LMFDB - Embedded newform 1690.2.l.g.1161.1

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			1161.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1690.1161
Dual form			1690.2.l.g.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.36603 - 2.36603i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-2.36603 + 1.36603i) q^{6} +(2.59808 - 1.50000i) q^{7} -1.00000i q^{8} +(-2.23205 - 3.86603i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.36603 - 2.36603i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-2.36603 + 1.36603i) q^{6} +(2.59808 - 1.50000i) q^{7} -1.00000i q^{8} +(-2.23205 - 3.86603i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(2.59808 + 1.50000i) q^{11} +2.73205 q^{12} -3.00000 q^{14} +(-2.36603 - 1.36603i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.09808 + 1.90192i) q^{17} +4.46410i q^{18} +(5.59808 - 3.23205i) q^{19} +(0.866025 - 0.500000i) q^{20} -8.19615i q^{21} +(-1.50000 - 2.59808i) q^{22} +(-1.26795 + 2.19615i) q^{23} +(-2.36603 - 1.36603i) q^{24} -1.00000 q^{25} -4.00000 q^{27} +(2.59808 + 1.50000i) q^{28} +(4.73205 - 8.19615i) q^{29} +(1.36603 + 2.36603i) q^{30} +1.26795i q^{31} +(0.866025 - 0.500000i) q^{32} +(7.09808 - 4.09808i) q^{33} -2.19615i q^{34} +(-1.50000 - 2.59808i) q^{35} +(2.23205 - 3.86603i) q^{36} +(-9.69615 - 5.59808i) q^{37} -6.46410 q^{38} -1.00000 q^{40} +(9.00000 + 5.19615i) q^{41} +(-4.09808 + 7.09808i) q^{42} +(-1.00000 - 1.73205i) q^{43} +3.00000i q^{44} +(-3.86603 + 2.23205i) q^{45} +(2.19615 - 1.26795i) q^{46} +3.00000i q^{47} +(1.36603 + 2.36603i) q^{48} +(1.00000 - 1.73205i) q^{49} +(0.866025 + 0.500000i) q^{50} +6.00000 q^{51} -6.46410 q^{53} +(3.46410 + 2.00000i) q^{54} +(1.50000 - 2.59808i) q^{55} +(-1.50000 - 2.59808i) q^{56} -17.6603i q^{57} +(-8.19615 + 4.73205i) q^{58} +(-9.00000 + 5.19615i) q^{59} -2.73205i q^{60} +(2.09808 + 3.63397i) q^{61} +(0.633975 - 1.09808i) q^{62} +(-11.5981 - 6.69615i) q^{63} -1.00000 q^{64} -8.19615 q^{66} +(-1.09808 + 1.90192i) q^{68} +(3.46410 + 6.00000i) q^{69} +3.00000i q^{70} +(-5.19615 + 3.00000i) q^{71} +(-3.86603 + 2.23205i) q^{72} -5.66025i q^{73} +(5.59808 + 9.69615i) q^{74} +(-1.36603 + 2.36603i) q^{75} +(5.59808 + 3.23205i) q^{76} +9.00000 q^{77} +6.19615 q^{79} +(0.866025 + 0.500000i) q^{80} +(1.23205 - 2.13397i) q^{81} +(-5.19615 - 9.00000i) q^{82} +2.19615i q^{83} +(7.09808 - 4.09808i) q^{84} +(1.90192 - 1.09808i) q^{85} +2.00000i q^{86} +(-12.9282 - 22.3923i) q^{87} +(1.50000 - 2.59808i) q^{88} +(14.8923 + 8.59808i) q^{89} +4.46410 q^{90} -2.53590 q^{92} +(3.00000 + 1.73205i) q^{93} +(1.50000 - 2.59808i) q^{94} +(-3.23205 - 5.59808i) q^{95} -2.73205i q^{96} +(-13.0981 + 7.56218i) q^{97} +(-1.73205 + 1.00000i) q^{98} -13.3923i 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
$3$	1.36603	−	2.36603i	0.788675	−	1.36603i	−0.138104	−	0.990418i	$-0.544101\pi$
$3$	1.36603	−	2.36603i	0.788675	−	1.36603i	0.926779	−	0.375608i	$-0.122566\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−2.36603	+	1.36603i	−0.965926	+	0.557678i
$7$	2.59808	−	1.50000i	0.981981	−	0.566947i	0.0791130	−	0.996866i	$-0.474791\pi$
$7$	2.59808	−	1.50000i	0.981981	−	0.566947i	0.902867	+	0.429919i	$0.141458\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−2.23205	−	3.86603i	−0.744017	−	1.28868i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	2.59808	+	1.50000i	0.783349	+	0.452267i	0.837616	−	0.546259i	$-0.183949\pi$
$11$	2.59808	+	1.50000i	0.783349	+	0.452267i	−0.0542666	+	0.998526i	$0.517282\pi$
$12$	2.73205			0.788675
$13$		0			0
$13$		0			0
$14$	−3.00000			−0.801784
$15$	−2.36603	−	1.36603i	−0.610905	−	0.352706i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.09808	+	1.90192i	0.266323	+	0.461284i	0.967909	−	0.251300i	$-0.0808580\pi$
$17$	1.09808	+	1.90192i	0.266323	+	0.461284i	−0.701587	+	0.712584i	$0.747525\pi$
$18$			4.46410i			1.05220i
$19$	5.59808	−	3.23205i	1.28429	−	0.741483i	0.306658	−	0.951820i	$-0.400789\pi$
$19$	5.59808	−	3.23205i	1.28429	−	0.741483i	0.977629	+	0.210337i	$0.0674560\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$		−	8.19615i		−	1.78855i
$22$	−1.50000	−	2.59808i	−0.319801	−	0.553912i
$23$	−1.26795	+	2.19615i	−0.264386	+	0.457929i	−0.967402	−	0.253244i	$-0.918503\pi$
$23$	−1.26795	+	2.19615i	−0.264386	+	0.457929i	0.703017	+	0.711173i	$0.251836\pi$
$24$	−2.36603	−	1.36603i	−0.482963	−	0.278839i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−4.00000			−0.769800
$28$	2.59808	+	1.50000i	0.490990	+	0.283473i
$29$	4.73205	−	8.19615i	0.878720	−	1.52199i	0.0259731	−	0.999663i	$-0.491732\pi$
$29$	4.73205	−	8.19615i	0.878720	−	1.52199i	0.852747	−	0.522325i	$-0.174935\pi$
$30$	1.36603	+	2.36603i	0.249401	+	0.431975i
$31$			1.26795i			0.227730i	0.993496	+	0.113865i	$0.0363232\pi$
$31$			1.26795i			0.227730i	−0.993496	+	0.113865i	$0.963677\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	7.09808	−	4.09808i	1.23562	−	0.713384i
$34$		−	2.19615i		−	0.376637i
$35$	−1.50000	−	2.59808i	−0.253546	−	0.439155i
$36$	2.23205	−	3.86603i	0.372008	−	0.644338i
$37$	−9.69615	−	5.59808i	−1.59404	−	0.920318i	−0.992604	−	0.121395i	$-0.961263\pi$
$37$	−9.69615	−	5.59808i	−1.59404	−	0.920318i	−0.601433	−	0.798923i	$-0.705403\pi$
$38$	−6.46410			−1.04862
$39$		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	$0.365317\pi$
$42$	−4.09808	+	7.09808i	−0.632347	+	1.09526i
$43$	−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
$45$	−3.86603	+	2.23205i	−0.576313	+	0.332734i
$46$	2.19615	−	1.26795i	0.323805	−	0.186949i
$47$			3.00000i			0.437595i	0.975770	+	0.218797i	$0.0702134\pi$
$47$			3.00000i			0.437595i	−0.975770	+	0.218797i	$0.929787\pi$
$48$	1.36603	+	2.36603i	0.197169	+	0.341506i
$49$	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
$53$	−6.46410			−0.887913			−0.443956	−	0.896048i	$-0.646425\pi$
$53$	−6.46410			−0.887913			−0.443956	+	0.896048i	$0.646425\pi$
$54$	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
$57$		−	17.6603i		−	2.33916i
$58$	−8.19615	+	4.73205i	−1.07621	+	0.621349i
$59$	−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	$0.569829\pi$
$60$		−	2.73205i		−	0.352706i
$61$	2.09808	+	3.63397i	0.268631	+	0.465283i	0.968509	−	0.248980i	$-0.0800954\pi$
$61$	2.09808	+	3.63397i	0.268631	+	0.465283i	−0.699877	+	0.714263i	$0.746762\pi$
$62$	0.633975	−	1.09808i	0.0805149	−	0.139456i
$63$	−11.5981	−	6.69615i	−1.46122	−	0.843636i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−8.19615			−1.00888
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$	−1.09808	+	1.90192i	−0.133161	+	0.230642i
$69$	3.46410	+	6.00000i	0.417029	+	0.722315i
$70$			3.00000i			0.358569i
$71$	−5.19615	+	3.00000i	−0.616670	+	0.356034i	−0.775571	−	0.631260i	$-0.782538\pi$
$71$	−5.19615	+	3.00000i	−0.616670	+	0.356034i	0.158901	+	0.987294i	$0.449205\pi$
$72$	−3.86603	+	2.23205i	−0.455615	+	0.263050i
$73$		−	5.66025i		−	0.662483i	−0.943546	−	0.331241i	$-0.892533\pi$
$73$		−	5.66025i		−	0.662483i	0.943546	−	0.331241i	$-0.107467\pi$
$74$	5.59808	+	9.69615i	0.650763	+	1.12715i
$75$	−1.36603	+	2.36603i	−0.157735	+	0.273205i
$76$	5.59808	+	3.23205i	0.642143	+	0.370742i
$77$	9.00000			1.02565
$78$		0			0
$79$	6.19615			0.697122			0.348561	−	0.937286i	$-0.386670\pi$
$79$	6.19615			0.697122			0.348561	+	0.937286i	$0.386670\pi$
$80$	0.866025	+	0.500000i	0.0968246	+	0.0559017i
$81$	1.23205	−	2.13397i	0.136895	−	0.237108i
$82$	−5.19615	−	9.00000i	−0.573819	−	0.993884i
$83$			2.19615i			0.241059i	0.992710	+	0.120530i	$0.0384592\pi$
$83$			2.19615i			0.241059i	−0.992710	+	0.120530i	$0.961541\pi$
$84$	7.09808	−	4.09808i	0.774464	−	0.447137i
$85$	1.90192	−	1.09808i	0.206293	−	0.119103i
$86$			2.00000i			0.215666i
$87$	−12.9282	−	22.3923i	−1.38605	−	2.40071i
