LMFDB - Embedded newform 1690.2.e.l.191.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1690,2,Mod(191,1690)]

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, 4]))

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

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

chi := DirichletCharacter("1690.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.e (of order $3$, 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 $\Q(\zeta_{3})$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1690.191
Dual form			1690.2.e.l.991.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−0.366025	+	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
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.366025	−	0.633975i	−0.149429	−	0.258819i
$7$	1.50000	+	2.59808i	0.566947	+	0.981981i	0.996866	+	0.0791130i	$0.0252088\pi$
$7$	1.50000	+	2.59808i	0.566947	+	0.981981i	−0.429919	+	0.902867i	$0.641458\pi$
$8$	1.00000			0.353553
$9$	1.23205	+	2.13397i	0.410684	+	0.711325i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$	0.732051			0.211325
$13$		0			0
$13$		0			0
$14$	−3.00000			−0.801784
$15$	0.366025	−	0.633975i	0.0945074	−	0.163692i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.09808	+	7.09808i	0.993929	+	1.72154i	0.592244	+	0.805759i	$0.298242\pi$
$17$	4.09808	+	7.09808i	0.993929	+	1.72154i	0.401685	+	0.915778i	$0.368425\pi$
$18$	−2.46410			−0.580794
$19$	0.232051	+	0.401924i	0.0532361	+	0.0922076i	0.891415	−	0.453187i	$-0.149713\pi$
$19$	0.232051	+	0.401924i	0.0532361	+	0.0922076i	−0.838179	+	0.545395i	$0.816380\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	−2.19615			−0.479240
$22$	−1.50000	−	2.59808i	−0.319801	−	0.553912i
$23$	4.73205	−	8.19615i	0.986701	−	1.70902i	0.352581	−	0.935781i	$-0.385304\pi$
$23$	4.73205	−	8.19615i	0.986701	−	1.70902i	0.634120	−	0.773234i	$-0.281362\pi$
$24$	−0.366025	+	0.633975i	−0.0747146	+	0.129410i
$25$	1.00000			0.200000
$26$		0			0
$27$	−4.00000			−0.769800
$28$	1.50000	−	2.59808i	0.283473	−	0.490990i
$29$	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
$31$	4.73205			0.849901			0.424951	−	0.905216i	$-0.360291\pi$
$31$	4.73205			0.849901			0.424951	+	0.905216i	$0.360291\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.09808	−	1.90192i	−0.191151	−	0.331082i
$34$	−8.19615			−1.40563
$35$	−1.50000	−	2.59808i	−0.253546	−	0.439155i
$36$	1.23205	−	2.13397i	0.205342	−	0.355662i
$37$	0.401924	−	0.696152i	0.0660759	−	0.114447i	−0.831095	−	0.556131i	$-0.812285\pi$
$37$	0.401924	−	0.696152i	0.0660759	−	0.114447i	0.897171	+	0.441684i	$0.145619\pi$
$38$	−0.464102			−0.0752872
$39$		0			0
$40$	−1.00000			−0.158114
$41$	−5.19615	+	9.00000i	−0.811503	+	1.40556i	0.100309	+	0.994956i	$0.468017\pi$
$41$	−5.19615	+	9.00000i	−0.811503	+	1.40556i	−0.911812	+	0.410608i	$0.865317\pi$
$42$	1.09808	−	1.90192i	0.169437	−	0.293473i
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	0.932145	−	0.362084i	$-0.117935\pi$
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	−0.779647	+	0.626219i	$0.784601\pi$
$44$	3.00000			0.452267
$45$	−1.23205	−	2.13397i	−0.183663	−	0.318114i
$46$	4.73205	+	8.19615i	0.697703	+	1.20846i
$47$	−3.00000			−0.437595			−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000			−0.437595			−0.218797	+	0.975770i	$0.570213\pi$
$48$	−0.366025	−	0.633975i	−0.0528312	−	0.0915064i
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−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	$0.489852\pi$
$54$	2.00000	−	3.46410i	0.272166	−	0.471405i
$55$	1.50000	−	2.59808i	0.202260	−	0.350325i
$56$	1.50000	+	2.59808i	0.200446	+	0.347183i
$57$	−0.339746			−0.0450005
$58$	1.26795	+	2.19615i	0.166490	+	0.288369i
$59$	5.19615	+	9.00000i	0.676481	+	1.17170i	0.976034	+	0.217620i	$0.0698294\pi$
$59$	5.19615	+	9.00000i	0.676481	+	1.17170i	−0.299552	+	0.954080i	$0.596837\pi$
$60$	−0.732051			−0.0945074
$61$	−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
$63$	−3.69615	+	6.40192i	−0.465671	+	0.806567i
$64$	1.00000			0.125000
$65$		0			0
$66$	2.19615			0.270328
$67$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$67$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$68$	4.09808	−	7.09808i	0.496965	−	0.860768i
$69$	3.46410	+	6.00000i	0.417029	+	0.722315i
$70$	3.00000			0.358569
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$	1.23205	+	2.13397i	0.145199	+	0.251491i
$73$	−11.6603			−1.36473			−0.682365	−	0.731012i	$-0.739048\pi$
$73$	−11.6603			−1.36473			−0.682365	+	0.731012i	$0.739048\pi$
$74$	0.401924	+	0.696152i	0.0467227	+	0.0809261i
$75$	−0.366025	+	0.633975i	−0.0422650	+	0.0732051i
$76$	0.232051	−	0.401924i	0.0266181	−	0.0461038i
$77$	−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	$0.575854\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−2.23205	+	3.86603i	−0.248006	+	0.429558i
$82$	−5.19615	−	9.00000i	−0.573819	−	0.993884i
$83$	−8.19615			−0.899645			−0.449822	−	0.893118i	$-0.648513\pi$
$83$	−8.19615			−0.899645			−0.449822	+	0.893118i	$0.648513\pi$
$84$	1.09808	+	1.90192i	0.119810	+	0.207517i
$85$	−4.09808	−	7.09808i	−0.444499	−	0.769894i
$86$	−2.00000			−0.215666
$87$	0.928203	+	1.60770i	0.0995138	+	0.172363i
$88$	−1.50000	+	2.59808i	−0.159901	+	0.276956i
$89$	−3.40192	+	5.89230i	−0.360603	+	0.624583i	−0.988060	−	0.154068i	$-0.950762\pi$
$89$	−3.40192	+	5.89230i	−0.360603	+	0.624583i	0.627457	+	0.778651i	$0.284096\pi$
$90$	2.46410			0.259739
$91$		0			0
$92$	−9.46410			−0.986701
$93$	−1.73205	+	3.00000i	−0.179605	+	0.311086i
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$	−0.232051	−	0.401924i	−0.0238079	−	0.0412365i
$96$	0.732051			0.0747146
$97$	−4.56218	−	7.90192i	−0.463219	−	0.802319i	0.535900	−	0.844281i	$-0.319972\pi$
$97$	−4.56218	−	7.90192i	−0.463219	−	0.802319i	−0.999119	+	0.0419625i	$0.986639\pi$
$98$	−1.00000	−	1.73205i	−0.101015	−	0.174964i
$99$	−7.39230			−0.742955
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	5.36603	−	9.29423i	0.533939	−	0.924810i	−0.465274	−	0.885167i	$-0.654044\pi$
$101$	5.36603	−	9.29423i	0.533939	−	0.924810i	0.999214	−	0.0396438i	$-0.0126223\pi$
$102$	3.00000	−	5.19615i	0.297044	−	0.514496i
$103$	9.19615			0.906124			0.453062	−	0.891479i	$-0.350332\pi$
$103$	9.19615			0.906124			0.453062	+	0.891479i	$0.350332\pi$
$104$		0			0
$105$	2.19615			0.214323
$106$	−0.232051	+	0.401924i	−0.0225388	+	0.0390383i
$107$	−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
$109$	−8.53590			−0.817591			−0.408795	−	0.912626i	$-0.634051\pi$
$109$	−8.53590			−0.817591			−0.408795	+	0.912626i	$0.634051\pi$
$110$	1.50000	+	2.59808i	0.143019	+	0.247717i
$111$	0.294229	+	0.509619i	0.0279269	+	0.0483709i
$112$	−3.00000			−0.283473
$113$	−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
