LMFDB - Embedded newform 1690.2.l.g.1161.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1690,2,Mod(361,1690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1690, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("1690.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.l (of order $6$, degree $2$, not 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:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1161.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1690.1161
Dual form			1690.2.l.g.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.366025 + 0.633975i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-0.633975 + 0.366025i) q^{6} +(-2.59808 + 1.50000i) q^{7} +1.00000i q^{8} +(1.23205 + 2.13397i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.366025 + 0.633975i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-0.633975 + 0.366025i) q^{6} +(-2.59808 + 1.50000i) q^{7} +1.00000i q^{8} +(1.23205 + 2.13397i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-2.59808 - 1.50000i) q^{11} -0.732051 q^{12} -3.00000 q^{14} +(-0.633975 - 0.366025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-4.09808 - 7.09808i) q^{17} +2.46410i q^{18} +(0.401924 - 0.232051i) q^{19} +(-0.866025 + 0.500000i) q^{20} -2.19615i q^{21} +(-1.50000 - 2.59808i) q^{22} +(-4.73205 + 8.19615i) q^{23} +(-0.633975 - 0.366025i) q^{24} -1.00000 q^{25} -4.00000 q^{27} +(-2.59808 - 1.50000i) q^{28} +(1.26795 - 2.19615i) q^{29} +(-0.366025 - 0.633975i) q^{30} -4.73205i q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.90192 - 1.09808i) q^{33} -8.19615i q^{34} +(-1.50000 - 2.59808i) q^{35} +(-1.23205 + 2.13397i) q^{36} +(0.696152 + 0.401924i) q^{37} +0.464102 q^{38} -1.00000 q^{40} +(9.00000 + 5.19615i) q^{41} +(1.09808 - 1.90192i) q^{42} +(-1.00000 - 1.73205i) q^{43} -3.00000i q^{44} +(-2.13397 + 1.23205i) q^{45} +(-8.19615 + 4.73205i) q^{46} -3.00000i q^{47} +(-0.366025 - 0.633975i) q^{48} +(1.00000 - 1.73205i) q^{49} +(-0.866025 - 0.500000i) q^{50} +6.00000 q^{51} +0.464102 q^{53} +(-3.46410 - 2.00000i) q^{54} +(1.50000 - 2.59808i) q^{55} +(-1.50000 - 2.59808i) q^{56} +0.339746i q^{57} +(2.19615 - 1.26795i) q^{58} +(-9.00000 + 5.19615i) q^{59} -0.732051i q^{60} +(-3.09808 - 5.36603i) q^{61} +(2.36603 - 4.09808i) q^{62} +(-6.40192 - 3.69615i) q^{63} -1.00000 q^{64} +2.19615 q^{66} +(4.09808 - 7.09808i) q^{68} +(-3.46410 - 6.00000i) q^{69} -3.00000i q^{70} +(5.19615 - 3.00000i) q^{71} +(-2.13397 + 1.23205i) q^{72} -11.6603i q^{73} +(0.401924 + 0.696152i) q^{74} +(0.366025 - 0.633975i) q^{75} +(0.401924 + 0.232051i) q^{76} +9.00000 q^{77} -4.19615 q^{79} +(-0.866025 - 0.500000i) q^{80} +(-2.23205 + 3.86603i) q^{81} +(5.19615 + 9.00000i) q^{82} +8.19615i q^{83} +(1.90192 - 1.09808i) q^{84} +(7.09808 - 4.09808i) q^{85} -2.00000i q^{86} +(0.928203 + 1.60770i) q^{87} +(1.50000 - 2.59808i) q^{88} +(-5.89230 - 3.40192i) q^{89} -2.46410 q^{90} -9.46410 q^{92} +(3.00000 + 1.73205i) q^{93} +(1.50000 - 2.59808i) q^{94} +(0.232051 + 0.401924i) q^{95} -0.732051i q^{96} +(-7.90192 + 4.56218i) q^{97} +(1.73205 - 1.00000i) q^{98} -7.39230i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} - 6 q^{6} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^6 - 2 * q^9	$ 4 q + 2 q^{3} + 2 q^{4} - 6 q^{6} - 2 q^{9} - 2 q^{10} + 4 q^{12} - 12 q^{14} - 6 q^{15} - 2 q^{16} - 6 q^{17} + 12 q^{19} - 6 q^{22} - 12 q^{23} - 6 q^{24} - 4 q^{25} - 16 q^{27} + 12 q^{29} + 2 q^{30} + 18 q^{33} - 6 q^{35} + 2 q^{36} - 18 q^{37} - 12 q^{38} - 4 q^{40} + 36 q^{41} - 6 q^{42} - 4 q^{43} - 12 q^{45} - 12 q^{46} + 2 q^{48} + 4 q^{49} + 24 q^{51} - 12 q^{53} + 6 q^{55} - 6 q^{56} - 12 q^{58} - 36 q^{59} - 2 q^{61} + 6 q^{62} - 36 q^{63} - 4 q^{64} - 12 q^{66} + 6 q^{68} - 12 q^{72} + 12 q^{74} - 2 q^{75} + 12 q^{76} + 36 q^{77} + 4 q^{79} - 2 q^{81} + 18 q^{84} + 18 q^{85} - 24 q^{87} + 6 q^{88} + 18 q^{89} + 4 q^{90} - 24 q^{92} + 12 q^{93} + 6 q^{94} - 6 q^{95} - 42 q^{97}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^6 - 2 * q^9 - 2 * q^10 + 4 * q^12 - 12 * q^14 - 6 * q^15 - 2 * q^16 - 6 * q^17 + 12 * q^19 - 6 * q^22 - 12 * q^23 - 6 * q^24 - 4 * q^25 - 16 * q^27 + 12 * q^29 + 2 * q^30 + 18 * q^33 - 6 * q^35 + 2 * q^36 - 18 * q^37 - 12 * q^38 - 4 * q^40 + 36 * q^41 - 6 * q^42 - 4 * q^43 - 12 * q^45 - 12 * q^46 + 2 * q^48 + 4 * q^49 + 24 * q^51 - 12 * q^53 + 6 * q^55 - 6 * q^56 - 12 * q^58 - 36 * q^59 - 2 * q^61 + 6 * q^62 - 36 * q^63 - 4 * q^64 - 12 * q^66 + 6 * q^68 - 12 * q^72 + 12 * q^74 - 2 * q^75 + 12 * q^76 + 36 * q^77 + 4 * q^79 - 2 * q^81 + 18 * q^84 + 18 * q^85 - 24 * q^87 + 6 * q^88 + 18 * q^89 + 4 * q^90 - 24 * q^92 + 12 * q^93 + 6 * q^94 - 6 * q^95 - 42 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.366025	+	0.633975i	−0.211325	+	0.366025i	−0.952129	−	0.305695i	$-0.901111\pi$
$3$	−0.366025	+	0.633975i	−0.211325	+	0.366025i	0.740805	+	0.671721i	$0.234444\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−0.633975	+	0.366025i	−0.258819	+	0.149429i
$7$	−2.59808	+	1.50000i	−0.981981	+	0.566947i	−0.902867	−	0.429919i	$-0.858542\pi$
$7$	−2.59808	+	1.50000i	−0.981981	+	0.566947i	−0.0791130	+	0.996866i	$0.525209\pi$
$8$			1.00000i			0.353553i
$9$	1.23205	+	2.13397i	0.410684	+	0.711325i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−2.59808	−	1.50000i	−0.783349	−	0.452267i	0.0542666	−	0.998526i	$-0.482718\pi$
$11$	−2.59808	−	1.50000i	−0.783349	−	0.452267i	−0.837616	+	0.546259i	$0.816051\pi$
$12$	−0.732051			−0.211325
$13$		0			0
$13$		0			0
$14$	−3.00000			−0.801784
$15$	−0.633975	−	0.366025i	−0.163692	−	0.0945074i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.09808	−	7.09808i	−0.993929	−	1.72154i	−0.592244	−	0.805759i	$-0.701758\pi$
$17$	−4.09808	−	7.09808i	−0.993929	−	1.72154i	−0.401685	−	0.915778i	$-0.631575\pi$
$18$			2.46410i			0.580794i
$19$	0.401924	−	0.232051i	0.0922076	−	0.0532361i	−0.453187	−	0.891415i	$-0.649713\pi$
$19$	0.401924	−	0.232051i	0.0922076	−	0.0532361i	0.545395	+	0.838179i	$0.316380\pi$
$20$	−0.866025	+	0.500000i	−0.193649	+	0.111803i
$21$		−	2.19615i		−	0.479240i
$22$	−1.50000	−	2.59808i	−0.319801	−	0.553912i
$23$	−4.73205	+	8.19615i	−0.986701	+	1.70902i	−0.352581	+	0.935781i	$0.614696\pi$
$23$	−4.73205	+	8.19615i	−0.986701	+	1.70902i	−0.634120	+	0.773234i	$0.718638\pi$
$24$	−0.633975	−	0.366025i	−0.129410	−	0.0747146i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−4.00000			−0.769800
$28$	−2.59808	−	1.50000i	−0.490990	−	0.283473i
$29$	1.26795	−	2.19615i	0.235452	−	0.407815i	−0.723952	−	0.689851i	$-0.757676\pi$
$29$	1.26795	−	2.19615i	0.235452	−	0.407815i	0.959404	+	0.282035i	$0.0910095\pi$
$30$	−0.366025	−	0.633975i	−0.0668268	−	0.115747i
$31$		−	4.73205i		−	0.849901i	−0.905216	−	0.424951i	$-0.860291\pi$
$31$		−	4.73205i		−	0.849901i	0.905216	−	0.424951i	$-0.139709\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	1.90192	−	1.09808i	0.331082	−	0.191151i
$34$		−	8.19615i		−	1.40563i
$35$	−1.50000	−	2.59808i	−0.253546	−	0.439155i
$36$	−1.23205	+	2.13397i	−0.205342	+	0.355662i
$37$	0.696152	+	0.401924i	0.114447	+	0.0660759i	0.556131	−	0.831095i	$-0.312285\pi$
$37$	0.696152	+	0.401924i	0.114447	+	0.0660759i	−0.441684	+	0.897171i	$0.645619\pi$
$38$	0.464102			0.0752872
$39$		0			0
$40$	−1.00000			−0.158114
$41$	9.00000	+	5.19615i	1.40556	+	0.811503i	0.994956	−	0.100309i	$-0.0319833\pi$
$41$	9.00000	+	5.19615i	1.40556	+	0.811503i	0.410608	+	0.911812i	$0.365317\pi$
$42$	1.09808	−	1.90192i	0.169437	−	0.293473i
$43$	−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	$0.882065\pi$
$44$		−	3.00000i		−	0.452267i
$45$	−2.13397	+	1.23205i	−0.318114	+	0.183663i
$46$	−8.19615	+	4.73205i	−1.20846	+	0.697703i
$47$		−	3.00000i		−	0.437595i	−0.975770	−	0.218797i	$-0.929787\pi$
$47$		−	3.00000i		−	0.437595i	0.975770	−	0.218797i	$-0.0702134\pi$
$48$	−0.366025	−	0.633975i	−0.0528312	−	0.0915064i
$49$	1.00000	−	1.73205i	0.142857	−	0.247436i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$	6.00000			0.840168
$52$		0			0
$53$	0.464102			0.0637493			0.0318746	−	0.999492i	$-0.489852\pi$
$53$	0.464102			0.0637493			0.0318746	+	0.999492i	$0.489852\pi$
$54$	−3.46410	−	2.00000i	−0.471405	−	0.272166i
$55$	1.50000	−	2.59808i	0.202260	−	0.350325i
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$			0.339746i			0.0450005i
$58$	2.19615	−	1.26795i	0.288369	−	0.166490i
$59$	−9.00000	+	5.19615i	−1.17170	+	0.676481i	−0.954080	−	0.299552i	$-0.903163\pi$
$59$	−9.00000	+	5.19615i	−1.17170	+	0.676481i	−0.217620	+	0.976034i	$0.569829\pi$
$60$		−	0.732051i		−	0.0945074i
