LMFDB - Embedded newform 570.2.s.a.221.1

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			221.1
Character	$\chi$	$=$	570.221
Dual form			570.2.s.a.521.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.62233 + 0.606673i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.33656 + 1.10164i) q^{6} -1.76552 q^{7} +1.00000 q^{8} +(2.26390 - 1.96845i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.62233 + 0.606673i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.33656 + 1.10164i) q^{6} -1.76552 q^{7} +1.00000 q^{8} +(2.26390 - 1.96845i) q^{9} +(-0.866025 - 0.500000i) q^{10} +3.02678i q^{11} +(0.285770 - 1.70831i) q^{12} +(-3.25407 - 1.87874i) q^{13} +(0.882761 + 1.52899i) q^{14} +(-1.10164 + 1.33656i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.76712 - 1.59760i) q^{17} +(-2.83667 - 0.976368i) q^{18} +(4.29047 - 0.769325i) q^{19} +1.00000i q^{20} +(2.86426 - 1.07109i) q^{21} +(2.62126 - 1.51339i) q^{22} +(-0.844837 - 0.487767i) q^{23} +(-1.62233 + 0.606673i) q^{24} +(0.500000 - 0.866025i) q^{25} +3.75748i q^{26} +(-2.47858 + 4.56691i) q^{27} +(0.882761 - 1.52899i) q^{28} +(3.19725 - 5.53779i) q^{29} +(1.70831 + 0.285770i) q^{30} -7.64334i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.83626 - 4.91042i) q^{33} +(-2.76712 - 1.59760i) q^{34} +(-1.52899 + 0.882761i) q^{35} +(0.572776 + 2.94481i) q^{36} -8.22349i q^{37} +(-2.81149 - 3.33099i) q^{38} +(6.41896 + 1.07377i) q^{39} +(0.866025 - 0.500000i) q^{40} +(-0.0664620 - 0.115116i) q^{41} +(-2.35972 - 1.94497i) q^{42} +(-4.92098 - 8.52339i) q^{43} +(-2.62126 - 1.51339i) q^{44} +(0.976368 - 2.83667i) q^{45} +0.975534i q^{46} +(7.38774 + 4.26531i) q^{47} +(1.33656 + 1.10164i) q^{48} -3.88293 q^{49} -1.00000 q^{50} +(-3.51996 + 4.27057i) q^{51} +(3.25407 - 1.87874i) q^{52} +(5.92218 - 10.2575i) q^{53} +(5.19435 - 0.136943i) q^{54} +(1.51339 + 2.62126i) q^{55} -1.76552 q^{56} +(-6.49382 + 3.85101i) q^{57} -6.39449 q^{58} +(-3.82758 - 6.62956i) q^{59} +(-0.606673 - 1.62233i) q^{60} +(-1.00006 + 1.73216i) q^{61} +(-6.61932 + 3.82167i) q^{62} +(-3.99696 + 3.47533i) q^{63} +1.00000 q^{64} -3.75748 q^{65} +(-3.33442 + 4.04546i) q^{66} +(0.649931 + 0.375238i) q^{67} +3.19520i q^{68} +(1.66652 + 0.278778i) q^{69} +(1.52899 + 0.882761i) q^{70} +(8.14418 + 14.1061i) q^{71} +(2.26390 - 1.96845i) q^{72} +(0.477929 + 0.827798i) q^{73} +(-7.12175 + 4.11174i) q^{74} +(-0.285770 + 1.70831i) q^{75} +(-1.47898 + 4.10032i) q^{76} -5.34384i q^{77} +(-2.27956 - 6.09587i) q^{78} +(2.26576 - 1.30814i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(1.25044 - 8.91271i) q^{81} +(-0.0664620 + 0.115116i) q^{82} -4.67129i q^{83} +(-0.504532 + 3.01607i) q^{84} +(1.59760 - 2.76712i) q^{85} +(-4.92098 + 8.52339i) q^{86} +(-1.82735 + 10.9238i) q^{87} +3.02678i q^{88} +(4.36131 - 7.55401i) q^{89} +(-2.94481 + 0.572776i) q^{90} +(5.74514 + 3.31696i) q^{91} +(0.844837 - 0.487767i) q^{92} +(4.63701 + 12.4000i) q^{93} -8.53062i q^{94} +(3.33099 - 2.81149i) q^{95} +(0.285770 - 1.70831i) q^{96} +(-12.4237 + 7.17285i) q^{97} +(1.94147 + 3.36272i) q^{98} +(5.95804 + 6.85230i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9}+O(q^{10}) $ 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * q^9	$ 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 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} + 4 q^{24} + 12 q^{25} + 28 q^{27} + 6 q^{28} - 12 q^{32} - 22 q^{33} - 12 q^{34} + 2 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} - 2 q^{48} + 12 q^{49} - 24 q^{50} - 20 q^{51} - 18 q^{52} + 8 q^{53} + 4 q^{54} - 12 q^{56} + 26 q^{59} + 22 q^{61} - 18 q^{62} + 6 q^{63} + 24 q^{64} + 8 q^{65} + 8 q^{66} - 48 q^{67} - 64 q^{69} + 24 q^{71} - 4 q^{72} - 8 q^{73} + 30 q^{74} + 2 q^{75} - 12 q^{76} - 38 q^{78} + 18 q^{79} - 12 q^{81} + 6 q^{82} + 12 q^{84} - 22 q^{86} - 24 q^{87} + 28 q^{89} + 8 q^{90} + 18 q^{91} + 2 q^{93} - 2 q^{96} + 6 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) $ 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * 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 + 4 * q^24 + 12 * q^25 + 28 * q^27 + 6 * q^28 - 12 * q^32 - 22 * q^33 - 12 * q^34 + 2 * 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 - 2 * q^48 + 12 * q^49 - 24 * q^50 - 20 * q^51 - 18 * q^52 + 8 * q^53 + 4 * q^54 - 12 * q^56 + 26 * q^59 + 22 * q^61 - 18 * q^62 + 6 * q^63 + 24 * q^64 + 8 * q^65 + 8 * q^66 - 48 * q^67 - 64 * q^69 + 24 * q^71 - 4 * q^72 - 8 * q^73 + 30 * q^74 + 2 * q^75 - 12 * q^76 - 38 * q^78 + 18 * q^79 - 12 * q^81 + 6 * q^82 + 12 * q^84 - 22 * q^86 - 24 * q^87 + 28 * q^89 + 8 * q^90 + 18 * q^91 + 2 * q^93 - 2 * q^96 + 6 * q^97 - 6 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−1.62233	+	0.606673i	−0.936651	+	0.350263i
$3$	−1.62233	+	0.606673i	−0.936651	+	0.350263i
$4$	−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
$6$	1.33656	+	1.10164i	0.545648	+	0.449743i
$7$	−1.76552			−0.667305			−0.333652	−	0.942696i	$-0.608281\pi$
$7$	−1.76552			−0.667305			−0.333652	+	0.942696i	$0.608281\pi$
$8$	1.00000			0.353553
$9$	2.26390	−	1.96845i	0.754632	−	0.656148i
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$			3.02678i			0.912607i	0.889824	+	0.456304i	$0.150827\pi$
$11$			3.02678i			0.912607i	−0.889824	+	0.456304i	$0.849173\pi$
$12$	0.285770	−	1.70831i	0.0824946	−	0.493148i
$13$	−3.25407	−	1.87874i	−0.902518	−	0.521069i	−0.0245016	−	0.999700i	$-0.507800\pi$
$13$	−3.25407	−	1.87874i	−0.902518	−	0.521069i	−0.878016	+	0.478631i	$0.841133\pi$
$14$	0.882761	+	1.52899i	0.235928	+	0.408639i
$15$	−1.10164	+	1.33656i	−0.284442	+	0.345098i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.76712	−	1.59760i	0.671126	−	0.387475i	−0.125377	−	0.992109i	$-0.540014\pi$
$17$	2.76712	−	1.59760i	0.671126	−	0.387475i	0.796503	+	0.604634i	$0.206681\pi$
$18$	−2.83667	−	0.976368i	−0.668610	−	0.230132i
$19$	4.29047	−	0.769325i	0.984301	−	0.176495i
$19$	4.29047	−	0.769325i	0.984301	−	0.176495i
$20$			1.00000i			0.223607i
$21$	2.86426	−	1.07109i	0.625032	−	0.233732i
$22$	2.62126	−	1.51339i	0.558855	−	0.322655i
$23$	−0.844837	−	0.487767i	−0.176161	−	0.101706i	0.409327	−	0.912388i	$-0.365764\pi$
$23$	−0.844837	−	0.487767i	−0.176161	−	0.101706i	−0.585488	+	0.810681i	$0.699097\pi$
$24$	−1.62233	+	0.606673i	−0.331156	+	0.123837i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$			3.75748i			0.736903i
$27$	−2.47858	+	4.56691i	−0.477002	+	0.878902i
$28$	0.882761	−	1.52899i	0.166826	−	0.288951i
$29$	3.19725	−	5.53779i	0.593714	−	1.02834i	−0.400014	−	0.916509i	$-0.630995\pi$
$29$	3.19725	−	5.53779i	0.593714	−	1.02834i	0.993727	−	0.111833i	$-0.0356721\pi$
$30$	1.70831	+	0.285770i	0.311894	+	0.0521741i
$31$		−	7.64334i		−	1.37278i	−0.727232	−	0.686392i	$-0.759194\pi$
$31$		−	7.64334i		−	1.37278i	0.727232	−	0.686392i	$-0.240806\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.83626	−	4.91042i	−0.319652	−	0.854795i
$34$	−2.76712	−	1.59760i	−0.474558	−	0.273986i
$35$	−1.52899	+	0.882761i	−0.258446	+	0.149214i
$36$	0.572776	+	2.94481i	0.0954627	+	0.490802i
$37$		−	8.22349i		−	1.35193i	−0.736932	−	0.675966i	$-0.763726\pi$
$37$		−	8.22349i		−	1.35193i	0.736932	−	0.675966i	$-0.236274\pi$
$38$	−2.81149	−	3.33099i	−0.456084	−	0.540359i
$39$	6.41896	+	1.07377i	1.02786	+	0.171941i
$40$	0.866025	−	0.500000i	0.136931	−	0.0790569i
$41$	−0.0664620	−	0.115116i	−0.0103796	−	0.0179780i	0.860789	−	0.508962i	$-0.169971\pi$
$41$	−0.0664620	−	0.115116i	−0.0103796	−	0.0179780i	−0.871169	+	0.490984i	$0.836637\pi$
$42$	−2.35972	−	1.94497i	−0.364113	−	0.300115i
$43$	−4.92098	−	8.52339i	−0.750443	−	1.29981i	−0.947608	−	0.319435i	$-0.896507\pi$
$43$	−4.92098	−	8.52339i	−0.750443	−	1.29981i	0.197165	−	0.980370i	$-0.436826\pi$
$44$	−2.62126	−	1.51339i	−0.395170	−	0.228152i
$45$	0.976368	−	2.83667i	0.145548	−	0.422866i
$46$			0.975534i			0.143835i
$47$	7.38774	+	4.26531i	1.07761	+	0.622160i	0.930251	−	0.366923i	$-0.119589\pi$
$47$	7.38774	+	4.26531i	1.07761	+	0.622160i	0.147361	+	0.989083i	$0.452922\pi$
$48$	1.33656	+	1.10164i	0.192916	+	0.159008i
$49$	−3.88293			−0.554705
$50$	−1.00000			−0.141421
$51$	−3.51996	+	4.27057i	−0.492893	+	0.597999i
$52$	3.25407	−	1.87874i	0.451259	−	0.260534i
$53$	5.92218	−	10.2575i	0.813474	−	1.40898i	−0.0969441	−	0.995290i	$-0.530907\pi$
$53$	5.92218	−	10.2575i	0.813474	−	1.40898i	0.910418	−	0.413689i	$-0.135760\pi$
$54$	5.19435	−	0.136943i	0.706861	−	0.0186356i
$55$	1.51339	+	2.62126i	0.204065	+	0.353451i
$56$	−1.76552			−0.235928
$57$	−6.49382	+	3.85101i	−0.860128	+	0.510079i
$58$	−6.39449			−0.839638
$59$	−3.82758	−	6.62956i	−0.498308	−	0.863095i	0.501690	−	0.865047i	$-0.332712\pi$
$59$	−3.82758	−	6.62956i	−0.498308	−	0.863095i	−0.999998	+	0.00195269i	$0.999378\pi$
$60$	−0.606673	−	1.62233i	−0.0783212	−	0.209442i
$61$	−1.00006	+	1.73216i	−0.128045	+	0.221780i	−0.922919	−	0.384994i	$-0.874204\pi$
$61$	−1.00006	+	1.73216i	−0.128045	+	0.221780i	0.794874	+	0.606774i	$0.207537\pi$
$62$	−6.61932	+	3.82167i	−0.840655	+	0.485352i
$63$	−3.99696	+	3.47533i	−0.503569	+	0.437851i
$64$	1.00000			0.125000
$65$	−3.75748			−0.466058
