LMFDB - Embedded newform 798.2.k.n.463.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(463,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("798.463");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.k (of order $3$, 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:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.70858800.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 18x^{4} + 81x^{2} + 48 $ x^6 + 18x^4 + 81x^2 + 48
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			463.2
Root			$2.49452i$ of defining polynomial
Character	$\chi$	$=$	798.463
Dual form			798.2.k.n.505.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} -1.22263 q^{11} -1.00000 q^{12} +(0.111315 - 0.192804i) q^{13} +(0.500000 + 0.866025i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.93195 - 6.81034i) q^{17} +1.00000 q^{18} +(4.04327 - 1.62849i) q^{19} +1.00000 q^{20} +(-0.500000 - 0.866025i) q^{21} +(0.611315 + 1.05883i) q^{22} +(3.43195 - 5.94431i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.00000 - 3.46410i) q^{25} -0.222631 q^{26} -1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(-2.00000 + 3.46410i) q^{29} -1.00000 q^{30} -0.445262 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.611315 - 1.05883i) q^{33} +(-3.93195 + 6.81034i) q^{34} +(0.500000 + 0.866025i) q^{35} +(-0.500000 - 0.866025i) q^{36} -1.22263 q^{37} +(-3.43195 - 2.68732i) q^{38} +0.222631 q^{39} +(-0.500000 - 0.866025i) q^{40} +(1.38868 + 2.40527i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(-1.00000 - 1.73205i) q^{43} +(0.611315 - 1.05883i) q^{44} +1.00000 q^{45} -6.86390 q^{46} +(4.54327 - 7.86917i) q^{47} +(0.500000 - 0.866025i) q^{48} +1.00000 q^{49} -4.00000 q^{50} +(3.93195 - 6.81034i) q^{51} +(0.111315 + 0.192804i) q^{52} +(4.32064 - 7.48356i) q^{53} +(0.500000 + 0.866025i) q^{54} +(0.611315 + 1.05883i) q^{55} -1.00000 q^{56} +(3.43195 + 2.68732i) q^{57} +4.00000 q^{58} +(-6.65458 - 11.5261i) q^{59} +(0.500000 + 0.866025i) q^{60} +(-2.88868 + 5.00335i) q^{61} +(0.222631 + 0.385608i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} -0.222631 q^{65} +(-0.611315 + 1.05883i) q^{66} +(-6.32064 + 10.9477i) q^{67} +7.86390 q^{68} +6.86390 q^{69} +(0.500000 - 0.866025i) q^{70} +(-5.65458 - 9.79402i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-3.32064 - 5.75151i) q^{73} +(0.611315 + 1.05883i) q^{74} +4.00000 q^{75} +(-0.611315 + 4.31582i) q^{76} +1.22263 q^{77} +(-0.111315 - 0.192804i) q^{78} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.38868 - 2.40527i) q^{82} +10.8639 q^{83} +1.00000 q^{84} +(-3.93195 + 6.81034i) q^{85} +(-1.00000 + 1.73205i) q^{86} -4.00000 q^{87} -1.22263 q^{88} +(-2.93195 + 5.07829i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-0.111315 + 0.192804i) q^{91} +(3.43195 + 5.94431i) q^{92} +(-0.222631 - 0.385608i) q^{93} -9.08653 q^{94} +(-3.43195 - 2.68732i) q^{95} -1.00000 q^{96} +(-1.77737 - 3.07849i) q^{97} +(-0.500000 - 0.866025i) q^{98} +(0.611315 - 1.05883i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 3 q^{6} - 6 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 3 * q^6 - 6 * q^7 + 6 * q^8 - 3 * q^9	$ 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 3 q^{6} - 6 q^{7} + 6 q^{8} - 3 q^{9} - 3 q^{10} - 6 q^{11} - 6 q^{12} + 3 q^{14} + 3 q^{15} - 3 q^{16} + 3 q^{17} + 6 q^{18} - 3 q^{19} + 6 q^{20} - 3 q^{21} + 3 q^{22} - 6 q^{23} + 3 q^{24} + 12 q^{25} - 6 q^{27} + 3 q^{28} - 12 q^{29} - 6 q^{30} - 3 q^{32} - 3 q^{33} + 3 q^{34} + 3 q^{35} - 3 q^{36} - 6 q^{37} + 6 q^{38} - 3 q^{40} + 9 q^{41} - 3 q^{42} - 6 q^{43} + 3 q^{44} + 6 q^{45} + 12 q^{46} + 3 q^{48} + 6 q^{49} - 24 q^{50} - 3 q^{51} + 3 q^{54} + 3 q^{55} - 6 q^{56} - 6 q^{57} + 24 q^{58} - 12 q^{59} + 3 q^{60} - 18 q^{61} + 3 q^{63} + 6 q^{64} - 3 q^{66} - 12 q^{67} - 6 q^{68} - 12 q^{69} + 3 q^{70} - 6 q^{71} - 3 q^{72} + 6 q^{73} + 3 q^{74} + 24 q^{75} - 3 q^{76} + 6 q^{77} - 3 q^{80} - 3 q^{81} + 9 q^{82} + 12 q^{83} + 6 q^{84} + 3 q^{85} - 6 q^{86} - 24 q^{87} - 6 q^{88} + 9 q^{89} - 3 q^{90} - 6 q^{92} + 6 q^{95} - 6 q^{96} - 12 q^{97} - 3 q^{98} + 3 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 3 * q^6 - 6 * q^7 + 6 * q^8 - 3 * q^9 - 3 * q^10 - 6 * q^11 - 6 * q^12 + 3 * q^14 + 3 * q^15 - 3 * q^16 + 3 * q^17 + 6 * q^18 - 3 * q^19 + 6 * q^20 - 3 * q^21 + 3 * q^22 - 6 * q^23 + 3 * q^24 + 12 * q^25 - 6 * q^27 + 3 * q^28 - 12 * q^29 - 6 * q^30 - 3 * q^32 - 3 * q^33 + 3 * q^34 + 3 * q^35 - 3 * q^36 - 6 * q^37 + 6 * q^38 - 3 * q^40 + 9 * q^41 - 3 * q^42 - 6 * q^43 + 3 * q^44 + 6 * q^45 + 12 * q^46 + 3 * q^48 + 6 * q^49 - 24 * q^50 - 3 * q^51 + 3 * q^54 + 3 * q^55 - 6 * q^56 - 6 * q^57 + 24 * q^58 - 12 * q^59 + 3 * q^60 - 18 * q^61 + 3 * q^63 + 6 * q^64 - 3 * q^66 - 12 * q^67 - 6 * q^68 - 12 * q^69 + 3 * q^70 - 6 * q^71 - 3 * q^72 + 6 * q^73 + 3 * q^74 + 24 * q^75 - 3 * q^76 + 6 * q^77 - 3 * q^80 - 3 * q^81 + 9 * q^82 + 12 * q^83 + 6 * q^84 + 3 * q^85 - 6 * q^86 - 24 * q^87 - 6 * q^88 + 9 * q^89 - 3 * q^90 - 6 * q^92 + 6 * q^95 - 6 * q^96 - 12 * q^97 - 3 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−1.22263			−0.368637			−0.184319	−	0.982867i	$-0.559008\pi$
$11$	−1.22263			−0.368637			−0.184319	+	0.982867i	$0.559008\pi$
$12$	−1.00000			−0.288675
$13$	0.111315	−	0.192804i	0.0308734	−	0.0534742i	−0.850176	−	0.526499i	$-0.823504\pi$
$13$	0.111315	−	0.192804i	0.0308734	−	0.0534742i	0.881049	+	0.473025i	$0.156838\pi$
$14$	0.500000	+	0.866025i	0.133631	+	0.231455i
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.93195	−	6.81034i	−0.953638	−	1.65175i	−0.737454	−	0.675397i	$-0.763972\pi$
$17$	−3.93195	−	6.81034i	−0.953638	−	1.65175i	−0.216184	−	0.976353i	$-0.569361\pi$
$18$	1.00000			0.235702
$19$	4.04327	−	1.62849i	0.927589	−	0.373602i
$19$	4.04327	−	1.62849i	0.927589	−	0.373602i
$20$	1.00000			0.223607
$21$	−0.500000	−	0.866025i	−0.109109	−	0.188982i
$22$	0.611315	+	1.05883i	0.130333	+	0.225743i
$23$	3.43195	−	5.94431i	0.715611	−	1.23948i	−0.247112	−	0.968987i	$-0.579482\pi$
$23$	3.43195	−	5.94431i	0.715611	−	1.23948i	0.962723	−	0.270488i	$-0.0871851\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	−0.222631			−0.0436615
$27$	−1.00000			−0.192450
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	−2.00000	+	3.46410i	−0.371391	+	0.643268i	−0.989780	−	0.142605i	$-0.954452\pi$
$29$	−2.00000	+	3.46410i	−0.371391	+	0.643268i	0.618389	+	0.785872i	$0.287786\pi$
$30$	−1.00000			−0.182574
$31$	−0.445262			−0.0799714			−0.0399857	−	0.999200i	$-0.512731\pi$
$31$	−0.445262			−0.0799714			−0.0399857	+	0.999200i	$0.512731\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.611315	−	1.05883i	−0.106416	−	0.184319i
$34$	−3.93195	+	6.81034i	−0.674324	+	1.16796i
$35$	0.500000	+	0.866025i	0.0845154	+	0.146385i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−1.22263			−0.200999			−0.100500	−	0.994937i	$-0.532044\pi$
$37$	−1.22263			−0.200999			−0.100500	+	0.994937i	$0.532044\pi$
$38$	−3.43195	−	2.68732i	−0.556736	−	0.435942i
$39$	0.222631			0.0356495
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	1.38868	+	2.40527i	0.216876	+	0.375640i	0.953851	−	0.300279i	$-0.0970799\pi$
$41$	1.38868	+	2.40527i	0.216876	+	0.375640i	−0.736975	+	0.675920i	$0.763747\pi$
$42$	−0.500000	+	0.866025i	−0.0771517	+	0.133631i
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	0.779647	−	0.626219i	$-0.215399\pi$
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	−0.932145	+	0.362084i	$0.882065\pi$
$44$	0.611315	−	1.05883i	0.0921593	−	0.159625i
$45$	1.00000			0.149071
$46$	−6.86390			−1.01203
$47$	4.54327	−	7.86917i	0.662704	−	1.14784i	−0.317199	−	0.948359i	$-0.602742\pi$
$47$	4.54327	−	7.86917i	0.662704	−	1.14784i	0.979902	−	0.199477i	$-0.0639244\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	1.00000			0.142857
$50$	−4.00000			−0.565685
$51$	3.93195	−	6.81034i	0.550583	−	0.953638i
$52$	0.111315	+	0.192804i	0.0154367	+	0.0267371i
$53$	4.32064	−	7.48356i	0.593485	−	1.02795i	−0.400274	−	0.916396i	$-0.631085\pi$
$53$	4.32064	−	7.48356i	0.593485	−	1.02795i	0.993759	−	0.111551i	$-0.0355817\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	0.611315	+	1.05883i	0.0824298	+	0.142773i
$56$	−1.00000			−0.133631
$57$	3.43195	+	2.68732i	0.454573	+	0.355945i
$58$	4.00000			0.525226
$59$	−6.65458	−	11.5261i	−0.866353	−	1.50057i	−0.865698	−	0.500567i	$-0.833125\pi$
$59$	−6.65458	−	11.5261i	−0.866353	−	1.50057i	−0.000655145	−	1.00000i	$-0.500209\pi$
$60$	0.500000	+	0.866025i	0.0645497	+	0.111803i
$61$	−2.88868	+	5.00335i	−0.369858	+	0.640613i	−0.989543	−	0.144238i	$-0.953927\pi$
$61$	−2.88868	+	5.00335i	−0.369858	+	0.640613i	0.619685	+	0.784851i	$0.287260\pi$
