LMFDB - Embedded newform 570.2.s.b.521.3

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			521.3
Character	$\chi$	$=$	570.521
Dual form			570.2.s.b.221.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.33656 - 1.10164i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.62233 + 0.606673i) q^{6} -1.76552 q^{7} -1.00000 q^{8} +(0.572776 + 2.94481i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.33656 - 1.10164i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.62233 + 0.606673i) q^{6} -1.76552 q^{7} -1.00000 q^{8} +(0.572776 + 2.94481i) 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} +(0.606673 + 1.62233i) 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} +(2.35972 + 1.94497i) q^{21} +(2.62126 + 1.51339i) q^{22} +(0.844837 - 0.487767i) q^{23} +(1.33656 + 1.10164i) 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} +(3.33442 - 4.04546i) q^{33} +(-2.76712 + 1.59760i) q^{34} +(1.52899 + 0.882761i) q^{35} +(2.26390 - 1.96845i) 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} +(2.86426 - 1.07109i) 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} +(1.62233 - 0.606673i) q^{48} -3.88293 q^{49} +1.00000 q^{50} +(1.93844 + 5.18366i) q^{51} +(3.25407 + 1.87874i) q^{52} +(-5.92218 - 10.2575i) q^{53} +(-2.71577 - 4.42997i) q^{54} +(1.51339 - 2.62126i) q^{55} +1.76552 q^{56} +(-4.88694 - 5.75480i) q^{57} -6.39449 q^{58} +(3.82758 - 6.62956i) q^{59} +(1.10164 - 1.33656i) q^{60} +(-1.00006 - 1.73216i) q^{61} +(6.61932 + 3.82167i) q^{62} +(-1.01125 - 5.19913i) q^{63} +1.00000 q^{64} +3.75748 q^{65} +(-1.83626 - 4.91042i) 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} +(-0.572776 - 2.94481i) 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} +(4.13939 - 5.02209i) q^{78} +(2.26576 + 1.30814i) q^{79} +(0.866025 - 0.500000i) q^{80} +(-8.34386 + 3.37344i) 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} +(-1.96845 - 2.26390i) q^{90} +(5.74514 - 3.31696i) q^{91} +(-0.844837 - 0.487767i) q^{92} +(8.42021 - 10.2158i) 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} +(-8.91329 + 1.73366i) 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
$3$	−1.33656	−	1.10164i	−0.771662	−	0.636032i
$3$	−1.33656	−	1.10164i	−0.771662	−	0.636032i
$4$	−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
$6$	−1.62233	+	0.606673i	−0.662313	+	0.247673i
$7$	−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
$9$	0.572776	+	2.94481i	0.190925	+	0.981605i
$10$	−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	−0.878016	−	0.478631i	$-0.841133\pi$
$13$	−3.25407	+	1.87874i	−0.902518	+	0.521069i	−0.0245016	+	0.999700i	$0.507800\pi$
$14$	−0.882761	+	1.52899i	−0.235928	+	0.408639i
$15$	0.606673	+	1.62233i	0.156642	+	0.418883i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.76712	−	1.59760i	−0.671126	−	0.387475i	0.125377	−	0.992109i	$-0.459986\pi$
$17$	−2.76712	−	1.59760i	−0.671126	−	0.387475i	−0.796503	+	0.604634i	$0.793319\pi$
$18$	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
$21$	2.35972	+	1.94497i	0.514934	+	0.424427i
$22$	2.62126	+	1.51339i	0.558855	+	0.322655i
$23$	0.844837	−	0.487767i	0.176161	−	0.101706i	−0.409327	−	0.912388i	$-0.634236\pi$
$23$	0.844837	−	0.487767i	0.176161	−	0.101706i	0.585488	+	0.810681i	$0.300903\pi$
$24$	1.33656	+	1.10164i	0.272824	+	0.224871i
$25$	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	−0.993727	−	0.111833i	$-0.964328\pi$
$29$	−3.19725	−	5.53779i	−0.593714	−	1.02834i	0.400014	−	0.916509i	$-0.369005\pi$
$30$	1.70831	+	0.285770i	0.311894	+	0.0521741i
$31$			7.64334i			1.37278i	0.727232	+	0.686392i	$0.240806\pi$
$31$			7.64334i			1.37278i	−0.727232	+	0.686392i	$0.759194\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	3.33442	−	4.04546i	0.580448	−	0.704224i
$34$	−2.76712	+	1.59760i	−0.474558	+	0.273986i
$35$	1.52899	+	0.882761i	0.258446	+	0.149214i
$36$	2.26390	−	1.96845i	0.377316	−	0.328074i
$37$			8.22349i			1.35193i	0.736932	+	0.675966i	$0.236274\pi$
$37$			8.22349i			1.35193i	−0.736932	+	0.675966i	$0.763726\pi$
$38$	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	$-0.830029\pi$
$41$	0.0664620	−	0.115116i	0.0103796	−	0.0179780i	0.871169	+	0.490984i	$0.163363\pi$
$42$	2.86426	−	1.07109i	0.441964	−	0.165274i
$43$	−4.92098	+	8.52339i	−0.750443	+	1.29981i	0.197165	+	0.980370i	$0.436826\pi$
$43$	−4.92098	+	8.52339i	−0.750443	+	1.29981i	−0.947608	+	0.319435i	$0.896507\pi$
$44$	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	$-0.880411\pi$
$47$	−7.38774	+	4.26531i	−1.07761	+	0.622160i	−0.147361	+	0.989083i	$0.547078\pi$
$48$	1.62233	−	0.606673i	0.234163	−	0.0875657i
$49$	−3.88293			−0.554705
$50$	1.00000			0.141421
$51$	1.93844	+	5.18366i	0.271436	+	0.725857i
$52$	3.25407	+	1.87874i	0.451259	+	0.260534i
$53$	−5.92218	−	10.2575i	−0.813474	−	1.40898i	−0.910418	−	0.413689i	$-0.864240\pi$
$53$	−5.92218	−	10.2575i	−0.813474	−	1.40898i	0.0969441	−	0.995290i	$-0.469093\pi$
$54$	−2.71577	−	4.42997i	−0.369569	−	0.602842i
$55$	1.51339	−	2.62126i	0.204065	−	0.353451i
$56$	1.76552			0.235928
$57$	−4.88694	−	5.75480i	−0.647292	−	0.762242i
$58$	−6.39449			−0.839638
$59$	3.82758	−	6.62956i	0.498308	−	0.863095i	−0.501690	−	0.865047i	$-0.667288\pi$
$59$	3.82758	−	6.62956i	0.498308	−	0.863095i	0.999998	+	0.00195269i	$0.000621562\pi$
$60$	1.10164	−	1.33656i	0.142221	−	0.172549i
$61$	−1.00006	−	1.73216i	−0.128045	−	0.221780i	0.794874	−	0.606774i	$-0.207537\pi$
$61$	−1.00006	−	1.73216i	−0.128045	−	0.221780i	−0.922919	+	0.384994i	$0.874204\pi$
$62$	6.61932	+	3.82167i	0.840655	+	0.485352i
$63$	−1.01125	−	5.19913i	−0.127405	−	0.655029i
$64$	1.00000			0.125000
$65$	3.75748			0.466058
$66$	−1.83626	−	4.91042i	−0.226028	−	0.604431i
$67$	0.649931	−	0.375238i	0.0794017	−	0.0458426i	−0.459773	−	0.888036i	$-0.652069\pi$
$67$	0.649931	−	0.375238i	0.0794017	−	0.0458426i	0.539175	+	0.842194i	$0.318736\pi$
$68$			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	−0.261106	+	0.965310i	$0.584087\pi$
$71$	−8.14418	+	14.1061i	−0.966536	+	1.67409i	−0.705430	+	0.708779i	$0.749246\pi$
$72$	−0.572776	−	2.94481i	−0.0675023	−	0.347050i
$73$	0.477929	−	0.827798i	0.0559374	−	0.0968864i	−0.836701	−	0.547660i	$-0.815519\pi$
$73$	0.477929	−	0.827798i	0.0559374	−	0.0968864i	0.892638	+	0.450774i	$0.148852\pi$
$74$	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
$78$	4.13939	−	5.02209i	0.468694	−	0.568640i
$79$	2.26576	+	1.30814i	0.254918	+	0.147177i	0.622014	−	0.783006i	$-0.286315\pi$
