LMFDB - Embedded newform 1386.2.ba.a.989.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(989,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("1386.989");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			989.6
Character	$\chi$	$=$	1386.989
Dual form			1386.2.ba.a.1187.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.42385 - 0.822059i) q^{5} +(-2.58759 + 0.551706i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.42385 - 0.822059i) q^{5} +(-2.58759 + 0.551706i) q^{7} +1.00000 q^{8} +(1.42385 - 0.822059i) q^{10} +(0.578609 + 3.26576i) q^{11} -1.29335i q^{13} +(0.816004 - 2.51677i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.68534 + 2.91910i) q^{17} +(0.340140 + 0.196380i) q^{19} +1.64412i q^{20} +(-3.11754 - 1.13179i) q^{22} +(-0.455476 - 0.262969i) q^{23} +(-1.14844 - 1.98915i) q^{25} +(1.12007 + 0.646675i) q^{26} +(1.77159 + 1.96507i) q^{28} -1.33002 q^{29} +(-2.86951 - 4.97013i) q^{31} +(-0.500000 - 0.866025i) q^{32} -3.37069 q^{34} +(4.13787 + 1.34161i) q^{35} +(1.50973 - 2.61493i) q^{37} +(-0.340140 + 0.196380i) q^{38} +(-1.42385 - 0.822059i) q^{40} +10.9253 q^{41} -10.5847i q^{43} +(2.53893 - 2.13397i) q^{44} +(0.455476 - 0.262969i) q^{46} +(-4.48768 - 2.59096i) q^{47} +(6.39124 - 2.85518i) q^{49} +2.29687 q^{50} +(-1.12007 + 0.646675i) q^{52} +(-1.43915 + 0.830895i) q^{53} +(1.86080 - 5.12560i) q^{55} +(-2.58759 + 0.551706i) q^{56} +(0.665012 - 1.15183i) q^{58} +(8.26233 - 4.77026i) q^{59} +(3.32010 + 1.91686i) q^{61} +5.73902 q^{62} +1.00000 q^{64} +(-1.06321 + 1.84153i) q^{65} +(-6.80137 - 11.7803i) q^{67} +(1.68534 - 2.91910i) q^{68} +(-3.23080 + 2.91270i) q^{70} +1.62169i q^{71} +(8.82651 - 5.09599i) q^{73} +(1.50973 + 2.61493i) q^{74} -0.392760i q^{76} +(-3.29894 - 8.13123i) q^{77} +(-7.22793 - 4.17305i) q^{79} +(1.42385 - 0.822059i) q^{80} +(-5.46264 + 9.46156i) q^{82} +5.98532 q^{83} -5.54181i q^{85} +(9.16665 + 5.29237i) q^{86} +(0.578609 + 3.26576i) q^{88} +(-8.32280 - 4.80517i) q^{89} +(0.713549 + 3.34666i) q^{91} +0.525938i q^{92} +(4.48768 - 2.59096i) q^{94} +(-0.322872 - 0.559231i) q^{95} +8.31783 q^{97} +(-0.722965 + 6.96257i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8}+O(q^{10}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 2 q^{11} - 16 q^{16} - 4 q^{17} + 4 q^{22} + 4 q^{25} - 16 q^{29} + 4 q^{31} - 16 q^{32} + 8 q^{34} - 16 q^{35} + 4 q^{37} + 32 q^{41} - 2 q^{44} + 20 q^{49} - 8 q^{50} - 12 q^{55} + 8 q^{58} - 8 q^{62} + 32 q^{64} - 8 q^{67} - 4 q^{68} - 4 q^{70} + 4 q^{74} - 14 q^{77} - 16 q^{82} - 88 q^{83} - 2 q^{88} + 24 q^{95} - 32 q^{97} + 8 q^{98}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 2 * q^11 - 16 * q^16 - 4 * q^17 + 4 * q^22 + 4 * q^25 - 16 * q^29 + 4 * q^31 - 16 * q^32 + 8 * q^34 - 16 * q^35 + 4 * q^37 + 32 * q^41 - 2 * q^44 + 20 * q^49 - 8 * q^50 - 12 * q^55 + 8 * q^58 - 8 * q^62 + 32 * q^64 - 8 * q^67 - 4 * q^68 - 4 * q^70 + 4 * q^74 - 14 * q^77 - 16 * q^82 - 88 * q^83 - 2 * q^88 + 24 * q^95 - 32 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.42385	−	0.822059i	−0.636764	−	0.367636i	0.146603	−	0.989195i	$-0.453166\pi$
$5$	−1.42385	−	0.822059i	−0.636764	−	0.367636i	−0.783367	+	0.621559i	$0.786499\pi$
$6$		0			0
$7$	−2.58759	+	0.551706i	−0.978017	+	0.208525i
$7$	−2.58759	+	0.551706i	−0.978017	+	0.208525i
$8$	1.00000			0.353553
$9$		0			0
$10$	1.42385	−	0.822059i	0.450260	−	0.259958i
$11$	0.578609	+	3.26576i	0.174457	+	0.984665i
$11$	0.578609	+	3.26576i	0.174457	+	0.984665i
$12$		0			0
$13$		−	1.29335i		−	0.358711i	−0.983784	−	0.179355i	$-0.942599\pi$
$13$		−	1.29335i		−	0.358711i	0.983784	−	0.179355i	$-0.0574012\pi$
$14$	0.816004	−	2.51677i	0.218086	−	0.672635i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.68534	+	2.91910i	0.408756	+	0.707986i	0.994751	−	0.102329i	$-0.0326294\pi$
$17$	1.68534	+	2.91910i	0.408756	+	0.707986i	−0.585995	+	0.810315i	$0.699296\pi$
$18$		0			0
$19$	0.340140	+	0.196380i	0.0780335	+	0.0450527i	0.538509	−	0.842620i	$-0.318988\pi$
$19$	0.340140	+	0.196380i	0.0780335	+	0.0450527i	−0.460476	+	0.887672i	$0.652321\pi$
$20$			1.64412i			0.367636i
$21$		0			0
$22$	−3.11754	−	1.13179i	−0.664661	−	0.241299i
$23$	−0.455476	−	0.262969i	−0.0949733	−	0.0548329i	0.451761	−	0.892139i	$-0.350796\pi$
$23$	−0.455476	−	0.262969i	−0.0949733	−	0.0548329i	−0.546734	+	0.837306i	$0.684129\pi$
$24$		0			0
$25$	−1.14844	−	1.98915i	−0.229687	−	0.397830i
$26$	1.12007	+	0.646675i	0.219665	+	0.126823i
$27$		0			0
$28$	1.77159	+	1.96507i	0.334798	+	0.371362i
$29$	−1.33002			−0.246979			−0.123490	−	0.992346i	$-0.539409\pi$
$29$	−1.33002			−0.246979			−0.123490	+	0.992346i	$0.539409\pi$
$30$		0			0
$31$	−2.86951	−	4.97013i	−0.515379	−	0.892662i	−0.999841	−	0.0178500i	$-0.994318\pi$
$31$	−2.86951	−	4.97013i	−0.515379	−	0.892662i	0.484462	−	0.874812i	$-0.339015\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−3.37069			−0.578068
$35$	4.13787	+	1.34161i	0.699428	+	0.226773i
$36$		0			0
$37$	1.50973	−	2.61493i	0.248198	−	0.429892i	−0.714828	−	0.699300i	$-0.753495\pi$
$37$	1.50973	−	2.61493i	0.248198	−	0.429892i	0.963026	+	0.269409i	$0.0868283\pi$
$38$	−0.340140	+	0.196380i	−0.0551780	+	0.0318570i
$39$		0			0
$40$	−1.42385	−	0.822059i	−0.225130	−	0.129979i
$41$	10.9253			1.70624			0.853120	−	0.521714i	$-0.174707\pi$
$41$	10.9253			1.70624			0.853120	+	0.521714i	$0.174707\pi$
$42$		0			0
$43$		−	10.5847i		−	1.61416i	−0.590444	−	0.807079i	$-0.701047\pi$
$43$		−	10.5847i		−	1.61416i	0.590444	−	0.807079i	$-0.298953\pi$
$44$	2.53893	−	2.13397i	0.382758	−	0.321708i
$45$		0			0
$46$	0.455476	−	0.262969i	0.0671563	−	0.0387727i
$47$	−4.48768	−	2.59096i	−0.654595	−	0.377931i	0.135619	−	0.990761i	$-0.456698\pi$
$47$	−4.48768	−	2.59096i	−0.654595	−	0.377931i	−0.790215	+	0.612830i	$0.790031\pi$
$48$		0			0
$49$	6.39124	−	2.85518i	0.913034	−	0.407882i
$50$	2.29687			0.324827
$51$		0			0
$52$	−1.12007	+	0.646675i	−0.155326	+	0.0896777i
$53$	−1.43915	+	0.830895i	−0.197683	+	0.114132i	−0.595574	−	0.803300i	$-0.703075\pi$
$53$	−1.43915	+	0.830895i	−0.197683	+	0.114132i	0.397891	+	0.917433i	$0.369742\pi$
$54$		0			0
$55$	1.86080	−	5.12560i	0.250910	−	0.691136i
$56$	−2.58759	+	0.551706i	−0.345781	+	0.0737248i
$57$		0			0
$58$	0.665012	−	1.15183i	0.0873203	−	0.151243i
$59$	8.26233	−	4.77026i	1.07566	−	0.621035i	0.145941	−	0.989293i	$-0.453379\pi$
$59$	8.26233	−	4.77026i	1.07566	−	0.621035i	0.929724	+	0.368258i	$0.120046\pi$
$60$		0			0
$61$	3.32010	+	1.91686i	0.425095	+	0.245429i	0.697255	−	0.716823i	$-0.254405\pi$
$61$	3.32010	+	1.91686i	0.425095	+	0.245429i	−0.272160	+	0.962252i	$0.587738\pi$
$62$	5.73902			0.728856
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.06321	+	1.84153i	−0.131875	+	0.228414i
$66$		0			0
$67$	−6.80137	−	11.7803i	−0.830919	−	1.43919i	−0.897310	−	0.441401i	$-0.854482\pi$
$67$	−6.80137	−	11.7803i	−0.830919	−	1.43919i	0.0663907	−	0.997794i	$-0.478852\pi$
$68$	1.68534	−	2.91910i	0.204378	−	0.353993i
$69$		0			0
$70$	−3.23080	+	2.91270i	−0.386155	+	0.348134i
$71$			1.62169i			0.192459i	0.995359	+	0.0962296i	$0.0306783\pi$
$71$			1.62169i			0.192459i	−0.995359	+	0.0962296i	$0.969322\pi$
$72$		0			0
$73$	8.82651	−	5.09599i	1.03307	−	0.596440i	0.115204	−	0.993342i	$-0.463248\pi$
$73$	8.82651	−	5.09599i	1.03307	−	0.596440i	0.917861	+	0.396901i	$0.129915\pi$