$62$	0.222631	+	0.385608i	0.0282742	+	0.0489723i
$63$	0.500000	−	0.866025i	0.0629941	−	0.109109i
$64$	1.00000			0.125000
$65$	−0.222631			−0.0276140
$66$	−0.611315	+	1.05883i	−0.0752477	+	0.130333i
$67$	−6.32064	+	10.9477i	−0.772189	+	1.33747i	0.164173	+	0.986432i	$0.447505\pi$
$67$	−6.32064	+	10.9477i	−0.772189	+	1.33747i	−0.936361	+	0.351038i	$0.885829\pi$
$68$	7.86390			0.953638
$69$	6.86390			0.826317
$70$	0.500000	−	0.866025i	0.0597614	−	0.103510i
$71$	−5.65458	−	9.79402i	−0.671075	−	1.16234i	−0.977599	−	0.210474i	$-0.932499\pi$
$71$	−5.65458	−	9.79402i	−0.671075	−	1.16234i	0.306524	−	0.951863i	$-0.400834\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−3.32064	−	5.75151i	−0.388651	−	0.673163i	0.603617	−	0.797274i	$-0.293725\pi$
$73$	−3.32064	−	5.75151i	−0.388651	−	0.673163i	−0.992268	+	0.124111i	$0.960392\pi$
$74$	0.611315	+	1.05883i	0.0710640	+	0.123086i
$75$	4.00000			0.461880
$76$	−0.611315	+	4.31582i	−0.0701227	+	0.495058i
$77$	1.22263			0.139332
$78$	−0.111315	−	0.192804i	−0.0126040	−	0.0218308i
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.38868	−	2.40527i	0.153355	−	0.265618i
$83$	10.8639			1.19247			0.596234	−	0.802811i	$-0.296663\pi$
$83$	10.8639			1.19247			0.596234	+	0.802811i	$0.296663\pi$
$84$	1.00000			0.109109
$85$	−3.93195	+	6.81034i	−0.426480	+	0.738685i
$86$	−1.00000	+	1.73205i	−0.107833	+	0.186772i
$87$	−4.00000			−0.428845
$88$	−1.22263			−0.130333
$89$	−2.93195	+	5.07829i	−0.310786	+	0.538297i	−0.978533	−	0.206091i	$-0.933926\pi$
$89$	−2.93195	+	5.07829i	−0.310786	+	0.538297i	0.667747	+	0.744389i	$0.267259\pi$
$90$	−0.500000	−	0.866025i	−0.0527046	−	0.0912871i
$91$	−0.111315	+	0.192804i	−0.0116690	+	0.0202114i
$92$	3.43195	+	5.94431i	0.357806	+	0.619738i
$93$	−0.222631	−	0.385608i	−0.0230858	−	0.0399857i
$94$	−9.08653			−0.937204
$95$	−3.43195	−	2.68732i	−0.352111	−	0.275714i
$96$	−1.00000			−0.102062
$97$	−1.77737	−	3.07849i	−0.180464	−	0.312574i	0.761574	−	0.648078i	$-0.224427\pi$
$97$	−1.77737	−	3.07849i	−0.180464	−	0.312574i	−0.942039	+	0.335504i	$0.891093\pi$
$98$	−0.500000	−	0.866025i	−0.0505076	−	0.0874818i
$99$	0.611315	−	1.05883i	0.0614395	−	0.106416i
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	−0.833946	+	1.44444i	−0.0829808	+	0.143727i	−0.904529	−	0.426412i	$-0.859777\pi$
$101$	−0.833946	+	1.44444i	−0.0829808	+	0.143727i	0.821548	+	0.570139i	$0.193111\pi$
$102$	−7.86390			−0.778642
$103$	8.30916			0.818726			0.409363	−	0.912372i	$-0.365751\pi$
$103$	8.30916			0.818726			0.409363	+	0.912372i	$0.365751\pi$
$104$	0.111315	−	0.192804i	0.0109154	−	0.0189060i
$105$	−0.500000	+	0.866025i	−0.0487950	+	0.0845154i
$106$	−8.64127			−0.839314
$107$	−9.08653			−0.878428			−0.439214	−	0.898382i	$-0.644743\pi$
$107$	−9.08653			−0.878428			−0.439214	+	0.898382i	$0.644743\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	4.15458	+	7.19595i	0.397937	+	0.689247i	0.993471	−	0.114083i	$-0.0363930\pi$
$109$	4.15458	+	7.19595i	0.397937	+	0.689247i	−0.595534	+	0.803330i	$0.703060\pi$
$110$	0.611315	−	1.05883i	0.0582866	−	0.100955i
$111$	−0.611315	−	1.05883i	−0.0580235	−	0.100500i
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$	10.2226			0.961664			0.480832	−	0.876813i	$-0.340335\pi$
$113$	10.2226			0.961664			0.480832	+	0.876813i	$0.340335\pi$
$114$	0.611315	−	4.31582i	0.0572549	−	0.404213i
$115$	−6.86390			−0.640062
$116$	−2.00000	−	3.46410i	−0.185695	−	0.321634i
$117$	0.111315	+	0.192804i	0.0102911	+	0.0178247i
$118$	−6.65458	+	11.5261i	−0.612604	+	1.06106i
$119$	3.93195	+	6.81034i	0.360441	+	0.624303i
$120$	0.500000	−	0.866025i	0.0456435	−	0.0790569i
$121$	−9.50517			−0.864107
$122$	5.77737			0.523058
$123$	−1.38868	+	2.40527i	−0.125213	+	0.216876i
$124$	0.222631	−	0.385608i	0.0199928	−	0.0346286i
$125$	−9.00000			−0.804984
$126$	−1.00000			−0.0890871
$127$	−4.65458	+	8.06197i	−0.413027	+	0.715384i	−0.995219	−	0.0976671i	$-0.968862\pi$
$127$	−4.65458	+	8.06197i	−0.413027	+	0.715384i	0.582192	+	0.813052i	$0.302195\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	1.00000	−	1.73205i	0.0880451	−	0.152499i
$130$	0.111315	+	0.192804i	0.00976301	+	0.0169100i
$131$	5.43195	+	9.40842i	0.474592	+	0.822017i	0.999577	−	0.0290945i	$-0.00926237\pi$
$131$	5.43195	+	9.40842i	0.474592	+	0.822017i	−0.524985	+	0.851112i	$0.675929\pi$
$132$	1.22263			0.106416
$133$	−4.04327	+	1.62849i	−0.350596	+	0.141208i
$134$	12.6413			1.09204
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	−3.93195	−	6.81034i	−0.337162	−	0.583982i
$137$	−10.9752	+	19.0096i	−0.937676	+	1.62410i	−0.167885	+	0.985807i	$0.553694\pi$
$137$	−10.9752	+	19.0096i	−0.937676	+	1.62410i	−0.769791	+	0.638296i	$0.779640\pi$
$138$	−3.43195	−	5.94431i	−0.292147	−	0.506014i
$139$	5.38868	−	9.33348i	0.457062	−	0.791655i	−0.541742	−	0.840545i	$-0.682235\pi$
$139$	5.38868	−	9.33348i	0.457062	−	0.791655i	0.998804	+	0.0488898i	$0.0155683\pi$
$140$	−1.00000			−0.0845154
$141$	9.08653			0.765224
$142$	−5.65458	+	9.79402i	−0.474522	+	0.821896i
$143$	−0.136098	+	0.235728i	−0.0113811	+	0.0197126i
$144$	1.00000			0.0833333
$145$	4.00000			0.332182
$146$	−3.32064	+	5.75151i	−0.274818	+	0.475998i
$147$	0.500000	+	0.866025i	0.0412393	+	0.0714286i
$148$	0.611315	−	1.05883i	0.0502498	−	0.0870352i
$149$	−2.77737	−	4.81054i	−0.227531	−	0.394095i	0.729545	−	0.683933i	$-0.239732\pi$
$149$	−2.77737	−	4.81054i	−0.227531	−	0.394095i	−0.957076	+	0.289838i	$0.906399\pi$
$150$	−2.00000	−	3.46410i	−0.163299	−	0.282843i
$151$	19.3092			1.57136			0.785679	−	0.618635i	$-0.212314\pi$
$151$	19.3092			1.57136			0.785679	+	0.618635i	$0.212314\pi$
$152$	4.04327	−	1.62849i	0.327952	−	0.132088i
$153$	7.86390			0.635759
$154$	−0.611315	−	1.05883i	−0.0492612	−	0.0853229i
$155$	0.222631	+	0.385608i	0.0178821	+	0.0309728i
$156$	−0.111315	+	0.192804i	−0.00891237	+	0.0154367i
$157$	1.66605	+	2.88569i	0.132966	+	0.230303i	0.924818	−	0.380409i	$-0.124217\pi$
$157$	1.66605	+	2.88569i	0.132966	+	0.230303i	−0.791853	+	0.610712i	$0.790883\pi$
$158$		0			0
$159$	8.64127			0.685297
$160$	1.00000			0.0790569
$161$	−3.43195	+	5.94431i	−0.270476	+	0.468478i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	−18.6413			−1.46010			−0.730049	−	0.683395i	$-0.760503\pi$
$163$	−18.6413			−1.46010			−0.730049	+	0.683395i	$0.760503\pi$
$164$	−2.77737			−0.216876
$165$	−0.611315	+	1.05883i	−0.0475908	+	0.0824298i
$166$	−5.43195	−	9.40842i	−0.421601	−	0.730235i
$167$	5.76590	−	9.98683i	0.446179	−	0.772804i	−0.551955	−	0.833874i	$-0.686118\pi$
$167$	5.76590	−	9.98683i	0.446179	−	0.772804i	0.998133	+	0.0610700i	$0.0194513\pi$
$168$	−0.500000	−	0.866025i	−0.0385758	−	0.0668153i
$169$	6.47522	+	11.2154i	0.498094	+	0.862724i
$170$	7.86390			0.603134
$171$	−0.611315	+	4.31582i	−0.0467485	+	0.330039i
$172$	2.00000			0.152499
$173$	0.975218	+	1.68913i	0.0741444	+	0.128422i	0.900714	−	0.434413i	$-0.143044\pi$
$173$	0.975218	+	1.68913i	0.0741444	+	0.128422i	−0.826569	+	0.562835i	$0.809711\pi$
$174$	2.00000	+	3.46410i	0.151620	+	0.262613i
$175$	−2.00000	+	3.46410i	−0.151186	+	0.261861i
$176$	0.611315	+	1.05883i	0.0460796	+	0.0798123i
$177$	6.65458	−	11.5261i	0.500189	−	0.866353i
$178$	5.86390			0.439518
$179$	−6.30916			−0.471569			−0.235785	−	0.971805i	$-0.575766\pi$
$179$	−6.30916			−0.471569			−0.235785	+	0.971805i	$0.575766\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	−3.11132	+	5.38896i	−0.231262	+	0.400558i	−0.958180	−	0.286167i	$-0.907619\pi$
$181$	−3.11132	+	5.38896i	−0.231262	+	0.400558i	0.726918	+	0.686725i	$0.240952\pi$
$182$	0.222631			0.0165025
$183$	−5.77737			−0.427075
$184$	3.43195	−	5.94431i	0.253007	−	0.438221i
$185$	0.611315	+	1.05883i	0.0449448	+	0.0778467i
$186$	−0.222631	+	0.385608i	−0.0163241	+	0.0282742i
$187$	4.80733	+	8.32653i	0.351546	+	0.608896i
$188$	4.54327	+	7.86917i	0.331352	+	0.573918i
$189$	1.00000			0.0727393
$190$	−0.611315	+	4.31582i	−0.0443495	+	0.313102i
$191$	−2.86390			−0.207225			−0.103612	−	0.994618i	$-0.533040\pi$
$191$	−2.86390			−0.207225			−0.103612	+	0.994618i	$0.533040\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	3.36390	+	5.82645i	0.242139	+	0.419397i	0.961323	−	0.275422i	$-0.0888177\pi$
$193$	3.36390	+	5.82645i	0.242139	+	0.419397i	−0.719184	+	0.694819i	$0.755484\pi$
$194$	−1.77737	+	3.07849i	−0.127608	+	0.221023i
$195$	−0.111315	−	0.192804i	−0.00797147	−	0.0138070i
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	17.5318			1.24909			0.624544	−	0.780989i	$-0.285285\pi$
$197$	17.5318			1.24909			0.624544	+	0.780989i	$0.285285\pi$
$198$	−1.22263			−0.0868886
$199$	6.54327	−	11.3333i	0.463840	−	0.803394i	−0.535308	−	0.844657i	$-0.679805\pi$
$199$	6.54327	−	11.3333i	0.463840	−	0.803394i	0.999148	+	0.0412624i	$0.0131380\pi$
