LMFDB - Embedded newform 572.2.i.b.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(133,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("572.133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.1
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	572.529
Dual form			572.2.i.b.133.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23025 + 2.13086i) q^{3} -2.05408 q^{5} +(-1.43346 - 2.48283i) q^{7} +(-1.52704 - 2.64491i) q^{9} +O(q^{10})$	\(q+(-1.23025 + 2.13086i) q^{3} -2.05408 q^{5} +(-1.43346 - 2.48283i) q^{7} +(-1.52704 - 2.64491i) q^{9} +(0.500000 - 0.866025i) q^{11} +(2.50000 - 2.59808i) q^{13} +(2.52704 - 4.37697i) q^{15} +(2.82383 + 4.89102i) q^{17} +(-1.73025 - 2.99689i) q^{19} +7.05408 q^{21} +(4.28434 - 7.42069i) q^{23} -0.780738 q^{25} +0.133074 q^{27} +(-3.39397 + 5.87852i) q^{29} +10.8420 q^{31} +(1.23025 + 2.13086i) q^{33} +(2.94445 + 5.09994i) q^{35} +(-1.12062 + 1.94097i) q^{37} +(2.46050 + 8.52344i) q^{39} +(2.82383 - 4.89102i) q^{41} +(-4.71420 - 8.16524i) q^{43} +(3.13667 + 5.43288i) q^{45} +5.32743 q^{47} +(-0.609631 + 1.05591i) q^{49} -13.8961 q^{51} +10.9751 q^{53} +(-1.02704 + 1.77889i) q^{55} +8.51459 q^{57} +(-6.39397 - 11.0747i) q^{59} +(-5.71780 - 9.90352i) q^{61} +(-4.37792 + 7.58277i) q^{63} +(-5.13521 + 5.33667i) q^{65} +(-0.429864 + 0.744547i) q^{67} +(10.5416 + 18.2586i) q^{69} +(-3.81138 - 6.60150i) q^{71} +4.37432 q^{73} +(0.960505 - 1.66364i) q^{75} -2.86693 q^{77} -16.4825 q^{79} +(4.41741 - 7.65118i) q^{81} +7.97509 q^{83} +(-5.80039 - 10.0466i) q^{85} +(-8.35087 - 14.4641i) q^{87} +(0.0811263 - 0.140515i) q^{89} +(-10.0342 - 2.48283i) q^{91} +(-13.3384 + 23.1028i) q^{93} +(3.55408 + 6.15585i) q^{95} +(-5.42101 - 9.38946i) q^{97} -3.05408 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} + 6 q^{5} - 5 q^{7}+O(q^{10}) $ 6 * q - q^3 + 6 * q^5 - 5 * q^7	$ 6 q - q^{3} + 6 q^{5} - 5 q^{7} + 3 q^{11} + 15 q^{13} + 6 q^{15} + 5 q^{17} - 4 q^{19} + 24 q^{21} + q^{23} + 12 q^{25} + 8 q^{27} - 4 q^{29} + 14 q^{31} + q^{33} - 9 q^{35} + 8 q^{37} + 2 q^{39} + 5 q^{41} - 8 q^{43} + 18 q^{45} + 12 q^{47} - 12 q^{49} - 14 q^{51} + 22 q^{53} + 3 q^{55} + 20 q^{57} - 22 q^{59} - 6 q^{61} + 4 q^{63} + 15 q^{65} - 7 q^{67} + 23 q^{69} + 11 q^{71} + 4 q^{73} - 7 q^{75} - 10 q^{77} - 40 q^{79} + 9 q^{81} + 4 q^{83} - 24 q^{85} - 29 q^{87} - 27 q^{89} - 35 q^{91} - 37 q^{93} + 3 q^{95} - 7 q^{97}+O(q^{100}) $ 6 * q - q^3 + 6 * q^5 - 5 * q^7 + 3 * q^11 + 15 * q^13 + 6 * q^15 + 5 * q^17 - 4 * q^19 + 24 * q^21 + q^23 + 12 * q^25 + 8 * q^27 - 4 * q^29 + 14 * q^31 + q^33 - 9 * q^35 + 8 * q^37 + 2 * q^39 + 5 * q^41 - 8 * q^43 + 18 * q^45 + 12 * q^47 - 12 * q^49 - 14 * q^51 + 22 * q^53 + 3 * q^55 + 20 * q^57 - 22 * q^59 - 6 * q^61 + 4 * q^63 + 15 * q^65 - 7 * q^67 + 23 * q^69 + 11 * q^71 + 4 * q^73 - 7 * q^75 - 10 * q^77 - 40 * q^79 + 9 * q^81 + 4 * q^83 - 24 * q^85 - 29 * q^87 - 27 * q^89 - 35 * q^91 - 37 * q^93 + 3 * q^95 - 7 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.23025	+	2.13086i	−0.710287	+	1.23025i	0.254463	+	0.967083i	$0.418101\pi$
$3$	−1.23025	+	2.13086i	−0.710287	+	1.23025i	−0.964750	+	0.263170i	$0.915232\pi$
$4$		0			0
$5$	−2.05408			−0.918614			−0.459307	−	0.888277i	$-0.651902\pi$
$5$	−2.05408			−0.918614			−0.459307	+	0.888277i	$0.651902\pi$
$6$		0			0
$7$	−1.43346	−	2.48283i	−0.541798	−	0.938422i	−0.998801	−	0.0489565i	$-0.984410\pi$
$7$	−1.43346	−	2.48283i	−0.541798	−	0.938422i	0.457003	−	0.889465i	$-0.348923\pi$
$8$		0			0
$9$	−1.52704	−	2.64491i	−0.509014	−	0.881638i
$10$		0			0
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$14$		0			0
$15$	2.52704	−	4.37697i	0.652479	−	1.13013i
$16$		0			0
$17$	2.82383	+	4.89102i	0.684880	+	1.18625i	0.973475	+	0.228795i	$0.0734786\pi$
$17$	2.82383	+	4.89102i	0.684880	+	1.18625i	−0.288595	+	0.957451i	$0.593188\pi$
$18$		0			0
$19$	−1.73025	−	2.99689i	−0.396947	−	0.687533i	0.596400	−	0.802687i	$-0.296597\pi$
$19$	−1.73025	−	2.99689i	−0.396947	−	0.687533i	−0.993348	+	0.115154i	$0.963264\pi$
$20$		0			0
$21$	7.05408			1.53933
$22$		0			0
$23$	4.28434	−	7.42069i	0.893346	−	1.54732i	0.0575075	−	0.998345i	$-0.481685\pi$
$23$	4.28434	−	7.42069i	0.893346	−	1.54732i	0.835838	−	0.548975i	$-0.184982\pi$
$24$		0			0
$25$	−0.780738			−0.156148
$26$		0			0
$27$	0.133074			0.0256102
$28$		0			0
$29$	−3.39397	+	5.87852i	−0.630244	+	1.09161i	0.357258	+	0.934006i	$0.383712\pi$
$29$	−3.39397	+	5.87852i	−0.630244	+	1.09161i	−0.987502	+	0.157609i	$0.949622\pi$
$30$		0			0
$31$	10.8420			1.94728			0.973642	−	0.228081i	$-0.0732452\pi$
$31$	10.8420			1.94728			0.973642	+	0.228081i	$0.0732452\pi$
$32$		0			0
$33$	1.23025	+	2.13086i	0.214159	+	0.370935i
$34$		0			0
$35$	2.94445	+	5.09994i	0.497703	+	0.862048i
$36$		0			0
$37$	−1.12062	+	1.94097i	−0.184229	+	0.319094i	−0.943316	−	0.331895i	$-0.892312\pi$
$37$	−1.12062	+	1.94097i	−0.184229	+	0.319094i	0.759087	+	0.650989i	$0.225645\pi$
$38$		0			0
$39$	2.46050	+	8.52344i	0.393996	+	1.36484i
$40$		0			0
$41$	2.82383	−	4.89102i	0.441008	−	0.763849i	−0.556756	−	0.830676i	$-0.687954\pi$
$41$	2.82383	−	4.89102i	0.441008	−	0.763849i	0.997765	+	0.0668270i	$0.0212876\pi$
$42$		0			0
$43$	−4.71420	−	8.16524i	−0.718909	−	1.24519i	−0.961432	−	0.275041i	$-0.911309\pi$
$43$	−4.71420	−	8.16524i	−0.718909	−	1.24519i	0.242524	−	0.970146i	$-0.422025\pi$
$44$		0			0
$45$	3.13667	+	5.43288i	0.467588	+	0.809886i
$46$		0			0
$47$	5.32743			0.777086			0.388543	−	0.921431i	$-0.372979\pi$
$47$	5.32743			0.777086			0.388543	+	0.921431i	$0.372979\pi$
$48$		0			0
$49$	−0.609631	+	1.05591i	−0.0870901	+	0.150845i
$50$		0			0
$51$	−13.8961			−1.94584
$52$		0			0
$53$	10.9751			1.50755			0.753773	−	0.657135i	$-0.228232\pi$
$53$	10.9751			1.50755			0.753773	+	0.657135i	$0.228232\pi$
$54$		0			0
$55$	−1.02704	+	1.77889i	−0.138486	+	0.239865i
$56$		0			0
$57$	8.51459			1.12778
$58$		0			0
$59$	−6.39397	−	11.0747i	−0.832424	−	1.44180i	−0.896111	−	0.443830i	$-0.853619\pi$
$59$	−6.39397	−	11.0747i	−0.832424	−	1.44180i	0.0636872	−	0.997970i	$-0.479714\pi$
$60$		0			0
$61$	−5.71780	−	9.90352i	−0.732089	−	1.26802i	−0.955989	−	0.293403i	$-0.905212\pi$
$61$	−5.71780	−	9.90352i	−0.732089	−	1.26802i	0.223900	−	0.974612i	$-0.428121\pi$
$62$		0			0
$63$	−4.37792	+	7.58277i	−0.551566	+	0.955340i
$64$		0			0
$65$	−5.13521	+	5.33667i	−0.636944	+	0.661932i
$66$		0			0
$67$	−0.429864	+	0.744547i	−0.0525163	+	0.0909608i	−0.891088	−	0.453830i	$-0.850057\pi$
$67$	−0.429864	+	0.744547i	−0.0525163	+	0.0909608i	0.838572	+	0.544790i	$0.183391\pi$
