LMFDB - Embedded newform 252.2.x.a.41.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(41,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("252.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.x (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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3x^{14} - 9x^{12} - 9x^{10} + 225x^{8} - 81x^{6} - 729x^{4} - 2187x^{2} + 6561 $ x^16 - 3x^14 - 9x^12 - 9x^10 + 225x^8 - 81x^6 - 729x^4 - 2187*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.8
Root			$-0.744857 + 1.56371i$ of defining polynomial
Character	$\chi$	$=$	252.41
Dual form			252.2.x.a.209.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72664 - 0.136790i) q^{3} +(0.276914 - 0.479629i) q^{5} +(-1.98718 - 1.74675i) q^{7} +(2.96258 - 0.472374i) q^{9} +O(q^{10})$	\(q+(1.72664 - 0.136790i) q^{3} +(0.276914 - 0.479629i) q^{5} +(-1.98718 - 1.74675i) q^{7} +(2.96258 - 0.472374i) q^{9} +(4.03478 - 2.32948i) q^{11} +(3.58265 + 2.06844i) q^{13} +(0.412522 - 0.866025i) q^{15} -7.24527 q^{17} +6.71715i q^{19} +(-3.67008 - 2.74418i) q^{21} +(-4.85295 - 2.80185i) q^{23} +(2.34664 + 4.06450i) q^{25} +(5.05069 - 1.22087i) q^{27} +(1.16599 - 0.673187i) q^{29} +(-0.830741 - 0.479629i) q^{31} +(6.64796 - 4.57409i) q^{33} +(-1.38807 + 0.469409i) q^{35} -7.06956 q^{37} +(6.46889 + 3.08139i) q^{39} +(-2.39152 + 4.14224i) q^{41} +(-1.02846 - 1.78135i) q^{43} +(0.593814 - 1.55174i) q^{45} +(-4.90301 - 8.49226i) q^{47} +(0.897752 + 6.94219i) q^{49} +(-12.5100 + 0.991080i) q^{51} +8.43202i q^{53} -2.58026i q^{55} +(0.918838 + 11.5981i) q^{57} +(3.89955 - 6.75422i) q^{59} +(-5.37336 + 3.10231i) q^{61} +(-6.71229 - 4.23618i) q^{63} +(1.98417 - 1.14556i) q^{65} +(1.68814 - 2.92394i) q^{67} +(-8.76257 - 4.17396i) q^{69} +0.407556i q^{71} +8.63566i q^{73} +(4.60778 + 6.69693i) q^{75} +(-12.0868 - 2.41864i) q^{77} +(-0.318176 - 0.551097i) q^{79} +(8.55373 - 2.79889i) q^{81} +(2.78840 + 4.82965i) q^{83} +(-2.00632 + 3.47504i) q^{85} +(1.92117 - 1.32185i) q^{87} -6.93137 q^{89} +(-3.50632 - 10.3683i) q^{91} +(-1.50000 - 0.714509i) q^{93} +(3.22174 + 1.86007i) q^{95} +(7.48798 - 4.32318i) q^{97} +(10.8530 - 8.80719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{7}+O(q^{10}) $ 16 * q - q^7	$ 16 q - q^{7} + 6 q^{11} - 12 q^{15} + 9 q^{21} + 6 q^{23} - 8 q^{25} - 12 q^{29} + 4 q^{37} + 18 q^{39} + 4 q^{43} - 5 q^{49} - 18 q^{51} - 42 q^{57} - 27 q^{63} - 24 q^{65} + 14 q^{67} - 21 q^{77} + 20 q^{79} - 36 q^{81} + 6 q^{85} - 18 q^{91} - 24 q^{93} - 60 q^{95} + 90 q^{99}+O(q^{100}) $ 16 * q - q^7 + 6 * q^11 - 12 * q^15 + 9 * q^21 + 6 * q^23 - 8 * q^25 - 12 * q^29 + 4 * q^37 + 18 * q^39 + 4 * q^43 - 5 * q^49 - 18 * q^51 - 42 * q^57 - 27 * q^63 - 24 * q^65 + 14 * q^67 - 21 * q^77 + 20 * q^79 - 36 * q^81 + 6 * q^85 - 18 * q^91 - 24 * q^93 - 60 * q^95 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.72664	−	0.136790i	0.996877	−	0.0789757i
$3$	1.72664	−	0.136790i	0.996877	−	0.0789757i
$4$		0			0
$5$	0.276914	−	0.479629i	0.123840	−	0.214496i	−0.797439	−	0.603399i	$-0.793813\pi$
$5$	0.276914	−	0.479629i	0.123840	−	0.214496i	0.921279	+	0.388903i	$0.127146\pi$
$6$		0			0
$7$	−1.98718	−	1.74675i	−0.751083	−	0.660208i
$7$	−1.98718	−	1.74675i	−0.751083	−	0.660208i
$8$		0			0
$9$	2.96258	−	0.472374i	0.987526	−	0.157458i
$10$		0			0
$11$	4.03478	−	2.32948i	1.21653	−	0.702365i	0.252357	−	0.967634i	$-0.418794\pi$
$11$	4.03478	−	2.32948i	1.21653	−	0.702365i	0.964174	+	0.265270i	$0.0854610\pi$
$12$		0			0
$13$	3.58265	+	2.06844i	0.993648	+	0.573683i	0.906363	−	0.422500i	$-0.138847\pi$
$13$	3.58265	+	2.06844i	0.993648	+	0.573683i	0.0872856	+	0.996183i	$0.472181\pi$
$14$		0			0
$15$	0.412522	−	0.866025i	0.106513	−	0.223607i
$16$		0			0
$17$	−7.24527			−1.75724			−0.878619	−	0.477524i	$-0.841534\pi$
$17$	−7.24527			−1.75724			−0.878619	+	0.477524i	$0.841534\pi$
$18$		0			0
$19$			6.71715i			1.54102i	0.637428	+	0.770510i	$0.279998\pi$
$19$			6.71715i			1.54102i	−0.637428	+	0.770510i	$0.720002\pi$
$20$		0			0
$21$	−3.67008	−	2.74418i	−0.800877	−	0.598829i
$22$		0			0
$23$	−4.85295	−	2.80185i	−1.01191	−	0.584227i	−0.100160	−	0.994971i	$-0.531936\pi$
$23$	−4.85295	−	2.80185i	−1.01191	−	0.584227i	−0.911751	+	0.410744i	$0.865269\pi$
$24$		0			0
$25$	2.34664	+	4.06450i	0.469328	+	0.812899i
$26$		0			0
$27$	5.05069	−	1.22087i	0.972006	−	0.234957i
$28$		0			0
$29$	1.16599	−	0.673187i	0.216520	−	0.125008i	−0.387818	−	0.921736i	$-0.626771\pi$
$29$	1.16599	−	0.673187i	0.216520	−	0.125008i	0.604338	+	0.796728i	$0.293438\pi$
$30$		0			0
$31$	−0.830741	−	0.479629i	−0.149206	−	0.0861438i	0.423539	−	0.905878i	$-0.360788\pi$
$31$	−0.830741	−	0.479629i	−0.149206	−	0.0861438i	−0.572744	+	0.819734i	$0.694121\pi$
$32$		0			0
$33$	6.64796	−	4.57409i	1.15726	−	0.796247i
$34$		0			0
$35$	−1.38807	+	0.469409i	−0.234626	+	0.0793447i
$36$		0			0
$37$	−7.06956			−1.16223			−0.581114	−	0.813822i	$-0.697383\pi$
$37$	−7.06956			−1.16223			−0.581114	+	0.813822i	$0.697383\pi$
$38$		0			0
$39$	6.46889	+	3.08139i	1.03585	+	0.493417i
$40$		0			0
$41$	−2.39152	+	4.14224i	−0.373493	+	0.646909i	−0.990100	−	0.140362i	$-0.955173\pi$
$41$	−2.39152	+	4.14224i	−0.373493	+	0.646909i	0.616607	+	0.787271i	$0.288507\pi$
$42$		0			0
$43$	−1.02846	−	1.78135i	−0.156839	−	0.271653i	0.776888	−	0.629639i	$-0.216797\pi$
$43$	−1.02846	−	1.78135i	−0.156839	−	0.271653i	−0.933727	+	0.357986i	$0.883464\pi$
$44$		0			0
$45$	0.593814	−	1.55174i	0.0885206	−	0.231320i
$46$		0			0
$47$	−4.90301	−	8.49226i	−0.715177	−	1.23872i	−0.962891	−	0.269890i	$-0.913013\pi$
$47$	−4.90301	−	8.49226i	−0.715177	−	1.23872i	0.247714	−	0.968833i	$-0.420321\pi$
$48$		0			0
$49$	0.897752	+	6.94219i	0.128250	+	0.991742i
$50$		0			0
$51$	−12.5100	+	0.991080i	−1.75175	+	0.138779i
$52$		0			0
$53$			8.43202i			1.15823i	0.815247	+	0.579114i	$0.196601\pi$
$53$			8.43202i			1.15823i	−0.815247	+	0.579114i	$0.803399\pi$
$54$		0			0
$55$		−	2.58026i		−	0.347922i
$56$		0			0
$57$	0.918838	+	11.5981i	0.121703	+	1.53621i
$58$		0			0
$59$	3.89955	−	6.75422i	0.507678	−	0.879325i	−0.492282	−	0.870436i	$-0.663837\pi$
$59$	3.89955	−	6.75422i	0.507678	−	0.879325i	0.999960	−	0.00888893i	$-0.00282947\pi$
$60$		0			0
$61$	−5.37336	+	3.10231i	−0.687989	+	0.397211i	−0.802858	−	0.596170i	$-0.796688\pi$
$61$	−5.37336	+	3.10231i	−0.687989	+	0.397211i	0.114869	+	0.993381i	$0.463355\pi$
$62$		0			0
$63$	−6.71229	−	4.23618i	−0.845668	−	0.533709i
$64$		0			0
$65$	1.98417	−	1.14556i	0.246106	−	0.142089i
$66$		0			0
$67$	1.68814	−	2.92394i	0.206239	−	0.357217i	−0.744288	−	0.667859i	$-0.767211\pi$
$67$	1.68814	−	2.92394i	0.206239	−	0.357217i	0.950527	+	0.310642i	$0.100544\pi$
$68$		0			0
$69$	−8.76257	−	4.17396i	−1.05489	−	0.502486i
$70$		0			0
$71$			0.407556i			0.0483680i	0.999708	+	0.0241840i	$0.00769875\pi$
$71$			0.407556i			0.0483680i	−0.999708	+	0.0241840i	$0.992301\pi$
$72$		0			0
$73$			8.63566i			1.01073i	0.862906	+	0.505364i	$0.168642\pi$
