LMFDB - Embedded newform 252.2.x.a.209.1

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			209.1
Root			$0.744857 + 1.56371i$ of defining polynomial
Character	$\chi$	$=$	252.209
Dual form			252.2.x.a.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72664 - 0.136790i) q^{3} +(-0.276914 - 0.479629i) q^{5} +(-0.519138 + 2.59432i) q^{7} +(2.96258 + 0.472374i) q^{9} +O(q^{10})$	\(q+(-1.72664 - 0.136790i) q^{3} +(-0.276914 - 0.479629i) q^{5} +(-0.519138 + 2.59432i) q^{7} +(2.96258 + 0.472374i) q^{9} +(4.03478 + 2.32948i) q^{11} +(-3.58265 + 2.06844i) q^{13} +(0.412522 + 0.866025i) q^{15} +7.24527 q^{17} +6.71715i q^{19} +(1.25124 - 4.40845i) q^{21} +(-4.85295 + 2.80185i) q^{23} +(2.34664 - 4.06450i) q^{25} +(-5.05069 - 1.22087i) q^{27} +(1.16599 + 0.673187i) q^{29} +(0.830741 - 0.479629i) q^{31} +(-6.64796 - 4.57409i) q^{33} +(1.38807 - 0.469409i) q^{35} -7.06956 q^{37} +(6.46889 - 3.08139i) q^{39} +(2.39152 + 4.14224i) q^{41} +(-1.02846 + 1.78135i) q^{43} +(-0.593814 - 1.55174i) q^{45} +(4.90301 - 8.49226i) q^{47} +(-6.46099 - 2.69362i) q^{49} +(-12.5100 - 0.991080i) q^{51} -8.43202i q^{53} -2.58026i q^{55} +(0.918838 - 11.5981i) q^{57} +(-3.89955 - 6.75422i) q^{59} +(5.37336 + 3.10231i) q^{61} +(-2.76348 + 7.44065i) q^{63} +(1.98417 + 1.14556i) q^{65} +(1.68814 + 2.92394i) q^{67} +(8.76257 - 4.17396i) q^{69} -0.407556i q^{71} +8.63566i q^{73} +(-4.60778 + 6.69693i) q^{75} +(-8.13802 + 9.25818i) q^{77} +(-0.318176 + 0.551097i) q^{79} +(8.55373 + 2.79889i) q^{81} +(-2.78840 + 4.82965i) q^{83} +(-2.00632 - 3.47504i) q^{85} +(-1.92117 - 1.32185i) q^{87} +6.93137 q^{89} +(-3.50632 - 10.3683i) q^{91} +(-1.50000 + 0.714509i) q^{93} +(3.22174 - 1.86007i) q^{95} +(-7.48798 - 4.32318i) q^{97} +(10.8530 + 8.80719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−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	$-0.206187\pi$
$5$	−0.276914	−	0.479629i	−0.123840	−	0.214496i	−0.921279	+	0.388903i	$0.872854\pi$
$6$		0			0
$7$	−0.519138	+	2.59432i	−0.196216	+	0.980561i
$7$	−0.519138	+	2.59432i	−0.196216	+	0.980561i
$8$		0			0
$9$	2.96258	+	0.472374i	0.987526	+	0.157458i
$10$		0			0
$11$	4.03478	+	2.32948i	1.21653	+	0.702365i	0.964174	−	0.265270i	$-0.0854610\pi$
$11$	4.03478	+	2.32948i	1.21653	+	0.702365i	0.252357	+	0.967634i	$0.418794\pi$
$12$		0			0
$13$	−3.58265	+	2.06844i	−0.993648	+	0.573683i	−0.906363	−	0.422500i	$-0.861153\pi$
$13$	−3.58265	+	2.06844i	−0.993648	+	0.573683i	−0.0872856	+	0.996183i	$0.527819\pi$
$14$		0			0
$15$	0.412522	+	0.866025i	0.106513	+	0.223607i
$16$		0			0
$17$	7.24527			1.75724			0.878619	−	0.477524i	$-0.158466\pi$
$17$	7.24527			1.75724			0.878619	+	0.477524i	$0.158466\pi$
$18$		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
$21$	1.25124	−	4.40845i	0.273043	−	0.962002i
$22$		0			0
$23$	−4.85295	+	2.80185i	−1.01191	+	0.584227i	−0.911751	−	0.410744i	$-0.865269\pi$
$23$	−4.85295	+	2.80185i	−1.01191	+	0.584227i	−0.100160	+	0.994971i	$0.531936\pi$
$24$		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	0.604338	−	0.796728i	$-0.293438\pi$
$29$	1.16599	+	0.673187i	0.216520	+	0.125008i	−0.387818	+	0.921736i	$0.626771\pi$
$30$		0			0
$31$	0.830741	−	0.479629i	0.149206	−	0.0861438i	−0.423539	−	0.905878i	$-0.639212\pi$
$31$	0.830741	−	0.479629i	0.149206	−	0.0861438i	0.572744	+	0.819734i	$0.305879\pi$
$32$		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	$-0.0448265\pi$
$41$	2.39152	+	4.14224i	0.373493	+	0.646909i	−0.616607	+	0.787271i	$0.711493\pi$
$42$		0			0
$43$	−1.02846	+	1.78135i	−0.156839	+	0.271653i	−0.933727	−	0.357986i	$-0.883464\pi$
$43$	−1.02846	+	1.78135i	−0.156839	+	0.271653i	0.776888	+	0.629639i	$0.216797\pi$
$44$		0			0
$45$	−0.593814	−	1.55174i	−0.0885206	−	0.231320i
$46$		0			0
$47$	4.90301	−	8.49226i	0.715177	−	1.23872i	−0.247714	−	0.968833i	$-0.579679\pi$
$47$	4.90301	−	8.49226i	0.715177	−	1.23872i	0.962891	−	0.269890i	$-0.0869874\pi$
$48$		0			0
$49$	−6.46099	−	2.69362i	−0.922999	−	0.384803i
$50$		0			0
$51$	−12.5100	−	0.991080i	−1.75175	−	0.138779i
$52$		0			0
$53$		−	8.43202i		−	1.15823i	−0.815247	−	0.579114i	$-0.803399\pi$
$53$		−	8.43202i		−	1.15823i	0.815247	−	0.579114i	$-0.196601\pi$
$54$		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	−0.999960	−	0.00888893i	$-0.997171\pi$
$59$	−3.89955	−	6.75422i	−0.507678	−	0.879325i	0.492282	−	0.870436i	$-0.336163\pi$
$60$		0			0
$61$	5.37336	+	3.10231i	0.687989	+	0.397211i	0.802858	−	0.596170i	$-0.203312\pi$
$61$	5.37336	+	3.10231i	0.687989	+	0.397211i	−0.114869	+	0.993381i	$0.536645\pi$
$62$		0			0
$63$	−2.76348	+	7.44065i	−0.348165	+	0.937433i
