LMFDB - Embedded newform 504.2.bs.a.257.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(257,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("504.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			257.11
Character	$\chi$	$=$	504.257
Dual form			504.2.bs.a.353.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.419673 - 1.68044i) q^{3} +(1.02449 + 1.77447i) q^{5} +(-2.64365 + 0.105420i) q^{7} +(-2.64775 + 1.41047i) q^{9} +O(q^{10})$	\(q+(-0.419673 - 1.68044i) q^{3} +(1.02449 + 1.77447i) q^{5} +(-2.64365 + 0.105420i) q^{7} +(-2.64775 + 1.41047i) q^{9} +(-5.11564 - 2.95352i) q^{11} +(0.139269 + 0.0804071i) q^{13} +(2.55194 - 2.46630i) q^{15} +(-2.77904 - 4.81345i) q^{17} +(-4.02056 - 2.32127i) q^{19} +(1.28662 + 4.39825i) q^{21} +(0.375194 - 0.216618i) q^{23} +(0.400830 - 0.694257i) q^{25} +(3.48140 + 3.85744i) q^{27} +(-1.95524 + 1.12886i) q^{29} +2.97708i q^{31} +(-2.81630 + 9.83603i) q^{33} +(-2.89547 - 4.58308i) q^{35} +(2.17904 - 3.77422i) q^{37} +(0.0766716 - 0.267778i) q^{39} +(-2.35740 + 4.08313i) q^{41} +(1.82369 + 3.15873i) q^{43} +(-5.21544 - 3.25334i) q^{45} +0.130095 q^{47} +(6.97777 - 0.557389i) q^{49} +(-6.92241 + 6.69009i) q^{51} +(-10.7936 + 6.23170i) q^{53} -12.1034i q^{55} +(-2.21343 + 7.73049i) q^{57} -6.44809 q^{59} -6.90990i q^{61} +(6.85103 - 4.00792i) q^{63} +0.329506i q^{65} +15.2919 q^{67} +(-0.521473 - 0.539582i) q^{69} +1.48027i q^{71} +(-2.60881 + 1.50620i) q^{73} +(-1.33487 - 0.382208i) q^{75} +(13.8353 + 7.26877i) q^{77} +17.3851 q^{79} +(5.02114 - 7.46914i) q^{81} +(-7.62399 - 13.2051i) q^{83} +(5.69422 - 9.86268i) q^{85} +(2.71754 + 2.81191i) q^{87} +(-4.04757 + 7.01059i) q^{89} +(-0.376655 - 0.197886i) q^{91} +(5.00280 - 1.24940i) q^{93} -9.51251i q^{95} +(-2.61123 + 1.50759i) q^{97} +(17.7108 + 0.604706i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9}+O(q^{10}) $ 48 * q - 4 * q^9	$ 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75} - 36 q^{77} - 12 q^{79} - 24 q^{87} + 18 q^{89} + 6 q^{91} + 16 q^{93} - 64 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.419673	−	1.68044i	−0.242299	−	0.970202i
$3$	−0.419673	−	1.68044i	−0.242299	−	0.970202i
$4$		0			0
$5$	1.02449	+	1.77447i	0.458167	+	0.793569i	0.998864	−	0.0476488i	$-0.0151728\pi$
$5$	1.02449	+	1.77447i	0.458167	+	0.793569i	−0.540697	+	0.841217i	$0.681839\pi$
$6$		0			0
$7$	−2.64365	+	0.105420i	−0.999206	+	0.0398451i
$7$	−2.64365	+	0.105420i	−0.999206	+	0.0398451i
$8$		0			0
$9$	−2.64775	+	1.41047i	−0.882583	+	0.470157i
$10$		0			0
$11$	−5.11564	−	2.95352i	−1.54242	−	0.890518i	−0.998685	−	0.0512635i	$-0.983675\pi$
$11$	−5.11564	−	2.95352i	−1.54242	−	0.890518i	−0.543738	−	0.839255i	$-0.682992\pi$
$12$		0			0
$13$	0.139269	+	0.0804071i	0.0386263	+	0.0223009i	0.519189	−	0.854660i	$-0.326234\pi$
$13$	0.139269	+	0.0804071i	0.0386263	+	0.0223009i	−0.480562	+	0.876960i	$0.659567\pi$
$14$		0			0
$15$	2.55194	−	2.46630i	0.658908	−	0.636795i
$16$		0			0
$17$	−2.77904	−	4.81345i	−0.674017	−	1.16743i	−0.976755	−	0.214358i	$-0.931234\pi$
$17$	−2.77904	−	4.81345i	−0.674017	−	1.16743i	0.302738	−	0.953074i	$-0.402099\pi$
$18$		0			0
$19$	−4.02056	−	2.32127i	−0.922381	−	0.532537i	−0.0379869	−	0.999278i	$-0.512095\pi$
$19$	−4.02056	−	2.32127i	−0.922381	−	0.532537i	−0.884394	+	0.466741i	$0.845428\pi$
$20$		0			0
$21$	1.28662	+	4.39825i	0.280764	+	0.959777i
$22$		0			0
$23$	0.375194	−	0.216618i	0.0782334	−	0.0451681i	−0.460373	−	0.887726i	$-0.652284\pi$
$23$	0.375194	−	0.216618i	0.0782334	−	0.0451681i	0.538606	+	0.842558i	$0.318951\pi$
$24$		0			0
$25$	0.400830	−	0.694257i	0.0801659	−	0.138851i
$26$		0			0
$27$	3.48140	+	3.85744i	0.669996	+	0.742365i
$28$		0			0
$29$	−1.95524	+	1.12886i	−0.363079	+	0.209623i	−0.670430	−	0.741972i	$-0.733890\pi$
$29$	−1.95524	+	1.12886i	−0.363079	+	0.209623i	0.307352	+	0.951596i	$0.400557\pi$
$30$		0			0
$31$			2.97708i			0.534700i	0.963600	+	0.267350i	$0.0861479\pi$
$31$			2.97708i			0.534700i	−0.963600	+	0.267350i	$0.913852\pi$
$32$		0			0
$33$	−2.81630	+	9.83603i	−0.490256	+	1.71223i
$34$		0			0
$35$	−2.89547	−	4.58308i	−0.489423	−	0.774683i
$36$		0			0
$37$	2.17904	−	3.77422i	0.358233	−	0.620477i	−0.629433	−	0.777055i	$-0.716713\pi$
$37$	2.17904	−	3.77422i	0.358233	−	0.620477i	0.987666	+	0.156578i	$0.0500461\pi$
$38$		0			0
$39$	0.0766716	−	0.267778i	0.0122773	−	0.0428788i
$40$		0			0
$41$	−2.35740	+	4.08313i	−0.368163	+	0.637678i	−0.989278	−	0.146042i	$-0.953347\pi$
$41$	−2.35740	+	4.08313i	−0.368163	+	0.637678i	0.621115	+	0.783719i	$0.286680\pi$
$42$		0			0
$43$	1.82369	+	3.15873i	0.278111	+	0.481702i	0.970915	−	0.239424i	$-0.0769585\pi$
$43$	1.82369	+	3.15873i	0.278111	+	0.481702i	−0.692805	+	0.721125i	$0.743625\pi$
$44$		0			0
$45$	−5.21544	−	3.25334i	−0.777472	−	0.484980i
$46$		0			0
$47$	0.130095			0.0189764			0.00948818	−	0.999955i	$-0.496980\pi$
$47$	0.130095			0.0189764			0.00948818	+	0.999955i	$0.496980\pi$
$48$		0			0
$49$	6.97777	−	0.557389i	0.996825	−	0.0796270i
$50$		0			0
$51$	−6.92241	+	6.69009i	−0.969331	+	0.936800i
$52$		0			0
$53$	−10.7936	+	6.23170i	−1.48262	+	0.855990i	−0.999805	−	0.0197331i	$-0.993718\pi$
$53$	−10.7936	+	6.23170i	−1.48262	+	0.855990i	−0.482813	+	0.875723i	$0.660385\pi$
$54$		0			0
$55$		−	12.1034i		−	1.63202i
$56$		0			0
$57$	−2.21343	+	7.73049i	−0.293177	+	1.02393i
$58$		0			0
$59$	−6.44809			−0.839470			−0.419735	−	0.907647i	$-0.637877\pi$
$59$	−6.44809			−0.839470			−0.419735	+	0.907647i	$0.637877\pi$
$60$		0			0
$61$		−	6.90990i		−	0.884722i	−0.896837	−	0.442361i	$-0.854141\pi$
$61$		−	6.90990i		−	0.884722i	0.896837	−	0.442361i	$-0.145859\pi$
$62$		0			0
$63$	6.85103	−	4.00792i	0.863148	−	0.504950i
$64$		0			0
$65$			0.329506i			0.0408702i
$66$		0			0
$67$	15.2919			1.86820			0.934102	−	0.357006i	$-0.116202\pi$
$67$	15.2919			1.86820			0.934102	+	0.357006i	$0.116202\pi$
$68$		0			0
$69$	−0.521473	−	0.539582i	−0.0627780	−	0.0649580i
$70$		0			0
$71$			1.48027i			0.175675i	0.996135	+	0.0878376i	$0.0279957\pi$
$71$			1.48027i			0.175675i	−0.996135	+	0.0878376i	$0.972004\pi$
$72$		0			0
$73$	−2.60881	+	1.50620i	−0.305339	+	0.176287i	−0.644839	−	0.764319i	$-0.723075\pi$
$73$	−2.60881	+	1.50620i	−0.305339	+	0.176287i	0.339500	+	0.940606i	$0.389742\pi$
$74$		0			0
$75$	−1.33487	−	0.382208i	−0.154138	−	0.0441336i
$76$		0			0
$77$	13.8353	+	7.26877i	1.57668	+	0.828353i
$78$		0			0
$79$	17.3851			1.95598			0.977991	−	0.208648i	$-0.0669063\pi$
$79$	17.3851			1.95598			0.977991	+	0.208648i	$0.0669063\pi$
$80$		0			0
$81$	5.02114	−	7.46914i	0.557905	−	0.829905i
$82$		0			0
$83$	−7.62399	−	13.2051i	−0.836841	−	1.44945i	−0.892522	−	0.451003i	$-0.851066\pi$
