LMFDB - Embedded newform 38.2.c.b.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,2,Mod(7,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("38.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	38.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.303431527681$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.1
Root			$1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	38.7
Dual form			38.2.c.b.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.32288 - 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.822876 + 1.42526i) q^{5} +(-1.32288 + 2.29129i) q^{6} +3.64575 q^{7} +1.00000 q^{8} +(-2.00000 + 3.46410i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.32288 - 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.822876 + 1.42526i) q^{5} +(-1.32288 + 2.29129i) q^{6} +3.64575 q^{7} +1.00000 q^{8} +(-2.00000 + 3.46410i) q^{9} +(0.822876 - 1.42526i) q^{10} -4.64575 q^{11} +2.64575 q^{12} +(-1.00000 + 1.73205i) q^{13} +(-1.82288 - 3.15731i) q^{14} +(2.17712 - 3.77089i) q^{15} +(-0.500000 - 0.866025i) q^{16} +4.00000 q^{18} +(1.67712 + 4.02334i) q^{19} -1.64575 q^{20} +(-4.82288 - 8.35347i) q^{21} +(2.32288 + 4.02334i) q^{22} +(0.822876 - 1.42526i) q^{23} +(-1.32288 - 2.29129i) q^{24} +(1.14575 - 1.98450i) q^{25} +2.00000 q^{26} +2.64575 q^{27} +(-1.82288 + 3.15731i) q^{28} +(-0.822876 + 1.42526i) q^{29} -4.35425 q^{30} -5.64575 q^{31} +(-0.500000 + 0.866025i) q^{32} +(6.14575 + 10.6448i) q^{33} +(3.00000 + 5.19615i) q^{35} +(-2.00000 - 3.46410i) q^{36} +0.354249 q^{37} +(2.64575 - 3.46410i) q^{38} +5.29150 q^{39} +(0.822876 + 1.42526i) q^{40} +(0.145751 + 0.252449i) q^{41} +(-4.82288 + 8.35347i) q^{42} +(-5.64575 - 9.77873i) q^{43} +(2.32288 - 4.02334i) q^{44} -6.58301 q^{45} -1.64575 q^{46} +(-2.17712 + 3.77089i) q^{47} +(-1.32288 + 2.29129i) q^{48} +6.29150 q^{49} -2.29150 q^{50} +(-1.00000 - 1.73205i) q^{52} +(6.29150 - 10.8972i) q^{53} +(-1.32288 - 2.29129i) q^{54} +(-3.82288 - 6.62141i) q^{55} +3.64575 q^{56} +(7.00000 - 9.16515i) q^{57} +1.64575 q^{58} +(3.96863 + 6.87386i) q^{59} +(2.17712 + 3.77089i) q^{60} +(-0.468627 + 0.811686i) q^{61} +(2.82288 + 4.88936i) q^{62} +(-7.29150 + 12.6293i) q^{63} +1.00000 q^{64} -3.29150 q^{65} +(6.14575 - 10.6448i) q^{66} +(-0.322876 + 0.559237i) q^{67} -4.35425 q^{69} +(3.00000 - 5.19615i) q^{70} +(1.35425 + 2.34563i) q^{71} +(-2.00000 + 3.46410i) q^{72} +(-0.854249 - 1.47960i) q^{73} +(-0.177124 - 0.306788i) q^{74} -6.06275 q^{75} +(-4.32288 - 0.559237i) q^{76} -16.9373 q^{77} +(-2.64575 - 4.58258i) q^{78} +(2.00000 + 3.46410i) q^{79} +(0.822876 - 1.42526i) q^{80} +(2.50000 + 4.33013i) q^{81} +(0.145751 - 0.252449i) q^{82} +7.93725 q^{83} +9.64575 q^{84} +(-5.64575 + 9.77873i) q^{86} +4.35425 q^{87} -4.64575 q^{88} +(3.29150 + 5.70105i) q^{90} +(-3.64575 + 6.31463i) q^{91} +(0.822876 + 1.42526i) q^{92} +(7.46863 + 12.9360i) q^{93} +4.35425 q^{94} +(-4.35425 + 5.70105i) q^{95} +2.64575 q^{96} +(1.85425 + 3.21165i) q^{97} +(-3.14575 - 5.44860i) q^{98} +(9.29150 - 16.0934i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 4 q^{7} + 4 q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 4 * q^7 + 4 * q^8 - 8 * q^9	$ 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 4 q^{7} + 4 q^{8} - 8 q^{9} - 2 q^{10} - 8 q^{11} - 4 q^{13} - 2 q^{14} + 14 q^{15} - 2 q^{16} + 16 q^{18} + 12 q^{19} + 4 q^{20} - 14 q^{21} + 4 q^{22} - 2 q^{23} - 6 q^{25} + 8 q^{26} - 2 q^{28} + 2 q^{29} - 28 q^{30} - 12 q^{31} - 2 q^{32} + 14 q^{33} + 12 q^{35} - 8 q^{36} + 12 q^{37} - 2 q^{40} - 10 q^{41} - 14 q^{42} - 12 q^{43} + 4 q^{44} + 16 q^{45} + 4 q^{46} - 14 q^{47} + 4 q^{49} + 12 q^{50} - 4 q^{52} + 4 q^{53} - 10 q^{55} + 4 q^{56} + 28 q^{57} - 4 q^{58} + 14 q^{60} + 14 q^{61} + 6 q^{62} - 8 q^{63} + 4 q^{64} + 8 q^{65} + 14 q^{66} + 4 q^{67} - 28 q^{69} + 12 q^{70} + 16 q^{71} - 8 q^{72} - 14 q^{73} - 6 q^{74} - 56 q^{75} - 12 q^{76} - 36 q^{77} + 8 q^{79} - 2 q^{80} + 10 q^{81} - 10 q^{82} + 28 q^{84} - 12 q^{86} + 28 q^{87} - 8 q^{88} - 8 q^{90} - 4 q^{91} - 2 q^{92} + 14 q^{93} + 28 q^{94} - 28 q^{95} + 18 q^{97} - 2 q^{98} + 16 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 4 * q^7 + 4 * q^8 - 8 * q^9 - 2 * q^10 - 8 * q^11 - 4 * q^13 - 2 * q^14 + 14 * q^15 - 2 * q^16 + 16 * q^18 + 12 * q^19 + 4 * q^20 - 14 * q^21 + 4 * q^22 - 2 * q^23 - 6 * q^25 + 8 * q^26 - 2 * q^28 + 2 * q^29 - 28 * q^30 - 12 * q^31 - 2 * q^32 + 14 * q^33 + 12 * q^35 - 8 * q^36 + 12 * q^37 - 2 * q^40 - 10 * q^41 - 14 * q^42 - 12 * q^43 + 4 * q^44 + 16 * q^45 + 4 * q^46 - 14 * q^47 + 4 * q^49 + 12 * q^50 - 4 * q^52 + 4 * q^53 - 10 * q^55 + 4 * q^56 + 28 * q^57 - 4 * q^58 + 14 * q^60 + 14 * q^61 + 6 * q^62 - 8 * q^63 + 4 * q^64 + 8 * q^65 + 14 * q^66 + 4 * q^67 - 28 * q^69 + 12 * q^70 + 16 * q^71 - 8 * q^72 - 14 * q^73 - 6 * q^74 - 56 * q^75 - 12 * q^76 - 36 * q^77 + 8 * q^79 - 2 * q^80 + 10 * q^81 - 10 * q^82 + 28 * q^84 - 12 * q^86 + 28 * q^87 - 8 * q^88 - 8 * q^90 - 4 * q^91 - 2 * q^92 + 14 * q^93 + 28 * q^94 - 28 * q^95 + 18 * q^97 - 2 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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
$3$	−1.32288	−	2.29129i	−0.763763	−	1.32288i	−0.940898	−	0.338689i	$-0.890016\pi$
$3$	−1.32288	−	2.29129i	−0.763763	−	1.32288i	0.177136	−	0.984186i	$-0.443317\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.822876	+	1.42526i	0.368001	+	0.637397i	0.989253	−	0.146214i	$-0.0467089\pi$
$5$	0.822876	+	1.42526i	0.368001	+	0.637397i	−0.621252	+	0.783611i	$0.713376\pi$
$6$	−1.32288	+	2.29129i	−0.540062	+	0.935414i
$7$	3.64575			1.37796			0.688982	−	0.724778i	$-0.258058\pi$
$7$	3.64575			1.37796			0.688982	+	0.724778i	$0.258058\pi$
$8$	1.00000			0.353553
$9$	−2.00000	+	3.46410i	−0.666667	+	1.15470i
$10$	0.822876	−	1.42526i	0.260216	−	0.450708i
$11$	−4.64575			−1.40075			−0.700373	−	0.713777i	$-0.746983\pi$
$11$	−4.64575			−1.40075			−0.700373	+	0.713777i	$0.746983\pi$
$12$	2.64575			0.763763
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	−1.82288	−	3.15731i	−0.487184	−	0.843827i
$15$	2.17712	−	3.77089i	0.562131	−	0.973640i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	4.00000			0.942809
$19$	1.67712	+	4.02334i	0.384759	+	0.923017i
$19$	1.67712	+	4.02334i	0.384759	+	0.923017i
$20$	−1.64575			−0.368001
$21$	−4.82288	−	8.35347i	−1.05244	−	1.82288i
$22$	2.32288	+	4.02334i	0.495239	+	0.857779i
$23$	0.822876	−	1.42526i	0.171581	−	0.297188i	−0.767391	−	0.641179i	$-0.778446\pi$
$23$	0.822876	−	1.42526i	0.171581	−	0.297188i	0.938973	+	0.343991i	$0.111779\pi$
$24$	−1.32288	−	2.29129i	−0.270031	−	0.467707i
$25$	1.14575	−	1.98450i	0.229150	−	0.396900i
$26$	2.00000			0.392232
$27$	2.64575			0.509175
$28$	−1.82288	+	3.15731i	−0.344491	+	0.596676i
$29$	−0.822876	+	1.42526i	−0.152804	+	0.264665i	−0.932257	−	0.361796i	$-0.882164\pi$
$29$	−0.822876	+	1.42526i	−0.152804	+	0.264665i	0.779453	+	0.626461i	$0.215497\pi$
$30$	−4.35425			−0.794973
$31$	−5.64575			−1.01401			−0.507003	−	0.861944i	$-0.669247\pi$
$31$	−5.64575			−1.01401			−0.507003	+	0.861944i	$0.669247\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	6.14575	+	10.6448i	1.06984	+	1.85301i
$34$		0			0
$35$	3.00000	+	5.19615i	0.507093	+	0.878310i
$36$	−2.00000	−	3.46410i	−0.333333	−	0.577350i
$37$	0.354249			0.0582381			0.0291191	−	0.999576i	$-0.490730\pi$
$37$	0.354249			0.0582381			0.0291191	+	0.999576i	$0.490730\pi$
$38$	2.64575	−	3.46410i	0.429198	−	0.561951i
$39$	5.29150			0.847319
$40$	0.822876	+	1.42526i	0.130108	+	0.225354i
$41$	0.145751	+	0.252449i	0.0227625	+	0.0394259i	0.877182	−	0.480158i	$-0.159421\pi$
$41$	0.145751	+	0.252449i	0.0227625	+	0.0394259i	−0.854420	+	0.519583i	$0.826087\pi$
$42$	−4.82288	+	8.35347i	−0.744186	+	1.28897i
$43$	−5.64575	−	9.77873i	−0.860969	−	1.49124i	−0.870995	−	0.491292i	$-0.836525\pi$
$43$	−5.64575	−	9.77873i	−0.860969	−	1.49124i	0.0100257	−	0.999950i	$-0.496809\pi$
$44$	2.32288	−	4.02334i	0.350187	−	0.606541i
$45$	−6.58301			−0.981336
$46$	−1.64575			−0.242653
$47$	−2.17712	+	3.77089i	−0.317566	+	0.550041i	−0.979980	−	0.199098i	$-0.936199\pi$
$47$	−2.17712	+	3.77089i	−0.317566	+	0.550041i	0.662413	+	0.749138i	$0.269532\pi$
$48$	−1.32288	+	2.29129i	−0.190941	+	0.330719i
$49$	6.29150			0.898786
$50$	−2.29150			−0.324067
$51$		0			0
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	6.29150	−	10.8972i	0.864204	−	1.49685i	−0.00363070	−	0.999993i	$-0.501156\pi$
$53$	6.29150	−	10.8972i	0.864204	−	1.49685i	0.867835	−	0.496852i	$-0.165511\pi$
$54$	−1.32288	−	2.29129i	−0.180021	−	0.311805i
$55$	−3.82288	−	6.62141i	−0.515476	−	0.892831i
$56$	3.64575			0.487184
$57$	7.00000	−	9.16515i	0.927173	−	1.21395i
$58$	1.64575			0.216098