$64$		0			0
$65$	1.98417	+	1.14556i	0.246106	+	0.142089i
$66$		0			0
$67$	1.68814	+	2.92394i	0.206239	+	0.357217i	0.950527	−	0.310642i	$-0.100544\pi$
$67$	1.68814	+	2.92394i	0.206239	+	0.357217i	−0.744288	+	0.667859i	$0.767211\pi$
$68$		0			0
$69$	8.76257	−	4.17396i	1.05489	−	0.502486i
$70$		0			0
$71$		−	0.407556i		−	0.0483680i	−0.999708	−	0.0241840i	$-0.992301\pi$
$71$		−	0.407556i		−	0.0483680i	0.999708	−	0.0241840i	$-0.00769875\pi$
$72$		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
$77$	−8.13802	+	9.25818i	−0.927414	+	1.05507i
$78$		0			0
$79$	−0.318176	+	0.551097i	−0.0357976	+	0.0620032i	−0.883369	−	0.468678i	$-0.844730\pi$
$79$	−0.318176	+	0.551097i	−0.0357976	+	0.0620032i	0.847572	+	0.530681i	$0.178064\pi$
$80$		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	$-0.932346\pi$
$83$	−2.78840	+	4.82965i	−0.306066	+	0.530123i	0.671432	+	0.741066i	$0.265680\pi$
$84$		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	$-0.380261\pi$
$89$	6.93137			0.734723			0.367362	+	0.930078i	$0.380261\pi$
$90$		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	$-0.477984\pi$
$97$	−7.48798	−	4.32318i	−0.760289	−	0.438953i	−0.829399	+	0.558656i	$0.811317\pi$
$98$		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	$-0.908209\pi$
$101$	−2.34227	+	4.05692i	−0.233064	+	0.403679i	0.725644	+	0.688070i	$0.241542\pi$
$102$		0			0
$103$	6.40804	−	3.69969i	0.631403	−	0.364541i	−0.149892	−	0.988702i	$-0.547893\pi$
$103$	6.40804	−	3.69969i	0.631403	−	0.364541i	0.781295	+	0.624162i	$0.214559\pi$
$104$		0			0
$105$	−2.46090	+	0.620628i	−0.240160	+	0.0605671i
$106$		0			0
$107$		−	5.06059i		−	0.489225i	−0.969621	−	0.244613i	$-0.921339\pi$
$107$		−	5.06059i		−	0.489225i	0.969621	−	0.244613i	$-0.0786608\pi$
$108$		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	−0.569741	−	0.821824i	$-0.692956\pi$
$113$	−1.51895	+	0.876965i	−0.142891	+	0.0824979i	0.426850	+	0.904322i	$0.359623\pi$
$114$		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
$119$	−3.76130	+	18.7966i	−0.344798	+	1.72308i
$120$		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	−0.914939	−	0.403592i	$-0.867762\pi$
$131$	−9.23643	−	15.9980i	−0.806990	−	1.39775i	0.107949	−	0.994156i	$-0.465572\pi$
$132$		0			0
$133$	−17.4264	−	3.48713i	−1.51106	−	0.302372i
$134$		0			0
$135$	0.813041	+	2.76053i	0.0699754	+	0.237589i
$136$		0			0
$137$	19.0537	+	11.0007i	1.62787	+	0.939851i	0.984727	+	0.174104i	$0.0557030\pi$
$137$	19.0537	+	11.0007i	1.62787	+	0.939851i	0.643142	+	0.765747i	$0.277630\pi$
$138$		0			0
$139$	8.55986	−	4.94204i	0.726038	−	0.419178i	−0.0909332	−	0.995857i	$-0.528985\pi$
$139$	8.55986	−	4.94204i	0.726038	−	0.419178i	0.816971	+	0.576679i	$0.195652\pi$
$140$		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
$147$	10.7874	+	5.53471i	0.889726	+	0.456495i
$148$		0			0
$149$	−6.36677	+	3.67585i	−0.521586	+	0.301138i	−0.737583	−	0.675256i	$-0.764033\pi$
$149$	−6.36677	+	3.67585i	−0.521586	+	0.301138i	0.215997	+	0.976394i	$0.430700\pi$
$150$		0			0
$151$	2.16599	−	3.75161i	0.176266	−	0.305302i	−0.764333	−	0.644822i	$-0.776931\pi$
$151$	2.16599	−	3.75161i	0.176266	−	0.305302i	0.940599	+	0.339520i	$0.110265\pi$
$152$		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	$-0.644038\pi$
$157$	1.54152	−	0.889998i	0.123027	−	0.0710296i	0.560251	+	0.828323i	$0.310705\pi$
$158$		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	$-0.107506\pi$
$167$	2.38803	+	4.13618i	0.184791	+	0.320067i	−0.758715	+	0.651423i	$0.774173\pi$
$168$		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	$-0.764116\pi$
$173$	2.83766	−	4.91497i	0.215743	−	0.373678i	0.953502	+	0.301386i	$0.0974493\pi$
$174$		0			0
$175$	9.32637	+	8.19796i	0.705008	+	0.619708i
$176$		0			0
$177$	5.80921	+	12.1955i	0.436647	+	0.916672i
$178$		0			0
$179$		−	12.6305i		−	0.944048i	−0.881586	−	0.472024i	$-0.843524\pi$
$179$		−	12.6305i		−	0.944048i	0.881586	−	0.472024i	$-0.156476\pi$
$180$		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
$189$	5.78934	−	12.4693i	0.421112	−	0.907009i
$190$		0			0
$191$	−10.0537	−	5.80452i	−0.727462	−	0.420000i	0.0900309	−	0.995939i	$-0.471303\pi$
$191$	−10.0537	−	5.80452i	−0.727462	−	0.420000i	−0.817493	+	0.575939i	$0.804637\pi$
$192$		0			0
$193$	−3.16599	−	5.48366i	−0.227893	−	0.394723i	0.729290	−	0.684204i	$-0.239850\pi$
$193$	−3.16599	−	5.48366i	−0.227893	−	0.394723i	−0.957184	+	0.289482i	$0.906517\pi$
$194$		0			0
$195$	−3.26925	−	2.24939i	−0.234116	−	0.161082i
$196$		0			0
$197$		−	3.10030i		−	0.220888i	−0.993882	−	0.110444i	$-0.964773\pi$
