LMFDB - Embedded newform 390.2.x.b.199.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(49,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("390.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.x (of order $6$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + \cdots + 2197 $ x^12 - 2x^11 - 8x^10 + 34x^9 + 8x^8 - 134x^7 + 98x^6 + 154x^5 + 104x^4 + 190x^3 - 1196x^2 - 338*x + 2197
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.4
Root			$2.00607 + 1.30680i$ of defining polynomial
Character	$\chi$	$=$	390.199
Dual form			390.2.x.b.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.26873 + 1.84128i) q^{5} +(0.866025 - 0.500000i) q^{6} +(2.17283 + 3.76344i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.26873 + 1.84128i) q^{5} +(0.866025 - 0.500000i) q^{6} +(2.17283 + 3.76344i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(0.960230 + 2.01940i) q^{10} +(-2.04055 - 1.17811i) q^{11} -1.00000i q^{12} +(3.18419 + 1.69144i) q^{13} +4.34565 q^{14} +(-2.01940 + 0.960230i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.60564 + 1.50437i) q^{17} +1.00000 q^{18} +(0.585872 - 0.338254i) q^{19} +(2.22896 + 0.178114i) q^{20} +4.34565i q^{21} +(-2.04055 + 1.17811i) q^{22} +(5.58405 + 3.22396i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-1.78064 - 4.67219i) q^{25} +(3.05692 - 1.91187i) q^{26} +1.00000i q^{27} +(2.17283 - 3.76344i) q^{28} +(4.82620 - 8.35922i) q^{29} +(-0.178114 + 2.22896i) q^{30} -7.11493i q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.17811 - 2.04055i) q^{33} +3.00874i q^{34} +(-9.68629 - 0.774021i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-3.74165 + 6.48073i) q^{37} -0.676507i q^{38} +(1.91187 + 3.05692i) q^{39} +(1.26873 - 1.84128i) q^{40} +(-2.60564 - 1.50437i) q^{41} +(3.76344 + 2.17283i) q^{42} +(5.91710 - 3.41624i) q^{43} +2.35623i q^{44} +(-2.22896 - 0.178114i) q^{45} +(5.58405 - 3.22396i) q^{46} -5.61529 q^{47} +(-0.866025 + 0.500000i) q^{48} +(-5.94234 + 10.2924i) q^{49} +(-4.93655 - 0.794019i) q^{50} -3.00874 q^{51} +(-0.127265 - 3.60330i) q^{52} -9.43400i q^{53} +(0.866025 + 0.500000i) q^{54} +(4.75816 - 2.26252i) q^{55} +(-2.17283 - 3.76344i) q^{56} +0.676507 q^{57} +(-4.82620 - 8.35922i) q^{58} +(-4.56364 + 2.63482i) q^{59} +(1.84128 + 1.26873i) q^{60} +(2.15646 + 3.73509i) q^{61} +(-6.16171 - 3.55746i) q^{62} +(-2.17283 + 3.76344i) q^{63} +1.00000 q^{64} +(-7.15429 + 3.71700i) q^{65} -2.35623 q^{66} +(2.91329 - 5.04596i) q^{67} +(2.60564 + 1.50437i) q^{68} +(3.22396 + 5.58405i) q^{69} +(-5.51347 + 8.00157i) q^{70} +(2.52520 - 1.45793i) q^{71} +(-0.500000 - 0.866025i) q^{72} +7.67804 q^{73} +(3.74165 + 6.48073i) q^{74} +(0.794019 - 4.93655i) q^{75} +(-0.585872 - 0.338254i) q^{76} -10.2393i q^{77} +(3.60330 - 0.127265i) q^{78} -3.74519 q^{79} +(-0.960230 - 2.01940i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.60564 + 1.50437i) q^{82} -10.3557 q^{83} +(3.76344 - 2.17283i) q^{84} +(0.535898 - 6.70637i) q^{85} -6.83247i q^{86} +(8.35922 - 4.82620i) q^{87} +(2.04055 + 1.17811i) q^{88} +(4.15208 + 2.39720i) q^{89} +(-1.26873 + 1.84128i) q^{90} +(0.553049 + 15.6587i) q^{91} -6.44791i q^{92} +(3.55746 - 6.16171i) q^{93} +(-2.80764 + 4.86298i) q^{94} +(-0.120495 + 1.50791i) q^{95} +1.00000i q^{96} +(8.17066 + 14.1520i) q^{97} +(5.94234 + 10.2924i) q^{98} -2.35623i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8} + 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 - 6 * q^4 + 2 * q^5 + 2 * q^7 - 12 * q^8 + 6 * q^9	$ 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8} + 6 q^{9} + 4 q^{10} + 6 q^{11} + 8 q^{13} + 4 q^{14} + 6 q^{15} - 6 q^{16} - 18 q^{17} + 12 q^{18} - 6 q^{19} + 2 q^{20} + 6 q^{22} - 6 q^{23} - 10 q^{25} - 2 q^{26} + 2 q^{28} + 14 q^{29} + 6 q^{30} + 6 q^{32} - 6 q^{33} - 22 q^{35} + 6 q^{36} + 12 q^{37} - 2 q^{39} - 2 q^{40} - 18 q^{41} + 12 q^{42} + 36 q^{43} - 2 q^{45} - 6 q^{46} - 16 q^{47} + 8 q^{49} - 20 q^{50} + 16 q^{51} - 10 q^{52} + 8 q^{55} - 2 q^{56} + 8 q^{57} - 14 q^{58} - 36 q^{59} + 10 q^{61} - 6 q^{62} - 2 q^{63} + 12 q^{64} - 44 q^{65} - 12 q^{66} - 4 q^{67} + 18 q^{68} + 16 q^{69} + 4 q^{70} - 12 q^{71} - 6 q^{72} - 28 q^{73} - 12 q^{74} + 16 q^{75} + 6 q^{76} + 2 q^{78} + 4 q^{79} - 4 q^{80} - 6 q^{81} - 18 q^{82} - 72 q^{83} + 12 q^{84} + 48 q^{85} - 6 q^{87} - 6 q^{88} + 18 q^{89} + 2 q^{90} + 2 q^{91} + 16 q^{93} - 8 q^{94} + 18 q^{95} + 48 q^{97} - 8 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 - 6 * q^4 + 2 * q^5 + 2 * q^7 - 12 * q^8 + 6 * q^9 + 4 * q^10 + 6 * q^11 + 8 * q^13 + 4 * q^14 + 6 * q^15 - 6 * q^16 - 18 * q^17 + 12 * q^18 - 6 * q^19 + 2 * q^20 + 6 * q^22 - 6 * q^23 - 10 * q^25 - 2 * q^26 + 2 * q^28 + 14 * q^29 + 6 * q^30 + 6 * q^32 - 6 * q^33 - 22 * q^35 + 6 * q^36 + 12 * q^37 - 2 * q^39 - 2 * q^40 - 18 * q^41 + 12 * q^42 + 36 * q^43 - 2 * q^45 - 6 * q^46 - 16 * q^47 + 8 * q^49 - 20 * q^50 + 16 * q^51 - 10 * q^52 + 8 * q^55 - 2 * q^56 + 8 * q^57 - 14 * q^58 - 36 * q^59 + 10 * q^61 - 6 * q^62 - 2 * q^63 + 12 * q^64 - 44 * q^65 - 12 * q^66 - 4 * q^67 + 18 * q^68 + 16 * q^69 + 4 * q^70 - 12 * q^71 - 6 * q^72 - 28 * q^73 - 12 * q^74 + 16 * q^75 + 6 * q^76 + 2 * q^78 + 4 * q^79 - 4 * q^80 - 6 * q^81 - 18 * q^82 - 72 * q^83 + 12 * q^84 + 48 * q^85 - 6 * q^87 - 6 * q^88 + 18 * q^89 + 2 * q^90 + 2 * q^91 + 16 * q^93 - 8 * q^94 + 18 * q^95 + 48 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.26873	+	1.84128i	−0.567394	+	0.823446i
$5$	−1.26873	+	1.84128i	−0.567394	+	0.823446i
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	2.17283	+	3.76344i	0.821251	+	1.42245i	0.904751	+	0.425940i	$0.140057\pi$
$7$	2.17283	+	3.76344i	0.821251	+	1.42245i	−0.0835003	+	0.996508i	$0.526610\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.960230	+	2.01940i	0.303651	+	0.638589i
$11$	−2.04055	−	1.17811i	−0.615250	−	0.355215i	0.159767	−	0.987155i	$-0.448926\pi$
$11$	−2.04055	−	1.17811i	−0.615250	−	0.355215i	−0.775017	+	0.631940i	$0.782259\pi$
$12$		−	1.00000i		−	0.288675i
$13$	3.18419	+	1.69144i	0.883134	+	0.469120i
$13$	3.18419	+	1.69144i	0.883134	+	0.469120i
$14$	4.34565			1.16142
$15$	−2.01940	+	0.960230i	−0.521406	+	0.247930i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.60564	+	1.50437i	−0.631962	+	0.364863i	−0.781511	−	0.623891i	$-0.785551\pi$
$17$	−2.60564	+	1.50437i	−0.631962	+	0.364863i	0.149550	+	0.988754i	$0.452218\pi$
$18$	1.00000			0.235702
$19$	0.585872	−	0.338254i	0.134408	−	0.0776007i	−0.431288	−	0.902214i	$-0.641941\pi$
$19$	0.585872	−	0.338254i	0.134408	−	0.0776007i	0.565696	+	0.824614i	$0.308607\pi$
$20$	2.22896	+	0.178114i	0.498411	+	0.0398275i
$21$			4.34565i			0.948299i
$22$	−2.04055	+	1.17811i	−0.435047	+	0.251175i
$23$	5.58405	+	3.22396i	1.16436	+	0.672241i	0.952344	−	0.305026i	$-0.0986651\pi$
$23$	5.58405	+	3.22396i	1.16436	+	0.672241i	0.212012	+	0.977267i	$0.431998\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	−1.78064	−	4.67219i	−0.356127	−	0.934438i
$26$	3.05692	−	1.91187i	0.599511	−	0.374948i
$27$			1.00000i			0.192450i
$28$	2.17283	−	3.76344i	0.410625	−	0.711224i
$29$	4.82620	−	8.35922i	0.896202	−	1.55227i	0.0638921	−	0.997957i	$-0.479649\pi$
$29$	4.82620	−	8.35922i	0.896202	−	1.55227i	0.832310	−	0.554311i	$-0.187018\pi$
$30$	−0.178114	+	2.22896i	−0.0325190	+	0.406951i
$31$		−	7.11493i		−	1.27788i	−0.769257	−	0.638939i	$-0.779374\pi$
$31$		−	7.11493i		−	1.27788i	0.769257	−	0.638939i	$-0.220626\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.17811	−	2.04055i	−0.205083	−	0.355215i
$34$			3.00874i			0.515995i
$35$	−9.68629	−	0.774021i	−1.63728	−	0.130833i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−3.74165	+	6.48073i	−0.615123	+	1.06542i	0.375240	+	0.926928i	$0.377560\pi$
$37$	−3.74165	+	6.48073i	−0.615123	+	1.06542i	−0.990363	+	0.138497i	$0.955773\pi$
$38$		−	0.676507i		−	0.109744i
$39$	1.91187	+	3.05692i	0.306144	+	0.489499i
$40$	1.26873	−	1.84128i	0.200604	−	0.291132i
$41$	−2.60564	−	1.50437i	−0.406933	−	0.234943i	0.282538	−	0.959256i	$-0.408824\pi$
$41$	−2.60564	−	1.50437i	−0.406933	−	0.234943i	−0.689471	+	0.724313i	$0.742157\pi$
$42$	3.76344	+	2.17283i	0.580712	+	0.335274i
$43$	5.91710	−	3.41624i	0.902349	−	0.520971i	0.0243872	−	0.999703i	$-0.492237\pi$
$43$	5.91710	−	3.41624i	0.902349	−	0.520971i	0.877961	+	0.478731i	$0.158903\pi$
$44$			2.35623i			0.355215i
$45$	−2.22896	−	0.178114i	−0.332274	−	0.0265517i
$46$	5.58405	−	3.22396i	0.823324	−	0.475346i
$47$	−5.61529			−0.819074			−0.409537	−	0.912294i	$-0.634310\pi$
$47$	−5.61529			−0.819074			−0.409537	+	0.912294i	$0.634310\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	−5.94234	+	10.2924i	−0.848906	+	1.47035i
$50$	−4.93655	−	0.794019i	−0.698134	−	0.112291i
$51$	−3.00874			−0.421308
$52$	−0.127265	−	3.60330i	−0.0176485	−	0.499688i
$53$		−	9.43400i		−	1.29586i	−0.761700	−	0.647930i	$-0.775635\pi$
$53$		−	9.43400i		−	1.29586i	0.761700	−	0.647930i	$-0.224365\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	4.75816	−	2.26252i	0.641590	−	0.305078i
$56$	−2.17283	−	3.76344i	−0.290356	−	0.502911i
$57$	0.676507			0.0896056
$58$	−4.82620	−	8.35922i	−0.633711	−	1.09762i
