LMFDB - Embedded newform 38.2.c.b.7.2

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			7.2
Root			$-1.32288 + 2.29129i$ of defining polynomial
Character	$\chi$	$=$	38.7
Dual form			38.2.c.b.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.32288 + 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.82288 - 3.15731i) q^{5} +(1.32288 - 2.29129i) q^{6} -1.64575 q^{7} +1.00000 q^{8} +(-2.00000 + 3.46410i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.32288 + 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.82288 - 3.15731i) q^{5} +(1.32288 - 2.29129i) q^{6} -1.64575 q^{7} +1.00000 q^{8} +(-2.00000 + 3.46410i) q^{9} +(-1.82288 + 3.15731i) q^{10} +0.645751 q^{11} -2.64575 q^{12} +(-1.00000 + 1.73205i) q^{13} +(0.822876 + 1.42526i) q^{14} +(4.82288 - 8.35347i) q^{15} +(-0.500000 - 0.866025i) q^{16} +4.00000 q^{18} +(4.32288 - 0.559237i) q^{19} +3.64575 q^{20} +(-2.17712 - 3.77089i) q^{21} +(-0.322876 - 0.559237i) q^{22} +(-1.82288 + 3.15731i) q^{23} +(1.32288 + 2.29129i) q^{24} +(-4.14575 + 7.18065i) q^{25} +2.00000 q^{26} -2.64575 q^{27} +(0.822876 - 1.42526i) q^{28} +(1.82288 - 3.15731i) q^{29} -9.64575 q^{30} -0.354249 q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.854249 + 1.47960i) q^{33} +(3.00000 + 5.19615i) q^{35} +(-2.00000 - 3.46410i) q^{36} +5.64575 q^{37} +(-2.64575 - 3.46410i) q^{38} -5.29150 q^{39} +(-1.82288 - 3.15731i) q^{40} +(-5.14575 - 8.91270i) q^{41} +(-2.17712 + 3.77089i) q^{42} +(-0.354249 - 0.613577i) q^{43} +(-0.322876 + 0.559237i) q^{44} +14.5830 q^{45} +3.64575 q^{46} +(-4.82288 + 8.35347i) q^{47} +(1.32288 - 2.29129i) q^{48} -4.29150 q^{49} +8.29150 q^{50} +(-1.00000 - 1.73205i) q^{52} +(-4.29150 + 7.43310i) q^{53} +(1.32288 + 2.29129i) q^{54} +(-1.17712 - 2.03884i) q^{55} -1.64575 q^{56} +(7.00000 + 9.16515i) q^{57} -3.64575 q^{58} +(-3.96863 - 6.87386i) q^{59} +(4.82288 + 8.35347i) q^{60} +(7.46863 - 12.9360i) q^{61} +(0.177124 + 0.306788i) q^{62} +(3.29150 - 5.70105i) q^{63} +1.00000 q^{64} +7.29150 q^{65} +(0.854249 - 1.47960i) q^{66} +(2.32288 - 4.02334i) q^{67} -9.64575 q^{69} +(3.00000 - 5.19615i) q^{70} +(6.64575 + 11.5108i) q^{71} +(-2.00000 + 3.46410i) q^{72} +(-6.14575 - 10.6448i) q^{73} +(-2.82288 - 4.88936i) q^{74} -21.9373 q^{75} +(-1.67712 + 4.02334i) q^{76} -1.06275 q^{77} +(2.64575 + 4.58258i) q^{78} +(2.00000 + 3.46410i) q^{79} +(-1.82288 + 3.15731i) q^{80} +(2.50000 + 4.33013i) q^{81} +(-5.14575 + 8.91270i) q^{82} -7.93725 q^{83} +4.35425 q^{84} +(-0.354249 + 0.613577i) q^{86} +9.64575 q^{87} +0.645751 q^{88} +(-7.29150 - 12.6293i) q^{90} +(1.64575 - 2.85052i) q^{91} +(-1.82288 - 3.15731i) q^{92} +(-0.468627 - 0.811686i) q^{93} +9.64575 q^{94} +(-9.64575 - 12.6293i) q^{95} -2.64575 q^{96} +(7.14575 + 12.3768i) q^{97} +(2.14575 + 3.71655i) q^{98} +(-1.29150 + 2.23695i) 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	$0.109984\pi$
$3$	1.32288	+	2.29129i	0.763763	+	1.32288i	−0.177136	+	0.984186i	$0.556683\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.82288	−	3.15731i	−0.815215	−	1.41199i	−0.909174	−	0.416417i	$-0.863286\pi$
$5$	−1.82288	−	3.15731i	−0.815215	−	1.41199i	0.0939588	−	0.995576i	$-0.470048\pi$
$6$	1.32288	−	2.29129i	0.540062	−	0.935414i
$7$	−1.64575			−0.622036			−0.311018	−	0.950404i	$-0.600670\pi$
$7$	−1.64575			−0.622036			−0.311018	+	0.950404i	$0.600670\pi$
$8$	1.00000			0.353553
$9$	−2.00000	+	3.46410i	−0.666667	+	1.15470i
$10$	−1.82288	+	3.15731i	−0.576444	+	0.998430i
$11$	0.645751			0.194701			0.0973507	−	0.995250i	$-0.468963\pi$
$11$	0.645751			0.194701			0.0973507	+	0.995250i	$0.468963\pi$
$12$	−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	$0.256123\pi$
$14$	0.822876	+	1.42526i	0.219923	+	0.380917i
$15$	4.82288	−	8.35347i	1.24526	−	2.15686i
$16$	−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
$19$	4.32288	−	0.559237i	0.991736	−	0.128298i
$19$	4.32288	−	0.559237i	0.991736	−	0.128298i
$20$	3.64575			0.815215
$21$	−2.17712	−	3.77089i	−0.475087	−	0.822876i
$22$	−0.322876	−	0.559237i	−0.0688373	−	0.119230i
$23$	−1.82288	+	3.15731i	−0.380096	+	0.658345i	−0.991076	−	0.133301i	$-0.957442\pi$
$23$	−1.82288	+	3.15731i	−0.380096	+	0.658345i	0.610980	+	0.791646i	$0.290776\pi$
$24$	1.32288	+	2.29129i	0.270031	+	0.467707i
$25$	−4.14575	+	7.18065i	−0.829150	+	1.43613i
$26$	2.00000			0.392232
$27$	−2.64575			−0.509175
$28$	0.822876	−	1.42526i	0.155509	−	0.269349i
$29$	1.82288	−	3.15731i	0.338500	−	0.586298i	−0.645651	−	0.763632i	$-0.723414\pi$
$29$	1.82288	−	3.15731i	0.338500	−	0.586298i	0.984151	+	0.177334i	$0.0567473\pi$
$30$	−9.64575			−1.76107
$31$	−0.354249			−0.0636249			−0.0318125	−	0.999494i	$-0.510128\pi$
$31$	−0.354249			−0.0636249			−0.0318125	+	0.999494i	$0.510128\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.854249	+	1.47960i	0.148706	+	0.257566i
$34$		0			0
$35$	3.00000	+	5.19615i	0.507093	+	0.878310i
$36$	−2.00000	−	3.46410i	−0.333333	−	0.577350i
$37$	5.64575			0.928156			0.464078	−	0.885794i	$-0.346386\pi$
$37$	5.64575			0.928156			0.464078	+	0.885794i	$0.346386\pi$
$38$	−2.64575	−	3.46410i	−0.429198	−	0.561951i
$39$	−5.29150			−0.847319
$40$	−1.82288	−	3.15731i	−0.288222	−	0.499215i
$41$	−5.14575	−	8.91270i	−0.803631	−	1.39193i	−0.917211	−	0.398401i	$-0.869565\pi$
$41$	−5.14575	−	8.91270i	−0.803631	−	1.39193i	0.113580	−	0.993529i	$-0.463768\pi$
$42$	−2.17712	+	3.77089i	−0.335938	+	0.581861i
$43$	−0.354249	−	0.613577i	−0.0540224	−	0.0935696i	0.837750	−	0.546055i	$-0.183871\pi$
$43$	−0.354249	−	0.613577i	−0.0540224	−	0.0935696i	−0.891772	+	0.452485i	$0.850538\pi$
$44$	−0.322876	+	0.559237i	−0.0486753	+	0.0843082i
$45$	14.5830			2.17391
$46$	3.64575			0.537537
$47$	−4.82288	+	8.35347i	−0.703489	+	1.21848i	0.263745	+	0.964592i	$0.415042\pi$
$47$	−4.82288	+	8.35347i	−0.703489	+	1.21848i	−0.967234	+	0.253886i	$0.918291\pi$
$48$	1.32288	−	2.29129i	0.190941	−	0.330719i
$49$	−4.29150			−0.613072
$50$	8.29150			1.17260
$51$		0			0
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	−4.29150	+	7.43310i	−0.589483	+	1.02101i	0.404817	+	0.914398i	$0.367335\pi$
$53$	−4.29150	+	7.43310i	−0.589483	+	1.02101i	−0.994300	+	0.106617i	$0.965998\pi$
$54$	1.32288	+	2.29129i	0.180021	+	0.311805i
$55$	−1.17712	−	2.03884i	−0.158723	−	0.274917i
$56$	−1.64575			−0.219923
$57$	7.00000	+	9.16515i	0.927173	+	1.21395i
$58$	−3.64575			−0.478711
$59$	−3.96863	−	6.87386i	−0.516671	−	0.894901i	−0.999813	−	0.0193585i	$-0.993838\pi$
$59$	−3.96863	−	6.87386i	−0.516671	−	0.894901i	0.483141	−	0.875542i	$-0.339496\pi$
$60$	4.82288	+	8.35347i	0.622631	+	1.07843i
$61$	7.46863	−	12.9360i	0.956260	−	1.65629i	0.224801	−	0.974405i	$-0.427827\pi$
$61$	7.46863	−	12.9360i	0.956260	−	1.65629i	0.731459	−	0.681886i	$-0.238840\pi$
$62$	0.177124	+	0.306788i	0.0224948	+	0.0389622i
$63$	3.29150	−	5.70105i	0.414690	−	0.718265i
$64$	1.00000			0.125000
$65$	7.29150			0.904400
$66$	0.854249	−	1.47960i	0.105151	−	0.182126i
$67$	2.32288	−	4.02334i	0.283784	−	0.491529i	−0.688529	−	0.725209i	$-0.741743\pi$
$67$	2.32288	−	4.02334i	0.283784	−	0.491529i	0.972314	+	0.233680i	$0.0750767\pi$
$68$		0			0
$69$	−9.64575			−1.16121
$70$	3.00000	−	5.19615i	0.358569	−	0.621059i
$71$	6.64575	+	11.5108i	0.788706	+	1.36608i	0.926760	+	0.375654i	$0.122582\pi$
$71$	6.64575	+	11.5108i	0.788706	+	1.36608i	−0.138055	+	0.990425i	$0.544085\pi$
$72$	−2.00000	+	3.46410i	−0.235702	+	0.408248i
$73$	−6.14575	−	10.6448i	−0.719306	−	1.24587i	−0.961275	−	0.275590i	$-0.911127\pi$
$73$	−6.14575	−	10.6448i	−0.719306	−	1.24587i	0.241969	−	0.970284i	$-0.422207\pi$
$74$	−2.82288	−	4.88936i	−0.328153	−	0.568377i
$75$	−21.9373			−2.53310
$76$	−1.67712	+	4.02334i	−0.192379	+	0.461509i
$77$	−1.06275			−0.121111
$78$	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	$0.761089\pi$
$80$	−1.82288	+	3.15731i	−0.203804	+	0.352998i
$81$	2.50000	+	4.33013i	0.277778	+	0.481125i
$82$	−5.14575	+	8.91270i	−0.568253	+	0.984243i
$83$	−7.93725			−0.871227			−0.435613	−	0.900134i	$-0.643469\pi$
$83$	−7.93725			−0.871227			−0.435613	+	0.900134i	$0.643469\pi$
