LMFDB - Embedded newform 441.2.w.a.251.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(62,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 11]))

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

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

chi := DirichletCharacter("441.62");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.w (of order $14$, degree $6$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			251.5
Character	$\chi$	$=$	441.251
Dual form			441.2.w.a.188.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.42590 - 1.13712i) q^{2} +(0.295114 + 1.29298i) q^{4} +(0.0720329 + 0.0346892i) q^{5} +(2.51149 - 0.832121i) q^{7} +(-0.533164 + 1.10713i) q^{8} +O(q^{10})$	\(q+(-1.42590 - 1.13712i) q^{2} +(0.295114 + 1.29298i) q^{4} +(0.0720329 + 0.0346892i) q^{5} +(2.51149 - 0.832121i) q^{7} +(-0.533164 + 1.10713i) q^{8} +(-0.0632661 - 0.131373i) q^{10} +(0.0489389 + 0.0390274i) q^{11} +(3.06781 + 2.44650i) q^{13} +(-4.52735 - 1.66934i) q^{14} +(4.40896 - 2.12324i) q^{16} +(0.399548 - 1.75053i) q^{17} +5.46553i q^{19} +(-0.0235945 + 0.103374i) q^{20} +(-0.0254032 - 0.111299i) q^{22} +(4.14363 - 0.945756i) q^{23} +(-3.11346 - 3.90416i) q^{25} +(-1.59244 - 6.97692i) q^{26} +(1.81709 + 3.00173i) q^{28} +(8.80774 + 2.01031i) q^{29} -6.38885i q^{31} +(-6.30510 - 1.43910i) q^{32} +(-2.56028 + 2.04175i) q^{34} +(0.209775 + 0.0271815i) q^{35} +(0.385319 - 1.68819i) q^{37} +(6.21495 - 7.79331i) q^{38} +(-0.0768107 + 0.0612545i) q^{40} +(-6.08257 - 2.92921i) q^{41} +(1.79918 - 0.866440i) q^{43} +(-0.0360191 + 0.0747945i) q^{44} +(-6.98384 - 3.36324i) q^{46} +(2.99901 - 3.76064i) q^{47} +(5.61515 - 4.17972i) q^{49} +9.10732i q^{50} +(-2.25792 + 4.68861i) q^{52} +(-0.0985022 + 0.0224825i) q^{53} +(0.00217138 + 0.00450891i) q^{55} +(-0.417772 + 3.22419i) q^{56} +(-10.2730 - 12.8819i) q^{58} +(3.52530 - 1.69769i) q^{59} +(-3.20273 - 0.731001i) q^{61} +(-7.26488 + 9.10987i) q^{62} +(1.25183 + 1.56975i) q^{64} +(0.136116 + 0.282648i) q^{65} -13.0206 q^{67} +2.38132 q^{68} +(-0.268210 - 0.277298i) q^{70} +(2.96758 - 0.677330i) q^{71} +(0.291084 - 0.232132i) q^{73} +(-2.46910 + 1.96904i) q^{74} +(-7.06682 + 1.61296i) q^{76} +(0.155385 + 0.0572939i) q^{77} +10.2856 q^{79} +0.391244 q^{80} +(5.34228 + 11.0934i) q^{82} +(10.5324 + 13.2072i) q^{83} +(0.0895053 - 0.112236i) q^{85} +(-3.55070 - 0.810424i) q^{86} +(-0.0693007 + 0.0333735i) q^{88} +(-3.24641 - 4.07086i) q^{89} +(9.74055 + 3.59156i) q^{91} +(2.44569 + 5.07852i) q^{92} +(-8.55259 + 1.95207i) q^{94} +(-0.189595 + 0.393698i) q^{95} +13.6406i q^{97} +(-12.7595 - 0.425217i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 24 q^{4}+O(q^{10}) $ 120 * q + 24 * q^4	$ 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) $ 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{9}{14}\right)$	$-1$

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 $

$2$	−1.42590	−	1.13712i	−1.00826	−	0.804064i	−0.0275717	−	0.999620i	$-0.508777\pi$
$2$	−1.42590	−	1.13712i	−1.00826	−	0.804064i	−0.980693	+	0.195556i	$0.937349\pi$
$3$		0			0
$3$		0			0
$4$	0.295114	+	1.29298i	0.147557	+	0.646490i
$5$	0.0720329	+	0.0346892i	0.0322141	+	0.0155135i	0.449921	−	0.893068i	$-0.351452\pi$
$5$	0.0720329	+	0.0346892i	0.0322141	+	0.0155135i	−0.417707	+	0.908582i	$0.637166\pi$
$6$		0			0
$7$	2.51149	−	0.832121i	0.949253	−	0.314512i
$7$	2.51149	−	0.832121i	0.949253	−	0.314512i
$8$	−0.533164	+	1.10713i	−0.188502	+	0.391428i
$9$		0			0
$10$	−0.0632661	−	0.131373i	−0.0200065	−	0.0415439i
$11$	0.0489389	+	0.0390274i	0.0147556	+	0.0117672i	0.630840	−	0.775913i	$-0.282710\pi$
$11$	0.0489389	+	0.0390274i	0.0147556	+	0.0117672i	−0.616084	+	0.787680i	$0.711282\pi$
$12$		0			0
$13$	3.06781	+	2.44650i	0.850857	+	0.678536i	0.948532	−	0.316682i	$-0.102569\pi$
$13$	3.06781	+	2.44650i	0.850857	+	0.678536i	−0.0976743	+	0.995218i	$0.531140\pi$
$14$	−4.52735	−	1.66934i	−1.20999	−	0.446149i
$15$		0			0
$16$	4.40896	−	2.12324i	1.10224	−	0.530810i
$17$	0.399548	−	1.75053i	0.0969046	−	0.424567i	−0.903083	−	0.429465i	$-0.858702\pi$
$17$	0.399548	−	1.75053i	0.0969046	−	0.424567i	0.999988	+	0.00489839i	$0.00155921\pi$
$18$		0			0
$19$			5.46553i			1.25388i	0.779068	+	0.626939i	$0.215693\pi$
$19$			5.46553i			1.25388i	−0.779068	+	0.626939i	$0.784307\pi$
$20$	−0.0235945	+	0.103374i	−0.00527590	+	0.0231152i
$21$		0			0
$22$	−0.0254032	−	0.111299i	−0.00541597	−	0.0237289i
$23$	4.14363	−	0.945756i	0.864006	−	0.197204i	0.232520	−	0.972592i	$-0.425303\pi$
$23$	4.14363	−	0.945756i	0.864006	−	0.197204i	0.631485	+	0.775388i	$0.282446\pi$
$24$		0			0
$25$	−3.11346	−	3.90416i	−0.622693	−	0.780832i
$26$	−1.59244	−	6.97692i	−0.312303	−	1.36829i
$27$		0			0
$28$	1.81709	+	3.00173i	0.343398	+	0.567274i
$29$	8.80774	+	2.01031i	1.63556	+	0.373305i	0.938924	−	0.344124i	$-0.111824\pi$
$29$	8.80774	+	2.01031i	1.63556	+	0.373305i	0.696632	+	0.717429i	$0.254681\pi$
$30$		0			0
$31$		−	6.38885i		−	1.14747i	−0.819040	−	0.573736i	$-0.805494\pi$
$31$		−	6.38885i		−	1.14747i	0.819040	−	0.573736i	$-0.194506\pi$
$32$	−6.30510	−	1.43910i	−1.11459	−	0.254399i
$33$		0			0
$34$	−2.56028	+	2.04175i	−0.439084	+	0.350158i
$35$	0.209775	+	0.0271815i	0.0354585	+	0.00459451i
$36$		0			0
$37$	0.385319	−	1.68819i	0.0633461	−	0.277537i	−0.933328	−	0.359024i	$-0.883110\pi$
$37$	0.385319	−	1.68819i	0.0633461	−	0.277537i	0.996674	+	0.0814866i	$0.0259668\pi$
$38$	6.21495	−	7.79331i	1.00820	−	1.26424i
$39$		0			0
$40$	−0.0768107	+	0.0612545i	−0.0121448	+	0.00968518i
$41$	−6.08257	−	2.92921i	−0.949938	−	0.457466i	−0.106274	−	0.994337i	$-0.533892\pi$
$41$	−6.08257	−	2.92921i	−0.949938	−	0.457466i	−0.843664	+	0.536871i	$0.819606\pi$
$42$		0			0
$43$	1.79918	−	0.866440i	0.274373	−	0.132131i	−0.291638	−	0.956529i	$-0.594200\pi$
$43$	1.79918	−	0.866440i	0.274373	−	0.132131i	0.566011	+	0.824398i	$0.308486\pi$
$44$	−0.0360191	+	0.0747945i	−0.00543009	+	0.0112757i
$45$		0			0
$46$	−6.98384	−	3.36324i	−1.02971	−	0.495882i
$47$	2.99901	−	3.76064i	0.437451	−	0.548546i	−0.513419	−	0.858138i	$-0.671621\pi$
$47$	2.99901	−	3.76064i	0.437451	−	0.548546i	0.950869	+	0.309592i	$0.100193\pi$
$48$		0			0
$49$	5.61515	−	4.17972i	0.802164	−	0.597103i
$50$			9.10732i			1.28797i
$51$		0			0
$52$	−2.25792	+	4.68861i	−0.313117	+	0.650193i
$53$	−0.0985022	+	0.0224825i	−0.0135303	+	0.00308821i	−0.229281	−	0.973360i	$-0.573637\pi$
$53$	−0.0985022	+	0.0224825i	−0.0135303	+	0.00308821i	0.215750	+	0.976449i	$0.430780\pi$
$54$		0			0
$55$	0.00217138	+	0.00450891i	0.000292788	+	0.000607981i
$56$	−0.417772	+	3.22419i	−0.0558272	+	0.430851i
$57$		0			0
$58$	−10.2730	−	12.8819i	−1.34891	−	1.69148i
$59$	3.52530	−	1.69769i	0.458955	−	0.221021i	−0.190097	−	0.981765i	$-0.560880\pi$
$59$	3.52530	−	1.69769i	0.458955	−	0.221021i	0.649052	+	0.760744i	$0.275166\pi$
$60$		0			0
$61$	−3.20273	−	0.731001i	−0.410067	−	0.0935951i	0.0125108	−	0.999922i	$-0.496018\pi$
$61$	−3.20273	−	0.731001i	−0.410067	−	0.0935951i	−0.422578	+	0.906327i	$0.638875\pi$
$62$	−7.26488	+	9.10987i	−0.922641	+	1.15695i
$63$		0			0
$64$	1.25183	+	1.56975i	0.156479	+	0.196219i
$65$	0.136116	+	0.282648i	0.0168831	+	0.0350582i
$66$		0			0
$67$	−13.0206			−1.59072			−0.795361	−	0.606135i	$-0.792719\pi$
$67$	−13.0206			−1.59072			−0.795361	+	0.606135i	$0.792719\pi$
$68$	2.38132			0.288777
$69$		0			0
$70$	−0.268210	−	0.277298i	−0.0320573	−	0.0331434i
$71$	2.96758	−	0.677330i	0.352187	−	0.0803843i	−0.0427678	−	0.999085i	$-0.513618\pi$
$71$	2.96758	−	0.677330i	0.352187	−	0.0803843i	0.394954	+	0.918701i	$0.370760\pi$
$72$		0			0
$73$	0.291084	−	0.232132i	0.0340688	−	0.0271690i	−0.606307	−	0.795230i	$-0.707350\pi$