$74$	1.50973	+	2.61493i	0.175503	+	0.303979i
$75$		0			0
$76$		−	0.392760i		−	0.0450527i
$77$	−3.29894	−	8.13123i	−0.375949	−	0.926640i
$78$		0			0
$79$	−7.22793	−	4.17305i	−0.813206	−	0.469505i	0.0348619	−	0.999392i	$-0.488901\pi$
$79$	−7.22793	−	4.17305i	−0.813206	−	0.469505i	−0.848068	+	0.529887i	$0.822234\pi$
$80$	1.42385	−	0.822059i	0.159191	−	0.0919090i
$81$		0			0
$82$	−5.46264	+	9.46156i	−0.603247	+	1.04485i
$83$	5.98532			0.656975			0.328487	−	0.944508i	$-0.393461\pi$
$83$	5.98532			0.656975			0.328487	+	0.944508i	$0.393461\pi$
$84$		0			0
$85$		−	5.54181i		−	0.601094i
$86$	9.16665	+	5.29237i	0.988466	+	0.570691i
$87$		0			0
$88$	0.578609	+	3.26576i	0.0616799	+	0.348132i
$89$	−8.32280	−	4.80517i	−0.882215	−	0.509347i	−0.0108269	−	0.999941i	$-0.503446\pi$
$89$	−8.32280	−	4.80517i	−0.882215	−	0.509347i	−0.871388	+	0.490594i	$0.836780\pi$
$90$		0			0
$91$	0.713549	+	3.34666i	0.0748003	+	0.350825i
$92$			0.525938i			0.0548329i
$93$		0			0
$94$	4.48768	−	2.59096i	0.462869	−	0.267237i
$95$	−0.322872	−	0.559231i	−0.0331260	−	0.0573759i
$96$		0			0
$97$	8.31783			0.844548			0.422274	−	0.906468i	$-0.361232\pi$
$97$	8.31783			0.844548			0.422274	+	0.906468i	$0.361232\pi$
$98$	−0.722965	+	6.96257i	−0.0730305	+	0.703325i
$99$		0			0
$100$	−1.14844	+	1.98915i	−0.114844	+	0.198915i
$101$	−2.53452	−	4.38992i	−0.252194	−	0.436813i	0.711935	−	0.702245i	$-0.247819\pi$
$101$	−2.53452	−	4.38992i	−0.252194	−	0.436813i	−0.964130	+	0.265432i	$0.914485\pi$
$102$		0			0
$103$	−3.64472	+	6.31283i	−0.359124	+	0.622022i	−0.987815	−	0.155634i	$-0.950258\pi$
$103$	−3.64472	+	6.31283i	−0.359124	+	0.622022i	0.628690	+	0.777656i	$0.283591\pi$
$104$		−	1.29335i		−	0.126823i
$105$		0			0
$106$		−	1.66179i		−	0.161407i
$107$	2.16028	−	3.74171i	0.208842	−	0.361725i	−0.742508	−	0.669837i	$-0.766364\pi$
$107$	2.16028	−	3.74171i	0.208842	−	0.361725i	0.951350	+	0.308112i	$0.0996972\pi$
$108$		0			0
$109$	5.84618	−	3.37529i	0.559962	−	0.323294i	−0.193168	−	0.981166i	$-0.561876\pi$
$109$	5.84618	−	3.37529i	0.559962	−	0.323294i	0.753130	+	0.657871i	$0.228543\pi$
$110$	3.50850	+	4.17430i	0.334523	+	0.398004i
$111$		0			0
$112$	0.816004	−	2.51677i	0.0771051	−	0.237813i
$113$		−	18.2771i		−	1.71936i	−0.510831	−	0.859681i	$-0.670662\pi$
$113$		−	18.2771i		−	1.71936i	0.510831	−	0.859681i	$-0.329338\pi$
$114$		0			0
$115$	0.432353	+	0.748857i	0.0403171	+	0.0698312i
$116$	0.665012	+	1.15183i	0.0617448	+	0.106945i
$117$		0			0
$118$			9.54052i			0.878276i
$119$	−5.97146	−	6.62362i	−0.547403	−	0.607186i
$120$		0			0
$121$	−10.3304	+	3.77920i	−0.939129	+	0.343564i
$122$	−3.32010	+	1.91686i	−0.300588	+	0.173544i
$123$		0			0
$124$	−2.86951	+	4.97013i	−0.257689	+	0.446331i
$125$			11.9969i			1.07304i
$126$		0			0
$127$			9.84411i			0.873524i	0.899577	+	0.436762i	$0.143875\pi$
$127$			9.84411i			0.873524i	−0.899577	+	0.436762i	$0.856125\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−1.06321	−	1.84153i	−0.0932497	−	0.161513i
$131$	−3.20488	+	5.55101i	−0.280011	+	0.484994i	−0.971387	−	0.237501i	$-0.923672\pi$
$131$	−3.20488	+	5.55101i	−0.280011	+	0.484994i	0.691376	+	0.722495i	$0.257005\pi$
$132$		0			0
$133$	−0.988487	−	0.320494i	−0.0857127	−	0.0277903i
$134$	13.6027			1.17510
$135$		0			0
$136$	1.68534	+	2.91910i	0.144517	+	0.250311i
$137$	14.4951	−	8.36876i	1.23840	−	0.714992i	0.269634	−	0.962963i	$-0.413097\pi$
$137$	14.4951	−	8.36876i	1.23840	−	0.714992i	0.968767	+	0.247971i	$0.0797639\pi$
$138$		0			0
$139$			3.66143i			0.310559i	0.987871	+	0.155279i	$0.0496278\pi$
$139$			3.66143i			0.310559i	−0.987871	+	0.155279i	$0.950372\pi$
$140$	−0.907070	−	4.25430i	−0.0766614	−	0.359554i
$141$		0			0
$142$	−1.40442	−	0.810845i	−0.117857	−	0.0680446i
$143$	4.22378	−	0.748344i	0.353210	−	0.0625797i
$144$		0			0
$145$	1.89375	+	1.09336i	0.157268	+	0.0907984i
$146$			10.1920i			0.843494i
$147$		0			0
$148$	−3.01946			−0.248198
$149$	−7.35277	+	12.7354i	−0.602363	+	1.04332i	0.390100	+	0.920773i	$0.372441\pi$
$149$	−7.35277	+	12.7354i	−0.602363	+	1.04332i	−0.992462	+	0.122550i	$0.960893\pi$
$150$		0			0
$151$	−8.55083	+	4.93683i	−0.695857	+	0.401753i	−0.805802	−	0.592184i	$-0.798266\pi$
$151$	−8.55083	+	4.93683i	−0.695857	+	0.401753i	0.109946	+	0.993938i	$0.464932\pi$
$152$	0.340140	+	0.196380i	0.0275890	+	0.0159285i
$153$		0			0
$154$	8.69133	+	1.20865i	0.700367	+	0.0973957i
$155$			9.43562i			0.757887i
$156$		0			0
$157$	4.33551	+	7.50933i	0.346012	+	0.599310i	0.985537	−	0.169460i	$-0.0542025\pi$
$157$	4.33551	+	7.50933i	0.346012	+	0.599310i	−0.639525	+	0.768770i	$0.720869\pi$
$158$	7.22793	−	4.17305i	0.575024	−	0.331990i
$159$		0			0
$160$			1.64412i			0.129979i
$161$	1.32367	+	0.429168i	0.104320	+	0.0338232i
$162$		0			0
$163$	6.06457	−	10.5041i	0.475014	−	0.822748i	−0.524577	−	0.851363i	$-0.675776\pi$
$163$	6.06457	−	10.5041i	0.475014	−	0.822748i	0.999591	+	0.0286150i	$0.00910968\pi$
$164$	−5.46264	−	9.46156i	−0.426560	−	0.738824i
$165$		0			0
$166$	−2.99266	+	5.18344i	−0.232276	+	0.402313i
$167$	1.42411			0.110201			0.0551006	−	0.998481i	$-0.482452\pi$
$167$	1.42411			0.110201			0.0551006	+	0.998481i	$0.482452\pi$
$168$		0			0
$169$	11.3272			0.871327
$170$	4.79935	+	2.77090i	0.368093	+	0.212519i
$171$		0			0
$172$	−9.16665	+	5.29237i	−0.698951	+	0.403539i
$173$	2.13167	−	3.69216i	0.162068	−	0.280709i	−0.773542	−	0.633745i	$-0.781517\pi$
$173$	2.13167	−	3.69216i	0.162068	−	0.280709i	0.935610	+	0.353035i	$0.114850\pi$
$174$		0			0
$175$	4.06911	+	4.51351i	0.307596	+	0.341189i
$176$	−3.11754	−	1.13179i	−0.234993	−	0.0853120i
$177$		0			0
$178$	8.32280	−	4.80517i	0.623820	−	0.360163i
$179$	−1.32093	+	0.762640i	−0.0987311	+	0.0570024i	−0.548553	−	0.836116i	$-0.684821\pi$
$179$	−1.32093	+	0.762640i	−0.0987311	+	0.0570024i	0.449821	+	0.893118i	$0.351488\pi$
$180$		0			0
$181$	19.7414			1.46736			0.733682	−	0.679493i	$-0.237800\pi$
$181$	19.7414			1.46736			0.733682	+	0.679493i	$0.237800\pi$
$182$	−3.25507	−	1.05538i	−0.241282	−	0.0782299i
$183$		0			0
$184$	−0.455476	−	0.262969i	−0.0335781	−	0.0193864i
$185$	−4.29925	+	2.48217i	−0.316087	+	0.182493i
$186$		0			0
$187$	−8.55794	+	7.19295i	−0.625818	+	0.526001i
$188$			5.18193i			0.377931i
$189$		0			0
$190$	0.645744			0.0468472
$191$	12.9424	+	7.47229i	0.936478	+	0.540676i	0.888854	−	0.458190i	$-0.151502\pi$
$191$	12.9424	+	7.47229i	0.936478	+	0.540676i	0.0476233	+	0.998865i	$0.484835\pi$
$192$		0			0
$193$	−3.47593	+	2.00683i	−0.250203	+	0.144455i	−0.619857	−	0.784715i	$-0.712810\pi$
$193$	−3.47593	+	2.00683i	−0.250203	+	0.144455i	0.369654	+	0.929169i	$0.379476\pi$
$194$	−4.15892	+	7.20346i	−0.298593	+	0.517178i
$195$		0			0
$196$	−5.66828	−	4.10739i	−0.404877	−	0.293385i
$197$	−21.4340			−1.52711			−0.763554	−	0.645744i	$-0.776547\pi$
$197$	−21.4340			−1.52711			−0.763554	+	0.645744i	$0.776547\pi$
$198$		0			0
$199$	−11.7097	−	20.2818i	−0.830079	−	1.43774i	−0.897975	−	0.440047i	$-0.854962\pi$
$199$	−11.7097	−	20.2818i	−0.830079	−	1.43774i	0.0678951	−	0.997692i	$-0.478372\pi$
$200$	−1.14844	−	1.98915i	−0.0812068	−	0.140654i
$201$		0			0
$202$	5.06904			0.356656
$203$	3.44156	−	0.733782i	0.241550	−	0.0515014i
$204$		0			0
$205$	−15.5559	−	8.98122i	−1.08647	−	0.627276i
$206$	−3.64472	−	6.31283i	−0.253939	−	0.439836i
$207$		0			0
