LMFDB - Embedded newform 280.2.l.a.29.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(29,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("280.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.l (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.11
Character	$\chi$	$=$	280.29
Dual form			280.2.l.a.29.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.752500 - 1.19739i) q^{2} -2.12140 q^{3} +(-0.867487 + 1.80207i) q^{4} +(-2.02293 + 0.952769i) q^{5} +(1.59636 + 2.54015i) q^{6} +1.00000i q^{7} +(2.81057 - 0.317339i) q^{8} +1.50036 q^{9} +O(q^{10})$	\(q+(-0.752500 - 1.19739i) q^{2} -2.12140 q^{3} +(-0.867487 + 1.80207i) q^{4} +(-2.02293 + 0.952769i) q^{5} +(1.59636 + 2.54015i) q^{6} +1.00000i q^{7} +(2.81057 - 0.317339i) q^{8} +1.50036 q^{9} +(2.66309 + 1.70527i) q^{10} -5.19834i q^{11} +(1.84029 - 3.82293i) q^{12} +6.02726 q^{13} +(1.19739 - 0.752500i) q^{14} +(4.29145 - 2.02121i) q^{15} +(-2.49493 - 3.12655i) q^{16} +2.84902i q^{17} +(-1.12902 - 1.79651i) q^{18} +1.52835i q^{19} +(0.0379041 - 4.47198i) q^{20} -2.12140i q^{21} +(-6.22444 + 3.91175i) q^{22} -4.80330i q^{23} +(-5.96235 + 0.673205i) q^{24} +(3.18446 - 3.85476i) q^{25} +(-4.53551 - 7.21698i) q^{26} +3.18135 q^{27} +(-1.80207 - 0.867487i) q^{28} +3.04559i q^{29} +(-5.64949 - 3.61758i) q^{30} +5.62454 q^{31} +(-1.86626 + 5.34014i) q^{32} +11.0278i q^{33} +(3.41139 - 2.14389i) q^{34} +(-0.952769 - 2.02293i) q^{35} +(-1.30154 + 2.70375i) q^{36} +4.69079 q^{37} +(1.83003 - 1.15008i) q^{38} -12.7863 q^{39} +(-5.38322 + 3.31978i) q^{40} +5.14767 q^{41} +(-2.54015 + 1.59636i) q^{42} -5.28583 q^{43} +(9.36779 + 4.50949i) q^{44} +(-3.03511 + 1.42949i) q^{45} +(-5.75143 + 3.61449i) q^{46} -6.17703i q^{47} +(5.29276 + 6.63268i) q^{48} -1.00000 q^{49} +(-7.01196 - 0.912336i) q^{50} -6.04393i q^{51} +(-5.22857 + 10.8616i) q^{52} +10.4728 q^{53} +(-2.39397 - 3.80932i) q^{54} +(4.95282 + 10.5159i) q^{55} +(0.317339 + 2.81057i) q^{56} -3.24224i q^{57} +(3.64676 - 2.29180i) q^{58} -0.438637i q^{59} +(-0.0804099 + 9.48687i) q^{60} +0.0169277i q^{61} +(-4.23247 - 6.73477i) q^{62} +1.50036i q^{63} +(7.79859 - 1.78381i) q^{64} +(-12.1927 + 5.74258i) q^{65} +(13.2046 - 8.29841i) q^{66} -3.18839 q^{67} +(-5.13415 - 2.47149i) q^{68} +10.1897i q^{69} +(-1.70527 + 2.66309i) q^{70} +5.46547 q^{71} +(4.21686 - 0.476122i) q^{72} +6.46618i q^{73} +(-3.52982 - 5.61670i) q^{74} +(-6.75554 + 8.17751i) q^{75} +(-2.75419 - 1.32582i) q^{76} +5.19834 q^{77} +(9.62166 + 15.3101i) q^{78} +10.3751 q^{79} +(8.02594 + 3.94769i) q^{80} -11.2500 q^{81} +(-3.87362 - 6.16377i) q^{82} -13.8900 q^{83} +(3.82293 + 1.84029i) q^{84} +(-2.71446 - 5.76337i) q^{85} +(3.97758 + 6.32920i) q^{86} -6.46092i q^{87} +(-1.64964 - 14.6103i) q^{88} -6.30493 q^{89} +(3.99558 + 2.55852i) q^{90} +6.02726i q^{91} +(8.65590 + 4.16680i) q^{92} -11.9319 q^{93} +(-7.39631 + 4.64821i) q^{94} +(-1.45616 - 3.09173i) q^{95} +(3.95910 - 11.3286i) q^{96} -3.58833i q^{97} +(0.752500 + 1.19739i) q^{98} -7.79937i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9}+O(q^{10}) $ 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9	$ 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9} - 8 q^{10} + 20 q^{16} - 24 q^{20} - 48 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{30} - 16 q^{31} + 12 q^{34} - 20 q^{36} - 32 q^{39} + 16 q^{40} - 8 q^{41} + 56 q^{44} - 36 q^{49} - 12 q^{50} - 52 q^{54} - 32 q^{55} + 12 q^{56} - 20 q^{60} - 20 q^{64} - 24 q^{65} - 28 q^{66} - 12 q^{70} + 56 q^{71} - 24 q^{74} + 48 q^{76} + 24 q^{79} + 64 q^{80} + 36 q^{81} + 24 q^{86} - 40 q^{89} - 52 q^{90} - 92 q^{94} + 40 q^{95} + 48 q^{96}+O(q^{100}) $ 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9 - 8 * q^10 + 20 * q^16 - 24 * q^20 - 48 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^30 - 16 * q^31 + 12 * q^34 - 20 * q^36 - 32 * q^39 + 16 * q^40 - 8 * q^41 + 56 * q^44 - 36 * q^49 - 12 * q^50 - 52 * q^54 - 32 * q^55 + 12 * q^56 - 20 * q^60 - 20 * q^64 - 24 * q^65 - 28 * q^66 - 12 * q^70 + 56 * q^71 - 24 * q^74 + 48 * q^76 + 24 * q^79 + 64 * q^80 + 36 * q^81 + 24 * q^86 - 40 * q^89 - 52 * q^90 - 92 * q^94 + 40 * q^95 + 48 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.752500	−	1.19739i	−0.532098	−	0.846683i
$2$	−0.752500	−	1.19739i	−0.532098	−	0.846683i
$3$	−2.12140			−1.22479			−0.612397	−	0.790551i	$-0.709794\pi$
$3$	−2.12140			−1.22479			−0.612397	+	0.790551i	$0.709794\pi$
$4$	−0.867487	+	1.80207i	−0.433744	+	0.901036i
$5$	−2.02293	+	0.952769i	−0.904680	+	0.426091i
$5$	−2.02293	+	0.952769i	−0.904680	+	0.426091i
$6$	1.59636	+	2.54015i	0.651710	+	1.03701i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	2.81057	−	0.317339i	0.993686	−	0.112196i
$9$	1.50036			0.500119
$10$	2.66309	+	1.70527i	0.842143	+	0.539255i
$11$		−	5.19834i		−	1.56736i	−0.621166	−	0.783679i	$-0.713341\pi$
$11$		−	5.19834i		−	1.56736i	0.621166	−	0.783679i	$-0.286659\pi$
$12$	1.84029	−	3.82293i	0.531246	−	1.10358i
$13$	6.02726			1.67166			0.835830	−	0.548988i	$-0.184987\pi$
$13$	6.02726			1.67166			0.835830	+	0.548988i	$0.184987\pi$
$14$	1.19739	−	0.752500i	0.320016	−	0.201114i
$15$	4.29145	−	2.02121i	1.10805	−	0.521874i
$16$	−2.49493	−	3.12655i	−0.623733	−	0.781637i
$17$			2.84902i			0.690990i	0.938421	+	0.345495i	$0.112289\pi$
$17$			2.84902i			0.690990i	−0.938421	+	0.345495i	$0.887711\pi$
$18$	−1.12902	−	1.79651i	−0.266112	−	0.423442i
$19$			1.52835i			0.350627i	0.984513	+	0.175313i	$0.0560939\pi$
$19$			1.52835i			0.350627i	−0.984513	+	0.175313i	$0.943906\pi$
$20$	0.0379041	−	4.47198i	0.00847561	−	0.999964i
$21$		−	2.12140i		−	0.462928i
$22$	−6.22444	+	3.91175i	−1.32706	+	0.833988i
$23$		−	4.80330i		−	1.00156i	−0.865575	−	0.500779i	$-0.833047\pi$
$23$		−	4.80330i		−	1.00156i	0.865575	−	0.500779i	$-0.166953\pi$
$24$	−5.96235	+	0.673205i	−1.21706	+	0.137417i
$25$	3.18446	−	3.85476i	0.636893	−	0.770952i
$26$	−4.53551	−	7.21698i	−0.889487	−	1.41537i
$27$	3.18135			0.612251
$28$	−1.80207	−	0.867487i	−0.340560	−	0.163940i
$29$			3.04559i			0.565551i	0.959186	+	0.282776i	$0.0912552\pi$
$29$			3.04559i			0.565551i	−0.959186	+	0.282776i	$0.908745\pi$
$30$	−5.64949	−	3.61758i	−1.03145	−	0.660476i
$31$	5.62454			1.01020			0.505099	−	0.863061i	$-0.331456\pi$
$31$	5.62454			1.01020			0.505099	+	0.863061i	$0.331456\pi$
$32$	−1.86626	+	5.34014i	−0.329912	+	0.944012i
$33$			11.0278i			1.91969i
$34$	3.41139	−	2.14389i	0.585049	−	0.367674i
$35$	−0.952769	−	2.02293i	−0.161047	−	0.341937i
$36$	−1.30154	+	2.70375i	−0.216923	+	0.450626i
$37$	4.69079			0.771160			0.385580	−	0.922674i	$-0.374001\pi$
$37$	4.69079			0.771160			0.385580	+	0.922674i	$0.374001\pi$
$38$	1.83003	−	1.15008i	0.296870	−	0.186568i
$39$	−12.7863			−2.04744
$40$	−5.38322	+	3.31978i	−0.851162	+	0.524903i
$41$	5.14767			0.803931			0.401965	−	0.915655i	$-0.368327\pi$
$41$	5.14767			0.803931			0.401965	+	0.915655i	$0.368327\pi$
$42$	−2.54015	+	1.59636i	−0.391954	+	0.246323i
$43$	−5.28583			−0.806081			−0.403040	−	0.915182i	$-0.632047\pi$
$43$	−5.28583			−0.806081			−0.403040	+	0.915182i	$0.632047\pi$
$44$	9.36779	+	4.50949i	1.41225	+	0.679832i
$45$	−3.03511	+	1.42949i	−0.452448	+	0.213096i
$46$	−5.75143	+	3.61449i	−0.848002	+	0.532927i
$47$		−	6.17703i		−	0.901012i	−0.892773	−	0.450506i	$-0.851244\pi$
$47$		−	6.17703i		−	0.901012i	0.892773	−	0.450506i	$-0.148756\pi$
$48$	5.29276	+	6.63268i	0.763944	+	0.957344i
$49$	−1.00000			−0.142857
$50$	−7.01196	−	0.912336i	−0.991641	−	0.129024i
$51$		−	6.04393i		−	0.846320i
$52$	−5.22857	+	10.8616i	−0.725072	+	1.50623i
$53$	10.4728			1.43855			0.719276	−	0.694725i	$-0.244474\pi$
$53$	10.4728			1.43855			0.719276	+	0.694725i	$0.244474\pi$
$54$	−2.39397	−	3.80932i	−0.325777	−	0.518382i
$55$	4.95282	+	10.5159i	0.667838	+	1.41796i
$56$	0.317339	+	2.81057i	0.0424062	+	0.375578i
$57$		−	3.24224i		−	0.429446i
$58$	3.64676	−	2.29180i	0.478842	−	0.300929i
$59$		−	0.438637i		−	0.0571056i	−0.999592	−	0.0285528i	$-0.990910\pi$
$59$		−	0.438637i		−	0.0571056i	0.999592	−	0.0285528i	$-0.00908988\pi$
$60$	−0.0804099	+	9.48687i	−0.0103809	+	1.22475i
$61$			0.0169277i			0.00216737i	0.999999	+	0.00108368i	$0.000344947\pi$
$61$			0.0169277i			0.00216737i	−0.999999	+	0.00108368i	$0.999655\pi$
$62$	−4.23247	−	6.73477i	−0.537524	−	0.855317i
