LMFDB - Embedded newform 624.2.cn.f.401.6

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			401.6
Character	$\chi$	$=$	624.401
Dual form			624.2.cn.f.305.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.315401 - 1.70309i) q^{3} +(-1.72616 + 1.72616i) q^{5} +(0.574711 + 2.14485i) q^{7} +(-2.80104 + 1.07431i) q^{9} +O(q^{10})$	\(q+(-0.315401 - 1.70309i) q^{3} +(-1.72616 + 1.72616i) q^{5} +(0.574711 + 2.14485i) q^{7} +(-2.80104 + 1.07431i) q^{9} +(1.47004 - 5.48627i) q^{11} +(2.76028 + 2.31967i) q^{13} +(3.48425 + 2.39538i) q^{15} +(1.40933 - 2.44104i) q^{17} +(7.85833 - 2.10563i) q^{19} +(3.47161 - 1.65527i) q^{21} +(1.84516 + 3.19592i) q^{23} -0.959270i q^{25} +(2.71311 + 4.43160i) q^{27} +(1.95737 - 1.13009i) q^{29} +(-3.13483 - 3.13483i) q^{31} +(-9.80727 - 0.773242i) q^{33} +(-4.69440 - 2.71031i) q^{35} +(7.36333 + 1.97300i) q^{37} +(3.08001 - 5.43263i) q^{39} +(7.02869 + 1.88333i) q^{41} +(0.416760 + 0.240616i) q^{43} +(2.98062 - 6.68949i) q^{45} +(-9.57953 - 9.57953i) q^{47} +(1.79209 - 1.03466i) q^{49} +(-4.60181 - 1.63032i) q^{51} +0.617097i q^{53} +(6.93266 + 12.0077i) q^{55} +(-6.06461 - 12.7193i) q^{57} +(-1.94720 + 0.521752i) q^{59} +(0.667748 - 1.15657i) q^{61} +(-3.91403 - 5.39040i) q^{63} +(-8.76881 + 0.760564i) q^{65} +(0.667631 - 2.49163i) q^{67} +(4.86098 - 4.15048i) q^{69} +(1.81372 + 6.76890i) q^{71} +(-6.75039 + 6.75039i) q^{73} +(-1.63372 + 0.302554i) q^{75} +12.6121 q^{77} +0.372617 q^{79} +(6.69170 - 6.01840i) q^{81} +(-4.99123 + 4.99123i) q^{83} +(1.78089 + 6.64636i) q^{85} +(-2.54201 - 2.97716i) q^{87} +(-2.17011 + 8.09895i) q^{89} +(-3.38898 + 7.25352i) q^{91} +(-4.35017 + 6.32762i) q^{93} +(-9.93009 + 17.1994i) q^{95} +(3.03688 - 0.813729i) q^{97} +(1.77632 + 16.9466i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

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
$3$	−0.315401	−	1.70309i	−0.182097	−	0.983281i
$3$	−0.315401	−	1.70309i	−0.182097	−	0.983281i
$4$		0			0
$5$	−1.72616	+	1.72616i	−0.771963	+	0.771963i	−0.978449	−	0.206486i	$-0.933797\pi$
$5$	−1.72616	+	1.72616i	−0.771963	+	0.771963i	0.206486	+	0.978449i	$0.433797\pi$
$6$		0			0
$7$	0.574711	+	2.14485i	0.217220	+	0.810677i	0.985373	+	0.170411i	$0.0545094\pi$
$7$	0.574711	+	2.14485i	0.217220	+	0.810677i	−0.768153	+	0.640266i	$0.778824\pi$
$8$		0			0
$9$	−2.80104	+	1.07431i	−0.933682	+	0.358104i
$10$		0			0
$11$	1.47004	−	5.48627i	0.443234	−	1.65417i	−0.277323	−	0.960777i	$-0.589447\pi$
$11$	1.47004	−	5.48627i	0.443234	−	1.65417i	0.720557	−	0.693396i	$-0.243886\pi$
$12$		0			0
$13$	2.76028	+	2.31967i	0.765564	+	0.643360i
$13$	2.76028	+	2.31967i	0.765564	+	0.643360i
$14$		0			0
$15$	3.48425	+	2.39538i	0.899628	+	0.618484i
$16$		0			0
$17$	1.40933	−	2.44104i	0.341813	−	0.592038i	−0.642956	−	0.765903i	$-0.722292\pi$
$17$	1.40933	−	2.44104i	0.341813	−	0.592038i	0.984770	+	0.173865i	$0.0556256\pi$
$18$		0			0
$19$	7.85833	−	2.10563i	1.80282	−	0.483065i	0.808411	−	0.588618i	$-0.200328\pi$
$19$	7.85833	−	2.10563i	1.80282	−	0.483065i	0.994414	+	0.105553i	$0.0336613\pi$
$20$		0			0
$21$	3.47161	−	1.65527i	0.757568	−	0.361210i
$22$		0			0
$23$	1.84516	+	3.19592i	0.384743	+	0.666395i	0.991734	−	0.128314i	$-0.0409566\pi$
$23$	1.84516	+	3.19592i	0.384743	+	0.666395i	−0.606990	+	0.794709i	$0.707623\pi$
$24$		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	$-0.599368\pi$
$29$	1.95737	−	1.13009i	0.363475	−	0.209853i	0.670604	+	0.741815i	$0.266035\pi$
$30$		0			0
$31$	−3.13483	−	3.13483i	−0.563031	−	0.563031i	0.367136	−	0.930167i	$-0.380338\pi$
$31$	−3.13483	−	3.13483i	−0.563031	−	0.563031i	−0.930167	+	0.367136i	$0.880338\pi$
$32$		0			0
$33$	−9.80727	−	0.773242i	−1.70723	−	0.134604i
$34$		0			0
$35$	−4.69440	−	2.71031i	−0.793499	−	0.458127i
$36$		0			0
$37$	7.36333	+	1.97300i	1.21052	+	0.324359i	0.806968	−	0.590596i	$-0.201107\pi$
$37$	7.36333	+	1.97300i	1.21052	+	0.324359i	0.403557	+	0.914955i	$0.367774\pi$
$38$		0			0
$39$	3.08001	−	5.43263i	0.493197	−	0.869918i
$40$		0			0
$41$	7.02869	+	1.88333i	1.09770	+	0.294127i	0.761826	−	0.647781i	$-0.224303\pi$
$41$	7.02869	+	1.88333i	1.09770	+	0.294127i	0.335870	+	0.941908i	$0.390970\pi$
$42$		0			0
$43$	0.416760	+	0.240616i	0.0635553	+	0.0366937i	0.531441	−	0.847095i	$-0.321651\pi$
$43$	0.416760	+	0.240616i	0.0635553	+	0.0366937i	−0.467886	+	0.883789i	$0.654984\pi$
$44$		0			0
$45$	2.98062	−	6.68949i	0.444324	−	0.997211i
$46$		0			0
$47$	−9.57953	−	9.57953i	−1.39732	−	1.39732i	−0.807633	−	0.589685i	$-0.799252\pi$
$47$	−9.57953	−	9.57953i	−1.39732	−	1.39732i	−0.589685	−	0.807633i	$-0.700748\pi$
$48$		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
$57$	−6.06461	−	12.7193i	−0.803277	−	1.68472i
$58$		0			0
$59$	−1.94720	+	0.521752i	−0.253504	+	0.0679263i	−0.383333	−	0.923610i	$-0.625224\pi$
$59$	−1.94720	+	0.521752i	−0.253504	+	0.0679263i	0.129829	+	0.991536i	$0.458557\pi$
$60$		0			0
$61$	0.667748	−	1.15657i	0.0854964	−	0.148084i	−0.820106	−	0.572211i	$-0.806086\pi$
$61$	0.667748	−	1.15657i	0.0854964	−	0.148084i	0.905603	+	0.424127i	$0.139419\pi$
$62$		0			0
$63$	−3.91403	−	5.39040i	−0.493121	−	0.679127i
$64$		0			0
$65$	−8.76881	+	0.760564i	−1.08764	+	0.0943364i
$66$		0			0
$67$	0.667631	−	2.49163i	0.0815641	−	0.304401i	−0.913077	−	0.407787i	$-0.866301\pi$
$67$	0.667631	−	2.49163i	0.0815641	−	0.304401i	0.994641	+	0.103385i	$0.0329674\pi$
$68$		0			0
$69$	4.86098	−	4.15048i	0.585193	−	0.499659i
$70$		0			0
$71$	1.81372	+	6.76890i	0.215249	+	0.803320i	0.986079	+	0.166279i	$0.0531752\pi$
$71$	1.81372	+	6.76890i	0.215249	+	0.803320i	−0.770830	+	0.637041i	$0.780158\pi$
$72$		0			0
$73$	−6.75039	+	6.75039i	−0.790073	+	0.790073i	−0.981506	−	0.191432i	$-0.938687\pi$
$73$	−6.75039	+	6.75039i	−0.790073	+	0.790073i	0.191432	+	0.981506i	$0.438687\pi$
$74$		0			0
