LMFDB - Embedded newform 368.2.j.c.93.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,2,Mod(93,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("368.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.j (of order $4$, 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:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.221124989353984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 2 x^{10} + 2 x^{9} + 12 x^{8} - 8 x^{7} - 14 x^{6} - 16 x^{5} + 48 x^{4} + 16 x^{3} + \cdots + 64 $ x^12 - 2x^11 - 2x^10 + 2x^9 + 12x^8 - 8x^7 - 14x^6 - 16x^5 + 48x^4 + 16x^3 - 32x^2 - 64*x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			93.4
Root			$1.41072 - 0.0993495i$ of defining polynomial
Character	$\chi$	$=$	368.93
Dual form			368.2.j.c.277.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.586784 - 1.28673i) q^{2} +(-0.955624 - 0.955624i) q^{3} +(-1.31137 - 1.51007i) q^{4} +(2.38359 - 2.38359i) q^{5} +(-1.79038 + 0.668889i) q^{6} +0.198699i q^{7} +(-2.71255 + 0.801301i) q^{8} -1.17357i q^{9} +(-1.66839 - 4.46569i) q^{10} +(-0.110168 + 0.110168i) q^{11} +(-0.189882 + 2.69623i) q^{12} +(1.69353 + 1.69353i) q^{13} +(0.255673 + 0.116593i) q^{14} -4.55562 q^{15} +(-0.560617 + 3.96052i) q^{16} -0.645369 q^{17} +(-1.51007 - 0.688630i) q^{18} +(0.173567 + 0.173567i) q^{19} +(-6.72515 - 0.473617i) q^{20} +(0.189882 - 0.189882i) q^{21} +(0.0771120 + 0.206401i) q^{22} -1.00000i q^{23} +(3.35792 + 1.82643i) q^{24} -6.36297i q^{25} +(3.17285 - 1.18538i) q^{26} +(-3.98836 + 3.98836i) q^{27} +(0.300049 - 0.260568i) q^{28} +(2.98858 + 2.98858i) q^{29} +(-2.67317 + 5.86188i) q^{30} -4.74204 q^{31} +(4.76717 + 3.04533i) q^{32} +0.210558 q^{33} +(-0.378692 + 0.830418i) q^{34} +(0.473617 + 0.473617i) q^{35} +(-1.77217 + 1.53898i) q^{36} +(-1.53702 + 1.53702i) q^{37} +(0.325181 - 0.121488i) q^{38} -3.23674i q^{39} +(-4.55562 + 8.37556i) q^{40} -9.42339i q^{41} +(-0.132908 - 0.355746i) q^{42} +(-2.46931 + 2.46931i) q^{43} +(0.310832 + 0.0218902i) q^{44} +(-2.79730 - 2.79730i) q^{45} +(-1.28673 - 0.586784i) q^{46} +10.2297 q^{47} +(4.32050 - 3.24903i) q^{48} +6.96052 q^{49} +(-8.18746 - 3.73369i) q^{50} +(0.616730 + 0.616730i) q^{51} +(0.336502 - 4.77818i) q^{52} +(6.13987 - 6.13987i) q^{53} +(2.79165 + 7.47226i) q^{54} +0.525189i q^{55} +(-0.159218 - 0.538981i) q^{56} -0.331730i q^{57} +(5.59916 - 2.09186i) q^{58} +(3.18941 - 3.18941i) q^{59} +(5.97411 + 6.87931i) q^{60} +(0.134023 + 0.134023i) q^{61} +(-2.78255 + 6.10175i) q^{62} +0.233187 q^{63} +(6.71583 - 4.34713i) q^{64} +8.07333 q^{65} +(0.123552 - 0.270932i) q^{66} +(8.34921 + 8.34921i) q^{67} +(0.846317 + 0.974552i) q^{68} +(-0.955624 + 0.955624i) q^{69} +(0.887329 - 0.331508i) q^{70} -4.76823i q^{71} +(0.940380 + 3.18336i) q^{72} -5.99750i q^{73} +(1.07584 + 2.87963i) q^{74} +(-6.08061 + 6.08061i) q^{75} +(0.0344876 - 0.489709i) q^{76} +(-0.0218902 - 0.0218902i) q^{77} +(-4.16483 - 1.89927i) q^{78} -0.630585 q^{79} +(8.10396 + 10.7765i) q^{80} +4.10204 q^{81} +(-12.1254 - 5.52949i) q^{82} +(0.711208 + 0.711208i) q^{83} +(-0.535739 - 0.0377293i) q^{84} +(-1.53829 + 1.53829i) q^{85} +(1.72840 + 4.62630i) q^{86} -5.71192i q^{87} +(0.210558 - 0.387113i) q^{88} +13.8549i q^{89} +(-5.24079 + 1.95797i) q^{90} +(-0.336502 + 0.336502i) q^{91} +(-1.51007 + 1.31137i) q^{92} +(4.53161 + 4.53161i) q^{93} +(6.00265 - 13.1630i) q^{94} +0.827425 q^{95} +(-1.64543 - 7.46582i) q^{96} +7.33230 q^{97} +(4.08432 - 8.95634i) q^{98} +(0.129289 + 0.129289i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 2 q^{3} - 4 q^{5} - 4 q^{8} - 6 q^{10} - 4 q^{11} - 8 q^{12} + 18 q^{13} - 2 q^{14} + 8 q^{16} - 8 q^{17} - 4 q^{18} - 8 q^{19} - 32 q^{20} + 8 q^{21} - 34 q^{22} + 12 q^{24} - 14 q^{26}+ \cdots + 36 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^5 - 4 * q^8 - 6 * q^10 - 4 * q^11 - 8 * q^12 + 18 * q^13 - 2 * q^14 + 8 * q^16 - 8 * q^17 - 4 * q^18 - 8 * q^19 - 32 * q^20 + 8 * q^21 - 34 * q^22 + 12 * q^24 - 14 * q^26 + 14 * q^27 + 12 * q^28 + 2 * q^29 - 30 * q^30 + 20 * q^31 - 8 * q^32 - 36 * q^33 + 10 * q^34 + 4 * q^35 + 4 * q^36 - 4 * q^37 + 24 * q^38 - 14 * q^42 + 20 * q^43 + 4 * q^44 - 20 * q^45 - 2 * q^46 - 16 * q^47 - 12 * q^48 + 52 * q^49 + 6 * q^50 - 4 * q^51 - 16 * q^53 + 16 * q^54 + 28 * q^56 + 14 * q^58 + 8 * q^59 + 48 * q^60 + 12 * q^61 - 44 * q^62 - 4 * q^63 + 24 * q^64 - 52 * q^65 + 34 * q^66 - 4 * q^67 - 16 * q^68 + 2 * q^69 + 28 * q^70 + 8 * q^72 - 26 * q^74 - 46 * q^75 - 8 * q^76 - 12 * q^77 - 44 * q^78 - 4 * q^79 + 4 * q^80 + 48 * q^81 - 6 * q^82 + 28 * q^83 + 12 * q^84 - 8 * q^85 + 44 * q^86 - 36 * q^88 + 4 * q^90 - 4 * q^92 - 14 * q^93 + 48 * q^95 + 32 * q^96 + 36 * q^97 - 2 * q^98 + 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.586784	−	1.28673i	0.414919	−	0.909859i
$2$	0.586784	−	1.28673i	0.414919	−	0.909859i
$3$	−0.955624	−	0.955624i	−0.551730	−	0.551730i	0.375210	−	0.926940i	$-0.377571\pi$
$3$	−0.955624	−	0.955624i	−0.551730	−	0.551730i	−0.926940	+	0.375210i	$0.877571\pi$
$4$	−1.31137	−	1.51007i	−0.655685	−	0.755035i
$5$	2.38359	−	2.38359i	1.06597	−	1.06597i	0.0683082	−	0.997664i	$-0.478240\pi$
$5$	2.38359	−	2.38359i	1.06597	−	1.06597i	0.997664	−	0.0683082i	$-0.0217601\pi$
$6$	−1.79038	+	0.668889i	−0.730919	+	0.273073i
$7$			0.198699i			0.0751012i	0.999295	+	0.0375506i	$0.0119555\pi$
$7$			0.198699i			0.0751012i	−0.999295	+	0.0375506i	$0.988044\pi$
$8$	−2.71255	+	0.801301i	−0.959031	+	0.283303i
$9$		−	1.17357i		−	0.391189i
$10$	−1.66839	−	4.46569i	−0.527592	−	1.41218i
$11$	−0.110168	+	0.110168i	−0.0332168	+	0.0332168i	−0.723520	−	0.690303i	$-0.757477\pi$
$11$	−0.110168	+	0.110168i	−0.0332168	+	0.0332168i	0.690303	+	0.723520i	$0.257477\pi$
$12$	−0.189882	+	2.69623i	−0.0548141	+	0.778336i
$13$	1.69353	+	1.69353i	0.469699	+	0.469699i	0.901817	−	0.432118i	$-0.142234\pi$
$13$	1.69353	+	1.69353i	0.469699	+	0.469699i	−0.432118	+	0.901817i	$0.642234\pi$
$14$	0.255673	+	0.116593i	0.0683315	+	0.0311609i
$15$	−4.55562			−1.17626
$16$	−0.560617	+	3.96052i	−0.140154	+	0.990130i
$17$	−0.645369			−0.156525			−0.0782625	−	0.996933i	$-0.524937\pi$
$17$	−0.645369			−0.156525			−0.0782625	+	0.996933i	$0.524937\pi$
$18$	−1.51007	−	0.688630i	−0.355927	−	0.162312i
$19$	0.173567	+	0.173567i	0.0398190	+	0.0398190i	0.726736	−	0.686917i	$-0.241036\pi$
$19$	0.173567	+	0.173567i	0.0398190	+	0.0398190i	−0.686917	+	0.726736i	$0.741036\pi$
$20$	−6.72515	−	0.473617i	−1.50379	−	0.105904i
$21$	0.189882	−	0.189882i	0.0414355	−	0.0414355i
$22$	0.0771120	+	0.206401i	0.0164403	+	0.0440049i
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$	3.35792	+	1.82643i	0.685432	+	0.372819i
$25$		−	6.36297i		−	1.27259i
$26$	3.17285	−	1.18538i	0.622247	−	0.232473i
$27$	−3.98836	+	3.98836i	−0.767560	+	0.767560i
$28$	0.300049	−	0.260568i	0.0567040	−	0.0492427i
$29$	2.98858	+	2.98858i	0.554966	+	0.554966i	0.927870	−	0.372904i	$-0.121638\pi$
$29$	2.98858	+	2.98858i	0.554966	+	0.554966i	−0.372904	+	0.927870i	$0.621638\pi$
$30$	−2.67317	+	5.86188i	−0.488051	+	1.07023i
$31$	−4.74204			−0.851696			−0.425848	−	0.904795i	$-0.640024\pi$
$31$	−4.74204			−0.851696			−0.425848	+	0.904795i	$0.640024\pi$
$32$	4.76717	+	3.04533i	0.842725	+	0.538344i
