LMFDB - Embedded newform 252.2.x.a.209.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(41,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("252.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.x (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.01223013094$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			209.7
Root			$-1.69483 - 0.357142i$ of defining polynomial
Character	$\chi$	$=$	252.209
Dual form			252.2.x.a.41.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15671 - 1.28920i) q^{3} +(1.21244 + 2.10001i) q^{5} +(1.05649 - 2.42566i) q^{7} +(-0.324049 - 2.98245i) q^{9} +O(q^{10})$	\(q+(1.15671 - 1.28920i) q^{3} +(1.21244 + 2.10001i) q^{5} +(1.05649 - 2.42566i) q^{7} +(-0.324049 - 2.98245i) q^{9} +(2.09680 + 1.21059i) q^{11} +(-4.73574 + 2.73418i) q^{13} +(4.10976 + 0.866025i) q^{15} +2.58069 q^{17} -0.402708i q^{19} +(-1.90510 - 4.16781i) q^{21} +(3.06895 - 1.77186i) q^{23} +(-0.440020 + 0.762137i) q^{25} +(-4.21979 - 3.03206i) q^{27} +(-6.31784 - 3.64761i) q^{29} +(-3.63732 + 2.10001i) q^{31} +(3.98607 - 1.30289i) q^{33} +(6.37484 - 0.722330i) q^{35} -3.19360 q^{37} +(-1.95298 + 9.26794i) q^{39} +(4.03924 + 6.99618i) q^{41} +(-4.22573 + 7.31918i) q^{43} +(5.87027 - 4.29654i) q^{45} +(-2.25769 + 3.91043i) q^{47} +(-4.76766 - 5.12537i) q^{49} +(2.98510 - 3.32701i) q^{51} +14.0288i q^{53} +5.87106i q^{55} +(-0.519169 - 0.465816i) q^{57} +(-0.0779043 - 0.134934i) q^{59} +(-10.2288 - 5.90561i) q^{61} +(-7.57676 - 2.36489i) q^{63} +(-11.4836 - 6.63005i) q^{65} +(2.53682 + 4.39390i) q^{67} +(1.26561 - 6.00600i) q^{69} +8.73987i q^{71} -8.80274i q^{73} +(0.473569 + 1.44884i) q^{75} +(5.15173 - 3.80715i) q^{77} +(5.66575 - 9.81337i) q^{79} +(-8.78998 + 1.93292i) q^{81} +(7.50937 - 13.0066i) q^{83} +(3.12893 + 5.41946i) q^{85} +(-12.0104 + 3.92571i) q^{87} -15.6668 q^{89} +(1.62893 + 14.3759i) q^{91} +(-1.50000 + 7.11831i) q^{93} +(0.845690 - 0.488259i) q^{95} +(4.97713 + 2.87355i) q^{97} +(2.93105 - 6.64589i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{7}+O(q^{10}) $ 16 * q - q^7	$ 16 q - q^{7} + 6 q^{11} - 12 q^{15} + 9 q^{21} + 6 q^{23} - 8 q^{25} - 12 q^{29} + 4 q^{37} + 18 q^{39} + 4 q^{43} - 5 q^{49} - 18 q^{51} - 42 q^{57} - 27 q^{63} - 24 q^{65} + 14 q^{67} - 21 q^{77} + 20 q^{79} - 36 q^{81} + 6 q^{85} - 18 q^{91} - 24 q^{93} - 60 q^{95} + 90 q^{99}+O(q^{100}) $ 16 * q - q^7 + 6 * q^11 - 12 * q^15 + 9 * q^21 + 6 * q^23 - 8 * q^25 - 12 * q^29 + 4 * q^37 + 18 * q^39 + 4 * q^43 - 5 * q^49 - 18 * q^51 - 42 * q^57 - 27 * q^63 - 24 * q^65 + 14 * q^67 - 21 * q^77 + 20 * q^79 - 36 * q^81 + 6 * q^85 - 18 * q^91 - 24 * q^93 - 60 * q^95 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.15671	−	1.28920i	0.667826	−	0.744317i
$3$	1.15671	−	1.28920i	0.667826	−	0.744317i
$4$		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
$7$	1.05649	−	2.42566i	0.399316	−	0.916813i
$7$	1.05649	−	2.42566i	0.399316	−	0.916813i
$8$		0			0
$9$	−0.324049	−	2.98245i	−0.108016	−	0.994149i
$10$		0			0
$11$	2.09680	+	1.21059i	0.632209	+	0.365006i	0.781607	−	0.623771i	$-0.214400\pi$
$11$	2.09680	+	1.21059i	0.632209	+	0.365006i	−0.149398	+	0.988777i	$0.547733\pi$
$12$		0			0
$13$	−4.73574	+	2.73418i	−1.31346	+	0.758325i	−0.982667	−	0.185380i	$-0.940648\pi$
$13$	−4.73574	+	2.73418i	−1.31346	+	0.758325i	−0.330790	+	0.943704i	$0.607315\pi$
$14$		0			0
$15$	4.10976	+	0.866025i	1.06114	+	0.223607i
$16$		0			0
$17$	2.58069			0.625909			0.312954	−	0.949768i	$-0.398681\pi$
$17$	2.58069			0.625909			0.312954	+	0.949768i	$0.398681\pi$
$18$		0			0
$19$		−	0.402708i		−	0.0923876i	−0.998932	−	0.0461938i	$-0.985291\pi$
$19$		−	0.402708i		−	0.0923876i	0.998932	−	0.0461938i	$-0.0147092\pi$
$20$		0			0
$21$	−1.90510	−	4.16781i	−0.415726	−	0.909490i
$22$		0			0
$23$	3.06895	−	1.77186i	0.639920	−	0.369458i	−0.144664	−	0.989481i	$-0.546210\pi$
$23$	3.06895	−	1.77186i	0.639920	−	0.369458i	0.784584	+	0.620023i	$0.212877\pi$
$24$		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	−0.218763	−	0.975778i	$-0.570202\pi$
$29$	−6.31784	−	3.64761i	−1.17319	−	0.677343i	−0.954430	+	0.298435i	$0.903535\pi$
$30$		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
$33$	3.98607	−	1.30289i	0.693887	−	0.226804i
$34$		0			0
$35$	6.37484	−	0.722330i	1.07754	−	0.122096i
$36$		0			0
$37$	−3.19360			−0.525025			−0.262513	−	0.964929i	$-0.584551\pi$
$37$	−3.19360			−0.525025			−0.262513	+	0.964929i	$0.584551\pi$
$38$		0			0
$39$	−1.95298	+	9.26794i	−0.312727	+	1.48406i
$40$		0			0
$41$	4.03924	+	6.99618i	0.630824	+	1.09262i	0.987384	+	0.158346i	$0.0506163\pi$
$41$	4.03924	+	6.99618i	0.630824	+	1.09262i	−0.356560	+	0.934273i	$0.616050\pi$
$42$		0			0
$43$	−4.22573	+	7.31918i	−0.644418	+	1.11616i	0.340018	+	0.940419i	$0.389567\pi$
$43$	−4.22573	+	7.31918i	−0.644418	+	1.11616i	−0.984436	+	0.175745i	$0.943766\pi$
$44$		0			0
$45$	5.87027	−	4.29654i	0.875088	−	0.640491i
$46$		0			0
$47$	−2.25769	+	3.91043i	−0.329317	+	0.570395i	−0.982377	−	0.186912i	$-0.940152\pi$
$47$	−2.25769	+	3.91043i	−0.329317	+	0.570395i	0.653059	+	0.757307i	$0.273485\pi$
$48$		0			0
$49$	−4.76766	−	5.12537i	−0.681094	−	0.732196i
$50$		0			0
$51$	2.98510	−	3.32701i	0.417998	−	0.465875i
$52$		0			0
$53$			14.0288i			1.92701i	0.267690	+	0.963505i	$0.413740\pi$
$53$			14.0288i			1.92701i	−0.267690	+	0.963505i	$0.586260\pi$