$84$	4.35425			0.475087
$85$		0			0
$86$	−0.354249	+	0.613577i	−0.0381996	+	0.0661637i
$87$	9.64575			1.03413
$88$	0.645751			0.0688373
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$	−7.29150	−	12.6293i	−0.768592	−	1.33124i
$91$	1.64575	−	2.85052i	0.172522	−	0.298816i
$92$	−1.82288	−	3.15731i	−0.190048	−	0.329173i
$93$	−0.468627	−	0.811686i	−0.0485944	−	0.0841679i
$94$	9.64575			0.994883
$95$	−9.64575	−	12.6293i	−0.989633	−	1.29573i
$96$	−2.64575			−0.270031
$97$	7.14575	+	12.3768i	0.725541	+	1.25667i	0.958751	+	0.284248i	$0.0917438\pi$
$97$	7.14575	+	12.3768i	0.725541	+	1.25667i	−0.233210	+	0.972426i	$0.574923\pi$
$98$	2.14575	+	3.71655i	0.216754	+	0.375428i
$99$	−1.29150	+	2.23695i	−0.129801	+	0.224822i
$100$	−4.14575	−	7.18065i	−0.414575	−	0.718065i
$101$	4.17712	−	7.23499i	0.415639	−	0.719909i	−0.579856	−	0.814719i	$-0.696891\pi$
$101$	4.17712	−	7.23499i	0.415639	−	0.719909i	0.995495	+	0.0948105i	$0.0302245\pi$
$102$		0			0
$103$	−2.70850			−0.266876			−0.133438	−	0.991057i	$-0.542602\pi$
$103$	−2.70850			−0.266876			−0.133438	+	0.991057i	$0.542602\pi$
$104$	−1.00000	+	1.73205i	−0.0980581	+	0.169842i
$105$	−7.93725	+	13.7477i	−0.774597	+	1.34164i
$106$	8.58301			0.833655
$107$	4.70850			0.455188			0.227594	−	0.973756i	$-0.426914\pi$
$107$	4.70850			0.455188			0.227594	+	0.973756i	$0.426914\pi$
$108$	1.32288	−	2.29129i	0.127294	−	0.220479i
$109$	3.29150	+	5.70105i	0.315269	+	0.546062i	0.979495	−	0.201470i	$-0.0645720\pi$
$109$	3.29150	+	5.70105i	0.315269	+	0.546062i	−0.664226	+	0.747532i	$0.731239\pi$
$110$	−1.17712	+	2.03884i	−0.112234	+	0.194396i
$111$	7.46863	+	12.9360i	0.708891	+	1.22783i
$112$	0.822876	+	1.42526i	0.0777544	+	0.134675i
$113$	5.58301			0.525205			0.262602	−	0.964904i	$-0.415419\pi$
$113$	5.58301			0.525205			0.262602	+	0.964904i	$0.415419\pi$
$114$	4.43725	−	10.6448i	0.415587	−	0.996973i
$115$	13.2915			1.23944
$116$	1.82288	+	3.15731i	0.169250	+	0.293149i
$117$	−4.00000	−	6.92820i	−0.369800	−	0.640513i
$118$	−3.96863	+	6.87386i	−0.365342	+	0.632790i
$119$		0			0
$120$	4.82288	−	8.35347i	0.440266	−	0.762564i
$121$	−10.5830			−0.962091
$122$	−14.9373			−1.35236
$123$	13.6144	−	23.5808i	1.22757	−	2.12621i
$124$	0.177124	−	0.306788i	0.0159062	−	0.0275504i
$125$	12.0000			1.07331
$126$	−6.58301			−0.586461
$127$	1.35425	−	2.34563i	0.120170	−	0.208141i	−0.799665	−	0.600447i	$-0.794989\pi$
$127$	1.35425	−	2.34563i	0.120170	−	0.208141i	0.919835	+	0.392306i	$0.128323\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	0.937254	−	1.62337i	0.0825206	−	0.142930i
$130$	−3.64575	−	6.31463i	−0.319754	−	0.553829i
$131$	6.96863	+	12.0700i	0.608852	+	1.05456i	0.991430	+	0.130639i	$0.0417029\pi$
$131$	6.96863	+	12.0700i	0.608852	+	1.05456i	−0.382578	+	0.923923i	$0.624964\pi$
$132$	−1.70850			−0.148706
$133$	−7.11438	+	0.920365i	−0.616895	+	0.0798058i
$134$	−4.64575			−0.401332
$135$	4.82288	+	8.35347i	0.415087	+	0.718952i
$136$		0			0
$137$	2.79150	−	4.83502i	0.238494	−	0.413084i	−0.721788	−	0.692114i	$-0.756680\pi$
$137$	2.79150	−	4.83502i	0.238494	−	0.413084i	0.960282	+	0.279030i	$0.0900129\pi$
$138$	4.82288	+	8.35347i	0.410550	+	0.711094i
$139$	−6.67712	+	11.5651i	−0.566346	+	0.980941i	0.430577	+	0.902554i	$0.358310\pi$
$139$	−6.67712	+	11.5651i	−0.566346	+	0.980941i	−0.996923	+	0.0783866i	$0.975023\pi$
$140$	−6.00000			−0.507093
$141$	−25.5203			−2.14919
$142$	6.64575	−	11.5108i	0.557699	−	0.965963i
$143$	−0.645751	+	1.11847i	−0.0540004	+	0.0935315i
$144$	4.00000			0.333333
$145$	−13.2915			−1.10380
$146$	−6.14575	+	10.6448i	−0.508626	+	0.880966i
$147$	−5.67712	−	9.83307i	−0.468241	−	0.811018i
$148$	−2.82288	+	4.88936i	−0.232039	+	0.401903i
$149$	2.46863	+	4.27579i	0.202238	+	0.350286i	0.949249	−	0.314525i	$-0.101845\pi$
$149$	2.46863	+	4.27579i	0.202238	+	0.350286i	−0.747011	+	0.664811i	$0.768512\pi$
$150$	10.9686	+	18.9982i	0.895585	+	1.55120i
$151$	−2.93725			−0.239030			−0.119515	−	0.992832i	$-0.538134\pi$
$151$	−2.93725			−0.239030			−0.119515	+	0.992832i	$0.538134\pi$
$152$	4.32288	−	0.559237i	0.350632	−	0.0453601i
$153$		0			0
$154$	0.531373	+	0.920365i	0.0428193	+	0.0741651i
$155$	0.645751	+	1.11847i	0.0518680	+	0.0898380i
$156$	2.64575	−	4.58258i	0.211830	−	0.366900i
$157$	−5.29150	−	9.16515i	−0.422308	−	0.731459i	0.573857	−	0.818956i	$-0.305447\pi$
$157$	−5.29150	−	9.16515i	−0.422308	−	0.731459i	−0.996165	+	0.0874969i	$0.972113\pi$
$158$	2.00000	−	3.46410i	0.159111	−	0.275589i
$159$	−22.7085			−1.80090
$160$	3.64575			0.288222
$161$	3.00000	−	5.19615i	0.236433	−	0.409514i
$162$	2.50000	−	4.33013i	0.196419	−	0.340207i
$163$	−11.9373			−0.934998			−0.467499	−	0.883994i	$-0.654845\pi$
$163$	−11.9373			−0.934998			−0.467499	+	0.883994i	$0.654845\pi$
$164$	10.2915			0.803631
$165$	3.11438	−	5.39426i	0.242454	−	0.419943i
$166$	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	$0.0129748\pi$
$168$	−2.17712	−	3.77089i	−0.167969	−	0.290930i
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$	−6.70850	+	16.0934i	−0.513012	+	1.23069i
$172$	0.708497			0.0540224
$173$	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	$0.760087\pi$
$174$	−4.82288	−	8.35347i	−0.365621	−	0.633275i
$175$	6.82288	−	11.8176i	0.515761	−	0.893324i
$176$	−0.322876	−	0.559237i	−0.0243377	−	0.0421541i
$177$	10.5000	−	18.1865i	0.789228	−	1.36698i
$178$		0			0
$179$	19.9373			1.49018			0.745090	−	0.666964i	$-0.232406\pi$
$179$	19.9373			1.49018			0.745090	+	0.666964i	$0.232406\pi$
$180$	−7.29150	+	12.6293i	−0.543477	+	0.941329i
$181$	2.11438	−	3.66221i	0.157160	−	0.272210i	−0.776683	−	0.629892i	$-0.783099\pi$
$181$	2.11438	−	3.66221i	0.157160	−	0.272210i	0.933844	+	0.357682i	$0.116433\pi$
$182$	−3.29150			−0.243982
$183$	39.5203			2.92142
$184$	−1.82288	+	3.15731i	−0.134384	+	0.232760i
$185$	−10.2915	−	17.8254i	−0.756646	−	1.31055i
$186$	−0.468627	+	0.811686i	−0.0343614	+	0.0595157i
$187$		0			0
$188$	−4.82288	−	8.35347i	−0.351744	−	0.609239i
$189$	4.35425			0.316725
$190$	−6.11438	+	14.6681i	−0.443584	+	1.06414i
$191$	−14.5830			−1.05519			−0.527595	−	0.849496i	$-0.676906\pi$
$191$	−14.5830			−1.05519			−0.527595	+	0.849496i	$0.676906\pi$
$192$	1.32288	+	2.29129i	0.0954703	+	0.165359i
$193$	3.29150	+	5.70105i	0.236928	+	0.410371i	0.959831	−	0.280578i	$-0.0905263\pi$
$193$	3.29150	+	5.70105i	0.236928	+	0.410371i	−0.722904	+	0.690949i	$0.757193\pi$
$194$	7.14575	−	12.3768i	0.513035	−	0.888603i
$195$	9.64575	+	16.7069i	0.690747	+	1.19641i
$196$	2.14575	−	3.71655i	0.153268	−	0.265468i
$197$	−2.35425			−0.167733			−0.0838666	−	0.996477i	$-0.526727\pi$
$197$	−2.35425			−0.167733			−0.0838666	+	0.996477i	$0.526727\pi$
$198$	2.58301			0.183566
$199$	−5.93725	+	10.2836i	−0.420881	+	0.728987i	−0.996026	−	0.0890645i	$-0.971612\pi$
$199$	−5.93725	+	10.2836i	−0.420881	+	0.728987i	0.575145	+	0.818051i	$0.304946\pi$
$200$	−4.14575	+	7.18065i	−0.293149	+	0.507749i
$201$	12.2915			0.866976
$202$	−8.35425			−0.587803
$203$	−3.00000	+	5.19615i	−0.210559	+	0.364698i
$204$		0			0
$205$	−18.7601	+	32.4935i	−1.31026	+	2.26944i
$206$	1.35425	+	2.34563i	0.0943550	+	0.163428i
$207$	−7.29150	−	12.6293i	−0.506794	−	0.877794i
$208$	2.00000			0.138675
$209$	2.79150	−	0.361128i	0.193092	−	0.0249797i
$210$	15.8745			1.09545
$211$	1.35425	+	2.34563i	0.0932303	+	0.161480i	0.908869	−	0.417082i	$-0.136947\pi$
$211$	1.35425	+	2.34563i	0.0932303	+	0.161480i	−0.815638	+	0.578562i	$0.803614\pi$
$212$	−4.29150	−	7.43310i	−0.294742	−	0.510507i
$213$	−17.5830	+	30.4547i	−1.20477	+	2.08672i
$214$	−2.35425	−	4.07768i	−0.160933	−	0.278744i
$215$	−1.29150	+	2.23695i	−0.0880797	+	0.152559i
$216$	−2.64575			−0.180021
$217$	0.583005			0.0395770
$218$	3.29150	−	5.70105i	0.222929	−	0.386124i
$219$	16.2601	−	28.1634i	1.09876	−	1.90310i
$220$	2.35425			0.158723
$221$		0			0
$222$	7.46863	−	12.9360i	0.501261	−	0.868210i
$223$	−14.4059	−	24.9517i	−0.964689	−	1.67089i	−0.710448	−	0.703750i	$-0.751508\pi$
$223$	−14.4059	−	24.9517i	−0.964689	−	1.67089i	−0.254241	−	0.967141i	$-0.581826\pi$
$224$	0.822876	−	1.42526i	0.0549807	−	0.0952294i