$61$	−3.09808	−	5.36603i	−0.396668	−	0.687049i	0.596645	−	0.802506i	$-0.296500\pi$
$61$	−3.09808	−	5.36603i	−0.396668	−	0.687049i	−0.993313	+	0.115456i	$0.963167\pi$
$62$	2.36603	−	4.09808i	0.300486	−	0.520456i
$63$	−6.40192	−	3.69615i	−0.806567	−	0.465671i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	2.19615			0.270328
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$	4.09808	−	7.09808i	0.496965	−	0.860768i
$69$	−3.46410	−	6.00000i	−0.417029	−	0.722315i
$70$		−	3.00000i		−	0.358569i
$71$	5.19615	−	3.00000i	0.616670	−	0.356034i	−0.158901	−	0.987294i	$-0.550795\pi$
$71$	5.19615	−	3.00000i	0.616670	−	0.356034i	0.775571	+	0.631260i	$0.217462\pi$
$72$	−2.13397	+	1.23205i	−0.251491	+	0.145199i
$73$		−	11.6603i		−	1.36473i	−0.731012	−	0.682365i	$-0.760952\pi$
$73$		−	11.6603i		−	1.36473i	0.731012	−	0.682365i	$-0.239048\pi$
$74$	0.401924	+	0.696152i	0.0467227	+	0.0809261i
$75$	0.366025	−	0.633975i	0.0422650	−	0.0732051i
$76$	0.401924	+	0.232051i	0.0461038	+	0.0266181i
$77$	9.00000			1.02565
$78$		0			0
$79$	−4.19615			−0.472104			−0.236052	−	0.971740i	$-0.575854\pi$
$79$	−4.19615			−0.472104			−0.236052	+	0.971740i	$0.575854\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	−2.23205	+	3.86603i	−0.248006	+	0.429558i
$82$	5.19615	+	9.00000i	0.573819	+	0.993884i
$83$			8.19615i			0.899645i	0.893118	+	0.449822i	$0.148513\pi$
$83$			8.19615i			0.899645i	−0.893118	+	0.449822i	$0.851487\pi$
$84$	1.90192	−	1.09808i	0.207517	−	0.119810i
$85$	7.09808	−	4.09808i	0.769894	−	0.444499i
$86$		−	2.00000i		−	0.215666i
$87$	0.928203	+	1.60770i	0.0995138	+	0.172363i
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	−5.89230	−	3.40192i	−0.624583	−	0.360603i	0.154068	−	0.988060i	$-0.450762\pi$
$89$	−5.89230	−	3.40192i	−0.624583	−	0.360603i	−0.778651	+	0.627457i	$0.784096\pi$
$90$	−2.46410			−0.259739
$91$		0			0
$92$	−9.46410			−0.986701
$93$	3.00000	+	1.73205i	0.311086	+	0.179605i
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$	0.232051	+	0.401924i	0.0238079	+	0.0412365i
$96$		−	0.732051i		−	0.0747146i
$97$	−7.90192	+	4.56218i	−0.802319	+	0.463219i	−0.844281	−	0.535900i	$-0.819972\pi$
$97$	−7.90192	+	4.56218i	−0.802319	+	0.463219i	0.0419625	+	0.999119i	$0.486639\pi$
$98$	1.73205	−	1.00000i	0.174964	−	0.101015i
$99$		−	7.39230i		−	0.742955i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−5.36603	+	9.29423i	−0.533939	+	0.924810i	0.465274	+	0.885167i	$0.345956\pi$
$101$	−5.36603	+	9.29423i	−0.533939	+	0.924810i	−0.999214	+	0.0396438i	$0.987378\pi$
$102$	5.19615	+	3.00000i	0.514496	+	0.297044i
$103$	−9.19615			−0.906124			−0.453062	−	0.891479i	$-0.649668\pi$
$103$	−9.19615			−0.906124			−0.453062	+	0.891479i	$0.649668\pi$
$104$		0			0
$105$	2.19615			0.214323
$106$	0.401924	+	0.232051i	0.0390383	+	0.0225388i
$107$	−8.83013	+	15.2942i	−0.853641	+	1.47855i	0.0242598	+	0.999706i	$0.492277\pi$
$107$	−8.83013	+	15.2942i	−0.853641	+	1.47855i	−0.877900	+	0.478843i	$0.841056\pi$
$108$	−2.00000	−	3.46410i	−0.192450	−	0.333333i
$109$			8.53590i			0.817591i	0.912626	+	0.408795i	$0.134051\pi$
$109$			8.53590i			0.817591i	−0.912626	+	0.408795i	$0.865949\pi$
$110$	2.59808	−	1.50000i	0.247717	−	0.143019i
$111$	−0.509619	+	0.294229i	−0.0483709	+	0.0279269i
$112$		−	3.00000i		−	0.283473i
$113$	−3.46410	−	6.00000i	−0.325875	−	0.564433i	0.655814	−	0.754923i	$-0.272326\pi$
$113$	−3.46410	−	6.00000i	−0.325875	−	0.564433i	−0.981689	+	0.190490i	$0.938992\pi$
$114$	−0.169873	+	0.294229i	−0.0159101	+	0.0275570i
$115$	−8.19615	−	4.73205i	−0.764295	−	0.441266i
$116$	2.53590			0.235452
$117$		0			0
$118$	−10.3923			−0.956689
$119$	21.2942	+	12.2942i	1.95204	+	1.12701i
$120$	0.366025	−	0.633975i	0.0334134	−	0.0578737i
$121$	−1.00000	−	1.73205i	−0.0909091	−	0.157459i
$122$		−	6.19615i		−	0.560973i
$123$	−6.58846	+	3.80385i	−0.594061	+	0.342981i
$124$	4.09808	−	2.36603i	0.368018	−	0.212475i
$125$		−	1.00000i		−	0.0894427i
$126$	−3.69615	−	6.40192i	−0.329279	−	0.570329i
$127$	−5.40192	+	9.35641i	−0.479343	+	0.830247i	−0.999719	−	0.0236904i	$-0.992458\pi$
$127$	−5.40192	+	9.35641i	−0.479343	+	0.830247i	0.520376	+	0.853937i	$0.325792\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	1.46410			0.128907
$130$		0			0
$131$	6.12436			0.535087			0.267544	−	0.963546i	$-0.413788\pi$
$131$	6.12436			0.535087			0.267544	+	0.963546i	$0.413788\pi$
$132$	1.90192	+	1.09808i	0.165541	+	0.0955753i
$133$	−0.696152	+	1.20577i	−0.0603641	+	0.104554i
$134$		0			0
$135$		−	4.00000i		−	0.344265i
$136$	7.09808	−	4.09808i	0.608655	−	0.351407i
$137$	−1.90192	+	1.09808i	−0.162492	+	0.0938150i	−0.579041	−	0.815298i	$-0.696573\pi$
$137$	−1.90192	+	1.09808i	−0.162492	+	0.0938150i	0.416549	+	0.909113i	$0.363240\pi$
$138$		−	6.92820i		−	0.589768i
$139$	−0.598076	−	1.03590i	−0.0507282	−	0.0878638i	0.839546	−	0.543288i	$-0.182821\pi$
$139$	−0.598076	−	1.03590i	−0.0507282	−	0.0878638i	−0.890274	+	0.455424i	$0.849488\pi$
$140$	1.50000	−	2.59808i	0.126773	−	0.219578i
$141$	1.90192	+	1.09808i	0.160171	+	0.0924747i
$142$	6.00000			0.503509
$143$		0			0
$144$	−2.46410			−0.205342
$145$	2.19615	+	1.26795i	0.182381	+	0.105297i
$146$	5.83013	−	10.0981i	0.482505	−	0.835723i
$147$	0.732051	+	1.26795i	0.0603785	+	0.104579i
$148$			0.803848i			0.0660759i
$149$	−5.19615	+	3.00000i	−0.425685	+	0.245770i	−0.697507	−	0.716578i	$-0.745707\pi$
$149$	−5.19615	+	3.00000i	−0.425685	+	0.245770i	0.271821	+	0.962348i	$0.412374\pi$
$150$	0.633975	−	0.366025i	0.0517638	−	0.0298858i
$151$			23.6603i			1.92544i	0.270492	+	0.962722i	$0.412813\pi$
$151$			23.6603i			1.92544i	−0.270492	+	0.962722i	$0.587187\pi$
$152$	0.232051	+	0.401924i	0.0188218	+	0.0326003i
$153$	10.0981	−	17.4904i	0.816381	−	1.41401i
$154$	7.79423	+	4.50000i	0.628077	+	0.362620i
$155$	4.73205			0.380087
$156$		0			0
$157$	−13.0000			−1.03751			−0.518756	−	0.854922i	$-0.673605\pi$
$157$	−13.0000			−1.03751			−0.518756	+	0.854922i	$0.673605\pi$
$158$	−3.63397	−	2.09808i	−0.289103	−	0.166914i
$159$	−0.169873	+	0.294229i	−0.0134718	+	0.0233338i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$		−	28.3923i		−	2.23763i
$162$	−3.86603	+	2.23205i	−0.303744	+	0.175366i
$163$	9.29423	−	5.36603i	0.727980	−	0.420300i	−0.0897026	−	0.995969i	$-0.528592\pi$
$163$	9.29423	−	5.36603i	0.727980	−	0.420300i	0.817683	+	0.575669i	$0.195258\pi$
$164$			10.3923i			0.811503i
$165$	1.09808	+	1.90192i	0.0854851	+	0.148065i
$166$	−4.09808	+	7.09808i	−0.318072	+	0.550918i
$167$	−2.59808	−	1.50000i	−0.201045	−	0.116073i	0.396098	−	0.918208i	$-0.370364\pi$
$167$	−2.59808	−	1.50000i	−0.201045	−	0.116073i	−0.597143	+	0.802135i	$0.703697\pi$
$168$	2.19615			0.169437
$169$		0			0
$170$	8.19615			0.628616
$171$	0.990381	+	0.571797i	0.0757363	+	0.0437264i
$172$	1.00000	−	1.73205i	0.0762493	−	0.132068i
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	0.996544	+	0.0830722i	$0.0264732\pi$
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	−0.426329	+	0.904568i	$0.640193\pi$
$174$			1.85641i			0.140734i
$175$	2.59808	−	1.50000i	0.196396	−	0.113389i
$176$	2.59808	−	1.50000i	0.195837	−	0.113067i
$177$		−	7.60770i		−	0.571829i
$178$	−3.40192	−	5.89230i	−0.254985	−	0.441647i
$179$	4.73205	−	8.19615i	0.353690	−	0.612609i	−0.633203	−	0.773986i	$-0.718260\pi$
$179$	4.73205	−	8.19615i	0.353690	−	0.612609i	0.986893	+	0.161377i	$0.0515934\pi$
$180$	−2.13397	−	1.23205i	−0.159057	−	0.0918316i
$181$	14.5885			1.08435			0.542176	−	0.840265i	$-0.317601\pi$
$181$	14.5885			1.08435			0.542176	+	0.840265i	$0.317601\pi$
$182$		0			0
$183$	4.53590			0.335303
$184$	−8.19615	−	4.73205i	−0.604228	−	0.348851i
$185$	−0.401924	+	0.696152i	−0.0295500	+	0.0511821i
$186$	1.73205	+	3.00000i	0.127000	+	0.219971i
$187$			24.5885i			1.79809i
$188$	2.59808	−	1.50000i	0.189484	−	0.109399i
$189$	10.3923	−	6.00000i	0.755929	−	0.436436i
$190$			0.464102i			0.0336695i
$191$	11.3660	+	19.6865i	0.822417	+	1.42447i	0.903878	+	0.427791i	$0.140708\pi$
$191$	11.3660	+	19.6865i	0.822417	+	1.42447i	−0.0814609	+	0.996677i	$0.525959\pi$
$192$	0.366025	−	0.633975i	0.0264156	−	0.0457532i
$193$	14.1962	+	8.19615i	1.02186	+	0.589972i	0.914643	−	0.404263i	$-0.132472\pi$
$193$	14.1962	+	8.19615i	1.02186	+	0.589972i	0.107219	+	0.994235i	$0.465805\pi$
$194$	−9.12436			−0.655091
$195$		0			0
$196$	2.00000			0.142857
$197$	−18.6962	−	10.7942i	−1.33205	−	0.769057i	−0.346433	−	0.938075i	$-0.612607\pi$
$197$	−18.6962	−	10.7942i	−1.33205	−	0.769057i	−0.985613	+	0.169018i	$0.945940\pi$
$198$	3.69615	−	6.40192i	0.262674	−	0.454965i
$199$	3.19615	+	5.53590i	0.226569	+	0.392429i	0.956789	−	0.290783i	$-0.0939157\pi$
$199$	3.19615	+	5.53590i	0.226569	+	0.392429i	−0.730220	+	0.683212i	$0.760582\pi$