$73$			8.63566i			1.01073i	−0.862906	+	0.505364i	$0.831358\pi$
$74$		0			0
$75$	4.60778	+	6.69693i	0.532061	+	0.773295i
$76$		0			0
$77$	−12.0868	−	2.41864i	−1.37742	−	0.275630i
$78$		0			0
$79$	−0.318176	−	0.551097i	−0.0357976	−	0.0620032i	0.847572	−	0.530681i	$-0.178064\pi$
$79$	−0.318176	−	0.551097i	−0.0357976	−	0.0620032i	−0.883369	+	0.468678i	$0.844730\pi$
$80$		0			0
$81$	8.55373	−	2.79889i	0.950414	−	0.310988i
$82$		0			0
$83$	2.78840	+	4.82965i	0.306066	+	0.530123i	0.977498	−	0.210944i	$-0.0676537\pi$
$83$	2.78840	+	4.82965i	0.306066	+	0.530123i	−0.671432	+	0.741066i	$0.734320\pi$
$84$		0			0
$85$	−2.00632	+	3.47504i	−0.217616	+	0.376921i
$86$		0			0
$87$	1.92117	−	1.32185i	0.205971	−	0.141717i
$88$		0			0
$89$	−6.93137			−0.734723			−0.367362	−	0.930078i	$-0.619739\pi$
$89$	−6.93137			−0.734723			−0.367362	+	0.930078i	$0.619739\pi$
$90$		0			0
$91$	−3.50632	−	10.3683i	−0.367562	−	1.08690i
$92$		0			0
$93$	−1.50000	−	0.714509i	−0.155543	−	0.0740912i
$94$		0			0
$95$	3.22174	+	1.86007i	0.330543	+	0.190839i
$96$		0			0
$97$	7.48798	−	4.32318i	0.760289	−	0.438953i	−0.0691107	−	0.997609i	$-0.522016\pi$
$97$	7.48798	−	4.32318i	0.760289	−	0.438953i	0.829399	+	0.558656i	$0.188683\pi$
$98$		0			0
$99$	10.8530	−	8.80719i	1.09076	−	0.885156i
$100$		0			0
$101$	2.34227	+	4.05692i	0.233064	+	0.403679i	0.958708	−	0.284391i	$-0.0917915\pi$
$101$	2.34227	+	4.05692i	0.233064	+	0.403679i	−0.725644	+	0.688070i	$0.758458\pi$
$102$		0			0
$103$	−6.40804	−	3.69969i	−0.631403	−	0.364541i	0.149892	−	0.988702i	$-0.452107\pi$
$103$	−6.40804	−	3.69969i	−0.631403	−	0.364541i	−0.781295	+	0.624162i	$0.785441\pi$
$104$		0			0
$105$	−2.33248	+	1.00037i	−0.227627	+	0.0976266i
$106$		0			0
$107$			5.06059i			0.489225i	0.969621	+	0.244613i	$0.0786608\pi$
$107$			5.06059i			0.489225i	−0.969621	+	0.244613i	$0.921339\pi$
$108$		0			0
$109$	11.7628			1.12667			0.563337	−	0.826227i	$-0.309517\pi$
$109$	11.7628			1.12667			0.563337	+	0.826227i	$0.309517\pi$
$110$		0			0
$111$	−12.2066	+	0.967044i	−1.15860	+	0.0917877i
$112$		0			0
$113$	−1.51895	−	0.876965i	−0.142891	−	0.0824979i	0.426850	−	0.904322i	$-0.359623\pi$
$113$	−1.51895	−	0.876965i	−0.142891	−	0.0824979i	−0.569741	+	0.821824i	$0.692956\pi$
$114$		0			0
$115$	−2.68770	+	1.55174i	−0.250629	+	0.144701i
$116$		0			0
$117$	11.5910	+	4.43557i	1.07158	+	0.410069i
$118$		0			0
$119$	14.3976	+	12.6557i	1.31983	+	1.16014i
$120$		0			0
$121$	5.35295	−	9.27159i	0.486632	−	0.842872i
$122$		0			0
$123$	−3.56269	+	7.47930i	−0.321237	+	0.674386i
$124$		0			0
$125$	5.36840			0.480164
$126$		0			0
$127$	11.0822			0.983385			0.491693	−	0.870769i	$-0.336378\pi$
$127$	11.0822			0.983385			0.491693	+	0.870769i	$0.336378\pi$
$128$		0			0
$129$	−2.01945	−	2.93506i	−0.177803	−	0.258418i
$130$		0			0
$131$	9.23643	−	15.9980i	0.806990	−	1.39775i	−0.107949	−	0.994156i	$-0.534428\pi$
$131$	9.23643	−	15.9980i	0.806990	−	1.39775i	0.914939	−	0.403592i	$-0.132238\pi$
$132$		0			0
$133$	11.7332	−	13.3482i	1.01739	−	1.15743i
$134$		0			0
$135$	0.813041	−	2.76053i	0.0699754	−	0.237589i
$136$		0			0
$137$	19.0537	−	11.0007i	1.62787	−	0.939851i	0.643142	−	0.765747i	$-0.277630\pi$
$137$	19.0537	−	11.0007i	1.62787	−	0.939851i	0.984727	−	0.174104i	$-0.0557030\pi$
$138$		0			0
$139$	−8.55986	−	4.94204i	−0.726038	−	0.419178i	0.0909332	−	0.995857i	$-0.471015\pi$
$139$	−8.55986	−	4.94204i	−0.726038	−	0.419178i	−0.816971	+	0.576679i	$0.804348\pi$
$140$		0			0
$141$	−9.62739	−	13.9924i	−0.810773	−	1.17837i
$142$		0			0
$143$	19.2736			1.61174
$144$		0			0
$145$		−	0.745659i		−	0.0619236i
$146$		0			0
$147$	2.49972	+	11.8639i	0.206173	+	0.978516i
$148$		0			0
$149$	−6.36677	−	3.67585i	−0.521586	−	0.301138i	0.215997	−	0.976394i	$-0.430700\pi$
$149$	−6.36677	−	3.67585i	−0.521586	−	0.301138i	−0.737583	+	0.675256i	$0.764033\pi$
$150$		0			0
$151$	2.16599	+	3.75161i	0.176266	+	0.305302i	0.940599	−	0.339520i	$-0.110265\pi$
$151$	2.16599	+	3.75161i	0.176266	+	0.305302i	−0.764333	+	0.644822i	$0.776931\pi$
$152$		0			0
$153$	−21.4647	+	3.42248i	−1.73532	+	0.276691i
$154$		0			0
$155$	−0.460087	+	0.265632i	−0.0369551	+	0.0213360i
$156$		0			0
$157$	−1.54152	−	0.889998i	−0.123027	−	0.0710296i	0.437224	−	0.899353i	$-0.355962\pi$
$157$	−1.54152	−	0.889998i	−0.123027	−	0.0710296i	−0.560251	+	0.828323i	$0.689295\pi$
$158$		0			0
$159$	1.15342	+	14.5591i	0.0914718	+	1.15461i
$160$		0			0
$161$	4.74955	+	14.0447i	0.374317	+	1.10687i
$162$		0			0
$163$	−5.63635			−0.441473			−0.220737	−	0.975333i	$-0.570846\pi$
$163$	−5.63635			−0.441473			−0.220737	+	0.975333i	$0.570846\pi$
$164$		0			0
$165$	−0.352954	−	4.45518i	−0.0274774	−	0.346835i
$166$		0			0
$167$	−2.38803	+	4.13618i	−0.184791	+	0.320067i	−0.943506	−	0.331355i	$-0.892494\pi$
$167$	−2.38803	+	4.13618i	−0.184791	+	0.320067i	0.758715	+	0.651423i	$0.225827\pi$
$168$		0			0
$169$	2.05692	+	3.56270i	0.158225	+	0.274054i
$170$		0			0
$171$	3.17301	+	19.9001i	0.242646	+	1.52180i
$172$		0			0
$173$	−2.83766	−	4.91497i	−0.215743	−	0.373678i	0.737759	−	0.675064i	$-0.235884\pi$
$173$	−2.83766	−	4.91497i	−0.215743	−	0.373678i	−0.953502	+	0.301386i	$0.902551\pi$
$174$		0			0
$175$	2.43646	−	12.1759i	0.184179	−	0.920408i
$176$		0			0
$177$	5.80921	−	12.1955i	0.436647	−	0.916672i
$178$		0			0
$179$			12.6305i			0.944048i	0.881586	+	0.472024i	$0.156476\pi$
$179$			12.6305i			0.944048i	−0.881586	+	0.472024i	$0.843524\pi$
$180$		0			0
$181$		−	22.7424i		−	1.69043i	−0.534426	−	0.845215i	$-0.679472\pi$
$181$		−	22.7424i		−	1.69043i	0.534426	−	0.845215i	$-0.320528\pi$
$182$		0			0
$183$	−8.85351	+	6.09160i	−0.654470	+	0.450304i
$184$		0			0
$185$	−1.95766	+	3.39076i	−0.143930	+	0.249294i
$186$		0			0
$187$	−29.2331	+	16.8777i	−2.13773	+	1.23422i
$188$		0			0
$189$	−12.1692	−	6.39619i	−0.885177	−	0.465254i
$190$		0			0
$191$	−10.0537	+	5.80452i	−0.727462	+	0.420000i	−0.817493	−	0.575939i	$-0.804637\pi$
$191$	−10.0537	+	5.80452i	−0.727462	+	0.420000i	0.0900309	+	0.995939i	$0.471303\pi$
$192$		0			0
$193$	−3.16599	+	5.48366i	−0.227893	+	0.394723i	−0.957184	−	0.289482i	$-0.906517\pi$
$193$	−3.16599	+	5.48366i	−0.227893	+	0.394723i	0.729290	+	0.684204i	$0.239850\pi$
$194$		0			0
$195$	3.26925	−	2.24939i	0.234116	−	0.161082i
$196$		0			0
$197$			3.10030i			0.220888i	0.993882	+	0.110444i	$0.0352272\pi$
$197$			3.10030i			0.220888i	−0.993882	+	0.110444i	$0.964773\pi$
$198$		0			0
$199$		−	15.7268i		−	1.11484i	−0.830229	−	0.557422i	$-0.811790\pi$
$199$		−	15.7268i		−	1.11484i	0.830229	−	0.557422i	$-0.188210\pi$
$200$		0			0
$201$	2.51485	−	5.27952i	0.177384	−	0.372389i
$202$		0			0
$203$	−3.49293	−	0.698954i	−0.245155	−	0.0490570i
$204$		0			0
$205$	1.32449	+	2.29409i	0.0925065	+	0.160226i
$206$		0			0
$207$	−15.7008	−	6.00830i	−1.09128	−	0.417606i
$208$		0			0
$209$	15.6475	+	27.1022i	1.08236	+	1.87470i
$210$		0			0
$211$	3.51263	−	6.08406i	0.241820	−	0.418844i	−0.719413	−	0.694582i	$-0.755589\pi$
