LMFDB - Embedded newform 420.2.i.a.139.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(139,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))

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

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

chi := DirichletCharacter("420.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.i (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.15
Character	$\chi$	$=$	420.139
Dual form			420.2.i.a.139.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.846354 + 1.13300i) q^{2} -1.00000i q^{3} +(-0.567368 - 1.91784i) q^{4} +(2.22361 + 0.235752i) q^{5} +(1.13300 + 0.846354i) q^{6} +(2.54904 + 0.708793i) q^{7} +(2.65310 + 0.980342i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.846354 + 1.13300i) q^{2} -1.00000i q^{3} +(-0.567368 - 1.91784i) q^{4} +(2.22361 + 0.235752i) q^{5} +(1.13300 + 0.846354i) q^{6} +(2.54904 + 0.708793i) q^{7} +(2.65310 + 0.980342i) q^{8} -1.00000 q^{9} +(-2.14906 + 2.31981i) q^{10} -5.27789i q^{11} +(-1.91784 + 0.567368i) q^{12} -2.60538 q^{13} +(-2.96045 + 2.28817i) q^{14} +(0.235752 - 2.22361i) q^{15} +(-3.35619 + 2.17624i) q^{16} +3.66896 q^{17} +(0.846354 - 1.13300i) q^{18} -6.51939 q^{19} +(-0.809470 - 4.39827i) q^{20} +(0.708793 - 2.54904i) q^{21} +(5.97984 + 4.46697i) q^{22} +3.54996 q^{23} +(0.980342 - 2.65310i) q^{24} +(4.88884 + 1.04844i) q^{25} +(2.20508 - 2.95189i) q^{26} +1.00000i q^{27} +(-0.0868958 - 5.29079i) q^{28} +6.64523 q^{29} +(2.31981 + 2.14906i) q^{30} +4.51142 q^{31} +(0.374851 - 5.64442i) q^{32} -5.27789 q^{33} +(-3.10524 + 4.15692i) q^{34} +(5.50096 + 2.17702i) q^{35} +(0.567368 + 1.91784i) q^{36} -0.593655i q^{37} +(5.51771 - 7.38645i) q^{38} +2.60538i q^{39} +(5.66833 + 2.80537i) q^{40} -8.01200i q^{41} +(2.28817 + 2.96045i) q^{42} -0.678893 q^{43} +(-10.1221 + 2.99451i) q^{44} +(-2.22361 - 0.235752i) q^{45} +(-3.00452 + 4.02210i) q^{46} +5.79334i q^{47} +(2.17624 + 3.35619i) q^{48} +(5.99522 + 3.61349i) q^{49} +(-5.32557 + 4.65170i) q^{50} -3.66896i q^{51} +(1.47821 + 4.99669i) q^{52} -1.21027i q^{53} +(-1.13300 - 0.846354i) q^{54} +(1.24427 - 11.7360i) q^{55} +(6.06800 + 4.37943i) q^{56} +6.51939i q^{57} +(-5.62422 + 7.52903i) q^{58} -10.4372 q^{59} +(-4.39827 + 0.809470i) q^{60} +11.9597i q^{61} +(-3.81826 + 5.11143i) q^{62} +(-2.54904 - 0.708793i) q^{63} +(6.07786 + 5.20189i) q^{64} +(-5.79334 - 0.614223i) q^{65} +(4.46697 - 5.97984i) q^{66} -8.59277 q^{67} +(-2.08165 - 7.03646i) q^{68} -3.54996i q^{69} +(-7.12232 + 4.39005i) q^{70} +0.618749i q^{71} +(-2.65310 - 0.980342i) q^{72} -1.27551 q^{73} +(0.672610 + 0.502443i) q^{74} +(1.04844 - 4.88884i) q^{75} +(3.69889 + 12.5031i) q^{76} +(3.74094 - 13.4536i) q^{77} +(-2.95189 - 2.20508i) q^{78} -6.11484i q^{79} +(-7.97589 + 4.04787i) q^{80} +1.00000 q^{81} +(9.07758 + 6.78099i) q^{82} +12.0472i q^{83} +(-5.29079 + 0.0868958i) q^{84} +(8.15831 + 0.864963i) q^{85} +(0.574584 - 0.769185i) q^{86} -6.64523i q^{87} +(5.17414 - 14.0028i) q^{88} -15.9259i q^{89} +(2.14906 - 2.31981i) q^{90} +(-6.64123 - 1.84668i) q^{91} +(-2.01413 - 6.80824i) q^{92} -4.51142i q^{93} +(-6.56384 - 4.90322i) q^{94} +(-14.4965 - 1.53696i) q^{95} +(-5.64442 - 0.374851i) q^{96} +0.241900 q^{97} +(-9.16816 + 3.73428i) q^{98} +5.27789i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{9}+O(q^{10}) $ 48 * q - 48 * q^9	$ 48 q - 48 q^{9} + 20 q^{14} - 16 q^{16} + 8 q^{25} - 16 q^{30} - 40 q^{44} + 16 q^{46} - 16 q^{49} + 48 q^{50} + 28 q^{56} - 32 q^{60} - 112 q^{74} + 48 q^{81} - 28 q^{84} + 56 q^{85} + 8 q^{86}+O(q^{100}) $ 48 * q - 48 * q^9 + 20 * q^14 - 16 * q^16 + 8 * q^25 - 16 * q^30 - 40 * q^44 + 16 * q^46 - 16 * q^49 + 48 * q^50 + 28 * q^56 - 32 * q^60 - 112 * q^74 + 48 * q^81 - 28 * q^84 + 56 * q^85 + 8 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	−0.846354	+	1.13300i	−0.598463	+	0.801150i
$2$	−0.846354	+	1.13300i	−0.598463	+	0.801150i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−0.567368	−	1.91784i	−0.283684	−	0.958918i
$5$	2.22361	+	0.235752i	0.994427	+	0.105431i
$5$	2.22361	+	0.235752i	0.994427	+	0.105431i
$6$	1.13300	+	0.846354i	0.462544	+	0.345523i
$7$	2.54904	+	0.708793i	0.963447	+	0.267899i
$7$	2.54904	+	0.708793i	0.963447	+	0.267899i
$8$	2.65310	+	0.980342i	0.938012	+	0.346603i
$9$	−1.00000			−0.333333
$10$	−2.14906	+	2.31981i	−0.679594	+	0.733589i
$11$		−	5.27789i		−	1.59134i	−0.605727	−	0.795672i	$-0.707118\pi$
$11$		−	5.27789i		−	1.59134i	0.605727	−	0.795672i	$-0.292882\pi$
$12$	−1.91784	+	0.567368i	−0.553631	+	0.163785i
$13$	−2.60538			−0.722603			−0.361302	−	0.932449i	$-0.617667\pi$
$13$	−2.60538			−0.722603			−0.361302	+	0.932449i	$0.617667\pi$
$14$	−2.96045	+	2.28817i	−0.791215	+	0.611539i
$15$	0.235752	−	2.22361i	0.0608708	−	0.574132i
$16$	−3.35619	+	2.17624i	−0.839047	+	0.544059i
$17$	3.66896			0.889853			0.444927	−	0.895567i	$-0.353230\pi$
$17$	3.66896			0.889853			0.444927	+	0.895567i	$0.353230\pi$
$18$	0.846354	−	1.13300i	0.199488	−	0.267050i
$19$	−6.51939			−1.49565			−0.747825	−	0.663896i	$-0.768902\pi$
$19$	−6.51939			−1.49565			−0.747825	+	0.663896i	$0.768902\pi$
$20$	−0.809470	−	4.39827i	−0.181003	−	0.983483i
$21$	0.708793	−	2.54904i	0.154671	−	0.556246i
$22$	5.97984	+	4.46697i	1.27491	+	0.952361i
$23$	3.54996			0.740218			0.370109	−	0.928988i	$-0.379320\pi$
$23$	3.54996			0.740218			0.370109	+	0.928988i	$0.379320\pi$
$24$	0.980342	−	2.65310i	0.200111	−	0.541561i
$25$	4.88884	+	1.04844i	0.977768	+	0.209688i
$26$	2.20508	−	2.95189i	0.432451	−	0.578914i
$27$			1.00000i			0.192450i
$28$	−0.0868958	−	5.29079i	−0.0164218	−	0.999865i
$29$	6.64523			1.23399			0.616994	−	0.786968i	$-0.288350\pi$
$29$	6.64523			1.23399			0.616994	+	0.786968i	$0.288350\pi$
$30$	2.31981	+	2.14906i	0.423538	+	0.392364i
$31$	4.51142			0.810275			0.405138	−	0.914256i	$-0.367224\pi$
$31$	4.51142			0.810275			0.405138	+	0.914256i	$0.367224\pi$
$32$	0.374851	−	5.64442i	0.0662649	−	0.997802i
$33$	−5.27789			−0.918763
$34$	−3.10524	+	4.15692i	−0.532544	+	0.712906i
$35$	5.50096	+	2.17702i	0.929832	+	0.367983i
$36$	0.567368	+	1.91784i	0.0945614	+	0.319639i
$37$		−	0.593655i		−	0.0975963i	−0.998809	−	0.0487981i	$-0.984461\pi$
$37$		−	0.593655i		−	0.0975963i	0.998809	−	0.0487981i	$-0.0155391\pi$
$38$	5.51771	−	7.38645i	0.895091	−	1.19824i
$39$			2.60538i			0.417195i
$40$	5.66833	+	2.80537i	0.896241	+	0.443567i
$41$		−	8.01200i		−	1.25126i	−0.780118	−	0.625632i	$-0.784841\pi$
$41$		−	8.01200i		−	1.25126i	0.780118	−	0.625632i	$-0.215159\pi$
$42$	2.28817	+	2.96045i	0.353072	+	0.456808i
$43$	−0.678893			−0.103530			−0.0517651	−	0.998659i	$-0.516485\pi$
$43$	−0.678893			−0.103530			−0.0517651	+	0.998659i	$0.516485\pi$
$44$	−10.1221	+	2.99451i	−1.52597	+	0.451439i
$45$	−2.22361	−	0.235752i	−0.331476	−	0.0351438i
$46$	−3.00452	+	4.02210i	−0.442993	+	0.593026i
$47$			5.79334i			0.845046i	0.906352	+	0.422523i	$0.138855\pi$
$47$			5.79334i			0.845046i	−0.906352	+	0.422523i	$0.861145\pi$
$48$	2.17624	+	3.35619i	0.314113	+	0.484424i
$49$	5.99522	+	3.61349i	0.856461	+	0.516212i
$50$	−5.32557	+	4.65170i	−0.753149	+	0.657849i
$51$		−	3.66896i		−	0.513757i
$52$	1.47821	+	4.99669i	0.204991	+	0.692917i
$53$		−	1.21027i		−	0.166243i	−0.996539	−	0.0831216i	$-0.973511\pi$
$53$		−	1.21027i		−	0.166243i	0.996539	−	0.0831216i	$-0.0264890\pi$
$54$	−1.13300	−	0.846354i	−0.154181	−	0.115174i
$55$	1.24427	−	11.7360i	0.167778	−	1.58248i
$56$	6.06800	+	4.37943i	0.810870	+	0.585226i
$57$			6.51939i			0.863514i
$58$	−5.62422	+	7.52903i	−0.738496	+	0.988610i
$59$	−10.4372			−1.35880			−0.679401	−	0.733767i	$-0.737760\pi$
$59$	−10.4372			−1.35880			−0.679401	+	0.733767i	$0.737760\pi$
$60$	−4.39827	+	0.809470i	−0.567814	+	0.104502i
$61$			11.9597i			1.53128i	0.643269	+	0.765640i	$0.277578\pi$
$61$			11.9597i			1.53128i	−0.643269	+	0.765640i	$0.722422\pi$
$62$	−3.81826	+	5.11143i	−0.484920	+	0.649153i
$63$	−2.54904	−	0.708793i	−0.321149	−	0.0892996i
$64$	6.07786	+	5.20189i	0.759732	+	0.650236i
$65$	−5.79334	−	0.614223i	−0.718576	−	0.0761850i
$66$	4.46697	−	5.97984i	0.549846	−	0.736068i
$67$	−8.59277			−1.04977			−0.524887	−	0.851172i	$-0.675892\pi$
$67$	−8.59277			−1.04977			−0.524887	+	0.851172i	$0.675892\pi$
$68$	−2.08165	−	7.03646i	−0.252437	−	0.853296i
$69$		−	3.54996i		−	0.427365i