$197$		−	3.10030i		−	0.220888i	0.993882	−	0.110444i	$-0.0352272\pi$
$198$		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
$203$	−2.35177	+	2.67549i	−0.165062	+	0.187782i
$204$		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	0.961233	−	0.275739i	$-0.0889225\pi$
$211$	3.51263	+	6.08406i	0.241820	+	0.418844i	−0.719413	+	0.694582i	$0.755589\pi$
$212$		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	$-0.642356\pi$
$223$	−21.3477	−	12.3251i	−1.42955	−	0.825350i	−0.997085	+	0.0763008i	$0.975689\pi$
$224$		0			0
$225$	8.87206	−	10.9329i	0.591470	−	0.728859i
$226$		0			0
$227$	10.0372	−	17.3849i	0.666190	−	1.15388i	−0.312771	−	0.949829i	$-0.601257\pi$
$227$	10.0372	−	17.3849i	0.666190	−	1.15388i	0.978961	−	0.204047i	$-0.0654095\pi$
$228$		0			0
$229$	−6.75865	+	3.90211i	−0.446624	+	0.257859i	−0.706403	−	0.707809i	$-0.749684\pi$
$229$	−6.75865	+	3.90211i	−0.446624	+	0.257859i	0.259779	+	0.965668i	$0.416350\pi$
$230$		0			0
$231$	15.3179	−	14.8724i	1.00784	−	0.978529i
$232$		0			0
$233$			7.96562i			0.521845i	0.965360	+	0.260922i	$0.0840267\pi$
$233$			7.96562i			0.521845i	−0.965360	+	0.260922i	$0.915973\pi$
$234$		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	0.501066	−	0.865409i	$-0.332941\pi$
$239$	23.2059	−	13.3979i	1.50107	−	0.866640i	0.999999	−	0.00123146i	$-0.000391987\pi$
$240$		0			0
$241$	−0.757259	−	0.437203i	−0.0487793	−	0.0281628i	0.475412	−	0.879763i	$-0.342299\pi$
$241$	−0.757259	−	0.437203i	−0.0487793	−	0.0281628i	−0.524191	+	0.851601i	$0.675632\pi$
$242$		0			0
$243$	−14.3864	−	6.00274i	−0.922885	−	0.385076i
$244$		0			0
$245$	0.497200	+	3.84478i	0.0317649	+	0.245634i
$246$		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	$-0.476665\pi$
$251$	2.32082			0.146489			0.0732445	+	0.997314i	$0.476665\pi$
$252$		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	−0.938989	−	0.343947i	$-0.888236\pi$
$257$	−12.3017	−	21.3072i	−0.767361	−	1.32911i	0.171628	−	0.985162i	$-0.445097\pi$
$258$		0			0
$259$	3.67007	−	18.3407i	0.228047	−	1.13963i
$260$		0			0
$261$	3.13635	+	2.54515i	0.194135	+	0.157541i
$262$		0			0
$263$	−20.5268	−	11.8512i	−1.26574	−	0.730775i	−0.291560	−	0.956552i	$-0.594174\pi$
$263$	−20.5268	−	11.8512i	−1.26574	−	0.730775i	−0.974179	+	0.225778i	$0.927508\pi$
$264$		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	$-0.283609\pi$
$269$	20.6212			1.25730			0.628648	+	0.777690i	$0.283609\pi$
$270$		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
$273$	4.63586	+	18.3820i	0.280575	+	1.11253i
$274$		0			0
$275$	18.9363	−	10.9329i	1.14190	−	0.659278i
$276$		0			0
$277$	−10.3940	+	18.0030i	−0.624518	+	1.08170i	0.364116	+	0.931354i	$0.381371\pi$
$277$	−10.3940	+	18.0030i	−0.624518	+	1.08170i	−0.988634	+	0.150343i	$0.951962\pi$
$278$		0			0
$279$	2.68770	−	1.02852i	0.160908	−	0.0615757i
$280$		0			0
$281$	−20.3371	−	11.7416i	−1.21321	−	0.700448i	−0.249754	−	0.968309i	$-0.580350\pi$
$281$	−20.3371	−	11.7416i	−1.21321	−	0.700448i	−0.963457	+	0.267862i	$0.913683\pi$
$282$		0			0
$283$	11.1906	−	6.46089i	0.665211	−	0.384060i	−0.129048	−	0.991638i	$-0.541192\pi$
$283$	11.1906	−	6.46089i	0.665211	−	0.384060i	0.794260	+	0.607578i	$0.207859\pi$
$284$		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	$-0.129555\pi$
$293$	1.99115	+	3.44878i	0.116324	+	0.201480i	−0.801984	+	0.597346i	$0.796222\pi$
$294$		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
$301$	−4.08747	−	3.59292i	−0.235598	−	0.207093i
$302$		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	$-0.0130604\pi$
$311$	8.18371	+	14.1746i	0.464056	+	0.803768i	−0.535103	+	0.844787i	$0.679727\pi$
$312$		0			0
$313$	16.5547	+	9.55785i	0.935726	+	0.540242i	0.888618	−	0.458648i	$-0.151666\pi$
$313$	16.5547	+	9.55785i	0.935726	+	0.540242i	0.0471079	+	0.998890i	$0.485000\pi$
$314$		0			0
$315$	4.33399	−	0.734975i	0.244193	−	0.0414111i
$316$		0			0
$317$	20.8798	+	12.0550i	1.17273	+	0.677074i	0.954321	−	0.298784i	$-0.0965811\pi$
$317$	20.8798	+	12.0550i	1.17273	+	0.677074i	0.218405	+	0.975858i	$0.429914\pi$
$318$		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
$329$	19.4863	+	17.1286i	1.07431	+	0.944332i
$330$		0			0
$331$	−5.70077	+	9.87403i	−0.313343	+	0.542726i	−0.979084	−	0.203457i	$-0.934782\pi$
$331$	−5.70077	+	9.87403i	−0.313343	+	0.542726i	0.665741	+	0.746183i	$0.268116\pi$
$332$		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	0.918971	−	0.394326i	$-0.129022\pi$
$337$	2.16599	+	3.75161i	0.117989	+	0.204363i	−0.800981	+	0.598689i	$0.795689\pi$
$338$		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	−0.618917	−	0.785456i	$-0.712428\pi$