$68$		0			0
$69$	10.5416	+	18.2586i	1.26906	+	2.19808i
$70$		0			0
$71$	−3.81138	−	6.60150i	−0.452327	−	0.783454i	0.546203	−	0.837653i	$-0.316073\pi$
$71$	−3.81138	−	6.60150i	−0.452327	−	0.783454i	−0.998530	+	0.0541989i	$0.982739\pi$
$72$		0			0
$73$	4.37432			0.511975			0.255988	−	0.966680i	$-0.417599\pi$
$73$	4.37432			0.511975			0.255988	+	0.966680i	$0.417599\pi$
$74$		0			0
$75$	0.960505	−	1.66364i	0.110910	−	0.192101i
$76$		0			0
$77$	−2.86693			−0.326716
$78$		0			0
$79$	−16.4825			−1.85442			−0.927212	−	0.374536i	$-0.877802\pi$
$79$	−16.4825			−1.85442			−0.927212	+	0.374536i	$0.877802\pi$
$80$		0			0
$81$	4.41741	−	7.65118i	0.490823	−	0.850131i
$82$		0			0
$83$	7.97509			0.875380			0.437690	−	0.899126i	$-0.355797\pi$
$83$	7.97509			0.875380			0.437690	+	0.899126i	$0.355797\pi$
$84$		0			0
$85$	−5.80039	−	10.0466i	−0.629140	−	1.08970i
$86$		0			0
$87$	−8.35087	−	14.4641i	−0.895308	−	1.55072i
$88$		0			0
$89$	0.0811263	−	0.140515i	0.00859937	−	0.0148946i	−0.861694	−	0.507429i	$-0.830596\pi$
$89$	0.0811263	−	0.140515i	0.00859937	−	0.0148946i	0.870293	+	0.492534i	$0.163929\pi$
$90$		0			0
$91$	−10.0342	−	2.48283i	−1.05187	−	0.260271i
$92$		0			0
$93$	−13.3384	+	23.1028i	−1.38313	+	2.39565i
$94$		0			0
$95$	3.55408	+	6.15585i	0.364641	+	0.631577i
$96$		0			0
$97$	−5.42101	−	9.38946i	−0.550420	−	0.953356i	−0.998244	−	0.0592339i	$-0.981134\pi$
$97$	−5.42101	−	9.38946i	−0.550420	−	0.953356i	0.447824	−	0.894122i	$-0.352199\pi$
$98$		0			0
$99$	−3.05408			−0.306947
$100$		0			0
$101$	−1.83628	+	3.18054i	−0.182717	+	0.316475i	−0.942805	−	0.333345i	$-0.891823\pi$
$101$	−1.83628	+	3.18054i	−0.182717	+	0.316475i	0.760088	+	0.649820i	$0.225156\pi$
$102$		0			0
$103$	9.54377			0.940375			0.470188	−	0.882566i	$-0.344186\pi$
$103$	9.54377			0.940375			0.470188	+	0.882566i	$0.344186\pi$
$104$		0			0
$105$	−14.4897			−1.41405
$106$		0			0
$107$	−1.30039	+	2.25234i	−0.125713	+	0.217742i	−0.922012	−	0.387162i	$-0.873455\pi$
$107$	−1.30039	+	2.25234i	−0.125713	+	0.217742i	0.796298	+	0.604904i	$0.206789\pi$
$108$		0			0
$109$	−0.165178			−0.0158212			−0.00791058	−	0.999969i	$-0.502518\pi$
$109$	−0.165178			−0.0158212			−0.00791058	+	0.999969i	$0.502518\pi$
$110$		0			0
$111$	−2.75729	−	4.77577i	−0.261711	−	0.453296i
$112$		0			0
$113$	0.136673	+	0.236725i	0.0128571	+	0.0222692i	0.872382	−	0.488824i	$-0.162574\pi$
$113$	0.136673	+	0.236725i	0.0128571	+	0.0222692i	−0.859525	+	0.511093i	$0.829241\pi$
$114$		0			0
$115$	−8.80039	+	15.2427i	−0.820640	+	1.42139i
$116$		0			0
$117$	−10.6893	−	2.64491i	−0.988226	−	0.244522i
$118$		0			0
$119$	8.09572	−	14.0222i	0.742133	−	1.28541i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$	6.94805	+	12.0344i	0.626485	+	1.08510i
$124$		0			0
$125$	11.8741			1.06205
$126$		0			0
$127$	−6.52704	+	11.3052i	−0.579181	+	1.00317i	0.416392	+	0.909185i	$0.363294\pi$
$127$	−6.52704	+	11.3052i	−0.579181	+	1.00317i	−0.995573	+	0.0939864i	$0.970039\pi$
$128$		0			0
$129$	23.1986			2.04253
$130$		0			0
$131$	−8.52179			−0.744552			−0.372276	−	0.928122i	$-0.621423\pi$
$131$	−8.52179			−0.744552			−0.372276	+	0.928122i	$0.621423\pi$
$132$		0			0
$133$	−4.96050	+	8.59185i	−0.430130	+	0.745008i
$134$		0			0
$135$	−0.273346			−0.0235259
$136$		0			0
$137$	2.11702	+	3.66679i	0.180869	+	0.313275i	0.942177	−	0.335116i	$-0.108776\pi$
$137$	2.11702	+	3.66679i	0.180869	+	0.313275i	−0.761307	+	0.648391i	$0.775442\pi$
$138$		0			0
$139$	−3.13307	−	5.42664i	−0.265744	−	0.460282i	0.702014	−	0.712163i	$-0.252284\pi$
$139$	−3.13307	−	5.42664i	−0.265744	−	0.460282i	−0.967758	+	0.251881i	$0.918951\pi$
$140$		0			0
$141$	−6.55408	+	11.3520i	−0.551953	+	0.956011i
$142$		0			0
$143$	−1.00000	−	3.46410i	−0.0836242	−	0.289683i
$144$		0			0
$145$	6.97150	−	12.0750i	0.578951	−	1.00277i
$146$		0			0
$147$	−1.50000	−	2.59808i	−0.123718	−	0.214286i
$148$		0			0
$149$	2.01245	+	3.48567i	0.164867	+	0.285557i	0.936608	−	0.350379i	$-0.113947\pi$
$149$	2.01245	+	3.48567i	0.164867	+	0.285557i	−0.771741	+	0.635937i	$0.780614\pi$
$150$		0			0
$151$	0.219262			0.0178433			0.00892164	−	0.999960i	$-0.497160\pi$
$151$	0.219262			0.0178433			0.00892164	+	0.999960i	$0.497160\pi$
$152$		0			0
$153$	8.62422	−	14.9376i	0.697227	−	1.20763i
$154$		0			0
$155$	−22.2704			−1.78880
$156$		0			0
$157$	−9.32743			−0.744410			−0.372205	−	0.928151i	$-0.621398\pi$
$157$	−9.32743			−0.744410			−0.372205	+	0.928151i	$0.621398\pi$
$158$		0			0
$159$	−13.5021	+	23.3864i	−1.07079	+	1.85466i
$160$		0			0
$161$	−24.5657			−1.93605
$162$		0			0
$163$	1.16731	+	2.02185i	0.0914311	+	0.158363i	0.908114	−	0.418724i	$-0.137523\pi$
$163$	1.16731	+	2.02185i	0.0914311	+	0.158363i	−0.816682	+	0.577087i	$0.804189\pi$
$164$		0			0
$165$	−2.52704	−	4.37697i	−0.196730	−	0.340746i
$166$		0			0
$167$	4.24484	−	7.35228i	0.328476	−	0.568937i	−0.653734	−	0.756725i	$-0.726798\pi$
$167$	4.24484	−	7.35228i	0.328476	−	0.568937i	0.982210	+	0.187788i	$0.0601318\pi$
$168$		0			0
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$		0			0
$171$	−5.28434	+	9.15274i	−0.404103	+	0.699927i
$172$		0			0
$173$	8.62422	+	14.9376i	0.655687	+	1.13568i	0.981721	+	0.190326i	$0.0609544\pi$
$173$	8.62422	+	14.9376i	0.655687	+	1.13568i	−0.326034	+	0.945358i	$0.605712\pi$
$174$		0			0
$175$	1.11916	+	1.93844i	0.0846005	+	0.146532i
$176$		0			0
$177$	31.4648			2.36504
$178$		0			0
$179$	−8.25370	+	14.2958i	−0.616910	+	1.06852i	0.373136	+	0.927777i	$0.378283\pi$
$179$	−8.25370	+	14.2958i	−0.616910	+	1.06852i	−0.990046	+	0.140743i	$0.955051\pi$
$180$		0			0
$181$	13.6840			1.01713			0.508563	−	0.861025i	$-0.330177\pi$
$181$	13.6840			1.01713			0.508563	+	0.861025i	$0.330177\pi$
$182$		0			0
$183$	28.1373			2.07997
$184$		0			0
$185$	2.30185	−	3.98692i	0.169235	−	0.293124i
$186$		0			0
$187$	5.64766			0.412998
$188$		0			0
$189$	−0.190757	−	0.330401i	−0.0138756	−	0.0240332i
$190$		0			0
$191$	−0.215663	−	0.373540i	−0.0156049	−	0.0270284i	0.858118	−	0.513453i	$-0.171634\pi$
$191$	−0.215663	−	0.373540i	−0.0156049	−	0.0270284i	−0.873722	+	0.486425i	$0.838301\pi$
$192$		0			0
$193$	−9.01459	+	15.6137i	−0.648884	+	1.12390i	0.334505	+	0.942394i	$0.391431\pi$
$193$	−9.01459	+	15.6137i	−0.648884	+	1.12390i	−0.983390	+	0.181507i	$0.941903\pi$
$194$		0			0
$195$	−5.05408	−	17.5079i	−0.361930	−	1.25376i
$196$		0			0
$197$	4.50000	−	7.79423i	0.320612	−	0.555316i	−0.660003	−	0.751263i	$-0.729445\pi$
$197$	4.50000	−	7.79423i	0.320612	−	0.555316i	0.980614	+	0.195947i	$0.0627782\pi$
$198$		0			0
