LMFDB - Embedded newform 504.2.cx.a.185.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(185,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5, 1]))

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

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

chi := DirichletCharacter("504.185");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cx (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.10
Character	$\chi$	$=$	504.185
Dual form			504.2.cx.a.425.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.601162 + 1.62438i) q^{3} -0.207028 q^{5} +(-1.37075 + 2.26297i) q^{7} +(-2.27721 - 1.95303i) q^{9} +O(q^{10})$	\(q+(-0.601162 + 1.62438i) q^{3} -0.207028 q^{5} +(-1.37075 + 2.26297i) q^{7} +(-2.27721 - 1.95303i) q^{9} +1.51705i q^{11} +(-3.39130 - 1.95797i) q^{13} +(0.124457 - 0.336292i) q^{15} +(-0.873421 + 1.51281i) q^{17} +(-0.968573 + 0.559206i) q^{19} +(-2.85188 - 3.58703i) q^{21} -1.44570i q^{23} -4.95714 q^{25} +(4.54143 - 2.52496i) q^{27} +(1.99711 - 1.15303i) q^{29} +(-5.15733 + 2.97759i) q^{31} +(-2.46426 - 0.911991i) q^{33} +(0.283783 - 0.468499i) q^{35} +(-2.13573 - 3.69920i) q^{37} +(5.21920 - 4.33170i) q^{39} +(-2.91134 + 5.04260i) q^{41} +(-0.213489 - 0.369774i) q^{43} +(0.471446 + 0.404332i) q^{45} +(-4.13407 + 7.16042i) q^{47} +(-3.24210 - 6.20393i) q^{49} +(-1.93231 - 2.32821i) q^{51} +(8.16638 + 4.71486i) q^{53} -0.314071i q^{55} +(-0.326092 - 1.90950i) q^{57} +(1.63405 + 2.83025i) q^{59} +(-10.5244 - 6.07629i) q^{61} +(7.54113 - 2.47615i) q^{63} +(0.702095 + 0.405354i) q^{65} +(3.24491 + 5.62035i) q^{67} +(2.34837 + 0.869102i) q^{69} -7.10884i q^{71} +(10.6188 + 6.13075i) q^{73} +(2.98005 - 8.05227i) q^{75} +(-3.43304 - 2.07949i) q^{77} +(-2.57806 + 4.46533i) q^{79} +(1.37135 + 8.89491i) q^{81} +(8.36457 + 14.4879i) q^{83} +(0.180823 - 0.313194i) q^{85} +(0.672371 + 3.93721i) q^{87} +(1.96290 + 3.39984i) q^{89} +(9.07945 - 4.99055i) q^{91} +(-1.73633 - 10.1675i) q^{93} +(0.200522 - 0.115771i) q^{95} +(-13.1184 + 7.57392i) q^{97} +(2.96284 - 3.45463i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{9}+O(q^{10}) $ 48 * q + 2 * q^9	$ 48 q + 2 q^{9} + 8 q^{15} - 10 q^{21} + 48 q^{25} + 18 q^{27} + 18 q^{29} + 18 q^{31} + 12 q^{33} - 4 q^{39} - 6 q^{41} - 6 q^{43} - 18 q^{45} + 18 q^{47} - 12 q^{49} + 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61} - 32 q^{63} - 36 q^{65} - 12 q^{77} + 6 q^{79} + 6 q^{81} - 54 q^{87} - 18 q^{89} + 6 q^{91} + 4 q^{93} - 54 q^{95} - 64 q^{99}+O(q^{100}) $ 48 * q + 2 * q^9 + 8 * q^15 - 10 * q^21 + 48 * q^25 + 18 * q^27 + 18 * q^29 + 18 * q^31 + 12 * q^33 - 4 * q^39 - 6 * q^41 - 6 * q^43 - 18 * q^45 + 18 * q^47 - 12 * q^49 + 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 - 32 * q^63 - 36 * q^65 - 12 * q^77 + 6 * q^79 + 6 * q^81 - 54 * q^87 - 18 * q^89 + 6 * q^91 + 4 * q^93 - 54 * q^95 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−0.601162	+	1.62438i	−0.347081	+	0.937835i
$3$	−0.601162	+	1.62438i	−0.347081	+	0.937835i
$4$		0			0
$5$	−0.207028			−0.0925858			−0.0462929	−	0.998928i	$-0.514741\pi$
$5$	−0.207028			−0.0925858			−0.0462929	+	0.998928i	$0.514741\pi$
$6$		0			0
$7$	−1.37075	+	2.26297i	−0.518094	+	0.855324i
$7$	−1.37075	+	2.26297i	−0.518094	+	0.855324i
$8$		0			0
$9$	−2.27721	−	1.95303i	−0.759069	−	0.651010i
$10$		0			0
$11$			1.51705i			0.457407i	0.973496	+	0.228703i	$0.0734486\pi$
$11$			1.51705i			0.457407i	−0.973496	+	0.228703i	$0.926551\pi$
$12$		0			0
$13$	−3.39130	−	1.95797i	−0.940578	−	0.543043i	−0.0504364	−	0.998727i	$-0.516061\pi$
$13$	−3.39130	−	1.95797i	−0.940578	−	0.543043i	−0.890141	+	0.455684i	$0.849395\pi$
$14$		0			0
$15$	0.124457	−	0.336292i	0.0321348	−	0.0868302i
$16$		0			0
$17$	−0.873421	+	1.51281i	−0.211836	+	0.366910i	−0.952289	−	0.305198i	$-0.901277\pi$
$17$	−0.873421	+	1.51281i	−0.211836	+	0.366910i	0.740453	+	0.672108i	$0.234611\pi$
$18$		0			0
$19$	−0.968573	+	0.559206i	−0.222206	+	0.128291i	−0.606971	−	0.794724i	$-0.707616\pi$
$19$	−0.968573	+	0.559206i	−0.222206	+	0.128291i	0.384765	+	0.923014i	$0.374282\pi$
$20$		0			0
$21$	−2.85188	−	3.58703i	−0.622332	−	0.782753i
$22$		0			0
$23$		−	1.44570i		−	0.301450i	−0.988576	−	0.150725i	$-0.951839\pi$
$23$		−	1.44570i		−	0.301450i	0.988576	−	0.150725i	$-0.0481608\pi$
$24$		0			0
$25$	−4.95714			−0.991428
$26$		0			0
$27$	4.54143	−	2.52496i	0.873999	−	0.485928i
$28$		0			0
$29$	1.99711	−	1.15303i	0.370853	−	0.214112i	−0.302978	−	0.952998i	$-0.597981\pi$
$29$	1.99711	−	1.15303i	0.370853	−	0.214112i	0.673831	+	0.738885i	$0.264648\pi$
$30$		0			0
$31$	−5.15733	+	2.97759i	−0.926285	+	0.534791i	−0.885635	−	0.464383i	$-0.846276\pi$
$31$	−5.15733	+	2.97759i	−0.926285	+	0.534791i	−0.0406501	+	0.999173i	$0.512943\pi$
$32$		0			0
$33$	−2.46426	−	0.911991i	−0.428972	−	0.158757i
$34$		0			0
$35$	0.283783	−	0.468499i	0.0479681	−	0.0791908i
$36$		0			0
$37$	−2.13573	−	3.69920i	−0.351113	−	0.608145i	0.635332	−	0.772239i	$-0.280863\pi$
$37$	−2.13573	−	3.69920i	−0.351113	−	0.608145i	−0.986445	+	0.164094i	$0.947530\pi$
$38$		0			0
$39$	5.21920	−	4.33170i	0.835742	−	0.693627i
$40$		0			0
$41$	−2.91134	+	5.04260i	−0.454676	+	0.787521i	−0.998669	−	0.0515680i	$-0.983578\pi$
$41$	−2.91134	+	5.04260i	−0.454676	+	0.787521i	0.543994	+	0.839089i	$0.316911\pi$
$42$		0			0
$43$	−0.213489	−	0.369774i	−0.0325568	−	0.0563900i	0.849288	−	0.527930i	$-0.177032\pi$
$43$	−0.213489	−	0.369774i	−0.0325568	−	0.0563900i	−0.881845	+	0.471540i	$0.843698\pi$
$44$		0			0
$45$	0.471446	+	0.404332i	0.0702790	+	0.0602743i
$46$		0			0
$47$	−4.13407	+	7.16042i	−0.603016	+	1.04445i	0.389346	+	0.921092i	$0.372701\pi$
$47$	−4.13407	+	7.16042i	−0.603016	+	1.04445i	−0.992362	+	0.123363i	$0.960632\pi$
$48$		0			0
$49$	−3.24210	−	6.20393i	−0.463158	−	0.886276i
$50$		0			0
$51$	−1.93231	−	2.32821i	−0.270577	−	0.326015i
$52$		0			0
$53$	8.16638	+	4.71486i	1.12174	+	0.647636i	0.941844	−	0.336050i	$-0.109091\pi$
$53$	8.16638	+	4.71486i	1.12174	+	0.647636i	0.179894	+	0.983686i	$0.442424\pi$
$54$		0			0
$55$		−	0.314071i		−	0.0423494i
$56$		0			0
$57$	−0.326092	−	1.90950i	−0.0431919	−	0.252920i
$58$		0			0
$59$	1.63405	+	2.83025i	0.212735	+	0.368467i	0.952569	−	0.304321i	$-0.0984297\pi$
$59$	1.63405	+	2.83025i	0.212735	+	0.368467i	−0.739835	+	0.672789i	$0.765096\pi$
$60$		0			0
$61$	−10.5244	−	6.07629i	−1.34752	−	0.777990i	−0.359620	−	0.933099i	$-0.617094\pi$
$61$	−10.5244	−	6.07629i	−1.34752	−	0.777990i	−0.987897	+	0.155109i	$0.950427\pi$
$62$		0			0
$63$	7.54113	−	2.47615i	0.950093	−	0.311966i
$64$		0			0
$65$	0.702095	+	0.405354i	0.0870841	+	0.0502780i
$66$		0			0
$67$	3.24491	+	5.62035i	0.396429	+	0.686635i	0.993282	−	0.115715i	$-0.0369160\pi$
$67$	3.24491	+	5.62035i	0.396429	+	0.686635i	−0.596854	+	0.802350i	$0.703583\pi$
$68$		0			0
$69$	2.34837	+	0.869102i	0.282710	+	0.104628i