$200$		−	1.00000i		−	0.0707107i
$201$		0			0
$202$	−9.29423	+	5.36603i	−0.653940	+	0.377552i
$203$			7.60770i			0.533956i
$204$	3.00000	+	5.19615i	0.210042	+	0.363803i
$205$	−5.19615	+	9.00000i	−0.362915	+	0.628587i
$206$	−7.96410	−	4.59808i	−0.554885	−	0.320363i
$207$	−23.3205			−1.62089
$208$		0			0
$209$	−1.39230			−0.0963077
$210$	1.90192	+	1.09808i	0.131245	+	0.0757745i
$211$	8.79423	−	15.2321i	0.605420	−	1.04862i	−0.386565	−	0.922262i	$-0.626339\pi$
$211$	8.79423	−	15.2321i	0.605420	−	1.04862i	0.991985	−	0.126356i	$-0.0403280\pi$
$212$	0.232051	+	0.401924i	0.0159373	+	0.0276042i
$213$			4.39230i			0.300956i
$214$	−15.2942	+	8.83013i	−1.04549	+	0.603615i
$215$	1.73205	−	1.00000i	0.118125	−	0.0681994i
$216$		−	4.00000i		−	0.272166i
$217$	7.09808	+	12.2942i	0.481849	+	0.834587i
$218$	−4.26795	+	7.39230i	−0.289062	+	0.500670i
$219$	7.39230	+	4.26795i	0.499526	+	0.288401i
$220$	3.00000			0.202260
$221$		0			0
$222$	−0.588457			−0.0394947
$223$	5.59808	+	3.23205i	0.374875	+	0.216434i	0.675586	−	0.737281i	$-0.263891\pi$
$223$	5.59808	+	3.23205i	0.374875	+	0.216434i	−0.300711	+	0.953715i	$0.597224\pi$
$224$	1.50000	−	2.59808i	0.100223	−	0.173591i
$225$	−1.23205	−	2.13397i	−0.0821367	−	0.142265i
$226$		−	6.92820i		−	0.460857i
$227$	−14.1962	+	8.19615i	−0.942232	+	0.543998i	−0.890659	−	0.454672i	$-0.849757\pi$
$227$	−14.1962	+	8.19615i	−0.942232	+	0.543998i	−0.0515725	+	0.998669i	$0.516423\pi$
$228$	−0.294229	+	0.169873i	−0.0194858	+	0.0112501i
$229$			1.26795i			0.0837884i	0.999122	+	0.0418942i	$0.0133392\pi$
$229$			1.26795i			0.0837884i	−0.999122	+	0.0418942i	$0.986661\pi$
$230$	−4.73205	−	8.19615i	−0.312022	−	0.540438i
$231$	−3.29423	+	5.70577i	−0.216744	+	0.375412i
$232$	2.19615	+	1.26795i	0.144184	+	0.0832449i
$233$	4.73205			0.310007			0.155003	−	0.987914i	$-0.450461\pi$
$233$	4.73205			0.310007			0.155003	+	0.987914i	$0.450461\pi$
$234$		0			0
$235$	3.00000			0.195698
$236$	−9.00000	−	5.19615i	−0.585850	−	0.338241i
$237$	1.53590	−	2.66025i	0.0997673	−	0.172802i
$238$	12.2942	+	21.2942i	0.796916	+	1.38030i
$239$		−	2.19615i		−	0.142057i	−0.997474	−	0.0710286i	$-0.977372\pi$
$239$		−	2.19615i		−	0.142057i	0.997474	−	0.0710286i	$-0.0226282\pi$
$240$	0.633975	−	0.366025i	0.0409229	−	0.0236268i
$241$	7.50000	−	4.33013i	0.483117	−	0.278928i	−0.238597	−	0.971119i	$-0.576688\pi$
$241$	7.50000	−	4.33013i	0.483117	−	0.278928i	0.721715	+	0.692191i	$0.243354\pi$
$242$		−	2.00000i		−	0.128565i
$243$	−7.63397	−	13.2224i	−0.489720	−	0.848219i
$244$	3.09808	−	5.36603i	0.198334	−	0.343525i
$245$	1.73205	+	1.00000i	0.110657	+	0.0638877i
$246$	−7.60770			−0.485049
$247$		0			0
$248$	4.73205			0.300486
$249$	−5.19615	−	3.00000i	−0.329293	−	0.190117i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−8.59808	−	14.8923i	−0.542706	−	0.939994i	−0.998747	−	0.0500355i	$-0.984067\pi$
$251$	−8.59808	−	14.8923i	−0.542706	−	0.939994i	0.456042	−	0.889958i	$-0.349267\pi$
$252$		−	7.39230i		−	0.465671i
$253$	24.5885	−	14.1962i	1.54586	−	0.892504i
$254$	−9.35641	+	5.40192i	−0.587073	+	0.338947i
$255$			6.00000i			0.375735i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.92820	−	12.0000i	0.432169	−	0.748539i	−0.564890	−	0.825166i	$-0.691082\pi$
$257$	6.92820	−	12.0000i	0.432169	−	0.748539i	0.997060	+	0.0766265i	$0.0244149\pi$
$258$	1.26795	+	0.732051i	0.0789391	+	0.0455755i
$259$	−2.41154			−0.149846
$260$		0			0
$261$	6.24871			0.386786
$262$	5.30385	+	3.06218i	0.327673	+	0.189182i
$263$	−1.79423	+	3.10770i	−0.110637	+	0.191629i	−0.916027	−	0.401116i	$-0.868622\pi$
$263$	−1.79423	+	3.10770i	−0.110637	+	0.191629i	0.805390	+	0.592745i	$0.201956\pi$
$264$	1.09808	+	1.90192i	0.0675819	+	0.117055i
$265$			0.464102i			0.0285095i
$266$	−1.20577	+	0.696152i	−0.0739306	+	0.0426838i
$267$	4.31347	−	2.49038i	0.263980	−	0.152409i
$268$		0			0
$269$	13.5622	+	23.4904i	0.826901	+	1.43223i	0.900458	+	0.434943i	$0.143231\pi$
$269$	13.5622	+	23.4904i	0.826901	+	1.43223i	−0.0735575	+	0.997291i	$0.523435\pi$
$270$	2.00000	−	3.46410i	0.121716	−	0.210819i
$271$	−8.19615	−	4.73205i	−0.497881	−	0.287452i	0.229957	−	0.973201i	$-0.426141\pi$
$271$	−8.19615	−	4.73205i	−0.497881	−	0.287452i	−0.727838	+	0.685749i	$0.759475\pi$
$272$	8.19615			0.496965
$273$		0			0
$274$	−2.19615			−0.132674
$275$	2.59808	+	1.50000i	0.156670	+	0.0904534i
$276$	3.46410	−	6.00000i	0.208514	−	0.361158i
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	0.880656	−	0.473757i	$-0.157103\pi$
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	−0.850613	+	0.525792i	$0.823769\pi$
$278$		−	1.19615i		−	0.0717405i
$279$	10.0981	−	5.83013i	0.604556	−	0.349041i
$280$	2.59808	−	1.50000i	0.155265	−	0.0896421i
$281$			10.3923i			0.619953i	0.950744	+	0.309976i	$0.100321\pi$
$281$			10.3923i			0.619953i	−0.950744	+	0.309976i	$0.899679\pi$
$282$	1.09808	+	1.90192i	0.0653895	+	0.113258i
$283$	4.80385	−	8.32051i	0.285559	−	0.494603i	−0.687186	−	0.726482i	$-0.741154\pi$
$283$	4.80385	−	8.32051i	0.285559	−	0.494603i	0.972745	+	0.231879i	$0.0744874\pi$
$284$	5.19615	+	3.00000i	0.308335	+	0.178017i
$285$	−0.339746			−0.0201248
$286$		0			0
$287$	−31.1769			−1.84032
$288$	−2.13397	−	1.23205i	−0.125746	−	0.0725993i
$289$	−25.0885	+	43.4545i	−1.47579	+	2.55615i
$290$	1.26795	+	2.19615i	0.0744565	+	0.128963i
$291$		−	6.67949i		−	0.391559i
$292$	10.0981	−	5.83013i	0.590945	−	0.341182i
$293$	−9.69615	+	5.59808i	−0.566455	+	0.327043i	−0.755732	−	0.654881i	$-0.772719\pi$
$293$	−9.69615	+	5.59808i	−0.566455	+	0.327043i	0.189277	+	0.981924i	$0.439386\pi$
$294$			1.46410i			0.0853881i
$295$	−5.19615	−	9.00000i	−0.302532	−	0.524000i
$296$	−0.401924	+	0.696152i	−0.0233613	+	0.0404630i
$297$	10.3923	+	6.00000i	0.603023	+	0.348155i
$298$	−6.00000			−0.347571
$299$		0			0
$300$	0.732051			0.0422650
$301$	5.19615	+	3.00000i	0.299501	+	0.172917i
$302$	−11.8301	+	20.4904i	−0.680747	+	1.17909i
$303$	−3.92820	−	6.80385i	−0.225669	−	0.390871i
$304$			0.464102i			0.0266181i
$305$	5.36603	−	3.09808i	0.307258	−	0.177395i
$306$	17.4904	−	10.0981i	0.999859	−	0.577269i
$307$			27.4641i			1.56746i	0.621102	+	0.783730i	$0.286685\pi$
$307$			27.4641i			1.56746i	−0.621102	+	0.783730i	$0.713315\pi$
$308$	4.50000	+	7.79423i	0.256411	+	0.444117i
$309$	3.36603	−	5.83013i	0.191486	−	0.331664i
$310$	4.09808	+	2.36603i	0.232755	+	0.134381i
$311$	−9.12436			−0.517395			−0.258697	−	0.965958i	$-0.583293\pi$
$311$	−9.12436			−0.517395			−0.258697	+	0.965958i	$0.583293\pi$
$312$		0			0
$313$	26.3923			1.49178			0.745891	−	0.666068i	$-0.232024\pi$
$313$	26.3923			1.49178			0.745891	+	0.666068i	$0.232024\pi$
$314$	−11.2583	−	6.50000i	−0.635344	−	0.366816i
$315$	3.69615	−	6.40192i	0.208255	−	0.360708i
$316$	−2.09808	−	3.63397i	−0.118026	−	0.204427i
$317$			23.1962i			1.30283i	0.758723	+	0.651413i	$0.225823\pi$
$317$			23.1962i			1.30283i	−0.758723	+	0.651413i	$0.774177\pi$
$318$	−0.294229	+	0.169873i	−0.0164995	+	0.00952600i
$319$	−6.58846	+	3.80385i	−0.368883	+	0.212975i
$320$		−	1.00000i		−	0.0559017i
$321$	−6.46410	−	11.1962i	−0.360791	−	0.624908i
$322$	14.1962	−	24.5885i	0.791121	−	1.37026i
$323$	−3.29423	−	1.90192i	−0.183296	−	0.105826i
$324$	−4.46410			−0.248006
$325$		0			0
$326$	10.7321			0.594393
$327$	−5.41154	−	3.12436i	−0.299259	−	0.172777i
$328$	−5.19615	+	9.00000i	−0.286910	+	0.496942i
$329$	4.50000	+	7.79423i	0.248093	+	0.429710i
$330$			2.19615i			0.120894i
$331$	−11.1962	+	6.46410i	−0.615396	+	0.355299i	−0.775074	−	0.631870i	$-0.782288\pi$
$331$	−11.1962	+	6.46410i	−0.615396	+	0.355299i	0.159678	+	0.987169i	$0.448954\pi$
$332$	−7.09808	+	4.09808i	−0.389558	+	0.224911i
$333$			1.98076i			0.108545i
$334$	−1.50000	−	2.59808i	−0.0820763	−	0.142160i
$335$		0			0
$336$	1.90192	+	1.09808i	0.103758	+	0.0599050i
$337$	6.19615			0.337526			0.168763	−	0.985657i	$-0.446023\pi$
$337$	6.19615			0.337526			0.168763	+	0.985657i	$0.446023\pi$
$338$		0			0
$339$	5.07180			0.275462
$340$	7.09808	+	4.09808i	0.384947	+	0.222249i
$341$	−7.09808	+	12.2942i	−0.384382	+	0.665770i
$342$	0.571797	+	0.990381i	0.0309192	+	0.0535537i
$343$		−	15.0000i		−	0.809924i
$344$	1.73205	−	1.00000i	0.0933859	−	0.0539164i
$345$	6.00000	−	3.46410i	0.323029	−	0.186501i
$346$			15.0000i			0.806405i
$347$	14.3660	+	24.8827i	0.771209	+	1.33577i	0.936901	+	0.349595i	$0.113681\pi$
$347$	14.3660	+	24.8827i	0.771209	+	1.33577i	−0.165692	+	0.986178i	$0.552986\pi$
$348$	−0.928203	+	1.60770i	−0.0497569	+	0.0861815i
$349$	3.50962	+	2.02628i	0.187866	+	0.108464i	0.590983	−	0.806684i	$-0.298740\pi$
$349$	3.50962	+	2.02628i	0.187866	+	0.108464i	−0.403117	+	0.915148i	$0.632073\pi$
