LMFDB - Embedded newform 576.2.p.c.95.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(95,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("576.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.p (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:	$4.59938315643$
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} + 11x^{14} + 85x^{12} + 332x^{10} + 940x^{8} + 1064x^{6} + 880x^{4} + 128x^{2} + 16 $ x^16 + 11x^14 + 85x^12 + 332x^10 + 940x^8 + 1064x^6 + 880x^4 + 128*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			95.8
Root			$0.539169 + 0.933868i$ of defining polynomial
Character	$\chi$	$=$	576.95
Dual form			576.2.p.c.479.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.68071 - 0.418594i) q^{3} +(-0.312371 + 0.541042i) q^{5} +(-0.751481 + 0.433868i) q^{7} +(2.64956 - 1.40707i) q^{9} +O(q^{10})$	\(q+(1.68071 - 0.418594i) q^{3} +(-0.312371 + 0.541042i) q^{5} +(-0.751481 + 0.433868i) q^{7} +(2.64956 - 1.40707i) q^{9} +(1.70560 - 0.984726i) q^{11} +(2.75578 + 1.59105i) q^{13} +(-0.298527 + 1.04009i) q^{15} -1.45005i q^{17} +2.81414 q^{19} +(-1.08141 + 1.04377i) q^{21} +(2.88357 - 4.99450i) q^{23} +(2.30485 + 3.99212i) q^{25} +(3.86414 - 3.47396i) q^{27} +(4.41107 + 7.64020i) q^{29} +(-7.14776 - 4.12676i) q^{31} +(2.45441 - 2.36899i) q^{33} -0.542111i q^{35} +4.26419i q^{37} +(5.29767 + 1.52054i) q^{39} +(-7.79610 - 4.50108i) q^{41} +(2.15855 + 3.73872i) q^{43} +(-0.0663618 + 1.87305i) q^{45} +(-5.29767 - 9.17583i) q^{47} +(-3.12352 + 5.41009i) q^{49} +(-0.606982 - 2.43711i) q^{51} -8.19740 q^{53} +1.23040i q^{55} +(4.72974 - 1.17798i) q^{57} +(-8.80475 - 5.08343i) q^{59} +(7.23321 - 4.17610i) q^{61} +(-1.38061 + 2.20694i) q^{63} +(-1.72165 + 0.993996i) q^{65} +(-2.55859 + 4.43161i) q^{67} +(2.75578 - 9.60134i) q^{69} +10.6284 q^{71} -0.776091 q^{73} +(5.54485 + 5.74478i) q^{75} +(-0.854482 + 1.48001i) q^{77} +(-12.1148 + 6.99450i) q^{79} +(5.04032 - 7.45622i) q^{81} +(-1.55157 + 0.895797i) q^{83} +(0.784539 + 0.452954i) q^{85} +(10.6119 + 10.9945i) q^{87} +2.66402i q^{89} -2.76122 q^{91} +(-13.7407 - 3.94387i) q^{93} +(-0.879054 + 1.52257i) q^{95} +(6.06063 + 10.4973i) q^{97} +(3.13350 - 5.00898i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{5} + 6 q^{9}+O(q^{10}) $ 16 * q + 6 * q^5 + 6 * q^9	$ 16 q + 6 q^{5} + 6 q^{9} + 6 q^{13} - 30 q^{21} - 14 q^{25} + 18 q^{29} - 48 q^{33} + 66 q^{45} + 6 q^{49} - 48 q^{53} + 18 q^{57} - 42 q^{61} + 54 q^{65} + 6 q^{69} + 28 q^{73} + 66 q^{77} - 6 q^{81} - 36 q^{85} - 102 q^{93} + 8 q^{97}+O(q^{100}) $ 16 * q + 6 * q^5 + 6 * q^9 + 6 * q^13 - 30 * q^21 - 14 * q^25 + 18 * q^29 - 48 * q^33 + 66 * q^45 + 6 * q^49 - 48 * q^53 + 18 * q^57 - 42 * q^61 + 54 * q^65 + 6 * q^69 + 28 * q^73 + 66 * q^77 - 6 * q^81 - 36 * q^85 - 102 * q^93 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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
$3$	1.68071	−	0.418594i	0.970357	−	0.241675i
$3$	1.68071	−	0.418594i	0.970357	−	0.241675i
$4$		0			0
$5$	−0.312371	+	0.541042i	−0.139697	+	0.241962i	−0.927382	−	0.374116i	$-0.877946\pi$
$5$	−0.312371	+	0.541042i	−0.139697	+	0.241962i	0.787685	+	0.616078i	$0.211279\pi$
$6$		0			0
$7$	−0.751481	+	0.433868i	−0.284033	+	0.163987i	−0.635248	−	0.772308i	$-0.719102\pi$
$7$	−0.751481	+	0.433868i	−0.284033	+	0.163987i	0.351215	+	0.936295i	$0.385769\pi$
$8$		0			0
$9$	2.64956	−	1.40707i	0.883186	−	0.469023i
$10$		0			0
$11$	1.70560	−	0.984726i	0.514256	−	0.296906i	−0.220325	−	0.975426i	$-0.570712\pi$
$11$	1.70560	−	0.984726i	0.514256	−	0.296906i	0.734582	+	0.678520i	$0.237379\pi$
$12$		0			0
$13$	2.75578	+	1.59105i	0.764316	+	0.441278i	0.830843	−	0.556506i	$-0.187859\pi$
$13$	2.75578	+	1.59105i	0.764316	+	0.441278i	−0.0665271	+	0.997785i	$0.521192\pi$
$14$		0			0
$15$	−0.298527	+	1.04009i	−0.0770794	+	0.268550i
$16$		0			0
$17$		−	1.45005i		−	0.351689i	−0.984418	−	0.175845i	$-0.943734\pi$
$17$		−	1.45005i		−	0.351689i	0.984418	−	0.175845i	$-0.0562656\pi$
$18$		0			0
$19$	2.81414			0.645607			0.322803	−	0.946466i	$-0.395375\pi$
$19$	2.81414			0.645607			0.322803	+	0.946466i	$0.395375\pi$
$20$		0			0
$21$	−1.08141	+	1.04377i	−0.235982	+	0.227769i
$22$		0			0
$23$	2.88357	−	4.99450i	0.601267	−	1.04142i	−0.391363	−	0.920237i	$-0.627996\pi$
$23$	2.88357	−	4.99450i	0.601267	−	1.04142i	0.992630	−	0.121188i	$-0.0386705\pi$
$24$		0			0
$25$	2.30485	+	3.99212i	0.460970	+	0.798423i
$26$		0			0
$27$	3.86414	−	3.47396i	0.743655	−	0.668564i
$28$		0			0
$29$	4.41107	+	7.64020i	0.819115	+	1.41875i	0.906335	+	0.422560i	$0.138869\pi$
$29$	4.41107	+	7.64020i	0.819115	+	1.41875i	−0.0872193	+	0.996189i	$0.527798\pi$
$30$		0			0
$31$	−7.14776	−	4.12676i	−1.28378	−	0.741188i	−0.306239	−	0.951955i	$-0.599071\pi$
$31$	−7.14776	−	4.12676i	−1.28378	−	0.741188i	−0.977537	+	0.210766i	$0.932404\pi$
$32$		0			0
$33$	2.45441	−	2.36899i	0.427257	−	0.412388i
$34$		0			0
$35$		−	0.542111i		−	0.0916335i
$36$		0			0
$37$			4.26419i			0.701028i	0.936557	+	0.350514i	$0.113993\pi$
$37$			4.26419i			0.701028i	−0.936557	+	0.350514i	$0.886007\pi$
$38$		0			0
$39$	5.29767	+	1.52054i	0.848306	+	0.243481i
$40$		0			0
$41$	−7.79610	−	4.50108i	−1.21755	−	0.702951i	−0.253154	−	0.967426i	$-0.581468\pi$
$41$	−7.79610	−	4.50108i	−1.21755	−	0.702951i	−0.964393	+	0.264475i	$0.914801\pi$
$42$		0			0
$43$	2.15855	+	3.73872i	0.329176	+	0.570149i	0.982349	−	0.187060i	$-0.0598958\pi$
$43$	2.15855	+	3.73872i	0.329176	+	0.570149i	−0.653173	+	0.757209i	$0.726563\pi$
$44$		0			0
$45$	−0.0663618	+	1.87305i	−0.00989264	+	0.279218i
$46$		0			0
$47$	−5.29767	−	9.17583i	−0.772744	−	1.33843i	−0.936054	−	0.351857i	$-0.885550\pi$
$47$	−5.29767	−	9.17583i	−0.772744	−	1.33843i	0.163309	−	0.986575i	$-0.447783\pi$
$48$		0			0
$49$	−3.12352	+	5.41009i	−0.446217	+	0.772870i
$50$		0			0
$51$	−0.606982	−	2.43711i	−0.0849945	−	0.341264i
$52$		0			0
$53$	−8.19740			−1.12600			−0.563000	−	0.826457i	$-0.690353\pi$
$53$	−8.19740			−1.12600			−0.563000	+	0.826457i	$0.690353\pi$
$54$		0			0
$55$			1.23040i			0.165907i
$56$		0			0
$57$	4.72974	−	1.17798i	0.626469	−	0.156027i
$58$		0			0
$59$	−8.80475	−	5.08343i	−1.14628	−	0.661806i	−0.198303	−	0.980141i	$-0.563543\pi$
$59$	−8.80475	−	5.08343i	−1.14628	−	0.661806i	−0.947978	+	0.318335i	$0.896876\pi$
$60$		0			0
$61$	7.23321	−	4.17610i	0.926118	−	0.534695i	0.0405364	−	0.999178i	$-0.487093\pi$
$61$	7.23321	−	4.17610i	0.926118	−	0.534695i	0.885582	+	0.464483i	$0.153760\pi$
$62$		0			0
$63$	−1.38061	+	2.20694i	−0.173941	+	0.278049i
$64$		0			0
$65$	−1.72165	+	0.993996i	−0.213545	+	0.123290i
$66$		0			0
$67$	−2.55859	+	4.43161i	−0.312582	+	0.541407i	−0.978920	−	0.204242i	$-0.934527\pi$
$67$	−2.55859	+	4.43161i	−0.312582	+	0.541407i	0.666339	+	0.745649i	$0.267860\pi$
$68$		0			0
$69$	2.75578	−	9.60134i	0.331757	−	1.15587i