$70$	−7.12232	+	4.39005i	−0.851280	+	0.524711i
$71$			0.618749i			0.0734320i	0.999326	+	0.0367160i	$0.0116897\pi$
$71$			0.618749i			0.0734320i	−0.999326	+	0.0367160i	$0.988310\pi$
$72$	−2.65310	−	0.980342i	−0.312671	−	0.115534i
$73$	−1.27551			−0.149287			−0.0746435	−	0.997210i	$-0.523782\pi$
$73$	−1.27551			−0.149287			−0.0746435	+	0.997210i	$0.523782\pi$
$74$	0.672610	+	0.502443i	0.0781893	+	0.0584078i
$75$	1.04844	−	4.88884i	0.121063	−	0.564515i
$76$	3.69889	+	12.5031i	0.424292	+	1.43421i
$77$	3.74094	−	13.4536i	0.426319	−	1.53318i
$78$	−2.95189	−	2.20508i	−0.334236	−	0.249676i
$79$		−	6.11484i		−	0.687973i	−0.938975	−	0.343986i	$-0.888223\pi$
$79$		−	6.11484i		−	0.687973i	0.938975	−	0.343986i	$-0.111777\pi$
$80$	−7.97589	+	4.04787i	−0.891731	+	0.452565i
$81$	1.00000			0.111111
$82$	9.07758	+	6.78099i	1.00245	+	0.748835i
$83$			12.0472i			1.32235i	0.750233	+	0.661174i	$0.229941\pi$
$83$			12.0472i			1.32235i	−0.750233	+	0.661174i	$0.770059\pi$
$84$	−5.29079	+	0.0868958i	−0.577272	+	0.00948110i
$85$	8.15831	+	0.864963i	0.884893	+	0.0938184i
$86$	0.574584	−	0.769185i	0.0619590	−	0.0829433i
$87$		−	6.64523i		−	0.712443i
$88$	5.17414	−	14.0028i	0.551565	−	1.49270i
$89$		−	15.9259i		−	1.68814i	−0.536234	−	0.844069i	$-0.680154\pi$
$89$		−	15.9259i		−	1.68814i	0.536234	−	0.844069i	$-0.319846\pi$
$90$	2.14906	−	2.31981i	0.226531	−	0.244530i
$91$	−6.64123	−	1.84668i	−0.696190	−	0.193584i
$92$	−2.01413	−	6.80824i	−0.209988	−	0.709808i
$93$		−	4.51142i		−	0.467813i
$94$	−6.56384	−	4.90322i	−0.677009	−	0.505729i
$95$	−14.4965	−	1.53696i	−1.48731	−	0.157689i
$96$	−5.64442	−	0.374851i	−0.576081	−	0.0382581i
$97$	0.241900			0.0245612			0.0122806	−	0.999925i	$-0.496091\pi$
$97$	0.241900			0.0245612			0.0122806	+	0.999925i	$0.496091\pi$
$98$	−9.16816	+	3.73428i	−0.926124	+	0.377220i
$99$			5.27789i			0.530448i
$100$	−0.763042	−	9.97085i	−0.0763042	−	0.997085i
$101$			11.3546i			1.12982i	0.825152	+	0.564911i	$0.191089\pi$
$101$			11.3546i			1.12982i	−0.825152	+	0.564911i	$0.808911\pi$
$102$	4.15692	+	3.10524i	0.411597	+	0.307464i
$103$			6.36010i			0.626679i	0.949641	+	0.313340i	$0.101448\pi$
$103$			6.36010i			0.626679i	−0.949641	+	0.313340i	$0.898552\pi$
$104$	−6.91233	−	2.55417i	−0.677810	−	0.250457i
$105$	2.17702	−	5.50096i	0.212455	−	0.536839i
$106$	1.37123	+	1.02432i	0.133186	+	0.0994904i
$107$	9.37779			0.906585			0.453292	−	0.891362i	$-0.350249\pi$
$107$	9.37779			0.906585			0.453292	+	0.891362i	$0.350249\pi$
$108$	1.91784	−	0.567368i	0.184544	−	0.0545950i
$109$	−12.4509			−1.19258			−0.596291	−	0.802768i	$-0.703360\pi$
$109$	−12.4509			−1.19258			−0.596291	+	0.802768i	$0.703360\pi$
$110$	12.2437	+	11.3425i	1.16739	+	1.08147i
$111$	−0.593655			−0.0563472
$112$	−10.0976	+	3.16848i	−0.954130	+	0.299393i
$113$			16.6576i			1.56702i	0.621382	+	0.783508i	$0.286572\pi$
$113$			16.6576i			1.56702i	−0.621382	+	0.783508i	$0.713428\pi$
$114$	−7.38645	−	5.51771i	−0.691805	−	0.516781i
$115$	7.89371	+	0.836909i	0.736092	+	0.0780422i
$116$	−3.77029	−	12.7445i	−0.350063	−	1.18329i
$117$	2.60538			0.240868
$118$	8.83354	−	11.8253i	0.813193	−	1.08860i
$119$	9.35233	+	2.60053i	0.857326	+	0.238390i
$120$	2.80537	−	5.66833i	0.256094	−	0.517445i
$121$	−16.8562			−1.53238
$122$	−13.5503	−	10.1221i	−1.22679	−	0.916415i
$123$	−8.01200			−0.722417
$124$	−2.55964	−	8.65217i	−0.229862	−	0.776988i
$125$	10.6237	+	3.48386i	0.950211	+	0.311606i
$126$	2.96045	−	2.28817i	0.263738	−	0.203846i
$127$	−8.75417			−0.776807			−0.388404	−	0.921489i	$-0.626973\pi$
$127$	−8.75417			−0.776807			−0.388404	+	0.921489i	$0.626973\pi$
$128$	−11.0377	+	2.48356i	−0.975608	+	0.219518i
$129$			0.678893i			0.0597732i
$130$	5.59913	−	6.04399i	0.491077	−	0.530093i
$131$	5.63278			0.492139			0.246069	−	0.969252i	$-0.420861\pi$
$131$	5.63278			0.492139			0.246069	+	0.969252i	$0.420861\pi$
$132$	2.99451	+	10.1221i	0.260639	+	0.881018i
$133$	−16.6182	−	4.62090i	−1.44098	−	0.400683i
$134$	7.27253	−	9.73558i	0.628250	−	0.841026i
$135$	−0.235752	+	2.22361i	−0.0202903	+	0.191377i
$136$	9.73411	+	3.59683i	0.834693	+	0.308426i
$137$			3.22716i			0.275715i	0.990452	+	0.137857i	$0.0440215\pi$
$137$			3.22716i			0.275715i	−0.990452	+	0.137857i	$0.955978\pi$
$138$	4.02210	+	3.00452i	0.342384	+	0.255762i
$139$	−9.83751			−0.834407			−0.417203	−	0.908813i	$-0.636990\pi$
$139$	−9.83751			−0.834407			−0.417203	+	0.908813i	$0.636990\pi$
$140$	1.05409	−	11.7851i	0.0890869	−	0.996024i
$141$	5.79334			0.487887
$142$	−0.701042	−	0.523681i	−0.0588301	−	0.0439464i
$143$			13.7509i			1.14991i
$144$	3.35619	−	2.17624i	0.279682	−	0.181353i
$145$	14.7764	+	1.56662i	1.22711	+	0.130101i
$146$	1.07953	−	1.44515i	0.0893428	−	0.119601i
$147$	3.61349	−	5.99522i	0.298035	−	0.494478i
$148$	−1.13853	+	0.336821i	−0.0935868	+	0.0276865i
$149$	−13.4804			−1.10436			−0.552179	−	0.833726i	$-0.686203\pi$
$149$	−13.4804			−1.10436			−0.552179	+	0.833726i	$0.686203\pi$
$150$	4.65170	+	5.32557i	0.379810	+	0.434831i
$151$			5.02129i			0.408627i	0.978905	+	0.204314i	$0.0654962\pi$
$151$			5.02129i			0.408627i	−0.978905	+	0.204314i	$0.934504\pi$
$152$	−17.2966	−	6.39123i	−1.40294	−	0.518397i
$153$	−3.66896			−0.296618
$154$	12.0767	+	15.6250i	0.973169	+	1.25910i
$155$	10.0316	+	1.06358i	0.805759	+	0.0854285i
$156$	4.99669	−	1.47821i	0.400056	−	0.118352i
$157$	−3.69893			−0.295206			−0.147603	−	0.989047i	$-0.547156\pi$
$157$	−3.69893			−0.295206			−0.147603	+	0.989047i	$0.547156\pi$
$158$	6.92810	+	5.17532i	0.551170	+	0.411726i
$159$	−1.21027			−0.0959805
$160$	2.16420	−	12.4626i	0.171095	−	0.985254i
$161$	9.04899	+	2.51619i	0.713160	+	0.198303i
$162$	−0.846354	+	1.13300i	−0.0664959	+	0.0890167i
$163$	4.53501			0.355209			0.177605	−	0.984102i	$-0.443165\pi$
$163$	4.53501			0.355209			0.177605	+	0.984102i	$0.443165\pi$
$164$	−15.3657	+	4.54575i	−1.19986	+	0.354964i
$165$	−11.7360	−	1.24427i	−0.913643	−	0.0968665i
$166$	−13.6494	−	10.1962i	−1.05940	−	0.791376i
$167$			9.44040i			0.730520i	0.930905	+	0.365260i	$0.119020\pi$
$167$			9.44040i			0.730520i	−0.930905	+	0.365260i	$0.880980\pi$
$168$	4.37943	−	6.06800i	0.337880	−	0.468156i
$169$	−6.21198			−0.477845
$170$	−7.88483	+	8.51129i	−0.604739	+	0.652786i
$171$	6.51939			0.498550
$172$	0.385182	+	1.30201i	0.0293699	+	0.0992770i
$173$	−12.8884			−0.979884			−0.489942	−	0.871755i	$-0.662982\pi$
$173$	−12.8884			−0.979884			−0.489942	+	0.871755i	$0.662982\pi$
$174$	7.52903	+	5.62422i	0.570774	+	0.426371i
$175$	11.7187	+	6.13769i	0.885853	+	0.463966i
$176$	11.4860	+	17.7136i	0.865786	+	1.33521i
$177$			10.4372i			0.784505i
$178$	18.0440	+	13.4789i	1.35245	+	1.01029i
$179$			16.3092i			1.21900i	0.792784	+	0.609502i	$0.208631\pi$
$179$			16.3092i			1.21900i	−0.792784	+	0.609502i	$0.791369\pi$
$180$	0.809470	+	4.39827i	0.0603343	+	0.327828i
$181$		−	16.7043i		−	1.24162i	−0.783960	−	0.620812i	$-0.786803\pi$
$181$		−	16.7043i		−	1.24162i	0.783960	−	0.620812i	$-0.213197\pi$
$182$	7.71311	−	5.96155i	0.571734	−	0.441900i
$183$	11.9597			0.884085
$184$	9.41839	+	3.48017i	0.694333	+	0.256562i
$185$	0.139955	−	1.32005i	0.0102897	−	0.0970523i
$186$	5.11143	+	3.81826i	0.374788	+	0.279969i
$187$		−	19.3644i		−	1.41606i
$188$	11.1107	−	3.28696i	0.810329	−	0.239726i
$189$	−0.708793	+	2.54904i	−0.0515571	+	0.185415i
$190$	14.0106	−	15.1237i	1.01643	−	1.09719i
$191$			3.06491i			0.221769i	0.993833	+	0.110884i	$0.0353684\pi$
$191$			3.06491i			0.221769i	−0.993833	+	0.110884i	$0.964632\pi$
$192$	5.20189	−	6.07786i	0.375414	−	0.438632i
$193$			26.6082i			1.91530i	0.287935	+	0.957650i	$0.407031\pi$
$193$			26.6082i			1.91530i	−0.287935	+	0.957650i	$0.592969\pi$
$194$	−0.204733	+	0.274072i	−0.0146990	+	0.0196773i
$195$	−0.614223	+	5.79334i	−0.0439854	+	0.414870i
$196$	3.52858	−	13.5480i	0.252041	−	0.967717i
$197$		−	15.4703i		−	1.10221i	−0.834435	−	0.551106i	$-0.814206\pi$
$197$		−	15.4703i		−	1.10221i	0.834435	−	0.551106i	$-0.185794\pi$
$198$	−5.97984	−	4.46697i	−0.424969	−	0.317454i
$199$	5.42099			0.384284			0.192142	−	0.981367i	$-0.438457\pi$
$199$	5.42099			0.384284			0.192142	+	0.981367i	$0.438457\pi$
$200$	11.9428	+	7.57434i	0.844480	+	0.535587i
$201$			8.59277i			0.606087i
$202$	−12.8647	−	9.60999i	−0.905157	−	0.676156i
$203$	16.9390	+	4.71009i	1.18888	+	0.330584i
$204$	−7.03646	+	2.08165i	−0.492651	+	0.145745i
