LMFDB - Embedded newform 576.2.y.a.335.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(47,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

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

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

chi := DirichletCharacter("576.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.y (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			335.3
Character	$\chi$	$=$	576.335
Dual form			576.2.y.a.239.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61259 - 0.632098i) q^{3} +(-3.81396 - 1.02195i) q^{5} +(-1.46715 + 2.54117i) q^{7} +(2.20090 + 2.03863i) q^{9} +O(q^{10})$	\(q+(-1.61259 - 0.632098i) q^{3} +(-3.81396 - 1.02195i) q^{5} +(-1.46715 + 2.54117i) q^{7} +(2.20090 + 2.03863i) q^{9} +(2.65006 - 0.710081i) q^{11} +(-2.34729 - 0.628955i) q^{13} +(5.50439 + 4.05878i) q^{15} -2.89808i q^{17} +(1.99906 + 1.99906i) q^{19} +(3.97218 - 3.17049i) q^{21} +(2.07141 - 1.19593i) q^{23} +(9.17180 + 5.29534i) q^{25} +(-2.26054 - 4.67867i) q^{27} +(8.46218 - 2.26743i) q^{29} +(0.439075 - 0.253500i) q^{31} +(-4.72230 - 0.530027i) q^{33} +(8.19258 - 8.19258i) q^{35} +(1.36407 + 1.36407i) q^{37} +(3.38766 + 2.49797i) q^{39} +(0.745739 + 1.29166i) q^{41} +(1.27136 + 4.74478i) q^{43} +(-6.31078 - 10.0245i) q^{45} +(3.25802 - 5.64306i) q^{47} +(-0.805035 - 1.39436i) q^{49} +(-1.83187 + 4.67343i) q^{51} +(-5.17979 + 5.17979i) q^{53} -10.8329 q^{55} +(-1.96006 - 4.48726i) q^{57} +(-0.664781 + 2.48100i) q^{59} +(2.99657 + 11.1833i) q^{61} +(-8.40956 + 2.60190i) q^{63} +(8.30972 + 4.79762i) q^{65} +(2.53505 - 9.46095i) q^{67} +(-4.09628 + 0.619209i) q^{69} +4.65399i q^{71} -4.91897i q^{73} +(-11.4432 - 14.3367i) q^{75} +(-2.08358 + 7.77604i) q^{77} +(3.61263 + 2.08575i) q^{79} +(0.687950 + 8.97367i) q^{81} +(3.37411 + 12.5924i) q^{83} +(-2.96169 + 11.0532i) q^{85} +(-15.0793 - 1.69249i) q^{87} +7.33327 q^{89} +(5.04210 - 5.04210i) q^{91} +(-0.868286 + 0.131254i) q^{93} +(-5.58139 - 9.66725i) q^{95} +(2.50134 - 4.33245i) q^{97} +(7.28011 + 3.83968i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.61259	−	0.632098i	−0.931030	−	0.364942i
$3$	−1.61259	−	0.632098i	−0.931030	−	0.364942i
$4$		0			0
$5$	−3.81396	−	1.02195i	−1.70566	−	0.457029i	−0.731302	−	0.682053i	$-0.761087\pi$
$5$	−3.81396	−	1.02195i	−1.70566	−	0.457029i	−0.974353	+	0.225024i	$0.927754\pi$
$6$		0			0
$7$	−1.46715	+	2.54117i	−0.554529	+	0.960473i	0.443411	+	0.896318i	$0.353768\pi$
$7$	−1.46715	+	2.54117i	−0.554529	+	0.960473i	−0.997940	+	0.0641541i	$0.979565\pi$
$8$		0			0
$9$	2.20090	+	2.03863i	0.733634	+	0.679544i
$10$		0			0
$11$	2.65006	−	0.710081i	0.799022	−	0.214097i	0.163868	−	0.986482i	$-0.447603\pi$
$11$	2.65006	−	0.710081i	0.799022	−	0.214097i	0.635155	+	0.772385i	$0.280936\pi$
$12$		0			0
$13$	−2.34729	−	0.628955i	−0.651021	−	0.174441i	−0.0818307	−	0.996646i	$-0.526077\pi$
$13$	−2.34729	−	0.628955i	−0.651021	−	0.174441i	−0.569191	+	0.822206i	$0.692743\pi$
$14$		0			0
$15$	5.50439	+	4.05878i	1.42123	+	1.04797i
$16$		0			0
$17$		−	2.89808i		−	0.702889i	−0.936209	−	0.351444i	$-0.885691\pi$
$17$		−	2.89808i		−	0.702889i	0.936209	−	0.351444i	$-0.114309\pi$
$18$		0			0
$19$	1.99906	+	1.99906i	0.458615	+	0.458615i	0.898201	−	0.439586i	$-0.144875\pi$
$19$	1.99906	+	1.99906i	0.458615	+	0.458615i	−0.439586	+	0.898201i	$0.644875\pi$
$20$		0			0
$21$	3.97218	−	3.17049i	0.866800	−	0.691858i
$22$		0			0
$23$	2.07141	−	1.19593i	0.431918	−	0.249368i	−0.268245	−	0.963351i	$-0.586444\pi$
$23$	2.07141	−	1.19593i	0.431918	−	0.249368i	0.700163	+	0.713983i	$0.253110\pi$
$24$		0			0
$25$	9.17180	+	5.29534i	1.83436	+	1.05907i
$26$		0			0
$27$	−2.26054	−	4.67867i	−0.435041	−	0.900410i
$28$		0			0
$29$	8.46218	−	2.26743i	1.57139	−	0.421052i	0.635141	−	0.772396i	$-0.280942\pi$
$29$	8.46218	−	2.26743i	1.57139	−	0.421052i	0.936246	+	0.351344i	$0.114275\pi$
$30$		0			0
$31$	0.439075	−	0.253500i	0.0788602	−	0.0455300i	−0.460051	−	0.887892i	$-0.652169\pi$
$31$	0.439075	−	0.253500i	0.0788602	−	0.0455300i	0.538912	+	0.842362i	$0.318836\pi$
$32$		0			0
$33$	−4.72230	−	0.530027i	−0.822047	−	0.0922658i
$34$		0			0
$35$	8.19258	−	8.19258i	1.38480	−	1.38480i
$36$		0			0
$37$	1.36407	+	1.36407i	0.224251	+	0.224251i	0.810286	−	0.586035i	$-0.199312\pi$
$37$	1.36407	+	1.36407i	0.224251	+	0.224251i	−0.586035	+	0.810286i	$0.699312\pi$
$38$		0			0
$39$	3.38766	+	2.49797i	0.542460	+	0.399995i
$40$		0			0
$41$	0.745739	+	1.29166i	0.116465	+	0.201723i	0.918364	−	0.395736i	$-0.129510\pi$
$41$	0.745739	+	1.29166i	0.116465	+	0.201723i	−0.801899	+	0.597459i	$0.796177\pi$
$42$		0			0
$43$	1.27136	+	4.74478i	0.193881	+	0.723572i	0.992554	+	0.121807i	$0.0388690\pi$
$43$	1.27136	+	4.74478i	0.193881	+	0.723572i	−0.798673	+	0.601765i	$0.794464\pi$
$44$		0			0
$45$	−6.31078	−	10.0245i	−0.940756	−	1.49436i
$46$		0			0
$47$	3.25802	−	5.64306i	0.475231	−	0.823124i	−0.524367	−	0.851493i	$-0.675698\pi$
$47$	3.25802	−	5.64306i	0.475231	−	0.823124i	0.999598	+	0.0283684i	$0.00903115\pi$
$48$		0			0
$49$	−0.805035	−	1.39436i	−0.115005	−	0.199195i
$50$		0			0
$51$	−1.83187	+	4.67343i	−0.256514	+	0.654411i
$52$		0			0
$53$	−5.17979	+	5.17979i	−0.711499	+	0.711499i	−0.966849	−	0.255349i	$-0.917809\pi$
$53$	−5.17979	+	5.17979i	−0.711499	+	0.711499i	0.255349	+	0.966849i	$0.417809\pi$
$54$		0			0
$55$	−10.8329			−1.46071
$56$		0			0
$57$	−1.96006	−	4.48726i	−0.259616	−	0.594352i
$58$		0			0
$59$	−0.664781	+	2.48100i	−0.0865472	+	0.322998i	−0.995603	−	0.0936766i	$-0.970138\pi$
$59$	−0.664781	+	2.48100i	−0.0865472	+	0.322998i	0.909056	+	0.416675i	$0.136805\pi$
$60$		0			0
$61$	2.99657	+	11.1833i	0.383671	+	1.43188i	0.840251	+	0.542198i	$0.182408\pi$
$61$	2.99657	+	11.1833i	0.383671	+	1.43188i	−0.456580	+	0.889682i	$0.650926\pi$
$62$		0			0
$63$	−8.40956	+	2.60190i	−1.05951	+	0.327809i
$64$		0			0
$65$	8.30972	+	4.79762i	1.03069	+	0.595071i
$66$		0			0
$67$	2.53505	−	9.46095i	0.309706	−	1.15584i	−0.619112	−	0.785303i	$-0.712507\pi$
$67$	2.53505	−	9.46095i	0.309706	−	1.15584i	0.928818	−	0.370536i	$-0.120826\pi$
$68$		0			0
$69$	−4.09628	+	0.619209i	−0.493134	+	0.0745440i
$70$		0			0
$71$			4.65399i			0.552327i	0.961111	+	0.276164i	$0.0890632\pi$
$71$			4.65399i			0.552327i	−0.961111	+	0.276164i	$0.910937\pi$
$72$		0			0
$73$		−	4.91897i		−	0.575722i	−0.957672	−	0.287861i	$-0.907056\pi$
$73$		−	4.91897i		−	0.575722i	0.957672	−	0.287861i	$-0.0929441\pi$
$74$		0			0
$75$	−11.4432	−	14.3367i	−1.32135	−	1.65546i
$76$		0			0
$77$	−2.08358	+	7.77604i	−0.237446	+	0.886162i
$78$		0			0
$79$	3.61263	+	2.08575i	0.406453	+	0.234666i	0.689264	−	0.724510i	$-0.257934\pi$
$79$	3.61263	+	2.08575i	0.406453	+	0.234666i	−0.282812	+	0.959175i	$0.591267\pi$
$80$		0			0
$81$	0.687950	+	8.97367i	0.0764389	+	0.997074i