$59$	−4.56364	+	2.63482i	−0.594135	+	0.343024i	−0.766731	−	0.641969i	$-0.778118\pi$
$59$	−4.56364	+	2.63482i	−0.594135	+	0.343024i	0.172596	+	0.984993i	$0.444785\pi$
$60$	1.84128	+	1.26873i	0.237708	+	0.163793i
$61$	2.15646	+	3.73509i	0.276106	+	0.478230i	0.970414	−	0.241449i	$-0.0776225\pi$
$61$	2.15646	+	3.73509i	0.276106	+	0.478230i	−0.694307	+	0.719679i	$0.744289\pi$
$62$	−6.16171	−	3.55746i	−0.782538	−	0.451798i
$63$	−2.17283	+	3.76344i	−0.273750	+	0.474149i
$64$	1.00000			0.125000
$65$	−7.15429	+	3.71700i	−0.887381	+	0.461037i
$66$	−2.35623			−0.290032
$67$	2.91329	−	5.04596i	0.355915	−	0.616463i	−0.631359	−	0.775490i	$-0.717503\pi$
$67$	2.91329	−	5.04596i	0.355915	−	0.616463i	0.987274	+	0.159028i	$0.0508360\pi$
$68$	2.60564	+	1.50437i	0.315981	+	0.182432i
$69$	3.22396	+	5.58405i	0.388119	+	0.672241i
$70$	−5.51347	+	8.00157i	−0.658986	+	0.956370i
$71$	2.52520	−	1.45793i	0.299686	−	0.173024i	−0.342616	−	0.939476i	$-0.611313\pi$
$71$	2.52520	−	1.45793i	0.299686	−	0.173024i	0.642302	+	0.766452i	$0.277980\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	7.67804			0.898647			0.449323	−	0.893369i	$-0.351665\pi$
$73$	7.67804			0.898647			0.449323	+	0.893369i	$0.351665\pi$
$74$	3.74165	+	6.48073i	0.434958	+	0.753369i
$75$	0.794019	−	4.93655i	0.0916854	−	0.570024i
$76$	−0.585872	−	0.338254i	−0.0672042	−	0.0388004i
$77$		−	10.2393i		−	1.16688i
$78$	3.60330	−	0.127265i	0.407994	−	0.0144099i
$79$	−3.74519			−0.421367			−0.210683	−	0.977554i	$-0.567569\pi$
$79$	−3.74519			−0.421367			−0.210683	+	0.977554i	$0.567569\pi$
$80$	−0.960230	−	2.01940i	−0.107357	−	0.225775i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.60564	+	1.50437i	−0.287745	+	0.166130i
$83$	−10.3557			−1.13668			−0.568341	−	0.822793i	$-0.692415\pi$
$83$	−10.3557			−1.13668			−0.568341	+	0.822793i	$0.692415\pi$
$84$	3.76344	−	2.17283i	0.410625	−	0.237075i
$85$	0.535898	−	6.70637i	0.0581263	−	0.727408i
$86$		−	6.83247i		−	0.736765i
$87$	8.35922	−	4.82620i	0.896202	−	0.517422i
$88$	2.04055	+	1.17811i	0.217524	+	0.125587i
$89$	4.15208	+	2.39720i	0.440119	+	0.254103i	0.703648	−	0.710549i	$-0.251553\pi$
$89$	4.15208	+	2.39720i	0.440119	+	0.254103i	−0.263529	+	0.964651i	$0.584886\pi$
$90$	−1.26873	+	1.84128i	−0.133736	+	0.194088i
$91$	0.553049	+	15.6587i	0.0579753	+	1.64148i
$92$		−	6.44791i		−	0.672241i
$93$	3.55746	−	6.16171i	0.368892	−	0.638939i
$94$	−2.80764	+	4.86298i	−0.289586	+	0.501578i
$95$	−0.120495	+	1.50791i	−0.0123626	+	0.154708i
$96$			1.00000i			0.102062i
$97$	8.17066	+	14.1520i	0.829605	+	1.43692i	0.898349	+	0.439283i	$0.144768\pi$
$97$	8.17066	+	14.1520i	0.829605	+	1.43692i	−0.0687436	+	0.997634i	$0.521899\pi$
$98$	5.94234	+	10.2924i	0.600267	+	1.03969i
$99$		−	2.35623i		−	0.236810i
$100$	−3.15592	+	3.87817i	−0.315592	+	0.387817i
$101$	−6.11911	+	10.5986i	−0.608875	+	1.05460i	0.382552	+	0.923934i	$0.375045\pi$
$101$	−6.11911	+	10.5986i	−0.608875	+	1.05460i	−0.991426	+	0.130668i	$0.958288\pi$
$102$	−1.50437	+	2.60564i	−0.148955	+	0.257997i
$103$		−	3.75144i		−	0.369640i	−0.982772	−	0.184820i	$-0.940830\pi$
$103$		−	3.75144i		−	0.369640i	0.982772	−	0.184820i	$-0.0591702\pi$
$104$	−3.18419	−	1.69144i	−0.312235	−	0.165859i
$105$	−8.00157	−	5.51347i	−0.780873	−	0.538060i
$106$	−8.17008	−	4.71700i	−0.793549	−	0.458156i
$107$	−14.3904	−	8.30831i	−1.39117	−	0.803194i	−0.397728	−	0.917503i	$-0.630201\pi$
$107$	−14.3904	−	8.30831i	−1.39117	−	0.803194i	−0.993445	+	0.114309i	$0.963535\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$		−	11.1116i		−	1.06430i	−0.846652	−	0.532148i	$-0.821385\pi$
$109$		−	11.1116i		−	1.06430i	0.846652	−	0.532148i	$-0.178615\pi$
$110$	0.419677	−	5.25194i	0.0400146	−	0.500753i
$111$	−6.48073	+	3.74165i	−0.615123	+	0.355142i
$112$	−4.34565			−0.410625
$113$	13.5620	−	7.83002i	1.27581	−	0.736587i	0.299731	−	0.954024i	$-0.403103\pi$
$113$	13.5620	−	7.83002i	1.27581	−	0.736587i	0.976074	+	0.217437i	$0.0697697\pi$
$114$	0.338254	−	0.585872i	0.0316804	−	0.0548720i
$115$	−13.0209	+	6.19148i	−1.21420	+	0.577358i
$116$	−9.65239			−0.896202
$117$	0.127265	+	3.60330i	0.0117657	+	0.333126i
$118$			5.26964i			0.485109i
$119$	−11.3232	−	6.53747i	−1.03800	−	0.599288i
$120$	2.01940	−	0.960230i	0.184345	−	0.0876566i
$121$	−2.72410	−	4.71827i	−0.247645	−	0.428934i
$122$	4.31292			0.390473
$123$	−1.50437	−	2.60564i	−0.135644	−	0.234943i
$124$	−6.16171	+	3.55746i	−0.553338	+	0.319470i
$125$	10.8620	+	2.64911i	0.971523	+	0.236943i
$126$	2.17283	+	3.76344i	0.193571	+	0.335274i
$127$	−11.7820	−	6.80236i	−1.04549	−	0.603611i	−0.124103	−	0.992269i	$-0.539605\pi$
$127$	−11.7820	−	6.80236i	−1.04549	−	0.603611i	−0.921382	+	0.388658i	$0.872939\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	6.83247			0.601566
$130$	−0.358130	+	8.05430i	−0.0314101	+	0.706409i
$131$	10.2122			0.892246			0.446123	−	0.894972i	$-0.352804\pi$
$131$	10.2122			0.892246			0.446123	+	0.894972i	$0.352804\pi$
$132$	−1.17811	+	2.04055i	−0.102542	+	0.177607i
$133$	2.54600	+	1.46993i	0.220766	+	0.127459i
$134$	−2.91329	−	5.04596i	−0.251670	−	0.435905i
$135$	−1.84128	−	1.26873i	−0.158472	−	0.109195i
$136$	2.60564	−	1.50437i	0.223432	−	0.128999i
$137$	6.20689	+	10.7506i	0.530290	+	0.918489i	0.999375	+	0.0353365i	$0.0112503\pi$
$137$	6.20689	+	10.7506i	0.530290	+	0.918489i	−0.469085	+	0.883153i	$0.655416\pi$
$138$	6.44791			0.548883
$139$	−7.80915	−	13.5258i	−0.662363	−	1.14725i	−0.979993	−	0.199032i	$-0.936220\pi$
$139$	−7.80915	−	13.5258i	−0.662363	−	1.14725i	0.317630	−	0.948215i	$-0.397113\pi$
$140$	4.17283	+	8.77559i	0.352668	+	0.741673i
$141$	−4.86298	−	2.80764i	−0.409537	−	0.236446i
$142$		−	2.91585i		−	0.244693i
$143$	−4.50479	−	7.20280i	−0.376710	−	0.602329i
$144$	−1.00000			−0.0833333
$145$	9.26852	+	19.4920i	0.769709	+	1.61872i
$146$	3.83902	−	6.64938i	0.317720	−	0.550307i
$147$	−10.2924	+	5.94234i	−0.848906	+	0.490116i
$148$	7.48330			0.615123
$149$	16.9104	−	9.76324i	1.38536	−	0.799836i	0.392569	−	0.919722i	$-0.371586\pi$
$149$	16.9104	−	9.76324i	1.38536	−	0.799836i	0.992788	+	0.119886i	$0.0382530\pi$
$150$	−3.87817	−	3.15592i	−0.316651	−	0.257679i
$151$			11.5027i			0.936079i	0.883707	+	0.468040i	$0.155040\pi$
$151$			11.5027i			0.936079i	−0.883707	+	0.468040i	$0.844960\pi$
$152$	−0.585872	+	0.338254i	−0.0475205	+	0.0274360i
$153$	−2.60564	−	1.50437i	−0.210654	−	0.121621i
$154$	−8.86753	−	5.11967i	−0.714566	−	0.412555i
$155$	13.1006	+	9.02694i	1.05226	+	0.725061i
$156$	1.69144	−	3.18419i	0.135423	−	0.254939i
$157$		−	4.47595i		−	0.357220i	−0.983920	−	0.178610i	$-0.942840\pi$
$157$		−	4.47595i		−	0.357220i	0.983920	−	0.178610i	$-0.0571600\pi$
$158$	−1.87260	+	3.24343i	−0.148976	+	0.258033i
$159$	4.71700	−	8.17008i	0.374082	−	0.647930i
$160$	−2.22896	−	0.178114i	−0.176215	−	0.0140811i
$161$			28.0204i			2.20831i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	−3.87774	−	6.71645i	−0.303728	−	0.526073i	0.673249	−	0.739416i	$-0.264898\pi$
$163$	−3.87774	−	6.71645i	−0.303728	−	0.526073i	−0.976977	+	0.213343i	$0.931565\pi$
$164$			3.00874i			0.234943i
$165$	5.25194	+	0.419677i	0.408863	+	0.0326718i
$166$	−5.17783	+	8.96827i	−0.401878	+	0.696073i
$167$	−0.339021	+	0.587202i	−0.0262342	+	0.0454390i	−0.878844	−	0.477108i	$-0.841685\pi$
$167$	−0.339021	+	0.587202i	−0.0262342	+	0.0454390i	0.852610	+	0.522547i	$0.175018\pi$
$168$		−	4.34565i		−	0.335274i
$169$	7.27808	+	10.7717i	0.559852	+	0.828593i
$170$	−5.53994	−	3.81729i	−0.424894	−	0.292772i
$171$	0.585872	+	0.338254i	0.0448028	+	0.0258669i
$172$	−5.91710	−	3.41624i	−0.451174	−	0.260486i
$173$	−0.625226	+	0.360974i	−0.0475350	+	0.0274444i	−0.523579	−	0.851977i	$-0.675404\pi$
$173$	−0.625226	+	0.360974i	−0.0475350	+	0.0274444i	0.476044	+	0.879421i	$0.342070\pi$
$174$		−	9.65239i		−	0.731746i
$175$	13.7145	−	16.8532i	1.03672	−	1.27398i
$176$	2.04055	−	1.17811i	0.153812	−	0.0888037i
$177$	−5.26964			−0.396090
$178$	4.15208	−	2.39720i	0.311211	−	0.179678i
$179$	3.18673	−	5.51958i	0.238187	−	0.412553i	−0.722007	−	0.691886i	$-0.756780\pi$
$179$	3.18673	−	5.51958i	0.238187	−	0.412553i	0.960194	+	0.279333i	$0.0901134\pi$
$180$	0.960230	+	2.01940i	0.0715713	+	0.150517i
$181$	22.0214			1.63683			0.818417	−	0.574624i	$-0.194852\pi$
$181$	22.0214			1.63683			0.818417	+	0.574624i	$0.194852\pi$
$182$	13.8374	+	7.35040i	1.02569	+	0.544848i
$183$			4.31292i			0.318820i
$184$	−5.58405	−	3.22396i	−0.411662	−	0.237673i
$185$	−7.18569	−	15.1117i	−0.528302	−	1.11104i
$186$	−3.55746	−	6.16171i	−0.260846	−	0.451798i
$187$	7.08928			0.518419
$188$	2.80764	+	4.86298i	0.204768	+	0.354669i
$189$	−3.76344	+	2.17283i	−0.273750	+	0.158050i
$190$	1.24564	+	0.858307i	0.0903682	+	0.0622681i
$191$	−0.293441	−	0.508255i	−0.0212326	−	0.0367760i	0.855214	−	0.518275i	$-0.173426\pi$
$191$	−0.293441	−	0.508255i	−0.0212326	−	0.0367760i	−0.876446	+	0.481499i	$0.840092\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	−11.3135	+	19.5955i	−0.814363	+	1.41052i	0.0954215	+	0.995437i	$0.469580\pi$
$193$	−11.3135	+	19.5955i	−0.814363	+	1.41052i	−0.909784	+	0.415081i	$0.863753\pi$
$194$	16.3413			1.17324
$195$	−8.05430	−	0.358130i	−0.576780	−	0.0256462i
$196$	11.8847			0.848906
