LMFDB - Embedded newform 576.2.y.a.47.9

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			47.9
Character	$\chi$	$=$	576.47
Dual form			576.2.y.a.527.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.632098 + 1.61259i) q^{3} +(-1.02195 + 3.81396i) q^{5} +(-1.46715 + 2.54117i) q^{7} +(-2.20090 - 2.03863i) q^{9} +O(q^{10})$	\(q+(-0.632098 + 1.61259i) q^{3} +(-1.02195 + 3.81396i) q^{5} +(-1.46715 + 2.54117i) q^{7} +(-2.20090 - 2.03863i) q^{9} +(0.710081 + 2.65006i) q^{11} +(0.628955 - 2.34729i) q^{13} +(-5.50439 - 4.05878i) q^{15} -2.89808i q^{17} +(1.99906 - 1.99906i) q^{19} +(-3.17049 - 3.97218i) q^{21} +(2.07141 - 1.19593i) q^{23} +(-9.17180 - 5.29534i) q^{25} +(4.67867 - 2.26054i) q^{27} +(2.26743 + 8.46218i) q^{29} +(-0.439075 + 0.253500i) q^{31} +(-4.72230 - 0.530027i) q^{33} +(-8.19258 - 8.19258i) q^{35} +(1.36407 - 1.36407i) q^{37} +(3.38766 + 2.49797i) q^{39} +(-0.745739 - 1.29166i) q^{41} +(-4.74478 + 1.27136i) q^{43} +(10.0245 - 6.31078i) q^{45} +(-3.25802 + 5.64306i) q^{47} +(-0.805035 - 1.39436i) q^{49} +(4.67343 + 1.83187i) q^{51} +(5.17979 + 5.17979i) q^{53} -10.8329 q^{55} +(1.96006 + 4.48726i) q^{57} +(-2.48100 - 0.664781i) q^{59} +(-11.1833 + 2.99657i) q^{61} +(8.40956 - 2.60190i) q^{63} +(8.30972 + 4.79762i) q^{65} +(-9.46095 - 2.53505i) q^{67} +(0.619209 + 4.09628i) q^{69} +4.65399i q^{71} +4.91897i q^{73} +(14.3367 - 11.4432i) q^{75} +(-7.77604 - 2.08358i) q^{77} +(-3.61263 - 2.08575i) q^{79} +(0.687950 + 8.97367i) q^{81} +(12.5924 - 3.37411i) q^{83} +(11.0532 + 2.96169i) q^{85} +(-15.0793 - 1.69249i) q^{87} -7.33327 q^{89} +(5.04210 + 5.04210i) q^{91} +(-0.131254 - 0.868286i) q^{93} +(5.58139 + 9.66725i) q^{95} +(2.50134 - 4.33245i) q^{97} +(3.83968 - 7.28011i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.632098	+	1.61259i	−0.364942	+	0.931030i
$3$	−0.632098	+	1.61259i	−0.364942	+	0.931030i
$4$		0			0
$5$	−1.02195	+	3.81396i	−0.457029	+	1.70566i	0.225024	+	0.974353i	$0.427754\pi$
$5$	−1.02195	+	3.81396i	−0.457029	+	1.70566i	−0.682053	+	0.731302i	$0.738913\pi$
$6$		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
$11$	0.710081	+	2.65006i	0.214097	+	0.799022i	0.986482	+	0.163868i	$0.0523970\pi$
$11$	0.710081	+	2.65006i	0.214097	+	0.799022i	−0.772385	+	0.635155i	$0.780936\pi$
$12$		0			0
$13$	0.628955	−	2.34729i	0.174441	−	0.651021i	−0.822206	−	0.569191i	$-0.807257\pi$
$13$	0.628955	−	2.34729i	0.174441	−	0.651021i	0.996646	−	0.0818307i	$-0.0260767\pi$
$14$		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	−0.439586	−	0.898201i	$-0.644875\pi$
$19$	1.99906	−	1.99906i	0.458615	−	0.458615i	0.898201	+	0.439586i	$0.144875\pi$
$20$		0			0
$21$	−3.17049	−	3.97218i	−0.691858	−	0.866800i
$22$		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
$27$	4.67867	−	2.26054i	0.900410	−	0.435041i
$28$		0			0
$29$	2.26743	+	8.46218i	0.421052	+	1.57139i	0.772396	+	0.635141i	$0.219058\pi$
$29$	2.26743	+	8.46218i	0.421052	+	1.57139i	−0.351344	+	0.936246i	$0.614275\pi$
$30$		0			0
$31$	−0.439075	+	0.253500i	−0.0788602	+	0.0455300i	−0.538912	−	0.842362i	$-0.681164\pi$
$31$	−0.439075	+	0.253500i	−0.0788602	+	0.0455300i	0.460051	+	0.887892i	$0.347831\pi$
$32$		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	−0.586035	−	0.810286i	$-0.699312\pi$
$37$	1.36407	−	1.36407i	0.224251	−	0.224251i	0.810286	+	0.586035i	$0.199312\pi$
$38$		0			0
$39$	3.38766	+	2.49797i	0.542460	+	0.399995i
$40$		0			0
$41$	−0.745739	−	1.29166i	−0.116465	−	0.201723i	0.801899	−	0.597459i	$-0.203823\pi$
$41$	−0.745739	−	1.29166i	−0.116465	−	0.201723i	−0.918364	+	0.395736i	$0.870490\pi$
$42$		0			0
$43$	−4.74478	+	1.27136i	−0.723572	+	0.193881i	−0.601765	−	0.798673i	$-0.705536\pi$
$43$	−4.74478	+	1.27136i	−0.723572	+	0.193881i	−0.121807	+	0.992554i	$0.538869\pi$
$44$		0			0
$45$	10.0245	−	6.31078i	1.49436	−	0.940756i
$46$		0			0
$47$	−3.25802	+	5.64306i	−0.475231	+	0.823124i	−0.999598	−	0.0283684i	$-0.990969\pi$
$47$	−3.25802	+	5.64306i	−0.475231	+	0.823124i	0.524367	+	0.851493i	$0.324302\pi$
$48$		0			0
$49$	−0.805035	−	1.39436i	−0.115005	−	0.199195i
$50$		0			0
$51$	4.67343	+	1.83187i	0.654411	+	0.256514i
$52$		0			0
$53$	5.17979	+	5.17979i	0.711499	+	0.711499i	0.966849	−	0.255349i	$-0.0821905\pi$
$53$	5.17979	+	5.17979i	0.711499	+	0.711499i	−0.255349	+	0.966849i	$0.582191\pi$
$54$		0			0
$55$	−10.8329			−1.46071
$56$		0			0
$57$	1.96006	+	4.48726i	0.259616	+	0.594352i
$58$		0			0
$59$	−2.48100	−	0.664781i	−0.322998	−	0.0865472i	0.0936766	−	0.995603i	$-0.470138\pi$
$59$	−2.48100	−	0.664781i	−0.322998	−	0.0865472i	−0.416675	+	0.909056i	$0.636805\pi$
$60$		0			0
$61$	−11.1833	+	2.99657i	−1.43188	+	0.383671i	−0.889682	−	0.456580i	$-0.849074\pi$
$61$	−11.1833	+	2.99657i	−1.43188	+	0.383671i	−0.542198	+	0.840251i	$0.682408\pi$
$62$		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
