LMFDB - Embedded newform 1890.2.t.b.1601.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(1151,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 1]))

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

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

chi := DirichletCharacter("1890.1151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.t (of order $6$, degree $2$, not 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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1601.4
Character	$\chi$	$=$	1890.1601
Dual form			1890.2.t.b.1151.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-1.17997 - 2.36805i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-1.17997 - 2.36805i) q^{7} +1.00000i q^{8} +(-0.866025 + 0.500000i) q^{10} +0.751037i q^{11} +(-2.72204 + 1.57157i) q^{13} +(2.20591 + 1.46081i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.433117 - 0.750180i) q^{17} +(1.23551 + 0.713322i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-0.375518 - 0.650417i) q^{22} +5.06153i q^{23} +1.00000 q^{25} +(1.57157 - 2.72204i) q^{26} +(-2.64078 - 0.162142i) q^{28} +(5.23368 + 3.02167i) q^{29} +(5.38301 + 3.10788i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.750180 + 0.433117i) q^{34} +(-1.17997 - 2.36805i) q^{35} +(3.60391 - 6.24216i) q^{37} -1.42664 q^{38} +1.00000i q^{40} +(2.08432 + 3.61015i) q^{41} +(3.69510 - 6.40010i) q^{43} +(0.650417 + 0.375518i) q^{44} +(-2.53076 - 4.38341i) q^{46} +(1.72922 + 2.99510i) q^{47} +(-4.21534 + 5.58846i) q^{49} +(-0.866025 + 0.500000i) q^{50} +3.14314i q^{52} +(0.790248 - 0.456250i) q^{53} +0.751037i q^{55} +(2.36805 - 1.17997i) q^{56} -6.04334 q^{58} +(4.21910 - 7.30769i) q^{59} +(9.30244 - 5.37077i) q^{61} -6.21576 q^{62} -1.00000 q^{64} +(-2.72204 + 1.57157i) q^{65} +(5.44637 - 9.43339i) q^{67} -0.866234 q^{68} +(2.20591 + 1.46081i) q^{70} -5.43339i q^{71} +(0.539702 - 0.311597i) q^{73} +7.20782i q^{74} +(1.23551 - 0.713322i) q^{76} +(1.77849 - 0.886201i) q^{77} +(-0.00292607 - 0.00506811i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-3.61015 - 2.08432i) q^{82} +(-1.01834 + 1.76381i) q^{83} +(-0.433117 - 0.750180i) q^{85} +7.39020i q^{86} -0.751037 q^{88} +(1.22452 - 2.12093i) q^{89} +(6.93349 + 4.59153i) q^{91} +(4.38341 + 2.53076i) q^{92} +(-2.99510 - 1.72922i) q^{94} +(1.23551 + 0.713322i) q^{95} +(9.23519 + 5.33194i) q^{97} +(0.856363 - 6.94742i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7}+O(q^{10}) $ 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7	$ 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7} - 6 q^{14} - 14 q^{16} + 6 q^{17} - 6 q^{19} + 14 q^{20} - 6 q^{22} + 28 q^{25} - 12 q^{26} - 8 q^{28} - 12 q^{31} - 4 q^{35} + 4 q^{37} + 12 q^{38} - 18 q^{41} + 28 q^{43} - 18 q^{46} - 30 q^{47} - 14 q^{49} + 42 q^{53} - 6 q^{56} - 12 q^{58} + 24 q^{59} + 24 q^{61} + 12 q^{62} - 28 q^{64} - 40 q^{67} + 12 q^{68} - 6 q^{70} + 6 q^{73} - 6 q^{76} + 24 q^{77} + 2 q^{79} - 14 q^{80} + 24 q^{82} + 18 q^{83} + 6 q^{85} - 12 q^{88} - 6 q^{89} + 66 q^{91} + 30 q^{92} + 42 q^{94} - 6 q^{95} - 72 q^{97} + 24 q^{98}+O(q^{100}) $ 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7 - 6 * q^14 - 14 * q^16 + 6 * q^17 - 6 * q^19 + 14 * q^20 - 6 * q^22 + 28 * q^25 - 12 * q^26 - 8 * q^28 - 12 * q^31 - 4 * q^35 + 4 * q^37 + 12 * q^38 - 18 * q^41 + 28 * q^43 - 18 * q^46 - 30 * q^47 - 14 * q^49 + 42 * q^53 - 6 * q^56 - 12 * q^58 + 24 * q^59 + 24 * q^61 + 12 * q^62 - 28 * q^64 - 40 * q^67 + 12 * q^68 - 6 * q^70 + 6 * q^73 - 6 * q^76 + 24 * q^77 + 2 * q^79 - 14 * q^80 + 24 * q^82 + 18 * q^83 + 6 * q^85 - 12 * q^88 - 6 * q^89 + 66 * q^91 + 30 * q^92 + 42 * q^94 - 6 * q^95 - 72 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−1.17997	−	2.36805i	−0.445987	−	0.895040i
$7$	−1.17997	−	2.36805i	−0.445987	−	0.895040i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.866025	+	0.500000i	−0.273861	+	0.158114i
$11$			0.751037i			0.226446i	0.993570	+	0.113223i	$0.0361175\pi$
$11$			0.751037i			0.226446i	−0.993570	+	0.113223i	$0.963883\pi$
$12$		0			0
$13$	−2.72204	+	1.57157i	−0.754958	+	0.435875i	−0.827483	−	0.561491i	$-0.810228\pi$
$13$	−2.72204	+	1.57157i	−0.754958	+	0.435875i	0.0725244	+	0.997367i	$0.476894\pi$
$14$	2.20591	+	1.46081i	0.589554	+	0.390417i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.433117	−	0.750180i	−0.105046	−	0.181945i	0.808711	−	0.588206i	$-0.200166\pi$
$17$	−0.433117	−	0.750180i	−0.105046	−	0.181945i	−0.913757	+	0.406261i	$0.866832\pi$
$18$		0			0
$19$	1.23551	+	0.713322i	0.283446	+	0.163647i	0.634982	−	0.772527i	$-0.281007\pi$
$19$	1.23551	+	0.713322i	0.283446	+	0.163647i	−0.351537	+	0.936174i	$0.614341\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$		0			0
$22$	−0.375518	−	0.650417i	−0.0800608	−	0.138669i
$23$			5.06153i			1.05540i	0.849430	+	0.527701i	$0.176946\pi$
$23$			5.06153i			1.05540i	−0.849430	+	0.527701i	$0.823054\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	1.57157	−	2.72204i	0.308210	−	0.533836i
$27$		0			0
$28$	−2.64078	−	0.162142i	−0.499060	−	0.0306420i
$29$	5.23368	+	3.02167i	0.971870	+	0.561110i	0.899806	−	0.436290i	$-0.143708\pi$
$29$	5.23368	+	3.02167i	0.971870	+	0.561110i	0.0720645	+	0.997400i	$0.477041\pi$
$30$		0			0
$31$	5.38301	+	3.10788i	0.966817	+	0.558192i	0.898264	−	0.439456i	$-0.144829\pi$
$31$	5.38301	+	3.10788i	0.966817	+	0.558192i	0.0685524	+	0.997648i	$0.478162\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	0.750180	+	0.433117i	0.128655	+	0.0742789i
$35$	−1.17997	−	2.36805i	−0.199451	−	0.400274i
$36$		0			0
$37$	3.60391	−	6.24216i	0.592479	−	1.02620i	−0.401418	−	0.915895i	$-0.631482\pi$
$37$	3.60391	−	6.24216i	0.592479	−	1.02620i	0.993897	−	0.110309i	$-0.0351842\pi$
$38$	−1.42664			−0.231432
$39$		0			0
$40$			1.00000i			0.158114i
$41$	2.08432	+	3.61015i	0.325516	+	0.563811i	0.981617	−	0.190863i	$-0.0611286\pi$
$41$	2.08432	+	3.61015i	0.325516	+	0.563811i	−0.656101	+	0.754673i	$0.727795\pi$
$42$		0			0
$43$	3.69510	−	6.40010i	0.563497	−	0.976006i	−0.433690	−	0.901062i	$-0.642789\pi$
$43$	3.69510	−	6.40010i	0.563497	−	0.976006i	0.997188	−	0.0749440i	$-0.0238778\pi$
$44$	0.650417	+	0.375518i	0.0980540	+	0.0566115i
$45$		0			0
$46$	−2.53076	−	4.38341i	−0.373141	−	0.646299i
$47$	1.72922	+	2.99510i	0.252233	+	0.436880i	0.964140	−	0.265393i	$-0.0855018\pi$
$47$	1.72922	+	2.99510i	0.252233	+	0.436880i	−0.711907	+	0.702273i	$0.752168\pi$
$48$		0			0
$49$	−4.21534	+	5.58846i	−0.602192	+	0.798352i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$		0			0
$52$			3.14314i			0.435875i
$53$	0.790248	−	0.456250i	0.108549	−	0.0626707i	−0.444743	−	0.895658i	$-0.646705\pi$
$53$	0.790248	−	0.456250i	0.108549	−	0.0626707i	0.553292	+	0.832988i	$0.313372\pi$
$54$		0			0
$55$			0.751037i			0.101270i
$56$	2.36805	−	1.17997i	0.316444	−	0.157680i
$57$		0			0
$58$	−6.04334			−0.793529
$59$	4.21910	−	7.30769i	0.549280	−	0.951381i	−0.449044	−	0.893510i	$-0.648235\pi$
$59$	4.21910	−	7.30769i	0.549280	−	0.951381i	0.998324	−	0.0578710i	$-0.0184312\pi$
$60$		0			0
$61$	9.30244	−	5.37077i	1.19106	−	0.687656i	0.232510	−	0.972594i	$-0.425306\pi$
$61$	9.30244	−	5.37077i	1.19106	−	0.687656i	0.958546	+	0.284938i	$0.0919729\pi$
$62$	−6.21576			−0.789403
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−2.72204	+	1.57157i	−0.337628	+	0.194929i
$66$		0			0
$67$	5.44637	−	9.43339i	0.665380	−	1.15247i	−0.313802	−	0.949489i	$-0.601603\pi$
