LMFDB - Embedded newform 784.2.x.l.557.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.1
Character	$\chi$	$=$	784.557
Dual form			784.2.x.l.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35072 + 0.418990i) q^{2} +(0.819585 - 0.219607i) q^{3} +(1.64889 - 1.13188i) q^{4} +(-1.33183 - 0.356864i) q^{5} +(-1.01502 + 0.640026i) q^{6} +(-1.75295 + 2.21972i) q^{8} +(-1.97458 + 1.14003i) q^{9} +O(q^{10})$	\(q+(-1.35072 + 0.418990i) q^{2} +(0.819585 - 0.219607i) q^{3} +(1.64889 - 1.13188i) q^{4} +(-1.33183 - 0.356864i) q^{5} +(-1.01502 + 0.640026i) q^{6} +(-1.75295 + 2.21972i) q^{8} +(-1.97458 + 1.14003i) q^{9} +(1.94846 - 0.0760019i) q^{10} +(-0.631061 - 2.35515i) q^{11} +(1.10284 - 1.28978i) q^{12} +(1.90592 + 1.90592i) q^{13} -1.16992 q^{15} +(1.43771 - 3.73269i) q^{16} +(-3.35849 + 5.81707i) q^{17} +(2.18945 - 2.36719i) q^{18} +(1.07944 - 4.02851i) q^{19} +(-2.59998 + 0.919042i) q^{20} +(1.83917 + 2.91674i) q^{22} +(-4.58892 + 2.64941i) q^{23} +(-0.949225 + 2.20421i) q^{24} +(-2.68370 - 1.54943i) q^{25} +(-3.37293 - 1.77581i) q^{26} +(-3.16792 + 3.16792i) q^{27} +(-3.03004 - 3.03004i) q^{29} +(1.58024 - 0.490185i) q^{30} +(-0.599978 + 1.03919i) q^{31} +(-0.377976 + 5.64421i) q^{32} +(-1.03442 - 1.79166i) q^{33} +(2.09908 - 9.26441i) q^{34} +(-1.96551 + 4.11477i) q^{36} +(3.07358 + 0.823563i) q^{37} +(0.229890 + 5.89367i) q^{38} +(1.98062 + 1.14351i) q^{39} +(3.12678 - 2.33073i) q^{40} +3.94994i q^{41} +(-7.02292 + 7.02292i) q^{43} +(-3.70630 - 3.16911i) q^{44} +(3.03665 - 0.813668i) q^{45} +(5.08827 - 5.50133i) q^{46} +(1.53093 + 2.65165i) q^{47} +(0.358595 - 3.37499i) q^{48} +(4.27413 + 0.968410i) q^{50} +(-1.47510 + 5.50513i) q^{51} +(5.29994 + 0.985393i) q^{52} +(-1.10495 - 4.12372i) q^{53} +(2.95164 - 5.60630i) q^{54} +3.36187i q^{55} -3.53876i q^{57} +(5.36229 + 2.82318i) q^{58} +(1.81836 + 6.78621i) q^{59} +(-1.92908 + 1.32421i) q^{60} +(-3.54750 + 13.2394i) q^{61} +(0.374991 - 1.65504i) q^{62} +(-1.85433 - 7.78212i) q^{64} +(-1.85822 - 3.21853i) q^{65} +(2.14790 + 1.98663i) q^{66} +(-4.85753 + 1.30157i) q^{67} +(1.04642 + 13.3931i) q^{68} +(-3.17918 + 3.17918i) q^{69} -11.5771i q^{71} +(0.930806 - 6.38144i) q^{72} +(-8.94350 - 5.16353i) q^{73} +(-4.49661 + 0.175396i) q^{74} +(-2.53979 - 0.680534i) q^{75} +(-2.77991 - 7.86439i) q^{76} +(-3.15439 - 0.714705i) q^{78} +(-2.03442 - 3.52371i) q^{79} +(-3.24685 + 4.45826i) q^{80} +(1.51940 - 2.63168i) q^{81} +(-1.65499 - 5.33527i) q^{82} +(9.17886 + 9.17886i) q^{83} +(6.54884 - 6.54884i) q^{85} +(6.54347 - 12.4285i) q^{86} +(-3.14879 - 1.81795i) q^{87} +(6.33400 + 2.72768i) q^{88} +(-14.6607 + 8.46436i) q^{89} +(-3.76075 + 2.37136i) q^{90} +(-4.56783 + 9.56270i) q^{92} +(-0.263519 + 0.983466i) q^{93} +(-3.17888 - 2.94019i) q^{94} +(-2.87526 + 4.98010i) q^{95} +(0.929726 + 4.70892i) q^{96} -2.51522 q^{97} +(3.93102 + 3.93102i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} - 4 q^{3} + 6 q^{4} - 4 q^{5} + 8 q^{6} - 8 q^{8}+O(q^{10}) $ 24 * q - 2 * q^2 - 4 * q^3 + 6 * q^4 - 4 * q^5 + 8 * q^6 - 8 * q^8	$ 24 q - 2 q^{2} - 4 q^{3} + 6 q^{4} - 4 q^{5} + 8 q^{6} - 8 q^{8} + 4 q^{10} - 8 q^{12} - 48 q^{15} - 10 q^{16} + 8 q^{17} - 40 q^{20} + 28 q^{22} + 8 q^{24} + 20 q^{26} + 8 q^{27} - 8 q^{29} + 28 q^{30} + 8 q^{31} - 12 q^{32} + 16 q^{34} - 32 q^{36} + 20 q^{37} - 16 q^{38} + 8 q^{40} + 32 q^{43} - 14 q^{44} - 40 q^{45} + 28 q^{46} - 16 q^{47} + 32 q^{48} + 88 q^{50} + 16 q^{51} + 16 q^{52} - 4 q^{53} - 64 q^{54} - 