$67$	−9.46095	−	2.53505i	−1.15584	−	0.309706i	−0.370536	−	0.928818i	$-0.620826\pi$
$67$	−9.46095	−	2.53505i	−1.15584	−	0.309706i	−0.785303	+	0.619112i	$0.787493\pi$
$68$		0			0
$69$	0.619209	+	4.09628i	0.0745440	+	0.493134i
$70$		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	$0.0929441\pi$
$73$			4.91897i			0.575722i	−0.957672	+	0.287861i	$0.907056\pi$
$74$		0			0
$75$	14.3367	−	11.4432i	1.65546	−	1.32135i
$76$		0			0
$77$	−7.77604	−	2.08358i	−0.886162	−	0.237446i
$78$		0			0
$79$	−3.61263	−	2.08575i	−0.406453	−	0.234666i	0.282812	−	0.959175i	$-0.408733\pi$
$79$	−3.61263	−	2.08575i	−0.406453	−	0.234666i	−0.689264	+	0.724510i	$0.742066\pi$
$80$		0			0
$81$	0.687950	+	8.97367i	0.0764389	+	0.997074i
$82$		0			0
$83$	12.5924	−	3.37411i	1.38219	−	0.370357i	0.510275	−	0.860011i	$-0.329544\pi$
$83$	12.5924	−	3.37411i	1.38219	−	0.370357i	0.871917	+	0.489654i	$0.162877\pi$
$84$		0			0
$85$	11.0532	+	2.96169i	1.19889	+	0.321241i
$86$		0			0
$87$	−15.0793	−	1.69249i	−1.61667	−	0.181453i
$88$		0			0
$89$	−7.33327			−0.777325			−0.388662	−	0.921380i	$-0.627063\pi$
$89$	−7.33327			−0.777325			−0.388662	+	0.921380i	$0.627063\pi$
$90$		0			0
$91$	5.04210	+	5.04210i	0.528556	+	0.528556i
$92$		0			0
$93$	−0.131254	−	0.868286i	−0.0136104	−	0.0900371i
$94$		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
$99$	3.83968	−	7.28011i	0.385902	−	0.731679i
$100$		0			0
$101$	−10.5592	+	2.82933i	−1.05068	+	0.281529i	−0.742533	−	0.669810i	$-0.766376\pi$
$101$	−10.5592	+	2.82933i	−1.05068	+	0.281529i	−0.308147	+	0.951339i	$0.599709\pi$
$102$		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	$-0.667672\pi$
$107$	3.74155	−	3.74155i	0.361709	−	0.361709i	0.864442	+	0.502733i	$0.167672\pi$
$108$		0			0
$109$	6.00859	+	6.00859i	0.575518	+	0.575518i	0.933665	−	0.358147i	$-0.116591\pi$
$109$	6.00859	+	6.00859i	0.575518	+	0.575518i	−0.358147	+	0.933665i	$0.616591\pi$
$110$		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
$115$	2.44435	+	9.12244i	0.227937	+	0.850672i
$116$		0			0
$117$	−6.16953	+	3.88395i	−0.570374	+	0.359071i
$118$		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
$123$	2.55430	−	0.386118i	0.230313	−	0.0348151i
$124$		0			0
$125$	15.6093	−	15.6093i	1.39613	−	1.39613i
$126$		0			0
$127$		−	17.9975i		−	1.59702i	−0.601983	−	0.798509i	$-0.705623\pi$
$127$		−	17.9975i		−	1.59702i	0.601983	−	0.798509i	$-0.294377\pi$
$128$		0			0
$129$	0.948984	−	8.45502i	0.0835533	−	0.744423i
$130$		0			0
$131$	−4.66555	+	17.4121i	−0.407631	+	1.52130i	0.391520	+	0.920170i	$0.371949\pi$
$131$	−4.66555	+	17.4121i	−0.407631	+	1.52130i	−0.799151	+	0.601131i	$0.794717\pi$
$132$		0			0
$133$	2.14704	+	8.01285i	0.186172	+	0.694802i
$134$		0			0
$135$	3.84026	+	20.1544i	0.330517	+	1.73462i
$136$		0			0
$137$	0.396155	−	0.686161i	0.0338458	−	0.0586227i	−0.848606	−	0.529025i	$-0.822558\pi$
$137$	0.396155	−	0.686161i	0.0338458	−	0.0586227i	0.882452	+	0.470402i	$0.155891\pi$
$138$		0			0
$139$	−5.49654	+	20.5134i	−0.466211	+	1.73992i	0.186633	+	0.982430i	$0.440242\pi$
$139$	−5.49654	+	20.5134i	−0.466211	+	1.73992i	−0.652844	+	0.757492i	$0.726424\pi$
$140$		0			0
$141$	−7.04056	−	8.82082i	−0.592922	−	0.742847i
$142$		0			0
$143$	6.66706			0.557528
$144$		0			0
$145$	−34.5916			−2.87268
$146$		0			0
$147$	2.75740	−	0.416819i	0.227426	−	0.0343787i
$148$		0			0
$149$	−3.02863	+	11.3030i	−0.248115	+	0.925977i	0.723677	+	0.690139i	$0.242450\pi$
$149$	−3.02863	+	11.3030i	−0.248115	+	0.925977i	−0.971792	+	0.235839i	$0.924216\pi$
$150$		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
$155$	−0.518128	−	1.93368i	−0.0416170	−	0.155317i
$156$		0			0
$157$	−0.947242	+	3.53516i	−0.0755981	+	0.282136i	−0.993368	−	0.114976i	$-0.963321\pi$
$157$	−0.947242	+	3.53516i	−0.0755981	+	0.282136i	0.917770	+	0.397112i	$0.129988\pi$
$158$		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	−0.539561	−	0.841946i	$-0.681410\pi$
$163$	3.86060	−	3.86060i	0.302385	−	0.302385i	0.841946	+	0.539561i	$0.181410\pi$
$164$		0			0
$165$	6.84745	−	17.4690i	0.533073	−	1.35996i
$166$		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
$171$	−8.47507	+	0.324387i	−0.648105	+	0.0248065i
$172$		0			0
$173$	1.03659	+	3.86859i	0.0788101	+	0.294123i	0.994070	−	0.108740i	$-0.0346816\pi$
$173$	1.03659	+	3.86859i	0.0788101	+	0.294123i	−0.915260	+	0.402863i	$0.868015\pi$
$174$		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	$-0.0715078\pi$
$179$	10.0625	+	10.0625i	0.752109	+	0.752109i	−0.222764	+	0.974872i	$0.571508\pi$
$180$		0			0
$181$	15.0346	−	15.0346i	1.11751	−	1.11751i	0.125405	−	0.992106i	$-0.459977\pi$
$181$	15.0346	−	15.0346i	1.11751	−	1.11751i	0.992106	−	0.125405i	$-0.0400229\pi$
$182$		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
$187$	7.68009	−	2.05787i	0.561624	−	0.150487i
$188$		0			0
$189$	−1.11987	+	15.2058i	−0.0814585	+	1.10606i
$190$		0			0
$191$	−10.9007	+	18.8806i	−0.788749	+	1.36615i	0.137984	+	0.990434i	$0.455938\pi$