$70$		0			0
$71$		−	7.10884i		−	0.843665i	−0.906674	−	0.421832i	$-0.861387\pi$
$71$		−	7.10884i		−	0.843665i	0.906674	−	0.421832i	$-0.138613\pi$
$72$		0			0
$73$	10.6188	+	6.13075i	1.24283	+	0.717549i	0.969670	−	0.244419i	$-0.0785971\pi$
$73$	10.6188	+	6.13075i	1.24283	+	0.717549i	0.273162	+	0.961968i	$0.411930\pi$
$74$		0			0
$75$	2.98005	−	8.05227i	0.344106	−	0.929796i
$76$		0			0
$77$	−3.43304	−	2.07949i	−0.391231	−	0.236980i
$78$		0			0
$79$	−2.57806	+	4.46533i	−0.290054	+	0.502389i	−0.973822	−	0.227311i	$-0.927007\pi$
$79$	−2.57806	+	4.46533i	−0.290054	+	0.502389i	0.683768	+	0.729700i	$0.260340\pi$
$80$		0			0
$81$	1.37135	+	8.89491i	0.152372	+	0.988323i
$82$		0			0
$83$	8.36457	+	14.4879i	0.918131	+	1.59025i	0.802252	+	0.596986i	$0.203635\pi$
$83$	8.36457	+	14.4879i	0.918131	+	1.59025i	0.115879	+	0.993263i	$0.463031\pi$
$84$		0			0
$85$	0.180823	−	0.313194i	0.0196130	−	0.0339707i
$86$		0			0
$87$	0.672371	+	3.93721i	0.0720857	+	0.422113i
$88$		0			0
$89$	1.96290	+	3.39984i	0.208067	+	0.360382i	0.951105	−	0.308866i	$-0.0999496\pi$
$89$	1.96290	+	3.39984i	0.208067	+	0.360382i	−0.743039	+	0.669248i	$0.766616\pi$
$90$		0			0
$91$	9.07945	−	4.99055i	0.951785	−	0.523151i
$92$		0			0
$93$	−1.73633	−	10.1675i	−0.180049	−	1.05432i
$94$		0			0
$95$	0.200522	−	0.115771i	0.0205731	−	0.0118779i
$96$		0			0
$97$	−13.1184	+	7.57392i	−1.33197	+	0.769016i	−0.985602	−	0.169082i	$-0.945920\pi$
$97$	−13.1184	+	7.57392i	−1.33197	+	0.769016i	−0.346372	+	0.938097i	$0.612586\pi$
$98$		0			0
$99$	2.96284	−	3.45463i	0.297776	−	0.347203i
$100$		0			0
$101$	10.2663			1.02153			0.510767	−	0.859719i	$-0.329361\pi$
$101$	10.2663			1.02153			0.510767	+	0.859719i	$0.329361\pi$
$102$		0			0
$103$			11.2576i			1.10924i	0.832103	+	0.554621i	$0.187137\pi$
$103$			11.2576i			1.10924i	−0.832103	+	0.554621i	$0.812863\pi$
$104$		0			0
$105$	0.590420	+	0.742615i	0.0576191	+	0.0724718i
$106$		0			0
$107$	9.87450	−	5.70104i	0.954604	−	0.551141i	0.0600957	−	0.998193i	$-0.480859\pi$
$107$	9.87450	−	5.70104i	0.954604	−	0.551141i	0.894508	+	0.447052i	$0.147526\pi$
$108$		0			0
$109$	1.50422	−	2.60538i	0.144078	−	0.249550i	−0.784951	−	0.619558i	$-0.787312\pi$
$109$	1.50422	−	2.60538i	0.144078	−	0.249550i	0.929029	+	0.370008i	$0.120645\pi$
$110$		0			0
$111$	7.29282	−	1.24542i	0.692204	−	0.118210i
$112$		0			0
$113$	14.2634	+	8.23500i	1.34179	+	0.774683i	0.987070	−	0.160289i	$-0.0512426\pi$
$113$	14.2634	+	8.23500i	1.34179	+	0.774683i	0.354721	+	0.934972i	$0.384576\pi$
$114$		0			0
$115$			0.299301i			0.0279100i
$116$		0			0
$117$	3.89873	+	11.0820i	0.360437	+	1.02453i
$118$		0			0
$119$	−2.22621	−	4.05021i	−0.204076	−	0.371282i
$120$		0			0
$121$	8.69857			0.790779
$122$		0			0
$123$	−6.44089	−	7.76054i	−0.580756	−	0.699745i
$124$		0			0
$125$	2.06141			0.184378
$126$		0			0
$127$	−8.52680			−0.756631			−0.378316	−	0.925677i	$-0.623497\pi$
$127$	−8.52680			−0.756631			−0.378316	+	0.925677i	$0.623497\pi$
$128$		0			0
$129$	0.728995	−	0.124493i	0.0641844	−	0.0109610i
$130$		0			0
$131$	−14.5546			−1.27164			−0.635821	−	0.771837i	$-0.719338\pi$
$131$	−14.5546			−1.27164			−0.635821	+	0.771837i	$0.719338\pi$
$132$		0			0
$133$	0.0622005	−	2.95838i	0.00539347	−	0.256524i
$134$		0			0
$135$	−0.940204	+	0.522737i	−0.0809198	+	0.0449900i
$136$		0			0
$137$			10.6840i			0.912797i	0.889776	+	0.456398i	$0.150861\pi$
$137$			10.6840i			0.912797i	−0.889776	+	0.456398i	$0.849139\pi$
$138$		0			0
$139$	7.46448	+	4.30962i	0.633129	+	0.365537i	0.781963	−	0.623325i	$-0.214219\pi$
$139$	7.46448	+	4.30962i	0.633129	+	0.365537i	−0.148834	+	0.988862i	$0.547552\pi$
$140$		0			0
$141$	−9.14598	−	11.0199i	−0.770230	−	0.928040i
$142$		0			0
$143$	2.97033	−	5.14476i	0.248391	−	0.430227i
$144$		0			0
$145$	−0.413457	+	0.238709i	−0.0343357	+	0.0198237i
$146$		0			0
$147$	12.0266	−	1.53683i	0.991934	−	0.126756i
$148$		0			0
$149$		−	22.0491i		−	1.80633i	−0.429292	−	0.903166i	$-0.641237\pi$
$149$		−	22.0491i		−	1.80633i	0.429292	−	0.903166i	$-0.358763\pi$
$150$		0			0
$151$	−8.80127			−0.716237			−0.358119	−	0.933676i	$-0.616582\pi$
$151$	−8.80127			−0.716237			−0.358119	+	0.933676i	$0.616582\pi$
$152$		0			0
$153$	4.94352	−	1.73916i	0.399660	−	0.140603i
$154$		0			0
$155$	1.06771	−	0.616444i	0.0857608	−	0.0495140i
$156$		0			0
$157$	9.13924	−	5.27654i	0.729391	−	0.421114i	−0.0888086	−	0.996049i	$-0.528306\pi$
$157$	9.13924	−	5.27654i	0.729391	−	0.421114i	0.818199	+	0.574935i	$0.194973\pi$
$158$		0			0
$159$	−12.5680	+	10.4309i	−0.996710	+	0.827223i
$160$		0			0
$161$	3.27159	+	1.98169i	0.257837	+	0.156179i
$162$		0			0
$163$	−4.64731	−	8.04937i	−0.364005	−	0.630475i	0.624611	−	0.780936i	$-0.285258\pi$
$163$	−4.64731	−	8.04937i	−0.364005	−	0.630475i	−0.988616	+	0.150461i	$0.951924\pi$
$164$		0			0
$165$	0.510170	+	0.188808i	0.0397167	+	0.0146987i
$166$		0			0
$167$	−4.44458	+	7.69824i	−0.343932	+	0.595707i	−0.985159	−	0.171644i	$-0.945092\pi$
$167$	−4.44458	+	7.69824i	−0.343932	+	0.595707i	0.641227	+	0.767351i	$0.278426\pi$
$168$		0			0
$169$	1.16728	+	2.02179i	0.0897910	+	0.155523i
$170$		0			0
$171$	3.29779	+	0.618224i	0.252188	+	0.0472768i
$172$		0			0
$173$	4.89970	−	8.48653i	0.372517	−	0.645219i	−0.617435	−	0.786622i	$-0.711828\pi$
$173$	4.89970	−	8.48653i	0.372517	−	0.645219i	0.989952	+	0.141403i	$0.0451614\pi$
$174$		0			0
$175$	6.79499	−	11.2179i	0.513653	−	0.847992i
$176$		0			0
$177$	−5.57972	+	0.952868i	−0.419398	+	0.0716219i
$178$		0			0
$179$	−14.3141	−	8.26425i	−1.06989	−	0.617699i	−0.141735	−	0.989905i	$-0.545268\pi$
$179$	−14.3141	−	8.26425i	−1.06989	−	0.617699i	−0.928150	+	0.372206i	$0.878602\pi$
$180$		0			0
$181$		−	23.8542i		−	1.77307i	−0.462664	−	0.886534i	$-0.653106\pi$
$181$		−	23.8542i		−	1.77307i	0.462664	−	0.886534i	$-0.346894\pi$
$182$		0			0
$183$	16.1971	−	13.4428i	1.19732	−	0.993723i
$184$		0			0
$185$	0.442157	+	0.765838i	0.0325080	+	0.0563056i
$186$		0			0
$187$	−2.29500	−	1.32502i	−0.167827	−	0.0968951i
$188$		0			0
$189$	−0.511241	+	13.7382i	−0.0371873	+	0.999308i
$190$		0			0
$191$	−19.3644	−	11.1800i	−1.40116	−	0.808960i	−0.406648	−	0.913585i	$-0.633302\pi$
$191$	−19.3644	−	11.1800i	−1.40116	−	0.808960i	−0.994512	+	0.104625i	$0.966636\pi$
$192$		0			0
$193$	4.32850	+	7.49719i	0.311572	+	0.539659i	0.978703	−	0.205282i	$-0.0658110\pi$
$193$	4.32850	+	7.49719i	0.311572	+	0.539659i	−0.667131	+	0.744941i	$0.732478\pi$
$194$		0			0
$195$	−1.08052	+	0.896783i	−0.0773778	+	0.0642200i
$196$		0			0
$197$			23.2821i			1.65878i	0.558668	+	0.829391i	$0.311313\pi$
$197$			23.2821i			1.65878i	−0.558668	+	0.829391i	$0.688687\pi$
$198$		0			0
$199$	8.80893	+	5.08584i	0.624449	+	0.360526i	0.778599	−	0.627522i	$-0.215931\pi$
$199$	8.80893	+	5.08584i	0.624449	+	0.360526i	−0.154150	+	0.988047i	$0.549264\pi$
$200$		0			0
$201$	−11.0803	+	1.89222i	−0.781543	+	0.133467i