$70$		0			0
$71$	10.6284			1.26136			0.630679	−	0.776044i	$-0.282776\pi$
$71$	10.6284			1.26136			0.630679	+	0.776044i	$0.282776\pi$
$72$		0			0
$73$	−0.776091			−0.0908346			−0.0454173	−	0.998968i	$-0.514462\pi$
$73$	−0.776091			−0.0908346			−0.0454173	+	0.998968i	$0.514462\pi$
$74$		0			0
$75$	5.54485	+	5.74478i	0.640264	+	0.663351i
$76$		0			0
$77$	−0.854482	+	1.48001i	−0.0973773	+	0.168662i
$78$		0			0
$79$	−12.1148	+	6.99450i	−1.36302	+	0.786943i	−0.990025	−	0.140889i	$-0.955004\pi$
$79$	−12.1148	+	6.99450i	−1.36302	+	0.786943i	−0.372999	+	0.927832i	$0.621671\pi$
$80$		0			0
$81$	5.04032	−	7.45622i	0.560036	−	0.828469i
$82$		0			0
$83$	−1.55157	+	0.895797i	−0.170307	+	0.0983265i	−0.582730	−	0.812666i	$-0.698016\pi$
$83$	−1.55157	+	0.895797i	−0.170307	+	0.0983265i	0.412424	+	0.910992i	$0.364682\pi$
$84$		0			0
$85$	0.784539	+	0.452954i	0.0850952	+	0.0491298i
$86$		0			0
$87$	10.6119	+	10.9945i	1.13771	+	1.17873i
$88$		0			0
$89$			2.66402i			0.282385i	0.989982	+	0.141193i	$0.0450937\pi$
$89$			2.66402i			0.282385i	−0.989982	+	0.141193i	$0.954906\pi$
$90$		0			0
$91$	−2.76122			−0.289455
$92$		0			0
$93$	−13.7407	−	3.94387i	−1.42485	−	0.408961i
$94$		0			0
$95$	−0.879054	+	1.52257i	−0.0901891	+	0.156212i
$96$		0			0
$97$	6.06063	+	10.4973i	0.615364	+	1.06584i	0.990321	+	0.138799i	$0.0443242\pi$
$97$	6.06063	+	10.4973i	0.615364	+	1.06584i	−0.374957	+	0.927042i	$0.622342\pi$
$98$		0			0
$99$	3.13350	−	5.00898i	0.314928	−	0.503421i
$100$		0			0
$101$	−1.47922	−	2.56209i	−0.147188	−	0.254938i	0.782999	−	0.622023i	$-0.213689\pi$
$101$	−1.47922	−	2.56209i	−0.147188	−	0.254938i	−0.930187	+	0.367085i	$0.880356\pi$
$102$		0			0
$103$	1.20966	+	0.698396i	0.119191	+	0.0688150i	0.558410	−	0.829565i	$-0.311412\pi$
$103$	1.20966	+	0.698396i	0.119191	+	0.0688150i	−0.439219	+	0.898380i	$0.644745\pi$
$104$		0			0
$105$	−0.226924	−	0.911130i	−0.0221455	−	0.0889172i
$106$		0			0
$107$			8.37526i			0.809667i	0.914390	+	0.404833i	$0.132670\pi$
$107$			8.37526i			0.809667i	−0.914390	+	0.404833i	$0.867330\pi$
$108$		0			0
$109$		−	16.3625i		−	1.56724i	−0.621239	−	0.783621i	$-0.713371\pi$
$109$		−	16.3625i		−	1.56724i	0.621239	−	0.783621i	$-0.286629\pi$
$110$		0			0
$111$	1.78496	+	7.16685i	0.169421	+	0.680248i
$112$		0			0
$113$	−14.3229	−	8.26933i	−1.34739	−	0.777913i	−0.359507	−	0.933142i	$-0.617055\pi$
$113$	−14.3229	−	8.26933i	−1.34739	−	0.777913i	−0.987878	+	0.155229i	$0.950388\pi$
$114$		0			0
$115$	1.80149	+	3.12027i	0.167990	+	0.290967i
$116$		0			0
$117$	9.54032	+	0.338012i	0.882003	+	0.0312492i
$118$		0			0
$119$	0.629131	+	1.08969i	0.0576723	+	0.0998914i
$120$		0			0
$121$	−3.56063	+	6.16719i	−0.323694	+	0.560654i
$122$		0			0
$123$	−14.9871	−	4.30160i	−1.35134	−	0.387863i
$124$		0			0
$125$	−6.00358			−0.536977
$126$		0			0
$127$			1.73547i			0.153998i	0.997031	+	0.0769991i	$0.0245339\pi$
$127$			1.73547i			0.153998i	−0.997031	+	0.0769991i	$0.975466\pi$
$128$		0			0
$129$	5.19289	+	5.38014i	0.457209	+	0.473695i
$130$		0			0
$131$	−14.8109	−	8.55109i	−1.29404	−	0.747112i	−0.314669	−	0.949202i	$-0.601893\pi$
$131$	−14.8109	−	8.55109i	−1.29404	−	0.747112i	−0.979367	+	0.202090i	$0.935227\pi$
$132$		0			0
$133$	−2.11477	+	1.22096i	−0.183374	+	0.105871i
$134$		0			0
$135$	0.672512	+	3.17583i	0.0578807	+	0.273332i
$136$		0			0
$137$	−2.19289	+	1.26607i	−0.187352	+	0.108167i	−0.590742	−	0.806860i	$-0.701165\pi$
$137$	−2.19289	+	1.26607i	−0.187352	+	0.108167i	0.403391	+	0.915028i	$0.367832\pi$
$138$		0			0
$139$	−4.25857	+	7.37605i	−0.361207	+	0.625629i	−0.988160	−	0.153428i	$-0.950969\pi$
$139$	−4.25857	+	7.37605i	−0.361207	+	0.625629i	0.626953	+	0.779057i	$0.284302\pi$
$140$		0			0
$141$	−12.7448	−	13.2043i	−1.07330	−	1.11200i
$142$		0			0
$143$	6.26700			0.524073
$144$		0			0
$145$	−5.51156			−0.457710
$146$		0			0
$147$	−2.98509	+	10.4003i	−0.246206	+	0.857800i
$148$		0			0
$149$	8.34997	−	14.4626i	0.684057	−	1.18482i	−0.289676	−	0.957125i	$-0.593547\pi$
$149$	8.34997	−	14.4626i	0.684057	−	1.18482i	0.973732	−	0.227696i	$-0.0731192\pi$
$150$		0			0
$151$	2.39854	−	1.38480i	0.195191	−	0.112693i	−0.399219	−	0.916855i	$-0.630719\pi$
$151$	2.39854	−	1.38480i	0.195191	−	0.112693i	0.594410	+	0.804162i	$0.297386\pi$
$152$		0			0
$153$	−2.04032	−	3.84200i	−0.164950	−	0.310607i
$154$		0			0
$155$	4.46551	−	2.57816i	0.358678	−	0.207083i
$156$		0			0
$157$	−4.02876	−	2.32600i	−0.321530	−	0.185635i	0.330544	−	0.943790i	$-0.392768\pi$
$157$	−4.02876	−	2.32600i	−0.321530	−	0.185635i	−0.652074	+	0.758155i	$0.726101\pi$
$158$		0			0
$159$	−13.7774	+	3.43138i	−1.09262	+	0.272126i
$160$		0			0
$161$			5.00436i			0.394399i
$162$		0			0
$163$	−9.82831			−0.769812			−0.384906	−	0.922956i	$-0.625766\pi$
$163$	−9.82831			−0.769812			−0.384906	+	0.922956i	$0.625766\pi$
$164$		0			0
$165$	0.515037	+	2.06794i	0.0400956	+	0.160989i
$166$		0			0
$167$	1.34854	−	2.33573i	0.104353	−	0.180744i	−0.809121	−	0.587642i	$-0.800056\pi$
$167$	1.34854	−	2.33573i	0.104353	−	0.180744i	0.913474	+	0.406898i	$0.133390\pi$
$168$		0			0
$169$	−1.43711	−	2.48915i	−0.110547	−	0.191473i
$170$		0			0
$171$	7.45622	−	3.95968i	0.570191	−	0.302804i
$172$		0			0
$173$	9.13451	+	15.8214i	0.694484	+	1.20288i	0.970354	+	0.241687i	$0.0777007\pi$
$173$	9.13451	+	15.8214i	0.694484	+	1.20288i	−0.275870	+	0.961195i	$0.588966\pi$
$174$		0			0
$175$	−3.46410	−	2.00000i	−0.261861	−	0.151186i
$176$		0			0
$177$	−16.9261	−	4.85814i	−1.27224	−	0.365160i
$178$		0			0
$179$			15.1453i			1.13201i	0.824400	+	0.566007i	$0.191513\pi$
$179$			15.1453i			1.13201i	−0.824400	+	0.566007i	$0.808487\pi$
$180$		0			0
$181$			17.2042i			1.27878i	0.768882	+	0.639391i	$0.220813\pi$
$181$			17.2042i			1.27878i	−0.768882	+	0.639391i	$0.779187\pi$
$182$		0			0
$183$	10.4088	−	10.0466i	0.769443	−	0.742665i
$184$		0			0
$185$	−2.30711	−	1.33201i	−0.169622	−	0.0979312i
$186$		0			0
$187$	−1.42790	−	2.47320i	−0.104419	−	0.180858i
$188$		0			0
$189$	−1.39659	+	4.28714i	−0.101587	+	0.311844i
$190$		0			0
$191$	−6.17672	−	10.6984i	−0.446932	−	0.774109i	0.551253	−	0.834338i	$-0.314150\pi$
$191$	−6.17672	−	10.6984i	−0.446932	−	0.774109i	−0.998185	+	0.0602296i	$0.980817\pi$
$192$		0			0
$193$	1.18640	−	2.05491i	0.0853993	−	0.147916i	−0.820162	−	0.572131i	$-0.806117\pi$
$193$	1.18640	−	2.05491i	0.0853993	−	0.147916i	0.905561	+	0.424215i	$0.139450\pi$
$194$		0			0
$195$	−2.47751	+	2.39129i	−0.177418	+	0.171244i
$196$		0			0
$197$	−17.8095			−1.26888			−0.634439	−	0.772973i	$-0.718769\pi$
$197$	−17.8095			−1.26888			−0.634439	+	0.772973i	$0.718769\pi$
$198$		0			0
$199$			1.90187i			0.134820i	0.997725	+	0.0674098i	$0.0214735\pi$
$199$			1.90187i			0.134820i	−0.997725	+	0.0674098i	$0.978527\pi$
$200$		0			0
$201$	−2.44520	+	8.51925i	−0.172471	+	0.600902i
$202$		0			0
