LMFDB - Embedded newform 624.2.cn.f.305.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(305,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 6, 5]))

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

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

chi := DirichletCharacter("624.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.cn (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			305.4
Character	$\chi$	$=$	624.305
Dual form			624.2.cn.f.401.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31722 + 1.12469i) q^{3} +(1.72616 + 1.72616i) q^{5} +(0.574711 - 2.14485i) q^{7} +(0.470140 - 2.96293i) q^{9} +O(q^{10})$	\(q+(-1.31722 + 1.12469i) q^{3} +(1.72616 + 1.72616i) q^{5} +(0.574711 - 2.14485i) q^{7} +(0.470140 - 2.96293i) q^{9} +(-1.47004 - 5.48627i) q^{11} +(2.76028 - 2.31967i) q^{13} +(-4.21513 - 0.332337i) q^{15} +(-1.40933 - 2.44104i) q^{17} +(7.85833 + 2.10563i) q^{19} +(1.65527 + 3.47161i) q^{21} +(-1.84516 + 3.19592i) q^{23} +0.959270i q^{25} +(2.71311 + 4.43160i) q^{27} +(-1.95737 - 1.13009i) q^{29} +(-3.13483 + 3.13483i) q^{31} +(8.10673 + 5.57328i) q^{33} +(4.69440 - 2.71031i) q^{35} +(7.36333 - 1.97300i) q^{37} +(-1.02699 + 6.15998i) q^{39} +(-7.02869 + 1.88333i) q^{41} +(0.416760 - 0.240616i) q^{43} +(5.92604 - 4.30296i) q^{45} +(9.57953 - 9.57953i) q^{47} +(1.79209 + 1.03466i) q^{49} +(4.60181 + 1.63032i) q^{51} +0.617097i q^{53} +(6.93266 - 12.0077i) q^{55} +(-12.7193 + 6.06461i) q^{57} +(1.94720 + 0.521752i) q^{59} +(0.667748 + 1.15657i) q^{61} +(-6.08485 - 2.71121i) q^{63} +(8.76881 + 0.760564i) q^{65} +(0.667631 + 2.49163i) q^{67} +(-1.16393 - 6.28497i) q^{69} +(-1.81372 + 6.76890i) q^{71} +(-6.75039 - 6.75039i) q^{73} +(-1.07888 - 1.26357i) q^{75} -12.6121 q^{77} +0.372617 q^{79} +(-8.55794 - 2.78599i) q^{81} +(4.99123 + 4.99123i) q^{83} +(1.78089 - 6.64636i) q^{85} +(3.84930 - 0.712863i) q^{87} +(2.17011 + 8.09895i) q^{89} +(-3.38898 - 7.25352i) q^{91} +(0.603546 - 7.65497i) q^{93} +(9.93009 + 17.1994i) q^{95} +(3.03688 + 0.813729i) q^{97} +(-16.9466 + 1.77632i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{7}+O(q^{10}) $ 56 * q - 4 * q^7	$ 56 q - 4 q^{7} + 8 q^{13} + 8 q^{15} - 4 q^{19} + 16 q^{21} - 24 q^{27} + 36 q^{31} + 28 q^{33} + 20 q^{37} - 16 q^{39} + 84 q^{43} + 12 q^{45} - 12 q^{49} + 24 q^{55} - 36 q^{57} - 24 q^{61} + 12 q^{63} + 32 q^{67} - 36 q^{69} - 20 q^{73} + 60 q^{75} + 32 q^{79} - 88 q^{85} + 16 q^{87} - 28 q^{91} - 88 q^{93} - 36 q^{97} - 44 q^{99}+O(q^{100}) $ 56 * q - 4 * q^7 + 8 * q^13 + 8 * q^15 - 4 * q^19 + 16 * q^21 - 24 * q^27 + 36 * q^31 + 28 * q^33 + 20 * q^37 - 16 * q^39 + 84 * q^43 + 12 * q^45 - 12 * q^49 + 24 * q^55 - 36 * q^57 - 24 * q^61 + 12 * q^63 + 32 * q^67 - 36 * q^69 - 20 * q^73 + 60 * q^75 + 32 * q^79 - 88 * q^85 + 16 * q^87 - 28 * q^91 - 88 * q^93 - 36 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.31722	+	1.12469i	−0.760498	+	0.649341i
$3$	−1.31722	+	1.12469i	−0.760498	+	0.649341i
$4$		0			0
$5$	1.72616	+	1.72616i	0.771963	+	0.771963i	0.978449	−	0.206486i	$-0.0662029\pi$
$5$	1.72616	+	1.72616i	0.771963	+	0.771963i	−0.206486	+	0.978449i	$0.566203\pi$
$6$		0			0
$7$	0.574711	−	2.14485i	0.217220	−	0.810677i	−0.768153	−	0.640266i	$-0.778824\pi$
$7$	0.574711	−	2.14485i	0.217220	−	0.810677i	0.985373	−	0.170411i	$-0.0545094\pi$
$8$		0			0
$9$	0.470140	−	2.96293i	0.156713	−	0.987644i
$10$		0			0
$11$	−1.47004	−	5.48627i	−0.443234	−	1.65417i	−0.720557	−	0.693396i	$-0.756114\pi$
$11$	−1.47004	−	5.48627i	−0.443234	−	1.65417i	0.277323	−	0.960777i	$-0.410553\pi$
$12$		0			0
$13$	2.76028	−	2.31967i	0.765564	−	0.643360i
$13$	2.76028	−	2.31967i	0.765564	−	0.643360i
$14$		0			0
$15$	−4.21513	−	0.332337i	−1.08834	−	0.0858091i
$16$		0			0
$17$	−1.40933	−	2.44104i	−0.341813	−	0.592038i	0.642956	−	0.765903i	$-0.277708\pi$
$17$	−1.40933	−	2.44104i	−0.341813	−	0.592038i	−0.984770	+	0.173865i	$0.944374\pi$
$18$		0			0
$19$	7.85833	+	2.10563i	1.80282	+	0.483065i	0.994414	−	0.105553i	$-0.0336613\pi$
$19$	7.85833	+	2.10563i	1.80282	+	0.483065i	0.808411	+	0.588618i	$0.200328\pi$
$20$		0			0
$21$	1.65527	+	3.47161i	0.361210	+	0.757568i
$22$		0			0
$23$	−1.84516	+	3.19592i	−0.384743	+	0.666395i	−0.991734	−	0.128314i	$-0.959043\pi$
$23$	−1.84516	+	3.19592i	−0.384743	+	0.666395i	0.606990	+	0.794709i	$0.292377\pi$
$24$		0			0
$25$			0.959270i			0.191854i
$26$		0			0
$27$	2.71311	+	4.43160i	0.522137	+	0.852861i
$28$		0			0
$29$	−1.95737	−	1.13009i	−0.363475	−	0.209853i	0.307129	−	0.951668i	$-0.400632\pi$
$29$	−1.95737	−	1.13009i	−0.363475	−	0.209853i	−0.670604	+	0.741815i	$0.733965\pi$
$30$		0			0
$31$	−3.13483	+	3.13483i	−0.563031	+	0.563031i	−0.930167	−	0.367136i	$-0.880338\pi$
$31$	−3.13483	+	3.13483i	−0.563031	+	0.563031i	0.367136	+	0.930167i	$0.380338\pi$
$32$		0			0
$33$	8.10673	+	5.57328i	1.41120	+	0.970184i
$34$		0			0
$35$	4.69440	−	2.71031i	0.793499	−	0.458127i
$36$		0			0
$37$	7.36333	−	1.97300i	1.21052	−	0.324359i	0.403557	−	0.914955i	$-0.367774\pi$
$37$	7.36333	−	1.97300i	1.21052	−	0.324359i	0.806968	+	0.590596i	$0.201107\pi$
$38$		0			0
$39$	−1.02699	+	6.15998i	−0.164449	+	0.986386i
$40$		0			0
$41$	−7.02869	+	1.88333i	−1.09770	+	0.294127i	−0.761826	−	0.647781i	$-0.775697\pi$
$41$	−7.02869	+	1.88333i	−1.09770	+	0.294127i	−0.335870	+	0.941908i	$0.609030\pi$
$42$		0			0
$43$	0.416760	−	0.240616i	0.0635553	−	0.0366937i	−0.467886	−	0.883789i	$-0.654984\pi$
$43$	0.416760	−	0.240616i	0.0635553	−	0.0366937i	0.531441	+	0.847095i	$0.321651\pi$
$44$		0			0
$45$	5.92604	−	4.30296i	0.883402	−	0.641448i
$46$		0			0
$47$	9.57953	−	9.57953i	1.39732	−	1.39732i	0.589685	−	0.807633i	$-0.299252\pi$
$47$	9.57953	−	9.57953i	1.39732	−	1.39732i	0.807633	−	0.589685i	$-0.200748\pi$
$48$		0			0
$49$	1.79209	+	1.03466i	0.256013	+	0.147809i
$50$		0			0
$51$	4.60181	+	1.63032i	0.644383	+	0.228290i
$52$		0			0
$53$			0.617097i			0.0847648i	0.999101	+	0.0423824i	$0.0134948\pi$
$53$			0.617097i			0.0847648i	−0.999101	+	0.0423824i	$0.986505\pi$
$54$		0			0
$55$	6.93266	−	12.0077i	0.934800	−	1.61912i
$56$		0			0
$57$	−12.7193	+	6.06461i	−1.68472	+	0.803277i
$58$		0			0
$59$	1.94720	+	0.521752i	0.253504	+	0.0679263i	0.383333	−	0.923610i	$-0.374776\pi$
$59$	1.94720	+	0.521752i	0.253504	+	0.0679263i	−0.129829	+	0.991536i	$0.541443\pi$
$60$		0			0
$61$	0.667748	+	1.15657i	0.0854964	+	0.148084i	0.905603	−	0.424127i	$-0.139419\pi$
$61$	0.667748	+	1.15657i	0.0854964	+	0.148084i	−0.820106	+	0.572211i	$0.806086\pi$
$62$		0			0
$63$	−6.08485	−	2.71121i	−0.766619	−	0.341580i
$64$		0			0
$65$	8.76881	+	0.760564i	1.08764	+	0.0943364i
$66$		0			0
$67$	0.667631	+	2.49163i	0.0815641	+	0.304401i	0.994641	−	0.103385i	$-0.0329674\pi$
$67$	0.667631	+	2.49163i	0.0815641	+	0.304401i	−0.913077	+	0.407787i	$0.866301\pi$
$68$		0			0
$69$	−1.16393	−	6.28497i	−0.140121	−	0.756621i
$70$		0			0
$71$	−1.81372	+	6.76890i	−0.215249	+	0.803320i	0.770830	+	0.637041i	$0.219842\pi$