$66$	−3.33442	+	4.04546i	−0.410439	+	0.497962i
$67$	0.649931	+	0.375238i	0.0794017	+	0.0458426i	0.539175	−	0.842194i	$-0.318736\pi$
$67$	0.649931	+	0.375238i	0.0794017	+	0.0458426i	−0.459773	+	0.888036i	$0.652069\pi$
$68$			3.19520i			0.387475i
$69$	1.66652	+	0.278778i	0.200625	+	0.0335609i
$70$	1.52899	+	0.882761i	0.182749	+	0.105510i
$71$	8.14418	+	14.1061i	0.966536	+	1.67409i	0.705430	+	0.708779i	$0.250754\pi$
$71$	8.14418	+	14.1061i	0.966536	+	1.67409i	0.261106	+	0.965310i	$0.415913\pi$
$72$	2.26390	−	1.96845i	0.266803	−	0.231984i
$73$	0.477929	+	0.827798i	0.0559374	+	0.0968864i	0.892638	−	0.450774i	$-0.148852\pi$
$73$	0.477929	+	0.827798i	0.0559374	+	0.0968864i	−0.836701	+	0.547660i	$0.815519\pi$
$74$	−7.12175	+	4.11174i	−0.827886	+	0.477980i
$75$	−0.285770	+	1.70831i	−0.0329978	+	0.197259i
$76$	−1.47898	+	4.10032i	−0.169651	+	0.470339i
$77$		−	5.34384i		−	0.608987i
$78$	−2.27956	−	6.09587i	−0.258110	−	0.690221i
$79$	2.26576	−	1.30814i	0.254918	−	0.147177i	−0.367096	−	0.930183i	$-0.619648\pi$
$79$	2.26576	−	1.30814i	0.254918	−	0.147177i	0.622014	+	0.783006i	$0.286315\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	1.25044	−	8.91271i	0.138938	−	0.990301i
$82$	−0.0664620	+	0.115116i	−0.00733950	+	0.0127124i
$83$		−	4.67129i		−	0.512741i	−0.966579	−	0.256370i	$-0.917473\pi$
$83$		−	4.67129i		−	0.512741i	0.966579	−	0.256370i	$-0.0825267\pi$
$84$	−0.504532	+	3.01607i	−0.0550490	+	0.329080i
$85$	1.59760	−	2.76712i	0.173284	−	0.300137i
$86$	−4.92098	+	8.52339i	−0.530643	+	0.919101i
$87$	−1.82735	+	10.9238i	−0.195913	+	1.17115i
$88$			3.02678i			0.322655i
$89$	4.36131	−	7.55401i	0.462298	−	0.800724i	−0.536777	−	0.843724i	$-0.680358\pi$
$89$	4.36131	−	7.55401i	0.462298	−	0.800724i	0.999075	+	0.0430003i	$0.0136917\pi$
$90$	−2.94481	+	0.572776i	−0.310411	+	0.0603759i
$91$	5.74514	+	3.31696i	0.602254	+	0.347712i
$92$	0.844837	−	0.487767i	0.0880803	−	0.0508532i
$93$	4.63701	+	12.4000i	0.480835	+	1.28582i
$94$		−	8.53062i		−	0.879867i
$95$	3.33099	−	2.81149i	0.341753	−	0.288453i
$96$	0.285770	−	1.70831i	0.0291662	−	0.174354i
$97$	−12.4237	+	7.17285i	−1.26144	+	0.728292i	−0.973353	−	0.229312i	$-0.926352\pi$
$97$	−12.4237	+	7.17285i	−1.26144	+	0.728292i	−0.288087	+	0.957604i	$0.593019\pi$
$98$	1.94147	+	3.36272i	0.196118	+	0.339686i
$99$	5.95804	+	6.85230i	0.598806	+	0.688682i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	13.7972	+	7.96584i	1.37288	+	0.792630i	0.991289	−	0.131703i	$-0.0420444\pi$
$101$	13.7972	+	7.96584i	1.37288	+	0.792630i	0.381587	+	0.924333i	$0.375378\pi$
$102$	5.45840	+	0.913090i	0.540462	+	0.0904094i
$103$			6.24459i			0.615298i	0.951500	+	0.307649i	$0.0995422\pi$
$103$			6.24459i			0.615298i	−0.951500	+	0.307649i	$0.900458\pi$
$104$	−3.25407	−	1.87874i	−0.319088	−	0.184226i
$105$	1.94497	−	2.35972i	0.189810	−	0.230285i
$106$	−11.8444			−1.15043
$107$	−2.50860			−0.242516			−0.121258	−	0.992621i	$-0.538693\pi$
$107$	−2.50860			−0.242516			−0.121258	+	0.992621i	$0.538693\pi$
$108$	−2.71577	−	4.42997i	−0.261325	−	0.426274i
$109$	−0.194529	+	0.112311i	−0.0186325	+	0.0107575i	−0.509287	−	0.860597i	$-0.670091\pi$
$109$	−0.194529	+	0.112311i	−0.0186325	+	0.0107575i	0.490655	+	0.871354i	$0.336758\pi$
$110$	1.51339	−	2.62126i	0.144296	−	0.249928i
$111$	4.98897	+	13.3412i	0.473532	+	1.26629i
$112$	0.882761	+	1.52899i	0.0834131	+	0.144476i
$113$	−12.6900			−1.19377			−0.596887	−	0.802326i	$-0.703596\pi$
$113$	−12.6900			−1.19377			−0.596887	+	0.802326i	$0.703596\pi$
$114$	6.58198	+	3.69831i	0.616459	+	0.346378i
$115$	−0.975534			−0.0909690
$116$	3.19725	+	5.53779i	0.296857	+	0.514171i
$117$	−11.0651	+	2.15220i	−1.02297	+	0.198971i
$118$	−3.82758	+	6.62956i	−0.352357	+	0.610300i
$119$	−4.88542	+	2.82060i	−0.447845	+	0.258564i
$120$	−1.10164	+	1.33656i	−0.100566	+	0.122011i
$121$	1.83863			0.167148
$122$	2.00013			0.181083
$123$	0.177661	+	0.146435i	0.0160191	+	0.0132036i
$124$	6.61932	+	3.82167i	0.594433	+	0.343196i
$125$		−	1.00000i		−	0.0894427i
$126$	5.00821	+	1.72380i	0.446166	+	0.153568i
$127$	3.90891	+	2.25681i	0.346860	+	0.200260i	0.663301	−	0.748352i	$-0.269155\pi$
$127$	3.90891	+	2.25681i	0.346860	+	0.200260i	−0.316442	+	0.948612i	$0.602488\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	13.1544	+	10.8423i	1.15818	+	0.954612i
$130$	1.87874	+	3.25407i	0.164776	+	0.285401i
$131$	3.84003	−	2.21704i	0.335505	−	0.193704i	−0.322778	−	0.946475i	$-0.604617\pi$
$131$	3.84003	−	2.21704i	0.335505	−	0.193704i	0.658282	+	0.752771i	$0.271283\pi$
$132$	5.17068	+	0.864960i	0.450050	+	0.0752851i
$133$	−7.57492	+	1.35826i	−0.656829	+	0.117776i
$134$		−	0.750475i		−	0.0648312i
$135$	0.136943	+	5.19435i	0.0117862	+	0.447058i
$136$	2.76712	−	1.59760i	0.237279	−	0.136993i
$137$	12.7182	+	7.34284i	1.08659	+	0.627341i	0.932666	−	0.360742i	$-0.117476\pi$
$137$	12.7182	+	7.34284i	1.08659	+	0.627341i	0.153921	+	0.988083i	$0.450810\pi$
$138$	−0.591830	−	1.58264i	−0.0503799	−	0.134723i
$139$	−9.42690	+	16.3279i	−0.799579	+	1.38491i	0.120311	+	0.992736i	$0.461611\pi$
$139$	−9.42690	+	16.3279i	−0.799579	+	1.38491i	−0.919890	+	0.392176i	$0.871722\pi$
$140$		−	1.76552i		−	0.149214i
$141$	−14.5730	−	2.43779i	−1.22727	−	0.205299i
$142$	8.14418	−	14.1061i	0.683444	−	1.18376i
$143$	5.68653	−	9.84935i	0.475531	−	0.823644i
$144$	−2.83667	−	0.976368i	−0.236389	−	0.0813640i
$145$		−	6.39449i		−	0.531033i
$146$	0.477929	−	0.827798i	0.0395537	−	0.0685090i
$147$	6.29939	−	2.35567i	0.519565	−	0.194292i
$148$	7.12175	+	4.11174i	0.585404	+	0.337983i
$149$	−2.37618	+	1.37189i	−0.194664	+	0.112390i	−0.594164	−	0.804344i	$-0.702517\pi$
$149$	−2.37618	+	1.37189i	−0.194664	+	0.112390i	0.399500	+	0.916733i	$0.369184\pi$
$150$	1.62233	−	0.606673i	0.132463	−	0.0495347i
$151$		−	22.7604i		−	1.85221i	−0.377263	−	0.926106i	$-0.623135\pi$
$151$		−	22.7604i		−	1.85221i	0.377263	−	0.926106i	$-0.376865\pi$
$152$	4.29047	−	0.769325i	0.348003	−	0.0624005i
$153$	3.11969	−	9.06373i	0.252212	−	0.732759i
$154$	−4.62790	+	2.67192i	−0.372927	+	0.215309i
$155$	−3.82167	−	6.61932i	−0.306964	−	0.531677i
$156$	−4.13939	+	5.02209i	−0.331417	+	0.402089i
$157$	4.01105	+	6.94734i	0.320117	+	0.554458i	0.980512	−	0.196460i	$-0.0629446\pi$
$157$	4.01105	+	6.94734i	0.320117	+	0.554458i	−0.660395	+	0.750918i	$0.729611\pi$
$158$	−2.26576	−	1.30814i	−0.180254	−	0.104070i
$159$	−3.38476	+	20.2339i	−0.268429	+	1.60465i
$160$			1.00000i			0.0790569i
$161$	1.49158	+	0.861163i	0.117553	+	0.0678692i
$162$	−8.34386	+	3.37344i	−0.655555	+	0.265042i
$163$	−3.70552			−0.290239			−0.145119	−	0.989414i	$-0.546357\pi$
$163$	−3.70552			−0.290239			−0.145119	+	0.989414i	$0.546357\pi$
$164$	0.132924			0.0103796
$165$	−4.04546	−	3.33442i	−0.314939	−	0.259584i
$166$	−4.04546	+	2.33564i	−0.313988	+	0.181281i
$167$	−0.0687715	+	0.119116i	−0.00532170	+	0.00921746i	−0.868674	−	0.495384i	$-0.835027\pi$
$167$	−0.0687715	+	0.119116i	−0.00532170	+	0.00921746i	0.863352	+	0.504602i	$0.168361\pi$
$168$	2.86426	−	1.07109i	0.220982	−	0.0826368i
$169$	0.559332	+	0.968791i	0.0430255	+	0.0745224i
$170$	−3.19520			−0.245061
$171$	8.19880	−	10.1872i	0.626978	−	0.779037i
$172$	9.84197			0.750443
$173$	−1.62087	−	2.80743i	−0.123232	−	0.213445i	0.797808	−	0.602911i	$-0.205993\pi$
$173$	−1.62087	−	2.80743i	−0.123232	−	0.213445i	−0.921041	+	0.389467i	$0.872659\pi$
$174$	10.3740	−	3.87937i	0.786448	−	0.294094i
$175$	−0.882761	+	1.52899i	−0.0667305	+	0.115581i
$176$	2.62126	−	1.51339i	0.197585	−	0.114076i
$177$	10.2316	+	8.43323i	0.769051	+	0.633880i
$178$	−8.72262			−0.653788
$179$	−18.0338			−1.34791			−0.673954	−	0.738773i	$-0.735406\pi$
$179$	−18.0338			−1.34791			−0.673954	+	0.738773i	$0.735406\pi$
$180$	1.96845	+	2.26390i	0.146719	+	0.168741i
$181$	9.17503	+	5.29721i	0.681974	+	0.393738i	0.800599	−	0.599201i	$-0.204515\pi$
$181$	9.17503	+	5.29721i	0.681974	+	0.393738i	−0.118624	+	0.992939i	$0.537848\pi$
$182$		−	6.63392i		−	0.491739i
$183$	0.571575	−	3.41684i	0.0422521	−	0.252580i
$184$	−0.844837	−	0.487767i	−0.0622822	−	0.0359586i
$185$	−4.11174	−	7.12175i	−0.302301	−	0.523601i
$186$	8.42021	−	10.2158i	0.617400	−	0.749056i
$187$	4.83557	+	8.37546i	0.353612	+	0.612474i
$188$	−7.38774	+	4.26531i	−0.538806	+	0.311080i
$189$	4.37598	−	8.06298i	0.318306	−	0.586495i
$190$	−4.10032	−	1.47898i	−0.297468	−	0.107297i
$191$		−	5.83776i		−	0.422406i	−0.977442	−	0.211203i	$-0.932262\pi$
$191$		−	5.83776i		−	0.422406i	0.977442	−	0.211203i	$-0.0677380\pi$
$192$	−1.62233	+	0.606673i	−0.117081	+	0.0437829i
$193$	12.2299	−	7.06095i	0.880329	−	0.508258i	0.00956246	−	0.999954i	$-0.496956\pi$
$193$	12.2299	−	7.06095i	0.880329	−	0.508258i	0.870767	+	0.491696i	$0.163623\pi$
$194$	12.4237	+	7.17285i	0.891973	+	0.514981i
$195$	6.09587	−	2.27956i	0.436534	−	0.163243i
$196$	1.94147	−	3.36272i	0.138676	−	0.240194i
$197$			0.287064i			0.0204525i	0.999948	+	0.0102262i	$0.00325517\pi$
$197$			0.287064i			0.0204525i	−0.999948	+	0.0102262i	$0.996745\pi$
$198$	2.95525	−	8.58597i	0.210020	−	0.610178i
$199$	9.44058	−	16.3516i	0.669225	−	1.15913i	−0.308896	−	0.951096i	$-0.599960\pi$