$33$	0.210558			0.0366534
$34$	−0.378692	+	0.830418i	−0.0649451	+	0.142416i
$35$	0.473617	+	0.473617i	0.0800558	+	0.0800558i
$36$	−1.77217	+	1.53898i	−0.295361	+	0.256497i
$37$	−1.53702	+	1.53702i	−0.252684	+	0.252684i	−0.822070	−	0.569386i	$-0.807181\pi$
$37$	−1.53702	+	1.53702i	−0.252684	+	0.252684i	0.569386	+	0.822070i	$0.307181\pi$
$38$	0.325181	−	0.121488i	0.0527514	−	0.0197080i
$39$		−	3.23674i		−	0.518294i
$40$	−4.55562	+	8.37556i	−0.720307	+	1.32429i
$41$		−	9.42339i		−	1.47169i	−0.677152	−	0.735843i	$-0.736786\pi$
$41$		−	9.42339i		−	1.47169i	0.677152	−	0.735843i	$-0.263214\pi$
$42$	−0.132908	−	0.355746i	−0.0205081	−	0.0548929i
$43$	−2.46931	+	2.46931i	−0.376566	+	0.376566i	−0.869862	−	0.493295i	$-0.835792\pi$
$43$	−2.46931	+	2.46931i	−0.376566	+	0.376566i	0.493295	+	0.869862i	$0.335792\pi$
$44$	0.310832	+	0.0218902i	0.0468597	+	0.00330008i
$45$	−2.79730	−	2.79730i	−0.416997	−	0.416997i
$46$	−1.28673	−	0.586784i	−0.189719	−	0.0865165i
$47$	10.2297			1.49216			0.746081	−	0.665855i	$-0.231933\pi$
$47$	10.2297			1.49216			0.746081	+	0.665855i	$0.231933\pi$
$48$	4.32050	−	3.24903i	0.623611	−	0.468956i
$49$	6.96052			0.994360
$50$	−8.18746	−	3.73369i	−1.15788	−	0.528023i
$51$	0.616730	+	0.616730i	0.0863594	+	0.0863594i
$52$	0.336502	−	4.77818i	0.0466644	−	0.662614i
$53$	6.13987	−	6.13987i	0.843377	−	0.843377i	−0.145920	−	0.989296i	$-0.546614\pi$
$53$	6.13987	−	6.13987i	0.843377	−	0.843377i	0.989296	+	0.145920i	$0.0466141\pi$
$54$	2.79165	+	7.47226i	0.379896	+	1.01685i
$55$			0.525189i			0.0708165i
$56$	−0.159218	−	0.538981i	−0.0212764	−	0.0720243i
$57$		−	0.331730i		−	0.0439387i
$58$	5.59916	−	2.09186i	0.735206	−	0.274675i
$59$	3.18941	−	3.18941i	0.415225	−	0.415225i	−0.468329	−	0.883554i	$-0.655144\pi$
$59$	3.18941	−	3.18941i	0.415225	−	0.415225i	0.883554	+	0.468329i	$0.155144\pi$
$60$	5.97411	+	6.87931i	0.771254	+	0.888115i
$61$	0.134023	+	0.134023i	0.0171599	+	0.0171599i	0.715635	−	0.698475i	$-0.246138\pi$
$61$	0.134023	+	0.134023i	0.0171599	+	0.0171599i	−0.698475	+	0.715635i	$0.746138\pi$
$62$	−2.78255	+	6.10175i	−0.353385	+	0.774923i
$63$	0.233187			0.0293788
$64$	6.71583	−	4.34713i	0.839479	−	0.543392i
$65$	8.07333			1.00137
$66$	0.123552	−	0.270932i	0.0152082	−	0.0333494i
$67$	8.34921	+	8.34921i	1.02002	+	1.02002i	0.999796	+	0.0202224i	$0.00643742\pi$
$67$	8.34921	+	8.34921i	1.02002	+	1.02002i	0.0202224	+	0.999796i	$0.493563\pi$
$68$	0.846317	+	0.974552i	0.102631	+	0.118182i
$69$	−0.955624	+	0.955624i	−0.115044	+	0.115044i
$70$	0.887329	−	0.331508i	0.106056	−	0.0396228i
$71$		−	4.76823i		−	0.565885i	−0.959137	−	0.282942i	$-0.908689\pi$
$71$		−	4.76823i		−	0.565885i	0.959137	−	0.282942i	$-0.0913105\pi$
$72$	0.940380	+	3.18336i	0.110825	+	0.375162i
$73$		−	5.99750i		−	0.701954i	−0.936384	−	0.350977i	$-0.885850\pi$
$73$		−	5.99750i		−	0.701954i	0.936384	−	0.350977i	$-0.114150\pi$
$74$	1.07584	+	2.87963i	0.125063	+	0.334750i
$75$	−6.08061	+	6.08061i	−0.702128	+	0.702128i
$76$	0.0344876	−	0.489709i	0.00395600	−	0.0561735i
$77$	−0.0218902	−	0.0218902i	−0.00249463	−	0.00249463i
$78$	−4.16483	−	1.89927i	−0.471574	−	0.215050i
$79$	−0.630585			−0.0709463			−0.0354732	−	0.999371i	$-0.511294\pi$
$79$	−0.630585			−0.0709463			−0.0354732	+	0.999371i	$0.511294\pi$
$80$	8.10396	+	10.7765i	0.906050	+	1.20485i
$81$	4.10204			0.455782
$82$	−12.1254	−	5.52949i	−1.33903	−	0.610630i
$83$	0.711208	+	0.711208i	0.0780653	+	0.0780653i	0.745061	−	0.666996i	$-0.232420\pi$
$83$	0.711208	+	0.711208i	0.0780653	+	0.0780653i	−0.666996	+	0.745061i	$0.732420\pi$
$84$	−0.535739	−	0.0377293i	−0.0584539	−	0.00411660i
$85$	−1.53829	+	1.53829i	−0.166851	+	0.166851i
$86$	1.72840	+	4.62630i	0.186378	+	0.498867i
$87$		−	5.71192i		−	0.612382i
$88$	0.210558	−	0.387113i	0.0224456	−	0.0412664i
$89$			13.8549i			1.46862i	0.678815	+	0.734310i	$0.262494\pi$
$89$			13.8549i			1.46862i	−0.678815	+	0.734310i	$0.737506\pi$
$90$	−5.24079	+	1.95797i	−0.552428	+	0.206388i
$91$	−0.336502	+	0.336502i	−0.0352750	+	0.0352750i
$92$	−1.51007	+	1.31137i	−0.157436	+	0.136720i
$93$	4.53161	+	4.53161i	0.469906	+	0.469906i
$94$	6.00265	−	13.1630i	0.619126	−	1.35766i
$95$	0.827425			0.0848920
$96$	−1.64543	−	7.46582i	−0.167936	−	0.761977i
$97$	7.33230			0.744482			0.372241	−	0.928136i	$-0.378589\pi$
$97$	7.33230			0.744482			0.372241	+	0.928136i	$0.378589\pi$
$98$	4.08432	−	8.95634i	0.412578	−	0.904727i
$99$	0.129289	+	0.129289i	0.0129941	+	0.0129941i
$100$	−9.60853	+	8.34421i	−0.960853	+	0.834421i
$101$	−9.48832	+	9.48832i	−0.944123	+	0.944123i	−0.998519	−	0.0543965i	$-0.982677\pi$
$101$	−9.48832	+	9.48832i	−0.944123	+	0.944123i	0.0543965	+	0.998519i	$0.482677\pi$
$102$	1.15545	−	0.431680i	0.114407	−	0.0427427i
$103$		−	17.8894i		−	1.76270i	−0.472467	−	0.881348i	$-0.656637\pi$
$103$		−	17.8894i		−	1.76270i	0.472467	−	0.881348i	$-0.343363\pi$
$104$	−5.95079	−	3.23674i	−0.583523	−	0.317389i
$105$		−	0.905198i		−	0.0883383i
$106$	−4.29761	−	11.5032i	−0.417421	−	1.11729i
$107$	−0.476373	+	0.476373i	−0.0460527	+	0.0460527i	−0.729758	−	0.683705i	$-0.760367\pi$
$107$	−0.476373	+	0.476373i	−0.0460527	+	0.0460527i	0.683705	+	0.729758i	$0.260367\pi$
$108$	11.2529	+	0.792483i	1.08281	+	0.0762567i
$109$	−13.5122	−	13.5122i	−1.29423	−	1.29423i	−0.932142	−	0.362092i	$-0.882063\pi$
$109$	−13.5122	−	13.5122i	−1.29423	−	1.29423i	−0.362092	−	0.932142i	$-0.617937\pi$
$110$	0.675779	+	0.308172i	0.0644330	+	0.0293831i
$111$	2.93762			0.278826
$112$	−0.786951	−	0.111394i	−0.0743599	−	0.0105258i
$113$	0.977296			0.0919363			0.0459681	−	0.998943i	$-0.485363\pi$
$113$	0.977296			0.0919363			0.0459681	+	0.998943i	$0.485363\pi$
$114$	−0.426848	−	0.194654i	−0.0399780	−	0.0182310i
$115$	−2.38359	−	2.38359i	−0.222271	−	0.222271i
$116$	0.593828	−	8.43210i	0.0551356	−	0.782901i
$117$	1.98747	−	1.98747i	0.183741	−	0.183741i
$118$	−2.23243	−	5.97541i	−0.205512	−	0.550081i
$119$		−	0.128234i		−	0.0117552i
$120$	12.3573	−	3.65043i	1.12807	−	0.333237i
$121$			10.9757i			0.997793i
$122$	0.251094	−	0.0938095i	0.0227330	−	0.00849311i
$123$	−9.00521	+	9.00521i	−0.811973	+	0.811973i
$124$	6.21857	+	7.16081i	0.558444	+	0.643060i
$125$	−3.24877	−	3.24877i	−0.290578	−	0.290578i
$126$	0.136830	−	0.300049i	0.0121898	−	0.0267305i
$127$	−15.5758			−1.38212			−0.691062	−	0.722795i	$-0.742857\pi$
$127$	−15.5758			−1.38212			−0.691062	+	0.722795i	$0.742857\pi$
$128$	−1.65287	−	11.1923i	−0.146094	−	0.989271i
$129$	4.71946			0.415526
$130$	4.73730	−	10.3882i	0.415488	−	0.911108i
$131$	5.80329	+	5.80329i	0.507036	+	0.507036i	0.913615	−	0.406579i	$-0.133279\pi$
$131$	5.80329	+	5.80329i	0.507036	+	0.507036i	−0.406579	+	0.913615i	$0.633279\pi$
$132$	−0.276119	−	0.317957i	−0.0240331	−	0.0276746i
$133$	−0.0344876	+	0.0344876i	−0.00299046	+	0.00299046i
$134$	15.6424	−	5.84403i	1.35130	−	0.504847i
$135$			19.0132i			1.63640i
$136$	1.75059	−	0.517135i	0.150112	−	0.0443439i
$137$			21.8496i			1.86674i	0.358915	+	0.933370i	$0.383147\pi$
$137$			21.8496i			1.86674i	−0.358915	+	0.933370i	$0.616853\pi$
$138$	0.668889	+	1.79038i	0.0569396	+	0.152407i
$139$	−11.8543	+	11.8543i	−1.00547	+	1.00547i	−0.00548673	+	0.999985i	$0.501746\pi$
$139$	−11.8543	+	11.8543i	−1.00547	+	1.00547i	−0.999985	+	0.00548673i	$0.998254\pi$