$347$	−4.62254	+	2.66882i	−0.248151	+	0.143270i	0.370766	+	0.928726i	$0.379095\pi$
$348$		0			0
$349$	−8.78031	−	5.06931i	−0.469999	−	0.271354i	0.246240	−	0.969209i	$-0.420805\pi$
$349$	−8.78031	−	5.06931i	−0.469999	−	0.271354i	−0.716239	+	0.697855i	$0.754138\pi$
$350$		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	$-0.699374\pi$
$353$	7.67564	−	13.2946i	0.408533	−	0.707600i	0.994726	+	0.102571i	$0.0327070\pi$
$354$		0			0
$355$	−0.195475	+	0.112858i	−0.0103748	+	0.00598987i
$356$		0			0
$357$	9.06559	−	31.9404i	0.479802	−	1.69047i
$358$		0			0
$359$			1.74800i			0.0922559i	0.998936	+	0.0461280i	$0.0146882\pi$
$359$			1.74800i			0.0922559i	−0.998936	+	0.0461280i	$0.985312\pi$
$360$		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	$-0.224024\pi$
$367$	11.1720	+	6.45018i	0.583176	+	0.336697i	−0.179219	+	0.983809i	$0.557357\pi$
$368$		0			0
$369$	5.12839	+	13.4014i	0.266973	+	0.697649i
$370$		0			0
$371$	21.8754	+	4.37738i	1.13571	+	0.227262i
$372$		0			0
$373$	5.34782	+	9.26269i	0.276900	+	0.479604i	0.970613	−	0.240647i	$-0.0773597\pi$
$373$	5.34782	+	9.26269i	0.276900	+	0.479604i	−0.693713	+	0.720251i	$0.744026\pi$
$374$		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	$-0.00662061\pi$
$383$	9.43059	+	16.3343i	0.481880	+	0.834641i	−0.517903	+	0.855439i	$0.673287\pi$
$384$		0			0
$385$	6.69402	+	1.33951i	0.341159	+	0.0682678i
$386$		0			0
$387$	−3.88836	+	4.79156i	−0.197656	+	0.243569i
$388$		0			0
$389$	14.3182	+	8.26660i	0.725960	+	0.419133i	0.816943	−	0.576719i	$-0.195667\pi$
$389$	14.3182	+	8.26660i	0.725960	+	0.419133i	−0.0909822	+	0.995853i	$0.529001\pi$
$390$		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
$399$	29.6122	+	8.40478i	1.48246	+	0.420765i
$400$		0			0
$401$	18.6395	−	10.7615i	0.930811	−	0.537404i	0.0437428	−	0.999043i	$-0.486072\pi$
$401$	18.6395	−	10.7615i	0.930811	−	0.537404i	0.887068	+	0.461639i	$0.152738\pi$
$402$		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	$-0.851886\pi$
$409$	−19.2516	+	11.1149i	−0.951933	+	0.549599i	−0.0582520	+	0.998302i	$0.518553\pi$
$410$		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	$-0.0586294\pi$
$419$	6.81490	+	11.8038i	0.332930	+	0.576651i	−0.650155	+	0.759802i	$0.725296\pi$
$420$		0			0
$421$	13.7071	−	23.7414i	0.668043	−	1.15708i	−0.310408	−	0.950603i	$-0.600466\pi$
$421$	13.7071	−	23.7414i	0.668043	−	1.15708i	0.978451	−	0.206480i	$-0.0662009\pi$
$422$		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
$427$	−10.8379	+	12.3297i	−0.524483	+	0.596676i
$428$		0			0
$429$	33.2786	+	2.63643i	1.60670	+	0.127288i
$430$		0			0
$431$			34.8331i			1.67785i	0.544248	+	0.838925i	$0.316815\pi$
$431$			34.8331i			1.67785i	−0.544248	+	0.838925i	$0.683185\pi$
$432$		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	$-0.572055\pi$
$439$	−24.7361	−	14.2814i	−1.18059	−	0.681614i	−0.956151	+	0.292874i	$0.905388\pi$
$440$		0			0
$441$	−17.8688	−	11.0321i	−0.850895	−	0.525336i
$442$		0			0
$443$	−21.8612	−	12.6216i	−1.03866	−	0.599669i	−0.119205	−	0.992870i	$-0.538034\pi$
$443$	−21.8612	−	12.6216i	−1.03866	−	0.599669i	−0.919453	+	0.393201i	$0.871368\pi$
$444$		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	$0.115998\pi$
$449$			15.1042i			0.712811i	−0.934331	+	0.356405i	$0.884002\pi$
$450$		0			0
$451$			22.2840i			1.04931i
$452$		0			0
$453$	−4.25308	+	6.18140i	−0.199827	+	0.290428i
$454$		0			0
$455$	−4.00201	+	4.55287i	−0.187617	+	0.213442i
$456$		0			0
$457$	−1.75138	+	3.03348i	−0.0819261	+	0.141900i	−0.904077	−	0.427369i	$-0.859440\pi$
$457$	−1.75138	+	3.03348i	−0.0819261	+	0.141900i	0.822151	+	0.569269i	$0.192774\pi$
$458$		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	$-0.862843\pi$
$461$	−1.98765	+	3.44272i	−0.0925743	+	0.160343i	0.816019	+	0.578025i	$0.196176\pi$
$462$		0			0
$463$	−5.18494	−	8.98058i	−0.240965	−	0.417363i	0.720025	−	0.693948i	$-0.244130\pi$
$463$	−5.18494	−	8.98058i	−0.240965	−	0.417363i	−0.960989	+	0.276585i	$0.910797\pi$
$464$		0			0
$465$	0.758070	+	0.521586i	0.0351546	+	0.0241879i
$466$		0			0
$467$	19.6190			0.907860			0.453930	−	0.891037i	$-0.350022\pi$
$467$	19.6190			0.907860			0.453930	+	0.891037i	$0.350022\pi$
$468$		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	0.236789	+	0.971561i	$0.423905\pi$
$479$	−15.8237	+	27.4074i	−0.723002	+	1.25228i	−0.959791	+	0.280715i	$0.909428\pi$
$480$		0			0
$481$	25.3277	−	14.6230i	1.15485	−	0.666751i
$482$		0			0
$483$	6.27960	+	24.8998i	0.285732	+	1.13298i
$484$		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	0.149806	−	0.988715i	$-0.452135\pi$