$205$	1.88884	−	17.8155i	0.131922	−	1.24429i
$206$	−7.20598	−	5.38290i	−0.502064	−	0.375044i
$207$	−3.54996			−0.246739
$208$	8.74415	−	5.66993i	0.606298	−	0.393139i
$209$			34.4086i			2.38010i
$210$	4.39005	+	7.12232i	0.302942	+	0.491487i
$211$			20.2200i			1.39200i	0.718040	+	0.696002i	$0.245039\pi$
$211$			20.2200i			1.39200i	−0.718040	+	0.696002i	$0.754961\pi$
$212$	−2.32110	+	0.686668i	−0.159414	+	0.0471605i
$213$	0.618749			0.0423960
$214$	−7.93693	+	10.6250i	−0.542558	+	0.726311i
$215$	−1.50959	−	0.160050i	−0.102953	−	0.0109153i
$216$	−0.980342	+	2.65310i	−0.0667038	+	0.180520i
$217$	11.4998	+	3.19767i	0.780658	+	0.217072i
$218$	10.5379	−	14.1069i	0.713716	−	0.955438i
$219$			1.27551i			0.0861909i
$220$	−23.2136	+	4.27230i	−1.56506	+	0.288038i
$221$	−9.55904			−0.643010
$222$	0.502443	−	0.672610i	0.0337217	−	0.0451426i
$223$		−	19.4080i		−	1.29966i	−0.760080	−	0.649829i	$-0.774840\pi$
$223$		−	19.4080i		−	1.29966i	0.760080	−	0.649829i	$-0.225160\pi$
$224$	4.95624	−	14.1222i	0.331153	−	0.943577i
$225$	−4.88884	−	1.04844i	−0.325923	−	0.0698958i
$226$	−18.8730	−	14.0982i	−1.25542	−	0.937801i
$227$		−	14.4509i		−	0.959141i	−0.877503	−	0.479571i	$-0.840792\pi$
$227$		−	14.4509i		−	0.959141i	0.877503	−	0.479571i	$-0.159208\pi$
$228$	12.5031	−	3.69889i	0.828039	−	0.244965i
$229$		−	15.3305i		−	1.01307i	−0.862219	−	0.506535i	$-0.830926\pi$
$229$		−	15.3305i		−	1.01307i	0.862219	−	0.506535i	$-0.169074\pi$
$230$	−7.62909	+	8.23523i	−0.503047	+	0.543015i
$231$	−13.4536	−	3.74094i	−0.885180	−	0.246136i
$232$	17.6304	+	6.51459i	1.15750	+	0.427704i
$233$		−	2.61653i		−	0.171415i	−0.996320	−	0.0857074i	$-0.972685\pi$
$233$		−	2.61653i		−	0.171415i	0.996320	−	0.0857074i	$-0.0273150\pi$
$234$	−2.20508	+	2.95189i	−0.144150	+	0.192971i
$235$	−1.36579	+	12.8821i	−0.0890943	+	0.840336i
$236$	5.92171	+	20.0168i	0.385471	+	1.30298i
$237$	−6.11484			−0.397201
$238$	−10.8618	+	8.39519i	−0.704065	+	0.544179i
$239$		−	2.17526i		−	0.140706i	−0.997522	−	0.0703528i	$-0.977588\pi$
$239$		−	2.17526i		−	0.140706i	0.997522	−	0.0703528i	$-0.0224125\pi$
$240$	4.04787	+	7.97589i	0.261289	+	0.514841i
$241$		−	1.94049i		−	0.124998i	−0.998045	−	0.0624988i	$-0.980093\pi$
$241$		−	1.94049i		−	0.124998i	0.998045	−	0.0624988i	$-0.0199070\pi$
$242$	14.2663	−	19.0980i	0.917071	−	1.22767i
$243$		−	1.00000i		−	0.0641500i
$244$	22.9367	−	6.78554i	1.46837	−	0.434400i
$245$	12.4791	+	9.44835i	0.797262	+	0.603633i
$246$	6.78099	−	9.07758i	0.432340	−	0.578765i
$247$	16.9855			1.08076
$248$	11.9692	+	4.42274i	0.760048	+	0.280844i
$249$	12.0472			0.763458
$250$	−12.9386	+	9.08803i	−0.818310	+	0.574777i
$251$	12.4952			0.788689			0.394344	−	0.918963i	$-0.370972\pi$
$251$	12.4952			0.788689			0.394344	+	0.918963i	$0.370972\pi$
$252$	0.0868958	+	5.29079i	0.00547392	+	0.333288i
$253$		−	18.7363i		−	1.17794i
$254$	7.40913	−	9.91846i	0.464890	−	0.622339i
$255$	0.864963	−	8.15831i	0.0541661	−	0.510893i
$256$	6.52798	−	14.6077i	0.407999	−	0.912983i
$257$	7.98037			0.497802			0.248901	−	0.968529i	$-0.419931\pi$
$257$	7.98037			0.497802			0.248901	+	0.968529i	$0.419931\pi$
$258$	−0.769185	−	0.574584i	−0.0478873	−	0.0357721i
$259$	0.420779	−	1.51325i	0.0261459	−	0.0940289i
$260$	2.10898	+	11.4592i	0.130793	+	0.710667i
$261$	−6.64523			−0.411329
$262$	−4.76733	+	6.38193i	−0.294527	+	0.394277i
$263$	−9.65240			−0.595192			−0.297596	−	0.954692i	$-0.596185\pi$
$263$	−9.65240			−0.595192			−0.297596	+	0.954692i	$0.596185\pi$
$264$	−14.0028	−	5.17414i	−0.861811	−	0.318446i
$265$	0.285323	−	2.69116i	0.0175272	−	0.165317i
$266$	19.3004	−	14.9175i	1.18338	−	0.914648i
$267$	−15.9259			−0.974647
$268$	4.87526	+	16.4795i	0.297804	+	1.00665i
$269$		−	19.9393i		−	1.21572i	−0.794043	−	0.607861i	$-0.792028\pi$
$269$		−	19.9393i		−	1.21572i	0.794043	−	0.607861i	$-0.207972\pi$
$270$	−2.31981	−	2.14906i	−0.141179	−	0.130788i
$271$	23.5830			1.43257			0.716283	−	0.697810i	$-0.245842\pi$
$271$	23.5830			1.43257			0.716283	+	0.697810i	$0.245842\pi$
$272$	−12.3137	+	7.98452i	−0.746628	+	0.484133i
$273$	−1.84668	+	6.64123i	−0.111766	+	0.401945i
$274$	−3.65636	−	2.73132i	−0.220889	−	0.165005i
$275$	5.53354	−	25.8028i	0.333685	−	1.55597i
$276$	−6.80824	+	2.01413i	−0.409808	+	0.121237i
$277$			26.8902i			1.61567i	0.589406	+	0.807837i	$0.299362\pi$
$277$			26.8902i			1.61567i	−0.589406	+	0.807837i	$0.700638\pi$
$278$	8.32602	−	11.1459i	0.499362	−	0.668485i
$279$	−4.51142			−0.270092
$280$	12.4604	+	11.1687i	0.744650	+	0.667455i
$281$	−2.53895			−0.151461			−0.0757304	−	0.997128i	$-0.524129\pi$
$281$	−2.53895			−0.151461			−0.0757304	+	0.997128i	$0.524129\pi$
$282$	−4.90322	+	6.56384i	−0.291983	+	0.390871i
$283$			30.8460i			1.83361i	0.399340	+	0.916803i	$0.369239\pi$
$283$			30.8460i			1.83361i	−0.399340	+	0.916803i	$0.630761\pi$
$284$	1.18666	−	0.351059i	0.0704153	−	0.0208315i
$285$	−1.53696	+	14.4965i	−0.0910415	+	0.858702i
$286$	−15.5798	−	11.6382i	−0.921251	−	0.688179i
$287$	5.67885	−	20.4229i	0.335212	−	1.20553i
$288$	−0.374851	+	5.64442i	−0.0220883	+	0.332601i
$289$	−3.53875			−0.208162
$290$	−14.2810	+	15.4157i	−0.838611	+	0.905239i
$291$		−	0.241900i		−	0.0141804i
$292$	0.723683	+	2.44622i	0.0423504	+	0.143154i
$293$	−2.41522			−0.141099			−0.0705493	−	0.997508i	$-0.522475\pi$
$293$	−2.41522			−0.141099			−0.0705493	+	0.997508i	$0.522475\pi$
$294$	3.73428	+	9.16816i	0.217788	+	0.534698i
$295$	−23.2081	−	2.46058i	−1.35123	−	0.143260i
$296$	0.581985	−	1.57503i	0.0338272	−	0.0915465i
$297$	5.27789			0.306254
$298$	11.4092	−	15.2733i	0.660917	−	0.884757i
$299$	−9.24900			−0.534883
$300$	−9.97085	+	0.763042i	−0.575667	+	0.0440543i
$301$	−1.73053	−	0.481195i	−0.0997459	−	0.0277356i
$302$	−5.68911	−	4.24979i	−0.327372	−	0.244548i
$303$	11.3546			0.652303
$304$	21.8803	−	14.1877i	1.25492	−	0.813723i
$305$	−2.81952	+	26.5936i	−0.161445	+	1.52275i
$306$	3.10524	−	4.15692i	0.177515	−	0.237635i
$307$		−	8.34794i		−	0.476442i	−0.971211	−	0.238221i	$-0.923436\pi$
$307$		−	8.34794i		−	0.476442i	0.971211	−	0.238221i	$-0.0765643\pi$
$308$	−27.9242	+	0.458627i	−1.59113	+	0.0261327i
$309$	6.36010			0.361813
$310$	−9.69534	+	10.4656i	−0.550658	+	0.594409i
$311$	−27.1508			−1.53958			−0.769791	−	0.638296i	$-0.779639\pi$
$311$	−27.1508			−1.53958			−0.769791	+	0.638296i	$0.779639\pi$
$312$	−2.55417	+	6.91233i	−0.144601	+	0.391334i
$313$	−28.7305			−1.62394			−0.811972	−	0.583697i	$-0.801606\pi$
$313$	−28.7305			−1.62394			−0.811972	+	0.583697i	$0.801606\pi$
$314$	3.13060	−	4.19087i	0.176670	−	0.236505i
$315$	−5.50096	−	2.17702i	−0.309944	−	0.122661i
$316$	−11.7273	+	3.46936i	−0.659709	+	0.195167i
$317$		−	25.4368i		−	1.42867i	−0.699803	−	0.714336i	$-0.746729\pi$
$317$		−	25.4368i		−	1.42867i	0.699803	−	0.714336i	$-0.253271\pi$
$318$	1.02432	−	1.37123i	0.0574408	−	0.0768949i
$319$		−	35.0728i		−	1.96370i
$320$	12.2884	+	12.9998i	0.686943	+	0.726711i
$321$		−	9.37779i		−	0.523417i
$322$	−10.5095	+	8.12290i	−0.585671	+	0.452672i
$323$	−23.9194			−1.33091
$324$	−0.567368	−	1.91784i	−0.0315205	−	0.106546i
$325$	−12.7373	−	2.73158i	−0.706538	−	0.151521i
$326$	−3.83823	+	5.13816i	−0.212580	+	0.284576i
$327$			12.4509i			0.688537i
$328$	7.85450	−	21.2566i	0.433692	−	1.17370i
$329$	−4.10628	+	14.7675i	−0.226387	+	0.814157i
$330$	11.3425	−	12.2437i	0.624386	−	0.673994i
$331$			1.85084i			0.101731i	0.998706	+	0.0508656i	$0.0161980\pi$
$331$			1.85084i			0.101731i	−0.998706	+	0.0508656i	$0.983802\pi$
$332$	23.1045	−	6.83517i	1.26802	−	0.375129i
$333$			0.593655i			0.0325321i
$334$	−10.6960	−	7.98993i	−0.585257	−	0.437189i
$335$	−19.1069	−	2.02576i	−1.04392	−	0.110679i
$336$	3.16848	+	10.0976i	0.172855	+	0.550867i
$337$		−	7.88387i		−	0.429462i	−0.976673	−	0.214731i	$-0.931113\pi$
$337$		−	7.88387i		−	0.429462i	0.976673	−	0.214731i	$-0.0688875\pi$
$338$	5.25754	−	7.03816i	0.285972	−	0.382826i
$339$	16.6576			0.904717
$340$	−2.96991	−	16.1371i	−0.161066	−	0.875155i
$341$		−	23.8108i		−	1.28943i
$342$	−5.51771	+	7.38645i	−0.298364	+	0.399414i
$343$	12.7209	+	13.4603i	0.686862	+	0.726788i
$344$	−1.80117	−	0.665548i	−0.0971126	−	0.0358839i
$345$	0.836909	−	7.89371i	0.0450577	−	0.424983i
$346$	10.9081	−	14.6025i	0.586425	−	0.785035i
$347$	−11.8601			−0.636684			−0.318342	−	0.947976i	$-0.603126\pi$