$115$	−4.73205	+	8.19615i	−0.441266	+	0.764295i
$116$	−2.53590			−0.235452
$117$		0			0
$118$	−10.3923			−0.956689
$119$	−12.2942	+	21.2942i	−1.12701	+	1.95204i
$120$	0.366025	−	0.633975i	0.0334134	−	0.0578737i
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	6.19615			0.560973
$123$	−3.80385	−	6.58846i	−0.342981	−	0.594061i
$124$	−2.36603	−	4.09808i	−0.212475	−	0.368018i
$125$	−1.00000			−0.0894427
$126$	−3.69615	−	6.40192i	−0.329279	−	0.570329i
$127$	5.40192	−	9.35641i	0.479343	−	0.830247i	−0.520376	−	0.853937i	$-0.674208\pi$
$127$	5.40192	−	9.35641i	0.479343	−	0.830247i	0.999719	+	0.0236904i	$0.00754158\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−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	$0.413788\pi$
$132$	−1.09808	+	1.90192i	−0.0955753	+	0.165541i
$133$	−0.696152	+	1.20577i	−0.0603641	+	0.104554i
$134$		0			0
$135$	4.00000			0.344265
$136$	4.09808	+	7.09808i	0.351407	+	0.608655i
$137$	1.09808	+	1.90192i	0.0938150	+	0.162492i	0.909113	−	0.416549i	$-0.136760\pi$
$137$	1.09808	+	1.90192i	0.0938150	+	0.162492i	−0.815298	+	0.579041i	$0.803427\pi$
$138$	−6.92820			−0.589768
$139$	−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
$141$	1.09808	−	1.90192i	0.0924747	−	0.160171i
$142$	−6.00000			−0.503509
$143$		0			0
$144$	−2.46410			−0.205342
$145$	−1.26795	+	2.19615i	−0.105297	+	0.182381i
$146$	5.83013	−	10.0981i	0.482505	−	0.835723i
$147$	−0.732051	−	1.26795i	−0.0603785	−	0.104579i
$148$	−0.803848			−0.0660759
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$	−0.366025	−	0.633975i	−0.0298858	−	0.0517638i
$151$	23.6603			1.92544			0.962722	−	0.270492i	$-0.0871865\pi$
$151$	23.6603			1.92544			0.962722	+	0.270492i	$0.0871865\pi$
$152$	0.232051	+	0.401924i	0.0188218	+	0.0326003i
$153$	−10.0981	+	17.4904i	−0.816381	+	1.41401i
$154$	4.50000	−	7.79423i	0.362620	−	0.628077i
$155$	−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	$0.673605\pi$
$158$	2.09808	−	3.63397i	0.166914	−	0.289103i
$159$	−0.169873	+	0.294229i	−0.0134718	+	0.0233338i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	28.3923			2.23763
$162$	−2.23205	−	3.86603i	−0.175366	−	0.303744i
$163$	−5.36603	−	9.29423i	−0.420300	−	0.727980i	0.575669	−	0.817683i	$-0.304742\pi$
$163$	−5.36603	−	9.29423i	−0.420300	−	0.727980i	−0.995969	+	0.0897026i	$0.971408\pi$
$164$	10.3923			0.811503
$165$	1.09808	+	1.90192i	0.0854851	+	0.148065i
$166$	4.09808	−	7.09808i	0.318072	−	0.550918i
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	−0.918208	−	0.396098i	$-0.870364\pi$
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	0.802135	+	0.597143i	$0.203697\pi$
$168$	−2.19615			−0.169437
$169$		0			0
$170$	8.19615			0.628616
$171$	−0.571797	+	0.990381i	−0.0437264	+	0.0757363i
$172$	1.00000	−	1.73205i	0.0762493	−	0.132068i
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	−0.996544	−	0.0830722i	$-0.973527\pi$
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	0.426329	−	0.904568i	$-0.359807\pi$
$174$	−1.85641			−0.140734
$175$	1.50000	+	2.59808i	0.113389	+	0.196396i
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$	−7.60770			−0.571829
$178$	−3.40192	−	5.89230i	−0.254985	−	0.441647i
$179$	−4.73205	+	8.19615i	−0.353690	+	0.612609i	−0.986893	−	0.161377i	$-0.948407\pi$
$179$	−4.73205	+	8.19615i	−0.353690	+	0.612609i	0.633203	+	0.773986i	$0.281740\pi$
$180$	−1.23205	+	2.13397i	−0.0918316	+	0.159057i
$181$	−14.5885			−1.08435			−0.542176	−	0.840265i	$-0.682399\pi$
$181$	−14.5885			−1.08435			−0.542176	+	0.840265i	$0.682399\pi$
$182$		0			0
$183$	4.53590			0.335303
$184$	4.73205	−	8.19615i	0.348851	−	0.604228i
$185$	−0.401924	+	0.696152i	−0.0295500	+	0.0511821i
$186$	−1.73205	−	3.00000i	−0.127000	−	0.219971i
$187$	−24.5885			−1.79809
$188$	1.50000	+	2.59808i	0.109399	+	0.189484i
$189$	−6.00000	−	10.3923i	−0.436436	−	0.755929i
$190$	0.464102			0.0336695
$191$	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
$193$	8.19615	−	14.1962i	0.589972	−	1.02186i	−0.404263	−	0.914643i	$-0.632472\pi$
$193$	8.19615	−	14.1962i	0.589972	−	1.02186i	0.994235	−	0.107219i	$-0.0341945\pi$
$194$	9.12436			0.655091
$195$		0			0
$196$	2.00000			0.142857
$197$	10.7942	−	18.6962i	0.769057	−	1.33205i	−0.169018	−	0.985613i	$-0.554060\pi$
$197$	10.7942	−	18.6962i	0.769057	−	1.33205i	0.938075	−	0.346433i	$-0.112607\pi$
$198$	3.69615	−	6.40192i	0.262674	−	0.454965i
$199$	−3.19615	−	5.53590i	−0.226569	−	0.392429i	0.730220	−	0.683212i	$-0.239418\pi$
$199$	−3.19615	−	5.53590i	−0.226569	−	0.392429i	−0.956789	+	0.290783i	$0.906084\pi$
$200$	1.00000			0.0707107
$201$		0			0
$202$	5.36603	+	9.29423i	0.377552	+	0.653940i
$203$	7.60770			0.533956
$204$	3.00000	+	5.19615i	0.210042	+	0.363803i
$205$	5.19615	−	9.00000i	0.362915	−	0.628587i
$206$	−4.59808	+	7.96410i	−0.320363	+	0.554885i
$207$	23.3205			1.62089
$208$		0			0
$209$	−1.39230			−0.0963077
$210$	−1.09808	+	1.90192i	−0.0757745	+	0.131245i
$211$	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
$213$	−4.39230			−0.300956
$214$	−8.83013	−	15.2942i	−0.603615	−	1.04549i
$215$	−1.00000	−	1.73205i	−0.0681994	−	0.118125i
$216$	−4.00000			−0.272166
$217$	7.09808	+	12.2942i	0.481849	+	0.834587i
$218$	4.26795	−	7.39230i	0.289062	−	0.500670i
$219$	4.26795	−	7.39230i	0.288401	−	0.499526i
$220$	−3.00000			−0.202260
$221$		0			0
$222$	−0.588457			−0.0394947
$223$	−3.23205	+	5.59808i	−0.216434	+	0.374875i	−0.953715	−	0.300711i	$-0.902776\pi$
$223$	−3.23205	+	5.59808i	−0.216434	+	0.374875i	0.737281	+	0.675586i	$0.236109\pi$
$224$	1.50000	−	2.59808i	0.100223	−	0.173591i
$225$	1.23205	+	2.13397i	0.0821367	+	0.142265i
$226$	6.92820			0.460857
$227$	−8.19615	−	14.1962i	−0.543998	−	0.942232i	−0.998669	−	0.0515725i	$-0.983577\pi$
$227$	−8.19615	−	14.1962i	−0.543998	−	0.942232i	0.454672	−	0.890659i	$-0.349757\pi$
$228$	0.169873	+	0.294229i	0.0112501	+	0.0194858i
$229$	1.26795			0.0837884			0.0418942	−	0.999122i	$-0.486661\pi$
$229$	1.26795			0.0837884			0.0418942	+	0.999122i	$0.486661\pi$
$230$	−4.73205	−	8.19615i	−0.312022	−	0.540438i
$231$	3.29423	−	5.70577i	0.216744	−	0.375412i
$232$	1.26795	−	2.19615i	0.0832449	−	0.144184i
$233$	−4.73205			−0.310007			−0.155003	−	0.987914i	$-0.549539\pi$
$233$	−4.73205			−0.310007			−0.155003	+	0.987914i	$0.549539\pi$
$234$		0			0
$235$	3.00000			0.195698
$236$	5.19615	−	9.00000i	0.338241	−	0.585850i
$237$	1.53590	−	2.66025i	0.0997673	−	0.172802i
$238$	−12.2942	−	21.2942i	−0.796916	−	1.38030i
$239$	2.19615			0.142057			0.0710286	−	0.997474i	$-0.477372\pi$
$239$	2.19615			0.142057			0.0710286	+	0.997474i	$0.477372\pi$
$240$	0.366025	+	0.633975i	0.0236268	+	0.0409229i
$241$	−4.33013	−	7.50000i	−0.278928	−	0.483117i	0.692191	−	0.721715i	$-0.256646\pi$
$241$	−4.33013	−	7.50000i	−0.278928	−	0.483117i	−0.971119	+	0.238597i	$0.923312\pi$
