LMFDB - Embedded newform 570.2.s.b.521.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(221,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("570.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.s (of order $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.11
Character	$\chi$	$=$	570.521
Dual form			570.2.s.b.221.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.54313 - 0.786608i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.0903420 - 1.72969i) q^{6} +2.34168 q^{7} -1.00000 q^{8} +(1.76250 - 2.42768i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.54313 - 0.786608i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.0903420 - 1.72969i) q^{6} +2.34168 q^{7} -1.00000 q^{8} +(1.76250 - 2.42768i) q^{9} +(-0.866025 + 0.500000i) q^{10} -2.39841i q^{11} +(-1.45279 - 0.943085i) q^{12} +(-0.414577 + 0.239356i) q^{13} +(1.17084 - 2.02795i) q^{14} +(-1.72969 - 0.0903420i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.40013 - 1.38572i) q^{17} +(-1.22118 - 2.74020i) q^{18} +(0.994947 + 4.24383i) q^{19} +1.00000i q^{20} +(3.61351 - 1.84198i) q^{21} +(-2.07709 - 1.19921i) q^{22} +(1.80040 - 1.03946i) q^{23} +(-1.54313 + 0.786608i) q^{24} +(0.500000 + 0.866025i) q^{25} +0.478712i q^{26} +(0.810128 - 5.13261i) q^{27} +(-1.17084 - 2.02795i) q^{28} +(-0.313727 - 0.543392i) q^{29} +(-0.943085 + 1.45279i) q^{30} +2.05113i q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.88661 - 3.70106i) q^{33} +(-2.40013 + 1.38572i) q^{34} +(-2.02795 - 1.17084i) q^{35} +(-2.98368 - 0.312528i) q^{36} -5.67577i q^{37} +(4.17274 + 1.26026i) q^{38} +(-0.451467 + 0.695467i) q^{39} +(0.866025 + 0.500000i) q^{40} +(1.04624 - 1.81214i) q^{41} +(0.211552 - 4.05038i) q^{42} +(-3.77271 + 6.53452i) q^{43} +(-2.07709 + 1.19921i) q^{44} +(-2.74020 + 1.22118i) q^{45} -2.07892i q^{46} +(1.94389 - 1.12231i) q^{47} +(-0.0903420 + 1.72969i) q^{48} -1.51654 q^{49} +1.00000 q^{50} +(-4.79373 - 0.250377i) q^{51} +(0.414577 + 0.239356i) q^{52} +(6.64114 + 11.5028i) q^{53} +(-4.03991 - 3.26790i) q^{54} +(-1.19921 + 2.07709i) q^{55} -2.34168 q^{56} +(4.87356 + 5.76614i) q^{57} -0.627455 q^{58} +(-3.13769 + 5.43465i) q^{59} +(0.786608 + 1.54313i) q^{60} +(1.25195 + 2.16845i) q^{61} +(1.77633 + 1.02556i) q^{62} +(4.12720 - 5.68484i) q^{63} +1.00000 q^{64} +0.478712 q^{65} +(-4.14852 - 0.216677i) q^{66} +(11.3258 - 6.53894i) q^{67} +2.77143i q^{68} +(1.96060 - 3.02023i) q^{69} +(-2.02795 + 1.17084i) q^{70} +(-2.68385 + 4.64856i) q^{71} +(-1.76250 + 2.42768i) q^{72} +(-5.81045 + 10.0640i) q^{73} +(-4.91536 - 2.83789i) q^{74} +(1.45279 + 0.943085i) q^{75} +(3.17779 - 2.98356i) q^{76} -5.61632i q^{77} +(0.376559 + 0.738715i) q^{78} +(10.1589 + 5.86527i) q^{79} +(0.866025 - 0.500000i) q^{80} +(-2.78722 - 8.55753i) q^{81} +(-1.04624 - 1.81214i) q^{82} +11.3081i q^{83} +(-3.40196 - 2.20840i) q^{84} +(1.38572 + 2.40013i) q^{85} +(3.77271 + 6.53452i) q^{86} +(-0.911558 - 0.591743i) q^{87} +2.39841i q^{88} +(-4.97362 - 8.61457i) q^{89} +(-0.312528 + 2.98368i) q^{90} +(-0.970806 + 0.560495i) q^{91} +(-1.80040 - 1.03946i) q^{92} +(1.61344 + 3.16516i) q^{93} -2.24461i q^{94} +(1.26026 - 4.17274i) q^{95} +(1.45279 + 0.943085i) q^{96} +(7.49209 + 4.32556i) q^{97} +(-0.758271 + 1.31336i) q^{98} +(-5.82257 - 4.22719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9	$ 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9} + 2 q^{12} + 18 q^{13} - 6 q^{14} - 12 q^{16} - 12 q^{17} - 2 q^{18} + 6 q^{19} + 6 q^{21} + 18 q^{22} - 2 q^{24} + 12 q^{25} - 28 q^{27} + 6 q^{28} + 12 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 6 q^{38} + 40 q^{39} - 6 q^{41} - 6 q^{42} - 22 q^{43} + 18 q^{44} + 8 q^{45} - 12 q^{47} - 4 q^{48} + 12 q^{49} + 24 q^{50} - 4 q^{51} - 18 q^{52} - 8 q^{53} - 32 q^{54} + 12 q^{56} - 20 q^{57} - 26 q^{59} + 22 q^{61} + 18 q^{62} + 30 q^{63} + 24 q^{64} - 8 q^{65} - 22 q^{66} - 48 q^{67} + 64 q^{69} - 24 q^{71} - 2 q^{72} - 8 q^{73} - 30 q^{74} - 2 q^{75} - 12 q^{76} + 2 q^{78} + 18 q^{79} - 6 q^{81} + 6 q^{82} - 12 q^{84} + 22 q^{86} - 24 q^{87} - 28 q^{89} + 16 q^{90} + 18 q^{91} + 14 q^{93} - 2 q^{96} + 6 q^{97} + 6 q^{98} - 52 q^{99}+O(q^{100}) $ 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9 + 2 * q^12 + 18 * q^13 - 6 * q^14 - 12 * q^16 - 12 * q^17 - 2 * q^18 + 6 * q^19 + 6 * q^21 + 18 * q^22 - 2 * q^24 + 12 * q^25 - 28 * q^27 + 6 * q^28 + 12 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 6 * q^38 + 40 * q^39 - 6 * q^41 - 6 * q^42 - 22 * q^43 + 18 * q^44 + 8 * q^45 - 12 * q^47 - 4 * q^48 + 12 * q^49 + 24 * q^50 - 4 * q^51 - 18 * q^52 - 8 * q^53 - 32 * q^54 + 12 * q^56 - 20 * q^57 - 26 * q^59 + 22 * q^61 + 18 * q^62 + 30 * q^63 + 24 * q^64 - 8 * q^65 - 22 * q^66 - 48 * q^67 + 64 * q^69 - 24 * q^71 - 2 * q^72 - 8 * q^73 - 30 * q^74 - 2 * q^75 - 12 * q^76 + 2 * q^78 + 18 * q^79 - 6 * q^81 + 6 * q^82 - 12 * q^84 + 22 * q^86 - 24 * q^87 - 28 * q^89 + 16 * q^90 + 18 * q^91 + 14 * q^93 - 2 * q^96 + 6 * q^97 + 6 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.54313	−	0.786608i	0.890926	−	0.454148i
$3$	1.54313	−	0.786608i	0.890926	−	0.454148i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	0.0903420	−	1.72969i	0.0368820	−	0.706144i
$7$	2.34168			0.885071			0.442536	−	0.896751i	$-0.354079\pi$
$7$	2.34168			0.885071			0.442536	+	0.896751i	$0.354079\pi$
$8$	−1.00000			−0.353553
$9$	1.76250	−	2.42768i	0.587498	−	0.809225i
$10$	−0.866025	+	0.500000i	−0.273861	+	0.158114i
$11$		−	2.39841i		−	0.723149i	−0.932343	−	0.361575i	$-0.882239\pi$
$11$		−	2.39841i		−	0.723149i	0.932343	−	0.361575i	$-0.117761\pi$
$12$	−1.45279	−	0.943085i	−0.419384	−	0.272245i
$13$	−0.414577	+	0.239356i	−0.114983	+	0.0663855i	−0.556389	−	0.830922i	$-0.687813\pi$
$13$	−0.414577	+	0.239356i	−0.114983	+	0.0663855i	0.441406	+	0.897308i	$0.354480\pi$
$14$	1.17084	−	2.02795i	0.312920	−	0.541993i
$15$	−1.72969	−	0.0903420i	−0.446605	−	0.0233262i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.40013	−	1.38572i	−0.582117	−	0.336086i	0.179857	−	0.983693i	$-0.442436\pi$
$17$	−2.40013	−	1.38572i	−0.582117	−	0.336086i	−0.761974	+	0.647607i	$0.775770\pi$
$18$	−1.22118	−	2.74020i	−0.287835	−	0.645872i
$19$	0.994947	+	4.24383i	0.228256	+	0.973601i
$19$	0.994947	+	4.24383i	0.228256	+	0.973601i
$20$			1.00000i			0.223607i
$21$	3.61351	−	1.84198i	0.788533	−	0.401954i
$22$	−2.07709	−	1.19921i	−0.442837	−	0.255672i
$23$	1.80040	−	1.03946i	0.375409	−	0.216743i	−0.300410	−	0.953810i	$-0.597123\pi$
$23$	1.80040	−	1.03946i	0.375409	−	0.216743i	0.675819	+	0.737068i	$0.263790\pi$
$24$	−1.54313	+	0.786608i	−0.314990	+	0.160566i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$			0.478712i			0.0938832i
$27$	0.810128	−	5.13261i	0.155909	−	0.987771i
$28$	−1.17084	−	2.02795i	−0.221268	−	0.383247i
$29$	−0.313727	−	0.543392i	−0.0582577	−	0.100905i	0.835426	−	0.549603i	$-0.185221\pi$
$29$	−0.313727	−	0.543392i	−0.0582577	−	0.100905i	−0.893683	+	0.448698i	$0.851888\pi$
$30$	−0.943085	+	1.45279i	−0.172183	+	0.265241i
$31$			2.05113i			0.368394i	0.982889	+	0.184197i	$0.0589684\pi$
$31$			2.05113i			0.368394i	−0.982889	+	0.184197i	$0.941032\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.88661	−	3.70106i	−0.328417	−	0.644272i
$34$	−2.40013	+	1.38572i	−0.411619	+	0.237648i
$35$	−2.02795	−	1.17084i	−0.342787	−	0.197908i
$36$	−2.98368	−	0.312528i	−0.497279	−	0.0520880i
$37$		−	5.67577i		−	0.933091i	−0.884497	−	0.466546i	$-0.845498\pi$
$37$		−	5.67577i		−	0.933091i	0.884497	−	0.466546i	$-0.154502\pi$
$38$	4.17274	+	1.26026i	0.676907	+	0.204442i
$39$	−0.451467	+	0.695467i	−0.0722925	+	0.111364i
$40$	0.866025	+	0.500000i	0.136931	+	0.0790569i
$41$	1.04624	−	1.81214i	0.163395	−	0.283008i	−0.772689	−	0.634785i	$-0.781089\pi$
$41$	1.04624	−	1.81214i	0.163395	−	0.283008i	0.936084	+	0.351776i	$0.114422\pi$
$42$	0.211552	−	4.05038i	0.0326432	−	0.624988i
$43$	−3.77271	+	6.53452i	−0.575333	+	0.996506i	0.420673	+	0.907213i	$0.361794\pi$
$43$	−3.77271	+	6.53452i	−0.575333	+	0.996506i	−0.996005	+	0.0892931i	$0.971539\pi$
$44$	−2.07709	+	1.19921i	−0.313133	+	0.180787i
$45$	−2.74020	+	1.22118i	−0.408485	+	0.182043i
$46$		−	2.07892i		−	0.306520i
$47$	1.94389	−	1.12231i	0.283546	−	0.163705i	−0.351482	−	0.936195i	$-0.614322\pi$
$47$	1.94389	−	1.12231i	0.283546	−	0.163705i	0.635028	+	0.772490i	$0.280989\pi$
$48$	−0.0903420	+	1.72969i	−0.0130397	+	0.249660i
$49$	−1.51654			−0.216649
$50$	1.00000			0.141421
$51$	−4.79373	−	0.250377i	−0.671256	−	0.0350597i
$52$	0.414577	+	0.239356i	0.0574915	+	0.0331927i
$53$	6.64114	+	11.5028i	0.912231	+	1.58003i	0.810906	+	0.585176i	$0.198975\pi$
$53$	6.64114	+	11.5028i	0.912231	+	1.58003i	0.101325	+	0.994853i	$0.467692\pi$
$54$	−4.03991	−	3.26790i	−0.549762	−	0.444704i
$55$	−1.19921	+	2.07709i	−0.161701	+	0.280074i
$56$	−2.34168			−0.312920
$57$	4.87356	+	5.76614i	0.645519	+	0.763744i
$58$	−0.627455			−0.0823889
$59$	−3.13769	+	5.43465i	−0.408493	+	0.707531i	−0.994721	−	0.102615i	$-0.967279\pi$
$59$	−3.13769	+	5.43465i	−0.408493	+	0.707531i	0.586228	+	0.810146i	$0.300612\pi$
$60$	0.786608	+	1.54313i	0.101551	+	0.199217i
$61$	1.25195	+	2.16845i	0.160296	+	0.277641i	0.934975	−	0.354714i	$-0.115422\pi$