$202$		0			0
$203$	−0.128252	+	6.09991i	−0.00900150	+	0.428130i
$204$		0			0
$205$	0.602730	−	1.04396i	0.0420965	−	0.0729132i
$206$		0			0
$207$	−2.82350	+	3.29216i	−0.196247	+	0.228821i
$208$		0			0
$209$	−0.848341	−	1.46937i	−0.0586810	−	0.101638i
$210$		0			0
$211$	−13.2184	+	22.8949i	−0.909991	+	1.57615i	−0.0959178	+	0.995389i	$0.530579\pi$
$211$	−13.2184	+	22.8949i	−0.909991	+	1.57615i	−0.814073	+	0.580762i	$0.802755\pi$
$212$		0			0
$213$	11.5475	+	4.27357i	0.791218	+	0.292820i
$214$		0			0
$215$	0.0441983	+	0.0765537i	0.00301430	+	0.00522092i
$216$		0			0
$217$	0.331198	−	15.7524i	0.0224832	−	1.06935i
$218$		0			0
$219$	−16.3422	+	13.5633i	−1.10431	+	0.916524i
$220$		0			0
$221$	5.92407	−	3.42026i	0.398496	−	0.230072i
$222$		0			0
$223$	−14.4887	+	8.36504i	−0.970233	+	0.560164i	−0.899307	−	0.437317i	$-0.855929\pi$
$223$	−14.4887	+	8.36504i	−0.970233	+	0.560164i	−0.0709258	+	0.997482i	$0.522595\pi$
$224$		0			0
$225$	11.2884	+	9.68144i	0.752562	+	0.645429i
$226$		0			0
$227$	−8.88921			−0.589998			−0.294999	−	0.955498i	$-0.595319\pi$
$227$	−8.88921			−0.589998			−0.294999	+	0.955498i	$0.595319\pi$
$228$		0			0
$229$			16.9536i			1.12032i	0.828383	+	0.560162i	$0.189261\pi$
$229$			16.9536i			1.12032i	−0.828383	+	0.560162i	$0.810739\pi$
$230$		0			0
$231$	5.44169	−	4.32644i	0.358037	−	0.284659i
$232$		0			0
$233$	−17.3861	+	10.0379i	−1.13900	+	0.657602i	−0.946183	−	0.323633i	$-0.895096\pi$
$233$	−17.3861	+	10.0379i	−1.13900	+	0.657602i	−0.192817	+	0.981235i	$0.561762\pi$
$234$		0			0
$235$	0.855868	−	1.48241i	0.0558307	−	0.0967016i
$236$		0			0
$237$	−5.70355	−	6.87213i	−0.370486	−	0.446393i
$238$		0			0
$239$	11.5629	+	6.67585i	0.747943	+	0.431825i	0.824950	−	0.565206i	$-0.191203\pi$
$239$	11.5629	+	6.67585i	0.747943	+	0.431825i	−0.0770074	+	0.997031i	$0.524536\pi$
$240$		0			0
$241$		−	12.7673i		−	0.822417i	−0.911541	−	0.411209i	$-0.865107\pi$
$241$		−	12.7673i		−	0.822417i	0.911541	−	0.411209i	$-0.134893\pi$
$242$		0			0
$243$	−15.2731	−	3.11970i	−0.979770	−	0.200129i
$244$		0			0
$245$	0.671206	+	1.28439i	0.0428818	+	0.0820565i
$246$		0			0
$247$	4.37963			0.278669
$248$		0			0
$249$	−28.5622	+	4.87767i	−1.81006	+	0.309110i
$250$		0			0
$251$	−17.8367			−1.12584			−0.562921	−	0.826511i	$-0.690322\pi$
$251$	−17.8367			−1.12584			−0.562921	+	0.826511i	$0.690322\pi$
$252$		0			0
$253$	2.19320			0.137885
$254$		0			0
$255$	0.400042	+	0.482005i	0.0250516	+	0.0301843i
$256$		0			0
$257$	1.63718			0.102124			0.0510621	−	0.998695i	$-0.483739\pi$
$257$	1.63718			0.102124			0.0510621	+	0.998695i	$0.483739\pi$
$258$		0			0
$259$	11.2987	+	0.237558i	0.702070	+	0.0147611i
$260$		0			0
$261$	−6.79972	−	1.27472i	−0.420892	−	0.0789032i
$262$		0			0
$263$		−	30.7251i		−	1.89459i	−0.320359	−	0.947296i	$-0.603803\pi$
$263$		−	30.7251i		−	1.89459i	0.320359	−	0.947296i	$-0.396197\pi$
$264$		0			0
$265$	−1.69067	−	0.976108i	−0.103857	−	0.0599619i
$266$		0			0
$267$	−6.70264	+	1.14463i	−0.410195	+	0.0700503i
$268$		0			0
$269$	0.491194	−	0.850773i	0.0299486	−	0.0518726i	−0.850663	−	0.525712i	$-0.823799\pi$
$269$	0.491194	−	0.850773i	0.0299486	−	0.0518726i	0.880611	+	0.473839i	$0.157132\pi$
$270$		0			0
$271$	−0.707412	+	0.408425i	−0.0429722	+	0.0248100i	−0.521332	−	0.853354i	$-0.674565\pi$
$271$	−0.707412	+	0.408425i	−0.0429722	+	0.0248100i	0.478360	+	0.878164i	$0.341231\pi$
$272$		0			0
$273$	2.64831	+	17.7486i	0.160283	+	1.07419i
$274$		0			0
$275$		−	7.52021i		−	0.453486i
$276$		0			0
$277$	10.6038			0.637118			0.318559	−	0.947903i	$-0.396801\pi$
$277$	10.6038			0.637118			0.318559	+	0.947903i	$0.396801\pi$
$278$		0			0
$279$	17.5596	+	3.29184i	1.05127	+	0.197077i
$280$		0			0
$281$	14.1764	−	8.18477i	0.845695	−	0.488262i	−0.0135009	−	0.999909i	$-0.504298\pi$
$281$	14.1764	−	8.18477i	0.845695	−	0.488262i	0.859196	+	0.511647i	$0.170964\pi$
$282$		0			0
$283$	−5.67689	+	3.27755i	−0.337456	+	0.194830i	−0.659146	−	0.752015i	$-0.729082\pi$
$283$	−5.67689	+	3.27755i	−0.337456	+	0.194830i	0.321691	+	0.946845i	$0.395749\pi$
$284$		0			0
$285$	0.0675102	+	0.395320i	0.00399896	+	0.0234168i
$286$		0			0
$287$	−7.42055	−	13.5004i	−0.438021	−	0.796905i
$288$		0			0
$289$	6.97427	+	12.0798i	0.410251	+	0.710576i
$290$		0			0
$291$	−4.41661	−	25.8624i	−0.258906	−	1.51608i
$292$		0			0
$293$	−7.02441	+	12.1666i	−0.410370	+	0.710782i	−0.994930	−	0.100568i	$-0.967934\pi$
$293$	−7.02441	+	12.1666i	−0.410370	+	0.710782i	0.584560	+	0.811351i	$0.301267\pi$
$294$		0			0
$295$	−0.338293	−	0.585941i	−0.0196962	−	0.0341148i
$296$		0			0
$297$	3.83048	+	6.88956i	0.222267	+	0.399773i
$298$		0			0
$299$	−2.83064	+	4.90281i	−0.163700	+	0.283537i
$300$		0			0
$301$	1.12943	+	0.0237464i	0.0650992	+	0.00136872i
$302$		0			0
$303$	−6.17171	+	16.6763i	−0.354556	+	0.958031i
$304$		0			0
$305$	2.17886	+	1.25796i	0.124761	+	0.0720308i
$306$		0			0
$307$		−	17.4335i		−	0.994982i	−0.867469	−	0.497491i	$-0.834255\pi$
$307$		−	17.4335i		−	0.994982i	0.867469	−	0.497491i	$-0.165745\pi$
$308$		0			0
$309$	−18.2866	−	6.76764i	−1.04029	−	0.384997i
$310$		0			0
$311$	−7.79813	−	13.5068i	−0.442191	−	0.765898i	0.555661	−	0.831409i	$-0.312465\pi$
$311$	−7.79813	−	13.5068i	−0.442191	−	0.765898i	−0.997852	+	0.0655116i	$0.979132\pi$
$312$		0			0
$313$	−1.93111	−	1.11493i	−0.109153	−	0.0630193i	0.444430	−	0.895814i	$-0.353406\pi$
$313$	−1.93111	−	1.11493i	−0.109153	−	0.0630193i	−0.553582	+	0.832794i	$0.686740\pi$
$314$		0			0
$315$	−1.56123	+	0.512633i	−0.0879651	+	0.0288836i
$316$		0			0
$317$	−29.7264	−	17.1625i	−1.66960	−	0.963943i	−0.967853	−	0.251515i	$-0.919071\pi$
$317$	−29.7264	−	17.1625i	−1.66960	−	0.963943i	−0.701745	−	0.712428i	$-0.747595\pi$
$318$		0			0
$319$	1.74920	+	3.02970i	0.0979364	+	0.169631i
$320$		0			0
$321$	3.32447	+	19.4672i	0.185554	+	1.08655i
$322$		0			0
$323$		−	1.95369i		−	0.108706i
$324$		0			0
$325$	16.8112	+	9.70592i	0.932515	+	0.538388i
$326$		0			0
$327$	3.32784	+	4.00967i	0.184030	+	0.221735i
$328$		0			0
$329$	−10.5371	−	19.1704i	−0.580928	−	1.05690i
$330$		0			0
$331$	11.2701	−	19.5205i	0.619463	−	1.07294i	−0.370121	−	0.928984i	$-0.620684\pi$
$331$	11.2701	−	19.5205i	0.619463	−	1.07294i	0.989584	−	0.143958i	$-0.0459829\pi$
$332$		0			0
$333$	−2.36114	+	12.5950i	−0.129390	+	0.690202i
$334$		0			0
$335$	−0.671787	−	1.16357i	−0.0367037	−	0.0635726i
$336$		0			0
$337$	−11.3776	+	19.7065i	−0.619776	+	1.07348i	0.369750	+	0.929131i	$0.379443\pi$
$337$	−11.3776	+	19.7065i	−0.619776	+	1.07348i	−0.989526	+	0.144353i	$0.953890\pi$
$338$		0			0
$339$	−21.9514	+	18.2186i	−1.19224	+	0.989500i
$340$		0			0
$341$	−4.51714	−	7.82392i	−0.244617	−	0.423689i
$342$		0			0
$343$	18.4834	+	1.16723i	0.998012	+	0.0630244i
$344$		0			0
$345$	−0.486178	−	0.179928i	−0.0261749	−	0.00968702i
$346$		0			0
$347$	6.46927	−	3.73504i	0.347289	−	0.200507i	−0.316202	−	0.948692i	$-0.602408\pi$