$242$	−2.00000			−0.128565
$243$	−7.63397	−	13.2224i	−0.489720	−	0.848219i
$244$	−3.09808	+	5.36603i	−0.198334	+	0.343525i
$245$	1.00000	−	1.73205i	0.0638877	−	0.110657i
$246$	7.60770			0.485049
$247$		0			0
$248$	4.73205			0.300486
$249$	3.00000	−	5.19615i	0.190117	−	0.329293i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	8.59808	+	14.8923i	0.542706	+	0.939994i	0.998747	+	0.0500355i	$0.0159335\pi$
$251$	8.59808	+	14.8923i	0.542706	+	0.939994i	−0.456042	+	0.889958i	$0.650733\pi$
$252$	7.39230			0.465671
$253$	14.1962	+	24.5885i	0.892504	+	1.54586i
$254$	5.40192	+	9.35641i	0.338947	+	0.587073i
$255$	6.00000			0.375735
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.92820	+	12.0000i	−0.432169	+	0.748539i	−0.997060	−	0.0766265i	$-0.975585\pi$
$257$	−6.92820	+	12.0000i	−0.432169	+	0.748539i	0.564890	+	0.825166i	$0.308918\pi$
$258$	0.732051	−	1.26795i	0.0455755	−	0.0789391i
$259$	2.41154			0.149846
$260$		0			0
$261$	6.24871			0.386786
$262$	−3.06218	+	5.30385i	−0.189182	+	0.327673i
$263$	−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
$265$	−0.464102			−0.0285095
$266$	−0.696152	−	1.20577i	−0.0426838	−	0.0739306i
$267$	−2.49038	−	4.31347i	−0.152409	−	0.263980i
$268$		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
$271$	−4.73205	+	8.19615i	−0.287452	+	0.497881i	−0.973201	−	0.229957i	$-0.926141\pi$
$271$	−4.73205	+	8.19615i	−0.287452	+	0.497881i	0.685749	+	0.727838i	$0.259475\pi$
$272$	−8.19615			−0.496965
$273$		0			0
$274$	−2.19615			−0.132674
$275$	−1.50000	+	2.59808i	−0.0904534	+	0.156670i
$276$	3.46410	−	6.00000i	0.208514	−	0.361158i
$277$	−0.500000	−	0.866025i	−0.0300421	−	0.0520344i	0.850613	−	0.525792i	$-0.176231\pi$
$277$	−0.500000	−	0.866025i	−0.0300421	−	0.0520344i	−0.880656	+	0.473757i	$0.842897\pi$
$278$	1.19615			0.0717405
$279$	5.83013	+	10.0981i	0.349041	+	0.604556i
$280$	−1.50000	−	2.59808i	−0.0896421	−	0.155265i
$281$	10.3923			0.619953			0.309976	−	0.950744i	$-0.399679\pi$
$281$	10.3923			0.619953			0.309976	+	0.950744i	$0.399679\pi$
$282$	1.09808	+	1.90192i	0.0653895	+	0.113258i
$283$	−4.80385	+	8.32051i	−0.285559	+	0.494603i	−0.972745	−	0.231879i	$-0.925513\pi$
$283$	−4.80385	+	8.32051i	−0.285559	+	0.494603i	0.687186	+	0.726482i	$0.258846\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$	0.339746			0.0201248
$286$		0			0
$287$	−31.1769			−1.84032
$288$	1.23205	−	2.13397i	0.0725993	−	0.125746i
$289$	−25.0885	+	43.4545i	−1.47579	+	2.55615i
$290$	−1.26795	−	2.19615i	−0.0744565	−	0.128963i
$291$	6.67949			0.391559
$292$	5.83013	+	10.0981i	0.341182	+	0.590945i
$293$	5.59808	+	9.69615i	0.327043	+	0.566455i	0.981924	−	0.189277i	$-0.0606144\pi$
$293$	5.59808	+	9.69615i	0.327043	+	0.566455i	−0.654881	+	0.755732i	$0.727281\pi$
$294$	1.46410			0.0853881
$295$	−5.19615	−	9.00000i	−0.302532	−	0.524000i
$296$	0.401924	−	0.696152i	0.0233613	−	0.0404630i
$297$	6.00000	−	10.3923i	0.348155	−	0.603023i
$298$	6.00000			0.347571
$299$		0			0
$300$	0.732051			0.0422650
$301$	−3.00000	+	5.19615i	−0.172917	+	0.299501i
$302$	−11.8301	+	20.4904i	−0.680747	+	1.17909i
$303$	3.92820	+	6.80385i	0.225669	+	0.390871i
$304$	−0.464102			−0.0266181
$305$	3.09808	+	5.36603i	0.177395	+	0.307258i
$306$	−10.0981	−	17.4904i	−0.577269	−	0.999859i
$307$	27.4641			1.56746			0.783730	−	0.621102i	$-0.213315\pi$
$307$	27.4641			1.56746			0.783730	+	0.621102i	$0.213315\pi$
$308$	4.50000	+	7.79423i	0.256411	+	0.444117i
$309$	−3.36603	+	5.83013i	−0.191486	+	0.331664i
$310$	2.36603	−	4.09808i	0.134381	−	0.232755i
$311$	9.12436			0.517395			0.258697	−	0.965958i	$-0.416707\pi$
$311$	9.12436			0.517395			0.258697	+	0.965958i	$0.416707\pi$
$312$		0			0
$313$	26.3923			1.49178			0.745891	−	0.666068i	$-0.232024\pi$
$313$	26.3923			1.49178			0.745891	+	0.666068i	$0.232024\pi$
$314$	6.50000	−	11.2583i	0.366816	−	0.635344i
$315$	3.69615	−	6.40192i	0.208255	−	0.360708i
$316$	2.09808	+	3.63397i	0.118026	+	0.204427i
$317$	−23.1962			−1.30283			−0.651413	−	0.758723i	$-0.725823\pi$
$317$	−23.1962			−1.30283			−0.651413	+	0.758723i	$0.725823\pi$
$318$	−0.169873	−	0.294229i	−0.00952600	−	0.0164995i
$319$	3.80385	+	6.58846i	0.212975	+	0.368883i
$320$	−1.00000			−0.0559017
$321$	−6.46410	−	11.1962i	−0.360791	−	0.624908i
$322$	−14.1962	+	24.5885i	−0.791121	+	1.37026i
$323$	−1.90192	+	3.29423i	−0.105826	+	0.183296i
$324$	4.46410			0.248006
$325$		0			0
$326$	10.7321			0.594393
$327$	3.12436	−	5.41154i	0.172777	−	0.299259i
$328$	−5.19615	+	9.00000i	−0.286910	+	0.496942i
$329$	−4.50000	−	7.79423i	−0.248093	−	0.429710i
$330$	−2.19615			−0.120894
$331$	−6.46410	−	11.1962i	−0.355299	−	0.615396i	0.631870	−	0.775074i	$-0.282288\pi$
$331$	−6.46410	−	11.1962i	−0.355299	−	0.615396i	−0.987169	+	0.159678i	$0.948954\pi$
$332$	4.09808	+	7.09808i	0.224911	+	0.389558i
$333$	1.98076			0.108545
$334$	−1.50000	−	2.59808i	−0.0820763	−	0.142160i
$335$		0			0
$336$	1.09808	−	1.90192i	0.0599050	−	0.103758i
$337$	−6.19615			−0.337526			−0.168763	−	0.985657i	$-0.553977\pi$
$337$	−6.19615			−0.337526			−0.168763	+	0.985657i	$0.553977\pi$
$338$		0			0
$339$	5.07180			0.275462
$340$	−4.09808	+	7.09808i	−0.222249	+	0.384947i
$341$	−7.09808	+	12.2942i	−0.384382	+	0.665770i
$342$	−0.571797	−	0.990381i	−0.0309192	−	0.0535537i
$343$	15.0000			0.809924
$344$	1.00000	+	1.73205i	0.0539164	+	0.0933859i
$345$	−3.46410	−	6.00000i	−0.186501	−	0.323029i
$346$	15.0000			0.806405
$347$	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
$349$	2.02628	−	3.50962i	0.108464	−	0.187866i	−0.806684	−	0.590983i	$-0.798740\pi$
$349$	2.02628	−	3.50962i	0.108464	−	0.187866i	0.915148	+	0.403117i	$0.132073\pi$
$350$	−3.00000			−0.160357
$351$		0			0
$352$	3.00000			0.159901
$353$	4.90192	−	8.49038i	0.260903	−	0.451897i	−0.705579	−	0.708631i	$-0.749313\pi$
$353$	4.90192	−	8.49038i	0.260903	−	0.451897i	0.966482	+	0.256734i	$0.0826464\pi$
$354$	3.80385	−	6.58846i	0.202172	−	0.350173i
$355$	−3.00000	−	5.19615i	−0.159223	−	0.275783i
$356$	6.80385			0.360603
$357$	−9.00000	−	15.5885i	−0.476331	−	0.825029i
$358$	−4.73205	−	8.19615i	−0.250097	−	0.433180i
$359$	−1.60770			−0.0848509			−0.0424255	−	0.999100i	$-0.513508\pi$
$359$	−1.60770			−0.0848509			−0.0424255	+	0.999100i	$0.513508\pi$
$360$	−1.23205	−	2.13397i	−0.0649348	−	0.112470i
$361$	9.39230	−	16.2679i	0.494332	−	0.856208i
$362$	7.29423	−	12.6340i	0.383376	−	0.664027i
$363$	−1.46410			−0.0768454
$364$		0			0
$365$	11.6603			0.610326
$366$	−2.26795	+	3.92820i	−0.118548	+	0.205330i
$367$	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
$369$	−25.6077			−1.33308
$370$	−0.401924	−	0.696152i	−0.0208950	−	0.0361912i
$371$	0.696152	+	1.20577i	0.0361424	+	0.0626005i
$372$	3.46410			0.179605
$373$	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
