LMFDB - Embedded newform 572.2.bh.a.57.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(57,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 2, 15]))

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

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

chi := DirichletCharacter("572.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bh (of order $20$, degree $8$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			57.8
Character	$\chi$	$=$	572.57
Dual form			572.2.bh.a.281.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.308779 - 0.224341i) q^{3} +(-3.55885 - 1.81333i) q^{5} +(-0.0145346 + 0.00230205i) q^{7} +(-0.882035 + 2.71463i) q^{9} +O(q^{10})$	\(q+(0.308779 - 0.224341i) q^{3} +(-3.55885 - 1.81333i) q^{5} +(-0.0145346 + 0.00230205i) q^{7} +(-0.882035 + 2.71463i) q^{9} +(-0.687132 + 3.24466i) q^{11} +(3.54014 + 0.683652i) q^{13} +(-1.50570 + 0.238480i) q^{15} +(1.45902 + 4.49041i) q^{17} +(-1.43800 - 0.227757i) q^{19} +(-0.00397154 + 0.00397154i) q^{21} +2.42920i q^{23} +(6.43836 + 8.86164i) q^{25} +(0.690478 + 2.12507i) q^{27} +(3.47408 - 4.78166i) q^{29} +(3.68056 + 7.22351i) q^{31} +(0.515740 + 1.15604i) q^{33} +(0.0559009 + 0.0181633i) q^{35} +(-0.308366 - 1.94695i) q^{37} +(1.24649 - 0.583103i) q^{39} +(-8.57953 - 1.35886i) q^{41} +1.10055 q^{43} +(8.06154 - 8.06154i) q^{45} +(-12.8939 - 2.04219i) q^{47} +(-6.65719 + 2.16305i) q^{49} +(1.45790 + 1.05923i) q^{51} +(-1.53644 + 4.72869i) q^{53} +(8.32904 - 10.3013i) q^{55} +(-0.495119 + 0.252276i) q^{57} +(1.16027 + 7.32567i) q^{59} +(-11.7635 + 3.82219i) q^{61} +(0.00657082 - 0.0414865i) q^{63} +(-11.3592 - 8.85246i) q^{65} +(8.72172 - 8.72172i) q^{67} +(0.544970 + 0.750086i) q^{69} +(2.40010 + 1.22291i) q^{71} +(-2.22327 + 0.352131i) q^{73} +(3.97606 + 1.29190i) q^{75} +(0.00251779 - 0.0487417i) q^{77} +(11.8112 + 3.83770i) q^{79} +(-6.23765 - 4.53192i) q^{81} +(-3.62220 + 7.10898i) q^{83} +(2.95013 - 18.6264i) q^{85} -2.25586i q^{87} +(-4.80029 - 4.80029i) q^{89} +(-0.0530284 - 0.00178700i) q^{91} +(2.75701 + 1.40477i) q^{93} +(4.70463 + 3.41812i) q^{95} +(2.70210 + 5.30317i) q^{97} +(-8.20198 - 4.72722i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 28 q^{9}+O(q^{10}) $ 112 * q - 28 * q^9	$ 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) $ 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.308779	−	0.224341i	0.178274	−	0.129523i	−0.495070	−	0.868853i	$-0.664858\pi$
$3$	0.308779	−	0.224341i	0.178274	−	0.129523i	0.673344	+	0.739330i	$0.264858\pi$
$4$		0			0
$5$	−3.55885	−	1.81333i	−1.59157	−	0.810944i	−0.999989	−	0.00469719i	$-0.998505\pi$
$5$	−3.55885	−	1.81333i	−1.59157	−	0.810944i	−0.591579	−	0.806247i	$-0.701495\pi$
$6$		0			0
$7$	−0.0145346	+	0.00230205i	−0.00549356	+	0.000870095i	−0.159181	−	0.987249i	$-0.550885\pi$
$7$	−0.0145346	+	0.00230205i	−0.00549356	+	0.000870095i	0.153687	+	0.988120i	$0.450885\pi$
$8$		0			0
$9$	−0.882035	+	2.71463i	−0.294012	+	0.904875i
$10$		0			0
$11$	−0.687132	+	3.24466i	−0.207178	+	0.978303i
$11$	−0.687132	+	3.24466i	−0.207178	+	0.978303i
$12$		0			0
$13$	3.54014	+	0.683652i	0.981859	+	0.189611i
$13$	3.54014	+	0.683652i	0.981859	+	0.189611i
$14$		0			0
$15$	−1.50570	+	0.238480i	−0.388771	+	0.0615753i
$16$		0			0
$17$	1.45902	+	4.49041i	0.353865	+	1.08908i	0.956665	+	0.291192i	$0.0940519\pi$
$17$	1.45902	+	4.49041i	0.353865	+	1.08908i	−0.602800	+	0.797893i	$0.705948\pi$
$18$		0			0
$19$	−1.43800	−	0.227757i	−0.329900	−	0.0522510i	−0.0107124	−	0.999943i	$-0.503410\pi$
$19$	−1.43800	−	0.227757i	−0.329900	−	0.0522510i	−0.319187	+	0.947692i	$0.603410\pi$
$20$		0			0
$21$	−0.00397154	+	0.00397154i	−0.000866660	+	0.000866660i
$22$		0			0
$23$			2.42920i			0.506523i	0.967398	+	0.253262i	$0.0815033\pi$
$23$			2.42920i			0.506523i	−0.967398	+	0.253262i	$0.918497\pi$
$24$		0			0
$25$	6.43836	+	8.86164i	1.28767	+	1.77233i
$26$		0			0
$27$	0.690478	+	2.12507i	0.132882	+	0.408970i
$28$		0			0
$29$	3.47408	−	4.78166i	0.645120	−	0.887932i	−0.353756	−	0.935338i	$-0.615096\pi$
$29$	3.47408	−	4.78166i	0.645120	−	0.887932i	0.998876	+	0.0474063i	$0.0150956\pi$
$30$		0			0
$31$	3.68056	+	7.22351i	0.661048	+	1.29738i	0.941338	+	0.337465i	$0.109569\pi$
$31$	3.68056	+	7.22351i	0.661048	+	1.29738i	−0.280290	+	0.959915i	$0.590431\pi$
$32$		0			0
$33$	0.515740	+	1.15604i	0.0897788	+	0.201240i
$34$		0			0
$35$	0.0559009	+	0.0181633i	0.00944898	+	0.00307016i
$36$		0			0
$37$	−0.308366	−	1.94695i	−0.0506951	−	0.320076i	−0.999984	−	0.00567101i	$-0.998195\pi$
$37$	−0.308366	−	1.94695i	−0.0506951	−	0.320076i	0.949289	−	0.314405i	$-0.101805\pi$
$38$		0			0
$39$	1.24649	−	0.583103i	0.199599	−	0.0933712i
$40$		0			0
$41$	−8.57953	−	1.35886i	−1.33990	−	0.212219i	−0.555003	−	0.831849i	$-0.687283\pi$
$41$	−8.57953	−	1.35886i	−1.33990	−	0.212219i	−0.784894	+	0.619630i	$0.787283\pi$
$42$		0			0
$43$	1.10055			0.167832			0.0839162	−	0.996473i	$-0.473257\pi$
$43$	1.10055			0.167832			0.0839162	+	0.996473i	$0.473257\pi$
$44$		0			0
$45$	8.06154	−	8.06154i	1.20174	−	1.20174i
$46$		0			0
$47$	−12.8939	−	2.04219i	−1.88077	−	0.297884i	−0.892551	−	0.450947i	$-0.851086\pi$
$47$	−12.8939	−	2.04219i	−1.88077	−	0.297884i	−0.988217	+	0.153062i	$0.951086\pi$
$48$		0			0
$49$	−6.65719	+	2.16305i	−0.951027	+	0.309007i
$50$		0			0
$51$	1.45790	+	1.05923i	0.204147	+	0.148321i
$52$		0			0
$53$	−1.53644	+	4.72869i	−0.211047	+	0.649535i	0.788364	+	0.615209i	$0.210928\pi$
$53$	−1.53644	+	4.72869i	−0.211047	+	0.649535i	−0.999411	+	0.0343261i	$0.989072\pi$
$54$		0			0
$55$	8.32904	−	10.3013i	1.12309	−	1.38903i
$56$		0			0
$57$	−0.495119	+	0.252276i	−0.0655802	+	0.0334148i
$58$		0			0
$59$	1.16027	+	7.32567i	0.151055	+	0.953721i	0.940474	+	0.339866i	$0.110382\pi$
$59$	1.16027	+	7.32567i	0.151055	+	0.953721i	−0.789419	+	0.613854i	$0.789618\pi$
$60$		0			0
$61$	−11.7635	+	3.82219i	−1.50616	+	0.489381i	−0.941807	−	0.336153i	$-0.890874\pi$
$61$	−11.7635	+	3.82219i	−1.50616	+	0.489381i	−0.564352	+	0.825534i	$0.690874\pi$
$62$		0			0
$63$	0.00657082	−	0.0414865i	0.000827845	−	0.00522681i
$64$		0			0
$65$	−11.3592	−	8.85246i	−1.40893	−	1.09801i
$66$		0			0
$67$	8.72172	−	8.72172i	1.06553	−	1.06553i	0.0678305	−	0.997697i	$-0.478392\pi$
$67$	8.72172	−	8.72172i	1.06553	−	1.06553i	0.997697	−	0.0678305i	$-0.0216077\pi$
$68$		0			0
$69$	0.544970	+	0.750086i	0.0656066	+	0.0902998i
$70$		0			0
$71$	2.40010	+	1.22291i	0.284839	+	0.145133i	0.590573	−	0.806984i	$-0.298902\pi$
$71$	2.40010	+	1.22291i	0.284839	+	0.145133i	−0.305734	+	0.952117i	$0.598902\pi$
$72$		0			0
$73$	−2.22327	+	0.352131i	−0.260214	+	0.0412138i	−0.285178	−	0.958475i	$-0.592053\pi$
$73$	−2.22327	+	0.352131i	−0.260214	+	0.0412138i	0.0249643	+	0.999688i	$0.492053\pi$
$74$		0			0
$75$	3.97606	+	1.29190i	0.459116	+	0.149176i
$76$		0			0
$77$	0.00251779	−	0.0487417i	0.000286929	−	0.00555464i