$347$	6.46927	−	3.73504i	0.347289	−	0.200507i	0.663491	+	0.748185i	$0.269074\pi$
$348$		0			0
$349$	7.60969	−	4.39346i	0.407337	−	0.235176i	−0.282308	−	0.959324i	$-0.591100\pi$
$349$	7.60969	−	4.39346i	0.407337	−	0.235176i	0.689645	+	0.724148i	$0.257767\pi$
$350$		0			0
$351$	−20.3451	−	0.329087i	−1.08594	−	0.0175654i
$352$		0			0
$353$	7.32610			0.389929			0.194965	−	0.980810i	$-0.437541\pi$
$353$	7.32610			0.389929			0.194965	+	0.980810i	$0.437541\pi$
$354$		0			0
$355$			1.47173i			0.0781113i
$356$		0			0
$357$	7.91738	−	1.18137i	0.419032	−	0.0625248i
$358$		0			0
$359$	11.0036	−	6.35295i	0.580749	−	0.335296i	−0.180682	−	0.983542i	$-0.557830\pi$
$359$	11.0036	−	6.35295i	0.580749	−	0.335296i	0.761431	+	0.648246i	$0.224497\pi$
$360$		0			0
$361$	−8.87458	+	15.3712i	−0.467083	+	0.809012i
$362$		0			0
$363$	−5.22925	+	14.1298i	−0.274465	+	0.741620i
$364$		0			0
$365$	−2.19838	−	1.26924i	−0.115069	−	0.0664349i
$366$		0			0
$367$		−	16.2728i		−	0.849435i	−0.905326	−	0.424717i	$-0.860374\pi$
$367$		−	16.2728i		−	0.849435i	0.905326	−	0.424717i	$-0.139626\pi$
$368$		0			0
$369$	16.4781	−	5.79709i	0.857814	−	0.301785i
$370$		0			0
$371$	−21.8636	+	12.0174i	−1.13510	+	0.623913i
$372$		0			0
$373$	15.8803			0.822251			0.411126	−	0.911579i	$-0.365136\pi$
$373$	15.8803			0.822251			0.411126	+	0.911579i	$0.365136\pi$
$374$		0			0
$375$	−1.23924	+	3.34850i	−0.0639941	+	0.172916i
$376$		0			0
$377$	−9.03038			−0.465088
$378$		0			0
$379$	−0.0882488			−0.00453304			−0.00226652	−	0.999997i	$-0.500721\pi$
$379$	−0.0882488			−0.00453304			−0.00226652	+	0.999997i	$0.500721\pi$
$380$		0			0
$381$	5.12599	−	13.8508i	0.262613	−	0.709595i
$382$		0			0
$383$	33.9273			1.73360			0.866802	−	0.498652i	$-0.166172\pi$
$383$	33.9273			1.73360			0.866802	+	0.498652i	$0.166172\pi$
$384$		0			0
$385$	0.710735	+	0.430512i	0.0362224	+	0.0219409i
$386$		0			0
$387$	−0.236021	+	1.25900i	−0.0119976	+	0.0639988i
$388$		0			0
$389$		−	11.3976i		−	0.577881i	−0.957347	−	0.288940i	$-0.906697\pi$
$389$		−	11.3976i		−	0.577881i	0.957347	−	0.288940i	$-0.0933029\pi$
$390$		0			0
$391$	2.18707	+	1.26271i	0.110605	+	0.0638578i
$392$		0			0
$393$	8.74968	−	23.6422i	0.441363	−	1.19259i
$394$		0			0
$395$	0.533731	−	0.924449i	0.0268549	−	0.0465141i
$396$		0			0
$397$	−3.81168	+	2.20068i	−0.191303	+	0.110449i	−0.592592	−	0.805503i	$-0.701895\pi$
$397$	−3.81168	+	2.20068i	−0.191303	+	0.110449i	0.401289	+	0.915951i	$0.368562\pi$
$398$		0			0
$399$	4.76814	+	1.87951i	0.238706	+	0.0940930i
$400$		0			0
$401$		−	8.48250i		−	0.423596i	−0.977313	−	0.211798i	$-0.932068\pi$
$401$		−	8.48250i		−	0.423596i	0.977313	−	0.211798i	$-0.0679318\pi$
$402$		0			0
$403$	23.3201			1.16166
$404$		0			0
$405$	−0.283908	−	1.84150i	−0.0141075	−	0.0915047i
$406$		0			0
$407$	5.61186	−	3.24001i	0.278170	−	0.160601i
$408$		0			0
$409$	10.0254	−	5.78819i	0.495726	−	0.286207i	−0.231221	−	0.972901i	$-0.574272\pi$
$409$	10.0254	−	5.78819i	0.495726	−	0.286207i	0.726947	+	0.686694i	$0.240939\pi$
$410$		0			0
$411$	−17.3549	−	6.42283i	−0.856053	−	0.316815i
$412$		0			0
$413$	−8.64465	−	0.181755i	−0.425375	−	0.00894359i
$414$		0			0
$415$	−1.73170	−	2.99939i	−0.0850059	−	0.147234i
$416$		0			0
$417$	−11.4878	+	9.53436i	−0.562561	+	0.466900i
$418$		0			0
$419$	−11.3173	+	19.6021i	−0.552885	+	0.957625i	0.445180	+	0.895441i	$0.353140\pi$
$419$	−11.3173	+	19.6021i	−0.552885	+	0.957625i	−0.998065	+	0.0621839i	$0.980193\pi$
$420$		0			0
$421$	−3.51429	−	6.08693i	−0.171276	−	0.296659i	0.767590	−	0.640941i	$-0.221456\pi$
$421$	−3.51429	−	6.08693i	−0.171276	−	0.296659i	−0.938866	+	0.344282i	$0.888122\pi$
$422$		0			0
$423$	23.3986	−	8.23180i	1.13768	−	0.400244i
$424$		0			0
$425$	4.32967	−	7.49921i	0.210020	−	0.363765i
$426$		0			0
$427$	28.1769	−	15.4875i	1.36357	−	0.749492i
$428$		0			0
$429$	6.57139	+	7.91778i	0.317270	+	0.382274i
$430$		0			0
$431$	0.267173	+	0.154252i	0.0128693	+	0.00743007i	0.506421	−	0.862286i	$-0.330968\pi$
$431$	0.267173	+	0.154252i	0.0128693	+	0.00743007i	−0.493552	+	0.869717i	$0.664302\pi$
$432$		0			0
$433$		−	32.8376i		−	1.57807i	−0.614347	−	0.789036i	$-0.710580\pi$
$433$		−	32.8376i		−	1.57807i	0.614347	−	0.789036i	$-0.289420\pi$
$434$		0			0
$435$	−0.139200	−	0.815113i	−0.00667411	−	0.0390817i
$436$		0			0
$437$	0.808445	+	1.40027i	0.0386732	+	0.0669839i
$438$		0			0
$439$	2.91256	+	1.68157i	0.139009	+	0.0802568i	0.567891	−	0.823103i	$-0.307759\pi$
$439$	2.91256	+	1.68157i	0.139009	+	0.0802568i	−0.428883	+	0.903360i	$0.641093\pi$
$440$		0			0
$441$	−4.73352	+	20.4596i	−0.225406	+	0.974265i
$442$		0			0
$443$	31.0997	+	17.9554i	1.47759	+	0.853087i	0.999679	−	0.0253206i	$-0.00806066\pi$
$443$	31.0997	+	17.9554i	1.47759	+	0.853087i	0.477911	+	0.878408i	$0.341394\pi$
$444$		0			0
$445$	−0.406375	−	0.703862i	−0.0192640	−	0.0333662i
$446$		0			0
$447$	35.8160	+	13.2551i	1.69404	+	0.626944i
$448$		0			0
$449$		−	13.9993i		−	0.660668i	−0.943864	−	0.330334i	$-0.892839\pi$
$449$		−	13.9993i		−	0.660668i	0.943864	−	0.330334i	$-0.107161\pi$
$450$		0			0
$451$	−7.64985	−	4.41664i	−0.360217	−	0.207972i
$452$		0			0
$453$	5.29099	−	14.2966i	0.248593	−	0.671712i
$454$		0			0
$455$	−1.87970	+	1.03318i	−0.0881217	+	0.0484364i
$456$		0			0
$457$	−3.97051	+	6.87713i	−0.185733	+	0.321699i	−0.943823	−	0.330451i	$-0.892799\pi$
$457$	−3.97051	+	6.87713i	−0.185733	+	0.321699i	0.758090	+	0.652149i	$0.226133\pi$
$458$		0			0
$459$	−0.146801	+	9.07567i	−0.00685208	+	0.423616i
$460$		0			0
$461$	2.12627	+	3.68281i	0.0990304	+	0.171526i	0.911284	−	0.411779i	$-0.135093\pi$
$461$	2.12627	+	3.68281i	0.0990304	+	0.171526i	−0.812253	+	0.583305i	$0.801759\pi$
$462$		0			0
$463$	−10.2557	+	17.7634i	−0.476622	+	0.825534i	−0.999641	−	0.0267869i	$-0.991472\pi$
$463$	−10.2557	+	17.7634i	−0.476622	+	0.825534i	0.523019	+	0.852321i	$0.324806\pi$
$464$		0			0
$465$	0.359470	+	2.10495i	0.0166700	+	0.0976148i
$466$		0			0
$467$	13.8842	+	24.0481i	0.642484	+	1.11281i	0.984877	+	0.173257i	$0.0554292\pi$
$467$	13.8842	+	24.0481i	0.642484	+	1.11281i	−0.342393	+	0.939557i	$0.611237\pi$
$468$		0			0
$469$	−17.1667	−	0.360932i	−0.792682	−	0.0166663i
$470$		0			0
$471$	3.07693	+	18.0176i	0.141778	+	0.830209i
$472$		0			0
$473$	0.560965	−	0.323873i	0.0257932	−	0.0148917i
$474$		0			0
$475$	4.80135	−	2.77206i	0.220301	−	0.127191i
$476$		0			0
$477$	−9.38827	−	26.6859i	−0.429860	−	1.22186i
$478$		0			0
$479$	−31.4128			−1.43529			−0.717643	−	0.696411i	$-0.754779\pi$
$479$	−31.4128			−1.43529			−0.717643	+	0.696411i	$0.754779\pi$
$480$		0			0
$481$			16.7268i			0.762677i
$482$		0			0
$483$	−5.18577	+	4.12297i	−0.235961	+	0.187602i
$484$		0			0
$485$	2.71588	−	1.56801i	0.123322	−	0.0711999i
$486$		0			0
$487$	−16.1798	+	28.0242i	−0.733176	+	1.26990i	0.222343	+	0.974968i	$0.428629\pi$