$83$	−7.62399	−	13.2051i	−0.836841	−	1.44945i	0.0556811	−	0.998449i	$-0.482267\pi$
$84$		0			0
$85$	5.69422	−	9.86268i	0.617625	−	1.06976i
$86$		0			0
$87$	2.71754	+	2.81191i	0.291350	+	0.301468i
$88$		0			0
$89$	−4.04757	+	7.01059i	−0.429041	+	0.743121i	−0.996788	−	0.0800819i	$-0.974482\pi$
$89$	−4.04757	+	7.01059i	−0.429041	+	0.743121i	0.567747	+	0.823203i	$0.307815\pi$
$90$		0			0
$91$	−0.376655	−	0.197886i	−0.0394842	−	0.0207441i
$92$		0			0
$93$	5.00280	−	1.24940i	0.518767	−	0.129557i
$94$		0			0
$95$		−	9.51251i		−	0.975963i
$96$		0			0
$97$	−2.61123	+	1.50759i	−0.265130	+	0.153073i	−0.626673	−	0.779283i	$-0.715584\pi$
$97$	−2.61123	+	1.50759i	−0.265130	+	0.153073i	0.361542	+	0.932356i	$0.382250\pi$
$98$		0			0
$99$	17.7108	+	0.604706i	1.78000	+	0.0607752i
$100$		0			0
$101$	7.56798	−	13.1081i	0.753042	−	1.30431i	−0.193300	−	0.981140i	$-0.561919\pi$
$101$	7.56798	−	13.1081i	0.753042	−	1.30431i	0.946342	−	0.323167i	$-0.104748\pi$
$102$		0			0
$103$	−9.28222	+	5.35909i	−0.914604	+	0.528047i	−0.881910	−	0.471418i	$-0.843742\pi$
$103$	−9.28222	+	5.35909i	−0.914604	+	0.528047i	−0.0326945	+	0.999465i	$0.510409\pi$
$104$		0			0
$105$	−6.48644	+	6.78905i	−0.633012	+	0.662544i
$106$		0			0
$107$	8.19081	+	4.72896i	0.791835	+	0.457166i	0.840608	−	0.541644i	$-0.182198\pi$
$107$	8.19081	+	4.72896i	0.791835	+	0.457166i	−0.0487731	+	0.998810i	$0.515531\pi$
$108$		0			0
$109$	−7.18065	−	12.4373i	−0.687782	−	1.19127i	−0.972554	−	0.232678i	$-0.925251\pi$
$109$	−7.18065	−	12.4373i	−0.687782	−	1.19127i	0.284772	−	0.958595i	$-0.408082\pi$
$110$		0			0
$111$	−7.25682	−	2.07781i	−0.688787	−	0.197217i
$112$		0			0
$113$	−1.15594	−	0.667384i	−0.108742	−	0.0627822i	0.444643	−	0.895708i	$-0.353331\pi$
$113$	−1.15594	−	0.667384i	−0.108742	−	0.0627822i	−0.553385	+	0.832926i	$0.686664\pi$
$114$		0			0
$115$	0.768767	+	0.443848i	0.0716879	+	0.0413890i
$116$		0			0
$117$	−0.482162	−	0.0164626i	−0.0445759	−	0.00152197i
$118$		0			0
$119$	7.85426	+	12.4321i	0.719999	+	1.13965i
$120$		0			0
$121$	11.9465	+	20.6920i	1.08605	+	1.88109i
$122$		0			0
$123$	7.85078	+	2.24788i	0.707881	+	0.202684i
$124$		0			0
$125$	11.8875			1.06325
$126$		0			0
$127$	−0.715218			−0.0634653			−0.0317326	−	0.999496i	$-0.510103\pi$
$127$	−0.715218			−0.0634653			−0.0317326	+	0.999496i	$0.510103\pi$
$128$		0			0
$129$	4.54270	−	4.39024i	0.399962	−	0.386539i
$130$		0			0
$131$	−9.14354	−	15.8371i	−0.798875	−	1.38369i	−0.920349	−	0.391097i	$-0.872096\pi$
$131$	−9.14354	−	15.8371i	−0.798875	−	1.38369i	0.121474	−	0.992595i	$-0.461238\pi$
$132$		0			0
$133$	10.8737	+	5.71279i	0.942867	+	0.495361i
$134$		0			0
$135$	−3.27826	+	10.1296i	−0.282148	+	0.871815i
$136$		0			0
$137$	2.64453	+	1.52682i	0.225938	+	0.130445i	0.608697	−	0.793403i	$-0.291693\pi$
$137$	2.64453	+	1.52682i	0.225938	+	0.130445i	−0.382759	+	0.923848i	$0.625026\pi$
$138$		0			0
$139$	−12.6377	−	7.29638i	−1.07192	−	0.618871i	−0.143211	−	0.989692i	$-0.545743\pi$
$139$	−12.6377	−	7.29638i	−1.07192	−	0.618871i	−0.928704	+	0.370821i	$0.879076\pi$
$140$		0			0
$141$	−0.0545976	−	0.218617i	−0.00459794	−	0.0184109i
$142$		0			0
$143$	−0.474967	−	0.822667i	−0.0397187	−	0.0687949i
$144$		0			0
$145$	−4.00625	−	2.31301i	−0.332701	−	0.192085i
$146$		0			0
$147$	−3.86504	−	11.4918i	−0.318783	−	0.947828i
$148$		0			0
$149$	3.45600	−	1.99532i	0.283127	−	0.163463i	−0.351711	−	0.936108i	$-0.614400\pi$
$149$	3.45600	−	1.99532i	0.283127	−	0.163463i	0.634838	+	0.772645i	$0.281067\pi$
$150$		0			0
$151$	−4.07003	+	7.04950i	−0.331214	+	0.573680i	−0.982750	−	0.184938i	$-0.940792\pi$
$151$	−4.07003	+	7.04950i	−0.331214	+	0.573680i	0.651536	+	0.758618i	$0.274125\pi$
$152$		0			0
$153$	14.1474	+	8.82503i	1.14375	+	0.713462i
$154$		0			0
$155$	−5.28275	+	3.05000i	−0.424321	+	0.244982i
$156$		0			0
$157$		−	7.20562i		−	0.575071i	−0.957770	−	0.287536i	$-0.907164\pi$
$157$		−	7.20562i		−	0.575071i	0.957770	−	0.287536i	$-0.0928360\pi$
$158$		0			0
$159$	15.0018	+	15.5227i	1.18972	+	1.23103i
$160$		0			0
$161$	−0.969046	+	0.612216i	−0.0763715	+	0.0482494i
$162$		0			0
$163$	−10.5854	+	18.3344i	−0.829111	+	1.43606i	0.0696247	+	0.997573i	$0.477820\pi$
$163$	−10.5854	+	18.3344i	−0.829111	+	1.43606i	−0.898736	+	0.438490i	$0.855514\pi$
$164$		0			0
$165$	−20.3391	+	5.07948i	−1.58339	+	0.395437i
$166$		0			0
$167$	−7.90489	+	13.6917i	−0.611699	+	1.05949i	0.379256	+	0.925292i	$0.376180\pi$
$167$	−7.90489	+	13.6917i	−0.611699	+	1.05949i	−0.990954	+	0.134201i	$0.957153\pi$
$168$		0			0
$169$	−6.48707	−	11.2359i	−0.499005	−	0.864303i
$170$		0			0
$171$	13.9195	+	0.475260i	1.06445	+	0.0363441i
$172$		0			0
$173$	−22.5823			−1.71690			−0.858449	−	0.512898i	$-0.828572\pi$
$173$	−22.5823			−1.71690			−0.858449	+	0.512898i	$0.828572\pi$
$174$		0			0
$175$	−0.986465	+	1.87763i	−0.0745697	+	0.141935i
$176$		0			0
$177$	2.70609	+	10.8356i	0.203402	+	0.814456i
$178$		0			0
$179$	−7.88911	+	4.55478i	−0.589660	+	0.340440i	−0.764963	−	0.644074i	$-0.777243\pi$
$179$	−7.88911	+	4.55478i	−0.589660	+	0.340440i	0.175303	+	0.984515i	$0.443909\pi$
$180$		0			0
$181$		−	7.60134i		−	0.565003i	−0.959267	−	0.282501i	$-0.908836\pi$
$181$		−	7.60134i		−	0.565003i	0.959267	−	0.282501i	$-0.0911642\pi$
$182$		0			0
$183$	−11.6117	+	2.89990i	−0.858359	+	0.214367i
$184$		0			0
$185$	8.92966			0.656522
$186$		0			0
$187$			32.8318i			2.40090i
$188$		0			0
$189$	−9.61026	−	9.83072i	−0.699043	−	0.715079i
$190$		0			0
$191$		−	10.3417i		−	0.748296i	−0.927369	−	0.374148i	$-0.877935\pi$
$191$		−	10.3417i		−	0.748296i	0.927369	−	0.374148i	$-0.122065\pi$
$192$		0			0
$193$	11.3169			0.814605			0.407302	−	0.913293i	$-0.366470\pi$
$193$	11.3169			0.814605			0.407302	+	0.913293i	$0.366470\pi$
$194$		0			0
$195$	0.553714	−	0.138285i	0.0396523	−	0.00990278i
$196$		0			0
$197$		−	22.1012i		−	1.57464i	−0.616543	−	0.787321i	$-0.711467\pi$
$197$		−	22.1012i		−	1.57464i	0.616543	−	0.787321i	$-0.288533\pi$
$198$		0			0
$199$	12.6214	−	7.28696i	0.894706	−	0.516559i	0.0192269	−	0.999815i	$-0.493879\pi$
$199$	12.6214	−	7.28696i	0.894706	−	0.516559i	0.875479	+	0.483257i	$0.160546\pi$
$200$		0			0
$201$	−6.41761	−	25.6971i	−0.452663	−	1.81254i
$202$		0			0
$203$	5.04996	−	3.19043i	0.354438	−	0.223924i
$204$		0			0
$205$	−9.66054			−0.674721
$206$		0			0
$207$	−0.687886	+	1.10275i	−0.0478114	+	0.0766465i
$208$		0			0
$209$	13.7118	+	23.7496i	0.948468	+	1.64279i
$210$		0			0
$211$	11.4970	−	19.9135i	0.791489	−	1.37090i	−0.133556	−	0.991041i	$-0.542640\pi$
$211$	11.4970	−	19.9135i	0.791489	−	1.37090i	0.925045	−	0.379858i	$-0.124027\pi$
$212$		0			0
$213$	2.48750	−	0.621228i	0.170440	−	0.0425659i
$214$		0			0