14 q^{58} + 16 q^{59} - 60 q^{60} + 20 q^{61} + 16 q^{62} - 36 q^{64} - 32 q^{65} - 12 q^{66} - 24 q^{67} + 28 q^{68} - 8 q^{69} - 6 q^{72} + 38 q^{74} + 40 q^{75} + 96 q^{76} - 152 q^{78} - 24 q^{79} - 24 q^{80} + 44 q^{81} + 16 q^{82} - 40 q^{83} - 16 q^{85} - 38 q^{86} + 14 q^{88} - 80 q^{90} + 64 q^{92} + 48 q^{93} + 24 q^{94} + 16 q^{96} + 96 q^{97} + 64 q^{99}+O(q^{100}) $ 24 * q - 2 * q^2 - 4 * q^3 + 6 * q^4 - 4 * q^5 + 8 * q^6 - 8 * q^8 + 4 * q^10 - 8 * q^12 - 48 * q^15 - 10 * q^16 + 8 * q^17 - 40 * q^20 + 28 * q^22 + 8 * q^24 + 20 * q^26 + 8 * q^27 - 8 * q^29 + 28 * q^30 + 8 * q^31 - 12 * q^32 + 16 * q^34 - 32 * q^36 + 20 * q^37 - 16 * q^38 + 8 * q^40 + 32 * q^43 - 14 * q^44 - 40 * q^45 + 28 * q^46 - 16 * q^47 + 32 * q^48 + 88 * q^50 + 16 * q^51 + 16 * q^52 - 4 * q^53 - 64 * q^54 - 14 * q^58 + 16 * q^59 - 60 * q^60 + 20 * q^61 + 16 * q^62 - 36 * q^64 - 32 * q^65 - 12 * q^66 - 24 * q^67 + 28 * q^68 - 8 * q^69 - 6 * q^72 + 38 * q^74 + 40 * q^75 + 96 * q^76 - 152 * q^78 - 24 * q^79 - 24 * q^80 + 44 * q^81 + 16 * q^82 - 40 * q^83 - 16 * q^85 - 38 * q^86 + 14 * q^88 - 80 * q^90 + 64 * q^92 + 48 * q^93 + 24 * q^94 + 16 * q^96 + 96 * q^97 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.35072	+	0.418990i	−0.955104	+	0.296271i
$2$	−1.35072	+	0.418990i	−0.955104	+	0.296271i
$3$	0.819585	−	0.219607i	0.473188	−	0.126790i	−0.0143411	−	0.999897i	$-0.504565\pi$
$3$	0.819585	−	0.219607i	0.473188	−	0.126790i	0.487529	+	0.873107i	$0.337898\pi$
$4$	1.64889	−	1.13188i	0.824447	−	0.565939i
$5$	−1.33183	−	0.356864i	−0.595614	−	0.159594i	−0.0515962	−	0.998668i	$-0.516431\pi$
$5$	−1.33183	−	0.356864i	−0.595614	−	0.159594i	−0.544018	+	0.839074i	$0.683098\pi$
$6$	−1.01502	+	0.640026i	−0.414379	+	0.261290i
$7$		0			0
$7$		0			0
$8$	−1.75295	+	2.21972i	−0.619762	+	0.784790i
$9$	−1.97458	+	1.14003i	−0.658195	+	0.380009i
$10$	1.94846	−	0.0760019i	0.616156	−	0.0240339i
$11$	−0.631061	−	2.35515i	−0.190272	−	0.710105i	−0.993440	−	0.114353i	$-0.963521\pi$
$11$	−0.631061	−	2.35515i	−0.190272	−	0.710105i	0.803168	−	0.595752i	$-0.203146\pi$
$12$	1.10284	−	1.28978i	0.318363	−	0.372327i
$13$	1.90592	+	1.90592i	0.528608	+	0.528608i	0.920157	−	0.391549i	$-0.128061\pi$
$13$	1.90592	+	1.90592i	0.528608	+	0.528608i	−0.391549	+	0.920157i	$0.628061\pi$
$14$		0			0
$15$	−1.16992			−0.302072
$16$	1.43771	−	3.73269i	0.359426	−	0.933173i
$17$	−3.35849	+	5.81707i	−0.814552	+	1.41085i	0.0950964	+	0.995468i	$0.469684\pi$
$17$	−3.35849	+	5.81707i	−0.814552	+	1.41085i	−0.909649	+	0.415378i	$0.863649\pi$
$18$	2.18945	−	2.36719i	0.516059	−	0.557952i
$19$	1.07944	−	4.02851i	0.247640	−	0.924205i	−0.724398	−	0.689382i	$-0.757882\pi$
$19$	1.07944	−	4.02851i	0.247640	−	0.924205i	0.972038	−	0.234823i	$-0.0754510\pi$
$20$	−2.59998	+	0.919042i	−0.581373	+	0.205504i
$21$		0			0
$22$	1.83917	+	2.91674i	0.392113	+	0.621852i
$23$	−4.58892	+	2.64941i	−0.956855	+	0.552441i	−0.895204	−	0.445657i	$-0.852970\pi$
$23$	−4.58892	+	2.64941i	−0.956855	+	0.552441i	−0.0616516	+	0.998098i	$0.519637\pi$
$24$	−0.949225	+	2.20421i	−0.193760	+	0.449933i
$25$	−2.68370	−	1.54943i	−0.536740	−	0.309887i
$26$	−3.37293	−	1.77581i	−0.661487	−	0.348264i
$27$	−3.16792	+	3.16792i	−0.609666	+	0.609666i
$28$		0			0
$29$	−3.03004	−	3.03004i	−0.562663	−	0.562663i	0.367400	−	0.930063i	$-0.380248\pi$
$29$	−3.03004	−	3.03004i	−0.562663	−	0.562663i	−0.930063	+	0.367400i	$0.880248\pi$
$30$	1.58024	−	0.490185i	0.288510	−	0.0894952i