$59$	3.96863	+	6.87386i	0.516671	+	0.894901i	0.999813	+	0.0193585i	$0.00616237\pi$
$59$	3.96863	+	6.87386i	0.516671	+	0.894901i	−0.483141	+	0.875542i	$0.660504\pi$
$60$	2.17712	+	3.77089i	0.281066	+	0.486820i
$61$	−0.468627	+	0.811686i	−0.0600015	+	0.103926i	−0.894466	−	0.447136i	$-0.852444\pi$
$61$	−0.468627	+	0.811686i	−0.0600015	+	0.103926i	0.834464	+	0.551062i	$0.185777\pi$
$62$	2.82288	+	4.88936i	0.358506	+	0.620950i
$63$	−7.29150	+	12.6293i	−0.918643	+	1.59114i
$64$	1.00000			0.125000
$65$	−3.29150			−0.408261
$66$	6.14575	−	10.6448i	0.756490	−	1.31028i
$67$	−0.322876	+	0.559237i	−0.0394455	+	0.0683217i	−0.885074	−	0.465450i	$-0.845892\pi$
$67$	−0.322876	+	0.559237i	−0.0394455	+	0.0683217i	0.845629	+	0.533772i	$0.179226\pi$
$68$		0			0
$69$	−4.35425			−0.524190
$70$	3.00000	−	5.19615i	0.358569	−	0.621059i
$71$	1.35425	+	2.34563i	0.160720	+	0.278375i	0.935127	−	0.354313i	$-0.115285\pi$
$71$	1.35425	+	2.34563i	0.160720	+	0.278375i	−0.774407	+	0.632687i	$0.781952\pi$
$72$	−2.00000	+	3.46410i	−0.235702	+	0.408248i
$73$	−0.854249	−	1.47960i	−0.0999822	−	0.173174i	0.811695	−	0.584082i	$-0.198545\pi$
$73$	−0.854249	−	1.47960i	−0.0999822	−	0.173174i	−0.911677	+	0.410907i	$0.865212\pi$
$74$	−0.177124	−	0.306788i	−0.0205903	−	0.0356634i
$75$	−6.06275			−0.700066
$76$	−4.32288	−	0.559237i	−0.495868	−	0.0641489i
$77$	−16.9373			−1.93018
$78$	−2.64575	−	4.58258i	−0.299572	−	0.518875i
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$	0.822876	−	1.42526i	0.0920003	−	0.159349i
$81$	2.50000	+	4.33013i	0.277778	+	0.481125i
$82$	0.145751	−	0.252449i	0.0160955	−	0.0278783i
$83$	7.93725			0.871227			0.435613	−	0.900134i	$-0.356531\pi$
$83$	7.93725			0.871227			0.435613	+	0.900134i	$0.356531\pi$
$84$	9.64575			1.05244
$85$		0			0
$86$	−5.64575	+	9.77873i	−0.608797	+	1.05447i
$87$	4.35425			0.466824
$88$	−4.64575			−0.495239
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$	3.29150	+	5.70105i	0.346955	+	0.600943i
$91$	−3.64575	+	6.31463i	−0.382179	+	0.661953i
$92$	0.822876	+	1.42526i	0.0857907	+	0.148594i
$93$	7.46863	+	12.9360i	0.774461	+	1.34141i
$94$	4.35425			0.449106
$95$	−4.35425	+	5.70105i	−0.446736	+	0.584915i
$96$	2.64575			0.270031
$97$	1.85425	+	3.21165i	0.188270	+	0.326094i	0.944674	−	0.328012i	$-0.106379\pi$
$97$	1.85425	+	3.21165i	0.188270	+	0.326094i	−0.756403	+	0.654106i	$0.773045\pi$
$98$	−3.14575	−	5.44860i	−0.317769	−	0.550392i
$99$	9.29150	−	16.0934i	0.933831	−	1.61744i
$100$	1.14575	+	1.98450i	0.114575	+	0.198450i
$101$	6.82288	−	11.8176i	0.678902	−	1.17589i	−0.296411	−	0.955061i	$-0.595790\pi$
$101$	6.82288	−	11.8176i	0.678902	−	1.17589i	0.975312	−	0.220831i	$-0.0708770\pi$
$102$		0			0
$103$	−13.2915			−1.30965			−0.654825	−	0.755780i	$-0.727258\pi$
$103$	−13.2915			−1.30965			−0.654825	+	0.755780i	$0.727258\pi$
$104$	−1.00000	+	1.73205i	−0.0980581	+	0.169842i
$105$	7.93725	−	13.7477i	0.774597	−	1.34164i
$106$	−12.5830			−1.22217
$107$	15.2915			1.47829			0.739143	−	0.673549i	$-0.235231\pi$
$107$	15.2915			1.47829			0.739143	+	0.673549i	$0.235231\pi$
$108$	−1.32288	+	2.29129i	−0.127294	+	0.220479i
$109$	−7.29150	−	12.6293i	−0.698399	−	1.20966i	−0.969021	−	0.246977i	$-0.920563\pi$
$109$	−7.29150	−	12.6293i	−0.698399	−	1.20966i	0.270622	−	0.962686i	$-0.412771\pi$
$110$	−3.82288	+	6.62141i	−0.364497	+	0.631327i
$111$	−0.468627	−	0.811686i	−0.0444801	−	0.0770418i
$112$	−1.82288	−	3.15731i	−0.172246	−	0.298338i
$113$	−15.5830			−1.46593			−0.732963	−	0.680269i	$-0.761863\pi$
$113$	−15.5830			−1.46593			−0.732963	+	0.680269i	$0.761863\pi$
$114$	−11.4373	−	1.47960i	−1.07120	−	0.138577i
$115$	2.70850			0.252569
$116$	−0.822876	−	1.42526i	−0.0764021	−	0.132332i
$117$	−4.00000	−	6.92820i	−0.369800	−	0.640513i
$118$	3.96863	−	6.87386i	0.365342	−	0.632790i
$119$		0			0
$120$	2.17712	−	3.77089i	0.198743	−	0.344234i
$121$	10.5830			0.962091
$122$	0.937254			0.0848550
$123$	0.385622	−	0.667916i	0.0347703	−	0.0602240i
$124$	2.82288	−	4.88936i	0.253502	−	0.439078i
$125$	12.0000			1.07331
$126$	14.5830			1.29916
$127$	6.64575	−	11.5108i	0.589715	−	1.02142i	−0.404554	−	0.914514i	$-0.632573\pi$
$127$	6.64575	−	11.5108i	0.589715	−	1.02142i	0.994270	−	0.106903i	$-0.0340933\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−14.9373	+	25.8721i	−1.31515	+	2.27791i
$130$	1.64575	+	2.85052i	0.144342	+	0.250008i
$131$	−0.968627	−	1.67771i	−0.0846293	−	0.146582i	0.820604	−	0.571497i	$-0.193637\pi$
$131$	−0.968627	−	1.67771i	−0.0846293	−	0.146582i	−0.905233	+	0.424915i	$0.860304\pi$
$132$	−12.2915			−1.06984
$133$	6.11438	+	14.6681i	0.530184	+	1.27188i
$134$	0.645751			0.0557844
$135$	2.17712	+	3.77089i	0.187377	+	0.324547i
$136$		0			0
$137$	−7.79150	+	13.4953i	−0.665673	+	1.15298i	0.313429	+	0.949612i	$0.398522\pi$
$137$	−7.79150	+	13.4953i	−0.665673	+	1.15298i	−0.979102	+	0.203368i	$0.934811\pi$
$138$	2.17712	+	3.77089i	0.185329	+	0.320999i
$139$	−9.32288	+	16.1477i	−0.790756	+	1.36963i	0.134743	+	0.990881i	$0.456979\pi$
$139$	−9.32288	+	16.1477i	−0.790756	+	1.36963i	−0.925499	+	0.378749i	$0.876354\pi$
$140$	−6.00000			−0.507093
$141$	11.5203			0.970181
$142$	1.35425	−	2.34563i	0.113646	−	0.196841i
$143$	4.64575	−	8.04668i	0.388497	−	0.672897i
$144$	4.00000			0.333333
$145$	−2.70850			−0.224928
$146$	−0.854249	+	1.47960i	−0.0706981	+	0.122453i
$147$	−8.32288	−	14.4156i	−0.686459	−	1.18898i
$148$	−0.177124	+	0.306788i	−0.0145595	+	0.0252178i
$149$	−5.46863	−	9.47194i	−0.448007	−	0.775972i	0.550249	−	0.835001i	$-0.314533\pi$
$149$	−5.46863	−	9.47194i	−0.448007	−	0.775972i	−0.998256	+	0.0590292i	$0.981200\pi$
$150$	3.03137	+	5.25049i	0.247511	+	0.428701i
$151$	12.9373			1.05282			0.526409	−	0.850231i	$-0.323538\pi$
$151$	12.9373			1.05282			0.526409	+	0.850231i	$0.323538\pi$
$152$	1.67712	+	4.02334i	0.136033	+	0.326336i
$153$		0			0
$154$	8.46863	+	14.6681i	0.682421	+	1.18199i
$155$	−4.64575	−	8.04668i	−0.373156	−	0.646325i
$156$	−2.64575	+	4.58258i	−0.211830	+	0.366900i
$157$	5.29150	+	9.16515i	0.422308	+	0.731459i	0.996165	−	0.0874969i	$-0.0278868\pi$
$157$	5.29150	+	9.16515i	0.422308	+	0.731459i	−0.573857	+	0.818956i	$0.694553\pi$
$158$	2.00000	−	3.46410i	0.159111	−	0.275589i
$159$	−33.2915			−2.64019
$160$	−1.64575			−0.130108
$161$	3.00000	−	5.19615i	0.236433	−	0.409514i
$162$	2.50000	−	4.33013i	0.196419	−	0.340207i
$163$	3.93725			0.308390			0.154195	−	0.988040i	$-0.450722\pi$
$163$	3.93725			0.308390			0.154195	+	0.988040i	$0.450722\pi$
$164$	−0.291503			−0.0227625
$165$	−10.1144	+	17.5186i	−0.787403	+	1.36382i
$166$	−3.96863	−	6.87386i	−0.308025	−	0.533515i
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	−0.534875	−	0.844931i	$-0.679641\pi$
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	0.999169	+	0.0407502i	$0.0129748\pi$
$168$	−4.82288	−	8.35347i	−0.372093	−	0.644484i
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$	−17.2915	−	2.23695i	−1.32231	−	0.171064i
$172$	11.2915			0.860969
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$	−2.17712	−	3.77089i	−0.165047	−	0.285870i
$175$	4.17712	−	7.23499i	0.315761	−	0.546914i
$176$	2.32288	+	4.02334i	0.175093	+	0.303271i
$177$	10.5000	−	18.1865i	0.789228	−	1.36698i
$178$		0			0
$179$	4.06275			0.303664			0.151832	−	0.988406i	$-0.451483\pi$
$179$	4.06275			0.303664			0.151832	+	0.988406i	$0.451483\pi$
$180$	3.29150	−	5.70105i	0.245334	−	0.424931i
$181$	−11.1144	+	19.2507i	−0.826125	+	1.43089i	0.0749311	+	0.997189i	$0.476126\pi$
$181$	−11.1144	+	19.2507i	−0.826125	+	1.43089i	−0.901056	+	0.433702i	$0.857207\pi$
$182$	7.29150			0.540482
$183$	2.47974			0.183308
$184$	0.822876	−	1.42526i	0.0606632	−	0.105072i
$185$	0.291503	+	0.504897i	0.0214317	+	0.0371208i
$186$	7.46863	−	12.9360i	0.547626	−	0.948517i
$187$		0			0
$188$	−2.17712	−	3.77089i	−0.158783	−	0.275020i
$189$	9.64575			0.701625
$190$	7.11438	+	0.920365i	0.516131	+	0.0667703i
$191$	6.58301			0.476330			0.238165	−	0.971225i	$-0.423454\pi$
$191$	6.58301			0.476330			0.238165	+	0.971225i	$0.423454\pi$
$192$	−1.32288	−	2.29129i	−0.0954703	−	0.165359i
$193$	−7.29150	−	12.6293i	−0.524854	−	0.909074i	−0.999581	−	0.0289406i	$-0.990787\pi$
$193$	−7.29150	−	12.6293i	−0.524854	−	0.909074i	0.474727	−	0.880133i	$-0.342547\pi$
$194$	1.85425	−	3.21165i	0.133127	−	0.230583i
$195$	4.35425	+	7.54178i	0.311814	+	0.540078i
$196$	−3.14575	+	5.44860i	−0.224697	+	0.389186i
$197$	−7.64575			−0.544737			−0.272369	−	0.962193i	$-0.587807\pi$
$197$	−7.64575			−0.544737			−0.272369	+	0.962193i	$0.587807\pi$
$198$	−18.5830			−1.32064
$199$	9.93725	−	17.2118i	0.704433	−	1.22011i	−0.262462	−	0.964942i	$-0.584535\pi$
$199$	9.93725	−	17.2118i	0.704433	−	1.22011i	0.966896	−	0.255172i	$-0.0821321\pi$
$200$	1.14575	−	1.98450i	0.0810169	−	0.140325i
$201$	1.70850			0.120508
