LMFDB - Embedded newform 280.2.l.a.29.26

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			29.26
Character	$\chi$	$=$	280.29
Dual form			280.2.l.a.29.25

$q$-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} +(0.381416 + 3.13919i) 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} +(-3.47182 + 2.81895i) 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} +(0.809138 + 6.65949i) 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} +(-5.98792 - 2.03587i) 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} +(-2.21935 + 6.71375i) 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} +(-7.36514 + 5.98012i) 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} +(3.13919 - 0.381416i) 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} +(-2.06819 - 8.70187i) 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} +(0.572261 + 4.70991i) 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	$-0.290206\pi$
$3$	2.12140			1.22479			0.612397	+	0.790551i	$0.290206\pi$
$4$	−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
$10$	0.381416	+	3.13919i	0.120614	+	0.992699i
$11$		−	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	$-0.815013\pi$
$13$	−6.02726			−1.67166			−0.835830	+	0.548988i	$0.815013\pi$
$14$	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	$-0.887711\pi$
$17$		−	2.84902i		−	0.690990i	0.938421	−	0.345495i	$-0.112289\pi$
$18$	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	$0.943906\pi$
$20$	−3.47182	+	2.81895i	−0.776323	+	0.630335i
$21$		−	2.12140i		−	0.462928i
$22$	6.22444	−	3.91175i	1.32706	−	0.833988i
$23$			4.80330i			1.00156i	0.865575	+	0.500779i	$0.166953\pi$
$23$			4.80330i			1.00156i	−0.865575	+	0.500779i	$0.833047\pi$
$24$	−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	$0.908745\pi$
$30$	0.809138	+	6.65949i	0.147728	+	1.21585i
$31$	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	$-0.625999\pi$
$37$	−4.69079			−0.771160			−0.385580	+	0.922674i	$0.625999\pi$
$38$	−1.83003	+	1.15008i	−0.296870	+	0.186568i
$39$	−12.7863			−2.04744
$40$	−5.98792	−	2.03587i	−0.946774	−	0.321899i
$41$	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	$-0.367953\pi$
$43$	5.28583			0.806081			0.403040	+	0.915182i	$0.367953\pi$
$44$	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	$0.148756\pi$
$47$			6.17703i			0.901012i	−0.892773	+	0.450506i	$0.851244\pi$
$48$	−5.29276	−	6.63268i	−0.763944	−	0.957344i
$49$	−1.00000			−0.142857
$50$	−2.21935	+	6.71375i	−0.313863	+	0.949468i
$51$		−	6.04393i		−	0.846320i
$52$	5.22857	−	10.8616i	0.725072	−	1.50623i
$53$	−10.4728			−1.43855			−0.719276	−	0.694725i	$-0.755526\pi$
$53$	−10.4728			−1.43855			−0.719276	+	0.694725i	$0.755526\pi$
$54$	−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	$-0.00908988\pi$
$60$	−7.36514	+	5.98012i	−0.950835	+	0.772031i
$61$			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	$-0.437607\pi$
$67$	3.18839			0.389524			0.194762	+	0.980851i	$0.437607\pi$
$68$	5.13415	+	2.47149i	0.622607	+	0.299712i
$69$			10.1897i			1.22670i
$70$	3.13919	−	0.381416i	0.375205	−	0.0455880i
$71$	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	$-0.876473\pi$
$73$		−	6.46618i		−	0.756809i	0.925640	−	0.378405i	$-0.123527\pi$
$74$	−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	$0.301625\pi$
$80$	−2.06819	−	8.70187i	−0.231230	−	0.972899i
$81$	−11.2500			−1.25000
$82$	3.87362	+	6.16377i	0.427770	+	0.680674i
$83$	13.8900			1.52463			0.762314	−	0.647207i	$-0.224063\pi$
$83$	13.8900			1.52463			0.762314	+	0.647207i	$0.224063\pi$
