LMFDB - Embedded newform 576.2.p.c.479.4

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			479.4
Root			$-1.16543 + 2.01859i$ of defining polynomial
Character	$\chi$	$=$	576.479
Dual form			576.2.p.c.95.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.231865 + 1.71646i) q^{3} +(0.959555 + 1.66200i) q^{5} +(2.63027 + 1.51859i) q^{7} +(-2.89248 - 0.795973i) q^{9} +O(q^{10})$	\(q+(-0.231865 + 1.71646i) q^{3} +(0.959555 + 1.66200i) q^{5} +(2.63027 + 1.51859i) q^{7} +(-2.89248 - 0.795973i) q^{9} +(3.87122 + 2.23505i) q^{11} +(-3.64938 + 2.10697i) q^{13} +(-3.07524 + 1.26168i) q^{15} -5.94600i q^{17} +1.59195 q^{19} +(-3.21646 + 4.16265i) q^{21} +(1.13870 + 1.97229i) q^{23} +(0.658507 - 1.14057i) q^{25} +(2.03692 - 4.78027i) q^{27} +(1.90160 - 3.29367i) q^{29} +(-8.67664 + 5.00946i) q^{31} +(-4.73397 + 6.12656i) q^{33} +5.82867i q^{35} +7.53794i q^{37} +(-2.77037 - 6.75256i) q^{39} +(-4.08347 + 2.35759i) q^{41} +(-1.83430 + 3.17709i) q^{43} +(-1.45259 - 5.57107i) q^{45} +(2.77037 - 4.79843i) q^{47} +(1.11221 + 1.92640i) q^{49} +(10.2061 + 1.37867i) q^{51} -5.72231 q^{53} +8.57861i q^{55} +(-0.369116 + 2.73251i) q^{57} +(1.08445 - 0.626109i) q^{59} +(-0.295196 - 0.170432i) q^{61} +(-6.39924 - 6.48610i) q^{63} +(-7.00357 - 4.04351i) q^{65} +(-3.66673 - 6.35096i) q^{67} +(-3.64938 + 1.49723i) q^{69} +15.9658 q^{71} +16.3731 q^{73} +(1.80506 + 1.39476i) q^{75} +(6.78823 + 11.7576i) q^{77} +(0.0479956 + 0.0277103i) q^{79} +(7.73285 + 4.60467i) q^{81} +(-8.37177 - 4.83345i) q^{83} +(9.88224 - 5.70551i) q^{85} +(5.21254 + 4.02771i) q^{87} -14.4661i q^{89} -12.7985 q^{91} +(-6.58674 - 16.0546i) q^{93} +(1.52756 + 2.64581i) q^{95} +(-1.99088 + 3.44830i) q^{97} +(-9.41837 - 9.54621i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

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

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
$3$	−0.231865	+	1.71646i	−0.133867	+	0.990999i
$3$	−0.231865	+	1.71646i	−0.133867	+	0.990999i
$4$		0			0
$5$	0.959555	+	1.66200i	0.429126	+	0.743268i	0.996796	−	0.0799881i	$-0.0254882\pi$
$5$	0.959555	+	1.66200i	0.429126	+	0.743268i	−0.567670	+	0.823256i	$0.692155\pi$
$6$		0			0
$7$	2.63027	+	1.51859i	0.994148	+	0.573972i	0.906512	−	0.422181i	$-0.138735\pi$
$7$	2.63027	+	1.51859i	0.994148	+	0.573972i	0.0876366	+	0.996153i	$0.472069\pi$
$8$		0			0
$9$	−2.89248	−	0.795973i	−0.964159	−	0.265324i
$10$		0			0
$11$	3.87122	+	2.23505i	1.16722	+	0.673892i	0.953023	−	0.302899i	$-0.0979545\pi$
$11$	3.87122	+	2.23505i	1.16722	+	0.673892i	0.214193	+	0.976791i	$0.431288\pi$
$12$		0			0
$13$	−3.64938	+	2.10697i	−1.01216	+	0.584369i	−0.911822	−	0.410585i	$-0.865325\pi$
$13$	−3.64938	+	2.10697i	−1.01216	+	0.584369i	−0.100334	+	0.994954i	$0.531991\pi$
$14$		0			0
$15$	−3.07524	+	1.26168i	−0.794024	+	0.325765i
$16$		0			0
$17$		−	5.94600i		−	1.44212i	−0.692875	−	0.721058i	$-0.743656\pi$
$17$		−	5.94600i		−	1.44212i	0.692875	−	0.721058i	$-0.256344\pi$
$18$		0			0
$19$	1.59195			0.365218			0.182609	−	0.983186i	$-0.441546\pi$
$19$	1.59195			0.365218			0.182609	+	0.983186i	$0.441546\pi$
$20$		0			0
$21$	−3.21646	+	4.16265i	−0.701889	+	0.908364i
$22$		0			0
$23$	1.13870	+	1.97229i	0.237436	+	0.411251i	0.959978	−	0.280076i	$-0.0903597\pi$
$23$	1.13870	+	1.97229i	0.237436	+	0.411251i	−0.722542	+	0.691327i	$0.757026\pi$
$24$		0			0
$25$	0.658507	−	1.14057i	0.131701	−	0.228114i
$26$		0			0
$27$	2.03692	−	4.78027i	0.392005	−	0.919963i
$28$		0			0
$29$	1.90160	−	3.29367i	0.353118	−	0.611619i	−0.633676	−	0.773599i	$-0.718455\pi$
$29$	1.90160	−	3.29367i	0.353118	−	0.611619i	0.986794	+	0.161980i	$0.0517879\pi$
$30$		0			0
$31$	−8.67664	+	5.00946i	−1.55837	+	0.899726i	−0.560958	+	0.827844i	$0.689567\pi$
$31$	−8.67664	+	5.00946i	−1.55837	+	0.899726i	−0.997413	+	0.0718819i	$0.977100\pi$
$32$		0			0
$33$	−4.73397	+	6.12656i	−0.824078	+	1.06650i
$34$		0			0
$35$			5.82867i			0.985225i
$36$		0			0
$37$			7.53794i			1.23923i	0.784906	+	0.619615i	$0.212711\pi$
$37$			7.53794i			1.23923i	−0.784906	+	0.619615i	$0.787289\pi$
$38$		0			0
$39$	−2.77037	−	6.75256i	−0.443615	−	1.08127i
$40$		0			0
$41$	−4.08347	+	2.35759i	−0.637731	+	0.368194i	−0.783740	−	0.621089i	$-0.786690\pi$
$41$	−4.08347	+	2.35759i	−0.637731	+	0.368194i	0.146009	+	0.989283i	$0.453357\pi$
$42$		0			0
$43$	−1.83430	+	3.17709i	−0.279727	+	0.484502i	−0.971317	−	0.237789i	$-0.923577\pi$
$43$	−1.83430	+	3.17709i	−0.279727	+	0.484502i	0.691589	+	0.722291i	$0.256911\pi$
$44$		0			0
$45$	−1.45259	−	5.57107i	−0.216539	−	0.830487i
$46$		0			0
$47$	2.77037	−	4.79843i	0.404101	−	0.699923i	−0.590116	−	0.807319i	$-0.700918\pi$
$47$	2.77037	−	4.79843i	0.404101	−	0.699923i	0.994216	+	0.107396i	$0.0342513\pi$
$48$		0			0
$49$	1.11221	+	1.92640i	0.158887	+	0.275201i
$50$		0			0
$51$	10.2061	+	1.37867i	1.42914	+	0.193052i
$52$		0			0
$53$	−5.72231			−0.786020			−0.393010	−	0.919534i	$-0.628566\pi$
$53$	−5.72231			−0.786020			−0.393010	+	0.919534i	$0.628566\pi$
$54$		0			0
$55$			8.57861i			1.15674i
$56$		0			0
$57$	−0.369116	+	2.73251i	−0.0488906	+	0.361930i
$58$		0			0
$59$	1.08445	−	0.626109i	0.141184	−	0.0815124i	−0.427744	−	0.903900i	$-0.640692\pi$
$59$	1.08445	−	0.626109i	0.141184	−	0.0815124i	0.568928	+	0.822387i	$0.307358\pi$
$60$		0			0
$61$	−0.295196	−	0.170432i	−0.0377960	−	0.0218215i	0.480983	−	0.876730i	$-0.340280\pi$
$61$	−0.295196	−	0.170432i	−0.0377960	−	0.0218215i	−0.518779	+	0.854908i	$0.673613\pi$
$62$		0			0
$63$	−6.39924	−	6.48610i	−0.806228	−	0.817172i
$64$		0			0
$65$	−7.00357	−	4.04351i	−0.868686	−	0.501536i
$66$		0			0
$67$	−3.66673	−	6.35096i	−0.447962	−	0.775893i	0.550291	−	0.834973i	$-0.314517\pi$
$67$	−3.66673	−	6.35096i	−0.447962	−	0.775893i	−0.998253	+	0.0590800i	$0.981183\pi$
$68$		0			0
$69$	−3.64938	+	1.49723i	−0.439334	+	0.180246i
$70$		0			0
$71$	15.9658			1.89480			0.947398	−	0.320058i	$-0.103703\pi$
$71$	15.9658			1.89480			0.947398	+	0.320058i	$0.103703\pi$
$72$		0			0
$73$	16.3731			1.91633			0.958164	−	0.286220i	$-0.0923988\pi$
$73$	16.3731			1.91633			0.958164	+	0.286220i	$0.0923988\pi$
$74$		0			0
$75$	1.80506	+	1.39476i	0.208430	+	0.161053i
$76$		0			0
$77$	6.78823	+	11.7576i	0.773590	+	1.33990i
$78$		0			0
$79$	0.0479956	+	0.0277103i	0.00539992	+	0.00311765i	0.502698	−	0.864462i	$-0.332341\pi$
$79$	0.0479956	+	0.0277103i	0.00539992	+	0.00311765i	−0.497298	+	0.867580i	$0.665674\pi$
$80$		0			0
$81$	7.73285	+	4.60467i	0.859206	+	0.511630i
$82$		0			0
$83$	−8.37177	−	4.83345i	−0.918922	−	0.530540i	−0.0356308	−	0.999365i	$-0.511344\pi$
$83$	−8.37177	−	4.83345i	−0.918922	−	0.530540i	−0.883291	+	0.468825i	$0.844677\pi$