$63$			1.50036i			0.189027i
$64$	7.79859	−	1.78381i	0.974824	−	0.222976i
$65$	−12.1927	+	5.74258i	−1.51232	+	0.712280i
$66$	13.2046	−	8.29841i	1.62537	−	1.02146i
$67$	−3.18839			−0.389524			−0.194762	−	0.980851i	$-0.562393\pi$
$67$	−3.18839			−0.389524			−0.194762	+	0.980851i	$0.562393\pi$
$68$	−5.13415	−	2.47149i	−0.622607	−	0.299712i
$69$			10.1897i			1.22670i
$70$	−1.70527	+	2.66309i	−0.203819	+	0.318300i
$71$	5.46547			0.648631			0.324316	−	0.945949i	$-0.394866\pi$
$71$	5.46547			0.648631			0.324316	+	0.945949i	$0.394866\pi$
$72$	4.21686	−	0.476122i	0.496961	−	0.0561116i
$73$			6.46618i			0.756809i	0.925640	+	0.378405i	$0.123527\pi$
$73$			6.46618i			0.756809i	−0.925640	+	0.378405i	$0.876473\pi$
$74$	−3.52982	−	5.61670i	−0.410333	−	0.652928i
$75$	−6.75554	+	8.17751i	−0.780062	+	0.944258i
$76$	−2.75419	−	1.32582i	−0.315928	−	0.152082i
$77$	5.19834			0.592406
$78$	9.62166	+	15.3101i	1.08944	+	1.73353i
$79$	10.3751			1.16729			0.583647	−	0.812008i	$-0.301625\pi$
$79$	10.3751			1.16729			0.583647	+	0.812008i	$0.301625\pi$
$80$	8.02594	+	3.94769i	0.897328	+	0.441365i
$81$	−11.2500			−1.25000
$82$	−3.87362	−	6.16377i	−0.427770	−	0.680674i
$83$	−13.8900			−1.52463			−0.762314	−	0.647207i	$-0.775937\pi$
$83$	−13.8900			−1.52463			−0.762314	+	0.647207i	$0.775937\pi$
$84$	3.82293	+	1.84029i	0.417115	+	0.200792i
$85$	−2.71446	−	5.76337i	−0.294425	−	0.625125i
$86$	3.97758	+	6.32920i	0.428914	+	0.682495i
$87$		−	6.46092i		−	0.692683i
$88$	−1.64964	−	14.6103i	−0.175852	−	1.55746i
$89$	−6.30493			−0.668321			−0.334161	−	0.942516i	$-0.608453\pi$
$89$	−6.30493			−0.668321			−0.334161	+	0.942516i	$0.608453\pi$
$90$	3.99558	+	2.55852i	0.421172	+	0.269692i
$91$			6.02726i			0.631828i
$92$	8.65590	+	4.16680i	0.902440	+	0.434419i
$93$	−11.9319			−1.23728
$94$	−7.39631	+	4.64821i	−0.762871	+	0.479427i
$95$	−1.45616	−	3.09173i	−0.149399	−	0.317205i
$96$	3.95910	−	11.3286i	0.404074	−	1.15622i
$97$		−	3.58833i		−	0.364340i	−0.983267	−	0.182170i	$-0.941688\pi$
$97$		−	3.58833i		−	0.364340i	0.983267	−	0.182170i	$-0.0583121\pi$
$98$	0.752500	+	1.19739i	0.0760140	+	0.120955i
$99$		−	7.79937i		−	0.783866i
$100$	4.18408	+	9.08259i	0.418408	+	0.908259i
$101$		−	19.0009i		−	1.89066i	−0.326118	−	0.945329i	$-0.605741\pi$
$101$		−	19.0009i		−	1.89066i	0.326118	−	0.945329i	$-0.394259\pi$
$102$	−7.23695	+	4.54806i	−0.716565	+	0.450325i
$103$			12.8903i			1.27012i	0.772462	+	0.635060i	$0.219025\pi$
$103$			12.8903i			1.27012i	−0.772462	+	0.635060i	$0.780975\pi$
$104$	16.9400	−	1.91269i	1.66111	−	0.187554i
$105$	2.02121	+	4.29145i	0.197250	+	0.418802i
$106$	−7.88079	−	12.5400i	−0.765450	−	1.21800i
$107$	16.2773			1.57358			0.786792	−	0.617218i	$-0.211740\pi$
$107$	16.2773			1.57358			0.786792	+	0.617218i	$0.211740\pi$
$108$	−2.75978	+	5.73302i	−0.265560	+	0.551660i
$109$		−	0.988397i		−	0.0946713i	−0.998879	−	0.0473356i	$-0.984927\pi$
$109$		−	0.988397i		−	0.0946713i	0.998879	−	0.0473356i	$-0.0150730\pi$
$110$	8.86459	−	13.8436i	0.845206	−	1.31994i
$111$	−9.95105			−0.944512
$112$	3.12655	−	2.49493i	0.295431	−	0.235749i
$113$		−	19.2081i		−	1.80695i	−0.428640	−	0.903475i	$-0.641007\pi$
$113$		−	19.2081i		−	1.80695i	0.428640	−	0.903475i	$-0.358993\pi$
$114$	−3.88223	+	2.43979i	−0.363604	+	0.228507i
$115$	4.57644	+	9.71673i	0.426755	+	0.906089i
$116$	−5.48837	−	2.64201i	−0.509582	−	0.245304i
$117$	9.04304			0.836030
$118$	−0.525219	+	0.330074i	−0.0483503	+	0.0303858i
$119$	−2.84902			−0.261170
$120$	11.4200	−	7.04259i	1.04250	−	0.642897i
$121$	−16.0227			−1.45661
$122$	0.0202690	−	0.0127381i	0.00183507	−	0.00115325i
$123$	−10.9203			−0.984649
$124$	−4.87922	+	10.1358i	−0.438167	+	0.910225i
$125$	−2.76924	+	10.8320i	−0.247688	+	0.968840i
$126$	1.79651	−	1.12902i	0.160046	−	0.100581i
$127$		−	4.54496i		−	0.403300i	−0.979458	−	0.201650i	$-0.935370\pi$
$127$		−	4.54496i		−	0.403300i	0.979458	−	0.201650i	$-0.0646303\pi$
$128$	−8.00435	−	7.99564i	−0.707492	−	0.706722i
$129$	11.2134			0.987283
$130$	16.0511	+	10.2781i	1.40778	+	0.901451i
$131$			9.57272i			0.836372i	0.908361	+	0.418186i	$0.137334\pi$
$131$			9.57272i			0.836372i	−0.908361	+	0.418186i	$0.862666\pi$
$132$	−19.8729	−	9.56646i	−1.72971	−	0.832653i
$133$	−1.52835			−0.132525
$134$	2.39926	+	3.81775i	0.207265	+	0.329803i
$135$	−6.43563	+	3.03109i	−0.553891	+	0.260875i
$136$	0.904107	+	8.00738i	0.0775266	+	0.686627i
$137$		−	19.4072i		−	1.65807i	−0.559199	−	0.829034i	$-0.688891\pi$
$137$		−	19.4072i		−	1.65807i	0.559199	−	0.829034i	$-0.311109\pi$
$138$	12.2011	−	7.66779i	1.03863	−	0.652725i
$139$		−	14.0670i		−	1.19315i	−0.802559	−	0.596573i	$-0.796529\pi$
$139$		−	14.0670i		−	1.19315i	0.802559	−	0.596573i	$-0.203471\pi$
$140$	4.47198	+	0.0379041i	0.377951	+	0.00320348i
$141$			13.1040i			1.10355i
$142$	−4.11276	−	6.54430i	−0.345135	−	0.549185i
$143$		−	31.3317i		−	2.62009i
$144$	−3.74329	−	4.69094i	−0.311941	−	0.390912i
$145$	−2.90174	−	6.16100i	−0.240976	−	0.511643i
$146$	7.74254	−	4.86580i	0.640777	−	0.402697i
$147$	2.12140			0.174971
$148$	−4.06920	+	8.45314i	−0.334486	+	0.694844i
$149$			18.0367i			1.47762i	0.673912	+	0.738812i	$0.264613\pi$
$149$			18.0367i			1.47762i	−0.673912	+	0.738812i	$0.735387\pi$
$150$	14.8752	+	1.93543i	1.21456	+	0.158028i
$151$	3.23596			0.263338			0.131669	−	0.991294i	$-0.457966\pi$
$151$	3.23596			0.263338			0.131669	+	0.991294i	$0.457966\pi$
$152$	0.485005	+	4.29553i	0.0393391	+	0.348413i
$153$			4.27456i			0.345577i
$154$	−3.91175	−	6.22444i	−0.315218	−	0.501580i
$155$	−11.3780	+	5.35889i	−0.913906	+	0.430436i
$156$	11.0919	−	23.0418i	0.888064	−	1.84482i
$157$	0.292472			0.0233418			0.0116709	−	0.999932i	$-0.496285\pi$
$157$	0.292472			0.0233418			0.0116709	+	0.999932i	$0.496285\pi$
$158$	−7.80729	−	12.4231i	−0.621114	−	0.988327i
$159$	−22.2171			−1.76193
$160$	−1.31260	−	12.5808i	−0.103770	−	0.994601i
$161$	4.80330			0.378553
$162$	8.46563	+	13.4706i	0.665122	+	1.05835i
$163$	13.0195			1.01976			0.509882	−	0.860245i	$-0.329689\pi$
$163$	13.0195			1.01976			0.509882	+	0.860245i	$0.329689\pi$
$164$	−4.46554	+	9.27647i	−0.348700	+	0.724371i
$165$	−10.5069	−	22.3084i	−0.817963	−	1.73671i
$166$	10.4522	+	16.6318i	0.811251	+	1.29088i
$167$			18.0140i			1.39397i	0.717087	+	0.696984i	$0.245475\pi$
$167$			18.0140i			1.39397i	−0.717087	+	0.696984i	$0.754525\pi$
$168$	−0.673205	−	5.96235i	−0.0519389	−	0.460006i
$169$	23.3279			1.79445
$170$	−4.85837	+	7.58720i	−0.372620	+	0.581912i
$171$			2.29307i			0.175355i
$172$	4.58539	−	9.52544i	0.349632	−	0.726308i
$173$	4.80116			0.365025			0.182513	−	0.983204i	$-0.441577\pi$
$173$	4.80116			0.365025			0.182513	+	0.983204i	$0.441577\pi$
$174$	−7.73624	+	4.86184i	−0.586483	+	0.368575i
$175$	3.85476	+	3.18446i	0.291393	+	0.240723i
$176$	−16.2529	+	12.9695i	−1.22511	+	0.977613i
$177$			0.930526i			0.0699426i
$178$	4.74446	+	7.54946i	0.355612	+	0.565856i
$179$			9.67391i			0.723062i	0.932360	+	0.361531i	$0.117746\pi$
$179$			9.67391i			0.723062i	−0.932360	+	0.361531i	$0.882254\pi$
$180$	0.0568697	−	6.70956i	0.00423881	−	0.500101i
$181$		−	7.37228i		−	0.547977i	−0.961733	−	0.273989i	$-0.911657\pi$
$181$		−	7.37228i		−	0.547977i	0.961733	−	0.273989i	$-0.0883431\pi$
$182$	7.21698	−	4.53551i	0.534958	−	0.336195i
$183$		−	0.0359105i		−	0.00265458i
$184$	−1.52428	−	13.5000i	−0.112371	−	0.995234i
$185$	−9.48911	+	4.46923i	−0.697654	+	0.328585i
$186$	8.97878	+	14.2872i	0.658356	+	1.04759i
$187$	14.8102			1.08303
$188$	11.1314	+	5.35849i	0.811844	+	0.390808i
$189$			3.18135i			0.231409i
$190$	−2.60625	+	4.07012i	−0.189077	+	0.295278i
$191$	10.2142			0.739076			0.369538	−	0.929216i	$-0.379516\pi$
$191$	10.2142			0.739076			0.369538	+	0.929216i	$0.379516\pi$
$192$	−16.5440	+	3.78418i	−1.19396	+	0.273099i
$193$			7.50867i			0.540486i	0.962792	+	0.270243i	$0.0871040\pi$
$193$			7.50867i			0.540486i	−0.962792	+	0.270243i	$0.912896\pi$
$194$	−4.29663	+	2.70022i	−0.308480	+	0.193864i
$195$	25.8657	−	12.1823i	1.85228	−	0.872396i
$196$	0.867487	−	1.80207i	0.0619634	−	0.128719i
$197$	5.98806			0.426632			0.213316	−	0.976983i	$-0.431574\pi$
$197$	5.98806			0.426632			0.213316	+	0.976983i	$0.431574\pi$
$198$	−9.33889	+	5.86903i	−0.663686	+	0.417093i
$199$	−11.2772			−0.799418			−0.399709	−	0.916642i	$-0.630889\pi$