$31$	−0.599978	+	1.03919i	−0.107759	+	0.186644i	−0.914862	−	0.403766i	$-0.867701\pi$
$31$	−0.599978	+	1.03919i	−0.107759	+	0.186644i	0.807103	+	0.590411i	$0.201034\pi$
$32$	−0.377976	+	5.64421i	−0.0668173	+	0.997765i
$33$	−1.03442	−	1.79166i	−0.180069	−	0.311888i
$34$	2.09908	−	9.26441i	0.359990	−	1.58883i
$35$		0			0
$36$	−1.96551	+	4.11477i	−0.327585	+	0.685795i
$37$	3.07358	+	0.823563i	0.505294	+	0.135393i	0.502456	−	0.864603i	$-0.332430\pi$
$37$	3.07358	+	0.823563i	0.505294	+	0.135393i	0.00283787	+	0.999996i	$0.499097\pi$
$38$	0.229890	+	5.89367i	0.0372931	+	0.956080i
$39$	1.98062	+	1.14351i	0.317153	+	0.183108i
$40$	3.12678	−	2.33073i	0.494387	−	0.368522i
$41$			3.94994i			0.616877i	0.951244	+	0.308438i	$0.0998064\pi$
$41$			3.94994i			0.616877i	−0.951244	+	0.308438i	$0.900194\pi$
$42$		0			0
$43$	−7.02292	+	7.02292i	−1.07098	+	1.07098i	−0.0737045	+	0.997280i	$0.523482\pi$
$43$	−7.02292	+	7.02292i	−1.07098	+	1.07098i	−0.997280	+	0.0737045i	$0.976518\pi$
$44$	−3.70630	−	3.16911i	−0.558745	−	0.477762i
$45$	3.03665	−	0.813668i	0.452677	−	0.121294i
$46$	5.08827	−	5.50133i	0.750224	−	0.811127i
$47$	1.53093	+	2.65165i	0.223309	+	0.386783i	0.955811	−	0.293982i	$-0.0949807\pi$
$47$	1.53093	+	2.65165i	0.223309	+	0.386783i	−0.732502	+	0.680765i	$0.761647\pi$
$48$	0.358595	−	3.37499i	0.0517588	−	0.487138i
$49$		0			0
$50$	4.27413	+	0.968410i	0.604453	+	0.136954i
$51$	−1.47510	+	5.50513i	−0.206555	+	0.770873i
$52$	5.29994	+	0.985393i	0.734969	+	0.136649i
$53$	−1.10495	−	4.12372i	−0.151776	−	0.566436i	−0.999360	−	0.0357747i	$-0.988610\pi$
$53$	−1.10495	−	4.12372i	−0.151776	−	0.566436i	0.847584	−	0.530662i	$-0.178057\pi$
$54$	2.95164	−	5.60630i	0.401668	−	0.762920i
$55$			3.36187i			0.453315i
$56$		0			0
$57$		−	3.53876i		−	0.468721i
$58$	5.36229	+	2.82318i	0.704103	+	0.370701i
$59$	1.81836	+	6.78621i	0.236730	+	0.883489i	0.977361	+	0.211577i	$0.0678600\pi$
$59$	1.81836	+	6.78621i	0.236730	+	0.883489i	−0.740631	+	0.671912i	$0.765473\pi$
$60$	−1.92908	+	1.32421i	−0.249043	+	0.170954i
$61$	−3.54750	+	13.2394i	−0.454210	+	1.69514i	0.236188	+	0.971707i	$0.424102\pi$
$61$	−3.54750	+	13.2394i	−0.454210	+	1.69514i	−0.690399	+	0.723429i	$0.742565\pi$
$62$	0.374991	−	1.65504i	0.0476240	−	0.210191i
$63$		0			0
$64$	−1.85433	−	7.78212i	−0.231791	−	0.972766i
$65$	−1.85822	−	3.21853i	−0.230483	−	0.399209i
$66$	2.14790	+	1.98663i	0.264388	+	0.244537i
$67$	−4.85753	+	1.30157i	−0.593442	+	0.159012i	−0.543026	−	0.839716i	$-0.682721\pi$
$67$	−4.85753	+	1.30157i	−0.593442	+	0.159012i	−0.0504163	+	0.998728i	$0.516055\pi$
$68$	1.04642	+	13.3931i	0.126897	+	1.62416i
$69$	−3.17918	+	3.17918i	−0.382728	+	0.382728i
$70$		0			0
$71$		−	11.5771i		−	1.37395i	−0.726682	−	0.686974i	$-0.758939\pi$
$71$		−	11.5771i		−	1.37395i	0.726682	−	0.686974i	$-0.241061\pi$
$72$	0.930806	−	6.38144i	0.109696	−	0.752059i
$73$	−8.94350	−	5.16353i	−1.04676	−	0.604346i	−0.125018	−	0.992154i	$-0.539899\pi$
$73$	−8.94350	−	5.16353i	−1.04676	−	0.604346i	−0.921740	+	0.387808i	$0.873232\pi$
$74$	−4.49661	+	0.175396i	−0.522721	+	0.0203894i
$75$	−2.53979	−	0.680534i	−0.293269	−	0.0785813i
$76$	−2.77991	−	7.86439i	−0.318877	−	0.902107i
$77$		0			0
$78$	−3.15439	−	0.714705i	−0.357164	−	0.0809244i
$79$	−2.03442	−	3.52371i	−0.228890	−	0.396449i	0.728590	−	0.684951i	$-0.240176\pi$
$79$	−2.03442	−	3.52371i	−0.228890	−	0.396449i	−0.957479	+	0.288502i	$0.906843\pi$
$80$	−3.24685	+	4.45826i	−0.363008	+	0.498449i
$81$	1.51940	−	2.63168i	0.168822	−	0.292408i