$211$	3.51263	−	6.08406i	0.241820	−	0.418844i	0.961233	+	0.275739i	$0.0889225\pi$
$212$		0			0
$213$	0.0557495	+	0.703702i	0.00381989	+	0.0482169i
$214$		0			0
$215$	−1.13918			−0.0776915
$216$		0			0
$217$	0.813041	+	2.40420i	0.0551928	+	0.163208i
$218$		0			0
$219$	1.18127	+	14.9107i	0.0798229	+	1.00757i
$220$		0			0
$221$	−25.9573	−	14.9864i	−1.74608	−	1.00810i
$222$		0			0
$223$	21.3477	−	12.3251i	1.42955	−	0.825350i	0.432464	−	0.901651i	$-0.357644\pi$
$223$	21.3477	−	12.3251i	1.42955	−	0.825350i	0.997085	+	0.0763008i	$0.0243109\pi$
$224$		0			0
$225$	8.87206	+	10.9329i	0.591470	+	0.728859i
$226$		0			0
$227$	−10.0372	−	17.3849i	−0.666190	−	1.15388i	−0.978961	−	0.204047i	$-0.934590\pi$
$227$	−10.0372	−	17.3849i	−0.666190	−	1.15388i	0.312771	−	0.949829i	$-0.398743\pi$
$228$		0			0
$229$	6.75865	+	3.90211i	0.446624	+	0.257859i	0.706403	−	0.707809i	$-0.250316\pi$
$229$	6.75865	+	3.90211i	0.446624	+	0.257859i	−0.259779	+	0.965668i	$0.583650\pi$
$230$		0			0
$231$	−21.2005	−	2.52277i	−1.39489	−	0.165986i
$232$		0			0
$233$		−	7.96562i		−	0.521845i	−0.965360	−	0.260922i	$-0.915973\pi$
$233$		−	7.96562i		−	0.521845i	0.965360	−	0.260922i	$-0.0840267\pi$
$234$		0			0
$235$	−5.43084			−0.354269
$236$		0			0
$237$	−0.624760	−	0.908023i	−0.0405825	−	0.0589824i
$238$		0			0
$239$	23.2059	+	13.3979i	1.50107	+	0.866640i	0.999999	+	0.00123146i	$0.000391987\pi$
$239$	23.2059	+	13.3979i	1.50107	+	0.866640i	0.501066	+	0.865409i	$0.332941\pi$
$240$		0			0
$241$	0.757259	−	0.437203i	0.0487793	−	0.0281628i	−0.475412	−	0.879763i	$-0.657701\pi$
$241$	0.757259	−	0.437203i	0.0487793	−	0.0281628i	0.524191	+	0.851601i	$0.324368\pi$
$242$		0			0
$243$	14.3864	−	6.00274i	0.922885	−	0.385076i
$244$		0			0
$245$	3.57827	+	1.49180i	0.228608	+	0.0953077i
$246$		0			0
$247$	−13.8940	+	24.0652i	−0.884057	+	1.53123i
$248$		0			0
$249$	5.47521	+	7.95764i	0.346977	+	0.504295i
$250$		0			0
$251$	−2.32082			−0.146489			−0.0732445	−	0.997314i	$-0.523335\pi$
$251$	−2.32082			−0.146489			−0.0732445	+	0.997314i	$0.523335\pi$
$252$		0			0
$253$	−26.1075			−1.64136
$254$		0			0
$255$	−2.98884	+	6.27459i	−0.187168	+	0.392930i
$256$		0			0
$257$	12.3017	−	21.3072i	0.767361	−	1.32911i	−0.171628	−	0.985162i	$-0.554903\pi$
$257$	12.3017	−	21.3072i	0.767361	−	1.32911i	0.938989	−	0.343947i	$-0.111764\pi$
$258$		0			0
$259$	14.0485	+	12.3487i	0.872929	+	0.767312i
$260$		0			0
$261$	3.13635	−	2.54515i	0.194135	−	0.157541i
$262$		0			0
$263$	−20.5268	+	11.8512i	−1.26574	+	0.730775i	−0.974179	−	0.225778i	$-0.927508\pi$
$263$	−20.5268	+	11.8512i	−1.26574	+	0.730775i	−0.291560	+	0.956552i	$0.594174\pi$
$264$		0			0
$265$	4.04424	+	2.33494i	0.248436	+	0.143434i
$266$		0			0
$267$	−11.9680	+	0.948141i	−0.732429	+	0.0580253i
$268$		0			0
$269$	−20.6212			−1.25730			−0.628648	−	0.777690i	$-0.716391\pi$
$269$	−20.6212			−1.25730			−0.628648	+	0.777690i	$0.716391\pi$
$270$		0			0
$271$			13.9454i			0.847123i	0.905867	+	0.423562i	$0.139220\pi$
$271$			13.9454i			0.847123i	−0.905867	+	0.423562i	$0.860780\pi$
$272$		0			0
$273$	−7.47243	−	17.4228i	−0.452252	−	1.05448i
$274$		0			0
$275$	18.9363	+	10.9329i	1.14190	+	0.659278i
$276$		0			0
$277$	−10.3940	−	18.0030i	−0.624518	−	1.08170i	−0.988634	−	0.150343i	$-0.951962\pi$
$277$	−10.3940	−	18.0030i	−0.624518	−	1.08170i	0.364116	−	0.931354i	$-0.381371\pi$
$278$		0			0
$279$	−2.68770	−	1.02852i	−0.160908	−	0.0615757i
$280$		0			0
$281$	−20.3371	+	11.7416i	−1.21321	+	0.700448i	−0.963457	−	0.267862i	$-0.913683\pi$
$281$	−20.3371	+	11.7416i	−1.21321	+	0.700448i	−0.249754	+	0.968309i	$0.580350\pi$
$282$		0			0
$283$	−11.1906	−	6.46089i	−0.665211	−	0.384060i	0.129048	−	0.991638i	$-0.458808\pi$
$283$	−11.1906	−	6.46089i	−0.665211	−	0.384060i	−0.794260	+	0.607578i	$0.792141\pi$
$284$		0			0
$285$	5.81722	+	2.77097i	0.344582	+	0.164138i
$286$		0			0
$287$	11.9878	−	4.05398i	0.707619	−	0.239299i
$288$		0			0
$289$	35.4940			2.08788
$290$		0			0
$291$	12.3377	−	8.48887i	0.723247	−	0.497626i
$292$		0			0
$293$	−1.99115	+	3.44878i	−0.116324	+	0.201480i	−0.918308	−	0.395866i	$-0.870445\pi$
$293$	−1.99115	+	3.44878i	−0.116324	+	0.201480i	0.801984	+	0.597346i	$0.203778\pi$
$294$		0			0
$295$	−2.15968	−	3.74067i	−0.125741	−	0.217790i
$296$		0			0
$297$	17.5344	−	16.6914i	1.01745	−	0.968535i
$298$		0			0
$299$	−11.5910	−	20.0761i	−0.670322	−	1.16103i
$300$		0			0
$301$	−1.06783	+	5.33632i	−0.0615485	+	0.307580i
$302$		0			0
$303$	4.59920	+	6.68445i	0.264217	+	0.384012i
$304$		0			0
$305$			3.43629i			0.196762i
$306$		0			0
$307$			22.3162i			1.27365i	0.771008	+	0.636825i	$0.219753\pi$
$307$			22.3162i			1.27365i	−0.771008	+	0.636825i	$0.780247\pi$
$308$		0			0
$309$	−11.5705	−	5.51147i	−0.658221	−	0.313537i
$310$		0			0
$311$	−8.18371	+	14.1746i	−0.464056	+	0.803768i	−0.999158	−	0.0410190i	$-0.986940\pi$
$311$	−8.18371	+	14.1746i	−0.464056	+	0.803768i	0.535103	+	0.844787i	$0.320273\pi$
$312$		0			0
$313$	−16.5547	+	9.55785i	−0.935726	+	0.540242i	−0.888618	−	0.458648i	$-0.848334\pi$
$313$	−16.5547	+	9.55785i	−0.935726	+	0.540242i	−0.0471079	+	0.998890i	$0.515000\pi$
$314$		0			0
$315$	−3.89052	+	2.04635i	−0.219206	+	0.115299i
$316$		0			0
$317$	20.8798	−	12.0550i	1.17273	−	0.677074i	0.218405	−	0.975858i	$-0.429914\pi$
$317$	20.8798	−	12.0550i	1.17273	−	0.677074i	0.954321	+	0.298784i	$0.0965811\pi$
$318$		0			0
$319$	3.13635	−	5.43232i	0.175602	−	0.304152i
$320$		0			0
$321$	0.692237	+	8.73781i	0.0386369	+	0.487697i
$322$		0			0
$323$		−	48.6676i		−	2.70794i
$324$		0			0
$325$			19.4156i			1.07698i
$326$		0			0
$327$	20.3102	−	1.60904i	1.12316	−	0.0889799i
$328$		0			0
$329$	−5.09068	+	25.4399i	−0.280658	+	1.40255i
$330$		0			0
$331$	−5.70077	−	9.87403i	−0.313343	−	0.542726i	0.665741	−	0.746183i	$-0.268116\pi$
$331$	−5.70077	−	9.87403i	−0.313343	−	0.542726i	−0.979084	+	0.203457i	$0.934782\pi$
$332$		0			0
$333$	−20.9441	+	3.33947i	−1.14773	+	0.183002i
$334$		0			0
$335$	−0.934938	−	1.61936i	−0.0510811	−	0.0884751i
$336$		0			0
$337$	2.16599	−	3.75161i	0.117989	−	0.204363i	−0.800981	−	0.598689i	$-0.795689\pi$
$337$	2.16599	−	3.75161i	0.117989	−	0.204363i	0.918971	+	0.394326i	$0.129022\pi$
$338$		0			0
$339$	−2.74264	−	1.30643i	−0.148960	−	0.0709554i
$340$		0			0
$341$	−4.46914			−0.242018
$342$		0			0
$343$	10.3423	−	15.3635i	0.558429	−	0.829552i
$344$		0			0
$345$	−4.42843	+	3.04695i	−0.238419	+	0.164042i
$346$		0			0
$347$	−4.62254	−	2.66882i	−0.248151	−	0.143270i	0.370766	−	0.928726i	$-0.379095\pi$
$347$	−4.62254	−	2.66882i	−0.248151	−	0.143270i	−0.618917	+	0.785456i	$0.712428\pi$
$348$		0			0
$349$	8.78031	−	5.06931i	0.469999	−	0.271354i	−0.246240	−	0.969209i	$-0.579195\pi$
$349$	8.78031	−	5.06931i	0.469999	−	0.271354i	0.716239	+	0.697855i	$0.245862\pi$
$350$		0			0
$351$	20.6202	+	6.07312i	1.10062	+	0.324159i
$352$		0			0
$353$	−7.67564	−	13.2946i	−0.408533	−	0.707600i	0.586192	−	0.810172i	$-0.300626\pi$