$199$	9.44058	−	16.3516i	0.669225	−	1.15913i	0.978121	−	0.208036i	$-0.0667071\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−1.28205	−	0.214463i	−0.0904287	−	0.0151271i
$202$		−	15.9317i		−	1.12095i
$203$	−5.64481	+	9.77709i	−0.396188	+	0.686217i
$204$	−1.93844	−	5.18366i	−0.135718	−	0.362929i
$205$	−0.115116	−	0.0664620i	−0.00804002	−	0.00464191i
$206$	5.40798	−	3.12230i	0.376791	−	0.217541i
$207$	−2.87276	+	0.558762i	−0.199671	+	0.0388367i
$208$			3.75748i			0.260534i
$209$	2.32857	+	12.9863i	0.161071	+	0.898281i
$210$	−3.01607	−	0.504532i	−0.208128	−	0.0348160i
$211$	−16.5023	+	9.52758i	−1.13606	+	0.655906i	−0.945453	−	0.325760i	$-0.894380\pi$
$211$	−16.5023	+	9.52758i	−1.13606	+	0.655906i	−0.190610	+	0.981666i	$0.561047\pi$
$212$	5.92218	+	10.2575i	0.406737	+	0.704489i
$213$	−21.7703	−	17.9439i	−1.49168	−	1.22950i
$214$	1.25430	+	2.17252i	0.0857423	+	0.148510i
$215$	−8.52339	−	4.92098i	−0.581291	−	0.335608i
$216$	−2.47858	+	4.56691i	−0.168646	+	0.310739i
$217$			13.4945i			0.916065i
$218$	0.194529	+	0.112311i	0.0131751	+	0.00760667i
$219$	−1.27756	−	1.05301i	−0.0863295	−	0.0711560i
$220$	−3.02678			−0.204065
$221$	−12.0059			−0.807604
$222$	9.05933	−	10.9912i	0.608022	−	0.737679i
$223$	−1.45190	+	0.838252i	−0.0972261	+	0.0561335i	−0.547825	−	0.836593i	$-0.684544\pi$
$223$	−1.45190	+	0.838252i	−0.0972261	+	0.0561335i	0.450599	+	0.892727i	$0.351211\pi$
$224$	0.882761	−	1.52899i	0.0589820	−	0.102160i
$225$	−0.572776	−	2.94481i	−0.0381851	−	0.196321i
$226$	6.34499	+	10.9898i	0.422063	+	0.731034i
$227$	−11.2504			−0.746714			−0.373357	−	0.927688i	$-0.621793\pi$
$227$	−11.2504			−0.746714			−0.373357	+	0.927688i	$0.621793\pi$
$228$	−0.0881621	−	7.54932i	−0.00583868	−	0.499966i
$229$	−22.6516			−1.49686			−0.748431	−	0.663213i	$-0.769192\pi$
$229$	−22.6516			−1.49686			−0.748431	+	0.663213i	$0.769192\pi$
$230$	0.487767	+	0.844837i	0.0321624	+	0.0557069i
$231$	3.24196	+	8.66946i	0.213306	+	0.570408i
$232$	3.19725	−	5.53779i	0.209909	−	0.363574i
$233$	9.24441	−	5.33726i	0.605622	−	0.349656i	−0.165628	−	0.986188i	$-0.552965\pi$
$233$	9.24441	−	5.33726i	0.605622	−	0.349656i	0.771250	+	0.636532i	$0.219632\pi$
$234$	7.39640	+	8.50654i	0.483518	+	0.556090i
$235$	8.53062			0.556477
$236$	7.65515			0.498308
$237$	−2.88219	+	3.49680i	−0.187218	+	0.227142i
$238$	4.88542	+	2.82060i	0.316674	+	0.182832i
$239$			21.9874i			1.42225i	0.703066	+	0.711124i	$0.251814\pi$
$239$			21.9874i			1.42225i	−0.703066	+	0.711124i	$0.748186\pi$
$240$	1.70831	+	0.285770i	0.110271	+	0.0184463i
$241$	1.68423	+	0.972389i	0.108491	+	0.0626371i	0.553263	−	0.833006i	$-0.313382\pi$
$241$	1.68423	+	0.972389i	0.108491	+	0.0626371i	−0.444773	+	0.895643i	$0.646716\pi$
$242$	−0.919316	−	1.59230i	−0.0590958	−	0.102357i
$243$	3.37847	+	15.2179i	0.216729	+	0.976232i
$244$	−1.00006	−	1.73216i	−0.0640225	−	0.110890i
$245$	−3.36272	+	1.94147i	−0.214836	+	0.124036i
$246$	0.0379857	−	0.227076i	0.00242188	−	0.0144778i
$247$	−15.4069	−	5.55724i	−0.980316	−	0.353599i
$248$		−	7.64334i		−	0.485352i
$249$	2.83395	+	7.57836i	0.179594	+	0.480259i
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$	−23.4450	−	13.5360i	−1.47983	−	0.854383i	−0.480095	−	0.877216i	$-0.659398\pi$
$251$	−23.4450	−	13.5360i	−1.47983	−	0.854383i	−0.999739	+	0.0228337i	$0.992731\pi$
$252$	−1.01125	−	5.19913i	−0.0637027	−	0.327515i
$253$	1.47636	−	2.55713i	0.0928180	−	0.160765i
$254$		−	4.51362i		−	0.283210i
$255$	−0.913090	+	5.45840i	−0.0571799	+	0.341818i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.4732	+	21.6042i	−0.778057	+	1.34764i	0.155002	+	0.987914i	$0.450461\pi$
$257$	−12.4732	+	21.6042i	−0.778057	+	1.34764i	−0.933060	+	0.359721i	$0.882872\pi$
$258$	2.81253	−	16.8132i	0.175101	−	1.04674i
$259$			14.5187i			0.902151i
$260$	1.87874	−	3.25407i	0.116515	−	0.201809i
$261$	−3.66261	−	18.8306i	−0.226710	−	1.16558i
$262$	−3.84003	−	2.21704i	−0.237238	−	0.136969i
$263$	−1.88439	+	1.08795i	−0.116196	+	0.0670860i	−0.556972	−	0.830531i	$-0.688037\pi$
$263$	−1.88439	+	1.08795i	−0.116196	+	0.0670860i	0.440775	+	0.897617i	$0.354704\pi$
$264$	−1.83626	−	4.91042i	−0.113014	−	0.302216i
$265$		−	11.8444i		−	0.727593i
$266$	4.96375	+	5.88094i	0.304347	+	0.360584i
$267$	−2.49266	+	14.9010i	−0.152548	+	0.911925i
$268$	−0.649931	+	0.375238i	−0.0397008	+	0.0229213i
$269$	−16.1461	−	27.9659i	−0.984447	−	1.70511i	−0.644368	−	0.764715i	$-0.722880\pi$
$269$	−16.1461	−	27.9659i	−0.984447	−	1.70511i	−0.340079	−	0.940397i	$-0.610454\pi$
$270$	4.42997	−	2.71577i	0.269599	−	0.165276i
$271$	1.71811	+	2.97585i	0.104368	+	0.180770i	0.913480	−	0.406884i	$-0.133385\pi$
$271$	1.71811	+	2.97585i	0.104368	+	0.180770i	−0.809112	+	0.587654i	$0.800052\pi$
$272$	−2.76712	−	1.59760i	−0.167781	−	0.0968687i
$273$	−11.3328	−	1.89577i	−0.685893	−	0.114737i
$274$		−	14.6857i		−	0.887194i
$275$	2.62126	+	1.51339i	0.158068	+	0.0912607i
$276$	−1.07469	+	1.30386i	−0.0646886	+	0.0784830i
$277$	10.6992			0.642854			0.321427	−	0.946934i	$-0.395838\pi$
$277$	10.6992			0.642854			0.321427	+	0.946934i	$0.395838\pi$
$278$	18.8538			1.13078
$279$	−15.0455	−	17.3037i	−0.900750	−	1.03595i
$280$	−1.52899	+	0.882761i	−0.0913744	+	0.0527551i
$281$	5.77482	−	10.0023i	0.344497	−	0.596687i	−0.640765	−	0.767737i	$-0.721383\pi$
$281$	5.77482	−	10.0023i	0.344497	−	0.596687i	0.985262	+	0.171050i	$0.0547161\pi$
$282$	5.17530	+	13.8395i	0.308185	+	0.824128i
$283$	−1.20364	−	2.08476i	−0.0715488	−	0.123926i	0.828031	−	0.560682i	$-0.189461\pi$
$283$	−1.20364	−	2.08476i	−0.0715488	−	0.123926i	−0.899580	+	0.436755i	$0.856128\pi$
$284$	−16.2884			−0.966536
$285$	−3.69831	+	6.58198i	−0.219069	+	0.389883i
$286$	−11.3731			−0.672503
$287$	0.117340	+	0.203239i	0.00692637	+	0.0119968i
$288$	0.572776	+	2.94481i	0.0337512	+	0.173525i
$289$	−3.39535	+	5.88093i	−0.199727	+	0.345937i
$290$	−5.53779	+	3.19725i	−0.325190	+	0.187749i
$291$	15.8038	−	19.1739i	0.926435	−	1.12399i
$292$	−0.955858			−0.0559374
$293$	12.2680			0.716707			0.358353	−	0.933586i	$-0.383338\pi$
$293$	12.2680			0.716707			0.358353	+	0.933586i	$0.383338\pi$
$294$	−5.18976	−	4.27760i	−0.302673	−	0.249474i
$295$	−6.62956	−	3.82758i	−0.385988	−	0.222850i
$296$		−	8.22349i		−	0.477980i
$297$	−13.8230	−	7.50210i	−0.802092	−	0.435316i
$298$	2.37618	+	1.37189i	0.137649	+	0.0794714i
$299$	1.83277	+	3.17446i	0.105992	+	0.183584i
$300$	−1.33656	−	1.10164i	−0.0771662	−	0.0636032i
$301$	8.68810	+	15.0482i	0.500774	+	0.867366i
$302$	−19.7111	+	11.3802i	−1.13424	+	0.654856i
$303$	−27.2163	−	4.55279i	−1.56354	−	0.261551i
$304$	−2.81149	−	3.33099i	−0.161250	−	0.191046i
$305$			2.00013i			0.114527i
$306$	−9.40926	+	1.83013i	−0.537892	+	0.104622i
$307$	18.5689	−	10.7208i	1.05978	−	0.611866i	0.134410	−	0.990926i	$-0.457086\pi$
$307$	18.5689	−	10.7208i	1.05978	−	0.611866i	0.925372	+	0.379060i	$0.123753\pi$
$308$	4.62790	+	2.67192i	0.263699	+	0.152247i
$309$	−3.78843	−	10.1308i	−0.215516	−	0.576320i
$310$	−3.82167	+	6.61932i	−0.217056	+	0.375952i
$311$			2.40119i			0.136159i	0.997680	+	0.0680795i	$0.0216872\pi$
$311$			2.40119i			0.136159i	−0.997680	+	0.0680795i	$0.978313\pi$
$312$	6.41896	+	1.07377i	0.363402	+	0.0607905i
$313$	3.85122	−	6.67052i	0.217684	−	0.377040i	−0.736415	−	0.676530i	$-0.763483\pi$
$313$	3.85122	−	6.67052i	0.217684	−	0.377040i	0.954100	+	0.299490i	$0.0968164\pi$
$314$	4.01105	−	6.94734i	0.226357	−	0.392061i
$315$	−1.72380	+	5.00821i	−0.0971251	+	0.282180i
$316$			2.61627i			0.147177i
$317$	10.1993	−	17.6656i	0.572848	−	0.992201i	−0.423424	−	0.905932i	$-0.639172\pi$
$317$	10.1993	−	17.6656i	0.572848	−	0.992201i	0.996272	−	0.0862698i	$-0.0274947\pi$
$318$	19.2154	−	7.18566i	1.07755	−	0.402952i
$319$	16.7616	+	9.67734i	0.938472	+	0.541827i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	4.06978	−	1.52190i	0.227153	−	0.0849443i
$322$		−	1.72233i		−	0.0959815i
$323$	10.6432	−	8.98327i	0.592203	−	0.499842i
$324$	7.09341	+	5.53927i	0.394078	+	0.307737i
$325$	−3.25407	+	1.87874i	−0.180504	+	0.104214i
$326$	1.85276	+	3.20908i	0.102615	+	0.177734i
$327$	0.247453	−	0.300221i	0.0136842	−	0.0166023i
$328$	−0.0664620	−	0.115116i	−0.00366975	−	0.00635620i
$329$	−13.0432	−	7.53050i	−0.719096	−	0.415170i
$330$	−0.864960	+	5.17068i	−0.0476145	+	0.284637i
$331$		−	25.4526i		−	1.39900i	−0.714631	−	0.699502i	$-0.753405\pi$
$331$		−	25.4526i		−	1.39900i	0.714631	−	0.699502i	$-0.246595\pi$
$332$	4.04546	+	2.33564i	0.222023	+	0.128185i
$333$	−16.1875	−	18.6171i	−0.887069	−	1.02021i
$334$	0.137543			0.00752602
$335$	0.750475			0.0410029
$336$	−2.35972	−	1.94497i	−0.128733	−	0.106107i
$337$	14.8031	−	8.54657i	0.806376	−	0.465561i	−0.0393200	−	0.999227i	$-0.512519\pi$
$337$	14.8031	−	8.54657i	0.806376	−	0.465561i	0.845696	+	0.533665i	$0.179186\pi$
$338$	0.559332	−	0.968791i	0.0304236	−	0.0526953i
$339$	20.5873	−	7.69867i	1.11815	−	0.418134i
$340$	1.59760	+	2.76712i	0.0866420	+	0.150068i
$341$	23.1347			1.25281
$342$	−12.9218	−	2.00676i	−0.698731	−	0.108513i
$343$	19.2141			1.03746
$344$	−4.92098	−	8.52339i	−0.265322	−	0.459551i
$345$	1.58264	−	0.591830i	0.0852062	−	0.0318631i
$346$	−1.62087	+	2.80743i	−0.0871384	+	0.150928i