$199$	−11.2772			−0.799418			−0.399709	+	0.916642i	$0.630889\pi$
$200$	7.72689	−	11.8446i	0.546373	−	0.837542i
$201$	6.76387			0.477086
$202$	−22.7515	+	14.2982i	−1.60079	+	1.00602i
$203$	−3.04559			−0.213758
$204$	10.8916	+	5.24303i	0.762565	+	0.367086i
$205$	−10.4134	+	4.90454i	−0.727300	+	0.342548i
$206$	15.4347	−	9.69997i	1.07539	−	0.675829i
$207$		−	7.20667i		−	0.500898i
$208$	−15.0376	−	18.8445i	−1.04267	−	1.30663i
$209$	7.94487			0.549558
$210$	3.61758	−	5.64949i	0.249636	−	0.389852i
$211$		−	8.35883i		−	0.575446i	−0.957714	−	0.287723i	$-0.907102\pi$
$211$		−	8.35883i		−	0.575446i	0.957714	−	0.287723i	$-0.0928982\pi$
$212$	−9.08503	+	18.8728i	−0.623962	+	1.29619i
$213$	−11.5945			−0.794440
$214$	−12.2487	−	19.4903i	−0.837301	−	1.33233i
$215$	10.6928	−	5.03617i	0.729245	−	0.343464i
$216$	8.94140	−	1.00957i	0.608385	−	0.0686923i
$217$			5.62454i			0.381819i
$218$	−1.18350	+	0.743769i	−0.0801565	+	0.0503744i
$219$		−	13.7174i		−	0.926935i
$220$	−23.2469	−	0.197038i	−1.56730	−	0.0132843i
$221$			17.1718i			1.15510i
$222$	7.48817	+	11.9153i	0.502573	+	0.799702i
$223$		−	1.25309i		−	0.0839129i	−0.999119	−	0.0419565i	$-0.986641\pi$
$223$		−	1.25309i		−	0.0839129i	0.999119	−	0.0419565i	$-0.0133591\pi$
$224$	−5.34014	−	1.86626i	−0.356803	−	0.124695i
$225$	4.77783	−	5.78352i	0.318522	−	0.385568i
$226$	−22.9997	+	14.4541i	−1.52991	+	0.961475i
$227$	0.654688			0.0434531			0.0217266	−	0.999764i	$-0.493084\pi$
$227$	0.654688			0.0434531			0.0217266	+	0.999764i	$0.493084\pi$
$228$	5.84276	+	2.81260i	0.386946	+	0.186269i
$229$		−	24.8058i		−	1.63922i	−0.572924	−	0.819608i	$-0.694191\pi$
$229$		−	24.8058i		−	1.63922i	0.572924	−	0.819608i	$-0.305809\pi$
$230$	8.19095	−	12.7916i	0.540095	−	0.843454i
$231$	−11.0278			−0.725575
$232$	0.966484	+	8.55983i	0.0634528	+	0.561980i
$233$			8.16996i			0.535232i	0.963526	+	0.267616i	$0.0862359\pi$
$233$			8.16996i			0.535232i	−0.963526	+	0.267616i	$0.913764\pi$
$234$	−6.80489	−	10.8281i	−0.444850	−	0.707852i
$235$	5.88528	+	12.4957i	0.383913	+	0.815128i
$236$	0.790455	+	0.380512i	0.0514542	+	0.0247692i
$237$	−22.0098			−1.42969
$238$	2.14389	+	3.41139i	0.138968	+	0.221128i
$239$	−9.55439			−0.618022			−0.309011	−	0.951058i	$-0.599998\pi$
$239$	−9.55439			−0.618022			−0.309011	+	0.951058i	$0.599998\pi$
$240$	−17.0263	−	8.37464i	−1.09904	−	0.540581i
$241$	20.4295			1.31598			0.657988	−	0.753028i	$-0.271408\pi$
$241$	20.4295			1.31598			0.657988	+	0.753028i	$0.271408\pi$
$242$	12.0571	+	19.1855i	0.775061	+	1.23329i
$243$	14.3218			0.918741
$244$	−0.0305049	−	0.0146845i	−0.00195288	−	0.000940081i
$245$	2.02293	−	0.952769i	0.129240	−	0.0608702i
$246$	8.21752	+	13.0758i	0.523930	+	0.833686i
$247$			9.21175i			0.586129i
$248$	15.8082	−	1.78489i	1.00382	−	0.113341i
$249$	29.4664			1.86735
$250$	15.0539	−	4.83519i	0.952094	−	0.305804i
$251$			22.6092i			1.42708i	0.700613	+	0.713541i	$0.252910\pi$
$251$			22.6092i			1.42708i	−0.700613	+	0.713541i	$0.747090\pi$
$252$	−2.70375	−	1.30154i	−0.170320	−	0.0819894i
$253$	−24.9692			−1.56980
$254$	−5.44209	+	3.42008i	−0.341467	+	0.214595i
$255$	5.75847	+	12.2264i	0.360609	+	0.765649i
$256$	−3.55063	+	15.6011i	−0.221914	+	0.975066i
$257$			17.7263i			1.10574i	0.833268	+	0.552869i	$0.186467\pi$
$257$			17.7263i			1.10574i	−0.833268	+	0.552869i	$0.813533\pi$
$258$	−8.43807	−	13.4268i	−0.525331	−	0.835915i
$259$			4.69079i			0.291471i
$260$	0.228458	−	26.9538i	0.0141683	−	1.67160i
$261$			4.56947i			0.282843i
$262$	11.4623	−	7.20347i	0.708142	−	0.445032i
$263$			22.9967i			1.41804i	0.705188	+	0.709020i	$0.250862\pi$
$263$			22.9967i			1.41804i	−0.705188	+	0.709020i	$0.749138\pi$
$264$	3.49955	+	30.9943i	0.215382	+	1.90757i
$265$	−21.1857	+	9.97817i	−1.30143	+	0.612954i
$266$	1.15008	+	1.83003i	0.0705160	+	0.112206i
$267$	13.3753			0.818556
$268$	2.76589	−	5.74571i	0.168953	−	0.350975i
$269$			0.882193i			0.0537882i	0.999638	+	0.0268941i	$0.00856170\pi$
$269$			0.882193i			0.0537882i	−0.999638	+	0.0268941i	$0.991438\pi$
$270$	8.47221	+	5.42507i	0.515602	+	0.330159i
$271$	−6.51642			−0.395845			−0.197922	−	0.980218i	$-0.563419\pi$
$271$	−6.51642			−0.395845			−0.197922	+	0.980218i	$0.563419\pi$
$272$	8.90762	−	7.10812i	0.540104	−	0.430993i
$273$		−	12.7863i		−	0.773859i
$274$	−23.2380	+	14.6039i	−1.40386	+	0.882254i
$275$	−20.0384	−	16.5539i	−1.20836	−	0.998239i
$276$	−18.3627	−	8.83947i	−1.10530	−	0.532074i
$277$	−4.54185			−0.272893			−0.136447	−	0.990647i	$-0.543568\pi$
$277$	−4.54185			−0.272893			−0.136447	+	0.990647i	$0.543568\pi$
$278$	−16.8437	+	10.5854i	−1.01022	+	0.634870i
$279$	8.43882			0.505219
$280$	−3.31978	−	5.38322i	−0.198395	−	0.321709i
$281$	−23.0187			−1.37318			−0.686589	−	0.727045i	$-0.740893\pi$
$281$	−23.0187			−1.37318			−0.686589	+	0.727045i	$0.740893\pi$
$282$	15.6906	−	9.86074i	0.934360	−	0.587198i
$283$	1.70754			0.101503			0.0507513	−	0.998711i	$-0.483838\pi$
$283$	1.70754			0.101503			0.0507513	+	0.998711i	$0.483838\pi$
$284$	−4.74122	+	9.84917i	−0.281340	+	0.584440i
$285$	3.08911	+	6.55882i	0.182983	+	0.388511i
$286$	−37.5163	+	23.5771i	−2.21839	+	1.39415i
$287$			5.14767i			0.303857i
$288$	−2.80006	+	8.01211i	−0.164995	+	0.472118i
$289$	8.88306			0.522533
$290$	−5.19356	+	8.11067i	−0.304976	+	0.476275i
$291$			7.61230i			0.446241i
$292$	−11.6525	−	5.60933i	−0.681913	−	0.328261i
$293$	11.9204			0.696397			0.348199	−	0.937421i	$-0.386793\pi$
$293$	11.9204			0.696397			0.348199	+	0.937421i	$0.386793\pi$
$294$	−1.59636	−	2.54015i	−0.0931014	−	0.148145i
$295$	0.417919	+	0.887330i	0.0243322	+	0.0516623i
$296$	13.1838	−	1.48857i	0.766291	−	0.0865214i
$297$		−	16.5377i		−	0.959617i
$298$	21.5970	−	13.5726i	1.25108	−	0.786241i
$299$		−	28.9507i		−	1.67426i
$300$	−8.87613	−	19.2679i	−0.512464	−	1.11243i
$301$		−	5.28583i		−	0.304670i
$302$	−2.43506	−	3.87470i	−0.140122	−	0.222964i
$303$			40.3085i			2.31567i
$304$	4.77845	−	3.81312i	0.274063	−	0.218698i
$305$	−0.0161282	−	0.0342434i	−0.000923496	−	0.00196077i
$306$	5.11831	−	3.21660i	0.292594	−	0.183881i
$307$	−10.3092			−0.588375			−0.294187	−	0.955748i	$-0.595049\pi$
$307$	−10.3092			−0.588375			−0.294187	+	0.955748i	$0.595049\pi$
$308$	−4.50949	+	9.36779i	−0.256952	+	0.533779i
$309$		−	27.3456i		−	1.55564i
$310$	14.9787	+	9.59139i	0.850730	+	0.544754i
$311$	9.05021			0.513190			0.256595	−	0.966519i	$-0.417399\pi$
$311$	9.05021			0.513190			0.256595	+	0.966519i	$0.417399\pi$
$312$	−35.9366	+	4.05758i	−2.03451	+	0.229715i
$313$		−	2.45855i		−	0.138965i	−0.997583	−	0.0694827i	$-0.977865\pi$
$313$		−	2.45855i		−	0.138965i	0.997583	−	0.0694827i	$-0.0221349\pi$
$314$	−0.220085	−	0.350203i	−0.0124201	−	0.0197631i
$315$	−1.42949	−	3.03511i	−0.0805428	−	0.171009i
$316$	−9.00029	+	18.6967i	−0.506306	+	1.05177i
$317$	0.793472			0.0445658			0.0222829	−	0.999752i	$-0.492907\pi$
$317$	0.793472			0.0445658			0.0222829	+	0.999752i	$0.492907\pi$
$318$	16.7183	+	26.6025i	0.937518	+	1.49179i
$319$	15.8320			0.886422
$320$	−14.0764	+	11.0388i	−0.786896	+	0.617086i
$321$	−34.5307			−1.92732
$322$	−3.61449	−	5.75143i	−0.201427	−	0.320515i
$323$	−4.35430			−0.242280
$324$	9.75923	−	20.2733i	0.542179	−	1.12630i
$325$	19.1936	−	23.2337i	1.06467	−	1.28877i
$326$	−9.79715	−	15.5894i	−0.542614	−	0.863416i
$327$			2.09679i			0.115953i
$328$	14.4679	−	1.63356i	0.798855	−	0.0901981i
$329$	6.17703			0.340550
$330$	−18.8054	+	29.3680i	−1.03520	+	1.61665i
$331$		−	6.17391i		−	0.339349i	−0.985500	−	0.169674i	$-0.945728\pi$
$331$		−	6.17391i		−	0.339349i	0.985500	−	0.169674i	$-0.0542716\pi$
$332$	12.0494	−	25.0308i	0.661298	−	1.37375i
$333$	7.03785			0.385672
$334$	21.5698	−	13.5556i	1.18025	−	0.741727i
$335$	6.44988	−	3.03780i	0.352395	−	0.165973i
$336$	−6.63268	+	5.29276i	−0.361842	+	0.288744i
$337$		−	8.99423i		−	0.489947i	−0.969530	−	0.244974i	$-0.921221\pi$
$337$		−	8.99423i		−	0.489947i	0.969530	−	0.244974i	$-0.0787793\pi$
$338$	−17.5542	−	27.9325i	−0.954823	−	1.51933i
$339$			40.7483i			2.21314i
$340$	12.7408	+	0.107990i	0.690965	+	0.00585656i
$341$		−	29.2383i		−	1.58334i
$342$	2.74570	−	1.72553i	0.148470	−	0.0933062i
$343$		−	1.00000i		−	0.0539949i
$344$	−14.8562	+	1.67740i	−0.800991	+	0.0904393i
$345$	−9.70847	−	20.6131i	−0.522687	−	1.10977i
$346$	−3.61287	−	5.74886i	−0.194229	−	0.309061i
