LMFDB - Embedded newform 390.2.x.a.199.3

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			199.3
Root			$2.00607 + 1.30680i$ of defining polynomial
Character	$\chi$	$=$	390.199
Dual form			390.2.x.a.49.3

$q$-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} +(-2.22896 + 0.178114i) q^{10} +(-2.04055 - 1.17811i) q^{11} +1.00000i q^{12} +(-3.18419 - 1.69144i) q^{13} +4.34565 q^{14} +(-0.178114 - 2.22896i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.60564 - 1.50437i) q^{17} -1.00000 q^{18} +(0.585872 - 0.338254i) q^{19} +(0.960230 - 2.01940i) 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} +(2.01940 + 0.960230i) q^{30} -7.11493i q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.17811 + 2.04055i) q^{33} +3.00874i q^{34} +(4.17283 - 8.77559i) 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} +(-0.960230 + 2.01940i) q^{45} +(5.58405 - 3.22396i) q^{46} +5.61529 q^{47} +(0.866025 - 0.500000i) q^{48} +(-5.94234 + 10.2924i) q^{49} +(-3.15592 - 3.87817i) q^{50} -3.00874 q^{51} +(0.127265 + 3.60330i) q^{52} +9.43400i q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.419677 - 5.25194i) 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} +(-0.925468 - 8.00896i) 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} +(3.87817 - 3.15592i) q^{75} +(-0.585872 - 0.338254i) q^{76} +10.2393i q^{77} +(-3.60330 + 0.127265i) q^{78} -3.74519 q^{79} +(-2.22896 + 0.178114i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.60564 - 1.50437i) q^{82} +10.3557 q^{83} +(3.76344 - 2.17283i) q^{84} +(6.07583 + 2.88908i) 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} +(1.36614 + 0.649603i) 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} - 2 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} + 4 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} + 26 q^{35} + 6 q^{36} - 12 q^{37} - 2 q^{39} - 2 q^{40} - 18 q^{41} - 12 q^{42} - 36 q^{43} - 4 q^{45} - 6 q^{46} + 16 q^{47} + 8 q^{49} - 10 q^{50} + 16 q^{51} + 10 q^{52} - 28 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} + 6 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} - 8 q^{75} + 6 q^{76} - 2 q^{78} + 4 q^{79} - 2 q^{80} - 6 q^{81} + 18 q^{82} + 72 q^{83} + 12 q^{84} + 18 q^{85} + 6 q^{87} + 6 q^{88} + 18 q^{89} + 2 q^{90} + 2 q^{91} - 16 q^{93} - 8 q^{94} - 42 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 - 2 * 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 + 4 * 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 + 26 * q^35 + 6 * q^36 - 12 * q^37 - 2 * q^39 - 2 * q^40 - 18 * q^41 - 12 * q^42 - 36 * q^43 - 4 * q^45 - 6 * q^46 + 16 * q^47 + 8 * q^49 - 10 * q^50 + 16 * q^51 + 10 * q^52 - 28 * 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 + 6 * 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 - 8 * q^75 + 6 * q^76 - 2 * q^78 + 4 * q^79 - 2 * q^80 - 6 * q^81 + 18 * q^82 + 72 * q^83 + 12 * q^84 + 18 * q^85 + 6 * q^87 + 6 * q^88 + 18 * q^89 + 2 * q^90 + 2 * q^91 - 16 * q^93 - 8 * q^94 - 42 * 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	$-0.859943\pi$
$7$	−2.17283	−	3.76344i	−0.821251	−	1.42245i	0.0835003	−	0.996508i	$-0.473390\pi$
$8$	1.00000			0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−2.22896	+	0.178114i	−0.704860	+	0.0563246i
$11$	−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
$15$	−0.178114	−	2.22896i	−0.0459888	−	0.575516i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.60564	−	1.50437i	0.631962	−	0.364863i	−0.149550	−	0.988754i	$-0.547782\pi$
$17$	2.60564	−	1.50437i	0.631962	−	0.364863i	0.781511	+	0.623891i	$0.214449\pi$
$18$	−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	$0.308607\pi$
$20$	0.960230	−	2.01940i	0.214714	−	0.451551i
$21$			4.34565i			0.948299i
$22$	2.04055	−	1.17811i	0.435047	−	0.251175i
$23$	−5.58405	−	3.22396i	−1.16436	−	0.672241i	−0.212012	−	0.977267i	$-0.568002\pi$