$203$	−6.62968	−	3.82765i	−0.465312	−	0.268648i
$204$		0			0
$205$	4.87055	−	2.81201i	0.340174	−	0.196400i
$206$		0			0
$207$	0.612603	−	17.2906i	0.0425788	−	1.20178i
$208$		0			0
$209$	4.79978	−	2.77115i	0.332007	−	0.191685i
$210$		0			0
$211$	2.65449	−	4.59771i	0.182742	−	0.316519i	−0.760071	−	0.649840i	$-0.774836\pi$
$211$	2.65449	−	4.59771i	0.182742	−	0.316519i	0.942813	+	0.333321i	$0.108169\pi$
$212$		0			0
$213$	17.8632	−	4.44898i	1.22397	−	0.304839i
$214$		0			0
$215$	−2.69707			−0.183939
$216$		0			0
$217$	7.16188			0.486180
$218$		0			0
$219$	−1.30438	+	0.324867i	−0.0881420	+	0.0219525i
$220$		0			0
$221$	2.30711	−	3.99602i	0.155193	−	0.268802i
$222$		0			0
$223$	5.71855	−	3.30160i	0.382942	−	0.221092i	−0.296155	−	0.955140i	$-0.595705\pi$
$223$	5.71855	−	3.30160i	0.382942	−	0.221092i	0.679098	+	0.734048i	$0.262371\pi$
$224$		0			0
$225$	11.7240	+	7.33426i	0.781601	+	0.488951i
$226$		0			0
$227$	20.3972	−	11.7763i	1.35381	−	0.781622i	0.365028	−	0.930997i	$-0.381059\pi$
$227$	20.3972	−	11.7763i	1.35381	−	0.781622i	0.988781	+	0.149375i	$0.0477260\pi$
$228$		0			0
$229$	7.42555	+	4.28714i	0.490694	+	0.283302i	0.724862	−	0.688894i	$-0.241903\pi$
$229$	7.42555	+	4.28714i	0.490694	+	0.283302i	−0.234168	+	0.972196i	$0.575237\pi$
$230$		0			0
$231$	−0.816613	+	2.84514i	−0.0537292	+	0.187196i
$232$		0			0
$233$			2.35596i			0.154344i	0.997018	+	0.0771720i	$0.0245891\pi$
$233$			2.35596i			0.154344i	−0.997018	+	0.0771720i	$0.975411\pi$
$234$		0			0
$235$	6.61935			0.431799
$236$		0			0
$237$	−17.4336	+	16.8269i	−1.13244	+	1.09302i
$238$		0			0
$239$	−11.3147	+	19.5977i	−0.731890	+	1.26767i	0.224185	+	0.974547i	$0.428028\pi$
$239$	−11.3147	+	19.5977i	−0.731890	+	1.26767i	−0.956075	+	0.293124i	$0.905305\pi$
$240$		0			0
$241$	−10.8858	−	18.8547i	−0.701215	−	1.21454i	−0.968040	−	0.250795i	$-0.919308\pi$
$241$	−10.8858	−	18.8547i	−0.701215	−	1.21454i	0.266825	−	0.963745i	$-0.414025\pi$
$242$		0			0
$243$	5.35018	−	14.6416i	0.343214	−	0.939257i
$244$		0			0
$245$	−1.95139	−	3.37991i	−0.124670	−	0.215935i
$246$		0			0
$247$	7.75514	+	4.47743i	0.493448	+	0.284892i
$248$		0			0
$249$	−2.23276	+	2.15505i	−0.141495	+	0.136571i
$250$		0			0
$251$			10.8742i			0.686375i	0.939267	+	0.343188i	$0.111507\pi$
$251$			10.8742i			0.686375i	−0.939267	+	0.343188i	$0.888493\pi$
$252$		0			0
$253$		−	11.3581i		−	0.714079i
$254$		0			0
$255$	1.50819	+	0.432880i	0.0944462	+	0.0271080i
$256$		0			0
$257$	20.7490	+	11.9794i	1.29429	+	0.747257i	0.979411	−	0.201875i	$-0.0647036\pi$
$257$	20.7490	+	11.9794i	1.29429	+	0.747257i	0.314876	+	0.949133i	$0.398037\pi$
$258$		0			0
$259$	−1.85009	−	3.20446i	−0.114959	−	0.199115i
$260$		0			0
$261$	22.4377	+	14.0365i	1.38886	+	0.868836i
$262$		0			0
$263$	3.58645	+	6.21192i	0.221150	+	0.383043i	0.955157	−	0.296098i	$-0.0956856\pi$
$263$	3.58645	+	6.21192i	0.221150	+	0.383043i	−0.734007	+	0.679142i	$0.762352\pi$
$264$		0			0
$265$	2.56063	−	4.43514i	0.157298	−	0.272449i
$266$		0			0
$267$	1.11514	+	4.47743i	0.0682455	+	0.274014i
$268$		0			0
$269$	13.0301			0.794458			0.397229	−	0.917720i	$-0.369972\pi$
$269$	13.0301			0.794458			0.397229	+	0.917720i	$0.369972\pi$
$270$		0			0
$271$		−	7.21940i		−	0.438547i	−0.975663	−	0.219274i	$-0.929631\pi$
$271$		−	7.21940i		−	0.438547i	0.975663	−	0.219274i	$-0.0703687\pi$
$272$		0			0
$273$	−4.64081	+	1.15583i	−0.280875	+	0.0699541i
$274$		0			0
$275$	7.86228	+	4.53929i	0.474113	+	0.273729i
$276$		0			0
$277$	−26.1861	+	15.1186i	−1.57337	+	0.908387i	−0.577620	+	0.816306i	$0.696018\pi$
$277$	−26.1861	+	15.1186i	−1.57337	+	0.908387i	−0.995752	+	0.0920808i	$0.970648\pi$
$278$		0			0
$279$	−24.7450	−	0.876713i	−1.48145	−	0.0524874i
$280$		0			0
$281$	22.8706	−	13.2043i	1.36434	−	0.787704i	0.374144	−	0.927371i	$-0.377937\pi$
$281$	22.8706	−	13.2043i	1.36434	−	0.787704i	0.990199	+	0.139667i	$0.0446032\pi$
$282$		0			0
$283$	14.4760	−	25.0732i	0.860509	−	1.49045i	−0.0109287	−	0.999940i	$-0.503479\pi$
$283$	14.4760	−	25.0732i	0.860509	−	1.49045i	0.871438	−	0.490506i	$-0.163188\pi$
$284$		0			0
$285$	−0.840097	+	2.92696i	−0.0497630	+	0.173378i
$286$		0			0
$287$	7.81150			0.461098
$288$		0			0
$289$	14.8974			0.876315
$290$		0			0
$291$	14.5803	+	15.1060i	0.854710	+	0.885529i
$292$		0			0
$293$	9.05188	−	15.6783i	0.528817	−	0.915937i	−0.470619	−	0.882337i	$-0.655969\pi$
$293$	9.05188	−	15.6783i	0.528817	−	0.915937i	0.999435	−	0.0336006i	$-0.0106974\pi$
$294$		0			0
$295$	5.50070	−	3.17583i	0.320263	−	0.184904i
$296$		0			0
$297$	3.16977	−	9.73029i	0.183929	−	0.564609i
$298$		0			0
$299$	15.8930	−	9.17583i	0.919116	−	0.530652i
$300$		0			0
$301$	−3.24422	−	1.87305i	−0.186994	−	0.107961i
$302$		0			0
$303$	−3.55862	−	3.68693i	−0.204437	−	0.211809i
$304$		0			0
$305$			5.21797i			0.298780i
$306$		0			0
$307$	23.6127			1.34765			0.673825	−	0.738891i	$-0.264650\pi$
$307$	23.6127			1.34765			0.673825	+	0.738891i	$0.264650\pi$
$308$		0			0
$309$	2.32543	+	0.667445i	0.132289	+	0.0379696i
$310$		0			0
$311$	−4.70159	+	8.14340i	−0.266603	+	0.461770i	−0.967982	−	0.251018i	$-0.919235\pi$
$311$	−4.70159	+	8.14340i	−0.266603	+	0.461770i	0.701379	+	0.712788i	$0.252568\pi$
$312$		0			0
$313$	−3.84517	−	6.66003i	−0.217342	−	0.376447i	0.736653	−	0.676271i	$-0.236405\pi$
$313$	−3.84517	−	6.66003i	−0.217342	−	0.376447i	−0.953994	+	0.299824i	$0.903072\pi$
$314$		0			0
$315$	−0.762787	−	1.43635i	−0.0429782	−	0.0809294i
$316$		0			0
$317$	16.4647	+	28.5178i	0.924752	+	1.60172i	0.791959	+	0.610574i	$0.209061\pi$
$317$	16.4647	+	28.5178i	0.924752	+	1.60172i	0.132793	+	0.991144i	$0.457605\pi$
$318$		0			0
$319$	15.0470	+	8.68739i	0.842471	+	0.486401i
$320$		0			0
$321$	3.50583	+	14.0764i	0.195676	+	0.785666i
$322$		0			0
$323$		−	4.08064i		−	0.227053i
$324$		0			0
$325$			14.6685i			0.813664i
$326$		0			0
$327$	−6.84923	−	27.5006i	−0.378764	−	1.52078i
$328$		0			0
$329$	7.96220	+	4.59698i	0.438970	+	0.253440i
$330$		0			0
$331$	−1.74858	−	3.02863i	−0.0961106	−	0.166468i	0.813961	−	0.580920i	$-0.197307\pi$
$331$	−1.74858	−	3.02863i	−0.0961106	−	0.166468i	−0.910072	+	0.414451i	$0.863974\pi$
$332$		0			0
$333$	6.00000	+	11.2982i	0.328798	+	0.619138i
$334$		0			0
$335$	−1.59846	−	2.76861i	−0.0873332	−	0.151265i
$336$		0			0
$337$	13.4890	−	23.3636i	0.734792	−	1.27270i	−0.220022	−	0.975495i	$-0.570613\pi$
$337$	13.4890	−	23.3636i	0.734792	−	1.27270i	0.954814	−	0.297203i	$-0.0960538\pi$
$338$		0			0
$339$	−27.5341	−	7.90285i	−1.49545	−	0.429224i
$340$		0			0
$341$	−16.2549			−0.880253
$342$		0			0
$343$		−	11.4949i		−	0.620668i
$344$		0			0
$345$	4.33391	+	4.49017i	0.233330	+	0.241743i
$346$		0			0
$347$	16.6779	+	9.62901i	0.895319	+	0.516912i	0.875678	−	0.482895i	$-0.160415\pi$
$347$	16.6779	+	9.62901i	0.895319	+	0.516912i	0.0196402	+	0.999807i	$0.493748\pi$