$79$	2.26576	+	1.30814i	0.254918	+	0.147177i	−0.367096	+	0.930183i	$0.619648\pi$
$80$	0.866025	−	0.500000i	0.0968246	−	0.0559017i
$81$	−8.34386	+	3.37344i	−0.927095	+	0.374826i
$82$	−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	$-0.319642\pi$
$89$	−4.36131	−	7.55401i	−0.462298	−	0.800724i	−0.999075	+	0.0430003i	$0.986308\pi$
$90$	−1.96845	−	2.26390i	−0.207492	−	0.238636i
$91$	5.74514	−	3.31696i	0.602254	−	0.347712i
$92$	−0.844837	−	0.487767i	−0.0880803	−	0.0508532i
$93$	8.42021	−	10.2158i	0.873135	−	1.05933i
$94$			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	−0.288087	−	0.957604i	$-0.593019\pi$
$97$	−12.4237	−	7.17285i	−1.26144	−	0.728292i	−0.973353	+	0.229312i	$0.926352\pi$
$98$	−1.94147	+	3.36272i	−0.196118	+	0.339686i
$99$	−8.91329	+	1.73366i	−0.895819	+	0.174240i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−13.7972	+	7.96584i	−1.37288	+	0.792630i	−0.991289	−	0.131703i	$-0.957956\pi$
$101$	−13.7972	+	7.96584i	−1.37288	+	0.792630i	−0.381587	+	0.924333i	$0.624622\pi$
$102$	5.45840	+	0.913090i	0.540462	+	0.0904094i
$103$		−	6.24459i		−	0.615298i	−0.951500	−	0.307649i	$-0.900458\pi$
$103$		−	6.24459i		−	0.615298i	0.951500	−	0.307649i	$-0.0995422\pi$
$104$	3.25407	−	1.87874i	0.319088	−	0.184226i
$105$	−1.07109	−	2.86426i	−0.104528	−	0.279523i
$106$	−11.8444			−1.15043
$107$	2.50860			0.242516			0.121258	−	0.992621i	$-0.461307\pi$
$107$	2.50860			0.242516			0.121258	+	0.992621i	$0.461307\pi$
$108$	−5.19435	+	0.136943i	−0.499826	+	0.0131773i
$109$	−0.194529	−	0.112311i	−0.0186325	−	0.0107575i	0.490655	−	0.871354i	$-0.336758\pi$
$109$	−0.194529	−	0.112311i	−0.0186325	−	0.0107575i	−0.509287	+	0.860597i	$0.670091\pi$
$110$	−1.51339	−	2.62126i	−0.144296	−	0.249928i
$111$	9.05933	−	10.9912i	0.859873	−	1.04324i
$112$	0.882761	−	1.52899i	0.0834131	−	0.144476i
$113$	12.6900			1.19377			0.596887	−	0.802326i	$-0.296404\pi$
$113$	12.6900			1.19377			0.596887	+	0.802326i	$0.296404\pi$
$114$	−7.42728	+	1.35482i	−0.695628	+	0.126890i
$115$	−0.975534			−0.0909690
$116$	−3.19725	+	5.53779i	−0.296857	+	0.514171i
$117$	−7.39640	−	8.50654i	−0.683797	−	0.786430i
$118$	−3.82758	−	6.62956i	−0.352357	−	0.610300i
$119$	4.88542	+	2.82060i	0.447845	+	0.258564i
$120$	−0.606673	−	1.62233i	−0.0553814	−	0.148098i
$121$	1.83863			0.167148
$122$	−2.00013			−0.181083
$123$	−0.215646	+	0.0806415i	−0.0194442	+	0.00727120i
$124$	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	−0.316442	−	0.948612i	$-0.602488\pi$
$127$	3.90891	−	2.25681i	0.346860	−	0.200260i	0.663301	+	0.748352i	$0.269155\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	15.9669	−	5.97086i	1.40581	−	0.525705i
$130$	1.87874	−	3.25407i	0.164776	−	0.285401i
$131$	−3.84003	−	2.21704i	−0.335505	−	0.193704i	0.322778	−	0.946475i	$-0.395383\pi$
$131$	−3.84003	−	2.21704i	−0.335505	−	0.193704i	−0.658282	+	0.752771i	$0.728717\pi$
$132$	−5.17068	−	0.864960i	−0.450050	−	0.0752851i
$133$	−7.57492	−	1.35826i	−0.656829	−	0.117776i
$134$		−	0.750475i		−	0.0648312i
$135$	−4.42997	+	2.71577i	−0.381271	+	0.233736i
$136$	2.76712	+	1.59760i	0.237279	+	0.136993i
$137$	−12.7182	+	7.34284i	−1.08659	+	0.627341i	−0.932666	−	0.360742i	$-0.882524\pi$
$137$	−12.7182	+	7.34284i	−1.08659	+	0.627341i	−0.153921	+	0.988083i	$0.549190\pi$
$138$	−1.07469	+	1.30386i	−0.0914835	+	0.110992i
$139$	−9.42690	−	16.3279i	−0.799579	−	1.38491i	−0.919890	−	0.392176i	$-0.871722\pi$
$139$	−9.42690	−	16.3279i	−0.799579	−	1.38491i	0.120311	−	0.992736i	$-0.461611\pi$
$140$		−	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
$147$	5.18976	+	4.27760i	0.428045	+	0.352810i
$148$	7.12175	−	4.11174i	0.585404	−	0.337983i
$149$	2.37618	+	1.37189i	0.194664	+	0.112390i	0.594164	−	0.804344i	$-0.297483\pi$
$149$	2.37618	+	1.37189i	0.194664	+	0.112390i	−0.399500	+	0.916733i	$0.630816\pi$
$150$	−1.33656	−	1.10164i	−0.109130	−	0.0899486i
$151$			22.7604i			1.85221i	0.377263	+	0.926106i	$0.376865\pi$
$151$			22.7604i			1.85221i	−0.377263	+	0.926106i	$0.623135\pi$
$152$	−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
$156$	−2.27956	−	6.09587i	−0.182511	−	0.488060i
$157$	4.01105	−	6.94734i	0.320117	−	0.554458i	−0.660395	−	0.750918i	$-0.729611\pi$
$157$	4.01105	−	6.94734i	0.320117	−	0.554458i	0.980512	+	0.196460i	$0.0629446\pi$
$158$	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
$162$	−1.25044	+	8.91271i	−0.0982442	+	0.700249i
$163$	−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
$165$	−4.91042	+	1.83626i	−0.382276	+	0.142953i
$166$	−4.04546	−	2.33564i	−0.313988	−	0.181281i
$167$	0.0687715	+	0.119116i	0.00532170	+	0.00921746i	0.868674	−	0.495384i	$-0.164973\pi$
$167$	0.0687715	+	0.119116i	0.00532170	+	0.00921746i	−0.863352	+	0.504602i	$0.831639\pi$
$168$	−2.35972	−	1.94497i	−0.182057	−	0.150058i
$169$	0.559332	−	0.968791i	0.0430255	−	0.0745224i
$170$	3.19520			0.245061
$171$	0.191961	+	13.0753i	0.0146796	+	0.999892i
$172$	9.84197			0.750443
$173$	1.62087	−	2.80743i	0.123232	−	0.213445i	−0.797808	−	0.602911i	$-0.794007\pi$
$173$	1.62087	−	2.80743i	0.123232	−	0.213445i	0.921041	+	0.389467i	$0.127341\pi$
$174$	8.54661	+	7.04443i	0.647917	+	0.534037i
$175$	−0.882761	−	1.52899i	−0.0667305	−	0.115581i
$176$	−2.62126	−	1.51339i	−0.197585	−	0.114076i
$177$	−12.4192	+	4.64418i	−0.933482	+	0.349078i
$178$	−8.72262			−0.653788
$179$	18.0338			1.34791			0.673954	−	0.738773i	$-0.264594\pi$
$179$	18.0338			1.34791			0.673954	+	0.738773i	$0.264594\pi$
$180$	−2.94481	+	0.572776i	−0.219493	+	0.0426922i
$181$	9.17503	−	5.29721i	0.681974	−	0.393738i	−0.118624	−	0.992939i	$-0.537848\pi$
$181$	9.17503	−	5.29721i	0.681974	−	0.393738i	0.800599	+	0.599201i	$0.204515\pi$
$182$		−	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
$186$	−4.63701	−	12.4000i	−0.340002	−	0.909212i
$187$	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	$-0.0677380\pi$
$192$	−1.33656	−	1.10164i	−0.0964578	−	0.0795041i
$193$	12.2299	+	7.06095i	0.880329	+	0.508258i	0.870767	−	0.491696i	$-0.163623\pi$
$193$	12.2299	+	7.06095i	0.880329	+	0.508258i	0.00956246	+	0.999954i	$0.496956\pi$
$194$	−12.4237	+	7.17285i	−0.891973	+	0.514981i
$195$	−5.02209	−	4.13939i	−0.359640	−	0.296428i
$196$	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	0.978121	+	0.208036i	$0.0667071\pi$
$199$	9.44058	+	16.3516i	0.669225	+	1.15913i	−0.308896	+	0.951096i	$0.599960\pi$
$200$	−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
$204$	3.51996	−	4.27057i	0.246446	−	0.299000i
$205$	−0.115116	+	0.0664620i	−0.00804002	+	0.00464191i