$487$	−16.1798	+	28.0242i	−0.733176	+	1.26990i	−0.955519	+	0.294929i	$0.904704\pi$
$488$		0			0
$489$	15.8690	−	2.71000i	0.717621	−	0.122551i
$490$		0			0
$491$	33.6617	+	19.4346i	1.51913	+	0.877071i	0.999746	+	0.0225309i	$0.00717243\pi$
$491$	33.6617	+	19.4346i	1.51913	+	0.877071i	0.519385	+	0.854540i	$0.326161\pi$
$492$		0			0
$493$			4.02832i			0.181426i
$494$		0			0
$495$	−0.613390	+	0.715205i	−0.0275699	+	0.0321461i
$496$		0			0
$497$	16.0871	+	9.74443i	0.721606	+	0.437097i
$498$		0			0
$499$	39.7540			1.77963			0.889816	−	0.456319i	$-0.150832\pi$
$499$	39.7540			1.77963			0.889816	+	0.456319i	$0.150832\pi$
$500$		0			0
$501$	−9.83293	−	11.8476i	−0.439303	−	0.529310i
$502$		0			0
$503$	−4.45463			−0.198622			−0.0993110	−	0.995056i	$-0.531664\pi$
$503$	−4.45463			−0.198622			−0.0993110	+	0.995056i	$0.531664\pi$
$504$		0			0
$505$	−2.12541			−0.0945796
$506$		0			0
$507$	−3.98588	+	0.680683i	−0.177019	+	0.0302302i
$508$		0			0
$509$	−19.8433			−0.879539			−0.439769	−	0.898111i	$-0.644940\pi$
$509$	−19.8433			−0.879539			−0.439769	+	0.898111i	$0.644940\pi$
$510$		0			0
$511$	−28.4294	+	15.6263i	−1.25764	+	0.691266i
$512$		0			0
$513$	−2.98673	+	4.98520i	−0.131868	+	0.220102i
$514$		0			0
$515$		−	2.33064i		−	0.102700i
$516$		0			0
$517$	−10.8627	−	6.27157i	−0.477740	−	0.275824i
$518$		0			0
$519$	10.8398	+	13.0607i	0.475815	+	0.573303i
$520$		0			0
$521$	−6.51527	+	11.2848i	−0.285439	+	0.494395i	−0.972716	−	0.232001i	$-0.925473\pi$
$521$	−6.51527	+	11.2848i	−0.285439	+	0.494395i	0.687277	+	0.726396i	$0.258806\pi$
$522$		0			0
$523$	28.6981	−	16.5688i	1.25488	−	0.724505i	0.282805	−	0.959177i	$-0.408735\pi$
$523$	28.6981	−	16.5688i	1.25488	−	0.724505i	0.972075	+	0.234672i	$0.0754017\pi$
$524$		0			0
$525$	14.1372	+	17.7814i	0.616997	+	0.776044i
$526$		0			0
$527$		−	10.4028i		−	0.453151i
$528$		0			0
$529$	20.9099			0.909128
$530$		0			0
$531$	1.80650	−	9.63641i	0.0783955	−	0.418185i
$532$		0			0
$533$	19.7465	−	11.4006i	0.855315	−	0.493817i
$534$		0			0
$535$	−2.04430	+	1.18028i	−0.0883827	+	0.0510278i
$536$		0			0
$537$	22.0294	−	18.2833i	0.950637	−	0.788985i
$538$		0			0
$539$	9.41165	−	4.91842i	0.405389	−	0.211851i
$540$		0			0
$541$	13.3022	+	23.0402i	0.571908	+	0.990574i	0.996370	+	0.0851281i	$0.0271300\pi$
$541$	13.3022	+	23.0402i	0.571908	+	0.990574i	−0.424462	+	0.905446i	$0.639537\pi$
$542$		0			0
$543$	38.7482	+	14.3402i	1.66284	+	0.615399i
$544$		0			0
$545$	−0.311415	+	0.539387i	−0.0133396	+	0.0231048i
$546$		0			0
$547$	−4.32361	−	7.48870i	−0.184864	−	0.320194i	0.758667	−	0.651479i	$-0.225851\pi$
$547$	−4.32361	−	7.48870i	−0.184864	−	0.320194i	−0.943531	+	0.331285i	$0.892518\pi$
$548$		0			0
$549$	12.0992	+	34.3915i	0.516380	+	1.46780i
$550$		0			0
$551$	−1.28956	+	2.23359i	−0.0549372	+	0.0951539i
$552$		0			0
$553$	−6.57106	−	11.9549i	−0.279430	−	0.508375i
$554$		0			0
$555$	−1.50982	+	0.257837i	−0.0640882	+	0.0109446i
$556$		0			0
$557$	19.1707	+	11.0682i	0.812289	+	0.468975i	0.847750	−	0.530396i	$-0.177957\pi$
$557$	19.1707	+	11.0682i	0.812289	+	0.468975i	−0.0354610	+	0.999371i	$0.511290\pi$
$558$		0			0
$559$			1.67202i			0.0707190i
$560$		0			0
$561$	3.53200	−	2.93140i	0.149121	−	0.123764i
$562$		0			0
$563$	6.10275	+	10.5703i	0.257200	+	0.445484i	0.965491	−	0.260437i	$-0.0838667\pi$
$563$	6.10275	+	10.5703i	0.257200	+	0.445484i	−0.708291	+	0.705921i	$0.750533\pi$
$564$		0			0
$565$	−2.95293	−	1.70488i	−0.124231	−	0.0717247i
$566$		0			0
$567$	−22.0087	−	9.08935i	−0.924279	−	0.381717i
$568$		0			0
$569$	−8.16135	−	4.71196i	−0.342142	−	0.197536i	0.319077	−	0.947729i	$-0.396627\pi$
$569$	−8.16135	−	4.71196i	−0.342142	−	0.197536i	−0.661219	+	0.750193i	$0.729960\pi$
$570$		0			0
$571$	−7.73579	−	13.3988i	−0.323733	−	0.560721i	0.657522	−	0.753435i	$-0.271604\pi$
$571$	−7.73579	−	13.3988i	−0.323733	−	0.560721i	−0.981255	+	0.192714i	$0.938271\pi$
$572$		0			0
$573$	29.8018	−	24.7341i	1.24499	−	1.03328i
$574$		0			0
$575$			7.16655i			0.298866i
$576$		0			0
$577$	−8.48608	−	4.89944i	−0.353280	−	0.203966i	0.312849	−	0.949803i	$-0.398717\pi$
$577$	−8.48608	−	4.89944i	−0.353280	−	0.203966i	−0.666129	+	0.745836i	$0.732050\pi$
$578$		0			0
$579$	−14.7804	+	2.52410i	−0.614252	+	0.104898i
$580$		0			0
$581$	−44.2514	−	0.930392i	−1.83586	−	0.0385992i
$582$		0			0
$583$	−7.15266	+	12.3888i	−0.296233	+	0.513091i
$584$		0			0
$585$	−0.807146	−	2.29429i	−0.0333714	−	0.0948571i
$586$		0			0
$587$	12.4297	+	21.5289i	0.513028	+	0.888591i	0.999886	+	0.0151097i	$0.00480974\pi$
$587$	12.4297	+	21.5289i	0.513028	+	0.888591i	−0.486858	+	0.873481i	$0.661857\pi$
$588$		0			0
$589$	3.33017	−	5.76802i	0.137217	−	0.237667i
$590$		0			0
$591$	−37.8190	−	13.9963i	−1.55566	−	0.575732i
$592$		0			0
$593$	−20.9831	−	36.3438i	−0.861673	−	1.49246i	−0.870313	−	0.492500i	$-0.836083\pi$
$593$	−20.9831	−	36.3438i	−0.861673	−	1.49246i	0.00863918	−	0.999963i	$-0.497250\pi$
$594$		0			0
$595$	0.460888	+	0.838507i	0.0188946	+	0.0343754i
$596$		0			0
$597$	−13.5569	+	11.2516i	−0.554848	+	0.460498i
$598$		0			0
$599$	26.2575	−	15.1598i	1.07285	−	0.619412i	0.143894	−	0.989593i	$-0.454038\pi$
$599$	26.2575	−	15.1598i	1.07285	−	0.619412i	0.928960	+	0.370181i	$0.120704\pi$
$600$		0			0
$601$	−2.71173	+	1.56562i	−0.110614	+	0.0638628i	−0.554286	−	0.832326i	$-0.687009\pi$
$601$	−2.71173	+	1.56562i	−0.110614	+	0.0638628i	0.443673	+	0.896189i	$0.353675\pi$
$602$		0			0
$603$	3.58738	−	19.1361i	0.146089	−	0.779282i
$604$		0			0
$605$	−1.80085			−0.0732149
$606$		0			0
$607$		−	14.3866i		−	0.583934i	−0.956428	−	0.291967i	$-0.905690\pi$
$607$		−	14.3866i		−	0.583934i	0.956428	−	0.291967i	$-0.0943097\pi$
$608$		0			0
$609$	−9.83146	−	3.87537i	−0.398391	−	0.157038i
$610$		0			0
$611$	28.0397	−	16.1888i	1.13437	−	0.654927i
$612$		0			0
$613$	−4.36863	+	7.56669i	−0.176447	+	0.305616i	−0.940661	−	0.339347i	$-0.889794\pi$
$613$	−4.36863	+	7.56669i	−0.176447	+	0.305616i	0.764214	+	0.644963i	$0.223127\pi$
$614$		0			0
$615$	1.33345	+	1.60665i	0.0537697	+	0.0647864i
$616$		0			0
$617$	−25.9444	−	14.9790i	−1.04448	−	0.603033i	−0.123384	−	0.992359i	$-0.539375\pi$
$617$	−25.9444	−	14.9790i	−1.04448	−	0.603033i	−0.921100	+	0.389326i	$0.872708\pi$
$618$		0			0
$619$		−	2.63070i		−	0.105737i	−0.998601	−	0.0528683i	$-0.983164\pi$
$619$		−	2.63070i		−	0.105737i	0.998601	−	0.0528683i	$-0.0168363\pi$
$620$		0			0
$621$	−3.65034	−	6.56556i	−0.146483	−	0.263467i
$622$		0			0
$623$	−10.3844	−	0.218333i	−0.416041	−	0.00874734i
$624$		0			0
$625$	24.3589			0.974357
$626$		0			0
$627$	2.89680	−	0.494697i	0.115687	−	0.0197563i
$628$		0			0
$629$	7.46158			0.297513
$630$		0			0
$631$	−18.0872			−0.720039			−0.360019	−	0.932945i	$-0.617230\pi$
$631$	−18.0872			−0.720039			−0.360019	+	0.932945i	$0.617230\pi$
$632$		0			0
$633$	−29.2436	−	35.2352i	−1.16233	−	1.40047i