$75$	−1.63372	+	0.302554i	−0.188646	+	0.0349360i
$76$		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
$81$	6.69170	−	6.01840i	0.743523	−	0.668711i
$82$		0			0
$83$	−4.99123	+	4.99123i	−0.547858	+	0.547858i	−0.925821	−	0.377963i	$-0.876625\pi$
$83$	−4.99123	+	4.99123i	−0.547858	+	0.547858i	0.377963	+	0.925821i	$0.376625\pi$
$84$		0			0
$85$	1.78089	+	6.64636i	0.193164	+	0.720899i
$86$		0			0
$87$	−2.54201	−	2.97716i	−0.272532	−	0.319185i
$88$		0			0
$89$	−2.17011	+	8.09895i	−0.230031	+	0.858487i	0.750295	+	0.661103i	$0.229911\pi$
$89$	−2.17011	+	8.09895i	−0.230031	+	0.858487i	−0.980326	+	0.197384i	$0.936755\pi$
$90$		0			0
$91$	−3.38898	+	7.25352i	−0.355261	+	0.760376i
$92$		0			0
$93$	−4.35017	+	6.32762i	−0.451092	+	0.656144i
$94$		0			0
$95$	−9.93009	+	17.1994i	−1.01881	+	1.76462i
$96$		0			0
$97$	3.03688	−	0.813729i	0.308348	−	0.0826217i	−0.101327	−	0.994853i	$-0.532309\pi$
$97$	3.03688	−	0.813729i	0.308348	−	0.0826217i	0.409675	+	0.912232i	$0.365642\pi$
$98$		0			0
$99$	1.77632	+	16.9466i	0.178527	+	1.70319i
$100$		0			0
$101$	−0.672751	−	1.16524i	−0.0669412	−	0.115946i	0.830612	−	0.556851i	$-0.187991\pi$
$101$	−0.672751	−	1.16524i	−0.0669412	−	0.115946i	−0.897553	+	0.440906i	$0.854657\pi$
$102$		0			0
$103$			10.0519i			0.990446i	0.868766	+	0.495223i	$0.164914\pi$
$103$			10.0519i			0.990446i	−0.868766	+	0.495223i	$0.835086\pi$
$104$		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	$-0.409828\pi$
$107$	12.9381	−	7.46982i	1.25077	−	0.722135i	0.971263	+	0.238008i	$0.0764943\pi$
$108$		0			0
$109$	−5.96629	−	5.96629i	−0.571467	−	0.571467i	0.361071	−	0.932538i	$-0.382411\pi$
$109$	−5.96629	−	5.96629i	−0.571467	−	0.571467i	−0.932538	+	0.361071i	$0.882411\pi$
$110$		0			0
$111$	1.03780	−	13.1627i	0.0985034	−	1.24935i
$112$		0			0
$113$	15.1400	+	8.74110i	1.42425	+	0.822294i	0.996659	−	0.0816760i	$-0.0260273\pi$
$113$	15.1400	+	8.74110i	1.42425	+	0.822294i	0.427596	+	0.903970i	$0.359361\pi$
$114$		0			0
$115$	−8.70173	−	2.33162i	−0.811440	−	0.217425i
$116$		0			0
$117$	−10.2237	−	3.53209i	−0.945183	−	0.326542i
$118$		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
$123$	0.990633	−	12.5645i	0.0893224	−	1.13290i
$124$		0			0
$125$	−6.97495	−	6.97495i	−0.623859	−	0.623859i
$126$		0			0
$127$	1.06716	−	0.616127i	0.0946954	−	0.0546724i	−0.451904	−	0.892066i	$-0.649255\pi$
$127$	1.06716	−	0.616127i	0.0946954	−	0.0546724i	0.546600	+	0.837394i	$0.315922\pi$
$128$		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
$135$	−12.3329	−	2.96640i	−1.06145	−	0.255307i
$136$		0			0
$137$	−11.6202	+	3.11363i	−0.992783	+	0.266015i	−0.718419	−	0.695611i	$-0.755134\pi$
$137$	−11.6202	+	3.11363i	−0.992783	+	0.266015i	−0.274364	+	0.961626i	$0.588467\pi$
$138$		0			0
$139$	−1.16445	+	2.01689i	−0.0987677	+	0.171071i	−0.911175	−	0.412020i	$-0.864823\pi$
$139$	−1.16445	+	2.01689i	−0.0987677	+	0.171071i	0.812407	+	0.583091i	$0.198157\pi$
$140$		0			0
$141$	−13.2934	+	19.3362i	−1.11951	+	1.62840i
$142$		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
$147$	−2.32735	−	2.72576i	−0.191957	−	0.224817i
$148$		0			0
$149$	−5.04901	−	18.8432i	−0.413631	−	1.54369i	−0.787562	−	0.616236i	$-0.788657\pi$
$149$	−5.04901	−	18.8432i	−0.413631	−	1.54369i	0.373930	−	0.927457i	$-0.378010\pi$
$150$		0			0
$151$	−0.712411	+	0.712411i	−0.0579752	+	0.0579752i	−0.735500	−	0.677525i	$-0.763053\pi$
$151$	−0.712411	+	0.712411i	−0.0579752	+	0.0579752i	0.677525	+	0.735500i	$0.263053\pi$
$152$		0			0
$153$	−1.32517	+	8.35151i	−0.107133	+	0.675180i
$154$		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
$159$	1.05097	−	0.194633i	0.0833476	−	0.0154354i
$160$		0			0
$161$	−5.79433	+	5.79433i	−0.456657	+	0.456657i
$162$		0			0
$163$	−2.57138	−	9.59651i	−0.201406	−	0.751657i	−0.990515	−	0.137404i	$-0.956124\pi$
$163$	−2.57138	−	9.59651i	−0.201406	−	0.751657i	0.789109	−	0.614253i	$-0.210542\pi$
$164$		0			0
$165$	18.2637	−	15.5942i	1.42183	−	1.21401i
$166$		0			0
$167$	2.68928	−	10.0365i	0.208102	−	0.776649i	−0.780379	−	0.625307i	$-0.784974\pi$
$167$	2.68928	−	10.0365i	0.208102	−	0.776649i	0.988481	−	0.151342i	$-0.0483595\pi$
$168$		0			0
$169$	2.23828	+	12.8059i	0.172175	+	0.985066i
$170$		0			0
$171$	−19.7494	+	14.3403i	−1.51028	+	1.09663i
$172$		0			0
$173$	−6.65624	+	11.5289i	−0.506064	+	0.876529i	0.493911	+	0.869512i	$0.335567\pi$
$173$	−6.65624	+	11.5289i	−0.506064	+	0.876529i	−0.999975	+	0.00701675i	$0.997766\pi$
$174$		0			0
$175$	2.05749	−	0.551303i	0.155532	−	0.0416746i
$176$		0			0
$177$	1.50274	+	3.15171i	0.112953	+	0.236897i
$178$		0			0
$179$	0.225490	+	0.390560i	0.0168539	+	0.0291918i	0.874329	−	0.485333i	$-0.161302\pi$
$179$	0.225490	+	0.390560i	0.0168539	+	0.0291918i	−0.857475	+	0.514525i	$0.827968\pi$
$180$		0			0
$181$			0.572791i			0.0425752i	0.999773	+	0.0212876i	$0.00677657\pi$
$181$			0.572791i			0.0425752i	−0.999773	+	0.0212876i	$0.993223\pi$
$182$		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
$189$	−7.94586	+	8.36609i	−0.577976	+	0.608544i
$190$		0			0
$191$	−7.87896	−	4.54892i	−0.570102	−	0.329148i	0.187088	−	0.982343i	$-0.440095\pi$
$191$	−7.87896	−	4.54892i	−0.570102	−	0.329148i	−0.757190	+	0.653195i	$0.773428\pi$
$192$		0			0
$193$	−13.9688	−	3.74292i	−1.00549	−	0.269421i	−0.281748	−	0.959488i	$-0.590914\pi$
$193$	−13.9688	−	3.74292i	−1.00549	−	0.269421i	−0.723745	+	0.690067i	$0.757581\pi$
$194$		0			0
$195$	4.06100	+	14.6942i	0.290814	+	1.05227i
$196$		0			0
$197$	−6.22190	−	1.66715i	−0.443292	−	0.118780i	0.0302668	−	0.999542i	$-0.490364\pi$
$197$	−6.22190	−	1.66715i	−0.443292	−	0.118780i	−0.473559	+	0.880762i	$0.657031\pi$
$198$		0			0
$199$	0.683303	+	0.394505i	0.0484381	+	0.0279657i	0.524023	−	0.851704i	$-0.324430\pi$
$199$	0.683303	+	0.394505i	0.0484381	+	0.0279657i	−0.475585	+	0.879670i	$0.657764\pi$