$82$	−1.65499	−	5.33527i	−0.182763	−	0.589182i
$83$	9.17886	+	9.17886i	1.00751	+	1.00751i	0.999972	+	0.00753873i	$0.00239967\pi$
$83$	9.17886	+	9.17886i	1.00751	+	1.00751i	0.00753873	+	0.999972i	$0.497600\pi$
$84$		0			0
$85$	6.54884	−	6.54884i	0.710322	−	0.710322i
$86$	6.54347	−	12.4285i	0.705600	−	1.34020i
$87$	−3.14879	−	1.81795i	−0.337586	−	0.194905i
$88$	6.33400	+	2.72768i	0.675207	+	0.290772i
$89$	−14.6607	+	8.46436i	−1.55403	+	0.897221i	−0.556225	+	0.831032i	$0.687751\pi$
$89$	−14.6607	+	8.46436i	−1.55403	+	0.897221i	−0.997807	+	0.0661891i	$0.978916\pi$
$90$	−3.76075	+	2.37136i	−0.396418	+	0.249964i
$91$		0			0
$92$	−4.56783	+	9.56270i	−0.476229	+	0.996980i
$93$	−0.263519	+	0.983466i	−0.0273256	+	0.101981i
$94$	−3.17888	−	2.94019i	−0.327876	−	0.303258i
$95$	−2.87526	+	4.98010i	−0.294996	+	0.510947i
$96$	0.929726	+	4.70892i	0.0948898	+	0.480602i
$97$	−2.51522			−0.255382			−0.127691	−	0.991814i	$-0.540757\pi$
$97$	−2.51522			−0.255382			−0.127691	+	0.991814i	$0.540757\pi$
$98$		0			0
$99$	3.93102	+	3.93102i	0.395082	+	0.395082i
$100$	−6.17891	+	0.482766i	−0.617891	+	0.0482766i
$101$	−3.13421	−	11.6970i	−0.311866	−	1.16390i	−0.926872	−	0.375377i	$-0.877513\pi$
$101$	−3.13421	−	11.6970i	−0.311866	−	1.16390i	0.615007	−	0.788522i	$-0.289153\pi$
$102$	−0.314154	−	8.05395i	−0.0311059	−	0.797460i
$103$	15.4461	−	8.91779i	1.52195	−	0.878696i	0.522282	−	0.852773i	$-0.325081\pi$
$103$	15.4461	−	8.91779i	1.52195	−	0.878696i	0.999664	−	0.0259230i	$-0.00825246\pi$
$104$	−7.57161	+	0.889630i	−0.742457	+	0.0872354i
$105$		0			0
$106$	3.22027	+	5.10703i	0.312781	+	0.496039i
$107$	−11.6014	−	3.10860i	−1.12155	−	0.300519i	−0.350042	−	0.936734i	$-0.613833\pi$
$107$	−11.6014	−	3.10860i	−1.12155	−	0.300519i	−0.771512	+	0.636215i	$0.780499\pi$
$108$	−1.63786	+	8.80925i	−0.157604	+	0.847671i
$109$	−9.92690	+	2.65991i	−0.950825	+	0.254773i	−0.700712	−	0.713444i	$-0.747134\pi$
$109$	−9.92690	+	2.65991i	−0.950825	+	0.254773i	−0.250113	+	0.968217i	$0.580468\pi$
$110$	−1.40859	−	4.54095i	−0.134304	−	0.432963i
$111$	2.69992			0.256265
$112$		0			0
$113$	−13.8351			−1.30150			−0.650749	−	0.759293i	$-0.725545\pi$
$113$	−13.8351			−1.30150			−0.650749	+	0.759293i	$0.725545\pi$
$114$	1.48271	+	4.77988i	0.138868	+	0.447677i
$115$	7.05715	−	1.89096i	0.658083	−	0.176333i
$116$	−8.42584	−	1.56658i	−0.782319	−	0.145453i
$117$	−5.93621	−	1.59060i	−0.548802	−	0.147051i
$118$	−5.29945	−	8.40440i	−0.487854	−	0.773688i
$119$		0			0
$120$	2.05081	−	2.59690i	0.187213	−	0.237063i
$121$	4.37778	−	2.52751i	0.397980	−	0.229774i
$122$	−0.755517	−	19.3692i	−0.0684013	−	1.75360i
$123$	0.867435	+	3.23731i	0.0782140	+	0.291899i
$124$	0.186939	+	2.39262i	0.0167876	+	0.214864i
$125$	7.89615	+	7.89615i	0.706253	+	0.706253i
$126$		0			0
$127$	14.1434			1.25502			0.627512	−	0.778607i	$-0.284073\pi$
$127$	14.1434			1.25502			0.627512	+	0.778607i	$0.284073\pi$
$128$	5.76532	+	9.73453i	0.509587	+	0.860419i
$129$	−4.21360	+	7.29816i	−0.370986	+	0.642567i
$130$	3.85846	+	3.56876i	0.338410	+	0.313001i
$131$	−1.11636	+	4.16631i	−0.0975368	+	0.364012i	−0.997392	−	0.0721767i	$-0.977005\pi$
$131$	−1.11636	+	4.16631i	−0.0975368	+	0.364012i	0.899855	+	0.436189i	$0.143672\pi$
$132$	−3.73359	−	1.78343i	−0.324967	−	0.155228i
$133$		0			0
$134$	6.01583	−	3.79332i	0.519688	−	0.327693i
$135$	5.34965	−	3.08862i	0.460424	−	0.265826i
$136$	−7.02501	−	17.6519i	−0.602390	−	1.51364i
$137$	−10.0295	−	5.79055i	−0.856880	−	0.494720i	0.00608624	−	0.999981i	$-0.498063\pi$