$347$	−11.8601			−0.636684			−0.318342	+	0.947976i	$0.603126\pi$
$348$	−12.7445	+	3.77029i	−0.683174	+	0.202109i
$349$			13.3335i			0.713725i	0.934157	+	0.356862i	$0.116153\pi$
$349$			13.3335i			0.713725i	−0.934157	+	0.356862i	$0.883847\pi$
$350$	−16.8722	+	8.08264i	−0.901857	+	0.432035i
$351$		−	2.60538i		−	0.139065i
$352$	−29.7907	−	1.97842i	−1.58785	−	0.105450i
$353$	21.6617			1.15294			0.576468	−	0.817120i	$-0.304431\pi$
$353$	21.6617			1.15294			0.576468	+	0.817120i	$0.304431\pi$
$354$	−11.8253	−	8.83354i	−0.628506	−	0.469497i
$355$	−0.145871	+	1.37585i	−0.00774204	+	0.0730228i
$356$	−30.5432	+	9.03583i	−1.61879	+	0.478898i
$357$	2.60053	−	9.35233i	0.137635	−	0.494978i
$358$	−18.4782	−	13.8033i	−0.976606	−	0.729529i
$359$			19.0353i			1.00465i	0.864680	+	0.502324i	$0.167521\pi$
$359$			19.0353i			1.00465i	−0.864680	+	0.502324i	$0.832479\pi$
$360$	−5.66833	−	2.80537i	−0.298747	−	0.147856i
$361$	23.5024			1.23697
$362$	18.9260	+	14.1378i	0.994727	+	0.743066i
$363$			16.8562i			0.884719i
$364$	0.226397	+	13.7845i	0.0118664	+	0.722506i
$365$	−2.83623	−	0.300703i	−0.148455	−	0.0157395i
$366$	−10.1221	+	13.5503i	−0.529092	+	0.708285i
$367$			3.71381i			0.193860i	0.995291	+	0.0969298i	$0.0309022\pi$
$367$			3.71381i			0.193860i	−0.995291	+	0.0969298i	$0.969098\pi$
$368$	−11.9143	+	7.72555i	−0.621077	+	0.402722i
$369$			8.01200i			0.417088i
$370$	1.37717	+	1.27580i	0.0715955	+	0.0663258i
$371$	0.857830	−	3.08502i	0.0445363	−	0.160167i
$372$	−8.65217	+	2.55964i	−0.448594	+	0.132711i
$373$		−	11.7956i		−	0.610756i	−0.952231	−	0.305378i	$-0.901217\pi$
$373$		−	11.7956i		−	0.610756i	0.952231	−	0.305378i	$-0.0987827\pi$
$374$	21.9398	+	16.3891i	1.13448	+	0.847461i
$375$	3.48386	−	10.6237i	0.179906	−	0.548605i
$376$	−5.67946	+	15.3703i	−0.292896	+	0.792663i
$377$	−17.3134			−0.891683
$378$	−2.28817	−	2.96045i	−0.117691	−	0.152269i
$379$		−	25.9889i		−	1.33496i	−0.744627	−	0.667480i	$-0.767373\pi$
$379$		−	25.9889i		−	1.33496i	0.744627	−	0.667480i	$-0.232627\pi$
$380$	5.27725	+	28.6740i	0.270717	+	1.47095i
$381$			8.75417i			0.448490i
$382$	−3.47253	−	2.59400i	−0.177670	−	0.132721i
$383$		−	1.22784i		−	0.0627397i	−0.999508	−	0.0313698i	$-0.990013\pi$
$383$		−	1.22784i		−	0.0627397i	0.999508	−	0.0313698i	$-0.00998697\pi$
$384$	2.48356	+	11.0377i	0.126739	+	0.563268i
$385$	11.4901	−	29.0335i	0.585588	−	1.47968i
$386$	−30.1470	−	22.5200i	−1.53444	−	1.14624i
$387$	0.678893			0.0345101
$388$	−0.137246	−	0.463925i	−0.00696763	−	0.0235522i
$389$	27.3654			1.38748			0.693741	−	0.720225i	$-0.255961\pi$
$389$	27.3654			1.38748			0.693741	+	0.720225i	$0.255961\pi$
$390$	−6.04399	−	5.59913i	−0.306049	−	0.283523i
$391$	13.0246			0.658685
$392$	12.3635	+	15.4643i	0.624449	+	0.781065i
$393$		−	5.63278i		−	0.284136i
$394$	17.5278	+	13.0934i	0.883038	+	0.659634i
$395$	1.44158	−	13.5970i	0.0725339	−	0.684139i
$396$	10.1221	−	2.99451i	0.508656	−	0.150480i
$397$	8.42589			0.422883			0.211442	−	0.977391i	$-0.432184\pi$
$397$	8.42589			0.422883			0.211442	+	0.977391i	$0.432184\pi$
$398$	−4.58808	+	6.14197i	−0.229980	+	0.307869i
$399$	−4.62090	+	16.6182i	−0.231334	+	0.831950i
$400$	−18.6895	+	7.12053i	−0.934476	+	0.356027i
$401$	23.6847			1.18276			0.591378	−	0.806395i	$-0.298584\pi$
$401$	23.6847			1.18276			0.591378	+	0.806395i	$0.298584\pi$
$402$	−9.73558	−	7.27253i	−0.485567	−	0.362721i
$403$	−11.7540			−0.585508
$404$	21.7762	−	6.44222i	1.08341	−	0.320512i
$405$	2.22361	+	0.235752i	0.110492	+	0.0117146i
$406$	−19.6729	+	15.2054i	−0.976349	+	0.754631i
$407$	−3.13325			−0.155309
$408$	3.59683	−	9.73411i	0.178070	−	0.481910i
$409$			9.16746i			0.453302i	0.973976	+	0.226651i	$0.0727776\pi$
$409$			9.16746i			0.453302i	−0.973976	+	0.226651i	$0.927222\pi$
$410$	18.5863	+	17.2183i	0.917913	+	0.850351i
$411$	3.22716			0.159184
$412$	12.1976	−	3.60852i	0.600934	−	0.177779i
$413$	−26.6047	−	7.39779i	−1.30913	−	0.364021i
$414$	3.00452	−	4.02210i	0.147664	−	0.197675i
$415$	−2.84014	+	26.7881i	−0.139417	+	1.31498i
$416$	−0.976630	+	14.7059i	−0.0478832	+	0.721015i
$417$			9.83751i			0.481745i
$418$	−38.9849	−	29.1219i	−1.90681	−	1.42440i
$419$	34.2720			1.67430			0.837148	−	0.546976i	$-0.184221\pi$
$419$	34.2720			1.67430			0.837148	+	0.546976i	$0.184221\pi$
$420$	−11.7851	−	1.05409i	−0.575055	−	0.0514344i
$421$	5.77768			0.281587			0.140794	−	0.990039i	$-0.455035\pi$
$421$	5.77768			0.281587			0.140794	+	0.990039i	$0.455035\pi$
$422$	−22.9092	−	17.1133i	−1.11520	−	0.833063i
$423$		−	5.79334i		−	0.281682i
$424$	1.18648	−	3.21096i	0.0576204	−	0.155938i
$425$	17.9370	+	3.84667i	0.870070	+	0.186591i
$426$	−0.523681	+	0.701042i	−0.0253724	+	0.0339656i
$427$	−8.47694	+	30.4857i	−0.410228	+	1.47531i
$428$	−5.32066	−	17.9851i	−0.257184	−	0.869340i
$429$	13.7509			0.663901
$430$	1.45899	−	1.57490i	0.0703585	−	0.0759486i
$431$		−	14.2304i		−	0.685456i	−0.939435	−	0.342728i	$-0.888649\pi$
$431$		−	14.2304i		−	0.685456i	0.939435	−	0.342728i	$-0.111351\pi$
$432$	−2.17624	−	3.35619i	−0.104704	−	0.161475i
$433$	19.3731			0.931012			0.465506	−	0.885045i	$-0.345872\pi$
$433$	19.3731			0.931012			0.465506	+	0.885045i	$0.345872\pi$
$434$	−13.3559	+	10.3229i	−0.641102	+	0.495515i
$435$	1.56662	−	14.7764i	0.0751139	−	0.708472i
$436$	7.06426	+	23.8788i	0.338317	+	1.14359i
$437$	−23.1436			−1.10711
$438$	−1.44515	−	1.07953i	−0.0690519	−	0.0515821i
$439$	7.17779			0.342577			0.171289	−	0.985221i	$-0.445207\pi$
$439$	7.17779			0.342577			0.171289	+	0.985221i	$0.445207\pi$
$440$	14.8064	−	29.9168i	0.705868	−	1.42623i
$441$	−5.99522	−	3.61349i	−0.285487	−	0.172071i
$442$	8.09033	−	10.8304i	0.384818	−	0.515148i
$443$	−6.51915			−0.309734			−0.154867	−	0.987935i	$-0.549495\pi$
$443$	−6.51915			−0.309734			−0.154867	+	0.987935i	$0.549495\pi$
$444$	0.336821	+	1.13853i	0.0159848	+	0.0540324i
$445$	3.75455	−	35.4128i	0.177983	−	1.67873i
$446$	21.9893	+	16.4261i	1.04122	+	0.777797i
$447$			13.4804i			0.637601i
$448$	11.8057	+	17.5678i	0.557765	+	0.829999i
$449$	13.3428			0.629686			0.314843	−	0.949144i	$-0.398048\pi$
$449$	13.3428			0.629686			0.314843	+	0.949144i	$0.398048\pi$
$450$	5.32557	−	4.65170i	0.251050	−	0.219283i
$451$	−42.2865			−1.99119
$452$	31.9465	−	9.45100i	1.50264	−	0.444537i
$453$	5.02129			0.235921
$454$	16.3729	+	12.2306i	0.768416	+	0.574011i
$455$	−14.3321	−	5.67196i	−0.671900	−	0.265906i
$456$	−6.39123	+	17.2966i	−0.299297	+	0.809987i
$457$			17.9090i			0.837748i	0.908044	+	0.418874i	$0.137575\pi$
$457$			17.9090i			0.837748i	−0.908044	+	0.418874i	$0.862425\pi$
$458$	17.3695	+	12.9751i	0.811622	+	0.606285i
$459$			3.66896i			0.171252i
$460$	−2.87358	−	15.6137i	−0.133982	−	0.727991i
$461$			23.2901i			1.08473i	0.840144	+	0.542363i	$0.182470\pi$
$461$			23.2901i			1.08473i	−0.840144	+	0.542363i	$0.817530\pi$
$462$	15.6250	−	12.0767i	0.726939	−	0.561859i
$463$	10.1120			0.469943			0.234971	−	0.972002i	$-0.424500\pi$
$463$	10.1120			0.469943			0.234971	+	0.972002i	$0.424500\pi$
$464$	−22.3026	+	14.4616i	−1.03537	+	0.671363i
$465$	1.06358	−	10.0316i	0.0493221	−	0.465205i
$466$	2.96453	+	2.21451i	0.137329	+	0.102585i
$467$			5.67471i			0.262594i	0.991343	+	0.131297i	$0.0419142\pi$
$467$			5.67471i			0.262594i	−0.991343	+	0.131297i	$0.958086\pi$
$468$	−1.47821	−	4.99669i	−0.0683303	−	0.230972i
$469$	−21.9033	−	6.09050i	−1.01140	−	0.281233i
$470$	−13.4395	−	12.4503i	−0.619916	−	0.574288i
$471$			3.69893i			0.170437i
$472$	−27.6908	−	10.2320i	−1.27457	−	0.470965i
$473$			3.58313i			0.164752i
$474$	5.17532	−	6.92810i	0.237710	−	0.318218i
$475$	−31.8723	−	6.83517i	−1.46240	−	0.313619i
$476$	−0.318817	−	19.4117i	−0.0146129	−	0.889733i
$477$			1.21027i			0.0554144i
$478$	2.46456	+	1.84104i	0.112726	+	0.0842071i
$479$	9.45565			0.432040			0.216020	−	0.976389i	$-0.430692\pi$
$479$	9.45565			0.432040			0.216020	+	0.976389i	$0.430692\pi$
$480$	−12.4626	−	2.16420i	−0.568837	−	0.0987819i
$481$			1.54670i			0.0705234i
$482$	2.19857	+	1.64234i	0.100142	+	0.0748065i
$483$	2.51619	−	9.04899i	0.114490	−	0.411743i
$484$	9.56365	+	32.3273i	0.434711	+	1.46942i
$485$	0.537891	+	0.0570284i	0.0244244	+	0.00258953i
$486$	1.13300	+	0.846354i	0.0513938	+	0.0383914i
$487$	−30.9220			−1.40121			−0.700604	−	0.713550i	$-0.747086\pi$
$487$	−30.9220			−1.40121			−0.700604	+	0.713550i	$0.747086\pi$
$488$	−11.7246	+	31.7302i	−0.530747	+	1.43636i