$23$	−5.58405	−	3.22396i	−1.16436	−	0.672241i	−0.952344	+	0.305026i	$0.901335\pi$
$24$	−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	$-0.187018\pi$
$30$	2.01940	+	0.960230i	0.368689	+	0.175313i
$31$		−	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
$35$	4.17283	−	8.77559i	0.705336	−	1.48335i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	3.74165	−	6.48073i	0.615123	−	1.06542i	−0.375240	−	0.926928i	$-0.622440\pi$
$37$	3.74165	−	6.48073i	0.615123	−	1.06542i	0.990363	−	0.138497i	$-0.0442271\pi$
$38$			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	−0.877961	−	0.478731i	$-0.841097\pi$
$43$	−5.91710	+	3.41624i	−0.902349	+	0.520971i	−0.0243872	+	0.999703i	$0.507763\pi$
$44$			2.35623i			0.355215i
$45$	−0.960230	+	2.01940i	−0.143143	+	0.301034i
$46$	5.58405	−	3.22396i	0.823324	−	0.475346i
$47$	5.61529			0.819074			0.409537	−	0.912294i	$-0.365690\pi$
$47$	5.61529			0.819074			0.409537	+	0.912294i	$0.365690\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	−5.94234	+	10.2924i	−0.848906	+	1.47035i
$50$	−3.15592	−	3.87817i	−0.446314	−	0.548456i
$51$	−3.00874			−0.421308
$52$	0.127265	+	3.60330i	0.0176485	+	0.499688i
$53$			9.43400i			1.29586i	0.761700	+	0.647930i	$0.224365\pi$
$53$			9.43400i			1.29586i	−0.761700	+	0.647930i	$0.775635\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	−0.419677	−	5.25194i	−0.0565892	−	0.708172i
$56$	−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
$65$	−0.925468	−	8.00896i	−0.114790	−	0.993390i
$66$	−2.35623			−0.290032
$67$	−2.91329	+	5.04596i	−0.355915	+	0.616463i	−0.987274	−	0.159028i	$-0.949164\pi$
$67$	−2.91329	+	5.04596i	−0.355915	+	0.616463i	0.631359	+	0.775490i	$0.282497\pi$
$68$	−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	$-0.648335\pi$
$73$	−7.67804			−0.898647			−0.449323	+	0.893369i	$0.648335\pi$
$74$	3.74165	+	6.48073i	0.434958	+	0.753369i
$75$	3.87817	−	3.15592i	0.447812	−	0.364414i
$76$	−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	$0.567569\pi$
$80$	−2.22896	+	0.178114i	−0.249206	+	0.0199137i
$81$	−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	$-0.307585\pi$
$83$	10.3557			1.13668			0.568341	+	0.822793i	$0.307585\pi$
$84$	3.76344	−	2.17283i	0.410625	−	0.237075i
$85$	6.07583	+	2.88908i	0.659017	+	0.313365i
$86$		−	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
$95$	1.36614	+	0.649603i	0.140163	+	0.0666478i
$96$			1.00000i			0.102062i
$97$	−8.17066	−	14.1520i	−0.829605	−	1.43692i	−0.898349	−	0.439283i	$-0.855232\pi$
$97$	−8.17066	−	14.1520i	−0.829605	−	1.43692i	0.0687436	−	0.997634i	$-0.478101\pi$
$98$	−5.94234	−	10.2924i	−0.600267	−	1.03969i
$99$		−	2.35623i		−	0.236810i
$100$	4.93655	−	0.794019i	0.493655	−	0.0794019i
$101$	−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	$0.0591702\pi$
$103$			3.75144i			0.369640i	−0.982772	+	0.184820i	$0.940830\pi$
$104$	−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	0.993445	−	0.114309i	$-0.0364654\pi$
$107$	14.3904	+	8.30831i	1.39117	+	0.803194i	0.397728	+	0.917503i	$0.369799\pi$
$108$	−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	$-0.178615\pi$
$110$	4.75816	+	2.26252i	0.453672	+	0.215723i
$111$	−6.48073	+	3.74165i	−0.615123	+	0.355142i
$112$	4.34565			0.410625
$113$	−13.5620	+	7.83002i	−1.27581	+	0.736587i	−0.976074	−	0.217437i	$-0.930230\pi$
$113$	−13.5620	+	7.83002i	−1.27581	+	0.736587i	−0.299731	+	0.954024i	$0.596897\pi$
$114$	0.338254	−	0.585872i	0.0316804	−	0.0548720i
$115$	−1.14846	−	14.3722i	−0.107095	−	1.34021i
$116$	−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
$120$	−0.178114	−	2.22896i	−0.0162595	−	0.203476i
$121$	−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	0.921382	−	0.388658i	$-0.127061\pi$
$127$	11.7820	+	6.80236i	1.04549	+	0.603611i	0.124103	+	0.992269i	$0.460395\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	6.83247			0.601566