$200$	2.00000	−	3.46410i	0.141421	−	0.244949i
$201$	−12.6413			−0.891647
$202$	1.66789			0.117353
$203$	2.00000	−	3.46410i	0.140372	−	0.243132i
$204$	3.93195	+	6.81034i	0.275292	+	0.476819i
$205$	1.38868	−	2.40527i	0.0969899	−	0.167991i
$206$	−4.15458	−	7.19595i	−0.289463	−	0.501365i
$207$	3.43195	+	5.94431i	0.238537	+	0.413158i
$208$	−0.222631			−0.0154367
$209$	−4.94342	+	1.99105i	−0.341944	+	0.137724i
$210$	1.00000			0.0690066
$211$	6.76590	+	11.7189i	0.465784	+	0.806761i	0.999237	−	0.0390689i	$-0.0124392\pi$
$211$	6.76590	+	11.7189i	0.465784	+	0.806761i	−0.533453	+	0.845830i	$0.679106\pi$
$212$	4.32064	+	7.48356i	0.296742	+	0.513973i
$213$	5.65458	−	9.79402i	0.387446	−	0.671075i
$214$	4.54327	+	7.86917i	0.310571	+	0.537925i
$215$	−1.00000	+	1.73205i	−0.0681994	+	0.118125i
$216$	−1.00000			−0.0680414
$217$	0.445262			0.0302263
$218$	4.15458	−	7.19595i	0.281384	−	0.487371i
$219$	3.32064	−	5.75151i	0.224388	−	0.388651i
$220$	−1.22263			−0.0824298
$221$	−1.75075			−0.117768
$222$	−0.611315	+	1.05883i	−0.0410288	+	0.0710640i
$223$	10.7093	+	18.5491i	0.717149	+	1.24214i	0.962125	+	0.272609i	$0.0878867\pi$
$223$	10.7093	+	18.5491i	0.717149	+	1.24214i	−0.244976	+	0.969529i	$0.578780\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$	2.00000	+	3.46410i	0.133333	+	0.230940i
$226$	−5.11132	−	8.85306i	−0.340000	−	0.588897i
$227$	26.8639			1.78302			0.891510	−	0.453001i	$-0.149647\pi$
$227$	26.8639			1.78302			0.891510	+	0.453001i	$0.149647\pi$
$228$	−4.04327	+	1.62849i	−0.267772	+	0.107850i
$229$	15.5052			1.02461			0.512305	−	0.858803i	$-0.328792\pi$
$229$	15.5052			1.02461			0.512305	+	0.858803i	$0.328792\pi$
$230$	3.43195	+	5.94431i	0.226296	+	0.391956i
$231$	0.611315	+	1.05883i	0.0402216	+	0.0696659i
$232$	−2.00000	+	3.46410i	−0.131306	+	0.227429i
$233$	4.66605	+	8.08184i	0.305683	+	0.529459i	0.977413	−	0.211337i	$-0.0677818\pi$
$233$	4.66605	+	8.08184i	0.305683	+	0.529459i	−0.671730	+	0.740796i	$0.734448\pi$
$234$	0.111315	−	0.192804i	0.00727692	−	0.0126040i
$235$	−9.08653			−0.592740
$236$	13.3092			0.866353
$237$		0			0
$238$	3.93195	−	6.81034i	0.254871	−	0.441449i
$239$	−6.35873			−0.411312			−0.205656	−	0.978624i	$-0.565933\pi$
$239$	−6.35873			−0.411312			−0.205656	+	0.978624i	$0.565933\pi$
$240$	−1.00000			−0.0645497
$241$	4.86390	−	8.42453i	0.313311	−	0.542671i	−0.665766	−	0.746161i	$-0.731895\pi$
$241$	4.86390	−	8.42453i	0.313311	−	0.542671i	0.979077	+	0.203489i	$0.0652283\pi$
$242$	4.75259	+	8.23172i	0.305508	+	0.529155i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−2.88868	−	5.00335i	−0.184929	−	0.320307i
$245$	−0.500000	−	0.866025i	−0.0319438	−	0.0553283i
$246$	2.77737			0.177079
$247$	0.136098	−	0.960835i	0.00865969	−	0.0611364i
$248$	−0.445262			−0.0282742
$249$	5.43195	+	9.40842i	0.344236	+	0.596234i
$250$	4.50000	+	7.79423i	0.284605	+	0.492950i
$251$	4.43195	−	7.67636i	0.279742	−	0.484528i	−0.691578	−	0.722301i	$-0.743084\pi$
$251$	4.43195	−	7.67636i	0.279742	−	0.484528i	0.971321	+	0.237774i	$0.0764176\pi$
$252$	0.500000	+	0.866025i	0.0314970	+	0.0545545i
$253$	−4.19601	+	7.26770i	−0.263801	+	0.456916i
$254$	9.30916			0.584109
$255$	−7.86390			−0.492457
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−13.6978	+	23.7254i	−0.854448	+	1.47995i	0.0227076	+	0.999742i	$0.492771\pi$
$257$	−13.6978	+	23.7254i	−0.854448	+	1.47995i	−0.877156	+	0.480206i	$0.840562\pi$
$258$	−2.00000			−0.124515
$259$	1.22263			0.0759706
$260$	0.111315	−	0.192804i	0.00690349	−	0.0119572i
$261$	−2.00000	−	3.46410i	−0.123797	−	0.214423i
$262$	5.43195	−	9.40842i	0.335587	−	0.581254i
$263$	−5.82064	−	10.0816i	−0.358916	−	0.621660i	0.628864	−	0.777515i	$-0.283520\pi$
$263$	−5.82064	−	10.0816i	−0.358916	−	0.621660i	−0.987780	+	0.155855i	$0.950187\pi$
$264$	−0.611315	−	1.05883i	−0.0376239	−	0.0651664i
$265$	−8.64127			−0.530829
$266$	3.43195	+	2.68732i	0.210426	+	0.164770i
$267$	−5.86390			−0.358865
$268$	−6.32064	−	10.9477i	−0.386094	−	0.668735i
$269$	−6.69785	−	11.6010i	−0.408375	−	0.707326i	0.586333	−	0.810070i	$-0.300571\pi$
$269$	−6.69785	−	11.6010i	−0.408375	−	0.707326i	−0.994708	+	0.102744i	$0.967238\pi$
$270$	0.500000	−	0.866025i	0.0304290	−	0.0527046i
$271$	−14.5732	−	25.2416i	−0.885260	−	1.53332i	−0.845415	−	0.534110i	$-0.820647\pi$
$271$	−14.5732	−	25.2416i	−0.885260	−	1.53332i	−0.0398451	−	0.999206i	$-0.512686\pi$
$272$	−3.93195	+	6.81034i	−0.238410	+	0.412937i
$273$	−0.222631			−0.0134742
$274$	21.9504			1.32607
$275$	−2.44526	+	4.23532i	−0.147455	+	0.255399i
$276$	−3.43195	+	5.94431i	−0.206579	+	0.357806i
$277$	14.0370			0.843400			0.421700	−	0.906735i	$-0.361434\pi$
$277$	14.0370			0.843400			0.421700	+	0.906735i	$0.361434\pi$
$278$	−10.7774			−0.646384
$279$	0.222631	−	0.385608i	0.0133286	−	0.0230858i
$280$	0.500000	+	0.866025i	0.0298807	+	0.0517549i
$281$	−15.9504	+	27.6270i	−0.951523	+	1.64809i	−0.209392	+	0.977832i	$0.567149\pi$
$281$	−15.9504	+	27.6270i	−0.951523	+	1.64809i	−0.742131	+	0.670255i	$0.766185\pi$
$282$	−4.54327	−	7.86917i	−0.270548	−	0.468602i
$283$	−13.8206	−	23.9380i	−0.821552	−	1.42297i	−0.904527	−	0.426417i	$-0.859776\pi$
$283$	−13.8206	−	23.9380i	−0.821552	−	1.42297i	0.0829750	−	0.996552i	$-0.473558\pi$
$284$	11.3092			0.671075
$285$	0.611315	−	4.31582i	0.0362112	−	0.255647i
$286$	0.272195			0.0160953
$287$	−1.38868	−	2.40527i	−0.0819715	−	0.141979i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	−22.4205	+	38.8334i	−1.31885	+	2.28432i
$290$	−2.00000	−	3.46410i	−0.117444	−	0.203419i
$291$	1.77737	−	3.07849i	0.104191	−	0.180464i
$292$	6.64127			0.388651
$293$	19.8373			1.15891			0.579453	−	0.815006i	$-0.303266\pi$
$293$	19.8373			1.15891			0.579453	+	0.815006i	$0.303266\pi$
$294$	0.500000	−	0.866025i	0.0291606	−	0.0505076i
$295$	−6.65458	+	11.5261i	−0.387445	+	0.671074i
$296$	−1.22263			−0.0710640
$297$	1.22263			0.0709442
$298$	−2.77737	+	4.81054i	−0.160889	+	0.278667i
$299$	−0.764058	−	1.32339i	−0.0441866	−	0.0765335i
$300$	−2.00000	+	3.46410i	−0.115470	+	0.200000i
$301$	1.00000	+	1.73205i	0.0576390	+	0.0998337i
$302$	−9.65458	−	16.7222i	−0.555559	−	0.962256i
$303$	−1.66789			−0.0958179
$304$	−3.43195	−	2.68732i	−0.196836	−	0.154129i
$305$	5.77737			0.330811
$306$	−3.93195	−	6.81034i	−0.224775	−	0.389321i
$307$	−3.87721	−	6.71553i	−0.221284	−	0.383276i	0.733914	−	0.679242i	$-0.237692\pi$
$307$	−3.87721	−	6.71553i	−0.221284	−	0.383276i	−0.955198	+	0.295967i	$0.904358\pi$
$308$	−0.611315	+	1.05883i	−0.0348329	+	0.0603324i
$309$	4.15458	+	7.19595i	0.236346	+	0.409363i
$310$	0.222631	−	0.385608i	0.0126446	−	0.0219011i
$311$	−23.5318			−1.33437			−0.667183	−	0.744894i	$-0.732500\pi$
$311$	−23.5318			−1.33437			−0.667183	+	0.744894i	$0.732500\pi$
$312$	0.222631			0.0126040
$313$	12.6413	−	21.8953i	0.714527	−	1.23760i	−0.248615	−	0.968602i	$-0.579975\pi$
$313$	12.6413	−	21.8953i	0.714527	−	1.23760i	0.963142	−	0.268994i	$-0.0866913\pi$
$314$	1.66605	−	2.88569i	0.0940208	−	0.162849i
$315$	−1.00000			−0.0563436
$316$		0			0
$317$	0.222631	−	0.385608i	0.0125042	−	0.0216579i	−0.859706	−	0.510790i	$-0.829353\pi$
$317$	0.222631	−	0.385608i	0.0125042	−	0.0216579i	0.872210	+	0.489132i	$0.162686\pi$
$318$	−4.32064	−	7.48356i	−0.242289	−	0.419657i
$319$	2.44526	−	4.23532i	0.136908	−	0.237132i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−4.54327	−	7.86917i	−0.253580	−	0.439214i
$322$	6.86390			0.382510
$323$	−26.9885	−	21.1329i	−1.50168	−	1.17586i
$324$	1.00000			0.0555556
$325$	−0.445262	−	0.771216i	−0.0246987	−	0.0427794i
$326$	9.32064	+	16.1438i	0.516222	+	0.894123i
$327$	−4.15458	+	7.19595i	−0.229749	+	0.397937i
$328$	1.38868	+	2.40527i	0.0766773	+	0.132809i
$329$	−4.54327	+	7.86917i	−0.250478	+	0.433841i
$330$	1.22263			0.0673036
$331$	−18.8143			−1.03413			−0.517065	−	0.855946i	$-0.672975\pi$
$331$	−18.8143			−1.03413			−0.517065	+	0.855946i	$0.672975\pi$
$332$	−5.43195	+	9.40842i	−0.298117	+	0.516354i
$333$	0.611315	−	1.05883i	0.0334999	−	0.0580235i
$334$	−11.5318			−0.630992
$335$	12.6413			0.690666
$336$	−0.500000	+	0.866025i	−0.0272772	+	0.0472456i
$337$	0.111315	+	0.192804i	0.00606374	+	0.0105027i	0.869041	−	0.494739i	$-0.164737\pi$
$337$	0.111315	+	0.192804i	0.00606374	+	0.0105027i	−0.862978	+	0.505242i	$0.831403\pi$
$338$	6.47522	−	11.2154i	0.352205	−	0.610038i
$339$	5.11132	+	8.85306i	0.277609	+	0.480832i
$340$	−3.93195	−	6.81034i	−0.213240	−	0.369342i
$341$	0.544391			0.0294804
$342$	4.04327	−	1.62849i	0.218635	−	0.0880589i
$343$	−1.00000			−0.0539949
$344$	−1.00000	−	1.73205i	−0.0539164	−	0.0933859i
$345$	−3.43195	−	5.94431i	−0.184770	−	0.320031i
$346$	0.975218	−	1.68913i	0.0524280	−	0.0908080i