$78$		0			0
$79$	11.8112	+	3.83770i	1.32887	+	0.431775i	0.885531	−	0.464581i	$-0.153795\pi$
$79$	11.8112	+	3.83770i	1.32887	+	0.431775i	0.443336	+	0.896356i	$0.353795\pi$
$80$		0			0
$81$	−6.23765	−	4.53192i	−0.693072	−	0.503546i
$82$		0			0
$83$	−3.62220	+	7.10898i	−0.397589	+	0.780312i	−0.999838	−	0.0179964i	$-0.994271\pi$
$83$	−3.62220	+	7.10898i	−0.397589	+	0.780312i	0.602249	+	0.798308i	$0.294271\pi$
$84$		0			0
$85$	2.95013	−	18.6264i	0.319987	−	2.02032i
$86$		0			0
$87$		−	2.25586i		−	0.241853i
$88$		0			0
$89$	−4.80029	−	4.80029i	−0.508830	−	0.508830i	0.405337	−	0.914167i	$-0.367154\pi$
$89$	−4.80029	−	4.80029i	−0.508830	−	0.508830i	−0.914167	+	0.405337i	$0.867154\pi$
$90$		0			0
$91$	−0.0530284	−	0.00178700i	−0.00555889	−	0.000187329i
$92$		0			0
$93$	2.75701	+	1.40477i	0.285889	+	0.145668i
$94$		0			0
$95$	4.70463	+	3.41812i	0.482685	+	0.350691i
$96$		0			0
$97$	2.70210	+	5.30317i	0.274356	+	0.538455i	0.986536	−	0.163542i	$-0.0522920\pi$
$97$	2.70210	+	5.30317i	0.274356	+	0.538455i	−0.712180	+	0.701997i	$0.752292\pi$
$98$		0			0
$99$	−8.20198	−	4.72722i	−0.824330	−	0.475103i
$100$		0			0
$101$	0.00930531	−	0.0286388i	0.000925913	−	0.00284967i	−0.950592	−	0.310441i	$-0.899523\pi$
$101$	0.00930531	−	0.0286388i	0.000925913	−	0.00284967i	0.951518	+	0.307592i	$0.0995231\pi$
$102$		0			0
$103$	6.80792	−	9.37030i	0.670805	−	0.923283i	−0.328974	−	0.944339i	$-0.606703\pi$
$103$	6.80792	−	9.37030i	0.670805	−	0.923283i	0.999778	+	0.0210558i	$0.00670276\pi$
$104$		0			0
$105$	0.0213358	−	0.00693243i	0.00208216	−	0.000676535i
$106$		0			0
$107$	11.7870	+	16.2235i	1.13950	+	1.56838i	0.768630	+	0.639694i	$0.220939\pi$
$107$	11.7870	+	16.2235i	1.13950	+	1.56838i	0.370865	+	0.928687i	$0.379061\pi$
$108$		0			0
$109$	2.71902	+	2.71902i	0.260435	+	0.260435i	0.825231	−	0.564796i	$-0.191045\pi$
$109$	2.71902	+	2.71902i	0.260435	+	0.260435i	−0.564796	+	0.825231i	$0.691045\pi$
$110$		0			0
$111$	−0.531998	−	0.531998i	−0.0504950	−	0.0504950i
$112$		0			0
$113$	−1.90399	+	1.38333i	−0.179113	+	0.130133i	−0.673729	−	0.738978i	$-0.735309\pi$
$113$	−1.90399	+	1.38333i	−0.179113	+	0.130133i	0.494616	+	0.869111i	$0.335309\pi$
$114$		0			0
$115$	4.40493	−	8.64517i	0.410762	−	0.806166i
$116$		0			0
$117$	−4.97839	+	9.00716i	−0.460252	+	0.832712i
$118$		0			0
$119$	−0.0315435	−	0.0619076i	−0.00289159	−	0.00567506i
$120$		0			0
$121$	−10.0557	−	4.45903i	−0.914154	−	0.405366i
$122$		0			0
$123$	−2.95403	+	1.50515i	−0.266356	+	0.135715i
$124$		0			0
$125$	−3.71998	−	23.4870i	−0.332725	−	2.10075i
$126$		0			0
$127$	4.30701	+	13.2556i	0.382185	+	1.17624i	0.938502	+	0.345274i	$0.112214\pi$
$127$	4.30701	+	13.2556i	0.382185	+	1.17624i	−0.556317	+	0.830970i	$0.687786\pi$
$128$		0			0
$129$	0.339827	−	0.246899i	0.0299201	−	0.0217382i
$130$		0			0
$131$		−	2.49282i		−	0.217799i	−0.994053	−	0.108900i	$-0.965267\pi$
$131$		−	2.49282i		−	0.217799i	0.994053	−	0.108900i	$-0.0347327\pi$
$132$		0			0
$133$	0.0214251			0.00185779
$134$		0			0
$135$	1.39614	−	8.81488i	0.120161	−	0.758664i
$136$		0			0
$137$	1.06097	−	2.08226i	0.0906444	−	0.177900i	−0.841233	−	0.540672i	$-0.818170\pi$
$137$	1.06097	−	2.08226i	0.0906444	−	0.177900i	0.931878	+	0.362773i	$0.118170\pi$
$138$		0			0
$139$	0.800620	−	1.10196i	0.0679077	−	0.0934669i	−0.773712	−	0.633537i	$-0.781602\pi$
$139$	0.800620	−	1.10196i	0.0679077	−	0.0934669i	0.841620	+	0.540070i	$0.181602\pi$
$140$		0			0
$141$	−4.43951	+	2.26204i	−0.373874	+	0.190499i
$142$		0			0
$143$	−4.65077	+	11.0168i	−0.388917	+	0.921273i
$144$		0			0
$145$	−21.0344	+	10.7176i	−1.74682	+	0.890047i
$146$		0			0
$147$	−1.57034	+	2.16139i	−0.129519	+	0.178268i
$148$		0			0
$149$	8.86376	−	17.3961i	0.726148	−	1.42514i	−0.171840	−	0.985125i	$-0.554971\pi$
$149$	8.86376	−	17.3961i	0.726148	−	1.42514i	0.897988	−	0.440020i	$-0.145029\pi$
$150$		0			0
$151$	0.478285	−	3.01977i	0.0389223	−	0.245745i	−0.960554	−	0.278092i	$-0.910298\pi$
$151$	0.478285	−	3.01977i	0.0389223	−	0.245745i	0.999477	+	0.0323465i	$0.0102980\pi$
$152$		0			0
$153$	−13.4767			−1.08953
$154$		0			0
$155$		−	32.3815i		−	2.60094i
$156$		0			0
$157$	7.64194	−	5.55219i	0.609893	−	0.443113i	−0.239484	−	0.970900i	$-0.576978\pi$
$157$	7.64194	−	5.55219i	0.609893	−	0.443113i	0.849377	+	0.527787i	$0.176978\pi$
$158$		0			0
$159$	0.586418	+	1.80481i	0.0465060	+	0.143131i
$160$		0			0
$161$	−0.00559215	−	0.0353075i	−0.000440723	−	0.00278262i
$162$		0			0
$163$	11.7559	−	5.98995i	0.920797	−	0.469169i	0.0717116	−	0.997425i	$-0.477154\pi$
$163$	11.7559	−	5.98995i	0.920797	−	0.469169i	0.849085	+	0.528256i	$0.177154\pi$
$164$		0			0
$165$	0.260829	−	5.04937i	0.0203055	−	0.393093i
$166$		0			0
$167$	−4.14991	−	8.14465i	−0.321129	−	0.630252i	0.672855	−	0.739775i	$-0.265068\pi$
$167$	−4.14991	−	8.14465i	−0.321129	−	0.630252i	−0.993984	+	0.109522i	$0.965068\pi$
$168$		0			0
$169$	12.0652	+	4.84045i	0.928095	+	0.372343i
$170$		0			0
$171$	1.88664	−	3.70274i	0.144275	−	0.283156i
$172$		0			0
$173$	9.03322	−	6.56302i	0.686783	−	0.498977i	−0.188818	−	0.982012i	$-0.560466\pi$
$173$	9.03322	−	6.56302i	0.686783	−	0.498977i	0.875601	+	0.483035i	$0.160466\pi$
$174$		0			0
$175$	−0.113979	−	0.113979i	−0.00861600	−	0.00861600i
$176$		0			0
$177$	2.00172	+	2.00172i	0.150458	+	0.150458i
$178$		0			0
$179$	−8.02030	−	11.0390i	−0.599466	−	0.825094i	0.396194	−	0.918167i	$-0.370331\pi$
$179$	−8.02030	−	11.0390i	−0.599466	−	0.825094i	−0.995659	+	0.0930734i	$0.970331\pi$
$180$		0			0
$181$	5.47281	−	1.77822i	0.406791	−	0.132174i	−0.0984720	−	0.995140i	$-0.531395\pi$
$181$	5.47281	−	1.77822i	0.406791	−	0.132174i	0.505263	+	0.862965i	$0.331395\pi$
$182$		0			0
$183$	−2.77484	+	3.81925i	−0.205122	+	0.282327i
$184$		0			0
$185$	−2.43302	+	7.48808i	−0.178879	+	0.550534i
$186$		0			0
$187$	−15.5724	+	1.64854i	−1.13877	+	0.120553i
$188$		0			0
$189$	−0.0149279	−	0.0292976i	−0.00108584	−	0.00213108i
$190$		0			0
$191$	11.2926	+	8.20458i	0.817106	+	0.593662i	0.915882	−	0.401447i	$-0.131493\pi$
$191$	11.2926	+	8.20458i	0.817106	+	0.593662i	−0.0987759	+	0.995110i	$0.531493\pi$
$192$		0			0
$193$	−8.39094	−	4.27540i	−0.603993	−	0.307750i	0.125122	−	0.992141i	$-0.460068\pi$
$193$	−8.39094	−	4.27540i	−0.603993	−	0.307750i	−0.729115	+	0.684392i	$0.760068\pi$
$194$		0			0
$195$	−5.49345	−	0.185124i	−0.393394	−	0.0132570i
$196$		0			0
$197$	−12.3966	−	12.3966i	−0.883223	−	0.883223i	0.110637	−	0.993861i	$-0.464711\pi$
$197$	−12.3966	−	12.3966i	−0.883223	−	0.883223i	−0.993861	+	0.110637i	$0.964711\pi$
$198$		0			0
$199$		−	1.65598i		−	0.117389i	−0.998276	−	0.0586945i	$-0.981306\pi$
$199$		−	1.65598i		−	0.117389i	0.998276	−	0.0586945i	$-0.0186938\pi$
$200$		0			0
$201$	0.736444	−	4.64973i	0.0519448	−	0.327966i
$202$		0			0
$203$	−0.0394867	+	0.0774970i	−0.00277142	+	0.00543922i
$204$		0			0
