LMFDB - Embedded newform 572.2.bn.a.491.61

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(95,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 21, 5]))

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

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

chi := DirichletCharacter("572.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bn (of order $30$, 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:	$640$
Relative dimension:	$80$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			491.61
Character	$\chi$	$=$	572.491
Dual form			572.2.bn.a.459.61

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.992718 + 1.00723i) q^{2} +(-0.548395 - 2.58000i) q^{3} +(-0.0290238 + 1.99979i) q^{4} +(-1.52195 - 2.09479i) q^{5} +(2.05425 - 3.11357i) q^{6} +(0.429806 - 2.02208i) q^{7} +(-2.04306 + 1.95599i) q^{8} +(-3.61501 + 1.60951i) q^{9} +O(q^{10})$	\(q+(0.992718 + 1.00723i) q^{2} +(-0.548395 - 2.58000i) q^{3} +(-0.0290238 + 1.99979i) q^{4} +(-1.52195 - 2.09479i) q^{5} +(2.05425 - 3.11357i) q^{6} +(0.429806 - 2.02208i) q^{7} +(-2.04306 + 1.95599i) q^{8} +(-3.61501 + 1.60951i) q^{9} +(0.599063 - 3.61249i) q^{10} +(-2.85263 - 1.69189i) q^{11} +(5.17537 - 1.02179i) q^{12} +(1.33053 + 3.35107i) q^{13} +(2.46338 - 1.57444i) q^{14} +(-4.56991 + 5.07540i) q^{15} +(-3.99832 - 0.116083i) q^{16} +(-7.36311 + 0.773894i) q^{17} +(-5.20983 - 2.04336i) q^{18} +(-0.342480 + 0.308370i) q^{19} +(4.23330 - 2.98278i) q^{20} -5.45266 q^{21} +(-1.12773 - 4.55282i) q^{22} +(5.13562 - 2.96505i) q^{23} +(6.16686 + 4.19843i) q^{24} +(-0.526709 + 1.62104i) q^{25} +(-2.05447 + 4.66682i) q^{26} +(1.48389 + 2.04240i) q^{27} +(4.03126 + 0.918211i) q^{28} +(-4.37157 - 3.93618i) q^{29} +(-9.64873 + 0.435488i) q^{30} +(2.58566 + 1.87859i) q^{31} +(-3.85228 - 4.14246i) q^{32} +(-2.80070 + 8.28761i) q^{33} +(-8.08898 - 6.64809i) q^{34} +(-4.88997 + 2.17715i) q^{35} +(-3.11375 - 7.27598i) q^{36} +(-2.63952 - 2.37664i) q^{37} +(-0.650586 - 0.0388314i) q^{38} +(7.91611 - 5.27047i) q^{39} +(7.20682 + 1.30285i) q^{40} +(6.82300 - 1.45027i) q^{41} +(-5.41295 - 5.49209i) q^{42} +(5.18381 - 8.97862i) q^{43} +(3.46622 - 5.65556i) q^{44} +(8.87345 + 5.12309i) q^{45} +(8.08471 + 2.22929i) q^{46} +(-0.0301227 + 0.0927082i) q^{47} +(1.89316 + 10.3793i) q^{48} +(2.49075 + 1.10895i) q^{49} +(-2.15564 + 1.07872i) q^{50} +(6.03454 + 18.5724i) q^{51} +(-6.74006 + 2.56351i) q^{52} +(-8.47246 - 6.15560i) q^{53} +(-0.584081 + 3.52214i) q^{54} +(0.797416 + 8.55063i) q^{55} +(3.07705 + 4.97193i) q^{56} +(0.983409 + 0.714488i) q^{57} +(-0.375097 - 8.31070i) q^{58} +(0.934660 + 0.198668i) q^{59} +(-10.0171 - 9.28617i) q^{60} +(4.75697 - 0.499978i) q^{61} +(0.674655 + 4.46926i) q^{62} +(1.70080 + 8.00162i) q^{63} +(0.348188 - 7.99242i) q^{64} +(4.99479 - 7.88734i) q^{65} +(-11.1278 + 5.40630i) q^{66} +(-3.70317 - 6.41407i) q^{67} +(-1.33392 - 14.7471i) q^{68} +(-10.4662 - 11.6239i) q^{69} +(-7.04725 - 2.76402i) q^{70} +(-0.413324 - 3.93251i) q^{71} +(4.23750 - 10.3593i) q^{72} +(4.91193 + 15.1174i) q^{73} +(-0.226481 - 5.01793i) q^{74} +(4.47113 + 0.469935i) q^{75} +(-0.606736 - 0.693838i) q^{76} +(-4.64722 + 5.04106i) q^{77} +(13.1670 + 2.74126i) q^{78} +(0.668752 + 0.485877i) q^{79} +(5.84207 + 8.55229i) q^{80} +(-3.48787 + 3.87368i) q^{81} +(8.23408 + 5.43262i) q^{82} +(0.341485 + 0.470014i) q^{83} +(0.158257 - 10.9042i) q^{84} +(12.8274 + 14.2463i) q^{85} +(14.1896 - 3.69195i) q^{86} +(-7.75799 + 13.4372i) q^{87} +(9.13742 - 2.12309i) q^{88} +(-1.45328 + 0.839052i) q^{89} +(3.64870 + 14.0234i) q^{90} +(7.34801 - 1.25012i) q^{91} +(5.78042 + 10.3562i) q^{92} +(3.42879 - 7.70119i) q^{93} +(-0.123282 + 0.0616926i) q^{94} +(1.16721 + 0.248098i) q^{95} +(-8.57497 + 12.2106i) q^{96} +(-6.73191 - 15.1201i) q^{97} +(1.35564 + 3.60963i) q^{98} +(13.0354 + 1.52488i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 15 q^{2} - 3 q^{4} - 15 q^{6} - 78 q^{9}+O(q^{10}) $ 640 * q - 15 * q^2 - 3 * q^4 - 15 * q^6 - 78 * q^9	$ 640 q - 15 q^{2} - 3 q^{4} - 15 q^{6} - 78 q^{9} - 4 q^{12} - 20 q^{13} - 12 q^{14} - 19 q^{16} - 10 q^{17} - 45 q^{20} - 15 q^{22} - 15 q^{24} + 104 q^{25} - 20 q^{26} - 15 q^{28} - 10 q^{29} + 45 q^{30} - 24 q^{33} + 4 q^{36} - 18 q^{37} - 14 q^{38} - 20 q^{40} - 30 q^{41} - 13 q^{42} - 108 q^{45} - 15 q^{46} + 35 q^{48} - 74 q^{49} - 90 q^{50} + 15 q^{52} - 8 q^{53} + 50 q^{56} + 27 q^{58} - 10 q^{61} - 5 q^{62} - 84 q^{64} - 146 q^{66} - 70 q^{68} - 26 q^{69} - 15 q^{72} - 55 q^{74} + 44 q^{77} + 24 q^{78} - 39 q^{80} + 30 q^{81} - 29 q^{82} + 30 q^{84} - 30 q^{85} - 75 q^{88} - 24 q^{89} + 30 q^{90} + 14 q^{92} + 66 q^{93} - 5 q^{94} - 30 q^{97}+O(q^{100}) $ 640 * q - 15 * q^2 - 3 * q^4 - 15 * q^6 - 78 * q^9 - 4 * q^12 - 20 * q^13 - 12 * q^14 - 19 * q^16 - 10 * q^17 - 45 * q^20 - 15 * q^22 - 15 * q^24 + 104 * q^25 - 20 * q^26 - 15 * q^28 - 10 * q^29 + 45 * q^30 - 24 * q^33 + 4 * q^36 - 18 * q^37 - 14 * q^38 - 20 * q^40 - 30 * q^41 - 13 * q^42 - 108 * q^45 - 15 * q^46 + 35 * q^48 - 74 * q^49 - 90 * q^50 + 15 * q^52 - 8 * q^53 + 50 * q^56 + 27 * q^58 - 10 * q^61 - 5 * q^62 - 84 * q^64 - 146 * q^66 - 70 * q^68 - 26 * q^69 - 15 * q^72 - 55 * q^74 + 44 * q^77 + 24 * q^78 - 39 * q^80 + 30 * q^81 - 29 * q^82 + 30 * q^84 - 30 * q^85 - 75 * q^88 - 24 * q^89 + 30 * q^90 + 14 * q^92 + 66 * q^93 - 5 * q^94 - 30 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.992718	+	1.00723i	0.701957	+	0.712219i
$2$	0.992718	+	1.00723i	0.701957	+	0.712219i
$3$	−0.548395	−	2.58000i	−0.316616	−	1.48956i	−0.792401	−	0.610000i	$-0.791169\pi$
$3$	−0.548395	−	2.58000i	−0.316616	−	1.48956i	0.475785	−	0.879562i	$-0.342164\pi$
$4$	−0.0290238	+	1.99979i	−0.0145119	+	0.999895i
$5$	−1.52195	−	2.09479i	−0.680637	−	0.936817i	0.319304	−	0.947652i	$-0.396551\pi$
$5$	−1.52195	−	2.09479i	−0.680637	−	0.936817i	−0.999941	+	0.0108354i	$0.996551\pi$
$6$	2.05425	−	3.11357i	0.838643	−	1.27111i
$7$	0.429806	−	2.02208i	0.162452	−	0.764274i	−0.819187	−	0.573526i	$-0.805575\pi$
$7$	0.429806	−	2.02208i	0.162452	−	0.764274i	0.981639	−	0.190748i	$-0.0610915\pi$
$8$	−2.04306	+	1.95599i	−0.722331	+	0.691548i
$9$	−3.61501	+	1.60951i	−1.20500	+	0.536502i
$10$	0.599063	−	3.61249i	0.189441	−	1.14237i
$11$	−2.85263	−	1.69189i	−0.860101	−	0.510124i
$11$	−2.85263	−	1.69189i	−0.860101	−	0.510124i
$12$	5.17537	−	1.02179i	1.49400	−	0.294966i
$13$	1.33053	+	3.35107i	0.369021	+	0.929421i
$13$	1.33053	+	3.35107i	0.369021	+	0.929421i
$14$	2.46338	−	1.57444i	0.658365	−	0.420787i
$15$	−4.56991	+	5.07540i	−1.17995	+	1.31046i
$16$	−3.99832	−	0.116083i	−0.999579	−	0.0290208i
$17$	−7.36311	+	0.773894i	−1.78582	+	0.187697i	−0.938937	−	0.344088i	$-0.888188\pi$
$17$	−7.36311	+	0.773894i	−1.78582	+	0.187697i	−0.846879	+	0.531785i	$0.821521\pi$
$18$	−5.20983	−	2.04336i	−1.22797	−	0.481625i
$19$	−0.342480	+	0.308370i	−0.0785703	+	0.0707450i	−0.707480	−	0.706733i	$-0.750168\pi$
$19$	−0.342480	+	0.308370i	−0.0785703	+	0.0707450i	0.628910	+	0.777478i	$0.283501\pi$
$20$	4.23330	−	2.98278i	0.946596	−	0.666971i
$21$	−5.45266			−1.18987
$22$	−1.12773	−	4.55282i	−0.240434	−	0.970666i
$23$	5.13562	−	2.96505i	1.07085	−	0.618256i	0.142437	−	0.989804i	$-0.454506\pi$
$23$	5.13562	−	2.96505i	1.07085	−	0.618256i	0.928414	+	0.371548i	$0.121173\pi$
$24$	6.16686	+	4.19843i	1.25880	+	0.857001i
$25$	−0.526709	+	1.62104i	−0.105342	+	0.324209i
$26$	−2.05447	+	4.66682i	−0.402914	+	0.915238i
$27$	1.48389	+	2.04240i	0.285574	+	0.393060i
$28$	4.03126	+	0.918211i	0.761836	+	0.173525i
$29$	−4.37157	−	3.93618i	−0.811781	−	0.730931i	0.154619	−	0.987974i	$-0.450585\pi$
$29$	−4.37157	−	3.93618i	−0.811781	−	0.730931i	−0.966400	+	0.257043i	$0.917252\pi$
$30$	−9.64873	+	0.435488i	−1.76161	+	0.0795089i
$31$	2.58566	+	1.87859i	0.464397	+	0.337404i	0.795254	−	0.606277i	$-0.207338\pi$
$31$	2.58566	+	1.87859i	0.464397	+	0.337404i	−0.330856	+	0.943681i	$0.607338\pi$
$32$	−3.85228	−	4.14246i	−0.680992	−	0.732290i
$33$	−2.80070	+	8.28761i	−0.487540	+	1.44269i
$34$	−8.08898	−	6.64809i	−1.38725	−	1.14014i
$35$	−4.88997	+	2.17715i	−0.826556	+	0.368006i
$36$	−3.11375	−	7.27598i	−0.518959	−	1.21266i
$37$	−2.63952	−	2.37664i	−0.433935	−	0.390716i	0.423010	−	0.906125i	$-0.360974\pi$
$37$	−2.63952	−	2.37664i	−0.433935	−	0.390716i	−0.856945	+	0.515409i	$0.827640\pi$
$38$	−0.650586	−	0.0388314i	−0.105539	−	0.00629928i
$39$	7.91611	−	5.27047i	1.26759	−	0.843950i
$40$	7.20682	+	1.30285i	1.13950	+	0.205999i
$41$	6.82300	−	1.45027i	1.06557	−	0.226495i	0.358425	−	0.933559i	$-0.383314\pi$
$41$	6.82300	−	1.45027i	1.06557	−	0.226495i	0.707150	+	0.707064i	$0.249981\pi$
$42$	−5.41295	−	5.49209i	−0.835237	−	0.847447i
$43$	5.18381	−	8.97862i	0.790524	−	1.36923i	−0.135119	−	0.990829i	$-0.543142\pi$
$43$	5.18381	−	8.97862i	0.790524	−	1.36923i	0.925643	−	0.378398i	$-0.123525\pi$
$44$	3.46622	−	5.65556i	0.522552	−	0.852607i
$45$	8.87345	+	5.12309i	1.32278	+	0.763705i
$46$	8.08471	+	2.22929i	1.19203	+	0.328691i
$47$	−0.0301227	+	0.0927082i	−0.00439385	+	0.0135229i	−0.953229	−	0.302248i	$-0.902263\pi$
$47$	−0.0301227	+	0.0927082i	−0.00439385	+	0.0135229i	0.948836	+	0.315771i	$0.102263\pi$
$48$	1.89316	+	10.3793i	0.273255	+	1.49812i
$49$	2.49075	+	1.10895i	0.355821	+	0.158422i
$50$	−2.15564	+	1.07872i	−0.304853	+	0.152554i
$51$	6.03454	+	18.5724i	0.845005	+	2.60066i
$52$	−6.74006	+	2.56351i	−0.934678	+	0.355495i
$53$	−8.47246	−	6.15560i	−1.16378	−	0.845537i	−0.173530	−	0.984829i	$-0.555517\pi$
$53$	−8.47246	−	6.15560i	−1.16378	−	0.845537i	−0.990251	+	0.139292i	$0.955517\pi$
$54$	−0.584081	+	3.52214i	−0.0794834	+	0.479303i
$55$	0.797416	+	8.55063i	0.107524	+	1.15297i
$56$	3.07705	+	4.97193i	0.411188	+	0.664402i
$57$	0.983409	+	0.714488i	0.130256	+	0.0946363i
$58$	−0.375097	−	8.31070i	−0.0492527	−	1.09125i