$347$	0.366418	−	0.211552i	0.0196703	−	0.0113567i	−0.490133	−	0.871648i	$-0.663052\pi$
$347$	0.366418	−	0.211552i	0.0196703	−	0.0113567i	0.509803	+	0.860291i	$0.329718\pi$
$348$	−8.54661	−	7.04443i	−0.458146	−	0.377621i
$349$	−29.6588			−1.58760			−0.793799	−	0.608180i	$-0.791900\pi$
$349$	−29.6588			−1.58760			−0.793799	+	0.608180i	$0.791900\pi$
$350$	1.76552			0.0943711
$351$	16.6455	−	10.2045i	0.888472	−	0.544673i
$352$	−2.62126	−	1.51339i	−0.139714	−	0.0806638i
$353$			29.5091i			1.57061i	0.619110	+	0.785304i	$0.287494\pi$
$353$			29.5091i			1.57061i	−0.619110	+	0.785304i	$0.712506\pi$
$354$	2.18761	−	13.0774i	0.116270	−	0.695056i
$355$	14.1061	+	8.14418i	0.748676	+	0.432248i
$356$	4.36131	+	7.55401i	0.231149	+	0.400362i
$357$	6.21457	−	7.53978i	0.328910	−	0.399048i
$358$	9.01690	+	15.6177i	0.476558	+	0.825422i
$359$	23.2838	−	13.4429i	1.22887	−	0.709490i	0.262079	−	0.965047i	$-0.415592\pi$
$359$	23.2838	−	13.4429i	1.22887	−	0.709490i	0.966794	+	0.255557i	$0.0822587\pi$
$360$	0.976368	−	2.83667i	0.0514591	−	0.149506i
$361$	17.8163	−	6.60153i	0.937699	−	0.347449i
$362$		−	10.5944i		−	0.556830i
$363$	−2.98286	+	1.11545i	−0.156560	+	0.0585458i
$364$	−5.74514	+	3.31696i	−0.301127	+	0.173856i
$365$	0.827798	+	0.477929i	0.0433289	+	0.0250160i
$366$	−3.24486	+	1.21342i	−0.169612	+	0.0634266i
$367$	−4.10312	+	7.10681i	−0.214181	+	0.370973i	−0.953019	−	0.302911i	$-0.902042\pi$
$367$	−4.10312	+	7.10681i	−0.214181	+	0.370973i	0.738838	+	0.673883i	$0.235375\pi$
$368$			0.975534i			0.0508532i
$369$	−0.377062	−	0.129783i	−0.0196291	−	0.00675622i
$370$	−4.11174	+	7.12175i	−0.213759	+	0.370242i
$371$	−10.4557	+	18.1099i	−0.542835	+	0.940218i
$372$	−13.0572	−	2.18423i	−0.676985	−	0.113247i
$373$		−	6.85659i		−	0.355021i	−0.984119	−	0.177510i	$-0.943196\pi$
$373$		−	6.85659i		−	0.355021i	0.984119	−	0.177510i	$-0.0568043\pi$
$374$	4.83557	−	8.37546i	0.250042	−	0.433085i
$375$	0.606673	+	1.62233i	0.0313285	+	0.0837767i
$376$	7.38774	+	4.26531i	0.380993	+	0.219967i
$377$	−20.8081	+	12.0136i	−1.07167	+	0.618731i
$378$	−9.17073	+	0.241776i	−0.471692	+	0.0124356i
$379$		−	4.08608i		−	0.209888i	−0.994478	−	0.104944i	$-0.966534\pi$
$379$		−	4.08608i		−	0.209888i	0.994478	−	0.104944i	$-0.0334663\pi$
$380$	0.769325	+	4.29047i	0.0394655	+	0.220097i
$381$	−7.71068	−	1.28986i	−0.395030	−	0.0660813i
$382$	−5.05565	+	2.91888i	−0.258670	+	0.149343i
$383$	15.1709	+	26.2767i	0.775196	+	1.34268i	0.934684	+	0.355479i	$0.115682\pi$
$383$	15.1709	+	26.2767i	0.775196	+	1.34268i	−0.159489	+	0.987200i	$0.550985\pi$
$384$	1.33656	+	1.10164i	0.0682060	+	0.0562179i
$385$	−2.67192	−	4.62790i	−0.136174	−	0.235860i
$386$	−12.2299	−	7.06095i	−0.622487	−	0.359393i
$387$	−27.9184	−	9.60938i	−1.41917	−	0.488472i
$388$		−	14.3457i		−	0.728292i
$389$	−0.212061	−	0.122434i	−0.0107519	−	0.00620763i	0.494614	−	0.869113i	$-0.335309\pi$
$389$	−0.212061	−	0.122434i	−0.0107519	−	0.00620763i	−0.505366	+	0.862905i	$0.668643\pi$
$390$	−5.02209	−	4.13939i	−0.254304	−	0.209606i
$391$	−3.11702			−0.157635
$392$	−3.88293			−0.196118
$393$	−4.88476	+	5.92641i	−0.246404	+	0.298948i
$394$	0.248605	−	0.143532i	0.0125245	−	0.00723103i
$395$	1.30814	−	2.26576i	0.0658195	−	0.114003i
$396$	−8.91329	+	1.73366i	−0.447910	+	0.0871199i
$397$	15.2157	+	26.3543i	0.763652	+	1.32268i	0.940957	+	0.338527i	$0.109929\pi$
$397$	15.2157	+	26.3543i	0.763652	+	1.32268i	−0.177305	+	0.984156i	$0.556738\pi$
$398$	−18.8812			−0.946427
$399$	11.4650	−	6.79904i	0.573967	−	0.340378i
$400$	−1.00000			−0.0500000
$401$	4.69167	+	8.12622i	0.234291	+	0.405804i	0.959066	−	0.283181i	$-0.0913898\pi$
$401$	4.69167	+	8.12622i	0.234291	+	0.405804i	−0.724775	+	0.688985i	$0.758056\pi$
$402$	0.455293	+	1.21752i	0.0227080	+	0.0607242i
$403$	−14.3598	+	24.8720i	−0.715315	+	1.23896i
$404$	−13.7972	+	7.96584i	−0.686438	+	0.396315i
$405$	−3.37344	−	8.34386i	−0.167627	−	0.414609i
$406$	11.2896			0.560294
$407$	24.8906			1.23378
$408$	−3.51996	+	4.27057i	−0.174264	+	0.211425i
$409$	−2.29099	−	1.32271i	−0.113282	−	0.0654036i	0.442288	−	0.896873i	$-0.354167\pi$
$409$	−2.29099	−	1.32271i	−0.113282	−	0.0654036i	−0.555571	+	0.831469i	$0.687500\pi$
$410$			0.132924i			0.00656465i
$411$	−25.0878	−	4.19672i	−1.23749	−	0.207009i
$412$	−5.40798	−	3.12230i	−0.266432	−	0.153824i
$413$	6.75767	+	11.7046i	0.332523	+	0.575947i
$414$	1.92028	+	2.20851i	0.0943769	+	0.108542i
$415$	−2.33564	−	4.04546i	−0.114652	−	0.198584i
$416$	3.25407	−	1.87874i	0.159544	−	0.0921128i
$417$	5.38784	−	32.2082i	0.263844	−	1.57724i
$418$	10.0822	−	8.50975i	0.493135	−	0.416225i
$419$		−	17.5775i		−	0.858719i	−0.903134	−	0.429359i	$-0.858739\pi$
$419$		−	17.5775i		−	0.858719i	0.903134	−	0.429359i	$-0.141261\pi$
$420$	1.07109	+	2.86426i	0.0522641	+	0.139761i
$421$	17.0375	−	9.83661i	0.830357	−	0.479407i	−0.0236179	−	0.999721i	$-0.507519\pi$
$421$	17.0375	−	9.83661i	0.830357	−	0.479407i	0.853975	+	0.520314i	$0.174185\pi$
$422$	16.5023	+	9.52758i	0.803317	+	0.463796i
$423$	25.1211	−	4.88614i	1.22143	−	0.237572i
$424$	5.92218	−	10.2575i	0.287607	−	0.498149i
$425$		−	3.19520i		−	0.154990i
$426$	−4.65472	+	27.8256i	−0.225522	+	1.34816i
$427$	1.76563	−	3.05817i	0.0854450	−	0.147995i
$428$	1.25430	−	2.17252i	0.0606290	−	0.105012i
$429$	−3.25007	+	19.4287i	−0.156915	+	0.938028i
$430$			9.84197i			0.474622i
$431$	−4.39080	+	7.60508i	−0.211497	+	0.366324i	−0.952183	−	0.305527i	$-0.901167\pi$
$431$	−4.39080	+	7.60508i	−0.211497	+	0.366324i	0.740686	+	0.671851i	$0.234501\pi$
$432$	5.19435	−	0.136943i	0.249913	−	0.00658867i
$433$	22.6952	+	13.1031i	1.09066	+	0.629693i	0.933752	−	0.357920i	$-0.116514\pi$
$433$	22.6952	+	13.1031i	1.09066	+	0.629693i	0.156908	+	0.987613i	$0.449847\pi$
$434$	11.6866	−	6.74724i	0.560973	−	0.323878i
$435$	3.87937	+	10.3740i	0.186001	+	0.497393i
$436$		−	0.224622i		−	0.0107575i
$437$	−4.00000	−	1.44280i	−0.191346	−	0.0690183i
$438$	−0.273155	+	1.63291i	−0.0130519	+	0.0780233i
$439$	−23.3862	+	13.5020i	−1.11616	+	0.644417i	−0.940419	−	0.340018i	$-0.889567\pi$
$439$	−23.3862	+	13.5020i	−1.11616	+	0.644417i	−0.175745	+	0.984436i	$0.556233\pi$
$440$	1.51339	+	2.62126i	0.0721479	+	0.124964i
$441$	−8.79055	+	7.64334i	−0.418598	+	0.363969i
$442$	6.00295	+	10.3974i	0.285531	+	0.494554i
$443$	12.9795	+	7.49371i	0.616674	+	0.356037i	0.775573	−	0.631258i	$-0.217461\pi$
$443$	12.9795	+	7.49371i	0.616674	+	0.356037i	−0.158899	+	0.987295i	$0.550794\pi$
$444$	−14.0483	−	2.35002i	−0.666703	−	0.111527i
$445$		−	8.72262i		−	0.413492i
$446$	1.45190	+	0.838252i	0.0687492	+	0.0396924i
$447$	3.02266	−	3.66722i	0.142967	−	0.173454i
$448$	−1.76552			−0.0834131
$449$	−1.07127			−0.0505565			−0.0252782	−	0.999680i	$-0.508047\pi$
$449$	−1.07127			−0.0505565			−0.0252782	+	0.999680i	$0.508047\pi$
$450$	−2.26390	+	1.96845i	−0.106721	+	0.0927934i
$451$	0.348429	−	0.201166i	0.0164069	−	0.00947252i
$452$	6.34499	−	10.9898i	0.298443	−	0.516919i
$453$	13.8081	+	36.9248i	0.648761	+	1.73488i
$454$	5.62519	+	9.74312i	0.264003	+	0.457267i
$455$	6.63392			0.311003
$456$	−6.49382	+	3.85101i	−0.304101	+	0.180340i
$457$	−7.60858			−0.355914			−0.177957	−	0.984038i	$-0.556949\pi$
$457$	−7.60858			−0.355914			−0.177957	+	0.984038i	$0.556949\pi$
$458$	11.3258	+	19.6169i	0.529220	+	0.916637i
$459$	0.437560	+	16.5970i	0.0204236	+	0.774680i
$460$	0.487767	−	0.844837i	0.0227422	−	0.0393907i
$461$	2.94051	−	1.69770i	0.136953	−	0.0790699i	−0.429958	−	0.902849i	$-0.641472\pi$
$461$	2.94051	−	1.69770i	0.136953	−	0.0790699i	0.566911	+	0.823779i	$0.308138\pi$
$462$	5.88699	−	7.14235i	0.273888	−	0.332292i
$463$	−14.1271			−0.656543			−0.328271	−	0.944583i	$-0.606466\pi$
$463$	−14.1271			−0.656543			−0.328271	+	0.944583i	$0.606466\pi$
$464$	−6.39449			−0.296857
$465$	10.2158	+	8.42021i	0.473745	+	0.390478i
$466$	−9.24441	−	5.33726i	−0.428239	−	0.247244i
$467$		−	11.4238i		−	0.528631i	−0.964436	−	0.264315i	$-0.914854\pi$
$467$		−	11.4238i		−	0.528631i	0.964436	−	0.264315i	$-0.0851460\pi$
$468$	3.66869	−	10.6587i	0.169585	−	0.492700i
$469$	−1.14747	−	0.662490i	−0.0529851	−	0.0305910i
$470$	−4.26531	−	7.38774i	−0.196744	−	0.340771i
$471$	−10.7220	−	8.83747i	−0.494044	−	0.407209i
$472$	−3.82758	−	6.62956i	−0.176178	−	0.305150i
$473$	25.7984	−	14.8947i	1.18621	−	0.684860i
$474$	4.46941	+	0.747651i	0.205287	+	0.0343407i
$475$	1.47898	−	4.10032i	0.0678603	−	0.188136i
$476$		−	5.64119i		−	0.258564i
$477$	−6.78417	−	34.8794i	−0.310626	−	1.59702i
$478$	19.0417	−	10.9937i	0.870946	−	0.502841i
$479$	−31.4439	−	18.1542i	−1.43671	−	0.829485i	−0.439091	−	0.898443i	$-0.644699\pi$
$479$	−31.4439	−	18.1542i	−1.43671	−	0.829485i	−0.997620	+	0.0689574i	$0.978033\pi$
$480$	−0.606673	−	1.62233i	−0.0276907	−	0.0740488i
$481$	−15.4498	+	26.7598i	−0.704450	+	1.22014i
$482$		−	1.94478i		−	0.0885822i
$483$	−2.94227	−	0.492188i	−0.133878	−	0.0223954i
$484$	−0.919316	+	1.59230i	−0.0417871	+	0.0723773i
$485$	−7.17285	+	12.4237i	−0.325702	+	0.564133i
$486$	11.4899	−	10.5348i	0.521192	−	0.477869i
$487$		−	9.01284i		−	0.408411i	−0.978928	−	0.204205i	$-0.934539\pi$