$82$		0			0
$83$	3.37411	+	12.5924i	0.370357	+	1.38219i	0.860011	+	0.510275i	$0.170456\pi$
$83$	3.37411	+	12.5924i	0.370357	+	1.38219i	−0.489654	+	0.871917i	$0.662877\pi$
$84$		0			0
$85$	−2.96169	+	11.0532i	−0.321241	+	1.19889i
$86$		0			0
$87$	−15.0793	−	1.69249i	−1.61667	−	0.181453i
$88$		0			0
$89$	7.33327			0.777325			0.388662	−	0.921380i	$-0.372937\pi$
$89$	7.33327			0.777325			0.388662	+	0.921380i	$0.372937\pi$
$90$		0			0
$91$	5.04210	−	5.04210i	0.528556	−	0.528556i
$92$		0			0
$93$	−0.868286	+	0.131254i	−0.0900371	+	0.0136104i
$94$		0			0
$95$	−5.58139	−	9.66725i	−0.572639	−	0.991839i
$96$		0			0
$97$	2.50134	−	4.33245i	0.253973	−	0.439893i	−0.710643	−	0.703552i	$-0.751596\pi$
$97$	2.50134	−	4.33245i	0.253973	−	0.439893i	0.964616	+	0.263659i	$0.0849294\pi$
$98$		0			0
$99$	7.28011	+	3.83968i	0.731679	+	0.385902i
$100$		0			0
$101$	−2.82933	−	10.5592i	−0.281529	−	1.05068i	−0.951339	−	0.308147i	$-0.900291\pi$
$101$	−2.82933	−	10.5592i	−0.281529	−	1.05068i	0.669810	−	0.742533i	$-0.266376\pi$
$102$		0			0
$103$	0.321949	+	0.557632i	0.0317226	+	0.0549451i	0.881451	−	0.472276i	$-0.156567\pi$
$103$	0.321949	+	0.557632i	0.0317226	+	0.0549451i	−0.849728	+	0.527221i	$0.823234\pi$
$104$		0			0
$105$	−18.3898	+	8.03277i	−1.79466	+	0.783918i
$106$		0			0
$107$	−3.74155	−	3.74155i	−0.361709	−	0.361709i	0.502733	−	0.864442i	$-0.332328\pi$
$107$	−3.74155	−	3.74155i	−0.361709	−	0.361709i	−0.864442	+	0.502733i	$0.832328\pi$
$108$		0			0
$109$	6.00859	−	6.00859i	0.575518	−	0.575518i	−0.358147	−	0.933665i	$-0.616591\pi$
$109$	6.00859	−	6.00859i	0.575518	−	0.575518i	0.933665	+	0.358147i	$0.116591\pi$
$110$		0			0
$111$	−1.33746	−	3.06191i	−0.126946	−	0.290623i
$112$		0			0
$113$	14.4387	−	8.33620i	1.35828	−	0.784204i	0.368889	−	0.929474i	$-0.379738\pi$
$113$	14.4387	−	8.33620i	1.35828	−	0.784204i	0.989392	+	0.145270i	$0.0464051\pi$
$114$		0			0
$115$	−9.12244	+	2.44435i	−0.850672	+	0.227937i
$116$		0			0
$117$	−3.88395	−	6.16953i	−0.359071	−	0.570374i
$118$		0			0
$119$	7.36453	+	4.25191i	0.675105	+	0.389772i
$120$		0			0
$121$	−3.00769	+	1.73649i	−0.273426	+	0.157863i
$122$		0			0
$123$	−0.386118	−	2.55430i	−0.0348151	−	0.230313i
$124$		0			0
$125$	−15.6093	−	15.6093i	−1.39613	−	1.39613i
$126$		0			0
$127$			17.9975i			1.59702i	0.601983	+	0.798509i	$0.294377\pi$
$127$			17.9975i			1.59702i	−0.601983	+	0.798509i	$0.705623\pi$
$128$		0			0
$129$	0.948984	−	8.45502i	0.0835533	−	0.744423i
$130$		0			0
$131$	−17.4121	−	4.66555i	−1.52130	−	0.407631i	−0.601131	−	0.799151i	$-0.705283\pi$
$131$	−17.4121	−	4.66555i	−1.52130	−	0.407631i	−0.920170	+	0.391520i	$0.871949\pi$
$132$		0			0
$133$	−8.01285	+	2.14704i	−0.694802	+	0.186172i
$134$		0			0
$135$	3.84026	+	20.1544i	0.330517	+	1.73462i
$136$		0			0
$137$	−0.396155	+	0.686161i	−0.0338458	+	0.0586227i	−0.882452	−	0.470402i	$-0.844109\pi$
$137$	−0.396155	+	0.686161i	−0.0338458	+	0.0586227i	0.848606	+	0.529025i	$0.177442\pi$
$138$		0			0
$139$	20.5134	+	5.49654i	1.73992	+	0.466211i	0.982430	−	0.186633i	$-0.0597576\pi$
$139$	20.5134	+	5.49654i	1.73992	+	0.466211i	0.757492	+	0.652844i	$0.226424\pi$
$140$		0			0
$141$	−8.82082	+	7.04056i	−0.742847	+	0.592922i
$142$		0			0
$143$	−6.66706			−0.557528
$144$		0			0
$145$	−34.5916			−2.87268
$146$		0			0
$147$	0.416819	+	2.75740i	0.0343787	+	0.227426i
$148$		0			0
$149$	−11.3030	−	3.02863i	−0.925977	−	0.248115i	−0.235839	−	0.971792i	$-0.575784\pi$
$149$	−11.3030	−	3.02863i	−0.925977	−	0.248115i	−0.690139	+	0.723677i	$0.742450\pi$
$150$		0			0
$151$	4.24025	−	7.34432i	0.345066	−	0.597673i	−0.640299	−	0.768125i	$-0.721190\pi$
$151$	4.24025	−	7.34432i	0.345066	−	0.597673i	0.985366	+	0.170453i	$0.0545230\pi$
$152$		0			0
$153$	5.90813	−	6.37840i	0.477644	−	0.515663i
$154$		0			0
$155$	−1.93368	+	0.518128i	−0.155317	+	0.0416170i
$156$		0			0
$157$	3.53516	+	0.947242i	0.282136	+	0.0755981i	0.397112	−	0.917770i	$-0.370012\pi$
$157$	3.53516	+	0.947242i	0.282136	+	0.0755981i	−0.114976	+	0.993368i	$0.536679\pi$
$158$		0			0
$159$	11.6270	−	5.07875i	0.922084	−	0.402771i
$160$		0			0
$161$			7.01840i			0.553127i
$162$		0			0
$163$	3.86060	+	3.86060i	0.302385	+	0.302385i	0.841946	−	0.539561i	$-0.181410\pi$
$163$	3.86060	+	3.86060i	0.302385	+	0.302385i	−0.539561	+	0.841946i	$0.681410\pi$
$164$		0			0
$165$	17.4690	+	6.84745i	1.35996	+	0.533073i
$166$		0			0
$167$	5.98224	−	3.45385i	0.462920	−	0.267267i	−0.250351	−	0.968155i	$-0.580546\pi$
$167$	5.98224	−	3.45385i	0.462920	−	0.267267i	0.713271	+	0.700888i	$0.247213\pi$
$168$		0			0
$169$	−6.14414	−	3.54732i	−0.472626	−	0.272871i
$170$		0			0
$171$	0.324387	+	8.47507i	0.0248065	+	0.648105i
$172$		0			0
$173$	3.86859	−	1.03659i	0.294123	−	0.0788101i	−0.108740	−	0.994070i	$-0.534682\pi$
$173$	3.86859	−	1.03659i	0.294123	−	0.0788101i	0.402863	+	0.915260i	$0.368015\pi$
$174$		0			0
$175$	−26.9127	+	15.5381i	−2.03441	+	1.17457i
$176$		0			0
$177$	2.64026	−	3.58063i	0.198454	−	0.269137i
$178$		0			0
$179$	−10.0625	+	10.0625i	−0.752109	+	0.752109i	−0.974872	−	0.222764i	$-0.928492\pi$
$179$	−10.0625	+	10.0625i	−0.752109	+	0.752109i	0.222764	+	0.974872i	$0.428492\pi$
$180$		0			0
$181$	15.0346	+	15.0346i	1.11751	+	1.11751i	0.992106	+	0.125405i	$0.0400229\pi$
$181$	15.0346	+	15.0346i	1.11751	+	1.11751i	0.125405	+	0.992106i	$0.459977\pi$
$182$		0			0
$183$	2.23673	−	19.9283i	0.165344	−	1.47314i
$184$		0			0
$185$	−3.80849	−	6.59651i	−0.280006	−	0.484985i
$186$		0			0
$187$	−2.05787	−	7.68009i	−0.150487	−	0.561624i
$188$		0			0
$189$	15.2058	+	1.11987i	1.10606	+	0.0814585i
$190$		0			0
$191$	10.9007	−	18.8806i	0.788749	−	1.36615i	−0.137984	−	0.990434i	$-0.544062\pi$
$191$	10.9007	−	18.8806i	0.788749	−	1.36615i	0.926734	−	0.375719i	$-0.122604\pi$
$192$		0			0
$193$	−2.34723	−	4.06553i	−0.168958	−	0.292643i	0.769096	−	0.639133i	$-0.220707\pi$
$193$	−2.34723	−	4.06553i	−0.168958	−	0.292643i	−0.938054	+	0.346490i	$0.887373\pi$
$194$		0			0
$195$	−10.3676	−	12.9892i	−0.742440	−	0.930173i
$196$		0			0
$197$	14.3226	−	14.3226i	1.02044	−	1.02044i	0.0206566	−	0.999787i	$-0.493424\pi$
$197$	14.3226	−	14.3226i	1.02044	−	1.02044i	0.999787	−	0.0206566i	$-0.00657567\pi$
$198$		0			0
$199$	14.4965			1.02763			0.513816	−	0.857901i	$-0.328232\pi$
$199$	14.4965			1.02763			0.513816	+	0.857901i	$0.328232\pi$
$200$		0			0
$201$	−10.0683	+	13.6542i	−0.710160	+	0.963096i
$202$		0			0
$203$	−6.65332	+	24.8305i	−0.466971	+	1.74276i
$204$		0			0
$205$	−1.52421	−	5.68844i	−0.106456	−	0.397298i
$206$		0			0
$207$	6.99702	+	1.59072i	0.486327	+	0.110563i
$208$		0			0
$209$	6.71710	+	3.87812i	0.464632	+	0.268255i
$210$		0			0
$211$	1.71268	−	6.39179i	0.117905	−	0.440029i	−0.881582	−	0.472030i	$-0.843521\pi$