$634$		0			0
$635$	1.76529			0.0700533
$636$		0			0
$637$	−1.15216	+	27.3873i	−0.0456501	+	1.08513i
$638$		0			0
$639$	−13.8838	+	16.1883i	−0.549234	+	0.640400i
$640$		0			0
$641$			41.1733i			1.62625i	0.582091	+	0.813124i	$0.302235\pi$
$641$			41.1733i			1.62625i	−0.582091	+	0.813124i	$0.697765\pi$
$642$		0			0
$643$	−31.3046	−	18.0737i	−1.23453	−	0.712758i	−0.266561	−	0.963818i	$-0.585887\pi$
$643$	−31.3046	−	18.0737i	−1.23453	−	0.712758i	−0.967971	+	0.251060i	$0.919221\pi$
$644$		0			0
$645$	−0.150922	+	0.0257735i	−0.00594256	+	0.00101483i
$646$		0			0
$647$	4.09812	−	7.09815i	0.161114	−	0.279057i	−0.774155	−	0.632996i	$-0.781825\pi$
$647$	4.09812	−	7.09815i	0.161114	−	0.279057i	0.935268	+	0.353939i	$0.115158\pi$
$648$		0			0
$649$	−4.29362	+	2.47892i	−0.168539	+	0.0973063i
$650$		0			0
$651$	25.3888	+	10.0078i	0.995066	+	0.392235i
$652$		0			0
$653$			26.9751i			1.05562i	0.849364	+	0.527808i	$0.176986\pi$
$653$			26.9751i			1.05562i	−0.849364	+	0.527808i	$0.823014\pi$
$654$		0			0
$655$	3.01321			0.117736
$656$		0			0
$657$	−12.2076	−	34.6997i	−0.476264	−	1.35377i
$658$		0			0
$659$	−2.60125	+	1.50183i	−0.101330	+	0.0585032i	−0.549809	−	0.835291i	$-0.685299\pi$
$659$	−2.60125	+	1.50183i	−0.101330	+	0.0585032i	0.448478	+	0.893794i	$0.351966\pi$
$660$		0			0
$661$	−31.2423	+	18.0377i	−1.21518	+	0.701586i	−0.963884	−	0.266323i	$-0.914191\pi$
$661$	−31.2423	+	18.0377i	−1.21518	+	0.701586i	−0.251299	+	0.967909i	$0.580858\pi$
$662$		0			0
$663$	1.99447	+	11.6791i	0.0774588	+	0.453577i
$664$		0			0
$665$	−0.0128773	+	0.612469i	−0.000499359	+	0.0237505i
$666$		0			0
$667$	−1.66694	−	2.88722i	−0.0645441	−	0.111794i
$668$		0			0
$669$	−4.87794	−	28.5638i	−0.188592	−	1.10434i
$670$		0			0
$671$	9.21802	−	15.9661i	0.355858	−	0.616364i
$672$		0			0
$673$	3.20540	+	5.55191i	0.123559	+	0.214010i	0.921169	−	0.389163i	$-0.127236\pi$
$673$	3.20540	+	5.55191i	0.123559	+	0.214010i	−0.797610	+	0.603174i	$0.793903\pi$
$674$		0			0
$675$	−22.5125	+	12.5166i	−0.866507	+	0.481763i
$676$		0			0
$677$	17.2249	−	29.8344i	0.662007	−	1.14663i	−0.318081	−	0.948064i	$-0.603038\pi$
$677$	17.2249	−	29.8344i	0.662007	−	1.14663i	0.980088	−	0.198566i	$-0.0636284\pi$
$678$		0			0
$679$	0.842449	−	40.0686i	0.0323302	−	1.53769i
$680$		0			0
$681$	5.34386	−	14.4394i	0.204777	−	0.553321i
$682$		0			0
$683$	2.53802	+	1.46533i	0.0971148	+	0.0560693i	0.547771	−	0.836628i	$-0.315477\pi$
$683$	2.53802	+	1.46533i	0.0971148	+	0.0560693i	−0.450656	+	0.892698i	$0.648810\pi$
$684$		0			0
$685$		−	2.21189i		−	0.0845120i
$686$		0			0
$687$	−27.5390	−	10.1919i	−1.05068	−	0.388843i
$688$		0			0
$689$	−18.4631	−	31.9790i	−0.703388	−	1.21830i
$690$		0			0
$691$	−3.29381	−	1.90168i	−0.125303	−	0.0723434i	0.436039	−	0.899928i	$-0.356381\pi$
$691$	−3.29381	−	1.90168i	−0.125303	−	0.0723434i	−0.561341	+	0.827585i	$0.689714\pi$
$692$		0			0
$693$	3.75644	+	11.4402i	0.142695	+	0.434579i
$694$		0			0
$695$	−1.54536	−	0.892213i	−0.0586188	−	0.0338436i
$696$		0			0
$697$	−5.08566	−	8.80862i	−0.192633	−	0.333650i
$698$		0			0
$699$	−5.85341	−	34.2759i	−0.221396	−	1.29643i
$700$		0			0
$701$			36.7042i			1.38630i	0.720795	+	0.693149i	$0.243777\pi$
$701$			36.7042i			1.38630i	−0.720795	+	0.693149i	$0.756223\pi$
$702$		0			0
$703$	4.13723	+	2.38863i	0.156039	+	0.0900889i
$704$		0			0
$705$	1.89347	+	2.28142i	0.0713124	+	0.0859233i
$706$		0			0
$707$	−14.0725	+	23.2324i	−0.529251	+	0.873743i
$708$		0			0
$709$	−10.4040	+	18.0202i	−0.390730	+	0.676764i	−0.992546	−	0.121870i	$-0.961111\pi$
$709$	−10.4040	+	18.0202i	−0.390730	+	0.676764i	0.601816	+	0.798635i	$0.294444\pi$
$710$		0			0
$711$	14.5917	−	5.13346i	0.547232	−	0.192520i
$712$		0			0
$713$	4.30471	+	7.45597i	0.161213	+	0.279228i
$714$		0			0
$715$	−0.614942	+	1.06511i	−0.0229975	+	0.0398329i
$716$		0			0
$717$	−17.7953	+	14.7693i	−0.664577	+	0.551569i
$718$		0			0
$719$	15.1577	+	26.2540i	0.565288	+	0.979108i	0.997023	+	0.0771074i	$0.0245684\pi$
$719$	15.1577	+	26.2540i	0.565288	+	0.979108i	−0.431734	+	0.902001i	$0.642098\pi$
$720$		0			0
$721$	−25.4756	−	15.4313i	−0.948761	−	0.574692i
$722$		0			0
$723$	20.7390	+	7.67525i	0.771292	+	0.285446i
$724$		0			0
$725$	−9.89993	+	5.71573i	−0.367674	+	0.212277i
$726$		0			0
$727$	−29.7259	+	17.1622i	−1.10247	+	0.636512i	−0.936869	−	0.349680i	$-0.886290\pi$
$727$	−29.7259	+	17.1622i	−1.10247	+	0.636512i	−0.165602	+	0.986193i	$0.552957\pi$
$728$		0			0
$729$	14.2492	−	22.9338i	0.527747	−	0.849401i
$730$		0			0
$731$	0.745864			0.0275868
$732$		0			0
$733$			6.18213i			0.228342i	0.993461	+	0.114171i	$0.0364212\pi$
$733$			6.18213i			0.228342i	−0.993461	+	0.114171i	$0.963579\pi$
$734$		0			0
$735$	−2.48984	+	0.318167i	−0.0918390	+	0.0117358i
$736$		0			0
$737$	−8.52633	+	4.92268i	−0.314071	+	0.181329i
$738$		0			0
$739$	−13.5892	+	23.5372i	−0.499887	+	0.865829i	−1.00000		0.000131035i	$-0.999958\pi$
$739$	−13.5892	+	23.5372i	−0.499887	+	0.865829i	0.500113	+	0.865960i	$0.333292\pi$
$740$		0			0
$741$	−2.63287	+	7.11417i	−0.0967208	+	0.261346i
$742$		0			0
$743$	24.3213	+	14.0419i	0.892262	+	0.515148i	0.874682	−	0.484698i	$-0.161070\pi$
$743$	24.3213	+	14.0419i	0.892262	+	0.515148i	0.0175804	+	0.999845i	$0.494404\pi$
$744$		0			0
$745$			4.56478i			0.167241i
$746$		0			0
$747$	9.24736	−	49.3281i	0.338343	−	1.80482i
$748$		0			0
$749$	−0.634128	+	30.1604i	−0.0231705	+	1.10204i
$750$		0			0
$751$	−42.1842			−1.53932			−0.769661	−	0.638453i	$-0.779575\pi$
$751$	−42.1842			−1.53932			−0.769661	+	0.638453i	$0.779575\pi$
$752$		0			0
$753$	10.7227	−	28.9735i	0.390759	−	1.05585i
$754$		0			0
$755$	1.82211			0.0663134
$756$		0			0
$757$	−32.6771			−1.18767			−0.593835	−	0.804587i	$-0.702387\pi$
$757$	−32.6771			−1.18767			−0.593835	+	0.804587i	$0.702387\pi$
$758$		0			0
$759$	−1.31847	+	3.56258i	−0.0478574	+	0.129314i
$760$		0			0
$761$	31.7567			1.15118			0.575589	−	0.817739i	$-0.304773\pi$
$761$	31.7567			1.15118			0.575589	+	0.817739i	$0.304773\pi$
$762$		0			0
$763$	3.83401	+	6.97532i	0.138800	+	0.252524i
$764$		0			0
$765$	−1.02345	+	0.360056i	−0.0370028	+	0.0130178i
$766$		0			0
$767$		−	12.7976i		−	0.462096i
$768$		0			0
$769$	−30.8593	−	17.8166i	−1.11281	−	0.642484i	−0.173258	−	0.984877i	$-0.555429\pi$
$769$	−30.8593	−	17.8166i	−1.11281	−	0.642484i	−0.939557	+	0.342393i	$0.888763\pi$
$770$		0			0
$771$	−0.984208	+	2.65939i	−0.0354454	+	0.0957756i
$772$		0			0
$773$	6.44721	−	11.1669i	0.231890	−	0.401645i	−0.726474	−	0.687194i	$-0.758842\pi$
$773$	6.44721	−	11.1669i	0.231890	−	0.401645i	0.958364	+	0.285548i	$0.0921757\pi$
$774$		0			0
$775$	25.5656	−	14.7603i	0.918344	−	0.530206i
$776$		0			0
$777$	−7.17827	+	18.2106i	−0.257519	+	0.653303i
$778$		0			0
$779$		−	6.51216i		−	0.233322i
$780$		0			0
$781$	10.7844			0.385898
$782$		0			0
$783$	6.15837	−	10.2790i	0.220082	−	0.367342i