$130$	7.39870	+	3.20300i	0.648909	+	0.280922i
$131$	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	$-0.988750\pi$
$137$	−6.20689	−	10.7506i	−0.530290	−	0.918489i	0.469085	−	0.883153i	$-0.344584\pi$
$138$	−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	$-0.397113\pi$
$140$	−9.68629	+	0.774021i	−0.818641	+	0.0654167i
$141$	−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
$145$	21.5148	−	1.71923i	1.78671	−	0.142774i
$146$	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	$0.0382530\pi$
$150$	0.794019	+	4.93655i	0.0648314	+	0.403068i
$151$			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	$0.0571600\pi$
$157$			4.47595i			0.357220i	−0.983920	+	0.178610i	$0.942840\pi$
$158$	1.87260	−	3.24343i	0.148976	−	0.258033i
$159$	4.71700	−	8.17008i	0.374082	−	0.647930i
$160$	0.960230	−	2.01940i	0.0759129	−	0.159647i
$161$			28.0204i			2.20831i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	3.87774	+	6.71645i	0.303728	+	0.526073i	0.976977	−	0.213343i	$-0.0684352\pi$
$163$	3.87774	+	6.71645i	0.303728	+	0.526073i	−0.673249	+	0.739416i	$0.735102\pi$
$164$			3.00874i			0.234943i
$165$	−2.26252	+	4.75816i	−0.176137	+	0.370422i
$166$	−5.17783	+	8.96827i	−0.401878	+	0.696073i
$167$	0.339021	−	0.587202i	0.0262342	−	0.0454390i	−0.852610	−	0.522547i	$-0.824982\pi$
$167$	0.339021	−	0.587202i	0.0262342	−	0.0454390i	0.878844	+	0.477108i	$0.158315\pi$
$168$			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	−0.476044	−	0.879421i	$-0.657930\pi$
$173$	0.625226	−	0.360974i	0.0475350	−	0.0274444i	0.523579	+	0.851977i	$0.324596\pi$
$174$		−	9.65239i		−	0.731746i
$175$	21.4525	−	3.45053i	1.62166	−	0.260835i
$176$	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	$0.0901134\pi$
$180$	2.22896	−	0.178114i	0.166137	−	0.0132758i
$181$	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
$185$	16.6800	−	1.33288i	1.22634	−	0.0979953i
$186$	−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	$-0.530420\pi$
$193$	11.3135	−	19.5955i	0.814363	−	1.41052i	0.909784	−	0.415081i	$-0.136247\pi$
$194$	16.3413			1.17324
$195$	−3.20300	+	7.39870i	−0.229372	+	0.529832i
$196$	11.8847			0.848906
$197$	−0.823770	+	1.42681i	−0.0586912	+	0.101656i	−0.893878	−	0.448310i	$-0.852026\pi$
$197$	−0.823770	+	1.42681i	−0.0586912	+	0.101656i	0.835187	+	0.549966i	$0.185359\pi$
$198$	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
$205$	−0.535898	−	6.70637i	−0.0374288	−	0.468393i
$206$	−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
$210$	−0.774021	−	9.68629i	−0.0534125	−	0.668418i
$211$	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
$215$	−13.7975	−	6.56075i	−0.940979	−	0.447439i
$216$		−	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	−0.777919	−	0.628364i	$-0.783725\pi$
$223$	2.31792	−	4.01476i	0.155220	−	0.268848i	0.933139	+	0.359516i	$0.117058\pi$
$224$	−2.17283	+	3.76344i	−0.145178	+	0.251456i
$225$	−4.93655	+	0.794019i	−0.329103	+	0.0529346i
$226$		−	15.6600i		−	1.04169i
$227$	−8.89213	−	15.4016i	−0.590192	−	1.02224i	−0.994206	−	0.107489i	$-0.965719\pi$
$227$	−8.89213	−	15.4016i	−0.590192	−	1.02224i	0.404015	−	0.914753i	$-0.367615\pi$
$228$	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	$-0.169142\pi$
$230$	13.0209	+	6.19148i	0.858572	+	0.408254i
$231$	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	$-0.918241\pi$
$233$		−	7.75548i		−	0.508079i	0.967194	−	0.254039i	$-0.0817593\pi$
$234$	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	$0.794016\pi$
$240$	2.01940	+	0.960230i	0.130351	+	0.0619826i
$241$	−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
$245$	−26.4905	+	2.11683i	−1.69242	+	0.135239i
$246$	−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
$250$	3.13679	−	10.7313i	0.198388	−	0.678706i
$251$	−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	0.832680	−	0.553755i	$-0.186806\pi$