$137$	−10.0295	−	5.79055i	−0.856880	−	0.494720i	−0.862966	+	0.505262i	$0.831396\pi$
$138$	2.96214	−	5.62623i	0.252154	−	0.478936i
$139$	−2.25088	+	2.25088i	−0.190917	+	0.190917i	−0.796092	−	0.605175i	$-0.793103\pi$
$139$	−2.25088	+	2.25088i	−0.190917	+	0.190917i	0.605175	+	0.796092i	$0.293103\pi$
$140$		0			0
$141$	1.83705	+	1.83705i	0.154708	+	0.154708i
$142$	4.85069	+	15.6374i	0.407061	+	1.31226i
$143$	3.28598	−	5.69149i	0.274788	−	0.475946i
$144$	1.41650	+	9.00954i	0.118042	+	0.750795i
$145$	2.95419	+	5.11681i	0.245332	+	0.424928i
$146$	14.2436	+	3.22725i	1.17881	+	0.267089i
$147$		0			0
$148$	6.00018	−	2.12095i	0.493212	−	0.174341i
$149$	3.14025	+	0.841428i	0.257260	+	0.0689325i	0.385144	−	0.922857i	$-0.374152\pi$
$149$	3.14025	+	0.841428i	0.257260	+	0.0689325i	−0.127884	+	0.991789i	$0.540819\pi$
$150$	3.71568	−	0.144935i	0.303384	−	0.0118339i
$151$	15.7259	+	9.07936i	1.27976	+	0.738868i	0.976804	−	0.214138i	$-0.0686941\pi$
$151$	15.7259	+	9.07936i	1.27976	+	0.738868i	0.302953	+	0.953005i	$0.402027\pi$
$152$	7.04998	+	9.45784i	0.571829	+	0.767132i
$153$		−	15.3150i		−	1.23815i
$154$		0			0
$155$	1.16992	−	1.16992i	0.0939703	−	0.0939703i
$156$	4.56015	−	0.356290i	0.365104	−	0.0285261i
$157$	14.7682	−	3.95712i	1.17863	−	0.315812i	0.384246	−	0.923231i	$-0.374461\pi$
$157$	14.7682	−	3.95712i	1.17863	−	0.315812i	0.794382	+	0.607418i	$0.207795\pi$
$158$	4.22433	+	3.90715i	0.336070	+	0.310836i
$159$	−1.81120	−	3.13709i	−0.143637	−	0.248787i
$160$	2.51761	−	7.38226i	0.199035	−	0.583619i
$161$		0			0
$162$	−0.949637	+	4.19127i	−0.0746106	+	0.329298i
$163$	−2.35393	+	8.78498i	−0.184374	+	0.688093i	0.810390	+	0.585891i	$0.199255\pi$
$163$	−2.35393	+	8.78498i	−0.184374	+	0.688093i	−0.994764	+	0.102202i	$0.967411\pi$
$164$	4.47085	+	6.51303i	0.349115	+	0.508582i
$165$	0.738291	+	2.75534i	0.0574759	+	0.214503i
$166$	−16.2439	−	8.55222i	−1.26077	−	0.663781i
$167$		−	0.661950i		−	0.0512232i	−0.999672	−	0.0256116i	$-0.991847\pi$
$167$		−	0.661950i		−	0.0512232i	0.999672	−	0.0256116i	$-0.00815332\pi$
$168$		0			0
$169$		−	5.73492i		−	0.441148i
$170$	−6.10176	+	11.5896i	−0.467983	+	0.888879i
$171$	2.46117	+	9.18523i	0.188211	+	0.702412i
$172$	−3.63096	+	19.5291i	−0.276858	+	1.48908i
$173$	2.32642	−	8.68232i	0.176874	−	0.660104i	−0.819350	−	0.573293i	$-0.805666\pi$
$173$	2.32642	−	8.68232i	0.176874	−	0.660104i	0.996225	−	0.0868112i	$-0.0276677\pi$
$174$	5.01484	+	1.13624i	0.380174	+	0.0861379i
$175$		0			0
$176$	−9.69834	−	1.03046i	−0.731040	−	0.0776735i
$177$	2.98060	+	5.16255i	0.224036	+	0.388041i
$178$	16.2560	−	17.5757i	1.21844	−	1.31735i
$179$	10.4037	−	2.78766i	0.777609	−	0.208360i	0.151878	−	0.988399i	$-0.451468\pi$
$179$	10.4037	−	2.78766i	0.777609	−	0.208360i	0.625730	+	0.780040i	$0.284801\pi$
$180$	4.08614	−	4.77877i	0.304563	−	0.356188i
$181$	13.9902	−	13.9902i	1.03989	−	1.03989i	0.0407146	−	0.999171i	$-0.487037\pi$
$181$	13.9902	−	13.9902i	1.03989	−	1.03989i	0.999171	−	0.0407146i	$-0.0129634\pi$
$182$		0			0
$183$			11.6299i			0.859707i
$184$	2.16319	−	14.8304i	0.159472	−	1.09331i
$185$	−3.79960	−	2.19370i	−0.279352	−	0.161284i
$186$	−0.0561222	−	1.43880i	−0.00411508	−	0.105498i
$187$	15.8195	+	4.23882i	1.15684	+	0.309973i
$188$	5.52569	+	2.63946i	0.403002	+	0.192503i
$189$		0			0
$190$	1.79706	−	7.93143i	0.130373	−	0.575406i
$191$	11.2211	+	19.4355i	0.811929	+	1.40630i	0.911512	+	0.411273i	$0.134916\pi$
$191$	11.2211	+	19.4355i	0.811929	+	1.40630i	−0.0995834	+	0.995029i	$0.531751\pi$
