LMFDB - Embedded newform 1764.2.w.a.509.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(509,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1764.509");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.w (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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3x^{14} - 9x^{12} - 9x^{10} + 225x^{8} - 81x^{6} - 729x^{4} - 2187x^{2} + 6561 $ x^16 - 3x^14 - 9x^12 - 9x^10 + 225x^8 - 81x^6 - 729x^4 - 2187*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			509.5
Root			$1.69483 + 0.357142i$ of defining polynomial
Character	$\chi$	$=$	1764.509
Dual form			1764.2.w.a.1109.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.538121 - 1.64634i) q^{3} +(1.21244 + 2.10001i) q^{5} +(-2.42085 - 1.77186i) q^{9} +O(q^{10})$	\(q+(0.538121 - 1.64634i) q^{3} +(1.21244 + 2.10001i) q^{5} +(-2.42085 - 1.77186i) q^{9} +(-2.09680 - 1.21059i) q^{11} +(-4.73574 - 2.73418i) q^{13} +(4.10976 - 0.866025i) q^{15} +(-1.29034 - 2.23494i) q^{17} +(-0.348755 - 0.201354i) q^{19} +(-3.06895 + 1.77186i) q^{23} +(-0.440020 + 0.762137i) q^{25} +(-4.21979 + 3.03206i) q^{27} +(-6.31784 + 3.64761i) q^{29} +4.20001i q^{31} +(-3.12137 + 2.80060i) q^{33} +(1.59680 - 2.76574i) q^{37} +(-7.04978 + 6.32530i) q^{39} +(4.03924 - 6.99618i) q^{41} +(-4.22573 - 7.31918i) q^{43} +(0.785780 - 7.23208i) q^{45} +4.51537 q^{47} +(-4.37383 + 0.921671i) q^{51} +(-12.1493 + 7.01442i) q^{53} -5.87106i q^{55} +(-0.519169 + 0.465816i) q^{57} +0.155809 q^{59} -11.8112i q^{61} -13.2601i q^{65} -5.07364 q^{67} +(1.26561 + 6.00600i) q^{69} -8.73987i q^{71} +(7.62339 - 4.40137i) q^{73} +(1.01795 + 1.13454i) q^{75} -11.3315 q^{79} +(2.72104 + 8.57881i) q^{81} +(7.50937 + 13.0066i) q^{83} +(3.12893 - 5.41946i) q^{85} +(2.60542 + 12.3641i) q^{87} +(7.83339 - 13.5678i) q^{89} +(6.91464 + 2.26012i) q^{93} -0.976519i q^{95} +(4.97713 - 2.87355i) q^{97} +(2.93105 + 6.64589i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{9}+O(q^{10}) $ 16 * q - 6 * q^9	$ 16 q - 6 q^{9} - 6 q^{11} - 12 q^{15} - 6 q^{23} - 8 q^{25} - 12 q^{29} - 2 q^{37} - 36 q^{39} + 4 q^{43} + 12 q^{51} + 36 q^{53} - 42 q^{57} - 28 q^{67} - 40 q^{79} - 18 q^{81} + 6 q^{85} - 6 q^{93} + 90 q^{99}+O(q^{100}) $ 16 * q - 6 * q^9 - 6 * q^11 - 12 * q^15 - 6 * q^23 - 8 * q^25 - 12 * q^29 - 2 * q^37 - 36 * q^39 + 4 * q^43 + 12 * q^51 + 36 * q^53 - 42 * q^57 - 28 * q^67 - 40 * q^79 - 18 * q^81 + 6 * q^85 - 6 * q^93 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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			0
$2$		0			0
$3$	0.538121	−	1.64634i	0.310685	−	0.950513i
$3$	0.538121	−	1.64634i	0.310685	−	0.950513i
$4$		0			0
$5$	1.21244	+	2.10001i	0.542220	+	0.939152i	0.998776	+	0.0494574i	$0.0157492\pi$
$5$	1.21244	+	2.10001i	0.542220	+	0.939152i	−0.456557	+	0.889694i	$0.650917\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2.42085	−	1.77186i	−0.806950	−	0.590619i
$10$		0			0
$11$	−2.09680	−	1.21059i	−0.632209	−	0.365006i	0.149398	−	0.988777i	$-0.452267\pi$
$11$	−2.09680	−	1.21059i	−0.632209	−	0.365006i	−0.781607	+	0.623771i	$0.785600\pi$
$12$		0			0
$13$	−4.73574	−	2.73418i	−1.31346	−	0.758325i	−0.330790	−	0.943704i	$-0.607315\pi$
$13$	−4.73574	−	2.73418i	−1.31346	−	0.758325i	−0.982667	+	0.185380i	$0.940648\pi$
$14$		0			0
$15$	4.10976	−	0.866025i	1.06114	−	0.223607i
$16$		0			0
$17$	−1.29034	−	2.23494i	−0.312954	−	0.542053i	0.666046	−	0.745911i	$-0.267985\pi$
$17$	−1.29034	−	2.23494i	−0.312954	−	0.542053i	−0.979001	+	0.203858i	$0.934652\pi$
$18$		0			0
$19$	−0.348755	−	0.201354i	−0.0800100	−	0.0461938i	0.459461	−	0.888198i	$-0.348043\pi$
$19$	−0.348755	−	0.201354i	−0.0800100	−	0.0461938i	−0.539471	+	0.842004i	$0.681376\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.06895	+	1.77186i	−0.639920	+	0.369458i	−0.784584	−	0.620023i	$-0.787123\pi$
$23$	−3.06895	+	1.77186i	−0.639920	+	0.369458i	0.144664	+	0.989481i	$0.453790\pi$
$24$		0			0
$25$	−0.440020	+	0.762137i	−0.0880040	+	0.152427i
$26$		0			0
$27$	−4.21979	+	3.03206i	−0.812098	+	0.583520i
$28$		0			0
$29$	−6.31784	+	3.64761i	−1.17319	+	0.677343i	−0.954430	−	0.298435i	$-0.903535\pi$
$29$	−6.31784	+	3.64761i	−1.17319	+	0.677343i	−0.218763	+	0.975778i	$0.570202\pi$
$30$		0			0
$31$			4.20001i			0.754345i	0.926143	+	0.377172i	$0.123104\pi$
$31$			4.20001i			0.754345i	−0.926143	+	0.377172i	$0.876896\pi$
$32$		0			0
$33$	−3.12137	+	2.80060i	−0.543361	+	0.487522i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.59680	−	2.76574i	0.262513	−	0.454685i	−0.704396	−	0.709807i	$-0.748782\pi$
$37$	1.59680	−	2.76574i	0.262513	−	0.454685i	0.966909	+	0.255122i	$0.0821155\pi$
$38$		0			0
$39$	−7.04978	+	6.32530i	−1.12887	+	1.01286i
$40$		0			0
$41$	4.03924	−	6.99618i	0.630824	−	1.09262i	−0.356560	−	0.934273i	$-0.616050\pi$
$41$	4.03924	−	6.99618i	0.630824	−	1.09262i	0.987384	−	0.158346i	$-0.0506163\pi$
$42$		0			0
$43$	−4.22573	−	7.31918i	−0.644418	−	1.11616i	−0.984436	−	0.175745i	$-0.943766\pi$
$43$	−4.22573	−	7.31918i	−0.644418	−	1.11616i	0.340018	−	0.940419i	$-0.389567\pi$
$44$		0			0
$45$	0.785780	−	7.23208i	0.117137	−	1.07809i
$46$		0			0
$47$	4.51537			0.658635			0.329317	−	0.944219i	$-0.393181\pi$
$47$	4.51537			0.658635			0.329317	+	0.944219i	$0.393181\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−4.37383	+	0.921671i	−0.612458	+	0.129060i
$52$		0			0
$53$	−12.1493	+	7.01442i	−1.66884	+	0.963505i	−0.700575	+	0.713579i	$0.747073\pi$
$53$	−12.1493	+	7.01442i	−1.66884	+	0.963505i	−0.968265	+	0.249926i	$0.919594\pi$
$54$		0			0
$55$		−	5.87106i		−	0.791654i
$56$		0			0
$57$	−0.519169	+	0.465816i	−0.0687657	+	0.0616989i
$58$		0			0
$59$	0.155809			0.0202846			0.0101423	−	0.999949i	$-0.496772\pi$
$59$	0.155809			0.0202846			0.0101423	+	0.999949i	$0.496772\pi$
$60$		0			0
$61$		−	11.8112i		−	1.51227i	−0.654415	−	0.756136i	$-0.727085\pi$
$61$		−	11.8112i		−	1.51227i	0.654415	−	0.756136i	$-0.272915\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	13.2601i		−	1.64471i
$66$		0			0
$67$	−5.07364			−0.619844			−0.309922	−	0.950762i	$-0.600303\pi$
$67$	−5.07364			−0.619844			−0.309922	+	0.950762i	$0.600303\pi$
$68$		0			0
$69$	1.26561	+	6.00600i	0.152361	+	0.723037i
$70$		0			0
$71$		−	8.73987i		−	1.03723i	−0.855007	−	0.518616i	$-0.826448\pi$
$71$		−	8.73987i		−	1.03723i	0.855007	−	0.518616i	$-0.173552\pi$
$72$		0			0
$73$	7.62339	−	4.40137i	0.892251	−	0.515141i	0.0175727	−	0.999846i	$-0.494406\pi$
$73$	7.62339	−	4.40137i	0.892251	−	0.515141i	0.874678	+	0.484704i	$0.161073\pi$
$74$		0			0
