LMFDB - Embedded newform 671.2.f.a.538.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(538,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("671.538");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.f (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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$60$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			538.10
Character	$\chi$	$=$	671.538
Dual form			671.2.f.a.560.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49884 - 1.49884i) q^{2} +0.414070i q^{3} +2.49306i q^{4} -2.38044i q^{5} +(0.620625 - 0.620625i) q^{6} +(0.200846 + 0.200846i) q^{7} +(0.739017 - 0.739017i) q^{8} +2.82855 q^{9} +O(q^{10})$	\(q+(-1.49884 - 1.49884i) q^{2} +0.414070i q^{3} +2.49306i q^{4} -2.38044i q^{5} +(0.620625 - 0.620625i) q^{6} +(0.200846 + 0.200846i) q^{7} +(0.739017 - 0.739017i) q^{8} +2.82855 q^{9} +(-3.56790 + 3.56790i) q^{10} +(2.58621 + 2.07642i) q^{11} -1.03230 q^{12} -2.91981i q^{13} -0.602073i q^{14} +0.985666 q^{15} +2.77078 q^{16} +(-3.33333 + 3.33333i) q^{17} +(-4.23955 - 4.23955i) q^{18} +6.98848 q^{19} +5.93457 q^{20} +(-0.0831643 + 0.0831643i) q^{21} +(-0.764090 - 6.98855i) q^{22} +(-0.146140 + 0.146140i) q^{23} +(0.306004 + 0.306004i) q^{24} -0.666476 q^{25} +(-4.37634 + 4.37634i) q^{26} +2.41342i q^{27} +(-0.500721 + 0.500721i) q^{28} +(0.0386866 - 0.0386866i) q^{29} +(-1.47736 - 1.47736i) q^{30} +(2.85647 + 2.85647i) q^{31} +(-5.63099 - 5.63099i) q^{32} +(-0.859783 + 1.07087i) q^{33} +9.99227 q^{34} +(0.478101 - 0.478101i) q^{35} +7.05173i q^{36} +(-4.12535 - 4.12535i) q^{37} +(-10.4746 - 10.4746i) q^{38} +1.20901 q^{39} +(-1.75918 - 1.75918i) q^{40} +0.823665 q^{41} +0.249300 q^{42} +(6.18141 - 6.18141i) q^{43} +(-5.17664 + 6.44757i) q^{44} -6.73317i q^{45} +0.438083 q^{46} +5.60710 q^{47} +1.14729i q^{48} -6.91932i q^{49} +(0.998942 + 0.998942i) q^{50} +(-1.38023 - 1.38023i) q^{51} +7.27927 q^{52} +(-2.78659 + 2.78659i) q^{53} +(3.61734 - 3.61734i) q^{54} +(4.94279 - 6.15630i) q^{55} +0.296857 q^{56} +2.89372i q^{57} -0.115970 q^{58} +(-9.55942 - 9.55942i) q^{59} +2.45732i q^{60} +(7.77469 - 0.744480i) q^{61} -8.56279i q^{62} +(0.568102 + 0.568102i) q^{63} +11.3384i q^{64} -6.95043 q^{65} +(2.89375 - 0.316386i) q^{66} +(-9.13584 - 9.13584i) q^{67} +(-8.31018 - 8.31018i) q^{68} +(-0.0605123 - 0.0605123i) q^{69} -1.43320 q^{70} +(-0.137784 - 0.137784i) q^{71} +(2.09034 - 2.09034i) q^{72} +9.40043i q^{73} +12.3665i q^{74} -0.275967i q^{75} +17.4227i q^{76} +(0.102389 + 0.936471i) q^{77} +(-1.81211 - 1.81211i) q^{78} +(-2.16657 - 2.16657i) q^{79} -6.59566i q^{80} +7.48631 q^{81} +(-1.23454 - 1.23454i) q^{82} -4.49513i q^{83} +(-0.207333 - 0.207333i) q^{84} +(7.93477 + 7.93477i) q^{85} -18.5299 q^{86} +(0.0160190 + 0.0160190i) q^{87} +(3.44576 - 0.376741i) q^{88} +(-4.18685 - 4.18685i) q^{89} +(-10.0920 + 10.0920i) q^{90} +(0.586433 - 0.586433i) q^{91} +(-0.364336 - 0.364336i) q^{92} +(-1.18278 + 1.18278i) q^{93} +(-8.40416 - 8.40416i) q^{94} -16.6356i q^{95} +(2.33162 - 2.33162i) q^{96} +5.62809i q^{97} +(-10.3710 + 10.3710i) q^{98} +(7.31521 + 5.87325i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 120 q^{9}+O(q^{10}) $ 120 * q - 120 * q^9	$ 120 q - 120 q^{9} - 4 q^{11} + 16 q^{12} + 16 q^{15} - 148 q^{16} + 56 q^{20} - 4 q^{22} - 4 q^{23} - 104 q^{25} + 40 q^{26} - 2 q^{33} - 8 q^{34} - 12 q^{37} + 20 q^{38} + 16 q^{42} - 10 q^{44} - 4 q^{53} + 50 q^{55} - 24 q^{56} + 64 q^{58} - 56 q^{67} + 68 q^{69} + 144 q^{70} - 12 q^{71} - 64 q^{77} + 84 q^{78} + 72 q^{81} + 40 q^{82} - 80 q^{86} + 4 q^{89} - 4 q^{91} + 4 q^{92} + 64 q^{93} + 24 q^{99}+O(q^{100}) $ 120 * q - 120 * q^9 - 4 * q^11 + 16 * q^12 + 16 * q^15 - 148 * q^16 + 56 * q^20 - 4 * q^22 - 4 * q^23 - 104 * q^25 + 40 * q^26 - 2 * q^33 - 8 * q^34 - 12 * q^37 + 20 * q^38 + 16 * q^42 - 10 * q^44 - 4 * q^53 + 50 * q^55 - 24 * q^56 + 64 * q^58 - 56 * q^67 + 68 * q^69 + 144 * q^70 - 12 * q^71 - 64 * q^77 + 84 * q^78 + 72 * q^81 + 40 * q^82 - 80 * q^86 + 4 * q^89 - 4 * q^91 + 4 * q^92 + 64 * q^93 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/671\mathbb{Z}\right)^\times$.

$n$	$123$	$551$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.49884	−	1.49884i	−1.05984	−	1.05984i	−0.998092	−	0.0617501i	$-0.980332\pi$
$2$	−1.49884	−	1.49884i	−1.05984	−	1.05984i	−0.0617501	−	0.998092i	$-0.519668\pi$
$3$			0.414070i			0.239063i	0.992830	+	0.119532i	$0.0381393\pi$
$3$			0.414070i			0.239063i	−0.992830	+	0.119532i	$0.961861\pi$
$4$			2.49306i			1.24653i
$5$		−	2.38044i		−	1.06456i	−0.846567	−	0.532282i	$-0.821335\pi$
$5$		−	2.38044i		−	1.06456i	0.846567	−	0.532282i	$-0.178665\pi$
$6$	0.620625	−	0.620625i	0.253369	−	0.253369i
$7$	0.200846	+	0.200846i	0.0759127	+	0.0759127i	0.744044	−	0.668131i	$-0.232905\pi$
$7$	0.200846	+	0.200846i	0.0759127	+	0.0759127i	−0.668131	+	0.744044i	$0.732905\pi$
$8$	0.739017	−	0.739017i	0.261282	−	0.261282i
$9$	2.82855			0.942849
$10$	−3.56790	+	3.56790i	−1.12827	+	1.12827i
$11$	2.58621	+	2.07642i	0.779771	+	0.626065i
$11$	2.58621	+	2.07642i	0.779771	+	0.626065i
$12$	−1.03230			−0.297999
$13$		−	2.91981i		−	0.809811i	−0.914359	−	0.404905i	$-0.867304\pi$
$13$		−	2.91981i		−	0.809811i	0.914359	−	0.404905i	$-0.132696\pi$
$14$		−	0.602073i		−	0.160911i
$15$	0.985666			0.254498
$16$	2.77078			0.692694
$17$	−3.33333	+	3.33333i	−0.808451	+	0.808451i	−0.984399	−	0.175949i	$-0.943701\pi$
$17$	−3.33333	+	3.33333i	−0.808451	+	0.808451i	0.175949	+	0.984399i	$0.443701\pi$
$18$	−4.23955	−	4.23955i	−0.999271	−	0.999271i
$19$	6.98848			1.60327			0.801634	−	0.597815i	$-0.203964\pi$
$19$	6.98848			1.60327			0.801634	+	0.597815i	$0.203964\pi$
$20$	5.93457			1.32701
$21$	−0.0831643	+	0.0831643i	−0.0181479	+	0.0181479i
$22$	−0.764090	−	6.98855i	−0.162905	−	1.48996i
$23$	−0.146140	+	0.146140i	−0.0304724	+	0.0304724i	−0.722179	−	0.691706i	$-0.756859\pi$
$23$	−0.146140	+	0.146140i	−0.0304724	+	0.0304724i	0.691706	+	0.722179i	$0.256859\pi$
$24$	0.306004	+	0.306004i	0.0624629	+	0.0624629i
$25$	−0.666476			−0.133295
$26$	−4.37634	+	4.37634i	−0.858271	+	0.858271i
$27$			2.41342i			0.464464i
$28$	−0.500721	+	0.500721i	−0.0946274	+	0.0946274i
$29$	0.0386866	−	0.0386866i	0.00718393	−	0.00718393i	−0.703506	−	0.710690i	$-0.748383\pi$
$29$	0.0386866	−	0.0386866i	0.00718393	−	0.00718393i	0.710690	+	0.703506i	$0.248383\pi$
$30$	−1.47736	−	1.47736i	−0.269728	−	0.269728i
$31$	2.85647	+	2.85647i	0.513037	+	0.513037i	0.915456	−	0.402419i	$-0.131830\pi$
$31$	2.85647	+	2.85647i	0.513037	+	0.513037i	−0.402419	+	0.915456i	$0.631830\pi$
$32$	−5.63099	−	5.63099i	−0.995428	−	0.995428i
$33$	−0.859783	+	1.07087i	−0.149669	+	0.186415i
$34$	9.99227			1.71366
$35$	0.478101	−	0.478101i	0.0808139	−	0.0808139i
$36$			7.05173i			1.17529i
$37$	−4.12535	−	4.12535i	−0.678204	−	0.678204i	0.281390	−	0.959594i	$-0.409205\pi$
$37$	−4.12535	−	4.12535i	−0.678204	−	0.678204i	−0.959594	+	0.281390i	$0.909205\pi$
$38$	−10.4746	−	10.4746i	−1.69921	−	1.69921i
$39$	1.20901			0.193596
$40$	−1.75918	−	1.75918i	−0.278151	−	0.278151i
$41$	0.823665			0.128635			0.0643174	−	0.997929i	$-0.479513\pi$
$41$	0.823665			0.128635			0.0643174	+	0.997929i	$0.479513\pi$
$42$	0.249300			0.0384679
$43$	6.18141	−	6.18141i	0.942656	−	0.942656i	−0.0557871	−	0.998443i	$-0.517767\pi$
$43$	6.18141	−	6.18141i	0.942656	−	0.942656i	0.998443	+	0.0557871i	$0.0177668\pi$
$44$	−5.17664	+	6.44757i	−0.780408	+	0.972008i
$45$		−	6.73317i		−	1.00372i
$46$	0.438083			0.0645918
$47$	5.60710			0.817880			0.408940	−	0.912561i	$-0.365899\pi$
$47$	5.60710			0.817880			0.408940	+	0.912561i	$0.365899\pi$
$48$			1.14729i			0.165598i
$49$		−	6.91932i		−	0.988475i
$50$	0.998942	+	0.998942i	0.141272	+	0.141272i
$51$	−1.38023	−	1.38023i	−0.193271	−	0.193271i
$52$	7.27927			1.00945
$53$	−2.78659	+	2.78659i	−0.382768	+	0.382768i	−0.872098	−	0.489331i	$-0.837241\pi$
$53$	−2.78659	+	2.78659i	−0.382768	+	0.382768i	0.489331	+	0.872098i	$0.337241\pi$
$54$	3.61734	−	3.61734i	0.492258	−	0.492258i
$55$	4.94279	−	6.15630i	0.666486	−	0.830116i
$56$	0.296857			0.0396692
$57$			2.89372i			0.383282i
$58$	−0.115970			−0.0152276
$59$	−9.55942	−	9.55942i	−1.24453	−	1.24453i	−0.958102	−	0.286429i	$-0.907532\pi$
$59$	−9.55942	−	9.55942i	−1.24453	−	1.24453i	−0.286429	−	0.958102i	$-0.592468\pi$
$60$			2.45732i			0.317239i