$73$	0.291084	−	0.232132i	0.0340688	−	0.0271690i	0.640376	+	0.768061i	$0.278778\pi$
$74$	−2.46910	+	1.96904i	−0.287027	+	0.228897i
$75$		0			0
$76$	−7.06682	+	1.61296i	−0.810620	+	0.185019i
$77$	0.155385	+	0.0572939i	0.0177078	+	0.00652925i
$78$		0			0
$79$	10.2856			1.15722			0.578609	−	0.815605i	$-0.303596\pi$
$79$	10.2856			1.15722			0.578609	+	0.815605i	$0.303596\pi$
$80$	0.391244			0.0437424
$81$		0			0
$82$	5.34228	+	11.0934i	0.589957	+	1.22506i
$83$	10.5324	+	13.2072i	1.15608	+	1.44968i	0.871074	+	0.491153i	$0.163424\pi$
$83$	10.5324	+	13.2072i	1.15608	+	1.44968i	0.285006	+	0.958526i	$0.408004\pi$
$84$		0			0
$85$	0.0895053	−	0.112236i	0.00970821	−	0.0121737i
$86$	−3.55070	−	0.810424i	−0.382882	−	0.0873903i
$87$		0			0
$88$	−0.0693007	+	0.0333735i	−0.00738748	+	0.00355762i
$89$	−3.24641	−	4.07086i	−0.344118	−	0.431511i	0.579413	−	0.815034i	$-0.303282\pi$
$89$	−3.24641	−	4.07086i	−0.344118	−	0.431511i	−0.923531	+	0.383523i	$0.874711\pi$
$90$		0			0
$91$	9.74055	+	3.59156i	1.02109	+	0.376498i
$92$	2.44569	+	5.07852i	0.254980	+	0.529472i
$93$		0			0
$94$	−8.55259	+	1.95207i	−0.882132	+	0.201341i
$95$	−0.189595	+	0.393698i	−0.0194520	+	0.0403926i
$96$		0			0
$97$			13.6406i			1.38499i	0.721422	+	0.692496i	$0.243489\pi$
$97$			13.6406i			1.38499i	−0.721422	+	0.692496i	$0.756511\pi$
$98$	−12.7595	−	0.425217i	−1.28890	−	0.0429534i
$99$		0			0
$100$	4.12917	−	5.17782i	0.412917	−	0.517782i
$101$	14.6900	+	7.07432i	1.46171	+	0.703921i	0.984584	−	0.174915i	$-0.0559650\pi$
$101$	14.6900	+	7.07432i	1.46171	+	0.703921i	0.477124	+	0.878836i	$0.341679\pi$
$102$		0			0
$103$	−6.01021	+	12.4803i	−0.592204	+	1.22972i	0.362449	+	0.932004i	$0.381941\pi$
$103$	−6.01021	+	12.4803i	−0.592204	+	1.22972i	−0.954653	+	0.297720i	$0.903774\pi$
$104$	−4.34422	+	2.09207i	−0.425986	+	0.205144i
$105$		0			0
$106$	0.166020	+	0.0799508i	0.0161252	+	0.00776551i
$107$	−4.53315	+	3.61507i	−0.438236	+	0.349482i	−0.817620	−	0.575758i	$-0.804707\pi$
$107$	−4.53315	+	3.61507i	−0.438236	+	0.349482i	0.379384	+	0.925239i	$0.376136\pi$
$108$		0			0
$109$	−1.20144	+	1.50656i	−0.115077	+	0.144302i	−0.836034	−	0.548678i	$-0.815131\pi$
$109$	−1.20144	+	1.50656i	−0.115077	+	0.144302i	0.720957	+	0.692980i	$0.243703\pi$
$110$	0.00203100	−	0.00889837i	0.000193648	−	0.000848427i
$111$		0			0
$112$	9.30625	−	9.00128i	0.879358	−	0.850541i
$113$	−4.97507	+	3.96749i	−0.468015	+	0.373230i	−0.828915	−	0.559375i	$-0.811041\pi$
$113$	−4.97507	+	3.96749i	−0.468015	+	0.373230i	0.360900	+	0.932605i	$0.382470\pi$
$114$		0			0
$115$	0.331285	+	0.0756136i	0.0308925	+	0.00705101i
$116$			11.9815i			1.11245i
$117$		0			0
$118$	−6.95721	−	1.58794i	−0.640463	−	0.146181i
$119$	−0.453195	−	4.72892i	−0.0415444	−	0.433499i
$120$		0			0
$121$	−2.44686	−	10.7204i	−0.222442	−	0.974581i
$122$	3.73554	+	4.68421i	0.338200	+	0.424089i
$123$		0			0
$124$	8.26066	−	1.88544i	0.741829	−	0.169318i
$125$	−0.177793	−	0.778961i	−0.0159023	−	0.0696724i
$126$		0			0
$127$	−2.40561	+	10.5397i	−0.213463	+	0.935244i	0.748730	+	0.662876i	$0.230664\pi$
$127$	−2.40561	+	10.5397i	−0.213463	+	0.935244i	−0.962193	+	0.272369i	$0.912193\pi$
$128$			9.27270i			0.819598i
$129$		0			0
$130$	0.127316	−	0.557808i	0.0111664	−	0.0489230i
$131$	−2.76634	+	1.33220i	−0.241697	+	0.116395i	−0.550811	−	0.834630i	$-0.685682\pi$
$131$	−2.76634	+	1.33220i	−0.241697	+	0.116395i	0.309115	+	0.951025i	$0.399967\pi$
$132$		0			0
$133$	4.54798	+	13.7266i	0.394360	+	1.19025i
$134$	18.5661	+	14.8060i	1.60387	+	1.27904i
$135$		0			0
$136$	1.72504	+	1.37567i	0.147921	+	0.117963i
$137$	−0.739039	−	1.53463i	−0.0631404	−	0.131112i	0.867011	−	0.498290i	$-0.166038\pi$
$137$	−0.739039	−	1.53463i	−0.0631404	−	0.131112i	−0.930151	+	0.367178i	$0.880324\pi$
$138$		0			0
$139$	−4.50183	+	9.34815i	−0.381840	+	0.792900i	0.618136	+	0.786071i	$0.287888\pi$
$139$	−4.50183	+	9.34815i	−0.381840	+	0.792900i	−0.999977	+	0.00682869i	$0.997826\pi$
$140$	0.0267626	+	0.279257i	0.00226185	+	0.0236015i
$141$		0			0
$142$	−5.00167	−	2.40868i	−0.419731	−	0.202132i
$143$	0.0546546	+	0.239458i	0.00457045	+	0.0200244i
$144$		0			0
$145$	0.564711	+	0.450342i	0.0468967	+	0.0373989i
$146$	−0.679018			−0.0561959
$147$		0			0
$148$	2.29651			0.188772
$149$	−15.6797	−	12.5041i	−1.28453	−	1.02438i	−0.997795	−	0.0663657i	$-0.978860\pi$
$149$	−15.6797	−	12.5041i	−1.28453	−	1.02438i	−0.286732	−	0.958011i	$-0.592569\pi$
$150$		0			0
$151$	−2.43375	−	10.6629i	−0.198056	−	0.867738i	−0.972093	−	0.234598i	$-0.924623\pi$
$151$	−2.43375	−	10.6629i	−0.198056	−	0.867738i	0.774037	−	0.633140i	$-0.218234\pi$
$152$	−6.05103	−	2.91402i	−0.490803	−	0.236358i
$153$		0			0
$154$	−0.156414	−	0.258386i	−0.0126042	−	0.0208214i
$155$	0.221624	−	0.460208i	0.0178013	−	0.0369648i
$156$		0			0
$157$	2.34186	+	4.86291i	0.186900	+	0.388103i	0.973273	−	0.229649i	$-0.0737579\pi$
$157$	2.34186	+	4.86291i	0.186900	+	0.388103i	−0.786373	+	0.617752i	$0.788044\pi$
$158$	−14.6662	−	11.6959i	−1.16678	−	0.930476i
$159$		0			0
$160$	−0.404253	−	0.322381i	−0.0319590	−	0.0254865i
$161$	9.61969	−	5.82325i	0.758137	−	0.458936i
$162$		0			0
$163$	1.10485	−	0.532066i	0.0865382	−	0.0416746i	−0.390114	−	0.920767i	$-0.627564\pi$
$163$	1.10485	−	0.532066i	0.0865382	−	0.0416746i	0.476652	+	0.879092i	$0.341850\pi$
$164$	1.99236	−	8.72909i	0.155577	−	0.681628i
$165$		0			0
$166$		−	30.8087i		−	2.39122i
$167$	−4.81868	+	21.1120i	−0.372881	+	1.63370i	0.345764	+	0.938321i	$0.387620\pi$
$167$	−4.81868	+	21.1120i	−0.372881	+	1.63370i	−0.718645	+	0.695377i	$0.755237\pi$
$168$		0			0
$169$	0.533339	+	2.33671i	0.0410260	+	0.179747i
$170$	−0.255251	+	0.0582594i	−0.0195769	+	0.00446829i
$171$		0			0
$172$	1.65125	+	2.07061i	0.125907	+	0.157882i
$173$	−3.33599	−	14.6159i	−0.253630	−	1.11123i	−0.927926	−	0.372765i	$-0.878410\pi$
$173$	−3.33599	−	14.6159i	−0.253630	−	1.11123i	0.674295	−	0.738462i	$-0.264447\pi$
$174$		0			0
$175$	−11.0682	−	7.21448i	−0.836674	−	0.545363i
$176$	0.298634	+	0.0681613i	0.0225104	+	0.00513785i
$177$		0			0
$178$			9.49620i			0.711770i
$179$	−3.72363	−	0.849895i	−0.278317	−	0.0635241i	0.0810837	−	0.996707i	$-0.474162\pi$
$179$	−3.72363	−	0.849895i	−0.278317	−	0.0635241i	−0.359401	+	0.933183i	$0.617019\pi$
$180$		0			0
$181$	14.2509	−	11.3647i	1.05926	−	0.844730i	0.0709924	−	0.997477i	$-0.477383\pi$
$181$	14.2509	−	11.3647i	1.05926	−	0.844730i	0.988265	+	0.152747i	$0.0488120\pi$
$182$	−9.80503	−	16.1974i	−0.726797	−	1.20063i
$183$		0			0
$184$	−1.16216	+	5.09176i	−0.0856756	+	0.375369i
$185$	0.0863178	−	0.108239i	0.00634621	−	0.00795790i
$186$		0			0
$187$	0.0878723	−	0.0700758i	0.00642586	−	0.00512445i
$188$	5.74749	+	2.76784i	0.419178	+	0.201866i
$189$		0			0
$190$	0.718025	−	0.345783i	0.0520910	−	0.0250857i
$191$	−2.12895	+	4.42080i	−0.154045	+	0.319878i	−0.963682	−	0.267054i	$-0.913950\pi$
$191$	−2.12895	+	4.42080i	−0.154045	+	0.319878i	0.809637	+	0.586932i	$0.199664\pi$
$192$		0			0
$193$	−0.0963446	−	0.0463971i	−0.00693503	−	0.00333974i	0.430413	−	0.902632i	$-0.358368\pi$
$193$	−0.0963446	−	0.0463971i	−0.00693503	−	0.00333974i	−0.437348	+	0.899292i	$0.644082\pi$
$194$	15.5110	−	19.4501i	1.11362	−	1.39644i
$195$		0			0
$196$	7.06141	+	6.02678i	0.504386	+	0.430484i
$197$		−	27.0265i		−	1.92556i	−0.270294	−	0.962778i	$-0.587121\pi$
$197$		−	27.0265i		−	1.92556i	0.270294	−	0.962778i	$-0.412879\pi$
$198$		0			0
$199$	−3.33989	+	6.93534i	−0.236758	+	0.491633i	−0.985166	−	0.171606i	$-0.945104\pi$
$199$	−3.33989	+	6.93534i	−0.236758	+	0.491633i	0.748408	+	0.663239i	$0.230819\pi$
$200$	5.98238	−	1.36544i	0.423018	−	0.0965512i
