LMFDB - Embedded newform 1764.2.bm.b.1697.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1685,1764)]

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, 1, 5]))

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

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

chi := DirichletCharacter("1764.1685");

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.bm (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			1697.7
Root			$1.69483 - 0.357142i$ of defining polynomial
Character	$\chi$	$=$	1764.1697
Dual form			1764.2.bm.b.1685.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.69483 - 0.357142i) q^{3} +2.42488 q^{5} +(2.74490 - 1.21059i) q^{9} +O(q^{10})$	\(q+(1.69483 - 0.357142i) q^{3} +2.42488 q^{5} +(2.74490 - 1.21059i) q^{9} +2.42118i q^{11} +(4.73574 + 2.73418i) q^{13} +(4.10976 - 0.866025i) q^{15} +(1.29034 - 2.23494i) q^{17} +(-0.348755 + 0.201354i) q^{19} -3.54372i q^{23} +0.880040 q^{25} +(4.21979 - 3.03206i) q^{27} +(-6.31784 + 3.64761i) q^{29} +(-3.63732 + 2.10001i) q^{31} +(0.864703 + 4.10349i) q^{33} +(1.59680 + 2.76574i) q^{37} +(9.00276 + 2.94264i) q^{39} +(-4.03924 + 6.99618i) q^{41} +(-4.22573 - 7.31918i) q^{43} +(6.65605 - 2.93553i) q^{45} +(2.25769 - 3.91043i) q^{47} +(1.38872 - 4.24868i) q^{51} +(12.1493 + 7.01442i) q^{53} +5.87106i q^{55} +(-0.519169 + 0.465816i) q^{57} +(0.0779043 + 0.134934i) q^{59} +(-10.2288 - 5.90561i) q^{61} +(11.4836 + 6.63005i) q^{65} +(2.53682 + 4.39390i) q^{67} +(-1.26561 - 6.00600i) q^{69} -8.73987i q^{71} +(7.62339 + 4.40137i) q^{73} +(1.49152 - 0.314299i) q^{75} +(5.66575 - 9.81337i) q^{79} +(6.06895 - 6.64589i) q^{81} +(-7.50937 - 13.0066i) q^{83} +(3.12893 - 5.41946i) q^{85} +(-9.40495 + 8.43843i) q^{87} +(-7.83339 - 13.5678i) q^{89} +(-5.41464 + 4.85819i) q^{93} +(-0.845690 + 0.488259i) q^{95} +(-4.97713 + 2.87355i) q^{97} +(2.93105 + 6.64589i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{9}+O(q^{10}) $ 16 * q + 6 * q^9	$ 16 q + 6 q^{9} - 12 q^{15} + 16 q^{25} - 12 q^{29} - 2 q^{37} + 18 q^{39} + 4 q^{43} + 6 q^{51} - 36 q^{53} - 42 q^{57} + 24 q^{65} + 14 q^{67} + 20 q^{79} + 54 q^{81} + 6 q^{85} + 30 q^{93} + 60 q^{95} + 90 q^{99}+O(q^{100}) $ 16 * q + 6 * q^9 - 12 * q^15 + 16 * q^25 - 12 * q^29 - 2 * q^37 + 18 * q^39 + 4 * q^43 + 6 * q^51 - 36 * q^53 - 42 * q^57 + 24 * q^65 + 14 * q^67 + 20 * q^79 + 54 * q^81 + 6 * q^85 + 30 * q^93 + 60 * q^95 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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			0
$2$		0			0
$3$	1.69483	−	0.357142i	0.978511	−	0.206196i
$3$	1.69483	−	0.357142i	0.978511	−	0.206196i
$4$		0			0
$5$	2.42488			1.08444			0.542220	−	0.840237i	$-0.317584\pi$
$5$	2.42488			1.08444			0.542220	+	0.840237i	$0.317584\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	2.74490	−	1.21059i	0.914967	−	0.403530i
$10$		0			0
$11$			2.42118i			0.730013i	0.931005	+	0.365006i	$0.118933\pi$
$11$			2.42118i			0.730013i	−0.931005	+	0.365006i	$0.881067\pi$
$12$		0			0
$13$	4.73574	+	2.73418i	1.31346	+	0.758325i	0.982667	−	0.185380i	$-0.0593516\pi$
$13$	4.73574	+	2.73418i	1.31346	+	0.758325i	0.330790	+	0.943704i	$0.392685\pi$
$14$		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	$-0.732015\pi$
$17$	1.29034	−	2.23494i	0.312954	−	0.542053i	0.979001	+	0.203858i	$0.0653480\pi$
$18$		0			0
$19$	−0.348755	+	0.201354i	−0.0800100	+	0.0461938i	−0.539471	−	0.842004i	$-0.681376\pi$
$19$	−0.348755	+	0.201354i	−0.0800100	+	0.0461938i	0.459461	+	0.888198i	$0.348043\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	3.54372i		−	0.738916i	−0.929247	−	0.369458i	$-0.879543\pi$
$23$		−	3.54372i		−	0.738916i	0.929247	−	0.369458i	$-0.120457\pi$
$24$		0			0
$25$	0.880040			0.176008
$26$		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
$31$	−3.63732	+	2.10001i	−0.653282	+	0.377172i	−0.789712	−	0.613477i	$-0.789770\pi$
$31$	−3.63732	+	2.10001i	−0.653282	+	0.377172i	0.136431	+	0.990650i	$0.456437\pi$
$32$		0			0
$33$	0.864703	+	4.10349i	0.150526	+	0.714325i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.59680	+	2.76574i	0.262513	+	0.454685i	0.966909	−	0.255122i	$-0.0821155\pi$
$37$	1.59680	+	2.76574i	0.262513	+	0.454685i	−0.704396	+	0.709807i	$0.748782\pi$
$38$		0			0
$39$	9.00276	+	2.94264i	1.44159	+	0.471199i
$40$		0			0
$41$	−4.03924	+	6.99618i	−0.630824	+	1.09262i	0.356560	+	0.934273i	$0.383950\pi$
$41$	−4.03924	+	6.99618i	−0.630824	+	1.09262i	−0.987384	+	0.158346i	$0.949384\pi$
$42$		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
$45$	6.65605	−	2.93553i	0.992225	−	0.437603i
$46$		0			0
$47$	2.25769	−	3.91043i	0.329317	−	0.570395i	−0.653059	−	0.757307i	$-0.726515\pi$
$47$	2.25769	−	3.91043i	0.329317	−	0.570395i	0.982377	+	0.186912i	$0.0598480\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	1.38872	−	4.24868i	0.194460	−	0.594934i
$52$		0			0
$53$	12.1493	+	7.01442i	1.66884	+	0.963505i	0.968265	+	0.249926i	$0.0804065\pi$
$53$	12.1493	+	7.01442i	1.66884	+	0.963505i	0.700575	+	0.713579i	$0.252927\pi$
$54$		0			0
$55$			5.87106i			0.791654i
$56$		0			0
$57$	−0.519169	+	0.465816i	−0.0687657	+	0.0616989i
$58$		0			0
$59$	0.0779043	+	0.134934i	0.0101423	+	0.0175669i	0.871052	−	0.491191i	$-0.163438\pi$
$59$	0.0779043	+	0.134934i	0.0101423	+	0.0175669i	−0.860910	+	0.508758i	$0.830105\pi$
$60$		0			0
$61$	−10.2288	−	5.90561i	−1.30967	−	0.756136i	−0.327626	−	0.944808i	$-0.606248\pi$
$61$	−10.2288	−	5.90561i	−1.30967	−	0.756136i	−0.982040	+	0.188672i	$0.939582\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	11.4836	+	6.63005i	1.42436	+	0.822357i
$66$		0			0