$84$		0			0
$85$	9.88224	−	5.70551i	1.07188	−	0.618850i
$86$		0			0
$87$	5.21254	+	4.02771i	0.558843	+	0.431816i
$88$		0			0
$89$		−	14.4661i		−	1.53341i	−0.642001	−	0.766704i	$-0.721895\pi$
$89$		−	14.4661i		−	1.53341i	0.642001	−	0.766704i	$-0.278105\pi$
$90$		0			0
$91$	−12.7985			−1.34165
$92$		0			0
$93$	−6.58674	−	16.0546i	−0.683013	−	1.66479i
$94$		0			0
$95$	1.52756	+	2.64581i	0.156724	+	0.271455i
$96$		0			0
$97$	−1.99088	+	3.44830i	−0.202143	+	0.350122i	−0.949219	−	0.314617i	$-0.898124\pi$
$97$	−1.99088	+	3.44830i	−0.202143	+	0.350122i	0.747076	+	0.664739i	$0.231457\pi$
$98$		0			0
$99$	−9.41837	−	9.54621i	−0.946582	−	0.959430i
$100$		0			0
$101$	8.70734	−	15.0816i	0.866412	−	1.50067i	0.000774625	−	1.00000i	$-0.499753\pi$
$101$	8.70734	−	15.0816i	0.866412	−	1.50067i	0.865638	−	0.500671i	$-0.166913\pi$
$102$		0			0
$103$	4.42671	−	2.55576i	0.436176	−	0.251826i	−0.265798	−	0.964029i	$-0.585635\pi$
$103$	4.42671	−	2.55576i	0.436176	−	0.251826i	0.701974	+	0.712202i	$0.252302\pi$
$104$		0			0
$105$	−10.0047	−	1.35146i	−0.976358	−	0.131889i
$106$		0			0
$107$			10.9191i			1.05559i	0.849372	+	0.527795i	$0.176981\pi$
$107$			10.9191i			1.05559i	−0.849372	+	0.527795i	$0.823019\pi$
$108$		0			0
$109$			3.26334i			0.312572i	0.987712	+	0.156286i	$0.0499521\pi$
$109$			3.26334i			0.312572i	−0.987712	+	0.156286i	$0.950048\pi$
$110$		0			0
$111$	−12.9386	−	1.74778i	−1.22808	−	0.165892i
$112$		0			0
$113$	9.93476	−	5.73584i	0.934584	−	0.539582i	0.0463256	−	0.998926i	$-0.485249\pi$
$113$	9.93476	−	5.73584i	0.934584	−	0.539582i	0.888258	+	0.459344i	$0.151915\pi$
$114$		0			0
$115$	−2.18530	+	3.78504i	−0.203780	+	0.352957i
$116$		0			0
$117$	12.2329	−	3.18956i	1.13093	−	0.294875i
$118$		0			0
$119$	9.02951	−	15.6396i	0.827734	−	1.43368i
$120$		0			0
$121$	4.49088	+	7.77843i	0.408261	+	0.707130i
$122$		0			0
$123$	−3.09990	−	7.55576i	−0.279509	−	0.681280i
$124$		0			0
$125$	12.1230			1.08432
$126$		0			0
$127$			6.07435i			0.539011i	0.962999	+	0.269506i	$0.0868603\pi$
$127$			6.07435i			0.539011i	−0.962999	+	0.269506i	$0.913140\pi$
$128$		0			0
$129$	−5.02805	−	3.88515i	−0.442695	−	0.342069i
$130$		0			0
$131$	11.6351	−	6.71754i	1.01656	−	0.586914i	0.103458	−	0.994634i	$-0.467009\pi$
$131$	11.6351	−	6.71754i	1.01656	−	0.586914i	0.913107	+	0.407720i	$0.133676\pi$
$132$		0			0
$133$	4.18725	+	2.41751i	0.363080	+	0.209625i
$134$		0			0
$135$	9.89934	−	1.20157i	0.851999	−	0.103415i
$136$		0			0
$137$	8.02805	+	4.63500i	0.685883	+	0.395994i	0.802068	−	0.597233i	$-0.203733\pi$
$137$	8.02805	+	4.63500i	0.685883	+	0.395994i	−0.116185	+	0.993228i	$0.537067\pi$
$138$		0			0
$139$	0.944348	+	1.63566i	0.0800986	+	0.138735i	0.903292	−	0.429026i	$-0.141143\pi$
$139$	0.944348	+	1.63566i	0.0800986	+	0.138735i	−0.823194	+	0.567761i	$0.807810\pi$
$140$		0			0
$141$	7.59396	+	5.86782i	0.639527	+	0.494160i
$142$		0			0
$143$	−18.8367			−1.57521
$144$		0			0
$145$	7.29877			0.606130
$146$		0			0
$147$	−3.56448	+	1.46240i	−0.293993	+	0.120617i
$148$		0			0
$149$	−7.03859	−	12.1912i	−0.576624	−	0.998742i	−0.995863	−	0.0908659i	$-0.971037\pi$
$149$	−7.03859	−	12.1912i	−0.576624	−	0.998742i	0.419239	−	0.907876i	$-0.362297\pi$
$150$		0			0
$151$	3.96519	+	2.28930i	0.322683	+	0.186301i	0.652588	−	0.757713i	$-0.273683\pi$
$151$	3.96519	+	2.28930i	0.322683	+	0.186301i	−0.329905	+	0.944014i	$0.607017\pi$
$152$		0			0
$153$	−4.73285	+	17.1987i	−0.382629	+	1.39043i
$154$		0			0
$155$	−16.6514	−	9.61371i	−1.33748	−	0.772192i
$156$		0			0
$157$	−19.5316	+	11.2766i	−1.55879	+	0.899970i	−0.561420	+	0.827531i	$0.689745\pi$
$157$	−19.5316	+	11.2766i	−1.55879	+	0.899970i	−0.997373	+	0.0724386i	$0.976922\pi$
$158$		0			0
$159$	1.32680	−	9.82213i	0.105222	−	0.778945i
$160$		0			0
$161$			6.91687i			0.545126i
$162$		0			0
$163$	−4.96379			−0.388794			−0.194397	−	0.980923i	$-0.562275\pi$
$163$	−4.96379			−0.388794			−0.194397	+	0.980923i	$0.562275\pi$
$164$		0			0
$165$	−14.7248	−	1.98908i	−1.14633	−	0.154849i
$166$		0			0
$167$	3.52022	+	6.09719i	0.272403	+	0.471815i	0.969477	−	0.245184i	$-0.0788484\pi$
$167$	3.52022	+	6.09719i	0.272403	+	0.471815i	−0.697074	+	0.716999i	$0.745515\pi$
$168$		0			0
$169$	2.37867	−	4.11997i	0.182974	−	0.316921i
$170$		0			0
$171$	−4.60467	−	1.26715i	−0.352128	−	0.0969011i
$172$		0			0
$173$	2.84365	−	4.92534i	0.216198	−	0.374467i	−0.737444	−	0.675408i	$-0.763968\pi$
$173$	2.84365	−	4.92534i	0.216198	−	0.374467i	0.953643	+	0.300941i	$0.0973008\pi$
$174$		0			0
$175$	3.46410	−	2.00000i	0.261861	−	0.151186i
$176$		0			0
$177$	0.823246	+	2.00659i	0.0618789	+	0.150825i
$178$		0			0
$179$			15.2828i			1.14229i	0.820848	+	0.571147i	$0.193501\pi$
$179$			15.2828i			1.14229i	−0.820848	+	0.571147i	$0.806499\pi$
$180$		0			0
$181$		−	20.4324i		−	1.51873i	−0.650665	−	0.759365i	$-0.725510\pi$
$181$		−	20.4324i		−	1.51873i	0.650665	−	0.759365i	$-0.274490\pi$
$182$		0			0
$183$	0.360985	−	0.467176i	0.0266848	−	0.0345346i
$184$		0			0
$185$	−12.5280	+	7.23307i	−0.921081	+	0.531786i
$186$		0			0
$187$	13.2896	−	23.0182i	0.971831	−	1.68326i
$188$		0			0
$189$	12.6169	−	9.48015i	0.917744	−	0.689579i
$190$		0			0
$191$	4.29793	−	7.44424i	0.310988	−	0.538646i	−0.667589	−	0.744530i	$-0.732674\pi$
$191$	4.29793	−	7.44424i	0.310988	−	0.538646i	0.978576	+	0.205884i	$0.0660069\pi$
$192$		0			0
$193$	0.766456	+	1.32754i	0.0551707	+	0.0955584i	0.892292	−	0.451459i	$-0.149096\pi$
$193$	0.766456	+	1.32754i	0.0551707	+	0.0955584i	−0.837121	+	0.547018i	$0.815763\pi$
$194$		0			0
$195$	8.56441	−	11.0838i	0.613310	−	0.793728i
$196$		0			0
$197$	−15.4255			−1.09902			−0.549512	−	0.835486i	$-0.685186\pi$
$197$	−15.4255			−1.09902			−0.549512	+	0.835486i	$0.685186\pi$
$198$		0			0
$199$		−	7.61578i		−	0.539868i	−0.962879	−	0.269934i	$-0.912998\pi$
$199$		−	7.61578i		−	0.539868i	0.962879	−	0.269934i	$-0.0870020\pi$
$200$		0			0
$201$	11.7514	−	4.82123i	0.828877	−	0.340063i
$202$		0			0
$203$	10.0034	−	5.77549i	0.702104	−	0.405360i
$204$		0			0
$205$	−7.83663	−	4.52448i	−0.547334	−	0.316003i
$206$		0			0
$207$	−1.72378	−	6.61118i	−0.119811	−	0.459509i
$208$		0			0
$209$	6.16277	+	3.55808i	0.426288	+	0.246117i
$210$		0			0
$211$	−2.38979	−	4.13923i	−0.164520	−	0.284956i	0.771965	−	0.635665i	$-0.219274\pi$
$211$	−2.38979	−	4.13923i	−0.164520	−	0.284956i	−0.936485	+	0.350709i	$0.885941\pi$
$212$		0			0
$213$	−3.70191	+	27.4047i	−0.253651	+	1.87774i
$214$		0			0
$215$	−7.04043			−0.480154
$216$		0			0
$217$	−30.4292			−2.06567
$218$		0			0
$219$	−3.79635	+	28.1038i	−0.256533	+	1.89908i
$220$		0			0