$202$	−13.6458			−0.960112
$203$	−3.00000	+	5.19615i	−0.210559	+	0.364698i
$204$		0			0
$205$	−0.239870	+	0.415468i	−0.0167533	+	0.0290175i
$206$	6.64575	+	11.5108i	0.463031	+	0.801994i
$207$	3.29150	+	5.70105i	0.228775	+	0.396250i
$208$	2.00000			0.138675
$209$	−7.79150	−	18.6914i	−0.538950	−	1.29291i
$210$	−15.8745			−1.09545
$211$	6.64575	+	11.5108i	0.457512	+	0.792435i	0.998829	−	0.0483843i	$-0.0154072\pi$
$211$	6.64575	+	11.5108i	0.457512	+	0.792435i	−0.541316	+	0.840819i	$0.682074\pi$
$212$	6.29150	+	10.8972i	0.432102	+	0.748423i
$213$	3.58301	−	6.20595i	0.245503	−	0.425224i
$214$	−7.64575	−	13.2428i	−0.522653	−	0.905261i
$215$	9.29150	−	16.0934i	0.633675	−	1.09756i
$216$	2.64575			0.180021
$217$	−20.5830			−1.39727
$218$	−7.29150	+	12.6293i	−0.493843	+	0.855361i
$219$	−2.26013	+	3.91466i	−0.152725	+	0.264528i
$220$	7.64575			0.515476
$221$		0			0
$222$	−0.468627	+	0.811686i	−0.0314522	+	0.0544768i
$223$	9.40588	+	16.2915i	0.629864	+	1.09096i	0.987579	+	0.157126i	$0.0502229\pi$
$223$	9.40588	+	16.2915i	0.629864	+	1.09096i	−0.357714	+	0.933831i	$0.616444\pi$
$224$	−1.82288	+	3.15731i	−0.121796	+	0.210957i
$225$	4.58301	+	7.93800i	0.305534	+	0.529200i
$226$	7.79150	+	13.4953i	0.518283	+	0.897693i
$227$	−7.35425			−0.488119			−0.244059	−	0.969760i	$-0.578479\pi$
$227$	−7.35425			−0.488119			−0.244059	+	0.969760i	$0.578479\pi$
$228$	4.43725	+	10.6448i	0.293864	+	0.704966i
$229$	20.0000			1.32164			0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000			1.32164			0.660819	+	0.750546i	$0.270209\pi$
$230$	−1.35425	−	2.34563i	−0.0892965	−	0.154666i
$231$	22.4059	+	38.8081i	1.47420	+	2.55339i
$232$	−0.822876	+	1.42526i	−0.0540244	+	0.0935731i
$233$	−9.43725	−	16.3458i	−0.618255	−	1.07085i	−0.989804	−	0.142436i	$-0.954507\pi$
$233$	−9.43725	−	16.3458i	−0.618255	−	1.07085i	0.371549	−	0.928413i	$-0.378827\pi$
$234$	−4.00000	+	6.92820i	−0.261488	+	0.452911i
$235$	−7.16601			−0.467459
$236$	−7.93725			−0.516671
$237$	5.29150	−	9.16515i	0.343720	−	0.595341i
$238$		0			0
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$	−4.35425			−0.281066
$241$	3.79150	−	6.56708i	0.244232	−	0.423022i	−0.717683	−	0.696370i	$-0.754797\pi$
$241$	3.79150	−	6.56708i	0.244232	−	0.423022i	0.961915	+	0.273347i	$0.0881308\pi$
$242$	−5.29150	−	9.16515i	−0.340151	−	0.589158i
$243$	10.5830	−	18.3303i	0.678900	−	1.17589i
$244$	−0.468627	−	0.811686i	−0.0300008	−	0.0519629i
$245$	5.17712	+	8.96704i	0.330754	+	0.572883i
$246$	−0.771243			−0.0491727
$247$	−8.64575	−	1.11847i	−0.550116	−	0.0711668i
$248$	−5.64575			−0.358506
$249$	−10.5000	−	18.1865i	−0.665410	−	1.15252i
$250$	−6.00000	−	10.3923i	−0.379473	−	0.657267i
$251$	−14.6144	+	25.3128i	−0.922451	+	1.59773i	−0.126842	+	0.991923i	$0.540484\pi$
$251$	−14.6144	+	25.3128i	−0.922451	+	1.59773i	−0.795610	+	0.605810i	$0.792849\pi$
$252$	−7.29150	−	12.6293i	−0.459321	−	0.795568i
$253$	−3.82288	+	6.62141i	−0.240342	+	0.416285i
$254$	−13.2915			−0.833983
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.14575	+	10.6448i	−0.383361	+	0.664001i	−0.991540	−	0.129798i	$-0.958567\pi$
$257$	−6.14575	+	10.6448i	−0.383361	+	0.664001i	0.608179	+	0.793800i	$0.291900\pi$
$258$	29.8745			1.85991
$259$	1.29150			0.0802501
$260$	1.64575	−	2.85052i	0.102065	−	0.176782i
$261$	−3.29150	−	5.70105i	−0.203739	−	0.352886i
$262$	−0.968627	+	1.67771i	−0.0598420	+	0.103649i
$263$	5.46863	+	9.47194i	0.337210	+	0.584065i	0.983907	−	0.178682i	$-0.0571834\pi$
$263$	5.46863	+	9.47194i	0.337210	+	0.584065i	−0.646697	+	0.762747i	$0.723850\pi$
$264$	6.14575	+	10.6448i	0.378245	+	0.655139i
$265$	20.7085			1.27211
$266$	9.64575	−	12.6293i	0.591419	−	0.774349i
$267$		0			0
$268$	−0.322876	−	0.559237i	−0.0197228	−	0.0341608i
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$	2.17712	−	3.77089i	0.132496	−	0.229489i
$271$	−6.17712	−	10.6991i	−0.375234	−	0.649924i	0.615128	−	0.788427i	$-0.289104\pi$
$271$	−6.17712	−	10.6991i	−0.375234	−	0.649924i	−0.990362	+	0.138503i	$0.955771\pi$
$272$		0			0
$273$	19.2915			1.16757
$274$	15.5830			0.941404
$275$	−5.32288	+	9.21949i	−0.320981	+	0.555956i
$276$	2.17712	−	3.77089i	0.131047	−	0.226981i
$277$	−27.5203			−1.65353			−0.826766	−	0.562546i	$-0.809822\pi$
$277$	−27.5203			−1.65353			−0.826766	+	0.562546i	$0.809822\pi$
$278$	18.6458			1.11830
$279$	11.2915	−	19.5575i	0.676005	−	1.17087i
$280$	3.00000	+	5.19615i	0.179284	+	0.310530i
$281$	−12.7288	+	22.0469i	−0.759334	+	1.31520i	0.183857	+	0.982953i	$0.441142\pi$
$281$	−12.7288	+	22.0469i	−0.759334	+	1.31520i	−0.943191	+	0.332252i	$0.892192\pi$
$282$	−5.76013	−	9.97684i	−0.343011	−	0.594112i
$283$	−15.3229	−	26.5400i	−0.910850	−	1.57764i	−0.812866	−	0.582451i	$-0.802094\pi$
$283$	−15.3229	−	26.5400i	−0.910850	−	1.57764i	−0.0979848	−	0.995188i	$-0.531240\pi$
$284$	−2.70850			−0.160720
$285$	18.8229	+	2.43506i	1.11497	+	0.144240i
$286$	−9.29150			−0.549418
$287$	0.531373	+	0.920365i	0.0313660	+	0.0543274i
$288$	−2.00000	−	3.46410i	−0.117851	−	0.204124i
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	1.35425	+	2.34563i	0.0795242	+	0.137740i
$291$	4.90588	−	8.49723i	0.287588	−	0.498117i
$292$	1.70850			0.0999822
$293$	28.9373			1.69053			0.845266	−	0.534345i	$-0.179442\pi$
$293$	28.9373			1.69053			0.845266	+	0.534345i	$0.179442\pi$
$294$	−8.32288	+	14.4156i	−0.485400	+	0.840737i
$295$	−6.53137	+	11.3127i	−0.380271	+	0.658649i
$296$	0.354249			0.0205903
$297$	−12.2915			−0.713225
$298$	−5.46863	+	9.47194i	−0.316789	+	0.548695i
$299$	1.64575	+	2.85052i	0.0951763	+	0.164850i
$300$	3.03137	−	5.25049i	0.175016	−	0.303137i
$301$	−20.5830	−	35.6508i	−1.18638	−	2.05488i
$302$	−6.46863	−	11.2040i	−0.372228	−	0.644717i
$303$	−36.1033			−2.07408
$304$	2.64575	−	3.46410i	0.151744	−	0.198680i
$305$	−1.54249			−0.0883225
$306$		0			0
$307$	−0.322876	−	0.559237i	−0.0184275	−	0.0319173i	0.856665	−	0.515874i	$-0.172533\pi$
$307$	−0.322876	−	0.559237i	−0.0184275	−	0.0319173i	−0.875092	+	0.483956i	$0.839199\pi$
$308$	8.46863	−	14.6681i	0.482545	−	0.835792i
$309$	17.5830	+	30.4547i	1.00026	+	1.73250i
$310$	−4.64575	+	8.04668i	−0.263861	+	0.457021i
$311$	13.6458			0.773780			0.386890	−	0.922126i	$-0.373549\pi$
$311$	13.6458			0.773780			0.386890	+	0.922126i	$0.373549\pi$
$312$	5.29150			0.299572
$313$	−4.43725	+	7.68555i	−0.250808	+	0.434413i	−0.963749	−	0.266812i	$-0.914030\pi$
$313$	−4.43725	+	7.68555i	−0.250808	+	0.434413i	0.712940	+	0.701225i	$0.247363\pi$
$314$	5.29150	−	9.16515i	0.298617	−	0.517219i
$315$	−24.0000			−1.35225
$316$	−4.00000			−0.225018
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	−0.769395	−	0.638774i	$-0.779442\pi$
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	0.937892	+	0.346929i	$0.112775\pi$
$318$	16.6458	+	28.8313i	0.933447	+	1.61678i
$319$	3.82288	−	6.62141i	0.214040	−	0.370728i
$320$	0.822876	+	1.42526i	0.0460001	+	0.0796746i
$321$	−20.2288	−	35.0372i	−1.12906	−	1.95559i
$322$	−6.00000			−0.334367
$323$		0			0
$324$	−5.00000			−0.277778
$325$	2.29150	+	3.96900i	0.127110	+	0.220160i
$326$	−1.96863	−	3.40976i	−0.109032	−	0.188849i
$327$	−19.2915	+	33.4139i	−1.06682	+	1.84779i
$328$	0.145751	+	0.252449i	0.00804777	+	0.0139391i
$329$	−7.93725	+	13.7477i	−0.437595	+	0.757937i
$330$	20.2288			1.11356
$331$	19.8118			1.08895			0.544476	−	0.838776i	$-0.316728\pi$
$331$	19.8118			1.08895			0.544476	+	0.838776i	$0.316728\pi$
$332$	−3.96863	+	6.87386i	−0.217807	+	0.377252i
$333$	−0.708497	+	1.22715i	−0.0388254	+	0.0672476i
$334$	−12.0000			−0.656611
$335$	−1.06275			−0.0580640
$336$	−4.82288	+	8.35347i	−0.263109	+	0.455719i
$337$	4.85425	+	8.40781i	0.264428	+	0.458002i	0.967414	−	0.253202i	$-0.0814836\pi$
$337$	4.85425	+	8.40781i	0.264428	+	0.458002i	−0.702986	+	0.711204i	$0.748150\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$	20.6144	+	35.7052i	1.11962	+	1.93924i
$340$		0			0
$341$	26.2288			1.42037
$342$	6.70850	+	16.0934i	0.362754	+	0.870229i
$343$	−2.58301			−0.139469
$344$	−5.64575	−	9.77873i	−0.304399	−	0.527234i
$345$	−3.58301	−	6.20595i	−0.192903	−	0.334117i
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	11.6144	+	20.1167i	0.623492	+	1.07992i	0.988830	+	0.149046i	$0.0476201\pi$
$347$	11.6144	+	20.1167i	0.623492	+	1.07992i	−0.365338	+	0.930875i	$0.619047\pi$
$348$	−2.17712	+	3.77089i	−0.116706	+	0.202141i
$349$	21.1660			1.13299			0.566495	−	0.824065i	$-0.308299\pi$
$349$	21.1660			1.13299			0.566495	+	0.824065i	$0.308299\pi$
$350$	−8.35425			−0.446553
$351$	−2.64575	+	4.58258i	−0.141220	+	0.244600i
$352$	2.32288	−	4.02334i	0.123810	−	0.214445i
$353$	12.8745			0.685241			0.342620	−	0.939474i	$-0.388686\pi$
$353$	12.8745			0.685241			0.342620	+	0.939474i	$0.388686\pi$
$354$	−21.0000			−1.11614
