LMFDB - Embedded newform 930.2.o.d.161.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(161,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, 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("930.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.o (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			161.9
Character	$\chi$	$=$	930.161
Dual form			930.2.o.d.491.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.68098 - 0.417505i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.417505 - 1.68098i) q^{6} +(2.16910 + 3.75699i) q^{7} +1.00000i q^{8} +(2.65138 - 1.40363i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.68098 - 0.417505i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.417505 - 1.68098i) q^{6} +(2.16910 + 3.75699i) q^{7} +1.00000i q^{8} +(2.65138 - 1.40363i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-2.88976 + 5.00521i) q^{11} +(-1.68098 + 0.417505i) q^{12} +(0.829513 + 0.478920i) q^{13} +(3.75699 - 2.16910i) q^{14} +(-1.66452 - 0.478920i) q^{15} +1.00000 q^{16} +(0.169223 + 0.293102i) q^{17} +(-1.40363 - 2.65138i) q^{18} +(0.915626 + 1.58591i) q^{19} +(0.866025 + 0.500000i) q^{20} +(5.21477 + 5.40981i) q^{21} +(5.00521 + 2.88976i) q^{22} +7.13933 q^{23} +(0.417505 + 1.68098i) q^{24} +(0.500000 + 0.866025i) q^{25} +(0.478920 - 0.829513i) q^{26} +(3.87089 - 3.46644i) q^{27} +(-2.16910 - 3.75699i) q^{28} -7.24694 q^{29} +(-0.478920 + 1.66452i) q^{30} +(4.75096 + 2.90317i) q^{31} -1.00000i q^{32} +(-2.76793 + 9.62014i) q^{33} +(0.293102 - 0.169223i) q^{34} -4.33820i q^{35} +(-2.65138 + 1.40363i) q^{36} +(-5.82791 + 3.36475i) q^{37} +(1.58591 - 0.915626i) q^{38} +(1.59435 + 0.458728i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-1.47141 - 0.849519i) q^{41} +(5.40981 - 5.21477i) q^{42} +(3.67927 - 2.12423i) q^{43} +(2.88976 - 5.00521i) q^{44} +(-2.99798 - 0.110108i) q^{45} -7.13933i q^{46} -2.77585i q^{47} +(1.68098 - 0.417505i) q^{48} +(-5.90998 + 10.2364i) q^{49} +(0.866025 - 0.500000i) q^{50} +(0.406831 + 0.422047i) q^{51} +(-0.829513 - 0.478920i) q^{52} +(4.01409 - 6.95261i) q^{53} +(-3.46644 - 3.87089i) q^{54} +(5.00521 - 2.88976i) q^{55} +(-3.75699 + 2.16910i) q^{56} +(2.20127 + 2.28360i) q^{57} +7.24694i q^{58} +(-0.461706 + 0.266566i) q^{59} +(1.66452 + 0.478920i) q^{60} -12.6523i q^{61} +(2.90317 - 4.75096i) q^{62} +(11.0245 + 6.91658i) q^{63} -1.00000 q^{64} +(-0.478920 - 0.829513i) q^{65} +(9.62014 + 2.76793i) q^{66} +(6.77532 - 11.7352i) q^{67} +(-0.169223 - 0.293102i) q^{68} +(12.0011 - 2.98071i) q^{69} -4.33820 q^{70} +(-5.72634 - 3.30610i) q^{71} +(1.40363 + 2.65138i) q^{72} +(5.51744 + 3.18550i) q^{73} +(3.36475 + 5.82791i) q^{74} +(1.20206 + 1.24702i) q^{75} +(-0.915626 - 1.58591i) q^{76} -25.0727 q^{77} +(0.458728 - 1.59435i) q^{78} +(-2.30975 + 1.33353i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(5.05963 - 7.44313i) q^{81} +(-0.849519 + 1.47141i) q^{82} +(-4.17413 + 7.22980i) q^{83} +(-5.21477 - 5.40981i) q^{84} -0.338445i q^{85} +(-2.12423 - 3.67927i) q^{86} +(-12.1819 + 3.02563i) q^{87} +(-5.00521 - 2.88976i) q^{88} +0.143194 q^{89} +(-0.110108 + 2.99798i) q^{90} +4.15530i q^{91} -7.13933 q^{92} +(9.19835 + 2.89662i) q^{93} -2.77585 q^{94} -1.83125i q^{95} +(-0.417505 - 1.68098i) q^{96} -13.3181 q^{97} +(10.2364 + 5.90998i) q^{98} +(-0.636370 + 17.3269i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9}+O(q^{10}) $ 36 * q - 36 * q^4 - 8 * q^7 + 8 * q^9	$ 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9} - 18 q^{10} + 36 q^{16} - 4 q^{18} - 4 q^{19} + 72 q^{21} - 18 q^{22} + 18 q^{25} + 8 q^{28} + 52 q^{31} - 36 q^{33} + 18 q^{34} - 8 q^{36} - 54 q^{37} - 8 q^{39} + 18 q^{40} + 12 q^{42} - 18 q^{43} + 4 q^{45} - 62 q^{49} - 10 q^{51} - 18 q^{55} + 12 q^{57} + 88 q^{63} - 36 q^{64} - 4 q^{66} + 10 q^{67} + 46 q^{69} + 16 q^{70} + 4 q^{72} + 24 q^{73} + 4 q^{76} + 92 q^{78} + 42 q^{79} + 4 q^{81} - 12 q^{82} - 72 q^{84} - 16 q^{87} + 18 q^{88} + 8 q^{90} + 48 q^{93} - 92 q^{94} - 80 q^{97} - 18 q^{99}+O(q^{100}) $ 36 * q - 36 * q^4 - 8 * q^7 + 8 * q^9 - 18 * q^10 + 36 * q^16 - 4 * q^18 - 4 * q^19 + 72 * q^21 - 18 * q^22 + 18 * q^25 + 8 * q^28 + 52 * q^31 - 36 * q^33 + 18 * q^34 - 8 * q^36 - 54 * q^37 - 8 * q^39 + 18 * q^40 + 12 * q^42 - 18 * q^43 + 4 * q^45 - 62 * q^49 - 10 * q^51 - 18 * q^55 + 12 * q^57 + 88 * q^63 - 36 * q^64 - 4 * q^66 + 10 * q^67 + 46 * q^69 + 16 * q^70 + 4 * q^72 + 24 * q^73 + 4 * q^76 + 92 * q^78 + 42 * q^79 + 4 * q^81 - 12 * q^82 - 72 * q^84 - 16 * q^87 + 18 * q^88 + 8 * q^90 + 48 * q^93 - 92 * q^94 - 80 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.68098	−	0.417505i	0.970514	−	0.241046i
$3$	1.68098	−	0.417505i	0.970514	−	0.241046i
$4$	−1.00000			−0.500000
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	−0.417505	−	1.68098i	−0.170446	−	0.686257i
$7$	2.16910	+	3.75699i	0.819842	+	1.42001i	0.905798	+	0.423709i	$0.139272\pi$
$7$	2.16910	+	3.75699i	0.819842	+	1.42001i	−0.0859560	+	0.996299i	$0.527394\pi$
$8$			1.00000i			0.353553i
$9$	2.65138	−	1.40363i	0.883793	−	0.467878i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−2.88976	+	5.00521i	−0.871295	+	1.50913i	−0.0106381	+	0.999943i	$0.503386\pi$
$11$	−2.88976	+	5.00521i	−0.871295	+	1.50913i	−0.860657	+	0.509185i	$0.829947\pi$
$12$	−1.68098	+	0.417505i	−0.485257	+	0.120523i
$13$	0.829513	+	0.478920i	0.230066	+	0.132828i	0.610602	−	0.791937i	$-0.290927\pi$
$13$	0.829513	+	0.478920i	0.230066	+	0.132828i	−0.380537	+	0.924766i	$0.624261\pi$
$14$	3.75699	−	2.16910i	1.00410	−	0.579716i
$15$	−1.66452	−	0.478920i	−0.429778	−	0.123657i
$16$	1.00000			0.250000
$17$	0.169223	+	0.293102i	0.0410425	+	0.0710877i	0.885817	−	0.464035i	$-0.153599\pi$
$17$	0.169223	+	0.293102i	0.0410425	+	0.0710877i	−0.844774	+	0.535123i	$0.820265\pi$
$18$	−1.40363	−	2.65138i	−0.330840	−	0.624936i
$19$	0.915626	+	1.58591i	0.210059	+	0.363833i	0.951733	−	0.306928i	$-0.0993011\pi$
$19$	0.915626	+	1.58591i	0.210059	+	0.363833i	−0.741674	+	0.670761i	$0.765968\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$	5.21477	+	5.40981i	1.13796	+	1.18052i
$22$	5.00521	+	2.88976i	1.06711	+	0.616099i
$23$	7.13933			1.48865			0.744327	−	0.667815i	$-0.232770\pi$
$23$	7.13933			1.48865			0.744327	+	0.667815i	$0.232770\pi$
$24$	0.417505	+	1.68098i	0.0852228	+	0.343128i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	0.478920	−	0.829513i	0.0939239	−	0.162681i
$27$	3.87089	−	3.46644i	0.744953	−	0.667117i
$28$	−2.16910	−	3.75699i	−0.409921	−	0.710004i
$29$	−7.24694			−1.34572			−0.672861	−	0.739769i	$-0.734935\pi$
$29$	−7.24694			−1.34572			−0.672861	+	0.739769i	$0.734935\pi$
$30$	−0.478920	+	1.66452i	−0.0874384	+	0.303899i
$31$	4.75096	+	2.90317i	0.853297	+	0.521425i
$31$	4.75096	+	2.90317i	0.853297	+	0.521425i
$32$		−	1.00000i		−	0.176777i
$33$	−2.76793	+	9.62014i	−0.481834	+	1.67465i
$34$	0.293102	−	0.169223i	0.0502666	−	0.0290214i
$35$		−	4.33820i		−	0.733289i
$36$	−2.65138	+	1.40363i	−0.441897	+	0.233939i
$37$	−5.82791	+	3.36475i	−0.958103	+	0.553161i	−0.895589	−	0.444883i	$-0.853245\pi$
$37$	−5.82791	+	3.36475i	−0.958103	+	0.553161i	−0.0625142	+	0.998044i	$0.519912\pi$
$38$	1.58591	−	0.915626i	0.257269	−	0.148534i
$39$	1.59435	+	0.458728i	0.255300	+	0.0734553i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−1.47141	−	0.849519i	−0.229796	−	0.132673i	0.380682	−	0.924706i	$-0.375689\pi$
$41$	−1.47141	−	0.849519i	−0.229796	−	0.132673i	−0.610478	+	0.792033i	$0.709023\pi$
$42$	5.40981	−	5.21477i	0.834752	−	0.804656i
$43$	3.67927	−	2.12423i	0.561084	−	0.323942i	−0.192496	−	0.981298i	$-0.561658\pi$
$43$	3.67927	−	2.12423i	0.561084	−	0.323942i	0.753581	+	0.657356i	$0.228325\pi$
$44$	2.88976	−	5.00521i	0.435648	−	0.754564i
$45$	−2.99798	−	0.110108i	−0.446912	−	0.0164139i
$46$		−	7.13933i		−	1.05264i
$47$		−	2.77585i		−	0.404900i	−0.979293	−	0.202450i	$-0.935110\pi$
$47$		−	2.77585i		−	0.404900i	0.979293	−	0.202450i	$-0.0648903\pi$
$48$	1.68098	−	0.417505i	0.242628	−	0.0602616i
$49$	−5.90998	+	10.2364i	−0.844282	+	1.46234i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	0.406831	+	0.422047i	0.0569678	+	0.0590985i
$52$	−0.829513	−	0.478920i	−0.115033	−	0.0664142i
$53$	4.01409	−	6.95261i	0.551378	−	0.955015i	−0.446797	−	0.894635i	$-0.647436\pi$
$53$	4.01409	−	6.95261i	0.551378	−	0.955015i	0.998175	−	0.0603796i	$-0.0192311\pi$
$54$	−3.46644	−	3.87089i	−0.471723	−	0.526761i
$55$	5.00521	−	2.88976i	0.674903	−	0.389655i
$56$	−3.75699	+	2.16910i	−0.502049	+	0.289858i
$57$	2.20127	+	2.28360i	0.291566	+	0.302471i
$58$			7.24694i			0.951569i
$59$	−0.461706	+	0.266566i	−0.0601089	+	0.0347039i	−0.529753	−	0.848152i	$-0.677715\pi$
$59$	−0.461706	+	0.266566i	−0.0601089	+	0.0347039i	0.469644	+	0.882856i	$0.344382\pi$
$60$	1.66452	+	0.478920i	0.214889	+	0.0618283i
$61$		−	12.6523i		−	1.61997i	−0.586454	−	0.809983i	$-0.699476\pi$
$61$		−	12.6523i		−	1.61997i	0.586454	−	0.809983i	$-0.300524\pi$
$62$	2.90317	−	4.75096i	0.368703	−	0.603372i
$63$	11.0245	+	6.91658i	1.38896	+	0.871408i