$140$	0.0941072	−	1.33628i	0.00795351	−	0.112936i
$141$	−9.77579	−	9.77579i	−0.823270	−	0.823270i
$142$	−6.13544	−	2.79792i	−0.514875	−	0.234796i
$143$	−0.373144			−0.0312039
$144$	4.64793	+	0.657922i	0.387328	+	0.0548268i
$145$	14.2471			1.18316
$146$	−7.71718	−	3.51923i	−0.638679	−	0.291254i
$147$	−6.65164	−	6.65164i	−0.548618	−	0.548618i
$148$	4.33660	+	0.305404i	0.356466	+	0.0251040i
$149$	−8.38711	+	8.38711i	−0.687099	+	0.687099i	−0.961590	−	0.274491i	$-0.911491\pi$
$149$	−8.38711	+	8.38711i	−0.687099	+	0.687099i	0.274491	+	0.961590i	$0.411491\pi$
$150$	4.25613	+	11.3921i	0.347511	+	0.930163i
$151$		−	15.0923i		−	1.22819i	−0.789230	−	0.614097i	$-0.789520\pi$
$151$		−	15.0923i		−	1.22819i	0.789230	−	0.614097i	$-0.210480\pi$
$152$	−0.609889	−	0.331730i	−0.0494685	−	0.0269068i
$153$			0.757384i			0.0612308i
$154$	−0.0410118	+	0.0153221i	−0.00330482	+	0.00123469i
$155$	−11.3031	+	11.3031i	−0.907884	+	0.907884i
$156$	−4.88771	+	4.24457i	−0.391330	+	0.339838i
$157$	11.9073	+	11.9073i	0.950307	+	0.950307i	0.998822	−	0.0485157i	$-0.0154491\pi$
$157$	11.9073	+	11.9073i	0.950307	+	0.950307i	−0.0485157	+	0.998822i	$0.515449\pi$
$158$	−0.370017	+	0.811395i	−0.0294370	+	0.0645511i
$159$	−11.7348			−0.930632
$160$	18.6218	−	4.10416i	1.47218	−	0.324462i
$161$	0.198699			0.0156597
$162$	2.40701	−	5.27823i	0.189112	−	0.414697i
$163$	4.28797	+	4.28797i	0.335860	+	0.335860i	0.854807	−	0.518947i	$-0.173676\pi$
$163$	4.28797	+	4.28797i	0.335860	+	0.335860i	−0.518947	+	0.854807i	$0.673676\pi$
$164$	−14.2300	+	12.3575i	−1.11117	+	0.964962i
$165$	0.501883	−	0.501883i	0.0390716	−	0.0390716i
$166$	1.33246	−	0.497811i	0.103419	−	0.0386376i
$167$			6.68260i			0.517115i	0.965996	+	0.258557i	$0.0832471\pi$
$167$			6.68260i			0.517115i	−0.965996	+	0.258557i	$0.916753\pi$
$168$	−0.362911	+	0.667215i	−0.0279992	+	0.0514768i
$169$		−	7.26395i		−	0.558765i
$170$	1.07673	+	2.88202i	0.0825813	+	0.221041i
$171$	0.203693	−	0.203693i	0.0155768	−	0.0155768i
$172$	6.96701	+	0.490650i	0.531230	+	0.0374117i
$173$	−3.18817	−	3.18817i	−0.242392	−	0.242392i	0.575447	−	0.817839i	$-0.304828\pi$
$173$	−3.18817	−	3.18817i	−0.242392	−	0.242392i	−0.817839	+	0.575447i	$0.804828\pi$
$174$	−7.34972	−	3.35166i	−0.557181	−	0.254089i
$175$	1.26432			0.0955734
$176$	−0.374560	−	0.498084i	−0.0282335	−	0.0375445i
$177$	−6.09574			−0.458184
$178$	17.8276	+	8.12984i	1.33624	+	0.609358i
$179$	−4.02322	−	4.02322i	−0.300709	−	0.300709i	0.540582	−	0.841291i	$-0.318204\pi$
$179$	−4.02322	−	4.02322i	−0.300709	−	0.300709i	−0.841291	+	0.540582i	$0.818204\pi$
$180$	−0.555821	+	7.89241i	−0.0414284	+	0.588266i
$181$	−7.39749	+	7.39749i	−0.549851	+	0.549851i	−0.926398	−	0.376546i	$-0.877112\pi$
$181$	−7.39749	+	7.39749i	−0.549851	+	0.549851i	0.376546	+	0.926398i	$0.377112\pi$
$182$	0.235535	+	0.630442i	0.0174590	+	0.0467315i
$183$		−	0.256151i		−	0.0189352i
$184$	0.801301	+	2.71255i	0.0590727	+	0.199972i
$185$			7.32722i			0.538708i
$186$	8.49005	−	3.17190i	0.622520	−	0.232575i
$187$	0.0710989	−	0.0710989i	0.00519926	−	0.00519926i
$188$	−13.4150	−	15.4476i	−0.978388	−	1.12663i
$189$	−0.792483	−	0.792483i	−0.0576447	−	0.0576447i
$190$	0.485519	−	1.06468i	0.0352233	−	0.0772397i
$191$	22.3903			1.62011			0.810054	−	0.586356i	$-0.199438\pi$
$191$	22.3903			1.62011			0.810054	+	0.586356i	$0.199438\pi$
$192$	−10.5720	−	2.26358i	−0.762971	−	0.163360i
$193$	18.2552			1.31404			0.657018	−	0.753875i	$-0.271818\pi$
$193$	18.2552			1.31404			0.657018	+	0.753875i	$0.271818\pi$
$194$	4.30247	−	9.43472i	0.308900	−	0.677374i
$195$	−7.71506	−	7.71506i	−0.552487	−	0.552487i
$196$	−9.12782	−	10.5109i	−0.651987	−	0.750776i
$197$	−8.05327	+	8.05327i	−0.573772	+	0.573772i	−0.933180	−	0.359409i	$-0.882978\pi$
$197$	−8.05327	+	8.05327i	−0.573772	+	0.573772i	0.359409	+	0.933180i	$0.382978\pi$
$198$	0.242226	−	0.0904962i	0.0172142	−	0.00643128i
$199$		−	17.8585i		−	1.26595i	−0.774170	−	0.632977i	$-0.781833\pi$
$199$		−	17.8585i		−	1.26595i	0.774170	−	0.632977i	$-0.218167\pi$
$200$	5.09866	+	17.2599i	0.360529	+	1.22046i
$201$		−	15.9574i		−	1.12555i
$202$	6.64135	+	17.7765i	0.467284	+	1.25075i
$203$	−0.593828	+	0.593828i	−0.0416786	+	0.0416786i
$204$	0.122544	−	1.74007i	0.00857977	−	0.121829i
$205$	−22.4615	−	22.4615i	−1.56878	−	1.56878i
$206$	−23.0189	−	10.4972i	−1.60380	−	0.731376i
$207$	−1.17357			−0.0815686
$208$	−7.65666	+	5.75782i	−0.530894	+	0.399233i
$209$	−0.0382430			−0.00264533
$210$	−1.16475	−	0.531156i	−0.0803754	−	0.0366532i
$211$	2.27372	+	2.27372i	0.156530	+	0.156530i	0.781027	−	0.624497i	$-0.214696\pi$
$211$	2.27372	+	2.27372i	0.156530	+	0.156530i	−0.624497	+	0.781027i	$0.714696\pi$
$212$	−17.3233	−	1.21999i	−1.18977	−	0.0837891i
$213$	−4.55663	+	4.55663i	−0.312215	+	0.312215i
$214$	0.333438	+	0.892494i	0.0227933	+	0.0610096i
$215$			11.7716i			0.802819i
$216$	7.62274	−	14.0145i	0.518662	−	0.953565i
$217$		−	0.942239i		−	0.0639634i
$218$	−25.3154	+	9.45788i	−1.71457	+	0.640568i
$219$	−5.73135	+	5.73135i	−0.387289	+	0.387289i
$220$	0.793072	−	0.688717i	0.0534689	−	0.0464333i
$221$	−1.09295	−	1.09295i	−0.0735197	−	0.0735197i
$222$	1.72375	−	3.77993i	0.115690	−	0.253692i
$223$	−3.29492			−0.220644			−0.110322	−	0.993896i	$-0.535188\pi$
$223$	−3.29492			−0.220644			−0.110322	+	0.993896i	$0.535188\pi$
$224$	−0.605105	+	0.947233i	−0.0404303	+	0.0632897i
$225$	−7.46738			−0.497825
$226$	0.573461	−	1.25752i	0.0381461	−	0.0836490i
$227$	18.7245	+	18.7245i	1.24279	+	1.24279i	0.958838	+	0.283953i	$0.0916459\pi$
$227$	18.7245	+	18.7245i	1.24279	+	1.24279i	0.283953	+	0.958838i	$0.408354\pi$
$228$	−0.500935	+	0.435021i	−0.0331752	+	0.0288099i
$229$	−9.90184	+	9.90184i	−0.654332	+	0.654332i	−0.954033	−	0.299701i	$-0.903113\pi$
$229$	−9.90184	+	9.90184i	−0.654332	+	0.654332i	0.299701	+	0.954033i	$0.403113\pi$
$230$	−4.46569	+	1.66839i	−0.294459	+	0.110011i
$231$			0.0418377i			0.00275272i
$232$	−10.5014	−	5.71192i	−0.689452	−	0.375006i
$233$			16.7592i			1.09793i	0.835846	+	0.548964i	$0.184978\pi$
$233$			16.7592i			1.09793i	−0.835846	+	0.548964i	$0.815022\pi$
$234$	−1.39113	−	3.72355i	−0.0909409	−	0.243416i
$235$	24.3835	−	24.3835i	1.59060	−	1.59060i
$236$	−8.99872	−	0.633732i	−0.585766	−	0.0412524i
$237$	0.602602	+	0.602602i	0.0391432	+	0.0391432i
$238$	−0.165003	−	0.0752457i	−0.0106956	−	0.00487746i
$239$	−16.9820			−1.09847			−0.549237	−	0.835667i	$-0.685082\pi$
$239$	−16.9820			−1.09847			−0.549237	+	0.835667i	$0.685082\pi$
$240$	2.55396	−	18.0426i	0.164858	−	1.16465i
$241$	−23.6419			−1.52291			−0.761455	−	0.648218i	$-0.775514\pi$
$241$	−23.6419			−1.52291			−0.761455	+	0.648218i	$0.775514\pi$
$242$	14.1228	+	6.44038i	0.907851	+	0.414003i
$243$	8.04507	+	8.04507i	0.516092	+	0.516092i
$244$	0.0266302	−	0.378138i	0.00170483	−	0.0242078i
$245$	16.5910	−	16.5910i	1.05996	−	1.05996i
$246$	6.30320	+	16.8714i	0.401878	+	1.07568i
$247$			0.587881i			0.0374060i
$248$	12.8630	−	3.79980i	0.816802	−	0.241288i
$249$		−	1.35929i		−	0.0861418i
$250$	−6.08662	+	2.27398i	−0.384952	+	0.143819i
$251$	10.3035	−	10.3035i	0.650352	−	0.650352i	−0.302726	−	0.953078i	$-0.597897\pi$
$251$	10.3035	−	10.3035i	0.650352	−	0.650352i	0.953078	+	0.302726i	$0.0978966\pi$