$347$	−14.7386			−0.791208			−0.395604	−	0.918421i	$-0.629465\pi$
$347$	−14.7386			−0.791208			−0.395604	+	0.918421i	$0.629465\pi$
$348$	11.6430	+	5.60477i	0.624133	+	0.300447i
$349$		−	3.64189i		−	0.194946i	−0.995238	−	0.0974729i	$-0.968924\pi$
$349$		−	3.64189i		−	0.194946i	0.995238	−	0.0974729i	$-0.0310759\pi$
$350$	0.912336	−	7.01196i	0.0487664	−	0.374805i
$351$	19.1748			1.02348
$352$	27.7598	+	9.70147i	1.47960	+	0.517090i
$353$		−	4.80763i		−	0.255884i	−0.991782	−	0.127942i	$-0.959163\pi$
$353$		−	4.80763i		−	0.255884i	0.991782	−	0.127942i	$-0.0408372\pi$
$354$	1.11420	−	0.700221i	0.0592192	−	0.0372163i
$355$	−11.0562	+	5.20732i	−0.586804	+	0.276376i
$356$	5.46945	−	11.3619i	0.289880	−	0.602182i
$357$	6.04393			0.319879
$358$	11.5834	−	7.27962i	0.612204	−	0.384740i
$359$	−4.34250			−0.229188			−0.114594	−	0.993412i	$-0.536557\pi$
$359$	−4.34250			−0.229188			−0.114594	+	0.993412i	$0.536557\pi$
$360$	−8.07676	+	4.98085i	−0.425683	+	0.262514i
$361$	16.6642			0.877061
$362$	−8.82750	+	5.54764i	−0.463963	+	0.291578i
$363$	33.9907			1.78405
$364$	−10.8616	−	5.22857i	−0.569300	−	0.274052i
$365$	−6.16077	−	13.0806i	−0.322470	−	0.684670i
$366$	−0.0429988	+	0.0270226i	−0.00224758	+	0.00141249i
$367$			17.2023i			0.897953i	0.893544	+	0.448976i	$0.148211\pi$
$367$			17.2023i			0.897953i	−0.893544	+	0.448976i	$0.851789\pi$
$368$	−15.0178	+	11.9839i	−0.782855	+	0.624705i
$369$	7.72334			0.402061
$370$	12.4920	+	7.99907i	0.649427	+	0.415852i
$371$			10.4728i			0.543721i
$372$	10.3508	−	21.5022i	0.536664	−	1.11484i
$373$	−17.1548			−0.888243			−0.444121	−	0.895967i	$-0.646484\pi$
$373$	−17.1548			−0.888243			−0.444121	+	0.895967i	$0.646484\pi$
$374$	−11.1447	−	17.7336i	−0.576278	−	0.916982i
$375$	5.87467	−	22.9790i	0.303367	−	1.18663i
$376$	−1.96021	−	17.3610i	−0.101090	−	0.895323i
$377$			18.3565i			0.945410i
$378$	3.80932	−	2.39397i	0.195930	−	0.123132i
$379$		−	24.9107i		−	1.27958i	−0.768552	−	0.639788i	$-0.779022\pi$
$379$		−	24.9107i		−	1.27958i	0.768552	−	0.639788i	$-0.220978\pi$
$380$	6.83473	+	0.0579306i	0.350614	+	0.00297178i
$381$			9.64170i			0.493959i
$382$	−7.68621	−	12.2304i	−0.393261	−	0.625763i
$383$		−	3.63723i		−	0.185854i	−0.995673	−	0.0929269i	$-0.970378\pi$
$383$		−	3.63723i		−	0.185854i	0.995673	−	0.0929269i	$-0.0296223\pi$
$384$	16.9805	+	16.9620i	0.866531	+	0.865588i
$385$	−10.5159	+	4.95282i	−0.535938	+	0.252419i
$386$	8.99081	−	5.65028i	0.457620	−	0.287591i
$387$	−7.93063			−0.403136
$388$	6.46643	+	3.11283i	0.328283	+	0.158030i
$389$			11.6754i			0.591968i	0.955193	+	0.295984i	$0.0956475\pi$
$389$			11.6754i			0.591968i	−0.955193	+	0.295984i	$0.904352\pi$
$390$	−34.0509	−	21.8041i	−1.72424	−	1.10409i
$391$	13.6847			0.692066
$392$	−2.81057	+	0.317339i	−0.141955	+	0.0160281i
$393$		−	20.3076i		−	1.02438i
$394$	−4.50602	−	7.17004i	−0.227010	−	0.361222i
$395$	−20.9881	+	9.88510i	−1.05603	+	0.497373i
$396$	14.0550	+	6.76585i	0.706292	+	0.339997i
$397$	4.98018			0.249948			0.124974	−	0.992160i	$-0.460115\pi$
$397$	4.98018			0.249948			0.124974	+	0.992160i	$0.460115\pi$
$398$	8.48607	+	13.5032i	0.425368	+	0.676853i
$399$	3.24224			0.162315
$400$	−19.9971	−	0.339012i	−0.999856	−	0.0169506i
$401$	17.6074			0.879273			0.439636	−	0.898176i	$-0.355107\pi$
$401$	17.6074			0.879273			0.439636	+	0.898176i	$0.355107\pi$
$402$	−5.08981	−	8.09899i	−0.253857	−	0.403941i
$403$	33.9006			1.68871
$404$	34.2410	+	16.4830i	1.70355	+	0.820061i
$405$	22.7579	−	10.7186i	1.13085	−	0.532614i
$406$	2.29180	+	3.64676i	0.113740	+	0.180985i
$407$		−	24.3843i		−	1.20868i
$408$	−1.91798	−	16.9869i	−0.0949540	−	0.840976i
$409$	−12.7284			−0.629380			−0.314690	−	0.949194i	$-0.601901\pi$
$409$	−12.7284			−0.629380			−0.314690	+	0.949194i	$0.601901\pi$
$410$	13.7087	+	8.77819i	0.677024	+	0.433524i
$411$			41.1705i			2.03079i
$412$	−23.2293	−	11.1822i	−1.14443	−	0.550907i
$413$	0.438637			0.0215839
$414$	−8.62920	+	5.42302i	−0.424102	+	0.266527i
$415$	28.0985	−	13.2340i	1.37930	−	0.649630i
$416$	−11.2485	+	32.1864i	−0.551501	+	1.57807i
$417$			29.8418i			1.46136i
$418$	−5.97852	−	9.51311i	−0.292419	−	0.465301i
$419$		−	19.7831i		−	0.966465i	−0.875492	−	0.483233i	$-0.839463\pi$
$419$		−	19.7831i		−	0.966465i	0.875492	−	0.483233i	$-0.160537\pi$
$420$	−9.48687	−	0.0804099i	−0.462912	−	0.00392360i
$421$			39.6263i			1.93127i	0.259908	+	0.965634i	$0.416308\pi$
$421$			39.6263i			1.93127i	−0.259908	+	0.965634i	$0.583692\pi$
$422$	−10.0088	+	6.29002i	−0.487220	+	0.306194i
$423$		−	9.26775i		−	0.450613i
$424$	29.4346	−	3.32343i	1.42947	−	0.161400i
$425$	10.9823	+	9.07261i	0.532720	+	0.440086i
$426$	8.72483	+	13.8831i	0.422720	+	0.672638i
$427$	−0.0169277			−0.000819188
$428$	−14.1203	+	29.3329i	−0.682532	+	1.41786i
$429$			66.4673i			3.20907i
$430$	−14.0766	−	9.01378i	−0.678835	−	0.434683i
$431$	−8.94297			−0.430768			−0.215384	−	0.976529i	$-0.569100\pi$
$431$	−8.94297			−0.430768			−0.215384	+	0.976529i	$0.569100\pi$
$432$	−7.93725	−	9.94665i	−0.381881	−	0.478558i
$433$		−	34.1417i		−	1.64075i	−0.571828	−	0.820374i	$-0.693765\pi$
$433$		−	34.1417i		−	1.64075i	0.571828	−	0.820374i	$-0.306235\pi$
$434$	6.73477	−	4.23247i	0.323279	−	0.203165i
$435$	6.15576	+	13.0700i	0.295146	+	0.626657i
$436$	1.78116	+	0.857422i	0.0853023	+	0.0410631i
$437$	7.34111			0.351173
$438$	−16.4251	+	10.3223i	−0.784820	+	0.493220i
$439$	−21.0065			−1.00259			−0.501293	−	0.865277i	$-0.667142\pi$
$439$	−21.0065			−1.00259			−0.501293	+	0.865277i	$0.667142\pi$
$440$	17.2573	+	27.9838i	0.822711	+	1.33408i
$441$	−1.50036			−0.0714456
$442$	20.5614	−	12.9218i	0.978004	−	0.614627i
$443$	22.8086			1.08367			0.541834	−	0.840486i	$-0.317730\pi$
$443$	22.8086			1.08367			0.541834	+	0.840486i	$0.317730\pi$
$444$	8.63241	−	17.9325i	0.409676	−	0.851040i
$445$	12.7544	−	6.00714i	0.604617	−	0.284766i
$446$	−1.50043	+	0.942949i	−0.0710477	+	0.0446499i
$447$		−	38.2631i		−	1.80978i
$448$	1.78381	+	7.79859i	0.0842770	+	0.368449i
$449$	−26.9912			−1.27379			−0.636897	−	0.770949i	$-0.719782\pi$
$449$	−26.9912			−1.27379			−0.636897	+	0.770949i	$0.719782\pi$
$450$	−10.5205	−	1.36883i	−0.495939	−	0.0645273i
$451$		−	26.7593i		−	1.26005i
$452$	34.6145	+	16.6628i	1.62813	+	0.783753i
$453$	−6.86477			−0.322535
$454$	−0.492653	−	0.783917i	−0.0231213	−	0.0367910i
$455$	−5.74258	−	12.1927i	−0.269216	−	0.571603i
$456$	−1.02889	−	9.11255i	−0.0481822	−	0.426734i
$457$		−	26.3304i		−	1.23169i	−0.787869	−	0.615843i	$-0.788816\pi$
$457$		−	26.3304i		−	1.23169i	0.787869	−	0.615843i	$-0.211184\pi$
$458$	−29.7023	+	18.6664i	−1.38790	+	0.872224i
$459$			9.06374i			0.423059i
$460$	−21.4802	−	0.182065i	−1.00152	−	0.00848881i
$461$			17.1623i			0.799326i	0.916662	+	0.399663i	$0.130873\pi$
$461$			17.1623i			0.799326i	−0.916662	+	0.399663i	$0.869127\pi$
$462$	8.29841	+	13.2046i	0.386077	+	0.614332i
$463$			7.15174i			0.332370i	0.986095	+	0.166185i	$0.0531448\pi$
$463$			7.15174i			0.332370i	−0.986095	+	0.166185i	$0.946855\pi$
$464$	9.52218	−	7.59853i	0.442056	−	0.352753i
$465$	24.1374	−	11.3684i	1.11935	−	0.527196i
$466$	9.78264	−	6.14790i	0.453172	−	0.284796i
$467$	−23.3584			−1.08090			−0.540449	−	0.841376i	$-0.681746\pi$
$467$	−23.3584			−1.08090			−0.540449	+	0.841376i	$0.681746\pi$
$468$	−7.84472	+	16.2962i	−0.362622	+	0.753293i
$469$		−	3.18839i		−	0.147226i
$470$	10.5335	−	16.4500i	0.485875	−	0.758780i
$471$	−0.620452			−0.0285889
$472$	−0.139197	−	1.23282i	−0.00640704	−	0.0567451i
$473$			27.4775i			1.26342i
$474$	16.5624	+	26.3544i	0.760737	+	1.21050i
$475$	5.89142	+	4.86697i	0.270317	+	0.223312i
$476$	2.47149	−	5.13415i	0.113281	−	0.235323i
$477$	15.7130			0.719447
$478$	7.18968	+	11.4403i	0.328848	+	0.523268i
$479$	−39.0636			−1.78486			−0.892432	−	0.451183i	$-0.851002\pi$
$479$	−39.0636			−1.78486			−0.892432	+	0.451183i	$0.851002\pi$
$480$	2.78456	+	26.6890i	0.127097	+	1.21818i
$481$	28.2726			1.28912
$482$	−15.3732	−	24.4620i	−0.700229	−	1.11422i
$483$	−10.1897			−0.463650
$484$	13.8995	−	28.8741i	0.631797	−	1.31246i
$485$	3.41885	+	7.25893i	0.155242	+	0.329611i
$486$	−10.7771	−	17.1487i	−0.488860	−	0.777882i
$487$		−	18.0575i		−	0.818262i	−0.912476	−	0.409131i	$-0.865832\pi$
$487$		−	18.0575i		−	0.818262i	0.912476	−	0.409131i	$-0.134168\pi$