$201$		0			0
$202$	−12.9021	−	26.7915i	−0.907790	−	1.88504i
$203$	23.7934	−	2.28023i	1.66997	−	0.160041i
$204$		0			0
$205$	−0.336533	−	0.421999i	−0.0235045	−	0.0294737i
$206$	22.7616	−	10.9614i	1.58587	−	0.763717i
$207$		0			0
$208$	18.7203	+	4.27280i	1.29802	+	0.296265i
$209$	−0.213306	+	0.267477i	−0.0147547	+	0.0185018i
$210$		0			0
$211$	−10.5551	−	13.2356i	−0.726641	−	0.911179i	0.272052	−	0.962283i	$-0.412298\pi$
$211$	−10.5551	−	13.2356i	−0.726641	−	0.911179i	−0.998693	+	0.0511032i	$0.983726\pi$
$212$	−0.0581388	−	0.120726i	−0.00399299	−	0.00829152i
$213$		0			0
$214$	10.5746			0.722863
$215$	0.159656			0.0108885
$216$		0			0
$217$	−5.31630	−	16.0455i	−0.360894	−	1.08924i
$218$	3.42627	−	0.782023i	0.232056	−	0.0529653i
$219$		0			0
$220$	−0.00518913	+	0.00413819i	−0.000349851	+	0.000278997i
$221$	5.50841	−	4.39281i	0.370536	−	0.295493i
$222$		0			0
$223$	−18.1221	+	4.13624i	−1.21354	+	0.276983i	−0.780943	−	0.624602i	$-0.785261\pi$
$223$	−18.1221	+	4.13624i	−1.21354	+	0.276983i	−0.432600	+	0.901586i	$0.642404\pi$
$224$	−17.0327	+	1.63233i	−1.13804	+	0.109064i
$225$		0			0
$226$	11.6055			0.771983
$227$	−10.6354			−0.705899			−0.352950	−	0.935642i	$-0.614821\pi$
$227$	−10.6354			−0.705899			−0.352950	+	0.935642i	$0.614821\pi$
$228$		0			0
$229$	6.60218	+	13.7096i	0.436285	+	0.905954i	0.996960	+	0.0779185i	$0.0248274\pi$
$229$	6.60218	+	13.7096i	0.436285	+	0.905954i	−0.560675	+	0.828036i	$0.689458\pi$
$230$	−0.386398	−	0.484528i	−0.0254783	−	0.0319488i
$231$		0			0
$232$	−6.92163	+	8.67945i	−0.454427	+	0.569834i
$233$	−27.6145	−	6.30283i	−1.80908	−	0.412912i	−0.821527	−	0.570169i	$-0.806878\pi$
$233$	−27.6145	−	6.30283i	−1.80908	−	0.412912i	−0.987558	+	0.157258i	$0.949735\pi$
$234$		0			0
$235$	0.346481	−	0.166857i	0.0226019	−	0.0108845i
$236$	3.23545	+	4.05713i	0.210610	+	0.264096i
$237$		0			0
$238$	−4.73113	+	7.25831i	−0.306673	+	0.470486i
$239$	−4.08821	−	8.48926i	−0.264444	−	0.549125i	0.725892	−	0.687808i	$-0.241427\pi$
$239$	−4.08821	−	8.48926i	−0.264444	−	0.549125i	−0.990337	+	0.138684i	$0.955713\pi$
$240$		0			0
$241$	17.7669	−	4.05517i	1.14446	−	0.261216i	0.392074	−	0.919934i	$-0.371758\pi$
$241$	17.7669	−	4.05517i	1.14446	−	0.261216i	0.752390	+	0.658717i	$0.228901\pi$
$242$	−8.70137	+	18.0686i	−0.559345	+	1.16149i
$243$		0			0
$244$		−	4.35679i		−	0.278915i
$245$	0.549467	−	0.106292i	0.0351042	−	0.00679078i
$246$		0			0
$247$	−13.3714	+	16.7672i	−0.850802	+	1.06687i
$248$	7.07326	+	3.40630i	0.449153	+	0.216301i
$249$		0			0
$250$	−0.632256	+	1.31289i	−0.0399874	+	0.0830347i
$251$	18.9959	−	9.14794i	1.19901	−	0.577413i	0.275617	−	0.961268i	$-0.411118\pi$
$251$	18.9959	−	9.14794i	1.19901	−	0.577413i	0.923393	+	0.383855i	$0.125404\pi$
$252$		0			0
$253$	0.239695	+	0.115431i	0.0150695	+	0.00725708i
$254$	15.4150	−	12.2931i	0.967224	−	0.771335i
$255$		0			0
$256$	13.0478	−	16.3614i	0.815489	−	1.02259i
$257$	−4.03415	+	17.6748i	−0.251644	+	1.10252i	0.678290	+	0.734794i	$0.262721\pi$
$257$	−4.03415	+	17.6748i	−0.251644	+	1.10252i	−0.929933	+	0.367728i	$0.880136\pi$
$258$		0			0
$259$	−0.437056	−	4.56051i	−0.0271574	−	0.283376i
$260$	−0.325289	+	0.259409i	−0.0201735	+	0.0160879i
$261$		0			0
$262$	5.45940	+	1.24607i	0.337283	+	0.0769826i
$263$			19.8437i			1.22361i	0.791007	+	0.611807i	$0.209557\pi$
$263$			19.8437i			1.22361i	−0.791007	+	0.611807i	$0.790443\pi$
$264$		0			0
$265$	−0.00787530	−	0.00179749i	−0.000483776	−	0.000110419i
$266$	9.12382	−	24.7444i	0.559417	−	1.51718i
$267$		0			0
$268$	−3.84257	−	16.8354i	−0.234722	−	1.02839i
$269$	−12.2821	−	15.4012i	−0.748852	−	0.939030i	0.250727	−	0.968058i	$-0.419330\pi$
$269$	−12.2821	−	15.4012i	−0.748852	−	0.939030i	−0.999579	+	0.0290276i	$0.990759\pi$
$270$		0			0
$271$	−10.3442	+	2.36100i	−0.628365	+	0.143420i	−0.524832	−	0.851206i	$-0.675872\pi$
$271$	−10.3442	+	2.36100i	−0.628365	+	0.143420i	−0.103533	+	0.994626i	$0.533015\pi$
$272$	−1.95522	−	8.56637i	−0.118552	−	0.519412i
$273$		0			0
$274$	−0.691259	+	3.02861i	−0.0417605	+	0.182965i
$275$		−	0.312576i		−	0.0188490i
$276$		0			0
$277$	2.67833	−	11.7345i	0.160925	−	0.705059i	−0.828497	−	0.559994i	$-0.810804\pi$
$277$	2.67833	−	11.7345i	0.160925	−	0.705059i	0.989422	−	0.145066i	$-0.0463393\pi$
$278$	17.0491	−	8.21042i	1.02254	−	0.492428i
$279$		0			0
$280$	−0.141938	+	0.217756i	−0.00848242	+	0.0130134i
$281$	−12.8009	−	10.2084i	−0.763638	−	0.608981i	0.162263	−	0.986748i	$-0.448121\pi$
$281$	−12.8009	−	10.2084i	−0.763638	−	0.608981i	−0.925901	+	0.377766i	$0.876692\pi$
$282$		0			0
$283$	4.21849	+	3.36413i	0.250763	+	0.199977i	0.740802	−	0.671724i	$-0.234446\pi$
$283$	4.21849	+	3.36413i	0.250763	+	0.199977i	−0.490038	+	0.871701i	$0.663017\pi$
$284$	1.75155	+	3.63713i	0.103935	+	0.215824i
$285$		0			0
$286$	0.194359	−	0.403591i	0.0114927	−	0.0238649i
$287$	−17.7138	−	2.29525i	−1.04561	−	0.135484i
$288$		0			0
$289$	12.4117	+	5.97718i	0.730102	+	0.351599i
$290$	−0.293130	−	1.28429i	−0.0172132	−	0.0754159i
$291$		0			0
$292$	0.386044	+	0.307860i	0.0225915	+	0.0180162i
$293$	−5.02608			−0.293627			−0.146813	−	0.989164i	$-0.546902\pi$
$293$	−5.02608			−0.293627			−0.146813	+	0.989164i	$0.546902\pi$
$294$		0			0
$295$	0.312829			0.0182136
$296$	1.66360	+	1.32668i	0.0966951	+	0.0771117i
$297$		0			0
$298$	8.13899	+	35.6592i	0.471479	+	2.06568i
$299$	15.0256	+	7.23597i	0.868955	+	0.418467i
$300$		0			0
$301$	3.79764	−	3.67319i	0.218892	−	0.211719i
$302$	−8.65475	+	17.9718i	−0.498025	+	1.03416i
$303$		0			0
$304$	11.6046	+	24.0973i	0.665572	+	1.38207i
$305$	−0.205344	−	0.163756i	−0.0117580	−	0.00937666i
$306$		0			0
$307$	21.7077	+	17.3113i	1.23892	+	0.988007i	0.999855	+	0.0170033i	$0.00541258\pi$
$307$	21.7077	+	17.3113i	1.23892	+	0.988007i	0.239066	+	0.971003i	$0.423159\pi$
$308$	−0.0282236	+	0.217818i	−0.00160819	+	0.0124113i
$309$		0			0
$310$	−0.839325	+	0.404198i	−0.0476704	+	0.0229569i
$311$	−7.38544	+	32.3577i	−0.418790	+	1.83484i	0.120492	+	0.992714i	$0.461553\pi$
$311$	−7.38544	+	32.3577i	−0.418790	+	1.83484i	−0.539282	+	0.842125i	$0.681304\pi$
$312$		0			0
$313$		−	21.9941i		−	1.24318i	−0.783344	−	0.621589i	$-0.786488\pi$
$313$		−	21.9941i		−	1.24318i	0.783344	−	0.621589i	$-0.213512\pi$
$314$	2.19045	−	9.59700i	0.123614	−	0.541590i
$315$		0			0
$316$	3.03542	+	13.2990i	0.170756	+	0.748129i
$317$	−32.1185	+	7.33084i	−1.80395	+	0.411741i	−0.986434	−	0.164159i	$-0.947509\pi$
$317$	−32.1185	+	7.33084i	−1.80395	+	0.411741i	−0.817520	+	0.575900i	$0.804652\pi$
$318$		0			0
$319$	0.352584	+	0.442126i	0.0197409	+	0.0247543i
$320$	0.0357198	+	0.156499i	0.00199680	+	0.00874855i
$321$		0			0
$322$	−20.3384	−	2.63534i	−1.13342	−	0.146862i
$323$	9.56760	+	2.18374i	0.532355	+	0.121507i
$324$		0			0
$325$		−	19.5943i		−	1.08690i
$326$	−2.18042	−	0.497667i	−0.120762	−	0.0275632i
$327$		0			0
$328$	6.48601	−	5.17242i	0.358130	−	0.285599i
$329$	4.40268	−	11.9404i	0.242727	−	0.658293i
$330$		0			0
$331$	−6.11936	+	26.8107i	−0.336350	+	1.47365i	0.470241	+	0.882538i	$0.344167\pi$
$331$	−6.11936	+	26.8107i	−0.336350	+	1.47365i	−0.806591	+	0.591109i	$0.798690\pi$
$332$	−13.9684	+	17.5158i	−0.766614	+	0.961304i
$333$		0			0
$334$	30.8778	−	24.6243i	1.68956	−	1.34738i
$335$	−0.937914	−	0.451675i	−0.0512437	−	0.0246777i
$336$		0			0
$337$	−16.9593	+	8.16718i	−0.923834	+	0.444895i	−0.834438	−	0.551101i	$-0.814208\pi$
$337$	−16.9593	+	8.16718i	−0.923834	+	0.444895i	−0.0893953	+	0.995996i	$0.528493\pi$
$338$	1.89663	−	3.93838i	0.103163	−	0.214220i
$339$		0			0
$340$	0.171533	+	0.0826060i	0.00930269	+	0.00447994i
$341$	0.249341	−	0.312663i	0.0135025	−	0.0169317i
$342$		0			0