$61$	1.25195	+	2.16845i	0.160296	+	0.277641i	−0.774679	+	0.632355i	$0.782088\pi$
$62$	1.77633	+	1.02556i	0.225594	+	0.130247i
$63$	4.12720	−	5.68484i	0.519978	−	0.716222i
$64$	1.00000			0.125000
$65$	0.478712			0.0593770
$66$	−4.14852	−	0.216677i	−0.510648	−	0.0266712i
$67$	11.3258	−	6.53894i	1.38366	−	0.798859i	0.391073	−	0.920360i	$-0.372104\pi$
$67$	11.3258	−	6.53894i	1.38366	−	0.798859i	0.992591	+	0.121501i	$0.0387707\pi$
$68$			2.77143i			0.336086i
$69$	1.96060	−	3.02023i	0.236028	−	0.363593i
$70$	−2.02795	+	1.17084i	−0.242387	+	0.139942i
$71$	−2.68385	+	4.64856i	−0.318514	+	0.551682i	−0.980178	−	0.198118i	$-0.936517\pi$
$71$	−2.68385	+	4.64856i	−0.318514	+	0.551682i	0.661664	+	0.749800i	$0.269850\pi$
$72$	−1.76250	+	2.42768i	−0.207712	+	0.286104i
$73$	−5.81045	+	10.0640i	−0.680062	+	1.17790i	0.294900	+	0.955528i	$0.404714\pi$
$73$	−5.81045	+	10.0640i	−0.680062	+	1.17790i	−0.974962	+	0.222373i	$0.928620\pi$
$74$	−4.91536	−	2.83789i	−0.571399	−	0.329898i
$75$	1.45279	+	0.943085i	0.167753	+	0.108898i
$76$	3.17779	−	2.98356i	0.364517	−	0.342238i
$77$		−	5.61632i		−	0.640038i
$78$	0.376559	+	0.738715i	0.0426369	+	0.0836430i
$79$	10.1589	+	5.86527i	1.14297	+	0.659894i	0.947164	−	0.320749i	$-0.103934\pi$
$79$	10.1589	+	5.86527i	1.14297	+	0.659894i	0.195806	+	0.980643i	$0.437268\pi$
$80$	0.866025	−	0.500000i	0.0968246	−	0.0559017i
$81$	−2.78722	−	8.55753i	−0.309691	−	0.950837i
$82$	−1.04624	−	1.81214i	−0.115538	−	0.200117i
$83$			11.3081i			1.24123i	0.784115	+	0.620615i	$0.213117\pi$
$83$			11.3081i			1.24123i	−0.784115	+	0.620615i	$0.786883\pi$
$84$	−3.40196	−	2.20840i	−0.371184	−	0.240956i
$85$	1.38572	+	2.40013i	0.150302	+	0.260331i
$86$	3.77271	+	6.53452i	0.406822	+	0.704636i
$87$	−0.911558	−	0.591743i	−0.0977293	−	0.0634415i
$88$			2.39841i			0.255672i
$89$	−4.97362	−	8.61457i	−0.527203	−	0.913142i	−0.999497	−	0.0317016i	$-0.989907\pi$
$89$	−4.97362	−	8.61457i	−0.527203	−	0.913142i	0.472294	−	0.881441i	$-0.343426\pi$
$90$	−0.312528	+	2.98368i	−0.0329433	+	0.314507i
$91$	−0.970806	+	0.560495i	−0.101768	+	0.0587559i
$92$	−1.80040	−	1.03946i	−0.187705	−	0.108371i
$93$	1.61344	+	3.16516i	0.167305	+	0.328212i
$94$		−	2.24461i		−	0.231514i
$95$	1.26026	−	4.17274i	0.129300	−	0.428114i
$96$	1.45279	+	0.943085i	0.148274	+	0.0962532i
$97$	7.49209	+	4.32556i	0.760706	+	0.439194i	0.829549	−	0.558434i	$-0.188597\pi$
$97$	7.49209	+	4.32556i	0.760706	+	0.439194i	−0.0688431	+	0.997627i	$0.521931\pi$
$98$	−0.758271	+	1.31336i	−0.0765970	+	0.132670i
$99$	−5.82257	−	4.22719i	−0.585191	−	0.424849i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	3.96069	−	2.28671i	0.394103	−	0.227536i	−0.289833	−	0.957077i	$-0.593600\pi$
$101$	3.96069	−	2.28671i	0.394103	−	0.227536i	0.683937	+	0.729542i	$0.260267\pi$
$102$	−2.61370	+	4.02630i	−0.258794	+	0.398663i
$103$		−	2.29913i		−	0.226540i	−0.993564	−	0.113270i	$-0.963867\pi$
$103$		−	2.29913i		−	0.226540i	0.993564	−	0.113270i	$-0.0361325\pi$
$104$	0.414577	−	0.239356i	0.0406526	−	0.0234708i
$105$	−4.05038	−	0.211552i	−0.395277	−	0.0206453i
$106$	13.2823			1.29009
$107$	−12.1841			−1.17788			−0.588939	−	0.808177i	$-0.700454\pi$
$107$	−12.1841			−1.17788			−0.588939	+	0.808177i	$0.700454\pi$
$108$	−4.85004	+	1.86471i	−0.466695	+	0.179432i
$109$	−0.624429	−	0.360514i	−0.0598095	−	0.0345310i	0.469797	−	0.882774i	$-0.344327\pi$
$109$	−0.624429	−	0.360514i	−0.0598095	−	0.0345310i	−0.529607	+	0.848243i	$0.677660\pi$
$110$	1.19921	+	2.07709i	0.114340	+	0.198043i
$111$	−4.46461	−	8.75845i	−0.423762	−	0.831315i
$112$	−1.17084	+	2.02795i	−0.110634	+	0.191624i
$113$	9.99505			0.940255			0.470128	−	0.882598i	$-0.344208\pi$
$113$	9.99505			0.940255			0.470128	+	0.882598i	$0.344208\pi$
$114$	7.43041	−	1.33756i	0.695921	−	0.125274i
$115$	−2.07892			−0.193860
$116$	−0.313727	+	0.543392i	−0.0291289	+	0.0504527i
$117$	−0.149611	+	1.42832i	−0.0138315	+	0.132049i
$118$	3.13769	+	5.43465i	0.288848	+	0.500300i
$119$	−5.62033	−	3.24490i	−0.515215	−	0.297460i
$120$	1.72969	+	0.0903420i	0.157899	+	0.00824706i
$121$	5.24761			0.477055
$122$	2.50391			0.226693
$123$	0.189038	−	3.61934i	0.0170450	−	0.326345i
$124$	1.77633	−	1.02556i	0.159519	−	0.0920984i
$125$		−	1.00000i		−	0.0894427i
$126$	−2.85961	−	6.41668i	−0.254755	−	0.571643i
$127$	9.58763	−	5.53542i	0.850764	−	0.491189i	−0.0101444	−	0.999949i	$-0.503229\pi$
$127$	9.58763	−	5.53542i	0.850764	−	0.491189i	0.860909	+	0.508760i	$0.169896\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−0.681668	+	13.0513i	−0.0600175	+	1.14910i
$130$	0.239356	−	0.414577i	0.0209929	−	0.0363608i
$131$	−13.3817	−	7.72594i	−1.16917	−	0.675018i	−0.215683	−	0.976464i	$-0.569198\pi$
$131$	−13.3817	−	7.72594i	−1.16917	−	0.675018i	−0.953484	+	0.301445i	$0.902531\pi$
$132$	−2.26191	+	3.48439i	−0.196874	+	0.303277i
$133$	2.32985	+	9.93768i	0.202023	+	0.861706i
$134$		−	13.0779i		−	1.12976i
$135$	−3.26790	+	4.03991i	−0.281256	+	0.347700i
$136$	2.40013	+	1.38572i	0.205810	+	0.118824i
$137$	−7.57874	+	4.37559i	−0.647496	+	0.373832i	−0.787496	−	0.616320i	$-0.788623\pi$
$137$	−7.57874	+	4.37559i	−0.647496	+	0.373832i	0.140000	+	0.990151i	$0.455290\pi$
$138$	−1.63530	−	3.20804i	−0.139206	−	0.273087i
$139$	3.74921	+	6.49383i	0.318004	+	0.550799i	0.980071	−	0.198645i	$-0.0636541\pi$
$139$	3.74921	+	6.49383i	0.318004	+	0.550799i	−0.662067	+	0.749444i	$0.730321\pi$
$140$			2.34168i			0.197908i
$141$	2.11686	−	3.26094i	0.178272	−	0.274621i
$142$	2.68385	+	4.64856i	0.225223	+	0.390098i
$143$	0.574075	+	0.994328i	0.0480066	+	0.0831499i
$144$	1.22118	+	2.74020i	0.101765	+	0.228350i
$145$			0.627455i			0.0521073i
$146$	5.81045	+	10.0640i	0.480876	+	0.832902i
$147$	−2.34022	+	1.19293i	−0.193018	+	0.0983908i
$148$	−4.91536	+	2.83789i	−0.404040	+	0.233273i
$149$	10.5955	+	6.11734i	0.868020	+	0.501152i	0.866690	−	0.498847i	$-0.166243\pi$
$149$	10.5955	+	6.11734i	0.868020	+	0.501152i	0.00133030	+	0.999999i	$0.499577\pi$
$150$	1.54313	−	0.786608i	0.125996	−	0.0642263i
$151$		−	16.0545i		−	1.30650i	−0.757143	−	0.653250i	$-0.773405\pi$
$151$		−	16.0545i		−	1.30650i	0.757143	−	0.653250i	$-0.226595\pi$
$152$	−0.994947	−	4.24383i	−0.0807009	−	0.344220i
$153$	−7.59429	+	3.38442i	−0.613962	+	0.273614i
$154$	−4.86387	−	2.80816i	−0.391942	−	0.226288i
$155$	1.02556	−	1.77633i	0.0823753	−	0.142678i
$156$	0.828026	+	0.0432478i	0.0662951	+	0.00346260i
$157$	−0.836254	+	1.44843i	−0.0667404	+	0.115598i	−0.897465	−	0.441086i	$-0.854593\pi$
$157$	−0.836254	+	1.44843i	−0.0667404	+	0.115598i	0.830724	+	0.556684i	$0.187927\pi$
$158$	10.1589	−	5.86527i	0.808202	−	0.466616i
$159$	19.2963	+	12.5263i	1.53030	+	0.993402i
$160$		−	1.00000i		−	0.0790569i
$161$	4.21595	−	2.43408i	0.332264	−	0.191833i
$162$	−8.80465	−	1.86496i	−0.691759	−	0.146525i
$163$	12.4272			0.973371			0.486686	−	0.873577i	$-0.338206\pi$
$163$	12.4272			0.973371			0.486686	+	0.873577i	$0.338206\pi$
$164$	−2.09248			−0.163395
$165$	−0.216677	+	4.14852i	−0.0168683	+	0.322962i
$166$	9.79314	+	5.65407i	0.760095	+	0.438841i
$167$	0.136815	+	0.236971i	0.0105871	+	0.0183374i	0.871270	−	0.490803i	$-0.163297\pi$
$167$	0.136815	+	0.236971i	0.0105871	+	0.0183374i	−0.860683	+	0.509141i	$0.829963\pi$
$168$	−3.61351	+	1.84198i	−0.278789	+	0.142112i
$169$	−6.38542	+	11.0599i	−0.491186	+	0.850759i
$170$	2.77143			0.212559
$171$	12.0562	+	5.06432i	0.921963	+	0.387278i
$172$	7.54542			0.575333
$173$	−12.1946	+	21.1216i	−0.927137	+	1.60585i	−0.139049	+	0.990286i	$0.544404\pi$
$173$	−12.1946	+	21.1216i	−0.927137	+	1.60585i	−0.788088	+	0.615563i	$0.788929\pi$
$174$	−0.968244	+	0.493561i	−0.0734024	+	0.0374168i
$175$	1.17084	+	2.02795i	0.0885071	+	0.153299i
$176$	2.07709	+	1.19921i	0.156566	+	0.0903936i
$177$	−0.566931	+	10.8545i	−0.0426131	+	0.815874i
$178$	−9.94725			−0.745578
$179$	−20.0769			−1.50062			−0.750309	−	0.661087i	$-0.770095\pi$
$179$	−20.0769			−1.50062			−0.750309	+	0.661087i	$0.770095\pi$
$180$	2.42768	+	1.76250i	0.180948	+	0.131369i
$181$	10.2054	−	5.89207i	0.758559	−	0.437954i	−0.0702194	−	0.997532i	$-0.522370\pi$
$181$	10.2054	−	5.89207i	0.758559	−	0.437954i	0.828778	+	0.559578i	$0.189037\pi$
$182$			1.12099i			0.0830933i
$183$	3.63765	+	2.36140i	0.268902	+	0.174560i
$184$	−1.80040	+	1.03946i	−0.132727	+	0.0766301i
$185$	−2.83789	+	4.91536i	−0.208646	+	0.361385i
$186$	3.54782	+	0.185303i	0.260139	+	0.0135871i
$187$	−3.32352	+	5.75651i	−0.243040	+	0.420958i
$188$	−1.94389	−	1.12231i	−0.141773	−	0.0818526i
$189$	1.89706	−	12.0189i	0.137991	−	0.874248i
$190$	−2.98356	−	3.17779i	−0.216450	−	0.230541i
$191$		−	7.36887i		−	0.533193i	−0.963808	−	0.266596i	$-0.914101\pi$
$191$		−	7.36887i		−	0.533193i	0.963808	−	0.266596i	$-0.0858991\pi$
$192$	1.54313	−	0.786608i	0.111366	−	0.0567686i
$193$	−6.47095	−	3.73601i	−0.465789	−	0.268924i	0.248686	−	0.968584i	$-0.420001\pi$
$193$	−6.47095	−	3.73601i	−0.465789	−	0.268924i	−0.714475	+	0.699661i	$0.753335\pi$
$194$	7.49209	−	4.32556i	0.537900	−	0.310557i
$195$	0.738715	−	0.376559i	0.0529005	−	0.0269660i
$196$	0.758271	+	1.31336i	0.0541622	+	0.0938118i
$197$			20.2370i			1.44183i	0.693025	+	0.720913i	$0.256277\pi$