$489$		−	4.53501i		−	0.205080i
$490$	−21.2667	+	6.14217i	−0.960733	+	0.277475i
$491$			6.70014i			0.302373i	0.988505	+	0.151187i	$0.0483094\pi$
$491$			6.70014i			0.302373i	−0.988505	+	0.151187i	$0.951691\pi$
$492$	4.54575	+	15.3657i	0.204938	+	0.692739i
$493$	24.3811			1.09807
$494$	−14.3758	+	19.2445i	−0.646796	+	0.865853i
$495$	−1.24427	+	11.7360i	−0.0559259	+	0.527492i
$496$	−15.1412	+	9.81793i	−0.679859	+	0.440838i
$497$	−0.438565	+	1.57722i	−0.0196723	+	0.0707479i
$498$	−10.1962	+	13.6494i	−0.456901	+	0.611644i
$499$		−	32.7953i		−	1.46812i	−0.679086	−	0.734059i	$-0.737623\pi$
$499$		−	32.7953i		−	1.46812i	0.679086	−	0.734059i	$-0.262377\pi$
$500$	0.653939	−	22.3511i	0.0292450	−	0.999572i
$501$	9.44040			0.421766
$502$	−10.5754	+	14.1570i	−0.472001	+	0.631858i
$503$		−	4.90734i		−	0.218808i	−0.993997	−	0.109404i	$-0.965106\pi$
$503$		−	4.90734i		−	0.218808i	0.993997	−	0.109404i	$-0.0348942\pi$
$504$	−6.06800	−	4.37943i	−0.270290	−	0.195075i
$505$	−2.67686	+	25.2481i	−0.119119	+	1.12352i
$506$	21.2282	+	15.8576i	0.943708	+	0.704954i
$507$			6.21198i			0.275884i
$508$	4.96684	+	16.7891i	0.220368	+	0.744894i
$509$		−	31.2970i		−	1.38722i	−0.720352	−	0.693608i	$-0.756020\pi$
$509$		−	31.2970i		−	1.38722i	0.720352	−	0.693608i	$-0.243980\pi$
$510$	8.51129	+	7.88483i	0.376886	+	0.349146i
$511$	−3.25132	−	0.904072i	−0.143830	−	0.0399938i
$512$	11.0255	+	19.7595i	0.487264	+	0.873255i
$513$		−	6.51939i		−	0.287838i
$514$	−6.75422	+	9.04174i	−0.297916	+	0.398814i
$515$	−1.49940	+	14.1423i	−0.0660716	+	0.623186i
$516$	1.30201	−	0.385182i	0.0573176	−	0.0169567i
$517$	30.5766			1.34476
$518$	1.35838	+	1.75749i	0.0596839	+	0.0772196i
$519$			12.8884i			0.565737i
$520$	−14.7682	−	7.30905i	−0.647626	−	0.320523i
$521$		−	9.74022i		−	0.426727i	−0.976973	−	0.213363i	$-0.931558\pi$
$521$		−	9.74022i		−	0.426727i	0.976973	−	0.213363i	$-0.0684419\pi$
$522$	5.62422	−	7.52903i	0.246165	−	0.329537i
$523$		−	27.3943i		−	1.19787i	−0.800798	−	0.598935i	$-0.795591\pi$
$523$		−	27.3943i		−	1.19787i	0.800798	−	0.598935i	$-0.204409\pi$
$524$	−3.19586	−	10.8028i	−0.139612	−	0.471920i
$525$	6.13769	−	11.7187i	0.267871	−	0.511448i
$526$	8.16935	−	10.9361i	0.356201	−	0.476839i
$527$	16.5522			0.721026
$528$	17.7136	−	11.4860i	0.770885	−	0.499862i
$529$	−10.3978			−0.452078
$530$	2.80759	+	2.60095i	0.121954	+	0.112978i
$531$	10.4372			0.452934
$532$	0.566507	+	34.4927i	0.0245612	+	1.49545i
$533$			20.8743i			0.904167i
$534$	13.4789	−	18.0440i	0.583290	−	0.780839i
$535$	20.8525	+	2.21083i	0.901532	+	0.0955825i
$536$	−22.7974	−	8.42385i	−0.984700	−	0.363855i
$537$	16.3092			0.703792
$538$	22.5912	+	16.8757i	0.973976	+	0.727565i
$539$	19.0716	−	31.6422i	0.821472	−	1.36292i
$540$	4.39827	−	0.809470i	0.189271	−	0.0348340i
$541$	41.4900			1.78379			0.891897	−	0.452238i	$-0.149374\pi$
$541$	41.4900			1.78379			0.891897	+	0.452238i	$0.149374\pi$
$542$	−19.9596	+	26.7195i	−0.857338	+	1.14770i
$543$	−16.7043			−0.716852
$544$	1.37531	−	20.7091i	0.0589660	−	0.887897i
$545$	−27.6859	−	2.93533i	−1.18594	−	0.125736i
$546$	−5.96155	−	7.71311i	−0.255131	−	0.330091i
$547$	37.8235			1.61722			0.808608	−	0.588348i	$-0.200222\pi$
$547$	37.8235			1.61722			0.808608	+	0.588348i	$0.200222\pi$
$548$	6.18916	−	1.83099i	0.264388	−	0.0782159i
$549$		−	11.9597i		−	0.510427i
$550$	24.5512	+	28.1078i	1.04687	+	1.19852i
$551$	−43.3228			−1.84561
$552$	3.48017	−	9.41839i	0.148126	−	0.400873i
$553$	4.33416	−	15.5870i	0.184307	−	0.662825i
$554$	−30.4665	−	22.7586i	−1.29440	−	0.966921i
$555$	−1.32005	−	0.139955i	−0.0560332	−	0.00594077i
$556$	5.58149	+	18.8667i	0.236708	+	0.800128i
$557$		−	1.38809i		−	0.0588151i	−0.999568	−	0.0294076i	$-0.990638\pi$
$557$		−	1.38809i		−	0.0588151i	0.999568	−	0.0294076i	$-0.00936206\pi$
$558$	3.81826	−	5.11143i	0.161640	−	0.216384i
$559$	1.76878			0.0748113
$560$	−23.2000	+	4.66493i	−0.980378	+	0.197129i
$561$	−19.3644			−0.817564
$562$	2.14885	−	2.87662i	0.0906437	−	0.121343i
$563$		−	41.8659i		−	1.76444i	−0.470839	−	0.882219i	$-0.656049\pi$
$563$		−	41.8659i		−	1.76444i	0.470839	−	0.882219i	$-0.343951\pi$
$564$	−3.28696	−	11.1107i	−0.138406	−	0.467844i
$565$	−3.92706	+	37.0399i	−0.165213	+	1.55828i
$566$	−34.9485	−	26.1067i	−1.46899	−	1.09735i
$567$	2.54904	+	0.708793i	0.107050	+	0.0297665i
$568$	−0.606586	+	1.64160i	−0.0254518	+	0.0688801i
$569$	26.6868			1.11877			0.559384	−	0.828909i	$-0.311038\pi$
$569$	26.6868			1.11877			0.559384	+	0.828909i	$0.311038\pi$
$570$	−15.1237	−	14.0106i	−0.633464	−	0.586839i
$571$			17.0316i			0.712748i	0.934343	+	0.356374i	$0.115987\pi$
$571$			17.0316i			0.712748i	−0.934343	+	0.356374i	$0.884013\pi$
$572$	26.3720	−	7.80184i	1.10267	−	0.326211i
$573$	3.06491			0.128038
$574$	18.3328	+	23.7191i	0.765196	+	0.990018i
$575$	17.3552	+	3.72191i	0.723761	+	0.155214i
$576$	−6.07786	−	5.20189i	−0.253244	−	0.216745i
$577$	−7.86773			−0.327538			−0.163769	−	0.986499i	$-0.552365\pi$
$577$	−7.86773			−0.327538			−0.163769	+	0.986499i	$0.552365\pi$
$578$	2.99503	−	4.00939i	0.124577	−	0.166769i
$579$	26.6082			1.10580
$580$	−5.37911	−	29.2275i	−0.223355	−	1.21361i
$581$	−8.53895	+	30.7087i	−0.354255	+	1.27401i
$582$	0.274072	+	0.204733i	0.0113607	+	0.00848647i
$583$	−6.38767			−0.264550
$584$	−3.38405	−	1.25043i	−0.140033	−	0.0517434i
$585$	5.79334	+	0.614223i	0.239525	+	0.0253950i
$586$	2.04413	−	2.73644i	0.0844423	−	0.113041i
$587$		−	18.4553i		−	0.761731i	−0.924630	−	0.380866i	$-0.875626\pi$
$587$		−	18.4553i		−	0.761731i	0.924630	−	0.380866i	$-0.124374\pi$
$588$	−13.5480	−	3.52858i	−0.558711	−	0.145516i
$589$	−29.4117			−1.21189
$590$	22.4301	−	24.2122i	0.923434	−	0.996802i
$591$	−15.4703			−0.636363
$592$	1.29193	+	1.99242i	0.0530982	+	0.0818878i
$593$	−37.1933			−1.52734			−0.763672	−	0.645604i	$-0.776606\pi$
$593$	−37.1933			−1.52734			−0.763672	+	0.645604i	$0.776606\pi$
$594$	−4.46697	+	5.97984i	−0.183282	+	0.245356i
$595$	20.1828	+	7.98739i	0.827414	+	0.327451i
$596$	7.64835	+	25.8532i	0.313289	+	1.05899i
$597$		−	5.42099i		−	0.221866i
$598$	7.82793	−	10.4791i	0.320108	−	0.428522i
$599$			5.93437i			0.242472i	0.992624	+	0.121236i	$0.0386858\pi$
$599$			5.93437i			0.242472i	−0.992624	+	0.121236i	$0.961314\pi$
$600$	7.57434	−	11.9428i	0.309221	−	0.487561i
$601$		−	30.5087i		−	1.24447i	−0.782829	−	0.622237i	$-0.786224\pi$
$601$		−	30.5087i		−	1.24447i	0.782829	−	0.622237i	$-0.213776\pi$
$602$	2.00983	−	1.55342i	0.0819147	−	0.0633128i
$603$	8.59277			0.349924
$604$	9.63002	−	2.84892i	0.391840	−	0.115921i
$605$	−37.4814	−	3.97387i	−1.52384	−	0.161561i
$606$	−9.60999	+	12.8647i	−0.390379	+	0.522593i
$607$			29.0986i			1.18108i	0.807010	+	0.590538i	$0.201084\pi$
$607$			29.0986i			1.18108i	−0.807010	+	0.590538i	$0.798916\pi$
$608$	−2.44380	+	36.7982i	−0.0991092	+	1.49236i
$609$	4.71009	−	16.9390i	0.190863	−	0.686401i
$610$	−27.7442	−	25.7021i	−1.12333	−	1.04065i
$611$		−	15.0939i		−	0.610633i
$612$	2.08165	+	7.03646i	0.0841457	+	0.284432i
$613$		−	2.83852i		−	0.114647i	−0.998356	−	0.0573235i	$-0.981743\pi$
$613$		−	2.83852i		−	0.114647i	0.998356	−	0.0573235i	$-0.0182566\pi$
$614$	9.45820	+	7.06532i	0.381702	+	0.285133i
$615$	−17.8155	−	1.88884i	−0.718391	−	0.0761655i
$616$	23.1142	−	32.0262i	0.931296	−	1.29037i
$617$		−	12.3980i		−	0.499125i	−0.968359	−	0.249562i	$-0.919713\pi$
$617$		−	12.3980i		−	0.499125i	0.968359	−	0.249562i	$-0.0802867\pi$
$618$	−5.38290	+	7.20598i	−0.216532	+	0.289867i
$619$	11.8664			0.476950			0.238475	−	0.971149i	$-0.423352\pi$
$619$	11.8664			0.476950			0.238475	+	0.971149i	$0.423352\pi$
$620$	−3.65186	−	19.8424i	−0.146662	−	0.796892i
$621$			3.54996i			0.142455i
$622$	22.9792	−	30.7618i	0.921382	−	1.23344i
$623$	11.2882	−	40.5957i	0.452250	−	1.62643i
$624$	−5.66993	−	8.74415i	−0.226979	−	0.350046i
$625$	22.8016	+	10.2513i	0.912062	+	0.410052i
$626$	24.3162	−	32.5516i	0.971870	−	1.30102i
$627$	34.4086			1.37415
$628$	2.09865	+	7.09393i	0.0837453	+	0.283079i
$629$		−	2.17810i		−	0.0868464i
$630$	7.12232	−	4.39005i	0.283760	−	0.174904i
$631$		−	31.7351i		−	1.26335i	−0.775232	−	0.631677i	$-0.782367\pi$
$631$		−	31.7351i		−	1.26335i	0.775232	−	0.631677i	$-0.217633\pi$
$632$	5.99463	−	16.2233i	0.238454	−	0.645327i
$633$	20.2200			0.803674
$634$	28.8198	+	21.5285i	1.14458	+	0.855007i