$206$	−5.40798	−	3.12230i	−0.376791	−	0.217541i
$207$	1.92028	+	2.20851i	0.133469	+	0.153502i
$208$		−	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	−0.190610	−	0.981666i	$-0.561047\pi$
$211$	−16.5023	−	9.52758i	−1.13606	−	0.655906i	−0.945453	+	0.325760i	$0.894380\pi$
$212$	−5.92218	+	10.2575i	−0.406737	+	0.704489i
$213$	26.4251	−	9.88171i	1.81061	−	0.677083i
$214$	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
$219$	−1.55072	+	0.579894i	−0.104788	+	0.0391856i
$220$	−3.02678			−0.204065
$221$	12.0059			0.807604
$222$	−4.98897	−	13.3412i	−0.334838	−	0.895402i
$223$	−1.45190	−	0.838252i	−0.0972261	−	0.0561335i	0.450599	−	0.892727i	$-0.351211\pi$
$223$	−1.45190	−	0.838252i	−0.0972261	−	0.0561335i	−0.547825	+	0.836593i	$0.684544\pi$
$224$	−0.882761	−	1.52899i	−0.0589820	−	0.102160i
$225$	−2.26390	+	1.96845i	−0.150926	+	0.131230i
$226$	6.34499	−	10.9898i	0.422063	−	0.731034i
$227$	11.2504			0.746714			0.373357	−	0.927688i	$-0.378207\pi$
$227$	11.2504			0.746714			0.373357	+	0.927688i	$0.378207\pi$
$228$	−2.54033	+	7.10962i	−0.168238	+	0.470846i
$229$	−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
$231$	−5.88699	+	7.14235i	−0.387335	+	0.469932i
$232$	3.19725	+	5.53779i	0.209909	+	0.363574i
$233$	−9.24441	−	5.33726i	−0.605622	−	0.349656i	0.165628	−	0.986188i	$-0.447035\pi$
$233$	−9.24441	−	5.33726i	−0.605622	−	0.349656i	−0.771250	+	0.636532i	$0.780368\pi$
$234$	−11.0651	+	2.15220i	−0.723347	+	0.140693i
$235$	8.53062			0.556477
$236$	−7.65515			−0.498308
$237$	−1.58722	−	4.24445i	−0.103101	−	0.275707i
$238$	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	−0.444773	−	0.895643i	$-0.646716\pi$
$241$	1.68423	−	0.972389i	0.108491	−	0.0626371i	0.553263	+	0.833006i	$0.313382\pi$
$242$	0.919316	−	1.59230i	0.0590958	−	0.102357i
$243$	14.8684	+	4.68313i	0.953806	+	0.300423i
$244$	−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
$249$	−5.14608	+	6.24345i	−0.326120	+	0.395663i
$250$	−0.866025	−	0.500000i	−0.0547723	−	0.0316228i
$251$	23.4450	−	13.5360i	1.47983	−	0.854383i	0.480095	−	0.877216i	$-0.340602\pi$
$251$	23.4450	−	13.5360i	1.47983	−	0.854383i	0.999739	+	0.0228337i	$0.00726884\pi$
$252$	−3.99696	+	3.47533i	−0.251785	+	0.218925i
$253$	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	0.933060	+	0.359721i	$0.117128\pi$
$257$	12.4732	+	21.6042i	0.778057	+	1.34764i	−0.155002	+	0.987914i	$0.549539\pi$
$258$	2.81253	−	16.8132i	0.175101	−	1.04674i
$259$		−	14.5187i		−	0.902151i
$260$	−1.87874	−	3.25407i	−0.116515	−	0.201809i
$261$	14.4765	−	12.5872i	0.896070	−	0.779128i
$262$	−3.84003	+	2.21704i	−0.237238	+	0.136969i
$263$	1.88439	+	1.08795i	0.116196	+	0.0670860i	0.556972	−	0.830531i	$-0.311963\pi$
$263$	1.88439	+	1.08795i	0.116196	+	0.0670860i	−0.440775	+	0.897617i	$0.645296\pi$
$264$	−3.33442	+	4.04546i	−0.205219	+	0.248981i
$265$			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	0.340079	−	0.940397i	$-0.389546\pi$
$269$	16.1461	−	27.9659i	0.984447	−	1.70511i	0.644368	−	0.764715i	$-0.277120\pi$
$270$	0.136943	+	5.19435i	0.00833409	+	0.316118i
$271$	1.71811	−	2.97585i	0.104368	−	0.180770i	−0.809112	−	0.587654i	$-0.800052\pi$
$271$	1.71811	−	2.97585i	0.104368	−	0.180770i	0.913480	+	0.406884i	$0.133385\pi$
$272$	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
$276$	0.591830	+	1.58264i	0.0356240	+	0.0952635i
$277$	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
$279$	−22.5082	+	4.37792i	−1.34753	+	0.262099i
$280$	−1.52899	−	0.882761i	−0.0913744	−	0.0527551i
$281$	−5.77482	−	10.0023i	−0.344497	−	0.596687i	0.640765	−	0.767737i	$-0.278617\pi$
$281$	−5.77482	−	10.0023i	−0.344497	−	0.596687i	−0.985262	+	0.171050i	$0.945284\pi$
$282$	9.39768	−	11.4017i	0.559624	−	0.678960i
$283$	−1.20364	+	2.08476i	−0.0715488	+	0.123926i	−0.899580	−	0.436755i	$-0.856128\pi$
$283$	−1.20364	+	2.08476i	−0.0715488	+	0.123926i	0.828031	+	0.560682i	$0.189461\pi$
$284$	16.2884			0.966536
$285$	1.35482	+	7.42728i	0.0802524	+	0.439954i
$286$	−11.3731			−0.672503
$287$	−0.117340	+	0.203239i	−0.00692637	+	0.0119968i
$288$	−2.26390	+	1.96845i	−0.133401	+	0.115992i
$289$	−3.39535	−	5.88093i	−0.199727	−	0.345937i
$290$	5.53779	+	3.19725i	0.325190	+	0.187749i
$291$	8.70315	+	23.2734i	0.510188	+	1.36431i
$292$	−0.955858			−0.0559374
$293$	−12.2680			−0.716707			−0.358353	−	0.933586i	$-0.616662\pi$
$293$	−12.2680			−0.716707			−0.358353	+	0.933586i	$0.616662\pi$
$294$	6.29939	−	2.35567i	0.367388	−	0.137385i
$295$	−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
$300$	−1.62233	+	0.606673i	−0.0936651	+	0.0350263i
$301$	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
$306$	−6.28957	−	7.23359i	−0.359551	−	0.413517i
$307$	18.5689	+	10.7208i	1.05978	+	0.611866i	0.925372	−	0.379060i	$-0.123753\pi$
$307$	18.5689	+	10.7208i	1.05978	+	0.611866i	0.134410	+	0.990926i	$0.457086\pi$
$308$	−4.62790	+	2.67192i	−0.263699	+	0.152247i
$309$	−6.87930	+	8.34626i	−0.391349	+	0.474802i
$310$	−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	0.954100	−	0.299490i	$-0.0968164\pi$
$313$	3.85122	+	6.67052i	0.217684	+	0.377040i	−0.736415	+	0.676530i	$0.763483\pi$
$314$	−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	−0.996272	−	0.0862698i	$-0.972505\pi$
$317$	−10.1993	−	17.6656i	−0.572848	−	0.992201i	0.423424	−	0.905932i	$-0.360828\pi$
$318$	15.8307	+	13.0482i	0.887741	+	0.731709i
$319$	16.7616	−	9.67734i	0.938472	−	0.541827i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	−3.35290	−	2.76358i	−0.187140	−	0.154248i
$322$			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
$327$	0.136272	+	0.364411i	0.00753588	+	0.0201520i
$328$	−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	$0.246595\pi$
$331$			25.4526i			1.39900i	−0.714631	+	0.699502i	$0.753405\pi$
$332$	−4.04546	+	2.33564i	−0.222023	+	0.128185i
$333$	−24.2166	+	4.71022i	−1.32706	+	0.258118i
$334$	0.137543			0.00752602
$335$	−0.750475			−0.0410029
$336$	−2.86426	+	1.07109i	−0.156258	+	0.0584330i
$337$	14.8031	+	8.54657i	0.806376	+	0.465561i	0.845696	−	0.533665i	$-0.179186\pi$
$337$	14.8031	+	8.54657i	0.806376	+	0.465561i	−0.0393200	+	0.999227i	$0.512519\pi$
$338$	−0.559332	−	0.968791i	−0.0304236	−	0.0526953i
$339$	−16.9609	−	13.9798i	−0.921190	−	0.759279i
$340$	1.59760	−	2.76712i	0.0866420	−	0.150068i
$341$	−23.1347			−1.25281
$342$	11.4195	+	6.37140i	0.617496	+	0.344526i
$343$	19.2141			1.03746
$344$	4.92098	−	8.52339i	0.265322	−	0.459551i
$345$	1.30386	+	1.07469i	0.0701973	+	0.0578592i
$346$	−1.62087	−	2.80743i	−0.0871384	−	0.150928i