$347$	−4.54327	−	7.86917i	−0.243895	−	0.422439i	0.717925	−	0.696120i	$-0.245092\pi$
$347$	−4.54327	−	7.86917i	−0.243895	−	0.422439i	−0.961820	+	0.273681i	$0.911759\pi$
$348$	2.00000	−	3.46410i	0.107211	−	0.185695i
$349$	34.6183			1.85308			0.926538	−	0.376200i	$-0.122770\pi$
$349$	34.6183			1.85308			0.926538	+	0.376200i	$0.122770\pi$
$350$	4.00000			0.213809
$351$	−0.111315	+	0.192804i	−0.00594158	+	0.0102911i
$352$	0.611315	−	1.05883i	0.0325832	−	0.0564358i
$353$	−17.8639			−0.950800			−0.475400	−	0.879770i	$-0.657697\pi$
$353$	−17.8639			−0.950800			−0.475400	+	0.879770i	$0.657697\pi$
$354$	−13.3092			−0.707374
$355$	−5.65458	+	9.79402i	−0.300114	+	0.519813i
$356$	−2.93195	−	5.07829i	−0.155393	−	0.269149i
$357$	−3.93195	+	6.81034i	−0.208101	+	0.360441i
$358$	3.15458	+	5.46390i	0.166725	+	0.288776i
$359$	−5.08653	−	8.81013i	−0.268457	−	0.464981i	0.700007	−	0.714136i	$-0.253180\pi$
$359$	−5.08653	−	8.81013i	−0.268457	−	0.464981i	−0.968464	+	0.249155i	$0.919847\pi$
$360$	1.00000			0.0527046
$361$	13.6960	−	13.1689i	0.720843	−	0.693099i
$362$	6.22263			0.327054
$363$	−4.75259	−	8.23172i	−0.249446	−	0.432053i
$364$	−0.111315	−	0.192804i	−0.00583452	−	0.0101057i
$365$	−3.32064	+	5.75151i	−0.173810	+	0.301048i
$366$	2.88868	+	5.00335i	0.150994	+	0.261529i
$367$	9.25259	−	16.0260i	0.482981	−	0.836548i	−0.516828	−	0.856089i	$-0.672887\pi$
$367$	9.25259	−	16.0260i	0.482981	−	0.836548i	0.999809	+	0.0195415i	$0.00622064\pi$
$368$	−6.86390			−0.357806
$369$	−2.77737			−0.144584
$370$	0.611315	−	1.05883i	0.0317808	−	0.0550459i
$371$	−4.32064	+	7.48356i	−0.224316	+	0.388527i
$372$	0.445262			0.0230858
$373$	24.7774			1.28292			0.641462	−	0.767155i	$-0.278328\pi$
$373$	24.7774			1.28292			0.641462	+	0.767155i	$0.278328\pi$
$374$	4.80733	−	8.32653i	0.248581	−	0.430555i
$375$	−4.50000	−	7.79423i	−0.232379	−	0.402492i
$376$	4.54327	−	7.86917i	0.234301	−	0.405821i
$377$	0.445262	+	0.771216i	0.0229322	+	0.0397196i
$378$	−0.500000	−	0.866025i	−0.0257172	−	0.0445435i
$379$	−1.72780			−0.0887514			−0.0443757	−	0.999015i	$-0.514130\pi$
$379$	−1.72780			−0.0887514			−0.0443757	+	0.999015i	$0.514130\pi$
$380$	4.04327	−	1.62849i	0.207415	−	0.0835400i
$381$	−9.30916			−0.476923
$382$	1.43195	+	2.48021i	0.0732650	+	0.126899i
$383$	3.23410	+	5.60163i	0.165255	+	0.286230i	0.936746	−	0.350010i	$-0.113822\pi$
$383$	3.23410	+	5.60163i	0.165255	+	0.286230i	−0.771491	+	0.636240i	$0.780489\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	−0.611315	−	1.05883i	−0.0311555	−	0.0539629i
$386$	3.36390	−	5.82645i	0.171218	−	0.296558i
$387$	2.00000			0.101666
$388$	3.55474			0.180464
$389$	−14.9619	+	25.9148i	−0.758599	+	1.31393i	0.184966	+	0.982745i	$0.440782\pi$
$389$	−14.9619	+	25.9148i	−0.758599	+	1.31393i	−0.943565	+	0.331187i	$0.892551\pi$
$390$	−0.111315	+	0.192804i	−0.00563668	+	0.00976301i
$391$	−53.9771			−2.72974
$392$	1.00000			0.0505076
$393$	−5.43195	+	9.40842i	−0.274006	+	0.474592i
$394$	−8.76590	−	15.1830i	−0.441620	−	0.764907i
$395$		0			0
$396$	0.611315	+	1.05883i	0.0307198	+	0.0532082i
$397$	−12.0865	−	20.9345i	−0.606606	−	1.05067i	−0.991796	−	0.127835i	$-0.959197\pi$
$397$	−12.0865	−	20.9345i	−0.606606	−	1.05067i	0.385190	−	0.922837i	$-0.374136\pi$
$398$	−13.0865			−0.655969
$399$	−3.43195	−	2.68732i	−0.171812	−	0.134534i
$400$	−4.00000			−0.200000
$401$	−17.3073	−	29.9772i	−0.864287	−	1.49699i	−0.867754	−	0.496994i	$-0.834437\pi$
$401$	−17.3073	−	29.9772i	−0.864287	−	1.49699i	0.00346726	−	0.999994i	$-0.498896\pi$
$402$	6.32064	+	10.9477i	0.315245	+	0.546020i
$403$	−0.0495645	+	0.0858483i	−0.00246898	+	0.00427641i
$404$	−0.833946	−	1.44444i	−0.0414904	−	0.0718635i
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$	−4.00000			−0.198517
$407$	1.49483			0.0740958
$408$	3.93195	−	6.81034i	0.194661	−	0.337162i
$409$	3.40717	−	5.90139i	0.168474	−	0.291805i	−0.769410	−	0.638756i	$-0.779450\pi$
$409$	3.40717	−	5.90139i	0.168474	−	0.291805i	0.937883	+	0.346951i	$0.112783\pi$
$410$	−2.77737			−0.137164
$411$	−21.9504			−1.08274
$412$	−4.15458	+	7.19595i	−0.204682	+	0.354519i
$413$	6.65458	+	11.5261i	0.327451	+	0.567161i
$414$	3.43195	−	5.94431i	0.168671	−	0.292147i
$415$	−5.43195	−	9.40842i	−0.266644	−	0.461841i
$416$	0.111315	+	0.192804i	0.00545769	+	0.00945300i
$417$	10.7774			0.527770
$418$	4.19601	+	3.28561i	0.205234	+	0.160704i
$419$	−6.44526			−0.314872			−0.157436	−	0.987529i	$-0.550323\pi$
$419$	−6.44526			−0.314872			−0.157436	+	0.987529i	$0.550323\pi$
$420$	−0.500000	−	0.866025i	−0.0243975	−	0.0422577i
$421$	−2.62279	−	4.54280i	−0.127827	−	0.221403i	0.795008	−	0.606600i	$-0.207467\pi$
$421$	−2.62279	−	4.54280i	−0.127827	−	0.221403i	−0.922834	+	0.385197i	$0.874134\pi$
$422$	6.76590	−	11.7189i	0.329359	−	0.570466i
$423$	4.54327	+	7.86917i	0.220901	+	0.382612i
$424$	4.32064	−	7.48356i	0.209829	−	0.363434i
$425$	−31.4556			−1.52582
$426$	−11.3092			−0.547931
$427$	2.88868	−	5.00335i	0.139793	−	0.242129i
$428$	4.54327	−	7.86917i	0.219607	−	0.380371i
$429$	−0.272195			−0.0131417
$430$	2.00000			0.0964486
$431$	10.0300	−	17.3724i	0.483126	−	0.836799i	−0.516686	−	0.856175i	$-0.672835\pi$
$431$	10.0300	−	17.3724i	0.483126	−	0.836799i	0.999812	+	0.0193761i	$0.00616798\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−2.76590	+	4.79068i	−0.132921	+	0.230225i	−0.924801	−	0.380451i	$-0.875769\pi$
$433$	−2.76590	+	4.79068i	−0.132921	+	0.230225i	0.791881	+	0.610676i	$0.209102\pi$
$434$	−0.222631	−	0.385608i	−0.0106866	−	0.0185098i
$435$	2.00000	+	3.46410i	0.0958927	+	0.166091i
$436$	−8.30916			−0.397937
$437$	4.19601	−	29.6234i	0.200722	−	1.41708i
$438$	−6.64127			−0.317332
$439$	−15.4637	−	26.7840i	−0.738044	−	1.27833i	−0.953375	−	0.301789i	$-0.902416\pi$
$439$	−15.4637	−	26.7840i	−0.738044	−	1.27833i	0.215330	−	0.976541i	$-0.430917\pi$
$440$	0.611315	+	1.05883i	0.0291433	+	0.0504777i
$441$	−0.500000	+	0.866025i	−0.0238095	+	0.0412393i
$442$	0.875374	+	1.51619i	0.0416373	+	0.0721179i
$443$	−3.77737	+	6.54260i	−0.179468	+	0.310848i	−0.941699	−	0.336458i	$-0.890771\pi$
$443$	−3.77737	+	6.54260i	−0.179468	+	0.310848i	0.762230	+	0.647306i	$0.224104\pi$
$444$	1.22263			0.0580235
$445$	5.86390			0.277976
$446$	10.7093	−	18.5491i	0.507101	−	0.878325i
$447$	2.77737	−	4.81054i	0.131365	−	0.227531i
$448$	−1.00000			−0.0472456
$449$	20.6147			0.972865			0.486433	−	0.873718i	$-0.338298\pi$
$449$	20.6147			0.972865			0.486433	+	0.873718i	$0.338298\pi$
$450$	2.00000	−	3.46410i	0.0942809	−	0.163299i
$451$	−1.69785	−	2.94076i	−0.0799486	−	0.138475i
$452$	−5.11132	+	8.85306i	−0.240416	+	0.416413i
$453$	9.65458	+	16.7222i	0.453612	+	0.785679i
$454$	−13.4320	−	23.2648i	−0.630393	−	1.09187i
$455$	0.222631			0.0104371
$456$	3.43195	+	2.68732i	0.160716	+	0.125845i
$457$	−11.0000			−0.514558			−0.257279	−	0.966337i	$-0.582826\pi$
$457$	−11.0000			−0.514558			−0.257279	+	0.966337i	$0.582826\pi$
$458$	−7.75259	−	13.4279i	−0.362255	−	0.627443i
$459$	3.93195	+	6.81034i	0.183528	+	0.317879i
$460$	3.43195	−	5.94431i	0.160016	−	0.277155i
$461$	12.0318	+	20.8397i	0.560377	+	0.970601i	0.997463	+	0.0711814i	$0.0226769\pi$
$461$	12.0318	+	20.8397i	0.560377	+	0.970601i	−0.437087	+	0.899419i	$0.643990\pi$
$462$	0.611315	−	1.05883i	0.0284410	−	0.0492612i
$463$	30.4186			1.41367			0.706837	−	0.707376i	$-0.250121\pi$
$463$	30.4186			1.41367			0.706837	+	0.707376i	$0.250121\pi$
$464$	4.00000			0.185695
$465$	−0.222631	+	0.385608i	−0.0103243	+	0.0178821i
$466$	4.66605	−	8.08184i	0.216151	−	0.374384i
$467$	−37.2825			−1.72523			−0.862615	−	0.505861i	$-0.831175\pi$
$467$	−37.2825			−1.72523			−0.862615	+	0.505861i	$0.831175\pi$
$468$	−0.222631			−0.0102911
$469$	6.32064	−	10.9477i	0.291860	−	0.505516i
$470$	4.54327	+	7.86917i	0.209565	+	0.362978i
$471$	−1.66605	+	2.88569i	−0.0767677	+	0.132966i
$472$	−6.65458	−	11.5261i	−0.306302	−	0.530531i
$473$	1.22263	+	2.11766i	0.0562166	+	0.0973701i
$474$		0			0
$475$	2.44526	−	17.2633i	0.112196	−	0.792093i
$476$	−7.86390			−0.360441
$477$	4.32064	+	7.48356i	0.197828	+	0.342649i
$478$	3.17936	+	5.50682i	0.145421	+	0.251876i
$479$	0.679364	−	1.17669i	0.0310409	−	0.0537645i	−0.850088	−	0.526641i	$-0.823451\pi$
$479$	0.679364	−	1.17669i	0.0310409	−	0.0537645i	0.881129	+	0.472877i	$0.156784\pi$
$480$	0.500000	+	0.866025i	0.0228218	+	0.0395285i
$481$	−0.136098	+	0.235728i	−0.00620552	+	0.0107483i
$482$	−9.72780			−0.443089
$483$	−6.86390			−0.312318
$484$	4.75259	−	8.23172i	0.216027	−	0.374169i
$485$	−1.77737	+	3.07849i	−0.0807062	+	0.139787i
$486$	−1.00000			−0.0453609
$487$	38.1731			1.72979			0.864893	−	0.501956i	$-0.167386\pi$
$487$	38.1731			1.72979			0.864893	+	0.501956i	$0.167386\pi$
$488$	−2.88868	+	5.00335i	−0.130765	+	0.226491i