$71$	−1.81372	+	6.76890i	−0.215249	+	0.803320i	−0.986079	+	0.166279i	$0.946825\pi$
$72$		0			0
$73$	−6.75039	−	6.75039i	−0.790073	−	0.790073i	0.191432	−	0.981506i	$-0.438687\pi$
$73$	−6.75039	−	6.75039i	−0.790073	−	0.790073i	−0.981506	+	0.191432i	$0.938687\pi$
$74$		0			0
$75$	−1.07888	−	1.26357i	−0.124579	−	0.145904i
$76$		0			0
$77$	−12.6121			−1.43728
$78$		0			0
$79$	0.372617			0.0419226			0.0209613	−	0.999780i	$-0.493327\pi$
$79$	0.372617			0.0419226			0.0209613	+	0.999780i	$0.493327\pi$
$80$		0			0
$81$	−8.55794	−	2.78599i	−0.950882	−	0.309554i
$82$		0			0
$83$	4.99123	+	4.99123i	0.547858	+	0.547858i	0.925821	−	0.377963i	$-0.123375\pi$
$83$	4.99123	+	4.99123i	0.547858	+	0.547858i	−0.377963	+	0.925821i	$0.623375\pi$
$84$		0			0
$85$	1.78089	−	6.64636i	0.193164	−	0.720899i
$86$		0			0
$87$	3.84930	−	0.712863i	0.412688	−	0.0764269i
$88$		0			0
$89$	2.17011	+	8.09895i	0.230031	+	0.858487i	0.980326	+	0.197384i	$0.0632446\pi$
$89$	2.17011	+	8.09895i	0.230031	+	0.858487i	−0.750295	+	0.661103i	$0.770089\pi$
$90$		0			0
$91$	−3.38898	−	7.25352i	−0.355261	−	0.760376i
$92$		0			0
$93$	0.603546	−	7.65497i	0.0625849	−	0.793783i
$94$		0			0
$95$	9.93009	+	17.1994i	1.01881	+	1.76462i
$96$		0			0
$97$	3.03688	+	0.813729i	0.308348	+	0.0826217i	0.409675	−	0.912232i	$-0.365642\pi$
$97$	3.03688	+	0.813729i	0.308348	+	0.0826217i	−0.101327	+	0.994853i	$0.532309\pi$
$98$		0			0
$99$	−16.9466	+	1.77632i	−1.70319	+	0.178527i
$100$		0			0
$101$	0.672751	−	1.16524i	0.0669412	−	0.115946i	−0.830612	−	0.556851i	$-0.812009\pi$
$101$	0.672751	−	1.16524i	0.0669412	−	0.115946i	0.897553	+	0.440906i	$0.145343\pi$
$102$		0			0
$103$		−	10.0519i		−	0.990446i	−0.868766	−	0.495223i	$-0.835086\pi$
$103$		−	10.0519i		−	0.990446i	0.868766	−	0.495223i	$-0.164914\pi$
$104$		0			0
$105$	−3.13530	+	8.84983i	−0.305974	+	0.863655i
$106$		0			0
$107$	−12.9381	−	7.46982i	−1.25077	−	0.722135i	−0.279511	−	0.960143i	$-0.590172\pi$
$107$	−12.9381	−	7.46982i	−1.25077	−	0.722135i	−0.971263	+	0.238008i	$0.923506\pi$
$108$		0			0
$109$	−5.96629	+	5.96629i	−0.571467	+	0.571467i	−0.932538	−	0.361071i	$-0.882411\pi$
$109$	−5.96629	+	5.96629i	−0.571467	+	0.571467i	0.361071	+	0.932538i	$0.382411\pi$
$110$		0			0
$111$	−7.48012	+	10.8803i	−0.709981	+	1.03272i
$112$		0			0
$113$	−15.1400	+	8.74110i	−1.42425	+	0.822294i	−0.996659	−	0.0816760i	$-0.973973\pi$
$113$	−15.1400	+	8.74110i	−1.42425	+	0.822294i	−0.427596	+	0.903970i	$0.640639\pi$
$114$		0			0
$115$	−8.70173	+	2.33162i	−0.811440	+	0.217425i
$116$		0			0
$117$	−5.57530	−	9.26909i	−0.515437	−	0.856927i
$118$		0			0
$119$	−6.04561	+	1.61992i	−0.554200	+	0.148498i
$120$		0			0
$121$	−18.4119	+	10.6301i	−1.67380	+	0.966372i
$122$		0			0
$123$	7.14017	−	10.3859i	0.643807	−	0.936462i
$124$		0			0
$125$	6.97495	−	6.97495i	0.623859	−	0.623859i
$126$		0			0
$127$	1.06716	+	0.616127i	0.0946954	+	0.0546724i	0.546600	−	0.837394i	$-0.315922\pi$
$127$	1.06716	+	0.616127i	0.0946954	+	0.0546724i	−0.451904	+	0.892066i	$0.649255\pi$
$128$		0			0
$129$	−0.278346	+	0.785671i	−0.0245070	+	0.0691745i
$130$		0			0
$131$			7.17983i			0.627305i	0.949538	+	0.313652i	$0.101553\pi$
$131$			7.17983i			0.627305i	−0.949538	+	0.313652i	$0.898447\pi$
$132$		0			0
$133$	9.03253	−	15.6448i	0.783220	−	1.35658i
$134$		0			0
$135$	−2.96640	+	12.3329i	−0.255307	+	1.06145i
$136$		0			0
$137$	11.6202	+	3.11363i	0.992783	+	0.266015i	0.718419	−	0.695611i	$-0.244866\pi$
$137$	11.6202	+	3.11363i	0.992783	+	0.266015i	0.274364	+	0.961626i	$0.411533\pi$
$138$		0			0
$139$	−1.16445	−	2.01689i	−0.0987677	−	0.171071i	0.812407	−	0.583091i	$-0.198157\pi$
$139$	−1.16445	−	2.01689i	−0.0987677	−	0.171071i	−0.911175	+	0.412020i	$0.864823\pi$
$140$		0			0
$141$	−1.84434	+	23.3924i	−0.155322	+	1.96999i
$142$		0			0
$143$	−16.7841	−	11.7336i	−1.40355	−	0.981215i
$144$		0			0
$145$	−1.42803	−	5.32947i	−0.118591	−	0.442588i
$146$		0			0
$147$	−3.52425	+	0.652667i	−0.290676	+	0.0538311i
$148$		0			0
$149$	5.04901	−	18.8432i	0.413631	−	1.54369i	−0.373930	−	0.927457i	$-0.621990\pi$
$149$	5.04901	−	18.8432i	0.413631	−	1.54369i	0.787562	−	0.616236i	$-0.211343\pi$
$150$		0			0
$151$	−0.712411	−	0.712411i	−0.0579752	−	0.0579752i	0.677525	−	0.735500i	$-0.263053\pi$
$151$	−0.712411	−	0.712411i	−0.0579752	−	0.0579752i	−0.735500	+	0.677525i	$0.763053\pi$
$152$		0			0
$153$	−7.89521	+	3.02813i	−0.638290	+	0.244810i
$154$		0			0
$155$	−10.8224			−0.869279
$156$		0			0
$157$	17.0306			1.35919			0.679594	−	0.733588i	$-0.262156\pi$
$157$	17.0306			1.35919			0.679594	+	0.733588i	$0.262156\pi$
$158$		0			0
$159$	−0.694044	−	0.812853i	−0.0550413	−	0.0644635i
$160$		0			0
$161$	5.79433	+	5.79433i	0.456657	+	0.456657i
$162$		0			0
$163$	−2.57138	+	9.59651i	−0.201406	+	0.751657i	0.789109	+	0.614253i	$0.210542\pi$
$163$	−2.57138	+	9.59651i	−0.201406	+	0.751657i	−0.990515	+	0.137404i	$0.956124\pi$
$164$		0			0
$165$	4.37313	+	23.6139i	0.340448	+	1.83834i
$166$		0			0
$167$	−2.68928	−	10.0365i	−0.208102	−	0.776649i	−0.988481	−	0.151342i	$-0.951640\pi$
$167$	−2.68928	−	10.0365i	−0.208102	−	0.776649i	0.780379	−	0.625307i	$-0.215026\pi$
$168$		0			0
$169$	2.23828	−	12.8059i	0.172175	−	0.985066i
$170$		0			0
$171$	9.93336	−	22.2938i	0.759623	−	1.70485i
$172$		0			0
$173$	6.65624	+	11.5289i	0.506064	+	0.876529i	0.999975	+	0.00701675i	$0.00223352\pi$
$173$	6.65624	+	11.5289i	0.506064	+	0.876529i	−0.493911	+	0.869512i	$0.664433\pi$
$174$		0			0
$175$	2.05749	+	0.551303i	0.155532	+	0.0416746i
$176$		0			0
$177$	−3.15171	+	1.50274i	−0.236897	+	0.112953i
$178$		0			0
$179$	−0.225490	+	0.390560i	−0.0168539	+	0.0291918i	−0.874329	−	0.485333i	$-0.838698\pi$
$179$	−0.225490	+	0.390560i	−0.0168539	+	0.0291918i	0.857475	+	0.514525i	$0.172032\pi$
$180$		0			0
$181$		−	0.572791i		−	0.0425752i	−0.999773	−	0.0212876i	$-0.993223\pi$
$181$		−	0.572791i		−	0.0425752i	0.999773	−	0.0212876i	$-0.00677657\pi$
$182$		0			0
$183$	−2.18036	−	0.772452i	−0.161177	−	0.0571013i
$184$		0			0
$185$	16.1160	+	9.30459i	1.18487	+	0.684087i
$186$		0			0
$187$	−11.3204	+	11.3204i	−0.827830	+	0.827830i
$188$		0			0
$189$	11.0644	−	3.27232i	0.804814	−	0.238026i
$190$		0			0
$191$	7.87896	−	4.54892i	0.570102	−	0.329148i	−0.187088	−	0.982343i	$-0.559905\pi$
$191$	7.87896	−	4.54892i	0.570102	−	0.329148i	0.757190	+	0.653195i	$0.226572\pi$
$192$		0			0
$193$	−13.9688	+	3.74292i	−1.00549	+	0.269421i	−0.723745	−	0.690067i	$-0.757581\pi$
$193$	−13.9688	+	3.74292i	−1.00549	+	0.269421i	−0.281748	+	0.959488i	$0.590914\pi$
$194$		0			0
$195$	−12.4059	+	8.86037i	−0.888402	+	0.634504i
$196$		0			0
$197$	6.22190	−	1.66715i	0.443292	−	0.118780i	−0.0302668	−	0.999542i	$-0.509636\pi$
$197$	6.22190	−	1.66715i	0.443292	−	0.118780i	0.473559	+	0.880762i	$0.342969\pi$
$198$		0			0
$199$	0.683303	−	0.394505i	0.0484381	−	0.0279657i	−0.475585	−	0.879670i	$-0.657764\pi$