$353$	−7.67564	−	13.2946i	−0.408533	−	0.707600i	−0.994726	+	0.102571i	$0.967293\pi$
$354$		0			0
$355$	0.195475	+	0.112858i	0.0103748	+	0.00598987i
$356$		0			0
$357$	26.5907	+	19.8823i	1.40733	+	1.05228i
$358$		0			0
$359$		−	1.74800i		−	0.0922559i	−0.998936	−	0.0461280i	$-0.985312\pi$
$359$		−	1.74800i		−	0.0922559i	0.998936	−	0.0461280i	$-0.0146882\pi$
$360$		0			0
$361$	−26.1201			−1.37474
$362$		0			0
$363$	7.97437	−	16.7409i	0.418546	−	0.878671i
$364$		0			0
$365$	4.14191	+	2.39133i	0.216798	+	0.125168i
$366$		0			0
$367$	−11.1720	+	6.45018i	−0.583176	+	0.336697i	−0.762394	−	0.647113i	$-0.775976\pi$
$367$	−11.1720	+	6.45018i	−0.583176	+	0.336697i	0.179219	+	0.983809i	$0.442643\pi$
$368$		0			0
$369$	−5.12839	+	13.4014i	−0.266973	+	0.697649i
$370$		0			0
$371$	14.7286	−	16.7559i	0.764671	−	0.869925i
$372$		0			0
$373$	5.34782	−	9.26269i	0.276900	−	0.479604i	−0.693713	−	0.720251i	$-0.744026\pi$
$373$	5.34782	−	9.26269i	0.276900	−	0.479604i	0.970613	+	0.240647i	$0.0773597\pi$
$374$		0			0
$375$	9.26930	−	0.734343i	0.478665	−	0.0379213i
$376$		0			0
$377$	5.56980			0.286859
$378$		0			0
$379$	0.566797			0.0291144			0.0145572	−	0.999894i	$-0.495366\pi$
$379$	0.566797			0.0291144			0.0145572	+	0.999894i	$0.495366\pi$
$380$		0			0
$381$	19.1350	−	1.51593i	0.980314	−	0.0776635i
$382$		0			0
$383$	−9.43059	+	16.3343i	−0.481880	+	0.834641i	−0.999784	−	0.0207978i	$-0.993379\pi$
$383$	−9.43059	+	16.3343i	−0.481880	+	0.834641i	0.517903	+	0.855439i	$0.326713\pi$
$384$		0			0
$385$	−4.50706	+	5.12744i	−0.229701	+	0.261318i
$386$		0			0
$387$	−3.88836	−	4.79156i	−0.197656	−	0.243569i
$388$		0			0
$389$	14.3182	−	8.26660i	0.725960	−	0.419133i	−0.0909822	−	0.995853i	$-0.529001\pi$
$389$	14.3182	−	8.26660i	0.725960	−	0.419133i	0.816943	+	0.576719i	$0.195667\pi$
$390$		0			0
$391$	35.1610	+	20.3002i	1.77817	+	1.02663i
$392$		0			0
$393$	13.7596	−	28.8862i	0.694082	−	1.45712i
$394$		0			0
$395$	−0.352429			−0.0177326
$396$		0			0
$397$			34.1080i			1.71183i	0.517114	+	0.855917i	$0.327006\pi$
$397$			34.1080i			1.71183i	−0.517114	+	0.855917i	$0.672994\pi$
$398$		0			0
$399$	18.4331	−	24.6525i	0.922807	−	1.23417i
$400$		0			0
$401$	18.6395	+	10.7615i	0.930811	+	0.537404i	0.887068	−	0.461639i	$-0.152738\pi$
$401$	18.6395	+	10.7615i	0.930811	+	0.537404i	0.0437428	+	0.999043i	$0.486072\pi$
$402$		0			0
$403$	−1.98417	−	3.43668i	−0.0988386	−	0.171193i
$404$		0			0
$405$	1.02622	−	4.87766i	0.0509931	−	0.242373i
$406$		0			0
$407$	−28.5241	+	16.4684i	−1.41389	+	0.816308i
$408$		0			0
$409$	19.2516	+	11.1149i	0.951933	+	0.549599i	0.893681	−	0.448703i	$-0.148114\pi$
$409$	19.2516	+	11.1149i	0.951933	+	0.549599i	0.0582520	+	0.998302i	$0.481447\pi$
$410$		0			0
$411$	31.3942	−	21.6006i	1.54856	−	1.06548i
$412$		0			0
$413$	−19.5470	+	6.61031i	−0.961846	+	0.325272i
$414$		0			0
$415$	3.08858			0.151613
$416$		0			0
$417$	−15.4558	−	7.36222i	−0.756875	−	0.360529i
$418$		0			0
$419$	−6.81490	+	11.8038i	−0.332930	+	0.576651i	−0.983085	−	0.183150i	$-0.941371\pi$
$419$	−6.81490	+	11.8038i	−0.332930	+	0.576651i	0.650155	+	0.759802i	$0.274704\pi$
$420$		0			0
$421$	13.7071	+	23.7414i	0.668043	+	1.15708i	0.978451	+	0.206480i	$0.0662009\pi$
$421$	13.7071	+	23.7414i	0.668043	+	1.15708i	−0.310408	+	0.950603i	$0.600466\pi$
$422$		0			0
$423$	−18.5371	−	22.8429i	−0.901303	−	1.11066i
$424$		0			0
$425$	−17.0020	−	29.4484i	−0.824720	−	1.42846i
$426$		0			0
$427$	16.0968	+	3.22106i	0.778978	+	0.155878i
$428$		0			0
$429$	33.2786	−	2.63643i	1.60670	−	0.127288i
$430$		0			0
$431$		−	34.8331i		−	1.67785i	−0.544248	−	0.838925i	$-0.683185\pi$
$431$		−	34.8331i		−	1.67785i	0.544248	−	0.838925i	$-0.316815\pi$
$432$		0			0
$433$		−	19.5648i		−	0.940223i	−0.882607	−	0.470112i	$-0.844214\pi$
$433$		−	19.5648i		−	0.940223i	0.882607	−	0.470112i	$-0.155786\pi$
$434$		0			0
$435$	−0.101999	−	1.28749i	−0.00489046	−	0.0617302i
$436$		0			0
$437$	18.8205	−	32.5980i	0.900305	−	1.55937i
$438$		0			0
$439$	24.7361	−	14.2814i	1.18059	−	0.681614i	0.224439	−	0.974488i	$-0.427945\pi$
$439$	24.7361	−	14.2814i	1.18059	−	0.681614i	0.956151	+	0.292874i	$0.0946116\pi$
$440$		0			0
$441$	5.93897	+	20.1427i	0.282808	+	0.959176i
$442$		0			0
$443$	−21.8612	+	12.6216i	−1.03866	+	0.599669i	−0.919453	−	0.393201i	$-0.871368\pi$
$443$	−21.8612	+	12.6216i	−1.03866	+	0.599669i	−0.119205	+	0.992870i	$0.538034\pi$
$444$		0			0
$445$	−1.91939	+	3.32448i	−0.0909878	+	0.157596i
$446$		0			0
$447$	−11.4959	−	5.47597i	−0.543739	−	0.259005i
$448$		0			0
$449$		−	15.1042i		−	0.712811i	−0.934331	−	0.356405i	$-0.884002\pi$
$449$		−	15.1042i		−	0.712811i	0.934331	−	0.356405i	$-0.115998\pi$
$450$		0			0
$451$			22.2840i			1.04931i
$452$		0			0
$453$	4.25308	+	6.18140i	0.199827	+	0.290428i
$454$		0			0
$455$	−5.94390	−	1.18941i	−0.278655	−	0.0557603i
$456$		0			0
$457$	−1.75138	−	3.03348i	−0.0819261	−	0.141900i	0.822151	−	0.569269i	$-0.192774\pi$
$457$	−1.75138	−	3.03348i	−0.0819261	−	0.141900i	−0.904077	+	0.427369i	$0.859440\pi$
$458$		0			0
$459$	−36.5936	+	8.84555i	−1.70804	+	0.412875i
$460$		0			0
$461$	1.98765	+	3.44272i	0.0925743	+	0.160343i	0.908594	−	0.417681i	$-0.137157\pi$
$461$	1.98765	+	3.44272i	0.0925743	+	0.160343i	−0.816019	+	0.578025i	$0.803824\pi$
$462$		0			0
$463$	−5.18494	+	8.98058i	−0.240965	+	0.417363i	−0.960989	−	0.276585i	$-0.910797\pi$
$463$	−5.18494	+	8.98058i	−0.240965	+	0.417363i	0.720025	+	0.693948i	$0.244130\pi$
$464$		0			0
$465$	−0.758070	+	0.521586i	−0.0351546	+	0.0241879i
$466$		0			0
$467$	−19.6190			−0.907860			−0.453930	−	0.891037i	$-0.649978\pi$
$467$	−19.6190			−0.907860			−0.453930	+	0.891037i	$0.649978\pi$
$468$		0			0
$469$	−8.46202	+	2.86164i	−0.390740	+	0.132138i
$470$		0			0
$471$	−2.78340	−	1.32584i	−0.128252	−	0.0610916i
$472$		0			0
$473$	−8.29923	−	4.79156i	−0.381599	−	0.220316i
$474$		0			0
$475$	−27.3018	+	15.7627i	−1.25269	+	0.723243i
$476$		0			0
$477$	3.98307	+	24.9805i	0.182372	+	1.14378i
$478$		0			0
$479$	15.8237	+	27.4074i	0.723002	+	1.25228i	0.959791	+	0.280715i	$0.0905717\pi$
$479$	15.8237	+	27.4074i	0.723002	+	1.25228i	−0.236789	+	0.971561i	$0.576095\pi$
$480$		0			0
$481$	−25.3277	−	14.6230i	−1.15485	−	0.666751i
$482$		0			0
$483$	10.1219	+	23.6004i	0.460564	+	1.07386i
$484$		0			0
$485$		−	4.78860i		−	0.217439i
$486$		0			0
$487$	−19.4585			−0.881747			−0.440874	−	0.897569i	$-0.645331\pi$
$487$	−19.4585			−0.881747			−0.440874	+	0.897569i	$0.645331\pi$
$488$		0			0
$489$	−9.73196	+	0.770996i	−0.440094	+	0.0348656i
$490$		0			0
$491$	23.9525	+	13.8290i	1.08096	+	0.624094i	0.931156	−	0.364622i	$-0.118802\pi$
$491$	23.9525	+	13.8290i	1.08096	+	0.624094i	0.149806	+	0.988715i	$0.452135\pi$
$492$		0			0
$493$	−8.44795	+	4.87743i	−0.380476	+	0.219668i
$494$		0			0
$495$	−1.21885	−	7.64422i	−0.0547831	−	0.343582i
$496$		0			0
$497$	0.711896	−	0.809886i	0.0319329	−	0.0363283i
$498$		0			0
$499$	4.50632	−	7.80517i	0.201730	−	0.349407i	−0.747356	−	0.664424i	$-0.768677\pi$