$347$	−0.366418	−	0.211552i	−0.0196703	−	0.0113567i	0.490133	−	0.871648i	$-0.336948\pi$
$347$	−0.366418	−	0.211552i	−0.0196703	−	0.0113567i	−0.509803	+	0.860291i	$0.670282\pi$
$348$	10.3740	−	3.87937i	0.556103	−	0.207956i
$349$	−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
$351$	0.514561	+	19.5177i	0.0274652	+	1.04178i
$352$	−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
$357$	−3.42236	−	9.15186i	−0.181130	−	0.484368i
$358$	9.01690	−	15.6177i	0.476558	−	0.825422i
$359$	−23.2838	−	13.4429i	−1.22887	−	0.709490i	−0.262079	−	0.965047i	$-0.584408\pi$
$359$	−23.2838	−	13.4429i	−1.22887	−	0.709490i	−0.966794	+	0.255557i	$0.917741\pi$
$360$	−0.976368	+	2.83667i	−0.0514591	+	0.149506i
$361$	17.8163	+	6.60153i	0.937699	+	0.347449i
$362$		−	10.5944i		−	0.556830i
$363$	−2.45744	−	2.02551i	−0.128982	−	0.106312i
$364$	−5.74514	−	3.31696i	−0.301127	−	0.173856i
$365$	−0.827798	+	0.477929i	−0.0433289	+	0.0250160i
$366$	2.67328	+	2.20342i	0.139735	+	0.115175i
$367$	−4.10312	−	7.10681i	−0.214181	−	0.370973i	0.738838	−	0.673883i	$-0.235375\pi$
$367$	−4.10312	−	7.10681i	−0.214181	−	0.370973i	−0.953019	+	0.302911i	$0.902042\pi$
$368$			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	$0.0568043\pi$
$373$			6.85659i			0.355021i	−0.984119	+	0.177510i	$0.943196\pi$
$374$	−4.83557	−	8.37546i	−0.250042	−	0.433085i
$375$	−1.10164	+	1.33656i	−0.0568885	+	0.0690196i
$376$	7.38774	−	4.26531i	0.380993	−	0.219967i
$377$	20.8081	+	12.0136i	1.07167	+	0.618731i
$378$	4.79475	+	7.82120i	0.246615	+	0.402279i
$379$			4.08608i			0.209888i	0.994478	+	0.104944i	$0.0334663\pi$
$379$			4.08608i			0.209888i	−0.994478	+	0.104944i	$0.966534\pi$
$380$	−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	0.159489	+	0.987200i	$0.449015\pi$
$383$	−15.1709	+	26.2767i	−0.775196	+	1.34268i	−0.934684	+	0.355479i	$0.884318\pi$
$384$	−1.62233	+	0.606673i	−0.0827891	+	0.0309592i
$385$	−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	$-0.664691\pi$
$389$	0.212061	−	0.122434i	0.0107519	−	0.00620763i	0.505366	+	0.862905i	$0.331357\pi$
$390$	−6.09587	+	2.27956i	−0.308676	+	0.115430i
$391$	−3.11702			−0.157635
$392$	3.88293			0.196118
$393$	2.69004	+	7.19353i	0.135694	+	0.362866i
$394$	0.248605	+	0.143532i	0.0125245	+	0.00723103i
$395$	−1.30814	−	2.26576i	−0.0658195	−	0.114003i
$396$	5.95804	+	6.85230i	0.299403	+	0.344341i
$397$	15.2157	−	26.3543i	0.763652	−	1.32268i	−0.177305	−	0.984156i	$-0.556738\pi$
$397$	15.2157	−	26.3543i	0.763652	−	1.32268i	0.940957	−	0.338527i	$-0.109929\pi$
$398$	18.8812			0.946427
$399$	8.62801	+	10.1602i	0.431941	+	0.508648i
$400$	−1.00000			−0.0500000
$401$	−4.69167	+	8.12622i	−0.234291	+	0.405804i	−0.959066	−	0.283181i	$-0.908610\pi$
$401$	−4.69167	+	8.12622i	−0.234291	+	0.405804i	0.724775	+	0.688985i	$0.241944\pi$
$402$	−0.826754	+	1.00305i	−0.0412347	+	0.0500278i
$403$	−14.3598	−	24.8720i	−0.715315	−	1.23896i
$404$	13.7972	+	7.96584i	0.686438	+	0.396315i
$405$	8.91271	+	1.25044i	0.442876	+	0.0621351i
$406$	11.2896			0.560294
$407$	−24.8906			−1.23378
$408$	−1.93844	−	5.18366i	−0.0959671	−	0.256629i
$409$	−2.29099	+	1.32271i	−0.113282	+	0.0654036i	−0.555571	−	0.831469i	$-0.687500\pi$
$409$	−2.29099	+	1.32271i	−0.113282	+	0.0654036i	0.442288	+	0.896873i	$0.354167\pi$
$410$			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
$414$	2.87276	−	0.558762i	0.141189	−	0.0274617i
$415$	−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	$-0.141261\pi$
$420$	−1.94497	+	2.35972i	−0.0949049	+	0.115143i
$421$	17.0375	+	9.83661i	0.830357	+	0.479407i	0.853975	−	0.520314i	$-0.174185\pi$
$421$	17.0375	+	9.83661i	0.830357	+	0.479407i	−0.0236179	+	0.999721i	$0.507519\pi$
$422$	−16.5023	+	9.52758i	−0.803317	+	0.463796i
$423$	−16.7921	−	19.3124i	−0.816458	−	0.939003i
$424$	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	$-0.0988327\pi$
$431$	4.39080	+	7.60508i	0.211497	+	0.366324i	−0.740686	+	0.671851i	$0.765499\pi$
$432$	2.71577	+	4.42997i	0.130663	+	0.213137i
$433$	22.6952	−	13.1031i	1.09066	−	0.629693i	0.156908	−	0.987613i	$-0.449847\pi$
$433$	22.6952	−	13.1031i	1.09066	−	0.629693i	0.933752	+	0.357920i	$0.116514\pi$
$434$	−11.6866	−	6.74724i	−0.560973	−	0.323878i
$435$	7.04443	−	8.54661i	0.337755	−	0.409779i
$436$			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	−0.175745	−	0.984436i	$-0.556233\pi$
$439$	−23.3862	−	13.5020i	−1.11616	−	0.644417i	−0.940419	+	0.340018i	$0.889567\pi$
$440$	−1.51339	+	2.62126i	−0.0721479	+	0.124964i
$441$	−2.22405	−	11.4345i	−0.105907	−	0.544501i
$442$	6.00295	−	10.3974i	0.285531	−	0.494554i
$443$	−12.9795	+	7.49371i	−0.616674	+	0.356037i	−0.775573	−	0.631258i	$-0.782539\pi$
$443$	−12.9795	+	7.49371i	−0.616674	+	0.356037i	0.158899	+	0.987295i	$0.449206\pi$
$444$	−14.0483	−	2.35002i	−0.666703	−	0.111527i
$445$			8.72262i			0.413492i
$446$	−1.45190	+	0.838252i	−0.0687492	+	0.0396924i
$447$	−1.66458	−	4.45131i	−0.0787318	−	0.210540i
$448$	−1.76552			−0.0834131
$449$	1.07127			0.0505565			0.0252782	−	0.999680i	$-0.491953\pi$
$449$	1.07127			0.0505565			0.0252782	+	0.999680i	$0.491953\pi$
$450$	0.572776	+	2.94481i	0.0270009	+	0.138820i
$451$	0.348429	+	0.201166i	0.0164069	+	0.00947252i
$452$	−6.34499	−	10.9898i	−0.298443	−	0.516919i
$453$	25.0737	−	30.4206i	1.17807	−	1.42928i
$454$	5.62519	−	9.74312i	0.264003	−	0.457267i
$455$	−6.63392			−0.311003
$456$	4.88694	+	5.75480i	0.228852	+	0.269493i
$457$	−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
$459$	−14.1546	+	8.67742i	−0.660681	+	0.405027i
$460$	0.487767	+	0.844837i	0.0227422	+	0.0393907i
$461$	−2.94051	−	1.69770i	−0.136953	−	0.0790699i	0.429958	−	0.902849i	$-0.358528\pi$
$461$	−2.94051	−	1.69770i	−0.136953	−	0.0790699i	−0.566911	+	0.823779i	$0.691862\pi$
$462$	3.24196	+	8.66946i	0.150830	+	0.403340i
$463$	−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
$465$	−12.4000	+	4.63701i	−0.575036	+	0.215036i
$466$	−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
$471$	−13.0145	+	4.86679i	−0.599675	+	0.224250i
$472$	−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
$477$	26.8144	−	23.3150i	1.22775	−	1.06752i
$478$	19.0417	+	10.9937i	0.870946	+	0.502841i
$479$	31.4439	−	18.1542i	1.43671	−	0.829485i	0.439091	−	0.898443i	$-0.355301\pi$
$479$	31.4439	−	18.1542i	1.43671	−	0.829485i	0.997620	+	0.0689574i	$0.0219673\pi$
$480$	−1.10164	+	1.33656i	−0.0502828	+	0.0610053i
$481$	−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	$0.0654610\pi$
