LMFDB - Embedded newform 1690.2.e.l.191.2

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			191.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1690.191
Dual form			1690.2.e.l.991.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.36603 - 2.36603i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(1.36603 + 2.36603i) q^{6} +(1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(-2.23205 - 3.86603i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.36603 - 2.36603i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(1.36603 + 2.36603i) q^{6} +(1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(-2.23205 - 3.86603i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-1.50000 + 2.59808i) q^{11} -2.73205 q^{12} -3.00000 q^{14} +(-1.36603 + 2.36603i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.09808 - 1.90192i) q^{17} +4.46410 q^{18} +(-3.23205 - 5.59808i) q^{19} +(0.500000 + 0.866025i) q^{20} +8.19615 q^{21} +(-1.50000 - 2.59808i) q^{22} +(1.26795 - 2.19615i) q^{23} +(1.36603 - 2.36603i) q^{24} +1.00000 q^{25} -4.00000 q^{27} +(1.50000 - 2.59808i) q^{28} +(4.73205 - 8.19615i) q^{29} +(-1.36603 - 2.36603i) q^{30} +1.26795 q^{31} +(-0.500000 - 0.866025i) q^{32} +(4.09808 + 7.09808i) q^{33} +2.19615 q^{34} +(-1.50000 - 2.59808i) q^{35} +(-2.23205 + 3.86603i) q^{36} +(5.59808 - 9.69615i) q^{37} +6.46410 q^{38} -1.00000 q^{40} +(5.19615 - 9.00000i) q^{41} +(-4.09808 + 7.09808i) q^{42} +(1.00000 + 1.73205i) q^{43} +3.00000 q^{44} +(2.23205 + 3.86603i) q^{45} +(1.26795 + 2.19615i) q^{46} -3.00000 q^{47} +(1.36603 + 2.36603i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(-0.500000 + 0.866025i) q^{50} -6.00000 q^{51} -6.46410 q^{53} +(2.00000 - 3.46410i) q^{54} +(1.50000 - 2.59808i) q^{55} +(1.50000 + 2.59808i) q^{56} -17.6603 q^{57} +(4.73205 + 8.19615i) q^{58} +(-5.19615 - 9.00000i) q^{59} +2.73205 q^{60} +(2.09808 + 3.63397i) q^{61} +(-0.633975 + 1.09808i) q^{62} +(6.69615 - 11.5981i) q^{63} +1.00000 q^{64} -8.19615 q^{66} +(-1.09808 + 1.90192i) q^{68} +(-3.46410 - 6.00000i) q^{69} +3.00000 q^{70} +(3.00000 + 5.19615i) q^{71} +(-2.23205 - 3.86603i) q^{72} +5.66025 q^{73} +(5.59808 + 9.69615i) q^{74} +(1.36603 - 2.36603i) q^{75} +(-3.23205 + 5.59808i) q^{76} -9.00000 q^{77} +6.19615 q^{79} +(0.500000 - 0.866025i) q^{80} +(1.23205 - 2.13397i) q^{81} +(5.19615 + 9.00000i) q^{82} +2.19615 q^{83} +(-4.09808 - 7.09808i) q^{84} +(1.09808 + 1.90192i) q^{85} -2.00000 q^{86} +(-12.9282 - 22.3923i) q^{87} +(-1.50000 + 2.59808i) q^{88} +(-8.59808 + 14.8923i) q^{89} -4.46410 q^{90} -2.53590 q^{92} +(1.73205 - 3.00000i) q^{93} +(1.50000 - 2.59808i) q^{94} +(3.23205 + 5.59808i) q^{95} -2.73205 q^{96} +(7.56218 + 13.0981i) q^{97} +(-1.00000 - 1.73205i) q^{98} +13.3923 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
$3$	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
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.36603	+	2.36603i	0.557678	+	0.965926i
$7$	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
$9$	−2.23205	−	3.86603i	−0.744017	−	1.28868i
$10$	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	$0.316051\pi$
$12$	−2.73205			−0.788675
$13$		0			0
$13$		0			0
$14$	−3.00000			−0.801784
$15$	−1.36603	+	2.36603i	−0.352706	+	0.610905i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.09808	−	1.90192i	−0.266323	−	0.461284i	0.701587	−	0.712584i	$-0.252475\pi$
$17$	−1.09808	−	1.90192i	−0.266323	−	0.461284i	−0.967909	+	0.251300i	$0.919142\pi$
$18$	4.46410			1.05220
$19$	−3.23205	−	5.59808i	−0.741483	−	1.28429i	−0.951820	−	0.306658i	$-0.900789\pi$
$19$	−3.23205	−	5.59808i	−0.741483	−	1.28429i	0.210337	−	0.977629i	$-0.432544\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	8.19615			1.78855
$22$	−1.50000	−	2.59808i	−0.319801	−	0.553912i
$23$	1.26795	−	2.19615i	0.264386	−	0.457929i	−0.703017	−	0.711173i	$-0.748164\pi$
$23$	1.26795	−	2.19615i	0.264386	−	0.457929i	0.967402	+	0.253244i	$0.0814975\pi$
$24$	1.36603	−	2.36603i	0.278839	−	0.482963i
$25$	1.00000			0.200000
$26$		0			0
$27$	−4.00000			−0.769800
$28$	1.50000	−	2.59808i	0.283473	−	0.490990i
$29$	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
$31$	1.26795			0.227730			0.113865	−	0.993496i	$-0.463677\pi$
$31$	1.26795			0.227730			0.113865	+	0.993496i	$0.463677\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	4.09808	+	7.09808i	0.713384	+	1.23562i
$34$	2.19615			0.376637
$35$	−1.50000	−	2.59808i	−0.253546	−	0.439155i
$36$	−2.23205	+	3.86603i	−0.372008	+	0.644338i
$37$	5.59808	−	9.69615i	0.920318	−	1.59404i	0.121395	−	0.992604i	$-0.461263\pi$
$37$	5.59808	−	9.69615i	0.920318	−	1.59404i	0.798923	−	0.601433i	$-0.205403\pi$
$38$	6.46410			1.04862
$39$		0			0
$40$	−1.00000			−0.158114
$41$	5.19615	−	9.00000i	0.811503	−	1.40556i	−0.100309	−	0.994956i	$-0.531983\pi$
$41$	5.19615	−	9.00000i	0.811503	−	1.40556i	0.911812	−	0.410608i	$-0.134683\pi$
$42$	−4.09808	+	7.09808i	−0.632347	+	1.09526i
$43$	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
$45$	2.23205	+	3.86603i	0.332734	+	0.576313i
$46$	1.26795	+	2.19615i	0.186949	+	0.323805i
$47$	−3.00000			−0.437595			−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000			−0.437595			−0.218797	+	0.975770i	$0.570213\pi$
$48$	1.36603	+	2.36603i	0.197169	+	0.341506i
$49$	−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
$53$	−6.46410			−0.887913			−0.443956	−	0.896048i	$-0.646425\pi$
$53$	−6.46410			−0.887913			−0.443956	+	0.896048i	$0.646425\pi$
$54$	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
$57$	−17.6603			−2.33916
$58$	4.73205	+	8.19615i	0.621349	+	1.07621i
$59$	−5.19615	−	9.00000i	−0.676481	−	1.17170i	−0.976034	−	0.217620i	$-0.930171\pi$
$59$	−5.19615	−	9.00000i	−0.676481	−	1.17170i	0.299552	−	0.954080i	$-0.403163\pi$
$60$	2.73205			0.352706
$61$	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
$63$	6.69615	−	11.5981i	0.843636	−	1.46122i
$64$	1.00000			0.125000
$65$		0			0
$66$	−8.19615			−1.00888
$67$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$67$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$68$	−1.09808	+	1.90192i	−0.133161	+	0.230642i
$69$	−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	$0.717462\pi$
$72$	−2.23205	−	3.86603i	−0.263050	−	0.455615i
$73$	5.66025			0.662483			0.331241	−	0.943546i	$-0.392533\pi$
$73$	5.66025			0.662483			0.331241	+	0.943546i	$0.392533\pi$
$74$	5.59808	+	9.69615i	0.650763	+	1.12715i
$75$	1.36603	−	2.36603i	0.157735	−	0.273205i
$76$	−3.23205	+	5.59808i	−0.370742	+	0.642143i
$77$	−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	$0.386670\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	1.23205	−	2.13397i	0.136895	−	0.237108i
$82$	5.19615	+	9.00000i	0.573819	+	0.993884i
$83$	2.19615			0.241059			0.120530	−	0.992710i	$-0.461541\pi$