$59$	0.934660	+	0.198668i	0.121682	+	0.0258644i	0.268350	−	0.963321i	$-0.413522\pi$
$59$	0.934660	+	0.198668i	0.121682	+	0.0258644i	−0.146668	+	0.989186i	$0.546855\pi$
$60$	−10.0171	−	9.28617i	−1.29320	−	1.19884i
$61$	4.75697	−	0.499978i	0.609068	−	0.0640156i	0.205027	−	0.978756i	$-0.434272\pi$
$61$	4.75697	−	0.499978i	0.609068	−	0.0640156i	0.404041	+	0.914741i	$0.367605\pi$
$62$	0.674655	+	4.46926i	0.0856813	+	0.567596i
$63$	1.70080	+	8.00162i	0.214280	+	1.00811i
$64$	0.348188	−	7.99242i	0.0435235	−	0.999052i
$65$	4.99479	−	7.88734i	0.619528	−	0.978304i
$66$	−11.1278	+	5.40630i	−1.36974	+	0.665469i
$67$	−3.70317	−	6.41407i	−0.452414	−	0.783604i	0.546122	−	0.837706i	$-0.316104\pi$
$67$	−3.70317	−	6.41407i	−0.452414	−	0.783604i	−0.998535	+	0.0541022i	$0.982770\pi$
$68$	−1.33392	−	14.7471i	−0.161762	−	1.78835i
$69$	−10.4662	−	11.6239i	−1.25998	−	1.39935i
$70$	−7.04725	−	2.76402i	−0.842308	−	0.330364i
$71$	−0.413324	−	3.93251i	−0.0490525	−	0.466703i	−0.991284	−	0.131741i	$-0.957943\pi$
$71$	−0.413324	−	3.93251i	−0.0490525	−	0.466703i	0.942232	−	0.334962i	$-0.108723\pi$
$72$	4.23750	−	10.3593i	0.499394	−	1.22085i
$73$	4.91193	+	15.1174i	0.574898	+	1.76935i	0.636527	+	0.771255i	$0.280370\pi$
$73$	4.91193	+	15.1174i	0.574898	+	1.76935i	−0.0616288	+	0.998099i	$0.519630\pi$
$74$	−0.226481	−	5.01793i	−0.0263278	−	0.583323i
$75$	4.47113	+	0.469935i	0.516282	+	0.0542634i
$76$	−0.606736	−	0.693838i	−0.0695974	−	0.0795887i
$77$	−4.64722	+	5.04106i	−0.529599	+	0.574482i
$78$	13.1670	+	2.74126i	1.49087	+	0.310386i
$79$	0.668752	+	0.485877i	0.0752405	+	0.0546654i	0.624770	−	0.780809i	$-0.285193\pi$
$79$	0.668752	+	0.485877i	0.0752405	+	0.0546654i	−0.549529	+	0.835475i	$0.685193\pi$
$80$	5.84207	+	8.55229i	0.653164	+	0.956175i
$81$	−3.48787	+	3.87368i	−0.387542	+	0.430409i
$82$	8.23408	+	5.43262i	0.909302	+	0.599933i
$83$	0.341485	+	0.470014i	0.0374829	+	0.0515907i	0.827347	−	0.561691i	$-0.189849\pi$
$83$	0.341485	+	0.470014i	0.0374829	+	0.0515907i	−0.789864	+	0.613282i	$0.789849\pi$
$84$	0.158257	−	10.9042i	0.0172673	−	1.18974i
$85$	12.8274	+	14.2463i	1.39133	+	1.54523i
$86$	14.1896	−	3.69195i	1.53010	−	0.398113i
$87$	−7.75799	+	13.4372i	−0.831744	+	1.44062i
$88$	9.13742	−	2.12309i	0.974052	−	0.226322i
$89$	−1.45328	+	0.839052i	−0.154047	+	0.0889393i	−0.575042	−	0.818124i	$-0.695014\pi$
$89$	−1.45328	+	0.839052i	−0.154047	+	0.0889393i	0.420995	+	0.907063i	$0.361681\pi$
$90$	3.64870	+	14.0234i	0.384607	+	1.47819i
$91$	7.34801	−	1.25012i	0.770281	−	0.131048i
$92$	5.78042	+	10.3562i	0.602651	+	1.07971i
$93$	3.42879	−	7.70119i	0.355549	−	0.798577i
$94$	−0.123282	+	0.0616926i	−0.0127155	+	0.00636310i
$95$	1.16721	+	0.248098i	0.119753	+	0.0254543i
$96$	−8.57497	+	12.2106i	−0.875179	+	1.24624i
$97$	−6.73191	−	15.1201i	−0.683522	−	1.53521i	−0.837083	−	0.547076i	$-0.815741\pi$
$97$	−6.73191	−	15.1201i	−0.683522	−	1.53521i	0.153561	−	0.988139i	$-0.450926\pi$
$98$	1.35564	+	3.60963i	0.136940	+	0.364628i
$99$	13.0354	+	1.52488i	1.31011	+	0.153256i
$100$	−3.22646	−	1.10036i	−0.322646	−	0.110036i
$101$	7.09193	+	0.745392i	0.705673	+	0.0741692i	0.450565	−	0.892743i	$-0.351222\pi$
$101$	7.09193	+	0.745392i	0.705673	+	0.0741692i	0.255108	+	0.966913i	$0.417889\pi$
$102$	−12.7161	+	24.5153i	−1.25908	+	2.42738i
$103$	3.14481	−	1.02181i	0.309867	−	0.100682i	−0.149956	−	0.988693i	$-0.547913\pi$
$103$	3.14481	−	1.02181i	0.309867	−	0.100682i	0.459822	+	0.888011i	$0.347913\pi$
$104$	−9.27302	−	4.24395i	−0.909294	−	0.416153i
$105$	8.29869	+	11.4222i	0.809869	+	1.11469i
$106$	−2.21065	−	14.6445i	−0.214717	−	1.42240i
$107$	9.67511	−	2.05651i	0.935328	−	0.198810i	0.285055	−	0.958511i	$-0.407988\pi$
$107$	9.67511	−	2.05651i	0.935328	−	0.198810i	0.650273	+	0.759701i	$0.274655\pi$
$108$	−4.12743	+	2.90819i	−0.397162	+	0.279840i
$109$	12.0417			1.15339			0.576694	−	0.816960i	$-0.304342\pi$
$109$	12.0417			1.15339			0.576694	+	0.816960i	$0.304342\pi$
$110$	−7.82084	+	9.29154i	−0.745688	+	0.885914i
$111$	−4.68421	+	8.11329i	−0.444606	+	0.770080i
$112$	−1.95323	+	8.03502i	−0.184563	+	0.759238i
$113$	4.98481	+	5.53619i	0.468931	+	0.520801i	0.930494	−	0.366307i	$-0.119378\pi$
$113$	4.98481	+	5.53619i	0.468931	+	0.520801i	−0.461563	+	0.887107i	$0.652711\pi$
$114$	0.256593	+	1.69980i	0.0240322	+	0.159201i
$115$	−14.0273	−	6.24536i	−1.30805	−	0.582383i
$116$	7.99842	−	8.62798i	0.742634	−	0.801088i
$117$	−10.2034	−	9.97268i	−0.943309	−	0.921975i
$118$	0.727749	+	1.13864i	0.0669947	+	0.104820i
$119$	−1.59984	+	15.2214i	−0.146657	+	1.39535i
$120$	−0.590842	−	19.3081i	−0.0539362	−	1.76258i
$121$	5.27501	+	9.65268i	0.479546	+	0.877516i
$122$	5.22592	+	4.29503i	0.473133	+	0.388853i
$123$	−7.48341	−	16.8080i	−0.674756	−	1.51553i
$124$	−3.83183	+	5.11624i	−0.344108	+	0.459452i
$125$	−8.11548	+	2.63688i	−0.725871	+	0.235850i
$126$	−6.37106	+	9.65644i	−0.567579	+	0.860264i
$127$	−7.44716	−	3.31569i	−0.660828	−	0.294220i	0.0487867	−	0.998809i	$-0.484465\pi$
$127$	−7.44716	−	3.31569i	−0.660828	−	0.294220i	−0.709615	+	0.704589i	$0.751131\pi$
$128$	8.39586	−	7.58351i	0.742096	−	0.670294i
$129$	−26.0076	−	8.45038i	−2.28984	−	0.744015i
$130$	12.9028	−	2.79900i	1.13165	−	0.245488i
$131$	20.8049			1.81774			0.908868	−	0.417083i	$-0.136948\pi$
$131$	20.8049			1.81774			0.908868	+	0.417083i	$0.136948\pi$
$132$	−16.4922	−	5.84136i	−1.43546	−	0.508425i
$133$	0.476349	+	0.825061i	0.0413047	+	0.0715419i
$134$	2.78425	−	10.0973i	0.240522	−	0.872274i
$135$	2.01998	−	6.21686i	0.173852	−	0.535062i
$136$	13.5295	−	15.9833i	1.16015	−	1.37056i
$137$	5.12450	−	0.538606i	0.437815	−	0.0460162i	0.116943	−	0.993139i	$-0.462691\pi$
$137$	5.12450	−	0.538606i	0.437815	−	0.0460162i	0.320872	+	0.947122i	$0.396024\pi$
$138$	1.31795	−	22.0811i	0.112191	−	1.87966i
$139$	−16.1428	−	3.43125i	−1.36921	−	0.291035i	−0.536106	−	0.844151i	$-0.680105\pi$
$139$	−16.1428	−	3.43125i	−1.36921	−	0.291035i	−0.833104	+	0.553116i	$0.813439\pi$
$140$	−4.21192	−	9.84210i	−0.355973	−	0.831809i
$141$	0.255706	+	0.0268758i	0.0215343	+	0.00226335i
$142$	3.55063	−	4.32019i	0.297962	−	0.362542i
$143$	1.87415	−	11.8105i	0.156725	−	0.987642i
$144$	14.6408	−	6.01567i	1.22007	−	0.501306i
$145$	−1.59214	+	15.1482i	−0.132220	+	1.25799i
$146$	−10.3505	+	19.9547i	−0.856614	+	1.65146i
$147$	1.49518	−	7.03426i	0.123320	−	0.580176i
$148$	4.82938	−	5.20951i	0.396973	−	0.428219i
$149$	0.551962	+	5.25157i	0.0452185	+	0.430225i	0.993588	+	0.113059i	$0.0360648\pi$
$149$	0.551962	+	5.25157i	0.0452185	+	0.430225i	−0.948370	+	0.317167i	$0.897269\pi$
$150$	3.96524	+	4.96997i	0.323760	+	0.405796i
$151$	−7.72558	−	2.51019i	−0.628699	−	0.204277i	−0.0227004	−	0.999742i	$-0.507226\pi$
$151$	−7.72558	−	2.51019i	−0.628699	−	0.204277i	−0.605999	+	0.795466i	$0.707226\pi$
$152$	0.0965371	−	1.29991i	0.00783019	−	0.105436i
$153$	25.3721	−	14.6486i	2.05122	−	1.18427i
$154$	−9.69088	+	0.323536i	−0.780913	+	0.0260712i
$155$		−	8.27552i		−	0.664705i
$156$	10.3101	+	15.9835i	0.825466	+	1.27971i
$157$	2.21363	−	6.81285i	0.176667	−	0.543725i	−0.823039	−	0.567985i	$-0.807723\pi$
$157$	2.21363	−	6.81285i	0.176667	−	0.543725i	0.999706	+	0.0242604i	$0.00772308\pi$
$158$	0.174492	+	1.15593i	0.0138819	+	0.0919605i
$159$	−11.2352	+	25.2346i	−0.891007	+	2.00123i
$160$	−2.81459	+	14.3743i	−0.222513	+	1.13639i
$161$	−3.78825	−	11.6590i	−0.298556	−	0.918860i
$162$	−7.36416	+	0.332376i	−0.578583	+	0.0261139i
$163$	−6.20792	+	2.76395i	−0.486242	+	0.216489i	−0.635190	−	0.772356i	$-0.719078\pi$
$163$	−6.20792	+	2.76395i	−0.486242	+	0.216489i	0.148948	+	0.988845i	$0.452411\pi$
$164$	2.70221	+	13.6867i	0.211007	+	1.06875i
$165$	21.6233	−	6.74646i	1.68337	−	0.525211i
$166$	−0.134414	+	0.810545i	−0.0104325	+	0.0629105i
$167$	−20.9252	−	2.19933i	−1.61924	−	0.170189i	−0.748917	−	0.662664i	$-0.769426\pi$
$167$	−20.9252	−	2.19933i	−1.61924	−	0.170189i	−0.870327	+	0.492475i	$0.836092\pi$
$168$	11.1401	−	10.6654i	0.859479	−	0.822851i
$169$	−9.45940	+	8.91738i	−0.727646	+	0.685952i
$170$	−1.61529	+	27.0627i	−0.123887	+	2.07562i
$171$	0.741745	−	1.66599i	0.0567226	−	0.127401i
$172$	17.8049	+	10.6271i	1.35761	+	0.810310i
$173$	−1.59254	+	1.43393i	−0.121078	+	0.109019i	−0.727446	−	0.686165i	$-0.759293\pi$
$173$	−1.59254	+	1.43393i	−0.121078	+	0.109019i	0.606367	+	0.795185i	$0.292626\pi$
$174$	−21.2359	+	5.52530i	−1.60989	+	0.418872i
$175$	3.05150	+	1.76178i	0.230671	+	0.133178i
$176$	11.2093	+	7.09585i	0.844934	+	0.534870i
$177$		−	2.52037i		−	0.189442i
$178$	−2.28782	−	0.630846i	−0.171479	−	0.0472839i
$179$	−3.67579	−	17.2932i	−0.274742	−	1.29256i	−0.871603	−	0.490213i	$-0.836919\pi$
$179$	−3.67579	−	17.2932i	−0.274742	−	1.29256i	0.596861	−	0.802345i	$-0.296414\pi$
$180$	−10.5026	+	17.5963i	−0.782820	+	1.31155i
$181$	1.47813	−	1.07392i	0.109868	−	0.0798240i	−0.531494	−	0.847062i	$-0.678369\pi$
$181$	1.47813	−	1.07392i	0.109868	−	0.0798240i	0.641363	+	0.767238i	$0.278369\pi$
$182$	8.55365	+	6.16012i	0.634039	+	0.456619i
$183$	−3.89864	−	11.9988i	−0.288196	−	0.886976i
$184$	−4.69276	+	16.1030i	−0.345955	+	1.18713i
$185$	−0.961321	+	9.14636i	−0.0706777	+	0.672453i
$186$	11.1607	−	4.19153i	0.818342	−	0.307338i
$187$	22.3136	+	10.2499i	1.63173	+	0.749550i
$188$	−0.184523	−	0.0629298i	−0.0134577	−	0.00458963i
$189$	4.76767	−	2.12271i	0.346797	−	0.154404i
$190$	0.908816	+	1.42194i	0.0659325	+	0.103158i
$191$	−3.53939	+	16.6515i	−0.256101	+	1.20486i	0.642565	+	0.766231i	$0.277870\pi$
$191$	−3.53939	+	16.6515i	−0.256101	+	1.20486i	−0.898667	+	0.438632i	$0.855463\pi$
$192$	−20.8114	+	3.48468i	−1.50193	+	0.251485i
$193$	15.3073	+	6.81527i	1.10185	+	0.490574i	0.875375	−	0.483444i	$-0.160614\pi$
$193$	15.3073	+	6.81527i	1.10185	+	0.490574i	0.226471	+	0.974018i	$0.427281\pi$
$194$	8.54655	−	21.7906i	0.613606	−	1.56447i
$195$	−23.0884	−	8.56117i	−1.65340	−	0.613078i