$487$			9.01284i			0.408411i	−0.978928	+	0.204205i	$0.934539\pi$
$488$	1.00006	+	1.73216i	0.0452707	+	0.0784112i
$489$	4.95265	+	4.08215i	0.223966	+	0.184601i
$490$	3.36272	−	1.94147i	0.151912	−	0.0877065i
$491$	−19.3513	−	11.1725i	−0.873313	−	0.504208i	−0.00486554	−	0.999988i	$-0.501549\pi$
$491$	−19.3513	−	11.1725i	−0.873313	−	0.504208i	−0.868448	+	0.495780i	$0.834882\pi$
$492$	0.177661	+	0.146435i	0.00800957	+	0.00660178i
$493$			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
$498$	2.83395	+	7.57836i	0.126992	+	0.339595i
$499$	19.8988	−	34.4658i	0.890795	−	1.54290i	0.0518700	−	0.998654i	$-0.483482\pi$
$499$	19.8988	−	34.4658i	0.890795	−	1.54290i	0.838925	−	0.544248i	$-0.183185\pi$
$500$	−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	$-0.945701\pi$
$503$	−29.8559	+	17.2373i	−1.33121	+	0.768575i	−0.345726	+	0.938336i	$0.612367\pi$
$504$	1.01125	+	5.19913i	0.0450446	+	0.231588i
$505$	15.9317			0.708950
$506$	2.95272			0.131264
$507$	−1.81484	+	0.678663i	−0.0805999	+	0.0301405i
$508$	−3.90891	−	2.25681i	−0.173430	−	0.100130i
$509$	18.5767	+	32.1758i	0.823398	+	1.42617i	0.903138	+	0.429351i	$0.141258\pi$
$509$	18.5767	+	32.1758i	0.823398	+	1.42617i	−0.0797396	+	0.996816i	$0.525409\pi$
$510$	−4.27057	−	3.51996i	−0.189104	−	0.155866i
$511$	−0.843794	+	1.46149i	−0.0373273	+	0.0646527i
$512$	−1.00000			−0.0441942
$513$	14.1477	−	17.6874i	0.624636	−	0.780916i
$514$	24.9464			1.10034
$515$	−3.12230	+	5.40798i	−0.137585	+	0.238304i
$516$	−13.1544	−	10.8423i	−0.579088	−	0.477306i
$517$	−12.9101	−	22.3610i	−0.567787	−	0.983437i
$518$	−12.5736	−	7.25937i	−0.552452	−	0.318959i
$519$	−5.25916	+	1.96667i	−0.230851	+	0.0863274i
$520$	−3.75748			−0.164776
$521$	18.7548			0.821664			0.410832	−	0.911711i	$-0.365238\pi$
$521$	18.7548			0.821664			0.410832	+	0.911711i	$0.365238\pi$
$522$	−3.66261	−	18.8306i	−0.160308	−	0.824192i
$523$	−11.5841	+	6.68808i	−0.506537	+	0.292449i	−0.731409	−	0.681939i	$-0.761137\pi$
$523$	−11.5841	+	6.68808i	−0.506537	+	0.292449i	0.224872	+	0.974388i	$0.427804\pi$
$524$			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
$528$	1.83626	+	4.91042i	0.0799131	+	0.213699i
$529$	−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
$534$	11.6583	+	9.60920i	0.504504	+	0.415831i
$535$	−2.17252	−	1.25430i	−0.0939260	−	0.0542282i
$536$	−0.649931	+	0.375238i	−0.0280727	+	0.0162078i
$537$	−24.1032	−	19.8668i	−1.04013	−	0.857314i
$538$	−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	−0.997662	−	0.0683416i	$-0.978229\pi$
$541$	−12.9791	−	22.4805i	−0.558017	−	0.966513i	0.439645	−	0.898171i	$-0.355104\pi$
$542$	−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
$546$	−7.30819	+	8.86661i	−0.312762	+	0.379456i
$547$	−21.9902	+	12.6960i	−0.940232	+	0.542843i	−0.890033	−	0.455896i	$-0.849319\pi$
$547$	−21.9902	+	12.6960i	−0.940232	+	0.542843i	−0.0501992	+	0.998739i	$0.515986\pi$
$548$	12.7182	+	7.34284i	0.543293	+	0.313671i
$549$	4.52808	−	3.93714i	0.193254	−	0.168033i
$550$			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
$555$	−13.3412	+	4.98897i	−0.566302	+	0.211770i
$556$	−9.42690	+	16.3279i	−0.399790	+	0.692456i
$557$	−29.9344	+	17.2826i	−1.26836	+	0.732288i	−0.974678	−	0.223615i	$-0.928214\pi$
$557$	−29.9344	+	17.2826i	−1.26836	+	0.732288i	−0.293683	+	0.955903i	$0.594881\pi$
$558$	−7.46271	+	21.6816i	−0.315922	+	0.917857i
$559$		−	36.9810i		−	1.56413i
$560$	−1.52899	+	0.882761i	−0.0646115	+	0.0373035i
$561$	−15.6898	+	5.86722i	−0.662423	+	0.247714i
$562$	−11.5496			−0.487193
$563$	37.7990			1.59304			0.796520	−	0.604612i	$-0.206672\pi$
$563$	37.7990			1.59304			0.796520	+	0.604612i	$0.206672\pi$
$564$	−5.17530	−	13.8395i	−0.217919	−	0.582747i
$565$	−10.9898	−	6.34499i	−0.462346	−	0.266936i
$566$	1.20364	+	2.08476i	0.0505926	+	0.0876290i
$567$	14.7313	−	5.95588i	0.618655	−	0.250123i
$568$	8.14418	−	14.1061i	0.341722	−	0.591880i
$569$	−36.6704			−1.53730			−0.768652	−	0.639667i	$-0.779072\pi$
$569$	−36.6704			−1.53730			−0.768652	+	0.639667i	$0.779072\pi$
$570$	7.10962	+	2.54033i	0.297789	+	0.106403i
$571$	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
$573$	−6.43111	+	7.80251i	−0.268664	+	0.325954i
$574$	0.117340	+	0.203239i	0.00489768	+	0.00848304i
$575$	0.844837	+	0.487767i	0.0352321	+	0.0203413i
$576$	0.572776	+	2.94481i	0.0238657	+	0.122701i
$577$	−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
$579$	−8.56738	−	22.9104i	−0.356048	−	0.952122i
$580$	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
$585$	2.15220	+	11.0651i	0.0889823	+	0.457485i
$586$	−6.13402	+	10.6244i	−0.253394	+	0.438891i
$587$	−11.3554	−	6.55606i	−0.468688	−	0.270597i	0.247002	−	0.969015i	$-0.420555\pi$
$587$	−11.3554	−	6.55606i	−0.468688	−	0.270597i	−0.715691	+	0.698418i	$0.753888\pi$
$588$	1.10962	−	6.63327i	0.0457601	−	0.273551i
$589$	−5.88021	+	32.7935i	−0.242290	+	1.35123i
$590$			7.65515i			0.315158i
$591$	0.316241	−	0.383678i	0.0130084	−	0.0157824i
$592$	−7.12175	−	4.11174i	−0.292702	−	0.168992i
$593$	−21.2078	+	12.2443i	−0.870900	+	0.502814i	−0.867647	−	0.497180i	$-0.834369\pi$
$593$	−21.2078	+	12.2443i	−0.870900	+	0.502814i	−0.00325292	+	0.999995i	$0.501035\pi$
$594$	13.4085	−	8.22003i	0.550158	−	0.337272i
$595$	−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	$-0.258860\pi$
$599$	−6.98997	−	12.1070i	−0.285603	−	0.494678i	−0.972755	+	0.231835i	$0.925527\pi$
$600$	−0.285770	+	1.70831i	−0.0116665	+	0.0697416i
$601$		−	41.6645i		−	1.69953i	−0.527161	−	0.849766i	$-0.676743\pi$
$601$		−	41.6645i		−	1.69953i	0.527161	−	0.849766i	$-0.323257\pi$
$602$	−8.68810	−	15.0482i	−0.354101	−	0.613320i
$603$	1.47727	+	1.69900i	0.0601591	+	0.0691885i
$604$	19.7111	−	11.3802i	0.802032	−	0.463053i
$605$	−1.59230	−	0.919316i	−0.0647362	−	0.0373755i
$606$	17.5510	−	21.2936i	0.712960	−	0.864994i
$607$		−	31.5810i		−	1.28183i	−0.767610	−	0.640917i	$-0.778554\pi$
$607$		−	31.5810i		−	1.28183i	0.767610	−	0.640917i	$-0.221446\pi$
$608$	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
$612$	−9.40926	+	1.83013i	−0.380347	+	0.0739787i
$613$	0.700918	−	1.21403i	0.0283098	−	0.0490340i	−0.851523	−	0.524317i	$-0.824321\pi$
$613$	0.700918	−	1.21403i	0.0283098	−	0.0490340i	0.879833	+	0.475283i	$0.157654\pi$
$614$	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	$-0.734786\pi$
$617$	−9.13701	+	5.27526i	−0.367842	+	0.212374i	0.304673	+	0.952457i	$0.401453\pi$
$618$	3.78843	+	10.1308i	0.152393	+	0.407520i
$619$	−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
