			0
$805$	−4.32456			−0.152421
$806$		0			0
$807$	4.51317			0.158871
$808$		0			0
$809$	−4.83772	+	8.37918i	−0.170085	+	0.294596i	−0.938449	−	0.345417i	$-0.887738\pi$
$809$	−4.83772	+	8.37918i	−0.170085	+	0.294596i	0.768364	+	0.640013i	$0.221071\pi$
$810$		0			0
$811$	33.9737			1.19298			0.596488	−	0.802622i	$-0.296562\pi$
$811$	33.9737			1.19298			0.596488	+	0.802622i	$0.296562\pi$
$812$		0			0
$813$	7.82456	+	13.5525i	0.274419	+	0.475308i
$814$		0			0
$815$	5.24342	+	9.08186i	0.183669	+	0.318124i
$816$		0			0
$817$	−3.83772	+	6.64713i	−0.134265	+	0.232554i
$818$		0			0
$819$	−6.83772	−	3.74517i	−0.238929	−	0.130867i
$820$		0			0
$821$	−21.0000	+	36.3731i	−0.732905	+	1.26943i	0.222731	+	0.974880i	$0.428503\pi$
$821$	−21.0000	+	36.3731i	−0.732905	+	1.26943i	−0.955636	+	0.294549i	$0.904831\pi$
$822$		0			0
$823$	2.83772	+	4.91508i	0.0989168	+	0.171329i	0.911237	−	0.411883i	$-0.135129\pi$
$823$	2.83772	+	4.91508i	0.0989168	+	0.171329i	−0.812320	+	0.583212i	$0.801796\pi$
$824$		0			0
$825$	−1.00000	−	1.73205i	−0.0348155	−	0.0603023i
$826$		0			0
$827$	28.4605			0.989669			0.494834	−	0.868987i	$-0.335229\pi$
$827$	28.4605			0.989669			0.494834	+	0.868987i	$0.335229\pi$
$828$		0			0
$829$	−7.82456	+	13.5525i	−0.271758	+	0.470699i	−0.969312	−	0.245833i	$-0.920938\pi$
$829$	−7.82456	+	13.5525i	−0.271758	+	0.470699i	0.697554	+	0.716532i	$0.254272\pi$
$830$		0			0
$831$	−24.3246			−0.843809
$832$		0			0
$833$	16.6491			0.576857
$834$		0			0
$835$	2.32456	−	4.02625i	0.0804446	−	0.139334i
$836$		0			0
$837$	−3.32456			−0.114913
$838$		0			0
$839$	7.51317	+	13.0132i	0.259383	+	0.449265i	0.966077	−	0.258255i	$-0.0831474\pi$
$839$	7.51317	+	13.0132i	0.259383	+	0.449265i	−0.706694	+	0.707520i	$0.749814\pi$
$840$		0			0
$841$	14.1491	+	24.5070i	0.487900	+	0.845068i
$842$		0			0
$843$	1.58114	−	2.73861i	0.0544573	−	0.0943228i
$844$		0			0
$845$	12.9868	−	0.584952i	0.446761	−	0.0201230i
$846$		0			0
$847$	−7.56797	+	13.1081i	−0.260039	+	0.450400i
$848$		0			0
$849$	−3.40569	−	5.89884i	−0.116883	−	0.202448i
$850$		0			0
$851$	−4.32456	−	7.49035i	−0.148244	−	0.256766i
$852$		0			0
$853$	37.7851			1.29374			0.646868	−	0.762602i	$-0.276079\pi$
$853$	37.7851			1.29374			0.646868	+	0.762602i	$0.276079\pi$
$854$		0			0
$855$	1.00000	−	1.73205i	0.0341993	−	0.0592349i
$856$		0			0
$857$	−15.4868			−0.529020			−0.264510	−	0.964383i	$-0.585210\pi$
$857$	−15.4868			−0.529020			−0.264510	+	0.964383i	$0.585210\pi$
$858$		0			0
$859$	32.9473			1.12415			0.562074	−	0.827087i	$-0.310004\pi$
$859$	32.9473			1.12415			0.562074	+	0.827087i	$0.310004\pi$
$860$		0			0
$861$	1.25658	−	2.17647i	0.0428243	−	0.0741738i
$862$		0			0
$863$	−24.3246			−0.828017			−0.414009	−	0.910273i	$-0.635872\pi$
$863$	−24.3246			−0.828017			−0.414009	+	0.910273i	$0.635872\pi$
$864$		0			0