$499$	4.50632	−	7.80517i	0.201730	−	0.349407i	0.949086	+	0.315017i	$0.102010\pi$
$500$		0			0
$501$	−3.55748	+	7.46836i	−0.158936	+	0.333662i
$502$		0			0
$503$	−27.1572			−1.21088			−0.605440	−	0.795891i	$-0.707003\pi$
$503$	−27.1572			−1.21088			−0.605440	+	0.795891i	$0.707003\pi$
$504$		0			0
$505$	2.59442			0.115450
$506$		0			0
$507$	4.03891	+	5.87013i	0.179374	+	0.260702i
$508$		0			0
$509$	−6.56799	+	11.3761i	−0.291121	+	0.504236i	−0.974075	−	0.226225i	$-0.927362\pi$
$509$	−6.56799	+	11.3761i	−0.291121	+	0.504236i	0.682954	+	0.730461i	$0.260695\pi$
$510$		0			0
$511$	15.0843	−	17.1606i	0.667291	−	0.759140i
$512$		0			0
$513$	8.20077	+	33.9262i	0.362073	+	1.49788i
$514$		0			0
$515$	−3.54895	+	2.04899i	−0.156385	+	0.0902892i
$516$		0			0
$517$	−39.5651	−	22.8429i	−1.74007	−	1.00463i
$518$		0			0
$519$	−5.57193	−	8.09822i	−0.244581	−	0.355472i
$520$		0			0
$521$	4.03219			0.176653			0.0883266	−	0.996092i	$-0.471848\pi$
$521$	4.03219			0.176653			0.0883266	+	0.996092i	$0.471848\pi$
$522$		0			0
$523$			0.595961i			0.0260595i	0.999915	+	0.0130298i	$0.00414762\pi$
$523$			0.595961i			0.0260595i	−0.999915	+	0.0130298i	$0.995852\pi$
$524$		0			0
$525$	2.54135	−	21.3566i	0.110914	−	0.932079i
$526$		0			0
$527$	6.01895	+	3.47504i	0.262189	+	0.151375i
$528$		0			0
$529$	4.20077	+	7.27595i	0.182642	+	0.316346i
$530$		0			0
$531$	8.36220	−	21.8519i	0.362889	−	0.948294i
$532$		0			0
$533$	−17.1360	+	9.89347i	−0.742242	+	0.428534i
$534$		0			0
$535$	2.42720	+	1.40135i	0.104937	+	0.0605855i
$536$		0			0
$537$	1.72773	+	21.8083i	0.0745569	+	0.941100i
$538$		0			0
$539$	19.7939	+	25.9189i	0.852585	+	1.11641i
$540$		0			0
$541$	−14.1012			−0.606259			−0.303129	−	0.952949i	$-0.598031\pi$
$541$	−14.1012			−0.606259			−0.303129	+	0.952949i	$0.598031\pi$
$542$		0			0
$543$	−3.11093	−	39.2680i	−0.133503	−	1.68515i
$544$		0			0
$545$	3.25729	−	5.64179i	0.139527	−	0.241668i
$546$		0			0
$547$	−18.9921	−	32.8952i	−0.812042	−	1.40650i	−0.911433	−	0.411450i	$-0.865023\pi$
$547$	−18.9921	−	32.8952i	−0.812042	−	1.40650i	0.0993905	−	0.995049i	$-0.468311\pi$
$548$		0			0
$549$	−14.4536	+	11.7291i	−0.616863	+	0.500585i
$550$		0			0
$551$	4.52190	+	7.83216i	0.192639	+	0.333661i
$552$		0			0
$553$	−0.330354	+	1.65090i	−0.0140481	+	0.0702034i
$554$		0			0
$555$	−2.91635	+	6.12241i	−0.123792	+	0.259882i
$556$		0			0
$557$			41.7056i			1.76712i	0.468313	+	0.883562i	$0.344862\pi$
$557$			41.7056i			1.76712i	−0.468313	+	0.883562i	$0.655138\pi$
$558$		0			0
$559$		−	8.50926i		−	0.359903i
$560$		0			0
$561$	−48.1663	+	33.1406i	−2.03358	+	1.39920i
$562$		0			0
$563$	−0.938436	+	1.62542i	−0.0395504	+	0.0685033i	−0.885123	−	0.465357i	$-0.845926\pi$
$563$	−0.938436	+	1.62542i	−0.0395504	+	0.0685033i	0.845573	+	0.533860i	$0.179259\pi$
$564$		0			0
$565$	−0.841235	+	0.485687i	−0.0353910	+	0.0204330i
$566$		0			0
$567$	−21.8867	−	9.37930i	−0.919156	−	0.393894i
$568$		0			0
$569$	−20.6391	+	11.9160i	−0.865237	+	0.499545i	−0.865762	−	0.500455i	$-0.833166\pi$
$569$	−20.6391	+	11.9160i	−0.865237	+	0.499545i	0.000525844		1.00000i	$0.499833\pi$
$570$		0			0
$571$	−14.8719	+	25.7589i	−0.622370	+	1.07798i	0.366674	+	0.930350i	$0.380497\pi$
$571$	−14.8719	+	25.7589i	−0.622370	+	1.07798i	−0.989043	+	0.147626i	$0.952837\pi$
$572$		0			0
$573$	−16.5652	+	11.3976i	−0.692020	+	0.476140i
$574$		0			0
$575$		−	26.2997i		−	1.09678i
$576$		0			0
$577$		−	14.6589i		−	0.610260i	−0.952311	−	0.305130i	$-0.901300\pi$
$577$		−	14.6589i		−	0.610260i	0.952311	−	0.305130i	$-0.0986999\pi$
$578$		0			0
$579$	−4.71643	+	9.90139i	−0.196008	+	0.411488i
$580$		0			0
$581$	2.89513	−	14.4680i	0.120110	−	0.600233i
$582$		0			0
$583$	19.6422	+	34.0213i	0.813498	+	1.40902i
$584$		0			0
$585$	5.33712	−	4.33108i	0.220663	−	0.179068i
$586$		0			0
$587$	−22.2189	−	38.4843i	−0.917074	−	1.58842i	−0.803836	−	0.594851i	$-0.797211\pi$
$587$	−22.2189	−	38.4843i	−0.917074	−	1.58842i	−0.113238	−	0.993568i	$-0.536122\pi$
$588$		0			0
$589$	3.22174	−	5.58021i	0.132749	−	0.229929i
$590$		0			0
$591$	0.424090	+	5.35311i	0.0174447	+	0.220198i
$592$		0			0
$593$	37.1186			1.52428			0.762140	−	0.647412i	$-0.224149\pi$
$593$	37.1186			1.52428			0.762140	+	0.647412i	$0.224149\pi$
$594$		0			0
$595$	10.0569	−	3.40100i	0.412294	−	0.139427i
$596$		0			0
$597$	−2.15127	−	27.1546i	−0.0880456	−	1.11136i
$598$		0			0
$599$	−12.0534	−	6.95901i	−0.492487	−	0.284338i	0.233119	−	0.972448i	$-0.425107\pi$
$599$	−12.0534	−	6.95901i	−0.492487	−	0.284338i	−0.725606	+	0.688111i	$0.758440\pi$
$600$		0			0
$601$	0.377613	−	0.218015i	0.0154032	−	0.00889301i	−0.492279	−	0.870438i	$-0.663836\pi$
$601$	0.377613	−	0.218015i	0.0154032	−	0.00889301i	0.507682	+	0.861545i	$0.330503\pi$
$602$		0			0
$603$	3.62005	−	9.45984i	0.147420	−	0.385235i
$604$		0			0
$605$	−2.96461	−	5.13486i	−0.120529	−	0.208762i
$606$		0			0
$607$	1.92117	+	1.10919i	0.0779778	+	0.0450205i	0.538482	−	0.842637i	$-0.318998\pi$
$607$	1.92117	+	1.10919i	0.0779778	+	0.0450205i	−0.460504	+	0.887658i	$0.652331\pi$
$608$		0			0
$609$	−6.12664	−	0.729046i	−0.248264	−	0.0295424i
$610$		0			0
$611$		−	40.5664i		−	1.64114i
$612$		0			0
$613$	38.2023			1.54298			0.771488	−	0.636244i	$-0.219513\pi$
$613$	38.2023			1.54298			0.771488	+	0.636244i	$0.219513\pi$
$614$		0			0
$615$	2.60073	+	3.77989i	0.104872	+	0.152420i
$616$		0			0
$617$	21.1043	+	12.1846i	0.849628	+	0.490533i	0.860525	−	0.509407i	$-0.170135\pi$
$617$	21.1043	+	12.1846i	0.849628	+	0.490533i	−0.0108970	+	0.999941i	$0.503469\pi$
$618$		0			0
$619$	25.4477	−	14.6922i	1.02283	−	0.590531i	0.107907	−	0.994161i	$-0.465585\pi$
$619$	25.4477	−	14.6922i	1.02283	−	0.590531i	0.914922	+	0.403630i	$0.132252\pi$
$620$		0			0
$621$	−27.9315	−	8.22647i	−1.12085	−	0.330117i
$622$		0			0
$623$	13.7739	+	12.1073i	0.551838	+	0.485070i
$624$		0			0
$625$	−10.2466	+	17.7476i	−0.409864	+	0.709906i
$626$		0			0
$627$	30.7249	+	44.6553i	1.22703	+	1.78336i
$628$		0			0
$629$	51.2209			2.04231
$630$		0			0
$631$	5.17077			0.205845			0.102923	−	0.994689i	$-0.467181\pi$
$631$	5.17077			0.205845			0.102923	+	0.994689i	$0.467181\pi$
$632$		0			0
$633$	5.23282	−	10.9855i	0.207986	−	0.436633i
$634$		0			0
$635$	3.06881	−	5.31533i	0.121782	−	0.210933i
$636$		0			0
$637$	−11.1432	+	26.7284i	−0.441510	+	1.05902i
$638$		0			0
$639$	0.192519	+	1.20741i	0.00761592	+	0.0477646i
$640$		0			0
$641$	−5.32405	+	3.07384i	−0.210287	+	0.121410i	−0.601445	−	0.798914i	$-0.705408\pi$
$641$	−5.32405	+	3.07384i	−0.210287	+	0.121410i	0.391158	+	0.920324i	$0.372075\pi$
$642$		0			0
$643$	23.9599	+	13.8333i	0.944886	+	0.545530i	0.891489	−	0.453043i	$-0.149662\pi$
$643$	23.9599	+	13.8333i	0.944886	+	0.545530i	0.0533976	+	0.998573i	$0.482995\pi$
$644$		0			0
$645$	−1.96696	+	0.155828i	−0.0774488	+	0.00613574i
$646$		0			0
$647$	4.81457			0.189280			0.0946402	−	0.995512i	$-0.469830\pi$
$647$	4.81457			0.189280			0.0946402	+	0.995512i	$0.469830\pi$