$211$	1.71268	−	6.39179i	0.117905	−	0.440029i	0.999488	+	0.0320010i	$0.0101880\pi$
$212$		0			0
$213$	2.94178	−	7.50499i	0.201568	−	0.514234i
$214$		0			0
$215$		−	19.3957i		−	1.32277i
$216$		0			0
$217$			1.48769i			0.100991i
$218$		0			0
$219$	−3.10927	+	7.93229i	−0.210105	+	0.536014i
$220$		0			0
$221$	−1.82276	+	6.80265i	−0.122612	+	0.457596i
$222$		0			0
$223$	−1.59599	−	0.921443i	−0.106875	−	0.0617044i	0.445610	−	0.895227i	$-0.352987\pi$
$223$	−1.59599	−	0.921443i	−0.106875	−	0.0617044i	−0.552485	+	0.833523i	$0.686320\pi$
$224$		0			0
$225$	9.39099	+	30.3525i	0.626066	+	2.02350i
$226$		0			0
$227$	0.184084	+	0.687012i	0.0122181	+	0.0455986i	0.971766	−	0.235948i	$-0.0758194\pi$
$227$	0.184084	+	0.687012i	0.0122181	+	0.0455986i	−0.959548	+	0.281546i	$0.909153\pi$
$228$		0			0
$229$	1.98433	−	7.40562i	0.131128	−	0.489377i	−0.868856	−	0.495066i	$-0.835144\pi$
$229$	1.98433	−	7.40562i	0.131128	−	0.489377i	0.999984	+	0.00568843i	$0.00181069\pi$
$230$		0			0
$231$	8.27520	−	11.2226i	0.544468	−	0.738390i
$232$		0			0
$233$	1.36925			0.0897024			0.0448512	−	0.998994i	$-0.485719\pi$
$233$	1.36925			0.0897024			0.0448512	+	0.998994i	$0.485719\pi$
$234$		0			0
$235$	−18.1929	+	18.1929i	−1.18677	+	1.18677i
$236$		0			0
$237$	−4.50730	−	5.64701i	−0.292780	−	0.366812i
$238$		0			0
$239$	0.773627	+	1.33996i	0.0500418	+	0.0866749i	0.889961	−	0.456036i	$-0.150731\pi$
$239$	0.773627	+	1.33996i	0.0500418	+	0.0866749i	−0.839919	+	0.542711i	$0.817398\pi$
$240$		0			0
$241$	3.83660	−	6.64519i	0.247137	−	0.428054i	−0.715593	−	0.698517i	$-0.753844\pi$
$241$	3.83660	−	6.64519i	0.247137	−	0.428054i	0.962730	+	0.270463i	$0.0871769\pi$
$242$		0			0
$243$	4.56286	−	14.9057i	0.292707	−	0.956202i
$244$		0			0
$245$	1.64541	+	6.14075i	0.105121	+	0.392318i
$246$		0			0
$247$	−3.43505	−	5.94968i	−0.218567	−	0.378569i
$248$		0			0
$249$	2.51855	−	22.4391i	0.159606	−	1.42202i
$250$		0			0
$251$	5.46632	+	5.46632i	0.345031	+	0.345031i	0.858255	−	0.513224i	$-0.171549\pi$
$251$	5.46632	+	5.46632i	0.345031	+	0.345031i	−0.513224	+	0.858255i	$0.671549\pi$
$252$		0			0
$253$	4.64014	−	4.64014i	0.291723	−	0.291723i
$254$		0			0
$255$	11.7627	−	15.9522i	0.736609	−	0.998965i
$256$		0			0
$257$	−20.5918	+	11.8887i	−1.28448	+	0.741596i	−0.977664	−	0.210172i	$-0.932598\pi$
$257$	−20.5918	+	11.8887i	−1.28448	+	0.741596i	−0.306818	+	0.951768i	$0.599264\pi$
$258$		0			0
$259$	−5.46761	+	1.46504i	−0.339741	+	0.0910333i
$260$		0			0
$261$	23.2469	+	12.2609i	1.43895	+	0.758929i
$262$		0			0
$263$	6.13704	+	3.54322i	0.378426	+	0.218484i	0.677133	−	0.735860i	$-0.263222\pi$
$263$	6.13704	+	3.54322i	0.378426	+	0.218484i	−0.298707	+	0.954345i	$0.596555\pi$
$264$		0			0
$265$	25.0490	−	14.4621i	1.53875	−	0.888397i
$266$		0			0
$267$	−11.8256	−	4.63535i	−0.723713	−	0.283679i
$268$		0			0
$269$	20.6616	+	20.6616i	1.25976	+	1.25976i	0.951207	+	0.308553i	$0.0998448\pi$
$269$	20.6616	+	20.6616i	1.25976	+	1.25976i	0.308553	+	0.951207i	$0.400155\pi$
$270$		0			0
$271$		−	16.6901i		−	1.01385i	−0.861989	−	0.506927i	$-0.830782\pi$
$271$		−	16.6901i		−	1.01385i	0.861989	−	0.506927i	$-0.169218\pi$
$272$		0			0
$273$	−11.3180	+	4.94374i	−0.684994	+	0.299209i
$274$		0			0
$275$	28.0659	+	7.52024i	1.69244	+	0.453487i
$276$		0			0
$277$	4.49217	−	1.20367i	0.269908	−	0.0723217i	−0.121326	−	0.992613i	$-0.538715\pi$
$277$	4.49217	−	1.20367i	0.269908	−	0.0723217i	0.391235	+	0.920291i	$0.372048\pi$
$278$		0			0
$279$	1.48316	+	0.337184i	0.0887942	+	0.0201867i
$280$		0			0
$281$	−11.4153	+	19.7719i	−0.680979	+	1.17949i	0.293703	+	0.955897i	$0.405112\pi$
$281$	−11.4153	+	19.7719i	−0.680979	+	1.17949i	−0.974682	+	0.223594i	$0.928221\pi$
$282$		0			0
$283$	24.9438	+	6.68368i	1.48276	+	0.397303i	0.907284	−	0.420518i	$-0.138152\pi$
$283$	24.9438	+	6.68368i	1.48276	+	0.397303i	0.575472	+	0.817822i	$0.304818\pi$
$284$		0			0
$285$	2.88985	+	19.1173i	0.171180	+	1.13241i
$286$		0			0
$287$	−4.37643			−0.258333
$288$		0			0
$289$	8.60110			0.505947
$290$		0			0
$291$	−6.77217	+	5.40538i	−0.396992	+	0.316869i
$292$		0			0
$293$	−2.76706	−	0.741431i	−0.161653	−	0.0433149i	0.177085	−	0.984196i	$-0.443333\pi$
$293$	−2.76706	−	0.741431i	−0.161653	−	0.0433149i	−0.338738	+	0.940881i	$0.610000\pi$
$294$		0			0
$295$	5.07090	−	8.78306i	0.295239	−	0.511370i
$296$		0			0
$297$	−9.31280	−	10.7936i	−0.540383	−	0.626307i
$298$		0			0
$299$	−5.61438	+	1.50437i	−0.324688	+	0.0869998i
$300$		0			0
$301$	−13.9226	−	3.73054i	−0.802484	−	0.215025i
$302$		0			0
$303$	−2.11190	+	18.8161i	−0.121326	+	1.08096i
$304$		0			0
$305$		−	45.7152i		−	2.61764i
$306$		0			0
$307$	7.67329	+	7.67329i	0.437938	+	0.437938i	0.891317	−	0.453380i	$-0.149782\pi$
$307$	7.67329	+	7.67329i	0.437938	+	0.437938i	−0.453380	+	0.891317i	$0.649782\pi$
$308$		0			0
$309$	−0.166694	−	1.10274i	−0.00948289	−	0.0627325i
$310$		0			0
$311$	−15.0777	+	8.70513i	−0.854980	+	0.493623i	−0.862328	−	0.506350i	$-0.830994\pi$
$311$	−15.0777	+	8.70513i	−0.854980	+	0.493623i	0.00734815	+	0.999973i	$0.497661\pi$
$312$		0			0
$313$	−21.3027	−	12.2991i	−1.20410	−	0.695189i	−0.242638	−	0.970117i	$-0.578013\pi$
$313$	−21.3027	−	12.2991i	−1.20410	−	0.695189i	−0.961465	+	0.274928i	$0.911346\pi$
$314$		0			0
$315$	34.7328	−	1.32941i	1.95697	−	0.0749039i
$316$		0			0
$317$	−7.99342	+	2.14183i	−0.448955	+	0.120297i	−0.476211	−	0.879331i	$-0.657990\pi$
$317$	−7.99342	+	2.14183i	−0.448955	+	0.120297i	0.0272552	+	0.999629i	$0.491323\pi$
$318$		0			0
$319$	20.8152	−	12.0177i	1.16543	−	0.672860i
$320$		0			0
$321$	3.66857	+	8.39862i	0.204759	+	0.468765i
$322$		0			0
$323$	5.79343	−	5.79343i	0.322355	−	0.322355i
$324$		0			0
$325$	−18.1983	−	18.1983i	−1.00946	−	1.00946i
$326$		0			0
$327$	−13.4874	+	5.89138i	−0.745856	+	0.325794i
$328$		0			0
$329$	9.55998	+	16.5584i	0.527059	+	0.912893i
$330$		0			0
$331$	−6.84245	−	25.5364i	−0.376095	−	1.40361i	−0.851738	−	0.523968i	$-0.824451\pi$
$331$	−6.84245	−	25.5364i	−0.376095	−	1.40361i	0.475643	−	0.879639i	$-0.342216\pi$
$332$		0			0
$333$	0.221347	+	5.78301i	0.0121298	+	0.316907i
$334$		0			0
$335$	−19.3372	+	33.4930i	−1.05650	+	1.82992i
$336$		0			0
$337$	12.3368	+	21.3679i	0.672026	+	1.16398i	0.977329	+	0.211728i	$0.0679092\pi$
$337$	12.3368	+	21.3679i	0.672026	+	1.16398i	−0.305302	+	0.952256i	$0.598757\pi$
$338$		0			0
$339$	−28.5531	+	4.31619i	−1.55079	+	0.234423i
$340$		0			0
$341$	0.983569	−	0.983569i	0.0532632	−	0.0532632i
$342$		0			0
$343$	−15.8156			−0.853964
$344$		0			0
$345$	16.2558	+	1.82454i	0.875185	+	0.0982300i
$346$		0			0
$347$	−6.16895	+	23.0228i	−0.331166	+	1.23593i	0.576799	+	0.816886i	$0.304301\pi$
$347$	−6.16895	+	23.0228i	−0.331166	+	1.23593i	−0.907966	+	0.419044i	$0.862365\pi$
$348$		0			0
$349$	6.94337	+	25.9130i	0.371670	+	1.38709i	0.858149	+	0.513400i	$0.171614\pi$