$205$	28.0692	+	20.3935i	1.96044	+	1.42434i
$206$		0			0
$207$	−6.59437	−	2.14264i	−0.458340	−	0.148924i
$208$		0			0
$209$	1.72709	−	4.50933i	0.119465	−	0.311917i
$210$		0			0
$211$	−20.4219	−	6.63548i	−1.40590	−	0.456806i	−0.494808	−	0.869002i	$-0.664762\pi$
$211$	−20.4219	−	6.63548i	−1.40590	−	0.456806i	−0.911095	+	0.412197i	$0.864762\pi$
$212$		0			0
$213$	1.01545	−	0.160831i	0.0695774	−	0.0110200i
$214$		0			0
$215$	−3.91670	−	1.99566i	−0.267117	−	0.136103i
$216$		0			0
$217$	−0.0701244	−	0.0965179i	−0.00476035	−	0.00655206i
$218$		0			0
$219$	−0.607501	+	0.607501i	−0.0410511	+	0.0410511i
$220$		0			0
$221$	2.09527	+	16.8942i	0.140943	+	1.13642i
$222$		0			0
$223$	−3.43514	+	21.6886i	−0.230034	+	1.45238i	0.554445	+	0.832221i	$0.312931\pi$
$223$	−3.43514	+	21.6886i	−0.230034	+	1.45238i	−0.784478	+	0.620156i	$0.787069\pi$
$224$		0			0
$225$	−29.7349	+	9.66146i	−1.98233	+	0.644097i
$226$		0			0
$227$	3.39495	+	21.4349i	0.225331	+	1.42268i	0.797882	+	0.602813i	$0.205954\pi$
$227$	3.39495	+	21.4349i	0.225331	+	1.42268i	−0.572552	+	0.819869i	$0.694046\pi$
$228$		0			0
$229$	18.6291	−	9.49202i	1.23105	−	0.627250i	0.287276	−	0.957848i	$-0.407250\pi$
$229$	18.6291	−	9.49202i	1.23105	−	0.627250i	0.943772	+	0.330598i	$0.107250\pi$
$230$		0			0
$231$	−0.0101573	−	0.0156153i	−0.000668304	−	0.00102741i
$232$		0			0
$233$	−3.33995	+	10.2793i	−0.218807	+	0.673420i	0.780054	+	0.625712i	$0.215192\pi$
$233$	−3.33995	+	10.2793i	−0.218807	+	0.673420i	−0.998861	+	0.0477074i	$0.984808\pi$
$234$		0			0
$235$	42.1843	+	30.6487i	2.75180	+	1.99930i
$236$		0			0
$237$	4.50801	−	1.46474i	0.292827	−	0.0951452i
$238$		0			0
$239$	14.4200	+	2.28390i	0.932750	+	0.147733i	0.604271	−	0.796779i	$-0.293464\pi$
$239$	14.4200	+	2.28390i	0.932750	+	0.147733i	0.328478	+	0.944512i	$0.393464\pi$
$240$		0			0
$241$	−9.25509	+	9.25509i	−0.596173	+	0.596173i	−0.939292	−	0.343119i	$-0.888517\pi$
$241$	−9.25509	+	9.25509i	−0.596173	+	0.596173i	0.343119	+	0.939292i	$0.388517\pi$
$242$		0			0
$243$	−9.64605			−0.618794
$244$		0			0
$245$	27.6143	+	4.37367i	1.76421	+	0.279424i
$246$		0			0
$247$	−4.93502	−	1.78938i	−0.314008	−	0.113856i
$248$		0			0
$249$	0.476375	+	3.00771i	0.0301890	+	0.190606i
$250$		0			0
$251$	11.3920	+	3.70147i	0.719054	+	0.233635i	0.645613	−	0.763665i	$-0.276602\pi$
$251$	11.3920	+	3.70147i	0.719054	+	0.233635i	0.0734412	+	0.997300i	$0.476602\pi$
$252$		0			0
$253$	−7.88194	−	1.66918i	−0.495533	−	0.104941i
$254$		0			0
$255$	−3.26773	−	6.41328i	−0.204633	−	0.401615i
$256$		0			0
$257$	8.59964	−	11.8364i	0.536431	−	0.738334i	−0.451662	−	0.892189i	$-0.649169\pi$
$257$	8.59964	−	11.8364i	0.536431	−	0.738334i	0.988093	+	0.153855i	$0.0491688\pi$
$258$		0			0
$259$	0.00896397	+	0.0275883i	0.000556994	+	0.00171425i
$260$		0			0
$261$	9.91615	+	13.6484i	0.613794	+	0.844816i
$262$		0			0
$263$			19.3113i			1.19078i	0.803436	+	0.595392i	$0.203003\pi$
$263$			19.3113i			1.19078i	−0.803436	+	0.595392i	$0.796997\pi$
$264$		0			0
$265$	14.0426	−	14.0426i	0.862632	−	0.862632i
$266$		0			0
$267$	−2.55913	−	0.405327i	−0.156616	−	0.0248056i
$268$		0			0
$269$	−4.41723	−	13.5948i	−0.269323	−	0.828892i	−0.990666	−	0.136313i	$-0.956475\pi$
$269$	−4.41723	−	13.5948i	−0.269323	−	0.828892i	0.721342	−	0.692579i	$-0.243525\pi$
$270$		0			0
$271$	15.3673	−	2.43395i	0.933500	−	0.147852i	0.328885	−	0.944370i	$-0.393327\pi$
$271$	15.3673	−	2.43395i	0.933500	−	0.147852i	0.604615	+	0.796518i	$0.293327\pi$
$272$		0			0
$273$	−0.0167750	+	0.0113447i	−0.00101527	+	0.000686610i
$274$		0			0
$275$	−33.1771	+	14.8012i	−2.00065	+	0.892546i
$276$		0			0
$277$	−8.39723	+	25.8440i	−0.504541	+	1.55282i	0.297000	+	0.954877i	$0.404014\pi$
$277$	−8.39723	+	25.8440i	−0.504541	+	1.55282i	−0.801541	+	0.597940i	$0.795986\pi$
$278$		0			0
$279$	−22.8555	+	3.61996i	−1.36832	+	0.216721i
$280$		0			0
$281$	14.1005	+	7.18457i	0.841166	+	0.428596i	0.820813	−	0.571197i	$-0.193521\pi$
$281$	14.1005	+	7.18457i	0.841166	+	0.428596i	0.0203536	+	0.999793i	$0.493521\pi$
$282$		0			0
$283$	−18.6245	+	13.5315i	−1.10711	+	0.804363i	−0.982206	−	0.187806i	$-0.939862\pi$
$283$	−18.6245	+	13.5315i	−1.10711	+	0.804363i	−0.124904	+	0.992169i	$0.539862\pi$
$284$		0			0
$285$	2.21952			0.131473
$286$		0			0
$287$	0.127828			0.00754546
$288$		0			0
$289$	−4.28175	+	3.11088i	−0.251868	+	0.182993i
$290$		0			0
$291$	2.02407	+	1.03132i	0.118653	+	0.0604568i
$292$		0			0
$293$	−32.4361	+	5.13738i	−1.89494	+	0.300129i	−0.991656	−	0.128916i	$-0.958850\pi$
$293$	−32.4361	+	5.13738i	−1.89494	+	0.300129i	−0.903283	+	0.429044i	$0.858850\pi$
$294$		0			0
$295$	9.15459	−	28.1749i	0.533001	−	1.64041i
$296$		0			0
$297$	−7.36960	+	0.780164i	−0.427627	+	0.0452697i
$298$		0			0
$299$	−1.66073	+	8.59972i	−0.0960424	+	0.497335i
$300$		0			0
$301$	−0.0159961	+	0.00253353i	−0.000921998	+	0.000146030i
$302$		0			0
$303$	−0.00355158	−	0.0109306i	−0.000204033	−	0.000627948i
$304$		0			0
$305$	48.7954	+	7.72843i	2.79402	+	0.442529i
$306$		0			0
$307$	10.4920	−	10.4920i	0.598812	−	0.598812i	−0.341184	−	0.939996i	$-0.610828\pi$
$307$	10.4920	−	10.4920i	0.598812	−	0.598812i	0.939996	+	0.341184i	$0.110828\pi$
$308$		0			0
$309$		−	4.42065i		−	0.251482i
$310$		0			0
$311$	−10.6326	−	14.6345i	−0.602920	−	0.829848i	0.393052	−	0.919516i	$-0.371419\pi$
$311$	−10.6326	−	14.6345i	−0.602920	−	0.829848i	−0.995972	+	0.0896687i	$0.971419\pi$
$312$		0			0
$313$	−1.03311	−	3.17958i	−0.0583947	−	0.179720i	0.917604	−	0.397495i	$-0.130120\pi$
$313$	−1.03311	−	3.17958i	−0.0583947	−	0.179720i	−0.975999	+	0.217774i	$0.930120\pi$
$314$		0			0
$315$	−0.0986131	+	0.135729i	−0.00555622	+	0.00764748i
$316$		0			0
$317$	−4.78415	−	9.38942i	−0.268705	−	0.527362i	0.716744	−	0.697336i	$-0.245632\pi$
$317$	−4.78415	−	9.38942i	−0.268705	−	0.527362i	−0.985449	+	0.169974i	$0.945632\pi$
$318$		0			0
$319$	13.1277	+	14.5578i	0.735012	+	0.815083i
$320$		0			0
$321$	7.27918	+	2.36515i	0.406284	+	0.132010i
$322$		0			0
$323$	−1.07535	−	6.78951i	−0.0598342	−	0.377778i
$324$		0			0
$325$	16.7344	+	35.7731i	0.928260	+	1.98433i
$326$		0			0
$327$	1.44956	+	0.229588i	0.0801610	+	0.0126963i
$328$		0			0
$329$	0.192109			0.0105913
$330$		0			0
$331$	11.9080	−	11.9080i	0.654522	−	0.654522i	−0.299556	−	0.954079i	$-0.596839\pi$
$331$	11.9080	−	11.9080i	0.654522	−	0.654522i	0.954079	+	0.299556i	$0.0968386\pi$
$332$		0			0
$333$	5.55723	+	0.880179i	0.304534	+	0.0482335i
$334$		0			0
$335$	−46.8546	+	15.2240i	−2.55994	+	0.831776i
$336$		0			0
$337$	−11.0885	−	8.05629i	−0.604030	−	0.438854i	0.243277	−	0.969957i	$-0.421778\pi$
$337$	−11.0885	−	8.05629i	−0.604030	−	0.438854i	−0.847307	+	0.531103i	$0.821778\pi$
$338$		0			0
$339$	−0.277575	+	0.854289i	−0.0150758	+	0.0463986i
$340$		0			0
$341$	−25.9669	+	6.97868i	−1.40619	+	0.377917i
$342$		0			0
$343$	0.183563	−	0.0935301i	0.00991148	−	0.00505015i