$54$		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	0.860910	−	0.508758i	$-0.169895\pi$
$59$	−0.0779043	−	0.134934i	−0.0101423	−	0.0175669i	−0.871052	+	0.491191i	$0.836562\pi$
$60$		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
$63$	−7.57676	−	2.36489i	−0.954582	−	0.297949i
$64$		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	$0.173552\pi$
$71$			8.73987i			1.03723i	−0.855007	+	0.518616i	$0.826448\pi$
$72$		0			0
$73$		−	8.80274i		−	1.03028i	−0.857105	−	0.515141i	$-0.827739\pi$
$73$		−	8.80274i		−	1.03028i	0.857105	−	0.515141i	$-0.172261\pi$
$74$		0			0
$75$	0.473569	+	1.44884i	0.0546830	+	0.167298i
$76$		0			0
$77$	5.15173	−	3.80715i	0.587094	−	0.433865i
$78$		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
$81$	−8.78998	+	1.93292i	−0.976665	+	0.214769i
$82$		0			0
$83$	7.50937	−	13.0066i	0.824260	−	1.42766i	−0.0782227	−	0.996936i	$-0.524925\pi$
$83$	7.50937	−	13.0066i	0.824260	−	1.42766i	0.902483	−	0.430725i	$-0.141742\pi$
$84$		0			0
$85$	3.12893	+	5.41946i	0.339380	+	0.587823i
$86$		0			0
$87$	−12.0104	+	3.92571i	−1.28765	+	0.420880i
$88$		0			0
$89$	−15.6668			−1.66068			−0.830338	−	0.557260i	$-0.811852\pi$
$89$	−15.6668			−1.66068			−0.830338	+	0.557260i	$0.811852\pi$
$90$		0			0
$91$	1.62893	+	14.3759i	0.170758	+	1.50701i
$92$		0			0
$93$	−1.50000	+	7.11831i	−0.155543	+	0.738135i
$94$		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	$-0.239091\pi$
$97$	4.97713	+	2.87355i	0.505351	+	0.291765i	−0.225569	+	0.974227i	$0.572424\pi$
$98$		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	$-0.268512\pi$
$103$	16.6863	−	9.63382i	1.64415	−	0.949249i	0.979337	−	0.202237i	$-0.0648212\pi$
$104$		0			0
$105$	6.44260	−	9.05393i	0.628734	−	0.883573i
$106$		0			0
$107$		−	1.09086i		−	0.105458i	−0.998609	−	0.0527288i	$-0.983208\pi$
$107$		−	1.09086i		−	0.105458i	0.998609	−	0.0527288i	$-0.0167919\pi$
$108$		0			0
$109$	2.31356			0.221599			0.110800	−	0.993843i	$-0.464659\pi$
$109$	2.31356			0.221599			0.110800	+	0.993843i	$0.464659\pi$
$110$		0			0
$111$	−3.69407	+	4.11718i	−0.350626	+	0.390785i
$112$		0			0
$113$	13.8868	−	8.01754i	1.30636	−	0.754227i	0.324872	−	0.945758i	$-0.394679\pi$
$113$	13.8868	−	8.01754i	1.30636	−	0.754227i	0.981487	+	0.191531i	$0.0613453\pi$
$114$		0			0
$115$	7.44183	+	4.29654i	0.693954	+	0.400655i
$116$		0			0
$117$	9.68915	+	13.2381i	0.895763	+	1.22386i
$118$		0			0
$119$	2.72647	−	6.25987i	0.249935	−	0.573842i
$120$		0			0
$121$	−2.56895	−	4.44955i	−0.233541	−	0.404505i
$122$		0			0
$123$	13.6917	+	2.88516i	1.23454	+	0.260146i
$124$		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
$129$	4.54791	+	13.9140i	0.400421	+	1.22506i
$130$		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
$133$	−0.976833	−	0.425457i	−0.0847022	−	0.0368918i
$134$		0			0
$135$	1.25111	−	12.5378i	0.107679	−	1.07908i
$136$		0			0
$137$	1.71002	+	0.987278i	0.146096	+	0.0843488i	0.571266	−	0.820765i	$-0.306452\pi$
$137$	1.71002	+	0.987278i	0.146096	+	0.0843488i	−0.425170	+	0.905114i	$0.639786\pi$
$138$		0			0
$139$	5.37804	−	3.10501i	0.456159	−	0.263364i	−0.254269	−	0.967134i	$-0.581835\pi$
$139$	5.37804	−	3.10501i	0.456159	−	0.263364i	0.710428	+	0.703770i	$0.248501\pi$
$140$		0			0
$141$	2.42982	+	7.43383i	0.204628	+	0.626041i
$142$		0			0
$143$	−13.2399			−1.10717
$144$		0			0
$145$		−	17.6900i		−	1.46907i
$146$		0			0
$147$	−12.1224	+	0.217875i	−0.999839	+	0.0179700i
$148$		0			0
$149$	10.5389	−	6.08462i	0.863378	−	0.498472i	−0.00176397	−	0.999998i	$-0.500561\pi$
$149$	10.5389	−	6.08462i	0.863378	−	0.498472i	0.865142	+	0.501527i	$0.167228\pi$
$150$		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
$157$	3.06154	−	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
$159$	18.0859	+	16.2273i	1.43431	+	1.28691i
$160$		0			0
$161$	−1.05561	−	9.31618i	−0.0831939	−	0.734218i
$162$		0			0
$163$	6.33150			0.495921			0.247961	−	0.968770i	$-0.420240\pi$
$163$	6.33150			0.495921			0.247961	+	0.968770i	$0.420240\pi$
$164$		0			0
$165$	7.56895	+	6.79111i	0.589242	+	0.528687i
$166$		0			0
$167$	−8.39779	−	14.5454i	−0.649840	−	1.12556i	−0.983161	−	0.182743i	$-0.941502\pi$
$167$	−8.39779	−	14.5454i	−0.649840	−	1.12556i	0.333320	−	0.942814i	$-0.391831\pi$
$168$		0			0
$169$	8.45146	−	14.6384i	0.650112	−	1.12603i
$170$		0			0
$171$	−1.20106	+	0.130497i	−0.0918470	+	0.00997937i
$172$		0			0
$173$	−8.30850	+	14.3907i	−0.631684	+	1.09411i	0.355524	+	0.934667i	$0.384303\pi$
$173$	−8.30850	+	14.3907i	−0.631684	+	1.09411i	−0.987207	+	0.159441i	$0.949031\pi$
$174$		0			0
$175$	1.38381	+	1.87253i	0.104606	+	0.141550i
$176$		0			0
$177$	−0.264069	−	0.0556457i	−0.0198487	−	0.00418259i
$178$		0			0
$179$		−	14.5587i		−	1.08817i	−0.839030	−	0.544086i	$-0.816877\pi$
$179$		−	14.5587i		−	1.08817i	0.839030	−	0.544086i	$-0.183123\pi$
$180$		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
$189$	−11.8129	+	7.03243i	−0.859263	+	0.511534i
$190$		0			0
$191$	7.28998	+	4.20887i	0.527485	+	0.304543i	0.739992	−	0.672616i	$-0.234829\pi$
$191$	7.28998	+	4.20887i	0.527485	+	0.304543i	−0.212507	+	0.977160i	$0.568163\pi$
$192$		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	$0.312292\pi$
$197$			23.3303i			1.66221i	−0.556112	+	0.831107i	$0.687708\pi$
$198$		0			0
$199$		−	14.1383i		−	1.00223i	−0.865379	−	0.501117i	$-0.832923\pi$
$199$		−	14.1383i		−	1.00223i	0.865379	−	0.501117i	$-0.167077\pi$
$200$		0			0