$67$	2.53682	+	4.39390i	0.309922	+	0.536801i	0.978345	−	0.206981i	$-0.0663637\pi$
$67$	2.53682	+	4.39390i	0.309922	+	0.536801i	−0.668423	+	0.743781i	$0.733030\pi$
$68$		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	0.874678	−	0.484704i	$-0.161073\pi$
$73$	7.62339	+	4.40137i	0.892251	+	0.515141i	0.0175727	+	0.999846i	$0.494406\pi$
$74$		0			0
$75$	1.49152	−	0.314299i	0.172226	−	0.0362921i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	5.66575	−	9.81337i	0.637447	−	1.10409i	−0.348544	−	0.937292i	$-0.613324\pi$
$79$	5.66575	−	9.81337i	0.637447	−	1.10409i	0.985991	−	0.166798i	$-0.0533427\pi$
$80$		0			0
$81$	6.06895	−	6.64589i	0.674328	−	0.738432i
$82$		0			0
$83$	−7.50937	−	13.0066i	−0.824260	−	1.42766i	−0.902483	−	0.430725i	$-0.858258\pi$
$83$	−7.50937	−	13.0066i	−0.824260	−	1.42766i	0.0782227	−	0.996936i	$-0.475075\pi$
$84$		0			0
$85$	3.12893	−	5.41946i	0.339380	−	0.587823i
$86$		0			0
$87$	−9.40495	+	8.43843i	−1.00832	+	0.904695i
$88$		0			0
$89$	−7.83339	−	13.5678i	−0.830338	−	1.43819i	−0.897771	−	0.440463i	$-0.854814\pi$
$89$	−7.83339	−	13.5678i	−0.830338	−	1.43819i	0.0674328	−	0.997724i	$-0.478519\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−5.41464	+	4.85819i	−0.561472	+	0.503771i
$94$		0			0
$95$	−0.845690	+	0.488259i	−0.0867660	+	0.0500944i
$96$		0			0
$97$	−4.97713	+	2.87355i	−0.505351	+	0.291765i	−0.730921	−	0.682462i	$-0.760909\pi$
$97$	−4.97713	+	2.87355i	−0.505351	+	0.291765i	0.225569	+	0.974227i	$0.427576\pi$
$98$		0			0
$99$	2.93105	+	6.64589i	0.294582	+	0.667937i
$100$		0			0
$101$	−9.67675			−0.962873			−0.481436	−	0.876481i	$-0.659885\pi$
$101$	−9.67675			−0.962873			−0.481436	+	0.876481i	$0.659885\pi$
$102$		0			0
$103$			19.2676i			1.89850i	0.314526	+	0.949249i	$0.398155\pi$
$103$			19.2676i			1.89850i	−0.314526	+	0.949249i	$0.601845\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.944715	−	0.545431i	0.0913290	−	0.0527288i	−0.453640	−	0.891185i	$-0.649875\pi$
$107$	0.944715	−	0.545431i	0.0913290	−	0.0527288i	0.544969	+	0.838456i	$0.316541\pi$
$108$		0			0
$109$	−1.15678	+	2.00360i	−0.110800	+	0.191910i	−0.916093	−	0.400966i	$-0.868674\pi$
$109$	−1.15678	+	2.00360i	−0.110800	+	0.191910i	0.805293	+	0.592877i	$0.202008\pi$
$110$		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
$115$		−	8.59309i		−	0.801309i
$116$		0			0
$117$	16.3091	+	1.77202i	1.50778	+	0.163823i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.13790			0.467082
$122$		0			0
$123$	−4.34721	+	13.2999i	−0.391974	+	1.19921i
$124$		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
$129$	−9.77588	−	10.8956i	−0.860718	−	0.959303i
$130$		0			0
$131$	−11.4630			−1.00153			−0.500765	−	0.865584i	$-0.666948\pi$
$131$	−11.4630			−1.00153			−0.500765	+	0.865584i	$0.666948\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	10.2325	−	7.35238i	0.880671	−	0.632792i
$136$		0			0
$137$			1.97456i			0.168698i	0.996436	+	0.0843488i	$0.0268810\pi$
$137$			1.97456i			0.168698i	−0.996436	+	0.0843488i	$0.973119\pi$
$138$		0			0
$139$	−5.37804	−	3.10501i	−0.456159	−	0.263364i	0.254269	−	0.967134i	$-0.418165\pi$
$139$	−5.37804	−	3.10501i	−0.456159	−	0.263364i	−0.710428	+	0.703770i	$0.751499\pi$
$140$		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
$149$		−	12.1692i		−	0.996943i	−0.866906	−	0.498472i	$-0.833895\pi$
$149$		−	12.1692i		−	0.996943i	0.866906	−	0.498472i	$-0.166105\pi$
$150$		0			0
$151$	10.6357			0.865519			0.432759	−	0.901509i	$-0.357540\pi$
$151$	10.6357			0.865519			0.432759	+	0.901509i	$0.357540\pi$
$152$		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
$157$	3.06154	−	1.76758i	0.244337	−	0.141068i	−0.372831	−	0.927899i	$-0.621613\pi$
$157$	3.06154	−	1.76758i	0.244337	−	0.141068i	0.617169	+	0.786831i	$0.288280\pi$
$158$		0			0
$159$	23.0962	+	7.54922i	1.83165	+	0.598692i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−3.16575	−	5.48324i	−0.247961	−	0.429481i	0.714999	−	0.699125i	$-0.246427\pi$
$163$	−3.16575	−	5.48324i	−0.247961	−	0.429481i	−0.962960	+	0.269645i	$0.913094\pi$
$164$		0			0
$165$	2.09680	+	9.95046i	0.163236	+	0.774642i
$166$		0			0
$167$	8.39779	−	14.5454i	0.649840	−	1.12556i	−0.333320	−	0.942814i	$-0.608169\pi$
$167$	8.39779	−	14.5454i	0.649840	−	1.12556i	0.983161	−	0.182743i	$-0.0584976\pi$
$168$		0			0
$169$	8.45146	+	14.6384i	0.650112	+	1.12603i
$170$		0			0
$171$	−0.713542	+	0.974896i	−0.0545659	+	0.0745522i
$172$		0			0
$173$	8.30850	−	14.3907i	0.631684	−	1.09411i	−0.355524	−	0.934667i	$-0.615697\pi$
$173$	8.30850	−	14.3907i	0.631684	−	1.09411i	0.987207	−	0.159441i	$-0.0509692\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.180225	+	0.200868i	0.0135466	+	0.0150981i
$178$		0			0
$179$	−12.6082	−	7.27937i	−0.942384	−	0.544086i	−0.0516773	−	0.998664i	$-0.516457\pi$
$179$	−12.6082	−	7.27937i	−0.942384	−	0.544086i	−0.890707	+	0.454578i	$0.849790\pi$
$180$		0			0
$181$			4.02355i			0.299068i	0.988757	+	0.149534i	$0.0477774\pi$
$181$			4.02355i			0.299068i	−0.988757	+	0.149534i	$0.952223\pi$
$182$		0			0
$183$	−19.4452	−	6.35587i	−1.43743	−	0.469839i
$184$		0			0
$185$	3.87205	+	6.70659i	0.284679	+	0.493078i
$186$		0			0
$187$	5.41119	+	3.12415i	0.395705	+	0.228461i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−7.28998	−	4.20887i	−0.527485	−	0.304543i	0.212507	−	0.977160i	$-0.431837\pi$
$191$	−7.28998	−	4.20887i	−0.527485	−	0.304543i	−0.739992	+	0.672616i	$0.765171\pi$
$192$		0			0
$193$	4.31784	+	7.47871i	0.310805	+	0.538330i	0.978537	−	0.206072i	$-0.0660681\pi$
$193$	4.31784	+	7.47871i	0.310805	+	0.538330i	−0.667732	+	0.744402i	$0.732735\pi$