$197$			20.2370i			1.44183i	−0.693025	+	0.720913i	$0.743723\pi$
$198$	−6.57214	+	2.92890i	−0.467062	+	0.208148i
$199$	−5.62306	−	9.73942i	−0.398608	−	0.690409i	0.594946	−	0.803765i	$-0.297173\pi$
$199$	−5.62306	−	9.73942i	−0.398608	−	0.690409i	−0.993554	+	0.113356i	$0.963840\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	12.3336	−	18.9994i	0.869942	−	1.34011i
$202$		−	4.57341i		−	0.321784i
$203$	−0.734649	−	1.27245i	−0.0515622	−	0.0893084i
$204$	2.18003	+	4.27668i	0.152633	+	0.299427i
$205$	−1.81214	+	1.04624i	−0.126565	+	0.0730725i
$206$	−1.99110	−	1.14956i	−0.138727	−	0.0800940i
$207$	0.649721	−	6.20283i	0.0451587	−	0.431126i
$208$		−	0.478712i		−	0.0331927i
$209$	10.1785	−	2.38630i	0.704059	−	0.165063i
$210$	−2.20840	+	3.40196i	−0.152394	+	0.234758i
$211$	−22.9716	−	13.2627i	−1.58143	−	0.913040i	−0.994651	−	0.103295i	$-0.967061\pi$
$211$	−22.9716	−	13.2627i	−1.58143	−	0.913040i	−0.586781	−	0.809745i	$-0.699605\pi$
$212$	6.64114	−	11.5028i	0.456115	−	0.790015i
$213$	−0.484928	+	9.28446i	−0.0332267	+	0.636161i
$214$	−6.09204	+	10.5517i	−0.416443	+	0.721301i
$215$	6.53452	−	3.77271i	0.445651	−	0.257297i
$216$	−0.810128	+	5.13261i	−0.0551222	+	0.349230i
$217$			4.80309i			0.326055i
$218$	−0.624429	+	0.360514i	−0.0422917	+	0.0244171i
$219$	−1.04985	+	20.1006i	−0.0709426	+	1.35827i
$220$	2.39841			0.161701
$221$	1.32672			0.0892448
$222$	−9.81735	−	0.512760i	−0.658897	−	0.0344142i
$223$	−13.2112	−	7.62747i	−0.884685	−	0.510773i	−0.0124845	−	0.999922i	$-0.503974\pi$
$223$	−13.2112	−	7.62747i	−0.884685	−	0.510773i	−0.872200	+	0.489149i	$0.837307\pi$
$224$	1.17084	+	2.02795i	0.0782300	+	0.135498i
$225$	2.98368	+	0.312528i	0.198912	+	0.0208352i
$226$	4.99753	−	8.65597i	0.332430	−	0.575786i
$227$	1.74109			0.115560			0.0577800	−	0.998329i	$-0.481598\pi$
$227$	1.74109			0.115560			0.0577800	+	0.998329i	$0.481598\pi$
$228$	2.55684	−	7.10370i	0.169331	−	0.470454i
$229$	−16.6454			−1.09996			−0.549979	−	0.835179i	$-0.685364\pi$
$229$	−16.6454			−1.09996			−0.549979	+	0.835179i	$0.685364\pi$
$230$	−1.03946	+	1.80040i	−0.0685400	+	0.118715i
$231$	−4.41784	−	8.66670i	−0.290672	−	0.570227i
$232$	0.313727	+	0.543392i	0.0205972	+	0.0356754i
$233$	7.51278	+	4.33751i	0.492179	+	0.284160i	0.725478	−	0.688245i	$-0.241619\pi$
$233$	7.51278	+	4.33751i	0.492179	+	0.284160i	−0.233299	+	0.972405i	$0.574952\pi$
$234$	1.16216	+	0.843728i	0.0759727	+	0.0551563i
$235$	−2.24461			−0.146422
$236$	6.27539			0.408493
$237$	20.2902	+	1.05976i	1.31799	+	0.0688388i
$238$	−5.62033	+	3.24490i	−0.364312	+	0.210336i
$239$		−	19.1483i		−	1.23860i	−0.785153	−	0.619302i	$-0.787416\pi$
$239$		−	19.1483i		−	1.23860i	0.785153	−	0.619302i	$-0.212584\pi$
$240$	0.943085	−	1.45279i	0.0608759	−	0.0937770i
$241$	−16.6382	+	9.60606i	−1.07176	+	0.618781i	−0.928662	−	0.370928i	$-0.879040\pi$
$241$	−16.6382	+	9.60606i	−1.07176	+	0.618781i	−0.143098	+	0.989709i	$0.545706\pi$
$242$	2.62380	−	4.54456i	0.168665	−	0.292135i
$243$	−11.0325	−	11.0129i	−0.707733	−	0.706480i
$244$	1.25195	−	2.16845i	0.0801481	−	0.138821i
$245$	1.31336	+	0.758271i	0.0839078	+	0.0484442i
$246$	−3.03992	−	1.97338i	−0.193818	−	0.125818i
$247$	−1.42827	−	1.52125i	−0.0908786	−	0.0967947i
$248$		−	2.05113i		−	0.130247i
$249$	8.89508	+	17.4499i	0.563703	+	1.10584i
$250$	−0.866025	−	0.500000i	−0.0547723	−	0.0316228i
$251$	−10.8299	+	6.25262i	−0.683574	+	0.394662i	−0.801200	−	0.598396i	$-0.795805\pi$
$251$	−10.8299	+	6.25262i	−0.683574	+	0.394662i	0.117626	+	0.993058i	$0.462472\pi$
$252$	−6.98681	−	0.731839i	−0.440128	−	0.0461016i
$253$	−2.49306	−	4.31810i	−0.156737	−	0.271477i
$254$		−	11.0708i		−	0.694646i
$255$	4.02630	+	2.61370i	0.252137	+	0.163676i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.733753	−	1.27090i	−0.0457702	−	0.0792764i	0.842233	−	0.539114i	$-0.181241\pi$
$257$	−0.733753	−	1.27090i	−0.0457702	−	0.0792764i	−0.888003	+	0.459838i	$0.847908\pi$
$258$	10.9619	+	7.11597i	0.682457	+	0.443021i
$259$		−	13.2908i		−	0.825852i
$260$	−0.239356	−	0.414577i	−0.0148442	−	0.0257110i
$261$	−1.87212	−	0.196097i	−0.115881	−	0.0121381i
$262$	−13.3817	+	7.72594i	−0.826725	+	0.477310i
$263$	−12.2015	−	7.04453i	−0.752376	−	0.434384i	0.0741759	−	0.997245i	$-0.476367\pi$
$263$	−12.2015	−	7.04453i	−0.752376	−	0.434384i	−0.826552	+	0.562861i	$0.809701\pi$
$264$	1.88661	+	3.70106i	0.116113	+	0.227785i
$265$		−	13.2823i		−	0.815924i
$266$	9.77121	+	2.95113i	0.599111	+	0.180946i
$267$	−14.4512	−	9.38110i	−0.884401	−	0.574114i
$268$	−11.3258	−	6.53894i	−0.691832	−	0.399429i
$269$	9.48574	−	16.4298i	0.578356	−	1.00174i	−0.417312	−	0.908763i	$-0.637028\pi$
$269$	9.48574	−	16.4298i	0.578356	−	1.00174i	0.995668	−	0.0929788i	$-0.0296389\pi$
$270$	1.86471	+	4.85004i	0.113483	+	0.295164i
$271$	12.6913	−	21.9819i	0.770940	−	1.33531i	−0.166108	−	0.986108i	$-0.553120\pi$
$271$	12.6913	−	21.9819i	0.770940	−	1.33531i	0.937048	−	0.349200i	$-0.113547\pi$
$272$	2.40013	−	1.38572i	0.145529	−	0.0840214i
$273$	−1.05719	+	1.62856i	−0.0639840	+	0.0985650i
$274$			8.75118i			0.528678i
$275$	2.07709	−	1.19921i	0.125253	−	0.0723149i
$276$	−3.59590	−	0.187814i	−0.216448	−	0.0113051i
$277$	8.10858			0.487198			0.243599	−	0.969876i	$-0.421672\pi$
$277$	8.10858			0.487198			0.243599	+	0.969876i	$0.421672\pi$
$278$	7.49842			0.449726
$279$	4.97948	+	3.61511i	0.298114	+	0.216431i
$280$	2.02795	+	1.17084i	0.121193	+	0.0699710i
$281$	−12.6467	−	21.9047i	−0.754438	−	1.30672i	−0.945653	−	0.325176i	$-0.894576\pi$
$281$	−12.6467	−	21.9047i	−0.754438	−	1.30672i	0.191216	−	0.981548i	$-0.438757\pi$
$282$	−1.76563	−	3.46373i	−0.105142	−	0.206262i
$283$	0.496185	−	0.859418i	0.0294952	−	0.0510871i	−0.850901	−	0.525326i	$-0.823943\pi$
$283$	0.496185	−	0.859418i	0.0294952	−	0.0510871i	0.880396	+	0.474239i	$0.157277\pi$
$284$	5.36769			0.318514
$285$	−1.33756	−	7.43041i	−0.0792301	−	0.440139i
$286$	1.14815			0.0678916
$287$	2.44995	−	4.24344i	0.144616	−	0.250483i
$288$	2.98368	+	0.312528i	0.175815	+	0.0184159i
$289$	−4.65958	−	8.07063i	−0.274093	−	0.474743i
$290$	0.543392	+	0.313727i	0.0319091	+	0.0184227i
$291$	14.9638	+	0.781559i	0.877192	+	0.0458158i
$292$	11.6209			0.680062
$293$	−23.3348			−1.36323			−0.681617	−	0.731709i	$-0.738723\pi$
$293$	−23.3348			−1.36323			−0.681617	+	0.731709i	$0.738723\pi$
$294$	−0.137007	+	2.62315i	−0.00799044	+	0.152985i
$295$	5.43465	−	3.13769i	0.316417	−	0.182684i
$296$			5.67577i			0.329898i
$297$	−12.3101	−	1.94302i	−0.714306	−	0.112746i
$298$	10.5955	−	6.11734i	0.613783	−	0.354368i
$299$	−0.497603	+	0.861873i	−0.0287771	+	0.0498434i
$300$	0.0903420	−	1.72969i	0.00521590	−	0.0998639i
$301$	−8.83447	+	15.3018i	−0.509210	+	0.881978i
$302$	−13.9036	−	8.02727i	−0.800064	−	0.461917i
$303$	4.31311	−	6.64419i	0.247782	−	0.381699i
$304$	−4.17274	−	1.26026i	−0.239323	−	0.0722811i
$305$		−	2.50391i		−	0.143373i
$306$	−0.866149	+	8.26906i	−0.0495145	+	0.472711i
$307$	−21.4512	−	12.3849i	−1.22429	−	0.706842i	−0.258458	−	0.966023i	$-0.583214\pi$
$307$	−21.4512	−	12.3849i	−1.22429	−	0.706842i	−0.965829	+	0.259180i	$0.916548\pi$
$308$	−4.86387	+	2.80816i	−0.277145	+	0.160010i
$309$	−1.80851	−	3.54785i	−0.102883	−	0.201830i
$310$	−1.02556	−	1.77633i	−0.0582482	−	0.100889i
$311$		−	11.2512i		−	0.637999i	−0.947755	−	0.318999i	$-0.896653\pi$
$311$		−	11.2512i		−	0.637999i	0.947755	−	0.318999i	$-0.103347\pi$
$312$	0.451467	−	0.695467i	0.0255593	−	0.0393731i
$313$	5.46644	+	9.46816i	0.308982	+	0.535172i	0.978140	−	0.207948i	$-0.0666785\pi$
$313$	5.46644	+	9.46816i	0.308982	+	0.535172i	−0.669158	+	0.743120i	$0.733345\pi$
$314$	0.836254	+	1.44843i	0.0471926	+	0.0817399i
$315$	−6.41668	+	2.85961i	−0.361539	+	0.161121i
$316$		−	11.7305i		−	0.659894i
$317$	8.95027	+	15.5023i	0.502697	+	0.870697i	0.999995	+	0.00311703i	$0.000992183\pi$
$317$	8.95027	+	15.5023i	0.502697	+	0.870697i	−0.497298	+	0.867580i	$0.665674\pi$
$318$	20.4963	−	10.4479i	1.14937	−	0.585892i
$319$	−1.30328	+	0.752448i	−0.0729696	+	0.0421290i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	−18.8016	+	9.58409i	−1.04940	+	0.534932i
$322$		−	4.86817i		−	0.271292i
$323$	3.49274	−	11.5645i	0.194341	−	0.643464i
$324$	−6.01743	+	6.69257i	−0.334302	+	0.371810i
$325$	−0.414577	−	0.239356i	−0.0229966	−	0.0132771i
$326$	6.21359	−	10.7622i	0.344139	−	0.596066i
$327$	−1.24716	−	0.0651391i	−0.0689680	−	0.00360220i
$328$	−1.04624	+	1.81214i	−0.0577688	+	0.100059i
$329$	4.55197	−	2.62808i	0.250958	−	0.144891i
$330$	3.48439	+	2.26191i	0.191809	+	0.124514i
$331$			10.3625i			0.569572i	0.958591	+	0.284786i	$0.0919226\pi$
$331$			10.3625i			0.569572i	−0.958591	+	0.284786i	$0.908077\pi$
$332$	9.79314	−	5.65407i	0.537468	−	0.310308i
$333$	−13.7789	−	10.0035i	−0.755081	−	0.548190i
$334$	0.273631			0.0149724
$335$	−13.0779			−0.714521
$336$	−0.211552	+	4.05038i	−0.0115411	+	0.220967i
$337$	−23.7499	−	13.7120i	−1.29374	−	0.746939i	−0.314422	−	0.949283i	$-0.601811\pi$
$337$	−23.7499	−	13.7120i	−1.29374	−	0.746939i	−0.979315	+	0.202344i	$0.935144\pi$
$338$	6.38542	+	11.0599i	0.347321	+	0.601577i
$339$	15.4237	−	7.86219i	0.837698	−	0.427015i
$340$	1.38572	−	2.40013i	0.0751510	−	0.130165i
$341$	4.91946			0.266404