$200$		0			0
$201$	−4.45405	−	0.351174i	−0.314164	−	0.0247699i
$202$		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	−0.923861	−	0.382729i	$-0.874984\pi$
$211$	−11.5246	−	19.9611i	−0.793383	−	1.37418i	0.130478	−	0.991451i	$-0.458349\pi$
$212$		0			0
$213$	10.9560	−	5.22385i	0.750693	−	0.357932i
$214$		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
$219$	13.6256	+	9.36746i	0.920734	+	0.632994i
$220$		0			0
$221$	9.55254	−	3.46875i	0.642574	−	0.233334i
$222$		0			0
$223$	−3.35292	+	12.5133i	−0.224528	+	0.837950i	0.758065	+	0.652179i	$0.226145\pi$
$223$	−3.35292	+	12.5133i	−0.224528	+	0.837950i	−0.982593	+	0.185771i	$0.940522\pi$
$224$		0			0
$225$	1.03056	+	2.68696i	0.0687037	+	0.179130i
$226$		0			0
$227$	2.62037	+	9.77935i	0.173920	+	0.649079i	0.996733	+	0.0807663i	$0.0257368\pi$
$227$	2.62037	+	9.77935i	0.173920	+	0.649079i	−0.822813	+	0.568312i	$0.807597\pi$
$228$		0			0
$229$	6.04210	−	6.04210i	0.399273	−	0.399273i	−0.478703	−	0.877977i	$-0.658893\pi$
$229$	6.04210	−	6.04210i	0.399273	−	0.399273i	0.877977	+	0.478703i	$0.158893\pi$
$230$		0			0
$231$	−3.97786	−	21.4795i	−0.261724	−	1.41325i
$232$		0			0
$233$	−9.52224			−0.623823			−0.311911	−	0.950111i	$-0.600969\pi$
$233$	−9.52224			−0.623823			−0.311911	+	0.950111i	$0.600969\pi$
$234$		0			0
$235$	33.0716			2.15736
$236$		0			0
$237$	−0.117524	−	0.634600i	−0.00763398	−	0.0412217i
$238$		0			0
$239$	0.346997	−	0.346997i	0.0224454	−	0.0224454i	−0.695795	−	0.718240i	$-0.744948\pi$
$239$	0.346997	−	0.346997i	0.0224454	−	0.0224454i	0.718240	+	0.695795i	$0.244948\pi$
$240$		0			0
$241$	−6.84098	−	25.5309i	−0.440667	−	1.64459i	−0.727131	−	0.686499i	$-0.759147\pi$
$241$	−6.84098	−	25.5309i	−0.440667	−	1.64459i	0.286464	−	0.958091i	$-0.407520\pi$
$242$		0			0
$243$	−12.3605	−	9.49838i	−0.792923	−	0.609321i
$244$		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
$249$	10.0748	+	6.92628i	0.638462	+	0.438935i
$250$		0			0
$251$	−6.74616	+	11.6847i	−0.425814	+	0.737531i	−0.996496	−	0.0836399i	$-0.973345\pi$
$251$	−6.74616	+	11.6847i	−0.425814	+	0.737531i	0.570682	+	0.821171i	$0.306679\pi$
$252$		0			0
$253$	20.2461	−	5.42494i	1.27286	−	0.341063i
$254$		0			0
$255$	10.7577	−	5.12928i	0.673671	−	0.321208i
$256$		0			0
$257$	1.24981	+	2.16473i	0.0779610	+	0.135032i	0.902370	−	0.430962i	$-0.141826\pi$
$257$	1.24981	+	2.16473i	0.0779610	+	0.135032i	−0.824409	+	0.565994i	$0.808492\pi$
$258$		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	$-0.570931\pi$
$263$	8.32134	−	4.80433i	0.513116	−	0.296248i	0.734114	+	0.679027i	$0.237598\pi$
$264$		0			0
$265$	−1.06521	−	1.06521i	−0.0654353	−	0.0654353i
$266$		0			0
$267$	14.4777	+	1.14148i	0.886021	+	0.0698572i
$268$		0			0
$269$	14.4109	+	8.32012i	0.878646	+	0.507286i	0.870212	−	0.492678i	$-0.163982\pi$
$269$	14.4109	+	8.32012i	0.878646	+	0.507286i	0.00843422	+	0.999964i	$0.497315\pi$
$270$		0			0
$271$	−30.2838	−	8.11452i	−1.83961	−	0.492922i	−0.840785	−	0.541369i	$-0.817906\pi$
$271$	−30.2838	−	8.11452i	−1.83961	−	0.492922i	−0.998826	+	0.0484469i	$0.984573\pi$
$272$		0			0
$273$	13.4223	+	3.48398i	0.812355	+	0.210860i
$274$		0			0
$275$	−5.26281	−	1.41017i	−0.317360	−	0.0850362i
$276$		0			0
$277$	−6.36855	−	3.67688i	−0.382649	−	0.220923i	0.296321	−	0.955088i	$-0.404240\pi$
$277$	−6.36855	−	3.67688i	−0.382649	−	0.220923i	−0.678970	+	0.734166i	$0.737573\pi$
$278$		0			0
$279$	12.1486	+	5.41300i	0.727316	+	0.324068i
$280$		0			0
$281$	5.52193	+	5.52193i	0.329411	+	0.329411i	0.852362	−	0.522952i	$-0.175169\pi$
$281$	5.52193	+	5.52193i	0.329411	+	0.329411i	−0.522952	+	0.852362i	$0.675169\pi$
$282$		0			0
$283$	−8.91761	+	5.14859i	−0.530097	+	0.306052i	−0.741056	−	0.671443i	$-0.765675\pi$
$283$	−8.91761	+	5.14859i	−0.530097	+	0.306052i	0.210959	+	0.977495i	$0.432341\pi$
$284$		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
$291$	−2.34369	−	4.91543i	−0.137390	−	0.288148i
$292$		0			0
$293$	27.2842	−	7.31077i	1.59396	−	0.427100i	0.650748	−	0.759294i	$-0.274456\pi$
$293$	27.2842	−	7.31077i	1.59396	−	0.427100i	0.943211	+	0.332194i	$0.107789\pi$
$294$		0			0
$295$	2.46056	−	4.26182i	0.143259	−	0.248133i
$296$		0			0
$297$	28.3013	−	8.37020i	1.64221	−	0.485688i
$298$		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
$303$	−1.77232	+	1.51327i	−0.101817	+	0.0869353i
$304$		0			0
$305$	0.843792	+	3.14907i	0.0483154	+	0.180315i
$306$		0			0
$307$	0.0722051	−	0.0722051i	0.00412096	−	0.00412096i	−0.705043	−	0.709164i	$-0.749072\pi$
$307$	0.0722051	−	0.0722051i	0.00412096	−	0.00412096i	0.709164	+	0.705043i	$0.249072\pi$
$308$		0			0
$309$	17.1194	−	3.17039i	0.973886	−	0.180357i
$310$		0			0
$311$	−20.0161			−1.13501			−0.567504	−	0.823370i	$-0.692091\pi$
$311$	−20.0161			−1.13501			−0.567504	+	0.823370i	$0.692091\pi$
$312$		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
$315$	16.0610	+	2.54845i	0.904932	+	0.143589i
$316$		0			0
$317$	−14.4492	+	14.4492i	−0.811546	+	0.811546i	−0.984866	−	0.173320i	$-0.944551\pi$
$317$	−14.4492	+	14.4492i	−0.811546	+	0.811546i	0.173320	+	0.984866i	$0.444551\pi$
$318$		0			0
$319$	−3.32256	−	12.4000i	−0.186028	−	0.694265i
$320$		0			0
$321$	−16.8025	−	19.6788i	−0.937823	−	1.09836i
$322$		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
$327$	−8.27938	+	12.0429i	−0.457850	+	0.665975i
$328$		0			0
$329$	15.0412	−	26.0521i	0.829248	−	1.43630i
$330$		0			0
$331$	9.05445	−	2.42613i	0.497678	−	0.133352i	−0.00124426	−	0.999999i	$-0.500396\pi$
$331$	9.05445	−	2.42613i	0.497678	−	0.133352i	0.498922	+	0.866647i	$0.333729\pi$
$332$		0			0
$333$	−22.7446	+	2.38407i	−1.24640	+	0.130646i
$334$		0			0
$335$	3.14852	+	5.45340i	0.172022	+	0.297951i
$336$		0			0
$337$			20.6022i			1.12227i	0.827724	+	0.561136i	$0.189635\pi$
$337$			20.6022i			1.12227i	−0.827724	+	0.561136i	$0.810365\pi$