$194$		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	0.866670	−	0.498882i	$-0.166256\pi$
$199$	12.2441	+	7.06913i	0.867960	+	0.501117i	0.00129041	+	0.999999i	$0.499589\pi$
$200$		0			0
$201$	5.86873	+	6.54092i	0.413948	+	0.461361i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−9.79468	+	16.9649i	−0.684090	+	1.18488i
$206$		0			0
$207$	−4.28998	−	9.72715i	−0.298175	−	0.676083i
$208$		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
$213$	−3.12137	−	14.8126i	−0.213873	−	1.01494i
$214$		0			0
$215$	−10.2469	−	17.7481i	−0.698832	−	1.21041i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	14.4923	+	4.73694i	0.979297	+	0.320093i
$220$		0			0
$221$	12.2215	−	7.05606i	0.822104	−	0.474642i
$222$		0			0
$223$	−13.4054	+	7.73961i	−0.897692	+	0.518283i	−0.876451	−	0.481492i	$-0.840095\pi$
$223$	−13.4054	+	7.73961i	−0.897692	+	0.518283i	−0.0212411	+	0.999774i	$0.506762\pi$
$224$		0			0
$225$	2.41562	−	1.06537i	0.161041	−	0.0710245i
$226$		0			0
$227$	15.0167			0.996694			0.498347	−	0.866978i	$-0.333941\pi$
$227$	15.0167			0.996694			0.498347	+	0.866978i	$0.333941\pi$
$228$		0			0
$229$			19.5935i			1.29478i	0.762160	+	0.647389i	$0.224139\pi$
$229$			19.5935i			1.29478i	−0.762160	+	0.647389i	$0.775861\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−16.9283	+	9.77356i	−1.10901	+	0.640287i	−0.938573	−	0.345081i	$-0.887851\pi$
$233$	−16.9283	+	9.77356i	−1.10901	+	0.640287i	−0.170437	+	0.985369i	$0.554518\pi$
$234$		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
$241$		−	8.33094i		−	0.536643i	−0.963329	−	0.268321i	$-0.913531\pi$
$241$		−	8.33094i		−	0.536643i	0.963329	−	0.268321i	$-0.0864689\pi$
$242$		0			0
$243$	7.91231	−	13.4311i	0.507575	−	0.861607i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−2.20215			−0.140120
$248$		0			0
$249$	−17.3723	−	19.3621i	−1.10093	−	1.22702i
$250$		0			0
$251$	−13.5763			−0.856928			−0.428464	−	0.903559i	$-0.640945\pi$
$251$	−13.5763			−0.856928			−0.428464	+	0.903559i	$0.640945\pi$
$252$		0			0
$253$	8.57997			0.539418
$254$		0			0
$255$	3.36749	−	10.3025i	0.210880	−	0.645170i
$256$		0			0
$257$	5.98060			0.373059			0.186530	−	0.982449i	$-0.440276\pi$
$257$	5.98060			0.373059			0.186530	+	0.982449i	$0.440276\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−12.9261	+	17.6606i	−0.800104	+	1.09316i
$262$		0			0
$263$		−	3.36602i		−	0.207558i	−0.994600	−	0.103779i	$-0.966907\pi$
$263$		−	3.36602i		−	0.207558i	0.994600	−	0.103779i	$-0.0330934\pi$
$264$		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	$-0.955495\pi$
$269$	−6.14112	+	10.6367i	−0.374431	+	0.648533i	0.615811	+	0.787894i	$0.288829\pi$
$270$		0			0
$271$	−25.4823	+	14.7122i	−1.54794	+	0.893703i	−0.549640	+	0.835402i	$0.685235\pi$
$271$	−25.4823	+	14.7122i	−1.54794	+	0.893703i	−0.998299	+	0.0583012i	$0.981432\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			2.13073i			0.128488i
$276$		0			0
$277$	−9.20215			−0.552904			−0.276452	−	0.961028i	$-0.589159\pi$
$277$	−9.20215			−0.552904			−0.276452	+	0.961028i	$0.589159\pi$
$278$		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
$283$	−10.5776	+	6.10696i	−0.628771	+	0.363021i	−0.780276	−	0.625435i	$-0.784921\pi$
$283$	−10.5776	+	6.10696i	−0.628771	+	0.363021i	0.151505	+	0.988457i	$0.451588\pi$
$284$		0			0
$285$	−1.25892	+	1.12955i	−0.0745722	+	0.0669086i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	5.17002	+	8.95475i	0.304119	+	0.526750i
$290$		0			0
$291$	−7.40913	+	6.64772i	−0.434331	+	0.389696i
$292$		0			0
$293$	−3.15082	+	5.45739i	−0.184073	+	0.318824i	−0.943264	−	0.332044i	$-0.892262\pi$
$293$	−3.15082	+	5.45739i	−0.184073	+	0.318824i	0.759191	+	0.650868i	$0.225595\pi$
$294$		0			0
$295$	0.188909	+	0.327199i	0.0109987	+	0.0190503i
$296$		0			0
$297$	7.34116	+	10.2169i	0.425977	+	0.592842i
$298$		0			0
$299$	9.68915	−	16.7821i	0.560338	−	0.970534i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−16.4004	+	3.45597i	−0.942181	+	0.198540i
$304$		0			0
$305$	−24.8036	−	14.3204i	−1.42025	−	0.819983i
$306$		0			0
$307$			28.7264i			1.63950i	0.572721	+	0.819750i	$0.305888\pi$
$307$			28.7264i			1.63950i	−0.572721	+	0.819750i	$0.694112\pi$
$308$		0			0
$309$	6.88128	+	32.6554i	0.391462	+	1.85770i
$310$		0			0
$311$	−8.86623	−	15.3568i	−0.502758	−	0.870802i	−0.999995	−	0.00318766i	$-0.998985\pi$
$311$	−8.86623	−	15.3568i	−0.502758	−	0.870802i	0.497237	−	0.867615i	$-0.334348\pi$
$312$		0			0
$313$	−23.4526	−	13.5404i	−1.32562	−	0.765348i	−0.341003	−	0.940062i	$-0.610767\pi$
$313$	−23.4526	−	13.5404i	−1.32562	−	0.765348i	−0.984619	+	0.174714i	$0.944100\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.65389	+	2.68692i	0.261388	+	0.150913i	0.624968	−	0.780651i	$-0.285112\pi$
$317$	4.65389	+	2.68692i	0.261388	+	0.150913i	−0.363579	+	0.931563i	$0.618445\pi$
$318$		0			0
$319$	−8.83150	−	15.2966i	−0.494469	−	0.856446i
$320$		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
$327$	−1.24498	+	3.80890i	−0.0688474	+	0.210633i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	3.72104	−	6.44502i	0.204527	−	0.354250i	−0.745455	−	0.666556i	$-0.767768\pi$
$331$	3.72104	−	6.44502i	0.204527	−	0.354250i	0.949982	+	0.312305i	$0.101101\pi$
$332$		0			0
$333$	7.73124	+	5.65861i	0.423669	+	0.310090i
$334$		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
$339$	26.3991	+	8.62882i	1.43380	+	0.468653i
$340$		0			0
$341$	−5.08449	−	8.80660i	−0.275341	−	0.476904i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−3.06895	−	14.5638i	−0.165227	−	0.784090i
$346$		0			0
$347$	1.63842	−	0.945944i	0.0879552	−	0.0507809i	−0.455377	−	0.890299i	$-0.650496\pi$