$257$	12.3353	+	7.12178i	0.769454	+	0.444244i	−0.0632261	+	0.997999i	$0.520139\pi$
$258$	−3.41624	+	5.91710i	−0.212686	+	0.368382i
$259$	−32.5198			−2.02068
$260$	−6.47323	+	4.80596i	−0.401453	+	0.298053i
$261$	9.65239			0.597468
$262$	−5.10611	+	8.84404i	−0.315457	+	0.546387i
$263$	13.3385	+	7.70101i	0.822490	+	0.474865i	0.851274	−	0.524721i	$-0.175830\pi$
$263$	13.3385	+	7.70101i	0.822490	+	0.474865i	−0.0287845	+	0.999586i	$0.509164\pi$
$264$	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	$0.531858\pi$
$270$	0.178114	+	2.22896i	0.0108397	+	0.135650i
$271$	−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
$275$	9.13785	−	7.43606i	0.551033	−	0.448411i
$276$	3.22396	−	5.58405i	0.194059	−	0.336121i
$277$	12.3861	−	7.15114i	0.744211	−	0.429671i	−0.0793871	−	0.996844i	$-0.525296\pi$
$277$	12.3861	−	7.15114i	0.744211	−	0.429671i	0.823599	+	0.567173i	$0.191963\pi$
$278$	15.6183			0.936723
$279$	6.16171	−	3.55746i	0.368892	−	0.212980i
$280$	4.17283	−	8.77559i	0.249374	−	0.524442i
$281$			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	0.0721756	−	0.997392i	$-0.477006\pi$
$283$	−12.7095	−	7.33785i	−0.755503	−	0.436190i	−0.827679	+	0.561202i	$0.810339\pi$
$284$	−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
$290$	−9.26852	+	19.4920i	−0.544266	+	1.14461i
$291$			16.3413i			0.957945i
$292$	3.83902	+	6.64938i	0.224662	+	0.389125i
$293$	−3.43198	−	5.94436i	−0.200498	−	0.347273i	0.748191	−	0.663484i	$-0.230923\pi$
$293$	−3.43198	−	5.94436i	−0.200498	−	0.347273i	−0.948689	+	0.316210i	$0.897589\pi$
$294$			11.8847i			0.693129i
$295$	−10.6415	−	5.06006i	−0.619571	−	0.294608i
$296$	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
$305$	−4.14139	+	8.70948i	−0.237135	+	0.498704i
$306$	−2.60564	+	1.50437i	−0.148955	+	0.0859991i
$307$	10.9917			0.627328			0.313664	−	0.949534i	$-0.398443\pi$
$307$	10.9917			0.627328			0.313664	+	0.949534i	$0.398443\pi$
$308$	8.86753	−	5.11967i	0.505275	−	0.291720i
$309$	1.87572	−	3.24884i	0.106706	−	0.184820i
$310$	1.26727	+	15.8589i	0.0719760	+	0.900725i
$311$	−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	$-0.868814\pi$
$313$		−	14.1734i		−	0.801130i	0.916268	−	0.400565i	$-0.131186\pi$
$314$	−3.87629	−	2.23798i	−0.218752	−	0.126296i
$315$	9.68629	−	0.774021i	0.545761	−	0.0436111i
$316$	1.87260	+	3.24343i	0.105342	+	0.182457i
$317$	−3.20808			−0.180184			−0.0900920	−	0.995933i	$-0.528716\pi$
$317$	−3.20808			−0.180184			−0.0900920	+	0.995933i	$0.528716\pi$
$318$	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
$325$	13.5726	−	11.8653i	0.752872	−	0.658167i
$326$	−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
$335$	−12.9872	+	1.03779i	−0.709568	+	0.0567008i
$336$	−3.76344	−	2.17283i	−0.205313	−	0.118537i
$337$		−	0.772078i		−	0.0420578i	−0.999779	−	0.0210289i	$-0.993306\pi$
$337$		−	0.772078i		−	0.0420578i	0.999779	−	0.0210289i	$-0.00669420\pi$
$338$	−12.9676	+	0.917149i	−0.705345	+	0.0498863i
$339$	15.6600			0.850537
$340$	−0.535898	−	6.70637i	−0.0290632	−	0.363704i
$341$	−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
$345$	−6.19148	+	13.0209i	−0.333338	+	0.701021i
$346$			0.721948i			0.0388122i
$347$	21.7856	−	12.5779i	1.16951	−	0.675218i	0.215946	−	0.976405i	$-0.430716\pi$
$347$	21.7856	−	12.5779i	1.16951	−	0.675218i	0.953565	+	0.301188i	$0.0973830\pi$
$348$	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	−0.748462	−	0.663177i	$-0.769208\pi$
$353$	3.75948	−	6.51161i	0.200097	−	0.346578i	0.948559	+	0.316599i	$0.102541\pi$
$354$	−2.63482	+	4.56364i	−0.140039	+	0.242555i
$355$	5.88826	+	2.79989i	0.312516	+	0.148603i
$356$		−	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	$-0.0923463\pi$
$360$	−0.960230	+	2.01940i	−0.0506086	+	0.106431i
$361$	−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	0.660155	−	0.751130i	$-0.270491\pi$