$349$	6.94337	+	25.9130i	0.371670	+	1.38709i	−0.486479	+	0.873692i	$0.661719\pi$
$350$		0			0
$351$	2.36348	+	12.4040i	0.126153	+	0.662075i
$352$		0			0
$353$	5.54075	+	3.19895i	0.294904	+	0.170263i	0.640151	−	0.768249i	$-0.278872\pi$
$353$	5.54075	+	3.19895i	0.294904	+	0.170263i	−0.345247	+	0.938512i	$0.612205\pi$
$354$		0			0
$355$	4.75614	−	17.7502i	0.252430	−	0.942080i
$356$		0			0
$357$	−9.18835	−	11.5117i	−0.486299	−	0.609264i
$358$		0			0
$359$		−	17.2363i		−	0.909697i	−0.890569	−	0.454849i	$-0.849693\pi$
$359$		−	17.2363i		−	0.909697i	0.890569	−	0.454849i	$-0.150307\pi$
$360$		0			0
$361$		−	11.0076i		−	0.579345i
$362$		0			0
$363$	5.94781	−	0.899094i	0.312179	−	0.0471902i
$364$		0			0
$365$	−5.02693	+	18.7608i	−0.263121	+	0.981983i
$366$		0			0
$367$	1.26366	+	0.729575i	0.0659625	+	0.0380835i	0.532619	−	0.846355i	$-0.321208\pi$
$367$	1.26366	+	0.729575i	0.0659625	+	0.0380835i	−0.466656	+	0.884439i	$0.654541\pi$
$368$		0			0
$369$	−0.991918	+	4.36310i	−0.0516372	+	0.227134i
$370$		0			0
$371$	−5.56323	−	20.7623i	−0.288829	−	1.07792i
$372$		0			0
$373$	−2.08247	+	7.77189i	−0.107826	+	0.402413i	−0.998650	−	0.0519349i	$-0.983461\pi$
$373$	−2.08247	+	7.77189i	−0.107826	+	0.402413i	0.890824	+	0.454348i	$0.150128\pi$
$374$		0			0
$375$	15.3048	+	35.0379i	0.790335	+	1.80935i
$376$		0			0
$377$	−21.2893			−1.09646
$378$		0			0
$379$	16.4748	−	16.4748i	0.846255	−	0.846255i	−0.143409	−	0.989664i	$-0.545806\pi$
$379$	16.4748	−	16.4748i	0.846255	−	0.846255i	0.989664	+	0.143409i	$0.0458063\pi$
$380$		0			0
$381$	11.3762	−	29.0226i	0.582819	−	1.48687i
$382$		0			0
$383$	5.19654	+	9.00067i	0.265531	+	0.459913i	0.967703	−	0.252095i	$-0.0811195\pi$
$383$	5.19654	+	9.00067i	0.265531	+	0.459913i	−0.702172	+	0.712008i	$0.747786\pi$
$384$		0			0
$385$	15.8934	−	27.5282i	0.810004	−	1.40297i
$386$		0			0
$387$	−6.87473	+	13.0346i	−0.349462	+	0.662588i
$388$		0			0
$389$	6.24292	+	23.2989i	0.316529	+	1.18130i	0.922558	+	0.385859i	$0.126095\pi$
$389$	6.24292	+	23.2989i	0.316529	+	1.18130i	−0.606029	+	0.795442i	$0.707239\pi$
$390$		0			0
$391$	−3.46590	−	6.00311i	−0.175278	−	0.303590i
$392$		0			0
$393$	25.1295	+	18.5298i	1.26761	+	0.934704i
$394$		0			0
$395$	−11.6469	−	11.6469i	−0.586019	−	0.586019i
$396$		0			0
$397$	8.37131	−	8.37131i	0.420144	−	0.420144i	−0.465109	−	0.885253i	$-0.653985\pi$
$397$	8.37131	−	8.37131i	0.420144	−	0.420144i	0.885253	+	0.465109i	$0.153985\pi$
$398$		0			0
$399$	14.2786	+	1.60262i	0.714824	+	0.0802312i
$400$		0			0
$401$	−3.16266	+	1.82596i	−0.157936	+	0.0911842i	−0.576885	−	0.816825i	$-0.695732\pi$
$401$	−3.16266	+	1.82596i	−0.157936	+	0.0911842i	0.418949	+	0.908010i	$0.362399\pi$
$402$		0			0
$403$	−1.19008	+	0.318880i	−0.0592820	+	0.0158846i
$404$		0			0
$405$	6.54681	−	34.9283i	0.325313	−	1.73560i
$406$		0			0
$407$	4.58345	+	2.64626i	0.227193	+	0.131170i
$408$		0			0
$409$	−12.1263	+	7.00113i	−0.599607	+	0.346184i	−0.768887	−	0.639385i	$-0.779189\pi$
$409$	−12.1263	+	7.00113i	−0.599607	+	0.346184i	0.169280	+	0.985568i	$0.445856\pi$
$410$		0			0
$411$	1.07256	−	0.856089i	0.0529054	−	0.0422277i
$412$		0			0
$413$	−5.32931	−	5.32931i	−0.262238	−	0.262238i
$414$		0			0
$415$		−	51.4750i		−	2.52681i
$416$		0			0
$417$	−29.6053	−	21.8302i	−1.44978	−	1.06903i
$418$		0			0
$419$	−0.601258	−	0.161107i	−0.0293734	−	0.00787057i	0.244102	−	0.969749i	$-0.421507\pi$
$419$	−0.601258	−	0.161107i	−0.0293734	−	0.00787057i	−0.273476	+	0.961879i	$0.588173\pi$
$420$		0			0
$421$	17.3705	−	4.65440i	0.846585	−	0.226842i	0.190649	−	0.981658i	$-0.438941\pi$
$421$	17.3705	−	4.65440i	0.846585	−	0.226842i	0.655936	+	0.754816i	$0.272274\pi$
$422$		0			0
$423$	18.6747	−	5.77791i	0.907995	−	0.280932i
$424$		0			0
$425$	15.3463	−	26.5806i	0.744407	−	1.28935i
$426$		0			0
$427$	−32.8152	−	8.79280i	−1.58804	−	0.425514i
$428$		0			0
$429$	10.7513	+	4.21424i	0.519075	+	0.203465i
$430$		0			0
$431$	−6.34380			−0.305570			−0.152785	−	0.988259i	$-0.548824\pi$
$431$	−6.34380			−0.305570			−0.152785	+	0.988259i	$0.548824\pi$
$432$		0			0
$433$	26.7319			1.28465			0.642327	−	0.766430i	$-0.277969\pi$
$433$	26.7319			1.28465			0.642327	+	0.766430i	$0.277969\pi$
$434$		0			0
$435$	55.7822	+	21.8653i	2.67455	+	1.04836i
$436$		0			0
$437$	6.53158	+	1.75013i	0.312448	+	0.0837202i
$438$		0			0
$439$	−0.347800	+	0.602407i	−0.0165996	+	0.0287513i	−0.874206	−	0.485555i	$-0.838617\pi$
$439$	−0.347800	+	0.602407i	−0.0165996	+	0.0287513i	0.857606	+	0.514307i	$0.171951\pi$
$440$		0			0
$441$	1.07079	−	4.71003i	0.0509899	−	0.224287i
$442$		0			0
$443$	15.8656	−	4.25119i	0.753800	−	0.201980i	0.138597	−	0.990349i	$-0.455741\pi$
$443$	15.8656	−	4.25119i	0.753800	−	0.201980i	0.615203	+	0.788369i	$0.289074\pi$
$444$		0			0
$445$	−27.9688	−	7.49422i	−1.32585	−	0.355260i
$446$		0			0
$447$	16.3127	+	12.0285i	0.771565	+	0.568931i
$448$		0			0
$449$			12.0759i			0.569896i	0.958543	+	0.284948i	$0.0919763\pi$
$449$			12.0759i			0.569896i	−0.958543	+	0.284948i	$0.908024\pi$
$450$		0			0
$451$	2.89343	+	2.89343i	0.136247	+	0.136247i
$452$		0			0
$453$	−11.4801	+	9.16314i	−0.539383	+	0.430522i
$454$		0			0
$455$	−24.3831	+	14.0776i	−1.14310	+	0.659969i
$456$		0			0
$457$	−10.6069	−	6.12391i	−0.496171	−	0.286464i	0.230960	−	0.972963i	$-0.425813\pi$
$457$	−10.6069	−	6.12391i	−0.496171	−	0.286464i	−0.727131	+	0.686499i	$0.759147\pi$
$458$		0			0
$459$	−13.5592	+	6.55124i	−0.632888	+	0.305786i
$460$		0			0
$461$	−30.3154	+	8.12298i	−1.41193	+	0.378325i	−0.882613	−	0.470101i	$-0.844217\pi$
$461$	−30.3154	+	8.12298i	−1.41193	+	0.378325i	−0.529314	+	0.848426i	$0.677551\pi$
$462$		0			0
$463$	−30.9163	+	17.8495i	−1.43680	+	0.829538i	−0.997626	−	0.0688633i	$-0.978063\pi$
$463$	−30.9163	+	17.8495i	−1.43680	+	0.829538i	−0.439176	+	0.898401i	$0.644729\pi$
$464$		0			0
$465$	3.44574	+	0.386747i	0.159793	+	0.0179350i
$466$		0			0
$467$	7.64586	−	7.64586i	0.353808	−	0.353808i	−0.507716	−	0.861524i	$-0.669510\pi$
$467$	7.64586	−	7.64586i	0.353808	−	0.353808i	0.861524	+	0.507716i	$0.169510\pi$
$468$		0			0
$469$	20.3226	+	20.3226i	0.938411	+	0.938411i
$470$		0			0
$471$	−5.10201	−	3.76208i	−0.235088	−	0.173348i
$472$		0			0
$473$	6.73836	+	11.6712i	0.309830	+	0.536641i
$474$		0			0
$475$	7.74926	+	28.9206i	0.355560	+	1.32697i
$476$		0			0
$477$	−21.9599	+	0.840526i	−1.00548	+	0.0384851i
$478$		0			0
$479$	3.03628	−	5.25898i	0.138731	−	0.240289i	−0.788286	−	0.615310i	$-0.789031\pi$
$479$	3.03628	−	5.25898i	0.138731	−	0.240289i	0.927017	+	0.375020i	$0.122364\pi$
$480$		0			0
$481$	−2.34393	−	4.05980i	−0.106874	−	0.185111i
$482$		0			0
$483$	4.43632	−	11.3178i	0.201859	−	0.514978i
$484$		0			0
$485$	−13.9675	+	13.9675i	−0.634234	+	0.634234i
$486$		0			0