$221$	12.5280	+	21.6992i	0.842728	+	1.45965i
$222$		0			0
$223$	−11.3549	−	6.55576i	−0.760381	−	0.439006i	0.0690516	−	0.997613i	$-0.478003\pi$
$223$	−11.3549	−	6.55576i	−0.760381	−	0.439006i	−0.829432	+	0.558607i	$0.811336\pi$
$224$		0			0
$225$	−2.81258	+	2.77491i	−0.187505	+	0.184994i
$226$		0			0
$227$	5.02631	+	2.90194i	0.333608	+	0.192609i	0.657442	−	0.753505i	$-0.271639\pi$
$227$	5.02631	+	2.90194i	0.333608	+	0.192609i	−0.323834	+	0.946114i	$0.604972\pi$
$228$		0			0
$229$	16.4201	−	9.48015i	1.08507	−	0.626466i	0.152811	−	0.988255i	$-0.451167\pi$
$229$	16.4201	−	9.48015i	1.08507	−	0.626466i	0.932260	+	0.361790i	$0.117834\pi$
$230$		0			0
$231$	−21.7553	+	8.92557i	−1.43140	+	0.587259i
$232$		0			0
$233$		−	5.46503i		−	0.358026i	−0.983847	−	0.179013i	$-0.942710\pi$
$233$		−	5.46503i		−	0.358026i	0.983847	−	0.179013i	$-0.0572904\pi$
$234$		0			0
$235$	10.6333			0.693640
$236$		0			0
$237$	−0.0586921	+	0.0759575i	−0.00381246	+	0.00493397i
$238$		0			0
$239$	11.0500	+	19.1392i	0.714768	+	1.23801i	0.963049	+	0.269326i	$0.0868009\pi$
$239$	11.0500	+	19.1392i	0.714768	+	1.23801i	−0.248281	+	0.968688i	$0.579866\pi$
$240$		0			0
$241$	9.55610	−	16.5516i	0.615562	−	1.06619i	−0.374723	−	0.927137i	$-0.622262\pi$
$241$	9.55610	−	16.5516i	0.615562	−	1.06619i	0.990286	−	0.139049i	$-0.0444044\pi$
$242$		0			0
$243$	−9.69671	+	12.2055i	−0.622044	+	0.782982i
$244$		0			0
$245$	−2.13445	+	3.69698i	−0.136365	+	0.236192i
$246$		0			0
$247$	−5.80962	+	3.35419i	−0.369657	+	0.213422i
$248$		0			0
$249$	10.2375	−	13.2491i	0.648778	−	0.839629i
$250$		0			0
$251$			3.24267i			0.204675i	0.994750	+	0.102338i	$0.0326322\pi$
$251$			3.24267i			0.204675i	−0.994750	+	0.102338i	$0.967368\pi$
$252$		0			0
$253$			10.1802i			0.640025i
$254$		0			0
$255$	7.50195	+	18.2854i	0.469790	+	1.14508i
$256$		0			0
$257$	−21.2580	+	12.2733i	−1.32604	+	0.765589i	−0.984684	−	0.174346i	$-0.944219\pi$
$257$	−21.2580	+	12.2733i	−1.32604	+	0.765589i	−0.341354	+	0.939935i	$0.610885\pi$
$258$		0			0
$259$	−11.4470	+	19.8268i	−0.711283	+	1.23198i
$260$		0			0
$261$	−8.12201	+	8.01324i	−0.502740	+	0.496007i
$262$		0			0
$263$	−15.1239	+	26.1953i	−0.932578	+	1.61527i	−0.153682	+	0.988120i	$0.549113\pi$
$263$	−15.1239	+	26.1953i	−0.932578	+	1.61527i	−0.778896	+	0.627153i	$0.784220\pi$
$264$		0			0
$265$	−5.49088	−	9.51048i	−0.337302	−	0.584224i
$266$		0			0
$267$	24.8306	+	3.35419i	1.51961	+	0.205273i
$268$		0			0
$269$	−17.4497			−1.06393			−0.531963	−	0.846767i	$-0.678546\pi$
$269$	−17.4497			−1.06393			−0.531963	+	0.846767i	$0.678546\pi$
$270$		0			0
$271$		−	0.634028i		−	0.0385145i	−0.999815	−	0.0192572i	$-0.993870\pi$
$271$		−	0.634028i		−	0.0385145i	0.999815	−	0.0192572i	$-0.00613015\pi$
$272$		0			0
$273$	2.96751	−	21.9681i	0.179602	−	1.32957i
$274$		0			0
$275$	5.09845	−	2.94359i	0.307448	−	0.177505i
$276$		0			0
$277$	19.6367	+	11.3372i	1.17985	+	0.681189i	0.955981	−	0.293430i	$-0.0947966\pi$
$277$	19.6367	+	11.3372i	1.17985	+	0.681189i	0.223873	+	0.974618i	$0.428130\pi$
$278$		0			0
$279$	29.0844	−	7.58338i	1.74124	−	0.454005i
$280$		0			0
$281$	10.1634	+	5.86782i	0.606296	+	0.350045i	0.771514	−	0.636212i	$-0.219500\pi$
$281$	10.1634	+	5.86782i	0.606296	+	0.350045i	−0.165219	+	0.986257i	$0.552833\pi$
$282$		0			0
$283$	7.24946	+	12.5564i	0.430936	+	0.746403i	0.996954	−	0.0779899i	$-0.0248502\pi$
$283$	7.24946	+	12.5564i	0.430936	+	0.746403i	−0.566018	+	0.824393i	$0.691517\pi$
$284$		0			0
$285$	−4.89562	+	2.00853i	−0.289992	+	0.118975i
$286$		0			0
$287$	−14.3208			−0.845332
$288$		0			0
$289$	−18.3549			−1.07970
$290$		0			0
$291$	−5.45726	−	4.21680i	−0.319910	−	0.247193i
$292$		0			0
$293$	−1.06591	−	1.84622i	−0.0622713	−	0.107857i	0.833209	−	0.552958i	$-0.186501\pi$
$293$	−1.06591	−	1.84622i	−0.0622713	−	0.107857i	−0.895480	+	0.445101i	$0.853168\pi$
$294$		0			0
$295$	2.08118	+	1.20157i	0.121171	+	0.0699582i
$296$		0			0
$297$	18.5695	−	13.9528i	1.07751	−	0.809626i
$298$		0			0
$299$	−8.31112	−	4.79843i	−0.480645	−	0.277500i
$300$		0			0
$301$	−9.64938	+	5.57107i	−0.556181	+	0.321111i
$302$		0			0
$303$	23.8680	+	18.4427i	1.37118	+	1.05950i
$304$		0			0
$305$		−	0.654154i		−	0.0374568i
$306$		0			0
$307$	26.4666			1.51053			0.755265	−	0.655419i	$-0.227508\pi$
$307$	26.4666			1.51053			0.755265	+	0.655419i	$0.227508\pi$
$308$		0			0
$309$	3.36047	+	8.19086i	0.191170	+	0.465962i
$310$		0			0
$311$	−9.70670	−	16.8125i	−0.550416	−	0.953349i	−0.998244	−	0.0592293i	$-0.981136\pi$
$311$	−9.70670	−	16.8125i	−0.550416	−	0.953349i	0.447828	−	0.894120i	$-0.352198\pi$
$312$		0			0
$313$	−4.89136	+	8.47208i	−0.276476	+	0.478871i	−0.970506	−	0.241075i	$-0.922500\pi$
$313$	−4.89136	+	8.47208i	−0.276476	+	0.478871i	0.694030	+	0.719946i	$0.255833\pi$
$314$		0			0
$315$	4.63947	−	16.8593i	0.261404	−	0.949914i
$316$		0			0
$317$	−5.22584	+	9.05141i	−0.293512	+	0.508378i	−0.974638	−	0.223789i	$-0.928157\pi$
$317$	−5.22584	+	9.05141i	−0.293512	+	0.508378i	0.681125	+	0.732167i	$0.261491\pi$
$318$		0			0
$319$	14.7230	−	8.50034i	0.824331	−	0.475928i
$320$		0			0
$321$	−18.7422	−	2.53176i	−1.04609	−	0.141309i
$322$		0			0
$323$		−	9.46571i		−	0.526686i
$324$		0			0
$325$			5.54983i			0.307849i
$326$		0			0
$327$	−5.60140	−	0.756654i	−0.309758	−	0.0418430i
$328$		0			0
$329$	14.5737	−	8.41410i	0.803472	−	0.463885i
$330$		0			0
$331$	−9.02124	+	15.6252i	−0.495852	+	0.858841i	−0.999989	−	0.00478295i	$-0.998478\pi$
$331$	−9.02124	+	15.6252i	−0.495852	+	0.858841i	0.504136	+	0.863624i	$0.331811\pi$
$332$		0			0
$333$	6.00000	−	21.8033i	0.328798	−	1.19482i
$334$		0			0
$335$	7.03685	−	12.1882i	0.384464	−	0.665912i
$336$		0			0
$337$	−0.444579	−	0.770034i	−0.0242178	−	0.0419464i	0.853663	−	0.520827i	$-0.174376\pi$
$337$	−0.444579	−	0.770034i	−0.0242178	−	0.0419464i	−0.877880	+	0.478880i	$0.841043\pi$
$338$		0			0
$339$	7.54182	+	18.3826i	0.409616	+	0.998404i
$340$		0			0
$341$	−44.7856			−2.42527
$342$		0			0
$343$		−	14.5043i		−	0.783157i
$344$		0			0
$345$	−5.99019	−	4.62859i	−0.322501	−	0.249195i
$346$		0			0
$347$	6.28499	−	3.62864i	0.337396	−	0.194796i	−0.321724	−	0.946834i	$-0.604262\pi$
$347$	6.28499	−	3.62864i	0.337396	−	0.194796i	0.659120	+	0.752038i	$0.270929\pi$
$348$		0			0
$349$	−20.5877	−	11.8863i	−1.10204	−	0.636260i	−0.165280	−	0.986247i	$-0.552853\pi$
$349$	−20.5877	−	11.8863i	−1.10204	−	0.636260i	−0.936755	+	0.349986i	$0.886186\pi$
$350$		0			0
$351$	2.63839	+	21.7368i	0.140827	+	1.16022i
$352$		0			0
$353$	10.4377	+	6.02618i	0.555540	+	0.320741i	0.751354	−	0.659900i	$-0.229401\pi$
$353$	10.4377	+	6.02618i	0.555540	+	0.320741i	−0.195813	+	0.980641i	$0.562735\pi$