$367$	6.50838	+	3.75761i	0.339735	+	0.196146i	−0.320420	+	0.947276i	$0.603824\pi$
$368$	5.58405	−	3.22396i	0.291089	−	0.168060i
$369$		−	3.00874i		−	0.156629i
$370$	−7.18569	+	15.1117i	−0.373566	+	0.785622i
$371$	35.5043	−	20.4984i	1.84329	−	1.06423i
$372$	7.11493			0.368892
$373$	19.8135	−	11.4393i	1.02590	−	0.592305i	0.110095	−	0.993921i	$-0.464885\pi$
$373$	19.8135	−	11.4393i	1.02590	−	0.592305i	0.915808	+	0.401616i	$0.131551\pi$
$374$	3.54464	−	6.13949i	0.183289	−	0.317466i
$375$	10.7313	+	3.13679i	0.554161	+	0.161983i
$376$	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	$0.900667\pi$
$380$	−0.120495	−	1.50791i	−0.00618128	−	0.0773541i
$381$	−6.80236	−	11.7820i	−0.348495	−	0.603611i
$382$	0.586882			0.0300275
$383$	6.84652	+	11.8585i	0.349841	+	0.605942i	0.986221	−	0.165434i	$-0.0529024\pi$
$383$	6.84652	+	11.8585i	0.349841	+	0.605942i	−0.636380	+	0.771376i	$0.719569\pi$
$384$	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	$0.282127\pi$
$390$	−4.80596	−	6.47323i	−0.243359	−	0.327785i
$391$	−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	$0.0939662\pi$
$397$	14.5517	+	25.2043i	0.730328	+	1.26497i	−0.226415	+	0.974031i	$0.572700\pi$
$398$	10.2733			0.514954
$399$	1.46993	+	2.54600i	0.0735887	+	0.127459i
$400$	−3.15592	−	3.87817i	−0.157796	−	0.193908i
$401$	−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
$405$	−2.22896	+	0.178114i	−0.110758	+	0.00885055i
$406$	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	$0.125115\pi$
$410$	6.07583	+	2.88908i	0.300064	+	0.142682i
$411$			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	$0.936336\pi$
$420$	8.77559	+	4.17283i	0.428205	+	0.203613i
$421$		−	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
$425$	2.38900	+	14.8528i	0.115883	+	0.720466i
$426$	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	−0.570168	−	0.821528i	$-0.693122\pi$
$433$	−2.99201	+	1.72744i	−0.143787	+	0.0830155i	0.426381	+	0.904544i	$0.359788\pi$
$434$		−	30.9190i		−	1.48416i
$435$	−19.4920	−	9.26852i	−0.934570	−	0.444391i
$436$	−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	$0.970269\pi$
$440$	−0.419677	−	5.25194i	−0.0200073	−	0.250377i
$441$	−11.8847			−0.565937
$442$	5.08909	−	9.58038i	0.242064	−	0.455692i
$443$		−	13.1629i		−	0.625390i	−0.949854	−	0.312695i	$-0.898768\pi$
$443$		−	13.1629i		−	0.625390i	0.949854	−	0.312695i	$-0.101232\pi$
$444$	6.48073	+	3.74165i	0.307562	+	0.177571i
$445$	0.853950	+	10.6865i	0.0404811	+	0.506591i
$446$	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
$455$	−28.1304	+	20.8850i	−1.31877	+	0.979105i
$456$	−0.676507			−0.0316804
$457$	5.38493	−	9.32698i	0.251897	−	0.436298i	−0.712151	−	0.702026i	$-0.752279\pi$
$457$	5.38493	−	9.32698i	0.251897	−	0.436298i	0.964048	+	0.265728i	$0.0856124\pi$
$458$	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	$-0.255024\pi$
$463$	29.9462			1.39172			0.695860	+	0.718178i	$0.255024\pi$
$464$	4.82620	+	8.35922i	0.224051	+	0.388067i
$465$	−15.8589	+	1.26727i	−0.735439	+	0.0587681i
$466$	6.71645	+	3.87774i	0.311133	+	0.179633i
$467$		−	21.8940i		−	1.01313i	−0.862201	−	0.506566i	$-0.830915\pi$
$467$		−	21.8940i		−	1.01313i	0.862201	−	0.506566i	$-0.169085\pi$
$468$	−3.05692	+	1.91187i	−0.141306	+	0.0883761i
$469$	25.3203			1.16918
$470$	−12.5163	+	1.00016i	−0.577332	+	0.0461340i
$471$	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
$475$	0.537159	+	3.33961i	0.0246466	+	0.153232i
$476$			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
$485$	15.6914	−	32.9996i	0.712511	−	1.49843i
$486$			1.00000i			0.0453609i
$487$	−10.8587	−	18.8079i	−0.492056	−	0.852265i	0.507902	−	0.861415i	$-0.330421\pi$
$487$	−10.8587	−	18.8079i	−0.492056	−	0.852265i	−0.999958	+	0.00914916i	$0.997088\pi$
$488$	2.15646	+	3.73509i	0.0976183	+	0.169080i
$489$		−	7.75548i		−	0.350715i
$490$	11.4120	−	23.9999i	0.515543	−	1.08420i