$635$	−19.4658	−	2.06381i	−0.772478	−	0.0818998i
$636$	0.686668	+	2.32110i	0.0272282	+	0.0920375i
$637$	−15.6198	−	9.41452i	−0.618881	−	0.373017i
$638$	39.7374	+	29.6840i	1.57322	+	1.17520i
$639$		−	0.618749i		−	0.0244773i
$640$	−25.1291	+	2.92029i	−0.993315	+	0.115435i
$641$	−36.5496			−1.44362			−0.721811	−	0.692090i	$-0.756690\pi$
$641$	−36.5496			−1.44362			−0.721811	+	0.692090i	$0.756690\pi$
$642$	10.6250	+	7.93693i	0.419336	+	0.313246i
$643$			11.0262i			0.434830i	0.976079	+	0.217415i	$0.0697625\pi$
$643$			11.0262i			0.434830i	−0.976079	+	0.217415i	$0.930238\pi$
$644$	−0.308476	−	18.7821i	−0.0121557	−	0.740118i
$645$	−0.160050	+	1.50959i	−0.00630197	+	0.0594401i
$646$	20.2443	−	27.1006i	0.796500	−	1.06626i
$647$			10.0350i			0.394515i	0.980352	+	0.197258i	$0.0632036\pi$
$647$			10.0350i			0.394515i	−0.980352	+	0.197258i	$0.936796\pi$
$648$	2.65310	+	0.980342i	0.104224	+	0.0385115i
$649$			55.0862i			2.16232i
$650$	13.8751	−	12.1195i	0.544228	−	0.475364i
$651$	3.19767	−	11.4998i	0.125326	−	0.450713i
$652$	−2.57302	−	8.69740i	−0.100767	−	0.340617i
$653$			10.8509i			0.424630i	0.977201	+	0.212315i	$0.0681003\pi$
$653$			10.8509i			0.424630i	−0.977201	+	0.212315i	$0.931900\pi$
$654$	−14.1069	−	10.5379i	−0.551622	−	0.412064i
$655$	12.5251	+	1.32794i	0.489396	+	0.0518868i
$656$	17.4360	+	26.8898i	0.680762	+	1.04987i
$657$	1.27551			0.0497623
$658$	−13.2561	−	17.1509i	−0.516778	−	0.668613i
$659$		−	4.25681i		−	0.165822i	−0.996557	−	0.0829108i	$-0.973578\pi$
$659$		−	4.25681i		−	0.165822i	0.996557	−	0.0829108i	$-0.0264217\pi$
$660$	4.27230	+	23.2136i	0.166299	+	0.903588i
$661$			23.6227i			0.918817i	0.888225	+	0.459409i	$0.151939\pi$
$661$			23.6227i			0.918817i	−0.888225	+	0.459409i	$0.848061\pi$
$662$	−2.09699	−	1.56646i	−0.0815019	−	0.0608823i
$663$			9.55904i			0.371242i
$664$	−11.8103	+	31.9623i	−0.458330	+	1.24038i
$665$	−35.8629	−	14.1928i	−1.39070	−	0.550374i
$666$	−0.672610	−	0.502443i	−0.0260631	−	0.0194693i
$667$	23.5903			0.913419
$668$	18.1051	−	5.35618i	0.700509	−	0.207237i
$669$	−19.4080			−0.750358
$670$	18.4664	−	19.9336i	0.713420	−	0.770102i
$671$	63.1219			2.43680
$672$	−14.1222	−	4.95624i	−0.544775	−	0.191191i
$673$			38.6495i			1.48983i	0.667161	+	0.744914i	$0.267509\pi$
$673$			38.6495i			1.48983i	−0.667161	+	0.744914i	$0.732491\pi$
$674$	8.93241	+	6.67255i	0.344064	+	0.257017i
$675$	−1.04844	+	4.88884i	−0.0403544	+	0.188172i
$676$	3.52448	+	11.9136i	0.135557	+	0.458214i
$677$	−15.5833			−0.598916			−0.299458	−	0.954109i	$-0.596806\pi$
$677$	−15.5833			−0.598916			−0.299458	+	0.954109i	$0.596806\pi$
$678$	−14.0982	+	18.8730i	−0.541440	+	0.724814i
$679$	0.616614	+	0.171457i	0.0236635	+	0.00657993i
$680$	20.7969	+	10.2928i	0.797523	+	0.394710i
$681$	−14.4509			−0.553760
$682$	26.9776	+	20.1524i	1.03303	+	0.771675i
$683$	3.11917			0.119352			0.0596759	−	0.998218i	$-0.480993\pi$
$683$	3.11917			0.119352			0.0596759	+	0.998218i	$0.480993\pi$
$684$	−3.69889	−	12.5031i	−0.141431	−	0.478069i
$685$	−0.760808	+	7.17592i	−0.0290690	+	0.274178i
$686$	−26.0169	+	3.02052i	−0.993328	+	0.115324i
$687$	−15.3305			−0.584897
$688$	2.27849	−	1.47743i	0.0868667	−	0.0563266i
$689$			3.15321i			0.120128i
$690$	8.23523	+	7.62909i	0.313510	+	0.290435i
$691$	−16.1917			−0.615962			−0.307981	−	0.951393i	$-0.599653\pi$
$691$	−16.1917			−0.615962			−0.307981	+	0.951393i	$0.599653\pi$
$692$	7.31245	+	24.7178i	0.277978	+	0.939629i
$693$	−3.74094	+	13.4536i	−0.142106	+	0.511059i
$694$	10.0379	−	13.4375i	0.381032	−	0.510080i
$695$	−21.8747	−	2.31921i	−0.829756	−	0.0879727i
$696$	6.51459	−	17.6304i	0.246935	−	0.668280i
$697$		−	29.3957i		−	1.11344i
$698$	−15.1068	−	11.2848i	−0.571801	−	0.427138i
$699$	−2.61653			−0.0989664
$700$	5.12224	−	25.9569i	0.193603	−	0.981080i
$701$	−43.7596			−1.65278			−0.826389	−	0.563099i	$-0.809609\pi$
$701$	−43.7596			−1.65278			−0.826389	+	0.563099i	$0.809609\pi$
$702$	2.95189	+	2.20508i	0.111412	+	0.0832253i
$703$			3.87027i			0.145970i
$704$	27.4550	−	32.0783i	1.03475	−	1.20900i
$705$	12.8821	+	1.36579i	0.485168	+	0.0514386i
$706$	−18.3335	+	24.5426i	−0.689989	+	0.923675i
$707$	−8.04804	+	28.9433i	−0.302678	+	1.08852i
$708$	20.0168	−	5.92171i	0.752276	−	0.222552i
$709$	−8.80386			−0.330636			−0.165318	−	0.986240i	$-0.552865\pi$
$709$	−8.80386			−0.330636			−0.165318	+	0.986240i	$0.552865\pi$
$710$	−1.43538	−	1.32973i	−0.0538689	−	0.0499040i
$711$			6.11484i			0.229324i
$712$	15.6128	−	42.2529i	0.585114	−	1.58349i
$713$	16.0154			0.599780
$714$	8.39519	+	10.8618i	0.314182	+	0.406492i
$715$	−3.24181	+	30.5766i	−0.121237	+	1.14350i
$716$	31.2783	−	9.25330i	1.16892	−	0.345812i
$717$	−2.17526			−0.0812364
$718$	−21.5670	−	16.1107i	−0.804874	−	0.601244i
$719$	−33.1425			−1.23601			−0.618003	−	0.786176i	$-0.712058\pi$
$719$	−33.1425			−1.23601			−0.618003	+	0.786176i	$0.712058\pi$
$720$	7.97589	−	4.04787i	0.297244	−	0.150855i
$721$	−4.50800	+	16.2122i	−0.167887	+	0.603772i
$722$	−19.8914	+	26.6282i	−0.740281	+	0.990999i
$723$	−1.94049			−0.0721674
$724$	−32.0362	+	9.47751i	−1.19061	+	0.352229i
$725$	32.4875	+	6.96711i	1.20655	+	0.258752i
$726$	−19.0980	−	14.2663i	−0.708793	−	0.529471i
$727$		−	32.7448i		−	1.21444i	−0.794535	−	0.607218i	$-0.792285\pi$
$727$		−	32.7448i		−	1.21444i	0.794535	−	0.607218i	$-0.207715\pi$
$728$	−15.8095	−	11.4101i	−0.585937	−	0.422886i
$729$	−1.00000			−0.0370370
$730$	2.74115	−	2.95894i	0.101455	−	0.109515i
$731$	−2.49083			−0.0921267
$732$	−6.78554	−	22.9367i	−0.250801	−	0.847765i
$733$	34.0689			1.25836			0.629181	−	0.777259i	$-0.283390\pi$
$733$	34.0689			1.25836			0.629181	+	0.777259i	$0.283390\pi$
$734$	−4.20774	−	3.14320i	−0.155311	−	0.116018i
$735$	9.44835	−	12.4791i	0.348508	−	0.460300i
$736$	1.33071	−	20.0375i	0.0490505	−	0.738591i
$737$			45.3517i			1.67055i
$738$	−9.07758	−	6.78099i	−0.334150	−	0.249612i
$739$			33.6009i			1.23603i	0.786167	+	0.618015i	$0.212063\pi$
$739$			33.6009i			1.23603i	−0.786167	+	0.618015i	$0.787937\pi$
$740$	−2.61105	+	0.480546i	−0.0959842	+	0.0176652i
$741$		−	16.9855i		−	0.623978i
$742$	2.76930	+	3.58294i	0.101664	+	0.131534i
$743$	−6.51915			−0.239164			−0.119582	−	0.992824i	$-0.538156\pi$
$743$	−6.51915			−0.239164			−0.119582	+	0.992824i	$0.538156\pi$
$744$	4.42274	−	11.9692i	0.162145	−	0.438814i
$745$	−29.9751	−	3.17803i	−1.09820	−	0.116434i
$746$	13.3644	+	9.98330i	0.489307	+	0.365515i
$747$		−	12.0472i		−	0.440782i
$748$	−37.1377	+	10.9867i	−1.35789	+	0.401715i
$749$	23.9044	+	6.64691i	0.873447	+	0.242873i
$750$	9.08803	+	12.9386i	0.331848	+	0.472451i
$751$			27.5873i			1.00668i	0.864090	+	0.503338i	$0.167895\pi$
$751$			27.5873i			1.00668i	−0.864090	+	0.503338i	$0.832105\pi$
$752$	−12.6077	−	19.4435i	−0.459755	−	0.709033i
$753$		−	12.4952i		−	0.455350i
$754$	14.6532	−	19.6160i	0.533639	−	0.714373i
$755$	−1.18378	+	11.1654i	−0.0430821	+	0.406350i
$756$	5.29079	−	0.0868958i	0.192424	−	0.00316037i
$757$			7.70156i			0.279918i	0.990157	+	0.139959i	$0.0446971\pi$
$757$			7.70156i			0.279918i	−0.990157	+	0.139959i	$0.955303\pi$
$758$	29.4454	+	21.9958i	1.06950	+	0.798925i
$759$	−18.7363			−0.680085
$760$	−36.9540	−	18.2893i	−1.34046	−	0.663422i
$761$		−	42.4206i		−	1.53775i	−0.639401	−	0.768873i	$-0.720818\pi$
$761$		−	42.4206i		−	1.53775i	0.639401	−	0.768873i	$-0.279182\pi$
$762$	−9.91846	−	7.40913i	−0.359308	−	0.268405i
$763$	−31.7379	−	8.82513i	−1.14899	−	0.319491i
$764$	5.87799	−	1.73893i	0.212658	−	0.0629123i
$765$	−8.15831	−	0.864963i	−0.294964	−	0.0312728i
$766$	1.39114	+	1.03919i	0.0502639	+	0.0375474i
$767$	27.1928			0.981875
$768$	−14.6077	−	6.52798i	−0.527111	−	0.235558i
$769$			11.0121i			0.397107i	0.980090	+	0.198554i	$0.0636244\pi$
$769$			11.0121i			0.397107i	−0.980090	+	0.198554i	$0.936376\pi$
$770$	23.1702	+	37.5909i	0.834997	+	1.35468i
$771$		−	7.98037i		−	0.287406i
$772$	51.0301	−	15.0966i	1.83662	−	0.543340i
$773$	48.8768			1.75798			0.878989	−	0.476842i	$-0.158219\pi$
$773$	48.8768			1.75798			0.878989	+	0.476842i	$0.158219\pi$
$774$	−0.574584	+	0.769185i	−0.0206530	+	0.0276478i
$775$	22.0556	+	4.72995i	0.792262	+	0.169905i
$776$	0.641785	+	0.237145i	0.0230387	+	0.00851300i
$777$	−1.51325	−	0.420779i	−0.0542876	−	0.0150954i
$778$	−23.1608	+	31.0050i	−0.830357	+	1.11158i
$779$			52.2333i			1.87145i