$487$	7.15811			0.324365			0.162183	−	0.986761i	$-0.448147\pi$
$487$	7.15811			0.324365			0.162183	+	0.986761i	$0.448147\pi$
$488$		0			0
$489$	−3.78529	−	8.66584i	−0.171177	−	0.391883i
$490$		0			0
$491$	7.24226	−	27.0285i	0.326838	−	1.21978i	−0.585612	−	0.810591i	$-0.699146\pi$
$491$	7.24226	−	27.0285i	0.326838	−	1.21978i	0.912451	−	0.409187i	$-0.134187\pi$
$492$		0			0
$493$	−6.57122	−	24.5241i	−0.295953	−	1.10451i
$494$		0			0
$495$	−23.8421	−	22.0843i	−1.07162	−	0.992614i
$496$		0			0
$497$	−11.8266	−	6.82809i	−0.530495	−	0.306282i
$498$		0			0
$499$	−11.4708	+	42.8097i	−0.513505	+	1.91643i	−0.134937	+	0.990854i	$0.543083\pi$
$499$	−11.4708	+	42.8097i	−0.513505	+	1.91643i	−0.378568	+	0.925573i	$0.623584\pi$
$500$		0			0
$501$	−11.8301	+	1.78828i	−0.528529	+	0.0798945i
$502$		0			0
$503$			3.93000i			0.175230i	0.996154	+	0.0876151i	$0.0279245\pi$
$503$			3.93000i			0.175230i	−0.996154	+	0.0876151i	$0.972075\pi$
$504$		0			0
$505$			43.1638i			1.92077i
$506$		0			0
$507$	7.66573	+	9.60408i	0.340447	+	0.426532i
$508$		0			0
$509$	10.8415	−	40.4609i	0.480539	−	1.79340i	−0.118819	−	0.992916i	$-0.537911\pi$
$509$	10.8415	−	40.4609i	0.480539	−	1.79340i	0.599358	−	0.800481i	$-0.295423\pi$
$510$		0			0
$511$	12.4999	+	7.21684i	0.552965	+	0.319254i
$512$		0			0
$513$	4.83397	−	13.8719i	0.213425	−	0.612458i
$514$		0			0
$515$	−0.658030	−	2.45580i	−0.0289963	−	0.108216i
$516$		0			0
$517$	4.62691	−	17.2679i	0.203491	−	0.759441i
$518$		0			0
$519$	−6.89368	−	0.773740i	−0.302599	−	0.0339634i
$520$		0			0
$521$	−26.1826			−1.14708			−0.573540	−	0.819178i	$-0.694430\pi$
$521$	−26.1826			−1.14708			−0.573540	+	0.819178i	$0.694430\pi$
$522$		0			0
$523$	−7.29036	+	7.29036i	−0.318785	+	0.318785i	−0.848300	−	0.529515i	$-0.822374\pi$
$523$	−7.29036	+	7.29036i	−0.318785	+	0.318785i	0.529515	+	0.848300i	$0.322374\pi$
$524$		0			0
$525$	53.2208	−	8.04507i	2.32275	−	0.351116i
$526$		0			0
$527$	−0.734665	−	1.27248i	−0.0320025	−	0.0554300i
$528$		0			0
$529$	−8.63952	+	14.9641i	−0.375631	+	0.650612i
$530$		0			0
$531$	−6.52096	+	4.10519i	−0.282986	+	0.178150i
$532$		0			0
$533$	−0.938073	−	3.50093i	−0.0406324	−	0.151642i
$534$		0			0
$535$	10.4465	+	18.0938i	0.451640	+	0.782263i
$536$		0			0
$537$	22.5873	−	9.86624i	0.974712	−	0.425760i
$538$		0			0
$539$	−3.12350	−	3.12350i	−0.134539	−	0.134539i
$540$		0			0
$541$	13.6906	−	13.6906i	0.588607	−	0.588607i	−0.348647	−	0.937254i	$-0.613359\pi$
$541$	13.6906	−	13.6906i	0.588607	−	0.588607i	0.937254	+	0.348647i	$0.113359\pi$
$542$		0			0
$543$	−14.7413	−	33.7479i	−0.632609	−	1.44826i
$544$		0			0
$545$	−29.0570	+	16.7761i	−1.24466	+	0.718607i
$546$		0			0
$547$	−29.0133	+	7.77408i	−1.24052	+	0.332396i	−0.818666	−	0.574269i	$-0.805286\pi$
$547$	−29.0133	+	7.77408i	−1.24052	+	0.332396i	−0.421851	+	0.906665i	$0.638620\pi$
$548$		0			0
$549$	−16.2036	+	30.7224i	−0.691552	+	1.31120i
$550$		0			0
$551$	21.4491	+	12.3836i	0.913762	+	0.527561i
$552$		0			0
$553$	−10.6005	+	6.12021i	−0.450780	+	0.260258i
$554$		0			0
$555$	1.97191	+	13.0448i	0.0837027	+	0.553721i
$556$		0			0
$557$	−1.85284	−	1.85284i	−0.0785074	−	0.0785074i	0.666763	−	0.745270i	$-0.267679\pi$
$557$	−1.85284	−	1.85284i	−0.0785074	−	0.0785074i	−0.745270	+	0.666763i	$0.767679\pi$
$558$		0			0
$559$		−	11.9370i		−	0.504882i
$560$		0			0
$561$	−1.53606	+	13.6856i	−0.0648526	+	0.577808i
$562$		0			0
$563$	−26.1400	−	7.00420i	−1.10167	−	0.295192i	−0.338226	−	0.941065i	$-0.609827\pi$
$563$	−26.1400	−	7.00420i	−1.10167	−	0.295192i	−0.763445	+	0.645873i	$0.776494\pi$
$564$		0			0
$565$	−63.5879	+	17.0383i	−2.67516	+	0.716808i
$566$		0			0
$567$	−23.8130	−	11.4175i	−1.00005	−	0.479489i
$568$		0			0
$569$	5.84691	−	10.1271i	0.245115	−	0.424552i	−0.717049	−	0.697023i	$-0.754508\pi$
$569$	5.84691	−	10.1271i	0.245115	−	0.424552i	0.962164	+	0.272471i	$0.0878409\pi$
$570$		0			0
$571$	−44.1127	−	11.8200i	−1.84606	−	0.494650i	−0.846756	−	0.531982i	$-0.821447\pi$
$571$	−44.1127	−	11.8200i	−1.84606	−	0.494650i	−0.999303	+	0.0373319i	$0.988114\pi$
$572$		0			0
$573$	−29.5128	+	23.5564i	−1.23292	+	0.984082i
$574$		0			0
$575$	25.3314			1.05639
$576$		0			0
$577$	−32.6884			−1.36083			−0.680417	−	0.732825i	$-0.738202\pi$
$577$	−32.6884			−1.36083			−0.680417	+	0.732825i	$0.738202\pi$
$578$		0			0
$579$	1.21532	+	8.03972i	0.0505068	+	0.334119i
$580$		0			0
$581$	−36.9497	−	9.90064i	−1.53293	−	0.410748i
$582$		0			0
$583$	−10.0487	+	17.4048i	−0.416174	+	0.720834i
$584$		0			0
$585$	8.50830	+	27.4996i	0.351775	+	1.13697i
$586$		0			0
$587$	−28.3101	+	7.58567i	−1.16848	+	0.313094i	−0.790349	−	0.612657i	$-0.790101\pi$
$587$	−28.3101	+	7.58567i	−1.16848	+	0.313094i	−0.378134	+	0.925751i	$0.623434\pi$
$588$		0			0
$589$	1.38450	+	0.370975i	0.0570472	+	0.0152858i
$590$		0			0
$591$	−32.1498	+	14.0432i	−1.32247	+	0.577661i
$592$		0			0
$593$			43.9681i			1.80555i	0.430111	+	0.902776i	$0.358474\pi$
$593$			43.9681i			1.80555i	−0.430111	+	0.902776i	$0.641526\pi$
$594$		0			0
$595$	−23.7428	−	23.7428i	−0.973360	−	0.973360i
$596$		0			0
$597$	−23.3770	−	9.16323i	−0.956756	−	0.375026i
$598$		0			0
$599$	−2.81411	+	1.62473i	−0.114982	+	0.0663846i	−0.556388	−	0.830923i	$-0.687813\pi$
$599$	−2.81411	+	1.62473i	−0.114982	+	0.0663846i	0.441406	+	0.897307i	$0.354480\pi$
$600$		0			0
$601$	12.6206	+	7.28651i	0.514806	+	0.297223i	0.734807	−	0.678276i	$-0.237273\pi$
$601$	12.6206	+	7.28651i	0.514806	+	0.297223i	−0.220001	+	0.975500i	$0.570606\pi$
$602$		0			0
$603$	24.8668	−	15.6546i	1.01266	−	0.637504i
$604$		0			0
$605$	13.2458	−	3.54920i	0.538519	−	0.144296i
$606$		0			0
$607$	−32.0317	+	18.4935i	−1.30013	+	0.750629i	−0.980426	−	0.196889i	$-0.936916\pi$
$607$	−32.0317	+	18.4935i	−1.30013	+	0.750629i	−0.319702	+	0.947518i	$0.603583\pi$
$608$		0			0
$609$	26.4244	−	35.8359i	1.07077	−	1.45214i
$610$		0			0
$611$	−11.1967	+	11.1967i	−0.452972	+	0.452972i
$612$		0			0
$613$	3.34985	+	3.34985i	0.135299	+	0.135299i	0.771513	−	0.636214i	$-0.219500\pi$
$613$	3.34985	+	3.34985i	0.135299	+	0.135299i	−0.636214	+	0.771513i	$0.719500\pi$
$614$		0			0
$615$	−1.13772	+	10.1366i	−0.0458774	+	0.408747i
$616$		0			0
$617$	−4.04358	−	7.00369i	−0.162789	−	0.281958i	0.773079	−	0.634309i	$-0.218715\pi$
$617$	−4.04358	−	7.00369i	−0.162789	−	0.281958i	−0.935868	+	0.352352i	$0.885382\pi$
$618$		0			0
$619$	−11.6692	−	43.5499i	−0.469023	−	1.75042i	−0.643194	−	0.765703i	$-0.722391\pi$
$619$	−11.6692	−	43.5499i	−0.469023	−	1.75042i	0.174171	−	0.984715i	$-0.444275\pi$
$620$		0			0
$621$	−10.2778	−	6.98798i	−0.412436	−	0.280418i
$622$		0			0
$623$	−10.7590	+	18.6351i	−0.431049	+	0.746599i
$624$		0			0
$625$	17.1046	+	29.6260i	0.684182	+	1.18504i
$626$		0			0
$627$	−8.38059	−	10.4997i	−0.334689	−	0.419318i
$628$		0			0