$784$		0			0
$785$	−1.89208	+	1.09239i	−0.0675312	+	0.0389892i
$786$		0			0
$787$	−15.3158	+	8.84260i	−0.545950	+	0.315205i	−0.747487	−	0.664276i	$-0.768740\pi$
$787$	−15.3158	+	8.84260i	−0.545950	+	0.315205i	0.201537	+	0.979481i	$0.435406\pi$
$788$		0			0
$789$	49.9092	+	18.4708i	1.77682	+	0.657578i
$790$		0			0
$791$	−38.1871	+	20.9897i	−1.35778	+	0.746307i
$792$		0			0
$793$	23.7944	+	41.2131i	0.844963	+	1.46352i
$794$		0			0
$795$	2.60194	−	2.15949i	0.0922812	−	0.0765891i
$796$		0			0
$797$	−22.8391	+	39.5585i	−0.809003	+	1.40123i	0.104553	+	0.994519i	$0.466659\pi$
$797$	−22.8391	+	39.5585i	−0.809003	+	1.40123i	−0.913555	+	0.406714i	$0.866674\pi$
$798$		0			0
$799$	−7.22156	−	12.5081i	−0.255481	−	0.442505i
$800$		0			0
$801$	2.17006	−	11.5757i	0.0766753	−	0.409008i
$802$		0			0
$803$	−9.30063	+	16.1092i	−0.328212	+	0.568480i
$804$		0			0
$805$	−0.677310	−	0.410266i	−0.0238721	−	0.0144600i
$806$		0			0
$807$	1.08669	+	1.30934i	0.0382533	+	0.0460909i
$808$		0			0
$809$	−10.8291	−	6.25218i	−0.380731	−	0.219815i	0.297405	−	0.954751i	$-0.403879\pi$
$809$	−10.8291	−	6.25218i	−0.380731	−	0.219815i	−0.678136	+	0.734936i	$0.737212\pi$
$810$		0			0
$811$		−	9.57778i		−	0.336322i	−0.985760	−	0.168161i	$-0.946217\pi$
$811$		−	9.57778i		−	0.336322i	0.985760	−	0.168161i	$-0.0537828\pi$
$812$		0			0
$813$	−0.238166	−	1.39463i	−0.00835286	−	0.0489119i
$814$		0			0
$815$	0.962123	+	1.66645i	0.0337017	+	0.0583730i
$816$		0			0
$817$	0.413560	+	0.238769i	0.0144686	+	0.00835346i
$818$		0			0
$819$	−30.4225	−	6.36793i	−1.06305	−	0.222513i
$820$		0			0
$821$	24.1379	+	13.9360i	0.842420	+	0.486371i	0.858086	−	0.513506i	$-0.171654\pi$
$821$	24.1379	+	13.9360i	0.842420	+	0.486371i	−0.0156664	+	0.999877i	$0.504987\pi$
$822$		0			0
$823$	−23.6383	−	40.9428i	−0.823980	−	1.42717i	−0.902697	−	0.430278i	$-0.858416\pi$
$823$	−23.6383	−	40.9428i	−0.823980	−	1.42717i	0.0787167	−	0.996897i	$-0.474918\pi$
$824$		0			0
$825$	12.2157	+	4.52087i	0.425295	+	0.157396i
$826$		0			0
$827$		−	24.1672i		−	0.840377i	−0.907437	−	0.420188i	$-0.861964\pi$
$827$		−	24.1672i		−	0.840377i	0.907437	−	0.420188i	$-0.138036\pi$
$828$		0			0
$829$	23.0216	+	13.2915i	0.799572	+	0.461633i	0.843322	−	0.537409i	$-0.180597\pi$
$829$	23.0216	+	13.2915i	0.799572	+	0.461633i	−0.0437494	+	0.999043i	$0.513930\pi$
$830$		0			0
$831$	−6.37458	+	17.2245i	−0.221132	+	0.597512i
$832$		0			0
$833$	12.2171	+	0.513960i	0.423297	+	0.0178076i
$834$		0			0
$835$	0.920152	−	1.59375i	0.0318432	−	0.0551540i
$836$		0			0
$837$	−15.9034	+	26.5446i	−0.549702	+	0.917514i
$838$		0			0
$839$	4.03255	+	6.98459i	0.139219	+	0.241135i	0.927201	−	0.374563i	$-0.122207\pi$
$839$	4.03255	+	6.98459i	0.139219	+	0.241135i	−0.787982	+	0.615698i	$0.788874\pi$
$840$		0			0
$841$	−11.8410	+	20.5093i	−0.408312	+	0.707217i
$842$		0			0
$843$	4.77282	+	27.9483i	0.164385	+	0.962589i
$844$		0			0
$845$	−0.241660	−	0.418568i	−0.00831337	−	0.0143992i
$846$		0			0
$847$	−11.9235	+	19.6846i	−0.409698	+	0.676372i
$848$		0			0
$849$	−1.91125	−	11.1917i	−0.0655940	−	0.384100i
$850$		0			0
$851$	−5.34794	+	3.08764i	−0.183325	+	0.105843i
$852$		0			0
$853$	−11.6046	+	6.69994i	−0.397335	+	0.229402i	−0.685334	−	0.728229i	$-0.740344\pi$
$853$	−11.6046	+	6.69994i	−0.397335	+	0.229402i	0.287998	+	0.957631i	$0.407010\pi$
$854$		0			0
$855$	−0.682734	−	0.127990i	−0.0233490	−	0.00437716i
$856$		0			0
$857$	−44.6679			−1.52583			−0.762914	−	0.646500i	$-0.776232\pi$
$857$	−44.6679			−1.52583			−0.762914	+	0.646500i	$0.776232\pi$
$858$		0			0
$859$		−	50.5104i		−	1.72339i	−0.507425	−	0.861696i	$-0.669403\pi$
$859$		−	50.5104i		−	1.72339i	0.507425	−	0.861696i	$-0.330597\pi$
$860$		0			0
$861$	26.3907	−	3.93783i	0.899394	−	0.134201i
$862$		0			0
$863$	0.227203	−	0.131176i	0.00773408	−	0.00446528i	−0.496128	−	0.868249i	$-0.665245\pi$
$863$	0.227203	−	0.131176i	0.00773408	−	0.00446528i	0.503862	+	0.863784i	$0.331912\pi$
$864$		0			0
$865$	−1.01438	+	1.75695i	−0.0344898	+	0.0597381i
$866$		0			0
$867$	−23.8148	+	4.06694i	−0.808794	+	0.138120i
$868$		0			0
$869$	−6.77412	−	3.91104i	−0.229796	−	0.132673i
$870$		0			0
$871$		−	25.4137i		−	0.861111i
$872$		0			0
$873$	44.6655	+	8.37327i	1.51170	+	0.283392i
$874$		0			0
$875$	−2.82567	+	4.66491i	−0.0955250	+	0.157703i
$876$		0			0
$877$	−9.26607			−0.312893			−0.156446	−	0.987686i	$-0.550004\pi$
$877$	−9.26607			−0.312893			−0.156446	+	0.987686i	$0.550004\pi$
$878$		0			0
$879$	−15.5404	−	18.7244i	−0.524165	−	0.631559i
$880$		0			0
$881$	41.5555			1.40004			0.700021	−	0.714122i	$-0.253174\pi$
$881$	41.5555			1.40004			0.700021	+	0.714122i	$0.253174\pi$
$882$		0			0
$883$	−29.4547			−0.991231			−0.495615	−	0.868542i	$-0.665057\pi$
$883$	−29.4547			−0.991231			−0.495615	+	0.868542i	$0.665057\pi$
$884$		0			0
$885$	1.15516	−	0.197270i	0.0388303	−	0.00663117i
$886$		0			0
$887$	15.5824			0.523207			0.261603	−	0.965175i	$-0.415749\pi$
$887$	15.5824			0.523207			0.261603	+	0.965175i	$0.415749\pi$
$888$		0			0
$889$	11.6881	−	19.2959i	0.392006	−	0.647165i
$890$		0			0
$891$	−13.4940	+	2.08040i	−0.452066	+	0.0696960i
$892$		0			0
$893$		−	9.24718i		−	0.309445i
$894$		0			0
$895$	2.96342	+	1.71093i	0.0990562	+	0.0571901i
$896$		0			0
$897$	−6.26235	−	7.54542i	−0.209094	−	0.251934i
$898$		0			0
$899$	−6.86649	+	11.8931i	−0.229010	+	0.396658i
$900$		0			0
$901$	−14.2654	+	8.23612i	−0.475248	+	0.274385i
$902$		0			0
$903$	−0.717544	+	1.82034i	−0.0238784	+	0.0605773i
$904$		0			0
$905$			4.93849i			0.164161i
$906$		0			0
$907$	20.5208			0.681383			0.340692	−	0.940175i	$-0.389339\pi$
$907$	20.5208			0.681383			0.340692	+	0.940175i	$0.389339\pi$
$908$		0			0
$909$	−23.3785	−	20.0504i	−0.775416	−	0.665029i
$910$		0			0
$911$	−15.0554	+	8.69226i	−0.498809	+	0.287987i	−0.728222	−	0.685342i	$-0.759653\pi$
$911$	−15.0554	+	8.69226i	−0.498809	+	0.287987i	0.229413	+	0.973329i	$0.426319\pi$
$912$		0			0
$913$	−21.9788	+	12.6894i	−0.727391	+	0.419959i
$914$		0			0
$915$	−3.35325	+	2.78305i	−0.110855	+	0.0920046i
$916$		0			0
$917$	19.9507	−	32.9367i	0.658830	−	1.08767i
$918$		0			0
$919$	17.1002	+	29.6183i	0.564082	+	0.977019i	0.997134	+	0.0756501i	$0.0241032\pi$
$919$	17.1002	+	29.6183i	0.564082	+	0.977019i	−0.433052	+	0.901369i	$0.642563\pi$
$920$		0			0
$921$	28.3186	+	10.4804i	0.933129	+	0.345340i
$922$		0			0
$923$	−13.9189	+	24.1082i	−0.458146	+	0.793532i
$924$		0			0
$925$	10.5871	+	18.3375i	0.348103	+	0.602932i
$926$		0			0
$927$	21.9864	−	25.6358i	0.722128	−	0.841992i
$928$		0			0
$929$	−1.49596	+	2.59108i	−0.0490808	+	0.0850105i	−0.889522	−	0.456892i	$-0.848963\pi$
$929$	−1.49596	+	2.59108i	−0.0490808	+	0.0850105i	0.840441	+	0.541903i	$0.182296\pi$
$930$		0			0
$931$	6.60949	+	4.19596i	0.216617	+	0.137517i
$932$		0			0
$933$	26.6280	−	4.54735i	0.871762	−	0.148874i
$934$		0			0