$252$	−0.305794	−	0.352128i	−0.0192632	−	0.0221820i
$253$	0.110168	+	0.110168i	0.00692619	+	0.00692619i
$254$	−9.13960	+	20.0419i	−0.573469	+	1.25754i
$255$	2.94006			0.184114
$256$	−15.3714	−	4.44067i	−0.960714	−	0.277542i
$257$	0.589308			0.0367600			0.0183800	−	0.999831i	$-0.494149\pi$
$257$	0.589308			0.0367600			0.0183800	+	0.999831i	$0.494149\pi$
$258$	2.76930	−	6.07270i	0.172409	−	0.378070i
$259$	−0.305404	−	0.305404i	−0.0189769	−	0.0189769i
$260$	−10.5871	−	12.1913i	−0.656585	−	0.756071i
$261$	3.50730	−	3.50730i	0.217096	−	0.217096i
$262$	10.8726	−	4.06202i	0.671710	−	0.250952i
$263$		−	5.79720i		−	0.357471i	−0.983897	−	0.178735i	$-0.942799\pi$
$263$		−	5.79720i		−	0.357471i	0.983897	−	0.178735i	$-0.0572006\pi$
$264$	−0.571149	+	0.168720i	−0.0351518	+	0.0103840i
$265$		−	29.2699i		−	1.79803i
$266$	0.0241396	+	0.0646132i	0.00148010	+	0.00396169i
$267$	13.2401	−	13.2401i	0.810281	−	0.810281i
$268$	1.65898	−	23.5568i	0.101338	−	1.43896i
$269$	5.32110	+	5.32110i	0.324433	+	0.324433i	0.850465	−	0.526032i	$-0.176321\pi$
$269$	5.32110	+	5.32110i	0.324433	+	0.324433i	−0.526032	+	0.850465i	$0.676321\pi$
$270$	24.4649	+	11.1566i	1.48889	+	0.678971i
$271$	−17.3009			−1.05096			−0.525479	−	0.850807i	$-0.676114\pi$
$271$	−17.3009			−1.05096			−0.525479	+	0.850807i	$0.676114\pi$
$272$	0.361805	−	2.55600i	0.0219376	−	0.154980i
$273$	0.643138			0.0389245
$274$	28.1147	+	12.8210i	1.69847	+	0.774545i
$275$	0.700995	+	0.700995i	0.0422716	+	0.0422716i
$276$	2.69623	+	0.189882i	0.162294	+	0.0114295i
$277$	−7.24556	+	7.24556i	−0.435343	+	0.435343i	−0.890441	−	0.455098i	$-0.849604\pi$
$277$	−7.24556	+	7.24556i	−0.435343	+	0.435343i	0.455098	+	0.890441i	$0.349604\pi$
$278$	8.29745	+	22.2093i	0.497648	+	1.33203i
$279$			5.56510i			0.333174i
$280$	−1.66422	−	0.905198i	−0.0994560	−	0.0540959i
$281$		−	4.03701i		−	0.240828i	−0.992724	−	0.120414i	$-0.961578\pi$
$281$		−	4.03701i		−	0.240828i	0.992724	−	0.120414i	$-0.0384221\pi$
$282$	−18.3151	+	6.84257i	−1.09065	+	0.407469i
$283$	10.6603	−	10.6603i	0.633689	−	0.633689i	−0.315303	−	0.948991i	$-0.602106\pi$
$283$	10.6603	−	10.6603i	0.633689	−	0.633689i	0.948991	+	0.315303i	$0.102106\pi$
$284$	−7.20036	+	6.25291i	−0.427262	+	0.371042i
$285$	−0.790707	−	0.790707i	−0.0468374	−	0.0468374i
$286$	−0.218955	+	0.480137i	−0.0129471	+	0.0283911i
$287$	1.87242			0.110525
$288$	3.57390	−	5.59460i	0.210594	−	0.329665i
$289$	−16.5835			−0.975500
$290$	8.35996	−	18.3322i	0.490913	−	1.07650i
$291$	−7.00692	−	7.00692i	−0.410753	−	0.410753i
$292$	−9.05663	+	7.86494i	−0.529999	+	0.460261i
$293$	9.87783	−	9.87783i	0.577069	−	0.577069i	−0.357026	−	0.934095i	$-0.616209\pi$
$293$	9.87783	−	9.87783i	0.577069	−	0.577069i	0.934095	+	0.357026i	$0.116209\pi$
$294$	−12.4620	+	4.65582i	−0.726796	+	0.271533i
$295$		−	15.2045i		−	0.885238i
$296$	2.93762	−	5.40084i	0.170746	−	0.313918i
$297$		−	0.878778i		−	0.0509919i
$298$	5.87057	+	15.7134i	0.340073	+	0.910253i
$299$	1.69353	−	1.69353i	0.0979391	−	0.0979391i
$300$	17.1561	+	1.20821i	0.990506	+	0.0697561i
$301$	−0.490650	−	0.490650i	−0.0282806	−	0.0282806i
$302$	−19.4198	−	8.85592i	−1.11748	−	0.509601i
$303$	18.1345			1.04180
$304$	−0.784721	+	0.590111i	−0.0450068	+	0.0338452i
$305$	0.638911			0.0365839
$306$	0.974552	+	0.444420i	0.0557114	+	0.0254058i
$307$	13.7274	+	13.7274i	0.783464	+	0.783464i	0.980414	−	0.196950i	$-0.0631036\pi$
$307$	13.7274	+	13.7274i	0.783464	+	0.783464i	−0.196950	+	0.980414i	$0.563104\pi$
$308$	−0.00434957	+	0.0617620i	−0.000247840	+	0.00351922i
$309$	−17.0955	+	17.0955i	−0.972532	+	0.972532i
$310$	7.91159	+	21.1765i	0.449348	+	1.20274i
$311$			27.0977i			1.53657i	0.640110	+	0.768284i	$0.278889\pi$
$311$			27.0977i			1.53657i	−0.640110	+	0.768284i	$0.721111\pi$
$312$	2.59361	+	8.77983i	0.146834	+	0.497060i
$313$			8.78013i			0.496282i	0.968724	+	0.248141i	$0.0798196\pi$
$313$			8.78013i			0.496282i	−0.968724	+	0.248141i	$0.920180\pi$
$314$	22.3086	−	8.33453i	1.25894	−	0.470345i
$315$	0.555821	−	0.555821i	0.0313170	−	0.0313170i
$316$	0.826930	+	0.952227i	0.0465185	+	0.0535669i
$317$	−5.92370	−	5.92370i	−0.332708	−	0.332708i	0.520906	−	0.853614i	$-0.325594\pi$
$317$	−5.92370	−	5.92370i	−0.332708	−	0.332708i	−0.853614	+	0.520906i	$0.825594\pi$
$318$	−6.88580	+	15.0996i	−0.386136	+	0.846743i
$319$	−0.658491			−0.0368684
$320$	5.64600	−	26.3695i	0.315621	−	1.47410i
$321$	0.910467			0.0508173
$322$	0.116593	−	0.255673i	0.00649749	−	0.0142481i
$323$	−0.112015	−	0.112015i	−0.00623267	−	0.00623267i
$324$	−5.37929	−	6.19436i	−0.298849	−	0.344131i
$325$	10.7759	−	10.7759i	0.597737	−	0.597737i
$326$	8.03360	−	3.00137i	0.444940	−	0.166231i
$327$			25.8252i			1.42813i
$328$	7.55097	+	25.5614i	0.416933	+	1.41139i
$329$			2.03264i			0.112063i
$330$	−0.351293	−	0.940287i	−0.0193381	−	0.0517611i
$331$	21.1008	−	21.1008i	1.15981	−	1.15981i	0.175289	−	0.984517i	$-0.443914\pi$
$331$	21.1008	−	21.1008i	1.15981	−	1.15981i	0.984517	−	0.175289i	$-0.0560860\pi$
$332$	0.141316	−	2.00663i	0.00775575	−	0.110128i
$333$	1.80379	+	1.80379i	0.0988472	+	0.0988472i
$334$	8.59873	+	3.92124i	0.470501	+	0.214561i
$335$	39.8021			2.17462
$336$	0.645578	+	0.858480i	0.0352192	+	0.0468339i
$337$	−13.0955			−0.713357			−0.356678	−	0.934227i	$-0.616091\pi$
$337$	−13.0955			−0.713357			−0.356678	+	0.934227i	$0.616091\pi$
$338$	−9.34677	−	4.26236i	−0.508397	−	0.231842i
$339$	−0.933927	−	0.933927i	−0.0507239	−	0.0507239i
$340$	4.34020	+	0.305657i	0.235380	+	0.0165766i
$341$	0.522420	−	0.522420i	0.0282907	−	0.0282907i
$342$	−0.142575	−	0.381622i	−0.00770957	−	0.0206358i
$343$			2.77394i			0.149779i
$344$	4.71946	−	8.67679i	0.254456	−	0.467821i
$345$			4.55562i			0.245267i
$346$	−5.97309	+	2.23156i	−0.321116	+	0.119970i
$347$	−18.5247	+	18.5247i	−0.994460	+	0.994460i	−0.999985	−	0.00552468i	$-0.998241\pi$
$347$	−18.5247	+	18.5247i	−0.994460	+	0.994460i	0.00552468	+	0.999985i	$0.498241\pi$
$348$	−8.62539	+	7.49044i	−0.462369	+	0.401530i
$349$	14.6830	+	14.6830i	0.785961	+	0.785961i	0.980829	−	0.194868i	$-0.0624279\pi$
$349$	14.6830	+	14.6830i	0.785961	+	0.785961i	−0.194868	+	0.980829i	$0.562428\pi$
$350$	0.741881	−	1.62684i	0.0396552	−	0.0869583i
$351$	−13.5088			−0.721045
$352$	−0.860687	+	0.189691i	−0.0458748	+	0.0101106i
$353$	1.40458			0.0747581			0.0373790	−	0.999301i	$-0.488099\pi$
$353$	1.40458			0.0747581			0.0373790	+	0.999301i	$0.488099\pi$
$354$	−3.57688	+	7.84360i	−0.190109	+	0.416883i
$355$	−11.3655	−	11.3655i	−0.603217	−	0.603217i
$356$	20.9219	−	18.1689i	1.10886	−	0.962952i
$357$	−0.122544	+	0.122544i	−0.00648570	+	0.00648570i
$358$	−7.53757	+	2.81605i	−0.398373	+	0.148833i
$359$		−	27.5559i		−	1.45435i	−0.686454	−	0.727174i	$-0.740834\pi$
$359$		−	27.5559i		−	1.45435i	0.686454	−	0.727174i	$-0.259166\pi$
$360$	9.82929	+	5.34633i	0.518049	+	0.281776i
$361$		−	18.9397i		−	0.996829i
$362$	5.17788	+	13.8593i	0.272143	+	0.728430i
$363$	10.4887	−	10.4887i	0.550512	−	0.550512i
$364$	0.949420	+	0.0668626i	0.0497631	+	0.00350455i
$365$	−14.2956	−	14.2956i	−0.748264	−	0.748264i
$366$	−0.329598	−	0.150305i	−0.0172284	−	0.00785658i
$367$	2.58686			0.135033			0.0675165	−	0.997718i	$-0.478492\pi$