$350$	3.00000			0.160357
$351$		0			0
$352$	3.00000			0.159901
$353$	−8.49038	−	4.90192i	−0.451897	−	0.260903i	0.256734	−	0.966482i	$-0.417354\pi$
$353$	−8.49038	−	4.90192i	−0.451897	−	0.260903i	−0.708631	+	0.705579i	$0.750687\pi$
$354$	3.80385	−	6.58846i	0.202172	−	0.350173i
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$		−	6.80385i		−	0.360603i
$357$	−15.5885	+	9.00000i	−0.825029	+	0.476331i
$358$	8.19615	−	4.73205i	0.433180	−	0.250097i
$359$		−	1.60770i		−	0.0848509i	−0.999100	−	0.0424255i	$-0.986492\pi$
$359$		−	1.60770i		−	0.0848509i	0.999100	−	0.0424255i	$-0.0135085\pi$
$360$	−1.23205	−	2.13397i	−0.0649348	−	0.112470i
$361$	−9.39230	+	16.2679i	−0.494332	+	0.856208i
$362$	12.6340	+	7.29423i	0.664027	+	0.383376i
$363$	1.46410			0.0768454
$364$		0			0
$365$	11.6603			0.610326
$366$	3.92820	+	2.26795i	0.205330	+	0.118548i
$367$	2.80385	−	4.85641i	0.146360	−	0.253502i	−0.783520	−	0.621367i	$-0.786578\pi$
$367$	2.80385	−	4.85641i	0.146360	−	0.253502i	0.929879	+	0.367865i	$0.119911\pi$
$368$	−4.73205	−	8.19615i	−0.246675	−	0.427254i
$369$			25.6077i			1.33308i
$370$	−0.696152	+	0.401924i	−0.0361912	+	0.0208950i
$371$	−1.20577	+	0.696152i	−0.0626005	+	0.0361424i
$372$			3.46410i			0.179605i
$373$	0.196152	+	0.339746i	0.0101564	+	0.0175914i	0.871059	−	0.491179i	$-0.163434\pi$
$373$	0.196152	+	0.339746i	0.0101564	+	0.0175914i	−0.860903	+	0.508770i	$0.830100\pi$
$374$	−12.2942	+	21.2942i	−0.635719	+	1.10110i
$375$	0.633975	+	0.366025i	0.0327383	+	0.0189015i
$376$	3.00000			0.154713
$377$		0			0
$378$	12.0000			0.617213
$379$	−25.7942	−	14.8923i	−1.32496	−	0.764966i	−0.340445	−	0.940264i	$-0.610578\pi$
$379$	−25.7942	−	14.8923i	−1.32496	−	0.764966i	−0.984515	+	0.175298i	$0.943911\pi$
$380$	−0.232051	+	0.401924i	−0.0119040	+	0.0206183i
$381$	−3.95448	−	6.84936i	−0.202594	−	0.350904i
$382$			22.7321i			1.16307i
$383$	−19.3923	+	11.1962i	−0.990900	+	0.572097i	−0.905543	−	0.424254i	$-0.860536\pi$
$383$	−19.3923	+	11.1962i	−0.990900	+	0.572097i	−0.0853571	+	0.996350i	$0.527203\pi$
$384$	0.633975	−	0.366025i	0.0323524	−	0.0186787i
$385$			9.00000i			0.458682i
$386$	8.19615	+	14.1962i	0.417173	+	0.722565i
$387$	2.46410	−	4.26795i	0.125257	−	0.216952i
$388$	−7.90192	−	4.56218i	−0.401159	−	0.231609i
$389$	22.7321			1.15256			0.576280	−	0.817252i	$-0.304504\pi$
$389$	22.7321			1.15256			0.576280	+	0.817252i	$0.304504\pi$
$390$		0			0
$391$	77.5692			3.92284
$392$	1.73205	+	1.00000i	0.0874818	+	0.0505076i
$393$	−2.24167	+	3.88269i	−0.113077	+	0.195856i
$394$	−10.7942	−	18.6962i	−0.543805	−	0.941899i
$395$		−	4.19615i		−	0.211131i
$396$	6.40192	−	3.69615i	0.321709	−	0.185739i
$397$	9.69615	−	5.59808i	0.486636	−	0.280959i	−0.236542	−	0.971621i	$-0.576014\pi$
$397$	9.69615	−	5.59808i	0.486636	−	0.280959i	0.723178	+	0.690662i	$0.242681\pi$
$398$			6.39230i			0.320417i
$399$	−0.509619	−	0.882686i	−0.0255129	−	0.0441896i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	4.50000	+	2.59808i	0.224719	+	0.129742i	0.608134	−	0.793835i	$-0.291919\pi$
$401$	4.50000	+	2.59808i	0.224719	+	0.129742i	−0.383414	+	0.923576i	$0.625252\pi$
$402$		0			0
$403$		0			0
$404$	−10.7321			−0.533939
$405$	−3.86603	−	2.23205i	−0.192104	−	0.110911i
$406$	−3.80385	+	6.58846i	−0.188782	+	0.326980i
$407$	−1.20577	−	2.08846i	−0.0597679	−	0.103521i
$408$			6.00000i			0.297044i
$409$	14.0885	−	8.13397i	0.696629	−	0.402199i	−0.109461	−	0.993991i	$-0.534913\pi$
$409$	14.0885	−	8.13397i	0.696629	−	0.402199i	0.806091	+	0.591792i	$0.201579\pi$
$410$	−9.00000	+	5.19615i	−0.444478	+	0.256620i
$411$		−	1.60770i		−	0.0793018i
$412$	−4.59808	−	7.96410i	−0.226531	−	0.392363i
$413$	15.5885	−	27.0000i	0.767058	−	1.32858i
$414$	−20.1962	−	11.6603i	−0.992587	−	0.573070i
$415$	−8.19615			−0.402333
$416$		0			0
$417$	0.875644			0.0428805
$418$	−1.20577	−	0.696152i	−0.0589762	−	0.0340499i
$419$	8.66025	−	15.0000i	0.423081	−	0.732798i	−0.573158	−	0.819445i	$-0.694282\pi$
$419$	8.66025	−	15.0000i	0.423081	−	0.732798i	0.996239	+	0.0866469i	$0.0276152\pi$
$420$	1.09808	+	1.90192i	0.0535806	+	0.0928044i
$421$		−	2.87564i		−	0.140150i	−0.997542	−	0.0700752i	$-0.977676\pi$
$421$		−	2.87564i		−	0.140150i	0.997542	−	0.0700752i	$-0.0223239\pi$
$422$	15.2321	−	8.79423i	0.741485	−	0.428096i
$423$	6.40192	−	3.69615i	0.311272	−	0.179713i
$424$			0.464102i			0.0225388i
$425$	4.09808	+	7.09808i	0.198786	+	0.344307i
$426$	−2.19615	+	3.80385i	−0.106404	+	0.184297i
$427$	16.0981	+	9.29423i	0.779041	+	0.449779i
$428$	−17.6603			−0.853641
$429$		0			0
$430$	2.00000			0.0964486
$431$	7.09808	+	4.09808i	0.341902	+	0.197397i	0.661113	−	0.750286i	$-0.270084\pi$
$431$	7.09808	+	4.09808i	0.341902	+	0.197397i	−0.319211	+	0.947684i	$0.603418\pi$
$432$	2.00000	−	3.46410i	0.0962250	−	0.166667i
$433$	−4.19615	−	7.26795i	−0.201654	−	0.349275i	0.747407	−	0.664366i	$-0.231298\pi$
$433$	−4.19615	−	7.26795i	−0.201654	−	0.349275i	−0.949062	+	0.315091i	$0.897965\pi$
$434$			14.1962i			0.681437i
$435$	−1.60770	+	0.928203i	−0.0770831	+	0.0445039i
$436$	−7.39230	+	4.26795i	−0.354027	+	0.204398i
$437$			4.39230i			0.210112i
$438$	4.26795	+	7.39230i	0.203931	+	0.353218i
$439$	1.70577	−	2.95448i	0.0814120	−	0.141010i	−0.822445	−	0.568845i	$-0.807390\pi$
$439$	1.70577	−	2.95448i	0.0814120	−	0.141010i	0.903857	+	0.427835i	$0.140724\pi$
$440$	2.59808	+	1.50000i	0.123858	+	0.0715097i
$441$	4.92820			0.234676
$442$		0			0
$443$	−22.3923			−1.06389			−0.531945	−	0.846779i	$-0.678539\pi$
$443$	−22.3923			−1.06389			−0.531945	+	0.846779i	$0.678539\pi$
$444$	−0.509619	−	0.294229i	−0.0241854	−	0.0139635i
$445$	3.40192	−	5.89230i	0.161267	−	0.279322i
$446$	3.23205	+	5.59808i	0.153042	+	0.265077i
$447$		−	4.39230i		−	0.207749i
$448$	2.59808	−	1.50000i	0.122748	−	0.0708683i
$449$	−13.5000	+	7.79423i	−0.637104	+	0.367832i	−0.783498	−	0.621394i	$-0.786567\pi$
$449$	−13.5000	+	7.79423i	−0.637104	+	0.367832i	0.146394	+	0.989226i	$0.453233\pi$
$450$		−	2.46410i		−	0.116159i
$451$	−15.5885	−	27.0000i	−0.734032	−	1.27138i
$452$	3.46410	−	6.00000i	0.162938	−	0.282216i
$453$	−15.0000	−	8.66025i	−0.704761	−	0.406894i
$454$	−16.3923			−0.769329
$455$		0			0
$456$	−0.339746			−0.0159101
$457$	−15.8827	−	9.16987i	−0.742961	−	0.428949i	0.0801841	−	0.996780i	$-0.474449\pi$
$457$	−15.8827	−	9.16987i	−0.742961	−	0.428949i	−0.823145	+	0.567832i	$0.807783\pi$
$458$	−0.633975	+	1.09808i	−0.0296237	+	0.0513097i
$459$	16.3923	+	28.3923i	0.765127	+	1.32524i
$460$		−	9.46410i		−	0.441266i
$461$	26.4904	−	15.2942i	1.23378	−	0.712323i	0.265964	−	0.963983i	$-0.414310\pi$
$461$	26.4904	−	15.2942i	1.23378	−	0.712323i	0.967816	+	0.251660i	$0.0809764\pi$
$462$	−5.70577	+	3.29423i	−0.265457	+	0.153261i
$463$		−	12.9282i		−	0.600825i	−0.953809	−	0.300412i	$-0.902876\pi$
$463$		−	12.9282i		−	0.600825i	0.953809	−	0.300412i	$-0.0971243\pi$
$464$	1.26795	+	2.19615i	0.0588631	+	0.101954i
$465$	−1.73205	+	3.00000i	−0.0803219	+	0.139122i
$466$	4.09808	+	2.36603i	0.189840	+	0.109604i
$467$	−37.8564			−1.75179			−0.875893	−	0.482506i	$-0.839727\pi$
$467$	−37.8564			−1.75179			−0.875893	+	0.482506i	$0.839727\pi$
$468$		0			0
$469$		0			0
$470$	2.59808	+	1.50000i	0.119840	+	0.0691898i
$471$	4.75833	−	8.24167i	0.219252	−	0.379756i
$472$	−5.19615	−	9.00000i	−0.239172	−	0.414259i
$473$			6.00000i			0.275880i
$474$	2.66025	−	1.53590i	0.122190	−	0.0705461i
$475$	−0.401924	+	0.232051i	−0.0184415	+	0.0106472i
$476$			24.5885i			1.12701i
$477$	0.571797	+	0.990381i	0.0261808	+	0.0453464i
$478$	1.09808	−	1.90192i	0.0502248	−	0.0869920i
$479$	35.4904	+	20.4904i	1.62160	+	0.936229i	0.986493	+	0.163803i	$0.0523760\pi$
$479$	35.4904	+	20.4904i	1.62160	+	0.936229i	0.635104	+	0.772427i	$0.280957\pi$
$480$	0.732051			0.0334134
$481$		0			0
$482$	8.66025			0.394464
$483$	18.0000	+	10.3923i	0.819028	+	0.472866i
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	−4.56218	−	7.90192i	−0.207158	−	0.358808i
$486$		−	15.2679i		−	0.692568i
$487$	13.2058	−	7.62436i	0.598411	−	0.345493i	−0.170005	−	0.985443i	$-0.554379\pi$
$487$	13.2058	−	7.62436i	0.598411	−	0.345493i	0.768416	+	0.639951i	$0.221045\pi$
$488$	5.36603	−	3.09808i	0.242909	−	0.140243i
$489$			7.85641i			0.355279i
$490$	1.00000	+	1.73205i	0.0451754	+	0.0782461i
$491$	−10.3301	+	17.8923i	−0.466192	+	0.807468i	−0.999254	−	0.0386076i	$-0.987708\pi$
$491$	−10.3301	+	17.8923i	−0.466192	+	0.807468i	0.533062	+	0.846076i	$0.321041\pi$
$492$	−6.58846	−	3.80385i	−0.297031	−	0.171491i
$493$	−20.7846			−0.936092
$494$		0			0
$495$	7.39230			0.332259
$496$	4.09808	+	2.36603i	0.184009	+	0.106238i