$201$	8.59896	+	1.81201i	0.606524	+	0.127809i
$202$		0			0
$203$	−15.5226	+	11.4713i	−1.08947	+	0.805125i
$204$		0			0
$205$	−9.79468	+	16.9649i	−0.684090	+	1.18488i
$206$		0			0
$207$	−6.27896	−	8.57881i	−0.436418	−	0.596268i
$208$		0			0
$209$	0.487514	−	0.844399i	0.0337221	−	0.0584083i
$210$		0			0
$211$	−6.75786	−	11.7050i	−0.465230	−	0.805802i	0.533982	−	0.845496i	$-0.320695\pi$
$211$	−6.75786	−	11.7050i	−0.465230	−	0.805802i	−0.999212	+	0.0396938i	$0.987362\pi$
$212$		0			0
$213$	11.2674	+	10.1095i	0.772029	+	0.692690i
$214$		0			0
$215$	−20.4938			−1.39766
$216$		0			0
$217$	1.25111	+	11.0415i	0.0849310	+	0.749548i
$218$		0			0
$219$	−11.3484	−	10.1822i	−0.766857	−	0.688050i
$220$		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	$-0.159905\pi$
$223$	13.4054	+	7.73961i	0.897692	+	0.518283i	0.0212411	+	0.999774i	$0.493238\pi$
$224$		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	0.179575	−	0.983744i	$-0.442528\pi$
$229$	16.9685	−	9.79677i	1.12131	−	0.647389i	0.941735	+	0.336355i	$0.109194\pi$
$230$		0			0
$231$	1.05089	−	11.0454i	0.0691432	−	0.726731i
$232$		0			0
$233$			19.5471i			1.28057i	0.768136	+	0.640287i	$0.221185\pi$
$233$			19.5471i			1.28057i	−0.768136	+	0.640287i	$0.778815\pi$
$234$		0			0
$235$	−10.9492			−0.714249
$236$		0			0
$237$	−6.09772	−	18.6555i	−0.396090	−	1.21180i
$238$		0			0
$239$	7.36210	−	4.25051i	0.476215	−	0.274943i	−0.242623	−	0.970121i	$-0.578008\pi$
$239$	7.36210	−	4.25051i	0.476215	−	0.274943i	0.718838	+	0.695178i	$0.244674\pi$
$240$		0			0
$241$	7.21480	+	4.16547i	0.464746	+	0.268321i	0.714038	−	0.700107i	$-0.246864\pi$
$241$	7.21480	+	4.16547i	0.464746	+	0.268321i	−0.249292	+	0.968428i	$0.580198\pi$
$242$		0			0
$243$	−7.67554	+	13.5678i	−0.492386	+	0.870377i
$244$		0			0
$245$	4.98283	−	16.2263i	0.318341	−	1.03666i
$246$		0			0
$247$	1.10108	+	1.90712i	0.0700598	+	0.121347i
$248$		0			0
$249$	−8.08191	−	24.7259i	−0.512170	−	1.56694i
$250$		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
$255$	10.6060	+	2.23494i	0.664174	+	0.139957i
$256$		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
$259$	−3.37401	+	7.74660i	−0.209651	+	0.481350i
$260$		0			0
$261$	−8.83150	+	20.0246i	−0.546656	+	1.23949i
$262$		0			0
$263$	−2.91506	−	1.68301i	−0.179750	−	0.103779i	0.407425	−	0.913239i	$-0.366427\pi$
$263$	−2.91506	−	1.68301i	−0.179750	−	0.103779i	−0.587175	+	0.809460i	$0.699760\pi$
$264$		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
$269$	−12.2822			−0.748862			−0.374431	−	0.927255i	$-0.622162\pi$
$269$	−12.2822			−0.748862			−0.374431	+	0.927255i	$0.622162\pi$
$270$		0			0
$271$		−	29.4244i		−	1.78741i	−0.448659	−	0.893703i	$-0.648098\pi$
$271$		−	29.4244i		−	1.78741i	0.448659	−	0.893703i	$-0.351902\pi$
$272$		0			0
$273$	20.4176	+	14.5287i	1.23573	+	0.879320i
$274$		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	0.531066	−	0.847331i	$-0.321792\pi$
$281$	1.05254	+	0.607682i	0.0627891	+	0.0362513i	−0.468277	+	0.883582i	$0.655125\pi$
$282$		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
$285$	0.348755	−	1.65503i	0.0206585	−	0.0980357i
$286$		0			0
$287$	21.2378	−	2.40644i	1.25363	−	0.142048i
$288$		0			0
$289$	−10.3400			−0.608238
$290$		0			0
$291$	9.46166	−	3.09264i	0.554652	−	0.181294i
$292$		0			0
$293$	3.15082	+	5.45739i	0.184073	+	0.318824i	0.943264	−	0.332044i	$-0.107738\pi$
$293$	3.15082	+	5.45739i	0.184073	+	0.318824i	−0.759191	+	0.650868i	$0.774405\pi$
$294$		0			0
$295$	0.188909	−	0.327199i	0.0109987	−	0.0190503i
$296$		0			0
$297$	−5.17748	−	11.4661i	−0.300428	−	0.665328i
$298$		0			0
$299$	−9.68915	+	16.7821i	−0.560338	+	0.970534i
$300$		0			0
$301$	13.2894	+	17.9828i	0.765988	+	1.03651i
$302$		0			0
$303$	5.20727	+	15.9312i	0.299150	+	0.915223i
$304$		0			0
$305$		−	28.6408i		−	1.63997i
$306$		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	$0.00101467\pi$
$311$	8.86623	+	15.3568i	0.502758	+	0.870802i	−0.497237	+	0.867615i	$0.665652\pi$
$312$		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
$315$	−4.22007	−	18.7785i	−0.237774	−	1.05805i
$316$		0			0
$317$	−4.65389	−	2.68692i	−0.261388	−	0.150913i	0.363579	−	0.931563i	$-0.381555\pi$
$317$	−4.65389	−	2.68692i	−0.261388	−	0.150913i	−0.624968	+	0.780651i	$0.714888\pi$
$318$		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
$325$		−	4.81237i		−	0.266942i
$326$		0			0
$327$	2.67612	−	2.98263i	0.147990	−	0.164940i
$328$		0			0
$329$	7.10015	+	9.60771i	0.391444	+	0.529690i
$330$		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
$333$	1.03488	+	9.52475i	0.0567113	+	0.521953i
$334$		0			0
$335$	−6.15149	+	10.6547i	−0.336092	+	0.582128i
$336$		0			0
$337$	−5.31784	−	9.21076i	−0.289681	−	0.501742i	0.684053	−	0.729433i	$-0.260216\pi$
$337$	−5.31784	−	9.21076i	−0.289681	−	0.501742i	−0.973734	+	0.227690i	$0.926883\pi$
$338$		0			0
$339$	5.72679	−	27.1767i	0.311037	−	1.47604i
$340$		0			0
$341$	−10.1690			−0.550681
$342$		0			0
$343$	−17.4694	+	6.14981i	−0.943259	+	0.332058i
$344$		0			0
$345$	14.1471	−	4.62412i	0.761655	−	0.248954i
$346$		0			0
$347$	−1.63842	+	0.945944i	−0.0879552	+	0.0507809i	−0.543332	−	0.839518i	$-0.682838\pi$
$347$	−1.63842	+	0.945944i	−0.0879552	+	0.0507809i	0.455377	+	0.890299i	$0.349504\pi$
$348$		0			0
$349$	−16.1105	−	9.30140i	−0.862375	−	0.497892i	0.00243201	−	0.999997i	$-0.499226\pi$