$199$	0.683303	−	0.394505i	0.0484381	−	0.0279657i	0.524023	+	0.851704i	$0.324430\pi$
$200$		0			0
$201$	−3.68173	−	2.53115i	−0.259689	−	0.178534i
$202$		0			0
$203$	−3.54880	+	3.54880i	−0.249077	+	0.249077i
$204$		0			0
$205$	−15.3836	−	8.88172i	−1.07444	−	0.620326i
$206$		0			0
$207$	8.60181	+	6.96963i	0.597867	+	0.484423i
$208$		0			0
$209$		−	46.2083i		−	3.19629i
$210$		0			0
$211$	−11.5246	+	19.9611i	−0.793383	+	1.37418i	0.130478	+	0.991451i	$0.458349\pi$
$211$	−11.5246	+	19.9611i	−0.793383	+	1.37418i	−0.923861	+	0.382729i	$0.874984\pi$
$212$		0			0
$213$	−5.22385	−	10.9560i	−0.357932	−	0.750693i
$214$		0			0
$215$	1.13474	+	0.304052i	0.0773885	+	0.0207362i
$216$		0			0
$217$	4.92211	+	8.52535i	0.334135	+	0.578738i
$218$		0			0
$219$	16.4839	+	1.29965i	1.11388	+	0.0878221i
$220$		0			0
$221$	−9.55254	−	3.46875i	−0.642574	−	0.233334i
$222$		0			0
$223$	−3.35292	−	12.5133i	−0.224528	−	0.837950i	−0.982593	−	0.185771i	$-0.940522\pi$
$223$	−3.35292	−	12.5133i	−0.224528	−	0.837950i	0.758065	−	0.652179i	$-0.226145\pi$
$224$		0			0
$225$	2.84225	+	0.450991i	0.189483	+	0.0300661i
$226$		0			0
$227$	−2.62037	+	9.77935i	−0.173920	+	0.649079i	0.822813	+	0.568312i	$0.192403\pi$
$227$	−2.62037	+	9.77935i	−0.173920	+	0.649079i	−0.996733	+	0.0807663i	$0.974263\pi$
$228$		0			0
$229$	6.04210	+	6.04210i	0.399273	+	0.399273i	0.877977	−	0.478703i	$-0.158893\pi$
$229$	6.04210	+	6.04210i	0.399273	+	0.399273i	−0.478703	+	0.877977i	$0.658893\pi$
$230$		0			0
$231$	16.6129	−	14.1847i	1.09305	−	0.933284i
$232$		0			0
$233$	9.52224			0.623823			0.311911	−	0.950111i	$-0.399031\pi$
$233$	9.52224			0.623823			0.311911	+	0.950111i	$0.399031\pi$
$234$		0			0
$235$	33.0716			2.15736
$236$		0			0
$237$	−0.490818	+	0.419079i	−0.0318821	+	0.0272221i
$238$		0			0
$239$	−0.346997	−	0.346997i	−0.0224454	−	0.0224454i	0.695795	−	0.718240i	$-0.255052\pi$
$239$	−0.346997	−	0.346997i	−0.0224454	−	0.0224454i	−0.718240	+	0.695795i	$0.755052\pi$
$240$		0			0
$241$	−6.84098	+	25.5309i	−0.440667	+	1.64459i	0.286464	+	0.958091i	$0.407520\pi$
$241$	−6.84098	+	25.5309i	−0.440667	+	1.64459i	−0.727131	+	0.686499i	$0.759147\pi$
$242$		0			0
$243$	14.4061	−	5.95528i	0.924149	−	0.382031i
$244$		0			0
$245$	1.30744	+	4.87943i	0.0835293	+	0.311736i
$246$		0			0
$247$	26.5756	−	12.4166i	1.69096	−	0.790049i
$248$		0			0
$249$	−12.1881	−	0.960958i	−0.772392	−	0.0608983i
$250$		0			0
$251$	6.74616	+	11.6847i	0.425814	+	0.737531i	0.996496	−	0.0836399i	$-0.0266545\pi$
$251$	6.74616	+	11.6847i	0.425814	+	0.737531i	−0.570682	+	0.821171i	$0.693321\pi$
$252$		0			0
$253$	20.2461	+	5.42494i	1.27286	+	0.341063i
$254$		0			0
$255$	5.12928	+	10.7577i	0.321208	+	0.673671i
$256$		0			0
$257$	−1.24981	+	2.16473i	−0.0779610	+	0.135032i	−0.902370	−	0.430962i	$-0.858174\pi$
$257$	−1.24981	+	2.16473i	−0.0779610	+	0.135032i	0.824409	+	0.565994i	$0.191508\pi$
$258$		0			0
$259$		−	16.9271i		−	1.05180i
$260$		0			0
$261$	−4.26862	+	5.26827i	−0.264221	+	0.326098i
$262$		0			0
$263$	−8.32134	−	4.80433i	−0.513116	−	0.296248i	0.220998	−	0.975274i	$-0.429069\pi$
$263$	−8.32134	−	4.80433i	−0.513116	−	0.296248i	−0.734114	+	0.679027i	$0.762402\pi$
$264$		0			0
$265$	−1.06521	+	1.06521i	−0.0654353	+	0.0654353i
$266$		0			0
$267$	−11.9673	−	8.22740i	−0.732388	−	0.503509i
$268$		0			0
$269$	−14.4109	+	8.32012i	−0.878646	+	0.507286i	−0.870212	−	0.492678i	$-0.836018\pi$
$269$	−14.4109	+	8.32012i	−0.878646	+	0.507286i	−0.00843422	+	0.999964i	$0.502685\pi$
$270$		0			0
$271$	−30.2838	+	8.11452i	−1.83961	+	0.492922i	−0.998826	−	0.0484469i	$-0.984573\pi$
$271$	−30.2838	+	8.11452i	−1.83961	+	0.492922i	−0.840785	+	0.541369i	$0.817906\pi$
$272$		0			0
$273$	12.6220	+	5.74293i	0.763918	+	0.347578i
$274$		0			0
$275$	5.26281	−	1.41017i	0.317360	−	0.0850362i
$276$		0			0
$277$	−6.36855	+	3.67688i	−0.382649	+	0.220923i	−0.678970	−	0.734166i	$-0.737573\pi$
$277$	−6.36855	+	3.67688i	−0.382649	+	0.220923i	0.296321	+	0.955088i	$0.404240\pi$
$278$		0			0
$279$	7.81447	+	10.7621i	0.467840	+	0.644309i
$280$		0			0
$281$	−5.52193	+	5.52193i	−0.329411	+	0.329411i	−0.852362	−	0.522952i	$-0.824831\pi$
$281$	−5.52193	+	5.52193i	−0.329411	+	0.329411i	0.522952	+	0.852362i	$0.324831\pi$
$282$		0			0
$283$	−8.91761	−	5.14859i	−0.530097	−	0.306052i	0.210959	−	0.977495i	$-0.432341\pi$
$283$	−8.91761	−	5.14859i	−0.530097	−	0.306052i	−0.741056	+	0.671443i	$0.765675\pi$
$284$		0			0
$285$	−32.4241	−	11.4871i	−1.92064	−	0.680440i
$286$		0			0
$287$			16.1578i			0.953768i
$288$		0			0
$289$	4.52756	−	7.84197i	0.266327	−	0.461292i
$290$		0			0
$291$	−4.91543	+	2.34369i	−0.288148	+	0.137390i
$292$		0			0
$293$	−27.2842	−	7.31077i	−1.59396	−	0.427100i	−0.650748	−	0.759294i	$-0.725544\pi$
$293$	−27.2842	−	7.31077i	−1.59396	−	0.427100i	−0.943211	+	0.332194i	$0.892211\pi$
$294$		0			0
$295$	2.46056	+	4.26182i	0.143259	+	0.248133i
$296$		0			0
$297$	20.3246	−	21.3995i	1.17935	−	1.24172i
$298$		0			0
$299$	2.32030	+	13.1018i	0.134187	+	0.757696i
$300$		0			0
$301$	−0.276570	−	1.03217i	−0.0159412	−	0.0594934i
$302$		0			0
$303$	0.424372	+	2.29151i	0.0243796	+	0.131644i
$304$		0			0
$305$	−0.843792	+	3.14907i	−0.0483154	+	0.180315i
$306$		0			0
$307$	0.0722051	+	0.0722051i	0.00412096	+	0.00412096i	0.709164	−	0.705043i	$-0.249072\pi$
$307$	0.0722051	+	0.0722051i	0.00412096	+	0.00412096i	−0.705043	+	0.709164i	$0.749072\pi$
$308$		0			0
$309$	11.3053	+	13.2406i	0.643137	+	0.753232i
$310$		0			0
$311$	20.0161			1.13501			0.567504	−	0.823370i	$-0.307909\pi$
$311$	20.0161			1.13501			0.567504	+	0.823370i	$0.307909\pi$
$312$		0			0
$313$	0.626697			0.0354230			0.0177115	−	0.999843i	$-0.494362\pi$
$313$	0.626697			0.0354230			0.0177115	+	0.999843i	$0.494362\pi$
$314$		0			0
$315$	−5.82345	−	15.1834i	−0.328114	−	0.855489i
$316$		0			0
$317$	14.4492	+	14.4492i	0.811546	+	0.811546i	0.984866	−	0.173320i	$-0.0554493\pi$
$317$	14.4492	+	14.4492i	0.811546	+	0.811546i	−0.173320	+	0.984866i	$0.555449\pi$
$318$		0			0
$319$	−3.32256	+	12.4000i	−0.186028	+	0.694265i
$320$		0			0
$321$	25.4436	−	4.71197i	1.42012	−	0.262997i
$322$		0			0
$323$	−5.93508	−	22.1500i	−0.330236	−	1.23246i
$324$		0			0
$325$	2.22519	+	2.64785i	0.123431	+	0.146876i
$326$		0			0
$327$	1.14869	−	14.5692i	0.0635226	−	0.805677i
$328$		0			0
$329$	−15.0412	−	26.0521i	−0.829248	−	1.43630i
$330$		0			0
$331$	9.05445	+	2.42613i	0.497678	+	0.133352i	0.498922	−	0.866647i	$-0.333729\pi$
$331$	9.05445	+	2.42613i	0.497678	+	0.133352i	−0.00124426	+	0.999999i	$0.500396\pi$
$332$		0			0
$333$	−2.38407	−	22.7446i	−0.130646	−	1.24640i
$334$		0			0
$335$	−3.14852	+	5.45340i	−0.172022	+	0.297951i
$336$		0			0
$337$		−	20.6022i		−	1.12227i	−0.827724	−	0.561136i	$-0.810365\pi$
$337$		−	20.6022i		−	1.12227i	0.827724	−	0.561136i	$-0.189635\pi$
$338$		0			0
$339$	10.1117	−	28.5418i	0.549194	−	1.55018i
$340$		0			0
$341$	21.8068	+	12.5902i	1.18091	+	0.681796i
$342$		0			0
$343$	14.2401	−	14.2401i	0.768893	−	0.768893i