$61$	7.77469	−	0.744480i	0.995447	−	0.0953209i
$61$	7.77469	−	0.744480i	0.995447	−	0.0953209i
$62$		−	8.56279i		−	1.08748i
$63$	0.568102	+	0.568102i	0.0715742	+	0.0715742i
$64$			11.3384i			1.41730i
$65$	−6.95043			−0.862095
$66$	2.89375	−	0.316386i	0.356195	−	0.0389445i
$67$	−9.13584	−	9.13584i	−1.11612	−	1.11612i	−0.992305	−	0.123815i	$-0.960487\pi$
$67$	−9.13584	−	9.13584i	−1.11612	−	1.11612i	−0.123815	−	0.992305i	$-0.539513\pi$
$68$	−8.31018	−	8.31018i	−1.00776	−	1.00776i
$69$	−0.0605123	−	0.0605123i	−0.00728482	−	0.00728482i
$70$	−1.43320			−0.171300
$71$	−0.137784	−	0.137784i	−0.0163519	−	0.0163519i	0.698884	−	0.715235i	$-0.253681\pi$
$71$	−0.137784	−	0.137784i	−0.0163519	−	0.0163519i	−0.715235	+	0.698884i	$0.753681\pi$
$72$	2.09034	−	2.09034i	0.246349	−	0.246349i
$73$			9.40043i			1.10024i	0.835087	+	0.550118i	$0.185417\pi$
$73$			9.40043i			1.10024i	−0.835087	+	0.550118i	$0.814583\pi$
$74$			12.3665i			1.43758i
$75$		−	0.275967i		−	0.0318660i
$76$			17.4227i			1.99852i
$77$	0.102389	+	0.936471i	0.0116683	+	0.106721i
$78$	−1.81211	−	1.81211i	−0.205181	−	0.205181i
$79$	−2.16657	−	2.16657i	−0.243758	−	0.243758i	0.574645	−	0.818403i	$-0.305140\pi$
$79$	−2.16657	−	2.16657i	−0.243758	−	0.243758i	−0.818403	+	0.574645i	$0.805140\pi$
$80$		−	6.59566i		−	0.737417i
$81$	7.48631			0.831813
$82$	−1.23454	−	1.23454i	−0.136333	−	0.136333i
$83$		−	4.49513i		−	0.493405i	−0.969091	−	0.246703i	$-0.920653\pi$
$83$		−	4.49513i		−	0.493405i	0.969091	−	0.246703i	$-0.0793470\pi$
$84$	−0.207333	−	0.207333i	−0.0226219	−	0.0226219i
$85$	7.93477	+	7.93477i	0.860647	+	0.860647i
$86$	−18.5299			−1.99813
$87$	0.0160190	+	0.0160190i	0.00171741	+	0.00171741i
$88$	3.44576	−	0.376741i	0.367320	−	0.0401607i
$89$	−4.18685	−	4.18685i	−0.443805	−	0.443805i	0.449484	−	0.893289i	$-0.351608\pi$
$89$	−4.18685	−	4.18685i	−0.443805	−	0.443805i	−0.893289	+	0.449484i	$0.851608\pi$
$90$	−10.0920	+	10.0920i	−1.06379	+	1.06379i
$91$	0.586433	−	0.586433i	0.0614749	−	0.0614749i
$92$	−0.364336	−	0.364336i	−0.0379847	−	0.0379847i
$93$	−1.18278	+	1.18278i	−0.122648	+	0.122648i
$94$	−8.40416	−	8.40416i	−0.866823	−	0.866823i
$95$		−	16.6356i		−	1.70678i
$96$	2.33162	−	2.33162i	0.237970	−	0.237970i
$97$			5.62809i			0.571446i	0.958312	+	0.285723i	$0.0922338\pi$
$97$			5.62809i			0.571446i	−0.958312	+	0.285723i	$0.907766\pi$
$98$	−10.3710	+	10.3710i	−1.04763	+	1.04763i
$99$	7.31521	+	5.87325i	0.735206	+	0.590284i
$100$		−	1.66156i		−	0.166156i
$101$	−5.04222	−	5.04222i	−0.501720	−	0.501720i	0.410252	−	0.911972i	$-0.365441\pi$
$101$	−5.04222	−	5.04222i	−0.501720	−	0.501720i	−0.911972	+	0.410252i	$0.865441\pi$
$102$			4.13749i			0.409673i
$103$	1.76883			0.174288			0.0871442	−	0.996196i	$-0.472226\pi$
$103$	1.76883			0.174288			0.0871442	+	0.996196i	$0.472226\pi$
$104$	−2.15779	−	2.15779i	−0.211589	−	0.211589i
$105$	0.197967	+	0.197967i	0.0193196	+	0.0193196i
$106$	8.35332			0.811347
$107$	2.53362			0.244935			0.122467	−	0.992473i	$-0.460919\pi$
$107$	2.53362			0.244935			0.122467	+	0.992473i	$0.460919\pi$
$108$	−6.01681			−0.578968
$109$	−10.3444			−0.990818			−0.495409	−	0.868660i	$-0.664982\pi$
$109$	−10.3444			−0.990818			−0.495409	+	0.868660i	$0.664982\pi$
$110$	−16.6358	+	1.81887i	−1.58616	+	0.173422i
$111$	1.70818	−	1.70818i	0.162134	−	0.162134i
$112$	0.556500	+	0.556500i	0.0525843	+	0.0525843i
$113$			11.0286i			1.03748i	0.854931	+	0.518741i	$0.173599\pi$
$113$			11.0286i			1.03748i	−0.854931	+	0.518741i	$0.826401\pi$
$114$	4.33723	−	4.33723i	0.406219	−	0.406219i
$115$	0.347878	+	0.347878i	0.0324398	+	0.0324398i
$116$	0.0964480	+	0.0964480i	0.00895497	+	0.00895497i
$117$		−	8.25883i		−	0.763529i
$118$			28.6561i			2.63801i
$119$	−1.33897			−0.122743
$120$	0.728424	−	0.728424i	0.0664957	−	0.0664957i
$121$	2.37695	+	10.7401i	0.216086	+	0.976374i
$122$	−12.7689	−	10.5372i	−1.15604	−	0.953991i
$123$			0.341055i			0.0307519i
$124$	−7.12134	+	7.12134i	−0.639515	+	0.639515i
$125$		−	10.3157i		−	0.922662i
$126$		−	1.70299i		−	0.151715i
$127$	12.5581			1.11435			0.557176	−	0.830394i	$-0.311885\pi$
$127$	12.5581			1.11435			0.557176	+	0.830394i	$0.311885\pi$
$128$	5.73248	−	5.73248i	0.506684	−	0.506684i
$129$	2.55953	+	2.55953i	0.225354	+	0.225354i
$130$	10.4176	+	10.4176i	0.913684	+	0.913684i
$131$			11.3435i			0.991086i	0.868583	+	0.495543i	$0.165031\pi$
$131$			11.3435i			0.991086i	−0.868583	+	0.495543i	$0.834969\pi$
$132$	−2.66974	−	2.14349i	−0.232371	−	0.186567i
$133$	1.40361	+	1.40361i	0.121708	+	0.121708i
$134$			27.3864i			2.36582i
$135$	5.74500			0.494451
$136$			4.92677i			0.422467i
$137$	3.89264			0.332571			0.166286	−	0.986078i	$-0.446823\pi$
$137$	3.89264			0.332571			0.166286	+	0.986078i	$0.446823\pi$
$138$			0.181397i			0.0154415i
$139$	−5.56492	+	5.56492i	−0.472011	+	0.472011i	−0.902565	−	0.430554i	$-0.858318\pi$
$139$	−5.56492	+	5.56492i	−0.472011	+	0.472011i	0.430554	+	0.902565i	$0.358318\pi$
$140$	1.19193	+	1.19193i	0.100737	+	0.100737i
$141$			2.32173i			0.195525i
$142$			0.413032i			0.0346608i
$143$	6.06276	−	7.55125i	0.506994	−	0.631467i
$144$	7.83727			0.653106
$145$	−0.0920910	−	0.0920910i	−0.00764774	−	0.00764774i
$146$	14.0898	−	14.0898i	1.16608	−	1.16608i
$147$	2.86508			0.236308
$148$	10.2847	−	10.2847i	0.845401	−	0.845401i
$149$	17.0154			1.39396			0.696979	−	0.717091i	$-0.254527\pi$
$149$	17.0154			1.39396			0.696979	+	0.717091i	$0.254527\pi$
$150$	−0.413632	+	0.413632i	−0.0337729	+	0.0337729i
$151$	14.4072	−	14.4072i	1.17244	−	1.17244i	0.190814	−	0.981626i	$-0.438887\pi$
$151$	14.4072	−	14.4072i	1.17244	−	1.17244i	0.981626	−	0.190814i	$-0.0611126\pi$
$152$	5.16461	−	5.16461i	0.418905	−	0.418905i
$153$	−9.42847	+	9.42847i	−0.762247	+	0.762247i
$154$	1.25016	−	1.55709i	0.100741	−	0.125474i
$155$	6.79964	−	6.79964i	0.546160	−	0.546160i
$156$			3.01412i			0.241323i
$157$	8.94365	+	8.94365i	0.713781	+	0.713781i	0.967324	−	0.253543i	$-0.0815959\pi$
$157$	8.94365	+	8.94365i	0.713781	+	0.713781i	−0.253543	+	0.967324i	$0.581596\pi$
$158$			6.49470i			0.516690i
$159$	−1.15384	−	1.15384i	−0.0915057	−	0.0915057i
$160$	−13.4042	+	13.4042i	−1.05970	+	1.05970i
$161$	−0.0587034			−0.00462648
$162$	−11.2208	−	11.2208i	−0.881590	−	0.881590i
$163$			17.4133i			1.36391i	0.731392	+	0.681957i	$0.238871\pi$
$163$			17.4133i			1.36391i	−0.731392	+	0.681957i	$0.761129\pi$
$164$			2.05345i			0.160347i
$165$	2.54914	+	2.04666i	0.198450	+	0.159332i
$166$	−6.73750	+	6.73750i	−0.522931	+	0.522931i
$167$	18.5886			1.43843			0.719214	−	0.694789i	$-0.244502\pi$
$167$	18.5886			1.43843			0.719214	+	0.694789i	$0.244502\pi$
$168$			0.122920i			0.00948345i
$169$	4.47469			0.344207
$170$		−	23.7860i		−	1.82430i
$171$	19.7673			1.51164
$172$	15.4106	+	15.4106i	1.17505	+	1.17505i
$173$	0.321493	+	0.321493i	0.0244427	+	0.0244427i	0.719223	−	0.694780i	$-0.244498\pi$
$173$	0.321493	+	0.321493i	0.0244427	+	0.0244427i	−0.694780	+	0.719223i	$0.744498\pi$
$174$		−	0.0480198i		−	0.00364037i
$175$	−0.133859	−	0.133859i	−0.0101188	−	0.0101188i
$176$	7.16581	+	5.75330i	0.540143	+	0.433671i
$177$	3.95826	−	3.95826i	0.297521	−	0.297521i
$178$			12.5508i			0.940726i
$179$	−4.72485			−0.353152			−0.176576	−	0.984287i	$-0.556502\pi$
$179$	−4.72485			−0.353152			−0.176576	+	0.984287i	$0.556502\pi$
$180$	16.7862			1.25117
$181$	−0.987042	−	0.987042i	−0.0733663	−	0.0733663i	0.669471	−	0.742838i	$-0.266521\pi$
$181$	−0.987042	−	0.987042i	−0.0733663	−	0.0733663i	−0.742838	+	0.669471i	$0.766521\pi$
$182$	−1.75794			−0.130307
$183$	0.308266	+	3.21926i	0.0227877	+	0.237975i
$184$			0.216000i			0.0159238i
$185$	−9.82014	+	9.82014i	−0.721991	+	0.721991i
$186$	3.54559			0.259975
$187$	−15.5421	+	1.69929i	−1.13655	+	0.124264i
$188$			13.9788i			1.01951i
$189$	−0.484727	+	0.484727i	−0.0352587	+	0.0352587i
$190$	−24.9342	+	24.9342i	−1.80892	+	1.80892i
$191$	8.57897	+	8.57897i	0.620753	+	0.620753i	0.945724	−	0.324971i	$-0.105355\pi$
$191$	8.57897	+	8.57897i	0.620753	+	0.620753i	−0.324971	+	0.945724i	$0.605355\pi$
$192$	−4.69488			−0.338824
$193$	−10.6433	+	10.6433i	−0.766123	+	0.766123i	−0.977422	−	0.211298i	$-0.932231\pi$
$193$	−10.6433	+	10.6433i	−0.766123	+	0.766123i	0.211298	+	0.977422i	$0.432231\pi$
$194$	8.43563	−	8.43563i	0.605643	−	0.605643i
$195$		−	2.87796i		−	0.206095i
$196$	17.2503			1.23216
$197$	7.02298			0.500367			0.250183	−	0.968198i	$-0.419509\pi$