$349$	−16.1105	−	9.30140i	−0.862375	−	0.497892i	−0.864807	+	0.502105i	$0.832559\pi$
$350$		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
$357$	−4.91646	−	10.7558i	−0.260207	−	0.569258i
$358$		0			0
$359$		−	8.62553i		−	0.455238i	−0.973750	−	0.227619i	$-0.926906\pi$
$359$		−	8.62553i		−	0.455238i	0.973750	−	0.227619i	$-0.0730940\pi$
$360$		0			0
$361$	18.8378			0.991465
$362$		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	0.0248966	−	0.999690i	$-0.492074\pi$
$367$	−15.8701	−	9.16260i	−0.828412	−	0.478284i	−0.853309	+	0.521406i	$0.825408\pi$
$368$		0			0
$369$	19.5568	−	14.3139i	1.01809	−	0.745154i
$370$		0			0
$371$	34.0292	+	14.8213i	1.76671	+	0.769486i
$372$		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
$375$	11.5560	−	12.8796i	0.596749	−	0.665099i
$376$		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
$381$	−3.54445	+	3.95042i	−0.181588	+	0.202386i
$382$		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
$385$	14.2412	+	6.20272i	0.725799	+	0.316120i
$386$		0			0
$387$	23.1984	+	10.2312i	1.17924	+	0.520083i
$388$		0			0
$389$	8.33425	+	4.81178i	0.422563	+	0.243967i	0.696173	−	0.717874i	$-0.254884\pi$
$389$	8.33425	+	4.81178i	0.422563	+	0.243967i	−0.273610	+	0.961841i	$0.588218\pi$
$390$		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
$395$	27.4775			1.38254
$396$		0			0
$397$			23.4807i			1.17846i	0.807964	+	0.589232i	$0.200570\pi$
$397$			23.4807i			1.17846i	−0.807964	+	0.589232i	$0.799430\pi$
$398$		0			0
$399$	−1.67841	+	0.767199i	−0.0840256	+	0.0384080i
$400$		0			0
$401$	−22.2019	+	12.8183i	−1.10871	+	0.640113i	−0.938495	−	0.345294i	$-0.887779\pi$
$401$	−22.2019	+	12.8183i	−1.10871	+	0.640113i	−0.170214	+	0.985407i	$0.554446\pi$
$402$		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
$409$	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
$411$	3.25078	−	1.06255i	0.160349	−	0.0524118i
$412$		0			0
$413$	−0.409610	+	0.0464127i	−0.0201556	+	0.00228382i
$414$		0			0
$415$	36.4186			1.78772
$416$		0			0
$417$	2.21786	−	10.5249i	0.108609	−	0.515408i
$418$		0			0
$419$	7.10643	+	12.3087i	0.347172	+	0.601319i	0.985746	−	0.168241i	$-0.0538088\pi$
$419$	7.10643	+	12.3087i	0.347172	+	0.601319i	−0.638574	+	0.769560i	$0.720475\pi$
$420$		0			0
$421$	−0.849964	+	1.47218i	−0.0414247	+	0.0717497i	−0.885994	−	0.463696i	$-0.846523\pi$
$421$	−0.849964	+	1.47218i	−0.0414247	+	0.0717497i	0.844570	+	0.535446i	$0.179856\pi$
$422$		0			0
$423$	12.3942	+	5.46626i	0.602629	+	0.265779i
$424$		0			0
$425$	−1.13555	+	1.96684i	−0.0550825	+	0.0954057i
$426$		0			0
$427$	−25.1317	+	18.5724i	−1.21621	+	0.898782i
$428$		0			0
$429$	−15.3147	+	17.0688i	−0.739399	+	0.824088i
$430$		0			0
$431$		−	32.6628i		−	1.57331i	−0.617392	−	0.786656i	$-0.711811\pi$
$431$		−	32.6628i		−	1.57331i	0.617392	−	0.786656i	$-0.288189\pi$
$432$		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
$441$	−13.7412	+	15.8802i	−0.654343	+	0.756198i
$442$		0			0
$443$	21.3562	+	12.3300i	1.01466	+	0.585816i	0.912554	−	0.408957i	$-0.134107\pi$
$443$	21.3562	+	12.3300i	1.01466	+	0.585816i	0.102109	+	0.994773i	$0.467441\pi$
$444$		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	$-0.965283\pi$
$449$		−	4.61306i		−	0.217704i	0.994058	−	0.108852i	$-0.0347174\pi$
$450$		0			0
$451$			19.5595i			0.921019i
$452$		0			0
$453$	5.72328	+	17.5099i	0.268903	+	0.822687i
$454$		0			0
$455$	−28.2146	+	20.8507i	−1.32272	+	0.977496i
$456$		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
$459$	−10.8900	−	7.82480i	−0.508300	−	0.365231i
$460$		0			0
$461$	9.28621	−	16.0842i	0.432502	−	0.749115i	−0.564586	−	0.825374i	$-0.690964\pi$
$461$	9.28621	−	16.0842i	0.432502	−	0.749115i	0.997088	+	0.0762589i	$0.0242975\pi$
$462$		0			0
$463$	17.7046	+	30.6653i	0.822804	+	1.42514i	0.903586	+	0.428406i	$0.140925\pi$
$463$	17.7046	+	30.6653i	0.822804	+	1.42514i	−0.0807828	+	0.996732i	$0.525742\pi$
$464$		0			0
$465$	−16.7672	+	5.48051i	−0.777559	+	0.254153i
$466$		0			0
$467$	15.8433			0.733141			0.366571	−	0.930390i	$-0.380532\pi$
$467$	15.8433			0.733141			0.366571	+	0.930390i	$0.380532\pi$
$468$		0			0
$469$	13.3382	−	1.51135i	0.615903	−	0.0697877i
$470$		0			0
$471$	1.26255	−	5.99149i	0.0581753	−	0.276073i
$472$		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
$479$	−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
$483$	−13.2314	−	9.41522i	−0.602050	−	0.428407i
$484$		0			0
$485$			13.9360i			0.632802i
$486$		0			0
$487$	−7.00939			−0.317626			−0.158813	−	0.987309i	$-0.550767\pi$
$487$	−7.00939			−0.317626			−0.158813	+	0.987309i	$0.550767\pi$
$488$		0			0
$489$	7.32370	−	8.16254i	0.331189	−	0.369123i
$490$		0			0
$491$	−16.4508	+	9.49785i	−0.742413	+	0.428632i	−0.822946	−	0.568120i	$-0.807671\pi$
$491$	−16.4508	+	9.49785i	−0.742413	+	0.428632i	0.0805333	+	0.996752i	$0.474338\pi$
$492$		0			0
$493$	−16.3044	−	9.41333i	−0.734312	−	0.423955i
$494$		0			0
$495$	17.5101	−	1.90251i	0.787022	−	0.0855116i
$496$		0			0
$497$	21.2000	+	9.23359i	0.950948	+	0.414183i
$498$		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
$501$	−28.4657	−	5.99840i	−1.27175	−	0.267989i
$502$		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
$507$	−9.09582	−	27.8279i	−0.403960	−	1.23588i
$508$		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
$511$	−21.3524	−	9.30001i	−0.944577	−	0.411408i
$512$		0			0
$513$	−1.22104	+	1.69934i	−0.0539100	+	0.0750278i