$344$		0			0
$345$	8.83974	−	12.8580i	0.475916	−	0.692252i
$346$		0			0
$347$	20.7808	−	11.9978i	1.11557	−	0.644076i	0.175306	−	0.984514i	$-0.443909\pi$
$347$	20.7808	−	11.9978i	1.11557	−	0.644076i	0.940267	+	0.340437i	$0.110575\pi$
$348$		0			0
$349$	−29.5949	+	7.92992i	−1.58418	+	0.424479i	−0.940216	−	0.340579i	$-0.889377\pi$
$349$	−29.5949	+	7.92992i	−1.58418	+	0.424479i	−0.643961	+	0.765058i	$0.722710\pi$
$350$		0			0
$351$	17.7688	+	5.93894i	0.948427	+	0.316997i
$352$		0			0
$353$	−28.6149	+	7.66733i	−1.52302	+	0.408091i	−0.920733	−	0.390193i	$-0.872408\pi$
$353$	−28.6149	+	7.66733i	−1.52302	+	0.408091i	−0.602282	+	0.798283i	$0.705742\pi$
$354$		0			0
$355$	−14.8150	+	8.55343i	−0.786298	+	0.453969i
$356$		0			0
$357$	6.14150	−	8.93324i	0.325043	−	0.472797i
$358$		0			0
$359$	−9.69605	+	9.69605i	−0.511738	+	0.511738i	−0.915059	−	0.403321i	$-0.867856\pi$
$359$	−9.69605	+	9.69605i	−0.511738	+	0.511738i	0.403321	+	0.915059i	$0.367856\pi$
$360$		0			0
$361$	40.8652	+	23.5935i	2.15080	+	1.24176i
$362$		0			0
$363$	12.2969	−	34.7098i	0.645420	−	1.82179i
$364$		0			0
$365$		−	23.3045i		−	1.21981i
$366$		0			0
$367$	5.92261	−	10.2583i	0.309158	−	0.535477i	−0.669020	−	0.743244i	$-0.733286\pi$
$367$	5.92261	−	10.2583i	0.309158	−	0.535477i	0.978178	+	0.207767i	$0.0666195\pi$
$368$		0			0
$369$	2.27572	+	21.7110i	0.118469	+	1.13023i
$370$		0			0
$371$	1.32358	+	0.354652i	0.0687169	+	0.0184126i
$372$		0			0
$373$	12.5599	+	21.7543i	0.650325	+	1.12640i	0.983044	+	0.183369i	$0.0587004\pi$
$373$	12.5599	+	21.7543i	0.650325	+	1.12640i	−0.332719	+	0.943026i	$0.607966\pi$
$374$		0			0
$375$	−1.34288	+	17.0322i	−0.0693463	+	0.879540i
$376$		0			0
$377$	−8.02434	+	1.42109i	−0.413274	+	0.0731901i
$378$		0			0
$379$	7.78147	+	29.0409i	0.399707	+	1.49173i	0.813612	+	0.581408i	$0.197498\pi$
$379$	7.78147	+	29.0409i	0.399707	+	1.49173i	−0.413904	+	0.910320i	$0.635835\pi$
$380$		0			0
$381$	−2.09864	+	0.388654i	−0.107517	+	0.0199113i
$382$		0			0
$383$	3.42225	−	12.7720i	0.174869	−	0.652620i	−0.821705	−	0.569913i	$-0.806977\pi$
$383$	3.42225	−	12.7720i	0.174869	−	0.652620i	0.996574	−	0.0827069i	$-0.0263565\pi$
$384$		0			0
$385$	−21.7705	−	21.7705i	−1.10953	−	1.10953i
$386$		0			0
$387$	−0.516995	−	1.34795i	−0.0262803	−	0.0685204i
$388$		0			0
$389$	35.5709			1.80352			0.901759	−	0.432239i	$-0.142276\pi$
$389$	35.5709			1.80352			0.901759	+	0.432239i	$0.142276\pi$
$390$		0			0
$391$	10.4018			0.526042
$392$		0			0
$393$	−8.07509	−	9.45742i	−0.407334	−	0.477064i
$394$		0			0
$395$	0.643197	+	0.643197i	0.0323627	+	0.0323627i
$396$		0			0
$397$	0.0698912	−	0.260837i	0.00350774	−	0.0130911i	−0.964150	−	0.265359i	$-0.914510\pi$
$397$	0.0698912	−	0.260837i	0.00350774	−	0.0130911i	0.967658	+	0.252268i	$0.0811763\pi$
$398$		0			0
$399$	5.69774	+	30.7665i	0.285244	+	1.54025i
$400$		0			0
$401$	3.32674	+	12.4156i	0.166130	+	0.620004i	0.997893	+	0.0648745i	$0.0206647\pi$
$401$	3.32674	+	12.4156i	0.166130	+	0.620004i	−0.831764	+	0.555130i	$0.812669\pi$
$402$		0			0
$403$	−1.38124	+	15.9248i	−0.0688043	+	0.793268i
$404$		0			0
$405$	−9.96332	−	19.5814i	−0.495081	−	0.973010i
$406$		0			0
$407$	−21.6488	−	37.4968i	−1.07309	−	1.85865i
$408$		0			0
$409$	−14.0337	−	3.76033i	−0.693924	−	0.185936i	−0.105417	−	0.994428i	$-0.533618\pi$
$409$	−14.0337	−	3.76033i	−0.693924	−	0.185936i	−0.588508	+	0.808492i	$0.700284\pi$
$410$		0			0
$411$	−18.8083	+	8.96782i	−0.927743	+	0.442350i
$412$		0			0
$413$	2.23816	−	3.87660i	0.110133	−	0.190755i
$414$		0			0
$415$			17.2313i			0.845853i
$416$		0			0
$417$	3.80223	+	1.34704i	0.186196	+	0.0659650i
$418$		0			0
$419$	28.4856	+	16.4462i	1.39161	+	0.803448i	0.993494	−	0.113887i	$-0.0363301\pi$
$419$	28.4856	+	16.4462i	1.39161	+	0.803448i	0.398118	+	0.917334i	$0.369663\pi$
$420$		0			0
$421$	−12.6319	+	12.6319i	−0.615641	+	0.615641i	−0.944410	−	0.328769i	$-0.893366\pi$
$421$	−12.6319	+	12.6319i	−0.615641	+	0.615641i	0.328769	+	0.944410i	$0.393366\pi$
$422$		0			0
$423$	−23.8798	−	32.8872i	−1.16107	−	1.59903i
$424$		0			0
$425$	2.34161	−	1.35193i	0.113585	−	0.0655782i
$426$		0			0
$427$	2.86444	−	0.767524i	0.138620	−	0.0371431i
$428$		0			0
$429$	35.3050	−	3.42110i	1.70454	−	0.165172i
$430$		0			0
$431$	−21.3199	+	5.71266i	−1.02694	+	0.275169i	−0.732693	−	0.680559i	$-0.761737\pi$
$431$	−21.3199	+	5.71266i	−1.02694	+	0.275169i	−0.294252	+	0.955728i	$0.595070\pi$
$432$		0			0
$433$	32.4780	−	18.7512i	1.56079	−	0.901125i	0.563618	−	0.826035i	$-0.309409\pi$
$433$	32.4780	−	18.7512i	1.56079	−	0.901125i	0.997177	−	0.0750900i	$-0.0239244\pi$
$434$		0			0
$435$	7.87503	+	5.41399i	0.377579	+	0.259581i
$436$		0			0
$437$	−21.2293	+	21.2293i	−1.01554	+	1.01554i
$438$		0			0
$439$	−18.7404	−	10.8198i	−0.894431	−	0.516400i	−0.0190419	−	0.999819i	$-0.506062\pi$
$439$	−18.7404	−	10.8198i	−0.894431	−	0.516400i	−0.875389	+	0.483419i	$0.839395\pi$
$440$		0			0
$441$	3.90817	−	4.82340i	0.186103	−	0.229686i
$442$		0			0
$443$		−	7.66009i		−	0.363942i	−0.983304	−	0.181971i	$-0.941752\pi$
$443$		−	7.66009i		−	0.363942i	0.983304	−	0.181971i	$-0.0582477\pi$
$444$		0			0
$445$	−10.2341	+	17.7260i	−0.485145	+	0.840295i
$446$		0			0
$447$	14.5421	+	30.4992i	0.687817	+	1.44256i
$448$		0			0
$449$	8.38164	+	2.24585i	0.395554	+	0.105988i	0.451113	−	0.892467i	$-0.351027\pi$
$449$	8.38164	+	2.24585i	0.395554	+	0.105988i	−0.0555585	+	0.998455i	$0.517694\pi$
$450$		0			0
$451$	20.6649	+	35.7927i	0.973073	+	1.68541i
$452$		0			0
$453$	1.73964	+	0.137160i	0.0817356	+	0.00644434i
$454$		0			0
$455$	6.67083	−	18.3707i	0.312733	−	0.861231i
$456$		0			0
$457$	10.2516	+	38.2595i	0.479550	+	1.78970i	0.603439	+	0.797409i	$0.293796\pi$
$457$	10.2516	+	38.2595i	0.479550	+	1.78970i	−0.123890	+	0.992296i	$0.539537\pi$
$458$		0			0
$459$	6.99402	−	12.8684i	0.326453	−	0.600645i
$460$		0			0
$461$	−2.25094	+	8.40062i	−0.104837	+	0.391256i	−0.998327	−	0.0578275i	$-0.981583\pi$
$461$	−2.25094	+	8.40062i	−0.104837	+	0.391256i	0.893490	+	0.449083i	$0.148249\pi$
$462$		0			0
$463$	−13.9840	−	13.9840i	−0.649893	−	0.649893i	0.303074	−	0.952967i	$-0.401987\pi$
$463$	−13.9840	−	13.9840i	−0.649893	−	0.649893i	−0.952967	+	0.303074i	$0.901987\pi$
$464$		0			0
$465$	14.2555	−	12.1719i	0.661085	−	0.564458i
$466$		0			0
$467$	−29.4617			−1.36333			−0.681663	−	0.731666i	$-0.738743\pi$
$467$	−29.4617			−1.36333			−0.681663	+	0.731666i	$0.738743\pi$
$468$		0			0
$469$	5.72787			0.264489
$470$		0			0
$471$	−22.4330	+	19.1541i	−1.03366	+	0.882576i
$472$		0			0
$473$	−1.93274	−	1.93274i	−0.0888675	−	0.0888675i
$474$		0			0
$475$	−2.01987	+	7.53826i	−0.0926780	+	0.345879i
$476$		0			0
$477$	1.82842	+	0.290122i	0.0837175	+	0.0132838i
$478$		0			0
$479$	8.50742	+	31.7501i	0.388714	+	1.45070i	0.832228	+	0.554433i	$0.187065\pi$
$479$	8.50742	+	31.7501i	0.388714	+	1.45070i	−0.443514	+	0.896267i	$0.646268\pi$
$480$		0			0
$481$	15.7481	−	22.5265i	0.718054	−	1.02712i