$191$	−10.9007	+	18.8806i	−0.788749	+	1.36615i	−0.926734	+	0.375719i	$0.877396\pi$
$192$		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
$195$	−12.9892	+	10.3676i	−0.930173	+	0.742440i
$196$		0			0
$197$	−14.3226	−	14.3226i	−1.02044	−	1.02044i	−0.999787	−	0.0206566i	$-0.993424\pi$
$197$	−14.3226	−	14.3226i	−1.02044	−	1.02044i	−0.0206566	−	0.999787i	$-0.506576\pi$
$198$		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
$203$	−24.8305	−	6.65332i	−1.74276	−	0.466971i
$204$		0			0
$205$	5.68844	−	1.52421i	0.397298	−	0.106456i
$206$		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
$211$	−6.39179	−	1.71268i	−0.440029	−	0.117905i	0.0320010	−	0.999488i	$-0.489812\pi$
$211$	−6.39179	−	1.71268i	−0.440029	−	0.117905i	−0.472030	+	0.881582i	$0.656479\pi$
$212$		0			0
$213$	−7.50499	−	2.94178i	−0.514234	−	0.201568i
$214$		0			0
$215$		−	19.3957i		−	1.32277i
$216$		0			0
$217$		−	1.48769i		−	0.100991i
$218$		0			0
$219$	−7.93229	−	3.10927i	−0.536014	−	0.210105i
$220$		0			0
$221$	−6.80265	−	1.82276i	−0.457596	−	0.122612i
$222$		0			0
$223$	1.59599	+	0.921443i	0.106875	+	0.0617044i	0.552485	−	0.833523i	$-0.313680\pi$
$223$	1.59599	+	0.921443i	0.106875	+	0.0617044i	−0.445610	+	0.895227i	$0.647013\pi$
$224$		0			0
$225$	9.39099	+	30.3525i	0.626066	+	2.02350i
$226$		0			0
$227$	0.687012	−	0.184084i	0.0455986	−	0.0122181i	−0.235948	−	0.971766i	$-0.575819\pi$
$227$	0.687012	−	0.184084i	0.0455986	−	0.0122181i	0.281546	+	0.959548i	$0.409153\pi$
$228$		0			0
$229$	−7.40562	−	1.98433i	−0.489377	−	0.131128i	0.00568843	−	0.999984i	$-0.498189\pi$
$229$	−7.40562	−	1.98433i	−0.489377	−	0.131128i	−0.495066	+	0.868856i	$0.664856\pi$
$230$		0			0
$231$	8.27520	−	11.2226i	0.544468	−	0.738390i
$232$		0			0
$233$	−1.36925			−0.0897024			−0.0448512	−	0.998994i	$-0.514281\pi$
$233$	−1.36925			−0.0897024			−0.0448512	+	0.998994i	$0.514281\pi$
$234$		0			0
$235$	−18.1929	−	18.1929i	−1.18677	−	1.18677i
$236$		0			0
$237$	5.64701	−	4.50730i	0.366812	−	0.292780i
$238$		0			0
$239$	−0.773627	−	1.33996i	−0.0500418	−	0.0866749i	0.839919	−	0.542711i	$-0.182602\pi$
$239$	−0.773627	−	1.33996i	−0.0500418	−	0.0866749i	−0.889961	+	0.456036i	$0.849269\pi$
$240$		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
$243$	−14.9057	−	4.56286i	−0.956202	−	0.292707i
$244$		0			0
$245$	6.14075	−	1.64541i	0.392318	−	0.105121i
$246$		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	$-0.828451\pi$
$251$	−5.46632	+	5.46632i	−0.345031	+	0.345031i	0.513224	+	0.858255i	$0.328451\pi$
$252$		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
$259$	1.46504	+	5.46761i	0.0910333	+	0.339741i
$260$		0			0
$261$	12.2609	−	23.2469i	0.758929	−	1.43895i
$262$		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
$267$	4.63535	−	11.8256i	0.283679	−	0.723713i
$268$		0			0
$269$	−20.6616	+	20.6616i	−1.25976	+	1.25976i	−0.308553	+	0.951207i	$0.599845\pi$
$269$	−20.6616	+	20.6616i	−1.25976	+	1.25976i	−0.951207	+	0.308553i	$0.900155\pi$
$270$		0			0
$271$			16.6901i			1.01385i	0.861989	+	0.506927i	$0.169218\pi$
$271$			16.6901i			1.01385i	−0.861989	+	0.506927i	$0.830782\pi$
$272$		0			0
$273$	−11.3180	+	4.94374i	−0.684994	+	0.299209i
$274$		0			0
$275$	7.52024	−	28.0659i	0.453487	−	1.69244i
$276$		0			0
$277$	−1.20367	−	4.49217i	−0.0723217	−	0.269908i	0.920291	−	0.391235i	$-0.127952\pi$
$277$	−1.20367	−	4.49217i	−0.0723217	−	0.269908i	−0.992613	+	0.121326i	$0.961285\pi$
$278$		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	$-0.594888\pi$
$281$	11.4153	−	19.7719i	0.680979	−	1.17949i	0.974682	−	0.223594i	$-0.0717790\pi$
$282$		0			0
$283$	−6.68368	+	24.9438i	−0.397303	+	1.48276i	0.420518	+	0.907284i	$0.361848\pi$
$283$	−6.68368	+	24.9438i	−0.397303	+	1.48276i	−0.817822	+	0.575472i	$0.804818\pi$
$284$		0			0
$285$	−19.1173	+	2.88985i	−1.13241	+	0.171180i
$286$		0			0
$287$	4.37643			0.258333
$288$		0			0
$289$	8.60110			0.505947
$290$		0			0
$291$	5.40538	+	6.77217i	0.316869	+	0.396992i
$292$		0			0
$293$	−0.741431	+	2.76706i	−0.0433149	+	0.161653i	−0.984196	−	0.177085i	$-0.943333\pi$
$293$	−0.741431	+	2.76706i	−0.0433149	+	0.161653i	0.940881	+	0.338738i	$0.110000\pi$
$294$		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
$299$	−1.50437	−	5.61438i	−0.0869998	−	0.324688i
$300$		0			0
$301$	3.73054	−	13.9226i	0.215025	−	0.802484i
$302$		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	−0.453380	−	0.891317i	$-0.649782\pi$
$307$	7.67329	−	7.67329i	0.437938	−	0.437938i	0.891317	+	0.453380i	$0.149782\pi$
$308$		0			0
$309$	−1.10274	+	0.166694i	−0.0627325	+	0.00948289i
$310$		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	0.961465	−	0.274928i	$-0.0886540\pi$
$313$	21.3027	+	12.2991i	1.20410	+	0.695189i	0.242638	+	0.970117i	$0.421987\pi$
$314$		0			0
$315$	1.32941	+	34.7328i	0.0749039	+	1.95697i
$316$		0			0