$192$	−3.22879	−	5.97089i	−0.233018	−	0.430912i
$193$	3.15704	−	5.46816i	0.227249	−	0.393607i	−0.729743	−	0.683722i	$-0.760360\pi$
$193$	3.15704	−	5.46816i	0.227249	−	0.393607i	0.956992	+	0.290115i	$0.0936936\pi$
$194$	3.39737	−	1.05385i	0.243917	−	0.0756623i
$195$	−2.22978	−	2.22978i	−0.159678	−	0.159678i
$196$		0			0
$197$	3.81709	−	3.81709i	0.271957	−	0.271957i	−0.557931	−	0.829887i	$-0.688405\pi$
$197$	3.81709	−	3.81709i	0.271957	−	0.271957i	0.829887	+	0.557931i	$0.188405\pi$
$198$	−6.95677	−	3.66265i	−0.494396	−	0.260293i
$199$	−22.1966	−	12.8152i	−1.57347	−	0.908445i	−0.995739	−	0.0922198i	$-0.970604\pi$
$199$	−22.1966	−	12.8152i	−1.57347	−	0.908445i	−0.577734	−	0.816225i	$-0.696063\pi$
$200$	8.14371	−	3.24098i	0.575847	−	0.229172i
$201$	−3.69533	+	2.13350i	−0.260648	+	0.150485i
$202$	9.13439	+	14.4862i	0.642693	+	1.01925i
$203$		0			0
$204$	3.79886	+	10.7470i	0.265973	+	0.752441i
$205$	1.40959	−	5.26066i	0.0984500	−	0.367420i
$206$	−17.1269	+	18.5172i	−1.19328	+	1.29015i
$207$	6.04080	−	10.4630i	0.419865	−	0.727227i
$208$	9.85438	−	4.37407i	0.683278	−	0.303287i
$209$	−10.1690			−0.703401
$210$		0			0
$211$	0.737145	+	0.737145i	0.0507472	+	0.0507472i	0.732025	−	0.681278i	$-0.238575\pi$
$211$	0.737145	+	0.737145i	0.0507472	+	0.0507472i	−0.681278	+	0.732025i	$0.738575\pi$
$212$	−6.48949	−	5.54891i	−0.445700	−	0.381101i
$213$	−2.54241	−	9.48841i	−0.174203	−	0.650135i
$214$	16.9728	−	0.662044i	1.16024	−	0.0452564i
$215$	11.8596	−	6.84713i	0.808816	−	0.466970i
$216$	−1.47869	−	12.5851i	−0.100612	−	0.856307i
$217$		0			0
$218$	12.2940	−	7.75207i	0.832655	−	0.525036i
$219$	−8.46391	−	2.26790i	−0.571938	−	0.153250i
$220$	3.80523	+	5.54337i	0.256548	+	0.373734i
$221$	−17.4879	+	4.68587i	−1.17636	+	0.315206i
$222$	−3.64684	+	1.13124i	−0.244760	+	0.0759239i
$223$	−5.76178			−0.385838			−0.192919	−	0.981215i	$-0.561795\pi$
$223$	−5.76178			−0.385838			−0.192919	+	0.981215i	$0.561795\pi$
$224$		0			0
$225$	7.06558			0.471039
$226$	18.6874	−	5.79678i	1.24307	−	0.385596i
$227$	24.8861	−	6.66820i	1.65175	−	0.442584i	0.691645	−	0.722237i	$-0.256886\pi$
$227$	24.8861	−	6.66820i	1.65175	−	0.442584i	0.960101	+	0.279653i	$0.0902195\pi$
$228$	−4.00545	−	5.83505i	−0.265267	−	0.386435i
$229$	−0.700446	−	0.187684i	−0.0462868	−	0.0124025i	0.235601	−	0.971850i	$-0.424294\pi$
$229$	−0.700446	−	0.187684i	−0.0462868	−	0.0124025i	−0.281888	+	0.959447i	$0.590961\pi$
$230$	−8.73995	+	5.51103i	−0.576295	+	0.363387i
$231$		0			0
$232$	12.0373	−	1.41433i	0.790290	−	0.0928556i
$233$	12.5076	−	7.22125i	0.819399	−	0.473080i	−0.0308104	−	0.999525i	$-0.509809\pi$
$233$	12.5076	−	7.22125i	0.819399	−	0.473080i	0.850209	+	0.526445i	$0.176475\pi$
$234$	8.68460	−	0.338753i	0.567730	−	0.0221450i
$235$	−1.09267	−	4.07789i	−0.0712778	−	0.266012i
$236$	10.6794	+	9.13158i	0.695172	+	0.594415i
$237$	−2.44121	−	2.44121i	−0.158574	−	0.158574i
$238$		0			0
$239$	−7.34716			−0.475248			−0.237624	−	0.971357i	$-0.576369\pi$
$239$	−7.34716			−0.475248			−0.237624	+	0.971357i	$0.576369\pi$
$240$	−1.68200	+	4.36696i	−0.108573	+	0.281886i
$241$	−1.62674	+	2.81759i	−0.104787	+	0.181497i	−0.913651	−	0.406499i	$-0.866750\pi$
$241$	−1.62674	+	2.81759i	−0.104787	+	0.181497i	0.808864	+	0.587996i	$0.200083\pi$
$242$	−4.85415	+	5.24821i	−0.312037	+	0.337368i
$243$	4.14595	−	15.4729i	0.265963	−	0.992588i
$244$	9.13598	+	25.8458i	0.584871	+	1.65461i
$245$		0			0
$246$	−2.52806	−	4.00926i	−0.161184	−	0.255621i