$75$	1.01795	+	1.13454i	0.117543	+	0.131006i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−11.3315			−1.27489			−0.637447	−	0.770494i	$-0.720009\pi$
$79$	−11.3315			−1.27489			−0.637447	+	0.770494i	$0.720009\pi$
$80$		0			0
$81$	2.72104	+	8.57881i	0.302337	+	0.953201i
$82$		0			0
$83$	7.50937	+	13.0066i	0.824260	+	1.42766i	0.902483	+	0.430725i	$0.141742\pi$
$83$	7.50937	+	13.0066i	0.824260	+	1.42766i	−0.0782227	+	0.996936i	$0.524925\pi$
$84$		0			0
$85$	3.12893	−	5.41946i	0.339380	−	0.587823i
$86$		0			0
$87$	2.60542	+	12.3641i	0.279331	+	1.32558i
$88$		0			0
$89$	7.83339	−	13.5678i	0.830338	−	1.43819i	−0.0674328	−	0.997724i	$-0.521481\pi$
$89$	7.83339	−	13.5678i	0.830338	−	1.43819i	0.897771	−	0.440463i	$-0.145186\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	6.91464	+	2.26012i	0.717015	+	0.234363i
$94$		0			0
$95$		−	0.976519i		−	0.100189i
$96$		0			0
$97$	4.97713	−	2.87355i	0.505351	−	0.291765i	−0.225569	−	0.974227i	$-0.572424\pi$
$97$	4.97713	−	2.87355i	0.505351	−	0.291765i	0.730921	+	0.682462i	$0.239091\pi$
$98$		0			0
$99$	2.93105	+	6.64589i	0.294582	+	0.667937i
$100$		0			0
$101$	−4.83838	+	8.38031i	−0.481436	+	0.833872i	−0.999773	−	0.0213045i	$-0.993218\pi$
$101$	−4.83838	+	8.38031i	−0.481436	+	0.833872i	0.518337	+	0.855177i	$0.326551\pi$
$102$		0			0
$103$	−16.6863	+	9.63382i	−1.64415	+	0.949249i	−0.664811	+	0.747012i	$0.731488\pi$
$103$	−16.6863	+	9.63382i	−1.64415	+	0.949249i	−0.979337	+	0.202237i	$0.935179\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.944715	−	0.545431i	−0.0913290	−	0.0527288i	0.453640	−	0.891185i	$-0.350125\pi$
$107$	−0.944715	−	0.545431i	−0.0913290	−	0.0527288i	−0.544969	+	0.838456i	$0.683459\pi$
$108$		0			0
$109$	−1.15678	−	2.00360i	−0.110800	−	0.191910i	0.805293	−	0.592877i	$-0.202008\pi$
$109$	−1.15678	−	2.00360i	−0.110800	−	0.191910i	−0.916093	+	0.400966i	$0.868674\pi$
$110$		0			0
$111$	−3.69407	−	4.11718i	−0.350626	−	0.390785i
$112$		0			0
$113$	13.8868	+	8.01754i	1.30636	+	0.754227i	0.981487	−	0.191531i	$-0.0613453\pi$
$113$	13.8868	+	8.01754i	1.30636	+	0.754227i	0.324872	+	0.945758i	$0.394679\pi$
$114$		0			0
$115$	−7.44183	−	4.29654i	−0.693954	−	0.400655i
$116$		0			0
$117$	6.61993	+	15.0101i	0.612013	+	1.38768i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−2.56895	−	4.44955i	−0.233541	−	0.404505i
$122$		0			0
$123$	−9.34446	−	10.4147i	−0.842561	−	0.939066i
$124$		0			0
$125$	9.99041			0.893569
$126$		0			0
$127$	−3.06425			−0.271909			−0.135954	−	0.990715i	$-0.543410\pi$
$127$	−3.06425			−0.271909			−0.135954	+	0.990715i	$0.543410\pi$
$128$		0			0
$129$	−14.3238	+	3.01837i	−1.26114	+	0.265753i
$130$		0			0
$131$	−5.73151	−	9.92727i	−0.500765	−	0.867350i	−1.00000		0.000883062i	$-0.999719\pi$
$131$	−5.73151	−	9.92727i	−0.500765	−	0.867350i	0.499235	−	0.866467i	$-0.333614\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−11.4836	−	5.18539i	−0.988350	−	0.446288i
$136$		0			0
$137$	−1.71002	−	0.987278i	−0.146096	−	0.0843488i	0.425170	−	0.905114i	$-0.360214\pi$
$137$	−1.71002	−	0.987278i	−0.146096	−	0.0843488i	−0.571266	+	0.820765i	$0.693548\pi$
$138$		0			0
$139$	5.37804	+	3.10501i	0.456159	+	0.263364i	0.710428	−	0.703770i	$-0.248501\pi$
$139$	5.37804	+	3.10501i	0.456159	+	0.263364i	−0.254269	+	0.967134i	$0.581835\pi$
$140$		0			0
$141$	2.42982	−	7.43383i	0.204628	−	0.626041i
$142$		0			0
$143$	6.61993	+	11.4661i	0.553587	+	0.958840i
$144$		0			0
$145$	−15.3200	−	8.84500i	−1.27226	−	0.734537i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−10.5389	+	6.08462i	−0.863378	+	0.498472i	−0.865142	−	0.501527i	$-0.832772\pi$
$149$	−10.5389	+	6.08462i	−0.863378	+	0.498472i	0.00176397	+	0.999998i	$0.499439\pi$
$150$		0			0
$151$	−5.31784	+	9.21076i	−0.432759	+	0.749561i	−0.997110	−	0.0759740i	$-0.975793\pi$
$151$	−5.31784	+	9.21076i	−0.432759	+	0.749561i	0.564350	+	0.825535i	$0.309127\pi$
$152$		0			0
$153$	−0.836270	+	7.69677i	−0.0676084	+	0.622247i
$154$		0			0
$155$	−8.82006	+	5.09226i	−0.708444	+	0.409021i
$156$		0			0
$157$		−	3.53516i		−	0.282136i	−0.990000	−	0.141068i	$-0.954946\pi$
$157$		−	3.53516i		−	0.282136i	0.990000	−	0.141068i	$-0.0450537\pi$
$158$		0			0
$159$	5.01029	+	23.7765i	0.397341	+	1.88560i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−3.16575	+	5.48324i	−0.247961	+	0.429481i	−0.962960	−	0.269645i	$-0.913094\pi$
$163$	−3.16575	+	5.48324i	−0.247961	+	0.429481i	0.714999	+	0.699125i	$0.246427\pi$
$164$		0			0
$165$	−9.66575	−	3.15935i	−0.752478	−	0.245955i
$166$		0			0
$167$	−8.39779	+	14.5454i	−0.649840	+	1.12556i	0.333320	+	0.942814i	$0.391831\pi$
$167$	−8.39779	+	14.5454i	−0.649840	+	1.12556i	−0.983161	+	0.182743i	$0.941502\pi$
$168$		0			0
$169$	8.45146	+	14.6384i	0.650112	+	1.12603i
$170$		0			0
$171$	0.487514	+	1.10539i	0.0372811	+	0.0845316i
$172$		0			0
$173$	16.6170			1.26337			0.631684	−	0.775226i	$-0.282364\pi$
$173$	16.6170			1.26337			0.631684	+	0.775226i	$0.282364\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.0838440	−	0.256513i	0.00630210	−	0.0192807i
$178$		0			0
$179$	12.6082	−	7.27937i	0.942384	−	0.544086i	0.0516773	−	0.998664i	$-0.483543\pi$
$179$	12.6082	−	7.27937i	0.942384	−	0.544086i	0.890707	+	0.454578i	$0.150210\pi$
$180$		0			0
$181$		−	4.02355i		−	0.299068i	−0.988757	−	0.149534i	$-0.952223\pi$
$181$		−	4.02355i		−	0.299068i	0.988757	−	0.149534i	$-0.0477774\pi$
$182$		0			0
$183$	−19.4452	−	6.35587i	−1.43743	−	0.469839i
$184$		0			0
$185$	7.74410			0.569358
$186$		0			0
$187$			6.24830i			0.456921i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			8.41775i			0.609087i	0.952498	+	0.304543i	$0.0985039\pi$
$191$			8.41775i			0.609087i	−0.952498	+	0.304543i	$0.901496\pi$
$192$		0			0
$193$	−8.63567			−0.621609			−0.310805	−	0.950474i	$-0.600599\pi$
$193$	−8.63567			−0.621609			−0.310805	+	0.950474i	$0.600599\pi$
$194$		0			0
$195$	−21.8306	−	7.13555i	−1.56332	−	0.510987i
$196$		0			0
$197$		−	23.3303i		−	1.66221i	−0.556112	−	0.831107i	$-0.687708\pi$
$197$		−	23.3303i		−	1.66221i	0.556112	−	0.831107i	$-0.312292\pi$
$198$		0			0
$199$	12.2441	−	7.06913i	0.867960	−	0.501117i	0.00129041	−	0.999999i	$-0.499589\pi$
$199$	12.2441	−	7.06913i	0.867960	−	0.501117i	0.866670	+	0.498882i	$0.166256\pi$
$200$		0			0
$201$	−2.73024	+	8.35293i	−0.192576	+	0.589170i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	19.5894			1.36818
$206$		0			0
$207$	10.5689	+	1.14834i	0.734593	+	0.0798150i
$208$		0			0
$209$	0.487514	+	0.844399i	0.0337221	+	0.0584083i
$210$		0			0
$211$	−6.75786	+	11.7050i	−0.465230	+	0.805802i	−0.999212	−	0.0396938i	$-0.987362\pi$
$211$	−6.75786	+	11.7050i	−0.465230	+	0.805802i	0.533982	+	0.845496i	$0.320695\pi$