$215$	−3.73672	+	6.47219i	−0.254842	+	0.441400i
$216$		0			0
$217$	−0.313845	−	7.87036i	−0.0213052	−	0.534275i
$218$		0			0
$219$	3.62593	+	3.75184i	0.245017	+	0.253526i
$220$		0			0
$221$		−	0.893820i		−	0.0601248i
$222$		0			0
$223$	−16.8616	+	9.73506i	−1.12914	+	0.651908i	−0.943718	−	0.330751i	$-0.892698\pi$
$223$	−16.8616	+	9.73506i	−1.12914	+	0.651908i	−0.185420	+	0.982659i	$0.559364\pi$
$224$		0			0
$225$	−0.0820663	+	2.40358i	−0.00547109	+	0.160238i
$226$		0			0
$227$	7.00737	−	12.1371i	0.465095	−	0.805569i	−0.534110	−	0.845415i	$-0.679353\pi$
$227$	7.00737	−	12.1371i	0.465095	−	0.805569i	0.999206	+	0.0398459i	$0.0126867\pi$
$228$		0			0
$229$	16.2431	−	9.37798i	1.07338	−	0.619714i	0.144275	−	0.989538i	$-0.453915\pi$
$229$	16.2431	−	9.37798i	1.07338	−	0.619714i	0.929102	+	0.369823i	$0.120582\pi$
$230$		0			0
$231$	6.40841	−	26.2999i	0.421642	−	1.73041i
$232$		0			0
$233$	3.05734	+	1.76516i	0.200293	+	0.115639i	0.596792	−	0.802396i	$-0.296442\pi$
$233$	3.05734	+	1.76516i	0.200293	+	0.115639i	−0.396499	+	0.918035i	$0.629775\pi$
$234$		0			0
$235$	0.133282	+	0.230851i	0.00869434	+	0.0150590i
$236$		0			0
$237$	−7.29608	−	29.2147i	−0.473932	−	1.89770i
$238$		0			0
$239$	−16.9732	−	9.79950i	−1.09791	−	0.633877i	−0.162236	−	0.986752i	$-0.551871\pi$
$239$	−16.9732	−	9.79950i	−1.09791	−	0.633877i	−0.935670	+	0.352875i	$0.885204\pi$
$240$		0			0
$241$	−10.5857	−	6.11166i	−0.681885	−	0.393687i	0.118680	−	0.992933i	$-0.462134\pi$
$241$	−10.5857	−	6.11166i	−0.681885	−	0.393687i	−0.800565	+	0.599246i	$0.795467\pi$
$242$		0			0
$243$	−14.6587	−	5.30312i	−0.940355	−	0.340195i
$244$		0			0
$245$	8.13775	+	11.8108i	0.519902	+	0.754566i
$246$		0			0
$247$	−0.373294	−	0.646564i	−0.0237521	−	0.0411399i
$248$		0			0
$249$	−18.9908	+	18.3535i	−1.20350	+	1.16310i
$250$		0			0
$251$	−8.48303			−0.535444			−0.267722	−	0.963496i	$-0.586271\pi$
$251$	−8.48303			−0.535444			−0.267722	+	0.963496i	$0.586271\pi$
$252$		0			0
$253$	−2.55914			−0.160892
$254$		0			0
$255$	−18.9633	−	5.42969i	−1.18753	−	0.340020i
$256$		0			0
$257$	8.41130	+	14.5688i	0.524682	+	0.908776i	0.999587	+	0.0287390i	$0.00914917\pi$
$257$	8.41130	+	14.5688i	0.524682	+	0.908776i	−0.474905	+	0.880037i	$0.657517\pi$
$258$		0			0
$259$	−5.36275	+	10.2074i	−0.333225	+	0.634258i
$260$		0			0
$261$	3.58476	−	5.74674i	0.221891	−	0.355714i
$262$		0			0
$263$	23.4545	+	13.5415i	1.44627	+	0.835003i	0.998256	−	0.0590255i	$-0.0187993\pi$
$263$	23.4545	+	13.5415i	1.44627	+	0.835003i	0.448011	+	0.894028i	$0.352133\pi$
$264$		0			0
$265$	−22.1160	−	12.7687i	−1.35857	−	0.784373i
$266$		0			0
$267$	13.4795	+	3.85953i	0.824933	+	0.236199i
$268$		0			0
$269$	−2.61318	−	4.52615i	−0.159328	−	0.275964i	0.775298	−	0.631595i	$-0.217599\pi$
$269$	−2.61318	−	4.52615i	−0.159328	−	0.275964i	−0.934627	+	0.355631i	$0.884266\pi$
$270$		0			0
$271$	−10.6766	−	6.16413i	−0.648557	−	0.374444i	0.139346	−	0.990244i	$-0.455500\pi$
$271$	−10.6766	−	6.16413i	−0.648557	−	0.374444i	−0.787903	+	0.615799i	$0.788833\pi$
$272$		0			0
$273$	−0.174464	+	0.715994i	−0.0105590	+	0.0433339i
$274$		0			0
$275$	−4.10100	+	2.36771i	−0.247300	+	0.142778i
$276$		0			0
$277$	−10.8371	+	18.7704i	−0.651138	+	1.12780i	0.331709	+	0.943382i	$0.392375\pi$
$277$	−10.8371	+	18.7704i	−0.651138	+	1.12780i	−0.982847	+	0.184423i	$0.940958\pi$
$278$		0			0
$279$	−4.19909	−	7.88256i	−0.251393	−	0.471917i
$280$		0			0
$281$	−9.39885	+	5.42643i	−0.560688	+	0.323714i	−0.753422	−	0.657538i	$-0.771598\pi$
$281$	−9.39885	+	5.42643i	−0.560688	+	0.323714i	0.192733	+	0.981251i	$0.438265\pi$
$282$		0			0
$283$			30.4132i			1.80788i	0.427662	+	0.903939i	$0.359337\pi$
$283$			30.4132i			1.80788i	−0.427662	+	0.903939i	$0.640663\pi$
$284$		0			0
$285$	−15.9852	+	3.99215i	−0.946881	+	0.236474i
$286$		0			0
$287$	5.80168	−	11.0429i	0.342463	−	0.651841i
$288$		0			0
$289$	−6.94618	+	12.0311i	−0.408599	+	0.707714i
$290$		0			0
$291$	3.62928	+	3.75531i	0.212752	+	0.220140i
$292$		0			0
$293$	−2.22993	+	3.86235i	−0.130274	+	0.225641i	−0.923782	−	0.382919i	$-0.874919\pi$
$293$	−2.22993	+	3.86235i	−0.130274	+	0.225641i	0.793508	+	0.608559i	$0.208252\pi$
$294$		0			0
$295$	−6.60602	−	11.4420i	−0.384618	−	0.666177i
$296$		0			0
$297$	−6.41657	−	30.0156i	−0.372327	−	1.74168i
$298$		0			0
$299$	0.0696706			0.00402916
$300$		0			0
$301$	−5.15420	−	8.15832i	−0.297083	−	0.470238i
$302$		0			0
$303$	−25.2035	−	7.21639i	−1.44790	−	0.414571i
$304$		0			0
$305$	12.2614	−	7.07914i	0.702087	−	0.405350i
$306$		0			0
$307$			9.43048i			0.538226i	0.963109	+	0.269113i	$0.0867305\pi$
$307$			9.43048i			0.538226i	−0.963109	+	0.269113i	$0.913269\pi$
$308$		0			0
$309$	12.9011	+	13.3491i	0.733919	+	0.759405i
$310$		0			0
$311$	6.96708			0.395067			0.197533	−	0.980296i	$-0.436707\pi$
$311$	6.96708			0.395067			0.197533	+	0.980296i	$0.436707\pi$
$312$		0			0
$313$		−	6.63255i		−	0.374894i	−0.982275	−	0.187447i	$-0.939979\pi$
$313$		−	6.63255i		−	0.374894i	0.982275	−	0.187447i	$-0.0600212\pi$
$314$		0			0
$315$	14.1308	+	8.05088i	0.796179	+	0.453616i
$316$		0			0
$317$		−	15.0437i		−	0.844940i	−0.906377	−	0.422470i	$-0.861163\pi$
$317$		−	15.0437i		−	0.844940i	0.906377	−	0.422470i	$-0.138837\pi$
$318$		0			0
$319$	13.3364			0.746694
$320$		0			0
$321$	4.50927	−	15.7488i	0.251683	−	0.879010i
$322$		0			0
$323$			25.8037i			1.43576i
$324$		0			0
$325$	0.111646	−	0.0644591i	0.00619303	−	0.00357555i
$326$		0			0
$327$	−17.8865	+	17.2862i	−0.989127	+	0.955931i
$328$		0			0
$329$	−0.343927	+	0.0137147i	−0.0189613	+	0.000756116i
$330$		0			0
$331$	−30.3001			−1.66544			−0.832722	−	0.553691i	$-0.813219\pi$
$331$	−30.3001			−1.66544			−0.832722	+	0.553691i	$0.813219\pi$
$332$		0			0
$333$	−0.446140	+	13.0667i	−0.0244483	+	0.716048i
$334$		0			0
$335$	15.6665	+	27.1351i	0.855950	+	1.48255i
$336$		0			0
$337$	−3.02011	+	5.23099i	−0.164516	+	0.284950i	−0.936483	−	0.350712i	$-0.885940\pi$
$337$	−3.02011	+	5.23099i	−0.164516	+	0.284950i	0.771967	+	0.635662i	$0.219273\pi$
$338$		0			0
$339$	−0.636379	+	2.22257i	−0.0345634	+	0.120714i
$340$		0			0
$341$	8.79286	−	15.2297i	0.476160	−	0.824733i
$342$		0			0
$343$	−18.3880	+	2.20914i	−0.992860	+	0.119282i
$344$		0			0
$345$	0.423228	−	1.47814i	0.0227858	−	0.0795802i
$346$		0			0
$347$		−	6.50010i		−	0.348944i	−0.984662	−	0.174472i	$-0.944178\pi$
$347$		−	6.50010i		−	0.348944i	0.984662	−	0.174472i	$-0.0558218\pi$
$348$		0			0
$349$	−10.6732	+	6.16218i	−0.571324	+	0.329854i	−0.757678	−	0.652629i	$-0.773666\pi$
$349$	−10.6732	+	6.16218i	−0.571324	+	0.329854i	0.186354	+	0.982483i	$0.440333\pi$
$350$		0			0
$351$	0.174686	+	0.817152i	0.00932405	+	0.0436163i