$83$	2.19615			0.241059			0.120530	+	0.992710i	$0.461541\pi$
$84$	−4.09808	−	7.09808i	−0.447137	−	0.774464i
$85$	1.09808	+	1.90192i	0.119103	+	0.206293i
$86$	−2.00000			−0.215666
$87$	−12.9282	−	22.3923i	−1.38605	−	2.40071i
$88$	−1.50000	+	2.59808i	−0.159901	+	0.276956i
$89$	−8.59808	+	14.8923i	−0.911394	+	1.57858i	−0.0992979	+	0.995058i	$0.531660\pi$
$89$	−8.59808	+	14.8923i	−0.911394	+	1.57858i	−0.812096	+	0.583523i	$0.801674\pi$
$90$	−4.46410			−0.470558
$91$		0			0
$92$	−2.53590			−0.264386
$93$	1.73205	−	3.00000i	0.179605	−	0.311086i
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$	3.23205	+	5.59808i	0.331601	+	0.574351i
$96$	−2.73205			−0.278839
$97$	7.56218	+	13.0981i	0.767823	+	1.32991i	0.938741	+	0.344623i	$0.111993\pi$
$97$	7.56218	+	13.0981i	0.767823	+	1.32991i	−0.170918	+	0.985285i	$0.554673\pi$
$98$	−1.00000	−	1.73205i	−0.101015	−	0.174964i
$99$	13.3923			1.34598
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	3.63397	−	6.29423i	0.361594	−	0.626299i	−0.626629	−	0.779317i	$-0.715566\pi$
$101$	3.63397	−	6.29423i	0.361594	−	0.626299i	0.988223	+	0.153018i	$0.0488993\pi$
$102$	3.00000	−	5.19615i	0.297044	−	0.514496i
$103$	−1.19615			−0.117860			−0.0589302	−	0.998262i	$-0.518769\pi$
$103$	−1.19615			−0.117860			−0.0589302	+	0.998262i	$0.518769\pi$
$104$		0			0
$105$	−8.19615			−0.799863
$106$	3.23205	−	5.59808i	0.313925	−	0.543733i
$107$	−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
$109$	−15.4641			−1.48119			−0.740596	−	0.671950i	$-0.765457\pi$
$109$	−15.4641			−1.48119			−0.740596	+	0.671950i	$0.765457\pi$
$110$	1.50000	+	2.59808i	0.143019	+	0.247717i
$111$	−15.2942	−	26.4904i	−1.45166	−	2.51436i
$112$	−3.00000			−0.283473
$113$	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
$115$	−1.26795	+	2.19615i	−0.118237	+	0.204792i
$116$	−9.46410			−0.878720
$117$		0			0
$118$	10.3923			0.956689
$119$	3.29423	−	5.70577i	0.301981	−	0.523047i
$120$	−1.36603	+	2.36603i	−0.124700	+	0.215988i
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−4.19615			−0.379902
$123$	−14.1962	−	24.5885i	−1.28002	−	2.21707i
$124$	−0.633975	−	1.09808i	−0.0569326	−	0.0986102i
$125$	−1.00000			−0.0894427
$126$	6.69615	+	11.5981i	0.596541	+	1.03324i
$127$	10.5981	−	18.3564i	0.940427	−	1.62887i	0.175769	−	0.984431i	$-0.443759\pi$
$127$	10.5981	−	18.3564i	0.940427	−	1.62887i	0.764658	−	0.644436i	$-0.222908\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	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	$0.790838\pi$
$132$	4.09808	−	7.09808i	0.356692	−	0.617808i
$133$	9.69615	−	16.7942i	0.840763	−	1.45624i
$134$		0			0
$135$	4.00000			0.344265
$136$	−1.09808	−	1.90192i	−0.0941593	−	0.163089i
$137$	−4.09808	−	7.09808i	−0.350122	−	0.606430i	0.636148	−	0.771567i	$-0.280527\pi$
$137$	−4.09808	−	7.09808i	−0.350122	−	0.606430i	−0.986271	+	0.165137i	$0.947193\pi$
$138$	6.92820			0.589768
$139$	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
$141$	−4.09808	+	7.09808i	−0.345120	+	0.597766i
$142$	−6.00000			−0.503509
$143$		0			0
$144$	4.46410			0.372008
$145$	−4.73205	+	8.19615i	−0.392975	+	0.680653i
$146$	−2.83013	+	4.90192i	−0.234223	+	0.405686i
$147$	2.73205	+	4.73205i	0.225336	+	0.390293i
$148$	−11.1962			−0.920318
$149$	−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	$0.912374\pi$
$150$	1.36603	+	2.36603i	0.111536	+	0.193185i
$151$	6.33975			0.515921			0.257961	−	0.966155i	$-0.416950\pi$
$151$	6.33975			0.515921			0.257961	+	0.966155i	$0.416950\pi$
$152$	−3.23205	−	5.59808i	−0.262154	−	0.454064i
$153$	−4.90192	+	8.49038i	−0.396297	+	0.686407i
$154$	4.50000	−	7.79423i	0.362620	−	0.628077i
$155$	−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	$0.673605\pi$
$158$	−3.09808	+	5.36603i	−0.246470	+	0.426898i
$159$	−8.83013	+	15.2942i	−0.700275	+	1.21291i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	7.60770			0.599570
$162$	1.23205	+	2.13397i	0.0967991	+	0.167661i
$163$	−3.63397	−	6.29423i	−0.284635	−	0.493002i	0.687886	−	0.725819i	$-0.258539\pi$
$163$	−3.63397	−	6.29423i	−0.284635	−	0.493002i	−0.972521	+	0.232817i	$0.925206\pi$
$164$	−10.3923			−0.811503
$165$	−4.09808	−	7.09808i	−0.319035	−	0.552584i
$166$	−1.09808	+	1.90192i	−0.0852272	+	0.147618i
$167$	−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	$0.203697\pi$
$168$	8.19615			0.632347
$169$		0			0
$170$	−2.19615			−0.168437
$171$	−14.4282	+	24.9904i	−1.10335	+	1.91106i
$172$	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	$-0.359807\pi$
$174$	25.8564			1.96017
$175$	1.50000	+	2.59808i	0.113389	+	0.196396i
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$	−28.3923			−2.13410
$178$	−8.59808	−	14.8923i	−0.644453	−	1.11623i
$179$	−1.26795	+	2.19615i	−0.0947710	+	0.164148i	−0.909513	−	0.415675i	$-0.863545\pi$
$179$	−1.26795	+	2.19615i	−0.0947710	+	0.164148i	0.814742	+	0.579824i	$0.196879\pi$
$180$	2.23205	−	3.86603i	0.166367	−	0.288157i
$181$	16.5885			1.23301			0.616505	−	0.787351i	$-0.288548\pi$
$181$	16.5885			1.23301			0.616505	+	0.787351i	$0.288548\pi$
$182$		0			0
$183$	11.4641			0.847451
$184$	1.26795	−	2.19615i	0.0934745	−	0.161903i
$185$	−5.59808	+	9.69615i	−0.411579	+	0.712875i
$186$	1.73205	+	3.00000i	0.127000	+	0.219971i
$187$	6.58846			0.481796
$188$	1.50000	+	2.59808i	0.109399	+	0.189484i
$189$	−6.00000	−	10.3923i	−0.436436	−	0.755929i
$190$	−6.46410			−0.468955
$191$	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
$193$	−2.19615	+	3.80385i	−0.158083	+	0.273807i	−0.934177	−	0.356809i	$-0.883865\pi$
$193$	−2.19615	+	3.80385i	−0.158083	+	0.273807i	0.776095	+	0.630616i	$0.217198\pi$
$194$	−15.1244			−1.08587
$195$		0			0
$196$	2.00000			0.142857
$197$	−4.79423	+	8.30385i	−0.341575	+	0.591625i	−0.984725	−	0.174115i	$-0.944294\pi$
$197$	−4.79423	+	8.30385i	−0.341575	+	0.591625i	0.643151	+	0.765740i	$0.277627\pi$
$198$	−6.69615	+	11.5981i	−0.475875	+	0.824239i
$199$	7.19615	+	12.4641i	0.510122	+	0.883557i	0.999931	+	0.0117273i	$0.00373299\pi$
$199$	7.19615	+	12.4641i	0.510122	+	0.883557i	−0.489810	+	0.871829i	$0.662934\pi$
$200$	1.00000			0.0707107
$201$		0			0
$202$	3.63397	+	6.29423i	0.255686	+	0.442860i
$203$	28.3923			1.99275
$204$	3.00000	+	5.19615i	0.210042	+	0.363803i
$205$	−5.19615	+	9.00000i	−0.362915	+	0.628587i
$206$	0.598076	−	1.03590i	0.0416699	−	0.0721745i
$207$	−11.3205			−0.786830
$208$		0			0
$209$	19.3923			1.34139
$210$	4.09808	−	7.09808i	0.282794	−	0.489814i
$211$	−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
$213$	16.3923			1.12318
$214$	−0.169873	−	0.294229i	−0.0116123	−	0.0201131i
$215$	−1.00000	−	1.73205i	−0.0681994	−	0.118125i
$216$	−4.00000			−0.272166
$217$	1.90192	+	3.29423i	0.129111	+	0.223627i
$218$	7.73205	−	13.3923i	0.523681	−	0.907041i
$219$	7.73205	−	13.3923i	0.522484	−	0.904968i
$220$	−3.00000			−0.202260
$221$		0			0
$222$	30.5885			2.05296