$491$	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	$0.924565\pi$
$500$	7.72518	+	8.08218i	0.345480	+	0.361446i
$501$	−0.587202	+	0.339021i	−0.0262342	+	0.0151463i
$502$	7.12807			0.318142
$503$	7.14818	−	4.12700i	0.318722	−	0.184014i	−0.332101	−	0.943244i	$-0.607757\pi$
$503$	7.14818	−	4.12700i	0.318722	−	0.184014i	0.650823	+	0.759230i	$0.274424\pi$
$504$	2.17283	−	3.76344i	0.0967853	−	0.167637i
$505$	−27.2786	+	2.17980i	−1.21388	+	0.0969998i
$506$	−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	$0.618873\pi$
$510$	6.70637	−	0.535898i	0.296963	−	0.0237300i
$511$	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
$520$	−0.925468	−	8.00896i	−0.0405844	−	0.351216i
$521$	−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	0.558338	−	0.829614i	$-0.311439\pi$
$523$	2.72235	+	1.57175i	0.119040	+	0.0687279i	−0.439298	+	0.898342i	$0.644773\pi$
$524$	−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
$530$	−1.68033	−	21.0280i	−0.0729887	−	0.913400i
$531$	−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
$535$	2.95965	+	37.0378i	0.127957	+	1.60128i
$536$	−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
$540$	−2.01940	−	0.960230i	−0.0869009	−	0.0413217i
$541$		−	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	$0.337428\pi$
$547$			40.8067i			1.74477i	−0.488820	+	0.872385i	$0.662572\pi$
$548$	−6.20689	+	10.7506i	−0.265145	+	0.459245i
$549$	−2.15646	+	3.73509i	−0.0920354	+	0.159410i
$550$	1.87089	+	11.6316i	0.0797750	+	0.495975i
$551$		−	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
$555$	−15.1117	−	7.18569i	−0.641457	−	0.305015i
$556$	−7.80915	+	13.5258i	−0.331182	+	0.573623i
$557$	12.6109	−	21.8427i	0.534340	−	0.925504i	−0.464855	−	0.885387i	$-0.653894\pi$
$557$	12.6109	−	21.8427i	0.534340	−	0.925504i	0.999195	−	0.0401170i	$-0.0127731\pi$
$558$			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	−0.985155	−	0.171664i	$-0.945086\pi$
$563$	−31.5356	+	18.2071i	−1.32907	+	0.767337i	−0.343912	+	0.939002i	$0.611752\pi$
$564$			5.61529i			0.236446i
$565$	−31.6238	−	15.0372i	−1.33042	−	0.632622i
$566$	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	$0.972306\pi$
$570$	1.50791	−	0.120495i	0.0631594	−	0.00504700i
$571$	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
$575$	25.0061	−	20.3491i	1.04283	−	0.848615i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	31.1697			1.29761			0.648806	−	0.760954i	$-0.275269\pi$
$577$	31.1697			1.29761			0.648806	+	0.760954i	$0.275269\pi$
$578$	−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
$585$	6.47323	−	4.80596i	0.267635	−	0.198702i
$586$	6.86396			0.283547
$587$	7.61411	−	13.1880i	0.314268	−	0.544328i	−0.665014	−	0.746831i	$-0.731574\pi$
$587$	7.61411	−	13.1880i	0.314268	−	0.544328i	0.979282	+	0.202503i	$0.0649076\pi$
$588$	−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	$-0.600976\pi$
$593$	−15.1921			−0.623865			−0.311933	+	0.950104i	$0.600976\pi$
$594$	−1.17811	−	2.04055i	−0.0483386	−	0.0837249i
$595$	−2.32883	−	29.1435i	−0.0954726	−	1.19477i
$596$	−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	$0.471698\pi$
$600$	3.87817	−	3.15592i	0.158326	−	0.128840i
$601$	−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
$605$	5.23152	−	11.0021i	0.212691	−	0.447297i
$606$			12.2382i			0.497144i
$607$	−37.6094	+	21.7138i	−1.52652	+	0.881335i	−0.527012	+	0.849858i	$0.676688\pi$
$607$	−37.6094	+	21.7138i	−1.52652	+	0.881335i	−0.999504	+	0.0314772i	$0.989979\pi$
$608$	−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	$-0.604147\pi$
$613$	16.3258	−	28.2771i	0.659392	−	1.14210i	0.980773	−	0.195150i	$-0.0625194\pi$
$614$	−5.49584	+	9.51907i	−0.221794	+	0.384159i
$615$	−2.88908	+	6.07583i	−0.116499	+	0.245001i
$616$			10.2393i			0.412555i
$617$	−4.83488	−	8.37426i	−0.194645	−	0.337135i	0.752139	−	0.659004i	$-0.229022\pi$