$317$	−2.14183	−	7.99342i	−0.120297	−	0.448955i	0.879331	−	0.476211i	$-0.157990\pi$
$317$	−2.14183	−	7.99342i	−0.120297	−	0.448955i	−0.999629	+	0.0272552i	$0.991323\pi$
$318$		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
$331$	25.5364	−	6.84245i	1.40361	−	0.376095i	0.523968	−	0.851738i	$-0.324451\pi$
$331$	25.5364	−	6.84245i	1.40361	−	0.376095i	0.879639	+	0.475643i	$0.157784\pi$
$332$		0			0
$333$	−5.78301	+	0.221347i	−0.316907	+	0.0121298i
$334$		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
$339$	4.31619	+	28.5531i	0.234423	+	1.55079i
$340$		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
$347$	−23.0228	−	6.16895i	−1.23593	−	0.331166i	−0.419044	−	0.907966i	$-0.637635\pi$
$347$	−23.0228	−	6.16895i	−1.23593	−	0.331166i	−0.816886	+	0.576799i	$0.804301\pi$
$348$		0			0
$349$	−25.9130	+	6.94337i	−1.38709	+	0.371670i	−0.873692	−	0.486479i	$-0.838281\pi$
$349$	−25.9130	+	6.94337i	−1.38709	+	0.371670i	−0.513400	+	0.858149i	$0.671614\pi$
$350$		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
$355$	−17.7502	−	4.75614i	−0.942080	−	0.252430i
$356$		0			0
$357$	−11.5117	+	9.18835i	−0.609264	+	0.486299i
$358$		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
$363$	0.899094	+	5.94781i	0.0471902	+	0.312179i
$364$		0			0
$365$	−18.7608	−	5.02693i	−0.981983	−	0.263121i
$366$		0			0
$367$	−1.26366	−	0.729575i	−0.0659625	−	0.0380835i	0.466656	−	0.884439i	$-0.345459\pi$
$367$	−1.26366	−	0.729575i	−0.0659625	−	0.0380835i	−0.532619	+	0.846355i	$0.678792\pi$
$368$		0			0
$369$	−0.991918	+	4.36310i	−0.0516372	+	0.227134i
$370$		0			0
$371$	−20.7623	+	5.56323i	−1.07792	+	0.288829i
$372$		0			0
$373$	7.77189	+	2.08247i	0.402413	+	0.107826i	0.454348	−	0.890824i	$-0.349872\pi$
$373$	7.77189	+	2.08247i	0.402413	+	0.107826i	−0.0519349	+	0.998650i	$0.516539\pi$
$374$		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	0.989664	−	0.143409i	$-0.0458063\pi$
$379$	16.4748	+	16.4748i	0.846255	+	0.846255i	−0.143409	+	0.989664i	$0.545806\pi$
$380$		0			0
$381$	29.0226	+	11.3762i	1.48687	+	0.582819i
$382$		0			0
$383$	−5.19654	−	9.00067i	−0.265531	−	0.459913i	0.702172	−	0.712008i	$-0.252214\pi$
$383$	−5.19654	−	9.00067i	−0.265531	−	0.459913i	−0.967703	+	0.252095i	$0.918881\pi$
$384$		0			0
$385$	15.8934	−	27.5282i	0.810004	−	1.40297i
$386$		0			0
$387$	13.0346	+	6.87473i	0.662588	+	0.349462i
$388$		0			0
$389$	23.2989	−	6.24292i	1.18130	−	0.316529i	0.385859	−	0.922558i	$-0.373905\pi$
$389$	23.2989	−	6.24292i	1.18130	−	0.316529i	0.795442	+	0.606029i	$0.207239\pi$
$390$		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	0.885253	−	0.465109i	$-0.153985\pi$
$397$	8.37131	+	8.37131i	0.420144	+	0.420144i	−0.465109	+	0.885253i	$0.653985\pi$
$398$		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
$403$	0.318880	+	1.19008i	0.0158846	+	0.0592820i
$404$		0			0
$405$	−34.9283	−	6.54681i	−1.73560	−	0.325313i
$406$		0			0
$407$	4.58345	+	2.64626i	0.227193	+	0.131170i
$408$		0			0
$409$	12.1263	−	7.00113i	0.599607	−	0.346184i	−0.169280	−	0.985568i	$-0.554144\pi$
$409$	12.1263	−	7.00113i	0.599607	−	0.346184i	0.768887	+	0.639385i	$0.220811\pi$
$410$		0			0
$411$	0.856089	+	1.07256i	0.0422277	+	0.0529054i
$412$		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
$419$	−0.161107	+	0.601258i	−0.00787057	+	0.0293734i	−0.969749	−	0.244102i	$-0.921507\pi$
$419$	−0.161107	+	0.601258i	−0.00787057	+	0.0293734i	0.961879	+	0.273476i	$0.0881733\pi$
$420$		0			0
$421$	−4.65440	−	17.3705i	−0.226842	−	0.846585i	−0.981658	−	0.190649i	$-0.938941\pi$
$421$	−4.65440	−	17.3705i	−0.226842	−	0.846585i	0.754816	−	0.655936i	$-0.227726\pi$
$422$		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
$427$	8.79280	−	32.8152i	0.425514	−	1.58804i
$428$		0			0
$429$	−4.21424	+	10.7513i	−0.203465	+	0.519075i
$430$		0			0
$431$	6.34380			0.305570			0.152785	−	0.988259i	$-0.451176\pi$
$431$	6.34380			0.305570			0.152785	+	0.988259i	$0.451176\pi$
$432$		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
$435$	21.8653	−	55.7822i	1.04836	−	2.67455i
$436$		0			0
$437$	1.75013	−	6.53158i	0.0837202	−	0.312448i
$438$		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
$443$	4.25119	+	15.8656i	0.201980	+	0.753800i	0.990349	+	0.138597i	$0.0442592\pi$
$443$	4.25119	+	15.8656i	0.201980	+	0.753800i	−0.788369	+	0.615203i	$0.789074\pi$
$444$		0			0
$445$	7.49422	−	27.9688i	0.355260	−	1.32585i
$446$		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
$453$	9.16314	+	11.4801i	0.430522	+	0.539383i
$454$		0			0
$455$	−24.3831	+	14.0776i	−1.14310	+	0.659969i
$456$		0			0
$457$	10.6069	+	6.12391i	0.496171	+	0.286464i	0.727131	−	0.686499i	$-0.240853\pi$
$457$	10.6069	+	6.12391i	0.496171	+	0.286464i	−0.230960	+	0.972963i	$0.574187\pi$
$458$		0			0
$459$	−6.55124	−	13.5592i	−0.305786	−	0.632888i
$460$		0			0
$461$	−8.12298	−	30.3154i	−0.378325	−	1.41193i	−0.848426	−	0.529314i	$-0.822449\pi$