$196$	−2.28996	+	4.94878i	−0.163569	+	0.353484i
$197$	5.36822	+	9.29803i	0.382470	+	0.662457i	0.991415	−	0.130756i	$-0.0417403\pi$
$197$	5.36822	+	9.29803i	0.382470	+	0.662457i	−0.608945	+	0.793212i	$0.708407\pi$
$198$	11.4046	+	14.6434i	0.810488	+	1.04066i
$199$	−16.1418	−	9.31948i	−1.14426	−	0.660640i	−0.196780	−	0.980448i	$-0.563048\pi$
$199$	−16.1418	−	9.31948i	−1.14426	−	0.660640i	−0.947483	+	0.319808i	$0.896382\pi$
$200$	−2.09465	−	4.34213i	−0.148114	−	0.307035i
$201$	−14.5175	+	13.0716i	−1.02398	+	0.922000i
$202$	6.28950	+	7.88316i	0.442528	+	0.554657i
$203$	−9.83821	+	7.14787i	−0.690507	+	0.501682i
$204$	−37.3160	+	11.5288i	−2.61265	+	0.807175i
$205$	−13.4223	−	12.0855i	−0.937454	−	0.844087i
$206$	4.15110	+	2.15317i	0.289221	+	0.150019i
$207$	−13.7931	+	18.9845i	−0.958684	+	1.31951i
$208$	−4.93086	−	13.5531i	−0.341893	−	0.939739i
$209$	1.49870	−	0.300228i	0.103667	−	0.0207672i
$210$	−3.26649	+	19.6977i	−0.225409	+	1.35927i
$211$	1.70833	−	16.2537i	0.117607	−	1.11895i	−0.763425	−	0.645896i	$-0.776484\pi$
$211$	1.70833	−	16.2537i	0.117607	−	1.11895i	0.881032	−	0.473056i	$-0.156849\pi$
$212$	12.5558	−	16.7645i	0.862336	−	1.15139i
$213$	−9.91921	+	3.22295i	−0.679653	+	0.220833i
$214$	11.6760	+	7.70353i	0.798157	+	0.526602i
$215$	−26.6978	+	2.80605i	−1.82077	+	0.191371i
$216$	−7.02659	−	1.27027i	−0.478099	−	0.0864306i
$217$	4.90999	−	4.42097i	0.333312	−	0.300115i
$218$	11.9540	+	12.1288i	0.809629	+	0.821465i
$219$	36.3091	−	20.9631i	2.45354	−	1.41655i
$220$	−17.1226	+	1.34649i	−1.15441	+	0.0907805i
$221$	−12.3902	−	23.6446i	−0.833454	−	1.59051i
$222$	−12.8220	+	3.33613i	−0.860560	+	0.223906i
$223$	11.2814	−	2.39793i	0.755455	−	0.160577i	0.185944	−	0.982560i	$-0.440466\pi$
$223$	11.2814	−	2.39793i	0.755455	−	0.160577i	0.569511	+	0.821983i	$0.307132\pi$
$224$	−10.0321	+	6.00915i	−0.670299	+	0.401503i
$225$	−0.705022	−	6.70783i	−0.0470014	−	0.447189i
$226$	−0.627709	+	10.5167i	−0.0417546	+	0.699561i
$227$	−0.389157	+	1.83084i	−0.0258293	+	0.121517i	−0.989173	−	0.146752i	$-0.953118\pi$
$227$	−0.389157	+	1.83084i	−0.0258293	+	0.121517i	0.963344	+	0.268269i	$0.0864515\pi$
$228$	−1.45737	+	1.94587i	−0.0965166	+	0.128869i
$229$	−11.1017	+	15.2801i	−0.733618	+	1.00974i	0.265342	+	0.964154i	$0.414515\pi$
$229$	−11.1017	+	15.2801i	−0.733618	+	1.00974i	−0.998960	+	0.0455847i	$0.985485\pi$
$230$	−7.63464	−	20.3286i	−0.503414	−	1.34043i
$231$	15.5544	+	9.22531i	1.02341	+	0.606981i
$232$	16.6305	−	0.508907i	1.09185	−	0.0334114i
$233$	2.76620	−	3.80735i	0.181220	−	0.249428i	−0.708737	−	0.705473i	$-0.750735\pi$
$233$	2.76620	−	3.80735i	0.181220	−	0.249428i	0.889956	+	0.456045i	$0.150735\pi$
$234$	−0.0843517	−	20.1773i	−0.00551424	−	1.31903i
$235$	0.240049	−	0.0779967i	0.0156591	−	0.00508794i
$236$	−0.424422	+	1.86336i	−0.0276275	+	0.121294i
$237$	0.886821	−	1.99183i	0.0576052	−	0.129383i
$238$	−16.9197	+	13.4992i	−1.09674	+	0.875021i
$239$	−7.82580	−	2.54276i	−0.506209	−	0.164477i	0.0447687	−	0.998997i	$-0.485745\pi$
$239$	−7.82580	−	2.54276i	−0.506209	−	0.164477i	−0.550977	+	0.834520i	$0.685745\pi$
$240$	18.8611	−	19.7626i	1.21748	−	1.27567i
$241$	−8.10876	+	14.0448i	−0.522331	+	0.904705i	0.477331	+	0.878724i	$0.341604\pi$
$241$	−8.10876	+	14.0448i	−0.522331	+	0.904705i	−0.999662	+	0.0259810i	$0.991729\pi$
$242$	−4.48587	+	14.8955i	−0.288363	+	0.957521i
$243$	18.4658	+	10.6612i	1.18458	+	0.683917i
$244$	0.861785	+	9.52745i	0.0551701	+	0.609933i
$245$	−1.46778	−	6.90535i	−0.0937729	−	0.441167i
$246$	9.50062	−	24.2231i	0.605737	−	1.54441i
$247$	−1.48905	−	0.737381i	−0.0947460	−	0.0469185i
$248$	−8.95715	+	1.21945i	−0.568780	+	0.0774353i
$249$	1.02537	−	1.13878i	0.0649799	−	0.0721675i
$250$	−10.7123	−	5.55648i	−0.677507	−	0.351422i
$251$	−1.68834	−	3.79208i	−0.106567	−	0.239354i	0.852389	−	0.522908i	$-0.175153\pi$
$251$	−1.68834	−	3.79208i	−0.106567	−	0.239354i	−0.958956	+	0.283554i	$0.908486\pi$
$252$	−16.0509	+	3.16900i	−1.01111	+	0.199628i
$253$	−19.6666	−	0.230709i	−1.23643	−	0.0145046i
$254$	−4.05326	−	10.7925i	−0.254324	−	0.677184i
$255$	29.7209	−	40.9074i	1.86120	−	2.56172i
$256$	15.9730	+	0.928273i	0.998316	+	0.0580171i
$257$	13.3564	−	14.8338i	0.833149	−	0.925305i	−0.164990	−	0.986295i	$-0.552759\pi$
$257$	13.3564	−	14.8338i	0.833149	−	0.925305i	0.998138	+	0.0609900i	$0.0194258\pi$
$258$	−17.3067	−	34.5845i	−1.07747	−	2.15313i
$259$	−5.94023	+	4.31583i	−0.369108	+	0.268173i
$260$	15.6280	+	10.2174i	0.969210	+	0.633659i
$261$	22.1386	+	7.19327i	1.37035	+	0.445252i
$262$	20.6534	+	20.9554i	1.27597	+	1.29463i
$263$	−11.6881	−	20.2444i	−0.720720	−	1.24832i	−0.960712	−	0.277548i	$-0.910478\pi$
$263$	−11.6881	−	20.2444i	−0.720720	−	1.24832i	0.239992	−	0.970775i	$-0.422855\pi$
$264$	−10.4885	−	22.4102i	−0.645522	−	1.37925i
$265$			27.1165i			1.66575i
$266$	−0.358146	+	1.29885i	−0.0219593	+	0.0796374i
$267$	2.96172	+	3.28933i	0.181255	+	0.201304i
$268$	12.9343	−	7.21939i	0.790087	−	0.440995i
$269$	1.04965	+	9.98672i	0.0639981	+	0.608901i	0.978774	+	0.204941i	$0.0657001\pi$
$269$	1.04965	+	9.98672i	0.0639981	+	0.608901i	−0.914776	+	0.403961i	$0.867633\pi$
$270$	8.26707	−	4.13700i	0.503118	−	0.251770i
$271$	14.1473	+	12.7382i	0.859384	+	0.773793i	0.975629	−	0.219427i	$-0.0704189\pi$
$271$	14.1473	+	12.7382i	0.859384	+	0.773793i	−0.116244	+	0.993221i	$0.537086\pi$
$272$	29.5299	−	2.23954i	1.79051	−	0.135792i
$273$	−7.25491	−	18.2723i	−0.439087	−	1.10589i
$274$	5.62968	+	4.62686i	0.340101	+	0.279519i
$275$	4.24513	−	3.73310i	0.255991	−	0.225115i
$276$	23.5491	−	20.5928i	1.41749	−	1.23954i
$277$	−9.47406	−	21.2791i	−0.569241	−	1.27854i	−0.937232	−	0.348707i	$-0.886621\pi$
$277$	−9.47406	−	21.2791i	−0.569241	−	1.27854i	0.367991	−	0.929829i	$-0.380046\pi$
$278$	−12.5691	−	19.6657i	−0.753847	−	1.17947i
$279$	−12.3708	−	2.62949i	−0.740619	−	0.157423i
$280$	5.73200	−	14.0128i	0.342553	−	0.837425i
$281$	7.16760	−	5.20756i	0.427583	−	0.310657i	−0.353099	−	0.935586i	$-0.614872\pi$
$281$	7.16760	−	5.20756i	0.427583	−	0.310657i	0.780682	+	0.624929i	$0.214872\pi$
$282$	0.226774	+	0.284235i	0.0135042	+	0.0169259i
$283$	22.6787	−	4.82051i	1.34811	−	0.286550i	0.523392	−	0.852092i	$-0.324666\pi$
$283$	22.6787	−	4.82051i	1.34811	−	0.286550i	0.824719	+	0.565542i	$0.191333\pi$
$284$	7.87619	−	0.712424i	0.467366	−	0.0422746i
$285$		−	3.14745i		−	0.186439i
$286$	13.7564	−	9.83677i	0.813432	−	0.581660i
$287$		−	14.4200i		−	0.851185i
$288$	20.5933	+	8.77478i	1.21347	+	0.517059i
$289$	36.9880	−	7.86204i	2.17576	−	0.462473i
$290$	−16.8383	+	13.4342i	−0.988776	+	0.788885i
$291$	−35.3181	+	25.6601i	−2.07038	+	1.50422i
$292$	−30.3741	+	9.38406i	−1.77751	+	0.549161i
$293$	−13.6029	−	2.89139i	−0.794691	−	0.168917i	−0.207361	−	0.978264i	$-0.566488\pi$
$293$	−13.6029	−	2.89139i	−0.794691	−	0.168917i	−0.587330	+	0.809348i	$0.699821\pi$
$294$	8.56941	−	5.47705i	0.499778	−	0.319428i
$295$	−1.00634	−	2.26028i	−0.0585914	−	0.131598i
$296$	10.0414	−	0.307274i	0.583643	−	0.0178599i
$297$	−0.777474	−	8.33678i	−0.0451136	−	0.483749i
$298$	−4.74159	+	5.76928i	−0.274673	+	0.334205i
$299$	16.7692	+	13.2648i	0.969787	+	0.767121i
$300$	−1.06954	+	8.92768i	−0.0617499	+	0.515440i
$301$	−15.9275	−	14.3411i	−0.918043	−	0.826610i
$302$	−5.14098	−	10.2734i	−0.295830	−	0.591165i
$303$	−1.96607	−	18.7059i	−0.112948	−	1.07463i
$304$	1.40514	−	1.19321i	0.0805903	−	0.0684350i
$305$	−8.28723	−	9.20390i	−0.474525	−	0.527014i
$306$	39.9419	+	11.0136i	2.28333	+	0.629608i
$307$			31.6627i			1.80709i	0.428498	+	0.903543i	$0.359043\pi$
$307$			31.6627i			1.80709i	−0.428498	+	0.903543i	$0.640957\pi$
$308$	−9.94618	−	9.43977i	−0.566736	−	0.537881i
$309$	−4.36086	−	7.55324i	−0.248081	−	0.429689i
$310$	8.33535	−	8.21525i	0.473416	−	0.466595i
$311$	−24.4310	−	7.93811i	−1.38535	−	0.450129i	−0.480929	−	0.876760i	$-0.659700\pi$
$311$	−24.4310	−	7.93811i	−1.38535	−	0.450129i	−0.904426	+	0.426631i	$0.859700\pi$
$312$	−5.86410	+	26.2517i	−0.331989	+	1.48621i
$313$	18.2949	−	13.2920i	1.03409	−	0.751311i	0.0649675	−	0.997887i	$-0.479306\pi$
$313$	18.2949	−	13.2920i	1.03409	−	0.751311i	0.969123	+	0.246576i	$0.0793056\pi$
$314$	9.05962	−	4.53360i	0.511264	−	0.255846i
$315$	14.1731	−	15.7409i	0.798567	−	0.886898i
$316$	−0.991061	+	1.32326i	−0.0557516	+	0.0744393i
$317$	5.90814	−	8.13186i	0.331834	−	0.456731i	−0.610200	−	0.792247i	$-0.708911\pi$
$317$	5.90814	−	8.13186i	0.331834	−	0.456731i	0.942034	+	0.335517i	$0.108911\pi$
$318$	−36.5704	+	13.7344i	−2.05077	+	0.770189i
$319$	5.81090	+	18.6247i	0.325348	+	1.04278i
$320$	−17.2723	+	11.4347i	−0.965553	+	0.639219i
$321$	−10.6116	−	23.8340i	−0.592280	−	1.33028i
$322$	7.98266	−	15.3898i	0.444856	−	0.857638i
$323$	2.28307	−	2.53561i	0.127034	−	0.141085i
$324$	−7.64531	−	7.08744i	−0.424739	−	0.393747i
$325$	−6.13304	+	0.391799i	−0.340200	+	0.0217331i
$326$	−8.94664	−	3.50899i	−0.495509	−	0.194345i
$327$	−6.60363	−	31.0676i	−0.365181	−	1.71804i
$328$	−11.1031	+	16.3087i	−0.613065	+	0.900500i
$329$	0.174516	+	0.100757i	0.00962140	+	0.00555492i
$330$	28.2611	+	15.0823i	1.55572	+	0.830254i
$331$	−11.4132	+	19.7683i	−0.627329	+	1.08657i	0.360757	+	0.932660i	$0.382518\pi$
$331$	−11.4132	+	19.7683i	−0.627329	+	1.08657i	−0.988086	+	0.153905i	$0.950815\pi$
$332$	−0.949840	+	0.669257i	−0.0521292	+	0.0367302i
$333$	13.3671	+	4.34324i	0.732513	+	0.238008i
$334$	−18.5576	−	23.2598i	−1.01543	−	1.27272i
$335$	−7.80007	+	17.5193i	−0.426163	+	0.957179i
$336$	21.8015	+	0.632962i	1.18937	+	0.0345309i
$337$	13.6666	−	4.44056i	0.744470	−	0.241893i	0.0878699	−	0.996132i	$-0.471994\pi$
$337$	13.6666	−	4.44056i	0.744470	−	0.241893i	0.656600	+	0.754239i	$0.271994\pi$
$338$	−18.3724	−	0.675354i	−0.999325	−	0.0367344i
$339$	11.5497	−	15.8968i	0.627294	−	0.863396i
$340$	−28.8619	+	25.2387i	−1.56526	+	1.36876i