$352$		0			0
$353$	−4.84698	+	8.39522i	−0.257979	+	0.446833i	−0.965700	−	0.259659i	$-0.916390\pi$
$353$	−4.84698	+	8.39522i	−0.257979	+	0.446833i	0.707721	+	0.706492i	$0.249723\pi$
$354$		0			0
$355$	−2.62669	+	1.51652i	−0.139410	+	0.0804886i
$356$		0			0
$357$	17.5952	−	18.4160i	0.931235	−	0.974679i
$358$		0			0
$359$	20.8975	+	12.0652i	1.10293	+	0.636776i	0.936989	−	0.349360i	$-0.113601\pi$
$359$	20.8975	+	12.0652i	1.10293	+	0.636776i	0.165940	+	0.986136i	$0.446934\pi$
$360$		0			0
$361$	1.27663	+	2.21118i	0.0671908	+	0.116378i
$362$		0			0
$363$	29.7579	−	28.7592i	1.56189	−	1.50947i
$364$		0			0
$365$	−5.34542	−	3.08618i	−0.279792	−	0.161538i
$366$		0			0
$367$	−4.23692	−	2.44619i	−0.221165	−	0.127690i	0.385324	−	0.922781i	$-0.374090\pi$
$367$	−4.23692	−	2.44619i	−0.221165	−	0.127690i	−0.606490	+	0.795091i	$0.707423\pi$
$368$		0			0
$369$	0.482656	−	14.1361i	0.0251261	−	0.735898i
$370$		0			0
$371$	27.8776	−	17.6123i	1.44733	−	0.914386i
$372$		0			0
$373$	15.3974	+	26.6690i	0.797245	+	1.38087i	0.921404	+	0.388606i	$0.127043\pi$
$373$	15.3974	+	26.6690i	0.797245	+	1.38087i	−0.124159	+	0.992262i	$0.539623\pi$
$374$		0			0
$375$	−4.98887	−	19.9762i	−0.257624	−	1.03157i
$376$		0			0
$377$	−0.363072			−0.0186992
$378$		0			0
$379$	8.36682			0.429775			0.214887	−	0.976639i	$-0.431062\pi$
$379$	8.36682			0.429775			0.214887	+	0.976639i	$0.431062\pi$
$380$		0			0
$381$	0.300158	+	1.20188i	0.0153776	+	0.0615741i
$382$		0			0
$383$	1.75731	+	3.04375i	0.0897944	+	0.155528i	0.907424	−	0.420216i	$-0.138046\pi$
$383$	1.75731	+	3.04375i	0.0897944	+	0.155528i	−0.817630	+	0.575744i	$0.804712\pi$
$384$		0			0
$385$	1.27595	+	31.9972i	0.0650283	+	1.63073i
$386$		0			0
$387$	−9.28398	−	5.79125i	−0.471931	−	0.294386i
$388$		0			0
$389$	−22.9726	−	13.2632i	−1.16476	−	0.672472i	−0.212316	−	0.977201i	$-0.568101\pi$
$389$	−22.9726	−	13.2632i	−1.16476	−	0.672472i	−0.952439	+	0.304729i	$0.901434\pi$
$390$		0			0
$391$	−2.08536	−	1.20398i	−0.105461	−	0.0608881i
$392$		0			0
$393$	−22.7759	+	22.0116i	−1.14889	+	1.11034i
$394$		0			0
$395$	17.8110	+	30.8495i	0.896166	+	1.55221i
$396$		0			0
$397$	19.9734	+	11.5317i	1.00244	+	0.578758i	0.908969	−	0.416865i	$-0.136871\pi$
$397$	19.9734	+	11.5317i	1.00244	+	0.578758i	0.0934690	+	0.995622i	$0.470204\pi$
$398$		0			0
$399$	5.03660	−	20.6701i	0.252145	−	1.03480i
$400$		0			0
$401$	1.26384	−	0.729680i	0.0631133	−	0.0364385i	−0.468111	−	0.883670i	$-0.655065\pi$
$401$	1.26384	−	0.729680i	0.0631133	−	0.0364385i	0.531225	+	0.847231i	$0.321732\pi$
$402$		0			0
$403$	−0.239379	+	0.414616i	−0.0119243	+	0.0206535i
$404$		0			0
$405$	18.3979	+	1.25780i	0.914200	+	0.0625007i
$406$		0			0
$407$	−22.2944	+	12.8717i	−1.10509	+	0.638026i
$408$		0			0
$409$		−	25.8174i		−	1.27659i	−0.769793	−	0.638293i	$-0.779641\pi$
$409$		−	25.8174i		−	1.27659i	0.769793	−	0.638293i	$-0.220359\pi$
$410$		0			0
$411$	1.45589	−	5.08474i	0.0718137	−	0.250812i
$412$		0			0
$413$	17.0465	−	0.679760i	0.838804	−	0.0334488i
$414$		0			0
$415$	15.6214	−	27.0571i	0.766826	−	1.32818i
$416$		0			0
$417$	−6.95741	+	24.2990i	−0.340706	+	1.18993i
$418$		0			0
$419$	−4.15180	+	7.19113i	−0.202829	+	0.351310i	−0.949439	−	0.313952i	$-0.898347\pi$
$419$	−4.15180	+	7.19113i	−0.202829	+	0.351310i	0.746610	+	0.665262i	$0.231680\pi$
$420$		0			0
$421$	8.28977	+	14.3583i	0.404019	+	0.699781i	0.994207	−	0.107485i	$-0.0342798\pi$
$421$	8.28977	+	14.3583i	0.404019	+	0.699781i	−0.590188	+	0.807266i	$0.700946\pi$
$422$		0			0
$423$	−0.344460	+	0.183496i	−0.0167482	+	0.00892187i
$424$		0			0
$425$	−4.45569			−0.216133
$426$		0			0
$427$	0.728444	+	18.2674i	0.0352519	+	0.884019i
$428$		0			0
$429$	−1.18311	+	1.14340i	−0.0571211	+	0.0552041i
$430$		0			0
$431$	13.7217	−	7.92225i	0.660953	−	0.381601i	−0.131687	−	0.991291i	$-0.542039\pi$
$431$	13.7217	−	7.92225i	0.660953	−	0.381601i	0.792640	+	0.609690i	$0.208706\pi$
$432$		0			0
$433$			12.0650i			0.579808i	0.957056	+	0.289904i	$0.0936233\pi$
$433$			12.0650i			0.579808i	−0.957056	+	0.289904i	$0.906377\pi$
$434$		0			0
$435$	−2.20556	+	7.70297i	−0.105748	+	0.369329i
$436$		0			0
$437$	−2.01132			−0.0962146
$438$		0			0
$439$		−	20.1424i		−	0.961343i	−0.876901	−	0.480672i	$-0.840393\pi$
$439$		−	20.1424i		−	0.961343i	0.876901	−	0.480672i	$-0.159607\pi$
$440$		0			0
$441$	−17.6892	+	11.3178i	−0.842343	+	0.538942i
$442$		0			0
$443$		−	13.4653i		−	0.639755i	−0.947459	−	0.319877i	$-0.896358\pi$
$443$		−	13.4653i		−	0.639755i	0.947459	−	0.319877i	$-0.103642\pi$
$444$		0			0
$445$	−16.5868			−0.786290
$446$		0			0
$447$	−4.80341	−	4.97021i	−0.227194	−	0.235083i
$448$		0			0
$449$			7.63121i			0.360139i	0.983654	+	0.180069i	$0.0576323\pi$
$449$			7.63121i			0.360139i	−0.983654	+	0.180069i	$0.942368\pi$
$450$		0			0
$451$	24.1192	−	13.9252i	1.13573	−	0.655712i
$452$		0			0
$453$	13.5543	+	3.88095i	0.636838	+	0.182343i
$454$		0			0
$455$	−0.0347366	−	0.871098i	−0.00162848	−	0.0408377i
$456$		0			0
$457$	25.8702			1.21016			0.605079	−	0.796165i	$-0.293142\pi$
$457$	25.8702			1.21016			0.605079	+	0.796165i	$0.293142\pi$
$458$		0			0
$459$	8.89262	−	27.4775i	0.415072	−	1.28254i
$460$		0			0
$461$	11.4048	+	19.7537i	0.531176	+	0.920023i	0.999338	+	0.0363806i	$0.0115829\pi$
$461$	11.4048	+	19.7537i	0.531176	+	0.920023i	−0.468162	+	0.883642i	$0.655084\pi$
$462$		0			0
$463$	10.7397	−	18.6017i	0.499116	−	0.864494i	−0.500884	−	0.865515i	$-0.666992\pi$
$463$	10.7397	−	18.6017i	0.499116	−	0.864494i	0.999999	+	0.00102063i	$0.000324876\pi$
$464$		0			0
$465$	7.34237	+	7.59734i	0.340494	+	0.352318i
$466$		0			0
$467$	16.8577	−	29.1984i	0.780081	−	1.35114i	−0.151813	−	0.988409i	$-0.548511\pi$
$467$	16.8577	−	29.1984i	0.780081	−	1.35114i	0.931894	−	0.362730i	$-0.118155\pi$
$468$		0			0
$469$	−40.4265	+	1.61208i	−1.86672	+	0.0744389i
$470$		0			0
$471$	−12.1086	+	3.02401i	−0.557935	+	0.139339i
$472$		0			0
$473$		−	21.5452i		−	0.990650i
$474$		0			0
$475$	−3.22312	+	1.86087i	−0.147887	+	0.0853826i
$476$		0			0
$477$	19.7892	−	31.7241i	0.906084	−	1.45255i
$478$		0			0
$479$	−0.0580442	+	0.100536i	−0.00265211	+	0.00459358i	−0.867348	−	0.497701i	$-0.834178\pi$
$479$	−0.0580442	+	0.100536i	−0.00265211	+	0.00459358i	0.864696	+	0.502295i	$0.167511\pi$
$480$		0			0
$481$	0.606947	−	0.350421i	0.0276744	−	0.0159778i
$482$		0			0
$483$	1.43548	+	1.37149i	0.0653164	+	0.0624050i
$484$		0			0
$485$	−5.35037	−	3.08904i	−0.242948	−	0.140266i
$486$		0			0
$487$	−3.60826	−	6.24968i	−0.163506	−	0.283200i	0.772618	−	0.634871i	$-0.218947\pi$
$487$	−3.60826	−	6.24968i	−0.163506	−	0.283200i	−0.936124	+	0.351671i	$0.885614\pi$
$488$		0			0