$342$	10.4139	−	7.90884i	0.563122	−	0.427661i
$343$	−19.9430			−1.07682
$344$	3.77271	−	6.53452i	0.203411	−	0.352318i
$345$	−3.20804	+	1.63530i	−0.172715	+	0.0880414i
$346$	12.1946	+	21.1216i	0.655585	+	1.13551i
$347$	22.5112	+	12.9969i	1.20847	+	0.697709i	0.962424	−	0.271551i	$-0.0875364\pi$
$347$	22.5112	+	12.9969i	1.20847	+	0.697709i	0.246042	+	0.969259i	$0.420870\pi$
$348$	−0.0566855	+	1.08530i	−0.00303866	+	0.0581784i
$349$	8.16697			0.437168			0.218584	−	0.975818i	$-0.429856\pi$
$349$	8.16697			0.437168			0.218584	+	0.975818i	$0.429856\pi$
$350$	2.34168			0.125168
$351$	0.892662	+	2.32177i	0.0476468	+	0.123927i
$352$	2.07709	−	1.19921i	0.110709	−	0.0639180i
$353$			23.1015i			1.22957i	0.788696	+	0.614783i	$0.210757\pi$
$353$			23.1015i			1.22957i	−0.788696	+	0.614783i	$0.789243\pi$
$354$	9.11681	+	5.91823i	0.484553	+	0.314550i
$355$	4.64856	−	2.68385i	0.246720	−	0.142444i
$356$	−4.97362	+	8.61457i	−0.263602	+	0.456571i
$357$	−11.2254	−	0.586301i	−0.594109	−	0.0310304i
$358$	−10.0385	+	17.3871i	−0.530549	+	0.918937i
$359$	−17.3948	−	10.0429i	−0.918063	−	0.530044i	−0.0350462	−	0.999386i	$-0.511158\pi$
$359$	−17.3948	−	10.0429i	−0.918063	−	0.530044i	−0.883017	+	0.469342i	$0.844491\pi$
$360$	2.74020	−	1.22118i	0.144421	−	0.0643619i
$361$	−17.0202	+	8.44477i	−0.895798	+	0.444462i
$362$		−	11.7841i		−	0.619361i
$363$	8.09774	−	4.12781i	0.425021	−	0.216654i
$364$	0.970806	+	0.560495i	0.0508841	+	0.0293779i
$365$	10.0640	−	5.81045i	0.526773	−	0.304133i
$366$	3.86385	−	1.96959i	0.201967	−	0.102952i
$367$	4.83084	+	8.36726i	0.252168	+	0.436768i	0.964122	−	0.265458i	$-0.0855231\pi$
$367$	4.83084	+	8.36726i	0.252168	+	0.436768i	−0.711955	+	0.702226i	$0.752190\pi$
$368$			2.07892i			0.108371i
$369$	−2.55529	−	5.73381i	−0.133023	−	0.298490i
$370$	2.83789	+	4.91536i	0.147535	+	0.255538i
$371$	15.5514	+	26.9358i	0.807389	+	1.39844i
$372$	1.93439	−	2.97985i	0.100293	−	0.154498i
$373$			16.8317i			0.871515i	0.900064	+	0.435757i	$0.143519\pi$
$373$			16.8317i			0.871515i	−0.900064	+	0.435757i	$0.856481\pi$
$374$	3.32352	+	5.75651i	0.171855	+	0.297662i
$375$	−0.786608	−	1.54313i	−0.0406203	−	0.0796868i
$376$	−1.94389	+	1.12231i	−0.100249	+	0.0578785i
$377$	0.260128	+	0.150185i	0.0133973	+	0.00773493i
$378$	−9.46016	−	7.65236i	−0.486578	−	0.393595i
$379$		−	31.6110i		−	1.62375i	−0.583834	−	0.811873i	$-0.698448\pi$
$379$		−	31.6110i		−	1.62375i	0.583834	−	0.811873i	$-0.301552\pi$
$380$	−4.24383	+	0.994947i	−0.217704	+	0.0510397i
$381$	10.4407	−	16.0836i	0.534895	−	0.823986i
$382$	−6.38163	−	3.68444i	−0.326513	−	0.188512i
$383$	14.8637	−	25.7447i	0.759500	−	1.31549i	−0.183605	−	0.983000i	$-0.558777\pi$
$383$	14.8637	−	25.7447i	0.759500	−	1.31549i	0.943106	−	0.332493i	$-0.107890\pi$
$384$	0.0903420	−	1.72969i	0.00461024	−	0.0882680i
$385$	−2.80816	+	4.86387i	−0.143117	+	0.247886i
$386$	−6.47095	+	3.73601i	−0.329363	+	0.190158i
$387$	9.21432	+	20.6760i	0.468390	+	1.05102i
$388$		−	8.65112i		−	0.439194i
$389$	6.06103	−	3.49934i	0.307307	−	0.177424i	−0.338414	−	0.940997i	$-0.609890\pi$
$389$	6.06103	−	3.49934i	0.307307	−	0.177424i	0.645721	+	0.763574i	$0.276557\pi$
$390$	0.0432478	−	0.828026i	0.00218994	−	0.0419287i
$391$	−5.76159			−0.291376
$392$	1.51654			0.0765970
$393$	−26.7270	−	1.39595i	−1.34820	−	0.0704165i
$394$	17.5258	+	10.1185i	0.882935	+	0.509763i
$395$	−5.86527	−	10.1589i	−0.295114	−	0.511152i
$396$	−0.749571	+	7.15609i	−0.0376674	+	0.359607i
$397$	14.8564	−	25.7320i	0.745621	−	1.29145i	−0.204283	−	0.978912i	$-0.565486\pi$
$397$	14.8564	−	25.7320i	0.745621	−	1.29145i	0.949904	−	0.312542i	$-0.101180\pi$
$398$	−11.2461			−0.563717
$399$	11.4123	+	13.5024i	0.571330	+	0.675968i
$400$	−1.00000			−0.0500000
$401$	−14.8000	+	25.6344i	−0.739079	+	1.28012i	0.213831	+	0.976871i	$0.431406\pi$
$401$	−14.8000	+	25.6344i	−0.739079	+	1.28012i	−0.952910	+	0.303252i	$0.901928\pi$
$402$	−10.2872	−	20.1809i	−0.513077	−	1.00653i
$403$	−0.490951	−	0.850351i	−0.0244560	−	0.0423590i
$404$	−3.96069	−	2.28671i	−0.197052	−	0.113768i
$405$	−1.86496	+	8.80465i	−0.0926708	+	0.437507i
$406$	−1.46930			−0.0729200
$407$	−13.6129			−0.674764
$408$	4.79373	+	0.250377i	0.237325	+	0.0123955i
$409$	−1.05270	+	0.607777i	−0.0520527	+	0.0300526i	−0.525800	−	0.850608i	$-0.676234\pi$
$409$	−1.05270	+	0.607777i	−0.0520527	+	0.0300526i	0.473748	+	0.880661i	$0.342901\pi$
$410$			2.09248i			0.103340i
$411$	−8.25310	+	12.7136i	−0.407096	+	0.627116i
$412$	−1.99110	+	1.14956i	−0.0980947	+	0.0566350i
$413$	−7.34747	+	12.7262i	−0.361545	+	0.626215i
$414$	−5.04695	−	3.66409i	−0.248044	−	0.180080i
$415$	5.65407	−	9.79314i	0.277547	−	0.480726i
$416$	−0.414577	−	0.239356i	−0.0203263	−	0.0117354i
$417$	10.8936	+	7.07165i	0.533463	+	0.346300i
$418$	3.02264	−	10.0080i	0.147842	−	0.489505i
$419$			3.26405i			0.159459i	0.996817	+	0.0797297i	$0.0254057\pi$
$419$			3.26405i			0.159459i	−0.996817	+	0.0797297i	$0.974594\pi$
$420$	1.84198	+	3.61351i	0.0898796	+	0.176321i
$421$	−18.4508	−	10.6526i	−0.899236	−	0.519174i	−0.0222837	−	0.999752i	$-0.507094\pi$
$421$	−18.4508	−	10.6526i	−0.899236	−	0.519174i	−0.876952	+	0.480578i	$0.840427\pi$
$422$	−22.9716	+	13.2627i	−1.11824	+	0.645617i
$423$	0.701504	−	6.69720i	0.0341083	−	0.325629i
$424$	−6.64114	−	11.5028i	−0.322522	−	0.558625i
$425$		−	2.77143i		−	0.134434i
$426$	7.79812	+	5.06219i	0.377820	+	0.245264i
$427$	2.93167	+	5.07781i	0.141874	+	0.245732i
$428$	6.09204	+	10.5517i	0.294470	+	0.510037i
$429$	1.66802	+	1.08280i	0.0805327	+	0.0522783i
$430$		−	7.54542i		−	0.363872i
$431$	−2.14280	−	3.71143i	−0.103215	−	0.178774i	0.809793	−	0.586716i	$-0.199580\pi$
$431$	−2.14280	−	3.71143i	−0.103215	−	0.178774i	−0.913007	+	0.407943i	$0.866246\pi$
$432$	4.03991	+	3.26790i	0.194370	+	0.157227i
$433$	18.0367	−	10.4135i	0.866789	−	0.500441i	0.000509428	−	1.00000i	$-0.499838\pi$
$433$	18.0367	−	10.4135i	0.866789	−	0.500441i	0.866280	+	0.499559i	$0.166505\pi$
$434$	4.15959	+	2.40154i	0.199667	+	0.115278i
$435$	0.493561	+	0.968244i	0.0236644	+	0.0464237i
$436$			0.721029i			0.0345310i
$437$	6.20259	+	6.60638i	0.296710	+	0.316026i
$438$	16.8827	+	10.9595i	0.806686	+	0.523665i
$439$	14.9323	+	8.62117i	0.712680	+	0.411466i	0.812052	−	0.583584i	$-0.198350\pi$
$439$	14.9323	+	8.62117i	0.712680	+	0.411466i	−0.0993728	+	0.995050i	$0.531684\pi$
$440$	1.19921	−	2.07709i	0.0571700	−	0.0990213i
$441$	−2.67290	+	3.68167i	−0.127281	+	0.175318i
$442$	0.663360	−	1.14897i	0.0315528	−	0.0546510i
$443$	19.6711	−	11.3571i	0.934602	−	0.539592i	0.0463376	−	0.998926i	$-0.485245\pi$
$443$	19.6711	−	11.3571i	0.934602	−	0.539592i	0.888264	+	0.459333i	$0.151912\pi$
$444$	−5.35274	+	8.24569i	−0.254030	+	0.391323i
$445$			9.94725i			0.471545i
$446$	−13.2112	+	7.62747i	−0.625566	+	0.361171i
$447$	21.1622	+	1.10530i	1.00094	+	0.0522791i
$448$	2.34168			0.110634
$449$	24.4007			1.15154			0.575770	−	0.817612i	$-0.304702\pi$
$449$	24.4007			1.15154			0.575770	+	0.817612i	$0.304702\pi$
$450$	1.76250	−	2.42768i	0.0830848	−	0.114442i
$451$	−4.34626	−	2.50931i	−0.204657	−	0.118159i
$452$	−4.99753	−	8.65597i	−0.235064	−	0.407142i
$453$	−12.6286	−	24.7742i	−0.593345	−	1.16399i
$454$	0.870543	−	1.50782i	0.0408566	−	0.0707657i
$455$	1.12099			0.0525528
$456$	−4.87356	−	5.76614i	−0.228225	−	0.270024i
$457$	5.57921			0.260984			0.130492	−	0.991449i	$-0.458344\pi$
$457$	5.57921			0.260984			0.130492	+	0.991449i	$0.458344\pi$
$458$	−8.32269	+	14.4153i	−0.388894	+	0.673584i
$459$	−9.05675	+	11.1963i	−0.422733	+	0.522600i
$460$	1.03946	+	1.80040i	0.0484651	+	0.0839440i
$461$	13.2971	+	7.67711i	0.619310	+	0.357559i	0.776600	−	0.629994i	$-0.216943\pi$
$461$	13.2971	+	7.67711i	0.619310	+	0.357559i	−0.157291	+	0.987552i	$0.550276\pi$
$462$	−9.71450	−	0.507389i	−0.451960	−	0.0236059i
$463$	29.0927			1.35205			0.676027	−	0.736877i	$-0.263700\pi$
$463$	29.0927			1.35205			0.676027	+	0.736877i	$0.263700\pi$
$464$	0.627455			0.0291289
$465$	0.185303	−	3.54782i	0.00859322	−	0.164526i
$466$	7.51278	−	4.33751i	0.348023	−	0.200931i
$467$			30.7109i			1.42113i	0.703630	+	0.710567i	$0.251561\pi$
$467$			30.7109i			1.42113i	−0.703630	+	0.710567i	$0.748439\pi$
$468$	1.31177	−	0.584595i	0.0606366	−	0.0270229i
$469$	26.5213	−	15.3121i	1.22464	−	0.707047i
$470$	−1.12231	+	1.94389i	−0.0517681	+	0.0896650i
$471$	−0.151098	+	2.89293i	−0.00696221	+	0.133299i
$472$	3.13769	−	5.43465i	0.144424	−	0.250150i
$473$	15.6725	+	9.04852i	0.720622	+	0.416051i
$474$	11.0629	−	17.0420i	0.508135	−	0.782764i
$475$	−3.17779	+	2.98356i	−0.145807	+	0.136895i
$476$			6.48980i			0.297460i
$477$	39.6300	+	4.15108i	1.81453	+	0.190065i
$478$	−16.5830	−	9.57417i	−0.758487	−	0.437912i
$479$	−22.3097	+	12.8805i	−1.01935	+	0.588525i	−0.913917	−	0.405901i	$-0.866958\pi$
$479$	−22.3097	+	12.8805i	−1.01935	+	0.588525i	−0.105438	+	0.994426i	$0.533624\pi$
$480$	−0.786608	−	1.54313i	−0.0359036	−	0.0704339i
$481$	1.35853	+	2.35305i	0.0619437	+	0.107290i
$482$			19.2121i			0.875088i
$483$	4.59109	−	7.07241i	0.208902	−	0.321806i
$484$	−2.62380	−	4.54456i	−0.119264	−	0.206571i
$485$	−4.32556	−	7.49209i	−0.196413	−	0.340198i
$486$	−15.0537	+	4.04793i	−0.682850	+	0.183618i