$199$	8.20175	+	14.2058i	0.581406	+	1.00703i	0.995313	+	0.0967062i	$0.0308307\pi$
$199$	8.20175	+	14.2058i	0.581406	+	1.00703i	−0.413906	+	0.910319i	$0.635836\pi$
$200$		0			0
$201$	−1.05768	−	1.83196i	−0.0746032	−	0.129217i
$202$		0			0
$203$	19.4605			1.36586
$204$		0			0
$205$	−5.80039	+	10.0466i	−0.405117	+	0.701683i
$206$		0			0
$207$	−26.1694			−1.81890
$208$		0			0
$209$	−3.46050			−0.239368
$210$		0			0
$211$	−3.19076	+	5.52655i	−0.219661	+	0.380464i	−0.954704	−	0.297556i	$-0.903828\pi$
$211$	−3.19076	+	5.52655i	−0.219661	+	0.380464i	0.735043	+	0.678020i	$0.237162\pi$
$212$		0			0
$213$	18.7558			1.28513
$214$		0			0
$215$	9.68337	+	16.7721i	0.660400	+	1.14385i
$216$		0			0
$217$	−15.5416	−	26.9189i	−1.05503	−	1.82737i
$218$		0			0
$219$	−5.38151	+	9.32106i	−0.363649	+	0.629859i
$220$		0			0
$221$	19.7668	+	4.89102i	1.32966	+	0.329006i
$222$		0			0
$223$	12.4626	−	21.5859i	0.834560	−	1.44550i	−0.0598279	−	0.998209i	$-0.519055\pi$
$223$	12.4626	−	21.5859i	0.834560	−	1.44550i	0.894388	−	0.447292i	$-0.147611\pi$
$224$		0			0
$225$	1.19222	+	2.06499i	0.0794813	+	0.137666i
$226$		0			0
$227$	4.55768	+	7.89414i	0.302504	+	0.523952i	0.976702	−	0.214598i	$-0.0688441\pi$
$227$	4.55768	+	7.89414i	0.302504	+	0.523952i	−0.674198	+	0.738550i	$0.735511\pi$
$228$		0			0
$229$	−18.4107			−1.21661			−0.608306	−	0.793702i	$-0.708151\pi$
$229$	−18.4107			−1.21661			−0.608306	+	0.793702i	$0.708151\pi$
$230$		0			0
$231$	3.52704	−	6.10902i	0.232062	−	0.401944i
$232$		0			0
$233$	3.62568			0.237526			0.118763	−	0.992923i	$-0.462107\pi$
$233$	3.62568			0.237526			0.118763	+	0.992923i	$0.462107\pi$
$234$		0			0
$235$	−10.9430			−0.713842
$236$		0			0
$237$	20.2776	−	35.1219i	1.31717	−	2.28141i
$238$		0			0
$239$	−12.3566			−0.799283			−0.399641	−	0.916672i	$-0.630865\pi$
$239$	−12.3566			−0.799283			−0.399641	+	0.916672i	$0.630865\pi$
$240$		0			0
$241$	−11.3238	−	19.6135i	−0.729432	−	1.26341i	−0.957124	−	0.289680i	$-0.906451\pi$
$241$	−11.3238	−	19.6135i	−0.729432	−	1.26341i	0.227691	−	0.973733i	$-0.426882\pi$
$242$		0			0
$243$	11.0687	+	19.1715i	0.710056	+	1.22985i
$244$		0			0
$245$	1.25223	−	2.16893i	0.0800023	−	0.138568i
$246$		0			0
$247$	−12.1118	−	2.99689i	−0.770653	−	0.190687i
$248$		0			0
$249$	−9.81138	+	16.9938i	−0.621771	+	1.07694i
$250$		0			0
$251$	6.55408	+	11.3520i	0.413690	+	0.716532i	0.995290	−	0.0969427i	$-0.0309064\pi$
$251$	6.55408	+	11.3520i	0.413690	+	0.716532i	−0.581600	+	0.813475i	$0.697573\pi$
$252$		0			0
$253$	−4.28434	−	7.42069i	−0.269354	−	0.466535i
$254$		0			0
$255$	28.5438			1.78748
$256$		0			0
$257$	−1.08472	+	1.87880i	−0.0676633	+	0.117196i	−0.897872	−	0.440256i	$-0.854888\pi$
$257$	−1.08472	+	1.87880i	−0.0676633	+	0.117196i	0.830209	+	0.557452i	$0.188221\pi$
$258$		0			0
$259$	6.42548			0.399260
$260$		0			0
$261$	20.7309			1.28321
$262$		0			0
$263$	15.0972	−	26.1491i	0.930932	−	1.61242i	0.149200	−	0.988807i	$-0.452330\pi$
$263$	15.0972	−	26.1491i	0.930932	−	1.61242i	0.781732	−	0.623614i	$-0.214336\pi$
$264$		0			0
$265$	−22.5438			−1.38485
$266$		0			0
$267$	0.199612	+	0.345738i	0.0122160	+	0.0211588i
$268$		0			0
$269$	−3.08113	−	5.33667i	−0.187860	−	0.325382i	0.756677	−	0.653789i	$-0.226822\pi$
$269$	−3.08113	−	5.33667i	−0.187860	−	0.325382i	−0.944536	+	0.328407i	$0.893488\pi$
$270$		0			0
$271$	13.7865	−	23.8789i	0.837469	−	1.45054i	−0.0545360	−	0.998512i	$-0.517368\pi$
$271$	13.7865	−	23.8789i	0.837469	−	1.45054i	0.892005	−	0.452026i	$-0.149299\pi$
$272$		0			0
$273$	17.6352	−	18.3270i	1.06733	−	1.10920i
$274$		0			0
$275$	−0.390369	+	0.676139i	−0.0235401	+	0.0407727i
$276$		0			0
$277$	−2.40496	−	4.16551i	−0.144500	−	0.250281i	0.784686	−	0.619893i	$-0.212824\pi$
$277$	−2.40496	−	4.16551i	−0.144500	−	0.250281i	−0.929186	+	0.369612i	$0.879491\pi$
$278$		0			0
$279$	−16.5562	−	28.6762i	−0.991195	−	1.71680i
$280$		0			0
$281$	−7.84922			−0.468245			−0.234123	−	0.972207i	$-0.575222\pi$
$281$	−7.84922			−0.468245			−0.234123	+	0.972207i	$0.575222\pi$
$282$		0			0
$283$	−1.20175	+	2.08149i	−0.0714365	+	0.123732i	−0.899531	−	0.436857i	$-0.856092\pi$
$283$	−1.20175	+	2.08149i	−0.0714365	+	0.123732i	0.828095	+	0.560588i	$0.189425\pi$
$284$		0			0
$285$	−17.4897			−1.03600
$286$		0			0
$287$	−16.1914			−0.955750
$288$		0			0
$289$	−7.44805	+	12.9004i	−0.438121	+	0.758847i
$290$		0			0
$291$	26.6768			1.56382
$292$		0			0
$293$	5.05408	+	8.75393i	0.295263	+	0.511410i	0.975046	−	0.222003i	$-0.0712595\pi$
$293$	5.05408	+	8.75393i	0.295263	+	0.511410i	−0.679783	+	0.733413i	$0.737926\pi$
$294$		0			0
$295$	13.1337	+	22.7483i	0.764676	+	1.32446i
$296$		0			0
$297$	0.0665372	−	0.115246i	0.00386088	−	0.00668724i
$298$		0			0
$299$	−8.56867	−	29.6828i	−0.495539	−	1.71660i
$300$		0			0
$301$	−13.5153	+	23.4091i	−0.779007	+	1.34928i
$302$		0			0
$303$	−4.51819	−	7.82573i	−0.259563	−	0.449576i
$304$		0			0
$305$	11.7448	+	20.3427i	0.672508	+	1.16482i
$306$		0			0
$307$	16.6798			0.951965			0.475982	−	0.879455i	$-0.342093\pi$
$307$	16.6798			0.951965			0.475982	+	0.879455i	$0.342093\pi$
$308$		0			0
$309$	−11.7412	+	20.3364i	−0.667936	+	1.15690i
$310$		0			0
$311$	−24.2776			−1.37666			−0.688329	−	0.725399i	$-0.741655\pi$
$311$	−24.2776			−1.37666			−0.688329	+	0.725399i	$0.741655\pi$
$312$		0			0
$313$	5.16225			0.291788			0.145894	−	0.989300i	$-0.453394\pi$
$313$	5.16225			0.291788			0.145894	+	0.989300i	$0.453394\pi$
$314$		0			0
$315$	8.99261	−	15.5757i	0.506676	−	0.877589i
$316$		0			0
$317$	0.204868			0.0115065			0.00575325	−	0.999983i	$-0.498169\pi$
$317$	0.204868			0.0115065			0.00575325	+	0.999983i	$0.498169\pi$
$318$		0			0
$319$	3.39397	+	5.87852i	0.190026	+	0.329134i
$320$		0			0
$321$	−3.19961	−	5.54189i	−0.178585	−	0.309318i
$322$		0			0
$323$	9.77188	−	16.9254i	0.543722	−	0.941754i
$324$		0			0
$325$	−1.95185	+	2.02842i	−0.108269	+	0.112516i
$326$		0			0
$327$	0.203210	−	0.351971i	0.0112376	−	0.0194640i
$328$		0			0
$329$	−7.63667	−	13.2271i	−0.421023	−	0.729234i
$330$		0			0
$331$	−3.92101	−	6.79139i	−0.215518	−	0.373288i	0.737915	−	0.674894i	$-0.235811\pi$
$331$	−3.92101	−	6.79139i	−0.215518	−	0.373288i	−0.953433	+	0.301606i	$0.902477\pi$
$332$		0			0
$333$	6.84494			0.375101
$334$		0			0
$335$	0.882977	−	1.52936i	0.0482422	−	0.0835579i
$336$		0			0
$337$	17.1986			0.936869			0.468434	−	0.883498i	$-0.344818\pi$
$337$	17.1986			0.936869			0.468434	+	0.883498i	$0.344818\pi$
$338$		0			0
$339$	−0.672570			−0.0365290
$340$		0			0
$341$	5.42101	−	9.38946i	0.293564	−	0.508468i