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	14.8923	+	8.59808i	1.57858	+	0.911394i	0.995058	+	0.0992979i	$0.0316597\pi$
$89$	14.8923	+	8.59808i	1.57858	+	0.911394i	0.583523	+	0.812096i	$0.301674\pi$
$90$	4.46410			0.470558
$91$		0			0
$92$	−2.53590			−0.264386
$93$	3.00000	+	1.73205i	0.311086	+	0.179605i
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$	−3.23205	−	5.59808i	−0.331601	−	0.574351i
$96$		−	2.73205i		−	0.278839i
$97$	−13.0981	+	7.56218i	−1.32991	+	0.767823i	−0.985285	−	0.170918i	$-0.945327\pi$
$97$	−13.0981	+	7.56218i	−1.32991	+	0.767823i	−0.344623	+	0.938741i	$0.611993\pi$
$98$	−1.73205	+	1.00000i	−0.174964	+	0.101015i
$99$		−	13.3923i		−	1.34598i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−3.63397	+	6.29423i	−0.361594	+	0.626299i	−0.988223	−	0.153018i	$-0.951101\pi$
$101$	−3.63397	+	6.29423i	−0.361594	+	0.626299i	0.626629	+	0.779317i	$0.284434\pi$
$102$	−5.19615	−	3.00000i	−0.514496	−	0.297044i
$103$	1.19615			0.117860			0.0589302	−	0.998262i	$-0.481231\pi$
$103$	1.19615			0.117860			0.0589302	+	0.998262i	$0.481231\pi$
$104$		0			0
$105$	−8.19615			−0.799863
$106$	5.59808	+	3.23205i	0.543733	+	0.313925i
$107$	−0.169873	+	0.294229i	−0.0164222	+	0.0284442i	−0.874120	−	0.485710i	$-0.838561\pi$
$107$	−0.169873	+	0.294229i	−0.0164222	+	0.0284442i	0.857697	+	0.514155i	$0.171894\pi$
$108$	−2.00000	−	3.46410i	−0.192450	−	0.333333i
$109$		−	15.4641i		−	1.48119i	−0.671950	−	0.740596i	$-0.734543\pi$
$109$		−	15.4641i		−	1.48119i	0.671950	−	0.740596i	$-0.265457\pi$
$110$	−2.59808	+	1.50000i	−0.247717	+	0.143019i
$111$	−26.4904	+	15.2942i	−2.51436	+	1.45166i
$112$			3.00000i			0.283473i
$113$	3.46410	+	6.00000i	0.325875	+	0.564433i	0.981689	−	0.190490i	$-0.0610077\pi$
$113$	3.46410	+	6.00000i	0.325875	+	0.564433i	−0.655814	+	0.754923i	$0.727674\pi$
$114$	−8.83013	+	15.2942i	−0.827017	+	1.43244i
$115$	2.19615	+	1.26795i	0.204792	+	0.118237i
$116$	9.46410			0.878720
$117$		0			0
$118$	10.3923			0.956689
$119$	5.70577	+	3.29423i	0.523047	+	0.301981i
$120$	−1.36603	+	2.36603i	−0.124700	+	0.215988i
$121$	−1.00000	−	1.73205i	−0.0909091	−	0.157459i
$122$		−	4.19615i		−	0.379902i
$123$	24.5885	−	14.1962i	2.21707	−	1.28002i
$124$	−1.09808	+	0.633975i	−0.0986102	+	0.0569326i
$125$			1.00000i			0.0894427i
$126$	6.69615	+	11.5981i	0.596541	+	1.03324i
$127$	−10.5981	+	18.3564i	−0.940427	+	1.62887i	−0.175769	+	0.984431i	$0.556241\pi$
$127$	−10.5981	+	18.3564i	−0.940427	+	1.62887i	−0.764658	+	0.644436i	$0.777092\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−5.46410			−0.481087
$130$		0			0
$131$	−18.1244			−1.58353			−0.791766	−	0.610824i	$-0.790838\pi$
$131$	−18.1244			−1.58353			−0.791766	+	0.610824i	$0.790838\pi$
$132$	7.09808	+	4.09808i	0.617808	+	0.356692i
$133$	9.69615	−	16.7942i	0.840763	−	1.45624i
$134$		0			0
$135$			4.00000i			0.344265i
$136$	1.90192	−	1.09808i	0.163089	−	0.0941593i
$137$	−7.09808	+	4.09808i	−0.606430	+	0.350122i	−0.771567	−	0.636148i	$-0.780527\pi$
$137$	−7.09808	+	4.09808i	−0.606430	+	0.350122i	0.165137	+	0.986271i	$0.447193\pi$
$138$		−	6.92820i		−	0.589768i
$139$	4.59808	+	7.96410i	0.390004	+	0.675506i	0.992450	−	0.122653i	$-0.0391404\pi$
$139$	4.59808	+	7.96410i	0.390004	+	0.675506i	−0.602446	+	0.798160i	$0.705807\pi$
$140$	1.50000	−	2.59808i	0.126773	−	0.219578i
$141$	7.09808	+	4.09808i	0.597766	+	0.345120i
$142$	6.00000			0.503509
$143$		0			0
$144$	4.46410			0.372008
$145$	−8.19615	−	4.73205i	−0.680653	−	0.392975i
$146$	−2.83013	+	4.90192i	−0.234223	+	0.405686i
$147$	−2.73205	−	4.73205i	−0.225336	−	0.390293i
$148$		−	11.1962i		−	0.920318i
$149$	5.19615	−	3.00000i	0.425685	−	0.245770i	−0.271821	−	0.962348i	$-0.587626\pi$
$149$	5.19615	−	3.00000i	0.425685	−	0.245770i	0.697507	+	0.716578i	$0.254293\pi$
$150$	2.36603	−	1.36603i	0.193185	−	0.111536i
$151$		−	6.33975i		−	0.515921i	−0.966155	−	0.257961i	$-0.916950\pi$
$151$		−	6.33975i		−	0.515921i	0.966155	−	0.257961i	$-0.0830505\pi$
$152$	−3.23205	−	5.59808i	−0.262154	−	0.454064i
$153$	4.90192	−	8.49038i	0.396297	−	0.686407i
$154$	−7.79423	−	4.50000i	−0.628077	−	0.362620i
$155$	1.26795			0.101844
$156$		0			0
$157$	−13.0000			−1.03751			−0.518756	−	0.854922i	$-0.673605\pi$
$157$	−13.0000			−1.03751			−0.518756	+	0.854922i	$0.673605\pi$
$158$	−5.36603	−	3.09808i	−0.426898	−	0.246470i
$159$	−8.83013	+	15.2942i	−0.700275	+	1.21291i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$			7.60770i			0.599570i
$162$	−2.13397	+	1.23205i	−0.167661	+	0.0967991i
$163$	−6.29423	+	3.63397i	−0.493002	+	0.284635i	−0.725819	−	0.687886i	$-0.758539\pi$
$163$	−6.29423	+	3.63397i	−0.493002	+	0.284635i	0.232817	+	0.972521i	$0.425206\pi$
$164$			10.3923i			0.811503i
$165$	−4.09808	−	7.09808i	−0.319035	−	0.552584i
$166$	1.09808	−	1.90192i	0.0852272	−	0.147618i
$167$	2.59808	+	1.50000i	0.201045	+	0.116073i	0.597143	−	0.802135i	$-0.296303\pi$
$167$	2.59808	+	1.50000i	0.201045	+	0.116073i	−0.396098	+	0.918208i	$0.629636\pi$
$168$	−8.19615			−0.632347
$169$		0			0
$170$	−2.19615			−0.168437
$171$	−24.9904	−	14.4282i	−1.91106	−	1.10335i
$172$	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	$0.640193\pi$
$174$			25.8564i			1.96017i
$175$	−2.59808	+	1.50000i	−0.196396	+	0.113389i
$176$	−2.59808	+	1.50000i	−0.195837	+	0.113067i
$177$			28.3923i			2.13410i
$178$	−8.59808	−	14.8923i	−0.644453	−	1.11623i
$179$	1.26795	−	2.19615i	0.0947710	−	0.164148i	−0.814742	−	0.579824i	$-0.803121\pi$
$179$	1.26795	−	2.19615i	0.0947710	−	0.164148i	0.909513	+	0.415675i	$0.136455\pi$
$180$	−3.86603	−	2.23205i	−0.288157	−	0.166367i
$181$	−16.5885			−1.23301			−0.616505	−	0.787351i	$-0.711452\pi$
$181$	−16.5885			−1.23301			−0.616505	+	0.787351i	$0.711452\pi$
$182$		0			0
$183$	11.4641			0.847451
$184$	2.19615	+	1.26795i	0.161903	+	0.0934745i
$185$	−5.59808	+	9.69615i	−0.411579	+	0.712875i
$186$	−1.73205	−	3.00000i	−0.127000	−	0.219971i
$187$			6.58846i			0.481796i
$188$	−2.59808	+	1.50000i	−0.189484	+	0.109399i
$189$	−10.3923	+	6.00000i	−0.755929	+	0.436436i
$190$			6.46410i			0.468955i
$191$	9.63397	+	16.6865i	0.697090	+	1.20740i	0.969471	+	0.245206i	$0.0788555\pi$
$191$	9.63397	+	16.6865i	0.697090	+	1.20740i	−0.272381	+	0.962189i	$0.587811\pi$
$192$	−1.36603	+	2.36603i	−0.0985844	+	0.170753i
$193$	3.80385	+	2.19615i	0.273807	+	0.158083i	0.630616	−	0.776095i	$-0.282802\pi$
$193$	3.80385	+	2.19615i	0.273807	+	0.158083i	−0.356809	+	0.934177i	$0.616135\pi$
$194$	15.1244			1.08587
$195$		0			0
$196$	2.00000			0.142857
$197$	−8.30385	−	4.79423i	−0.591625	−	0.341575i	0.174115	−	0.984725i	$-0.444294\pi$
$197$	−8.30385	−	4.79423i	−0.591625	−	0.341575i	−0.765740	+	0.643151i	$0.777627\pi$
$198$	−6.69615	+	11.5981i	−0.475875	+	0.824239i
$199$	−7.19615	−	12.4641i	−0.510122	−	0.883557i	−0.999931	−	0.0117273i	$-0.996267\pi$
$199$	−7.19615	−	12.4641i	−0.510122	−	0.883557i	0.489810	−	0.871829i	$-0.337066\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	6.29423	−	3.63397i	0.442860	−	0.255686i
$203$		−	28.3923i		−	1.99275i
$204$	3.00000	+	5.19615i	0.210042	+	0.363803i
$205$	5.19615	−	9.00000i	0.362915	−	0.628587i
$206$	−1.03590	−	0.598076i	−0.0721745	−	0.0416699i
$207$	11.3205			0.786830
$208$		0			0
$209$	19.3923			1.34139
$210$	7.09808	+	4.09808i	0.489814	+	0.282794i
$211$	−6.79423	+	11.7679i	−0.467734	+	0.810139i	−0.999320	−	0.0368651i	$-0.988263\pi$
$211$	−6.79423	+	11.7679i	−0.467734	+	0.810139i	0.531586	+	0.847004i	$0.321596\pi$
$212$	−3.23205	−	5.59808i	−0.221978	−	0.384477i
$213$			16.3923i			1.12318i
$214$	0.294229	−	0.169873i	0.0201131	−	0.0116123i
$215$	−1.73205	+	1.00000i	−0.118125	+	0.0681994i
$216$			4.00000i			0.272166i
$217$	1.90192	+	3.29423i	0.129111	+	0.223627i
$218$	−7.73205	+	13.3923i	−0.523681	+	0.907041i
$219$	−13.3923	−	7.73205i	−0.904968	−	0.522484i
$220$	3.00000			0.202260
$221$		0			0
$222$	30.5885			2.05296