$621$	−0.133593	−	5.06726i	−0.00536088	−	0.203342i
$622$	2.07949	+	1.20060i	0.0833801	+	0.0481395i
$623$	7.69999	+	13.3368i	0.308494	+	0.534327i
$624$	−4.13939	+	5.02209i	−0.165708	+	0.201045i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	7.70245			0.307852
$627$	17.4185	−	14.7917i	0.695628	−	0.590723i
$628$	−8.02210			−0.320117
$629$	13.1378	−	22.7554i	0.523840	−	0.907317i
$630$	3.47533	+	3.99696i	0.138461	+	0.159243i
$631$	−4.99217	−	8.64668i	−0.198735	−	0.344219i	0.749384	−	0.662136i	$-0.230350\pi$
$631$	−4.99217	−	8.64668i	−0.198735	−	0.344219i	−0.948119	+	0.317917i	$0.897017\pi$
$632$	−2.26576	−	1.30814i	−0.0901270	−	0.0520349i
$633$	11.5603	+	30.9137i	0.459479	+	1.22871i
$634$	−20.3985			−0.810129
$635$	−4.51362			−0.179118
$636$	19.2154	−	7.18566i	0.761942	−	0.284930i
$637$	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	$-0.977466\pi$
$641$	−11.0764	+	19.1848i	−0.437490	+	0.757755i	0.560005	+	0.828489i	$0.310799\pi$
$642$	−4.06978	+	1.52190i	−0.160621	+	0.0600647i
$643$	−24.4476	+	42.3446i	−0.964121	+	1.66991i	−0.252163	+	0.967685i	$0.581142\pi$
$643$	−24.4476	+	42.3446i	−0.964121	+	1.66991i	−0.711958	+	0.702222i	$0.752191\pi$
$644$	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	$-0.0168842\pi$
$648$	8.34386	−	3.37344i	0.327778	−	0.132521i
$649$	20.0662	+	11.5852i	0.787666	+	0.454759i
$650$	−3.25407	+	1.87874i	−0.127635	+	0.0736903i
$651$	−14.8661	+	18.0362i	−0.582647	+	0.706893i
$652$	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	$-0.0230722\pi$
$659$	11.1918	+	19.3847i	0.435970	+	0.755121i	−0.561405	+	0.827541i	$0.689739\pi$
$660$	4.04546	+	3.33442i	0.157469	+	0.129792i
$661$	12.9940	−	7.50211i	0.505409	−	0.291798i	−0.225535	−	0.974235i	$-0.572413\pi$
$661$	12.9940	−	7.50211i	0.505409	−	0.291798i	0.730945	+	0.682437i	$0.239080\pi$
$662$	22.0426	+	12.7263i	0.856711	+	0.494622i
$663$	−16.0466	−	13.2262i	−0.623198	−	0.513662i
$664$			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
$669$	1.01709	+	2.71984i	0.0393230	+	0.105155i
$670$	−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	$-0.918164\pi$
$673$		−	13.1927i		−	0.508543i	0.967133	−	0.254271i	$-0.0818356\pi$
$674$	14.8031	−	8.54657i	0.570194	−	0.329202i
$675$	5.19435	−	0.136943i	0.199931	−	0.00527094i
$676$	−1.11866			−0.0430255
$677$	15.1704			0.583047			0.291523	−	0.956564i	$-0.405838\pi$
$677$	15.1704			0.583047			0.291523	+	0.956564i	$0.405838\pi$
$678$	−20.5873	+	7.69867i	−0.790651	+	0.295666i
$679$	21.9344	+	12.6638i	0.841764	+	0.485993i
$680$	−1.59760	−	2.76712i	−0.0612651	−	0.106114i
$681$	−15.0368	−	12.3939i	−0.576211	−	0.474934i
$682$	−11.5673	+	20.0352i	−0.442936	+	0.767188i
$683$	26.8136			1.02599			0.512997	−	0.858390i	$-0.328535\pi$
$683$	26.8136			1.02599			0.512997	+	0.858390i	$0.328535\pi$
$684$	11.2276	−	6.70389i	0.429296	−	0.256330i
$685$	14.6857			0.561111
$686$	9.60703	−	16.6399i	0.366798	−	0.635313i
$687$	30.2752	+	24.9539i	1.15507	+	0.952052i
$688$	−4.92098	−	8.52339i	−0.187611	−	0.324951i
$689$	38.5424	+	22.2525i	1.46835	+	0.847752i
$690$	1.58264	−	0.591830i	0.0602499	−	0.0225306i
$691$	−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
$693$	15.7366	−	3.06082i	0.597784	−	0.116271i
$694$	−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
$699$	6.47595	+	17.3176i	0.244943	+	0.655011i
$700$	−0.882761	+	1.52899i	−0.0333652	+	0.0577903i
$701$	−4.07681	−	2.35374i	−0.153979	−	0.0888997i	0.421031	−	0.907046i	$-0.361668\pi$
$701$	−4.07681	−	2.35374i	−0.153979	−	0.0888997i	−0.575010	+	0.818147i	$0.695002\pi$
$702$	17.1601	+	9.31321i	0.647665	+	0.351504i
$703$	−6.32653	+	35.2826i	−0.238610	+	1.33071i
$704$			3.02678i			0.114076i
$705$	−11.4017	−	9.39768i	−0.429412	−	0.353937i
$706$	25.5556	+	14.7545i	0.961798	+	0.555294i
$707$	24.3593	−	14.0639i	0.916127	−	0.528926i
$708$	10.2316	+	8.43323i	0.384525	+	0.316940i
$709$	15.3247	+	26.5431i	0.575531	+	0.996849i	0.995984	+	0.0895342i	$0.0285378\pi$
$709$	15.3247	+	26.5431i	0.575531	+	0.996849i	−0.420453	+	0.907314i	$0.638129\pi$
$710$		−	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
$717$	24.2222	−	29.3875i	0.904596	−	1.09750i
$718$	−23.2838	+	13.4429i	−0.868944	+	0.501685i
$719$	−20.3745	−	11.7632i	−0.759841	−	0.438694i	0.0693979	−	0.997589i	$-0.477892\pi$
$719$	−20.3745	−	11.7632i	−0.759841	−	0.438694i	−0.829239	+	0.558895i	$0.811226\pi$
$720$	1.96845	+	2.26390i	0.0733596	+	0.0843704i
$721$			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
$726$	−2.98286	+	1.11545i	−0.110704	+	0.0413982i
$727$	0.310241	−	0.537354i	0.0115062	−	0.0199293i	−0.860215	−	0.509932i	$-0.829671\pi$
$727$	0.310241	−	0.537354i	0.0115062	−	0.0199293i	0.871721	+	0.490002i	$0.163004\pi$
$728$	−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
$732$	3.24486	−	1.21342i	0.119933	−	0.0448494i
$733$	−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
$735$	−2.35567	−	6.29939i	−0.0868902	−	0.232356i
$736$	0.844837	+	0.487767i	0.0311411	+	0.0179793i
$737$	1.13576	+	1.96719i	0.0418363	+	0.0724625i
$738$	0.300926	−	0.261654i	0.0110772	−	0.00963161i
$739$	10.7620	−	18.6403i	0.395886	−	0.685694i	−0.597328	−	0.801997i	$-0.703771\pi$
$739$	10.7620	−	18.6403i	0.395886	−	0.685694i	0.993214	+	0.116303i	$0.0371044\pi$
$740$	−8.22349			−0.302301
$741$	26.7143	+	9.54526i	0.981373	+	0.350654i
$742$	20.9115			0.767685
$743$	−16.8709	+	29.2213i	−0.618935	+	1.07203i	0.370746	+	0.928734i	$0.379102\pi$
$743$	−16.8709	+	29.2213i	−0.618935	+	1.07203i	−0.989680	+	0.143292i	$0.954231\pi$
$744$	−8.42021	+	10.2158i	−0.308700	+	0.374528i
$745$	−1.37189	−	2.37618i	−0.0502622	−	0.0870566i
$746$	5.93798	+	3.42829i	0.217405	+	0.125519i
$747$	13.7561	−	2.67560i	0.503309	−	0.0978952i
$748$	−9.67115			−0.353612
$749$	−4.42900			−0.161832
$750$	0.606673	+	1.62233i	0.0221526	+	0.0592390i
$751$	−37.8615	+	21.8593i	−1.38158	+	0.797658i	−0.992347	−	0.123479i	$-0.960595\pi$
$751$	−37.8615	+	21.8593i	−1.38158	+	0.797658i	−0.389237	+	0.921137i	$0.627261\pi$
$752$		−	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
$756$	9.17073	−	0.241776i	0.333536	−	0.00879331i
$757$	−9.68232	+	16.7703i	−0.351910	+	0.609526i	−0.986584	−	0.163254i	$-0.947801\pi$
$757$	−9.68232	+	16.7703i	−0.351910	+	0.609526i	0.634674	+	0.772780i	$0.281134\pi$
$758$	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	$-0.227345\pi$
$762$	−4.97239	+	6.03272i	−0.180131	+	0.218542i
$763$	0.343445	+	0.198288i	0.0124335	+	0.00717850i
$764$	−5.05565	+	2.91888i	−0.182907	+	0.105601i