$488$	0.00537182	+	0.0475764i	0.000243171	+	0.00215368i
$489$	−27.6196			−1.24900
$490$	−2.66309	−	1.70527i	−0.120306	−	0.0770364i
$491$		−	28.2637i		−	1.27552i	−0.770235	−	0.637760i	$-0.779861\pi$
$491$		−	28.2637i		−	1.27552i	0.770235	−	0.637760i	$-0.220139\pi$
$492$	9.47321	−	19.6792i	0.427085	−	0.887205i
$493$	−8.67695			−0.390790
$494$	11.0301	−	6.93184i	0.496266	−	0.311878i
$495$	7.43099	+	15.7775i	0.333998	+	0.709148i
$496$	−14.0329	−	17.5854i	−0.630094	−	0.789608i
$497$			5.46547i			0.245160i
$498$	−22.1734	−	35.2827i	−0.993615	−	1.58106i
$499$		−	2.52606i		−	0.113082i	−0.998400	−	0.0565411i	$-0.981993\pi$
$499$		−	2.52606i		−	0.113082i	0.998400	−	0.0565411i	$-0.0180072\pi$
$500$	−17.1177	−	14.3870i	−0.765527	−	0.643404i
$501$		−	38.2150i		−	1.70732i
$502$	27.0721	−	17.0135i	1.20829	−	0.759347i
$503$		−	2.49511i		−	0.111252i	−0.998452	−	0.0556258i	$-0.982285\pi$
$503$		−	2.49511i		−	0.111252i	0.998452	−	0.0556258i	$-0.0177154\pi$
$504$	0.476122	+	4.21686i	0.0212082	+	0.187834i
$505$	18.1034	+	38.4374i	0.805593	+	1.71044i
$506$	18.7893	+	29.8979i	0.835287	+	1.32912i
$507$	−49.4878			−2.19783
$508$	8.19035	+	3.94269i	0.363388	+	0.174929i
$509$			14.7415i			0.653404i	0.945127	+	0.326702i	$0.105937\pi$
$509$			14.7415i			0.653404i	−0.945127	+	0.326702i	$0.894063\pi$
$510$	10.3066	−	16.0955i	0.456382	−	0.712722i
$511$	−6.46618			−0.286047
$512$	21.3524	−	7.48831i	0.943652	−	0.330940i
$513$			4.86221i			0.214672i
$514$	21.2253	−	13.3391i	0.936209	−	0.588361i
$515$	−12.2815	−	26.0762i	−0.541187	−	1.14905i
$516$	−9.72746	+	20.2073i	−0.428227	+	0.889578i
$517$	−32.1103			−1.41221
$518$	5.61670	−	3.52982i	0.246784	−	0.155091i
$519$	−10.1852			−0.447080
$520$	−32.4461	+	20.0091i	−1.42285	+	0.877459i
$521$	−35.5594			−1.55788			−0.778942	−	0.627096i	$-0.784243\pi$
$521$	−35.5594			−1.55788			−0.778942	+	0.627096i	$0.784243\pi$
$522$	5.47144	−	3.43853i	0.239478	−	0.150500i
$523$	−37.3619			−1.63372			−0.816860	−	0.576835i	$-0.804287\pi$
$523$	−37.3619			−1.63372			−0.816860	+	0.576835i	$0.804287\pi$
$524$	−17.2507	−	8.30421i	−0.753602	−	0.362771i
$525$	−8.17751	−	6.75554i	−0.356896	−	0.294836i
$526$	27.5361	−	17.3051i	1.20063	−	0.754536i
$527$			16.0245i			0.698036i
$528$	34.4789	−	27.5136i	1.50050	−	1.19737i
$529$	−0.0717106			−0.00311785
$530$	27.8900	+	17.8590i	1.21147	+	0.775746i
$531$		−	0.658112i		−	0.0285596i
$532$	1.32582	−	2.75419i	0.0574817	−	0.119409i
$533$	31.0263			1.34390
$534$	−10.0649	−	16.0155i	−0.435552	−	0.693057i
$535$	−32.9278	+	15.5085i	−1.42359	+	0.670490i
$536$	−8.96119	+	1.01180i	−0.387064	+	0.0437032i
$537$		−	20.5223i		−	0.885601i
$538$	1.05633	−	0.663850i	0.0455416	−	0.0286206i
$539$			5.19834i			0.223908i
$540$	0.120586	−	14.2269i	0.00518920	−	0.612229i
$541$		−	5.18769i		−	0.223036i	−0.993762	−	0.111518i	$-0.964429\pi$
$541$		−	5.18769i		−	0.223036i	0.993762	−	0.111518i	$-0.0355713\pi$
$542$	4.90361	+	7.80270i	0.210628	+	0.335155i
$543$			15.6396i			0.671159i
$544$	−15.2142	−	5.31703i	−0.652303	−	0.227966i
$545$	0.941714	+	1.99945i	0.0403386	+	0.0856472i
$546$	−15.3101	+	9.62166i	−0.655213	+	0.411769i
$547$	17.8859			0.764746			0.382373	−	0.924008i	$-0.375107\pi$
$547$	17.8859			0.764746			0.382373	+	0.924008i	$0.375107\pi$
$548$	34.9731	+	16.8355i	1.49398	+	0.719176i
$549$			0.0253976i			0.00108394i
$550$	−4.74263	+	36.4506i	−0.202227	+	1.55426i
$551$	−4.65471			−0.198297
$552$	3.23361	+	28.6390i	0.137631	+	1.21896i
$553$			10.3751i			0.441195i
$554$	3.41774	+	5.43836i	0.145206	+	0.231054i
$555$	20.1302	−	9.48105i	0.854482	−	0.402448i
$556$	25.3497	+	12.2029i	1.07507	+	0.517519i
$557$	−41.2170			−1.74642			−0.873211	−	0.487342i	$-0.837966\pi$
$557$	−41.2170			−1.74642			−0.873211	+	0.487342i	$0.837966\pi$
$558$	−6.35022	−	10.1046i	−0.268826	−	0.427760i
$559$	−31.8590			−1.34749
$560$	−3.94769	+	8.02594i	−0.166820	+	0.339158i
$561$	−31.4184			−1.32649
$562$	17.3216	+	27.5623i	0.730666	+	1.16265i
$563$	3.19209			0.134530			0.0672652	−	0.997735i	$-0.478573\pi$
$563$	3.19209			0.134530			0.0672652	+	0.997735i	$0.478573\pi$
$564$	−23.6143	−	11.3675i	−0.994342	−	0.478659i
$565$	18.3009	+	38.8567i	0.769926	+	1.63471i
$566$	−1.28492	−	2.04459i	−0.0540093	−	0.0859404i
$567$		−	11.2500i		−	0.472456i
$568$	15.3611	−	1.73441i	0.644536	−	0.0727741i
$569$	−28.7302			−1.20443			−0.602217	−	0.798333i	$-0.705716\pi$
$569$	−28.7302			−1.20443			−0.602217	+	0.798333i	$0.705716\pi$
$570$	5.52891	−	8.63438i	0.231581	−	0.361654i
$571$			10.9823i			0.459596i	0.973238	+	0.229798i	$0.0738066\pi$
$571$			10.9823i			0.459596i	−0.973238	+	0.229798i	$0.926193\pi$
$572$	56.4621	+	27.1799i	2.36080	+	1.13645i
$573$	−21.6685			−0.905215
$574$	6.16377	−	3.87362i	0.257271	−	0.161682i
$575$	−18.5156	−	15.2959i	−0.772153	−	0.637885i
$576$	11.7007	−	2.67635i	0.487528	−	0.111515i
$577$			17.8148i			0.741638i	0.928705	+	0.370819i	$0.120923\pi$
$577$			17.8148i			0.741638i	−0.928705	+	0.370819i	$0.879077\pi$
$578$	−6.68450	−	10.6365i	−0.278039	−	0.442420i
$579$		−	15.9289i		−	0.661984i
$580$	13.6198	+	0.115440i	0.565531	+	0.00479339i
$581$		−	13.8900i		−	0.576255i
$582$	9.11489	−	5.72826i	0.377825	−	0.237444i
$583$		−	54.4412i		−	2.25473i
$584$	2.05197	+	18.1736i	0.0849112	+	0.752031i
$585$	−18.2934	+	8.61593i	−0.756339	+	0.356225i
$586$	−8.97010	−	14.2734i	−0.370552	−	0.589628i
$587$	−31.7501			−1.31047			−0.655234	−	0.755426i	$-0.727430\pi$
$587$	−31.7501			−1.31047			−0.655234	+	0.755426i	$0.727430\pi$
$588$	−1.84029	+	3.82293i	−0.0758923	+	0.157655i
$589$			8.59626i			0.354203i
$590$	0.747996	−	1.16813i	0.0307945	−	0.0480911i
$591$	−12.7031			−0.522536
$592$	−11.7032	−	14.6660i	−0.480998	−	0.602768i
$593$			10.6769i			0.438448i	0.975675	+	0.219224i	$0.0703525\pi$
$593$			10.6769i			0.438448i	−0.975675	+	0.219224i	$0.929648\pi$
$594$	−19.8021	+	12.4446i	−0.812491	+	0.510610i
$595$	5.76337	−	2.71446i	0.236275	−	0.111282i
$596$	−32.5034	−	15.6466i	−1.33139	−	0.640910i
$597$	23.9234			0.979121
$598$	−34.6653	+	21.7854i	−1.41757	+	0.890873i
$599$	21.0247			0.859045			0.429523	−	0.903056i	$-0.358682\pi$
$599$	21.0247			0.859045			0.429523	+	0.903056i	$0.358682\pi$
$600$	−16.3918	+	25.1273i	−0.669194	+	1.02582i
$601$	47.1712			1.92415			0.962077	−	0.272779i	$-0.0879429\pi$
$601$	47.1712			1.92415			0.962077	+	0.272779i	$0.0879429\pi$
$602$	−6.32920	+	3.97758i	−0.257959	+	0.162114i
$603$	−4.78372			−0.194808
$604$	−2.80715	+	5.83143i	−0.114221	+	0.237278i
$605$	32.4128	−	15.2660i	1.31777	−	0.620650i
$606$	48.2651	−	30.3322i	1.96063	−	1.23216i
$607$			25.4193i			1.03174i	0.856668	+	0.515868i	$0.172530\pi$
$607$			25.4193i			1.03174i	−0.856668	+	0.515868i	$0.827470\pi$
$608$	−8.16158	−	2.85230i	−0.330996	−	0.115676i
$609$	6.46092			0.261810
$610$	−0.0288663	+	0.0450799i	−0.00116876	+	0.00182523i
$611$		−	37.2305i		−	1.50619i
$612$	−7.70306	−	3.70812i	−0.311378	−	0.149892i
$613$	20.4828			0.827294			0.413647	−	0.910437i	$-0.364255\pi$
$613$	20.4828			0.827294			0.413647	+	0.910437i	$0.364255\pi$
$614$	7.75764	+	12.3441i	0.313073	+	0.498167i
$615$	22.0909	−	10.4045i	0.890793	−	0.419550i
$616$	14.6103	−	1.64964i	0.588665	−	0.0664658i
$617$			44.2279i			1.78055i	0.455425	+	0.890274i	$0.349487\pi$
$617$			44.2279i			1.78055i	−0.455425	+	0.890274i	$0.650513\pi$
$618$	−32.7433	+	20.5776i	−1.31713	+	0.827751i
$619$		−	12.1807i		−	0.489583i	−0.969576	−	0.244791i	$-0.921281\pi$
$619$		−	12.1807i		−	0.489583i	0.969576	−	0.244791i	$-0.0787195\pi$
$620$	0.213193	−	25.1528i	0.00856204	−	1.01016i
$621$		−	15.2810i		−	0.613205i
$622$	−6.81028	−	10.8366i	−0.273067	−	0.434509i
$623$		−	6.30493i		−	0.252602i
$624$	31.9008	+	39.9769i	1.27706	+	1.60036i
$625$	−4.71839	−	24.5507i	−0.188735	−	0.982028i
$626$	−2.94384	+	1.85006i	−0.117660	+	0.0739433i
$627$	−16.8543			−0.673095
$628$	−0.253716	+	0.527056i	−0.0101244	+	0.0210318i
$629$			13.3642i			0.532864i
$630$	−2.55852	+	3.99558i	−0.101934	+	0.159188i
$631$	10.2466			0.407912			0.203956	−	0.978980i	$-0.434620\pi$
$631$	10.2466			0.407912			0.203956	+	0.978980i	$0.434620\pi$
$632$	29.1600	−	3.29244i	1.15992	−	0.130966i
$633$			17.7325i			0.704802i
$634$	−0.597087	−	0.950095i	−0.0237134	−	0.0377331i
$635$	4.33029	+	9.19412i	0.171842	+	0.364857i