$497$	−9.00000	+	15.5885i	−0.403705	+	0.699238i
$498$	−3.00000	−	5.19615i	−0.134433	−	0.232845i
$499$		−	25.8564i		−	1.15749i	−0.815508	−	0.578746i	$-0.803542\pi$
$499$		−	25.8564i		−	1.15749i	0.815508	−	0.578746i	$-0.196458\pi$
$500$	0.866025	−	0.500000i	0.0387298	−	0.0223607i
$501$	1.90192	−	1.09808i	0.0849717	−	0.0490584i
$502$		−	17.1962i		−	0.767502i
$503$	13.3301	+	23.0885i	0.594361	+	1.02946i	0.993637	+	0.112633i	$0.0359283\pi$
$503$	13.3301	+	23.0885i	0.594361	+	1.02946i	−0.399276	+	0.916831i	$0.630738\pi$
$504$	3.69615	−	6.40192i	0.164640	−	0.285164i
$505$	−9.29423	−	5.36603i	−0.413588	−	0.238785i
$506$	28.3923			1.26219
$507$		0			0
$508$	−10.8038			−0.479343
$509$	19.3923	+	11.1962i	0.859549	+	0.496261i	0.863861	−	0.503730i	$-0.168039\pi$
$509$	19.3923	+	11.1962i	0.859549	+	0.496261i	−0.00431237	+	0.999991i	$0.501373\pi$
$510$	−3.00000	+	5.19615i	−0.132842	+	0.230089i
$511$	17.4904	+	30.2942i	0.773729	+	1.34014i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.60770	+	0.928203i	−0.0709815	+	0.0409812i
$514$	12.0000	−	6.92820i	0.529297	−	0.305590i
$515$		−	9.19615i		−	0.405231i
$516$	0.732051	+	1.26795i	0.0322267	+	0.0558184i
$517$	−4.50000	+	7.79423i	−0.197910	+	0.342790i
$518$	−2.08846	−	1.20577i	−0.0917615	−	0.0529786i
$519$	−10.9808			−0.482002
$520$		0			0
$521$	6.46410			0.283197			0.141599	−	0.989924i	$-0.454776\pi$
$521$	6.46410			0.283197			0.141599	+	0.989924i	$0.454776\pi$
$522$	5.41154	+	3.12436i	0.236857	+	0.136749i
$523$	1.19615	−	2.07180i	0.0523041	−	0.0905933i	−0.838688	−	0.544612i	$-0.816677\pi$
$523$	1.19615	−	2.07180i	0.0523041	−	0.0905933i	0.890992	+	0.454019i	$0.150010\pi$
$524$	3.06218	+	5.30385i	0.133772	+	0.231700i
$525$			2.19615i			0.0958479i
$526$	−3.10770	+	1.79423i	−0.135502	+	0.0782321i
$527$	−33.5885	+	19.3923i	−1.46314	+	0.844742i
$528$			2.19615i			0.0955753i
$529$	−33.2846	−	57.6506i	−1.44716	−	2.50655i
$530$	−0.232051	+	0.401924i	−0.0100796	+	0.0174585i
$531$	−22.1769	−	12.8038i	−0.962396	−	0.555640i
$532$	−1.39230			−0.0603641
$533$		0			0
$534$	4.98076			0.215539
$535$	−15.2942	−	8.83013i	−0.661227	−	0.381760i
$536$		0			0
$537$	3.46410	+	6.00000i	0.149487	+	0.258919i
$538$			27.1244i			1.16941i
$539$	−5.19615	+	3.00000i	−0.223814	+	0.129219i
$540$	3.46410	−	2.00000i	0.149071	−	0.0860663i
$541$		−	22.0526i		−	0.948114i	−0.880494	−	0.474057i	$-0.842789\pi$
$541$		−	22.0526i		−	0.948114i	0.880494	−	0.474057i	$-0.157211\pi$
$542$	−4.73205	−	8.19615i	−0.203259	−	0.352055i
$543$	−5.33975	+	9.24871i	−0.229150	+	0.396900i
$544$	7.09808	+	4.09808i	0.304328	+	0.175704i
$545$	−8.53590			−0.365638
$546$		0			0
$547$	−6.78461			−0.290089			−0.145044	−	0.989425i	$-0.546333\pi$
$547$	−6.78461			−0.290089			−0.145044	+	0.989425i	$0.546333\pi$
$548$	−1.90192	−	1.09808i	−0.0812462	−	0.0469075i
$549$	7.63397	−	13.2224i	0.325810	−	0.564320i
$550$	1.50000	+	2.59808i	0.0639602	+	0.110782i
$551$		−	1.17691i		−	0.0501382i
$552$	6.00000	−	3.46410i	0.255377	−	0.147442i
$553$	10.9019	−	6.29423i	0.463597	−	0.267658i
$554$			1.00000i			0.0424859i
$555$	−0.294229	−	0.509619i	−0.0124893	−	0.0216321i
$556$	0.598076	−	1.03590i	0.0253641	−	0.0439319i
$557$	5.89230	+	3.40192i	0.249665	+	0.144144i	0.619611	−	0.784909i	$-0.287290\pi$
$557$	5.89230	+	3.40192i	0.249665	+	0.144144i	−0.369946	+	0.929053i	$0.620624\pi$
$558$	11.6603			0.493618
$559$		0			0
$560$	3.00000			0.126773
$561$	−15.5885	−	9.00000i	−0.658145	−	0.379980i
$562$	−5.19615	+	9.00000i	−0.219186	+	0.379642i
$563$	−7.26795	−	12.5885i	−0.306308	−	0.530540i	0.671244	−	0.741236i	$-0.265760\pi$
$563$	−7.26795	−	12.5885i	−0.306308	−	0.530540i	−0.977552	+	0.210696i	$0.932427\pi$
$564$			2.19615i			0.0924747i
$565$	6.00000	−	3.46410i	0.252422	−	0.145736i
$566$	8.32051	−	4.80385i	0.349737	−	0.201921i
$567$		−	13.3923i		−	0.562424i
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	13.6244	−	23.5981i	0.571163	−	0.989283i	−0.425284	−	0.905060i	$-0.639826\pi$
$569$	13.6244	−	23.5981i	0.571163	−	0.989283i	0.996447	−	0.0842230i	$-0.0268408\pi$
$570$	−0.294229	−	0.169873i	−0.0123239	−	0.00711520i
$571$	−38.3731			−1.60586			−0.802931	−	0.596071i	$-0.796728\pi$
$571$	−38.3731			−1.60586			−0.802931	+	0.596071i	$0.796728\pi$
$572$		0			0
$573$	−16.6410			−0.695188
$574$	−27.0000	−	15.5885i	−1.12696	−	0.650650i
$575$	4.73205	−	8.19615i	0.197340	−	0.341803i
$576$	−1.23205	−	2.13397i	−0.0513355	−	0.0889156i
$577$			26.4449i			1.10091i	0.834863	+	0.550457i	$0.185547\pi$
$577$			26.4449i			1.10091i	−0.834863	+	0.550457i	$0.814453\pi$
$578$	−43.4545	+	25.0885i	−1.80747	+	1.04354i
$579$	−10.3923	+	6.00000i	−0.431889	+	0.249351i
$580$			2.53590i			0.105297i
$581$	−12.2942	−	21.2942i	−0.510051	−	0.883433i
$582$	3.33975	−	5.78461i	0.138437	−	0.239780i
$583$	−1.20577	−	0.696152i	−0.0499379	−	0.0288317i
$584$	11.6603			0.482505
$585$		0			0
$586$	−11.1962			−0.462509
$587$	−25.9808	−	15.0000i	−1.07234	−	0.619116i	−0.143521	−	0.989647i	$-0.545842\pi$
$587$	−25.9808	−	15.0000i	−1.07234	−	0.619116i	−0.928820	+	0.370531i	$0.879176\pi$
$588$	−0.732051	+	1.26795i	−0.0301893	+	0.0522893i
$589$	−1.09808	−	1.90192i	−0.0452454	−	0.0783674i
$590$		−	10.3923i		−	0.427844i
$591$	13.6865	−	7.90192i	0.562989	−	0.325042i
$592$	−0.696152	+	0.401924i	−0.0286117	+	0.0165190i
$593$			20.7846i			0.853522i	0.904365	+	0.426761i	$0.140345\pi$
$593$			20.7846i			0.853522i	−0.904365	+	0.426761i	$0.859655\pi$
$594$	6.00000	+	10.3923i	0.246183	+	0.426401i
$595$	−12.2942	+	21.2942i	−0.504014	+	0.872978i
$596$	−5.19615	−	3.00000i	−0.212843	−	0.122885i
$597$	−4.67949			−0.191519
$598$		0			0
$599$	−19.8564			−0.811311			−0.405655	−	0.914026i	$-0.632957\pi$
$599$	−19.8564			−0.811311			−0.405655	+	0.914026i	$0.632957\pi$
$600$	0.633975	+	0.366025i	0.0258819	+	0.0149429i
$601$	18.8923	−	32.7224i	0.770633	−	1.33478i	−0.166583	−	0.986027i	$-0.553273\pi$
$601$	18.8923	−	32.7224i	0.770633	−	1.33478i	0.937216	−	0.348748i	$-0.113393\pi$
$602$	3.00000	+	5.19615i	0.122271	+	0.211779i
$603$		0			0
$604$	−20.4904	+	11.8301i	−0.833742	+	0.481361i
$605$	1.73205	−	1.00000i	0.0704179	−	0.0406558i
$606$		−	7.85641i		−	0.319145i
$607$	18.7942	+	32.5526i	0.762834	+	1.32127i	0.941384	+	0.337337i	$0.109526\pi$
$607$	18.7942	+	32.5526i	0.762834	+	1.32127i	−0.178550	+	0.983931i	$0.557141\pi$
$608$	−0.232051	+	0.401924i	−0.00941090	+	0.0163002i
$609$	−4.82309	−	2.78461i	−0.195441	−	0.112838i
$610$	6.19615			0.250875
$611$		0			0
$612$	20.1962			0.816381
$613$	−33.6962	−	19.4545i	−1.36097	−	0.785759i	−0.371221	−	0.928545i	$-0.621061\pi$
$613$	−33.6962	−	19.4545i	−1.36097	−	0.785759i	−0.989754	+	0.142785i	$0.954394\pi$
$614$	−13.7321	+	23.7846i	−0.554180	+	0.959869i
$615$	−3.80385	−	6.58846i	−0.153386	−	0.265672i
$616$			9.00000i			0.362620i
$617$	−15.5885	+	9.00000i	−0.627568	+	0.362326i	−0.779809	−	0.626017i	$-0.784684\pi$
$617$	−15.5885	+	9.00000i	−0.627568	+	0.362326i	0.152242	+	0.988343i	$0.451351\pi$
$618$	5.83013	−	3.36603i	0.234522	−	0.135401i
$619$			31.3923i			1.26176i	0.775879	+	0.630882i	$0.217307\pi$
$619$			31.3923i			1.26176i	−0.775879	+	0.630882i	$0.782693\pi$
$620$	2.36603	+	4.09808i	0.0950219	+	0.164583i
$621$	18.9282	−	32.7846i	0.759563	−	1.31560i
$622$	−7.90192	−	4.56218i	−0.316838	−	0.182927i
$623$	20.4115			0.817771
$624$		0			0
$625$	1.00000			0.0400000
$626$	22.8564	+	13.1962i	0.913526	+	0.527424i
$627$	0.509619	−	0.882686i	0.0203522	−	0.0352511i
$628$	−6.50000	−	11.2583i	−0.259378	−	0.449256i
$629$		−	6.58846i		−	0.262699i
$630$	6.40192	−	3.69615i	0.255059	−	0.147258i
$631$	18.0000	−	10.3923i	0.716569	−	0.413711i	−0.0969198	−	0.995292i	$-0.530899\pi$
$631$	18.0000	−	10.3923i	0.716569	−	0.413711i	0.813488	+	0.581581i	$0.197566\pi$
$632$		−	4.19615i		−	0.166914i
$633$	6.43782	+	11.1506i	0.255880	+	0.443198i
$634$	−11.5981	+	20.0885i	−0.460618	+	0.797815i
$635$	−9.35641	−	5.40192i	−0.371298	−	0.214369i
$636$	−0.339746			−0.0134718
$637$		0			0
$638$	−7.60770			−0.301192
$639$	12.8038	+	7.39230i	0.506512	+	0.292435i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−16.0359	−	27.7750i	−0.633380	−	1.09705i	−0.986856	−	0.161603i	$-0.948334\pi$
$641$	−16.0359	−	27.7750i	−0.633380	−	1.09705i	0.353476	−	0.935444i	$-0.385000\pi$
$642$		−	12.9282i		−	0.510235i
$643$	9.29423	−	5.36603i	0.366529	−	0.211615i	−0.305412	−	0.952220i	$-0.598794\pi$
$643$	9.29423	−	5.36603i	0.366529	−	0.211615i	0.671941	+	0.740605i	$0.265461\pi$
$644$	24.5885	−	14.1962i	0.968921	−	0.559407i
$645$			1.46410i			0.0576489i
$646$	−1.90192	−	3.29423i	−0.0748302	−	0.129610i
$647$	0.401924	−	0.696152i	0.0158013	−	0.0273686i	−0.858017	−	0.513622i	$-0.828303\pi$