$342$		0			0
$343$	−16.5729			−0.894855
$344$		0			0
$345$	−21.6534	−	37.5048i	−1.16578	−	2.01919i
$346$		0			0
$347$	−0.144065	−	0.249528i	−0.00773381	−	0.0133954i	0.862133	−	0.506683i	$-0.169128\pi$
$347$	−0.144065	−	0.249528i	−0.00773381	−	0.0133954i	−0.869866	+	0.493287i	$0.835795\pi$
$348$		0			0
$349$	0.620621	−	1.07495i	0.0332211	−	0.0575406i	−0.848937	−	0.528494i	$-0.822757\pi$
$349$	0.620621	−	1.07495i	0.0332211	−	0.0575406i	0.882158	+	0.470954i	$0.156090\pi$
$350$		0			0
$351$	0.332686	−	0.345738i	0.0177575	−	0.0184541i
$352$		0			0
$353$	−4.30252	+	7.45219i	−0.229000	+	0.396640i	−0.957512	−	0.288393i	$-0.906879\pi$
$353$	−4.30252	+	7.45219i	−0.229000	+	0.396640i	0.728512	+	0.685033i	$0.240212\pi$
$354$		0			0
$355$	7.82889	+	13.5600i	0.415514	+	0.719692i
$356$		0			0
$357$	19.9195	+	34.5017i	1.05425	+	1.82602i
$358$		0			0
$359$	34.7850			1.83588			0.917941	−	0.396716i	$-0.129850\pi$
$359$	34.7850			1.83588			0.917941	+	0.396716i	$0.129850\pi$
$360$		0			0
$361$	3.51245	−	6.08375i	0.184866	−	0.320197i
$362$		0			0
$363$	2.46050			0.129143
$364$		0			0
$365$	−8.98522			−0.470308
$366$		0			0
$367$	−0.519650	+	0.900061i	−0.0271255	+	0.0469828i	−0.879269	−	0.476325i	$-0.841969\pi$
$367$	−0.519650	+	0.900061i	−0.0271255	+	0.0469828i	0.852144	+	0.523307i	$0.175302\pi$
$368$		0			0
$369$	−17.2484			−0.897918
$370$		0			0
$371$	−15.7324	−	27.2493i	−0.816785	−	1.41471i
$372$		0			0
$373$	−3.66158	−	6.34204i	−0.189589	−	0.328378i	0.755524	−	0.655121i	$-0.227382\pi$
$373$	−3.66158	−	6.34204i	−0.189589	−	0.328378i	−0.945113	+	0.326743i	$0.894049\pi$
$374$		0			0
$375$	−14.6082	+	25.3021i	−0.754363	+	1.30659i
$376$		0			0
$377$	6.78794	+	23.5141i	0.349596	+	1.21104i
$378$		0			0
$379$	0.991146	−	1.71671i	0.0509117	−	0.0881817i	−0.839446	−	0.543442i	$-0.817121\pi$
$379$	0.991146	−	1.71671i	0.0509117	−	0.0881817i	0.890358	+	0.455261i	$0.150454\pi$
$380$		0			0
$381$	−16.0598	−	27.8164i	−0.822769	−	1.42508i
$382$		0			0
$383$	13.5182	+	23.4142i	0.690747	+	1.19641i	0.971593	+	0.236656i	$0.0760516\pi$
$383$	13.5182	+	23.4142i	0.690747	+	1.19641i	−0.280846	+	0.959753i	$0.590615\pi$
$384$		0			0
$385$	5.88891			0.300126
$386$		0			0
$387$	−14.3976	+	24.9373i	−0.731869	+	1.26764i
$388$		0			0
$389$	23.2527			1.17896			0.589480	−	0.807783i	$-0.299333\pi$
$389$	23.2527			1.17896			0.589480	+	0.807783i	$0.299333\pi$
$390$		0			0
$391$	48.3930			2.44734
$392$		0			0
$393$	10.4839	−	18.1587i	0.528845	−	0.915987i
$394$		0			0
$395$	33.8564			1.70350
$396$		0			0
$397$	2.72286	+	4.71613i	0.136656	+	0.236696i	0.926229	−	0.376961i	$-0.123031\pi$
$397$	2.72286	+	4.71613i	0.136656	+	0.236696i	−0.789573	+	0.613657i	$0.789698\pi$
$398$		0			0
$399$	−12.2053	−	21.1403i	−0.611032	−	1.05834i
$400$		0			0
$401$	−15.6426	+	27.0938i	−0.781154	+	1.35300i	0.150115	+	0.988668i	$0.452035\pi$
$401$	−15.6426	+	27.0938i	−0.781154	+	1.35300i	−0.931270	+	0.364330i	$0.881298\pi$
$402$		0			0
$403$	27.1050	−	28.1684i	1.35020	−	1.40317i
$404$		0			0
$405$	−9.07373	+	15.7162i	−0.450877	+	0.780943i
$406$		0			0
$407$	1.12062	+	1.94097i	0.0555471	+	0.0962105i
$408$		0			0
$409$	3.22879	+	5.59243i	0.159653	+	0.276528i	0.934744	−	0.355323i	$-0.115629\pi$
$409$	3.22879	+	5.59243i	0.159653	+	0.276528i	−0.775090	+	0.631850i	$0.782296\pi$
$410$		0			0
$411$	−10.4179			−0.513877
$412$		0			0
$413$	−18.3310	+	31.7503i	−0.902011	+	1.56233i
$414$		0			0
$415$	−16.3815			−0.804137
$416$		0			0
$417$	15.4179			0.755017
$418$		0			0
$419$	7.06867	−	12.2433i	0.345327	−	0.598124i	−0.640086	−	0.768303i	$-0.721101\pi$
$419$	7.06867	−	12.2433i	0.345327	−	0.598124i	0.985413	+	0.170179i	$0.0544346\pi$
$420$		0			0
$421$	35.6984			1.73984			0.869918	−	0.493197i	$-0.164172\pi$
$421$	35.6984			1.73984			0.869918	+	0.493197i	$0.164172\pi$
$422$		0			0
$423$	−8.13521	−	14.0906i	−0.395547	−	0.685108i
$424$		0			0
$425$	−2.20467	−	3.81861i	−0.106942	−	0.185230i
$426$		0			0
$427$	−16.3925	+	28.3927i	−0.793289	+	1.37402i
$428$		0			0
$429$	8.61177	+	2.13086i	0.415780	+	0.102879i
$430$		0			0
$431$	−16.7178	+	28.9561i	−0.805268	+	1.39477i	0.110842	+	0.993838i	$0.464645\pi$
$431$	−16.7178	+	28.9561i	−0.805268	+	1.39477i	−0.916110	+	0.400927i	$0.868688\pi$
$432$		0			0
$433$	5.73239	+	9.92879i	0.275481	+	0.477147i	0.970256	−	0.242080i	$-0.0778295\pi$
$433$	5.73239	+	9.92879i	0.275481	+	0.477147i	−0.694775	+	0.719227i	$0.744496\pi$
$434$		0			0
$435$	17.1534	+	29.7106i	0.822442	+	1.42451i
$436$		0			0
$437$	−29.6519			−1.41844
$438$		0			0
$439$	−1.84874	+	3.20211i	−0.0882354	+	0.152828i	−0.906765	−	0.421636i	$-0.861456\pi$
$439$	−1.84874	+	3.20211i	−0.0882354	+	0.152828i	0.818530	+	0.574464i	$0.194789\pi$
$440$		0			0
$441$	3.72373			0.177320
$442$		0			0
$443$	7.50739			0.356687			0.178343	−	0.983968i	$-0.442926\pi$
$443$	7.50739			0.356687			0.178343	+	0.983968i	$0.442926\pi$
$444$		0			0
$445$	−0.166640	+	0.288629i	−0.00789951	+	0.0136823i
$446$		0			0
$447$	−9.90330			−0.468410
$448$		0			0
$449$	9.58832	+	16.6075i	0.452501	+	0.783755i	0.998541	−	0.0540046i	$-0.0171986\pi$
$449$	9.58832	+	16.6075i	0.452501	+	0.783755i	−0.546040	+	0.837759i	$0.683865\pi$
$450$		0			0
$451$	−2.82383	−	4.89102i	−0.132969	−	0.230309i
$452$		0			0
$453$	−0.269748	+	0.467216i	−0.0126738	+	0.0219517i
$454$		0			0
$455$	20.6112	+	5.09994i	0.966267	+	0.239089i
$456$		0			0
$457$	−2.12422	+	3.67926i	−0.0993668	+	0.172108i	−0.911423	−	0.411471i	$-0.865015\pi$
$457$	−2.12422	+	3.67926i	−0.0993668	+	0.172108i	0.812056	+	0.583580i	$0.198348\pi$
$458$		0			0
$459$	0.375780	+	0.650870i	0.0175399	+	0.0303800i
$460$		0			0
$461$	−11.5921	−	20.0781i	−0.539899	−	0.935132i	−0.998909	−	0.0467010i	$-0.985129\pi$
$461$	−11.5921	−	20.0781i	−0.539899	−	0.935132i	0.459010	−	0.888431i	$-0.348204\pi$
$462$		0			0
$463$	−38.9836			−1.81172			−0.905862	−	0.423574i	$-0.860775\pi$
$463$	−38.9836			−1.81172			−0.905862	+	0.423574i	$0.860775\pi$
$464$		0			0
$465$	27.3982	−	47.4551i	1.27056	−	2.20068i
$466$		0			0
$467$	5.88891			0.272506			0.136253	−	0.990674i	$-0.456494\pi$
$467$	5.88891			0.272506			0.136253	+	0.990674i	$0.456494\pi$
$468$		0			0
$469$	2.46478			0.113813
$470$		0			0
$471$	11.4751	−	19.8754i	0.528744	−	0.915812i
$472$		0			0
$473$	−9.42840			−0.433518
$474$		0			0
$475$	1.35087	+	2.33978i	0.0619823	+	0.107357i
$476$		0			0
$477$	−16.7594	−	29.0282i	−0.767362	−	1.32911i
$478$		0			0
$479$	−0.777139	+	1.34604i	−0.0355084	+	0.0615024i	−0.883233	−	0.468934i	$-0.844638\pi$