$487$		−	9.01284i		−	0.408411i	0.978928	−	0.204205i	$-0.0654610\pi$
$488$	−1.00006	+	1.73216i	−0.0452707	+	0.0784112i
$489$	6.01157	−	2.24804i	0.271853	−	0.101660i
$490$	3.36272	+	1.94147i	0.151912	+	0.0877065i
$491$	19.3513	−	11.1725i	0.873313	−	0.504208i	0.00486554	−	0.999988i	$-0.498451\pi$
$491$	19.3513	−	11.1725i	0.873313	−	0.504208i	0.868448	+	0.495780i	$0.165118\pi$
$492$	−0.215646	+	0.0806415i	−0.00972209	+	0.00363560i
$493$		−	20.4317i		−	0.920196i
$494$	2.89072	+	16.1214i	0.130060	+	0.725334i
$495$	8.58597	+	2.95525i	0.385911	+	0.132828i
$496$	−6.61932	+	3.82167i	−0.297216	+	0.171598i
$497$	−14.3787	−	24.9047i	−0.644974	−	1.11713i
$498$	5.14608	−	6.24345i	0.230601	−	0.279776i
$499$	19.8988	+	34.4658i	0.890795	+	1.54290i	0.838925	+	0.544248i	$0.183185\pi$
$499$	19.8988	+	34.4658i	0.890795	+	1.54290i	0.0518700	+	0.998654i	$0.483482\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	0.0393056	−	0.234967i	0.00175605	−	0.0104975i
$502$			27.0719i			1.20828i
$503$	29.8559	+	17.2373i	1.33121	+	0.768575i	0.985485	−	0.169761i	$-0.0542995\pi$
$503$	29.8559	+	17.2373i	1.33121	+	0.768575i	0.345726	+	0.938336i	$0.387633\pi$
$504$	−3.99696	+	3.47533i	−0.178039	+	0.154804i
$505$	15.9317			0.708950
$506$	−2.95272			−0.131264
$507$	−1.49516	−	1.23237i	−0.0664024	−	0.0547313i
$508$	−3.90891	+	2.25681i	−0.173430	+	0.100130i
$509$	−18.5767	+	32.1758i	−0.823398	+	1.42617i	0.0797396	+	0.996816i	$0.474591\pi$
$509$	−18.5767	+	32.1758i	−0.823398	+	1.42617i	−0.903138	+	0.429351i	$0.858742\pi$
$510$	5.18366	−	1.93844i	0.229536	−	0.0858356i
$511$	−0.843794	−	1.46149i	−0.0373273	−	0.0646527i
$512$	1.00000			0.0441942
$513$	−7.12083	+	21.5010i	−0.314392	+	0.949293i
$514$	24.9464			1.10034
$515$	3.12230	+	5.40798i	0.137585	+	0.238304i
$516$	−15.9669	+	5.97086i	−0.702903	+	0.262852i
$517$	−12.9101	+	22.3610i	−0.567787	+	0.983437i
$518$	12.5736	−	7.25937i	0.552452	−	0.318959i
$519$	4.33277	+	3.57123i	0.190187	+	0.156759i
$520$	−3.75748			−0.164776
$521$	−18.7548			−0.821664			−0.410832	−	0.911711i	$-0.634762\pi$
$521$	−18.7548			−0.821664			−0.410832	+	0.911711i	$0.634762\pi$
$522$	−14.4765	+	12.5872i	−0.633617	+	0.550927i
$523$	−11.5841	−	6.68808i	−0.506537	−	0.292449i	0.224872	−	0.974388i	$-0.427804\pi$
$523$	−11.5841	−	6.68808i	−0.506537	−	0.292449i	−0.731409	+	0.681939i	$0.761137\pi$
$524$			4.43408i			0.193704i
$525$	0.504532	−	3.01607i	0.0220196	−	0.131632i
$526$	1.88439	+	1.08795i	0.0821633	+	0.0474370i
$527$	−12.2110	−	21.1500i	−0.531919	−	0.921310i
$528$	−3.33442	+	4.04546i	−0.145112	+	0.176056i
$529$	−11.0242	−	19.0944i	−0.479312	−	0.830192i
$530$	−10.2575	+	5.92218i	−0.445558	+	0.257243i
$531$	−21.7152	−	7.47425i	−0.942357	−	0.324355i
$532$	2.61117	−	7.23920i	0.113209	−	0.313859i
$533$			0.499460i			0.0216340i
$534$	14.1510	−	5.29178i	0.612372	−	0.228998i
$535$	−2.17252	+	1.25430i	−0.0939260	+	0.0542282i
$536$	0.649931	+	0.375238i	0.0280727	+	0.0162078i
$537$	29.2567	−	10.9406i	1.26252	−	0.472122i
$538$	−16.1461	+	27.9659i	−0.696109	+	1.20570i
$539$		−	11.7528i		−	0.506227i
$540$	−4.56691	−	2.47858i	−0.196528	−	0.106661i
$541$	−12.9791	+	22.4805i	−0.558017	+	0.966513i	0.439645	+	0.898171i	$0.355104\pi$
$541$	−12.9791	+	22.4805i	−0.558017	+	0.966513i	−0.997662	+	0.0683416i	$0.978229\pi$
$542$	1.71811	−	2.97585i	0.0737990	−	0.127824i
$543$	−18.0986	−	3.02756i	−0.776684	−	0.129925i
$544$			3.19520i			0.136993i
$545$	−0.112311	+	0.194529i	−0.00481088	+	0.00833269i
$546$	4.02462	+	10.7624i	0.172238	+	0.460588i
$547$	−21.9902	−	12.6960i	−0.940232	−	0.542843i	−0.0501992	−	0.998739i	$-0.515986\pi$
$547$	−21.9902	−	12.6960i	−0.940232	−	0.542843i	−0.890033	+	0.455896i	$0.849319\pi$
$548$	−12.7182	+	7.34284i	−0.543293	+	0.313671i
$549$	1.14562	+	5.89000i	0.0488941	+	0.251379i
$550$		−	3.02678i		−	0.129062i
$551$	9.45733	−	26.2194i	0.402896	−	1.11699i
$552$	1.66652	+	0.278778i	0.0709317	+	0.0118656i
$553$	−4.00025	+	2.30954i	−0.170108	+	0.0982118i
$554$	−5.34961	−	9.26579i	−0.227283	−	0.393666i
$555$	10.9912	+	9.05933i	0.466549	+	0.384547i
$556$	−9.42690	−	16.3279i	−0.399790	−	0.692456i
$557$	29.9344	+	17.2826i	1.26836	+	0.732288i	0.974678	−	0.223615i	$-0.0717857\pi$
$557$	29.9344	+	17.2826i	1.26836	+	0.732288i	0.293683	+	0.955903i	$0.405119\pi$
$558$	−7.46271	+	21.6816i	−0.315922	+	0.917857i
$559$			36.9810i			1.56413i
$560$	1.52899	+	0.882761i	0.0646115	+	0.0373035i
$561$	−12.9261	−	10.6541i	−0.545738	−	0.449818i
$562$	−11.5496			−0.487193
$563$	−37.7990			−1.59304			−0.796520	−	0.604612i	$-0.793328\pi$
$563$	−37.7990			−1.59304			−0.796520	+	0.604612i	$0.793328\pi$
$564$	9.39768	−	11.4017i	0.395714	−	0.480097i
$565$	−10.9898	+	6.34499i	−0.462346	+	0.266936i
$566$	−1.20364	+	2.08476i	−0.0505926	+	0.0876290i
$567$	−2.20769	+	15.7356i	−0.0927142	+	0.660832i
$568$	8.14418	+	14.1061i	0.341722	+	0.591880i
$569$	36.6704			1.53730			0.768652	−	0.639667i	$-0.220928\pi$
$569$	36.6704			1.53730			0.768652	+	0.639667i	$0.220928\pi$
$570$	7.54932	−	0.0881621i	0.316206	−	0.00369270i
$571$	29.7545			1.24519			0.622593	−	0.782546i	$-0.286079\pi$
$571$	29.7545			1.24519			0.622593	+	0.782546i	$0.286079\pi$
$572$	5.68653	+	9.84935i	0.237766	+	0.411822i
$573$	3.54161	+	9.47076i	0.147953	+	0.395647i
$574$	0.117340	−	0.203239i	0.00489768	−	0.00848304i
$575$	−0.844837	+	0.487767i	−0.0352321	+	0.0203413i
$576$	2.26390	−	1.96845i	0.0943290	−	0.0820186i
$577$	−16.0955			−0.670064			−0.335032	−	0.942207i	$-0.608747\pi$
$577$	−16.0955			−0.670064			−0.335032	+	0.942207i	$0.608747\pi$
$578$	6.79071			0.282456
$579$	−15.5573	+	18.8747i	−0.646538	+	0.784408i
$580$	5.53779	+	3.19725i	0.229944	+	0.132758i
$581$			8.24726i			0.342154i
$582$	−24.5070	−	4.09956i	−1.01585	−	0.169932i
$583$	31.0472	+	17.9251i	1.28584	+	0.742382i
$584$	0.477929	+	0.827798i	0.0197769	+	0.0342545i
$585$	−8.50654	+	7.39640i	−0.351702	+	0.305803i
$586$	−6.13402	−	10.6244i	−0.253394	−	0.438891i
$587$	11.3554	−	6.55606i	0.468688	−	0.270597i	−0.247002	−	0.969015i	$-0.579445\pi$
$587$	11.3554	−	6.55606i	0.468688	−	0.270597i	0.715691	+	0.698418i	$0.246112\pi$
$588$	−1.10962	+	6.63327i	−0.0457601	+	0.273551i
$589$	−5.88021	−	32.7935i	−0.242290	−	1.35123i
$590$			7.65515i			0.315158i
$591$	−0.174154	−	0.465712i	−0.00716374	−	0.0191568i
$592$	−7.12175	+	4.11174i	−0.292702	+	0.168992i
$593$	21.2078	+	12.2443i	0.870900	+	0.502814i	0.867647	−	0.497180i	$-0.165631\pi$
$593$	21.2078	+	12.2443i	0.870900	+	0.502814i	0.00325292	+	0.999995i	$0.498965\pi$
$594$	0.414496	+	15.7221i	0.0170070	+	0.645087i
$595$	−2.82060	+	4.88542i	−0.115633	+	0.200283i
$596$		−	2.74378i		−	0.112390i
$597$	−5.39566	+	32.2549i	−0.220830	+	1.32011i
$598$	1.83277	−	3.17446i	0.0749477	−	0.129813i
$599$	6.98997	−	12.1070i	0.285603	−	0.494678i	−0.687153	−	0.726513i	$-0.741140\pi$
$599$	6.98997	−	12.1070i	0.285603	−	0.494678i	0.972755	+	0.231835i	$0.0744730\pi$
$600$	−0.285770	+	1.70831i	−0.0116665	+	0.0697416i
$601$			41.6645i			1.69953i	0.527161	+	0.849766i	$0.323257\pi$
$601$			41.6645i			1.69953i	−0.527161	+	0.849766i	$0.676743\pi$
$602$	8.68810	−	15.0482i	0.354101	−	0.613320i
$603$	2.21001	−	0.429854i	0.0899986	−	0.0175050i
$604$	19.7111	+	11.3802i	0.802032	+	0.463053i
$605$	1.59230	−	0.919316i	0.0647362	−	0.0373755i
$606$	9.66532	+	25.8464i	0.392627	+	1.04994i
$607$			31.5810i			1.28183i	0.767610	+	0.640917i	$0.221446\pi$
$607$			31.5810i			1.28183i	−0.767610	+	0.640917i	$0.778554\pi$
$608$	−1.47898	+	4.10032i	−0.0599806	+	0.166290i
$609$	3.22623	−	19.2862i	0.130733	−	0.781516i
$610$	1.73216	−	1.00006i	0.0701331	−	0.0404914i
$611$	−16.0268	−	27.7593i	−0.648376	−	1.12302i
$612$	6.28957	+	7.23359i	0.254241	+	0.292401i
$613$	0.700918	+	1.21403i	0.0283098	+	0.0490340i	0.879833	−	0.475283i	$-0.157654\pi$
$613$	0.700918	+	1.21403i	0.0283098	+	0.0490340i	−0.851523	+	0.524317i	$0.824321\pi$
$614$	−18.5689	−	10.7208i	−0.749379	−	0.432654i
$615$	0.227076	+	0.0379857i	0.00915659	+	0.00153173i
$616$		−	5.34384i		−	0.215309i
$617$	9.13701	+	5.27526i	0.367842	+	0.212374i	0.672515	−	0.740083i	$-0.265214\pi$
$617$	9.13701	+	5.27526i	0.367842	+	0.212374i	−0.304673	+	0.952457i	$0.598547\pi$
$618$	−6.87930	+	8.34626i	−0.276726	+	0.335736i
$619$	−4.98387			−0.200318			−0.100159	−	0.994971i	$-0.531935\pi$
$619$	−4.98387			−0.200318			−0.100159	+	0.994971i	$0.531935\pi$
$620$	7.64334			0.306964
$621$	4.32158	−	2.64933i	0.173419	−	0.106314i
$622$	2.07949	−	1.20060i	0.0833801	−	0.0481395i
$623$	−7.69999	+	13.3368i	−0.308494	+	0.534327i
$624$	−2.27956	−	6.09587i	−0.0912555	−	0.244030i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−7.70245			−0.307852
$627$	−11.6561	−	19.6553i	−0.465502	−	0.784959i
$628$	−8.02210			−0.320117
$629$	−13.1378	−	22.7554i	−0.523840	−	0.907317i
$630$	5.19913	−	1.01125i	0.207138	−	0.0402891i
$631$	−4.99217	+	8.64668i	−0.198735	+	0.344219i	−0.948119	−	0.317917i	$-0.897017\pi$
$631$	−4.99217	+	8.64668i	−0.198735	+	0.344219i	0.749384	+	0.662136i	$0.230350\pi$
$632$	2.26576	−	1.30814i	0.0901270	−	0.0520349i
$633$	20.9919	−	25.4683i	0.834355	−	1.01228i
$634$	−20.3985			−0.810129
$635$	4.51362			0.179118