$343$	10.6244	−	15.1698i	0.573661	−	0.819093i
$344$			2.45388i			0.132304i
$345$		0			0
$346$	−11.8632	+	24.6342i	−0.637771	+	1.32435i
$347$	−6.86589	+	1.56709i	−0.368580	+	0.0841260i	−0.402799	−	0.915288i	$-0.631963\pi$
$347$	−6.86589	+	1.56709i	−0.368580	+	0.0841260i	0.0342191	+	0.999414i	$0.489106\pi$
$348$		0			0
$349$	−12.1607	−	25.2520i	−0.650947	−	1.35171i	−0.921265	−	0.388935i	$-0.872843\pi$
$349$	−12.1607	−	25.2520i	−0.650947	−	1.35171i	0.270318	−	0.962771i	$-0.412871\pi$
$350$	7.57839	+	22.8729i	0.405082	+	1.22261i
$351$		0			0
$352$	−0.252400	−	0.316500i	−0.0134530	−	0.0168695i
$353$	−22.4618	+	10.8170i	−1.19552	+	0.575732i	−0.922395	−	0.386247i	$-0.873771\pi$
$353$	−22.4618	+	10.8170i	−1.19552	+	0.575732i	−0.273124	+	0.961979i	$0.588057\pi$
$354$		0			0
$355$	0.237259	+	0.0541529i	0.0125924	+	0.00287414i
$356$	4.30548	−	5.39891i	0.228190	−	0.286141i
$357$		0			0
$358$	4.34310	+	5.44608i	0.229540	+	0.287834i
$359$	4.16953	+	8.65812i	0.220059	+	0.456958i	0.981547	−	0.191221i	$-0.0612449\pi$
$359$	4.16953	+	8.65812i	0.220059	+	0.456958i	−0.761487	+	0.648180i	$0.775531\pi$
$360$		0			0
$361$	−10.8720			−0.572212
$362$	−33.2433			−1.74723
$363$		0			0
$364$	−1.76924	+	13.6543i	−0.0927334	+	0.715677i
$365$	0.0290201	−	0.00662364i	0.00151898	−	0.000346697i
$366$		0			0
$367$	16.2513	−	12.9600i	0.848310	−	0.676505i	−0.0996053	−	0.995027i	$-0.531758\pi$
$367$	16.2513	−	12.9600i	0.848310	−	0.676505i	0.947915	+	0.318522i	$0.103187\pi$
$368$	16.2610	−	12.9677i	0.847663	−	0.675989i
$369$		0			0
$370$	−0.246161	+	0.0561847i	−0.0127973	+	0.00292090i
$371$	−0.228679	+	0.138430i	−0.0118724	+	0.00718694i
$372$		0			0
$373$	23.7079			1.22755			0.613774	−	0.789482i	$-0.289650\pi$
$373$	23.7079			1.22755			0.613774	+	0.789482i	$0.289650\pi$
$374$	−0.204982			−0.0105993
$375$		0			0
$376$	2.56454	+	5.32532i	0.132256	+	0.274633i
$377$	22.1023	+	27.7154i	1.13832	+	1.42741i
$378$		0			0
$379$	−17.2796	+	21.6679i	−0.887594	+	1.11301i	0.105352	+	0.994435i	$0.466403\pi$
$379$	−17.2796	+	21.6679i	−0.887594	+	1.11301i	−0.992945	+	0.118572i	$0.962168\pi$
$380$	−0.564996	−	0.128957i	−0.0289837	−	0.00661533i
$381$		0			0
$382$	8.06264	−	3.88276i	0.412521	−	0.198659i
$383$	22.3799	+	28.0635i	1.14356	+	1.43398i	0.883527	+	0.468380i	$0.155162\pi$
$383$	22.3799	+	28.0635i	1.14356	+	1.43398i	0.260033	+	0.965600i	$0.416267\pi$
$384$		0			0
$385$	0.00920535	+	0.00951723i	0.000469148	+	0.000485043i
$386$	0.0846188	+	0.175713i	0.00430699	+	0.00894355i
$387$		0			0
$388$	−17.6370	+	4.02553i	−0.895384	+	0.204365i
$389$	−7.63642	+	15.8572i	−0.387182	+	0.803992i	0.612724	+	0.790297i	$0.290074\pi$
$389$	−7.63642	+	15.8572i	−0.387182	+	0.803992i	−0.999906	+	0.0136948i	$0.995641\pi$
$390$		0			0
$391$		−	7.63143i		−	0.385938i
$392$	1.63369	+	8.44515i	0.0825136	+	0.426545i
$393$		0			0
$394$	−30.7323	+	38.5371i	−1.54827	+	1.94147i
$395$	0.740899	+	0.356798i	0.0372787	+	0.0179525i
$396$		0			0
$397$	−8.96807	+	18.6224i	−0.450094	+	0.934630i	0.545252	+	0.838272i	$0.316434\pi$
$397$	−8.96807	+	18.6224i	−0.450094	+	0.934630i	−0.995347	+	0.0963585i	$0.969280\pi$
$398$	12.6487	−	6.09127i	0.634020	−	0.305328i
$399$		0			0
$400$	−22.0166	−	10.6026i	−1.10083	−	0.530132i
$401$	29.6733	−	23.6636i	1.48181	−	1.18171i	0.541827	−	0.840490i	$-0.317733\pi$
$401$	29.6733	−	23.6636i	1.48181	−	1.18171i	0.939985	−	0.341216i	$-0.110839\pi$
$402$		0			0
$403$	15.6303	−	19.5998i	0.778601	−	0.976335i
$404$	−4.81173	+	21.0816i	−0.239393	+	1.04885i
$405$		0			0
$406$	−36.5199	−	23.8045i	−1.81245	−	1.18140i
$407$	0.0847430	−	0.0675803i	0.00420055	−	0.00334983i
$408$		0			0
$409$	4.32746	+	0.987715i	0.213979	+	0.0488394i	0.328167	−	0.944620i	$-0.393569\pi$
$409$	4.32746	+	0.987715i	0.213979	+	0.0488394i	−0.114187	+	0.993459i	$0.536426\pi$
$410$			0.984407i			0.0486164i
$411$		0			0
$412$	−17.9105	−	4.08796i	−0.882388	−	0.201399i
$413$	7.44106	−	7.19722i	0.366151	−	0.354152i
$414$		0			0
$415$	0.300531	+	1.31671i	0.0147525	+	0.0646349i
$416$	−15.8221	−	19.8403i	−0.775742	−	0.972750i
$417$		0			0
$418$	0.608306	−	0.138842i	0.0297532	−	0.00679097i
$419$	−6.17213	−	27.0419i	−0.301528	−	1.32108i	−0.867820	−	0.496878i	$-0.834480\pi$
$419$	−6.17213	−	27.0419i	−0.301528	−	1.32108i	0.566292	−	0.824205i	$-0.308377\pi$
$420$		0			0
$421$	1.22091	−	5.34915i	0.0595035	−	0.260702i	−0.936423	−	0.350874i	$-0.885885\pi$
$421$	1.22091	−	5.34915i	0.0595035	−	0.260702i	0.995926	+	0.0901721i	$0.0287417\pi$
$422$			30.8751i			1.50298i
$423$		0			0
$424$	0.0276269	−	0.121041i	0.00134168	−	0.00587828i
$425$	−8.07834	+	3.89032i	−0.391857	+	0.188708i
$426$		0			0
$427$	−8.65189	+	0.829153i	−0.418694	+	0.0401255i
$428$	−6.01200	−	4.79441i	−0.290601	−	0.231747i
$429$		0			0
$430$	−0.227654	−	0.181548i	−0.0109785	−	0.00875503i
$431$	9.97595	+	20.7153i	0.480525	+	0.997819i	0.990485	+	0.137622i	$0.0439458\pi$
$431$	9.97595	+	20.7153i	0.480525	+	0.997819i	−0.509960	+	0.860198i	$0.670340\pi$
$432$		0			0
$433$	−2.52920	+	5.25193i	−0.121545	+	0.252392i	−0.952860	−	0.303411i	$-0.901875\pi$
$433$	−2.52920	+	5.25193i	−0.121545	+	0.252392i	0.831314	+	0.555802i	$0.187589\pi$
$434$	−10.6652	+	28.9246i	−0.511944	+	1.38843i
$435$		0			0
$436$	−2.30251	−	1.10883i	−0.110270	−	0.0531033i
$437$	5.16906	+	22.6471i	0.247270	+	1.08336i
$438$		0			0
$439$	−21.0324	−	16.7728i	−1.00382	−	0.800522i	−0.0238631	−	0.999715i	$-0.507597\pi$
$439$	−21.0324	−	16.7728i	−1.00382	−	0.800522i	−0.979960	+	0.199193i	$0.936168\pi$
$440$	−0.00614963			−0.000293172
$441$		0			0
$442$	−12.8496			−0.611193
$443$	−7.69731	−	6.13840i	−0.365710	−	0.291644i	0.423342	−	0.905970i	$-0.360857\pi$
$443$	−7.69731	−	6.13840i	−0.365710	−	0.291644i	−0.789053	+	0.614325i	$0.789428\pi$
$444$		0			0
$445$	−0.0926330	−	0.405851i	−0.00439122	−	0.0192392i
$446$	30.5437	+	14.7091i	1.44628	+	0.696494i
$447$		0			0
$448$	4.45019	+	2.90073i	0.210252	+	0.137047i
$449$	7.61349	−	15.8096i	0.359303	−	0.746100i	−0.640458	−	0.767993i	$-0.721255\pi$
$449$	7.61349	−	15.8096i	0.359303	−	0.746100i	0.999760	+	0.0218939i	$0.00696960\pi$
$450$		0			0
$451$	−0.183354	−	0.380739i	−0.00863383	−	0.0179283i
$452$	−6.59809	−	5.26180i	−0.310348	−	0.247494i
$453$		0			0
$454$	15.1651	+	12.0938i	0.711733	+	0.567588i
$455$	0.577052	+	0.596603i	0.0270526	+	0.0279692i
$456$		0			0
$457$	15.7239	−	7.57225i	0.735535	−	0.354215i	−0.0283235	−	0.999599i	$-0.509017\pi$
$457$	15.7239	−	7.57225i	0.735535	−	0.354215i	0.763858	+	0.645384i	$0.223303\pi$
$458$	6.17535	−	27.0560i	0.288555	−	1.26424i
$459$		0			0
$460$			0.450659i			0.0210121i
$461$	0.302478	−	1.32524i	0.0140878	−	0.0617227i	−0.967395	−	0.253271i	$-0.918494\pi$
$461$	0.302478	−	1.32524i	0.0140878	−	0.0617227i	0.981483	+	0.191548i	$0.0613508\pi$
$462$		0			0
$463$	−4.63599	−	20.3116i	−0.215453	−	0.943961i	−0.960791	−	0.277274i	$-0.910569\pi$
$463$	−4.63599	−	20.3116i	−0.215453	−	0.943961i	0.745338	−	0.666687i	$-0.232288\pi$
$464$	43.1013	−	9.83760i	2.00093	−	0.456699i
$465$		0			0
$466$	32.2085	+	40.3881i	1.49203	+	1.87094i
$467$	−4.83052	−	21.1639i	−0.223530	−	0.979349i	−0.954797	−	0.297258i	$-0.903928\pi$
$467$	−4.83052	−	21.1639i	−0.223530	−	0.979349i	0.731267	−	0.682091i	$-0.238929\pi$
$468$		0			0
$469$	−32.7012	+	10.8347i	−1.51000	+	0.500302i
$470$	−0.683784	−	0.156069i	−0.0315406	−	0.00719893i
$471$		0			0
$472$			4.80810i			0.221311i
$473$	0.121865	+	0.0278149i	0.00560335	+	0.00127893i
$474$		0			0
$475$	21.3383	−	17.0167i	0.979069	−	0.780781i
$476$	5.98065	−	1.98154i	0.274123	−	0.0908239i
$477$		0			0
$478$	−3.82390	+	16.7536i	−0.174901	+	0.766293i