$489$	35.2523	+	10.0936i	1.59416	+	0.456449i
$490$		0			0
$491$	−13.2127	−	7.62833i	−0.596279	−	0.344262i	0.171298	−	0.985219i	$-0.445204\pi$
$491$	−13.2127	−	7.62833i	−0.596279	−	0.344262i	−0.767576	+	0.640958i	$0.778537\pi$
$492$		0			0
$493$	10.8674	+	6.27429i	0.489442	+	0.282580i
$494$		0			0
$495$	17.0715	+	32.0468i	0.767308	+	1.44040i
$496$		0			0
$497$	−0.156050	−	3.91331i	−0.00699981	−	0.175536i
$498$		0			0
$499$	−8.24154	−	14.2748i	−0.368942	−	0.639026i	0.620458	−	0.784239i	$-0.286947\pi$
$499$	−8.24154	−	14.2748i	−0.368942	−	0.639026i	−0.989400	+	0.145213i	$0.953613\pi$
$500$		0			0
$501$	26.3255	+	7.53765i	1.17614	+	0.336757i
$502$		0			0
$503$	−6.95709			−0.310201			−0.155101	−	0.987899i	$-0.549570\pi$
$503$	−6.95709			−0.310201			−0.155101	+	0.987899i	$0.549570\pi$
$504$		0			0
$505$	31.0134			1.38008
$506$		0			0
$507$	−16.1588	+	15.6165i	−0.717640	+	0.693555i
$508$		0			0
$509$	13.1345	+	22.7496i	0.582177	+	1.00836i	0.995221	+	0.0976491i	$0.0311323\pi$
$509$	13.1345	+	22.7496i	0.582177	+	1.00836i	−0.413044	+	0.910711i	$0.635534\pi$
$510$		0			0
$511$	6.73801	−	4.25689i	0.298072	−	0.188314i
$512$		0			0
$513$	−5.04301	−	23.5904i	−0.222654	−	1.04154i
$514$		0			0
$515$	−19.0191	−	10.9807i	−0.838083	−	0.483867i
$516$		0			0
$517$	−0.665521	−	0.384239i	−0.0292696	−	0.0168988i
$518$		0			0
$519$	9.47718	+	37.9481i	0.416002	+	1.66574i
$520$		0			0
$521$	−9.46686	−	16.3971i	−0.414750	−	0.718369i	0.580652	−	0.814152i	$-0.302798\pi$
$521$	−9.46686	−	16.3971i	−0.414750	−	0.718369i	−0.995402	+	0.0957832i	$0.969464\pi$
$522$		0			0
$523$	−8.19679	−	4.73242i	−0.358421	−	0.206934i	0.309967	−	0.950747i	$-0.399682\pi$
$523$	−8.19679	−	4.73242i	−0.358421	−	0.206934i	−0.668388	+	0.743813i	$0.733015\pi$
$524$		0			0
$525$	3.56923	+	0.869702i	0.155774	+	0.0379569i
$526$		0			0
$527$	14.3300	−	8.27344i	0.624226	−	0.360397i
$528$		0			0
$529$	−11.4062	+	19.7560i	−0.495920	+	0.858958i
$530$		0			0
$531$	17.0729	−	9.09485i	0.740902	−	0.394683i
$532$		0			0
$533$	−0.656625	+	0.379103i	−0.0284416	+	0.0164208i
$534$		0			0
$535$			19.3792i			0.837834i
$536$		0			0
$537$	10.9649	+	11.3456i	0.473170	+	0.489601i
$538$		0			0
$539$	−37.3420	−	17.7576i	−1.60843	−	0.764872i
$540$		0			0
$541$	−9.96877	+	17.2664i	−0.428591	+	0.742341i	−0.996748	−	0.0805787i	$-0.974323\pi$
$541$	−9.96877	+	17.2664i	−0.428591	+	0.742341i	0.568157	+	0.822920i	$0.307656\pi$
$542$		0			0
$543$	−12.7736	+	3.19008i	−0.548167	+	0.136899i
$544$		0			0
$545$	14.7131	−	25.4838i	0.630238	−	1.09160i
$546$		0			0
$547$	−9.19529	−	15.9267i	−0.393162	−	0.680977i	0.599702	−	0.800223i	$-0.295286\pi$
$547$	−9.19529	−	15.9267i	−0.393162	−	0.680977i	−0.992865	+	0.119246i	$0.961952\pi$
$548$		0			0
$549$	9.74621	+	18.2957i	0.415958	+	0.780840i
$550$		0			0
$551$	10.4815			0.446529
$552$		0			0
$553$	−45.9602	+	1.83275i	−1.95443	+	0.0779364i
$554$		0			0
$555$	−3.74754	−	15.0057i	−0.159074	−	0.636958i
$556$		0			0
$557$	17.1334	−	9.89198i	0.725966	−	0.419137i	−0.0909787	−	0.995853i	$-0.529000\pi$
$557$	17.1334	−	9.89198i	0.725966	−	0.419137i	0.816945	+	0.576716i	$0.195666\pi$
$558$		0			0
$559$			0.586551i			0.0248085i
$560$		0			0
$561$	55.1718	−	13.7786i	2.32936	−	0.581735i
$562$		0			0
$563$	23.6408			0.996342			0.498171	−	0.867079i	$-0.334005\pi$
$563$	23.6408			0.996342			0.498171	+	0.867079i	$0.334005\pi$
$564$		0			0
$565$		−	2.73492i		−	0.115059i
$566$		0			0
$567$	−12.4867	+	20.2751i	−0.524394	+	0.851476i
$568$		0			0
$569$			0.248951i			0.0104366i	0.999986	+	0.00521829i	$0.00166104\pi$
$569$			0.248951i			0.0104366i	−0.999986	+	0.00521829i	$0.998339\pi$
$570$		0			0
$571$	21.4095			0.895959			0.447979	−	0.894044i	$-0.352144\pi$
$571$	21.4095			0.895959			0.447979	+	0.894044i	$0.352144\pi$
$572$		0			0
$573$	−17.3785	+	4.34012i	−0.725998	+	0.181311i
$574$		0			0
$575$		−	0.347308i		−	0.0144838i
$576$		0			0
$577$	−15.1856	+	8.76740i	−0.632184	+	0.364991i	−0.781597	−	0.623783i	$-0.785595\pi$
$577$	−15.1856	+	8.76740i	−0.632184	+	0.364991i	0.149414	+	0.988775i	$0.452261\pi$
$578$		0			0
$579$	−4.74938	−	19.0173i	−0.197378	−	0.790331i
$580$		0			0
$581$	21.5472	+	34.1060i	0.893930	+	1.41496i
$582$		0			0
$583$	73.6217			3.04910
$584$		0			0
$585$	−0.464758	−	0.872449i	−0.0192154	−	0.0360713i
$586$		0			0
$587$	0.868296	+	1.50393i	0.0358384	+	0.0620739i	0.883388	−	0.468642i	$-0.155257\pi$
$587$	0.868296	+	1.50393i	0.0358384	+	0.0620739i	−0.847550	+	0.530716i	$0.821923\pi$
$588$		0			0
$589$	6.91062	−	11.9696i	0.284747	−	0.493197i
$590$		0			0
$591$	−37.1397	+	9.27527i	−1.52772	+	0.381534i
$592$		0			0
$593$	−1.20172	+	2.08145i	−0.0493489	+	0.0854749i	−0.889645	−	0.456653i	$-0.849048\pi$
$593$	−1.20172	+	2.08145i	−0.0493489	+	0.0854749i	0.840296	+	0.542128i	$0.182381\pi$
$594$		0			0
$595$	−14.0138	+	26.6738i	−0.574510	+	1.09352i
$596$		0			0
$597$	−17.5421	−	18.1513i	−0.717952	−	0.742884i
$598$		0			0
$599$			0.0915006i			0.00373861i	0.999998	+	0.00186931i	$0.000595019\pi$
$599$			0.0915006i			0.00373861i	−0.999998	+	0.00186931i	$0.999405\pi$
$600$		0			0
$601$	23.2642	−	13.4316i	0.948968	−	0.547887i	0.0562081	−	0.998419i	$-0.482099\pi$
$601$	23.2642	−	13.4316i	0.948968	−	0.547887i	0.892760	+	0.450532i	$0.148766\pi$
$602$		0			0
$603$	−40.4891	+	21.5688i	−1.64885	+	0.878349i
$604$		0			0
$605$	−24.4782	+	42.3975i	−0.995181	+	1.72370i
$606$		0			0
$607$	17.2245	−	9.94456i	0.699120	−	0.403637i	−0.107899	−	0.994162i	$-0.534412\pi$
$607$	17.2245	−	9.94456i	0.699120	−	0.403637i	0.807020	+	0.590524i	$0.201079\pi$
$608$		0			0
$609$	−7.48065	−	7.14721i	−0.303131	−	0.289620i
$610$		0			0
$611$	0.0181183	+	0.0104606i	0.000732987	+	0.000423190i
$612$		0			0
$613$	−21.2209	−	36.7558i	−0.857106	−	1.48455i	−0.874678	−	0.484705i	$-0.838927\pi$
$613$	−21.2209	−	36.7558i	−0.857106	−	1.48455i	0.0175716	−	0.999846i	$-0.494406\pi$
$614$		0			0
$615$	4.05427	+	16.2339i	0.163484	+	0.654616i
$616$		0			0
$617$	−13.9907	−	8.07756i	−0.563246	−	0.325190i	0.191201	−	0.981551i	$-0.438762\pi$
$617$	−13.9907	−	8.07756i	−0.563246	−	0.325190i	−0.754447	+	0.656361i	$0.772095\pi$
$618$		0			0
$619$	−30.3820	−	17.5410i	−1.22115	−	0.705034i	−0.255990	−	0.966679i	$-0.582402\pi$
$619$	−30.3820	−	17.5410i	−1.22115	−	0.705034i	−0.965164	+	0.261646i	$0.915735\pi$
$620$		0			0
$621$	2.14179	+	0.693154i	0.0859472	+	0.0278153i
$622$		0			0
$623$	9.96129	−	18.9602i	0.399091	−	0.759626i
$624$		0			0
$625$	10.1745	+	17.6228i	0.406981	+	0.704912i
$626$		0			0
$627$	34.1553	−	33.0090i	1.36403	−	1.31825i
$628$		0			0
$629$	−24.2226			−0.965820
$630$		0			0
$631$	13.0916			0.521170			0.260585	−	0.965451i	$-0.416085\pi$