$197$	0.823770	−	1.42681i	0.0586912	−	0.101656i	−0.835187	−	0.549966i	$-0.814641\pi$
$197$	0.823770	−	1.42681i	0.0586912	−	0.101656i	0.893878	+	0.448310i	$0.147974\pi$
$198$	−2.04055	−	1.17811i	−0.145016	−	0.0837249i
$199$	−5.13665	−	8.89694i	−0.364127	−	0.630687i	0.624508	−	0.781018i	$-0.285299\pi$
$199$	−5.13665	−	8.89694i	−0.364127	−	0.630687i	−0.988636	+	0.150331i	$0.951966\pi$
$200$	1.78064	+	4.67219i	0.125910	+	0.330374i
$201$	5.04596	−	2.91329i	0.355915	−	0.205488i
$202$	6.11911	+	10.5986i	0.430539	+	0.745716i
$203$	41.9459			2.94403
$204$	1.50437	+	2.60564i	0.105327	+	0.182432i
$205$	6.07583	−	2.88908i	0.424355	−	0.201782i
$206$	−3.24884	−	1.87572i	−0.226357	−	0.130688i
$207$			6.44791i			0.448161i
$208$	−3.05692	+	1.91187i	−0.211959	+	0.132564i
$209$	−1.59401			−0.110260
$210$	−8.77559	+	4.17283i	−0.605573	+	0.287952i
$211$	12.1905	−	21.1145i	0.839226	−	1.45358i	−0.0513166	−	0.998682i	$-0.516342\pi$
$211$	12.1905	−	21.1145i	0.839226	−	1.45358i	0.890543	−	0.454900i	$-0.150325\pi$
$212$	−8.17008	+	4.71700i	−0.561124	+	0.323965i
$213$	2.91585			0.199791
$214$	−14.3904	+	8.30831i	−0.983708	+	0.567944i
$215$	−1.21696	+	15.2293i	−0.0829959	+	1.03863i
$216$		−	1.00000i		−	0.0680414i
$217$	26.7766	−	15.4595i	1.81772	−	1.04946i
$218$	−9.62290	−	5.55578i	−0.651745	−	0.376285i
$219$	6.64938	+	3.83902i	0.449323	+	0.259417i
$220$	−4.33848	−	2.98942i	−0.292500	−	0.201547i
$221$	−10.8414	+	0.382907i	−0.729272	+	0.0257571i
$222$			7.48330i			0.502246i
$223$	−2.31792	+	4.01476i	−0.155220	+	0.268848i	−0.933139	−	0.359516i	$-0.882942\pi$
$223$	−2.31792	+	4.01476i	−0.155220	+	0.268848i	0.777919	+	0.628364i	$0.216275\pi$
$224$	−2.17283	+	3.76344i	−0.145178	+	0.251456i
$225$	3.15592	−	3.87817i	0.210394	−	0.258545i
$226$		−	15.6600i		−	1.04169i
$227$	8.89213	+	15.4016i	0.590192	+	1.02224i	0.994206	+	0.107489i	$0.0342812\pi$
$227$	8.89213	+	15.4016i	0.590192	+	1.02224i	−0.404015	+	0.914753i	$0.632385\pi$
$228$	−0.338254	−	0.585872i	−0.0224014	−	0.0388004i
$229$		−	15.3361i		−	1.01344i	−0.862111	−	0.506720i	$-0.830858\pi$
$229$		−	15.3361i		−	1.01344i	0.862111	−	0.506720i	$-0.169142\pi$
$230$	−1.14846	+	14.3722i	−0.0757274	+	0.947672i
$231$	5.11967	−	8.86753i	0.336850	−	0.583441i
$232$	−4.82620	+	8.35922i	−0.316855	+	0.548809i
$233$			7.75548i			0.508079i	0.967194	+	0.254039i	$0.0817593\pi$
$233$			7.75548i			0.508079i	−0.967194	+	0.254039i	$0.918241\pi$
$234$	3.18419	+	1.69144i	0.208157	+	0.110573i
$235$	7.12430	−	10.3393i	0.464738	−	0.674463i
$236$	4.56364	+	2.63482i	0.297068	+	0.171512i
$237$	−3.24343	−	1.87260i	−0.210683	−	0.121638i
$238$	−11.3232	+	6.53747i	−0.733975	+	0.423761i
$239$			18.6409i			1.20578i	0.797824	+	0.602890i	$0.205984\pi$
$239$			18.6409i			1.20578i	−0.797824	+	0.602890i	$0.794016\pi$
$240$	0.178114	−	2.22896i	0.0114972	−	0.143879i
$241$	−2.65884	+	1.53508i	−0.171271	+	0.0988833i	−0.583185	−	0.812339i	$-0.698194\pi$
$241$	−2.65884	+	1.53508i	−0.171271	+	0.0988833i	0.411914	+	0.911223i	$0.364860\pi$
$242$	−5.44819			−0.350223
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	2.15646	−	3.73509i	0.138053	−	0.239115i
$245$	−11.4120	−	23.9999i	−0.729088	−	1.53330i
$246$	−3.00874			−0.191830
$247$	2.43766	−	0.0860957i	0.155105	−	0.00547814i
$248$			7.11493i			0.451798i
$249$	−8.96827	−	5.17783i	−0.568341	−	0.328132i
$250$	7.72518	−	8.08218i	0.488583	−	0.511162i
$251$	−3.56404	−	6.17309i	−0.224960	−	0.389642i	0.731347	−	0.682005i	$-0.238892\pi$
$251$	−3.56404	−	6.17309i	−0.224960	−	0.389642i	−0.956307	+	0.292363i	$0.905558\pi$
$252$	4.34565			0.273750
$253$	−7.59637	−	13.1573i	−0.477580	−	0.827193i
$254$	−11.7820	+	6.80236i	−0.739270	+	0.426818i
$255$	3.81729	−	5.53994i	0.239048	−	0.346924i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−12.3353	−	7.12178i	−0.769454	−	0.444244i	0.0632261	−	0.997999i	$-0.479861\pi$
$257$	−12.3353	−	7.12178i	−0.769454	−	0.444244i	−0.832680	+	0.553755i	$0.813194\pi$
$258$	3.41624	−	5.91710i	0.212686	−	0.368382i
$259$	−32.5198			−2.02068
$260$	6.79616	+	4.33730i	0.421480	+	0.268988i
$261$	9.65239			0.597468
$262$	5.10611	−	8.84404i	0.315457	−	0.546387i
$263$	−13.3385	−	7.70101i	−0.822490	−	0.474865i	0.0287845	−	0.999586i	$-0.490836\pi$
$263$	−13.3385	−	7.70101i	−0.822490	−	0.474865i	−0.851274	+	0.524721i	$0.824170\pi$
$264$	1.17811	+	2.04055i	0.0725079	+	0.125587i
$265$	17.3707	+	11.9692i	1.06707	+	0.735264i
$266$	2.54600	−	1.46993i	0.156105	−	0.0901273i
$267$	2.39720	+	4.15208i	0.146706	+	0.254103i
$268$	−5.82658			−0.355915
$269$	13.3134	+	23.0595i	0.811732	+	1.40596i	0.911651	+	0.410966i	$0.134808\pi$
$269$	13.3134	+	23.0595i	0.811732	+	1.40596i	−0.0999185	+	0.994996i	$0.531858\pi$
$270$	−2.01940	+	0.960230i	−0.122896	+	0.0584378i
$271$	−6.66899	−	3.85034i	−0.405112	−	0.233892i	0.283575	−	0.958950i	$-0.408479\pi$
$271$	−6.66899	−	3.85034i	−0.405112	−	0.233892i	−0.688687	+	0.725058i	$0.741813\pi$
$272$		−	3.00874i		−	0.182432i
$273$	−7.35040	+	13.8374i	−0.444866	+	0.837475i
$274$	12.4138			0.749943
$275$	−1.87089	+	11.6316i	−0.112819	+	0.701414i
$276$	3.22396	−	5.58405i	0.194059	−	0.336121i
$277$	−12.3861	+	7.15114i	−0.744211	+	0.429671i	−0.823599	−	0.567173i	$-0.808037\pi$
$277$	−12.3861	+	7.15114i	−0.744211	+	0.429671i	0.0793871	+	0.996844i	$0.474704\pi$
$278$	−15.6183			−0.936723
$279$	6.16171	−	3.55746i	0.368892	−	0.212980i
$280$	9.68629	+	0.774021i	0.578867	+	0.0462566i
$281$			7.96746i			0.475299i	0.971351	+	0.237649i	$0.0763769\pi$
$281$			7.96746i			0.475299i	−0.971351	+	0.237649i	$0.923623\pi$
$282$	−4.86298	+	2.80764i	−0.289586	+	0.167193i
$283$	12.7095	+	7.33785i	0.755503	+	0.436190i	0.827679	−	0.561202i	$-0.189661\pi$
$283$	12.7095	+	7.33785i	0.755503	+	0.436190i	−0.0721756	+	0.997392i	$0.522994\pi$
$284$	−2.52520	−	1.45793i	−0.149843	−	0.0865120i
$285$	−0.858307	+	1.24564i	−0.0508417	+	0.0737854i
$286$	−8.49021	+	0.299865i	−0.502036	+	0.0177314i
$287$		−	13.0749i		−	0.771789i
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−3.97374	+	6.88273i	−0.233750	+	0.404866i
$290$	21.5148	+	1.71923i	1.26339	+	0.100956i
$291$			16.3413i			0.957945i
$292$	−3.83902	−	6.64938i	−0.224662	−	0.389125i
$293$	3.43198	+	5.94436i	0.200498	+	0.347273i	0.948689	−	0.316210i	$-0.102411\pi$
$293$	3.43198	+	5.94436i	0.200498	+	0.347273i	−0.748191	+	0.663484i	$0.769077\pi$
$294$			11.8847i			0.693129i
$295$	0.938596	−	11.7458i	0.0546472	−	0.683868i
$296$	3.74165	−	6.48073i	0.217479	−	0.376685i
$297$	1.17811	−	2.04055i	0.0683611	−	0.118405i
$298$		−	19.5265i		−	1.13114i
$299$	12.3275	+	19.7108i	0.712921	+	1.13990i
$300$	−4.67219	+	1.78064i	−0.269749	+	0.102805i
$301$	25.7136	+	14.8458i	1.48211	+	0.855696i
$302$	9.96166	+	5.75137i	0.573229	+	0.330954i
$303$	−10.5986	+	6.11911i	−0.608875	+	0.351534i
$304$			0.676507i			0.0388004i
$305$	−9.61333	−	0.768190i	−0.550458	−	0.0439865i
$306$	−2.60564	+	1.50437i	−0.148955	+	0.0859991i
$307$	−10.9917			−0.627328			−0.313664	−	0.949534i	$-0.601557\pi$
$307$	−10.9917			−0.627328			−0.313664	+	0.949534i	$0.601557\pi$
$308$	−8.86753	+	5.11967i	−0.505275	+	0.291720i
$309$	1.87572	−	3.24884i	0.106706	−	0.184820i
$310$	14.3678	−	6.83197i	0.816039	−	0.388030i
$311$	−13.9044			−0.788446			−0.394223	−	0.919015i	$-0.628986\pi$
$311$	−13.9044			−0.788446			−0.394223	+	0.919015i	$0.628986\pi$
$312$	−1.91187	−	3.05692i	−0.108238	−	0.173064i
$313$			14.1734i			0.801130i	0.916268	+	0.400565i	$0.131186\pi$
$313$			14.1734i			0.801130i	−0.916268	+	0.400565i	$0.868814\pi$
$314$	−3.87629	−	2.23798i	−0.218752	−	0.126296i
$315$	−4.17283	−	8.77559i	−0.235112	−	0.494448i
$316$	1.87260	+	3.24343i	0.105342	+	0.182457i
$317$	3.20808			0.180184			0.0900920	−	0.995933i	$-0.471284\pi$
$317$	3.20808			0.180184			0.0900920	+	0.995933i	$0.471284\pi$
$318$	−4.71700	−	8.17008i	−0.264516	−	0.458156i
$319$	−19.6962	+	11.3716i	−1.10278	+	0.636688i
$320$	−1.26873	+	1.84128i	−0.0709243	+	0.102931i
$321$	−8.30831	−	14.3904i	−0.463724	−	0.803194i
$322$	24.2664	+	14.0102i	1.35231	+	0.780757i
$323$	−1.01772	+	1.76274i	−0.0566273	+	0.0980813i
$324$	1.00000			0.0555556
$325$	2.23284	−	17.8889i	0.123856	−	0.992300i
$326$	−7.75548			−0.429537
$327$	5.55578	−	9.62290i	0.307236	−	0.532148i
$328$	2.60564	+	1.50437i	0.143873	+	0.0830649i
$329$	−12.2010	−	21.1328i	−0.672665	−	1.16509i
$330$	2.98942	−	4.33848i	0.164562	−	0.238825i
$331$	−22.3066	+	12.8787i	−1.22608	+	0.707878i	−0.966208	−	0.257765i	$-0.917014\pi$
$331$	−22.3066	+	12.8787i	−1.22608	+	0.707878i	−0.259873	+	0.965643i	$0.583681\pi$
$332$	5.17783	+	8.96827i	0.284170	+	0.492198i
$333$	−7.48330			−0.410082
$334$	0.339021	+	0.587202i	0.0185504	+	0.0321302i
$335$	5.59485	+	11.7662i	0.305680	+	0.642854i
$336$	−3.76344	−	2.17283i	−0.205313	−	0.118537i
$337$			0.772078i			0.0420578i	0.999779	+	0.0210289i	$0.00669420\pi$
$337$			0.772078i			0.0420578i	−0.999779	+	0.0210289i	$0.993306\pi$
$338$	12.9676	−	0.917149i	0.705345	−	0.0498863i
$339$	15.6600			0.850537
$340$	−6.07583	+	2.88908i	−0.329508	+	0.156682i
$341$	−8.38219	+	14.5184i	−0.453921	+	0.786215i
$342$	0.585872	−	0.338254i	0.0316804	−	0.0182907i
$343$	−21.2271			−1.14616
$344$	−5.91710	+	3.41624i	−0.319028	+	0.184191i