$765$	−7.23359	+	6.28957i	−0.261531	+	0.227400i
$766$	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	0.954079	+	0.299555i	$0.0968382\pi$
$769$	20.4227	+	35.3732i	0.736462	+	1.27559i	−0.217617	+	0.976034i	$0.569828\pi$
$770$	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	0.694064	+	0.719914i	$0.255819\pi$
$773$	26.9826	+	46.7352i	0.970495	+	1.68095i	0.276432	+	0.961034i	$0.410848\pi$
$774$	−22.2812	+	19.3734i	−0.800881	+	0.696362i
$775$	−6.61932	+	3.82167i	−0.237773	+	0.137278i
$776$	12.4237	+	7.17285i	0.445986	+	0.257490i
$777$	−15.9944	+	19.4052i	−0.573797	+	0.696156i
$778$		−	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
$783$	−33.2152	+	0.875681i	−1.18701	+	0.0312943i
$784$	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	$0.148921\pi$
$787$			25.3024i			0.901933i	−0.892541	+	0.450967i	$0.851079\pi$
$788$	0.248605	−	0.143532i	0.00885617	−	0.00511311i
$789$	−1.32006	−	3.53003i	−0.0469955	−	0.125672i
$790$	−2.61627			−0.0930828
$791$	−22.4044			−0.796610
$792$	8.91329	−	1.73366i	0.316720	−	0.0616031i
$793$	6.50856	+	3.75772i	0.231126	+	0.133440i
$794$	−15.2157	−	26.3543i	−0.539983	−	0.935278i
$795$	13.0482	−	15.8307i	0.462773	−	0.561456i
$796$	9.44058	−	16.3516i	0.334612	−	0.579566i
$797$	−50.5277			−1.78978			−0.894891	−	0.446284i	$-0.852747\pi$
$797$	−50.5277			−1.78978			−0.894891	+	0.446284i	$0.852747\pi$
$798$	13.1130	−	2.39196i	0.464196	−	0.0846744i
$799$	27.2570			0.964285
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	19.7471	−	17.1700i	0.697730	−	0.606672i
$802$	4.69167	+	8.12622i	0.165669	+	0.286947i
$803$	2.50556	+	1.44658i	0.0884192	+	0.0510489i
$804$	0.455293	+	1.21752i	0.0160570	+	0.0429385i
$805$	1.72233			0.0607040
$806$	−28.7197			−1.01161
$807$	−52.3886	+	19.5908i	−1.84417	+	0.689631i
$808$	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	0.277775	−	0.960646i	$-0.410403\pi$
$811$	35.5579	−	20.5294i	1.24861	−	0.720883i	0.970831	+	0.239763i	$0.0770697\pi$
$812$	5.64481	−	9.77709i	0.198094	−	0.343109i
$813$	−5.57466	+	2.08466i	−0.195512	+	0.0731121i
$814$	−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
$819$	13.0585	+	15.0185i	0.456301	+	0.524789i
$820$	0.115116	+	0.0664620i	0.00402001	+	0.00232096i
$821$	7.15533	−	4.13113i	0.249723	−	0.144178i	−0.369915	−	0.929066i	$-0.620613\pi$
$821$	7.15533	−	4.13113i	0.249723	−	0.144178i	0.619637	+	0.784888i	$0.287280\pi$
$822$	16.1783	−	19.6283i	0.564284	−	0.684614i
$823$	20.6142	+	35.7048i	0.718566	+	1.24459i	0.961568	+	0.274566i	$0.0885343\pi$
$823$	20.6142	+	35.7048i	0.718566	+	1.24459i	−0.243003	+	0.970026i	$0.578132\pi$
$824$			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	$-0.151043\pi$
$827$	1.41094	+	2.44382i	0.0490632	+	0.0849800i	−0.840451	+	0.541888i	$0.817710\pi$
$828$	0.952480	−	2.76727i	0.0331010	−	0.0961692i
$829$			44.2077i			1.53540i	0.640811	+	0.767699i	$0.278598\pi$
$829$			44.2077i			1.53540i	−0.640811	+	0.767699i	$0.721402\pi$
$830$	2.33564	+	4.04546i	0.0810714	+	0.140420i
$831$	−14.3001	−	11.7867i	−0.496066	−	0.408876i
$832$	−3.25407	+	1.87874i	−0.112815	+	0.0651336i
$833$	10.7445	+	6.20337i	0.372277	+	0.214934i
$834$	25.1992	+	20.7701i	0.872577	+	0.719210i
$835$		−	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	$-0.760083\pi$
$839$	6.60690	−	11.4435i	0.228096	−	0.395073i	0.957244	+	0.289283i	$0.0934168\pi$
$840$	1.07109	+	2.86426i	0.0369563	+	0.0988262i
$841$	−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
$846$	−25.1211	+	4.88614i	−0.863681	+	0.167989i
$847$	−3.24614			−0.111539
$848$	11.8444			0.406737
$849$	3.90539	−	1.46043i	0.134033	−	0.0501218i
$850$	−2.76712	−	1.59760i	−0.0949115	−	0.0547972i
$851$	4.01114	+	6.94751i	0.137500	+	0.238157i
$852$	−21.7703	−	17.9439i	−0.745839	−	0.614748i
$853$	1.06604	−	1.84644i	0.0365006	−	0.0632208i	−0.847198	−	0.531277i	$-0.821712\pi$
$853$	1.06604	−	1.84644i	0.0365006	−	0.0632208i	0.883699	+	0.468056i	$0.155046\pi$
$854$	3.53127			0.120837
$855$	6.37140	−	11.4195i	0.217897	−	0.390539i
$856$	−2.50860			−0.0857423
$857$	−25.1218	+	43.5123i	−0.858145	+	1.48635i	0.0155507	+	0.999879i	$0.495050\pi$
$857$	−25.1218	+	43.5123i	−0.858145	+	1.48635i	−0.873696	+	0.486472i	$0.838283\pi$
$858$	15.2007	+	12.5290i	0.518945	+	0.427734i
$859$	1.48228	+	2.56738i	0.0505746	+	0.0875978i	0.890204	−	0.455561i	$-0.150561\pi$
$859$	1.48228	+	2.56738i	0.0505746	+	0.0875978i	−0.839630	+	0.543159i	$0.817228\pi$
$860$	−8.52339	−	4.92098i	−0.290645	−	0.167804i
$861$	0.380729	−	0.142374i	0.0129752	−	0.00485210i
$862$	8.78159			0.299102
$863$	−0.298281			−0.0101536			−0.00507680	−	0.999987i	$-0.501616\pi$
$863$	−0.298281			−0.0101536			−0.00507680	+	0.999987i	$0.501616\pi$
$864$	5.19435	−	0.136943i	0.176715	−	0.00465890i
$865$	−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
$870$	−3.87937	−	10.3740i	−0.131523	−	0.351710i
$871$	−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
$876$	1.27756	+	1.05301i	0.0431648	+	0.0355780i
$877$	31.2808	+	18.0600i	1.05628	+	0.609843i	0.924401	−	0.381423i	$-0.124566\pi$
$877$	31.2808	+	18.0600i	1.05628	+	0.609843i	0.131878	+	0.991266i	$0.457899\pi$
$878$	−23.3862	+	13.5020i	−0.789247	+	0.455672i
$879$	16.3970	+	13.5150i	0.553055	+	0.455849i
$880$	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	0.988408	+	0.151818i	$0.0485128\pi$
$883$	18.5924	+	32.2029i	0.625683	+	1.08371i	−0.362726	+	0.931896i	$0.618154\pi$
$884$	−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	$-0.0780966\pi$
$887$	8.18050	+	14.1690i	0.274674	+	0.475750i	−0.695379	+	0.718644i	$0.744763\pi$
$888$	−9.05933	+	10.9912i	−0.304011	+	0.368839i
$889$	−6.90127	+	3.98445i	−0.231461	+	0.133634i
$890$	7.55401	+	4.36131i	0.253211	+	0.146192i
$891$	−10.2106	−	25.2550i	−0.342069	−	0.846073i
$892$			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
$897$	5.94672	−	2.22379i	0.198555	−	0.0742502i
$898$	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
$903$	−28.1899	+	10.5417i	−0.938101	+	0.350805i
$904$	−12.6900			−0.422063
$905$	−10.5944			−0.352170
$906$	−13.8081	−	36.9248i	−0.458744	−	1.22674i
$907$	−37.5272	−	21.6663i	−1.24607	−	0.719418i	−0.275746	−	0.961230i	$-0.588925\pi$
$907$	−37.5272	−	21.6663i	−1.24607	−	0.719418i	−0.970323	+	0.241812i	$0.922258\pi$
$908$	−5.62519	−	9.74312i	−0.186679	−	0.323337i
$909$	−31.3606	−	36.0676i	−1.04017	−	1.19629i
$910$	−3.31696	+	5.74514i	−0.109956	+	0.190450i
$911$	35.9636			1.19153			0.595764	−	0.803159i	$-0.296849\pi$
$911$	35.9636			1.19153			0.595764	+	0.803159i	$0.296849\pi$