$348$		0			0
$349$	15.3570	−	8.86639i	0.822043	−	0.474607i	−0.0290775	−	0.999577i	$-0.509257\pi$
$349$	15.3570	−	8.86639i	0.822043	−	0.474607i	0.851120	+	0.524970i	$0.175924\pi$
$350$		0			0
$351$	16.1760	−	3.42542i	0.863410	−	0.182835i
$352$		0			0
$353$	15.2735	−	8.81818i	0.812928	−	0.469344i	−0.0350435	−	0.999386i	$-0.511157\pi$
$353$	15.2735	−	8.81818i	0.812928	−	0.469344i	0.847972	+	0.530041i	$0.177824\pi$
$354$		0			0
$355$	−3.32000	+	5.75041i	−0.176207	+	0.305200i
$356$		0			0
$357$	1.51352	+	1.56809i	0.0801040	+	0.0829924i
$358$		0			0
$359$	−29.1550			−1.53874			−0.769372	−	0.638801i	$-0.779431\pi$
$359$	−29.1550			−1.53874			−0.769372	+	0.638801i	$0.779431\pi$
$360$		0			0
$361$	−11.0806			−0.583192
$362$		0			0
$363$	−3.40283	+	11.8557i	−0.178602	+	0.622263i
$364$		0			0
$365$	0.242428	−	0.419898i	0.0126893	−	0.0219785i
$366$		0			0
$367$	25.2952	−	14.6042i	1.32040	−	0.762333i	0.336607	−	0.941645i	$-0.390721\pi$
$367$	25.2952	−	14.6042i	1.32040	−	0.762333i	0.983792	+	0.179312i	$0.0573873\pi$
$368$		0			0
$369$	−26.9896	−	0.956235i	−1.40502	−	0.0497796i
$370$		0			0
$371$	6.16019	−	3.55659i	0.319821	−	0.184649i
$372$		0			0
$373$	−8.99633	−	5.19403i	−0.465812	−	0.268937i	0.248673	−	0.968588i	$-0.420006\pi$
$373$	−8.99633	−	5.19403i	−0.465812	−	0.268937i	−0.714485	+	0.699651i	$0.753339\pi$
$374$		0			0
$375$	−10.0903	+	2.51306i	−0.521059	+	0.129774i
$376$		0			0
$377$			28.0730i			1.44583i
$378$		0			0
$379$	−9.40043			−0.482868			−0.241434	−	0.970417i	$-0.577618\pi$
$379$	−9.40043			−0.482868			−0.241434	+	0.970417i	$0.577618\pi$
$380$		0			0
$381$	0.726458	+	2.91682i	0.0372176	+	0.149433i
$382$		0			0
$383$	−14.1080	+	24.4358i	−0.720887	+	1.24861i	0.239757	+	0.970833i	$0.422932\pi$
$383$	−14.1080	+	24.4358i	−0.720887	+	1.24861i	−0.960645	+	0.277780i	$0.910401\pi$
$384$		0			0
$385$	−0.533831	−	0.924622i	−0.0272065	−	0.0471231i
$386$		0			0
$387$	10.9798	+	6.86872i	0.558136	+	0.349157i
$388$		0			0
$389$	−9.67663	−	16.7604i	−0.490624	−	0.849786i	0.509317	−	0.860579i	$-0.329898\pi$
$389$	−9.67663	−	16.7604i	−0.490624	−	0.849786i	−0.999942	+	0.0107924i	$0.996565\pi$
$390$		0			0
$391$	−7.24228	−	4.18133i	−0.366258	−	0.211459i
$392$		0			0
$393$	−28.4723	−	8.17212i	−1.43624	−	0.412229i
$394$		0			0
$395$		−	8.73951i		−	0.439733i
$396$		0			0
$397$			4.42212i			0.221940i	0.993824	+	0.110970i	$0.0353958\pi$
$397$			4.42212i			0.221940i	−0.993824	+	0.110970i	$0.964604\pi$
$398$		0			0
$399$	−3.04322	+	2.93731i	−0.152352	+	0.147050i
$400$		0			0
$401$	−9.31867	−	5.38014i	−0.465352	−	0.268671i	0.248940	−	0.968519i	$-0.419918\pi$
$401$	−9.31867	−	5.38014i	−0.465352	−	0.268671i	−0.714292	+	0.699848i	$0.753251\pi$
$402$		0			0
$403$	−13.1318	−	22.7449i	−0.654140	−	1.13300i
$404$		0			0
$405$	2.45968	+	5.05613i	0.122222	+	0.251241i
$406$		0			0
$407$	4.19905	+	7.27298i	0.208139	+	0.360508i
$408$		0			0
$409$	7.62126	−	13.2004i	0.376847	−	0.652718i	−0.613755	−	0.789497i	$-0.710342\pi$
$409$	7.62126	−	13.2004i	0.376847	−	0.652718i	0.990602	+	0.136779i	$0.0436749\pi$
$410$		0			0
$411$	−3.15565	+	3.04582i	−0.155657	+	0.150239i
$412$		0			0
$413$	8.82214			0.434109
$414$		0			0
$415$		−	1.11928i		−	0.0549435i
$416$		0			0
$417$	−4.06984	+	14.1796i	−0.199301	+	0.694378i
$418$		0			0
$419$	−9.87593	−	5.70187i	−0.482471	−	0.278555i	0.238975	−	0.971026i	$-0.423189\pi$
$419$	−9.87593	−	5.70187i	−0.482471	−	0.278555i	−0.721446	+	0.692471i	$0.756522\pi$
$420$		0			0
$421$	−22.3821	+	12.9223i	−1.09084	+	0.629795i	−0.933799	−	0.357797i	$-0.883528\pi$
$421$	−22.3821	+	12.9223i	−1.09084	+	0.629795i	−0.157038	+	0.987593i	$0.550195\pi$
$422$		0			0
$423$	−26.9475	−	16.8577i	−1.31023	−	0.819650i
$424$		0			0
$425$	5.78877	−	3.34215i	0.280797	−	0.162118i
$426$		0			0
$427$	−3.62375	+	6.27652i	−0.175366	+	0.303742i
$428$		0			0
$429$	10.5330	−	2.62333i	0.508538	−	0.126655i
$430$		0			0
$431$	34.4831			1.66099			0.830496	−	0.557025i	$-0.188057\pi$
$431$	34.4831			1.66099			0.830496	+	0.557025i	$0.188057\pi$
$432$		0			0
$433$	−22.5245			−1.08246			−0.541230	−	0.840874i	$-0.682041\pi$
$433$	−22.5245			−1.08246			−0.541230	+	0.840874i	$0.682041\pi$
$434$		0			0
$435$	−9.26333	+	2.30711i	−0.444143	+	0.110617i
$436$		0			0
$437$	8.11477	−	14.0552i	0.388182	−	0.672351i
$438$		0			0
$439$	2.11034	−	1.21841i	0.100721	−	0.0581514i	−0.448793	−	0.893636i	$-0.648146\pi$
$439$	2.11034	−	1.21841i	0.100721	−	0.0581514i	0.549514	+	0.835484i	$0.314813\pi$
$440$		0			0
$441$	−0.663578	+	18.7294i	−0.0315989	+	0.891874i
$442$		0			0
$443$	−7.57955	+	4.37605i	−0.360115	+	0.207913i	−0.669131	−	0.743144i	$-0.733334\pi$
$443$	−7.57955	+	4.37605i	−0.360115	+	0.207913i	0.309016	+	0.951057i	$0.400000\pi$
$444$		0			0
$445$	−1.44135	−	0.832161i	−0.0683263	−	0.0394482i
$446$		0			0
$447$	7.97992	−	27.8026i	0.377437	−	1.31502i
$448$		0			0
$449$			15.1485i			0.714903i	0.933932	+	0.357451i	$0.116354\pi$
$449$			15.1485i			0.714903i	−0.933932	+	0.357451i	$0.883646\pi$
$450$		0			0
$451$	−17.7293			−0.834841
$452$		0			0
$453$	3.45158	−	3.33146i	0.162170	−	0.156526i
$454$		0			0
$455$	0.862526	−	1.49394i	0.0404359	−	0.0700370i
$456$		0			0
$457$	−6.54907	−	11.3433i	−0.306352	−	0.530618i	0.671209	−	0.741268i	$-0.265775\pi$
$457$	−6.54907	−	11.3433i	−0.306352	−	0.530618i	−0.977562	+	0.210650i	$0.932442\pi$
$458$		0			0
$459$	−5.03742	−	5.60321i	−0.235127	−	0.261535i
$460$		0			0
$461$	0.472168	+	0.817819i	0.0219911	+	0.0380896i	0.876812	−	0.480834i	$-0.159666\pi$
$461$	0.472168	+	0.817819i	0.0219911	+	0.0380896i	−0.854820	+	0.518924i	$0.826333\pi$
$462$		0			0
$463$	27.0864	+	15.6383i	1.25881	+	0.726775i	0.972843	−	0.231465i	$-0.0743518\pi$
$463$	27.0864	+	15.6383i	1.25881	+	0.726775i	0.285967	+	0.958239i	$0.407685\pi$
$464$		0			0
$465$	6.42601	−	6.20237i	0.297999	−	0.287628i
$466$		0			0
$467$			37.1248i			1.71793i	0.512033	+	0.858966i	$0.328893\pi$
$467$			37.1248i			1.71793i	−0.512033	+	0.858966i	$0.671107\pi$
$468$		0			0
$469$		−	4.44036i		−	0.205037i
$470$		0			0
$471$	−7.74482	−	2.22292i	−0.356862	−	0.102427i
$472$		0			0
$473$	7.36322	+	4.25116i	0.338561	+	0.195468i
$474$		0			0
$475$	6.48616	+	11.2344i	0.297605	+	0.515467i
$476$		0			0
$477$	−21.7195	+	11.5343i	−0.994467	+	0.528119i
$478$		0			0
$479$	0.922436	+	1.59771i	0.0421472	+	0.0730010i	0.886329	−	0.463055i	$-0.153247\pi$
$479$	0.922436	+	1.59771i	0.0421472	+	0.0730010i	−0.844182	+	0.536056i	$0.819913\pi$
$480$		0			0
$481$	−6.78454	+	11.7512i	−0.309348	+	0.535807i
$482$		0			0
$483$	2.09480	+	8.41087i	0.0953165	+	0.382708i
$484$		0			0
$485$	−7.57266			−0.343857
$486$		0			0
$487$			15.0231i			0.680763i	0.940287	+	0.340381i	$0.110556\pi$
$487$			15.0231i			0.680763i	−0.940287	+	0.340381i	$0.889444\pi$
$488$		0			0
$489$	−16.5185	+	4.11407i	−0.746993	+	0.186045i