$84$	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	$0.608453\pi$
$90$	0.572261	+	4.70991i	0.0603216	+	0.496468i
$91$			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	$0.0583121\pi$
$97$			3.58833i			0.364340i	−0.983267	+	0.182170i	$0.941688\pi$
$98$	−0.752500	−	1.19739i	−0.0760140	−	0.120955i
$99$		−	7.79937i		−	0.783866i
$100$	−9.70904	+	2.39468i	−0.970904	+	0.239468i
$101$		−	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	$-0.780975\pi$
$103$		−	12.8903i		−	1.27012i	0.772462	−	0.635060i	$-0.219025\pi$
$104$	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	$-0.788260\pi$
$107$	−16.2773			−1.57358			−0.786792	+	0.617218i	$0.788260\pi$
$108$	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	$-0.0150730\pi$
$110$	16.3186	−	1.98273i	1.55592	−	0.189046i
$111$	−9.95105			−0.944512
$112$	−3.12655	+	2.49493i	−0.295431	+	0.235749i
$113$			19.2081i			1.80695i	0.428640	+	0.903475i	$0.358993\pi$
$113$			19.2081i			1.80695i	−0.428640	+	0.903475i	$0.641007\pi$
$114$	−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
$120$	−12.7028	−	4.31890i	−1.15960	−	0.394260i
$121$	−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	$0.0646303\pi$
$127$			4.54496i			0.403300i	−0.979458	+	0.201650i	$0.935370\pi$
$128$	8.00435	+	7.99564i	0.707492	+	0.706722i
$129$	11.2134			0.987283
$130$	−2.29890	−	18.9207i	−0.201626	−	1.65946i
$131$			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	$0.311109\pi$
$137$			19.4072i			1.65807i	−0.559199	+	0.829034i	$0.688891\pi$
$138$	−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	$-0.203471\pi$
$140$	2.81895	+	3.47182i	0.238244	+	0.293422i
$141$			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	$0.735387\pi$
$150$	−4.70813	+	14.2426i	−0.384417	+	1.16290i
$151$	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	$-0.503715\pi$
$157$	−0.292472			−0.0233418			−0.0116709	+	0.999932i	$0.503715\pi$
$158$	7.80729	+	12.4231i	0.621114	+	0.988327i
$159$	−22.2171			−1.76193
$160$	8.86323	−	9.02459i	0.700700	−	0.713456i
$161$	4.80330			0.378553
$162$	−8.46563	−	13.4706i	−0.665122	−	1.05835i
$163$	−13.0195			−1.01976			−0.509882	−	0.860245i	$-0.670311\pi$
$163$	−13.0195			−1.01976			−0.509882	+	0.860245i	$0.670311\pi$
$164$	−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	$-0.754525\pi$
$167$		−	18.0140i		−	1.39397i	0.717087	−	0.696984i	$-0.245475\pi$
$168$	0.673205	+	5.96235i	0.0519389	+	0.460006i
$169$	23.3279			1.79445
$170$	8.94363	−	1.08666i	0.685945	−	0.0833434i
$171$			2.29307i			0.175355i
$172$	−4.58539	+	9.52544i	−0.349632	+	0.726308i
$173$	−4.80116			−0.365025			−0.182513	−	0.983204i	$-0.558423\pi$
$173$	−4.80116			−0.365025			−0.182513	+	0.983204i	$0.558423\pi$
$174$	−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	$0.882254\pi$
$180$	−5.20897	+	4.22943i	−0.388254	+	0.315243i
$181$		−	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
$190$	−4.79777	+	0.582937i	−0.348067	+	0.0422907i
$191$	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	$-0.912896\pi$
$193$		−	7.50867i		−	0.540486i	0.962792	−	0.270243i	$-0.0871040\pi$
$194$	−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	$-0.568426\pi$
$197$	−5.98806			−0.426632			−0.213316	+	0.976983i	$0.568426\pi$
$198$	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	$0.630889\pi$
$200$	−10.1734	−	9.82352i	−0.719369	−	0.694628i
$201$	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
$210$	6.65949	−	0.809138i	0.459549	−	0.0558359i
$211$		−	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
$220$	14.6538	+	18.0477i	0.987962	+	1.21678i