$489$	−9.32064	−	16.1438i	−0.421494	−	0.730049i
$490$	−0.500000	+	0.866025i	−0.0225877	+	0.0391230i
$491$	17.7093	+	30.6734i	0.799210	+	1.38427i	0.920131	+	0.391611i	$0.128082\pi$
$491$	17.7093	+	30.6734i	0.799210	+	1.38427i	−0.120920	+	0.992662i	$0.538585\pi$
$492$	−1.38868	−	2.40527i	−0.0626067	−	0.108438i
$493$	31.4556			1.41669
$494$	−0.900156	+	0.362553i	−0.0404999	+	0.0163120i
$495$	−1.22263			−0.0549532
$496$	0.222631	+	0.385608i	0.00999642	+	0.0173143i
$497$	5.65458	+	9.79402i	0.253643	+	0.439322i
$498$	5.43195	−	9.40842i	0.243412	−	0.421601i
$499$	13.7544	+	23.8234i	0.615733	+	1.06648i	0.990255	+	0.139263i	$0.0444732\pi$
$499$	13.7544	+	23.8234i	0.615733	+	1.06648i	−0.374523	+	0.927218i	$0.622193\pi$
$500$	4.50000	−	7.79423i	0.201246	−	0.348569i
$501$	11.5318			0.515203
$502$	−8.86390			−0.395615
$503$	12.0865	−	20.9345i	0.538912	−	0.933423i	−0.460051	−	0.887892i	$-0.652169\pi$
$503$	12.0865	−	20.9345i	0.538912	−	0.933423i	0.998963	−	0.0455303i	$-0.0144978\pi$
$504$	0.500000	−	0.866025i	0.0222718	−	0.0385758i
$505$	1.66789			0.0742203
$506$	8.39202			0.373071
$507$	−6.47522	+	11.2154i	−0.287575	+	0.498094i
$508$	−4.65458	−	8.06197i	−0.206514	−	0.357692i
$509$	−13.8092	+	23.9182i	−0.612080	+	1.06015i	0.378809	+	0.925475i	$0.376334\pi$
$509$	−13.8092	+	23.9182i	−0.612080	+	1.06015i	−0.990889	+	0.134679i	$0.957000\pi$
$510$	3.93195	+	6.81034i	0.174110	+	0.301567i
$511$	3.32064	+	5.75151i	0.146896	+	0.254432i
$512$	1.00000			0.0441942
$513$	−4.04327	+	1.62849i	−0.178515	+	0.0718998i
$514$	27.3957			1.20837
$515$	−4.15458	−	7.19595i	−0.183073	−	0.317091i
$516$	1.00000	+	1.73205i	0.0440225	+	0.0762493i
$517$	−5.55474	+	9.62109i	−0.244297	+	0.423135i
$518$	−0.611315	−	1.05883i	−0.0268597	−	0.0465223i
$519$	−0.975218	+	1.68913i	−0.0428073	+	0.0741444i
$520$	−0.222631			−0.00976301
$521$	−11.2825			−0.494297			−0.247149	−	0.968978i	$-0.579494\pi$
$521$	−11.2825			−0.494297			−0.247149	+	0.968978i	$0.579494\pi$
$522$	−2.00000	+	3.46410i	−0.0875376	+	0.151620i
$523$	−2.16605	+	3.75171i	−0.0947149	+	0.164051i	−0.909490	−	0.415727i	$-0.863527\pi$
$523$	−2.16605	+	3.75171i	−0.0947149	+	0.164051i	0.814775	+	0.579778i	$0.196861\pi$
$524$	−10.8639			−0.474592
$525$	−4.00000			−0.174574
$526$	−5.82064	+	10.0816i	−0.253792	+	0.439580i
$527$	1.75075	+	3.03238i	0.0762638	+	0.132093i
$528$	−0.611315	+	1.05883i	−0.0266041	+	0.0460796i
$529$	−12.0566	−	20.8826i	−0.524199	−	0.907939i
$530$	4.32064	+	7.48356i	0.187676	+	0.325065i
$531$	13.3092			0.577569
$532$	0.611315	−	4.31582i	0.0265039	−	0.187114i
$533$	0.618328			0.0267828
$534$	2.93195	+	5.07829i	0.126878	+	0.219759i
$535$	4.54327	+	7.86917i	0.196423	+	0.340214i
$536$	−6.32064	+	10.9477i	−0.273010	+	0.472867i
$537$	−3.15458	−	5.46390i	−0.136130	−	0.235785i
$538$	−6.69785	+	11.6010i	−0.288765	+	0.500155i
$539$	−1.22263			−0.0526624
$540$	−1.00000			−0.0430331
$541$	6.29068	−	10.8958i	0.270457	−	0.468446i	−0.698522	−	0.715589i	$-0.746158\pi$
$541$	6.29068	−	10.8958i	0.270457	−	0.468446i	0.968979	+	0.247143i	$0.0794917\pi$
$542$	−14.5732	+	25.2416i	−0.625974	+	1.08422i
$543$	−6.22263			−0.267039
$544$	7.86390			0.337162
$545$	4.15458	−	7.19595i	0.177963	−	0.308241i
$546$	0.111315	+	0.192804i	0.00476386	+	0.00825125i
$547$	10.4072	−	18.0257i	0.444978	−	0.770725i	−0.553072	−	0.833133i	$-0.686545\pi$
$547$	10.4072	−	18.0257i	0.444978	−	0.770725i	0.998051	+	0.0624080i	$0.0198780\pi$
$548$	−10.9752	−	19.0096i	−0.468838	−	0.812051i
$549$	−2.88868	−	5.00335i	−0.123286	−	0.213538i
$550$	4.89052			0.208533
$551$	−2.44526	+	17.2633i	−0.104172	+	0.735440i
$552$	6.86390			0.292147
$553$		0			0
$554$	−7.01848	−	12.1564i	−0.298187	−	0.516475i
$555$	−0.611315	+	1.05883i	−0.0259489	+	0.0449448i
$556$	5.38868	+	9.33348i	0.228531	+	0.395828i
$557$	−14.2226	+	24.6343i	−0.602632	+	1.04379i	0.389789	+	0.920904i	$0.372548\pi$
$557$	−14.2226	+	24.6343i	−0.602632	+	1.04379i	−0.992421	+	0.122885i	$0.960785\pi$
$558$	−0.445262			−0.0188494
$559$	−0.445262			−0.0188326
$560$	0.500000	−	0.866025i	0.0211289	−	0.0365963i
$561$	−4.80733	+	8.32653i	−0.202965	+	0.351546i
$562$	31.9009			1.34566
$563$	23.7544			1.00113			0.500565	−	0.865699i	$-0.333126\pi$
$563$	23.7544			1.00113			0.500565	+	0.865699i	$0.333126\pi$
$564$	−4.54327	+	7.86917i	−0.191306	+	0.331352i
$565$	−5.11132	−	8.85306i	−0.215035	−	0.372451i
$566$	−13.8206	+	23.9380i	−0.580925	+	1.00619i
$567$	0.500000	+	0.866025i	0.0209980	+	0.0363696i
$568$	−5.65458	−	9.79402i	−0.237261	−	0.410948i
$569$	29.9504			1.25559			0.627794	−	0.778380i	$-0.283958\pi$
$569$	29.9504			1.25559			0.627794	+	0.778380i	$0.283958\pi$
$570$	−4.04327	+	1.62849i	−0.169354	+	0.0682101i
$571$	−3.80399			−0.159192			−0.0795960	−	0.996827i	$-0.525363\pi$
$571$	−3.80399			−0.159192			−0.0795960	+	0.996827i	$0.525363\pi$
$572$	−0.136098	−	0.235728i	−0.00569053	−	0.00985629i
$573$	−1.43195	−	2.48021i	−0.0598206	−	0.103612i
$574$	−1.38868	+	2.40527i	−0.0579626	+	0.100394i
$575$	−13.7278	−	23.7773i	−0.572489	−	0.991580i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−11.9771			−0.498611			−0.249306	−	0.968425i	$-0.580202\pi$
$577$	−11.9771			−0.498611			−0.249306	+	0.968425i	$0.580202\pi$
$578$	44.8410			1.86514
$579$	−3.36390	+	5.82645i	−0.139799	+	0.242139i
$580$	−2.00000	+	3.46410i	−0.0830455	+	0.143839i
$581$	−10.8639			−0.450711
$582$	−3.55474			−0.147349
$583$	−5.28254	+	9.14963i	−0.218781	+	0.378939i
$584$	−3.32064	−	5.75151i	−0.137409	−	0.237999i
$585$	0.111315	−	0.192804i	0.00460233	−	0.00797147i
$586$	−9.91864	−	17.1796i	−0.409735	−	0.709682i
$587$	8.30916	+	14.3919i	0.342956	+	0.594017i	0.984980	−	0.172667i	$-0.0552385\pi$
$587$	8.30916	+	14.3919i	0.342956	+	0.594017i	−0.642024	+	0.766684i	$0.721905\pi$
$588$	−1.00000			−0.0412393
$589$	−1.80031	+	0.725107i	−0.0741806	+	0.0298775i
$590$	13.3092			0.547930
$591$	8.76590	+	15.1830i	0.360581	+	0.624544i
$592$	0.611315	+	1.05883i	0.0251249	+	0.0435176i
$593$	12.8073	−	22.1829i	0.525934	−	0.910944i	−0.473610	−	0.880735i	$-0.657049\pi$
$593$	12.8073	−	22.1829i	0.525934	−	0.910944i	0.999544	−	0.0302093i	$-0.00961738\pi$
$594$	−0.611315	−	1.05883i	−0.0250826	−	0.0434443i
$595$	3.93195	−	6.81034i	0.161194	−	0.279197i
$596$	5.55474			0.227531
$597$	13.0865			0.535596
$598$	−0.764058	+	1.32339i	−0.0312447	+	0.0541174i
$599$	11.5980	−	20.0883i	0.473882	−	0.820787i	−0.525671	−	0.850688i	$-0.676186\pi$
$599$	11.5980	−	20.0883i	0.473882	−	0.820787i	0.999553	+	0.0299007i	$0.00951912\pi$
$600$	4.00000			0.163299
$601$	−19.2596			−0.785615			−0.392808	−	0.919621i	$-0.628496\pi$
$601$	−19.2596			−0.785615			−0.392808	+	0.919621i	$0.628496\pi$
$602$	1.00000	−	1.73205i	0.0407570	−	0.0705931i
$603$	−6.32064	−	10.9477i	−0.257396	−	0.445823i
$604$	−9.65458	+	16.7222i	−0.392839	+	0.680418i
$605$	4.75259	+	8.23172i	0.193220	+	0.334667i
$606$	0.833946	+	1.44444i	0.0338768	+	0.0586763i
$607$	18.1731			0.737622			0.368811	−	0.929504i	$-0.379765\pi$
$607$	18.1731			0.737622			0.368811	+	0.929504i	$0.379765\pi$
$608$	−0.611315	+	4.31582i	−0.0247921	+	0.175030i
$609$	4.00000			0.162088
$610$	−2.88868	−	5.00335i	−0.116959	−	0.202580i
$611$	−1.01147	−	1.75192i	−0.0409198	−	0.0708751i
$612$	−3.93195	+	6.81034i	−0.158940	+	0.275292i
$613$	5.79585	+	10.0387i	0.234092	+	0.405460i	0.959009	−	0.283377i	$-0.0914549\pi$
$613$	5.79585	+	10.0387i	0.234092	+	0.405460i	−0.724916	+	0.688837i	$0.758122\pi$
$614$	−3.87721	+	6.71553i	−0.156472	+	0.271017i
$615$	2.77737			0.111994
$616$	1.22263			0.0492612
$617$	−4.55658	+	7.89222i	−0.183441	+	0.317729i	−0.943050	−	0.332651i	$-0.892057\pi$
$617$	−4.55658	+	7.89222i	−0.183441	+	0.317729i	0.759609	+	0.650380i	$0.225390\pi$
$618$	4.15458	−	7.19595i	0.167122	−	0.289463i
$619$	−5.13610			−0.206437			−0.103219	−	0.994659i	$-0.532914\pi$
$619$	−5.13610			−0.206437			−0.103219	+	0.994659i	$0.532914\pi$
$620$	−0.445262			−0.0178821
$621$	−3.43195	+	5.94431i	−0.137719	+	0.238537i
$622$	11.7659	+	20.3791i	0.471770	+	0.817129i
$623$	2.93195	−	5.07829i	0.117466	−	0.203457i
$624$	−0.111315	−	0.192804i	−0.00445618	−	0.00771834i
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	−25.2825			−1.01049
$627$	−4.19601	−	3.28561i	−0.167572	−	0.131214i
$628$	−3.33211			−0.132966
$629$	4.80733	+	8.32653i	0.191681	+	0.332001i
$630$	0.500000	+	0.866025i	0.0199205	+	0.0345033i
$631$	−22.3092	+	38.6406i	−0.888114	+	1.53826i	−0.0460112	+	0.998941i	$0.514651\pi$
$631$	−22.3092	+	38.6406i	−0.888114	+	1.53826i	−0.842103	+	0.539317i	$0.818682\pi$
$632$		0			0
$633$	−6.76590	+	11.7189i	−0.268920	+	0.465784i
$634$	−0.445262			−0.0176836
$635$	9.30916			0.369423
$636$	−4.32064	+	7.48356i	−0.171324	+	0.296742i
$637$	0.111315	−	0.192804i	0.00441048	−	0.00763917i