$355$	−2.22876	+	3.86032i	−0.118290	+	0.204884i
$356$		0			0
$357$		0			0
$358$	−2.03137	−	3.51844i	−0.107361	−	0.185955i
$359$	2.46863	+	4.27579i	0.130289	+	0.225667i	0.923788	−	0.382904i	$-0.125076\pi$
$359$	2.46863	+	4.27579i	0.130289	+	0.225667i	−0.793499	+	0.608572i	$0.791743\pi$
$360$	−6.58301			−0.346955
$361$	−13.3745	+	13.4953i	−0.703921	+	0.710278i
$362$	22.2288			1.16832
$363$	−14.0000	−	24.2487i	−0.734809	−	1.27273i
$364$	−3.64575	−	6.31463i	−0.191089	−	0.330976i
$365$	1.40588	−	2.43506i	0.0735872	−	0.127457i
$366$	−1.23987	−	2.14752i	−0.0648091	−	0.112253i
$367$	−8.11438	+	14.0545i	−0.423567	+	0.733640i	−0.996285	−	0.0861125i	$-0.972556\pi$
$367$	−8.11438	+	14.0545i	−0.423567	+	0.733640i	0.572718	+	0.819752i	$0.305889\pi$
$368$	−1.64575			−0.0857907
$369$	−1.16601			−0.0607001
$370$	0.291503	−	0.504897i	0.0151545	−	0.0262484i
$371$	22.9373	−	39.7285i	1.19084	−	2.06260i
$372$	−14.9373			−0.774461
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$		0			0
$375$	−15.8745	−	27.4955i	−0.819756	−	1.41986i
$376$	−2.17712	+	3.77089i	−0.112277	+	0.194469i
$377$	−1.64575	−	2.85052i	−0.0847605	−	0.146810i
$378$	−4.82288	−	8.35347i	−0.248062	−	0.429656i
$379$	10.7085			0.550059			0.275029	−	0.961436i	$-0.411312\pi$
$379$	10.7085			0.550059			0.275029	+	0.961436i	$0.411312\pi$
$380$	−2.76013	−	6.62141i	−0.141592	−	0.339671i
$381$	−35.1660			−1.80161
$382$	−3.29150	−	5.70105i	−0.168408	−	0.291691i
$383$	−2.76013	−	4.78068i	−0.141036	−	0.244282i	0.786851	−	0.617143i	$-0.211710\pi$
$383$	−2.76013	−	4.78068i	−0.141036	−	0.244282i	−0.927887	+	0.372861i	$0.878377\pi$
$384$	−1.32288	+	2.29129i	−0.0675077	+	0.116927i
$385$	−13.9373	−	24.1400i	−0.710308	−	1.23029i
$386$	−7.29150	+	12.6293i	−0.371128	+	0.642812i
$387$	45.1660			2.29592
$388$	−3.70850			−0.188270
$389$	−6.00000	+	10.3923i	−0.304212	+	0.526911i	−0.977086	−	0.212847i	$-0.931726\pi$
$389$	−6.00000	+	10.3923i	−0.304212	+	0.526911i	0.672874	+	0.739758i	$0.265060\pi$
$390$	4.35425	−	7.54178i	0.220486	−	0.381893i
$391$		0			0
$392$	6.29150			0.317769
$393$	−2.56275	+	4.43881i	−0.129273	+	0.223908i
$394$	3.82288	+	6.62141i	0.192594	+	0.333582i
$395$	−3.29150	+	5.70105i	−0.165613	+	0.286851i
$396$	9.29150	+	16.0934i	0.466916	+	0.808721i
$397$	−10.5314	−	18.2409i	−0.528554	−	0.915483i	−0.999446	−	0.0332919i	$-0.989401\pi$
$397$	−10.5314	−	18.2409i	−0.528554	−	0.915483i	0.470891	−	0.882191i	$-0.343932\pi$
$398$	−19.8745			−0.996219
$399$	25.5203	−	33.4139i	1.27761	−	1.67279i
$400$	−2.29150			−0.114575
$401$	−13.7915	−	23.8876i	−0.688715	−	1.19289i	−0.972254	−	0.233928i	$-0.924842\pi$
$401$	−13.7915	−	23.8876i	−0.688715	−	1.19289i	0.283539	−	0.958961i	$-0.408491\pi$
$402$	−0.854249	−	1.47960i	−0.0426061	−	0.0737958i
$403$	5.64575	−	9.77873i	0.281235	−	0.487113i
$404$	6.82288	+	11.8176i	0.339451	+	0.587946i
$405$	−4.11438	+	7.12631i	−0.204445	+	0.354109i
$406$	6.00000			0.297775
$407$	−1.64575			−0.0815769
$408$		0			0
$409$	3.79150	−	6.56708i	0.187478	−	0.324721i	−0.756931	−	0.653495i	$-0.773302\pi$
$409$	3.79150	−	6.56708i	0.187478	−	0.324721i	0.944409	+	0.328774i	$0.106635\pi$
$410$	0.479741			0.0236927
$411$	41.2288			2.03366
$412$	6.64575	−	11.5108i	0.327413	−	0.567095i
$413$	14.4686	+	25.0604i	0.711955	+	1.23314i
$414$	3.29150	−	5.70105i	0.161769	−	0.280191i
$415$	6.53137	+	11.3127i	0.320612	+	0.555317i
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$	49.3320			2.41580
$418$	−12.2915	+	16.0934i	−0.601197	+	0.787152i
$419$	−31.7490			−1.55104			−0.775520	−	0.631322i	$-0.782512\pi$
$419$	−31.7490			−1.55104			−0.775520	+	0.631322i	$0.782512\pi$
$420$	7.93725	+	13.7477i	0.387298	+	0.670820i
$421$	12.4059	+	21.4876i	0.604626	+	1.04724i	0.992111	+	0.125366i	$0.0400106\pi$
$421$	12.4059	+	21.4876i	0.604626	+	1.04724i	−0.387485	+	0.921876i	$0.626656\pi$
$422$	6.64575	−	11.5108i	0.323510	−	0.560336i
$423$	−8.70850	−	15.0836i	−0.423422	−	0.733388i
$424$	6.29150	−	10.8972i	0.305542	−	0.529215i
$425$		0			0
$426$	−7.16601			−0.347194
$427$	−1.70850	+	2.95920i	−0.0826800	+	0.143206i
$428$	−7.64575	+	13.2428i	−0.369571	+	0.640116i
$429$	−24.5830			−1.18688
$430$	−18.5830			−0.896152
$431$	−13.9373	+	24.1400i	−0.671334	+	1.16278i	0.306192	+	0.951970i	$0.400945\pi$
$431$	−13.9373	+	24.1400i	−0.671334	+	1.16278i	−0.977526	+	0.210815i	$0.932388\pi$
$432$	−1.32288	−	2.29129i	−0.0636469	−	0.110240i
$433$	−8.93725	+	15.4798i	−0.429497	+	0.743911i	−0.996829	−	0.0795788i	$-0.974642\pi$
$433$	−8.93725	+	15.4798i	−0.429497	+	0.743911i	0.567332	+	0.823489i	$0.307976\pi$
$434$	10.2915	+	17.8254i	0.494008	+	0.855647i
$435$	3.58301	+	6.20595i	0.171792	+	0.297552i
$436$	14.5830			0.698399
$437$	7.11438	+	0.920365i	0.340327	+	0.0440270i
$438$	4.52026			0.215986
$439$	−5.40588	−	9.36326i	−0.258009	−	0.446884i	0.707700	−	0.706513i	$-0.249733\pi$
$439$	−5.40588	−	9.36326i	−0.258009	−	0.446884i	−0.965708	+	0.259629i	$0.916400\pi$
$440$	−3.82288	−	6.62141i	−0.182248	−	0.315664i
$441$	−12.5830	+	21.7944i	−0.599191	+	1.03783i
$442$		0			0
$443$	−5.32288	+	9.21949i	−0.252897	+	0.438031i	−0.964322	−	0.264731i	$-0.914717\pi$
$443$	−5.32288	+	9.21949i	−0.252897	+	0.438031i	0.711425	+	0.702762i	$0.248050\pi$
$444$	0.937254			0.0444801
$445$		0			0
$446$	9.40588	−	16.2915i	0.445381	−	0.771423i
$447$	−14.4686	+	25.0604i	−0.684343	+	1.18532i
$448$	3.64575			0.172246
$449$	−24.2915			−1.14639			−0.573193	−	0.819420i	$-0.694296\pi$
$449$	−24.2915			−1.14639			−0.573193	+	0.819420i	$0.694296\pi$
$450$	4.58301	−	7.93800i	0.216045	−	0.374201i
$451$	−0.677124	−	1.17281i	−0.0318845	−	0.0552256i
$452$	7.79150	−	13.4953i	0.366481	−	0.634765i
$453$	−17.1144	−	29.6430i	−0.804104	−	1.39275i
$454$	3.67712	+	6.36897i	0.172576	+	0.298910i
$455$	−12.0000			−0.562569
$456$	7.00000	−	9.16515i	0.327805	−	0.429198i
$457$	32.8745			1.53780			0.768902	−	0.639366i	$-0.220803\pi$
$457$	32.8745			1.53780			0.768902	+	0.639366i	$0.220803\pi$
$458$	−10.0000	−	17.3205i	−0.467269	−	0.809334i
$459$		0			0
$460$	−1.35425	+	2.34563i	−0.0631422	+	0.109365i
$461$	−9.58301	−	16.5983i	−0.446325	−	0.773058i	0.551818	−	0.833964i	$-0.313934\pi$
$461$	−9.58301	−	16.5983i	−0.446325	−	0.773058i	−0.998143	+	0.0609066i	$0.980601\pi$
$462$	22.4059	−	38.8081i	1.04242	−	1.80552i
$463$	−38.4575			−1.78727			−0.893636	−	0.448792i	$-0.851854\pi$
$463$	−38.4575			−1.78727			−0.893636	+	0.448792i	$0.851854\pi$
$464$	1.64575			0.0764021
$465$	−12.2915	+	21.2895i	−0.570005	+	0.987277i
$466$	−9.43725	+	16.3458i	−0.437172	+	0.757205i
$467$	−19.3542			−0.895608			−0.447804	−	0.894132i	$-0.647794\pi$
$467$	−19.3542			−0.895608			−0.447804	+	0.894132i	$0.647794\pi$
$468$	8.00000			0.369800
$469$	−1.17712	+	2.03884i	−0.0543546	+	0.0941448i
$470$	3.58301	+	6.20595i	0.165272	+	0.286259i
$471$	14.0000	−	24.2487i	0.645086	−	1.11732i
$472$	3.96863	+	6.87386i	0.182671	+	0.316395i
$473$	26.2288	+	45.4295i	1.20600	+	2.08885i
$474$	−10.5830			−0.486094
$475$	9.90588	+	1.28149i	0.454513	+	0.0587989i
$476$		0			0
$477$	25.1660	+	43.5888i	1.15227	+	1.99579i
$478$	6.00000	+	10.3923i	0.274434	+	0.475333i
$479$	−3.29150	+	5.70105i	−0.150393	+	0.260488i	−0.931372	−	0.364069i	$-0.881387\pi$
$479$	−3.29150	+	5.70105i	−0.150393	+	0.260488i	0.780979	+	0.624557i	$0.214720\pi$
$480$	2.17712	+	3.77089i	0.0993717	+	0.172117i
$481$	−0.354249	+	0.613577i	−0.0161523	+	0.0279767i
$482$	−7.58301			−0.345396
$483$	−15.8745			−0.722315
$484$	−5.29150	+	9.16515i	−0.240523	+	0.416598i
$485$	−3.05163	+	5.28558i	−0.138567	+	0.240006i
$486$	−21.1660			−0.960110
$487$	4.22876			0.191623			0.0958116	−	0.995399i	$-0.469455\pi$
$487$	4.22876			0.191623			0.0958116	+	0.995399i	$0.469455\pi$
$488$	−0.468627	+	0.811686i	−0.0212137	+	0.0367433i
$489$	−5.20850	−	9.02138i	−0.235536	−	0.407961i
$490$	5.17712	−	8.96704i	0.233879	−	0.405090i
$491$	−19.6458	−	34.0274i	−0.886600	−	1.53564i	−0.843868	−	0.536550i	$-0.819727\pi$
$491$	−19.6458	−	34.0274i	−0.886600	−	1.53564i	−0.0427320	−	0.999087i	$-0.513606\pi$
$492$	0.385622	+	0.667916i	0.0173852	+	0.0301120i
$493$		0			0
$494$	3.35425	+	8.04668i	0.150915	+	0.362037i
$495$	30.5830			1.37460
$496$	2.82288	+	4.88936i	0.126751	+	0.219539i
$497$	4.93725	+	8.55157i	0.221466	+	0.383591i
$498$	−10.5000	+	18.1865i	−0.470516	+	0.814958i
$499$	2.38562	+	4.13202i	0.106795	+	0.184975i	0.914470	−	0.404653i	$-0.132608\pi$
$499$	2.38562	+	4.13202i	0.106795	+	0.184975i	−0.807675	+	0.589628i	$0.799274\pi$
$500$	−6.00000	+	10.3923i	−0.268328	+	0.464758i
$501$	−31.7490			−1.41844
$502$	29.2288			1.30454
$503$	20.4686	−	35.4527i	0.912651	−	1.58076i	0.102346	−	0.994749i	$-0.467365\pi$
$503$	20.4686	−	35.4527i	0.912651	−	1.58076i	0.810305	−	0.586009i	$-0.199302\pi$
$504$	−7.29150	+	12.6293i	−0.324789	+	0.562552i