$64$	−1.00000			−0.125000
$65$	−0.478920	−	0.829513i	−0.0594027	−	0.102888i
$66$	9.62014	+	2.76793i	1.18416	+	0.340708i
$67$	6.77532	−	11.7352i	0.827737	−	1.43368i	−0.0720727	−	0.997399i	$-0.522961\pi$
$67$	6.77532	−	11.7352i	0.827737	−	1.43368i	0.899810	−	0.436283i	$-0.143705\pi$
$68$	−0.169223	−	0.293102i	−0.0205213	−	0.0355439i
$69$	12.0011	−	2.98071i	1.44476	−	0.358835i
$70$	−4.33820			−0.518514
$71$	−5.72634	−	3.30610i	−0.679592	−	0.392362i	0.120110	−	0.992761i	$-0.461675\pi$
$71$	−5.72634	−	3.30610i	−0.679592	−	0.392362i	−0.799701	+	0.600398i	$0.795009\pi$
$72$	1.40363	+	2.65138i	0.165420	+	0.312468i
$73$	5.51744	+	3.18550i	0.645768	+	0.372834i	0.786833	−	0.617166i	$-0.211719\pi$
$73$	5.51744	+	3.18550i	0.645768	+	0.372834i	−0.141065	+	0.990000i	$0.545053\pi$
$74$	3.36475	+	5.82791i	0.391144	+	0.677481i
$75$	1.20206	+	1.24702i	0.138802	+	0.143993i
$76$	−0.915626	−	1.58591i	−0.105030	−	0.181916i
$77$	−25.0727			−2.85730
$78$	0.458728	−	1.59435i	0.0519407	−	0.180524i
$79$	−2.30975	+	1.33353i	−0.259867	+	0.150034i	−0.624274	−	0.781206i	$-0.714605\pi$
$79$	−2.30975	+	1.33353i	−0.259867	+	0.150034i	0.364407	+	0.931240i	$0.381272\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	5.05963	−	7.44313i	0.562181	−	0.827014i
$82$	−0.849519	+	1.47141i	−0.0938137	+	0.162490i
$83$	−4.17413	+	7.22980i	−0.458170	+	0.793574i	−0.998864	−	0.0476452i	$-0.984828\pi$
$83$	−4.17413	+	7.22980i	−0.458170	+	0.793574i	0.540694	+	0.841219i	$0.318162\pi$
$84$	−5.21477	−	5.40981i	−0.568978	−	0.590259i
$85$		−	0.338445i		−	0.0367095i
$86$	−2.12423	−	3.67927i	−0.229062	−	0.396746i
$87$	−12.1819	+	3.02563i	−1.30604	+	0.324382i
$88$	−5.00521	−	2.88976i	−0.533557	−	0.308049i
$89$	0.143194			0.0151786			0.00758928	−	0.999971i	$-0.497584\pi$
$89$	0.143194			0.0151786			0.00758928	+	0.999971i	$0.497584\pi$
$90$	−0.110108	+	2.99798i	−0.0116064	+	0.316015i
$91$			4.15530i			0.435593i
$92$	−7.13933			−0.744327
$93$	9.19835	+	2.89662i	0.953824	+	0.300365i
$94$	−2.77585			−0.286307
$95$		−	1.83125i		−	0.187882i
$96$	−0.417505	−	1.68098i	−0.0426114	−	0.171564i
$97$	−13.3181			−1.35225			−0.676125	−	0.736786i	$-0.736342\pi$
$97$	−13.3181			−1.35225			−0.676125	+	0.736786i	$0.736342\pi$
$98$	10.2364	+	5.90998i	1.03403	+	0.596998i
$99$	−0.636370	+	17.3269i	−0.0639576	+	1.74142i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$			3.40652i			0.338961i	0.985534	+	0.169481i	$0.0542090\pi$
$101$			3.40652i			0.338961i	−0.985534	+	0.169481i	$0.945791\pi$
$102$	0.422047	−	0.406831i	0.0417889	−	0.0402823i
$103$	−5.55266	+	9.61750i	−0.547120	+	0.947640i	0.451350	+	0.892347i	$0.350943\pi$
$103$	−5.55266	+	9.61750i	−0.547120	+	0.947640i	−0.998470	+	0.0552930i	$0.982391\pi$
$104$	−0.478920	+	0.829513i	−0.0469619	+	0.0813405i
$105$	−1.81122	−	7.29242i	−0.176757	−	0.711667i
$106$	−6.95261	−	4.01409i	−0.675297	−	0.389883i
$107$	11.2294	−	6.48331i	1.08559	−	0.626765i	0.153190	−	0.988197i	$-0.451045\pi$
$107$	11.2294	−	6.48331i	1.08559	−	0.626765i	0.932399	+	0.361431i	$0.117712\pi$
$108$	−3.87089	+	3.46644i	−0.372477	+	0.333558i
$109$	13.4893			1.29204			0.646022	−	0.763319i	$-0.276432\pi$
$109$	13.4893			1.29204			0.646022	+	0.763319i	$0.276432\pi$
$110$	−2.88976	−	5.00521i	−0.275528	−	0.477228i
$111$	−8.39180	+	8.08925i	−0.796514	+	0.767798i
$112$	2.16910	+	3.75699i	0.204961	+	0.355002i
$113$	11.1201	+	6.42019i	1.04609	+	0.603960i	0.921552	−	0.388255i	$-0.126922\pi$
$113$	11.1201	+	6.42019i	1.04609	+	0.603960i	0.124538	+	0.992215i	$0.460255\pi$
$114$	2.28360	−	2.20127i	0.213879	−	0.206168i
$115$	−6.18284	−	3.56967i	−0.576553	−	0.332873i
$116$	7.24694			0.672861
$117$	2.87158	+	0.105466i	0.265478	+	0.00975029i
$118$	0.266566	+	0.461706i	0.0245394	+	0.0425034i
$119$	−0.734121	+	1.27154i	−0.0672968	+	0.116561i
$120$	0.478920	−	1.66452i	0.0437192	−	0.151949i
$121$	−11.2014	−	19.4014i	−1.01831	−	1.76377i
$122$	−12.6523			−1.14549
$123$	−2.82809	−	0.813703i	−0.255000	−	0.0733691i
$124$	−4.75096	−	2.90317i	−0.426649	−	0.260712i
$125$		−	1.00000i		−	0.0894427i
$126$	6.91658	−	11.0245i	0.616178	−	0.982144i
$127$	−18.3605	+	10.6004i	−1.62923	+	0.940637i	−0.644909	+	0.764260i	$0.723105\pi$
$127$	−18.3605	+	10.6004i	−1.62923	+	0.940637i	−0.984323	+	0.176377i	$0.943562\pi$
$128$			1.00000i			0.0883883i
$129$	5.29791	−	5.10690i	0.466455	−	0.449637i
$130$	−0.829513	+	0.478920i	−0.0727531	+	0.0420040i
$131$	17.8493	−	10.3053i	1.55950	−	0.900378i	0.562196	−	0.827004i	$-0.309957\pi$
$131$	17.8493	−	10.3053i	1.55950	−	0.900378i	0.997305	−	0.0733736i	$-0.0233766\pi$
$132$	2.76793	−	9.62014i	0.240917	−	0.837326i
$133$	−3.97217	+	6.87999i	−0.344430	+	0.596571i
$134$	−11.7352	−	6.77532i	−1.01377	−	0.585298i
$135$	−5.08551	+	1.06658i	−0.437691	+	0.0917967i
$136$	−0.293102	+	0.169223i	−0.0251333	+	0.0145107i
$137$	4.77791	−	8.27559i	0.408205	−	0.707031i	−0.586484	−	0.809961i	$-0.699488\pi$
$137$	4.77791	−	8.27559i	0.408205	−	0.707031i	0.994689	+	0.102929i	$0.0328216\pi$
$138$	−2.98071	−	12.0011i	−0.253734	−	1.02160i
$139$		−	15.0058i		−	1.27277i	−0.771370	−	0.636387i	$-0.780428\pi$
$139$		−	15.0058i		−	1.27277i	0.771370	−	0.636387i	$-0.219572\pi$
$140$			4.33820i			0.366645i
$141$	−1.15893	−	4.66615i	−0.0975997	−	0.392961i
$142$	−3.30610	+	5.72634i	−0.277442	+	0.480544i
$143$	−4.79419	+	2.76793i	−0.400910	+	0.231466i
$144$	2.65138	−	1.40363i	0.220948	−	0.116969i
$145$	6.27603	+	3.62347i	0.521196	+	0.300913i
$146$	3.18550	−	5.51744i	0.263634	−	0.456627i
$147$	−5.66081	+	19.6746i	−0.466896	+	1.62273i
$148$	5.82791	−	3.36475i	0.479051	−	0.276580i
$149$	7.45745	−	4.30556i	0.610938	−	0.352725i	−0.162395	−	0.986726i	$-0.551922\pi$
$149$	7.45745	−	4.30556i	0.610938	−	0.352725i	0.773332	+	0.634001i	$0.218588\pi$
$150$	1.24702	−	1.20206i	0.101819	−	0.0981477i
$151$			17.7682i			1.44595i	0.690872	+	0.722977i	$0.257227\pi$
$151$			17.7682i			1.44595i	−0.690872	+	0.722977i	$0.742773\pi$
$152$	−1.58591	+	0.915626i	−0.128634	+	0.0742671i
$153$	0.860082	+	0.539599i	0.0695335	+	0.0436240i
$154$			25.0727i			2.02042i
$155$	−2.66287	−	4.88970i	−0.213887	−	0.392750i
$156$	−1.59435	−	0.458728i	−0.127650	−	0.0367276i
$157$	−14.6635			−1.17027			−0.585136	−	0.810935i	$-0.698959\pi$
$157$	−14.6635			−1.17027			−0.585136	+	0.810935i	$0.698959\pi$
$158$	1.33353	+	2.30975i	0.106090	+	0.183754i
$159$	3.84486	−	13.3631i	0.304917	−	1.05976i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	15.4859	+	26.8224i	1.22046	+	2.11390i
$162$	−7.44313	−	5.05963i	−0.584787	−	0.397522i
$163$	−10.7485			−0.841889			−0.420945	−	0.907086i	$-0.638301\pi$
$163$	−10.7485			−0.841889			−0.420945	+	0.907086i	$0.638301\pi$
$164$	1.47141	+	0.849519i	0.114898	+	0.0663363i
$165$	7.20717	−	6.94733i	0.561077	−	0.540849i
$166$	7.22980	+	4.17413i	0.561142	+	0.323975i
$167$	−3.76944	−	6.52887i	−0.291688	−	0.505219i	0.682521	−	0.730866i	$-0.260884\pi$
$167$	−3.76944	−	6.52887i	−0.291688	−	0.505219i	−0.974209	+	0.225647i	$0.927550\pi$
$168$	−5.40981	+	5.21477i	−0.417376	+	0.402328i
$169$	−6.04127	−	10.4638i	−0.464713	−	0.804907i
$170$	−0.338445			−0.0259576
$171$	4.65371	+	2.91965i	0.355878	+	0.223271i
$172$	−3.67927	+	2.12423i	−0.280542	+	0.161971i
$173$	1.18142	+	0.682091i	0.0898215	+	0.0518584i	0.544238	−	0.838931i	$-0.316819\pi$
$173$	1.18142	+	0.682091i	0.0898215	+	0.0518584i	−0.454416	+	0.890789i	$0.650152\pi$
$174$	3.02563	+	12.1819i	0.229372	+	0.923511i
$175$	−2.16910	+	3.75699i	−0.163968	+	0.284002i
$176$	−2.88976	+	5.00521i	−0.217824	+	0.377282i
$177$	−0.664825	+	0.640856i	−0.0499713	+	0.0481697i
$178$		−	0.143194i		−	0.0107329i
$179$	5.20586	+	9.01681i	0.389104	+	0.673948i	0.992329	−	0.123623i	$-0.0394513\pi$
$179$	5.20586	+	9.01681i	0.389104	+	0.673948i	−0.603225	+	0.797571i	$0.706118\pi$
$180$	2.99798	+	0.110108i	0.223456	+	0.00820694i
$181$	5.65582	+	3.26539i	0.420394	+	0.242714i	0.695246	−	0.718772i	$-0.255296\pi$
$181$	5.65582	+	3.26539i	0.420394	+	0.242714i	−0.274852	+	0.961487i	$0.588629\pi$
$182$	4.15530			0.308011
$183$	−5.28241	−	21.2683i	−0.390487	−	1.57220i
$184$			7.13933i			0.526319i
$185$	6.72949			0.494762
$186$	2.89662	−	9.19835i	0.212390	−	0.674456i
$187$	−1.95605			−0.143041
$188$			2.77585i			0.202450i
$189$	21.4197	+	7.02384i	1.55806	+	0.510909i
$190$	−1.83125			−0.132853
$191$	13.7963	+	7.96528i	0.998263	+	0.576347i	0.907734	−	0.419547i	$-0.137811\pi$
$191$	13.7963	+	7.96528i	0.998263	+	0.576347i	0.0905288	+	0.995894i	$0.471144\pi$
$192$	−1.68098	+	0.417505i	−0.121314	+	0.0301308i
$193$	−4.98917	−	8.64149i	−0.359128	−	0.622028i	0.628687	−	0.777658i	$-0.283593\pi$
$193$	−4.98917	−	8.64149i	−0.359128	−	0.622028i	−0.987815	+	0.155630i	$0.950259\pi$
$194$			13.3181i			0.956186i
$195$	−1.15138	−	1.19444i	−0.0824520	−	0.0855358i
$196$	5.90998	−	10.2364i	0.422141	−	0.731170i
$197$	−11.4302	+	19.7976i	−0.814365	+	1.41052i	0.0954178	+	0.995437i	$0.469581\pi$
$197$	−11.4302	+	19.7976i	−0.814365	+	1.41052i	−0.909783	+	0.415084i	$0.863752\pi$
$198$	17.3269	+	0.636370i	1.23137	+	0.0452248i