$479$	−0.777139	+	1.34604i	−0.0355084	+	0.0615024i	0.847725	+	0.530436i	$0.177972\pi$
$480$		0			0
$481$	2.24124	+	7.76389i	0.102192	+	0.354003i
$482$		0			0
$483$	30.2221	−	52.3462i	1.37515	−	2.38183i
$484$		0			0
$485$	11.1352	+	19.2868i	0.505624	+	0.875766i
$486$		0			0
$487$	−7.51459	−	13.0157i	−0.340519	−	0.589795i	0.644011	−	0.765017i	$-0.277269\pi$
$487$	−7.51459	−	13.0157i	−0.340519	−	0.589795i	−0.984529	+	0.175221i	$0.943936\pi$
$488$		0			0
$489$	−5.74436			−0.259769
$490$		0			0
$491$	−10.6154	+	18.3864i	−0.479065	+	0.829764i	−0.999712	−	0.0240075i	$-0.992357\pi$
$491$	−10.6154	+	18.3864i	−0.479065	+	0.829764i	0.520647	+	0.853772i	$0.325691\pi$
$492$		0			0
$493$	−38.3360			−1.72657
$494$		0			0
$495$	6.27335			0.281966
$496$		0			0
$497$	−10.9269	+	18.9260i	−0.490140	+	0.848948i
$498$		0			0
$499$	−32.7060			−1.46412			−0.732061	−	0.681239i	$-0.761442\pi$
$499$	−32.7060			−1.46412			−0.732061	+	0.681239i	$0.761442\pi$
$500$		0			0
$501$	10.4445	+	18.0903i	0.466624	+	0.808216i
$502$		0			0
$503$	1.44445	+	2.50187i	0.0644050	+	0.111553i	0.896430	−	0.443186i	$-0.146152\pi$
$503$	1.44445	+	2.50187i	0.0644050	+	0.111553i	−0.832025	+	0.554738i	$0.812818\pi$
$504$		0			0
$505$	3.77188	−	6.53309i	0.167847	−	0.290719i
$506$		0			0
$507$	28.2958	+	14.9160i	1.25666	+	0.662444i
$508$		0			0
$509$	−16.5885	+	28.7322i	−0.735273	+	1.27353i	0.219330	+	0.975651i	$0.429613\pi$
$509$	−16.5885	+	28.7322i	−0.735273	+	1.27353i	−0.954603	+	0.297880i	$0.903721\pi$
$510$		0			0
$511$	−6.27042	−	10.8607i	−0.277387	−	0.480449i
$512$		0			0
$513$	−0.230252	−	0.398809i	−0.0101659	−	0.0176078i
$514$		0			0
$515$	−19.6037			−0.863842
$516$		0			0
$517$	2.66372	−	4.61369i	0.117150	−	0.202910i
$518$		0			0
$519$	−42.4399			−1.86290
$520$		0			0
$521$	−23.9253			−1.04819			−0.524093	−	0.851661i	$-0.675596\pi$
$521$	−23.9253			−1.04819			−0.524093	+	0.851661i	$0.675596\pi$
$522$		0			0
$523$	6.08472	−	10.5391i	0.266066	−	0.460841i	−0.701776	−	0.712398i	$-0.747609\pi$
$523$	6.08472	−	10.5391i	0.266066	−	0.460841i	0.967842	+	0.251557i	$0.0809426\pi$
$524$		0			0
$525$	−5.50739			−0.240362
$526$		0			0
$527$	30.6160	+	53.0285i	1.33366	+	2.30996i
$528$		0			0
$529$	−25.2111	−	43.6669i	−1.09613	−	1.89856i
$530$		0			0
$531$	−19.5277	+	33.8230i	−0.847431	+	1.46779i
$532$		0			0
$533$	−5.64766	−	19.5641i	−0.244627	−	0.847414i
$534$		0			0
$535$	2.67111	−	4.62649i	0.115482	−	0.200021i
$536$		0			0
$537$	−20.3083	−	35.1749i	−0.876366	−	1.51791i
$538$		0			0
$539$	0.609631	+	1.05591i	0.0262587	+	0.0454813i
$540$		0			0
$541$	−12.3169			−0.529546			−0.264773	−	0.964311i	$-0.585297\pi$
$541$	−12.3169			−0.529546			−0.264773	+	0.964311i	$0.585297\pi$
$542$		0			0
$543$	−16.8348	+	29.1588i	−0.722451	+	1.25132i
$544$		0			0
$545$	0.339289			0.0145335
$546$		0			0
$547$	−10.9823			−0.469569			−0.234784	−	0.972047i	$-0.575438\pi$
$547$	−10.9823			−0.469569			−0.234784	+	0.972047i	$0.575438\pi$
$548$		0			0
$549$	−17.4626	+	30.2462i	−0.745287	+	1.29088i
$550$		0			0
$551$	23.4897			1.00069
$552$		0			0
$553$	23.6270	+	40.9232i	1.00472	+	1.74023i
$554$		0			0
$555$	5.66372	+	9.80984i	0.240411	+	0.416405i
$556$		0			0
$557$	11.9648	−	20.7236i	0.506964	−	0.878087i	−0.493004	−	0.870027i	$-0.664101\pi$
$557$	11.9648	−	20.7236i	0.506964	−	0.878087i	0.999968	−	0.00805994i	$-0.00256559\pi$
$558$		0			0
$559$	−32.9994	−	8.16524i	−1.39573	−	0.345353i
$560$		0			0
$561$	−6.94805	+	12.0344i	−0.293347	+	0.508092i
$562$		0			0
$563$	−20.3456	−	35.2396i	−0.857466	−	1.48517i	−0.874339	−	0.485316i	$-0.838704\pi$
$563$	−20.3456	−	35.2396i	−0.857466	−	1.48517i	0.0168731	−	0.999858i	$-0.494629\pi$
$564$		0			0
$565$	−0.280738	−	0.486253i	−0.0118107	−	0.0204568i
$566$		0			0
$567$	−25.3288			−1.06371
$568$		0			0
$569$	−0.233851	+	0.405042i	−0.00980355	+	0.0169802i	−0.870886	−	0.491486i	$-0.836454\pi$
$569$	−0.233851	+	0.405042i	−0.00980355	+	0.0169802i	0.861082	+	0.508466i	$0.169787\pi$
$570$		0			0
$571$	−42.1780			−1.76509			−0.882547	−	0.470224i	$-0.844173\pi$
$571$	−42.1780			−1.76509			−0.882547	+	0.470224i	$0.844173\pi$
$572$		0			0
$573$	1.06128			0.0443357
$574$		0			0
$575$	−3.34494	+	5.79361i	−0.139494	+	0.241610i
$576$		0			0
$577$	22.8142			0.949767			0.474884	−	0.880049i	$-0.342490\pi$
$577$	22.8142			0.949767			0.474884	+	0.880049i	$0.342490\pi$
$578$		0			0
$579$	−22.1804	−	38.4176i	−0.921788	−	1.59658i
$580$		0			0
$581$	−11.4320	−	19.8008i	−0.474279	−	0.821476i
$582$		0			0
$583$	5.48755	−	9.50471i	0.227271	−	0.393645i
$584$		0			0
$585$	21.9567	+	5.43288i	0.907798	+	0.224622i
$586$		0			0
$587$	−3.71634	+	6.43688i	−0.153390	+	0.265679i	−0.932471	−	0.361244i	$-0.882352\pi$
$587$	−3.71634	+	6.43688i	−0.153390	+	0.265679i	0.779082	+	0.626922i	$0.215686\pi$
$588$		0			0
$589$	−18.7594	−	32.4923i	−0.772969	−	1.33882i
$590$		0			0
$591$	11.0723	+	19.1777i	0.455452	+	0.788867i
$592$		0			0
$593$	25.0761			1.02975			0.514875	−	0.857265i	$-0.327838\pi$
$593$	25.0761			1.02975			0.514875	+	0.857265i	$0.327838\pi$
$594$		0			0
$595$	−16.6293	+	28.8028i	−0.681734	+	1.18080i
$596$		0			0
$597$	−40.3609			−1.65186
$598$		0			0
$599$	9.86693			0.403152			0.201576	−	0.979473i	$-0.435394\pi$
$599$	9.86693			0.403152			0.201576	+	0.979473i	$0.435394\pi$
$600$		0			0
$601$	−1.22306	+	2.11839i	−0.0498895	+	0.0864111i	−0.889892	−	0.456172i	$-0.849220\pi$
$601$	−1.22306	+	2.11839i	−0.0498895	+	0.0864111i	0.840002	+	0.542583i	$0.182554\pi$
$602$		0			0
$603$	2.62568			0.106926
$604$		0			0
$605$	1.02704	+	1.77889i	0.0417552	+	0.0723221i
$606$		0			0
$607$	17.0438	+	29.5207i	0.691785	+	1.19821i	0.971252	+	0.238052i	$0.0765088\pi$
$607$	17.0438	+	29.5207i	0.691785	+	1.19821i	−0.279467	+	0.960155i	$0.590158\pi$
$608$		0			0
$609$	−23.9413	+	41.4676i	−0.970152	+	1.68035i
$610$		0			0
$611$	13.3186	−	13.8411i	0.538812	−	0.559950i
$612$		0			0
$613$	4.35087	−	7.53593i	0.175730	−	0.304374i	−0.764684	−	0.644406i	$-0.777105\pi$
$613$	4.35087	−	7.53593i	0.175730	−	0.304374i	0.940414	+	0.340032i	$0.110438\pi$
$614$		0			0
$615$	−14.2719	−	24.7196i	−0.575498	−	0.996792i
$616$		0			0
$617$	−19.5854	−	33.9229i	−0.788478	−	1.36568i	−0.926899	−	0.375311i	$-0.877536\pi$
$617$	−19.5854	−	33.9229i	−0.788478	−	1.36568i	0.138420	−	0.990374i	$-0.455797\pi$
$618$		0			0
$619$	35.8391			1.44049			0.720247	−	0.693717i	$-0.244028\pi$
$619$	35.8391			1.44049			0.720247	+	0.693717i	$0.244028\pi$
$620$		0			0
$621$	0.570136	−	0.987504i	0.0228788	−	0.0396272i
$622$		0			0
$623$	−0.465166			−0.0186365
$624$		0			0
$625$	−20.4868			−0.819470