$636$	19.2730	−	40.0368i	0.764225	−	1.58756i
$637$	−6.02726			−0.238809
$638$	−11.9136	−	18.9571i	−0.471663	−	0.750518i
$639$	8.20015			0.324393
$640$	23.8102	+	8.54830i	0.941182	+	0.337901i
$641$	−22.9323			−0.905770			−0.452885	−	0.891569i	$-0.649605\pi$
$641$	−22.9323			−0.905770			−0.452885	+	0.891569i	$0.649605\pi$
$642$	25.9844	+	41.3467i	1.02552	+	1.63183i
$643$	−17.5511			−0.692147			−0.346074	−	0.938207i	$-0.612485\pi$
$643$	−17.5511			−0.692147			−0.346074	+	0.938207i	$0.612485\pi$
$644$	−4.16680	+	8.65590i	−0.164195	+	0.341090i
$645$	−22.6838	+	10.6838i	−0.893175	+	0.420672i
$646$	3.27661	+	5.21380i	0.128917	+	0.205134i
$647$			15.9490i			0.627021i	0.949585	+	0.313511i	$0.101505\pi$
$647$			15.9490i			0.627021i	−0.949585	+	0.313511i	$0.898495\pi$
$648$	−31.6189	+	3.57007i	−1.24211	+	0.140245i
$649$	−2.28018			−0.0895050
$650$	−42.2629	−	5.49889i	−1.65769	−	0.215684i
$651$		−	11.9319i		−	0.467649i
$652$	−11.2942	+	23.4620i	−0.442316	+	0.918844i
$653$	20.5764			0.805218			0.402609	−	0.915372i	$-0.368103\pi$
$653$	20.5764			0.805218			0.402609	+	0.915372i	$0.368103\pi$
$654$	2.51068	−	1.57784i	0.0981752	−	0.0616982i
$655$	−9.12059	−	19.3649i	−0.356371	−	0.756650i
$656$	−12.8431	−	16.0944i	−0.501438	−	0.628382i
$657$			9.70158i			0.378495i
$658$	−4.64821	−	7.39631i	−0.181206	−	0.288338i
$659$			47.6592i			1.85654i	0.371907	+	0.928270i	$0.378704\pi$
$659$			47.6592i			1.85654i	−0.371907	+	0.928270i	$0.621296\pi$
$660$	49.3160	+	0.417998i	1.91962	+	0.0162705i
$661$			15.3338i			0.596417i	0.954501	+	0.298208i	$0.0963890\pi$
$661$			15.3338i			0.596417i	−0.954501	+	0.298208i	$0.903611\pi$
$662$	−7.39258	+	4.64587i	−0.287321	+	0.180567i
$663$		−	36.4284i		−	1.41476i
$664$	−39.0389	+	4.40785i	−1.51500	+	0.171058i
$665$	3.09173	−	1.45616i	0.119892	−	0.0564675i
$666$	−5.29599	−	8.42706i	−0.205215	−	0.326542i
$667$	14.6289			0.566432
$668$	−32.4626	−	15.6269i	−1.25602	−	0.604624i
$669$			2.65831i			0.102776i
$670$	−8.49097	−	5.43708i	−0.328035	−	0.210053i
$671$	0.0879958			0.00339704
$672$	11.3286	+	3.95910i	0.437010	+	0.152726i
$673$			12.4825i			0.481165i	0.970629	+	0.240583i	$0.0773385\pi$
$673$			12.4825i			0.481165i	−0.970629	+	0.240583i	$0.922661\pi$
$674$	−10.7696	+	6.76816i	−0.414830	+	0.260700i
$675$	10.1309	−	12.2633i	0.389938	−	0.472016i
$676$	−20.2366	+	42.0385i	−0.778331	+	1.61686i
$677$	10.2605			0.394343			0.197172	−	0.980369i	$-0.436824\pi$
$677$	10.2605			0.394343			0.197172	+	0.980369i	$0.436824\pi$
$678$	48.7916	−	30.6631i	1.87383	−	1.17761i
$679$	3.58833			0.137707
$680$	−9.45812	−	15.3369i	−0.362702	−	0.588145i
$681$	−1.38886			−0.0532211
$682$	−35.0096	+	22.0018i	−1.34059	+	0.842493i
$683$	−26.9367			−1.03071			−0.515353	−	0.856978i	$-0.672339\pi$
$683$	−26.9367			−1.03071			−0.515353	+	0.856978i	$0.672339\pi$
$684$	−4.13227	−	1.98921i	−0.158001	−	0.0760592i
$685$	18.4906	+	39.2593i	0.706488	+	1.50002i
$686$	−1.19739	+	0.752500i	−0.0457166	+	0.0287306i
$687$			52.6232i			2.00770i
$688$	13.1878	+	16.5264i	0.502779	+	0.630063i
$689$	63.1223			2.40477
$690$	−17.3763	+	27.1362i	−0.661505	+	1.03306i
$691$			33.8769i			1.28874i	0.764714	+	0.644369i	$0.222880\pi$
$691$			33.8769i			1.28874i	−0.764714	+	0.644369i	$0.777120\pi$
$692$	−4.16494	+	8.65203i	−0.158327	+	0.328901i
$693$	7.79937			0.296274
$694$	11.0908	+	17.6478i	0.421000	+	0.669902i
$695$	13.4026	+	28.4565i	0.508389	+	1.07942i
$696$	−2.05030	−	18.1589i	−0.0777166	−	0.688310i
$697$			14.6658i			0.555508i
$698$	−4.36076	+	2.74052i	−0.165057	+	0.103730i
$699$		−	17.3318i		−	0.655549i
$700$	−9.08259	+	4.18408i	−0.343290	+	0.158143i
$701$			31.5922i			1.19322i	0.802531	+	0.596610i	$0.203486\pi$
$701$			31.5922i			1.19322i	−0.802531	+	0.596610i	$0.796514\pi$
$702$	−14.4290	−	22.9597i	−0.544589	−	0.866559i
$703$			7.16915i			0.270390i
$704$	−9.27284	−	40.5397i	−0.349483	−	1.52790i
$705$	−12.4851	−	26.5084i	−0.470214	−	0.998363i
$706$	−5.75661	+	3.61774i	−0.216653	+	0.136156i
$707$	19.0009			0.714601
$708$	−1.67687	−	0.807219i	−0.0630208	−	0.0303371i
$709$		−	47.3591i		−	1.77861i	−0.457315	−	0.889305i	$-0.651189\pi$
$709$		−	47.3591i		−	1.77861i	0.457315	−	0.889305i	$-0.348811\pi$
$710$	14.5550	+	9.32012i	0.546240	+	0.349778i
$711$	15.5664			0.583786
$712$	−17.7204	+	2.00080i	−0.664102	+	0.0749832i
$713$		−	27.0164i		−	1.01177i
$714$	−4.54806	−	7.23695i	−0.170207	−	0.270836i
$715$	29.8519	+	63.3818i	1.11640	+	2.37035i
$716$	−17.4331	−	8.39199i	−0.651505	−	0.313623i
$717$	20.2687			0.756949
$718$	3.26773	+	5.19966i	0.121951	+	0.194050i
$719$	38.1859			1.42409			0.712047	−	0.702132i	$-0.247768\pi$
$719$	38.1859			1.42409			0.712047	+	0.702132i	$0.247768\pi$
$720$	12.0418	+	5.92294i	0.448771	+	0.220735i
$721$	−12.8903			−0.480061
$722$	−12.5398	−	19.9535i	−0.466682	−	0.742592i
$723$	−43.3391			−1.61180
$724$	13.2854	+	6.39536i	0.493748	+	0.237682i
$725$	11.7400	+	9.69856i	0.436013	+	0.360195i
$726$	−25.5780	−	40.7002i	−0.949289	−	1.51052i
$727$			10.6304i			0.394262i	0.980377	+	0.197131i	$0.0631624\pi$
$727$			10.6304i			0.394262i	−0.980377	+	0.197131i	$0.936838\pi$
$728$	1.91269	+	16.9400i	0.0708889	+	0.627839i
$729$	3.36776			0.124732
$730$	−11.0266	+	17.2200i	−0.408113	+	0.637341i
$731$		−	15.0594i		−	0.556994i
$732$	0.0647132	+	0.0311519i	0.00239187	+	0.00115141i
$733$	3.83559			0.141671			0.0708354	−	0.997488i	$-0.477433\pi$
$733$	3.83559			0.141671			0.0708354	+	0.997488i	$0.477433\pi$
$734$	20.5979	−	12.9447i	0.760281	−	0.477799i
$735$	−4.29145	+	2.02121i	−0.158292	+	0.0745534i
$736$	25.6503	+	8.96423i	0.945482	+	0.330426i
$737$			16.5743i			0.610524i
$738$	−5.81182	−	9.24786i	−0.213936	−	0.340418i
$739$			41.3288i			1.52031i	0.649744	+	0.760153i	$0.274876\pi$
$739$			41.3288i			1.52031i	−0.649744	+	0.760153i	$0.725124\pi$
$740$	0.177800	−	20.9771i	0.00653605	−	0.771133i
$741$		−	19.5418i		−	0.717887i
$742$	12.5400	−	7.88079i	0.460359	−	0.289313i
$743$		−	4.38109i		−	0.160727i	−0.996766	−	0.0803633i	$-0.974392\pi$
$743$		−	4.38109i		−	0.160727i	0.996766	−	0.0803633i	$-0.0256080\pi$
$744$	−33.5355	+	3.78647i	−1.22947	+	0.138819i
$745$	−17.1848	−	36.4869i	−0.629602	−	1.33678i
$746$	12.9090	+	20.5410i	0.472632	+	0.752060i
$747$	−20.8400			−0.762496
$748$	−12.8477	+	26.6891i	−0.469757	+	0.975849i
$749$			16.2773i			0.594759i
$750$	−31.9355	+	10.2574i	−1.16612	+	0.374547i
$751$	−16.3956			−0.598285			−0.299143	−	0.954208i	$-0.596701\pi$
$751$	−16.3956			−0.598285			−0.299143	+	0.954208i	$0.596701\pi$
$752$	−19.3128	+	15.4113i	−0.704265	+	0.561991i
$753$		−	47.9633i		−	1.74788i
$754$	21.9799	−	13.8133i	0.800462	−	0.503051i
$755$	−6.54610	+	3.08312i	−0.238237	+	0.112206i
$756$	−5.73302	−	2.75978i	−0.208508	−	0.100372i
$757$	−39.7528			−1.44484			−0.722420	−	0.691454i	$-0.756970\pi$
$757$	−39.7528			−1.44484			−0.722420	+	0.691454i	$0.756970\pi$
$758$	−29.8278	+	18.7453i	−1.08339	+	0.680859i
$759$	52.9698			1.92268
$760$	−5.07377	−	8.22743i	−0.184045	−	0.298440i
$761$	4.22709			0.153232			0.0766160	−	0.997061i	$-0.475588\pi$
$761$	4.22709			0.153232			0.0766160	+	0.997061i	$0.475588\pi$
$762$	11.5449	−	7.25538i	0.418227	−	0.262835i
$763$	0.988397			0.0357824
$764$	−8.86071	+	18.4068i	−0.320569	+	0.665934i
$765$	−4.07266	−	8.64711i	−0.147247	−	0.312637i
$766$	−4.35519	+	2.73702i	−0.157359	+	0.0988925i
$767$		−	2.64378i		−	0.0954612i
$768$	7.53232	−	33.0962i	0.271799	−	1.19425i
$769$	−17.1527			−0.618542			−0.309271	−	0.950974i	$-0.600085\pi$
$769$	−17.1527			−0.618542			−0.309271	+	0.950974i	$0.600085\pi$
$770$	13.8436	+	8.86459i	0.498890	+	0.319458i
$771$		−	37.6047i		−	1.35430i
$772$	−13.5312	−	6.51367i	−0.486997	−	0.234432i
$773$	32.4384			1.16673			0.583364	−	0.812211i	$-0.301736\pi$
$773$	32.4384			1.16673			0.583364	+	0.812211i	$0.301736\pi$
$774$	5.96780	+	9.49606i	0.214508	+	0.341329i
$775$	17.9112	−	21.6813i	0.643388	−	0.778814i
$776$	−1.13872	−	10.0852i	−0.0408776	−	0.362039i
$777$		−	9.95105i		−	0.356992i
$778$	13.9801	−	8.78577i	0.501209	−	0.314985i
$779$			7.86743i			0.281880i
$780$	−0.484651	+	57.1798i	−0.0173533	+	2.04737i
$781$		−	28.4113i		−	1.01664i
$782$	−10.2978	−	16.3860i	−0.368247	−	0.585961i
$783$			9.68907i			0.346259i
$784$	2.49493	+	3.12655i	0.0891047	+	0.111662i
$785$	−0.591650	+	0.278658i	−0.0211169	+	0.00994574i