$514$		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
$521$	−13.6999			−0.600203			−0.300102	−	0.953907i	$-0.597021\pi$
$521$	−13.6999			−0.600203			−0.300102	+	0.953907i	$0.597021\pi$
$522$		0			0
$523$		−	24.4881i		−	1.07079i	−0.844602	−	0.535394i	$-0.820163\pi$
$523$		−	24.4881i		−	1.07079i	0.844602	−	0.535394i	$-0.179837\pi$
$524$		0			0
$525$	4.01472	+	0.381972i	0.175217	+	0.0166706i
$526$		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
$535$	2.29082	−	1.32261i	0.0990408	−	0.0571812i
$536$		0			0
$537$	−18.7691	−	16.8402i	−0.809945	−	0.726709i
$538$		0			0
$539$	−3.79211	−	16.5186i	−0.163338	−	0.711505i
$540$		0			0
$541$	−37.1608			−1.59767			−0.798833	−	0.601552i	$-0.794549\pi$
$541$	−37.1608			−1.59767			−0.798833	+	0.601552i	$0.794549\pi$
$542$		0			0
$543$	5.18714	+	4.65408i	0.222602	+	0.199726i
$544$		0			0
$545$	2.80506	+	4.85850i	0.120155	+	0.208115i
$546$		0			0
$547$	−3.31826	+	5.74739i	−0.141878	+	0.245741i	−0.928204	−	0.372072i	$-0.878648\pi$
$547$	−3.31826	+	5.74739i	−0.141878	+	0.245741i	0.786326	+	0.617812i	$0.211981\pi$
$548$		0			0
$549$	−14.2985	+	32.4206i	−0.610247	+	1.38368i
$550$		0			0
$551$	−1.46892	+	2.54424i	−0.0625781	+	0.108388i
$552$		0			0
$553$	−17.8181	−	24.1109i	−0.757702	−	1.02530i
$554$		0			0
$555$	−13.1249	−	2.76574i	−0.557123	−	0.117399i
$556$		0			0
$557$		−	24.6188i		−	1.04313i	−0.853211	−	0.521565i	$-0.825348\pi$
$557$		−	24.6188i		−	1.04313i	0.853211	−	0.521565i	$-0.174652\pi$
$558$		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	0.967539	−	0.252724i	$-0.0813263\pi$
$563$	6.28555	+	10.8869i	0.264904	+	0.458828i	−0.702634	+	0.711551i	$0.747993\pi$
$564$		0			0
$565$	33.6738	+	19.4416i	1.41667	+	0.817913i
$566$		0			0
$567$	−4.59793	+	23.3636i	−0.193095	+	0.981180i
$568$		0			0
$569$	−12.8872	−	7.44043i	−0.540260	−	0.311919i	0.204924	−	0.978778i	$-0.434305\pi$
$569$	−12.8872	−	7.44043i	−0.540260	−	0.311919i	−0.745184	+	0.666859i	$0.767638\pi$
$570$		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
$577$			20.9013i			0.870133i	0.900398	+	0.435067i	$0.143275\pi$
$577$			20.9013i			0.870133i	−0.900398	+	0.435067i	$0.856725\pi$
$578$		0			0
$579$	14.6360	+	3.08416i	0.608252	+	0.128173i
$580$		0			0
$581$	−23.6160	−	31.9565i	−0.979759	−	1.32578i
$582$		0			0
$583$	−16.9832	+	29.4157i	−0.703371	+	1.21827i
$584$		0			0
$585$	−16.0525	+	36.3977i	−0.663691	+	1.50486i
$586$		0			0
$587$	14.8542	−	25.7283i	0.613100	−	1.06192i	−0.377615	−	0.925963i	$-0.623256\pi$
$587$	14.8542	−	25.7283i	0.613100	−	1.06192i	0.990715	−	0.135957i	$-0.0434109\pi$
$588$		0			0
$589$	0.845690	+	1.46478i	0.0348461	+	0.0603551i
$590$		0			0
$591$	30.0773	+	26.9864i	1.23721	+	1.11007i
$592$		0			0
$593$	11.7921			0.484241			0.242121	−	0.970246i	$-0.422157\pi$
$593$	11.7921			0.484241			0.242121	+	0.970246i	$0.422157\pi$
$594$		0			0
$595$	16.4515	−	1.86411i	0.674444	−	0.0764210i
$596$		0			0
$597$	−18.2270	−	16.3538i	−0.745980	−	0.669318i
$598$		0			0
$599$	−27.7991	+	16.0498i	−1.13584	+	0.655778i	−0.945397	−	0.325921i	$-0.894326\pi$
$599$	−27.7991	+	16.0498i	−1.13584	+	0.655778i	−0.190443	+	0.981698i	$0.560992\pi$
$600$		0			0
$601$	16.1636	+	9.33208i	0.659329	+	0.380664i	0.792021	−	0.610494i	$-0.209029\pi$
$601$	16.1636	+	9.33208i	0.659329	+	0.380664i	−0.132692	+	0.991157i	$0.542362\pi$
$602$		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	−0.723531	−	0.690292i	$-0.757482\pi$
$607$	−12.0104	+	6.93419i	−0.487486	+	0.281450i	0.236045	+	0.971742i	$0.424149\pi$
$608$		0			0
$609$	−3.16641	+	33.2806i	−0.128309	+	1.34860i
$610$		0			0
$611$		−	24.6917i		−	0.998918i
$612$		0			0
$613$	−20.9021			−0.844227			−0.422114	−	0.906543i	$-0.638712\pi$
$613$	−20.9021			−0.844227			−0.422114	+	0.906543i	$0.638712\pi$
$614$		0			0
$615$	10.5415	+	32.2507i	0.425072	+	1.30047i
$616$		0			0
$617$	15.2904	−	8.82792i	0.615569	−	0.355399i	−0.159573	−	0.987186i	$-0.551012\pi$
$617$	15.2904	−	8.82792i	0.615569	−	0.355399i	0.775142	+	0.631787i	$0.217678\pi$
$618$		0			0
$619$	−4.78789	−	2.76429i	−0.192441	−	0.111106i	0.400684	−	0.916216i	$-0.368773\pi$
$619$	−4.78789	−	2.76429i	−0.192441	−	0.111106i	−0.593125	+	0.805110i	$0.702106\pi$
$620$		0			0
$621$	−18.3227	−	1.82837i	−0.735264	−	0.0733701i
$622$		0			0
$623$	−16.5518	+	38.0023i	−0.663134	+	1.52253i
$624$		0			0
$625$	14.3129	+	24.7906i	0.572515	+	0.991624i
$626$		0			0
$627$	−0.524684	−	1.60522i	−0.0209538	−	0.0641065i
$628$		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
$633$	−22.9068	−	4.82702i	−0.910465	−	0.191857i
$634$		0			0
$635$	−3.71522	−	6.43496i	−0.147434	−	0.255363i
$636$		0			0
$637$	36.5920	+	11.2368i	1.44983	+	0.445218i
$638$		0			0
$639$	26.0662	−	2.83215i	1.03116	−	0.112038i
$640$		0			0
$641$	25.3174	+	14.6170i	0.999978	+	0.577337i	0.908242	−	0.418446i	$-0.137425\pi$
$641$	25.3174	+	14.6170i	0.999978	+	0.577337i	0.0917361	+	0.995783i	$0.470758\pi$
$642$		0			0
$643$	34.6535	−	20.0072i	1.36660	−	0.789008i	0.376109	−	0.926575i	$-0.377262\pi$
$643$	34.6535	−	20.0072i	1.36660	−	0.789008i	0.990492	+	0.137567i	$0.0439284\pi$
$644$		0			0
$645$	−23.7053	+	26.4205i	−0.933396	+	1.04031i
$646$		0			0
$647$	7.56553			0.297432			0.148716	−	0.988880i	$-0.452486\pi$
$647$	7.56553			0.297432			0.148716	+	0.988880i	$0.452486\pi$
$648$		0			0
$649$		−	0.377240i		−	0.0148080i
$650$		0			0
$651$	15.6819	+	11.1589i	0.614621	+	0.437352i