$225$	−16.5830	−	28.7226i	−1.10553	−	1.91484i
$226$	−2.79150	−	4.83502i	−0.185688	−	0.321621i
$227$	−12.6458			−0.839328			−0.419664	−	0.907680i	$-0.637852\pi$
$227$	−12.6458			−0.839328			−0.419664	+	0.907680i	$0.637852\pi$
$228$	−11.4373	+	1.47960i	−0.757451	+	0.0979890i
$229$	20.0000			1.32164			0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000			1.32164			0.660819	+	0.750546i	$0.270209\pi$
$230$	−6.64575	−	11.5108i	−0.438208	−	0.758998i
$231$	−1.40588	−	2.43506i	−0.0925002	−	0.160215i
$232$	1.82288	−	3.15731i	0.119678	−	0.207288i
$233$	6.43725	+	11.1497i	0.421719	+	0.730438i	0.996108	−	0.0881444i	$-0.0280937\pi$
$233$	6.43725	+	11.1497i	0.421719	+	0.730438i	−0.574389	+	0.818582i	$0.694760\pi$
$234$	−4.00000	+	6.92820i	−0.261488	+	0.452911i
$235$	35.1660			2.29398
$236$	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	$0.626871\pi$
$240$	−9.64575			−0.622631
$241$	−6.79150	+	11.7632i	−0.437479	+	0.757736i	−0.997494	−	0.0707462i	$-0.977462\pi$
$241$	−6.79150	+	11.7632i	−0.437479	+	0.757736i	0.560015	+	0.828482i	$0.310795\pi$
$242$	5.29150	+	9.16515i	0.340151	+	0.589158i
$243$	−10.5830	+	18.3303i	−0.678900	+	1.17589i
$244$	7.46863	+	12.9360i	0.478130	+	0.828145i
$245$	7.82288	+	13.5496i	0.499785	+	0.865653i
$246$	−27.2288			−1.73604
$247$	−3.35425	+	8.04668i	−0.213426	+	0.511998i
$248$	−0.354249			−0.0224948
$249$	−10.5000	−	18.1865i	−0.665410	−	1.15252i
$250$	−6.00000	−	10.3923i	−0.379473	−	0.657267i
$251$	−1.38562	+	2.39997i	−0.0874597	+	0.151485i	−0.906437	−	0.422342i	$-0.861208\pi$
$251$	−1.38562	+	2.39997i	−0.0874597	+	0.151485i	0.818977	+	0.573826i	$0.194542\pi$
$252$	3.29150	+	5.70105i	0.207345	+	0.359132i
$253$	−1.17712	+	2.03884i	−0.0740052	+	0.128181i
$254$	−2.70850			−0.169946
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.854249	+	1.47960i	−0.0532866	+	0.0922950i	−0.891438	−	0.453142i	$-0.850303\pi$
$257$	−0.854249	+	1.47960i	−0.0532866	+	0.0922950i	0.838152	+	0.545437i	$0.183636\pi$
$258$	−1.87451			−0.116702
$259$	−9.29150			−0.577346
$260$	−3.64575	+	6.31463i	−0.226100	+	0.391617i
$261$	7.29150	+	12.6293i	0.451333	+	0.781731i
$262$	6.96863	−	12.0700i	0.430523	−	0.745688i
$263$	−2.46863	−	4.27579i	−0.152222	−	0.263656i	0.779822	−	0.626001i	$-0.215310\pi$
$263$	−2.46863	−	4.27579i	−0.152222	−	0.263656i	−0.932044	+	0.362345i	$0.881976\pi$
$264$	0.854249	+	1.47960i	0.0525754	+	0.0910632i
$265$	31.2915			1.92222
$266$	4.35425	+	5.70105i	0.266976	+	0.349554i
$267$		0			0
$268$	2.32288	+	4.02334i	0.141892	+	0.245765i
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$	4.82288	−	8.35347i	0.293511	−	0.508376i
$271$	−8.82288	−	15.2817i	−0.535952	−	0.928295i	−0.999117	−	0.0420233i	$-0.986620\pi$
$271$	−8.82288	−	15.2817i	−0.535952	−	0.928295i	0.463165	−	0.886272i	$-0.346714\pi$
$272$		0			0
$273$	8.70850			0.527062
$274$	−5.58301			−0.337282
$275$	−2.67712	+	4.63692i	−0.161437	+	0.279617i
$276$	4.82288	−	8.35347i	0.290303	−	0.502820i
$277$	9.52026			0.572017			0.286008	−	0.958227i	$-0.407671\pi$
$277$	9.52026			0.572017			0.286008	+	0.958227i	$0.407671\pi$
$278$	13.3542			0.800935
$279$	0.708497	−	1.22715i	0.0424166	−	0.0734678i
$280$	3.00000	+	5.19615i	0.179284	+	0.310530i
$281$	13.7288	−	23.7789i	0.818989	−	1.41853i	−0.0874389	−	0.996170i	$-0.527868\pi$
$281$	13.7288	−	23.7789i	0.818989	−	1.41853i	0.906428	−	0.422361i	$-0.138798\pi$
$282$	12.7601	+	22.1012i	0.759855	+	1.31611i
$283$	−12.6771	−	21.9574i	−0.753577	−	1.30523i	−0.946079	−	0.323937i	$-0.894993\pi$
$283$	−12.6771	−	21.9574i	−0.753577	−	1.30523i	0.192502	−	0.981297i	$-0.438340\pi$
$284$	−13.2915			−0.788706
$285$	16.1771	−	38.8081i	0.958250	−	2.29879i
$286$	1.29150			0.0763682
$287$	8.46863	+	14.6681i	0.499887	+	0.865830i
$288$	−2.00000	−	3.46410i	−0.117851	−	0.204124i
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	6.64575	+	11.5108i	0.390252	+	0.675936i
$291$	−18.9059	+	32.7459i	−1.10828	+	1.91960i
$292$	12.2915			0.719306
$293$	13.0627			0.763134			0.381567	−	0.924341i	$-0.375385\pi$
$293$	13.0627			0.763134			0.381567	+	0.924341i	$0.375385\pi$
$294$	−5.67712	+	9.83307i	−0.331097	+	0.573476i
$295$	−14.4686	+	25.0604i	−0.842396	+	1.45907i
$296$	5.64575			0.328153
$297$	−1.70850			−0.0991371
$298$	2.46863	−	4.27579i	0.143004	−	0.247690i
$299$	−3.64575	−	6.31463i	−0.210839	−	0.365184i
$300$	10.9686	−	18.9982i	0.633274	−	1.09686i
$301$	0.583005	+	1.00979i	0.0336039	+	0.0582036i
$302$	1.46863	+	2.54374i	0.0845100	+	0.146376i
$303$	22.1033			1.26980
$304$	−2.64575	−	3.46410i	−0.151744	−	0.198680i
$305$	−54.4575			−3.11823
$306$		0			0
$307$	2.32288	+	4.02334i	0.132574	+	0.229624i	0.924668	−	0.380775i	$-0.124343\pi$
$307$	2.32288	+	4.02334i	0.132574	+	0.229624i	−0.792094	+	0.610399i	$0.791009\pi$
$308$	0.531373	−	0.920365i	0.0302778	−	0.0524427i
$309$	−3.58301	−	6.20595i	−0.203830	−	0.353044i
$310$	0.645751	−	1.11847i	0.0366762	−	0.0635251i
$311$	8.35425			0.473726			0.236863	−	0.971543i	$-0.423881\pi$
$311$	8.35425			0.473726			0.236863	+	0.971543i	$0.423881\pi$
$312$	−5.29150			−0.299572
$313$	11.4373	−	19.8099i	0.646472	−	1.11972i	−0.337488	−	0.941330i	$-0.609577\pi$
$313$	11.4373	−	19.8099i	0.646472	−	1.11972i	0.983959	−	0.178392i	$-0.0570895\pi$
$314$	−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	$0.112775\pi$
$318$	11.3542	+	19.6661i	0.636715	+	1.10282i
$319$	1.17712	−	2.03884i	0.0659063	−	0.114153i
$320$	−1.82288	−	3.15731i	−0.101902	−	0.176499i
$321$	6.22876	+	10.7885i	0.347655	+	0.602157i
$322$	−6.00000			−0.334367
$323$		0			0
$324$	−5.00000			−0.277778
$325$	−8.29150	−	14.3613i	−0.459930	−	0.796622i
$326$	5.96863	+	10.3380i	0.330572	+	0.572567i
$327$	−8.70850	+	15.0836i	−0.481581	+	0.834123i
$328$	−5.14575	−	8.91270i	−0.284127	−	0.492122i
$329$	7.93725	−	13.7477i	0.437595	−	0.757937i
$330$	−6.22876			−0.342882
$331$	−27.8118			−1.52867			−0.764336	−	0.644818i	$-0.776933\pi$
$331$	−27.8118			−1.52867			−0.764336	+	0.644818i	$0.776933\pi$
$332$	3.96863	−	6.87386i	0.217807	−	0.377252i
$333$	−11.2915	+	19.5575i	−0.618771	+	1.07174i
$334$	−12.0000			−0.656611
$335$	−16.9373			−0.925381
$336$	−2.17712	+	3.77089i	−0.118772	+	0.205719i
$337$	10.1458	+	17.5730i	0.552674	+	0.957260i	0.998080	+	0.0619313i	$0.0197260\pi$
$337$	10.1458	+	17.5730i	0.552674	+	0.957260i	−0.445406	+	0.895329i	$0.646941\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$	7.38562	+	12.7923i	0.401132	+	0.694781i
$340$		0			0
$341$	−0.228757			−0.0123879
$342$	17.2915	−	2.23695i	0.935017	−	0.120960i
$343$	18.5830			1.00339
$344$	−0.354249	−	0.613577i	−0.0190998	−	0.0330818i
$345$	17.5830	+	30.4547i	0.946637	+	1.63962i
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	−1.61438	−	2.79619i	−0.0866644	−	0.150107i	0.819435	−	0.573172i	$-0.194287\pi$
$347$	−1.61438	−	2.79619i	−0.0866644	−	0.150107i	−0.906099	+	0.423065i	$0.860954\pi$
$348$	−4.82288	+	8.35347i	−0.258533	+	0.447793i
$349$	−21.1660			−1.13299			−0.566495	−	0.824065i	$-0.691701\pi$
$349$	−21.1660			−1.13299			−0.566495	+	0.824065i	$0.691701\pi$
$350$	−13.6458			−0.729396
$351$	2.64575	−	4.58258i	0.141220	−	0.244600i
$352$	−0.322876	+	0.559237i	−0.0172093	+	0.0298074i
$353$	−18.8745			−1.00459			−0.502294	−	0.864697i	$-0.667511\pi$
$353$	−18.8745			−1.00459			−0.502294	+	0.864697i	$0.667511\pi$
$354$	−21.0000			−1.11614
$355$	24.2288	−	41.9654i	1.28593	−	2.22729i
$356$		0			0
$357$		0			0
$358$	−9.96863	−	17.2662i	−0.526858	−	0.912545i
$359$	−5.46863	−	9.47194i	−0.288623	−	0.499910i	0.684858	−	0.728676i	$-0.259864\pi$
$359$	−5.46863	−	9.47194i	−0.288623	−	0.499910i	−0.973481	+	0.228766i	$0.926531\pi$
$360$	14.5830			0.768592
$361$	18.3745	−	4.83502i	0.967079	−	0.254475i
$362$	−4.22876			−0.222259
$363$	−14.0000	−	24.2487i	−0.734809	−	1.27273i
$364$	1.64575	+	2.85052i	0.0862608	+	0.149408i
$365$	−22.4059	+	38.8081i	−1.17278	+	2.03131i
$366$	−19.7601	−	34.2255i	−1.03288	−	1.78900i
$367$	5.11438	−	8.85836i	0.266968	−	0.462403i	−0.701109	−	0.713054i	$-0.747311\pi$
$367$	5.11438	−	8.85836i	0.266968	−	0.462403i	0.968077	+	0.250651i	$0.0806447\pi$