$208$	1.12007	+	0.646675i	0.0776632	+	0.0448389i
$209$	−0.444523	+	1.22444i	−0.0307483	+	0.0846966i
$210$		0			0
$211$		−	2.15572i		−	0.148406i	−0.997243	−	0.0742028i	$-0.976359\pi$
$211$		−	2.15572i		−	0.148406i	0.997243	−	0.0742028i	$-0.0236412\pi$
$212$	1.43915	+	0.830895i	0.0988414	+	0.0570661i
$213$		0			0
$214$	2.16028	+	3.74171i	0.147674	+	0.255778i
$215$	−8.70128	+	15.0711i	−0.593423	+	1.02784i
$216$		0			0
$217$	10.1672	+	11.2775i	0.690192	+	0.765569i
$218$			6.75058i			0.457207i
$219$		0			0
$220$	−5.36930	+	0.951302i	−0.361998	+	0.0641367i
$221$	3.77542	−	2.17974i	0.253962	−	0.146625i
$222$		0			0
$223$	7.01103			0.469493			0.234747	−	0.972057i	$-0.424574\pi$
$223$	7.01103			0.469493			0.234747	+	0.972057i	$0.424574\pi$
$224$	1.77159	+	1.96507i	0.118369	+	0.131296i
$225$		0			0
$226$	15.8284	+	9.13854i	1.05289	+	0.607886i
$227$	−10.0653	−	17.4337i	−0.668060	−	1.15711i	−0.978446	−	0.206503i	$-0.933792\pi$
$227$	−10.0653	−	17.4337i	−0.668060	−	1.15711i	0.310387	−	0.950610i	$-0.399542\pi$
$228$		0			0
$229$	4.19825	−	7.27158i	0.277428	−	0.480520i	−0.693317	−	0.720633i	$-0.743851\pi$
$229$	4.19825	−	7.27158i	0.277428	−	0.480520i	0.970745	+	0.240113i	$0.0771846\pi$
$230$	−0.864705			−0.0570170
$231$		0			0
$232$	−1.33002			−0.0873203
$233$	6.15876	−	10.6673i	0.403474	−	0.698838i	−0.590669	−	0.806914i	$-0.701136\pi$
$233$	6.15876	−	10.6673i	0.403474	−	0.698838i	0.994143	+	0.108077i	$0.0344692\pi$
$234$		0			0
$235$	4.25985	+	7.37828i	0.277882	+	0.481306i
$236$	−8.26233	−	4.77026i	−0.537832	−	0.310518i
$237$		0			0
$238$	8.72196	−	1.85963i	0.565360	−	0.120542i
$239$	−6.66725			−0.431268			−0.215634	−	0.976474i	$-0.569182\pi$
$239$	−6.66725			−0.431268			−0.215634	+	0.976474i	$0.569182\pi$
$240$		0			0
$241$	−4.40382	+	2.54255i	−0.283675	+	0.163780i	−0.635086	−	0.772441i	$-0.719035\pi$
$241$	−4.40382	+	2.54255i	−0.283675	+	0.163780i	0.351411	+	0.936221i	$0.385702\pi$
$242$	1.89233	−	10.8360i	0.121644	−	0.696565i
$243$		0			0
$244$		−	3.83372i		−	0.245429i
$245$	−11.4473	−	1.18864i	−0.731340	−	0.0759394i
$246$		0			0
$247$	0.253988	−	0.439920i	0.0161609	−	0.0279915i
$248$	−2.86951	−	4.97013i	−0.182214	−	0.315604i
$249$		0			0
$250$	−10.3896	−	5.99846i	−0.657099	−	0.379376i
$251$			15.5033i			0.978563i	0.872126	+	0.489281i	$0.162741\pi$
$251$			15.5033i			0.978563i	−0.872126	+	0.489281i	$0.837259\pi$
$252$		0			0
$253$	0.595253	−	1.63963i	0.0374232	−	0.103083i
$254$	−8.52525	−	4.92206i	−0.534922	−	0.308837i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−11.4588	−	6.61574i	−0.714780	−	0.412678i	0.0980485	−	0.995182i	$-0.468740\pi$
$257$	−11.4588	−	6.61574i	−0.714780	−	0.412678i	−0.812828	+	0.582503i	$0.802073\pi$
$258$		0			0
$259$	−2.46389	+	7.59929i	−0.153099	+	0.472197i
$260$	2.12642			0.131875
$261$		0			0
$262$	−3.20488	−	5.55101i	−0.197998	−	0.342942i
$263$	2.38841	+	4.13684i	0.147275	+	0.255088i	0.930220	−	0.367004i	$-0.119616\pi$
$263$	2.38841	+	4.13684i	0.147275	+	0.255088i	−0.782944	+	0.622092i	$0.786283\pi$
$264$		0			0
$265$	2.73218			0.167837
$266$	0.771799	−	0.695808i	0.0473220	−	0.0426627i
$267$		0			0
$268$	−6.80137	+	11.7803i	−0.415460	+	0.719597i
$269$	9.14107	−	5.27760i	0.557341	−	0.321781i	−0.194737	−	0.980856i	$-0.562385\pi$
$269$	9.14107	−	5.27760i	0.557341	−	0.321781i	0.752077	+	0.659075i	$0.229052\pi$
$270$		0			0
$271$	21.4275	+	12.3712i	1.30163	+	0.751496i	0.980683	−	0.195602i	$-0.0626660\pi$
$271$	21.4275	+	12.3712i	1.30163	+	0.751496i	0.320946	+	0.947098i	$0.395999\pi$
$272$	−3.37069			−0.204378
$273$		0			0
$274$			16.7375i			1.01115i
$275$	5.83160	−	4.90146i	0.351659	−	0.295569i
$276$		0			0
$277$	−10.2245	+	5.90312i	−0.614331	+	0.354684i	−0.774659	−	0.632380i	$-0.782078\pi$
$277$	−10.2245	+	5.90312i	−0.614331	+	0.354684i	0.160328	+	0.987064i	$0.448745\pi$
$278$	−3.17089	−	1.83072i	−0.190178	−	0.109799i
$279$		0			0
$280$	4.13787	+	1.34161i	0.247285	+	0.0801763i
$281$	−16.1488			−0.963359			−0.481680	−	0.876347i	$-0.659973\pi$
$281$	−16.1488			−0.963359			−0.481680	+	0.876347i	$0.659973\pi$
$282$		0			0
$283$	11.4555	−	6.61385i	0.680960	−	0.393153i	−0.119257	−	0.992863i	$-0.538051\pi$
$283$	11.4555	−	6.61385i	0.680960	−	0.393153i	0.800217	+	0.599711i	$0.204718\pi$
$284$	1.40442	−	0.810845i	0.0833373	−	0.0481148i
$285$		0			0
$286$	−1.46380	+	4.03207i	−0.0865565	+	0.238421i
$287$	−28.2701	+	6.02754i	−1.66873	+	0.355794i
$288$		0			0
$289$	2.81923	−	4.88306i	0.165837	−	0.287239i
$290$	−1.89375	+	1.09336i	−0.111205	+	0.0642042i
$291$		0			0
$292$	−8.82651	−	5.09599i	−0.516533	−	0.298220i
$293$	−14.9415			−0.872894			−0.436447	−	0.899730i	$-0.643763\pi$
$293$	−14.9415			−0.872894			−0.436447	+	0.899730i	$0.643763\pi$
$294$		0			0
$295$	−15.6857			−0.913260
$296$	1.50973	−	2.61493i	0.0877513	−	0.151990i
$297$		0			0
$298$	−7.35277	−	12.7354i	−0.425935	−	0.737741i
$299$	−0.340111	+	0.589090i	−0.0196691	+	0.0340680i
$300$		0			0
$301$	5.83966	+	27.3890i	0.336593	+	1.57867i
$302$		−	9.87365i		−	0.568165i
$303$		0			0
$304$	−0.340140	+	0.196380i	−0.0195084	+	0.0112632i
$305$	−3.15154	−	5.45863i	−0.180457	−	0.312561i
$306$		0			0
$307$			32.9465i			1.88036i	0.340683	+	0.940178i	$0.389342\pi$
$307$			32.9465i			1.88036i	−0.340683	+	0.940178i	$0.610658\pi$
$308$	−5.39238	+	6.92259i	−0.307260	+	0.394451i
$309$		0			0
$310$	−8.17149	−	4.71781i	−0.464109	−	0.267954i
$311$	−16.8425	+	9.72400i	−0.955049	+	0.551398i	−0.894646	−	0.446776i	$-0.852572\pi$
$311$	−16.8425	+	9.72400i	−0.955049	+	0.551398i	−0.0604031	+	0.998174i	$0.519239\pi$
$312$		0			0
$313$	−4.28905	+	7.42885i	−0.242431	+	0.419904i	−0.961406	−	0.275132i	$-0.911278\pi$
$313$	−4.28905	+	7.42885i	−0.242431	+	0.419904i	0.718975	+	0.695036i	$0.244612\pi$
$314$	−8.67102			−0.489334
$315$		0			0
$316$			8.34610i			0.469505i
$317$	−1.74470	−	1.00730i	−0.0979923	−	0.0565759i	0.450203	−	0.892926i	$-0.351352\pi$
$317$	−1.74470	−	1.00730i	−0.0979923	−	0.0565759i	−0.548195	+	0.836350i	$0.684685\pi$
$318$		0			0
$319$	−0.769563	−	4.34354i	−0.0430873	−	0.243192i
$320$	−1.42385	−	0.822059i	−0.0795955	−	0.0459545i
$321$		0			0
$322$	−1.03350	+	0.931745i	−0.0575949	+	0.0519241i
$323$			1.32387i			0.0736622i
$324$		0			0
$325$	−2.57267	+	1.48533i	−0.142706	+	0.0823914i
$326$	6.06457	+	10.5041i	0.335886	+	0.581771i
$327$		0			0
$328$	10.9253			0.603247
$329$	13.0417	+	4.22847i	0.719013	+	0.233123i
$330$		0			0
$331$	9.13936	−	15.8298i	0.502345	−	0.870086i	−0.497652	−	0.867377i	$-0.665804\pi$
$331$	9.13936	−	15.8298i	0.502345	−	0.870086i	0.999996	−	0.00270934i	$-0.000862412\pi$
$332$	−2.99266	−	5.18344i	−0.164244	−	0.284478i
$333$		0			0
$334$	−0.712056	+	1.23332i	−0.0389620	+	0.0674841i
$335$			22.3645i			1.22190i
$336$		0			0
$337$			1.04529i			0.0569406i	0.999595	+	0.0284703i	$0.00906361\pi$
$337$			1.04529i			0.0569406i	−0.999595	+	0.0284703i	$0.990936\pi$
$338$	−5.66362	+	9.80968i	−0.308060	+	0.533576i
$339$		0			0
$340$	−4.79935	+	2.77090i	−0.260281	+	0.150273i
$341$	14.5710	−	12.2469i	0.789062	−	0.663207i
$342$		0			0
$343$	−14.9627	+	10.9141i	−0.807909	+	0.589307i
$344$		−	10.5847i		−	0.570691i
$345$		0			0
$346$	2.13167	+	3.69216i	0.114599	+	0.198492i
$347$	−12.0831	−	20.9286i	−0.648657	−	1.12351i	−0.983444	−	0.181212i	$-0.941998\pi$
$347$	−12.0831	−	20.9286i	−0.648657	−	1.12351i	0.334787	−	0.942294i	$-0.391336\pi$