$197$	7.02298			0.500367			0.250183	+	0.968198i	$0.419509\pi$
$198$	−2.16126	−	19.7674i	−0.153594	−	1.40481i
$199$	−25.3620			−1.79786			−0.898932	−	0.438088i	$-0.855656\pi$
$199$	−25.3620			−1.79786			−0.898932	+	0.438088i	$0.855656\pi$
$200$	−0.492537	+	0.492537i	−0.0348276	+	0.0348276i
$201$	3.78287	−	3.78287i	0.266823	−	0.266823i
$202$			15.1150i			1.06349i
$203$	0.0155401			0.00109070
$204$	3.44099	−	3.44099i	0.240918	−	0.240918i
$205$		−	1.96068i		−	0.136940i
$206$	−2.65120	−	2.65120i	−0.184718	−	0.184718i
$207$	−0.413365	+	0.413365i	−0.0287308	+	0.0287308i
$208$		−	8.09015i		−	0.560951i
$209$	18.0737	+	14.5110i	1.25018	+	1.00375i
$210$		−	0.593443i		−	0.0409515i
$211$	−8.19668	+	8.19668i	−0.564283	+	0.564283i	−0.930521	−	0.366238i	$-0.880646\pi$
$211$	−8.19668	+	8.19668i	−0.564283	+	0.564283i	0.366238	+	0.930521i	$0.380646\pi$
$212$	−6.94714	−	6.94714i	−0.477131	−	0.477131i
$213$	0.0570520	−	0.0570520i	0.00390914	−	0.00390914i
$214$	−3.79750	−	3.79750i	−0.259592	−	0.259592i
$215$	−14.7144	−	14.7144i	−1.00352	−	1.00352i
$216$	1.78356	+	1.78356i	0.121356	+	0.121356i
$217$			1.14742i			0.0778920i
$218$	15.5047	+	15.5047i	1.05011	+	1.05011i
$219$	−3.89243			−0.263026
$220$	15.3480	+	12.3227i	1.03476	+	0.830794i
$221$	9.73270	+	9.73270i	0.654692	+	0.654692i
$222$	−5.12060			−0.343672
$223$	9.07714	−	9.07714i	0.607850	−	0.607850i	−0.334534	−	0.942384i	$-0.608579\pi$
$223$	9.07714	−	9.07714i	0.607850	−	0.607850i	0.942384	+	0.334534i	$0.108579\pi$
$224$		−	2.26193i		−	0.151131i
$225$	−1.88516			−0.125677
$226$	16.5301	−	16.5301i	1.09957	−	1.09957i
$227$	−8.89306	−	8.89306i	−0.590253	−	0.590253i	0.347447	−	0.937700i	$-0.387049\pi$
$227$	−8.89306	−	8.89306i	−0.590253	−	0.590253i	−0.937700	+	0.347447i	$0.887049\pi$
$228$	−7.21421			−0.477773
$229$		−	17.9135i		−	1.18376i	−0.806027	−	0.591878i	$-0.798387\pi$
$229$		−	17.9135i		−	1.18376i	0.806027	−	0.591878i	$-0.201613\pi$
$230$		−	1.04283i		−	0.0687620i
$231$	−0.387764	+	0.0423960i	−0.0255130	+	0.00278945i
$232$		−	0.0571801i		−	0.00375406i
$233$	−1.84216	−	1.84216i	−0.120684	−	0.120684i	0.644186	−	0.764869i	$-0.277196\pi$
$233$	−1.84216	−	1.84216i	−0.120684	−	0.120684i	−0.764869	+	0.644186i	$0.777196\pi$
$234$	−12.3787	+	12.3787i	−0.809220	+	0.809220i
$235$		−	13.3473i		−	0.870685i
$236$	23.8322	−	23.8322i	1.55134	−	1.55134i
$237$	0.897111	−	0.897111i	0.0582736	−	0.0582736i
$238$	2.00691	+	2.00691i	0.130089	+	0.130089i
$239$		−	2.40422i		−	0.155516i	−0.996972	−	0.0777579i	$-0.975224\pi$
$239$		−	2.40422i		−	0.155516i	0.996972	−	0.0777579i	$-0.0247761\pi$
$240$	2.73106			0.176289
$241$			15.0300i			0.968166i	0.875022	+	0.484083i	$0.160847\pi$
$241$			15.0300i			0.968166i	−0.875022	+	0.484083i	$0.839153\pi$
$242$	12.5351	−	19.6604i	0.805785	−	1.26382i
$243$			10.3401i			0.663319i
$244$	1.85603	+	19.3827i	0.118820	+	1.24085i
$245$	−16.4710			−1.05229
$246$	0.511187	−	0.511187i	0.0325921	−	0.0325921i
$247$		−	20.4051i		−	1.29834i
$248$	4.22196			0.268094
$249$	1.86130			0.117955
$250$	−15.4616	+	15.4616i	−0.977876	+	0.977876i
$251$	−13.7642	+	13.7642i	−0.868791	+	0.868791i	−0.992339	−	0.123548i	$-0.960573\pi$
$251$	−13.7642	+	13.7642i	−0.868791	+	0.868791i	0.123548	+	0.992339i	$0.460573\pi$
$252$	−1.41631	+	1.41631i	−0.0892193	+	0.0892193i
$253$	−0.681398	+	0.0745004i	−0.0428391	+	0.00468380i
$254$	−18.8226	−	18.8226i	−1.18104	−	1.18104i
$255$	−3.28555	+	3.28555i	−0.205749	+	0.205749i
$256$	5.49262			0.343289
$257$	−28.3781			−1.77018			−0.885090	−	0.465420i	$-0.845903\pi$
$257$	−28.3781			−1.77018			−0.885090	+	0.465420i	$0.845903\pi$
$258$		−	7.67267i		−	0.477680i
$259$		−	1.65712i		−	0.102969i
$260$		−	17.3278i		−	1.07463i
$261$	0.109427	−	0.109427i	0.00677336	−	0.00677336i
$262$	17.0021	−	17.0021i	1.05039	−	1.05039i
$263$	−14.8885			−0.918062			−0.459031	−	0.888420i	$-0.651803\pi$
$263$	−14.8885			−0.918062			−0.459031	+	0.888420i	$0.651803\pi$
$264$	0.155997	+	1.42679i	0.00960095	+	0.0878126i
$265$	6.63330	+	6.63330i	0.407481	+	0.407481i
$266$		−	4.20758i		−	0.257983i
$267$	1.73365	−	1.73365i	0.106097	−	0.106097i
$268$	22.7762	−	22.7762i	1.39128	−	1.39128i
$269$	−16.0279			−0.977236			−0.488618	−	0.872498i	$-0.662499\pi$
$269$	−16.0279			−0.977236			−0.488618	+	0.872498i	$0.662499\pi$
$270$	−8.61085	−	8.61085i	−0.524040	−	0.524040i
$271$	−12.5446			−0.762030			−0.381015	−	0.924569i	$-0.624425\pi$
$271$	−12.5446			−0.762030			−0.381015	+	0.924569i	$0.624425\pi$
$272$	−9.23591	+	9.23591i	−0.560009	+	0.560009i
$273$	0.242824	+	0.242824i	0.0146964	+	0.0146964i
$274$	−5.83446	−	5.83446i	−0.352473	−	0.352473i
$275$	−1.72365	−	1.38388i	−0.103940	−	0.0834514i
$276$	0.150861	−	0.150861i	0.00908074	−	0.00908074i
$277$	7.85870	+	7.85870i	0.472183	+	0.472183i	0.902621	−	0.430437i	$-0.141641\pi$
$277$	7.85870	+	7.85870i	0.472183	+	0.472183i	−0.430437	+	0.902621i	$0.641641\pi$
$278$	16.6819			1.00051
$279$	8.07965	+	8.07965i	0.483716	+	0.483716i
$280$		−	0.706650i		−	0.0422304i
$281$	−12.8791	+	12.8791i	−0.768300	+	0.768300i	−0.977807	−	0.209507i	$-0.932814\pi$
$281$	−12.8791	+	12.8791i	−0.768300	+	0.768300i	0.209507	+	0.977807i	$0.432814\pi$
$282$	3.47991	−	3.47991i	0.207225	−	0.207225i
$283$	−26.8258			−1.59463			−0.797315	−	0.603564i	$-0.793747\pi$
$283$	−26.8258			−1.59463			−0.797315	+	0.603564i	$0.793747\pi$
$284$	0.343502	−	0.343502i	0.0203831	−	0.0203831i
$285$	6.88831			0.408028
$286$	−20.4053	+	2.23100i	−1.20659	+	0.131922i
$287$	0.165430	+	0.165430i	0.00976502	+	0.00976502i
$288$	−15.9275	−	15.9275i	−0.938538	−	0.938538i
$289$		−	5.22215i		−	0.307186i
$290$			0.276060i			0.0162108i
$291$	−2.33042			−0.136612
$292$	−23.4358			−1.37148
$293$	21.0492			1.22970			0.614852	−	0.788642i	$-0.289216\pi$
$293$	21.0492			1.22970			0.614852	+	0.788642i	$0.289216\pi$
$294$	−4.29431	−	4.29431i	−0.250449	−	0.250449i
$295$	−22.7556	+	22.7556i	−1.32488	+	1.32488i
$296$	−6.09741			−0.354405
$297$	−5.01129	+	6.24162i	−0.290784	+	0.362175i
$298$	−25.5035	−	25.5035i	−1.47738	−	1.47738i
$299$	0.426702	+	0.426702i	0.0246768	+	0.0246768i
$300$	0.688003			0.0397219
$301$	2.48302			0.143119
$302$	−43.1882			−2.48520
$303$	2.08783	−	2.08783i	0.119943	−	0.119943i
$304$	19.3635			1.11057
$305$	−1.77219	−	18.5071i	−0.101475	−	1.05972i
$306$	28.2636			1.61572
$307$	18.3632	+	18.3632i	1.04804	+	1.04804i	0.998786	+	0.0492563i	$0.0156851\pi$
$307$	18.3632	+	18.3632i	1.04804	+	1.04804i	0.0492563	+	0.998786i	$0.484315\pi$
$308$	−2.33468	+	0.255261i	−0.133031	+	0.0145448i
$309$			0.732421i			0.0416660i
$310$	−20.3832			−1.15769
$311$	15.6902	+	15.6902i	0.889707	+	0.889707i	0.994495	−	0.104787i	$-0.0334162\pi$
$311$	15.6902	+	15.6902i	0.889707	+	0.889707i	−0.104787	+	0.994495i	$0.533416\pi$
$312$	0.893476	−	0.893476i	0.0505831	−	0.0505831i
$313$	−3.36910	−	3.36910i	−0.190433	−	0.190433i	0.605450	−	0.795883i	$-0.292993\pi$
$313$	−3.36910	−	3.36910i	−0.190433	−	0.190433i	−0.795883	+	0.605450i	$0.792993\pi$
$314$		−	26.8103i		−	1.51299i
$315$	1.35233	−	1.35233i	0.0761953	−	0.0761953i
$316$	5.40139	−	5.40139i	0.303852	−	0.303852i
$317$	−5.17427			−0.290616			−0.145308	−	0.989386i	$-0.546417\pi$
$317$	−5.17427			−0.290616			−0.145308	+	0.989386i	$0.546417\pi$
$318$			3.45886i			0.193963i
$319$	0.180381	−	0.0197219i	0.0100994	−	0.00110422i
$320$	26.9903			1.50880
$321$			1.04910i			0.0585549i
$322$	0.0879872	+	0.0879872i	0.00490333	+	0.00490333i
$323$	−23.2949	+	23.2949i	−1.29616	+	1.29616i
$324$			18.6638i			1.03688i
$325$			1.94598i			0.107944i
$326$	26.0998	−	26.0998i	1.44553	−	1.44553i
$327$		−	4.28332i		−	0.236868i
$328$	0.608703	−	0.608703i	0.0336100	−	0.0336100i
$329$	1.12616	+	1.12616i	0.0620874	+	0.0620874i
$330$	−0.753138	−	6.88838i	−0.0414589	−	0.379193i
$331$	16.7933	−	16.7933i	0.923043	−	0.923043i	−0.0742008	−	0.997243i	$-0.523641\pi$
$331$	16.7933	−	16.7933i	0.923043	−	0.923043i	0.997243	+	0.0742008i	$0.0236406\pi$
$332$	11.2066			0.615044
$333$	−11.6688	−	11.6688i	−0.639444	−	0.639444i
$334$	−27.8614	−	27.8614i	−1.52451	−	1.52451i
$335$	−21.7473	+	21.7473i	−1.18818	+	1.18818i
$336$	−0.230430	+	0.230430i	−0.0125710	+	0.0125710i
$337$	−9.14234	−	9.14234i	−0.498015	−	0.498015i	0.412804	−	0.910820i	$-0.364549\pi$
$337$	−9.14234	−	9.14234i	−0.498015	−	0.498015i	−0.910820	+	0.412804i	$0.864549\pi$
$338$	−6.70685	−	6.70685i	−0.364805	−	0.364805i