$67$	5.44637	−	9.43339i	0.665380	−	1.15247i	0.979182	−	0.202984i	$-0.0650639\pi$
$68$	−0.866234			−0.105046
$69$		0			0
$70$	2.20591	+	1.46081i	0.263657	+	0.174600i
$71$		−	5.43339i		−	0.644825i	−0.946599	−	0.322413i	$-0.895506\pi$
$71$		−	5.43339i		−	0.644825i	0.946599	−	0.322413i	$-0.104494\pi$
$72$		0			0
$73$	0.539702	−	0.311597i	0.0631673	−	0.0364697i	−0.468084	−	0.883684i	$-0.655055\pi$
$73$	0.539702	−	0.311597i	0.0631673	−	0.0364697i	0.531251	+	0.847214i	$0.321722\pi$
$74$			7.20782i			0.837892i
$75$		0			0
$76$	1.23551	−	0.713322i	0.141723	−	0.0818237i
$77$	1.77849	−	0.886201i	0.202678	−	0.100992i
$78$		0			0
$79$	−0.00292607	−	0.00506811i	−0.000329209	−	0.000570206i	0.865861	−	0.500285i	$-0.166771\pi$
$79$	−0.00292607	−	0.00506811i	−0.000329209	−	0.000570206i	−0.866190	+	0.499715i	$0.833438\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$		0			0
$82$	−3.61015	−	2.08432i	−0.398674	−	0.230175i
$83$	−1.01834	+	1.76381i	−0.111777	+	0.193603i	−0.916487	−	0.400065i	$-0.868988\pi$
$83$	−1.01834	+	1.76381i	−0.111777	+	0.193603i	0.804710	+	0.593668i	$0.202321\pi$
$84$		0			0
$85$	−0.433117	−	0.750180i	−0.0469781	−	0.0813685i
$86$			7.39020i			0.796905i
$87$		0			0
$88$	−0.751037			−0.0800608
$89$	1.22452	−	2.12093i	0.129799	−	0.224819i	−0.793800	−	0.608179i	$-0.791900\pi$
$89$	1.22452	−	2.12093i	0.129799	−	0.224819i	0.923599	+	0.383361i	$0.125233\pi$
$90$		0			0
$91$	6.93349	+	4.59153i	0.726827	+	0.481323i
$92$	4.38341	+	2.53076i	0.457002	+	0.263850i
$93$		0			0
$94$	−2.99510	−	1.72922i	−0.308921	−	0.178355i
$95$	1.23551	+	0.713322i	0.126761	+	0.0731853i
$96$		0			0
$97$	9.23519	+	5.33194i	0.937692	+	0.541377i	0.889236	−	0.457449i	$-0.151237\pi$
$97$	9.23519	+	5.33194i	0.937692	+	0.541377i	0.0484558	+	0.998825i	$0.484570\pi$
$98$	0.856363	−	6.94742i	0.0865057	−	0.701795i
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	5.74239			0.571389			0.285695	−	0.958321i	$-0.407776\pi$
$101$	5.74239			0.571389			0.285695	+	0.958321i	$0.407776\pi$
$102$		0			0
$103$		−	15.6548i		−	1.54251i	−0.636526	−	0.771255i	$-0.719629\pi$
$103$		−	15.6548i		−	1.54251i	0.636526	−	0.771255i	$-0.280371\pi$
$104$	−1.57157	−	2.72204i	−0.154105	−	0.266918i
$105$		0			0
$106$	−0.456250	+	0.790248i	−0.0443149	+	0.0767557i
$107$	−11.6558	−	6.72947i	−1.12681	−	0.650562i	−0.183677	−	0.982987i	$-0.558800\pi$
$107$	−11.6558	−	6.72947i	−1.12681	−	0.650562i	−0.943130	+	0.332425i	$0.892133\pi$
$108$		0			0
$109$	−6.28955	−	10.8938i	−0.602430	−	1.04344i	−0.992452	−	0.122634i	$-0.960866\pi$
$109$	−6.28955	−	10.8938i	−0.602430	−	1.04344i	0.390022	−	0.920806i	$-0.372467\pi$
$110$	−0.375518	−	0.650417i	−0.0358043	−	0.0620148i
$111$		0			0
$112$	−1.46081	+	2.20591i	−0.138033	+	0.208439i
$113$	2.91695	−	1.68410i	0.274404	−	0.158427i	−0.356484	−	0.934302i	$-0.616024\pi$
$113$	2.91695	−	1.68410i	0.274404	−	0.158427i	0.630887	+	0.775875i	$0.282691\pi$
$114$		0			0
$115$			5.06153i			0.471990i
$116$	5.23368	−	3.02167i	0.485935	−	0.280555i
$117$		0			0
$118$			8.43820i			0.776799i
$119$	−1.26540	+	1.91083i	−0.115999	+	0.175166i
$120$		0			0
$121$	10.4359			0.948722
$122$	−5.37077	+	9.30244i	−0.486246	+	0.842204i
$123$		0			0
$124$	5.38301	−	3.10788i	0.483408	−	0.279096i
$125$	1.00000			0.0894427
$126$		0			0
$127$	6.31880			0.560703			0.280352	−	0.959897i	$-0.409549\pi$
$127$	6.31880			0.560703			0.280352	+	0.959897i	$0.409549\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	1.57157	−	2.72204i	0.137836	−	0.238739i
$131$	−10.9728			−0.958699			−0.479350	−	0.877624i	$-0.659127\pi$
$131$	−10.9728			−0.958699			−0.479350	+	0.877624i	$0.659127\pi$
$132$		0			0
$133$	0.231319	−	3.76745i	0.0200579	−	0.326680i
$134$			10.8927i			0.940990i
$135$		0			0
$136$	0.750180	−	0.433117i	0.0643274	−	0.0371395i
$137$			21.2377i			1.81446i	0.420637	+	0.907229i	$0.361807\pi$
$137$			21.2377i			1.81446i	−0.420637	+	0.907229i	$0.638193\pi$
$138$		0			0
$139$	−8.99525	+	5.19341i	−0.762967	+	0.440499i	−0.830360	−	0.557227i	$-0.811865\pi$
$139$	−8.99525	+	5.19341i	−0.762967	+	0.440499i	0.0673930	+	0.997727i	$0.478532\pi$
$140$	−2.64078	−	0.162142i	−0.223187	−	0.0137035i
$141$		0			0
$142$	2.71670	+	4.70546i	0.227980	+	0.394873i
$143$	−1.18031	−	2.04435i	−0.0987023	−	0.170957i
$144$		0			0
$145$	5.23368	+	3.02167i	0.434634	+	0.250936i
$146$	−0.311597	+	0.539702i	−0.0257880	+	0.0446660i
$147$		0			0
$148$	−3.60391	−	6.24216i	−0.296240	−	0.513102i
$149$			12.9684i			1.06241i	0.847242	+	0.531207i	$0.178261\pi$
$149$			12.9684i			1.06241i	−0.847242	+	0.531207i	$0.821739\pi$
$150$		0			0
$151$	22.9105			1.86443			0.932217	−	0.361900i	$-0.117872\pi$
$151$	22.9105			1.86443			0.932217	+	0.361900i	$0.117872\pi$
$152$	−0.713322	+	1.23551i	−0.0578581	+	0.100213i
$153$		0			0
$154$	−1.09712	+	1.65672i	−0.0884085	+	0.133502i
$155$	5.38301	+	3.10788i	0.432374	+	0.249631i
$156$		0			0
$157$	7.74720	+	4.47285i	0.618294	+	0.356972i	0.776204	−	0.630481i	$-0.217143\pi$
$157$	7.74720	+	4.47285i	0.618294	+	0.356972i	−0.157911	+	0.987453i	$0.550476\pi$
$158$	0.00506811	+	0.00292607i	0.000403197	+	0.000232786i
$159$		0			0
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	11.9860	−	5.97245i	0.944626	−	0.470695i
$162$		0			0
$163$	−8.68748	+	15.0472i	−0.680456	+	1.17858i	0.294386	+	0.955687i	$0.404885\pi$
$163$	−8.68748	+	15.0472i	−0.680456	+	1.17858i	−0.974842	+	0.222898i	$0.928448\pi$
$164$	4.16864			0.325516
$165$		0			0
$166$		−	2.03667i		−	0.158076i
$167$	−8.49076	−	14.7064i	−0.657035	−	1.13802i	−0.981380	−	0.192079i	$-0.938477\pi$
$167$	−8.49076	−	14.7064i	−0.657035	−	1.13802i	0.324345	−	0.945939i	$-0.394856\pi$
$168$		0			0
$169$	−1.56033	+	2.70257i	−0.120025	+	0.207890i
$170$	0.750180	+	0.433117i	0.0575362	+	0.0332185i
$171$		0			0
$172$	−3.69510	−	6.40010i	−0.281749	−	0.488003i
$173$	4.57540	+	7.92483i	0.347861	+	0.602514i	0.985869	−	0.167516i	$-0.0535746\pi$
$173$	4.57540	+	7.92483i	0.347861	+	0.602514i	−0.638008	+	0.770030i	$0.720241\pi$
$174$		0			0
$175$	−1.17997	−	2.36805i	−0.0891973	−	0.179008i
$176$	0.650417	−	0.375518i	0.0490270	−	0.0283058i
$177$		0			0
$178$			2.44904i			0.183564i
$179$	17.2805	−	9.97688i	1.29160	−	0.745707i	0.312664	−	0.949864i	$-0.398779\pi$
$179$	17.2805	−	9.97688i	1.29160	−	0.745707i	0.978938	+	0.204157i	$0.0654452\pi$
$180$		0			0
$181$			21.6898i			1.61219i	0.591784	+	0.806097i	$0.298424\pi$
$181$			21.6898i			1.61219i	−0.591784	+	0.806097i	$0.701576\pi$
$182$	−8.30034	−	0.509636i	−0.615262	−	0.0377767i
$183$		0			0
$184$	−5.06153			−0.373141
$185$	3.60391	−	6.24216i	0.264965	−	0.458933i
$186$		0			0
$187$	0.563413	−	0.325287i	0.0412008	−	0.0237873i
$188$	3.45844			0.252233
$189$		0			0
$190$	−1.42664			−0.103500
$191$	6.10266	−	3.52337i	0.441573	−	0.254942i	−0.262692	−	0.964880i	$-0.584610\pi$
$191$	6.10266	−	3.52337i	0.441573	−	0.254942i	0.704265	+	0.709938i	$0.251277\pi$
$192$		0			0
$193$	1.20239	−	2.08260i	0.0865498	−	0.149909i	−0.819501	−	0.573078i	$-0.805749\pi$
$193$	1.20239	−	2.08260i	0.0865498	−	0.149909i	0.906051	+	0.423169i	$0.139083\pi$
$194$	−10.6639			−0.765622
$195$		0			0
$196$	2.73208	+	6.44482i	0.195148	+	0.460345i
$197$		−	1.58424i		−	0.112873i	−0.998406	−	0.0564364i	$-0.982026\pi$
$197$		−	1.58424i		−	0.112873i	0.998406	−	0.0564364i	$-0.0179738\pi$
$198$		0			0
$199$	6.71297	−	3.87574i	0.475870	−	0.274744i	−0.242824	−	0.970070i	$-0.578074\pi$