$505$	22.4575			0.999346
$506$	7.64575			0.339895
$507$	11.9059	−	20.6216i	0.528759	−	0.915837i
$508$	6.64575	+	11.5108i	0.294858	+	0.510708i
$509$	15.8745	−	27.4955i	0.703625	−	1.21871i	−0.263560	−	0.964643i	$-0.584897\pi$
$509$	15.8745	−	27.4955i	0.703625	−	1.21871i	0.967185	−	0.254072i	$-0.0817699\pi$
$510$		0			0
$511$	−3.11438	−	5.39426i	−0.137772	−	0.238628i
$512$	1.00000			0.0441942
$513$	4.43725	+	10.6448i	0.195910	+	0.469977i
$514$	12.2915			0.542155
$515$	−10.9373	−	18.9439i	−0.481953	−	0.834767i
$516$	−14.9373	−	25.8721i	−0.657576	−	1.13895i
$517$	10.1144	−	17.5186i	0.444830	−	0.770468i
$518$	−0.645751	−	1.11847i	−0.0283727	−	0.0491429i
$519$	7.93725	−	13.7477i	0.348407	−	0.603458i
$520$	−3.29150			−0.144342
$521$	−11.7085			−0.512959			−0.256479	−	0.966550i	$-0.582563\pi$
$521$	−11.7085			−0.512959			−0.256479	+	0.966550i	$0.582563\pi$
$522$	−3.29150	+	5.70105i	−0.144065	+	0.249528i
$523$	0.937254	−	1.62337i	0.0409833	−	0.0709851i	−0.844806	−	0.535072i	$-0.820284\pi$
$523$	0.937254	−	1.62337i	0.0409833	−	0.0709851i	0.885789	+	0.464087i	$0.153618\pi$
$524$	1.93725			0.0846293
$525$	−22.1033			−0.964666
$526$	5.46863	−	9.47194i	0.238443	−	0.412996i
$527$		0			0
$528$	6.14575	−	10.6448i	0.267459	−	0.463253i
$529$	10.1458	+	17.5730i	0.441120	+	0.764042i
$530$	−10.3542	−	17.9341i	−0.449760	−	0.779007i
$531$	−31.7490			−1.37779
$532$	−15.7601	−	2.03884i	−0.683288	−	0.0883949i
$533$	−0.583005			−0.0252528
$534$		0			0
$535$	12.5830	+	21.7944i	0.544011	+	0.942254i
$536$	−0.322876	+	0.559237i	−0.0139461	+	0.0241554i
$537$	−5.37451	−	9.30892i	−0.231927	−	0.401710i
$538$		0			0
$539$	−29.2288			−1.25897
$540$	−4.35425			−0.187377
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	−0.939110	−	0.343617i	$-0.888348\pi$
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	0.767136	+	0.641484i	$0.221681\pi$
$542$	−6.17712	+	10.6991i	−0.265330	+	0.459565i
$543$	58.8118			2.52385
$544$		0			0
$545$	12.0000	−	20.7846i	0.514024	−	0.890315i
$546$	−9.64575	−	16.7069i	−0.412800	−	0.714991i
$547$	−5.64575	+	9.77873i	−0.241395	+	0.418108i	−0.961112	−	0.276159i	$-0.910938\pi$
$547$	−5.64575	+	9.77873i	−0.241395	+	0.418108i	0.719717	+	0.694268i	$0.244272\pi$
$548$	−7.79150	−	13.4953i	−0.332836	−	0.576490i
$549$	−1.87451	−	3.24674i	−0.0800020	−	0.138568i
$550$	10.6458			0.453936
$551$	−7.11438	−	0.920365i	−0.303083	−	0.0392089i
$552$	−4.35425			−0.185329
$553$	7.29150	+	12.6293i	0.310066	+	0.537050i
$554$	13.7601	+	23.8332i	0.584612	+	1.01258i
$555$	0.771243	−	1.33583i	0.0327375	−	0.0567029i
$556$	−9.32288	−	16.1477i	−0.395378	−	0.684815i
$557$	2.70850	−	4.69126i	0.114763	−	0.198775i	−0.802922	−	0.596084i	$-0.796723\pi$
$557$	2.70850	−	4.69126i	0.114763	−	0.198775i	0.917685	+	0.397309i	$0.130056\pi$
$558$	−22.5830			−0.956015
$559$	22.5830			0.955159
$560$	3.00000	−	5.19615i	0.126773	−	0.219578i
$561$		0			0
$562$	25.4575			1.07386
$563$	10.0627			0.424094			0.212047	−	0.977259i	$-0.431987\pi$
$563$	10.0627			0.424094			0.212047	+	0.977259i	$0.431987\pi$
$564$	−5.76013	+	9.97684i	−0.242545	+	0.420101i
$565$	−12.8229	−	22.2099i	−0.539462	−	0.934376i
$566$	−15.3229	+	26.5400i	−0.644069	+	1.11556i
$567$	9.11438	+	15.7866i	0.382768	+	0.662973i
$568$	1.35425	+	2.34563i	0.0568230	+	0.0984203i
$569$	6.58301			0.275974			0.137987	−	0.990434i	$-0.455937\pi$
$569$	6.58301			0.275974			0.137987	+	0.990434i	$0.455937\pi$
$570$	−7.30262	−	17.5186i	−0.305873	−	0.733774i
$571$	7.81176			0.326912			0.163456	−	0.986551i	$-0.447736\pi$
$571$	7.81176			0.326912			0.163456	+	0.986551i	$0.447736\pi$
$572$	4.64575	+	8.04668i	0.194249	+	0.336448i
$573$	−8.70850	−	15.0836i	−0.363803	−	0.630125i
$574$	0.531373	−	0.920365i	0.0221791	−	0.0384153i
$575$	−1.88562	−	3.26599i	−0.0786359	−	0.136201i
$576$	−2.00000	+	3.46410i	−0.0833333	+	0.144338i
$577$	11.0000			0.457936			0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000			0.457936			0.228968	+	0.973434i	$0.426465\pi$
$578$	−17.0000			−0.707107
$579$	−19.2915	+	33.4139i	−0.801727	+	1.38863i
$580$	1.35425	−	2.34563i	0.0562321	−	0.0973969i
$581$	28.9373			1.20052
$582$	−9.81176			−0.406711
$583$	−29.2288	+	50.6257i	−1.21053	+	2.09670i
$584$	−0.854249	−	1.47960i	−0.0353491	−	0.0612264i
$585$	6.58301	−	11.4021i	0.272174	−	0.471419i
$586$	−14.4686	−	25.0604i	−0.597693	−	1.03524i
$587$	7.06275	+	12.2330i	0.291511	+	0.504911i	0.974167	−	0.225828i	$-0.0725088\pi$
$587$	7.06275	+	12.2330i	0.291511	+	0.504911i	−0.682656	+	0.730739i	$0.739175\pi$
$588$	16.6458			0.686459
$589$	−9.46863	−	22.7148i	−0.390148	−	0.935946i
$590$	13.0627			0.537785
$591$	10.1144	+	17.5186i	0.416050	+	0.720620i
$592$	−0.177124	−	0.306788i	−0.00727977	−	0.0126089i
$593$	−14.8542	+	25.7283i	−0.609991	+	1.05654i	0.381250	+	0.924472i	$0.375494\pi$
$593$	−14.8542	+	25.7283i	−0.609991	+	1.05654i	−0.991241	+	0.132063i	$0.957840\pi$
$594$	6.14575	+	10.6448i	0.252163	+	0.436760i
$595$		0			0
$596$	10.9373			0.448007
$597$	−52.5830			−2.15208
$598$	1.64575	−	2.85052i	0.0672998	−	0.116567i
$599$	8.46863	−	14.6681i	0.346019	−	0.599322i	−0.639520	−	0.768775i	$-0.720867\pi$
$599$	8.46863	−	14.6681i	0.346019	−	0.599322i	0.985538	+	0.169453i	$0.0542000\pi$
$600$	−6.06275			−0.247511
$601$	10.4170			0.424918			0.212459	−	0.977170i	$-0.431853\pi$
$601$	10.4170			0.424918			0.212459	+	0.977170i	$0.431853\pi$
$602$	−20.5830	+	35.6508i	−0.838901	+	1.45302i
$603$	−1.29150	−	2.23695i	−0.0525941	−	0.0910956i
$604$	−6.46863	+	11.2040i	−0.263205	+	0.455884i
$605$	8.70850	+	15.0836i	0.354051	+	0.613234i
$606$	18.0516	+	31.2663i	0.733297	+	1.27011i
$607$	6.93725			0.281574			0.140787	−	0.990040i	$-0.455037\pi$
$607$	6.93725			0.281574			0.140787	+	0.990040i	$0.455037\pi$
$608$	−4.32288	−	0.559237i	−0.175316	−	0.0226801i
$609$	15.8745			0.643268
$610$	0.771243	+	1.33583i	0.0312267	+	0.0540863i
$611$	−4.35425	−	7.54178i	−0.176154	−	0.305108i
$612$		0			0
$613$	−3.70850	−	6.42331i	−0.149785	−	0.259435i	0.781363	−	0.624077i	$-0.214525\pi$
$613$	−3.70850	−	6.42331i	−0.149785	−	0.259435i	−0.931148	+	0.364642i	$0.881191\pi$
$614$	−0.322876	+	0.559237i	−0.0130302	+	0.0225690i
$615$	1.26927			0.0511821
$616$	−16.9373			−0.682421
$617$	15.4373	−	26.7381i	0.621480	−	1.07644i	−0.367730	−	0.929933i	$-0.619865\pi$
$617$	15.4373	−	26.7381i	0.621480	−	1.07644i	0.989210	−	0.146503i	$-0.0468018\pi$
$618$	17.5830	−	30.4547i	0.707292	−	1.22507i
$619$	−8.45751			−0.339936			−0.169968	−	0.985450i	$-0.554366\pi$
$619$	−8.45751			−0.339936			−0.169968	+	0.985450i	$0.554366\pi$
$620$	9.29150			0.373156
$621$	2.17712	−	3.77089i	0.0873650	−	0.151321i
$622$	−6.82288	−	11.8176i	−0.273572	−	0.473841i
$623$		0			0
$624$	−2.64575	−	4.58258i	−0.105915	−	0.183450i
$625$	4.14575	+	7.18065i	0.165830	+	0.287226i
$626$	8.87451			0.354697
$627$	−32.5203	+	42.5790i	−1.29873	+	1.70044i
$628$	−10.5830			−0.422308
$629$		0			0
$630$	12.0000	+	20.7846i	0.478091	+	0.828079i
$631$	12.4059	−	21.4876i	0.493870	−	0.855408i	−0.506105	−	0.862472i	$-0.668915\pi$
$631$	12.4059	−	21.4876i	0.493870	−	0.855408i	0.999975	+	0.00706354i	$0.00224841\pi$
$632$	2.00000	+	3.46410i	0.0795557	+	0.137795i
$633$	17.5830	−	30.4547i	0.698862	−	1.21046i
$634$	−6.00000			−0.238290
$635$	21.8745			0.868063
$636$	16.6458	−	28.8313i	0.660047	−	1.14323i
$637$	−6.29150	+	10.8972i	−0.249278	+	0.431763i
$638$	−7.64575			−0.302698
$639$	−10.8340			−0.428586
$640$	0.822876	−	1.42526i	0.0325270	−	0.0563384i
$641$	−6.43725	−	11.1497i	−0.254256	−	0.440385i	0.710437	−	0.703761i	$-0.248497\pi$
$641$	−6.43725	−	11.1497i	−0.254256	−	0.440385i	−0.964693	+	0.263376i	$0.915164\pi$
$642$	−20.2288	+	35.0372i	−0.798365	+	1.38281i
$643$	3.26013	+	5.64671i	0.128567	+	0.222685i	0.923122	−	0.384508i	$-0.125629\pi$
$643$	3.26013	+	5.64671i	0.128567	+	0.222685i	−0.794555	+	0.607193i	$0.792296\pi$
$644$	3.00000	+	5.19615i	0.118217	+	0.204757i
$645$	−49.1660			−1.93591
$646$		0			0
$647$	−22.4575			−0.882896			−0.441448	−	0.897287i	$-0.645535\pi$
$647$	−22.4575			−0.882896			−0.441448	+	0.897287i	$0.645535\pi$
$648$	2.50000	+	4.33013i	0.0982093	+	0.170103i
$649$	−18.4373	−	31.9343i	−0.723726	−	1.25353i
$650$	2.29150	−	3.96900i	0.0898801	−	0.155677i
$651$	27.2288	+	47.1616i	1.06718	+	1.84841i
$652$	−1.96863	+	3.40976i	−0.0770974	+	0.133537i
$653$	24.0000			0.939193			0.469596	−	0.882881i	$-0.344399\pi$
$653$	24.0000			0.939193			0.469596	+	0.882881i	$0.344399\pi$
$654$	38.5830			1.50871
$655$	1.59412	−	2.76110i	0.0622874	−	0.107885i
$656$	0.145751	−	0.252449i	0.00569063	−	0.00985646i
$657$	6.83399			0.266619
$658$	15.8745			0.618853
$659$	9.29150	−	16.0934i	0.361946	−	0.626908i	−0.626335	−	0.779554i	$-0.715446\pi$
$659$	9.29150	−	16.0934i	0.361946	−	0.626908i	0.988281	+	0.152646i	$0.0487793\pi$