$223$	0.232051	−	0.401924i	0.0155393	−	0.0269148i	−0.858151	−	0.513397i	$-0.828387\pi$
$223$	0.232051	−	0.401924i	0.0155393	−	0.0269148i	0.873690	+	0.486482i	$0.161720\pi$
$224$	1.50000	−	2.59808i	0.100223	−	0.173591i
$225$	−2.23205	−	3.86603i	−0.148803	−	0.257735i
$226$	−6.92820			−0.460857
$227$	2.19615	+	3.80385i	0.145764	+	0.252470i	0.929658	−	0.368425i	$-0.120103\pi$
$227$	2.19615	+	3.80385i	0.145764	+	0.252470i	−0.783894	+	0.620895i	$0.786769\pi$
$228$	8.83013	+	15.2942i	0.584789	+	1.01289i
$229$	4.73205			0.312703			0.156351	−	0.987701i	$-0.450027\pi$
$229$	4.73205			0.312703			0.156351	+	0.987701i	$0.450027\pi$
$230$	−1.26795	−	2.19615i	−0.0836061	−	0.144810i
$231$	−12.2942	+	21.2942i	−0.808901	+	1.40106i
$232$	4.73205	−	8.19615i	0.310674	−	0.538104i
$233$	−1.26795			−0.0830661			−0.0415331	−	0.999137i	$-0.513224\pi$
$233$	−1.26795			−0.0830661			−0.0415331	+	0.999137i	$0.513224\pi$
$234$		0			0
$235$	3.00000			0.195698
$236$	−5.19615	+	9.00000i	−0.338241	+	0.585850i
$237$	8.46410	−	14.6603i	0.549802	−	0.952286i
$238$	3.29423	+	5.70577i	0.213533	+	0.369850i
$239$	−8.19615			−0.530165			−0.265083	−	0.964226i	$-0.585399\pi$
$239$	−8.19615			−0.530165			−0.265083	+	0.964226i	$0.585399\pi$
$240$	−1.36603	−	2.36603i	−0.0881766	−	0.152726i
$241$	4.33013	+	7.50000i	0.278928	+	0.483117i	0.971119	−	0.238597i	$-0.0766876\pi$
$241$	4.33013	+	7.50000i	0.278928	+	0.483117i	−0.692191	+	0.721715i	$0.743354\pi$
$242$	−2.00000			−0.128565
$243$	−9.36603	−	16.2224i	−0.600831	−	1.04067i
$244$	2.09808	−	3.63397i	0.134316	−	0.232641i
$245$	1.00000	−	1.73205i	0.0638877	−	0.110657i
$246$	28.3923			1.81023
$247$		0			0
$248$	1.26795			0.0805149
$249$	3.00000	−	5.19615i	0.190117	−	0.329293i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	3.40192	+	5.89230i	0.214728	+	0.371919i	0.953188	−	0.302378i	$-0.0977803\pi$
$251$	3.40192	+	5.89230i	0.214728	+	0.371919i	−0.738461	+	0.674296i	$0.764447\pi$
$252$	−13.3923			−0.843636
$253$	3.80385	+	6.58846i	0.239146	+	0.414213i
$254$	10.5981	+	18.3564i	0.664982	+	1.15178i
$255$	6.00000			0.375735
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.92820	−	12.0000i	0.432169	−	0.748539i	−0.564890	−	0.825166i	$-0.691082\pi$
$257$	6.92820	−	12.0000i	0.432169	−	0.748539i	0.997060	+	0.0766265i	$0.0244149\pi$
$258$	−2.73205	+	4.73205i	−0.170090	+	0.294605i
$259$	33.5885			2.08709
$260$		0			0
$261$	−42.2487			−2.61513
$262$	9.06218	−	15.6962i	0.559863	−	0.969712i
$263$	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
$265$	6.46410			0.397087
$266$	9.69615	+	16.7942i	0.594509	+	1.02972i
$267$	23.4904	+	40.6865i	1.43759	+	2.48998i
$268$		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
$271$	−1.26795	+	2.19615i	−0.0770224	+	0.133407i	−0.901964	−	0.431811i	$-0.857875\pi$
$271$	−1.26795	+	2.19615i	−0.0770224	+	0.133407i	0.824942	+	0.565218i	$0.191208\pi$
$272$	2.19615			0.133161
$273$		0			0
$274$	8.19615			0.495148
$275$	−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	$0.842897\pi$
$278$	−9.19615			−0.551549
$279$	−2.83013	−	4.90192i	−0.169435	−	0.293471i
$280$	−1.50000	−	2.59808i	−0.0896421	−	0.155265i
$281$	−10.3923			−0.619953			−0.309976	−	0.950744i	$-0.600321\pi$
$281$	−10.3923			−0.619953			−0.309976	+	0.950744i	$0.600321\pi$
$282$	−4.09808	−	7.09808i	−0.244037	−	0.422684i
$283$	−15.1962	+	26.3205i	−0.903317	+	1.56459i	−0.0801576	+	0.996782i	$0.525542\pi$
$283$	−15.1962	+	26.3205i	−0.903317	+	1.56459i	−0.823160	+	0.567810i	$0.807791\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$	17.6603			1.04610
$286$		0			0
$287$	31.1769			1.84032
$288$	−2.23205	+	3.86603i	−0.131525	+	0.227808i
$289$	6.08846	−	10.5455i	0.358145	−	0.620325i
$290$	−4.73205	−	8.19615i	−0.277876	−	0.481295i
$291$	41.3205			2.42225
$292$	−2.83013	−	4.90192i	−0.165621	−	0.286863i
$293$	0.401924	+	0.696152i	0.0234806	+	0.0406697i	0.877527	−	0.479527i	$-0.159192\pi$
$293$	0.401924	+	0.696152i	0.0234806	+	0.0406697i	−0.854046	+	0.520197i	$0.825859\pi$
$294$	−5.46410			−0.318673
$295$	5.19615	+	9.00000i	0.302532	+	0.524000i
$296$	5.59808	−	9.69615i	0.325382	−	0.563577i
$297$	6.00000	−	10.3923i	0.348155	−	0.603023i
$298$	6.00000			0.347571
$299$		0			0
$300$	−2.73205			−0.157735
$301$	−3.00000	+	5.19615i	−0.172917	+	0.299501i
$302$	−3.16987	+	5.49038i	−0.182406	+	0.315936i
$303$	−9.92820	−	17.1962i	−0.570360	−	0.987893i
$304$	6.46410			0.370742
$305$	−2.09808	−	3.63397i	−0.120135	−	0.208081i
$306$	−4.90192	−	8.49038i	−0.280224	−	0.485363i
$307$	20.5359			1.17205			0.586023	−	0.810295i	$-0.300693\pi$
$307$	20.5359			1.17205			0.586023	+	0.810295i	$0.300693\pi$
$308$	4.50000	+	7.79423i	0.256411	+	0.444117i
$309$	−1.63397	+	2.83013i	−0.0929536	+	0.161000i
$310$	0.633975	−	1.09808i	0.0360073	−	0.0623665i
$311$	−15.1244			−0.857624			−0.428812	−	0.903394i	$-0.641068\pi$
$311$	−15.1244			−0.857624			−0.428812	+	0.903394i	$0.641068\pi$
$312$		0			0
$313$	5.60770			0.316966			0.158483	−	0.987362i	$-0.449340\pi$
$313$	5.60770			0.316966			0.158483	+	0.987362i	$0.449340\pi$
$314$	6.50000	−	11.2583i	0.366816	−	0.635344i
$315$	−6.69615	+	11.5981i	−0.377285	+	0.653478i
$316$	−3.09808	−	5.36603i	−0.174280	−	0.301863i
$317$	−12.8038			−0.719136			−0.359568	−	0.933119i	$-0.617076\pi$
$317$	−12.8038			−0.719136			−0.359568	+	0.933119i	$0.617076\pi$
$318$	−8.83013	−	15.2942i	−0.495169	−	0.857658i
$319$	14.1962	+	24.5885i	0.794832	+	1.37669i
$320$	−1.00000			−0.0559017
$321$	0.464102	+	0.803848i	0.0259036	+	0.0448664i
$322$	−3.80385	+	6.58846i	−0.211980	+	0.367160i
$323$	−7.09808	+	12.2942i	−0.394948	+	0.684069i
$324$	−2.46410			−0.136895
$325$		0			0
$326$	7.26795			0.402534
$327$	−21.1244	+	36.5885i	−1.16818	+	2.02335i
$328$	5.19615	−	9.00000i	0.286910	−	0.496942i
$329$	−4.50000	−	7.79423i	−0.248093	−	0.429710i
$330$	8.19615			0.451183
$331$	0.464102	+	0.803848i	0.0255093	+	0.0441835i	0.878498	−	0.477746i	$-0.158546\pi$
$331$	0.464102	+	0.803848i	0.0255093	+	0.0441835i	−0.852989	+	0.521929i	$0.825213\pi$
$332$	−1.09808	−	1.90192i	−0.0602648	−	0.104382i
$333$	−49.9808			−2.73893
$334$	−1.50000	−	2.59808i	−0.0820763	−	0.142160i
$335$		0			0
$336$	−4.09808	+	7.09808i	−0.223568	+	0.387232i
$337$	4.19615			0.228579			0.114289	−	0.993447i	$-0.463541\pi$
$337$	4.19615			0.228579			0.114289	+	0.993447i	$0.463541\pi$
$338$		0			0
$339$	18.9282			1.02804
$340$	1.09808	−	1.90192i	0.0595515	−	0.103146i
$341$	−1.90192	+	3.29423i	−0.102995	+	0.178392i
$342$	−14.4282	−	24.9904i	−0.780188	−	1.35133i
$343$	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
$347$	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
$349$	−17.0263	+	29.4904i	−0.911396	+	1.57858i	−0.0993018	+	0.995057i	$0.531661\pi$
$349$	−17.0263	+	29.4904i	−0.911396	+	1.57858i	−0.812094	+	0.583527i	$0.801672\pi$
$350$	−3.00000			−0.160357
$351$		0			0