$344$		0			0
$345$	−0.579316	−	3.65766i	−0.0311893	−	0.196922i
$346$		0			0
$347$	0.661676	−	0.214992i	0.0355206	−	0.0115414i	−0.291203	−	0.956661i	$-0.594055\pi$
$347$	0.661676	−	0.214992i	0.0355206	−	0.0115414i	0.326723	+	0.945120i	$0.394055\pi$
$348$		0			0
$349$	−1.18789	+	7.50007i	−0.0635865	+	0.401469i	0.935282	+	0.353904i	$0.115146\pi$
$349$	−1.18789	+	7.50007i	−0.0635865	+	0.401469i	−0.998868	+	0.0475651i	$0.984854\pi$
$350$		0			0
$351$	0.991581	+	7.99511i	0.0529267	+	0.426747i
$352$		0			0
$353$	−4.75290	+	4.75290i	−0.252971	+	0.252971i	−0.822188	−	0.569216i	$-0.807247\pi$
$353$	−4.75290	+	4.75290i	−0.252971	+	0.252971i	0.569216	+	0.822188i	$0.307247\pi$
$354$		0			0
$355$	−6.32406	−	8.70432i	−0.335646	−	0.461977i
$356$		0			0
$357$	−0.0236284	−	0.0120393i	−0.00125055	−	0.000637186i
$358$		0			0
$359$	30.9345	−	4.89955i	1.63266	−	0.258588i	0.728269	−	0.685291i	$-0.240325\pi$
$359$	30.9345	−	4.89955i	1.63266	−	0.258588i	0.904392	+	0.426703i	$0.140325\pi$
$360$		0			0
$361$	−16.0541	−	5.21629i	−0.844953	−	0.274542i
$362$		0			0
$363$	−4.10533	+	0.879053i	−0.215474	+	0.0461383i
$364$		0			0
$365$	8.55082	+	2.77833i	0.447570	+	0.145424i
$366$		0			0
$367$	−7.88148	−	5.72623i	−0.411410	−	0.298907i	0.362763	−	0.931882i	$-0.381834\pi$
$367$	−7.88148	−	5.72623i	−0.411410	−	0.298907i	−0.774172	+	0.632975i	$0.781834\pi$
$368$		0			0
$369$	11.2563	−	22.0916i	0.585977	−	1.15004i
$370$		0			0
$371$	0.0114459	−	0.0722666i	0.000594242	−	0.00375189i
$372$		0			0
$373$		−	1.32539i		−	0.0686259i	−0.999411	−	0.0343130i	$-0.989076\pi$
$373$		−	1.32539i		−	0.0686259i	0.999411	−	0.0343130i	$-0.0109243\pi$
$374$		0			0
$375$	−6.41777	−	6.41777i	−0.331412	−	0.331412i
$376$		0			0
$377$	15.5677	−	14.5527i	0.801779	−	0.749502i
$378$		0			0
$379$	−1.41816	−	0.722590i	−0.0728462	−	0.0371170i	0.417188	−	0.908820i	$-0.363016\pi$
$379$	−1.41816	−	0.722590i	−0.0728462	−	0.0371170i	−0.490034	+	0.871703i	$0.663016\pi$
$380$		0			0
$381$	4.30369	+	3.12681i	0.220485	+	0.160192i
$382$		0			0
$383$	1.21481	+	2.38420i	0.0620740	+	0.121827i	0.919959	−	0.392015i	$-0.128222\pi$
$383$	1.21481	+	2.38420i	0.0620740	+	0.121827i	−0.857885	+	0.513842i	$0.828222\pi$
$384$		0			0
$385$	−0.0973451	+	0.168899i	−0.00496117	+	0.00860790i
$386$		0			0
$387$	−0.970724	+	2.98758i	−0.0493447	+	0.151867i
$388$		0			0
$389$	5.57416	−	7.67218i	0.282621	−	0.388995i	−0.643979	−	0.765044i	$-0.722717\pi$
$389$	5.57416	−	7.67218i	0.282621	−	0.388995i	0.926600	+	0.376049i	$0.122717\pi$
$390$		0			0
$391$	−10.9081	+	3.54426i	−0.551647	+	0.179241i
$392$		0			0
$393$	−0.559243	−	0.769732i	−0.0282101	−	0.0388278i
$394$		0			0
$395$	−35.0754	−	35.0754i	−1.76484	−	1.76484i
$396$		0			0
$397$	−15.6862	−	15.6862i	−0.787269	−	0.787269i	0.193777	−	0.981046i	$-0.437926\pi$
$397$	−15.6862	−	15.6862i	−0.787269	−	0.787269i	−0.981046	+	0.193777i	$0.937926\pi$
$398$		0			0
$399$	0.00661561	−	0.00480652i	0.000331195	−	0.000240627i
$400$		0			0
$401$	−7.07077	+	13.8772i	−0.353097	+	0.692993i	−0.997422	−	0.0717595i	$-0.977139\pi$
$401$	−7.07077	+	13.8772i	−0.353097	+	0.692993i	0.644325	+	0.764752i	$0.277139\pi$
$402$		0			0
$403$	8.09135	+	28.0885i	0.403059	+	1.39919i
$404$		0			0
$405$	13.9810	+	27.4393i	0.694723	+	1.36347i
$406$		0			0
$407$	6.52909	+	0.337265i	0.323635	+	0.0167176i
$408$		0			0
$409$	17.6676	−	9.00207i	0.873604	−	0.445124i	0.0411083	−	0.999155i	$-0.486911\pi$
$409$	17.6676	−	9.00207i	0.873604	−	0.445124i	0.832496	+	0.554031i	$0.186911\pi$
$410$		0			0
$411$	−0.139533	−	0.880977i	−0.00688266	−	0.0434554i
$412$		0			0
$413$	−0.0337282	−	0.103805i	−0.00165966	−	0.00510789i
$414$		0			0
$415$	25.7818	−	18.7316i	1.26558	−	0.919497i
$416$		0			0
$417$		−	0.519874i		−	0.0254583i
$418$		0			0
$419$	36.9320			1.80424			0.902122	−	0.431481i	$-0.142009\pi$
$419$	36.9320			1.80424			0.902122	+	0.431481i	$0.142009\pi$
$420$		0			0
$421$	−4.80458	+	30.3349i	−0.234161	+	1.47843i	0.537967	+	0.842966i	$0.319192\pi$
$421$	−4.80458	+	30.3349i	−0.234161	+	1.47843i	−0.772128	+	0.635467i	$0.780808\pi$
$422$		0			0
$423$	16.9167	−	33.2008i	0.822516	−	1.61428i
$424$		0			0
$425$	−30.3987	+	41.8402i	−1.47455	+	2.02955i
$426$		0			0
$427$	0.162179	−	0.0826341i	0.00784837	−	0.00399895i
$428$		0			0
$429$	1.03547	+	4.44512i	0.0499928	+	0.214613i
$430$		0			0
$431$	−22.9687	+	11.7031i	−1.10636	+	0.563719i	−0.909077	−	0.416627i	$-0.863212\pi$
$431$	−22.9687	+	11.7031i	−1.10636	+	0.563719i	−0.197284	+	0.980346i	$0.563212\pi$
$432$		0			0
$433$	−4.90017	+	6.74450i	−0.235487	+	0.324120i	−0.910363	−	0.413811i	$-0.864197\pi$
$433$	−4.90017	+	6.74450i	−0.235487	+	0.324120i	0.674876	+	0.737932i	$0.264197\pi$
$434$		0			0
$435$	−4.09060	+	8.02826i	−0.196129	+	0.384926i
$436$		0			0
$437$	0.553267	−	3.49319i	0.0264663	−	0.167102i
$438$		0			0
$439$	−1.01486			−0.0484364			−0.0242182	−	0.999707i	$-0.507710\pi$
$439$	−1.01486			−0.0484364			−0.0242182	+	0.999707i	$0.507710\pi$
$440$		0			0
$441$		−	19.9797i		−	0.951413i
$442$		0			0
$443$	14.8265	−	10.7721i	0.704430	−	0.511799i	−0.176942	−	0.984221i	$-0.556620\pi$
$443$	14.8265	−	10.7721i	0.704430	−	0.511799i	0.881372	+	0.472423i	$0.156620\pi$
$444$		0			0
$445$	8.37904	+	25.7880i	0.397205	+	1.22247i
$446$		0			0
$447$	−1.16572	−	7.36006i	−0.0551366	−	0.348119i
$448$		0			0
$449$	7.83044	−	3.98981i	0.369541	−	0.188291i	−0.259351	−	0.965783i	$-0.583509\pi$
$449$	7.83044	−	3.98981i	0.369541	−	0.188291i	0.628892	+	0.777492i	$0.283509\pi$
$450$		0			0
$451$	10.3043	−	26.9040i	0.485212	−	1.26686i
$452$		0			0
$453$	−0.529775	−	1.03974i	−0.0248910	−	0.0488513i
$454$		0			0
$455$	0.185480	+	0.102517i	0.00869543	+	0.00480609i
$456$		0			0
$457$	−12.2350	+	24.0126i	−0.572330	+	1.12326i	0.405546	+	0.914075i	$0.367082\pi$
$457$	−12.2350	+	24.0126i	−0.572330	+	1.12326i	−0.977876	+	0.209186i	$0.932918\pi$
$458$		0			0
$459$	−8.53502	+	6.20106i	−0.398381	+	0.289441i
$460$		0			0
$461$	7.48947	+	7.48947i	0.348819	+	0.348819i	0.859670	−	0.510850i	$-0.170669\pi$
$461$	7.48947	+	7.48947i	0.348819	+	0.348819i	−0.510850	+	0.859670i	$0.670669\pi$
$462$		0			0
$463$	−11.9070	−	11.9070i	−0.553363	−	0.553363i	0.374047	−	0.927410i	$-0.377970\pi$
$463$	−11.9070	−	11.9070i	−0.553363	−	0.553363i	−0.927410	+	0.374047i	$0.877970\pi$
$464$		0			0
$465$	−7.26450	−	9.99872i	−0.336883	−	0.463680i
$466$		0			0
$467$	24.9291	−	8.09997i	1.15358	−	0.374822i	0.331091	−	0.943599i	$-0.392583\pi$
$467$	24.9291	−	8.09997i	1.15358	−	0.374822i	0.822492	+	0.568777i	$0.192583\pi$
$468$		0			0
$469$	−0.106689	+	0.146845i	−0.00492643	+	0.00678065i
$470$		0			0
$471$	1.11409	−	3.42880i	0.0513343	−	0.157991i
$472$		0			0
$473$	−0.756223	+	3.57092i	−0.0347712	+	0.164191i
$474$		0			0
$475$	−7.24006	−	14.2094i	−0.332197	−	0.651973i
$476$		0			0
$477$	−11.4814	−	8.34174i	−0.525698	−	0.381942i
$478$		0			0