$199$	6.71297	−	3.87574i	0.475870	−	0.274744i	0.718694	+	0.695327i	$0.244740\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	−4.97305	+	2.87119i	−0.349903	+	0.202017i
$203$	0.979879	−	15.9591i	0.0687740	−	1.12011i
$204$		0			0
$205$	2.08432	+	3.61015i	0.145575	+	0.252144i
$206$	7.82738	+	13.5574i	0.545360	+	0.944591i
$207$		0			0
$208$	2.72204	+	1.57157i	0.188740	+	0.108969i
$209$	−0.535731	+	0.927914i	−0.0370573	+	0.0641851i
$210$		0			0
$211$	6.64182	+	11.5040i	0.457242	+	0.791966i	0.998814	−	0.0486881i	$-0.0155040\pi$
$211$	6.64182	+	11.5040i	0.457242	+	0.791966i	−0.541572	+	0.840654i	$0.682171\pi$
$212$		−	0.912500i		−	0.0626707i
$213$		0			0
$214$	13.4589			0.920034
$215$	3.69510	−	6.40010i	0.252004	−	0.436483i
$216$		0			0
$217$	1.00784	−	16.4144i	0.0684164	−	1.11429i
$218$	10.8938	+	6.28955i	0.737823	+	0.425982i
$219$		0			0
$220$	0.650417	+	0.375518i	0.0438511	+	0.0253174i
$221$	2.35792	+	1.36135i	0.158611	+	0.0915742i
$222$		0			0
$223$	−13.8018	−	7.96848i	−0.924237	−	0.533609i	−0.0392529	−	0.999229i	$-0.512498\pi$
$223$	−13.8018	−	7.96848i	−0.924237	−	0.533609i	−0.884984	+	0.465621i	$0.845831\pi$
$224$	0.162142	−	2.64078i	0.0108336	−	0.176444i
$225$		0			0
$226$	−1.68410	+	2.91695i	−0.112025	+	0.194033i
$227$	13.1879			0.875314			0.437657	−	0.899142i	$-0.355808\pi$
$227$	13.1879			0.875314			0.437657	+	0.899142i	$0.355808\pi$
$228$		0			0
$229$			19.7537i			1.30536i	0.757633	+	0.652681i	$0.226356\pi$
$229$			19.7537i			1.30536i	−0.757633	+	0.652681i	$0.773644\pi$
$230$	−2.53076	−	4.38341i	−0.166874	−	0.289034i
$231$		0			0
$232$	−3.02167	+	5.23368i	−0.198382	+	0.343608i
$233$	−23.8501	−	13.7699i	−1.56247	−	0.902094i	−0.997006	−	0.0773231i	$-0.975363\pi$
$233$	−23.8501	−	13.7699i	−1.56247	−	0.902094i	−0.565467	−	0.824771i	$-0.691304\pi$
$234$		0			0
$235$	1.72922	+	2.99510i	0.112802	+	0.195379i
$236$	−4.21910	−	7.30769i	−0.274640	−	0.475690i
$237$		0			0
$238$	0.140453	−	2.28753i	0.00910421	−	0.148279i
$239$	−6.52234	+	3.76567i	−0.421895	+	0.243581i	−0.695888	−	0.718151i	$-0.744989\pi$
$239$	−6.52234	+	3.76567i	−0.421895	+	0.243581i	0.273993	+	0.961732i	$0.411656\pi$
$240$		0			0
$241$			11.9813i			0.771785i	0.922544	+	0.385892i	$0.126106\pi$
$241$			11.9813i			0.771785i	−0.922544	+	0.385892i	$0.873894\pi$
$242$	−9.03779	+	5.21797i	−0.580971	+	0.335424i
$243$		0			0
$244$		−	10.7415i		−	0.687656i
$245$	−4.21534	+	5.58846i	−0.269308	+	0.357034i
$246$		0			0
$247$	−4.48415			−0.285319
$248$	−3.10788	+	5.38301i	−0.197351	+	0.341821i
$249$		0			0
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$	30.3694			1.91690			0.958449	−	0.285265i	$-0.0920816\pi$
$251$	30.3694			1.91690			0.958449	+	0.285265i	$0.0920816\pi$
$252$		0			0
$253$	−3.80139			−0.238992
$254$	−5.47224	+	3.15940i	−0.343359	+	0.198238i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.800054			0.0499060			0.0249530	−	0.999689i	$-0.492056\pi$
$257$	0.800054			0.0499060			0.0249530	+	0.999689i	$0.492056\pi$
$258$		0			0
$259$	−19.0343	−	1.16869i	−1.18273	−	0.0726190i
$260$			3.14314i			0.194929i
$261$		0			0
$262$	9.50274	−	5.48641i	0.587081	−	0.338951i
$263$		−	20.8541i		−	1.28592i	−0.765900	−	0.642960i	$-0.777706\pi$
$263$		−	20.8541i		−	1.28592i	0.765900	−	0.642960i	$-0.222294\pi$
$264$		0			0
$265$	0.790248	−	0.456250i	0.0485445	−	0.0280272i
$266$	1.68340	+	3.37837i	0.103216	+	0.207141i
$267$		0			0
$268$	−5.44637	−	9.43339i	−0.332690	−	0.576236i
$269$	15.0545	+	26.0752i	0.917889	+	1.58983i	0.802616	+	0.596497i	$0.203441\pi$
$269$	15.0545	+	26.0752i	0.917889	+	1.58983i	0.115273	+	0.993334i	$0.463226\pi$
$270$		0			0
$271$	−12.3296	−	7.11850i	−0.748970	−	0.432418i	0.0763514	−	0.997081i	$-0.475673\pi$
$271$	−12.3296	−	7.11850i	−0.748970	−	0.432418i	−0.825322	+	0.564663i	$0.809006\pi$
$272$	−0.433117	+	0.750180i	−0.0262616	+	0.0454864i
$273$		0			0
$274$	−10.6188	−	18.3924i	−0.641508	−	1.11112i
$275$			0.751037i			0.0452892i
$276$		0			0
$277$	−16.9306			−1.01726			−0.508631	−	0.860985i	$-0.669848\pi$
$277$	−16.9306			−1.01726			−0.508631	+	0.860985i	$0.669848\pi$
$278$	5.19341	−	8.99525i	0.311480	−	0.539499i
$279$		0			0
$280$	2.36805	−	1.17997i	0.141518	−	0.0705167i
$281$	16.7637	+	9.67853i	1.00004	+	0.577373i	0.908260	−	0.418407i	$-0.137411\pi$
$281$	16.7637	+	9.67853i	1.00004	+	0.577373i	0.0917791	+	0.995779i	$0.470745\pi$
$282$		0			0
$283$	26.4542	+	15.2734i	1.57254	+	0.907907i	0.995856	+	0.0909409i	$0.0289874\pi$
$283$	26.4542	+	15.2734i	1.57254	+	0.907907i	0.576685	+	0.816966i	$0.304346\pi$
$284$	−4.70546	−	2.71670i	−0.279218	−	0.161206i
$285$		0			0
$286$	2.04435	+	1.18031i	0.120885	+	0.0697930i
$287$	6.08958	−	9.19565i	0.359457	−	0.542802i
$288$		0			0
$289$	8.12482	−	14.0726i	0.477931	−	0.827800i
$290$	−6.04334			−0.354877
$291$		0			0
$292$		−	0.623194i		−	0.0364697i
$293$	−0.844143	−	1.46210i	−0.0493154	−	0.0854167i	0.840314	−	0.542100i	$-0.182371\pi$
$293$	−0.844143	−	1.46210i	−0.0493154	−	0.0854167i	−0.889629	+	0.456683i	$0.849037\pi$
$294$		0			0
$295$	4.21910	−	7.30769i	0.245645	−	0.425470i
$296$	6.24216	+	3.60391i	0.362818	+	0.209473i
$297$		0			0
$298$	−6.48421	−	11.2310i	−0.375620	−	0.650593i
$299$	−7.95455	−	13.7777i	−0.460024	−	0.796784i
$300$		0			0
$301$	−19.5159	−	1.19826i	−1.12488	−	0.0690667i
$302$	−19.8411	+	11.4553i	−1.14173	+	0.659177i
$303$		0			0
$304$		−	1.42664i		−	0.0818237i
$305$	9.30244	−	5.37077i	0.532656	−	0.307529i
$306$		0			0
$307$			7.15873i			0.408570i	0.978911	+	0.204285i	$0.0654869\pi$
$307$			7.15873i			0.408570i	−0.978911	+	0.204285i	$0.934513\pi$
$308$	0.121775	−	1.98332i	0.00693876	−	0.113010i
$309$		0			0
$310$	−6.21576			−0.353032
$311$	−12.3177	+	21.3350i	−0.698475	+	1.20979i	0.270520	+	0.962714i	$0.412804\pi$
$311$	−12.3177	+	21.3350i	−0.698475	+	1.20979i	−0.968995	+	0.247080i	$0.920529\pi$
$312$		0			0
$313$	−11.0002	+	6.35095i	−0.621766	+	0.358977i	−0.777556	−	0.628813i	$-0.783541\pi$
$313$	−11.0002	+	6.35095i	−0.621766	+	0.358977i	0.155790	+	0.987790i	$0.450208\pi$
$314$	−8.94569			−0.504835
$315$		0			0
$316$	−0.00585214			−0.000329209
$317$	−22.1158	+	12.7685i	−1.24214	+	0.717152i	−0.969530	−	0.244971i	$-0.921222\pi$
$317$	−22.1158	+	12.7685i	−1.24214	+	0.717152i	−0.272614	+	0.962123i	$0.587888\pi$
$318$		0			0
$319$	−2.26938	+	3.93069i	−0.127061	+	0.220076i
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	−7.39392	+	11.1653i	−0.412047	+	0.622217i
$323$		−	1.23581i		−	0.0687622i
$324$		0			0
$325$	−2.72204	+	1.57157i	−0.150992	+	0.0871751i
$326$		−	17.3750i		−	0.962310i
$327$		0			0
$328$	−3.61015	+	2.08432i	−0.199337	+	0.115087i
$329$	5.05212	−	7.62901i	0.278532	−	0.420601i
$330$		0			0
$331$	7.01463	+	12.1497i	0.385559	+	0.667807i	0.991847	−	0.127438i	$-0.0406754\pi$
$331$	7.01463	+	12.1497i	0.385559	+	0.667807i	−0.606288	+	0.795245i	$0.707342\pi$
$332$	1.01834	+	1.76381i	0.0558884	+	0.0968016i
$333$		0			0
$334$	14.7064	+	8.49076i	0.804700	+	0.464594i
$335$	5.44637	−	9.43339i	0.297567	−	0.515401i
$336$		0			0
$337$	13.7946	+	23.8930i	0.751442	+	1.30154i	0.947124	+	0.320868i	$0.103975\pi$
$337$	13.7946	+	23.8930i	0.751442	+	1.30154i	−0.195682	+	0.980667i	$0.562692\pi$
$338$		−	3.12066i		−	0.169741i
$339$		0			0
$340$	−0.866234			−0.0469781
$341$	−2.33413	+	4.04284i	−0.126400	+	0.218932i
$342$		0			0
$343$	18.2077	+	3.38793i	0.983126	+	0.182931i
$344$	6.40010	+	3.69510i	0.345070	+	0.199226i