$487$		−	19.2342i		−	0.871583i	−0.900048	−	0.435791i	$-0.856469\pi$
$487$		−	19.2342i		−	0.871583i	0.900048	−	0.435791i	$-0.143531\pi$
$488$	−1.25195	−	2.16845i	−0.0566733	−	0.0981610i
$489$	19.1767	−	9.77532i	0.867202	−	0.442055i
$490$	1.31336	−	0.758271i	0.0593318	−	0.0342552i
$491$	−18.7155	−	10.8054i	−0.844619	−	0.487641i	0.0142124	−	0.999899i	$-0.495476\pi$
$491$	−18.7155	−	10.8054i	−0.844619	−	0.487641i	−0.858832	+	0.512258i	$0.828809\pi$
$492$	−3.22896	+	1.64596i	−0.145573	+	0.0742056i
$493$			1.73895i			0.0783183i
$494$	−2.03157	+	0.476294i	−0.0914048	+	0.0214295i
$495$	2.92890	+	6.57214i	0.131644	+	0.295396i
$496$	−1.77633	−	1.02556i	−0.0797596	−	0.0460492i
$497$	−6.28470	+	10.8854i	−0.281908	+	0.488278i
$498$	19.5596	+	1.02160i	0.876488	+	0.0457790i
$499$	−9.49912	+	16.4530i	−0.425239	+	0.736535i	−0.996443	−	0.0842728i	$-0.973143\pi$
$499$	−9.49912	+	16.4530i	−0.425239	+	0.736535i	0.571204	+	0.820808i	$0.306477\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	0.397527	+	0.258057i	0.0177602	+	0.0115291i
$502$			12.5052i			0.558136i
$503$	−17.2526	+	9.96081i	−0.769256	+	0.444130i	−0.832609	−	0.553861i	$-0.813154\pi$
$503$	−17.2526	+	9.96081i	−0.769256	+	0.444130i	0.0633529	+	0.997991i	$0.479821\pi$
$504$	−4.12720	+	5.68484i	−0.183840	+	0.253223i
$505$	−4.57341			−0.203514
$506$	−4.98612			−0.221660
$507$	−1.15374	+	22.0896i	−0.0512395	+	0.981035i
$508$	−9.58763	−	5.53542i	−0.425382	−	0.245594i
$509$	−15.7560	−	27.2902i	−0.698372	−	1.20962i	−0.969031	−	0.246941i	$-0.920575\pi$
$509$	−15.7560	−	27.2902i	−0.698372	−	1.20962i	0.270658	−	0.962675i	$-0.412759\pi$
$510$	4.27668	−	2.18003i	0.189374	−	0.0965334i
$511$	−13.6062	+	23.5666i	−0.601903	+	1.04253i
$512$	−1.00000			−0.0441942
$513$	22.5880	−	1.66863i	0.997283	−	0.0736718i
$514$	−1.46751			−0.0647289
$515$	−1.14956	+	1.99110i	−0.0506559	+	0.0877385i
$516$	11.6436	−	5.93529i	0.512579	−	0.261286i
$517$	−2.69176	−	4.66226i	−0.118383	−	0.205046i
$518$	−11.5102	−	6.64542i	−0.505729	−	0.291983i
$519$	−2.20336	+	42.1858i	−0.0967170	+	1.85175i
$520$	−0.478712			−0.0209929
$521$	11.3505			0.497273			0.248637	−	0.968597i	$-0.420018\pi$
$521$	11.3505			0.497273			0.248637	+	0.968597i	$0.420018\pi$
$522$	−1.10589	+	1.52326i	−0.0484033	+	0.0666712i
$523$	31.9970	−	18.4735i	1.39913	−	0.807788i	0.404828	−	0.914393i	$-0.367331\pi$
$523$	31.9970	−	18.4735i	1.39913	−	0.807788i	0.994301	+	0.106605i	$0.0339980\pi$
$524$			15.4519i			0.675018i
$525$	3.40196	+	2.20840i	0.148474	+	0.0963825i
$526$	−12.2015	+	7.04453i	−0.532010	+	0.307156i
$527$	2.84228	−	4.92298i	0.123812	−	0.214448i
$528$	4.14852	+	0.216677i	0.180541	+	0.00942968i
$529$	−9.33904	+	16.1757i	−0.406045	+	0.703291i
$530$	−11.5028	−	6.64114i	−0.499649	−	0.288473i
$531$	7.66339	+	17.1958i	0.332563	+	0.746236i
$532$	7.44136	−	6.98655i	0.322624	−	0.302905i
$533$			1.00169i			0.0433882i
$534$	−15.3499	+	7.82459i	−0.664255	+	0.338603i
$535$	10.5517	+	6.09204i	0.456191	+	0.263382i
$536$	−11.3258	+	6.53894i	−0.489199	+	0.282439i
$537$	−30.9813	+	15.7927i	−1.33694	+	0.681503i
$538$	−9.48574	−	16.4298i	−0.408959	−	0.708339i
$539$			3.63730i			0.156670i
$540$	5.13261	+	0.810128i	0.220872	+	0.0348624i
$541$	15.2223	+	26.3657i	0.654456	+	1.13355i	0.982030	+	0.188725i	$0.0604356\pi$
$541$	15.2223	+	26.3657i	0.654456	+	1.13355i	−0.327574	+	0.944826i	$0.606231\pi$
$542$	−12.6913	−	21.9819i	−0.545137	−	0.944205i
$543$	11.1134	−	17.1198i	0.476924	−	0.734683i
$544$		−	2.77143i		−	0.118824i
$545$	0.360514	+	0.624429i	0.0154427	+	0.0267476i
$546$	0.881780	+	1.72983i	0.0377367	+	0.0740300i
$547$	−7.08775	+	4.09212i	−0.303050	+	0.174966i	−0.643812	−	0.765183i	$-0.722648\pi$
$547$	−7.08775	+	4.09212i	−0.303050	+	0.174966i	0.340762	+	0.940150i	$0.389315\pi$
$548$	7.57874	+	4.37559i	0.323748	+	0.186916i
$549$	7.47085	+	0.782541i	0.318848	+	0.0333980i
$550$		−	2.39841i		−	0.102269i
$551$	1.99392	−	1.87205i	0.0849438	−	0.0797521i
$552$	−1.96060	+	3.02023i	−0.0834487	+	0.128550i
$553$	23.7890	+	13.7346i	1.01161	+	0.584053i
$554$	4.05429	−	7.02224i	0.172250	−	0.298346i
$555$	−0.512760	+	9.81735i	−0.0217655	+	0.416723i
$556$	3.74921	−	6.49383i	0.159002	−	0.275400i
$557$	1.37346	−	0.792970i	0.0581956	−	0.0335992i	−0.470620	−	0.882336i	$-0.655970\pi$
$557$	1.37346	−	0.792970i	0.0581956	−	0.0335992i	0.528815	+	0.848737i	$0.322636\pi$
$558$	5.62051	−	2.50480i	0.237935	−	0.106037i
$559$		−	3.61209i		−	0.152775i
$560$	2.02795	−	1.17084i	0.0856966	−	0.0494770i
$561$	−0.600507	+	11.4973i	−0.0253534	+	0.485418i
$562$	−25.2934			−1.06694
$563$	12.2083			0.514519			0.257260	−	0.966342i	$-0.417180\pi$
$563$	12.2083			0.514519			0.257260	+	0.966342i	$0.417180\pi$
$564$	−3.88249	−	0.202783i	−0.163482	−	0.00853869i
$565$	−8.65597	−	4.99753i	−0.364159	−	0.210247i
$566$	−0.496185	−	0.859418i	−0.0208562	−	0.0361240i
$567$	−6.52677	−	20.0390i	−0.274099	−	0.841559i
$568$	2.68385	−	4.64856i	0.112612	−	0.195049i
$569$	30.1807			1.26524			0.632620	−	0.774462i	$-0.281979\pi$
$569$	30.1807			1.26524			0.632620	+	0.774462i	$0.281979\pi$
$570$	−7.10370	−	2.55684i	−0.297541	−	0.107094i
$571$	−35.1445			−1.47075			−0.735375	−	0.677660i	$-0.762994\pi$
$571$	−35.1445			−1.47075			−0.735375	+	0.677660i	$0.762994\pi$
$572$	0.574075	−	0.994328i	0.0240033	−	0.0415749i
$573$	−5.79641	−	11.3711i	−0.242149	−	0.475035i
$574$	−2.44995	−	4.24344i	−0.102259	−	0.177118i
$575$	1.80040	+	1.03946i	0.0750818	+	0.0433485i
$576$	1.76250	−	2.42768i	0.0734373	−	0.101153i
$577$	3.33452			0.138818			0.0694088	−	0.997588i	$-0.477889\pi$
$577$	3.33452			0.138818			0.0694088	+	0.997588i	$0.477889\pi$
$578$	−9.31916			−0.387626
$579$	−12.9243	−	0.675036i	−0.537115	−	0.0280536i
$580$	0.543392	−	0.313727i	0.0225631	−	0.0130268i
$581$			26.4800i			1.09858i
$582$	8.15874	−	12.5682i	0.338191	−	0.520970i
$583$	27.5885	−	15.9282i	1.14260	−	0.659679i
$584$	5.81045	−	10.0640i	0.240438	−	0.416451i
$585$	0.843728	−	1.16216i	0.0348839	−	0.0480493i
$586$	−11.6674	+	20.2085i	−0.481976	+	0.834807i
$587$	6.62612	+	3.82559i	0.273489	+	0.157899i	0.630472	−	0.776212i	$-0.282861\pi$
$587$	6.62612	+	3.82559i	0.273489	+	0.157899i	−0.356983	+	0.934111i	$0.616195\pi$
$588$	2.20321	+	1.43023i	0.0908590	+	0.0589816i
$589$	−8.70464	+	2.04077i	−0.358668	+	0.0840883i
$590$		−	6.27539i		−	0.258354i
$591$	15.9186	+	31.2283i	0.654803	+	1.28456i
$592$	4.91536	+	2.83789i	0.202020	+	0.116636i
$593$	−16.7538	+	9.67281i	−0.687996	+	0.397215i	−0.802861	−	0.596166i	$-0.796690\pi$
$593$	−16.7538	+	9.67281i	−0.687996	+	0.397215i	0.114865	+	0.993381i	$0.463357\pi$
$594$	−7.83777	+	9.68937i	−0.321588	+	0.397560i
$595$	3.24490	+	5.62033i	0.133028	+	0.230411i
$596$		−	12.2347i		−	0.501152i
$597$	−16.3382	−	10.6060i	−0.668678	−	0.434076i
$598$	0.497603	+	0.861873i	0.0203485	+	0.0352446i
$599$	−0.00576144	−	0.00997910i	−0.000235406	−	0.000407735i	0.865908	−	0.500204i	$-0.166742\pi$
$599$	−0.00576144	−	0.00997910i	−0.000235406	−	0.000407735i	−0.866143	+	0.499796i	$0.833408\pi$
$600$	−1.45279	−	0.943085i	−0.0593098	−	0.0385013i
$601$			19.6294i			0.800698i	0.916363	+	0.400349i	$0.131111\pi$
$601$			19.6294i			0.800698i	−0.916363	+	0.400349i	$0.868889\pi$
$602$	8.83447	+	15.3018i	0.360066	+	0.623653i
$603$	4.08720	−	39.0202i	0.166444	−	1.58902i
$604$	−13.9036	+	8.02727i	−0.565731	+	0.326625i
$605$	−4.54456	−	2.62380i	−0.184763	−	0.106673i
$606$	−3.59748	−	7.05736i	−0.146138	−	0.286686i
$607$			48.4715i			1.96740i	0.179821	+	0.983699i	$0.442448\pi$
$607$			48.4715i			1.96740i	−0.179821	+	0.983699i	$0.557552\pi$
$608$	−3.17779	+	2.98356i	−0.128876	+	0.120999i
$609$	−2.13458	−	1.38567i	−0.0864974	−	0.0561503i
$610$	−2.16845	−	1.25195i	−0.0877979	−	0.0506901i
$611$	−0.537262	+	0.930565i	−0.0217353	+	0.0376466i
$612$	6.72814	+	4.88464i	0.271969	+	0.197450i
$613$	17.8645	−	30.9422i	0.721539	−	1.24974i	−0.238843	−	0.971058i	$-0.576768\pi$
$613$	17.8645	−	30.9422i	0.721539	−	1.24974i	0.960383	−	0.278685i	$-0.0898985\pi$
$614$	−21.4512	+	12.3849i	−0.865702	+	0.499813i
$615$	−1.97338	+	3.03992i	−0.0795745	+	0.122582i
$616$			5.61632i			0.226288i
$617$	28.5725	−	16.4963i	1.15028	−	0.664117i	0.201328	−	0.979524i	$-0.435474\pi$
$617$	28.5725	−	16.4963i	1.15028	−	0.664117i	0.948957	+	0.315407i	$0.102141\pi$
$618$	−3.97679	−	0.207708i	−0.159970	−	0.00835524i
$619$	−33.4945			−1.34626			−0.673129	−	0.739525i	$-0.735050\pi$
$619$	−33.4945			−1.34626			−0.673129	+	0.739525i	$0.735050\pi$
$620$	−2.05113			−0.0823753
$621$	−3.87659	−	10.0828i	−0.155562	−	0.404611i
$622$	−9.74385	−	5.62562i	−0.390693	−	0.225567i
$623$	−11.6466	−	20.1725i	−0.466612	−	0.808196i
$624$	−0.376559	−	0.738715i	−0.0150744	−	0.0295723i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	10.9329			0.436966
$627$	13.8296	−	11.6888i	0.552301	−	0.466807i
$628$	1.67251			0.0667404
$629$	−7.86501	+	13.6226i	−0.313598	+	0.543169i
$630$	−0.731839	+	6.98681i	−0.0291572	+	0.278361i
$631$	−11.0092	−	19.0686i	−0.438271	−	0.759108i	0.559285	−	0.828975i	$-0.311076\pi$
$631$	−11.0092	−	19.0686i	−0.438271	−	0.759108i	−0.997556	+	0.0698675i	$0.977742\pi$
$632$	−10.1589	−	5.86527i	−0.404101	−	0.233308i
$633$	−45.8807	−	2.39635i	−1.82359	−	0.0952465i