$638$	−4.89052			−0.193618
$639$	11.3092			0.447384
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−6.66605	−	11.5459i	−0.263293	−	0.456037i	0.703822	−	0.710377i	$-0.251475\pi$
$641$	−6.66605	−	11.5459i	−0.263293	−	0.456037i	−0.967115	+	0.254339i	$0.918142\pi$
$642$	−4.54327	+	7.86917i	−0.179308	+	0.310571i
$643$	2.26590	+	3.92465i	0.0893583	+	0.154773i	0.907240	−	0.420613i	$-0.138185\pi$
$643$	2.26590	+	3.92465i	0.0893583	+	0.154773i	−0.817882	+	0.575386i	$0.804852\pi$
$644$	−3.43195	−	5.94431i	−0.135238	−	0.234239i
$645$	−2.00000			−0.0787499
$646$	−4.80733	+	33.9392i	−0.189142	+	1.33532i
$647$	17.7278			0.696952			0.348476	−	0.937318i	$-0.386699\pi$
$647$	17.7278			0.696952			0.348476	+	0.937318i	$0.386699\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	8.13610	+	14.0921i	0.319370	+	0.553165i
$650$	−0.445262	+	0.771216i	−0.0174646	+	0.0302496i
$651$	0.222631	+	0.385608i	0.00872559	+	0.0151132i
$652$	9.32064	−	16.1438i	0.365024	−	0.632241i
$653$	14.6413			0.572957			0.286479	−	0.958087i	$-0.407515\pi$
$653$	14.6413			0.572957			0.286479	+	0.958087i	$0.407515\pi$
$654$	8.30916			0.324914
$655$	5.43195	−	9.40842i	0.212244	−	0.367617i
$656$	1.38868	−	2.40527i	0.0542190	−	0.0939101i
$657$	6.64127			0.259101
$658$	9.08653			0.354230
$659$	12.6978	−	21.9933i	0.494638	−	0.856738i	−0.505343	−	0.862919i	$-0.668634\pi$
$659$	12.6978	−	21.9933i	0.494638	−	0.856738i	0.999981	+	0.00618053i	$0.00196734\pi$
$660$	−0.611315	−	1.05883i	−0.0237954	−	0.0412149i
$661$	6.97522	−	12.0814i	0.271305	−	0.469913i	−0.697892	−	0.716203i	$-0.745878\pi$
$661$	6.97522	−	12.0814i	0.271305	−	0.469913i	0.969196	+	0.246290i	$0.0792116\pi$
$662$	9.40717	+	16.2937i	0.365620	+	0.633272i
$663$	−0.875374	−	1.51619i	−0.0339967	−	0.0588840i
$664$	10.8639			0.421601
$665$	3.43195	+	2.68732i	0.133085	+	0.104210i
$666$	−1.22263			−0.0473760
$667$	13.7278	+	23.7773i	0.531543	+	0.920659i
$668$	5.76590	+	9.98683i	0.223089	+	0.386402i
$669$	−10.7093	+	18.5491i	−0.414046	+	0.717149i
$670$	−6.32064	−	10.9477i	−0.244187	−	0.422945i
$671$	3.53180	−	6.11725i	0.136343	−	0.236154i
$672$	1.00000			0.0385758
$673$	−7.44526			−0.286994			−0.143497	−	0.989651i	$-0.545835\pi$
$673$	−7.44526			−0.286994			−0.143497	+	0.989651i	$0.545835\pi$
$674$	0.111315	−	0.192804i	0.00428771	−	0.00742653i
$675$	−2.00000	+	3.46410i	−0.0769800	+	0.133333i
$676$	−12.9504			−0.498094
$677$	8.77737			0.337342			0.168671	−	0.985672i	$-0.446053\pi$
$677$	8.77737			0.337342			0.168671	+	0.985672i	$0.446053\pi$
$678$	5.11132	−	8.85306i	0.196299	−	0.340000i
$679$	1.77737	+	3.07849i	0.0682092	+	0.118142i
$680$	−3.93195	+	6.81034i	−0.150783	+	0.261165i
$681$	13.4320	+	23.2648i	0.514713	+	0.891510i
$682$	−0.272195	−	0.471456i	−0.0104229	−	0.0180530i
$683$	0.996322			0.0381232			0.0190616	−	0.999818i	$-0.493932\pi$
$683$	0.996322			0.0381232			0.0190616	+	0.999818i	$0.493932\pi$
$684$	−3.43195	−	2.68732i	−0.131224	−	0.102752i
$685$	21.9504			0.838683
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$	7.75259	+	13.4279i	0.295780	+	0.512305i
$688$	−1.00000	+	1.73205i	−0.0381246	+	0.0660338i
$689$	−0.961907	−	1.66607i	−0.0366457	−	0.0634723i
$690$	−3.43195	+	5.94431i	−0.130652	+	0.226296i
$691$	37.3691			1.42159			0.710793	−	0.703401i	$-0.248336\pi$
$691$	37.3691			1.42159			0.710793	+	0.703401i	$0.248336\pi$
$692$	−1.95044			−0.0741444
$693$	−0.611315	+	1.05883i	−0.0232220	+	0.0402216i
$694$	−4.54327	+	7.86917i	−0.172460	+	0.298710i
$695$	−10.7774			−0.408809
$696$	−4.00000			−0.151620
$697$	10.9205	−	18.9148i	0.413643	−	0.716450i
$698$	−17.3092	−	29.9804i	−0.655162	−	1.13477i
$699$	−4.66605	+	8.08184i	−0.176486	+	0.305683i
$700$	−2.00000	−	3.46410i	−0.0755929	−	0.130931i
$701$	−6.67936	−	11.5690i	−0.252276	−	0.436955i	0.711876	−	0.702305i	$-0.247846\pi$
$701$	−6.67936	−	11.5690i	−0.252276	−	0.436955i	−0.964152	+	0.265350i	$0.914512\pi$
$702$	0.222631			0.00840266
$703$	−4.94342	+	1.99105i	−0.186445	+	0.0750938i
$704$	−1.22263			−0.0460796
$705$	−4.54327	−	7.86917i	−0.171109	−	0.296370i
$706$	8.93195	+	15.4706i	0.336158	+	0.582243i
$707$	0.833946	−	1.44444i	0.0313638	−	0.0543237i
$708$	6.65458	+	11.5261i	0.250095	+	0.433176i
$709$	−17.2526	+	29.8824i	−0.647934	+	1.12226i	0.335681	+	0.941976i	$0.391034\pi$
$709$	−17.2526	+	29.8824i	−0.647934	+	1.12226i	−0.983615	+	0.180280i	$0.942300\pi$
$710$	11.3092			0.424425
$711$		0			0
$712$	−2.93195	+	5.07829i	−0.109880	+	0.190317i
$713$	−1.52812	+	2.64678i	−0.0572284	+	0.0991225i
$714$	7.86390			0.294299
$715$	0.272195			0.0101795
$716$	3.15458	−	5.46390i	0.117892	−	0.204195i
$717$	−3.17936	−	5.50682i	−0.118736	−	0.205656i
$718$	−5.08653	+	8.81013i	−0.189828	+	0.328791i
$719$	−16.4072	−	28.4181i	−0.611884	−	1.05981i	−0.990923	−	0.134434i	$-0.957079\pi$
$719$	−16.4072	−	28.4181i	−0.611884	−	1.05981i	0.379038	−	0.925381i	$-0.376255\pi$
$720$	−0.500000	−	0.866025i	−0.0186339	−	0.0322749i
$721$	−8.30916			−0.309449
$722$	−18.2526	−	5.27665i	−0.679291	−	0.196377i
$723$	9.72780			0.361781
$724$	−3.11132	−	5.38896i	−0.115631	−	0.200279i
$725$	8.00000	+	13.8564i	0.297113	+	0.514614i
$726$	−4.75259	+	8.23172i	−0.176385	+	0.305508i
$727$	−0.475218	−	0.823101i	−0.0176249	−	0.0305271i	0.857078	−	0.515186i	$-0.172277\pi$
$727$	−0.475218	−	0.823101i	−0.0176249	−	0.0305271i	−0.874703	+	0.484659i	$0.838944\pi$
$728$	−0.111315	+	0.192804i	−0.00412563	+	0.00714579i
$729$	1.00000			0.0370370
$730$	6.64127			0.245804
$731$	−7.86390	+	13.6207i	−0.290857	+	0.503779i
$732$	2.88868	−	5.00335i	0.106769	−	0.184929i
$733$	30.3957			1.12269			0.561345	−	0.827582i	$-0.310284\pi$
$733$	30.3957			1.12269			0.561345	+	0.827582i	$0.310284\pi$
$734$	−18.5052			−0.683038
$735$	0.500000	−	0.866025i	0.0184428	−	0.0319438i
$736$	3.43195	+	5.94431i	0.126503	+	0.219110i
$737$	7.72780	−	13.3850i	0.284657	−	0.493041i
$738$	1.38868	+	2.40527i	0.0511182	+	0.0885393i
$739$	−3.22263	−	5.58176i	−0.118546	−	0.205328i	0.800645	−	0.599138i	$-0.204490\pi$
$739$	−3.22263	−	5.58176i	−0.118546	−	0.205328i	−0.919192	+	0.393810i	$0.871157\pi$
$740$	−1.22263			−0.0449448
$741$	0.900156	−	0.362553i	0.0330681	−	0.0133187i
$742$	8.64127			0.317231
$743$	−12.1298	−	21.0094i	−0.444999	−	0.770761i	0.553053	−	0.833146i	$-0.313463\pi$
$743$	−12.1298	−	21.0094i	−0.444999	−	0.770761i	−0.998052	+	0.0623849i	$0.980129\pi$
$744$	−0.222631	−	0.385608i	−0.00816205	−	0.0141371i
$745$	−2.77737	+	4.81054i	−0.101755	+	0.176245i
$746$	−12.3887	−	21.4578i	−0.453582	−	0.785627i
$747$	−5.43195	+	9.40842i	−0.198745	+	0.344236i
$748$	−9.61465			−0.351546
$749$	9.08653			0.332015
$750$	−4.50000	+	7.79423i	−0.164317	+	0.284605i
$751$	−6.30916	+	10.9278i	−0.230225	+	0.398761i	−0.957874	−	0.287188i	$-0.907279\pi$
$751$	−6.30916	+	10.9278i	−0.230225	+	0.398761i	0.727649	+	0.685949i	$0.240613\pi$
$752$	−9.08653			−0.331352
$753$	8.86390			0.323019
$754$	0.445262	−	0.771216i	0.0162155	−	0.0280860i
$755$	−9.65458	−	16.7222i	−0.351366	−	0.608584i
$756$	−0.500000	+	0.866025i	−0.0181848	+	0.0314970i
$757$	−11.3506	−	19.6598i	−0.412544	−	0.714548i	0.582623	−	0.812743i	$-0.302026\pi$
$757$	−11.3506	−	19.6598i	−0.412544	−	0.714548i	−0.995167	+	0.0981950i	$0.968693\pi$
$758$	0.863902	+	1.49632i	0.0313783	+	0.0543489i
$759$	−8.39202			−0.304611
$760$	−3.43195	−	2.68732i	−0.124490	−	0.0974795i
$761$	−41.6516			−1.50987			−0.754935	−	0.655800i	$-0.772332\pi$
$761$	−41.6516			−1.50987			−0.754935	+	0.655800i	$0.772332\pi$
$762$	4.65458	+	8.06197i	0.168618	+	0.292054i
$763$	−4.15458	−	7.19595i	−0.150406	−	0.260511i
$764$	1.43195	−	2.48021i	0.0518062	−	0.0897309i
$765$	−3.93195	−	6.81034i	−0.142160	−	0.246228i
$766$	3.23410	−	5.60163i	0.116853	−	0.202395i
$767$	−2.96303			−0.106989
$768$	−1.00000			−0.0360844
$769$	7.13610	−	12.3601i	0.257334	−	0.445716i	−0.708193	−	0.706019i	$-0.750489\pi$
$769$	7.13610	−	12.3601i	0.257334	−	0.445716i	0.965527	+	0.260303i	$0.0838225\pi$
$770$	−0.611315	+	1.05883i	−0.0220303	+	0.0381576i
$771$	−27.3957			−0.986632
$772$	−6.72780			−0.242139
$773$	−11.9186	+	20.6437i	−0.428684	+	0.742502i	−0.996757	−	0.0804763i	$-0.974356\pi$
$773$	−11.9186	+	20.6437i	−0.428684	+	0.742502i	0.568073	+	0.822978i	$0.307689\pi$
$774$	−1.00000	−	1.73205i	−0.0359443	−	0.0622573i
$775$	−0.890524	+	1.54243i	−0.0319886	+	0.0554058i
$776$	−1.77737	−	3.07849i	−0.0638038	−	0.110511i
$777$	0.611315	+	1.05883i	0.0219308	+	0.0379853i
$778$	29.9238			1.07282
$779$	9.53180	+	7.46369i	0.341512	+	0.267414i
$780$	0.222631			0.00797147
$781$	6.91347	+	11.9745i	0.247383	+	0.428480i
$782$	26.9885	+	46.7455i	0.965108	+	1.67162i
$783$	2.00000	−	3.46410i	0.0714742	−	0.123797i
$784$	−0.500000	−	0.866025i	−0.0178571	−	0.0309295i