$629$	3.95318	−	3.95318i	0.157624	−	0.157624i
$630$		0			0
$631$	3.49919			0.139300			0.0696502	−	0.997571i	$-0.477812\pi$
$631$	3.49919			0.139300			0.0696502	+	0.997571i	$0.477812\pi$
$632$		0			0
$633$	−6.80209	+	9.22477i	−0.270359	+	0.366652i
$634$		0			0
$635$	18.3925	−	68.6417i	0.729883	−	2.72396i
$636$		0			0
$637$	1.01266	+	3.77930i	0.0401231	+	0.149741i
$638$		0			0
$639$	−9.48779	+	10.2430i	−0.375331	+	0.405206i
$640$		0			0
$641$	4.01739	+	2.31944i	0.158677	+	0.0916125i	0.577236	−	0.816577i	$-0.304131\pi$
$641$	4.01739	+	2.31944i	0.158677	+	0.0916125i	−0.418559	+	0.908190i	$0.637465\pi$
$642$		0			0
$643$	10.6535	−	39.7595i	0.420134	−	1.56796i	−0.354190	−	0.935173i	$-0.615243\pi$
$643$	10.6535	−	39.7595i	0.420134	−	1.56796i	0.774324	−	0.632789i	$-0.218090\pi$
$644$		0			0
$645$	−12.2600	+	31.2773i	−0.482736	+	1.23154i
$646$		0			0
$647$			2.08960i			0.0821505i	0.999156	+	0.0410752i	$0.0130783\pi$
$647$			2.08960i			0.0821505i	−0.999156	+	0.0410752i	$0.986922\pi$
$648$		0			0
$649$			7.04684i			0.276613i
$650$		0			0
$651$	0.940365	−	2.39903i	0.0368558	−	0.0940255i
$652$		0			0
$653$	4.75454	−	17.7442i	0.186059	−	0.694383i	−0.808342	−	0.588713i	$-0.799635\pi$
$653$	4.75454	−	17.7442i	0.186059	−	0.694383i	0.994401	−	0.105670i	$-0.0336987\pi$
$654$		0			0
$655$	61.6410	+	35.5885i	2.40851	+	1.39056i
$656$		0			0
$657$	10.0280	−	10.8262i	0.391228	−	0.422369i
$658$		0			0
$659$	7.84088	+	29.2626i	0.305437	+	1.13991i	0.932568	+	0.360994i	$0.117562\pi$
$659$	7.84088	+	29.2626i	0.305437	+	1.13991i	−0.627131	+	0.778914i	$0.715771\pi$
$660$		0			0
$661$	12.5011	−	46.6546i	0.486235	−	1.81465i	−0.0881985	−	0.996103i	$-0.528111\pi$
$661$	12.5011	−	46.6546i	0.486235	−	1.81465i	0.574434	−	0.818551i	$-0.305222\pi$
$662$		0			0
$663$	7.23932	−	9.81773i	0.281152	−	0.381289i
$664$		0			0
$665$	32.7549			1.27018
$666$		0			0
$667$	14.8169	−	14.8169i	0.573714	−	0.573714i
$668$		0			0
$669$	1.99123	+	2.49473i	0.0769854	+	0.0964519i
$670$		0			0
$671$	15.8822	+	27.5087i	0.613124	+	1.06196i
$672$		0			0
$673$	8.92590	−	15.4601i	0.344068	−	0.595944i	−0.641116	−	0.767444i	$-0.721528\pi$
$673$	8.92590	−	15.4601i	0.344068	−	0.595944i	0.985184	+	0.171500i	$0.0548615\pi$
$674$		0			0
$675$	4.04192	−	54.8822i	0.155574	−	2.11241i
$676$		0			0
$677$	0.575049	+	2.14611i	0.0221009	+	0.0824818i	0.976095	−	0.217342i	$-0.0697387\pi$
$677$	0.575049	+	2.14611i	0.0221009	+	0.0824818i	−0.953995	+	0.299824i	$0.903072\pi$
$678$		0			0
$679$	7.33966	+	12.7127i	0.281670	+	0.487867i
$680$		0			0
$681$	0.137406	−	1.22423i	0.00526543	−	0.0469126i
$682$		0			0
$683$	−0.857818	−	0.857818i	−0.0328235	−	0.0328235i	0.690505	−	0.723328i	$-0.257389\pi$
$683$	−0.857818	−	0.857818i	−0.0328235	−	0.0328235i	−0.723328	+	0.690505i	$0.757389\pi$
$684$		0			0
$685$	2.21214	−	2.21214i	0.0845216	−	0.0845216i
$686$		0			0
$687$	−7.88099	+	10.6879i	−0.300679	+	0.407771i
$688$		0			0
$689$	15.4163	−	8.90063i	0.587316	−	0.339087i
$690$		0			0
$691$	37.8791	−	10.1497i	1.44099	−	0.386112i	0.548109	−	0.836407i	$-0.315348\pi$
$691$	37.8791	−	10.1497i	1.44099	−	0.386112i	0.892880	+	0.450295i	$0.148681\pi$
$692$		0			0
$693$	−20.4383	+	12.8667i	−0.776386	+	0.488764i
$694$		0			0
$695$	−72.6201	−	41.9272i	−2.75464	−	1.59039i
$696$		0			0
$697$	3.74334	−	2.16122i	0.141789	−	0.0818619i
$698$		0			0
$699$	−2.20804	−	0.865499i	−0.0835156	−	0.0327362i
$700$		0			0
$701$	−14.3403	−	14.3403i	−0.541627	−	0.541627i	0.382379	−	0.924006i	$-0.375105\pi$
$701$	−14.3403	−	14.3403i	−0.541627	−	0.541627i	−0.924006	+	0.382379i	$0.875105\pi$
$702$		0			0
$703$			5.45369i			0.205690i
$704$		0			0
$705$	40.8374	−	17.8380i	1.53802	−	0.671817i
$706$		0			0
$707$	30.9838	+	8.30208i	1.16527	+	0.312232i
$708$		0			0
$709$	−4.26177	+	1.14194i	−0.160054	+	0.0428864i	−0.337956	−	0.941162i	$-0.609736\pi$
$709$	−4.26177	+	1.14194i	−0.160054	+	0.0428864i	0.177902	+	0.984048i	$0.443069\pi$
$710$		0			0
$711$	3.69896	+	11.9554i	0.138722	+	0.448361i
$712$		0			0
$713$	0.606335	−	1.05020i	0.0227074	−	0.0393304i
$714$		0			0
$715$	25.4279	+	6.81339i	0.950951	+	0.254806i
$716$		0			0
$717$	−0.400557	−	2.64982i	−0.0149591	−	0.0989593i
$718$		0			0
$719$	49.2509			1.83675			0.918374	−	0.395714i	$-0.129503\pi$
$719$	49.2509			1.83675			0.918374	+	0.395714i	$0.129503\pi$
$720$		0			0
$721$	−1.88938			−0.0703644
$722$		0			0
$723$	−10.3873	+	8.29086i	−0.386307	+	0.308340i
$724$		0			0
$725$	89.6203	+	24.0137i	3.32841	+	0.891846i
$726$		0			0
$727$	2.18154	−	3.77855i	0.0809090	−	0.140139i	−0.822732	−	0.568430i	$-0.807551\pi$
$727$	2.18154	−	3.77855i	0.0809090	−	0.140139i	0.903641	+	0.428291i	$0.140884\pi$
$728$		0			0
$729$	−16.7799	+	21.1527i	−0.621478	+	0.783432i
$730$		0			0
$731$	13.7508	−	3.68451i	0.508591	−	0.136277i
$732$		0			0
$733$	30.7314	+	8.23445i	1.13509	+	0.304146i	0.776975	−	0.629532i	$-0.216753\pi$
$733$	30.7314	+	8.23445i	1.13509	+	0.304146i	0.358114	+	0.933678i	$0.383420\pi$
$734$		0			0
$735$	1.22818	−	10.9426i	0.0453023	−	0.403623i
$736$		0			0
$737$		−	26.8722i		−	0.989849i
$738$		0			0
$739$	32.4463	+	32.4463i	1.19356	+	1.19356i	0.976061	+	0.217495i	$0.0697887\pi$
$739$	32.4463	+	32.4463i	1.19356	+	1.19356i	0.217495	+	0.976061i	$0.430211\pi$
$740$		0			0
$741$	1.77855	+	11.7657i	0.0653366	+	0.432224i
$742$		0			0
$743$	10.8406	−	6.25880i	0.397702	−	0.229613i	−0.287790	−	0.957693i	$-0.592921\pi$
$743$	10.8406	−	6.25880i	0.397702	−	0.229613i	0.685492	+	0.728080i	$0.259587\pi$
$744$		0			0
$745$	40.0141	+	23.1021i	1.46600	+	0.846397i
$746$		0			0
$747$	−18.2451	+	34.5932i	−0.667554	+	1.26570i
$748$		0			0
$749$	14.9973	−	4.01852i	0.547990	−	0.146834i
$750$		0			0
$751$	34.0479	−	19.6575i	1.24242	−	0.717314i	0.272837	−	0.962060i	$-0.412038\pi$
$751$	34.0479	−	19.6575i	1.24242	−	0.717314i	0.969587	+	0.244747i	$0.0787047\pi$
$752$		0			0
$753$	−5.35969	−	12.2702i	−0.195318	−	0.447151i
$754$		0			0
$755$	−23.6777	+	23.6777i	−0.861718	+	0.861718i
$756$		0			0
$757$	−25.3026	−	25.3026i	−0.919640	−	0.919640i	0.0773631	−	0.997003i	$-0.475350\pi$
$757$	−25.3026	−	25.3026i	−0.919640	−	0.919640i	−0.997003	+	0.0773631i	$0.975350\pi$
$758$		0			0
$759$	−10.4157	+	4.54963i	−0.378065	+	0.165141i
$760$		0			0
$761$	11.0907	+	19.2097i	0.402039	+	0.696352i	0.993972	−	0.109635i	$-0.0349683\pi$
$761$	11.0907	+	19.2097i	0.402039	+	0.696352i	−0.591933	+	0.805987i	$0.701635\pi$
$762$		0			0
$763$	6.45338	+	24.0843i	0.233628	+	0.871911i
$764$		0			0
$765$	−29.0518	+	18.2892i	−1.05037	+	0.661247i
$766$		0			0
$767$	3.12087	−	5.40551i	0.112688	−	0.195182i
$768$		0			0
$769$	0.792978	+	1.37348i	0.0285955	+	0.0495289i	0.879969	−	0.475031i	$-0.157563\pi$
$769$	0.792978	+	1.37348i	0.0285955	+	0.0495289i	−0.851374	+	0.524560i	$0.824230\pi$