$367$	2.58686			0.135033			0.0675165	+	0.997718i	$0.478492\pi$
$368$	3.96052	+	0.560617i	0.206456	+	0.0292242i
$369$	−11.0590			−0.575707
$370$	9.42819	+	4.29949i	0.490148	+	0.223520i
$371$	1.21999	+	1.21999i	0.0633386	+	0.0633386i
$372$	0.900426	−	12.7857i	0.0466849	−	0.662905i
$373$	−6.22966	+	6.22966i	−0.322560	+	0.322560i	−0.849748	−	0.527189i	$-0.823246\pi$
$373$	−6.22966	+	6.22966i	−0.322560	+	0.322560i	0.527189	+	0.849748i	$0.323246\pi$
$374$	−0.0497657	−	0.133205i	−0.00257332	−	0.00688787i
$375$			6.20919i			0.320641i
$376$	−27.7487	+	8.19710i	−1.43103	+	0.422733i
$377$			10.1225i			0.521334i
$378$	−1.48473	+	0.554699i	−0.0763664	+	0.0285306i
$379$	1.65615	−	1.65615i	0.0850706	−	0.0850706i	−0.663291	−	0.748362i	$-0.730841\pi$
$379$	1.65615	−	1.65615i	0.0850706	−	0.0850706i	0.748362	+	0.663291i	$0.230841\pi$
$380$	−1.08506	−	1.24947i	−0.0556624	−	0.0640964i
$381$	14.8846	+	14.8846i	0.762559	+	0.762559i
$382$	13.1383	−	28.8104i	0.672213	−	1.47407i
$383$	17.3779			0.887968			0.443984	−	0.896035i	$-0.353565\pi$
$383$	17.3779			0.887968			0.443984	+	0.896035i	$0.353565\pi$
$384$	−9.11613	+	12.2752i	−0.465205	+	0.626414i
$385$	−0.104355			−0.00531840
$386$	10.7118	−	23.4895i	0.545218	−	1.19559i
$387$	2.89790	+	2.89790i	0.147309	+	0.147309i
$388$	−9.61536	−	11.0723i	−0.488146	−	0.562110i
$389$	10.5112	−	10.5112i	0.532941	−	0.532941i	−0.388505	−	0.921446i	$-0.627008\pi$
$389$	10.5112	−	10.5112i	0.532941	−	0.532941i	0.921446	+	0.388505i	$0.127008\pi$
$390$	−14.4543	+	5.40016i	−0.731922	+	0.273448i
$391$			0.645369i			0.0326377i
$392$	−18.8807	+	5.57747i	−0.953621	+	0.281705i
$393$		−	11.0915i		−	0.559494i
$394$	5.63689	+	15.0879i	0.283982	+	0.760120i
$395$	−1.50305	+	1.50305i	−0.0756269	+	0.0756269i
$396$	0.0256897	−	0.364782i	0.00129095	−	0.0183310i
$397$	23.9835	+	23.9835i	1.20370	+	1.20370i	0.973033	+	0.230666i	$0.0740906\pi$
$397$	23.9835	+	23.9835i	1.20370	+	1.20370i	0.230666	+	0.973033i	$0.425909\pi$
$398$	−22.9791	−	10.4791i	−1.15184	−	0.525268i
$399$	0.0659144			0.00329985
$400$	25.2007	+	3.56719i	1.26003	+	0.178360i
$401$	−6.10812			−0.305025			−0.152513	−	0.988302i	$-0.548736\pi$
$401$	−6.10812			−0.305025			−0.152513	+	0.988302i	$0.548736\pi$
$402$	−20.5329	−	9.36354i	−1.02409	−	0.467011i
$403$	−8.03077	−	8.03077i	−0.400041	−	0.400041i
$404$	26.7707	+	1.88532i	1.33189	+	0.0937982i
$405$	9.77757	−	9.77757i	0.485851	−	0.485851i
$406$	0.415650	+	1.11255i	0.0206284	+	0.0552148i
$407$		−	0.338659i		−	0.0167867i
$408$	−2.16709	−	1.17872i	−0.107287	−	0.0583555i
$409$			32.3334i			1.59878i	0.600810	+	0.799392i	$0.294845\pi$
$409$			32.3334i			1.59878i	−0.600810	+	0.799392i	$0.705155\pi$
$410$	−42.0820	+	15.7219i	−2.07828	+	0.776450i
$411$	20.8800	−	20.8800i	1.02994	−	1.02994i
$412$	−27.0143	+	23.4596i	−1.33090	+	1.15577i
$413$	0.633732	+	0.633732i	0.0311839	+	0.0311839i
$414$	−0.688630	+	1.51007i	−0.0338443	+	0.0742158i
$415$	3.39045			0.166431
$416$	2.91598	+	13.2307i	0.142968	+	0.648687i
$417$	22.6566			1.10950
$418$	−0.0224404	+	0.0492086i	−0.00109760	+	0.00240687i
$419$	9.28588	+	9.28588i	0.453645	+	0.453645i	0.896562	−	0.442917i	$-0.146057\pi$
$419$	9.28588	+	9.28588i	0.453645	+	0.453645i	−0.442917	+	0.896562i	$0.646057\pi$
$420$	−1.36691	+	1.18705i	−0.0666985	+	0.0579221i
$421$	−4.53002	+	4.53002i	−0.220779	+	0.220779i	−0.808827	−	0.588047i	$-0.799897\pi$
$421$	−4.53002	+	4.53002i	−0.220779	+	0.220779i	0.588047	+	0.808827i	$0.299897\pi$
$422$	4.25986	−	1.59149i	0.207367	−	0.0774727i
$423$		−	12.0053i		−	0.583717i
$424$	−11.7348	+	21.5746i	−0.569893	+	1.04775i
$425$			4.10646i			0.199193i
$426$	3.18942	+	8.53693i	0.154528	+	0.413616i
$427$	−0.0266302	+	0.0266302i	−0.00128873	+	0.00128873i
$428$	1.34406	+	0.0946550i	0.0649675	+	0.00457532i
$429$	0.356585	+	0.356585i	0.0172161	+	0.0172161i
$430$	15.1470	+	6.90740i	0.730452	+	0.333105i
$431$	24.7717			1.19321			0.596605	−	0.802535i	$-0.296516\pi$
$431$	24.7717			1.19321			0.596605	+	0.802535i	$0.296516\pi$
$432$	−13.5600	−	18.0319i	−0.652407	−	0.867561i
$433$	18.8955			0.908059			0.454030	−	0.890987i	$-0.349986\pi$
$433$	18.8955			0.908059			0.454030	+	0.890987i	$0.349986\pi$
$434$	−1.21241	−	0.552891i	−0.0581976	−	0.0265396i
$435$	−13.6148	−	13.6148i	−0.652782	−	0.652782i
$436$	−2.68486	+	38.1239i	−0.128582	+	1.82580i
$437$	0.173567	−	0.173567i	0.00830285	−	0.00830285i
$438$	4.01166	+	10.7378i	0.191685	+	0.513071i
$439$		−	11.0160i		−	0.525766i	−0.964828	−	0.262883i	$-0.915327\pi$
$439$		−	11.0160i		−	0.525766i	0.964828	−	0.262883i	$-0.0846733\pi$
$440$	−0.420835	−	1.42460i	−0.0200625	−	0.0679152i
$441$		−	8.16864i		−	0.388983i
$442$	−2.04766	+	0.765010i	−0.0973972	+	0.0363878i
$443$	3.85949	−	3.85949i	0.183370	−	0.183370i	−0.609453	−	0.792822i	$-0.708611\pi$
$443$	3.85949	−	3.85949i	0.183370	−	0.183370i	0.792822	+	0.609453i	$0.208611\pi$
$444$	−3.85230	−	4.43601i	−0.182822	−	0.210523i
$445$	33.0244	+	33.0244i	1.56551	+	1.56551i
$446$	−1.93340	+	4.23968i	−0.0915493	+	0.200755i
$447$	16.0298			0.758186
$448$	0.863772	+	1.33443i	0.0408094	+	0.0630459i
$449$	−38.5451			−1.81905			−0.909527	−	0.415644i	$-0.863556\pi$
$449$	−38.5451			−1.81905			−0.909527	+	0.415644i	$0.863556\pi$
$450$	−4.38173	+	9.60853i	−0.206557	+	0.452950i
$451$	1.03815	+	1.03815i	0.0488848	+	0.0488848i
$452$	−1.28160	−	1.47578i	−0.0602812	−	0.0694150i
$453$	−14.4226	+	14.4226i	−0.677631	+	0.677631i
$454$	35.0808	−	13.1063i	1.64642	−	0.615107i
$455$			1.60416i			0.0752043i
$456$	0.265815	+	0.899833i	0.0124479	+	0.0421385i
$457$		−	18.3632i		−	0.858996i	−0.903068	−	0.429498i	$-0.858691\pi$
$457$		−	18.3632i		−	0.858996i	0.903068	−	0.429498i	$-0.141309\pi$
$458$	6.93080	+	18.5513i	0.323855	+	0.866844i
$459$	2.57396	−	2.57396i	0.120142	−	0.120142i
$460$	−0.473617	+	6.72515i	−0.0220825	+	0.313562i
$461$	8.09188	+	8.09188i	0.376876	+	0.376876i	0.869974	−	0.493098i	$-0.164135\pi$
$461$	8.09188	+	8.09188i	0.376876	+	0.376876i	−0.493098	+	0.869974i	$0.664135\pi$
$462$	0.0538340	+	0.0245497i	0.00250458	+	0.00114215i
$463$	−26.6880			−1.24030			−0.620148	−	0.784485i	$-0.712927\pi$
$463$	−26.6880			−1.24030			−0.620148	+	0.784485i	$0.712927\pi$
$464$	−13.5118	+	10.1609i	−0.627269	+	0.471707i
$465$	21.6030			1.00181
$466$	21.5646	+	9.83399i	0.998960	+	0.455551i
$467$	10.7335	+	10.7335i	0.496689	+	0.496689i	0.910406	−	0.413717i	$-0.135770\pi$
$467$	10.7335	+	10.7335i	0.496689	+	0.496689i	−0.413717	+	0.910406i	$0.635770\pi$
$468$	−5.60751	−	0.394908i	−0.259207	−	0.0182546i
$469$	−1.65898	+	1.65898i	−0.0766046	+	0.0766046i
$470$	−17.0672	−	45.6829i	−0.787253	−	2.10720i
$471$		−	22.7578i		−	1.04862i
$472$	−6.09574	+	11.2071i	−0.280579	+	0.515848i
$473$		−	0.544077i		−	0.0250167i
$474$	1.12899	−	0.421792i	0.0518560	−	0.0193735i
$475$	1.10440	−	1.10440i	0.0506735	−	0.0506735i
$476$	−0.193643	+	0.168162i	−0.00887559	+	0.00770771i
$477$	−7.20556	−	7.20556i	−0.329920	−	0.329920i
$478$	−9.96476	+	21.8513i	−0.455777	+	0.999456i
$479$	−15.0208			−0.686317			−0.343159	−	0.939277i	$-0.611497\pi$
$479$	−15.0208			−0.686317			−0.343159	+	0.939277i	$0.611497\pi$
$480$	−21.7175	−	13.8734i	−0.991261	−	0.633231i
$481$	−5.20595			−0.237371
$482$	−13.8727	+	30.4209i	−0.631883	+	1.38563i