$221$			17.1718i			1.15510i
$222$	−7.48817	−	11.9153i	−0.502573	−	0.799702i
$223$			1.25309i			0.0839129i	0.999119	+	0.0419565i	$0.0133591\pi$
$223$			1.25309i			0.0839129i	−0.999119	+	0.0419565i	$0.986641\pi$
$224$	−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	$-0.506916\pi$
$227$	−0.654688			−0.0434531			−0.0217266	+	0.999764i	$0.506916\pi$
$228$	−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	$-0.305809\pi$
$230$	−15.0785	+	1.83206i	−0.994246	+	0.120802i
$231$	−11.0278			−0.725575
$232$	−0.966484	−	8.55983i	−0.0634528	−	0.561980i
$233$		−	8.16996i		−	0.535232i	−0.963526	−	0.267616i	$-0.913764\pi$
$233$		−	8.16996i		−	0.535232i	0.963526	−	0.267616i	$-0.0862359\pi$
$234$	−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	$0.599998\pi$
$240$	−4.38746	−	18.4602i	−0.283209	−	1.19160i
$241$	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
$250$	−10.8862	+	11.4669i	−0.688506	+	0.725231i
$251$			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	$-0.813533\pi$
$257$		−	17.7263i		−	1.10574i	0.833268	−	0.552869i	$-0.186467\pi$
$258$	8.43807	+	13.4268i	0.525331	+	0.835915i
$259$			4.69079i			0.291471i
$260$	20.9256	−	16.9905i	1.29775	−	1.05371i
$261$			4.56947i			0.282843i
$262$	−11.4623	+	7.20347i	−0.708142	+	0.445032i
$263$		−	22.9967i		−	1.41804i	−0.705188	−	0.709020i	$-0.749138\pi$
$263$		−	22.9967i		−	1.41804i	0.705188	−	0.709020i	$-0.250862\pi$
$264$	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	$0.991438\pi$
$270$	−1.21342	−	9.98686i	−0.0738463	−	0.607781i
$271$	−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	$-0.456432\pi$
$277$	4.54185			0.272893			0.136447	+	0.990647i	$0.456432\pi$
$278$	16.8437	−	10.5854i	1.01022	−	0.634870i
$279$	8.43882			0.505219
$280$	−2.03587	+	5.98792i	−0.121666	+	0.357847i
$281$	−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	$-0.516162\pi$
$283$	−1.70754			−0.101503			−0.0507513	+	0.998711i	$0.516162\pi$
$284$	−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
$290$	−9.56068	+	1.16164i	−0.561422	+	0.0682136i
$291$			7.61230i			0.446241i
$292$	11.6525	+	5.60933i	0.681913	+	0.328261i
$293$	−11.9204			−0.696397			−0.348199	−	0.937421i	$-0.613207\pi$
$293$	−11.9204			−0.696397			−0.348199	+	0.937421i	$0.613207\pi$
$294$	−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
$300$	−20.5968	+	5.08008i	−1.18916	+	0.293299i
$301$		−	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	$-0.404951\pi$
$307$	10.3092			0.588375			0.294187	+	0.955748i	$0.404951\pi$
$308$	4.50949	−	9.36779i	0.256952	−	0.533779i
$309$		−	27.3456i		−	1.55564i
$310$	2.14529	+	17.6565i	0.121844	+	1.00282i
$311$	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	$0.0221349\pi$
$313$			2.45855i			0.138965i	−0.997583	+	0.0694827i	$0.977865\pi$
$314$	−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	$-0.507093\pi$
$317$	−0.793472			−0.0445658			−0.0222829	+	0.999752i	$0.507093\pi$
$318$	−16.7183	−	26.6025i	−0.937518	−	1.49179i
$319$	15.8320			0.886422
$320$	17.4755	+	3.82174i	0.976912	+	0.213642i
$321$	−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
$330$	34.6183	−	4.20618i	1.90568	−	0.231542i
$331$		−	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	$0.0787793\pi$
$337$			8.99423i			0.489947i	−0.969530	+	0.244974i	$0.921221\pi$
$338$	17.5542	+	27.9325i	0.954823	+	1.51933i
$339$			40.7483i			2.21314i
$340$	8.03125	+	9.89130i	0.435556	+	0.536431i
$341$		−	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	$-0.370535\pi$
$347$	14.7386			0.791208			0.395604	+	0.918421i	$0.370535\pi$