$636$	−15.8307	−	13.0482i	−0.627727	−	0.517396i
$637$	12.6353	+	7.29502i	0.500631	+	0.289039i
$638$		−	19.3547i		−	0.766259i
$639$	46.2047	+	15.9034i	1.82783	+	0.629130i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$	11.0764	+	19.1848i	0.437490	+	0.757755i	0.997495	−	0.0707341i	$-0.0225342\pi$
$641$	11.0764	+	19.1848i	0.437490	+	0.757755i	−0.560005	+	0.828489i	$0.689201\pi$
$642$	−3.35290	−	2.76358i	−0.132328	−	0.109070i
$643$	−24.4476	−	42.3446i	−0.964121	−	1.66991i	−0.711958	−	0.702222i	$-0.752191\pi$
$643$	−24.4476	−	42.3446i	−0.964121	−	1.66991i	−0.252163	−	0.967685i	$-0.581142\pi$
$644$	−1.49158	+	0.861163i	−0.0587764	+	0.0339346i
$645$	16.8132	+	2.81253i	0.662018	+	0.110743i
$646$	−13.1013	−	4.72564i	−0.515465	−	0.185928i
$647$		−	2.69718i		−	0.106037i	−0.998594	−	0.0530185i	$-0.983116\pi$
$647$		−	2.69718i		−	0.106037i	0.998594	−	0.0530185i	$-0.0168842\pi$
$648$	1.25044	−	8.91271i	0.0491221	−	0.350124i
$649$	20.0662	−	11.5852i	0.787666	−	0.454759i
$650$	3.25407	+	1.87874i	0.127635	+	0.0736903i
$651$	−8.18674	−	21.8925i	−0.320863	−	0.858033i
$652$	1.85276	−	3.20908i	0.0725597	−	0.125677i
$653$			0.588679i			0.0230368i	0.999934	+	0.0115184i	$0.00366650\pi$
$653$			0.588679i			0.0230368i	−0.999934	+	0.0115184i	$0.996334\pi$
$654$	−0.383725	−	0.0641902i	−0.0150049	−	0.00251004i
$655$	2.21704	−	3.84003i	0.0866269	−	0.150042i
$656$	−0.0664620	+	0.115116i	−0.00259491	+	0.00449451i
$657$	2.71146	+	0.933270i	0.105784	+	0.0364103i
$658$			15.0610i			0.587139i
$659$	−11.1918	+	19.3847i	−0.435970	+	0.755121i	−0.997374	−	0.0724200i	$-0.976928\pi$
$659$	−11.1918	+	19.3847i	−0.435970	+	0.755121i	0.561405	+	0.827541i	$0.310261\pi$
$660$	4.91042	−	1.83626i	0.191138	−	0.0714765i
$661$	12.9940	+	7.50211i	0.505409	+	0.291798i	0.730945	−	0.682437i	$-0.239080\pi$
$661$	12.9940	+	7.50211i	0.505409	+	0.291798i	−0.225535	+	0.974235i	$0.572413\pi$
$662$	−22.0426	+	12.7263i	−0.856711	+	0.494622i
$663$	19.4775	−	7.28365i	0.756443	−	0.282874i
$664$		−	4.67129i		−	0.181281i
$665$	−5.88094	+	4.96375i	−0.228053	+	0.192486i
$666$	−8.02915	+	23.3273i	−0.311123	+	0.903916i
$667$	−5.40230	+	3.11902i	−0.209178	+	0.120769i
$668$	−0.0687715	−	0.119116i	−0.00266085	−	0.00460873i
$669$	1.84691	−	2.24075i	0.0714055	−	0.0866323i
$670$	−0.375238	−	0.649931i	−0.0144967	−	0.0251090i
$671$	−5.24286	−	3.02697i	−0.202398	−	0.116855i
$672$	−0.504532	+	3.01607i	−0.0194628	+	0.116347i
$673$			13.1927i			0.508543i	0.967133	+	0.254271i	$0.0818356\pi$
$673$			13.1927i			0.508543i	−0.967133	+	0.254271i	$0.918164\pi$
$674$	−14.8031	−	8.54657i	−0.570194	−	0.329202i
$675$	2.71577	+	4.42997i	0.104530	+	0.170509i
$676$	−1.11866			−0.0430255
$677$	−15.1704			−0.583047			−0.291523	−	0.956564i	$-0.594162\pi$
$677$	−15.1704			−0.583047			−0.291523	+	0.956564i	$0.594162\pi$
$678$	−16.9609	−	13.9798i	−0.651380	−	0.536891i
$679$	21.9344	−	12.6638i	0.841764	−	0.485993i
$680$	1.59760	−	2.76712i	0.0612651	−	0.106114i
$681$	18.2518	−	6.82531i	0.699411	−	0.261546i
$682$	−11.5673	−	20.0352i	−0.442936	−	0.767188i
$683$	−26.8136			−1.02599			−0.512997	−	0.858390i	$-0.671465\pi$
$683$	−26.8136			−1.02599			−0.512997	+	0.858390i	$0.671465\pi$
$684$	4.72300	+	12.1940i	0.180588	+	0.466249i
$685$	14.6857			0.561111
$686$	−9.60703	−	16.6399i	−0.366798	−	0.635313i
$687$	36.7484	−	13.7421i	1.40204	−	0.524295i
$688$	−4.92098	+	8.52339i	−0.187611	+	0.324951i
$689$	−38.5424	+	22.2525i	−1.46835	+	0.847752i
$690$	−1.30386	−	1.07469i	−0.0496370	−	0.0409127i
$691$	−18.3997			−0.699959			−0.349980	−	0.936757i	$-0.613811\pi$
$691$	−18.3997			−0.699959			−0.349980	+	0.936757i	$0.613811\pi$
$692$	3.24174			0.123232
$693$	−10.5191	−	12.0979i	−0.399586	−	0.459561i
$694$	−0.366418	−	0.211552i	−0.0139090	−	0.00803039i
$695$			18.8538i			0.715166i
$696$	−1.82735	+	10.9238i	−0.0692656	+	0.414065i
$697$	−0.367817	−	0.212359i	−0.0139321	−	0.00804368i
$698$	14.8294	+	25.6853i	0.561301	+	0.972201i
$699$	−11.7595	+	14.2671i	−0.444785	+	0.539632i
$700$	−0.882761	−	1.52899i	−0.0333652	−	0.0577903i
$701$	4.07681	−	2.35374i	0.153979	−	0.0888997i	−0.421031	−	0.907046i	$-0.638332\pi$
$701$	4.07681	−	2.35374i	0.153979	−	0.0888997i	0.575010	+	0.818147i	$0.304998\pi$
$702$	−17.1601	−	9.31321i	−0.647665	−	0.351504i
$703$	−6.32653	−	35.2826i	−0.238610	−	1.33071i
$704$			3.02678i			0.114076i
$705$	−13.8395	+	5.17530i	−0.521225	+	0.194913i
$706$	25.5556	−	14.7545i	0.961798	−	0.555294i
$707$	−24.3593	−	14.0639i	−0.916127	−	0.528926i
$708$	−12.4192	+	4.64418i	−0.466741	+	0.174539i
$709$	15.3247	−	26.5431i	0.575531	−	0.996849i	−0.420453	−	0.907314i	$-0.638129\pi$
$709$	15.3247	−	26.5431i	0.575531	−	0.996849i	0.995984	−	0.0895342i	$-0.0285378\pi$
$710$		−	16.2884i		−	0.611291i
$711$	2.55444	−	7.42150i	0.0957992	−	0.278328i
$712$	4.36131	−	7.55401i	0.163447	−	0.283099i
$713$	−3.72817	+	6.45737i	−0.139621	+	0.241830i
$714$	−9.63693	−	1.61208i	−0.360653	−	0.0603306i
$715$		−	11.3731i		−	0.425328i
$716$	9.01690	−	15.6177i	0.336977	−	0.583662i
$717$	−13.3392	−	35.6708i	−0.498161	−	1.33215i
$718$	−23.2838	−	13.4429i	−0.868944	−	0.501685i
$719$	20.3745	−	11.7632i	0.759841	−	0.438694i	−0.0693979	−	0.997589i	$-0.522108\pi$
$719$	20.3745	−	11.7632i	0.759841	−	0.438694i	0.829239	+	0.558895i	$0.188774\pi$
$720$	−2.94481	+	0.572776i	−0.109747	+	0.0213461i
$721$		−	11.0250i		−	0.410591i
$722$	−14.6252	−	12.1286i	−0.544295	−	0.451379i
$723$	−3.32229	−	0.555758i	−0.123557	−	0.0206689i
$724$	−9.17503	+	5.29721i	−0.340987	+	0.196869i
$725$	−3.19725	−	5.53779i	−0.118743	−	0.205668i
$726$	2.45744	+	2.02551i	0.0912041	+	0.0751737i
$727$	0.310241	+	0.537354i	0.0115062	+	0.0199293i	0.871721	−	0.490002i	$-0.163004\pi$
$727$	0.310241	+	0.537354i	0.0115062	+	0.0199293i	−0.860215	+	0.509932i	$0.829671\pi$
$728$	5.74514	+	3.31696i	0.212929	+	0.122935i
$729$	−14.7133	−	22.6389i	−0.544937	−	0.838477i
$730$		−	0.955858i		−	0.0353779i
$731$	−27.2339	−	15.7235i	−1.00728	−	0.581555i
$732$	2.67328	+	2.20342i	0.0988075	+	0.0814407i
$733$	−46.1349			−1.70403			−0.852016	−	0.523515i	$-0.824620\pi$
$733$	−46.1349			−1.70403			−0.852016	+	0.523515i	$0.824620\pi$
$734$	8.20624			0.302898
$735$	4.27760	−	5.18976i	0.157781	−	0.191427i
$736$	0.844837	−	0.487767i	0.0311411	−	0.0179793i
$737$	−1.13576	+	1.96719i	−0.0418363	+	0.0724625i
$738$	0.0761357	+	0.391437i	0.00280259	+	0.0144090i
$739$	10.7620	+	18.6403i	0.395886	+	0.685694i	0.993214	−	0.116303i	$-0.0371044\pi$
$739$	10.7620	+	18.6403i	0.395886	+	0.685694i	−0.597328	+	0.801997i	$0.703771\pi$
$740$	8.22349			0.302301
$741$	28.3664	−	0.331267i	1.04207	−	0.0121694i
$742$	20.9115			0.767685
$743$	16.8709	+	29.2213i	0.618935	+	1.07203i	0.989680	+	0.143292i	$0.0457688\pi$
$743$	16.8709	+	29.2213i	0.618935	+	1.07203i	−0.370746	+	0.928734i	$0.620898\pi$
$744$	4.63701	+	12.4000i	0.170001	+	0.454606i
$745$	−1.37189	+	2.37618i	−0.0502622	+	0.0870566i
$746$	−5.93798	+	3.42829i	−0.217405	+	0.125519i
$747$	−9.19518	−	10.5753i	−0.336434	−	0.386930i
$748$	−9.67115			−0.353612
$749$	4.42900			0.161832
$750$	1.10164	−	1.33656i	0.0402262	−	0.0488042i
$751$	−37.8615	−	21.8593i	−1.38158	−	0.797658i	−0.389237	−	0.921137i	$-0.627261\pi$
$751$	−37.8615	−	21.8593i	−1.38158	−	0.797658i	−0.992347	+	0.123479i	$0.960595\pi$
$752$		−	8.53062i		−	0.311080i
$753$	46.2474	+	7.73634i	1.68535	+	0.281928i
$754$	20.8081	+	12.0136i	0.757788	+	0.437509i
$755$	−11.3802	−	19.7111i	−0.414167	−	0.717359i
$756$	4.79475	+	7.82120i	0.174383	+	0.284454i
$757$	−9.68232	−	16.7703i	−0.351910	−	0.609526i	0.634674	−	0.772780i	$-0.281134\pi$
$757$	−9.68232	−	16.7703i	−0.351910	−	0.609526i	−0.986584	+	0.163254i	$0.947801\pi$
$758$	−3.53865	+	2.04304i	−0.128529	+	0.0742065i
$759$	−0.843798	+	5.04417i	−0.0306279	+	0.183092i
$760$	3.33099	−	2.81149i	0.120828	−	0.101983i
$761$		−	36.1398i		−	1.31007i	−0.755600	−	0.655033i	$-0.772655\pi$
$761$		−	36.1398i		−	1.31007i	0.755600	−	0.655033i	$-0.227345\pi$
$762$	2.73829	+	7.32257i	0.0991979	+	0.265269i
$763$	0.343445	−	0.198288i	0.0124335	−	0.00717850i
$764$	5.05565	+	2.91888i	0.182907	+	0.105601i
$765$	−1.83013	−	9.40926i	−0.0661686	−	0.340193i
$766$	15.1709	−	26.2767i	0.548146	−	0.949417i
$767$			28.7641i			1.03861i
$768$	0.285770	−	1.70831i	0.0103118	−	0.0616435i
$769$	20.4227	−	35.3732i	0.736462	−	1.27559i	−0.217617	−	0.976034i	$-0.569828\pi$
$769$	20.4227	−	35.3732i	0.736462	−	1.27559i	0.954079	−	0.299555i	$-0.0968382\pi$
$770$	−2.67192	+	4.62790i	−0.0962893	+	0.166778i
$771$	7.12893	−	42.6163i	0.256742	−	1.53479i
$772$			14.1219i			0.508258i
$773$	−26.9826	+	46.7352i	−0.970495	+	1.68095i	−0.276432	+	0.961034i	$0.589152\pi$
$773$	−26.9826	+	46.7352i	−0.970495	+	1.68095i	−0.694064	+	0.719914i	$0.744181\pi$
$774$	5.63724	+	28.9828i	0.202627	+	1.04176i
$775$	−6.61932	−	3.82167i	−0.237773	−	0.137278i
$776$	−12.4237	+	7.17285i	−0.445986	+	0.257490i
$777$	−8.80813	−	23.5542i	−0.315990	−	0.845001i
$778$			0.244867i			0.00877891i
$779$	−0.373715	−	0.442769i	−0.0133897	−	0.0158639i
$780$	−1.07377	+	6.41896i	−0.0384473	+	0.229836i
$781$	−42.6961	+	24.6506i	−1.52779	+	0.882068i
$782$	1.55851	+	2.69942i	0.0557323	+	0.0965311i