$223$	0.401924	+	0.232051i	0.0269148	+	0.0155393i	0.513397	−	0.858151i	$-0.328387\pi$
$223$	0.401924	+	0.232051i	0.0269148	+	0.0155393i	−0.486482	+	0.873690i	$0.661720\pi$
$224$	1.50000	−	2.59808i	0.100223	−	0.173591i
$225$	2.23205	+	3.86603i	0.148803	+	0.257735i
$226$		−	6.92820i		−	0.460857i
$227$	−3.80385	+	2.19615i	−0.252470	+	0.145764i	−0.620895	−	0.783894i	$-0.713231\pi$
$227$	−3.80385	+	2.19615i	−0.252470	+	0.145764i	0.368425	+	0.929658i	$0.379897\pi$
$228$	15.2942	−	8.83013i	1.01289	−	0.584789i
$229$		−	4.73205i		−	0.312703i	−0.987701	−	0.156351i	$-0.950027\pi$
$229$		−	4.73205i		−	0.312703i	0.987701	−	0.156351i	$-0.0499732\pi$
$230$	−1.26795	−	2.19615i	−0.0836061	−	0.144810i
$231$	12.2942	−	21.2942i	0.808901	−	1.40106i
$232$	−8.19615	−	4.73205i	−0.538104	−	0.310674i
$233$	1.26795			0.0830661			0.0415331	−	0.999137i	$-0.486776\pi$
$233$	1.26795			0.0830661			0.0415331	+	0.999137i	$0.486776\pi$
$234$		0			0
$235$	3.00000			0.195698
$236$	−9.00000	−	5.19615i	−0.585850	−	0.338241i
$237$	8.46410	−	14.6603i	0.549802	−	0.952286i
$238$	−3.29423	−	5.70577i	−0.213533	−	0.369850i
$239$		−	8.19615i		−	0.530165i	−0.964226	−	0.265083i	$-0.914601\pi$
$239$		−	8.19615i		−	0.530165i	0.964226	−	0.265083i	$-0.0853992\pi$
$240$	2.36603	−	1.36603i	0.152726	−	0.0881766i
$241$	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
$243$	−9.36603	−	16.2224i	−0.600831	−	1.04067i
$244$	−2.09808	+	3.63397i	−0.134316	+	0.232641i
$245$	−1.73205	−	1.00000i	−0.110657	−	0.0638877i
$246$	−28.3923			−1.81023
$247$		0			0
$248$	1.26795			0.0805149
$249$	5.19615	+	3.00000i	0.329293	+	0.190117i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−3.40192	−	5.89230i	−0.214728	−	0.371919i	0.738461	−	0.674296i	$-0.235553\pi$
$251$	−3.40192	−	5.89230i	−0.214728	−	0.371919i	−0.953188	+	0.302378i	$0.902220\pi$
$252$		−	13.3923i		−	0.843636i
$253$	−6.58846	+	3.80385i	−0.414213	+	0.239146i
$254$	18.3564	−	10.5981i	1.15178	−	0.664982i
$255$		−	6.00000i		−	0.375735i
$256$	−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	$0.308918\pi$
$258$	4.73205	+	2.73205i	0.294605	+	0.170090i
$259$	−33.5885			−2.08709
$260$		0			0
$261$	−42.2487			−2.61513
$262$	15.6962	+	9.06218i	0.969712	+	0.559863i
$263$	13.7942	−	23.8923i	0.850589	−	1.47326i	−0.0300894	−	0.999547i	$-0.509579\pi$
$263$	13.7942	−	23.8923i	0.850589	−	1.47326i	0.880678	−	0.473715i	$-0.157087\pi$
$264$	−4.09808	−	7.09808i	−0.252219	−	0.436856i
$265$			6.46410i			0.397087i
$266$	−16.7942	+	9.69615i	−1.02972	+	0.594509i
$267$	40.6865	−	23.4904i	2.48998	−	1.43759i
$268$		0			0
$269$	1.43782	+	2.49038i	0.0876656	+	0.151841i	0.906524	−	0.422154i	$-0.138726\pi$
$269$	1.43782	+	2.49038i	0.0876656	+	0.151841i	−0.818858	+	0.573996i	$0.805393\pi$
$270$	2.00000	−	3.46410i	0.121716	−	0.210819i
$271$	2.19615	+	1.26795i	0.133407	+	0.0770224i	0.565218	−	0.824942i	$-0.308792\pi$
$271$	2.19615	+	1.26795i	0.133407	+	0.0770224i	−0.431811	+	0.901964i	$0.642125\pi$
$272$	−2.19615			−0.133161
$273$		0			0
$274$	8.19615			0.495148
$275$	−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	$0.823769\pi$
$278$		−	9.19615i		−	0.551549i
$279$	4.90192	−	2.83013i	0.293471	−	0.169435i
$280$	−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	$0.899679\pi$
$282$	−4.09808	−	7.09808i	−0.244037	−	0.422684i
$283$	15.1962	−	26.3205i	0.903317	−	1.56459i	0.0801576	−	0.996782i	$-0.474458\pi$
$283$	15.1962	−	26.3205i	0.903317	−	1.56459i	0.823160	−	0.567810i	$-0.192209\pi$
$284$	−5.19615	−	3.00000i	−0.308335	−	0.178017i
$285$	−17.6603			−1.04610
$286$		0			0
$287$	31.1769			1.84032
$288$	−3.86603	−	2.23205i	−0.227808	−	0.131525i
$289$	6.08846	−	10.5455i	0.358145	−	0.620325i
$290$	4.73205	+	8.19615i	0.277876	+	0.481295i
$291$			41.3205i			2.42225i
$292$	4.90192	−	2.83013i	0.286863	−	0.165621i
$293$	0.696152	−	0.401924i	0.0406697	−	0.0234806i	−0.479527	−	0.877527i	$-0.659192\pi$
$293$	0.696152	−	0.401924i	0.0406697	−	0.0234806i	0.520197	+	0.854046i	$0.325859\pi$
$294$			5.46410i			0.318673i
$295$	5.19615	+	9.00000i	0.302532	+	0.524000i
$296$	−5.59808	+	9.69615i	−0.325382	+	0.563577i
$297$	−10.3923	−	6.00000i	−0.603023	−	0.348155i
$298$	−6.00000			−0.347571
$299$		0			0
$300$	−2.73205			−0.157735
$301$	−5.19615	−	3.00000i	−0.299501	−	0.172917i
$302$	−3.16987	+	5.49038i	−0.182406	+	0.315936i
$303$	9.92820	+	17.1962i	0.570360	+	0.987893i
$304$			6.46410i			0.370742i
$305$	3.63397	−	2.09808i	0.208081	−	0.120135i
$306$	−8.49038	+	4.90192i	−0.485363	+	0.280224i
$307$		−	20.5359i		−	1.17205i	−0.810295	−	0.586023i	$-0.800693\pi$
$307$		−	20.5359i		−	1.17205i	0.810295	−	0.586023i	$-0.199307\pi$
$308$	4.50000	+	7.79423i	0.256411	+	0.444117i
$309$	1.63397	−	2.83013i	0.0929536	−	0.161000i
$310$	−1.09808	−	0.633975i	−0.0623665	−	0.0360073i
$311$	15.1244			0.857624			0.428812	−	0.903394i	$-0.358932\pi$
$311$	15.1244			0.857624			0.428812	+	0.903394i	$0.358932\pi$
$312$		0			0
$313$	5.60770			0.316966			0.158483	−	0.987362i	$-0.449340\pi$
$313$	5.60770			0.316966			0.158483	+	0.987362i	$0.449340\pi$
$314$	11.2583	+	6.50000i	0.635344	+	0.366816i
$315$	−6.69615	+	11.5981i	−0.377285	+	0.653478i
$316$	3.09808	+	5.36603i	0.174280	+	0.301863i
$317$		−	12.8038i		−	0.719136i	−0.933119	−	0.359568i	$-0.882924\pi$
$317$		−	12.8038i		−	0.719136i	0.933119	−	0.359568i	$-0.117076\pi$
$318$	15.2942	−	8.83013i	0.857658	−	0.495169i
$319$	24.5885	−	14.1962i	1.37669	−	0.794832i
$320$			1.00000i			0.0559017i
$321$	0.464102	+	0.803848i	0.0259036	+	0.0448664i
$322$	3.80385	−	6.58846i	0.211980	−	0.367160i
$323$	12.2942	+	7.09808i	0.684069	+	0.394948i
$324$	2.46410			0.136895
$325$		0			0
$326$	7.26795			0.402534
$327$	−36.5885	−	21.1244i	−2.02335	−	1.16818i
$328$	5.19615	−	9.00000i	0.286910	−	0.496942i
$329$	4.50000	+	7.79423i	0.248093	+	0.429710i
$330$			8.19615i			0.451183i
$331$	−0.803848	+	0.464102i	−0.0441835	+	0.0255093i	−0.521929	−	0.852989i	$-0.674787\pi$
$331$	−0.803848	+	0.464102i	−0.0441835	+	0.0255093i	0.477746	+	0.878498i	$0.341454\pi$
$332$	−1.90192	+	1.09808i	−0.104382	+	0.0602648i
$333$			49.9808i			2.73893i
$334$	−1.50000	−	2.59808i	−0.0820763	−	0.142160i
$335$		0			0
$336$	7.09808	+	4.09808i	0.387232	+	0.223568i
$337$	−4.19615			−0.228579			−0.114289	−	0.993447i	$-0.536459\pi$
$337$	−4.19615			−0.228579			−0.114289	+	0.993447i	$0.536459\pi$
$338$		0			0
$339$	18.9282			1.02804
$340$	1.90192	+	1.09808i	0.103146	+	0.0595515i
$341$	−1.90192	+	3.29423i	−0.102995	+	0.178392i
$342$	14.4282	+	24.9904i	0.780188	+	1.35133i
$343$			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
$347$	12.6340	+	21.8827i	0.678227	+	1.17472i	0.975514	+	0.219936i	$0.0705848\pi$
$347$	12.6340	+	21.8827i	0.678227	+	1.17472i	−0.297287	+	0.954788i	$0.596082\pi$
$348$	12.9282	−	22.3923i	0.693024	−	1.20035i
$349$	29.4904	+	17.0263i	1.57858	+	0.911396i	0.995057	+	0.0993018i	$0.0316609\pi$
$349$	29.4904	+	17.0263i	1.57858	+	0.911396i	0.583527	+	0.812094i	$0.301672\pi$
$350$	3.00000			0.160357
$351$		0			0
$352$	3.00000			0.159901
$353$	17.4904	+	10.0981i	0.930919	+	0.537466i	0.887102	−	0.461573i	$-0.152715\pi$
$353$	17.4904	+	10.0981i	0.930919	+	0.537466i	0.0438169	+	0.999040i	$0.486048\pi$
$354$	14.1962	−	24.5885i	0.754517	−	1.30686i
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$			17.1962i			0.911394i
$357$	15.5885	−	9.00000i	0.825029	−	0.476331i
$358$	−2.19615	+	1.26795i	−0.116070	+	0.0670132i
$359$			22.3923i			1.18182i	0.806737	+	0.590910i	$0.201231\pi$
$359$			22.3923i			1.18182i	−0.806737	+	0.590910i	$0.798769\pi$
$360$	2.23205	+	3.86603i	0.117639	+	0.203757i
$361$	11.3923	−	19.7321i	0.599595	−	1.03853i
$362$	14.3660	+	8.29423i	0.755062	+	0.435935i
$363$	−5.46410			−0.286791
$364$		0			0
$365$	−5.66025			−0.296271
$366$	−9.92820	−	5.73205i	−0.518955	−	0.299619i
$367$	13.1962	−	22.8564i	0.688834	−	1.19309i	−0.283382	−	0.959007i	$-0.591456\pi$