$368$	3.64575			0.190048
$369$	41.1660			2.14302
$370$	−10.2915	+	17.8254i	−0.535030	+	0.926699i
$371$	7.06275	−	12.2330i	0.366680	−	0.635108i
$372$	0.937254			0.0485944
$373$	−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
$376$	−4.82288	+	8.35347i	−0.248721	+	0.430797i
$377$	3.64575	+	6.31463i	0.187766	+	0.325220i
$378$	−2.17712	−	3.77089i	−0.111979	−	0.193954i
$379$	21.2915			1.09367			0.546836	−	0.837240i	$-0.315832\pi$
$379$	21.2915			1.09367			0.546836	+	0.837240i	$0.315832\pi$
$380$	15.7601	−	2.03884i	0.808478	−	0.104590i
$381$	7.16601			0.367126
$382$	7.29150	+	12.6293i	0.373066	+	0.646169i
$383$	15.7601	+	27.2973i	0.805305	+	1.39483i	0.916085	+	0.400984i	$0.131332\pi$
$383$	15.7601	+	27.2973i	0.805305	+	1.39483i	−0.110780	+	0.993845i	$0.535335\pi$
$384$	1.32288	−	2.29129i	0.0675077	−	0.116927i
$385$	1.93725	+	3.35542i	0.0987316	+	0.171008i
$386$	3.29150	−	5.70105i	0.167533	−	0.290176i
$387$	2.83399			0.144060
$388$	−14.2915			−0.725541
$389$	−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	$0.265060\pi$
$390$	9.64575	−	16.7069i	0.488432	−	0.845988i
$391$		0			0
$392$	−4.29150			−0.216754
$393$	−18.4373	+	31.9343i	−0.930036	+	1.61087i
$394$	1.17712	+	2.03884i	0.0593027	+	0.102715i
$395$	7.29150	−	12.6293i	0.366875	−	0.635447i
$396$	−1.29150	−	2.23695i	−0.0649004	−	0.112411i
$397$	−18.4686	−	31.9886i	−0.926914	−	1.60546i	−0.788454	−	0.615094i	$-0.789118\pi$
$397$	−18.4686	−	31.9886i	−0.926914	−	1.60546i	−0.138460	−	0.990368i	$-0.544215\pi$
$398$	11.8745			0.595215
$399$	−11.5203	−	15.0836i	−0.576734	−	0.755122i
$400$	8.29150			0.414575
$401$	−3.20850	−	5.55728i	−0.160225	−	0.277517i	0.774724	−	0.632299i	$-0.217889\pi$
$401$	−3.20850	−	5.55728i	−0.160225	−	0.277517i	−0.934949	+	0.354782i	$0.884555\pi$
$402$	−6.14575	−	10.6448i	−0.306522	−	0.530912i
$403$	0.354249	−	0.613577i	0.0176464	−	0.0305644i
$404$	4.17712	+	7.23499i	0.207820	+	0.359954i
$405$	9.11438	−	15.7866i	0.452897	−	0.784441i
$406$	6.00000			0.297775
$407$	3.64575			0.180713
$408$		0			0
$409$	−6.79150	+	11.7632i	−0.335818	+	0.581654i	−0.983642	−	0.180136i	$-0.942346\pi$
$409$	−6.79150	+	11.7632i	−0.335818	+	0.581654i	0.647823	+	0.761790i	$0.275679\pi$
$410$	37.5203			1.85299
$411$	14.7712			0.728612
$412$	1.35425	−	2.34563i	0.0667190	−	0.115561i
$413$	6.53137	+	11.3127i	0.321388	+	0.556660i
$414$	−7.29150	+	12.6293i	−0.358358	+	0.620694i
$415$	14.4686	+	25.0604i	0.710237	+	1.23017i
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$	−35.3320			−1.73022
$418$	−1.70850	−	2.23695i	−0.0835653	−	0.109413i
$419$	31.7490			1.55104			0.775520	−	0.631322i	$-0.217488\pi$
$419$	31.7490			1.55104			0.775520	+	0.631322i	$0.217488\pi$
$420$	−7.93725	−	13.7477i	−0.387298	−	0.670820i
$421$	−11.4059	−	19.7556i	−0.555889	−	0.962827i	−0.997834	−	0.0657853i	$-0.979045\pi$
$421$	−11.4059	−	19.7556i	−0.555889	−	0.962827i	0.441945	−	0.897042i	$-0.354289\pi$
$422$	1.35425	−	2.34563i	0.0659238	−	0.114183i
$423$	−19.2915	−	33.4139i	−0.937985	−	1.62464i
$424$	−4.29150	+	7.43310i	−0.208414	+	0.360983i
$425$		0			0
$426$	35.1660			1.70380
$427$	−12.2915	+	21.2895i	−0.594828	+	1.03027i
$428$	−2.35425	+	4.07768i	−0.113797	+	0.197102i
$429$	−3.41699			−0.164974
$430$	2.58301			0.124564
$431$	1.93725	−	3.35542i	0.0933142	−	0.161625i	−0.815590	−	0.578631i	$-0.803587\pi$
$431$	1.93725	−	3.35542i	0.0933142	−	0.161625i	0.908904	+	0.417006i	$0.136921\pi$
$432$	1.32288	+	2.29129i	0.0636469	+	0.110240i
$433$	6.93725	−	12.0157i	0.333383	−	0.577437i	−0.649790	−	0.760114i	$-0.725143\pi$
$433$	6.93725	−	12.0157i	0.333383	−	0.577437i	0.983173	+	0.182677i	$0.0584764\pi$
$434$	−0.291503	−	0.504897i	−0.0139926	−	0.0242358i
$435$	−17.5830	−	30.4547i	−0.843041	−	1.46019i
$436$	−6.58301			−0.315269
$437$	−6.11438	+	14.6681i	−0.292490	+	0.701670i
$438$	−32.5203			−1.55388
$439$	18.4059	+	31.8799i	0.878465	+	1.52155i	0.853025	+	0.521869i	$0.174765\pi$
$439$	18.4059	+	31.8799i	0.878465	+	1.52155i	0.0254393	+	0.999676i	$0.491902\pi$
$440$	−1.17712	−	2.03884i	−0.0561172	−	0.0971978i
$441$	8.58301	−	14.8662i	0.408715	−	0.707914i
$442$		0			0
$443$	−2.67712	+	4.63692i	−0.127194	+	0.220306i	−0.922588	−	0.385786i	$-0.873930\pi$
$443$	−2.67712	+	4.63692i	−0.127194	+	0.220306i	0.795394	+	0.606092i	$0.207264\pi$
$444$	−14.9373			−0.708891
$445$		0			0
$446$	−14.4059	+	24.9517i	−0.682138	+	1.18150i
$447$	−6.53137	+	11.3127i	−0.308923	+	0.535071i
$448$	−1.64575			−0.0777544
$449$	−13.7085			−0.646944			−0.323472	−	0.946238i	$-0.604850\pi$
$449$	−13.7085			−0.646944			−0.323472	+	0.946238i	$0.604850\pi$
$450$	−16.5830	+	28.7226i	−0.781730	+	1.35400i
$451$	−3.32288	−	5.75539i	−0.156468	−	0.271011i
$452$	−2.79150	+	4.83502i	−0.131301	+	0.227420i
$453$	−3.88562	−	6.73009i	−0.182562	−	0.316207i
$454$	6.32288	+	10.9515i	0.296747	+	0.513981i
$455$	−12.0000			−0.562569
$456$	7.00000	+	9.16515i	0.327805	+	0.429198i
$457$	1.12549			0.0526483			0.0263242	−	0.999653i	$-0.491620\pi$
$457$	1.12549			0.0526483			0.0263242	+	0.999653i	$0.491620\pi$
$458$	−10.0000	−	17.3205i	−0.467269	−	0.809334i
$459$		0			0
$460$	−6.64575	+	11.5108i	−0.309860	+	0.536693i
$461$	11.5830	+	20.0624i	0.539474	+	0.934397i	0.998932	+	0.0461975i	$0.0147103\pi$
$461$	11.5830	+	20.0624i	0.539474	+	0.934397i	−0.459458	+	0.888200i	$0.651956\pi$
$462$	−1.40588	+	2.43506i	−0.0654075	+	0.113289i
$463$	14.4575			0.671898			0.335949	−	0.941880i	$-0.390943\pi$
$463$	14.4575			0.671898			0.335949	+	0.941880i	$0.390943\pi$
$464$	−3.64575			−0.169250
$465$	−1.70850	+	2.95920i	−0.0792297	+	0.137230i
$466$	6.43725	−	11.1497i	0.298200	−	0.516498i
$467$	−24.6458			−1.14047			−0.570235	−	0.821482i	$-0.693148\pi$
$467$	−24.6458			−1.14047			−0.570235	+	0.821482i	$0.693148\pi$
$468$	8.00000			0.369800
$469$	−3.82288	+	6.62141i	−0.176524	+	0.305749i
$470$	−17.5830	−	30.4547i	−0.811044	−	1.40477i
$471$	14.0000	−	24.2487i	0.645086	−	1.11732i
$472$	−3.96863	−	6.87386i	−0.182671	−	0.316395i
$473$	−0.228757	−	0.396218i	−0.0105182	−	0.0182181i
$474$	10.5830			0.486094
$475$	−13.9059	+	33.3595i	−0.638046	+	1.53064i
$476$		0			0
$477$	−17.1660	−	29.7324i	−0.785978	−	1.36135i
$478$	6.00000	+	10.3923i	0.274434	+	0.475333i
$479$	7.29150	−	12.6293i	0.333157	−	0.577045i	−0.649972	−	0.759958i	$-0.725219\pi$
$479$	7.29150	−	12.6293i	0.333157	−	0.577045i	0.983129	+	0.182913i	$0.0585527\pi$
$480$	4.82288	+	8.35347i	0.220133	+	0.381282i
$481$	−5.64575	+	9.77873i	−0.257424	+	0.445872i
$482$	13.5830			0.618689
$483$	15.8745			0.722315
$484$	5.29150	−	9.16515i	0.240523	−	0.416598i
$485$	26.0516	−	45.1228i	1.18294	−	2.04892i
$486$	21.1660			0.960110
$487$	−22.2288			−1.00728			−0.503641	−	0.863913i	$-0.668006\pi$
$487$	−22.2288			−1.00728			−0.503641	+	0.863913i	$0.668006\pi$
$488$	7.46863	−	12.9360i	0.338089	−	0.585587i
$489$	−15.7915	−	27.3517i	−0.714116	−	1.23689i
$490$	7.82288	−	13.5496i	0.353401	−	0.612109i
$491$	−14.3542	−	24.8623i	−0.647798	−	1.12202i	−0.983648	−	0.180104i	$-0.942357\pi$
$491$	−14.3542	−	24.8623i	−0.647798	−	1.12202i	0.335849	−	0.941916i	$-0.390977\pi$
$492$	13.6144	+	23.5808i	0.613784	+	1.06310i
$493$		0			0
$494$	8.64575	−	1.11847i	0.388991	−	0.0503225i
$495$	9.41699			0.423262
$496$	0.177124	+	0.306788i	0.00795312	+	0.0137752i
$497$	−10.9373	−	18.9439i	−0.490603	−	0.849749i
$498$	−10.5000	+	18.1865i	−0.470516	+	0.814958i
$499$	15.6144	+	27.0449i	0.698996	+	1.21070i	0.968815	+	0.247785i	$0.0797026\pi$
$499$	15.6144	+	27.0449i	0.698996	+	1.21070i	−0.269819	+	0.962911i	$0.586964\pi$
$500$	−6.00000	+	10.3923i	−0.268328	+	0.464758i
$501$	31.7490			1.41844
$502$	2.77124			0.123687
$503$	12.5314	−	21.7050i	0.558746	−	0.967777i	−0.438855	−	0.898558i	$-0.644616\pi$
$503$	12.5314	−	21.7050i	0.558746	−	0.967777i	0.997601	−	0.0692192i	$-0.0220508\pi$
$504$	3.29150	−	5.70105i	0.146615	−	0.253945i
$505$	−30.4575			−1.35534
$506$	2.35425			0.104659
$507$	−11.9059	+	20.6216i	−0.528759	+	0.915837i
$508$	1.35425	+	2.34563i	0.0600851	+	0.104070i
$509$	−15.8745	+	27.4955i	−0.703625	+	1.21871i	0.263560	+	0.964643i	$0.415103\pi$