$338$		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
$345$	−1.22643	+	15.5552i	−0.0660289	+	0.837466i
$346$		0			0
$347$	−20.7808	−	11.9978i	−1.11557	−	0.644076i	−0.175306	−	0.984514i	$-0.556091\pi$
$347$	−20.7808	−	11.9978i	−1.11557	−	0.644076i	−0.940267	+	0.340437i	$0.889425\pi$
$348$		0			0
$349$	−29.5949	−	7.92992i	−1.58418	−	0.424479i	−0.643961	−	0.765058i	$-0.722710\pi$
$349$	−29.5949	−	7.92992i	−1.58418	−	0.424479i	−0.940216	+	0.340579i	$0.889377\pi$
$350$		0			0
$351$	−2.79091	+	18.5259i	−0.148968	+	0.988842i
$352$		0			0
$353$	28.6149	+	7.66733i	1.52302	+	0.408091i	0.920733	−	0.390193i	$-0.127592\pi$
$353$	28.6149	+	7.66733i	1.52302	+	0.408091i	0.602282	+	0.798283i	$0.294258\pi$
$354$		0			0
$355$	−14.8150	−	8.55343i	−0.786298	−	0.453969i
$356$		0			0
$357$	0.852077	−	10.8072i	0.0450967	−	0.571976i
$358$		0			0
$359$	9.69605	+	9.69605i	0.511738	+	0.511738i	0.915059	−	0.403321i	$-0.132144\pi$
$359$	9.69605	+	9.69605i	0.511738	+	0.511738i	−0.403321	+	0.915059i	$0.632144\pi$
$360$		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	0.978178	−	0.207767i	$-0.0666195\pi$
$367$	5.92261	+	10.2583i	0.309158	+	0.535477i	−0.669020	+	0.743244i	$0.733286\pi$
$368$		0			0
$369$	−21.7110	+	2.27572i	−1.13023	+	0.118469i
$370$		0			0
$371$	−1.32358	+	0.354652i	−0.0687169	+	0.0184126i
$372$		0			0
$373$	12.5599	−	21.7543i	0.650325	−	1.12640i	−0.332719	−	0.943026i	$-0.607966\pi$
$373$	12.5599	−	21.7543i	0.650325	−	1.12640i	0.983044	−	0.183369i	$-0.0587004\pi$
$374$		0			0
$375$	−9.67908	+	14.0789i	−0.499826	+	0.727031i
$376$		0			0
$377$	8.02434	+	1.42109i	0.413274	+	0.0731901i
$378$		0			0
$379$	7.78147	−	29.0409i	0.399707	−	1.49173i	−0.413904	−	0.910320i	$-0.635835\pi$
$379$	7.78147	−	29.0409i	0.399707	−	1.49173i	0.813612	−	0.581408i	$-0.197498\pi$
$380$		0			0
$381$	−1.38590	−	1.62315i	−0.0710020	−	0.0831565i
$382$		0			0
$383$	−3.42225	−	12.7720i	−0.174869	−	0.652620i	−0.996574	−	0.0827069i	$-0.973643\pi$
$383$	−3.42225	−	12.7720i	−0.174869	−	0.652620i	0.821705	−	0.569913i	$-0.193023\pi$
$384$		0			0
$385$	−21.7705	+	21.7705i	−1.10953	+	1.10953i
$386$		0			0
$387$	−1.42586	−	0.226247i	−0.0724806	−	0.0115008i
$388$		0			0
$389$	−35.5709			−1.80352			−0.901759	−	0.432239i	$-0.857724\pi$
$389$	−35.5709			−1.80352			−0.901759	+	0.432239i	$0.857724\pi$
$390$		0			0
$391$	10.4018			0.526042
$392$		0			0
$393$	12.2279	−	2.26452i	0.616817	−	0.114230i
$394$		0			0
$395$	−0.643197	+	0.643197i	−0.0323627	+	0.0323627i
$396$		0			0
$397$	0.0698912	+	0.260837i	0.00350774	+	0.0130911i	0.967658	−	0.252268i	$-0.0811763\pi$
$397$	0.0698912	+	0.260837i	0.00350774	+	0.0130911i	−0.964150	+	0.265359i	$0.914510\pi$
$398$		0			0
$399$	23.7957	−	20.3176i	1.19127	−	1.01715i
$400$		0			0
$401$	−3.32674	+	12.4156i	−0.166130	+	0.620004i	0.831764	+	0.555130i	$0.187331\pi$
$401$	−3.32674	+	12.4156i	−0.166130	+	0.620004i	−0.997893	+	0.0648745i	$0.979335\pi$
$402$		0			0
$403$	−1.38124	−	15.9248i	−0.0688043	−	0.793268i
$404$		0			0
$405$	−1.16223	+	21.9397i	−0.0577519	+	1.09019i
$406$		0			0
$407$	21.6488	−	37.4968i	1.07309	−	1.85865i
$408$		0			0
$409$	−14.0337	+	3.76033i	−0.693924	+	0.185936i	−0.588508	−	0.808492i	$-0.700284\pi$
$409$	−14.0337	+	3.76033i	−0.693924	+	0.185936i	−0.105417	+	0.994428i	$0.533618\pi$
$410$		0			0
$411$	8.96782	+	18.8083i	0.442350	+	0.927743i
$412$		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	$-0.963670\pi$
$419$	−28.4856	+	16.4462i	−1.39161	+	0.803448i	−0.398118	+	0.917334i	$0.630337\pi$
$420$		0			0
$421$	−12.6319	−	12.6319i	−0.615641	−	0.615641i	0.328769	−	0.944410i	$-0.393366\pi$
$421$	−12.6319	−	12.6319i	−0.615641	−	0.615641i	−0.944410	+	0.328769i	$0.893366\pi$
$422$		0			0
$423$	37.1241	+	16.5413i	1.80504	+	0.804265i
$424$		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
$429$	−25.2771	−	24.8840i	−1.22039	−	1.20141i
$430$		0			0
$431$	21.3199	+	5.71266i	1.02694	+	0.275169i	0.732693	−	0.680559i	$-0.238263\pi$
$431$	21.3199	+	5.71266i	1.02694	+	0.275169i	0.294252	+	0.955728i	$0.404930\pi$
$432$		0			0
$433$	32.4780	+	18.7512i	1.56079	+	0.901125i	0.997177	+	0.0750900i	$0.0239244\pi$
$433$	32.4780	+	18.7512i	1.56079	+	0.901125i	0.563618	+	0.826035i	$0.309409\pi$
$434$		0			0
$435$	9.52697	+	0.751142i	0.456783	+	0.0360145i
$436$		0			0
$437$	21.2293	+	21.2293i	1.01554	+	1.01554i
$438$		0			0
$439$	−18.7404	+	10.8198i	−0.894431	+	0.516400i	−0.875389	−	0.483419i	$-0.839395\pi$
$439$	−18.7404	+	10.8198i	−0.894431	+	0.516400i	−0.0190419	+	0.999819i	$0.506062\pi$
$440$		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
$447$	−30.4992	+	14.5421i	−1.44256	+	0.687817i
$448$		0			0
$449$	−8.38164	+	2.24585i	−0.395554	+	0.105988i	−0.451113	−	0.892467i	$-0.648973\pi$
$449$	−8.38164	+	2.24585i	−0.395554	+	0.105988i	0.0555585	+	0.998455i	$0.482306\pi$
$450$		0			0
$451$	20.6649	−	35.7927i	0.973073	−	1.68541i
$452$		0			0
$453$	1.43800	+	0.988606i	0.0675629	+	0.0464488i
$454$		0			0
$455$	−6.67083	−	18.3707i	−0.312733	−	0.861231i
$456$		0			0
$457$	10.2516	−	38.2595i	0.479550	−	1.78970i	−0.123890	−	0.992296i	$-0.539537\pi$
$457$	10.2516	−	38.2595i	0.479550	−	1.78970i	0.603439	−	0.797409i	$-0.293796\pi$
$458$		0			0
$459$	14.6414	−	0.377192i	0.683400	−	0.0176058i
$460$		0			0
$461$	2.25094	+	8.40062i	0.104837	+	0.391256i	0.998327	−	0.0578275i	$-0.0184173\pi$
$461$	2.25094	+	8.40062i	0.104837	+	0.391256i	−0.893490	+	0.449083i	$0.851751\pi$
$462$		0			0
$463$	−13.9840	+	13.9840i	−0.649893	+	0.649893i	−0.952967	−	0.303074i	$-0.901987\pi$
$463$	−13.9840	+	13.9840i	−0.649893	+	0.649893i	0.303074	+	0.952967i	$0.401987\pi$
$464$		0			0
$465$	−3.41340	−	18.4316i	−0.158293	−	0.854745i
$466$		0			0
$467$	29.4617			1.36333			0.681663	−	0.731666i	$-0.261257\pi$