$341$	−4.19755	−	9.73357i	−0.227310	−	0.527102i
$342$	2.41437	−	0.906746i	0.130554	−	0.0490312i
$343$	11.8186	−	16.2670i	0.638146	−	0.878333i
$344$	6.97128	+	28.4834i	0.375866	+	1.53572i
$345$	−8.42050	+	39.6154i	−0.453345	+	2.13282i
$346$	−3.02523	−	0.180567i	−0.162638	−	0.00970732i
$347$	−0.868848	−	8.26653i	−0.0466422	−	0.443771i	−0.992775	−	0.119992i	$-0.961713\pi$
$347$	−0.868848	−	8.26653i	−0.0466422	−	0.443771i	0.946133	−	0.323779i	$-0.104953\pi$
$348$	−26.6465	−	15.9043i	−1.42840	−	0.852563i
$349$	−9.01992	+	1.91724i	−0.482825	+	0.102628i	−0.442893	−	0.896575i	$-0.646048\pi$
$349$	−9.01992	+	1.91724i	−0.482825	+	0.102628i	−0.0399326	+	0.999202i	$0.512714\pi$
$350$	1.25475	+	4.82251i	0.0670694	+	0.257774i
$351$	−4.86987	+	7.69008i	−0.259935	+	0.410466i
$352$	3.98053	+	18.3345i	0.212163	+	0.977234i
$353$	12.8691	−	7.43000i	0.684955	−	0.395459i	−0.116764	−	0.993160i	$-0.537252\pi$
$353$	12.8691	−	7.43000i	0.684955	−	0.395459i	0.801719	+	0.597701i	$0.203919\pi$
$354$	2.53859	−	2.50201i	0.134925	−	0.132981i
$355$	−7.60872	+	6.85092i	−0.403829	+	0.363609i
$356$	−1.63575	−	2.93061i	−0.0866944	−	0.155322i
$357$	40.1486	−	4.21978i	2.12489	−	0.223335i
$358$	13.7692	−	20.8697i	0.727727	−	1.10300i
$359$	25.9089	−	8.41831i	1.36742	−	0.444301i	0.468906	−	0.883248i	$-0.344648\pi$
$359$	25.9089	−	8.41831i	1.36742	−	0.444301i	0.898513	+	0.438947i	$0.144648\pi$
$360$	−28.1497	+	6.88962i	−1.48362	+	0.363115i
$361$	−1.96384	+	18.6847i	−0.103360	+	0.983405i
$362$	2.54905	+	0.422712i	0.133975	+	0.0222173i
$363$	22.0111	−	18.9030i	1.15528	−	0.992150i
$364$	2.28670	+	14.7308i	0.119856	+	0.772101i
$365$	24.1919	−	33.2973i	1.26626	−	1.74286i
$366$	8.21529	−	15.8382i	0.429420	−	0.827878i
$367$	16.8630	+	15.1835i	0.880240	+	0.792571i	0.979280	−	0.202512i	$-0.0649106\pi$
$367$	16.8630	+	15.1835i	0.880240	+	0.792571i	−0.0990402	+	0.995083i	$0.531577\pi$
$368$	−20.8780	+	11.2591i	−1.08834	+	0.586919i
$369$	−22.3310	+	16.2244i	−1.16251	+	0.844610i
$370$	−10.1668	+	8.11148i	−0.528547	+	0.421696i
$371$	−16.0886	+	14.4863i	−0.835280	+	0.752089i
$372$	15.3012	+	7.08038i	0.793333	+	0.367101i
$373$	−16.8996	−	9.75698i	−0.875027	−	0.505197i	−0.00601163	−	0.999982i	$-0.501914\pi$
$373$	−16.8996	−	9.75698i	−0.875027	−	0.505197i	−0.869016	+	0.494785i	$0.835247\pi$
$374$	11.8270	+	32.6502i	0.611562	+	1.68830i
$375$	11.2536	+	19.4919i	0.581135	+	1.00656i
$376$	−0.119794	−	0.248328i	−0.00617790	−	0.0128066i
$377$	7.37395	−	19.8867i	0.379778	−	1.02422i
$378$	6.87101	+	2.69490i	0.353406	+	0.138611i
$379$	−8.50203	−	3.78535i	−0.436720	−	0.194440i	0.176587	−	0.984285i	$-0.443494\pi$
$379$	−8.50203	−	3.78535i	−0.436720	−	0.194440i	−0.613307	+	0.789845i	$0.710161\pi$
$380$	−0.530020	+	2.32697i	−0.0271894	+	0.119371i
$381$	−4.47048	+	21.0320i	−0.229030	+	1.07750i
$382$	−20.2855	+	12.9653i	−1.03790	+	0.663362i
$383$	−21.7808	+	9.69743i	−1.11295	+	0.495516i	−0.879042	−	0.476744i	$-0.841817\pi$
$383$	−21.7808	+	9.69743i	−1.11295	+	0.495516i	−0.233904	+	0.972260i	$0.575150\pi$
$384$	−24.1697	−	17.5025i	−1.23340	−	0.893172i
$385$	17.6328	+	2.06267i	0.898650	+	0.105124i
$386$	8.33132	+	22.1836i	0.424053	+	1.12912i
$387$	−4.28838	+	40.8012i	−0.217991	+	2.07404i
$388$	30.4324	−	13.0236i	1.54497	−	0.661171i
$389$	−4.83905	−	14.8931i	−0.245350	−	0.755109i	−0.995579	−	0.0939309i	$-0.970057\pi$
$389$	−4.83905	−	14.8931i	−0.245350	−	0.755109i	0.750229	−	0.661178i	$-0.229943\pi$
$390$	−14.2972	−	31.7542i	−0.723968	−	1.60794i
$391$	−35.5195	+	25.8064i	−1.79630	+	1.30509i
$392$	−7.25784	+	2.60623i	−0.366576	+	0.131634i
$393$	−11.4093	−	53.6767i	−0.575525	−	2.70763i
$394$	−4.03612	+	14.6373i	−0.203337	+	0.737419i
$395$		−	2.14037i		−	0.107694i
$396$	−3.42777	+	26.0238i	−0.172252	+	1.30775i
$397$	−24.4968	−	14.1433i	−1.22946	−	0.709830i	−0.262544	−	0.964920i	$-0.584562\pi$
$397$	−24.4968	−	14.1433i	−1.22946	−	0.709830i	−0.966917	+	0.255090i	$0.917895\pi$
$398$	−6.63740	−	25.5101i	−0.332703	−	1.27871i
$399$	1.86743	−	1.68144i	0.0934883	−	0.0841773i
$400$	2.29412	−	6.42030i	0.114706	−	0.321015i
$401$	−11.9712	+	26.8877i	−0.597811	+	1.34271i	0.320651	+	0.947198i	$0.396098\pi$
$401$	−11.9712	+	26.8877i	−0.597811	+	1.34271i	−0.918462	+	0.395509i	$0.870568\pi$
$402$	−27.5779	−	1.64604i	−1.37546	−	0.0820968i
$403$	−2.85501	+	11.1642i	−0.142218	+	0.556130i
$404$	−1.69646	+	14.1607i	−0.0844021	+	0.704522i
$405$	13.4229	+	1.41080i	0.666989	+	0.0701034i
$406$	−16.9661	−	2.81351i	−0.842014	−	0.139632i
$407$	3.50857	+	11.2454i	0.173913	+	0.557416i
$408$	−48.6564	−	26.1410i	−2.40885	−	1.29417i
$409$	−4.31793	+	1.92247i	−0.213508	+	0.0950598i	−0.510704	−	0.859757i	$-0.670615\pi$
$409$	−4.31793	+	1.92247i	−0.213508	+	0.0950598i	0.297196	+	0.954816i	$0.403948\pi$
$410$	−1.15168	−	25.5168i	−0.0568776	−	1.26019i
$411$	−4.19985	−	12.9258i	−0.207163	−	0.637584i
$412$	1.95213	+	6.31861i	0.0961745	+	0.311295i
$413$	0.803445	−	1.80457i	0.0395350	−	0.0887970i
$414$	−32.8144	+	4.95348i	−1.61274	+	0.243450i
$415$	0.464855	−	1.43068i	0.0228188	−	0.0702291i
$416$	8.75614	−	18.4209i	0.429305	−	0.903159i
$417$			43.5299i			2.13167i
$418$	1.79018	+	1.21149i	0.0875607	+	0.0592560i
$419$	7.21017	−	4.16279i	0.352240	−	0.203366i	−0.313431	−	0.949611i	$-0.601479\pi$
$419$	7.21017	−	4.16279i	0.352240	−	0.203366i	0.665671	+	0.746245i	$0.268145\pi$
$420$	−23.0828	+	16.2641i	−1.12632	+	0.793607i
$421$	32.0022	+	10.3982i	1.55969	+	0.506775i	0.956726	−	0.290991i	$-0.0939851\pi$
$421$	32.0022	+	10.3982i	1.55969	+	0.506775i	0.602967	+	0.797766i	$0.293985\pi$
$422$	18.0671	−	14.4147i	0.879494	−	0.701695i
$423$	−0.0403205	−	0.383624i	−0.00196045	−	0.0186524i
$424$	29.3500	−	3.99580i	1.42536	−	0.194053i
$425$	2.62370	−	12.3435i	0.127268	−	0.598750i
$426$	−13.0932	−	6.79145i	−0.634368	−	0.329047i
$427$	1.03358	−	9.83387i	0.0500185	−	0.475894i
$428$	3.83177	+	19.4079i	0.185216	+	0.938115i
$429$	−31.4988	+	1.64150i	−1.52078	+	0.0792525i
$430$	−29.3297	−	24.1052i	−1.41440	−	1.16246i
$431$	−19.9434	−	2.09614i	−0.960640	−	0.100967i	−0.388791	−	0.921326i	$-0.627107\pi$
$431$	−19.9434	−	2.09614i	−0.960640	−	0.100967i	−0.571849	+	0.820359i	$0.693774\pi$
$432$	−5.69597	−	8.33840i	−0.274047	−	0.401182i
$433$	6.34030	+	1.34767i	0.304695	+	0.0647650i	0.357722	−	0.933828i	$-0.383554\pi$
$433$	6.34030	+	1.34767i	0.304695	+	0.0647650i	−0.0530267	+	0.998593i	$0.516887\pi$
$434$	9.32716	+	0.556709i	0.447718	+	0.0267229i
$435$	39.9554	−	4.19948i	1.91572	−	0.201350i
$436$	−0.349497	+	24.0809i	−0.0167379	+	1.15327i
$437$	−0.844513	+	2.59914i	−0.0403985	+	0.124334i
$438$	57.1593	+	15.7612i	2.73118	+	0.753099i
$439$	10.9141	+	18.9037i	0.520900	+	0.902226i	0.999705	+	0.0243040i	$0.00773697\pi$
$439$	10.9141	+	18.9037i	0.520900	+	0.902226i	−0.478804	+	0.877922i	$0.658930\pi$
$440$	−18.3541	−	15.9097i	−0.874999	−	0.758466i
$441$	−10.7889			−0.513759
$442$	11.5156	−	35.9522i	0.547743	−	1.71007i
$443$	−6.82312	−	2.21697i	−0.324176	−	0.105331i	0.142408	−	0.989808i	$-0.454516\pi$
$443$	−6.82312	−	2.21697i	−0.324176	−	0.105331i	−0.466584	+	0.884477i	$0.654516\pi$
$444$	−16.0889	−	9.60291i	−0.763546	−	0.455734i
$445$	3.96946	+	1.76732i	0.188170	+	0.0837788i
$446$	13.6145	+	8.98245i	0.644663	+	0.425331i
$447$	13.2463	−	4.30400i	0.626530	−	0.203572i
$448$	−16.0117	−	4.13926i	−0.756480	−	0.195561i
$449$	3.37598	+	7.58258i	0.159322	+	0.357844i	0.975514	−	0.219937i	$-0.0705853\pi$
$449$	3.37598	+	7.58258i	0.159322	+	0.357844i	−0.816192	+	0.577781i	$0.803919\pi$
$450$	6.05644	−	7.36910i	0.285503	−	0.347383i
$451$	−21.9172	−	7.40668i	−1.03204	−	0.348767i
$452$	−11.2159	+	9.80788i	−0.527551	+	0.461324i
$453$	−2.23962	+	21.3086i	−0.105227	+	1.00116i
$454$	−2.23040	+	1.42554i	−0.104678	+	0.0669038i
$455$	−13.8020	−	13.4899i	−0.647049	−	0.632416i
$456$	−3.40670	+	0.463798i	−0.159533	+	0.0217193i
$457$	11.9728	+	5.33062i	0.560062	+	0.249356i	0.667188	−	0.744890i	$-0.267498\pi$
$457$	11.9728	+	5.33062i	0.560062	+	0.249356i	−0.107125	+	0.994246i	$0.534165\pi$
$458$	−26.4114	+	3.98692i	−1.23412	+	0.186297i
$459$	−12.5066	−	13.8900i	−0.583760	−	0.648331i
$460$	12.8965	−	27.8704i	0.601304	−	1.29946i
$461$	−4.63311	+	8.02478i	−0.215785	+	0.373751i	−0.953515	−	0.301345i	$-0.902565\pi$
$461$	−4.63311	+	8.02478i	−0.215785	+	0.373751i	0.737730	+	0.675096i	$0.235898\pi$
$462$	6.14916	+	24.8250i	0.286085	+	1.15496i
$463$	−6.33104			−0.294228			−0.147114	−	0.989120i	$-0.546998\pi$
$463$	−6.33104			−0.294228			−0.147114	+	0.989120i	$0.546998\pi$
$464$	17.0220	+	16.2456i	0.790227	+	0.754182i
$465$	−21.3508	+	4.53825i	−0.990120	+	0.210457i
$466$	6.58093	−	0.993421i	0.304856	−	0.0460194i
$467$	3.83075	+	5.27258i	0.177266	+	0.243986i	0.888399	−	0.459071i	$-0.151818\pi$
$467$	3.83075	+	5.27258i	0.177266	+	0.243986i	−0.711133	+	0.703057i	$0.751818\pi$
$468$	20.2394	−	20.1153i	0.935567	−	0.929830i
$469$	−14.5614	+	4.73129i	−0.672383	+	0.218471i
$470$	0.316862	+	0.164356i	0.0146157	+	0.00758118i
$471$	−18.7911	−	1.97502i	−0.865847	−	0.0910042i
$472$	−2.29816	+	1.42230i	−0.105781	+	0.0654665i
$473$	−29.9783	+	16.8423i	−1.37841	+	0.774408i
$474$	2.88659	−	1.08409i	0.132586	−	0.0497941i
$475$	−0.319494	−	0.717596i	−0.0146594	−	0.0329256i
$476$	−30.3932	−	3.64112i	−1.39307	−	0.166890i
$477$	40.5355	+	8.61609i	1.85599	+	0.394504i
$478$	−5.20767	−	10.4066i	−0.238193	−	0.475987i
$479$	2.43049	−	5.45897i	0.111052	−	0.249427i	−0.849467	−	0.527642i	$-0.823076\pi$
$479$	2.43049	−	5.45897i	0.111052	−	0.249427i	0.960519	+	0.278215i	$0.0897429\pi$
$480$	38.6292	−	0.621166i	1.76317	−	0.0283522i
$481$	4.45233	−	12.0074i	0.203009	−	0.547491i
$482$	−22.1960	+	5.77512i	−1.01100	+	0.263050i
$483$	−28.0028	+	16.1674i	−1.27417	+	0.735643i
$484$	−19.4564	+	10.2688i	−0.884383	+	0.466762i
$485$	−21.4278	+	37.1140i	−0.972985	+	1.68526i