$660$	−10.1144	−	17.5186i	−0.393702	−	0.681911i
$661$	−8.11438	+	14.0545i	−0.315613	+	0.546657i	−0.979568	−	0.201115i	$-0.935543\pi$
$661$	−8.11438	+	14.0545i	−0.315613	+	0.546657i	0.663955	+	0.747773i	$0.268877\pi$
$662$	−9.90588	−	17.1575i	−0.385003	−	0.666845i
$663$		0			0
$664$	7.93725			0.308025
$665$	−15.8745	+	20.7846i	−0.615587	+	0.805993i
$666$	1.41699			0.0549074
$667$	1.35425	+	2.34563i	0.0524367	+	0.0908231i
$668$	6.00000	+	10.3923i	0.232147	+	0.402090i
$669$	24.8856	−	43.1032i	0.962134	−	1.66646i
$670$	0.531373	+	0.920365i	0.0205287	+	0.0355568i
$671$	2.17712	−	3.77089i	0.0840470	−	0.145574i
$672$	9.64575			0.372093
$673$	−13.8745			−0.534823			−0.267411	−	0.963582i	$-0.586168\pi$
$673$	−13.8745			−0.534823			−0.267411	+	0.963582i	$0.586168\pi$
$674$	4.85425	−	8.40781i	0.186979	−	0.323857i
$675$	3.03137	−	5.25049i	0.116678	−	0.202092i
$676$	−9.00000			−0.346154
$677$	−11.4170			−0.438791			−0.219395	−	0.975636i	$-0.570408\pi$
$677$	−11.4170			−0.438791			−0.219395	+	0.975636i	$0.570408\pi$
$678$	20.6144	−	35.7052i	0.791690	−	1.37125i
$679$	6.76013	+	11.7089i	0.259430	+	0.449346i
$680$		0			0
$681$	9.72876	+	16.8507i	0.372807	+	0.645720i
$682$	−13.1144	−	22.7148i	−0.502175	−	0.869793i
$683$	−5.41699			−0.207276			−0.103638	−	0.994615i	$-0.533048\pi$
$683$	−5.41699			−0.207276			−0.103638	+	0.994615i	$0.533048\pi$
$684$	10.5830	−	13.8564i	0.404651	−	0.529813i
$685$	−25.6458			−0.979874
$686$	1.29150	+	2.23695i	0.0493098	+	0.0854071i
$687$	−26.4575	−	45.8258i	−1.00942	−	1.74836i
$688$	−5.64575	+	9.77873i	−0.215242	+	0.372811i
$689$	12.5830	+	21.7944i	0.479374	+	0.830301i
$690$	−3.58301	+	6.20595i	−0.136403	+	0.236256i
$691$	2.58301			0.0982622			0.0491311	−	0.998792i	$-0.484355\pi$
$691$	2.58301			0.0982622			0.0491311	+	0.998792i	$0.484355\pi$
$692$	−6.00000			−0.228086
$693$	33.8745	−	58.6724i	1.28679	−	2.22878i
$694$	11.6144	−	20.1167i	0.440876	−	0.763619i
$695$	−30.6863			−1.16400
$696$	4.35425			0.165047
$697$		0			0
$698$	−10.5830	−	18.3303i	−0.400573	−	0.693812i
$699$	−24.9686	+	43.2469i	−0.944400	+	1.63575i
$700$	4.17712	+	7.23499i	0.157880	+	0.273457i
$701$	−5.17712	−	8.96704i	−0.195537	−	0.338681i	0.751539	−	0.659688i	$-0.229312\pi$
$701$	−5.17712	−	8.96704i	−0.195537	−	0.338681i	−0.947077	+	0.321008i	$0.895978\pi$
$702$	5.29150			0.199715
$703$	0.594119	+	1.42526i	0.0224076	+	0.0537548i
$704$	−4.64575			−0.175093
$705$	9.47974	+	16.4194i	0.357028	+	0.618390i
$706$	−6.43725	−	11.1497i	−0.242269	−	0.419623i
$707$	24.8745	−	43.0839i	0.935502	−	1.62034i
$708$	10.5000	+	18.1865i	0.394614	+	0.683492i
$709$	−1.82288	+	3.15731i	−0.0684595	+	0.118575i	−0.898223	−	0.439539i	$-0.855142\pi$
$709$	−1.82288	+	3.15731i	−0.0684595	+	0.118575i	0.829764	+	0.558115i	$0.188475\pi$
$710$	4.45751			0.167287
$711$	−16.0000			−0.600047
$712$		0			0
$713$	−4.64575	+	8.04668i	−0.173985	+	0.301350i
$714$		0			0
$715$	15.2915			0.571870
$716$	−2.03137	+	3.51844i	−0.0759160	+	0.131490i
$717$	15.8745	+	27.4955i	0.592844	+	1.02684i
$718$	2.46863	−	4.27579i	0.0921283	−	0.159571i
$719$	−1.35425	−	2.34563i	−0.0505050	−	0.0874771i	0.839668	−	0.543100i	$-0.182750\pi$
$719$	−1.35425	−	2.34563i	−0.0505050	−	0.0874771i	−0.890173	+	0.455623i	$0.849416\pi$
$720$	3.29150	+	5.70105i	0.122667	+	0.212466i
$721$	−48.4575			−1.80465
$722$	18.3745	+	4.83502i	0.683828	+	0.179941i
$723$	−20.0627			−0.746142
$724$	−11.1144	−	19.2507i	−0.413063	−	0.715445i
$725$	1.88562	+	3.26599i	0.0700302	+	0.121296i
$726$	−14.0000	+	24.2487i	−0.519589	+	0.899954i
$727$	−0.708497	−	1.22715i	−0.0262767	−	0.0455126i	0.852588	−	0.522584i	$-0.175032\pi$
$727$	−0.708497	−	1.22715i	−0.0262767	−	0.0455126i	−0.878865	+	0.477071i	$0.841698\pi$
$728$	−3.64575	+	6.31463i	−0.135121	+	0.234036i
$729$	−41.0000			−1.51852
$730$	−2.81176			−0.104068
$731$		0			0
$732$	−1.23987	+	2.14752i	−0.0458269	+	0.0793746i
$733$	−16.1033			−0.594788			−0.297394	−	0.954755i	$-0.596117\pi$
$733$	−16.1033			−0.594788			−0.297394	+	0.954755i	$0.596117\pi$
$734$	16.2288			0.599014
$735$	13.6974	−	23.7246i	0.505236	−	0.875094i
$736$	0.822876	+	1.42526i	0.0303316	+	0.0525359i
$737$	1.50000	−	2.59808i	0.0552532	−	0.0957014i
$738$	0.583005	+	1.00979i	0.0214607	+	0.0371711i
$739$	16.9059	+	29.2818i	0.621893	+	1.07715i	0.989133	+	0.147024i	$0.0469694\pi$
$739$	16.9059	+	29.2818i	0.621893	+	1.07715i	−0.367240	+	0.930126i	$0.619697\pi$
$740$	−0.583005			−0.0214317
$741$	8.87451	+	21.2895i	0.326013	+	0.782090i
$742$	−45.8745			−1.68411
$743$	23.7601	+	41.1538i	0.871675	+	1.50978i	0.860263	+	0.509850i	$0.170299\pi$
$743$	23.7601	+	41.1538i	0.871675	+	1.50978i	0.0114112	+	0.999935i	$0.496368\pi$
$744$	7.46863	+	12.9360i	0.273813	+	0.474258i
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$	2.00000	+	3.46410i	0.0732252	+	0.126830i
$747$	−15.8745	+	27.4955i	−0.580818	+	1.00601i
$748$		0			0
$749$	55.7490			2.03702
$750$	−15.8745	+	27.4955i	−0.579655	+	1.00399i
$751$	3.93725	−	6.81952i	0.143672	−	0.248848i	−0.785204	−	0.619237i	$-0.787442\pi$
$751$	3.93725	−	6.81952i	0.143672	−	0.248848i	0.928877	+	0.370389i	$0.120775\pi$
$752$	4.35425			0.158783
$753$	77.3320			2.81814
$754$	−1.64575	+	2.85052i	−0.0599347	+	0.103810i
$755$	10.6458	+	18.4390i	0.387439	+	0.671063i
$756$	−4.82288	+	8.35347i	−0.175406	+	0.303813i
$757$	2.29150	+	3.96900i	0.0832861	+	0.144256i	0.904660	−	0.426135i	$-0.140125\pi$
$757$	2.29150	+	3.96900i	0.0832861	+	0.144256i	−0.821374	+	0.570391i	$0.806792\pi$
$758$	−5.35425	−	9.27383i	−0.194475	−	0.336841i
$759$	20.2288			0.734257
$760$	−4.35425	+	5.70105i	−0.157945	+	0.206799i
$761$	42.8745			1.55420			0.777100	−	0.629377i	$-0.216690\pi$
$761$	42.8745			1.55420			0.777100	+	0.629377i	$0.216690\pi$
$762$	17.5830	+	30.4547i	0.636965	+	1.10326i
$763$	−26.5830	−	46.0431i	−0.962369	−	1.66687i
$764$	−3.29150	+	5.70105i	−0.119082	+	0.206257i
$765$		0			0
$766$	−2.76013	+	4.78068i	−0.0997275	+	0.172733i
$767$	−15.8745			−0.573195
$768$	2.64575			0.0954703
$769$	−17.6458	+	30.5633i	−0.636322	+	1.10214i	0.349911	+	0.936783i	$0.386212\pi$
$769$	−17.6458	+	30.5633i	−0.636322	+	1.10214i	−0.986233	+	0.165359i	$0.947122\pi$
$770$	−13.9373	+	24.1400i	−0.502264	+	0.869946i
$771$	32.5203			1.17119
$772$	14.5830			0.524854
$773$	2.46863	−	4.27579i	0.0887903	−	0.153789i	−0.818210	−	0.574920i	$-0.805033\pi$
$773$	2.46863	−	4.27579i	0.0887903	−	0.153789i	0.907000	+	0.421130i	$0.138367\pi$
$774$	−22.5830	−	39.1149i	−0.811729	−	1.40596i
$775$	−6.46863	+	11.2040i	−0.232360	+	0.402459i
$776$	1.85425	+	3.21165i	0.0665636	+	0.115292i
$777$	−1.70850	−	2.95920i	−0.0612920	−	0.106161i
$778$	12.0000			0.430221
$779$	−0.771243	+	1.00979i	−0.0276327	+	0.0361796i
$780$	−8.70850			−0.311814
$781$	−6.29150	−	10.8972i	−0.225128	−	0.389933i
$782$		0			0
$783$	−2.17712	+	3.77089i	−0.0778041	+	0.134761i
$784$	−3.14575	−	5.44860i	−0.112348	−	0.194593i
$785$	−8.70850	+	15.0836i	−0.310820	+	0.538355i
$786$	5.12549			0.182820
$787$	−42.5203			−1.51568			−0.757842	−	0.652438i	$-0.773746\pi$
$787$	−42.5203			−1.51568			−0.757842	+	0.652438i	$0.773746\pi$
$788$	3.82288	−	6.62141i	0.136184	−	0.235878i
$789$	14.4686	−	25.0604i	0.515097	−	0.892174i
$790$	6.58301			0.234213
$791$	−56.8118			−2.01999
$792$	9.29150	−	16.0934i	0.330159	−	0.571852i
$793$	−0.937254	−	1.62337i	−0.0332829	−	0.0576476i
$794$	−10.5314	+	18.2409i	−0.373744	+	0.647344i
$795$	−27.3948	−	47.4491i	−0.971592	−	1.68285i
$796$	9.93725	+	17.2118i	0.352217	+	0.610057i
$797$	−44.8118			−1.58731			−0.793657	−	0.608365i	$-0.791826\pi$
$797$	−44.8118			−1.58731			−0.793657	+	0.608365i	$0.791826\pi$
$798$	−41.6974	−	5.39426i	−1.47607	−	0.190955i
$799$		0			0
$800$	1.14575	+	1.98450i	0.0405084	+	0.0701627i
$801$		0			0
$802$	−13.7915	+	23.8876i	−0.486995	+	0.843500i
$803$	3.96863	+	6.87386i	0.140050	+	0.242573i
$804$	−0.854249	+	1.47960i	−0.0301270	+	0.0521815i
$805$	9.87451			0.348031
$806$	−11.2915			−0.397726
$807$		0			0
$808$	6.82288	−	11.8176i	0.240028	−	0.415741i
$809$	−9.00000			−0.316423			−0.158212	−	0.987405i	$-0.550573\pi$
$809$	−9.00000			−0.316423			−0.158212	+	0.987405i	$0.550573\pi$
$810$	8.22876			0.289129
$811$	15.6458	−	27.0992i	0.549397	−	0.951583i	−0.448919	−	0.893572i	$-0.648191\pi$
$811$	15.6458	−	27.0992i	0.549397	−	0.951583i	0.998316	−	0.0580106i	$-0.0184757\pi$
$812$	−3.00000	−	5.19615i	−0.105279	−	0.182349i
$813$	−16.3431	+	28.3071i	−0.573179	+	0.992775i
$814$	0.822876	+	1.42526i	0.0288418	+	0.0499554i
$815$	3.23987	+	5.61162i	0.113488	+	0.196566i
$816$		0			0
$817$	29.8745	−	39.1149i	1.04518	−	1.36846i
$818$	−7.58301			−0.265134
$819$	−14.5830	−	25.2585i	−0.509571	−	0.882604i
$820$	−0.239870	−	0.415468i	−0.00837664	−	0.0145088i