$461$	−8.12298	−	30.3154i	−0.378325	−	1.41193i	0.470101	−	0.882613i	$-0.344217\pi$
$462$		0			0
$463$	30.9163	−	17.8495i	1.43680	−	0.829538i	0.439176	−	0.898401i	$-0.355271\pi$
$463$	30.9163	−	17.8495i	1.43680	−	0.829538i	0.997626	+	0.0688633i	$0.0219372\pi$
$464$		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	$-0.330490\pi$
$467$	−7.64586	−	7.64586i	−0.353808	−	0.353808i	−0.861524	+	0.507716i	$0.830490\pi$
$468$		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
$475$	−28.9206	+	7.74926i	−1.32697	+	0.355560i
$476$		0			0
$477$	−0.840526	−	21.9599i	−0.0384851	−	1.00548i
$478$		0			0
$479$	−3.03628	+	5.25898i	−0.138731	+	0.240289i	−0.927017	−	0.375020i	$-0.877636\pi$
$479$	−3.03628	+	5.25898i	−0.138731	+	0.240289i	0.788286	+	0.615310i	$0.210969\pi$
$480$		0			0
$481$	−2.34393	−	4.05980i	−0.106874	−	0.185111i
$482$		0			0
$483$	−11.3178	−	4.43632i	−0.514978	−	0.201859i
$484$		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
$491$	27.0285	+	7.24226i	1.21978	+	0.326838i	0.810591	−	0.585612i	$-0.199146\pi$
$491$	27.0285	+	7.24226i	1.21978	+	0.326838i	0.409187	+	0.912451i	$0.365813\pi$
$492$		0			0
$493$	24.5241	−	6.57122i	1.10451	−	0.295953i
$494$		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
$499$	42.8097	+	11.4708i	1.91643	+	0.513505i	0.990854	+	0.134937i	$0.0430832\pi$
$499$	42.8097	+	11.4708i	1.91643	+	0.513505i	0.925573	+	0.378568i	$0.123584\pi$
$500$		0			0
$501$	1.78828	+	11.8301i	0.0798945	+	0.528529i
$502$		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
$507$	−9.60408	+	7.66573i	−0.426532	+	0.340447i
$508$		0			0
$509$	40.4609	+	10.8415i	1.79340	+	0.480539i	0.992916	−	0.118819i	$-0.0379108\pi$
$509$	40.4609	+	10.8415i	1.79340	+	0.480539i	0.800481	+	0.599358i	$0.204577\pi$
$510$		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
$515$	−2.45580	+	0.658030i	−0.108216	+	0.0289963i
$516$		0			0
$517$	−17.2679	−	4.62691i	−0.759441	−	0.203491i
$518$		0			0
$519$	−6.89368	−	0.773740i	−0.302599	−	0.0339634i
$520$		0			0
$521$	26.1826			1.14708			0.573540	−	0.819178i	$-0.305570\pi$
$521$	26.1826			1.14708			0.573540	+	0.819178i	$0.305570\pi$
$522$		0			0
$523$	−7.29036	−	7.29036i	−0.318785	−	0.318785i	0.529515	−	0.848300i	$-0.322374\pi$
$523$	−7.29036	−	7.29036i	−0.318785	−	0.318785i	−0.848300	+	0.529515i	$0.822374\pi$
$524$		0			0
$525$	8.04507	+	53.2208i	0.351116	+	2.32275i
$526$		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
$531$	4.10519	+	6.52096i	0.178150	+	0.282986i
$532$		0			0
$533$	−3.50093	+	0.938073i	−0.151642	+	0.0406324i
$534$		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	0.937254	−	0.348647i	$-0.113359\pi$
$541$	13.6906	+	13.6906i	0.588607	+	0.588607i	−0.348647	+	0.937254i	$0.613359\pi$
$542$		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
$547$	7.77408	+	29.0133i	0.332396	+	1.24052i	0.906665	+	0.421851i	$0.138620\pi$
$547$	7.77408	+	29.0133i	0.332396	+	1.24052i	−0.574269	+	0.818666i	$0.694714\pi$
$548$		0			0
$549$	30.7224	+	16.2036i	1.31120	+	0.691552i
$550$		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
$555$	−13.0448	+	1.97191i	−0.553721	+	0.0837027i
$556$		0			0
$557$	1.85284	−	1.85284i	0.0785074	−	0.0785074i	−0.666763	−	0.745270i	$-0.732321\pi$
$557$	1.85284	−	1.85284i	0.0785074	−	0.0785074i	0.745270	+	0.666763i	$0.232321\pi$
$558$		0			0
$559$			11.9370i			0.504882i
$560$		0			0
$561$	−1.53606	+	13.6856i	−0.0648526	+	0.577808i
$562$		0			0
$563$	−7.00420	+	26.1400i	−0.295192	+	1.10167i	0.645873	+	0.763445i	$0.276494\pi$
$563$	−7.00420	+	26.1400i	−0.295192	+	1.10167i	−0.941065	+	0.338226i	$0.890173\pi$
$564$		0			0
$565$	17.0383	+	63.5879i	0.716808	+	2.67516i
$566$		0			0
$567$	−23.8130	−	11.4175i	−1.00005	−	0.479489i
$568$		0			0
$569$	−5.84691	+	10.1271i	−0.245115	+	0.424552i	−0.962164	−	0.272471i	$-0.912159\pi$
$569$	−5.84691	+	10.1271i	−0.245115	+	0.424552i	0.717049	+	0.697023i	$0.245492\pi$
$570$		0			0
$571$	11.8200	−	44.1127i	0.494650	−	1.84606i	−0.0373319	−	0.999303i	$-0.511886\pi$
$571$	11.8200	−	44.1127i	0.494650	−	1.84606i	0.531982	−	0.846756i	$-0.321447\pi$
$572$		0			0
$573$	−23.5564	−	29.5128i	−0.984082	−	1.23292i
$574$		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
$579$	8.03972	−	1.21532i	0.334119	−	0.0505068i
$580$		0			0
$581$	−9.90064	+	36.9497i	−0.410748	+	1.53293i
$582$		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
$587$	−7.58567	−	28.3101i	−0.313094	−	1.16848i	−0.925751	−	0.378134i	$-0.876566\pi$
$587$	−7.58567	−	28.3101i	−0.313094	−	1.16848i	0.612657	−	0.790349i	$-0.290101\pi$
$588$		0			0
$589$	−0.370975	+	1.38450i	−0.0152858	+	0.0570472i
$590$		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
$597$	−9.16323	+	23.3770i	−0.375026	+	0.956756i
$598$		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	0.220001	−	0.975500i	$-0.429394\pi$
$601$	−12.6206	−	7.28651i	−0.514806	−	0.297223i	−0.734807	+	0.678276i	$0.762727\pi$