$345$	−14.3722	−	1.14846i	−0.773771	−	0.0618312i
$346$			0.721948i			0.0388122i
$347$	−21.7856	+	12.5779i	−1.16951	+	0.675218i	−0.953565	−	0.301188i	$-0.902617\pi$
$347$	−21.7856	+	12.5779i	−1.16951	+	0.675218i	−0.215946	+	0.976405i	$0.569284\pi$
$348$	−8.35922	−	4.82620i	−0.448101	−	0.258711i
$349$	−23.6602	−	13.6602i	−1.26650	−	0.731214i	−0.292176	−	0.956365i	$-0.594379\pi$
$349$	−23.6602	−	13.6602i	−1.26650	−	0.731214i	−0.974324	+	0.225151i	$0.927713\pi$
$350$	−7.73802	−	20.3037i	−0.413614	−	1.08528i
$351$	−1.69144	+	3.18419i	−0.0902823	+	0.169959i
$352$		−	2.35623i		−	0.125587i
$353$	−3.75948	+	6.51161i	−0.200097	+	0.346578i	−0.948559	−	0.316599i	$-0.897459\pi$
$353$	−3.75948	+	6.51161i	−0.200097	+	0.346578i	0.748462	+	0.663177i	$0.230792\pi$
$354$	−2.63482	+	4.56364i	−0.140039	+	0.242555i
$355$	−0.519354	+	6.49932i	−0.0275644	+	0.344948i
$356$		−	4.79440i		−	0.254103i
$357$	−6.53747	−	11.3232i	−0.345999	−	0.599288i
$358$	−3.18673	−	5.51958i	−0.168424	−	0.291719i
$359$		−	10.8402i		−	0.572124i	−0.958211	−	0.286062i	$-0.907654\pi$
$359$		−	10.8402i		−	0.572124i	0.958211	−	0.286062i	$-0.0923463\pi$
$360$	2.22896	+	0.178114i	0.117477	+	0.00938743i
$361$	−9.27117	+	16.0581i	−0.487956	+	0.845165i
$362$	11.0107	−	19.0711i	0.578708	−	1.00235i
$363$		−	5.44819i		−	0.285956i
$364$	13.2843	−	8.30831i	0.696287	−	0.435474i
$365$	−9.74138	+	14.1374i	−0.509887	+	0.739987i
$366$	3.73509	+	2.15646i	0.195237	+	0.112720i
$367$	−6.50838	−	3.75761i	−0.339735	−	0.196146i	0.320420	−	0.947276i	$-0.396176\pi$
$367$	−6.50838	−	3.75761i	−0.339735	−	0.196146i	−0.660155	+	0.751130i	$0.729509\pi$
$368$	−5.58405	+	3.22396i	−0.291089	+	0.168060i
$369$		−	3.00874i		−	0.156629i
$370$	−16.6800	−	1.33288i	−0.867151	−	0.0692931i
$371$	35.5043	−	20.4984i	1.84329	−	1.06423i
$372$	−7.11493			−0.368892
$373$	−19.8135	+	11.4393i	−1.02590	+	0.592305i	−0.915808	−	0.401616i	$-0.868449\pi$
$373$	−19.8135	+	11.4393i	−1.02590	+	0.592305i	−0.110095	+	0.993921i	$0.535115\pi$
$374$	3.54464	−	6.13949i	0.183289	−	0.317466i
$375$	8.08218	+	7.72518i	0.417362	+	0.398926i
$376$	5.61529			0.289586
$377$	29.5066	−	18.4541i	1.51967	−	0.950434i
$378$			4.34565i			0.223516i
$379$	−22.6152	−	13.0569i	−1.16166	−	0.670687i	−0.209962	−	0.977710i	$-0.567334\pi$
$379$	−22.6152	−	13.0569i	−1.16166	−	0.670687i	−0.951702	+	0.307022i	$0.900667\pi$
$380$	1.36614	−	0.649603i	0.0700813	−	0.0333239i
$381$	−6.80236	−	11.7820i	−0.348495	−	0.603611i
$382$	−0.586882			−0.0300275
$383$	−6.84652	−	11.8585i	−0.349841	−	0.605942i	0.636380	−	0.771376i	$-0.280431\pi$
$383$	−6.84652	−	11.8585i	−0.349841	−	0.605942i	−0.986221	+	0.165434i	$0.947098\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$	18.8535	+	12.9910i	0.960864	+	0.662082i
$386$	11.3135	+	19.5955i	0.575842	+	0.997387i
$387$	5.91710	+	3.41624i	0.300783	+	0.173657i
$388$	8.17066	−	14.1520i	0.414802	−	0.718459i
$389$	24.9403			1.26452			0.632261	−	0.774755i	$-0.282127\pi$
$389$	24.9403			1.26452			0.632261	+	0.774755i	$0.282127\pi$
$390$	−4.33730	+	6.79616i	−0.219628	+	0.344137i
$391$	−19.4001			−0.981104
$392$	5.94234	−	10.2924i	0.300134	−	0.519847i
$393$	8.84404	+	5.10611i	0.446123	+	0.257569i
$394$	−0.823770	−	1.42681i	−0.0415009	−	0.0718817i
$395$	4.75165	−	6.89595i	0.239081	−	0.346973i
$396$	−2.04055	+	1.17811i	−0.102542	+	0.0592025i
$397$	−14.5517	−	25.2043i	−0.730328	−	1.26497i	−0.956743	−	0.290934i	$-0.906034\pi$
$397$	−14.5517	−	25.2043i	−0.730328	−	1.26497i	0.226415	−	0.974031i	$-0.427300\pi$
$398$	−10.2733			−0.514954
$399$	1.46993	+	2.54600i	0.0735887	+	0.127459i
$400$	4.93655	+	0.794019i	0.246828	+	0.0397009i
$401$	−14.4596	−	8.34823i	−0.722076	−	0.416891i	0.0934404	−	0.995625i	$-0.470214\pi$
$401$	−14.4596	−	8.34823i	−0.722076	−	0.416891i	−0.815516	+	0.578734i	$0.803547\pi$
$402$		−	5.82658i		−	0.290603i
$403$	12.0345	−	22.6552i	0.599479	−	1.12854i
$404$	12.2382			0.608875
$405$	−0.960230	−	2.01940i	−0.0477142	−	0.100345i
$406$	20.9730	−	36.3262i	1.04087	−	1.80284i
$407$	15.2701	−	8.81618i	0.756909	−	0.437002i
$408$	3.00874			0.148955
$409$	21.3140	−	12.3056i	1.05391	−	0.608475i	0.130168	−	0.991492i	$-0.458448\pi$
$409$	21.3140	−	12.3056i	1.05391	−	0.608475i	0.923741	+	0.383017i	$0.125115\pi$
$410$	0.535898	−	6.70637i	0.0264661	−	0.331204i
$411$			12.4138i			0.612326i
$412$	−3.24884	+	1.87572i	−0.160059	+	0.0924100i
$413$	−19.8320	−	11.4500i	−0.975868	−	0.563418i
$414$	5.58405	+	3.22396i	0.274441	+	0.158449i
$415$	13.1386	−	19.0677i	0.644947	−	0.935996i
$416$	0.127265	+	3.60330i	0.00623968	+	0.176667i
$417$		−	15.6183i		−	0.764831i
$418$	−0.797003	+	1.38045i	−0.0389827	+	0.0675200i
$419$	−13.5527	+	23.4739i	−0.662091	+	1.14678i	0.317974	+	0.948099i	$0.396998\pi$
$419$	−13.5527	+	23.4739i	−0.662091	+	1.14678i	−0.980065	+	0.198676i	$0.936336\pi$
$420$	−0.774021	+	9.68629i	−0.0377684	+	0.472643i
$421$		−	32.9996i		−	1.60830i	−0.594425	−	0.804151i	$-0.702620\pi$
$421$		−	32.9996i		−	1.60830i	0.594425	−	0.804151i	$-0.297380\pi$
$422$	−12.1905	−	21.1145i	−0.593422	−	1.02784i
$423$	−2.80764	−	4.86298i	−0.136512	−	0.236446i
$424$			9.43400i			0.458156i
$425$	11.6684	+	9.49533i	0.566000	+	0.460591i
$426$	1.45793	−	2.52520i	0.0706367	−	0.122346i
$427$	−9.37121	+	16.2314i	−0.453505	+	0.785493i
$428$			16.6166i			0.803194i
$429$	−0.299865	−	8.49021i	−0.0144776	−	0.409911i
$430$	12.5805	+	8.66858i	0.606686	+	0.418036i
$431$	7.45678	+	4.30517i	0.359180	+	0.207373i	0.668721	−	0.743513i	$-0.266842\pi$
$431$	7.45678	+	4.30517i	0.359180	+	0.207373i	−0.309541	+	0.950886i	$0.600175\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	2.99201	−	1.72744i	0.143787	−	0.0830155i	−0.426381	−	0.904544i	$-0.640212\pi$
$433$	2.99201	−	1.72744i	0.143787	−	0.0830155i	0.570168	+	0.821528i	$0.306878\pi$
$434$		−	30.9190i		−	1.48416i
$435$	−1.71923	+	21.5148i	−0.0824305	+	1.03156i
$436$	−9.62290	+	5.55578i	−0.460853	+	0.266074i
$437$	4.36206			0.208666
$438$	6.64938	−	3.83902i	0.317720	−	0.183436i
$439$	−12.1229	+	20.9974i	−0.578593	+	1.00215i	0.417049	+	0.908884i	$0.363064\pi$
$439$	−12.1229	+	20.9974i	−0.578593	+	1.00215i	−0.995641	+	0.0932675i	$0.970269\pi$
$440$	−4.75816	+	2.26252i	−0.226836	+	0.107861i
$441$	−11.8847			−0.565937
$442$	−5.08909	+	9.58038i	−0.242064	+	0.455692i
$443$			13.1629i			0.625390i	0.949854	+	0.312695i	$0.101232\pi$
$443$			13.1629i			0.625390i	−0.949854	+	0.312695i	$0.898768\pi$
$444$	6.48073	+	3.74165i	0.307562	+	0.177571i
$445$	−9.68180	+	4.60373i	−0.458961	+	0.218238i
$446$	2.31792	+	4.01476i	0.109757	+	0.190104i
$447$	19.5265			0.923571
$448$	2.17283	+	3.76344i	0.102656	+	0.177806i
$449$	2.17774	−	1.25732i	0.102774	−	0.0593365i	−0.447732	−	0.894168i	$-0.647768\pi$
$449$	2.17774	−	1.25732i	0.102774	−	0.0593365i	0.550506	+	0.834831i	$0.314435\pi$
$450$	−1.78064	−	4.67219i	−0.0839399	−	0.220249i
$451$	3.54464	+	6.13949i	0.166910	+	0.289097i
$452$	−13.5620	−	7.83002i	−0.637903	−	0.368293i
$453$	−5.75137	+	9.96166i	−0.270223	+	0.468040i
$454$	17.7843			0.834657
$455$	−29.5338	−	18.8484i	−1.38456	−	0.883626i
$456$	−0.676507			−0.0316804
$457$	−5.38493	+	9.32698i	−0.251897	+	0.436298i	−0.964048	−	0.265728i	$-0.914388\pi$
$457$	−5.38493	+	9.32698i	−0.251897	+	0.436298i	0.712151	+	0.702026i	$0.247721\pi$
$458$	−13.2815	−	7.66806i	−0.620602	−	0.358305i
$459$	−1.50437	−	2.60564i	−0.0702180	−	0.121621i
$460$	11.8724	+	8.18068i	0.553554	+	0.381426i
$461$	10.2984	−	5.94576i	0.479642	−	0.276922i	−0.240625	−	0.970618i	$-0.577352\pi$
$461$	10.2984	−	5.94576i	0.479642	−	0.276922i	0.720267	+	0.693697i	$0.244019\pi$
$462$	−5.11967	−	8.86753i	−0.238189	−	0.412555i
$463$	−29.9462			−1.39172			−0.695860	−	0.718178i	$-0.744976\pi$
$463$	−29.9462			−1.39172			−0.695860	+	0.718178i	$0.744976\pi$
$464$	4.82620	+	8.35922i	0.224051	+	0.388067i
$465$	6.83197	+	14.3678i	0.316825	+	0.666293i
$466$	6.71645	+	3.87774i	0.311133	+	0.179633i
$467$			21.8940i			1.01313i	0.862201	+	0.506566i	$0.169085\pi$
$467$			21.8940i			1.01313i	−0.862201	+	0.506566i	$0.830915\pi$
$468$	3.05692	−	1.91187i	0.141306	−	0.0883761i
$469$	25.3203			1.16918
$470$	−5.39197	−	11.3395i	−0.248713	−	0.523051i
$471$	2.23798	−	3.87629i	0.103121	−	0.178610i
$472$	4.56364	−	2.63482i	0.210059	−	0.121277i
$473$	−16.0989			−0.740227
$474$	−3.24343	+	1.87260i	−0.148976	+	0.0860112i
$475$	−2.62361	−	2.13500i	−0.120379	−	0.0979605i
$476$			13.0749i			0.599288i
$477$	8.17008	−	4.71700i	0.374082	−	0.215977i
$478$	16.1435	+	9.32045i	0.738386	+	0.426307i
$479$	−7.90106	−	4.56168i	−0.361009	−	0.208429i	0.308514	−	0.951220i	$-0.400168\pi$
$479$	−7.90106	−	4.56168i	−0.361009	−	0.208429i	−0.669523	+	0.742791i	$0.733502\pi$
$480$	−1.84128	−	1.26873i	−0.0840426	−	0.0579095i
$481$	−22.8758	+	14.3071i	−1.04305	+	0.652346i
$482$			3.07016i			0.139842i
$483$	−14.0102	+	24.2664i	−0.637486	+	1.10416i
$484$	−2.72410	+	4.71827i	−0.123823	+	0.214467i
$485$	−36.4242	−	2.91062i	−1.65394	−	0.132164i
$486$			1.00000i			0.0453609i
$487$	10.8587	+	18.8079i	0.492056	+	0.852265i	0.999958	−	0.00914916i	$-0.00291231\pi$
$487$	10.8587	+	18.8079i	0.492056	+	0.852265i	−0.507902	+	0.861415i	$0.669579\pi$