$352$	3.00000			0.159901
$353$	10.0981	−	17.4904i	0.537466	−	0.930919i	−0.461573	−	0.887102i	$-0.652715\pi$
$353$	10.0981	−	17.4904i	0.537466	−	0.930919i	0.999040	−	0.0438169i	$-0.0139518\pi$
$354$	14.1962	−	24.5885i	0.754517	−	1.30686i
$355$	−3.00000	−	5.19615i	−0.159223	−	0.275783i
$356$	17.1962			0.911394
$357$	−9.00000	−	15.5885i	−0.476331	−	0.825029i
$358$	−1.26795	−	2.19615i	−0.0670132	−	0.116070i
$359$	−22.3923			−1.18182			−0.590910	−	0.806737i	$-0.701231\pi$
$359$	−22.3923			−1.18182			−0.590910	+	0.806737i	$0.701231\pi$
$360$	2.23205	+	3.86603i	0.117639	+	0.203757i
$361$	−11.3923	+	19.7321i	−0.599595	+	1.03853i
$362$	−8.29423	+	14.3660i	−0.435935	+	0.755062i
$363$	5.46410			0.286791
$364$		0			0
$365$	−5.66025			−0.296271
$366$	−5.73205	+	9.92820i	−0.299619	+	0.518955i
$367$	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
$369$	−46.3923			−2.41509
$370$	−5.59808	−	9.69615i	−0.291030	−	0.504079i
$371$	−9.69615	−	16.7942i	−0.503399	−	0.871913i
$372$	−3.46410			−0.179605
$373$	−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
$375$	−1.36603	+	2.36603i	−0.0705412	+	0.122181i
$376$	−3.00000			−0.154713
$377$		0			0
$378$	12.0000			0.617213
$379$	−5.89230	+	10.2058i	−0.302667	+	0.524235i	−0.976739	−	0.214430i	$-0.931210\pi$
$379$	−5.89230	+	10.2058i	−0.302667	+	0.524235i	0.674072	+	0.738666i	$0.264544\pi$
$380$	3.23205	−	5.59808i	0.165801	−	0.287175i
$381$	−28.9545	−	50.1506i	−1.48338	−	2.56929i
$382$	−19.2679			−0.985834
$383$	−0.803848	−	1.39230i	−0.0410747	−	0.0711435i	0.844757	−	0.535150i	$-0.179745\pi$
$383$	−0.803848	−	1.39230i	−0.0410747	−	0.0711435i	−0.885832	+	0.464006i	$0.846411\pi$
$384$	1.36603	+	2.36603i	0.0697097	+	0.120741i
$385$	9.00000			0.458682
$386$	−2.19615	−	3.80385i	−0.111781	−	0.193611i
$387$	4.46410	−	7.73205i	0.226923	−	0.393042i
$388$	7.56218	−	13.0981i	0.383911	−	0.664954i
$389$	−19.2679			−0.976924			−0.488462	−	0.872585i	$-0.662442\pi$
$389$	−19.2679			−0.976924			−0.488462	+	0.872585i	$0.662442\pi$
$390$		0			0
$391$	−5.56922			−0.281648
$392$	−1.00000	+	1.73205i	−0.0505076	+	0.0874818i
$393$	−24.7583	+	42.8827i	−1.24889	+	2.16315i
$394$	−4.79423	−	8.30385i	−0.241530	−	0.418342i
$395$	−6.19615			−0.311762
$396$	−6.69615	−	11.5981i	−0.336494	−	0.582825i
$397$	−0.401924	−	0.696152i	−0.0201720	−	0.0349389i	0.855763	−	0.517368i	$-0.173088\pi$
$397$	−0.401924	−	0.696152i	−0.0201720	−	0.0349389i	−0.875935	+	0.482429i	$0.839755\pi$
$398$	−14.3923			−0.721421
$399$	−26.4904	−	45.8827i	−1.32618	−	2.29701i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−2.59808	+	4.50000i	−0.129742	+	0.224719i	−0.923576	−	0.383414i	$-0.874748\pi$
$401$	−2.59808	+	4.50000i	−0.129742	+	0.224719i	0.793835	+	0.608134i	$0.208081\pi$
$402$		0			0
$403$		0			0
$404$	−7.26795			−0.361594
$405$	−1.23205	+	2.13397i	−0.0612211	+	0.106038i
$406$	−14.1962	+	24.5885i	−0.704543	+	1.22030i
$407$	16.7942	+	29.0885i	0.832459	+	1.44186i
$408$	−6.00000			−0.297044
$409$	9.86603	+	17.0885i	0.487844	+	0.844970i	0.999902	−	0.0139806i	$-0.00445032\pi$
$409$	9.86603	+	17.0885i	0.487844	+	0.844970i	−0.512059	+	0.858950i	$0.671117\pi$
$410$	−5.19615	−	9.00000i	−0.256620	−	0.444478i
$411$	−22.3923			−1.10453
$412$	0.598076	+	1.03590i	0.0294651	+	0.0510351i
$413$	15.5885	−	27.0000i	0.767058	−	1.32858i
$414$	5.66025	−	9.80385i	0.278186	−	0.481833i
$415$	−2.19615			−0.107805
$416$		0			0
$417$	25.1244			1.23034
$418$	−9.69615	+	16.7942i	−0.474254	+	0.821433i
$419$	−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
$421$	27.1244			1.32196			0.660980	−	0.750403i	$-0.270141\pi$
$421$	27.1244			1.32196			0.660980	+	0.750403i	$0.270141\pi$
$422$	−6.79423	−	11.7679i	−0.330738	−	0.572855i
$423$	6.69615	+	11.5981i	0.325578	+	0.563918i
$424$	−6.46410			−0.313925
$425$	−1.09808	−	1.90192i	−0.0532645	−	0.0922569i
$426$	−8.19615	+	14.1962i	−0.397105	+	0.687806i
$427$	−6.29423	+	10.9019i	−0.304599	+	0.527581i
$428$	0.339746			0.0164222
$429$		0			0
$430$	2.00000			0.0964486
$431$	1.09808	−	1.90192i	0.0528925	−	0.0916124i	−0.838367	−	0.545106i	$-0.816489\pi$
$431$	1.09808	−	1.90192i	0.0528925	−	0.0916124i	0.891259	+	0.453494i	$0.149823\pi$
$432$	2.00000	−	3.46410i	0.0962250	−	0.166667i
$433$	−6.19615	−	10.7321i	−0.297768	−	0.515749i	0.677857	−	0.735194i	$-0.262909\pi$
$433$	−6.19615	−	10.7321i	−0.297768	−	0.515749i	−0.975625	+	0.219444i	$0.929576\pi$
$434$	−3.80385			−0.182591
$435$	12.9282	+	22.3923i	0.619860	+	1.07363i
$436$	7.73205	+	13.3923i	0.370298	+	0.641375i
$437$	−16.3923			−0.784150
$438$	7.73205	+	13.3923i	0.369452	+	0.639909i
$439$	−17.2942	+	29.9545i	−0.825408	+	1.42965i	0.0761982	+	0.997093i	$0.475722\pi$
$439$	−17.2942	+	29.9545i	−0.825408	+	1.42965i	−0.901607	+	0.432557i	$0.857612\pi$
$440$	1.50000	−	2.59808i	0.0715097	−	0.123858i
$441$	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	$0.512160\pi$
$444$	−15.2942	+	26.4904i	−0.725832	+	1.25718i
$445$	8.59808	−	14.8923i	0.407588	−	0.705963i
$446$	0.232051	+	0.401924i	0.0109879	+	0.0190316i
$447$	−16.3923			−0.775329
$448$	1.50000	+	2.59808i	0.0708683	+	0.122748i
$449$	−7.79423	−	13.5000i	−0.367832	−	0.637104i	0.621394	−	0.783498i	$-0.286567\pi$
$449$	−7.79423	−	13.5000i	−0.367832	−	0.637104i	−0.989226	+	0.146394i	$0.953233\pi$
$450$	4.46410			0.210440
$451$	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
$454$	−4.39230			−0.206141
$455$		0			0
$456$	−17.6603			−0.827017
$457$	17.8301	−	30.8827i	0.834058	−	1.44463i	−0.0607368	−	0.998154i	$-0.519345\pi$
$457$	17.8301	−	30.8827i	0.834058	−	1.44463i	0.894795	−	0.446477i	$-0.147322\pi$
$458$	−2.36603	+	4.09808i	−0.110557	+	0.191491i
$459$	4.39230	+	7.60770i	0.205015	+	0.355097i
$460$	2.53590			0.118237
$461$	−0.294229	−	0.509619i	−0.0137036	−	0.0237353i	0.859092	−	0.511821i	$-0.171029\pi$
$461$	−0.294229	−	0.509619i	−0.0137036	−	0.0237353i	−0.872796	+	0.488085i	$0.837695\pi$
$462$	−12.2942	−	21.2942i	−0.571979	−	0.990697i
$463$	0.928203			0.0431373			0.0215686	−	0.999767i	$-0.493134\pi$
$463$	0.928203			0.0431373			0.0215686	+	0.999767i	$0.493134\pi$
$464$	4.73205	+	8.19615i	0.219680	+	0.380497i
$465$	−1.73205	+	3.00000i	−0.0803219	+	0.139122i
$466$	0.633975	−	1.09808i	0.0293683	−	0.0508674i
$467$	10.1436			0.469390			0.234695	−	0.972069i	$-0.424591\pi$
$467$	10.1436			0.469390			0.234695	+	0.972069i	$0.424591\pi$
$468$		0			0
$469$		0			0
$470$	−1.50000	+	2.59808i	−0.0691898	+	0.119840i
$471$	−17.7583	+	30.7583i	−0.818261	+	1.41727i
$472$	−5.19615	−	9.00000i	−0.239172	−	0.414259i
$473$	−6.00000			−0.275880
$474$	8.46410	+	14.6603i	0.388769	+	0.673368i
$475$	−3.23205	−	5.59808i	−0.148297	−	0.256857i
$476$	−6.58846			−0.301981
$477$	14.4282	+	24.9904i	0.660622	+	1.14423i
$478$	4.09808	−	7.09808i	0.187442	−	0.324658i
$479$	−5.49038	+	9.50962i	−0.250862	+	0.434506i	−0.963763	−	0.266759i	$-0.914047\pi$