$780$	11.4592	−	2.10898i	0.410304	−	0.0755135i
$781$	3.26569			0.116856
$782$	−11.0235	+	14.7569i	−0.394198	+	0.527706i
$783$			6.64523i			0.237481i
$784$	−27.9849	+	0.919494i	−0.999461	+	0.0328391i
$785$	−8.22495	−	0.872028i	−0.293561	−	0.0311240i
$786$	6.38193	+	4.76733i	0.227636	+	0.170045i
$787$			22.4181i			0.799118i	0.916707	+	0.399559i	$0.130837\pi$
$787$			22.4181i			0.799118i	−0.916707	+	0.399559i	$0.869163\pi$
$788$	−29.6695	+	8.77735i	−1.05693	+	0.312680i
$789$			9.65240i			0.343634i
$790$	14.1853	+	13.1412i	0.504689	+	0.467542i
$791$	−11.8068	+	42.4609i	−0.419802	+	1.50974i
$792$	−5.17414	+	14.0028i	−0.183855	+	0.497567i
$793$		−	31.1595i		−	1.10651i
$794$	−7.13129	+	9.54651i	−0.253080	+	0.338793i
$795$	−2.69116	−	0.285323i	−0.0954456	−	0.0101194i
$796$	−3.07570	−	10.3966i	−0.109015	−	0.368496i
$797$	10.7307			0.380100			0.190050	−	0.981774i	$-0.439135\pi$
$797$	10.7307			0.380100			0.190050	+	0.981774i	$0.439135\pi$
$798$	−14.9175	−	19.3004i	−0.528072	−	0.683225i
$799$			21.2555i			0.751967i
$800$	7.75041	−	27.2017i	0.274018	−	0.961724i
$801$			15.9259i			0.562713i
$802$	−20.0456	+	26.8347i	−0.707836	+	0.947565i
$803$			6.73200i			0.237567i
$804$	16.4795	−	4.87526i	0.581188	−	0.171937i
$805$	19.5282	+	7.72832i	0.688278	+	0.272388i
$806$	9.94803	−	13.3172i	0.350405	−	0.469080i
$807$	−19.9393			−0.701898
$808$	−11.1314	+	30.1248i	−0.391600	+	1.05979i
$809$	−15.1335			−0.532066			−0.266033	−	0.963964i	$-0.585713\pi$
$809$	−15.1335			−0.532066			−0.266033	+	0.963964i	$0.585713\pi$
$810$	−2.14906	+	2.31981i	−0.0755104	+	0.0815098i
$811$	38.6616			1.35759			0.678795	−	0.734327i	$-0.262502\pi$
$811$	38.6616			1.35759			0.678795	+	0.734327i	$0.262502\pi$
$812$	−0.577442	−	35.1585i	−0.0202642	−	1.23382i
$813$		−	23.5830i		−	0.827093i
$814$	2.65184	−	3.54996i	0.0929469	−	0.124426i
$815$	10.0841	+	1.06914i	0.353230	+	0.0374502i
$816$	7.98452	+	12.3137i	0.279514	+	0.431066i
$817$	4.42597			0.154845
$818$	−10.3867	−	7.75892i	−0.363163	−	0.271284i
$819$	6.64123	+	1.84668i	0.232063	+	0.0645281i
$820$	−35.2389	+	6.48547i	−1.23060	+	0.226482i
$821$	−13.2483			−0.462370			−0.231185	−	0.972910i	$-0.574260\pi$
$821$	−13.2483			−0.462370			−0.231185	+	0.972910i	$0.574260\pi$
$822$	−2.73132	+	3.65636i	−0.0952657	+	0.127530i
$823$	33.6127			1.17166			0.585832	−	0.810432i	$-0.300768\pi$
$823$	33.6127			1.17166			0.585832	+	0.810432i	$0.300768\pi$
$824$	−6.23507	+	16.8740i	−0.217209	+	0.587832i
$825$	−25.8028	−	5.53354i	−0.898338	−	0.192653i
$826$	30.8987	−	23.8820i	1.07510	−	0.830960i
$827$	−33.8094			−1.17567			−0.587834	−	0.808982i	$-0.700019\pi$
$827$	−33.8094			−1.17567			−0.587834	+	0.808982i	$0.700019\pi$
$828$	2.01413	+	6.80824i	0.0699960	+	0.236603i
$829$		−	17.5043i		−	0.607949i	−0.952680	−	0.303974i	$-0.901686\pi$
$829$		−	17.5043i		−	0.607949i	0.952680	−	0.303974i	$-0.0983137\pi$
$830$	−27.9471	−	25.8901i	−0.970059	−	0.898659i
$831$	26.8902			0.932810
$832$	−15.8351	−	13.5529i	−0.548985	−	0.469862i
$833$	21.9962	+	13.2577i	0.762124	+	0.459353i
$834$	−11.1459	−	8.32602i	−0.385950	−	0.288307i
$835$	−2.22559	+	20.9917i	−0.0770198	+	0.726449i
$836$	65.9901	−	19.5224i	2.28232	−	0.675195i
$837$			4.51142i			0.155938i
$838$	−29.0063	+	38.8301i	−1.00200	+	1.34136i
$839$	−37.1221			−1.28160			−0.640798	−	0.767709i	$-0.721396\pi$
$839$	−37.1221			−1.28160			−0.640798	+	0.767709i	$0.721396\pi$
$840$	11.1687	−	12.4604i	0.385356	−	0.429924i
$841$	15.1591			0.522726
$842$	−4.88997	+	6.54610i	−0.168519	+	0.225594i
$843$			2.53895i			0.0874459i
$844$	38.7787	−	11.4722i	1.33482	−	0.394889i
$845$	−13.8130	−	1.46449i	−0.475182	−	0.0503798i
$846$	6.56384	+	4.90322i	0.225670	+	0.168576i
$847$	−42.9670	−	11.9475i	−1.47636	−	0.410522i
$848$	2.63383	+	4.06189i	0.0904462	+	0.139486i
$849$	30.8460			1.05863
$850$	−19.5393	+	17.0669i	−0.670192	+	0.585389i
$851$		−	2.10745i		−	0.0722425i
$852$	−0.351059	−	1.18666i	−0.0120271	−	0.0406543i
$853$	−9.12797			−0.312536			−0.156268	−	0.987715i	$-0.549946\pi$
$853$	−9.12797			−0.312536			−0.156268	+	0.987715i	$0.549946\pi$
$854$	−27.3658	−	35.4061i	−0.936437	−	1.21157i
$855$	14.4965	+	1.53696i	0.495772	+	0.0525628i
$856$	24.8802	+	9.19344i	0.850387	+	0.314225i
$857$	−14.2373			−0.486336			−0.243168	−	0.969984i	$-0.578187\pi$
$857$	−14.2373			−0.486336			−0.243168	+	0.969984i	$0.578187\pi$
$858$	−11.6382	+	15.5798i	−0.397320	+	0.531885i
$859$	−12.3261			−0.420560			−0.210280	−	0.977641i	$-0.567438\pi$
$859$	−12.3261			−0.420560			−0.210280	+	0.977641i	$0.567438\pi$
$860$	0.549544	+	2.98595i	0.0187393	+	0.101820i
$861$	−20.4229	−	5.67885i	−0.696011	−	0.193535i
$862$	16.1231	+	12.0440i	0.549153	+	0.410220i
$863$	17.6039			0.599242			0.299621	−	0.954058i	$-0.403140\pi$
$863$	17.6039			0.599242			0.299621	+	0.954058i	$0.403140\pi$
$864$	5.64442	+	0.374851i	0.192027	+	0.0127527i
$865$	−28.6586	−	3.03846i	−0.974423	−	0.103311i
$866$	−16.3965	+	21.9497i	−0.557176	+	0.745881i
$867$			3.53875i			0.120182i
$868$	−0.392024	−	23.8690i	−0.0133061	−	0.810166i
$869$	−32.2735			−1.09480
$870$	15.4157	+	14.2810i	0.522640	+	0.484172i
$871$	22.3874			0.758569
$872$	−33.0335	−	12.2062i	−1.11866	−	0.413353i
$873$	−0.241900			−0.00818708
$874$	19.5877	−	26.2216i	0.662562	−	0.886959i
$875$	24.6109	+	16.4105i	0.831999	+	0.554777i
$876$	2.44622	−	0.723683i	0.0826500	−	0.0244510i
$877$			1.12429i			0.0379646i	0.999820	+	0.0189823i	$0.00604262\pi$
$877$			1.12429i			0.0379646i	−0.999820	+	0.0189823i	$0.993957\pi$
$878$	−6.07495	+	8.13242i	−0.205020	+	0.274456i
$879$			2.41522i			0.0814634i
$880$	21.3642	+	42.0959i	0.720187	+	1.41905i
$881$		−	15.1406i		−	0.510101i	−0.966928	−	0.255051i	$-0.917908\pi$
$881$		−	15.1406i		−	0.510101i	0.966928	−	0.255051i	$-0.0820922\pi$
$882$	9.16816	−	3.73428i	0.308708	−	0.125740i
$883$	−9.65260			−0.324836			−0.162418	−	0.986722i	$-0.551929\pi$
$883$	−9.65260			−0.324836			−0.162418	+	0.986722i	$0.551929\pi$
$884$	5.42349	+	18.3327i	0.182412	+	0.616594i
$885$	−2.46058	+	23.2081i	−0.0827114	+	0.780132i
$886$	5.51751	−	7.38618i	0.185364	−	0.248144i
$887$		−	42.5999i		−	1.43036i	−0.698939	−	0.715182i	$-0.746344\pi$
$887$		−	42.5999i		−	1.43036i	0.698939	−	0.715182i	$-0.253656\pi$
$888$	−1.57503	−	0.581985i	−0.0528544	−	0.0195301i
$889$	−22.3147	−	6.20490i	−0.748412	−	0.208106i
$890$	36.9450	+	34.2257i	1.23840	+	1.14725i
$891$		−	5.27789i		−	0.176816i
$892$	−37.2214	+	11.0115i	−1.24627	+	0.368692i
$893$		−	37.7691i		−	1.26389i
$894$	−15.2733	−	11.4092i	−0.510814	−	0.381581i
$895$	−3.84491	+	36.2651i	−0.128521	+	1.21221i
$896$	−29.8960	−	1.49278i	−0.998756	−	0.0498703i
$897$			9.24900i			0.308815i
$898$	−11.2927	+	15.1174i	−0.376844	+	0.504473i
$899$	29.9794			0.999870
$900$	0.763042	+	9.97085i	0.0254347	+	0.332362i
$901$		−	4.44042i		−	0.147932i
$902$	35.7893	−	47.9105i	1.19165	−	1.59524i
$903$	−0.481195	+	1.73053i	−0.0160132	+	0.0575883i
$904$	−16.3301	+	44.1943i	−0.543133	+	1.46988i
$905$	3.93808	−	37.1439i	0.130906	−	1.23470i
$906$	−4.24979	+	5.68911i	−0.141190	+	0.189008i
$907$	−1.57855			−0.0524148			−0.0262074	−	0.999657i	$-0.508343\pi$
$907$	−1.57855			−0.0524148			−0.0262074	+	0.999657i	$0.508343\pi$
$908$	−27.7145	+	8.19899i	−0.919738	+	0.272093i
$909$		−	11.3546i		−	0.376607i
$910$	18.5564	−	11.4378i	0.615138	−	0.379158i
$911$		−	18.8412i		−	0.624235i	−0.950043	−	0.312118i	$-0.898962\pi$
$911$		−	18.8412i		−	0.624235i	0.950043	−	0.312118i	$-0.101038\pi$
$912$	−14.1877	−	21.8803i	−0.469803	−	0.724529i
$913$	63.5836			2.10431
$914$	−20.2909	−	15.1574i	−0.671162	−	0.501361i
$915$	26.5936	+	2.81952i	0.879158	+	0.0932103i
$916$	−29.4015	+	8.69806i	−0.971451	+	0.287392i
$917$	14.3582	+	3.99248i	0.474149	+	0.131843i
$918$	−4.15692	−	3.10524i	−0.137199	−	0.102488i
$919$		−	32.8286i		−	1.08292i	−0.840728	−	0.541458i	$-0.817872\pi$
$919$		−	32.8286i		−	1.08292i	0.840728	−	0.541458i	$-0.182128\pi$
$920$	20.1223	+	9.95893i	0.663413	+	0.328336i
$921$	−8.34794			−0.275074
$922$	−26.3876	−	19.7117i	−0.869030	−	0.649169i
$923$		−	1.61208i		−	0.0530622i
$924$	0.458627	+	27.9242i	0.0150877	+	0.918639i
$925$	0.622410	−	2.90229i	0.0204647	−	0.0954266i
$926$	−8.55830	+	11.4568i	−0.281243	+	0.376495i
$927$		−	6.36010i		−	0.208893i
$928$	2.49097	−	37.5085i	0.0817701	−	1.23128i
$929$		−	13.7857i		−	0.452295i	−0.974093	−	0.226148i	$-0.927387\pi$