$347$	1.63842	−	0.945944i	0.0879552	−	0.0507809i	0.543332	+	0.839518i	$0.317162\pi$
$348$		0			0
$349$	16.1105	−	9.30140i	0.862375	−	0.497892i	−0.00243201	−	0.999997i	$-0.500774\pi$
$349$	16.1105	−	9.30140i	0.862375	−	0.497892i	0.864807	+	0.502105i	$0.167441\pi$
$350$		0			0
$351$	28.2740	−	2.82139i	1.50915	−	0.150595i
$352$		0			0
$353$	−3.89010			−0.207049			−0.103525	−	0.994627i	$-0.533012\pi$
$353$	−3.89010			−0.207049			−0.103525	+	0.994627i	$0.533012\pi$
$354$		0			0
$355$		−	21.1931i		−	1.12481i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	7.46992	−	4.31276i	0.394248	−	0.227619i	−0.289751	−	0.957102i	$-0.593573\pi$
$359$	7.46992	−	4.31276i	0.394248	−	0.227619i	0.683999	+	0.729483i	$0.260239\pi$
$360$		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
$367$			18.3252i			0.956568i	0.878205	+	0.478284i	$0.158741\pi$
$367$			18.3252i			0.956568i	−0.878205	+	0.478284i	$0.841259\pi$
$368$		0			0
$369$	−2.61783	+	24.0937i	−0.136279	+	1.25427i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−7.69583			−0.398475			−0.199237	−	0.979951i	$-0.563846\pi$
$373$	−7.69583			−0.398475			−0.199237	+	0.979951i	$0.563846\pi$
$374$		0			0
$375$	−16.9320	+	3.56799i	−0.874367	+	0.184250i
$376$		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
$381$	−5.19339	+	1.09437i	−0.266065	+	0.0560664i
$382$		0			0
$383$	−3.40934			−0.174209			−0.0871047	−	0.996199i	$-0.527761\pi$
$383$	−3.40934			−0.174209			−0.0871047	+	0.996199i	$0.527761\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−20.4597	−	14.9748i	−1.04003	−	0.761211i
$388$		0			0
$389$			9.62356i			0.487934i	0.969784	+	0.243967i	$0.0784489\pi$
$389$			9.62356i			0.487934i	−0.969784	+	0.243967i	$0.921551\pi$
$390$		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	0.106308	−	0.994333i	$-0.466097\pi$
$397$	20.3349	−	11.7404i	1.02058	−	0.589232i	0.914272	+	0.405101i	$0.132764\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			25.6365i			1.28023i	0.768281	+	0.640113i	$0.221113\pi$
$401$			25.6365i			1.28023i	−0.768281	+	0.640113i	$0.778887\pi$
$402$		0			0
$403$	−22.9672			−1.14408
$404$		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
$409$	13.3646	−	7.71603i	0.660835	−	0.381533i	−0.131760	−	0.991282i	$-0.542063\pi$
$409$	13.3646	−	7.71603i	0.660835	−	0.381533i	0.792595	+	0.609748i	$0.208730\pi$
$410$		0			0
$411$	0.705196	+	3.34654i	0.0347848	+	0.165073i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−18.2093	−	31.5395i	−0.893860	−	1.54821i
$416$		0			0
$417$	−10.2238	−	3.34175i	−0.500661	−	0.163646i
$418$		0			0
$419$	−7.10643	+	12.3087i	−0.347172	+	0.601319i	−0.985746	−	0.168241i	$-0.946191\pi$
$419$	−7.10643	+	12.3087i	−0.347172	+	0.601319i	0.638574	+	0.769560i	$0.279525\pi$
$420$		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
$423$	1.46320	−	13.4669i	0.0711433	−	0.654781i
$424$		0			0
$425$	1.13555	−	1.96684i	0.0550825	−	0.0954057i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−7.12465	+	21.7973i	−0.343982	+	1.05238i
$430$		0			0
$431$	−28.2868	−	16.3314i	−1.36253	−	0.786656i	−0.372568	−	0.928005i	$-0.621523\pi$
$431$	−28.2868	−	16.3314i	−1.36253	−	0.786656i	−0.989960	+	0.141349i	$0.954856\pi$
$432$		0			0
$433$			13.6919i			0.657992i	0.944331	+	0.328996i	$0.106710\pi$
$433$			13.6919i			0.657992i	−0.944331	+	0.328996i	$0.893290\pi$
$434$		0			0
$435$	−22.8059	+	20.4622i	−1.09346	+	0.981087i
$436$		0			0
$437$	0.713542	+	1.23589i	0.0341333	+	0.0591207i
$438$		0			0
$439$	−7.64139	−	4.41176i	−0.364704	−	0.210562i	0.306438	−	0.951890i	$-0.400863\pi$
$439$	−7.64139	−	4.41176i	−0.364704	−	0.210562i	−0.671142	+	0.741329i	$0.734196\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−21.3562	−	12.3300i	−1.01466	−	0.585816i	−0.102109	−	0.994773i	$-0.532559\pi$
$443$	−21.3562	−	12.3300i	−1.01466	−	0.585816i	−0.912554	+	0.408957i	$0.865893\pi$
$444$		0			0
$445$	−18.9950	−	32.9004i	−0.900451	−	1.55963i
$446$		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
$453$	18.0257	−	3.79844i	0.846920	−	0.178466i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−3.85935	+	6.68460i	−0.180533	+	0.312692i	−0.942062	−	0.335438i	$-0.891116\pi$
$457$	−3.85935	+	6.68460i	−0.180533	+	0.312692i	0.761529	+	0.648131i	$0.224449\pi$
$458$		0			0
$459$	−1.33150	−	13.3434i	−0.0621491	−	0.622816i
$460$		0			0
$461$	−9.28621	−	16.0842i	−0.432502	−	0.749115i	0.564586	−	0.825374i	$-0.309036\pi$
$461$	−9.28621	−	16.0842i	−0.432502	−	0.749115i	−0.997088	+	0.0762589i	$0.975702\pi$
$462$		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
$465$	−13.1298	+	11.7805i	−0.608882	+	0.546309i
$466$		0			0
$467$	7.92166	+	13.7207i	0.366571	+	0.634919i	0.989027	−	0.147736i	$-0.0471985\pi$
$467$	7.92166	+	13.7207i	0.366571	+	0.634919i	−0.622456	+	0.782655i	$0.713865\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	4.55751	−	4.08915i	0.209999	−	0.188418i
$472$		0			0
$473$	17.7210	−	10.2312i	0.814814	−	0.470433i
$474$		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
$479$	−26.5025			−1.21093			−0.605465	−	0.795872i	$-0.707013\pi$
$479$	−26.5025			−1.21093			−0.605465	+	0.795872i	$0.707013\pi$
$480$		0			0
$481$			17.4638i			0.796279i
$482$		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	−0.775628	−	0.631190i	$-0.782567\pi$
$487$	3.50469	−	6.07031i	0.158813	−	0.275072i	0.934441	+	0.356118i	$0.115900\pi$
$488$		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
$493$			18.8267i			0.847910i
$494$		0			0
$495$	7.10745	+	16.1155i	0.319456	+	0.724337i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	1.25786			0.0563094			0.0281547	−	0.999604i	$-0.491037\pi$