$488$	−2.15646	−	3.73509i	−0.0976183	−	0.169080i
$489$		−	7.75548i		−	0.350715i
$490$	−26.4905	−	2.11683i	−1.19672	−	0.0956285i
$491$	16.5438	−	28.6548i	0.746613	−	1.29317i	−0.202824	−	0.979215i	$-0.565012\pi$
$491$	16.5438	−	28.6548i	0.746613	−	1.29317i	0.949437	−	0.313957i	$-0.101655\pi$
$492$	−1.50437	+	2.60564i	−0.0678222	+	0.117472i
$493$			29.0415i			1.30796i
$494$	1.14427	−	2.15412i	0.0514831	−	0.0969187i
$495$	4.33848	+	2.98942i	0.195000	+	0.134365i
$496$	6.16171	+	3.55746i	0.276669	+	0.159735i
$497$	10.9736	+	6.33564i	0.492235	+	0.284192i
$498$	−8.96827	+	5.17783i	−0.401878	+	0.232024i
$499$			10.4889i			0.469546i	0.972050	+	0.234773i	$0.0754347\pi$
$499$			10.4889i			0.469546i	−0.972050	+	0.234773i	$0.924565\pi$
$500$	−3.13679	−	10.7313i	−0.140281	−	0.479918i
$501$	−0.587202	+	0.339021i	−0.0262342	+	0.0151463i
$502$	−7.12807			−0.318142
$503$	−7.14818	+	4.12700i	−0.318722	+	0.184014i	−0.650823	−	0.759230i	$-0.725576\pi$
$503$	−7.14818	+	4.12700i	−0.318722	+	0.184014i	0.332101	+	0.943244i	$0.392243\pi$
$504$	2.17283	−	3.76344i	0.0967853	−	0.167637i
$505$	−11.7515	−	24.7138i	−0.522936	−	1.09975i
$506$	−15.1927			−0.675400
$507$	0.917149	+	12.9676i	0.0407320	+	0.575912i
$508$			13.6047i			0.603611i
$509$	5.84526	+	3.37476i	0.259087	+	0.149584i	0.623918	−	0.781490i	$-0.285540\pi$
$509$	5.84526	+	3.37476i	0.259087	+	0.149584i	−0.364831	+	0.931074i	$0.618873\pi$
$510$	−2.88908	−	6.07583i	−0.127931	−	0.269042i
$511$	16.6830	+	28.8959i	0.738014	+	1.27828i
$512$	−1.00000			−0.0441942
$513$	0.338254	+	0.585872i	0.0149343	+	0.0258669i
$514$	−12.3353	+	7.12178i	−0.544086	+	0.314128i
$515$	6.90745	+	4.75957i	0.304379	+	0.209732i
$516$	−3.41624	−	5.91710i	−0.150391	−	0.260486i
$517$	11.4583	+	6.61545i	0.503935	+	0.290947i
$518$	−16.2599	+	28.1630i	−0.714419	+	1.23741i
$519$	−0.721948			−0.0316900
$520$	7.15429	−	3.71700i	0.313737	−	0.163001i
$521$	−30.4048			−1.33206			−0.666029	−	0.745926i	$-0.732007\pi$
$521$	−30.4048			−1.33206			−0.666029	+	0.745926i	$0.732007\pi$
$522$	4.82620	−	8.35922i	0.211237	−	0.365873i
$523$	−2.72235	−	1.57175i	−0.119040	−	0.0687279i	0.439298	−	0.898342i	$-0.355227\pi$
$523$	−2.72235	−	1.57175i	−0.119040	−	0.0687279i	−0.558338	+	0.829614i	$0.688561\pi$
$524$	−5.10611	−	8.84404i	−0.223062	−	0.386354i
$525$	20.3037	−	7.73802i	0.886126	−	0.337715i
$526$	−13.3385	+	7.70101i	−0.581588	+	0.335780i
$527$	10.7035	+	18.5390i	0.466251	+	0.807570i
$528$	2.35623			0.102542
$529$	9.28778	+	16.0869i	0.403816	+	0.699431i
$530$	19.0510	−	9.05881i	0.827522	−	0.393490i
$531$	−4.56364	−	2.63482i	−0.198045	−	0.114341i
$532$		−	2.93986i		−	0.127459i
$533$	−5.75231	−	9.19748i	−0.249160	−	0.398387i
$534$	4.79440			0.207474
$535$	33.5555	−	15.9558i	1.45073	−	0.689828i
$536$	−2.91329	+	5.04596i	−0.125835	+	0.217952i
$537$	5.51958	−	3.18673i	0.238187	−	0.137518i
$538$	26.6268			1.14796
$539$	24.2513	−	14.0015i	1.04458	−	0.603088i
$540$	−0.178114	+	2.22896i	−0.00766480	+	0.0959193i
$541$		−	17.6144i		−	0.757301i	−0.925540	−	0.378650i	$-0.876388\pi$
$541$		−	17.6144i		−	0.757301i	0.925540	−	0.378650i	$-0.123612\pi$
$542$	−6.66899	+	3.85034i	−0.286458	+	0.165386i
$543$	19.0711	+	11.0107i	0.818417	+	0.472513i
$544$	−2.60564	−	1.50437i	−0.111716	−	0.0644993i
$545$	20.4595	+	14.0976i	0.876390	+	0.603875i
$546$	8.30831	+	13.2843i	0.355563	+	0.568516i
$547$		−	40.8067i		−	1.74477i	−0.488820	−	0.872385i	$-0.662572\pi$
$547$		−	40.8067i		−	1.74477i	0.488820	−	0.872385i	$-0.337428\pi$
$548$	6.20689	−	10.7506i	0.265145	−	0.459245i
$549$	−2.15646	+	3.73509i	−0.0920354	+	0.159410i
$550$	9.13785	+	7.43606i	0.389639	+	0.317075i
$551$		−	6.52991i		−	0.278184i
$552$	−3.22396	−	5.58405i	−0.137221	−	0.237673i
$553$	−8.13765	−	14.0948i	−0.346048	−	0.599373i
$554$			14.3023i			0.607646i
$555$	1.33288	−	16.6800i	0.0565776	−	0.708026i
$556$	−7.80915	+	13.5258i	−0.331182	+	0.573623i
$557$	−12.6109	+	21.8427i	−0.534340	+	0.925504i	0.464855	+	0.885387i	$0.346106\pi$
$557$	−12.6109	+	21.8427i	−0.534340	+	0.925504i	−0.999195	+	0.0401170i	$0.987227\pi$
$558$		−	7.11493i		−	0.301199i
$559$	24.6195	−	0.869535i	1.04129	−	0.0367774i
$560$	5.51347	−	8.00157i	0.232987	−	0.338128i
$561$	6.13949	+	3.54464i	0.259210	+	0.149655i
$562$	6.90002	+	3.98373i	0.291060	+	0.168043i
$563$	31.5356	−	18.2071i	1.32907	−	0.767337i	0.343912	−	0.939002i	$-0.388248\pi$
$563$	31.5356	−	18.2071i	1.32907	−	0.767337i	0.985155	+	0.171664i	$0.0549145\pi$
$564$			5.61529i			0.236446i
$565$	−2.78927	+	34.9057i	−0.117346	+	1.46849i
$566$	12.7095	−	7.33785i	0.534222	−	0.308433i
$567$	−4.34565			−0.182500
$568$	−2.52520	+	1.45793i	−0.105955	+	0.0611732i
$569$	−13.6768	+	23.6888i	−0.573360	+	0.993088i	0.422858	+	0.906196i	$0.361027\pi$
$569$	−13.6768	+	23.6888i	−0.573360	+	0.993088i	−0.996218	+	0.0868922i	$0.972306\pi$
$570$	0.649603	+	1.36614i	0.0272089	+	0.0572211i
$571$	45.7020			1.91257			0.956285	−	0.292438i	$-0.0944664\pi$
$571$	45.7020			1.91257			0.956285	+	0.292438i	$0.0944664\pi$
$572$	−3.98541	+	7.50267i	−0.166638	+	0.313702i
$573$		−	0.586882i		−	0.0245174i
$574$	−11.3232	−	6.53747i	−0.472622	−	0.272869i
$575$	5.11976	−	31.8304i	0.213509	−	1.32742i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−31.1697			−1.29761			−0.648806	−	0.760954i	$-0.724731\pi$
$577$	−31.1697			−1.29761			−0.648806	+	0.760954i	$0.724731\pi$
$578$	3.97374	+	6.88273i	0.165286	+	0.286284i
$579$	−19.5955	+	11.3135i	−0.814363	+	0.470173i
$580$	12.2463	−	17.7728i	0.508500	−	0.737974i
$581$	−22.5011	−	38.9730i	−0.933501	−	1.61687i
$582$	14.1520	+	8.17066i	0.586619	+	0.338685i
$583$	−11.1143	+	19.2506i	−0.460308	+	0.797278i
$584$	−7.67804			−0.317720
$585$	−6.79616	−	4.33730i	−0.280987	−	0.179325i
$586$	6.86396			0.283547
$587$	−7.61411	+	13.1880i	−0.314268	+	0.544328i	−0.979282	−	0.202503i	$-0.935092\pi$
$587$	−7.61411	+	13.1880i	−0.314268	+	0.544328i	0.665014	+	0.746831i	$0.268426\pi$
$588$	10.2924	+	5.94234i	0.424453	+	0.245058i
$589$	−2.40665	−	4.16844i	−0.0991643	−	0.171758i
$590$	−9.70288	−	6.68576i	−0.399461	−	0.275248i
$591$	1.42681	−	0.823770i	0.0586912	−	0.0338854i
$592$	−3.74165	−	6.48073i	−0.153781	−	0.266356i
$593$	15.1921			0.623865			0.311933	−	0.950104i	$-0.399024\pi$
$593$	15.1921			0.623865			0.311933	+	0.950104i	$0.399024\pi$
$594$	−1.17811	−	2.04055i	−0.0483386	−	0.0837249i
$595$	26.4035	−	12.5549i	1.08244	−	0.514703i
$596$	−16.9104	−	9.76324i	−0.692678	−	0.399918i
$597$		−	10.2733i		−	0.420458i
$598$	23.2338	−	0.820594i	0.950100	−	0.0335566i
$599$	4.34655			0.177595			0.0887975	−	0.996050i	$-0.471698\pi$
$599$	4.34655			0.177595			0.0887975	+	0.996050i	$0.471698\pi$
$600$	−0.794019	+	4.93655i	−0.0324157	+	0.201534i
$601$	−5.14622	+	8.91351i	−0.209918	+	0.363590i	−0.951689	−	0.307065i	$-0.900653\pi$
$601$	−5.14622	+	8.91351i	−0.209918	+	0.363590i	0.741770	+	0.670654i	$0.233987\pi$
$602$	25.7136	−	14.8458i	1.04801	−	0.605069i
$603$	5.82658			0.237277
$604$	9.96166	−	5.75137i	0.405334	−	0.234020i
$605$	12.1438	+	0.970399i	0.493716	+	0.0394523i
$606$			12.2382i			0.497144i
$607$	37.6094	−	21.7138i	1.52652	−	0.881335i	0.527012	−	0.849858i	$-0.323312\pi$
$607$	37.6094	−	21.7138i	1.52652	−	0.881335i	0.999504	−	0.0314772i	$-0.0100212\pi$
$608$	0.585872	+	0.338254i	0.0237603	+	0.0137180i
$609$	36.3262	+	20.9730i	1.47201	+	0.849867i
$610$	−5.47194	+	7.94129i	−0.221552	+	0.321534i
$611$	−17.8801	−	9.49791i	−0.723352	−	0.384244i
$612$			3.00874i			0.121621i
$613$	−16.3258	+	28.2771i	−0.659392	+	1.14210i	0.321382	+	0.946950i	$0.395853\pi$
$613$	−16.3258	+	28.2771i	−0.659392	+	1.14210i	−0.980773	+	0.195150i	$0.937481\pi$
$614$	−5.49584	+	9.51907i	−0.221794	+	0.384159i
$615$	6.70637	+	0.535898i	0.270427	+	0.0216095i
$616$			10.2393i			0.412555i
$617$	4.83488	+	8.37426i	0.194645	+	0.337135i	0.946784	−	0.321869i	$-0.104311\pi$
$617$	4.83488	+	8.37426i	0.194645	+	0.337135i	−0.752139	+	0.659004i	$0.770978\pi$
$618$	−1.87572	−	3.24884i	−0.0754525	−	0.130688i
$619$			5.20064i			0.209031i	0.994523	+	0.104516i	$0.0333292\pi$
$619$			5.20064i			0.209031i	−0.994523	+	0.104516i	$0.966671\pi$
$620$	1.26727	−	15.8589i	0.0508947	−	0.636909i
$621$	−3.22396	+	5.58405i	−0.129373	+	0.224080i
$622$	−6.95220	+	12.0416i	−0.278758	+	0.482823i
$623$			20.8348i			0.834729i
$624$	−3.60330	+	0.127265i	−0.144248	+	0.00509468i
$625$	−18.6587	+	16.6389i	−0.746347	+	0.665557i
$626$	12.2746	+	7.08672i	0.490590	+	0.283242i
$627$	−1.38045	−	0.797003i	−0.0551298	−	0.0318292i
$628$	−3.87629	+	2.23798i	−0.154681	+	0.0893050i
$629$		−	22.5153i		−	0.897743i
$630$	−9.68629	−	0.774021i	−0.385911	−	0.0308377i
$631$	−6.86811	+	3.96531i	−0.273415	+	0.157856i	−0.630439	−	0.776239i	$-0.717125\pi$
$631$	−6.86811	+	3.96531i	−0.273415	+	0.157856i	0.357023	+	0.934095i	$0.383792\pi$
$632$	3.74519			0.148976
$633$	21.1145	−	12.1905i	0.839226	−	0.484527i
$634$	1.60404	−	2.77828i	0.0637046	−	0.110340i
$635$	27.4733	−	13.0637i	1.09024	−	0.518415i
$636$	−9.43400			−0.374082
$637$	−36.3305	+	22.7219i	−1.43947	+	0.900276i
$638$			22.7432i			0.900413i
$639$	2.52520	+	1.45793i	0.0998954	+	0.0576746i
$640$	0.960230	+	2.01940i	0.0379564	+	0.0798236i