$367$	13.1962	−	22.8564i	0.688834	−	1.19309i	0.972216	−	0.234088i	$-0.0752102\pi$
$368$	−1.26795	−	2.19615i	−0.0660964	−	0.114482i
$369$		−	46.3923i		−	2.41509i
$370$	9.69615	−	5.59808i	0.504079	−	0.291030i
$371$	−16.7942	+	9.69615i	−0.871913	+	0.503399i
$372$			3.46410i			0.179605i
$373$	−10.1962	−	17.6603i	−0.527937	−	0.914413i	−0.999470	−	0.0325648i	$-0.989632\pi$
$373$	−10.1962	−	17.6603i	−0.527937	−	0.914413i	0.471533	−	0.881848i	$-0.343701\pi$
$374$	3.29423	−	5.70577i	0.170341	−	0.295038i
$375$	2.36603	+	1.36603i	0.122181	+	0.0705412i
$376$	3.00000			0.154713
$377$		0			0
$378$	12.0000			0.617213
$379$	−10.2058	−	5.89230i	−0.524235	−	0.302667i	0.214430	−	0.976739i	$-0.431210\pi$
$379$	−10.2058	−	5.89230i	−0.524235	−	0.302667i	−0.738666	+	0.674072i	$0.764544\pi$
$380$	3.23205	−	5.59808i	0.165801	−	0.287175i
$381$	28.9545	+	50.1506i	1.48338	+	2.56929i
$382$		−	19.2679i		−	0.985834i
$383$	1.39230	−	0.803848i	0.0711435	−	0.0410747i	−0.464006	−	0.885832i	$-0.653589\pi$
$383$	1.39230	−	0.803848i	0.0711435	−	0.0410747i	0.535150	+	0.844757i	$0.320255\pi$
$384$	2.36603	−	1.36603i	0.120741	−	0.0697097i
$385$		−	9.00000i		−	0.458682i
$386$	−2.19615	−	3.80385i	−0.111781	−	0.193611i
$387$	−4.46410	+	7.73205i	−0.226923	+	0.393042i
$388$	−13.0981	−	7.56218i	−0.664954	−	0.383911i
$389$	19.2679			0.976924			0.488462	−	0.872585i	$-0.337558\pi$
$389$	19.2679			0.976924			0.488462	+	0.872585i	$0.337558\pi$
$390$		0			0
$391$	−5.56922			−0.281648
$392$	−1.73205	−	1.00000i	−0.0874818	−	0.0505076i
$393$	−24.7583	+	42.8827i	−1.24889	+	2.16315i
$394$	4.79423	+	8.30385i	0.241530	+	0.418342i
$395$		−	6.19615i		−	0.311762i
$396$	11.5981	−	6.69615i	0.582825	−	0.336494i
$397$	−0.696152	+	0.401924i	−0.0349389	+	0.0201720i	−0.517368	−	0.855763i	$-0.673088\pi$
$397$	−0.696152	+	0.401924i	−0.0349389	+	0.0201720i	0.482429	+	0.875935i	$0.339755\pi$
$398$			14.3923i			0.721421i
$399$	−26.4904	−	45.8827i	−1.32618	−	2.29701i
$400$	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
$404$	−7.26795			−0.361594
$405$	−2.13397	−	1.23205i	−0.106038	−	0.0612211i
$406$	−14.1962	+	24.5885i	−0.704543	+	1.22030i
$407$	−16.7942	−	29.0885i	−0.832459	−	1.44186i
$408$		−	6.00000i		−	0.297044i
$409$	−17.0885	+	9.86603i	−0.844970	+	0.487844i	−0.858950	−	0.512059i	$-0.828883\pi$
$409$	−17.0885	+	9.86603i	−0.844970	+	0.487844i	0.0139806	+	0.999902i	$0.495550\pi$
$410$	−9.00000	+	5.19615i	−0.444478	+	0.256620i
$411$			22.3923i			1.10453i
$412$	0.598076	+	1.03590i	0.0294651	+	0.0510351i
$413$	−15.5885	+	27.0000i	−0.767058	+	1.32858i
$414$	−9.80385	−	5.66025i	−0.481833	−	0.278186i
$415$	2.19615			0.107805
$416$		0			0
$417$	25.1244			1.23034
$418$	−16.7942	−	9.69615i	−0.821433	−	0.474254i
$419$	−8.66025	+	15.0000i	−0.423081	+	0.732798i	−0.996239	−	0.0866469i	$-0.972385\pi$
$419$	−8.66025	+	15.0000i	−0.423081	+	0.732798i	0.573158	+	0.819445i	$0.305718\pi$
$420$	−4.09808	−	7.09808i	−0.199966	−	0.346351i
$421$			27.1244i			1.32196i	0.750403	+	0.660980i	$0.229859\pi$
$421$			27.1244i			1.32196i	−0.750403	+	0.660980i	$0.770141\pi$
$422$	11.7679	−	6.79423i	0.572855	−	0.330738i
$423$	11.5981	−	6.69615i	0.563918	−	0.325578i
$424$			6.46410i			0.313925i
$425$	−1.09808	−	1.90192i	−0.0532645	−	0.0922569i
$426$	8.19615	−	14.1962i	0.397105	−	0.687806i
$427$	10.9019	+	6.29423i	0.527581	+	0.304599i
$428$	−0.339746			−0.0164222
$429$		0			0
$430$	2.00000			0.0964486
$431$	1.90192	+	1.09808i	0.0916124	+	0.0528925i	0.545106	−	0.838367i	$-0.316489\pi$
$431$	1.90192	+	1.09808i	0.0916124	+	0.0528925i	−0.453494	+	0.891259i	$0.649823\pi$
$432$	2.00000	−	3.46410i	0.0962250	−	0.166667i
$433$	6.19615	+	10.7321i	0.297768	+	0.515749i	0.975625	−	0.219444i	$-0.0704245\pi$
$433$	6.19615	+	10.7321i	0.297768	+	0.515749i	−0.677857	+	0.735194i	$0.737091\pi$
$434$		−	3.80385i		−	0.182591i
$435$	−22.3923	+	12.9282i	−1.07363	+	0.619860i
$436$	13.3923	−	7.73205i	0.641375	−	0.370298i
$437$			16.3923i			0.784150i
$438$	7.73205	+	13.3923i	0.369452	+	0.639909i
$439$	17.2942	−	29.9545i	0.825408	−	1.42965i	−0.0761982	−	0.997093i	$-0.524278\pi$
$439$	17.2942	−	29.9545i	0.825408	−	1.42965i	0.901607	−	0.432557i	$-0.142388\pi$
$440$	−2.59808	−	1.50000i	−0.123858	−	0.0715097i
$441$	−8.92820			−0.425153
$442$		0			0
$443$	−1.60770			−0.0763839			−0.0381920	−	0.999270i	$-0.512160\pi$
$443$	−1.60770			−0.0763839			−0.0381920	+	0.999270i	$0.512160\pi$
$444$	−26.4904	−	15.2942i	−1.25718	−	0.725832i
$445$	8.59808	−	14.8923i	0.407588	−	0.705963i
$446$	−0.232051	−	0.401924i	−0.0109879	−	0.0190316i
$447$		−	16.3923i		−	0.775329i
$448$	−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	$0.453233\pi$
$450$		−	4.46410i		−	0.210440i
$451$	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
$454$	4.39230			0.206141
$455$		0			0
$456$	−17.6603			−0.827017
$457$	30.8827	+	17.8301i	1.44463	+	0.834058i	0.998154	−	0.0607368i	$-0.0193450\pi$
$457$	30.8827	+	17.8301i	1.44463	+	0.834058i	0.446477	+	0.894795i	$0.352678\pi$
$458$	−2.36603	+	4.09808i	−0.110557	+	0.191491i
$459$	−4.39230	−	7.60770i	−0.205015	−	0.355097i
$460$			2.53590i			0.118237i
$461$	0.509619	−	0.294229i	0.0237353	−	0.0137036i	−0.488085	−	0.872796i	$-0.662305\pi$
$461$	0.509619	−	0.294229i	0.0237353	−	0.0137036i	0.511821	+	0.859092i	$0.328971\pi$
$462$	−21.2942	+	12.2942i	−0.990697	+	0.571979i
$463$		−	0.928203i		−	0.0431373i	−0.999767	−	0.0215686i	$-0.993134\pi$
$463$		−	0.928203i		−	0.0431373i	0.999767	−	0.0215686i	$-0.00686604\pi$
$464$	4.73205	+	8.19615i	0.219680	+	0.380497i
$465$	1.73205	−	3.00000i	0.0803219	−	0.139122i
$466$	−1.09808	−	0.633975i	−0.0508674	−	0.0293683i
$467$	−10.1436			−0.469390			−0.234695	−	0.972069i	$-0.575409\pi$
$467$	−10.1436			−0.469390			−0.234695	+	0.972069i	$0.575409\pi$
$468$		0			0
$469$		0			0
$470$	−2.59808	−	1.50000i	−0.119840	−	0.0691898i
$471$	−17.7583	+	30.7583i	−0.818261	+	1.41727i
$472$	5.19615	+	9.00000i	0.239172	+	0.414259i
$473$		−	6.00000i		−	0.275880i
$474$	−14.6603	+	8.46410i	−0.673368	+	0.388769i
$475$	−5.59808	+	3.23205i	−0.256857	+	0.148297i
$476$			6.58846i			0.301981i
$477$	14.4282	+	24.9904i	0.660622	+	1.14423i
$478$	−4.09808	+	7.09808i	−0.187442	+	0.324658i
$479$	9.50962	+	5.49038i	0.434506	+	0.250862i	0.701264	−	0.712901i	$-0.252619\pi$
$479$	9.50962	+	5.49038i	0.434506	+	0.250862i	−0.266759	+	0.963763i	$0.585953\pi$
$480$	−2.73205			−0.124700
$481$		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
$485$	7.56218	+	13.0981i	0.343381	+	0.594753i
$486$			18.7321i			0.849703i
$487$	28.7942	−	16.6244i	1.30479	−	0.753321i	0.323569	−	0.946204i	$-0.395117\pi$
$487$	28.7942	−	16.6244i	1.30479	−	0.753321i	0.981222	+	0.192883i	$0.0617838\pi$
$488$	3.63397	−	2.09808i	0.164502	−	0.0949754i
$489$			19.8564i			0.897938i
$490$	1.00000	+	1.73205i	0.0451754	+	0.0782461i
$491$	−1.66987	+	2.89230i	−0.0753603	+	0.130528i	−0.901243	−	0.433314i	$-0.857344\pi$
$491$	−1.66987	+	2.89230i	−0.0753603	+	0.130528i	0.825883	+	0.563842i	$0.190677\pi$
$492$	24.5885	+	14.1962i	1.10853	+	0.640012i
$493$	20.7846			0.936092
$494$		0			0
$495$	−13.3923			−0.601939
$496$	−1.09808	−	0.633975i	−0.0493051	−	0.0284663i
$497$	−9.00000	+	15.5885i	−0.403705	+	0.699238i
$498$	−3.00000	−	5.19615i	−0.134433	−	0.232845i
$499$		−	1.85641i		−	0.0831042i	−0.999136	−	0.0415521i	$-0.986770\pi$
$499$		−	1.85641i		−	0.0831042i	0.999136	−	0.0415521i	$-0.0132302\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	7.09808	−	4.09808i	0.317119	−	0.183089i
$502$			6.80385i			0.303671i
$503$	4.66987	+	8.08846i	0.208219	+	0.360646i	0.951154	−	0.308718i	$-0.0998999\pi$
$503$	4.66987	+	8.08846i	0.208219	+	0.360646i	−0.742934	+	0.669364i	$0.766567\pi$
$504$	−6.69615	+	11.5981i	−0.298270	+	0.516619i
$505$	6.29423	+	3.63397i	0.280089	+	0.161710i
$506$	7.60770			0.338203