$354$		0			0
$355$	15.3201	+	26.5352i	0.813106	+	1.40834i
$356$		0			0
$357$	24.7511	+	19.1251i	1.30997	+	1.01221i
$358$		0			0
$359$	−19.3505			−1.02128			−0.510640	−	0.859795i	$-0.670591\pi$
$359$	−19.3505			−1.02128			−0.510640	+	0.859795i	$0.670591\pi$
$360$		0			0
$361$	−16.4657			−0.866616
$362$		0			0
$363$	−14.3926	+	5.90487i	−0.755418	+	0.309925i
$364$		0			0
$365$	15.7109	+	27.2121i	0.822347	+	1.42435i
$366$		0			0
$367$	−7.52528	−	4.34472i	−0.392817	−	0.226793i	0.290563	−	0.956856i	$-0.406157\pi$
$367$	−7.52528	−	4.34472i	−0.392817	−	0.226793i	−0.683380	+	0.730063i	$0.739491\pi$
$368$		0			0
$369$	13.6879	−	3.56895i	0.712565	−	0.185792i
$370$		0			0
$371$	−15.0512	−	8.68983i	−0.781421	−	0.451153i
$372$		0			0
$373$	−3.92070	+	2.26362i	−0.203006	+	0.117206i	−0.598057	−	0.801454i	$-0.704060\pi$
$373$	−3.92070	+	2.26362i	−0.203006	+	0.117206i	0.395051	+	0.918659i	$0.370727\pi$
$374$		0			0
$375$	−2.81091	+	20.8087i	−0.145155	+	1.07456i
$376$		0			0
$377$			16.0265i			0.825406i
$378$		0			0
$379$	9.28133			0.476750			0.238375	−	0.971173i	$-0.423385\pi$
$379$	9.28133			0.476750			0.238375	+	0.971173i	$0.423385\pi$
$380$		0			0
$381$	−10.4264	−	1.40843i	−0.534160	−	0.0721558i
$382$		0			0
$383$	−4.62746	−	8.01500i	−0.236452	−	0.409548i	0.723241	−	0.690595i	$-0.242651\pi$
$383$	−4.62746	−	8.01500i	−0.236452	−	0.409548i	−0.959694	+	0.281048i	$0.909318\pi$
$384$		0			0
$385$	−13.0274	+	22.5640i	−0.663936	+	1.14997i
$386$		0			0
$387$	7.83454	−	7.72962i	0.398252	−	0.392919i
$388$		0			0
$389$	2.98502	−	5.17021i	0.151347	−	0.262140i	−0.780376	−	0.625310i	$-0.784972\pi$
$389$	2.98502	−	5.17021i	0.151347	−	0.262140i	0.931723	+	0.363170i	$0.118306\pi$
$390$		0			0
$391$	11.7272	−	6.77072i	0.593071	−	0.342410i
$392$		0			0
$393$	8.83262	+	21.5288i	0.445547	+	1.08598i
$394$		0			0
$395$			0.106358i			0.00535146i
$396$		0			0
$397$		−	17.5213i		−	0.879367i	−0.898153	−	0.439684i	$-0.855091\pi$
$397$		−	17.5213i		−	0.879367i	0.898153	−	0.439684i	$-0.144909\pi$
$398$		0			0
$399$	−5.12043	+	6.62671i	−0.256342	+	0.331751i
$400$		0			0
$401$	−6.72928	+	3.88515i	−0.336044	+	0.194015i	−0.658521	−	0.752562i	$-0.728818\pi$
$401$	−6.72928	+	3.88515i	−0.336044	+	0.194015i	0.322477	+	0.946577i	$0.395484\pi$
$402$		0			0
$403$	21.1096	−	36.5629i	1.05154	−	1.82133i
$404$		0			0
$405$	−0.232853	+	17.2704i	−0.0115706	+	0.858174i
$406$		0			0
$407$	−16.8477	+	29.1810i	−0.835108	+	1.44645i
$408$		0			0
$409$	−8.48175	−	14.6908i	−0.419396	−	0.726415i	0.576483	−	0.817109i	$-0.304425\pi$
$409$	−8.48175	−	14.6908i	−0.419396	−	0.726415i	−0.995879	+	0.0906945i	$0.971091\pi$
$410$		0			0
$411$	−9.81721	+	12.7051i	−0.484247	+	0.626698i
$412$		0			0
$413$	3.80320			0.187143
$414$		0			0
$415$		−	18.5518i		−	0.910674i
$416$		0			0
$417$	−3.02651	+	1.24169i	−0.148209	+	0.0608056i
$418$		0			0
$419$	0.0314545	−	0.0181603i	0.00153665	−	0.000887187i	−0.499231	−	0.866469i	$-0.666384\pi$
$419$	0.0314545	−	0.0181603i	0.00153665	−	0.000887187i	0.500768	+	0.865581i	$0.333051\pi$
$420$		0			0
$421$	3.13540	+	1.81022i	0.152810	+	0.0882249i	0.574455	−	0.818536i	$-0.305214\pi$
$421$	3.13540	+	1.81022i	0.152810	+	0.0882249i	−0.421645	+	0.906761i	$0.638547\pi$
$422$		0			0
$423$	−11.8327	+	11.6742i	−0.575324	+	0.567619i
$424$		0			0
$425$	−6.78181	−	3.91548i	−0.328966	−	0.189929i
$426$		0			0
$427$	−0.517630	−	0.896562i	−0.0250499	−	0.0433877i
$428$		0			0
$429$	4.36757	−	32.3325i	0.210868	−	1.56103i
$430$		0			0
$431$	−9.58181			−0.461539			−0.230770	−	0.973008i	$-0.574124\pi$
$431$	−9.58181			−0.461539			−0.230770	+	0.973008i	$0.574124\pi$
$432$		0			0
$433$	9.88778			0.475176			0.237588	−	0.971366i	$-0.423643\pi$
$433$	9.88778			0.475176			0.237588	+	0.971366i	$0.423643\pi$
$434$		0			0
$435$	−1.69233	+	12.5280i	−0.0811408	+	0.600674i
$436$		0			0
$437$	1.81275	+	3.13978i	0.0867157	+	0.150196i
$438$		0			0
$439$	−19.7468	−	11.4008i	−0.942464	−	0.544132i	−0.0517319	−	0.998661i	$-0.516474\pi$
$439$	−19.7468	−	11.4008i	−0.942464	−	0.544132i	−0.890732	+	0.454529i	$0.849807\pi$
$440$		0			0
$441$	−1.68368	−	6.45737i	−0.0801751	−	0.307494i
$442$		0			0
$443$	−2.36311	−	1.36434i	−0.112275	−	0.0648218i	0.442811	−	0.896615i	$-0.353981\pi$
$443$	−2.36311	−	1.36434i	−0.112275	−	0.0648218i	−0.555086	+	0.831793i	$0.687315\pi$
$444$		0			0
$445$	24.0427	−	13.8811i	1.13973	−	0.658026i
$446$		0			0
$447$	22.5577	−	9.25476i	1.06694	−	0.437735i
$448$		0			0
$449$			17.1488i			0.809302i	0.914471	+	0.404651i	$0.132607\pi$
$449$			17.1488i			0.809302i	−0.914471	+	0.404651i	$0.867393\pi$
$450$		0			0
$451$	−21.0773			−0.992493
$452$		0			0
$453$	−4.84889	+	6.27529i	−0.227821	+	0.294839i
$454$		0			0
$455$	−12.2809	−	21.2711i	−0.575735	−	0.997203i
$456$		0			0
$457$	−11.3079	+	19.5858i	−0.528961	+	0.916187i	0.470469	+	0.882417i	$0.344085\pi$
$457$	−11.3079	+	19.5858i	−0.528961	+	0.916187i	−0.999430	+	0.0337704i	$0.989249\pi$
$458$		0			0
$459$	−28.4234	−	12.1115i	−1.32669	−	0.565317i
$460$		0			0
$461$	10.8418	−	18.7785i	0.504953	−	0.874604i	−0.495031	−	0.868875i	$-0.664843\pi$
$461$	10.8418	−	18.7785i	0.504953	−	0.874604i	0.999984	−	0.00572824i	$-0.00182336\pi$
$462$		0			0
$463$	10.9262	−	6.30823i	0.507782	−	0.293168i	−0.224139	−	0.974557i	$-0.571957\pi$
$463$	10.9262	−	6.30823i	0.507782	−	0.293168i	0.731922	+	0.681389i	$0.238624\pi$
$464$		0			0
$465$	20.3624	−	26.3525i	0.944286	−	1.22207i
$466$		0			0
$467$		−	29.0822i		−	1.34577i	−0.739749	−	0.672883i	$-0.765056\pi$
$467$		−	29.0822i		−	1.34577i	0.739749	−	0.672883i	$-0.234944\pi$
$468$		0			0
$469$		−	22.2730i		−	1.02847i
$470$		0			0
$471$	−14.8271	−	36.1399i	−0.683198	−	1.66524i
$472$		0			0
$473$	−14.2019	+	8.19948i	−0.653005	+	0.377012i
$474$		0			0
$475$	1.04831	−	1.81572i	0.0480997	−	0.0833111i
$476$		0			0
$477$	16.5517	+	4.55481i	0.757849	+	0.208550i
$478$		0			0
$479$	−0.657735	+	1.13923i	−0.0300527	+	0.0520527i	−0.880661	−	0.473748i	$-0.842901\pi$
$479$	−0.657735	+	1.13923i	−0.0300527	+	0.0520527i	0.850608	+	0.525801i	$0.176234\pi$
$480$		0			0
$481$	−15.8822	−	27.5088i	−0.724168	−	1.25430i
$482$		0			0
$483$	−11.8725	−	1.60378i	−0.540219	−	0.0729744i
$484$		0			0
$485$	−7.64142			−0.346979
$486$		0			0
$487$		−	10.5975i		−	0.480220i	−0.970746	−	0.240110i	$-0.922816\pi$
$487$		−	10.5975i		−	0.480220i	0.970746	−	0.240110i	$-0.0771835\pi$
$488$		0			0
$489$	1.15093	−	8.52015i	0.0520467	−	0.385294i
$490$		0			0
$491$	12.2744	−	7.08665i	0.553938	−	0.319816i	−0.196771	−	0.980450i	$-0.563045\pi$
$491$	12.2744	−	7.08665i	0.553938	−	0.319816i	0.750709	+	0.660633i	$0.229712\pi$