$785$	1.66605	−	2.88569i	0.0594640	−	0.102995i
$786$	10.8639			0.387503
$787$	54.4327			1.94031			0.970157	−	0.242476i	$-0.0779594\pi$
$787$	54.4327			1.94031			0.970157	+	0.242476i	$0.0779594\pi$
$788$	−8.76590	+	15.1830i	−0.312272	+	0.540871i
$789$	5.82064	−	10.0816i	0.207220	−	0.358916i
$790$		0			0
$791$	−10.2226			−0.363475
$792$	0.611315	−	1.05883i	0.0217221	−	0.0376239i
$793$	0.643110	+	1.11390i	0.0228375	+	0.0395557i
$794$	−12.0865	+	20.9345i	−0.428935	+	0.742937i
$795$	−4.32064	−	7.48356i	−0.153237	−	0.265415i
$796$	6.54327	+	11.3333i	0.231920	+	0.401697i
$797$	20.2825			0.718445			0.359222	−	0.933252i	$-0.383042\pi$
$797$	20.2825			0.718445			0.359222	+	0.933252i	$0.383042\pi$
$798$	−0.611315	+	4.31582i	−0.0216403	+	0.152778i
$799$	−71.4556			−2.52792
$800$	2.00000	+	3.46410i	0.0707107	+	0.122474i
$801$	−2.93195	−	5.07829i	−0.103595	−	0.179432i
$802$	−17.3073	+	29.9772i	−0.611143	+	1.05853i
$803$	4.05991	+	7.03197i	0.143271	+	0.248153i
$804$	6.32064	−	10.9477i	0.222912	−	0.386094i
$805$	6.86390			0.241921
$806$	0.0991290			0.00349167
$807$	6.69785	−	11.6010i	0.235775	−	0.408375i
$808$	−0.833946	+	1.44444i	−0.0293381	+	0.0508151i
$809$	−13.6782			−0.480901			−0.240451	−	0.970661i	$-0.577295\pi$
$809$	−13.6782			−0.480901			−0.240451	+	0.970661i	$0.577295\pi$
$810$	1.00000			0.0351364
$811$	20.0300	−	34.6929i	0.703347	−	1.21823i	−0.263938	−	0.964540i	$-0.585021\pi$
$811$	20.0300	−	34.6929i	0.703347	−	1.21823i	0.967285	−	0.253693i	$-0.0816453\pi$
$812$	2.00000	+	3.46410i	0.0701862	+	0.121566i
$813$	14.5732	−	25.2416i	0.511105	−	0.885260i
$814$	−0.747413	−	1.29456i	−0.0261968	−	0.0453742i
$815$	9.32064	+	16.1438i	0.326488	+	0.565493i
$816$	−7.86390			−0.275292
$817$	−6.86390	−	5.37465i	−0.240138	−	0.188035i
$818$	−6.81434			−0.238258
$819$	−0.111315	−	0.192804i	−0.00388968	−	0.00673712i
$820$	1.38868	+	2.40527i	0.0484950	+	0.0839957i
$821$	−8.32064	+	14.4118i	−0.290392	+	0.502974i	−0.973902	−	0.226967i	$-0.927119\pi$
$821$	−8.32064	+	14.4118i	−0.290392	+	0.502974i	0.683510	+	0.729941i	$0.260452\pi$
$822$	10.9752	+	19.0096i	0.382805	+	0.663037i
$823$	−6.65458	+	11.5261i	−0.231964	+	0.401774i	−0.958386	−	0.285475i	$-0.907849\pi$
$823$	−6.65458	+	11.5261i	−0.231964	+	0.401774i	0.726422	+	0.687249i	$0.241182\pi$
$824$	8.30916			0.289463
$825$	−4.89052			−0.170266
$826$	6.65458	−	11.5261i	0.231543	−	0.401043i
$827$	6.01848	−	10.4243i	0.209283	−	0.362489i	−0.742206	−	0.670172i	$-0.766220\pi$
$827$	6.01848	−	10.4243i	0.209283	−	0.362489i	0.951489	+	0.307683i	$0.0995536\pi$
$828$	−6.86390			−0.238537
$829$	15.3321			0.532506			0.266253	−	0.963903i	$-0.414214\pi$
$829$	15.3321			0.532506			0.266253	+	0.963903i	$0.414214\pi$
$830$	−5.43195	+	9.40842i	−0.188546	+	0.326571i
$831$	7.01848	+	12.1564i	0.243469	+	0.421700i
$832$	0.111315	−	0.192804i	0.00385917	−	0.00668428i
$833$	−3.93195	−	6.81034i	−0.136234	−	0.235964i
$834$	−5.38868	−	9.33348i	−0.186595	−	0.323192i
$835$	−11.5318			−0.399074
$836$	0.747413	−	5.27665i	0.0258498	−	0.182497i
$837$	0.445262			0.0153905
$838$	3.22263	+	5.58176i	0.111324	+	0.192819i
$839$	24.8524	+	43.0457i	0.858001	+	1.48610i	0.873833	+	0.486227i	$0.161627\pi$
$839$	24.8524	+	43.0457i	0.858001	+	1.48610i	−0.0158314	+	0.999875i	$0.505039\pi$
$840$	−0.500000	+	0.866025i	−0.0172516	+	0.0298807i
$841$	6.50000	+	11.2583i	0.224138	+	0.388218i
$842$	−2.62279	+	4.54280i	−0.0903872	+	0.156555i
$843$	−31.9009			−1.09872
$844$	−13.5318			−0.465784
$845$	6.47522	−	11.2154i	0.222754	−	0.385822i
$846$	4.54327	−	7.86917i	0.156201	−	0.270548i
$847$	9.50517			0.326602
$848$	−8.64127			−0.296742
$849$	13.8206	−	23.9380i	0.474323	−	0.821552i
$850$	15.7278	+	27.2414i	0.539459	+	0.934371i
$851$	−4.19601	+	7.26770i	−0.143837	+	0.249134i
$852$	5.65458	+	9.79402i	0.193723	+	0.335538i
$853$	4.86390	+	8.42453i	0.166537	+	0.288450i	0.937200	−	0.348792i	$-0.113408\pi$
$853$	4.86390	+	8.42453i	0.166537	+	0.288450i	−0.770663	+	0.637243i	$0.780075\pi$
$854$	−5.77737			−0.197698
$855$	4.04327	−	1.62849i	0.138277	−	0.0556933i
$856$	−9.08653			−0.310571
$857$	10.6978	+	18.5292i	0.365432	+	0.632946i	0.988845	−	0.148946i	$-0.0475881\pi$
$857$	10.6978	+	18.5292i	0.365432	+	0.632946i	−0.623414	+	0.781892i	$0.714255\pi$
$858$	0.136098	+	0.235728i	0.00464630	+	0.00804763i
$859$	−10.8073	+	18.7188i	−0.368741	+	0.638678i	−0.989369	−	0.145427i	$-0.953544\pi$
$859$	−10.8073	+	18.7188i	−0.368741	+	0.638678i	0.620628	+	0.784105i	$0.286878\pi$
$860$	−1.00000	−	1.73205i	−0.0340997	−	0.0590624i
$861$	1.38868	−	2.40527i	0.0473262	−	0.0819715i
$862$	−20.0599			−0.683243
$863$	48.6782			1.65703			0.828513	−	0.559969i	$-0.189187\pi$
$863$	48.6782			1.65703			0.828513	+	0.559969i	$0.189187\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	0.975218	−	1.68913i	0.0331584	−	0.0574320i
$866$	5.53180			0.187978
$867$	−44.8410			−1.52288
$868$	−0.222631	+	0.385608i	−0.00755659	+	0.0130884i
$869$		0			0
$870$	2.00000	−	3.46410i	0.0678064	−	0.117444i
$871$	1.40717	+	2.43729i	0.0476801	+	0.0825844i
$872$	4.15458	+	7.19595i	0.140692	+	0.243686i
$873$	3.55474			0.120310
$874$	−27.7526	+	11.1778i	−0.938745	+	0.378096i
$875$	9.00000			0.304256
$876$	3.32064	+	5.75151i	0.112194	+	0.194326i
$877$	−0.0114716	−	0.0198694i	−0.000387368	−	0.000670941i	0.865832	−	0.500335i	$-0.166790\pi$
$877$	−0.0114716	−	0.0198694i	−0.000387368	−	0.000670941i	−0.866219	+	0.499664i	$0.833457\pi$
$878$	−15.4637	+	26.7840i	−0.521876	+	0.903916i
$879$	9.91864	+	17.1796i	0.334547	+	0.579453i
$880$	0.611315	−	1.05883i	0.0206074	−	0.0356931i
$881$	−15.8410			−0.533695			−0.266848	−	0.963739i	$-0.585982\pi$
$881$	−15.8410			−0.533695			−0.266848	+	0.963739i	$0.585982\pi$
$882$	1.00000			0.0336718
$883$	1.91347	−	3.31422i	0.0643933	−	0.111532i	−0.832031	−	0.554729i	$-0.812822\pi$
$883$	1.91347	−	3.31422i	0.0643933	−	0.111532i	0.896425	+	0.443196i	$0.146155\pi$
$884$	0.875374	−	1.51619i	0.0294420	−	0.0509951i
$885$	−13.3092			−0.447383
$886$	7.55474			0.253806
$887$	2.10948	−	3.65372i	0.0708293	−	0.122680i	−0.828436	−	0.560084i	$-0.810769\pi$
$887$	2.10948	−	3.65372i	0.0708293	−	0.122680i	0.899265	+	0.437404i	$0.144102\pi$
$888$	−0.611315	−	1.05883i	−0.0205144	−	0.0355320i
$889$	4.65458	−	8.06197i	0.156110	−	0.270390i
$890$	−2.93195	−	5.07829i	−0.0982792	−	0.170225i
$891$	0.611315	+	1.05883i	0.0204798	+	0.0354721i
$892$	−21.4186			−0.717149
$893$	5.55474	−	39.2158i	0.185882	−	1.31231i
$894$	−5.55474			−0.185778
$895$	3.15458	+	5.46390i	0.105446	+	0.182638i
$896$	0.500000	+	0.866025i	0.0167038	+	0.0289319i
$897$	0.764058	−	1.32339i	0.0255112	−	0.0441866i
$898$	−10.3073	−	17.8528i	−0.343960	−	0.595756i
$899$	0.890524	−	1.54243i	0.0297006	−	0.0514430i
$900$	−4.00000			−0.133333
$901$	−67.9541			−2.26388
$902$	−1.69785	+	2.94076i	−0.0565322	+	0.0979166i
$903$	−1.00000	+	1.73205i	−0.0332779	+	0.0576390i
$904$	10.2226			0.340000
$905$	6.22263			0.206847
$906$	9.65458	−	16.7222i	0.320752	−	0.555559i
$907$	−14.2825	−	24.7381i	−0.474244	−	0.821415i	0.525321	−	0.850904i	$-0.323945\pi$
$907$	−14.2825	−	24.7381i	−0.474244	−	0.821415i	−0.999565	+	0.0294893i	$0.990612\pi$
$908$	−13.4320	+	23.2648i	−0.445755	+	0.772070i
$909$	−0.833946	−	1.44444i	−0.0276603	−	0.0479090i
$910$	−0.111315	−	0.192804i	−0.00369007	−	0.00639139i
$911$	11.9135			0.394711			0.197355	−	0.980332i	$-0.436765\pi$
$911$	11.9135			0.394711			0.197355	+	0.980332i	$0.436765\pi$
$912$	0.611315	−	4.31582i	0.0202427	−	0.142911i
$913$	−13.2825			−0.439588
$914$	5.50000	+	9.52628i	0.181924	+	0.315101i
$915$	2.88868	+	5.00335i	0.0954970	+	0.165406i
$916$	−7.75259	+	13.4279i	−0.256153	+	0.443669i
$917$	−5.43195	−	9.40842i	−0.179379	−	0.310693i
$918$	3.93195	−	6.81034i	0.129774	−	0.224775i
$919$	14.6449			0.483092			0.241546	−	0.970389i	$-0.422345\pi$
$919$	14.6449			0.483092			0.241546	+	0.970389i	$0.422345\pi$
$920$	−6.86390			−0.226296
$921$	3.87721	−	6.71553i	0.127759	−	0.221284i
$922$	12.0318	−	20.8397i	0.396246	−	0.686318i
$923$	−2.51777			−0.0828734
$924$	−1.22263			−0.0402216
$925$	−2.44526	+	4.23532i	−0.0803997	+	0.139256i
$926$	−15.2093	−	26.3433i	−0.499809	−	0.865695i
$927$	−4.15458	+	7.19595i	−0.136454	+	0.236346i
$928$	−2.00000	−	3.46410i	−0.0656532	−	0.113715i
$929$	10.4752	+	18.1436i	0.343681	+	0.595273i	0.985113	−	0.171907i	$-0.0549929\pi$
$929$	10.4752	+	18.1436i	0.343681	+	0.595273i	−0.641432	+	0.767180i	$0.721660\pi$
$930$	0.445262			0.0146007
$931$	4.04327	−	1.62849i	0.132513	−	0.0533718i
$932$	−9.33211			−0.305683
$933$	−11.7659	−	20.3791i	−0.385198	−	0.667183i
$934$	18.6413	+	32.2876i	0.609961	+	1.05648i
$935$	4.80733	−	8.32653i	0.157216	−	0.272307i
$936$	0.111315	+	0.192804i	0.00363846	+	0.00630200i