$479$	0.615662	−	0.772016i	0.0281303	−	0.0352743i	−0.767567	−	0.640968i	$-0.778533\pi$
$479$	0.615662	−	0.772016i	0.0281303	−	0.0352743i	0.795698	+	0.605694i	$0.207104\pi$
$480$		0			0
$481$	5.31225	−	4.23638i	0.242218	−	0.193162i
$482$	−29.9450	−	14.4207i	−1.36396	−	0.656847i
$483$		0			0
$484$	13.1391	−	6.32748i	0.597234	−	0.287613i
$485$	−0.473182	+	0.982572i	−0.0214861	+	0.0446163i
$486$		0			0
$487$	−31.5848	−	15.2104i	−1.43124	−	0.689251i	−0.452016	−	0.892010i	$-0.649295\pi$
$487$	−31.5848	−	15.2104i	−1.43124	−	0.689251i	−0.979229	+	0.202759i	$0.935009\pi$
$488$	2.51689	−	3.15608i	0.113934	−	0.142869i
$489$		0			0
$490$	−0.904352	−	0.473246i	−0.0408545	−	0.0213791i
$491$			11.8176i			0.533321i	0.963791	+	0.266660i	$0.0859202\pi$
$491$			11.8176i			0.533321i	−0.963791	+	0.266660i	$0.914080\pi$
$492$		0			0
$493$	7.03823	−	14.6150i	0.316986	−	0.658228i
$494$	38.1326	−	8.70352i	1.71567	−	0.391590i
$495$		0			0
$496$	−13.5651	−	28.1682i	−0.609090	−	1.26479i
$497$	6.88942	−	4.17049i	0.309033	−	0.187072i
$498$		0			0
$499$	−24.7503	−	31.0359i	−1.10798	−	1.38936i	−0.912711	−	0.408607i	$-0.866015\pi$
$499$	−24.7503	−	31.0359i	−1.10798	−	1.38936i	−0.195265	−	0.980751i	$-0.562557\pi$
$500$	0.954712	−	0.459765i	0.0426960	−	0.0205613i
$501$		0			0
$502$	−37.4886	−	8.55652i	−1.67320	−	0.381896i
$503$	2.94170	−	3.68878i	0.131164	−	0.164474i	−0.711912	−	0.702268i	$-0.752171\pi$
$503$	2.94170	−	3.68878i	0.131164	−	0.164474i	0.843076	+	0.537794i	$0.180742\pi$
$504$		0			0
$505$	0.812759	+	1.01917i	0.0361673	+	0.0453524i
$506$	−0.210522	−	0.437154i	−0.00935886	−	0.0194339i
$507$		0			0
$508$	−14.3375			−0.636124
$509$	13.6927			0.606918			0.303459	−	0.952845i	$-0.401858\pi$
$509$	13.6927			0.606918			0.303459	+	0.952845i	$0.401858\pi$
$510$		0			0
$511$	0.537892	−	0.825213i	0.0237950	−	0.0365053i
$512$	−19.1294	+	4.36616i	−0.845407	+	0.192959i
$513$		0			0
$514$	25.8506	−	20.6152i	1.14022	−	0.909297i
$515$	−0.865866	+	0.690505i	−0.0381546	+	0.0304273i
$516$		0			0
$517$	0.293536	−	0.0669978i	0.0129097	−	0.00294656i
$518$	−4.56264	+	6.99982i	−0.200471	+	0.307555i
$519$		0			0
$520$	−0.385499			−0.0169053
$521$	−33.0259			−1.44689			−0.723446	−	0.690381i	$-0.757443\pi$
$521$	−33.0259			−1.44689			−0.723446	+	0.690381i	$0.757443\pi$
$522$		0			0
$523$	1.79046	+	3.71793i	0.0782913	+	0.162574i	0.936440	−	0.350827i	$-0.114100\pi$
$523$	1.79046	+	3.71793i	0.0782913	+	0.162574i	−0.858149	+	0.513401i	$0.828385\pi$
$524$	−2.53890	−	3.18368i	−0.110912	−	0.139079i
$525$		0			0
$526$	22.5646	−	28.2951i	0.983863	−	1.23373i
$527$	−11.1839	−	2.55265i	−0.487179	−	0.111195i
$528$		0			0
$529$	−4.44710	+	2.14161i	−0.193352	+	0.0931136i
$530$	0.00918544	+	0.0115182i	0.000398990	+	0.000500318i
$531$		0			0
$532$	−16.4061	+	9.93137i	−0.711293	+	0.430579i
$533$	−11.4939	−	23.8673i	−0.497855	−	1.03381i
$534$		0			0
$535$	−0.451940	+	0.103152i	−0.0195391	+	0.00445966i
$536$	6.94213	−	14.4155i	0.299854	−	0.622654i
$537$		0			0
$538$			35.9268i			1.54892i
$539$	0.437923	+	0.0145940i	0.0188627	+	0.000628609i
$540$		0			0
$541$	−4.69692	+	5.88975i	−0.201936	+	0.253220i	−0.872480	−	0.488650i	$-0.837489\pi$
$541$	−4.69692	+	5.88975i	−0.201936	+	0.253220i	0.670544	+	0.741870i	$0.266061\pi$
$542$	17.4345	+	8.39603i	0.748877	+	0.360640i
$543$		0			0
$544$	−5.03838	+	10.4623i	−0.216019	+	0.448567i
$545$	−0.138804	+	0.0668447i	−0.00594573	+	0.00286331i
$546$		0			0
$547$	9.81461	+	4.72647i	0.419642	+	0.202089i	0.631775	−	0.775152i	$-0.282327\pi$
$547$	9.81461	+	4.72647i	0.419642	+	0.202089i	−0.212133	+	0.977241i	$0.568041\pi$
$548$	1.76614	−	1.40845i	0.0754460	−	0.0601662i
$549$		0			0
$550$	−0.355435	+	0.445702i	−0.0151558	+	0.0190048i
$551$	−10.9874	+	48.1390i	−0.468079	+	2.05079i
$552$		0			0
$553$	25.8321	−	8.55884i	1.09849	−	0.363959i
$554$	−17.1626	+	13.6867i	−0.729168	+	0.581492i
$555$		0			0
$556$	−13.4155	−	3.06200i	−0.568945	−	0.129858i
$557$			20.9491i			0.887641i	0.896116	+	0.443821i	$0.146377\pi$
$557$			20.9491i			0.887641i	−0.896116	+	0.443821i	$0.853623\pi$
$558$		0			0
$559$	7.63929	+	1.74362i	0.323108	+	0.0737472i
$560$	0.982604	−	0.325562i	0.0415226	−	0.0137575i
$561$		0			0
$562$	6.64469	+	29.1123i	0.280289	+	1.22803i
$563$	−7.84657	−	9.83929i	−0.330694	−	0.414677i	0.588491	−	0.808504i	$-0.299722\pi$
$563$	−7.84657	−	9.83929i	−0.330694	−	0.414677i	−0.919185	+	0.393827i	$0.871151\pi$
$564$		0			0
$565$	−0.495998	+	0.113208i	−0.0208668	+	0.00476271i
$566$	−2.18973	−	9.59384i	−0.0920413	−	0.403259i
$567$		0			0
$568$	−0.832315	+	3.64661i	−0.0349231	+	0.153008i
$569$			23.8454i			0.999649i	0.866127	+	0.499825i	$0.166602\pi$
$569$			23.8454i			0.999649i	−0.866127	+	0.499825i	$0.833398\pi$
$570$		0			0
$571$	−1.44405	+	6.32680i	−0.0604317	+	0.264769i	−0.996114	−	0.0880756i	$-0.971928\pi$
$571$	−1.44405	+	6.32680i	−0.0604317	+	0.264769i	0.935682	+	0.352844i	$0.114785\pi$
$572$	−0.293484	+	0.141335i	−0.0122712	+	0.00590950i
$573$		0			0
$574$	22.6481	+	23.4154i	0.945314	+	0.977342i
$575$	−16.5934	−	13.2328i	−0.691993	−	0.551846i
$576$		0			0
$577$	−33.3975	−	26.6336i	−1.39036	−	1.10877i	−0.980477	−	0.196633i	$-0.936999\pi$
$577$	−33.3975	−	26.6336i	−1.39036	−	1.10877i	−0.409880	−	0.912140i	$-0.634429\pi$
$578$	−10.9012	−	22.6365i	−0.453428	−	0.941553i
$579$		0			0
$580$	−0.415629	+	0.863062i	−0.0172580	+	0.0358367i
$581$	37.4420	+	24.4055i	1.55335	+	1.01251i
$582$		0			0
$583$	−0.00569802	−	0.00274402i	−0.000235988	−	0.000113646i
$584$	0.101804	+	0.446031i	0.00421266	+	0.0184569i
$585$		0			0
$586$	7.16670	+	5.71525i	0.296053	+	0.236095i
$587$	15.7350			0.649452			0.324726	−	0.945808i	$-0.394728\pi$
$587$	15.7350			0.649452			0.324726	+	0.945808i	$0.394728\pi$
$588$		0			0
$589$	34.9185			1.43879
$590$	−0.446064	−	0.355724i	−0.0183641	−	0.0146449i
$591$		0			0
$592$	−1.88559	−	8.26130i	−0.0774972	−	0.339537i
$593$	−23.1968	−	11.1710i	−0.952580	−	0.458738i	−0.107990	−	0.994152i	$-0.534441\pi$
$593$	−23.1968	−	11.1710i	−0.952580	−	0.458738i	−0.844590	+	0.535414i	$0.820156\pi$
$594$		0			0
$595$	0.131397	−	0.356359i	0.00538677	−	0.0146093i
$596$	11.5403	−	23.9636i	0.472708	−	0.981588i
$597$		0			0
$598$	−13.1969	−	27.4037i	−0.539663	−	1.12062i
$599$	−32.7391	−	26.1085i	−1.33768	−	1.06677i	−0.991707	−	0.128522i	$-0.958977\pi$
$599$	−32.7391	−	26.1085i	−1.33768	−	1.06677i	−0.345975	−	0.938244i	$-0.612452\pi$
$600$		0			0
$601$	12.1095	+	9.65701i	0.493957	+	0.393918i	0.838542	−	0.544838i	$-0.183409\pi$
$601$	12.1095	+	9.65701i	0.493957	+	0.393918i	−0.344584	+	0.938755i	$0.611980\pi$
$602$	−9.59192	+	0.919240i	−0.390937	+	0.0374654i
$603$		0			0
$604$	13.0687	−	6.29357i	0.531759	−	0.256082i
$605$	0.195628	−	0.857100i	0.00795339	−	0.0348461i
$606$		0			0
$607$		−	6.82644i		−	0.277077i	−0.990357	−	0.138538i	$-0.955760\pi$
$607$		−	6.82644i		−	0.277077i	0.990357	−	0.138538i	$-0.0442404\pi$
$608$	7.86543	−	34.4607i	0.318985	−	1.39757i
$609$		0			0
$610$	0.106590	+	0.467000i	0.00431569	+	0.0189083i
$611$	18.4008	−	4.19986i	0.744417	−	0.169908i
$612$		0			0
$613$	5.74752	+	7.20716i	0.232140	+	0.291095i	0.884234	−	0.467043i	$-0.154681\pi$
$613$	5.74752	+	7.20716i	0.232140	+	0.291095i	−0.652094	+	0.758138i	$0.726109\pi$
$614$	−11.2680	−	49.3683i	−0.454739	−	1.99234i
$615$		0			0
$616$	−0.146277	+	0.141484i	−0.00589368	+	0.00570054i
$617$	−17.3111	−	3.95114i	−0.696918	−	0.159067i	−0.140637	−	0.990061i	$-0.544915\pi$
$617$	−17.3111	−	3.95114i	−0.696918	−	0.159067i	−0.556281	+	0.830994i	$0.687772\pi$
$618$		0			0
$619$			4.78926i			0.192497i	0.995357	+	0.0962483i	$0.0306843\pi$
$619$			4.78926i			0.192497i	−0.995357	+	0.0962483i	$0.969316\pi$