$348$		0			0
$349$		−	30.8063i		−	1.64902i	−0.565846	−	0.824511i	$-0.691450\pi$
$349$		−	30.8063i		−	1.64902i	0.565846	−	0.824511i	$-0.308550\pi$
$350$	−5.94337	+	1.26720i	−0.317686	+	0.0677346i
$351$		0			0
$352$	2.53893	−	2.13397i	0.135325	−	0.113741i
$353$	−8.94782	+	5.16602i	−0.476244	+	0.274960i	−0.718850	−	0.695165i	$-0.755331\pi$
$353$	−8.94782	+	5.16602i	−0.476244	+	0.274960i	0.242606	+	0.970125i	$0.421998\pi$
$354$		0			0
$355$	1.33313	−	2.30904i	0.0707549	−	0.122551i
$356$			9.61034i			0.509347i
$357$		0			0
$358$		−	1.52528i		−	0.0806136i
$359$	−10.1350	+	17.5542i	−0.534902	+	0.926478i	0.464266	+	0.885696i	$0.346318\pi$
$359$	−10.1350	+	17.5542i	−0.534902	+	0.926478i	−0.999168	+	0.0407819i	$0.987015\pi$
$360$		0			0
$361$	−9.42287	−	16.3209i	−0.495941	−	0.858994i
$362$	−9.87068	+	17.0965i	−0.518792	+	0.898573i
$363$		0			0
$364$	2.54152	−	2.29128i	0.133212	−	0.120096i
$365$	−16.7568			−0.877092
$366$		0			0
$367$	−4.97708	−	8.62055i	−0.259801	−	0.449989i	0.706387	−	0.707826i	$-0.250324\pi$
$367$	−4.97708	−	8.62055i	−0.259801	−	0.449989i	−0.966189	+	0.257836i	$0.916990\pi$
$368$	0.455476	−	0.262969i	0.0237433	−	0.0137082i
$369$		0			0
$370$		−	4.96435i		−	0.258084i
$371$	3.26553	−	2.94401i	0.169538	−	0.152845i
$372$		0			0
$373$	−10.3112	−	5.95317i	−0.533894	−	0.308244i	0.208707	−	0.977978i	$-0.433075\pi$
$373$	−10.3112	−	5.95317i	−0.533894	−	0.308244i	−0.742601	+	0.669735i	$0.766408\pi$
$374$	−1.95031	−	11.0079i	−0.100848	−	0.569203i
$375$		0			0
$376$	−4.48768	−	2.59096i	−0.231434	−	0.133619i
$377$			1.72019i			0.0885941i
$378$		0			0
$379$	−18.3862			−0.944437			−0.472218	−	0.881482i	$-0.656547\pi$
$379$	−18.3862			−0.944437			−0.472218	+	0.881482i	$0.656547\pi$
$380$	−0.322872	+	0.559231i	−0.0165630	+	0.0286879i
$381$		0			0
$382$	−12.9424	+	7.47229i	−0.662190	+	0.382315i
$383$	−33.5005	−	19.3415i	−1.71180	−	0.988306i	−0.932141	−	0.362096i	$-0.882061\pi$
$383$	−33.5005	−	19.3415i	−1.71180	−	0.988306i	−0.779655	−	0.626209i	$-0.784606\pi$
$384$		0			0
$385$	−1.98716	+	14.2896i	−0.101275	+	0.728264i
$386$		−	4.01366i		−	0.204290i
$387$		0			0
$388$	−4.15892	−	7.20346i	−0.211137	−	0.365700i
$389$	27.7566	−	16.0253i	1.40731	−	0.812513i	0.412185	−	0.911100i	$-0.364766\pi$
$389$	27.7566	−	16.0253i	1.40731	−	0.812513i	0.995128	+	0.0985872i	$0.0314323\pi$
$390$		0			0
$391$		−	1.77277i		−	0.0896530i
$392$	6.39124	−	2.85518i	0.322806	−	0.144208i
$393$		0			0
$394$	10.7170	−	18.5624i	0.539914	−	0.935159i
$395$	6.86099	+	11.8836i	0.345214	+	0.597928i
$396$		0			0
$397$	16.4657	−	28.5193i	0.826387	−	1.43134i	−0.0744670	−	0.997223i	$-0.523726\pi$
$397$	16.4657	−	28.5193i	0.826387	−	1.43134i	0.900854	−	0.434121i	$-0.142941\pi$
$398$	23.4194			1.17391
$399$		0			0
$400$	2.29687			0.114844
$401$	8.94782	+	5.16602i	0.446833	+	0.257979i	0.706492	−	0.707721i	$-0.250277\pi$
$401$	8.94782	+	5.16602i	0.446833	+	0.257979i	−0.259659	+	0.965700i	$0.583610\pi$
$402$		0			0
$403$	−6.42812	+	3.71128i	−0.320208	+	0.184872i
$404$	−2.53452	+	4.38992i	−0.126097	+	0.218407i
$405$		0			0
$406$	−1.08530	+	3.34736i	−0.0538627	+	0.166127i
$407$	9.41328	+	3.41740i	0.466599	+	0.169394i
$408$		0			0
$409$	−13.7011	+	7.91033i	−0.677476	+	0.391141i	−0.798903	−	0.601459i	$-0.794586\pi$
$409$	−13.7011	+	7.91033i	−0.677476	+	0.391141i	0.121428	+	0.992600i	$0.461253\pi$
$410$	15.5559	−	8.98122i	0.768253	−	0.443551i
$411$		0			0
$412$	7.28943			0.359124
$413$	−18.7478	+	16.9019i	−0.922516	+	0.831686i
$414$		0			0
$415$	−8.52220	−	4.92029i	−0.418338	−	0.241528i
$416$	−1.12007	+	0.646675i	−0.0549162	+	0.0317059i
$417$		0			0
$418$	−0.838139	−	0.997190i	−0.0409947	−	0.0487742i
$419$			32.3275i			1.57930i	0.613556	+	0.789651i	$0.289739\pi$
$419$			32.3275i			1.57930i	−0.613556	+	0.789651i	$0.710261\pi$
$420$		0			0
$421$	−10.8176			−0.527217			−0.263609	−	0.964630i	$-0.584913\pi$
$421$	−10.8176			−0.527217			−0.263609	+	0.964630i	$0.584913\pi$
$422$	1.86691	+	1.07786i	0.0908795	+	0.0524693i
$423$		0			0
$424$	−1.43915	+	0.830895i	−0.0698914	+	0.0403518i
$425$	3.87102	−	6.70481i	0.187772	−	0.325231i
$426$		0			0
$427$	−9.64859	−	3.12833i	−0.466928	−	0.151390i
$428$	−4.32056			−0.208842
$429$		0			0
$430$	−8.70128	−	15.0711i	−0.419613	−	0.726791i
$431$	−17.9409	−	31.0745i	−0.864183	−	1.49681i	−0.867856	−	0.496815i	$-0.834503\pi$
$431$	−17.9409	−	31.0745i	−0.864183	−	1.49681i	0.00367384	−	0.999993i	$-0.498831\pi$
$432$		0			0
$433$	23.8240			1.14491			0.572454	−	0.819937i	$-0.305991\pi$
$433$	23.8240			1.14491			0.572454	+	0.819937i	$0.305991\pi$
$434$	−14.8502	+	3.16625i	−0.712833	+	0.151985i
$435$		0			0
$436$	−5.84618	−	3.37529i	−0.279981	−	0.161647i
$437$	−0.103284	−	0.178893i	−0.00494074	−	0.00855760i
$438$		0			0
$439$	18.4555	+	10.6553i	0.880834	+	0.508550i	0.870933	−	0.491401i	$-0.163515\pi$
$439$	18.4555	+	10.6553i	0.880834	+	0.508550i	0.00990091	+	0.999951i	$0.496848\pi$
$440$	1.86080	−	5.12560i	0.0887102	−	0.244354i
$441$		0			0
$442$			4.35948i			0.207359i
$443$	27.1827	+	15.6939i	1.29149	+	0.745642i	0.978918	−	0.204252i	$-0.0654763\pi$
$443$	27.1827	+	15.6939i	1.29149	+	0.745642i	0.312571	+	0.949894i	$0.398810\pi$
$444$		0			0
$445$	7.90027	+	13.6837i	0.374509	+	0.648668i
$446$	−3.50552	+	6.07173i	−0.165991	+	0.287505i
$447$		0			0
$448$	−2.58759	+	0.551706i	−0.122252	+	0.0260657i
$449$			20.7653i			0.979973i	0.871730	+	0.489987i	$0.162998\pi$
$449$			20.7653i			0.979973i	−0.871730	+	0.489987i	$0.837002\pi$
$450$		0			0
$451$	6.32146	+	35.6794i	0.297666	+	1.68008i
$452$	−15.8284	+	9.13854i	−0.744506	+	0.429841i
$453$		0			0
$454$	20.1307			0.944779
$455$	1.73517	−	5.35172i	0.0813459	−	0.250892i
$456$		0			0
$457$	−3.43048	−	1.98059i	−0.160471	−	0.0926479i	0.417614	−	0.908625i	$-0.362866\pi$
$457$	−3.43048	−	1.98059i	−0.160471	−	0.0926479i	−0.578085	+	0.815977i	$0.696200\pi$
$458$	4.19825	+	7.27158i	0.196171	+	0.339779i
$459$		0			0
$460$	0.432353	−	0.748857i	0.0201585	−	0.0349156i
$461$	4.46540			0.207975			0.103987	−	0.994579i	$-0.466840\pi$
$461$	4.46540			0.207975			0.103987	+	0.994579i	$0.466840\pi$
$462$		0			0
$463$	−33.8033			−1.57097			−0.785486	−	0.618879i	$-0.787587\pi$
$463$	−33.8033			−1.57097			−0.785486	+	0.618879i	$0.787587\pi$
$464$	0.665012	−	1.15183i	0.0308724	−	0.0534726i
$465$		0			0
$466$	6.15876	+	10.6673i	0.285299	+	0.494153i
$467$	−2.67151	−	1.54240i	−0.123623	−	0.0713735i	0.436914	−	0.899504i	$-0.356072\pi$
$467$	−2.67151	−	1.54240i	−0.123623	−	0.0713735i	−0.560536	+	0.828130i	$0.689405\pi$
$468$		0			0
$469$	24.0984	+	26.7303i	1.11276	+	1.23429i
$470$	−8.51970			−0.392984
$471$		0			0
$472$	8.26233	−	4.77026i	0.380305	−	0.219569i
$473$	34.5673	−	6.12442i	1.58940	−	0.281601i
$474$		0			0
$475$		−	0.902120i		−	0.0413921i
$476$	−2.75049	+	8.48325i	−0.126069	+	0.388829i
$477$		0			0
$478$	3.33362	−	5.77400i	0.152476	−	0.264097i
$479$	7.85049	+	13.5974i	0.358698	+	0.621283i	0.987744	−	0.156085i	$-0.0498875\pi$
$479$	7.85049	+	13.5974i	0.358698	+	0.621283i	−0.629046	+	0.777368i	$0.716554\pi$
$480$		0			0
$481$	−3.38202	−	1.95261i	−0.154207	−	0.0890313i
$482$		−	5.08510i		−	0.231620i
$483$		0			0
$484$	8.43809	+	7.05681i	0.383550	+	0.320764i
$485$	−11.8433	−	6.83775i	−0.537778	−	0.310486i
$486$		0			0
$487$	−14.0970	−	24.4167i	−0.638795	−	1.10643i	−0.985698	−	0.168524i	$-0.946100\pi$