$929$		−	13.7857i		−	0.452295i	0.974093	−	0.226148i	$-0.0726132\pi$
$930$	10.4656	+	9.69534i	0.343182	+	0.317923i
$931$	−39.0852	−	23.5577i	−1.28097	−	0.772073i
$932$	−5.01808	+	1.48454i	−0.164373	+	0.0486276i
$933$			27.1508i			0.888878i
$934$	−6.42943	−	4.80282i	−0.210377	−	0.157153i
$935$	4.56518	−	43.0587i	0.149297	−	1.40817i
$936$	6.91233	+	2.55417i	0.225937	+	0.0834855i
$937$	−49.6812			−1.62301			−0.811507	−	0.584342i	$-0.801353\pi$
$937$	−49.6812			−1.62301			−0.811507	+	0.584342i	$0.801353\pi$
$938$	25.4385	−	19.6617i	0.830596	−	0.641977i
$939$			28.7305i			0.937584i
$940$	25.4807	−	4.68954i	0.831088	−	0.152956i
$941$			26.5101i			0.864206i	0.901824	+	0.432103i	$0.142228\pi$
$941$			26.5101i			0.864206i	−0.901824	+	0.432103i	$0.857772\pi$
$942$	−4.19087	−	3.13060i	−0.136546	−	0.102001i
$943$		−	28.4423i		−	0.926207i
$944$	35.0290	−	22.7137i	1.14010	−	0.739269i
$945$	−2.17702	+	5.50096i	−0.0708184	+	0.178946i
$946$	−4.05967	−	3.03260i	−0.131991	−	0.0985982i
$947$	−39.0954			−1.27043			−0.635214	−	0.772336i	$-0.719088\pi$
$947$	−39.0954			−1.27043			−0.635214	+	0.772336i	$0.719088\pi$
$948$	3.46936	+	11.7273i	0.112680	+	0.380883i
$949$	3.32319			0.107875
$950$	34.7195	−	30.3262i	1.12645	−	0.983913i
$951$	−25.4368			−0.824844
$952$	22.2632	+	16.0679i	0.721555	+	0.520765i
$953$		−	47.5395i		−	1.53996i	−0.638070	−	0.769978i	$-0.720267\pi$
$953$		−	47.5395i		−	1.53996i	0.638070	−	0.769978i	$-0.279733\pi$
$954$	−1.37123	−	1.02432i	−0.0443953	−	0.0331635i
$955$	−0.722557	+	6.81515i	−0.0233814	+	0.220533i
$956$	−4.17178	+	1.23417i	−0.134925	+	0.0399159i
$957$	−35.0728			−1.13374
$958$	−8.00283	+	10.7132i	−0.258560	+	0.346129i
$959$	−2.28739	+	8.22616i	−0.0738636	+	0.265636i
$960$	12.9998	−	12.2884i	0.419567	−	0.396607i
$961$	−10.6471			−0.343454
$962$	−1.75241	−	1.30906i	−0.0564998	−	0.0422056i
$963$	−9.37779			−0.302195
$964$	−3.72153	+	1.10097i	−0.119862	+	0.0354598i
$965$	−6.27293	+	59.1661i	−0.201933	+	1.90463i
$966$	8.12290	+	10.5095i	0.261350	+	0.338137i
$967$	35.6130			1.14524			0.572619	−	0.819822i	$-0.305928\pi$
$967$	35.6130			1.14524			0.572619	+	0.819822i	$0.305928\pi$
$968$	−44.7210	−	16.5248i	−1.43739	−	0.531127i
$969$			23.9194i			0.768401i
$970$	−0.519859	+	0.561163i	−0.0166917	+	0.0180178i
$971$	10.4073			0.333987			0.166994	−	0.985958i	$-0.446594\pi$
$971$	10.4073			0.333987			0.166994	+	0.985958i	$0.446594\pi$
$972$	−1.91784	+	0.567368i	−0.0615146	+	0.0181983i
$973$	−25.0762	−	6.97276i	−0.803907	−	0.223537i
$974$	26.1709	−	35.0345i	0.838571	−	1.12258i
$975$	−2.73158	+	12.7373i	−0.0874806	+	0.407920i
$976$	−26.0271	−	40.1389i	−0.833108	−	1.28482i
$977$		−	11.0699i		−	0.354157i	−0.984197	−	0.177079i	$-0.943335\pi$
$977$		−	11.0699i		−	0.354157i	0.984197	−	0.177079i	$-0.0566647\pi$
$978$	5.13816	+	3.83823i	0.164300	+	0.122733i
$979$	−84.0550			−2.68641
$980$	11.0401	−	29.2936i	0.352664	−	0.935750i
$981$	12.4509			0.397527
$982$	−7.59125	−	5.67069i	−0.242246	−	0.180959i
$983$			35.8579i			1.14369i	0.820362	+	0.571845i	$0.193772\pi$
$983$			35.8579i			1.14369i	−0.820362	+	0.571845i	$0.806228\pi$
$984$	−21.2566	−	7.85450i	−0.677636	−	0.250392i
$985$	3.64715	−	34.3998i	0.116208	−	1.09607i
$986$	−20.6350	+	27.6237i	−0.657153	+	0.879718i
$987$	14.7675	+	4.10628i	0.470054	+	0.130704i
$988$	−9.63703	−	32.5754i	−0.306595	−	1.03636i
$989$	−2.41004			−0.0766349
$990$	−12.2437	−	11.3425i	−0.389131	−	0.360489i
$991$		−	6.47576i		−	0.205709i	−0.994696	−	0.102855i	$-0.967202\pi$
$991$		−	6.47576i		−	0.205709i	0.994696	−	0.102855i	$-0.0327977\pi$
$992$	1.69111	−	25.4644i	0.0536928	−	0.808495i
$993$	1.85084			0.0587345
$994$	−1.41580	−	1.83178i	−0.0449065	−	0.0581005i
$995$	12.0541	+	1.27801i	0.382142	+	0.0405156i
$996$	−6.83517	−	23.1045i	−0.216581	−	0.732093i
$997$	−44.6666			−1.41460			−0.707302	−	0.706911i	$-0.750088\pi$
$997$	−44.6666			−1.41460			−0.707302	+	0.706911i	$0.750088\pi$
$998$	37.1570	+	27.7564i	1.17618	+	0.878614i
$999$	0.593655			0.0187824

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.i.a.139.15	yes	48
4.3	odd	2	inner	420.2.i.a.139.36	yes	48
5.4	even	2	inner	420.2.i.a.139.34	yes	48
7.6	odd	2	inner	420.2.i.a.139.16	yes	48
20.19	odd	2	inner	420.2.i.a.139.13	✓	48
28.27	even	2	inner	420.2.i.a.139.35	yes	48
35.34	odd	2	inner	420.2.i.a.139.33	yes	48
140.139	even	2	inner	420.2.i.a.139.14	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.i.a.139.13	✓	48	20.19	odd	2	inner
420.2.i.a.139.14	yes	48	140.139	even	2	inner
420.2.i.a.139.15	yes	48	1.1	even	1	trivial
420.2.i.a.139.16	yes	48	7.6	odd	2	inner
420.2.i.a.139.33	yes	48	35.34	odd	2	inner
420.2.i.a.139.34	yes	48	5.4	even	2	inner
420.2.i.a.139.35	yes	48	28.27	even	2	inner
420.2.i.a.139.36	yes	48	4.3	odd	2	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:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.846354 + 1.13300i) q^{2} -1.00000i q^{3} +(-0.567368 - 1.91784i) q^{4} +(2.22361 + 0.235752i) q^{5} +(1.13300 + 0.846354i) q^{6} +(2.54904 + 0.708793i) q^{7} +(2.65310 + 0.980342i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.846354 + 1.13300i) q^{2} -1.00000i q^{3} +(-0.567368 - 1.91784i) q^{4} +(2.22361 + 0.235752i) q^{5} +(1.13300 + 0.846354i) q^{6} +(2.54904 + 0.708793i) q^{7} +(2.65310 + 0.980342i) q^{8} -1.00000 q^{9} +(-2.14906 + 2.31981i) q^{10} -5.27789i q^{11} +(-1.91784 + 0.567368i) q^{12} -2.60538 q^{13} +(-2.96045 + 2.28817i) q^{14} +(0.235752 - 2.22361i) q^{15} +(-3.35619 + 2.17624i) q^{16} +3.66896 q^{17} +(0.846354 - 1.13300i) q^{18} -6.51939 q^{19} +(-0.809470 - 4.39827i) q^{20} +(0.708793 - 2.54904i) q^{21} +(5.97984 + 4.46697i) q^{22} +3.54996 q^{23} +(0.980342 - 2.65310i) q^{24} +(4.88884 + 1.04844i) q^{25} +(2.20508 - 2.95189i) q^{26} +1.00000i q^{27} +(-0.0868958 - 5.29079i) q^{28} +6.64523 q^{29} +(2.31981 + 2.14906i) q^{30} +4.51142 q^{31} +(0.374851 - 5.64442i) q^{32} -5.27789 q^{33} +(-3.10524 + 4.15692i) q^{34} +(5.50096 + 2.17702i) q^{35} +(0.567368 + 1.91784i) q^{36} -0.593655i q^{37} +(5.51771 - 7.38645i) q^{38} +2.60538i q^{39} +(5.66833 + 2.80537i) q^{40} -8.01200i q^{41} +(2.28817 + 2.96045i) q^{42} -0.678893 q^{43} +(-10.1221 + 2.99451i) q^{44} +(-2.22361 - 0.235752i) q^{45} +(-3.00452 + 4.02210i) q^{46} +5.79334i q^{47} +(2.17624 + 3.35619i) q^{48} +(5.99522 + 3.61349i) q^{49} +(-5.32557 + 4.65170i) q^{50} -3.66896i q^{51} +(1.47821 + 4.99669i) q^{52} -1.21027i q^{53} +(-1.13300 - 0.846354i) q^{54} +(1.24427 - 11.7360i) q^{55} +(6.06800 + 4.37943i) q^{56} +6.51939i q^{57} +(-5.62422 + 7.52903i) q^{58} -10.4372 q^{59} +(-4.39827 + 0.809470i) q^{60} +11.9597i q^{61} +(-3.81826 + 5.11143i) q^{62} +(-2.54904 - 0.708793i) q^{63} +(6.07786 + 5.20189i) q^{64} +(-5.79334 - 0.614223i) q^{65} +(4.46697 - 5.97984i) q^{66} -8.59277 q^{67} +(-2.08165 - 7.03646i) q^{68} -3.54996i q^{69} +(-7.12232 + 4.39005i) q^{70} +0.618749i q^{71} +(-2.65310 - 0.980342i) q^{72} -1.27551 q^{73} +(0.672610 + 0.502443i) q^{74} +(1.04844 - 4.88884i) q^{75} +(3.69889 + 12.5031i) q^{76} +(3.74094 - 13.4536i) q^{77} +(-2.95189 - 2.20508i) q^{78} -6.11484i q^{79} +(-7.97589 + 4.04787i) q^{80} +1.00000 q^{81} +(9.07758 + 6.78099i) q^{82} +12.0472i q^{83} +(-5.29079 + 0.0868958i) q^{84} +(8.15831 + 0.864963i) q^{85} +(0.574584 - 0.769185i) q^{86} -6.64523i q^{87} +(5.17414 - 14.0028i) q^{88} -15.9259i q^{89} +(2.14906 - 2.31981i) q^{90} +(-6.64123 - 1.84668i) q^{91} +(-2.01413 - 6.80824i) q^{92} -4.51142i q^{93} +(-6.56384 - 4.90322i) q^{94} +(-14.4965 - 1.53696i) q^{95} +(-5.64442 - 0.374851i) q^{96} +0.241900 q^{97} +(-9.16816 + 3.73428i) q^{98} +5.27789i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{9}+O(q^{10}) \) 48 * q - 48 * q^9	\( 48 q - 48 q^{9} + 20 q^{14} - 16 q^{16} + 8 q^{25} - 16 q^{30} - 40 q^{44} + 16 q^{46} - 16 q^{49} + 48 q^{50} + 28 q^{56} - 32 q^{60} - 112 q^{74} + 48 q^{81} - 28 q^{84} + 56 q^{85} + 8 q^{86}+O(q^{100}) \) 48 * q - 48 * q^9 + 20 * q^14 - 16 * q^16 + 8 * q^25 - 16 * q^30 - 40 * q^44 + 16 * q^46 - 16 * q^49 + 48 * q^50 + 28 * q^56 - 32 * q^60 - 112 * q^74 + 48 * q^81 - 28 * q^84 + 56 * q^85 + 8 * q^86

Introduction

L-functions

Modular forms

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Database

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