$491$	23.9525	−	13.8290i	1.08096	−	0.624094i	0.931156	+	0.364622i	$0.118802\pi$
$492$		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
$497$	1.05733	+	0.211578i	0.0474277	+	0.00949055i
$498$		0			0
$499$	4.50632	+	7.80517i	0.201730	+	0.349407i	0.949086	−	0.315017i	$-0.102010\pi$
$499$	4.50632	+	7.80517i	0.201730	+	0.349407i	−0.747356	+	0.664424i	$0.768677\pi$
$500$		0			0
$501$	−3.55748	−	7.46836i	−0.158936	−	0.333662i
$502$		0			0
$503$	27.1572			1.21088			0.605440	−	0.795891i	$-0.292997\pi$
$503$	27.1572			1.21088			0.605440	+	0.795891i	$0.292997\pi$
$504$		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	$-0.0726384\pi$
$509$	6.56799	+	11.3761i	0.291121	+	0.504236i	−0.682954	+	0.730461i	$0.739305\pi$
$510$		0			0
$511$	−22.4037	−	4.48310i	−0.991080	−	0.198321i
$512$		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	$-0.528152\pi$
$521$	−4.03219			−0.176653			−0.0883266	+	0.996092i	$0.528152\pi$
$522$		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
$525$	−14.9819	−	15.4307i	−0.653864	−	0.673451i
$526$		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	0.0993905	+	0.995049i	$0.468311\pi$
$547$	−18.9921	+	32.8952i	−0.812042	+	1.40650i	−0.911433	+	0.411450i	$0.865023\pi$
$548$		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
$553$	−1.26454	−	1.11155i	−0.0537739	−	0.0472677i
$554$		0			0
$555$	−2.91635	−	6.12241i	−0.123792	−	0.259882i
$556$		0			0
$557$		−	41.7056i		−	1.76712i	−0.468313	−	0.883562i	$-0.655138\pi$
$557$		−	41.7056i		−	1.76712i	0.468313	−	0.883562i	$-0.344862\pi$
$558$		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	$-0.154074\pi$
$563$	0.938436	+	1.62542i	0.0395504	+	0.0685033i	−0.845573	+	0.533860i	$0.820741\pi$
$564$		0			0
$565$	0.841235	+	0.485687i	0.0353910	+	0.0204330i
$566$		0			0
$567$	−11.7018	+	20.7381i	−0.491428	+	0.870918i
$568$		0			0
$569$	−20.6391	−	11.9160i	−0.865237	−	0.499545i	0.000525844	−	1.00000i	$-0.499833\pi$
$569$	−20.6391	−	11.9160i	−0.865237	−	0.499545i	−0.865762	+	0.500455i	$0.833166\pi$
$570$		0			0
$571$	−14.8719	−	25.7589i	−0.622370	−	1.07798i	−0.989043	−	0.147626i	$-0.952837\pi$
$571$	−14.8719	−	25.7589i	−0.622370	−	1.07798i	0.366674	−	0.930350i	$-0.380497\pi$
$572$		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
$581$	−11.0821	−	9.74125i	−0.459762	−	0.404135i
$582$		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	0.113238	−	0.993568i	$-0.463878\pi$
$587$	22.2189	−	38.4843i	0.917074	−	1.58842i	0.803836	−	0.594851i	$-0.202789\pi$
$588$		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	$-0.775851\pi$
$593$	−37.1186			−1.52428			−0.762140	+	0.647412i	$0.775851\pi$
$594$		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	−0.725606	−	0.688111i	$-0.758440\pi$
$599$	−12.0534	+	6.95901i	−0.492487	+	0.284338i	0.233119	+	0.972448i	$0.425107\pi$
$600$		0			0
$601$	−0.377613	−	0.218015i	−0.0154032	−	0.00889301i	0.492279	−	0.870438i	$-0.336164\pi$
$601$	−0.377613	−	0.218015i	−0.0154032	−	0.00889301i	−0.507682	+	0.861545i	$0.669497\pi$
$602$		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	$-0.681002\pi$
$607$	−1.92117	+	1.10919i	−0.0779778	+	0.0450205i	0.460504	+	0.887658i	$0.347669\pi$
$608$		0			0
$609$	4.42665	−	4.29790i	0.179377	−	0.174160i
$610$		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	−0.0108970	−	0.999941i	$-0.503469\pi$
$617$	21.1043	−	12.1846i	0.849628	−	0.490533i	0.860525	+	0.509407i	$0.170135\pi$
$618$		0			0
$619$	−25.4477	−	14.6922i	−1.02283	−	0.590531i	−0.107907	−	0.994161i	$-0.534415\pi$
$619$	−25.4477	−	14.6922i	−1.02283	−	0.590531i	−0.914922	+	0.403630i	$0.867748\pi$
$620$		0			0
$621$	27.9315	−	8.22647i	1.12085	−	0.330117i
$622$		0			0
$623$	−3.59834	+	17.9822i	−0.144164	+	0.720441i
$624$		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
$637$	28.7191	−	3.71390i	1.13789	−	0.147150i
$638$		0			0
$639$	0.192519	−	1.20741i	0.00761592	−	0.0477646i
$640$		0			0
$641$	−5.32405	−	3.07384i	−0.210287	−	0.121410i	0.391158	−	0.920324i	$-0.372075\pi$
$641$	−5.32405	−	3.07384i	−0.210287	−	0.121410i	−0.601445	+	0.798914i	$0.705408\pi$
$642$		0			0
$643$	−23.9599	+	13.8333i	−0.944886	+	0.545530i	−0.891489	−	0.453043i	$-0.850338\pi$
$643$	−23.9599	+	13.8333i	−0.944886	+	0.545530i	−0.0533976	+	0.998573i	$0.517005\pi$
$644$		0			0
$645$	−1.96696	−	0.155828i	−0.0774488	−	0.00613574i
$646$		0			0
$647$	−4.81457			−0.189280			−0.0946402	−	0.995512i	$-0.530170\pi$
$647$	−4.81457			−0.189280			−0.0946402	+	0.995512i	$0.530170\pi$
$648$		0			0
$649$		−	36.3357i		−	1.42630i
$650$		0			0