$212$		0			0
$213$	−14.3888	−	4.70311i	−0.985902	−	0.322252i
$214$		0			0
$215$	10.2469	−	17.7481i	0.698832	−	1.21041i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−3.14382	−	14.9191i	−0.212440	−	1.00814i
$220$		0			0
$221$			14.1121i			0.949284i
$222$		0			0
$223$	13.4054	−	7.73961i	0.897692	−	0.518283i	0.0212411	−	0.999774i	$-0.493238\pi$
$223$	13.4054	−	7.73961i	0.897692	−	0.518283i	0.876451	+	0.481492i	$0.159905\pi$
$224$		0			0
$225$	2.41562	−	1.06537i	0.161041	−	0.0710245i
$226$		0			0
$227$	7.50835	−	13.0048i	0.498347	−	0.863162i	−0.501651	−	0.865070i	$-0.667274\pi$
$227$	7.50835	−	13.0048i	0.498347	−	0.863162i	0.999998	+	0.00190793i	$0.000607314\pi$
$228$		0			0
$229$	−16.9685	+	9.79677i	−1.12131	+	0.647389i	−0.941735	−	0.336355i	$-0.890806\pi$
$229$	−16.9685	+	9.79677i	−1.12131	+	0.647389i	−0.179575	+	0.983744i	$0.557472\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	16.9283	+	9.77356i	1.10901	+	0.640287i	0.938573	−	0.345081i	$-0.112149\pi$
$233$	16.9283	+	9.77356i	1.10901	+	0.640287i	0.170437	+	0.985369i	$0.445482\pi$
$234$		0			0
$235$	5.47462	+	9.48232i	0.357125	+	0.618558i
$236$		0			0
$237$	−6.09772	+	18.6555i	−0.396090	+	1.21180i
$238$		0			0
$239$	7.36210	+	4.25051i	0.476215	+	0.274943i	0.718838	−	0.695178i	$-0.244674\pi$
$239$	7.36210	+	4.25051i	0.476215	+	0.274943i	−0.242623	+	0.970121i	$0.578008\pi$
$240$		0			0
$241$	−7.21480	−	4.16547i	−0.464746	−	0.268321i	0.249292	−	0.968428i	$-0.419802\pi$
$241$	−7.21480	−	4.16547i	−0.464746	−	0.268321i	−0.714038	+	0.700107i	$0.753136\pi$
$242$		0			0
$243$	15.5879	+	0.136700i	0.999962	+	0.00876928i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.10108	+	1.90712i	0.0700598	+	0.121347i
$248$		0			0
$249$	25.4542	−	5.36382i	1.61310	−	0.339918i
$250$		0			0
$251$	13.5763			0.856928			0.428464	−	0.903559i	$-0.359055\pi$
$251$	13.5763			0.856928			0.428464	+	0.903559i	$0.359055\pi$
$252$		0			0
$253$	8.57997			0.539418
$254$		0			0
$255$	−7.23852	−	8.06760i	−0.453294	−	0.505213i
$256$		0			0
$257$	2.99030	+	5.17935i	0.186530	+	0.323079i	0.944091	−	0.329685i	$-0.106943\pi$
$257$	2.99030	+	5.17935i	0.186530	+	0.323079i	−0.757561	+	0.652764i	$0.773609\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	21.7576	+	2.36401i	1.34676	+	0.146328i
$262$		0			0
$263$	2.91506	+	1.68301i	0.179750	+	0.103779i	0.587175	−	0.809460i	$-0.300240\pi$
$263$	2.91506	+	1.68301i	0.179750	+	0.103779i	−0.407425	+	0.913239i	$0.633573\pi$
$264$		0			0
$265$	−29.4607	−	17.0091i	−1.80976	−	1.04486i
$266$		0			0
$267$	−18.1219	−	20.1975i	−1.10904	−	1.23607i
$268$		0			0
$269$	6.14112	+	10.6367i	0.374431	+	0.648533i	0.990242	−	0.139361i	$-0.0445048\pi$
$269$	6.14112	+	10.6367i	0.374431	+	0.648533i	−0.615811	+	0.787894i	$0.711171\pi$
$270$		0			0
$271$	−25.4823	−	14.7122i	−1.54794	−	0.893703i	−0.998299	−	0.0583012i	$-0.981432\pi$
$271$	−25.4823	−	14.7122i	−1.54794	−	0.893703i	−0.549640	−	0.835402i	$-0.685235\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.84527	−	1.06537i	0.111274	−	0.0642440i
$276$		0			0
$277$	4.60108	−	7.96930i	0.276452	−	0.478829i	−0.694049	−	0.719928i	$-0.744175\pi$
$277$	4.60108	−	7.96930i	0.276452	−	0.478829i	0.970500	+	0.241100i	$0.0775080\pi$
$278$		0			0
$279$	7.44183	−	10.1676i	0.445531	−	0.608719i
$280$		0			0
$281$	1.05254	−	0.607682i	0.0627891	−	0.0362513i	−0.468277	−	0.883582i	$-0.655125\pi$
$281$	1.05254	−	0.607682i	0.0627891	−	0.0362513i	0.531066	+	0.847331i	$0.321792\pi$
$282$		0			0
$283$			12.2139i			0.726043i	0.931781	+	0.363021i	$0.118255\pi$
$283$			12.2139i			0.726043i	−0.931781	+	0.363021i	$0.881745\pi$
$284$		0			0
$285$	−1.60768	−	0.525486i	−0.0952307	−	0.0311271i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	5.17002	−	8.95475i	0.304119	−	0.526750i
$290$		0			0
$291$	−2.05253	−	9.74036i	−0.120321	−	0.570990i
$292$		0			0
$293$	3.15082	−	5.45739i	0.184073	−	0.318824i	−0.759191	−	0.650868i	$-0.774405\pi$
$293$	3.15082	−	5.45739i	0.184073	−	0.318824i	0.943264	+	0.332044i	$0.107738\pi$
$294$		0			0
$295$	0.188909	+	0.327199i	0.0109987	+	0.0190503i
$296$		0			0
$297$	12.5186	−	1.24920i	0.726405	−	0.0724860i
$298$		0			0
$299$	19.3783			1.12068
$300$		0			0
$301$		0			0
$302$		0			0
$303$	11.1932	+	12.4752i	0.643032	+	0.716683i
$304$		0			0
$305$	24.8036	−	14.3204i	1.42025	−	0.819983i
$306$		0			0
$307$		−	28.7264i		−	1.63950i	−0.572721	−	0.819750i	$-0.694112\pi$
$307$		−	28.7264i		−	1.63950i	0.572721	−	0.819750i	$-0.305888\pi$
$308$		0			0
$309$	6.88128	+	32.6554i	0.391462	+	1.85770i
$310$		0			0
$311$	−17.7325			−1.00552			−0.502758	−	0.864427i	$-0.667681\pi$
$311$	−17.7325			−1.00552			−0.502758	+	0.864427i	$0.667681\pi$
$312$		0			0
$313$		−	27.0808i		−	1.53070i	−0.643616	−	0.765348i	$-0.722567\pi$
$313$		−	27.0808i		−	1.53070i	0.643616	−	0.765348i	$-0.277433\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	5.37385i		−	0.301825i	−0.988547	−	0.150913i	$-0.951779\pi$
$317$		−	5.37385i		−	0.301825i	0.988547	−	0.150913i	$-0.0482212\pi$
$318$		0			0
$319$	17.6630			0.988938
$320$		0			0
$321$	−1.40633	+	1.26181i	−0.0784940	+	0.0704274i
$322$		0			0
$323$			1.03926i			0.0578262i
$324$		0			0
$325$	4.16764	−	2.40619i	0.231179	−	0.133471i
$326$		0			0
$327$	−3.92110	+	0.826270i	−0.216837	+	0.0456928i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−7.44207			−0.409053			−0.204527	−	0.978861i	$-0.565565\pi$
$331$	−7.44207			−0.409053			−0.204527	+	0.978861i	$0.565565\pi$
$332$		0			0
$333$	−8.76612	+	3.86614i	−0.480380	+	0.211863i
$334$		0			0
$335$	−6.15149	−	10.6547i	−0.336092	−	0.582128i
$336$		0			0
$337$	−5.31784	+	9.21076i	−0.289681	+	0.501742i	−0.973734	−	0.227690i	$-0.926883\pi$
$337$	−5.31784	+	9.21076i	−0.289681	+	0.501742i	0.684053	+	0.729433i	$0.260216\pi$
$338$		0			0
$339$	20.6723	−	18.5479i	1.12277	−	1.00738i
$340$		0			0
$341$	5.08449	−	8.80660i	0.275341	−	0.476904i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−11.0782	+	9.93970i	−0.596428	+	0.535135i
$346$		0			0
$347$			1.89189i			0.101562i	0.998710	+	0.0507809i	$0.0161710\pi$
$347$			1.89189i			0.101562i	−0.998710	+	0.0507809i	$0.983829\pi$
$348$		0			0
$349$	−16.1105	+	9.30140i	−0.862375	+	0.497892i	−0.864807	−	0.502105i	$-0.832559\pi$
$349$	−16.1105	+	9.30140i	−0.862375	+	0.497892i	0.00243201	+	0.999997i	$0.499226\pi$
$350$		0			0
$351$	28.2740	−	2.82139i	1.50915	−	0.150595i
$352$		0			0
$353$	−1.94505	+	3.36893i	−0.103525	+	0.179310i	−0.913134	−	0.407659i	$-0.866345\pi$
$353$	−1.94505	+	3.36893i	−0.103525	+	0.179310i	0.809610	+	0.586968i	$0.199679\pi$
$354$		0			0