$348$	−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	$-0.0310759\pi$
$350$	6.71375	+	2.21935i	0.358865	+	0.118629i
$351$	19.1748			1.02348
$352$	−27.7598	−	9.70147i	−1.47960	−	0.517090i
$353$			4.80763i			0.255884i	0.991782	+	0.127942i	$0.0408372\pi$
$353$			4.80763i			0.255884i	−0.991782	+	0.127942i	$0.959163\pi$
$354$	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	$0.536557\pi$
$360$	−8.98403	−	3.05453i	−0.473500	−	0.160988i
$361$	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	$-0.851789\pi$
$367$		−	17.2023i		−	0.897953i	0.893544	−	0.448976i	$-0.148211\pi$
$368$	15.0178	−	11.9839i	0.782855	−	0.624705i
$369$	7.72334			0.402061
$370$	−1.78914	−	14.7253i	−0.0930131	−	0.765530i
$371$			10.4728i			0.543721i
$372$	−10.3508	+	21.5022i	−0.536664	+	1.11484i
$373$	17.1548			0.888243			0.444121	−	0.895967i	$-0.353516\pi$
$373$	17.1548			0.888243			0.444121	+	0.895967i	$0.353516\pi$
$374$	−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	$-0.220978\pi$
$380$	−4.30833	−	5.30615i	−0.221013	−	0.272200i
$381$			9.64170i			0.493959i
$382$	7.68621	+	12.2304i	0.393261	+	0.625763i
$383$			3.63723i			0.185854i	0.995673	+	0.0929269i	$0.0296223\pi$
$383$			3.63723i			0.185854i	−0.995673	+	0.0929269i	$0.970378\pi$
$384$	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	$0.904352\pi$
$390$	−4.87689	−	40.1385i	−0.246951	−	2.03249i
$391$	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	$-0.539885\pi$
$397$	−4.98018			−0.249948			−0.124974	+	0.992160i	$0.539885\pi$
$398$	−8.48607	−	13.5032i	−0.425368	−	0.676853i
$399$	3.24224			0.162315
$400$	4.10709	−	19.5738i	0.205354	−	0.978688i
$401$	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	$0.601901\pi$
$410$	1.96341	+	16.1595i	0.0969657	+	0.798062i
$411$			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	$-0.160537\pi$
$420$	5.98012	+	7.36514i	0.291800	+	0.359382i
$421$			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
$430$	2.01610	+	16.5932i	0.0972250	+	0.800196i
$431$	−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	$0.306235\pi$
$433$			34.1417i			1.64075i	−0.571828	+	0.820374i	$0.693765\pi$
$434$	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	$0.667142\pi$
$440$	−10.5831	+	31.1273i	−0.504531	+	1.48393i
$441$	−1.50036			−0.0714456
$442$	−20.5614	+	12.9218i	−0.978004	+	0.614627i
$443$	−22.8086			−1.08367			−0.541834	−	0.840486i	$-0.682270\pi$
$443$	−22.8086			−1.08367			−0.541834	+	0.840486i	$0.682270\pi$
$444$	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	$0.719782\pi$
$450$	−3.32981	+	10.0730i	−0.156969	+	0.474847i
$451$		−	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	$0.211184\pi$
$457$			26.3304i			1.23169i	−0.787869	+	0.615843i	$0.788816\pi$
$458$	29.7023	−	18.6664i	1.38790	−	0.872224i
$459$			9.06374i			0.423059i
$460$	−13.5402	−	16.6762i	−0.631317	−	0.777532i
$461$			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	$-0.946855\pi$
$463$		−	7.15174i		−	0.332370i	0.986095	−	0.166185i	$-0.0531448\pi$
$464$	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	$-0.318254\pi$
$467$	23.3584			1.08090			0.540449	+	0.841376i	$0.318254\pi$
$468$	7.84472	−	16.2962i	0.362622	−	0.753293i
$469$		−	3.18839i		−	0.147226i
$470$	−19.3909	+	2.35602i	−0.894434	+	0.108675i
$471$	−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	$0.851002\pi$
$480$	18.8025	−	19.1448i	0.858213	−	0.873837i
$481$	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	$0.134168\pi$
$487$			18.0575i			0.818262i	−0.912476	+	0.409131i	$0.865832\pi$