$339$	−4.56660			−0.248024
$340$	−19.7819	+	19.7819i	−1.07282	+	1.07282i
$341$	1.45619	+	13.3187i	0.0788571	+	0.721245i
$342$	−29.6280	−	29.6280i	−1.60210	−	1.60210i
$343$	2.79564	−	2.79564i	0.150950	−	0.150950i
$344$		−	9.13633i		−	0.492598i
$345$	−0.144046	+	0.144046i	−0.00775515	+	0.00775515i
$346$		−	0.963736i		−	0.0518108i
$347$		−	34.0483i		−	1.82781i	−0.405927	−	0.913906i	$-0.633051\pi$
$347$		−	34.0483i		−	1.82781i	0.405927	−	0.913906i	$-0.366949\pi$
$348$	−0.0399362	+	0.0399362i	−0.00214080	+	0.00214080i
$349$	−21.1279	−	21.1279i	−1.13095	−	1.13095i	−0.990019	−	0.140933i	$-0.954990\pi$
$349$	−21.1279	−	21.1279i	−1.13095	−	1.13095i	−0.140933	−	0.990019i	$-0.545010\pi$
$350$			0.401267i			0.0214486i
$351$	7.04675			0.376128
$352$	−2.87060	−	26.2552i	−0.153004	−	1.39941i
$353$		−	20.2288i		−	1.07667i	−0.842730	−	0.538336i	$-0.819053\pi$
$353$		−	20.2288i		−	1.07667i	0.842730	−	0.538336i	$-0.180947\pi$
$354$	−11.8656			−0.630651
$355$	−0.327985	+	0.327985i	−0.0174076	+	0.0174076i
$356$	10.4381	−	10.4381i	0.553216	−	0.553216i
$357$		−	0.554428i		−	0.0293434i
$358$	7.08180	+	7.08180i	0.374285	+	0.374285i
$359$	−7.10927	+	7.10927i	−0.375213	+	0.375213i	−0.869372	−	0.494159i	$-0.835476\pi$
$359$	−7.10927	+	7.10927i	−0.375213	+	0.375213i	0.494159	+	0.869372i	$0.335476\pi$
$360$	−4.97593	−	4.97593i	−0.262255	−	0.262255i
$361$	29.8389			1.57047
$362$			2.95884i			0.155513i
$363$	−4.44716	+	0.984221i	−0.233415	+	0.0516582i
$364$	1.46201	+	1.46201i	0.0766303	+	0.0766303i
$365$	22.3771			1.17127
$366$	4.36312	−	5.28721i	0.228064	−	0.276367i
$367$	−16.1853			−0.844866			−0.422433	−	0.906394i	$-0.638824\pi$
$367$	−16.1853			−0.844866			−0.422433	+	0.906394i	$0.638824\pi$
$368$	−0.404922	+	0.404922i	−0.0211080	+	0.0211080i
$369$	2.32978			0.121283
$370$	29.4377			1.53039
$371$	−1.11935			−0.0581139
$372$	−2.94873	−	2.94873i	−0.152885	−	0.152885i
$373$	7.95385	+	7.95385i	0.411835	+	0.411835i	0.882377	−	0.470543i	$-0.155942\pi$
$373$	7.95385	+	7.95385i	0.411835	+	0.411835i	−0.470543	+	0.882377i	$0.655942\pi$
$374$	25.8421	+	20.7482i	1.33626	+	1.07286i
$375$	4.27141			0.220575
$376$	4.14374	−	4.14374i	0.213697	−	0.213697i
$377$	−0.112958	−	0.112958i	−0.00581762	−	0.00581762i
$378$	1.45306			0.0747373
$379$	22.2672			1.14379			0.571894	−	0.820327i	$-0.306209\pi$
$379$	22.2672			1.14379			0.571894	+	0.820327i	$0.306209\pi$
$380$	41.4736			2.12755
$381$			5.19993i			0.266401i
$382$		−	25.7171i		−	1.31580i
$383$	−5.85499	−	5.85499i	−0.299176	−	0.299176i	0.541515	−	0.840691i	$-0.317851\pi$
$383$	−5.85499	−	5.85499i	−0.299176	−	0.299176i	−0.840691	+	0.541515i	$0.817851\pi$
$384$	2.37364	+	2.37364i	0.121130	+	0.121130i
$385$	2.22921	−	0.243730i	0.113611	−	0.0124216i
$386$	31.9053			1.62394
$387$	17.4844	−	17.4844i	0.888782	−	0.888782i
$388$	−14.0312			−0.712325
$389$	−13.1119	+	13.1119i	−0.664798	+	0.664798i	−0.956507	−	0.291709i	$-0.905776\pi$
$389$	−13.1119	+	13.1119i	−0.664798	+	0.664798i	0.291709	+	0.956507i	$0.405776\pi$
$390$	−4.31361	+	4.31361i	−0.218428	+	0.218428i
$391$		−	0.974267i		−	0.0492708i
$392$	−5.11350	−	5.11350i	−0.258271	−	0.258271i
$393$	−4.69700			−0.236932
$394$	−10.5263	−	10.5263i	−0.530309	−	0.530309i
$395$	−5.15738	+	5.15738i	−0.259496	+	0.259496i
$396$	−14.6424	+	18.2372i	−0.735807	+	0.916456i
$397$	22.8131	+	22.8131i	1.14496	+	1.14496i	0.987530	+	0.157428i	$0.0503203\pi$
$397$	22.8131	+	22.8131i	1.14496	+	1.14496i	0.157428	+	0.987530i	$0.449680\pi$
$398$	38.0136	+	38.0136i	1.90545	+	1.90545i
$399$	−0.581192	+	0.581192i	−0.0290960	+	0.0290960i
$400$	−1.84666			−0.0923328
$401$	21.0459	+	21.0459i	1.05098	+	1.05098i	0.998629	+	0.0523540i	$0.0166724\pi$
$401$	21.0459	+	21.0459i	1.05098	+	1.05098i	0.0523540	+	0.998629i	$0.483328\pi$
$402$	−11.3399			−0.565581
$403$	8.34035	−	8.34035i	0.415463	−	0.415463i
$404$	12.5706	−	12.5706i	0.625409	−	0.625409i
$405$		−	17.8207i		−	0.885517i
$406$	−0.0232922	−	0.0232922i	−0.00115597	−	0.00115597i
$407$	−2.10305	−	19.2350i	−0.104244	−	0.953443i
$408$	−2.04003			−0.100996
$409$	−27.5779	+	27.5779i	−1.36364	+	1.36364i	−0.494408	+	0.869230i	$0.664615\pi$
$409$	−27.5779	+	27.5779i	−1.36364	+	1.36364i	−0.869230	+	0.494408i	$0.835385\pi$
$410$	−2.93875	+	2.93875i	−0.145135	+	0.145135i
$411$			1.61183i			0.0795055i
$412$			4.40981i			0.217256i
$413$		−	3.83994i		−	0.188951i
$414$	1.23914			0.0609003
$415$	−10.7004			−0.525261
$416$	−16.4414	+	16.4414i	−0.806108	+	0.806108i
$417$	−2.30427	−	2.30427i	−0.112840	−	0.112840i
$418$	−5.33983	−	48.8394i	−0.261180	−	2.38881i
$419$	17.3042	−	17.3042i	0.845366	−	0.845366i	−0.144185	−	0.989551i	$-0.546056\pi$
$419$	17.3042	−	17.3042i	0.845366	−	0.845366i	0.989551	+	0.144185i	$0.0460559\pi$
$420$	−0.493544	+	0.493544i	−0.0240825	+	0.0240825i
$421$	7.41956	−	7.41956i	0.361607	−	0.361607i	−0.502797	−	0.864404i	$-0.667696\pi$
$421$	7.41956	−	7.41956i	0.361607	−	0.361607i	0.864404	+	0.502797i	$0.167696\pi$
$422$	24.5711			1.19610
$423$	15.8599			0.771137
$424$			4.11868i			0.200021i
$425$	2.22158	−	2.22158i	0.107763	−	0.107763i
$426$	−0.171024			−0.00828613
$427$	1.71104	+	1.41199i	0.0828031	+	0.0683310i
$428$			6.31647i			0.305318i
$429$	3.12674	+	2.51041i	0.150961	+	0.121204i
$430$			44.1093i			2.12714i
$431$	−14.8300			−0.714336			−0.357168	−	0.934040i	$-0.616258\pi$
$431$	−14.8300			−0.714336			−0.357168	+	0.934040i	$0.616258\pi$
$432$			6.68706i			0.321731i
$433$	−16.8401	−	16.8401i	−0.809285	−	0.809285i	0.175241	−	0.984526i	$-0.443930\pi$
$433$	−16.8401	−	16.8401i	−0.809285	−	0.809285i	−0.984526	+	0.175241i	$0.943930\pi$
$434$	1.71980	−	1.71980i	0.0825532	−	0.0825532i
$435$	0.0381321	−	0.0381321i	0.00182829	−	0.00182829i
$436$		−	25.7893i		−	1.23508i
$437$	−1.02130	+	1.02130i	−0.0488554	+	0.0488554i
$438$	5.83414	+	5.83414i	0.278766	+	0.278766i
$439$		−	6.97952i		−	0.333114i	−0.986032	−	0.166557i	$-0.946735\pi$
$439$		−	6.97952i		−	0.333114i	0.986032	−	0.166557i	$-0.0532650\pi$
$440$	−0.896808	−	8.20242i	−0.0427536	−	0.391035i
$441$		−	19.5716i		−	0.931982i
$442$		−	29.1756i		−	1.38774i
$443$	40.0155			1.90119			0.950597	−	0.310429i	$-0.100473\pi$
$443$	40.0155			1.90119			0.950597	+	0.310429i	$0.100473\pi$
$444$	4.25860	+	4.25860i	0.202104	+	0.202104i
$445$	−9.96652	+	9.96652i	−0.472458	+	0.472458i
$446$	−27.2104			−1.28845
$447$			7.04558i			0.333244i
$448$	−2.27727	+	2.27727i	−0.107591	+	0.107591i
$449$	−9.40219			−0.443717			−0.221858	−	0.975079i	$-0.571212\pi$
$449$	−9.40219			−0.443717			−0.221858	+	0.975079i	$0.571212\pi$
$450$	2.82555	+	2.82555i	0.133198	+	0.133198i
$451$	2.13017	+	1.71028i	0.100306	+	0.0805338i
$452$	−27.4949			−1.29325
$453$	5.96558	+	5.96558i	0.280287	+	0.280287i
$454$			26.6586i			1.25115i
$455$	−1.39597	−	1.39597i	−0.0654439	−	0.0654439i
$456$	2.13851	+	2.13851i	0.100145	+	0.100145i
$457$	4.85972	+	4.85972i	0.227328	+	0.227328i	0.811576	−	0.584247i	$-0.198610\pi$
$457$	4.85972	+	4.85972i	0.227328	+	0.227328i	−0.584247	+	0.811576i	$0.698610\pi$
$458$	−26.8495	+	26.8495i	−1.25459	+	1.25459i
$459$	−8.04473	−	8.04473i	−0.375496	−	0.375496i
$460$	−0.867279	+	0.867279i	−0.0404371	+	0.0404371i
$461$		−	20.6833i		−	0.963316i	−0.876359	−	0.481658i	$-0.840035\pi$
$461$		−	20.6833i		−	0.963316i	0.876359	−	0.481658i	$-0.159965\pi$
$462$	0.644742	+	0.517653i	0.0299961	+	0.0240834i
$463$			25.3304i			1.17721i	0.808422	+	0.588603i	$0.200322\pi$
$463$			25.3304i			1.17721i	−0.808422	+	0.588603i	$0.799678\pi$
$464$	0.107192	−	0.107192i	0.00497626	−	0.00497626i
$465$	2.81552	+	2.81552i	0.130567	+	0.130567i
$466$			5.52221i			0.255811i
$467$	−3.62766	+	3.62766i	−0.167868	+	0.167868i	−0.786042	−	0.618174i	$-0.787873\pi$
$467$	−3.62766	+	3.62766i	−0.167868	+	0.167868i	0.618174	+	0.786042i	$0.287873\pi$
$468$	20.5897			0.951761
$469$		−	3.66979i		−	0.169455i
$470$	−20.0056	+	20.0056i	−0.922788	+	0.922788i
$471$	−3.70330	+	3.70330i	−0.170639	+	0.170639i
$472$	−14.1291			−0.650347
$473$	28.8216	−	3.15120i	1.32522	−	0.144892i
$474$	−2.68926			−0.123522
$475$	−4.65766			−0.213708
$476$		−	3.33814i		−	0.153003i
$477$	−7.88200	+	7.88200i	−0.360892	+	0.360892i
$478$	−3.60354	+	3.60354i	−0.164822	+	0.164822i
$479$	−39.5665			−1.80784			−0.903919	−	0.427704i	$-0.859323\pi$
$479$	−39.5665			−1.80784			−0.903919	+	0.427704i	$0.859323\pi$