$647$	0.401924	−	0.696152i	0.0158013	−	0.0273686i	0.873818	+	0.486253i	$0.161637\pi$
$648$	−3.86603	−	2.23205i	−0.151872	−	0.0876832i
$649$	31.1769			1.22380
$650$		0			0
$651$	−10.3923			−0.407307
$652$	9.29423	+	5.36603i	0.363990	+	0.210150i
$653$	−0.696152	+	1.20577i	−0.0272425	+	0.0471855i	−0.879325	−	0.476222i	$-0.842006\pi$
$653$	−0.696152	+	1.20577i	−0.0272425	+	0.0471855i	0.852083	+	0.523407i	$0.175339\pi$
$654$	−3.12436	−	5.41154i	−0.122172	−	0.211608i
$655$			6.12436i			0.239298i
$656$	−9.00000	+	5.19615i	−0.351391	+	0.202876i
$657$	24.8827	−	14.3660i	0.970766	−	0.560472i
$658$			9.00000i			0.350857i
$659$	2.66025	+	4.60770i	0.103629	+	0.179490i	0.913177	−	0.407563i	$-0.133621\pi$
$659$	2.66025	+	4.60770i	0.103629	+	0.179490i	−0.809548	+	0.587053i	$0.800288\pi$
$660$	−1.09808	+	1.90192i	−0.0427426	+	0.0740323i
$661$	−31.0981	−	17.9545i	−1.20957	−	0.698348i	−0.246909	−	0.969039i	$-0.579415\pi$
$661$	−31.0981	−	17.9545i	−1.20957	−	0.698348i	−0.962666	+	0.270690i	$0.912748\pi$
$662$	−12.9282			−0.502469
$663$		0			0
$664$	−8.19615			−0.318072
$665$	−1.20577	−	0.696152i	−0.0467578	−	0.0269956i
$666$	−0.990381	+	1.71539i	−0.0383765	+	0.0664700i
$667$	12.0000	+	20.7846i	0.464642	+	0.804783i
$668$		−	3.00000i		−	0.116073i
$669$	−4.09808	+	2.36603i	−0.158441	+	0.0914758i
$670$		0			0
$671$			18.5885i			0.717599i
$672$	1.09808	+	1.90192i	0.0423592	+	0.0733683i
$673$	−12.1962	+	21.1244i	−0.470127	+	0.814284i	−0.999416	−	0.0341573i	$-0.989125\pi$
$673$	−12.1962	+	21.1244i	−0.470127	+	0.814284i	0.529289	+	0.848441i	$0.322459\pi$
$674$	5.36603	+	3.09808i	0.206692	+	0.119333i
$675$	4.00000			0.153960
$676$		0			0
$677$	−25.8564			−0.993742			−0.496871	−	0.867824i	$-0.665518\pi$
$677$	−25.8564			−0.993742			−0.496871	+	0.867824i	$0.665518\pi$
$678$	4.39230	+	2.53590i	0.168685	+	0.0973906i
$679$	13.6865	−	23.7058i	0.525241	−	0.909744i
$680$	4.09808	+	7.09808i	0.157154	+	0.272199i
$681$		−	12.0000i		−	0.459841i
$682$	−12.2942	+	7.09808i	−0.470770	+	0.271799i
$683$	−27.0000	+	15.5885i	−1.03313	+	0.596476i	−0.917879	−	0.396861i	$-0.870099\pi$
$683$	−27.0000	+	15.5885i	−1.03313	+	0.596476i	−0.115248	+	0.993337i	$0.536766\pi$
$684$			1.14359i			0.0437264i
$685$	−1.09808	−	1.90192i	−0.0419553	−	0.0726688i
$686$	7.50000	−	12.9904i	0.286351	−	0.495975i
$687$	−0.803848	−	0.464102i	−0.0306687	−	0.0177066i
$688$	2.00000			0.0762493
$689$		0			0
$690$	6.92820			0.263752
$691$	31.7942	+	18.3564i	1.20951	+	0.698311i	0.962652	−	0.270741i	$-0.0872688\pi$
$691$	31.7942	+	18.3564i	1.20951	+	0.698311i	0.246857	+	0.969052i	$0.420602\pi$
$692$	−7.50000	+	12.9904i	−0.285107	+	0.493820i
$693$	11.0885	+	19.2058i	0.421216	+	0.729567i
$694$			28.7321i			1.09065i
$695$	1.03590	−	0.598076i	0.0392939	−	0.0226863i
$696$	−1.60770	+	0.928203i	−0.0609395	+	0.0351835i
$697$		−	85.1769i		−	3.22631i
$698$	2.02628	+	3.50962i	0.0766958	+	0.132841i
$699$	−1.73205	+	3.00000i	−0.0655122	+	0.113470i
$700$	2.59808	+	1.50000i	0.0981981	+	0.0566947i
$701$	35.9090			1.35626			0.678131	−	0.734941i	$-0.262790\pi$
$701$	35.9090			1.35626			0.678131	+	0.734941i	$0.262790\pi$
$702$		0			0
$703$	0.373067			0.0140705
$704$	2.59808	+	1.50000i	0.0979187	+	0.0565334i
$705$	−1.09808	+	1.90192i	−0.0413559	+	0.0716306i
$706$	−4.90192	−	8.49038i	−0.184486	−	0.319540i
$707$		−	32.1962i		−	1.21086i
$708$	6.58846	−	3.80385i	0.247609	−	0.142957i
$709$	−9.50962	+	5.49038i	−0.357141	+	0.206196i	−0.667826	−	0.744317i	$-0.732775\pi$
$709$	−9.50962	+	5.49038i	−0.357141	+	0.206196i	0.310685	+	0.950513i	$0.399442\pi$
$710$			6.00000i			0.225176i
$711$	−5.16987	−	8.95448i	−0.193885	−	0.335819i
$712$	3.40192	−	5.89230i	0.127492	−	0.220823i
$713$	38.7846	+	22.3923i	1.45250	+	0.838598i
$714$	−18.0000			−0.673633
$715$		0			0
$716$	9.46410			0.353690
$717$	1.39230	+	0.803848i	0.0519966	+	0.0300202i
$718$	0.803848	−	1.39230i	0.0299993	−	0.0519604i
$719$	−12.9282	−	22.3923i	−0.482141	−	0.835092i	0.517649	−	0.855593i	$-0.326807\pi$
$719$	−12.9282	−	22.3923i	−0.482141	−	0.835092i	−0.999790	+	0.0205009i	$0.993474\pi$
$720$		−	2.46410i		−	0.0918316i
$721$	23.8923	−	13.7942i	0.889796	−	0.513724i
$722$	−16.2679	+	9.39230i	−0.605430	+	0.349545i
$723$			6.33975i			0.235778i
$724$	7.29423	+	12.6340i	0.271088	+	0.469538i
$725$	−1.26795	+	2.19615i	−0.0470905	+	0.0815631i
$726$	1.26795	+	0.732051i	0.0470580	+	0.0271690i
$727$	34.3731			1.27483			0.637413	−	0.770522i	$-0.280004\pi$
$727$	34.3731			1.27483			0.637413	+	0.770522i	$0.280004\pi$
$728$		0			0
$729$	−2.21539			−0.0820515
$730$	10.0981	+	5.83013i	0.373747	+	0.215783i
$731$	−8.19615	+	14.1962i	−0.303146	+	0.525064i
$732$	2.26795	+	3.92820i	0.0838258	+	0.145191i
$733$		−	14.9090i		−	0.550675i	−0.961348	−	0.275338i	$-0.911210\pi$
$733$		−	14.9090i		−	0.550675i	0.961348	−	0.275338i	$-0.0887896\pi$
$734$	4.85641	−	2.80385i	0.179253	−	0.103492i
$735$	−1.26795	+	0.732051i	−0.0467690	+	0.0270021i
$736$		−	9.46410i		−	0.348851i
$737$		0			0
$738$	−12.8038	+	22.1769i	−0.471316	+	0.816344i
$739$	−28.2058	−	16.2846i	−1.03757	−	0.599039i	−0.118423	−	0.992963i	$-0.537784\pi$
$739$	−28.2058	−	16.2846i	−1.03757	−	0.599039i	−0.919143	+	0.393924i	$0.871117\pi$
$740$	−0.803848			−0.0295500
$741$		0			0
$742$	−1.39230			−0.0511131
$743$	11.7846	+	6.80385i	0.432335	+	0.249609i	0.700341	−	0.713808i	$-0.253031\pi$
$743$	11.7846	+	6.80385i	0.432335	+	0.249609i	−0.268006	+	0.963417i	$0.586365\pi$
$744$	−1.73205	+	3.00000i	−0.0635001	+	0.109985i
$745$	−3.00000	−	5.19615i	−0.109911	−	0.190372i
$746$			0.392305i			0.0143633i
$747$	−17.4904	+	10.0981i	−0.639940	+	0.369469i
$748$	−21.2942	+	12.2942i	−0.778594	+	0.449522i
$749$		−	52.9808i		−	1.93587i
$750$	0.366025	+	0.633975i	0.0133654	+	0.0231495i
$751$	10.1962	−	17.6603i	0.372063	−	0.644432i	−0.617820	−	0.786320i	$-0.711984\pi$
$751$	10.1962	−	17.6603i	0.372063	−	0.644432i	0.989883	+	0.141888i	$0.0453172\pi$
$752$	2.59808	+	1.50000i	0.0947421	+	0.0546994i
$753$	12.5885			0.458749
$754$		0			0
$755$	−23.6603			−0.861085
$756$	10.3923	+	6.00000i	0.377964	+	0.218218i
$757$	18.8923	−	32.7224i	0.686652	−	1.18932i	−0.286262	−	0.958151i	$-0.592413\pi$
$757$	18.8923	−	32.7224i	0.686652	−	1.18932i	0.972914	−	0.231166i	$-0.0742539\pi$
$758$	−14.8923	−	25.7942i	−0.540913	−	0.936889i
$759$			20.7846i			0.754434i
$760$	−0.401924	+	0.232051i	−0.0145793	+	0.00841737i
$761$	−16.2846	+	9.40192i	−0.590317	+	0.340819i	−0.765223	−	0.643766i	$-0.777371\pi$
$761$	−16.2846	+	9.40192i	−0.590317	+	0.340819i	0.174906	+	0.984585i	$0.444038\pi$
$762$		−	7.90897i		−	0.286512i
$763$	−12.8038	−	22.1769i	−0.463530	−	0.802858i
$764$	−11.3660	+	19.6865i	−0.411208	+	0.712234i
$765$	17.4904	+	10.0981i	0.632366	+	0.365097i
$766$	−22.3923			−0.809067
$767$		0			0
$768$	0.732051			0.0264156
$769$	33.0000	+	19.0526i	1.19001	+	0.687053i	0.958309	−	0.285734i	$-0.0922374\pi$
$769$	33.0000	+	19.0526i	1.19001	+	0.687053i	0.231701	+	0.972787i	$0.425571\pi$
$770$	−4.50000	+	7.79423i	−0.162169	+	0.280885i
$771$	5.07180	+	8.78461i	0.182656	+	0.316370i
$772$			16.3923i			0.589972i
$773$	−2.08846	+	1.20577i	−0.0751166	+	0.0433686i	−0.537088	−	0.843526i	$-0.680476\pi$
$773$	−2.08846	+	1.20577i	−0.0751166	+	0.0433686i	0.461971	+	0.886895i	$0.347142\pi$
$774$	4.26795	−	2.46410i	0.153408	−	0.0885703i
$775$			4.73205i			0.169980i
$776$	−4.56218	−	7.90192i	−0.163773	−	0.283663i
$777$	0.882686	−	1.52886i	0.0316662	−	0.0548474i
$778$	19.6865	+	11.3660i	0.705796	+	0.407492i
$779$	4.82309			0.172805
$780$		0			0
$781$	−18.0000			−0.644091
$782$	67.1769	+	38.7846i	2.40224	+	1.38693i
$783$	−5.07180	+	8.78461i	−0.181251	+	0.313936i
$784$	1.00000	+	1.73205i	0.0357143	+	0.0618590i
$785$		−	13.0000i		−	0.463990i
$786$	−3.88269	+	2.24167i	−0.138491	+	0.0799577i
$787$	37.0981	−	21.4186i	1.32240	−	0.763490i	0.338292	−	0.941041i	$-0.390151\pi$
$787$	37.0981	−	21.4186i	1.32240	−	0.763490i	0.984112	+	0.177551i	$0.0568175\pi$
$788$		−	21.5885i		−	0.769057i
$789$	−1.31347	−	2.27499i	−0.0467606	−	0.0809918i
$790$	2.09808	−	3.63397i	0.0746462	−	0.129291i
$791$	18.0000	+	10.3923i	0.640006	+	0.369508i
$792$	7.39230			0.262674
$793$		0			0
$794$	11.1962			0.397337
$795$	−0.294229	−	0.169873i	−0.0104352	−	0.00602477i
$796$	−3.19615	+	5.53590i	−0.113285	+	0.196215i
$797$	6.46410	+	11.1962i	0.228970	+	0.396588i	0.957503	−	0.288423i	$-0.0931308\pi$
$797$	6.46410	+	11.1962i	0.228970	+	0.396588i	−0.728533	+	0.685011i	$0.759797\pi$
$798$		−	1.01924i		−	0.0360806i
$799$	−21.2942	+	12.2942i	−0.753336	+	0.434939i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$		−	16.7654i		−	0.592375i