$620$	0.660444	+	0.150742i	0.0265241	+	0.00605394i
$621$		0			0
$622$	47.3255	−	37.7408i	1.89758	−	1.51327i
$623$	−11.5408	−	7.52253i	−0.462371	−	0.301384i
$624$		0			0
$625$	−5.54170	+	24.2798i	−0.221668	+	0.971190i
$626$	−25.0098	+	31.3613i	−0.999594	+	1.25345i
$627$		0			0
$628$	−5.59653	+	4.46309i	−0.223326	+	0.178097i
$629$	−2.80129	−	1.34903i	−0.111695	−	0.0537893i
$630$		0			0
$631$	18.1773	−	8.75372i	0.723626	−	0.348480i	−0.0355476	−	0.999368i	$-0.511318\pi$
$631$	18.1773	−	8.75372i	0.723626	−	0.348480i	0.759174	+	0.650888i	$0.225603\pi$
$632$	−5.48389	+	11.3874i	−0.218138	+	0.452967i
$633$		0			0
$634$	54.1338	+	26.0695i	2.14993	+	1.03535i
$635$	−0.538896	+	0.675754i	−0.0213854	+	0.0268165i
$636$		0			0
$637$	27.4519	+	0.914849i	1.08768	+	0.0362476i
$638$		−	1.03136i		−	0.0408318i
$639$		0			0
$640$	−0.321663	+	0.667939i	−0.0127148	+	0.0264026i
$641$	40.9493	−	9.34640i	1.61740	−	0.369161i	0.684419	−	0.729089i	$-0.260056\pi$
$641$	40.9493	−	9.34640i	1.61740	−	0.369161i	0.932980	+	0.359928i	$0.117199\pi$
$642$		0			0
$643$	19.3615	+	40.2045i	0.763541	+	1.58551i	0.809888	+	0.586585i	$0.199528\pi$
$643$	19.3615	+	40.2045i	0.763541	+	1.58551i	−0.0463464	+	0.998925i	$0.514758\pi$
$644$	10.3683	+	10.7195i	0.408566	+	0.422409i
$645$		0			0
$646$	−11.1593	−	13.9933i	−0.439056	−	0.550559i
$647$	23.4669	−	11.3011i	0.922578	−	0.444290i	0.0885873	−	0.996068i	$-0.471765\pi$
$647$	23.4669	−	11.3011i	0.922578	−	0.444290i	0.833991	+	0.551778i	$0.186051\pi$
$648$		0			0
$649$	0.238781	+	0.0545002i	0.00937297	+	0.00213932i
$650$	−22.2810	+	27.9395i	−0.873934	+	1.09588i
$651$		0			0
$652$	1.01401	+	1.27152i	0.0397115	+	0.0497967i
$653$	−1.66044	−	3.44795i	−0.0649782	−	0.134929i	0.865950	−	0.500130i	$-0.166714\pi$
$653$	−1.66044	−	3.44795i	−0.0649782	−	0.134929i	−0.930929	+	0.365201i	$0.881000\pi$
$654$		0			0
$655$	−0.245481			−0.00959173
$656$	−33.0372			−1.28989
$657$		0			0
$658$	−19.8554	+	12.0194i	−0.774043	+	0.468565i
$659$	10.8991	−	2.48764i	0.424567	−	0.0969047i	−0.00489821	−	0.999988i	$-0.501559\pi$
$659$	10.8991	−	2.48764i	0.424567	−	0.0969047i	0.429465	+	0.903083i	$0.358702\pi$
$660$		0			0
$661$	−25.5622	+	20.3852i	−0.994256	+	0.792893i	−0.978345	−	0.206981i	$-0.933636\pi$
$661$	−25.5622	+	20.3852i	−0.994256	+	0.792893i	−0.0159108	+	0.999873i	$0.505065\pi$
$662$	39.2125	−	31.2709i	1.52404	−	1.21538i
$663$		0			0
$664$	−20.2375	+	4.61908i	−0.785368	+	0.179255i
$665$	−0.148561	+	1.14653i	−0.00576096	+	0.0444607i
$666$		0			0
$667$	38.3972			1.48675
$668$	−28.7195			−1.11119
$669$		0			0
$670$	0.823764	+	1.71056i	0.0318248	+	0.0660848i
$671$	−0.128209	−	0.160769i	−0.00494944	−	0.00620640i
$672$		0			0
$673$	26.9597	−	33.8063i	1.03922	−	1.30314i	0.0875005	−	0.996164i	$-0.472112\pi$
$673$	26.9597	−	33.8063i	1.03922	−	1.30314i	0.951718	−	0.306974i	$-0.0993165\pi$
$674$	33.4694	+	7.63917i	1.28919	+	0.294250i
$675$		0			0
$676$	−2.86392	+	1.37919i	−0.110151	+	0.0530458i
$677$	−6.81052	−	8.54012i	−0.261750	−	0.328224i	0.633539	−	0.773711i	$-0.281602\pi$
$677$	−6.81052	−	8.54012i	−0.261750	−	0.328224i	−0.895288	+	0.445488i	$0.853030\pi$
$678$		0			0
$679$	11.3506	+	34.2582i	0.435597	+	1.31471i
$680$	0.0765385	+	0.158934i	0.00293512	+	0.00609483i
$681$		0			0
$682$	−0.711070	+	0.162297i	−0.0272283	+	0.00621468i
$683$	0.211166	−	0.438491i	0.00808005	−	0.0167784i	−0.896890	−	0.442254i	$-0.854179\pi$
$683$	0.211166	−	0.438491i	0.00808005	−	0.0167784i	0.904970	+	0.425476i	$0.139893\pi$
$684$		0			0
$685$		−	0.136181i		−	0.00520319i
$686$	−32.3991	+	9.54951i	−1.23700	+	0.364602i
$687$		0			0
$688$	6.09285	−	7.64020i	0.232288	−	0.291280i
$689$	−0.357189	−	0.172013i	−0.0136078	−	0.00655318i
$690$		0			0
$691$	−13.8343	+	28.7273i	−0.526283	+	1.09284i	0.453219	+	0.891399i	$0.350276\pi$
$691$	−13.8343	+	28.7273i	−0.526283	+	1.09284i	−0.979501	+	0.201438i	$0.935439\pi$
$692$	17.9136	−	8.62672i	0.680972	−	0.327939i
$693$		0			0
$694$	11.5721	+	5.57281i	0.439269	+	0.211541i
$695$	−0.648560	+	0.517209i	−0.0246013	+	0.0196189i
$696$		0			0
$697$	−7.55796	+	9.47739i	−0.286278	+	0.358982i
$698$	−11.3745	+	49.8349i	−0.430531	+	1.88628i
$699$		0			0
$700$	6.06180	−	16.4400i	0.229114	−	0.621374i
$701$	18.2624	−	14.5638i	0.689762	−	0.550067i	−0.214669	−	0.976687i	$-0.568867\pi$
$701$	18.2624	−	14.5638i	0.689762	−	0.550067i	0.904431	+	0.426620i	$0.140296\pi$
$702$		0			0
$703$	9.22688	+	2.10597i	0.347998	+	0.0794283i
$704$			0.125678i			0.00473666i
$705$		0			0
$706$	44.3285	+	10.1177i	1.66832	+	0.380784i
$707$	42.7804	+	5.54324i	1.60892	+	0.208475i
$708$		0			0
$709$	−8.46035	−	37.0672i	−0.317735	−	1.39209i	−0.841514	−	0.540235i	$-0.818336\pi$
$709$	−8.46035	−	37.0672i	−0.317735	−	1.39209i	0.523779	−	0.851854i	$-0.324522\pi$
$710$	−0.276730	−	0.347008i	−0.0103855	−	0.0130230i
$711$		0			0
$712$	6.23782	−	1.42374i	0.233772	−	0.0533570i
$713$	−6.04229	−	26.4730i	−0.226286	−	0.991422i
$714$		0			0
$715$	−0.00436966	+	0.0191447i	−0.000163416	+	0.000715973i
$716$		−	5.06540i		−	0.189303i
$717$		0			0
$718$	3.89997	−	17.0869i	0.145545	−	0.637676i
$719$	−26.8474	+	12.9290i	−1.00124	+	0.482171i	−0.861359	−	0.507997i	$-0.830386\pi$
$719$	−26.8474	+	12.9290i	−1.00124	+	0.482171i	−0.139880	+	0.990168i	$0.544672\pi$
$720$		0			0
$721$	−4.70943	+	36.3454i	−0.175389	+	1.35358i
$722$	15.5024	+	12.3628i	0.576941	+	0.460095i
$723$		0			0
$724$	18.8999	+	15.0722i	0.702410	+	0.560154i
$725$	−19.5740	−	40.6458i	−0.726960	−	1.50955i
$726$		0			0
$727$	−13.4164	+	27.8594i	−0.497586	+	1.03325i	0.489343	+	0.872091i	$0.337237\pi$
$727$	−13.4164	+	27.8594i	−0.497586	+	1.03325i	−0.986929	+	0.161156i	$0.948478\pi$
$728$	−9.16962	+	8.86912i	−0.339849	+	0.328712i
$729$		0			0
$730$	−0.0489116	−	0.0235546i	−0.00181030	−	0.000871795i
$731$	−0.797874	−	3.49571i	−0.0295104	−	0.129294i
$732$		0			0
$733$	−11.7287	−	9.35330i	−0.433208	−	0.345472i	0.382480	−	0.923964i	$-0.375070\pi$
$733$	−11.7287	−	9.35330i	−0.433208	−	0.345472i	−0.815688	+	0.578492i	$0.803641\pi$
$734$	−37.9097			−1.39927
$735$		0			0
$736$	−27.4870			−1.01318
$737$	−0.637215	−	0.508162i	−0.0234721	−	0.0187184i
$738$		0			0
$739$	7.06950	+	30.9735i	0.260056	+	1.13938i	0.921191	+	0.389112i	$0.127218\pi$
$739$	7.06950	+	30.9735i	0.260056	+	1.13938i	−0.661135	+	0.750267i	$0.729925\pi$
$740$	0.165425	+	0.0796643i	0.00608113	+	0.00292852i
$741$		0			0
$742$	0.483485	+	0.0626472i	0.0177493	+	0.00229985i
$743$	−9.78269	+	20.3140i	−0.358892	+	0.745247i	−0.999749	−	0.0224137i	$-0.992865\pi$
$743$	−9.78269	+	20.3140i	−0.358892	+	0.745247i	0.640857	+	0.767660i	$0.278579\pi$
$744$		0			0
$745$	−0.695693	−	1.44462i	−0.0254882	−	0.0529269i
$746$	−33.8051	−	26.9587i	−1.23769	−	0.987027i
$747$		0			0
$748$	0.116539	+	0.0929367i	0.00426109	+	0.00339810i
$749$	−8.37678	+	12.8513i	−0.306081	+	0.469577i
$750$		0			0
$751$	3.53737	−	1.70351i	0.129081	−	0.0621620i	−0.368229	−	0.929735i	$-0.620036\pi$
$751$	3.53737	−	1.70351i	0.129081	−	0.0621620i	0.497309	+	0.867573i	$0.334321\pi$
$752$	5.23776	−	22.9481i	0.191002	−	0.836833i
$753$		0			0
$754$		−	64.6522i		−	2.35450i
$755$	0.194579	−	0.852508i	0.00708147	−	0.0310259i
$756$		0			0
$757$	−2.49190	−	10.9177i	−0.0905696	−	0.396811i	0.909241	−	0.416270i	$-0.136663\pi$
$757$	−2.49190	−	10.9177i	−0.0905696	−	0.396811i	−0.999811	+	0.0194586i	$0.993806\pi$
$758$	49.2780	−	11.2474i	1.78986	−	0.408523i
$759$		0			0
$760$	−0.334788	−	0.419811i	−0.0121440	−	0.0152281i
$761$	−0.918025	−	4.02213i	−0.0332784	−	0.145802i	0.955559	−	0.294799i	$-0.0952527\pi$
$761$	−0.918025	−	4.02213i	−0.0332784	−	0.145802i	−0.988838	+	0.148997i	$0.952396\pi$