$499$	1.25786			0.0563094			0.0281547	+	0.999604i	$0.491037\pi$
$500$		0			0
$501$	9.03806	−	27.6512i	0.403791	−	1.23536i
$502$		0			0
$503$	37.9507			1.69214			0.846070	−	0.533072i	$-0.178963\pi$
$503$	37.9507			1.69214			0.846070	+	0.533072i	$0.178963\pi$
$504$		0			0
$505$	−23.4650			−1.04418
$506$		0			0
$507$	19.5518	+	21.7912i	0.868324	+	0.967780i
$508$		0			0
$509$	5.80942			0.257498			0.128749	−	0.991677i	$-0.458904\pi$
$509$	5.80942			0.257498			0.128749	+	0.991677i	$0.458904\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−0.861156	+	1.90712i	−0.0380210	+	0.0842014i
$514$		0			0
$515$			46.7217i			2.05881i
$516$		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	$-0.930354\pi$
$521$	−6.84995	+	11.8645i	−0.300102	+	0.519791i	0.676057	+	0.736849i	$0.263687\pi$
$522$		0			0
$523$	−21.2073	+	12.2440i	−0.927330	+	0.535394i	−0.885966	−	0.463750i	$-0.846504\pi$
$523$	−21.2073	+	12.2440i	−0.927330	+	0.535394i	−0.0413640	+	0.999144i	$0.513170\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			10.8389i			0.472151i
$528$		0			0
$529$	10.4421			0.454003
$530$		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
$535$	2.29082	−	1.32261i	0.0990408	−	0.0571812i
$536$		0			0
$537$	−23.9686	−	7.83437i	−1.03432	−	0.338078i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	18.5804	+	32.1822i	0.798833	+	1.38362i	0.920376	+	0.391034i	$0.127882\pi$
$541$	18.5804	+	32.1822i	0.798833	+	1.38362i	−0.121543	+	0.992586i	$0.538784\pi$
$542$		0			0
$543$	1.43698	+	6.81924i	0.0616666	+	0.292641i
$544$		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
$549$	−35.2263	−	3.82741i	−1.50342	−	0.163350i
$550$		0			0
$551$	1.46892	−	2.54424i	0.0625781	−	0.108388i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	8.95767	+	9.98366i	0.380232	+	0.423783i
$556$		0			0
$557$	−21.3205	−	12.3094i	−0.903378	−	0.521565i	−0.0250832	−	0.999685i	$-0.507985\pi$
$557$	−21.3205	−	12.3094i	−0.903378	−	0.521565i	−0.878295	+	0.478120i	$0.841318\pi$
$558$		0			0
$559$		−	46.2156i		−	1.95471i
$560$		0			0
$561$	10.2868	+	3.36235i	0.434310	+	0.141958i
$562$		0			0
$563$	−6.28555	−	10.8869i	−0.264904	−	0.458828i	0.702634	−	0.711551i	$-0.252007\pi$
$563$	−6.28555	−	10.8869i	−0.264904	−	0.458828i	−0.967539	+	0.252724i	$0.918674\pi$
$564$		0			0
$565$	33.6738	+	19.4416i	1.41667	+	0.817913i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	12.8872	+	7.44043i	0.540260	+	0.311919i	0.745184	−	0.666859i	$-0.232362\pi$
$569$	12.8872	+	7.44043i	0.540260	+	0.311919i	−0.204924	+	0.978778i	$0.565695\pi$
$570$		0			0
$571$	8.45573	+	14.6458i	0.353861	+	0.612906i	0.986922	−	0.161196i	$-0.0515351\pi$
$571$	8.45573	+	14.6458i	0.353861	+	0.612906i	−0.633061	+	0.774102i	$0.718202\pi$
$572$		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	0.0734203	−	0.997301i	$-0.476609\pi$
$577$	−18.1011	−	10.4507i	−0.753558	−	0.435067i	−0.826978	+	0.562234i	$0.809942\pi$
$578$		0			0
$579$	9.98896	+	11.1331i	0.415127	+	0.462675i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−16.9832	+	29.4157i	−0.703371	+	1.21827i
$584$		0			0
$585$	39.5476	+	4.29692i	1.63509	+	0.177656i
$586$		0			0
$587$	−14.8542	−	25.7283i	−0.613100	−	1.06192i	−0.990715	−	0.135957i	$-0.956589\pi$
$587$	−14.8542	−	25.7283i	−0.613100	−	1.06192i	0.377615	−	0.925963i	$-0.376744\pi$
$588$		0			0
$589$	0.845690	−	1.46478i	0.0348461	−	0.0603551i
$590$		0			0
$591$	−8.33222	−	39.5409i	−0.342742	−	1.62649i
$592$		0			0
$593$	5.89603	+	10.2122i	0.242121	+	0.419365i	0.961318	−	0.275440i	$-0.0888237\pi$
$593$	5.89603	+	10.2122i	0.242121	+	0.419365i	−0.719197	+	0.694806i	$0.755490\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	23.2763	+	7.60810i	0.952637	+	0.311379i
$598$		0			0
$599$	27.7991	−	16.0498i	1.13584	−	0.655778i	0.190443	−	0.981698i	$-0.439008\pi$
$599$	27.7991	−	16.0498i	1.13584	−	0.655778i	0.945397	+	0.325921i	$0.105674\pi$
$600$		0			0
$601$	−16.1636	+	9.33208i	−0.659329	+	0.380664i	−0.792021	−	0.610494i	$-0.790971\pi$
$601$	−16.1636	+	9.33208i	−0.659329	+	0.380664i	0.132692	+	0.991157i	$0.457638\pi$
$602$		0			0
$603$	12.2825	+	8.98978i	0.500183	+	0.366092i
$604$		0			0
$605$	12.4588			0.506522
$606$		0			0
$607$		−	13.8684i		−	0.562900i	−0.959576	−	0.281450i	$-0.909185\pi$
$607$		−	13.8684i		−	0.562900i	0.959576	−	0.281450i	$-0.0908154\pi$
$608$		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	−0.574032	−	0.818833i	$-0.694622\pi$
$613$	10.4510	−	18.1017i	0.422114	−	0.731122i	0.996146	+	0.0877104i	$0.0279550\pi$
$614$		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
$619$			5.52857i			0.222212i	0.993809	+	0.111106i	$0.0354393\pi$
$619$			5.52857i			0.222212i	−0.993809	+	0.111106i	$0.964561\pi$
$620$		0			0
$621$	−10.7448	−	14.9537i	−0.431173	−	0.600073i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−28.6257			−1.14503
$626$		0			0
$627$	−1.12782	−	1.25700i	−0.0450409	−	0.0501998i
$628$		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
$633$	−7.27310	+	22.2514i	−0.289080	+	0.884415i
$634$		0			0
$635$	−7.43045			−0.294868
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−10.5804	−	23.9901i	−0.418554	−	0.949032i
$640$		0			0
$641$			29.2340i			1.15467i	0.816506	+	0.577337i	$0.195908\pi$
$641$			29.2340i			1.15467i	−0.816506	+	0.577337i	$0.804092\pi$
$642$		0			0
$643$	−34.6535	−	20.0072i	−1.36660	−	0.789008i	−0.376109	−	0.926575i	$-0.622738\pi$
$643$	−34.6535	−	20.0072i	−1.36660	−	0.789008i	−0.990492	+	0.137567i	$0.956072\pi$
$644$		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	$-0.785819\pi$
$647$	3.78276	−	6.55194i	0.148716	−	0.257583i	0.930753	+	0.365648i	$0.119153\pi$