$479$	−5.49038	+	9.50962i	−0.250862	+	0.434506i	0.712901	+	0.701264i	$0.247381\pi$
$480$	2.73205			0.124700
$481$		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
$485$	−7.56218	−	13.0981i	−0.343381	−	0.594753i
$486$	18.7321			0.849703
$487$	−16.6244	−	28.7942i	−0.753321	−	1.30479i	−0.946204	−	0.323569i	$-0.895117\pi$
$487$	−16.6244	−	28.7942i	−0.753321	−	1.30479i	0.192883	−	0.981222i	$-0.438216\pi$
$488$	2.09808	+	3.63397i	0.0949754	+	0.164502i
$489$	−19.8564			−0.897938
$490$	1.00000	+	1.73205i	0.0451754	+	0.0782461i
$491$	1.66987	−	2.89230i	0.0753603	−	0.130528i	−0.825883	−	0.563842i	$-0.809323\pi$
$491$	1.66987	−	2.89230i	0.0753603	−	0.130528i	0.901243	+	0.433314i	$0.142656\pi$
$492$	−14.1962	+	24.5885i	−0.640012	+	1.10853i
$493$	−20.7846			−0.936092
$494$		0			0
$495$	−13.3923			−0.601939
$496$	−0.633975	+	1.09808i	−0.0284663	+	0.0493051i
$497$	−9.00000	+	15.5885i	−0.403705	+	0.699238i
$498$	3.00000	+	5.19615i	0.134433	+	0.232845i
$499$	−1.85641			−0.0831042			−0.0415521	−	0.999136i	$-0.513230\pi$
$499$	−1.85641			−0.0831042			−0.0415521	+	0.999136i	$0.513230\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	4.09808	+	7.09808i	0.183089	+	0.317119i
$502$	−6.80385			−0.303671
$503$	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
$505$	−3.63397	+	6.29423i	−0.161710	+	0.280089i
$506$	−7.60770			−0.338203
$507$		0			0
$508$	−21.1962			−0.940427
$509$	−0.803848	+	1.39230i	−0.0356299	+	0.0617128i	−0.883290	−	0.468826i	$-0.844677\pi$
$509$	−0.803848	+	1.39230i	−0.0356299	+	0.0617128i	0.847661	+	0.530539i	$0.178010\pi$
$510$	−3.00000	+	5.19615i	−0.132842	+	0.230089i
$511$	8.49038	+	14.7058i	0.375592	+	0.650545i
$512$	1.00000			0.0441942
$513$	12.9282	+	22.3923i	0.570794	+	0.988644i
$514$	6.92820	+	12.0000i	0.305590	+	0.529297i
$515$	1.19615			0.0527088
$516$	−2.73205	−	4.73205i	−0.120272	−	0.208317i
$517$	4.50000	−	7.79423i	0.197910	−	0.342790i
$518$	−16.7942	+	29.0885i	−0.737896	+	1.27807i
$519$	−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	$0.503236\pi$
$522$	21.1244	−	36.5885i	0.924588	−	1.60143i
$523$	−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
$525$	8.19615			0.357709
$526$	13.7942	+	23.8923i	0.601457	+	1.04175i
$527$	−1.39230	−	2.41154i	−0.0606498	−	0.105048i
$528$	−8.19615			−0.356692
$529$	8.28461	+	14.3494i	0.360200	+	0.623885i
$530$	−3.23205	+	5.59808i	−0.140391	+	0.243165i
$531$	−23.1962	+	40.1769i	−1.00663	+	1.74353i
$532$	−19.3923			−0.840763
$533$		0			0
$534$	−46.9808			−2.03306
$535$	0.169873	−	0.294229i	0.00734425	−	0.0127206i
$536$		0			0
$537$	3.46410	+	6.00000i	0.149487	+	0.258919i
$538$	−2.87564			−0.123978
$539$	−3.00000	−	5.19615i	−0.129219	−	0.223814i
$540$	−2.00000	−	3.46410i	−0.0860663	−	0.149071i
$541$	16.0526			0.690153			0.345077	−	0.938574i	$-0.387853\pi$
$541$	16.0526			0.690153			0.345077	+	0.938574i	$0.387853\pi$
$542$	−1.26795	−	2.19615i	−0.0544631	−	0.0943328i
$543$	22.6603	−	39.2487i	0.972445	−	1.68432i
$544$	−1.09808	+	1.90192i	−0.0470796	+	0.0815443i
$545$	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	$0.233097\pi$
$548$	−4.09808	+	7.09808i	−0.175061	+	0.303215i
$549$	9.36603	−	16.2224i	0.399732	−	0.692357i
$550$	−1.50000	−	2.59808i	−0.0639602	−	0.110782i
$551$	−61.1769			−2.60622
$552$	−3.46410	−	6.00000i	−0.147442	−	0.255377i
$553$	9.29423	+	16.0981i	0.395231	+	0.684560i
$554$	1.00000			0.0424859
$555$	15.2942	+	26.4904i	0.649204	+	1.12445i
$556$	4.59808	−	7.96410i	0.195002	−	0.337753i
$557$	8.59808	−	14.8923i	0.364312	−	0.631007i	−0.624353	−	0.781142i	$-0.714637\pi$
$557$	8.59808	−	14.8923i	0.364312	−	0.631007i	0.988666	+	0.150135i	$0.0479708\pi$
$558$	5.66025			0.239618
$559$		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
$563$	10.7321	+	18.5885i	0.452302	+	0.783410i	0.998529	−	0.0542274i	$-0.0172696\pi$
$563$	10.7321	+	18.5885i	0.452302	+	0.783410i	−0.546227	+	0.837637i	$0.683936\pi$
$564$	8.19615			0.345120
$565$	−3.46410	−	6.00000i	−0.145736	−	0.252422i
$566$	−15.1962	−	26.3205i	−0.638742	−	1.10633i
$567$	7.39230			0.310448
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	10.6244	−	18.4019i	0.445396	−	0.771449i	−0.552684	−	0.833391i	$-0.686396\pi$
$569$	10.6244	−	18.4019i	0.445396	−	0.771449i	0.998080	+	0.0619424i	$0.0197295\pi$
$570$	−8.83013	+	15.2942i	−0.369853	+	0.640605i
$571$	−34.3731			−1.43847			−0.719234	−	0.694768i	$-0.755507\pi$
$571$	−34.3731			−1.43847			−0.719234	+	0.694768i	$0.755507\pi$
$572$		0			0
$573$	52.6410			2.19911
$574$	−15.5885	+	27.0000i	−0.650650	+	1.12696i
$575$	1.26795	−	2.19615i	0.0528771	−	0.0915859i
$576$	−2.23205	−	3.86603i	−0.0930021	−	0.161084i
$577$	32.4449			1.35070			0.675349	−	0.737499i	$-0.263993\pi$
$577$	32.4449			1.35070			0.675349	+	0.737499i	$0.263993\pi$
$578$	6.08846	+	10.5455i	0.253246	+	0.438636i
$579$	6.00000	+	10.3923i	0.249351	+	0.431889i
$580$	9.46410			0.392975
$581$	3.29423	+	5.70577i	0.136668	+	0.236715i
$582$	−20.6603	+	35.7846i	−0.856395	+	1.48332i
$583$	9.69615	−	16.7942i	0.401574	−	0.695546i
$584$	5.66025			0.234223
$585$		0			0
$586$	−0.803848			−0.0332066
$587$	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	$-0.0458424\pi$
$588$	2.73205	−	4.73205i	0.112668	−	0.195146i
$589$	−4.09808	−	7.09808i	−0.168858	−	0.292471i
$590$	−10.3923			−0.427844
$591$	13.0981	+	22.6865i	0.538783	+	0.933199i
$592$	5.59808	+	9.69615i	0.230080	+	0.398509i
$593$	−20.7846			−0.853522			−0.426761	−	0.904365i	$-0.640345\pi$
$593$	−20.7846			−0.853522			−0.426761	+	0.904365i	$0.640345\pi$
$594$	6.00000	+	10.3923i	0.246183	+	0.426401i
$595$	−3.29423	+	5.70577i	−0.135050	+	0.233914i
$596$	−3.00000	+	5.19615i	−0.122885	+	0.212843i
$597$	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	$0.448689\pi$
$600$	1.36603	−	2.36603i	0.0557678	−	0.0965926i
$601$	−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
$604$	−3.16987	−	5.49038i	−0.128980	−	0.223400i
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$	19.8564			0.806611
$607$	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
$609$	38.7846	−	67.1769i	1.57163	−	2.72215i
$610$	4.19615			0.169897
$611$		0			0
$612$	9.80385			0.396297
$613$	−13.4545	+	23.3038i	−0.543421	+	0.941234i	0.455283	+	0.890347i	$0.349538\pi$
$613$	−13.4545	+	23.3038i	−0.543421	+	0.941234i	−0.998704	+	0.0508868i	$0.983795\pi$
$614$	−10.2679	+	17.7846i	−0.414381	+	0.717728i
$615$	14.1962	+	24.5885i	0.572444	+	0.991502i
$616$	−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	$0.951351\pi$
$618$	−1.63397	−	2.83013i	−0.0657281	−	0.113844i
$619$	10.6077			0.426359			0.213180	−	0.977013i	$-0.431618\pi$
$619$	10.6077			0.426359			0.213180	+	0.977013i	$0.431618\pi$
$620$	0.633975	+	1.09808i	0.0254610	+	0.0440998i
$621$	−5.07180	+	8.78461i	−0.203524	+	0.352514i
$622$	7.56218	−	13.0981i	0.303216	−	0.525185i