$648$		0			0
$649$		−	36.3357i		−	1.42630i
$650$		0			0
$651$	1.73270	+	4.03998i	0.0679099	+	0.158339i
$652$		0			0
$653$	21.1759	+	12.2259i	0.828677	+	0.478437i	0.853400	−	0.521257i	$-0.174537\pi$
$653$	21.1759	+	12.2259i	0.828677	+	0.478437i	−0.0247223	+	0.999694i	$0.507870\pi$
$654$		0			0
$655$	−5.11539	−	8.86011i	−0.199875	−	0.346193i
$656$		0			0
$657$	4.07926	+	25.5838i	0.159147	+	0.998120i
$658$		0			0
$659$	−20.7514	+	11.9808i	−0.808359	+	0.466706i	−0.846386	−	0.532570i	$-0.821226\pi$
$659$	−20.7514	+	11.9808i	−0.808359	+	0.466706i	0.0380267	+	0.999277i	$0.487893\pi$
$660$		0			0
$661$	−6.73275	−	3.88715i	−0.261874	−	0.151193i	0.363315	−	0.931666i	$-0.381645\pi$
$661$	−6.73275	−	3.88715i	−0.261874	−	0.151193i	−0.625189	+	0.780473i	$0.714978\pi$
$662$		0			0
$663$	−46.8689	−	22.3255i	−1.82024	−	0.867051i
$664$		0			0
$665$	−3.15309	−	9.32385i	−0.122272	−	0.361563i
$666$		0			0
$667$	−7.54469			−0.292131
$668$		0			0
$669$	35.1739	−	24.2012i	1.35990	−	0.935672i
$670$		0			0
$671$	−14.4536	+	25.0343i	−0.557973	+	0.966438i
$672$		0			0
$673$	−14.7281	−	25.5097i	−0.567725	−	0.983328i	−0.996790	−	0.0800548i	$-0.974490\pi$
$673$	−14.7281	−	25.5097i	−0.567725	−	0.983328i	0.429066	−	0.903273i	$-0.358843\pi$
$674$		0			0
$675$	16.8144	+	17.6636i	0.647185	+	0.679871i
$676$		0			0
$677$	17.8293	+	30.8812i	0.685235	+	1.18686i	0.973363	+	0.229270i	$0.0736337\pi$
$677$	17.8293	+	30.8812i	0.685235	+	1.18686i	−0.288128	+	0.957592i	$0.593033\pi$
$678$		0			0
$679$	−22.4314	−	4.48866i	−0.860840	−	0.172259i
$680$		0			0
$681$	−19.7087	−	28.6445i	−0.755238	−	1.09766i
$682$		0			0
$683$			13.0969i			0.501139i	0.968099	+	0.250570i	$0.0806179\pi$
$683$			13.0969i			0.501139i	−0.968099	+	0.250570i	$0.919382\pi$
$684$		0			0
$685$		−	12.1850i		−	0.465563i
$686$		0			0
$687$	12.2035	+	5.81302i	0.465594	+	0.221781i
$688$		0			0
$689$	−17.4412	+	30.2090i	−0.664456	+	1.15087i
$690$		0			0
$691$	7.81992	−	4.51483i	0.297484	−	0.171752i	−0.343828	−	0.939033i	$-0.611724\pi$
$691$	7.81992	−	4.51483i	0.297484	−	0.171752i	0.641312	+	0.767280i	$0.278390\pi$
$692$		0			0
$693$	−36.9507	−	1.45591i	−1.40364	−	0.0553055i
$694$		0			0
$695$	−4.74068	+	2.73704i	−0.179824	+	0.103822i
$696$		0			0
$697$	17.3273	−	30.0117i	0.656316	−	1.13677i
$698$		0			0
$699$	−1.08962	−	13.7538i	−0.0412131	−	0.520215i
$700$		0			0
$701$		−	0.259274i		−	0.00979264i	−0.999988	−	0.00489632i	$-0.998441\pi$
$701$		−	0.259274i		−	0.00979264i	0.999988	−	0.00489632i	$-0.00155855\pi$
$702$		0			0
$703$		−	47.4873i		−	1.79102i
$704$		0			0
$705$	−9.37711	+	0.742884i	−0.353163	+	0.0279786i
$706$		0			0
$707$	2.43192	−	12.1532i	0.0914617	−	0.457067i
$708$		0			0
$709$	−3.08574	−	5.34467i	−0.115888	−	0.200723i	0.802247	−	0.596993i	$-0.203638\pi$
$709$	−3.08574	−	5.34467i	−0.115888	−	0.200723i	−0.918134	+	0.396270i	$0.870305\pi$
$710$		0			0
$711$	−1.20294	−	1.48237i	−0.0451139	−	0.0555932i
$712$		0			0
$713$	2.68770	+	4.65523i	0.100655	+	0.174340i
$714$		0			0
$715$	5.33712	−	9.24417i	0.199597	−	0.345712i
$716$		0			0
$717$	41.9010	+	19.9591i	1.56482	+	0.745386i
$718$		0			0
$719$	19.5275			0.728253			0.364127	−	0.931349i	$-0.381368\pi$
$719$	19.5275			0.728253			0.364127	+	0.931349i	$0.381368\pi$
$720$		0			0
$721$	6.27151	+	18.5452i	0.233563	+	0.690658i
$722$		0			0
$723$	1.24771	−	0.858479i	0.0464028	−	0.0319272i
$724$		0			0
$725$	5.47233	+	3.15945i	0.203237	+	0.117339i
$726$		0			0
$727$	0.425312	−	0.245554i	0.0157740	−	0.00910710i	−0.492092	−	0.870543i	$-0.663768\pi$
$727$	0.425312	−	0.245554i	0.0157740	−	0.00910710i	0.507866	+	0.861436i	$0.330434\pi$
$728$		0			0
$729$	24.0189	−	12.3325i	0.889591	−	0.456759i
$730$		0			0
$731$	7.45149	+	12.9064i	0.275603	+	0.477359i
$732$		0			0
$733$	6.68424	+	3.85915i	0.246888	+	0.142541i	0.618338	−	0.785912i	$-0.287806\pi$
$733$	6.68424	+	3.85915i	0.246888	+	0.142541i	−0.371450	+	0.928453i	$0.621139\pi$
$734$		0			0
$735$	6.38246	+	2.08633i	0.235421	+	0.0769555i
$736$		0			0
$737$		−	15.7300i		−	0.579420i
$738$		0			0
$739$	10.9083			0.401270			0.200635	−	0.979666i	$-0.435700\pi$
$739$	10.9083			0.401270			0.200635	+	0.979666i	$0.435700\pi$
$740$		0			0
$741$	−20.6982	+	43.4525i	−0.760366	+	1.59627i
$742$		0			0
$743$	27.0051	+	15.5914i	0.990722	+	0.571994i	0.905490	−	0.424367i	$-0.139503\pi$
$743$	27.0051	+	15.5914i	0.990722	+	0.571994i	0.0852322	+	0.996361i	$0.472837\pi$
$744$		0			0
$745$	−3.52609	+	2.03579i	−0.129186	+	0.0745855i
$746$		0			0
$747$	10.5422	+	12.9910i	0.385721	+	0.475317i
$748$		0			0
$749$	8.83956	−	10.0563i	0.322991	−	0.367449i
$750$		0			0
$751$	23.0367	−	39.9008i	0.840622	−	1.45600i	−0.0487482	−	0.998811i	$-0.515523\pi$
$751$	23.0367	−	39.9008i	0.840622	−	1.45600i	0.889370	−	0.457188i	$-0.151143\pi$
$752$		0			0
$753$	−4.00723	+	0.317465i	−0.146032	+	0.0115691i
$754$		0			0
$755$	2.39917			0.0873149
$756$		0			0
$757$	40.6419			1.47715			0.738577	−	0.674169i	$-0.235498\pi$
$757$	40.6419			1.47715			0.738577	+	0.674169i	$0.235498\pi$
$758$		0			0
$759$	−45.0782	+	3.57124i	−1.63623	+	0.129628i
$760$		0			0
$761$	3.64190	−	6.30795i	0.132019	−	0.228663i	−0.792436	−	0.609955i	$-0.791187\pi$
$761$	3.64190	−	6.30795i	0.132019	−	0.228663i	0.924455	+	0.381292i	$0.124521\pi$
$762$		0			0
$763$	−23.3748	−	20.5467i	−0.846226	−	0.743840i
$764$		0			0
$765$	−4.30235	+	11.2428i	−0.155552	+	0.406485i
$766$		0			0
$767$	27.9415	−	16.1320i	1.00891	−	0.582493i
$768$		0			0
$769$	−35.8261	−	20.6842i	−1.29192	−	0.745892i	−0.312927	−	0.949777i	$-0.601310\pi$
$769$	−35.8261	−	20.6842i	−1.29192	−	0.745892i	−0.978995	+	0.203886i	$0.934643\pi$
$770$		0			0
$771$	18.3261	−	38.4727i	0.659997	−	1.38556i
$772$		0			0
$773$	17.1183			0.615702			0.307851	−	0.951435i	$-0.400390\pi$
$773$	17.1183			0.615702			0.307851	+	0.951435i	$0.400390\pi$
$774$		0			0
$775$		−	4.50206i		−	0.161719i
$776$		0			0
$777$	25.9458	+	19.4001i	0.930802	+	0.695975i
$778$		0			0
$779$	−27.8241	−	16.0642i	−0.996900	−	0.575561i
$780$		0			0
$781$	0.949393	+	1.64440i	0.0339719	+	0.0588411i
$782$		0			0
$783$	5.06720	−	4.82359i	0.181087	−	0.172381i
$784$		0			0
$785$	−0.853737	+	0.492906i	−0.0304712	+	0.0175926i
$786$		0			0
$787$	−25.7426	−	14.8625i	−0.917623	−	0.529790i	−0.0347472	−	0.999396i	$-0.511063\pi$
$787$	−25.7426	−	14.8625i	−0.917623	−	0.529790i	−0.882876	+	0.469606i	$0.844396\pi$
$788$		0			0
$789$	−33.8214	+	23.2706i	−1.20407	+	0.828455i
$790$		0			0
$791$	1.48658	+	4.39590i	0.0528568	+	0.156300i
$792$		0			0
$793$	−25.6679			−0.911492
$794$		0			0
$795$	7.30235	+	3.47840i	0.258988	+	0.123366i
$796$		0			0
$797$	20.6019	−	35.6836i	0.729757	−	1.26398i	−0.227229	−	0.973841i	$-0.572966\pi$
$797$	20.6019	−	35.6836i	0.729757	−	1.26398i	0.956986	−	0.290135i	$-0.0937002\pi$
$798$		0			0
$799$	35.5236	+	61.5288i	1.25674	+	2.17673i
$800$		0			0
$801$	−20.5347	+	3.27420i	−0.725558	+	0.115688i
$802$		0			0
$803$	20.1166	+	34.8430i	0.709900	+	1.22958i