$199$	−9.17917	−	5.29960i	−0.650694	−	0.375678i	0.138028	−	0.990428i	$-0.455924\pi$
$199$	−9.17917	−	5.29960i	−0.650694	−	0.375678i	−0.788722	+	0.614750i	$0.789257\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	6.48967	−	22.5553i	0.457746	−	1.59093i
$202$	3.40652			0.239682
$203$	−15.7193	−	27.2267i	−1.10328	−	1.91094i
$204$	−0.406831	−	0.422047i	−0.0284839	−	0.0295492i
$205$	0.849519	+	1.47141i	0.0593330	+	0.102768i
$206$	9.61750	+	5.55266i	0.670083	+	0.386872i
$207$	18.9291	−	10.0210i	1.31566	−	0.696508i
$208$	0.829513	+	0.478920i	0.0575164	+	0.0332071i
$209$	−10.5838			−0.732094
$210$	−7.29242	+	1.81122i	−0.503225	+	0.124986i
$211$	−1.34322	−	2.32653i	−0.0924713	−	0.160165i	0.816079	−	0.577940i	$-0.196143\pi$
$211$	−1.34322	−	2.32653i	−0.0924713	−	0.160165i	−0.908550	+	0.417775i	$0.862810\pi$
$212$	−4.01409	+	6.95261i	−0.275689	+	0.477507i
$213$	−11.0062	−	3.16672i	−0.754130	−	0.216980i
$214$	−6.48331	−	11.2294i	−0.443190	−	0.767627i
$215$	−4.24846			−0.289743
$216$	3.46644	+	3.87089i	0.235861	+	0.263381i
$217$	−0.601878	+	24.1466i	−0.0408581	+	1.63918i
$218$		−	13.4893i		−	0.913613i
$219$	10.6047	+	3.05120i	0.716597	+	0.206181i
$220$	−5.00521	+	2.88976i	−0.337451	+	0.194828i
$221$			0.324176i			0.0218065i
$222$	8.08925	+	8.39180i	0.542915	+	0.563221i
$223$	13.2239	−	7.63482i	0.885538	−	0.511265i	0.0130575	−	0.999915i	$-0.495844\pi$
$223$	13.2239	−	7.63482i	0.885538	−	0.511265i	0.872480	+	0.488649i	$0.162510\pi$
$224$	3.75699	−	2.16910i	0.251024	−	0.144929i
$225$	2.54127	+	1.59435i	0.169418	+	0.106290i
$226$	6.42019	−	11.1201i	0.427064	−	0.739697i
$227$	−21.3686	−	12.3371i	−1.41828	−	0.818845i	−0.422133	−	0.906534i	$-0.638719\pi$
$227$	−21.3686	−	12.3371i	−1.41828	−	0.818845i	−0.996148	+	0.0876888i	$0.972052\pi$
$228$	−2.20127	−	2.28360i	−0.145783	−	0.151235i
$229$	17.2277	−	9.94643i	1.13844	−	0.657279i	0.192396	−	0.981317i	$-0.438374\pi$
$229$	17.2277	−	9.94643i	1.13844	−	0.657279i	0.946044	+	0.324039i	$0.105041\pi$
$230$	−3.56967	+	6.18284i	−0.235377	+	0.407685i
$231$	−42.1467	+	10.4680i	−2.77305	+	0.688742i
$232$		−	7.24694i		−	0.475785i
$233$			10.7147i			0.701944i	0.936386	+	0.350972i	$0.114149\pi$
$233$			10.7147i			0.701944i	−0.936386	+	0.350972i	$0.885851\pi$
$234$	0.105466	−	2.87158i	0.00689450	−	0.187721i
$235$	−1.38793	+	2.40396i	−0.0905384	+	0.156817i
$236$	0.461706	−	0.266566i	0.0300545	−	0.0173520i
$237$	−3.32588	+	3.20597i	−0.216039	+	0.208250i
$238$	1.27154	+	0.734121i	0.0824214	+	0.0475860i
$239$	−9.02709	+	15.6354i	−0.583914	+	1.01137i	0.411096	+	0.911592i	$0.365146\pi$
$239$	−9.02709	+	15.6354i	−0.583914	+	1.01137i	−0.995010	+	0.0997762i	$0.968187\pi$
$240$	−1.66452	−	0.478920i	−0.107444	−	0.0309141i
$241$	−15.8738	+	9.16476i	−1.02252	+	0.590354i	−0.914834	−	0.403831i	$-0.867678\pi$
$241$	−15.8738	+	9.16476i	−1.02252	+	0.590354i	−0.107689	+	0.994185i	$0.534345\pi$
$242$	−19.4014	+	11.2014i	−1.24717	+	0.720055i
$243$	5.39758	−	14.6242i	0.346255	−	0.938140i
$244$			12.6523i			0.809983i
$245$	10.2364	−	5.90998i	0.653978	−	0.377575i
$246$	−0.813703	+	2.82809i	−0.0518798	+	0.180312i
$247$			1.75405i			0.111607i
$248$	−2.90317	+	4.75096i	−0.184351	+	0.301686i
$249$	−3.99815	+	13.8959i	−0.253372	+	0.880615i
$250$	−1.00000			−0.0632456
$251$	−12.8794	−	22.3077i	−0.812938	−	1.40805i	−0.910799	−	0.412850i	$-0.864533\pi$
$251$	−12.8794	−	22.3077i	−0.812938	−	1.40805i	0.0978612	−	0.995200i	$-0.468800\pi$
$252$	−11.0245	−	6.91658i	−0.694481	−	0.435704i
$253$	−20.6310	+	35.7339i	−1.29706	+	2.24657i
$254$	10.6004	+	18.3605i	0.665131	+	1.15204i
$255$	−0.141303	−	0.568919i	−0.00884871	−	0.0356271i
$256$	1.00000			0.0625000
$257$	−2.25748	−	1.30335i	−0.140818	−	0.0813010i	0.427936	−	0.903809i	$-0.359241\pi$
$257$	−2.25748	−	1.30335i	−0.140818	−	0.0813010i	−0.568754	+	0.822508i	$0.692574\pi$
$258$	−5.10690	−	5.29791i	−0.317942	−	0.329833i
$259$	−25.2826	−	14.5969i	−1.57099	−	0.907009i
$260$	0.478920	+	0.829513i	0.0297013	+	0.0514442i
$261$	−19.2144	+	10.1720i	−1.18934	+	0.629633i
$262$	−10.3053	−	17.8493i	−0.636663	−	1.10273i
$263$	14.5026			0.894272			0.447136	−	0.894466i	$-0.352444\pi$
$263$	14.5026			0.894272			0.447136	+	0.894466i	$0.352444\pi$
$264$	−9.62014	−	2.76793i	−0.592079	−	0.170354i
$265$	−6.95261	+	4.01409i	−0.427096	+	0.246584i
$266$	6.87999	+	3.97217i	0.421839	+	0.243549i
$267$	0.240706	−	0.0597843i	0.0147310	−	0.00365874i
$268$	−6.77532	+	11.7352i	−0.413868	+	0.716841i
$269$	1.36344	−	2.36155i	0.0831307	−	0.143987i	−0.821462	−	0.570263i	$-0.806841\pi$
$269$	1.36344	−	2.36155i	0.0831307	−	0.143987i	0.904593	+	0.426276i	$0.140175\pi$
$270$	1.06658	+	5.08551i	0.0649101	+	0.309494i
$271$			19.1303i			1.16208i	0.813875	+	0.581040i	$0.197354\pi$
$271$			19.1303i			1.16208i	−0.813875	+	0.581040i	$0.802646\pi$
$272$	0.169223	+	0.293102i	0.0102606	+	0.0177719i
$273$	1.73486	+	6.98496i	0.104998	+	0.422749i
$274$	−8.27559	−	4.77791i	−0.499947	−	0.288644i
$275$	−5.77952			−0.348518
$276$	−12.0011	+	2.98071i	−0.722379	+	0.179417i
$277$		−	14.5670i		−	0.875246i	−0.899159	−	0.437623i	$-0.855820\pi$
$277$		−	14.5670i		−	0.875246i	0.899159	−	0.437623i	$-0.144180\pi$
$278$	−15.0058			−0.899987
$279$	16.6716	+	1.02880i	0.998101	+	0.0615927i
$280$	4.33820			0.259257
$281$			7.59637i			0.453161i	0.973992	+	0.226581i	$0.0727547\pi$
$281$			7.59637i			0.453161i	−0.973992	+	0.226581i	$0.927245\pi$
$282$	−4.66615	+	1.15893i	−0.277865	+	0.0690134i
$283$	−5.87807			−0.349415			−0.174708	−	0.984620i	$-0.555898\pi$
$283$	−5.87807			−0.349415			−0.174708	+	0.984620i	$0.555898\pi$
$284$	5.72634	+	3.30610i	0.339796	+	0.196181i
$285$	−0.764556	−	3.07830i	−0.0452884	−	0.182343i
$286$	2.76793	+	4.79419i	0.163671	+	0.283486i
$287$		−	7.37076i		−	0.435082i
$288$	−1.40363	−	2.65138i	−0.0827099	−	0.156234i
$289$	8.44273	−	14.6232i	0.496631	−	0.860190i
$290$	3.62347	−	6.27603i	0.212777	−	0.368541i
$291$	−22.3875	+	5.56038i	−1.31238	+	0.325955i
$292$	−5.51744	−	3.18550i	−0.322884	−	0.186417i
$293$	−2.32910	+	1.34471i	−0.136067	+	0.0785586i	−0.566488	−	0.824070i	$-0.691698\pi$
$293$	−2.32910	+	1.34471i	−0.136067	+	0.0785586i	0.430421	+	0.902628i	$0.358365\pi$
$294$	19.6746	+	5.66081i	1.14744	+	0.330145i
$295$	0.533132			0.0310401
$296$	−3.36475	−	5.82791i	−0.195572	−	0.338741i
$297$	6.16433	+	29.3918i	0.357691	+	1.70549i
$298$	−4.30556	−	7.45745i	−0.249414	−	0.431998i
$299$	5.92217	+	3.41917i	0.342488	+	0.197736i
$300$	−1.20206	−	1.24702i	−0.0694009	−	0.0719966i
$301$	15.9614	+	9.21533i	0.920001	+	0.531163i
$302$	17.7682			1.02244
$303$	1.42224	+	5.72629i	0.0817054	+	0.328967i
$304$	0.915626	+	1.58591i	0.0525148	+	0.0909582i
$305$	−6.32617	+	10.9572i	−0.362235	+	0.627410i
$306$	0.539599	−	0.860082i	0.0308468	−	0.0491676i
$307$	1.29217	+	2.23811i	0.0737483	+	0.127736i	0.900541	−	0.434771i	$-0.143171\pi$
$307$	1.29217	+	2.23811i	0.0737483	+	0.127736i	−0.826793	+	0.562506i	$0.809837\pi$
$308$	25.0727			1.42865
$309$	−5.31856	+	18.4851i	−0.302562	+	1.05158i
$310$	−4.88970	+	2.66287i	−0.277716	+	0.151241i
$311$		−	5.04909i		−	0.286308i	−0.989700	−	0.143154i	$-0.954276\pi$
$311$		−	5.04909i		−	0.286308i	0.989700	−	0.143154i	$-0.0457244\pi$
$312$	−0.458728	+	1.59435i	−0.0259704	+	0.0902620i
$313$	10.1401	−	5.85439i	0.573153	−	0.330910i	−0.185255	−	0.982691i	$-0.559311\pi$
$313$	10.1401	−	5.85439i	0.573153	−	0.330910i	0.758408	+	0.651781i	$0.225978\pi$
$314$			14.6635i			0.827508i
$315$	−6.08924	−	11.5022i	−0.343090	−	0.648076i
$316$	2.30975	−	1.33353i	0.129934	−	0.0750172i
$317$	4.37197	−	2.52416i	0.245554	−	0.141771i	−0.372173	−	0.928164i	$-0.621387\pi$
$317$	4.37197	−	2.52416i	0.245554	−	0.141771i	0.617727	+	0.786393i	$0.288054\pi$
$318$	−13.3631	−	3.84486i	−0.749365	−	0.215609i
$319$	20.9419	−	36.2724i	1.17252	−	2.03087i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	16.1696	−	15.5866i	0.902499	−	0.869962i
$322$	26.8224	−	15.4859i	1.49475	−	0.862996i
$323$	−0.309889	+	0.536744i	−0.0172427	+	0.0298652i
$324$	−5.05963	+	7.44313i	−0.281090	+	0.413507i
$325$			0.957839i			0.0531314i
$326$			10.7485i			0.595306i
$327$	22.6753	−	5.63186i	1.25395	−	0.311442i
$328$	0.849519	−	1.47141i	0.0469069	−	0.0812451i
$329$	10.4289	−	6.02110i	0.574961	−	0.331954i
$330$	−6.94733	−	7.20717i	−0.382438	−	0.396741i
$331$	−13.6225	−	7.86495i	−0.748760	−	0.432297i	0.0764857	−	0.997071i	$-0.475630\pi$
$331$	−13.6225	−	7.86495i	−0.748760	−	0.432297i	−0.825246	+	0.564774i	$0.808963\pi$
$332$	4.17413	−	7.22980i	0.229085	−	0.396787i
$333$	−10.7291	+	17.1015i	−0.587953	+	0.937155i
$334$	−6.52887	+	3.76944i	−0.357244	+	0.206255i
$335$	−11.7352	+	6.77532i	−0.641162	+	0.370175i
$336$	5.21477	+	5.40981i	0.284489	+	0.295129i
$337$		−	0.335775i		−	0.0182908i	−0.999958	−	0.00914541i	$-0.997089\pi$
$337$		−	0.335775i		−	0.0182908i	0.999958	−	0.00914541i	$-0.00291111\pi$
$338$	−10.4638	+	6.04127i	−0.569155	+	0.328602i
$339$	21.3731	+	6.14951i	1.16083	+	0.333995i
$340$			0.338445i			0.0183548i
$341$	−28.2601	+	15.3901i	−1.53037	+	0.833420i
$342$	2.91965	−	4.65371i	0.157876	−	0.251644i