$480$	−5.55028	−	5.55028i	−0.253334	−	0.253334i
$481$	−12.0453	+	12.0453i	−0.549217	+	0.549217i
$482$	22.5276	−	22.5276i	1.02610	−	1.02610i
$483$		−	0.0243073i		−	0.00110602i
$484$	−26.7757	+	5.92587i	−1.21708	+	0.269358i
$485$	13.3973			0.608341
$486$	15.4982	−	15.4982i	0.703014	−	0.703014i
$487$		−	5.53548i		−	0.250837i	−0.992104	−	0.125418i	$-0.959973\pi$
$487$		−	5.53548i		−	0.250837i	0.992104	−	0.125418i	$-0.0400273\pi$
$488$	5.19544	−	6.29581i	0.235187	−	0.284998i
$489$	−7.21032			−0.326062
$490$	24.6874	+	24.6874i	1.11526	+	1.11526i
$491$	−18.2867			−0.825267			−0.412634	−	0.910897i	$-0.635391\pi$
$491$	−18.2867			−0.825267			−0.412634	+	0.910897i	$0.635391\pi$
$492$	−0.850269			−0.0383331
$493$			0.257910i			0.0116157i
$494$	−30.5840	+	30.5840i	−1.37604	+	1.37604i
$495$	13.9809	−	17.4134i	0.628395	−	0.782674i
$496$	7.91463	+	7.91463i	0.355378	+	0.355378i
$497$		−	0.0553466i		−	0.00248263i
$498$	−2.78979	−	2.78979i	−0.125014	−	0.125014i
$499$	8.25914	+	8.25914i	0.369730	+	0.369730i	0.867379	−	0.497649i	$-0.165803\pi$
$499$	8.25914	+	8.25914i	0.369730	+	0.369730i	−0.497649	+	0.867379i	$0.665803\pi$
$500$	25.7176			1.15013
$501$			7.69697i			0.343875i
$502$	41.2608			1.84156
$503$		−	28.9860i		−	1.29242i	−0.763159	−	0.646211i	$-0.776353\pi$
$503$		−	28.9860i		−	1.29242i	0.763159	−	0.646211i	$-0.223647\pi$
$504$	0.839675			0.0374021
$505$	−12.0027	+	12.0027i	−0.534113	+	0.534113i
$506$	1.13297	+	0.909644i	0.0503668	+	0.0404386i
$507$			1.85283i			0.0822872i
$508$			31.3081i			1.38907i
$509$	12.6653	+	12.6653i	0.561381	+	0.561381i	0.929700	−	0.368318i	$-0.120066\pi$
$509$	12.6653	+	12.6653i	0.561381	+	0.561381i	−0.368318	+	0.929700i	$0.620066\pi$
$510$	9.84904			0.436123
$511$	−1.88804	+	1.88804i	−0.0835219	+	0.0835219i
$512$	−19.6975	−	19.6975i	−0.870516	−	0.870516i
$513$			16.8662i			0.744660i
$514$	42.5344	+	42.5344i	1.87611	+	1.87611i
$515$		−	4.21060i		−	0.185541i
$516$	−6.38106	+	6.38106i	−0.280911	+	0.280911i
$517$	14.5011	+	11.6427i	0.637759	+	0.512045i
$518$	−2.48377	+	2.48377i	−0.109130	+	0.109130i
$519$	−0.133121	+	0.133121i	−0.00584335	+	0.00584335i
$520$	−5.13649	+	5.13649i	−0.225250	+	0.225250i
$521$	−28.3737	+	28.3737i	−1.24308	+	1.24308i	−0.284357	+	0.958719i	$0.591780\pi$
$521$	−28.3737	+	28.3737i	−1.24308	+	1.24308i	−0.958719	+	0.284357i	$0.908220\pi$
$522$	−0.328027			−0.0143574
$523$	−6.46298	+	6.46298i	−0.282607	+	0.282607i	−0.834148	−	0.551541i	$-0.814040\pi$
$523$	−6.46298	+	6.46298i	−0.282607	+	0.282607i	0.551541	+	0.834148i	$0.314040\pi$
$524$	−28.2800			−1.23542
$525$	0.0554270	−	0.0554270i	0.00241903	−	0.00241903i
$526$	22.3155	+	22.3155i	0.973001	+	0.973001i
$527$	−19.0431			−0.829530
$528$	−2.38227	+	2.96714i	−0.103675	+	0.129128i
$529$			22.9573i			0.998143i
$530$		−	19.8846i		−	0.863730i
$531$	−27.0393	−	27.0393i	−1.17340	−	1.17340i
$532$	−3.49928	+	3.49928i	−0.151713	+	0.151713i
$533$		−	2.40495i		−	0.104170i
$534$	−5.19693			−0.224893
$535$		−	6.03113i		−	0.260748i
$536$	−13.5031			−0.583244
$537$		−	1.95642i		−	0.0844256i
$538$	24.0232	+	24.0232i	1.03572	+	1.03572i
$539$	14.3674	−	17.8948i	0.618849	−	0.770784i
$540$			14.3226i			0.616348i
$541$	−29.5020	−	29.5020i	−1.26839	−	1.26839i	−0.946920	−	0.321470i	$-0.895823\pi$
$541$	−29.5020	−	29.5020i	−1.26839	−	1.26839i	−0.321470	−	0.946920i	$-0.604177\pi$
$542$	18.8024	+	18.8024i	0.807631	+	0.807631i
$543$	0.408704	−	0.408704i	0.0175392	−	0.0175392i
$544$	37.5399			1.60951
$545$			24.6243i			1.05479i
$546$		−	0.727910i		−	0.0311517i
$547$	−1.29793	+	1.29793i	−0.0554953	+	0.0554953i	−0.734310	−	0.678815i	$-0.762494\pi$
$547$	−1.29793	+	1.29793i	−0.0554953	+	0.0554953i	0.678815	+	0.734310i	$0.262494\pi$
$548$			9.70459i			0.414559i
$549$	21.9911	−	2.10580i	0.938556	−	0.0898732i
$550$	0.509247	+	4.65770i	0.0217144	+	0.198605i
$551$	0.270361	−	0.270361i	0.0115178	−	0.0115178i
$552$	−0.0894392			−0.00380678
$553$		−	0.870294i		−	0.0370087i
$554$		−	23.5579i		−	1.00088i
$555$	−4.06622	−	4.06622i	−0.172601	−	0.172601i
$556$	−13.8737	−	13.8737i	−0.588375	−	0.588375i
$557$	4.71757	−	4.71757i	0.199890	−	0.199890i	−0.600063	−	0.799953i	$-0.704858\pi$
$557$	4.71757	−	4.71757i	0.199890	−	0.199890i	0.799953	+	0.600063i	$0.204858\pi$
$558$		−	24.2202i		−	1.02532i
$559$	−18.0486	−	18.0486i	−0.763373	−	0.763373i
$560$	1.32471	−	1.32471i	0.0559793	−	0.0559793i
$561$	−0.703623	−	6.43550i	−0.0297070	−	0.271707i
$562$	38.6073			1.62855
$563$	−6.28066			−0.264698			−0.132349	−	0.991203i	$-0.542252\pi$
$563$	−6.28066			−0.264698			−0.132349	+	0.991203i	$0.542252\pi$
$564$	−5.78821			−0.243728
$565$	26.2528			1.10447
$566$	40.2077	+	40.2077i	1.69006	+	1.69006i
$567$	1.50360	+	1.50360i	0.0631451	+	0.0631451i
$568$	−0.203649			−0.00854491
$569$			26.1553i			1.09649i	0.836319	+	0.548244i	$0.184703\pi$
$569$			26.1553i			1.09649i	−0.836319	+	0.548244i	$0.815297\pi$
$570$	−10.3245	−	10.3245i	−0.432446	−	0.432446i
$571$			38.5184i			1.61194i	0.591954	+	0.805972i	$0.298357\pi$
$571$			38.5184i			1.61194i	−0.591954	+	0.805972i	$0.701643\pi$
$572$	18.8257	+	15.1148i	0.787142	+	0.631983i
$573$	−3.55229	+	3.55229i	−0.148399	+	0.148399i
$574$		−	0.495907i		−	0.0206988i
$575$	0.0973990	−	0.0973990i	0.00406182	−	0.00406182i
$576$			32.0712i			1.33630i
$577$	−22.8201	−	22.8201i	−0.950014	−	0.950014i	0.0487952	−	0.998809i	$-0.484462\pi$
$577$	−22.8201	−	22.8201i	−0.950014	−	0.950014i	−0.998809	+	0.0487952i	$0.984462\pi$
$578$	−7.82719	+	7.82719i	−0.325568	+	0.325568i
$579$	−4.40708	−	4.40708i	−0.183152	−	0.183152i
$580$	0.229588	−	0.229588i	0.00953314	−	0.00953314i
$581$	0.902830	−	0.902830i	0.0374557	−	0.0374557i
$582$	3.49294	+	3.49294i	0.144787	+	0.144787i
$583$	−12.9928	+	1.42057i	−0.538109	+	0.0588339i
$584$	6.94707	+	6.94707i	0.287472	+	0.287472i
$585$	−19.6596			−0.812825
$586$	−31.5494	−	31.5494i	−1.30329	−	1.30329i
$587$	−3.23549	−	3.23549i	−0.133543	−	0.133543i	0.637176	−	0.770719i	$-0.280103\pi$
$587$	−3.23549	−	3.23549i	−0.133543	−	0.133543i	−0.770719	+	0.637176i	$0.780103\pi$
$588$			7.14281i			0.294565i
$589$	19.9624	+	19.9624i	0.822536	+	0.822536i
$590$	68.2141			2.80833
$591$			2.90800i			0.119619i
$592$	−11.4304	−	11.4304i	−0.469788	−	0.469788i
$593$	0.836884	+	0.836884i	0.0343667	+	0.0343667i	0.724081	−	0.689715i	$-0.242264\pi$
$593$	0.836884	+	0.836884i	0.0343667	+	0.0343667i	−0.689715	+	0.724081i	$0.742264\pi$
$594$	16.8663	−	1.84407i	0.692034	−	0.0756632i
$595$			3.18734i			0.130668i
$596$			42.4205i			1.73761i
$597$		−	10.5016i		−	0.429803i
$598$		−	1.27912i		−	0.0523071i
$599$	29.0777	−	29.0777i	1.18808	−	1.18808i	0.210486	−	0.977597i	$-0.432495\pi$
$599$	29.0777	−	29.0777i	1.18808	−	1.18808i	0.977597	−	0.210486i	$-0.0675045\pi$
$600$	−0.203945	−	0.203945i	−0.00832600	−	0.00832600i
$601$	−11.5208			−0.469942			−0.234971	−	0.972002i	$-0.575500\pi$
$601$	−11.5208			−0.469942			−0.234971	+	0.972002i	$0.575500\pi$
$602$	−3.72166	−	3.72166i	−0.151684	−	0.151684i
$603$	−25.8411	−	25.8411i	−1.05233	−	1.05233i
$604$	35.9179	+	35.9179i	1.46148	+	1.46148i
$605$	25.5662	−	5.65817i	1.03941	−	0.230037i
$606$	−6.25866			−0.254241
$607$		−	19.4327i		−	0.788749i	−0.918950	−	0.394374i	$-0.870961\pi$
$607$		−	19.4327i		−	0.788749i	0.918950	−	0.394374i	$-0.129039\pi$
$608$	−39.3521	−	39.3521i	−1.59594	−	1.59594i
$609$			0.00643469i			0.000260747i
$610$	−25.0831	+	30.3955i	−1.01558	+	1.23068i
$611$		−	16.3717i		−	0.662328i
$612$	−23.5057	−	23.5057i	−0.950163	−	0.950163i
$613$	−27.0160			−1.09116			−0.545582	−	0.838057i	$-0.683691\pi$
$613$	−27.0160			−1.09116			−0.545582	+	0.838057i	$0.683691\pi$
$614$		−	55.0471i		−	2.22152i
$615$	0.811859			0.0327373
$616$	0.767735	+	0.616401i	0.0309329	+	0.0248355i
$617$	−16.4834	+	16.4834i	−0.663597	+	0.663597i	−0.956226	−	0.292629i	$-0.905470\pi$
$617$	−16.4834	+	16.4834i	−0.663597	+	0.663597i	0.292629	+	0.956226i	$0.405470\pi$
$618$	1.09778	−	1.09778i	0.0441593	−	0.0441593i
$619$	35.6717			1.43377			0.716884	−	0.697192i	$-0.245568\pi$
$619$	35.6717			1.43377			0.716884	+	0.697192i	$0.245568\pi$
$620$	16.9519	+	16.9519i	0.680804	+	0.680804i
$621$	−0.352698	−	0.352698i	−0.0141533	−	0.0141533i
$622$		−	47.0342i		−	1.88590i
$623$		−	1.68182i		−	0.0673808i
$624$	3.34989			0.134103
$625$	−27.8882			−1.11553
$626$			10.0995i			0.403657i
$627$	−6.00858	+	7.48376i	−0.239960	+	0.298873i