$865$	−9.74342	−	16.8761i	−0.331286	−	0.573804i
$866$		0			0
$867$	17.1491	+	29.7031i	0.582414	+	1.00877i
$868$		0			0
$869$	11.0000	−	19.0526i	0.373149	−	0.646314i
$870$		0			0
$871$	12.1359	+	6.64713i	0.411211	+	0.225229i
$872$		0			0
$873$	−9.40569	+	16.2911i	−0.318335	+	0.551372i
$874$		0			0
$875$	−1.08114	−	1.87259i	−0.0365492	−	0.0633050i
$876$		0			0
$877$	−5.83772	−	10.1112i	−0.197126	−	0.341432i	0.750469	−	0.660905i	$-0.229827\pi$
$877$	−5.83772	−	10.1112i	−0.197126	−	0.341432i	−0.947595	+	0.319473i	$0.896494\pi$
$878$		0			0
$879$	−8.51317			−0.287142
$880$		0			0
$881$	1.16228	−	2.01312i	0.0391581	−	0.0678239i	−0.845782	−	0.533528i	$-0.820866\pi$
$881$	1.16228	−	2.01312i	0.0391581	−	0.0678239i	0.884940	+	0.465705i	$0.154199\pi$
$882$		0			0
$883$	−51.4605			−1.73178			−0.865892	−	0.500231i	$-0.833248\pi$
$883$	−51.4605			−1.73178			−0.865892	+	0.500231i	$0.833248\pi$
$884$		0			0
$885$	−0.837722			−0.0281597
$886$		0			0
$887$	9.23025	−	15.9873i	0.309921	−	0.536800i	−0.668423	−	0.743781i	$-0.733031\pi$
$887$	9.23025	−	15.9873i	0.309921	−	0.536800i	0.978345	+	0.206981i	$0.0663639\pi$
$888$		0			0
$889$	13.3246			0.446891
$890$		0			0
$891$	1.00000	+	1.73205i	0.0335013	+	0.0580259i
$892$		0			0
$893$	−11.4868	−	19.8958i	−0.384392	−	0.665787i
$894$		0			0
$895$	9.74342	−	16.8761i	0.325686	−	0.564106i
$896$		0			0
$897$	−6.16228	+	3.74517i	−0.205752	+	0.125048i
$898$		0			0
$899$	1.39253	−	2.41193i	0.0464434	−	0.0804423i
$900$		0			0
$901$	22.6491	+	39.2294i	0.754551	+	1.30692i
$902$		0			0
$903$	−4.14911	−	7.18647i	−0.138074	−	0.239151i
$904$		0			0
$905$	−0.649111			−0.0215772
$906$		0			0
$907$	17.6491	−	30.5692i	0.586029	−	1.01503i	−0.408717	−	0.912661i	$-0.634024\pi$
$907$	17.6491	−	30.5692i	0.586029	−	1.01503i	0.994746	−	0.102371i	$-0.0326429\pi$
$908$		0			0
$909$	−12.3246			−0.408780
$910$		0			0
$911$	30.9737			1.02620			0.513102	−	0.858328i	$-0.328496\pi$
$911$	30.9737			1.02620			0.513102	+	0.858328i	$0.328496\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	13.0000			0.429767
$916$		0			0
$917$	−17.0943	−	29.6082i	−0.564504	−	0.977749i
$918$		0			0
$919$	7.83772	+	13.5753i	0.258543	+	0.447809i	0.965852	−	0.259095i	$-0.0834244\pi$
$919$	7.83772	+	13.5753i	0.258543	+	0.447809i	−0.707309	+	0.706904i	$0.750091\pi$
$920$		0			0
$921$	−8.91886	+	15.4479i	−0.293886	+	0.509026i
$922$		0			0
$923$	41.5548	−	25.2553i	1.36779	−	0.831287i
$924$		0			0
$925$	2.16228	−	3.74517i	0.0710953	−	0.123141i
$926$		0			0
$927$	−4.24342	−	7.34981i	−0.139372	−	0.241400i
$928$		0			0
$929$	−7.67544	−	13.2943i	−0.251823	−	0.436171i	0.712205	−	0.701972i	$-0.247697\pi$
$929$	−7.67544	−	13.2943i	−0.251823	−	0.436171i	−0.964028	+	0.265801i	$0.914363\pi$
$930$		0			0
$931$	−4.64911			−0.152368
$932$		0			0
$933$	−2.90569	+	5.03281i	−0.0951282	+	0.164767i
$934$		0			0