$783$	17.3660	+	28.3274i	0.620609	+	1.01234i
$784$	1.94147	+	3.36272i	0.0693381	+	0.120097i
$785$	6.94734	+	4.01105i	0.247961	+	0.143161i
$786$	7.57480	+	1.26713i	0.270184	+	0.0451969i
$787$		−	25.3024i		−	0.901933i	−0.892541	−	0.450967i	$-0.851079\pi$
$787$		−	25.3024i		−	0.901933i	0.892541	−	0.450967i	$-0.148921\pi$
$788$	−0.248605	−	0.143532i	−0.00885617	−	0.00511311i
$789$	2.39707	−	2.90822i	0.0853378	−	0.103536i
$790$	−2.61627			−0.0930828
$791$	22.4044			0.796610
$792$	5.95804	+	6.85230i	0.211710	+	0.243486i
$793$	6.50856	−	3.75772i	0.231126	−	0.133440i
$794$	15.2157	−	26.3543i	0.539983	−	0.935278i
$795$	7.18566	+	19.2154i	0.254849	+	0.681501i
$796$	9.44058	+	16.3516i	0.334612	+	0.579566i
$797$	50.5277			1.78978			0.894891	−	0.446284i	$-0.147253\pi$
$797$	50.5277			1.78978			0.894891	+	0.446284i	$0.147253\pi$
$798$	−11.6206	−	6.52945i	−0.411366	−	0.231140i
$799$	27.2570			0.964285
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	−4.99611	−	25.6865i	−0.176529	−	0.907588i
$802$	4.69167	−	8.12622i	0.165669	−	0.286947i
$803$	−2.50556	+	1.44658i	−0.0884192	+	0.0510489i
$804$	0.826754	−	1.00305i	0.0291574	−	0.0353750i
$805$	1.72233			0.0607040
$806$	28.7197			1.01161
$807$	43.1605	+	35.5745i	1.51932	+	1.25228i
$808$	13.7972	+	7.96584i	0.485385	+	0.280237i
$809$			27.9215i			0.981667i	0.871253	+	0.490833i	$0.163308\pi$
$809$			27.9215i			0.981667i	−0.871253	+	0.490833i	$0.836692\pi$
$810$	−5.53927	+	7.09341i	−0.194630	+	0.249237i
$811$	35.5579	+	20.5294i	1.24861	+	0.720883i	0.970831	−	0.239763i	$-0.0770697\pi$
$811$	35.5579	+	20.5294i	1.24861	+	0.720883i	0.277775	+	0.960646i	$0.410403\pi$
$812$	−5.64481	−	9.77709i	−0.198094	−	0.343109i
$813$	−4.59270	−	3.78547i	−0.161073	−	0.132762i
$814$	−12.4453	−	21.5559i	−0.436208	−	0.755535i
$815$	−3.20908	+	1.85276i	−0.112409	+	0.0648994i
$816$	5.45840	+	0.913090i	0.191082	+	0.0319646i
$817$	−27.6706	−	32.7835i	−0.968071	−	1.14695i
$818$			2.64541i			0.0924947i
$819$	19.5356	−	3.79975i	0.682631	−	0.132774i
$820$	0.115116	−	0.0664620i	0.00402001	−	0.00232096i
$821$	−7.15533	−	4.13113i	−0.249723	−	0.144178i	0.369915	−	0.929066i	$-0.379387\pi$
$821$	−7.15533	−	4.13113i	−0.249723	−	0.144178i	−0.619637	+	0.784888i	$0.712720\pi$
$822$	8.90941	+	23.8250i	0.310751	+	0.830992i
$823$	20.6142	−	35.7048i	0.718566	−	1.24459i	−0.243003	−	0.970026i	$-0.578132\pi$
$823$	20.6142	−	35.7048i	0.718566	−	1.24459i	0.961568	−	0.274566i	$-0.0885343\pi$
$824$			6.24459i			0.217541i
$825$	−5.17068	−	0.864960i	−0.180020	−	0.0301141i
$826$	6.75767	−	11.7046i	0.235129	−	0.407256i
$827$	−1.41094	+	2.44382i	−0.0490632	+	0.0849800i	−0.889514	−	0.456908i	$-0.848957\pi$
$827$	−1.41094	+	2.44382i	−0.0490632	+	0.0849800i	0.840451	+	0.541888i	$0.182290\pi$
$828$	0.952480	−	2.76727i	0.0331010	−	0.0961692i
$829$		−	44.2077i		−	1.53540i	−0.640811	−	0.767699i	$-0.721402\pi$
$829$		−	44.2077i		−	1.53540i	0.640811	−	0.767699i	$-0.278598\pi$
$830$	−2.33564	+	4.04546i	−0.0810714	+	0.140420i
$831$	−17.3576	+	6.49093i	−0.602130	+	0.225168i
$832$	−3.25407	−	1.87874i	−0.112815	−	0.0651336i
$833$	−10.7445	+	6.20337i	−0.372277	+	0.214934i
$834$	−30.5871	+	11.4381i	−1.05914	+	0.396069i
$835$			0.137543i			0.00475987i
$836$	−12.4107	−	4.47654i	−0.429235	−	0.154824i
$837$	34.9064	+	18.9446i	1.20654	+	0.654821i
$838$	−15.2226	+	8.78877i	−0.525856	+	0.303603i
$839$	−6.60690	−	11.4435i	−0.228096	−	0.395073i	0.729148	−	0.684356i	$-0.239917\pi$
$839$	−6.60690	−	11.4435i	−0.228096	−	0.395073i	−0.957244	+	0.289283i	$0.906583\pi$
$840$	1.94497	−	2.35972i	0.0671079	−	0.0814182i
$841$	−5.94475	−	10.2966i	−0.204991	−	0.355056i
$842$	−17.0375	−	9.83661i	−0.587151	−	0.338992i
$843$	−3.30054	+	19.7304i	−0.113677	+	0.679552i
$844$		−	19.0552i		−	0.655906i
$845$	0.968791	+	0.559332i	0.0333274	+	0.0192416i
$846$	−16.7921	−	19.3124i	−0.577323	−	0.663975i
$847$	−3.24614			−0.111539
$848$	−11.8444			−0.406737
$849$	3.21746	+	2.65195i	0.110423	+	0.0910147i
$850$	−2.76712	+	1.59760i	−0.0949115	+	0.0547972i
$851$	−4.01114	+	6.94751i	−0.137500	+	0.238157i
$852$	26.4251	−	9.88171i	0.905307	−	0.338542i
$853$	1.06604	+	1.84644i	0.0365006	+	0.0632208i	0.883699	−	0.468056i	$-0.155046\pi$
$853$	1.06604	+	1.84644i	0.0365006	+	0.0632208i	−0.847198	+	0.531277i	$0.821712\pi$
$854$	−3.53127			−0.120837
$855$	2.00676	−	12.9218i	0.0686297	−	0.441916i
$856$	−2.50860			−0.0857423
$857$	25.1218	+	43.5123i	0.858145	+	1.48635i	0.873696	+	0.486472i	$0.161717\pi$
$857$	25.1218	+	43.5123i	0.858145	+	1.48635i	−0.0155507	+	0.999879i	$0.504950\pi$
$858$	18.4508	−	6.89972i	0.629901	−	0.235553i
$859$	1.48228	−	2.56738i	0.0505746	−	0.0875978i	−0.839630	−	0.543159i	$-0.817228\pi$
$859$	1.48228	−	2.56738i	0.0505746	−	0.0875978i	0.890204	+	0.455561i	$0.150561\pi$
$860$	8.52339	−	4.92098i	0.290645	−	0.167804i
$861$	−0.313664	−	0.258533i	−0.0106896	−	0.00881080i
$862$	8.78159			0.299102
$863$	0.298281			0.0101536			0.00507680	−	0.999987i	$-0.498384\pi$
$863$	0.298281			0.0101536			0.00507680	+	0.999987i	$0.498384\pi$
$864$	−2.71577	−	4.42997i	−0.0923924	−	0.150710i
$865$	−2.80743	−	1.62087i	−0.0954553	−	0.0551112i
$866$		−	26.2061i		−	0.890520i
$867$	1.94058	−	11.6007i	0.0659055	−	0.393979i
$868$	−11.6866	−	6.74724i	−0.396668	−	0.229016i
$869$	3.95943	+	6.85794i	0.134315	+	0.232640i
$870$	7.04443	−	8.54661i	0.238829	−	0.289757i
$871$	−1.40995	−	2.44210i	−0.0477743	−	0.0827475i
$872$	−0.194529	+	0.112311i	−0.00658757	+	0.00380334i
$873$	−14.0067	+	40.6940i	−0.474054	+	1.37728i
$874$	0.750502	+	4.18550i	0.0253861	+	0.141577i
$875$			1.76552i			0.0596855i
$876$	1.55072	−	0.579894i	0.0523938	−	0.0195928i
$877$	31.2808	−	18.0600i	1.05628	−	0.609843i	0.131878	−	0.991266i	$-0.457899\pi$
$877$	31.2808	−	18.0600i	1.05628	−	0.609843i	0.924401	+	0.381423i	$0.124566\pi$
$878$	23.3862	+	13.5020i	0.789247	+	0.455672i
$879$	−19.9028	+	7.44269i	−0.671304	+	0.251036i
$880$	1.51339	−	2.62126i	0.0510163	−	0.0883628i
$881$			24.2198i			0.815986i	0.912985	+	0.407993i	$0.133771\pi$
$881$			24.2198i			0.815986i	−0.912985	+	0.407993i	$0.866229\pi$
$882$	11.0146	+	3.79117i	0.370881	+	0.127655i
$883$	18.5924	−	32.2029i	0.625683	−	1.08371i	−0.362726	−	0.931896i	$-0.618154\pi$
$883$	18.5924	−	32.2029i	0.625683	−	1.08371i	0.988408	−	0.151818i	$-0.0485128\pi$
$884$	6.00295	−	10.3974i	0.201901	−	0.349703i
$885$	13.0774	+	2.18761i	0.439592	+	0.0735357i
$886$		−	14.9874i		−	0.503512i
$887$	−8.18050	+	14.1690i	−0.274674	+	0.475750i	−0.970053	−	0.242894i	$-0.921903\pi$
$887$	−8.18050	+	14.1690i	−0.274674	+	0.475750i	0.695379	+	0.718644i	$0.255237\pi$
$888$	4.98897	+	13.3412i	0.167419	+	0.447701i
$889$	−6.90127	−	3.98445i	−0.231461	−	0.133634i
$890$	−7.55401	+	4.36131i	−0.253211	+	0.146192i
$891$	26.9768	+	3.78482i	0.903756	+	0.126796i
$892$		−	1.67650i		−	0.0561335i
$893$	34.9783	+	12.6166i	1.17050	+	0.422199i
$894$	−4.68724	−	0.784089i	−0.156765	−	0.0262239i
$895$	−15.6177	+	9.01690i	−0.522043	+	0.301402i
$896$	0.882761	+	1.52899i	0.0294910	+	0.0510799i
$897$	−4.89922	−	4.03812i	−0.163580	−	0.134829i
$898$	0.535636	+	0.927749i	0.0178744	+	0.0309594i
$899$	−42.3272	−	24.4376i	−1.41169	−	0.815040i
$900$	2.83667	+	0.976368i	0.0945557	+	0.0325456i
$901$		−	37.8451i		−	1.26080i
$902$	−0.348429	−	0.201166i	−0.0116014	−	0.00669808i
$903$	−23.2243	−	19.1423i	−0.772857	−	0.637017i
$904$	−12.6900			−0.422063
$905$	10.5944			0.352170
$906$	25.0737	−	30.4206i	0.833019	−	1.01066i
$907$	−37.5272	+	21.6663i	−1.24607	+	0.719418i	−0.970323	−	0.241812i	$-0.922258\pi$
$907$	−37.5272	+	21.6663i	−1.24607	+	0.719418i	−0.275746	+	0.961230i	$0.588925\pi$
$908$	5.62519	−	9.74312i	0.186679	−	0.323337i
$909$	46.9158	−	9.12528i	1.55610	−	0.302666i
$910$	−3.31696	−	5.74514i	−0.109956	−	0.190450i
$911$	−35.9636			−1.19153			−0.595764	−	0.803159i	$-0.703151\pi$
$911$	−35.9636			−1.19153			−0.595764	+	0.803159i	$0.703151\pi$
$912$	6.58198	+	3.69831i	0.217951	+	0.122463i
$913$	14.1389			0.467931
$914$	3.80429	+	6.58922i	0.125835	+	0.217952i
$915$	−1.21342	−	3.24486i	−0.0401145	−	0.107272i
$916$	11.3258	−	19.6169i	0.374215	−	0.648160i
$917$	−6.77965	+	3.91423i	−0.223884	+	0.129259i
$918$	14.1546	−	8.67742i	0.467172	−	0.286398i
$919$	39.6618			1.30832			0.654161	−	0.756355i	$-0.273022\pi$
$919$	39.6618			1.30832			0.654161	+	0.756355i	$0.273022\pi$
$920$	−0.975534			−0.0321624
$921$	−23.6208	+	28.6578i	−0.778333	+	0.944307i
$922$	−2.94051	−	1.69770i	−0.0968405	−	0.0559109i
$923$		−	61.2032i		−	2.01453i
$924$	−9.12895	−	1.52711i	−0.300320	−	0.0502381i
$925$	−7.12175	−	4.11174i	−0.234162	−	0.135193i
$926$	7.06356	+	12.2344i	0.232123	+	0.402049i
$927$	12.2921	+	14.1371i	0.403727	+	0.464323i
$928$	3.19725	+	5.53779i	0.104955	+	0.181787i
$929$	8.50595	−	4.91091i	0.279071	−	0.161122i	−0.353932	−	0.935271i	$-0.615155\pi$
$929$	8.50595	−	4.91091i	0.279071	−	0.161122i	0.633003	+	0.774150i	$0.281822\pi$
$930$	2.18423	−	13.0572i	0.0716238	−	0.428163i
$931$	−16.6596	+	2.98724i	−0.545997	+	0.0979027i
$932$			10.6745i			0.349656i
$933$	−1.45674	−	3.89552i	−0.0476915	−	0.127534i
$934$	−9.89331	+	5.71190i	−0.323719	+	0.186899i