$345$		0			0
$346$	−7.92483	−	4.57540i	−0.426041	−	0.245975i
$347$	10.1962	+	5.88676i	0.547359	+	0.316018i	0.748056	−	0.663635i	$-0.230987\pi$
$347$	10.1962	+	5.88676i	0.547359	+	0.316018i	−0.200697	+	0.979653i	$0.564321\pi$
$348$		0			0
$349$	−25.3085	−	14.6119i	−1.35473	−	0.782155i	−0.365824	−	0.930684i	$-0.619213\pi$
$349$	−25.3085	−	14.6119i	−1.35473	−	0.782155i	−0.988908	+	0.148530i	$0.952546\pi$
$350$	2.20591	+	1.46081i	0.117911	+	0.0780835i
$351$		0			0
$352$	−0.375518	+	0.650417i	−0.0200152	+	0.0346673i
$353$	−0.301856			−0.0160662			−0.00803309	−	0.999968i	$-0.502557\pi$
$353$	−0.301856			−0.0160662			−0.00803309	+	0.999968i	$0.502557\pi$
$354$		0			0
$355$		−	5.43339i		−	0.288375i
$356$	−1.22452	−	2.12093i	−0.0648995	−	0.112409i
$357$		0			0
$358$	−9.97688	+	17.2805i	−0.527294	+	0.913301i
$359$	−22.8586	−	13.1974i	−1.20643	−	0.696534i	−0.244455	−	0.969661i	$-0.578609\pi$
$359$	−22.8586	−	13.1974i	−1.20643	−	0.696534i	−0.961978	+	0.273126i	$0.911942\pi$
$360$		0			0
$361$	−8.48234	−	14.6918i	−0.446439	−	0.773255i
$362$	−10.8449	−	18.7840i	−0.569996	−	0.987263i
$363$		0			0
$364$	7.44312	−	3.70881i	0.390126	−	0.194395i
$365$	0.539702	−	0.311597i	0.0282493	−	0.0163097i
$366$		0			0
$367$		−	9.73338i		−	0.508079i	−0.967194	−	0.254039i	$-0.918241\pi$
$367$		−	9.73338i		−	0.508079i	0.967194	−	0.254039i	$-0.0817592\pi$
$368$	4.38341	−	2.53076i	0.228501	−	0.131925i
$369$		0			0
$370$			7.20782i			0.374717i
$371$	−2.01289	−	1.33299i	−0.104504	−	0.0692052i
$372$		0			0
$373$	−19.2585			−0.997168			−0.498584	−	0.866841i	$-0.666146\pi$
$373$	−19.2585			−0.997168			−0.498584	+	0.866841i	$0.666146\pi$
$374$	−0.325287	+	0.563413i	−0.0168202	+	0.0291334i
$375$		0			0
$376$	−2.99510	+	1.72922i	−0.154460	+	0.0891777i
$377$	−18.9951			−0.978296
$378$		0			0
$379$	−29.4361			−1.51203			−0.756015	−	0.654554i	$-0.772856\pi$
$379$	−29.4361			−1.51203			−0.756015	+	0.654554i	$0.772856\pi$
$380$	1.23551	−	0.713322i	0.0633804	−	0.0365927i
$381$		0			0
$382$	−3.52337	+	6.10266i	−0.180271	+	0.312239i
$383$	−17.8073			−0.909912			−0.454956	−	0.890514i	$-0.650345\pi$
$383$	−17.8073			−0.909912			−0.454956	+	0.890514i	$0.650345\pi$
$384$		0			0
$385$	1.77849	−	0.886201i	0.0906405	−	0.0451650i
$386$			2.40478i			0.122400i
$387$		0			0
$388$	9.23519	−	5.33194i	0.468846	−	0.270688i
$389$			12.5302i			0.635306i	0.948207	+	0.317653i	$0.102895\pi$
$389$			12.5302i			0.635306i	−0.948207	+	0.317653i	$0.897105\pi$
$390$		0			0
$391$	3.79706	−	2.19223i	0.192026	−	0.110866i
$392$	−5.58846	−	4.21534i	−0.282260	−	0.212907i
$393$		0			0
$394$	0.792122	+	1.37200i	0.0399066	+	0.0691202i
$395$	−0.00292607	−	0.00506811i	−0.000147227	−	0.000255004i
$396$		0			0
$397$	−26.6549	−	15.3892i	−1.33777	−	0.772361i	−0.351293	−	0.936266i	$-0.614258\pi$
$397$	−26.6549	−	15.3892i	−1.33777	−	0.772361i	−0.986476	+	0.163905i	$0.947591\pi$
$398$	−3.87574	+	6.71297i	−0.194273	+	0.336491i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$		−	7.17154i		−	0.358129i	−0.983837	−	0.179065i	$-0.942693\pi$
$401$		−	7.17154i		−	0.358129i	0.983837	−	0.179065i	$-0.0573071\pi$
$402$		0			0
$403$	−19.5370			−0.973208
$404$	2.87119	−	4.97305i	0.142847	−	0.247419i
$405$		0			0
$406$	7.13096	+	14.3109i	0.353903	+	0.710240i
$407$	4.68809	+	2.70667i	0.232380	+	0.134165i
$408$		0			0
$409$	23.0919	+	13.3321i	1.14182	+	0.659232i	0.946881	−	0.321583i	$-0.104215\pi$
$409$	23.0919	+	13.3321i	1.14182	+	0.659232i	0.194942	+	0.980815i	$0.437548\pi$
$410$	−3.61015	−	2.08432i	−0.178293	−	0.102937i
$411$		0			0
$412$	−13.5574	−	7.82738i	−0.667926	−	0.385627i
$413$	−22.2834	−	1.36819i	−1.09649	−	0.0673241i
$414$		0			0
$415$	−1.01834	+	1.76381i	−0.0499881	+	0.0865820i
$416$	−3.14314			−0.154105
$417$		0			0
$418$		−	1.07146i		−	0.0524070i
$419$	−12.2128	−	21.1533i	−0.596636	−	1.03340i	−0.993314	−	0.115446i	$-0.963170\pi$
$419$	−12.2128	−	21.1533i	−0.596636	−	1.03340i	0.396677	−	0.917958i	$-0.370163\pi$
$420$		0			0
$421$	8.84702	−	15.3235i	0.431177	−	0.746821i	−0.565798	−	0.824544i	$-0.691432\pi$
$421$	8.84702	−	15.3235i	0.431177	−	0.746821i	0.996975	+	0.0777229i	$0.0247649\pi$
$422$	−11.5040	−	6.64182i	−0.560005	−	0.323319i
$423$		0			0
$424$	0.456250	+	0.790248i	0.0221574	+	0.0383778i
$425$	−0.433117	−	0.750180i	−0.0210093	−	0.0363891i
$426$		0			0
$427$	−23.6949	−	15.6913i	−1.14667	−	0.759356i
$428$	−11.6558	+	6.72947i	−0.563403	+	0.325281i
$429$		0			0
$430$			7.39020i			0.356387i
$431$	20.5184	−	11.8463i	0.988335	−	0.570616i	0.0835591	−	0.996503i	$-0.473371\pi$
$431$	20.5184	−	11.8463i	0.988335	−	0.570616i	0.904776	+	0.425887i	$0.140038\pi$
$432$		0			0
$433$			24.1077i			1.15854i	0.815135	+	0.579271i	$0.196663\pi$
$433$			24.1077i			1.15854i	−0.815135	+	0.579271i	$0.803337\pi$
$434$	7.33441	+	14.7192i	0.352063	+	0.706547i
$435$		0			0
$436$	−12.5791			−0.602430
$437$	−3.61050	+	6.25357i	−0.172714	+	0.299149i
$438$		0			0
$439$	−0.925536	+	0.534359i	−0.0441734	+	0.0255035i	−0.521924	−	0.852992i	$-0.674786\pi$
$439$	−0.925536	+	0.534359i	−0.0441734	+	0.0255035i	0.477751	+	0.878495i	$0.341452\pi$
$440$	−0.751037			−0.0358043
$441$		0			0
$442$	−2.72270			−0.129505
$443$	26.8115	−	15.4796i	1.27385	−	0.735459i	0.298142	−	0.954522i	$-0.403633\pi$
$443$	26.8115	−	15.4796i	1.27385	−	0.735459i	0.975711	+	0.219062i	$0.0702998\pi$
$444$		0			0
$445$	1.22452	−	2.12093i	0.0580479	−	0.100542i
$446$	15.9370			0.754637
$447$		0			0
$448$	1.17997	+	2.36805i	0.0557483	+	0.111880i
$449$		−	22.4824i		−	1.06101i	−0.847682	−	0.530505i	$-0.822002\pi$
$449$		−	22.4824i		−	1.06101i	0.847682	−	0.530505i	$-0.177998\pi$
$450$		0			0
$451$	−2.71135	+	1.56540i	−0.127673	+	0.0737119i
$452$		−	3.36820i		−	0.158427i
$453$		0			0
$454$	−11.4211	+	6.59397i	−0.536018	+	0.309470i
$455$	6.93349	+	4.59153i	0.325047	+	0.215254i
$456$		0			0
$457$	−20.6626	−	35.7886i	−0.966554	−	1.67412i	−0.705380	−	0.708829i	$-0.749224\pi$
$457$	−20.6626	−	35.7886i	−0.966554	−	1.67412i	−0.261174	−	0.965292i	$-0.584110\pi$
$458$	−9.87685	−	17.1072i	−0.461515	−	0.799367i
$459$		0			0
$460$	4.38341	+	2.53076i	0.204378	+	0.117997i
$461$	13.0109	−	22.5356i	0.605979	−	1.04959i	−0.385917	−	0.922533i	$-0.626115\pi$
$461$	13.0109	−	22.5356i	0.605979	−	1.04959i	0.991896	−	0.127052i	$-0.0405516\pi$
$462$		0			0
$463$	−5.54762	−	9.60876i	−0.257820	−	0.446557i	0.707838	−	0.706375i	$-0.249671\pi$
$463$	−5.54762	−	9.60876i	−0.257820	−	0.446557i	−0.965658	+	0.259818i	$0.916337\pi$
$464$		−	6.04334i		−	0.280555i
$465$		0			0
$466$	27.5397			1.27575
$467$	−18.7366	+	32.4527i	−0.867025	+	1.50173i	−0.00200339	+	0.999998i	$0.500638\pi$
$467$	−18.7366	+	32.4527i	−0.867025	+	1.50173i	−0.865022	+	0.501734i	$0.832696\pi$
$468$		0			0
$469$	−28.7653	−	1.76617i	−1.32826	−	0.0815543i
$470$	−2.99510	−	1.72922i	−0.138154	−	0.0797630i
$471$		0			0
$472$	7.30769	+	4.21910i	0.336364	+	0.194200i
$473$	4.80671	+	2.77515i	0.221013	+	0.127602i
$474$		0			0
$475$	1.23551	+	0.713322i	0.0566891	+	0.0327295i
$476$	1.02213	+	2.05129i	0.0468492	+	0.0940206i
$477$		0			0
$478$	3.76567	−	6.52234i	0.172238	−	0.298325i
$479$	−13.9632			−0.637996			−0.318998	−	0.947755i	$-0.603346\pi$
$479$	−13.9632			−0.637996			−0.318998	+	0.947755i	$0.603346\pi$
$480$		0			0
$481$			22.6552i			1.03299i
$482$	−5.99066	−	10.3761i	−0.272867	−	0.472620i
$483$		0			0
$484$	5.21797	−	9.03779i	0.237181	−	0.410809i
$485$	9.23519	+	5.33194i	0.419349	+	0.242111i