$762$		0			0
$763$	−1.76376	+	4.78344i	−0.0638525	+	0.173172i
$764$	−6.34429	−	1.44804i	−0.229528	−	0.0523883i
$765$		0			0
$766$		−	65.4644i		−	2.36533i
$767$	14.9684	+	3.41643i	0.540476	+	0.123360i
$768$		0			0
$769$	−33.1561	+	26.4411i	−1.19564	+	0.953491i	−0.999632	−	0.0271112i	$-0.991369\pi$
$769$	−33.1561	+	26.4411i	−1.19564	+	0.953491i	−0.196008	+	0.980602i	$0.562798\pi$
$770$	−0.00230370	−	0.0240382i	−8.30195e−5	−	0.000866276i
$771$		0			0
$772$	0.0315579	−	0.138264i	0.00113579	−	0.00497623i
$773$	−5.38928	+	6.75794i	−0.193839	+	0.243066i	−0.869247	−	0.494378i	$-0.835396\pi$
$773$	−5.38928	+	6.75794i	−0.193839	+	0.243066i	0.675408	+	0.737444i	$0.263967\pi$
$774$		0			0
$775$	−24.9431	+	19.8915i	−0.895983	+	0.714522i
$776$	−15.1019	−	7.27267i	−0.542125	−	0.261074i
$777$		0			0
$778$	28.9203	−	13.9273i	1.03684	−	0.499317i
$779$	16.0097	−	33.2445i	0.573607	−	1.19111i
$780$		0			0
$781$	0.171664	+	0.0826692i	0.00614263	+	0.00295814i
$782$	−8.67784	+	10.8817i	−0.310319	+	0.389128i
$783$		0			0
$784$	15.8824	−	30.3505i	0.567228	−	1.08395i
$785$			0.431527i			0.0154019i
$786$		0			0
$787$	16.5245	−	34.3135i	0.589035	−	1.22314i	−0.367090	−	0.930185i	$-0.619646\pi$
$787$	16.5245	−	34.3135i	0.589035	−	1.22314i	0.956125	−	0.292958i	$-0.0946397\pi$
$788$	34.9447	−	7.97589i	1.24485	−	0.284129i
$789$		0			0
$790$	−0.650727	−	1.35125i	−0.0231518	−	0.0480753i
$791$	−9.19340	+	14.1042i	−0.326880	+	0.501486i
$792$		0			0
$793$	−8.03696	−	10.0780i	−0.285401	−	0.357881i
$794$	33.9634	−	16.3559i	1.20532	−	0.580450i
$795$		0			0
$796$	−9.95291	−	2.27169i	−0.352771	−	0.0805178i
$797$	−31.4962	+	39.4950i	−1.11565	+	1.39898i	−0.208581	+	0.978005i	$0.566885\pi$
$797$	−31.4962	+	39.4950i	−1.11565	+	1.39898i	−0.907071	+	0.420978i	$0.861687\pi$
$798$		0			0
$799$	−5.38488	−	6.75243i	−0.190503	−	0.238884i
$800$	14.0122	+	29.0967i	0.495407	+	1.02872i
$801$		0			0
$802$	−69.2195			−2.44423
$803$	0.0233048			0.000822409
$804$		0			0
$805$	0.894938	−	0.0857663i	0.0315424	−	0.00302287i
$806$	−44.5745	+	10.1738i	−1.57007	+	0.358359i
$807$		0			0
$808$	−15.6643	+	12.4919i	−0.551069	+	0.439463i
$809$	24.8019	−	19.7788i	0.871987	−	0.695386i	−0.0815478	−	0.996669i	$-0.525986\pi$
$809$	24.8019	−	19.7788i	0.871987	−	0.695386i	0.953535	+	0.301283i	$0.0974149\pi$
$810$		0			0
$811$	−14.1169	+	3.22209i	−0.495711	+	0.113143i	−0.463065	−	0.886324i	$-0.653250\pi$
$811$	−14.1169	+	3.22209i	−0.495711	+	0.113143i	−0.0326458	+	0.999467i	$0.510393\pi$
$812$	9.97005	+	30.0914i	0.349880	+	1.05600i
$813$		0			0
$814$	−0.197682			−0.00692874
$815$	0.0980422			0.00343427
$816$		0			0
$817$	4.73556	+	9.83349i	0.165676	+	0.344030i
$818$	−5.04739	−	6.32922i	−0.176478	−	0.221296i
$819$		0			0
$820$	0.446321	−	0.559669i	0.0155862	−	0.0195445i
$821$	2.04355	+	0.466428i	0.0713205	+	0.0162784i	0.258032	−	0.966136i	$-0.416926\pi$
$821$	2.04355	+	0.466428i	0.0713205	+	0.0162784i	−0.186712	+	0.982415i	$0.559783\pi$
$822$		0			0
$823$	−14.9013	+	7.17608i	−0.519426	+	0.250142i	−0.675179	−	0.737654i	$-0.735934\pi$
$823$	−14.9013	+	7.17608i	−0.519426	+	0.250142i	0.155753	+	0.987796i	$0.450219\pi$
$824$	−10.6129	−	13.3081i	−0.369717	−	0.463610i
$825$		0			0
$826$	−18.7943	+	1.80115i	−0.653937	+	0.0626700i
$827$	−2.37577	−	4.93334i	−0.0826137	−	0.171549i	0.855570	−	0.517688i	$-0.173207\pi$
$827$	−2.37577	−	4.93334i	−0.0826137	−	0.171549i	−0.938183	+	0.346138i	$0.887493\pi$
$828$		0			0
$829$	−33.3488	+	7.61165i	−1.15825	+	0.264364i	−0.758133	−	0.652099i	$-0.773888\pi$
$829$	−33.3488	+	7.61165i	−1.15825	+	0.264364i	−0.400119	+	0.916463i	$0.631031\pi$
$830$	1.06873	−	2.21924i	0.0370962	−	0.0770310i
$831$		0			0
$832$			7.87831i			0.273131i
$833$	−5.07323	−	11.4995i	−0.175777	−	0.398434i
$834$		0			0
$835$	−1.07946	+	1.35360i	−0.0373564	+	0.0468434i
$836$	−0.408792	−	0.196864i	−0.0141384	−	0.00680867i
$837$		0			0
$838$	−21.9490	+	45.5775i	−0.758214	+	1.57445i
$839$	31.9275	−	15.3755i	1.10226	−	0.530820i	0.207891	−	0.978152i	$-0.433340\pi$
$839$	31.9275	−	15.3755i	1.10226	−	0.530820i	0.894368	+	0.447332i	$0.147626\pi$
$840$		0			0
$841$	47.4068	+	22.8299i	1.63472	+	0.787239i
$842$	−7.82351	+	6.23904i	−0.269616	+	0.215012i
$843$		0			0
$844$	13.9985	−	17.5535i	0.481847	−	0.604217i
$845$	−0.0426407	+	0.186821i	−0.00146688	+	0.00642684i
$846$		0			0
$847$	−15.0659	−	24.8880i	−0.517671	−	0.855163i
$848$	−0.386556	+	0.308268i	−0.0132744	+	0.0105860i
$849$		0			0
$850$	15.9427	+	3.63881i	0.546829	+	0.124810i
$851$		−	7.35966i		−	0.252286i
$852$		0			0
$853$	9.95445	+	2.27204i	0.340834	+	0.0777931i	0.389512	−	0.921021i	$-0.372644\pi$
$853$	9.95445	+	2.27204i	0.340834	+	0.0777931i	−0.0486780	+	0.998815i	$0.515501\pi$
$854$	13.2796	+	8.65593i	0.454418	+	0.296200i
$855$		0			0
$856$	−1.58542	−	6.94619i	−0.0541886	−	0.237416i
$857$	4.92636	+	6.17746i	0.168281	+	0.211018i	0.858820	−	0.512277i	$-0.171198\pi$
$857$	4.92636	+	6.17746i	0.168281	+	0.211018i	−0.690539	+	0.723295i	$0.742627\pi$
$858$		0			0
$859$	−14.6463	+	3.34292i	−0.499725	+	0.114059i	−0.464951	−	0.885336i	$-0.653928\pi$
$859$	−14.6463	+	3.34292i	−0.499725	+	0.114059i	−0.0347737	+	0.999395i	$0.511071\pi$
$860$	0.0471169	+	0.206433i	0.00160667	+	0.00703929i
$861$		0			0
$862$	9.33099	−	40.8818i	0.317815	−	1.39244i
$863$			2.09035i			0.0711565i	0.999367	+	0.0355783i	$0.0113273\pi$
$863$			2.09035i			0.0711565i	−0.999367	+	0.0355783i	$0.988673\pi$
$864$		0			0
$865$	0.266714	−	1.16855i	0.00906854	−	0.0397319i
$866$	9.57845	−	4.61274i	0.325489	−	0.156747i
$867$		0			0
$868$	19.1776	−	11.6091i	0.650931	−	0.394040i
$869$	0.503364	+	0.401419i	0.0170755	+	0.0136172i
$870$		0			0
$871$	−39.9448	−	31.8549i	−1.35348	−	1.07936i
$872$	−1.02738	−	2.13339i	−0.0347916	−	0.0722456i
$873$		0			0
$874$	18.3819	−	38.1704i	0.621776	−	1.29113i
$875$	−1.09471	−	1.80841i	−0.0370081	−	0.0611353i
$876$		0			0
$877$	−10.6555	−	5.13144i	−0.359812	−	0.173276i	0.245240	−	0.969462i	$-0.421133\pi$
$877$	−10.6555	−	5.13144i	−0.359812	−	0.173276i	−0.605052	+	0.796186i	$0.706848\pi$
$878$	10.9175	+	47.8327i	0.368448	+	1.61428i
$879$		0			0
$880$	0.0191470	+	0.0152692i	0.000645446	+	0.000514726i
$881$	−0.697841			−0.0235109			−0.0117554	−	0.999931i	$-0.503742\pi$
$881$	−0.697841			−0.0235109			−0.0117554	+	0.999931i	$0.503742\pi$
$882$		0			0
$883$	22.0445			0.741855			0.370928	−	0.928662i	$-0.379040\pi$
$883$	22.0445			0.741855			0.370928	+	0.928662i	$0.379040\pi$
$884$	7.30543	+	5.82588i	0.245708	+	0.195946i
$885$		0			0
$886$	3.99552	+	17.5055i	0.134232	+	0.588109i
$887$	7.91096	+	3.80972i	0.265624	+	0.127918i	0.561956	−	0.827167i	$-0.310049\pi$
$887$	7.91096	+	3.80972i	0.265624	+	0.127918i	−0.296332	+	0.955085i	$0.595763\pi$
$888$		0			0
$889$	2.72861	+	28.4720i	0.0915147	+	0.954921i
$890$	−0.329416	+	0.684039i	−0.0110420	+	0.0229290i
$891$		0			0
$892$	−10.6962	−	22.2108i	−0.358134	−	0.743673i
$893$	20.5539	+	16.3912i	0.687810	+	0.548510i
$894$		0			0
$895$	−0.238742	−	0.190390i	−0.00798026	−	0.00636405i
$896$	7.71600	+	23.2883i	0.257774	+	0.778007i
$897$		0			0
$898$	−28.8334	+	13.8854i	−0.962184	+	0.463363i
$899$	12.8436	−	56.2714i	0.428357	−	1.87675i
$900$		0			0
$901$			0.181414i			0.00604378i
$902$	−0.171500	+	0.751393i	−0.00571034	+	0.0250186i
$903$		0			0
$904$	−1.73998	−	7.62335i	−0.0578708	−	0.253549i
$905$	1.42076	−	0.324280i	0.0472277	−	0.0107794i
$906$		0			0
$907$	−7.76200	−	9.73324i	−0.257733	−	0.323187i	0.636083	−	0.771621i	$-0.280554\pi$
$907$	−7.76200	−	9.73324i	−0.257733	−	0.323187i	−0.893816	+	0.448434i	$0.851982\pi$
$908$	−3.13867	−	13.7514i	−0.104160	−	0.456357i