$467$	29.4617			1.36333			0.681663	+	0.731666i	$0.261257\pi$
$468$		0			0
$469$	5.72787			0.264489
$470$		0			0
$471$	−5.37146	−	29.0047i	−0.247504	−	1.33646i
$472$		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
$477$	−0.662956	−	1.72852i	−0.0303547	−	0.0791434i
$478$		0			0
$479$	−8.50742	+	31.7501i	−0.388714	+	1.45070i	0.443514	+	0.896267i	$0.353732\pi$
$479$	−8.50742	+	31.7501i	−0.388714	+	1.45070i	−0.832228	+	0.554433i	$0.812935\pi$
$480$		0			0
$481$	15.7481	+	22.5265i	0.718054	+	1.02712i
$482$		0			0
$483$	11.6958	+	8.04074i	0.532178	+	0.365866i
$484$		0			0
$485$	−3.83752	+	6.64677i	−0.174253	+	0.301814i
$486$		0			0
$487$	−11.0631	+	2.96434i	−0.501316	+	0.134327i	−0.500611	−	0.865672i	$-0.666891\pi$
$487$	−11.0631	+	2.96434i	−0.501316	+	0.134327i	−0.000705427		1.00000i	$0.500225\pi$
$488$		0			0
$489$	−15.5327	+	7.40604i	−0.702414	+	0.334913i
$490$		0			0
$491$	0.607370	+	1.05200i	0.0274102	+	0.0474759i	0.879405	−	0.476074i	$-0.157941\pi$
$491$	0.607370	+	1.05200i	0.0274102	+	0.0474759i	−0.851995	+	0.523550i	$0.824607\pi$
$492$		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	0.0440068	−	0.999031i	$-0.485988\pi$
$499$	−21.3336	−	21.3336i	−0.955024	−	0.955024i	−0.999031	+	0.0440068i	$0.985988\pi$
$500$		0			0
$501$	−17.9413	−	1.41456i	−0.801559	−	0.0631979i
$502$		0			0
$503$	−19.6423	−	11.3405i	−0.875808	−	0.505648i	−0.00653389	−	0.999979i	$-0.502080\pi$
$503$	−19.6423	−	11.3405i	−0.875808	−	0.505648i	−0.869274	+	0.494331i	$0.835413\pi$
$504$		0			0
$505$	3.17267	+	0.850114i	0.141182	+	0.0378296i
$506$		0			0
$507$	21.1036	−	7.85097i	0.937244	−	0.348674i
$508$		0			0
$509$	−19.3215	−	5.17719i	−0.856412	−	0.229475i	−0.196209	−	0.980562i	$-0.562863\pi$
$509$	−19.3215	−	5.17719i	−0.856412	−	0.229475i	−0.660203	+	0.751087i	$0.729530\pi$
$510$		0			0
$511$	−18.3581	−	10.5991i	−0.812114	−	0.468874i
$512$		0			0
$513$	30.6518	+	29.1122i	1.35331	+	1.28533i
$514$		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	0.998048	−	0.0624482i	$-0.0198908\pi$
$523$	10.1755	+	17.6244i	0.444942	+	0.770663i	−0.553106	+	0.833111i	$0.686557\pi$
$524$		0			0
$525$	−1.58785	−	3.33021i	−0.0692996	−	0.145342i
$526$		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
$531$	4.89368	−	3.55336i	0.212368	−	0.154203i
$532$		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
$537$	0.594040	−	0.507213i	0.0256347	−	0.0218879i
$538$		0			0
$539$	−3.04200	−	11.3529i	−0.131028	−	0.489003i
$540$		0			0
$541$	5.28291	−	5.28291i	0.227130	−	0.227130i	−0.584363	−	0.811493i	$-0.698655\pi$
$541$	5.28291	−	5.28291i	0.227130	−	0.227130i	0.811493	+	0.584363i	$0.198655\pi$
$542$		0			0
$543$	0.975516	−	0.180659i	0.0418634	−	0.00775281i
$544$		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
$549$	−0.627870	+	3.95698i	−0.0267968	+	0.168880i
$550$		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
$555$	20.9296	+	24.5124i	0.888411	+	1.04049i
$556$		0			0
$557$	1.77202	−	6.61326i	0.0750828	−	0.280213i	−0.918169	−	0.396188i	$-0.870333\pi$
$557$	1.77202	−	6.61326i	0.0750828	−	0.280213i	0.993252	+	0.115975i	$0.0369994\pi$
$558$		0			0
$559$	0.592223	+	1.63091i	0.0250484	+	0.0689803i
$560$		0			0
$561$	−15.7092	+	22.8502i	−0.663244	+	0.964734i
$562$		0			0
$563$	−9.52928	+	16.5052i	−0.401611	+	0.695611i	−0.993921	−	0.110099i	$-0.964883\pi$
$563$	−9.52928	+	16.5052i	−0.401611	+	0.695611i	0.592309	+	0.805711i	$0.298216\pi$
$564$		0			0
$565$	−41.2227	+	11.0456i	−1.73425	+	0.464692i
$566$		0			0
$567$	16.7544	+	10.8939i	0.703617	+	0.457499i
$568$		0			0
$569$	3.18974	+	5.52479i	0.133721	+	0.231611i	0.925108	−	0.379704i	$-0.123974\pi$
$569$	3.18974	+	5.52479i	0.133721	+	0.231611i	−0.791387	+	0.611315i	$0.790641\pi$
$570$		0			0
$571$		−	4.64342i		−	0.194321i	−0.995269	−	0.0971605i	$-0.969024\pi$
$571$		−	4.64342i		−	0.194321i	0.995269	−	0.0971605i	$-0.0309760\pi$
$572$		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	0.280233	−	0.959932i	$-0.409588\pi$
$577$	−16.3269	−	16.3269i	−0.679699	−	0.679699i	−0.959932	+	0.280233i	$0.909588\pi$
$578$		0			0
$579$	−1.96878	+	24.9706i	−0.0818195	+	1.03774i
$580$		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
$585$	23.7447	−	11.5508i	0.981724	−	0.477568i
$586$		0			0
$587$	17.6852	+	4.73874i	0.729948	+	0.195589i	0.604606	−	0.796525i	$-0.293331\pi$
$587$	17.6852	+	4.73874i	0.729948	+	0.195589i	0.125342	+	0.992114i	$0.459997\pi$
$588$		0			0
$589$	−31.2353	−	18.0337i	−1.28703	−	0.743066i
$590$		0			0
$591$	−0.876924	+	11.1223i	−0.0360718	+	0.457510i
$592$		0			0
$593$	11.8285	+	11.8285i	0.485739	+	0.485739i	0.906959	−	0.421220i	$-0.138398\pi$
$593$	11.8285	+	11.8285i	0.485739	+	0.485739i	−0.421220	+	0.906959i	$0.638398\pi$
$594$		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	0.821185	−	0.570662i	$-0.193313\pi$
$601$	−2.04984	−	3.55043i	−0.0836147	−	0.144825i	−0.904800	+	0.425837i	$0.859980\pi$
$602$		0			0
$603$	0.806729	+	7.69642i	0.0328525	+	0.313422i
$604$		0			0
$605$	50.1311	−	13.4326i	2.03812	−	0.546112i
$606$		0			0
$607$	−4.15357	+	7.19419i	−0.168588	+	0.292003i	−0.937924	−	0.346842i	$-0.887254\pi$
$607$	−4.15357	+	7.19419i	−0.168588	+	0.292003i	0.769336	+	0.638845i	$0.220587\pi$
$608$		0			0
$609$	4.92464	−	7.16323i	0.199556	−	0.290269i
$610$		0			0
$611$	−4.22084	−	48.6635i	−0.170757	−	1.96872i
$612$		0			0
$613$	−1.42881	+	5.33239i	−0.0577091	+	0.215373i	−0.988759	−	0.149519i	$-0.952227\pi$
$613$	−1.42881	+	5.33239i	−0.0577091	+	0.215373i	0.931050	+	0.364892i	$0.118894\pi$
$614$		0			0
$615$	19.9784	+	23.3984i	0.805606	+	0.943513i
$616$		0			0
$617$	−6.17063	−	23.0291i	−0.248420	−	0.927117i	−0.971633	−	0.236492i	$-0.924002\pi$
$617$	−6.17063	−	23.0291i	−0.248420	−	0.927117i	0.723213	−	0.690625i	$-0.242664\pi$
$618$		0			0
$619$	−19.4317	+	19.4317i	−0.781028	+	0.781028i	−0.980004	−	0.198976i	$-0.936238\pi$