$509$	−15.8745	+	27.4955i	−0.703625	+	1.21871i	−0.967185	+	0.254072i	$0.918230\pi$
$510$		0			0
$511$	10.1144	+	17.5186i	0.447434	+	0.774978i
$512$	1.00000			0.0441942
$513$	−11.4373	+	1.47960i	−0.504967	+	0.0653260i
$514$	1.70850			0.0753586
$515$	4.93725	+	8.55157i	0.217561	+	0.376827i
$516$	0.937254	+	1.62337i	0.0412603	+	0.0714649i
$517$	−3.11438	+	5.39426i	−0.136970	+	0.237239i
$518$	4.64575	+	8.04668i	0.204123	+	0.353551i
$519$	−7.93725	+	13.7477i	−0.348407	+	0.603458i
$520$	7.29150			0.319754
$521$	−22.2915			−0.976608			−0.488304	−	0.872673i	$-0.662384\pi$
$521$	−22.2915			−0.976608			−0.488304	+	0.872673i	$0.662384\pi$
$522$	7.29150	−	12.6293i	0.319140	−	0.552767i
$523$	−14.9373	+	25.8721i	−0.653161	+	1.13131i	0.329191	+	0.944263i	$0.393224\pi$
$523$	−14.9373	+	25.8721i	−0.653161	+	1.13131i	−0.982352	+	0.187044i	$0.940109\pi$
$524$	−13.9373			−0.608852
$525$	36.1033			1.57568
$526$	−2.46863	+	4.27579i	−0.107637	+	0.186433i
$527$		0			0
$528$	0.854249	−	1.47960i	0.0371764	−	0.0643914i
$529$	4.85425	+	8.40781i	0.211054	+	0.365557i
$530$	−15.6458	−	27.0992i	−0.679608	−	1.17712i
$531$	31.7490			1.37779
$532$	2.76013	−	6.62141i	0.119667	−	0.287075i
$533$	20.5830			0.891549
$534$		0			0
$535$	−8.58301	−	14.8662i	−0.371076	−	0.642722i
$536$	2.32288	−	4.02334i	0.100333	−	0.173782i
$537$	26.3745	+	45.6820i	1.13814	+	1.97132i
$538$		0			0
$539$	−2.77124			−0.119366
$540$	−9.64575			−0.415087
$541$	−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	$0.221681\pi$
$542$	−8.82288	+	15.2817i	−0.378975	+	0.656404i
$543$	11.1882			0.480133
$544$		0			0
$545$	12.0000	−	20.7846i	0.514024	−	0.890315i
$546$	−4.35425	−	7.54178i	−0.186345	−	0.322758i
$547$	−0.354249	+	0.613577i	−0.0151466	+	0.0262346i	−0.873499	−	0.486825i	$-0.838155\pi$
$547$	−0.354249	+	0.613577i	−0.0151466	+	0.0262346i	0.858353	+	0.513060i	$0.171488\pi$
$548$	2.79150	+	4.83502i	0.119247	+	0.206542i
$549$	29.8745	+	51.7442i	1.27501	+	2.20839i
$550$	5.35425			0.228306
$551$	6.11438	−	14.6681i	0.260481	−	0.624882i
$552$	−9.64575			−0.410550
$553$	−3.29150	−	5.70105i	−0.139969	−	0.242433i
$554$	−4.76013	−	8.24479i	−0.202239	−	0.350287i
$555$	27.2288	−	47.1616i	1.15580	−	2.00190i
$556$	−6.67712	−	11.5651i	−0.283173	−	0.490470i
$557$	13.2915	−	23.0216i	0.563179	−	0.975455i	−0.434037	−	0.900895i	$-0.642911\pi$
$557$	13.2915	−	23.0216i	0.563179	−	0.975455i	0.997217	−	0.0745599i	$-0.0237552\pi$
$558$	−1.41699			−0.0599862
$559$	1.41699			0.0599325
$560$	3.00000	−	5.19615i	0.126773	−	0.219578i
$561$		0			0
$562$	−27.4575			−1.15823
$563$	25.9373			1.09312			0.546562	−	0.837418i	$-0.315936\pi$
$563$	25.9373			1.09312			0.546562	+	0.837418i	$0.315936\pi$
$564$	12.7601	−	22.1012i	0.537298	−	0.930628i
$565$	−10.1771	−	17.6273i	−0.428155	−	0.741586i
$566$	−12.6771	+	21.9574i	−0.532859	+	0.922939i
$567$	−4.11438	−	7.12631i	−0.172788	−	0.299277i
$568$	6.64575	+	11.5108i	0.278850	+	0.482982i
$569$	−14.5830			−0.611351			−0.305676	−	0.952136i	$-0.598882\pi$
$569$	−14.5830			−0.611351			−0.305676	+	0.952136i	$0.598882\pi$
$570$	−41.6974	+	5.39426i	−1.74651	+	0.225941i
$571$	−39.8118			−1.66607			−0.833035	−	0.553220i	$-0.813399\pi$
$571$	−39.8118			−1.66607			−0.833035	+	0.553220i	$0.813399\pi$
$572$	−0.645751	−	1.11847i	−0.0270002	−	0.0467658i
$573$	−19.2915	−	33.4139i	−0.805914	−	1.39588i
$574$	8.46863	−	14.6681i	0.353474	−	0.612234i
$575$	−15.1144	−	26.1789i	−0.630313	−	1.09173i
$576$	−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
$579$	−8.70850	+	15.0836i	−0.361913	+	0.626851i
$580$	6.64575	−	11.5108i	0.275950	−	0.477959i
$581$	13.0627			0.541934
$582$	37.8118			1.56735
$583$	−2.77124	+	4.79993i	−0.114773	+	0.198793i
$584$	−6.14575	−	10.6448i	−0.254313	−	0.440483i
$585$	−14.5830	+	25.2585i	−0.602933	+	1.04431i
$586$	−6.53137	−	11.3127i	−0.269809	−	0.467322i
$587$	22.9373	+	39.7285i	0.946722	+	1.63977i	0.752267	+	0.658859i	$0.228961\pi$
$587$	22.9373	+	39.7285i	0.946722	+	1.63977i	0.194455	+	0.980911i	$0.437706\pi$
$588$	11.3542			0.468241
$589$	−1.53137	+	0.198109i	−0.0630991	+	0.00816294i
$590$	28.9373			1.19133
$591$	−3.11438	−	5.39426i	−0.128108	−	0.221890i
$592$	−2.82288	−	4.88936i	−0.116019	−	0.200952i
$593$	−20.1458	+	34.8935i	−0.827287	+	1.43290i	0.0728721	+	0.997341i	$0.476784\pi$
$593$	−20.1458	+	34.8935i	−0.827287	+	1.43290i	−0.900159	+	0.435562i	$0.856550\pi$
$594$	0.854249	+	1.47960i	0.0350502	+	0.0607088i
$595$		0			0
$596$	−4.93725			−0.202238
$597$	−31.4170			−1.28581
$598$	−3.64575	+	6.31463i	−0.149086	+	0.258224i
$599$	0.531373	−	0.920365i	0.0217113	−	0.0376051i	−0.854966	−	0.518685i	$-0.826422\pi$
$599$	0.531373	−	0.920365i	0.0217113	−	0.0376051i	0.876677	+	0.481080i	$0.159755\pi$
$600$	−21.9373			−0.895585
$601$	31.5830			1.28830			0.644149	−	0.764900i	$-0.277212\pi$
$601$	31.5830			1.28830			0.644149	+	0.764900i	$0.277212\pi$
$602$	0.583005	−	1.00979i	0.0237615	−	0.0411562i
$603$	9.29150	+	16.0934i	0.378379	+	0.655372i
$604$	1.46863	−	2.54374i	0.0597576	−	0.103503i
$605$	19.2915	+	33.4139i	0.784311	+	1.35847i
$606$	−11.0516	−	19.1420i	−0.448942	−	0.777590i
$607$	−8.93725			−0.362752			−0.181376	−	0.983414i	$-0.558055\pi$
$607$	−8.93725			−0.362752			−0.181376	+	0.983414i	$0.558055\pi$
$608$	−1.67712	+	4.02334i	−0.0680164	+	0.163168i
$609$	−15.8745			−0.643268
$610$	27.2288	+	47.1616i	1.10246	+	1.90952i
$611$	−9.64575	−	16.7069i	−0.390225	−	0.675890i
$612$		0			0
$613$	−14.2915	−	24.7536i	−0.577228	−	0.999789i	−0.995796	−	0.0916030i	$-0.970801\pi$
$613$	−14.2915	−	24.7536i	−0.577228	−	0.999789i	0.418567	−	0.908186i	$-0.362532\pi$
$614$	2.32288	−	4.02334i	0.0937436	−	0.162369i
$615$	−99.2693			−4.00292
$616$	−1.06275			−0.0428193
$617$	−0.437254	+	0.757346i	−0.0176032	+	0.0304896i	−0.874693	−	0.484678i	$-0.838937\pi$
$617$	−0.437254	+	0.757346i	−0.0176032	+	0.0304896i	0.857090	+	0.515167i	$0.172270\pi$
$618$	−3.58301	+	6.20595i	−0.144130	+	0.249640i
$619$	44.4575			1.78690			0.893449	−	0.449164i	$-0.148278\pi$
$619$	44.4575			1.78690			0.893449	+	0.449164i	$0.148278\pi$
$620$	−1.29150			−0.0518680
$621$	4.82288	−	8.35347i	0.193535	−	0.335213i
$622$	−4.17712	−	7.23499i	−0.167487	−	0.290097i
$623$		0			0
$624$	2.64575	+	4.58258i	0.105915	+	0.183450i
$625$	−1.14575	−	1.98450i	−0.0458301	−	0.0793800i
$626$	−22.8745			−0.914249
$627$	4.52026	+	5.91841i	0.180522	+	0.236358i
$628$	10.5830			0.422308
$629$		0			0
$630$	12.0000	+	20.7846i	0.478091	+	0.828079i
$631$	−11.4059	+	19.7556i	−0.454061	+	0.786457i	−0.998634	−	0.0522570i	$-0.983359\pi$
$631$	−11.4059	+	19.7556i	−0.454061	+	0.786457i	0.544573	+	0.838714i	$0.316692\pi$
$632$	2.00000	+	3.46410i	0.0795557	+	0.137795i
$633$	−3.58301	+	6.20595i	−0.142412	+	0.246664i
$634$	−6.00000			−0.238290
$635$	−9.87451			−0.391858
$636$	11.3542	−	19.6661i	0.450225	−	0.779813i
$637$	4.29150	−	7.43310i	0.170036	−	0.294510i
$638$	−2.35425			−0.0932056
$639$	−53.1660			−2.10321
$640$	−1.82288	+	3.15731i	−0.0720555	+	0.124804i
$641$	9.43725	+	16.3458i	0.372749	+	0.645620i	0.989987	−	0.141156i	$-0.0450819\pi$
$641$	9.43725	+	16.3458i	0.372749	+	0.645620i	−0.617238	+	0.786776i	$0.711749\pi$
$642$	6.22876	−	10.7885i	0.245829	−	0.425789i
$643$	−15.2601	−	26.4313i	−0.601801	−	1.04235i	−0.992548	−	0.121852i	$-0.961117\pi$
$643$	−15.2601	−	26.4313i	−0.601801	−	1.04235i	0.390748	−	0.920498i	$-0.372217\pi$
$644$	3.00000	+	5.19615i	0.118217	+	0.204757i
$645$	−6.83399			−0.269088
$646$		0			0
$647$	30.4575			1.19741			0.598704	−	0.800970i	$-0.295683\pi$
$647$	30.4575			1.19741			0.598704	+	0.800970i	$0.295683\pi$
$648$	2.50000	+	4.33013i	0.0982093	+	0.170103i
$649$	−2.56275	−	4.43881i	−0.100597	−	0.174238i
$650$	−8.29150	+	14.3613i	−0.325219	+	0.563297i
$651$	0.771243	+	1.33583i	0.0302274	+	0.0523554i
$652$	5.96863	−	10.3380i	0.233749	−	0.404866i
$653$	24.0000			0.939193			0.469596	−	0.882881i	$-0.344399\pi$
$653$	24.0000			0.939193			0.469596	+	0.882881i	$0.344399\pi$
$654$	17.4170			0.681058
$655$	25.4059	−	44.0043i	0.992690	−	1.71939i
$656$	−5.14575	+	8.91270i	−0.200908	+	0.347983i