$247$	9.73536	−	5.62071i	0.619446	−	0.357637i
$248$	−1.25499	−	3.15344i	−0.0796917	−	0.200243i
$249$	9.53860	+	5.50711i	0.604484	+	0.348999i
$250$	−13.9739	−	7.35709i	−0.883787	−	0.465303i
$251$	2.08074	−	2.08074i	0.131335	−	0.131335i	−0.638383	−	0.769719i	$-0.720396\pi$
$251$	2.08074	−	2.08074i	0.131335	−	0.131335i	0.769719	+	0.638383i	$0.220396\pi$
$252$		0			0
$253$	9.13566	+	9.13566i	0.574354	+	0.574354i
$254$	−19.1038	+	5.92595i	−1.19868	+	0.371827i
$255$	3.92916	−	6.80551i	0.246054	−	0.426177i
$256$	−11.8660	−	10.7330i	−0.741626	−	0.670814i
$257$	−5.48098	−	9.49334i	−0.341894	−	0.592178i	0.642890	−	0.765958i	$-0.277735\pi$
$257$	−5.48098	−	9.49334i	−0.341894	−	0.592178i	−0.984784	+	0.173780i	$0.944402\pi$
$258$	2.63353	−	11.6232i	0.163957	−	0.723631i
$259$		0			0
$260$	−6.70698	−	3.20373i	−0.415949	−	0.198687i
$261$	9.43738	+	2.52874i	0.584159	+	0.156525i
$262$	−0.237753	−	6.09527i	−0.0146884	−	0.376567i
$263$	8.82750	+	5.09656i	0.544327	+	0.314267i	0.746831	−	0.665014i	$-0.231575\pi$
$263$	8.82750	+	5.09656i	0.544327	+	0.314267i	−0.202504	+	0.979281i	$0.564908\pi$
$264$	5.79027	+	0.844578i	0.356367	+	0.0519802i
$265$			5.88642i			0.361600i
$266$		0			0
$267$	−10.1569	+	10.1569i	−0.621590	+	0.621590i
$268$	−6.53634	+	7.64429i	−0.399270	+	0.466949i
$269$	−2.40123	+	0.643406i	−0.146405	+	0.0392292i	−0.331277	−	0.943533i	$-0.607480\pi$
$269$	−2.40123	+	0.643406i	−0.146405	+	0.0392292i	0.184872	+	0.982763i	$0.440813\pi$
$270$	−5.93178	+	6.41332i	−0.360997	+	0.390302i
$271$	2.83083	+	4.90314i	0.171961	+	0.297845i	0.939105	−	0.343630i	$-0.111656\pi$
$271$	2.83083	+	4.90314i	0.171961	+	0.297845i	−0.767145	+	0.641474i	$0.778323\pi$
$272$	16.8848	+	20.8994i	1.02379	+	1.26721i
$273$		0			0
$274$	15.9733	+	3.61914i	0.964981	+	0.218640i
$275$	−1.95558	+	7.29831i	−0.117926	+	0.440104i
$276$	−1.64369	+	8.84057i	−0.0989384	+	0.532140i
$277$	7.80837	+	29.1412i	0.469159	+	1.75093i	0.642718	+	0.766103i	$0.277807\pi$
$277$	7.80837	+	29.1412i	0.469159	+	1.75093i	−0.173559	+	0.984824i	$0.555527\pi$
$278$	2.09721	−	3.98341i	0.125782	−	0.238909i
$279$		−	2.73596i		−	0.163798i
$280$		0			0
$281$		−	1.60009i		−	0.0954532i	−0.998860	−	0.0477266i	$-0.984802\pi$
$281$		−	1.60009i		−	0.0954532i	0.998860	−	0.0477266i	$-0.0151976\pi$
$282$	−3.25105	−	1.71164i	−0.193597	−	0.101926i
$283$	5.26857	+	19.6626i	0.313184	+	1.16882i	0.925668	+	0.378336i	$0.123504\pi$
$283$	5.26857	+	19.6626i	0.313184	+	1.16882i	−0.612484	+	0.790483i	$0.709830\pi$
$284$	−13.1038	−	19.0894i	−0.777570	−	1.13275i
$285$	−1.26286	+	4.71304i	−0.0748051	+	0.279177i
$286$	−2.05377	+	9.06441i	−0.121442	+	0.535990i
$287$		0			0
$288$	−5.68821	−	11.5759i	−0.335181	−	0.682115i
$289$	−14.0589	−	24.3506i	−0.826991	−	1.43239i
$290$	−6.13418	−	5.67361i	−0.360212	−	0.333166i
$291$	−2.06144	+	0.552361i	−0.120844	+	0.0323800i
$292$	−20.5914	+	1.60883i	−1.20502	+	0.0941497i
$293$	0.267863	−	0.267863i	0.0156487	−	0.0156487i	−0.699239	−	0.714888i	$-0.746478\pi$
$293$	0.267863	−	0.267863i	0.0156487	−	0.0156487i	0.714888	+	0.699239i	$0.246478\pi$
$294$		0			0
$295$		−	9.68700i		−	0.563999i
$296$	−7.21592	+	5.37883i	−0.419417	+	0.312638i
$297$	9.46007	+	5.46177i	0.548929	+	0.316924i
$298$	−4.59416	+	0.179201i	−0.266132	+	0.0103808i
$299$	−13.7957	−	3.69655i	−0.797826	−	0.213777i
$300$	−4.95812	+	1.75260i	−0.286257	+	0.101186i
$301$		0			0
$302$	−25.0455	−	5.67468i	−1.44121	−	0.326541i
$303$	−5.13751	−	8.89842i	−0.295142	−	0.511201i