$651$	−1.07496	−	4.26241i	−0.0421310	−	0.167057i
$652$		0			0
$653$	21.1759	−	12.2259i	0.828677	−	0.478437i	−0.0247223	−	0.999694i	$-0.507870\pi$
$653$	21.1759	−	12.2259i	0.828677	−	0.478437i	0.853400	+	0.521257i	$0.174537\pi$
$654$		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	0.0380267	−	0.999277i	$-0.487893\pi$
$659$	−20.7514	−	11.9808i	−0.808359	−	0.466706i	−0.846386	+	0.532570i	$0.821226\pi$
$660$		0			0
$661$	6.73275	−	3.88715i	0.261874	−	0.151193i	−0.363315	−	0.931666i	$-0.618355\pi$
$661$	6.73275	−	3.88715i	0.261874	−	0.151193i	0.625189	+	0.780473i	$0.285022\pi$
$662$		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	0.429066	+	0.903273i	$0.358843\pi$
$673$	−14.7281	+	25.5097i	−0.567725	+	0.983328i	−0.996790	+	0.0800548i	$0.974490\pi$
$674$		0			0
$675$	−16.8144	+	17.6636i	−0.647185	+	0.679871i
$676$		0			0
$677$	−17.8293	+	30.8812i	−0.685235	+	1.18686i	0.288128	+	0.957592i	$0.406967\pi$
$677$	−17.8293	+	30.8812i	−0.685235	+	1.18686i	−0.973363	+	0.229270i	$0.926366\pi$
$678$		0			0
$679$	15.1030	−	17.1819i	0.579601	−	0.659380i
$680$		0			0
$681$	−19.7087	+	28.6445i	−0.755238	+	1.09766i
$682$		0			0
$683$		−	13.0969i		−	0.501139i	−0.968099	−	0.250570i	$-0.919382\pi$
$683$		−	13.0969i		−	0.501139i	0.968099	−	0.250570i	$-0.0806179\pi$
$684$		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	$-0.388276\pi$
$691$	−7.81992	−	4.51483i	−0.297484	−	0.171752i	−0.641312	+	0.767280i	$0.721610\pi$
$692$		0			0
$693$	−28.4828	+	23.5839i	−1.08197	+	0.895878i
$694$		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	$0.00155855\pi$
$701$			0.259274i			0.00979264i	−0.999988	+	0.00489632i	$0.998441\pi$
$702$		0			0
$703$		−	47.4873i		−	1.79102i
$704$		0			0
$705$	9.37711	+	0.742884i	0.353163	+	0.0279786i
$706$		0			0
$707$	−9.30900	−	8.18269i	−0.350101	−	0.307742i
$708$		0			0
$709$	−3.08574	+	5.34467i	−0.115888	+	0.200723i	−0.918134	−	0.396270i	$-0.870305\pi$
$709$	−3.08574	+	5.34467i	−0.115888	+	0.200723i	0.802247	+	0.596993i	$0.203638\pi$
$710$		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	$-0.618632\pi$
$719$	−19.5275			−0.728253			−0.364127	+	0.931349i	$0.618632\pi$
$720$		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	$-0.336232\pi$
$727$	−0.425312	−	0.245554i	−0.0157740	−	0.00910710i	−0.507866	+	0.861436i	$0.669566\pi$
$728$		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	$-0.712194\pi$
$733$	−6.68424	+	3.85915i	−0.246888	+	0.142541i	0.371450	+	0.928453i	$0.378861\pi$
$734$		0			0
$735$	−0.332559	−	6.70656i	−0.0122666	−	0.247375i
$736$		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	0.0852322	−	0.996361i	$-0.472837\pi$
$743$	27.0051	−	15.5914i	0.990722	−	0.571994i	0.905490	+	0.424367i	$0.139503\pi$
$744$		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
$749$	13.1288	+	2.62714i	0.479715	+	0.0959937i
$750$		0			0
$751$	23.0367	+	39.9008i	0.840622	+	1.45600i	0.889370	+	0.457188i	$0.151143\pi$
$751$	23.0367	+	39.9008i	0.840622	+	1.45600i	−0.0487482	+	0.998811i	$0.515523\pi$
$752$		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	$-0.208813\pi$
$761$	−3.64190	−	6.30795i	−0.132019	−	0.228663i	−0.924455	+	0.381292i	$0.875479\pi$
$762$		0			0
$763$	−6.10653	+	30.5165i	−0.221071	+	1.10477i
$764$		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	$-0.398690\pi$
$769$	35.8261	−	20.6842i	1.29192	−	0.745892i	0.978995	+	0.203886i	$0.0653570\pi$
$770$		0			0
$771$	18.3261	+	38.4727i	0.659997	+	1.38556i
$772$		0			0
$773$	−17.1183			−0.615702			−0.307851	−	0.951435i	$-0.599610\pi$
$773$	−17.1183			−0.615702			−0.307851	+	0.951435i	$0.599610\pi$
$774$		0			0
$775$		−	4.50206i		−	0.161719i
$776$		0			0
$777$	−8.84572	+	31.1658i	−0.317339	+	1.11807i
$778$		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	$-0.488937\pi$
$787$	25.7426	−	14.8625i	0.917623	−	0.529790i	0.882876	+	0.469606i	$0.155604\pi$
$788$		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	−0.956986	−	0.290135i	$-0.906300\pi$
$797$	−20.6019	−	35.6836i	−0.729757	−	1.26398i	0.227229	−	0.973841i	$-0.427034\pi$
$798$		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
$805$	−5.42101	+	6.16718i	−0.191065	+	0.217365i
$806$		0			0
$807$	−35.6054	−	2.82077i	−1.25337	−	0.0992957i
$808$		0			0
$809$		−	12.4233i		−	0.436780i	−0.975862	−	0.218390i	$-0.929920\pi$
$809$		−	12.4233i		−	0.436780i	0.975862	−	0.218390i	$-0.0700805\pi$
$810$		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
$819$	−5.48999	−	32.3733i	−0.191836	−	1.13122i
$820$		0			0
$821$	−11.7411	−	6.77873i	−0.409768	−	0.236579i	0.280922	−	0.959731i	$-0.409360\pi$