$487$	−14.0970	−	24.4167i	−0.638795	−	1.10643i	0.346903	−	0.937901i	$-0.387233\pi$
$488$	3.32010	+	1.91686i	0.150294	+	0.0867722i
$489$		0			0
$490$	6.75303	−	9.31932i	0.305071	−	0.421004i
$491$	−14.6613			−0.661655			−0.330828	−	0.943691i	$-0.607328\pi$
$491$	−14.6613			−0.661655			−0.330828	+	0.943691i	$0.607328\pi$
$492$		0			0
$493$	−2.24155	−	3.88247i	−0.100954	−	0.174858i
$494$	0.253988	+	0.439920i	0.0114275	+	0.0197930i
$495$		0			0
$496$	5.73902			0.257689
$497$	−0.894696	−	4.19627i	−0.0401326	−	0.188228i
$498$		0			0
$499$	−19.5576	+	33.8747i	−0.875517	+	1.51644i	−0.0193055	+	0.999814i	$0.506146\pi$
$499$	−19.5576	+	33.8747i	−0.875517	+	1.51644i	−0.856211	+	0.516626i	$0.827188\pi$
$500$	10.3896	−	5.99846i	0.464639	−	0.268259i
$501$		0			0
$502$	−13.4263	−	7.75167i	−0.599245	−	0.345974i
$503$	39.2496			1.75005			0.875027	−	0.484074i	$-0.160844\pi$
$503$	39.2496			1.75005			0.875027	+	0.484074i	$0.160844\pi$
$504$		0			0
$505$			8.33410i			0.370863i
$506$	1.12234	+	1.33532i	0.0498940	+	0.0593623i
$507$		0			0
$508$	8.52525	−	4.92206i	0.378247	−	0.218381i
$509$	3.76989	+	2.17655i	0.167098	+	0.0964738i	0.581217	−	0.813749i	$-0.302577\pi$
$509$	3.76989	+	2.17655i	0.167098	+	0.0964738i	−0.414119	+	0.910223i	$0.635910\pi$
$510$		0			0
$511$	−20.0279	+	18.0560i	−0.885982	+	0.798749i
$512$	1.00000			0.0441942
$513$		0			0
$514$	11.4588	−	6.61574i	0.505426	−	0.291808i
$515$	10.3790	−	5.99234i	0.457355	−	0.264054i
$516$		0			0
$517$	5.86486	−	16.1549i	0.257936	−	0.710490i
$518$	−5.34923	−	5.93344i	−0.235032	−	0.260700i
$519$		0			0
$520$	−1.06321	+	1.84153i	−0.0466249	+	0.0807566i
$521$	17.8760	−	10.3207i	0.783161	−	0.452158i	−0.0543883	−	0.998520i	$-0.517321\pi$
$521$	17.8760	−	10.3207i	0.783161	−	0.452158i	0.837549	+	0.546362i	$0.183988\pi$
$522$		0			0
$523$	23.0273	+	13.2948i	1.00691	+	0.581343i	0.910287	−	0.413978i	$-0.135861\pi$
$523$	23.0273	+	13.2948i	1.00691	+	0.581343i	0.0966280	+	0.995321i	$0.469194\pi$
$524$	6.40975			0.280011
$525$		0			0
$526$	−4.77681			−0.208279
$527$	9.67221	−	16.7528i	0.421328	−	0.729762i
$528$		0			0
$529$	−11.3617	−	19.6790i	−0.493987	−	0.855610i
$530$	−1.36609	+	2.36614i	−0.0593392	+	0.102778i
$531$		0			0
$532$	0.216688	+	1.01630i	0.00939462	+	0.0440623i
$533$		−	14.1302i		−	0.612047i
$534$		0			0
$535$	−6.15182	+	3.55175i	−0.265966	+	0.153556i
$536$	−6.80137	−	11.7803i	−0.293774	−	0.508832i
$537$		0			0
$538$			10.5552i			0.455067i
$539$	13.0224	+	19.2203i	0.560913	+	0.827875i
$540$		0			0
$541$	22.7295	+	13.1229i	0.977218	+	0.564197i	0.901429	−	0.432927i	$-0.142519\pi$
$541$	22.7295	+	13.1229i	0.977218	+	0.564197i	0.0757888	+	0.997124i	$0.475853\pi$
$542$	−21.4275	+	12.3712i	−0.920391	+	0.531388i
$543$		0			0
$544$	1.68534	−	2.91910i	0.0722585	−	0.125155i
$545$	−11.0988			−0.475419
$546$		0			0
$547$		−	37.4556i		−	1.60149i	−0.599008	−	0.800743i	$-0.704438\pi$
$547$		−	37.4556i		−	1.60149i	0.599008	−	0.800743i	$-0.295562\pi$
$548$	−14.4951	−	8.36876i	−0.619201	−	0.357496i
$549$		0			0
$550$	1.32899	+	7.50105i	0.0566684	+	0.319846i
$551$	−0.452394	−	0.261190i	−0.0192727	−	0.0111271i
$552$		0			0
$553$	21.0052	+	6.81045i	0.893233	+	0.289610i
$554$		−	11.8062i		−	0.501599i
$555$		0			0
$556$	3.17089	−	1.83072i	0.134476	−	0.0776397i
$557$	−6.80146	−	11.7805i	−0.288187	−	0.499155i	0.685190	−	0.728365i	$-0.259719\pi$
$557$	−6.80146	−	11.7805i	−0.288187	−	0.499155i	−0.973377	+	0.229210i	$0.926386\pi$
$558$		0			0
$559$	−13.6898			−0.579016
$560$	−3.23080	+	2.91270i	−0.136526	+	0.123084i
$561$		0			0
$562$	8.07442	−	13.9853i	0.340599	−	0.589935i
$563$	6.85190	+	11.8678i	0.288773	+	0.500170i	0.973517	−	0.228614i	$-0.0734193\pi$
$563$	6.85190	+	11.8678i	0.288773	+	0.500170i	−0.684744	+	0.728784i	$0.740086\pi$
$564$		0			0
$565$	−15.0248	+	26.0238i	−0.632100	+	1.09483i
$566$			13.2277i			0.556002i
$567$		0			0
$568$			1.62169i			0.0680446i
$569$	−16.1147	+	27.9115i	−0.675565	+	1.17011i	0.300738	+	0.953707i	$0.402767\pi$
$569$	−16.1147	+	27.9115i	−0.675565	+	1.17011i	−0.976303	+	0.216406i	$0.930566\pi$
$570$		0			0
$571$	26.5520	−	15.3298i	1.11117	−	0.641532i	0.172035	−	0.985091i	$-0.444966\pi$
$571$	26.5520	−	15.3298i	1.11117	−	0.641532i	0.939131	+	0.343558i	$0.111632\pi$
$572$	−2.75997	−	3.28373i	−0.115400	−	0.137299i
$573$		0			0
$574$	8.91506	−	27.4964i	0.372107	−	1.14768i
$575$			1.20801i			0.0503777i
$576$		0			0
$577$	17.7360	+	30.7197i	0.738360	+	1.27888i	0.953233	+	0.302235i	$0.0977329\pi$
$577$	17.7360	+	30.7197i	0.738360	+	1.27888i	−0.214873	+	0.976642i	$0.568934\pi$
$578$	2.81923	+	4.88306i	0.117265	+	0.203108i
$579$		0			0
$580$		−	2.18672i		−	0.0907984i
$581$	−15.4876	+	3.30214i	−0.642532	+	0.136996i
$582$		0			0
$583$	−3.54621	−	4.21917i	−0.146869	−	0.174740i
$584$	8.82651	−	5.09599i	0.365244	−	0.210874i
$585$		0			0
$586$	7.47077	−	12.9398i	0.308615	−	0.534536i
$587$		−	17.6758i		−	0.729557i	−0.931094	−	0.364778i	$-0.881145\pi$
$587$		−	17.6758i		−	0.729557i	0.931094	−	0.364778i	$-0.118855\pi$
$588$		0			0
$589$		−	2.25406i		−	0.0928768i
$590$	7.84287	−	13.5843i	0.322886	−	0.559255i
$591$		0			0
$592$	1.50973	+	2.61493i	0.0620495	+	0.107473i
$593$	−1.53418	+	2.65729i	−0.0630014	+	0.109122i	−0.895806	−	0.444446i	$-0.853401\pi$
$593$	−1.53418	+	2.65729i	−0.0630014	+	0.109122i	0.832804	+	0.553568i	$0.186734\pi$
$594$		0			0
$595$	3.05745	+	14.3399i	0.125343	+	0.587880i
$596$	14.7055			0.602363
$597$		0			0
$598$	−0.340111	−	0.589090i	−0.0139082	−	0.0240897i
$599$	−1.84155	+	1.06322i	−0.0752436	+	0.0434419i	−0.537150	−	0.843487i	$-0.680499\pi$
$599$	−1.84155	+	1.06322i	−0.0752436	+	0.0434419i	0.461906	+	0.886929i	$0.347166\pi$
$600$		0			0
$601$			3.74930i			0.152937i	0.997072	+	0.0764686i	$0.0243645\pi$
$601$			3.74930i			0.152937i	−0.997072	+	0.0764686i	$0.975635\pi$
$602$	−26.6394	−	8.63718i	−1.08574	−	0.352025i
$603$		0			0
$604$	8.55083	+	4.93683i	0.347928	+	0.200877i
$605$	17.8157	+	3.11121i	0.724311	+	0.126489i
$606$		0			0
$607$	−16.2817	−	9.40025i	−0.660855	−	0.381545i	0.131748	−	0.991283i	$-0.457941\pi$
$607$	−16.2817	−	9.40025i	−0.660855	−	0.381545i	−0.792602	+	0.609739i	$0.791274\pi$
$608$		−	0.392760i		−	0.0159285i
$609$		0			0
$610$	6.30309			0.255205
$611$	−3.35102	+	5.80414i	−0.135568	+	0.234810i
$612$		0			0
$613$	17.7160	−	10.2283i	0.715542	−	0.413118i	−0.0975676	−	0.995229i	$-0.531106\pi$
$613$	17.7160	−	10.2283i	0.715542	−	0.413118i	0.813110	+	0.582110i	$0.197773\pi$
$614$	−28.5325	−	16.4733i	−1.15148	−	0.664806i
$615$		0			0
$616$	−3.29894	−	8.13123i	−0.132918	−	0.327617i
$617$		−	29.3351i		−	1.18099i	−0.807043	−	0.590493i	$-0.798933\pi$
$617$		−	29.3351i		−	1.18099i	0.807043	−	0.590493i	$-0.201067\pi$
$618$		0			0
$619$	−6.16332	−	10.6752i	−0.247725	−	0.429072i	0.715169	−	0.698951i	$-0.246350\pi$
$619$	−6.16332	−	10.6752i	−0.247725	−	0.429072i	−0.962894	+	0.269879i	$0.913016\pi$
$620$	8.17149	−	4.71781i	0.328175	−	0.189472i
$621$		0			0
$622$		−	19.4480i		−	0.779794i
$623$	24.1870	+	7.84207i	0.969033	+	0.314186i
$624$		0			0
$625$	4.12000	−	7.13605i	0.164800	−	0.285442i
$626$	−4.28905	−	7.42885i	−0.171425	−	0.296917i
$627$		0			0
$628$	4.33551	−	7.50933i	0.173006	−	0.299655i
$629$	10.1777			0.405810
$630$		0			0
$631$	−14.7738			−0.588136			−0.294068	−	0.955784i	$-0.595009\pi$