$912$	7.42728	−	1.35482i	0.245942	−	0.0448624i
$913$	14.1389			0.467931
$914$	−3.80429	+	6.58922i	−0.125835	+	0.217952i
$915$	2.20342	−	2.67328i	0.0728428	−	0.0883761i
$916$	11.3258	+	19.6169i	0.374215	+	0.648160i
$917$	6.77965	+	3.91423i	0.223884	+	0.129259i
$918$	0.437560	+	16.5970i	0.0144416	+	0.547782i
$919$	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
$921$	−13.0080	−	34.7852i	−0.428628	−	1.14621i
$922$	−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
$927$	18.3892	−	3.57675i	0.603979	−	0.117476i
$928$	3.19725	−	5.53779i	0.104955	−	0.181787i
$929$	−8.50595	−	4.91091i	−0.279071	−	0.161122i	0.353932	−	0.935271i	$-0.384845\pi$
$929$	−8.50595	−	4.91091i	−0.279071	−	0.161122i	−0.633003	+	0.774150i	$0.718178\pi$
$930$	−2.18423	+	13.0572i	−0.0716238	+	0.428163i
$931$	−16.6596	−	2.98724i	−0.545997	−	0.0979027i
$932$			10.6745i			0.349656i
$933$	2.64525	−	3.20933i	0.0866016	−	0.105069i
$934$	−9.89331	−	5.71190i	−0.323719	−	0.186899i
$935$	−8.37546	+	4.83557i	−0.273907	+	0.158140i
$936$	7.39640	+	8.50654i	0.241759	+	0.278045i
$937$	−14.1222	−	24.4603i	−0.461351	−	0.799084i	0.537677	−	0.843151i	$-0.319302\pi$
$937$	−14.1222	−	24.4603i	−0.461351	−	0.799084i	−0.999029	+	0.0440667i	$0.985969\pi$
$938$			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	$-0.277224\pi$
$941$	−10.4415	−	18.0853i	−0.340385	−	0.589563i	−0.984504	+	0.175361i	$0.943891\pi$
$942$	−2.29247	+	13.7043i	−0.0746928	+	0.446509i
$943$		−	0.129672i		−	0.00422270i
$944$	3.82758	+	6.62956i	0.124577	+	0.215774i
$945$	7.82120	−	4.79475i	0.254424	−	0.155973i
$946$	−25.7984	+	14.8947i	−0.838778	+	0.484269i
$947$	51.7967	+	29.9048i	1.68317	+	0.971777i	0.959534	+	0.281591i	$0.0908622\pi$
$947$	51.7967	+	29.9048i	1.68317	+	0.971777i	0.723632	+	0.690186i	$0.242471\pi$
$948$	−2.88219	+	3.49680i	−0.0936092	+	0.113571i
$949$			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	$-0.859730\pi$
$953$	−2.55708	+	4.42900i	−0.0828321	+	0.143469i	0.821633	+	0.570016i	$0.193063\pi$
$954$	−6.78417	−	34.8794i	−0.219646	−	1.12926i
$955$	−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
$960$	0.606673	+	1.62233i	0.0195803	+	0.0523604i
$961$	−27.4206			−0.884535
$962$	−30.8996			−0.996243
$963$	1.43687	+	7.38737i	0.0463024	+	0.238055i
$964$	−1.68423	−	0.972389i	−0.0542453	−	0.0313185i
$965$	−7.06095	−	12.2299i	−0.227300	−	0.393695i
$966$	1.89738	−	2.30199i	0.0610473	−	0.0740653i
$967$	−14.7197	+	25.4953i	−0.473354	+	0.819873i	−0.999535	−	0.0304996i	$-0.990290\pi$
$967$	−14.7197	+	25.4953i	−0.473354	+	0.819873i	0.526181	+	0.850373i	$0.323623\pi$
$968$	−1.83863			−0.0590958
$969$	4.32891	+	23.7316i	0.139065	+	0.762370i
$970$	14.3457			0.460613
$971$	−9.07896	+	15.7252i	−0.291358	+	0.504646i	−0.974131	−	0.225984i	$-0.927440\pi$
$971$	−9.07896	+	15.7252i	−0.291358	+	0.504646i	0.682773	+	0.730630i	$0.260774\pi$
$972$	−3.37847	−	15.2179i	−0.108364	−	0.488116i
$973$	16.6434	+	28.8272i	0.533563	+	0.924158i
$974$	7.80535	+	4.50642i	0.250099	+	0.144395i
$975$	2.27956	+	6.09587i	0.0730044	+	0.195224i
$976$	2.00013			0.0640225
$977$	37.0070			1.18396			0.591980	−	0.805953i	$-0.298346\pi$
$977$	37.0070			1.18396			0.591980	+	0.805953i	$0.298346\pi$
$978$	6.01157	−	2.24804i	0.192229	−	0.0718844i
$979$	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	$-0.876720\pi$
$983$	−4.26025	+	7.37898i	−0.135881	+	0.235353i	0.790053	+	0.613039i	$0.210053\pi$
$984$	0.215646	−	0.0806415i	0.00687456	−	0.00257076i
$985$	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
$990$	6.85230	−	5.95804i	0.217780	−	0.189359i
$991$	−7.55231	−	4.36033i	−0.239907	−	0.138510i	0.375227	−	0.926933i	$-0.377565\pi$
$991$	−7.55231	−	4.36033i	−0.239907	−	0.138510i	−0.615134	+	0.788423i	$0.710898\pi$
$992$	−6.61932	+	3.82167i	−0.210164	+	0.121338i
$993$	28.0397	−	34.0189i	0.889812	−	1.07956i
$994$	−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	0.932258	−	0.361793i	$-0.117835\pi$
$997$	4.82494	+	8.35704i	0.152807	+	0.264670i	−0.779451	+	0.626463i	$0.784502\pi$
$998$	−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.b.521.3	yes	24
3.2	odd	2		570.2.s.a.521.1	yes	24
19.12	odd	6		570.2.s.a.221.1	✓	24
57.50	even	6	inner	570.2.s.b.221.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.s.a.221.1	✓	24	19.12	odd	6
570.2.s.a.521.1	yes	24	3.2	odd	2
570.2.s.b.221.3	yes	24	57.50	even	6	inner
570.2.s.b.521.3	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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.33656 - 1.10164i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.62233 + 0.606673i) q^{6} -1.76552 q^{7} -1.00000 q^{8} +(0.572776 + 2.94481i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.33656 - 1.10164i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.62233 + 0.606673i) q^{6} -1.76552 q^{7} -1.00000 q^{8} +(0.572776 + 2.94481i) 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} +(0.606673 + 1.62233i) 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} +(2.35972 + 1.94497i) q^{21} +(2.62126 + 1.51339i) q^{22} +(0.844837 - 0.487767i) q^{23} +(1.33656 + 1.10164i) 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} +(3.33442 - 4.04546i) q^{33} +(-2.76712 + 1.59760i) q^{34} +(1.52899 + 0.882761i) q^{35} +(2.26390 - 1.96845i) 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} +(2.86426 - 1.07109i) 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} +(1.62233 - 0.606673i) q^{48} -3.88293 q^{49} +1.00000 q^{50} +(1.93844 + 5.18366i) q^{51} +(3.25407 + 1.87874i) q^{52} +(-5.92218 - 10.2575i) q^{53} +(-2.71577 - 4.42997i) q^{54} +(1.51339 - 2.62126i) q^{55} +1.76552 q^{56} +(-4.88694 - 5.75480i) q^{57} -6.39449 q^{58} +(3.82758 - 6.62956i) q^{59} +(1.10164 - 1.33656i) q^{60} +(-1.00006 - 1.73216i) q^{61} +(6.61932 + 3.82167i) q^{62} +(-1.01125 - 5.19913i) q^{63} +1.00000 q^{64} +3.75748 q^{65} +(-1.83626 - 4.91042i) 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} +(-0.572776 - 2.94481i) 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} +(4.13939 - 5.02209i) q^{78} +(2.26576 + 1.30814i) q^{79} +(0.866025 - 0.500000i) q^{80} +(-8.34386 + 3.37344i) 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} +(-1.96845 - 2.26390i) q^{90} +(5.74514 - 3.31696i) q^{91} +(-0.844837 - 0.487767i) q^{92} +(8.42021 - 10.2158i) 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} +(-8.91329 + 1.73366i) 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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