$486$		0			0
$487$	1.90704	+	3.30309i	0.0864163	+	0.149677i	0.905994	−	0.423291i	$-0.139125\pi$
$487$	1.90704	+	3.30309i	0.0864163	+	0.149677i	−0.819578	+	0.572968i	$0.805792\pi$
$488$	5.37077	+	9.30244i	0.243123	+	0.421102i
$489$		0			0
$490$	0.856363	−	6.94742i	0.0386865	−	0.313852i
$491$	−23.7383	+	13.7053i	−1.07129	+	0.618512i	−0.928535	−	0.371245i	$-0.878931\pi$
$491$	−23.7383	+	13.7053i	−1.07129	+	0.618512i	−0.142760	+	0.989757i	$0.545598\pi$
$492$		0			0
$493$		−	5.23494i		−	0.235770i
$494$	3.88339	−	2.24207i	0.174722	−	0.100876i
$495$		0			0
$496$		−	6.21576i		−	0.279096i
$497$	−12.8666	+	6.41124i	−0.577144	+	0.287584i
$498$		0			0
$499$	25.7894			1.15449			0.577247	−	0.816570i	$-0.304127\pi$
$499$	25.7894			1.15449			0.577247	+	0.816570i	$0.304127\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		0			0
$502$	−26.3006	+	15.1847i	−1.17386	+	0.677726i
$503$	−17.3517			−0.773675			−0.386838	−	0.922148i	$-0.626433\pi$
$503$	−17.3517			−0.773675			−0.386838	+	0.922148i	$0.626433\pi$
$504$		0			0
$505$	5.74239			0.255533
$506$	3.29210	−	1.90070i	0.146352	−	0.0844963i
$507$		0			0
$508$	3.15940	−	5.47224i	0.140176	−	0.242792i
$509$	−28.1334			−1.24699			−0.623497	−	0.781826i	$-0.714288\pi$
$509$	−28.1334			−1.24699			−0.623497	+	0.781826i	$0.714288\pi$
$510$		0			0
$511$	−1.37471	−	0.910367i	−0.0608136	−	0.0402723i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−0.692867	+	0.400027i	−0.0305611	+	0.0176444i
$515$		−	15.6548i		−	0.689831i
$516$		0			0
$517$	−2.24943	+	1.29871i	−0.0989298	+	0.0571171i
$518$	17.0685	−	8.50501i	0.749947	−	0.373689i
$519$		0			0
$520$	−1.57157	−	2.72204i	−0.0689179	−	0.119369i
$521$	−3.97534	−	6.88549i	−0.174163	−	0.301659i	0.765708	−	0.643188i	$-0.222389\pi$
$521$	−3.97534	−	6.88549i	−0.174163	−	0.301659i	−0.939871	+	0.341529i	$0.889055\pi$
$522$		0			0
$523$	0.614490	+	0.354776i	0.0268698	+	0.0155133i	0.513375	−	0.858165i	$-0.328395\pi$
$523$	0.614490	+	0.354776i	0.0268698	+	0.0155133i	−0.486505	+	0.873678i	$0.661728\pi$
$524$	−5.48641	+	9.50274i	−0.239675	+	0.415129i
$525$		0			0
$526$	10.4271	+	18.0602i	0.454641	+	0.787462i
$527$		−	5.38430i		−	0.234544i
$528$		0			0
$529$	−2.61907			−0.113873
$530$	−0.456250	+	0.790248i	−0.0198182	+	0.0343262i
$531$		0			0
$532$	−3.14705	−	2.08405i	−0.136442	−	0.0903552i
$533$	−11.3472	−	6.55131i	−0.491502	−	0.283769i
$534$		0			0
$535$	−11.6558	−	6.72947i	−0.503923	−	0.290940i
$536$	9.43339	+	5.44637i	0.407461	+	0.235247i
$537$		0			0
$538$	−26.0752	−	15.0545i	−1.12418	−	0.649046i
$539$	−4.19714	−	3.16588i	−0.180784	−	0.136364i
$540$		0			0
$541$	−0.152089	+	0.263426i	−0.00653882	+	0.0113256i	−0.869276	−	0.494327i	$-0.835415\pi$
$541$	−0.152089	+	0.263426i	−0.00653882	+	0.0113256i	0.862737	+	0.505652i	$0.168748\pi$
$542$	14.2370			0.611532
$543$		0			0
$544$		−	0.866234i		−	0.0371395i
$545$	−6.28955	−	10.8938i	−0.269415	−	0.466640i
$546$		0			0
$547$	4.14876	−	7.18586i	0.177388	−	0.307245i	−0.763597	−	0.645693i	$-0.776569\pi$
$547$	4.14876	−	7.18586i	0.177388	−	0.307245i	0.940985	+	0.338448i	$0.109902\pi$
$548$	18.3924	+	10.6188i	0.785684	+	0.453615i
$549$		0			0
$550$	−0.375518	−	0.650417i	−0.0160122	−	0.0277339i
$551$	4.31085	+	7.46661i	0.183648	+	0.318088i
$552$		0			0
$553$	−0.00854886	+	0.0129093i	−0.000363535	+	0.000548959i
$554$	14.6623	−	8.46531i	0.622943	−	0.359657i
$555$		0			0
$556$			10.3868i			0.440499i
$557$	2.70966	−	1.56442i	0.114812	−	0.0662867i	−0.441494	−	0.897264i	$-0.645551\pi$
$557$	2.70966	−	1.56442i	0.114812	−	0.0662867i	0.556306	+	0.830977i	$0.312218\pi$
$558$		0			0
$559$			23.2284i			0.982458i
$560$	−1.46081	+	2.20591i	−0.0617304	+	0.0932167i
$561$		0			0
$562$	−19.3571			−0.816528
$563$	−10.4373	+	18.0780i	−0.439881	+	0.761897i	−0.997680	−	0.0680796i	$-0.978313\pi$
$563$	−10.4373	+	18.0780i	−0.439881	+	0.761897i	0.557799	+	0.829976i	$0.311646\pi$
$564$		0			0
$565$	2.91695	−	1.68410i	0.122717	−	0.0708507i
$566$	−30.5467			−1.28397
$567$		0			0
$568$	5.43339			0.227980
$569$	−20.0446	+	11.5727i	−0.840313	+	0.485155i	−0.857371	−	0.514700i	$-0.827903\pi$
$569$	−20.0446	+	11.5727i	−0.840313	+	0.485155i	0.0170577	+	0.999855i	$0.494570\pi$
$570$		0			0
$571$	12.3844	−	21.4504i	0.518271	−	0.897671i	−0.481504	−	0.876444i	$-0.659909\pi$
$571$	12.3844	−	21.4504i	0.518271	−	0.897671i	0.999775	−	0.0212272i	$-0.00675732\pi$
$572$	−2.36061			−0.0987023
$573$		0			0
$574$	−0.675912	+	11.0085i	−0.0282120	+	0.459484i
$575$			5.06153i			0.211080i
$576$		0			0
$577$	31.6396	−	18.2671i	1.31717	−	0.760470i	0.333900	−	0.942609i	$-0.391635\pi$
$577$	31.6396	−	18.2671i	1.31717	−	0.760470i	0.983273	+	0.182138i	$0.0583019\pi$
$578$			16.2496i			0.675896i
$579$		0			0
$580$	5.23368	−	3.02167i	0.217317	−	0.125468i
$581$	5.37840	+	0.330230i	0.223134	+	0.0137003i
$582$		0			0
$583$	0.342660	+	0.593505i	0.0141915	+	0.0245805i
$584$	0.311597	+	0.539702i	0.0128940	+	0.0223330i
$585$		0			0
$586$	1.46210	+	0.844143i	0.0603987	+	0.0348712i
$587$	12.1405	−	21.0280i	0.501092	−	0.867918i	−0.498907	−	0.866656i	$-0.666265\pi$
$587$	12.1405	−	21.0280i	0.501092	−	0.867918i	0.999999	−	0.00126186i	$-0.000401662\pi$
$588$		0			0
$589$	4.43384	+	7.67964i	0.182693	+	0.316434i
$590$			8.43820i			0.347395i
$591$		0			0
$592$	−7.20782			−0.296240
$593$	−19.7837	+	34.2664i	−0.812419	+	1.40715i	0.0987467	+	0.995113i	$0.468517\pi$
$593$	−19.7837	+	34.2664i	−0.812419	+	1.40715i	−0.911166	+	0.412039i	$0.864817\pi$
$594$		0			0
$595$	−1.26540	+	1.91083i	−0.0518764	+	0.0783365i
$596$	11.2310	+	6.48421i	0.460039	+	0.265604i
$597$		0			0
$598$	13.7777	+	7.95455i	0.563411	+	0.325286i
$599$	−35.4500	−	20.4671i	−1.44845	−	0.836263i	−0.450060	−	0.892998i	$-0.648598\pi$
$599$	−35.4500	−	20.4671i	−1.44845	−	0.836263i	−0.998389	+	0.0567354i	$0.981931\pi$
$600$		0			0
$601$	4.48642	+	2.59023i	0.183005	+	0.105658i	0.588704	−	0.808349i	$-0.299639\pi$
$601$	4.48642	+	2.59023i	0.183005	+	0.105658i	−0.405699	+	0.914007i	$0.632972\pi$
$602$	17.5004	−	8.72021i	0.713262	−	0.355409i
$603$		0			0
$604$	11.4553	−	19.8411i	0.466108	−	0.807323i
$605$	10.4359			0.424281
$606$		0			0
$607$			3.09536i			0.125637i	0.998025	+	0.0628183i	$0.0200089\pi$
$607$			3.09536i			0.125637i	−0.998025	+	0.0628183i	$0.979991\pi$
$608$	0.713322	+	1.23551i	0.0289290	+	0.0501066i
$609$		0			0
$610$	−5.37077	+	9.30244i	−0.217456	+	0.376645i
$611$	−9.41402	−	5.43519i	−0.380850	−	0.219884i
$612$		0			0
$613$	−1.39906	−	2.42324i	−0.0565075	−	0.0978739i	0.836388	−	0.548138i	$-0.184663\pi$
$613$	−1.39906	−	2.42324i	−0.0565075	−	0.0978739i	−0.892895	+	0.450264i	$0.851330\pi$
$614$	−3.57936	−	6.19964i	−0.144451	−	0.250197i
$615$		0			0
$616$	0.886201	+	1.77849i	0.0357060	+	0.0716576i
$617$	20.0878	−	11.5977i	0.808706	−	0.466906i	−0.0378006	−	0.999285i	$-0.512035\pi$
$617$	20.0878	−	11.5977i	0.808706	−	0.466906i	0.846506	+	0.532379i	$0.178702\pi$
$618$		0			0
$619$			9.82235i			0.394793i	0.980324	+	0.197397i	$0.0632487\pi$
$619$			9.82235i			0.394793i	−0.980324	+	0.197397i	$0.936751\pi$
$620$	5.38301	−	3.10788i	0.216187	−	0.124816i
$621$		0			0
$622$		−	24.6355i		−	0.987793i
$623$	−6.46738	−	0.397093i	−0.259110	−	0.0159092i
$624$		0			0
$625$	1.00000			0.0400000
$626$	6.35095	−	11.0002i	0.253835	−	0.439655i
$627$		0			0
$628$	7.74720	−	4.47285i	0.309147	−	0.178486i
$629$	−6.24366			−0.248951
$630$		0			0