$602$		0			0
$603$	15.6546	+	24.8668i	0.637504	+	1.01266i
$604$		0			0
$605$	3.54920	+	13.2458i	0.144296	+	0.538519i
$606$		0			0
$607$	32.0317	−	18.4935i	1.30013	−	0.750629i	0.319702	−	0.947518i	$-0.396417\pi$
$607$	32.0317	−	18.4935i	1.30013	−	0.750629i	0.980426	+	0.196889i	$0.0630838\pi$
$608$		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	−0.636214	−	0.771513i	$-0.719500\pi$
$613$	3.34985	−	3.34985i	0.135299	−	0.135299i	0.771513	+	0.636214i	$0.219500\pi$
$614$		0			0
$615$	−1.13772	+	10.1366i	−0.0458774	+	0.408747i
$616$		0			0
$617$	4.04358	+	7.00369i	0.162789	+	0.281958i	0.935868	−	0.352352i	$-0.114618\pi$
$617$	4.04358	+	7.00369i	0.162789	+	0.281958i	−0.773079	+	0.634309i	$0.781285\pi$
$618$		0			0
$619$	43.5499	−	11.6692i	1.75042	−	0.469023i	0.765703	−	0.643194i	$-0.222391\pi$
$619$	43.5499	−	11.6692i	1.75042	−	0.469023i	0.984715	+	0.174171i	$0.0557246\pi$
$620$		0			0
$621$	6.98798	−	10.2778i	0.280418	−	0.412436i
$622$		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
$627$	−10.4997	+	8.38059i	−0.419318	+	0.334689i
$628$		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
$635$	68.6417	+	18.3925i	2.72396	+	0.729883i
$636$		0			0
$637$	−3.77930	+	1.01266i	−0.149741	+	0.0401231i
$638$		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
$643$	−39.7595	−	10.6535i	−1.56796	−	0.420134i	−0.632789	−	0.774324i	$-0.718090\pi$
$643$	−39.7595	−	10.6535i	−1.56796	−	0.420134i	−0.935173	+	0.354190i	$0.884757\pi$
$644$		0			0
$645$	31.2773	+	12.2600i	1.23154	+	0.482736i
$646$		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
$651$	2.39903	+	0.940365i	0.0940255	+	0.0368558i
$652$		0			0
$653$	17.7442	+	4.75454i	0.694383	+	0.186059i	0.588713	−	0.808342i	$-0.299635\pi$
$653$	17.7442	+	4.75454i	0.694383	+	0.186059i	0.105670	+	0.994401i	$0.466301\pi$
$654$		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
$659$	29.2626	−	7.84088i	1.13991	−	0.305437i	0.360994	−	0.932568i	$-0.382438\pi$
$659$	29.2626	−	7.84088i	1.13991	−	0.305437i	0.778914	+	0.627131i	$0.215771\pi$
$660$		0			0
$661$	−46.6546	−	12.5011i	−1.81465	−	0.486235i	−0.818551	−	0.574434i	$-0.805222\pi$
$661$	−46.6546	−	12.5011i	−1.81465	−	0.486235i	−0.996103	+	0.0881985i	$0.971889\pi$
$662$		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
$669$	−2.49473	+	1.99123i	−0.0964519	+	0.0769854i
$670$		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
$675$	−54.8822	−	4.04192i	−2.11241	−	0.155574i
$676$		0			0
$677$	2.14611	−	0.575049i	0.0824818	−	0.0221009i	−0.217342	−	0.976095i	$-0.569739\pi$
$677$	2.14611	−	0.575049i	0.0824818	−	0.0221009i	0.299824	+	0.953995i	$0.403072\pi$
$678$		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	$-0.742611\pi$
$683$	0.857818	−	0.857818i	0.0328235	−	0.0328235i	0.723328	+	0.690505i	$0.242611\pi$
$684$		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
$691$	−10.1497	−	37.8791i	−0.386112	−	1.44099i	−0.836407	−	0.548109i	$-0.815348\pi$
$691$	−10.1497	−	37.8791i	−0.386112	−	1.44099i	0.450295	−	0.892880i	$-0.351319\pi$
$692$		0			0
$693$	12.8667	+	20.4383i	0.488764	+	0.776386i
$694$		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
$699$	0.865499	−	2.20804i	0.0327362	−	0.0835156i
$700$		0			0
$701$	14.3403	−	14.3403i	0.541627	−	0.541627i	−0.382379	−	0.924006i	$-0.624895\pi$
$701$	14.3403	−	14.3403i	0.541627	−	0.541627i	0.924006	+	0.382379i	$0.124895\pi$
$702$		0			0
$703$		−	5.45369i		−	0.205690i
$704$		0			0
$705$	40.8374	−	17.8380i	1.53802	−	0.671817i
$706$		0			0
$707$	8.30208	−	30.9838i	0.312232	−	1.16527i
$708$		0			0
$709$	1.14194	+	4.26177i	0.0428864	+	0.160054i	0.984048	−	0.177902i	$-0.0569311\pi$
$709$	1.14194	+	4.26177i	0.0428864	+	0.160054i	−0.941162	+	0.337956i	$0.890264\pi$
$710$		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
$715$	−6.81339	+	25.4279i	−0.254806	+	0.950951i
$716$		0			0
$717$	2.64982	−	0.400557i	0.0989593	−	0.0149591i
$718$		0			0
$719$	−49.2509			−1.83675			−0.918374	−	0.395714i	$-0.870497\pi$
$719$	−49.2509			−1.83675			−0.918374	+	0.395714i	$0.870497\pi$
$720$		0			0
$721$	−1.88938			−0.0703644
$722$		0			0
$723$	8.29086	+	10.3873i	0.308340	+	0.386307i
$724$		0			0
$725$	24.0137	−	89.6203i	0.891846	−	3.32841i
$726$		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
$731$	3.68451	+	13.7508i	0.136277	+	0.508591i
$732$		0			0
$733$	−8.23445	+	30.7314i	−0.304146	+	1.13509i	0.629532	+	0.776975i	$0.283247\pi$
$733$	−8.23445	+	30.7314i	−0.304146	+	1.13509i	−0.933678	+	0.358114i	$0.883420\pi$
$734$		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	0.217495	−	0.976061i	$-0.430211\pi$
$739$	32.4463	−	32.4463i	1.19356	−	1.19356i	0.976061	−	0.217495i	$-0.0697887\pi$
$740$		0			0
$741$	11.7657	−	1.77855i	0.432224	−	0.0653366i
$742$		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
$747$	−34.5932	−	18.2451i	−1.26570	−	0.667554i