$821$	−11.7411	−	6.77873i	−0.409768	−	0.236579i	−0.690690	+	0.723151i	$0.742693\pi$
$822$		0			0
$823$	12.2565	+	21.2289i	0.427235	+	0.739993i	0.996626	−	0.0820737i	$-0.0261543\pi$
$823$	12.2565	+	21.2289i	0.427235	+	0.739993i	−0.569391	+	0.822067i	$0.692821\pi$
$824$		0			0
$825$	−34.1917	+	16.2869i	−1.19040	+	0.567036i
$826$		0			0
$827$			14.7323i			0.512292i	0.966638	+	0.256146i	$0.0824527\pi$
$827$			14.7323i			0.512292i	−0.966638	+	0.256146i	$0.917547\pi$
$828$		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
$833$	−46.8117	−	19.5160i	−1.62193	−	0.676190i
$834$		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	$-0.827716\pi$
$839$	0.511154	−	0.885345i	0.0176470	−	0.0305655i	0.874714	+	0.484639i	$0.161049\pi$
$840$		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	$-0.388394\pi$
$853$	−8.70682	−	5.02689i	−0.298116	−	0.172117i	−0.641596	+	0.767043i	$0.721727\pi$
$854$		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	$-0.673035\pi$
$857$	14.1272	−	24.4690i	0.482575	−	0.835844i	0.999800	+	0.0200052i	$0.00636826\pi$
$858$		0			0
$859$	−26.9800	+	15.5769i	−0.920544	+	0.531476i	−0.883809	−	0.467849i	$-0.845029\pi$
$859$	−26.9800	+	15.5769i	−0.920544	+	0.531476i	−0.0367356	+	0.999325i	$0.511696\pi$
$860$		0			0
$861$	21.2532	−	5.35996i	0.724308	−	0.182667i
$862$		0			0
$863$		−	57.1234i		−	1.94450i	−0.233938	−	0.972252i	$-0.575161\pi$
$863$		−	57.1234i		−	1.94450i	0.233938	−	0.972252i	$-0.424839\pi$
$864$		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
$875$	2.78694	−	13.9274i	0.0942158	−	0.470830i
$876$		0			0
$877$	15.6691	+	27.1397i	0.529108	+	0.916443i	0.999424	+	0.0339441i	$0.0108068\pi$
$877$	15.6691	+	27.1397i	0.529108	+	0.916443i	−0.470315	+	0.882498i	$0.655860\pi$
$878$		0			0
$879$	−2.96625	−	6.22717i	−0.100049	−	0.210037i
$880$		0			0
$881$	−12.2822			−0.413799			−0.206900	−	0.978362i	$-0.566337\pi$
$881$	−12.2822			−0.413799			−0.206900	+	0.978362i	$0.566337\pi$
$882$		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	$-0.0639734\pi$
$887$	9.44264	+	16.3551i	0.317053	+	0.549152i	−0.662819	+	0.748780i	$0.730640\pi$
$888$		0			0
$889$	−5.75318	+	28.7507i	−0.192956	+	0.964269i
$890$		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
$903$	6.56612	+	6.76281i	0.218507	+	0.225052i
$904$		0			0
$905$	−10.9079	+	6.29769i	−0.362591	+	0.209342i
$906$		0			0
$907$	28.8802	−	50.0219i	0.958950	−	1.66095i	0.233891	−	0.972263i	$-0.424854\pi$
$907$	28.8802	−	50.0219i	0.958950	−	1.66095i	0.725059	−	0.688687i	$-0.241813\pi$
$908$		0			0
$909$	−8.85553	+	10.9125i	−0.293719	+	0.361945i
$910$		0			0
$911$	−33.7810	−	19.5034i	−1.11921	−	0.646178i	−0.178013	−	0.984028i	$-0.556967\pi$
$911$	−33.7810	−	19.5034i	−1.11921	−	0.646178i	−0.941200	+	0.337850i	$0.890300\pi$
$912$		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	0.363824	+	0.931468i	$0.381471\pi$
$929$	−19.0424	+	32.9825i	−0.624762	+	1.08212i	−0.988587	+	0.150653i	$0.951863\pi$
$930$		0			0
$931$	18.0934	−	43.3994i	0.592989	−	1.42236i
$932$		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	$-0.157973\pi$
$941$	0.837737	+	1.45100i	0.0273094	+	0.0473014i	−0.852048	+	0.523464i	$0.824639\pi$
$942$		0			0
$943$	−23.2119	−	13.4014i	−0.755884	−	0.436410i
$944$		0			0
$945$	−7.58378	+	0.676191i	−0.246700	+	0.0219965i
$946$		0			0
$947$	19.2331	+	11.1042i	0.624992	+	0.360839i	0.778810	−	0.627260i	$-0.215824\pi$
$947$	19.2331	+	11.1042i	0.624992	+	0.360839i	−0.153818	+	0.988099i	$0.549157\pi$
$948$		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	$0.144931\pi$
$953$			27.1505i			0.879491i	−0.898122	+	0.439746i	$0.855069\pi$
$954$		0			0
$955$			6.42941i			0.208051i
$956$		0			0
$957$	−4.67227	−	9.80869i	−0.151033	−	0.317070i
$958$		0			0
$959$	−38.4308	+	43.7206i	−1.24099	+	1.41181i
$960$		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	−0.998968	−	0.0454157i	$-0.985539\pi$
$967$	−16.7553	−	29.0211i	−0.538815	−	0.933255i	0.460153	−	0.887840i	$-0.347795\pi$
$968$		0			0
$969$	6.65723	−	84.0314i	0.213861	−	2.69948i
$970$		0			0
$971$	35.7465			1.14716			0.573580	−	0.819149i	$-0.305554\pi$
$971$	35.7465			1.14716			0.573580	+	0.819149i	$0.305554\pi$
$972$		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	−0.974218	−	0.225610i	$-0.927562\pi$
$977$	−39.5696	+	22.8455i	−1.26594	+	0.730892i	−0.291725	+	0.956502i	$0.594229\pi$
$978$		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	$-0.929589\pi$
$983$	−9.33713	+	16.1724i	−0.297808	+	0.515819i	0.677826	+	0.735222i	$0.262922\pi$
$984$		0			0
$985$	−1.48699	+	0.858517i	−0.0473796	+	0.0273546i