$631$	13.0916			0.521170			0.260585	+	0.965451i	$0.416085\pi$
$632$		0			0
$633$	−38.2883	−	10.9629i	−1.52182	−	0.435737i
$634$		0			0
$635$	−0.732735	−	1.26913i	−0.0290777	−	0.0503641i
$636$		0			0
$637$	1.01661	+	0.483435i	0.0402794	+	0.0191544i
$638$		0			0
$639$	−2.08787	−	3.91937i	−0.0825949	−	0.155048i
$640$		0			0
$641$	−3.45066	−	1.99224i	−0.136293	−	0.0786887i	0.430303	−	0.902684i	$-0.358407\pi$
$641$	−3.45066	−	1.99224i	−0.136293	−	0.0786887i	−0.566596	+	0.823996i	$0.691740\pi$
$642$		0			0
$643$	−24.9128	−	14.3834i	−0.982467	−	0.567227i	−0.0794528	−	0.996839i	$-0.525317\pi$
$643$	−24.9128	−	14.3834i	−0.982467	−	0.567227i	−0.903014	+	0.429611i	$0.858651\pi$
$644$		0			0
$645$	12.4443	+	3.56312i	0.489995	+	0.140298i
$646$		0			0
$647$	11.4786	+	19.8815i	0.451270	+	0.781623i	0.998465	−	0.0553822i	$-0.0176377\pi$
$647$	11.4786	+	19.8815i	0.451270	+	0.781623i	−0.547195	+	0.837005i	$0.684304\pi$
$648$		0			0
$649$	32.9861	+	19.0445i	1.29482	+	0.747564i
$650$		0			0
$651$	−13.0940	+	3.83038i	−0.513192	+	0.150124i
$652$		0			0
$653$	−1.61080	+	0.929996i	−0.0630355	+	0.0363936i	−0.531187	−	0.847255i	$-0.678254\pi$
$653$	−1.61080	+	0.929996i	−0.0630355	+	0.0363936i	0.468151	+	0.883648i	$0.344920\pi$
$654$		0			0
$655$	18.7350	−	32.4499i	0.732036	−	1.26792i
$656$		0			0
$657$	4.78303	−	7.66769i	0.186604	−	0.299145i
$658$		0			0
$659$	−9.04167	+	5.22021i	−0.352213	+	0.203351i	−0.665660	−	0.746255i	$-0.731850\pi$
$659$	−9.04167	+	5.22021i	−0.352213	+	0.203351i	0.313446	+	0.949606i	$0.398516\pi$
$660$		0			0
$661$			39.9788i			1.55500i	0.628885	+	0.777498i	$0.283512\pi$
$661$			39.9788i			1.55500i	−0.628885	+	0.777498i	$0.716488\pi$
$662$		0			0
$663$	−1.50201	+	0.375112i	−0.0583332	+	0.0145682i
$664$		0			0
$665$	1.00281	+	25.1478i	0.0388874	+	0.975188i
$666$		0			0
$667$	−0.489063	+	0.847081i	−0.0189366	+	0.0327991i
$668$		0			0
$669$	23.4355	+	24.2494i	0.906071	+	0.937535i
$670$		0			0
$671$	−20.4085	+	35.3485i	−0.787861	+	1.36462i
$672$		0			0
$673$	−17.1038	−	29.6247i	−0.659303	−	1.14195i	−0.980796	−	0.195035i	$-0.937518\pi$
$673$	−17.1038	−	29.6247i	−0.659303	−	1.14195i	0.321493	−	0.946912i	$-0.395815\pi$
$674$		0			0
$675$	4.07351	−	0.870810i	0.156789	−	0.0335175i
$676$		0			0
$677$	−22.0224			−0.846389			−0.423195	−	0.906039i	$-0.639091\pi$
$677$	−22.0224			−0.846389			−0.423195	+	0.906039i	$0.639091\pi$
$678$		0			0
$679$	6.74425	−	4.26083i	0.258820	−	0.163516i
$680$		0			0
$681$	−23.3365	−	6.68183i	−0.894256	−	0.256048i
$682$		0			0
$683$	−28.8171	+	16.6375i	−1.10265	+	0.636618i	−0.936917	−	0.349552i	$-0.886334\pi$
$683$	−28.8171	+	16.6375i	−1.10265	+	0.636618i	−0.165737	+	0.986170i	$0.553000\pi$
$684$		0			0
$685$			6.25687i			0.239063i
$686$		0			0
$687$	−22.5759	−	23.3599i	−0.861326	−	0.891236i
$688$		0			0
$689$	−2.00429			−0.0763575
$690$		0			0
$691$		−	43.9547i		−	1.67212i	−0.548641	−	0.836058i	$-0.684855\pi$
$691$		−	43.9547i		−	1.67212i	0.548641	−	0.836058i	$-0.315145\pi$
$692$		0			0
$693$	−46.8848	+	0.268445i	−1.78101	+	0.0101974i
$694$		0			0
$695$		−	29.9003i		−	1.13418i
$696$		0			0
$697$	26.2052			0.992594
$698$		0			0
$699$	1.68315	−	5.87846i	0.0636627	−	0.222344i
$700$		0			0
$701$			20.6866i			0.781321i	0.920535	+	0.390661i	$0.127753\pi$
$701$			20.6866i			0.781321i	−0.920535	+	0.390661i	$0.872247\pi$
$702$		0			0
$703$	−17.5220	+	10.1163i	−0.660854	+	0.381544i
$704$		0			0
$705$	0.331996	−	0.320854i	0.0125037	−	0.0120841i
$706$		0			0
$707$	−18.6252	+	35.4511i	−0.700474	+	1.33328i
$708$		0			0
$709$	−3.51311			−0.131938			−0.0659688	−	0.997822i	$-0.521014\pi$
$709$	−3.51311			−0.131938			−0.0659688	+	0.997822i	$0.521014\pi$
$710$		0			0
$711$	−46.0315	+	24.5212i	−1.72632	+	0.919618i
$712$		0			0
$713$	0.644891	+	1.11698i	0.0241514	+	0.0418314i
$714$		0			0
$715$	0.973201	−	1.68563i	0.0363956	−	0.0630391i
$716$		0			0
$717$	−9.34424	+	32.6351i	−0.348967	+	1.21878i
$718$		0			0
$719$	−6.36853	+	11.0306i	−0.237506	+	0.411372i	−0.959998	−	0.280007i	$-0.909663\pi$
$719$	−6.36853	+	11.0306i	−0.237506	+	0.411372i	0.722492	+	0.691379i	$0.242997\pi$
$720$		0			0
$721$	23.9740	−	15.1461i	0.892838	−	0.564070i
$722$		0			0
$723$	−5.82773	+	20.3535i	−0.216736	+	0.756956i
$724$		0			0
$725$			1.80992i			0.0672187i
$726$		0			0
$727$	17.7538	−	10.2502i	0.658454	−	0.380158i	−0.133234	−	0.991085i	$-0.542536\pi$
$727$	17.7538	−	10.2502i	0.658454	−	0.380158i	0.791687	+	0.610926i	$0.209203\pi$
$728$		0			0
$729$	−2.75971	+	26.8586i	−0.102212	+	0.994763i
$730$		0			0
$731$	10.1362	−	17.5565i	0.374903	−	0.649351i
$732$		0			0
$733$	−16.5292	+	9.54315i	−0.610521	+	0.352484i	−0.773169	−	0.634200i	$-0.781330\pi$
$733$	−16.5292	+	9.54315i	−0.610521	+	0.352484i	0.162649	+	0.986684i	$0.447996\pi$
$734$		0			0
$735$	16.4322	−	18.6317i	0.606110	−	0.687240i
$736$		0			0
$737$	−78.2279	−	45.1649i	−2.88156	−	1.66367i
$738$		0			0
$739$	17.3600	+	30.0685i	0.638599	+	1.10609i	0.985740	+	0.168274i	$0.0538193\pi$
$739$	17.3600	+	30.0685i	0.638599	+	1.10609i	−0.347141	+	0.937813i	$0.612847\pi$
$740$		0			0
$741$	−0.929849	+	0.898643i	−0.0341589	+	0.0330125i
$742$		0			0
$743$	21.7742	+	12.5713i	0.798816	+	0.461197i	0.843057	−	0.537824i	$-0.180754\pi$
$743$	21.7742	+	12.5713i	0.798816	+	0.461197i	−0.0442408	+	0.999021i	$0.514087\pi$
$744$		0			0
$745$	7.08130	+	4.08839i	0.259439	+	0.149787i
$746$		0			0
$747$	38.8119	+	24.2105i	1.42005	+	0.885814i
$748$		0			0
$749$	−22.1522	−	11.6382i	−0.809422	−	0.425252i
$750$		0			0
$751$	−22.6348	−	39.2046i	−0.825955	−	1.43060i	−0.901187	−	0.433430i	$-0.857303\pi$
$751$	−22.6348	−	39.2046i	−0.825955	−	1.43060i	0.0752321	−	0.997166i	$-0.476030\pi$
$752$		0			0
$753$	3.56010	+	14.2552i	0.129737	+	0.519489i
$754$		0			0
$755$	−16.6789			−0.607006
$756$		0			0
$757$	−5.73623			−0.208487			−0.104243	−	0.994552i	$-0.533242\pi$
$757$	−5.73623			−0.208487			−0.104243	+	0.994552i	$0.533242\pi$
$758$		0			0
$759$	1.07400	+	4.30048i	0.0389839	+	0.156098i
$760$		0			0
$761$	−8.21001	−	14.2202i	−0.297613	−	0.515480i	0.677977	−	0.735084i	$-0.262857\pi$
$761$	−8.21001	−	14.2202i	−0.297613	−	0.515480i	−0.975589	+	0.219603i	$0.929524\pi$
$762$		0			0
$763$	20.2943	+	32.1228i	0.734702	+	1.16292i
$764$		0			0
$765$	−1.16584	+	34.1454i	−0.0421511	+	1.23453i
$766$		0			0
$767$	−0.898021	−	0.518472i	−0.0324256	−	0.0187210i
$768$		0			0
$769$	−45.8286	−	26.4592i	−1.65262	−	0.954142i	−0.975989	−	0.217822i	$-0.930105\pi$
$769$	−45.8286	−	26.4592i	−1.65262	−	0.954142i	−0.676633	−	0.736320i	$-0.736562\pi$
$770$		0			0
$771$	20.9520	−	20.2488i	0.754567	−	0.729243i
$772$		0			0
$773$	−14.1328	−	24.4788i	−0.508322	−	0.880440i	−0.999954	−	0.00963659i	$-0.996933\pi$