$935$	−14.3246			−0.468463
$936$		0			0
$937$	−16.9737			−0.554505			−0.277253	−	0.960797i	$-0.589424\pi$
$937$	−16.9737			−0.554505			−0.277253	+	0.960797i	$0.589424\pi$
$938$		0			0
$939$	−0.243416	+	0.421610i	−0.00794360	+	0.0137587i
$940$		0			0
$941$	16.4605			0.536597			0.268298	−	0.963336i	$-0.413539\pi$
$941$	16.4605			0.536597			0.268298	+	0.963336i	$0.413539\pi$
$942$		0			0
$943$	−1.16228	−	2.01312i	−0.0378490	−	0.0655563i
$944$		0			0
$945$	1.08114	+	1.87259i	0.0351694	+	0.0609153i
$946$		0			0
$947$	−8.23025	+	14.2552i	−0.267447	+	0.463232i	−0.968202	−	0.250170i	$-0.919513\pi$
$947$	−8.23025	+	14.2552i	−0.267447	+	0.463232i	0.700755	+	0.713402i	$0.252847\pi$
$948$		0			0
$949$	−0.0131670	−	0.584952i	−0.000427420	−	0.0189884i
$950$		0			0
$951$	5.16228	−	8.94133i	0.167398	−	0.289942i
$952$		0			0
$953$	28.1623	+	48.7785i	0.912266	+	1.58009i	0.810856	+	0.585246i	$0.199002\pi$
$953$	28.1623	+	48.7785i	0.912266	+	1.58009i	0.101410	+	0.994845i	$0.467665\pi$
$954$		0			0
$955$	−9.90569	−	17.1572i	−0.320541	−	0.555193i
$956$		0			0
$957$	−1.67544			−0.0541594
$958$		0			0
$959$	20.7171	−	35.8830i	0.668989	−	1.15872i
$960$		0			0
$961$	−19.9473			−0.643462
$962$		0			0
$963$	−0.513167			−0.0165366
$964$		0			0
$965$	3.08114	−	5.33669i	0.0991854	−	0.171794i
$966$		0			0
$967$	6.97367			0.224258			0.112129	−	0.993694i	$-0.464233\pi$
$967$	6.97367			0.224258			0.112129	+	0.993694i	$0.464233\pi$
$968$		0			0
$969$	−7.16228	−	12.4054i	−0.230086	−	0.398520i
$970$		0			0
$971$	17.8114	+	30.8502i	0.571595	+	0.990031i	0.996402	+	0.0847474i	$0.0270083\pi$
$971$	17.8114	+	30.8502i	0.571595	+	0.990031i	−0.424808	+	0.905284i	$0.639658\pi$
$972$		0			0
$973$	−12.2434	+	21.2062i	−0.392506	+	0.679840i
$974$		0			0
$975$	−3.16228	−	1.73205i	−0.101274	−	0.0554700i
$976$		0			0
$977$	7.48683	−	12.9676i	0.239525	−	0.414869i	−0.721053	−	0.692880i	$-0.756342\pi$
$977$	7.48683	−	12.9676i	0.239525	−	0.414869i	0.960578	+	0.278010i	$0.0896750\pi$
$978$		0			0
$979$	3.48683	+	6.03937i	0.111440	+	0.193019i
$980$		0			0
$981$	2.66228	+	4.61120i	0.0850000	+	0.147224i
$982$		0			0
$983$	−53.6228			−1.71030			−0.855150	−	0.518380i	$-0.826535\pi$
$983$	−53.6228			−1.71030			−0.855150	+	0.518380i	$0.826535\pi$
$984$		0			0
$985$	9.16228	−	15.8695i	0.291934	−	0.505645i
$986$		0			0
$987$	24.8377			0.790593
$988$		0			0
$989$	−7.67544			−0.244065
$990$		0			0
$991$	−8.81139	+	15.2618i	−0.279903	+	0.484806i	−0.971360	−	0.237611i	$-0.923636\pi$
$991$	−8.81139	+	15.2618i	−0.279903	+	0.484806i	0.691457	+	0.722417i	$0.256969\pi$
$992$		0			0
$993$	15.3246			0.486310
$994$		0			0
$995$	−9.66228	−	16.7356i	−0.306315	−	0.530553i
$996$		0			0
$997$	−16.2434	−	28.1344i	−0.514434	−	0.891026i	−0.999860	−	0.0167481i	$-0.994669\pi$
$997$	−16.2434	−	28.1344i	−0.514434	−	0.891026i	0.485426	−	0.874278i	$-0.338665\pi$