$641$	−1.69937	−	2.94340i	−0.0671212	−	0.116257i	0.830512	−	0.557001i	$-0.188048\pi$
$641$	−1.69937	−	2.94340i	−0.0671212	−	0.116257i	−0.897633	+	0.440744i	$0.854715\pi$
$642$	−16.6166			−0.655805
$643$	−4.69916	−	8.13918i	−0.185317	−	0.320978i	0.758367	−	0.651828i	$-0.225998\pi$
$643$	−4.69916	−	8.13918i	−0.185317	−	0.320978i	−0.943683	+	0.330851i	$0.892664\pi$
$644$	24.2664	−	14.0102i	0.956228	−	0.552079i
$645$	−8.66858	+	12.5805i	−0.341325	+	0.495357i
$646$	1.01772	+	1.76274i	0.0400415	+	0.0693540i
$647$	34.6972	+	20.0324i	1.36409	+	0.787555i	0.990165	−	0.139905i	$-0.0446798\pi$
$647$	34.6972	+	20.0324i	1.36409	+	0.787555i	0.373921	+	0.927461i	$0.378013\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	12.4165			0.487389
$650$	−14.3759	−	10.8782i	−0.563868	−	0.426677i
$651$	30.9190			1.21181
$652$	−3.87774	+	6.71645i	−0.151864	+	0.263036i
$653$	−27.1900	−	15.6981i	−1.06403	−	0.614316i	−0.137483	−	0.990504i	$-0.543901\pi$
$653$	−27.1900	−	15.6981i	−1.06403	−	0.614316i	−0.926543	+	0.376189i	$0.877234\pi$
$654$	−5.55578	−	9.62290i	−0.217248	−	0.376285i
$655$	−12.9566	+	18.8036i	−0.506255	+	0.734717i
$656$	2.60564	−	1.50437i	0.101733	−	0.0587358i
$657$	3.83902	+	6.64938i	0.149774	+	0.259417i
$658$	−24.4021			−0.951292
$659$	9.48950	+	16.4363i	0.369659	+	0.640268i	0.989512	−	0.144450i	$-0.0461413\pi$
$659$	9.48950	+	16.4363i	0.369659	+	0.640268i	−0.619853	+	0.784718i	$0.712808\pi$
$660$	−2.26252	−	4.75816i	−0.0880685	−	0.185211i
$661$	11.4484	+	6.60972i	0.445290	+	0.257088i	0.705839	−	0.708372i	$-0.250570\pi$
$661$	11.4484	+	6.60972i	0.445290	+	0.257088i	−0.260549	+	0.965461i	$0.583904\pi$
$662$			25.7574i			1.00109i
$663$	−9.58038	−	5.08909i	−0.372071	−	0.197644i
$664$	10.3557			0.401878
$665$	−5.93675	+	2.82295i	−0.230217	+	0.109469i
$666$	−3.74165	+	6.48073i	−0.144986	+	0.251123i
$667$	53.8995	−	31.1189i	2.08700	−	1.20493i
$668$	0.678042			0.0262342
$669$	−4.01476	+	2.31792i	−0.155220	+	0.0896161i
$670$	12.9872	+	1.03779i	0.501740	+	0.0400935i
$671$		−	10.1622i		−	0.392308i
$672$	−3.76344	+	2.17283i	−0.145178	+	0.0838186i
$673$	−7.44817	−	4.30020i	−0.287106	−	0.165761i	0.349530	−	0.936925i	$-0.386341\pi$
$673$	−7.44817	−	4.30020i	−0.287106	−	0.165761i	−0.636636	+	0.771164i	$0.719675\pi$
$674$	0.668639	+	0.386039i	0.0257550	+	0.0148697i
$675$	4.67219	−	1.78064i	0.179833	−	0.0685367i
$676$	5.68953	−	11.6889i	0.218828	−	0.449571i
$677$		−	25.8539i		−	0.993646i	−0.867852	−	0.496823i	$-0.834500\pi$
$677$		−	25.8539i		−	0.993646i	0.867852	−	0.496823i	$-0.165500\pi$
$678$	7.83002	−	13.5620i	0.300710	−	0.520845i
$679$	−35.5068	+	61.4997i	−1.36263	+	2.36014i
$680$	−0.535898	+	6.70637i	−0.0205508	+	0.257177i
$681$			17.7843i			0.681495i
$682$	8.38219	+	14.5184i	0.320971	+	0.555938i
$683$	−10.4524	−	18.1041i	−0.399950	−	0.692734i	0.593769	−	0.804636i	$-0.297639\pi$
$683$	−10.4524	−	18.1041i	−0.399950	−	0.692734i	−0.993719	+	0.111901i	$0.964306\pi$
$684$		−	0.676507i		−	0.0258669i
$685$	−27.6698	−	2.21107i	−1.05721	−	0.0844805i
$686$	−10.6136	+	18.3832i	−0.405228	+	0.701875i
$687$	7.66806	−	13.2815i	0.292555	−	0.506720i
$688$			6.83247i			0.260486i
$689$	15.9570	−	30.0396i	0.607914	−	1.14442i
$690$	−8.18068	+	11.8724i	−0.311433	+	0.451975i
$691$	−42.3440	−	24.4473i	−1.61084	−	0.930019i	−0.989176	−	0.146736i	$-0.953123\pi$
$691$	−42.3440	−	24.4473i	−1.61084	−	0.930019i	−0.621665	−	0.783283i	$-0.713543\pi$
$692$	0.625226	+	0.360974i	0.0237675	+	0.0137222i
$693$	8.86753	−	5.11967i	0.336850	−	0.194480i
$694$			25.1558i			0.954902i
$695$	34.8126	+	2.78184i	1.32052	+	0.105521i
$696$	−8.35922	+	4.82620i	−0.316855	+	0.182936i
$697$	9.05251			0.342888
$698$	−23.6602	+	13.6602i	−0.895551	+	0.517046i
$699$	−3.87774	+	6.71645i	−0.146670	+	0.254039i
$700$	−21.4525	−	3.45053i	−0.810829	−	0.130418i
$701$	31.9805			1.20789			0.603944	−	0.797027i	$-0.293595\pi$
$701$	31.9805			1.20789			0.603944	+	0.797027i	$0.293595\pi$
$702$	1.91187	+	3.05692i	0.0721588	+	0.115376i
$703$			5.06250i			0.190936i
$704$	−2.04055	−	1.17811i	−0.0769062	−	0.0444018i
$705$	11.3395	−	5.39197i	0.427070	−	0.203073i
$706$	3.75948	+	6.51161i	0.141490	+	0.245068i
$707$	−53.1831			−2.00016
$708$	2.63482	+	4.56364i	0.0990225	+	0.171512i
$709$	−5.42026	+	3.12939i	−0.203562	+	0.117527i	−0.598316	−	0.801260i	$-0.704163\pi$
$709$	−5.42026	+	3.12939i	−0.203562	+	0.117527i	0.394754	+	0.918787i	$0.370830\pi$
$710$	5.36890	+	3.69944i	0.201491	+	0.138837i
$711$	−1.87260	−	3.24343i	−0.0702278	−	0.121638i
$712$	−4.15208	−	2.39720i	−0.155606	−	0.0898389i
$713$	22.9382	−	39.7301i	0.859043	−	1.48791i
$714$	−13.0749			−0.489317
$715$	18.9778	+	0.843835i	0.709728	+	0.0315577i
$716$	−6.37346			−0.238187
$717$	−9.32045	+	16.1435i	−0.348079	+	0.602890i
$718$	−9.38789	−	5.42010i	−0.350353	−	0.202276i
$719$	−9.52308	−	16.4945i	−0.355151	−	0.615140i	0.631993	−	0.774974i	$-0.282237\pi$
$719$	−9.52308	−	16.4945i	−0.355151	−	0.615140i	−0.987144	+	0.159835i	$0.948904\pi$
$720$	1.26873	−	1.84128i	0.0472829	−	0.0686205i
$721$	14.1183	−	8.15122i	0.525794	−	0.303567i
$722$	9.27117	+	16.0581i	0.345037	+	0.597622i
$723$	−3.07016			−0.114181
$724$	−11.0107	−	19.0711i	−0.409209	−	0.708770i
$725$	−47.6495	−	7.66418i	−1.76966	−	0.284640i
$726$	−4.71827	−	2.72410i	−0.175111	−	0.101101i
$727$			28.2602i			1.04811i	0.851684	+	0.524056i	$0.175582\pi$
$727$			28.2602i			1.04811i	−0.851684	+	0.524056i	$0.824418\pi$
$728$	−0.553049	−	15.6587i	−0.0204974	−	0.580350i
$729$	−1.00000			−0.0370370
$730$	7.37269	+	15.5050i	0.272875	+	0.573866i
$731$	−10.2786	+	17.8030i	−0.380166	+	0.658468i
$732$	3.73509	−	2.15646i	0.138053	−	0.0797050i
$733$	5.28165			0.195082			0.0975410	−	0.995232i	$-0.468902\pi$
$733$	5.28165			0.195082			0.0975410	+	0.995232i	$0.468902\pi$
$734$	−6.50838	+	3.75761i	−0.240229	+	0.138696i
$735$	2.11683	−	26.4905i	0.0780804	−	0.977117i
$736$			6.44791i			0.237673i
$737$	−11.8894	+	6.86437i	−0.437953	+	0.252852i
$738$	−2.60564	−	1.50437i	−0.0959151	−	0.0553766i
$739$	34.5736	+	19.9611i	1.27181	+	0.734280i	0.975329	−	0.220758i	$-0.0708533\pi$
$739$	34.5736	+	19.9611i	1.27181	+	0.734280i	0.296482	+	0.955038i	$0.404187\pi$
$740$	−9.49430	+	13.7789i	−0.349018	+	0.506521i
$741$	2.15412	+	1.14427i	0.0791337	+	0.0420358i
$742$		−	40.9969i		−	1.50504i
$743$	9.28543	−	16.0828i	0.340650	−	0.590022i	−0.643904	−	0.765106i	$-0.722686\pi$
$743$	9.28543	−	16.0828i	0.340650	−	0.590022i	0.984553	+	0.175084i	$0.0560197\pi$
$744$	−3.55746	+	6.16171i	−0.130423	+	0.225899i
$745$	−3.47794	+	43.5238i	−0.127422	+	1.59459i
$746$			22.8786i			0.837646i
$747$	−5.17783	−	8.96827i	−0.189447	−	0.328132i
$748$	−3.54464	−	6.13949i	−0.129605	−	0.224482i
$749$		−	72.2100i		−	2.63850i
$750$	10.7313	−	3.13679i	0.391851	−	0.114539i
$751$	15.1001	−	26.1541i	0.551010	−	0.954377i	−0.447192	−	0.894438i	$-0.647576\pi$
$751$	15.1001	−	26.1541i	0.551010	−	0.954377i	0.998202	−	0.0599394i	$-0.0190907\pi$
$752$	2.80764	−	4.86298i	0.102384	−	0.177335i
$753$		−	7.12807i		−	0.259761i
$754$	−1.22841	−	34.7805i	−0.0447361	−	1.26663i
$755$	−21.1798	−	14.5939i	−0.770811	−	0.531126i
$756$	3.76344	+	2.17283i	0.136875	+	0.0790249i
$757$	4.85341	+	2.80211i	0.176400	+	0.101845i	0.585600	−	0.810600i	$-0.300859\pi$
$757$	4.85341	+	2.80211i	0.176400	+	0.101845i	−0.409200	+	0.912445i	$0.634192\pi$
$758$	−22.6152	+	13.0569i	−0.821421	+	0.474247i
$759$		−	15.1927i		−	0.551462i
$760$	0.120495	−	1.50791i	0.00437083	−	0.0546976i
$761$	−5.77640	+	3.33501i	−0.209394	+	0.120894i	−0.601030	−	0.799227i	$-0.705243\pi$
$761$	−5.77640	+	3.33501i	−0.209394	+	0.120894i	0.391635	+	0.920120i	$0.371909\pi$
$762$	−13.6047			−0.492847
$763$	41.8178	−	24.1435i	1.51391	−	0.874053i
$764$	−0.293441	+	0.508255i	−0.0106163	+	0.0183880i
$765$	6.07583	−	2.88908i	0.219672	−	0.104455i
$766$	−13.6930			−0.494750
$767$	−18.9881	+	0.670640i	−0.685621	+	0.0242154i
$768$		−	1.00000i		−	0.0360844i
$769$	6.03234	+	3.48277i	0.217532	+	0.125592i	0.604807	−	0.796372i	$-0.293250\pi$
$769$	6.03234	+	3.48277i	0.217532	+	0.125592i	−0.387275	+	0.921964i	$0.626584\pi$
$770$	20.6773	−	9.83213i	0.745158	−	0.354325i
$771$	−7.12178	−	12.3353i	−0.256485	−	0.444244i
$772$	22.6270			0.814363
$773$	10.6748	+	18.4893i	0.383945	+	0.665013i	0.991622	−	0.129172i	$-0.0412318\pi$
$773$	10.6748	+	18.4893i	0.383945	+	0.665013i	−0.607677	+	0.794184i	$0.707898\pi$
$774$	5.91710	−	3.41624i	0.212686	−	0.122794i
$775$	−33.2423	+	12.6691i	−1.19410	+	0.455087i
$776$	−8.17066	−	14.1520i	−0.293310	−	0.508027i
$777$	−28.1630	−	16.2599i	−1.01034	−	0.583321i
$778$	12.4701	−	21.5989i	0.447076	−	0.774359i
$779$	−2.03543			−0.0729270
$780$	3.71700	+	7.15429i	0.133090	+	0.256165i
$781$	−6.87041			−0.245843
$782$	−9.70004	+	16.8010i	−0.346873	+	0.600801i
$783$	8.35922	+	4.82620i	0.298734	+	0.172474i
$784$	−5.94234	−	10.2924i	−0.212226	−	0.367587i
$785$	8.24149	+	5.67879i	0.294151	+	0.202685i
$786$	8.84404	−	5.10611i	0.315457	−	0.182129i
$787$	−9.61648	−	16.6562i	−0.342791	−	0.593731i	0.642159	−	0.766571i	$-0.278039\pi$
$787$	−9.61648	−	16.6562i	−0.342791	−	0.593731i	−0.984950	+	0.172841i	$0.944705\pi$
$788$	−1.64754			−0.0586912
$789$	−7.70101	−	13.3385i	−0.274163	−	0.474865i