$488$	−0.00537182	−	0.0475764i	−0.000243171	−	0.00215368i
$489$	−27.6196			−1.24900
$490$	−0.381416	−	3.13919i	−0.0172306	−	0.141814i
$491$		−	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	$-0.0180072\pi$
$500$	−21.9223	−	4.40622i	−0.980393	−	0.197052i
$501$		−	38.2150i		−	1.70732i
$502$	−27.0721	+	17.0135i	−1.20829	+	0.759347i
$503$			2.49511i			0.111252i	0.998452	+	0.0556258i	$0.0177154\pi$
$503$			2.49511i			0.111252i	−0.998452	+	0.0556258i	$0.982285\pi$
$504$	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	$0.894063\pi$
$510$	18.9731	−	2.30526i	0.840141	−	0.102078i
$511$	−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
$520$	36.0908	+	12.2707i	1.58269	+	0.538106i
$521$	−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	$-0.195713\pi$
$523$	37.3619			1.63372			0.816860	+	0.576835i	$0.195713\pi$
$524$	−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
$530$	−3.99450	−	32.8762i	−0.173510	−	1.42805i
$531$		−	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
$540$	11.0451	−	8.96805i	0.475304	−	0.385923i
$541$		−	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	$-0.624893\pi$
$547$	−17.8859			−0.764746			−0.382373	+	0.924008i	$0.624893\pi$
$548$	−34.9731	−	16.8355i	−1.49398	−	0.719176i
$549$			0.0253976i			0.00108394i
$550$	34.9004	+	11.5369i	1.48816	+	0.491936i
$551$	−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	$-0.162034\pi$
$557$	41.2170			1.74642			0.873211	+	0.487342i	$0.162034\pi$
$558$	6.35022	+	10.1046i	0.268826	+	0.427760i
$559$	−31.8590			−1.34749
$560$	−8.70187	+	2.06819i	−0.367721	+	0.0873968i
$561$	−31.4184			−1.32649
$562$	−17.3216	−	27.5623i	−0.730666	−	1.16265i
$563$	−3.19209			−0.134530			−0.0672652	−	0.997735i	$-0.521427\pi$
$563$	−3.19209			−0.134530			−0.0672652	+	0.997735i	$0.521427\pi$
$564$	−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	$0.705716\pi$
$570$	−10.1780	+	1.23664i	−0.426310	+	0.0517973i
$571$			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	$-0.879077\pi$
$577$		−	17.8148i		−	0.741638i	0.928705	−	0.370819i	$-0.120923\pi$
$578$	6.68450	+	10.6365i	0.278039	+	0.442420i
$579$		−	15.9289i		−	0.661984i
$580$	−8.58534	−	10.5737i	−0.356487	−	0.439050i
$581$		−	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	$-0.272570\pi$
$587$	31.7501			1.31047			0.655234	+	0.755426i	$0.272570\pi$
$588$	1.84029	−	3.82293i	0.0758923	−	0.157655i
$589$			8.59626i			0.354203i
$590$	1.37696	−	0.167303i	0.0566887	−	0.00688776i
$591$	−12.7031			−0.522536
$592$	11.7032	+	14.6660i	0.480998	+	0.602768i
$593$		−	10.6769i		−	0.438448i	−0.975675	−	0.219224i	$-0.929648\pi$
$593$		−	10.6769i		−	0.438448i	0.975675	−	0.219224i	$-0.0703525\pi$
$594$	−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	$0.358682\pi$
$600$	−21.5819	−	20.8397i	−0.881079	−	0.850775i
$601$	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	$-0.827470\pi$
$607$		−	25.4193i		−	1.03174i	0.856668	−	0.515868i	$-0.172530\pi$
$608$	8.16158	+	2.85230i	0.330996	+	0.115676i
$609$	6.46092			0.261810
$610$	−0.0531392	+	0.00645649i	−0.00215154	+	0.000261416i
$611$		−	37.2305i		−	1.50619i
$612$	7.70306	+	3.70812i	0.311378	+	0.149892i
$613$	−20.4828			−0.827294			−0.413647	−	0.910437i	$-0.635745\pi$
$613$	−20.4828			−0.827294			−0.413647	+	0.910437i	$0.635745\pi$
$614$	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	$-0.650513\pi$
$617$		−	44.2279i		−	1.78055i	0.455425	−	0.890274i	$-0.349487\pi$
$618$	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	$-0.0787195\pi$
$620$	−19.5274	+	15.8553i	−0.784240	+	0.636763i