$486$	7.59299	+	29.1828i	0.344425	+	1.32376i
$487$	8.68274	+	9.64316i	0.393452	+	0.436973i	0.907027	−	0.421072i	$-0.138346\pi$
$487$	8.68274	+	9.64316i	0.393452	+	0.436973i	−0.513575	+	0.858045i	$0.671679\pi$
$488$	−8.74083	+	10.3261i	−0.395679	+	0.467440i
$489$	10.5354	+	14.5007i	0.476426	+	0.655744i
$490$	5.49819	−	8.33345i	0.248383	−	0.376467i
$491$	−3.48941	+	3.87539i	−0.157475	+	0.174894i	−0.816719	−	0.577035i	$-0.804210\pi$
$491$	−3.48941	+	3.87539i	−0.157475	+	0.174894i	0.659244	+	0.751929i	$0.270876\pi$
$492$	33.8297	−	14.4774i	1.52516	−	0.652692i
$493$	35.2346	+	25.5994i	1.58689	+	1.15294i
$494$	−0.735494	−	2.23183i	−0.0330914	−	0.100415i
$495$	−16.6450	−	29.6272i	−0.748136	−	1.33164i
$496$	−10.1202	−	7.81134i	−0.454410	−	0.350740i
$497$	−8.12950	−	0.854445i	−0.364658	−	0.0383271i
$498$	2.16492	−	0.0977119i	0.0970122	−	0.00437857i
$499$	−3.13790	−	9.65746i	−0.140472	−	0.432327i	0.855929	−	0.517093i	$-0.172986\pi$
$499$	−3.13790	−	9.65746i	−0.140472	−	0.432327i	−0.996401	+	0.0847657i	$0.972986\pi$
$500$	−5.03766	−	16.3058i	−0.225291	−	0.729217i
$501$	5.80103	+	55.1932i	0.259171	+	2.46585i
$502$	2.14345	−	5.46501i	0.0956668	−	0.243915i
$503$	12.2871	+	13.6462i	0.547853	+	0.608453i	0.951946	−	0.306265i	$-0.0990794\pi$
$503$	12.2871	+	13.6462i	0.547853	+	0.608453i	−0.404093	+	0.914718i	$0.632413\pi$
$504$	−19.1259	−	13.0210i	−0.851937	−	0.580003i
$505$	−9.23213	−	15.9905i	−0.410824	−	0.711569i
$506$	−19.2910	−	20.0378i	−0.857588	−	0.890788i
$507$	28.1943	+	19.5150i	1.25215	+	0.866691i
$508$	6.84682	−	14.7965i	0.303779	−	0.656489i
$509$	3.26903	+	15.3796i	0.144897	+	0.681687i	0.989290	+	0.145963i	$0.0466280\pi$
$509$	3.26903	+	15.3796i	0.144897	+	0.681687i	−0.844393	+	0.535724i	$0.820039\pi$
$510$	70.7076	−	10.6736i	3.13099	−	0.472637i
$511$	32.6797	−	3.43477i	1.44566	−	0.151945i
$512$	14.9217	+	17.0100i	0.659454	+	0.751745i
$513$	−1.13802	−	0.241893i	−0.0502447	−	0.0106798i
$514$	28.2001	−	1.27279i	1.24385	−	0.0561405i
$515$	−6.92671	−	5.03255i	−0.305228	−	0.221761i
$516$	17.6538	−	51.7645i	0.777166	−	2.27880i
$517$	0.242781	−	0.213498i	0.0106775	−	0.00938963i
$518$	−10.2440	−	1.69878i	−0.450095	−	0.0746400i
$519$	4.57287	+	3.32238i	0.200727	+	0.145836i
$520$	5.22292	+	25.8841i	0.229040	+	1.13509i
$521$	0.292796	+	0.901135i	0.0128276	+	0.0394794i	0.957265	−	0.289211i	$-0.0933928\pi$
$521$	0.292796	+	0.901135i	0.0128276	+	0.0394794i	−0.944438	+	0.328690i	$0.893393\pi$
$522$	14.7321	+	29.4395i	0.644807	+	1.28853i
$523$	22.7131	+	10.1125i	0.993176	+	0.442190i	0.837985	−	0.545694i	$-0.183734\pi$
$523$	22.7131	+	10.1125i	0.993176	+	0.442190i	0.155191	+	0.987884i	$0.450401\pi$
$524$	−0.603839	+	41.6055i	−0.0263788	+	1.81755i
$525$	2.87197	−	8.83900i	0.125343	−	0.385766i
$526$	8.78777	−	31.8696i	0.383165	−	1.38958i
$527$	−20.4923	−	11.8312i	−0.892658	−	0.515377i
$528$	12.1601	−	32.8113i	0.529202	−	1.42793i
$529$	6.08306	−	10.5362i	0.264481	−	0.458095i
$530$	−27.3126	+	26.9190i	−1.18638	+	1.16929i
$531$	−3.69856	+	0.786154i	−0.160504	+	0.0341162i
$532$	−1.66377	+	0.928652i	−0.0721338	+	0.0402622i
$533$	13.9382	+	20.9348i	0.603729	+	0.906786i
$534$	−0.372954	+	6.24851i	−0.0161393	+	0.270399i
$535$	−19.0330	−	17.1374i	−0.822868	−	0.740913i
$536$	20.1117	+	5.86097i	0.868692	+	0.253155i
$537$	−42.6007	+	18.9671i	−1.83836	+	0.818489i
$538$	−9.01692	+	10.9712i	−0.388747	+	0.473003i
$539$	−5.22896	−	7.37750i	−0.225227	−	0.317771i
$540$	12.3738	+	4.21997i	0.532483	+	0.181599i
$541$	−22.6840	−	16.4809i	−0.975260	−	0.708568i	−0.0186157	−	0.999827i	$-0.505926\pi$
$541$	−22.6840	−	16.4809i	−0.975260	−	0.708568i	−0.956644	+	0.291259i	$0.905926\pi$
$542$	1.21389	+	26.8950i	0.0521409	+	1.15524i
$543$	−3.58131	−	3.22463i	−0.153689	−	0.138382i
$544$	31.5706	+	27.5201i	1.35358	+	1.17992i
$545$	−18.3269	−	25.2248i	−0.785039	−	1.08051i
$546$	11.2023	−	25.4466i	0.479415	−	1.08901i
$547$	3.58018	−	11.0187i	0.153077	−	0.471123i	−0.844884	−	0.534950i	$-0.820330\pi$
$547$	3.58018	−	11.0187i	0.153077	−	0.471123i	0.997961	+	0.0638265i	$0.0203304\pi$
$548$	0.928367	+	10.2635i	0.0396579	+	0.438437i
$549$	−16.3918	+	9.46381i	−0.699585	+	0.403905i
$550$	7.97431	+	0.569907i	0.340026	+	0.0243009i
$551$	2.71098			0.115492
$552$	44.1192	+	3.27650i	1.87784	+	0.139457i
$553$	1.26992	−	1.14344i	0.0540023	−	0.0486239i
$554$	12.0279	−	30.6667i	0.511015	−	1.30290i
$555$	24.1248	−	2.53561i	1.02404	−	0.107631i
$556$	7.33030	−	32.1825i	0.310874	−	1.36484i
$557$	−18.8658	+	20.9526i	−0.799369	+	0.887790i	−0.995689	−	0.0927503i	$-0.970434\pi$
$557$	−18.8658	+	20.9526i	−0.799369	+	0.887790i	0.196320	+	0.980540i	$0.437101\pi$
$558$	−9.63219	−	15.0706i	−0.407763	−	0.637987i
$559$	36.9852	+	5.42505i	1.56431	+	0.229455i
$560$	19.8044	−	8.13731i	0.836887	−	0.343864i
$561$	14.2082	−	63.1900i	0.599869	−	2.66788i
$562$	12.3606	+	2.04978i	0.521401	+	0.0864646i
$563$	13.5102	−	6.01511i	0.569385	−	0.253507i	−0.101789	−	0.994806i	$-0.532457\pi$
$563$	13.5102	−	6.01511i	0.569385	−	0.253507i	0.671175	+	0.741299i	$0.265790\pi$
$564$	−0.0611675	+	0.510578i	−0.00257562	+	0.0214992i
$565$	4.01050	−	18.8679i	0.168723	−	0.793779i
$566$	27.3689	+	18.0573i	1.15040	+	0.759004i
$567$	6.33377	+	8.71769i	0.265993	+	0.366109i
$568$	8.53641	+	7.22590i	0.358180	+	0.303192i
$569$	7.21446	+	33.9414i	0.302446	+	1.42290i	0.822501	+	0.568764i	$0.192578\pi$
$569$	7.21446	+	33.9414i	0.302446	+	1.42290i	−0.520055	+	0.854133i	$0.674088\pi$
$570$	3.17020	−	3.12453i	0.132785	−	0.130872i
$571$	8.01751			0.335522			0.167761	−	0.985828i	$-0.446346\pi$
$571$	8.01751			0.335522			0.167761	+	0.985828i	$0.446346\pi$
$572$	23.5641	+	4.09070i	0.985264	+	0.171041i
$573$	44.9019			1.87580
$574$	14.5242	−	14.3150i	0.606230	−	0.597496i
$575$	2.10150	+	9.88678i	0.0876386	+	0.412307i
$576$	11.6051	+	29.4531i	0.483548	+	1.22721i
$577$	−18.3973	−	25.3217i	−0.765889	−	1.05416i	−0.996701	−	0.0811575i	$-0.974138\pi$
$577$	−18.3973	−	25.3217i	−0.765889	−	1.05416i	0.230812	−	0.972998i	$-0.425862\pi$
$578$	44.6375	+	29.4506i	1.85668	+	1.22498i
$579$	9.18889	−	43.2303i	0.381877	−	1.79659i
$580$	−30.2470	−	3.62360i	−1.25594	−	0.150462i
$581$	1.09718	−	0.488495i	0.0455186	−	0.0202662i
$582$	−60.9065	−	10.1002i	−2.52466	−	0.418667i
$583$	13.7542	+	31.8941i	0.569640	+	1.32092i
$584$	−39.6048	−	21.2780i	−1.63886	−	0.880489i
$585$	−5.36150	+	36.5520i	−0.221671	+	1.51124i
$586$	−10.5916	−	16.5716i	−0.437534	−	0.684567i
$587$	−0.883102	+	0.980784i	−0.0364495	+	0.0404813i	−0.761094	−	0.648642i	$-0.775337\pi$
$587$	−0.883102	+	0.980784i	−0.0364495	+	0.0404813i	0.724644	+	0.689123i	$0.242004\pi$
$588$	14.0236	+	3.19420i	0.578325	+	0.131727i
$589$	−1.46484	+	0.153960i	−0.0603575	+	0.00634383i
$590$	1.27761	−	3.25743i	0.0525982	−	0.134106i
$591$	21.0450	−	18.9490i	0.865675	−	0.779457i
$592$	10.2777	+	9.80894i	0.422413	+	0.403145i
$593$	39.7791			1.63353			0.816766	−	0.576969i	$-0.195765\pi$
$593$	39.7791			1.63353			0.816766	+	0.576969i	$0.195765\pi$
$594$	7.62525	−	9.05917i	0.312868	−	0.371702i
$595$	34.3205	−	19.8149i	1.40700	−	0.812334i
$596$	−10.5181	+	0.951387i	−0.430836	+	0.0389703i
$597$	−15.1921	+	46.7566i	−0.621773	+	1.91362i
$598$	3.28639	+	30.0586i	0.134390	+	1.22919i
$599$	−15.0107	−	20.6605i	−0.613322	−	0.844165i	0.383524	−	0.923531i	$-0.374710\pi$
$599$	−15.0107	−	20.6605i	−0.613322	−	0.844165i	−0.996846	+	0.0793661i	$0.974710\pi$
$600$	−10.0540	+	7.78539i	−0.410452	+	0.317837i
$601$	−5.88729	−	5.30094i	−0.240147	−	0.216230i	0.540265	−	0.841495i	$-0.318324\pi$
$601$	−5.88729	−	5.30094i	−0.240147	−	0.216230i	−0.780412	+	0.625265i	$0.784991\pi$
$602$	−1.36663	−	30.2793i	−0.0556999	−	1.23409i
$603$	23.7105	+	17.2267i	0.965566	+	0.701524i
$604$	5.24409	−	15.3767i	0.213379	−	0.625668i
$605$	12.1920	−	25.7409i	0.495675	−	1.04652i
$606$	16.8894	−	20.5500i	0.686085	−	0.834786i
$607$	8.95901	−	3.98881i	0.363635	−	0.161901i	−0.216782	−	0.976220i	$-0.569556\pi$
$607$	8.95901	−	3.98881i	0.363635	−	0.161901i	0.580417	+	0.814319i	$0.302890\pi$
$608$	2.59674	+	0.230782i	0.105312	+	0.00935945i
$609$	23.8367	+	21.4627i	0.965913	+	0.869712i
$610$	1.04357	−	17.4840i	0.0422527	−	0.707907i
$611$	−0.350751	+	0.0224071i	−0.0141899	+	0.000906496i
$612$	28.5577	+	51.1641i	1.15438	+	2.06819i
$613$	8.28509	−	1.76105i	0.334632	−	0.0711282i	−0.0375315	−	0.999295i	$-0.511949\pi$
$613$	8.28509	−	1.76105i	0.334632	−	0.0711282i	0.372163	+	0.928167i	$0.378616\pi$
$614$	−31.8916	+	31.4321i	−1.28704	+	1.26850i
$615$	−23.8198	+	41.2571i	−0.960507	+	1.66365i
$616$	−0.365737	−	19.3891i	−0.0147360	−	0.781210i
$617$	−13.7921	−	7.96289i	−0.555250	−	0.320574i	0.195987	−	0.980607i	$-0.437209\pi$
$617$	−13.7921	−	7.96289i	−0.555250	−	0.320574i	−0.751237	+	0.660033i	$0.770542\pi$
$618$	3.27874	−	11.8906i	0.131890	−	0.478311i
$619$	11.6414	−	35.8285i	0.467906	−	1.44007i	−0.387384	−	0.921918i	$-0.626621\pi$
$619$	11.6414	−	35.8285i	0.467906	−	1.44007i	0.855290	−	0.518149i	$-0.173379\pi$
$620$	16.5493	+	0.240187i	0.664635	+	0.00964615i
$621$	13.6765	+	6.08917i	0.548819	+	0.244350i
$622$	−16.2576	−	32.4879i	−0.651869	−	1.30265i
$623$	1.07200	+	3.29928i	0.0429488	+	0.132183i
$624$	−32.2629	+	20.1541i	−1.29155	+	0.806808i
$625$	24.7698	+	17.9963i	0.990791	+	0.719852i
$626$	31.5499	+	5.23195i	1.26099	+	0.209111i
$627$	−1.59647	−	3.70199i	−0.0637567	−	0.147843i
$628$	13.5600	+	4.62453i	0.541104	+	0.184539i
$629$	21.2743	+	15.4567i	0.848264	+	0.616300i
$630$	29.9246	−	1.35063i	1.19223	−	0.0538102i
$631$	7.25640	+	1.54239i	0.288873	+	0.0614018i	0.350069	−	0.936724i	$-0.386158\pi$
$631$	7.25640	+	1.54239i	0.288873	+	0.0614018i	−0.0611962	+	0.998126i	$0.519492\pi$
$632$	−2.31667	+	0.315399i	−0.0921523	+	0.0125459i
$633$	−42.8714	+	4.50597i	−1.70399	+	0.179096i
$634$	14.0558	−	2.12178i	0.558226	−	0.0842668i