$986$		0			0
$987$	−31.3028	−	32.2405i	−0.996380	−	1.02623i
$988$		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	$-0.0236946\pi$
$997$	45.1982	+	26.0952i	1.43144	+	0.826442i	0.434209	+	0.900812i	$0.357028\pi$
$998$		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.209.1	yes	16
3.2	odd	2		756.2.x.a.629.6		16
4.3	odd	2		1008.2.cc.c.209.8		16
7.2	even	3		1764.2.w.a.1109.6		16
7.3	odd	6		1764.2.bm.b.1685.3		16
7.4	even	3		1764.2.bm.b.1685.6		16
7.5	odd	6		1764.2.w.a.1109.3		16
7.6	odd	2	inner	252.2.x.a.209.8	yes	16
9.2	odd	6		2268.2.f.b.1133.5		16
9.4	even	3		756.2.x.a.125.3		16
9.5	odd	6	inner	252.2.x.a.41.8	yes	16
9.7	even	3		2268.2.f.b.1133.11		16
12.11	even	2		3024.2.cc.c.2897.6		16
21.2	odd	6		5292.2.w.a.521.6		16
21.5	even	6		5292.2.w.a.521.3		16
21.11	odd	6		5292.2.bm.b.4625.3		16
21.17	even	6		5292.2.bm.b.4625.6		16
21.20	even	2		756.2.x.a.629.3		16
28.27	even	2		1008.2.cc.c.209.1		16
36.23	even	6		1008.2.cc.c.545.1		16
36.31	odd	6		3024.2.cc.c.881.3		16
63.4	even	3		5292.2.w.a.1097.3		16
63.5	even	6		1764.2.bm.b.1697.6		16
63.13	odd	6		756.2.x.a.125.6		16
63.20	even	6		2268.2.f.b.1133.12		16
63.23	odd	6		1764.2.bm.b.1697.3		16
63.31	odd	6		5292.2.w.a.1097.6		16
63.32	odd	6		1764.2.w.a.509.3		16
63.34	odd	6		2268.2.f.b.1133.6		16
63.40	odd	6		5292.2.bm.b.2285.3		16
63.41	even	6	inner	252.2.x.a.41.1	✓	16
63.58	even	3		5292.2.bm.b.2285.6		16
63.59	even	6		1764.2.w.a.509.6		16
84.83	odd	2		3024.2.cc.c.2897.3		16
252.139	even	6		3024.2.cc.c.881.6		16
252.167	odd	6		1008.2.cc.c.545.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.x.a.41.1	✓	16	63.41	even	6	inner
252.2.x.a.41.8	yes	16	9.5	odd	6	inner
252.2.x.a.209.1	yes	16	1.1	even	1	trivial
252.2.x.a.209.8	yes	16	7.6	odd	2	inner
756.2.x.a.125.3		16	9.4	even	3
756.2.x.a.125.6		16	63.13	odd	6
756.2.x.a.629.3		16	21.20	even	2
756.2.x.a.629.6		16	3.2	odd	2
1008.2.cc.c.209.1		16	28.27	even	2
1008.2.cc.c.209.8		16	4.3	odd	2
1008.2.cc.c.545.1		16	36.23	even	6
1008.2.cc.c.545.8		16	252.167	odd	6
1764.2.w.a.509.3		16	63.32	odd	6
1764.2.w.a.509.6		16	63.59	even	6
1764.2.w.a.1109.3		16	7.5	odd	6
1764.2.w.a.1109.6		16	7.2	even	3
1764.2.bm.b.1685.3		16	7.3	odd	6
1764.2.bm.b.1685.6		16	7.4	even	3
1764.2.bm.b.1697.3		16	63.23	odd	6
1764.2.bm.b.1697.6		16	63.5	even	6
2268.2.f.b.1133.5		16	9.2	odd	6
2268.2.f.b.1133.6		16	63.34	odd	6
2268.2.f.b.1133.11		16	9.7	even	3
2268.2.f.b.1133.12		16	63.20	even	6
3024.2.cc.c.881.3		16	36.31	odd	6
3024.2.cc.c.881.6		16	252.139	even	6
3024.2.cc.c.2897.3		16	84.83	odd	2
3024.2.cc.c.2897.6		16	12.11	even	2
5292.2.w.a.521.3		16	21.5	even	6
5292.2.w.a.521.6		16	21.2	odd	6
5292.2.w.a.1097.3		16	63.4	even	3
5292.2.w.a.1097.6		16	63.31	odd	6
5292.2.bm.b.2285.3		16	63.40	odd	6
5292.2.bm.b.2285.6		16	63.58	even	3
5292.2.bm.b.4625.3		16	21.11	odd	6
5292.2.bm.b.4625.6		16	21.17	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72664 - 0.136790i) q^{3} +(-0.276914 - 0.479629i) q^{5} +(-0.519138 + 2.59432i) q^{7} +(2.96258 + 0.472374i) q^{9} +O(q^{10})\)	\(q+(-1.72664 - 0.136790i) q^{3} +(-0.276914 - 0.479629i) q^{5} +(-0.519138 + 2.59432i) q^{7} +(2.96258 + 0.472374i) q^{9} +(4.03478 + 2.32948i) q^{11} +(-3.58265 + 2.06844i) q^{13} +(0.412522 + 0.866025i) q^{15} +7.24527 q^{17} +6.71715i q^{19} +(1.25124 - 4.40845i) q^{21} +(-4.85295 + 2.80185i) q^{23} +(2.34664 - 4.06450i) q^{25} +(-5.05069 - 1.22087i) q^{27} +(1.16599 + 0.673187i) q^{29} +(0.830741 - 0.479629i) q^{31} +(-6.64796 - 4.57409i) q^{33} +(1.38807 - 0.469409i) q^{35} -7.06956 q^{37} +(6.46889 - 3.08139i) q^{39} +(2.39152 + 4.14224i) q^{41} +(-1.02846 + 1.78135i) q^{43} +(-0.593814 - 1.55174i) q^{45} +(4.90301 - 8.49226i) q^{47} +(-6.46099 - 2.69362i) q^{49} +(-12.5100 - 0.991080i) q^{51} -8.43202i q^{53} -2.58026i q^{55} +(0.918838 - 11.5981i) q^{57} +(-3.89955 - 6.75422i) q^{59} +(5.37336 + 3.10231i) q^{61} +(-2.76348 + 7.44065i) q^{63} +(1.98417 + 1.14556i) q^{65} +(1.68814 + 2.92394i) q^{67} +(8.76257 - 4.17396i) q^{69} -0.407556i q^{71} +8.63566i q^{73} +(-4.60778 + 6.69693i) q^{75} +(-8.13802 + 9.25818i) q^{77} +(-0.318176 + 0.551097i) q^{79} +(8.55373 + 2.79889i) q^{81} +(-2.78840 + 4.82965i) q^{83} +(-2.00632 - 3.47504i) q^{85} +(-1.92117 - 1.32185i) q^{87} +6.93137 q^{89} +(-3.50632 - 10.3683i) q^{91} +(-1.50000 + 0.714509i) q^{93} +(3.22174 - 1.86007i) q^{95} +(-7.48798 - 4.32318i) q^{97} +(10.8530 + 8.80719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7}+O(q^{10}) \) 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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