$631$	−14.7738			−0.588136			−0.294068	+	0.955784i	$0.595009\pi$
$632$	−7.22793	−	4.17305i	−0.287512	−	0.165995i
$633$		0			0
$634$	1.74470	−	1.00730i	0.0692910	−	0.0400052i
$635$	8.09244	−	14.0165i	0.321139	−	0.556229i
$636$		0			0
$637$	−3.69274	−	8.26611i	−0.146312	−	0.327515i
$638$	4.14640	+	1.50531i	0.164158	+	0.0595958i
$639$		0			0
$640$	1.42385	−	0.822059i	0.0562826	−	0.0324947i
$641$	17.1907	−	9.92508i	0.678994	−	0.392017i	−0.120482	−	0.992716i	$-0.538444\pi$
$641$	17.1907	−	9.92508i	0.678994	−	0.392017i	0.799476	+	0.600698i	$0.205111\pi$
$642$		0			0
$643$	2.60504			0.102733			0.0513664	−	0.998680i	$-0.483642\pi$
$643$	2.60504			0.102733			0.0513664	+	0.998680i	$0.483642\pi$
$644$	−0.290163	−	1.36091i	−0.0114340	−	0.0536275i
$645$		0			0
$646$	−1.14651	−	0.661936i	−0.0451087	−	0.0260435i
$647$	−11.2756	+	6.50996i	−0.443289	+	0.255933i	−0.704992	−	0.709216i	$-0.749049\pi$
$647$	−11.2756	+	6.50996i	−0.443289	+	0.255933i	0.261703	+	0.965149i	$0.415716\pi$
$648$		0			0
$649$	20.3592	+	24.2227i	0.799169	+	0.950825i
$650$		−	2.97066i		−	0.116519i
$651$		0			0
$652$	−12.1291			−0.475014
$653$	34.0245	+	19.6441i	1.33148	+	0.768732i	0.985527	−	0.169518i	$-0.0542212\pi$
$653$	34.0245	+	19.6441i	1.33148	+	0.768732i	0.345956	+	0.938251i	$0.387554\pi$
$654$		0			0
$655$	9.12652	−	5.26920i	0.356602	−	0.205885i
$656$	−5.46264	+	9.46156i	−0.213280	+	0.369412i
$657$		0			0
$658$	−10.1828	+	9.18023i	−0.396968	+	0.357883i
$659$	21.8725			0.852033			0.426017	−	0.904715i	$-0.359917\pi$
$659$	21.8725			0.852033			0.426017	+	0.904715i	$0.359917\pi$
$660$		0			0
$661$	−14.6974	−	25.4567i	−0.571665	−	0.990152i	−0.996395	−	0.0848322i	$-0.972965\pi$
$661$	−14.6974	−	25.4567i	−0.571665	−	0.990152i	0.424731	−	0.905320i	$-0.360369\pi$
$662$	9.13936	+	15.8298i	0.355211	+	0.615244i
$663$		0			0
$664$	5.98532			0.232276
$665$	1.14399	+	1.26893i	0.0443621	+	0.0492070i
$666$		0			0
$667$	0.605794	+	0.349755i	0.0234564	+	0.0135426i
$668$	−0.712056	−	1.23332i	−0.0275503	−	0.0477185i
$669$		0			0
$670$	−19.3682	−	11.1823i	−0.748260	−	0.432008i
$671$	−4.33897	+	11.9518i	−0.167504	+	0.461393i
$672$		0			0
$673$		−	18.0026i		−	0.693949i	−0.937875	−	0.346975i	$-0.887209\pi$
$673$		−	18.0026i		−	0.693949i	0.937875	−	0.346975i	$-0.112791\pi$
$674$	−0.905249	−	0.522645i	−0.0348689	−	0.0201316i
$675$		0			0
$676$	−5.66362	−	9.80968i	−0.217832	−	0.377295i
$677$	17.7248	−	30.7003i	0.681219	−	1.17991i	−0.293390	−	0.955993i	$-0.594783\pi$
$677$	17.7248	−	30.7003i	0.681219	−	1.17991i	0.974609	−	0.223914i	$-0.0718834\pi$
$678$		0			0
$679$	−21.5231	+	4.58900i	−0.825982	+	0.176110i
$680$		−	5.54181i		−	0.212519i
$681$		0			0
$682$	3.32065	+	18.7423i	0.127154	+	0.717679i
$683$	−4.85527	+	2.80319i	−0.185782	+	0.107261i	−0.590006	−	0.807399i	$-0.700875\pi$
$683$	−4.85527	+	2.80319i	−0.185782	+	0.107261i	0.404225	+	0.914660i	$0.367541\pi$
$684$		0			0
$685$	−27.5185			−1.05143
$686$	−1.97055	−	18.4151i	−0.0752360	−	0.703093i
$687$		0			0
$688$	9.16665	+	5.29237i	0.349475	+	0.201770i
$689$	1.07464	+	1.86133i	0.0409405	+	0.0709110i
$690$		0			0
$691$	−16.7993	+	29.0972i	−0.639074	+	1.10691i	0.346562	+	0.938027i	$0.387349\pi$
$691$	−16.7993	+	29.0972i	−0.639074	+	1.10691i	−0.985636	+	0.168882i	$0.945984\pi$
$692$	−4.26333			−0.162068
$693$		0			0
$694$	24.1663			0.917339
$695$	3.00992	−	5.21333i	0.114173	−	0.197753i
$696$		0			0
$697$	18.4128	+	31.8920i	0.697436	+	1.20799i
$698$	26.6790	+	15.4031i	1.00982	+	0.583017i
$699$		0			0
$700$	1.87426	−	5.78071i	0.0708403	−	0.218490i
$701$	43.4126			1.63967			0.819835	−	0.572600i	$-0.194065\pi$
$701$	43.4126			1.63967			0.819835	+	0.572600i	$0.194065\pi$
$702$		0			0
$703$	1.02704	−	0.592962i	0.0387355	−	0.0223640i
$704$	0.578609	+	3.26576i	0.0218071	+	0.123083i
$705$		0			0
$706$		−	10.3320i		−	0.388852i
$707$	8.98024	+	9.96100i	0.337737	+	0.374622i
$708$		0			0
$709$	−1.34801	+	2.33482i	−0.0506255	+	0.0876859i	−0.890228	−	0.455516i	$-0.849455\pi$
$709$	−1.34801	+	2.33482i	−0.0506255	+	0.0876859i	0.839602	+	0.543202i	$0.182788\pi$
$710$	1.33313	+	2.30904i	0.0500313	+	0.0866567i
$711$		0			0
$712$	−8.32280	−	4.80517i	−0.311910	−	0.180081i
$713$			3.01837i			0.113039i
$714$		0			0
$715$	−6.62920	−	2.40667i	−0.247918	−	0.0900042i
$716$	1.32093	+	0.762640i	0.0493655	+	0.0285012i
$717$		0			0
$718$	−10.1350	−	17.5542i	−0.378233	−	0.655119i
$719$	−6.61138	−	3.81708i	−0.246563	−	0.142353i	0.371627	−	0.928382i	$-0.378800\pi$
$719$	−6.61138	−	3.81708i	−0.246563	−	0.142353i	−0.618189	+	0.786029i	$0.712134\pi$
$720$		0			0
$721$	5.94820	−	18.3458i	0.221523	−	0.683234i
$722$	18.8457			0.701366
$723$		0			0
$724$	−9.87068	−	17.0965i	−0.366841	−	0.635387i
$725$	1.52745	+	2.64562i	0.0567280	+	0.0982558i
$726$		0			0
$727$	16.8096			0.623435			0.311717	−	0.950175i	$-0.399096\pi$
$727$	16.8096			0.623435			0.311717	+	0.950175i	$0.399096\pi$
$728$	0.713549	+	3.34666i	0.0264459	+	0.124035i
$729$		0			0
$730$	8.37841	−	14.5118i	0.310099	−	0.537107i
$731$	30.8979	−	17.8389i	1.14280	−	0.659796i
$732$		0			0
$733$	−2.28623	−	1.31996i	−0.0844440	−	0.0487537i	0.457183	−	0.889372i	$-0.348858\pi$
$733$	−2.28623	−	1.31996i	−0.0844440	−	0.0487537i	−0.541627	+	0.840619i	$0.682192\pi$
$734$	9.95416			0.367415
$735$		0			0
$736$			0.525938i			0.0193864i
$737$	34.5364	−	29.0279i	1.27216	−	1.06925i
$738$		0			0
$739$	2.14077	−	1.23598i	0.0787496	−	0.0454661i	−0.460108	−	0.887863i	$-0.652189\pi$
$739$	2.14077	−	1.23598i	0.0787496	−	0.0454661i	0.538858	+	0.842397i	$0.318856\pi$
$740$	4.29925	+	2.48217i	0.158044	+	0.0912465i
$741$		0			0
$742$	0.916820	+	4.30003i	0.0336575	+	0.157859i
$743$	9.82643			0.360497			0.180248	−	0.983621i	$-0.442310\pi$
$743$	9.82643			0.360497			0.180248	+	0.983621i	$0.442310\pi$
$744$		0			0
$745$	20.9385	−	12.0888i	0.767126	−	0.442901i
$746$	10.3112	−	5.95317i	0.377520	−	0.217961i
$747$		0			0
$748$	10.5082	+	3.81492i	0.384220	+	0.139487i
$749$	−3.52559	+	10.8739i	−0.128822	+	0.397322i
$750$		0			0
$751$	−5.78977	+	10.0282i	−0.211272	+	0.365934i	−0.952113	−	0.305747i	$-0.901094\pi$
$751$	−5.78977	+	10.0282i	−0.211272	+	0.365934i	0.740841	+	0.671680i	$0.234427\pi$
$752$	4.48768	−	2.59096i	0.163649	−	0.0944827i
$753$		0			0
$754$	−1.48973	−	0.860093i	−0.0542526	−	0.0313227i
$755$	16.2335			0.590796
$756$		0			0
$757$	25.5191			0.927507			0.463753	−	0.885964i	$-0.346502\pi$
$757$	25.5191			0.927507			0.463753	+	0.885964i	$0.346502\pi$
$758$	9.19311	−	15.9229i	0.333909	−	0.578347i
$759$		0			0
$760$	−0.322872	−	0.559231i	−0.0117118	−	0.0202854i
$761$	5.09089	−	8.81767i	0.184544	−	0.319640i	−0.758878	−	0.651232i	$-0.774252\pi$
$761$	5.09089	−	8.81767i	0.184544	−	0.319640i	0.943423	+	0.331592i	$0.107586\pi$
$762$		0			0
$763$	−13.2653	+	11.9592i	−0.480237	+	0.432954i
$764$		−	14.9446i		−	0.540676i
$765$		0			0
$766$	33.5005	−	19.3415i	1.21042	−	0.698838i
$767$	−6.16962	−	10.6861i	−0.222772	−	0.385852i
$768$		0			0
$769$		−	22.7648i		−	0.820921i	−0.911878	−	0.410461i	$-0.865368\pi$
$769$		−	22.7648i		−	0.820921i	0.911878	−	0.410461i	$-0.134632\pi$
$770$	−11.3816	−	8.86572i	−0.410163	−	0.319498i
$771$		0			0
$772$	3.47593	+	2.00683i	0.125102	+	0.0722274i
$773$	−1.09140	+	0.630122i	−0.0392551	+	0.0226639i	−0.519499	−	0.854471i	$-0.673881\pi$