$621$		−	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
$630$	4.70991	−	0.572261i	0.187647	−	0.0227994i
$631$	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
$640$	8.57422	+	23.8009i	0.338926	+	0.940813i
$641$	−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	$-0.387515\pi$
$643$	17.5511			0.692147			0.346074	+	0.938207i	$0.387515\pi$
$644$	−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	$-0.898495\pi$
$647$		−	15.9490i		−	0.627021i	0.949585	−	0.313511i	$-0.101505\pi$
$648$	31.6189	−	3.57007i	1.24211	−	0.140245i
$649$	−2.28018			−0.0895050
$650$	13.3766	−	40.4655i	0.524672	−	1.58719i
$651$		−	11.9319i		−	0.467649i
$652$	11.2942	−	23.4620i	0.442316	−	0.918844i
$653$	−20.5764			−0.805218			−0.402609	−	0.915372i	$-0.631897\pi$
$653$	−20.5764			−0.805218			−0.402609	+	0.915372i	$0.631897\pi$
$654$	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	$0.621296\pi$
$660$	31.0867	+	38.2865i	1.21005	+	1.49030i
$661$			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
$670$	1.21610	+	10.0090i	0.0469822	+	0.386680i
$671$	0.0879958			0.00339704
$672$	−11.3286	−	3.95910i	−0.437010	−	0.152726i
$673$		−	12.4825i		−	0.481165i	−0.970629	−	0.240583i	$-0.922661\pi$
$673$		−	12.4825i		−	0.481165i	0.970629	−	0.240583i	$-0.0773385\pi$
$674$	−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	$-0.563176\pi$
$677$	−10.2605			−0.394343			−0.197172	+	0.980369i	$0.563176\pi$
$678$	−48.7916	+	30.6631i	−1.87383	+	1.17761i
$679$	3.58833			0.137707
$680$	−5.80024	+	17.0597i	−0.222429	+	0.654211i
$681$	−1.38886			−0.0532211
$682$	35.0096	−	22.0018i	1.34059	−	0.842493i
$683$	26.9367			1.03071			0.515353	−	0.856978i	$-0.327661\pi$
$683$	26.9367			1.03071			0.515353	+	0.856978i	$0.327661\pi$
$684$	−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
$690$	−31.9876	+	3.88654i	−1.21775	+	0.147958i
$691$			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
$700$	2.39468	+	9.70904i	0.0905103	+	0.366967i
$701$			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	$-0.348811\pi$
$710$	2.08462	+	17.1571i	0.0782343	+	0.643896i
$711$	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	$0.247768\pi$
$720$	−3.10302	−	13.0559i	−0.115643	−	0.486565i
$721$	−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	$-0.936838\pi$
$727$		−	10.6304i		−	0.394262i	0.980377	−	0.197131i	$-0.0631624\pi$
$728$	−1.91269	−	16.9400i	−0.0708889	−	0.627839i
$729$	3.36776			0.124732
$730$	20.2986	−	2.46631i	0.751284	−	0.0912821i
$731$		−	15.0594i		−	0.556994i
$732$	−0.0647132	−	0.0311519i	−0.00239187	−	0.00115141i
$733$	−3.83559			−0.141671			−0.0708354	−	0.997488i	$-0.522567\pi$
$733$	−3.83559			−0.141671			−0.0708354	+	0.997488i	$0.522567\pi$
$734$	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	$0.725124\pi$
$740$	16.2856	−	13.2231i	0.598669	−	0.486090i
$741$		−	19.5418i		−	0.717887i
$742$	−12.5400	+	7.88079i	−0.460359	+	0.289313i
$743$			4.38109i			0.160727i	0.996766	+	0.0803633i	$0.0256080\pi$
$743$			4.38109i			0.160727i	−0.996766	+	0.0803633i	$0.974392\pi$
$744$	−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
$750$	−23.0941	+	24.3260i	−0.843277	+	0.888258i
$751$	−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	$-0.243030\pi$
$757$	39.7528			1.44484			0.722420	+	0.691454i	$0.243030\pi$
$758$	29.8278	−	18.7453i	1.08339	−	0.680859i
$759$	52.9698			1.92268
$760$	3.11151	−	9.15163i	0.112866	−	0.331964i
$761$	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	$0.600085\pi$
$770$	−1.98273	−	16.3186i	−0.0714527	−	0.588081i
$771$		−	37.6047i		−	1.35430i