$483$	−0.189882	−	0.189882i	−0.00863991	−	0.00863991i
$484$	16.5741	−	14.3932i	0.753368	−	0.654238i
$485$	17.4772	−	17.4772i	0.793598	−	0.793598i
$486$	15.0726	−	5.63115i	0.683706	−	0.255434i
$487$		−	35.4382i		−	1.60586i	−0.596073	−	0.802930i	$-0.703273\pi$
$487$		−	35.4382i		−	1.60586i	0.596073	−	0.802930i	$-0.296727\pi$
$488$	−0.470936	−	0.256151i	−0.0213183	−	0.0115954i
$489$		−	8.19538i		−	0.370608i
$490$	−11.6129	−	31.0835i	−0.524617	−	1.40421i
$491$	−19.3127	+	19.3127i	−0.871572	+	0.871572i	−0.992644	−	0.121072i	$-0.961367\pi$
$491$	−19.3127	+	19.3127i	−0.871572	+	0.871572i	0.121072	+	0.992644i	$0.461367\pi$
$492$	25.4077	+	1.78933i	1.14547	+	0.0806691i
$493$	−1.92874	−	1.92874i	−0.0868659	−	0.0868659i
$494$	0.756446	+	0.344959i	0.0340341	+	0.0155204i
$495$	0.616345			0.0277026
$496$	2.65847	−	18.7809i	0.119369	−	0.843289i
$497$	0.947443			0.0424986
$498$	−1.74905	−	0.797612i	−0.0783769	−	0.0357418i
$499$	−17.7085	−	17.7085i	−0.792743	−	0.792743i	0.189197	−	0.981939i	$-0.439412\pi$
$499$	−17.7085	−	17.7085i	−0.792743	−	0.792743i	−0.981939	+	0.189197i	$0.939412\pi$
$500$	−0.645527	+	9.16619i	−0.0288688	+	0.409925i
$501$	6.38605	−	6.38605i	0.285308	−	0.285308i
$502$	−7.21195	−	19.3038i	−0.321885	−	0.861571i
$503$			36.4638i			1.62584i	0.582375	+	0.812921i	$0.302124\pi$
$503$			36.4638i			1.62584i	−0.582375	+	0.812921i	$0.697876\pi$
$504$	−0.632530	+	0.186853i	−0.0281751	+	0.00832308i
$505$			45.2325i			2.01282i
$506$	0.206401	−	0.0771120i	0.00917566	−	0.00342805i
$507$	−6.94160	+	6.94160i	−0.308287	+	0.308287i
$508$	20.4256	+	23.5205i	0.906238	+	1.04355i
$509$	−15.9196	−	15.9196i	−0.705624	−	0.705624i	0.259988	−	0.965612i	$-0.416281\pi$
$509$	−15.9196	−	15.9196i	−0.705624	−	0.705624i	−0.965612	+	0.259988i	$0.916281\pi$
$510$	1.72518	−	3.78307i	0.0763921	−	0.167517i
$511$	1.19170			0.0527176
$512$	−14.7337	+	17.1732i	−0.651142	+	0.758956i
$513$	−1.38450			−0.0611270
$514$	0.345796	−	0.758282i	0.0152524	−	0.0334464i
$515$	−42.6410	−	42.6410i	−1.87899	−	1.87899i
$516$	−6.18896	−	7.12672i	−0.272454	−	0.313736i
$517$	−1.12699	+	1.12699i	−0.0495649	+	0.0495649i
$518$	−0.572179	+	0.213767i	−0.0251401	+	0.00939240i
$519$			6.09338i			0.267470i
$520$	−21.8993	+	6.46917i	−0.960347	+	0.283692i
$521$		−	33.2196i		−	1.45538i	−0.685909	−	0.727688i	$-0.740595\pi$
$521$		−	33.2196i		−	1.45538i	0.685909	−	0.727688i	$-0.259405\pi$
$522$	−2.45494	−	6.57099i	−0.107450	−	0.287604i
$523$	−27.4509	+	27.4509i	−1.20034	+	1.20034i	−0.226282	+	0.974062i	$0.572657\pi$
$523$	−27.4509	+	27.4509i	−1.20034	+	1.20034i	−0.974062	+	0.226282i	$0.927343\pi$
$524$	1.15311	−	16.3736i	0.0503738	−	0.715286i
$525$	−1.20821	−	1.20821i	−0.0527307	−	0.0527307i
$526$	−7.45946	−	3.40170i	−0.325248	−	0.148321i
$527$	3.06037			0.133312
$528$	−0.118042	+	0.833919i	−0.00513714	+	0.0362917i
$529$	−1.00000			−0.0434783
$530$	−37.6625	−	17.1751i	−1.63596	−	0.746037i
$531$	−3.74298	−	3.74298i	−0.162432	−	0.162432i
$532$	0.0973048	+	0.00685266i	0.00421870	+	0.000297101i
$533$	15.9587	−	15.9587i	0.691250	−	0.691250i
$534$	−9.26741	−	24.8056i	−0.401040	−	1.07344i
$535$			2.27095i			0.0981819i
$536$	−29.3378	−	15.9574i	−1.26720	−	0.689255i
$537$			7.68936i			0.331821i
$538$	9.96917	−	3.72451i	0.429802	−	0.160575i
$539$	−0.766825	+	0.766825i	−0.0330295	+	0.0330295i
$540$	28.7112	−	24.9333i	1.23554	−	1.07296i
$541$	−19.2548	−	19.2548i	−0.827830	−	0.827830i	0.159386	−	0.987216i	$-0.449048\pi$
$541$	−19.2548	−	19.2548i	−0.827830	−	0.827830i	−0.987216	+	0.159386i	$0.949048\pi$
$542$	−10.1519	+	22.2617i	−0.436062	+	0.956222i
$543$	14.1384			0.606738
$544$	−3.07659	−	1.96536i	−0.131908	−	0.0842642i
$545$	−64.4150			−2.75924
$546$	0.377383	−	0.827548i	0.0161505	−	0.0354158i
$547$	13.3090	+	13.3090i	0.569051	+	0.569051i	0.931862	−	0.362812i	$-0.118183\pi$
$547$	13.3090	+	13.3090i	0.569051	+	0.569051i	−0.362812	+	0.931862i	$0.618183\pi$
$548$	32.9945	−	28.6530i	1.40945	−	1.22399i
$549$	0.157285	−	0.157285i	0.00671276	−	0.00671276i
$550$	1.31333	−	0.490662i	0.0560004	−	0.0209219i
$551$			1.03744i			0.0441964i
$552$	1.82643	−	3.35792i	0.0777381	−	0.142922i
$553$		−	0.125297i		−	0.00532816i
$554$	5.07153	+	13.5747i	0.215469	+	0.576733i
$555$	7.00207	−	7.00207i	0.297221	−	0.297221i
$556$	33.4463	+	2.35545i	1.41844	+	0.0998932i
$557$	−15.1073	−	15.1073i	−0.640118	−	0.640118i	0.310467	−	0.950584i	$-0.399515\pi$
$557$	−15.1073	−	15.1073i	−0.640118	−	0.640118i	−0.950584	+	0.310467i	$0.899515\pi$
$558$	7.16081	+	3.26551i	0.303141	+	0.138240i
$559$	−8.36368			−0.353746
$560$	−2.14128	+	1.61025i	−0.0904858	+	0.0680455i
$561$	−0.135888			−0.00573718
$562$	−5.19455	−	2.36885i	−0.219119	−	0.0999239i
$563$	−18.6896	−	18.6896i	−0.787673	−	0.787673i	0.193439	−	0.981112i	$-0.438036\pi$
$563$	−18.6896	−	18.6896i	−0.787673	−	0.787673i	−0.981112	+	0.193439i	$0.938036\pi$
$564$	−1.94244	+	27.5818i	−0.0817915	+	1.16140i
$565$	2.32947	−	2.32947i	0.0980015	−	0.0980015i
$566$	−7.46168	−	19.9722i	−0.313638	−	0.839496i
$567$			0.815071i			0.0342298i
$568$	3.82079	+	12.9341i	0.160317	+	0.542701i
$569$		−	11.4387i		−	0.479536i	−0.970830	−	0.239768i	$-0.922929\pi$
$569$		−	11.4387i		−	0.479536i	0.970830	−	0.239768i	$-0.0770714\pi$
$570$	−1.48140	+	0.553456i	−0.0620492	+	0.0231817i
$571$	−11.6909	+	11.6909i	−0.489249	+	0.489249i	−0.908069	−	0.418820i	$-0.862444\pi$
$571$	−11.6909	+	11.6909i	−0.489249	+	0.489249i	0.418820	+	0.908069i	$0.362444\pi$
$572$	0.489330	+	0.563473i	0.0204599	+	0.0235600i
$573$	−21.3967	−	21.3967i	−0.893861	−	0.893861i
$574$	1.09870	−	2.40931i	0.0458590	−	0.100562i
$575$	−6.36297			−0.265354
$576$	−5.10165	−	7.88148i	−0.212569	−	0.328395i
$577$	−35.4727			−1.47675			−0.738374	−	0.674391i	$-0.764406\pi$
$577$	−35.4727			−1.47675			−0.738374	+	0.674391i	$0.764406\pi$
$578$	−9.73093	+	21.3386i	−0.404753	+	0.887567i
$579$	−17.4451	−	17.4451i	−0.724992	−	0.724992i
$580$	−18.6832	−	21.5141i	−0.775778	−	0.893324i
$581$	−0.141316	+	0.141316i	−0.00586279	+	0.00586279i
$582$	−13.1276	+	4.90450i	−0.544156	+	0.203298i
$583$			1.35283i			0.0560286i
$584$	4.80580	+	16.2685i	0.198865	+	0.673195i
$585$		−	9.47459i		−	0.391726i
$586$	−6.91399	−	18.5063i	−0.285614	−	0.764488i
$587$	9.32268	−	9.32268i	0.384788	−	0.384788i	−0.488036	−	0.872824i	$-0.662286\pi$
$587$	9.32268	−	9.32268i	0.384788	−	0.384788i	0.872824	+	0.488036i	$0.162286\pi$
$588$	−1.32167	+	18.7672i	−0.0545049	+	0.773946i
$589$	−0.823063	−	0.823063i	−0.0339137	−	0.0339137i
$590$	−19.5641	−	8.92172i	−0.805441	−	0.367302i
$591$	15.3918			0.633134
$592$	−5.22570	−	6.94906i	−0.214775	−	0.285605i
$593$	8.32328			0.341796			0.170898	−	0.985289i	$-0.445333\pi$
$593$	8.32328			0.341796			0.170898	+	0.985289i	$0.445333\pi$
$594$	−1.13075	−	0.515652i	−0.0463954	−	0.0211575i
$595$	−0.305657	−	0.305657i	−0.0125307	−	0.0125307i
$596$	23.6637	+	1.66651i	0.969304	+	0.0682630i
$597$	−17.0660	+	17.0660i	−0.698464	+	0.698464i
$598$	−1.18538	−	3.17285i	−0.0484740	−	0.129747i
$599$		−	40.0370i		−	1.63587i	−0.575313	−	0.817933i	$-0.695120\pi$
$599$		−	40.0370i		−	1.63587i	0.575313	−	0.817933i	$-0.304880\pi$
$600$	11.6215	−	21.3663i	0.474448	−	0.872277i
$601$			9.90326i			0.403963i	0.979389	+	0.201981i	$0.0647380\pi$