$773$	−1.09140	+	0.630122i	−0.0392551	+	0.0226639i	0.480244	+	0.877135i	$0.340548\pi$
$774$		0			0
$775$	−6.59090	+	11.4158i	−0.236752	+	0.410067i
$776$	8.31783			0.298593
$777$		0			0
$778$			32.0505i			1.14907i
$779$	3.71612	+	2.14551i	0.133144	+	0.0768707i
$780$		0			0
$781$	−5.29606	+	0.938324i	−0.189508	+	0.0335759i
$782$	1.53527	+	0.886387i	0.0549010	+	0.0316971i
$783$		0			0
$784$	−0.722965	+	6.96257i	−0.0258202	+	0.248663i
$785$		−	14.2562i		−	0.508825i
$786$		0			0
$787$	−39.6470	+	22.8902i	−1.41326	+	0.815948i	−0.995694	−	0.0926980i	$-0.970451\pi$
$787$	−39.6470	+	22.8902i	−1.41326	+	0.815948i	−0.417568	+	0.908646i	$0.637118\pi$
$788$	10.7170	+	18.5624i	0.381777	+	0.661257i
$789$		0			0
$790$	−13.7220			−0.488206
$791$	10.0836	+	47.2936i	0.358530	+	1.68157i
$792$		0			0
$793$	2.47917	−	4.29405i	0.0880379	−	0.152486i
$794$	16.4657	+	28.5193i	0.584344	+	1.01211i
$795$		0			0
$796$	−11.7097	+	20.2818i	−0.415040	+	0.718870i
$797$			2.29098i			0.0811508i	0.999176	+	0.0405754i	$0.0129191\pi$
$797$			2.29098i			0.0811508i	−0.999176	+	0.0405754i	$0.987081\pi$
$798$		0			0
$799$		−	17.4666i		−	0.617926i
$800$	−1.14844	+	1.98915i	−0.0406034	+	0.0703271i
$801$		0			0
$802$	−8.94782	+	5.16602i	−0.315958	+	0.182419i
$803$	21.7494	+	25.8767i	0.767519	+	0.913170i
$804$		0			0
$805$	−1.53190	−	1.69920i	−0.0539924	−	0.0598890i
$806$		−	7.42256i		−	0.261448i
$807$		0			0
$808$	−2.53452	−	4.38992i	−0.0891641	−	0.154437i
$809$	12.5840	+	21.7961i	0.442430	+	0.766311i	0.997869	−	0.0652458i	$-0.0207832\pi$
$809$	12.5840	+	21.7961i	0.442430	+	0.766311i	−0.555439	+	0.831557i	$0.687450\pi$
$810$		0			0
$811$			12.0031i			0.421487i	0.977541	+	0.210744i	$0.0675885\pi$
$811$			12.0031i			0.421487i	−0.977541	+	0.210744i	$0.932411\pi$
$812$	−2.35625	−	2.61358i	−0.0826882	−	0.0917188i
$813$		0			0
$814$	−7.66620	+	6.44344i	−0.268700	+	0.225842i
$815$	−17.2701	+	9.97088i	−0.604944	+	0.349265i
$816$		0			0
$817$	2.07863	−	3.60029i	0.0727221	−	0.125958i
$818$		−	15.8207i		−	0.553157i
$819$		0			0
$820$			17.9624i			0.627276i
$821$	5.69313	−	9.86078i	0.198691	−	0.344144i	−0.749413	−	0.662103i	$-0.769664\pi$
$821$	5.69313	−	9.86078i	0.198691	−	0.344144i	0.948104	+	0.317959i	$0.102997\pi$
$822$		0			0
$823$	−27.8850	−	48.2982i	−0.972010	−	1.68357i	−0.689469	−	0.724315i	$-0.742156\pi$
$823$	−27.8850	−	48.2982i	−0.972010	−	1.68357i	−0.282540	−	0.959255i	$-0.591177\pi$
$824$	−3.64472	+	6.31283i	−0.126970	+	0.219918i
$825$		0			0
$826$	−5.26356	−	24.6870i	−0.183143	−	0.858969i
$827$	−13.7158			−0.476946			−0.238473	−	0.971149i	$-0.576647\pi$
$827$	−13.7158			−0.476946			−0.238473	+	0.971149i	$0.576647\pi$
$828$		0			0
$829$	20.2816	+	35.1287i	0.704408	+	1.22007i	0.966905	+	0.255137i	$0.0821207\pi$
$829$	20.2816	+	35.1287i	0.704408	+	1.22007i	−0.262497	+	0.964933i	$0.584546\pi$
$830$	8.52220	−	4.92029i	0.295810	−	0.170786i
$831$		0			0
$832$		−	1.29335i		−	0.0448389i
$833$	19.1060	+	13.8447i	0.661983	+	0.479691i
$834$		0			0
$835$	−2.02772	−	1.17071i	−0.0701722	−	0.0405139i
$836$	1.28266	−	0.227254i	0.0443618	−	0.00785976i
$837$		0			0
$838$	−27.9965	−	16.1638i	−0.967121	−	0.558368i
$839$			38.8580i			1.34153i	0.741672	+	0.670763i	$0.234033\pi$
$839$			38.8580i			1.34153i	−0.741672	+	0.670763i	$0.765967\pi$
$840$		0			0
$841$	−27.2310			−0.939001
$842$	5.40880	−	9.36831i	0.186399	−	0.322853i
$843$		0			0
$844$	−1.86691	+	1.07786i	−0.0642615	+	0.0371014i
$845$	−16.1283	−	9.31167i	−0.554830	−	0.320331i
$846$		0			0
$847$	24.6459	−	15.4784i	0.846843	−	0.531843i
$848$		−	1.66179i		−	0.0570661i
$849$		0			0
$850$	3.87102	+	6.70481i	0.132775	+	0.229973i
$851$	−1.37529	+	0.794025i	−0.0471444	+	0.0272188i
$852$		0			0
$853$		−	51.3490i		−	1.75816i	−0.476677	−	0.879078i	$-0.658159\pi$
$853$		−	51.3490i		−	1.75816i	0.476677	−	0.879078i	$-0.341841\pi$
$854$	7.53351	−	6.79176i	0.257791	−	0.232409i
$855$		0			0
$856$	2.16028	−	3.74171i	0.0738368	−	0.127889i
$857$	−20.2462	−	35.0674i	−0.691596	−	1.19788i	−0.971315	−	0.237797i	$-0.923575\pi$
$857$	−20.2462	−	35.0674i	−0.691596	−	1.19788i	0.279719	−	0.960082i	$-0.409759\pi$
$858$		0			0
$859$	10.6853	−	18.5075i	0.364577	−	0.631467i	−0.624131	−	0.781320i	$-0.714547\pi$
$859$	10.6853	−	18.5075i	0.364577	−	0.631467i	0.988708	+	0.149853i	$0.0478801\pi$
$860$	17.4026			0.593423
$861$		0			0
$862$	35.8818			1.22214
$863$	−18.8633	−	10.8907i	−0.642113	−	0.370724i	0.143315	−	0.989677i	$-0.454224\pi$
$863$	−18.8633	−	10.8907i	−0.642113	−	0.370724i	−0.785428	+	0.618953i	$0.787557\pi$
$864$		0			0
$865$	−6.07034	+	3.50471i	−0.206398	+	0.119164i
$866$	−11.9120	+	20.6322i	−0.404786	+	0.701110i
$867$		0			0
$868$	4.68306	−	14.4438i	0.158953	−	0.490254i
$869$	9.44605	−	26.0193i	0.320435	−	0.882644i
$870$		0			0
$871$	−15.2361	+	8.79655i	−0.516255	+	0.298060i
$872$	5.84618	−	3.37529i	0.197977	−	0.114302i
$873$		0			0
$874$	0.206568			0.00698725
$875$	−6.61877	−	31.0431i	−0.223755	−	1.04945i
$876$		0			0
$877$	10.1630	+	5.86760i	0.343180	+	0.198135i	0.661677	−	0.749789i	$-0.269845\pi$
$877$	10.1630	+	5.86760i	0.343180	+	0.198135i	−0.318498	+	0.947924i	$0.603178\pi$
$878$	−18.4555	+	10.6553i	−0.622844	+	0.359599i
$879$		0			0
$880$	3.50850	+	4.17430i	0.118272	+	0.140716i
$881$			9.90728i			0.333785i	0.985975	+	0.166892i	$0.0533732\pi$
$881$			9.90728i			0.333785i	−0.985975	+	0.166892i	$0.946627\pi$
$882$		0			0
$883$	8.62510			0.290258			0.145129	−	0.989413i	$-0.453640\pi$
$883$	8.62510			0.290258			0.145129	+	0.989413i	$0.453640\pi$
$884$	−3.77542	−	2.17974i	−0.126981	−	0.0733126i
$885$		0			0
$886$	−27.1827	+	15.6939i	−0.913221	+	0.527248i
$887$	−3.00576	+	5.20614i	−0.100924	+	0.174805i	−0.912065	−	0.410045i	$-0.865513\pi$
$887$	−3.00576	+	5.20614i	−0.100924	+	0.174805i	0.811142	+	0.584850i	$0.198846\pi$
$888$		0			0
$889$	−5.43106	−	25.4725i	−0.182152	−	0.854321i
$890$	−15.8005			−0.529635
$891$		0			0
$892$	−3.50552	−	6.07173i	−0.117373	−	0.203297i
$893$	−1.01763	−	1.76258i	−0.0340536	−	0.0589825i
$894$		0			0
$895$	2.50774			0.0838246
$896$	0.816004	−	2.51677i	0.0272608	−	0.0840794i
$897$		0			0
$898$	−17.9832	−	10.3826i	−0.600109	−	0.346473i
$899$	3.81651	+	6.61039i	0.127288	+	0.220469i
$900$		0			0
$901$	−4.85093	−	2.80069i	−0.161608	−	0.0933045i
$902$	−34.0600	−	12.3651i	−1.13407	−	0.411714i
$903$		0			0
$904$		−	18.2771i		−	0.607886i
$905$	−28.1087	−	16.2286i	−0.934365	−	0.539456i
$906$		0			0
$907$	11.3959	+	19.7383i	0.378395	+	0.655400i	0.990829	−	0.135122i	$-0.0431426\pi$
$907$	11.3959	+	19.7383i	0.378395	+	0.655400i	−0.612434	+	0.790522i	$0.709809\pi$
$908$	−10.0653	+	17.4337i	−0.334030	+	0.578557i
$909$		0			0
$910$	3.76714	+	4.17856i	0.124879	+	0.138518i
$911$		−	8.07918i		−	0.267675i	−0.991003	−	0.133838i	$-0.957270\pi$
$911$		−	8.07918i		−	0.267675i	0.991003	−	0.133838i	$-0.0427300\pi$
$912$		0			0
$913$	3.46316	+	19.5467i	0.114614	+	0.646900i
$914$	3.43048	−	1.98059i	0.113470	−	0.0655120i
$915$		0			0
$916$	−8.39650			−0.277428
$917$	5.23038	−	16.1319i	0.172722	−	0.532722i
$918$		0			0
$919$	35.9595	+	20.7612i	1.18619	+	0.684850i	0.957440	−	0.288634i	$-0.0932011\pi$
$919$	35.9595	+	20.7612i	1.18619	+	0.684850i	0.228755	+	0.973484i	$0.426534\pi$
$920$	0.432353	+	0.748857i	0.0142542	+	0.0246891i
$921$		0			0
$922$	−2.23270	+	3.86715i	−0.0735301	+	0.127358i