$628$	−22.2971	+	22.2971i	−0.889749	+	0.889749i
$629$	27.5023			1.09659
$630$	−4.05386			−0.161510
$631$	−1.56159	−	1.56159i	−0.0621658	−	0.0621658i	0.675340	−	0.737506i	$-0.263997\pi$
$631$	−1.56159	−	1.56159i	−0.0621658	−	0.0621658i	−0.737506	+	0.675340i	$0.763997\pi$
$632$	−3.20226			−0.127379
$633$	−3.39400	−	3.39400i	−0.134899	−	0.134899i
$634$	7.75541	+	7.75541i	0.308007	+	0.308007i
$635$		−	29.8938i		−	1.18630i
$636$	2.87660	−	2.87660i	0.114065	−	0.114065i
$637$	−20.2031			−0.800477
$638$	−0.299923	−	0.240803i	−0.0118741	−	0.00953349i
$639$	−0.389727	−	0.389727i	−0.0154174	−	0.0154174i
$640$	−13.6458	−	13.6458i	−0.539397	−	0.539397i
$641$	−2.58863	−	2.58863i	−0.102245	−	0.102245i	0.654134	−	0.756379i	$-0.273033\pi$
$641$	−2.58863	−	2.58863i	−0.102245	−	0.102245i	−0.756379	+	0.654134i	$0.773033\pi$
$642$	1.57243	−	1.57243i	0.0620589	−	0.0620589i
$643$	12.8895	−	12.8895i	0.508313	−	0.508313i	−0.405695	−	0.914008i	$-0.632971\pi$
$643$	12.8895	−	12.8895i	0.508313	−	0.508313i	0.914008	+	0.405695i	$0.132971\pi$
$644$		−	0.146351i		−	0.00576704i
$645$	6.09280	−	6.09280i	0.239904	−	0.239904i
$646$	69.8308			2.74746
$647$	4.10623	+	4.10623i	0.161433	+	0.161433i	0.783201	−	0.621768i	$-0.213586\pi$
$647$	4.10623	+	4.10623i	0.161433	+	0.161433i	−0.621768	+	0.783201i	$0.713586\pi$
$648$	5.53251	−	5.53251i	0.217338	−	0.217338i
$649$	−4.87326	−	44.5720i	−0.191292	−	1.74961i
$650$	2.91673	−	2.91673i	0.114403	−	0.114403i
$651$	−0.475112			−0.0186211
$652$	−43.4124			−1.70016
$653$	26.3786	+	26.3786i	1.03227	+	1.03227i	0.999462	+	0.0328113i	$0.0104460\pi$
$653$	26.3786	+	26.3786i	1.03227	+	1.03227i	0.0328113	+	0.999462i	$0.489554\pi$
$654$	−6.42002	+	6.42002i	−0.251043	+	0.251043i
$655$	27.0025			1.05507
$656$	2.28219			0.0891046
$657$			26.5895i			1.03736i
$658$		−	3.37589i		−	0.131606i
$659$	−0.615650			−0.0239823			−0.0119912	−	0.999928i	$-0.503817\pi$
$659$	−0.615650			−0.0239823			−0.0119912	+	0.999928i	$0.503817\pi$
$660$	−5.10244	+	6.35515i	−0.198612	+	0.247374i
$661$	8.51097	−	8.51097i	0.331039	−	0.331039i	−0.521942	−	0.852981i	$-0.674792\pi$
$661$	8.51097	−	8.51097i	0.331039	−	0.331039i	0.852981	+	0.521942i	$0.174792\pi$
$662$	−50.3410			−1.95656
$663$	−4.03001	+	4.03001i	−0.156513	+	0.156513i
$664$	−3.32198	−	3.32198i	−0.128918	−	0.128918i
$665$	3.34120	−	3.34120i	0.129566	−	0.129566i
$666$			34.9792i			1.35542i
$667$			0.0113073i			0.000437822i
$668$			46.3424i			1.79304i
$669$	3.75857	+	3.75857i	0.145315	+	0.145315i
$670$	65.1915			2.51857
$671$	21.6528	+	14.2181i	0.835898	+	0.548885i
$672$	0.936595			0.0361299
$673$	27.3989	+	27.3989i	1.05615	+	1.05615i	0.998327	+	0.0578235i	$0.0184161\pi$
$673$	27.3989	+	27.3989i	1.05615	+	1.05615i	0.0578235	+	0.998327i	$0.481584\pi$
$674$			27.4059i			1.05563i
$675$		−	1.60849i		−	0.0619107i
$676$			11.1557i			0.429064i
$677$	−9.20555	+	9.20555i	−0.353798	+	0.353798i	−0.861521	−	0.507722i	$-0.830488\pi$
$677$	−9.20555	+	9.20555i	−0.353798	+	0.353798i	0.507722	+	0.861521i	$0.330488\pi$
$678$	6.84462	+	6.84462i	0.262866	+	0.262866i
$679$	−1.13038	+	1.13038i	−0.0433800	+	0.0433800i
$680$	11.7279			0.449743
$681$	3.68234	−	3.68234i	0.141108	−	0.141108i
$682$	17.7800	−	22.1452i	0.680830	−	0.847982i
$683$	−22.5619			−0.863307			−0.431653	−	0.902040i	$-0.642070\pi$
$683$	−22.5619			−0.863307			−0.431653	+	0.902040i	$0.642070\pi$
$684$			49.2809i			1.88430i
$685$		−	9.26619i		−	0.354043i
$686$	−8.38045			−0.319967
$687$	7.41743			0.282993
$688$	17.1273	−	17.1273i	0.652972	−	0.652972i
$689$	8.13633	+	8.13633i	0.309969	+	0.309969i
$690$	0.431803			0.0164385
$691$	−9.24086			−0.351539			−0.175769	−	0.984431i	$-0.556241\pi$
$691$	−9.24086			−0.351539			−0.175769	+	0.984431i	$0.556241\pi$
$692$	−0.801502	+	0.801502i	−0.0304685	+	0.0304685i
$693$	0.289611	+	2.64885i	0.0110014	+	0.100622i
$694$	−51.0331	+	51.0331i	−1.93719	+	1.93719i
$695$	13.2469	+	13.2469i	0.502485	+	0.502485i
$696$	0.0236766			0.000897458
$697$	−2.74555	+	2.74555i	−0.103995	+	0.103995i
$698$			63.3349i			2.39726i
$699$	0.762781	−	0.762781i	0.0288510	−	0.0288510i
$700$	0.333718	−	0.333718i	0.0126134	−	0.0126134i
$701$	18.8469	+	18.8469i	0.711837	+	0.711837i	0.966919	−	0.255082i	$-0.0821025\pi$
$701$	18.8469	+	18.8469i	0.711837	+	0.711837i	−0.255082	+	0.966919i	$0.582102\pi$
$702$	−10.5620	−	10.5620i	−0.398636	−	0.398636i
$703$	−28.8300	−	28.8300i	−1.08734	−	1.08734i
$704$	−23.5433	+	29.3234i	−0.887321	+	1.10517i
$705$	5.52673			0.208149
$706$	−30.3198	+	30.3198i	−1.14110	+	1.14110i
$707$		−	2.02542i		−	0.0761738i
$708$	9.86819	+	9.86819i	0.370869	+	0.370869i
$709$	−15.4745	−	15.4745i	−0.581157	−	0.581157i	0.354064	−	0.935221i	$-0.384799\pi$
$709$	−15.4745	−	15.4745i	−0.581157	−	0.581157i	−0.935221	+	0.354064i	$0.884799\pi$
$710$	0.983195			0.0368987
$711$	−6.12825	−	6.12825i	−0.229827	−	0.229827i
$712$	−6.18830			−0.231916
$713$	−0.834890			−0.0312669
$714$	−0.831000	+	0.831000i	−0.0310994	+	0.0310994i
$715$	−17.9753	−	14.4320i	−0.672237	−	0.539727i
$716$		−	11.7793i		−	0.440214i
$717$	0.995513			0.0371781
$718$	21.3113			0.795332
$719$			2.59416i			0.0967458i	0.998829	+	0.0483729i	$0.0154036\pi$
$719$			2.59416i			0.0967458i	−0.998829	+	0.0483729i	$0.984596\pi$
$720$		−	18.6561i		−	0.695273i
$721$	0.355263	+	0.355263i	0.0132307	+	0.0132307i
$722$	−44.7238	−	44.7238i	−1.66445	−	1.66445i
$723$	−6.22346			−0.231453
$724$	2.46075	−	2.46075i	0.0914532	−	0.0914532i
$725$	−0.0257837	+	0.0257837i	−0.000957582	+	0.000957582i
$726$	8.14078	+	5.19039i	0.302133	+	0.192634i
$727$	−24.0052			−0.890302			−0.445151	−	0.895456i	$-0.646850\pi$
$727$	−24.0052			−0.890302			−0.445151	+	0.895456i	$0.646850\pi$
$728$		−	0.866768i		−	0.0321246i
$729$	18.1774			0.673237
$730$	−33.5398	−	33.5398i	−1.24136	−	1.24136i
$731$			41.2093i			1.52418i
$732$	−8.02581	+	0.768526i	−0.296642	+	0.0284055i
$733$			10.6009i			0.391552i	0.980649	+	0.195776i	$0.0627225\pi$
$733$			10.6009i			0.391552i	−0.980649	+	0.195776i	$0.937278\pi$
$734$	24.2592	+	24.2592i	0.895425	+	0.895425i
$735$		−	6.82014i		−	0.251565i
$736$	1.64583			0.0606661
$737$	−4.65733	−	42.5970i	−0.171555	−	1.56908i
$738$	−3.49197	−	3.49197i	−0.128541	−	0.128541i
$739$	19.6984	+	19.6984i	0.724618	+	0.724618i	0.969542	−	0.244924i	$-0.0787631\pi$
$739$	19.6984	+	19.6984i	0.724618	+	0.724618i	−0.244924	+	0.969542i	$0.578763\pi$
$740$	−24.4822	−	24.4822i	−0.899983	−	0.899983i
$741$	8.44912			0.310386
$742$	1.67773	+	1.67773i	0.0615915	+	0.0615915i
$743$	35.5458	−	35.5458i	1.30405	−	1.30405i	0.378412	−	0.925637i	$-0.376470\pi$
$743$	35.5458	−	35.5458i	1.30405	−	1.30405i	0.925637	−	0.378412i	$-0.123530\pi$
$744$			1.74818i			0.0640915i
$745$		−	40.5042i		−	1.48396i
$746$		−	23.8431i		−	0.872959i
$747$		−	12.7147i		−	0.465206i
$748$	−4.23642	−	38.7473i	−0.154899	−	1.41674i
$749$	0.508868	+	0.508868i	0.0185936	+	0.0185936i
$750$	−6.40217	−	6.40217i	−0.233774	−	0.233774i
$751$			12.1634i			0.443849i	0.975064	+	0.221924i	$0.0712338\pi$
$751$			12.1634i			0.443849i	−0.975064	+	0.221924i	$0.928766\pi$
$752$	15.5360			0.566540
$753$	−5.69935	−	5.69935i	−0.207696	−	0.207696i
$754$			0.338612i			0.0123315i
$755$	−34.2954	−	34.2954i	−1.24814	−	1.24814i
$756$	−1.20845	−	1.20845i	−0.0439510	−	0.0439510i
$757$	−50.4951			−1.83527			−0.917637	−	0.397419i	$-0.869906\pi$
$757$	−50.4951			−1.83527			−0.917637	+	0.397419i	$0.869906\pi$
$758$	−33.3750	−	33.3750i	−1.21223	−	1.21223i
$759$	−0.0308483	−	0.282146i	−0.00111972	−	0.0102413i
$760$	−12.2940	−	12.2940i	−0.445951	−	0.445951i
$761$	−5.81308	+	5.81308i	−0.210724	+	0.210724i	−0.804575	−	0.593851i	$-0.797607\pi$
$761$	−5.81308	+	5.81308i	−0.210724	+	0.210724i	0.593851	+	0.804575i	$0.297607\pi$
$762$	7.79388	−	7.79388i	0.282342	−	0.282342i
$763$	−2.07764	−	2.07764i	−0.0752156	−	0.0752156i
$764$	−21.3879	+	21.3879i	−0.773786	+	0.773786i
$765$	22.4439	+	22.4439i	0.811460	+	0.811460i
$766$			17.5514i			0.634158i
$767$	−27.9117	+	27.9117i	−1.00783	+	1.00783i
$768$			2.27433i			0.0820677i
$769$	−12.3444	+	12.3444i	−0.445151	+	0.445151i	−0.893739	−	0.448588i	$-0.851927\pi$
$769$	−12.3444	+	12.3444i	−0.445151	+	0.445151i	0.448588	+	0.893739i	$0.351927\pi$
$770$	−3.70655	−	2.97592i	−0.133575	−	0.107245i
$771$		−	11.7505i		−	0.423185i
$772$	−26.5344	−	26.5344i	−0.954995	−	0.954995i
$773$			13.0566i			0.469614i	0.972042	+	0.234807i	$0.0754458\pi$