$790$	−3.59625	−	7.56302i	−0.127949	−	0.269080i
$791$	58.9357	+	34.0265i	2.09551	+	1.20984i
$792$			2.35623i			0.0837249i
$793$	0.548883	+	15.5407i	0.0194914	+	0.551868i
$794$	−29.1034			−1.03284
$795$	9.05881	+	19.0510i	0.321283	+	0.675669i
$796$	−5.13665	+	8.89694i	−0.182064	+	0.315344i
$797$	19.7080	−	11.3784i	0.698094	−	0.403044i	−0.108543	−	0.994092i	$-0.534619\pi$
$797$	19.7080	−	11.3784i	0.698094	−	0.403044i	0.806637	+	0.591047i	$0.201285\pi$
$798$	2.93986			0.104070
$799$	14.6314	−	8.44747i	0.517623	−	0.298850i
$800$	3.15592	−	3.87817i	0.111578	−	0.137114i
$801$			4.79440i			0.169402i
$802$	−14.4596	+	8.34823i	−0.510585	+	0.294786i
$803$	−15.6675	−	9.04561i	−0.552892	−	0.319213i
$804$	−5.04596	−	2.91329i	−0.177957	−	0.102744i
$805$	−51.5934	−	35.5504i	−1.81843	−	1.25299i
$806$	−13.6028	−	21.7498i	−0.479138	−	0.766103i
$807$			26.6268i			0.937308i
$808$	6.11911	−	10.5986i	0.215270	−	0.372858i
$809$	−17.7054	+	30.6667i	−0.622490	+	1.07818i	0.366530	+	0.930406i	$0.380546\pi$
$809$	−17.7054	+	30.6667i	−0.622490	+	1.07818i	−0.989020	+	0.147779i	$0.952788\pi$
$810$	−2.22896	−	0.178114i	−0.0783178	−	0.00625829i
$811$		−	1.41268i		−	0.0496060i	−0.999692	−	0.0248030i	$-0.992104\pi$
$811$		−	1.41268i		−	0.0496060i	0.999692	−	0.0248030i	$-0.00789586\pi$
$812$	−20.9730	−	36.3262i	−0.736007	−	1.27480i
$813$	−3.85034	−	6.66899i	−0.135037	−	0.233892i
$814$		−	17.6324i		−	0.618014i
$815$	17.2867	+	1.38136i	0.605526	+	0.0483869i
$816$	1.50437	−	2.60564i	0.0526635	−	0.0912158i
$817$	2.31111	−	4.00296i	0.0808555	−	0.140046i
$818$		−	24.6113i		−	0.860513i
$819$	−13.2843	+	8.30831i	−0.464191	+	0.290316i
$820$	−5.53994	−	3.81729i	−0.193463	−	0.133305i
$821$	14.7591	+	8.52118i	0.515097	+	0.297391i	0.734926	−	0.678147i	$-0.237217\pi$
$821$	14.7591	+	8.52118i	0.515097	+	0.297391i	−0.219829	+	0.975538i	$0.570550\pi$
$822$	10.7506	+	6.20689i	0.374972	+	0.216490i
$823$	−3.83623	+	2.21485i	−0.133723	+	0.0772047i	−0.565369	−	0.824838i	$-0.691266\pi$
$823$	−3.83623	+	2.21485i	−0.133723	+	0.0772047i	0.431646	+	0.902043i	$0.357933\pi$
$824$			3.75144i			0.130688i
$825$	−7.43606	+	9.13785i	−0.258890	+	0.318139i
$826$	−19.8320	+	11.4500i	−0.690043	+	0.398396i
$827$	−41.2574			−1.43466			−0.717330	−	0.696734i	$-0.754636\pi$
$827$	−41.2574			−1.43466			−0.717330	+	0.696734i	$0.754636\pi$
$828$	5.58405	−	3.22396i	0.194059	−	0.112040i
$829$	21.3857	−	37.0411i	0.742756	−	1.28649i	−0.208479	−	0.978027i	$-0.566851\pi$
$829$	21.3857	−	37.0411i	0.742756	−	1.28649i	0.951236	−	0.308465i	$-0.0998153\pi$
$830$	−9.94382	−	20.9122i	−0.345155	−	0.725873i
$831$	−14.3023			−0.496141
$832$	3.18419	+	1.69144i	0.110392	+	0.0586400i
$833$		−	35.7579i		−	1.23894i
$834$	−13.5258	−	7.80915i	−0.468361	−	0.270409i
$835$	−0.651076	−	1.36923i	−0.0225314	−	0.0473843i
$836$	0.797003	+	1.38045i	0.0275649	+	0.0477438i
$837$	7.11493			0.245928
$838$	13.5527	+	23.4739i	0.468169	+	0.810893i
$839$	−0.249908	+	0.144284i	−0.00862777	+	0.00498124i	−0.504308	−	0.863524i	$-0.668252\pi$
$839$	−0.249908	+	0.144284i	−0.00862777	+	0.00498124i	0.495680	+	0.868505i	$0.334919\pi$
$840$	8.00157	+	5.51347i	0.276080	+	0.190233i
$841$	−32.0843	−	55.5717i	−1.10636	−	1.91626i
$842$	−28.5785	−	16.4998i	−0.984880	−	0.568621i
$843$	−3.98373	+	6.90002i	−0.137207	+	0.237649i
$844$	−24.3809			−0.839226
$845$	−29.0677	−	0.265420i	−0.999958	−	0.00913072i
$846$	−5.61529			−0.193058
$847$	11.8380	−	20.5040i	0.406757	−	0.704524i
$848$	8.17008	+	4.71700i	0.280562	+	0.161982i
$849$	7.33785	+	12.7095i	0.251834	+	0.436190i
$850$	14.0574	−	5.35747i	0.482165	−	0.183760i
$851$	−41.7871	+	24.1258i	−1.43244	+	0.827022i
$852$	−1.45793	−	2.52520i	−0.0499477	−	0.0865120i
$853$	42.9336			1.47002			0.735009	−	0.678058i	$-0.237178\pi$
$853$	42.9336			1.47002			0.735009	+	0.678058i	$0.237178\pi$
$854$	9.37121	+	16.2314i	0.320676	+	0.555428i
$855$	−1.36614	+	0.649603i	−0.0467209	+	0.0222159i
$856$	14.3904	+	8.30831i	0.491854	+	0.283972i
$857$			43.6929i			1.49252i	0.665654	+	0.746261i	$0.268153\pi$
$857$			43.6929i			1.49252i	−0.665654	+	0.746261i	$0.731847\pi$
$858$	−7.50267	−	3.98541i	−0.256137	−	0.136060i
$859$	−50.5362			−1.72427			−0.862137	−	0.506676i	$-0.830874\pi$
$859$	−50.5362			−1.72427			−0.862137	+	0.506676i	$0.830874\pi$
$860$	13.7975	−	6.56075i	0.470490	−	0.223720i
$861$	6.53747	−	11.3232i	0.222796	−	0.385894i
$862$	7.45678	−	4.30517i	0.253979	−	0.146635i
$863$	9.24937			0.314852			0.157426	−	0.987531i	$-0.449680\pi$
$863$	9.24937			0.314852			0.157426	+	0.987531i	$0.449680\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	0.128589	−	1.60920i	0.00437216	−	0.0547143i
$866$		−	3.45488i		−	0.117402i
$867$	−6.88273	+	3.97374i	−0.233750	+	0.134955i
$868$	−26.7766	−	15.4595i	−0.908858	−	0.524729i
$869$	7.64226	+	4.41226i	0.259246	+	0.149676i
$870$	17.7728	+	12.2463i	0.602553	+	0.415189i
$871$	17.8114	−	11.1396i	0.603516	−	0.377452i
$872$			11.1116i			0.376285i
$873$	−8.17066	+	14.1520i	−0.276535	+	0.478973i
$874$	2.18103	−	3.77765i	0.0737744	−	0.127781i
$875$	13.6314	+	46.6344i	0.460825	+	1.57653i
$876$		−	7.67804i		−	0.259417i
$877$	−28.4654	−	49.3035i	−0.961208	−	1.66486i	−0.719476	−	0.694517i	$-0.755618\pi$
$877$	−28.4654	−	49.3035i	−0.961208	−	1.66486i	−0.241731	−	0.970343i	$-0.577715\pi$
$878$	12.1229	+	20.9974i	0.409127	+	0.708628i
$879$			6.86396i			0.231515i
$880$	−0.419677	+	5.25194i	−0.0141473	+	0.177043i
$881$	7.98900	−	13.8374i	0.269156	−	0.466192i	−0.699488	−	0.714644i	$-0.746588\pi$
$881$	7.98900	−	13.8374i	0.269156	−	0.466192i	0.968644	+	0.248452i	$0.0799218\pi$
$882$	−5.94234	+	10.2924i	−0.200089	+	0.346564i
$883$			0.189481i			0.00637654i	0.999995	+	0.00318827i	$0.00101486\pi$
$883$			0.189481i			0.00637654i	−0.999995	+	0.00318827i	$0.998985\pi$
$884$	5.75231	+	9.19748i	0.193471	+	0.309345i
$885$	6.68576	−	9.70288i	0.224739	−	0.326159i
$886$	11.3994	+	6.58147i	0.382972	+	0.221109i
$887$	15.5339	+	8.96852i	0.521578	+	0.301133i	0.737580	−	0.675260i	$-0.235968\pi$
$887$	15.5339	+	8.96852i	0.521578	+	0.301133i	−0.216002	+	0.976393i	$0.569302\pi$
$888$	6.48073	−	3.74165i	0.217479	−	0.125562i
$889$		−	59.1213i		−	1.98287i
$890$	−0.853950	+	10.6865i	−0.0286245	+	0.358214i
$891$	2.04055	−	1.17811i	0.0683611	−	0.0394683i
$892$	4.63585			0.155220
$893$	−3.28984	+	1.89939i	−0.110090	+	0.0635607i
$894$	9.76324	−	16.9104i	0.326532	−	0.565570i
$895$	6.11999	+	12.8705i	0.204569	+	0.430215i
$896$	4.34565			0.145178
$897$	0.820594	+	23.2338i	0.0273988	+	0.775754i
$898$		−	2.51464i		−	0.0839145i
$899$	−59.4752	−	34.3380i	−1.98361	−	1.14524i
$900$	−4.93655	−	0.794019i	−0.164552	−	0.0264673i
$901$	14.1922	+	24.5817i	0.472812	+	0.818934i
$902$	7.08928			0.236047
$903$	14.8458	+	25.7136i	0.494036	+	0.855696i
$904$	−13.5620	+	7.83002i	−0.451065	+	0.260423i
$905$	−27.9392	+	40.5475i	−0.928731	+	1.34784i
$906$	5.75137	+	9.96166i	0.191076	+	0.330954i
$907$	−28.5874	−	16.5050i	−0.949230	−	0.548038i	−0.0563882	−	0.998409i	$-0.517958\pi$
$907$	−28.5874	−	16.5050i	−0.949230	−	0.548038i	−0.892842	+	0.450371i	$0.851292\pi$
$908$	8.89213	−	15.4016i	0.295096	−	0.511121i
$909$	−12.2382			−0.405916
$910$	−31.0901	+	16.1528i	−1.03063	+	0.535460i
$911$	13.9676			0.462768			0.231384	−	0.972863i	$-0.425675\pi$
$911$	13.9676			0.462768			0.231384	+	0.972863i	$0.425675\pi$
$912$	−0.338254	+	0.585872i	−0.0112007	+	0.0194002i
$913$	21.1313	+	12.2002i	0.699344	+	0.403766i
$914$	5.38493	+	9.32698i	0.178118	+	0.308509i
$915$	−7.94129	−	5.47194i	−0.262531	−	0.180897i
$916$	−13.2815	+	7.66806i	−0.438832	+	0.253360i
$917$	22.1894	+	38.4331i	0.732758	+	1.26917i
$918$	−3.00874			−0.0993032
$919$	9.50273	+	16.4592i	0.313466	+	0.542939i	0.979110	−	0.203330i	$-0.0651764\pi$
$919$	9.50273	+	16.4592i	0.313466	+	0.542939i	−0.665644	+	0.746269i	$0.731843\pi$
$920$	13.0209	−	6.19148i	0.429286	−	0.204127i
$921$	−9.51907	−	5.49584i	−0.313664	−	0.181094i
$922$		−	11.8915i		−	0.391626i
$923$	10.5067	−	0.371086i	0.345832	−	0.0122144i
$924$	−10.2393			−0.336850
$925$	36.9417	+	5.94188i	1.21463	+	0.195368i
$926$	−14.9731	+	25.9342i	−0.492047	+	0.852250i
$927$	3.24884	−	1.87572i	0.106706	−	0.0616067i
$928$	9.65239			0.316855
$929$	−50.0606	+	28.9025i	−1.64243	+	0.948259i	−0.662468	+	0.749090i	$0.730491\pi$
$929$	−50.0606	+	28.9025i	−1.64243	+	0.948259i	−0.979965	+	0.199169i	$0.936176\pi$
$930$	15.8589	+	1.26727i	0.520034	+	0.0415553i
$931$			8.04007i			0.263503i
$932$	6.71645	−	3.87774i	0.220005	−	0.127020i
$933$	−12.0416	−	6.95220i	−0.394223	−	0.227605i
$934$	18.9607	+	10.9470i	0.620414	+	0.358196i
$935$	−8.99439	+	13.0534i	−0.294148	+	0.426890i
$936$	−0.127265	−	3.60330i	−0.00415979	−	0.117778i
$937$			39.7996i			1.30020i	0.759850	+	0.650099i	$0.225273\pi$
$937$			39.7996i			1.30020i	−0.759850	+	0.650099i	$0.774727\pi$
$938$	12.6601	−	21.9280i	0.413368	−	0.715974i
$939$	−7.08672	+	12.2746i	−0.231266	+	0.400565i
$940$	−12.5163	−	1.00016i	−0.408236	−	0.0326217i
$941$			1.26326i			0.0411810i	0.999788	+	0.0205905i	$0.00655462\pi$
$941$			1.26326i			0.0411810i	−0.999788	+	0.0205905i	$0.993445\pi$
$942$	−2.23798	−	3.87629i	−0.0729172	−	0.126296i
$943$	−9.70004	−	16.8010i	−0.315877	−	0.547115i