$773$	−14.1328	−	24.4788i	−0.508322	−	0.880440i	0.491631	−	0.870803i	$-0.336401\pi$
$774$		0			0
$775$	2.06686	+	1.19330i	0.0742438	+	0.0428647i
$776$		0			0
$777$	19.4035	+	4.72799i	0.696098	+	0.169616i
$778$		0			0
$779$	18.9561	−	10.9443i	0.679174	−	0.392121i
$780$		0			0
$781$	4.37199	−	7.57251i	0.156442	−	0.270966i
$782$		0			0
$783$	−11.1615	−	3.61221i	−0.398878	−	0.129090i
$784$		0			0
$785$	12.7862	−	7.38211i	0.456359	−	0.263479i
$786$		0			0
$787$			11.4245i			0.407238i	0.979050	+	0.203619i	$0.0652705\pi$
$787$			11.4245i			0.407238i	−0.979050	+	0.203619i	$0.934730\pi$
$788$		0			0
$789$	12.9124	−	45.0969i	0.459693	−	1.60549i
$790$		0			0
$791$	3.12627	+	1.64247i	0.111157	+	0.0583995i
$792$		0			0
$793$	0.555605	−	0.962336i	0.0197301	−	0.0341735i
$794$		0			0
$795$	−12.1755	+	42.5232i	−0.431820	+	1.50814i
$796$		0			0
$797$	−2.29457	+	3.97432i	−0.0812780	+	0.140778i	−0.903799	−	0.427957i	$-0.859233\pi$
$797$	−2.29457	+	3.97432i	−0.0812780	+	0.140778i	0.822521	+	0.568735i	$0.192567\pi$
$798$		0			0
$799$	−0.361541	−	0.626207i	−0.0127904	−	0.0221536i
$800$		0			0
$801$	0.828703	−	24.2713i	0.0292808	−	0.857583i
$802$		0			0
$803$	17.7943			0.627948
$804$		0			0
$805$	−2.07914	−	1.09234i	−0.0732801	−	0.0384998i
$806$		0			0
$807$	−6.50924	+	6.29079i	−0.229136	+	0.221446i
$808$		0			0
$809$	12.1693	−	7.02597i	0.427851	−	0.247020i	−0.270579	−	0.962698i	$-0.587215\pi$
$809$	12.1693	−	7.02597i	0.427851	−	0.247020i	0.698431	+	0.715678i	$0.253882\pi$
$810$		0			0
$811$			33.6468i			1.18150i	0.806855	+	0.590749i	$0.201168\pi$
$811$			33.6468i			1.18150i	−0.806855	+	0.590749i	$0.798832\pi$
$812$		0			0
$813$	−5.87777	+	20.5283i	−0.206142	+	0.719958i
$814$		0			0
$815$	−43.3786			−1.51949
$816$		0			0
$817$		−	16.9332i		−	0.592416i
$818$		0			0
$819$	1.27640	−	0.00730819i	0.0446011	−	0.000255369i
$820$		0			0
$821$		−	48.3267i		−	1.68661i	−0.537433	−	0.843306i	$-0.680606\pi$
$821$		−	48.3267i		−	1.68661i	0.537433	−	0.843306i	$-0.319394\pi$
$822$		0			0
$823$	32.1328			1.12008			0.560040	−	0.828466i	$-0.310786\pi$
$823$	32.1328			1.12008			0.560040	+	0.828466i	$0.310786\pi$
$824$		0			0
$825$	5.69988	+	5.89781i	0.198444	+	0.205335i
$826$		0			0
$827$			4.51801i			0.157107i	0.996910	+	0.0785533i	$0.0250301\pi$
$827$			4.51801i			0.157107i	−0.996910	+	0.0785533i	$0.974970\pi$
$828$		0			0
$829$	33.6077	−	19.4034i	1.16724	−	0.673909i	0.214215	−	0.976787i	$-0.431281\pi$
$829$	33.6077	−	19.4034i	1.16724	−	0.673909i	0.953029	+	0.302878i	$0.0979475\pi$
$830$		0			0
$831$	36.0906	+	10.3336i	1.25197	+	0.358470i
$832$		0			0
$833$	−22.0745	−	32.0381i	−0.764836	−	1.11006i
$834$		0			0
$835$	−32.3940			−1.12104
$836$		0			0
$837$	−11.4839	+	10.3644i	−0.396942	+	0.358247i
$838$		0			0
$839$	8.38179	+	14.5177i	0.289372	+	0.501206i	0.973660	−	0.228005i	$-0.0732203\pi$
$839$	8.38179	+	14.5177i	0.289372	+	0.501206i	−0.684288	+	0.729212i	$0.739887\pi$
$840$		0			0
$841$	−11.9514	+	20.7004i	−0.412116	+	0.713806i
$842$		0			0
$843$	13.0632	+	13.5169i	0.449922	+	0.465546i
$844$		0			0
$845$	13.2919	−	23.0223i	0.457256	−	0.791990i
$846$		0			0
$847$	−33.7637	−	53.4429i	−1.16014	−	1.83632i
$848$		0			0
$849$	51.1075	−	12.7636i	1.75401	−	0.438046i
$850$		0			0
$851$		−	1.88808i		−	0.0647227i
$852$		0			0
$853$	14.0552	−	8.11477i	0.481241	−	0.277844i	−0.239693	−	0.970849i	$-0.577047\pi$
$853$	14.0552	−	8.11477i	0.481241	−	0.277844i	0.720933	+	0.693004i	$0.243713\pi$
$854$		0			0
$855$	13.4171	+	25.1867i	0.458856	+	0.861368i
$856$		0			0
$857$	23.3778	−	40.4915i	0.798570	−	1.38316i	−0.121978	−	0.992533i	$-0.538924\pi$
$857$	23.3778	−	40.4915i	0.798570	−	1.38316i	0.920547	−	0.390631i	$-0.127743\pi$
$858$		0			0
$859$	−7.64627	+	4.41457i	−0.260887	+	0.150623i	−0.624739	−	0.780833i	$-0.714795\pi$
$859$	−7.64627	+	4.41457i	−0.260887	+	0.150623i	0.363852	+	0.931457i	$0.381461\pi$
$860$		0			0
$861$	−20.9917	−	5.11497i	−0.715395	−	0.174318i
$862$		0			0
$863$	8.96721	+	5.17722i	0.305247	+	0.176235i	0.644798	−	0.764353i	$-0.276942\pi$
$863$	8.96721	+	5.17722i	0.305247	+	0.176235i	−0.339550	+	0.940588i	$0.610275\pi$
$864$		0			0
$865$	−23.1354	−	40.0716i	−0.786626	−	1.36248i
$866$		0			0
$867$	23.1327	+	6.62348i	0.785628	+	0.224945i
$868$		0			0
$869$	−88.9361	−	51.3473i	−3.01695	−	1.74184i
$870$		0			0
$871$	2.12969	+	1.22958i	0.0721619	+	0.0416627i
$872$		0			0
$873$	4.78746	−	7.67479i	0.162031	−	0.259752i
$874$		0			0
$875$	−31.4264	+	1.25319i	−1.06241	+	0.0423654i
$876$		0			0
$877$	−19.7407	−	34.1919i	−0.666597	−	1.15458i	−0.978850	−	0.204580i	$-0.934417\pi$
$877$	−19.7407	−	34.1919i	−0.666597	−	1.15458i	0.312253	−	0.949999i	$-0.398916\pi$
$878$		0			0
$879$	7.42628	+	2.12633i	0.250482	+	0.0717194i
$880$		0			0
$881$	−14.9886			−0.504980			−0.252490	−	0.967599i	$-0.581250\pi$
$881$	−14.9886			−0.504980			−0.252490	+	0.967599i	$0.581250\pi$
$882$		0			0
$883$	−0.888235			−0.0298915			−0.0149458	−	0.999888i	$-0.504758\pi$
$883$	−0.888235			−0.0298915			−0.0149458	+	0.999888i	$0.504758\pi$
$884$		0			0
$885$	−16.4552	+	15.9029i	−0.553134	+	0.534571i
$886$		0			0
$887$	−0.549031	−	0.950950i	−0.0184347	−	0.0319298i	0.856661	−	0.515880i	$-0.172535\pi$
$887$	−0.549031	−	0.950950i	−0.0184347	−	0.0319298i	−0.875096	+	0.483950i	$0.839202\pi$
$888$		0			0
$889$	1.89079	−	0.0753985i	0.0634149	−	0.00252878i
$890$		0			0
$891$	−47.7466	+	23.3794i	−1.59957	+	0.783240i
$892$		0			0
$893$	−0.523057	−	0.301987i	−0.0175034	−	0.0101056i
$894$		0			0
$895$	−16.1647	−	9.33268i	−0.540326	−	0.311957i
$896$		0			0
$897$	−0.0292389	−	0.117077i	−0.000976259	−	0.00390909i
$898$		0			0
$899$	−3.36070	−	5.82090i	−0.112086	−	0.194138i
$900$		0			0
$901$	59.9919	+	34.6364i	1.99862	+	1.15390i
$902$		0			0
$903$	−11.5465	+	12.0851i	−0.384243	+	0.402169i
$904$		0			0
$905$	13.4884	−	7.78751i	0.448369	−	0.258866i
$906$		0			0
$907$	12.9292	−	22.3940i	0.429307	−	0.743581i	−0.567505	−	0.823370i	$-0.692091\pi$
$907$	12.9292	−	22.3940i	0.429307	−	0.743581i	0.996812	+	0.0797889i	$0.0254246\pi$
$908$		0			0
$909$	−1.54948	+	45.3814i	−0.0513929	+	1.50521i
$910$		0			0
$911$	32.9640	−	19.0318i	1.09215	−	0.630551i	0.157999	−	0.987439i	$-0.449496\pi$
$911$	32.9640	−	19.0318i	1.09215	−	0.630551i	0.934147	+	0.356888i	$0.116162\pi$
$912$		0			0
$913$			90.0703i			2.98089i
$914$		0			0
$915$	−17.0419	−	17.6337i	−0.563386	−	0.582951i
$916$		0			0
$917$	25.8419	+	40.9038i	0.853374	+	1.35076i
$918$		0			0
$919$	−4.90995	+	8.50428i	−0.161964	+	0.280530i	−0.935573	−	0.353133i	$-0.885116\pi$
$919$	−4.90995	+	8.50428i	−0.161964	+	0.280530i	0.773609	+	0.633663i	$0.218450\pi$