$355$	18.3538	−	10.5966i	0.974118	−	0.562407i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−7.46992	−	4.31276i	−0.394248	−	0.227619i	0.289751	−	0.957102i	$-0.406427\pi$
$359$	−7.46992	−	4.31276i	−0.394248	−	0.227619i	−0.683999	+	0.729483i	$0.739761\pi$
$360$		0			0
$361$	−9.41891	−	16.3140i	−0.495732	−	0.858633i
$362$		0			0
$363$	−8.70786	+	1.83496i	−0.457044	+	0.0963103i
$364$		0			0
$365$	18.4858	+	10.6728i	0.967592	+	0.558639i
$366$		0			0
$367$	15.8701	+	9.16260i	0.828412	+	0.478284i	0.853309	−	0.521406i	$-0.174592\pi$
$367$	15.8701	+	9.16260i	0.828412	+	0.478284i	−0.0248966	+	0.999690i	$0.507926\pi$
$368$		0			0
$369$	−22.1746	+	9.77973i	−1.15437	+	0.509112i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	3.84791	+	6.66478i	0.199237	+	0.345089i	0.948281	−	0.317431i	$-0.102820\pi$
$373$	3.84791	+	6.66478i	0.199237	+	0.345089i	−0.749044	+	0.662520i	$0.769487\pi$
$374$		0			0
$375$	5.37605	−	16.4476i	0.277618	−	0.849349i
$376$		0			0
$377$	39.8928			2.05458
$378$		0			0
$379$	−7.52510			−0.386539			−0.193269	−	0.981146i	$-0.561909\pi$
$379$	−7.52510			−0.386539			−0.193269	+	0.981146i	$0.561909\pi$
$380$		0			0
$381$	−1.64894	+	5.04479i	−0.0844778	+	0.258453i
$382$		0			0
$383$	−1.70467	−	2.95258i	−0.0871047	−	0.150870i	0.819181	−	0.573534i	$-0.194428\pi$
$383$	−1.70467	−	2.95258i	−0.0871047	−	0.150870i	−0.906286	+	0.422665i	$0.861095\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.73869	+	25.2060i	−0.139215	+	1.28129i
$388$		0			0
$389$	−8.33425	−	4.81178i	−0.422563	−	0.243967i	0.273610	−	0.961841i	$-0.411782\pi$
$389$	−8.33425	−	4.81178i	−0.422563	−	0.243967i	−0.696173	+	0.717874i	$0.745116\pi$
$390$		0			0
$391$	7.92000	+	4.57261i	0.400532	+	0.231247i
$392$		0			0
$393$	−19.4279	+	4.09392i	−0.980007	+	0.206511i
$394$		0			0
$395$	−13.7388	−	23.7962i	−0.691272	−	1.19732i
$396$		0			0
$397$	20.3349	+	11.7404i	1.02058	+	0.589232i	0.914272	−	0.405101i	$-0.132764\pi$
$397$	20.3349	+	11.7404i	1.02058	+	0.589232i	0.106308	+	0.994333i	$0.466097\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	22.2019	−	12.8183i	1.10871	−	0.640113i	0.170214	−	0.985407i	$-0.445554\pi$
$401$	22.2019	−	12.8183i	1.10871	−	0.640113i	0.938495	+	0.345294i	$0.112221\pi$
$402$		0			0
$403$	11.4836	−	19.8902i	0.572038	−	0.990799i
$404$		0			0
$405$	−14.7165	+	16.1155i	−0.731267	+	0.800785i
$406$		0			0
$407$	−6.69635	+	3.86614i	−0.331926	+	0.191637i
$408$		0			0
$409$		−	15.4321i		−	0.763066i	−0.924355	−	0.381533i	$-0.875396\pi$
$409$		−	15.4321i		−	0.763066i	0.924355	−	0.381533i	$-0.124604\pi$
$410$		0			0
$411$	−2.54559	+	2.28399i	−0.125565	+	0.112661i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−18.2093	+	31.5395i	−0.893860	+	1.54821i
$416$		0			0
$417$	8.00593	−	7.18319i	0.392052	−	0.351762i
$418$		0			0
$419$	7.10643	−	12.3087i	0.347172	−	0.601319i	−0.638574	−	0.769560i	$-0.720475\pi$
$419$	7.10643	−	12.3087i	0.347172	−	0.601319i	0.985746	+	0.168241i	$0.0538088\pi$
$420$		0			0
$421$	−0.849964	−	1.47218i	−0.0414247	−	0.0717497i	0.844570	−	0.535446i	$-0.179856\pi$
$421$	−0.849964	−	1.47218i	−0.0414247	−	0.0717497i	−0.885994	+	0.463696i	$0.846523\pi$
$422$		0			0
$423$	−10.9310	−	8.00060i	−0.531486	−	0.389003i
$424$		0			0
$425$	2.27111			0.110165
$426$		0			0
$427$		0			0
$428$		0			0
$429$	22.4393	−	4.72851i	1.08338	−	0.228294i
$430$		0			0
$431$	28.2868	−	16.3314i	1.36253	−	0.786656i	0.372568	−	0.928005i	$-0.378477\pi$
$431$	28.2868	−	16.3314i	1.36253	−	0.786656i	0.989960	+	0.141349i	$0.0451440\pi$
$432$		0			0
$433$		−	13.6919i		−	0.657992i	−0.944331	−	0.328996i	$-0.893290\pi$
$433$		−	13.6919i		−	0.657992i	0.944331	−	0.328996i	$-0.106710\pi$
$434$		0			0
$435$	−22.8059	+	20.4622i	−1.09346	+	0.981087i
$436$		0			0
$437$	1.42708			0.0682667
$438$		0			0
$439$		−	8.82352i		−	0.421124i	−0.977581	−	0.210562i	$-0.932471\pi$
$439$		−	8.82352i		−	0.421124i	0.977581	−	0.210562i	$-0.0675293\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			24.6600i			1.17163i	0.810444	+	0.585816i	$0.199226\pi$
$443$			24.6600i			1.17163i	−0.810444	+	0.585816i	$0.800774\pi$
$444$		0			0
$445$	37.9901			1.80090
$446$		0			0
$447$	4.34614	+	20.6248i	0.205566	+	0.975520i
$448$		0			0
$449$			4.61306i			0.217704i	0.994058	+	0.108852i	$0.0347174\pi$
$449$			4.61306i			0.217704i	−0.994058	+	0.108852i	$0.965283\pi$
$450$		0			0
$451$	−16.9390	+	9.77973i	−0.797626	+	0.460509i
$452$		0			0
$453$	12.3024	+	13.7115i	0.578016	+	0.644221i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	7.71871			0.361066			0.180533	−	0.983569i	$-0.442218\pi$
$457$	7.71871			0.361066			0.180533	+	0.983569i	$0.442218\pi$
$458$		0			0
$459$	12.2215	+	5.51858i	0.570449	+	0.257585i
$460$		0			0
$461$	9.28621	+	16.0842i	0.432502	+	0.749115i	0.997088	−	0.0762589i	$-0.0242975\pi$
$461$	9.28621	+	16.0842i	0.432502	+	0.749115i	−0.564586	+	0.825374i	$0.690964\pi$
$462$		0			0
$463$	17.7046	−	30.6653i	0.822804	−	1.42514i	−0.0807828	−	0.996732i	$-0.525742\pi$
$463$	17.7046	−	30.6653i	0.822804	−	1.42514i	0.903586	−	0.428406i	$-0.140925\pi$
$464$		0			0
$465$	3.63732	+	17.2610i	0.168677	+	0.800462i
$466$		0			0
$467$	−7.92166	+	13.7207i	−0.366571	+	0.634919i	−0.989027	−	0.147736i	$-0.952802\pi$
$467$	−7.92166	+	13.7207i	−0.366571	+	0.634919i	0.622456	+	0.782655i	$0.286135\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−5.82006	−	1.90234i	−0.268174	−	0.0876554i
$472$		0			0
$473$			20.4625i			0.940866i
$474$		0			0
$475$	0.306919	−	0.177200i	0.0140824	−	0.00813048i
$476$		0			0
$477$	41.8403	+	4.54603i	1.91574	+	0.208149i
$478$		0			0
$479$	−13.2512	+	22.9518i	−0.605465	+	1.04870i	0.386513	+	0.922284i	$0.373679\pi$
$479$	−13.2512	+	22.9518i	−0.605465	+	1.04870i	−0.991978	+	0.126412i	$0.959654\pi$
$480$		0			0
$481$	−15.1241	+	8.73188i	−0.689598	+	0.398139i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	12.0689	+	6.96801i	0.548023	+	0.316401i
$486$		0			0
$487$	3.50469	+	6.07031i	0.158813	+	0.275072i	0.934441	−	0.356118i	$-0.115900\pi$
$487$	3.50469	+	6.07031i	0.158813	+	0.275072i	−0.775628	+	0.631190i	$0.782567\pi$
$488$		0			0
$489$	7.32370	+	8.16254i	0.331189	+	0.369123i
$490$		0			0
$491$	−16.4508	−	9.49785i	−0.742413	−	0.428632i	0.0805333	−	0.996752i	$-0.474338\pi$
$491$	−16.4508	−	9.49785i	−0.742413	−	0.428632i	−0.822946	+	0.568120i	$0.807671\pi$
$492$		0			0
$493$	16.3044	+	9.41333i	0.734312	+	0.423955i
$494$		0			0
$495$	−10.4027	+	14.2130i	−0.467566	+	0.638826i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−0.628929	−	1.08934i	−0.0281547	−	0.0487654i	0.851605	−	0.524184i	$-0.175630\pi$