$804$		0			0
$805$	8.05144	+	1.61114i	0.283776	+	0.0567852i
$806$		0			0
$807$	−35.6054	+	2.82077i	−1.25337	+	0.0992957i
$808$		0			0
$809$			12.4233i			0.436780i	0.975862	+	0.218390i	$0.0700805\pi$
$809$			12.4233i			0.436780i	−0.975862	+	0.218390i	$0.929920\pi$
$810$		0			0
$811$			32.8713i			1.15427i	0.816650	+	0.577133i	$0.195829\pi$
$811$			32.8713i			1.15427i	−0.816650	+	0.577133i	$0.804171\pi$
$812$		0			0
$813$	1.90759	+	24.0787i	0.0669021	+	0.844477i
$814$		0			0
$815$	−1.56078	+	2.70336i	−0.0546719	+	0.0946944i
$816$		0			0
$817$	11.9656	−	6.90833i	0.418623	−	0.241692i
$818$		0			0
$819$	−15.2855	−	29.0607i	−0.534118	−	1.01546i
$820$		0			0
$821$	−11.7411	+	6.77873i	−0.409768	+	0.236579i	−0.690690	−	0.723151i	$-0.742693\pi$
$821$	−11.7411	+	6.77873i	−0.409768	+	0.236579i	0.280922	+	0.959731i	$0.409360\pi$
$822$		0			0
$823$	12.2565	−	21.2289i	0.427235	−	0.739993i	−0.569391	−	0.822067i	$-0.692821\pi$
$823$	12.2565	−	21.2289i	0.427235	−	0.739993i	0.996626	+	0.0820737i	$0.0261543\pi$
$824$		0			0
$825$	34.1917	+	16.2869i	1.19040	+	0.567036i
$826$		0			0
$827$		−	14.7323i		−	0.512292i	−0.966638	−	0.256146i	$-0.917547\pi$
$827$		−	14.7323i		−	0.512292i	0.966638	−	0.256146i	$-0.0824527\pi$
$828$		0			0
$829$		−	13.5191i		−	0.469539i	−0.972051	−	0.234770i	$-0.924566\pi$
$829$		−	13.5191i		−	0.469539i	0.972051	−	0.234770i	$-0.0754336\pi$
$830$		0			0
$831$	−20.4094	−	29.6629i	−0.707995	−	1.02900i
$832$		0			0
$833$	−6.50446	−	50.2981i	−0.225366	−	1.74273i
$834$		0			0
$835$	1.32255	+	2.29073i	0.0457689	+	0.0792740i
$836$		0			0
$837$	−4.78138	−	1.40823i	−0.165269	−	0.0486755i
$838$		0			0
$839$	−0.511154	−	0.885345i	−0.0176470	−	0.0305655i	0.857067	−	0.515205i	$-0.172284\pi$
$839$	−0.511154	−	0.885345i	−0.0176470	−	0.0305655i	−0.874714	+	0.484639i	$0.838951\pi$
$840$		0			0
$841$	−13.5936	+	23.5449i	−0.468746	+	0.811892i
$842$		0			0
$843$	−33.5088	+	23.0555i	−1.15410	+	0.794074i
$844$		0			0
$845$	2.27836			0.0783780
$846$		0			0
$847$	−26.8324	+	9.07404i	−0.921972	+	0.311788i
$848$		0			0
$849$	−20.2059	−	9.62487i	−0.693465	−	0.330325i
$850$		0			0
$851$	34.3082	+	19.8079i	1.17607	+	0.679005i
$852$		0			0
$853$	8.70682	−	5.02689i	0.298116	−	0.172117i	−0.343480	−	0.939160i	$-0.611606\pi$
$853$	8.70682	−	5.02689i	0.298116	−	0.172117i	0.641596	+	0.767043i	$0.278273\pi$
$854$		0			0
$855$	10.4233	+	3.98874i	0.356469	+	0.136412i
$856$		0			0
$857$	−14.1272	−	24.4690i	−0.482575	−	0.835844i	0.517225	−	0.855850i	$-0.326965\pi$
$857$	−14.1272	−	24.4690i	−0.482575	−	0.835844i	−0.999800	+	0.0200052i	$0.993632\pi$
$858$		0			0
$859$	26.9800	+	15.5769i	0.920544	+	0.531476i	0.883809	−	0.467849i	$-0.154971\pi$
$859$	26.9800	+	15.5769i	0.920544	+	0.531476i	0.0367356	+	0.999325i	$0.488304\pi$
$860$		0			0
$861$	20.1441	−	8.63959i	0.686510	−	0.294436i
$862$		0			0
$863$			57.1234i			1.94450i	0.233938	+	0.972252i	$0.424839\pi$
$863$			57.1234i			1.94450i	−0.233938	+	0.972252i	$0.575161\pi$
$864$		0			0
$865$	−3.14314			−0.106870
$866$		0			0
$867$	61.2854	−	4.85522i	2.08136	−	0.164892i
$868$		0			0
$869$	−2.56754	−	1.48237i	−0.0870978	−	0.0502859i
$870$		0			0
$871$	12.0960	−	6.98365i	0.409858	−	0.236632i
$872$		0			0
$873$	20.1415	−	16.3449i	0.681688	−	0.553191i
$874$		0			0
$875$	−10.6680	−	9.37724i	−0.360643	−	0.317009i
$876$		0			0
$877$	15.6691	−	27.1397i	0.529108	−	0.916443i	−0.470315	−	0.882498i	$-0.655860\pi$
$877$	15.6691	−	27.1397i	0.529108	−	0.916443i	0.999424	−	0.0339441i	$-0.0108068\pi$
$878$		0			0
$879$	−2.96625	+	6.22717i	−0.100049	+	0.210037i
$880$		0			0
$881$	12.2822			0.413799			0.206900	−	0.978362i	$-0.433663\pi$
$881$	12.2822			0.413799			0.206900	+	0.978362i	$0.433663\pi$
$882$		0			0
$883$	3.61496			0.121653			0.0608266	−	0.998148i	$-0.480626\pi$
$883$	3.61496			0.121653			0.0608266	+	0.998148i	$0.480626\pi$
$884$		0			0
$885$	−4.24068	−	6.16338i	−0.142549	−	0.207180i
$886$		0			0
$887$	−9.44264	+	16.3551i	−0.317053	+	0.549152i	−0.979872	−	0.199628i	$-0.936027\pi$
$887$	−9.44264	+	16.3551i	−0.317053	+	0.549152i	0.662819	+	0.748780i	$0.269360\pi$
$888$		0			0
$889$	−22.0223	−	19.3578i	−0.738603	−	0.649239i
$890$		0			0
$891$	27.9924	−	31.2186i	0.937781	−	1.04586i
$892$		0			0
$893$	57.0438	−	32.9342i	1.90890	−	1.10210i
$894$		0			0
$895$	6.05795	+	3.49756i	0.202495	+	0.116911i
$896$		0			0
$897$	−22.7596	−	33.0787i	−0.759922	−	1.10447i
$898$		0			0
$899$	−1.29152			−0.0430746
$900$		0			0
$901$		−	61.0923i		−	2.03528i
$902$		0			0
$903$	−1.11380	+	9.35997i	−0.0370649	+	0.311480i
$904$		0			0
$905$	−10.9079	−	6.29769i	−0.362591	−	0.209342i
$906$		0			0
$907$	28.8802	+	50.0219i	0.958950	+	1.66095i	0.725059	+	0.688687i	$0.241813\pi$
$907$	28.8802	+	50.0219i	0.958950	+	1.66095i	0.233891	+	0.972263i	$0.424854\pi$
$908$		0			0
$909$	8.85553	+	10.9125i	0.293719	+	0.361945i
$910$		0			0
$911$	−33.7810	+	19.5034i	−1.11921	+	0.646178i	−0.941200	−	0.337850i	$-0.890300\pi$
$911$	−33.7810	+	19.5034i	−1.11921	+	0.646178i	−0.178013	+	0.984028i	$0.556967\pi$
$912$		0			0
$913$	22.5011	+	12.9910i	0.744679	+	0.429940i
$914$		0			0
$915$	0.470050	+	5.93324i	0.0155394	+	0.196147i
$916$		0			0
$917$	−46.2988	+	15.6571i	−1.52892	+	0.517043i
$918$		0			0
$919$	−31.8095			−1.04930			−0.524649	−	0.851319i	$-0.675803\pi$
$919$	−31.8095			−1.04930			−0.524649	+	0.851319i	$0.675803\pi$
$920$		0			0
$921$	3.05262	+	38.5320i	0.100587	+	1.26967i
$922$		0			0
$923$	−0.843006	+	1.46013i	−0.0277479	+	0.0480607i
$924$		0			0
$925$	−16.5897	−	28.7342i	−0.545465	−	0.944774i
$926$		0			0
$927$	−20.7320	−	7.93361i	−0.680927	−	0.260574i
$928$		0			0
$929$	19.0424	+	32.9825i	0.624762	+	1.08212i	0.988587	+	0.150653i	$0.0481375\pi$
$929$	19.0424	+	32.9825i	0.624762	+	1.08212i	−0.363824	+	0.931468i	$0.618529\pi$
$930$		0			0
$931$	−46.6317	+	6.03033i	−1.52829	+	0.197636i
$932$		0			0
$933$	−12.1914	+	25.5939i	−0.399128	+	0.837907i
$934$		0			0
$935$			18.6947i			0.611382i
$936$		0			0
$937$			37.6261i			1.22919i	0.788842	+	0.614596i	$0.210681\pi$
$937$			37.6261i			1.22919i	−0.788842	+	0.614596i	$0.789319\pi$
$938$		0			0
$939$	−27.2766	+	18.7675i	−0.890137	+	0.612454i
$940$		0			0
$941$	−0.837737	+	1.45100i	−0.0273094	+	0.0473014i	−0.879357	−	0.476163i	$-0.842027\pi$
$941$	−0.837737	+	1.45100i	−0.0273094	+	0.0473014i	0.852048	+	0.523464i	$0.175361\pi$
$942$		0			0
$943$	23.2119	−	13.4014i	0.755884	−	0.436410i
$944$		0			0
$945$	−6.43761	+	4.06549i	−0.209415	+	0.132250i
$946$		0			0
$947$	19.2331	−	11.1042i	0.624992	−	0.360839i	−0.153818	−	0.988099i	$-0.549157\pi$
$947$	19.2331	−	11.1042i	0.624992	−	0.360839i	0.778810	+	0.627260i	$0.215824\pi$
$948$		0			0
$949$	−17.8624	+	30.9386i	−0.579838	+	1.00431i
$950$		0			0
$951$	34.4029	−	23.6707i	1.11559	−	0.767576i
$952$		0			0
$953$		−	27.1505i		−	0.879491i	−0.898122	−	0.439746i	$-0.855069\pi$
$953$		−	27.1505i		−	0.879491i	0.898122	−	0.439746i	$-0.144931\pi$
$954$		0			0