$490$		0			0
$491$	−6.61877	−	3.82135i	−0.298701	−	0.172455i	0.343158	−	0.939278i	$-0.388503\pi$
$491$	−6.61877	−	3.82135i	−0.298701	−	0.172455i	−0.641859	+	0.766823i	$0.721837\pi$
$492$		0			0
$493$	11.0787	−	6.39628i	0.498959	−	0.288074i
$494$		0			0
$495$	1.73125	+	3.26001i	0.0778141	+	0.146527i
$496$		0			0
$497$	−7.98704	+	4.61132i	−0.358268	+	0.206846i
$498$		0			0
$499$	14.5388	−	25.1820i	0.650848	−	1.12730i	−0.332069	−	0.943255i	$-0.607747\pi$
$499$	14.5388	−	25.1820i	0.650848	−	1.12730i	0.982917	−	0.184047i	$-0.0589199\pi$
$500$		0			0
$501$	1.28877	−	4.49017i	0.0575781	−	0.200606i
$502$		0			0
$503$	−31.4130			−1.40064			−0.700318	−	0.713831i	$-0.746959\pi$
$503$	−31.4130			−1.40064			−0.700318	+	0.713831i	$0.746959\pi$
$504$		0			0
$505$	1.84827			0.0822468
$506$		0			0
$507$	−3.45731	−	3.58197i	−0.153545	−	0.159081i
$508$		0			0
$509$	9.59946	−	16.6268i	0.425489	−	0.736968i	−0.570977	−	0.820966i	$-0.693436\pi$
$509$	9.59946	−	16.6268i	0.425489	−	0.736968i	0.996466	+	0.0839980i	$0.0267689\pi$
$510$		0			0
$511$	0.583218	−	0.336721i	0.0258000	−	0.0148957i
$512$		0			0
$513$	10.8742	−	9.77619i	0.480109	−	0.431629i
$514$		0			0
$515$	−0.755724	+	0.436317i	−0.0333012	+	0.0192264i
$516$		0			0
$517$	−18.0714	−	10.4335i	−0.794777	−	0.458865i
$518$		0			0
$519$	21.9752	+	22.7676i	0.964605	+	0.999386i
$520$		0			0
$521$		−	25.7108i		−	1.12641i	−0.826317	−	0.563205i	$-0.809568\pi$
$521$		−	25.7108i		−	1.12641i	0.826317	−	0.563205i	$-0.190432\pi$
$522$		0			0
$523$	−20.4567			−0.894509			−0.447254	−	0.894407i	$-0.647598\pi$
$523$	−20.4567			−0.894509			−0.447254	+	0.894407i	$0.647598\pi$
$524$		0			0
$525$	−6.65933	−	1.91136i	−0.290637	−	0.0834188i
$526$		0			0
$527$	−5.98402	+	10.3646i	−0.260668	+	0.451490i
$528$		0			0
$529$	−5.13001	−	8.88543i	−0.223044	−	0.386323i
$530$		0			0
$531$	−30.4814	−	1.07995i	−1.32278	−	0.0468659i
$532$		0			0
$533$	−14.3229	−	24.8080i	−0.620394	−	1.07455i
$534$		0			0
$535$	−4.53137	−	2.61619i	−0.195908	−	0.113108i
$536$		0			0
$537$	6.33974	+	25.4549i	0.273580	+	1.09846i
$538$		0			0
$539$			12.3032i			0.529938i
$540$		0			0
$541$		−	25.9547i		−	1.11588i	−0.829881	−	0.557940i	$-0.811592\pi$
$541$		−	25.9547i		−	1.11588i	0.829881	−	0.557940i	$-0.188408\pi$
$542$		0			0
$543$	7.20159	+	28.9153i	0.309050	+	1.24087i
$544$		0			0
$545$	8.85280	+	5.11117i	0.379212	+	0.218938i
$546$		0			0
$547$	9.48679	+	16.4316i	0.405626	+	0.702565i	0.994394	−	0.105737i	$-0.0337202\pi$
$547$	9.48679	+	16.4316i	0.405626	+	0.702565i	−0.588768	+	0.808302i	$0.700387\pi$
$548$		0			0
$549$	13.2888	−	21.2424i	0.567151	−	0.906605i
$550$		0			0
$551$	12.4134	+	21.5006i	0.528827	+	0.915955i
$552$		0			0
$553$	6.06938	−	10.5125i	0.258096	−	0.447036i
$554$		0			0
$555$	−4.43514	−	1.27298i	−0.188261	−	0.0540348i
$556$		0			0
$557$	0.319595			0.0135417			0.00677083	−	0.999977i	$-0.497845\pi$
$557$	0.319595			0.0135417			0.00677083	+	0.999977i	$0.497845\pi$
$558$		0			0
$559$			13.7374i			0.581032i
$560$		0			0
$561$	−3.43515	−	3.55902i	−0.145032	−	0.150262i
$562$		0			0
$563$	5.97840	+	3.45163i	0.251959	+	0.145469i	0.620661	−	0.784079i	$-0.286864\pi$
$563$	5.97840	+	3.45163i	0.251959	+	0.145469i	−0.368702	+	0.929548i	$0.620198\pi$
$564$		0			0
$565$	8.94812	−	5.16620i	0.376450	−	0.217344i
$566$		0			0
$567$	−0.552693	+	7.79004i	−0.0232109	+	0.327151i
$568$		0			0
$569$	−13.6038	+	7.85414i	−0.570300	+	0.329263i	−0.757269	−	0.653103i	$-0.773467\pi$
$569$	−13.6038	+	7.85414i	−0.570300	+	0.329263i	0.186969	+	0.982366i	$0.440133\pi$
$570$		0			0
$571$	−10.9368	+	18.9432i	−0.457693	+	0.792747i	−0.998839	−	0.0481816i	$-0.984657\pi$
$571$	−10.9368	+	18.9432i	−0.457693	+	0.792747i	0.541146	+	0.840929i	$0.317991\pi$
$572$		0			0
$573$	−14.8595	−	15.3953i	−0.620767	−	0.643150i
$574$		0			0
$575$	26.5848			1.10866
$576$		0			0
$577$	17.5347			0.729979			0.364989	−	0.931012i	$-0.381073\pi$
$577$	17.5347			0.729979			0.364989	+	0.931012i	$0.381073\pi$
$578$		0			0
$579$	1.13383	−	3.95033i	0.0471202	−	0.164170i
$580$		0			0
$581$	0.777316	−	1.34635i	0.0322485	−	0.0558560i
$582$		0			0
$583$	−13.9814	+	8.07219i	−0.579052	+	0.334316i
$584$		0			0
$585$	−3.16300	+	5.05613i	−0.130774	+	0.209045i
$586$		0			0
$587$	−9.86502	+	5.69557i	−0.407173	+	0.235081i	−0.689574	−	0.724215i	$-0.742202\pi$
$587$	−9.86502	+	5.69557i	−0.407173	+	0.235081i	0.282401	+	0.959296i	$0.408869\pi$
$588$		0			0
$589$	−20.1148	−	11.6133i	−0.828815	−	0.478516i
$590$		0			0
$591$	−29.9326	+	7.45497i	−1.23126	+	0.306656i
$592$		0			0
$593$		−	14.5507i		−	0.597524i	−0.954328	−	0.298762i	$-0.903426\pi$
$593$		−	14.5507i		−	0.597524i	0.954328	−	0.298762i	$-0.0965737\pi$
$594$		0			0
$595$	−0.786089			−0.0322265
$596$		0			0
$597$	0.796109	+	3.19648i	0.0325826	+	0.130823i
$598$		0			0
$599$	4.01255	−	6.94994i	0.163948	−	0.283967i	−0.772333	−	0.635218i	$-0.780910\pi$
$599$	4.01255	−	6.94994i	0.163948	−	0.283967i	0.936281	+	0.351251i	$0.114244\pi$
$600$		0			0
$601$	8.02650	+	13.9023i	0.327408	+	0.567087i	0.981997	−	0.188898i	$-0.0604916\pi$
$601$	8.02650	+	13.9023i	0.327408	+	0.567087i	−0.654589	+	0.755985i	$0.727158\pi$
$602$		0			0
$603$	−0.543562	+	15.3419i	−0.0221355	+	0.624771i
$604$		0			0
$605$	−2.22447	−	3.85290i	−0.0904378	−	0.156643i
$606$		0			0
$607$	2.03660	+	1.17583i	0.0826629	+	0.0477255i	0.540762	−	0.841176i	$-0.318136\pi$
$607$	2.03660	+	1.17583i	0.0826629	+	0.0477255i	−0.458099	+	0.888901i	$0.651469\pi$
$608$		0			0
$609$	−12.7448	−	3.65801i	−0.516444	−	0.148230i
$610$		0			0
$611$		−	33.7154i		−	1.36398i
$612$		0			0
$613$			14.7623i			0.596244i	0.954528	+	0.298122i	$0.0963603\pi$
$613$			14.7623i			0.596244i	−0.954528	+	0.298122i	$0.903640\pi$
$614$		0			0
$615$	7.00888	−	6.76496i	0.282625	−	0.272789i
$616$		0			0
$617$	14.2845	+	8.24718i	0.575074	+	0.332019i	0.759173	−	0.650889i	$-0.225603\pi$
$617$	14.2845	+	8.24718i	0.575074	+	0.332019i	−0.184099	+	0.982908i	$0.558937\pi$
$618$		0			0
$619$	−20.6263	−	35.7258i	−0.829040	−	1.43594i	−0.898792	−	0.438375i	$-0.855554\pi$
$619$	−20.6263	−	35.7258i	−0.829040	−	1.43594i	0.0697522	−	0.997564i	$-0.477779\pi$
$620$		0			0
$621$	−6.20813	−	29.3169i	−0.249124	−	1.17645i
$622$		0			0
$623$	−1.15583	−	2.00196i	−0.0463074	−	0.0802068i
$624$		0			0
$625$	−9.64890	+	16.7124i	−0.385956	+	0.668495i
$626$		0			0
$627$	6.90703	−	6.66665i	0.275840	−	0.266240i
$628$		0			0
$629$	6.18329			0.246544
$630$		0			0
$631$		−	2.49407i		−	0.0992873i	−0.998767	−	0.0496437i	$-0.984191\pi$
$631$		−	2.49407i		−	0.0992873i	0.998767	−	0.0496437i	$-0.0158086\pi$
$632$		0			0
$633$	2.53685	−	8.83855i	0.100831	−	0.351301i
$634$		0			0
$635$	−0.938964	−	0.542111i	−0.0372616	−	0.0215130i
$636$		0			0
$637$	−17.2155	+	9.93935i	−0.682101	+	0.393811i
$638$		0			0