$648$		0			0
$649$	−0.326700	+	0.188620i	−0.0128241	+	0.00740399i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	39.1877i		−	1.53353i	−0.641927	−	0.766766i	$-0.721865\pi$
$653$		−	39.1877i		−	1.53353i	0.641927	−	0.766766i	$-0.278135\pi$
$654$		0			0
$655$	−27.7965			−1.08610
$656$		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
$661$	27.3501	−	15.7906i	1.06380	−	0.614184i	0.137317	−	0.990527i	$-0.456152\pi$
$661$	27.3501	−	15.7906i	1.06380	−	0.614184i	0.926480	+	0.376343i	$0.122819\pi$
$662$		0			0
$663$	18.1933	−	16.3236i	0.706568	−	0.633957i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	12.9261	+	22.3886i	0.500500	+	0.866891i
$668$		0			0
$669$	−19.9557	+	17.9049i	−0.771533	+	0.692245i
$670$		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
$675$	3.71358	−	2.66834i	0.142936	−	0.102704i
$676$		0			0
$677$	−17.2099	+	29.8084i	−0.661430	+	1.14563i	0.318809	+	0.947819i	$0.396717\pi$
$677$	−17.2099	+	29.8084i	−0.661430	+	1.14563i	−0.980240	+	0.197812i	$0.936616\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	25.4508	−	5.36309i	0.975275	−	0.205514i
$682$		0			0
$683$	16.4694	+	9.50861i	0.630184	+	0.363837i	0.780823	−	0.624752i	$-0.214800\pi$
$683$	16.4694	+	9.50861i	0.630184	+	0.363837i	−0.150639	+	0.988589i	$0.548133\pi$
$684$		0			0
$685$			4.78806i			0.182942i
$686$		0			0
$687$	6.99767	+	33.2077i	0.266978	+	1.26695i
$688$		0			0
$689$	38.3574	+	66.4369i	1.46130	+	2.53104i
$690$		0			0
$691$	16.7795	+	9.68764i	0.638321	+	0.368535i	0.783968	−	0.620802i	$-0.213193\pi$
$691$	16.7795	+	9.68764i	0.638321	+	0.368535i	−0.145646	+	0.989337i	$0.546526\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−13.0411	−	7.52928i	−0.494677	−	0.285602i
$696$		0			0
$697$	10.4240	+	18.0549i	0.394838	+	0.683880i
$698$		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
$705$	5.89202	−	18.0261i	0.221906	−	0.678903i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	20.4119	−	35.3544i	0.766585	−	1.32776i	−0.172820	−	0.984953i	$-0.555288\pi$
$709$	20.4119	−	35.3544i	0.766585	−	1.32776i	0.939405	−	0.342810i	$-0.111379\pi$
$710$		0			0
$711$	3.67196	−	33.7956i	0.137709	−	1.26743i
$712$		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
$717$	13.9955	+	4.57458i	0.522673	+	0.170841i
$718$		0			0
$719$	−21.1578	−	36.6464i	−0.789054	−	1.36668i	−0.926547	−	0.376178i	$-0.877238\pi$
$719$	−21.1578	−	36.6464i	−0.789054	−	1.36668i	0.137494	−	0.990503i	$-0.456095\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−2.97532	−	14.1195i	−0.110654	−	0.525111i
$724$		0			0
$725$	−5.55995	+	3.21004i	−0.206491	+	0.119218i
$726$		0			0
$727$	4.58754	−	2.64862i	0.170142	−	0.0982318i	−0.412511	−	0.910953i	$-0.635348\pi$
$727$	4.58754	−	2.64862i	0.170142	−	0.0982318i	0.582653	+	0.812721i	$0.302015\pi$
$728$		0			0
$729$	8.61321	−	25.5893i	0.319008	−	0.947752i
$730$		0			0
$731$	−21.8106			−0.806694
$732$		0			0
$733$		−	18.6499i		−	0.688852i	−0.938814	−	0.344426i	$-0.888074\pi$
$733$		−	18.6499i		−	0.688852i	0.938814	−	0.344426i	$-0.111926\pi$
$734$		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	0.186648	+	0.982427i	$0.440238\pi$
$739$	−20.5918	+	35.6661i	−0.757483	+	1.31200i	−0.944131	+	0.329572i	$0.893096\pi$
$740$		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
$745$		−	29.5089i		−	1.08112i
$746$		0			0
$747$	−36.3581	−	26.6111i	−1.33027	−	0.973649i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	18.1230			0.661318			0.330659	−	0.943750i	$-0.392729\pi$
$751$	18.1230			0.661318			0.330659	+	0.943750i	$0.392729\pi$
$752$		0			0
$753$	−23.0095	+	4.84866i	−0.838513	+	0.176695i
$754$		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
$759$	14.5416	−	3.06426i	0.527826	−	0.111226i
$760$		0			0
$761$	−11.8107			−0.428139			−0.214070	−	0.976818i	$-0.568672\pi$
$761$	−11.8107			−0.428139			−0.214070	+	0.976818i	$0.568672\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	2.02785	−	18.6637i	0.0733172	−	0.674789i
$766$		0			0
$767$			0.852017i			0.0307646i
$768$		0			0
$769$	−3.14015	−	1.81297i	−0.113237	−	0.0653773i	0.442312	−	0.896861i	$-0.354158\pi$
$769$	−3.14015	−	1.81297i	−0.113237	−	0.0653773i	−0.555549	+	0.831484i	$0.687492\pi$
$770$		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	$-0.903222\pi$
$773$	−6.05553	+	10.4885i	−0.217802	+	0.377245i	0.736333	+	0.676619i	$0.236555\pi$
$774$		0			0
$775$	−3.20099	+	1.84809i	−0.114983	+	0.0663854i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	3.25327i		−	0.116561i
$780$		0			0
$781$	21.1608			0.757192
$782$		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
$787$	−17.5995	+	10.1611i	−0.627354	+	0.362203i	−0.779727	−	0.626120i	$-0.784642\pi$
$787$	−17.5995	+	10.1611i	−0.627354	+	0.362203i	0.152372	+	0.988323i	$0.451309\pi$
$788$		0			0
$789$	−1.20215	−	5.70483i	−0.0427975	−	0.203097i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−32.2940	−	55.9348i	−1.14679	−	1.98630i
$794$		0			0
$795$	56.0055	+	18.3060i	1.98631	+	0.649245i
$796$		0			0
$797$	−16.8973	+	29.2669i	−0.598532	+	1.03669i	0.394506	+	0.918893i	$0.370916\pi$
$797$	−16.8973	+	29.2669i	−0.598532	+	1.03669i	−0.993038	+	0.117795i	$0.962418\pi$
$798$		0			0
$799$	−5.82639	−	10.0916i	−0.206123	−	0.357015i
$800$		0			0
$801$	−37.9269	−	27.7593i	−1.34008	−	0.980827i
$802$		0			0
$803$	−10.6565	+	18.4576i	−0.376060	+	0.651354i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−6.60934	+	20.2207i	−0.232660	+	0.711803i
$808$		0			0
$809$	4.19308	+	2.42087i	0.147421	+	0.0851134i	0.571896	−	0.820326i	$-0.306208\pi$
$809$	4.19308	+	2.42087i	0.147421	+	0.0851134i	−0.424475	+	0.905440i	$0.639541\pi$