$748$		0			0
$749$	4.01852	+	14.9973i	0.146834	+	0.547990i
$750$		0			0
$751$	−34.0479	+	19.6575i	−1.24242	+	0.717314i	−0.969587	−	0.244747i	$-0.921295\pi$
$751$	−34.0479	+	19.6575i	−1.24242	+	0.717314i	−0.272837	+	0.962060i	$0.587962\pi$
$752$		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	−0.997003	−	0.0773631i	$-0.975350\pi$
$757$	−25.3026	+	25.3026i	−0.919640	+	0.919640i	0.0773631	+	0.997003i	$0.475350\pi$
$758$		0			0
$759$	−10.4157	+	4.54963i	−0.378065	+	0.165141i
$760$		0			0
$761$	−11.0907	−	19.2097i	−0.402039	−	0.696352i	0.591933	−	0.805987i	$-0.298365\pi$
$761$	−11.0907	−	19.2097i	−0.402039	−	0.696352i	−0.993972	+	0.109635i	$0.965032\pi$
$762$		0			0
$763$	−24.0843	+	6.45338i	−0.871911	+	0.233628i
$764$		0			0
$765$	−18.2892	−	29.0518i	−0.661247	−	1.05037i
$766$		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
$771$	−6.15555	−	40.7210i	−0.221687	−	1.46653i
$772$		0			0
$773$	0.198602	+	0.198602i	0.00714323	+	0.00714323i	0.710669	−	0.703526i	$-0.248392\pi$
$773$	0.198602	+	0.198602i	0.00714323	+	0.00714323i	−0.703526	+	0.710669i	$0.748392\pi$
$774$		0			0
$775$	5.36948			0.192877
$776$		0			0
$777$	−9.74308	−	1.09355i	−0.349531	−	0.0392310i
$778$		0			0
$779$	−4.07287	−	1.09132i	−0.145926	−	0.0391007i
$780$		0			0
$781$	−12.3334	+	3.30471i	−0.441322	+	0.118252i
$782$		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
$787$	−14.0581	−	3.76684i	−0.501116	−	0.134274i	−0.000597888	−	1.00000i	$-0.500190\pi$
$787$	−14.0581	−	3.76684i	−0.501116	−	0.134274i	−0.500518	+	0.865726i	$0.666857\pi$
$788$		0			0
$789$	−9.59298	+	7.65687i	−0.341519	+	0.272592i
$790$		0			0
$791$			48.9217i			1.73946i
$792$		0			0
$793$			28.1353i			0.999112i
$794$		0			0
$795$	−7.48795	−	49.5353i	−0.265570	−	1.75683i
$796$		0			0
$797$	−11.6520	−	3.12214i	−0.412734	−	0.110592i	0.0464762	−	0.998919i	$-0.485201\pi$
$797$	−11.6520	−	3.12214i	−0.412734	−	0.110592i	−0.459210	+	0.888328i	$0.651868\pi$
$798$		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
$803$	−13.0355	+	3.49286i	−0.460015	+	0.123261i
$804$		0			0
$805$	−26.7679	−	7.17244i	−0.943445	−	0.252795i
$806$		0			0
$807$	−20.2586	−	46.3789i	−0.713135	−	1.63261i
$808$		0			0
$809$	5.40097			0.189888			0.0949441	−	0.995483i	$-0.469733\pi$
$809$	5.40097			0.189888			0.0949441	+	0.995483i	$0.469733\pi$
$810$		0			0
$811$	−19.4041	−	19.4041i	−0.681371	−	0.681371i	0.278938	−	0.960309i	$-0.410018\pi$
$811$	−19.4041	−	19.4041i	−0.681371	−	0.681371i	−0.960309	+	0.278938i	$0.910018\pi$
$812$		0			0
$813$	−26.9144	−	10.5498i	−0.943928	−	0.369998i
$814$		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
$819$	−0.818183	−	21.3762i	−0.0285896	−	0.746944i
$820$		0			0
$821$	−20.6449	+	5.53178i	−0.720512	+	0.193061i	−0.600400	−	0.799700i	$-0.704992\pi$
$821$	−20.6449	+	5.53178i	−0.720512	+	0.193061i	−0.120112	+	0.992760i	$0.538325\pi$
$822$		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	$-0.840484\pi$
$827$	−11.4058	+	11.4058i	−0.396617	+	0.396617i	0.480421	+	0.877038i	$0.340484\pi$
$828$		0			0
$829$	−15.8083	−	15.8083i	−0.549043	−	0.549043i	0.377121	−	0.926164i	$-0.376914\pi$
$829$	−15.8083	−	15.8083i	−0.549043	−	0.549043i	−0.926164	+	0.377121i	$0.876914\pi$
$830$		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
$835$	7.05931	+	26.3457i	0.244297	+	0.911730i
$836$		0			0
$837$	−1.48124	+	2.17859i	−0.0511992	+	0.0753031i
$838$		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
$843$	24.6684	+	30.9060i	0.849624	+	1.06446i
$844$		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
$851$	1.19421	−	4.45686i	0.0409371	−	0.152779i
$852$		0			0
$853$	−10.3756	−	38.7224i	−0.355255	−	1.32583i	−0.880163	−	0.474672i	$-0.842567\pi$
$853$	−10.3756	−	38.7224i	−0.355255	−	1.32583i	0.524907	−	0.851159i	$-0.324100\pi$
$854$		0			0
$855$	7.42388	−	32.6551i	0.253891	−	1.11678i
$856$		0			0
$857$	0.0140657	−	0.0243624i	0.000480474	−	0.000832205i	−0.865785	−	0.500416i	$-0.833180\pi$
$857$	0.0140657	−	0.0243624i	0.000480474	−	0.000832205i	0.866266	+	0.499584i	$0.166514\pi$
$858$		0			0
$859$	3.15104	−	11.7598i	0.107512	−	0.401240i	−0.891106	−	0.453795i	$-0.850070\pi$
$859$	3.15104	−	11.7598i	0.107512	−	0.401240i	0.998618	+	0.0525549i	$0.0167364\pi$
$860$		0			0
$861$	−2.76634	+	7.05740i	−0.0942765	+	0.240516i
$862$		0			0
$863$	40.1140			1.36550			0.682748	−	0.730654i	$-0.260785\pi$
$863$	40.1140			1.36550			0.682748	+	0.730654i	$0.260785\pi$
$864$		0			0
$865$	−15.8140			−0.537692
$866$		0			0
$867$	−5.43674	+	13.8701i	−0.184642	+	0.471052i
$868$		0			0
$869$	2.96211	−	11.0547i	0.100483	−	0.375006i
$870$		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
$875$	16.7647	+	62.5669i	0.566752	+	2.11515i
$876$		0			0
$877$	12.2948	−	45.8849i	0.415167	−	1.54942i	−0.369334	−	0.929297i	$-0.620414\pi$
$877$	12.2948	−	45.8849i	0.415167	−	1.54942i	0.784501	−	0.620127i	$-0.212919\pi$