$343$	−20.9099			−1.12903
$344$	2.12423	+	3.67927i	0.114531	+	0.198373i
$345$	−11.8836	−	3.41917i	−0.639791	−	0.184082i
$346$	0.682091	−	1.18142i	0.0366695	−	0.0635134i
$347$	−15.7546	−	27.2878i	−0.845754	−	1.46489i	−0.884965	−	0.465657i	$-0.845818\pi$
$347$	−15.7546	−	27.2878i	−0.845754	−	1.46489i	0.0392114	−	0.999231i	$-0.487515\pi$
$348$	12.1819	−	3.02563i	0.653021	−	0.162191i
$349$	−27.5332			−1.47382			−0.736909	−	0.675992i	$-0.763715\pi$
$349$	−27.5332			−1.47382			−0.736909	+	0.675992i	$0.763715\pi$
$350$	3.75699	+	2.16910i	0.200820	+	0.115943i
$351$	4.87110	−	1.02161i	0.260000	−	0.0545297i
$352$	5.00521	+	2.88976i	0.266779	+	0.154025i
$353$	4.02900	+	6.97842i	0.214442	+	0.371424i	0.953100	−	0.302656i	$-0.0978734\pi$
$353$	4.02900	+	6.97842i	0.214442	+	0.371424i	−0.738658	+	0.674080i	$0.764540\pi$
$354$	0.640856	+	0.664825i	0.0340611	+	0.0353350i
$355$	3.30610	+	5.72634i	0.175470	+	0.303923i
$356$	−0.143194			−0.00758928
$357$	−0.703170	+	2.44392i	−0.0372157	+	0.129346i
$358$	9.01681	−	5.20586i	0.476553	−	0.275138i
$359$	20.1011	+	11.6054i	1.06090	+	0.612509i	0.925680	−	0.378307i	$-0.123494\pi$
$359$	20.1011	+	11.6054i	1.06090	+	0.612509i	0.135216	+	0.990816i	$0.456827\pi$
$360$	0.110108	−	2.99798i	0.00580319	−	0.158007i
$361$	7.82326	−	13.5503i	0.411750	−	0.713173i
$362$	3.26539	−	5.65582i	0.171625	−	0.297263i
$363$	−26.9296	−	27.9368i	−1.41344	−	1.46630i
$364$		−	4.15530i		−	0.217797i
$365$	−3.18550	−	5.51744i	−0.166737	−	0.288796i
$366$	−21.2683	+	5.28241i	−1.11171	+	0.276116i
$367$	7.60499	+	4.39074i	0.396977	+	0.229195i	0.685179	−	0.728375i	$-0.259724\pi$
$367$	7.60499	+	4.39074i	0.396977	+	0.229195i	−0.288202	+	0.957570i	$0.593057\pi$
$368$	7.13933			0.372163
$369$	−5.09368	−	0.187077i	−0.265166	−	0.00973885i
$370$		−	6.72949i		−	0.349850i
$371$	34.8278			1.80817
$372$	−9.19835	−	2.89662i	−0.476912	−	0.150183i
$373$	6.26703			0.324495			0.162247	−	0.986750i	$-0.448126\pi$
$373$	6.26703			0.324495			0.162247	+	0.986750i	$0.448126\pi$
$374$			1.95605i			0.101145i
$375$	−0.417505	−	1.68098i	−0.0215599	−	0.0868054i
$376$	2.77585			0.143154
$377$	−6.01143	−	3.47070i	−0.309604	−	0.178750i
$378$	7.02384	−	21.4197i	0.361267	−	1.10171i
$379$	12.6057	+	21.8337i	0.647511	+	1.12152i	0.983715	+	0.179733i	$0.0575233\pi$
$379$	12.6057	+	21.8337i	0.647511	+	1.12152i	−0.336205	+	0.941789i	$0.609143\pi$
$380$			1.83125i			0.0939412i
$381$	−26.4379	+	25.4847i	−1.35445	+	1.30562i
$382$	7.96528	−	13.7963i	0.407539	−	0.705878i
$383$	1.21970	−	2.11259i	0.0623239	−	0.107948i	−0.833180	−	0.553002i	$-0.813482\pi$
$383$	1.21970	−	2.11259i	0.0623239	−	0.107948i	0.895504	+	0.445054i	$0.146815\pi$
$384$	0.417505	+	1.68098i	0.0213057	+	0.0857821i
$385$	21.7136	+	12.5363i	1.10663	+	0.638911i
$386$	−8.64149	+	4.98917i	−0.439840	+	0.253942i
$387$	6.77351	−	10.7965i	0.344317	−	0.548817i
$388$	13.3181			0.676125
$389$	2.01268	+	3.48606i	0.102047	+	0.176750i	0.912528	−	0.409015i	$-0.134127\pi$
$389$	2.01268	+	3.48606i	0.102047	+	0.176750i	−0.810481	+	0.585765i	$0.800794\pi$
$390$	−1.19444	+	1.15138i	−0.0604830	+	0.0583024i
$391$	1.20814	+	2.09255i	0.0610981	+	0.105825i
$392$	−10.2364	−	5.90998i	−0.517015	−	0.298499i
$393$	25.7018	−	24.7751i	1.29648	−	1.24974i
$394$	19.7976	+	11.4302i	0.997389	+	0.575843i
$395$	2.66707			0.134195
$396$	0.636370	−	17.3269i	0.0319788	−	0.870708i
$397$	−10.2922	−	17.8267i	−0.516552	−	0.894694i	−0.999815	−	0.0192190i	$-0.993882\pi$
$397$	−10.2922	−	17.8267i	−0.516552	−	0.894694i	0.483263	−	0.875475i	$-0.339451\pi$
$398$	−5.29960	+	9.17917i	−0.265645	+	0.460110i
$399$	−3.80470	+	13.2235i	−0.190473	+	0.662004i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−2.12457			−0.106096			−0.0530479	−	0.998592i	$-0.516894\pi$
$401$	−2.12457			−0.106096			−0.0530479	+	0.998592i	$0.516894\pi$
$402$	−22.5553	−	6.48967i	−1.12496	−	0.323675i
$403$	2.55060	+	4.68355i	0.127054	+	0.233304i
$404$		−	3.40652i		−	0.169481i
$405$	−8.10333	+	3.91613i	−0.402658	+	0.194594i
$406$	−27.2267	+	15.7193i	−1.35124	+	0.780137i
$407$		−	38.8932i		−	1.92787i
$408$	−0.422047	+	0.406831i	−0.0208945	+	0.0201411i
$409$	30.3848	−	17.5427i	1.50243	−	0.867431i	0.502438	−	0.864613i	$-0.332437\pi$
$409$	30.3848	−	17.5427i	1.50243	−	0.867431i	0.999996	−	0.00281712i	$-0.000896719\pi$
$410$	1.47141	−	0.849519i	0.0726678	−	0.0419548i
$411$	4.57647	−	15.9059i	0.225741	−	0.784580i
$412$	5.55266	−	9.61750i	0.273560	−	0.473820i
$413$	−2.00297	−	1.15641i	−0.0985597	−	0.0569035i
$414$	−10.0210	−	18.9291i	−0.492506	−	0.930314i
$415$	7.22980	−	4.17413i	0.354897	−	0.204900i
$416$	0.478920	−	0.829513i	0.0234810	−	0.0406702i
$417$	−6.26499	−	25.2244i	−0.306798	−	1.23524i
$418$			10.5838i			0.517669i
$419$		−	30.0425i		−	1.46767i	−0.679327	−	0.733836i	$-0.737728\pi$
$419$		−	30.0425i		−	1.46767i	0.679327	−	0.733836i	$-0.262272\pi$
$420$	1.81122	+	7.29242i	0.0883784	+	0.355834i
$421$	8.88135	−	15.3829i	0.432850	−	0.749719i	−0.564267	−	0.825592i	$-0.690841\pi$
$421$	8.88135	−	15.3829i	0.432850	−	0.749719i	0.997117	+	0.0758735i	$0.0241745\pi$
$422$	−2.32653	+	1.34322i	−0.113254	+	0.0653871i
$423$	−3.89628	−	7.35984i	−0.189444	−	0.357848i
$424$	6.95261	+	4.01409i	0.337649	+	0.194942i
$425$	−0.169223	+	0.293102i	−0.00820850	+	0.0142175i
$426$	−3.16672	+	11.0062i	−0.153428	+	0.533251i
$427$	47.5347	−	27.4442i	2.30036	−	1.32812i
$428$	−11.2294	+	6.48331i	−0.542795	+	0.313383i
$429$	−6.90331	+	6.65442i	−0.333295	+	0.321278i
$430$			4.24846i			0.204879i
$431$	26.1760	−	15.1127i	1.26085	−	0.727954i	0.287614	−	0.957746i	$-0.407138\pi$
$431$	26.1760	−	15.1127i	1.26085	−	0.727954i	0.973240	+	0.229792i	$0.0738047\pi$
$432$	3.87089	−	3.46644i	0.186238	−	0.166779i
$433$		−	18.0413i		−	0.867010i	−0.901151	−	0.433505i	$-0.857277\pi$
$433$		−	18.0413i		−	0.867010i	0.901151	−	0.433505i	$-0.142723\pi$
$434$	24.1466	+	0.601878i	1.15907	+	0.0288911i
$435$	12.0627	+	3.47070i	0.578362	+	0.166407i
$436$	−13.4893			−0.646022
$437$	6.53696	+	11.3223i	0.312705	+	0.541621i
$438$	3.05120	−	10.6047i	0.145792	−	0.506711i
$439$	−7.32870	+	12.6937i	−0.349780	+	0.605836i	−0.986210	−	0.165498i	$-0.947077\pi$
$439$	−7.32870	+	12.6937i	−0.349780	+	0.605836i	0.636431	+	0.771334i	$0.280410\pi$
$440$	2.88976	+	5.00521i	0.137764	+	0.238614i
$441$	−1.30147	+	35.4360i	−0.0619747	+	1.68743i
$442$	0.324176			0.0154195
$443$	−13.4664	−	7.77486i	−0.639810	−	0.369395i	0.144731	−	0.989471i	$-0.453768\pi$
$443$	−13.4664	−	7.77486i	−0.639810	−	0.369395i	−0.784541	+	0.620076i	$0.787102\pi$
$444$	8.39180	−	8.08925i	0.398257	−	0.383899i
$445$	−0.124010	−	0.0715971i	−0.00587863	−	0.00339403i
$446$	−7.63482	−	13.2239i	−0.361519	−	0.626170i
$447$	10.7382	−	10.3511i	0.507900	−	0.489589i
$448$	−2.16910	−	3.75699i	−0.102480	−	0.177501i
$449$	−15.2448			−0.719449			−0.359724	−	0.933059i	$-0.617129\pi$
$449$	−15.2448			−0.719449			−0.359724	+	0.933059i	$0.617129\pi$
$450$	1.59435	−	2.54127i	0.0751582	−	0.119797i
$451$	8.50405	−	4.90981i	0.400440	−	0.231194i
$452$	−11.1201	−	6.42019i	−0.523045	−	0.301980i
$453$	7.41830	+	29.8679i	0.348542	+	1.40332i
$454$	−12.3371	+	21.3686i	−0.579011	+	1.00288i
$455$	2.07765	−	3.59859i	0.0974016	−	0.168705i
$456$	−2.28360	+	2.20127i	−0.106940	+	0.103084i
$457$			15.6182i			0.730590i	0.930892	+	0.365295i	$0.119032\pi$
$457$			15.6182i			0.730590i	−0.930892	+	0.365295i	$0.880968\pi$
$458$	−9.94643	−	17.2277i	−0.464766	−	0.804999i
$459$	1.67106	+	0.547966i	0.0779986	+	0.0255769i
$460$	6.18284	+	3.56967i	0.288277	+	0.166437i
$461$	23.2167			1.08131			0.540654	−	0.841245i	$-0.318177\pi$
$461$	23.2167			1.08131			0.540654	+	0.841245i	$0.318177\pi$
$462$	10.4680	+	42.1467i	0.487014	+	1.96084i
$463$			8.21847i			0.381945i	0.981595	+	0.190972i	$0.0611641\pi$
$463$			8.21847i			0.381945i	−0.981595	+	0.190972i	$0.938836\pi$
$464$	−7.24694			−0.336431
$465$	−6.51769	−	7.10772i	−0.302251	−	0.329613i
$466$	10.7147			0.496350
$467$			18.3605i			0.849622i	0.905282	+	0.424811i	$0.139659\pi$
$467$			18.3605i			0.849622i	−0.905282	+	0.424811i	$0.860341\pi$
$468$	−2.87158	−	0.105466i	−0.132739	−	0.00487514i
$469$	58.7853			2.71445
$470$	2.40396	+	1.38793i	0.110886	+	0.0640203i
$471$	−24.6490	+	6.12207i	−1.13577	+	0.282090i
$472$	−0.266566	−	0.461706i	−0.0122697	−	0.0212517i
$473$			24.5541i			1.12900i
$474$	3.20597	+	3.32588i	0.147255	+	0.152763i
$475$	−0.915626	+	1.58591i	−0.0420118	+	0.0727666i
$476$	0.734121	−	1.27154i	0.0336484	−	0.0582807i
$477$	0.883965	−	24.0683i	0.0404740	−	1.10201i
$478$	15.6354	+	9.02709i	0.715145	+	0.412889i
$479$	13.3330	−	7.69783i	0.609202	−	0.351723i	−0.163451	−	0.986551i	$-0.552263\pi$
$479$	13.3330	−	7.69783i	0.609202	−	0.351723i	0.772653	+	0.634829i	$0.218929\pi$
$480$	−0.478920	+	1.66452i	−0.0218596	+	0.0759747i
$481$	−6.44577			−0.293902
$482$	9.16476	+	15.8738i	0.417443	+	0.723033i
$483$	37.2300	+	38.6224i	1.69402	+	1.75738i
$484$	11.2014	+	19.4014i	0.509156	+	0.881884i
$485$	11.5338	+	6.65906i	0.523725	+	0.302373i
$486$	−14.6242	−	5.39758i	−0.663365	−	0.244839i