$375$	0.366025	−	0.633975i	0.0189015	−	0.0327383i
$376$	−3.00000			−0.154713
$377$		0			0
$378$	12.0000			0.617213
$379$	14.8923	−	25.7942i	0.764966	−	1.32496i	−0.175298	−	0.984515i	$-0.556089\pi$
$379$	14.8923	−	25.7942i	0.764966	−	1.32496i	0.940264	−	0.340445i	$-0.110578\pi$
$380$	−0.232051	+	0.401924i	−0.0119040	+	0.0206183i
$381$	3.95448	+	6.84936i	0.202594	+	0.350904i
$382$	−22.7321			−1.16307
$383$	−11.1962	−	19.3923i	−0.572097	−	0.990900i	−0.996350	−	0.0853571i	$-0.972797\pi$
$383$	−11.1962	−	19.3923i	−0.572097	−	0.990900i	0.424254	−	0.905543i	$-0.360536\pi$
$384$	−0.366025	−	0.633975i	−0.0186787	−	0.0323524i
$385$	9.00000			0.458682
$386$	8.19615	+	14.1962i	0.417173	+	0.722565i
$387$	−2.46410	+	4.26795i	−0.125257	+	0.216952i
$388$	−4.56218	+	7.90192i	−0.231609	+	0.401159i
$389$	−22.7321			−1.15256			−0.576280	−	0.817252i	$-0.695496\pi$
$389$	−22.7321			−1.15256			−0.576280	+	0.817252i	$0.695496\pi$
$390$		0			0
$391$	77.5692			3.92284
$392$	−1.00000	+	1.73205i	−0.0505076	+	0.0874818i
$393$	−2.24167	+	3.88269i	−0.113077	+	0.195856i
$394$	10.7942	+	18.6962i	0.543805	+	0.941899i
$395$	4.19615			0.211131
$396$	3.69615	+	6.40192i	0.185739	+	0.321709i
$397$	−5.59808	−	9.69615i	−0.280959	−	0.486636i	0.690662	−	0.723178i	$-0.257319\pi$
$397$	−5.59808	−	9.69615i	−0.280959	−	0.486636i	−0.971621	+	0.236542i	$0.923986\pi$
$398$	6.39230			0.320417
$399$	−0.509619	−	0.882686i	−0.0255129	−	0.0441896i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	2.59808	−	4.50000i	0.129742	−	0.224719i	−0.793835	−	0.608134i	$-0.791919\pi$
$401$	2.59808	−	4.50000i	0.129742	−	0.224719i	0.923576	+	0.383414i	$0.125252\pi$
$402$		0			0
$403$		0			0
$404$	−10.7321			−0.533939
$405$	2.23205	−	3.86603i	0.110911	−	0.192104i
$406$	−3.80385	+	6.58846i	−0.188782	+	0.326980i
$407$	1.20577	+	2.08846i	0.0597679	+	0.103521i
$408$	−6.00000			−0.297044
$409$	8.13397	+	14.0885i	0.402199	+	0.696629i	0.993991	−	0.109461i	$-0.0349126\pi$
$409$	8.13397	+	14.0885i	0.402199	+	0.696629i	−0.591792	+	0.806091i	$0.701579\pi$
$410$	5.19615	+	9.00000i	0.256620	+	0.444478i
$411$	−1.60770			−0.0793018
$412$	−4.59808	−	7.96410i	−0.226531	−	0.392363i
$413$	−15.5885	+	27.0000i	−0.767058	+	1.32858i
$414$	−11.6603	+	20.1962i	−0.573070	+	0.992587i
$415$	8.19615			0.402333
$416$		0			0
$417$	0.875644			0.0428805
$418$	0.696152	−	1.20577i	0.0340499	−	0.0589762i
$419$	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
$421$	2.87564			0.140150			0.0700752	−	0.997542i	$-0.477676\pi$
$421$	2.87564			0.140150			0.0700752	+	0.997542i	$0.477676\pi$
$422$	8.79423	+	15.2321i	0.428096	+	0.741485i
$423$	−3.69615	−	6.40192i	−0.179713	−	0.311272i
$424$	0.464102			0.0225388
$425$	4.09808	+	7.09808i	0.198786	+	0.344307i
$426$	2.19615	−	3.80385i	0.106404	−	0.184297i
$427$	9.29423	−	16.0981i	0.449779	−	0.779041i
$428$	17.6603			0.853641
$429$		0			0
$430$	2.00000			0.0964486
$431$	−4.09808	+	7.09808i	−0.197397	+	0.341902i	−0.947684	−	0.319211i	$-0.896582\pi$
$431$	−4.09808	+	7.09808i	−0.197397	+	0.341902i	0.750286	+	0.661113i	$0.229916\pi$
$432$	2.00000	−	3.46410i	0.0962250	−	0.166667i
$433$	4.19615	+	7.26795i	0.201654	+	0.349275i	0.949062	−	0.315091i	$-0.102035\pi$
$433$	4.19615	+	7.26795i	0.201654	+	0.349275i	−0.747407	+	0.664366i	$0.768702\pi$
$434$	−14.1962			−0.681437
$435$	−0.928203	−	1.60770i	−0.0445039	−	0.0770831i
$436$	4.26795	+	7.39230i	0.204398	+	0.354027i
$437$	4.39230			0.210112
$438$	4.26795	+	7.39230i	0.203931	+	0.353218i
$439$	−1.70577	+	2.95448i	−0.0814120	+	0.141010i	−0.903857	−	0.427835i	$-0.859276\pi$
$439$	−1.70577	+	2.95448i	−0.0814120	+	0.141010i	0.822445	+	0.568845i	$0.192610\pi$
$440$	1.50000	−	2.59808i	0.0715097	−	0.123858i
$441$	−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	$0.678539\pi$
$444$	0.294229	−	0.509619i	0.0139635	−	0.0241854i
$445$	3.40192	−	5.89230i	0.161267	−	0.279322i
$446$	−3.23205	−	5.59808i	−0.153042	−	0.265077i
$447$	4.39230			0.207749
$448$	1.50000	+	2.59808i	0.0708683	+	0.122748i
$449$	7.79423	+	13.5000i	0.367832	+	0.637104i	0.989226	−	0.146394i	$-0.0467667\pi$
$449$	7.79423	+	13.5000i	0.367832	+	0.637104i	−0.621394	+	0.783498i	$0.713433\pi$
$450$	−2.46410			−0.116159
$451$	−15.5885	−	27.0000i	−0.734032	−	1.27138i
$452$	−3.46410	+	6.00000i	−0.162938	+	0.282216i
$453$	−8.66025	+	15.0000i	−0.406894	+	0.704761i
$454$	16.3923			0.769329
$455$		0			0
$456$	−0.339746			−0.0159101
$457$	9.16987	−	15.8827i	0.428949	−	0.742961i	−0.567832	−	0.823145i	$-0.692217\pi$
$457$	9.16987	−	15.8827i	0.428949	−	0.742961i	0.996780	+	0.0801841i	$0.0255508\pi$
$458$	−0.633975	+	1.09808i	−0.0296237	+	0.0513097i
$459$	−16.3923	−	28.3923i	−0.765127	−	1.32524i
$460$	9.46410			0.441266
$461$	15.2942	+	26.4904i	0.712323	+	1.23378i	0.963983	+	0.265964i	$0.0856903\pi$
$461$	15.2942	+	26.4904i	0.712323	+	1.23378i	−0.251660	+	0.967816i	$0.580976\pi$
$462$	3.29423	+	5.70577i	0.153261	+	0.265457i
$463$	−12.9282			−0.600825			−0.300412	−	0.953809i	$-0.597124\pi$
$463$	−12.9282			−0.600825			−0.300412	+	0.953809i	$0.597124\pi$
$464$	1.26795	+	2.19615i	0.0588631	+	0.101954i
$465$	1.73205	−	3.00000i	0.0803219	−	0.139122i
$466$	2.36603	−	4.09808i	0.109604	−	0.189840i
$467$	37.8564			1.75179			0.875893	−	0.482506i	$-0.160273\pi$
$467$	37.8564			1.75179			0.875893	+	0.482506i	$0.160273\pi$
$468$		0			0
$469$		0			0
$470$	−1.50000	+	2.59808i	−0.0691898	+	0.119840i
$471$	4.75833	−	8.24167i	0.219252	−	0.379756i
$472$	5.19615	+	9.00000i	0.239172	+	0.414259i
$473$	−6.00000			−0.275880
$474$	1.53590	+	2.66025i	0.0705461	+	0.122190i
$475$	0.232051	+	0.401924i	0.0106472	+	0.0184415i
$476$	24.5885			1.12701
$477$	0.571797	+	0.990381i	0.0261808	+	0.0453464i
$478$	−1.09808	+	1.90192i	−0.0502248	+	0.0869920i
$479$	20.4904	−	35.4904i	0.936229	−	1.62160i	0.163803	−	0.986493i	$-0.447624\pi$
$479$	20.4904	−	35.4904i	0.936229	−	1.62160i	0.772427	−	0.635104i	$-0.219043\pi$
$480$	−0.732051			−0.0334134
$481$		0			0
$482$	8.66025			0.394464
$483$	−10.3923	+	18.0000i	−0.472866	+	0.819028i
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	4.56218	+	7.90192i	0.207158	+	0.358808i
$486$	15.2679			0.692568
$487$	7.62436	+	13.2058i	0.345493	+	0.598411i	0.985443	−	0.170005i	$-0.0543785\pi$
$487$	7.62436	+	13.2058i	0.345493	+	0.598411i	−0.639951	+	0.768416i	$0.721045\pi$
$488$	−3.09808	−	5.36603i	−0.140243	−	0.242909i
$489$	7.85641			0.355279
$490$	1.00000	+	1.73205i	0.0451754	+	0.0782461i
$491$	10.3301	−	17.8923i	0.466192	−	0.807468i	−0.533062	−	0.846076i	$-0.678959\pi$
$491$	10.3301	−	17.8923i	0.466192	−	0.807468i	0.999254	+	0.0386076i	$0.0122922\pi$
$492$	−3.80385	+	6.58846i	−0.171491	+	0.297031i
$493$	20.7846			0.936092
$494$		0			0
$495$	7.39230			0.332259
$496$	−2.36603	+	4.09808i	−0.106238	+	0.184009i