$479$	−9.79408	−	4.99033i	−0.447503	−	0.228014i	0.215691	−	0.976462i	$-0.430800\pi$
$479$	−9.79408	−	4.99033i	−0.447503	−	0.228014i	−0.663194	+	0.748448i	$0.730800\pi$
$480$		0			0
$481$	0.239374	−	7.10330i	0.0109145	−	0.323882i
$482$		0			0
$483$	−0.00964766	−	0.00964766i	−0.000438984	−	0.000438984i
$484$		0			0
$485$		−	23.7730i		−	1.07948i
$486$		0			0
$487$	−2.82971	+	17.8661i	−0.128226	+	0.809589i	0.836814	+	0.547487i	$0.184416\pi$
$487$	−2.82971	+	17.8661i	−0.128226	+	0.809589i	−0.965040	+	0.262102i	$0.915584\pi$
$488$		0			0
$489$	2.28620	−	4.48692i	0.103385	−	0.202905i
$490$		0			0
$491$	35.0436	+	25.4606i	1.58149	+	1.14902i	0.914957	+	0.403550i	$0.132224\pi$
$491$	35.0436	+	25.4606i	1.58149	+	1.14902i	0.666537	+	0.745472i	$0.267776\pi$
$492$		0			0
$493$	26.5404	+	8.62349i	1.19532	+	0.388382i
$494$		0			0
$495$	20.6176	+	31.6963i	0.926694	+	1.42464i
$496$		0			0
$497$	−0.0376997	−	0.0122494i	−0.00169106	−	0.000549459i
$498$		0			0
$499$	20.5816	−	3.25980i	0.921358	−	0.145929i	0.322303	−	0.946637i	$-0.395543\pi$
$499$	20.5816	−	3.25980i	0.921358	−	0.145929i	0.599055	+	0.800708i	$0.295543\pi$
$500$		0			0
$501$	−3.10859	−	1.58390i	−0.138881	−	0.0707636i
$502$		0			0
$503$	−23.2159	−	31.9539i	−1.03514	−	1.42475i	−0.901014	−	0.433790i	$-0.857176\pi$
$503$	−23.2159	−	31.9539i	−1.03514	−	1.42475i	−0.134130	−	0.990964i	$-0.542824\pi$
$504$		0			0
$505$	−0.0850478	+	0.0850478i	−0.00378458	+	0.00378458i
$506$		0			0
$507$	4.81141	−	1.21210i	0.213682	−	0.0538312i
$508$		0			0
$509$	4.04433	−	25.5349i	0.179262	−	1.13181i	−0.719861	−	0.694118i	$-0.755795\pi$
$509$	4.04433	−	25.5349i	0.179262	−	1.13181i	0.899123	−	0.437696i	$-0.144205\pi$
$510$		0			0
$511$	0.0315037	−	0.0102362i	0.00139364	−	0.000452822i
$512$		0			0
$513$	−0.508907	−	3.21311i	−0.0224688	−	0.141862i
$514$		0			0
$515$	−41.2198	+	21.0025i	−1.81636	+	0.925483i
$516$		0			0
$517$	15.4860	−	40.4331i	0.681075	−	1.77825i
$518$		0			0
$519$	1.31692	−	4.05305i	0.0578062	−	0.177909i
$520$		0			0
$521$	3.17863	+	2.30941i	0.139258	+	0.101177i	0.655233	−	0.755427i	$-0.272570\pi$
$521$	3.17863	+	2.30941i	0.139258	+	0.101177i	−0.515975	+	0.856604i	$0.672570\pi$
$522$		0			0
$523$	−4.18291	+	1.35911i	−0.182906	+	0.0594297i	−0.399038	−	0.916934i	$-0.630656\pi$
$523$	−4.18291	+	1.35911i	−0.182906	+	0.0594297i	0.216132	+	0.976364i	$0.430656\pi$
$524$		0			0
$525$	−0.0607645	−	0.00962416i	−0.00265198	−	0.000420033i
$526$		0			0
$527$	−27.0665	+	27.0665i	−1.17903	+	1.17903i
$528$		0			0
$529$	17.0990			0.743434
$530$		0			0
$531$	−20.9098	−	3.31179i	−0.907410	−	0.143720i
$532$		0			0
$533$	−29.4438	−	10.6760i	−1.27535	−	0.462428i
$534$		0			0
$535$	−12.5299	−	79.1106i	−0.541715	−	3.42025i
$536$		0			0
$537$	−4.95300	−	1.60933i	−0.213738	−	0.0694477i
$538$		0			0
$539$	−2.44401	−	23.0867i	−0.105271	−	0.994412i
$540$		0			0
$541$	−15.5351	−	30.4894i	−0.667908	−	1.31084i	−0.937539	−	0.347879i	$-0.886902\pi$
$541$	−15.5351	−	30.4894i	−0.667908	−	1.31084i	0.269631	−	0.962964i	$-0.413098\pi$
$542$		0			0
$543$	1.29096	−	1.77686i	0.0554005	−	0.0762522i
$544$		0			0
$545$	−4.74612	−	14.6070i	−0.203301	−	0.625697i
$546$		0			0
$547$	−10.5001	−	14.4522i	−0.448953	−	0.617931i	0.523219	−	0.852198i	$-0.324731\pi$
$547$	−10.5001	−	14.4522i	−0.448953	−	0.617931i	−0.972172	+	0.234267i	$0.924731\pi$
$548$		0			0
$549$		−	35.3048i		−	1.50677i
$550$		0			0
$551$	−6.08478	+	6.08478i	−0.259220	+	0.259220i
$552$		0			0
$553$	−0.180506	−	0.0285893i	−0.00767590	−	0.00121574i
$554$		0			0
$555$	0.928617	+	2.85799i	0.0394176	+	0.121315i
$556$		0			0
$557$	3.30458	−	0.523393i	0.140019	−	0.0221769i	−0.0860313	−	0.996292i	$-0.527419\pi$
$557$	3.30458	−	0.523393i	0.140019	−	0.0221769i	0.226051	+	0.974116i	$0.427419\pi$
$558$		0			0
$559$	3.89611	+	0.752394i	0.164788	+	0.0318229i
$560$		0			0
$561$	−4.43860	+	4.00257i	−0.187398	+	0.168989i
$562$		0			0
$563$	−2.80727	+	8.63990i	−0.118312	+	0.364128i	−0.992623	−	0.121238i	$-0.961314\pi$
$563$	−2.80727	+	8.63990i	−0.118312	+	0.364128i	0.874311	+	0.485366i	$0.161314\pi$
$564$		0			0
$565$	9.28447	−	1.47052i	0.390601	−	0.0618651i
$566$		0			0
$567$	0.101094	+	0.0515102i	0.00424557	+	0.00216323i
$568$		0			0
$569$	−27.5751	+	20.0345i	−1.15601	+	0.839889i	−0.989268	−	0.146112i	$-0.953324\pi$
$569$	−27.5751	+	20.0345i	−1.15601	+	0.839889i	−0.166740	+	0.986001i	$0.553324\pi$
$570$		0			0
$571$	−0.831361			−0.0347914			−0.0173957	−	0.999849i	$-0.505538\pi$
$571$	−0.831361			−0.0347914			−0.0173957	+	0.999849i	$0.505538\pi$
$572$		0			0
$573$	5.32756			0.222562
$574$		0			0
$575$	−21.5267	+	15.6401i	−0.897726	+	0.652236i
$576$		0			0
$577$	20.4416	+	10.4155i	0.850994	+	0.433603i	0.824376	−	0.566043i	$-0.191526\pi$
$577$	20.4416	+	10.4155i	0.850994	+	0.433603i	0.0266178	+	0.999646i	$0.491526\pi$
$578$		0			0
$579$	−3.55009	+	0.562280i	−0.147537	+	0.0233675i
$580$		0			0
$581$	0.0362820	−	0.111665i	0.00150523	−	0.00463263i
$582$		0			0
$583$	−14.2873	−	8.23448i	−0.591718	−	0.341037i
$584$		0			0
$585$	34.0503	−	23.0277i	1.40781	−	0.952079i
$586$		0			0
$587$	−38.6934	+	6.12843i	−1.59705	+	0.252948i	−0.890590	−	0.454807i	$-0.849708\pi$
$587$	−38.6934	+	6.12843i	−1.59705	+	0.252948i	−0.706458	+	0.707755i	$0.749708\pi$
$588$		0			0
$589$	−3.64744	−	11.2257i	−0.150290	−	0.462546i
$590$		0			0
$591$	−6.60890	−	1.04675i	−0.271854	−	0.0430574i
$592$		0			0
$593$	−1.11251	+	1.11251i	−0.0456853	+	0.0456853i	−0.729580	−	0.683895i	$-0.760285\pi$
$593$	−1.11251	+	1.11251i	−0.0456853	+	0.0456853i	0.683895	+	0.729580i	$0.260285\pi$
$594$		0			0
$595$			0.277519i			0.0113772i
$596$		0			0
$597$	−0.371503	−	0.511331i	−0.0152046	−	0.0209274i
$598$		0			0
$599$	−3.19771	−	9.84153i	−0.130655	−	0.402114i	0.864234	−	0.503090i	$-0.167804\pi$
$599$	−3.19771	−	9.84153i	−0.130655	−	0.402114i	−0.994889	+	0.100976i	$0.967804\pi$
$600$		0			0
$601$	27.2610	−	37.5216i	1.11200	−	1.53054i	0.293563	−	0.955940i	$-0.405159\pi$
$601$	27.2610	−	37.5216i	1.11200	−	1.53054i	0.818437	−	0.574597i	$-0.194841\pi$
$602$		0			0
$603$	15.9833	+	31.3691i	0.650892	+	1.27745i
$604$		0			0
$605$	27.7011	+	34.1033i	1.12621	+	1.38650i
$606$		0			0
$607$	21.9297	+	7.12539i	0.890098	+	0.289210i	0.718144	−	0.695894i	$-0.244992\pi$
$607$	21.9297	+	7.12539i	0.890098	+	0.289210i	0.171954	+	0.985105i	$0.444992\pi$
$608$		0			0
$609$	0.00519310	+	0.0327880i	0.000210435	+	0.00132864i
$610$		0			0
$611$	−44.2501	−	16.0446i	−1.79017	−	0.649095i
$612$		0			0
$613$	35.8478	+	5.67774i	1.44788	+	0.229322i	0.830357	−	0.557231i	$-0.188136\pi$
$613$	35.8478	+	5.67774i	1.44788	+	0.229322i	0.617523	+	0.786553i	$0.288136\pi$
$614$		0			0
$615$	13.2423			0.533981
$616$		0			0
$617$	5.99987	−	5.99987i	0.241546	−	0.241546i	−0.575944	−	0.817489i	$-0.695365\pi$
$617$	5.99987	−	5.99987i	0.241546	−	0.241546i	0.817489	+	0.575944i	$0.195365\pi$