$487$	13.0311	+	7.52353i	0.590497	+	0.340924i	0.765294	−	0.643681i	$-0.222593\pi$
$487$	13.0311	+	7.52353i	0.590497	+	0.340924i	−0.174797	+	0.984605i	$0.555927\pi$
$488$	12.6523			0.572744
$489$	−18.0680	+	4.48756i	−0.817065	+	0.202934i
$490$	−5.90998	−	10.2364i	−0.266986	−	0.462433i
$491$	18.2622	−	31.6310i	0.824159	−	1.42749i	−0.0784006	−	0.996922i	$-0.524981\pi$
$491$	18.2622	−	31.6310i	0.824159	−	1.42749i	0.902560	−	0.430564i	$-0.141685\pi$
$492$	2.82809	+	0.813703i	0.127500	+	0.0366846i
$493$	−1.22635	−	2.12409i	−0.0552318	−	0.0956643i
$494$	1.75405			0.0789182
$495$	9.21455	−	14.6873i	0.414163	−	0.660146i
$496$	4.75096	+	2.90317i	0.213324	+	0.130356i
$497$		−	28.6851i		−	1.28670i
$498$	13.8959	+	3.99815i	0.622689	+	0.179161i
$499$	0.704675	−	0.406844i	0.0315456	−	0.0182128i	−0.484144	−	0.874988i	$-0.660869\pi$
$499$	0.704675	−	0.406844i	0.0315456	−	0.0182128i	0.515690	+	0.856775i	$0.327536\pi$
$500$			1.00000i			0.0447214i
$501$	−9.06219	−	9.40113i	−0.404869	−	0.420011i
$502$	−22.3077	+	12.8794i	−0.995642	+	0.574834i
$503$	−5.03784	+	2.90860i	−0.224626	+	0.129688i	−0.608091	−	0.793868i	$-0.708064\pi$
$503$	−5.03784	+	2.90860i	−0.224626	+	0.129688i	0.383464	+	0.923556i	$0.374731\pi$
$504$	−6.91658	+	11.0245i	−0.308089	+	0.491072i
$505$	1.70326	−	2.95013i	0.0757941	−	0.131279i
$506$	35.7339	+	20.6310i	1.58856	+	0.917158i
$507$	−14.5239	−	15.0671i	−0.645030	−	0.669156i
$508$	18.3605	−	10.6004i	0.814616	−	0.470319i
$509$	−12.6093	+	21.8399i	−0.558897	+	0.968038i	0.438692	+	0.898637i	$0.355442\pi$
$509$	−12.6093	+	21.8399i	−0.558897	+	0.968038i	−0.997589	+	0.0694002i	$0.977891\pi$
$510$	−0.568919	+	0.141303i	−0.0251922	+	0.00625698i
$511$			27.6386i			1.22266i
$512$		−	1.00000i		−	0.0441942i
$513$	9.04175	+	2.96492i	0.399203	+	0.130904i
$514$	−1.30335	+	2.25748i	−0.0574885	+	0.0995730i
$515$	9.61750	−	5.55266i	0.423797	−	0.244680i
$516$	−5.29791	+	5.10690i	−0.233227	+	0.224819i
$517$	13.8937	+	8.02155i	0.611046	+	0.352787i
$518$	−14.5969	+	25.2826i	−0.641352	+	1.11086i
$519$	2.27071	+	0.653334i	0.0996732	+	0.0286782i
$520$	0.829513	−	0.478920i	0.0363766	−	0.0210020i
$521$	21.3703	−	12.3381i	0.936250	−	0.540544i	0.0474671	−	0.998873i	$-0.484885\pi$
$521$	21.3703	−	12.3381i	0.936250	−	0.540544i	0.888783	+	0.458329i	$0.151552\pi$
$522$	10.1720	+	19.2144i	0.445218	+	0.840990i
$523$		−	6.76591i		−	0.295853i	−0.988998	−	0.147926i	$-0.952740\pi$
$523$		−	6.76591i		−	0.295853i	0.988998	−	0.147926i	$-0.0472598\pi$
$524$	−17.8493	+	10.3053i	−0.779750	+	0.450189i
$525$	−2.07765	+	7.22103i	−0.0906760	+	0.315151i
$526$		−	14.5026i		−	0.632345i
$527$	−0.0469556	+	1.88380i	−0.00204542	+	0.0820596i
$528$	−2.76793	+	9.62014i	−0.120459	+	0.418663i
$529$	27.9701			1.21609
$530$	4.01409	+	6.95261i	0.174361	+	0.302002i
$531$	−0.849996	+	1.35483i	−0.0368867	+	0.0587947i
$532$	3.97217	−	6.87999i	0.172215	−	0.298286i
$533$	−0.813703	−	1.40938i	−0.0352454	−	0.0610468i
$534$	−0.0597843	−	0.240706i	−0.00258712	−	0.0104164i
$535$	−12.9666			−0.560596
$536$	11.7352	+	6.77532i	0.506883	+	0.292649i
$537$	12.5155	+	12.9836i	0.540084	+	0.560284i
$538$	−2.36155	−	1.36344i	−0.101814	−	0.0587823i
$539$	−34.1568	−	59.1614i	−1.47124	−	2.54826i
$540$	5.08551	−	1.06658i	0.218845	−	0.0458984i
$541$	8.17497	+	14.1595i	0.351469	+	0.608763i	0.986507	−	0.163718i	$-0.0523488\pi$
$541$	8.17497	+	14.1595i	0.351469	+	0.608763i	−0.635038	+	0.772481i	$0.719015\pi$
$542$	19.1303			0.821715
$543$	10.8706	+	3.12772i	0.466503	+	0.134223i
$544$	0.293102	−	0.169223i	0.0125667	−	0.00725536i
$545$	−11.6821	−	6.74466i	−0.500406	−	0.288910i
$546$	6.98496	−	1.73486i	0.298929	−	0.0742450i
$547$	−6.91136	+	11.9708i	−0.295508	+	0.511835i	−0.975103	−	0.221752i	$-0.928822\pi$
$547$	−6.91136	+	11.9708i	−0.295508	+	0.511835i	0.679595	+	0.733588i	$0.262156\pi$
$548$	−4.77791	+	8.27559i	−0.204102	+	0.353516i
$549$	−17.7592	−	33.5461i	−0.757946	−	1.43171i
$550$			5.77952i			0.246440i
$551$	−6.63548	−	11.4930i	−0.282681	−	0.489618i
$552$	2.98071	+	12.0011i	0.126867	+	0.510799i
$553$	−10.0201	−	5.78513i	−0.426100	−	0.246009i
$554$	−14.5670			−0.618892
$555$	11.3121	−	2.80960i	0.480173	−	0.119261i
$556$			15.0058i			0.636387i
$557$	−37.9053			−1.60610			−0.803049	−	0.595914i	$-0.796790\pi$
$557$	−37.9053			−1.60610			−0.803049	+	0.595914i	$0.796790\pi$
$558$	1.02880	−	16.6716i	0.0435526	−	0.705764i
$559$	4.06934			0.172115
$560$		−	4.33820i		−	0.183322i
$561$	−3.28808	+	0.816661i	−0.138823	+	0.0344794i
$562$	7.59637			0.320434
$563$	−7.71129	−	4.45212i	−0.324992	−	0.187634i	0.328623	−	0.944461i	$-0.393415\pi$
$563$	−7.71129	−	4.45212i	−0.324992	−	0.187634i	−0.653616	+	0.756827i	$0.726749\pi$
$564$	1.15893	+	4.66615i	0.0487998	+	0.196480i
$565$	−6.42019	−	11.1201i	−0.270099	−	0.467826i
$566$			5.87807i			0.247074i
$567$	38.9386	+	2.86408i	1.63527	+	0.120280i
$568$	3.30610	−	5.72634i	0.138721	−	0.240272i
$569$	−11.7789	+	20.4017i	−0.493798	+	0.855283i	−0.999974	−	0.00714674i	$-0.997725\pi$
$569$	−11.7789	+	20.4017i	−0.493798	+	0.855283i	0.506176	+	0.862430i	$0.331058\pi$
$570$	−3.07830	+	0.764556i	−0.128936	+	0.0320237i
$571$	−9.66054	−	5.57752i	−0.404281	−	0.233412i	0.284048	−	0.958810i	$-0.408322\pi$
$571$	−9.66054	−	5.57752i	−0.404281	−	0.233412i	−0.688330	+	0.725398i	$0.741656\pi$
$572$	4.79419	−	2.76793i	0.200455	−	0.115733i
$573$	26.5168	+	7.62946i	1.10775	+	0.318725i
$574$	−7.37076			−0.307650
$575$	3.56967	+	6.18284i	0.148865	+	0.257842i
$576$	−2.65138	+	1.40363i	−0.110474	+	0.0584847i
$577$	16.1937	+	28.0483i	0.674152	+	1.16766i	0.976716	+	0.214536i	$0.0688239\pi$
$577$	16.1937	+	28.0483i	0.674152	+	1.16766i	−0.302565	+	0.953129i	$0.597843\pi$
$578$	−14.6232	−	8.44273i	−0.608246	−	0.351171i
$579$	−11.9945	−	12.4432i	−0.498476	−	0.517120i
$580$	−6.27603	−	3.62347i	−0.260598	−	0.150456i
$581$	−36.2164			−1.50251
$582$	5.56038	+	22.3875i	0.230485	+	0.927991i
$583$	23.1995	+	40.1828i	0.960826	+	1.66420i
$584$	−3.18550	+	5.51744i	−0.131817	+	0.228313i
$585$	−2.43413	−	1.52713i	−0.100639	−	0.0631389i
$586$	1.34471	+	2.32910i	0.0555493	+	0.0962142i
$587$	−9.72871			−0.401547			−0.200773	−	0.979638i	$-0.564346\pi$
$587$	−9.72871			−0.401547			−0.200773	+	0.979638i	$0.564346\pi$
$588$	5.66081	−	19.6746i	0.233448	−	0.811366i
$589$	−0.254066	+	10.1928i	−0.0104686	+	0.419988i
$590$		−	0.533132i		−	0.0219487i
$591$	−10.9483	+	38.0515i	−0.450351	+	1.56523i
$592$	−5.82791	+	3.36475i	−0.239526	+	0.138290i
$593$		−	33.4833i		−	1.37499i	−0.726187	−	0.687497i	$-0.758709\pi$
$593$		−	33.4833i		−	1.37499i	0.726187	−	0.687497i	$-0.241291\pi$
$594$	29.3918	−	6.16433i	1.20596	−	0.252926i
$595$	1.27154	−	0.734121i	0.0521279	−	0.0300960i
$596$	−7.45745	+	4.30556i	−0.305469	+	0.176363i
$597$	−17.6426	−	5.07616i	−0.722063	−	0.207753i
$598$	3.41917	−	5.92217i	0.139820	−	0.242176i
$599$	−19.1920	−	11.0805i	−0.784164	−	0.452737i	0.0537401	−	0.998555i	$-0.482886\pi$
$599$	−19.1920	−	11.0805i	−0.784164	−	0.452737i	−0.837904	+	0.545818i	$0.816219\pi$
$600$	−1.24702	+	1.20206i	−0.0509093	+	0.0490739i
$601$	20.2842	−	11.7111i	0.827409	−	0.477705i	−0.0255558	−	0.999673i	$-0.508136\pi$
$601$	20.2842	−	11.7111i	0.827409	−	0.477705i	0.852965	+	0.521969i	$0.174802\pi$
$602$	9.21533	−	15.9614i	0.375589	−	0.650539i
$603$	1.49203	−	40.6245i	0.0607601	−	1.65436i
$604$		−	17.7682i		−	0.722977i
$605$			22.4029i			0.910806i
$606$	5.72629	−	1.42224i	0.232614	−	0.0577745i
$607$	7.70723	−	13.3493i	0.312827	−	0.541832i	−0.666146	−	0.745821i	$-0.732057\pi$
$607$	7.70723	−	13.3493i	0.312827	−	0.541832i	0.978973	+	0.203989i	$0.0653908\pi$
$608$	1.58591	−	0.915626i	0.0643172	−	0.0371335i
$609$	−37.7911	−	39.2045i	−1.53137	−	1.58865i
$610$	10.9572	+	6.32617i	0.443646	+	0.256139i
$611$	1.32941	−	2.30261i	0.0537822	−	0.0931535i
$612$	−0.860082	−	0.539599i	−0.0347667	−	0.0218120i
$613$	−39.1725	+	22.6163i	−1.58216	+	0.913462i	−0.587619	+	0.809138i	$0.699935\pi$
$613$	−39.1725	+	22.6163i	−1.58216	+	0.913462i	−0.994543	+	0.104324i	$0.966732\pi$
$614$	2.23811	−	1.29217i	0.0903228	−	0.0521479i
$615$	2.04234	+	2.11873i	0.0823553	+	0.0854355i
$616$		−	25.0727i		−	1.01021i
$617$	−13.2494	+	7.64955i	−0.533401	+	0.307959i	−0.742400	−	0.669957i	$-0.766313\pi$
$617$	−13.2494	+	7.64955i	−0.533401	+	0.307959i	0.208999	+	0.977916i	$0.432979\pi$
$618$	18.4851	+	5.31856i	0.743579	+	0.213944i
$619$		−	29.4236i		−	1.18264i	−0.806438	−	0.591318i	$-0.798608\pi$
$619$		−	29.4236i		−	1.18264i	0.806438	−	0.591318i	$-0.201392\pi$
$620$	2.66287	+	4.88970i	0.106943	+	0.196375i
$621$	27.6356	−	24.7481i	1.10898	−	0.993106i
$622$	−5.04909			−0.202450
$623$	0.310602	+	0.537979i	0.0124440	+	0.0215537i
$624$	1.59435	+	0.458728i	0.0638249	+	0.0183638i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−5.85439	−	10.1401i	−0.233989	−	0.405280i
$627$	−17.7911	+	4.41877i	−0.710507	+	0.176469i
$628$	14.6635			0.585136
$629$	−1.97243	−	1.13878i	−0.0786459	−	0.0454062i
$630$	−11.5022	+	6.08924i	−0.458259	+	0.242601i
$631$	−26.5372	−	15.3213i	−1.05643	−	0.609930i	−0.131987	−	0.991251i	$-0.542136\pi$