$631$	26.4402			1.05257			0.526285	−	0.850308i	$-0.323585\pi$
$631$	26.4402			1.05257			0.526285	+	0.850308i	$0.323585\pi$
$632$	0.00506811	−	0.00292607i	0.000201598	−	0.000116393i
$633$		0			0
$634$	12.7685	−	22.1158i	0.507103	−	0.878329i
$635$	6.31880			0.250754
$636$		0			0
$637$	2.69167	−	21.8367i	0.106648	−	0.865203i
$638$		−	4.53877i		−	0.179692i
$639$		0			0
$640$	0.866025	−	0.500000i	0.0342327	−	0.0197642i
$641$		−	27.8267i		−	1.09909i	−0.835465	−	0.549543i	$-0.814802\pi$
$641$		−	27.8267i		−	1.09909i	0.835465	−	0.549543i	$-0.185198\pi$
$642$		0			0
$643$	36.4628	−	21.0518i	1.43795	−	0.830203i	0.440246	−	0.897877i	$-0.354891\pi$
$643$	36.4628	−	21.0518i	1.43795	−	0.830203i	0.997707	+	0.0676745i	$0.0215580\pi$
$644$	0.820687	−	13.3664i	0.0323396	−	0.526709i
$645$		0			0
$646$	0.617904	+	1.07024i	0.0243111	+	0.0421081i
$647$	11.5301	+	19.9708i	0.453296	+	0.785132i	0.998588	−	0.0531139i	$-0.0169146\pi$
$647$	11.5301	+	19.9708i	0.453296	+	0.785132i	−0.545292	+	0.838246i	$0.683581\pi$
$648$		0			0
$649$	5.48835	+	3.16870i	0.215436	+	0.124382i
$650$	1.57157	−	2.72204i	0.0616421	−	0.106767i
$651$		0			0
$652$	8.68748	+	15.0472i	0.340228	+	0.589292i
$653$			25.7997i			1.00962i	0.863230	+	0.504810i	$0.168437\pi$
$653$			25.7997i			1.00962i	−0.863230	+	0.504810i	$0.831563\pi$
$654$		0			0
$655$	−10.9728			−0.428743
$656$	2.08432	−	3.61015i	0.0813790	−	0.140953i
$657$		0			0
$658$	−0.560759	+	9.13298i	−0.0218607	+	0.356040i
$659$	−25.3231	−	14.6203i	−0.986447	−	0.569525i	−0.0822364	−	0.996613i	$-0.526206\pi$
$659$	−25.3231	−	14.6203i	−0.986447	−	0.569525i	−0.904210	+	0.427088i	$0.859540\pi$
$660$		0			0
$661$	22.4429	+	12.9574i	0.872926	+	0.503984i	0.868320	−	0.496005i	$-0.165200\pi$
$661$	22.4429	+	12.9574i	0.872926	+	0.503984i	0.00460675	+	0.999989i	$0.498534\pi$
$662$	−12.1497	−	7.01463i	−0.472211	−	0.272631i
$663$		0			0
$664$	−1.76381	−	1.01834i	−0.0684491	−	0.0395191i
$665$	0.231319	−	3.76745i	0.00897017	−	0.146096i
$666$		0			0
$667$	−15.2943	+	26.4904i	−0.592196	+	1.02571i
$668$	−16.9815			−0.657035
$669$		0			0
$670$			10.8927i			0.420823i
$671$	4.03364	+	6.98648i	0.155717	+	0.269710i
$672$		0			0
$673$	−4.62323	+	8.00767i	−0.178212	+	0.308673i	−0.941268	−	0.337660i	$-0.890365\pi$
$673$	−4.62323	+	8.00767i	−0.178212	+	0.308673i	0.763056	+	0.646332i	$0.223698\pi$
$674$	−23.8930	−	13.7946i	−0.920325	−	0.531350i
$675$		0			0
$676$	1.56033	+	2.70257i	0.0600127	+	0.103945i
$677$	12.3613	+	21.4103i	0.475082	+	0.822866i	0.999593	−	0.0285376i	$-0.00908502\pi$
$677$	12.3613	+	21.4103i	0.475082	+	0.822866i	−0.524511	+	0.851404i	$0.675752\pi$
$678$		0			0
$679$	1.72906	−	28.1610i	0.0663554	−	1.08072i
$680$	0.750180	−	0.433117i	0.0287681	−	0.0166093i
$681$		0			0
$682$		−	4.66827i		−	0.178757i
$683$	26.9472	−	15.5580i	1.03111	−	0.595309i	0.113804	−	0.993503i	$-0.463696\pi$
$683$	26.9472	−	15.5580i	1.03111	−	0.595309i	0.917301	+	0.398194i	$0.130363\pi$
$684$		0			0
$685$			21.2377i			0.811451i
$686$	−17.4623	+	6.16984i	−0.666715	+	0.235565i
$687$		0			0
$688$	−7.39020			−0.281749
$689$	−1.43406	+	2.48386i	−0.0546333	+	0.0946276i
$690$		0			0
$691$	27.9609	−	16.1432i	1.06368	−	0.614118i	0.137235	−	0.990539i	$-0.456179\pi$
$691$	27.9609	−	16.1432i	1.06368	−	0.614118i	0.926449	+	0.376421i	$0.122845\pi$
$692$	9.15080			0.347861
$693$		0			0
$694$	−11.7735			−0.446917
$695$	−8.99525	+	5.19341i	−0.341209	+	0.196997i
$696$		0			0
$697$	1.80551	−	3.12723i	0.0683885	−	0.118452i
$698$	29.2237			1.10613
$699$		0			0
$700$	−2.64078	−	0.162142i	−0.0998120	−	0.00612839i
$701$		−	26.3883i		−	0.996673i	−0.866984	−	0.498337i	$-0.833944\pi$
$701$		−	26.3883i		−	0.996673i	0.866984	−	0.498337i	$-0.166056\pi$
$702$		0			0
$703$	8.90534	−	5.14150i	0.335871	−	0.193915i
$704$		−	0.751037i		−	0.0283058i
$705$		0			0
$706$	0.261415	−	0.150928i	0.00983849	−	0.00568025i
$707$	−6.77585	−	13.5983i	−0.254832	−	0.511416i
$708$		0			0
$709$	4.53937	+	7.86242i	0.170480	+	0.295279i	0.938588	−	0.345041i	$-0.112135\pi$
$709$	4.53937	+	7.86242i	0.170480	+	0.295279i	−0.768108	+	0.640320i	$0.778802\pi$
$710$	2.71670	+	4.70546i	0.101956	+	0.176593i
$711$		0			0
$712$	2.12093	+	1.22452i	0.0794854	+	0.0458909i
$713$	−15.7306	+	27.2462i	−0.589117	+	1.02038i
$714$		0			0
$715$	−1.18031	−	2.04435i	−0.0441410	−	0.0764545i
$716$		−	19.9538i		−	0.745707i
$717$		0			0
$718$	26.3949			0.985048
$719$	−19.1759	+	33.2136i	−0.715140	+	1.23866i	0.247766	+	0.968820i	$0.420304\pi$
$719$	−19.1759	+	33.2136i	−0.715140	+	1.23866i	−0.962906	+	0.269839i	$0.913030\pi$
$720$		0			0
$721$	−37.0713	+	18.4722i	−1.38061	+	0.687939i
$722$	14.6918	+	8.48234i	0.546774	+	0.315680i
$723$		0			0
$724$	18.7840	+	10.8449i	0.698100	+	0.403048i
$725$	5.23368	+	3.02167i	0.194374	+	0.112222i
$726$		0			0
$727$	8.55880	+	4.94142i	0.317428	+	0.183267i	0.650246	−	0.759724i	$-0.274666\pi$
$727$	8.55880	+	4.94142i	0.317428	+	0.183267i	−0.332817	+	0.942991i	$0.607999\pi$
$728$	−4.59153	+	6.93349i	−0.170173	+	0.256972i
$729$		0			0
$730$	−0.311597	+	0.539702i	−0.0115327	+	0.0199753i
$731$	−6.40164			−0.236773
$732$		0			0
$733$			6.99187i			0.258251i	0.991628	+	0.129125i	$0.0412169\pi$
$733$			6.99187i			0.258251i	−0.991628	+	0.129125i	$0.958783\pi$
$734$	4.86669	+	8.42936i	0.179633	+	0.311133i
$735$		0			0
$736$	−2.53076	+	4.38341i	−0.0932852	+	0.161575i
$737$	7.08483	+	4.09043i	0.260973	+	0.150673i
$738$		0			0
$739$	9.75535	+	16.8968i	0.358856	+	0.621558i	0.987770	−	0.155918i	$-0.0498334\pi$
$739$	9.75535	+	16.8968i	0.358856	+	0.621558i	−0.628914	+	0.777475i	$0.716500\pi$
$740$	−3.60391	−	6.24216i	−0.132482	−	0.229466i
$741$		0			0
$742$	2.40971	+	0.147955i	0.0884632	+	0.00543158i
$743$	−33.4098	+	19.2892i	−1.22569	+	0.707651i	−0.966125	−	0.258075i	$-0.916912\pi$
$743$	−33.4098	+	19.2892i	−1.22569	+	0.707651i	−0.259563	+	0.965726i	$0.583578\pi$
$744$		0			0
$745$			12.9684i			0.475126i
$746$	16.6784	−	9.62926i	0.610638	−	0.352552i
$747$		0			0
$748$		−	0.650573i		−	0.0237873i
$749$	−2.18226	+	35.5421i	−0.0797380	+	1.29868i
$750$		0			0
$751$	−19.7427			−0.720423			−0.360211	−	0.932871i	$-0.617295\pi$
$751$	−19.7427			−0.720423			−0.360211	+	0.932871i	$0.617295\pi$
$752$	1.72922	−	2.99510i	0.0630582	−	0.109220i
$753$		0			0
$754$	16.4502	−	9.49753i	0.599081	−	0.345880i
$755$	22.9105			0.833800
$756$		0			0
$757$	−21.2004			−0.770540			−0.385270	−	0.922804i	$-0.625892\pi$
$757$	−21.2004			−0.770540			−0.385270	+	0.922804i	$0.625892\pi$
$758$	25.4924	−	14.7180i	0.925926	−	0.534584i
$759$		0			0
$760$	−0.713322	+	1.23551i	−0.0258749	+	0.0448167i
$761$	−1.39505			−0.0505706			−0.0252853	−	0.999680i	$-0.508049\pi$
$761$	−1.39505			−0.0505706			−0.0252853	+	0.999680i	$0.508049\pi$
$762$		0			0
$763$	−18.3757	+	27.7484i	−0.665244	+	1.00456i
$764$		−	7.04674i		−	0.254942i
$765$		0			0
$766$	15.4216	−	8.90367i	0.557205	−	0.321703i
$767$			26.5224i			0.957670i
$768$		0			0
$769$	−10.8209	+	6.24747i	−0.390213	+	0.225289i	−0.682252	−	0.731117i	$-0.738999\pi$
$769$	−10.8209	+	6.24747i	−0.390213	+	0.225289i	0.292040	+	0.956406i	$0.405666\pi$
$770$	−1.09712	+	1.65672i	−0.0395375	+	0.0597040i
$771$		0			0
$772$	−1.20239	−	2.08260i	−0.0432749	−	0.0749543i
$773$	19.4887	+	33.7554i	0.700960	+	1.21410i	0.968130	+	0.250449i	$0.0805783\pi$
$773$	19.4887	+	33.7554i	0.700960	+	1.21410i	−0.267169	+	0.963650i	$0.586088\pi$
$774$		0			0
$775$	5.38301	+	3.10788i	0.193363	+	0.111638i