$601$			9.90326i			0.403963i	−0.979389	+	0.201981i	$0.935262\pi$
$602$	−0.919241	+	0.343431i	−0.0374655	+	0.0139972i
$603$	9.79835	−	9.79835i	0.399020	−	0.399020i
$604$	−22.7904	+	19.7916i	−0.927330	+	0.805309i
$605$	26.1616	+	26.1616i	1.06362	+	1.06362i
$606$	10.6410	−	23.3343i	0.432263	−	0.947891i
$607$	−33.7530			−1.36999			−0.684995	−	0.728548i	$-0.740196\pi$
$607$	−33.7530			−1.36999			−0.684995	+	0.728548i	$0.740196\pi$
$608$	0.298855	+	1.35599i	0.0121202	+	0.0549929i
$609$	1.13495			0.0459906
$610$	0.374902	−	0.822108i	0.0151794	−	0.0332862i
$611$	17.3243	+	17.3243i	0.700867	+	0.700867i
$612$	1.14370	−	0.993210i	0.0462314	−	0.0401481i
$613$	12.9941	−	12.9941i	0.524827	−	0.524827i	−0.394198	−	0.919026i	$-0.628978\pi$
$613$	12.9941	−	12.9941i	0.524827	−	0.524827i	0.919026	+	0.394198i	$0.128978\pi$
$614$	25.7185	−	9.60850i	1.03791	−	0.387767i
$615$			42.9294i			1.73108i
$616$	0.0769190	+	0.0418377i	0.00309916	+	0.00168569i
$617$			42.9224i			1.72799i	0.503501	+	0.863995i	$0.332045\pi$
$617$			42.9224i			1.72799i	−0.503501	+	0.863995i	$0.667955\pi$
$618$	11.9660	+	32.0288i	0.481345	+	1.28839i
$619$	4.50065	−	4.50065i	0.180896	−	0.180896i	−0.610850	−	0.791746i	$-0.709172\pi$
$619$	4.50065	−	4.50065i	0.180896	−	0.180896i	0.791746	+	0.610850i	$0.209172\pi$
$620$	31.8909	+	2.24591i	1.28077	+	0.0901979i
$621$	3.98836	+	3.98836i	0.160047	+	0.160047i
$622$	34.8675	+	15.9005i	1.39806	+	0.637550i
$623$	−2.75296			−0.110295
$624$	12.8192	+	1.81458i	0.513178	+	0.0726412i
$625$	16.3274			0.653097
$626$	11.2977	+	5.15203i	0.451546	+	0.205917i
$627$	0.0365460	+	0.0365460i	0.00145950	+	0.00145950i
$628$	2.36597	−	33.5957i	0.0944125	−	1.34062i
$629$	0.991942	−	0.991942i	0.0395513	−	0.0395513i
$630$	−0.389047	−	1.04134i	−0.0155000	−	0.0414880i
$631$			21.5372i			0.857383i	0.903451	+	0.428691i	$0.141025\pi$
$631$			21.5372i			0.857383i	−0.903451	+	0.428691i	$0.858975\pi$
$632$	1.71049	−	0.505288i	0.0680397	−	0.0200993i
$633$		−	4.34565i		−	0.172724i
$634$	−11.0982	+	4.14630i	−0.440764	+	0.164670i
$635$	−37.1262	+	37.1262i	−1.47331	+	1.47331i
$636$	15.3887	+	17.7204i	0.610201	+	0.702659i
$637$	11.7878	+	11.7878i	0.467050	+	0.467050i
$638$	−0.386392	+	0.847303i	−0.0152974	+	0.0335450i
$639$	−5.59584			−0.221368
$640$	−30.6176	−	22.7381i	−1.21027	−	0.898803i
$641$	19.9600			0.788373			0.394187	−	0.919030i	$-0.371026\pi$
$641$	19.9600			0.788373			0.394187	+	0.919030i	$0.371026\pi$
$642$	0.534247	−	1.17153i	0.0210851	−	0.0462366i
$643$	11.5859	+	11.5859i	0.456905	+	0.456905i	0.897638	−	0.440733i	$-0.145282\pi$
$643$	11.5859	+	11.5859i	0.456905	+	0.456905i	−0.440733	+	0.897638i	$0.645282\pi$
$644$	−0.260568	−	0.300049i	−0.0102678	−	0.0118236i
$645$	11.2493	−	11.2493i	0.442939	−	0.442939i
$646$	−0.209862	+	0.0784049i	−0.00825690	+	0.00308480i
$647$			21.3677i			0.840053i	0.907512	+	0.420026i	$0.137979\pi$
$647$			21.3677i			0.840053i	−0.907512	+	0.420026i	$0.862021\pi$
$648$	−11.1270	+	3.28697i	−0.437109	+	0.129124i
$649$			0.702740i			0.0275850i
$650$	−7.54257	−	20.1888i	−0.295844	−	0.791868i
$651$	−0.900426	+	0.900426i	−0.0352905	+	0.0352905i
$652$	0.852017	−	12.0983i	0.0333675	−	0.473804i
$653$	−35.5745	−	35.5745i	−1.39214	−	1.39214i	−0.820522	−	0.571615i	$-0.806317\pi$
$653$	−35.5745	−	35.5745i	−1.39214	−	1.39214i	−0.571615	−	0.820522i	$-0.693683\pi$
$654$	33.2301	+	15.1538i	1.29940	+	0.592560i
$655$	27.6653			1.08097
$656$	37.3215	+	5.28292i	1.45716	+	0.206263i
$657$	−7.03847			−0.274597
$658$	2.61547	+	1.19272i	0.101962	+	0.0464971i
$659$	23.0602	+	23.0602i	0.898296	+	0.898296i	0.995285	−	0.0969891i	$-0.0309212\pi$
$659$	23.0602	+	23.0602i	0.898296	+	0.898296i	−0.0969891	+	0.995285i	$0.530921\pi$
$660$	−1.41603	−	0.0997237i	−0.0551190	−	0.00388174i
$661$	−26.3968	+	26.3968i	−1.02671	+	1.02671i	−0.0270814	+	0.999633i	$0.508621\pi$
$661$	−26.3968	+	26.3968i	−1.02671	+	1.02671i	−0.999633	+	0.0270814i	$0.991379\pi$
$662$	−14.7695	−	39.5328i	−0.574034	−	1.53648i
$663$			2.08889i			0.0811259i
$664$	−2.49908	−	1.35929i	−0.0969831	−	0.0527509i
$665$			0.164409i			0.00637549i
$666$	3.37944	−	1.26257i	0.130950	−	0.0489234i
$667$	2.98858	−	2.98858i	0.115718	−	0.115718i
$668$	10.0912	−	8.76336i	0.390440	−	0.339064i
$669$	3.14870	+	3.14870i	0.121736	+	0.121736i
$670$	23.3552	−	51.2147i	0.902291	−	1.97860i
$671$	−0.0295300			−0.00113999
$672$	1.48345	−	0.326946i	0.0572254	−	0.0126122i
$673$	−26.3257			−1.01478			−0.507391	−	0.861716i	$-0.669390\pi$
$673$	−26.3257			−1.01478			−0.507391	+	0.861716i	$0.669390\pi$
$674$	−7.68422	+	16.8504i	−0.295985	+	0.649054i
$675$	25.3778	+	25.3778i	0.976793	+	0.976793i
$676$	−10.9691	+	9.52572i	−0.421887	+	0.366374i
$677$	34.7259	−	34.7259i	1.33462	−	1.33462i	0.433445	−	0.901180i	$-0.357298\pi$
$677$	34.7259	−	34.7259i	1.33462	−	1.33462i	0.901180	−	0.433445i	$-0.142702\pi$
$678$	−1.74973	+	0.653703i	−0.0671979	+	0.0251053i
$679$			1.45692i			0.0559115i
$680$	2.94006	−	5.40533i	0.112746	−	0.207285i
$681$		−	35.7872i		−	1.37137i
$682$	−0.365669	−	0.978764i	−0.0140022	−	0.0374788i
$683$	−21.2863	+	21.2863i	−0.814498	+	0.814498i	−0.985305	−	0.170807i	$-0.945363\pi$
$683$	−21.2863	+	21.2863i	−0.814498	+	0.814498i	0.170807	+	0.985305i	$0.445363\pi$
$684$	−0.574707	−	0.0404736i	−0.0219745	−	0.00154755i
$685$	52.0805	+	52.0805i	1.98989	+	1.98989i
$686$	3.56933	+	1.62770i	0.136278	+	0.0621460i
$687$	18.9249			0.722029
$688$	−8.39541	−	11.1641i	−0.320072	−	0.425627i
$689$	20.7961			0.792267
$690$	5.86188	+	2.67317i	0.223158	+	0.101766i
$691$	−16.7977	−	16.7977i	−0.639016	−	0.639016i	0.311296	−	0.950313i	$-0.399237\pi$
$691$	−16.7977	−	16.7977i	−0.639016	−	0.639016i	−0.950313	+	0.311296i	$0.899237\pi$
$692$	−0.633487	+	8.99523i	−0.0240815	+	0.341947i
$693$	−0.0256897	+	0.0256897i	−0.000975870	+	0.000975870i
$694$	12.9664	+	34.7064i	0.492198	+	1.31744i
$695$			56.5117i			2.14361i
$696$	4.57696	+	15.4938i	0.173489	+	0.587293i
$697$			6.08156i			0.230356i
$698$	27.5088	−	10.2774i	1.04122	−	0.389004i
$699$	16.0154	−	16.0154i	0.605760	−	0.605760i
$700$	−1.65799	−	1.90921i	−0.0626660	−	0.0721612i
$701$	9.14173	+	9.14173i	0.345279	+	0.345279i	0.858347	−	0.513069i	$-0.171491\pi$
$701$	9.14173	+	9.14173i	0.345279	+	0.345279i	−0.513069	+	0.858347i	$0.671491\pi$
$702$	−7.92673	+	17.3822i	−0.299175	+	0.656049i
$703$	−0.533551			−0.0201233
$704$	−0.260954	+	1.21878i	−0.00983509	+	0.0459346i
$705$	−46.6029			−1.75517
$706$	0.824182	−	1.80732i	0.0310185	−	0.0680193i
$707$	−1.88532	−	1.88532i	−0.0709048	−	0.0709048i
$708$	7.99378	+	9.20499i	0.300424	+	0.345945i
$709$	6.26542	−	6.26542i	0.235303	−	0.235303i	−0.579599	−	0.814902i	$-0.696791\pi$
$709$	6.26542	−	6.26542i	0.235303	−	0.235303i	0.814902	+	0.579599i	$0.196791\pi$
$710$	−21.2934	+	7.95528i	−0.799129	+	0.298556i
$711$			0.740034i			0.0277534i
$712$	−11.1020	−	37.5822i	−0.416064	−	1.40845i
$713$			4.74204i			0.177591i
$714$	0.0857745	+	0.229588i	0.00321003	+	0.00859210i
$715$	−0.889421	+	0.889421i	−0.0332625	+	0.0332625i
$716$	−0.799410	+	11.3513i	−0.0298753	+	0.424217i
$717$	16.2284	+	16.2284i	0.606061	+	0.606061i
$718$	−35.4572	−	16.1694i	−1.32325	−	0.603436i
$719$	−14.6826			−0.547569			−0.273784	−	0.961791i	$-0.588275\pi$