$631$	−26.5372	−	15.3213i	−1.05643	−	0.609930i	−0.924442	+	0.381322i	$0.875469\pi$
$632$	−1.33353	−	2.30975i	−0.0530451	−	0.0918769i
$633$	−3.22927	−	3.35005i	−0.128352	−	0.133152i
$634$	−2.52416	−	4.37197i	−0.100247	−	0.173633i
$635$	21.2009			0.841331
$636$	−3.84486	+	13.3631i	−0.152458	+	0.529881i
$637$	−9.80481	+	5.66081i	−0.388481	+	0.224289i
$638$	−36.2724	−	20.9419i	−1.43604	−	0.829098i
$639$	−19.8233	−	0.728055i	−0.784196	−	0.0288014i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	20.7547	−	35.9482i	0.819761	−	1.41987i	−0.0860974	−	0.996287i	$-0.527440\pi$
$641$	20.7547	−	35.9482i	0.819761	−	1.41987i	0.905858	−	0.423581i	$-0.139227\pi$
$642$	−15.5866	−	16.1696i	−0.615156	−	0.638163i
$643$		−	19.6554i		−	0.775133i	−0.921842	−	0.387566i	$-0.873316\pi$
$643$		−	19.6554i		−	0.775133i	0.921842	−	0.387566i	$-0.126684\pi$
$644$	−15.4859	−	26.8224i	−0.610231	−	1.05695i
$645$	−7.14157	+	1.77375i	−0.281199	+	0.0698414i
$646$	0.536744	+	0.309889i	0.0211179	+	0.0121924i
$647$	−26.1942			−1.02980			−0.514900	−	0.857250i	$-0.672171\pi$
$647$	−26.1942			−1.02980			−0.514900	+	0.857250i	$0.672171\pi$
$648$	7.44313	+	5.05963i	0.292394	+	0.198761i
$649$		−	3.08124i		−	0.120949i
$650$	0.957839			0.0375696
$651$	9.06956	+	40.8411i	0.355464	+	1.60069i
$652$	10.7485			0.420945
$653$			3.14858i			0.123213i	0.998101	+	0.0616067i	$0.0196224\pi$
$653$			3.14858i			0.123213i	−0.998101	+	0.0616067i	$0.980378\pi$
$654$	−5.63186	−	22.6753i	−0.220223	−	0.886673i
$655$	−20.6106			−0.805322
$656$	−1.47141	−	0.849519i	−0.0574489	−	0.0331682i
$657$	19.1001	+	0.701496i	0.745166	+	0.0273680i
$658$	−6.02110	−	10.4289i	−0.234727	−	0.406559i
$659$			13.1254i			0.511293i	0.966770	+	0.255646i	$0.0822883\pi$
$659$			13.1254i			0.511293i	−0.966770	+	0.255646i	$0.917712\pi$
$660$	−7.20717	+	6.94733i	−0.280539	+	0.270424i
$661$	6.59803	−	11.4281i	0.256634	−	0.444503i	−0.708704	−	0.705506i	$-0.750720\pi$
$661$	6.59803	−	11.4281i	0.256634	−	0.444503i	0.965338	+	0.261003i	$0.0840533\pi$
$662$	−7.86495	+	13.6225i	−0.305680	+	0.529453i
$663$	0.135345	+	0.544933i	0.00525637	+	0.0211635i
$664$	−7.22980	−	4.17413i	−0.280571	−	0.161988i
$665$	6.87999	−	3.97217i	0.266795	−	0.154034i
$666$	17.1015	+	10.7291i	0.662669	+	0.415746i
$667$	−51.7383			−2.00331
$668$	3.76944	+	6.52887i	0.145844	+	0.252609i
$669$	19.0415	−	18.3550i	0.736188	−	0.709646i
$670$	6.77532	+	11.7352i	0.261753	+	0.453370i
$671$	63.3276	+	36.5622i	2.44474	+	1.41147i
$672$	5.40981	−	5.21477i	0.208688	−	0.201164i
$673$	33.1800	+	19.1565i	1.27900	+	0.738429i	0.976664	−	0.214773i	$-0.0689013\pi$
$673$	33.1800	+	19.1565i	1.27900	+	0.738429i	0.302333	+	0.953202i	$0.402235\pi$
$674$	−0.335775			−0.0129336
$675$	4.93747	+	1.61907i	0.190043	+	0.0623180i
$676$	6.04127	+	10.4638i	0.232357	+	0.402453i
$677$	−13.8127	+	23.9243i	−0.530866	+	0.919487i	0.468485	+	0.883471i	$0.344800\pi$
$677$	−13.8127	+	23.9243i	−0.530866	+	0.919487i	−0.999351	+	0.0360159i	$0.988533\pi$
$678$	6.14951	−	21.3731i	0.236170	−	0.820829i
$679$	−28.8883	−	50.0361i	−1.10863	−	1.92021i
$680$	0.338445			0.0129788
$681$	−41.0709	−	11.8170i	−1.57384	−	0.452829i
$682$	15.3901	+	28.2601i	0.589317	+	1.08214i
$683$			23.0912i			0.883559i	0.897124	+	0.441779i	$0.145653\pi$
$683$			23.0912i			0.883559i	−0.897124	+	0.441779i	$0.854347\pi$
$684$	−4.65371	−	2.91965i	−0.177939	−	0.111636i
$685$	−8.27559	+	4.77791i	−0.316194	+	0.182555i
$686$			20.9099i			0.798344i
$687$	24.8068	−	23.9124i	0.946437	−	0.912315i
$688$	3.67927	−	2.12423i	0.140271	−	0.0809855i
$689$	6.65949	−	3.84486i	0.253706	−	0.146477i
$690$	−3.41917	+	11.8836i	−0.130165	+	0.452400i
$691$	10.3702	−	17.9617i	0.394500	−	0.683295i	−0.598537	−	0.801095i	$-0.704251\pi$
$691$	10.3702	−	17.9617i	0.394500	−	0.683295i	0.993037	+	0.117800i	$0.0375843\pi$
$692$	−1.18142	−	0.682091i	−0.0449107	−	0.0259292i
$693$	−66.4772	+	35.1929i	−2.52526	+	1.33687i
$694$	−27.2878	+	15.7546i	−1.03583	+	0.598038i
$695$	−7.50289	+	12.9954i	−0.284601	+	0.492943i
$696$	−3.02563	−	12.1819i	−0.114686	−	0.461755i
$697$		−	0.575032i		−	0.0217809i
$698$			27.5332i			1.04215i
$699$	4.47345	+	18.0112i	0.169201	+	0.681247i
$700$	2.16910	−	3.75699i	0.0819842	−	0.142001i
$701$	12.0910	−	6.98074i	0.456670	−	0.263659i	−0.253973	−	0.967211i	$-0.581737\pi$
$701$	12.0910	−	6.98074i	0.456670	−	0.263659i	0.710643	+	0.703553i	$0.248404\pi$
$702$	−1.02161	−	4.87110i	−0.0385583	−	0.183848i
$703$	−10.6724	−	6.16170i	−0.402516	−	0.232393i
$704$	2.88976	−	5.00521i	0.108912	−	0.188641i
$705$	−1.32941	+	4.62047i	−0.0500685	+	0.174017i
$706$	6.97842	−	4.02900i	0.262636	−	0.151633i
$707$	−12.7983	+	7.38908i	−0.481328	+	0.277895i
$708$	0.664825	−	0.640856i	0.0249856	−	0.0240848i
$709$			18.6132i			0.699033i	0.936930	+	0.349516i	$0.113654\pi$
$709$			18.6132i			0.699033i	−0.936930	+	0.349516i	$0.886346\pi$
$710$	5.72634	−	3.30610i	0.214906	−	0.124076i
$711$	−4.25223	+	6.77775i	−0.159471	+	0.254185i
$712$			0.143194i			0.00536643i
$713$	33.9187	+	20.7267i	1.27026	+	0.776221i
$714$	2.44392	+	0.703170i	0.0914615	+	0.0263155i
$715$	5.53585			0.207029
$716$	−5.20586	−	9.01681i	−0.194552	−	0.336974i
$717$	−8.64650	+	30.0516i	−0.322909	+	1.12230i
$718$	11.6054	−	20.1011i	0.433109	−	0.750167i
$719$	−3.10759	−	5.38250i	−0.115893	−	0.200733i	0.802243	−	0.596997i	$-0.203640\pi$
$719$	−3.10759	−	5.38250i	−0.115893	−	0.200733i	−0.918137	+	0.396264i	$0.870306\pi$
$720$	−2.99798	−	0.110108i	−0.111728	−	0.00410347i
$721$	−48.1771			−1.79421
$722$	−13.5503	−	7.82326i	−0.504289	−	0.291152i
$723$	−22.8572	+	22.0332i	−0.850070	+	0.819422i
$724$	−5.65582	−	3.26539i	−0.210197	−	0.121357i
$725$	−3.62347	−	6.27603i	−0.134572	−	0.233086i
$726$	−27.9368	+	26.9296i	−1.03683	+	0.999450i
$727$	12.1101	+	20.9754i	0.449141	+	0.777934i	0.998330	−	0.0577635i	$-0.0183969\pi$
$727$	12.1101	+	20.9754i	0.449141	+	0.777934i	−0.549190	+	0.835698i	$0.685064\pi$
$728$	−4.15530			−0.154006
$729$	2.96757	−	26.8364i	0.109910	−	0.993942i
$730$	−5.51744	+	3.18550i	−0.204210	+	0.117901i
$731$	1.24523	+	0.718936i	0.0460566	+	0.0265908i
$732$	5.28241	+	21.2683i	0.195243	+	0.786099i
$733$	25.5424	−	44.2407i	0.943430	−	1.63407i	0.184565	−	0.982820i	$-0.440912\pi$
$733$	25.5424	−	44.2407i	0.943430	−	1.63407i	0.758865	−	0.651248i	$-0.225754\pi$
$734$	4.39074	−	7.60499i	0.162065	−	0.280705i
$735$	14.7397	−	14.2083i	0.543682	−	0.524080i
$736$		−	7.13933i		−	0.263159i
$737$	39.1581	+	67.8238i	1.44241	+	2.49832i
$738$	−0.187077	+	5.09368i	−0.00688641	+	0.187501i
$739$	35.7770	+	20.6559i	1.31608	+	0.759839i	0.983096	−	0.183093i	$-0.0586111\pi$
$739$	35.7770	+	20.6559i	1.31608	+	0.759839i	0.332984	+	0.942932i	$0.391944\pi$
$740$	−6.72949			−0.247381
$741$	0.732322	+	2.94851i	0.0269025	+	0.108316i
$742$		−	34.8278i		−	1.27857i
$743$	−19.2139			−0.704889			−0.352445	−	0.935833i	$-0.614650\pi$
$743$	−19.2139			−0.704889			−0.352445	+	0.935833i	$0.614650\pi$
$744$	−2.89662	+	9.19835i	−0.106195	+	0.337228i
$745$	−8.61112			−0.315487
$746$		−	6.26703i		−	0.229452i
$747$	−0.919208	+	25.0279i	−0.0336321	+	0.915723i
$748$	1.95605			0.0715203
$749$	48.7154	+	28.1259i	1.78002	+	1.02770i
$750$	−1.68098	+	0.417505i	−0.0613807	+	0.0152451i
$751$	−15.6599	−	27.1237i	−0.571437	−	0.989758i	−0.996419	−	0.0845560i	$-0.973053\pi$
$751$	−15.6599	−	27.1237i	−0.571437	−	0.989758i	0.424982	−	0.905202i	$-0.360281\pi$
$752$		−	2.77585i		−	0.101225i
$753$	−30.9635	−	32.1216i	−1.12837	−	1.17058i
$754$	−3.47070	+	6.01143i	−0.126395	+	0.218923i
$755$	8.88409	−	15.3877i	0.323325	−	0.560016i
$756$	−21.4197	−	7.02384i	−0.779028	−	0.255454i
$757$	−14.0423	−	8.10734i	−0.510377	−	0.294666i	0.222612	−	0.974907i	$-0.428542\pi$
$757$	−14.0423	−	8.10734i	−0.510377	−	0.294666i	−0.732988	+	0.680241i	$0.761875\pi$
$758$	21.8337	−	12.6057i	0.793036	−	0.457859i
$759$	−19.7611	+	68.6814i	−0.717284	+	2.49298i
$760$	1.83125			0.0664265
$761$	7.90266	+	13.6878i	0.286471	+	0.496183i	0.972965	−	0.230953i	$-0.0741844\pi$
$761$	7.90266	+	13.6878i	0.286471	+	0.496183i	−0.686494	+	0.727136i	$0.740851\pi$
$762$	25.4847	+	26.4379i	0.923214	+	0.957743i
$763$	29.2597	+	50.6793i	1.05927	+	1.83471i
$764$	−13.7963	−	7.96528i	−0.499131	−	0.288174i
$765$	−0.475053	−	0.897347i	−0.0171756	−	0.0324436i
$766$	−2.11259	−	1.21970i	−0.0763309	−	0.0440696i
$767$	−0.510654			−0.0184387
$768$	1.68098	−	0.417505i	0.0606571	−	0.0150654i
$769$	10.0816	+	17.4619i	0.363552	+	0.629691i	0.988543	−	0.150941i	$-0.0482304\pi$
$769$	10.0816	+	17.4619i	0.363552	+	0.629691i	−0.624990	+	0.780633i	$0.714897\pi$
$770$	12.5363	−	21.7136i	0.451779	−	0.782504i
$771$	−4.33893	−	1.24840i	−0.156263	−	0.0449602i
$772$	4.98917	+	8.64149i	0.179564	+	0.311014i
$773$	28.2917			1.01758			0.508790	−	0.860891i	$-0.330093\pi$
$773$	28.2917			1.01758			0.508790	+	0.860891i	$0.330093\pi$
$774$	−10.7965	−	6.77351i	−0.388072	−	0.243469i
$775$	−0.138739	+	5.56604i	−0.00498366	+	0.199938i
$776$		−	13.3181i		−	0.478093i
$777$	−48.5939	−	13.9815i	−1.74329	−	0.501584i