$786$	−24.3161	+	15.2815i	−0.867328	+	0.545072i
$787$	14.6777			0.523203			0.261602	−	0.965176i	$-0.415749\pi$
$787$	14.6777			0.523203			0.261602	+	0.965176i	$0.415749\pi$
$788$	−5.19456	+	10.7909i	−0.185049	+	0.384411i
$789$		−	48.7854i		−	1.73681i
$790$	27.6299	+	17.6924i	0.983027	+	0.629469i
$791$	19.2081			0.682963
$792$	−2.47505	−	21.9207i	−0.0879469	−	0.778917i
$793$			0.102027i			0.00362310i
$794$	−3.74758	−	5.96321i	−0.132997	−	0.211627i
$795$	44.9435	−	21.1677i	1.59398	−	0.750742i
$796$	9.78280	−	20.3223i	0.346742	−	0.720304i
$797$	8.78616			0.311222			0.155611	−	0.987818i	$-0.450265\pi$
$797$	8.78616			0.311222			0.155611	+	0.987818i	$0.450265\pi$
$798$	−2.43979	−	3.88223i	−0.0863676	−	0.137429i
$799$	17.5985			0.622590
$800$	14.6419	+	24.1995i	0.517670	+	0.855581i
$801$	−9.45965			−0.334240
$802$	−13.2496	−	21.0830i	−0.467859	−	0.744465i
$803$	33.6134			1.18619
$804$	−5.86757	+	12.1890i	−0.206933	+	0.429872i
$805$	−9.71673	+	4.57644i	−0.342470	+	0.161298i
$806$	−25.5102	−	40.5922i	−0.898558	−	1.42980i
$807$		−	1.87149i		−	0.0658795i
$808$	−6.02972	−	53.4033i	−0.212125	−	1.87872i
$809$	−3.35869			−0.118085			−0.0590426	−	0.998255i	$-0.518805\pi$
$809$	−3.35869			−0.118085			−0.0590426	+	0.998255i	$0.518805\pi$
$810$	−29.9597	−	19.1843i	−1.05268	−	0.674069i
$811$		−	31.8199i		−	1.11735i	−0.829388	−	0.558673i	$-0.811311\pi$
$811$		−	31.8199i		−	1.11735i	0.829388	−	0.558673i	$-0.188689\pi$
$812$	2.64201	−	5.48837i	0.0927163	−	0.192604i
$813$	13.8240			0.484828
$814$	−29.1975	+	18.3492i	−1.02337	+	0.643139i
$815$	−26.3374	+	12.4045i	−0.922560	+	0.434512i
$816$	−18.8967	+	15.0792i	−0.661515	+	0.527878i
$817$		−	8.07858i		−	0.282634i
$818$	9.57814	+	15.2409i	0.334892	+	0.532885i
$819$			9.04304i			0.315989i
$820$	0.195118	−	23.0202i	0.00681380	−	0.803902i
$821$		−	18.4178i		−	0.642785i	−0.946946	−	0.321392i	$-0.895849\pi$
$821$		−	18.4178i		−	0.642785i	0.946946	−	0.321392i	$-0.104151\pi$
$822$	49.2971	−	30.9808i	1.71943	−	1.08058i
$823$			35.4510i			1.23574i	0.786279	+	0.617872i	$0.212005\pi$
$823$			35.4510i			1.23574i	−0.786279	+	0.617872i	$0.787995\pi$
$824$	4.09060	+	36.2291i	0.142503	+	1.26210i
$825$	42.5095	+	35.1176i	1.47999	+	1.22264i
$826$	−0.330074	−	0.525219i	−0.0114847	−	0.0182747i
$827$	5.08845			0.176943			0.0884714	−	0.996079i	$-0.471802\pi$
$827$	5.08845			0.176943			0.0884714	+	0.996079i	$0.471802\pi$
$828$	12.9869	+	6.25169i	0.451327	+	0.217261i
$829$		−	5.21215i		−	0.181025i	−0.995895	−	0.0905127i	$-0.971149\pi$
$829$		−	5.21215i		−	0.181025i	0.995895	−	0.0905127i	$-0.0288506\pi$
$830$	−36.9904	−	23.6863i	−1.28395	−	0.822163i
$831$	9.63510			0.334238
$832$	47.0041	−	10.7515i	1.62958	−	0.372740i
$833$		−	2.84902i		−	0.0987129i
$834$	35.7322	−	22.4559i	1.23731	−	0.777585i
$835$	−17.1632	−	36.4411i	−0.593957	−	1.26109i
$836$	−6.89207	+	14.3172i	−0.238367	+	0.495172i
$837$	17.8936			0.618494
$838$	−23.6880	+	14.8867i	−0.818290	+	0.514254i
$839$	19.4837			0.672651			0.336326	−	0.941746i	$-0.390816\pi$
$839$	19.4837			0.672651			0.336326	+	0.941746i	$0.390816\pi$
$840$	7.04259	+	11.4200i	0.242992	+	0.394027i
$841$	19.7244			0.680152
$842$	47.4481	−	29.8188i	1.63517	−	1.02762i
$843$	48.8319			1.68186
$844$	15.0632	+	7.25118i	0.518498	+	0.249596i
$845$	−47.1905	+	22.2260i	−1.62340	+	0.764599i
$846$	−11.0971	+	6.97398i	−0.381526	+	0.239770i
$847$		−	16.0227i		−	0.550548i
$848$	−26.1290	−	32.7438i	−0.897272	−	1.12443i
$849$	−3.62238			−0.124320
$850$	2.59927	−	19.9773i	0.0891542	−	0.685214i
$851$		−	22.5313i		−	0.772362i
$852$	10.0580	−	20.8941i	0.344583	−	0.715819i
$853$	−24.4612			−0.837537			−0.418768	−	0.908093i	$-0.637538\pi$
$853$	−24.4612			−0.837537			−0.418768	+	0.908093i	$0.637538\pi$
$854$	0.0127381	+	0.0202690i	0.000435888	+	0.000693592i
$855$	−2.18476	−	4.63871i	−0.0747173	−	0.158640i
$856$	45.7484	−	5.16542i	1.56365	−	0.176550i
$857$		−	55.7585i		−	1.90467i	−0.305047	−	0.952337i	$-0.598672\pi$
$857$		−	55.7585i		−	1.90467i	0.305047	−	0.952337i	$-0.401328\pi$
$858$	79.5873	−	50.0167i	2.71707	−	1.70754i
$859$		−	34.5757i		−	1.17971i	−0.807510	−	0.589854i	$-0.799185\pi$
$859$		−	34.5757i		−	1.17971i	0.807510	−	0.589854i	$-0.200815\pi$
$860$	−0.200354	+	23.6381i	−0.00683203	+	0.806052i
$861$		−	10.9203i		−	0.372162i
$862$	6.72959	+	10.7082i	0.229211	+	0.364724i
$863$		−	30.9858i		−	1.05477i	−0.849626	−	0.527385i	$-0.823173\pi$
$863$		−	30.9858i		−	1.05477i	0.849626	−	0.527385i	$-0.176827\pi$
$864$	−5.93724	+	16.9888i	−0.201989	+	0.577972i
$865$	−9.71239	+	4.57439i	−0.330231	+	0.155534i
$866$	−40.8810	+	25.6917i	−1.38919	+	0.873038i
$867$	−18.8446			−0.639995
$868$	−10.1358	−	4.87922i	−0.344033	−	0.165611i
$869$		−	53.9335i		−	1.82957i
$870$	11.0176	−	17.2060i	0.373533	−	0.583338i
$871$	−19.2173			−0.651152
$872$	−0.313657	−	2.77796i	−0.0106218	−	0.0940735i
$873$		−	5.38378i		−	0.182213i
$874$	−5.52419	−	8.79018i	−0.186858	−	0.297332i
$875$	−10.8320	−	2.76924i	−0.366187	−	0.0936173i
$876$	24.7197	+	11.8997i	0.835202	+	0.402052i
$877$	−28.7071			−0.969371			−0.484686	−	0.874688i	$-0.661066\pi$
$877$	−28.7071			−0.969371			−0.484686	+	0.874688i	$0.661066\pi$
$878$	15.8074	+	25.1530i	0.533474	+	0.848873i
$879$	−25.2880			−0.852943
$880$	20.5214	−	41.7216i	0.691777	−	1.40643i
$881$	24.1693			0.814286			0.407143	−	0.913365i	$-0.366525\pi$
$881$	24.1693			0.814286			0.407143	+	0.913365i	$0.366525\pi$
$882$	1.12902	+	1.79651i	0.0380161	+	0.0604918i
$883$	−48.2581			−1.62402			−0.812008	−	0.583647i	$-0.801625\pi$
$883$	−48.2581			−1.62402			−0.812008	+	0.583647i	$0.801625\pi$
$884$	−30.9448	−	14.8963i	−1.04079	−	0.501018i
$885$	−0.886576	−	1.88238i	−0.0298019	−	0.0632757i
$886$	−17.1634	−	27.3108i	−0.576617	−	0.917523i
$887$		−	24.3795i		−	0.818584i	−0.912404	−	0.409292i	$-0.865776\pi$
$887$		−	24.3795i		−	0.818584i	0.912404	−	0.409292i	$-0.134224\pi$
$888$	−27.9681	+	3.15786i	−0.938549	+	0.105971i
$889$	4.54496			0.152433
$890$	−16.7906	−	10.7516i	−0.562822	−	0.360396i
$891$			58.4813i			1.95920i
$892$	2.25815	+	1.08704i	0.0756086	+	0.0363967i
$893$	9.44064			0.315919
$894$	−45.8159	+	28.7930i	−1.53231	+	0.962982i
$895$	−9.21700	−	19.5696i	−0.308090	−	0.654140i
$896$	7.99564	−	8.00435i	0.267116	−	0.267407i
$897$			61.4162i			2.05063i
$898$	20.3109	+	32.3190i	0.677783	+	1.07850i
$899$			17.1300i			0.571319i
$900$	6.27762	+	13.6271i	0.209254	+	0.454238i
$901$			29.8373i			0.994024i
$902$	−32.0414	+	20.1364i	−1.06686	+	0.670469i
$903$			11.2134i			0.373158i
$904$	−6.09550	−	53.9858i	−0.202733	−	1.79554i
$905$	7.02408	+	14.9136i	0.233488	+	0.495744i
$906$	5.16574	+	8.21981i	0.171620	+	0.273085i
$907$	14.6514			0.486492			0.243246	−	0.969965i	$-0.421788\pi$
$907$	14.6514			0.486492			0.243246	+	0.969965i	$0.421788\pi$
$908$	−0.567933	+	1.17979i	−0.0188475	+	0.0391529i
$909$		−	28.5081i		−	0.945554i
$910$	−10.2781	+	16.0511i	−0.340717	+	0.532090i
$911$	36.3676			1.20491			0.602456	−	0.798152i	$-0.294189\pi$
$911$	36.3676			1.20491			0.602456	+	0.798152i	$0.294189\pi$
$912$	−10.1370	+	8.08918i	−0.335671	+	0.267859i
$913$			72.2051i			2.38964i
$914$	−31.5278	+	19.8137i	−1.04285	+	0.655377i
$915$	0.0342144	+	0.0726442i	0.00113109	+	0.00240154i
$916$	44.7019	+	21.5188i	1.47699	+	0.711000i
$917$	−9.57272			−0.316119
$918$	10.8528	−	6.82047i	0.358197	−	0.225109i
$919$	24.9391			0.822666			0.411333	−	0.911485i	$-0.365063\pi$
$919$	24.9391			0.822666			0.411333	+	0.911485i	$0.365063\pi$
$920$	15.9459	+	25.8572i	0.525720	+	0.852488i
$921$	21.8699			0.720638
$922$	20.5499	−	12.9146i	0.676776	−	0.425320i
$923$	32.9418			1.08429
$924$	9.56646	−	19.8729i	0.314713	−	0.653769i
$925$	14.9376	−	18.0819i	0.491146	−	0.594528i
$926$	8.56342	−	5.38168i	0.281412	−	0.176853i
$927$			19.3401i			0.635212i
$928$	−16.2638	−	5.68387i	−0.533887	−	0.186582i
$929$	−15.3284			−0.502909			−0.251455	−	0.967869i	$-0.580909\pi$
$929$	−15.3284			−0.502909			−0.251455	+	0.967869i	$0.580909\pi$
$930$	−31.7758	−	20.3472i	−1.04197	−	0.667211i
$931$		−	1.52835i		−	0.0500896i
$932$	−14.7229	−	7.08734i	−0.482264	−	0.232153i
$933$	−19.1991			−0.628552
$934$	17.5772	+	27.9692i	0.575144	+	0.915179i
$935$	−29.9599	+	14.1107i	−0.979795	+	0.461469i
$936$	25.4161	−	2.86971i	0.830751	−	0.0937995i