$776$	−5.33194	+	9.23519i	−0.191406	+	0.331524i
$777$		0			0
$778$	−6.26510	−	10.8515i	−0.224615	−	0.389044i
$779$			5.94717i			0.213079i
$780$		0			0
$781$	4.08068			0.146018
$782$	−2.19223	+	3.79706i	−0.0783941	+	0.135783i
$783$		0			0
$784$	6.94742	+	0.856363i	0.248122	+	0.0305844i
$785$	7.74720	+	4.47285i	0.276509	+	0.159643i
$786$		0			0
$787$	−24.6682	−	14.2422i	−0.879326	−	0.507679i	−0.00888998	−	0.999960i	$-0.502830\pi$
$787$	−24.6682	−	14.2422i	−0.879326	−	0.507679i	−0.870436	+	0.492281i	$0.836163\pi$
$788$	−1.37200	−	0.792122i	−0.0488753	−	0.0282182i
$789$		0			0
$790$	0.00506811	+	0.00292607i	0.000180315	+	0.000104105i
$791$	−7.42996	−	4.92030i	−0.264179	−	0.174946i
$792$		0			0
$793$	−16.8811	+	29.2389i	−0.599465	+	1.03830i
$794$	30.7784			1.09228
$795$		0			0
$796$		−	7.75147i		−	0.274744i
$797$	−3.94399	−	6.83119i	−0.139703	−	0.241973i	0.787681	−	0.616083i	$-0.211282\pi$
$797$	−3.94399	−	6.83119i	−0.139703	−	0.241973i	−0.927384	+	0.374110i	$0.877948\pi$
$798$		0			0
$799$	1.49791	−	2.59445i	0.0529922	−	0.0917852i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$		0			0
$802$	3.58577	+	6.21073i	0.126618	+	0.219309i
$803$	0.234021	+	0.405336i	0.00825841	+	0.0143040i
$804$		0			0
$805$	11.9860	−	5.97245i	0.422450	−	0.210501i
$806$	16.9196	−	9.76851i	0.595966	−	0.344081i
$807$		0			0
$808$			5.74239i			0.202017i
$809$	−2.59994	+	1.50108i	−0.0914092	+	0.0527751i	−0.545008	−	0.838431i	$-0.683473\pi$
$809$	−2.59994	+	1.50108i	−0.0914092	+	0.0527751i	0.453599	+	0.891206i	$0.350140\pi$
$810$		0			0
$811$			7.71594i			0.270943i	0.990781	+	0.135472i	$0.0432549\pi$
$811$			7.71594i			0.270943i	−0.990781	+	0.135472i	$0.956745\pi$
$812$	−13.3311	−	8.82816i	−0.467828	−	0.309808i
$813$		0			0
$814$	−5.41334			−0.189737
$815$	−8.68748	+	15.0472i	−0.304309	+	0.527079i
$816$		0			0
$817$	9.13067	−	5.27159i	0.319442	−	0.184430i
$818$	−26.6643			−0.932295
$819$		0			0
$820$	4.16864			0.145575
$821$	42.1560	−	24.3388i	1.47125	−	0.849429i	0.471775	−	0.881719i	$-0.343613\pi$
$821$	42.1560	−	24.3388i	1.47125	−	0.849429i	0.999479	+	0.0322902i	$0.0102801\pi$
$822$		0			0
$823$	24.3935	−	42.2508i	0.850304	−	1.47277i	−0.0306307	−	0.999531i	$-0.509752\pi$
$823$	24.3935	−	42.2508i	0.850304	−	1.47277i	0.880934	−	0.473238i	$-0.156915\pi$
$824$	15.6548			0.545360
$825$		0			0
$826$	19.9821	−	9.95682i	0.695266	−	0.346442i
$827$		−	28.6190i		−	0.995181i	−0.867412	−	0.497591i	$-0.834218\pi$
$827$		−	28.6190i		−	0.995181i	0.867412	−	0.497591i	$-0.165782\pi$
$828$		0			0
$829$	−22.2964	+	12.8728i	−0.774386	+	0.447092i	−0.834437	−	0.551103i	$-0.814207\pi$
$829$	−22.2964	+	12.8728i	−0.774386	+	0.447092i	0.0600511	+	0.998195i	$0.480874\pi$
$830$		−	2.03667i		−	0.0706939i
$831$		0			0
$832$	2.72204	−	1.57157i	0.0943698	−	0.0544844i
$833$	6.01809	+	0.741810i	0.208514	+	0.0257022i
$834$		0			0
$835$	−8.49076	−	14.7064i	−0.293835	−	0.508937i
$836$	0.535731	+	0.927914i	0.0185287	+	0.0320926i
$837$		0			0
$838$	21.1533	+	12.2128i	0.730727	+	0.421886i
$839$	−16.6271	+	28.7990i	−0.574032	+	0.994252i	0.422114	+	0.906543i	$0.361288\pi$
$839$	−16.6271	+	28.7990i	−0.574032	+	0.994252i	−0.996146	+	0.0877095i	$0.972045\pi$
$840$		0			0
$841$	3.76096	+	6.51417i	0.129688	+	0.224626i
$842$			17.6940i			0.609777i
$843$		0			0
$844$	13.2836			0.457242
$845$	−1.56033	+	2.70257i	−0.0536770	+	0.0929712i
$846$		0			0
$847$	−12.3141	−	24.7129i	−0.423117	−	0.849144i
$848$	−0.790248	−	0.456250i	−0.0271372	−	0.0156677i
$849$		0			0
$850$	0.750180	+	0.433117i	0.0257310	+	0.0148558i
$851$	31.5949	+	18.2413i	1.08306	+	0.625304i
$852$		0			0
$853$	0.801658	+	0.462837i	0.0274482	+	0.0158473i	0.513661	−	0.857993i	$-0.328289\pi$
$853$	0.801658	+	0.462837i	0.0274482	+	0.0158473i	−0.486213	+	0.873840i	$0.661622\pi$
$854$	28.3660	+	1.74165i	0.970665	+	0.0595982i
$855$		0			0
$856$	6.72947	−	11.6558i	0.230008	−	0.398386i
$857$	16.2250			0.554236			0.277118	−	0.960836i	$-0.410621\pi$
$857$	16.2250			0.554236			0.277118	+	0.960836i	$0.410621\pi$
$858$		0			0
$859$		−	22.9123i		−	0.781759i	−0.920442	−	0.390880i	$-0.872171\pi$
$859$		−	22.9123i		−	0.781759i	0.920442	−	0.390880i	$-0.127829\pi$
$860$	−3.69510	−	6.40010i	−0.126002	−	0.218242i
$861$		0			0
$862$	−11.8463	+	20.5184i	−0.403486	+	0.698859i
$863$	1.28485	+	0.741810i	0.0437369	+	0.0252515i	0.521709	−	0.853123i	$-0.325295\pi$
$863$	1.28485	+	0.741810i	0.0437369	+	0.0252515i	−0.477972	+	0.878375i	$0.658628\pi$
$864$		0			0
$865$	4.57540	+	7.92483i	0.155568	+	0.269452i
$866$	−12.0538	−	20.8779i	−0.409606	−	0.709459i
$867$		0			0
$868$	−13.7114	−	9.08004i	−0.465396	−	0.308197i
$869$	0.00380633	−	0.00219759i	0.000129121	−	7.45481e-5i
$870$		0			0
$871$			34.2374i			1.16009i
$872$	10.8938	−	6.28955i	0.368911	−	0.212991i
$873$		0			0
$874$		−	7.22100i		−	0.244254i
$875$	−1.17997	−	2.36805i	−0.0398903	−	0.0800548i
$876$		0			0
$877$	−40.6373			−1.37222			−0.686112	−	0.727496i	$-0.740684\pi$
$877$	−40.6373			−1.37222			−0.686112	+	0.727496i	$0.740684\pi$
$878$	0.534359	−	0.925536i	0.0180337	−	0.0312353i
$879$		0			0
$880$	0.650417	−	0.375518i	0.0219255	−	0.0126587i
$881$	−5.36428			−0.180727			−0.0903636	−	0.995909i	$-0.528803\pi$
$881$	−5.36428			−0.180727			−0.0903636	+	0.995909i	$0.528803\pi$
$882$		0			0
$883$	9.15422			0.308064			0.154032	−	0.988066i	$-0.450774\pi$
$883$	9.15422			0.308064			0.154032	+	0.988066i	$0.450774\pi$
$884$	2.35792	−	1.36135i	0.0793055	−	0.0457871i
$885$		0			0
$886$	−15.4796	+	26.8115i	−0.520048	+	0.900750i
$887$	36.1166			1.21268			0.606338	−	0.795207i	$-0.292638\pi$
$887$	36.1166			1.21268			0.606338	+	0.795207i	$0.292638\pi$
$888$		0			0
$889$	−7.45600	−	14.9633i	−0.250066	−	0.501851i
$890$			2.44904i			0.0820921i
$891$		0			0
$892$	−13.8018	+	7.96848i	−0.462119	+	0.266804i
$893$			4.93397i			0.165109i
$894$		0			0
$895$	17.2805	−	9.97688i	0.577622	−	0.333490i
$896$	−2.20591	−	1.46081i	−0.0736943	−	0.0488022i
$897$		0			0
$898$	11.2412	+	19.4703i	0.375123	+	0.649733i
$899$	18.7820	+	32.5313i	0.626414	+	1.08498i
$900$		0			0
$901$	−0.684539	−	0.395219i	−0.0228053	−	0.0131667i
$902$	1.56540	−	2.71135i	0.0521222	−	0.0902782i
$903$		0			0
$904$	1.68410	+	2.91695i	0.0560124	+	0.0970163i
$905$			21.6898i			0.720995i
$906$		0			0
$907$	23.0774			0.766272			0.383136	−	0.923692i	$-0.374844\pi$
$907$	23.0774			0.766272			0.383136	+	0.923692i	$0.374844\pi$
$908$	6.59397	−	11.4211i	0.218828	−	0.379022i
$909$		0			0
$910$	−8.30034	−	0.509636i	−0.275154	−	0.0168943i
$911$	−30.4817	−	17.5986i	−1.00990	−	0.583068i	−0.0987403	−	0.995113i	$-0.531481\pi$
$911$	−30.4817	−	17.5986i	−1.00990	−	0.583068i	−0.911163	+	0.412045i	$0.864815\pi$
$912$		0			0
$913$	−1.32469	−	0.764808i	−0.0438407	−	0.0253114i
$914$	35.7886	+	20.6626i	1.18378	+	0.683457i
$915$		0			0
$916$	17.1072	+	9.87685i	0.565238	+	0.326340i
$917$	12.9476	+	25.9842i	0.427567	+	0.858074i
$918$		0			0
$919$	9.86747	−	17.0910i	0.325498	−	0.563779i	−0.656115	−	0.754661i	$-0.727801\pi$
$919$	9.86747	−	17.0910i	0.325498	−	0.563779i	0.981613	+	0.190882i	$0.0611348\pi$
$920$	−5.06153			−0.166874
$921$		0			0
$922$			26.0218i			0.856983i
$923$	8.53897	+	14.7899i	0.281063	+	0.486816i
$924$		0			0
$925$	3.60391	−	6.24216i	0.118496	−	0.205241i
$926$	9.60876	+	5.54762i	0.315763	+	0.182306i
$927$		0			0
$928$	3.02167	+	5.23368i	0.0991911	+	0.171804i
$929$	−26.1679	−	45.3241i	−0.858540	−	1.48703i	−0.873322	−	0.487144i	$-0.838039\pi$