$778$	3.48606	−	2.01268i	0.124981	−	0.0721580i
$779$		−	3.11137i		−	0.111476i
$780$	1.15138	+	1.19444i	0.0412260	+	0.0427679i
$781$	33.0955	−	19.1077i	1.18425	−	0.683727i
$782$	2.09255	−	1.20814i	0.0748296	−	0.0432029i
$783$	−28.0521	+	25.1211i	−1.00250	+	0.897754i
$784$	−5.90998	+	10.2364i	−0.211071	+	0.365585i
$785$	12.6989	+	7.33174i	0.453245	+	0.261681i
$786$	−24.7751	−	25.7018i	−0.883700	−	0.916752i
$787$	6.13803	−	3.54379i	0.218797	−	0.126323i	−0.386596	−	0.922249i	$-0.626349\pi$
$787$	6.13803	−	3.54379i	0.218797	−	0.126323i	0.605393	+	0.795927i	$0.293016\pi$
$788$	11.4302	−	19.7976i	0.407183	−	0.705261i
$789$	24.3786	−	6.05492i	0.867903	−	0.215561i
$790$		−	2.66707i		−	0.0948900i
$791$			55.7041i			1.98061i
$792$	−17.3269	−	0.636370i	−0.615684	−	0.0226124i
$793$	6.05945	−	10.4953i	0.215177	−	0.372698i
$794$	−17.8267	+	10.2922i	−0.632644	+	0.365257i
$795$	−10.0113	+	9.65035i	−0.355064	+	0.342263i
$796$	9.17917	+	5.29960i	0.325347	+	0.187839i
$797$	1.69939	−	2.94344i	0.0601956	−	0.104262i	−0.834357	−	0.551224i	$-0.814161\pi$
$797$	1.69939	−	2.94344i	0.0601956	−	0.104262i	0.894553	+	0.446962i	$0.147494\pi$
$798$	13.2235	+	3.80470i	0.468108	+	0.134685i
$799$	0.813609	−	0.469737i	0.0287834	−	0.0166181i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	0.379662	−	0.200992i	0.0134147	−	0.00710171i
$802$			2.12457i			0.0750211i
$803$	−31.8882	+	18.4106i	−1.12531	+	0.649698i
$804$	−6.48967	+	22.5553i	−0.228873	+	0.795466i
$805$		−	30.9718i		−	1.09161i
$806$	4.68355	−	2.55060i	0.164971	−	0.0898410i
$807$	1.30596	−	4.53897i	0.0459720	−	0.159779i
$808$	−3.40652			−0.119841
$809$	−17.6125	−	30.5057i	−0.619222	−	1.07252i	−0.989628	−	0.143653i	$-0.954115\pi$
$809$	−17.6125	−	30.5057i	−0.619222	−	1.07252i	0.370406	−	0.928870i	$-0.379218\pi$
$810$	3.91613	+	8.10333i	0.137599	+	0.284722i
$811$	−11.5089	+	19.9340i	−0.404133	+	0.699979i	−0.994220	−	0.107361i	$-0.965760\pi$
$811$	−11.5089	+	19.9340i	−0.404133	+	0.699979i	0.590087	+	0.807339i	$0.299093\pi$
$812$	15.7193	+	27.2267i	0.551640	+	0.955468i
$813$	7.98697	+	32.1576i	0.280115	+	1.12781i
$814$	−38.8932			−1.36321
$815$	9.30850	+	5.37426i	0.326062	+	0.188252i
$816$	0.406831	+	0.422047i	0.0142419	+	0.0147746i
$817$	6.73768	+	3.89000i	0.235722	+	0.136094i
$818$	−17.5427	−	30.3848i	−0.613366	−	1.06238i
$819$	5.83251	+	11.0173i	0.203804	+	0.384974i
$820$	−0.849519	−	1.47141i	−0.0296665	−	0.0513839i
$821$	−10.5703			−0.368904			−0.184452	−	0.982841i	$-0.559051\pi$
$821$	−10.5703			−0.368904			−0.184452	+	0.982841i	$0.559051\pi$
$822$	−15.9059	−	4.57647i	−0.554782	−	0.159623i
$823$	−27.2600	+	15.7385i	−0.950223	+	0.548611i	−0.893150	−	0.449759i	$-0.851510\pi$
$823$	−27.2600	+	15.7385i	−0.950223	+	0.548611i	−0.0570726	+	0.998370i	$0.518177\pi$
$824$	−9.61750	−	5.55266i	−0.335041	−	0.193436i
$825$	−9.71525	+	2.41298i	−0.338242	+	0.0840091i
$826$	−1.15641	+	2.00297i	−0.0402368	+	0.0696922i
$827$	10.1100	−	17.5111i	0.351561	−	0.608921i	−0.634962	−	0.772543i	$-0.718984\pi$
$827$	10.1100	−	17.5111i	0.351561	−	0.608921i	0.986523	+	0.163622i	$0.0523177\pi$
$828$	−18.9291	+	10.0210i	−0.657831	+	0.348254i
$829$			26.9721i			0.936781i	0.883522	+	0.468390i	$0.155166\pi$
$829$			26.9721i			0.936781i	−0.883522	+	0.468390i	$0.844834\pi$
$830$	−4.17413	−	7.22980i	−0.144886	−	0.250950i
$831$	−6.08179	−	24.4868i	−0.210975	−	0.849438i
$832$	−0.829513	−	0.478920i	−0.0287582	−	0.0166036i
$833$	−4.00041			−0.138606
$834$	−25.2244	+	6.26499i	−0.873450	+	0.216939i
$835$			7.53889i			0.260894i
$836$	10.5838			0.366047
$837$	28.4541	−	5.23107i	0.983518	−	0.180812i
$838$	−30.0425			−1.03780
$839$		−	40.5964i		−	1.40154i	−0.713386	−	0.700771i	$-0.752840\pi$
$839$		−	40.5964i		−	1.40154i	0.713386	−	0.700771i	$-0.247160\pi$
$840$	7.29242	−	1.81122i	0.251612	−	0.0624930i
$841$	23.5181			0.810968
$842$	−15.3829	−	8.88135i	−0.530131	−	0.306071i
$843$	3.17152	+	12.7693i	0.109233	+	0.439799i
$844$	1.34322	+	2.32653i	0.0462357	+	0.0800825i
$845$			12.0825i			0.415652i
$846$	−7.35984	+	3.89628i	−0.253037	+	0.133957i
$847$	48.5940	−	84.1673i	1.66971	−	2.89202i
$848$	4.01409	−	6.95261i	0.137845	−	0.238754i
$849$	−9.88092	+	2.45412i	−0.339112	+	0.0842253i
$850$	0.293102	+	0.169223i	0.0100533	+	0.00580429i
$851$	−41.6074	+	24.0220i	−1.42628	+	0.823465i
$852$	11.0062	+	3.16672i	0.377065	+	0.108490i
$853$	−47.0016			−1.60931			−0.804653	−	0.593746i	$-0.797648\pi$
$853$	−47.0016			−1.60931			−0.804653	+	0.593746i	$0.797648\pi$
$854$	−27.4442	−	47.5347i	−0.939120	−	1.62660i
$855$	−2.57041	−	4.85534i	−0.0879060	−	0.166049i
$856$	6.48331	+	11.2294i	0.221595	+	0.383814i
$857$	20.7126	+	11.9585i	0.707530	+	0.408493i	0.810146	−	0.586228i	$-0.199388\pi$
$857$	20.7126	+	11.9585i	0.707530	+	0.408493i	−0.102616	+	0.994721i	$0.532721\pi$
$858$	6.65442	+	6.90331i	0.227178	+	0.235675i
$859$	9.81718	+	5.66795i	0.334958	+	0.193388i	0.658040	−	0.752983i	$-0.271386\pi$
$859$	9.81718	+	5.66795i	0.334958	+	0.193388i	−0.323082	+	0.946371i	$0.604719\pi$
$860$	4.24846			0.144871
$861$	−3.07733	−	12.3901i	−0.104875	−	0.422253i
$862$	−15.1127	−	26.1760i	−0.514741	−	0.891558i
$863$	22.1314	−	38.3327i	0.753362	−	1.30486i	−0.192823	−	0.981234i	$-0.561764\pi$
$863$	22.1314	−	38.3327i	0.753362	−	1.30486i	0.946185	−	0.323627i	$-0.104902\pi$
$864$	−3.46644	−	3.87089i	−0.117931	−	0.131690i
$865$	−0.682091	−	1.18142i	−0.0231918	−	0.0401694i
$866$	−18.0413			−0.613069
$867$	8.08678	−	28.1062i	0.274641	−	0.954537i
$868$	0.601878	−	24.1466i	0.0204291	−	0.819588i
$869$		−	15.4144i		−	0.522897i
$870$	3.47070	−	12.0627i	0.117668	−	0.408963i
$871$	11.2404	−	6.48967i	0.380868	−	0.219894i
$872$			13.4893i			0.456806i
$873$	−35.3114	+	18.6938i	−1.19511	+	0.632688i
$874$	11.3223	−	6.53696i	0.382984	−	0.221116i
$875$	3.75699	−	2.16910i	0.127009	−	0.0733289i
$876$	−10.6047	−	3.05120i	−0.358298	−	0.103090i
$877$	−26.8199	+	46.4534i	−0.905643	+	1.56862i	−0.0855921	+	0.996330i	$0.527278\pi$
$877$	−26.8199	+	46.4534i	−0.905643	+	1.56862i	−0.820051	+	0.572290i	$0.806055\pi$
$878$	12.6937	+	7.32870i	0.428391	+	0.247332i
$879$	−3.35375	+	3.23283i	−0.113119	+	0.109041i
$880$	5.00521	−	2.88976i	0.168726	−	0.0974138i
$881$	−14.6650	+	25.4005i	−0.494077	+	0.855766i	−0.999977	−	0.00682624i	$-0.997827\pi$
$881$	−14.6650	+	25.4005i	−0.494077	+	0.855766i	0.505900	+	0.862592i	$0.331160\pi$
$882$	35.4360	+	1.30147i	1.19319	+	0.0438227i
$883$			53.8031i			1.81062i	0.424753	+	0.905309i	$0.360361\pi$
$883$			53.8031i			1.81062i	−0.424753	+	0.905309i	$0.639639\pi$
$884$		−	0.324176i		−	0.0109032i
$885$	0.896183	−	0.222585i	0.0301249	−	0.00748211i
$886$	−7.77486	+	13.4664i	−0.261201	+	0.452414i
$887$	−32.7721	+	18.9210i	−1.10038	+	0.635304i	−0.936321	−	0.351146i	$-0.885792\pi$
$887$	−32.7721	+	18.9210i	−1.10038	+	0.635304i	−0.164059	+	0.986451i	$0.552459\pi$
$888$	−8.08925	−	8.39180i	−0.271457	−	0.281610i
$889$	−79.6515	−	45.9868i	−2.67142	−	1.54235i
$890$	−0.0715971	+	0.124010i	−0.00239994	+	0.00415682i
$891$	22.6333	+	46.8334i	0.758245	+	1.56898i
$892$	−13.2239	+	7.63482i	−0.442769	+	0.255633i
$893$	4.40226	−	2.54164i	0.147316	−	0.0850529i
$894$	−10.3511	−	10.7382i	−0.346192	−	0.359140i
$895$		−	10.4117i		−	0.348025i
$896$	−3.75699	+	2.16910i	−0.125512	+	0.0724645i
$897$	11.3826	+	3.27501i	0.380053	+	0.109349i
$898$			15.2448i			0.508727i
$899$	−34.4299	−	21.0391i	−1.14830	−	0.701693i
$900$	−2.54127	−	1.59435i	−0.0847091	−	0.0531448i
$901$	2.71710			0.0905198
$902$	−4.90981	−	8.50405i	−0.163479	−	0.283154i
$903$	30.6782	+	8.82680i	1.02091	+	0.293738i
$904$	−6.42019	+	11.1201i	−0.213532	+	0.369849i
$905$	−3.26539	−	5.65582i	−0.108545	−	0.188006i
$906$	29.8679	−	7.41830i	0.992296	−	0.246456i
$907$	35.8033			1.18883			0.594414	−	0.804159i	$-0.297384\pi$
$907$	35.8033			1.18883			0.594414	+	0.804159i	$0.297384\pi$
$908$	21.3686	+	12.3371i	0.709141	+	0.409423i
$909$	4.78150	+	9.03197i	0.158592	+	0.299572i
$910$	−3.59859	−	2.07765i	−0.119292	−	0.0688734i
$911$	−14.8312	−	25.6883i	−0.491379	−	0.851093i	0.508572	−	0.861019i	$-0.330174\pi$
$911$	−14.8312	−	25.6883i	−0.491379	−	0.851093i	−0.999951	+	0.00992656i	$0.996840\pi$
$912$	2.20127	+	2.28360i	0.0728914	+	0.0756177i
$913$	−24.1245	−	41.7848i	−0.798403	−	1.38287i
$914$	15.6182			0.516605
$915$	−6.05945	+	21.0601i	−0.200319	+	0.696225i
$916$	−17.2277	+	9.94643i	−0.569220	+	0.328639i
$917$	77.4338	+	44.7064i	2.55709	+	1.47634i
$918$	0.547966	−	1.67106i	0.0180856	−	0.0551533i
$919$	−16.9354	+	29.3330i	−0.558649	+	0.967608i	0.438961	+	0.898506i	$0.355347\pi$
$919$	−16.9354	+	29.3330i	−0.558649	+	0.967608i	−0.997610	+	0.0691016i	$0.977987\pi$
$920$	3.56967	−	6.18284i	0.117688	−	0.203842i
$921$	3.10654	+	3.22273i	0.102364	+	0.106193i
$922$		−	23.2167i		−	0.764600i
$923$	−3.16672	−	5.48491i	−0.104234	−	0.180538i
$924$	42.1467	−	10.4680i	1.38652	−	0.344371i
$925$	−5.82791	−	3.36475i	−0.191621	−	0.110632i
$926$	8.21847			0.270076
$927$	−1.22278	+	33.2935i	−0.0401614	+	1.09350i
$928$			7.24694i			0.237892i
$929$	−25.8944			−0.849568			−0.424784	−	0.905295i	$-0.639650\pi$