$499$	−0.628929	−	1.08934i	−0.0281547	−	0.0487654i	−0.879759	+	0.475419i	$0.842296\pi$
$500$		0			0
$501$	19.4276	+	21.6528i	0.867961	+	0.967375i
$502$		0			0
$503$	−37.9507			−1.69214			−0.846070	−	0.533072i	$-0.821037\pi$
$503$	−37.9507			−1.69214			−0.846070	+	0.533072i	$0.821037\pi$
$504$		0			0
$505$	−23.4650			−1.04418
$506$		0			0
$507$	28.6476	−	6.03674i	1.27228	−	0.268101i
$508$		0			0
$509$	2.90471	+	5.03110i	0.128749	+	0.223000i	0.923192	−	0.384339i	$-0.125571\pi$
$509$	2.90471	+	5.03110i	0.128749	+	0.223000i	−0.794443	+	0.607338i	$0.792237\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	2.08219	−	0.207776i	0.0919310	−	0.00917355i
$514$		0			0
$515$	−40.4622	−	23.3609i	−1.78298	−	1.02940i
$516$		0			0
$517$	−9.46784	−	5.46626i	−0.416395	−	0.240406i
$518$		0			0
$519$	8.94197	−	27.3572i	0.392509	−	1.20085i
$520$		0			0
$521$	6.84995	+	11.8645i	0.300102	+	0.519791i	0.976159	−	0.217058i	$-0.0696461\pi$
$521$	6.84995	+	11.8645i	0.300102	+	0.519791i	−0.676057	+	0.736849i	$0.736313\pi$
$522$		0			0
$523$	−21.2073	−	12.2440i	−0.927330	−	0.535394i	−0.0413640	−	0.999144i	$-0.513170\pi$
$523$	−21.2073	−	12.2440i	−0.927330	−	0.535394i	−0.885966	+	0.463750i	$0.846504\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	9.38679	−	5.41946i	0.408895	−	0.236076i
$528$		0			0
$529$	−5.22104	+	9.04310i	−0.227002	+	0.393178i
$530$		0			0
$531$	−0.377189	−	0.276071i	−0.0163686	−	0.0119805i
$532$		0			0
$533$	−38.2576	+	22.0880i	−1.65712	+	0.956739i
$534$		0			0
$535$		−	2.64521i		−	0.114362i
$536$		0			0
$537$	−5.19953	−	24.6746i	−0.224376	−	1.06479i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	18.5804	−	32.1822i	0.798833	−	1.38362i	−0.121543	−	0.992586i	$-0.538784\pi$
$541$	18.5804	−	32.1822i	0.798833	−	1.38362i	0.920376	−	0.391034i	$-0.127882\pi$
$542$		0			0
$543$	−6.62412	−	2.16516i	−0.284268	−	0.0929159i
$544$		0			0
$545$	2.80506	−	4.85850i	0.120155	−	0.208115i
$546$		0			0
$547$	−3.31826	−	5.74739i	−0.141878	−	0.245741i	0.786326	−	0.617812i	$-0.211981\pi$
$547$	−3.31826	−	5.74739i	−0.141878	−	0.245741i	−0.928204	+	0.372072i	$0.878648\pi$
$548$		0			0
$549$	−20.9278	+	28.5932i	−0.893177	+	1.22033i
$550$		0			0
$551$	2.93784			0.125156
$552$		0			0
$553$		0			0
$554$		0			0
$555$	4.16727	−	12.7494i	0.176891	−	0.541182i
$556$		0			0
$557$	21.3205	−	12.3094i	0.903378	−	0.521565i	0.0250832	−	0.999685i	$-0.492015\pi$
$557$	21.3205	−	12.3094i	0.903378	−	0.521565i	0.878295	+	0.478120i	$0.158682\pi$
$558$		0			0
$559$			46.2156i			1.95471i
$560$		0			0
$561$	10.2868	+	3.36235i	0.434310	+	0.141958i
$562$		0			0
$563$	−12.5711			−0.529808			−0.264904	−	0.964275i	$-0.585340\pi$
$563$	−12.5711			−0.529808			−0.264904	+	0.964275i	$0.585340\pi$
$564$		0			0
$565$			38.8831i			1.63583i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	14.8809i		−	0.623838i	−0.950109	−	0.311919i	$-0.899028\pi$
$569$		−	14.8809i		−	0.623838i	0.950109	−	0.311919i	$-0.100972\pi$
$570$		0			0
$571$	−16.9115			−0.707723			−0.353861	−	0.935298i	$-0.615132\pi$
$571$	−16.9115			−0.707723			−0.353861	+	0.935298i	$0.615132\pi$
$572$		0			0
$573$	13.8585	+	4.52977i	0.578945	+	0.189234i
$574$		0			0
$575$		−	3.11861i		−	0.130055i
$576$		0			0
$577$	−18.1011	+	10.4507i	−0.753558	+	0.435067i	−0.826978	−	0.562234i	$-0.809942\pi$
$577$	−18.1011	+	10.4507i	−0.753558	+	0.435067i	0.0734203	+	0.997301i	$0.476609\pi$
$578$		0			0
$579$	−4.64704	+	14.2172i	−0.193124	+	0.590848i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	33.9663			1.40674
$584$		0			0
$585$	−23.4950	+	32.1007i	−0.971400	+	1.32720i
$586$		0			0
$587$	14.8542	+	25.7283i	0.613100	+	1.06192i	0.990715	+	0.135957i	$0.0434109\pi$
$587$	14.8542	+	25.7283i	0.613100	+	1.06192i	−0.377615	+	0.925963i	$0.623256\pi$
$588$		0			0
$589$	0.845690	−	1.46478i	0.0348461	−	0.0603551i
$590$		0			0
$591$	−38.4095	−	12.5545i	−1.57996	−	0.516424i
$592$		0			0
$593$	−5.89603	+	10.2122i	−0.242121	+	0.419365i	−0.961318	−	0.275440i	$-0.911176\pi$
$593$	−5.89603	+	10.2122i	−0.242121	+	0.419365i	0.719197	+	0.694806i	$0.244510\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−5.04936	−	23.9619i	−0.206657	−	0.980697i
$598$		0			0
$599$			32.0996i			1.31156i	0.754954	+	0.655778i	$0.227659\pi$
$599$			32.0996i			1.31156i	−0.754954	+	0.655778i	$0.772341\pi$
$600$		0			0
$601$	16.1636	−	9.33208i	0.659329	−	0.380664i	−0.132692	−	0.991157i	$-0.542362\pi$
$601$	16.1636	−	9.33208i	0.659329	−	0.380664i	0.792021	+	0.610494i	$0.209029\pi$
$602$		0			0
$603$	12.2825	+	8.98978i	0.500183	+	0.366092i
$604$		0			0
$605$	6.22939	−	10.7896i	0.253261	−	0.438661i
$606$		0			0
$607$	12.0104	−	6.93419i	0.487486	−	0.281450i	−0.236045	−	0.971742i	$-0.575851\pi$
$607$	12.0104	−	6.93419i	0.487486	−	0.281450i	0.723531	+	0.690292i	$0.242518\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−21.3836	−	12.3458i	−0.865089	−	0.499459i
$612$		0			0
$613$	10.4510	+	18.1017i	0.422114	+	0.731122i	0.996146	−	0.0877104i	$-0.0279550\pi$
$613$	10.4510	+	18.1017i	0.422114	+	0.731122i	−0.574032	+	0.818833i	$0.694622\pi$
$614$		0			0
$615$	10.5415	−	32.2507i	0.425072	−	1.30047i
$616$		0			0
$617$	15.2904	+	8.82792i	0.615569	+	0.355399i	0.775142	−	0.631787i	$-0.217678\pi$
$617$	15.2904	+	8.82792i	0.615569	+	0.355399i	−0.159573	+	0.987186i	$0.551012\pi$
$618$		0			0
$619$	4.78789	+	2.76429i	0.192441	+	0.111106i	0.593125	−	0.805110i	$-0.297894\pi$
$619$	4.78789	+	2.76429i	0.192441	+	0.111106i	−0.400684	+	0.916216i	$0.631227\pi$
$620$		0			0
$621$	7.57793	−	16.7821i	0.304092	−	0.673443i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	14.3129	+	24.7906i	0.572515	+	0.991624i
$626$		0			0
$627$	1.65251	−	0.348223i	0.0659948	−	0.0139067i
$628$		0			0
$629$	−8.24169			−0.328618
$630$		0			0
$631$	24.3544			0.969533			0.484766	−	0.874644i	$-0.338905\pi$
$631$	24.3544			0.969533			0.484766	+	0.874644i	$0.338905\pi$
$632$		0			0
$633$	15.6337	+	17.4244i	0.621386	+	0.692558i
$634$		0			0
$635$	−3.71522	−	6.43496i	−0.147434	−	0.255363i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−15.4858	+	21.1579i	−0.612609	+	0.836994i
$640$		0			0
$641$	−25.3174	−	14.6170i	−0.999978	−	0.577337i	−0.0917361	−	0.995783i	$-0.529242\pi$
$641$	−25.3174	−	14.6170i	−0.999978	−	0.577337i	−0.908242	+	0.418446i	$0.862575\pi$
$642$		0			0
$643$	34.6535	+	20.0072i	1.36660	+	0.789008i	0.990492	−	0.137567i	$-0.0439284\pi$
$643$	34.6535	+	20.0072i	1.36660	+	0.789008i	0.376109	+	0.926575i	$0.377262\pi$
$644$		0			0
$645$	−23.7053	−	26.4205i	−0.933396	−	1.04031i
$646$		0			0
$647$	−3.78276	−	6.55194i	−0.148716	−	0.257583i	0.782037	−	0.623232i	$-0.214181\pi$