$634$	17.9005			0.710921
$635$	−11.0708			−0.439333
$636$	1.19995	−	22.9743i	0.0475810	−	0.910989i
$637$	0.628724	−	0.362994i	0.0249110	−	0.0143823i
$638$			1.50490i			0.0595794i
$639$	6.55493	+	14.7086i	0.259309	+	0.581862i
$640$	−0.866025	+	0.500000i	−0.0342327	+	0.0197642i
$641$	7.33431	−	12.7034i	0.289688	−	0.501754i	−0.684047	−	0.729438i	$-0.739782\pi$
$641$	7.33431	−	12.7034i	0.289688	−	0.501754i	0.973735	+	0.227684i	$0.0731152\pi$
$642$	−1.10073	+	21.0747i	−0.0434425	+	0.831752i
$643$	−15.3180	+	26.5315i	−0.604082	+	1.04630i	0.388114	+	0.921612i	$0.373127\pi$
$643$	−15.3180	+	26.5315i	−0.604082	+	1.04630i	−0.992196	+	0.124690i	$0.960207\pi$
$644$	−4.21595	−	2.43408i	−0.166132	−	0.0959163i
$645$	7.11597	−	10.9619i	0.280191	−	0.431624i
$646$	−8.26874	−	8.80703i	−0.325329	−	0.346508i
$647$		−	9.82606i		−	0.386302i	−0.981169	−	0.193151i	$-0.938129\pi$
$647$		−	9.82606i		−	0.386302i	0.981169	−	0.193151i	$-0.0618707\pi$
$648$	2.78722	+	8.55753i	0.109492	+	0.336172i
$649$	13.0345	+	7.52549i	0.511650	+	0.295401i
$650$	−0.414577	+	0.239356i	−0.0162611	+	0.00938832i
$651$	3.77815	+	7.41178i	0.148077	+	0.290491i
$652$	−6.21359	−	10.7622i	−0.243343	−	0.421482i
$653$			31.4026i			1.22888i	0.788964	+	0.614440i	$0.210618\pi$
$653$			31.4026i			1.22888i	−0.788964	+	0.614440i	$0.789382\pi$
$654$	−0.679991	+	1.04750i	−0.0265898	+	0.0409605i
$655$	7.72594	+	13.3817i	0.301877	+	0.522867i
$656$	1.04624	+	1.81214i	0.0408487	+	0.0707521i
$657$	14.1912	+	31.8436i	0.553652	+	1.24234i
$658$		−	5.25616i		−	0.204906i
$659$	1.68244	+	2.91407i	0.0655385	+	0.113516i	0.896933	−	0.442167i	$-0.145790\pi$
$659$	1.68244	+	2.91407i	0.0655385	+	0.113516i	−0.831394	+	0.555683i	$0.812457\pi$
$660$	3.70106	−	1.88661i	0.144064	−	0.0734363i
$661$	−6.16334	+	3.55840i	−0.239726	+	0.138406i	−0.615051	−	0.788487i	$-0.710865\pi$
$661$	−6.16334	+	3.55840i	−0.239726	+	0.138406i	0.375325	+	0.926893i	$0.377531\pi$
$662$	8.97416	+	5.18123i	0.348790	+	0.201374i
$663$	2.04730	−	1.04361i	0.0795105	−	0.0405304i
$664$		−	11.3081i		−	0.438841i
$665$	2.95113	−	9.77121i	0.114440	−	0.378911i
$666$	−15.5528	+	6.93115i	−0.602658	+	0.268577i
$667$	−1.12967	−	0.652215i	−0.0437410	−	0.0252539i
$668$	0.136815	−	0.236971i	0.00529355	−	0.00916869i
$669$	−26.3864	−	1.37816i	−1.02016	−	0.0532828i
$670$	−6.53894	+	11.3258i	−0.252621	+	0.437553i
$671$	5.20084	−	3.00270i	0.200776	−	0.115918i
$672$	3.40196	+	2.20840i	0.131233	+	0.0851909i
$673$		−	26.5117i		−	1.02195i	−0.859596	−	0.510975i	$-0.829284\pi$
$673$		−	26.5117i		−	1.02195i	0.859596	−	0.510975i	$-0.170716\pi$
$674$	−23.7499	+	13.7120i	−0.914810	+	0.528166i
$675$	4.85004	−	1.86471i	0.186678	−	0.0717729i
$676$	12.7708			0.491186
$677$	42.3166			1.62636			0.813179	−	0.582013i	$-0.197735\pi$
$677$	42.3166			1.62636			0.813179	+	0.582013i	$0.197735\pi$
$678$	0.902972	−	17.2884i	0.0346784	−	0.663956i
$679$	17.5441	+	10.1291i	0.673279	+	0.388718i
$680$	−1.38572	−	2.40013i	−0.0531398	−	0.0920408i
$681$	2.68672	−	1.36955i	0.102955	−	0.0524813i
$682$	2.45973	−	4.26038i	0.0941879	−	0.163138i
$683$	−11.0677			−0.423493			−0.211746	−	0.977325i	$-0.567915\pi$
$683$	−11.0677			−0.423493			−0.211746	+	0.977325i	$0.567915\pi$
$684$	−1.64229	−	12.9732i	−0.0627944	−	0.496041i
$685$	8.75118			0.334365
$686$	−9.97150	+	17.2711i	−0.380714	+	0.659415i
$687$	−25.6860	+	13.0934i	−0.979981	+	0.499544i
$688$	−3.77271	−	6.53452i	−0.143833	−	0.249126i
$689$	−5.50653	−	3.17920i	−0.209782	−	0.121118i
$690$	−0.187814	+	3.59590i	−0.00714995	+	0.136893i
$691$	20.2406			0.769990			0.384995	−	0.922919i	$-0.374203\pi$
$691$	20.2406			0.769990			0.384995	+	0.922919i	$0.374203\pi$
$692$	24.3892			0.927137
$693$	−13.6346	−	9.89873i	−0.517935	−	0.376022i
$694$	22.5112	−	12.9969i	0.854515	−	0.493354i
$695$		−	7.49842i		−	0.284431i
$696$	0.911558	+	0.591743i	0.0345525	+	0.0224300i
$697$	−5.02222	+	2.89958i	−0.190230	+	0.109829i
$698$	4.08348	−	7.07280i	0.154562	−	0.267710i
$699$	15.0051	+	0.783718i	0.567545	+	0.0296429i
$700$	1.17084	−	2.02795i	0.0442536	−	0.0766494i
$701$	12.8127	+	7.39742i	0.483929	+	0.279397i	0.722053	−	0.691838i	$-0.243199\pi$
$701$	12.8127	+	7.39742i	0.483929	+	0.279397i	−0.238123	+	0.971235i	$0.576532\pi$
$702$	2.45704	+	0.387819i	0.0927352	+	0.0146373i
$703$	24.0870	−	5.64709i	0.908459	−	0.212984i
$704$		−	2.39841i		−	0.0903936i
$705$	−3.46373	+	1.76563i	−0.130452	+	0.0664975i
$706$	20.0065	+	11.5507i	0.752953	+	0.434718i
$707$	9.27466	−	5.35473i	0.348810	−	0.201385i
$708$	9.68374	−	4.93627i	0.363937	−	0.185516i
$709$	−0.506440	−	0.877179i	−0.0190197	−	0.0329432i	0.856359	−	0.516381i	$-0.172721\pi$
$709$	−0.506440	−	0.877179i	−0.0190197	−	0.0329432i	−0.875379	+	0.483438i	$0.839388\pi$
$710$		−	5.36769i		−	0.201446i
$711$	32.1440	−	14.3251i	1.20550	−	0.537234i
$712$	4.97362	+	8.61457i	0.186394	+	0.322845i
$713$	2.13207	+	3.69285i	0.0798466	+	0.138298i
$714$	−6.12044	+	9.42830i	−0.229052	+	0.352845i
$715$		−	1.14815i		−	0.0429384i
$716$	10.0385	+	17.3871i	0.375155	+	0.649787i
$717$	−15.0622	−	29.5484i	−0.562510	−	1.10350i
$718$	−17.3948	+	10.0429i	−0.649168	+	0.374798i
$719$	−2.95761	−	1.70758i	−0.110300	−	0.0636819i	0.443835	−	0.896109i	$-0.353618\pi$
$719$	−2.95761	−	1.70758i	−0.110300	−	0.0636819i	−0.554135	+	0.832427i	$0.686951\pi$
$720$	0.312528	−	2.98368i	0.0116472	−	0.111195i
$721$		−	5.38382i		−	0.200504i
$722$	−1.19670	+	18.9623i	−0.0445364	+	0.705703i
$723$	−18.1187	+	27.9111i	−0.673840	+	1.03803i
$724$	−10.2054	−	5.89207i	−0.379279	−	0.218977i
$725$	0.313727	−	0.543392i	0.0116515	−	0.0201811i
$726$	0.474079	−	9.07675i	0.0175947	−	0.336870i
$727$	−20.0624	+	34.7491i	−0.744074	+	1.28877i	0.206552	+	0.978436i	$0.433776\pi$
$727$	−20.0624	+	34.7491i	−0.744074	+	1.28877i	−0.950626	+	0.310338i	$0.899558\pi$
$728$	0.970806	−	0.560495i	0.0359805	−	0.0207733i
$729$	−25.6874	−	8.31615i	−0.951385	−	0.308005i
$730$		−	11.6209i		−	0.430109i
$731$	18.1100	−	10.4558i	0.669822	−	0.386722i
$732$	0.226208	−	4.33099i	0.00836089	−	0.160078i
$733$	42.4761			1.56889			0.784446	−	0.620197i	$-0.212947\pi$
$733$	42.4761			1.56889			0.784446	+	0.620197i	$0.212947\pi$
$734$	9.66168			0.356619
$735$	2.62315	+	0.137007i	0.0967565	+	0.00505360i
$736$	1.80040	+	1.03946i	0.0663636	+	0.0383150i
$737$	−15.6831	−	27.1639i	−0.577694	−	1.00060i
$738$	−6.24327	−	0.653957i	−0.229818	−	0.0240725i
$739$	−25.6660	+	44.4548i	−0.944139	+	1.63530i	−0.186673	+	0.982422i	$0.559770\pi$
$739$	−25.6660	+	44.4548i	−0.944139	+	1.63530i	−0.757466	+	0.652874i	$0.773563\pi$
$740$	5.67577			0.208646
$741$	−3.40063	−	1.22399i	−0.124925	−	0.0449645i
$742$	31.1028			1.14182
$743$	14.7044	−	25.4688i	0.539454	−	0.934361i	−0.459480	−	0.888188i	$-0.651964\pi$
$743$	14.7044	−	25.4688i	0.539454	−	0.934361i	0.998933	−	0.0461730i	$-0.0147025\pi$
$744$	−1.61344	−	3.16516i	−0.0591514	−	0.116040i
$745$	−6.11734	−	10.5955i	−0.224122	−	0.388190i
$746$	14.5767	+	8.41587i	0.533692	+	0.308127i
$747$	27.4525	+	19.9306i	1.00443	+	0.729221i
$748$	6.64704			0.243040
$749$	−28.5312			−1.04251
$750$	−1.72969	−	0.0903420i	−0.0631595	−	0.00329882i
$751$	9.26493	−	5.34911i	0.338082	−	0.195192i	−0.321342	−	0.946963i	$-0.604134\pi$
$751$	9.26493	−	5.34911i	0.338082	−	0.195192i	0.659424	+	0.751772i	$0.270800\pi$
$752$			2.24461i			0.0818526i
$753$	−11.7935	+	18.1675i	−0.429779	+	0.662059i
$754$	0.260128	−	0.150185i	0.00947332	−	0.00546942i
$755$	−8.02727	+	13.9036i	−0.292142	+	0.506005i
$756$	−11.3572	+	4.36656i	−0.413058	+	0.158810i
$757$	−8.59944	+	14.8947i	−0.312552	+	0.541356i	−0.978914	−	0.204272i	$-0.934517\pi$
$757$	−8.59944	+	14.8947i	−0.312552	+	0.541356i	0.666362	+	0.745628i	$0.267851\pi$
$758$	−27.3759	−	15.8055i	−0.994337	−	0.574081i
$759$	−7.24376	−	4.70233i	−0.262932	−	0.170684i
$760$	−1.26026	+	4.17274i	−0.0457146	+	0.151361i
$761$			35.2476i			1.27772i	0.769321	+	0.638862i	$0.220595\pi$
$761$			35.2476i			1.27772i	−0.769321	+	0.638862i	$0.779405\pi$
$762$	−8.70841	−	17.0837i	−0.315472	−	0.618878i
$763$	−1.46221	−	0.844208i	−0.0529356	−	0.0305624i
$764$	−6.38163	+	3.68444i	−0.230879	+	0.133298i
$765$	8.26906	+	0.866149i	0.298968	+	0.0313157i
$766$	−14.8637	−	25.7447i	−0.537048	−	0.930194i
$767$		−	3.00411i		−	0.108472i
$768$	−1.45279	−	0.943085i	−0.0524229	−	0.0340306i
$769$	−16.3809	−	28.3725i	−0.590710	−	1.02314i	−0.994137	−	0.108128i	$-0.965514\pi$
$769$	−16.3809	−	28.3725i	−0.590710	−	1.02314i	0.403427	−	0.915012i	$-0.367819\pi$
$770$	2.80816	+	4.86387i	0.101199	+	0.175282i
$771$	−2.13197	−	1.38398i	−0.0767811	−	0.0498429i
$772$			7.47201i			0.268924i
$773$	−9.83728	−	17.0387i	−0.353822	−	0.612838i	0.633093	−	0.774075i	$-0.281785\pi$
$773$	−9.83728	−	17.0387i	−0.353822	−	0.612838i	−0.986916	+	0.161237i	$0.948452\pi$
$774$	22.5131	+	2.35815i	0.809216	+	0.0847620i
$775$	−1.77633	+	1.02556i	−0.0638077	+	0.0368394i
$776$	−7.49209	−	4.32556i	−0.268950	−	0.155278i
$777$	−10.4547	−	20.5095i	−0.375059	−	0.735773i
$778$		−	6.99868i		−	0.250915i
$779$	8.73135	+	2.63707i	0.312833	+	0.0944830i
$780$	−0.695467	−	0.451467i	−0.0249017	−	0.0161651i
$781$	11.1492	+	6.43698i	0.398949	+	0.230333i
$782$	−2.88079	+	4.98968i	−0.103017	+	0.178431i