$626$		0			0
$627$	4.25729	−	7.37385i	0.170020	−	0.294483i
$628$		0			0
$629$	−12.6578			−0.504699
$630$		0			0
$631$	4.03803	+	6.99408i	0.160752	+	0.278430i	0.935138	−	0.354283i	$-0.115275\pi$
$631$	4.03803	+	6.99408i	0.160752	+	0.278430i	−0.774387	+	0.632712i	$0.781942\pi$
$632$		0			0
$633$	−7.85087	−	13.5981i	−0.312044	−	0.540476i
$634$		0			0
$635$	13.4071	−	23.2218i	0.532044	−	0.921528i
$636$		0			0
$637$	1.21926	+	4.22365i	0.0483089	+	0.167347i
$638$		0			0
$639$	−11.6403	+	20.1615i	−0.460482	+	0.797578i
$640$		0			0
$641$	20.7812	+	35.9941i	0.820809	+	1.42168i	0.905081	+	0.425240i	$0.139810\pi$
$641$	20.7812	+	35.9941i	0.820809	+	1.42168i	−0.0842721	+	0.996443i	$0.526856\pi$
$642$		0			0
$643$	5.22519	+	9.05030i	0.206061	+	0.356909i	0.950470	−	0.310815i	$-0.100602\pi$
$643$	5.22519	+	9.05030i	0.206061	+	0.356909i	−0.744409	+	0.667724i	$0.767269\pi$
$644$		0			0
$645$	−47.6519			−1.87629
$646$		0			0
$647$	−6.03424	+	10.4516i	−0.237230	+	0.410895i	−0.959919	−	0.280279i	$-0.909573\pi$
$647$	−6.03424	+	10.4516i	−0.237230	+	0.410895i	0.722688	+	0.691174i	$0.242906\pi$
$648$		0			0
$649$	−12.7879			−0.501970
$650$		0			0
$651$	76.4805			2.99751
$652$		0			0
$653$	6.96624	−	12.0659i	0.272610	−	0.472174i	−0.696919	−	0.717150i	$-0.745446\pi$
$653$	6.96624	−	12.0659i	0.272610	−	0.472174i	0.969529	+	0.244975i	$0.0787798\pi$
$654$		0			0
$655$	17.5045			0.683956
$656$		0			0
$657$	−6.67977	−	11.5697i	−0.260603	−	0.451377i
$658$		0			0
$659$	−8.87412	−	15.3704i	−0.345687	−	0.598747i	0.639792	−	0.768548i	$-0.279021\pi$
$659$	−8.87412	−	15.3704i	−0.345687	−	0.598747i	−0.985478	+	0.169801i	$0.945687\pi$
$660$		0			0
$661$	15.8384	−	27.4329i	0.616043	−	1.06702i	−0.374157	−	0.927365i	$-0.622068\pi$
$661$	15.8384	−	27.4329i	0.616043	−	1.06702i	0.990201	−	0.139653i	$-0.0445987\pi$
$662$		0			0
$663$	−34.7403	+	36.1031i	−1.34920	+	1.40213i
$664$		0			0
$665$	10.1893	−	17.6484i	0.395124	−	0.684375i
$666$		0			0
$667$	29.0818	+	50.3712i	1.12605	+	1.95038i
$668$		0			0
$669$	30.6644	+	53.1123i	1.18555	+	2.05344i
$670$		0			0
$671$	−11.4356			−0.441466
$672$		0			0
$673$	−18.2367	+	31.5868i	−0.702972	+	1.21758i	0.264447	+	0.964400i	$0.414811\pi$
$673$	−18.2367	+	31.5868i	−0.702972	+	1.21758i	−0.967419	+	0.253182i	$0.918523\pi$
$674$		0			0
$675$	−0.103896			−0.00399897
$676$		0			0
$677$	−28.5586			−1.09759			−0.548797	−	0.835956i	$-0.684914\pi$
$677$	−28.5586			−1.09759			−0.548797	+	0.835956i	$0.684914\pi$
$678$		0			0
$679$	−15.5416	+	26.9189i	−0.596433	+	1.03305i
$680$		0			0
$681$	−22.4284			−0.859458
$682$		0			0
$683$	12.5059	+	21.6609i	0.478526	+	0.828831i	0.999697	−	0.0246209i	$-0.00783787\pi$
$683$	12.5059	+	21.6609i	0.478526	+	0.828831i	−0.521171	+	0.853452i	$0.674505\pi$
$684$		0			0
$685$	−4.34854	−	7.53190i	−0.166149	−	0.287779i
$686$		0			0
$687$	22.6498	−	39.2306i	0.864144	−	1.49674i
$688$		0			0
$689$	27.4377	−	28.5141i	1.04529	−	1.08630i
$690$		0			0
$691$	−10.3918	+	17.9992i	−0.395324	+	0.684721i	−0.993142	−	0.116910i	$-0.962701\pi$
$691$	−10.3918	+	17.9992i	−0.395324	+	0.684721i	0.597819	+	0.801631i	$0.296034\pi$
$692$		0			0
$693$	4.37792	+	7.58277i	0.166303	+	0.288046i
$694$		0			0
$695$	6.43560	+	11.1468i	0.244116	+	0.422822i
$696$		0			0
$697$	31.8961			1.20815
$698$		0			0
$699$	−4.46050	+	7.72582i	−0.168712	+	0.292217i
$700$		0			0
$701$	8.79513			0.332188			0.166094	−	0.986110i	$-0.446885\pi$
$701$	8.79513			0.332188			0.166094	+	0.986110i	$0.446885\pi$
$702$		0			0
$703$	7.75583			0.292517
$704$		0			0
$705$	13.4626	−	23.3180i	0.507032	−	0.878206i
$706$		0			0
$707$	10.5290			0.395983
$708$		0			0
$709$	6.81498	+	11.8039i	0.255942	+	0.443304i	0.965151	−	0.261694i	$-0.0842811\pi$
$709$	6.81498	+	11.8039i	0.255942	+	0.443304i	−0.709209	+	0.704998i	$0.750948\pi$
$710$		0			0
$711$	25.1694	+	43.5948i	0.943928	+	1.63493i
$712$		0			0
$713$	46.4509	−	80.4553i	1.73960	−	3.01307i
$714$		0			0
$715$	2.05408	+	7.11556i	0.0768184	+	0.266107i
$716$		0			0
$717$	15.2017	−	26.3302i	0.567720	−	0.983319i
$718$		0			0
$719$	0.811379	+	1.40535i	0.0302593	+	0.0524107i	0.880758	−	0.473566i	$-0.157033\pi$
$719$	0.811379	+	1.40535i	0.0302593	+	0.0524107i	−0.850499	+	0.525976i	$0.823700\pi$
$720$		0			0
$721$	−13.6806	−	23.6956i	−0.509493	−	0.882469i
$722$		0			0
$723$	55.7247			2.07242
$724$		0			0
$725$	2.64980	−	4.58959i	0.0984111	−	0.170453i
$726$		0			0
$727$	31.0115			1.15015			0.575076	−	0.818100i	$-0.304973\pi$
$727$	31.0115			1.15015			0.575076	+	0.818100i	$0.304973\pi$
$728$		0			0
$729$	−27.9646			−1.03573
$730$		0			0
$731$	26.6242	−	46.1145i	0.984732	−	1.70561i
$732$		0			0
$733$	−9.55389			−0.352881			−0.176440	−	0.984311i	$-0.556458\pi$
$733$	−9.55389			−0.352881			−0.176440	+	0.984311i	$0.556458\pi$
$734$		0			0
$735$	3.08113	+	5.33667i	0.113649	+	0.196846i
$736$		0			0
$737$	0.429864	+	0.744547i	0.0158342	+	0.0274257i
$738$		0			0
$739$	−8.32383	+	14.4173i	−0.306197	+	0.530349i	−0.977527	−	0.210810i	$-0.932390\pi$
$739$	−8.32383	+	14.4173i	−0.306197	+	0.530349i	0.671330	+	0.741159i	$0.265723\pi$
$740$		0			0
$741$	21.2865	−	22.1216i	0.781978	−	0.812655i
$742$		0			0
$743$	−5.05622	+	8.75763i	−0.185495	+	0.321286i	−0.943743	−	0.330679i	$-0.892722\pi$
$743$	−5.05622	+	8.75763i	−0.185495	+	0.321286i	0.758248	+	0.651966i	$0.226055\pi$
$744$		0			0
$745$	−4.13375	−	7.15986i	−0.151449	−	0.262317i
$746$		0			0
$747$	−12.1783	−	21.0934i	−0.445581	−	0.771769i
$748$		0			0
$749$	7.45623			0.272445
$750$		0			0
$751$	23.0364	−	39.9002i	0.840609	−	1.45598i	−0.0487711	−	0.998810i	$-0.515530\pi$
$751$	23.0364	−	39.9002i	0.840609	−	1.45598i	0.889380	−	0.457168i	$-0.151136\pi$
$752$		0			0
$753$	−32.2527			−1.17535
$754$		0			0
$755$	−0.450383			−0.0163911
$756$		0			0
$757$	13.0541	−	22.6103i	0.474459	−	0.821787i	−0.525113	−	0.851032i	$-0.675977\pi$
$757$	13.0541	−	22.6103i	0.474459	−	0.821787i	0.999572	+	0.0292455i	$0.00931047\pi$
$758$		0			0
$759$	21.0833			0.765274
$760$		0			0
$761$	−9.63521	−	16.6887i	−0.349276	−	0.604964i	0.636845	−	0.770992i	$-0.280239\pi$
$761$	−9.63521	−	16.6887i	−0.349276	−	0.604964i	−0.986121	+	0.166028i	$0.946906\pi$
$762$		0			0
$763$	0.236776	+	0.410108i	0.00857187	+	0.0148469i
$764$		0			0
$765$	−17.7149	+	30.6831i	−0.640483	+	1.10935i
$766$		0			0
$767$	−44.7578	−	11.0747i	−1.61611	−	0.399883i
$768$		0			0
$769$	27.0890	−	46.9195i	0.976854	−	1.69196i	0.303179	−	0.952934i	$-0.401952\pi$
$769$	27.0890	−	46.9195i	0.976854	−	1.69196i	0.673675	−	0.739027i	$-0.264715\pi$