$647$	−3.78276	−	6.55194i	−0.148716	−	0.257583i	−0.930753	+	0.365648i	$0.880847\pi$
$648$		0			0
$649$	−0.326700	−	0.188620i	−0.0128241	−	0.00740399i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−33.9375	+	19.5938i	−1.32808	+	0.766766i	−0.985002	−	0.172542i	$-0.944802\pi$
$653$	−33.9375	+	19.5938i	−1.32808	+	0.766766i	−0.343076	+	0.939308i	$0.611469\pi$
$654$		0			0
$655$	13.8982	−	24.0724i	0.543049	−	0.940588i
$656$		0			0
$657$	−26.2537	−	2.85252i	−1.02425	−	0.111287i
$658$		0			0
$659$	−22.8594	+	13.1979i	−0.890474	+	0.514115i	−0.874098	−	0.485751i	$-0.838546\pi$
$659$	−22.8594	+	13.1979i	−0.890474	+	0.514115i	−0.0163765	+	0.999866i	$0.505213\pi$
$660$		0			0
$661$		−	31.5812i		−	1.22837i	−0.789163	−	0.614184i	$-0.789485\pi$
$661$		−	31.5812i		−	1.22837i	0.789163	−	0.614184i	$-0.210515\pi$
$662$		0			0
$663$	23.2333	+	7.59404i	0.902307	+	0.294928i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	12.9261	−	22.3886i	0.500500	−	0.866891i
$668$		0			0
$669$	−5.52827	−	26.2346i	−0.213735	−	1.01429i
$670$		0			0
$671$	−14.2985	+	24.7658i	−0.551989	+	0.956073i
$672$		0			0
$673$	−7.21676	−	12.4998i	−0.278186	−	0.481832i	0.692748	−	0.721180i	$-0.256400\pi$
$673$	−7.21676	−	12.4998i	−0.278186	−	0.481832i	−0.970934	+	0.239348i	$0.923066\pi$
$674$		0			0
$675$	−0.454055	−	4.55022i	−0.0174766	−	0.175138i
$676$		0			0
$677$	−34.4198			−1.32286			−0.661430	−	0.750006i	$-0.730050\pi$
$677$	−34.4198			−1.32286			−0.661430	+	0.750006i	$0.730050\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−17.3700	−	19.3595i	−0.665618	−	0.741856i
$682$		0			0
$683$	−16.4694	+	9.50861i	−0.630184	+	0.363837i	−0.780823	−	0.624752i	$-0.785200\pi$
$683$	−16.4694	+	9.50861i	−0.630184	+	0.363837i	0.150639	+	0.988589i	$0.451867\pi$
$684$		0			0
$685$		−	4.78806i		−	0.182942i
$686$		0			0
$687$	6.99767	+	33.2077i	0.266978	+	1.26695i
$688$		0			0
$689$	76.7147			2.92260
$690$		0			0
$691$			19.3753i			0.737070i	0.929614	+	0.368535i	$0.120141\pi$
$691$			19.3753i			0.737070i	−0.929614	+	0.368535i	$0.879859\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			15.0586i			0.571204i
$696$		0			0
$697$	−20.8481			−0.789676
$698$		0			0
$699$	25.2001	−	22.6103i	0.953154	−	0.855201i
$700$		0			0
$701$		−	23.0297i		−	0.869819i	−0.900474	−	0.434910i	$-0.856780\pi$
$701$		−	23.0297i		−	0.869819i	0.900474	−	0.434910i	$-0.143220\pi$
$702$		0			0
$703$	−1.11379	+	0.643045i	−0.0420073	+	0.0242529i
$704$		0			0
$705$	18.5571	−	3.91043i	0.698901	−	0.147275i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−40.8238			−1.53317			−0.766585	−	0.642143i	$-0.778045\pi$
$709$	−40.8238			−1.53317			−0.766585	+	0.642143i	$0.778045\pi$
$710$		0			0
$711$	27.4319	+	20.0778i	1.02878	+	0.752977i
$712$		0			0
$713$	−7.44183	−	12.8896i	−0.278699	−	0.482720i
$714$		0			0
$715$	−16.0525	+	27.8038i	−0.600331	+	1.03980i
$716$		0			0
$717$	10.9595	−	9.83321i	0.409289	−	0.367228i
$718$		0			0
$719$	21.1578	−	36.6464i	0.789054	−	1.36668i	−0.137494	−	0.990503i	$-0.543905\pi$
$719$	21.1578	−	36.6464i	0.789054	−	1.36668i	0.926547	−	0.376178i	$-0.122762\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−10.7402	+	9.63647i	−0.399433	+	0.358384i
$724$		0			0
$725$		−	6.42008i		−	0.238436i
$726$		0			0
$727$	−4.58754	+	2.64862i	−0.170142	+	0.0982318i	−0.582653	−	0.812721i	$-0.697985\pi$
$727$	−4.58754	+	2.64862i	−0.170142	+	0.0982318i	0.412511	+	0.910953i	$0.364652\pi$
$728$		0			0
$729$	8.61321	−	25.5893i	0.319008	−	0.947752i
$730$		0			0
$731$	−10.9053	+	18.8885i	−0.403347	+	0.698617i
$732$		0			0
$733$	16.1513	−	9.32497i	0.596563	−	0.344426i	−0.171125	−	0.985249i	$-0.554740\pi$
$733$	16.1513	−	9.32497i	0.596563	−	0.344426i	0.767688	+	0.640824i	$0.221407\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	10.6384	+	6.14210i	0.391871	+	0.226247i
$738$		0			0
$739$	−20.5918	−	35.6661i	−0.757483	−	1.31200i	−0.944131	−	0.329572i	$-0.893096\pi$
$739$	−20.5918	−	35.6661i	−0.757483	−	1.31200i	0.186648	−	0.982427i	$-0.440238\pi$
$740$		0			0
$741$	3.73227	−	0.786480i	0.137108	−	0.0288921i
$742$		0			0
$743$	20.5831	+	11.8837i	0.755122	+	0.435970i	0.827542	−	0.561404i	$-0.189739\pi$
$743$	20.5831	+	11.8837i	0.755122	+	0.435970i	−0.0724196	+	0.997374i	$0.523072\pi$
$744$		0			0
$745$	−25.5555	−	14.7545i	−0.936281	−	0.540562i
$746$		0			0
$747$	4.86681	−	44.7926i	0.178067	−	1.63888i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−9.06151	−	15.6950i	−0.330659	−	0.572718i	0.651982	−	0.758234i	$-0.273938\pi$
$751$	−9.06151	−	15.6950i	−0.330659	−	0.572718i	−0.982641	+	0.185516i	$0.940604\pi$
$752$		0			0
$753$	7.30569	−	22.3511i	0.266234	−	0.814521i
$754$		0			0
$755$	−25.7902			−0.938603
$756$		0			0
$757$	37.1059			1.34864			0.674319	−	0.738440i	$-0.264437\pi$
$757$	37.1059			1.34864			0.674319	+	0.738440i	$0.264437\pi$
$758$		0			0
$759$	4.61707	−	14.1255i	0.167589	−	0.512724i
$760$		0			0
$761$	−5.90537	−	10.2284i	−0.214070	−	0.370779i	0.738915	−	0.673799i	$-0.235339\pi$
$761$	−5.90537	−	10.2284i	−0.214070	−	0.370779i	−0.952984	+	0.303020i	$0.902005\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−17.1772	+	7.57569i	−0.621043	+	0.273900i
$766$		0			0
$767$	−0.737868	−	0.426009i	−0.0266429	−	0.0153823i
$768$		0			0
$769$	3.14015	+	1.81297i	0.113237	+	0.0653773i	0.555549	−	0.831484i	$-0.312508\pi$
$769$	3.14015	+	1.81297i	0.113237	+	0.0653773i	−0.442312	+	0.896861i	$0.645842\pi$
$770$		0			0
$771$	10.1361	−	2.13592i	0.365043	−	0.0769233i
$772$		0			0
$773$	6.05553	+	10.4885i	0.217802	+	0.377245i	0.954136	−	0.299374i	$-0.0967778\pi$
$773$	6.05553	+	10.4885i	0.217802	+	0.377245i	−0.736333	+	0.676619i	$0.763445\pi$
$774$		0			0
$775$	−3.20099	−	1.84809i	−0.114983	−	0.0663854i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.81742	+	1.62664i	−0.100944	+	0.0582803i
$780$		0			0
$781$	−10.5804	+	18.3258i	−0.378596	+	0.655748i
$782$		0			0
$783$	15.6002	−	34.5482i	0.557505	−	1.23465i
$784$		0			0
$785$	7.42386	−	4.28617i	0.264969	−	0.152980i
$786$		0			0
$787$			20.3222i			0.724406i	0.932099	+	0.362203i	$0.117975\pi$
$787$			20.3222i			0.724406i	−0.932099	+	0.362203i	$0.882025\pi$
$788$		0			0
$789$	4.33946	−	3.89351i	0.154489	−	0.138612i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−32.2940	+	55.9348i	−1.14679	+	1.98630i
$794$		0			0
$795$	−43.8562	+	39.3492i	−1.55542	+	1.39557i
$796$		0			0
$797$	16.8973	−	29.2669i	0.598532	−	1.03669i	−0.394506	−	0.918893i	$-0.629084\pi$
$797$	16.8973	−	29.2669i	0.598532	−	1.03669i	0.993038	−	0.117795i	$-0.0375824\pi$
$798$		0			0
$799$	−5.82639	−	10.0916i	−0.206123	−	0.357015i
$800$		0			0