$482$		0			0
$483$	−14.1492	−	1.11558i	−0.643813	−	0.0507606i
$484$		0			0
$485$	3.83752	+	6.64677i	0.174253	+	0.301814i
$486$		0			0
$487$	−11.0631	−	2.96434i	−0.501316	−	0.134327i	−0.000705427	−	1.00000i	$-0.500225\pi$
$487$	−11.0631	−	2.96434i	−0.501316	−	0.134327i	−0.500611	+	0.865672i	$0.666891\pi$
$488$		0			0
$489$	−7.40604	−	15.5327i	−0.334913	−	0.702414i
$490$		0			0
$491$	−0.607370	+	1.05200i	−0.0274102	+	0.0474759i	−0.879405	−	0.476074i	$-0.842059\pi$
$491$	−0.607370	+	1.05200i	−0.0274102	+	0.0474759i	0.851995	+	0.523550i	$0.175393\pi$
$492$		0			0
$493$			6.37070i			0.286922i
$494$		0			0
$495$	−32.3187	−	26.1863i	−1.45262	−	1.17699i
$496$		0			0
$497$	13.4759	+	7.78031i	0.604477	+	0.348995i
$498$		0			0
$499$	−21.3336	+	21.3336i	−0.955024	+	0.955024i	−0.999031	−	0.0440068i	$-0.985988\pi$
$499$	−21.3336	+	21.3336i	−0.955024	+	0.955024i	0.0440068	+	0.999031i	$0.485988\pi$
$500$		0			0
$501$	14.8304	+	10.1957i	0.662571	+	0.455510i
$502$		0			0
$503$	19.6423	−	11.3405i	0.875808	−	0.505648i	0.00653389	−	0.999979i	$-0.497920\pi$
$503$	19.6423	−	11.3405i	0.875808	−	0.505648i	0.869274	+	0.494331i	$0.164587\pi$
$504$		0			0
$505$	3.17267	−	0.850114i	0.141182	−	0.0378296i
$506$		0			0
$507$	11.4543	+	19.3855i	0.508705	+	0.860941i
$508$		0			0
$509$	19.3215	−	5.17719i	0.856412	−	0.229475i	0.196209	−	0.980562i	$-0.437137\pi$
$509$	19.3215	−	5.17719i	0.856412	−	0.229475i	0.660203	+	0.751087i	$0.270470\pi$
$510$		0			0
$511$	−18.3581	+	10.5991i	−0.812114	+	0.468874i
$512$		0			0
$513$	11.9892	+	40.5378i	0.529334	+	1.78979i
$514$		0			0
$515$	17.3513	−	17.3513i	0.764588	−	0.764588i
$516$		0			0
$517$	−66.6382	−	38.4736i	−2.93075	−	1.69207i
$518$		0			0
$519$	−21.7342	−	7.69995i	−0.954027	−	0.337990i
$520$		0			0
$521$			19.4238i			0.850973i	0.904965	+	0.425486i	$0.139897\pi$
$521$			19.4238i			0.850973i	−0.904965	+	0.425486i	$0.860103\pi$
$522$		0			0
$523$	10.1755	−	17.6244i	0.444942	−	0.770663i	−0.553106	−	0.833111i	$-0.686557\pi$
$523$	10.1755	−	17.6244i	0.444942	−	0.770663i	0.998048	+	0.0624482i	$0.0198908\pi$
$524$		0			0
$525$	−3.33021	+	1.58785i	−0.145342	+	0.0692996i
$526$		0			0
$527$	12.0702	+	3.23421i	0.525788	+	0.140884i
$528$		0			0
$529$	4.69074	+	8.12459i	0.203945	+	0.353243i
$530$		0			0
$531$	2.46137	−	5.52414i	0.106814	−	0.239727i
$532$		0			0
$533$	−15.0324	+	21.5027i	−0.651127	+	0.931387i
$534$		0			0
$535$	−9.43915	−	35.2274i	−0.408090	−	1.52301i
$536$		0			0
$537$	−0.142239	−	0.768060i	−0.00613808	−	0.0331442i
$538$		0			0
$539$	3.04200	−	11.3529i	0.131028	−	0.489003i
$540$		0			0
$541$	5.28291	+	5.28291i	0.227130	+	0.227130i	0.811493	−	0.584363i	$-0.198655\pi$
$541$	5.28291	+	5.28291i	0.227130	+	0.227130i	−0.584363	+	0.811493i	$0.698655\pi$
$542$		0			0
$543$	0.644213	+	0.754492i	0.0276458	+	0.0323784i
$544$		0			0
$545$	−20.5976			−0.882303
$546$		0			0
$547$	−15.2518			−0.652122			−0.326061	−	0.945349i	$-0.605721\pi$
$547$	−15.2518			−0.652122			−0.326061	+	0.945349i	$0.605721\pi$
$548$		0			0
$549$	3.74078	−	1.43474i	0.159653	−	0.0612332i
$550$		0			0
$551$	−13.0021	−	13.0021i	−0.553910	−	0.553910i
$552$		0			0
$553$	0.214147	−	0.799207i	0.00910645	−	0.0339857i
$554$		0			0
$555$	−31.6931	+	5.86935i	−1.34530	+	0.249140i
$556$		0			0
$557$	−1.77202	−	6.61326i	−0.0750828	−	0.280213i	0.918169	−	0.396188i	$-0.129667\pi$
$557$	−1.77202	−	6.61326i	−0.0750828	−	0.280213i	−0.993252	+	0.115975i	$0.963001\pi$
$558$		0			0
$559$	0.592223	−	1.63091i	0.0250484	−	0.0689803i
$560$		0			0
$561$	2.17951	−	27.6434i	0.0920190	−	1.16711i
$562$		0			0
$563$	9.52928	+	16.5052i	0.401611	+	0.695611i	0.993921	−	0.110099i	$-0.0351169\pi$
$563$	9.52928	+	16.5052i	0.401611	+	0.695611i	−0.592309	+	0.805711i	$0.701784\pi$
$564$		0			0
$565$	−41.2227	−	11.0456i	−1.73425	−	0.464692i
$566$		0			0
$567$	−10.8939	+	16.7544i	−0.457499	+	0.703617i
$568$		0			0
$569$	−3.18974	+	5.52479i	−0.133721	+	0.231611i	−0.925108	−	0.379704i	$-0.876026\pi$
$569$	−3.18974	+	5.52479i	−0.133721	+	0.231611i	0.791387	+	0.611315i	$0.209359\pi$
$570$		0			0
$571$			4.64342i			0.194321i	0.995269	+	0.0971605i	$0.0309760\pi$
$571$			4.64342i			0.194321i	−0.995269	+	0.0971605i	$0.969024\pi$
$572$		0			0
$573$	−5.26220	+	14.8533i	−0.219832	+	0.620507i
$574$		0			0
$575$	−3.06575	−	1.77001i	−0.127851	−	0.0738145i
$576$		0			0
$577$	−16.3269	+	16.3269i	−0.679699	+	0.679699i	−0.959932	−	0.280233i	$-0.909588\pi$
$577$	−16.3269	+	16.3269i	−0.679699	+	0.679699i	0.280233	+	0.959932i	$0.409588\pi$
$578$		0			0
$579$	14.1903	−	20.6408i	0.589729	−	0.857802i
$580$		0			0
$581$	13.5739	−	7.83692i	0.563142	−	0.325130i
$582$		0			0
$583$	3.38556	−	0.907159i	0.140216	−	0.0375707i
$584$		0			0
$585$	6.37607	−	25.6238i	0.263618	−	1.05941i
$586$		0			0
$587$	−17.6852	+	4.73874i	−0.729948	+	0.195589i	−0.604606	−	0.796525i	$-0.706669\pi$
$587$	−17.6852	+	4.73874i	−0.729948	+	0.195589i	−0.125342	+	0.992114i	$0.540003\pi$
$588$		0			0
$589$	−31.2353	+	18.0337i	−1.28703	+	0.743066i
$590$		0			0
$591$	−6.32059	+	9.19373i	−0.259994	+	0.378179i
$592$		0			0
$593$	−11.8285	+	11.8285i	−0.485739	+	0.485739i	−0.906959	−	0.421220i	$-0.861602\pi$
$593$	−11.8285	+	11.8285i	−0.485739	+	0.485739i	0.421220	+	0.906959i	$0.361602\pi$
$594$		0			0
$595$	−13.2319	−	7.63947i	−0.542457	−	0.313188i
$596$		0			0
$597$	−0.456364	+	1.28816i	−0.0186777	+	0.0527207i
$598$		0			0
$599$			36.6793i			1.49867i	0.662188	+	0.749337i	$0.269628\pi$
$599$			36.6793i			1.49867i	−0.662188	+	0.749337i	$0.730372\pi$
$600$		0			0
$601$	−2.04984	+	3.55043i	−0.0836147	+	0.144825i	−0.904800	−	0.425837i	$-0.859980\pi$
$601$	−2.04984	+	3.55043i	−0.0836147	+	0.144825i	0.821185	+	0.570662i	$0.193313\pi$
$602$		0			0
$603$	7.69642	−	0.806729i	0.313422	−	0.0328525i
$604$		0			0
$605$	−50.1311	−	13.4326i	−2.03812	−	0.546112i
$606$		0			0
$607$	−4.15357	−	7.19419i	−0.168588	−	0.292003i	0.769336	−	0.638845i	$-0.220587\pi$
$607$	−4.15357	−	7.19419i	−0.168588	−	0.292003i	−0.937924	+	0.346842i	$0.887254\pi$
$608$		0			0
$609$	0.683249	−	8.66585i	0.0276866	−	0.351158i
$610$		0			0
$611$	4.22084	−	48.6635i	0.170757	−	1.96872i
$612$		0			0
$613$	−1.42881	−	5.33239i	−0.0577091	−	0.215373i	0.931050	−	0.364892i	$-0.118894\pi$
$613$	−1.42881	−	5.33239i	−0.0577091	−	0.215373i	−0.988759	+	0.149519i	$0.952227\pi$
$614$		0			0
$615$	30.2528	−	5.60260i	1.21991	−	0.225919i
$616$		0			0
$617$	6.17063	−	23.0291i	0.248420	−	0.927117i	−0.723213	−	0.690625i	$-0.757336\pi$
$617$	6.17063	−	23.0291i	0.248420	−	0.927117i	0.971633	−	0.236492i	$-0.0759978\pi$
$618$		0			0
$619$	−19.4317	−	19.4317i	−0.781028	−	0.781028i	0.198976	−	0.980004i	$-0.436238\pi$
$619$	−19.4317	−	19.4317i	−0.781028	−	0.781028i	−0.980004	+	0.198976i	$0.936238\pi$
$620$		0			0
$621$	−19.1692	+	0.493838i	−0.769232	+	0.0198170i
$622$		0			0
$623$	18.6182			0.745923
$624$		0			0
$625$	28.8762			1.15505
$626$		0			0