$623$	−51.5885			−2.06685
$624$		0			0
$625$	1.00000			0.0400000
$626$	−2.80385	+	4.85641i	−0.112064	+	0.194101i
$627$	26.4904	−	45.8827i	1.05792	−	1.83238i
$628$	6.50000	+	11.2583i	0.259378	+	0.449256i
$629$	−24.5885			−0.980406
$630$	−6.69615	−	11.5981i	−0.266781	−	0.462078i
$631$	10.3923	+	18.0000i	0.413711	+	0.716569i	0.995292	−	0.0969198i	$-0.0308990\pi$
$631$	10.3923	+	18.0000i	0.413711	+	0.716569i	−0.581581	+	0.813488i	$0.697566\pi$
$632$	6.19615			0.246470
$633$	18.5622	+	32.1506i	0.737780	+	1.27787i
$634$	6.40192	−	11.0885i	0.254253	−	0.440379i
$635$	−10.5981	+	18.3564i	−0.420572	+	0.728452i
$636$	17.6603			0.700275
$637$		0			0
$638$	−28.3923			−1.12406
$639$	13.3923	−	23.1962i	0.529791	−	0.917626i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	22.9641	+	39.7750i	0.907027	+	1.57102i	0.818172	+	0.574973i	$0.194988\pi$
$641$	22.9641	+	39.7750i	0.907027	+	1.57102i	0.0888552	+	0.996045i	$0.471679\pi$
$642$	−0.928203			−0.0366333
$643$	3.63397	+	6.29423i	0.143310	+	0.248220i	0.928741	−	0.370729i	$-0.120892\pi$
$643$	3.63397	+	6.29423i	0.143310	+	0.248220i	−0.785431	+	0.618949i	$0.787559\pi$
$644$	−3.80385	−	6.58846i	−0.149893	−	0.259622i
$645$	−5.46410			−0.215149
$646$	−7.09808	−	12.2942i	−0.279270	−	0.483710i
$647$	−5.59808	+	9.69615i	−0.220083	+	0.381195i	−0.954833	−	0.297143i	$-0.903966\pi$
$647$	−5.59808	+	9.69615i	−0.220083	+	0.381195i	0.734750	+	0.678338i	$0.237300\pi$
$648$	1.23205	−	2.13397i	0.0483995	−	0.0838304i
$649$	31.1769			1.22380
$650$		0			0
$651$	10.3923			0.407307
$652$	−3.63397	+	6.29423i	−0.142317	+	0.246501i
$653$	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
$655$	18.1244			0.708177
$656$	5.19615	+	9.00000i	0.202876	+	0.351391i
$657$	−12.6340	−	21.8827i	−0.492898	−	0.853725i
$658$	9.00000			0.350857
$659$	−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
$661$	14.9545	−	25.9019i	0.581662	−	1.00747i	−0.413621	−	0.910449i	$-0.635736\pi$
$661$	14.9545	−	25.9019i	0.581662	−	1.00747i	0.995283	−	0.0970187i	$-0.0309307\pi$
$662$	−0.928203			−0.0360756
$663$		0			0
$664$	2.19615			0.0852272
$665$	−9.69615	+	16.7942i	−0.376001	+	0.651252i
$666$	24.9904	−	43.2846i	0.968358	−	1.67724i
$667$	−12.0000	−	20.7846i	−0.464642	−	0.804783i
$668$	3.00000			0.116073
$669$	−0.633975	−	1.09808i	−0.0245109	−	0.0424541i
$670$		0			0
$671$	−12.5885			−0.485972
$672$	−4.09808	−	7.09808i	−0.158087	−	0.273814i
$673$	1.80385	−	3.12436i	0.0695332	−	0.120435i	−0.829163	−	0.559007i	$-0.811182\pi$
$673$	1.80385	−	3.12436i	0.0695332	−	0.120435i	0.898696	+	0.438572i	$0.144516\pi$
$674$	−2.09808	+	3.63397i	−0.0808149	+	0.139975i
$675$	−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	$0.488642\pi$
$678$	−9.46410	+	16.3923i	−0.363467	+	0.629543i
$679$	−22.6865	+	39.2942i	−0.870629	+	1.50797i
$680$	1.09808	+	1.90192i	0.0421093	+	0.0729354i
$681$	12.0000			0.459841
$682$	−1.90192	−	3.29423i	−0.0728284	−	0.126143i
$683$	−15.5885	−	27.0000i	−0.596476	−	1.03313i	−0.993337	−	0.115248i	$-0.963234\pi$
$683$	−15.5885	−	27.0000i	−0.596476	−	1.03313i	0.396861	−	0.917879i	$-0.370099\pi$
$684$	28.8564			1.10335
$685$	4.09808	+	7.09808i	0.156579	+	0.271204i
$686$	−7.50000	+	12.9904i	−0.286351	+	0.495975i
$687$	6.46410	−	11.1962i	0.246621	−	0.427160i
$688$	−2.00000			−0.0762493
$689$		0			0
$690$	−6.92820			−0.263752
$691$	9.35641	−	16.2058i	0.355934	−	0.616497i	−0.631343	−	0.775504i	$-0.717496\pi$
$691$	9.35641	−	16.2058i	0.355934	−	0.616497i	0.987277	+	0.159007i	$0.0508293\pi$
$692$	−7.50000	+	12.9904i	−0.285107	+	0.493820i
$693$	20.0885	+	34.7942i	0.763097	+	1.32172i
$694$	−25.2679			−0.959158
$695$	−4.59808	−	7.96410i	−0.174415	−	0.302096i
$696$	−12.9282	−	22.3923i	−0.490042	−	0.848778i
$697$	−22.8231			−0.864486
$698$	−17.0263	−	29.4904i	−0.644454	−	1.11623i
$699$	−1.73205	+	3.00000i	−0.0655122	+	0.113470i
$700$	1.50000	−	2.59808i	0.0566947	−	0.0981981i
$701$	29.9090			1.12965			0.564823	−	0.825212i	$-0.308944\pi$
$701$	29.9090			1.12965			0.564823	+	0.825212i	$0.308944\pi$
$702$		0			0
$703$	−72.3731			−2.72960
$704$	−1.50000	+	2.59808i	−0.0565334	+	0.0979187i
$705$	4.09808	−	7.09808i	0.154342	−	0.267329i
$706$	10.0981	+	17.4904i	0.380046	+	0.658259i
$707$	21.8038			0.820018
$708$	14.1962	+	24.5885i	0.533524	+	0.924091i
$709$	−20.4904	−	35.4904i	−0.769532	−	1.33287i	−0.937817	−	0.347131i	$-0.887156\pi$
$709$	−20.4904	−	35.4904i	−0.769532	−	1.33287i	0.168284	−	0.985738i	$-0.446177\pi$
$710$	6.00000			0.225176
$711$	−13.8301	−	23.9545i	−0.518670	−	0.898363i
$712$	−8.59808	+	14.8923i	−0.322227	+	0.558113i
$713$	1.60770	−	2.78461i	0.0602087	−	0.104284i
$714$	18.0000			0.673633
$715$		0			0
$716$	2.53590			0.0947710
$717$	−11.1962	+	19.3923i	−0.418128	+	0.724219i
$718$	11.1962	−	19.3923i	0.417837	−	0.723714i
$719$	−0.928203	−	1.60770i	−0.0346161	−	0.0599569i	0.848198	−	0.529679i	$-0.177688\pi$
$719$	−0.928203	−	1.60770i	−0.0346161	−	0.0599569i	−0.882814	+	0.469722i	$0.844354\pi$
$720$	−4.46410			−0.166367
$721$	−1.79423	−	3.10770i	−0.0668206	−	0.115737i
$722$	−11.3923	−	19.7321i	−0.423978	−	0.734351i
$723$	23.6603			0.879934
$724$	−8.29423	−	14.3660i	−0.308253	−	0.533909i
$725$	4.73205	−	8.19615i	0.175744	−	0.304397i
$726$	−2.73205	+	4.73205i	−0.101396	+	0.175623i
$727$	38.3731			1.42318			0.711589	−	0.702596i	$-0.247976\pi$
$727$	38.3731			1.42318			0.711589	+	0.702596i	$0.247976\pi$
$728$		0			0
$729$	−43.7846			−1.62165
$730$	2.83013	−	4.90192i	0.104748	−	0.181428i
$731$	2.19615	−	3.80385i	0.0812276	−	0.140690i
$732$	−5.73205	−	9.92820i	−0.211863	−	0.366957i
$733$	−50.9090			−1.88037			−0.940183	−	0.340670i	$-0.889346\pi$
$733$	−50.9090			−1.88037			−0.940183	+	0.340670i	$0.889346\pi$
$734$	13.1962	+	22.8564i	0.487079	+	0.843645i
$735$	−2.73205	−	4.73205i	−0.100773	−	0.174544i
$736$	−2.53590			−0.0934745
$737$		0			0
$738$	23.1962	−	40.1769i	0.853862	−	1.47893i
$739$	25.2846	−	43.7942i	0.930109	−	1.61100i	0.146979	−	0.989140i	$-0.453045\pi$
$739$	25.2846	−	43.7942i	0.930109	−	1.61100i	0.783131	−	0.621857i	$-0.213622\pi$
$740$	11.1962			0.411579
$741$		0			0
$742$	19.3923			0.711914
$743$	−17.1962	+	29.7846i	−0.630866	+	1.09269i	0.356509	+	0.934292i	$0.383967\pi$
$743$	−17.1962	+	29.7846i	−0.630866	+	1.09269i	−0.987375	+	0.158400i	$0.949367\pi$
$744$	1.73205	−	3.00000i	0.0635001	−	0.109985i
$745$	3.00000	+	5.19615i	0.109911	+	0.190372i
$746$	20.3923			0.746615
$747$	−4.90192	−	8.49038i	−0.179352	−	0.310647i
$748$	−3.29423	−	5.70577i	−0.120449	−	0.208624i
$749$	−1.01924			−0.0372421
$750$	−1.36603	−	2.36603i	−0.0498802	−	0.0863950i
$751$	0.196152	−	0.339746i	0.00715770	−	0.0123975i	−0.862424	−	0.506186i	$-0.831055\pi$
$751$	0.196152	−	0.339746i	0.00715770	−	0.0123975i	0.869582	+	0.493788i	$0.164388\pi$
$752$	1.50000	−	2.59808i	0.0546994	−	0.0947421i
$753$	18.5885			0.677401
$754$		0			0