$801$	−43.0037	+	18.9660i	−1.51946	+	0.670132i
$802$		0			0
$803$	−21.3130			−0.752119
$804$		0			0
$805$		0			0
$806$		0			0
$807$	20.8163	−	4.38650i	0.732769	−	0.154412i
$808$		0			0
$809$	−4.19308	+	2.42087i	−0.147421	+	0.0851134i	−0.571896	−	0.820326i	$-0.693792\pi$
$809$	−4.19308	+	2.42087i	−0.147421	+	0.0851134i	0.424475	+	0.905440i	$0.360459\pi$
$810$		0			0
$811$		−	0.493486i		−	0.0173286i	−0.999962	−	0.00866432i	$-0.997242\pi$
$811$		−	0.493486i		−	0.0173286i	0.999962	−	0.00866432i	$-0.00275797\pi$
$812$		0			0
$813$	−37.9338	+	34.0355i	−1.33040	+	1.19368i
$814$		0			0
$815$	−15.3531			−0.537797
$816$		0			0
$817$			3.40347i			0.119072i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	30.8225i		−	1.07571i	−0.843036	−	0.537857i	$-0.819234\pi$
$821$		−	30.8225i		−	1.07571i	0.843036	−	0.537857i	$-0.180766\pi$
$822$		0			0
$823$	−15.8850			−0.553716			−0.276858	−	0.960911i	$-0.589293\pi$
$823$	−15.8850			−0.553716			−0.276858	+	0.960911i	$0.589293\pi$
$824$		0			0
$825$	−0.760974	−	3.61123i	−0.0264937	−	0.125727i
$826$		0			0
$827$		−	35.6756i		−	1.24056i	−0.784379	−	0.620282i	$-0.787018\pi$
$827$		−	35.6756i		−	1.24056i	0.784379	−	0.620282i	$-0.212982\pi$
$828$		0			0
$829$	2.87997	−	1.66275i	0.100026	−	0.0577498i	−0.449153	−	0.893455i	$-0.648274\pi$
$829$	2.87997	−	1.66275i	0.100026	−	0.0577498i	0.549178	+	0.835705i	$0.314941\pi$
$830$		0			0
$831$	−10.6442	−	11.8634i	−0.369244	−	0.411536i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−40.7273			−1.40942
$836$		0			0
$837$	−12.7347	−	17.7232i	−0.440176	−	0.612602i
$838$		0			0
$839$	−20.9689	−	36.3192i	−0.723926	−	1.25388i	−0.959414	−	0.282000i	$-0.909002\pi$
$839$	−20.9689	−	36.3192i	−0.723926	−	1.25388i	0.235488	−	0.971877i	$-0.424331\pi$
$840$		0			0
$841$	12.1100	−	20.9752i	0.417588	−	0.723283i
$842$		0			0
$843$	−0.434057	−	2.05984i	−0.0149497	−	0.0709445i
$844$		0			0
$845$	−20.4938	+	35.4963i	−0.705007	+	1.22111i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	20.1082	+	6.57258i	0.690113	+	0.225570i
$850$		0			0
$851$			11.3172i			0.387949i
$852$		0			0
$853$	−12.5330	+	7.23594i	−0.429122	+	0.247754i	−0.698973	−	0.715149i	$-0.746359\pi$
$853$	−12.5330	+	7.23594i	−0.429122	+	0.247754i	0.269851	+	0.962902i	$0.413026\pi$
$854$		0			0
$855$	−1.73025	+	2.36401i	−0.0591734	+	0.0808473i
$856$		0			0
$857$	23.7329	−	41.1065i	0.810699	−	1.40417i	−0.101676	−	0.994818i	$-0.532421\pi$
$857$	23.7329	−	41.1065i	0.810699	−	1.40417i	0.912375	−	0.409355i	$-0.134246\pi$
$858$		0			0
$859$	5.20316	−	3.00405i	0.177530	−	0.102497i	−0.408602	−	0.912713i	$-0.633984\pi$
$859$	5.20316	−	3.00405i	0.177530	−	0.102497i	0.586131	+	0.810216i	$0.300650\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−27.1064	−	15.6499i	−0.922714	−	0.532729i	−0.0382141	−	0.999270i	$-0.512167\pi$
$863$	−27.1064	−	15.6499i	−0.922714	−	0.532729i	−0.884500	+	0.466540i	$0.845500\pi$
$864$		0			0
$865$	20.1471	+	34.8958i	0.685022	+	1.18649i
$866$		0			0
$867$	−11.9604	−	13.3303i	−0.406197	−	0.452722i
$868$		0			0
$869$	23.7599	+	13.7178i	0.806000	+	0.465344i
$870$		0			0
$871$	24.0274	+	13.8722i	0.814139	+	0.470043i
$872$		0			0
$873$	−17.1404	−	1.86234i	−0.580115	−	0.0630307i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−20.6882	−	35.8330i	−0.698591	−	1.21000i	−0.968955	−	0.247237i	$-0.920477\pi$
$877$	−20.6882	−	35.8330i	−0.698591	−	1.21000i	0.270364	−	0.962758i	$-0.412856\pi$
$878$		0			0
$879$	−7.28917	−	8.12406i	−0.245858	−	0.274018i
$880$		0			0
$881$	−39.7350			−1.33870			−0.669352	−	0.742945i	$-0.733428\pi$
$881$	−39.7350			−1.33870			−0.669352	+	0.742945i	$0.733428\pi$
$882$		0			0
$883$	−48.1324			−1.61978			−0.809892	−	0.586579i	$-0.800474\pi$
$883$	−48.1324			−1.61978			−0.809892	+	0.586579i	$0.800474\pi$
$884$		0			0
$885$	0.640336	−	0.134934i	0.0215247	−	0.00453576i
$886$		0			0
$887$	14.0561	+	24.3459i	0.471958	+	0.817456i	0.999485	−	0.0320827i	$-0.0102140\pi$
$887$	14.0561	+	24.3459i	0.471958	+	0.817456i	−0.527527	+	0.849538i	$0.676881\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	4.67994	−	21.2821i	0.156784	−	0.712978i
$892$		0			0
$893$	−1.57476	−	0.909189i	−0.0526974	−	0.0304248i
$894$		0			0
$895$	30.5735	+	17.6516i	1.02196	+	0.590028i
$896$		0			0
$897$	10.4279	−	31.9032i	0.348177	−	1.06522i
$898$		0			0
$899$	−15.3200	−	26.5350i	−0.510950	−	0.884992i
$900$		0			0
$901$	31.3537	+	18.1020i	1.04454	+	0.603066i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	8.44949	−	4.87831i	0.280870	−	0.162161i
$906$		0			0
$907$	−29.7430	+	51.5163i	−0.987599	+	1.71057i	−0.357836	+	0.933784i	$0.616485\pi$
$907$	−29.7430	+	51.5163i	−0.987599	+	1.71057i	−0.629763	+	0.776788i	$0.716848\pi$
$908$		0			0
$909$	26.5617	−	11.7146i	0.880996	−	0.388548i
$910$		0			0
$911$	25.4502	−	14.6937i	0.843204	−	0.486824i	−0.0151480	−	0.999885i	$-0.504822\pi$
$911$	25.4502	−	14.6937i	0.843204	−	0.486824i	0.858352	+	0.513061i	$0.171489\pi$
$912$		0			0
$913$		−	36.3630i		−	1.20344i
$914$		0			0
$915$	−10.2288	−	48.5413i	−0.338154	−	1.60472i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	20.7994	−	36.0256i	0.686108	−	1.18837i	−0.286979	−	0.957937i	$-0.592651\pi$
$919$	20.7994	−	36.0256i	0.686108	−	1.18837i	0.973087	−	0.230437i	$-0.0740156\pi$
$920$		0			0
$921$	−47.2933	−	15.4583i	−1.55837	−	0.509367i
$922$		0			0
$923$	−23.8964	+	41.3897i	−0.786558	+	1.36236i
$924$		0			0
$925$	1.40525	+	2.43396i	0.0462043	+	0.0800282i
$926$		0			0
$927$	57.4648	+	6.24366i	1.88739	+	0.205069i
$928$		0			0
$929$	2.43228			0.0798004			0.0399002	−	0.999204i	$-0.487296\pi$
$929$	2.43228			0.0798004			0.0399002	+	0.999204i	$0.487296\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−9.54222	+	29.1936i	−0.312398	+	0.955756i
$934$		0			0
$935$	−13.1215	+	7.57569i	−0.429118	+	0.247752i
$936$		0			0
$937$		−	7.29837i		−	0.238427i	−0.992869	−	0.119214i	$-0.961963\pi$
$937$		−	7.29837i		−	0.238427i	0.992869	−	0.119214i	$-0.0380374\pi$
$938$		0			0
$939$	−44.5841	−	14.5728i	−1.45495	−	0.475564i
$940$		0			0
$941$	−42.4735			−1.38460			−0.692298	−	0.721612i	$-0.743402\pi$
$941$	−42.4735			−1.38460			−0.692298	+	0.721612i	$0.743402\pi$
$942$		0			0
$943$			28.6279i			0.932252i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	54.6311i		−	1.77527i	−0.460546	−	0.887636i	$-0.652346\pi$
$947$		−	54.6311i		−	1.77527i	0.460546	−	0.887636i	$-0.347654\pi$
$948$		0			0
$949$	−48.1365			−1.56258
$950$		0			0
$951$	−8.84717	−	2.89178i	−0.286889	−	0.0937725i
$952$		0			0
$953$		−	17.1877i		−	0.556764i	−0.960470	−	0.278382i	$-0.910202\pi$
$953$		−	17.1877i		−	0.556764i	0.960470	−	0.278382i	$-0.0897981\pi$