$635$	4.38855	+	20.6465i	0.174154	+	0.819332i
$636$	−50.1378	−	23.2004i	−1.98809	−	0.919955i
$637$	−0.402179	+	9.82216i	−0.0159349	+	0.389168i
$638$	−12.9908	+	24.3420i	−0.514310	+	0.963708i
$639$	7.82358	+	13.5508i	0.309496	+	0.536063i
$640$	−28.6639	−	6.04579i	−1.13304	−	0.238981i
$641$	−30.0730	−	33.3994i	−1.18781	−	1.31920i	−0.936241	−	0.351357i	$-0.885720\pi$
$641$	−30.0730	−	33.3994i	−1.18781	−	1.31920i	−0.251569	−	0.967839i	$-0.580946\pi$
$642$	13.4720	−	34.3487i	0.531697	−	1.35563i
$643$	3.36040	+	31.9721i	0.132521	+	1.26086i	0.835438	+	0.549584i	$0.185214\pi$
$643$	3.36040	+	31.9721i	0.132521	+	1.26086i	−0.702917	+	0.711272i	$0.748119\pi$
$644$	23.4256	−	7.23731i	0.923096	−	0.285190i
$645$	21.8806	+	67.3414i	0.861546	+	2.65157i
$646$	4.82039	−	0.217565i	0.189656	−	0.00855997i
$647$	1.91889	+	0.201683i	0.0754393	+	0.00792899i	0.142173	−	0.989842i	$-0.454591\pi$
$647$	1.91889	+	0.201683i	0.0754393	+	0.00792899i	−0.0667336	+	0.997771i	$0.521258\pi$
$648$	−0.450946	−	14.7364i	−0.0177148	−	0.578901i
$649$	−2.33012	−	2.14807i	−0.0914650	−	0.0843191i
$650$	−6.48300	−	5.78843i	−0.254284	−	0.227041i
$651$	−14.0987	−	10.2433i	−0.552572	−	0.401467i
$652$	−5.34713	−	12.4948i	−0.209410	−	0.489332i
$653$	−2.28784	+	2.54091i	−0.0895302	+	0.0994334i	−0.786245	−	0.617915i	$-0.787978\pi$
$653$	−2.28784	+	2.54091i	−0.0895302	+	0.0994334i	0.696715	+	0.717348i	$0.254644\pi$
$654$	24.7367	−	37.4927i	0.967281	−	1.46608i
$655$	−31.6641	−	43.5819i	−1.23722	−	1.70289i
$656$	−27.4489	+	5.00662i	−1.07170	+	0.195476i
$657$	−42.0882	−	46.7437i	−1.64202	−	1.82364i
$658$	0.0717600	+	0.275802i	0.00279749	+	0.0107519i
$659$	5.75851	−	9.97403i	0.224320	−	0.388533i	−0.731796	−	0.681524i	$-0.761317\pi$
$659$	5.75851	−	9.97403i	0.224320	−	0.388533i	0.956115	+	0.292991i	$0.0946507\pi$
$660$	12.8639	+	43.4379i	0.500727	+	1.69082i
$661$	10.2029	−	5.89067i	0.396848	−	0.229120i	−0.288275	−	0.957548i	$-0.593082\pi$
$661$	10.2029	−	5.89067i	0.396848	−	0.229120i	0.685123	+	0.728427i	$0.259748\pi$
$662$	−31.2414	+	8.12860i	−1.21423	+	0.315927i
$663$	−54.2084	+	44.9333i	−2.10528	+	1.74506i
$664$	−1.61702	−	0.292324i	−0.0627525	−	0.0113444i
$665$	1.00335	−	2.25355i	0.0389081	−	0.0873890i
$666$	8.89513	+	17.7754i	0.344679	+	0.688781i
$667$	−34.1217	−	7.25280i	−1.32120	−	0.280829i
$668$	5.00553	−	41.7822i	0.193670	−	1.61660i
$669$	−12.3733	−	27.7909i	−0.478379	−	1.07446i
$670$	−25.3892	+	9.53520i	−0.980870	+	0.368377i
$671$	−14.4158	−	6.62202i	−0.556516	−	0.255640i
$672$	21.0052	+	22.5874i	0.810292	+	0.871329i
$673$	−4.30986	−	0.452985i	−0.166133	−	0.0174613i	0.0210967	−	0.999777i	$-0.493284\pi$
$673$	−4.30986	−	0.452985i	−0.166133	−	0.0174613i	−0.187230	+	0.982316i	$0.559951\pi$
$674$	18.0398	+	9.35723i	0.694867	+	0.360427i
$675$	−4.09239	+	1.32970i	−0.157516	+	0.0511801i
$676$	−17.5583	−	19.1756i	−0.675321	−	0.737524i
$677$	13.2133	+	18.1865i	0.507827	+	0.698964i	0.983551	−	0.180630i	$-0.0578138\pi$
$677$	13.2133	+	18.1865i	0.507827	+	0.698964i	−0.475724	+	0.879595i	$0.657814\pi$
$678$	27.4773	−	4.14783i	1.05526	−	0.159296i
$679$	−33.4675	+	7.11373i	−1.28436	+	0.273000i
$680$	−54.0729	−	4.01570i	−2.07360	−	0.153995i
$681$	4.93698			0.189185
$682$	5.63695	−	13.8906i	0.215850	−	0.531898i
$683$	−3.14706	+	5.45087i	−0.120419	+	0.208572i	−0.919933	−	0.392076i	$-0.871757\pi$
$683$	−3.14706	+	5.45087i	−0.120419	+	0.208572i	0.799514	+	0.600648i	$0.205090\pi$
$684$	3.31009	+	1.53169i	0.126565	+	0.0585655i
$685$	−8.92750	−	9.91499i	−0.341102	−	0.378832i
$686$	28.1171	−	4.24441i	1.07352	−	0.162052i
$687$	45.5108	+	20.2627i	1.73634	+	0.773070i
$688$	−21.7688	+	35.2976i	−0.829927	+	1.34571i
$689$	9.35505	−	36.5820i	0.356399	−	1.39366i
$690$	−48.2610	+	30.8455i	−1.83726	+	1.17427i
$691$	−1.83387	+	17.4482i	−0.0697639	+	0.663759i	0.902631	+	0.430416i	$0.141633\pi$
$691$	−1.83387	+	17.4482i	−0.0697639	+	0.663759i	−0.972394	+	0.233343i	$0.925034\pi$
$692$	−2.82133	−	3.22636i	−0.107251	−	0.122648i
$693$	8.68612	−	25.7032i	0.329958	−	0.976385i
$694$	7.46378	−	9.08146i	0.283321	−	0.344728i
$695$	17.3808	+	39.0378i	0.659289	+	1.48079i
$696$	−10.4331	−	42.6276i	−0.395465	−	1.61580i
$697$	−49.1162	+	15.9588i	−1.86041	+	0.604483i
$698$	−10.8853	−	7.18185i	−0.412016	−	0.271837i
$699$	−11.3399	−	5.04886i	−0.428915	−	0.190965i
$700$	−3.61176	+	6.05121i	−0.136512	+	0.228714i
$701$	3.51339	+	1.14157i	0.132699	+	0.0431165i	0.374614	−	0.927181i	$-0.377775\pi$
$701$	3.51339	+	1.14157i	0.132699	+	0.0431165i	−0.241915	+	0.970298i	$0.577775\pi$
$702$	−12.5801	+	2.72900i	−0.474805	+	0.102999i
$703$	1.63687			0.0617356
$704$	−14.5156	+	22.2103i	−0.547075	+	0.837083i
$705$	−0.332873	−	0.576553i	−0.0125367	−	0.0217143i
$706$	20.2591	+	5.58629i	0.762463	+	0.210243i
$707$	4.55540	−	14.0201i	0.171323	−	0.527279i
$708$	5.04021	+	0.0731507i	0.189423	+	0.00274917i
$709$	−12.2730	+	1.28995i	−0.460923	+	0.0484450i	−0.332145	−	0.943228i	$-0.607772\pi$
$709$	−12.2730	+	1.28995i	−0.460923	+	0.0484450i	−0.128778	+	0.991673i	$0.541106\pi$
$710$	−14.4538	−	0.862699i	−0.542440	−	0.0323765i
$711$	−3.19957	−	0.680090i	−0.119993	−	0.0255053i
$712$	1.32796	−	4.55684i	0.0497674	−	0.170775i
$713$	18.8491	+	1.98112i	0.705903	+	0.0741934i
$714$	44.1065	+	36.2498i	1.65064	+	1.35661i
$715$	−27.5928	+	14.0490i	−1.03191	+	0.525404i
$716$	34.6895	−	6.84889i	1.29641	−	0.255955i
$717$	−2.26867	+	21.5850i	−0.0847251	+	0.806105i
$718$	34.1994	+	17.7392i	1.27631	+	0.662021i
$719$	−7.40112	+	34.8195i	−0.276015	+	1.29855i	0.593577	+	0.804777i	$0.297715\pi$
$719$	−7.40112	+	34.8195i	−0.276015	+	1.29855i	−0.869592	+	0.493771i	$0.835618\pi$
$720$	−34.8841	−	21.5138i	−1.30005	−	0.801771i
$721$	−0.714523	−	6.79823i	−0.0266102	−	0.253179i
$722$	−20.7693	+	16.5706i	−0.772954	+	0.616693i
$723$	40.6823	+	13.2185i	1.51299	+	0.491601i
$724$	2.10472	+	2.98711i	0.0782212	+	0.111015i
$725$	8.68327	−	5.01329i	0.322489	−	0.186189i
$726$	40.8905	+	3.40490i	1.51759	+	0.126368i
$727$		−	26.2692i		−	0.974269i	−0.873327	−	0.487135i	$-0.838042\pi$
$727$		−	26.2692i		−	0.974269i	0.873327	−	0.487135i	$-0.161958\pi$
$728$	−12.5672	+	16.9267i	−0.465772	+	0.627346i
$729$	12.5471	−	38.6159i	0.464706	−	1.43022i
$730$	57.5538	−	8.68802i	2.13016	−	0.321558i
$731$	−31.2205	+	70.1223i	−1.15473	+	2.59357i
$732$	24.1082	−	7.44821i	0.891065	−	0.275294i
$733$	−5.13929	−	15.8171i	−0.189824	−	0.584218i	0.810174	−	0.586189i	$-0.199373\pi$
$733$	−5.13929	−	15.8171i	−0.189824	−	0.584218i	−0.999998	+	0.00197134i	$0.999373\pi$
$734$	1.44691	+	32.0578i	0.0534062	+	1.18327i
$735$	−17.0109	+	7.57372i	−0.627455	+	0.279361i
$736$	−32.0664	−	9.85191i	−1.18198	−	0.363146i
$737$	−0.288141	+	24.5623i	−0.0106138	+	0.904765i
$738$	−38.5101	−	6.38619i	−1.41758	−	0.235079i
$739$	−4.01152	−	0.421628i	−0.147566	−	0.0155098i	0.0304573	−	0.999536i	$-0.490304\pi$
$739$	−4.01152	−	0.421628i	−0.147566	−	0.0155098i	−0.178023	+	0.984026i	$0.556970\pi$
$740$	−18.2629	−	2.18790i	−0.671357	−	0.0804288i
$741$	−1.08585	+	4.24612i	−0.0398898	+	0.155985i
$742$	−30.5625	−	1.82418i	−1.12198	−	0.0669676i
$743$	20.5597	−	46.1779i	0.754263	−	1.69410i	0.0349782	−	0.999388i	$-0.488864\pi$
$743$	20.5597	−	46.1779i	0.754263	−	1.69410i	0.719285	−	0.694715i	$-0.244470\pi$
$744$	8.05825	+	22.4407i	0.295430	+	0.822716i
$745$	10.1609	−	9.14888i	0.372265	−	0.335189i
$746$	−6.94899	−	26.7077i	−0.254421	−	0.977838i
$747$	−1.99096	−	1.14948i	−0.0728455	−	0.0420574i
$748$	−21.1454	+	44.3250i	−0.773151	+	1.62068i
$749$		−	20.4477i		−	0.747144i
$750$	−8.46111	+	30.6849i	−0.308956	+	1.12045i
$751$	−5.93795	−	27.9359i	−0.216679	−	1.01939i	−0.943194	−	0.332243i	$-0.892194\pi$
$751$	−5.93795	−	27.9359i	−0.216679	−	1.01939i	0.726515	−	0.687151i	$-0.241139\pi$
$752$	0.131202	−	0.367180i	0.00478444	−	0.0133897i
$753$	−8.85768	+	6.43548i	−0.322792	+	0.234522i
$754$	27.3507	−	12.3146i	0.996054	−	0.448470i
$755$	6.49964	+	20.0038i	0.236546	+	0.728014i
$756$	4.10659	+	9.59595i	0.149355	+	0.349001i
$757$	−0.339202	+	3.22729i	−0.0123285	+	0.117298i	−0.998955	−	0.0456976i	$-0.985449\pi$
$757$	−0.339202	+	3.22729i	−0.0123285	+	0.117298i	0.986627	+	0.162996i	$0.0521156\pi$
$758$	−4.62740	−	12.3213i	−0.168075	−	0.447529i
$759$	10.1898	+	50.8662i	0.369867	+	1.84633i
$760$	−2.86995	+	1.77617i	−0.104104	+	0.0644285i
$761$	11.9642	−	5.32681i	0.433702	−	0.193097i	−0.178260	−	0.983983i	$-0.557047\pi$
$761$	11.9642	−	5.32681i	0.433702	−	0.193097i	0.611963	+	0.790887i	$0.290380\pi$
$762$	−25.6219	+	16.3760i	−0.928185	+	0.593240i
$763$	5.17561	−	24.3493i	0.187370	−	0.881505i
$764$	−33.1968	−	7.56133i	−1.20102	−	0.273559i
$765$	−69.3009	−	30.8547i	−2.50558	−	1.11556i
$766$	−31.3897	−	12.3114i	−1.13416	−	0.444831i
$767$	0.577837	+	3.39645i	0.0208645	+	0.122639i
$768$	−6.36460	−	41.7195i	−0.229663	−	1.50542i
$769$	−16.2844	−	28.2055i	−0.587231	−	1.01711i	−0.994593	−	0.103848i	$-0.966885\pi$
$769$	−16.2844	−	28.2055i	−0.587231	−	1.01711i	0.407362	−	0.913267i	$-0.366449\pi$
$770$	15.4268	+	19.8079i	0.555943	+	0.713828i
$771$	−45.5957	−	26.3247i	−1.64209	−	0.948060i
$772$	−14.0734	+	30.4136i	−0.506512	+	1.09461i
$773$	4.92394	−	4.43354i	0.177102	−	0.159463i	−0.575812	−	0.817582i	$-0.695314\pi$
$773$	4.92394	−	4.43354i	0.177102	−	0.159463i	0.752914	+	0.658119i	$0.228647\pi$
$774$	−45.3533	+	36.1847i	−1.63019	+	1.30063i
$775$	−4.40716	+	3.20199i	−0.158310	+	0.115019i
$776$	43.3285	+	17.7237i	1.55540	+	0.636245i
$777$	14.3924	+	12.9590i	0.516325	+	0.464901i
$778$	10.1969	−	19.6587i	0.365578	−	0.704797i
$779$	−1.88952	+	2.60070i	−0.0676991	+	0.0931798i
$780$	17.7906	−	45.9235i	0.637007	−	1.64433i
$781$	−5.47432	+	11.9173i	−0.195887	+	0.426435i
$782$	−61.2538	−	10.1578i	−2.19043	−	0.363242i
$783$	1.55232	−	14.7693i	0.0554754	−	0.527813i
$784$	−9.83006	−	4.72307i	−0.351073	−	0.168681i