$955$			6.42941i			0.208051i
$956$		0			0
$957$	4.67227	−	9.80869i	0.151033	−	0.317070i
$958$		0			0
$959$	−57.0785	−	11.4217i	−1.84316	−	0.368827i
$960$		0			0
$961$	−15.0399	−	26.0499i	−0.485158	−	0.840319i
$962$		0			0
$963$	2.39049	+	14.9924i	0.0770325	+	0.483123i
$964$		0			0
$965$	1.75341	+	3.03700i	0.0564444	+	0.0977646i
$966$		0			0
$967$	−16.7553	+	29.0211i	−0.538815	+	0.933255i	0.460153	+	0.887840i	$0.347795\pi$
$967$	−16.7553	+	29.0211i	−0.538815	+	0.933255i	−0.998968	+	0.0454157i	$0.985539\pi$
$968$		0			0
$969$	−6.65723	−	84.0314i	−0.213861	−	2.69948i
$970$		0			0
$971$	−35.7465			−1.14716			−0.573580	−	0.819149i	$-0.694446\pi$
$971$	−35.7465			−1.14716			−0.573580	+	0.819149i	$0.694446\pi$
$972$		0			0
$973$	8.37748	+	24.7726i	0.268570	+	0.794173i
$974$		0			0
$975$	2.65585	+	33.5237i	0.0850553	+	1.07362i
$976$		0			0
$977$	−39.5696	−	22.8455i	−1.26594	−	0.730892i	−0.291725	−	0.956502i	$-0.594229\pi$
$977$	−39.5696	−	22.8455i	−1.26594	−	0.730892i	−0.974218	+	0.225610i	$0.927562\pi$
$978$		0			0
$979$	−27.9665	+	16.1465i	−0.893814	+	0.516044i
$980$		0			0
$981$	34.8483	−	5.55646i	1.11262	−	0.177404i
$982$		0			0
$983$	9.33713	+	16.1724i	0.297808	+	0.515819i	0.975634	−	0.219404i	$-0.0704111\pi$
$983$	9.33713	+	16.1724i	0.297808	+	0.515819i	−0.677826	+	0.735222i	$0.737078\pi$
$984$		0			0
$985$	1.48699	+	0.858517i	0.0473796	+	0.0273546i
$986$		0			0
$987$	−5.30984	+	44.6220i	−0.169014	+	1.42033i
$988$		0			0
$989$			11.5264i			0.366518i
$990$		0			0
$991$	48.5612			1.54260			0.771299	−	0.636473i	$-0.219608\pi$
$991$	48.5612			1.54260			0.771299	+	0.636473i	$0.219608\pi$
$992$		0			0
$993$	−11.1939	−	16.2691i	−0.355226	−	0.516284i
$994$		0			0
$995$	−7.54303	−	4.35497i	−0.239130	−	0.138062i
$996$		0			0
$997$	−45.1982	+	26.0952i	−1.43144	+	0.826442i	−0.997231	−	0.0743700i	$-0.976305\pi$
$997$	−45.1982	+	26.0952i	−1.43144	+	0.826442i	−0.434209	+	0.900812i	$0.642972\pi$
$998$		0			0
$999$	−35.7061	+	8.63102i	−1.12969	+	0.273073i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.x.a.41.8	yes	16
3.2	odd	2		756.2.x.a.125.3		16
4.3	odd	2		1008.2.cc.c.545.1		16
7.2	even	3		1764.2.bm.b.1697.3		16
7.3	odd	6		1764.2.w.a.509.6		16
7.4	even	3		1764.2.w.a.509.3		16
7.5	odd	6		1764.2.bm.b.1697.6		16
7.6	odd	2	inner	252.2.x.a.41.1	✓	16
9.2	odd	6	inner	252.2.x.a.209.1	yes	16
9.4	even	3		2268.2.f.b.1133.5		16
9.5	odd	6		2268.2.f.b.1133.11		16
9.7	even	3		756.2.x.a.629.6		16
12.11	even	2		3024.2.cc.c.881.3		16
21.2	odd	6		5292.2.bm.b.2285.6		16
21.5	even	6		5292.2.bm.b.2285.3		16
21.11	odd	6		5292.2.w.a.1097.3		16
21.17	even	6		5292.2.w.a.1097.6		16
21.20	even	2		756.2.x.a.125.6		16
28.27	even	2		1008.2.cc.c.545.8		16
36.7	odd	6		3024.2.cc.c.2897.6		16
36.11	even	6		1008.2.cc.c.209.8		16
63.2	odd	6		1764.2.w.a.1109.6		16
63.11	odd	6		1764.2.bm.b.1685.6		16
63.13	odd	6		2268.2.f.b.1133.12		16
63.16	even	3		5292.2.w.a.521.6		16
63.20	even	6	inner	252.2.x.a.209.8	yes	16
63.25	even	3		5292.2.bm.b.4625.3		16
63.34	odd	6		756.2.x.a.629.3		16
63.38	even	6		1764.2.bm.b.1685.3		16
63.41	even	6		2268.2.f.b.1133.6		16
63.47	even	6		1764.2.w.a.1109.3		16
63.52	odd	6		5292.2.bm.b.4625.6		16
63.61	odd	6		5292.2.w.a.521.3		16
84.83	odd	2		3024.2.cc.c.881.6		16
252.83	odd	6		1008.2.cc.c.209.1		16
252.223	even	6		3024.2.cc.c.2897.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.x.a.41.1	✓	16	7.6	odd	2	inner
252.2.x.a.41.8	yes	16	1.1	even	1	trivial
252.2.x.a.209.1	yes	16	9.2	odd	6	inner
252.2.x.a.209.8	yes	16	63.20	even	6	inner
756.2.x.a.125.3		16	3.2	odd	2
756.2.x.a.125.6		16	21.20	even	2
756.2.x.a.629.3		16	63.34	odd	6
756.2.x.a.629.6		16	9.7	even	3
1008.2.cc.c.209.1		16	252.83	odd	6
1008.2.cc.c.209.8		16	36.11	even	6
1008.2.cc.c.545.1		16	4.3	odd	2
1008.2.cc.c.545.8		16	28.27	even	2
1764.2.w.a.509.3		16	7.4	even	3
1764.2.w.a.509.6		16	7.3	odd	6
1764.2.w.a.1109.3		16	63.47	even	6
1764.2.w.a.1109.6		16	63.2	odd	6
1764.2.bm.b.1685.3		16	63.38	even	6
1764.2.bm.b.1685.6		16	63.11	odd	6
1764.2.bm.b.1697.3		16	7.2	even	3
1764.2.bm.b.1697.6		16	7.5	odd	6
2268.2.f.b.1133.5		16	9.4	even	3
2268.2.f.b.1133.6		16	63.41	even	6
2268.2.f.b.1133.11		16	9.5	odd	6
2268.2.f.b.1133.12		16	63.13	odd	6
3024.2.cc.c.881.3		16	12.11	even	2
3024.2.cc.c.881.6		16	84.83	odd	2
3024.2.cc.c.2897.3		16	252.223	even	6
3024.2.cc.c.2897.6		16	36.7	odd	6
5292.2.w.a.521.3		16	63.61	odd	6
5292.2.w.a.521.6		16	63.16	even	3
5292.2.w.a.1097.3		16	21.11	odd	6
5292.2.w.a.1097.6		16	21.17	even	6
5292.2.bm.b.2285.3		16	21.5	even	6
5292.2.bm.b.2285.6		16	21.2	odd	6
5292.2.bm.b.4625.3		16	63.25	even	3
5292.2.bm.b.4625.6		16	63.52	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72664 - 0.136790i) q^{3} +(0.276914 - 0.479629i) q^{5} +(-1.98718 - 1.74675i) q^{7} +(2.96258 - 0.472374i) q^{9} +O(q^{10})\)	\(q+(1.72664 - 0.136790i) q^{3} +(0.276914 - 0.479629i) q^{5} +(-1.98718 - 1.74675i) q^{7} +(2.96258 - 0.472374i) q^{9} +(4.03478 - 2.32948i) q^{11} +(3.58265 + 2.06844i) q^{13} +(0.412522 - 0.866025i) q^{15} -7.24527 q^{17} +6.71715i q^{19} +(-3.67008 - 2.74418i) q^{21} +(-4.85295 - 2.80185i) q^{23} +(2.34664 + 4.06450i) q^{25} +(5.05069 - 1.22087i) q^{27} +(1.16599 - 0.673187i) q^{29} +(-0.830741 - 0.479629i) q^{31} +(6.64796 - 4.57409i) q^{33} +(-1.38807 + 0.469409i) q^{35} -7.06956 q^{37} +(6.46889 + 3.08139i) q^{39} +(-2.39152 + 4.14224i) q^{41} +(-1.02846 - 1.78135i) q^{43} +(0.593814 - 1.55174i) q^{45} +(-4.90301 - 8.49226i) q^{47} +(0.897752 + 6.94219i) q^{49} +(-12.5100 + 0.991080i) q^{51} +8.43202i q^{53} -2.58026i q^{55} +(0.918838 + 11.5981i) q^{57} +(3.89955 - 6.75422i) q^{59} +(-5.37336 + 3.10231i) q^{61} +(-6.71229 - 4.23618i) q^{63} +(1.98417 - 1.14556i) q^{65} +(1.68814 - 2.92394i) q^{67} +(-8.76257 - 4.17396i) q^{69} +0.407556i q^{71} +8.63566i q^{73} +(4.60778 + 6.69693i) q^{75} +(-12.0868 - 2.41864i) q^{77} +(-0.318176 - 0.551097i) q^{79} +(8.55373 - 2.79889i) q^{81} +(2.78840 + 4.82965i) q^{83} +(-2.00632 + 3.47504i) q^{85} +(1.92117 - 1.32185i) q^{87} -6.93137 q^{89} +(-3.50632 - 10.3683i) q^{91} +(-1.50000 - 0.714509i) q^{93} +(3.22174 + 1.86007i) q^{95} +(7.48798 - 4.32318i) q^{97} +(10.8530 - 8.80719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7}+O(q^{10}) \) 16 * q - q^7	\( 16 q - q^{7} + 6 q^{11} - 12 q^{15} + 9 q^{21} + 6 q^{23} - 8 q^{25} - 12 q^{29} + 4 q^{37} + 18 q^{39} + 4 q^{43} - 5 q^{49} - 18 q^{51} - 42 q^{57} - 27 q^{63} - 24 q^{65} + 14 q^{67} - 21 q^{77} + 20 q^{79} - 36 q^{81} + 6 q^{85} - 18 q^{91} - 24 q^{93} - 60 q^{95} + 90 q^{99}+O(q^{100}) \) 16 * q - q^7 + 6 * q^11 - 12 * q^15 + 9 * q^21 + 6 * q^23 - 8 * q^25 - 12 * q^29 + 4 * q^37 + 18 * q^39 + 4 * q^43 - 5 * q^49 - 18 * q^51 - 42 * q^57 - 27 * q^63 - 24 * q^65 + 14 * q^67 - 21 * q^77 + 20 * q^79 - 36 * q^81 + 6 * q^85 - 18 * q^91 - 24 * q^93 - 60 * q^95 + 90 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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