$507$		0			0
$508$	−21.1962			−0.940427
$509$	−1.39230	−	0.803848i	−0.0617128	−	0.0356299i	0.468826	−	0.883290i	$-0.344677\pi$
$509$	−1.39230	−	0.803848i	−0.0617128	−	0.0356299i	−0.530539	+	0.847661i	$0.678010\pi$
$510$	−3.00000	+	5.19615i	−0.132842	+	0.230089i
$511$	−8.49038	−	14.7058i	−0.375592	−	0.650545i
$512$			1.00000i			0.0441942i
$513$	−22.3923	+	12.9282i	−0.988644	+	0.570794i
$514$	12.0000	−	6.92820i	0.529297	−	0.305590i
$515$		−	1.19615i		−	0.0527088i
$516$	−2.73205	−	4.73205i	−0.120272	−	0.208317i
$517$	−4.50000	+	7.79423i	−0.197910	+	0.342790i
$518$	29.0885	+	16.7942i	1.27807	+	0.737896i
$519$	40.9808			1.79886
$520$		0			0
$521$	−0.464102			−0.0203327			−0.0101663	−	0.999948i	$-0.503236\pi$
$521$	−0.464102			−0.0203327			−0.0101663	+	0.999948i	$0.503236\pi$
$522$	36.5885	+	21.1244i	1.60143	+	0.924588i
$523$	−9.19615	+	15.9282i	−0.402120	+	0.696492i	−0.993982	−	0.109548i	$-0.965060\pi$
$523$	−9.19615	+	15.9282i	−0.402120	+	0.696492i	0.591862	+	0.806039i	$0.298393\pi$
$524$	−9.06218	−	15.6962i	−0.395883	−	0.685690i
$525$			8.19615i			0.357709i
$526$	−23.8923	+	13.7942i	−1.04175	+	0.601457i
$527$	−2.41154	+	1.39230i	−0.105048	+	0.0606498i
$528$			8.19615i			0.356692i
$529$	8.28461	+	14.3494i	0.360200	+	0.623885i
$530$	3.23205	−	5.59808i	0.140391	−	0.243165i
$531$	40.1769	+	23.1962i	1.74353	+	1.00663i
$532$	19.3923			0.840763
$533$		0			0
$534$	−46.9808			−2.03306
$535$	0.294229	+	0.169873i	0.0127206	+	0.00734425i
$536$		0			0
$537$	−3.46410	−	6.00000i	−0.149487	−	0.258919i
$538$		−	2.87564i		−	0.123978i
$539$	5.19615	−	3.00000i	0.223814	−	0.129219i
$540$	−3.46410	+	2.00000i	−0.149071	+	0.0860663i
$541$		−	16.0526i		−	0.690153i	−0.938574	−	0.345077i	$-0.887853\pi$
$541$		−	16.0526i		−	0.690153i	0.938574	−	0.345077i	$-0.112147\pi$
$542$	−1.26795	−	2.19615i	−0.0544631	−	0.0943328i
$543$	−22.6603	+	39.2487i	−0.972445	+	1.68432i
$544$	1.90192	+	1.09808i	0.0815443	+	0.0470796i
$545$	−15.4641			−0.662409
$546$		0			0
$547$	34.7846			1.48728			0.743641	−	0.668579i	$-0.233097\pi$
$547$	34.7846			1.48728			0.743641	+	0.668579i	$0.233097\pi$
$548$	−7.09808	−	4.09808i	−0.303215	−	0.175061i
$549$	9.36603	−	16.2224i	0.399732	−	0.692357i
$550$	1.50000	+	2.59808i	0.0639602	+	0.110782i
$551$		−	61.1769i		−	2.60622i
$552$	6.00000	−	3.46410i	0.255377	−	0.147442i
$553$	16.0981	−	9.29423i	0.684560	−	0.395231i
$554$		−	1.00000i		−	0.0424859i
$555$	15.2942	+	26.4904i	0.649204	+	1.12445i
$556$	−4.59808	+	7.96410i	−0.195002	+	0.337753i
$557$	−14.8923	−	8.59808i	−0.631007	−	0.364312i	0.150135	−	0.988666i	$-0.452029\pi$
$557$	−14.8923	−	8.59808i	−0.631007	−	0.364312i	−0.781142	+	0.624353i	$0.785363\pi$
$558$	−5.66025			−0.239618
$559$		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
$563$	−10.7321	−	18.5885i	−0.452302	−	0.783410i	0.546227	−	0.837637i	$-0.316064\pi$
$563$	−10.7321	−	18.5885i	−0.452302	−	0.783410i	−0.998529	+	0.0542274i	$0.982730\pi$
$564$			8.19615i			0.345120i
$565$	6.00000	−	3.46410i	0.252422	−	0.145736i
$566$	−26.3205	+	15.1962i	−1.10633	+	0.638742i
$567$		−	7.39230i		−	0.310448i
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	−10.6244	+	18.4019i	−0.445396	+	0.771449i	−0.998080	−	0.0619424i	$-0.980270\pi$
$569$	−10.6244	+	18.4019i	−0.445396	+	0.771449i	0.552684	+	0.833391i	$0.313604\pi$
$570$	15.2942	+	8.83013i	0.640605	+	0.369853i
$571$	34.3731			1.43847			0.719234	−	0.694768i	$-0.244493\pi$
$571$	34.3731			1.43847			0.719234	+	0.694768i	$0.244493\pi$
$572$		0			0
$573$	52.6410			2.19911
$574$	−27.0000	−	15.5885i	−1.12696	−	0.650650i
$575$	1.26795	−	2.19615i	0.0528771	−	0.0915859i
$576$	2.23205	+	3.86603i	0.0930021	+	0.161084i
$577$			32.4449i			1.35070i	0.737499	+	0.675349i	$0.236007\pi$
$577$			32.4449i			1.35070i	−0.737499	+	0.675349i	$0.763993\pi$
$578$	−10.5455	+	6.08846i	−0.438636	+	0.253246i
$579$	10.3923	−	6.00000i	0.431889	−	0.249351i
$580$		−	9.46410i		−	0.392975i
$581$	3.29423	+	5.70577i	0.136668	+	0.236715i
$582$	20.6603	−	35.7846i	0.856395	−	1.48332i
$583$	−16.7942	−	9.69615i	−0.695546	−	0.401574i
$584$	−5.66025			−0.234223
$585$		0			0
$586$	−0.803848			−0.0332066
$587$	25.9808	+	15.0000i	1.07234	+	0.619116i	0.928820	−	0.370531i	$-0.120824\pi$
$587$	25.9808	+	15.0000i	1.07234	+	0.619116i	0.143521	+	0.989647i	$0.454158\pi$
$588$	2.73205	−	4.73205i	0.112668	−	0.195146i
$589$	4.09808	+	7.09808i	0.168858	+	0.292471i
$590$		−	10.3923i		−	0.427844i
$591$	−22.6865	+	13.0981i	−0.933199	+	0.538783i
$592$	9.69615	−	5.59808i	0.398509	−	0.230080i
$593$			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
$595$	3.29423	−	5.70577i	0.135050	−	0.233914i
$596$	5.19615	+	3.00000i	0.212843	+	0.122885i
$597$	−39.3205			−1.60928
$598$		0			0
$599$	7.85641			0.321004			0.160502	−	0.987036i	$-0.448689\pi$
$599$	7.85641			0.321004			0.160502	+	0.987036i	$0.448689\pi$
$600$	2.36603	+	1.36603i	0.0965926	+	0.0557678i
$601$	−1.89230	+	3.27757i	−0.0771887	+	0.133695i	−0.902036	−	0.431661i	$-0.857928\pi$
$601$	−1.89230	+	3.27757i	−0.0771887	+	0.133695i	0.824847	+	0.565356i	$0.191261\pi$
$602$	3.00000	+	5.19615i	0.122271	+	0.211779i
$603$		0			0
$604$	5.49038	−	3.16987i	0.223400	−	0.128980i
$605$	−1.73205	+	1.00000i	−0.0704179	+	0.0406558i
$606$		−	19.8564i		−	0.806611i
$607$	3.20577	+	5.55256i	0.130118	+	0.225371i	0.923722	−	0.383064i	$-0.125131\pi$
$607$	3.20577	+	5.55256i	0.130118	+	0.225371i	−0.793604	+	0.608435i	$0.791798\pi$
$608$	3.23205	−	5.59808i	0.131077	−	0.227032i
$609$	−67.1769	−	38.7846i	−2.72215	−	1.57163i
$610$	−4.19615			−0.169897
$611$		0			0
$612$	9.80385			0.396297
$613$	−23.3038	−	13.4545i	−0.941234	−	0.543421i	−0.0508868	−	0.998704i	$-0.516205\pi$
$613$	−23.3038	−	13.4545i	−0.941234	−	0.543421i	−0.890347	+	0.455283i	$0.849538\pi$
$614$	−10.2679	+	17.7846i	−0.414381	+	0.717728i
$615$	−14.1962	−	24.5885i	−0.572444	−	0.991502i
$616$		−	9.00000i		−	0.362620i
$617$	15.5885	−	9.00000i	0.627568	−	0.362326i	−0.152242	−	0.988343i	$-0.548649\pi$
$617$	15.5885	−	9.00000i	0.627568	−	0.362326i	0.779809	+	0.626017i	$0.215316\pi$
$618$	−2.83013	+	1.63397i	−0.113844	+	0.0657281i
$619$		−	10.6077i		−	0.426359i	−0.977013	−	0.213180i	$-0.931618\pi$
$619$		−	10.6077i		−	0.426359i	0.977013	−	0.213180i	$-0.0683820\pi$
$620$	0.633975	+	1.09808i	0.0254610	+	0.0440998i
$621$	5.07180	−	8.78461i	0.203524	−	0.352514i
$622$	−13.0981	−	7.56218i	−0.525185	−	0.303216i
$623$	51.5885			2.06685
$624$		0			0
$625$	1.00000			0.0400000
$626$	−4.85641	−	2.80385i	−0.194101	−	0.112064i
$627$	26.4904	−	45.8827i	1.05792	−	1.83238i
$628$	−6.50000	−	11.2583i	−0.259378	−	0.449256i
$629$		−	24.5885i		−	0.980406i
$630$	11.5981	−	6.69615i	0.462078	−	0.266781i
$631$	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	$0.197566\pi$
$632$		−	6.19615i		−	0.246470i
$633$	18.5622	+	32.1506i	0.737780	+	1.27787i
$634$	−6.40192	+	11.0885i	−0.254253	+	0.440379i
$635$	18.3564	+	10.5981i	0.728452	+	0.420572i
$636$	−17.6603			−0.700275
$637$		0			0
$638$	−28.3923			−1.12406
$639$	23.1962	+	13.3923i	0.917626	+	0.529791i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−22.9641	−	39.7750i	−0.907027	−	1.57102i	−0.818172	−	0.574973i	$-0.805012\pi$
$641$	−22.9641	−	39.7750i	−0.907027	−	1.57102i	−0.0888552	−	0.996045i	$-0.528321\pi$
$642$		−	0.928203i		−	0.0366333i
$643$	−6.29423	+	3.63397i	−0.248220	+	0.143310i	−0.618949	−	0.785431i	$-0.712441\pi$
$643$	−6.29423	+	3.63397i	−0.248220	+	0.143310i	0.370729	+	0.928741i	$0.379108\pi$
$644$	−6.58846	+	3.80385i	−0.259622	+	0.149893i
$645$			5.46410i			0.215149i
$646$	−7.09808	−	12.2942i	−0.279270	−	0.483710i
$647$	5.59808	−	9.69615i	0.220083	−	0.381195i	−0.734750	−	0.678338i	$-0.762700\pi$
$647$	5.59808	−	9.69615i	0.220083	−	0.381195i	0.954833	+	0.297143i	$0.0960338\pi$
$648$	−2.13397	−	1.23205i	−0.0838304	−	0.0483995i