$929$	−25.8944			−0.849568			−0.424784	+	0.905295i	$0.639650\pi$
$930$	−7.10772	+	6.51769i	−0.233071	+	0.213724i
$931$	−21.6453			−0.709396
$932$		−	10.7147i		−	0.350972i
$933$	−2.10802	−	8.48742i	−0.0690135	−	0.277866i
$934$	18.3605			0.600773
$935$	1.69399	+	0.978026i	0.0553994	+	0.0319849i
$936$	−0.105466	+	2.87158i	−0.00344725	+	0.0938606i
$937$	18.6102	+	32.2338i	0.607968	+	1.05303i	0.991575	+	0.129534i	$0.0413483\pi$
$937$	18.6102	+	32.2338i	0.607968	+	1.05303i	−0.383607	+	0.923496i	$0.625318\pi$
$938$		−	58.7853i		−	1.91941i
$939$	14.6011	−	14.0747i	0.476488	−	0.459309i
$940$	1.38793	−	2.40396i	0.0452692	−	0.0784085i
$941$	−11.2426	+	19.4727i	−0.366497	+	0.634792i	−0.989015	−	0.147814i	$-0.952776\pi$
$941$	−11.2426	+	19.4727i	−0.366497	+	0.634792i	0.622518	+	0.782605i	$0.286110\pi$
$942$	6.12207	+	24.6490i	0.199468	+	0.803107i
$943$	−10.5049	−	6.06500i	−0.342086	−	0.197504i
$944$	−0.461706	+	0.266566i	−0.0150272	+	0.00867598i
$945$	−15.0381	−	16.7927i	−0.489190	−	0.546266i
$946$	24.5541			0.798321
$947$	−16.3484	−	28.3163i	−0.531252	−	0.920156i	−0.999335	−	0.0364709i	$-0.988388\pi$
$947$	−16.3484	−	28.3163i	−0.531252	−	0.920156i	0.468083	−	0.883685i	$-0.344945\pi$
$948$	3.32588	−	3.20597i	0.108020	−	0.104125i
$949$	3.05120	+	5.28482i	0.0990460	+	0.171553i
$950$	1.58591	+	0.915626i	0.0514537	+	0.0297068i
$951$	6.29534	−	6.06837i	0.204140	−	0.196781i
$952$	−1.27154	−	0.734121i	−0.0412107	−	0.0237930i
$953$	−40.6741			−1.31756			−0.658782	−	0.752334i	$-0.728928\pi$
$953$	−40.6741			−1.31756			−0.658782	+	0.752334i	$0.728928\pi$
$954$	−24.0683	−	0.883965i	−0.779241	−	0.0286194i
$955$	−7.96528	−	13.7963i	−0.257750	−	0.446437i
$956$	9.02709	−	15.6354i	0.291957	−	0.505684i
$957$	20.0590	−	69.7165i	0.648415	−	2.25362i
$958$	−7.69783	−	13.3330i	−0.248706	−	0.430771i
$959$	41.4551			1.33865
$960$	1.66452	+	0.478920i	0.0537222	+	0.0154571i
$961$	14.1432	+	27.5857i	0.456233	+	0.889860i
$962$			6.44577i			0.207820i
$963$	20.6733	−	32.9517i	0.666187	−	1.06185i
$964$	15.8738	−	9.16476i	0.511261	−	0.295177i
$965$			9.97834i			0.321214i
$966$	38.6224	−	37.2300i	1.24266	−	1.19785i
$967$	45.3740	−	26.1967i	1.45913	−	0.842429i	0.460161	−	0.887836i	$-0.347792\pi$
$967$	45.3740	−	26.1967i	1.45913	−	0.842429i	0.998969	+	0.0454068i	$0.0144584\pi$
$968$	19.4014	−	11.2014i	0.623586	−	0.360028i
$969$	−0.296824	+	1.03164i	−0.00953537	+	0.0331409i
$970$	6.65906	−	11.5338i	0.213810	−	0.370329i
$971$	−37.9151	−	21.8903i	−1.21675	−	0.702493i	−0.252532	−	0.967589i	$-0.581263\pi$
$971$	−37.9151	−	21.8903i	−1.21675	−	0.702493i	−0.964222	+	0.265095i	$0.914597\pi$
$972$	−5.39758	+	14.6242i	−0.173128	+	0.469070i
$973$	56.3766	−	32.5490i	1.80735	−	1.04347i
$974$	7.52353	−	13.0311i	0.241070	−	0.417545i
$975$	0.399902	+	1.61011i	0.0128071	+	0.0515647i
$976$		−	12.6523i		−	0.404991i
$977$		−	11.7865i		−	0.377085i	−0.982065	−	0.188542i	$-0.939624\pi$
$977$		−	11.7865i		−	0.377085i	0.982065	−	0.188542i	$-0.0603763\pi$
$978$	4.48756	+	18.0680i	0.143496	+	0.577752i
$979$	−0.413797	+	0.716717i	−0.0132250	+	0.0229064i
$980$	−10.2364	+	5.90998i	−0.326989	+	0.188787i
$981$	35.7653	−	18.9341i	1.14190	−	0.604518i
$982$	−31.6310	−	18.2622i	−1.00939	−	0.582769i
$983$	−14.0778	+	24.3835i	−0.449013	+	0.777714i	−0.998322	−	0.0579056i	$-0.981558\pi$
$983$	−14.0778	+	24.3835i	−0.449013	+	0.777714i	0.549309	+	0.835619i	$0.314891\pi$
$984$	0.813703	−	2.82809i	0.0259399	−	0.0901562i
$985$	19.7976	−	11.4302i	0.630805	−	0.364195i
$986$	−2.12409	+	1.22635i	−0.0676449	+	0.0390548i
$987$	15.0168	−	14.4754i	0.477991	−	0.460758i
$988$		−	1.75405i		−	0.0558036i
$989$	26.2676	−	15.1656i	0.835260	−	0.482238i
$990$	−14.6873	−	9.21455i	−0.466794	−	0.292858i
$991$		−	10.7035i		−	0.340009i	−0.985443	−	0.170005i	$-0.945622\pi$
$991$		−	10.7035i		−	0.340009i	0.985443	−	0.170005i	$-0.0543783\pi$
$992$	2.90317	−	4.75096i	0.0921757	−	0.150843i
$993$	−26.1828	−	7.53336i	−0.830885	−	0.239064i
$994$	−28.6851			−0.909835
$995$	5.29960	+	9.17917i	0.168008	+	0.290999i
$996$	3.99815	−	13.8959i	0.126686	−	0.440307i
$997$	8.36197	−	14.4834i	0.264826	−	0.458693i	−0.702692	−	0.711494i	$-0.748019\pi$
$997$	8.36197	−	14.4834i	0.264826	−	0.458693i	0.967518	+	0.252802i	$0.0813521\pi$
$998$	−0.406844	−	0.704675i	−0.0128784	−	0.0223061i
$999$	−10.8955	+	33.2267i	−0.344719	+	1.05125i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.o.d.161.9	✓	36
3.2	odd	2	inner	930.2.o.d.161.16	yes	36
31.26	odd	6	inner	930.2.o.d.491.7	yes	36
93.26	even	6	inner	930.2.o.d.491.18	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.o.d.161.9	✓	36	1.1	even	1	trivial
930.2.o.d.161.16	yes	36	3.2	odd	2	inner
930.2.o.d.491.7	yes	36	31.26	odd	6	inner
930.2.o.d.491.18	yes	36	93.26	even	6	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.68098 - 0.417505i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.417505 - 1.68098i) q^{6} +(2.16910 + 3.75699i) q^{7} +1.00000i q^{8} +(2.65138 - 1.40363i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.68098 - 0.417505i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.417505 - 1.68098i) q^{6} +(2.16910 + 3.75699i) q^{7} +1.00000i q^{8} +(2.65138 - 1.40363i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-2.88976 + 5.00521i) q^{11} +(-1.68098 + 0.417505i) q^{12} +(0.829513 + 0.478920i) q^{13} +(3.75699 - 2.16910i) q^{14} +(-1.66452 - 0.478920i) q^{15} +1.00000 q^{16} +(0.169223 + 0.293102i) q^{17} +(-1.40363 - 2.65138i) q^{18} +(0.915626 + 1.58591i) q^{19} +(0.866025 + 0.500000i) q^{20} +(5.21477 + 5.40981i) q^{21} +(5.00521 + 2.88976i) q^{22} +7.13933 q^{23} +(0.417505 + 1.68098i) q^{24} +(0.500000 + 0.866025i) q^{25} +(0.478920 - 0.829513i) q^{26} +(3.87089 - 3.46644i) q^{27} +(-2.16910 - 3.75699i) q^{28} -7.24694 q^{29} +(-0.478920 + 1.66452i) q^{30} +(4.75096 + 2.90317i) q^{31} -1.00000i q^{32} +(-2.76793 + 9.62014i) q^{33} +(0.293102 - 0.169223i) q^{34} -4.33820i q^{35} +(-2.65138 + 1.40363i) q^{36} +(-5.82791 + 3.36475i) q^{37} +(1.58591 - 0.915626i) q^{38} +(1.59435 + 0.458728i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-1.47141 - 0.849519i) q^{41} +(5.40981 - 5.21477i) q^{42} +(3.67927 - 2.12423i) q^{43} +(2.88976 - 5.00521i) q^{44} +(-2.99798 - 0.110108i) q^{45} -7.13933i q^{46} -2.77585i q^{47} +(1.68098 - 0.417505i) q^{48} +(-5.90998 + 10.2364i) q^{49} +(0.866025 - 0.500000i) q^{50} +(0.406831 + 0.422047i) q^{51} +(-0.829513 - 0.478920i) q^{52} +(4.01409 - 6.95261i) q^{53} +(-3.46644 - 3.87089i) q^{54} +(5.00521 - 2.88976i) q^{55} +(-3.75699 + 2.16910i) q^{56} +(2.20127 + 2.28360i) q^{57} +7.24694i q^{58} +(-0.461706 + 0.266566i) q^{59} +(1.66452 + 0.478920i) q^{60} -12.6523i q^{61} +(2.90317 - 4.75096i) q^{62} +(11.0245 + 6.91658i) q^{63} -1.00000 q^{64} +(-0.478920 - 0.829513i) q^{65} +(9.62014 + 2.76793i) q^{66} +(6.77532 - 11.7352i) q^{67} +(-0.169223 - 0.293102i) q^{68} +(12.0011 - 2.98071i) q^{69} -4.33820 q^{70} +(-5.72634 - 3.30610i) q^{71} +(1.40363 + 2.65138i) q^{72} +(5.51744 + 3.18550i) q^{73} +(3.36475 + 5.82791i) q^{74} +(1.20206 + 1.24702i) q^{75} +(-0.915626 - 1.58591i) q^{76} -25.0727 q^{77} +(0.458728 - 1.59435i) q^{78} +(-2.30975 + 1.33353i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(5.05963 - 7.44313i) q^{81} +(-0.849519 + 1.47141i) q^{82} +(-4.17413 + 7.22980i) q^{83} +(-5.21477 - 5.40981i) q^{84} -0.338445i q^{85} +(-2.12423 - 3.67927i) q^{86} +(-12.1819 + 3.02563i) q^{87} +(-5.00521 - 2.88976i) q^{88} +0.143194 q^{89} +(-0.110108 + 2.99798i) q^{90} +4.15530i q^{91} -7.13933 q^{92} +(9.19835 + 2.89662i) q^{93} -2.77585 q^{94} -1.83125i q^{95} +(-0.417505 - 1.68098i) q^{96} -13.3181 q^{97} +(10.2364 + 5.90998i) q^{98} +(-0.636370 + 17.3269i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9}+O(q^{10}) \) 36 * q - 36 * q^4 - 8 * q^7 + 8 * q^9	\( 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9} - 18 q^{10} + 36 q^{16} - 4 q^{18} - 4 q^{19} + 72 q^{21} - 18 q^{22} + 18 q^{25} + 8 q^{28} + 52 q^{31} - 36 q^{33} + 18 q^{34} - 8 q^{36} - 54 q^{37} - 8 q^{39} + 18 q^{40} + 12 q^{42} - 18 q^{43} + 4 q^{45} - 62 q^{49} - 10 q^{51} - 18 q^{55} + 12 q^{57} + 88 q^{63} - 36 q^{64} - 4 q^{66} + 10 q^{67} + 46 q^{69} + 16 q^{70} + 4 q^{72} + 24 q^{73} + 4 q^{76} + 92 q^{78} + 42 q^{79} + 4 q^{81} - 12 q^{82} - 72 q^{84} - 16 q^{87} + 18 q^{88} + 8 q^{90} + 48 q^{93} - 92 q^{94} - 80 q^{97} - 18 q^{99}+O(q^{100}) \) 36 * q - 36 * q^4 - 8 * q^7 + 8 * q^9 - 18 * q^10 + 36 * q^16 - 4 * q^18 - 4 * q^19 + 72 * q^21 - 18 * q^22 + 18 * q^25 + 8 * q^28 + 52 * q^31 - 36 * q^33 + 18 * q^34 - 8 * q^36 - 54 * q^37 - 8 * q^39 + 18 * q^40 + 12 * q^42 - 18 * q^43 + 4 * q^45 - 62 * q^49 - 10 * q^51 - 18 * q^55 + 12 * q^57 + 88 * q^63 - 36 * q^64 - 4 * q^66 + 10 * q^67 + 46 * q^69 + 16 * q^70 + 4 * q^72 + 24 * q^73 + 4 * q^76 + 92 * q^78 + 42 * q^79 + 4 * q^81 - 12 * q^82 - 72 * q^84 - 16 * q^87 + 18 * q^88 + 8 * q^90 + 48 * q^93 - 92 * q^94 - 80 * q^97 - 18 * q^99

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