$998$		0			0
$999$	−2.16228	+	3.74517i	−0.0684114	+	0.118492i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1560.2.bg.e.601.2	✓	4	13.3	even	3	inner
1560.2.bg.e.841.2	yes	4	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} -1.00000 q^{5} +(1.08114 + 1.87259i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} -1.00000 q^{5} +(1.08114 + 1.87259i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} +(-0.0811388 - 3.60464i) q^{13} +(-0.500000 + 0.866025i) q^{15} +(3.58114 + 6.20271i) q^{17} +(-1.00000 - 1.73205i) q^{19} +2.16228 q^{21} +(1.00000 - 1.73205i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(0.418861 - 0.725489i) q^{29} +3.32456 q^{31} +(-1.00000 - 1.73205i) q^{33} +(-1.08114 - 1.87259i) q^{35} +(2.16228 - 3.74517i) q^{37} +(-3.16228 - 1.73205i) q^{39} +(0.581139 - 1.00656i) q^{41} +(-1.91886 - 3.32357i) q^{43} +(0.500000 + 0.866025i) q^{45} +11.4868 q^{47} +(1.16228 - 2.01312i) q^{49} +7.16228 q^{51} +6.32456 q^{53} +(-1.00000 + 1.73205i) q^{55} -2.00000 q^{57} +(0.418861 + 0.725489i) q^{59} +(-6.50000 - 11.2583i) q^{61} +(1.08114 - 1.87259i) q^{63} +(0.0811388 + 3.60464i) q^{65} +(-1.91886 + 3.32357i) q^{67} +(-1.00000 - 1.73205i) q^{69} +(6.74342 + 11.6799i) q^{71} +0.162278 q^{73} +(0.500000 - 0.866025i) q^{75} +4.32456 q^{77} +11.0000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-3.58114 - 6.20271i) q^{85} +(-0.418861 - 0.725489i) q^{87} +(-1.74342 + 3.01969i) q^{89} +(6.66228 - 4.04905i) q^{91} +(1.66228 - 2.87915i) q^{93} +(1.00000 + 1.73205i) q^{95} +(-9.40569 - 16.2911i) q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 4 q^{5} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 - 2 * q^9	\( 4 q + 2 q^{3} - 4 q^{5} - 2 q^{7} - 2 q^{9} + 4 q^{11} + 6 q^{13} - 2 q^{15} + 8 q^{17} - 4 q^{19} - 4 q^{21} + 4 q^{23} + 4 q^{25} - 4 q^{27} + 8 q^{29} - 12 q^{31} - 4 q^{33} + 2 q^{35} - 4 q^{37} - 4 q^{41} - 14 q^{43} + 2 q^{45} + 8 q^{47} - 8 q^{49} + 16 q^{51} - 4 q^{55} - 8 q^{57} + 8 q^{59} - 26 q^{61} - 2 q^{63} - 6 q^{65} - 14 q^{67} - 4 q^{69} + 8 q^{71} - 12 q^{73} + 2 q^{75} - 8 q^{77} + 44 q^{79} - 2 q^{81} - 8 q^{85} - 8 q^{87} + 12 q^{89} + 14 q^{91} - 6 q^{93} + 4 q^{95} - 6 q^{97} - 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 - 2 * q^9 + 4 * q^11 + 6 * q^13 - 2 * q^15 + 8 * q^17 - 4 * q^19 - 4 * q^21 + 4 * q^23 + 4 * q^25 - 4 * q^27 + 8 * q^29 - 12 * q^31 - 4 * q^33 + 2 * q^35 - 4 * q^37 - 4 * q^41 - 14 * q^43 + 2 * q^45 + 8 * q^47 - 8 * q^49 + 16 * q^51 - 4 * q^55 - 8 * q^57 + 8 * q^59 - 26 * q^61 - 2 * q^63 - 6 * q^65 - 14 * q^67 - 4 * q^69 + 8 * q^71 - 12 * q^73 + 2 * q^75 - 8 * q^77 + 44 * q^79 - 2 * q^81 - 8 * q^85 - 8 * q^87 + 12 * q^89 + 14 * q^91 - 6 * q^93 + 4 * q^95 - 6 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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