$810$		0			0
$811$			0.493486i			0.0173286i	0.999962	+	0.00866432i	$0.00275797\pi$
$811$			0.493486i			0.0173286i	−0.999962	+	0.00866432i	$0.997242\pi$
$812$		0			0
$813$	−37.9338	+	34.0355i	−1.33040	+	1.19368i
$814$		0			0
$815$	−7.67656	−	13.2962i	−0.268898	−	0.465745i
$816$		0			0
$817$	2.94749	+	1.70174i	0.103120	+	0.0595362i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	26.6931	+	15.4113i	0.931595	+	0.537857i	0.887316	−	0.461163i	$-0.152568\pi$
$821$	26.6931	+	15.4113i	0.931595	+	0.537857i	0.0442792	+	0.999019i	$0.485901\pi$
$822$		0			0
$823$	7.94249	+	13.7568i	0.276858	+	0.479532i	0.970602	−	0.240690i	$-0.0773736\pi$
$823$	7.94249	+	13.7568i	0.276858	+	0.479532i	−0.693744	+	0.720221i	$0.744040\pi$
$824$		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	0.549178	−	0.835705i	$-0.314941\pi$
$829$	2.87997	+	1.66275i	0.100026	+	0.0577498i	−0.449153	+	0.893455i	$0.648274\pi$
$830$		0			0
$831$	−15.5961	+	3.28647i	−0.541022	+	0.114006i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	20.3636	−	35.2708i	0.704712	−	1.22060i
$836$		0			0
$837$	−8.98136	+	19.8902i	−0.310441	+	0.687504i
$838$		0			0
$839$	20.9689	+	36.3192i	0.723926	+	1.25388i	0.959414	+	0.282000i	$0.0909978\pi$
$839$	20.9689	+	36.3192i	0.723926	+	1.25388i	−0.235488	+	0.971877i	$0.575669\pi$
$840$		0			0
$841$	12.1100	−	20.9752i	0.417588	−	0.723283i
$842$		0			0
$843$	1.56684	−	1.40582i	0.0539649	−	0.0484191i
$844$		0			0
$845$	20.4938	+	35.4963i	0.705007	+	1.22111i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−15.7461	+	14.1280i	−0.540406	+	0.484870i
$850$		0			0
$851$	9.80100	−	5.65861i	0.335974	−	0.193975i
$852$		0			0
$853$	12.5330	−	7.23594i	0.429122	−	0.247754i	−0.269851	−	0.962902i	$-0.586974\pi$
$853$	12.5330	−	7.23594i	0.429122	−	0.247754i	0.698973	+	0.715149i	$0.253641\pi$
$854$		0			0
$855$	−1.73025	+	2.36401i	−0.0591734	+	0.0808473i
$856$		0			0
$857$	47.4657			1.62140			0.810699	−	0.585463i	$-0.199087\pi$
$857$	47.4657			1.62140			0.810699	+	0.585463i	$0.199087\pi$
$858$		0			0
$859$		−	6.00809i		−	0.204993i	−0.994733	−	0.102497i	$-0.967317\pi$
$859$		−	6.00809i		−	0.204993i	0.994733	−	0.102497i	$-0.0326831\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	27.1064	−	15.6499i	0.922714	−	0.532729i	0.0382141	−	0.999270i	$-0.487833\pi$
$863$	27.1064	−	15.6499i	0.922714	−	0.532729i	0.884500	+	0.466540i	$0.154500\pi$
$864$		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
$871$			27.7445i			0.940086i
$872$		0			0
$873$	−10.1830	+	13.9129i	−0.344644	+	0.470879i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	41.3764			1.39718			0.698591	−	0.715521i	$-0.253811\pi$
$877$	41.3764			1.39718			0.698591	+	0.715521i	$0.253811\pi$
$878$		0			0
$879$	−3.39105	+	10.3746i	−0.114377	+	0.349928i
$880$		0			0
$881$	39.7350			1.33870			0.669352	−	0.742945i	$-0.266572\pi$
$881$	39.7350			1.33870			0.669352	+	0.742945i	$0.266572\pi$
$882$		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
$885$	0.437024	+	0.487080i	0.0146904	+	0.0163730i
$886$		0			0
$887$	28.1122			0.943916			0.471958	−	0.881621i	$-0.343547\pi$
$887$	28.1122			0.943916			0.471958	+	0.881621i	$0.343547\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	16.0909	+	14.6940i	0.539065	+	0.492268i
$892$		0			0
$893$			1.81838i			0.0608497i
$894$		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
$905$			9.75663i			0.324321i
$906$		0			0
$907$	59.4859			1.97520			0.987599	−	0.156997i	$-0.0501812\pi$
$907$	59.4859			1.97520			0.987599	+	0.156997i	$0.0501812\pi$
$908$		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
$913$	31.4913	−	18.1815i	1.04221	−	0.601721i
$914$		0			0
$915$	−47.1524	−	15.4122i	−1.55881	−	0.509512i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	20.7994	+	36.0256i	0.686108	+	1.18837i	0.973087	+	0.230437i	$0.0740156\pi$
$919$	20.7994	+	36.0256i	0.686108	+	1.18837i	−0.286979	+	0.957937i	$0.592651\pi$
$920$		0			0
$921$	10.2594	+	48.6863i	0.338058	+	1.60427i
$922$		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
$927$	23.3252	+	52.8878i	0.766100	+	1.73706i
$928$		0			0
$929$	1.21614	−	2.10641i	0.0399002	−	0.0691092i	−0.845386	−	0.534156i	$-0.820629\pi$
$929$	1.21614	−	2.10641i	0.0399002	−	0.0691092i	0.885286	+	0.465047i	$0.153963\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−20.5113	−	22.8606i	−0.671510	−	0.748423i
$934$		0			0
$935$	13.1215	+	7.57569i	0.429118	+	0.247752i
$936$		0			0
$937$			7.29837i			0.238427i	0.992869	+	0.119214i	$0.0380374\pi$
$937$			7.29837i			0.238427i	−0.992869	+	0.119214i	$0.961963\pi$
$938$		0			0
$939$	−44.5841	−	14.5728i	−1.45495	−	0.475564i
$940$		0			0
$941$	−21.2367	−	36.7831i	−0.692298	−	1.19910i	−0.971083	−	0.238742i	$-0.923265\pi$
$941$	−21.2367	−	36.7831i	−0.692298	−	1.19910i	0.278785	−	0.960354i	$-0.410068\pi$
$942$		0			0
$943$	24.7925	+	14.3139i	0.807354	+	0.466126i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	47.3119	+	27.3155i	1.53743	+	0.887636i	0.998988	+	0.0449739i	$0.0143205\pi$
$947$	47.3119	+	27.3155i	1.53743	+	0.887636i	0.538443	+	0.842662i	$0.319013\pi$
$948$		0			0
$949$	24.0683	+	41.6874i	0.781288	+	1.35323i
$950$		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
$957$	−20.4310	−	22.7711i	−0.660439	−	0.736084i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−6.67994	+	11.5700i	−0.215482	+	0.373226i
$962$		0			0
$963$	1.93285	−	2.64082i	0.0622854	−	0.0850991i
$964$		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
$969$	0.371164	+	1.76138i	0.0119235	+	0.0565836i
$970$		0			0
$971$	27.1241	+	46.9803i	0.870453	+	1.50767i	0.861529	+	0.507708i	$0.169507\pi$