$492$		0			0
$493$	−19.5841	−	11.3069i	−0.882026	−	0.509238i
$494$		0			0
$495$	6.82834	−	24.8134i	0.306911	−	1.11528i
$496$		0			0
$497$	41.9944	+	24.2455i	1.88371	+	1.08756i
$498$		0			0
$499$	−20.3136	−	35.1842i	−0.909363	−	1.57506i	−0.814951	−	0.579529i	$-0.803236\pi$
$499$	−20.3136	−	35.1842i	−0.909363	−	1.57506i	−0.0944115	−	0.995533i	$-0.530097\pi$
$500$		0			0
$501$	−11.2818	+	4.62859i	−0.504034	+	0.206790i
$502$		0			0
$503$	4.81878			0.214859			0.107429	−	0.994213i	$-0.465738\pi$
$503$	4.81878			0.214859			0.107429	+	0.994213i	$0.465738\pi$
$504$		0			0
$505$	33.4207			1.48720
$506$		0			0
$507$	6.52024	+	5.03816i	0.289574	+	0.223753i
$508$		0			0
$509$	−10.8768	−	18.8392i	−0.482106	−	0.835032i	0.517683	−	0.855573i	$-0.326795\pi$
$509$	−10.8768	−	18.8392i	−0.482106	−	0.835032i	−0.999789	+	0.0205402i	$0.993461\pi$
$510$		0			0
$511$	43.0657	+	24.8640i	1.90511	+	1.09992i
$512$		0			0
$513$	3.24267	−	7.60993i	0.143167	−	0.335987i
$514$		0			0
$515$	8.49534	+	4.90479i	0.374349	+	0.216131i
$516$		0			0
$517$	21.4494	−	12.3838i	0.943345	−	0.544640i
$518$		0			0
$519$	7.79482	+	6.02302i	0.342154	+	0.264381i
$520$		0			0
$521$			9.89853i			0.433662i	0.976209	+	0.216831i	$0.0695721\pi$
$521$			9.89853i			0.433662i	−0.976209	+	0.216831i	$0.930428\pi$
$522$		0			0
$523$	−20.9296			−0.915188			−0.457594	−	0.889161i	$-0.651289\pi$
$523$	−20.9296			−0.915188			−0.457594	+	0.889161i	$0.651289\pi$
$524$		0			0
$525$	2.62972	+	6.40972i	0.114770	+	0.279743i
$526$		0			0
$527$	29.7862	+	51.5913i	1.29751	+	2.24735i
$528$		0			0
$529$	8.90672	−	15.4269i	0.387248	−	0.670734i
$530$		0			0
$531$	−3.63512	+	0.947811i	−0.157751	+	0.0411315i
$532$		0			0
$533$	9.93476	−	17.2075i	0.430322	−	0.745340i
$534$		0			0
$535$	−18.1475	+	10.4775i	−0.784587	+	0.452981i
$536$		0			0
$537$	−26.2324	−	3.54355i	−1.13201	−	0.152916i
$538$		0			0
$539$			9.94337i			0.428291i
$540$		0			0
$541$			24.6577i			1.06012i	0.847961	+	0.530058i	$0.177830\pi$
$541$			24.6577i			1.06012i	−0.847961	+	0.530058i	$0.822170\pi$
$542$		0			0
$543$	35.0714	+	4.73755i	1.50506	+	0.203308i
$544$		0			0
$545$	−5.42367	+	3.13136i	−0.232325	+	0.134133i
$546$		0			0
$547$	−3.26148	+	5.64904i	−0.139451	+	0.241536i	−0.927289	−	0.374347i	$-0.877867\pi$
$547$	−3.26148	+	5.64904i	−0.139451	+	0.241536i	0.787838	+	0.615882i	$0.211200\pi$
$548$		0			0
$549$	0.718189	+	0.727938i	0.0306516	+	0.0310676i
$550$		0			0
$551$	3.02725	−	5.24335i	0.128965	−	0.223374i
$552$		0			0
$553$	0.0841609	+	0.145771i	0.00357888	+	0.00619881i
$554$		0			0
$555$	−9.51048	−	23.1810i	−0.403697	−	0.983979i
$556$		0			0
$557$	23.6027			1.00008			0.500039	−	0.866003i	$-0.333319\pi$
$557$	23.6027			1.00008			0.500039	+	0.866003i	$0.333319\pi$
$558$		0			0
$559$		−	15.4592i		−	0.653856i
$560$		0			0
$561$	36.4285	+	28.1482i	1.53801	+	1.18842i
$562$		0			0
$563$	−38.2685	+	22.0943i	−1.61283	+	0.931166i	−0.624115	+	0.781332i	$0.714540\pi$
$563$	−38.2685	+	22.0943i	−1.61283	+	0.931166i	−0.988711	+	0.149833i	$0.952126\pi$
$564$		0			0
$565$	19.0659	+	11.0077i	0.802109	+	0.463098i
$566$		0			0
$567$	13.3469	+	23.8545i	0.560517	+	1.00180i
$568$		0			0
$569$	6.63183	+	3.82889i	0.278021	+	0.160515i	0.632527	−	0.774538i	$-0.282018\pi$
$569$	6.63183	+	3.82889i	0.278021	+	0.160515i	−0.354506	+	0.935054i	$0.615351\pi$
$570$		0			0
$571$	−2.68452	−	4.64972i	−0.112344	−	0.194585i	0.804371	−	0.594127i	$-0.202502\pi$
$571$	−2.68452	−	4.64972i	−0.112344	−	0.194585i	−0.916715	+	0.399542i	$0.869169\pi$
$572$		0			0
$573$	11.7812	+	9.10329i	0.492167	+	0.380296i
$574$		0			0
$575$	2.99937			0.125083
$576$		0			0
$577$	−20.8963			−0.869924			−0.434962	−	0.900449i	$-0.643238\pi$
$577$	−20.8963			−0.869924			−0.434962	+	0.900449i	$0.643238\pi$
$578$		0			0
$579$	−2.45639	+	1.00778i	−0.102084	+	0.0418820i
$580$		0			0
$581$	−14.6800	−	25.4265i	−0.609030	−	1.05487i
$582$		0			0
$583$	−22.1523	−	12.7896i	−0.917455	−	0.529693i
$584$		0			0
$585$	17.0391	+	17.2704i	0.704482	+	0.714044i
$586$		0			0
$587$	2.30245	+	1.32932i	0.0950324	+	0.0548670i	0.546763	−	0.837287i	$-0.315860\pi$
$587$	2.30245	+	1.32932i	0.0950324	+	0.0548670i	−0.451731	+	0.892154i	$0.649193\pi$
$588$		0			0
$589$	−13.8128	+	7.97480i	−0.569145	+	0.328596i
$590$		0			0
$591$	3.57663	−	26.4773i	0.147123	−	1.08913i
$592$		0			0
$593$		−	19.5587i		−	0.803180i	−0.915820	−	0.401590i	$-0.868458\pi$
$593$		−	19.5587i		−	0.803180i	0.915820	−	0.401590i	$-0.131542\pi$
$594$		0			0
$595$	34.6573			1.42081
$596$		0			0
$597$	13.0722	+	1.76583i	0.535009	+	0.0722706i
$598$		0			0
$599$	−10.9459	−	18.9589i	−0.447239	−	0.774640i	0.550967	−	0.834527i	$-0.314259\pi$
$599$	−10.9459	−	18.9589i	−0.447239	−	0.774640i	−0.998205	+	0.0598874i	$0.980926\pi$
$600$		0			0
$601$	11.6621	−	20.1993i	0.475706	−	0.823947i	−0.523907	−	0.851776i	$-0.675526\pi$
$601$	11.6621	−	20.1993i	0.475706	−	0.823947i	0.999613	+	0.0278286i	$0.00885926\pi$
$602$		0			0
$603$	5.55073	+	21.2886i	0.226043	+	0.866939i
$604$		0			0
$605$	−8.61849	+	14.9277i	−0.350391	+	0.606896i
$606$		0			0
$607$	5.54529	−	3.20157i	0.225076	−	0.129948i	−0.383222	−	0.923656i	$-0.625186\pi$
$607$	5.54529	−	3.20157i	0.225076	−	0.129948i	0.608299	+	0.793708i	$0.291852\pi$
$608$		0			0
$609$	7.59396	+	18.5097i	0.307723	+	0.750049i
$610$		0			0
$611$			23.3484i			0.944575i
$612$		0			0
$613$		−	25.2674i		−	1.02054i	−0.860014	−	0.510271i	$-0.829545\pi$
$613$		−	25.2674i		−	1.02054i	0.860014	−	0.510271i	$-0.170455\pi$
$614$		0			0
$615$	9.58313	−	12.4022i	0.386429	−	0.500105i
$616$		0			0
$617$	23.3822	−	13.4997i	0.941333	−	0.543479i	0.0509554	−	0.998701i	$-0.483773\pi$
$617$	23.3822	−	13.4997i	0.941333	−	0.543479i	0.890378	+	0.455222i	$0.150440\pi$
$618$		0			0
$619$	−8.55480	+	14.8173i	−0.343846	+	0.595559i	−0.985143	−	0.171733i	$-0.945063\pi$
$619$	−8.55480	+	14.8173i	−0.343846	+	0.595559i	0.641297	+	0.767293i	$0.278397\pi$
$620$		0			0
$621$	11.7475	−	1.42590i	0.471412	−	0.0572195i
$622$		0			0
$623$	21.9681	−	38.0499i	0.880133	−	1.52444i
$624$		0			0
$625$	8.34020	+	14.4457i	0.333608	+	0.577826i
$626$		0			0
$627$	−7.53623	+	9.75316i	−0.300968	+	0.389504i
$628$		0			0
$629$	44.8206			1.78711
$630$		0			0
$631$			14.4488i			0.575199i	0.957751	+	0.287600i	$0.0928572\pi$
$631$			14.4488i			0.575199i	−0.957751	+	0.287600i	$0.907143\pi$
$632$		0			0
$633$	7.65893	−	3.14223i	0.304415	−	0.124893i
$634$		0			0
$635$	−10.0956	+	5.82867i	−0.400630	+	0.231304i
$636$		0			0
$637$	−8.11776	−	4.68679i	−0.321637	−	0.185697i
$638$		0			0
$639$	−46.1808	−	12.7084i	−1.82688	−	0.502736i
$640$		0			0