$619$	−19.4317	+	19.4317i	−0.781028	+	0.781028i	0.198976	+	0.980004i	$0.436238\pi$
$620$		0			0
$621$	−9.15690	+	16.8479i	−0.367454	+	0.676083i
$622$		0			0
$623$	−18.6182			−0.745923
$624$		0			0
$625$	28.8762			1.15505
$626$		0			0
$627$	−78.6970	+	14.5741i	−3.14285	+	0.582035i
$628$		0			0
$629$	15.1935	−	15.1935i	0.605806	−	0.605806i
$630$		0			0
$631$	3.00162	+	11.2022i	0.119493	+	0.445953i	0.999584	−	0.0288524i	$-0.00918527\pi$
$631$	3.00162	+	11.2022i	0.119493	+	0.445953i	−0.880091	+	0.474805i	$0.842519\pi$
$632$		0			0
$633$	−30.3608	+	25.9231i	−1.20673	+	1.03035i
$634$		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
$639$	−12.3522	−	17.0115i	−0.488646	−	0.672964i
$640$		0			0
$641$	9.29977	−	16.1077i	0.367319	−	0.636215i	−0.621826	−	0.783155i	$-0.713609\pi$
$641$	9.29977	−	16.1077i	0.367319	−	0.636215i	0.989145	+	0.146940i	$0.0469424\pi$
$642$		0			0
$643$	−28.9091	+	7.74616i	−1.14006	+	0.305479i	−0.778976	−	0.627054i	$-0.784261\pi$
$643$	−28.9091	+	7.74616i	−1.14006	+	0.305479i	−0.361086	+	0.932532i	$0.617594\pi$
$644$		0			0
$645$	0.875726	+	1.83667i	0.0344817	+	0.0723186i
$646$		0			0
$647$	10.6735	+	18.4871i	0.419619	+	0.726802i	0.995901	−	0.0904492i	$-0.0288303\pi$
$647$	10.6735	+	18.4871i	0.419619	+	0.726802i	−0.576282	+	0.817251i	$0.695497\pi$
$648$		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	$-0.530704\pi$
$653$	18.3357	−	10.5861i	0.717533	−	0.414268i	0.813844	+	0.581084i	$0.197371\pi$
$654$		0			0
$655$	−12.3936	−	12.3936i	−0.484256	−	0.484256i
$656$		0			0
$657$	11.6561	−	26.1602i	0.454748	−	1.02061i
$658$		0			0
$659$	30.9228	+	17.8533i	1.20458	+	0.695464i	0.961570	−	0.274559i	$-0.0885320\pi$
$659$	30.9228	+	17.8533i	1.20458	+	0.695464i	0.243010	+	0.970024i	$0.421865\pi$
$660$		0			0
$661$	−17.7357	−	4.75228i	−0.689840	−	0.184842i	−0.103165	−	0.994664i	$-0.532897\pi$
$661$	−17.7357	−	4.75228i	−0.689840	−	0.184842i	−0.586675	+	0.809822i	$0.699564\pi$
$662$		0			0
$663$	−8.92049	−	15.1748i	−0.346443	−	0.589341i
$664$		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
$669$	22.3688	+	1.76364i	0.864826	+	0.0681861i
$670$		0			0
$671$	−5.36366	−	5.36366i	−0.207062	−	0.207062i
$672$		0			0
$673$	−25.8577	+	14.9289i	−0.996740	+	0.575468i	−0.907282	−	0.420522i	$-0.861847\pi$
$673$	−25.8577	+	14.9289i	−0.996740	+	0.575468i	−0.0894579	+	0.995991i	$0.528513\pi$
$674$		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
$681$	15.8287	−	7.54715i	0.606556	−	0.289207i
$682$		0			0
$683$	−33.6457	+	9.01534i	−1.28742	+	0.344962i	−0.836679	−	0.547694i	$-0.815506\pi$
$683$	−33.6457	+	9.01534i	−1.28742	+	0.344962i	−0.450738	+	0.892656i	$0.648839\pi$
$684$		0			0
$685$	14.6838	−	25.4330i	0.561038	−	0.971746i
$686$		0			0
$687$	−12.1959	−	8.38457i	−0.465304	−	0.319891i
$688$		0			0
$689$	−1.43146	+	1.70336i	−0.0545343	+	0.0648929i
$690$		0			0
$691$	7.05147	−	26.3164i	0.268250	−	1.00112i	−0.691980	−	0.721916i	$-0.743262\pi$
$691$	7.05147	−	26.3164i	0.268250	−	1.00112i	0.960231	−	0.279208i	$-0.0900718\pi$
$692$		0			0
$693$	−35.3270	+	13.5493i	−1.34196	+	0.514696i
$694$		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
$699$	3.00332	+	16.2172i	0.113596	+	0.613393i
$700$		0			0
$701$	−7.80915			−0.294948			−0.147474	−	0.989066i	$-0.547114\pi$
$701$	−7.80915			−0.294948			−0.147474	+	0.989066i	$0.547114\pi$
$702$		0			0
$703$	62.0179			2.33905
$704$		0			0
$705$	−10.4308	−	56.3241i	−0.392848	−	2.12129i
$706$		0			0
$707$	2.11262	−	2.11262i	0.0794534	−	0.0794534i
$708$		0			0
$709$	8.07769	+	30.1463i	0.303364	+	1.13217i	0.934345	+	0.356371i	$0.115986\pi$
$709$	8.07769	+	30.1463i	0.303364	+	1.13217i	−0.630981	+	0.775799i	$0.717347\pi$
$710$		0			0
$711$	−1.04372	+	0.400307i	−0.0391424	+	0.0150127i
$712$		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
$717$	−0.700411	−	0.481525i	−0.0261573	−	0.0179829i
$718$		0			0
$719$	−2.01546	+	3.49089i	−0.0751641	+	0.130188i	−0.901158	−	0.433492i	$-0.857281\pi$
$719$	−2.01546	+	3.49089i	−0.0751641	+	0.130188i	0.825993	+	0.563680i	$0.190615\pi$
$720$		0			0
$721$	−21.5599	+	5.77695i	−0.802932	+	0.215145i
$722$		0			0
$723$	−41.3238	+	19.7033i	−1.53685	+	0.732773i
$724$		0			0
$725$	−1.08406	−	1.87765i	−0.0402611	−	0.0697342i
$726$		0			0
$727$		−	26.5507i		−	0.984711i	−0.870394	−	0.492356i	$-0.836136\pi$
$727$		−	26.5507i		−	0.984711i	0.870394	−	0.492356i	$-0.163864\pi$
$728$		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	0.934909	−	0.354888i	$-0.115481\pi$
$733$	15.7035	+	15.7035i	0.580021	+	0.580021i	−0.354888	+	0.934909i	$0.615481\pi$
$734$		0			0
$735$	8.72249	+	0.687714i	0.321734	+	0.0253667i
$736$		0			0
$737$	−12.6883	−	7.32561i	−0.467380	−	0.269842i
$738$		0			0
$739$	6.55841	+	1.75732i	0.241255	+	0.0646441i	0.377420	−	0.926042i	$-0.376811\pi$
$739$	6.55841	+	1.75732i	0.241255	+	0.0646441i	−0.136165	+	0.990686i	$0.543478\pi$
$740$		0			0
$741$	12.7646	−	49.1768i	0.468921	−	1.80656i
$742$		0			0
$743$	−40.6931	−	10.9037i	−1.49288	−	0.400017i	−0.582174	−	0.813064i	$-0.697798\pi$
$743$	−40.6931	−	10.9037i	−1.49288	−	0.400017i	−0.910709	+	0.413047i	$0.864464\pi$
$744$		0			0
$745$	41.2418	+	23.8110i	1.51098	+	0.872366i
$746$		0			0
$747$	8.61851	−	19.3428i	0.315335	−	0.707716i
$748$		0			0
$749$	23.4573	+	23.4573i	0.857112	+	0.857112i
$750$		0			0
$751$	31.3813	−	18.1180i	1.14512	−	0.661135i	0.197426	−	0.980318i	$-0.436742\pi$
$751$	31.3813	−	18.1180i	1.14512	−	0.661135i	0.947693	+	0.319183i	$0.103408\pi$
$752$		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	0.802470	−	0.596692i	$-0.203519\pi$
$757$	−3.17824	−	5.50487i	−0.115515	−	0.200078i	−0.917986	+	0.396614i	$0.870185\pi$
$758$		0			0
$759$	−15.6248	−	32.7700i	−0.567145	−	1.18948i
$760$		0			0