$617$	−4.83488	−	8.37426i	−0.194645	−	0.337135i	−0.946784	+	0.321869i	$0.895689\pi$
$618$	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	$0.966671\pi$
$620$	−14.3678	−	6.83197i	−0.577027	−	0.274378i
$621$	−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
$630$	−4.17283	+	8.77559i	−0.166249	+	0.349628i
$631$	−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
$635$	2.42319	+	30.3244i	0.0961613	+	1.20339i
$636$	−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
$640$	−2.22896	+	0.178114i	−0.0881075	+	0.00704057i
$641$	−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	0.943683	−	0.330851i	$-0.107336\pi$
$643$	4.69916	+	8.13918i	0.185317	+	0.320978i	−0.758367	+	0.651828i	$0.774002\pi$
$644$	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	−0.373921	−	0.927461i	$-0.621987\pi$
$647$	−34.6972	−	20.0324i	−1.36409	−	0.787555i	−0.990165	+	0.139905i	$0.955320\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	12.4165			0.487389
$650$	3.48934	+	17.6868i	0.136863	+	0.693735i
$651$	30.9190			1.21181
$652$	3.87774	−	6.71645i	0.151864	−	0.263036i
$653$	27.1900	+	15.6981i	1.06403	+	0.614316i	0.926543	−	0.376189i	$-0.122766\pi$
$653$	27.1900	+	15.6981i	1.06403	+	0.614316i	0.137483	+	0.990504i	$0.456099\pi$
$654$	−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	$0.712808\pi$
$660$	5.25194	−	0.419677i	0.204432	−	0.0163359i
$661$	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
$665$	−0.523631	−	6.55285i	−0.0203055	−	0.254109i
$666$	−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
$670$	5.59485	−	11.7662i	0.216148	−	0.454566i
$671$		−	10.1622i		−	0.392308i
$672$	3.76344	−	2.17283i	0.145178	−	0.0838186i
$673$	7.44817	+	4.30020i	0.287106	+	0.165761i	0.636636	−	0.771164i	$-0.280325\pi$
$673$	7.44817	+	4.30020i	0.287106	+	0.165761i	−0.349530	+	0.936925i	$0.613659\pi$
$674$	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	$0.165500\pi$
$677$			25.8539i			0.993646i	−0.867852	+	0.496823i	$0.834500\pi$
$678$	−7.83002	+	13.5620i	−0.300710	+	0.520845i
$679$	−35.5068	+	61.4997i	−1.36263	+	2.36014i
$680$	6.07583	+	2.88908i	0.232998	+	0.110791i
$681$			17.7843i			0.681495i
$682$	−8.38219	−	14.5184i	−0.320971	−	0.555938i
$683$	10.4524	+	18.1041i	0.399950	+	0.692734i	0.993719	−	0.111901i	$-0.0356941\pi$
$683$	10.4524	+	18.1041i	0.399950	+	0.692734i	−0.593769	+	0.804636i	$0.702361\pi$
$684$		−	0.676507i		−	0.0258669i
$685$	11.9201	−	25.0683i	0.455443	−	0.957811i
$686$	−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
$695$	14.9972	−	31.5395i	0.568875	−	1.19636i
$696$	−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
$700$	−13.7145	−	16.8532i	−0.518360	−	0.636990i
$701$	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
$705$	−1.00016	−	12.5163i	−0.0376682	−	0.471390i
$706$	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
$715$	−7.54701	+	17.4330i	−0.282242	+	0.651958i
$716$	−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
$725$	30.4621	+	37.4336i	1.13134	+	1.39025i
$726$	−4.71827	−	2.72410i	−0.175111	−	0.101101i
$727$		−	28.2602i		−	1.04811i	−0.851684	−	0.524056i	$-0.824418\pi$
$727$		−	28.2602i		−	1.04811i	0.851684	−	0.524056i	$-0.175582\pi$
$728$	0.553049	+	15.6587i	0.0204974	+	0.580350i
$729$	−1.00000			−0.0370370
$730$	17.1141	−	1.36757i	0.633420	−	0.0506159i
$731$	−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	$-0.531098\pi$
$733$	−5.28165			−0.195082			−0.0975410	+	0.995232i	$0.531098\pi$
$734$	−6.50838	+	3.75761i	−0.240229	+	0.138696i
$735$	23.9999	+	11.4120i	0.885249	+	0.420939i
$736$			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	−0.984553	−	0.175084i	$-0.943980\pi$
$743$	−9.28543	+	16.0828i	−0.340650	+	0.590022i	0.643904	+	0.765106i	$0.277314\pi$
$744$	−3.55746	+	6.16171i	−0.130423	+	0.225899i
$745$	39.4317	+	18.7499i	1.44467	+	0.686944i