$783$	−3.04318	+	1.17002i	−0.108754	+	0.0418132i
$784$	0.758271	−	1.31336i	0.0270811	−	0.0469059i
$785$	1.44843	−	0.836254i	0.0516969	−	0.0298472i
$786$	−14.5724	+	22.4483i	−0.519781	+	0.800704i
$787$			42.0288i			1.49816i	0.662478	+	0.749082i	$0.269505\pi$
$787$			42.0288i			1.49816i	−0.662478	+	0.749082i	$0.730495\pi$
$788$	17.5258	−	10.1185i	0.624329	−	0.360457i
$789$	−24.3698	−	1.27283i	−0.867586	−	0.0453141i
$790$	−11.7305			−0.417354
$791$	23.4052			0.832193
$792$	5.82257	+	4.22719i	0.206896	+	0.150207i
$793$	−1.03806	−	0.599326i	−0.0368627	−	0.0212827i
$794$	−14.8564	−	25.7320i	−0.527234	−	0.913196i
$795$	−10.4479	−	20.4963i	−0.370551	−	0.726928i
$796$	−5.62306	+	9.73942i	−0.199304	+	0.345205i
$797$	31.9447			1.13154			0.565769	−	0.824564i	$-0.308579\pi$
$797$	31.9447			1.13154			0.565769	+	0.824564i	$0.308579\pi$
$798$	17.3996	−	3.13213i	0.615940	−	0.110876i
$799$	−6.22079			−0.220076
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−29.6794	−	3.10879i	−1.04867	−	0.109844i
$802$	14.8000	+	25.6344i	0.522608	+	0.905183i
$803$	24.1376	+	13.9359i	0.851798	+	0.491786i
$804$	−22.6207	−	1.18148i	−0.797772	−	0.0416677i
$805$	−4.86817			−0.171580
$806$	−0.981901			−0.0345860
$807$	1.71392	−	32.8149i	0.0603329	−	1.15514i
$808$	−3.96069	+	2.28671i	−0.139337	+	0.0804460i
$809$		−	45.3248i		−	1.59354i	−0.604285	−	0.796768i	$-0.706541\pi$
$809$		−	45.3248i		−	1.59354i	0.604285	−	0.796768i	$-0.293459\pi$
$810$	6.69257	+	6.01743i	0.235153	+	0.211431i
$811$	−22.3241	+	12.8888i	−0.783907	+	0.452589i	−0.837813	−	0.545957i	$-0.816166\pi$
$811$	−22.3241	+	12.8888i	−0.783907	+	0.452589i	0.0539064	+	0.998546i	$0.482833\pi$
$812$	−0.734649	+	1.27245i	−0.0257811	+	0.0446542i
$813$	2.29311	−	43.9040i	0.0804229	−	1.53978i
$814$	−6.80643	+	11.7891i	−0.238565	+	0.413207i
$815$	−10.7622	−	6.21359i	−0.376985	−	0.217652i
$816$	2.61370	−	4.02630i	0.0914977	−	0.140949i
$817$	−31.4850	−	9.50923i	−1.10152	−	0.332686i
$818$			1.21555i			0.0425008i
$819$	−0.350341	+	3.34467i	−0.0122419	+	0.116872i
$820$	1.81214	+	1.04624i	0.0632826	+	0.0365362i
$821$	−1.49955	+	0.865764i	−0.0523345	+	0.0302154i	−0.525939	−	0.850522i	$-0.676286\pi$
$821$	−1.49955	+	0.865764i	−0.0523345	+	0.0302154i	0.473604	+	0.880738i	$0.342953\pi$
$822$	6.88375	+	13.5042i	0.240098	+	0.471013i
$823$	−14.3880	−	24.9207i	−0.501534	−	0.868682i	−0.999998	−	0.00177204i	$-0.999436\pi$
$823$	−14.3880	−	24.9207i	−0.501534	−	0.868682i	0.498465	−	0.866910i	$-0.333897\pi$
$824$			2.29913i			0.0800940i
$825$	2.26191	−	3.48439i	0.0787496	−	0.121311i
$826$	7.34747	+	12.7262i	0.255651	+	0.442801i
$827$	−15.2033	−	26.3329i	−0.528671	−	0.915684i	−0.999441	−	0.0334287i	$-0.989357\pi$
$827$	−15.2033	−	26.3329i	−0.528671	−	0.915684i	0.470770	−	0.882256i	$-0.343976\pi$
$828$	−5.69667	+	2.53874i	−0.197973	+	0.0882273i
$829$		−	6.37093i		−	0.221272i	−0.993861	−	0.110636i	$-0.964711\pi$
$829$		−	6.37093i		−	0.221272i	0.993861	−	0.110636i	$-0.0352887\pi$
$830$	−5.65407	−	9.79314i	−0.196256	−	0.339925i
$831$	12.5126	−	6.37828i	0.434057	−	0.221260i
$832$	−0.414577	+	0.239356i	−0.0143729	+	0.00829818i
$833$	3.63990	+	2.10150i	0.126115	+	0.0728126i
$834$	11.5710	−	5.89832i	0.400672	−	0.204242i
$835$		−	0.273631i		−	0.00946938i
$836$	−7.15582	−	7.62166i	−0.247489	−	0.263601i
$837$	10.5276	+	1.66168i	0.363889	+	0.0574360i
$838$	2.82675	+	1.63203i	0.0976485	+	0.0563774i
$839$	8.20502	−	14.2115i	0.283269	−	0.490636i	−0.688919	−	0.724838i	$-0.741914\pi$
$839$	8.20502	−	14.2115i	0.283269	−	0.490636i	0.972188	+	0.234202i	$0.0752478\pi$
$840$	4.05038	+	0.211552i	0.139752	+	0.00729923i
$841$	14.3032	−	24.7738i	0.493212	−	0.854268i
$842$	−18.4508	+	10.6526i	−0.635856	+	0.367112i
$843$	−36.7459	−	23.8538i	−1.26560	−	0.821568i
$844$			26.5254i			0.913040i
$845$	11.0599	−	6.38542i	0.380471	−	0.219665i
$846$	−5.44919	−	3.95612i	−0.187347	−	0.136014i
$847$	12.2882			0.422228
$848$	−13.2823			−0.456115
$849$	0.0896527	−	1.71650i	0.00307687	−	0.0589100i
$850$	−2.40013	−	1.38572i	−0.0823238	−	0.0475297i
$851$	−5.89974	−	10.2187i	−0.202241	−	0.350291i
$852$	8.28304	−	4.22227i	0.283772	−	0.144653i
$853$	−18.9054	+	32.7451i	−0.647308	+	1.12117i	0.336456	+	0.941699i	$0.390772\pi$
$853$	−18.9054	+	32.7451i	−0.647308	+	1.12117i	−0.983763	+	0.179470i	$0.942562\pi$
$854$	5.86335			0.200640
$855$	−7.90884	−	10.4139i	−0.270477	−	0.356149i
$856$	12.1841			0.416443
$857$	−0.203026	+	0.351652i	−0.00693525	+	0.0120122i	−0.869472	−	0.493982i	$-0.835541\pi$
$857$	−0.203026	+	0.351652i	−0.00693525	+	0.0120122i	0.862537	+	0.505994i	$0.168874\pi$
$858$	1.77175	−	0.903145i	0.0604864	−	0.0308329i
$859$	2.87993	+	4.98819i	0.0982621	+	0.170195i	0.910965	−	0.412483i	$-0.135338\pi$
$859$	2.87993	+	4.98819i	0.0982621	+	0.170195i	−0.812703	+	0.582678i	$0.802005\pi$
$860$	−6.53452	−	3.77271i	−0.222825	−	0.128648i
$861$	0.442667	−	8.47534i	0.0150861	−	0.288839i
$862$	−4.28560			−0.145968
$863$	26.1179			0.889065			0.444532	−	0.895763i	$-0.353370\pi$
$863$	26.1179			0.889065			0.444532	+	0.895763i	$0.353370\pi$
$864$	4.85004	−	1.86471i	0.165002	−	0.0634388i
$865$	21.1216	−	12.1946i	0.718157	−	0.414628i
$866$		−	20.8270i		−	0.707731i
$867$	−13.5388	−	8.78876i	−0.459800	−	0.298482i
$868$	4.15959	−	2.40154i	0.141186	−	0.0815137i
$869$	14.0673	−	24.3653i	0.477202	−	0.826538i
$870$	1.08530	+	0.0566855i	0.0367953	+	0.00192182i
$871$	−3.13027	+	5.42179i	−0.106065	+	0.183710i
$872$	0.624429	+	0.360514i	0.0211458	+	0.0122086i
$873$	23.7058	−	10.5646i	0.802320	−	0.357557i
$874$	8.82259	−	2.06842i	0.298428	−	0.0699652i
$875$		−	2.34168i		−	0.0791632i
$876$	17.9325	−	9.14109i	0.605885	−	0.308849i
$877$	7.26280	+	4.19318i	0.245247	+	0.141594i	0.617586	−	0.786503i	$-0.288111\pi$
$877$	7.26280	+	4.19318i	0.245247	+	0.141594i	−0.372339	+	0.928097i	$0.621444\pi$
$878$	14.9323	−	8.62117i	0.503941	−	0.290950i
$879$	−36.0086	+	18.3554i	−1.21454	+	0.619111i
$880$	−1.19921	−	2.07709i	−0.0404253	−	0.0700186i
$881$		−	41.7995i		−	1.40826i	−0.710071	−	0.704130i	$-0.751337\pi$
$881$		−	41.7995i		−	1.40826i	0.710071	−	0.704130i	$-0.248663\pi$
$882$	1.85197	+	4.15564i	0.0623592	+	0.139928i
$883$	1.58994	+	2.75386i	0.0535057	+	0.0926746i	0.891538	−	0.452946i	$-0.149627\pi$
$883$	1.58994	+	2.75386i	0.0535057	+	0.0926746i	−0.838032	+	0.545621i	$0.816294\pi$
$884$	−0.663360	−	1.14897i	−0.0223112	−	0.0386441i
$885$	5.91823	−	9.11681i	0.198939	−	0.306458i
$886$		−	22.7142i		−	0.763099i
$887$	−24.1827	−	41.8857i	−0.811976	−	1.40638i	−0.911479	−	0.411346i	$-0.865059\pi$
$887$	−24.1827	−	41.8857i	−0.811976	−	1.40638i	0.0995032	−	0.995037i	$-0.468275\pi$
$888$	4.46461	+	8.75845i	0.149822	+	0.293914i
$889$	22.4511	−	12.9622i	0.752987	−	0.434737i
$890$	8.61457	+	4.97362i	0.288761	+	0.166716i
$891$	−20.5245	+	6.68491i	−0.687597	+	0.223953i
$892$			15.2549i			0.510773i
$893$	6.69694	+	7.13291i	0.224105	+	0.238694i
$894$	11.5383	−	17.7744i	0.385900	−	0.594464i
$895$	17.3871	+	10.0385i	0.581187	+	0.335548i
$896$	1.17084	−	2.02795i	0.0391150	−	0.0677491i
$897$	−0.0899088	+	1.72140i	−0.00300197	+	0.0574759i
$898$	12.2004	−	21.1316i	0.407131	−	0.705172i
$899$	1.11457	−	0.643496i	0.0371729	−	0.0214618i
$900$	−1.22118	−	2.74020i	−0.0407060	−	0.0913401i
$901$		−	36.8109i		−	1.22635i
$902$	−4.34626	+	2.50931i	−0.144715	+	0.0835510i
$903$	−1.59625	+	30.5618i	−0.0531198	+	1.01703i
$904$	−9.99505			−0.332430
$905$	−11.7841			−0.391718
$906$	−27.7694	−	1.45040i	−0.922577	−	0.0481862i
$907$	−38.0067	−	21.9432i	−1.26199	−	0.728612i	−0.288533	−	0.957470i	$-0.593167\pi$
$907$	−38.0067	−	21.9432i	−1.26199	−	0.728612i	−0.973460	+	0.228858i	$0.926501\pi$
$908$	−0.870543	−	1.50782i	−0.0288900	−	0.0500389i
$909$	1.42932	−	13.6456i	0.0474075	−	0.452595i
$910$	0.560495	−	0.970806i	0.0185802	−	0.0321819i
$911$	59.7244			1.97876			0.989378	−	0.145363i	$-0.0464350\pi$
$911$	59.7244			1.97876			0.989378	+	0.145363i	$0.0464350\pi$
$912$	−7.43041	+	1.33756i	−0.246045	+	0.0442909i
$913$	27.1216			0.897595
$914$	2.78960	−	4.83173i	0.0922719	−	0.159820i
$915$	−1.96959	−	3.86385i	−0.0651128	−	0.127735i
$916$	8.32269	+	14.4153i	0.274989	+	0.476296i
$917$	−31.3357	−	18.0917i	−1.03480	−	0.597439i
$918$	5.16793	+	13.4415i	0.170567	+	0.443637i
$919$	47.4923			1.56663			0.783313	−	0.621628i	$-0.213528\pi$
$919$	47.4923			1.56663			0.783313	+	0.621628i	$0.213528\pi$
$920$	2.07892			0.0685400
$921$	−42.8441	−	2.23775i	−1.41176	−	0.0737363i
$922$	13.2971	−	7.67711i	0.437918	−	0.252832i
$923$		−	2.56958i		−	0.0845788i
$924$	−5.29666	+	8.15931i	−0.174247	+	0.268422i
$925$	4.91536	−	2.83789i	0.161616	−	0.0933091i
$926$	14.5464	−	25.1950i	0.478023	−	0.827960i
$927$	−5.58154	−	4.05220i	−0.183322	−	0.133092i
$928$	0.313727	−	0.543392i	0.0102986	−	0.0178377i
$929$	10.2174	+	5.89900i	0.335221	+	0.193540i	0.658157	−	0.752881i	$-0.271336\pi$
$929$	10.2174	+	5.89900i	0.335221	+	0.193540i	−0.322936	+	0.946421i	$0.604670\pi$
$930$	−2.97985	−	1.93439i	−0.0977133	−	0.0634311i
$931$	−1.50888	−	6.43595i	−0.0494515	−	0.210930i
$932$		−	8.67501i		−	0.284160i
$933$	−8.85031	−	17.3621i	−0.289746	−	0.568410i
$934$	26.5965	+	15.3555i	0.870263	+	0.502446i
$935$	5.75651	−	3.32352i	0.188258	−	0.108691i