$944$		−	5.26964i		−	0.171512i
$945$	0.774021	−	9.68629i	0.0251789	−	0.315095i
$946$	−8.04943	+	13.9420i	−0.261710	+	0.453294i
$947$	4.47761	−	7.75545i	0.145503	−	0.252018i	−0.784058	−	0.620688i	$-0.786853\pi$
$947$	4.47761	−	7.75545i	0.145503	−	0.252018i	0.929560	+	0.368670i	$0.120187\pi$
$948$			3.74519i			0.121638i
$949$	24.4483	+	12.9869i	0.793626	+	0.421574i
$950$	−3.16077	+	1.20461i	−0.102549	+	0.0390828i
$951$	2.77828	+	1.60404i	0.0900920	+	0.0520146i
$952$	11.3232	+	6.53747i	0.366988	+	0.211880i
$953$	10.7128	−	6.18504i	0.347022	−	0.200353i	−0.316351	−	0.948642i	$-0.602458\pi$
$953$	10.7128	−	6.18504i	0.347022	−	0.200353i	0.663373	+	0.748289i	$0.269124\pi$
$954$		−	9.43400i		−	0.305437i
$955$	1.30814	+	0.104532i	0.0423304	+	0.00338257i
$956$	16.1435	−	9.32045i	0.522118	−	0.301445i
$957$	−22.7432			−0.735184
$958$	−7.90106	+	4.56168i	−0.255272	+	0.147381i
$959$	−26.9730	+	46.7185i	−0.871002	+	1.50862i
$960$	−2.01940	+	0.960230i	−0.0651757	+	0.0309913i
$961$	−19.6222			−0.632973
$962$	0.952362	+	26.9646i	0.0307054	+	0.869374i
$963$		−	16.6166i		−	0.535463i
$964$	2.65884	+	1.53508i	0.0856354	+	0.0494416i
$965$	−21.7271	−	45.6928i	−0.699421	−	1.47090i
$966$	14.0102	+	24.2664i	0.450770	+	0.780757i
$967$	−6.35606			−0.204397			−0.102198	−	0.994764i	$-0.532588\pi$
$967$	−6.35606			−0.204397			−0.102198	+	0.994764i	$0.532588\pi$
$968$	2.72410	+	4.71827i	0.0875557	+	0.151651i
$969$	−1.76274	+	1.01772i	−0.0566273	+	0.0326938i
$970$	−20.7328	+	30.0890i	−0.665689	+	0.966099i
$971$	23.6660	+	40.9907i	0.759477	+	1.31545i	0.943117	+	0.332460i	$0.107879\pi$
$971$	23.6660	+	40.9907i	0.759477	+	1.31545i	−0.183640	+	0.982994i	$0.558788\pi$
$972$	0.866025	+	0.500000i	0.0277778	+	0.0160375i
$973$	33.9358	−	58.7786i	1.08793	−	1.88435i
$974$	21.7174			0.695872
$975$	10.8782	−	14.3759i	0.348380	−	0.460396i
$976$	−4.31292			−0.138053
$977$	24.5952	−	42.6002i	0.786871	−	1.36290i	−0.141005	−	0.990009i	$-0.545033\pi$
$977$	24.5952	−	42.6002i	0.786871	−	1.36290i	0.927875	−	0.372891i	$-0.121633\pi$
$978$	−6.71645	−	3.87774i	−0.214768	−	0.123997i
$979$	−5.64835	−	9.78324i	−0.180522	−	0.312674i
$980$	−15.0785	+	21.8830i	−0.481665	+	0.699028i
$981$	9.62290	−	5.55578i	0.307236	−	0.177383i
$982$	−16.5438	−	28.6548i	−0.527935	−	0.914411i
$983$	22.1542			0.706609			0.353304	−	0.935508i	$-0.385058\pi$
$983$	22.1542			0.706609			0.353304	+	0.935508i	$0.385058\pi$
$984$	1.50437	+	2.60564i	0.0479576	+	0.0830649i
$985$	1.58202	+	3.32703i	0.0504073	+	0.106008i
$986$	25.1507	+	14.5208i	0.800961	+	0.462435i
$987$		−	24.4021i		−	0.776727i
$988$	−1.29339	−	2.06803i	−0.0411483	−	0.0657928i
$989$	44.0552			1.40087
$990$	4.75816	−	2.26252i	0.151224	−	0.0719076i
$991$	24.0251	−	41.6127i	0.763182	−	1.32187i	−0.178020	−	0.984027i	$-0.556969\pi$
$991$	24.0251	−	41.6127i	0.763182	−	1.32187i	0.941202	−	0.337843i	$-0.109697\pi$
$992$	6.16171	−	3.55746i	0.195634	−	0.112950i
$993$	−25.7574			−0.817387
$994$	10.9736	−	6.33564i	0.348063	−	0.200954i
$995$	22.8988	+	1.82982i	0.725941	+	0.0580091i
$996$			10.3557i			0.328132i
$997$	41.0355	−	23.6919i	1.29961	−	0.750329i	0.319271	−	0.947663i	$-0.396562\pi$
$997$	41.0355	−	23.6919i	1.29961	−	0.750329i	0.980336	+	0.197335i	$0.0632286\pi$
$998$	9.08363	+	5.24444i	0.287537	+	0.166010i
$999$	−6.48073	−	3.74165i	−0.205041	−	0.118381i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.x.b.199.4	yes	12
3.2	odd	2		1170.2.bj.c.199.5		12
5.2	odd	4		1950.2.bc.j.901.4		12
5.3	odd	4		1950.2.bc.i.901.3		12
5.4	even	2		390.2.x.a.199.3	yes	12
13.10	even	6		390.2.x.a.49.3	✓	12
15.14	odd	2		1170.2.bj.d.199.2		12
39.23	odd	6		1170.2.bj.d.829.2		12
65.23	odd	12		1950.2.bc.i.751.3		12
65.49	even	6	inner	390.2.x.b.49.4	yes	12
65.62	odd	12		1950.2.bc.j.751.4		12
195.179	odd	6		1170.2.bj.c.829.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.3	✓	12	13.10	even	6
390.2.x.a.199.3	yes	12	5.4	even	2
390.2.x.b.49.4	yes	12	65.49	even	6	inner
390.2.x.b.199.4	yes	12	1.1	even	1	trivial
1170.2.bj.c.199.5		12	3.2	odd	2
1170.2.bj.c.829.5		12	195.179	odd	6
1170.2.bj.d.199.2		12	15.14	odd	2
1170.2.bj.d.829.2		12	39.23	odd	6
1950.2.bc.i.751.3		12	65.23	odd	12
1950.2.bc.i.901.3		12	5.3	odd	4
1950.2.bc.j.751.4		12	65.62	odd	12
1950.2.bc.j.901.4		12	5.2	odd	4

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.26873 + 1.84128i) q^{5} +(0.866025 - 0.500000i) q^{6} +(2.17283 + 3.76344i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.26873 + 1.84128i) q^{5} +(0.866025 - 0.500000i) q^{6} +(2.17283 + 3.76344i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(0.960230 + 2.01940i) q^{10} +(-2.04055 - 1.17811i) q^{11} -1.00000i q^{12} +(3.18419 + 1.69144i) q^{13} +4.34565 q^{14} +(-2.01940 + 0.960230i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.60564 + 1.50437i) q^{17} +1.00000 q^{18} +(0.585872 - 0.338254i) q^{19} +(2.22896 + 0.178114i) q^{20} +4.34565i q^{21} +(-2.04055 + 1.17811i) q^{22} +(5.58405 + 3.22396i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-1.78064 - 4.67219i) q^{25} +(3.05692 - 1.91187i) q^{26} +1.00000i q^{27} +(2.17283 - 3.76344i) q^{28} +(4.82620 - 8.35922i) q^{29} +(-0.178114 + 2.22896i) q^{30} -7.11493i q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.17811 - 2.04055i) q^{33} +3.00874i q^{34} +(-9.68629 - 0.774021i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-3.74165 + 6.48073i) q^{37} -0.676507i q^{38} +(1.91187 + 3.05692i) q^{39} +(1.26873 - 1.84128i) q^{40} +(-2.60564 - 1.50437i) q^{41} +(3.76344 + 2.17283i) q^{42} +(5.91710 - 3.41624i) q^{43} +2.35623i q^{44} +(-2.22896 - 0.178114i) q^{45} +(5.58405 - 3.22396i) q^{46} -5.61529 q^{47} +(-0.866025 + 0.500000i) q^{48} +(-5.94234 + 10.2924i) q^{49} +(-4.93655 - 0.794019i) q^{50} -3.00874 q^{51} +(-0.127265 - 3.60330i) q^{52} -9.43400i q^{53} +(0.866025 + 0.500000i) q^{54} +(4.75816 - 2.26252i) q^{55} +(-2.17283 - 3.76344i) q^{56} +0.676507 q^{57} +(-4.82620 - 8.35922i) q^{58} +(-4.56364 + 2.63482i) q^{59} +(1.84128 + 1.26873i) q^{60} +(2.15646 + 3.73509i) q^{61} +(-6.16171 - 3.55746i) q^{62} +(-2.17283 + 3.76344i) q^{63} +1.00000 q^{64} +(-7.15429 + 3.71700i) q^{65} -2.35623 q^{66} +(2.91329 - 5.04596i) q^{67} +(2.60564 + 1.50437i) q^{68} +(3.22396 + 5.58405i) q^{69} +(-5.51347 + 8.00157i) q^{70} +(2.52520 - 1.45793i) q^{71} +(-0.500000 - 0.866025i) q^{72} +7.67804 q^{73} +(3.74165 + 6.48073i) q^{74} +(0.794019 - 4.93655i) q^{75} +(-0.585872 - 0.338254i) q^{76} -10.2393i q^{77} +(3.60330 - 0.127265i) q^{78} -3.74519 q^{79} +(-0.960230 - 2.01940i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.60564 + 1.50437i) q^{82} -10.3557 q^{83} +(3.76344 - 2.17283i) q^{84} +(0.535898 - 6.70637i) q^{85} -6.83247i q^{86} +(8.35922 - 4.82620i) q^{87} +(2.04055 + 1.17811i) q^{88} +(4.15208 + 2.39720i) q^{89} +(-1.26873 + 1.84128i) q^{90} +(0.553049 + 15.6587i) q^{91} -6.44791i q^{92} +(3.55746 - 6.16171i) q^{93} +(-2.80764 + 4.86298i) q^{94} +(-0.120495 + 1.50791i) q^{95} +1.00000i q^{96} +(8.17066 + 14.1520i) q^{97} +(5.94234 + 10.2924i) q^{98} -2.35623i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8} + 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 - 6 * q^4 + 2 * q^5 + 2 * q^7 - 12 * q^8 + 6 * q^9	\( 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8} + 6 q^{9} + 4 q^{10} + 6 q^{11} + 8 q^{13} + 4 q^{14} + 6 q^{15} - 6 q^{16} - 18 q^{17} + 12 q^{18} - 6 q^{19} + 2 q^{20} + 6 q^{22} - 6 q^{23} - 10 q^{25} - 2 q^{26} + 2 q^{28} + 14 q^{29} + 6 q^{30} + 6 q^{32} - 6 q^{33} - 22 q^{35} + 6 q^{36} + 12 q^{37} - 2 q^{39} - 2 q^{40} - 18 q^{41} + 12 q^{42} + 36 q^{43} - 2 q^{45} - 6 q^{46} - 16 q^{47} + 8 q^{49} - 20 q^{50} + 16 q^{51} - 10 q^{52} + 8 q^{55} - 2 q^{56} + 8 q^{57} - 14 q^{58} - 36 q^{59} + 10 q^{61} - 6 q^{62} - 2 q^{63} + 12 q^{64} - 44 q^{65} - 12 q^{66} - 4 q^{67} + 18 q^{68} + 16 q^{69} + 4 q^{70} - 12 q^{71} - 6 q^{72} - 28 q^{73} - 12 q^{74} + 16 q^{75} + 6 q^{76} + 2 q^{78} + 4 q^{79} - 4 q^{80} - 6 q^{81} - 18 q^{82} - 72 q^{83} + 12 q^{84} + 48 q^{85} - 6 q^{87} - 6 q^{88} + 18 q^{89} + 2 q^{90} + 2 q^{91} + 16 q^{93} - 8 q^{94} + 18 q^{95} + 48 q^{97} - 8 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 + 2 * q^5 + 2 * q^7 - 12 * q^8 + 6 * q^9 + 4 * q^10 + 6 * q^11 + 8 * q^13 + 4 * q^14 + 6 * q^15 - 6 * q^16 - 18 * q^17 + 12 * q^18 - 6 * q^19 + 2 * q^20 + 6 * q^22 - 6 * q^23 - 10 * q^25 - 2 * q^26 + 2 * q^28 + 14 * q^29 + 6 * q^30 + 6 * q^32 - 6 * q^33 - 22 * q^35 + 6 * q^36 + 12 * q^37 - 2 * q^39 - 2 * q^40 - 18 * q^41 + 12 * q^42 + 36 * q^43 - 2 * q^45 - 6 * q^46 - 16 * q^47 + 8 * q^49 - 20 * q^50 + 16 * q^51 - 10 * q^52 + 8 * q^55 - 2 * q^56 + 8 * q^57 - 14 * q^58 - 36 * q^59 + 10 * q^61 - 6 * q^62 - 2 * q^63 + 12 * q^64 - 44 * q^65 - 12 * q^66 - 4 * q^67 + 18 * q^68 + 16 * q^69 + 4 * q^70 - 12 * q^71 - 6 * q^72 - 28 * q^73 - 12 * q^74 + 16 * q^75 + 6 * q^76 + 2 * q^78 + 4 * q^79 - 4 * q^80 - 6 * q^81 - 18 * q^82 - 72 * q^83 + 12 * q^84 + 48 * q^85 - 6 * q^87 - 6 * q^88 + 18 * q^89 + 2 * q^90 + 2 * q^91 + 16 * q^93 - 8 * q^94 + 18 * q^95 + 48 * q^97 - 8 * q^98

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