$755$	−6.33975			−0.230727
$756$	−6.00000	+	10.3923i	−0.218218	+	0.377964i
$757$	−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
$759$	20.7846			0.754434
$760$	3.23205	+	5.59808i	0.117239	+	0.203064i
$761$	14.5981	+	25.2846i	0.529180	+	0.916566i	0.999421	+	0.0340283i	$0.0108337\pi$
$761$	14.5981	+	25.2846i	0.529180	+	0.916566i	−0.470241	+	0.882538i	$0.655833\pi$
$762$	57.9090			2.09782
$763$	−23.1962	−	40.1769i	−0.839757	−	1.45450i
$764$	9.63397	−	16.6865i	0.348545	−	0.603698i
$765$	4.90192	−	8.49038i	0.177229	−	0.306970i
$766$	1.60770			0.0580884
$767$		0			0
$768$	−2.73205			−0.0985844
$769$	19.0526	−	33.0000i	0.687053	−	1.19001i	−0.285734	−	0.958309i	$-0.592237\pi$
$769$	19.0526	−	33.0000i	0.687053	−	1.19001i	0.972787	−	0.231701i	$-0.0744293\pi$
$770$	−4.50000	+	7.79423i	−0.162169	+	0.280885i
$771$	−18.9282	−	32.7846i	−0.681683	−	1.18071i
$772$	4.39230			0.158083
$773$	−16.7942	−	29.0885i	−0.604046	−	1.04624i	−0.992201	−	0.124645i	$-0.960221\pi$
$773$	−16.7942	−	29.0885i	−0.604046	−	1.04624i	0.388155	−	0.921594i	$-0.373113\pi$
$774$	4.46410	+	7.73205i	0.160459	+	0.277923i
$775$	1.26795			0.0455461
$776$	7.56218	+	13.0981i	0.271466	+	0.470194i
$777$	45.8827	−	79.4711i	1.64603	−	2.85101i
$778$	9.63397	−	16.6865i	0.345395	−	0.598241i
$779$	−67.1769			−2.40686
$780$		0			0
$781$	−18.0000			−0.644091
$782$	2.78461	−	4.82309i	0.0995774	−	0.172473i
$783$	−18.9282	+	32.7846i	−0.676439	+	1.17163i
$784$	−1.00000	−	1.73205i	−0.0357143	−	0.0618590i
$785$	13.0000			0.463990
$786$	−24.7583	−	42.8827i	−0.883100	−	1.52957i
$787$	18.4186	+	31.9019i	0.656552	+	1.13718i	0.981502	+	0.191450i	$0.0613189\pi$
$787$	18.4186	+	31.9019i	0.656552	+	1.13718i	−0.324951	+	0.945731i	$0.605348\pi$
$788$	9.58846			0.341575
$789$	−37.6865	−	65.2750i	−1.34168	−	2.32385i
$790$	3.09808	−	5.36603i	0.110225	−	0.190915i
$791$	−10.3923	+	18.0000i	−0.369508	+	0.640006i
$792$	13.3923			0.475875
$793$		0			0
$794$	0.803848			0.0285275
$795$	8.83013	−	15.2942i	0.313172	−	0.542430i
$796$	7.19615	−	12.4641i	0.255061	−	0.441778i
$797$	0.464102	+	0.803848i	0.0164393	+	0.0284737i	0.874128	−	0.485696i	$-0.161434\pi$
$797$	0.464102	+	0.803848i	0.0164393	+	0.0284737i	−0.857689	+	0.514169i	$0.828100\pi$
$798$	52.9808			1.87550
$799$	3.29423	+	5.70577i	0.116541	+	0.201856i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	76.7654			2.71237
$802$	−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
$808$	3.63397	−	6.29423i	0.127843	−	0.221430i
$809$	−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
$811$	22.6077			0.793864			0.396932	−	0.917848i	$-0.370075\pi$
$811$	22.6077			0.793864			0.396932	+	0.917848i	$0.370075\pi$
$812$	−14.1962	−	24.5885i	−0.498187	−	0.862886i
$813$	3.46410	+	6.00000i	0.121491	+	0.210429i
$814$	−33.5885			−1.17727
$815$	3.63397	+	6.29423i	0.127293	+	0.220477i
$816$	3.00000	−	5.19615i	0.105021	−	0.181902i
$817$	6.46410	−	11.1962i	0.226150	−	0.391704i
$818$	−19.7321			−0.689915
$819$		0			0
$820$	10.3923			0.362915
$821$	4.90192	−	8.49038i	0.171078	−	0.296316i	−0.767719	−	0.640787i	$-0.778608\pi$
$821$	4.90192	−	8.49038i	0.171078	−	0.296316i	0.938797	+	0.344471i	$0.111942\pi$
$822$	11.1962	−	19.3923i	0.390511	−	0.676384i
$823$	−8.40192	−	14.5526i	−0.292873	−	0.507270i	0.681615	−	0.731711i	$-0.261278\pi$
$823$	−8.40192	−	14.5526i	−0.292873	−	0.507270i	−0.974488	+	0.224441i	$0.927945\pi$
$824$	−1.19615			−0.0416699
$825$	4.09808	+	7.09808i	0.142677	+	0.247123i
$826$	15.5885	+	27.0000i	0.542392	+	0.939450i
$827$	11.4115			0.396818			0.198409	−	0.980119i	$-0.436423\pi$
$827$	11.4115			0.396818			0.198409	+	0.980119i	$0.436423\pi$
$828$	5.66025	+	9.80385i	0.196707	+	0.340707i
$829$	−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	$0.279573\pi$
$830$	1.09808	−	1.90192i	0.0381148	−	0.0660167i
$831$	−2.73205			−0.0947738
$832$		0			0
$833$	4.39230			0.152184
$834$	−12.5622	+	21.7583i	−0.434993	+	0.753429i
$835$	1.50000	−	2.59808i	0.0519096	−	0.0899101i
$836$	−9.69615	−	16.7942i	−0.335348	−	0.580841i
$837$	−5.07180			−0.175307
$838$	−8.66025	−	15.0000i	−0.299164	−	0.518166i
$839$	16.0981	+	27.8827i	0.555767	+	0.962617i	0.997843	+	0.0656397i	$0.0209088\pi$
$839$	16.0981	+	27.8827i	0.555767	+	0.962617i	−0.442076	+	0.896978i	$0.645758\pi$
$840$	−8.19615			−0.282794
$841$	−30.2846	−	52.4545i	−1.04430	−	1.80878i
$842$	−13.5622	+	23.4904i	−0.467384	+	0.809532i
$843$	−14.1962	+	24.5885i	−0.488941	+	0.846871i
$844$	13.5885			0.467734
$845$		0			0
$846$	−13.3923			−0.460437
$847$	−3.00000	+	5.19615i	−0.103081	+	0.178542i
$848$	3.23205	−	5.59808i	0.110989	−	0.192239i
$849$	41.5167	+	71.9090i	1.42485	+	2.46791i
$850$	2.19615			0.0753274
$851$	−14.1962	−	24.5885i	−0.486638	−	0.842881i
$852$	−8.19615	−	14.1962i	−0.280796	−	0.486352i
$853$	13.8564			0.474434			0.237217	−	0.971457i	$-0.423765\pi$
$853$	13.8564			0.474434			0.237217	+	0.971457i	$0.423765\pi$
$854$	−6.29423	−	10.9019i	−0.215384	−	0.373056i
$855$	14.4282	−	24.9904i	0.493434	−	0.854653i
$856$	−0.169873	+	0.294229i	−0.00580614	+	0.0100565i
$857$	13.2679			0.453225			0.226612	−	0.973985i	$-0.427235\pi$
$857$	13.2679			0.453225			0.226612	+	0.973985i	$0.427235\pi$
$858$		0			0
$859$	52.3731			1.78695			0.893473	−	0.449117i	$-0.148261\pi$
$859$	52.3731			1.78695			0.893473	+	0.449117i	$0.148261\pi$
$860$	−1.00000	+	1.73205i	−0.0340997	+	0.0590624i
$861$	42.5885	−	73.7654i	1.45141	−	2.51392i
$862$	1.09808	+	1.90192i	0.0374006	+	0.0647798i
$863$	−19.1769			−0.652790			−0.326395	−	0.945234i	$-0.605834\pi$
$863$	−19.1769			−0.652790			−0.326395	+	0.945234i	$0.605834\pi$
$864$	2.00000	+	3.46410i	0.0680414	+	0.117851i
$865$	7.50000	+	12.9904i	0.255008	+	0.441686i
$866$	12.3923			0.421108
$867$	−16.6340	−	28.8109i	−0.564919	−	0.978469i
$868$	1.90192	−	3.29423i	0.0645555	−	0.111813i
$869$	−9.29423	+	16.0981i	−0.315285	+	0.546090i
$870$	−25.8564			−0.876614
$871$		0			0
$872$	−15.4641			−0.523681
$873$	33.7583	−	58.4711i	1.14255	−	1.97895i
$874$	8.19615	−	14.1962i	0.277239	−	0.480192i
$875$	−1.50000	−	2.59808i	−0.0507093	−	0.0878310i
$876$	−15.4641			−0.522484
$877$	10.2679	+	17.7846i	0.346724	+	0.600544i	0.985665	−	0.168712i	$-0.0539607\pi$
$877$	10.2679	+	17.7846i	0.346724	+	0.600544i	−0.638941	+	0.769255i	$0.720627\pi$
$878$	−17.2942	−	29.9545i	−0.583652	−	1.01091i
$879$	2.19615			0.0740744
$880$	1.50000	+	2.59808i	0.0505650	+	0.0875811i
$881$	−4.16025	+	7.20577i	−0.140163	+	0.242769i	−0.927558	−	0.373680i	$-0.878096\pi$
$881$	−4.16025	+	7.20577i	−0.140163	+	0.242769i	0.787395	+	0.616449i	$0.211429\pi$
$882$	−4.46410	+	7.73205i	−0.150314	+	0.260352i
$883$	26.5885			0.894773			0.447386	−	0.894341i	$-0.352355\pi$
$883$	26.5885			0.894773			0.447386	+	0.894341i	$0.352355\pi$
$884$		0			0
$885$	28.3923			0.954397
$886$	0.803848	−	1.39230i	0.0270058	−	0.0467754i