$935$	0.475130	+	0.274316i	0.0155384	+	0.00897110i
$936$		0			0
$937$		−	10.9928i		−	0.359120i	−0.983747	−	0.179560i	$-0.942533\pi$
$937$		−	10.9928i		−	0.359120i	0.983747	−	0.179560i	$-0.0574674\pi$
$938$		0			0
$939$	2.97197	−	2.46660i	0.0969865	−	0.0804943i
$940$		0			0
$941$	−4.95300	−	8.57884i	−0.161463	−	0.279662i	0.773931	−	0.633271i	$-0.218288\pi$
$941$	−4.95300	−	8.57884i	−0.161463	−	0.279662i	−0.935394	+	0.353608i	$0.884955\pi$
$942$		0			0
$943$	7.29009	+	4.20894i	0.237398	+	0.137062i
$944$		0			0
$945$	0.105841	−	2.84420i	0.00344301	−	0.0925217i
$946$		0			0
$947$	23.4219	+	13.5227i	0.761110	+	0.439427i	0.829694	−	0.558218i	$-0.188515\pi$
$947$	23.4219	+	13.5227i	0.761110	+	0.439427i	−0.0685840	+	0.997645i	$0.521848\pi$
$948$		0			0
$949$	−24.0076	−	41.5824i	−0.779320	−	1.34982i
$950$		0			0
$951$	45.7488	−	37.9694i	1.48351	−	1.23124i
$952$		0			0
$953$			51.9958i			1.68431i	0.539236	+	0.842155i	$0.318713\pi$
$953$			51.9958i			1.68431i	−0.539236	+	0.842155i	$0.681287\pi$
$954$		0			0
$955$	4.00898	+	2.31458i	0.129727	+	0.0748982i
$956$		0			0
$957$	−5.97293	+	1.02002i	−0.193078	+	0.0329725i
$958$		0			0
$959$	−24.1776	−	14.6451i	−0.780737	−	0.472914i
$960$		0			0
$961$	2.23207	−	3.86605i	0.0720022	−	0.124711i
$962$		0			0
$963$	−33.6206	−	6.30273i	−1.08341	−	0.203103i
$964$		0			0
$965$	−0.896121	−	1.55213i	−0.0288472	−	0.0499648i
$966$		0			0
$967$	8.23005	−	14.2549i	0.264660	−	0.458405i	−0.702814	−	0.711374i	$-0.748073\pi$
$967$	8.23005	−	14.2549i	0.264660	−	0.458405i	0.967475	+	0.252968i	$0.0814068\pi$
$968$		0			0
$969$	3.17353	+	1.17448i	0.101948	+	0.0377299i
$970$		0			0
$971$	−6.09724	−	10.5607i	−0.195670	−	0.338910i	0.751450	−	0.659790i	$-0.229355\pi$
$971$	−6.09724	−	10.5607i	−0.195670	−	0.338910i	−0.947120	+	0.320880i	$0.896021\pi$
$972$		0			0
$973$	−19.9845	+	10.9845i	−0.640673	+	0.352148i
$974$		0			0
$975$	−25.8723	+	21.4728i	−0.828577	+	0.687681i
$976$		0			0
$977$	18.8425	−	10.8787i	0.602824	−	0.348040i	−0.167328	−	0.985901i	$-0.553514\pi$
$977$	18.8425	−	10.8787i	0.602824	−	0.348040i	0.770152	+	0.637861i	$0.220181\pi$
$978$		0			0
$979$	−5.15771	+	2.97781i	−0.164841	+	0.0951711i
$980$		0			0
$981$	−8.51380	+	2.99521i	−0.271825	+	0.0956297i
$982$		0			0
$983$	62.4746			1.99263			0.996316	−	0.0857622i	$-0.0273325\pi$
$983$	62.4746			1.99263			0.996316	+	0.0857622i	$0.0273325\pi$
$984$		0			0
$985$		−	4.82005i		−	0.153580i
$986$		0			0
$987$	37.4745	−	5.59166i	1.19283	−	0.177984i
$988$		0			0
$989$	−0.534583	+	0.308642i	−0.0169988	+	0.00981424i
$990$		0			0
$991$	−27.5362	+	47.6942i	−0.874717	+	1.51505i	−0.0176535	+	0.999844i	$0.505620\pi$
$991$	−27.5362	+	47.6942i	−0.874717	+	1.51505i	−0.857064	+	0.515210i	$0.827714\pi$
$992$		0			0
$993$	24.9334	+	30.0419i	0.791238	+	0.953352i
$994$		0			0
$995$	−1.82370	−	1.05291i	−0.0578151	−	0.0333795i
$996$		0			0
$997$		−	23.8706i		−	0.755990i	−0.925808	−	0.377995i	$-0.876614\pi$
$997$		−	23.8706i		−	0.755990i	0.925808	−	0.377995i	$-0.123386\pi$
$998$		0			0
$999$	−19.0396	−	11.4070i	−0.602387	−	0.360902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cx.a.185.10	yes	48
3.2	odd	2		1512.2.cx.a.17.12		48
4.3	odd	2		1008.2.df.e.689.15		48
7.5	odd	6		504.2.bs.a.257.19	✓	48
9.2	odd	6		504.2.bs.a.353.19	yes	48
9.7	even	3		1512.2.bs.a.521.12		48
12.11	even	2		3024.2.df.e.17.12		48
21.5	even	6		1512.2.bs.a.1097.12		48
28.19	even	6		1008.2.ca.e.257.6		48
36.7	odd	6		3024.2.ca.e.2033.12		48
36.11	even	6		1008.2.ca.e.353.6		48
63.47	even	6	inner	504.2.cx.a.425.10	yes	48
63.61	odd	6		1512.2.cx.a.89.12		48
84.47	odd	6		3024.2.ca.e.2609.12		48
252.47	odd	6		1008.2.df.e.929.15		48
252.187	even	6		3024.2.df.e.1601.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.19	✓	48	7.5	odd	6
504.2.bs.a.353.19	yes	48	9.2	odd	6
504.2.cx.a.185.10	yes	48	1.1	even	1	trivial
504.2.cx.a.425.10	yes	48	63.47	even	6	inner
1008.2.ca.e.257.6		48	28.19	even	6
1008.2.ca.e.353.6		48	36.11	even	6
1008.2.df.e.689.15		48	4.3	odd	2
1008.2.df.e.929.15		48	252.47	odd	6
1512.2.bs.a.521.12		48	9.7	even	3
1512.2.bs.a.1097.12		48	21.5	even	6
1512.2.cx.a.17.12		48	3.2	odd	2
1512.2.cx.a.89.12		48	63.61	odd	6
3024.2.ca.e.2033.12		48	36.7	odd	6
3024.2.ca.e.2609.12		48	84.47	odd	6
3024.2.df.e.17.12		48	12.11	even	2
3024.2.df.e.1601.12		48	252.187	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cx (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.601162 + 1.62438i) q^{3} -0.207028 q^{5} +(-1.37075 + 2.26297i) q^{7} +(-2.27721 - 1.95303i) q^{9} +O(q^{10})\)	\(q+(-0.601162 + 1.62438i) q^{3} -0.207028 q^{5} +(-1.37075 + 2.26297i) q^{7} +(-2.27721 - 1.95303i) q^{9} +1.51705i q^{11} +(-3.39130 - 1.95797i) q^{13} +(0.124457 - 0.336292i) q^{15} +(-0.873421 + 1.51281i) q^{17} +(-0.968573 + 0.559206i) q^{19} +(-2.85188 - 3.58703i) q^{21} -1.44570i q^{23} -4.95714 q^{25} +(4.54143 - 2.52496i) q^{27} +(1.99711 - 1.15303i) q^{29} +(-5.15733 + 2.97759i) q^{31} +(-2.46426 - 0.911991i) q^{33} +(0.283783 - 0.468499i) q^{35} +(-2.13573 - 3.69920i) q^{37} +(5.21920 - 4.33170i) q^{39} +(-2.91134 + 5.04260i) q^{41} +(-0.213489 - 0.369774i) q^{43} +(0.471446 + 0.404332i) q^{45} +(-4.13407 + 7.16042i) q^{47} +(-3.24210 - 6.20393i) q^{49} +(-1.93231 - 2.32821i) q^{51} +(8.16638 + 4.71486i) q^{53} -0.314071i q^{55} +(-0.326092 - 1.90950i) q^{57} +(1.63405 + 2.83025i) q^{59} +(-10.5244 - 6.07629i) q^{61} +(7.54113 - 2.47615i) q^{63} +(0.702095 + 0.405354i) q^{65} +(3.24491 + 5.62035i) q^{67} +(2.34837 + 0.869102i) q^{69} -7.10884i q^{71} +(10.6188 + 6.13075i) q^{73} +(2.98005 - 8.05227i) q^{75} +(-3.43304 - 2.07949i) q^{77} +(-2.57806 + 4.46533i) q^{79} +(1.37135 + 8.89491i) q^{81} +(8.36457 + 14.4879i) q^{83} +(0.180823 - 0.313194i) q^{85} +(0.672371 + 3.93721i) q^{87} +(1.96290 + 3.39984i) q^{89} +(9.07945 - 4.99055i) q^{91} +(-1.73633 - 10.1675i) q^{93} +(0.200522 - 0.115771i) q^{95} +(-13.1184 + 7.57392i) q^{97} +(2.96284 - 3.45463i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{9}+O(q^{10}) \) 48 * q + 2 * q^9	\( 48 q + 2 q^{9} + 8 q^{15} - 10 q^{21} + 48 q^{25} + 18 q^{27} + 18 q^{29} + 18 q^{31} + 12 q^{33} - 4 q^{39} - 6 q^{41} - 6 q^{43} - 18 q^{45} + 18 q^{47} - 12 q^{49} + 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61} - 32 q^{63} - 36 q^{65} - 12 q^{77} + 6 q^{79} + 6 q^{81} - 54 q^{87} - 18 q^{89} + 6 q^{91} + 4 q^{93} - 54 q^{95} - 64 q^{99}+O(q^{100}) \) 48 * q + 2 * q^9 + 8 * q^15 - 10 * q^21 + 48 * q^25 + 18 * q^27 + 18 * q^29 + 18 * q^31 + 12 * q^33 - 4 * q^39 - 6 * q^41 - 6 * q^43 - 18 * q^45 + 18 * q^47 - 12 * q^49 + 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 - 32 * q^63 - 36 * q^65 - 12 * q^77 + 6 * q^79 + 6 * q^81 - 54 * q^87 - 18 * q^89 + 6 * q^91 + 4 * q^93 - 54 * q^95 - 64 * q^99

Introduction

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