$772$	13.5312	+	6.51367i	0.486997	+	0.234432i
$773$	−32.4384			−1.16673			−0.583364	−	0.812211i	$-0.698264\pi$
$773$	−32.4384			−1.16673			−0.583364	+	0.812211i	$0.698264\pi$
$774$	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
$780$	44.3916	−	36.0438i	1.58947	−	1.29057i
$781$		−	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	$-0.584251\pi$
$787$	−14.6777			−0.523203			−0.261602	+	0.965176i	$0.584251\pi$
$788$	5.19456	−	10.7909i	0.185049	−	0.384411i
$789$		−	48.7854i		−	1.73681i
$790$	3.95724	+	32.5695i	0.140792	+	1.15877i
$791$	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	$-0.549735\pi$
$797$	−8.78616			−0.311222			−0.155611	+	0.987818i	$0.549735\pi$
$798$	2.43979	+	3.88223i	0.0863676	+	0.137429i
$799$	17.5985			0.622590
$800$	26.5280	−	9.81147i	0.937907	−	0.346888i
$801$	−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	$0.518805\pi$
$810$	−4.29093	−	35.3159i	−0.150768	−	1.24087i
$811$		−	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
$820$	−17.8718	+	14.5110i	−0.624110	+	0.506746i
$821$		−	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	$-0.787995\pi$
$823$		−	35.4510i		−	1.23574i	0.786279	−	0.617872i	$-0.212005\pi$
$824$	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	$-0.528198\pi$
$827$	−5.08845			−0.176943			−0.0884714	+	0.996079i	$0.528198\pi$
$828$	−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	$-0.0288506\pi$
$830$	5.29788	+	43.6034i	0.183892	+	1.51350i
$831$	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	$0.390816\pi$
$840$	−4.31890	+	12.7028i	−0.149016	+	0.438289i
$841$	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
$850$	19.1277	+	6.32297i	0.656073	+	0.216876i
$851$		−	22.5313i		−	0.772362i
$852$	−10.0580	+	20.8941i	−0.344583	+	0.715819i
$853$	24.4612			0.837537			0.418768	−	0.908093i	$-0.362462\pi$
$853$	24.4612			0.837537			0.418768	+	0.908093i	$0.362462\pi$
$854$	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	$0.401328\pi$
$857$			55.7585i			1.90467i	−0.305047	+	0.952337i	$0.598672\pi$
$858$	−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	$-0.200815\pi$
$860$	−18.3514	+	14.9005i	−0.625779	+	0.508101i
$861$		−	10.9203i		−	0.372162i
$862$	−6.72959	−	10.7082i	−0.229211	−	0.364724i
$863$			30.9858i			1.05477i	0.849626	+	0.527385i	$0.176827\pi$
$863$			30.9858i			1.05477i	−0.849626	+	0.527385i	$0.823173\pi$
$864$	−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
$870$	−20.2821	+	2.46430i	−0.687626	+	0.0835476i
$871$	−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	$-0.338934\pi$
$877$	28.7071			0.969371			0.484686	+	0.874688i	$0.338934\pi$
$878$	−15.8074	−	25.1530i	−0.533474	−	0.848873i
$879$	−25.2880			−0.852943
$880$	−45.2353	+	10.7511i	−1.52488	+	0.362421i
$881$	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	$-0.198375\pi$
$883$	48.2581			1.62402			0.812008	+	0.583647i	$0.198375\pi$
$884$	−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	$0.134224\pi$
$887$			24.3795i			0.818584i	−0.912404	+	0.409292i	$0.865776\pi$
$888$	27.9681	−	3.15786i	0.938549	−	0.105971i
$889$	4.54496			0.152433
$890$	−2.40480	−	19.7924i	−0.0806092	−	0.663442i
$891$			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
$900$	−14.5670	+	3.59287i	−0.485568	+	0.119762i
$901$			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	$-0.578212\pi$
$907$	−14.6514			−0.486492			−0.243246	+	0.969965i	$0.578212\pi$
$908$	0.567933	−	1.17979i	0.0188475	−	0.0391529i
$909$		−	28.5081i		−	0.945554i
$910$	−18.9207	+	2.29890i	−0.627216	+	0.0762076i