$746$			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
$750$	−8.08218	+	7.72518i	−0.295120	+	0.282084i
$751$	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	0.409200	−	0.912445i	$-0.365808\pi$
$757$	−4.85341	−	2.80211i	−0.176400	−	0.101845i	−0.585600	+	0.810600i	$0.699141\pi$
$758$	22.6152	−	13.0569i	0.821421	−	0.474247i
$759$		−	15.1927i		−	0.551462i
$760$	1.36614	+	0.649603i	0.0495549	+	0.0235636i
$761$	−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
$765$	0.535898	+	6.70637i	0.0193754	+	0.242469i
$766$	−13.6930			−0.494750
$767$	18.9881	−	0.670640i	0.685621	−	0.0242154i
$768$			1.00000i

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} +(-2.22896 + 0.178114i) q^{10} +(-2.04055 - 1.17811i) q^{11} +1.00000i q^{12} +(-3.18419 - 1.69144i) q^{13} +4.34565 q^{14} +(-0.178114 - 2.22896i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.60564 - 1.50437i) q^{17} -1.00000 q^{18} +(0.585872 - 0.338254i) q^{19} +(0.960230 - 2.01940i) 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} +(2.01940 + 0.960230i) q^{30} -7.11493i q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.17811 + 2.04055i) q^{33} +3.00874i q^{34} +(4.17283 - 8.77559i) 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} +(-0.960230 + 2.01940i) q^{45} +(5.58405 - 3.22396i) q^{46} +5.61529 q^{47} +(0.866025 - 0.500000i) q^{48} +(-5.94234 + 10.2924i) q^{49} +(-3.15592 - 3.87817i) q^{50} -3.00874 q^{51} +(0.127265 + 3.60330i) q^{52} +9.43400i q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.419677 - 5.25194i) 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} +(-0.925468 - 8.00896i) 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} +(3.87817 - 3.15592i) q^{75} +(-0.585872 - 0.338254i) q^{76} +10.2393i q^{77} +(-3.60330 + 0.127265i) q^{78} -3.74519 q^{79} +(-2.22896 + 0.178114i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.60564 - 1.50437i) q^{82} +10.3557 q^{83} +(3.76344 - 2.17283i) q^{84} +(6.07583 + 2.88908i) 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} +(1.36614 + 0.649603i) 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	\( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} - 2 q^{7} + 12 q^{8} + 6 q^{9} - 2 q^{10} + 6 q^{11} - 8 q^{13} + 4 q^{14} + 6 q^{15} - 6 q^{16} + 18 q^{17} - 12 q^{18} - 6 q^{19} + 4 q^{20} - 6 q^{22} + 6 q^{23} - 10 q^{25} - 2 q^{26} - 2 q^{28} + 14 q^{29} - 6 q^{30} - 6 q^{32} + 6 q^{33} + 26 q^{35} + 6 q^{36} - 12 q^{37} - 2 q^{39} - 2 q^{40} - 18 q^{41} - 12 q^{42} - 36 q^{43} - 4 q^{45} - 6 q^{46} + 16 q^{47} + 8 q^{49} - 10 q^{50} + 16 q^{51} + 10 q^{52} - 28 q^{55} - 2 q^{56} - 8 q^{57} + 14 q^{58} - 36 q^{59} + 10 q^{61} + 6 q^{62} + 2 q^{63} + 12 q^{64} + 6 q^{65} - 12 q^{66} + 4 q^{67} - 18 q^{68} + 16 q^{69} - 4 q^{70} - 12 q^{71} + 6 q^{72} + 28 q^{73} - 12 q^{74} - 8 q^{75} + 6 q^{76} - 2 q^{78} + 4 q^{79} - 2 q^{80} - 6 q^{81} + 18 q^{82} + 72 q^{83} + 12 q^{84} + 18 q^{85} + 6 q^{87} + 6 q^{88} + 18 q^{89} + 2 q^{90} + 2 q^{91} - 16 q^{93} - 8 q^{94} - 42 q^{95} - 48 q^{97} + 8 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 - 2 * q^7 + 12 * q^8 + 6 * q^9 - 2 * 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 + 4 * 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 + 26 * q^35 + 6 * q^36 - 12 * q^37 - 2 * q^39 - 2 * q^40 - 18 * q^41 - 12 * q^42 - 36 * q^43 - 4 * q^45 - 6 * q^46 + 16 * q^47 + 8 * q^49 - 10 * q^50 + 16 * q^51 + 10 * q^52 - 28 * 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 + 6 * 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 - 8 * q^75 + 6 * q^76 - 2 * q^78 + 4 * q^79 - 2 * q^80 - 6 * q^81 + 18 * q^82 + 72 * q^83 + 12 * q^84 + 18 * q^85 + 6 * q^87 + 6 * q^88 + 18 * q^89 + 2 * q^90 + 2 * q^91 - 16 * q^93 - 8 * q^94 - 42 * q^95 - 48 * q^97 + 8 * q^98

Introduction

L-functions

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