$920$		0			0
$921$	15.8473	−	3.95772i	0.522188	−	0.130411i
$922$		0			0
$923$	−0.119024	+	0.206155i	−0.00391772	+	0.00678569i
$924$		0			0
$925$	−1.74685	−	3.02563i	−0.0574361	−	0.0994823i
$926$		0			0
$927$	17.0181	−	27.2818i	0.558949	−	0.896053i
$928$		0			0
$929$	−11.9943			−0.393520			−0.196760	−	0.980452i	$-0.563042\pi$
$929$	−11.9943			−0.393520			−0.196760	+	0.980452i	$0.563042\pi$
$930$		0			0
$931$	−29.3484	−	13.9563i	−0.961856	−	0.457399i
$932$		0			0
$933$	−2.92390	−	11.7077i	−0.0957241	−	0.383294i
$934$		0			0
$935$	−58.2592	+	33.6359i	−1.90528	+	1.10001i
$936$		0			0
$937$		−	36.5712i		−	1.19473i	−0.801970	−	0.597364i	$-0.796215\pi$
$937$		−	36.5712i		−	1.19473i	0.801970	−	0.597364i	$-0.203785\pi$
$938$		0			0
$939$	−11.1456	+	2.78350i	−0.363723	+	0.0908362i
$940$		0			0
$941$	24.0309			0.783385			0.391693	−	0.920096i	$-0.371890\pi$
$941$	24.0309			0.783385			0.391693	+	0.920096i	$0.371890\pi$
$942$		0			0
$943$			2.04262i			0.0665169i
$944$		0			0
$945$	7.59871	−	27.1246i	0.247186	−	0.882365i
$946$		0			0
$947$		−	9.06932i		−	0.294713i	−0.989083	−	0.147357i	$-0.952924\pi$
$947$		−	9.06932i		−	0.294713i	0.989083	−	0.147357i	$-0.0470765\pi$
$948$		0			0
$949$	−0.484436			−0.0157255
$950$		0			0
$951$	−25.2801	+	6.31346i	−0.819763	+	0.204728i
$952$		0			0
$953$			26.8728i			0.870495i	0.900311	+	0.435247i	$0.143339\pi$
$953$			26.8728i			0.870495i	−0.900311	+	0.435247i	$0.856661\pi$
$954$		0			0
$955$	18.3510	−	10.5949i	0.593824	−	0.342845i
$956$		0			0
$957$	−5.59693	−	22.4110i	−0.180923	−	0.724444i
$958$		0			0
$959$	−7.15217	−	3.75759i	−0.230956	−	0.121339i
$960$		0			0
$961$	22.1370			0.714096
$962$		0			0
$963$	−28.3573	−	0.968213i	−0.913800	−	0.0312002i
$964$		0			0
$965$	11.5940	+	20.0815i	0.373225	+	0.646445i
$966$		0			0
$967$	0.193927	−	0.335892i	0.00623628	−	0.0108015i	−0.862890	−	0.505391i	$-0.831348\pi$
$967$	0.193927	−	0.335892i	0.00623628	−	0.0108015i	0.869127	+	0.494590i	$0.164682\pi$
$968$		0			0
$969$	43.3615	−	10.8291i	1.39297	−	0.347882i
$970$		0			0
$971$	−12.5732	+	21.7775i	−0.403494	+	0.698872i	−0.994145	−	0.108055i	$-0.965538\pi$
$971$	−12.5732	+	21.7775i	−0.403494	+	0.698872i	0.590651	+	0.806927i	$0.298871\pi$
$972$		0			0
$973$	34.1788	+	17.9568i	1.09572	+	0.575669i
$974$		0			0
$975$	−0.155175	−	0.160563i	−0.00496956	−	0.00514214i
$976$		0			0
$977$		−	11.9971i		−	0.383823i	−0.981412	−	0.191911i	$-0.938531\pi$
$977$		−	11.9971i		−	0.383823i	0.981412	−	0.191911i	$-0.0614686\pi$
$978$		0			0
$979$	41.4118	−	23.9091i	1.32353	−	0.764138i
$980$		0			0
$981$	36.5549	+	22.8026i	1.16711	+	0.728032i
$982$		0			0
$983$	−17.7390	+	30.7249i	−0.565787	+	0.979972i	0.431189	+	0.902262i	$0.358094\pi$
$983$	−17.7390	+	30.7249i	−0.565787	+	0.979972i	−0.996976	+	0.0777106i	$0.975239\pi$
$984$		0			0
$985$	39.2179	−	22.6425i	1.24959	−	0.721449i
$986$		0			0
$987$	0.167384	+	0.572192i	0.00532788	+	0.0182131i
$988$		0			0
$989$	1.36848	+	0.790091i	0.0435151	+	0.0251234i
$990$		0			0
$991$	4.77487	+	8.27032i	0.151679	+	0.262715i	0.931845	−	0.362857i	$-0.118199\pi$
$991$	4.77487	+	8.27032i	0.151679	+	0.262715i	−0.780166	+	0.625573i	$0.784865\pi$
$992$		0			0
$993$	12.7161	+	50.9175i	0.403535	+	1.61582i
$994$		0			0
$995$	25.8610	+	14.9309i	0.819849	+	0.473340i
$996$		0			0
$997$	−22.6750	−	13.0914i	−0.718124	−	0.414609i	0.0959378	−	0.995387i	$-0.469415\pi$
$997$	−22.6750	−	13.0914i	−0.718124	−	0.414609i	−0.814062	+	0.580778i	$0.802748\pi$
$998$		0			0
$999$	22.1449	−	4.73402i	0.700635	−	0.149778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bs.a.257.11	✓	48
3.2	odd	2		1512.2.bs.a.1097.8		48
4.3	odd	2		1008.2.ca.e.257.14		48
7.3	odd	6		504.2.cx.a.185.19	yes	48
9.2	odd	6		504.2.cx.a.425.19	yes	48
9.7	even	3		1512.2.cx.a.89.8		48
12.11	even	2		3024.2.ca.e.2609.8		48
21.17	even	6		1512.2.cx.a.17.8		48
28.3	even	6		1008.2.df.e.689.6		48
36.7	odd	6		3024.2.df.e.1601.8		48
36.11	even	6		1008.2.df.e.929.6		48
63.38	even	6	inner	504.2.bs.a.353.11	yes	48
63.52	odd	6		1512.2.bs.a.521.8		48
84.59	odd	6		3024.2.df.e.17.8		48
252.115	even	6		3024.2.ca.e.2033.8		48
252.227	odd	6		1008.2.ca.e.353.14		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.11	✓	48	1.1	even	1	trivial
504.2.bs.a.353.11	yes	48	63.38	even	6	inner
504.2.cx.a.185.19	yes	48	7.3	odd	6
504.2.cx.a.425.19	yes	48	9.2	odd	6
1008.2.ca.e.257.14		48	4.3	odd	2
1008.2.ca.e.353.14		48	252.227	odd	6
1008.2.df.e.689.6		48	28.3	even	6
1008.2.df.e.929.6		48	36.11	even	6
1512.2.bs.a.521.8		48	63.52	odd	6
1512.2.bs.a.1097.8		48	3.2	odd	2
1512.2.cx.a.17.8		48	21.17	even	6
1512.2.cx.a.89.8		48	9.7	even	3
3024.2.ca.e.2033.8		48	252.115	even	6
3024.2.ca.e.2609.8		48	12.11	even	2
3024.2.df.e.17.8		48	84.59	odd	6
3024.2.df.e.1601.8		48	36.7	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.419673 - 1.68044i) q^{3} +(1.02449 + 1.77447i) q^{5} +(-2.64365 + 0.105420i) q^{7} +(-2.64775 + 1.41047i) q^{9} +O(q^{10})\)	\(q+(-0.419673 - 1.68044i) q^{3} +(1.02449 + 1.77447i) q^{5} +(-2.64365 + 0.105420i) q^{7} +(-2.64775 + 1.41047i) q^{9} +(-5.11564 - 2.95352i) q^{11} +(0.139269 + 0.0804071i) q^{13} +(2.55194 - 2.46630i) q^{15} +(-2.77904 - 4.81345i) q^{17} +(-4.02056 - 2.32127i) q^{19} +(1.28662 + 4.39825i) q^{21} +(0.375194 - 0.216618i) q^{23} +(0.400830 - 0.694257i) q^{25} +(3.48140 + 3.85744i) q^{27} +(-1.95524 + 1.12886i) q^{29} +2.97708i q^{31} +(-2.81630 + 9.83603i) q^{33} +(-2.89547 - 4.58308i) q^{35} +(2.17904 - 3.77422i) q^{37} +(0.0766716 - 0.267778i) q^{39} +(-2.35740 + 4.08313i) q^{41} +(1.82369 + 3.15873i) q^{43} +(-5.21544 - 3.25334i) q^{45} +0.130095 q^{47} +(6.97777 - 0.557389i) q^{49} +(-6.92241 + 6.69009i) q^{51} +(-10.7936 + 6.23170i) q^{53} -12.1034i q^{55} +(-2.21343 + 7.73049i) q^{57} -6.44809 q^{59} -6.90990i q^{61} +(6.85103 - 4.00792i) q^{63} +0.329506i q^{65} +15.2919 q^{67} +(-0.521473 - 0.539582i) q^{69} +1.48027i q^{71} +(-2.60881 + 1.50620i) q^{73} +(-1.33487 - 0.382208i) q^{75} +(13.8353 + 7.26877i) q^{77} +17.3851 q^{79} +(5.02114 - 7.46914i) q^{81} +(-7.62399 - 13.2051i) q^{83} +(5.69422 - 9.86268i) q^{85} +(2.71754 + 2.81191i) q^{87} +(-4.04757 + 7.01059i) q^{89} +(-0.376655 - 0.197886i) q^{91} +(5.00280 - 1.24940i) q^{93} -9.51251i q^{95} +(-2.61123 + 1.50759i) q^{97} +(17.7108 + 0.604706i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9}+O(q^{10}) \) 48 * q - 4 * q^9	\( 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75} - 36 q^{77} - 12 q^{79} - 24 q^{87} + 18 q^{89} + 6 q^{91} + 16 q^{93} - 64 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Introduction

L-functions

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