$657$	49.1660			1.91815
$658$	−15.8745			−0.618853
$659$	−1.29150	+	2.23695i	−0.0503098	+	0.0871391i	−0.890084	−	0.455797i	$-0.849354\pi$
$659$	−1.29150	+	2.23695i	−0.0503098	+	0.0871391i	0.839774	+	0.542936i	$0.182688\pi$
$660$	3.11438	+	5.39426i	0.121227	+	0.209971i
$661$	5.11438	−	8.85836i	0.198926	−	0.344550i	−0.749254	−	0.662282i	$-0.769588\pi$
$661$	5.11438	−	8.85836i	0.198926	−	0.344550i	0.948181	+	0.317732i	$0.102921\pi$
$662$	13.9059	+	24.0857i	0.540467	+	0.936117i
$663$		0			0
$664$	−7.93725			−0.308025
$665$	15.8745	+	20.7846i	0.615587	+	0.805993i
$666$	22.5830			0.875074
$667$	6.64575	+	11.5108i	0.257325	+	0.445699i
$668$	6.00000	+	10.3923i	0.232147	+	0.402090i
$669$	38.1144	−	66.0160i	1.47359	−	2.55233i
$670$	8.46863	+	14.6681i	0.327172	+	0.566678i
$671$	4.82288	−	8.35347i	0.186185	−	0.322482i
$672$	4.35425			0.167969
$673$	17.8745			0.689012			0.344506	−	0.938784i	$-0.388046\pi$
$673$	17.8745			0.689012			0.344506	+	0.938784i	$0.388046\pi$
$674$	10.1458	−	17.5730i	0.390800	−	0.676885i
$675$	10.9686	−	18.9982i	0.422183	−	0.731242i
$676$	−9.00000			−0.346154
$677$	−32.5830			−1.25227			−0.626133	−	0.779716i	$-0.715363\pi$
$677$	−32.5830			−1.25227			−0.626133	+	0.779716i	$0.715363\pi$
$678$	7.38562	−	12.7923i	0.283643	−	0.491284i
$679$	−11.7601	−	20.3691i	−0.451312	−	0.781696i
$680$		0			0
$681$	−16.7288	−	28.9751i	−0.641047	−	1.11033i
$682$	0.114378	+	0.198109i	0.00437977	+	0.00758599i
$683$	−26.5830			−1.01717			−0.508585	−	0.861012i	$-0.669831\pi$
$683$	−26.5830			−1.01717			−0.508585	+	0.861012i	$0.669831\pi$
$684$	−10.5830	−	13.8564i	−0.404651	−	0.529813i
$685$	−20.3542			−0.777696
$686$	−9.29150	−	16.0934i	−0.354751	−	0.614447i
$687$	26.4575	+	45.8258i	1.00942	+	1.74836i
$688$	−0.354249	+	0.613577i	−0.0135056	+	0.0233924i
$689$	−8.58301	−	14.8662i	−0.326986	−	0.566357i
$690$	17.5830	−	30.4547i	0.669374	−	1.15939i
$691$	−18.5830			−0.706931			−0.353465	−	0.935448i	$-0.614997\pi$
$691$	−18.5830			−0.706931			−0.353465	+	0.935448i	$0.614997\pi$
$692$	−6.00000			−0.228086
$693$	2.12549	−	3.68146i	0.0807408	−	0.139847i
$694$	−1.61438	+	2.79619i	−0.0612810	+	0.106142i
$695$	48.6863			1.84678
$696$	9.64575			0.365621
$697$		0			0
$698$	10.5830	+	18.3303i	0.400573	+	0.693812i
$699$	−17.0314	+	29.4992i	−0.644186	+	1.11576i
$700$	6.82288	+	11.8176i	0.257880	+	0.446662i
$701$	−7.82288	−	13.5496i	−0.295466	−	0.511762i	0.679627	−	0.733558i	$-0.262142\pi$
$701$	−7.82288	−	13.5496i	−0.295466	−	0.511762i	−0.975093	+	0.221796i	$0.928808\pi$
$702$	−5.29150			−0.199715
$703$	24.4059	−	3.15731i	0.920485	−	0.119080i
$704$	0.645751			0.0243377
$705$	46.5203	+	80.5755i	1.75205	+	3.03465i
$706$	9.43725	+	16.3458i	0.355176	+	0.615182i
$707$	−6.87451	+	11.9070i	−0.258542	+	0.447809i
$708$	10.5000	+	18.1865i	0.394614	+	0.683492i
$709$	0.822876	−	1.42526i	0.0309037	−	0.0535269i	−0.850160	−	0.526525i	$-0.823495\pi$
$709$	0.822876	−	1.42526i	0.0309037	−	0.0535269i	0.881064	+	0.472998i	$0.156828\pi$
$710$	−48.4575			−1.81858
$711$	−16.0000			−0.600047
$712$		0			0
$713$	0.645751	−	1.11847i	0.0241836	−	0.0418872i
$714$		0			0
$715$	4.70850			0.176088
$716$	−9.96863	+	17.2662i	−0.372545	+	0.645267i
$717$	−15.8745	−	27.4955i	−0.592844	−	1.02684i
$718$	−5.46863	+	9.47194i	−0.204087	+	0.353490i
$719$	−6.64575	−	11.5108i	−0.247845	−	0.429280i	0.715083	−	0.699040i	$-0.246389\pi$
$719$	−6.64575	−	11.5108i	−0.247845	−	0.429280i	−0.962928	+	0.269760i	$0.913056\pi$
$720$	−7.29150	−	12.6293i	−0.271738	−	0.470664i
$721$	4.45751			0.166006
$722$	−13.3745	−	13.4953i	−0.497748	−	0.502242i
$723$	−35.9373			−1.33652
$724$	2.11438	+	3.66221i	0.0785802	+	0.136105i
$725$	15.1144	+	26.1789i	0.561334	+	0.972259i
$726$	−14.0000	+	24.2487i	−0.519589	+	0.899954i
$727$	−11.2915	−	19.5575i	−0.418779	−	0.725346i	0.577038	−	0.816717i	$-0.304208\pi$
$727$	−11.2915	−	19.5575i	−0.418779	−	0.725346i	−0.995817	+	0.0913712i	$0.970875\pi$
$728$	1.64575	−	2.85052i	0.0609956	−	0.105647i
$729$	−41.0000			−1.51852
$730$	44.8118			1.65856
$731$		0			0
$732$	−19.7601	+	34.2255i	−0.730355	+	1.26501i
$733$	42.1033			1.55512			0.777560	−	0.628809i	$-0.216457\pi$
$733$	42.1033			1.55512			0.777560	+	0.628809i	$0.216457\pi$
$734$	−10.2288			−0.377550
$735$	−20.6974	+	35.8489i	−0.763434	+	1.32231i
$736$	−1.82288	−	3.15731i	−0.0671921	−	0.116380i
$737$	1.50000	−	2.59808i	0.0552532	−	0.0957014i
$738$	−20.5830	−	35.6508i	−0.757671	−	1.31232i
$739$	−6.90588	−	11.9613i	−0.254037	−	0.440005i	0.710597	−	0.703600i	$-0.248425\pi$
$739$	−6.90588	−	11.9613i	−0.254037	−	0.440005i	−0.964633	+	0.263595i	$0.915092\pi$
$740$	20.5830			0.756646
$741$	−22.8745	+	2.95920i	−0.840316	+	0.108709i
$742$	−14.1255			−0.518563
$743$	5.23987	+	9.07572i	0.192232	+	0.332956i	0.945990	−	0.324197i	$-0.105094\pi$
$743$	5.23987	+	9.07572i	0.192232	+	0.332956i	−0.753757	+	0.657153i	$0.771761\pi$
$744$	−0.468627	−	0.811686i	−0.0171807	−	0.0297578i
$745$	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
$749$	−7.74902			−0.283143
$750$	15.8745	−	27.4955i	0.579655	−	1.00399i
$751$	−11.9373	+	20.6759i	−0.435597	+	0.754475i	−0.997344	−	0.0728333i	$-0.976796\pi$
$751$	−11.9373	+	20.6759i	−0.435597	+	0.754475i	0.561748	+	0.827309i	$0.310129\pi$
$752$	9.64575			0.351744
$753$	−7.33202			−0.267194
$754$	3.64575	−	6.31463i	0.132770	−	0.229965i
$755$	5.35425	+	9.27383i	0.194861	+	0.337509i
$756$	−2.17712	+	3.77089i	−0.0791812	+	0.137146i
$757$	−8.29150	−	14.3613i	−0.301360	−	0.521970i	0.675084	−	0.737740i	$-0.264107\pi$
$757$	−8.29150	−	14.3613i	−0.301360	−	0.521970i	−0.976444	+	0.215770i	$0.930774\pi$
$758$	−10.6458	−	18.4390i	−0.386671	−	0.669734i
$759$	−6.22876			−0.226090
$760$	−9.64575	−	12.6293i	−0.349888	−	0.458111i
$761$	11.1255			0.403299			0.201649	−	0.979458i	$-0.435370\pi$
$761$	11.1255			0.403299			0.201649	+	0.979458i	$0.435370\pi$
$762$	−3.58301	−	6.20595i	−0.129799	−	0.224818i
$763$	−5.41699	−	9.38251i	−0.196108	−	0.339670i
$764$	7.29150	−	12.6293i	0.263797	−	0.456910i
$765$		0			0
$766$	15.7601	−	27.2973i	0.569437	−	0.986293i
$767$	15.8745			0.573195
$768$	−2.64575			−0.0954703
$769$	−12.3542	+	21.3982i	−0.445506	+	0.771638i	−0.998087	−	0.0618204i	$-0.980309\pi$
$769$	−12.3542	+	21.3982i	−0.445506	+	0.771638i	0.552582	+	0.833459i	$0.313643\pi$
$770$	1.93725	−	3.35542i	0.0698138	−	0.120921i
$771$	−4.52026			−0.162793
$772$	−6.58301			−0.236928
$773$	−5.46863	+	9.47194i	−0.196693	+	0.340682i	−0.947454	−	0.319892i	$-0.896354\pi$
$773$	−5.46863	+	9.47194i	−0.196693	+	0.340682i	0.750761	+	0.660574i	$0.229687\pi$
$774$	−1.41699	−	2.45431i	−0.0509328	−	0.0882182i
$775$	1.46863	−	2.54374i	0.0527546	−	0.0913737i
$776$	7.14575	+	12.3768i	0.256518	+	0.444301i
$777$	−12.2915	−	21.2895i	−0.440955	−	0.763757i
$778$	12.0000			0.430221
$779$	−27.2288	−	35.6508i	−0.975571	−	1.27732i
$780$	−19.2915			−0.690747
$781$	4.29150	+	7.43310i	0.153562	+	0.265977i
$782$		0			0
$783$	−4.82288	+	8.35347i	−0.172356	+	0.298529i
$784$	2.14575	+	3.71655i	0.0766340	+	0.132734i
$785$	−19.2915	+	33.4139i	−0.688543	+	1.19259i
$786$	36.8745			1.31527
$787$	−5.47974			−0.195332			−0.0976658	−	0.995219i	$-0.531138\pi$
$787$	−5.47974			−0.195332			−0.0976658	+	0.995219i	$0.531138\pi$
$788$	1.17712	−	2.03884i	0.0419333	−	0.0726306i
$789$	6.53137	−	11.3127i	0.232523	−	0.402742i
$790$	−14.5830			−0.518840
$791$	−9.18824			−0.326696
$792$	−1.29150	+	2.23695i	−0.0458915	+	0.0794865i
$793$	14.9373	+	25.8721i	0.530437	+	0.918745i
$794$	−18.4686	+	31.9886i	−0.655427	+	1.13523i
$795$	41.3948	+	71.6978i	1.46812	+	2.54286i
$796$	−5.93725	−	10.2836i	−0.210440	−	0.364493i
$797$	2.81176			0.0995977			0.0497989	−	0.998759i	$-0.484142\pi$
$797$	2.81176			0.0995977			0.0497989	+	0.998759i	$0.484142\pi$
$798$	−7.30262	+	17.5186i	−0.258510	+	0.620152i
$799$		0			0
$800$	−4.14575	−	7.18065i	−0.146574	−	0.253874i
$801$		0			0
$802$	−3.20850	+	5.55728i	−0.113296	+	0.196234i
$803$	−3.96863	−	6.87386i	−0.140050	−	0.242573i
$804$	−6.14575	+	10.6448i	−0.216744	+	0.375412i
$805$	−21.8745			−0.770975
$806$	−0.708497			−0.0249558