$971$	27.1241	+	46.9803i	0.870453	+	1.50767i	0.00892375	+	0.999960i	$0.497159\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	7.92279	+	2.58964i	0.253732	+	0.0829349i
$976$		0			0
$977$	35.6936	−	20.6077i	1.14194	−	0.659299i	0.195029	−	0.980797i	$-0.437520\pi$
$977$	35.6936	−	20.6077i	1.14194	−	0.659299i	0.946910	+	0.321498i	$0.104186\pi$
$978$		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
$983$	18.4394			0.588125			0.294062	−	0.955786i	$-0.404993\pi$
$983$	18.4394			0.588125			0.294062	+	0.955786i	$0.404993\pi$
$984$		0			0
$985$		−	56.5731i		−	1.80257i
$986$		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	−0.834950	−	0.550326i	$-0.814503\pi$
$991$	1.86116	−	3.22362i	0.0591216	−	0.102402i	0.894071	+	0.447925i	$0.147837\pi$
$992$		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
$997$			0.475330i			0.0150539i	0.999972	+	0.00752693i	$0.00239592\pi$
$997$			0.475330i			0.0150539i	−0.999972	+	0.00752693i	$0.997604\pi$
$998$		0			0
$999$	15.1241	+	6.82924i	0.478504	+	0.216068i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.bm.b.1697.7		16
3.2	odd	2		5292.2.bm.b.2285.2		16
7.2	even	3		1764.2.w.a.509.4		16
7.3	odd	6		252.2.x.a.41.7	yes	16
7.4	even	3		252.2.x.a.41.2	✓	16
7.5	odd	6		1764.2.w.a.509.5		16
7.6	odd	2	inner	1764.2.bm.b.1697.2		16
9.2	odd	6		1764.2.w.a.1109.5		16
9.7	even	3		5292.2.w.a.521.2		16
21.2	odd	6		5292.2.w.a.1097.7		16
21.5	even	6		5292.2.w.a.1097.2		16
21.11	odd	6		756.2.x.a.125.7		16
21.17	even	6		756.2.x.a.125.2		16
21.20	even	2		5292.2.bm.b.2285.7		16
28.3	even	6		1008.2.cc.c.545.2		16
28.11	odd	6		1008.2.cc.c.545.7		16
63.2	odd	6	inner	1764.2.bm.b.1685.2		16
63.4	even	3		2268.2.f.b.1133.14		16
63.11	odd	6		252.2.x.a.209.7	yes	16
63.16	even	3		5292.2.bm.b.4625.7		16
63.20	even	6		1764.2.w.a.1109.4		16
63.25	even	3		756.2.x.a.629.2		16
63.31	odd	6		2268.2.f.b.1133.3		16
63.32	odd	6		2268.2.f.b.1133.4		16
63.34	odd	6		5292.2.w.a.521.7		16
63.38	even	6		252.2.x.a.209.2	yes	16
63.47	even	6	inner	1764.2.bm.b.1685.7		16
63.52	odd	6		756.2.x.a.629.7		16
63.59	even	6		2268.2.f.b.1133.13		16
63.61	odd	6		5292.2.bm.b.4625.2		16
84.11	even	6		3024.2.cc.c.881.7		16
84.59	odd	6		3024.2.cc.c.881.2		16
252.11	even	6		1008.2.cc.c.209.2		16
252.115	even	6		3024.2.cc.c.2897.7		16
252.151	odd	6		3024.2.cc.c.2897.2		16
252.227	odd	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	7.4	even	3
252.2.x.a.41.7	yes	16	7.3	odd	6
252.2.x.a.209.2	yes	16	63.38	even	6
252.2.x.a.209.7	yes	16	63.11	odd	6
756.2.x.a.125.2		16	21.17	even	6
756.2.x.a.125.7		16	21.11	odd	6
756.2.x.a.629.2		16	63.25	even	3
756.2.x.a.629.7		16	63.52	odd	6
1008.2.cc.c.209.2		16	252.11	even	6
1008.2.cc.c.209.7		16	252.227	odd	6
1008.2.cc.c.545.2		16	28.3	even	6
1008.2.cc.c.545.7		16	28.11	odd	6
1764.2.w.a.509.4		16	7.2	even	3
1764.2.w.a.509.5		16	7.5	odd	6
1764.2.w.a.1109.4		16	63.20	even	6
1764.2.w.a.1109.5		16	9.2	odd	6
1764.2.bm.b.1685.2		16	63.2	odd	6	inner
1764.2.bm.b.1685.7		16	63.47	even	6	inner
1764.2.bm.b.1697.2		16	7.6	odd	2	inner
1764.2.bm.b.1697.7		16	1.1	even	1	trivial
2268.2.f.b.1133.3		16	63.31	odd	6
2268.2.f.b.1133.4		16	63.32	odd	6
2268.2.f.b.1133.13		16	63.59	even	6
2268.2.f.b.1133.14		16	63.4	even	3
3024.2.cc.c.881.2		16	84.59	odd	6
3024.2.cc.c.881.7		16	84.11	even	6
3024.2.cc.c.2897.2		16	252.151	odd	6
3024.2.cc.c.2897.7		16	252.115	even	6
5292.2.w.a.521.2		16	9.7	even	3
5292.2.w.a.521.7		16	63.34	odd	6
5292.2.w.a.1097.2		16	21.5	even	6
5292.2.w.a.1097.7		16	21.2	odd	6
5292.2.bm.b.2285.2		16	3.2	odd	2
5292.2.bm.b.2285.7		16	21.20	even	2
5292.2.bm.b.4625.2		16	63.61	odd	6
5292.2.bm.b.4625.7		16	63.16	even	3

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.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.69483 - 0.357142i) q^{3} +2.42488 q^{5} +(2.74490 - 1.21059i) q^{9} +O(q^{10})\)	\(q+(1.69483 - 0.357142i) q^{3} +2.42488 q^{5} +(2.74490 - 1.21059i) q^{9} +2.42118i q^{11} +(4.73574 + 2.73418i) q^{13} +(4.10976 - 0.866025i) q^{15} +(1.29034 - 2.23494i) q^{17} +(-0.348755 + 0.201354i) q^{19} -3.54372i q^{23} +0.880040 q^{25} +(4.21979 - 3.03206i) q^{27} +(-6.31784 + 3.64761i) q^{29} +(-3.63732 + 2.10001i) q^{31} +(0.864703 + 4.10349i) q^{33} +(1.59680 + 2.76574i) q^{37} +(9.00276 + 2.94264i) q^{39} +(-4.03924 + 6.99618i) q^{41} +(-4.22573 - 7.31918i) q^{43} +(6.65605 - 2.93553i) q^{45} +(2.25769 - 3.91043i) q^{47} +(1.38872 - 4.24868i) q^{51} +(12.1493 + 7.01442i) q^{53} +5.87106i q^{55} +(-0.519169 + 0.465816i) q^{57} +(0.0779043 + 0.134934i) q^{59} +(-10.2288 - 5.90561i) q^{61} +(11.4836 + 6.63005i) q^{65} +(2.53682 + 4.39390i) q^{67} +(-1.26561 - 6.00600i) q^{69} -8.73987i q^{71} +(7.62339 + 4.40137i) q^{73} +(1.49152 - 0.314299i) q^{75} +(5.66575 - 9.81337i) q^{79} +(6.06895 - 6.64589i) q^{81} +(-7.50937 - 13.0066i) q^{83} +(3.12893 - 5.41946i) q^{85} +(-9.40495 + 8.43843i) q^{87} +(-7.83339 - 13.5678i) q^{89} +(-5.41464 + 4.85819i) q^{93} +(-0.845690 + 0.488259i) q^{95} +(-4.97713 + 2.87355i) q^{97} +(2.93105 + 6.64589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{9}+O(q^{10}) \) 16 * q + 6 * q^9	\( 16 q + 6 q^{9} - 12 q^{15} + 16 q^{25} - 12 q^{29} - 2 q^{37} + 18 q^{39} + 4 q^{43} + 6 q^{51} - 36 q^{53} - 42 q^{57} + 24 q^{65} + 14 q^{67} + 20 q^{79} + 54 q^{81} + 6 q^{85} + 30 q^{93} + 60 q^{95} + 90 q^{99}+O(q^{100}) \) 16 * q + 6 * q^9 - 12 * q^15 + 16 * q^25 - 12 * q^29 - 2 * q^37 + 18 * q^39 + 4 * q^43 + 6 * q^51 - 36 * q^53 - 42 * q^57 + 24 * q^65 + 14 * q^67 + 20 * q^79 + 54 * q^81 + 6 * q^85 + 30 * q^93 + 60 * q^95 + 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more