$929$	−26.1679	−	45.3241i	−0.858540	−	1.48703i	0.0147821	−	0.999891i	$-0.495295\pi$
$930$		0			0
$931$	−9.19447	+	3.89771i	−0.301337	+	0.127742i
$932$	−23.8501	+	13.7699i	−0.781236	+	0.451047i
$933$		0			0
$934$		−	37.4732i		−	1.22616i
$935$	0.563413	−	0.325287i	0.0184256	−	0.0106380i
$936$		0			0
$937$			36.5989i			1.19563i	0.801633	+	0.597816i	$0.203965\pi$
$937$			36.5989i			1.19563i	−0.801633	+	0.597816i	$0.796035\pi$
$938$	25.7946	−	12.8531i	0.842223	−	0.419669i
$939$		0			0
$940$	3.45844			0.112802
$941$	−6.92046	+	11.9866i	−0.225601	+	0.390752i	−0.956499	−	0.291734i	$-0.905768\pi$
$941$	−6.92046	+	11.9866i	−0.225601	+	0.390752i	0.730899	+	0.682486i	$0.239101\pi$
$942$		0			0
$943$	−18.2729	+	10.5498i	−0.595047	+	0.343550i
$944$	−8.43820			−0.274640
$945$		0			0
$946$	−5.55031			−0.180456
$947$	18.8005	−	10.8545i	0.610935	−	0.352724i	−0.162396	−	0.986726i	$-0.551922\pi$
$947$	18.8005	−	10.8545i	0.610935	−	0.352724i	0.773331	+	0.634002i	$0.218589\pi$
$948$		0			0
$949$	−0.979394	+	1.69636i	−0.0317925	+	0.0550662i
$950$	−1.42664			−0.0462865
$951$		0			0
$952$	−1.91083	−	1.26540i	−0.0619305	−	0.0410119i
$953$		−	7.37332i		−	0.238845i	−0.992844	−	0.119423i	$-0.961896\pi$
$953$		−	7.37332i		−	0.238845i	0.992844	−	0.119423i	$-0.0381043\pi$
$954$		0			0
$955$	6.10266	−	3.52337i	0.197477	−	0.114014i
$956$			7.53135i			0.243581i
$957$		0			0
$958$	12.0925	−	6.98162i	0.390691	−	0.225566i
$959$	50.2920	−	25.0598i	1.62401	−	0.809224i
$960$		0			0
$961$	3.81785	+	6.61271i	0.123156	+	0.213313i
$962$	−11.3276	−	19.6200i	−0.365217	−	0.632574i
$963$		0			0
$964$	10.3761	+	5.99066i	0.334193	+	0.192946i
$965$	1.20239	−	2.08260i	0.0387062	−	0.0670412i
$966$		0			0
$967$	3.66184	+	6.34250i	0.117757	+	0.203961i	0.918878	−	0.394541i	$-0.129096\pi$
$967$	3.66184	+	6.34250i	0.117757	+	0.203961i	−0.801122	+	0.598502i	$0.795763\pi$
$968$			10.4359i			0.335424i
$969$		0			0
$970$	−10.6639			−0.342397
$971$	−25.1933	+	43.6361i	−0.808491	+	1.40035i	0.105418	+	0.994428i	$0.466382\pi$
$971$	−25.1933	+	43.6361i	−0.808491	+	1.40035i	−0.913909	+	0.405920i	$0.866951\pi$
$972$		0			0
$973$	22.9124	+	15.1731i	0.734537	+	0.486429i
$974$	−3.30309	−	1.90704i	−0.105838	−	0.0611055i
$975$		0			0
$976$	−9.30244	−	5.37077i	−0.297764	−	0.171914i
$977$	51.0807	+	29.4915i	1.63422	+	0.943515i	0.982773	+	0.184818i	$0.0591696\pi$
$977$	51.0807	+	29.4915i	1.63422	+	0.943515i	0.651444	+	0.758697i	$0.274164\pi$
$978$		0			0
$979$	1.59290	+	0.919661i	0.0509093	+	0.0293925i
$980$	2.73208	+	6.44482i	0.0872730	+	0.205872i
$981$		0			0
$982$	13.7053	−	23.7383i	0.437354	−	0.757520i
$983$	10.7629			0.343284			0.171642	−	0.985159i	$-0.445093\pi$
$983$	10.7629			0.343284			0.171642	+	0.985159i	$0.445093\pi$
$984$		0			0
$985$		−	1.58424i		−	0.0504782i
$986$	2.61747	+	4.53359i	0.0833572	+	0.144379i
$987$		0			0
$988$	−2.24207	+	3.88339i	−0.0713299	+	0.123547i
$989$	32.3943	+	18.7028i	1.03008	+	0.594716i
$990$		0			0
$991$	−23.9427	−	41.4700i	−0.760566	−	1.31734i	−0.942559	−	0.334039i	$-0.891588\pi$
$991$	−23.9427	−	41.4700i	−0.760566	−	1.31734i	0.181993	−	0.983300i	$-0.441745\pi$
$992$	3.10788	+	5.38301i	0.0986753	+	0.170911i
$993$		0			0
$994$	7.93715	−	11.9856i	0.251751	−	0.380160i
$995$	6.71297	−	3.87574i	0.212816	−	0.122869i
$996$		0			0
$997$		−	27.4211i		−	0.868435i	−0.900808	−	0.434217i	$-0.857025\pi$
$997$		−	27.4211i		−	0.868435i	0.900808	−	0.434217i	$-0.142975\pi$
$998$	−22.3343	+	12.8947i	−0.706980	+	0.408175i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.t.b.1601.4		28
3.2	odd	2		630.2.t.b.551.12	yes	28
7.3	odd	6		1890.2.bk.b.521.10		28
9.4	even	3		630.2.bk.b.131.6	yes	28
9.5	odd	6		1890.2.bk.b.341.10		28
21.17	even	6		630.2.bk.b.101.13	yes	28
63.31	odd	6		630.2.t.b.311.12	✓	28
63.59	even	6	inner	1890.2.t.b.1151.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.12	✓	28	63.31	odd	6
630.2.t.b.551.12	yes	28	3.2	odd	2
630.2.bk.b.101.13	yes	28	21.17	even	6
630.2.bk.b.131.6	yes	28	9.4	even	3
1890.2.t.b.1151.4		28	63.59	even	6	inner
1890.2.t.b.1601.4		28	1.1	even	1	trivial
1890.2.bk.b.341.10		28	9.5	odd	6
1890.2.bk.b.521.10		28	7.3	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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-1.17997 - 2.36805i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-1.17997 - 2.36805i) q^{7} +1.00000i q^{8} +(-0.866025 + 0.500000i) q^{10} +0.751037i q^{11} +(-2.72204 + 1.57157i) q^{13} +(2.20591 + 1.46081i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.433117 - 0.750180i) q^{17} +(1.23551 + 0.713322i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-0.375518 - 0.650417i) q^{22} +5.06153i q^{23} +1.00000 q^{25} +(1.57157 - 2.72204i) q^{26} +(-2.64078 - 0.162142i) q^{28} +(5.23368 + 3.02167i) q^{29} +(5.38301 + 3.10788i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.750180 + 0.433117i) q^{34} +(-1.17997 - 2.36805i) q^{35} +(3.60391 - 6.24216i) q^{37} -1.42664 q^{38} +1.00000i q^{40} +(2.08432 + 3.61015i) q^{41} +(3.69510 - 6.40010i) q^{43} +(0.650417 + 0.375518i) q^{44} +(-2.53076 - 4.38341i) q^{46} +(1.72922 + 2.99510i) q^{47} +(-4.21534 + 5.58846i) q^{49} +(-0.866025 + 0.500000i) q^{50} +3.14314i q^{52} +(0.790248 - 0.456250i) q^{53} +0.751037i q^{55} +(2.36805 - 1.17997i) q^{56} -6.04334 q^{58} +(4.21910 - 7.30769i) q^{59} +(9.30244 - 5.37077i) q^{61} -6.21576 q^{62} -1.00000 q^{64} +(-2.72204 + 1.57157i) q^{65} +(5.44637 - 9.43339i) q^{67} -0.866234 q^{68} +(2.20591 + 1.46081i) q^{70} -5.43339i q^{71} +(0.539702 - 0.311597i) q^{73} +7.20782i q^{74} +(1.23551 - 0.713322i) q^{76} +(1.77849 - 0.886201i) q^{77} +(-0.00292607 - 0.00506811i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-3.61015 - 2.08432i) q^{82} +(-1.01834 + 1.76381i) q^{83} +(-0.433117 - 0.750180i) q^{85} +7.39020i q^{86} -0.751037 q^{88} +(1.22452 - 2.12093i) q^{89} +(6.93349 + 4.59153i) q^{91} +(4.38341 + 2.53076i) q^{92} +(-2.99510 - 1.72922i) q^{94} +(1.23551 + 0.713322i) q^{95} +(9.23519 + 5.33194i) q^{97} +(0.856363 - 6.94742i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7}+O(q^{10}) \) 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7	\( 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7} - 6 q^{14} - 14 q^{16} + 6 q^{17} - 6 q^{19} + 14 q^{20} - 6 q^{22} + 28 q^{25} - 12 q^{26} - 8 q^{28} - 12 q^{31} - 4 q^{35} + 4 q^{37} + 12 q^{38} - 18 q^{41} + 28 q^{43} - 18 q^{46} - 30 q^{47} - 14 q^{49} + 42 q^{53} - 6 q^{56} - 12 q^{58} + 24 q^{59} + 24 q^{61} + 12 q^{62} - 28 q^{64} - 40 q^{67} + 12 q^{68} - 6 q^{70} + 6 q^{73} - 6 q^{76} + 24 q^{77} + 2 q^{79} - 14 q^{80} + 24 q^{82} + 18 q^{83} + 6 q^{85} - 12 q^{88} - 6 q^{89} + 66 q^{91} + 30 q^{92} + 42 q^{94} - 6 q^{95} - 72 q^{97} + 24 q^{98}+O(q^{100}) \) 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7 - 6 * q^14 - 14 * q^16 + 6 * q^17 - 6 * q^19 + 14 * q^20 - 6 * q^22 + 28 * q^25 - 12 * q^26 - 8 * q^28 - 12 * q^31 - 4 * q^35 + 4 * q^37 + 12 * q^38 - 18 * q^41 + 28 * q^43 - 18 * q^46 - 30 * q^47 - 14 * q^49 + 42 * q^53 - 6 * q^56 - 12 * q^58 + 24 * q^59 + 24 * q^61 + 12 * q^62 - 28 * q^64 - 40 * q^67 + 12 * q^68 - 6 * q^70 + 6 * q^73 - 6 * q^76 + 24 * q^77 + 2 * q^79 - 14 * q^80 + 24 * q^82 + 18 * q^83 + 6 * q^85 - 12 * q^88 - 6 * q^89 + 66 * q^91 + 30 * q^92 + 42 * q^94 - 6 * q^95 - 72 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more