$497$	−9.00000	+	15.5885i	−0.403705	+	0.699238i
$498$	3.00000	+	5.19615i	0.134433	+	0.232845i
$499$	25.8564			1.15749			0.578746	−	0.815508i	$-0.303542\pi$
$499$	25.8564			1.15749			0.578746	+	0.815508i	$0.303542\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−1.09808	−	1.90192i	−0.0490584	−	0.0849717i
$502$	−17.1962			−0.767502
$503$	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
$505$	−5.36603	+	9.29423i	−0.238785	+	0.413588i
$506$	−28.3923			−1.26219
$507$		0			0
$508$	−10.8038			−0.479343
$509$	−11.1962	+	19.3923i	−0.496261	+	0.859549i	−0.999991	−	0.00431237i	$-0.998627\pi$
$509$	−11.1962	+	19.3923i	−0.496261	+	0.859549i	0.503730	+	0.863861i	$0.331961\pi$
$510$	−3.00000	+	5.19615i	−0.132842	+	0.230089i
$511$	−17.4904	−	30.2942i	−0.773729	−	1.34014i
$512$	1.00000			0.0441942
$513$	−0.928203	−	1.60770i	−0.0409812	−	0.0709815i
$514$	−6.92820	−	12.0000i	−0.305590	−	0.529297i
$515$	−9.19615			−0.405231
$516$	0.732051	+	1.26795i	0.0322267	+	0.0558184i
$517$	4.50000	−	7.79423i	0.197910	−	0.342790i
$518$	−1.20577	+	2.08846i	−0.0529786	+	0.0917615i
$519$	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	$0.454776\pi$
$522$	−3.12436	+	5.41154i	−0.136749	+	0.236857i
$523$	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
$525$	−2.19615			−0.0958479
$526$	−1.79423	−	3.10770i	−0.0782321	−	0.135502i
$527$	19.3923	+	33.5885i	0.844742	+	1.46314i
$528$	2.19615			0.0955753
$529$	−33.2846	−	57.6506i	−1.44716	−	2.50655i
$530$	0.232051	−	0.401924i	0.0100796	−	0.0174585i
$531$	−12.8038	+	22.1769i	−0.555640	+	0.962396i
$532$	1.39230			0.0603641
$533$		0			0
$534$	4.98076			0.215539
$535$	8.83013	−	15.2942i	0.381760	−	0.661227i
$536$		0			0
$537$	−3.46410	−	6.00000i	−0.149487	−	0.258919i
$538$	−27.1244			−1.16941
$539$	−3.00000	−	5.19615i	−0.129219	−	0.223814i
$540$	−2.00000	−	3.46410i	−0.0860663	−	0.149071i
$541$	−22.0526			−0.948114			−0.474057	−	0.880494i	$-0.657211\pi$
$541$	−22.0526			−0.948114			−0.474057	+	0.880494i	$0.657211\pi$
$542$	−4.73205	−	8.19615i	−0.203259	−	0.352055i
$543$	5.33975	−	9.24871i	0.229150	−	0.396900i
$544$	4.09808	−	7.09808i	0.175704	−	0.304328i
$545$	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	$0.546333\pi$
$548$	1.09808	−	1.90192i	0.0469075	−	0.0812462i
$549$	7.63397	−	13.2224i	0.325810	−	0.564320i
$550$	−1.50000	−	2.59808i	−0.0639602	−	0.110782i
$551$	1.17691			0.0501382
$552$	3.46410	+	6.00000i	0.147442	+	0.255377i
$553$	−6.29423	−	10.9019i	−0.267658	−	0.463597i
$554$	1.00000			0.0424859
$555$	−0.294229	−	0.509619i	−0.0124893	−	0.0216321i
$556$	−0.598076	+	1.03590i	−0.0253641	+	0.0439319i
$557$	3.40192	−	5.89230i	0.144144	−	0.249665i	−0.784909	−	0.619611i	$-0.787290\pi$
$557$	3.40192	−	5.89230i	0.144144	−	0.249665i	0.929053	+	0.369946i	$0.120624\pi$
$558$	−11.6603			−0.493618
$559$		0			0
$560$	3.00000			0.126773
$561$	9.00000	−	15.5885i	0.379980	−	0.658145i
$562$	−5.19615	+	9.00000i	−0.219186	+	0.379642i
$563$	7.26795	+	12.5885i	0.306308	+	0.530540i	0.977552	−	0.210696i	$-0.0675731\pi$
$563$	7.26795	+	12.5885i	0.306308	+	0.530540i	−0.671244	+	0.741236i	$0.734240\pi$
$564$	−2.19615			−0.0924747
$565$	3.46410	+	6.00000i	0.145736	+	0.252422i
$566$	−4.80385	−	8.32051i	−0.201921	−	0.349737i
$567$	−13.3923			−0.562424
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	−13.6244	+	23.5981i	−0.571163	+	0.989283i	0.425284	+	0.905060i	$0.360174\pi$
$569$	−13.6244	+	23.5981i	−0.571163	+	0.989283i	−0.996447	+	0.0842230i	$0.973159\pi$
$570$	−0.169873	+	0.294229i	−0.00711520	+	0.0123239i
$571$	38.3731			1.60586			0.802931	−	0.596071i	$-0.203272\pi$
$571$	38.3731			1.60586			0.802931	+	0.596071i	$0.203272\pi$
$572$		0			0
$573$	−16.6410			−0.695188
$574$	15.5885	−	27.0000i	0.650650	−	1.12696i
$575$	4.73205	−	8.19615i	0.197340	−	0.341803i
$576$	1.23205	+	2.13397i	0.0513355	+	0.0889156i
$577$	−26.4449			−1.10091			−0.550457	−	0.834863i	$-0.685547\pi$
$577$	−26.4449			−1.10091			−0.550457	+	0.834863i	$0.685547\pi$
$578$	−25.0885	−	43.4545i	−1.04354	−	1.80747i
$579$	6.00000	+	10.3923i	0.249351	+	0.431889i
$580$	2.53590			0.105297
$581$	−12.2942	−	21.2942i	−0.510051	−	0.883433i
$582$	−3.33975	+	5.78461i	−0.138437	+	0.239780i
$583$	−0.696152	+	1.20577i	−0.0288317	+	0.0499379i
$584$	−11.6603			−0.482505
$585$		0			0
$586$	−11.1962			−0.462509
$587$	15.0000	−	25.9808i	0.619116	−	1.07234i	−0.370531	−	0.928820i	$-0.620824\pi$
$587$	15.0000	−	25.9808i	0.619116	−	1.07234i	0.989647	−	0.143521i	$-0.0458424\pi$
$588$	−0.732051	+	1.26795i	−0.0301893	+	0.0522893i
$589$	1.09808	+	1.90192i	0.0452454	+	0.0783674i
$590$	10.3923			0.427844
$591$	7.90192	+	13.6865i	0.325042	+	0.562989i
$592$	0.401924	+	0.696152i	0.0165190	+	0.0286117i
$593$	20.7846			0.853522			0.426761	−	0.904365i	$-0.359655\pi$
$593$	20.7846			0.853522			0.426761	+	0.904365i	$0.359655\pi$
$594$	6.00000	+	10.3923i	0.246183	+	0.426401i
$595$	12.2942	−	21.2942i	0.504014	−	0.872978i
$596$	−3.00000	+	5.19615i	−0.122885	+	0.212843i
$597$	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	$0.632957\pi$
$600$	−0.366025	+	0.633975i	−0.0149429	+	0.0258819i
$601$	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
$604$	−11.8301	−	20.4904i	−0.481361	−	0.833742i
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$	−7.85641			−0.319145
$607$	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
$609$	−2.78461	+	4.82309i	−0.112838	+	0.195441i
$610$	−6.19615			−0.250875
$611$		0			0
$612$	20.1962			0.816381
$613$	19.4545	−	33.6962i	0.785759	−	1.36097i	−0.142785	−	0.989754i	$-0.545606\pi$
$613$	19.4545	−	33.6962i	0.785759	−	1.36097i	0.928545	−	0.371221i	$-0.121061\pi$
$614$	−13.7321	+	23.7846i	−0.554180	+	0.959869i
$615$	3.80385	+	6.58846i	0.153386	+	0.265672i
$616$	−9.00000			−0.362620
$617$	−9.00000	−	15.5885i	−0.362326	−	0.627568i	0.626017	−	0.779809i	$-0.284684\pi$
$617$	−9.00000	−	15.5885i	−0.362326	−	0.627568i	−0.988343	+	0.152242i	$0.951351\pi$
$618$	−3.36603	−	5.83013i	−0.135401	−	0.234522i
$619$	31.3923			1.26176			0.630882	−	0.775879i	$-0.282693\pi$
$619$	31.3923			1.26176			0.630882	+	0.775879i	$0.282693\pi$
$620$	2.36603	+	4.09808i	0.0950219	+	0.164583i
$621$	−18.9282	+	32.7846i	−0.759563	+	1.31560i
$622$	−4.56218	+	7.90192i	−0.182927	+	0.316838i
$623$	−20.4115			−0.817771
$624$		0			0
$625$	1.00000			0.0400000
$626$	−13.1962	+	22.8564i	−0.527424	+	0.913526i
$627$	0.509619	−	0.882686i	0.0203522	−	0.0352511i
$628$	6.50000	+	11.2583i	0.259378	+	0.449256i
$629$	6.58846			0.262699
$630$	3.69615	+	6.40192i	0.147258	+	0.255059i
$631$	−10.3923	−	18.0000i	−0.413711	−	0.716569i	0.581581	−	0.813488i	$-0.302434\pi$
$631$	−10.3923	−	18.0000i	−0.413711	−	0.716569i	−0.995292	+	0.0969198i	$0.969101\pi$
$632$	−4.19615			−0.166914
$633$	6.43782	+	11.1506i	0.255880	+	0.443198i