$618$		0			0
$619$	−22.3677	−	3.54269i	−0.899032	−	0.142393i	−0.310222	−	0.950664i	$-0.600403\pi$
$619$	−22.3677	−	3.54269i	−0.899032	−	0.142393i	−0.588810	+	0.808271i	$0.700403\pi$
$620$		0			0
$621$	−5.16222	+	1.67731i	−0.207153	+	0.0673081i
$622$		0			0
$623$	0.0808209	+	0.0587198i	0.00323802	+	0.00235256i
$624$		0			0
$625$	−12.4266	+	38.2451i	−0.497063	+	1.52980i
$626$		0			0
$627$	−0.478339	−	1.77984i	−0.0191030	−	0.0710801i
$628$		0			0
$629$	8.29269	−	4.22534i	0.330651	−	0.168475i
$630$		0			0
$631$	1.92570	+	12.1584i	0.0766611	+	0.484019i	0.995911	+	0.0903438i	$0.0287966\pi$
$631$	1.92570	+	12.1584i	0.0766611	+	0.484019i	−0.919250	+	0.393675i	$0.871203\pi$
$632$		0			0
$633$	−7.79448	+	2.53258i	−0.309803	+	0.100661i
$634$		0			0
$635$	8.70873	−	54.9848i	0.345595	−	2.18200i
$636$		0			0
$637$	−25.0462	+	3.10631i	−0.992366	+	0.123077i
$638$		0			0
$639$	−5.43671	+	5.43671i	−0.215073	+	0.215073i
$640$		0			0
$641$	12.8737	+	17.7191i	0.508479	+	0.699862i	0.983662	−	0.180025i	$-0.0576180\pi$
$641$	12.8737	+	17.7191i	0.508479	+	0.699862i	−0.475183	+	0.879887i	$0.657618\pi$
$642$		0			0
$643$	5.47869	+	2.79153i	0.216058	+	0.110087i	0.558670	−	0.829390i	$-0.311312\pi$
$643$	5.47869	+	2.79153i	0.216058	+	0.110087i	−0.342612	+	0.939477i	$0.611312\pi$
$644$		0			0
$645$	−1.65710	+	0.262459i	−0.0652484	+	0.0103343i
$646$		0			0
$647$	19.1466	+	6.22110i	0.752730	+	0.244577i	0.660156	−	0.751129i	$-0.270490\pi$
$647$	19.1466	+	6.22110i	0.752730	+	0.244577i	0.0925746	+	0.995706i	$0.470490\pi$
$648$		0			0
$649$	−24.5666	−	1.26901i	−0.964323	−	0.0498129i
$650$		0			0
$651$	−0.0433059	−	0.0140709i	−0.00169729	−	0.000551484i
$652$		0			0
$653$	−11.5809	−	8.41404i	−0.453197	−	0.329267i	0.337660	−	0.941268i	$-0.390365\pi$
$653$	−11.5809	−	8.41404i	−0.453197	−	0.329267i	−0.790857	+	0.612001i	$0.790365\pi$
$654$		0			0
$655$	−4.52030	+	8.87159i	−0.176623	+	0.346642i
$656$		0			0
$657$	1.00510	−	6.34593i	0.0392126	−	0.247578i
$658$		0			0
$659$		−	23.7384i		−	0.924717i	−0.886693	−	0.462358i	$-0.847003\pi$
$659$		−	23.7384i		−	0.924717i	0.886693	−	0.462358i	$-0.152997\pi$
$660$		0			0
$661$	10.5879	+	10.5879i	0.411823	+	0.411823i	0.882373	−	0.470550i	$-0.155945\pi$
$661$	10.5879	+	10.5879i	0.411823	+	0.411823i	−0.470550	+	0.882373i	$0.655945\pi$
$662$		0			0
$663$	4.43703	+	4.74651i	0.172320	+	0.184339i
$664$		0			0
$665$	−0.0762486	−	0.0388506i	−0.00295680	−	0.00150656i
$666$		0			0
$667$	11.6156	+	8.43923i	0.449758	+	0.326768i
$668$		0			0
$669$	3.80495	+	7.46763i	0.147108	+	0.288715i
$670$		0			0
$671$	−4.31865	−	40.7949i	−0.166720	−	1.57487i
$672$		0			0
$673$	−9.76045	+	30.0396i	−0.376238	+	1.15794i	0.566402	+	0.824129i	$0.308335\pi$
$673$	−9.76045	+	30.0396i	−0.376238	+	1.15794i	−0.942640	+	0.333811i	$0.891665\pi$
$674$		0			0
$675$	−14.3861	+	19.8007i	−0.553721	+	0.762131i
$676$		0			0
$677$	30.3645	−	9.86602i	1.16700	−	0.379182i	0.339479	−	0.940614i	$-0.389749\pi$
$677$	30.3645	−	9.86602i	1.16700	−	0.379182i	0.827523	+	0.561432i	$0.189749\pi$
$678$		0			0
$679$	−0.0514821	−	0.0708590i	−0.00197570	−	0.00271932i
$680$		0			0
$681$	5.85701	+	5.85701i	0.224441	+	0.224441i
$682$		0			0
$683$	9.63676	+	9.63676i	0.368740	+	0.368740i	0.867018	−	0.498277i	$-0.166034\pi$
$683$	9.63676	+	9.63676i	0.368740	+	0.368740i	−0.498277	+	0.867018i	$0.666034\pi$
$684$		0			0
$685$	−7.55164	+	5.48659i	−0.288533	+	0.209632i
$686$		0			0
$687$	3.62284	−	7.11022i	0.138220	−	0.271272i
$688$		0			0
$689$	−8.67201	+	15.6898i	−0.330377	+	0.597736i
$690$		0			0
$691$	15.1421	+	29.7180i	0.576032	+	1.13053i	0.976761	+	0.214330i	$0.0687567\pi$
$691$	15.1421	+	29.7180i	0.576032	+	1.13053i	−0.400730	+	0.916196i	$0.631243\pi$
$692$		0			0
$693$	0.130095	+	0.0498268i	0.00494189	+	0.00189276i
$694$		0			0
$695$	−4.84750	+	2.46993i	−0.183876	+	0.0936896i
$696$		0			0
$697$	−6.41587	−	40.5082i	−0.243018	−	1.53436i
$698$		0			0
$699$	1.27476	+	3.92332i	0.0482160	+	0.148394i
$700$		0			0
$701$	−5.41521	+	3.93438i	−0.204530	+	0.148600i	−0.685335	−	0.728228i	$-0.740344\pi$
$701$	−5.41521	+	3.93438i	−0.204530	+	0.148600i	0.480806	+	0.876827i	$0.340344\pi$
$702$		0			0
$703$			2.86994i			0.108242i
$704$		0			0
$705$	19.9014			0.749530
$706$		0			0
$707$	−6.93209e−5	0	0.000437675i	−2.60708e−6	0	1.64605e-5i
$708$		0			0
$709$	20.2940	−	39.8292i	0.762156	−	1.49582i	−0.103202	−	0.994660i	$-0.532909\pi$
$709$	20.2940	−	39.8292i	0.762156	−	1.49582i	0.865358	−	0.501155i	$-0.167091\pi$
$710$		0			0
$711$	−20.8358	+	28.6781i	−0.781405	+	1.07551i
$712$		0			0
$713$	−17.5473	+	8.94082i	−0.657153	+	0.334836i
$714$		0			0
$715$	36.5285	−	30.7739i	1.36609	−	1.15088i
$716$		0			0
$717$	4.96495	−	2.52977i	0.185420	−	0.0944760i
$718$		0			0
$719$	10.6779	−	14.6969i	0.398220	−	0.548103i	−0.562076	−	0.827086i	$-0.689997\pi$
$719$	10.6779	−	14.6969i	0.398220	−	0.548103i	0.960296	+	0.278982i	$0.0899971\pi$
$720$		0			0
$721$	−0.0773795	+	0.151866i	−0.00288176	+	0.00565578i
$722$		0			0
$723$	−0.781481	+	4.93408i	−0.0290636	+	0.183500i
$724$		0			0
$725$	64.7407			2.40441
$726$		0			0
$727$			36.4865i			1.35321i	0.736347	+	0.676604i	$0.236549\pi$
$727$			36.4865i			1.35321i	−0.736347	+	0.676604i	$0.763451\pi$
$728$		0			0
$729$	15.7344	−	11.4317i	0.582757	−	0.423398i
$730$		0			0
$731$	1.60573	+	4.94192i	0.0593900	+	0.182784i
$732$		0			0
$733$	4.63581	+	29.2693i	0.171227	+	1.08109i	0.912258	+	0.409616i	$0.134337\pi$
$733$	4.63581	+	29.2693i	0.171227	+	1.08109i	−0.741031	+	0.671471i	$0.765663\pi$
$734$		0			0
$735$	9.50791	−	4.84452i	0.350705	−	0.178693i
$736$		0			0
$737$	22.3061	+	34.2920i	0.821655	+	1.26316i
$738$		0			0
$739$	−5.26745	−	10.3380i	−0.193766	−	0.380288i	0.773598	−	0.633676i	$-0.218455\pi$
$739$	−5.26745	−	10.3380i	−0.193766	−	0.380288i	−0.967365	+	0.253389i	$0.918455\pi$
$740$		0			0
$741$	−1.92526	+	0.554604i	−0.0707263	+	0.0203739i
$742$		0			0
$743$	6.49616	−	12.7494i	0.238321	−	0.467731i	−0.740607	−	0.671939i	$-0.765462\pi$
$743$	6.49616	−	12.7494i	0.238321	−	0.467731i	0.978928	+	0.204208i	$0.0654617\pi$
$744$		0			0
$745$	−63.0897	+	45.8373i	−2.31143	+	1.67935i
$746$		0			0
$747$	−16.1033	−	16.1033i	−0.589189	−	0.589189i
$748$		0			0
$749$	−0.208667	−	0.208667i	−0.00762453	−	0.00762453i
$750$		0			0
$751$	−2.10634	−	2.89913i	−0.0768615	−	0.105791i	0.768855	−	0.639423i	$-0.220827\pi$
$751$	−2.10634	−	2.89913i	−0.0768615	−	0.105791i	−0.845717	+	0.533632i	$0.820827\pi$
$752$		0			0
$753$	4.34799	−	1.41275i	0.158450	−	0.0514834i
$754$		0			0
$755$	−7.17798	+	9.87964i	−0.261233	+	0.359557i
$756$		0			0
$757$	−5.05625	+	15.5615i	−0.183773	+	0.565594i	−0.999925	−	0.0122428i	$-0.996103\pi$
$757$	−5.05625	+	15.5615i	−0.183773	+	0.565594i	0.816153	+	0.577837i	$0.196103\pi$
$758$		0			0
$759$	−2.80824	+	1.25284i	−0.101933	+	0.0454751i
$760$		0			0