$785$	−17.6405	+	5.73175i	−0.629617	+	0.204575i
$786$	42.7385	−	64.7776i	1.52443	−	2.31054i
$787$	−9.67768	+	1.01717i	−0.344972	+	0.0362580i	−0.275430	−	0.961321i	$-0.588820\pi$
$787$	−9.67768	+	1.01717i	−0.344972	+	0.0362580i	−0.0695417	+	0.997579i	$0.522154\pi$
$788$	−18.7499	+	10.4654i	−0.667937	+	0.372816i
$789$	−45.8208	+	41.2572i	−1.63126	+	1.46880i
$790$	2.15585	−	2.12479i	0.0767017	−	0.0755965i
$791$	13.3371	−	7.70018i	0.474213	−	0.273787i
$792$	−29.6148	+	22.3817i	−1.05231	+	0.795301i
$793$	8.00474	+	15.2757i	0.284257	+	0.542457i
$794$	−10.0729	−	38.7142i	−0.357475	−	1.37392i
$795$	69.9605	−	14.8706i	2.48124	−	0.527405i
$796$	19.1055	−	32.0097i	0.677176	−	1.13455i
$797$	−0.173734	−	1.65297i	−0.00615398	−	0.0585512i	0.991014	−	0.133759i	$-0.0427047\pi$
$797$	−0.173734	−	1.65297i	−0.00615398	−	0.0585512i	−0.997168	+	0.0752076i	$0.976038\pi$
$798$	3.54742	+	0.211734i	0.125577	+	0.00749532i
$799$	0.150051	−	0.705933i	0.00530841	−	0.0249741i
$800$	8.74413	−	4.06283i	0.309152	−	0.143643i
$801$	3.90317	−	5.37225i	0.137912	−	0.189819i
$802$	−38.9661	+	14.6342i	−1.37594	+	0.516750i
$803$	11.5650	−	51.4347i	0.408120	−	1.81509i
$804$	−25.7191	−	29.4113i	−0.907043	−	1.03726i
$805$	−18.6576	+	25.6800i	−0.657596	+	0.905103i
$806$	−14.0792	+	8.20728i	−0.495918	+	0.289089i
$807$	25.1901	−	8.18476i	0.886734	−	0.288117i
$808$	−15.9472	+	12.3489i	−0.561021	+	0.434432i
$809$	−6.56097	+	14.7362i	−0.230671	+	0.518096i	−0.991383	−	0.130993i	$-0.958183\pi$
$809$	−6.56097	+	14.7362i	−0.230671	+	0.518096i	0.760712	+	0.649090i	$0.224850\pi$
$810$	11.9041	+	14.9205i	0.418269	+	0.524252i
$811$	19.0851	+	6.20112i	0.670168	+	0.217751i	0.624286	−	0.781196i	$-0.285390\pi$
$811$	19.0851	+	6.20112i	0.670168	+	0.217751i	0.0458823	+	0.998947i	$0.485390\pi$
$812$	−14.0087	−	19.8818i	−0.491609	−	0.697714i
$813$	25.1063	−	43.4855i	0.880518	−	1.52510i
$814$	−7.84373	+	14.6975i	−0.274922	+	0.515147i
$815$	15.2380	+	8.79768i	0.533765	+	0.308169i
$816$	−21.9721	−	74.9588i	−0.769176	−	2.62408i
$817$	0.993390	+	4.67353i	0.0347543	+	0.163506i
$818$	−6.22285	−	2.44068i	−0.217577	−	0.0853364i
$819$	−24.5511	+	16.3459i	−0.857884	+	0.571170i
$820$	24.5580	−	26.4910i	0.857603	−	0.925106i
$821$	23.6087	−	26.2202i	0.823951	−	0.915090i	−0.173616	−	0.984814i	$-0.555545\pi$
$821$	23.6087	−	26.2202i	0.823951	−	0.915090i	0.997566	+	0.0697234i	$0.0222117\pi$
$822$	8.85000	−	17.0619i	0.308679	−	0.595102i
$823$	12.9670	+	29.1243i	0.452000	+	1.01521i	0.985541	+	0.169434i	$0.0541941\pi$
$823$	12.9670	+	29.1243i	0.452000	+	1.01521i	−0.533542	+	0.845774i	$0.679139\pi$
$824$	−4.42638	+	8.23883i	−0.154200	+	0.287013i
$825$	−11.9594	−	8.90522i	−0.416373	−	0.310040i
$826$	2.61521	−	0.982172i	0.0909947	−	0.0341741i
$827$	3.13233	−	4.31128i	0.108922	−	0.149918i	−0.751076	−	0.660216i	$-0.770465\pi$
$827$	3.13233	−	4.31128i	0.108922	−	0.149918i	0.859998	+	0.510298i	$0.170465\pi$
$828$	−37.5647	−	28.1342i	−1.30546	−	0.977731i
$829$	−9.12507	+	10.1344i	−0.316927	+	0.351983i	−0.880468	−	0.474105i	$-0.842772\pi$
$829$	−9.12507	+	10.1344i	−0.316927	+	0.351983i	0.563542	+	0.826088i	$0.309438\pi$
$830$	1.90249	−	0.952042i	0.0660364	−	0.0330459i
$831$	−49.7044	+	36.1124i	−1.72423	+	1.25273i
$832$	27.2465	−	9.46731i	0.944601	−	0.328220i
$833$	−19.1979	−	6.23776i	−0.665166	−	0.216126i
$834$	−43.8446	+	43.2129i	−1.51822	+	1.49634i
$835$	27.2401	+	47.1812i	0.942681	+	1.63277i
$836$	0.556895	+	3.00579i	0.0192606	+	0.103958i
$837$			8.06855i			0.278890i
$838$	11.3506	+	3.12982i	0.392098	+	0.108118i
$839$	18.5347	+	20.5849i	0.639889	+	0.710669i	0.972633	−	0.232349i	$-0.0746410\pi$
$839$	18.5347	+	20.5849i	0.639889	+	0.710669i	−0.332744	+	0.943017i	$0.607974\pi$
$840$	−39.2964	−	7.10400i	−1.35585	−	0.245111i
$841$	0.585798	+	5.57350i	0.0201999	+	0.192190i
$842$	21.2958	+	42.5560i	0.733903	+	1.46658i
$843$	−17.3662	−	15.6366i	−0.598123	−	0.538552i
$844$	32.4544	+	3.88806i	1.11713	+	0.133832i
$845$	33.0768	+	6.24361i	1.13788	+	0.214787i
$846$	0.346371	−	0.421442i	0.0119085	−	0.0144895i
$847$	21.7857	−	6.51771i	0.748566	−	0.223951i
$848$	33.1610	+	25.5955i	1.13875	+	0.878954i
$849$	−24.8738	−	55.8675i	−0.853667	−	1.91737i
$850$	15.0374	−	9.61098i	0.515778	−	0.329654i
$851$	−20.6024	−	4.37918i	−0.706242	−	0.150116i
$852$	−6.15732	−	19.9299i	−0.210946	−	0.682786i
$853$	−8.28461	+	6.01912i	−0.283660	+	0.206091i	−0.720512	−	0.693442i	$-0.756093\pi$
$853$	−8.28461	+	6.01912i	−0.283660	+	0.206091i	0.436852	+	0.899533i	$0.356093\pi$
$854$	10.9310	−	8.72120i	0.374052	−	0.298433i
$855$	−4.61878	+	0.981753i	−0.157959	+	0.0335752i
$856$	−15.7443	+	23.1260i	−0.538129	+	0.790431i
$857$		−	53.9557i		−	1.84309i	−0.388269	−	0.921546i	$-0.626927\pi$
$857$		−	53.9557i		−	1.84309i	0.388269	−	0.921546i	$-0.373073\pi$
$858$	−32.9228	−	30.0970i	−1.12397	−	1.02749i
$859$		−	18.0327i		−	0.615269i	−0.951505	−	0.307634i	$-0.900463\pi$
$859$		−	18.0327i		−	0.615269i	0.951505	−	0.307634i	$-0.0995374\pi$
$860$	−4.83664	−	53.4714i	−0.164928	−	1.82336i
$861$	−37.2035	+	7.90786i	−1.26789	+	0.269499i
$862$	−17.6869	−	22.1685i	−0.602417	−	0.755061i
$863$	8.26658	−	6.00602i	0.281398	−	0.204447i	−0.438129	−	0.898912i	$-0.644359\pi$
$863$	8.26658	−	6.00602i	0.281398	−	0.204447i	0.719527	+	0.694465i	$0.244359\pi$
$864$	2.74420	−	14.0148i	0.0933597	−	0.476794i
$865$	5.42753	+	1.15366i	0.184542	+	0.0392255i
$866$	4.93671	+	7.72400i	0.167756	+	0.262472i
$867$	−40.5681	−	91.1174i	−1.37776	−	3.09451i
$868$	8.69851	+	9.94725i	0.295247	+	0.337632i
$869$	−1.08565	−	2.51748i	−0.0368283	−	0.0853998i
$870$	43.8943	+	36.0754i	1.48816	+	1.22307i
$871$	16.5669	−	20.9437i	0.561347	−	0.709649i
$872$	−24.6020	+	23.5535i	−0.833128	+	0.797623i
$873$	48.6718	+	43.8243i	1.64729	+	1.48323i
$874$	−3.45630	+	1.72960i	−0.116911	+	0.0585045i
$875$	1.84390	+	17.5435i	0.0623350	+	0.593078i
$876$	40.8679	+	73.2189i	1.38080	+	2.47384i
$877$	31.6474	+	35.1480i	1.06866	+	1.18686i	0.981657	+	0.190654i	$0.0610607\pi$
$877$	31.6474	+	35.1480i	1.06866	+	1.18686i	0.0869981	+	0.996208i	$0.472273\pi$
$878$	−8.20581	+	29.7590i	−0.276933	+	1.00432i
$879$			36.6811i			1.23722i
$880$	−2.19574	−	34.2807i	−0.0740184	−	1.15560i
$881$	20.0929	+	34.8019i	0.676947	+	1.17251i	0.975896	+	0.218238i	$0.0700308\pi$
$881$	20.0929	+	34.8019i	0.676947	+	1.17251i	−0.298949	+	0.954269i	$0.596636\pi$
$882$	−10.7104	−	10.8669i	−0.360637	−	0.365909i
$883$	49.6331	+	16.1268i	1.67029	+	0.542709i	0.982989	−	0.183667i	$-0.0587967\pi$
$883$	49.6331	+	16.1268i	1.67029	+	0.542709i	0.687298	+	0.726376i	$0.258797\pi$
$884$	47.6439	−	24.0915i	1.60244	−	0.810285i
$885$	−5.27963	+	3.83588i	−0.177473	+	0.128942i
$886$	−4.54044	−	9.07328i	−0.152539	−	0.304823i
$887$	1.46537	−	1.62745i	0.0492022	−	0.0546446i	−0.718041	−	0.696000i	$-0.754961\pi$
$887$	1.46537	−	1.62745i	0.0492022	−	0.0546446i	0.767243	+	0.641356i	$0.221628\pi$
$888$	−6.29941	−	25.7382i	−0.211394	−	0.863718i
$889$	−9.90542	+	13.6336i	−0.332217	+	0.457258i
$890$	2.16046	+	5.75260i	0.0724187	+	0.192828i
$891$	16.5035	−	5.14907i	0.552887	−	0.172500i
$892$	4.46792	+	22.6299i	0.149597	+	0.757706i
$893$	−0.0182720	−	0.0410397i	−0.000611450	−	0.00137334i
$894$	17.4850	+	9.06946i	0.584785	+	0.303328i
$895$	−30.6313	+	34.0195i	−1.02389	+	1.13715i
$896$	−11.7259	−	20.2365i	−0.391734	−	0.676055i
$897$	25.0269	−	50.5388i	0.835625	−	1.68744i
$898$	−4.28600	+	10.9277i	−0.143026	+	0.364664i
$899$	−3.90892	−	18.3900i	−0.130370	−	0.613341i
$900$	13.4347	−	1.21521i	0.447824	−	0.0405069i
$901$	67.1474	+	38.7676i	2.23700	+	1.29154i
$902$	−14.2974	−	29.4284i	−0.476051	−	0.979859i
$903$	−28.2656	+	48.9574i	−0.940619	+	1.62920i
$904$	−21.0130	−	1.56052i	−0.698882	−	0.0519022i
$905$	−4.49928	−	1.46190i	−0.149561	−	0.0485953i
$906$	−23.6859	+	18.8976i	−0.786912	+	0.627830i
$907$	17.3829	−	39.0426i	0.577189	−	1.29639i	−0.355152	−	0.934809i	$-0.615571\pi$
$907$	17.3829	−	39.0426i	0.577189	−	1.29639i	0.932341	−	0.361580i	$-0.117762\pi$
$908$	−3.65000	−	0.831371i	−0.121130	−	0.0275900i
$909$	−26.8371	+	8.71991i	−0.890131	+	0.289221i
$910$	−0.114101	−	27.2935i	−0.00378242	−	0.904770i
$911$	29.6889	−	40.8633i	0.983638	−	1.35386i	0.0487923	−	0.998809i	$-0.484463\pi$
$911$	29.6889	−	40.8633i	0.983638	−	1.35386i	0.934846	−	0.355053i	$-0.115537\pi$
$912$	−3.84904	−	2.97091i	−0.127454	−	0.0983766i
$913$	−0.178919	−	1.91853i	−0.00592135	−	0.0634941i
$914$	6.51642	+	17.3511i	0.215544	+	0.573924i
$915$	−19.2014	+	26.4284i	−0.634777	+	0.873696i
$916$	−30.2348	−	22.6445i	−0.998986	−	0.748194i
$917$	8.94210	−	42.0693i	0.295294	−	1.38925i
$918$	1.57489	−	26.3859i	0.0519792	−	0.870865i
$919$	−5.44687	−	51.8235i	−0.179676	−	1.70950i	−0.598244	−	0.801314i	$-0.704135\pi$
$919$	−5.44687	−	51.8235i	−0.179676	−	1.70950i	0.418569	−	0.908185i	$-0.362532\pi$
$920$	40.8745	−	14.6777i	1.34759	−	0.483908i
$921$	81.6896	−	17.3637i	2.69177	−	0.572152i
$922$	−12.6822	+	3.29974i	−0.417665	+	0.108671i
$923$	12.6282	−	6.61739i	0.415662	−	0.217814i
$924$	−18.9001	+	30.8378i	−0.621769	+	1.01449i
$925$	5.24289	−	3.02698i	0.172385	−	0.0995266i
$926$	−6.28493	−	6.37681i	−0.206536	−	0.209555i
$927$	−9.72390	+	8.75544i	−0.319375	+	0.287566i
$928$	0.535026	+	33.2723i	0.0175631	+	1.09222i
$929$	49.2631	−	5.17776i	1.61627	−	0.169877i	0.747211	−	0.664587i	$-0.231393\pi$
$929$	49.2631	−	5.17776i	1.61627	−	0.169877i	0.869058	+	0.494711i	$0.164726\pi$
$930$	−25.7664	−	17.0000i	−0.844913	−	0.557451i
$931$	−1.19500	+	0.388279i	−0.0391645	+	0.0127253i
$932$	7.53361	+	5.64232i	0.246771	+	0.184820i
$933$	−7.08246	+	67.3851i	−0.231869	+	2.20609i
$934$	−1.50784	+	9.09263i	−0.0493381	+	0.297520i
$935$	−12.4887	−	62.3421i	−0.408426	−	2.03881i
$936$	40.3527	+	0.416936i	1.31897	+	0.0136280i
$937$	−20.4300	+	28.1195i	−0.667419	+	0.918624i	−0.999698	−	0.0245571i	$-0.992182\pi$