$639$	28.1605	−	14.9549i	1.11401	−	0.591605i
$640$		0			0
$641$	3.03469	−	1.75208i	0.119863	−	0.0692029i	−0.438870	−	0.898551i	$-0.644621\pi$
$641$	3.03469	−	1.75208i	0.119863	−	0.0692029i	0.558733	+	0.829348i	$0.311288\pi$
$642$		0			0
$643$	−21.6711	+	37.5354i	−0.854623	+	1.48025i	0.0223710	+	0.999750i	$0.492879\pi$
$643$	−21.6711	+	37.5354i	−0.854623	+	1.48025i	−0.876994	+	0.480501i	$0.840455\pi$
$644$		0			0
$645$	−4.53299	+	1.12898i	−0.178486	+	0.0444535i
$646$		0			0
$647$	−30.1547			−1.18551			−0.592753	−	0.805385i	$-0.701959\pi$
$647$	−30.1547			−1.18551			−0.592753	+	0.805385i	$0.701959\pi$
$648$		0			0
$649$	−20.0231			−0.785976
$650$		0			0
$651$	12.0370	−	2.99792i	0.471768	−	0.117498i
$652$		0			0
$653$	−8.50977	+	14.7394i	−0.333013	+	0.576796i	−0.983101	−	0.183063i	$-0.941399\pi$
$653$	−8.50977	+	14.7394i	−0.333013	+	0.576796i	0.650088	+	0.759859i	$0.274732\pi$
$654$		0			0
$655$	9.25300	−	5.34222i	0.361545	−	0.208738i
$656$		0			0
$657$	−2.05630	+	1.09201i	−0.0802238	+	0.0426035i
$658$		0			0
$659$	−22.1524	+	12.7897i	−0.862934	+	0.498215i	−0.864994	−	0.501783i	$-0.832678\pi$
$659$	−22.1524	+	12.7897i	−0.862934	+	0.498215i	0.00205997	+	0.999998i	$0.499344\pi$
$660$		0			0
$661$	38.6746	+	22.3288i	1.50427	+	0.868488i	0.999988	+	0.00494722i	$0.00157475\pi$
$661$	38.6746	+	22.3288i	1.50427	+	0.868488i	0.504278	+	0.863541i	$0.331759\pi$
$662$		0			0
$663$	2.20486	−	7.68189i	0.0856297	−	0.298340i
$664$		0			0
$665$		−	1.52557i		−	0.0591592i
$666$		0			0
$667$	50.8786			1.97003
$668$		0			0
$669$	8.22917	−	7.94278i	0.318158	−	0.307086i
$670$		0			0
$671$	8.22462	−	14.2455i	0.317508	−	0.549940i
$672$		0			0
$673$	8.87704	+	15.3755i	0.342185	+	0.592681i	0.984838	−	0.173476i	$-0.0554998\pi$
$673$	8.87704	+	15.3755i	0.342185	+	0.592681i	−0.642653	+	0.766157i	$0.722166\pi$
$674$		0			0
$675$	22.7747	+	7.41916i	0.876599	+	0.285564i
$676$		0			0
$677$	4.79339	+	8.30239i	0.184225	+	0.319087i	0.943315	−	0.331899i	$-0.107689\pi$
$677$	4.79339	+	8.30239i	0.184225	+	0.319087i	−0.759090	+	0.650985i	$0.774356\pi$
$678$		0			0
$679$	−9.10890	−	5.25903i	−0.349568	−	0.201823i
$680$		0			0
$681$	29.3522	−	28.3307i	1.12478	−	1.08563i
$682$		0			0
$683$		−	24.7701i		−	0.947800i	−0.880579	−	0.473900i	$-0.842846\pi$
$683$		−	24.7701i		−	0.947800i	0.880579	−	0.473900i	$-0.157154\pi$
$684$		0			0
$685$		−	1.58193i		−	0.0604425i
$686$		0			0
$687$	14.2748	+	4.09715i	0.544616	+	0.156316i
$688$		0			0
$689$	−22.5902	−	13.0425i	−0.860620	−	0.496879i
$690$		0			0
$691$	9.61477	+	16.6533i	0.365763	+	0.633520i	0.988898	−	0.148594i	$-0.0474748\pi$
$691$	9.61477	+	16.6533i	0.365763	+	0.633520i	−0.623135	+	0.782114i	$0.714141\pi$
$692$		0			0
$693$	−0.181531	+	5.12368i	−0.00689579	+	0.194632i
$694$		0			0
$695$	−2.66051	−	4.60813i	−0.100919	−	0.174796i
$696$		0			0
$697$	−6.52680	+	11.3047i	−0.247220	+	0.428198i
$698$		0			0
$699$	0.986190	+	3.95968i	0.0373011	+	0.149769i
$700$		0			0
$701$	−10.5311			−0.397754			−0.198877	−	0.980024i	$-0.563729\pi$
$701$	−10.5311			−0.397754			−0.198877	+	0.980024i	$0.563729\pi$
$702$		0			0
$703$			12.0000i			0.452589i
$704$		0			0
$705$	11.1252	−	2.77082i	0.418999	−	0.104355i
$706$		0			0
$707$	2.22322	+	1.28358i	0.0836127	+	0.0482738i
$708$		0			0
$709$	16.7893	−	9.69332i	0.630537	−	0.364040i	−0.150423	−	0.988622i	$-0.548064\pi$
$709$	16.7893	−	9.69332i	0.630537	−	0.364040i	0.780960	+	0.624581i	$0.214730\pi$
$710$		0			0
$711$	−22.2572	+	35.5787i	−0.834710	+	1.33431i
$712$		0			0
$713$	−41.2222	+	23.7997i	−1.54378	+	0.891304i
$714$		0			0
$715$	−1.95763	+	3.39071i	−0.0732111	+	0.126805i
$716$		0			0
$717$	−10.8133	+	37.6743i	−0.403830	+	1.40697i
$718$		0			0
$719$	12.9401			0.482583			0.241291	−	0.970453i	$-0.422429\pi$
$719$	12.9401			0.482583			0.241291	+	0.970453i	$0.422429\pi$
$720$		0			0
$721$	−1.21205			−0.0451390
$722$		0			0
$723$	−26.1883	−	27.1326i	−0.973954	−	1.00907i
$724$		0			0
$725$	−20.3337	+	35.2190i	−0.755175	+	1.30800i
$726$		0			0
$727$	−11.6566	+	6.72997i	−0.432321	+	0.249601i	−0.700335	−	0.713814i	$-0.746966\pi$
$727$	−11.6566	+	6.72997i	−0.432321	+	0.249601i	0.268014	+	0.963415i	$0.413633\pi$
$728$		0			0
$729$	2.86322	−	26.8478i	0.106045	−	0.994361i
$730$		0			0
$731$	5.42133	−	3.13001i	0.200515	−	0.115767i
$732$		0			0
$733$	8.61900	+	4.97618i	0.318350	+	0.183800i	0.650657	−	0.759372i	$-0.274494\pi$
$733$	8.61900	+	4.97618i	0.318350	+	0.183800i	−0.332307	+	0.943171i	$0.607827\pi$
$734$		0			0
$735$	−4.69453	−	4.86380i	−0.173160	−	0.179404i
$736$		0			0
$737$			10.0780i			0.371230i
$738$		0			0
$739$	−20.2128			−0.743540			−0.371770	−	0.928325i	$-0.621249\pi$
$739$	−20.2128			−0.743540			−0.371770	+	0.928325i	$0.621249\pi$
$740$		0			0
$741$	14.9084	+	4.27900i	0.547672	+	0.157193i
$742$		0			0
$743$	22.5392	−	39.0391i	0.826883	−	1.43220i	−0.0735881	−	0.997289i	$-0.523445\pi$
$743$	22.5392	−	39.0391i	0.826883	−	1.43220i	0.900471	−	0.434915i	$-0.143222\pi$
$744$		0			0
$745$	5.21658	+	9.03538i	0.191121	+	0.331031i
$746$		0			0
$747$	−2.85052	+	4.55663i	−0.104295	+	0.166718i
$748$		0			0
$749$	−3.63376	−	6.29385i	−0.132775	−	0.229972i
$750$		0			0
$751$	−37.1455	−	21.4460i	−1.35546	−	0.782575i	−0.366452	−	0.930437i	$-0.619428\pi$
$751$	−37.1455	−	21.4460i	−1.35546	−	0.782575i	−0.989008	+	0.147862i	$0.952761\pi$
$752$		0			0
$753$	4.55188	+	18.2764i	0.165880	+	0.666029i
$754$		0			0
$755$			1.73029i			0.0629715i
$756$		0			0
$757$		−	18.3964i		−	0.668628i	−0.942462	−	0.334314i	$-0.891495\pi$
$757$		−	18.3964i		−	0.668628i	0.942462	−	0.334314i	$-0.108505\pi$
$758$		0			0
$759$	−4.75444	−	19.0897i	−0.172575	−	0.692912i
$760$		0			0
$761$	−30.0623	−	17.3565i	−1.08976	−	0.629172i	−0.156246	−	0.987718i	$-0.549939\pi$
$761$	−30.0623	−	17.3565i	−1.08976	−	0.629172i	−0.933512	+	0.358546i	$0.883273\pi$
$762$		0			0
$763$	7.09916	+	12.2961i	0.257007	+	0.445149i
$764$		0			0
$765$	2.71602	+	0.0962281i	0.0981979	+	0.00347913i
$766$		0			0
$767$	−16.1760	−	28.0176i	−0.584081	−	1.01166i
$768$		0			0
$769$	3.41906	−	5.92199i	0.123294	−	0.213552i	−0.797771	−	0.602961i	$-0.793987\pi$
$769$	3.41906	−	5.92199i	0.123294	−	0.213552i	0.921065	+	0.389409i	$0.127321\pi$
$770$		0			0
$771$	39.8875	+	11.4485i	1.43651	+	0.412309i
$772$		0			0
$773$	40.5131			1.45715			0.728577	−	0.684964i	$-0.240182\pi$
$773$	40.5131			1.45715			0.728577	+	0.684964i	$0.240182\pi$
$774$		0			0
$775$		−	38.0463i		−	1.36666i
$776$		0			0
$777$	−4.45083	−	4.61132i	−0.159673	−	0.165430i
$778$		0			0
$779$	−21.9393	−	12.6667i	−0.786057	−	0.453830i
$780$		0			0
$781$	18.1277	−	10.4661i	0.648661	−	0.374505i
$782$		0			0
$783$	43.5868	+	14.1990i	1.55766	+	0.507429i
$784$		0			0
$785$	2.51693	−	1.45315i	0.0898332	−	0.0518652i
$786$		0			0
$787$	21.6672	−	37.5286i	0.772351	−	1.33775i	−0.163921	−	0.986473i	$-0.552414\pi$