$770$		0			0
$771$	40.7210	−	6.15555i	1.46653	−	0.221687i
$772$		0			0
$773$	−0.198602	+	0.198602i	−0.00714323	+	0.00714323i	−0.710669	−	0.703526i	$-0.751608\pi$
$773$	−0.198602	+	0.198602i	−0.00714323	+	0.00714323i	0.703526	+	0.710669i	$0.251608\pi$
$774$		0			0
$775$	5.36948			0.192877
$776$		0			0
$777$	9.74308	+	1.09355i	0.349531	+	0.0392310i
$778$		0			0
$779$	−1.09132	+	4.07287i	−0.0391007	+	0.145926i
$780$		0			0
$781$	3.30471	+	12.3334i	0.118252	+	0.441322i
$782$		0			0
$783$	−29.7377	−	34.4661i	−1.06274	−	1.23172i
$784$		0			0
$785$	−12.5149	−	7.22549i	−0.446676	−	0.257889i
$786$		0			0
$787$	3.76684	−	14.0581i	0.134274	−	0.501116i	−0.865726	−	0.500518i	$-0.833143\pi$
$787$	3.76684	−	14.0581i	0.134274	−	0.501116i	1.00000		0.000597888i	$-0.000190314\pi$
$788$		0			0
$789$	−7.65687	−	9.59298i	−0.272592	−	0.341519i
$790$		0			0
$791$			48.9217i			1.73946i
$792$		0			0
$793$		−	28.1353i		−	0.999112i
$794$		0			0
$795$	−49.5353	+	7.48795i	−1.75683	+	0.265570i
$796$		0			0
$797$	−3.12214	+	11.6520i	−0.110592	+	0.412734i	−0.998919	−	0.0464762i	$-0.985201\pi$
$797$	−3.12214	+	11.6520i	−0.110592	+	0.412734i	0.888328	+	0.459210i	$0.151868\pi$
$798$		0			0
$799$	−16.3541	−	9.44202i	−0.578565	−	0.334035i
$800$		0			0
$801$	16.1398	+	14.9498i	0.570272	+	0.528227i
$802$		0			0
$803$	−3.49286	−	13.0355i	−0.123261	−	0.460015i
$804$		0			0
$805$	7.17244	−	26.7679i	0.252795	−	0.943445i
$806$		0			0
$807$	−20.2586	−	46.3789i	−0.713135	−	1.63261i
$808$		0			0
$809$	−5.40097			−0.189888			−0.0949441	−	0.995483i	$-0.530267\pi$
$809$	−5.40097			−0.189888			−0.0949441	+	0.995483i	$0.530267\pi$
$810$		0			0
$811$	−19.4041	+	19.4041i	−0.681371	+	0.681371i	−0.960309	−	0.278938i	$-0.910018\pi$
$811$	−19.4041	+	19.4041i	−0.681371	+	0.681371i	0.278938	+	0.960309i	$0.410018\pi$
$812$		0			0
$813$	−10.5498	+	26.9144i	−0.369998	+	0.943928i
$814$		0			0
$815$	−10.7788	−	18.6695i	−0.377566	−	0.653964i
$816$		0			0
$817$	−6.94356	+	12.0266i	−0.242924	+	0.420758i
$818$		0			0
$819$	21.3762	−	0.818183i	0.746944	−	0.0285896i
$820$		0			0
$821$	−5.53178	−	20.6449i	−0.193061	−	0.720512i	−0.992760	−	0.120112i	$-0.961675\pi$
$821$	−5.53178	−	20.6449i	−0.193061	−	0.720512i	0.799700	−	0.600400i	$-0.204992\pi$
$822$		0			0
$823$	15.8047	+	27.3746i	0.550918	+	0.954217i	0.998209	+	0.0598289i	$0.0190555\pi$
$823$	15.8047	+	27.3746i	0.550918	+	0.954217i	−0.447291	+	0.894389i	$0.647611\pi$
$824$		0			0
$825$	−40.5053	−	29.8675i	−1.41021	−	1.03985i
$826$		0			0
$827$	11.4058	+	11.4058i	0.396617	+	0.396617i	0.877038	−	0.480421i	$-0.159516\pi$
$827$	11.4058	+	11.4058i	0.396617	+	0.396617i	−0.480421	+	0.877038i	$0.659516\pi$
$828$		0			0
$829$	−15.8083	+	15.8083i	−0.549043	+	0.549043i	−0.926164	−	0.377121i	$-0.876914\pi$
$829$	−15.8083	+	15.8083i	−0.549043	+	0.549043i	0.377121	+	0.926164i	$0.376914\pi$
$830$		0			0
$831$	−8.00487	−	0.898459i	−0.277686	−	0.0311672i
$832$		0			0
$833$	−4.04098	+	2.33306i	−0.140012	+	0.0808357i
$834$		0			0
$835$	−26.3457	+	7.05931i	−0.911730	+	0.244297i
$836$		0			0
$837$	−2.17859	−	1.48124i	−0.0753031	−	0.0511992i
$838$		0			0
$839$	28.2922	+	16.3345i	0.976755	+	0.563930i	0.901289	−	0.433219i	$-0.142622\pi$
$839$	28.2922	+	16.3345i	0.976755	+	0.563930i	0.0754662	+	0.997148i	$0.475956\pi$
$840$		0			0
$841$	41.3525	−	23.8749i	1.42595	−	0.823272i
$842$		0			0
$843$	30.9060	−	24.6684i	1.06446	−	0.849624i
$844$		0			0
$845$	19.8083	+	19.8083i	0.681428	+	0.681428i
$846$		0			0
$847$		−	10.1907i		−	0.350158i
$848$		0			0
$849$	−35.9994	−	26.5450i	−1.23550	−	0.911021i
$850$		0			0
$851$	4.45686	+	1.19421i	0.152779	+	0.0409371i
$852$		0			0
$853$	38.7224	−	10.3756i	1.32583	−	0.355255i	0.474672	−	0.880163i	$-0.342567\pi$
$853$	38.7224	−	10.3756i	1.32583	−	0.355255i	0.851159	+	0.524907i	$0.175900\pi$
$854$		0			0
$855$	7.42388	−	32.6551i	0.253891	−	1.11678i
$856$		0			0
$857$	−0.0140657	+	0.0243624i	−0.000480474	+	0.000832205i	−0.866266	−	0.499584i	$-0.833486\pi$
$857$	−0.0140657	+	0.0243624i	−0.000480474	+	0.000832205i	0.865785	+	0.500416i	$0.166820\pi$
$858$		0			0
$859$	−11.7598	−	3.15104i	−0.401240	−	0.107512i	0.0525549	−	0.998618i	$-0.483264\pi$
$859$	−11.7598	−	3.15104i	−0.401240	−	0.107512i	−0.453795	+	0.891106i	$0.649930\pi$
$860$		0			0
$861$	7.05740	+	2.76634i	0.240516	+	0.0942765i
$862$		0			0
$863$	−40.1140			−1.36550			−0.682748	−	0.730654i	$-0.739215\pi$
$863$	−40.1140			−1.36550			−0.682748	+	0.730654i	$0.739215\pi$
$864$		0			0
$865$	−15.8140			−0.537692
$866$		0			0
$867$	−13.8701	−	5.43674i	−0.471052	−	0.184642i
$868$		0			0
$869$	11.0547	+	2.96211i	0.375006	+	0.100483i
$870$		0			0
$871$	−11.9010	+	20.6132i	−0.403251	+	0.698451i
$872$		0			0
$873$	14.3375	−	4.43598i	0.485250	−	0.150135i
$874$		0			0
$875$	62.5669	−	16.7647i	2.11515	−	0.566752i
$876$		0			0
$877$	−45.8849	−	12.2948i	−1.54942	−	0.415167i	−0.620127	−	0.784501i	$-0.712919\pi$
$877$	−45.8849	−	12.2948i	−1.54942	−	0.415167i	−0.929297	+	0.369334i	$0.879586\pi$
$878$		0			0
$879$	3.99348	+	2.94468i	0.134697	+	0.0993216i
$880$		0			0
$881$			20.6694i			0.696371i	0.937426	+	0.348186i	$0.113202\pi$
$881$			20.6694i			0.696371i	−0.937426	+	0.348186i	$0.886798\pi$
$882$		0			0
$883$	37.7611	+	37.7611i	1.27076	+	1.27076i	0.945688	+	0.325075i	$0.105390\pi$
$883$	37.7611	+	37.7611i	1.27076	+	1.27076i	0.325075	+	0.945688i	$0.394610\pi$
$884$		0			0
$885$	−13.7291	+	10.9582i	−0.461497	+	0.368355i
$886$		0			0
$887$	24.4908	−	14.1398i	0.822322	−	0.474768i	−0.0288948	−	0.999582i	$-0.509199\pi$
$887$	24.4908	−	14.1398i	0.822322	−	0.474768i	0.851216	+	0.524815i	$0.175865\pi$
$888$		0			0
$889$	−45.7347	−	26.4049i	−1.53389	−	0.885593i
$890$		0			0
$891$	8.19514	+	23.2922i	0.274547	+	0.780319i
$892$		0			0
$893$	17.7937	−	4.76782i	0.595445	−	0.159549i
$894$		0			0
$895$	48.6615	−	28.0947i	1.62657	−	0.939103i
$896$		0			0
$897$	10.0046	+	1.12291i	0.334044	+	0.0374928i
$898$		0			0
$899$	3.14074	−	3.14074i	0.104750	−	0.104750i
$900$		0			0
$901$	15.0115	+	15.0115i	0.500105	+	0.500105i
$902$		0			0
$903$	20.0934	+	14.8163i	0.668665	+	0.493055i
$904$		0			0
$905$	−41.9767	−	72.7058i	−1.39535	−	2.41682i
$906$		0			0
$907$	9.12179	+	34.0430i	0.302884	+	1.13038i	0.934751	+	0.355302i	$0.115622\pi$
$907$	9.12179	+	34.0430i	0.302884	+	1.13038i	−0.631867	+	0.775077i	$0.717711\pi$
$908$		0			0
$909$	15.2993	−	29.0078i	0.507444	−	0.962126i
$910$		0			0
$911$	8.81619	−	15.2701i	0.292093	−	0.505921i	−0.682211	−	0.731155i	$-0.738982\pi$
$911$	8.81619	−	15.2701i	0.292093	−	0.505921i	0.974305	+	0.225235i	$0.0723149\pi$
$912$		0			0
$913$	17.8832	+	30.9746i	0.591847	+	1.02511i
$914$		0			0
$915$	−28.8965	+	73.7199i	−0.955288	+	2.43710i
$916$		0			0
$917$	37.4020	−	37.4020i	1.23512	−	1.23512i
$918$		0			0