$641$	−35.3963	−	20.4361i	−1.39807	−	0.807176i	−0.403879	−	0.914812i	$-0.632338\pi$
$641$	−35.3963	−	20.4361i	−1.39807	−	0.807176i	−0.994190	+	0.107636i	$0.965672\pi$
$642$		0			0
$643$	3.76272	+	6.51722i	0.148387	+	0.257014i	0.930631	−	0.365958i	$-0.119259\pi$
$643$	3.76272	+	6.51722i	0.148387	+	0.257014i	−0.782244	+	0.622972i	$0.785925\pi$
$644$		0			0
$645$	1.63243	−	12.0846i	0.0642768	−	0.475832i
$646$		0			0
$647$	22.8778			0.899419			0.449709	−	0.893175i	$-0.351528\pi$
$647$	22.8778			0.899419			0.449709	+	0.893175i	$0.351528\pi$
$648$		0			0
$649$	5.59753			0.219722
$650$		0			0
$651$	7.05546	−	52.2306i	0.276525	−	2.04708i
$652$		0			0
$653$	−4.76276	−	8.24934i	−0.186381	−	0.322822i	0.757660	−	0.652650i	$-0.226343\pi$
$653$	−4.76276	−	8.24934i	−0.186381	−	0.322822i	−0.944041	+	0.329828i	$0.893009\pi$
$654$		0			0
$655$	22.3291	+	12.8917i	0.872469	+	0.503720i
$656$		0			0
$657$	−47.3589	−	13.0326i	−1.84765	−	0.508449i
$658$		0			0
$659$	−41.1574	−	23.7622i	−1.60326	−	0.925645i	−0.990829	−	0.135125i	$-0.956856\pi$
$659$	−41.1574	−	23.7622i	−1.60326	−	0.925645i	−0.612436	−	0.790520i	$-0.709810\pi$
$660$		0			0
$661$	5.66209	−	3.26901i	0.220230	−	0.127150i	−0.385827	−	0.922571i	$-0.626084\pi$
$661$	5.66209	−	3.26901i	0.220230	−	0.127150i	0.606057	+	0.795421i	$0.292750\pi$
$662$		0			0
$663$	−40.1507	+	16.4726i	−1.55932	+	0.639744i
$664$		0			0
$665$			9.27893i			0.359822i
$666$		0			0
$667$	8.66143			0.335372
$668$		0			0
$669$	13.8855	−	17.9702i	0.536845	−	0.694768i
$670$		0			0
$671$	−0.761845	−	1.31955i	−0.0294107	−	0.0509408i
$672$		0			0
$673$	−13.6311	+	23.6098i	−0.525442	+	0.910092i	0.474119	+	0.880461i	$0.342767\pi$
$673$	−13.6311	+	23.6098i	−0.525442	+	0.910092i	−0.999561	+	0.0296310i	$0.990567\pi$
$674$		0			0
$675$	−4.11089	−	5.47109i	−0.158228	−	0.210582i
$676$		0			0
$677$	−15.7284	+	27.2424i	−0.604492	+	1.04701i	0.387639	+	0.921811i	$0.373291\pi$
$677$	−15.7284	+	27.2424i	−0.604492	+	1.04701i	−0.992132	+	0.125200i	$0.960043\pi$
$678$		0			0
$679$	−10.4731	+	6.04664i	−0.401920	+	0.232049i
$680$		0			0
$681$	−6.14649	+	7.95461i	−0.235534	+	0.304821i
$682$		0			0
$683$		−	22.3637i		−	0.855725i	−0.903844	−	0.427862i	$-0.859267\pi$
$683$		−	22.3637i		−	0.855725i	0.903844	−	0.427862i	$-0.140733\pi$
$684$		0			0
$685$			17.7901i			0.679726i
$686$		0			0
$687$	12.4651	+	30.3826i	0.475572	+	1.15917i
$688$		0			0
$689$	20.8829	−	12.0568i	0.795576	−	0.459326i
$690$		0			0
$691$	−6.43897	+	11.1526i	−0.244950	+	0.424265i	−0.962117	−	0.272635i	$-0.912105\pi$
$691$	−6.43897	+	11.1526i	−0.244950	+	0.424265i	0.717168	+	0.696901i	$0.245438\pi$
$692$		0			0
$693$	−10.2761	−	39.4117i	−0.390357	−	1.49713i
$694$		0			0
$695$	−1.81231	+	3.13901i	−0.0687448	+	0.119069i
$696$		0			0
$697$	14.0182	+	24.2803i	0.530979	+	0.919682i
$698$		0			0
$699$	9.38051	+	1.26715i	0.354803	+	0.0479279i
$700$		0			0
$701$	9.77325			0.369131			0.184565	−	0.982820i	$-0.440912\pi$
$701$	9.77325			0.369131			0.184565	+	0.982820i	$0.440912\pi$
$702$		0			0
$703$			12.0000i			0.452589i
$704$		0			0
$705$	−2.46549	+	18.2517i	−0.0928556	+	0.687397i
$706$		0			0
$707$	45.8053	−	26.4457i	1.72268	−	0.994593i
$708$		0			0
$709$	−22.5252	−	13.0049i	−0.845950	−	0.488409i	0.0133323	−	0.999911i	$-0.495756\pi$
$709$	−22.5252	−	13.0049i	−0.845950	−	0.488409i	−0.859282	+	0.511502i	$0.829089\pi$
$710$		0			0
$711$	−0.116770	−	0.118354i	−0.00437920	−	0.00443864i
$712$		0			0
$713$	−19.7602	−	11.4086i	−0.740026	−	0.427254i
$714$		0			0
$715$	−18.0749	−	31.3066i	−0.675963	−	1.17080i
$716$		0			0
$717$	−35.4139	+	14.5293i	−1.32255	+	0.542605i
$718$		0			0
$719$	−27.9704			−1.04312			−0.521559	−	0.853215i	$-0.674649\pi$
$719$	−27.9704			−1.04312			−0.521559	+	0.853215i	$0.674649\pi$
$720$		0			0
$721$	15.5246			0.578165
$722$		0			0
$723$	26.1945	+	20.2404i	0.974185	+	0.752749i
$724$		0			0
$725$	−2.50444	−	4.33781i	−0.0930124	−	0.161102i
$726$		0			0
$727$	7.10497	+	4.10206i	0.263509	+	0.152137i	0.625934	−	0.779876i	$-0.284718\pi$
$727$	7.10497	+	4.10206i	0.263509	+	0.152137i	−0.362425	+	0.932013i	$0.618051\pi$
$728$		0			0
$729$	−18.7019	−	19.4740i	−0.692663	−	0.721261i
$730$		0			0
$731$	18.8910	+	10.9067i	0.698708	+	0.403399i
$732$		0			0
$733$	−19.3513	+	11.1725i	−0.714756	+	0.412665i	−0.812820	−	0.582515i	$-0.802069\pi$
$733$	−19.3513	+	11.1725i	−0.714756	+	0.412665i	0.0980633	+	0.995180i	$0.468735\pi$
$734$		0			0
$735$	−5.85082	−	4.52091i	−0.215811	−	0.166756i
$736$		0			0
$737$		−	32.7812i		−	1.20751i
$738$		0			0
$739$	−35.6888			−1.31283			−0.656417	−	0.754399i	$-0.727929\pi$
$739$	−35.6888			−1.31283			−0.656417	+	0.754399i	$0.727929\pi$
$740$		0			0
$741$	−4.41029	−	10.7497i	−0.162016	−	0.394900i
$742$		0			0
$743$	−7.56128	−	13.0965i	−0.277396	−	0.480465i	0.693341	−	0.720610i	$-0.256138\pi$
$743$	−7.56128	−	13.0965i	−0.277396	−	0.480465i	−0.970737	+	0.240145i	$0.922805\pi$
$744$		0			0
$745$	13.5078	−	23.3963i	0.494889	−	0.857172i
$746$		0			0
$747$	20.3679	+	20.6443i	0.745222	+	0.755337i
$748$		0			0
$749$	−16.5816	+	28.7202i	−0.605879	+	1.04941i
$750$		0			0
$751$	−29.4856	+	17.0235i	−1.07595	+	0.621197i	−0.929800	−	0.368066i	$-0.880020\pi$
$751$	−29.4856	+	17.0235i	−1.07595	+	0.621197i	−0.146146	+	0.989263i	$0.546687\pi$
$752$		0			0
$753$	−5.56591	−	0.751860i	−0.202833	−	0.0273993i
$754$		0			0
$755$			8.78686i			0.319786i
$756$		0			0
$757$			45.3866i			1.64960i	0.565423	+	0.824801i	$0.308713\pi$
$757$			45.3866i			1.64960i	−0.565423	+	0.824801i	$0.691287\pi$
$758$		0			0
$759$	−17.4739	−	2.36043i	−0.634264	−	0.0856782i
$760$		0			0
$761$	−12.6558	+	7.30686i	−0.458774	+	0.264873i	−0.711529	−	0.702657i	$-0.751997\pi$
$761$	−12.6558	+	7.30686i	−0.458774	+	0.264873i	0.252755	+	0.967530i	$0.418663\pi$
$762$		0			0
$763$	−4.95567	+	8.58347i	−0.179407	+	0.310742i
$764$		0			0
$765$	−33.1256	+	8.63707i	−1.19766	+	0.312274i
$766$		0			0
$767$	−2.63839	+	4.56982i	−0.0952667	+	0.165007i
$768$		0			0
$769$	22.2146	+	38.4768i	0.801079	+	1.38751i	0.918906	+	0.394476i	$0.129074\pi$
$769$	22.2146	+	38.4768i	0.801079	+	1.38751i	−0.117827	+	0.993034i	$0.537593\pi$
$770$		0			0
$771$	−16.1377	−	39.3343i	−0.581185	−	1.41659i
$772$		0			0
$773$	−10.7747			−0.387539			−0.193770	−	0.981047i	$-0.562071\pi$
$773$	−10.7747			−0.387539			−0.193770	+	0.981047i	$0.562071\pi$
$774$		0			0
$775$			13.1951i			0.473981i
$776$		0			0
$777$	−31.3778	−	24.2455i	−1.12567	−	0.869802i
$778$		0			0
$779$	−6.50067	+	3.75316i	−0.232911	+	0.134471i
$780$		0			0
$781$	61.8072	+	35.6844i	2.21164	+	1.27689i
$782$		0			0
$783$	−11.8712	−	15.7991i	−0.424243	−	0.564614i