$909$		0			0
$910$	−0.144411	−	1.50687i	−0.00478718	−	0.0499523i
$911$	−33.4396	−	7.63236i	−1.10790	−	0.252871i	−0.370840	−	0.928697i	$-0.620930\pi$
$911$	−33.4396	−	7.63236i	−1.10790	−	0.252871i	−0.737062	+	0.675825i	$0.763787\pi$
$912$		0			0
$913$			1.05740i			0.0349947i
$914$	−31.0313	−	7.08270i	−1.02643	−	0.234275i
$915$		0			0
$916$	−15.7778	+	12.5824i	−0.521313	+	0.415734i
$917$	−5.83909	+	5.64774i	−0.192824	+	0.186505i
$918$		0			0
$919$	6.41309	−	28.0976i	0.211548	−	0.926854i	−0.751967	−	0.659201i	$-0.770895\pi$
$919$	6.41309	−	28.0976i	0.211548	−	0.926854i	0.963515	−	0.267653i	$-0.0862481\pi$
$920$	−0.260343	+	0.326460i	−0.00858325	+	0.0107631i
$921$		0			0
$922$	−1.93826	+	1.54571i	−0.0638332	+	0.0509053i
$923$	10.7610	+	5.18225i	0.354204	+	0.170576i
$924$		0			0
$925$	−7.79066	+	3.75178i	−0.256155	+	0.123358i
$926$	−16.4862	+	34.2340i	−0.541771	+	1.12500i
$927$		0			0
$928$	−52.6406	−	25.3504i	−1.72801	−	0.832167i
$929$	23.0930	−	28.9577i	0.757657	−	0.950071i	−0.242140	−	0.970241i	$-0.577849\pi$
$929$	23.0930	−	28.9577i	0.757657	−	0.950071i	0.999797	+	0.0201700i	$0.00642074\pi$
$930$		0			0
$931$	22.8444	+	30.6898i	0.748695	+	1.00582i
$932$		−	37.5650i		−	1.23048i
$933$		0			0
$934$	−17.1780	+	35.6705i	−0.562082	+	1.16717i
$935$	0.00876057	−	0.00199954i	0.000286501	−	6.53921e-5i
$936$		0			0
$937$	−4.38680	−	9.10928i	−0.143310	−	0.297587i	0.816942	−	0.576719i	$-0.195667\pi$
$937$	−4.38680	−	9.10928i	−0.143310	−	0.297587i	−0.960253	+	0.279132i	$0.909953\pi$
$938$	58.9490	+	21.7358i	1.92475	+	0.709700i
$939$		0			0
$940$	0.317994	+	0.398752i	0.0103718	+	0.0130058i
$941$	−35.1459	+	16.9254i	−1.14572	+	0.551751i	−0.907746	−	0.419519i	$-0.862199\pi$
$941$	−35.1459	+	16.9254i	−1.14572	+	0.551751i	−0.237977	+	0.971271i	$0.576484\pi$
$942$		0			0
$943$	−27.9742	−	6.38493i	−0.910966	−	0.207922i
$944$	11.9383	−	14.9701i	0.388558	−	0.487236i
$945$		0			0
$946$	−0.142138	−	0.178236i	−0.00462132	−	0.00579495i
$947$	11.7073	+	24.3105i	0.380437	+	0.789987i	0.999987	+	0.00502923i	$0.00160086\pi$
$947$	11.7073	+	24.3105i	0.380437	+	0.789987i	−0.619550	+	0.784957i	$0.712685\pi$
$948$		0			0
$949$	1.46090			0.0474228
$950$	−49.7763			−1.61496
$951$		0			0
$952$	5.47713	+	2.01954i	0.177515	+	0.0654538i
$953$	46.6988	−	10.6587i	1.51272	−	0.345269i	0.615958	−	0.787779i	$-0.288769\pi$
$953$	46.6988	−	10.6587i	1.51272	−	0.345269i	0.896764	+	0.442510i	$0.145912\pi$
$954$		0			0
$955$	−0.306708	+	0.244592i	−0.00992485	+	0.00791480i
$956$	9.76995	−	7.79128i	0.315983	−	0.251988i
$957$		0			0
$958$	−1.75575	+	0.400738i	−0.0567256	+	0.0129473i
$959$	−3.13309	−	3.23924i	−0.101173	−	0.104600i
$960$		0			0
$961$	−9.81745			−0.316692
$962$	−12.3920			−0.399534
$963$		0			0
$964$	10.4865	+	21.7754i	0.337748	+	0.701340i
$965$	−0.00533050	−	0.00668424i	−0.000171595	−	0.000215173i
$966$		0			0
$967$	−23.0916	+	28.9560i	−0.742577	+	0.931162i	−0.999377	−	0.0353024i	$-0.988761\pi$
$967$	−23.0916	+	28.9560i	−0.742577	+	0.931162i	0.256800	+	0.966465i	$0.417332\pi$
$968$	13.1734	+	3.00674i	0.423409	+	0.0966403i
$969$		0			0
$970$	1.79201	−	0.862986i	0.0575380	−	0.0277088i
$971$	37.0100	+	46.4091i	1.18771	+	1.48934i	0.832030	+	0.554731i	$0.187179\pi$
$971$	37.0100	+	46.4091i	1.18771	+	1.48934i	0.355678	+	0.934608i	$0.384250\pi$
$972$		0			0
$973$	−3.52751	+	27.2238i	−0.113087	+	0.872756i
$974$	27.7408	+	57.6043i	0.888871	+	1.84576i
$975$		0			0
$976$	−15.6728	+	3.57721i	−0.501673	+	0.114504i
$977$	−5.36951	+	11.1499i	−0.171786	+	0.356717i	−0.969031	−	0.246938i	$-0.920575\pi$
$977$	−5.36951	+	11.1499i	−0.171786	+	0.356717i	0.797245	+	0.603655i	$0.206290\pi$
$978$		0			0
$979$		−	0.325922i		−	0.0104165i
$980$	0.299589	+	0.679081i	0.00957003	+	0.0216925i
$981$		0			0
$982$	13.4380	−	16.8507i	0.428824	−	0.537728i
$983$	−28.2925	−	13.6250i	−0.902392	−	0.434569i	−0.0756395	−	0.997135i	$-0.524100\pi$
$983$	−28.2925	−	13.6250i	−0.902392	−	0.434569i	−0.826752	+	0.562566i	$0.809814\pi$
$984$		0			0
$985$	0.937527	−	1.94679i	0.0298721	−	0.0620300i
$986$	−26.6548	+	12.8363i	−0.848863	+	0.408791i
$987$		0			0
$988$	−25.6258	−	12.3407i	−0.815264	−	0.392610i
$989$	6.63570	−	5.29179i	0.211003	−	0.168269i
$990$		0			0
$991$	3.51077	−	4.40236i	0.111523	−	0.139846i	−0.722937	−	0.690914i	$-0.757208\pi$
$991$	3.51077	−	4.40236i	0.111523	−	0.139846i	0.834460	+	0.551068i	$0.185780\pi$
$992$	−9.19418	+	40.2823i	−0.291916	+	1.27897i
$993$		0			0
$994$	−14.5660	−	1.88737i	−0.462004	−	0.0598639i
$995$	−0.481163	+	0.383715i	−0.0152539	+	0.0121646i
$996$		0			0
$997$	18.9005	+	4.31391i	0.598584	+	0.136623i	0.511068	−	0.859540i	$-0.329250\pi$
$997$	18.9005	+	4.31391i	0.598584	+	0.136623i	0.0875158	+	0.996163i	$0.472107\pi$
$998$			72.3981i			2.29172i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.w.a.251.5	yes	120
3.2	odd	2	inner	441.2.w.a.251.16	yes	120
49.41	odd	14	inner	441.2.w.a.188.16	yes	120
147.41	even	14	inner	441.2.w.a.188.5	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.w.a.188.5	✓	120	147.41	even	14	inner
441.2.w.a.188.16	yes	120	49.41	odd	14	inner
441.2.w.a.251.5	yes	120	1.1	even	1	trivial
441.2.w.a.251.16	yes	120	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.w (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.42590 - 1.13712i) q^{2} +(0.295114 + 1.29298i) q^{4} +(0.0720329 + 0.0346892i) q^{5} +(2.51149 - 0.832121i) q^{7} +(-0.533164 + 1.10713i) q^{8} +O(q^{10})\)	\(q+(-1.42590 - 1.13712i) q^{2} +(0.295114 + 1.29298i) q^{4} +(0.0720329 + 0.0346892i) q^{5} +(2.51149 - 0.832121i) q^{7} +(-0.533164 + 1.10713i) q^{8} +(-0.0632661 - 0.131373i) q^{10} +(0.0489389 + 0.0390274i) q^{11} +(3.06781 + 2.44650i) q^{13} +(-4.52735 - 1.66934i) q^{14} +(4.40896 - 2.12324i) q^{16} +(0.399548 - 1.75053i) q^{17} +5.46553i q^{19} +(-0.0235945 + 0.103374i) q^{20} +(-0.0254032 - 0.111299i) q^{22} +(4.14363 - 0.945756i) q^{23} +(-3.11346 - 3.90416i) q^{25} +(-1.59244 - 6.97692i) q^{26} +(1.81709 + 3.00173i) q^{28} +(8.80774 + 2.01031i) q^{29} -6.38885i q^{31} +(-6.30510 - 1.43910i) q^{32} +(-2.56028 + 2.04175i) q^{34} +(0.209775 + 0.0271815i) q^{35} +(0.385319 - 1.68819i) q^{37} +(6.21495 - 7.79331i) q^{38} +(-0.0768107 + 0.0612545i) q^{40} +(-6.08257 - 2.92921i) q^{41} +(1.79918 - 0.866440i) q^{43} +(-0.0360191 + 0.0747945i) q^{44} +(-6.98384 - 3.36324i) q^{46} +(2.99901 - 3.76064i) q^{47} +(5.61515 - 4.17972i) q^{49} +9.10732i q^{50} +(-2.25792 + 4.68861i) q^{52} +(-0.0985022 + 0.0224825i) q^{53} +(0.00217138 + 0.00450891i) q^{55} +(-0.417772 + 3.22419i) q^{56} +(-10.2730 - 12.8819i) q^{58} +(3.52530 - 1.69769i) q^{59} +(-3.20273 - 0.731001i) q^{61} +(-7.26488 + 9.10987i) q^{62} +(1.25183 + 1.56975i) q^{64} +(0.136116 + 0.282648i) q^{65} -13.0206 q^{67} +2.38132 q^{68} +(-0.268210 - 0.277298i) q^{70} +(2.96758 - 0.677330i) q^{71} +(0.291084 - 0.232132i) q^{73} +(-2.46910 + 1.96904i) q^{74} +(-7.06682 + 1.61296i) q^{76} +(0.155385 + 0.0572939i) q^{77} +10.2856 q^{79} +0.391244 q^{80} +(5.34228 + 11.0934i) q^{82} +(10.5324 + 13.2072i) q^{83} +(0.0895053 - 0.112236i) q^{85} +(-3.55070 - 0.810424i) q^{86} +(-0.0693007 + 0.0333735i) q^{88} +(-3.24641 - 4.07086i) q^{89} +(9.74055 + 3.59156i) q^{91} +(2.44569 + 5.07852i) q^{92} +(-8.55259 + 1.95207i) q^{94} +(-0.189595 + 0.393698i) q^{95} +13.6406i q^{97} +(-12.7595 - 0.425217i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 24 q^{4}+O(q^{10}) \) 120 * q + 24 * q^4	\( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) \) 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

Introduction

L-functions

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