$936$	0.149611	−	1.42832i	0.00489019	−	0.0466862i
$937$	−24.8952	−	43.1198i	−0.813292	−	1.40866i	−0.910548	−	0.413404i	$-0.864340\pi$
$937$	−24.8952	−	43.1198i	−0.813292	−	1.40866i	0.0972554	−	0.995259i	$-0.468994\pi$
$938$		−	30.6242i		−	0.999916i
$939$	15.8832	+	10.3106i	0.518327	+	0.336475i
$940$	1.12231	+	1.94389i	0.0366056	+	0.0634027i
$941$	11.3241	+	19.6139i	0.369155	+	0.639396i	0.989434	−	0.144986i	$-0.0463136\pi$
$941$	11.3241	+	19.6139i	0.369155	+	0.639396i	−0.620278	+	0.784382i	$0.712980\pi$
$942$	2.42980	+	1.57732i	0.0791671	+	0.0513918i
$943$		−	4.35009i		−	0.141659i
$944$	−3.13769	−	5.43465i	−0.102123	−	0.176883i
$945$	−7.65236	+	9.46016i	−0.248931	+	0.307739i
$946$	15.6725	−	9.04852i	0.509557	−	0.294193i
$947$	−16.7901	−	9.69377i	−0.545605	−	0.315005i	0.201742	−	0.979439i	$-0.435340\pi$
$947$	−16.7901	−	9.69377i	−0.545605	−	0.315005i	−0.747347	+	0.664433i	$0.768673\pi$
$948$	−9.22733	−	18.1017i	−0.299690	−	0.587917i
$949$		−	5.56307i		−	0.180585i
$950$	0.994947	+	4.24383i	0.0322803	+	0.137688i
$951$	26.0057	+	16.8817i	0.843291	+	0.547427i
$952$	5.62033	+	3.24490i	0.182156	+	0.105168i
$953$	14.1707	−	24.5444i	0.459034	−	0.795070i	−0.539876	−	0.841744i	$-0.681529\pi$
$953$	14.1707	−	24.5444i	0.459034	−	0.795070i	0.998910	+	0.0466745i	$0.0148623\pi$
$954$	23.4100	−	32.2451i	0.757925	−	1.04397i
$955$	−3.68444	+	6.38163i	−0.119226	+	0.206505i
$956$	−16.5830	+	9.57417i	−0.536331	+	0.309651i
$957$	−1.41925	+	2.18630i	−0.0458777	+	0.0706729i
$958$			25.7610i			0.832299i
$959$	−17.7470	+	10.2462i	−0.573080	+	0.330868i
$960$	−1.72969	−	0.0903420i	−0.0558256	−	0.00291577i
$961$	26.7929			0.864286
$962$	2.71706			0.0876016
$963$	−21.4744	+	29.5790i	−0.692002	+	0.953169i
$964$	16.6382	+	9.60606i	0.535880	+	0.309390i
$965$	3.73601	+	6.47095i	0.120266	+	0.208307i
$966$	−3.82934	−	7.51221i	−0.123207	−	0.241701i
$967$	−19.7510	+	34.2097i	−0.635150	+	1.10011i	0.351334	+	0.936250i	$0.385728\pi$
$967$	−19.7510	+	34.2097i	−0.635150	+	1.10011i	−0.986483	+	0.163861i	$0.947605\pi$
$968$	−5.24761			−0.168665
$969$	−3.70695	−	20.5929i	−0.119084	−	0.661538i
$970$	−8.65112			−0.277771
$971$	−6.63173	+	11.4865i	−0.212822	+	0.368619i	−0.952597	−	0.304236i	$-0.901599\pi$
$971$	−6.63173	+	11.4865i	−0.212822	+	0.368619i	0.739774	+	0.672855i	$0.234932\pi$
$972$	−4.02124	+	15.0609i	−0.128981	+	0.483077i
$973$	8.77945	+	15.2065i	0.281456	+	0.487496i
$974$	−16.6573	−	9.61708i	−0.533733	−	0.308151i
$975$	−0.828026	−	0.0432478i	−0.0265180	−	0.00138504i
$976$	−2.50391			−0.0801481
$977$	−44.3642			−1.41934			−0.709668	−	0.704537i	$-0.751155\pi$
$977$	−44.3642			−1.41934			−0.709668	+	0.704537i	$0.751155\pi$
$978$	1.12270	−	21.4952i	0.0358998	−	0.687341i
$979$	−20.6613	+	11.9288i	−0.660338	+	0.381246i
$980$		−	1.51654i		−	0.0484442i
$981$	−1.97577	+	0.880507i	−0.0630813	+	0.0281124i
$982$	−18.7155	+	10.8054i	−0.597236	+	0.344814i
$983$	0.420338	−	0.728047i	0.0134067	−	0.0232211i	−0.859244	−	0.511566i	$-0.829066\pi$
$983$	0.420338	−	0.728047i	0.0134067	−	0.0232211i	0.872651	+	0.488345i	$0.162399\pi$
$984$	−0.189038	+	3.61934i	−0.00602633	+	0.115380i
$985$	10.1185	−	17.5258i	0.322402	−	0.558417i
$986$	1.50597	+	0.869474i	0.0479600	+	0.0276897i
$987$	4.95701	−	7.63608i	0.157783	−	0.243059i
$988$	−0.603304	+	1.99754i	−0.0191937	+	0.0635502i
$989$			15.6863i			0.498796i
$990$	7.15609	+	0.749571i	0.227436	+	0.0238229i
$991$	−3.01574	−	1.74114i	−0.0957982	−	0.0553091i	0.451336	−	0.892354i	$-0.350948\pi$
$991$	−3.01574	−	1.74114i	−0.0957982	−	0.0553091i	−0.547134	+	0.837045i	$0.684281\pi$
$992$	−1.77633	+	1.02556i	−0.0563985	+	0.0325617i
$993$	8.15120	+	15.9906i	0.258670	+	0.507447i
$994$	6.28470	+	10.8854i	0.199339	+	0.345265i
$995$			11.2461i			0.356526i
$996$	10.6645	−	16.4283i	0.337919	−	0.520551i
$997$	15.1353	+	26.2151i	0.479339	+	0.830240i	0.999719	−	0.0236947i	$-0.00754296\pi$
$997$	15.1353	+	26.2151i	0.479339	+	0.830240i	−0.520380	+	0.853935i	$0.674210\pi$
$998$	9.49912	+	16.4530i	0.300689	+	0.520809i
$999$	−29.1315	−	4.59810i	−0.921681	−	0.145478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.s.b.521.11	yes	24
3.2	odd	2		570.2.s.a.521.6	yes	24
19.12	odd	6		570.2.s.a.221.6	✓	24
57.50	even	6	inner	570.2.s.b.221.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.s.a.221.6	✓	24	19.12	odd	6
570.2.s.a.521.6	yes	24	3.2	odd	2
570.2.s.b.221.11	yes	24	57.50	even	6	inner
570.2.s.b.521.11	yes	24	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.54313 - 0.786608i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.0903420 - 1.72969i) q^{6} +2.34168 q^{7} -1.00000 q^{8} +(1.76250 - 2.42768i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.54313 - 0.786608i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.0903420 - 1.72969i) q^{6} +2.34168 q^{7} -1.00000 q^{8} +(1.76250 - 2.42768i) q^{9} +(-0.866025 + 0.500000i) q^{10} -2.39841i q^{11} +(-1.45279 - 0.943085i) q^{12} +(-0.414577 + 0.239356i) q^{13} +(1.17084 - 2.02795i) q^{14} +(-1.72969 - 0.0903420i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.40013 - 1.38572i) q^{17} +(-1.22118 - 2.74020i) q^{18} +(0.994947 + 4.24383i) q^{19} +1.00000i q^{20} +(3.61351 - 1.84198i) q^{21} +(-2.07709 - 1.19921i) q^{22} +(1.80040 - 1.03946i) q^{23} +(-1.54313 + 0.786608i) q^{24} +(0.500000 + 0.866025i) q^{25} +0.478712i q^{26} +(0.810128 - 5.13261i) q^{27} +(-1.17084 - 2.02795i) q^{28} +(-0.313727 - 0.543392i) q^{29} +(-0.943085 + 1.45279i) q^{30} +2.05113i q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.88661 - 3.70106i) q^{33} +(-2.40013 + 1.38572i) q^{34} +(-2.02795 - 1.17084i) q^{35} +(-2.98368 - 0.312528i) q^{36} -5.67577i q^{37} +(4.17274 + 1.26026i) q^{38} +(-0.451467 + 0.695467i) q^{39} +(0.866025 + 0.500000i) q^{40} +(1.04624 - 1.81214i) q^{41} +(0.211552 - 4.05038i) q^{42} +(-3.77271 + 6.53452i) q^{43} +(-2.07709 + 1.19921i) q^{44} +(-2.74020 + 1.22118i) q^{45} -2.07892i q^{46} +(1.94389 - 1.12231i) q^{47} +(-0.0903420 + 1.72969i) q^{48} -1.51654 q^{49} +1.00000 q^{50} +(-4.79373 - 0.250377i) q^{51} +(0.414577 + 0.239356i) q^{52} +(6.64114 + 11.5028i) q^{53} +(-4.03991 - 3.26790i) q^{54} +(-1.19921 + 2.07709i) q^{55} -2.34168 q^{56} +(4.87356 + 5.76614i) q^{57} -0.627455 q^{58} +(-3.13769 + 5.43465i) q^{59} +(0.786608 + 1.54313i) q^{60} +(1.25195 + 2.16845i) q^{61} +(1.77633 + 1.02556i) q^{62} +(4.12720 - 5.68484i) q^{63} +1.00000 q^{64} +0.478712 q^{65} +(-4.14852 - 0.216677i) q^{66} +(11.3258 - 6.53894i) q^{67} +2.77143i q^{68} +(1.96060 - 3.02023i) q^{69} +(-2.02795 + 1.17084i) q^{70} +(-2.68385 + 4.64856i) q^{71} +(-1.76250 + 2.42768i) q^{72} +(-5.81045 + 10.0640i) q^{73} +(-4.91536 - 2.83789i) q^{74} +(1.45279 + 0.943085i) q^{75} +(3.17779 - 2.98356i) q^{76} -5.61632i q^{77} +(0.376559 + 0.738715i) q^{78} +(10.1589 + 5.86527i) q^{79} +(0.866025 - 0.500000i) q^{80} +(-2.78722 - 8.55753i) q^{81} +(-1.04624 - 1.81214i) q^{82} +11.3081i q^{83} +(-3.40196 - 2.20840i) q^{84} +(1.38572 + 2.40013i) q^{85} +(3.77271 + 6.53452i) q^{86} +(-0.911558 - 0.591743i) q^{87} +2.39841i q^{88} +(-4.97362 - 8.61457i) q^{89} +(-0.312528 + 2.98368i) q^{90} +(-0.970806 + 0.560495i) q^{91} +(-1.80040 - 1.03946i) q^{92} +(1.61344 + 3.16516i) q^{93} -2.24461i q^{94} +(1.26026 - 4.17274i) q^{95} +(1.45279 + 0.943085i) q^{96} +(7.49209 + 4.32556i) q^{97} +(-0.758271 + 1.31336i) q^{98} +(-5.82257 - 4.22719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9	\( 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9} + 2 q^{12} + 18 q^{13} - 6 q^{14} - 12 q^{16} - 12 q^{17} - 2 q^{18} + 6 q^{19} + 6 q^{21} + 18 q^{22} - 2 q^{24} + 12 q^{25} - 28 q^{27} + 6 q^{28} + 12 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 6 q^{38} + 40 q^{39} - 6 q^{41} - 6 q^{42} - 22 q^{43} + 18 q^{44} + 8 q^{45} - 12 q^{47} - 4 q^{48} + 12 q^{49} + 24 q^{50} - 4 q^{51} - 18 q^{52} - 8 q^{53} - 32 q^{54} + 12 q^{56} - 20 q^{57} - 26 q^{59} + 22 q^{61} + 18 q^{62} + 30 q^{63} + 24 q^{64} - 8 q^{65} - 22 q^{66} - 48 q^{67} + 64 q^{69} - 24 q^{71} - 2 q^{72} - 8 q^{73} - 30 q^{74} - 2 q^{75} - 12 q^{76} + 2 q^{78} + 18 q^{79} - 6 q^{81} + 6 q^{82} - 12 q^{84} + 22 q^{86} - 24 q^{87} - 28 q^{89} + 16 q^{90} + 18 q^{91} + 14 q^{93} - 2 q^{96} + 6 q^{97} + 6 q^{98} - 52 q^{99}+O(q^{100}) \) 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9 + 2 * q^12 + 18 * q^13 - 6 * q^14 - 12 * q^16 - 12 * q^17 - 2 * q^18 + 6 * q^19 + 6 * q^21 + 18 * q^22 - 2 * q^24 + 12 * q^25 - 28 * q^27 + 6 * q^28 + 12 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 6 * q^38 + 40 * q^39 - 6 * q^41 - 6 * q^42 - 22 * q^43 + 18 * q^44 + 8 * q^45 - 12 * q^47 - 4 * q^48 + 12 * q^49 + 24 * q^50 - 4 * q^51 - 18 * q^52 - 8 * q^53 - 32 * q^54 + 12 * q^56 - 20 * q^57 - 26 * q^59 + 22 * q^61 + 18 * q^62 + 30 * q^63 + 24 * q^64 - 8 * q^65 - 22 * q^66 - 48 * q^67 + 64 * q^69 - 24 * q^71 - 2 * q^72 - 8 * q^73 - 30 * q^74 - 2 * q^75 - 12 * q^76 + 2 * q^78 + 18 * q^79 - 6 * q^81 + 6 * q^82 - 12 * q^84 + 22 * q^86 - 24 * q^87 - 28 * q^89 + 16 * q^90 + 18 * q^91 + 14 * q^93 - 2 * q^96 + 6 * q^97 + 6 * q^98 - 52 * q^99

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