$954$		0			0
$955$	−17.6773	+	10.2060i	−0.572025	+	0.330259i
$956$		0			0
$957$	9.50484	−	29.0793i	0.307248	−	0.939999i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	13.3599			0.430964
$962$		0			0
$963$	1.32059	+	2.99431i	0.0425553	+	0.0964902i
$964$		0			0
$965$	−10.4702	−	18.1350i	−0.337049	−	0.583786i
$966$		0			0
$967$	−11.1546	+	19.3203i	−0.358706	+	0.621298i	−0.987745	−	0.156076i	$-0.950115\pi$
$967$	−11.1546	+	19.3203i	−0.358706	+	0.621298i	0.629039	+	0.777374i	$0.283449\pi$
$968$		0			0
$969$	1.71098	+	0.559250i	0.0549646	+	0.0179657i
$970$		0			0
$971$	−27.1241	+	46.9803i	−0.870453	+	1.50767i	−0.00892375	+	0.999960i	$0.502841\pi$
$971$	−27.1241	+	46.9803i	−0.870453	+	1.50767i	−0.861529	+	0.507708i	$0.830493\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−1.71870	−	8.15616i	−0.0550424	−	0.261206i
$976$		0			0
$977$			41.2154i			1.31860i	0.751881	+	0.659299i	$0.229147\pi$
$977$			41.2154i			1.31860i	−0.751881	+	0.659299i	$0.770853\pi$
$978$		0			0
$979$	−32.8501	+	18.9660i	−1.04989	+	0.606157i
$980$		0			0
$981$	−0.749708	+	6.90008i	−0.0239363	+	0.220303i
$982$		0			0
$983$	9.21969	−	15.9690i	0.294062	−	0.509331i	−0.680704	−	0.732559i	$-0.738326\pi$
$983$	9.21969	−	15.9690i	0.294062	−	0.509331i	0.974766	+	0.223228i	$0.0716593\pi$
$984$		0			0
$985$	48.9938	−	28.2866i	1.56107	−	0.901285i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	25.9371	+	14.9748i	0.824752	+	0.476171i
$990$		0			0
$991$	1.86116	+	3.22362i	0.0591216	+	0.102402i	0.894071	−	0.447925i	$-0.147837\pi$
$991$	1.86116	+	3.22362i	0.0591216	+	0.102402i	−0.834950	+	0.550326i	$0.814503\pi$
$992$		0			0
$993$	−4.00474	+	12.2522i	−0.127087	+	0.388810i
$994$		0			0
$995$	29.6904	+	17.1418i	0.941250	+	0.543431i
$996$		0			0
$997$	0.411648	+	0.237665i	0.0130370	+	0.00752693i	0.506504	−	0.862237i	$-0.330937\pi$
$997$	0.411648	+	0.237665i	0.0130370	+	0.00752693i	−0.493467	+	0.869764i	$0.664271\pi$
$998$		0			0
$999$	1.64773	+	16.5124i	0.0521320	+	0.522431i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.w.a.509.5		16
3.2	odd	2		5292.2.w.a.1097.2		16
7.2	even	3		252.2.x.a.41.7	yes	16
7.3	odd	6		1764.2.bm.b.1697.7		16
7.4	even	3		1764.2.bm.b.1697.2		16
7.5	odd	6		252.2.x.a.41.2	✓	16
7.6	odd	2	inner	1764.2.w.a.509.4		16
9.2	odd	6		1764.2.bm.b.1685.7		16
9.7	even	3		5292.2.bm.b.4625.2		16
21.2	odd	6		756.2.x.a.125.2		16
21.5	even	6		756.2.x.a.125.7		16
21.11	odd	6		5292.2.bm.b.2285.7		16
21.17	even	6		5292.2.bm.b.2285.2		16
21.20	even	2		5292.2.w.a.1097.7		16
28.19	even	6		1008.2.cc.c.545.7		16
28.23	odd	6		1008.2.cc.c.545.2		16
63.2	odd	6		252.2.x.a.209.2	yes	16
63.5	even	6		2268.2.f.b.1133.4		16
63.11	odd	6	inner	1764.2.w.a.1109.4		16
63.16	even	3		756.2.x.a.629.7		16
63.20	even	6		1764.2.bm.b.1685.2		16
63.23	odd	6		2268.2.f.b.1133.13		16
63.25	even	3		5292.2.w.a.521.7		16
63.34	odd	6		5292.2.bm.b.4625.7		16
63.38	even	6	inner	1764.2.w.a.1109.5		16
63.40	odd	6		2268.2.f.b.1133.14		16
63.47	even	6		252.2.x.a.209.7	yes	16
63.52	odd	6		5292.2.w.a.521.2		16
63.58	even	3		2268.2.f.b.1133.3		16
63.61	odd	6		756.2.x.a.629.2		16
84.23	even	6		3024.2.cc.c.881.2		16
84.47	odd	6		3024.2.cc.c.881.7		16
252.47	odd	6		1008.2.cc.c.209.2		16
252.79	odd	6		3024.2.cc.c.2897.7		16
252.187	even	6		3024.2.cc.c.2897.2		16
252.191	even	6		1008.2.cc.c.209.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.x.a.41.2	✓	16	7.5	odd	6
252.2.x.a.41.7	yes	16	7.2	even	3
252.2.x.a.209.2	yes	16	63.2	odd	6
252.2.x.a.209.7	yes	16	63.47	even	6
756.2.x.a.125.2		16	21.2	odd	6
756.2.x.a.125.7		16	21.5	even	6
756.2.x.a.629.2		16	63.61	odd	6
756.2.x.a.629.7		16	63.16	even	3
1008.2.cc.c.209.2		16	252.47	odd	6
1008.2.cc.c.209.7		16	252.191	even	6
1008.2.cc.c.545.2		16	28.23	odd	6
1008.2.cc.c.545.7		16	28.19	even	6
1764.2.w.a.509.4		16	7.6	odd	2	inner
1764.2.w.a.509.5		16	1.1	even	1	trivial
1764.2.w.a.1109.4		16	63.11	odd	6	inner
1764.2.w.a.1109.5		16	63.38	even	6	inner
1764.2.bm.b.1685.2		16	63.20	even	6
1764.2.bm.b.1685.7		16	9.2	odd	6
1764.2.bm.b.1697.2		16	7.4	even	3
1764.2.bm.b.1697.7		16	7.3	odd	6
2268.2.f.b.1133.3		16	63.58	even	3
2268.2.f.b.1133.4		16	63.5	even	6
2268.2.f.b.1133.13		16	63.23	odd	6
2268.2.f.b.1133.14		16	63.40	odd	6
3024.2.cc.c.881.2		16	84.23	even	6
3024.2.cc.c.881.7		16	84.47	odd	6
3024.2.cc.c.2897.2		16	252.187	even	6
3024.2.cc.c.2897.7		16	252.79	odd	6
5292.2.w.a.521.2		16	63.52	odd	6
5292.2.w.a.521.7		16	63.25	even	3
5292.2.w.a.1097.2		16	3.2	odd	2
5292.2.w.a.1097.7		16	21.20	even	2
5292.2.bm.b.2285.2		16	21.17	even	6
5292.2.bm.b.2285.7		16	21.11	odd	6
5292.2.bm.b.4625.2		16	9.7	even	3
5292.2.bm.b.4625.7		16	63.34	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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.538121 - 1.64634i) q^{3} +(1.21244 + 2.10001i) q^{5} +(-2.42085 - 1.77186i) q^{9} +O(q^{10})\)	\(q+(0.538121 - 1.64634i) q^{3} +(1.21244 + 2.10001i) q^{5} +(-2.42085 - 1.77186i) q^{9} +(-2.09680 - 1.21059i) q^{11} +(-4.73574 - 2.73418i) q^{13} +(4.10976 - 0.866025i) q^{15} +(-1.29034 - 2.23494i) q^{17} +(-0.348755 - 0.201354i) q^{19} +(-3.06895 + 1.77186i) q^{23} +(-0.440020 + 0.762137i) q^{25} +(-4.21979 + 3.03206i) q^{27} +(-6.31784 + 3.64761i) q^{29} +4.20001i q^{31} +(-3.12137 + 2.80060i) q^{33} +(1.59680 - 2.76574i) q^{37} +(-7.04978 + 6.32530i) q^{39} +(4.03924 - 6.99618i) q^{41} +(-4.22573 - 7.31918i) q^{43} +(0.785780 - 7.23208i) q^{45} +4.51537 q^{47} +(-4.37383 + 0.921671i) q^{51} +(-12.1493 + 7.01442i) q^{53} -5.87106i q^{55} +(-0.519169 + 0.465816i) q^{57} +0.155809 q^{59} -11.8112i q^{61} -13.2601i q^{65} -5.07364 q^{67} +(1.26561 + 6.00600i) q^{69} -8.73987i q^{71} +(7.62339 - 4.40137i) q^{73} +(1.01795 + 1.13454i) q^{75} -11.3315 q^{79} +(2.72104 + 8.57881i) q^{81} +(7.50937 + 13.0066i) q^{83} +(3.12893 - 5.41946i) q^{85} +(2.60542 + 12.3641i) q^{87} +(7.83339 - 13.5678i) q^{89} +(6.91464 + 2.26012i) q^{93} -0.976519i q^{95} +(4.97713 - 2.87355i) q^{97} +(2.93105 + 6.64589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{9}+O(q^{10}) \) 16 * q - 6 * q^9	\( 16 q - 6 q^{9} - 6 q^{11} - 12 q^{15} - 6 q^{23} - 8 q^{25} - 12 q^{29} - 2 q^{37} - 36 q^{39} + 4 q^{43} + 12 q^{51} + 36 q^{53} - 42 q^{57} - 28 q^{67} - 40 q^{79} - 18 q^{81} + 6 q^{85} - 6 q^{93} + 90 q^{99}+O(q^{100}) \) 16 * q - 6 * q^9 - 6 * q^11 - 12 * q^15 - 6 * q^23 - 8 * q^25 - 12 * q^29 - 2 * q^37 - 36 * q^39 + 4 * q^43 + 12 * q^51 + 36 * q^53 - 42 * q^57 - 28 * q^67 - 40 * q^79 - 18 * q^81 + 6 * q^85 - 6 * q^93 + 90 * q^99

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