$770$		0			0
$771$	−2.66897	−	4.62279i	−0.0961206	−	0.166486i
$772$		0			0
$773$	−16.9069	−	29.2836i	−0.608099	−	1.05326i	−0.991553	−	0.129698i	$-0.958599\pi$
$773$	−16.9069	−	29.2836i	−0.608099	−	1.05326i	0.383455	−	0.923560i	$-0.374734\pi$
$774$		0			0
$775$	−8.46478			−0.304064
$776$		0			0
$777$	−7.90496	+	13.6918i	−0.283589	+	0.491190i
$778$		0			0
$779$	−19.5438			−0.700228
$780$		0			0
$781$	−7.62276			−0.272764
$782$		0			0
$783$	−0.451650	+	0.782282i	−0.0161407	+	0.0279565i
$784$		0			0
$785$	19.1593			0.683826
$786$		0			0
$787$	−1.39922	−	2.42353i	−0.0498769	−	0.0863894i	0.840009	−	0.542572i	$-0.182550\pi$
$787$	−1.39922	−	2.42353i	−0.0498769	−	0.0863894i	−0.889886	+	0.456183i	$0.849216\pi$
$788$		0			0
$789$	37.1467	+	64.3399i	1.32246	+	2.29056i
$790$		0			0
$791$	0.391832	−	0.678672i	0.0139319	−	0.0241308i
$792$		0			0
$793$	−40.0246	−	9.90352i	−1.42132	−	0.351684i
$794$		0			0
$795$	27.7345	−	48.0376i	0.983642	−	1.70372i
$796$		0			0
$797$	21.3245	+	36.9351i	0.755353	+	1.30831i	0.945199	+	0.326495i	$0.105868\pi$
$797$	21.3245	+	36.9351i	0.755353	+	1.30831i	−0.189846	+	0.981814i	$0.560799\pi$
$798$		0			0
$799$	15.0438	+	26.0566i	0.532210	+	0.921815i
$800$		0			0
$801$	−0.495533			−0.0175088
$802$		0			0
$803$	2.18716	−	3.78827i	0.0771832	−	0.133685i
$804$		0			0
$805$	50.4601			1.77849
$806$		0			0
$807$	15.1623			0.533737
$808$		0			0
$809$	−15.6352	+	27.0810i	−0.549705	+	0.952117i	0.448590	+	0.893738i	$0.351926\pi$
$809$	−15.6352	+	27.0810i	−0.549705	+	0.952117i	−0.998295	+	0.0583787i	$0.981407\pi$
$810$		0			0
$811$	37.4212			1.31404			0.657018	−	0.753875i	$-0.271817\pi$
$811$	37.4212			1.31404			0.657018	+	0.753875i	$0.271817\pi$
$812$		0			0
$813$	33.9217	+	58.7541i	1.18969	+	2.06060i
$814$		0			0
$815$	−2.39776	−	4.15304i	−0.0839899	−	0.145475i
$816$		0			0
$817$	−16.3135	+	28.2558i	−0.570738	+	0.988547i
$818$		0			0
$819$	8.75583	+	30.3311i	0.305954	+	1.05985i
$820$		0			0
$821$	−19.1190	+	33.1150i	−0.667256	+	1.15572i	0.311412	+	0.950275i	$0.399198\pi$
$821$	−19.1190	+	33.1150i	−0.667256	+	1.15572i	−0.978668	+	0.205447i	$0.934135\pi$
$822$		0			0
$823$	16.4694	+	28.5258i	0.574086	+	0.994346i	0.996140	+	0.0877753i	$0.0279757\pi$
$823$	16.4694	+	28.5258i	0.574086	+	0.994346i	−0.422055	+	0.906570i	$0.638691\pi$
$824$		0			0
$825$	−0.960505	−	1.66364i	−0.0334405	−	0.0579206i
$826$		0			0
$827$	−7.60117			−0.264318			−0.132159	−	0.991229i	$-0.542191\pi$
$827$	−7.60117			−0.264318			−0.132159	+	0.991229i	$0.542191\pi$
$828$		0			0
$829$	21.9356	−	37.9936i	0.761855	−	1.31957i	−0.180039	−	0.983660i	$-0.557622\pi$
$829$	21.9356	−	37.9936i	0.761855	−	1.31957i	0.941893	−	0.335912i	$-0.109044\pi$
$830$		0			0
$831$	11.8348			0.410545
$832$		0			0
$833$	−6.88598			−0.238585
$834$		0			0
$835$	−8.71926	+	15.1022i	−0.301743	+	0.522633i
$836$		0			0
$837$	1.44280			0.0498703
$838$		0			0
$839$	6.57441	+	11.3872i	0.226974	+	0.393130i	0.956910	−	0.290385i	$-0.0937835\pi$
$839$	6.57441	+	11.3872i	0.226974	+	0.393130i	−0.729936	+	0.683515i	$0.760450\pi$
$840$		0			0
$841$	−8.53803	−	14.7883i	−0.294415	−	0.509942i
$842$		0			0
$843$	9.65652	−	16.7256i	0.332588	−	0.576060i
$844$		0			0
$845$	1.02704	+	26.6833i	0.0353313	+	0.917935i
$846$		0			0
$847$	−1.43346	+	2.48283i	−0.0492544	+	0.0853111i
$848$		0			0
$849$	−2.95691	−	5.12151i	−0.101481	−	0.175770i
$850$		0			0
$851$	9.60224	+	16.6316i	0.329161	+	0.570123i
$852$		0			0
$853$	19.5792			0.670379			0.335189	−	0.942151i	$-0.391200\pi$
$853$	19.5792			0.670379			0.335189	+	0.942151i	$0.391200\pi$
$854$		0			0
$855$	10.8545	−	18.8005i	0.371215	−	0.642963i
$856$		0			0
$857$	−23.3360			−0.797142			−0.398571	−	0.917138i	$-0.630494\pi$
$857$	−23.3360			−0.797142			−0.398571	+	0.917138i	$0.630494\pi$
$858$		0			0
$859$	−30.5539			−1.04249			−0.521243	−	0.853409i	$-0.674531\pi$
$859$	−30.5539			−1.04249			−0.521243	+	0.853409i	$0.674531\pi$
$860$		0			0
$861$	19.9195	−	34.5017i	0.678856	−	1.17581i
$862$		0			0
$863$	−30.1708			−1.02703			−0.513513	−	0.858082i	$-0.671656\pi$
$863$	−30.1708			−1.02703			−0.513513	+	0.858082i	$0.671656\pi$
$864$		0			0
$865$	−17.7149	−	30.6831i	−0.602324	−	1.04326i
$866$		0			0
$867$	−18.3260	−	31.7415i	−0.622382	−	1.07800i
$868$		0			0
$869$	−8.24124	+	14.2743i	−0.279565	+	0.484221i
$870$		0			0
$871$	0.859728	+	2.97819i	0.0291308	+	0.100912i
$872$		0			0
$873$	−16.5562	+	28.6762i	−0.560343	+	0.970543i
$874$		0			0
$875$	−17.0211	−	29.4814i	−0.575419	−	0.996654i
$876$		0			0
$877$	5.64047	+	9.76957i	0.190465	+	0.329895i	0.945404	−	0.325899i	$-0.105667\pi$
$877$	5.64047	+	9.76957i	0.190465	+	0.329895i	−0.754939	+	0.655795i	$0.772334\pi$
$878$		0			0
$879$	−24.8712			−0.838885
$880$		0			0
$881$	28.4158	−	49.2175i	0.957351	−	1.65818i	0.228457	−	0.973554i	$-0.426632\pi$
$881$	28.4158	−	49.2175i	0.957351	−	1.65818i	0.728894	−	0.684627i	$-0.240035\pi$
$882$		0			0
$883$	−21.0478			−0.708316			−0.354158	−	0.935186i	$-0.615233\pi$
$883$	−21.0478			−0.708316			−0.354158	+	0.935186i	$0.615233\pi$
$884$		0			0
$885$	−64.6313			−2.17256
$886$		0			0
$887$	3.49427	−	6.05225i	0.117326	−	0.203215i	−0.801381	−	0.598154i	$-0.795901\pi$
$887$	3.49427	−	6.05225i	0.117326	−	0.203215i	0.918707	+	0.394939i	$0.129234\pi$
$888$		0			0
$889$	37.4251			1.25520
$890$		0			0
$891$	−4.41741	−	7.65118i	−0.147989	−	0.256324i
$892$		0			0
$893$	−9.21780	−	15.9657i	−0.308462	−	0.534272i
$894$		0			0
$895$	16.9538	−	29.3648i	0.566703	−	0.981558i
$896$		0			0
$897$	73.7914	+	18.2586i	2.46382	+	0.609638i
$898$		0			0
$899$	−36.7975	+	63.7351i	−1.22726	+	2.12568i
$900$		0			0
$901$	30.9918	+	53.6794i	1.03249	+	1.78832i
$902$		0			0
$903$	−33.2544	−	57.5983i	−1.10664	−	1.91675i
$904$		0			0
$905$	−28.1082			−0.934347
$906$		0			0
$907$	2.16012	−	3.74143i	0.0717255	−	0.124232i	−0.827932	−	0.560828i	$-0.810483\pi$
$907$	2.16012	−	3.74143i	0.0717255	−	0.124232i	0.899658	+	0.436596i	$0.143816\pi$
$908$		0			0
$909$	11.2163			0.372022
$910$		0			0
$911$	39.6447			1.31349			0.656744	−	0.754113i	$-0.271933\pi$
$911$	39.6447			1.31349			0.656744	+	0.754113i	$0.271933\pi$
$912$		0			0
$913$	3.98755	−	6.90663i	0.131969	−	0.228576i
$914$		0			0
$915$	−57.7965			−1.91069
$916$		0			0
$917$	12.2157	+	21.1581i	0.403397	+	0.698704i
$918$		0			0
$919$	−11.4253	−	19.7892i	−0.376885	−	0.652784i	0.613722	−	0.789522i	$-0.289672\pi$
$919$	−11.4253	−	19.7892i	−0.376885	−	0.652784i	−0.990607	+	0.136738i	$0.956338\pi$
$920$		0			0
$921$	−20.5203	+	35.5422i	−0.676168	+	1.17116i