$719$	−14.6826			−0.547569			−0.273784	+	0.961791i	$0.588275\pi$
$720$	12.6470	−	9.51054i	0.471325	−	0.354437i
$721$	3.55461			0.132381
$722$	−24.3704	−	11.1135i	−0.906973	−	0.413603i
$723$	22.5928	+	22.5928i	0.840234	+	0.840234i
$724$	20.8716	+	1.46988i	0.775686	+	0.0546275i
$725$	19.0163	−	19.0163i	0.706246	−	0.706246i
$726$	−7.34155	−	19.6507i	−0.272470	−	0.729306i
$727$			38.0962i			1.41291i	0.707757	+	0.706456i	$0.249707\pi$
$727$			38.0962i			1.41291i	−0.707757	+	0.706456i	$0.750293\pi$
$728$	0.643138	−	1.18242i	0.0238363	−	0.0438233i
$729$		−	27.6822i		−	1.02527i
$730$	−26.7830	+	10.0062i	−0.991282	+	0.370345i
$731$	1.59362	−	1.59362i	0.0589420	−	0.0589420i
$732$	−0.386806	+	0.335909i	−0.0142968	+	0.0124155i
$733$	−9.11245	−	9.11245i	−0.336576	−	0.336576i	0.518501	−	0.855077i	$-0.326490\pi$
$733$	−9.11245	−	9.11245i	−0.336576	−	0.336576i	−0.855077	+	0.518501i	$0.826490\pi$
$734$	1.51793	−	3.32860i	0.0560277	−	0.122861i
$735$	−31.7095			−1.16962
$736$	3.04533	−	4.76717i	0.112252	−	0.175720i
$737$	−1.83963			−0.0677636
$738$	−6.48923	+	14.2300i	−0.238872	+	0.523812i
$739$	−24.5125	−	24.5125i	−0.901708	−	0.901708i	0.0938755	−	0.995584i	$-0.470074\pi$
$739$	−24.5125	−	24.5125i	−0.901708	−	0.901708i	−0.995584	+	0.0938755i	$0.970074\pi$
$740$	11.0646	−	9.60870i	0.406743	−	0.353223i
$741$	0.561793	−	0.561793i	0.0206380	−	0.0206380i
$742$	2.28567	−	0.853931i	0.0839095	−	0.0313488i
$743$			35.3509i			1.29690i	0.761258	+	0.648449i	$0.224582\pi$
$743$			35.3509i			1.29690i	−0.761258	+	0.648449i	$0.775418\pi$
$744$	−15.9234	−	8.66102i	−0.583780	−	0.317528i
$745$			39.9828i			1.46486i
$746$	4.36045	+	11.6714i	0.159648	+	0.427320i
$747$	0.834651	−	0.834651i	0.0305383	−	0.0305383i
$748$	−0.200601	−	0.0141273i	−0.00733470	−	0.000516545i
$749$	−0.0946550	−	0.0946550i	−0.00345862	−	0.00345862i
$750$	7.98958	+	3.64345i	0.291738	+	0.133040i
$751$	−47.2423			−1.72390			−0.861948	−	0.506997i	$-0.830755\pi$
$751$	−47.2423			−1.72390			−0.861948	+	0.506997i	$0.830755\pi$
$752$	−5.73497	+	40.5151i	−0.209133	+	1.47743i
$753$	−19.6926			−0.717637
$754$	13.0249	+	5.93970i	0.474340	+	0.216311i
$755$	−35.9738	−	35.9738i	−1.30922	−	1.30922i
$756$	−0.157466	+	2.23594i	−0.00572697	+	0.0813205i
$757$	−3.51361	+	3.51361i	−0.127704	+	0.127704i	−0.768070	−	0.640366i	$-0.778783\pi$
$757$	−3.51361	+	3.51361i	−0.127704	+	0.127704i	0.640366	+	0.768070i	$0.278783\pi$
$758$	−1.15922	−	3.10282i	−0.0421048	−	0.112700i
$759$		−	0.210558i		−	0.00764277i
$760$	−2.24443	+	0.663016i	−0.0814140	+	0.0240501i
$761$		−	15.6852i		−	0.568587i	−0.958737	−	0.284294i	$-0.908241\pi$
$761$		−	15.6852i		−	0.568587i	0.958737	−	0.284294i	$-0.0917591\pi$
$762$	27.8865	−	10.4185i	1.01022	−	0.377421i
$763$	2.68486	−	2.68486i	0.0971986	−	0.0971986i
$764$	−29.3620	−	33.8109i	−1.06228	−	1.22324i
$765$	1.80529	+	1.80529i	0.0652704	+	0.0652704i
$766$	10.1971	−	22.3607i	0.368435	−	0.807925i
$767$	10.8027			0.390062
$768$	10.4457	+	18.9329i	0.376926	+	0.683182i
$769$	36.5815			1.31916			0.659582	−	0.751632i	$-0.270733\pi$
$769$	36.5815			1.31916			0.659582	+	0.751632i	$0.270733\pi$

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:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.586784 - 1.28673i) q^{2} +(-0.955624 - 0.955624i) q^{3} +(-1.31137 - 1.51007i) q^{4} +(2.38359 - 2.38359i) q^{5} +(-1.79038 + 0.668889i) q^{6} +0.198699i q^{7} +(-2.71255 + 0.801301i) q^{8} -1.17357i q^{9} +(-1.66839 - 4.46569i) q^{10} +(-0.110168 + 0.110168i) q^{11} +(-0.189882 + 2.69623i) q^{12} +(1.69353 + 1.69353i) q^{13} +(0.255673 + 0.116593i) q^{14} -4.55562 q^{15} +(-0.560617 + 3.96052i) q^{16} -0.645369 q^{17} +(-1.51007 - 0.688630i) q^{18} +(0.173567 + 0.173567i) q^{19} +(-6.72515 - 0.473617i) q^{20} +(0.189882 - 0.189882i) q^{21} +(0.0771120 + 0.206401i) q^{22} -1.00000i q^{23} +(3.35792 + 1.82643i) q^{24} -6.36297i q^{25} +(3.17285 - 1.18538i) q^{26} +(-3.98836 + 3.98836i) q^{27} +(0.300049 - 0.260568i) q^{28} +(2.98858 + 2.98858i) q^{29} +(-2.67317 + 5.86188i) q^{30} -4.74204 q^{31} +(4.76717 + 3.04533i) q^{32} +0.210558 q^{33} +(-0.378692 + 0.830418i) q^{34} +(0.473617 + 0.473617i) q^{35} +(-1.77217 + 1.53898i) q^{36} +(-1.53702 + 1.53702i) q^{37} +(0.325181 - 0.121488i) q^{38} -3.23674i q^{39} +(-4.55562 + 8.37556i) q^{40} -9.42339i q^{41} +(-0.132908 - 0.355746i) q^{42} +(-2.46931 + 2.46931i) q^{43} +(0.310832 + 0.0218902i) q^{44} +(-2.79730 - 2.79730i) q^{45} +(-1.28673 - 0.586784i) q^{46} +10.2297 q^{47} +(4.32050 - 3.24903i) q^{48} +6.96052 q^{49} +(-8.18746 - 3.73369i) q^{50} +(0.616730 + 0.616730i) q^{51} +(0.336502 - 4.77818i) q^{52} +(6.13987 - 6.13987i) q^{53} +(2.79165 + 7.47226i) q^{54} +0.525189i q^{55} +(-0.159218 - 0.538981i) q^{56} -0.331730i q^{57} +(5.59916 - 2.09186i) q^{58} +(3.18941 - 3.18941i) q^{59} +(5.97411 + 6.87931i) q^{60} +(0.134023 + 0.134023i) q^{61} +(-2.78255 + 6.10175i) q^{62} +0.233187 q^{63} +(6.71583 - 4.34713i) q^{64} +8.07333 q^{65} +(0.123552 - 0.270932i) q^{66} +(8.34921 + 8.34921i) q^{67} +(0.846317 + 0.974552i) q^{68} +(-0.955624 + 0.955624i) q^{69} +(0.887329 - 0.331508i) q^{70} -4.76823i q^{71} +(0.940380 + 3.18336i) q^{72} -5.99750i q^{73} +(1.07584 + 2.87963i) q^{74} +(-6.08061 + 6.08061i) q^{75} +(0.0344876 - 0.489709i) q^{76} +(-0.0218902 - 0.0218902i) q^{77} +(-4.16483 - 1.89927i) q^{78} -0.630585 q^{79} +(8.10396 + 10.7765i) q^{80} +4.10204 q^{81} +(-12.1254 - 5.52949i) q^{82} +(0.711208 + 0.711208i) q^{83} +(-0.535739 - 0.0377293i) q^{84} +(-1.53829 + 1.53829i) q^{85} +(1.72840 + 4.62630i) q^{86} -5.71192i q^{87} +(0.210558 - 0.387113i) q^{88} +13.8549i q^{89} +(-5.24079 + 1.95797i) q^{90} +(-0.336502 + 0.336502i) q^{91} +(-1.51007 + 1.31137i) q^{92} +(4.53161 + 4.53161i) q^{93} +(6.00265 - 13.1630i) q^{94} +0.827425 q^{95} +(-1.64543 - 7.46582i) q^{96} +7.33230 q^{97} +(4.08432 - 8.95634i) q^{98} +(0.129289 + 0.129289i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 2 q^{3} - 4 q^{5} - 4 q^{8} - 6 q^{10} - 4 q^{11} - 8 q^{12} + 18 q^{13} - 2 q^{14} + 8 q^{16} - 8 q^{17} - 4 q^{18} - 8 q^{19} - 32 q^{20} + 8 q^{21} - 34 q^{22} + 12 q^{24} - 14 q^{26}+ \cdots + 36 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^5 - 4 * q^8 - 6 * q^10 - 4 * q^11 - 8 * q^12 + 18 * q^13 - 2 * q^14 + 8 * q^16 - 8 * q^17 - 4 * q^18 - 8 * q^19 - 32 * q^20 + 8 * q^21 - 34 * q^22 + 12 * q^24 - 14 * q^26 + 14 * q^27 + 12 * q^28 + 2 * q^29 - 30 * q^30 + 20 * q^31 - 8 * q^32 - 36 * q^33 + 10 * q^34 + 4 * q^35 + 4 * q^36 - 4 * q^37 + 24 * q^38 - 14 * q^42 + 20 * q^43 + 4 * q^44 - 20 * q^45 - 2 * q^46 - 16 * q^47 - 12 * q^48 + 52 * q^49 + 6 * q^50 - 4 * q^51 - 16 * q^53 + 16 * q^54 + 28 * q^56 + 14 * q^58 + 8 * q^59 + 48 * q^60 + 12 * q^61 - 44 * q^62 - 4 * q^63 + 24 * q^64 - 52 * q^65 + 34 * q^66 - 4 * q^67 - 16 * q^68 + 2 * q^69 + 28 * q^70 + 8 * q^72 - 26 * q^74 - 46 * q^75 - 8 * q^76 - 12 * q^77 - 44 * q^78 - 4 * q^79 + 4 * q^80 + 48 * q^81 - 6 * q^82 + 28 * q^83 + 12 * q^84 - 8 * q^85 + 44 * q^86 - 36 * q^88 + 4 * q^90 - 4 * q^92 - 14 * q^93 + 48 * q^95 + 32 * q^96 + 36 * q^97 - 2 * q^98 + 36 * q^99

Introduction

L-functions

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