$911$	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	$0.365063\pi$
$920$	9.77889	−	28.7618i	0.322400	−	0.948249i
$921$	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	$0.580909\pi$
$930$	4.55103	+	37.4566i	0.149234	+	1.22825i
$931$		−	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	$0.449740\pi$
$937$			60.4593i			1.97512i	−0.157240	+	0.987560i	$0.550260\pi$
$938$	3.81775	−	2.39926i	0.124654	−	0.0783387i
$939$			5.21558i			0.170204i
$940$	−17.4127	−	21.4455i	−0.567940	−	0.699476i
$941$			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	$-0.518668\pi$
$947$	−3.60744			−0.117226			−0.0586131	+	0.998281i	$0.518668\pi$
$948$	−19.0933	+	39.6633i	−0.620120	+	1.28821i
$949$			38.9733i			1.26513i
$950$	−10.2609	−	3.39193i	−0.332909	−	0.110049i
$951$	−1.68327			−0.0545839
$952$	8.00738	−	0.904107i	0.259521	−	0.0293023i
$953$		−	28.5937i		−	0.926242i	−0.886295	−	0.463121i	$-0.846729\pi$
$953$		−	28.5937i		−	0.926242i	0.886295	−	0.463121i	$-0.153271\pi$
$954$	−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
$960$	37.0727	+	8.10746i	1.19652	+	0.261667i
$961$	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	$-0.984111\pi$
$967$		−	3.10316i		−	0.0997908i	0.998754	−	0.0498954i	$-0.0158888\pi$
$968$	45.0330	−	5.08465i	1.44742	−	0.163427i
$969$	9.23723			0.296743
$970$	−11.2645	+	1.36865i	−0.361680	+	0.0439446i
$971$		−	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	$0.121124\pi$
$977$			23.2180i			0.742811i	−0.928471	+	0.371406i	$0.878876\pi$
$978$	−20.7837	−	33.0714i	−0.664590	−	1.05751i
$979$			32.7752i			1.04750i
$980$	3.47182	−	2.81895i	0.110903	−	0.0900479i
$981$		−	1.48295i		−	0.0473469i
$982$	33.8426	−	21.2684i	1.07996	−	0.678702i
$983$			12.7854i			0.407791i	0.978993	+	0.203896i	$0.0653604\pi$
$983$			12.7854i			0.407791i	−0.978993	+	0.203896i	$0.934640\pi$
$984$	−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
$990$	24.4837	−	2.97481i	0.778143	−	0.0945456i
$991$	−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	$-0.439252\pi$
$997$	11.9789			0.379375			0.189688	+	0.981844i	$0.439252\pi$
$998$	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.29.26	yes	36
4.3	odd	2		1120.2.l.a.1009.7		36
5.4	even	2	inner	280.2.l.a.29.11	✓	36
8.3	odd	2		1120.2.l.a.1009.30		36
8.5	even	2	inner	280.2.l.a.29.12	yes	36
20.19	odd	2		1120.2.l.a.1009.29		36
40.19	odd	2		1120.2.l.a.1009.8		36
40.29	even	2	inner	280.2.l.a.29.25	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.l.a.29.11	✓	36	5.4	even	2	inner
280.2.l.a.29.12	yes	36	8.5	even	2	inner
280.2.l.a.29.25	yes	36	40.29	even	2	inner
280.2.l.a.29.26	yes	36	1.1	even	1	trivial
1120.2.l.a.1009.7		36	4.3	odd	2
1120.2.l.a.1009.8		36	40.19	odd	2
1120.2.l.a.1009.29		36	20.19	odd	2
1120.2.l.a.1009.30		36	8.3	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} +(0.381416 + 3.13919i) 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} +(-3.47182 + 2.81895i) 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} +(0.809138 + 6.65949i) 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} +(-5.98792 - 2.03587i) 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} +(-2.21935 + 6.71375i) 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} +(-7.36514 + 5.98012i) 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} +(3.13919 - 0.381416i) 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} +(-2.06819 - 8.70187i) 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} +(0.572261 + 4.70991i) 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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