$649$	−31.1769			−1.22380
$650$		0			0
$651$	10.3923			0.407307
$652$	−6.29423	−	3.63397i	−0.246501	−	0.142317i
$653$	9.69615	−	16.7942i	0.379440	−	0.657209i	−0.611541	−	0.791213i	$-0.709450\pi$
$653$	9.69615	−	16.7942i	0.379440	−	0.657209i	0.990981	+	0.134004i	$0.0427834\pi$
$654$	21.1244	+	36.5885i	0.826028	+	1.43072i
$655$			18.1244i			0.708177i
$656$	−9.00000	+	5.19615i	−0.351391	+	0.202876i
$657$	−21.8827	+	12.6340i	−0.853725	+	0.492898i
$658$		−	9.00000i		−	0.350857i
$659$	−14.6603	−	25.3923i	−0.571082	−	0.989144i	−0.996455	−	0.0841255i	$-0.973190\pi$
$659$	−14.6603	−	25.3923i	−0.571082	−	0.989144i	0.425373	−	0.905018i	$-0.360143\pi$
$660$	4.09808	−	7.09808i	0.159517	−	0.276292i
$661$	−25.9019	−	14.9545i	−1.00747	−	0.581662i	−0.0970187	−	0.995283i	$-0.530931\pi$
$661$	−25.9019	−	14.9545i	−1.00747	−	0.581662i	−0.910449	+	0.413621i	$0.864264\pi$
$662$	0.928203			0.0360756
$663$		0			0
$664$	2.19615			0.0852272
$665$	−16.7942	−	9.69615i	−0.651252	−	0.376001i
$666$	24.9904	−	43.2846i	0.968358	−	1.67724i
$667$	12.0000	+	20.7846i	0.464642	+	0.804783i
$668$			3.00000i			0.116073i
$669$	1.09808	−	0.633975i	0.0424541	−	0.0245109i
$670$		0			0
$671$			12.5885i			0.485972i
$672$	−4.09808	−	7.09808i	−0.158087	−	0.273814i
$673$	−1.80385	+	3.12436i	−0.0695332	+	0.120435i	−0.898696	−	0.438572i	$-0.855484\pi$
$673$	−1.80385	+	3.12436i	−0.0695332	+	0.120435i	0.829163	+	0.559007i	$0.188818\pi$
$674$	3.63397	+	2.09808i	0.139975	+	0.0808149i
$675$	4.00000			0.153960
$676$		0			0
$677$	1.85641			0.0713475			0.0356737	−	0.999363i	$-0.488642\pi$
$677$	1.85641			0.0713475			0.0356737	+	0.999363i	$0.488642\pi$
$678$	−16.3923	−	9.46410i	−0.629543	−	0.363467i
$679$	−22.6865	+	39.2942i	−0.870629	+	1.50797i
$680$	−1.09808	−	1.90192i	−0.0421093	−	0.0729354i
$681$			12.0000i			0.459841i
$682$	3.29423	−	1.90192i	0.126143	−	0.0728284i
$683$	−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	$0.536766\pi$
$684$		−	28.8564i		−	1.10335i
$685$	4.09808	+	7.09808i	0.156579	+	0.271204i
$686$	7.50000	−	12.9904i	0.286351	−	0.495975i
$687$	−11.1962	−	6.46410i	−0.427160	−	0.246621i
$688$	2.00000			0.0762493
$689$		0			0
$690$	−6.92820			−0.263752
$691$	16.2058	+	9.35641i	0.616497	+	0.355934i	0.775504	−	0.631343i	$-0.217496\pi$
$691$	16.2058	+	9.35641i	0.616497	+	0.355934i	−0.159007	+	0.987277i	$0.550829\pi$
$692$	−7.50000	+	12.9904i	−0.285107	+	0.493820i
$693$	−20.0885	−	34.7942i	−0.763097	−	1.32172i
$694$		−	25.2679i		−	0.959158i
$695$	7.96410	−	4.59808i	0.302096	−	0.174415i
$696$	−22.3923	+	12.9282i	−0.848778	+	0.490042i
$697$			22.8231i			0.864486i
$698$	−17.0263	−	29.4904i	−0.644454	−	1.11623i
$699$	1.73205	−	3.00000i	0.0655122	−	0.113470i
$700$	−2.59808	−	1.50000i	−0.0981981	−	0.0566947i
$701$	−29.9090			−1.12965			−0.564823	−	0.825212i	$-0.691056\pi$
$701$	−29.9090			−1.12965			−0.564823	+	0.825212i	$0.691056\pi$
$702$		0			0
$703$	−72.3731			−2.72960
$704$	−2.59808	−	1.50000i	−0.0979187	−	0.0565334i
$705$	4.09808	−	7.09808i	0.154342	−	0.267329i
$706$	−10.0981	−	17.4904i	−0.380046	−	0.658259i
$707$			21.8038i			0.820018i
$708$	−24.5885	+	14.1962i	−0.924091	+	0.533524i
$709$	−35.4904	+	20.4904i	−1.33287	+	0.769532i	−0.985738	−	0.168284i	$-0.946177\pi$
$709$	−35.4904	+	20.4904i	−1.33287	+	0.769532i	−0.347131	+	0.937817i	$0.612844\pi$
$710$		−	6.00000i		−	0.225176i
$711$	−13.8301	−	23.9545i	−0.518670	−	0.898363i
$712$	8.59808	−	14.8923i	0.322227	−	0.558113i
$713$	−2.78461	−	1.60770i	−0.104284	−	0.0602087i
$714$	−18.0000			−0.673633
$715$		0			0
$716$	2.53590			0.0947710
$717$	−19.3923	−	11.1962i	−0.724219	−	0.418128i
$718$	11.1962	−	19.3923i	0.417837	−	0.723714i
$719$	0.928203	+	1.60770i	0.0346161	+	0.0599569i	0.882814	−	0.469722i	$-0.155646\pi$
$719$	0.928203	+	1.60770i	0.0346161	+	0.0599569i	−0.848198	+	0.529679i	$0.822312\pi$
$720$		−	4.46410i		−	0.166367i
$721$	3.10770	−	1.79423i	0.115737	−	0.0668206i
$722$	−19.7321	+	11.3923i	−0.734351	+	0.423978i
$723$		−	23.6603i		−	0.879934i
$724$	−8.29423	−	14.3660i	−0.308253	−	0.533909i
$725$	−4.73205	+	8.19615i	−0.175744	+	0.304397i
$726$	4.73205	+	2.73205i	0.175623	+	0.101396i
$727$	−38.3731			−1.42318			−0.711589	−	0.702596i	$-0.752024\pi$
$727$	−38.3731			−1.42318			−0.711589	+	0.702596i	$0.752024\pi$
$728$		0			0
$729$	−43.7846			−1.62165
$730$	4.90192	+	2.83013i	0.181428	+	0.104748i
$731$	2.19615	−	3.80385i	0.0812276	−	0.140690i
$732$	5.73205	+	9.92820i	0.211863	+	0.366957i
$733$		−	50.9090i		−	1.88037i	−0.340670	−	0.940183i	$-0.610654\pi$
$733$		−	50.9090i		−	1.88037i	0.340670	−	0.940183i	$-0.389346\pi$
$734$	−22.8564	+	13.1962i	−0.843645	+	0.487079i
$735$	−4.73205	+	2.73205i	−0.174544	+	0.100773i
$736$			2.53590i			0.0934745i
$737$		0			0
$738$	−23.1962	+	40.1769i	−0.853862	+	1.47893i
$739$	−43.7942	−	25.2846i	−1.61100	−	0.930109i	−0.989140	−	0.146979i	$-0.953045\pi$
$739$	−43.7942	−	25.2846i	−1.61100	−	0.930109i	−0.621857	−	0.783131i	$-0.713622\pi$
$740$	−11.1962			−0.411579
$741$		0			0
$742$	19.3923			0.711914
$743$	−29.7846	−	17.1962i	−1.09269	−	0.630866i	−0.158400	−	0.987375i	$-0.550633\pi$
$743$	−29.7846	−	17.1962i	−1.09269	−	0.630866i	−0.934292	+	0.356509i	$0.883967\pi$
$744$	1.73205	−	3.00000i	0.0635001	−	0.109985i
$745$	−3.00000	−	5.19615i	−0.109911	−	0.190372i
$746$			20.3923i			0.746615i
$747$	8.49038	−	4.90192i	0.310647	−	0.179352i
$748$	−5.70577	+	3.29423i	−0.208624	+	0.120449i
$749$			1.01924i			0.0372421i
$750$	−1.36603	−	2.36603i	−0.0498802	−	0.0863950i
$751$	−0.196152	+	0.339746i	−0.00715770	+	0.0123975i	−0.869582	−	0.493788i	$-0.835612\pi$
$751$	−0.196152	+	0.339746i	−0.00715770	+	0.0123975i	0.862424	+	0.506186i	$0.168945\pi$
$752$	−2.59808	−	1.50000i	−0.0947421	−	0.0546994i
$753$	−18.5885			−0.677401
$754$		0			0
$755$	−6.33975			−0.230727
$756$	−10.3923	−	6.00000i	−0.377964	−	0.218218i
$757$	−1.89230	+	3.27757i	−0.0687770	+	0.119125i	−0.898363	−	0.439253i	$-0.855243\pi$
$757$	−1.89230	+	3.27757i	−0.0687770	+	0.119125i	0.829586	+	0.558379i	$0.188576\pi$
$758$	5.89230	+	10.2058i	0.214018	+	0.370690i
$759$			20.7846i			0.754434i
$760$	−5.59808	+	3.23205i	−0.203064	+	0.117239i
$761$	25.2846	−	14.5981i	0.916566	−	0.529180i	0.0340283	−	0.999421i	$-0.489166\pi$
$761$	25.2846	−	14.5981i	0.916566	−	0.529180i	0.882538	+	0.470241i	$0.155833\pi$
$762$		−	57.9090i		−	2.09782i
$763$	−23.1962	−	40.1769i	−0.839757	−	1.45450i
$764$	−9.63397	+	16.6865i	−0.348545	+	0.603698i
$765$	−8.49038	−	4.90192i	−0.306970	−	0.177229i
$766$	−1.60770			−0.0580884
$767$		0			0
$768$	−2.73205			−0.0985844
$769$	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
$771$	18.9282	+	32.7846i	0.681683	+	1.18071i
$772$			4.39230i			0.158083i
$773$	29.0885	−	16.7942i	1.04624	−	0.604046i	0.124645	−	0.992201i	$-0.460221\pi$
$773$	29.0885	−	16.7942i	1.04624	−	0.604046i	0.921594	+	0.388155i	$0.126887\pi$
$774$	7.73205	−	4.46410i	0.277923	−	0.160459i
$775$		−	1.26795i		−	0.0455461i
$776$	7.56218	+	13.0981i	0.271466	+	0.470194i
$777$	−45.8827	+	79.4711i	−1.64603	+	2.85101i
$778$	−16.6865	−	9.63397i	−0.598241	−	0.345395i
$779$	67.1769			2.40686
$780$		0			0
$781$	−18.0000			−0.644091
$782$	4.82309	+	2.78461i	0.172473	+	0.0995774i
$783$	−18.9282	+	32.7846i	−0.676439	+	1.17163i
$784$	1.00000	+	1.73205i	0.0357143	+	0.0618590i
$785$			13.0000i			0.463990i
$786$	42.8827	−	24.7583i	1.52957	−	0.883100i
$787$	31.9019	−	18.4186i	1.13718	−	0.656552i	0.191450	−	0.981502i	$-0.438681\pi$
$787$	31.9019	−	18.4186i	1.13718	−	0.656552i	0.945731	+	0.324951i	$0.105348\pi$
$788$		−	9.58846i		−	0.341575i
$789$	−37.6865	−	65.2750i	−1.34168	−	2.32385i
$790$	−3.09808	+	5.36603i	−0.110225	+	0.190915i
$791$	18.0000	+	10.3923i	0.640006	+	0.369508i
$792$	−13.3923			−0.475875
$793$		0			0
$794$	0.803848			0.0285275
$795$	15.2942	+	8.83013i	0.542430	+	0.313172i
$796$	7.19615	−	12.4641i	0.255061	−	0.441778i