$652$		0			0
$653$	33.9375	−	19.5938i	1.32808	−	0.766766i	0.343076	−	0.939308i	$-0.388531\pi$
$653$	33.9375	−	19.5938i	1.32808	−	0.766766i	0.985002	+	0.172542i	$0.0551980\pi$
$654$		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	−0.0163765	−	0.999866i	$-0.505213\pi$
$659$	−22.8594	−	13.1979i	−0.890474	−	0.514115i	−0.874098	+	0.485751i	$0.838546\pi$
$660$		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
$663$	−5.04003	+	23.9177i	−0.195738	+	0.928885i
$664$		0			0
$665$	−0.290888	−	2.56720i	−0.0112802	−	0.0995517i
$666$		0			0
$667$	−25.8522			−1.00100
$668$		0			0
$669$	25.4840	−	8.32970i	0.985269	−	0.322045i
$670$		0			0
$671$	−14.2985	−	24.7658i	−0.551989	−	0.956073i
$672$		0			0
$673$	−7.21676	+	12.4998i	−0.278186	+	0.481832i	−0.970934	−	0.239348i	$-0.923066\pi$
$673$	−7.21676	+	12.4998i	−0.278186	+	0.481832i	0.692748	+	0.721180i	$0.256400\pi$
$674$		0			0
$675$	4.16764	−	1.88189i	0.160412	−	0.0724340i
$676$		0			0
$677$	17.2099	−	29.8084i	0.661430	−	1.14563i	−0.318809	−	0.947819i	$-0.603283\pi$
$677$	17.2099	−	29.8084i	0.661430	−	1.14563i	0.980240	−	0.197812i	$-0.0633837\pi$
$678$		0			0
$679$	12.2285	−	9.03696i	0.469289	−	0.346807i
$680$		0			0
$681$	−8.08081	−	24.7226i	−0.309657	−	0.947370i
$682$		0			0
$683$			19.0172i			0.727674i	0.931463	+	0.363837i	$0.118533\pi$
$683$			19.0172i			0.727674i	−0.931463	+	0.363837i	$0.881467\pi$
$684$		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
$693$	−13.0240	−	14.1311i	−0.494743	−	0.536794i
$694$		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	$0.143220\pi$
$701$			23.0297i			0.869819i	−0.900474	+	0.434910i	$0.856780\pi$
$702$		0			0
$703$			1.28609i			0.0485058i
$704$		0			0
$705$	−12.6651	+	14.1157i	−0.476995	+	0.531628i
$706$		0			0
$707$	15.2161	+	20.5900i	0.572260	+	0.774366i
$708$		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
$711$	−31.1038	−	13.7178i	−1.16648	−	0.514457i
$712$		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
$717$	3.03607	−	14.4078i	0.113384	−	0.538069i
$718$		0			0
$719$	−42.3156			−1.57811			−0.789054	−	0.614324i	$-0.789429\pi$
$719$	−42.3156			−1.57811			−0.789054	+	0.614324i	$0.789429\pi$
$720$		0			0
$721$	−5.73950	−	50.6533i	−0.213750	−	1.88643i
$722$		0			0
$723$	13.7155	−	4.48306i	0.510086	−	0.166727i
$724$		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	$-0.364652\pi$
$727$	−4.58754	−	2.64862i	−0.170142	−	0.0982318i	−0.582653	+	0.812721i	$0.697985\pi$
$728$		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	−0.767688	−	0.640824i	$-0.778593\pi$
$733$	−16.1513	+	9.32497i	−0.596563	+	0.344426i	0.171125	+	0.985249i	$0.445260\pi$
$734$		0			0
$735$	−15.1552	−	25.1930i	−0.559009	−	0.929256i
$736$		0			0
$737$			12.2842i			0.452494i
$738$		0			0
$739$	41.1837			1.51497			0.757483	−	0.652855i	$-0.226429\pi$
$739$	41.1837			1.51497			0.757483	+	0.652855i	$0.226429\pi$
$740$		0			0
$741$	3.73227	+	0.786480i	0.137108	+	0.0288921i
$742$		0			0
$743$	20.5831	−	11.8837i	0.755122	−	0.435970i	−0.0724196	−	0.997374i	$-0.523072\pi$
$743$	20.5831	−	11.8837i	0.755122	−	0.435970i	0.827542	+	0.561404i	$0.189739\pi$
$744$		0			0
$745$	25.5555	+	14.7545i	0.936281	+	0.540562i
$746$		0			0
$747$	−41.2249	−	18.1815i	−1.50834	−	0.665227i
$748$		0			0
$749$	−2.64606	−	1.15249i	−0.0966850	−	0.0421109i
$750$		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
$753$	15.7038	−	17.5025i	0.572279	−	0.637826i
$754$		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
$759$	9.92453	−	11.0613i	0.360237	−	0.401498i
$760$		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
$763$	2.44426	−	5.61192i	0.0884880	−	0.203165i
$764$		0			0
$765$	15.1493	−	11.0880i	0.547725	−	0.400889i
$766$		0			0
$767$	0.737868	+	0.426009i	0.0266429	+	0.0153823i
$768$		0			0
$769$	3.14015	−	1.81297i	0.113237	−	0.0653773i	−0.442312	−	0.896861i	$-0.645842\pi$
$769$	3.14015	−	1.81297i	0.113237	−	0.0653773i	0.555549	+	0.831484i	$0.312508\pi$
$770$		0			0
$771$	10.1361	+	2.13592i	0.365043	+	0.0769233i
$772$		0			0
$773$	−12.1111			−0.435605			−0.217802	−	0.975993i	$-0.569889\pi$
$773$	−12.1111			−0.435605			−0.217802	+	0.975993i	$0.569889\pi$
$774$		0			0
$775$		−	3.69618i		−	0.132771i
$776$		0			0
$777$	6.08413	+	13.3103i	0.218267	+	0.477505i
$778$		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
$787$	−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
$789$	−5.54160	+	1.81133i	−0.197286	+	0.0644850i
$790$		0			0
$791$	−4.77657	−	42.1551i	−0.169835	−	1.49886i
$792$		0			0
$793$	64.5880			2.29359
$794$		0			0
$795$	−12.1493	+	57.6552i	−0.430893	+	2.04482i
$796$		0			0
$797$	16.8973	+	29.2669i	0.598532	+	1.03669i	0.993038	+	0.117795i	$0.0375824\pi$
$797$	16.8973	+	29.2669i	0.598532	+	1.03669i	−0.394506	+	0.918893i	$0.629084\pi$
$798$		0			0
$799$	−5.82639	+	10.0916i	−0.206123	+	0.357015i
$800$		0			0
$801$	5.07681	+	46.7254i	0.179380	+	1.65096i
$802$		0			0
$803$	10.6565	−	18.4576i	0.376060	−	0.651354i
$804$		0			0
$805$	18.2842	−	13.5121i	0.644433	−	0.476239i
$806$		0			0
$807$	−14.2070	+	15.8342i	−0.500109	+	0.557391i
$808$		0			0
$809$			4.84175i			0.170227i	0.996371	+	0.0851134i	$0.0271253\pi$
$809$			4.84175i			0.170227i	−0.996371	+	0.0851134i	$0.972875\pi$
$810$		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
$819$	42.3476	−	9.51670i	1.47974	−	0.332540i
$820$		0			0