$937$	−20.4300	+	28.1195i	−0.667419	+	0.918624i	0.332279	+	0.943181i	$0.392182\pi$
$938$	−19.2209	−	9.96985i	−0.627583	−	0.325527i
$939$	−44.3263	−	39.9116i	−1.44653	−	1.30247i
$940$	0.149010	+	0.482312i	0.00486017	+	0.0157313i
$941$	1.30376	−	0.947237i	0.0425014	−	0.0308790i	−0.566332	−	0.824177i	$-0.691638\pi$
$941$	1.30376	−	0.947237i	0.0425014	−	0.0308790i	0.608833	+	0.793298i	$0.291638\pi$
$942$	−16.6649	−	20.8876i	−0.542973	−	0.680554i
$943$	30.7402	−	27.6786i	1.00104	−	0.901340i
$944$	−3.71400	−	0.902836i	−0.120880	−	0.0293848i
$945$	−11.7028	−	6.75660i	−0.380692	−	0.219792i
$946$	−46.7241	−	13.4755i	−1.51913	−	0.438126i
$947$	−10.6465	−	18.4402i	−0.345963	−	0.599226i	0.639565	−	0.768737i	$-0.279114\pi$
$947$	−10.6465	−	18.4402i	−0.345963	−	0.599226i	−0.985528	+	0.169511i	$0.945781\pi$
$948$	3.95750	+	1.83126i	0.128534	+	0.0594767i
$949$	−44.1240	+	36.5743i	−1.43232	+	1.18725i
$950$	0.405617	−	1.03417i	0.0131599	−	0.0335531i
$951$	−24.2202	−	10.7835i	−0.785393	−	0.349679i
$952$	−26.5044	−	34.2275i	−0.859013	−	1.10932i
$953$	7.80178	−	36.7045i	0.252724	−	1.18897i	−0.650399	−	0.759593i	$-0.725398\pi$
$953$	7.80178	−	36.7045i	0.252724	−	1.18897i	0.903123	−	0.429382i	$-0.141268\pi$
$954$	31.5619	+	49.3819i	1.02186	+	1.59880i
$955$	40.2682	−	17.9286i	1.30305	−	0.580154i
$956$	5.31211	−	15.5761i	0.171806	−	0.503768i
$957$	44.8650	−	25.2058i	1.45028	−	0.814788i
$958$	7.91123	−	2.97116i	0.255600	−	0.0959937i
$959$	1.11344	−	10.5936i	0.0359547	−	0.342086i
$960$	38.9735	+	38.2918i	1.25787	+	1.23586i
$961$	−6.42301	−	19.7680i	−0.207194	−	0.637677i
$962$	16.5141	−	7.43544i	0.532437	−	0.239728i
$963$	−31.6657	+	23.0065i	−1.02041	+	0.741373i
$964$	−27.8513	−	16.6235i	−0.897029	−	0.535405i
$965$	−9.02050	−	42.4381i	−0.290380	−	1.36613i
$966$	−44.0832	−	12.1556i	−1.41835	−	0.391099i
$967$			1.67215i			0.0537729i	0.999638	+	0.0268864i	$0.00855925\pi$
$967$			1.67215i			0.0537729i	−0.999638	+	0.0268864i	$0.991441\pi$
$968$	−29.6577	−	9.40313i	−0.953236	−	0.302228i
$969$	−7.79389	−	4.49980i	−0.250376	−	0.144555i
$970$	−58.6540	+	15.2610i	−1.88327	+	0.490002i
$971$	−20.2031	+	18.1910i	−0.648349	+	0.583776i	−0.926285	−	0.376823i	$-0.877016\pi$
$971$	−20.2031	+	18.1910i	−0.648349	+	0.583776i	0.277936	+	0.960600i	$0.410350\pi$
$972$	−21.8561	+	36.6182i	−0.701036	+	1.17453i
$973$	−13.8765	+	31.1672i	−0.444861	+	0.999173i
$974$	−1.09337	+	18.3184i	−0.0350338	+	0.586961i
$975$	4.37417	+	15.6084i	0.140085	+	0.499867i
$976$	−19.0779	+	1.44687i	−0.610669	+	0.0463130i
$977$	29.5126	+	3.10190i	0.944193	+	0.0992387i	0.564097	−	0.825708i	$-0.309224\pi$
$977$	29.5126	+	3.10190i	0.944193	+	0.0992387i	0.380096	+	0.924947i	$0.375891\pi$
$978$	−4.14688	+	25.0066i	−0.132603	+	0.799624i
$979$	5.56526	+	0.0652862i	0.177866	+	0.00208656i
$980$	13.8518	−	2.73483i	0.442481	−	0.0873608i
$981$	−43.5310	+	19.3812i	−1.38984	+	0.618795i
$982$	−7.36741	+	0.332523i	−0.235103	+	0.0106112i
$983$	−4.71452	−	14.5098i	−0.150370	−	0.462791i	0.847293	−	0.531126i	$-0.178231\pi$
$983$	−4.71452	−	14.5098i	−0.150370	−	0.462791i	−0.997662	+	0.0683358i	$0.978231\pi$
$984$	48.1654	+	19.7023i	1.53546	+	0.628086i
$985$	11.3072	−	25.3964i	0.360278	−	0.809197i
$986$	9.19348	+	60.9023i	0.292780	+	1.93952i
$987$	0.164249	−	0.505507i	0.00522811	−	0.0160905i
$988$	1.51783	−	2.95639i	0.0482885	−	0.0940552i
$989$		−	61.4811i		−	1.95498i
$990$	13.3176	−	46.1767i	0.423262	−	1.46759i
$991$	−3.10954	+	1.79529i	−0.0987778	+	0.0570294i	−0.548575	−	0.836101i	$-0.684830\pi$
$991$	−3.10954	+	1.79529i	−0.0987778	+	0.0570294i	0.449797	+	0.893131i	$0.351496\pi$
$992$	−2.17868	−	17.9478i	−0.0691731	−	0.569844i
$993$	57.2612	+	18.6053i	1.81713	+	0.590421i
$994$	−7.20968	−	9.03650i	−0.228677	−	0.286620i
$995$	5.04473	+	47.9974i	0.159929	+	1.52162i
$996$	2.24757	+	2.08357i	0.0712169	+	0.0660203i
$997$	10.4105	−	48.9775i	0.329704	−	1.55113i	−0.431192	−	0.902260i	$-0.641907\pi$
$997$	10.4105	−	48.9775i	0.329704	−	1.55113i	0.760896	−	0.648874i	$-0.224760\pi$
$998$	6.61223	−	12.7477i	0.209307	−	0.403522i
$999$	0.937279	−	8.91761i	0.0296542	−	0.282141i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bn.a.491.61	yes	640
4.3	odd	2	inner	572.2.bn.a.491.16	yes	640
11.8	odd	10	inner	572.2.bn.a.283.12	yes	640
13.4	even	6	inner	572.2.bn.a.95.34	yes	640
44.19	even	10	inner	572.2.bn.a.283.34	yes	640
52.43	odd	6	inner	572.2.bn.a.95.12	✓	640
143.30	odd	30	inner	572.2.bn.a.459.16	yes	640
572.459	even	30	inner	572.2.bn.a.459.61	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bn.a.95.12	✓	640	52.43	odd	6	inner
572.2.bn.a.95.34	yes	640	13.4	even	6	inner
572.2.bn.a.283.12	yes	640	11.8	odd	10	inner
572.2.bn.a.283.34	yes	640	44.19	even	10	inner
572.2.bn.a.459.16	yes	640	143.30	odd	30	inner
572.2.bn.a.459.61	yes	640	572.459	even	30	inner
572.2.bn.a.491.16	yes	640	4.3	odd	2	inner
572.2.bn.a.491.61	yes	640	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bn (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.992718 + 1.00723i) q^{2} +(-0.548395 - 2.58000i) q^{3} +(-0.0290238 + 1.99979i) q^{4} +(-1.52195 - 2.09479i) q^{5} +(2.05425 - 3.11357i) q^{6} +(0.429806 - 2.02208i) q^{7} +(-2.04306 + 1.95599i) q^{8} +(-3.61501 + 1.60951i) q^{9} +O(q^{10})\)	\(q+(0.992718 + 1.00723i) q^{2} +(-0.548395 - 2.58000i) q^{3} +(-0.0290238 + 1.99979i) q^{4} +(-1.52195 - 2.09479i) q^{5} +(2.05425 - 3.11357i) q^{6} +(0.429806 - 2.02208i) q^{7} +(-2.04306 + 1.95599i) q^{8} +(-3.61501 + 1.60951i) q^{9} +(0.599063 - 3.61249i) q^{10} +(-2.85263 - 1.69189i) q^{11} +(5.17537 - 1.02179i) q^{12} +(1.33053 + 3.35107i) q^{13} +(2.46338 - 1.57444i) q^{14} +(-4.56991 + 5.07540i) q^{15} +(-3.99832 - 0.116083i) q^{16} +(-7.36311 + 0.773894i) q^{17} +(-5.20983 - 2.04336i) q^{18} +(-0.342480 + 0.308370i) q^{19} +(4.23330 - 2.98278i) q^{20} -5.45266 q^{21} +(-1.12773 - 4.55282i) q^{22} +(5.13562 - 2.96505i) q^{23} +(6.16686 + 4.19843i) q^{24} +(-0.526709 + 1.62104i) q^{25} +(-2.05447 + 4.66682i) q^{26} +(1.48389 + 2.04240i) q^{27} +(4.03126 + 0.918211i) q^{28} +(-4.37157 - 3.93618i) q^{29} +(-9.64873 + 0.435488i) q^{30} +(2.58566 + 1.87859i) q^{31} +(-3.85228 - 4.14246i) q^{32} +(-2.80070 + 8.28761i) q^{33} +(-8.08898 - 6.64809i) q^{34} +(-4.88997 + 2.17715i) q^{35} +(-3.11375 - 7.27598i) q^{36} +(-2.63952 - 2.37664i) q^{37} +(-0.650586 - 0.0388314i) q^{38} +(7.91611 - 5.27047i) q^{39} +(7.20682 + 1.30285i) q^{40} +(6.82300 - 1.45027i) q^{41} +(-5.41295 - 5.49209i) q^{42} +(5.18381 - 8.97862i) q^{43} +(3.46622 - 5.65556i) q^{44} +(8.87345 + 5.12309i) q^{45} +(8.08471 + 2.22929i) q^{46} +(-0.0301227 + 0.0927082i) q^{47} +(1.89316 + 10.3793i) q^{48} +(2.49075 + 1.10895i) q^{49} +(-2.15564 + 1.07872i) q^{50} +(6.03454 + 18.5724i) q^{51} +(-6.74006 + 2.56351i) q^{52} +(-8.47246 - 6.15560i) q^{53} +(-0.584081 + 3.52214i) q^{54} +(0.797416 + 8.55063i) q^{55} +(3.07705 + 4.97193i) q^{56} +(0.983409 + 0.714488i) q^{57} +(-0.375097 - 8.31070i) q^{58} +(0.934660 + 0.198668i) q^{59} +(-10.0171 - 9.28617i) q^{60} +(4.75697 - 0.499978i) q^{61} +(0.674655 + 4.46926i) q^{62} +(1.70080 + 8.00162i) q^{63} +(0.348188 - 7.99242i) q^{64} +(4.99479 - 7.88734i) q^{65} +(-11.1278 + 5.40630i) q^{66} +(-3.70317 - 6.41407i) q^{67} +(-1.33392 - 14.7471i) q^{68} +(-10.4662 - 11.6239i) q^{69} +(-7.04725 - 2.76402i) q^{70} +(-0.413324 - 3.93251i) q^{71} +(4.23750 - 10.3593i) q^{72} +(4.91193 + 15.1174i) q^{73} +(-0.226481 - 5.01793i) q^{74} +(4.47113 + 0.469935i) q^{75} +(-0.606736 - 0.693838i) q^{76} +(-4.64722 + 5.04106i) q^{77} +(13.1670 + 2.74126i) q^{78} +(0.668752 + 0.485877i) q^{79} +(5.84207 + 8.55229i) q^{80} +(-3.48787 + 3.87368i) q^{81} +(8.23408 + 5.43262i) q^{82} +(0.341485 + 0.470014i) q^{83} +(0.158257 - 10.9042i) q^{84} +(12.8274 + 14.2463i) q^{85} +(14.1896 - 3.69195i) q^{86} +(-7.75799 + 13.4372i) q^{87} +(9.13742 - 2.12309i) q^{88} +(-1.45328 + 0.839052i) q^{89} +(3.64870 + 14.0234i) q^{90} +(7.34801 - 1.25012i) q^{91} +(5.78042 + 10.3562i) q^{92} +(3.42879 - 7.70119i) q^{93} +(-0.123282 + 0.0616926i) q^{94} +(1.16721 + 0.248098i) q^{95} +(-8.57497 + 12.2106i) q^{96} +(-6.73191 - 15.1201i) q^{97} +(1.35564 + 3.60963i) q^{98} +(13.0354 + 1.52488i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 15 q^{2} - 3 q^{4} - 15 q^{6} - 78 q^{9}+O(q^{10}) \) 640 * q - 15 * q^2 - 3 * q^4 - 15 * q^6 - 78 * q^9	\( 640 q - 15 q^{2} - 3 q^{4} - 15 q^{6} - 78 q^{9} - 4 q^{12} - 20 q^{13} - 12 q^{14} - 19 q^{16} - 10 q^{17} - 45 q^{20} - 15 q^{22} - 15 q^{24} + 104 q^{25} - 20 q^{26} - 15 q^{28} - 10 q^{29} + 45 q^{30} - 24 q^{33} + 4 q^{36} - 18 q^{37} - 14 q^{38} - 20 q^{40} - 30 q^{41} - 13 q^{42} - 108 q^{45} - 15 q^{46} + 35 q^{48} - 74 q^{49} - 90 q^{50} + 15 q^{52} - 8 q^{53} + 50 q^{56} + 27 q^{58} - 10 q^{61} - 5 q^{62} - 84 q^{64} - 146 q^{66} - 70 q^{68} - 26 q^{69} - 15 q^{72} - 55 q^{74} + 44 q^{77} + 24 q^{78} - 39 q^{80} + 30 q^{81} - 29 q^{82} + 30 q^{84} - 30 q^{85} - 75 q^{88} - 24 q^{89} + 30 q^{90} + 14 q^{92} + 66 q^{93} - 5 q^{94} - 30 q^{97}+O(q^{100}) \) 640 * q - 15 * q^2 - 3 * q^4 - 15 * q^6 - 78 * q^9 - 4 * q^12 - 20 * q^13 - 12 * q^14 - 19 * q^16 - 10 * q^17 - 45 * q^20 - 15 * q^22 - 15 * q^24 + 104 * q^25 - 20 * q^26 - 15 * q^28 - 10 * q^29 + 45 * q^30 - 24 * q^33 + 4 * q^36 - 18 * q^37 - 14 * q^38 - 20 * q^40 - 30 * q^41 - 13 * q^42 - 108 * q^45 - 15 * q^46 + 35 * q^48 - 74 * q^49 - 90 * q^50 + 15 * q^52 - 8 * q^53 + 50 * q^56 + 27 * q^58 - 10 * q^61 - 5 * q^62 - 84 * q^64 - 146 * q^66 - 70 * q^68 - 26 * q^69 - 15 * q^72 - 55 * q^74 + 44 * q^77 + 24 * q^78 - 39 * q^80 + 30 * q^81 - 29 * q^82 + 30 * q^84 - 30 * q^85 - 75 * q^88 - 24 * q^89 + 30 * q^90 + 14 * q^92 + 66 * q^93 - 5 * q^94 - 30 * q^97

Introduction

L-functions

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