$773$			13.0566i			0.469614i	−0.972042	+	0.234807i	$0.924554\pi$
$774$	−52.4127			−1.88394
$775$	−1.90377	−	1.90377i	−0.0683853	−	0.0683853i
$776$	4.15926	+	4.15926i	0.149309	+	0.149309i
$777$	0.686164			0.0246160
$778$	39.3052			1.40916
$779$	5.75617			0.206236
$780$	7.17493			0.256904
$781$	−0.0702402	−	0.642434i	−0.00251339	−	0.0229881i
$782$	−1.46027	+	1.46027i	−0.0522193	+	0.0522193i
$783$	0.0933672	+	0.0933672i	0.00333667	+	0.00333667i
$784$		−	19.1719i		−	0.684710i
$785$	21.2898	−	21.2898i	0.759865	−	0.759865i
$786$	7.04006	+	7.04006i	0.251111	+	0.251111i
$787$	19.8121	+	19.8121i	0.706226	+	0.706226i	0.965739	−	0.259514i	$-0.0835622\pi$
$787$	19.8121	+	19.8121i	0.706226	+	0.706226i	−0.259514	+	0.965739i	$0.583562\pi$
$788$			17.5087i			0.623722i
$789$		−	6.16486i		−	0.219475i
$790$	15.4602			0.550050
$791$	−2.21505	+	2.21505i	−0.0787581	+	0.0787581i
$792$	9.74650	−	1.06563i	0.346327	−	0.0378655i
$793$	−2.17374	−	22.7006i	−0.0771918	−	0.806123i
$794$		−	68.3866i		−	2.42695i
$795$	−2.74665	+	2.74665i	−0.0974136	+	0.0974136i
$796$		−	63.2289i		−	2.24109i
$797$			0.145215i			0.00514377i	0.999997	+	0.00257188i	$0.000818657\pi$
$797$			0.145215i			0.00514377i	−0.999997	+	0.00257188i	$0.999181\pi$
$798$	1.74223			0.0616743
$799$	−18.6903	+	18.6903i	−0.661215	+	0.661215i
$800$	3.75292	+	3.75292i	0.132686	+	0.132686i
$801$	−11.8427	−	11.8427i	−0.418441	−	0.418441i
$802$		−	63.0890i		−	2.22775i
$803$	−19.5192	+	24.3115i	−0.688819	+	0.857933i
$804$	9.43092	+	9.43092i	0.332603	+	0.332603i
$805$			0.139740i			0.00492518i
$806$	−25.0018			−0.880649
$807$		−	6.63665i		−	0.233621i
$808$	−7.45258			−0.262181
$809$			38.3512i			1.34836i	0.738569	+	0.674178i	$0.235502\pi$
$809$			38.3512i			1.34836i	−0.738569	+	0.674178i	$0.764498\pi$
$810$	−26.7104	+	26.7104i	−0.938508	+	0.938508i
$811$	1.58172	+	1.58172i	0.0555418	+	0.0555418i	0.734332	−	0.678790i	$-0.237495\pi$
$811$	1.58172	+	1.58172i	0.0555418	+	0.0555418i	−0.678790	+	0.734332i	$0.737495\pi$
$812$			0.0387424i			0.00135959i
$813$		−	5.19433i		−	0.182173i
$814$	−25.6781	+	31.9824i	−0.900016	+	1.12098i
$815$	41.4512			1.45197
$816$	−3.82431	−	3.82431i	−0.133878	−	0.133878i
$817$	43.1987	−	43.1987i	1.51133	−	1.51133i
$818$	82.6698			2.89048
$819$	1.65875	−	1.65875i	0.0579615	−	0.0579615i
$820$	4.88810			0.170700
$821$	−36.7051	+	36.7051i	−1.28102	+	1.28102i	−0.340926	+	0.940090i	$0.610741\pi$
$821$	−36.7051	+	36.7051i	−1.28102	+	1.28102i	−0.940090	+	0.340926i	$0.889259\pi$
$822$	2.41587	−	2.41587i	0.0842632	−	0.0842632i
$823$	−0.532920	+	0.532920i	−0.0185764	+	0.0185764i	−0.716334	−	0.697758i	$-0.754181\pi$
$823$	−0.532920	+	0.532920i	−0.0185764	+	0.0185764i	0.697758	+	0.716334i	$0.254181\pi$
$824$	1.30720	−	1.30720i	0.0455384	−	0.0455384i
$825$	0.573025	−	0.713709i	0.0199502	−	0.0248482i
$826$	−5.75547	+	5.75547i	−0.200258	+	0.200258i
$827$			44.5849i			1.55037i	0.631736	+	0.775184i	$0.282343\pi$
$827$			44.5849i			1.55037i	−0.631736	+	0.775184i	$0.717657\pi$
$828$	−1.03054	−	1.03054i	−0.0358138	−	0.0358138i
$829$		−	19.5130i		−	0.677715i	−0.940838	−	0.338857i	$-0.889960\pi$
$829$		−	19.5130i		−	0.677715i	0.940838	−	0.338857i	$-0.110040\pi$
$830$	16.0382	+	16.0382i	0.556693	+	0.556693i
$831$	−3.25405	+	3.25405i	−0.112882	+	0.112882i
$832$	33.1060			1.14774
$833$	23.0644	+	23.0644i	0.799133	+	0.799133i
$834$			6.90746i			0.239186i
$835$		−	44.2489i		−	1.53130i
$836$	−36.1769	+	45.0587i	−1.25120	+	1.55839i
$837$	−6.89387	+	6.89387i	−0.238287	+	0.238287i
$838$	−51.8726			−1.79191
$839$		−	7.68239i		−	0.265226i	−0.991168	−	0.132613i	$-0.957663\pi$
$839$		−	7.68239i		−	0.265226i	0.991168	−	0.132613i	$-0.0423367\pi$
$840$	0.292602			0.0100957
$841$			28.9970i			0.999897i
$842$	−22.2415			−0.766493
$843$	−5.33282	−	5.33282i	−0.183672	−	0.183672i
$844$	−20.4348	−	20.4348i	−0.703395	−	0.703395i
$845$		−	10.6517i		−	0.366430i
$846$	−23.7716	−	23.7716i	−0.817283	−	0.817283i
$847$	−1.67971	+	2.63451i	−0.0577155	+	0.0905229i
$848$	−7.72102	+	7.72102i	−0.265141	+	0.265141i
$849$		−	11.1078i		−	0.381217i
$850$	−6.65960			−0.228423
$851$	1.20576			0.0413329
$852$	0.142234	+	0.142234i	0.00487285	+	0.00487285i
$853$	19.3475			0.662445			0.331222	−	0.943553i	$-0.392539\pi$
$853$	19.3475			0.662445			0.331222	+	0.943553i	$0.392539\pi$
$854$	−0.448231	−	4.68093i	−0.0153382	−	0.160178i
$855$		−	47.0547i		−	1.60924i
$856$	1.87239	−	1.87239i	0.0639970	−	0.0639970i
$857$	−33.6907			−1.15085			−0.575427	−	0.817853i	$-0.695164\pi$
$857$	−33.6907			−1.15085			−0.575427	+	0.817853i	$0.695164\pi$
$858$	−0.923790	−	8.44920i	−0.0315377	−	0.288451i
$859$			9.56782i			0.326450i	0.986589	+	0.163225i	$0.0521896\pi$
$859$			9.56782i			0.326450i	−0.986589	+	0.163225i	$0.947810\pi$
$860$	36.6840	−	36.6840i	1.25091	−	1.25091i
$861$	−0.0684995	+	0.0684995i	−0.00233446	+	0.00233446i
$862$	22.2279	+	22.2279i	0.757084	+	0.757084i
$863$	−31.2672			−1.06435			−0.532174	−	0.846635i	$-0.678625\pi$
$863$	−31.2672			−1.06435			−0.532174	+	0.846635i	$0.678625\pi$
$864$	13.5900	−	13.5900i	0.462340	−	0.462340i
$865$	0.765294	−	0.765294i	0.0260208	−	0.0260208i
$866$			50.4814i			1.71543i
$867$	2.16234			0.0734368
$868$	−2.86059			−0.0970946
$869$	−1.10449	−	10.1019i	−0.0374672	−	0.342684i
$870$	−0.114308			−0.00387541
$871$	−26.6749	+	26.6749i	−0.903846	+	0.903846i
$872$	−7.64472	+	7.64472i	−0.258883	+	0.258883i
$873$			15.9193i			0.538788i
$874$	3.06153			0.103558
$875$	2.07186	−	2.07186i	0.0700418	−	0.0700418i
$876$		−	9.70406i		−	0.327870i
$877$	12.7563	+	12.7563i	0.430750	+	0.430750i	0.888884	−	0.458133i	$-0.151482\pi$
$877$	12.7563	+	12.7563i	0.430750	+	0.430750i	−0.458133	+	0.888884i	$0.651482\pi$
$878$	−10.4612	+	10.4612i	−0.353048	+	0.353048i
$879$			8.71581i			0.293977i
$880$	13.6954	−	17.0577i	0.461671	−	0.575016i
$881$			3.91743i			0.131981i	0.997820	+	0.0659907i	$0.0210208\pi$
$881$			3.91743i			0.131981i	−0.997820	+	0.0659907i	$0.978979\pi$
$882$	−29.3348	+	29.3348i	−0.987753	+	0.987753i
$883$	8.00374	+	8.00374i	0.269347	+	0.269347i	0.828837	−	0.559490i	$-0.189003\pi$
$883$	8.00374	+	8.00374i	0.269347	+	0.269347i	−0.559490	+	0.828837i	$0.689003\pi$
$884$	−24.2642	+	24.2642i	−0.816093	+	0.816093i
$885$	−9.42240	−	9.42240i	−0.316730	−	0.316730i
$886$	−59.9769	−	59.9769i	−2.01496	−	2.01496i
$887$	−21.2869	−	21.2869i	−0.714743	−	0.714743i	0.252781	−	0.967524i	$-0.418655\pi$
$887$	−21.2869	−	21.2869i	−0.714743	−	0.714743i	−0.967524	+	0.252781i	$0.918655\pi$
$888$		−	2.52475i		−	0.0847252i
$889$	2.52225	+	2.52225i	0.0845935	+	0.0845935i
$890$	29.8765			1.00146
$891$	19.3612	+	15.5447i	0.648623	+	0.520768i
$892$	22.6298	+	22.6298i	0.757703	+	0.757703i
$893$	39.1851			1.31128
$894$	10.5602	−	10.5602i	0.353186	−	0.353186i
$895$			11.2472i			0.375952i
$896$	2.30269			0.0769275
$897$	−0.176685	+	0.176685i	−0.00589932	+	0.00589932i
$898$	14.0924	+	14.0924i	0.470269	+	0.470269i
$899$	0.221014			0.00737124
$900$		−	4.69981i		−	0.156660i
$901$		−	18.5772i		−	0.618898i
$902$	−0.629354	−	5.75622i	−0.0209552	−	0.191661i
$903$			1.02814i			0.0342145i
$904$	8.15031	+	8.15031i	0.271075	+	0.271075i
$905$	−2.34959	+	2.34959i	−0.0781030	+	0.0781030i
$906$		−	17.8829i		−	0.594120i
$907$	−8.99133	+	8.99133i	−0.298552	+	0.298552i	−0.840447	−	0.541894i	$-0.817707\pi$
$907$	−8.99133	+	8.99133i	−0.298552	+	0.298552i	0.541894	+	0.840447i	$0.317707\pi$
$908$	22.1709	−	22.1709i	0.735767	−	0.735767i
$909$	−14.2622	−	14.2622i	−0.473046	−	0.473046i
$910$			4.18467i			0.138720i
$911$	−21.6959			−0.718816			−0.359408	−	0.933181i	$-0.617021\pi$
$911$	−21.6959			−0.718816			−0.359408	+	0.933181i	$0.617021\pi$
$912$			8.01785i			0.265498i
$913$	9.33379	−	11.6254i	0.308903	−	0.384743i
$914$		−	14.5679i		−	0.481864i
$915$	7.66325	−	0.733809i	0.253339	−	0.0242590i
$916$	44.6594			1.47559
$917$	−2.27830	+	2.27830i	−0.0752360	+	0.0752360i
$918$			24.1156i			0.795933i
$919$	22.5849			0.745007			0.372504	−	0.928031i	$-0.378499\pi$
$919$	22.5849			0.745007			0.372504	+	0.928031i	$0.378499\pi$
$920$	0.514175			0.0169518
$921$	−7.60364	+	7.60364i	−0.250548	+	0.250548i
$922$	−31.0010	+	31.0010i	−1.02096	+	1.02096i
$923$	−0.402302	+	0.402302i	−0.0132419	+	0.0132419i
$924$	−0.105696	−	0.966719i	−0.00347714	−	0.0318027i
$925$	2.74945	+	2.74945i	0.0904013	+	0.0904013i