$797$	−0.464102	−	0.803848i	−0.0164393	−	0.0284737i	0.857689	−	0.514169i	$-0.171900\pi$
$797$	−0.464102	−	0.803848i	−0.0164393	−	0.0284737i	−0.874128	+	0.485696i	$0.838566\pi$
$798$			52.9808i			1.87550i
$799$	−5.70577	+	3.29423i	−0.201856	+	0.116541i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		−	76.7654i		−	2.71237i
$802$	−2.59808	−	4.50000i	−0.0917413	−	0.158901i
$803$	8.49038	−	14.7058i	0.299619	−	0.518955i
$804$		0			0
$805$	7.60770			0.268136
$806$		0			0
$807$	7.85641			0.276559
$808$	6.29423	+	3.63397i	0.221430	+	0.127843i
$809$	−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	$0.305302\pi$
$810$	1.23205	+	2.13397i	0.0432899	+	0.0749802i
$811$			22.6077i			0.793864i	0.917848	+	0.396932i	$0.129925\pi$
$811$			22.6077i			0.793864i	−0.917848	+	0.396932i	$0.870075\pi$
$812$	24.5885	−	14.1962i	0.862886	−	0.498187i
$813$	6.00000	−	3.46410i	0.210429	−	0.121491i
$814$			33.5885i			1.17727i
$815$	3.63397	+	6.29423i	0.127293	+	0.220477i
$816$	−3.00000	+	5.19615i	−0.105021	+	0.181902i
$817$	−11.1962	−	6.46410i	−0.391704	−	0.226150i
$818$	19.7321			0.689915
$819$		0			0
$820$	10.3923			0.362915
$821$	8.49038	+	4.90192i	0.296316	+	0.171078i	0.640787	−	0.767719i	$-0.278608\pi$
$821$	8.49038	+	4.90192i	0.296316	+	0.171078i	−0.344471	+	0.938797i	$0.611942\pi$
$822$	11.1962	−	19.3923i	0.390511	−	0.676384i
$823$	8.40192	+	14.5526i	0.292873	+	0.507270i	0.974488	−	0.224441i	$-0.0720555\pi$
$823$	8.40192	+	14.5526i	0.292873	+	0.507270i	−0.681615	+	0.731711i	$0.738722\pi$
$824$		−	1.19615i		−	0.0416699i
$825$	−7.09808	+	4.09808i	−0.247123	+	0.142677i
$826$	27.0000	−	15.5885i	0.939450	−	0.542392i
$827$		−	11.4115i		−	0.396818i	−0.980119	−	0.198409i	$-0.936423\pi$
$827$		−	11.4115i		−	0.396818i	0.980119	−	0.198409i	$-0.0635775\pi$
$828$	5.66025	+	9.80385i	0.196707	+	0.340707i
$829$	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	$0.0537604\pi$
$830$	−1.90192	−	1.09808i	−0.0660167	−	0.0381148i
$831$	2.73205			0.0947738
$832$		0			0
$833$	4.39230			0.152184
$834$	−21.7583	−	12.5622i	−0.753429	−	0.434993i
$835$	1.50000	−	2.59808i	0.0519096	−	0.0899101i
$836$	9.69615	+	16.7942i	0.335348	+	0.580841i
$837$		−	5.07180i		−	0.175307i
$838$	15.0000	−	8.66025i	0.518166	−	0.299164i
$839$	27.8827	−	16.0981i	0.962617	−	0.555767i	0.0656397	−	0.997843i	$-0.479091\pi$
$839$	27.8827	−	16.0981i	0.962617	−	0.555767i	0.896978	+	0.442076i	$0.145758\pi$
$840$			8.19615i			0.282794i
$841$	−30.2846	−	52.4545i	−1.04430	−	1.80878i
$842$	13.5622	−	23.4904i	0.467384	−	0.809532i
$843$	24.5885	+	14.1962i	0.846871	+	0.488941i
$844$	−13.5885			−0.467734
$845$		0			0
$846$	−13.3923			−0.460437
$847$	−5.19615	−	3.00000i	−0.178542	−	0.103081i
$848$	3.23205	−	5.59808i	0.110989	−	0.192239i
$849$	−41.5167	−	71.9090i	−1.42485	−	2.46791i
$850$			2.19615i			0.0753274i
$851$	24.5885	−	14.1962i	0.842881	−	0.486638i
$852$	−14.1962	+	8.19615i	−0.486352	+	0.280796i
$853$		−	13.8564i		−	0.474434i	−0.971457	−	0.237217i	$-0.923765\pi$
$853$		−	13.8564i		−	0.474434i	0.971457	−	0.237217i	$-0.0762353\pi$
$854$	−6.29423	−	10.9019i	−0.215384	−	0.373056i
$855$	−14.4282	+	24.9904i	−0.493434	+	0.854653i
$856$	0.294229	+	0.169873i	0.0100565	+	0.00580614i
$857$	−13.2679			−0.453225			−0.226612	−	0.973985i	$-0.572765\pi$
$857$	−13.2679			−0.453225			−0.226612	+	0.973985i	$0.572765\pi$
$858$		0			0
$859$	52.3731			1.78695			0.893473	−	0.449117i	$-0.148261\pi$
$859$	52.3731			1.78695			0.893473	+	0.449117i	$0.148261\pi$
$860$	−1.73205	−	1.00000i	−0.0590624	−	0.0340997i
$861$	42.5885	−	73.7654i	1.45141	−	2.51392i
$862$	−1.09808	−	1.90192i	−0.0374006	−	0.0647798i
$863$		−	19.1769i		−	0.652790i	−0.945234	−	0.326395i	$-0.894166\pi$
$863$		−	19.1769i		−	0.652790i	0.945234	−	0.326395i	$-0.105834\pi$
$864$	−3.46410	+	2.00000i	−0.117851	+	0.0680414i
$865$	12.9904	−	7.50000i	0.441686	−	0.255008i
$866$		−	12.3923i		−	0.421108i
$867$	−16.6340	−	28.8109i	−0.564919	−	0.978469i
$868$	−1.90192	+	3.29423i	−0.0645555	+	0.111813i
$869$	16.0981	+	9.29423i	0.546090	+	0.315285i
$870$	25.8564			0.876614
$871$		0			0
$872$	−15.4641			−0.523681
$873$	58.4711	+	33.7583i	1.97895	+	1.14255i
$874$	8.19615	−	14.1962i	0.277239	−	0.480192i
$875$	1.50000	+	2.59808i	0.0507093	+	0.0878310i
$876$		−	15.4641i		−	0.522484i
$877$	−17.7846	+	10.2679i	−0.600544	+	0.346724i	−0.769255	−	0.638941i	$-0.779373\pi$
$877$	−17.7846	+	10.2679i	−0.600544	+	0.346724i	0.168712	+	0.985665i	$0.446039\pi$
$878$	−29.9545	+	17.2942i	−1.01091	+	0.583652i
$879$		−	2.19615i		−	0.0740744i
$880$	1.50000	+	2.59808i	0.0505650	+	0.0875811i
$881$	4.16025	−	7.20577i	0.140163	−	0.242769i	−0.787395	−	0.616449i	$-0.788571\pi$
$881$	4.16025	−	7.20577i	0.140163	−	0.242769i	0.927558	+	0.373680i	$0.121904\pi$
$882$	7.73205	+	4.46410i	0.260352	+	0.150314i
$883$	−26.5885			−0.894773			−0.447386	−	0.894341i	$-0.647645\pi$
$883$	−26.5885			−0.894773			−0.447386	+	0.894341i	$0.647645\pi$
$884$		0			0
$885$	28.3923			0.954397
$886$	1.39230	+	0.803848i	0.0467754	+	0.0270058i
$887$	−26.3827	+	45.6962i	−0.885844	+	1.53433i	−0.0411005	+	0.999155i	$0.513086\pi$
$887$	−26.3827	+	45.6962i	−0.885844	+	1.53433i	−0.844743	+	0.535172i	$0.820247\pi$
$888$	15.2942	+	26.4904i	0.513241	+	0.888959i
$889$			63.5885i			2.13269i
$890$	−14.8923	+	8.59808i	−0.499191	+	0.288208i
$891$	6.40192	−	3.69615i	0.214473	−	0.123826i
$892$			0.464102i			0.0155393i
$893$	9.69615	+	16.7942i	0.324469	+	0.561997i
$894$	−8.19615	+	14.1962i	−0.274120	+	0.474790i
$895$	−2.19615	−	1.26795i	−0.0734093	−	0.0423829i
$896$	3.00000			0.100223
$897$		0			0
$898$	15.5885			0.520194
$899$	10.3923	+	6.00000i	0.346603	+	0.200111i
$900$	−2.23205	+	3.86603i	−0.0744017	+	0.128868i
$901$	−7.09808	−	12.2942i	−0.236471	−	0.409580i
$902$		−	31.1769i		−	1.03808i
$903$	−14.1962	+	8.19615i	−0.472418	+	0.272751i
$904$	6.00000	−	3.46410i	0.199557	−	0.115214i
$905$			16.5885i			0.551419i
$906$	8.66025	+	15.0000i	0.287718	+	0.498342i
$907$	13.2942	−	23.0263i	0.441428	−	0.764575i	−0.556368	−	0.830936i	$-0.687806\pi$
$907$	13.2942	−	23.0263i	0.441428	−	0.764575i	0.997796	+	0.0663609i	$0.0211389\pi$
$908$	−3.80385	−	2.19615i	−0.126235	−	0.0728819i
$909$	32.4449			1.07613
$910$		0			0
$911$	−14.5359			−0.481596			−0.240798	−	0.970575i	$-0.577409\pi$
$911$	−14.5359			−0.481596			−0.240798	+	0.970575i	$0.577409\pi$
$912$	15.2942	+	8.83013i	0.506443	+	0.292395i
$913$	−3.29423	+	5.70577i	−0.109023	+	0.188833i
$914$	−17.8301	−	30.8827i	−0.589768	−	1.02151i
$915$		−	11.4641i		−	0.378992i
$916$	4.09808	−	2.36603i	0.135404	−	0.0781757i
$917$	−47.0885	+	27.1865i	−1.55500	+	0.897778i
$918$			8.78461i			0.289935i
$919$	5.39230	+	9.33975i	0.177876	+	0.308090i	0.941153	−	0.337982i	$-0.109744\pi$
$919$	5.39230	+	9.33975i	0.177876	+	0.308090i	−0.763277	+	0.646071i	$0.776411\pi$
$920$	1.26795	−	2.19615i	0.0418030	−	0.0724050i
$921$	−48.5885	−	28.0526i	−1.60104	−	0.924363i
$922$	−0.588457			−0.0193798
$923$		0			0
$924$	24.5885			0.808901
$925$	9.69615	+	5.59808i	0.318808	+	0.184064i
$926$	−0.464102	+	0.803848i	−0.0152513	+	0.0264161i
$927$	−2.66987	−	4.62436i	−0.0876901	−	0.151884i
$928$		−	9.46410i		−	0.310674i
$929$	−38.7846	+	22.3923i	−1.27248	+	0.734668i	−0.975454	−	0.220201i	$-0.929329\pi$
$929$	−38.7846	+	22.3923i	−1.27248	+	0.734668i	−0.297027	+	0.954869i	$0.595995\pi$
$930$	−3.00000	+	1.73205i	−0.0983739	+	0.0567962i
$931$		−	12.9282i		−	0.423705i
$932$	0.633975	+	1.09808i	0.0207665	+	0.0359687i
$933$	20.6603	−	35.7846i	0.676386	−	1.17154i
$934$	8.78461	+	5.07180i	0.287441	+	0.165954i
$935$	6.58846			0.215466
$936$		0			0
$937$	−30.3923			−0.992873			−0.496437	−	0.868073i	$-0.665359\pi$
$937$	−30.3923			−0.992873			−0.496437	+	0.868073i	$0.665359\pi$
$938$		0			0
$939$	7.66025	−	13.2679i	0.249983	−	0.432983i