$627$	51.9701	+	60.8665i	2.07548	+	2.43077i
$628$		0			0
$629$	−15.1935	−	15.1935i	−0.605806	−	0.605806i
$630$		0			0
$631$	3.00162	−	11.2022i	0.119493	−	0.445953i	−0.880091	−	0.474805i	$-0.842519\pi$
$631$	3.00162	−	11.2022i	0.119493	−	0.445953i	0.999584	+	0.0288524i	$0.00918527\pi$
$632$		0			0
$633$	−7.26971	−	39.2548i	−0.288945	−	1.56024i
$634$		0			0
$635$	0.778561	+	2.90563i	0.0308963	+	0.115306i
$636$		0			0
$637$	7.34674	−	1.30109i	0.291089	−	0.0515512i
$638$		0			0
$639$	19.2031	+	8.55626i	0.759662	+	0.338480i
$640$		0			0
$641$	−9.29977	−	16.1077i	−0.367319	−	0.636215i	0.621826	−	0.783155i	$-0.286391\pi$
$641$	−9.29977	−	16.1077i	−0.367319	−	0.636215i	−0.989145	+	0.146940i	$0.953058\pi$
$642$		0			0
$643$	−28.9091	−	7.74616i	−1.14006	−	0.305479i	−0.361086	−	0.932532i	$-0.617594\pi$
$643$	−28.9091	−	7.74616i	−1.14006	−	0.305479i	−0.778976	+	0.627054i	$0.784261\pi$
$644$		0			0
$645$	−1.83667	+	0.875726i	−0.0723186	+	0.0344817i
$646$		0			0
$647$	−10.6735	+	18.4871i	−0.419619	+	0.726802i	−0.995901	−	0.0904492i	$-0.971170\pi$
$647$	−10.6735	+	18.4871i	−0.419619	+	0.726802i	0.576282	+	0.817251i	$0.304503\pi$
$648$		0			0
$649$		−	11.4499i		−	0.449447i
$650$		0			0
$651$	−16.0719	−	5.69391i	−0.629907	−	0.223162i
$652$		0			0
$653$	−18.3357	−	10.5861i	−0.717533	−	0.414268i	0.0963112	−	0.995351i	$-0.469296\pi$
$653$	−18.3357	−	10.5861i	−0.717533	−	0.414268i	−0.813844	+	0.581084i	$0.802629\pi$
$654$		0			0
$655$	−12.3936	+	12.3936i	−0.484256	+	0.484256i
$656$		0			0
$657$	−23.1746	+	16.8273i	−0.904126	+	0.656496i
$658$		0			0
$659$	−30.9228	+	17.8533i	−1.20458	+	0.695464i	−0.961570	−	0.274559i	$-0.911468\pi$
$659$	−30.9228	+	17.8533i	−1.20458	+	0.695464i	−0.243010	+	0.970024i	$0.578135\pi$
$660$		0			0
$661$	−17.7357	+	4.75228i	−0.689840	+	0.184842i	−0.586675	−	0.809822i	$-0.699564\pi$
$661$	−17.7357	+	4.75228i	−0.689840	+	0.184842i	−0.103165	+	0.994664i	$0.532897\pi$
$662$		0			0
$663$	16.4841	−	6.17455i	0.640189	−	0.239800i
$664$		0			0
$665$	42.5971	−	11.4139i	1.65184	−	0.442610i
$666$		0			0
$667$	7.22336	−	4.17041i	0.279690	−	0.161479i
$668$		0			0
$669$	18.4901	+	12.7117i	0.714868	+	0.491464i
$670$		0			0
$671$	5.36366	−	5.36366i	0.207062	−	0.207062i
$672$		0			0
$673$	−25.8577	−	14.9289i	−0.996740	−	0.575468i	−0.0894579	−	0.995991i	$-0.528513\pi$
$673$	−25.8577	−	14.9289i	−0.996740	−	0.575468i	−0.907282	+	0.420522i	$0.861847\pi$
$674$		0			0
$675$	−4.25110	+	2.60260i	−0.163625	+	0.100174i
$676$		0			0
$677$			21.5956i			0.829988i	0.909824	+	0.414994i	$0.136216\pi$
$677$			21.5956i			0.829988i	−0.909824	+	0.414994i	$0.863784\pi$
$678$		0			0
$679$	3.49065	−	6.04599i	0.133959	−	0.232024i
$680$		0			0
$681$	−7.54715	−	15.8287i	−0.289207	−	0.606556i
$682$		0			0
$683$	33.6457	+	9.01534i	1.28742	+	0.344962i	0.836679	−	0.547694i	$-0.184494\pi$
$683$	33.6457	+	9.01534i	1.28742	+	0.344962i	0.450738	+	0.892656i	$0.351161\pi$
$684$		0			0
$685$	14.6838	+	25.4330i	0.561038	+	0.971746i
$686$		0			0
$687$	−14.7543	−	1.16328i	−0.562911	−	0.0443820i
$688$		0			0
$689$	1.43146	+	1.70336i	0.0545343	+	0.0648929i
$690$		0			0
$691$	7.05147	+	26.3164i	0.268250	+	1.00112i	0.960231	+	0.279208i	$0.0900718\pi$
$691$	7.05147	+	26.3164i	0.268250	+	1.00112i	−0.691980	+	0.721916i	$0.743262\pi$
$692$		0			0
$693$	−5.92944	+	37.3687i	−0.225241	+	1.41952i
$694$		0			0
$695$	1.47145	−	5.49152i	0.0558152	−	0.208305i
$696$		0			0
$697$	14.5030	+	14.5030i	0.549342	+	0.549342i
$698$		0			0
$699$	−12.5429	+	10.7096i	−0.474416	+	0.405073i
$700$		0			0
$701$	7.80915			0.294948			0.147474	−	0.989066i	$-0.452886\pi$
$701$	7.80915			0.294948			0.147474	+	0.989066i	$0.452886\pi$
$702$		0			0
$703$	62.0179			2.33905
$704$		0			0
$705$	−43.5627	+	37.1954i	−1.64066	+	1.40086i
$706$		0			0
$707$	−2.11262	−	2.11262i	−0.0794534	−	0.0794534i
$708$		0			0
$709$	8.07769	−	30.1463i	0.303364	−	1.13217i	−0.630981	−	0.775799i	$-0.717347\pi$
$709$	8.07769	−	30.1463i	0.303364	−	1.13217i	0.934345	−	0.356371i	$-0.115986\pi$
$710$		0			0
$711$	0.175182	−	1.10404i	0.00656984	−	0.0414047i
$712$		0			0
$713$	−4.23438	−	15.8029i	−0.158579	−	0.591824i
$714$		0			0
$715$	−8.71785	−	49.2261i	−0.326029	−	1.84095i
$716$		0			0
$717$	0.847337	+	0.0668072i	0.0316444	+	0.00249496i
$718$		0			0
$719$	2.01546	+	3.49089i	0.0751641	+	0.130188i	0.901158	−	0.433492i	$-0.142719\pi$
$719$	2.01546	+	3.49089i	0.0751641	+	0.130188i	−0.825993	+	0.563680i	$0.809385\pi$
$720$		0			0
$721$	−21.5599	−	5.77695i	−0.802932	−	0.215145i
$722$		0			0
$723$	−19.7033	−	41.3238i	−0.732773	−	1.53685i
$724$		0			0
$725$	1.08406	−	1.87765i	0.0402611	−	0.0697342i
$726$		0			0
$727$			26.5507i			0.984711i	0.870394	+	0.492356i	$0.163864\pi$
$727$			26.5507i			0.984711i	−0.870394	+	0.492356i	$0.836136\pi$
$728$		0			0
$729$	−12.2781	+	24.0468i	−0.454745	+	0.890622i
$730$		0			0
$731$	−1.17471	−	0.678217i	−0.0434481	−	0.0250848i
$732$		0			0
$733$	15.7035	−	15.7035i	0.580021	−	0.580021i	−0.354888	−	0.934909i	$-0.615481\pi$
$733$	15.7035	−	15.7035i	0.580021	−	0.580021i	0.934909	+	0.354888i	$0.115481\pi$
$734$		0			0
$735$	−7.21004	−	4.95682i	−0.265946	−	0.182835i
$736$		0			0
$737$	12.6883	−	7.32561i	0.467380	−	0.269842i
$738$		0			0
$739$	6.55841	−	1.75732i	0.241255	−	0.0646441i	−0.136165	−	0.990686i	$-0.543478\pi$
$739$	6.55841	−	1.75732i	0.241255	−	0.0646441i	0.377420	+	0.926042i	$0.376811\pi$
$740$		0			0
$741$	−21.0410	+	46.2447i	−0.772962	+	1.69884i
$742$		0			0
$743$	40.6931	−	10.9037i	1.49288	−	0.400017i	0.582174	−	0.813064i	$-0.302202\pi$
$743$	40.6931	−	10.9037i	1.49288	−	0.400017i	0.910709	+	0.413047i	$0.135536\pi$
$744$		0			0
$745$	41.2418	−	23.8110i	1.51098	−	0.872366i
$746$		0			0
$747$	17.1352	−	12.4421i	0.626946	−	0.455232i
$748$		0			0
$749$	−23.4573	+	23.4573i	−0.857112	+	0.857112i
$750$		0			0
$751$	31.3813	+	18.1180i	1.14512	+	0.661135i	0.947693	−	0.319183i	$-0.103408\pi$
$751$	31.3813	+	18.1180i	1.14512	+	0.661135i	0.197426	+	0.980318i	$0.436742\pi$
$752$		0			0
$753$	−22.0278	−	7.80397i	−0.802739	−	0.284392i
$754$		0			0
$755$		−	2.45947i		−	0.0895093i
$756$		0			0
$757$	−3.17824	+	5.50487i	−0.115515	+	0.200078i	−0.917986	−	0.396614i	$-0.870185\pi$
$757$	−3.17824	+	5.50487i	−0.115515	+	0.200078i	0.802470	+	0.596692i	$0.203519\pi$
$758$		0			0
$759$	−32.7700	+	15.6248i	−1.18948	+	0.567145i
$760$		0			0
$761$	−21.0411	−	5.63796i	−0.762741	−	0.204376i	−0.143579	−	0.989639i	$-0.545861\pi$
$761$	−21.0411	−	5.63796i	−0.762741	−	0.204376i	−0.619162	+	0.785263i	$0.712528\pi$
$762$		0			0
$763$	9.36791	+	16.2257i	0.339141	+	0.587410i
$764$		0			0
$765$	−18.8554	−	8.40137i	−0.681720	−	0.303752i
$766$		0			0
$767$	6.58512	−	3.07669i	0.237775	−	0.111093i
$768$		0			0
$769$	−3.69721	−	13.7982i	−0.133325	−	0.497575i	0.866674	−	0.498874i	$-0.166253\pi$
$769$	−3.69721	−	13.7982i	−0.133325	−	0.497575i	−0.999999	+	0.00129915i	$0.999586\pi$
$770$		0			0