$887$	−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
$889$	63.5885			2.13269
$890$	8.59808	+	14.8923i	0.288208	+	0.499191i
$891$	3.69615	+	6.40192i	0.123826	+	0.214473i
$892$	−0.464102			−0.0155393
$893$	9.69615	+	16.7942i	0.324469	+	0.561997i
$894$	8.19615	−	14.1962i	0.274120	−	0.474790i
$895$	1.26795	−	2.19615i	0.0423829	−	0.0734093i
$896$	−3.00000			−0.100223
$897$		0			0
$898$	15.5885			0.520194
$899$	6.00000	−	10.3923i	0.200111	−	0.346603i
$900$	−2.23205	+	3.86603i	−0.0744017	+	0.128868i
$901$	7.09808	+	12.2942i	0.236471	+	0.409580i
$902$	−31.1769			−1.03808
$903$	8.19615	+	14.1962i	0.272751	+	0.472418i
$904$	3.46410	+	6.00000i	0.115214	+	0.199557i
$905$	−16.5885			−0.551419
$906$	8.66025	+	15.0000i	0.287718	+	0.498342i
$907$	−13.2942	+	23.0263i	−0.441428	+	0.764575i	−0.997796	−	0.0663609i	$-0.978861\pi$
$907$	−13.2942	+	23.0263i	−0.441428	+	0.764575i	0.556368	+	0.830936i	$0.312194\pi$
$908$	2.19615	−	3.80385i	0.0728819	−	0.126235i
$909$	−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	$0.577409\pi$
$912$	8.83013	−	15.2942i	0.292395	−	0.506443i
$913$	−3.29423	+	5.70577i	−0.109023	+	0.188833i
$914$	17.8301	+	30.8827i	0.589768	+	1.02151i
$915$	−11.4641			−0.378992
$916$	−2.36603	−	4.09808i	−0.0781757	−	0.135404i
$917$	−27.1865	−	47.0885i	−0.897778	−	1.55500i
$918$	−8.78461			−0.289935
$919$	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
$921$	28.0526	−	48.5885i	0.924363	−	1.60104i
$922$	0.588457			0.0193798
$923$		0			0
$924$	24.5885			0.808901
$925$	5.59808	−	9.69615i	0.184064	−	0.318808i
$926$	−0.464102	+	0.803848i	−0.0152513	+	0.0264161i
$927$	2.66987	+	4.62436i	0.0876901	+	0.151884i
$928$	−9.46410			−0.310674
$929$	22.3923	+	38.7846i	0.734668	+	1.27248i	0.954869	+	0.297027i	$0.0959952\pi$
$929$	22.3923	+	38.7846i	0.734668	+	1.27248i	−0.220201	+	0.975454i	$0.570671\pi$
$930$	−1.73205	−	3.00000i	−0.0567962	−	0.0983739i
$931$	12.9282			0.423705
$932$	0.633975	+	1.09808i	0.0207665	+	0.0359687i
$933$	−20.6603	+	35.7846i	−0.676386	+	1.17154i
$934$	−5.07180	+	8.78461i	−0.165954	+	0.287441i
$935$	−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
$941$	44.7846			1.45994			0.729968	−	0.683481i	$-0.239535\pi$
$941$	44.7846			1.45994			0.729968	+	0.683481i	$0.239535\pi$
$942$	−17.7583	−	30.7583i	−0.578598	−	1.00216i
$943$	−13.1769	−	22.8231i	−0.429099	−	0.743222i
$944$	10.3923			0.338241
$945$	6.00000	+	10.3923i	0.195180	+	0.338062i
$946$	3.00000	−	5.19615i	0.0975384	−	0.168941i
$947$	28.6865	−	49.6865i	0.932187	−	1.61460i	0.152612	−	0.988286i	$-0.451231\pi$
$947$	28.6865	−	49.6865i	0.932187	−	1.61460i	0.779575	−	0.626309i	$-0.215435\pi$
$948$	−16.9282			−0.549802
$949$		0			0
$950$	6.46410			0.209723
$951$	−17.4904	+	30.2942i	−0.567164	+	0.982358i
$952$	3.29423	−	5.70577i	0.106767	−	0.184925i
$953$	12.2942	+	21.2942i	0.398249	+	0.689788i	0.993510	−	0.113745i	$-0.0362846\pi$
$953$	12.2942	+	21.2942i	0.398249	+	0.689788i	−0.595261	+	0.803533i	$0.702951\pi$
$954$	−28.8564			−0.934261
$955$	−9.63397	−	16.6865i	−0.311748	−	0.539964i
$956$	4.09808	+	7.09808i	0.132541	+	0.229568i
$957$	77.5692			2.50746
$958$	−5.49038	−	9.50962i	−0.177386	−	0.307242i
$959$	12.2942	−	21.2942i	0.397001	−	0.687627i
$960$	−1.36603	+	2.36603i	−0.0440883	+	0.0763631i
$961$	−29.3923			−0.948139
$962$		0			0
$963$	1.51666			0.0488737
$964$	4.33013	−	7.50000i	0.139464	−	0.241559i
$965$	2.19615	−	3.80385i	0.0706966	−	0.122450i
$966$	10.3923	+	18.0000i	0.334367	+	0.579141i
$967$	38.5692			1.24030			0.620151	−	0.784482i	$-0.287071\pi$
$967$	38.5692			1.24030			0.620151	+	0.784482i	$0.287071\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$	19.3923	+	33.5885i	0.622971	+	1.07902i
$970$	15.1244			0.485614
$971$	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
$973$	−13.7942	+	23.8923i	−0.442223	+	0.765952i
$974$	33.2487			1.06536
$975$		0			0
$976$	−4.19615			−0.134316
$977$	−2.19615	+	3.80385i	−0.0702611	+	0.121696i	−0.899016	−	0.437916i	$-0.855717\pi$
$977$	−2.19615	+	3.80385i	−0.0702611	+	0.121696i	0.828755	+	0.559612i	$0.189050\pi$
$978$	9.92820	−	17.1962i	0.317469	−	0.549872i
$979$	−25.7942	−	44.6769i	−0.824387	−	1.42788i
$980$	−2.00000			−0.0638877
$981$	34.5167	+	59.7846i	1.10203	+	1.90878i
$982$	1.66987	+	2.89230i	0.0532878	+	0.0922972i
$983$	38.5692			1.23017			0.615084	−	0.788462i	$-0.289122\pi$
$983$	38.5692			1.23017			0.615084	+	0.788462i	$0.289122\pi$
$984$	−14.1962	−	24.5885i	−0.452557	−	0.783851i
$985$	4.79423	−	8.30385i	0.152757	−	0.264583i
$986$	10.3923	−	18.0000i	0.330958	−	0.573237i
$987$	−24.5885			−0.782659
$988$		0			0
$989$	5.07180			0.161274
$990$	6.69615	−	11.5981i	0.212818	−	0.368611i
$991$	−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
$993$	2.53590			0.0804743
$994$	−9.00000	−	15.5885i	−0.285463	−	0.494436i
$995$	−7.19615	−	12.4641i	−0.228133	−	0.395139i
$996$	−6.00000			−0.190117
$997$	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
$999$	−22.3923	+	38.7846i	−0.708461	+	1.22709i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.e.l.191.2		4
13.2	odd	12		1690.2.l.g.361.1		4
13.3	even	3	inner	1690.2.e.l.991.2		4
13.4	even	6		1690.2.a.j.1.1		2
13.5	odd	4		130.2.l.a.121.2	yes	4
13.6	odd	12		1690.2.d.f.1351.1		4
13.7	odd	12		1690.2.d.f.1351.3		4
13.8	odd	4		1690.2.l.g.1161.1		4
13.9	even	3		1690.2.a.m.1.1		2
13.10	even	6		1690.2.e.n.991.2		4
13.11	odd	12		130.2.l.a.101.2	✓	4
13.12	even	2		1690.2.e.n.191.2		4
39.5	even	4		1170.2.bs.c.901.1		4
39.11	even	12		1170.2.bs.c.361.1		4
52.11	even	12		1040.2.da.a.881.1		4
52.31	even	4		1040.2.da.a.641.1		4
65.4	even	6		8450.2.a.bm.1.2		2
65.9	even	6		8450.2.a.bf.1.2		2
65.18	even	4		650.2.n.b.199.2		4
65.24	odd	12		650.2.m.a.101.1		4
65.37	even	12		650.2.n.b.49.2		4
65.44	odd	4		650.2.m.a.251.1		4
65.57	even	4		650.2.n.a.199.1		4
65.63	even	12		650.2.n.a.49.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.a.101.2	✓	4	13.11	odd	12
130.2.l.a.121.2	yes	4	13.5	odd	4
650.2.m.a.101.1		4	65.24	odd	12
650.2.m.a.251.1		4	65.44	odd	4
650.2.n.a.49.1		4	65.63	even	12
650.2.n.a.199.1		4	65.57	even	4
650.2.n.b.49.2		4	65.37	even	12
650.2.n.b.199.2		4	65.18	even	4
1040.2.da.a.641.1		4	52.31	even	4
1040.2.da.a.881.1		4	52.11	even	12
1170.2.bs.c.361.1		4	39.11	even	12
1170.2.bs.c.901.1		4	39.5	even	4
1690.2.a.j.1.1		2	13.4	even	6
1690.2.a.m.1.1		2	13.9	even	3
1690.2.d.f.1351.1		4	13.6	odd	12
1690.2.d.f.1351.3		4	13.7	odd	12
1690.2.e.l.191.2		4	1.1	even	1	trivial
1690.2.e.l.991.2		4	13.3	even	3	inner
1690.2.e.n.191.2		4	13.12	even	2
1690.2.e.n.991.2		4	13.10	even	6
1690.2.l.g.361.1		4	13.2	odd	12
1690.2.l.g.1161.1		4	13.8	odd	4
8450.2.a.bf.1.2		2	65.9	even	6
8450.2.a.bm.1.2		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)

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

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