$787$	21.6672	−	37.5286i	0.772351	−	1.33775i	0.936272	−	0.351277i	$-0.114252\pi$
$788$		0			0
$789$	8.62805	+	8.93915i	0.307167	+	0.318242i
$790$		0			0
$791$	14.3512			0.510270
$792$		0			0
$793$	26.5775			0.943796
$794$		0			0
$795$	2.44715	−	8.52604i	0.0867914	−	0.302388i
$796$		0			0
$797$	−21.1110	+	36.5654i	−0.747791	+	1.29521i	0.201089	+	0.979573i	$0.435552\pi$
$797$	−21.1110	+	36.5654i	−0.747791	+	1.29521i	−0.948880	+	0.315639i	$0.897781\pi$
$798$		0			0
$799$	−13.3054	+	7.68189i	−0.470712	+	0.271766i
$800$		0			0
$801$	3.74845	+	7.05847i	0.132445	+	0.249399i
$802$		0			0
$803$	−1.32370	+	0.764237i	−0.0467122	+	0.0269693i
$804$		0			0
$805$	−2.70757	−	1.56322i	−0.0954294	−	0.0550962i
$806$		0			0
$807$	21.8998	−	5.45431i	0.770908	−	0.192001i
$808$		0			0
$809$		−	31.6048i		−	1.11117i	−0.831461	−	0.555583i	$-0.812495\pi$
$809$		−	31.6048i		−	1.11117i	0.831461	−	0.555583i	$-0.187505\pi$
$810$		0			0
$811$	−19.9542			−0.700688			−0.350344	−	0.936621i	$-0.613935\pi$
$811$	−19.9542			−0.700688			−0.350344	+	0.936621i	$0.613935\pi$
$812$		0			0
$813$	−3.02199	−	12.1337i	−0.105986	−	0.425547i
$814$		0			0
$815$	3.07008	−	5.31753i	0.107540	−	0.186265i
$816$		0			0
$817$	6.07445	+	10.5213i	0.212518	+	0.368092i
$818$		0			0
$819$	−7.31603	+	3.88523i	−0.255643	+	0.135761i
$820$		0			0
$821$	15.1074	+	26.1669i	0.527253	+	0.913230i	0.999496	+	0.0317607i	$0.0101114\pi$
$821$	15.1074	+	26.1669i	0.527253	+	0.913230i	−0.472242	+	0.881469i	$0.656555\pi$
$822$		0			0
$823$	−26.8460	−	15.4996i	−0.935794	−	0.540281i	−0.0471548	−	0.998888i	$-0.515015\pi$
$823$	−26.8460	−	15.4996i	−0.935794	−	0.540281i	−0.888639	+	0.458607i	$0.848349\pi$
$824$		0			0
$825$	15.1143	+	4.33812i	0.526213	+	0.151034i
$826$		0			0
$827$			25.1412i			0.874245i	0.899402	+	0.437122i	$0.144002\pi$
$827$			25.1412i			0.874245i	−0.899402	+	0.437122i	$0.855998\pi$
$828$		0			0
$829$			32.9471i			1.14430i	0.820149	+	0.572149i	$0.193890\pi$
$829$			32.9471i			1.14430i	−0.820149	+	0.572149i	$0.806110\pi$
$830$		0			0
$831$	−37.6827	+	36.3712i	−1.30720	+	1.26170i
$832$		0			0
$833$	7.84491	+	4.52926i	0.271810	+	0.156930i
$834$		0			0
$835$	0.842487	+	1.45923i	0.0291555	+	0.0504987i
$836$		0			0
$837$	−41.9562	+	8.88462i	−1.45022	+	0.307098i
$838$		0			0
$839$	1.28863	+	2.23197i	0.0444883	+	0.0770560i	0.887412	−	0.460977i	$-0.152501\pi$
$839$	1.28863	+	2.23197i	0.0444883	+	0.0770560i	−0.842924	+	0.538033i	$0.819168\pi$
$840$		0			0
$841$	−24.4151	+	42.2882i	−0.841900	+	1.45821i
$842$		0			0
$843$	32.9115	−	31.7661i	1.13353	−	1.09408i
$844$		0			0
$845$	1.79565			0.0617722
$846$		0			0
$847$		−	6.17937i		−	0.212326i
$848$		0			0
$849$	13.8345	−	48.2003i	0.474798	−	1.65423i
$850$		0			0
$851$	21.2975	+	12.2961i	0.730068	+	0.421505i
$852$		0			0
$853$	2.50789	−	1.44793i	0.0858685	−	0.0495762i	−0.456451	−	0.889749i	$-0.650880\pi$
$853$	2.50789	−	1.44793i	0.0858685	−	0.0495762i	0.542319	+	0.840172i	$0.317546\pi$
$854$		0			0
$855$	−0.186751	+	5.27102i	−0.00638676	+	0.180265i
$856$		0			0
$857$	16.9352	−	9.77752i	0.578494	−	0.333994i	−0.182041	−	0.983291i	$-0.558270\pi$
$857$	16.9352	−	9.77752i	0.578494	−	0.333994i	0.760535	+	0.649297i	$0.224937\pi$
$858$		0			0
$859$	5.09073	−	8.81740i	0.173693	−	0.300846i	−0.766015	−	0.642823i	$-0.777763\pi$
$859$	5.09073	−	8.81740i	0.173693	−	0.300846i	0.939708	+	0.341977i	$0.111096\pi$
$860$		0			0
$861$	13.1289	−	3.26985i	0.447430	−	0.111436i
$862$		0			0
$863$	−5.38174			−0.183197			−0.0915983	−	0.995796i	$-0.529198\pi$
$863$	−5.38174			−0.183197			−0.0915983	+	0.995796i	$0.529198\pi$
$864$		0			0
$865$	−11.4134			−0.388068
$866$		0			0
$867$	25.0381	−	6.23594i	0.850338	−	0.211784i
$868$		0			0
$869$	−13.7753	+	23.8596i	−0.467296	+	0.809380i
$870$		0			0
$871$	−14.1018	+	8.14170i	−0.477823	+	0.275871i
$872$		0			0
$873$	30.8284	+	19.2855i	1.04338	+	0.652717i
$874$		0			0
$875$	4.51158	−	2.60476i	0.152519	−	0.0880570i
$876$		0			0
$877$	37.0499	+	21.3908i	1.25109	+	0.722315i	0.971325	−	0.237754i	$-0.0764112\pi$
$877$	37.0499	+	21.3908i	1.25109	+	0.722315i	0.279762	+	0.960069i	$0.409745\pi$
$878$		0			0
$879$	8.65072	−	30.1397i	0.291782	−	1.01659i
$880$		0			0
$881$		−	20.4046i		−	0.687448i	−0.939071	−	0.343724i	$-0.888312\pi$
$881$		−	20.4046i		−	0.687448i	0.939071	−	0.343724i	$-0.111688\pi$
$882$		0			0
$883$	51.0790			1.71895			0.859473	−	0.511181i	$-0.170792\pi$
$883$	51.0790			1.71895			0.859473	+	0.511181i	$0.170792\pi$
$884$		0			0
$885$	7.91568	−	7.64020i	0.266083	−	0.256823i
$886$		0			0
$887$	19.2192	−	33.2886i	0.645318	−	1.11772i	−0.338910	−	0.940819i	$-0.610058\pi$
$887$	19.2192	−	33.2886i	0.645318	−	1.11772i	0.984228	−	0.176904i	$-0.0566084\pi$
$888$		0			0
$889$	−0.752966	−	1.30417i	−0.0252537	−	0.0437406i
$890$		0			0
$891$	1.25442	−	17.6806i	0.0420246	−	0.592323i
$892$		0			0
$893$	−14.9084	−	25.8220i	−0.498889	−	0.864101i
$894$		0			0
$895$	−8.19426	−	4.73096i	−0.273904	−	0.158138i
$896$		0			0
$897$	22.8706	−	22.0746i	0.763625	−	0.737050i
$898$		0			0
$899$		−	72.8138i		−	2.42848i
$900$		0			0
$901$			11.8867i			0.396002i
$902$		0			0
$903$	−6.23663	−	1.79004i	−0.207542	−	0.0595688i
$904$		0			0
$905$	−9.30822	−	5.37411i	−0.309416	−	0.178641i
$906$		0			0
$907$	28.8075	+	49.8961i	0.956538	+	1.65677i	0.730809	+	0.682582i	$0.239143\pi$
$907$	28.8075	+	49.8961i	0.956538	+	1.65677i	0.225729	+	0.974190i	$0.427524\pi$
$908$		0			0
$909$	−7.52433	−	4.70704i	−0.249566	−	0.156123i
$910$		0			0
$911$	−17.2250	−	29.8346i	−0.570690	−	0.988464i	−0.996495	−	0.0836493i	$-0.973342\pi$
$911$	−17.2250	−	29.8346i	−0.570690	−	0.988464i	0.425805	−	0.904815i	$-0.359991\pi$
$912$		0			0
$913$	−1.76423	+	3.05574i	−0.0583875	+	0.101130i
$914$		0			0
$915$	2.18421	+	8.76988i	0.0722077	+	0.289923i
$916$		0			0
$917$	14.8402			0.490066
$918$		0			0
$919$			41.9650i			1.38430i	0.721755	+	0.692149i	$0.243336\pi$
$919$			41.9650i			1.38430i	−0.721755	+	0.692149i	$0.756664\pi$
$920$		0			0
$921$	39.6861	−	9.88415i	1.30770	−	0.325694i
$922$		0			0
$923$	29.2895	+	16.9103i	0.964076	+	0.556610i
$924$		0			0
$925$	−17.0231	+	9.82831i	−0.559717	+	0.323153i
$926$		0			0
$927$	4.18775	+	0.148371i	0.137544	+	0.00487315i
$928$		0			0
$929$	−16.6300	+	9.60134i	−0.545613	+	0.315010i	−0.747351	−	0.664430i	$-0.768674\pi$
$929$	−16.6300	+	9.60134i	−0.545613	+	0.315010i	0.201738	+	0.979440i	$0.435341\pi$
$930$		0			0
$931$	−8.79000	+	15.2247i	−0.288081	+	0.498970i
$932$		0			0
$933$	−4.49323	+	15.6547i	−0.147102	+	0.512513i
$934$		0			0
$935$	1.78414			0.0583477
$936$		0			0
$937$	56.0541			1.83121			0.915604	−	0.402081i	$-0.131713\pi$
$937$	56.0541			1.83121			0.915604	+	0.402081i	$0.131713\pi$
$938$		0			0
$939$	−9.25045	−	9.58400i	−0.301877	−	0.312762i
$940$		0			0