$878$		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	0.325075	−	0.945688i	$-0.394610\pi$
$883$	37.7611	−	37.7611i	1.27076	−	1.27076i	0.945688	−	0.325075i	$-0.105390\pi$
$884$		0			0
$885$	10.9582	+	13.7291i	0.368355	+	0.461497i
$886$		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
$891$	−23.2922	+	8.19514i	−0.780319	+	0.274547i
$892$		0			0
$893$	4.76782	+	17.7937i	0.159549	+	0.595445i
$894$		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
$907$	−34.0430	+	9.12179i	−1.13038	+	0.302884i	−0.775077	−	0.631867i	$-0.782289\pi$
$907$	−34.0430	+	9.12179i	−1.13038	+	0.302884i	−0.355302	+	0.934751i	$0.615622\pi$
$908$		0			0
$909$	29.0078	+	15.2993i	0.962126	+	0.507444i
$910$		0			0
$911$	−8.81619	+	15.2701i	−0.292093	+	0.505921i	−0.974305	−	0.225235i	$-0.927685\pi$
$911$	−8.81619	+	15.2701i	−0.292093	+	0.505921i	0.682211	+	0.731155i	$0.261018\pi$
$912$		0			0
$913$	17.8832	+	30.9746i	0.591847	+	1.02511i
$914$		0			0
$915$	73.7199	+	28.8965i	2.43710	+	0.955288i
$916$		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
$923$	10.9243	+	2.92715i	0.359577	+	0.0963483i
$924$		0			0
$925$	−19.7341	+	5.28775i	−0.648855	+	0.173860i
$926$		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
$931$	−4.39672	−	1.17810i	−0.144097	−	0.0386106i
$932$		0			0
$933$	−4.50721	−	29.8167i	−0.147560	−	0.976156i
$934$		0			0
$935$			31.3946i			1.02671i
$936$		0			0
$937$		−	47.0464i		−	1.53694i	−0.639886	−	0.768470i	$-0.721018\pi$
$937$		−	47.0464i		−	1.53694i	0.639886	−	0.768470i	$-0.278982\pi$
$938$		0			0
$939$	−33.2989	+	26.5784i	−1.08667	+	0.867352i
$940$		0			0
$941$	2.40748	+	0.645083i	0.0784816	+	0.0210291i	0.297846	−	0.954614i	$-0.403732\pi$
$941$	2.40748	+	0.645083i	0.0784816	+	0.0210291i	−0.219365	+	0.975643i	$0.570398\pi$
$942$		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
$947$	−50.2676	+	13.4692i	−1.63348	+	0.437689i	−0.954921	−	0.296859i	$-0.904061\pi$
$947$	−50.2676	+	13.4692i	−1.63348	+	0.437689i	−0.678557	+	0.734548i	$0.737394\pi$
$948$		0			0
$949$	11.5462	+	3.09381i	0.374807	+	0.100429i
$950$		0			0
$951$	14.2440	+	1.59873i	0.461893	+	0.0518424i
$952$		0			0
$953$	−61.2734			−1.98484			−0.992420	−	0.122896i	$-0.960782\pi$
$953$	−61.2734			−1.98484			−0.992420	+	0.122896i	$0.960782\pi$
$954$		0			0
$955$	−60.8700	−	60.8700i	−1.96971	−	1.96971i
$956$		0			0
$957$	−6.22233	−	41.1628i	−0.201139	−	1.33060i
$958$		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
$963$	−15.8624	+	0.607142i	−0.511160	+	0.0195649i
$964$		0			0
$965$	17.9045	−	4.79750i	0.576367	−	0.154437i
$966$		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	$-0.904417\pi$
$971$	−20.5494	+	20.5494i	−0.659461	+	0.659461i	0.295791	+	0.955253i	$0.404417\pi$
$972$		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
$979$	−5.20721	−	19.4336i	−0.166423	−	0.621100i
$980$		0			0
$981$	−0.975015	−	25.4736i	−0.0311298	−	0.813310i
$982$		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
$987$	32.7447	−	4.94982i	1.04228	−	0.157555i
$988$		0			0
$989$	−8.30792	+	8.30792i	−0.264176	+	0.264176i
$990$		0			0
$991$		−	20.2358i		−	0.642812i	−0.946942	−	0.321406i	$-0.895845\pi$
$991$		−	20.2358i		−	0.642812i	0.946942	−	0.321406i	$-0.104155\pi$
$992$		0			0
$993$	−5.10742	+	45.5049i	−0.162079	+	1.44405i
$994$		0			0
$995$	−14.8147	+	55.2892i	−0.469657	+	1.75278i
$996$		0			0
$997$	−0.173576	−	0.647795i	−0.00549721	−	0.0205159i	0.963123	−	0.269062i	$-0.0867138\pi$
$997$	−0.173576	−	0.647795i	−0.00549721	−	0.0205159i	−0.968620	+	0.248547i	$0.920047\pi$
$998$		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.47.9		88
3.2	odd	2		1728.2.z.a.1007.22		88
4.3	odd	2		144.2.u.a.83.18	yes	88
9.4	even	3		1728.2.z.a.1583.22		88
9.5	odd	6	inner	576.2.y.a.239.3		88
12.11	even	2		432.2.v.a.35.5		88
16.5	even	4		144.2.u.a.11.20	✓	88
16.11	odd	4	inner	576.2.y.a.335.3		88
36.23	even	6		144.2.u.a.131.20	yes	88
36.31	odd	6		432.2.v.a.179.3		88
48.5	odd	4		432.2.v.a.251.3		88
48.11	even	4		1728.2.z.a.143.22		88
144.5	odd	12		144.2.u.a.59.18	yes	88
144.59	even	12	inner	576.2.y.a.527.9		88
144.85	even	12		432.2.v.a.395.5		88
144.139	odd	12		1728.2.z.a.719.22		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.20	✓	88	16.5	even	4
144.2.u.a.59.18	yes	88	144.5	odd	12
144.2.u.a.83.18	yes	88	4.3	odd	2
144.2.u.a.131.20	yes	88	36.23	even	6
432.2.v.a.35.5		88	12.11	even	2
432.2.v.a.179.3		88	36.31	odd	6
432.2.v.a.251.3		88	48.5	odd	4
432.2.v.a.395.5		88	144.85	even	12
576.2.y.a.47.9		88	1.1	even	1	trivial
576.2.y.a.239.3		88	9.5	odd	6	inner
576.2.y.a.335.3		88	16.11	odd	4	inner
576.2.y.a.527.9		88	144.59	even	12	inner
1728.2.z.a.143.22		88	48.11	even	4
1728.2.z.a.719.22		88	144.139	odd	12
1728.2.z.a.1007.22		88	3.2	odd	2
1728.2.z.a.1583.22		88	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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