$923$	2.09741			0.0690372
$924$		0			0
$925$	−6.93532			−0.228032
$926$	16.9017	−	29.2745i	0.555423	−	0.962020i
$927$		0			0
$928$	0.665012	+	1.15183i	0.0218301	+	0.0378108i
$929$	−18.1293	−	10.4670i	−0.594803	−	0.343410i	0.172191	−	0.985064i	$-0.444915\pi$
$929$	−18.1293	−	10.4670i	−0.594803	−	0.343410i	−0.766994	+	0.641654i	$0.778249\pi$
$930$		0			0
$931$	2.73462	+	0.283952i	0.0896235	+	0.00930614i
$932$	−12.3175			−0.403474
$933$		0			0
$934$	2.67151	−	1.54240i	0.0874144	−	0.0504687i
$935$	18.0982	−	3.20654i	0.591876	−	0.104865i
$936$		0			0
$937$			7.24085i			0.236548i	0.992981	+	0.118274i	$0.0377362\pi$
$937$			7.24085i			0.236548i	−0.992981	+	0.118274i	$0.962264\pi$
$938$	−35.1983	+	7.50471i	−1.14927	+	0.245037i
$939$		0			0
$940$	4.25985	−	7.37828i	0.138941	−	0.240653i
$941$	27.6924	+	47.9646i	0.902745	+	1.56360i	0.823916	+	0.566713i	$0.191785\pi$
$941$	27.6924	+	47.9646i	0.902745	+	1.56360i	0.0788298	+	0.996888i	$0.474882\pi$
$942$		0			0
$943$	−4.97620	−	2.87301i	−0.162047	−	0.0935581i
$944$			9.54052i			0.310518i
$945$		0			0
$946$	−11.9797	+	32.9983i	−0.389494	+	1.07287i
$947$	−16.0090	−	9.24283i	−0.520224	−	0.300352i	0.216802	−	0.976216i	$-0.430437\pi$
$947$	−16.0090	−	9.24283i	−0.520224	−	0.300352i	−0.737026	+	0.675864i	$0.763771\pi$
$948$		0			0
$949$	−6.59090	−	11.4158i	−0.213950	−	0.370572i
$950$	0.781259	+	0.451060i	0.0253474	+	0.0146343i
$951$		0			0
$952$	−5.97146	−	6.62362i	−0.193536	−	0.214673i
$953$	−42.1993			−1.36697			−0.683485	−	0.729964i	$-0.739537\pi$
$953$	−42.1993			−1.36697			−0.683485	+	0.729964i	$0.739537\pi$
$954$		0			0
$955$	−12.2853	−	21.2788i	−0.397544	−	0.688566i
$956$	3.33362	+	5.77400i	0.107817	+	0.186745i
$957$		0			0
$958$	−15.7010			−0.507275
$959$	−32.8903	+	29.6520i	−1.06208	+	0.957512i
$960$		0			0
$961$	−0.968154	+	1.67689i	−0.0312308	+	0.0540933i
$962$	3.38202	−	1.95261i	0.109041	−	0.0629547i
$963$		0			0
$964$	4.40382	+	2.54255i	0.141838	+	0.0818900i
$965$	6.59894			0.212427
$966$		0			0
$967$		−	28.8707i		−	0.928420i	−0.885725	−	0.464210i	$-0.846338\pi$
$967$		−	28.8707i		−	0.928420i	0.885725	−	0.464210i	$-0.153662\pi$
$968$	−10.3304	+	3.77920i	−0.332032	+	0.121468i
$969$		0			0
$970$	11.8433	−	6.83775i	0.380267	−	0.219547i
$971$	33.5960	+	19.3967i	1.07815	+	0.622469i	0.930396	−	0.366556i	$-0.119463\pi$
$971$	33.5960	+	19.3967i	1.07815	+	0.622469i	0.147752	+	0.989024i	$0.452796\pi$
$972$		0			0
$973$	−2.02003	−	9.47429i	−0.0647593	−	0.303732i
$974$	28.1940			0.903393
$975$		0			0
$976$	−3.32010	+	1.91686i	−0.106274	+	0.0613572i
$977$	−51.7993	+	29.9064i	−1.65721	+	0.956789i	−0.683212	+	0.730220i	$0.739418\pi$
$977$	−51.7993	+	29.9064i	−1.65721	+	0.956789i	−0.973995	+	0.226569i	$0.927249\pi$
$978$		0			0
$979$	10.8769	−	29.9606i	0.347627	−	0.957545i
$980$	4.69425	+	10.5080i	0.149952	+	0.335664i
$981$		0			0
$982$	7.33065	−	12.6971i	0.233931	−	0.405180i
$983$	26.0949	−	15.0659i	0.832298	−	0.480528i	−0.0223406	−	0.999750i	$-0.507112\pi$
$983$	26.0949	−	15.0659i	0.832298	−	0.480528i	0.854639	+	0.519223i	$0.173779\pi$
$984$		0			0
$985$	30.5187	+	17.6200i	0.972408	+	0.561420i
$986$	4.48309			0.142771
$987$		0			0
$988$	−0.507976			−0.0161609
$989$	−2.78346	+	4.82110i	−0.0885089	+	0.153302i
$990$		0			0
$991$	−24.6850	−	42.7557i	−0.784146	−	1.35818i	−0.929508	−	0.368802i	$-0.879768\pi$
$991$	−24.6850	−	42.7557i	−0.784146	−	1.35818i	0.145362	−	0.989379i	$-0.453565\pi$
$992$	−2.86951	+	4.97013i	−0.0911070	+	0.157802i
$993$		0			0
$994$	4.08142	+	1.32330i	0.129455	+	0.0419727i
$995$			38.5043i			1.22067i
$996$		0			0
$997$	−41.8425	+	24.1578i	−1.32517	+	0.765085i	−0.984548	−	0.175117i	$-0.943970\pi$
$997$	−41.8425	+	24.1578i	−1.32517	+	0.765085i	−0.340618	+	0.940202i	$0.610636\pi$
$998$	−19.5576	−	33.8747i	−0.619084	−	1.07228i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.ba.a.989.6	✓	32
3.2	odd	2		1386.2.ba.b.989.11	yes	32
7.4	even	3	inner	1386.2.ba.a.1187.11	yes	32
11.10	odd	2		1386.2.ba.b.989.6	yes	32
21.11	odd	6		1386.2.ba.b.1187.6	yes	32
33.32	even	2	inner	1386.2.ba.a.989.11	yes	32
77.32	odd	6		1386.2.ba.b.1187.11	yes	32
231.32	even	6	inner	1386.2.ba.a.1187.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.ba.a.989.6	✓	32	1.1	even	1	trivial
1386.2.ba.a.989.11	yes	32	33.32	even	2	inner
1386.2.ba.a.1187.6	yes	32	231.32	even	6	inner
1386.2.ba.a.1187.11	yes	32	7.4	even	3	inner
1386.2.ba.b.989.6	yes	32	11.10	odd	2
1386.2.ba.b.989.11	yes	32	3.2	odd	2
1386.2.ba.b.1187.6	yes	32	21.11	odd	6
1386.2.ba.b.1187.11	yes	32	77.32	odd	6

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.42385 - 0.822059i) q^{5} +(-2.58759 + 0.551706i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.42385 - 0.822059i) q^{5} +(-2.58759 + 0.551706i) q^{7} +1.00000 q^{8} +(1.42385 - 0.822059i) q^{10} +(0.578609 + 3.26576i) q^{11} -1.29335i q^{13} +(0.816004 - 2.51677i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.68534 + 2.91910i) q^{17} +(0.340140 + 0.196380i) q^{19} +1.64412i q^{20} +(-3.11754 - 1.13179i) q^{22} +(-0.455476 - 0.262969i) q^{23} +(-1.14844 - 1.98915i) q^{25} +(1.12007 + 0.646675i) q^{26} +(1.77159 + 1.96507i) q^{28} -1.33002 q^{29} +(-2.86951 - 4.97013i) q^{31} +(-0.500000 - 0.866025i) q^{32} -3.37069 q^{34} +(4.13787 + 1.34161i) q^{35} +(1.50973 - 2.61493i) q^{37} +(-0.340140 + 0.196380i) q^{38} +(-1.42385 - 0.822059i) q^{40} +10.9253 q^{41} -10.5847i q^{43} +(2.53893 - 2.13397i) q^{44} +(0.455476 - 0.262969i) q^{46} +(-4.48768 - 2.59096i) q^{47} +(6.39124 - 2.85518i) q^{49} +2.29687 q^{50} +(-1.12007 + 0.646675i) q^{52} +(-1.43915 + 0.830895i) q^{53} +(1.86080 - 5.12560i) q^{55} +(-2.58759 + 0.551706i) q^{56} +(0.665012 - 1.15183i) q^{58} +(8.26233 - 4.77026i) q^{59} +(3.32010 + 1.91686i) q^{61} +5.73902 q^{62} +1.00000 q^{64} +(-1.06321 + 1.84153i) q^{65} +(-6.80137 - 11.7803i) q^{67} +(1.68534 - 2.91910i) q^{68} +(-3.23080 + 2.91270i) q^{70} +1.62169i q^{71} +(8.82651 - 5.09599i) q^{73} +(1.50973 + 2.61493i) q^{74} -0.392760i q^{76} +(-3.29894 - 8.13123i) q^{77} +(-7.22793 - 4.17305i) q^{79} +(1.42385 - 0.822059i) q^{80} +(-5.46264 + 9.46156i) q^{82} +5.98532 q^{83} -5.54181i q^{85} +(9.16665 + 5.29237i) q^{86} +(0.578609 + 3.26576i) q^{88} +(-8.32280 - 4.80517i) q^{89} +(0.713549 + 3.34666i) q^{91} +0.525938i q^{92} +(4.48768 - 2.59096i) q^{94} +(-0.322872 - 0.559231i) q^{95} +8.31783 q^{97} +(-0.722965 + 6.96257i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8}+O(q^{10}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 2 q^{11} - 16 q^{16} - 4 q^{17} + 4 q^{22} + 4 q^{25} - 16 q^{29} + 4 q^{31} - 16 q^{32} + 8 q^{34} - 16 q^{35} + 4 q^{37} + 32 q^{41} - 2 q^{44} + 20 q^{49} - 8 q^{50} - 12 q^{55} + 8 q^{58} - 8 q^{62} + 32 q^{64} - 8 q^{67} - 4 q^{68} - 4 q^{70} + 4 q^{74} - 14 q^{77} - 16 q^{82} - 88 q^{83} - 2 q^{88} + 24 q^{95} - 32 q^{97} + 8 q^{98}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 2 * q^11 - 16 * q^16 - 4 * q^17 + 4 * q^22 + 4 * q^25 - 16 * q^29 + 4 * q^31 - 16 * q^32 + 8 * q^34 - 16 * q^35 + 4 * q^37 + 32 * q^41 - 2 * q^44 + 20 * q^49 - 8 * q^50 - 12 * q^55 + 8 * q^58 - 8 * q^62 + 32 * q^64 - 8 * q^67 - 4 * q^68 - 4 * q^70 + 4 * q^74 - 14 * q^77 - 16 * q^82 - 88 * q^83 - 2 * q^88 + 24 * q^95 - 32 * q^97 + 8 * q^98

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