$634$	11.5981	−	20.0885i	0.460618	−	0.797815i
$635$	−5.40192	+	9.35641i	−0.214369	+	0.371298i
$636$	0.339746			0.0134718
$637$		0			0
$638$	−7.60770			−0.301192
$639$	−7.39230	+	12.8038i	−0.292435	+	0.506512i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	16.0359	+	27.7750i	0.633380	+	1.09705i	0.986856	+	0.161603i	$0.0516663\pi$
$641$	16.0359	+	27.7750i	0.633380	+	1.09705i	−0.353476	+	0.935444i	$0.615000\pi$
$642$	12.9282			0.510235
$643$	5.36603	+	9.29423i	0.211615	+	0.366529i	0.952220	−	0.305412i	$-0.0987943\pi$
$643$	5.36603	+	9.29423i	0.211615	+	0.366529i	−0.740605	+	0.671941i	$0.765461\pi$
$644$	−14.1962	−	24.5885i	−0.559407	−	0.968921i
$645$	1.46410			0.0576489
$646$	−1.90192	−	3.29423i	−0.0748302	−	0.129610i
$647$	−0.401924	+	0.696152i	−0.0158013	+	0.0273686i	−0.873818	−	0.486253i	$-0.838363\pi$
$647$	−0.401924	+	0.696152i	−0.0158013	+	0.0273686i	0.858017	+	0.513622i	$0.171697\pi$
$648$	−2.23205	+	3.86603i	−0.0876832	+	0.151872i
$649$	−31.1769			−1.22380
$650$		0			0
$651$	−10.3923			−0.407307
$652$	−5.36603	+	9.29423i	−0.210150	+	0.363990i
$653$	−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
$655$	−6.12436			−0.239298
$656$	−5.19615	−	9.00000i	−0.202876	−	0.351391i
$657$	−14.3660	−	24.8827i	−0.560472	−	0.970766i
$658$	9.00000			0.350857
$659$	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
$661$	−17.9545	+	31.0981i	−0.698348	+	1.20957i	0.270690	+	0.962666i	$0.412748\pi$
$661$	−17.9545	+	31.0981i	−0.698348	+	1.20957i	−0.969039	+	0.246909i	$0.920585\pi$
$662$	12.9282			0.502469
$663$		0			0
$664$	−8.19615			−0.318072
$665$	0.696152	−	1.20577i	0.0269956	−	0.0467578i
$666$	−0.990381	+	1.71539i	−0.0383765	+	0.0664700i
$667$	−12.0000	−	20.7846i	−0.464642	−	0.804783i
$668$	3.00000			0.116073
$669$	−2.36603	−	4.09808i	−0.0914758	−	0.158441i
$670$		0			0
$671$	18.5885			0.717599
$672$	1.09808	+	1.90192i	0.0423592	+	0.0733683i
$673$	12.1962	−	21.1244i	0.470127	−	0.814284i	−0.529289	−	0.848441i	$-0.677541\pi$
$673$	12.1962	−	21.1244i	0.470127	−	0.814284i	0.999416	+	0.0341573i	$0.0108747\pi$
$674$	3.09808	−	5.36603i	0.119333	−	0.206692i
$675$	−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	$0.665518\pi$
$678$	−2.53590	+	4.39230i	−0.0973906	+	0.168685i
$679$	13.6865	−	23.7058i	0.525241	−	0.909744i
$680$	−4.09808	−	7.09808i	−0.157154	−	0.272199i
$681$	12.0000			0.459841
$682$	−7.09808	−	12.2942i	−0.271799	−	0.470770i
$683$	15.5885	+	27.0000i	0.596476	+	1.03313i	0.993337	+	0.115248i	$0.0367661\pi$
$683$	15.5885	+	27.0000i	0.596476	+	1.03313i	−0.396861	+	0.917879i	$0.629901\pi$
$684$	1.14359			0.0437264
$685$	−1.09808	−	1.90192i	−0.0419553	−	0.0726688i
$686$	−7.50000	+	12.9904i	−0.286351	+	0.495975i
$687$	−0.464102	+	0.803848i	−0.0177066	+	0.0306687i
$688$	−2.00000			−0.0762493
$689$		0			0
$690$	6.92820			0.263752
$691$	−18.3564	+	31.7942i	−0.698311	+	1.20951i	0.270741	+	0.962652i	$0.412731\pi$
$691$	−18.3564	+	31.7942i	−0.698311	+	1.20951i	−0.969052	+	0.246857i	$0.920602\pi$
$692$	−7.50000	+	12.9904i	−0.285107	+	0.493820i
$693$	−11.0885	−	19.2058i	−0.421216	−	0.729567i
$694$	−28.7321			−1.09065
$695$	0.598076	+	1.03590i	0.0226863	+	0.0392939i
$696$	0.928203	+	1.60770i	0.0351835	+	0.0609395i
$697$	−85.1769			−3.22631
$698$	2.02628	+	3.50962i	0.0766958	+	0.132841i
$699$	1.73205	−	3.00000i	0.0655122	−	0.113470i
$700$	1.50000	−	2.59808i	0.0566947	−	0.0981981i
$701$	−35.9090			−1.35626			−0.678131	−	0.734941i	$-0.737210\pi$
$701$	−35.9090			−1.35626			−0.678131	+	0.734941i	$0.737210\pi$
$702$		0			0
$703$	0.373067			0.0140705
$704$	−1.50000	+	2.59808i	−0.0565334	+	0.0979187i
$705$	−1.09808	+	1.90192i	−0.0413559	+	0.0716306i
$706$	4.90192	+	8.49038i	0.184486	+	0.319540i
$707$	32.1962			1.21086
$708$	3.80385	+	6.58846i	0.142957	+	0.247609i
$709$	5.49038	+	9.50962i	0.206196	+	0.357141i	0.950513	−	0.310685i	$-0.100558\pi$
$709$	5.49038	+	9.50962i	0.206196	+	0.357141i	−0.744317	+	0.667826i	$0.767225\pi$
$710$	6.00000			0.225176
$711$	−5.16987	−	8.95448i	−0.193885	−	0.335819i
$712$	−3.40192	+	5.89230i	−0.127492	+	0.220823i
$713$	22.3923	−	38.7846i	0.838598	−	1.45250i
$714$	18.0000			0.673633
$715$		0			0
$716$	9.46410			0.353690
$717$	−0.803848	+	1.39230i	−0.0300202	+	0.0519966i
$718$	0.803848	−	1.39230i	0.0299993	−	0.0519604i
$719$	12.9282	+	22.3923i	0.482141	+	0.835092i	0.999790	−	0.0205009i	$-0.00652609\pi$
$719$	12.9282	+	22.3923i	0.482141	+	0.835092i	−0.517649	+	0.855593i	$0.673193\pi$
$720$	2.46410			0.0918316
$721$	13.7942	+	23.8923i	0.513724	+	0.889796i
$722$	9.39230	+	16.2679i	0.349545	+	0.605430i
$723$	6.33975			0.235778
$724$	7.29423	+	12.6340i	0.271088	+	0.469538i
$725$	1.26795	−	2.19615i	0.0470905	−	0.0815631i
$726$	0.732051	−	1.26795i	0.0271690	−	0.0470580i
$727$	−34.3731			−1.27483			−0.637413	−	0.770522i	$-0.719996\pi$
$727$	−34.3731			−1.27483			−0.637413	+	0.770522i	$0.719996\pi$
$728$		0			0
$729$	−2.21539			−0.0820515
$730$	−5.83013	+	10.0981i	−0.215783	+	0.373747i
$731$	−8.19615	+	14.1962i	−0.303146	+	0.525064i
$732$	−2.26795	−	3.92820i	−0.0838258	−	0.145191i
$733$	14.9090			0.550675			0.275338	−	0.961348i	$-0.411210\pi$
$733$	14.9090			0.550675			0.275338	+	0.961348i	$0.411210\pi$
$734$	2.80385	+	4.85641i	0.103492	+	0.179253i
$735$	0.732051	+	1.26795i	0.0270021	+	0.0467690i
$736$	−9.46410			−0.348851
$737$		0			0
$738$	12.8038	−	22.1769i	0.471316	−	0.816344i
$739$	−16.2846	+	28.2058i	−0.599039	+	1.03757i	0.393924	+	0.919143i	$0.371117\pi$
$739$	−16.2846	+	28.2058i	−0.599039	+	1.03757i	−0.992963	+	0.118423i	$0.962216\pi$
$740$	0.803848			0.0295500
$741$		0			0
$742$	−1.39230			−0.0511131
$743$	−6.80385	+	11.7846i	−0.249609	+	0.432335i	−0.963417	−	0.268006i	$-0.913635\pi$
$743$	−6.80385	+	11.7846i	−0.249609	+	0.432335i	0.713808	+	0.700341i	$0.246969\pi$
$744$	−1.73205	+	3.00000i	−0.0635001	+	0.109985i
$745$	3.00000	+	5.19615i	0.109911	+	0.190372i
$746$	−0.392305			−0.0143633
$747$	−10.0981	−	17.4904i	−0.369469	−	0.639940i
$748$	12.2942	+	21.2942i	0.449522	+	0.778594i
$749$	−52.9808			−1.93587
$750$	0.366025	+	0.633975i	0.0133654	+	0.0231495i
$751$	−10.1962	+	17.6603i	−0.372063	+	0.644432i	−0.989883	−	0.141888i	$-0.954683\pi$
$751$	−10.1962	+	17.6603i	−0.372063	+	0.644432i	0.617820	+	0.786320i	$0.288016\pi$
$752$	1.50000	−	2.59808i	0.0546994	−	0.0947421i
$753$	−12.5885			−0.458749
$754$		0			0
$755$	−23.6603			−0.861085
$756$	−6.00000	+	10.3923i	−0.218218	+	0.377964i
$757$	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
$759$	−20.7846			−0.754434
$760$	−0.232051	−	0.401924i	−0.00841737	−	0.0145793i
$761$	9.40192	+	16.2846i	0.340819	+	0.590317i	0.984585	−	0.174906i	$-0.0559622\pi$
$761$	9.40192	+	16.2846i	0.340819	+	0.590317i	−0.643766	+	0.765223i	$0.722629\pi$
$762$	−7.90897			−0.286512
$763$	−12.8038	−	22.1769i	−0.463530	−	0.802858i