$761$	21.0411	−	5.63796i	0.762741	−	0.204376i	0.143579	−	0.989639i	$-0.454139\pi$
$761$	21.0411	−	5.63796i	0.762741	−	0.204376i	0.619162	+	0.785263i	$0.287472\pi$
$762$		0			0
$763$	9.36791	−	16.2257i	0.339141	−	0.587410i
$764$		0			0
$765$	−12.1286	−	16.7035i	−0.438511	−	0.603917i
$766$		0			0
$767$	−6.58512	−	3.07669i	−0.237775	−	0.111093i
$768$		0			0
$769$	−3.69721	+	13.7982i	−0.133325	+	0.497575i	−0.999999	−	0.00129915i	$-0.999586\pi$
$769$	−3.69721	+	13.7982i	−0.133325	+	0.497575i	0.866674	+	0.498874i	$0.166253\pi$
$770$		0			0
$771$	3.29255	−	2.81130i	0.118578	−	0.101246i
$772$		0			0
$773$	2.17937	+	8.13353i	0.0783866	+	0.292543i	0.993980	−	0.109563i	$-0.0349451\pi$
$773$	2.17937	+	8.13353i	0.0783866	+	0.292543i	−0.915593	+	0.402106i	$0.868278\pi$
$774$		0			0
$775$	−3.00714	+	3.00714i	−0.108020	+	0.108020i
$776$		0			0
$777$	28.8285	−	5.33883i	1.03422	−	0.191530i
$778$		0			0
$779$	59.1994			2.12104
$780$		0			0
$781$	39.8022			1.42424
$782$		0			0
$783$	10.3187	+	5.60824i	0.368759	+	0.200422i
$784$		0			0
$785$	−29.3975	+	29.3975i	−1.04924	+	1.04924i
$786$		0			0
$787$	−8.57267	−	31.9936i	−0.305583	−	1.14045i	−0.932443	−	0.361318i	$-0.882327\pi$
$787$	−8.57267	−	31.9936i	−0.305583	−	1.14045i	0.626860	−	0.779132i	$-0.284340\pi$
$788$		0			0
$789$	−10.8068	−	12.6567i	−0.384731	−	0.450591i
$790$		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
$795$	−1.47818	+	2.15012i	−0.0524257	+	0.0762568i
$796$		0			0
$797$	−27.4840	+	47.6037i	−0.973534	+	1.68621i	−0.288843	+	0.957376i	$0.593271\pi$
$797$	−27.4840	+	47.6037i	−0.973534	+	1.68621i	−0.684691	+	0.728834i	$0.740063\pi$
$798$		0			0
$799$	−36.8847	+	9.88323i	−1.30489	+	0.349644i
$800$		0			0
$801$	−2.62224	−	25.0169i	−0.0926523	−	0.883928i
$802$		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	$-0.476488\pi$
$809$	27.7137	−	16.0005i	0.974361	−	0.562547i	0.900563	+	0.434726i	$0.143155\pi$
$810$		0			0
$811$	34.5566	+	34.5566i	1.21344	+	1.21344i	0.969886	+	0.243559i	$0.0783148\pi$
$811$	34.5566	+	34.5566i	1.21344	+	1.21344i	0.243559	+	0.969886i	$0.421685\pi$
$812$		0			0
$813$	−4.26824	+	54.1355i	−0.149694	+	1.89861i
$814$		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
$819$	1.70013	−	23.9583i	0.0594073	−	0.837169i
$820$		0			0
$821$	6.31469	+	1.69202i	0.220384	+	0.0590518i	0.367321	−	0.930094i	$-0.380275\pi$
$821$	6.31469	+	1.69202i	0.220384	+	0.0590518i	−0.146937	+	0.989146i	$0.546942\pi$
$822$		0			0
$823$	9.88316	+	5.70605i	0.344505	+	0.198900i	0.662263	−	0.749272i	$-0.269596\pi$
$823$	9.88316	+	5.70605i	0.344505	+	0.198900i	−0.317757	+	0.948172i	$0.602930\pi$
$824$		0			0
$825$	−0.741748	+	9.40782i	−0.0258243	+	0.327538i
$826$		0			0
$827$	−16.1511	−	16.1511i	−0.561628	−	0.561628i	0.368142	−	0.929770i	$-0.379994\pi$
$827$	−16.1511	−	16.1511i	−0.561628	−	0.561628i	−0.929770	+	0.368142i	$0.879994\pi$
$828$		0			0
$829$	10.4973	−	6.06059i	0.364585	−	0.210493i	−0.306505	−	0.951869i	$-0.599160\pi$
$829$	10.4973	−	6.06059i	0.364585	−	0.210493i	0.671090	+	0.741376i	$0.265826\pi$
$830$		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
$837$	5.38717	−	22.3974i	0.186208	−	0.774168i
$838$		0			0
$839$	−32.4519	+	8.69547i	−1.12036	+	0.300201i	−0.771031	−	0.636798i	$-0.780259\pi$
$839$	−32.4519	+	8.69547i	−1.12036	+	0.300201i	−0.349334	+	0.936998i	$0.613592\pi$
$840$		0			0
$841$	−11.9458	+	20.6907i	−0.411924	+	0.713473i
$842$		0			0
$843$	7.66274	−	11.1460i	0.263919	−	0.383888i
$844$		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
$849$	11.5811	+	13.5636i	0.397464	+	0.465503i
$850$		0			0
$851$	7.28102	+	27.1731i	0.249590	+	0.931483i
$852$		0			0
$853$	14.0421	−	14.0421i	0.480792	−	0.480792i	−0.424592	−	0.905385i	$-0.639583\pi$
$853$	14.0421	−	14.0421i	0.480792	−	0.480792i	0.905385	+	0.424592i	$0.139583\pi$
$854$		0			0
$855$	9.33706	−	58.8444i	0.319321	−	2.01243i
$856$		0			0
$857$	−29.0059			−0.990824			−0.495412	−	0.868658i	$-0.664983\pi$
$857$	−29.0059			−0.990824			−0.495412	+	0.868658i	$0.664983\pi$
$858$		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
$861$	27.5183	−	5.09620i	0.937821	−	0.173678i
$862$		0			0
$863$	21.8394	−	21.8394i	0.743422	−	0.743422i	−0.229813	−	0.973235i	$-0.573811\pi$
$863$	21.8394	−	21.8394i	0.743422	−	0.743422i	0.973235	+	0.229813i	$0.0738115\pi$
$864$		0			0
$865$	−8.41108	−	31.3906i	−0.285985	−	1.06731i
$866$		0			0
$867$	11.9276	−	10.1842i	0.405082	−	0.345874i
$868$		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
$873$	−7.63223	+	5.54185i	−0.258312	+	0.187563i
$874$		0			0
$875$	10.9516	−	18.9688i	0.370233	−	0.641263i
$876$		0			0
$877$	51.5387	−	13.8098i	1.74034	−	0.466322i	0.757816	−	0.652468i	$-0.226266\pi$
$877$	51.5387	−	13.8098i	1.74034	−	0.466322i	0.982522	+	0.186146i	$0.0595996\pi$
$878$		0			0
$879$	−21.0564	−	44.1616i	−0.710214	−	1.48954i
$880$		0			0
$881$	−23.5586	−	40.8048i	−0.793711	−	1.37475i	−0.923654	−	0.383226i	$-0.874813\pi$
$881$	−23.5586	−	40.8048i	−0.793711	−	1.37475i	0.129943	−	0.991521i	$-0.458520\pi$
$882$		0			0
$883$			21.4475i			0.721765i	0.932611	+	0.360882i	$0.117524\pi$
$883$			21.4475i			0.721765i	−0.932611	+	0.360882i	$0.882476\pi$
$884$		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	$-0.528494\pi$
$887$	21.6954	−	12.5259i	0.728461	−	0.420577i	0.817859	+	0.575419i	$0.195161\pi$
$888$		0			0
$889$	1.93481	+	1.93481i	0.0648914	+	0.0648914i
$890$		0			0
$891$	−23.1815	−	45.5598i	−0.776609	−	1.52631i
$892$		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
$897$	23.0454	−	0.180626i	0.769463	−	0.00603092i
$898$		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
$903$	1.84511	+	0.145476i	0.0614016	+	0.00484113i
$904$		0			0
$905$	−0.988730	−	0.988730i	−0.0328665	−	0.0328665i
$906$		0			0
$907$	−24.8693	+	14.3583i	−0.825772	+	0.476760i	−0.852403	−	0.522886i	$-0.824856\pi$