$922$		0			0
$923$	−26.6797	−	6.60150i	−0.878171	−	0.217291i
$924$		0			0
$925$	0.874912	−	1.51539i	0.0287669	−	0.0498258i
$926$		0			0
$927$	−14.5737	−	25.2424i	−0.478664	−	0.829071i
$928$		0			0
$929$	−11.9935	−	20.7733i	−0.393493	−	0.681550i	0.599414	−	0.800439i	$-0.295400\pi$
$929$	−11.9935	−	20.7733i	−0.393493	−	0.681550i	−0.992908	+	0.118889i	$0.962067\pi$
$930$		0			0
$931$	4.21926			0.138281
$932$		0			0
$933$	29.8676	−	51.7322i	0.977821	−	1.69364i
$934$		0			0
$935$	−11.6008			−0.379386
$936$		0			0
$937$	38.5979			1.26094			0.630468	−	0.776215i	$-0.282863\pi$
$937$	38.5979			1.26094			0.630468	+	0.776215i	$0.282863\pi$
$938$		0			0
$939$	−6.35087	+	11.0000i	−0.207253	+	0.358973i
$940$		0			0
$941$	4.97937			0.162323			0.0811613	−	0.996701i	$-0.474137\pi$
$941$	4.97937			0.162323			0.0811613	+	0.996701i	$0.474137\pi$
$942$		0			0
$943$	−24.1965	−	41.9096i	−0.787946	−	1.36476i
$944$		0			0
$945$	0.391832	+	0.678672i	0.0127463	+	0.0220772i
$946$		0			0
$947$	14.7106	−	25.4795i	0.478030	−	0.827973i	−0.521652	−	0.853158i	$-0.674684\pi$
$947$	14.7106	−	25.4795i	0.478030	−	0.827973i	0.999683	+	0.0251852i	$0.00801756\pi$
$948$		0			0
$949$	10.9358	−	11.3648i	0.354991	−	0.368917i
$950$		0			0
$951$	−0.252039	+	0.436544i	−0.00817292	+	0.0141559i
$952$		0			0
$953$	−19.6249	−	33.9913i	−0.635713	−	1.10109i	−0.986364	−	0.164580i	$-0.947373\pi$
$953$	−19.6249	−	33.9913i	−0.635713	−	1.10109i	0.350651	−	0.936506i	$-0.385960\pi$
$954$		0			0
$955$	0.442991	+	0.767282i	0.0143348	+	0.0248287i
$956$		0			0
$957$	−16.7017			−0.539891
$958$		0			0
$959$	6.06935	−	10.5124i	0.195989	−	0.339464i
$960$		0			0
$961$	86.5494			2.79192
$962$		0			0
$963$	7.94299			0.255959
$964$		0			0
$965$	18.5167	−	32.0719i	0.596074	−	1.03243i
$966$		0			0
$967$	13.3465			0.429194			0.214597	−	0.976703i	$-0.431156\pi$
$967$	13.3465			0.429194			0.214597	+	0.976703i	$0.431156\pi$
$968$		0			0
$969$	24.0438	+	41.6450i	0.772397	+	1.33783i
$970$		0			0
$971$	5.18862	+	8.98696i	0.166511	+	0.288405i	0.937191	−	0.348817i	$-0.113417\pi$
$971$	5.18862	+	8.98696i	0.166511	+	0.288405i	−0.770680	+	0.637222i	$0.780083\pi$
$972$		0			0
$973$	−8.98229	+	15.5578i	−0.287959	+	0.498760i
$974$		0			0
$975$	−1.92101	−	6.65457i	−0.0615215	−	0.213117i
$976$		0			0
$977$	20.2848	−	35.1343i	0.648969	−	1.12405i	−0.334401	−	0.942431i	$-0.608534\pi$
$977$	20.2848	−	35.1343i	0.648969	−	1.12405i	0.983370	−	0.181616i	$-0.0581327\pi$
$978$		0			0
$979$	−0.0811263	−	0.140515i	−0.00259281	−	0.00449088i
$980$		0			0
$981$	0.252233	+	0.436881i	0.00805319	+	0.0139485i
$982$		0			0
$983$	−33.3072			−1.06233			−0.531167	−	0.847267i	$-0.678246\pi$
$983$	−33.3072			−1.06233			−0.531167	+	0.847267i	$0.678246\pi$
$984$		0			0
$985$	−9.24338	+	16.0100i	−0.294519	+	0.510121i
$986$		0			0
$987$	37.5801			1.19619
$988$		0			0
$989$	−80.7889			−2.56894
$990$		0			0
$991$	−22.6426	+	39.2181i	−0.719266	+	1.24581i	0.242025	+	0.970270i	$0.422188\pi$
$991$	−22.6426	+	39.2181i	−0.719266	+	1.24581i	−0.961291	+	0.275535i	$0.911145\pi$
$992$		0			0
$993$	19.2953			0.612319
$994$		0			0
$995$	−16.8471	−	29.1800i	−0.534088	−	0.925068i
$996$		0			0
$997$	2.85087	+	4.93786i	0.0902881	+	0.156384i	0.907632	−	0.419766i	$-0.137888\pi$
$997$	2.85087	+	4.93786i	0.0902881	+	0.156384i	−0.817344	+	0.576150i	$0.804555\pi$
$998$		0			0
$999$	−0.149126	+	0.258294i	−0.00471814	+	0.00817206i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.i.b.529.1	yes	6
13.3	even	3	inner	572.2.i.b.133.1	✓	6
13.4	even	6		7436.2.a.m.1.3		3
13.9	even	3		7436.2.a.n.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.i.b.133.1	✓	6	13.3	even	3	inner
572.2.i.b.529.1	yes	6	1.1	even	1	trivial
7436.2.a.m.1.3		3	13.4	even	6
7436.2.a.n.1.3		3	13.9	even	3

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23025 + 2.13086i) q^{3} -2.05408 q^{5} +(-1.43346 - 2.48283i) q^{7} +(-1.52704 - 2.64491i) q^{9} +O(q^{10})\)	\(q+(-1.23025 + 2.13086i) q^{3} -2.05408 q^{5} +(-1.43346 - 2.48283i) q^{7} +(-1.52704 - 2.64491i) q^{9} +(0.500000 - 0.866025i) q^{11} +(2.50000 - 2.59808i) q^{13} +(2.52704 - 4.37697i) q^{15} +(2.82383 + 4.89102i) q^{17} +(-1.73025 - 2.99689i) q^{19} +7.05408 q^{21} +(4.28434 - 7.42069i) q^{23} -0.780738 q^{25} +0.133074 q^{27} +(-3.39397 + 5.87852i) q^{29} +10.8420 q^{31} +(1.23025 + 2.13086i) q^{33} +(2.94445 + 5.09994i) q^{35} +(-1.12062 + 1.94097i) q^{37} +(2.46050 + 8.52344i) q^{39} +(2.82383 - 4.89102i) q^{41} +(-4.71420 - 8.16524i) q^{43} +(3.13667 + 5.43288i) q^{45} +5.32743 q^{47} +(-0.609631 + 1.05591i) q^{49} -13.8961 q^{51} +10.9751 q^{53} +(-1.02704 + 1.77889i) q^{55} +8.51459 q^{57} +(-6.39397 - 11.0747i) q^{59} +(-5.71780 - 9.90352i) q^{61} +(-4.37792 + 7.58277i) q^{63} +(-5.13521 + 5.33667i) q^{65} +(-0.429864 + 0.744547i) q^{67} +(10.5416 + 18.2586i) q^{69} +(-3.81138 - 6.60150i) q^{71} +4.37432 q^{73} +(0.960505 - 1.66364i) q^{75} -2.86693 q^{77} -16.4825 q^{79} +(4.41741 - 7.65118i) q^{81} +7.97509 q^{83} +(-5.80039 - 10.0466i) q^{85} +(-8.35087 - 14.4641i) q^{87} +(0.0811263 - 0.140515i) q^{89} +(-10.0342 - 2.48283i) q^{91} +(-13.3384 + 23.1028i) q^{93} +(3.55408 + 6.15585i) q^{95} +(-5.42101 - 9.38946i) q^{97} -3.05408 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} + 6 q^{5} - 5 q^{7}+O(q^{10}) \) 6 * q - q^3 + 6 * q^5 - 5 * q^7	\( 6 q - q^{3} + 6 q^{5} - 5 q^{7} + 3 q^{11} + 15 q^{13} + 6 q^{15} + 5 q^{17} - 4 q^{19} + 24 q^{21} + q^{23} + 12 q^{25} + 8 q^{27} - 4 q^{29} + 14 q^{31} + q^{33} - 9 q^{35} + 8 q^{37} + 2 q^{39} + 5 q^{41} - 8 q^{43} + 18 q^{45} + 12 q^{47} - 12 q^{49} - 14 q^{51} + 22 q^{53} + 3 q^{55} + 20 q^{57} - 22 q^{59} - 6 q^{61} + 4 q^{63} + 15 q^{65} - 7 q^{67} + 23 q^{69} + 11 q^{71} + 4 q^{73} - 7 q^{75} - 10 q^{77} - 40 q^{79} + 9 q^{81} + 4 q^{83} - 24 q^{85} - 29 q^{87} - 27 q^{89} - 35 q^{91} - 37 q^{93} + 3 q^{95} - 7 q^{97}+O(q^{100}) \) 6 * q - q^3 + 6 * q^5 - 5 * q^7 + 3 * q^11 + 15 * q^13 + 6 * q^15 + 5 * q^17 - 4 * q^19 + 24 * q^21 + q^23 + 12 * q^25 + 8 * q^27 - 4 * q^29 + 14 * q^31 + q^33 - 9 * q^35 + 8 * q^37 + 2 * q^39 + 5 * q^41 - 8 * q^43 + 18 * q^45 + 12 * q^47 - 12 * q^49 - 14 * q^51 + 22 * q^53 + 3 * q^55 + 20 * q^57 - 22 * q^59 - 6 * q^61 + 4 * q^63 + 15 * q^65 - 7 * q^67 + 23 * q^69 + 11 * q^71 + 4 * q^73 - 7 * q^75 - 10 * q^77 - 40 * q^79 + 9 * q^81 + 4 * q^83 - 24 * q^85 - 29 * q^87 - 27 * q^89 - 35 * q^91 - 37 * q^93 + 3 * q^95 - 7 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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