$761$	18.4714	+	36.2521i	0.669587	+	1.31414i	0.936585	+	0.350441i	$0.113968\pi$
$761$	18.4714	+	36.2521i	0.669587	+	1.31414i	−0.266998	+	0.963697i	$0.586032\pi$
$762$		0			0
$763$	−0.0457792	−	0.0332605i	−0.00165732	−	0.00120411i
$764$		0			0
$765$	47.9616	+	24.4377i	1.73405	+	0.883545i
$766$		0			0
$767$	−0.900679	+	26.7271i	−0.0325216	+	0.965061i
$768$		0			0
$769$	−18.5196	−	18.5196i	−0.667833	−	0.667833i	0.289381	−	0.957214i	$-0.406551\pi$
$769$	−18.5196	−	18.5196i	−0.667833	−	0.667833i	−0.957214	+	0.289381i	$0.906551\pi$
$770$		0			0
$771$		−	5.58409i		−	0.201106i
$772$		0			0
$773$	−2.70960	+	17.1077i	−0.0974576	+	0.615323i	0.889819	+	0.456313i	$0.150830\pi$
$773$	−2.70960	+	17.1077i	−0.0974576	+	0.615323i	−0.987277	+	0.159010i	$0.949170\pi$
$774$		0			0
$775$	−40.3154	+	79.1234i	−1.44817	+	2.84219i
$776$		0			0
$777$	0.00895707	+	0.00650769i	0.000321333	+	0.000233462i
$778$		0			0
$779$	12.0279	+	3.90809i	0.430943	+	0.140022i
$780$		0			0
$781$	−5.61712	+	6.94721i	−0.200996	+	0.248591i
$782$		0			0
$783$	12.5601	+	4.08104i	0.448863	+	0.145844i
$784$		0			0
$785$	−37.2645	+	5.90211i	−1.33003	+	0.210655i
$786$		0			0
$787$	−17.3892	−	8.86026i	−0.619859	−	0.315834i	0.115710	−	0.993283i	$-0.463086\pi$
$787$	−17.3892	−	8.86026i	−0.619859	−	0.315834i	−0.735570	+	0.677449i	$0.763086\pi$
$788$		0			0
$789$	4.33231	+	5.96291i	0.154234	+	0.212285i
$790$		0			0
$791$	0.0244893	−	0.0244893i	0.000870739	−	0.000870739i
$792$		0			0
$793$	−44.2575	+	5.48896i	−1.57163	+	0.194919i
$794$		0			0
$795$	1.18573	−	7.48642i	0.0420536	−	0.265516i
$796$		0			0
$797$	33.3509	−	10.8364i	1.18135	−	0.383844i	0.348482	−	0.937316i	$-0.386697\pi$
$797$	33.3509	−	10.8364i	1.18135	−	0.383844i	0.832868	+	0.553472i	$0.186697\pi$
$798$		0			0
$799$	−9.64220	−	60.8785i	−0.341117	−	2.15373i
$800$		0			0
$801$	17.2650	−	8.79697i	0.610030	−	0.310826i
$802$		0			0
$803$	0.385131	−	7.45572i	0.0135910	−	0.263107i
$804$		0			0
$805$	−0.0441223	+	0.135794i	−0.00155511	+	0.00478613i
$806$		0			0
$807$	−4.41383	−	3.20684i	−0.155374	−	0.112886i
$808$		0			0
$809$	43.3385	−	14.0815i	1.52370	−	0.495080i	0.576876	−	0.816832i	$-0.304272\pi$
$809$	43.3385	−	14.0815i	1.52370	−	0.495080i	0.946824	+	0.321752i	$0.104272\pi$
$810$		0			0
$811$	−36.3332	−	5.75462i	−1.27583	−	0.202072i	−0.518487	−	0.855086i	$-0.673504\pi$
$811$	−36.3332	−	5.75462i	−1.27583	−	0.202072i	−0.757346	+	0.653014i	$0.773504\pi$
$812$		0			0
$813$	4.19908	−	4.19908i	0.147268	−	0.147268i
$814$		0			0
$815$	−52.6994			−1.84598
$816$		0			0
$817$	−1.58259	−	0.250658i	−0.0553678	−	0.00876941i
$818$		0			0
$819$	0.0516240	−	0.142376i	0.00180389	−	0.00497502i
$820$		0			0
$821$	−5.78193	−	36.5057i	−0.201791	−	1.27406i	−0.855696	−	0.517479i	$-0.826870\pi$
$821$	−5.78193	−	36.5057i	−0.201791	−	1.27406i	0.653905	−	0.756577i	$-0.273130\pi$
$822$		0			0
$823$	−21.1661	−	6.87729i	−0.737805	−	0.239727i	−0.0840793	−	0.996459i	$-0.526795\pi$
$823$	−21.1661	−	6.87729i	−0.737805	−	0.239727i	−0.653726	+	0.756732i	$0.726795\pi$
$824$		0			0
$825$	−6.92387	+	12.0133i	−0.241058	+	0.418249i
$826$		0			0
$827$	12.5866	+	24.7027i	0.437681	+	0.858996i	0.999496	+	0.0317341i	$0.0101030\pi$
$827$	12.5866	+	24.7027i	0.437681	+	0.858996i	−0.561816	+	0.827262i	$0.689897\pi$
$828$		0			0
$829$	18.8548	−	25.9514i	0.654855	−	0.901331i	−0.344442	−	0.938807i	$-0.611932\pi$
$829$	18.8548	−	25.9514i	0.654855	−	0.901331i	0.999298	+	0.0374767i	$0.0119320\pi$
$830$		0			0
$831$	3.20499	+	9.86394i	0.111180	+	0.342176i
$832$		0			0
$833$	−19.4260	−	26.7376i	−0.673071	−	0.926402i
$834$		0			0
$835$			36.5108i			1.26351i
$836$		0			0
$837$	−12.8091	+	12.8091i	−0.442748	+	0.442748i
$838$		0			0
$839$	34.1438	+	5.40784i	1.17877	+	0.186699i	0.714916	−	0.699210i	$-0.246465\pi$
$839$	34.1438	+	5.40784i	1.17877	+	0.186699i	0.463858	+	0.885910i	$0.346465\pi$
$840$		0			0
$841$	−1.83354	−	5.64306i	−0.0632256	−	0.194588i
$842$		0			0
$843$	5.96574	−	0.944881i	0.205471	−	0.0325434i
$844$		0			0
$845$	−34.1611	−	39.1047i	−1.17518	−	1.34524i
$846$		0			0
$847$	0.156421	+	0.0416614i	0.00537467	+	0.00143150i
$848$		0			0
$849$	−2.71518	+	8.35647i	−0.0931848	+	0.286793i
$850$		0			0
$851$	4.72953	−	0.749084i	0.162126	−	0.0256783i
$852$		0			0
$853$	−28.0930	−	14.3141i	−0.961885	−	0.490105i	−0.0987690	−	0.995110i	$-0.531490\pi$
$853$	−28.0930	−	14.3141i	−0.961885	−	0.490105i	−0.863116	+	0.505005i	$0.831490\pi$
$854$		0			0
$855$	−13.4286	+	9.75642i	−0.459247	+	0.333662i
$856$		0			0
$857$	26.1357			0.892777			0.446389	−	0.894839i	$-0.352710\pi$
$857$	26.1357			0.892777			0.446389	+	0.894839i	$0.352710\pi$
$858$		0			0
$859$	37.2719			1.27170			0.635850	−	0.771812i	$-0.280650\pi$
$859$	37.2719			1.27170			0.635850	+	0.771812i	$0.280650\pi$
$860$		0			0
$861$	0.0394707	−	0.0286771i	0.00134516	−	0.000977314i
$862$		0			0
$863$	25.8694	+	13.1811i	0.880604	+	0.448690i	0.834988	−	0.550269i	$-0.185475\pi$
$863$	25.8694	+	13.1811i	0.880604	+	0.448690i	0.0456166	+	0.998959i	$0.485475\pi$
$864$		0			0
$865$	−44.0488	+	6.97665i	−1.49770	+	0.237213i
$866$		0			0
$867$	−0.624219	+	1.92115i	−0.0211996	+	0.0652456i
$868$		0			0
$869$	−20.5679	+	35.6865i	−0.697719	+	1.21058i
$870$		0			0
$871$	36.8388	−	24.9135i	1.24823	−	0.844162i
$872$		0			0
$873$	−16.7795	+	2.65760i	−0.567899	+	0.0899463i
$874$		0			0
$875$	0.108137	+	0.332811i	0.00365570	+	0.0112511i
$876$		0			0
$877$	−27.2968	−	4.32339i	−0.921747	−	0.145990i	−0.322514	−	0.946565i	$-0.604528\pi$
$877$	−27.2968	−	4.32339i	−0.921747	−	0.145990i	−0.599233	+	0.800574i	$0.704528\pi$
$878$		0			0
$879$	−8.86308	+	8.86308i	−0.298944	+	0.298944i
$880$		0			0
$881$			34.0555i			1.14736i	0.819080	+	0.573680i	$0.194485\pi$
$881$			34.0555i			1.14736i	−0.819080	+	0.573680i	$0.805515\pi$
$882$		0			0
$883$	13.2584	+	18.2486i	0.446180	+	0.614114i	0.971571	−	0.236747i	$-0.0760812\pi$
$883$	13.2584	+	18.2486i	0.446180	+	0.614114i	−0.525392	+	0.850860i	$0.676081\pi$
$884$		0			0
$885$	−3.49405	−	10.7536i	−0.117451	−	0.361478i
$886$		0			0
$887$	20.0698	−	27.6238i	0.673880	−	0.927516i	−0.325961	−	0.945383i	$-0.605688\pi$
$887$	20.0698	−	27.6238i	0.673880	−	0.927516i	0.999840	+	0.0178677i	$0.00568777\pi$
$888$		0			0
$889$	−0.0931157	−	0.182750i	−0.00312300	−	0.00612924i
$890$		0			0
$891$	18.9906	−	17.1251i	0.636210	−	0.573711i
$892$		0			0
$893$	18.0763	+	5.87334i	0.604900	+	0.196544i
$894$		0			0
$895$	8.52577	+	53.8296i	0.284985	+	1.79933i
$896$		0			0
$897$	1.41647	+	3.02798i	0.0472947	+	0.101101i
$898$		0			0
$899$	47.3269	+	7.49584i	1.57844	+	0.250000i
$900$		0			0
$901$	−23.4755			−0.782081
$902$		0			0
$903$	−0.00437088	+	0.00437088i	−0.000145454	+	0.000145454i
$904$		0			0
$905$	−22.7014	−	3.59556i	−0.754622	−	0.119520i
$906$		0			0
$907$	−35.5861	+	11.5626i	−1.18162	+	0.383931i	−0.832967	−	0.553322i	$-0.813360\pi$