$802$	2.59808	+	4.50000i	0.0917413	+	0.158901i
$803$	−17.4904	+	30.2942i	−0.617222	+	1.06906i
$804$		0			0
$805$	28.3923			1.00070
$806$		0			0
$807$	−19.8564			−0.698979
$808$	−9.29423	−	5.36603i	−0.326970	−	0.188776i
$809$	−12.0000	+	20.7846i	−0.421898	+	0.730748i	−0.996125	−	0.0879478i	$-0.971969\pi$
$809$	−12.0000	+	20.7846i	−0.421898	+	0.730748i	0.574228	+	0.818696i	$0.305302\pi$
$810$	−2.23205	−	3.86603i	−0.0784263	−	0.135838i
$811$		−	43.3923i		−	1.52371i	−0.647748	−	0.761855i	$-0.724289\pi$
$811$		−	43.3923i		−	1.52371i	0.647748	−	0.761855i	$-0.275711\pi$
$812$	−6.58846	+	3.80385i	−0.231210	+	0.133489i
$813$	6.00000	−	3.46410i	0.210429	−	0.121491i
$814$		−	2.41154i		−	0.0845245i
$815$	5.36603	+	9.29423i	0.187964	+	0.325563i
$816$	−3.00000	+	5.19615i	−0.105021	+	0.181902i
$817$	−0.803848	−	0.464102i	−0.0281231	−	0.0162369i
$818$	16.2679			0.568796
$819$		0			0
$820$	−10.3923			−0.362915
$821$	−17.4904	−	10.0981i	−0.610419	−	0.352425i	0.162711	−	0.986674i	$-0.447976\pi$
$821$	−17.4904	−	10.0981i	−0.610419	−	0.352425i	−0.773129	+	0.634249i	$0.781310\pi$
$822$	0.803848	−	1.39230i	0.0280374	−	0.0485622i
$823$	13.5981	+	23.5526i	0.473999	+	0.820991i	0.999557	−	0.0297674i	$-0.00947664\pi$
$823$	13.5981	+	23.5526i	0.473999	+	0.820991i	−0.525558	+	0.850758i	$0.676143\pi$
$824$		−	9.19615i		−	0.320363i
$825$	−1.90192	+	1.09808i	−0.0662165	+	0.0382301i
$826$	27.0000	−	15.5885i	0.939450	−	0.542392i
$827$			42.5885i			1.48095i	0.672086	+	0.740473i	$0.265398\pi$
$827$			42.5885i			1.48095i	−0.672086	+	0.740473i	$0.734602\pi$
$828$	−11.6603	−	20.1962i	−0.405222	−	0.701865i
$829$	10.0000	−	17.3205i	0.347314	−	0.601566i	−0.638457	−	0.769657i	$-0.720427\pi$
$829$	10.0000	−	17.3205i	0.347314	−	0.601566i	0.985771	+	0.168091i	$0.0537604\pi$
$830$	−7.09808	−	4.09808i	−0.246378	−	0.142246i
$831$	−0.732051			−0.0253946
$832$		0			0
$833$	−16.3923			−0.567960
$834$	0.758330	+	0.437822i	0.0262588	+	0.0151605i
$835$	1.50000	−	2.59808i	0.0519096	−	0.0899101i
$836$	−0.696152	−	1.20577i	−0.0240769	−	0.0417025i
$837$			18.9282i			0.654254i
$838$	15.0000	−	8.66025i	0.518166	−	0.299164i
$839$	−18.8827	+	10.9019i	−0.651903	+	0.376376i	−0.789185	−	0.614156i	$-0.789497\pi$
$839$	−18.8827	+	10.9019i	−0.651903	+	0.376376i	0.137282	+	0.990532i	$0.456163\pi$
$840$			2.19615i			0.0757745i
$841$	11.2846	+	19.5455i	0.389124	+	0.673983i
$842$	1.43782	−	2.49038i	0.0495506	−	0.0858242i
$843$	−6.58846	−	3.80385i	−0.226919	−	0.131011i
$844$	17.5885			0.605420
$845$		0			0
$846$	7.39230			0.254153
$847$	5.19615	+	3.00000i	0.178542	+	0.103081i
$848$	−0.232051	+	0.401924i	−0.00796866	+	0.0138021i
$849$	3.51666	+	6.09103i	0.120691	+	0.209044i
$850$			8.19615i			0.281126i
$851$	−6.58846	+	3.80385i	−0.225849	+	0.130394i
$852$	−3.80385	+	2.19615i	−0.130318	+	0.0752389i
$853$		−	13.8564i		−	0.474434i	−0.971457	−	0.237217i	$-0.923765\pi$
$853$		−	13.8564i		−	0.474434i	0.971457	−	0.237217i	$-0.0762353\pi$
$854$	9.29423	+	16.0981i	0.318042	+	0.550865i
$855$	−0.571797	+	0.990381i	−0.0195550	+	0.0338703i
$856$	−15.2942	−	8.83013i	−0.522746	−	0.301808i
$857$	−16.7321			−0.571556			−0.285778	−	0.958296i	$-0.592252\pi$
$857$	−16.7321			−0.571556			−0.285778	+	0.958296i	$0.592252\pi$
$858$		0			0
$859$	−20.3731			−0.695120			−0.347560	−	0.937658i	$-0.612990\pi$
$859$	−20.3731			−0.695120			−0.347560	+	0.937658i	$0.612990\pi$
$860$	1.73205	+	1.00000i	0.0590624	+	0.0340997i
$861$	11.4115	−	19.7654i	0.388904	−	0.673602i
$862$	4.09808	+	7.09808i	0.139581	+	0.241761i
$863$		−	43.1769i		−	1.46976i	−0.678198	−	0.734880i	$-0.737239\pi$
$863$		−	43.1769i		−	1.46976i	0.678198	−	0.734880i	$-0.262761\pi$
$864$	3.46410	−	2.00000i	0.117851	−	0.0680414i
$865$	−12.9904	+	7.50000i	−0.441686	+	0.255008i
$866$		−	8.39230i		−	0.285182i
$867$	−18.3660	−	31.8109i	−0.623743	−	1.08035i
$868$	−7.09808	+	12.2942i	−0.240924	+	0.417293i
$869$	10.9019	+	6.29423i	0.369822	+	0.213517i
$870$	−1.85641			−0.0629381
$871$		0			0
$872$	−8.53590			−0.289062
$873$	−19.4711	−	11.2417i	−0.658998	−	0.380473i
$874$	−2.19615	+	3.80385i	−0.0742860	+	0.128667i
$875$	1.50000	+	2.59808i	0.0507093	+	0.0878310i
$876$			8.53590i			0.288401i
$877$	23.7846	−	13.7321i	0.803149	−	0.463698i	−0.0414220	−	0.999142i	$-0.513189\pi$
$877$	23.7846	−	13.7321i	0.803149	−	0.463698i	0.844571	+	0.535443i	$0.179855\pi$
$878$	2.95448	−	1.70577i	0.0997090	−	0.0575670i
$879$		−	8.19615i		−	0.276449i
$880$	1.50000	+	2.59808i	0.0505650	+	0.0875811i
$881$	−13.1603	+	22.7942i	−0.443380	+	0.767957i	−0.997938	−	0.0641883i	$-0.979554\pi$
$881$	−13.1603	+	22.7942i	−0.443380	+	0.767957i	0.554558	+	0.832145i	$0.312888\pi$
$882$	4.26795	+	2.46410i	0.143709	+	0.0829706i
$883$	4.58846			0.154414			0.0772069	−	0.997015i	$-0.475400\pi$
$883$	4.58846			0.154414			0.0772069	+	0.997015i	$0.475400\pi$
$884$		0			0
$885$	7.60770			0.255730
$886$	−19.3923	−	11.1962i	−0.651497	−	0.376142i
$887$	20.3827	−	35.3038i	0.684384	−	1.18539i	−0.289246	−	0.957255i	$-0.593405\pi$
$887$	20.3827	−	35.3038i	0.684384	−	1.18539i	0.973630	−	0.228133i	$-0.0732620\pi$
$888$	−0.294229	−	0.509619i	−0.00987367	−	0.0171017i
$889$		−	32.4115i		−	1.08705i
$890$	5.89230	−	3.40192i	0.197511	−	0.114033i
$891$	11.5981	−	6.69615i	0.388550	−	0.224330i
$892$			6.46410i			0.216434i
$893$	−0.696152	−	1.20577i	−0.0232959	−	0.0403496i
$894$	2.19615	−	3.80385i	0.0734503	−	0.127220i
$895$	8.19615	+	4.73205i	0.273967	+	0.158175i
$896$	3.00000			0.100223
$897$		0			0
$898$	−15.5885			−0.520194
$899$	−10.3923	−	6.00000i	−0.346603	−	0.200111i
$900$	1.23205	−	2.13397i	0.0410684	−	0.0711325i
$901$	−1.90192	−	3.29423i	−0.0633623	−	0.109747i
$902$		−	31.1769i		−	1.03808i
$903$	−3.80385	+	2.19615i	−0.126584	+	0.0730834i
$904$	6.00000	−	3.46410i	0.199557	−	0.115214i
$905$			14.5885i			0.484937i
$906$	−8.66025	−	15.0000i	−0.287718	−	0.498342i
$907$	−2.29423	+	3.97372i	−0.0761786	+	0.131945i	−0.901598	−	0.432574i	$-0.857605\pi$
$907$	−2.29423	+	3.97372i	−0.0761786	+	0.131945i	0.825420	+	0.564520i	$0.190939\pi$
$908$	−14.1962	−	8.19615i	−0.471116	−	0.271999i
$909$	−26.4449			−0.877121
$910$		0			0
$911$	−21.4641			−0.711137			−0.355569	−	0.934650i	$-0.615713\pi$
$911$	−21.4641			−0.711137			−0.355569	+	0.934650i	$0.615713\pi$
$912$	−0.294229	−	0.169873i	−0.00974288	−	0.00562506i
$913$	12.2942	−	21.2942i	0.406880	−	0.704736i
$914$	−9.16987	−	15.8827i	−0.303312	−	0.525353i
$915$			4.53590i			0.149952i
$916$	−1.09808	+	0.633975i	−0.0362815	+	0.0209471i
$917$	−15.9115	+	9.18653i	−0.525445	+	0.303366i
$918$			32.7846i			1.08205i
$919$	−15.3923	−	26.6603i	−0.507745	−	0.879441i	−0.999960	−	0.00896670i	$-0.997146\pi$
$919$	−15.3923	−	26.6603i	−0.507745	−	0.879441i	0.492215	−	0.870474i	$-0.336188\pi$
$920$	4.73205	−	8.19615i	0.156011	−	0.270219i
$921$	−17.4115	−	10.0526i	−0.573730	−	0.331243i
$922$	30.5885			1.00738
$923$		0			0
$924$	−6.58846			−0.216744
$925$	−0.696152	−	0.401924i	−0.0228894	−	0.0132152i
$926$	6.46410	−	11.1962i	0.212424	−	0.367928i
$927$	−11.3301	−	19.6244i	−0.372130	−	0.644548i
$928$			2.53590i			0.0832449i
$929$	2.78461	−	1.60770i	0.0913601	−	0.0527468i	−0.453624	−	0.891193i	$-0.649869\pi$
$929$	2.78461	−	1.60770i	0.0913601	−	0.0527468i	0.544984	+	0.838446i	$0.316536\pi$
$930$	−3.00000	+	1.73205i	−0.0983739	+	0.0567962i
$931$		−	0.928203i		−	0.0304206i
$932$	2.36603	+	4.09808i	0.0775017	+	0.134237i
$933$	3.33975	−	5.78461i	0.109338	−	0.189380i
$934$	−32.7846	−	18.9282i	−1.07275	−	0.619350i
$935$	−24.5885			−0.804129
$936$		0			0
$937$	−9.60770			−0.313870			−0.156935	−	0.987609i	$-0.550161\pi$
$937$	−9.60770			−0.313870			−0.156935	+	0.987609i	$0.550161\pi$
$938$		0			0
$939$	−9.66025	+	16.7321i	−0.315250	+	0.546030i
$940$	1.50000	+	2.59808i	0.0489246	+	0.0847399i
$941$		−	3.21539i		−	0.104819i	−0.998626	−	0.0524094i	$-0.983310\pi$
$941$		−	3.21539i		−	0.104819i	0.998626	−	0.0524094i	$-0.0166901\pi$
$942$	8.24167	−	4.75833i	0.268528	−	0.155035i
$943$	−85.1769	+	49.1769i	−2.77374	+	1.60142i
$944$		−	10.3923i		−	0.338241i
$945$	6.00000	+	10.3923i	0.195180	+	0.338062i
$946$	−3.00000	+	5.19615i	−0.0975384	+	0.168941i
$947$	−13.3135	−	7.68653i	−0.432630	−	0.249779i	0.267837	−	0.963464i	$-0.413691\pi$
$947$	−13.3135	−	7.68653i	−0.432630	−	0.249779i	−0.700466	+	0.713686i	$0.747025\pi$
$948$	3.07180			0.0997673
$949$		0			0
$950$	−0.464102			−0.0150574
$951$	−14.7058	−	8.49038i	−0.476867	−	0.275319i
$952$	−12.2942	+	21.2942i	−0.398458	+	0.690150i
$953$	3.29423	+	5.70577i	0.106711	+	0.184828i	0.914436	−	0.404731i	$-0.132635\pi$
$953$	3.29423	+	5.70577i	0.106711	+	0.184828i	−0.807725	+	0.589559i	$0.799302\pi$