$941$	−5.98561	+	10.3674i	−0.195125	+	0.337967i	−0.946942	−	0.321406i	$-0.895845\pi$
$941$	−5.98561	+	10.3674i	−0.195125	+	0.337967i	0.751816	+	0.659373i	$0.229178\pi$
$942$		0			0
$943$	−44.9613	+	25.9584i	−1.46414	+	0.845322i
$944$		0			0
$945$	−1.88327	−	2.09480i	−0.0612628	−	0.0681437i
$946$		0			0
$947$	−28.4040	+	16.3991i	−0.923007	+	0.532898i	−0.884593	−	0.466364i	$-0.845564\pi$
$947$	−28.4040	+	16.3991i	−0.923007	+	0.532898i	−0.0384138	+	0.999262i	$0.512230\pi$
$948$		0			0
$949$	−2.13874	−	1.23480i	−0.0694263	−	0.0400833i
$950$		0			0
$951$	39.6098	+	41.0380i	1.28444	+	1.33075i
$952$		0			0
$953$			5.01998i			0.162613i	0.996689	+	0.0813065i	$0.0259093\pi$
$953$			5.01998i			0.162613i	−0.996689	+	0.0813065i	$0.974091\pi$
$954$		0			0
$955$	7.71771			0.249739
$956$		0			0
$957$	28.9261	+	8.30239i	0.935048	+	0.268378i
$958$		0			0
$959$	1.09861	−	1.90285i	0.0354761	−	0.0614463i
$960$		0			0
$961$	18.5603	+	32.1474i	0.598720	+	1.03701i
$962$		0			0
$963$	11.7846	+	22.1907i	0.379752	+	0.715086i
$964$		0			0
$965$	0.741197	+	1.28379i	0.0238600	+	0.0413267i
$966$		0			0
$967$	38.2768	+	22.0991i	1.23090	+	0.710660i	0.967217	−	0.253950i	$-0.0817298\pi$
$967$	38.2768	+	22.0991i	1.23090	+	0.710660i	0.263682	+	0.964610i	$0.415063\pi$
$968$		0			0
$969$	−1.70813	−	6.85837i	−0.0548731	−	0.220322i
$970$		0			0
$971$		−	51.9018i		−	1.66561i	−0.553567	−	0.832805i	$-0.686734\pi$
$971$		−	51.9018i		−	1.66561i	0.553567	−	0.832805i	$-0.313266\pi$
$972$		0			0
$973$		−	7.39062i		−	0.236932i
$974$		0			0
$975$	6.14015	+	24.6535i	0.196642	+	0.789544i
$976$		0			0
$977$	11.6452	+	6.72338i	0.372564	+	0.215100i	0.674578	−	0.738203i	$-0.264326\pi$
$977$	11.6452	+	6.72338i	0.372564	+	0.215100i	−0.302014	+	0.953304i	$0.597659\pi$
$978$		0			0
$979$	2.62333	+	4.54373i	0.0838419	+	0.145218i
$980$		0			0
$981$	−23.0231	−	43.3534i	−0.735072	−	1.38417i
$982$		0			0
$983$	13.0997	+	22.6894i	0.417816	+	0.723678i	0.995719	−	0.0924270i	$-0.0294625\pi$
$983$	13.0997	+	22.6894i	0.417816	+	0.723678i	−0.577904	+	0.816105i	$0.696129\pi$
$984$		0			0
$985$	5.56319	−	9.63572i	0.177258	−	0.307020i
$986$		0			0
$987$	15.3064	+	4.39325i	0.487208	+	0.139839i
$988$		0			0
$989$	24.8974			0.791690
$990$		0			0
$991$		−	40.2335i		−	1.27806i	−0.769182	−	0.639030i	$-0.779336\pi$
$991$		−	40.2335i		−	1.27806i	0.769182	−	0.639030i	$-0.220664\pi$
$992$		0			0
$993$	−4.20661	−	4.35829i	−0.133493	−	0.138306i
$994$		0			0
$995$	−1.02899	−	0.594087i	−0.0326212	−	0.0188338i
$996$		0			0
$997$	43.5866	−	25.1647i	1.38040	−	0.796975i	0.388194	−	0.921578i	$-0.373099\pi$
$997$	43.5866	−	25.1647i	1.38040	−	0.796975i	0.992207	+	0.124603i	$0.0397658\pi$
$998$		0			0
$999$	14.8136	+	16.4774i	0.468682	+	0.521323i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.p.c.95.8	yes	16
3.2	odd	2		1728.2.p.a.287.5		16
4.3	odd	2	inner	576.2.p.c.95.1	yes	16
8.3	odd	2		576.2.p.a.95.8	yes	16
8.5	even	2		576.2.p.a.95.1	✓	16
9.2	odd	6		576.2.p.a.479.8	yes	16
9.4	even	3		5184.2.f.a.2591.9		16
9.5	odd	6		5184.2.f.f.2591.5		16
9.7	even	3		1728.2.p.c.1439.4		16
12.11	even	2		1728.2.p.a.287.6		16
24.5	odd	2		1728.2.p.c.287.3		16
24.11	even	2		1728.2.p.c.287.4		16
36.7	odd	6		1728.2.p.c.1439.3		16
36.11	even	6		576.2.p.a.479.1	yes	16
36.23	even	6		5184.2.f.f.2591.7		16
36.31	odd	6		5184.2.f.a.2591.11		16
72.5	odd	6		5184.2.f.a.2591.10		16
72.11	even	6	inner	576.2.p.c.479.8	yes	16
72.13	even	6		5184.2.f.f.2591.6		16
72.29	odd	6	inner	576.2.p.c.479.1	yes	16
72.43	odd	6		1728.2.p.a.1439.5		16
72.59	even	6		5184.2.f.a.2591.12		16
72.61	even	6		1728.2.p.a.1439.6		16
72.67	odd	6		5184.2.f.f.2591.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
576.2.p.a.95.1	✓	16	8.5	even	2
576.2.p.a.95.8	yes	16	8.3	odd	2
576.2.p.a.479.1	yes	16	36.11	even	6
576.2.p.a.479.8	yes	16	9.2	odd	6
576.2.p.c.95.1	yes	16	4.3	odd	2	inner
576.2.p.c.95.8	yes	16	1.1	even	1	trivial
576.2.p.c.479.1	yes	16	72.29	odd	6	inner
576.2.p.c.479.8	yes	16	72.11	even	6	inner
1728.2.p.a.287.5		16	3.2	odd	2
1728.2.p.a.287.6		16	12.11	even	2
1728.2.p.a.1439.5		16	72.43	odd	6
1728.2.p.a.1439.6		16	72.61	even	6
1728.2.p.c.287.3		16	24.5	odd	2
1728.2.p.c.287.4		16	24.11	even	2
1728.2.p.c.1439.3		16	36.7	odd	6
1728.2.p.c.1439.4		16	9.7	even	3
5184.2.f.a.2591.9		16	9.4	even	3
5184.2.f.a.2591.10		16	72.5	odd	6
5184.2.f.a.2591.11		16	36.31	odd	6
5184.2.f.a.2591.12		16	72.59	even	6
5184.2.f.f.2591.5		16	9.5	odd	6
5184.2.f.f.2591.6		16	72.13	even	6
5184.2.f.f.2591.7		16	36.23	even	6
5184.2.f.f.2591.8		16	72.67	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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.68071 - 0.418594i) q^{3} +(-0.312371 + 0.541042i) q^{5} +(-0.751481 + 0.433868i) q^{7} +(2.64956 - 1.40707i) q^{9} +O(q^{10})\)	\(q+(1.68071 - 0.418594i) q^{3} +(-0.312371 + 0.541042i) q^{5} +(-0.751481 + 0.433868i) q^{7} +(2.64956 - 1.40707i) q^{9} +(1.70560 - 0.984726i) q^{11} +(2.75578 + 1.59105i) q^{13} +(-0.298527 + 1.04009i) q^{15} -1.45005i q^{17} +2.81414 q^{19} +(-1.08141 + 1.04377i) q^{21} +(2.88357 - 4.99450i) q^{23} +(2.30485 + 3.99212i) q^{25} +(3.86414 - 3.47396i) q^{27} +(4.41107 + 7.64020i) q^{29} +(-7.14776 - 4.12676i) q^{31} +(2.45441 - 2.36899i) q^{33} -0.542111i q^{35} +4.26419i q^{37} +(5.29767 + 1.52054i) q^{39} +(-7.79610 - 4.50108i) q^{41} +(2.15855 + 3.73872i) q^{43} +(-0.0663618 + 1.87305i) q^{45} +(-5.29767 - 9.17583i) q^{47} +(-3.12352 + 5.41009i) q^{49} +(-0.606982 - 2.43711i) q^{51} -8.19740 q^{53} +1.23040i q^{55} +(4.72974 - 1.17798i) q^{57} +(-8.80475 - 5.08343i) q^{59} +(7.23321 - 4.17610i) q^{61} +(-1.38061 + 2.20694i) q^{63} +(-1.72165 + 0.993996i) q^{65} +(-2.55859 + 4.43161i) q^{67} +(2.75578 - 9.60134i) q^{69} +10.6284 q^{71} -0.776091 q^{73} +(5.54485 + 5.74478i) q^{75} +(-0.854482 + 1.48001i) q^{77} +(-12.1148 + 6.99450i) q^{79} +(5.04032 - 7.45622i) q^{81} +(-1.55157 + 0.895797i) q^{83} +(0.784539 + 0.452954i) q^{85} +(10.6119 + 10.9945i) q^{87} +2.66402i q^{89} -2.76122 q^{91} +(-13.7407 - 3.94387i) q^{93} +(-0.879054 + 1.52257i) q^{95} +(6.06063 + 10.4973i) q^{97} +(3.13350 - 5.00898i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{5} + 6 q^{9}+O(q^{10}) \) 16 * q + 6 * q^5 + 6 * q^9	\( 16 q + 6 q^{5} + 6 q^{9} + 6 q^{13} - 30 q^{21} - 14 q^{25} + 18 q^{29} - 48 q^{33} + 66 q^{45} + 6 q^{49} - 48 q^{53} + 18 q^{57} - 42 q^{61} + 54 q^{65} + 6 q^{69} + 28 q^{73} + 66 q^{77} - 6 q^{81} - 36 q^{85} - 102 q^{93} + 8 q^{97}+O(q^{100}) \) 16 * q + 6 * q^5 + 6 * q^9 + 6 * q^13 - 30 * q^21 - 14 * q^25 + 18 * q^29 - 48 * q^33 + 66 * q^45 + 6 * q^49 - 48 * q^53 + 18 * q^57 - 42 * q^61 + 54 * q^65 + 6 * q^69 + 28 * q^73 + 66 * q^77 - 6 * q^81 - 36 * q^85 - 102 * q^93 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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