$771$	−0.788382	−	4.25708i	−0.0283929	−	0.153315i
$772$		0			0
$773$	−2.17937	+	8.13353i	−0.0783866	+	0.292543i	−0.993980	−	0.109563i	$-0.965055\pi$
$773$	−2.17937	+	8.13353i	−0.0783866	+	0.292543i	0.915593	+	0.402106i	$0.131722\pi$
$774$		0			0
$775$	−3.00714	−	3.00714i	−0.108020	−	0.108020i
$776$		0			0
$777$	19.0378	+	22.2968i	0.682978	+	0.799893i
$778$		0			0
$779$	−59.1994			−2.12104
$780$		0			0
$781$	39.8022			1.42424
$782$		0			0
$783$	−0.302456	−	11.7404i	−0.0108089	−	0.419566i
$784$		0			0
$785$	29.3975	+	29.3975i	1.04924	+	1.04924i
$786$		0			0
$787$	−8.57267	+	31.9936i	−0.305583	+	1.14045i	0.626860	+	0.779132i	$0.284340\pi$
$787$	−8.57267	+	31.9936i	−0.305583	+	1.14045i	−0.932443	+	0.361318i	$0.882327\pi$
$788$		0			0
$789$	16.3644	−	3.03058i	0.582589	−	0.107891i
$790$		0			0
$791$	10.0472	+	37.4967i	0.357238	+	1.33323i
$792$		0			0
$793$	4.52604	+	1.64351i	0.160724	+	0.0583628i
$794$		0			0
$795$	0.205084	−	2.60115i	0.00727359	−	0.0922532i
$796$		0			0
$797$	27.4840	+	47.6037i	0.973534	+	1.68621i	0.684691	+	0.728834i	$0.259937\pi$
$797$	27.4840	+	47.6037i	0.973534	+	1.68621i	0.288843	+	0.957376i	$0.406729\pi$
$798$		0			0
$799$	−36.8847	−	9.88323i	−1.30489	−	0.349644i
$800$		0			0
$801$	25.0169	−	2.62224i	0.883928	−	0.0926523i
$802$		0			0
$803$	−27.1111	+	46.9578i	−0.956730	+	1.65711i
$804$		0			0
$805$			20.0039i			0.705045i
$806$		0			0
$807$	9.62473	−	27.1672i	0.338806	−	0.956331i
$808$		0			0
$809$	−27.7137	−	16.0005i	−0.974361	−	0.562547i	−0.0737978	−	0.997273i	$-0.523512\pi$
$809$	−27.7137	−	16.0005i	−0.974361	−	0.562547i	−0.900563	+	0.434726i	$0.856845\pi$
$810$		0			0
$811$	34.5566	−	34.5566i	1.21344	−	1.21344i	0.243559	−	0.969886i	$-0.421685\pi$
$811$	34.5566	−	34.5566i	1.21344	−	1.21344i	0.969886	−	0.243559i	$-0.0783148\pi$
$812$		0			0
$813$	30.7641	−	44.7486i	1.07895	−	1.56940i
$814$		0			0
$815$	−21.0037	+	12.1265i	−0.735729	+	0.424773i
$816$		0			0
$817$	3.78169	−	1.01330i	0.132304	−	0.0354509i
$818$		0			0
$819$	−23.0850	+	6.63114i	−0.806655	+	0.231711i
$820$		0			0
$821$	−6.31469	+	1.69202i	−0.220384	+	0.0590518i	−0.367321	−	0.930094i	$-0.619725\pi$
$821$	−6.31469	+	1.69202i	−0.220384	+	0.0590518i	0.146937	+	0.989146i	$0.453058\pi$
$822$		0			0
$823$	9.88316	−	5.70605i	0.344505	−	0.198900i	−0.317757	−	0.948172i	$-0.602930\pi$
$823$	9.88316	−	5.70605i	0.344505	−	0.198900i	0.662263	+	0.749272i	$0.269596\pi$
$824$		0			0
$825$	−5.34628	+	7.77654i	−0.186134	+	0.270744i
$826$		0			0
$827$	16.1511	−	16.1511i	0.561628	−	0.561628i	−0.368142	−	0.929770i	$-0.620006\pi$
$827$	16.1511	−	16.1511i	0.561628	−	0.561628i	0.929770	+	0.368142i	$0.120006\pi$
$828$		0			0
$829$	10.4973	+	6.06059i	0.364585	+	0.210493i	0.671090	−	0.741376i	$-0.265826\pi$
$829$	10.4973	+	6.06059i	0.364585	+	0.210493i	−0.306505	+	0.951869i	$0.599160\pi$
$830$		0			0
$831$	4.25343	−	12.0059i	0.147550	−	0.416481i
$832$		0			0
$833$		−	5.83274i		−	0.202092i
$834$		0			0
$835$	12.6825	−	21.9668i	0.438897	−	0.760192i
$836$		0			0
$837$	−22.3974	−	5.38717i	−0.774168	−	0.186208i
$838$		0			0
$839$	32.4519	+	8.69547i	1.12036	+	0.300201i	0.771031	−	0.636798i	$-0.219741\pi$
$839$	32.4519	+	8.69547i	1.12036	+	0.300201i	0.349334	+	0.936998i	$0.386408\pi$
$840$		0			0
$841$	−11.9458	−	20.6907i	−0.411924	−	0.713473i
$842$		0			0
$843$	1.06313	−	13.4841i	0.0366163	−	0.464416i
$844$		0			0
$845$	25.9686	−	18.2414i	0.893348	−	0.627522i
$846$		0			0
$847$	12.2185	+	45.5999i	0.419831	+	1.56683i
$848$		0			0
$849$	17.5370	−	3.24774i	0.601869	−	0.111462i
$850$		0			0
$851$	−7.28102	+	27.1731i	−0.249590	+	0.931483i
$852$		0			0
$853$	14.0421	+	14.0421i	0.480792	+	0.480792i	0.905385	−	0.424592i	$-0.139583\pi$
$853$	14.0421	+	14.0421i	0.480792	+	0.480792i	−0.424592	+	0.905385i	$0.639583\pi$
$854$		0			0
$855$	55.6292	−	21.3360i	1.90248	−	0.729677i
$856$		0			0
$857$	29.0059			0.990824			0.495412	−	0.868658i	$-0.335017\pi$
$857$	29.0059			0.990824			0.495412	+	0.868658i	$0.335017\pi$
$858$		0			0
$859$	11.0160			0.375859			0.187930	−	0.982182i	$-0.439822\pi$
$859$	11.0160			0.375859			0.187930	+	0.982182i	$0.439822\pi$
$860$		0			0
$861$	−18.1726	−	21.2835i	−0.619320	−	0.725338i
$862$		0			0
$863$	−21.8394	−	21.8394i	−0.743422	−	0.743422i	0.229813	−	0.973235i	$-0.426189\pi$
$863$	−21.8394	−	21.8394i	−0.743422	−	0.743422i	−0.973235	+	0.229813i	$0.926189\pi$
$864$		0			0
$865$	−8.41108	+	31.3906i	−0.285985	+	1.06731i
$866$		0			0
$867$	2.85599	+	15.4217i	0.0969946	+	0.523749i
$868$		0			0
$869$	−0.547762	−	2.04428i	−0.0185816	−	0.0693473i
$870$		0			0
$871$	7.62261	+	5.32892i	0.258282	+	0.180563i
$872$		0			0
$873$	3.83878	−	8.61550i	0.129923	−	0.291590i
$874$		0			0
$875$	−10.9516	−	18.9688i	−0.370233	−	0.641263i
$876$		0			0
$877$	51.5387	+	13.8098i	1.74034	+	0.466322i	0.982522	−	0.186146i	$-0.0595996\pi$
$877$	51.5387	+	13.8098i	1.74034	+	0.466322i	0.757816	+	0.652468i	$0.226266\pi$
$878$		0			0
$879$	44.1616	−	21.0564i	1.48954	−	0.710214i
$880$		0			0
$881$	23.5586	−	40.8048i	0.793711	−	1.37475i	−0.129943	−	0.991521i	$-0.541480\pi$
$881$	23.5586	−	40.8048i	0.793711	−	1.37475i	0.923654	−	0.383226i	$-0.125187\pi$
$882$		0			0
$883$		−	21.4475i		−	0.721765i	−0.932611	−	0.360882i	$-0.882476\pi$
$883$		−	21.4475i		−	0.721765i	0.932611	−	0.360882i	$-0.117524\pi$
$884$		0			0
$885$	−8.03433	−	2.84638i	−0.270071	−	0.0956801i
$886$		0			0
$887$	−21.6954	−	12.5259i	−0.728461	−	0.420577i	0.0893977	−	0.995996i	$-0.471506\pi$
$887$	−21.6954	−	12.5259i	−0.728461	−	0.420577i	−0.817859	+	0.575419i	$0.804839\pi$
$888$		0			0
$889$	1.93481	−	1.93481i	0.0648914	−	0.0648914i
$890$		0			0
$891$	−2.70415	+	51.0467i	−0.0905924	+	1.71013i
$892$		0			0
$893$	95.4501	−	55.1082i	3.19412	−	1.84412i
$894$		0			0
$895$	−1.06340	+	0.284938i	−0.0355456	+	0.00952442i
$896$		0			0
$897$	−17.7918	−	14.6483i	−0.594052	−	0.489094i
$898$		0			0
$899$	9.67867	−	2.59339i	0.322802	−	0.0864944i
$900$		0			0
$901$	1.50636	−	0.869695i	0.0501840	−	0.0289738i
$902$		0			0
$903$	1.52518	+	1.04854i	0.0507548	+	0.0348933i
$904$		0			0
$905$	0.988730	−	0.988730i	0.0328665	−	0.0328665i
$906$		0			0
$907$	−24.8693	−	14.3583i	−0.825772	−	0.476760i	0.0266307	−	0.999645i	$-0.491522\pi$
$907$	−24.8693	−	14.3583i	−0.825772	−	0.476760i	−0.852403	+	0.522886i	$0.824856\pi$
$908$		0			0
$909$	−3.13624	−	2.54114i	−0.104022	−	0.0842843i
$910$		0			0
$911$		−	30.6397i		−	1.01514i	−0.861611	−	0.507569i	$-0.830544\pi$
$911$		−	30.6397i		−	1.01514i	0.861611	−	0.507569i	$-0.169456\pi$
$912$		0			0
$913$	20.0459	−	34.7205i	0.663423	−	1.14908i
$914$		0			0
$915$	−2.43028	−	5.09703i	−0.0803424	−	0.168503i
$916$		0			0
$917$	15.3997	+	4.12633i	0.508542	+	0.136263i
$918$		0			0
$919$	5.08612	+	8.80943i	0.167776	+	0.290596i	0.937638	−	0.347615i	$-0.113008\pi$
$919$	5.08612	+	8.80943i	0.167776	+	0.290596i	−0.769862	+	0.638211i	$0.779675\pi$
$920$		0			0
$921$	−0.176318	−	0.0139016i	−0.00580989	−	0.000458074i