$764$	11.3660	−	19.6865i	0.411208	−	0.712234i
$765$	10.0981	−	17.4904i	0.365097	−	0.632366i
$766$	22.3923			0.809067
$767$		0			0
$768$	0.732051			0.0264156
$769$	−19.0526	+	33.0000i	−0.687053	+	1.19001i	0.285734	+	0.958309i	$0.407763\pi$
$769$	−19.0526	+	33.0000i	−0.687053	+	1.19001i	−0.972787	+	0.231701i	$0.925571\pi$
$770$	−4.50000	+	7.79423i	−0.162169	+	0.280885i
$771$	−5.07180	−	8.78461i	−0.182656	−	0.316370i
$772$	−16.3923			−0.589972
$773$	−1.20577	−	2.08846i	−0.0433686	−	0.0751166i	0.843526	−	0.537088i	$-0.180476\pi$
$773$	−1.20577	−	2.08846i	−0.0433686	−	0.0751166i	−0.886895	+	0.461971i	$0.847142\pi$
$774$	−2.46410	−	4.26795i	−0.0885703	−	0.153408i
$775$	4.73205			0.169980
$776$	−4.56218	−	7.90192i	−0.163773	−	0.283663i
$777$	−0.882686	+	1.52886i	−0.0316662	+	0.0548474i
$778$	11.3660	−	19.6865i	0.407492	−	0.705796i
$779$	−4.82309			−0.172805
$780$		0			0
$781$	−18.0000			−0.644091
$782$	−38.7846	+	67.1769i	−1.38693	+	2.40224i
$783$	−5.07180	+	8.78461i	−0.181251	+	0.313936i
$784$	−1.00000	−	1.73205i	−0.0357143	−	0.0618590i
$785$	13.0000			0.463990
$786$	−2.24167	−	3.88269i	−0.0799577	−	0.138491i
$787$	−21.4186	−	37.0981i	−0.763490	−	1.32240i	−0.941041	−	0.338292i	$-0.890151\pi$
$787$	−21.4186	−	37.0981i	−0.763490	−	1.32240i	0.177551	−	0.984112i	$-0.443182\pi$
$788$	−21.5885			−0.769057
$789$	−1.31347	−	2.27499i	−0.0467606	−	0.0809918i
$790$	−2.09808	+	3.63397i	−0.0746462	+	0.129291i
$791$	10.3923	−	18.0000i	0.369508	−	0.640006i
$792$	−7.39230			−0.262674
$793$		0			0
$794$	11.1962			0.397337
$795$	0.169873	−	0.294229i	0.00602477	−	0.0104352i
$796$	−3.19615	+	5.53590i	−0.113285	+	0.196215i
$797$	−6.46410	−	11.1962i	−0.228970	−	0.396588i	0.728533	−	0.685011i	$-0.240203\pi$
$797$	−6.46410	−	11.1962i	−0.228970	−	0.396588i	−0.957503	+	0.288423i	$0.906869\pi$
$798$	1.01924			0.0360806
$799$	−12.2942	−	21.2942i	−0.434939	−	0.753336i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−16.7654			−0.592375
$802$	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
$808$	5.36603	−	9.29423i	0.188776	−	0.326970i
$809$	−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
$811$	43.3923			1.52371			0.761855	−	0.647748i	$-0.224289\pi$
$811$	43.3923			1.52371			0.761855	+	0.647748i	$0.224289\pi$
$812$	−3.80385	−	6.58846i	−0.133489	−	0.231210i
$813$	−3.46410	−	6.00000i	−0.121491	−	0.210429i
$814$	−2.41154			−0.0845245
$815$	5.36603	+	9.29423i	0.187964	+	0.325563i
$816$	3.00000	−	5.19615i	0.105021	−	0.181902i
$817$	−0.464102	+	0.803848i	−0.0162369	+	0.0281231i
$818$	−16.2679			−0.568796
$819$		0			0
$820$	−10.3923			−0.362915
$821$	10.0981	−	17.4904i	0.352425	−	0.610419i	−0.634249	−	0.773129i	$-0.718690\pi$
$821$	10.0981	−	17.4904i	0.352425	−	0.610419i	0.986674	+	0.162711i	$0.0520237\pi$
$822$	0.803848	−	1.39230i	0.0280374	−	0.0485622i
$823$	−13.5981	−	23.5526i	−0.473999	−	0.820991i	0.525558	−	0.850758i	$-0.323857\pi$
$823$	−13.5981	−	23.5526i	−0.473999	−	0.820991i	−0.999557	+	0.0297674i	$0.990523\pi$
$824$	9.19615			0.320363
$825$	−1.09808	−	1.90192i	−0.0382301	−	0.0662165i
$826$	−15.5885	−	27.0000i	−0.542392	−	0.939450i
$827$	42.5885			1.48095			0.740473	−	0.672086i	$-0.234602\pi$
$827$	42.5885			1.48095			0.740473	+	0.672086i	$0.234602\pi$
$828$	−11.6603	−	20.1962i	−0.405222	−	0.701865i
$829$	−10.0000	+	17.3205i	−0.347314	+	0.601566i	−0.985771	−	0.168091i	$-0.946240\pi$
$829$	−10.0000	+	17.3205i	−0.347314	+	0.601566i	0.638457	+	0.769657i	$0.279573\pi$
$830$	−4.09808	+	7.09808i	−0.142246	+	0.246378i
$831$	0.732051			0.0253946
$832$		0			0
$833$	−16.3923			−0.567960
$834$	−0.437822	+	0.758330i	−0.0151605	+	0.0262588i
$835$	1.50000	−	2.59808i	0.0519096	−	0.0899101i
$836$	0.696152	+	1.20577i	0.0240769	+	0.0417025i
$837$	−18.9282			−0.654254
$838$	8.66025	+	15.0000i	0.299164	+	0.518166i
$839$	10.9019	+	18.8827i	0.376376	+	0.651903i	0.990532	−	0.137282i	$-0.0438367\pi$
$839$	10.9019	+	18.8827i	0.376376	+	0.651903i	−0.614156	+	0.789185i	$0.710503\pi$
$840$	2.19615			0.0757745
$841$	11.2846	+	19.5455i	0.389124	+	0.673983i
$842$	−1.43782	+	2.49038i	−0.0495506	+	0.0858242i
$843$	−3.80385	+	6.58846i	−0.131011	+	0.226919i
$844$	−17.5885			−0.605420
$845$		0			0
$846$	7.39230			0.254153
$847$	−3.00000	+	5.19615i	−0.103081	+	0.178542i
$848$	−0.232051	+	0.401924i	−0.00796866	+	0.0138021i
$849$	−3.51666	−	6.09103i	−0.120691	−	0.209044i
$850$	−8.19615			−0.281126
$851$	−3.80385	−	6.58846i	−0.130394	−	0.225849i
$852$	2.19615	+	3.80385i	0.0752389	+	0.130318i
$853$	−13.8564			−0.474434			−0.237217	−	0.971457i	$-0.576235\pi$
$853$	−13.8564			−0.474434			−0.237217	+	0.971457i	$0.576235\pi$
$854$	9.29423	+	16.0981i	0.318042	+	0.550865i
$855$	0.571797	−	0.990381i	0.0195550	−	0.0338703i
$856$	−8.83013	+	15.2942i	−0.301808	+	0.522746i
$857$	16.7321			0.571556			0.285778	−	0.958296i	$-0.407748\pi$
$857$	16.7321			0.571556			0.285778	+	0.958296i	$0.407748\pi$
$858$		0			0
$859$	−20.3731			−0.695120			−0.347560	−	0.937658i	$-0.612990\pi$
$859$	−20.3731			−0.695120			−0.347560	+	0.937658i	$0.612990\pi$
$860$	−1.00000	+	1.73205i	−0.0340997	+	0.0590624i
$861$	11.4115	−	19.7654i	0.388904	−	0.673602i
$862$	−4.09808	−	7.09808i	−0.139581	−	0.241761i
$863$	43.1769			1.46976			0.734880	−	0.678198i	$-0.237239\pi$
$863$	43.1769			1.46976			0.734880	+	0.678198i	$0.237239\pi$
$864$	2.00000	+	3.46410i	0.0680414	+	0.117851i
$865$	7.50000	+	12.9904i	0.255008	+	0.441686i
$866$	−8.39230			−0.285182
$867$	−18.3660	−	31.8109i	−0.623743	−	1.08035i
$868$	7.09808	−	12.2942i	0.240924	−	0.417293i
$869$	6.29423	−	10.9019i	0.213517	−	0.369822i
$870$	1.85641			0.0629381
$871$		0			0
$872$	−8.53590			−0.289062
$873$	11.2417	−	19.4711i	0.380473	−	0.658998i
$874$	−2.19615	+	3.80385i	−0.0742860	+	0.128667i
$875$	−1.50000	−	2.59808i	−0.0507093	−	0.0878310i
$876$	−8.53590			−0.288401
$877$	13.7321	+	23.7846i	0.463698	+	0.803149i	0.999142	−	0.0414220i	$-0.0131888\pi$
$877$	13.7321	+	23.7846i	0.463698	+	0.803149i	−0.535443	+	0.844571i	$0.679855\pi$
$878$	−1.70577	−	2.95448i	−0.0575670	−	0.0997090i
$879$	−8.19615			−0.276449
$880$	1.50000	+	2.59808i	0.0505650	+	0.0875811i
$881$	13.1603	−	22.7942i	0.443380	−	0.767957i	−0.554558	−	0.832145i	$-0.687112\pi$
$881$	13.1603	−	22.7942i	0.443380	−	0.767957i	0.997938	+	0.0641883i	$0.0204458\pi$
$882$	2.46410	−	4.26795i	0.0829706	−	0.143709i
$883$	−4.58846			−0.154414			−0.0772069	−	0.997015i	$-0.524600\pi$
$883$	−4.58846			−0.154414			−0.0772069	+	0.997015i	$0.524600\pi$
$884$		0			0
$885$	7.60770			0.255730
$886$	11.1962	−	19.3923i	0.376142	−	0.651497i
$887$	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
$889$	32.4115			1.08705
$890$	3.40192	+	5.89230i	0.114033	+	0.197511i
$891$	−6.69615	−	11.5981i	−0.224330	−	0.388550i
$892$	6.46410			0.216434