$784$		0			0
$785$	−37.4833	−	21.6410i	−1.33784	−	0.772401i
$786$		0			0
$787$	16.7959	+	29.0914i	0.598710	+	1.03700i	0.993012	+	0.118016i	$0.0376533\pi$
$787$	16.7959	+	29.0914i	0.598710	+	1.03700i	−0.394301	+	0.918981i	$0.629013\pi$
$788$		0			0
$789$	−41.4566	−	32.0333i	−1.47589	−	1.14042i
$790$		0			0
$791$	34.8415			1.23882
$792$		0			0
$793$	1.43638			0.0510073
$794$		0			0
$795$	17.5975	−	7.21973i	0.624119	−	0.256058i
$796$		0			0
$797$	12.1756	+	21.0887i	0.431281	+	0.747001i	0.996984	−	0.0776084i	$-0.0247284\pi$
$797$	12.1756	+	21.0887i	0.431281	+	0.747001i	−0.565703	+	0.824609i	$0.691395\pi$
$798$		0			0
$799$	−28.5314	−	16.4726i	−1.00937	−	0.582760i
$800$		0			0
$801$	−11.5147	+	41.8430i	−0.406851	+	1.47845i
$802$		0			0
$803$	63.3839	+	36.5947i	2.23677	+	1.29140i
$804$		0			0
$805$	−11.4958	+	6.63712i	−0.405175	+	0.233928i
$806$		0			0
$807$	4.04597	−	29.9517i	0.142425	−	1.05435i
$808$		0			0
$809$			16.9318i			0.595290i	0.954677	+	0.297645i	$0.0962012\pi$
$809$			16.9318i			0.595290i	−0.954677	+	0.297645i	$0.903799\pi$
$810$		0			0
$811$	24.5985			0.863771			0.431885	−	0.901929i	$-0.357849\pi$
$811$	24.5985			0.863771			0.431885	+	0.901929i	$0.357849\pi$
$812$		0			0
$813$	1.08828	+	0.147009i	0.0381678	+	0.00515582i
$814$		0			0
$815$	−4.76303	−	8.24981i	−0.166842	−	0.288978i
$816$		0			0
$817$	−2.92010	+	5.05776i	−0.102161	+	0.176949i
$818$		0			0
$819$	37.0193	+	10.1872i	1.29356	+	0.355971i
$820$		0			0
$821$	−0.0525282	+	0.0909815i	−0.00183325	+	0.00317528i	−0.866941	−	0.498412i	$-0.833917\pi$
$821$	−0.0525282	+	0.0909815i	−0.00183325	+	0.00317528i	0.865107	+	0.501587i	$0.167250\pi$
$822$		0			0
$823$	9.56689	−	5.52345i	0.333481	−	0.192535i	−0.323905	−	0.946090i	$-0.604996\pi$
$823$	9.56689	−	5.52345i	0.333481	−	0.192535i	0.657385	+	0.753554i	$0.271662\pi$
$824$		0			0
$825$	3.87041	+	9.43380i	0.134750	+	0.328443i
$826$		0			0
$827$		−	15.4229i		−	0.536308i	−0.963376	−	0.268154i	$-0.913586\pi$
$827$		−	15.4229i		−	0.536308i	0.963376	−	0.268154i	$-0.0864135\pi$
$828$		0			0
$829$		−	25.8278i		−	0.897038i	−0.893773	−	0.448519i	$-0.851952\pi$
$829$		−	25.8278i		−	0.897038i	0.893773	−	0.448519i	$-0.148048\pi$
$830$		0			0
$831$	−24.0130	+	31.0769i	−0.833001	+	1.07805i
$832$		0			0
$833$	11.4544	−	6.61320i	0.396871	−	0.229134i
$834$		0			0
$835$	−6.75569	+	11.7012i	−0.233790	+	0.404936i
$836$		0			0
$837$	6.27294	+	51.6806i	0.216824	+	1.78634i
$838$		0			0
$839$	−8.10290	+	14.0346i	−0.279743	+	0.484529i	−0.971321	−	0.237773i	$-0.923583\pi$
$839$	−8.10290	+	14.0346i	−0.279743	+	0.484529i	0.691578	+	0.722302i	$0.256916\pi$
$840$		0			0
$841$	7.26783	+	12.5882i	0.250615	+	0.434077i
$842$		0			0
$843$	−12.4284	+	16.0845i	−0.428057	+	0.553979i
$844$		0			0
$845$	9.12985			0.314076
$846$		0			0
$847$			27.2791i			0.937322i
$848$		0			0
$849$	−23.2335	+	9.53203i	−0.797373	+	0.327138i
$850$		0			0
$851$	−14.8670	+	8.58347i	−0.509634	+	0.294238i
$852$		0			0
$853$	−15.3781	−	8.87853i	−0.526535	−	0.303995i	0.213069	−	0.977037i	$-0.431654\pi$
$853$	−15.3781	−	8.87853i	−0.526535	−	0.303995i	−0.739604	+	0.673042i	$0.764987\pi$
$854$		0			0
$855$	−2.31244	−	8.86885i	−0.0790837	−	0.303308i
$856$		0			0
$857$	−22.9285	−	13.2378i	−0.783223	−	0.452194i	0.0543481	−	0.998522i	$-0.482692\pi$
$857$	−22.9285	−	13.2378i	−0.783223	−	0.452194i	−0.837571	+	0.546328i	$0.816025\pi$
$858$		0			0
$859$	12.9367	+	22.4071i	0.441395	+	0.764519i	0.997793	−	0.0663970i	$-0.0211504\pi$
$859$	12.9367	+	22.4071i	0.441395	+	0.764519i	−0.556398	+	0.830916i	$0.687817\pi$
$860$		0			0
$861$	3.32049	−	24.5812i	0.113162	−	0.837723i
$862$		0			0
$863$	48.6992			1.65774			0.828870	−	0.559441i	$-0.188984\pi$
$863$	48.6992			1.65774			0.828870	+	0.559441i	$0.188984\pi$
$864$		0			0
$865$	10.9145			0.371106
$866$		0			0
$867$	4.25584	−	31.5054i	0.144536	−	1.06998i
$868$		0			0
$869$	0.123867	+	0.214545i	0.00420192	+	0.00727793i
$870$		0			0
$871$	26.7626	+	15.4514i	0.906815	+	0.523550i
$872$		0			0
$873$	8.50332	−	8.38944i	0.287794	−	0.283940i
$874$		0			0
$875$	31.8869	+	18.4099i	1.07797	+	0.622368i
$876$		0			0
$877$	−9.11577	+	5.26299i	−0.307818	+	0.177719i	−0.645949	−	0.763380i	$-0.723538\pi$
$877$	−9.11577	+	5.26299i	−0.307818	+	0.177719i	0.338132	+	0.941099i	$0.390205\pi$
$878$		0			0
$879$	3.41611	−	1.40153i	0.115222	−	0.0472723i
$880$		0			0
$881$		−	23.5758i		−	0.794288i	−0.917756	−	0.397144i	$-0.870001\pi$
$881$		−	23.5758i		−	0.794288i	0.917756	−	0.397144i	$-0.129999\pi$
$882$		0			0
$883$	−53.1293			−1.78794			−0.893971	−	0.448124i	$-0.852092\pi$
$883$	−53.1293			−1.78794			−0.893971	+	0.448124i	$0.852092\pi$
$884$		0			0
$885$	−2.54501	+	3.29367i	−0.0855494	+	0.110716i
$886$		0			0
$887$	7.75882	+	13.4387i	0.260516	+	0.451227i	0.966379	−	0.257122i	$-0.0827741\pi$
$887$	7.75882	+	13.4387i	0.260516	+	0.451227i	−0.705863	+	0.708348i	$0.749441\pi$
$888$		0			0
$889$	−9.22442	+	15.9772i	−0.309377	+	0.535857i
$890$		0			0
$891$	19.6439	+	35.1090i	0.658095	+	1.17619i
$892$		0			0
$893$	4.41029	−	7.63884i	0.147585	−	0.255624i
$894$		0			0
$895$	−25.4001	+	14.6647i	−0.849031	+	0.490188i
$896$		0			0
$897$	10.1634	−	13.1531i	0.339345	−	0.439170i
$898$		0			0
$899$			38.1040i			1.27084i
$900$		0			0
$901$			34.0249i			1.13353i
$902$		0			0
$903$	−7.32518	−	17.8545i	−0.243767	−	0.594161i
$904$		0			0
$905$	33.9586	−	19.6060i	1.12882	−	0.651727i
$906$		0			0
$907$	6.92312	−	11.9912i	0.229879	−	0.398161i	−0.727893	−	0.685690i	$-0.759500\pi$
$907$	6.92312	−	11.9912i	0.229879	−	0.398161i	0.957772	+	0.287529i	$0.0928338\pi$
$908$		0			0
$909$	−37.1903	+	36.6922i	−1.23352	+	1.21700i
$910$		0			0
$911$	15.5442	−	26.9233i	0.515002	−	0.892010i	−0.484846	−	0.874599i	$-0.661124\pi$
$911$	15.5442	−	26.9233i	0.515002	−	0.892010i	0.999848	−	0.0174104i	$-0.00554219\pi$
$912$		0			0
$913$	−21.6060	−	37.4226i	−0.715053	−	1.23851i
$914$		0			0
$915$	1.12283	+	0.151675i	0.0371196	+	0.00501423i
$916$		0			0
$917$	40.8047			1.34749
$918$		0			0
$919$			33.6999i			1.11166i	0.831297	+	0.555828i	$0.187599\pi$
$919$			33.6999i			1.11166i	−0.831297	+	0.555828i	$0.812401\pi$
$920$		0			0
$921$	−6.13668	+	45.4290i	−0.202210	+	1.49693i
$922$		0			0
$923$	−58.2654	+	33.6396i	−1.91783	+	1.10726i
$924$		0			0
$925$	8.59753	+	4.96379i	0.282685	+	0.163208i
$926$		0			0
$927$	−14.8385	+	3.86894i	−0.487359	+	0.127073i
$928$		0			0
$929$	−2.59328	−	1.49723i	−0.0850829	−	0.0491226i	0.456855	−	0.889541i	$-0.348976\pi$
$929$	−2.59328	−	1.49723i	−0.0850829	−	0.0491226i	−0.541938	+	0.840419i	$0.682309\pi$
$930$		0			0
$931$	1.77058	+	3.06673i	0.0580284	+	0.100508i