$821$	−26.6931	−	15.4113i	−0.931595	−	0.537857i	−0.0442792	−	0.999019i	$-0.514099\pi$
$821$	−26.6931	−	15.4113i	−0.931595	−	0.537857i	−0.887316	+	0.461163i	$0.847432\pi$
$822$		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	$0.212982\pi$
$827$			35.6756i			1.24056i	−0.784379	+	0.620282i	$0.787018\pi$
$828$		0			0
$829$		−	3.32551i		−	0.115500i	−0.998331	−	0.0577498i	$-0.981607\pi$
$829$		−	3.32551i		−	0.115500i	0.998331	−	0.0577498i	$-0.0183926\pi$
$830$		0			0
$831$	−4.95188	−	15.1498i	−0.171779	−	0.525542i
$832$		0			0
$833$	−12.3038	−	13.2270i	−0.426303	−	0.458288i
$834$		0			0
$835$	20.3636	−	35.2708i	0.704712	−	1.22060i
$836$		0			0
$837$	21.7161	+	2.16699i	0.750617	+	0.0749021i
$838$		0			0
$839$	−20.9689	+	36.3192i	−0.723926	+	1.25388i	0.235488	+	0.971877i	$0.424331\pi$
$839$	−20.9689	+	36.3192i	−0.723926	+	1.25388i	−0.959414	+	0.282000i	$0.909002\pi$
$840$		0			0
$841$	12.1100	+	20.9752i	0.417588	+	0.723283i
$842$		0			0
$843$	2.00090	−	0.654014i	0.0689146	−	0.0225254i
$844$		0			0
$845$	40.9875			1.41001
$846$		0			0
$847$	−13.5072	+	1.53049i	−0.464112	+	0.0525883i
$848$		0			0
$849$	−4.36210	+	20.7005i	−0.149707	+	0.710441i
$850$		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	$-0.413026\pi$
$853$	−12.5330	−	7.23594i	−0.429122	−	0.247754i	−0.698973	+	0.715149i	$0.746359\pi$
$854$		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	−0.586131	−	0.810216i	$-0.699350\pi$
$859$	−5.20316	+	3.00405i	−0.177530	+	0.102497i	0.408602	+	0.912713i	$0.366016\pi$
$860$		0			0
$861$	21.4635	−	30.1632i	0.731476	−	1.02796i
$862$		0			0
$863$		−	31.2998i		−	1.06546i	−0.846286	−	0.532729i	$-0.821166\pi$
$863$		−	31.2998i		−	1.06546i	0.846286	−	0.532729i	$-0.178834\pi$
$864$		0			0
$865$	−40.2942			−1.37004
$866$		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
$873$	6.95737	−	15.7752i	0.235471	−	0.533910i
$874$		0			0
$875$	10.5548	−	24.2333i	0.356816	−	0.819236i
$876$		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
$879$	10.6802	+	2.25058i	0.360235	+	0.0759102i
$880$		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
$885$	−0.203311	−	0.622014i	−0.00683424	−	0.0209088i
$886$		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
$889$	−3.23735	+	7.43284i	−0.108577	+	0.249289i
$890$		0			0
$891$	−20.7708	−	6.58811i	−0.695849	−	0.220710i
$892$		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
$899$	30.6400			1.02190
$900$		0			0
$901$			36.2041i			1.20613i
$902$		0			0
$903$	38.5553	+	3.66827i	1.28304	+	0.122072i
$904$		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	0.858352	−	0.513061i	$-0.171489\pi$
$911$	25.4502	+	14.6937i	0.843204	+	0.486824i	−0.0151480	+	0.999885i	$0.504822\pi$
$912$		0			0
$913$	31.4913	−	18.1815i	1.04221	−	0.601721i
$914$		0			0
$915$	−36.9236	−	33.1291i	−1.22066	−	1.09521i
$916$		0			0
$917$	−30.1355	+	3.41464i	−0.995161	+	0.112761i
$918$		0			0
$919$	−41.5987			−1.37222			−0.686108	−	0.727500i	$-0.740682\pi$
$919$	−41.5987			−1.37222			−0.686108	+	0.727500i	$0.740682\pi$
$920$		0			0
$921$	37.0339	+	33.2280i	1.22031	+	1.09490i
$922$		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
$927$	−34.1395	−	46.6441i	−1.12129	−	1.53199i
$928$		0			0
$929$	−1.21614	+	2.10641i	−0.0399002	+	0.0691092i	−0.885286	−	0.465047i	$-0.846037\pi$
$929$	−1.21614	+	2.10641i	−0.0399002	+	0.0691092i	0.845386	+	0.534156i	$0.179371\pi$
$930$		0			0
$931$	−2.06403	+	1.91997i	−0.0676458	+	0.0629246i
$932$		0			0
$933$	30.0535	+	6.33300i	0.983908	+	0.207333i
$934$		0			0
$935$			15.1514i			0.495503i
$936$		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	$0.0767350\pi$
$941$	21.2367	+	36.7831i	0.692298	+	1.19910i	−0.278785	+	0.960354i	$0.589932\pi$
$942$		0			0
$943$	24.7925	+	14.3139i	0.807354	+	0.466126i
$944$		0			0
$945$	−29.0906	−	16.2808i	−0.946317	−	0.529615i
$946$		0			0
$947$	−47.3119	−	27.3155i	−1.53743	−	0.887636i	−0.998988	−	0.0449739i	$-0.985680\pi$
$947$	−47.3119	−	27.3155i	−1.53743	−	0.887636i	−0.538443	−	0.842662i	$-0.680987\pi$
$948$		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	$0.0897981\pi$
$953$			17.1877i			0.556764i	−0.960470	+	0.278382i	$0.910202\pi$
$954$		0			0
$955$			20.4120i			0.660518i
$956$		0			0
$957$	−29.9358	−	6.30819i	−0.967687	−	0.203915i
$958$		0			0
$959$	4.20142	−	3.10487i	0.135671	−	0.100261i
$960$		0			0
$961$	−6.67994	+	11.5700i	−0.215482	+	0.373226i
$962$		0			0
$963$	−3.25344	+	0.353493i	−0.104841	+	0.0113912i
$964$		0			0
$965$	−10.4702	+	18.1350i	−0.337049	+	0.583786i
$966$		0			0
$967$	−11.1546	−	19.3203i	−0.358706	−	0.621298i	0.629039	−	0.777374i	$-0.283449\pi$
$967$	−11.1546	−	19.3203i	−0.358706	−	0.621298i	−0.987745	+	0.156076i	$0.950115\pi$
$968$		0			0
$969$	−1.33981	−	1.20213i	−0.0430410	−	0.0386179i
$970$		0			0
$971$	54.2481			1.74091			0.870453	−	0.492252i	$-0.163826\pi$
$971$	54.2481			1.74091			0.870453	+	0.492252i	$0.163826\pi$
$972$		0			0
$973$	−1.84986	−	16.3257i	−0.0593037	−	0.523378i
$974$		0			0
$975$	−6.20409	−	5.56652i	−0.198690	−	0.178271i
$976$		0			0
$977$	−35.6936	+	20.6077i	−1.14194	+	0.659299i	−0.946910	−	0.321498i	$-0.895814\pi$
$977$	−35.6936	+	20.6077i	−1.14194	+	0.659299i	−0.195029	+	0.980797i	$0.562480\pi$
$978$		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
$987$	20.5990	+	1.95985i	0.655674	+	0.0623827i
$988$		0			0
$989$			29.9496i			0.952341i
$990$		0			0