$907$	−35.5861	+	11.5626i	−1.18162	+	0.383931i	−0.348650	+	0.937253i	$0.613360\pi$
$908$		0			0
$909$	0.0695360	+	0.0505209i	0.00230636	+	0.00167567i
$910$		0			0
$911$	12.6702	−	38.9949i	0.419782	−	1.29196i	−0.488120	−	0.872776i	$-0.662317\pi$
$911$	12.6702	−	38.9949i	0.419782	−	1.29196i	0.907903	−	0.419181i	$-0.137683\pi$
$912$		0			0
$913$	−20.5773	−	16.6376i	−0.681010	−	0.550626i
$914$		0			0
$915$	16.8008	−	8.56044i	0.555417	−	0.282999i
$916$		0			0
$917$	0.00573862	+	0.0362322i	0.000189506	+	0.00119649i
$918$		0			0
$919$	1.81797	−	0.590695i	0.0599694	−	0.0194852i	−0.278879	−	0.960326i	$-0.589963\pi$
$919$	1.81797	−	0.590695i	0.0599694	−	0.0194852i	0.338848	+	0.940841i	$0.389963\pi$
$920$		0			0
$921$	0.885926	−	5.59352i	0.0291923	−	0.184313i
$922$		0			0
$923$	7.66064	+	5.97011i	0.252153	+	0.196509i
$924$		0			0
$925$	15.2678	−	15.2678i	0.502002	−	0.502002i
$926$		0			0
$927$	19.4320	+	26.7459i	0.638232	+	0.878451i
$928$		0			0
$929$	20.4390	+	10.4142i	0.670582	+	0.341679i	0.755911	−	0.654674i	$-0.227194\pi$
$929$	20.4390	+	10.4142i	0.670582	+	0.341679i	−0.0853289	+	0.996353i	$0.527194\pi$
$930$		0			0
$931$	10.0657	−	1.59425i	0.329889	−	0.0522494i
$932$		0			0
$933$	−6.56625	−	2.13350i	−0.214969	−	0.0698478i
$934$		0			0
$935$	58.4093	+	22.3710i	1.91019	+	0.731609i
$936$		0			0
$937$	−26.6327	−	8.65349i	−0.870053	−	0.282697i	−0.160232	−	0.987079i	$-0.551224\pi$
$937$	−26.6327	−	8.65349i	−0.870053	−	0.282697i	−0.709821	+	0.704382i	$0.751224\pi$
$938$		0			0
$939$	−1.03231	−	0.750019i	−0.0336882	−	0.0244759i
$940$		0			0
$941$	−4.40332	+	8.64199i	−0.143544	+	0.281721i	−0.951574	−	0.307421i	$-0.900534\pi$
$941$	−4.40332	+	8.64199i	−0.143544	+	0.281721i	0.808030	+	0.589142i	$0.200534\pi$
$942$		0			0
$943$	3.30095	−	20.8414i	0.107494	−	0.678689i
$944$		0			0
$945$			0.131335i			0.00427232i
$946$		0			0
$947$	36.2042	+	36.2042i	1.17648	+	1.17648i	0.980635	+	0.195845i	$0.0627448\pi$
$947$	36.2042	+	36.2042i	1.17648	+	1.17648i	0.195845	+	0.980635i	$0.437255\pi$
$948$		0			0
$949$	−8.11143	−	0.273347i	−0.263308	−	0.00887322i
$950$		0			0
$951$	−3.58368	−	1.82598i	−0.116209	−	0.0592113i
$952$		0			0
$953$	16.3314	+	11.8655i	0.529027	+	0.384361i	0.819994	−	0.572373i	$-0.193977\pi$
$953$	16.3314	+	11.8655i	0.529027	+	0.384361i	−0.290967	+	0.956733i	$0.593977\pi$
$954$		0			0
$955$	−25.3113	−	49.6761i	−0.819053	−	1.60748i
$956$		0			0
$957$	7.31949	+	1.55007i	0.236606	+	0.0501067i
$958$		0			0
$959$	−0.0106272	+	0.0327073i	−0.000343171	+	0.00105617i
$960$		0			0
$961$	−20.4112	+	28.0936i	−0.658425	+	0.906244i
$962$		0			0
$963$	−54.4372	+	17.6877i	−1.75421	+	0.569979i
$964$		0			0
$965$	22.1094	+	30.4310i	0.711728	+	0.979609i
$966$		0			0
$967$	17.0179	+	17.0179i	0.547258	+	0.547258i	0.925647	−	0.378389i	$-0.123522\pi$
$967$	17.0179	+	17.0179i	0.547258	+	0.547258i	−0.378389	+	0.925647i	$0.623522\pi$
$968$		0			0
$969$	−1.85521	−	1.85521i	−0.0595980	−	0.0595980i
$970$		0			0
$971$	−21.6120	+	15.7020i	−0.693561	+	0.503901i	−0.877829	−	0.478975i	$-0.841009\pi$
$971$	−21.6120	+	15.7020i	−0.693561	+	0.503901i	0.184268	+	0.982876i	$0.441009\pi$
$972$		0			0
$973$	−0.00909992	+	0.0178596i	−0.000291730	+	0.000572553i
$974$		0			0
$975$	13.1926	+	7.29176i	0.422502	+	0.233523i
$976$		0			0
$977$	−3.72110	−	7.30307i	−0.119049	−	0.233646i	0.823790	−	0.566894i	$-0.191855\pi$
$977$	−3.72110	−	7.30307i	−0.119049	−	0.233646i	−0.942839	+	0.333248i	$0.891855\pi$
$978$		0			0
$979$	18.8738	−	12.2769i	0.603209	−	0.392372i
$980$		0			0
$981$	−9.77938	+	4.98284i	−0.312232	+	0.159090i
$982$		0			0
$983$	5.65232	+	35.6873i	0.180281	+	1.13825i	0.897374	+	0.441271i	$0.145472\pi$
$983$	5.65232	+	35.6873i	0.180281	+	1.13825i	−0.717093	+	0.696978i	$0.754528\pi$
$984$		0			0
$985$	21.6387	+	66.5969i	0.689465	+	2.12196i
$986$		0			0
$987$	0.0593192	−	0.0430979i	0.00188815	−	0.00137182i
$988$		0			0
$989$			2.67346i			0.0850110i
$990$		0			0
$991$	−19.7279			−0.626679			−0.313339	−	0.949641i	$-0.601448\pi$
$991$	−19.7279			−0.626679			−0.313339	+	0.949641i	$0.601448\pi$
$992$		0			0
$993$	1.00549	−	6.34839i	0.0319082	−	0.201460i
$994$		0			0
$995$	−3.00282	+	5.89337i	−0.0951959	+	0.186832i
$996$		0			0
$997$	1.38549	−	1.90696i	0.0438788	−	0.0603940i	−0.786514	−	0.617573i	$-0.788116\pi$
$997$	1.38549	−	1.90696i	0.0438788	−	0.0603940i	0.830393	+	0.557179i	$0.188116\pi$
$998$		0			0
$999$	3.92449	−	1.99963i	0.124165	−	0.0632654i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bh.a.57.8	✓	112
11.6	odd	10	inner	572.2.bh.a.369.8	yes	112
13.8	odd	4	inner	572.2.bh.a.541.8	yes	112
143.138	even	20	inner	572.2.bh.a.281.8	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bh.a.57.8	✓	112	1.1	even	1	trivial
572.2.bh.a.281.8	yes	112	143.138	even	20	inner
572.2.bh.a.369.8	yes	112	11.6	odd	10	inner
572.2.bh.a.541.8	yes	112	13.8	odd	4	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bh (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.308779 - 0.224341i) q^{3} +(-3.55885 - 1.81333i) q^{5} +(-0.0145346 + 0.00230205i) q^{7} +(-0.882035 + 2.71463i) q^{9} +O(q^{10})\)	\(q+(0.308779 - 0.224341i) q^{3} +(-3.55885 - 1.81333i) q^{5} +(-0.0145346 + 0.00230205i) q^{7} +(-0.882035 + 2.71463i) q^{9} +(-0.687132 + 3.24466i) q^{11} +(3.54014 + 0.683652i) q^{13} +(-1.50570 + 0.238480i) q^{15} +(1.45902 + 4.49041i) q^{17} +(-1.43800 - 0.227757i) q^{19} +(-0.00397154 + 0.00397154i) q^{21} +2.42920i q^{23} +(6.43836 + 8.86164i) q^{25} +(0.690478 + 2.12507i) q^{27} +(3.47408 - 4.78166i) q^{29} +(3.68056 + 7.22351i) q^{31} +(0.515740 + 1.15604i) q^{33} +(0.0559009 + 0.0181633i) q^{35} +(-0.308366 - 1.94695i) q^{37} +(1.24649 - 0.583103i) q^{39} +(-8.57953 - 1.35886i) q^{41} +1.10055 q^{43} +(8.06154 - 8.06154i) q^{45} +(-12.8939 - 2.04219i) q^{47} +(-6.65719 + 2.16305i) q^{49} +(1.45790 + 1.05923i) q^{51} +(-1.53644 + 4.72869i) q^{53} +(8.32904 - 10.3013i) q^{55} +(-0.495119 + 0.252276i) q^{57} +(1.16027 + 7.32567i) q^{59} +(-11.7635 + 3.82219i) q^{61} +(0.00657082 - 0.0414865i) q^{63} +(-11.3592 - 8.85246i) q^{65} +(8.72172 - 8.72172i) q^{67} +(0.544970 + 0.750086i) q^{69} +(2.40010 + 1.22291i) q^{71} +(-2.22327 + 0.352131i) q^{73} +(3.97606 + 1.29190i) q^{75} +(0.00251779 - 0.0487417i) q^{77} +(11.8112 + 3.83770i) q^{79} +(-6.23765 - 4.53192i) q^{81} +(-3.62220 + 7.10898i) q^{83} +(2.95013 - 18.6264i) q^{85} -2.25586i q^{87} +(-4.80029 - 4.80029i) q^{89} +(-0.0530284 - 0.00178700i) q^{91} +(2.75701 + 1.40477i) q^{93} +(4.70463 + 3.41812i) q^{95} +(2.70210 + 5.30317i) q^{97} +(-8.20198 - 4.72722i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 28 q^{9}+O(q^{10}) \) 112 * q - 28 * q^9	\( 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) \) 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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