$919$	−40.6483			−1.34086			−0.670431	−	0.741972i	$-0.733891\pi$
$919$	−40.6483			−1.34086			−0.670431	+	0.741972i	$0.733891\pi$
$920$		0			0
$921$	−7.52361	−	17.2242i	−0.247911	−	0.567555i
$922$		0			0
$923$	2.92715	−	10.9243i	0.0963483	−	0.359577i
$924$		0			0
$925$	5.28775	+	19.7341i	0.173860	+	0.648855i
$926$		0			0
$927$	−0.428229	+	1.88363i	−0.0140649	+	0.0618665i
$928$		0			0
$929$	−46.7331	−	26.9814i	−1.53326	−	0.885230i	−0.999208	−	0.0397807i	$-0.987334\pi$
$929$	−46.7331	−	26.9814i	−1.53326	−	0.885230i	−0.534055	−	0.845450i	$-0.679333\pi$
$930$		0			0
$931$	1.17810	−	4.39672i	0.0386106	−	0.144097i
$932$		0			0
$933$	29.8167	−	4.50721i	0.976156	−	0.147560i
$934$		0			0
$935$			31.3946i			1.02671i
$936$		0			0
$937$			47.0464i			1.53694i	0.639886	+	0.768470i	$0.278982\pi$
$937$			47.0464i			1.53694i	−0.639886	+	0.768470i	$0.721018\pi$
$938$		0			0
$939$	26.5784	+	33.2989i	0.867352	+	1.08667i
$940$		0			0
$941$	0.645083	−	2.40748i	0.0210291	−	0.0784816i	−0.954614	−	0.297846i	$-0.903732\pi$
$941$	0.645083	−	2.40748i	0.0210291	−	0.0784816i	0.975643	+	0.219365i	$0.0703984\pi$
$942$		0			0
$943$	3.08946	+	1.78370i	0.100607	+	0.0580853i
$944$		0			0
$945$	−56.8501	−	19.8107i	−1.84933	−	0.644443i
$946$		0			0
$947$	−13.4692	−	50.2676i	−0.437689	−	1.63348i	−0.734548	−	0.678557i	$-0.762606\pi$
$947$	−13.4692	−	50.2676i	−0.437689	−	1.63348i	0.296859	−	0.954921i	$-0.404061\pi$
$948$		0			0
$949$	−3.09381	+	11.5462i	−0.100429	+	0.374807i
$950$		0			0
$951$	14.2440	+	1.59873i	0.461893	+	0.0518424i
$952$		0			0
$953$	61.2734			1.98484			0.992420	−	0.122896i	$-0.0392181\pi$
$953$	61.2734			1.98484			0.992420	+	0.122896i	$0.0392181\pi$
$954$		0			0
$955$	−60.8700	+	60.8700i	−1.96971	+	1.96971i
$956$		0			0
$957$	−41.1628	+	6.22233i	−1.33060	+	0.201139i
$958$		0			0
$959$	−1.16244	−	2.01340i	−0.0375370	−	0.0650160i
$960$		0			0
$961$	−15.3715	+	26.6242i	−0.495854	+	0.858844i
$962$		0			0
$963$	−0.607142	−	15.8624i	−0.0195649	−	0.511160i
$964$		0			0
$965$	4.79750	+	17.9045i	0.154437	+	0.576367i
$966$		0			0
$967$	3.75805	+	6.50913i	0.120851	+	0.209319i	0.920103	−	0.391676i	$-0.128104\pi$
$967$	3.75805	+	6.50913i	0.120851	+	0.209319i	−0.799253	+	0.600995i	$0.794771\pi$
$968$		0			0
$969$	−13.0045	+	5.68042i	−0.417763	+	0.182481i
$970$		0			0
$971$	20.5494	+	20.5494i	0.659461	+	0.659461i	0.955253	−	0.295791i	$-0.0955833\pi$
$971$	20.5494	+	20.5494i	0.659461	+	0.659461i	−0.295791	+	0.955253i	$0.595583\pi$
$972$		0			0
$973$	−44.0638	+	44.0638i	−1.41262	+	1.41262i
$974$		0			0
$975$	17.8434	+	40.8496i	0.571445	+	1.30824i
$976$		0			0
$977$	48.8661	−	28.2129i	1.56337	−	0.902610i	0.566453	−	0.824094i	$-0.308315\pi$
$977$	48.8661	−	28.2129i	1.56337	−	0.902610i	0.996913	−	0.0785154i	$-0.0250180\pi$
$978$		0			0
$979$	19.4336	−	5.20721i	0.621100	−	0.166423i
$980$		0			0
$981$	25.4736	−	0.975015i	0.813310	−	0.0311298i
$982$		0			0
$983$	−5.17882	−	2.98999i	−0.165179	−	0.0953660i	0.415132	−	0.909761i	$-0.363735\pi$
$983$	−5.17882	−	2.98999i	−0.165179	−	0.0953660i	−0.580311	+	0.814395i	$0.697069\pi$
$984$		0			0
$985$	−69.2628	+	39.9889i	−2.20690	+	1.27415i
$986$		0			0
$987$	−4.94982	−	32.7447i	−0.157555	−	1.04228i
$988$		0			0
$989$	8.30792	+	8.30792i	0.264176	+	0.264176i
$990$		0			0
$991$			20.2358i			0.642812i	0.946942	+	0.321406i	$0.104155\pi$
$991$			20.2358i			0.642812i	−0.946942	+	0.321406i	$0.895845\pi$
$992$		0			0
$993$	−5.10742	+	45.5049i	−0.162079	+	1.44405i
$994$		0			0
$995$	−55.2892	−	14.8147i	−1.75278	−	0.469657i
$996$		0			0
$997$	0.647795	−	0.173576i	0.0205159	−	0.00549721i	−0.248547	−	0.968620i	$-0.579953\pi$
$997$	0.647795	−	0.173576i	0.0205159	−	0.00549721i	0.269062	+	0.963123i	$0.413286\pi$
$998$		0			0
$999$	3.29849	−	9.46555i	0.104360	−	0.299477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.y.a.335.3		88
3.2	odd	2		1728.2.z.a.143.22		88
4.3	odd	2		144.2.u.a.11.20	✓	88
9.4	even	3		1728.2.z.a.719.22		88
9.5	odd	6	inner	576.2.y.a.527.9		88
12.11	even	2		432.2.v.a.251.3		88
16.3	odd	4	inner	576.2.y.a.47.9		88
16.13	even	4		144.2.u.a.83.18	yes	88
36.23	even	6		144.2.u.a.59.18	yes	88
36.31	odd	6		432.2.v.a.395.5		88
48.29	odd	4		432.2.v.a.35.5		88
48.35	even	4		1728.2.z.a.1007.22		88
144.13	even	12		432.2.v.a.179.3		88
144.67	odd	12		1728.2.z.a.1583.22		88
144.77	odd	12		144.2.u.a.131.20	yes	88
144.131	even	12	inner	576.2.y.a.239.3		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.20	✓	88	4.3	odd	2
144.2.u.a.59.18	yes	88	36.23	even	6
144.2.u.a.83.18	yes	88	16.13	even	4
144.2.u.a.131.20	yes	88	144.77	odd	12
432.2.v.a.35.5		88	48.29	odd	4
432.2.v.a.179.3		88	144.13	even	12
432.2.v.a.251.3		88	12.11	even	2
432.2.v.a.395.5		88	36.31	odd	6
576.2.y.a.47.9		88	16.3	odd	4	inner
576.2.y.a.239.3		88	144.131	even	12	inner
576.2.y.a.335.3		88	1.1	even	1	trivial
576.2.y.a.527.9		88	9.5	odd	6	inner
1728.2.z.a.143.22		88	3.2	odd	2
1728.2.z.a.719.22		88	9.4	even	3
1728.2.z.a.1007.22		88	48.35	even	4
1728.2.z.a.1583.22		88	144.67	odd	12

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.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.61259 - 0.632098i) q^{3} +(-3.81396 - 1.02195i) q^{5} +(-1.46715 + 2.54117i) q^{7} +(2.20090 + 2.03863i) q^{9} +O(q^{10})\)	\(q+(-1.61259 - 0.632098i) q^{3} +(-3.81396 - 1.02195i) q^{5} +(-1.46715 + 2.54117i) q^{7} +(2.20090 + 2.03863i) q^{9} +(2.65006 - 0.710081i) q^{11} +(-2.34729 - 0.628955i) q^{13} +(5.50439 + 4.05878i) q^{15} -2.89808i q^{17} +(1.99906 + 1.99906i) q^{19} +(3.97218 - 3.17049i) q^{21} +(2.07141 - 1.19593i) q^{23} +(9.17180 + 5.29534i) q^{25} +(-2.26054 - 4.67867i) q^{27} +(8.46218 - 2.26743i) q^{29} +(0.439075 - 0.253500i) q^{31} +(-4.72230 - 0.530027i) q^{33} +(8.19258 - 8.19258i) q^{35} +(1.36407 + 1.36407i) q^{37} +(3.38766 + 2.49797i) q^{39} +(0.745739 + 1.29166i) q^{41} +(1.27136 + 4.74478i) q^{43} +(-6.31078 - 10.0245i) q^{45} +(3.25802 - 5.64306i) q^{47} +(-0.805035 - 1.39436i) q^{49} +(-1.83187 + 4.67343i) q^{51} +(-5.17979 + 5.17979i) q^{53} -10.8329 q^{55} +(-1.96006 - 4.48726i) q^{57} +(-0.664781 + 2.48100i) q^{59} +(2.99657 + 11.1833i) q^{61} +(-8.40956 + 2.60190i) q^{63} +(8.30972 + 4.79762i) q^{65} +(2.53505 - 9.46095i) q^{67} +(-4.09628 + 0.619209i) q^{69} +4.65399i q^{71} -4.91897i q^{73} +(-11.4432 - 14.3367i) q^{75} +(-2.08358 + 7.77604i) q^{77} +(3.61263 + 2.08575i) q^{79} +(0.687950 + 8.97367i) q^{81} +(3.37411 + 12.5924i) q^{83} +(-2.96169 + 11.0532i) q^{85} +(-15.0793 - 1.69249i) q^{87} +7.33327 q^{89} +(5.04210 - 5.04210i) q^{91} +(-0.868286 + 0.131254i) q^{93} +(-5.58139 - 9.66725i) q^{95} +(2.50134 - 4.33245i) q^{97} +(7.28011 + 3.83968i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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