$991$	−3.72231			−0.118243			−0.0591216	−	0.998251i	$-0.518830\pi$
$991$	−3.72231			−0.118243			−0.0591216	+	0.998251i	$0.518830\pi$
$992$		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	0.493467	−	0.869764i	$-0.335729\pi$
$997$	−0.411648	−	0.237665i	−0.0130370	−	0.00752693i	−0.506504	+	0.862237i	$0.669063\pi$
$998$		0			0
$999$	13.4763	+	9.68320i	0.426372	+	0.306363i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.x.a.209.7	yes	16
3.2	odd	2		756.2.x.a.629.2		16
4.3	odd	2		1008.2.cc.c.209.2		16
7.2	even	3		1764.2.w.a.1109.5		16
7.3	odd	6		1764.2.bm.b.1685.7		16
7.4	even	3		1764.2.bm.b.1685.2		16
7.5	odd	6		1764.2.w.a.1109.4		16
7.6	odd	2	inner	252.2.x.a.209.2	yes	16
9.2	odd	6		2268.2.f.b.1133.14		16
9.4	even	3		756.2.x.a.125.7		16
9.5	odd	6	inner	252.2.x.a.41.2	✓	16
9.7	even	3		2268.2.f.b.1133.4		16
12.11	even	2		3024.2.cc.c.2897.2		16
21.2	odd	6		5292.2.w.a.521.2		16
21.5	even	6		5292.2.w.a.521.7		16
21.11	odd	6		5292.2.bm.b.4625.7		16
21.17	even	6		5292.2.bm.b.4625.2		16
21.20	even	2		756.2.x.a.629.7		16
28.27	even	2		1008.2.cc.c.209.7		16
36.23	even	6		1008.2.cc.c.545.7		16
36.31	odd	6		3024.2.cc.c.881.7		16
63.4	even	3		5292.2.w.a.1097.7		16
63.5	even	6		1764.2.bm.b.1697.2		16
63.13	odd	6		756.2.x.a.125.2		16
63.20	even	6		2268.2.f.b.1133.3		16
63.23	odd	6		1764.2.bm.b.1697.7		16
63.31	odd	6		5292.2.w.a.1097.2		16
63.32	odd	6		1764.2.w.a.509.4		16
63.34	odd	6		2268.2.f.b.1133.13		16
63.40	odd	6		5292.2.bm.b.2285.7		16
63.41	even	6	inner	252.2.x.a.41.7	yes	16
63.58	even	3		5292.2.bm.b.2285.2		16
63.59	even	6		1764.2.w.a.509.5		16
84.83	odd	2		3024.2.cc.c.2897.7		16
252.139	even	6		3024.2.cc.c.881.2		16
252.167	odd	6		1008.2.cc.c.545.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.x.a.41.2	✓	16	9.5	odd	6	inner
252.2.x.a.41.7	yes	16	63.41	even	6	inner
252.2.x.a.209.2	yes	16	7.6	odd	2	inner
252.2.x.a.209.7	yes	16	1.1	even	1	trivial
756.2.x.a.125.2		16	63.13	odd	6
756.2.x.a.125.7		16	9.4	even	3
756.2.x.a.629.2		16	3.2	odd	2
756.2.x.a.629.7		16	21.20	even	2
1008.2.cc.c.209.2		16	4.3	odd	2
1008.2.cc.c.209.7		16	28.27	even	2
1008.2.cc.c.545.2		16	252.167	odd	6
1008.2.cc.c.545.7		16	36.23	even	6
1764.2.w.a.509.4		16	63.32	odd	6
1764.2.w.a.509.5		16	63.59	even	6
1764.2.w.a.1109.4		16	7.5	odd	6
1764.2.w.a.1109.5		16	7.2	even	3
1764.2.bm.b.1685.2		16	7.4	even	3
1764.2.bm.b.1685.7		16	7.3	odd	6
1764.2.bm.b.1697.2		16	63.5	even	6
1764.2.bm.b.1697.7		16	63.23	odd	6
2268.2.f.b.1133.3		16	63.20	even	6
2268.2.f.b.1133.4		16	9.7	even	3
2268.2.f.b.1133.13		16	63.34	odd	6
2268.2.f.b.1133.14		16	9.2	odd	6
3024.2.cc.c.881.2		16	252.139	even	6
3024.2.cc.c.881.7		16	36.31	odd	6
3024.2.cc.c.2897.2		16	12.11	even	2
3024.2.cc.c.2897.7		16	84.83	odd	2
5292.2.w.a.521.2		16	21.2	odd	6
5292.2.w.a.521.7		16	21.5	even	6
5292.2.w.a.1097.2		16	63.31	odd	6
5292.2.w.a.1097.7		16	63.4	even	3
5292.2.bm.b.2285.2		16	63.58	even	3
5292.2.bm.b.2285.7		16	63.40	odd	6
5292.2.bm.b.4625.2		16	21.17	even	6
5292.2.bm.b.4625.7		16	21.11	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15671 - 1.28920i) q^{3} +(1.21244 + 2.10001i) q^{5} +(1.05649 - 2.42566i) q^{7} +(-0.324049 - 2.98245i) q^{9} +O(q^{10})\)	\(q+(1.15671 - 1.28920i) q^{3} +(1.21244 + 2.10001i) q^{5} +(1.05649 - 2.42566i) q^{7} +(-0.324049 - 2.98245i) q^{9} +(2.09680 + 1.21059i) q^{11} +(-4.73574 + 2.73418i) q^{13} +(4.10976 + 0.866025i) q^{15} +2.58069 q^{17} -0.402708i q^{19} +(-1.90510 - 4.16781i) q^{21} +(3.06895 - 1.77186i) q^{23} +(-0.440020 + 0.762137i) q^{25} +(-4.21979 - 3.03206i) q^{27} +(-6.31784 - 3.64761i) q^{29} +(-3.63732 + 2.10001i) q^{31} +(3.98607 - 1.30289i) q^{33} +(6.37484 - 0.722330i) q^{35} -3.19360 q^{37} +(-1.95298 + 9.26794i) q^{39} +(4.03924 + 6.99618i) q^{41} +(-4.22573 + 7.31918i) q^{43} +(5.87027 - 4.29654i) q^{45} +(-2.25769 + 3.91043i) q^{47} +(-4.76766 - 5.12537i) q^{49} +(2.98510 - 3.32701i) q^{51} +14.0288i q^{53} +5.87106i q^{55} +(-0.519169 - 0.465816i) q^{57} +(-0.0779043 - 0.134934i) q^{59} +(-10.2288 - 5.90561i) q^{61} +(-7.57676 - 2.36489i) q^{63} +(-11.4836 - 6.63005i) q^{65} +(2.53682 + 4.39390i) q^{67} +(1.26561 - 6.00600i) q^{69} +8.73987i q^{71} -8.80274i q^{73} +(0.473569 + 1.44884i) q^{75} +(5.15173 - 3.80715i) q^{77} +(5.66575 - 9.81337i) q^{79} +(-8.78998 + 1.93292i) q^{81} +(7.50937 - 13.0066i) q^{83} +(3.12893 + 5.41946i) q^{85} +(-12.0104 + 3.92571i) q^{87} -15.6668 q^{89} +(1.62893 + 14.3759i) q^{91} +(-1.50000 + 7.11831i) q^{93} +(0.845690 - 0.488259i) q^{95} +(4.97713 + 2.87355i) q^{97} +(2.93105 - 6.64589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7}+O(q^{10}) \) 16 * q - q^7	\( 16 q - q^{7} + 6 q^{11} - 12 q^{15} + 9 q^{21} + 6 q^{23} - 8 q^{25} - 12 q^{29} + 4 q^{37} + 18 q^{39} + 4 q^{43} - 5 q^{49} - 18 q^{51} - 42 q^{57} - 27 q^{63} - 24 q^{65} + 14 q^{67} - 21 q^{77} + 20 q^{79} - 36 q^{81} + 6 q^{85} - 18 q^{91} - 24 q^{93} - 60 q^{95} + 90 q^{99}+O(q^{100}) \) 16 * q - q^7 + 6 * q^11 - 12 * q^15 + 9 * q^21 + 6 * q^23 - 8 * q^25 - 12 * q^29 + 4 * q^37 + 18 * q^39 + 4 * q^43 - 5 * q^49 - 18 * q^51 - 42 * q^57 - 27 * q^63 - 24 * q^65 + 14 * q^67 - 21 * q^77 + 20 * q^79 - 36 * q^81 + 6 * q^85 - 18 * q^91 - 24 * q^93 - 60 * q^95 + 90 * q^99

Introduction

L-functions

Modular forms

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Database

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