$937$	−2.67936	+	4.64080i	−0.0875310	+	0.151608i	−0.906467	−	0.422277i	$-0.861231\pi$
$937$	−2.67936	+	4.64080i	−0.0875310	+	0.151608i	0.818936	+	0.573885i	$0.194564\pi$
$938$	−12.6413			−0.412752
$939$	25.2825			0.825065
$940$	4.54327	−	7.86917i	0.148185	−	0.256664i
$941$	−6.94526	+	12.0295i	−0.226409	+	0.392152i	−0.956741	−	0.290940i	$-0.906032\pi$
$941$	−6.94526	+	12.0295i	−0.226409	+	0.392152i	0.730332	+	0.683092i	$0.239365\pi$
$942$	3.33211			0.108566
$943$	19.0636			0.620796
$944$	−6.65458	+	11.5261i	−0.216588	+	0.375142i
$945$	−0.500000	−	0.866025i	−0.0162650	−	0.0281718i
$946$	1.22263	−	2.11766i	0.0397512	−	0.0688510i
$947$	11.0300	+	19.1044i	0.358425	+	0.620811i	0.987698	−	0.156374i	$-0.0499804\pi$
$947$	11.0300	+	19.1044i	0.358425	+	0.620811i	−0.629273	+	0.777185i	$0.716647\pi$
$948$		0			0
$949$	−1.47855			−0.0479958
$950$	−16.1731	+	6.51398i	−0.524724	+	0.211341i
$951$	0.445262			0.0144386
$952$	3.93195	+	6.81034i	0.127435	+	0.220724i
$953$	−4.66789	−	8.08503i	−0.151208	−	0.261900i	0.780464	−	0.625201i	$-0.214983\pi$
$953$	−4.66789	−	8.08503i	−0.151208	−	0.261900i	−0.931672	+	0.363301i	$0.881650\pi$
$954$	4.32064	−	7.48356i	0.139886	−	0.242289i
$955$	1.43195	+	2.48021i	0.0463369	+	0.0802578i
$956$	3.17936	−	5.50682i	0.102828	−	0.178103i
$957$	4.89052			0.158088
$958$	−1.35873			−0.0438985
$959$	10.9752	−	19.0096i	0.354408	−	0.613853i
$960$	0.500000	−	0.866025i	0.0161374	−	0.0279508i
$961$	−30.8017			−0.993605
$962$	0.272195			0.00877593
$963$	4.54327	−	7.86917i	0.146405	−	0.253580i
$964$	4.86390	+	8.42453i	0.156656	+	0.271336i
$965$	3.36390	−	5.82645i	0.108288	−	0.187560i
$966$	3.43195	+	5.94431i	0.110421	+	0.191255i
$967$	−5.51848	−	9.55830i	−0.177462	−	0.307374i	0.763548	−	0.645751i	$-0.223456\pi$
$967$	−5.51848	−	9.55830i	−0.177462	−	0.307374i	−0.941011	+	0.338377i	$0.890122\pi$
$968$	−9.50517			−0.305508
$969$	4.80733	−	33.9392i	0.154434	−	1.09028i
$970$	3.55474			0.114136
$971$	10.5185	+	18.2185i	0.337554	+	0.584661i	0.983972	−	0.178323i	$-0.0570670\pi$
$971$	10.5185	+	18.2185i	0.337554	+	0.584661i	−0.646418	+	0.762984i	$0.723734\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−5.38868	+	9.33348i	−0.172753	+	0.299217i
$974$	−19.0865	−	33.0588i	−0.611572	−	1.05927i
$975$	0.445262	−	0.771216i	0.0142598	−	0.0246987i
$976$	5.77737			0.184929
$977$	−4.88685			−0.156344			−0.0781720	−	0.996940i	$-0.524908\pi$
$977$	−4.88685			−0.156344			−0.0781720	+	0.996940i	$0.524908\pi$
$978$	−9.32064	+	16.1438i	−0.298041	+	0.516222i
$979$	3.58469	−	6.20887i	0.114567	−	0.198436i
$980$	1.00000			0.0319438
$981$	−8.30916			−0.265291
$982$	17.7093	−	30.6734i	0.565127	−	0.978829i
$983$	27.0370	+	46.8294i	0.862345	+	1.49363i	0.869659	+	0.493653i	$0.164339\pi$
$983$	27.0370	+	46.8294i	0.862345	+	1.49363i	−0.00731373	+	0.999973i	$0.502328\pi$
$984$	−1.38868	+	2.40527i	−0.0442696	+	0.0766773i
$985$	−8.76590	−	15.1830i	−0.279305	−	0.483770i
$986$	−15.7278	−	27.2414i	−0.500875	−	0.867542i
$987$	−9.08653			−0.289228
$988$	0.764058	+	0.598281i	0.0243079	+	0.0190339i
$989$	−13.7278			−0.436519
$990$	0.611315	+	1.05883i	0.0194289	+	0.0336518i
$991$	−26.2463	−	45.4599i	−0.833741	−	1.44408i	−0.895052	−	0.445963i	$-0.852861\pi$
$991$	−26.2463	−	45.4599i	−0.833741	−	1.44408i	0.0613107	−	0.998119i	$-0.480472\pi$
$992$	0.222631	−	0.385608i	0.00706854	−	0.0122431i
$993$	−9.40717	−	16.2937i	−0.298527	−	0.517065i
$994$	5.65458	−	9.79402i	0.179352	−	0.310648i
$995$	−13.0865			−0.414871
$996$	−10.8639			−0.344236
$997$	26.3709	−	45.6758i	0.835175	−	1.44657i	−0.0587124	−	0.998275i	$-0.518699\pi$
$997$	26.3709	−	45.6758i	0.835175	−	1.44657i	0.893888	−	0.448291i	$-0.147967\pi$
$998$	13.7544	−	23.8234i	0.435389	−	0.754115i
$999$	1.22263			0.0386823

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.k.n.463.2	✓	6
3.2	odd	2		2394.2.o.t.1261.2		6
19.11	even	3	inner	798.2.k.n.505.2	yes	6
57.11	odd	6		2394.2.o.t.505.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.k.n.463.2	✓	6	1.1	even	1	trivial
798.2.k.n.505.2	yes	6	19.11	even	3	inner
2394.2.o.t.505.2		6	57.11	odd	6
2394.2.o.t.1261.2		6	3.2	odd	2

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} -1.22263 q^{11} -1.00000 q^{12} +(0.111315 - 0.192804i) q^{13} +(0.500000 + 0.866025i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.93195 - 6.81034i) q^{17} +1.00000 q^{18} +(4.04327 - 1.62849i) q^{19} +1.00000 q^{20} +(-0.500000 - 0.866025i) q^{21} +(0.611315 + 1.05883i) q^{22} +(3.43195 - 5.94431i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.00000 - 3.46410i) q^{25} -0.222631 q^{26} -1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(-2.00000 + 3.46410i) q^{29} -1.00000 q^{30} -0.445262 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.611315 - 1.05883i) q^{33} +(-3.93195 + 6.81034i) q^{34} +(0.500000 + 0.866025i) q^{35} +(-0.500000 - 0.866025i) q^{36} -1.22263 q^{37} +(-3.43195 - 2.68732i) q^{38} +0.222631 q^{39} +(-0.500000 - 0.866025i) q^{40} +(1.38868 + 2.40527i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(-1.00000 - 1.73205i) q^{43} +(0.611315 - 1.05883i) q^{44} +1.00000 q^{45} -6.86390 q^{46} +(4.54327 - 7.86917i) q^{47} +(0.500000 - 0.866025i) q^{48} +1.00000 q^{49} -4.00000 q^{50} +(3.93195 - 6.81034i) q^{51} +(0.111315 + 0.192804i) q^{52} +(4.32064 - 7.48356i) q^{53} +(0.500000 + 0.866025i) q^{54} +(0.611315 + 1.05883i) q^{55} -1.00000 q^{56} +(3.43195 + 2.68732i) q^{57} +4.00000 q^{58} +(-6.65458 - 11.5261i) q^{59} +(0.500000 + 0.866025i) q^{60} +(-2.88868 + 5.00335i) q^{61} +(0.222631 + 0.385608i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} -0.222631 q^{65} +(-0.611315 + 1.05883i) q^{66} +(-6.32064 + 10.9477i) q^{67} +7.86390 q^{68} +6.86390 q^{69} +(0.500000 - 0.866025i) q^{70} +(-5.65458 - 9.79402i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-3.32064 - 5.75151i) q^{73} +(0.611315 + 1.05883i) q^{74} +4.00000 q^{75} +(-0.611315 + 4.31582i) q^{76} +1.22263 q^{77} +(-0.111315 - 0.192804i) q^{78} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.38868 - 2.40527i) q^{82} +10.8639 q^{83} +1.00000 q^{84} +(-3.93195 + 6.81034i) q^{85} +(-1.00000 + 1.73205i) q^{86} -4.00000 q^{87} -1.22263 q^{88} +(-2.93195 + 5.07829i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-0.111315 + 0.192804i) q^{91} +(3.43195 + 5.94431i) q^{92} +(-0.222631 - 0.385608i) q^{93} -9.08653 q^{94} +(-3.43195 - 2.68732i) q^{95} -1.00000 q^{96} +(-1.77737 - 3.07849i) q^{97} +(-0.500000 - 0.866025i) q^{98} +(0.611315 - 1.05883i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 3 q^{6} - 6 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 3 * q^6 - 6 * q^7 + 6 * q^8 - 3 * q^9	\( 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 3 q^{6} - 6 q^{7} + 6 q^{8} - 3 q^{9} - 3 q^{10} - 6 q^{11} - 6 q^{12} + 3 q^{14} + 3 q^{15} - 3 q^{16} + 3 q^{17} + 6 q^{18} - 3 q^{19} + 6 q^{20} - 3 q^{21} + 3 q^{22} - 6 q^{23} + 3 q^{24} + 12 q^{25} - 6 q^{27} + 3 q^{28} - 12 q^{29} - 6 q^{30} - 3 q^{32} - 3 q^{33} + 3 q^{34} + 3 q^{35} - 3 q^{36} - 6 q^{37} + 6 q^{38} - 3 q^{40} + 9 q^{41} - 3 q^{42} - 6 q^{43} + 3 q^{44} + 6 q^{45} + 12 q^{46} + 3 q^{48} + 6 q^{49} - 24 q^{50} - 3 q^{51} + 3 q^{54} + 3 q^{55} - 6 q^{56} - 6 q^{57} + 24 q^{58} - 12 q^{59} + 3 q^{60} - 18 q^{61} + 3 q^{63} + 6 q^{64} - 3 q^{66} - 12 q^{67} - 6 q^{68} - 12 q^{69} + 3 q^{70} - 6 q^{71} - 3 q^{72} + 6 q^{73} + 3 q^{74} + 24 q^{75} - 3 q^{76} + 6 q^{77} - 3 q^{80} - 3 q^{81} + 9 q^{82} + 12 q^{83} + 6 q^{84} + 3 q^{85} - 6 q^{86} - 24 q^{87} - 6 q^{88} + 9 q^{89} - 3 q^{90} - 6 q^{92} + 6 q^{95} - 6 q^{96} - 12 q^{97} - 3 q^{98} + 3 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 3 * q^6 - 6 * q^7 + 6 * q^8 - 3 * q^9 - 3 * q^10 - 6 * q^11 - 6 * q^12 + 3 * q^14 + 3 * q^15 - 3 * q^16 + 3 * q^17 + 6 * q^18 - 3 * q^19 + 6 * q^20 - 3 * q^21 + 3 * q^22 - 6 * q^23 + 3 * q^24 + 12 * q^25 - 6 * q^27 + 3 * q^28 - 12 * q^29 - 6 * q^30 - 3 * q^32 - 3 * q^33 + 3 * q^34 + 3 * q^35 - 3 * q^36 - 6 * q^37 + 6 * q^38 - 3 * q^40 + 9 * q^41 - 3 * q^42 - 6 * q^43 + 3 * q^44 + 6 * q^45 + 12 * q^46 + 3 * q^48 + 6 * q^49 - 24 * q^50 - 3 * q^51 + 3 * q^54 + 3 * q^55 - 6 * q^56 - 6 * q^57 + 24 * q^58 - 12 * q^59 + 3 * q^60 - 18 * q^61 + 3 * q^63 + 6 * q^64 - 3 * q^66 - 12 * q^67 - 6 * q^68 - 12 * q^69 + 3 * q^70 - 6 * q^71 - 3 * q^72 + 6 * q^73 + 3 * q^74 + 24 * q^75 - 3 * q^76 + 6 * q^77 - 3 * q^80 - 3 * q^81 + 9 * q^82 + 12 * q^83 + 6 * q^84 + 3 * q^85 - 6 * q^86 - 24 * q^87 - 6 * q^88 + 9 * q^89 - 3 * q^90 - 6 * q^92 + 6 * q^95 - 6 * q^96 - 12 * q^97 - 3 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

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