$954$			1.14359i			0.0370252i
$955$	−19.6865	+	11.3660i	−0.637041	+	0.367796i
$956$	1.90192	−	1.09808i	0.0615126	−	0.0355143i
$957$		−	5.56922i		−	0.180027i
$958$	20.4904	+	35.4904i	0.662014	+	1.14664i
$959$	3.29423	−	5.70577i	0.106376	−	0.184249i
$960$	0.633975	+	0.366025i	0.0204614	+	0.0118134i
$961$	8.60770			0.277668
$962$		0			0
$963$	−43.5167			−1.40230
$964$	7.50000	+	4.33013i	0.241559	+	0.139464i
$965$	−8.19615	+	14.1962i	−0.263843	+	0.456990i
$966$	10.3923	+	18.0000i	0.334367	+	0.579141i
$967$			44.5692i			1.43325i	0.697459	+	0.716625i	$0.254314\pi$
$967$			44.5692i			1.43325i	−0.697459	+	0.716625i	$0.745686\pi$
$968$	1.73205	−	1.00000i	0.0556702	−	0.0321412i
$969$	2.41154	−	1.39230i	0.0774699	−	0.0447273i
$970$		−	9.12436i		−	0.292965i
$971$	−23.3827	−	40.5000i	−0.750386	−	1.29971i	−0.947636	−	0.319354i	$-0.896534\pi$
$971$	−23.3827	−	40.5000i	−0.750386	−	1.29971i	0.197250	−	0.980353i	$-0.436799\pi$
$972$	7.63397	−	13.2224i	0.244860	−	0.424110i
$973$	3.10770	+	1.79423i	0.0996281	+	0.0575203i
$974$	15.2487			0.488600
$975$		0			0
$976$	6.19615			0.198334
$977$	−14.1962	−	8.19615i	−0.454175	−	0.262218i	0.255417	−	0.966831i	$-0.417787\pi$
$977$	−14.1962	−	8.19615i	−0.454175	−	0.262218i	−0.709592	+	0.704613i	$0.751121\pi$
$978$	−3.92820	+	6.80385i	−0.125610	+	0.217563i
$979$	10.2058	+	17.6769i	0.326178	+	0.564957i
$980$			2.00000i			0.0638877i
$981$	−18.2154	+	10.5167i	−0.581573	+	0.335771i
$982$	−17.8923	+	10.3301i	−0.570966	+	0.329648i
$983$		−	44.5692i		−	1.42154i	−0.703426	−	0.710769i	$-0.748347\pi$
$983$		−	44.5692i		−	1.42154i	0.703426	−	0.710769i	$-0.251653\pi$
$984$	−3.80385	−	6.58846i	−0.121262	−	0.210032i
$985$	10.7942	−	18.6962i	0.343933	−	0.595709i
$986$	−18.0000	−	10.3923i	−0.573237	−	0.330958i
$987$	−6.58846			−0.209713
$988$		0			0
$989$	18.9282			0.601882
$990$	6.40192	+	3.69615i	0.203466	+	0.117471i
$991$	5.58846	−	9.67949i	0.177523	−	0.307479i	−0.763508	−	0.645798i	$-0.776525\pi$
$991$	5.58846	−	9.67949i	0.177523	−	0.307479i	0.941032	+	0.338319i	$0.109858\pi$
$992$	2.36603	+	4.09808i	0.0751214	+	0.130114i
$993$		−	9.46410i		−	0.300334i
$994$	−15.5885	+	9.00000i	−0.494436	+	0.285463i
$995$	−5.53590	+	3.19615i	−0.175500	+	0.101325i
$996$		−	6.00000i		−	0.190117i
$997$	−20.2846	−	35.1340i	−0.642420	−	1.11270i	−0.984891	−	0.173176i	$-0.944597\pi$
$997$	−20.2846	−	35.1340i	−0.642420	−	1.11270i	0.342471	−	0.939528i	$-0.388736\pi$
$998$	12.9282	−	22.3923i	0.409235	−	0.708816i
$999$	−2.78461	−	1.60770i	−0.0881012	−	0.0508652i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.l.g.1161.2		4
13.2	odd	12		1690.2.e.n.991.1		4
13.3	even	3		130.2.l.a.101.1	✓	4
13.4	even	6		1690.2.d.f.1351.4		4
13.5	odd	4		1690.2.e.n.191.1		4
13.6	odd	12		1690.2.a.j.1.2		2
13.7	odd	12		1690.2.a.m.1.2		2
13.8	odd	4		1690.2.e.l.191.1		4
13.9	even	3		1690.2.d.f.1351.2		4
13.10	even	6	inner	1690.2.l.g.361.2		4
13.11	odd	12		1690.2.e.l.991.1		4
13.12	even	2		130.2.l.a.121.1	yes	4
39.29	odd	6		1170.2.bs.c.361.2		4
39.38	odd	2		1170.2.bs.c.901.2		4
52.3	odd	6		1040.2.da.a.881.2		4
52.51	odd	2		1040.2.da.a.641.2		4
65.3	odd	12		650.2.n.b.49.1		4
65.12	odd	4		650.2.n.b.199.1		4
65.19	odd	12		8450.2.a.bm.1.1		2
65.29	even	6		650.2.m.a.101.2		4
65.38	odd	4		650.2.n.a.199.2		4
65.42	odd	12		650.2.n.a.49.2		4
65.59	odd	12		8450.2.a.bf.1.1		2
65.64	even	2		650.2.m.a.251.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.a.101.1	✓	4	13.3	even	3
130.2.l.a.121.1	yes	4	13.12	even	2
650.2.m.a.101.2		4	65.29	even	6
650.2.m.a.251.2		4	65.64	even	2
650.2.n.a.49.2		4	65.42	odd	12
650.2.n.a.199.2		4	65.38	odd	4
650.2.n.b.49.1		4	65.3	odd	12
650.2.n.b.199.1		4	65.12	odd	4
1040.2.da.a.641.2		4	52.51	odd	2
1040.2.da.a.881.2		4	52.3	odd	6
1170.2.bs.c.361.2		4	39.29	odd	6
1170.2.bs.c.901.2		4	39.38	odd	2
1690.2.a.j.1.2		2	13.6	odd	12
1690.2.a.m.1.2		2	13.7	odd	12
1690.2.d.f.1351.2		4	13.9	even	3
1690.2.d.f.1351.4		4	13.4	even	6
1690.2.e.l.191.1		4	13.8	odd	4
1690.2.e.l.991.1		4	13.11	odd	12
1690.2.e.n.191.1		4	13.5	odd	4
1690.2.e.n.991.1		4	13.2	odd	12
1690.2.l.g.361.2		4	13.10	even	6	inner
1690.2.l.g.1161.2		4	1.1	even	1	trivial
8450.2.a.bf.1.1		2	65.59	odd	12
8450.2.a.bm.1.1		2	65.19	odd	12

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:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.366025 + 0.633975i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-0.633975 + 0.366025i) q^{6} +(-2.59808 + 1.50000i) q^{7} +1.00000i q^{8} +(1.23205 + 2.13397i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.366025 + 0.633975i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-0.633975 + 0.366025i) q^{6} +(-2.59808 + 1.50000i) q^{7} +1.00000i q^{8} +(1.23205 + 2.13397i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-2.59808 - 1.50000i) q^{11} -0.732051 q^{12} -3.00000 q^{14} +(-0.633975 - 0.366025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-4.09808 - 7.09808i) q^{17} +2.46410i q^{18} +(0.401924 - 0.232051i) q^{19} +(-0.866025 + 0.500000i) q^{20} -2.19615i q^{21} +(-1.50000 - 2.59808i) q^{22} +(-4.73205 + 8.19615i) q^{23} +(-0.633975 - 0.366025i) q^{24} -1.00000 q^{25} -4.00000 q^{27} +(-2.59808 - 1.50000i) q^{28} +(1.26795 - 2.19615i) q^{29} +(-0.366025 - 0.633975i) q^{30} -4.73205i q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.90192 - 1.09808i) q^{33} -8.19615i q^{34} +(-1.50000 - 2.59808i) q^{35} +(-1.23205 + 2.13397i) q^{36} +(0.696152 + 0.401924i) q^{37} +0.464102 q^{38} -1.00000 q^{40} +(9.00000 + 5.19615i) q^{41} +(1.09808 - 1.90192i) q^{42} +(-1.00000 - 1.73205i) q^{43} -3.00000i q^{44} +(-2.13397 + 1.23205i) q^{45} +(-8.19615 + 4.73205i) q^{46} -3.00000i q^{47} +(-0.366025 - 0.633975i) q^{48} +(1.00000 - 1.73205i) q^{49} +(-0.866025 - 0.500000i) q^{50} +6.00000 q^{51} +0.464102 q^{53} +(-3.46410 - 2.00000i) q^{54} +(1.50000 - 2.59808i) q^{55} +(-1.50000 - 2.59808i) q^{56} +0.339746i q^{57} +(2.19615 - 1.26795i) q^{58} +(-9.00000 + 5.19615i) q^{59} -0.732051i q^{60} +(-3.09808 - 5.36603i) q^{61} +(2.36603 - 4.09808i) q^{62} +(-6.40192 - 3.69615i) q^{63} -1.00000 q^{64} +2.19615 q^{66} +(4.09808 - 7.09808i) q^{68} +(-3.46410 - 6.00000i) q^{69} -3.00000i q^{70} +(5.19615 - 3.00000i) q^{71} +(-2.13397 + 1.23205i) q^{72} -11.6603i q^{73} +(0.401924 + 0.696152i) q^{74} +(0.366025 - 0.633975i) q^{75} +(0.401924 + 0.232051i) q^{76} +9.00000 q^{77} -4.19615 q^{79} +(-0.866025 - 0.500000i) q^{80} +(-2.23205 + 3.86603i) q^{81} +(5.19615 + 9.00000i) q^{82} +8.19615i q^{83} +(1.90192 - 1.09808i) q^{84} +(7.09808 - 4.09808i) q^{85} -2.00000i q^{86} +(0.928203 + 1.60770i) q^{87} +(1.50000 - 2.59808i) q^{88} +(-5.89230 - 3.40192i) q^{89} -2.46410 q^{90} -9.46410 q^{92} +(3.00000 + 1.73205i) q^{93} +(1.50000 - 2.59808i) q^{94} +(0.232051 + 0.401924i) q^{95} -0.732051i q^{96} +(-7.90192 + 4.56218i) q^{97} +(1.73205 - 1.00000i) q^{98} -7.39230i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} - 6 q^{6} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^6 - 2 * q^9	\( 4 q + 2 q^{3} + 2 q^{4} - 6 q^{6} - 2 q^{9} - 2 q^{10} + 4 q^{12} - 12 q^{14} - 6 q^{15} - 2 q^{16} - 6 q^{17} + 12 q^{19} - 6 q^{22} - 12 q^{23} - 6 q^{24} - 4 q^{25} - 16 q^{27} + 12 q^{29} + 2 q^{30} + 18 q^{33} - 6 q^{35} + 2 q^{36} - 18 q^{37} - 12 q^{38} - 4 q^{40} + 36 q^{41} - 6 q^{42} - 4 q^{43} - 12 q^{45} - 12 q^{46} + 2 q^{48} + 4 q^{49} + 24 q^{51} - 12 q^{53} + 6 q^{55} - 6 q^{56} - 12 q^{58} - 36 q^{59} - 2 q^{61} + 6 q^{62} - 36 q^{63} - 4 q^{64} - 12 q^{66} + 6 q^{68} - 12 q^{72} + 12 q^{74} - 2 q^{75} + 12 q^{76} + 36 q^{77} + 4 q^{79} - 2 q^{81} + 18 q^{84} + 18 q^{85} - 24 q^{87} + 6 q^{88} + 18 q^{89} + 4 q^{90} - 24 q^{92} + 12 q^{93} + 6 q^{94} - 6 q^{95} - 42 q^{97}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^6 - 2 * q^9 - 2 * q^10 + 4 * q^12 - 12 * q^14 - 6 * q^15 - 2 * q^16 - 6 * q^17 + 12 * q^19 - 6 * q^22 - 12 * q^23 - 6 * q^24 - 4 * q^25 - 16 * q^27 + 12 * q^29 + 2 * q^30 + 18 * q^33 - 6 * q^35 + 2 * q^36 - 18 * q^37 - 12 * q^38 - 4 * q^40 + 36 * q^41 - 6 * q^42 - 4 * q^43 - 12 * q^45 - 12 * q^46 + 2 * q^48 + 4 * q^49 + 24 * q^51 - 12 * q^53 + 6 * q^55 - 6 * q^56 - 12 * q^58 - 36 * q^59 - 2 * q^61 + 6 * q^62 - 36 * q^63 - 4 * q^64 - 12 * q^66 + 6 * q^68 - 12 * q^72 + 12 * q^74 - 2 * q^75 + 12 * q^76 + 36 * q^77 + 4 * q^79 - 2 * q^81 + 18 * q^84 + 18 * q^85 - 24 * q^87 + 6 * q^88 + 18 * q^89 + 4 * q^90 - 24 * q^92 + 12 * q^93 + 6 * q^94 - 6 * q^95 - 42 * q^97

Introduction

L-functions

Modular forms

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Database

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