$907$	−24.8693	+	14.3583i	−0.825772	+	0.476760i	0.0266307	+	0.999645i	$0.491522\pi$
$908$		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
$915$	5.09703	−	2.43028i	0.168503	−	0.0803424i
$916$		0			0
$917$	−15.3997	+	4.12633i	−0.508542	+	0.136263i
$918$		0			0
$919$	5.08612	−	8.80943i	0.167776	−	0.290596i	−0.769862	−	0.638211i	$-0.779675\pi$
$919$	5.08612	−	8.80943i	0.167776	−	0.290596i	0.937638	+	0.347615i	$0.113008\pi$
$920$		0			0
$921$	−0.145745	−	0.100198i	−0.00480248	−	0.00330165i
$922$		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
$927$	−10.7989	−	28.1559i	−0.354683	−	0.924761i
$928$		0			0
$929$	6.27665	+	23.4248i	0.205930	+	0.768542i	0.989164	+	0.146815i	$0.0469022\pi$
$929$	6.27665	+	23.4248i	0.205930	+	0.768542i	−0.783234	+	0.621727i	$0.786431\pi$
$930$		0			0
$931$	11.9042	−	11.9042i	0.390145	−	0.390145i
$932$		0			0
$933$	6.31309	+	34.0892i	0.206681	+	1.11603i
$934$		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
$939$	−0.197661	−	1.06732i	−0.00645042	−	0.0348308i
$940$		0			0
$941$	−0.888058	+	0.888058i	−0.0289499	+	0.0289499i	−0.721434	−	0.692484i	$-0.756516\pi$
$941$	−0.888058	+	0.888058i	−0.0289499	+	0.0289499i	0.692484	+	0.721434i	$0.256516\pi$
$942$		0			0
$943$	6.95011	+	25.9382i	0.226327	+	0.844663i
$944$		0			0
$945$	−0.725386	−	28.1571i	−0.0235968	−	0.915949i
$946$		0			0
$947$	−0.622237	+	2.32222i	−0.0202200	+	0.0754620i	−0.975299	−	0.220891i	$-0.929104\pi$
$947$	−0.622237	+	2.32222i	−0.0202200	+	0.0754620i	0.955079	+	0.296352i	$0.0957703\pi$
$948$		0			0
$949$	−34.2916	+	2.97429i	−1.11315	+	0.0965496i
$950$		0			0
$951$	29.1655	+	20.0510i	0.945757	+	0.650198i
$952$		0			0
$953$	−6.06072	+	10.4975i	−0.196326	+	0.340046i	−0.947334	−	0.320246i	$-0.896234\pi$
$953$	−6.06072	+	10.4975i	−0.196326	+	0.340046i	0.751008	+	0.660293i	$0.229568\pi$
$954$		0			0
$955$	21.4525	−	5.74819i	0.694188	−	0.186007i
$956$		0			0
$957$	−20.0703	+	9.56959i	−0.648782	+	0.309341i
$958$		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	0.858013	−	0.513628i	$-0.171699\pi$
$967$	10.7092	+	10.7092i	0.344386	+	0.344386i	−0.513628	+	0.858013i	$0.671699\pi$
$968$		0			0
$969$	−39.5954	−	3.12185i	−1.27199	−	0.100288i
$970$		0			0
$971$	−10.1662	−	5.86945i	−0.326248	−	0.188360i	0.327926	−	0.944703i	$-0.393650\pi$
$971$	−10.1662	−	5.86945i	−0.326248	−	0.188360i	−0.654174	+	0.756344i	$0.726984\pi$
$972$		0			0
$973$	−4.99516	−	1.33845i	−0.160137	−	0.0429087i
$974$		0			0
$975$	−5.21136	−	2.95456i	−0.166897	−	0.0946218i
$976$		0			0
$977$	−16.0380	−	4.29736i	−0.513100	−	0.137485i	−0.00702677	−	0.999975i	$-0.502237\pi$
$977$	−16.0380	−	4.29736i	−0.513100	−	0.137485i	−0.506073	+	0.862491i	$0.668903\pi$
$978$		0			0
$979$	41.2429	+	23.8116i	1.31813	+	0.761021i
$980$		0			0
$981$	23.1215	+	10.3022i	0.738214	+	0.328924i
$982$		0			0
$983$	25.9952	+	25.9952i	0.829118	+	0.829118i	0.987395	−	0.158277i	$-0.0505938\pi$
$983$	25.9952	+	25.9952i	0.829118	+	0.829118i	−0.158277	+	0.987395i	$0.550594\pi$
$984$		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	0.991811	−	0.127712i	$-0.0407634\pi$
$991$	12.1294	+	21.0088i	0.385304	+	0.667366i	−0.606508	+	0.795078i	$0.707430\pi$
$992$		0			0
$993$	−6.98771	−	14.6554i	−0.221748	−	0.465074i
$994$		0			0
$995$	−1.86047	+	0.498512i	−0.0589809	+	0.0158039i
$996$		0			0
$997$	−27.5907	+	47.7884i	−0.873805	+	1.51347i	−0.0157748	+	0.999876i	$0.505021\pi$
$997$	−27.5907	+	47.7884i	−0.873805	+	1.51347i	−0.858030	+	0.513599i	$0.828312\pi$
$998$		0			0
$999$	11.2340	+	37.9843i	0.355427	+	1.20177i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bp.a.89.9	✓	56	4.3	odd	2
312.2.bp.a.89.11	yes	56	12.11	even	2
312.2.bp.a.305.9	yes	56	156.71	odd	12
312.2.bp.a.305.11	yes	56	52.19	even	12
624.2.cn.f.305.4		56	13.6	odd	12	inner
624.2.cn.f.305.6		56	39.32	even	12	inner
624.2.cn.f.401.4		56	3.2	odd	2	inner
624.2.cn.f.401.6		56	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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.cn (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.315401 - 1.70309i) q^{3} +(-1.72616 + 1.72616i) q^{5} +(0.574711 + 2.14485i) q^{7} +(-2.80104 + 1.07431i) q^{9} +O(q^{10})\)	\(q+(-0.315401 - 1.70309i) q^{3} +(-1.72616 + 1.72616i) q^{5} +(0.574711 + 2.14485i) q^{7} +(-2.80104 + 1.07431i) q^{9} +(1.47004 - 5.48627i) q^{11} +(2.76028 + 2.31967i) q^{13} +(3.48425 + 2.39538i) q^{15} +(1.40933 - 2.44104i) q^{17} +(7.85833 - 2.10563i) q^{19} +(3.47161 - 1.65527i) q^{21} +(1.84516 + 3.19592i) q^{23} -0.959270i q^{25} +(2.71311 + 4.43160i) q^{27} +(1.95737 - 1.13009i) q^{29} +(-3.13483 - 3.13483i) q^{31} +(-9.80727 - 0.773242i) q^{33} +(-4.69440 - 2.71031i) q^{35} +(7.36333 + 1.97300i) q^{37} +(3.08001 - 5.43263i) q^{39} +(7.02869 + 1.88333i) q^{41} +(0.416760 + 0.240616i) q^{43} +(2.98062 - 6.68949i) q^{45} +(-9.57953 - 9.57953i) q^{47} +(1.79209 - 1.03466i) q^{49} +(-4.60181 - 1.63032i) q^{51} +0.617097i q^{53} +(6.93266 + 12.0077i) q^{55} +(-6.06461 - 12.7193i) q^{57} +(-1.94720 + 0.521752i) q^{59} +(0.667748 - 1.15657i) q^{61} +(-3.91403 - 5.39040i) q^{63} +(-8.76881 + 0.760564i) q^{65} +(0.667631 - 2.49163i) q^{67} +(4.86098 - 4.15048i) q^{69} +(1.81372 + 6.76890i) q^{71} +(-6.75039 + 6.75039i) q^{73} +(-1.63372 + 0.302554i) q^{75} +12.6121 q^{77} +0.372617 q^{79} +(6.69170 - 6.01840i) q^{81} +(-4.99123 + 4.99123i) q^{83} +(1.78089 + 6.64636i) q^{85} +(-2.54201 - 2.97716i) q^{87} +(-2.17011 + 8.09895i) q^{89} +(-3.38898 + 7.25352i) q^{91} +(-4.35017 + 6.32762i) q^{93} +(-9.93009 + 17.1994i) q^{95} +(3.03688 - 0.813729i) q^{97} +(1.77632 + 16.9466i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{7}+O(q^{10}) \) 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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