$935$	8.37546	+	4.83557i	0.273907	+	0.158140i
$936$	−11.0651	+	2.15220i	−0.361674	+	0.0703467i
$937$	−14.1222	+	24.4603i	−0.461351	+	0.799084i	−0.999029	−	0.0440667i	$-0.985969\pi$
$937$	−14.1222	+	24.4603i	−0.461351	+	0.799084i	0.537677	+	0.843151i	$0.319302\pi$
$938$			1.32498i			0.0432622i
$939$	−2.20113	+	13.1582i	−0.0718310	+	0.429402i
$940$	−4.26531	+	7.38774i	−0.139119	+	0.240961i
$941$	10.4415	−	18.0853i	0.340385	−	0.589563i	−0.644119	−	0.764925i	$-0.722776\pi$
$941$	10.4415	−	18.0853i	0.340385	−	0.589563i	0.984504	+	0.175361i	$0.0561094\pi$
$942$	−2.29247	+	13.7043i	−0.0746928	+	0.446509i
$943$			0.129672i			0.00422270i
$944$	−3.82758	+	6.62956i	−0.124577	+	0.215774i
$945$	−0.241776	−	9.17073i	−0.00786497	−	0.298324i
$946$	−25.7984	−	14.8947i	−0.838778	−	0.484269i
$947$	−51.7967	+	29.9048i	−1.68317	+	0.971777i	−0.723632	+	0.690186i	$0.757529\pi$
$947$	−51.7967	+	29.9048i	−1.68317	+	0.971777i	−0.959534	+	0.281591i	$0.909138\pi$
$948$	−1.58722	−	4.24445i	−0.0515506	−	0.137853i
$949$		−	3.59162i		−	0.116589i
$950$	−4.29047	+	0.769325i	−0.139201	+	0.0249602i
$951$	−5.82928	+	34.8471i	−0.189027	+	1.12999i
$952$	−4.88542	+	2.82060i	−0.158337	+	0.0914160i
$953$	2.55708	+	4.42900i	0.0828321	+	0.143469i	0.904465	−	0.426547i	$-0.140270\pi$
$953$	2.55708	+	4.42900i	0.0828321	+	0.143469i	−0.821633	+	0.570016i	$0.806937\pi$
$954$	−26.8144	+	23.3150i	−0.868148	+	0.754850i
$955$	−2.91888	−	5.05565i	−0.0944528	−	0.163597i
$956$	−19.0417	−	10.9937i	−0.615852	−	0.355562i
$957$	−33.0639	−	5.53098i	−1.06880	−	0.178791i
$958$			36.3083i			1.17307i
$959$	−22.4542	−	12.9639i	−0.725084	−	0.418628i
$960$	−1.10164	+	1.33656i	−0.0355553	+	0.0431372i
$961$	−27.4206			−0.884535
$962$	30.8996			0.996243
$963$	−5.67922	+	4.93805i	−0.183010	+	0.159126i
$964$	−1.68423	+	0.972389i	−0.0542453	+	0.0313185i
$965$	7.06095	−	12.2299i	0.227300	−	0.393695i
$966$	1.04489	+	2.79418i	0.0336188	+	0.0899012i
$967$	−14.7197	−	25.4953i	−0.473354	−	0.819873i	0.526181	−	0.850373i	$-0.323623\pi$
$967$	−14.7197	−	25.4953i	−0.473354	−	0.819873i	−0.999535	+	0.0304996i	$0.990290\pi$
$968$	1.83863			0.0590958
$969$	−11.8168	+	21.0307i	−0.379611	+	0.675605i
$970$	14.3457			0.460613
$971$	9.07896	+	15.7252i	0.291358	+	0.504646i	0.974131	−	0.225984i	$-0.0725597\pi$
$971$	9.07896	+	15.7252i	0.291358	+	0.504646i	−0.682773	+	0.730630i	$0.739226\pi$
$972$	−14.8684	−	4.68313i	−0.476903	−	0.150212i
$973$	16.6434	−	28.8272i	0.533563	−	0.924158i
$974$	−7.80535	+	4.50642i	−0.250099	+	0.144395i
$975$	4.13939	−	5.02209i	0.132567	−	0.160836i
$976$	2.00013			0.0640225
$977$	−37.0070			−1.18396			−0.591980	−	0.805953i	$-0.701654\pi$
$977$	−37.0070			−1.18396			−0.591980	+	0.805953i	$0.701654\pi$
$978$	−4.95265	−	4.08215i	−0.158368	−	0.130533i
$979$	22.8643	+	13.2007i	0.730746	+	0.421897i
$980$		−	3.88293i		−	0.124036i
$981$	−0.219314	+	0.637180i	−0.00700216	+	0.0203436i
$982$	−19.3513	−	11.1725i	−0.617526	−	0.356529i
$983$	4.26025	+	7.37898i	0.135881	+	0.235353i	0.925934	−	0.377686i	$-0.123280\pi$
$983$	4.26025	+	7.37898i	0.135881	+	0.235353i	−0.790053	+	0.613039i	$0.789947\pi$
$984$	0.177661	+	0.146435i	0.00566362	+	0.00466816i
$985$	0.143532	+	0.248605i	0.00457331	+	0.00792120i
$986$	−17.6943	+	10.2158i	−0.563503	+	0.325338i
$987$	25.7289	+	4.30398i	0.818961	+	0.136997i
$988$	12.5161	−	10.5641i	0.398192	−	0.336089i
$989$			9.60117i			0.305299i
$990$	−1.73366	−	8.91329i	−0.0550995	−	0.283283i
$991$	−7.55231	+	4.36033i	−0.239907	+	0.138510i	−0.615134	−	0.788423i	$-0.710898\pi$
$991$	−7.55231	+	4.36033i	−0.239907	+	0.138510i	0.375227	+	0.926933i	$0.377565\pi$
$992$	6.61932	+	3.82167i	0.210164	+	0.121338i
$993$	15.4414	+	41.2925i	0.490019	+	1.31038i
$994$	−14.3787	+	24.9047i	−0.456065	+	0.789929i
$995$		−	18.8812i		−	0.598573i
$996$	−7.98003	−	1.33491i	−0.252857	−	0.0422983i
$997$	4.82494	−	8.35704i	0.152807	−	0.264670i	−0.779451	−	0.626463i	$-0.784502\pi$
$997$	4.82494	−	8.35704i	0.152807	−	0.264670i	0.932258	+	0.361793i	$0.117835\pi$
$998$	19.8988	−	34.4658i	0.629887	−	1.09100i
$999$	37.5559	+	20.3825i	1.18822	+	0.644875i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.s.a.221.1	✓	24
3.2	odd	2		570.2.s.b.221.3	yes	24
19.8	odd	6		570.2.s.b.521.3	yes	24
57.8	even	6	inner	570.2.s.a.521.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.s.a.221.1	✓	24	1.1	even	1	trivial
570.2.s.a.521.1	yes	24	57.8	even	6	inner
570.2.s.b.221.3	yes	24	3.2	odd	2
570.2.s.b.521.3	yes	24	19.8	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.62233 + 0.606673i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.33656 + 1.10164i) q^{6} -1.76552 q^{7} +1.00000 q^{8} +(2.26390 - 1.96845i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.62233 + 0.606673i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.33656 + 1.10164i) q^{6} -1.76552 q^{7} +1.00000 q^{8} +(2.26390 - 1.96845i) q^{9} +(-0.866025 - 0.500000i) q^{10} +3.02678i q^{11} +(0.285770 - 1.70831i) q^{12} +(-3.25407 - 1.87874i) q^{13} +(0.882761 + 1.52899i) q^{14} +(-1.10164 + 1.33656i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.76712 - 1.59760i) q^{17} +(-2.83667 - 0.976368i) q^{18} +(4.29047 - 0.769325i) q^{19} +1.00000i q^{20} +(2.86426 - 1.07109i) q^{21} +(2.62126 - 1.51339i) q^{22} +(-0.844837 - 0.487767i) q^{23} +(-1.62233 + 0.606673i) q^{24} +(0.500000 - 0.866025i) q^{25} +3.75748i q^{26} +(-2.47858 + 4.56691i) q^{27} +(0.882761 - 1.52899i) q^{28} +(3.19725 - 5.53779i) q^{29} +(1.70831 + 0.285770i) q^{30} -7.64334i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.83626 - 4.91042i) q^{33} +(-2.76712 - 1.59760i) q^{34} +(-1.52899 + 0.882761i) q^{35} +(0.572776 + 2.94481i) q^{36} -8.22349i q^{37} +(-2.81149 - 3.33099i) q^{38} +(6.41896 + 1.07377i) q^{39} +(0.866025 - 0.500000i) q^{40} +(-0.0664620 - 0.115116i) q^{41} +(-2.35972 - 1.94497i) q^{42} +(-4.92098 - 8.52339i) q^{43} +(-2.62126 - 1.51339i) q^{44} +(0.976368 - 2.83667i) q^{45} +0.975534i q^{46} +(7.38774 + 4.26531i) q^{47} +(1.33656 + 1.10164i) q^{48} -3.88293 q^{49} -1.00000 q^{50} +(-3.51996 + 4.27057i) q^{51} +(3.25407 - 1.87874i) q^{52} +(5.92218 - 10.2575i) q^{53} +(5.19435 - 0.136943i) q^{54} +(1.51339 + 2.62126i) q^{55} -1.76552 q^{56} +(-6.49382 + 3.85101i) q^{57} -6.39449 q^{58} +(-3.82758 - 6.62956i) q^{59} +(-0.606673 - 1.62233i) q^{60} +(-1.00006 + 1.73216i) q^{61} +(-6.61932 + 3.82167i) q^{62} +(-3.99696 + 3.47533i) q^{63} +1.00000 q^{64} -3.75748 q^{65} +(-3.33442 + 4.04546i) q^{66} +(0.649931 + 0.375238i) q^{67} +3.19520i q^{68} +(1.66652 + 0.278778i) q^{69} +(1.52899 + 0.882761i) q^{70} +(8.14418 + 14.1061i) q^{71} +(2.26390 - 1.96845i) q^{72} +(0.477929 + 0.827798i) q^{73} +(-7.12175 + 4.11174i) q^{74} +(-0.285770 + 1.70831i) q^{75} +(-1.47898 + 4.10032i) q^{76} -5.34384i q^{77} +(-2.27956 - 6.09587i) q^{78} +(2.26576 - 1.30814i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(1.25044 - 8.91271i) q^{81} +(-0.0664620 + 0.115116i) q^{82} -4.67129i q^{83} +(-0.504532 + 3.01607i) q^{84} +(1.59760 - 2.76712i) q^{85} +(-4.92098 + 8.52339i) q^{86} +(-1.82735 + 10.9238i) q^{87} +3.02678i q^{88} +(4.36131 - 7.55401i) q^{89} +(-2.94481 + 0.572776i) q^{90} +(5.74514 + 3.31696i) q^{91} +(0.844837 - 0.487767i) q^{92} +(4.63701 + 12.4000i) q^{93} -8.53062i q^{94} +(3.33099 - 2.81149i) q^{95} +(0.285770 - 1.70831i) q^{96} +(-12.4237 + 7.17285i) q^{97} +(1.94147 + 3.36272i) q^{98} +(5.95804 + 6.85230i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9}+O(q^{10}) \) 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * q^9	\( 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9} - 2 q^{12} + 18 q^{13} + 6 q^{14} - 12 q^{16} + 12 q^{17} + 2 q^{18} + 6 q^{19} - 6 q^{21} + 18 q^{22} + 4 q^{24} + 12 q^{25} + 28 q^{27} + 6 q^{28} - 12 q^{32} - 22 q^{33} - 12 q^{34} + 2 q^{36} + 6 q^{38} + 40 q^{39} + 6 q^{41} - 6 q^{42} - 22 q^{43} - 18 q^{44} + 8 q^{45} + 12 q^{47} - 2 q^{48} + 12 q^{49} - 24 q^{50} - 20 q^{51} - 18 q^{52} + 8 q^{53} + 4 q^{54} - 12 q^{56} + 26 q^{59} + 22 q^{61} - 18 q^{62} + 6 q^{63} + 24 q^{64} + 8 q^{65} + 8 q^{66} - 48 q^{67} - 64 q^{69} + 24 q^{71} - 4 q^{72} - 8 q^{73} + 30 q^{74} + 2 q^{75} - 12 q^{76} - 38 q^{78} + 18 q^{79} - 12 q^{81} + 6 q^{82} + 12 q^{84} - 22 q^{86} - 24 q^{87} + 28 q^{89} + 8 q^{90} + 18 q^{91} + 2 q^{93} - 2 q^{96} + 6 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * 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 + 4 * q^24 + 12 * q^25 + 28 * q^27 + 6 * q^28 - 12 * q^32 - 22 * q^33 - 12 * q^34 + 2 * 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 - 2 * q^48 + 12 * q^49 - 24 * q^50 - 20 * q^51 - 18 * q^52 + 8 * q^53 + 4 * q^54 - 12 * q^56 + 26 * q^59 + 22 * q^61 - 18 * q^62 + 6 * q^63 + 24 * q^64 + 8 * q^65 + 8 * q^66 - 48 * q^67 - 64 * q^69 + 24 * q^71 - 4 * q^72 - 8 * q^73 + 30 * q^74 + 2 * q^75 - 12 * q^76 - 38 * q^78 + 18 * q^79 - 12 * q^81 + 6 * q^82 + 12 * q^84 - 22 * q^86 - 24 * q^87 + 28 * q^89 + 8 * q^90 + 18 * q^91 + 2 * q^93 - 2 * q^96 + 6 * q^97 - 6 * q^98 + 2 * q^99

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