$937$		−	60.4593i		−	1.97512i	−0.157240	−	0.987560i	$-0.550260\pi$
$937$		−	60.4593i		−	1.97512i	0.157240	−	0.987560i	$-0.449740\pi$
$938$	−3.81775	+	2.39926i	−0.124654	+	0.0783387i
$939$			5.21558i			0.170204i
$940$	−27.6235	−	0.234134i	−0.900979	−	0.00763662i
$941$			17.1028i			0.557536i	0.960358	+	0.278768i	$0.0899261\pi$
$941$			17.1028i			0.557536i	−0.960358	+	0.278768i	$0.910074\pi$
$942$	0.466890	+	0.742923i	0.0152121	+	0.0242057i
$943$		−	24.7258i		−	0.805183i
$944$	−1.37142	+	1.09437i	−0.0446359	+	0.0356187i
$945$	−3.03109	−	6.43563i	−0.0986014	−	0.209351i
$946$	32.9013	−	20.6768i	1.06971	−	0.672262i
$947$	3.60744			0.117226			0.0586131	−	0.998281i	$-0.481332\pi$
$947$	3.60744			0.117226			0.0586131	+	0.998281i	$0.481332\pi$
$948$	19.0933	−	39.6633i	0.620120	−	1.28821i
$949$			38.9733i			1.26513i
$950$	1.39437	−	10.7167i	0.0452392	−	0.347696i
$951$	−1.68327			−0.0545839
$952$	−8.00738	+	0.904107i	−0.259521	+	0.0293023i
$953$			28.5937i			0.926242i	0.886295	+	0.463121i	$0.153271\pi$
$953$			28.5937i			0.926242i	−0.886295	+	0.463121i	$0.846729\pi$
$954$	−11.8240	−	18.8145i	−0.382816	−	0.609143i
$955$	−20.6626	+	9.73180i	−0.668627	+	0.314914i
$956$	8.28831	−	17.2177i	0.268063	−	0.556860i
$957$	−33.5861			−1.08568
$958$	29.3954	+	46.7744i	0.949722	+	1.51121i
$959$	19.4072			0.626690
$960$	29.8618	−	23.4177i	0.963785	−	0.755803i
$961$	0.635482			0.0204994
$962$	−21.2751	−	33.8533i	−0.685937	−	1.09147i
$963$	24.4217			0.786980
$964$	−17.7223	+	36.8154i	−0.570797	+	1.18574i
$965$	−7.15403	−	15.1895i	−0.230296	−	0.488967i
$966$	7.66779	+	12.2011i	0.246707	+	0.392564i
$967$			3.10316i			0.0997908i	0.998754	+	0.0498954i	$0.0158888\pi$
$967$			3.10316i			0.0997908i	−0.998754	+	0.0498954i	$0.984111\pi$
$968$	−45.0330	+	5.08465i	−1.44742	+	0.163427i
$969$	9.23723			0.296743
$970$	6.11909	−	9.55604i	0.196472	−	0.306826i
$971$		−	2.54166i		−	0.0815657i	−0.999168	−	0.0407828i	$-0.987015\pi$
$971$		−	2.54166i		−	0.0815657i	0.999168	−	0.0407828i	$-0.0129852\pi$
$972$	−12.4239	+	25.8088i	−0.398498	+	0.827819i
$973$	14.0670			0.450967
$974$	−21.6218	+	13.5882i	−0.692808	+	0.435395i
$975$	−40.7174	+	49.2880i	−1.30400	+	1.57848i
$976$	0.0529252	−	0.0422334i	0.00169410	−	0.00135186i
$977$		−	23.2180i		−	0.742811i	−0.928471	−	0.371406i	$-0.878876\pi$
$977$		−	23.2180i		−	0.742811i	0.928471	−	0.371406i	$-0.121124\pi$
$978$	20.7837	+	33.0714i	0.664590	+	1.05751i
$979$			32.7752i			1.04750i
$980$	−0.0379041	+	4.47198i	−0.00121080	+	0.142852i
$981$		−	1.48295i		−	0.0473469i
$982$	−33.8426	+	21.2684i	−1.07996	+	0.678702i
$983$		−	12.7854i		−	0.407791i	−0.978993	−	0.203896i	$-0.934640\pi$
$983$		−	12.7854i		−	0.407791i	0.978993	−	0.203896i	$-0.0653604\pi$
$984$	−30.6922	+	3.46544i	−0.978432	+	0.110474i
$985$	−12.1134	+	5.70524i	−0.385965	+	0.181784i
$986$	6.52941	+	10.3897i	0.207939	+	0.330875i
$987$	−13.1040			−0.417104
$988$	−16.6002	−	7.99107i	−0.528124	−	0.254230i
$989$			25.3894i			0.807336i
$990$	13.3001	−	20.7704i	0.422704	−	0.660127i
$991$	−59.5404			−1.89136			−0.945681	−	0.325096i	$-0.894603\pi$
$991$	−59.5404			−1.89136			−0.945681	+	0.325096i	$0.894603\pi$
$992$	−10.4969	+	30.0358i	−0.333276	+	0.953638i
$993$			13.0974i			0.415632i
$994$	6.54430	−	4.11276i	0.207572	−	0.130449i
$995$	22.8129	−	10.7445i	0.723217	−	0.340625i
$996$	−25.5617	+	53.1005i	−0.809953	+	1.68255i
$997$	−11.9789			−0.379375			−0.189688	−	0.981844i	$-0.560748\pi$
$997$	−11.9789			−0.379375			−0.189688	+	0.981844i	$0.560748\pi$
$998$	−3.02469	+	1.90086i	−0.0957447	+	0.0601708i
$999$	14.9230			0.472144

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.l.a.29.11	✓	36
4.3	odd	2		1120.2.l.a.1009.29		36
5.4	even	2	inner	280.2.l.a.29.26	yes	36
8.3	odd	2		1120.2.l.a.1009.8		36
8.5	even	2	inner	280.2.l.a.29.25	yes	36
20.19	odd	2		1120.2.l.a.1009.7		36
40.19	odd	2		1120.2.l.a.1009.30		36
40.29	even	2	inner	280.2.l.a.29.12	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.l.a.29.11	✓	36	1.1	even	1	trivial
280.2.l.a.29.12	yes	36	40.29	even	2	inner
280.2.l.a.29.25	yes	36	8.5	even	2	inner
280.2.l.a.29.26	yes	36	5.4	even	2	inner
1120.2.l.a.1009.7		36	20.19	odd	2
1120.2.l.a.1009.8		36	8.3	odd	2
1120.2.l.a.1009.29		36	4.3	odd	2
1120.2.l.a.1009.30		36	40.19	odd	2

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.752500 - 1.19739i) q^{2} -2.12140 q^{3} +(-0.867487 + 1.80207i) q^{4} +(-2.02293 + 0.952769i) q^{5} +(1.59636 + 2.54015i) q^{6} +1.00000i q^{7} +(2.81057 - 0.317339i) q^{8} +1.50036 q^{9} +O(q^{10})\)	\(q+(-0.752500 - 1.19739i) q^{2} -2.12140 q^{3} +(-0.867487 + 1.80207i) q^{4} +(-2.02293 + 0.952769i) q^{5} +(1.59636 + 2.54015i) q^{6} +1.00000i q^{7} +(2.81057 - 0.317339i) q^{8} +1.50036 q^{9} +(2.66309 + 1.70527i) q^{10} -5.19834i q^{11} +(1.84029 - 3.82293i) q^{12} +6.02726 q^{13} +(1.19739 - 0.752500i) q^{14} +(4.29145 - 2.02121i) q^{15} +(-2.49493 - 3.12655i) q^{16} +2.84902i q^{17} +(-1.12902 - 1.79651i) q^{18} +1.52835i q^{19} +(0.0379041 - 4.47198i) q^{20} -2.12140i q^{21} +(-6.22444 + 3.91175i) q^{22} -4.80330i q^{23} +(-5.96235 + 0.673205i) q^{24} +(3.18446 - 3.85476i) q^{25} +(-4.53551 - 7.21698i) q^{26} +3.18135 q^{27} +(-1.80207 - 0.867487i) q^{28} +3.04559i q^{29} +(-5.64949 - 3.61758i) q^{30} +5.62454 q^{31} +(-1.86626 + 5.34014i) q^{32} +11.0278i q^{33} +(3.41139 - 2.14389i) q^{34} +(-0.952769 - 2.02293i) q^{35} +(-1.30154 + 2.70375i) q^{36} +4.69079 q^{37} +(1.83003 - 1.15008i) q^{38} -12.7863 q^{39} +(-5.38322 + 3.31978i) q^{40} +5.14767 q^{41} +(-2.54015 + 1.59636i) q^{42} -5.28583 q^{43} +(9.36779 + 4.50949i) q^{44} +(-3.03511 + 1.42949i) q^{45} +(-5.75143 + 3.61449i) q^{46} -6.17703i q^{47} +(5.29276 + 6.63268i) q^{48} -1.00000 q^{49} +(-7.01196 - 0.912336i) q^{50} -6.04393i q^{51} +(-5.22857 + 10.8616i) q^{52} +10.4728 q^{53} +(-2.39397 - 3.80932i) q^{54} +(4.95282 + 10.5159i) q^{55} +(0.317339 + 2.81057i) q^{56} -3.24224i q^{57} +(3.64676 - 2.29180i) q^{58} -0.438637i q^{59} +(-0.0804099 + 9.48687i) q^{60} +0.0169277i q^{61} +(-4.23247 - 6.73477i) q^{62} +1.50036i q^{63} +(7.79859 - 1.78381i) q^{64} +(-12.1927 + 5.74258i) q^{65} +(13.2046 - 8.29841i) q^{66} -3.18839 q^{67} +(-5.13415 - 2.47149i) q^{68} +10.1897i q^{69} +(-1.70527 + 2.66309i) q^{70} +5.46547 q^{71} +(4.21686 - 0.476122i) q^{72} +6.46618i q^{73} +(-3.52982 - 5.61670i) q^{74} +(-6.75554 + 8.17751i) q^{75} +(-2.75419 - 1.32582i) q^{76} +5.19834 q^{77} +(9.62166 + 15.3101i) q^{78} +10.3751 q^{79} +(8.02594 + 3.94769i) q^{80} -11.2500 q^{81} +(-3.87362 - 6.16377i) q^{82} -13.8900 q^{83} +(3.82293 + 1.84029i) q^{84} +(-2.71446 - 5.76337i) q^{85} +(3.97758 + 6.32920i) q^{86} -6.46092i q^{87} +(-1.64964 - 14.6103i) q^{88} -6.30493 q^{89} +(3.99558 + 2.55852i) q^{90} +6.02726i q^{91} +(8.65590 + 4.16680i) q^{92} -11.9319 q^{93} +(-7.39631 + 4.64821i) q^{94} +(-1.45616 - 3.09173i) q^{95} +(3.95910 - 11.3286i) q^{96} -3.58833i q^{97} +(0.752500 + 1.19739i) q^{98} -7.79937i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9}+O(q^{10}) \) 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9	\( 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9} - 8 q^{10} + 20 q^{16} - 24 q^{20} - 48 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{30} - 16 q^{31} + 12 q^{34} - 20 q^{36} - 32 q^{39} + 16 q^{40} - 8 q^{41} + 56 q^{44} - 36 q^{49} - 12 q^{50} - 52 q^{54} - 32 q^{55} + 12 q^{56} - 20 q^{60} - 20 q^{64} - 24 q^{65} - 28 q^{66} - 12 q^{70} + 56 q^{71} - 24 q^{74} + 48 q^{76} + 24 q^{79} + 64 q^{80} + 36 q^{81} + 24 q^{86} - 40 q^{89} - 52 q^{90} - 92 q^{94} + 40 q^{95} + 48 q^{96}+O(q^{100}) \) 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9 - 8 * q^10 + 20 * q^16 - 24 * q^20 - 48 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^30 - 16 * q^31 + 12 * q^34 - 20 * q^36 - 32 * q^39 + 16 * q^40 - 8 * q^41 + 56 * q^44 - 36 * q^49 - 12 * q^50 - 52 * q^54 - 32 * q^55 + 12 * q^56 - 20 * q^60 - 20 * q^64 - 24 * q^65 - 28 * q^66 - 12 * q^70 + 56 * q^71 - 24 * q^74 + 48 * q^76 + 24 * q^79 + 64 * q^80 + 36 * q^81 + 24 * q^86 - 40 * q^89 - 52 * q^90 - 92 * q^94 + 40 * q^95 + 48 * q^96

Introduction

L-functions

Modular forms

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Database

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