$807$		0			0
$808$	4.17712	−	7.23499i	0.146951	−	0.254526i
$809$	−9.00000			−0.316423			−0.158212	−	0.987405i	$-0.550573\pi$
$809$	−9.00000			−0.316423			−0.158212	+	0.987405i	$0.550573\pi$
$810$	−18.2288			−0.640493
$811$	10.3542	−	17.9341i	0.363587	−	0.629751i	−0.624961	−	0.780656i	$-0.714885\pi$
$811$	10.3542	−	17.9341i	0.363587	−	0.629751i	0.988548	+	0.150905i	$0.0482187\pi$
$812$	−3.00000	−	5.19615i	−0.105279	−	0.182349i
$813$	23.3431	−	40.4315i	0.818679	−	1.41799i
$814$	−1.82288	−	3.15731i	−0.0638918	−	0.110664i
$815$	21.7601	+	37.6897i	0.762224	+	1.32021i
$816$		0			0
$817$	−1.87451	−	2.45431i	−0.0655807	−	0.0858653i
$818$	13.5830			0.474919
$819$	6.58301	+	11.4021i	0.230029	+	0.398422i
$820$	−18.7601	−	32.4935i	−0.655132	−	1.13472i
$821$	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	$0.133278\pi$
$822$	−7.38562	−	12.7923i	−0.257603	−	0.446182i
$823$	0.0627461	−	0.108679i	0.00218719	−	0.00378832i	−0.864930	−	0.501893i	$-0.832637\pi$
$823$	0.0627461	−	0.108679i	0.00218719	−	0.00378832i	0.867117	+	0.498105i	$0.165970\pi$
$824$	−2.70850			−0.0943550
$825$	−14.1660			−0.493197
$826$	6.53137	−	11.3127i	0.227256	−	0.393618i
$827$	23.6771	−	41.0100i	0.823334	−	1.42606i	−0.0798514	−	0.996807i	$-0.525445\pi$
$827$	23.6771	−	41.0100i	0.823334	−	1.42606i	0.903186	−	0.429250i	$-0.141222\pi$
$828$	14.5830			0.506794
$829$	25.1660			0.874052			0.437026	−	0.899449i	$-0.356032\pi$
$829$	25.1660			0.874052			0.437026	+	0.899449i	$0.356032\pi$
$830$	14.4686	−	25.0604i	0.502213	−	0.869859i
$831$	12.5941	+	21.8137i	0.436885	+	0.756707i
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$		0			0
$834$	17.6660	+	30.5984i	0.611724	+	1.05954i
$835$	−43.7490			−1.51400
$836$	−1.08301	+	2.59808i	−0.0374565	+	0.0898563i
$837$	0.937254			0.0323962
$838$	−15.8745	−	27.4955i	−0.548376	−	0.949815i
$839$	2.23987	+	3.87957i	0.0773289	+	0.133938i	0.902097	−	0.431534i	$-0.142028\pi$
$839$	2.23987	+	3.87957i	0.0773289	+	0.133938i	−0.824768	+	0.565472i	$0.808694\pi$
$840$	−7.93725	+	13.7477i	−0.273861	+	0.474342i
$841$	7.85425	+	13.6040i	0.270836	+	0.469102i
$842$	−11.4059	+	19.7556i	−0.393073	+	0.680822i
$843$	72.6458			2.50205
$844$	−2.70850			−0.0932303
$845$	16.4059	−	28.4158i	0.564379	−	0.977534i
$846$	−19.2915	+	33.4139i	−0.663256	+	1.14879i
$847$	17.4170			0.598455
$848$	8.58301			0.294742
$849$	33.5405	−	58.0939i	1.15111	−	1.99378i
$850$		0			0
$851$	−10.2915	+	17.8254i	−0.352788	+	0.611047i
$852$	−17.5830	−	30.4547i	−0.602384	−	1.04336i
$853$	6.29150	+	10.8972i	0.215417	+	0.373113i	0.953401	−	0.301705i	$-0.0975556\pi$
$853$	6.29150	+	10.8972i	0.215417	+	0.373113i	−0.737985	+	0.674818i	$0.764222\pi$
$854$	24.5830			0.841213
$855$	63.0405	−	8.15536i	2.15594	−	0.278907i
$856$	4.70850			0.160933
$857$	−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	$0.950104\pi$
$858$	1.70850	+	2.95920i	0.0583271	+	0.101026i
$859$	6.61438	−	11.4564i	0.225680	−	0.390889i	−0.730843	−	0.682545i	$-0.760873\pi$
$859$	6.61438	−	11.4564i	0.225680	−	0.390889i	0.956523	+	0.291656i	$0.0942064\pi$
$860$	−1.29150	−	2.23695i	−0.0440399	−	0.0762793i
$861$	−22.4059	+	38.8081i	−0.763590	+	1.32258i
$862$	−3.87451			−0.131966
$863$	−46.9373			−1.59776			−0.798881	−	0.601489i	$-0.794575\pi$
$863$	−46.9373			−1.59776			−0.798881	+	0.601489i	$0.794575\pi$
$864$	1.32288	−	2.29129i	0.0450051	−	0.0779512i
$865$	10.9373	−	18.9439i	0.371878	−	0.644111i
$866$	−13.8745			−0.471475
$867$	44.9778			1.52753
$868$	−0.291503	+	0.504897i	−0.00989424	+	0.0171373i
$869$	1.29150	+	2.23695i	0.0438112	+	0.0758833i
$870$	−17.5830	+	30.4547i	−0.596120	+	1.03251i
$871$	4.64575	+	8.04668i	0.157415	+	0.272651i
$872$	3.29150	+	5.70105i	0.111464	+	0.193062i
$873$	−57.1660			−1.93478
$874$	15.7601	−	2.03884i	0.533094	−	0.0689648i
$875$	−19.7490			−0.667639
$876$	16.2601	+	28.1634i	0.549379	+	0.951552i
$877$	18.1771	+	31.4837i	0.613798	+	1.06313i	0.990594	+	0.136833i	$0.0436924\pi$
$877$	18.1771	+	31.4837i	0.613798	+	1.06313i	−0.376796	+	0.926296i	$0.622974\pi$
$878$	18.4059	−	31.8799i	0.621168	−	1.07590i
$879$	17.2804	+	29.9305i	0.582853	+	1.00953i
$880$	−1.17712	+	2.03884i	−0.0396809	+	0.0687293i
$881$	−5.12549			−0.172682			−0.0863411	−	0.996266i	$-0.527517\pi$
$881$	−5.12549			−0.172682			−0.0863411	+	0.996266i	$0.527517\pi$
$882$	−17.1660			−0.578010
$883$	−20.1974	+	34.9829i	−0.679696	+	1.17727i	0.295376	+	0.955381i	$0.404555\pi$
$883$	−20.1974	+	34.9829i	−0.679696	+	1.17727i	−0.975072	+	0.221887i	$0.928778\pi$
$884$		0			0
$885$	−76.5608			−2.57356
$886$	5.35425			0.179880
$887$	19.2915	−	33.4139i	0.647745	−	1.12193i	−0.335915	−	0.941892i	$-0.609045\pi$
$887$	19.2915	−	33.4139i	0.647745	−	1.12193i	0.983660	−	0.180035i	$-0.0576212\pi$
$888$	7.46863	+	12.9360i	0.250631	+	0.434105i
$889$	−2.22876	+	3.86032i	−0.0747501	+	0.129471i
$890$		0			0
$891$	1.61438	+	2.79619i	0.0540837	+	0.0936757i
$892$	28.8118			0.964689
$893$	−16.1771	+	38.8081i	−0.541347	+	1.29866i
$894$	13.0627			0.436884
$895$	−36.3431	−	62.9482i	−1.21482	−	2.10412i
$896$	0.822876	+	1.42526i	0.0274903	+	0.0476147i
$897$	9.64575	−	16.7069i	0.322062	−	0.557828i
$898$	6.85425	+	11.8719i	0.228729	+	0.396171i
$899$	−0.645751	+	1.11847i	−0.0215370	+	0.0373032i
$900$	33.1660			1.10553
$901$		0			0
$902$	−3.32288	+	5.75539i	−0.110640	+	0.191634i
$903$	−1.54249	+	2.67167i	−0.0513307	+	0.0889075i
$904$	5.58301			0.185688
$905$	−15.4170			−0.512478
$906$	−3.88562	+	6.73009i	−0.129091	+	0.223592i
$907$	−12.0314	−	20.8389i	−0.399495	−	0.691946i	0.594168	−	0.804341i	$-0.297481\pi$
$907$	−12.0314	−	20.8389i	−0.399495	−	0.691946i	−0.993664	+	0.112395i	$0.964148\pi$
$908$	6.32288	−	10.9515i	0.209832	−	0.363440i
$909$	16.7085	+	28.9400i	0.554186	+	0.959878i
$910$	6.00000	+	10.3923i	0.198898	+	0.344502i
$911$	1.06275			0.0352103			0.0176052	−	0.999845i	$-0.494396\pi$
$911$	1.06275			0.0352103			0.0176052	+	0.999845i	$0.494396\pi$
$912$	4.43725	−	10.6448i	0.146932	−	0.352483i
$913$	−5.12549			−0.169629
$914$	−0.562746	−	0.974705i	−0.0186140	−	0.0322404i
$915$	−72.0405	−	124.778i	−2.38159	−	4.12503i
$916$	−10.0000	+	17.3205i	−0.330409	+	0.572286i
$917$	−11.4686	−	19.8642i	−0.378727	−	0.655975i
$918$		0			0
$919$	11.8745			0.391704			0.195852	−	0.980633i	$-0.437253\pi$
$919$	11.8745			0.391704			0.195852	+	0.980633i	$0.437253\pi$
$920$	13.2915			0.438208
$921$	−6.14575	+	10.6448i	−0.202509	+	0.350757i
$922$	11.5830	−	20.0624i	0.381466	−	0.660718i
$923$	−26.5830			−0.874990
$924$	2.81176			0.0925002
$925$	−23.4059	+	40.5402i	−0.769581	+	1.33295i
$926$	−7.22876	−	12.5206i	−0.237552	−	0.411452i
$927$	5.41699	−	9.38251i	0.177917	−	0.308162i
$928$	1.82288	+	3.15731i	0.0598388	+	0.103644i
$929$	−5.79150	−	10.0312i	−0.190013	−	0.329112i	0.755241	−	0.655447i	$-0.227520\pi$
$929$	−5.79150	−	10.0312i	−0.190013	−	0.329112i	−0.945254	+	0.326335i	$0.894186\pi$
$930$	3.41699			0.112048
$931$	−18.5516	+	2.39997i	−0.608005	+	0.0786557i
$932$	−12.8745			−0.421719
$933$	11.0516	+	19.1420i	0.361814	+	0.626681i
$934$	12.3229	+	21.3438i	0.403217	+	0.698392i
$935$		0			0
$936$	−4.00000	−	6.92820i	−0.130744	−	0.226455i
$937$	−19.4373	+	33.6663i	−0.634987	+	1.09983i	0.351530	+	0.936176i	$0.385661\pi$
$937$	−19.4373	+	33.6663i	−0.634987	+	1.09983i	−0.986518	+	0.163654i	$0.947672\pi$
$938$	7.64575			0.249643
$939$	60.5203			1.97500
$940$	−17.5830	+	30.4547i	−0.573494	+	0.993321i
$941$	−29.5830	+	51.2393i	−0.964378	+	1.67035i	−0.253103	+	0.967439i	$0.581451\pi$
$941$	−29.5830	+	51.2393i	−0.964378	+	1.67035i	−0.711276	+	0.702913i	$0.751882\pi$
$942$	−28.0000			−0.912289
$943$	37.5203			1.22183
$944$	−3.96863	+	6.87386i	−0.129168	+	0.223725i
$945$	−7.93725	−	13.7477i	−0.258199	−	0.447214i
$946$	−0.228757	+	0.396218i	−0.00743752	+	0.0128822i
$947$	−27.8745	−	48.2801i	−0.905800	−	1.56889i	−0.819840	−	0.572593i	$-0.805938\pi$
$947$	−27.8745	−	48.2801i	−0.905800	−	1.56889i	−0.0859598	−	0.996299i	$-0.527396\pi$
$948$	−5.29150	−	9.16515i	−0.171860	−	0.297670i
$949$	24.5830			0.797998
$950$	35.8431	−	4.63692i	1.16290	−	0.150441i