$821$	3.00000	−	5.19615i	0.104701	−	0.181347i	−0.808915	−	0.587925i	$-0.799945\pi$
$821$	3.00000	−	5.19615i	0.104701	−	0.181347i	0.913616	+	0.406578i	$0.133278\pi$
$822$	−20.6144	−	35.7052i	−0.719009	−	1.24536i
$823$	15.9373	−	27.6041i	0.555538	−	0.962220i	−0.442324	−	0.896855i	$-0.645846\pi$
$823$	15.9373	−	27.6041i	0.555538	−	0.962220i	0.997861	−	0.0653641i	$-0.0208209\pi$
$824$	−13.2915			−0.463031
$825$	28.1660			0.980615
$826$	14.4686	−	25.0604i	0.503428	−	0.871963i
$827$	26.3229	−	45.5926i	0.915336	−	1.58541i	0.108928	−	0.994050i	$-0.465258\pi$
$827$	26.3229	−	45.5926i	0.915336	−	1.58541i	0.806408	−	0.591359i	$-0.201408\pi$
$828$	−6.58301			−0.228775
$829$	−17.1660			−0.596200			−0.298100	−	0.954535i	$-0.596353\pi$
$829$	−17.1660			−0.596200			−0.298100	+	0.954535i	$0.596353\pi$
$830$	6.53137	−	11.3127i	0.226707	−	0.392669i
$831$	36.4059	+	63.0568i	1.26291	+	2.18742i
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$		0			0
$834$	−24.6660	−	42.7228i	−0.854114	−	1.47937i
$835$	19.7490			0.683443
$836$	20.0830	+	2.59808i	0.694585	+	0.0898563i
$837$	−14.9373			−0.516307
$838$	15.8745	+	27.4955i	0.548376	+	0.949815i
$839$	20.7601	+	35.9576i	0.716719	+	1.24139i	0.962293	+	0.272016i	$0.0876904\pi$
$839$	20.7601	+	35.9576i	0.716719	+	1.24139i	−0.245573	+	0.969378i	$0.578976\pi$
$840$	7.93725	−	13.7477i	0.273861	−	0.474342i
$841$	13.1458	+	22.7691i	0.453302	+	0.785142i
$842$	12.4059	−	21.4876i	0.427535	−	0.740512i
$843$	67.3542			2.31980
$844$	−13.2915			−0.457512
$845$	−7.40588	+	12.8274i	−0.254770	+	0.441275i
$846$	−8.70850	+	15.0836i	−0.299404	+	0.518583i
$847$	38.5830			1.32573
$848$	−12.5830			−0.432102
$849$	−40.5405	+	70.2182i	−1.39135	+	2.40988i
$850$		0			0
$851$	0.291503	−	0.504897i	0.00999258	−	0.0173077i
$852$	3.58301	+	6.20595i	0.122752	+	0.212612i
$853$	−4.29150	−	7.43310i	−0.146938	−	0.254505i	0.783156	−	0.621825i	$-0.213609\pi$
$853$	−4.29150	−	7.43310i	−0.146938	−	0.254505i	−0.930094	+	0.367321i	$0.880275\pi$
$854$	3.41699			0.116927
$855$	−11.0405	−	26.4857i	−0.377578	−	0.905790i
$856$	15.2915			0.522653
$857$	−10.5000	−	18.1865i	−0.358673	−	0.621240i	0.629066	−	0.777352i	$-0.283437\pi$
$857$	−10.5000	−	18.1865i	−0.358673	−	0.621240i	−0.987739	+	0.156112i	$0.950104\pi$
$858$	12.2915	+	21.2895i	0.419625	+	0.726812i
$859$	−6.61438	+	11.4564i	−0.225680	+	0.390889i	−0.956523	−	0.291656i	$-0.905794\pi$
$859$	−6.61438	+	11.4564i	−0.225680	+	0.390889i	0.730843	+	0.682545i	$0.239127\pi$
$860$	9.29150	+	16.0934i	0.316838	+	0.548779i
$861$	1.40588	−	2.43506i	0.0479123	−	0.0829865i
$862$	27.8745			0.949410
$863$	−31.0627			−1.05739			−0.528694	−	0.848812i	$-0.677318\pi$
$863$	−31.0627			−1.05739			−0.528694	+	0.848812i	$0.677318\pi$
$864$	−1.32288	+	2.29129i	−0.0450051	+	0.0779512i
$865$	−4.93725	+	8.55157i	−0.167872	+	0.290762i
$866$	17.8745			0.607401
$867$	−44.9778			−1.52753
$868$	10.2915	−	17.8254i	0.349316	−	0.605034i
$869$	−9.29150	−	16.0934i	−0.315193	−	0.545930i
$870$	3.58301	−	6.20595i	0.121475	−	0.210401i
$871$	−0.645751	−	1.11847i	−0.0218804	−	0.0378980i
$872$	−7.29150	−	12.6293i	−0.246921	−	0.427680i
$873$	−14.8340			−0.502054
$874$	−2.76013	−	6.62141i	−0.0933628	−	0.223973i
$875$	43.7490			1.47899
$876$	−2.26013	−	3.91466i	−0.0763627	−	0.132264i
$877$	20.8229	+	36.0663i	0.703139	+	1.21787i	0.967359	+	0.253409i	$0.0815520\pi$
$877$	20.8229	+	36.0663i	0.703139	+	1.21787i	−0.264221	+	0.964462i	$0.585115\pi$
$878$	−5.40588	+	9.36326i	−0.182440	+	0.315995i
$879$	−38.2804	−	66.3036i	−1.29117	−	2.23636i
$880$	−3.82288	+	6.62141i	−0.128869	+	0.223208i
$881$	−36.8745			−1.24233			−0.621167	−	0.783678i	$-0.713341\pi$
$881$	−36.8745			−1.24233			−0.621167	+	0.783678i	$0.713341\pi$
$882$	25.1660			0.847384
$883$	14.1974	−	24.5906i	0.477780	−	0.827539i	−0.521896	−	0.853009i	$-0.674775\pi$
$883$	14.1974	−	24.5906i	0.477780	−	0.827539i	0.999676	+	0.0254701i	$0.00810828\pi$
$884$		0			0
$885$	34.5608			1.16175
$886$	10.6458			0.357651
$887$	8.70850	−	15.0836i	0.292403	−	0.506456i	−0.681975	−	0.731376i	$-0.738879\pi$
$887$	8.70850	−	15.0836i	0.292403	−	0.506456i	0.974377	+	0.224919i	$0.0722119\pi$
$888$	−0.468627	−	0.811686i	−0.0157261	−	0.0272384i
$889$	24.2288	−	41.9654i	0.812606	−	1.40748i
$890$		0			0
$891$	−11.6144	−	20.1167i	−0.389096	−	0.673935i
$892$	−18.8118			−0.629864
$893$	−18.8229	−	2.43506i	−0.629884	−	0.0814861i
$894$	28.9373			0.967807
$895$	3.34313	+	5.79048i	0.111749	+	0.193554i
$896$	−1.82288	−	3.15731i	−0.0608980	−	0.105478i
$897$	4.35425	−	7.54178i	0.145384	−	0.251813i
$898$	12.1458	+	21.0371i	0.405309	+	0.702016i
$899$	4.64575	−	8.04668i	0.154944	−	0.268372i
$900$	−9.16601			−0.305534
$901$		0			0
$902$	−0.677124	+	1.17281i	−0.0225458	+	0.0390504i
$903$	−54.4575	+	94.3232i	−1.81223	+	3.13888i
$904$	−15.5830			−0.518283
$905$	−36.5830			−1.21606
$906$	−17.1144	+	29.6430i	−0.568587	+	0.984822i
$907$	−19.9686	−	34.5867i	−0.663047	−	1.14843i	−0.979811	−	0.199927i	$-0.935929\pi$
$907$	−19.9686	−	34.5867i	−0.663047	−	1.14843i	0.316763	−	0.948505i	$-0.397404\pi$
$908$	3.67712	−	6.36897i	0.122030	−	0.211362i
$909$	27.2915	+	47.2703i	0.905202	+	1.56786i
$910$	6.00000	+	10.3923i	0.198898	+	0.344502i
$911$	16.9373			0.561156			0.280578	−	0.959831i	$-0.409474\pi$
$911$	16.9373			0.561156			0.280578	+	0.959831i	$0.409474\pi$
$912$	−11.4373	−	1.47960i	−0.378725	−	0.0489945i
$913$	−36.8745			−1.22037
$914$	−16.4373	−	28.4702i	−0.543696	−	0.941709i
$915$	2.04052	+	3.53428i	0.0674575	+	0.116840i
$916$	−10.0000	+	17.3205i	−0.330409	+	0.572286i
$917$	−3.53137	−	6.11652i	−0.116616	−	0.201985i
$918$		0			0
$919$	−19.8745			−0.655600			−0.327800	−	0.944747i	$-0.606307\pi$
$919$	−19.8745			−0.655600			−0.327800	+	0.944747i	$0.606307\pi$
$920$	2.70850			0.0892965
$921$	−0.854249	+	1.47960i	−0.0281485	+	0.0487545i
$922$	−9.58301	+	16.5983i	−0.315599	+	0.546634i
$923$	−5.41699			−0.178303
$924$	−44.8118			−1.47420
$925$	0.405881	−	0.703006i	0.0133453	−	0.0231147i
$926$	19.2288	+	33.3052i	0.631896	+	1.09448i
$927$	26.5830	−	46.0431i	0.873100	−	1.51225i
$928$	−0.822876	−	1.42526i	−0.0270122	−	0.0467865i
$929$	4.79150	+	8.29913i	0.157204	+	0.272285i	0.933859	−	0.357640i	$-0.116419\pi$
$929$	4.79150	+	8.29913i	0.157204	+	0.272285i	−0.776655	+	0.629926i	$0.783085\pi$
$930$	24.5830			0.806108
$931$	10.5516	+	25.3128i	0.345816	+	0.829595i
$932$	18.8745			0.618255
$933$	−18.0516	−	31.2663i	−0.590984	−	1.02361i
$934$	9.67712	+	16.7613i	0.316645	+	0.548446i
$935$		0			0
$936$	−4.00000	−	6.92820i	−0.130744	−	0.226455i
$937$	−3.56275	+	6.17086i	−0.116390	+	0.201593i	−0.918334	−	0.395805i	$-0.870466\pi$
$937$	−3.56275	+	6.17086i	−0.116390	+	0.201593i	0.801945	+	0.597398i	$0.203799\pi$
$938$	2.35425			0.0768689
$939$	23.4797			0.766232
$940$	3.58301	−	6.20595i	0.116865	−	0.202416i
$941$	−8.41699	+	14.5787i	−0.274386	+	0.475251i	−0.969980	−	0.243184i	$-0.921808\pi$
$941$	−8.41699	+	14.5787i	−0.274386	+	0.475251i	0.695594	+	0.718435i	$0.255141\pi$
$942$	−28.0000			−0.912289
$943$	0.479741			0.0156225
$944$	3.96863	−	6.87386i	0.129168	−	0.223725i
$945$	7.93725	+	13.7477i	0.258199	+	0.447214i
$946$	26.2288	−	45.4295i	0.852770	−	1.47704i
$947$	3.87451	+	6.71084i	0.125905	+	0.218073i	0.922086	−	0.386985i	$-0.126483\pi$
$947$	3.87451	+	6.71084i	0.125905	+	0.218073i	−0.796182	+	0.605058i	$0.793150\pi$
$948$	5.29150	+	9.16515i	0.171860	+	0.297670i
$949$	3.41699			0.110920
$950$	−3.84313	−	9.21949i	−0.124688	−	0.299120i
$951$	−15.8745			−0.514766
$952$		0			0
$953$	6.72876	+	11.6545i	0.217966	+	0.377528i	0.954186	−	0.299214i	$-0.0967245\pi$
$953$	6.72876	+	11.6545i	0.217966	+	0.377528i	−0.736220	+	0.676742i	$0.763391\pi$
$954$	25.1660	−	43.5888i	0.814780	−	1.41124i
$955$	5.41699	+	9.38251i	0.175290	+	0.303611i
$956$	6.00000	−	10.3923i	0.194054	−	0.336111i
$957$	−20.2288			−0.653903
$958$	6.58301			0.212687
$959$	−28.4059	+	49.2004i	−0.917274	+	1.58876i
$960$	2.17712	−	3.77089i	0.0702664	−	0.121705i
$961$	0.874508			0.0282099
$962$	0.708497			0.0228429
$963$	−30.5830	+	52.9713i	−0.985524	+	1.70698i
$964$	3.79150	+	6.56708i	0.122116	+	0.211511i
$965$	12.0000	−	20.7846i	0.386294	−	0.669080i
$966$	7.93725	+	13.7477i	0.255377	+	0.442326i
$967$	6.64575	+	11.5108i	0.213713	+	0.370162i	0.952874	−	0.303367i	$-0.0981109\pi$
$967$	6.64575	+	11.5108i	0.213713	+	0.370162i	−0.739161	+	0.673529i	$0.764778\pi$
$968$	10.5830			0.340151
$969$		0			0
$970$	6.10326			0.195964
$971$	27.1974	+	47.1073i	0.872806	+	1.51174i	0.859082	+	0.511838i	$0.171035\pi$
$971$	27.1974	+	47.1073i	0.872806	+	1.51174i	0.0137234	+	0.999906i	$0.495632\pi$
$972$	10.5830	+	18.3303i	0.339450	+	0.587945i
$973$	−33.9889	+	58.8705i	−1.08963	+	1.88730i
$974$	−2.11438	−	3.66221i	−0.0677491	−	0.117345i