$940$	1.50000	+	2.59808i	0.0489246	+	0.0847399i
$941$			44.7846i			1.45994i	0.683481	+	0.729968i	$0.260465\pi$
$941$			44.7846i			1.45994i	−0.683481	+	0.729968i	$0.739535\pi$
$942$	30.7583	−	17.7583i	1.00216	−	0.578598i
$943$	−22.8231	+	13.1769i	−0.743222	+	0.429099i
$944$		−	10.3923i		−	0.338241i
$945$	6.00000	+	10.3923i	0.195180	+	0.338062i
$946$	−3.00000	+	5.19615i	−0.0975384	+	0.168941i
$947$	−49.6865	−	28.6865i	−1.61460	−	0.932187i	−0.988286	−	0.152612i	$-0.951231\pi$
$947$	−49.6865	−	28.6865i	−1.61460	−	0.932187i	−0.626309	−	0.779575i	$-0.715435\pi$
$948$	16.9282			0.549802
$949$		0			0
$950$	6.46410			0.209723
$951$	−30.2942	−	17.4904i	−0.982358	−	0.567164i
$952$	3.29423	−	5.70577i	0.106767	−	0.184925i
$953$	−12.2942	−	21.2942i	−0.398249	−	0.689788i	0.595261	−	0.803533i	$-0.297049\pi$
$953$	−12.2942	−	21.2942i	−0.398249	−	0.689788i	−0.993510	+	0.113745i	$0.963715\pi$
$954$		−	28.8564i		−	0.934261i
$955$	16.6865	−	9.63397i	0.539964	−	0.311748i
$956$	7.09808	−	4.09808i	0.229568	−	0.132541i
$957$		−	77.5692i		−	2.50746i
$958$	−5.49038	−	9.50962i	−0.177386	−	0.307242i
$959$	−12.2942	+	21.2942i	−0.397001	+	0.687627i
$960$	2.36603	+	1.36603i	0.0763631	+	0.0440883i
$961$	29.3923			0.948139
$962$		0			0
$963$	1.51666			0.0488737
$964$	7.50000	+	4.33013i	0.241559	+	0.139464i
$965$	2.19615	−	3.80385i	0.0706966	−	0.122450i
$966$	−10.3923	−	18.0000i	−0.334367	−	0.579141i
$967$			38.5692i			1.24030i	0.784482	+	0.620151i	$0.212929\pi$
$967$			38.5692i			1.24030i	−0.784482	+	0.620151i	$0.787071\pi$
$968$	−1.73205	+	1.00000i	−0.0556702	+	0.0321412i
$969$	33.5885	−	19.3923i	1.07902	−	0.622971i
$970$		−	15.1244i		−	0.485614i
$971$	23.3827	+	40.5000i	0.750386	+	1.29971i	0.947636	+	0.319354i	$0.103466\pi$
$971$	23.3827	+	40.5000i	0.750386	+	1.29971i	−0.197250	+	0.980353i	$0.563201\pi$
$972$	9.36603	−	16.2224i	0.300415	−	0.520335i
$973$	23.8923	+	13.7942i	0.765952	+	0.442223i
$974$	−33.2487			−1.06536
$975$		0			0
$976$	−4.19615			−0.134316
$977$	−3.80385	−	2.19615i	−0.121696	−	0.0702611i	0.437916	−	0.899016i	$-0.355717\pi$
$977$	−3.80385	−	2.19615i	−0.121696	−	0.0702611i	−0.559612	+	0.828755i	$0.689050\pi$
$978$	9.92820	−	17.1962i	0.317469	−	0.549872i
$979$	25.7942	+	44.6769i	0.824387	+	1.42788i
$980$		−	2.00000i		−	0.0638877i
$981$	−59.7846	+	34.5167i	−1.90878	+	1.10203i
$982$	2.89230	−	1.66987i	0.0922972	−	0.0532878i
$983$		−	38.5692i		−	1.23017i	−0.788462	−	0.615084i	$-0.789122\pi$
$983$		−	38.5692i		−	1.23017i	0.788462	−	0.615084i	$-0.210878\pi$
$984$	−14.1962	−	24.5885i	−0.452557	−	0.783851i
$985$	−4.79423	+	8.30385i	−0.152757	+	0.264583i
$986$	−18.0000	−	10.3923i	−0.573237	−	0.330958i
$987$	24.5885			0.782659
$988$		0			0
$989$	5.07180			0.161274
$990$	11.5981	+	6.69615i	0.368611	+	0.212818i
$991$	−25.5885	+	44.3205i	−0.812844	+	1.40789i	0.0980215	+	0.995184i	$0.468749\pi$
$991$	−25.5885	+	44.3205i	−0.812844	+	1.40789i	−0.910866	+	0.412703i	$0.864585\pi$
$992$	0.633975	+	1.09808i	0.0201287	+	0.0348640i
$993$			2.53590i			0.0804743i
$994$	15.5885	−	9.00000i	0.494436	−	0.285463i
$995$	−12.4641	+	7.19615i	−0.395139	+	0.228133i
$996$			6.00000i			0.190117i
$997$	21.2846	+	36.8660i	0.674090	+	1.16756i	0.976734	+	0.214455i	$0.0687975\pi$
$997$	21.2846	+	36.8660i	0.674090	+	1.16756i	−0.302644	+	0.953104i	$0.597869\pi$
$998$	−0.928203	+	1.60770i	−0.0293818	+	0.0508907i
$999$	38.7846	+	22.3923i	1.22709	+	0.708461i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.l.g.1161.1		4
13.2	odd	12		1690.2.e.l.991.2		4
13.3	even	3		130.2.l.a.101.2	✓	4
13.4	even	6		1690.2.d.f.1351.1		4
13.5	odd	4		1690.2.e.l.191.2		4
13.6	odd	12		1690.2.a.m.1.1		2
13.7	odd	12		1690.2.a.j.1.1		2
13.8	odd	4		1690.2.e.n.191.2		4
13.9	even	3		1690.2.d.f.1351.3		4
13.10	even	6	inner	1690.2.l.g.361.1		4
13.11	odd	12		1690.2.e.n.991.2		4
13.12	even	2		130.2.l.a.121.2	yes	4
39.29	odd	6		1170.2.bs.c.361.1		4
39.38	odd	2		1170.2.bs.c.901.1		4
52.3	odd	6		1040.2.da.a.881.1		4
52.51	odd	2		1040.2.da.a.641.1		4
65.3	odd	12		650.2.n.a.49.1		4
65.12	odd	4		650.2.n.a.199.1		4
65.19	odd	12		8450.2.a.bf.1.2		2
65.29	even	6		650.2.m.a.101.1		4
65.38	odd	4		650.2.n.b.199.2		4
65.42	odd	12		650.2.n.b.49.2		4
65.59	odd	12		8450.2.a.bm.1.2		2
65.64	even	2		650.2.m.a.251.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.a.101.2	✓	4	13.3	even	3
130.2.l.a.121.2	yes	4	13.12	even	2
650.2.m.a.101.1		4	65.29	even	6
650.2.m.a.251.1		4	65.64	even	2
650.2.n.a.49.1		4	65.3	odd	12
650.2.n.a.199.1		4	65.12	odd	4
650.2.n.b.49.2		4	65.42	odd	12
650.2.n.b.199.2		4	65.38	odd	4
1040.2.da.a.641.1		4	52.51	odd	2
1040.2.da.a.881.1		4	52.3	odd	6
1170.2.bs.c.361.1		4	39.29	odd	6
1170.2.bs.c.901.1		4	39.38	odd	2
1690.2.a.j.1.1		2	13.7	odd	12
1690.2.a.m.1.1		2	13.6	odd	12
1690.2.d.f.1351.1		4	13.4	even	6
1690.2.d.f.1351.3		4	13.9	even	3
1690.2.e.l.191.2		4	13.5	odd	4
1690.2.e.l.991.2		4	13.2	odd	12
1690.2.e.n.191.2		4	13.8	odd	4
1690.2.e.n.991.2		4	13.11	odd	12
1690.2.l.g.361.1		4	13.10	even	6	inner
1690.2.l.g.1161.1		4	1.1	even	1	trivial
8450.2.a.bf.1.2		2	65.19	odd	12
8450.2.a.bm.1.2		2	65.59	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.36603 - 2.36603i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-2.36603 + 1.36603i) q^{6} +(2.59808 - 1.50000i) q^{7} -1.00000i q^{8} +(-2.23205 - 3.86603i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.36603 - 2.36603i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-2.36603 + 1.36603i) q^{6} +(2.59808 - 1.50000i) q^{7} -1.00000i q^{8} +(-2.23205 - 3.86603i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(2.59808 + 1.50000i) q^{11} +2.73205 q^{12} -3.00000 q^{14} +(-2.36603 - 1.36603i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.09808 + 1.90192i) q^{17} +4.46410i q^{18} +(5.59808 - 3.23205i) q^{19} +(0.866025 - 0.500000i) q^{20} -8.19615i q^{21} +(-1.50000 - 2.59808i) q^{22} +(-1.26795 + 2.19615i) q^{23} +(-2.36603 - 1.36603i) q^{24} -1.00000 q^{25} -4.00000 q^{27} +(2.59808 + 1.50000i) q^{28} +(4.73205 - 8.19615i) q^{29} +(1.36603 + 2.36603i) q^{30} +1.26795i q^{31} +(0.866025 - 0.500000i) q^{32} +(7.09808 - 4.09808i) q^{33} -2.19615i q^{34} +(-1.50000 - 2.59808i) q^{35} +(2.23205 - 3.86603i) q^{36} +(-9.69615 - 5.59808i) q^{37} -6.46410 q^{38} -1.00000 q^{40} +(9.00000 + 5.19615i) q^{41} +(-4.09808 + 7.09808i) q^{42} +(-1.00000 - 1.73205i) q^{43} +3.00000i q^{44} +(-3.86603 + 2.23205i) q^{45} +(2.19615 - 1.26795i) q^{46} +3.00000i q^{47} +(1.36603 + 2.36603i) q^{48} +(1.00000 - 1.73205i) q^{49} +(0.866025 + 0.500000i) q^{50} +6.00000 q^{51} -6.46410 q^{53} +(3.46410 + 2.00000i) q^{54} +(1.50000 - 2.59808i) q^{55} +(-1.50000 - 2.59808i) q^{56} -17.6603i q^{57} +(-8.19615 + 4.73205i) q^{58} +(-9.00000 + 5.19615i) q^{59} -2.73205i q^{60} +(2.09808 + 3.63397i) q^{61} +(0.633975 - 1.09808i) q^{62} +(-11.5981 - 6.69615i) q^{63} -1.00000 q^{64} -8.19615 q^{66} +(-1.09808 + 1.90192i) q^{68} +(3.46410 + 6.00000i) q^{69} +3.00000i q^{70} +(-5.19615 + 3.00000i) q^{71} +(-3.86603 + 2.23205i) q^{72} -5.66025i q^{73} +(5.59808 + 9.69615i) q^{74} +(-1.36603 + 2.36603i) q^{75} +(5.59808 + 3.23205i) q^{76} +9.00000 q^{77} +6.19615 q^{79} +(0.866025 + 0.500000i) q^{80} +(1.23205 - 2.13397i) q^{81} +(-5.19615 - 9.00000i) q^{82} +2.19615i q^{83} +(7.09808 - 4.09808i) q^{84} +(1.90192 - 1.09808i) q^{85} +2.00000i q^{86} +(-12.9282 - 22.3923i) q^{87} +(1.50000 - 2.59808i) q^{88} +(14.8923 + 8.59808i) q^{89} +4.46410 q^{90} -2.53590 q^{92} +(3.00000 + 1.73205i) q^{93} +(1.50000 - 2.59808i) q^{94} +(-3.23205 - 5.59808i) q^{95} -2.73205i q^{96} +(-13.0981 + 7.56218i) q^{97} +(-1.73205 + 1.00000i) q^{98} -13.3923i 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

Varieties

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Database

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