$893$	−0.696152	−	1.20577i	−0.0232959	−	0.0403496i
$894$	−2.19615	+	3.80385i	−0.0734503	+	0.127220i
$895$	4.73205	−	8.19615i	0.158175	−	0.273967i
$896$	−3.00000			−0.100223
$897$		0			0
$898$	−15.5885			−0.520194
$899$	6.00000	−	10.3923i	0.200111	−	0.346603i
$900$	1.23205	−	2.13397i	0.0410684	−	0.0711325i
$901$	1.90192	+	3.29423i	0.0633623	+	0.109747i
$902$	31.1769			1.03808
$903$	−2.19615	−	3.80385i	−0.0730834	−	0.126584i
$904$	−3.46410	−	6.00000i	−0.115214	−	0.199557i
$905$	14.5885			0.484937
$906$	−8.66025	−	15.0000i	−0.287718	−	0.498342i
$907$	2.29423	−	3.97372i	0.0761786	−	0.131945i	−0.825420	−	0.564520i	$-0.809061\pi$
$907$	2.29423	−	3.97372i	0.0761786	−	0.131945i	0.901598	+	0.432574i	$0.142395\pi$
$908$	−8.19615	+	14.1962i	−0.271999	+	0.471116i
$909$	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	$0.615713\pi$
$912$	0.169873	−	0.294229i	0.00562506	−	0.00974288i
$913$	12.2942	−	21.2942i	0.406880	−	0.704736i
$914$	9.16987	+	15.8827i	0.303312	+	0.525353i
$915$	−4.53590			−0.149952
$916$	−0.633975	−	1.09808i	−0.0209471	−	0.0362815i
$917$	9.18653	+	15.9115i	0.303366	+	0.525445i
$918$	32.7846			1.08205
$919$	−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
$921$	−10.0526	+	17.4115i	−0.331243	+	0.573730i
$922$	−30.5885			−1.00738
$923$		0			0
$924$	−6.58846			−0.216744
$925$	0.401924	−	0.696152i	0.0132152	−	0.0228894i
$926$	6.46410	−	11.1962i	0.212424	−	0.367928i
$927$	11.3301	+	19.6244i	0.372130	+	0.644548i
$928$	−2.53590			−0.0832449
$929$	1.60770	+	2.78461i	0.0527468	+	0.0913601i	0.891193	−	0.453624i	$-0.149869\pi$
$929$	1.60770	+	2.78461i	0.0527468	+	0.0913601i	−0.838446	+	0.544984i	$0.816536\pi$
$930$	1.73205	+	3.00000i	0.0567962	+	0.0983739i
$931$	−0.928203			−0.0304206
$932$	2.36603	+	4.09808i	0.0775017	+	0.134237i
$933$	−3.33975	+	5.78461i	−0.109338	+	0.189380i
$934$	−18.9282	+	32.7846i	−0.619350	+	1.07275i
$935$	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
$941$	3.21539			0.104819			0.0524094	−	0.998626i	$-0.483310\pi$
$941$	3.21539			0.104819			0.0524094	+	0.998626i	$0.483310\pi$
$942$	4.75833	+	8.24167i	0.155035	+	0.268528i
$943$	49.1769	+	85.1769i	1.60142	+	2.77374i
$944$	−10.3923			−0.338241
$945$	6.00000	+	10.3923i	0.195180	+	0.338062i
$946$	3.00000	−	5.19615i	0.0975384	−	0.168941i
$947$	−7.68653	+	13.3135i	−0.249779	+	0.432630i	−0.963464	−	0.267837i	$-0.913691\pi$
$947$	−7.68653	+	13.3135i	−0.249779	+	0.432630i	0.713686	+	0.700466i	$0.247025\pi$
$948$	−3.07180			−0.0997673
$949$		0			0
$950$	−0.464102			−0.0150574
$951$	8.49038	−	14.7058i	0.275319	−	0.476867i
$952$	−12.2942	+	21.2942i	−0.398458	+	0.690150i
$953$	−3.29423	−	5.70577i	−0.106711	−	0.184828i	0.807725	−	0.589559i	$-0.200698\pi$
$953$	−3.29423	−	5.70577i	−0.106711	−	0.184828i	−0.914436	+	0.404731i	$0.867365\pi$
$954$	−1.14359			−0.0370252
$955$	−11.3660	−	19.6865i	−0.367796	−	0.637041i
$956$	−1.09808	−	1.90192i	−0.0355143	−	0.0615126i
$957$	−5.56922			−0.180027
$958$	20.4904	+	35.4904i	0.662014	+	1.14664i
$959$	−3.29423	+	5.70577i	−0.106376	+	0.184249i
$960$	0.366025	−	0.633975i	0.0118134	−	0.0204614i
$961$	−8.60770			−0.277668
$962$		0			0
$963$	−43.5167			−1.40230
$964$	−4.33013	+	7.50000i	−0.139464	+	0.241559i
$965$	−8.19615	+	14.1962i	−0.263843	+	0.456990i
$966$	−10.3923	−	18.0000i	−0.334367	−	0.579141i
$967$	−44.5692			−1.43325			−0.716625	−	0.697459i	$-0.754314\pi$
$967$	−44.5692			−1.43325			−0.716625	+	0.697459i	$0.754314\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$	−1.39230	−	2.41154i	−0.0447273	−	0.0774699i
$970$	−9.12436			−0.292965
$971$	−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
$973$	1.79423	−	3.10770i	0.0575203	−	0.0996281i
$974$	−15.2487			−0.488600
$975$		0			0
$976$	6.19615			0.198334
$977$	8.19615	−	14.1962i	0.262218	−	0.454175i	−0.704613	−	0.709592i	$-0.748879\pi$
$977$	8.19615	−	14.1962i	0.262218	−	0.454175i	0.966831	+	0.255417i	$0.0822127\pi$
$978$	−3.92820	+	6.80385i	−0.125610	+	0.217563i
$979$	−10.2058	−	17.6769i	−0.326178	−	0.564957i
$980$	−2.00000			−0.0638877
$981$	−10.5167	−	18.2154i	−0.335771	−	0.581573i
$982$	10.3301	+	17.8923i	0.329648	+	0.570966i
$983$	−44.5692			−1.42154			−0.710769	−	0.703426i	$-0.751653\pi$
$983$	−44.5692			−1.42154			−0.710769	+	0.703426i	$0.751653\pi$
$984$	−3.80385	−	6.58846i	−0.121262	−	0.210032i
$985$	−10.7942	+	18.6962i	−0.343933	+	0.595709i
$986$	−10.3923	+	18.0000i	−0.330958	+	0.573237i
$987$	6.58846			0.209713
$988$		0			0
$989$	18.9282			0.601882
$990$	−3.69615	+	6.40192i	−0.117471	+	0.203466i
$991$	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
$993$	9.46410			0.300334
$994$	−9.00000	−	15.5885i	−0.285463	−	0.494436i
$995$	3.19615	+	5.53590i	0.101325	+	0.175500i
$996$	−6.00000			−0.190117
$997$	−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
$999$	−1.60770	+	2.78461i	−0.0508652	+	0.0881012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.e.l.191.1		4
13.2	odd	12		130.2.l.a.101.1	✓	4
13.3	even	3	inner	1690.2.e.l.991.1		4
13.4	even	6		1690.2.a.j.1.2		2
13.5	odd	4		1690.2.l.g.1161.2		4
13.6	odd	12		1690.2.d.f.1351.2		4
13.7	odd	12		1690.2.d.f.1351.4		4
13.8	odd	4		130.2.l.a.121.1	yes	4
13.9	even	3		1690.2.a.m.1.2		2
13.10	even	6		1690.2.e.n.991.1		4
13.11	odd	12		1690.2.l.g.361.2		4
13.12	even	2		1690.2.e.n.191.1		4
39.2	even	12		1170.2.bs.c.361.2		4
39.8	even	4		1170.2.bs.c.901.2		4
52.15	even	12		1040.2.da.a.881.2		4
52.47	even	4		1040.2.da.a.641.2		4
65.2	even	12		650.2.n.a.49.2		4
65.4	even	6		8450.2.a.bm.1.1		2
65.8	even	4		650.2.n.a.199.2		4
65.9	even	6		8450.2.a.bf.1.1		2
65.28	even	12		650.2.n.b.49.1		4
65.34	odd	4		650.2.m.a.251.2		4
65.47	even	4		650.2.n.b.199.1		4
65.54	odd	12		650.2.m.a.101.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.a.101.1	✓	4	13.2	odd	12
130.2.l.a.121.1	yes	4	13.8	odd	4
650.2.m.a.101.2		4	65.54	odd	12
650.2.m.a.251.2		4	65.34	odd	4
650.2.n.a.49.2		4	65.2	even	12
650.2.n.a.199.2		4	65.8	even	4
650.2.n.b.49.1		4	65.28	even	12
650.2.n.b.199.1		4	65.47	even	4
1040.2.da.a.641.2		4	52.47	even	4
1040.2.da.a.881.2		4	52.15	even	12
1170.2.bs.c.361.2		4	39.2	even	12
1170.2.bs.c.901.2		4	39.8	even	4
1690.2.a.j.1.2		2	13.4	even	6
1690.2.a.m.1.2		2	13.9	even	3
1690.2.d.f.1351.2		4	13.6	odd	12
1690.2.d.f.1351.4		4	13.7	odd	12
1690.2.e.l.191.1		4	1.1	even	1	trivial
1690.2.e.l.991.1		4	13.3	even	3	inner
1690.2.e.n.191.1		4	13.12	even	2
1690.2.e.n.991.1		4	13.10	even	6
1690.2.l.g.361.2		4	13.11	odd	12
1690.2.l.g.1161.2		4	13.5	odd	4
8450.2.a.bf.1.1		2	65.9	even	6
8450.2.a.bm.1.1		2	65.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.e (of order \(3\), degree \(2\), not minimal)

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

Introduction

L-functions

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