$926$	37.9663	−	37.9663i	1.24765	−	1.24765i
$927$	5.00323			0.164328
$928$	−0.435688			−0.0143022
$929$			46.8503i			1.53711i	0.639785	+	0.768554i	$0.279023\pi$
$929$			46.8503i			1.53711i	−0.639785	+	0.768554i	$0.720977\pi$
$930$		−	8.44005i		−	0.276760i
$931$		−	48.3556i		−	1.58479i
$932$	4.59261	−	4.59261i	0.150436	−	0.150436i
$933$	−6.49682	+	6.49682i	−0.212696	+	0.212696i
$934$	10.8746			0.355827
$935$	4.04504	+	36.9969i	0.132287	+	1.20993i
$936$	−6.10341	−	6.10341i	−0.199496	−	0.199496i
$937$		−	45.6084i		−	1.48996i	−0.667085	−	0.744981i	$-0.732458\pi$
$937$		−	45.6084i		−	1.48996i	0.667085	−	0.744981i	$-0.267542\pi$
$938$	−5.50044	+	5.50044i	−0.179596	+	0.179596i
$939$	1.39504	−	1.39504i	0.0455254	−	0.0455254i
$940$	33.2757			1.08533
$941$	17.1116	+	17.1116i	0.557823	+	0.557823i	0.928687	−	0.370864i	$-0.120938\pi$
$941$	17.1116	+	17.1116i	0.557823	+	0.557823i	−0.370864	+	0.928687i	$0.620938\pi$
$942$	11.1013			0.361700
$943$	−0.120371	+	0.120371i	−0.00391981	+	0.00391981i
$944$	−26.4870	−	26.4870i	−0.862079	−	0.862079i
$945$	1.15386	+	1.15386i	0.0375351	+	0.0375351i
$946$	−47.9222	−	38.4759i	−1.55809	−	1.25096i
$947$	−11.8434	+	11.8434i	−0.384860	+	0.384860i	−0.872849	−	0.487990i	$-0.837730\pi$
$947$	−11.8434	+	11.8434i	−0.384860	+	0.384860i	0.487990	+	0.872849i	$0.337730\pi$
$948$	2.23655	+	2.23655i	0.0726398	+	0.0726398i
$949$	27.4475			0.890983
$950$	6.98109	+	6.98109i	0.226497	+	0.226497i
$951$		−	2.14251i		−	0.0694755i
$952$	−0.989523	+	0.989523i	−0.0320706	+	0.0320706i
$953$	11.5301	−	11.5301i	0.373496	−	0.373496i	−0.495253	−	0.868749i	$-0.664925\pi$
$953$	11.5301	−	11.5301i	0.373496	−	0.373496i	0.868749	+	0.495253i	$0.164925\pi$
$954$	23.6278			0.764977
$955$	20.4217	−	20.4217i	0.660830	−	0.660830i
$956$	5.99385			0.193855
$957$	0.00816625	+	0.0746905i	0.000263977	+	0.00241440i
$958$	59.3039	+	59.3039i	1.91602	+	1.91602i
$959$	0.781822	+	0.781822i	0.0252464	+	0.0252464i
$960$			11.1759i			0.360700i
$961$		−	14.6812i		−	0.473587i
$962$	36.1079			1.16417
$963$	7.16647			0.230936
$964$	−37.4706			−1.20685
$965$	25.3358	+	25.3358i	0.815587	+	0.815587i
$966$	−0.0364328	+	0.0364328i	−0.00117221	+	0.00117221i
$967$	1.15755			0.0372244			0.0186122	−	0.999827i	$-0.494075\pi$
$967$	1.15755			0.0372244			0.0186122	+	0.999827i	$0.494075\pi$
$968$	9.69373	+	6.18053i	0.311568	+	0.198650i
$969$	−9.64572	−	9.64572i	−0.309865	−	0.309865i
$970$	−20.0805	−	20.0805i	−0.644745	−	0.644745i
$971$	0.977007			0.0313537			0.0156768	−	0.999877i	$-0.495010\pi$
$971$	0.977007			0.0313537			0.0156768	+	0.999877i	$0.495010\pi$
$972$	−25.7785			−0.826847
$973$	−2.23539			−0.0716632
$974$	−8.29682	+	8.29682i	−0.265847	+	0.265847i
$975$	−0.805773			−0.0258054
$976$	21.5419	−	2.06279i	0.689540	−	0.0660282i
$977$	30.3260			0.970215			0.485107	−	0.874455i	$-0.338781\pi$
$977$	30.3260			0.970215			0.485107	+	0.874455i	$0.338781\pi$
$978$	10.8071	+	10.8071i	0.345574	+	0.345574i
$979$	−2.13440	−	19.5217i	−0.0682157	−	0.623917i
$980$		−	41.0632i		−	1.31171i
$981$	−29.2597			−0.934191
$982$	27.4089	+	27.4089i	0.874652	+	0.874652i
$983$	−21.5029	+	21.5029i	−0.685835	+	0.685835i	−0.961309	−	0.275473i	$-0.911165\pi$
$983$	−21.5029	+	21.5029i	−0.685835	+	0.685835i	0.275473	+	0.961309i	$0.411165\pi$
$984$	0.252045	+	0.252045i	0.00803491	+	0.00803491i
$985$		−	16.7178i		−	0.532672i
$986$	0.386567	−	0.386567i	0.0123108	−	0.0123108i
$987$	−0.466310	+	0.466310i	−0.0148428	+	0.0148428i
$988$	50.8710			1.61842
$989$			1.80670i			0.0574499i
$990$	−47.0551	+	5.14475i	−1.49551	+	0.163511i
$991$	24.5433			0.779644			0.389822	−	0.920890i	$-0.372537\pi$
$991$	24.5433			0.779644			0.389822	+	0.920890i	$0.372537\pi$
$992$		−	32.1695i		−	1.02138i
$993$	6.95359	+	6.95359i	0.220665	+	0.220665i
$994$	−0.0829558	+	0.0829558i	−0.00263120	+	0.00263120i
$995$			60.3726i			1.91394i
$996$			4.64033i			0.147034i
$997$	−2.10312	+	2.10312i	−0.0666065	+	0.0666065i	−0.739625	−	0.673019i	$-0.764997\pi$
$997$	−2.10312	+	2.10312i	−0.0666065	+	0.0666065i	0.673019	+	0.739625i	$0.264997\pi$
$998$		−	24.7583i		−	0.783710i
$999$	9.95623	−	9.95623i	0.315001	−	0.315001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.f.a.538.10	✓	120
11.10	odd	2	inner	671.2.f.a.538.51	yes	120
61.11	odd	4	inner	671.2.f.a.560.51	yes	120
671.560	even	4	inner	671.2.f.a.560.10	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.f.a.538.10	✓	120	1.1	even	1	trivial
671.2.f.a.538.51	yes	120	11.10	odd	2	inner
671.2.f.a.560.10	yes	120	671.560	even	4	inner
671.2.f.a.560.51	yes	120	61.11	odd	4	inner

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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.49884 - 1.49884i) q^{2} +0.414070i q^{3} +2.49306i q^{4} -2.38044i q^{5} +(0.620625 - 0.620625i) q^{6} +(0.200846 + 0.200846i) q^{7} +(0.739017 - 0.739017i) q^{8} +2.82855 q^{9} +O(q^{10})\)	\(q+(-1.49884 - 1.49884i) q^{2} +0.414070i q^{3} +2.49306i q^{4} -2.38044i q^{5} +(0.620625 - 0.620625i) q^{6} +(0.200846 + 0.200846i) q^{7} +(0.739017 - 0.739017i) q^{8} +2.82855 q^{9} +(-3.56790 + 3.56790i) q^{10} +(2.58621 + 2.07642i) q^{11} -1.03230 q^{12} -2.91981i q^{13} -0.602073i q^{14} +0.985666 q^{15} +2.77078 q^{16} +(-3.33333 + 3.33333i) q^{17} +(-4.23955 - 4.23955i) q^{18} +6.98848 q^{19} +5.93457 q^{20} +(-0.0831643 + 0.0831643i) q^{21} +(-0.764090 - 6.98855i) q^{22} +(-0.146140 + 0.146140i) q^{23} +(0.306004 + 0.306004i) q^{24} -0.666476 q^{25} +(-4.37634 + 4.37634i) q^{26} +2.41342i q^{27} +(-0.500721 + 0.500721i) q^{28} +(0.0386866 - 0.0386866i) q^{29} +(-1.47736 - 1.47736i) q^{30} +(2.85647 + 2.85647i) q^{31} +(-5.63099 - 5.63099i) q^{32} +(-0.859783 + 1.07087i) q^{33} +9.99227 q^{34} +(0.478101 - 0.478101i) q^{35} +7.05173i q^{36} +(-4.12535 - 4.12535i) q^{37} +(-10.4746 - 10.4746i) q^{38} +1.20901 q^{39} +(-1.75918 - 1.75918i) q^{40} +0.823665 q^{41} +0.249300 q^{42} +(6.18141 - 6.18141i) q^{43} +(-5.17664 + 6.44757i) q^{44} -6.73317i q^{45} +0.438083 q^{46} +5.60710 q^{47} +1.14729i q^{48} -6.91932i q^{49} +(0.998942 + 0.998942i) q^{50} +(-1.38023 - 1.38023i) q^{51} +7.27927 q^{52} +(-2.78659 + 2.78659i) q^{53} +(3.61734 - 3.61734i) q^{54} +(4.94279 - 6.15630i) q^{55} +0.296857 q^{56} +2.89372i q^{57} -0.115970 q^{58} +(-9.55942 - 9.55942i) q^{59} +2.45732i q^{60} +(7.77469 - 0.744480i) q^{61} -8.56279i q^{62} +(0.568102 + 0.568102i) q^{63} +11.3384i q^{64} -6.95043 q^{65} +(2.89375 - 0.316386i) q^{66} +(-9.13584 - 9.13584i) q^{67} +(-8.31018 - 8.31018i) q^{68} +(-0.0605123 - 0.0605123i) q^{69} -1.43320 q^{70} +(-0.137784 - 0.137784i) q^{71} +(2.09034 - 2.09034i) q^{72} +9.40043i q^{73} +12.3665i q^{74} -0.275967i q^{75} +17.4227i q^{76} +(0.102389 + 0.936471i) q^{77} +(-1.81211 - 1.81211i) q^{78} +(-2.16657 - 2.16657i) q^{79} -6.59566i q^{80} +7.48631 q^{81} +(-1.23454 - 1.23454i) q^{82} -4.49513i q^{83} +(-0.207333 - 0.207333i) q^{84} +(7.93477 + 7.93477i) q^{85} -18.5299 q^{86} +(0.0160190 + 0.0160190i) q^{87} +(3.44576 - 0.376741i) q^{88} +(-4.18685 - 4.18685i) q^{89} +(-10.0920 + 10.0920i) q^{90} +(0.586433 - 0.586433i) q^{91} +(-0.364336 - 0.364336i) q^{92} +(-1.18278 + 1.18278i) q^{93} +(-8.40416 - 8.40416i) q^{94} -16.6356i q^{95} +(2.33162 - 2.33162i) q^{96} +5.62809i q^{97} +(-10.3710 + 10.3710i) q^{98} +(7.31521 + 5.87325i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 120 q^{9}+O(q^{10}) \) 120 * q - 120 * q^9	\( 120 q - 120 q^{9} - 4 q^{11} + 16 q^{12} + 16 q^{15} - 148 q^{16} + 56 q^{20} - 4 q^{22} - 4 q^{23} - 104 q^{25} + 40 q^{26} - 2 q^{33} - 8 q^{34} - 12 q^{37} + 20 q^{38} + 16 q^{42} - 10 q^{44} - 4 q^{53} + 50 q^{55} - 24 q^{56} + 64 q^{58} - 56 q^{67} + 68 q^{69} + 144 q^{70} - 12 q^{71} - 64 q^{77} + 84 q^{78} + 72 q^{81} + 40 q^{82} - 80 q^{86} + 4 q^{89} - 4 q^{91} + 4 q^{92} + 64 q^{93} + 24 q^{99}+O(q^{100}) \) 120 * q - 120 * q^9 - 4 * q^11 + 16 * q^12 + 16 * q^15 - 148 * q^16 + 56 * q^20 - 4 * q^22 - 4 * q^23 - 104 * q^25 + 40 * q^26 - 2 * q^33 - 8 * q^34 - 12 * q^37 + 20 * q^38 + 16 * q^42 - 10 * q^44 - 4 * q^53 + 50 * q^55 - 24 * q^56 + 64 * q^58 - 56 * q^67 + 68 * q^69 + 144 * q^70 - 12 * q^71 - 64 * q^77 + 84 * q^78 + 72 * q^81 + 40 * q^82 - 80 * q^86 + 4 * q^89 - 4 * q^91 + 4 * q^92 + 64 * q^93 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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