$932$		0			0
$933$	31.1086	−	12.7629i	1.01845	−	0.417840i
$934$		0			0
$935$	51.0084			1.66815
$936$		0			0
$937$	9.83746			0.321376			0.160688	−	0.987005i	$-0.448629\pi$
$937$	9.83746			0.321376			0.160688	+	0.987005i	$0.448629\pi$
$938$		0			0
$939$	−13.4079	−	10.3602i	−0.437549	−	0.338093i
$940$		0			0
$941$	−17.6838	−	30.6293i	−0.576477	−	0.998487i	−0.995879	−	0.0906870i	$-0.971094\pi$
$941$	−17.6838	−	30.6293i	−0.576477	−	0.998487i	0.419402	−	0.907800i	$-0.362240\pi$
$942$		0			0
$943$	−9.29971	−	5.36919i	−0.302840	−	0.174845i
$944$		0			0
$945$	27.8626	+	11.8725i	0.906371	+	0.386214i
$946$		0			0
$947$	1.27322	+	0.735095i	0.0413741	+	0.0238874i	0.520544	−	0.853835i	$-0.325729\pi$
$947$	1.27322	+	0.735095i	0.0413741	+	0.0238874i	−0.479170	+	0.877722i	$0.659062\pi$
$948$		0			0
$949$	−59.7518	+	34.4977i	−1.93962	+	1.11984i
$950$		0			0
$951$	−14.3247	−	11.0686i	−0.464511	−	0.358926i
$952$		0			0
$953$		−	19.9312i		−	0.645634i	−0.946461	−	0.322817i	$-0.895370\pi$
$953$		−	19.9312i		−	0.645634i	0.946461	−	0.322817i	$-0.104630\pi$
$954$		0			0
$955$	16.4964			0.533812
$956$		0			0
$957$	11.1768	+	27.2424i	0.361293	+	0.880622i
$958$		0			0
$959$	14.0773	+	24.3826i	0.454579	+	0.787354i
$960$		0			0
$961$	34.6894	−	60.0839i	1.11901	−	1.93819i
$962$		0			0
$963$	8.69132	−	31.5833i	0.280074	−	1.01776i
$964$		0			0
$965$	−1.47091	+	2.54770i	−0.0473504	+	0.0820133i
$966$		0			0
$967$	−25.7192	+	14.8490i	−0.827074	+	0.477511i	−0.852850	−	0.522157i	$-0.825128\pi$
$967$	−25.7192	+	14.8490i	−0.827074	+	0.477511i	0.0257760	+	0.999668i	$0.491794\pi$
$968$		0			0
$969$	16.2475	+	2.19476i	0.521945	+	0.0705059i
$970$		0			0
$971$			21.5707i			0.692236i	0.938191	+	0.346118i	$0.112500\pi$
$971$			21.5707i			0.692236i	−0.938191	+	0.346118i	$0.887500\pi$
$972$		0			0
$973$			5.73630i			0.183897i
$974$		0			0
$975$	−9.52606	−	1.28681i	−0.305078	−	0.0412108i
$976$		0			0
$977$	−10.1262	+	5.84635i	−0.323965	+	0.187041i	−0.653159	−	0.757221i	$-0.726557\pi$
$977$	−10.1262	+	5.84635i	−0.323965	+	0.187041i	0.329193	+	0.944263i	$0.393223\pi$
$978$		0			0
$979$	32.3325	−	56.0016i	1.03335	−	1.78982i
$980$		0			0
$981$	2.59753	−	9.43915i	0.0829329	−	0.301369i
$982$		0			0
$983$	−23.9886	+	41.5495i	−0.765118	+	1.32522i	0.175066	+	0.984557i	$0.443986\pi$
$983$	−23.9886	+	41.5495i	−0.765118	+	1.32522i	−0.940184	+	0.340667i	$0.889347\pi$
$984$		0			0
$985$	−14.8016	−	25.6372i	−0.471620	−	0.816869i
$986$		0			0
$987$	11.0634	+	26.9660i	0.352151	+	0.858339i
$988$		0			0
$989$	−8.35487			−0.265669
$990$		0			0
$991$			39.4417i			1.25291i	0.779459	+	0.626453i	$0.215494\pi$
$991$			39.4417i			1.25291i	−0.779459	+	0.626453i	$0.784506\pi$
$992$		0			0
$993$	−24.7284	−	19.1075i	−0.784733	−	0.606360i
$994$		0			0
$995$	12.6574	−	7.30776i	0.401267	−	0.231672i
$996$		0			0
$997$	−4.96221	−	2.86494i	−0.157155	−	0.0907334i	0.419360	−	0.907820i	$-0.362254\pi$
$997$	−4.96221	−	2.86494i	−0.157155	−	0.0907334i	−0.576515	+	0.817087i	$0.695588\pi$
$998$		0			0
$999$	36.0334	+	15.3542i	1.14005	+	0.485785i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.p.c.479.4	yes	16
3.2	odd	2		1728.2.p.a.1439.4		16
4.3	odd	2	inner	576.2.p.c.479.5	yes	16
8.3	odd	2		576.2.p.a.479.4	yes	16
8.5	even	2		576.2.p.a.479.5	yes	16
9.2	odd	6		5184.2.f.f.2591.9		16
9.4	even	3		1728.2.p.c.287.5		16
9.5	odd	6		576.2.p.a.95.4	✓	16
9.7	even	3		5184.2.f.a.2591.5		16
12.11	even	2		1728.2.p.a.1439.3		16
24.5	odd	2		1728.2.p.c.1439.6		16
24.11	even	2		1728.2.p.c.1439.5		16
36.7	odd	6		5184.2.f.a.2591.7		16
36.11	even	6		5184.2.f.f.2591.11		16
36.23	even	6		576.2.p.a.95.5	yes	16
36.31	odd	6		1728.2.p.c.287.6		16
72.5	odd	6	inner	576.2.p.c.95.5	yes	16
72.11	even	6		5184.2.f.a.2591.8		16
72.13	even	6		1728.2.p.a.287.3		16
72.29	odd	6		5184.2.f.a.2591.6		16
72.43	odd	6		5184.2.f.f.2591.12		16
72.59	even	6	inner	576.2.p.c.95.4	yes	16
72.61	even	6		5184.2.f.f.2591.10		16
72.67	odd	6		1728.2.p.a.287.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
576.2.p.a.95.4	✓	16	9.5	odd	6
576.2.p.a.95.5	yes	16	36.23	even	6
576.2.p.a.479.4	yes	16	8.3	odd	2
576.2.p.a.479.5	yes	16	8.5	even	2
576.2.p.c.95.4	yes	16	72.59	even	6	inner
576.2.p.c.95.5	yes	16	72.5	odd	6	inner
576.2.p.c.479.4	yes	16	1.1	even	1	trivial
576.2.p.c.479.5	yes	16	4.3	odd	2	inner
1728.2.p.a.287.3		16	72.13	even	6
1728.2.p.a.287.4		16	72.67	odd	6
1728.2.p.a.1439.3		16	12.11	even	2
1728.2.p.a.1439.4		16	3.2	odd	2
1728.2.p.c.287.5		16	9.4	even	3
1728.2.p.c.287.6		16	36.31	odd	6
1728.2.p.c.1439.5		16	24.11	even	2
1728.2.p.c.1439.6		16	24.5	odd	2
5184.2.f.a.2591.5		16	9.7	even	3
5184.2.f.a.2591.6		16	72.29	odd	6
5184.2.f.a.2591.7		16	36.7	odd	6
5184.2.f.a.2591.8		16	72.11	even	6
5184.2.f.f.2591.9		16	9.2	odd	6
5184.2.f.f.2591.10		16	72.61	even	6
5184.2.f.f.2591.11		16	36.11	even	6
5184.2.f.f.2591.12		16	72.43	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)

\(f(q)\)	\(=\)	\(q+(-0.231865 + 1.71646i) q^{3} +(0.959555 + 1.66200i) q^{5} +(2.63027 + 1.51859i) q^{7} +(-2.89248 - 0.795973i) q^{9} +O(q^{10})\)	\(q+(-0.231865 + 1.71646i) q^{3} +(0.959555 + 1.66200i) q^{5} +(2.63027 + 1.51859i) q^{7} +(-2.89248 - 0.795973i) q^{9} +(3.87122 + 2.23505i) q^{11} +(-3.64938 + 2.10697i) q^{13} +(-3.07524 + 1.26168i) q^{15} -5.94600i q^{17} +1.59195 q^{19} +(-3.21646 + 4.16265i) q^{21} +(1.13870 + 1.97229i) q^{23} +(0.658507 - 1.14057i) q^{25} +(2.03692 - 4.78027i) q^{27} +(1.90160 - 3.29367i) q^{29} +(-8.67664 + 5.00946i) q^{31} +(-4.73397 + 6.12656i) q^{33} +5.82867i q^{35} +7.53794i q^{37} +(-2.77037 - 6.75256i) q^{39} +(-4.08347 + 2.35759i) q^{41} +(-1.83430 + 3.17709i) q^{43} +(-1.45259 - 5.57107i) q^{45} +(2.77037 - 4.79843i) q^{47} +(1.11221 + 1.92640i) q^{49} +(10.2061 + 1.37867i) q^{51} -5.72231 q^{53} +8.57861i q^{55} +(-0.369116 + 2.73251i) q^{57} +(1.08445 - 0.626109i) q^{59} +(-0.295196 - 0.170432i) q^{61} +(-6.39924 - 6.48610i) q^{63} +(-7.00357 - 4.04351i) q^{65} +(-3.66673 - 6.35096i) q^{67} +(-3.64938 + 1.49723i) q^{69} +15.9658 q^{71} +16.3731 q^{73} +(1.80506 + 1.39476i) q^{75} +(6.78823 + 11.7576i) q^{77} +(0.0479956 + 0.0277103i) q^{79} +(7.73285 + 4.60467i) q^{81} +(-8.37177 - 4.83345i) q^{83} +(9.88224 - 5.70551i) q^{85} +(5.21254 + 4.02771i) q^{87} -14.4661i q^{89} -12.7985 q^{91} +(-6.58674 - 16.0546i) q^{93} +(1.52756 + 2.64581i) q^{95} +(-1.99088 + 3.44830i) q^{97} +(-9.41837 - 9.54621i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{5} + 6 q^{9}+O(q^{10}) \) 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

Properties

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