$922$		0			0
$923$	10.6952	+	22.8913i	0.352037	+	0.753475i
$924$		0			0
$925$	1.89264	+	7.06342i	0.0622296	+	0.232244i
$926$		0			0
$927$	−29.7832	−	4.72581i	−0.978208	−	0.155216i
$928$		0			0
$929$	−6.27665	+	23.4248i	−0.205930	+	0.768542i	0.783234	+	0.621727i	$0.213569\pi$
$929$	−6.27665	+	23.4248i	−0.205930	+	0.768542i	−0.989164	+	0.146815i	$0.953098\pi$
$930$		0			0
$931$	11.9042	+	11.9042i	0.390145	+	0.390145i
$932$		0			0
$933$	−26.3656	+	22.5119i	−0.863171	+	0.737007i
$934$		0			0
$935$	−39.0817			−1.27811
$936$		0			0
$937$	16.1432			0.527376			0.263688	−	0.964608i	$-0.415061\pi$
$937$	16.1432			0.527376			0.263688	+	0.964608i	$0.415061\pi$
$938$		0			0
$939$	−0.825499	+	0.704841i	−0.0269391	+	0.0230016i
$940$		0			0
$941$	0.888058	+	0.888058i	0.0289499	+	0.0289499i	0.721434	−	0.692484i	$-0.243484\pi$
$941$	0.888058	+	0.888058i	0.0289499	+	0.0289499i	−0.692484	+	0.721434i	$0.743484\pi$
$942$		0			0
$943$	6.95011	−	25.9382i	0.226327	−	0.844663i
$944$		0			0
$945$	24.7474	+	13.4503i	0.805034	+	0.437539i
$946$		0			0
$947$	0.622237	+	2.32222i	0.0202200	+	0.0754620i	0.975299	−	0.220891i	$-0.0708964\pi$
$947$	0.622237	+	2.32222i	0.0202200	+	0.0754620i	−0.955079	+	0.296352i	$0.904230\pi$
$948$		0			0
$949$	−34.2916	−	2.97429i	−1.11315	−	0.0965496i
$950$		0			0
$951$	−35.2836	−	2.78189i	−1.14415	−	0.0902090i
$952$		0			0
$953$	6.06072	+	10.4975i	0.196326	+	0.340046i	0.947334	−	0.320246i	$-0.103766\pi$
$953$	6.06072	+	10.4975i	0.196326	+	0.340046i	−0.751008	+	0.660293i	$0.770432\pi$
$954$		0			0
$955$	21.4525	+	5.74819i	0.694188	+	0.186007i
$956$		0			0
$957$	−9.56959	−	20.0703i	−0.309341	−	0.648782i
$958$		0			0
$959$	13.3565	−	23.1342i	0.431305	−	0.747042i
$960$		0			0
$961$			11.3457i			0.365991i
$962$		0			0
$963$	−28.2153	+	34.8229i	−0.909225	+	1.12215i
$964$		0			0
$965$	−30.5732	−	17.6515i	−0.984187	−	0.568220i
$966$		0			0
$967$	10.7092	−	10.7092i	0.344386	−	0.344386i	−0.513628	−	0.858013i	$-0.671699\pi$
$967$	10.7092	−	10.7092i	0.344386	−	0.344386i	0.858013	+	0.513628i	$0.171699\pi$
$968$		0			0
$969$	32.7297	+	22.5013i	1.05143	+	0.722846i
$970$		0			0
$971$	10.1662	−	5.86945i	0.326248	−	0.188360i	−0.327926	−	0.944703i	$-0.606350\pi$
$971$	10.1662	−	5.86945i	0.326248	−	0.188360i	0.654174	+	0.756344i	$0.273016\pi$
$972$		0			0
$973$	−4.99516	+	1.33845i	−0.160137	+	0.0429087i
$974$		0			0
$975$	−5.90908	−	0.985156i	−0.189242	−	0.0315502i
$976$		0			0
$977$	16.0380	−	4.29736i	0.513100	−	0.137485i	0.00702677	−	0.999975i	$-0.497763\pi$
$977$	16.0380	−	4.29736i	0.513100	−	0.137485i	0.506073	+	0.862491i	$0.331097\pi$
$978$		0			0
$979$	41.2429	−	23.8116i	1.31813	−	0.761021i
$980$		0			0
$981$	14.8727	+	20.4827i	0.474850	+	0.653963i
$982$		0			0
$983$	−25.9952	+	25.9952i	−0.829118	+	0.829118i	−0.987395	−	0.158277i	$-0.949406\pi$
$983$	−25.9952	+	25.9952i	−0.829118	+	0.829118i	0.158277	+	0.987395i	$0.449406\pi$
$984$		0			0
$985$	13.6178	+	7.86223i	0.433899	+	0.250512i
$986$		0			0
$987$	49.1132	+	17.3997i	1.56329	+	0.553838i
$988$		0			0
$989$			1.77591i			0.0564706i
$990$		0			0
$991$	12.1294	−	21.0088i	0.385304	−	0.667366i	−0.606508	−	0.795078i	$-0.707430\pi$
$991$	12.1294	−	21.0088i	0.385304	−	0.667366i	0.991811	+	0.127712i	$0.0407634\pi$
$992$		0			0
$993$	−14.6554	+	6.98771i	−0.465074	+	0.221748i
$994$		0			0
$995$	1.86047	+	0.498512i	0.0589809	+	0.0158039i
$996$		0			0
$997$	−27.5907	−	47.7884i	−0.873805	−	1.51347i	−0.858030	−	0.513599i	$-0.828312\pi$
$997$	−27.5907	−	47.7884i	−0.873805	−	1.51347i	−0.0157748	−	0.999876i	$-0.505021\pi$
$998$		0			0
$999$	28.7210	+	27.2784i	0.908693	+	0.863050i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.cn.f.305.4		56
3.2	odd	2	inner	624.2.cn.f.305.6		56
4.3	odd	2		312.2.bp.a.305.11	yes	56
12.11	even	2		312.2.bp.a.305.9	yes	56
13.11	odd	12	inner	624.2.cn.f.401.6		56
39.11	even	12	inner	624.2.cn.f.401.4		56
52.11	even	12		312.2.bp.a.89.9	✓	56
156.11	odd	12		312.2.bp.a.89.11	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bp.a.89.9	✓	56	52.11	even	12
312.2.bp.a.89.11	yes	56	156.11	odd	12
312.2.bp.a.305.9	yes	56	12.11	even	2
312.2.bp.a.305.11	yes	56	4.3	odd	2
624.2.cn.f.305.4		56	1.1	even	1	trivial
624.2.cn.f.305.6		56	3.2	odd	2	inner
624.2.cn.f.401.4		56	39.11	even	12	inner
624.2.cn.f.401.6		56	13.11	odd	12	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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.cn (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.31722 + 1.12469i) q^{3} +(1.72616 + 1.72616i) q^{5} +(0.574711 - 2.14485i) q^{7} +(0.470140 - 2.96293i) q^{9} +O(q^{10})\)	\(q+(-1.31722 + 1.12469i) q^{3} +(1.72616 + 1.72616i) q^{5} +(0.574711 - 2.14485i) q^{7} +(0.470140 - 2.96293i) q^{9} +(-1.47004 - 5.48627i) q^{11} +(2.76028 - 2.31967i) q^{13} +(-4.21513 - 0.332337i) q^{15} +(-1.40933 - 2.44104i) q^{17} +(7.85833 + 2.10563i) q^{19} +(1.65527 + 3.47161i) q^{21} +(-1.84516 + 3.19592i) q^{23} +0.959270i q^{25} +(2.71311 + 4.43160i) q^{27} +(-1.95737 - 1.13009i) q^{29} +(-3.13483 + 3.13483i) q^{31} +(8.10673 + 5.57328i) q^{33} +(4.69440 - 2.71031i) q^{35} +(7.36333 - 1.97300i) q^{37} +(-1.02699 + 6.15998i) q^{39} +(-7.02869 + 1.88333i) q^{41} +(0.416760 - 0.240616i) q^{43} +(5.92604 - 4.30296i) q^{45} +(9.57953 - 9.57953i) q^{47} +(1.79209 + 1.03466i) q^{49} +(4.60181 + 1.63032i) q^{51} +0.617097i q^{53} +(6.93266 - 12.0077i) q^{55} +(-12.7193 + 6.06461i) q^{57} +(1.94720 + 0.521752i) q^{59} +(0.667748 + 1.15657i) q^{61} +(-6.08485 - 2.71121i) q^{63} +(8.76881 + 0.760564i) q^{65} +(0.667631 + 2.49163i) q^{67} +(-1.16393 - 6.28497i) q^{69} +(-1.81372 + 6.76890i) q^{71} +(-6.75039 - 6.75039i) q^{73} +(-1.07888 - 1.26357i) q^{75} -12.6121 q^{77} +0.372617 q^{79} +(-8.55794 - 2.78599i) q^{81} +(4.99123 + 4.99123i) q^{83} +(1.78089 - 6.64636i) q^{85} +(3.84930 - 0.712863i) q^{87} +(2.17011 + 8.09895i) q^{89} +(-3.38898 - 7.25352i) q^{91} +(0.603546 - 7.65497i) q^{93} +(9.93009 + 17.1994i) q^{95} +(3.03688 + 0.813729i) q^{97} +(-16.9466 + 1.77632i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{7}+O(q^{10}) \) 56 * q - 4 * q^7	\( 56 q - 4 q^{7} + 8 q^{13} + 8 q^{15} - 4 q^{19} + 16 q^{21} - 24 q^{27} + 36 q^{31} + 28 q^{33} + 20 q^{37} - 16 q^{39} + 84 q^{43} + 12 q^{45} - 12 q^{49} + 24 q^{55} - 36 q^{57} - 24 q^{61} + 12 q^{63} + 32 q^{67} - 36 q^{69} - 20 q^{73} + 60 q^{75} + 32 q^{79} - 88 q^{85} + 16 q^{87} - 28 q^{91} - 88 q^{93} - 36 q^{97} - 44 q^{99}+O(q^{100}) \) 56 * q - 4 * q^7 + 8 * q^13 + 8 * q^15 - 4 * q^19 + 16 * q^21 - 24 * q^27 + 36 * q^31 + 28 * q^33 + 20 * q^37 - 16 * q^39 + 84 * q^43 + 12 * q^45 - 12 * q^49 + 24 * q^55 - 36 * q^57 - 24 * q^61 + 12 * q^63 + 32 * q^67 - 36 * q^69 - 20 * q^73 + 60 * q^75 + 32 * q^79 - 88 * q^85 + 16 * q^87 - 28 * q^91 - 88 * q^93 - 36 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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