$951$	15.8745			0.514766
$952$		0			0
$953$	−19.7288	−	34.1712i	−0.639077	−	1.10691i	−0.985636	−	0.168886i	$-0.945983\pi$
$953$	−19.7288	−	34.1712i	−0.639077	−	1.10691i	0.346559	−	0.938028i	$-0.387350\pi$
$954$	−17.1660	+	29.7324i	−0.555770	+	0.962622i
$955$	26.5830	+	46.0431i	0.860206	+	1.48992i
$956$	6.00000	−	10.3923i	0.194054	−	0.336111i
$957$	6.22876			0.201347
$958$	−14.5830			−0.471156
$959$	−4.59412	+	7.95725i	−0.148352	+	0.256953i
$960$	4.82288	−	8.35347i	0.155658	−	0.269607i
$961$	−30.8745			−0.995952
$962$	11.2915			0.364053
$963$	−9.41699	+	16.3107i	−0.303458	+	0.525605i
$964$	−6.79150	−	11.7632i	−0.218740	−	0.378868i
$965$	12.0000	−	20.7846i	0.386294	−	0.669080i
$966$	−7.93725	−	13.7477i	−0.255377	−	0.442326i
$967$	1.35425	+	2.34563i	0.0435497	+	0.0754303i	0.886979	−	0.461810i	$-0.152800\pi$
$967$	1.35425	+	2.34563i	0.0435497	+	0.0754303i	−0.843429	+	0.537241i	$0.819467\pi$
$968$	−10.5830			−0.340151
$969$		0			0
$970$	−52.1033			−1.67293
$971$	−7.19738	−	12.4662i	−0.230975	−	0.400060i	0.727120	−	0.686510i	$-0.240858\pi$
$971$	−7.19738	−	12.4662i	−0.230975	−	0.400060i	−0.958095	+	0.286450i	$0.907525\pi$
$972$	−10.5830	−	18.3303i	−0.339450	−	0.587945i
$973$	10.9889	−	19.0333i	0.352288	−	0.610180i
$974$	11.1144	+	19.2507i	0.356128	+	0.616831i
$975$	21.9373	−	37.9964i	0.702554	−	1.21686i
$976$	−14.9373			−0.478130
$977$	45.4575			1.45431			0.727157	−	0.686471i	$-0.240841\pi$
$977$	45.4575			1.45431			0.727157	+	0.686471i	$0.240841\pi$
$978$	−15.7915	+	27.3517i	−0.504957	+	0.874610i
$979$		0			0
$980$	−15.6458			−0.499785
$981$	−26.3320			−0.840717
$982$	−14.3542	+	24.8623i	−0.458062	+	0.793387i
$983$	15.8745	+	27.4955i	0.506318	+	0.876969i	0.999973	+	0.00731102i	$0.00232719\pi$
$983$	15.8745	+	27.4955i	0.506318	+	0.876969i	−0.493655	+	0.869658i	$0.664339\pi$
$984$	13.6144	−	23.5808i	0.434011	−	0.751728i
$985$	4.29150	+	7.43310i	0.136739	+	0.236838i
$986$		0			0
$987$	42.0000			1.33687
$988$	−5.29150	−	6.92820i	−0.168345	−	0.220416i
$989$	2.58301			0.0821348
$990$	−4.70850	−	8.15536i	−0.149646	−	0.259194i
$991$	22.5830	+	39.1149i	0.717373	+	1.24253i	0.962037	+	0.272918i	$0.0879889\pi$
$991$	22.5830	+	39.1149i	0.717373	+	1.24253i	−0.244664	+	0.969608i	$0.578678\pi$
$992$	0.177124	−	0.306788i	0.00562370	−	0.00974054i
$993$	−36.7915	−	63.7248i	−1.16754	−	2.02224i
$994$	−10.9373	+	18.9439i	−0.346909	+	0.600863i
$995$	43.2915			1.37243
$996$	21.0000			0.665410
$997$	5.11438	−	8.85836i	0.161974	−	0.280547i	−0.773603	−	0.633671i	$-0.781547\pi$
$997$	5.11438	−	8.85836i	0.161974	−	0.280547i	0.935577	+	0.353124i	$0.114881\pi$
$998$	15.6144	−	27.0449i	0.494265	−	0.856091i
$999$	−14.9373			−0.472594

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.2.c.b.7.2	✓	4
3.2	odd	2		342.2.g.f.235.2		4
4.3	odd	2		304.2.i.e.273.1		4
5.2	odd	4		950.2.j.g.349.4		8
5.3	odd	4		950.2.j.g.349.1		8
5.4	even	2		950.2.e.k.501.1		4
8.3	odd	2		1216.2.i.k.577.2		4
8.5	even	2		1216.2.i.l.577.1		4
12.11	even	2		2736.2.s.v.577.2		4
19.2	odd	18		722.2.e.o.389.2		12
19.3	odd	18		722.2.e.o.595.1		12
19.4	even	9		722.2.e.n.245.1		12
19.5	even	9		722.2.e.n.99.1		12
19.6	even	9		722.2.e.n.423.1		12
19.7	even	3		722.2.a.j.1.1		2
19.8	odd	6		722.2.c.j.429.1		4
19.9	even	9		722.2.e.n.415.2		12
19.10	odd	18		722.2.e.o.415.1		12
19.11	even	3	inner	38.2.c.b.11.2	yes	4
19.12	odd	6		722.2.a.g.1.2		2
19.13	odd	18		722.2.e.o.423.2		12
19.14	odd	18		722.2.e.o.99.2		12
19.15	odd	18		722.2.e.o.245.2		12
19.16	even	9		722.2.e.n.595.2		12
19.17	even	9		722.2.e.n.389.1		12
19.18	odd	2		722.2.c.j.653.1		4
57.11	odd	6		342.2.g.f.163.2		4
57.26	odd	6		6498.2.a.ba.1.1		2
57.50	even	6		6498.2.a.bg.1.1		2
76.7	odd	6		5776.2.a.ba.1.2		2
76.11	odd	6		304.2.i.e.49.1		4
76.31	even	6		5776.2.a.z.1.1		2
95.49	even	6		950.2.e.k.201.1		4
95.68	odd	12		950.2.j.g.49.4		8
95.87	odd	12		950.2.j.g.49.1		8
152.11	odd	6		1216.2.i.k.961.2		4
152.125	even	6		1216.2.i.l.961.1		4
228.11	even	6		2736.2.s.v.1873.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.b.7.2	✓	4	1.1	even	1	trivial
38.2.c.b.11.2	yes	4	19.11	even	3	inner
304.2.i.e.49.1		4	76.11	odd	6
304.2.i.e.273.1		4	4.3	odd	2
342.2.g.f.163.2		4	57.11	odd	6
342.2.g.f.235.2		4	3.2	odd	2
722.2.a.g.1.2		2	19.12	odd	6
722.2.a.j.1.1		2	19.7	even	3
722.2.c.j.429.1		4	19.8	odd	6
722.2.c.j.653.1		4	19.18	odd	2
722.2.e.n.99.1		12	19.5	even	9
722.2.e.n.245.1		12	19.4	even	9
722.2.e.n.389.1		12	19.17	even	9
722.2.e.n.415.2		12	19.9	even	9
722.2.e.n.423.1		12	19.6	even	9
722.2.e.n.595.2		12	19.16	even	9
722.2.e.o.99.2		12	19.14	odd	18
722.2.e.o.245.2		12	19.15	odd	18
722.2.e.o.389.2		12	19.2	odd	18
722.2.e.o.415.1		12	19.10	odd	18
722.2.e.o.423.2		12	19.13	odd	18
722.2.e.o.595.1		12	19.3	odd	18
950.2.e.k.201.1		4	95.49	even	6
950.2.e.k.501.1		4	5.4	even	2
950.2.j.g.49.1		8	95.87	odd	12
950.2.j.g.49.4		8	95.68	odd	12
950.2.j.g.349.1		8	5.3	odd	4
950.2.j.g.349.4		8	5.2	odd	4
1216.2.i.k.577.2		4	8.3	odd	2
1216.2.i.k.961.2		4	152.11	odd	6
1216.2.i.l.577.1		4	8.5	even	2
1216.2.i.l.961.1		4	152.125	even	6
2736.2.s.v.577.2		4	12.11	even	2
2736.2.s.v.1873.2		4	228.11	even	6
5776.2.a.z.1.1		2	76.31	even	6
5776.2.a.ba.1.2		2	76.7	odd	6
6498.2.a.ba.1.1		2	57.26	odd	6
6498.2.a.bg.1.1		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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.32288 + 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.82288 - 3.15731i) q^{5} +(1.32288 - 2.29129i) q^{6} -1.64575 q^{7} +1.00000 q^{8} +(-2.00000 + 3.46410i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.32288 + 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.82288 - 3.15731i) q^{5} +(1.32288 - 2.29129i) q^{6} -1.64575 q^{7} +1.00000 q^{8} +(-2.00000 + 3.46410i) q^{9} +(-1.82288 + 3.15731i) q^{10} +0.645751 q^{11} -2.64575 q^{12} +(-1.00000 + 1.73205i) q^{13} +(0.822876 + 1.42526i) q^{14} +(4.82288 - 8.35347i) q^{15} +(-0.500000 - 0.866025i) q^{16} +4.00000 q^{18} +(4.32288 - 0.559237i) q^{19} +3.64575 q^{20} +(-2.17712 - 3.77089i) q^{21} +(-0.322876 - 0.559237i) q^{22} +(-1.82288 + 3.15731i) q^{23} +(1.32288 + 2.29129i) q^{24} +(-4.14575 + 7.18065i) q^{25} +2.00000 q^{26} -2.64575 q^{27} +(0.822876 - 1.42526i) q^{28} +(1.82288 - 3.15731i) q^{29} -9.64575 q^{30} -0.354249 q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.854249 + 1.47960i) q^{33} +(3.00000 + 5.19615i) q^{35} +(-2.00000 - 3.46410i) q^{36} +5.64575 q^{37} +(-2.64575 - 3.46410i) q^{38} -5.29150 q^{39} +(-1.82288 - 3.15731i) q^{40} +(-5.14575 - 8.91270i) q^{41} +(-2.17712 + 3.77089i) q^{42} +(-0.354249 - 0.613577i) q^{43} +(-0.322876 + 0.559237i) q^{44} +14.5830 q^{45} +3.64575 q^{46} +(-4.82288 + 8.35347i) q^{47} +(1.32288 - 2.29129i) q^{48} -4.29150 q^{49} +8.29150 q^{50} +(-1.00000 - 1.73205i) q^{52} +(-4.29150 + 7.43310i) q^{53} +(1.32288 + 2.29129i) q^{54} +(-1.17712 - 2.03884i) q^{55} -1.64575 q^{56} +(7.00000 + 9.16515i) q^{57} -3.64575 q^{58} +(-3.96863 - 6.87386i) q^{59} +(4.82288 + 8.35347i) q^{60} +(7.46863 - 12.9360i) q^{61} +(0.177124 + 0.306788i) q^{62} +(3.29150 - 5.70105i) q^{63} +1.00000 q^{64} +7.29150 q^{65} +(0.854249 - 1.47960i) q^{66} +(2.32288 - 4.02334i) q^{67} -9.64575 q^{69} +(3.00000 - 5.19615i) q^{70} +(6.64575 + 11.5108i) q^{71} +(-2.00000 + 3.46410i) q^{72} +(-6.14575 - 10.6448i) q^{73} +(-2.82288 - 4.88936i) q^{74} -21.9373 q^{75} +(-1.67712 + 4.02334i) q^{76} -1.06275 q^{77} +(2.64575 + 4.58258i) q^{78} +(2.00000 + 3.46410i) q^{79} +(-1.82288 + 3.15731i) q^{80} +(2.50000 + 4.33013i) q^{81} +(-5.14575 + 8.91270i) q^{82} -7.93725 q^{83} +4.35425 q^{84} +(-0.354249 + 0.613577i) q^{86} +9.64575 q^{87} +0.645751 q^{88} +(-7.29150 - 12.6293i) q^{90} +(1.64575 - 2.85052i) q^{91} +(-1.82288 - 3.15731i) q^{92} +(-0.468627 - 0.811686i) q^{93} +9.64575 q^{94} +(-9.64575 - 12.6293i) q^{95} -2.64575 q^{96} +(7.14575 + 12.3768i) q^{97} +(2.14575 + 3.71655i) q^{98} +(-1.29150 + 2.23695i) 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

L-functions

Modular forms

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