$975$	6.06275	−	10.5010i	0.194163	−	0.336301i
$976$	0.937254			0.0300008
$977$	−7.45751			−0.238587			−0.119293	−	0.992859i	$-0.538063\pi$
$977$	−7.45751			−0.238587			−0.119293	+	0.992859i	$0.538063\pi$
$978$	−5.20850	+	9.02138i	−0.166549	+	0.288472i
$979$		0			0
$980$	−10.3542			−0.330754
$981$	58.3320			1.86240
$982$	−19.6458	+	34.0274i	−0.626921	+	1.08586i
$983$	−15.8745	−	27.4955i	−0.506318	−	0.876969i	−0.999973	−	0.00731102i	$-0.997673\pi$
$983$	−15.8745	−	27.4955i	−0.506318	−	0.876969i	0.493655	−	0.869658i	$-0.335661\pi$
$984$	0.385622	−	0.667916i	0.0122932	−	0.0212924i
$985$	−6.29150	−	10.8972i	−0.200464	−	0.347214i
$986$		0			0
$987$	42.0000			1.33687
$988$	5.29150	−	6.92820i	0.168345	−	0.220416i
$989$	−18.5830			−0.590905
$990$	−15.2915	−	26.4857i	−0.485996	−	0.841770i
$991$	1.41699	+	2.45431i	0.0450123	+	0.0779636i	0.887654	−	0.460511i	$-0.152334\pi$
$991$	1.41699	+	2.45431i	0.0450123	+	0.0779636i	−0.842641	+	0.538475i	$0.819001\pi$
$992$	2.82288	−	4.88936i	0.0896264	−	0.155237i
$993$	−26.2085	−	45.3944i	−0.831702	−	1.44055i
$994$	4.93725	−	8.55157i	0.156600	−	0.271239i
$995$	32.7085			1.03693
$996$	21.0000			0.665410
$997$	−8.11438	+	14.0545i	−0.256985	+	0.445111i	−0.965433	−	0.260652i	$-0.916062\pi$
$997$	−8.11438	+	14.0545i	−0.256985	+	0.445111i	0.708448	+	0.705763i	$0.249396\pi$
$998$	2.38562	−	4.13202i	0.0755155	−	0.130797i
$999$	0.937254			0.0296534

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.2.c.b.7.1	✓	4
3.2	odd	2		342.2.g.f.235.1		4
4.3	odd	2		304.2.i.e.273.2		4
5.2	odd	4		950.2.j.g.349.3		8
5.3	odd	4		950.2.j.g.349.2		8
5.4	even	2		950.2.e.k.501.2		4
8.3	odd	2		1216.2.i.k.577.1		4
8.5	even	2		1216.2.i.l.577.2		4
12.11	even	2		2736.2.s.v.577.1		4
19.2	odd	18		722.2.e.o.389.1		12
19.3	odd	18		722.2.e.o.595.2		12
19.4	even	9		722.2.e.n.245.2		12
19.5	even	9		722.2.e.n.99.2		12
19.6	even	9		722.2.e.n.423.2		12
19.7	even	3		722.2.a.j.1.2		2
19.8	odd	6		722.2.c.j.429.2		4
19.9	even	9		722.2.e.n.415.1		12
19.10	odd	18		722.2.e.o.415.2		12
19.11	even	3	inner	38.2.c.b.11.1	yes	4
19.12	odd	6		722.2.a.g.1.1		2
19.13	odd	18		722.2.e.o.423.1		12
19.14	odd	18		722.2.e.o.99.1		12
19.15	odd	18		722.2.e.o.245.1		12
19.16	even	9		722.2.e.n.595.1		12
19.17	even	9		722.2.e.n.389.2		12
19.18	odd	2		722.2.c.j.653.2		4
57.11	odd	6		342.2.g.f.163.1		4
57.26	odd	6		6498.2.a.ba.1.2		2
57.50	even	6		6498.2.a.bg.1.2		2
76.7	odd	6		5776.2.a.ba.1.1		2
76.11	odd	6		304.2.i.e.49.2		4
76.31	even	6		5776.2.a.z.1.2		2
95.49	even	6		950.2.e.k.201.2		4
95.68	odd	12		950.2.j.g.49.3		8
95.87	odd	12		950.2.j.g.49.2		8
152.11	odd	6		1216.2.i.k.961.1		4
152.125	even	6		1216.2.i.l.961.2		4
228.11	even	6		2736.2.s.v.1873.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.b.7.1	✓	4	1.1	even	1	trivial
38.2.c.b.11.1	yes	4	19.11	even	3	inner
304.2.i.e.49.2		4	76.11	odd	6
304.2.i.e.273.2		4	4.3	odd	2
342.2.g.f.163.1		4	57.11	odd	6
342.2.g.f.235.1		4	3.2	odd	2
722.2.a.g.1.1		2	19.12	odd	6
722.2.a.j.1.2		2	19.7	even	3
722.2.c.j.429.2		4	19.8	odd	6
722.2.c.j.653.2		4	19.18	odd	2
722.2.e.n.99.2		12	19.5	even	9
722.2.e.n.245.2		12	19.4	even	9
722.2.e.n.389.2		12	19.17	even	9
722.2.e.n.415.1		12	19.9	even	9
722.2.e.n.423.2		12	19.6	even	9
722.2.e.n.595.1		12	19.16	even	9
722.2.e.o.99.1		12	19.14	odd	18
722.2.e.o.245.1		12	19.15	odd	18
722.2.e.o.389.1		12	19.2	odd	18
722.2.e.o.415.2		12	19.10	odd	18
722.2.e.o.423.1		12	19.13	odd	18
722.2.e.o.595.2		12	19.3	odd	18
950.2.e.k.201.2		4	95.49	even	6
950.2.e.k.501.2		4	5.4	even	2
950.2.j.g.49.2		8	95.87	odd	12
950.2.j.g.49.3		8	95.68	odd	12
950.2.j.g.349.2		8	5.3	odd	4
950.2.j.g.349.3		8	5.2	odd	4
1216.2.i.k.577.1		4	8.3	odd	2
1216.2.i.k.961.1		4	152.11	odd	6
1216.2.i.l.577.2		4	8.5	even	2
1216.2.i.l.961.2		4	152.125	even	6
2736.2.s.v.577.1		4	12.11	even	2
2736.2.s.v.1873.1		4	228.11	even	6
5776.2.a.z.1.2		2	76.31	even	6
5776.2.a.ba.1.1		2	76.7	odd	6
6498.2.a.ba.1.2		2	57.26	odd	6
6498.2.a.bg.1.2		2	57.50	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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.32288 - 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.822876 + 1.42526i) q^{5} +(-1.32288 + 2.29129i) q^{6} +3.64575 q^{7} +1.00000 q^{8} +(-2.00000 + 3.46410i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.32288 - 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.822876 + 1.42526i) q^{5} +(-1.32288 + 2.29129i) q^{6} +3.64575 q^{7} +1.00000 q^{8} +(-2.00000 + 3.46410i) q^{9} +(0.822876 - 1.42526i) q^{10} -4.64575 q^{11} +2.64575 q^{12} +(-1.00000 + 1.73205i) q^{13} +(-1.82288 - 3.15731i) q^{14} +(2.17712 - 3.77089i) q^{15} +(-0.500000 - 0.866025i) q^{16} +4.00000 q^{18} +(1.67712 + 4.02334i) q^{19} -1.64575 q^{20} +(-4.82288 - 8.35347i) q^{21} +(2.32288 + 4.02334i) q^{22} +(0.822876 - 1.42526i) q^{23} +(-1.32288 - 2.29129i) q^{24} +(1.14575 - 1.98450i) q^{25} +2.00000 q^{26} +2.64575 q^{27} +(-1.82288 + 3.15731i) q^{28} +(-0.822876 + 1.42526i) q^{29} -4.35425 q^{30} -5.64575 q^{31} +(-0.500000 + 0.866025i) q^{32} +(6.14575 + 10.6448i) q^{33} +(3.00000 + 5.19615i) q^{35} +(-2.00000 - 3.46410i) q^{36} +0.354249 q^{37} +(2.64575 - 3.46410i) q^{38} +5.29150 q^{39} +(0.822876 + 1.42526i) q^{40} +(0.145751 + 0.252449i) q^{41} +(-4.82288 + 8.35347i) q^{42} +(-5.64575 - 9.77873i) q^{43} +(2.32288 - 4.02334i) q^{44} -6.58301 q^{45} -1.64575 q^{46} +(-2.17712 + 3.77089i) q^{47} +(-1.32288 + 2.29129i) q^{48} +6.29150 q^{49} -2.29150 q^{50} +(-1.00000 - 1.73205i) q^{52} +(6.29150 - 10.8972i) q^{53} +(-1.32288 - 2.29129i) q^{54} +(-3.82288 - 6.62141i) q^{55} +3.64575 q^{56} +(7.00000 - 9.16515i) q^{57} +1.64575 q^{58} +(3.96863 + 6.87386i) q^{59} +(2.17712 + 3.77089i) q^{60} +(-0.468627 + 0.811686i) q^{61} +(2.82288 + 4.88936i) q^{62} +(-7.29150 + 12.6293i) q^{63} +1.00000 q^{64} -3.29150 q^{65} +(6.14575 - 10.6448i) q^{66} +(-0.322876 + 0.559237i) q^{67} -4.35425 q^{69} +(3.00000 - 5.19615i) q^{70} +(1.35425 + 2.34563i) q^{71} +(-2.00000 + 3.46410i) q^{72} +(-0.854249 - 1.47960i) q^{73} +(-0.177124 - 0.306788i) q^{74} -6.06275 q^{75} +(-4.32288 - 0.559237i) q^{76} -16.9373 q^{77} +(-2.64575 - 4.58258i) q^{78} +(2.00000 + 3.46410i) q^{79} +(0.822876 - 1.42526i) q^{80} +(2.50000 + 4.33013i) q^{81} +(0.145751 - 0.252449i) q^{82} +7.93725 q^{83} +9.64575 q^{84} +(-5.64575 + 9.77873i) q^{86} +4.35425 q^{87} -4.64575 q^{88} +(3.29150 + 5.70105i) q^{90} +(-3.64575 + 6.31463i) q^{91} +(0.822876 + 1.42526i) q^{92} +(7.46863 + 12.9360i) q^{93} +4.35425 q^{94} +(-4.35425 + 5.70105i) q^{95} +2.64575 q^{96} +(1.85425 + 3.21165i) q^{97} +(-3.14575 - 5.44860i) q^{98} +(9.29150 - 16.0934i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 4 q^{7} + 4 q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 4 * q^7 + 4 * q^8 - 8 * q^9	\( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 4 q^{7} + 4 q^{8} - 8 q^{9} - 2 q^{10} - 8 q^{11} - 4 q^{13} - 2 q^{14} + 14 q^{15} - 2 q^{16} + 16 q^{18} + 12 q^{19} + 4 q^{20} - 14 q^{21} + 4 q^{22} - 2 q^{23} - 6 q^{25} + 8 q^{26} - 2 q^{28} + 2 q^{29} - 28 q^{30} - 12 q^{31} - 2 q^{32} + 14 q^{33} + 12 q^{35} - 8 q^{36} + 12 q^{37} - 2 q^{40} - 10 q^{41} - 14 q^{42} - 12 q^{43} + 4 q^{44} + 16 q^{45} + 4 q^{46} - 14 q^{47} + 4 q^{49} + 12 q^{50} - 4 q^{52} + 4 q^{53} - 10 q^{55} + 4 q^{56} + 28 q^{57} - 4 q^{58} + 14 q^{60} + 14 q^{61} + 6 q^{62} - 8 q^{63} + 4 q^{64} + 8 q^{65} + 14 q^{66} + 4 q^{67} - 28 q^{69} + 12 q^{70} + 16 q^{71} - 8 q^{72} - 14 q^{73} - 6 q^{74} - 56 q^{75} - 12 q^{76} - 36 q^{77} + 8 q^{79} - 2 q^{80} + 10 q^{81} - 10 q^{82} + 28 q^{84} - 12 q^{86} + 28 q^{87} - 8 q^{88} - 8 q^{90} - 4 q^{91} - 2 q^{92} + 14 q^{93} + 28 q^{94} - 28 q^{95} + 18 q^{97} - 2 q^{98} + 16 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 4 * q^7 + 4 * q^8 - 8 * q^9 - 2 * q^10 - 8 * q^11 - 4 * q^13 - 2 * q^14 + 14 * q^15 - 2 * q^16 + 16 * q^18 + 12 * q^19 + 4 * q^20 - 14 * q^21 + 4 * q^22 - 2 * q^23 - 6 * q^25 + 8 * q^26 - 2 * q^28 + 2 * q^29 - 28 * q^30 - 12 * q^31 - 2 * q^32 + 14 * q^33 + 12 * q^35 - 8 * q^36 + 12 * q^37 - 2 * q^40 - 10 * q^41 - 14 * q^42 - 12 * q^43 + 4 * q^44 + 16 * q^45 + 4 * q^46 - 14 * q^47 + 4 * q^49 + 12 * q^50 - 4 * q^52 + 4 * q^53 - 10 * q^55 + 4 * q^56 + 28 * q^57 - 4 * q^58 + 14 * q^60 + 14 * q^61 + 6 * q^62 - 8 * q^63 + 4 * q^64 + 8 * q^65 + 14 * q^66 + 4 * q^67 - 28 * q^69 + 12 * q^70 + 16 * q^71 - 8 * q^72 - 14 * q^73 - 6 * q^74 - 56 * q^75 - 12 * q^76 - 36 * q^77 + 8 * q^79 - 2 * q^80 + 10 * q^81 - 10 * q^82 + 28 * q^84 - 12 * q^86 + 28 * q^87 - 8 * q^88 - 8 * q^90 - 4 * q^91 - 2 * q^92 + 14 * q^93 + 28 * q^94 - 28 * q^95 + 18 * q^97 - 2 * q^98 + 16 * q^99

Introduction

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