$304$	−13.4853	−	9.82103i	−0.773435	−	0.563274i
$305$	9.44935	−	16.3667i	0.541068	−	0.937157i
$306$	6.41686	+	20.6864i	0.366827	+	1.18256i
$307$	−12.3805	−	12.3805i	−0.706594	−	0.706594i	0.259223	−	0.965817i	$-0.416534\pi$
$307$	−12.3805	−	12.3805i	−0.706594	−	0.706594i	−0.965817	+	0.259223i	$0.916534\pi$
$308$		0			0
$309$	10.7010	−	10.7010i	0.608756	−	0.608756i
$310$	−1.09005	+	2.07042i	−0.0619107	+	0.117592i
$311$	−3.19969	−	1.84734i	−0.181438	−	0.104753i	0.406530	−	0.913637i	$-0.366739\pi$
$311$	−3.19969	−	1.84734i	−0.181438	−	0.104753i	−0.587968	+	0.808884i	$0.700072\pi$
$312$	−6.01021	+	2.39191i	−0.340261	+	0.135415i
$313$	9.06728	−	5.23500i	0.512513	−	0.295900i	−0.221353	−	0.975194i	$-0.571047\pi$
$313$	9.06728	−	5.23500i	0.512513	−	0.295900i	0.733866	+	0.679294i	$0.237714\pi$
$314$	−18.2897	+	11.5327i	−1.03215	+	0.650827i
$315$		0			0
$316$	−7.34295	−	3.50752i	−0.413073	−	0.197313i
$317$	−5.78104	+	21.5751i	−0.324695	+	1.21178i	0.589922	+	0.807460i	$0.299158\pi$
$317$	−5.78104	+	21.5751i	−0.324695	+	1.21178i	−0.914618	+	0.404320i	$0.867508\pi$
$318$	3.76083	+	3.47845i	0.210897	+	0.195062i
$319$	−5.22406	+	9.04833i	−0.292491	+	0.506609i
$320$	−0.307499	+	11.0262i	−0.0171897	+	0.616385i
$321$	−10.1910			−0.568809
$322$		0			0
$323$	19.8089	+	19.8089i	1.10219	+	1.10219i
$324$	−0.473408	−	6.05913i	−0.0263004	−	0.336618i
$325$	−2.16182	−	8.06803i	−0.119916	−	0.447534i
$326$	−0.501321	−	12.8523i	−0.0277656	−	0.711825i
$327$	−7.55181	+	4.36004i	−0.417616	+	0.241111i
$328$	−8.76777	−	6.92405i	−0.484119	−	0.382317i
$329$		0			0
$330$	−2.15169	−	3.41236i	−0.118446	−	0.187844i
$331$	−9.23788	−	2.47528i	−0.507760	−	0.136054i	−0.00416093	−	0.999991i	$-0.501324\pi$
$331$	−9.23788	−	2.47528i	−0.507760	−	0.136054i	−0.503599	+	0.863937i	$0.667991\pi$
$332$	25.5243	+	4.74562i	1.40083	+	0.260450i
$333$	−7.00793	+	1.87777i	−0.384032	+	0.102901i
$334$	0.277351	+	0.894110i	0.0151760	+	0.0489235i
$335$	6.93391			0.378840
$336$		0			0
$337$	−27.1949			−1.48140			−0.740700	−	0.671836i	$-0.765506\pi$
$337$	−27.1949			−1.48140			−0.740700	+	0.671836i	$0.765506\pi$
$338$	2.40287	+	7.74627i	0.130699	+	0.421342i
$339$	−11.3391	+	3.03829i	−0.615853	+	0.165017i
$340$	3.38586	−	18.2108i	0.183624	−	0.987621i
$341$	2.82608	+	0.757246i	0.153041	+	0.0410071i
$342$	−7.17288	−	11.3755i	−0.387865	−	0.615115i
$343$		0			0
$344$	−3.27810	−	27.8997i	−0.176743	−	1.50425i
$345$	5.36867	−	3.09960i	0.289039	−	0.166877i
$346$	0.495462	+	12.7021i	0.0266362	+	0.682871i
$347$	−1.53056	−	5.71214i	−0.0821649	−	0.306644i	0.912597	−	0.408859i	$-0.134073\pi$
$347$	−1.53056	−	5.71214i	−0.0821649	−	0.306644i	−0.994762	+	0.102216i	$0.967407\pi$
$348$	−7.24973	+	0.566430i	−0.388626	+	0.0303639i
$349$	−24.5827	−	24.5827i	−1.31588	−	1.31588i	−0.917004	−	0.398877i	$-0.869400\pi$
$349$	−24.5827	−	24.5827i	−1.31588	−	1.31588i	−0.398877	−	0.917004i	$-0.630600\pi$
$350$		0			0
$351$	−12.0756			−0.644548
$352$	13.5315	−	2.67165i	0.721232	−	0.142400i
$353$	−16.6729	+	28.8783i	−0.887409	+	1.53704i	−0.0444826	+	0.999010i	$0.514164\pi$
$353$	−16.6729	+	28.8783i	−0.887409	+	1.53704i	−0.842927	+	0.538028i	$0.819169\pi$
$354$	−6.18902	−	5.72433i	−0.328943	−	0.304244i
$355$	−4.13144	+	15.4187i	−0.219274	+	0.818342i
$356$	−14.5933	+	30.5510i	−0.773445	+	1.61920i
$357$		0			0
$358$	−12.8845	+	8.12440i	−0.680966	+	0.429388i
$359$	6.84072	−	3.94949i	0.361039	−	0.208446i	−0.308497	−	0.951225i	$-0.599826\pi$
$359$	6.84072	−	3.94949i	0.361039	−	0.208446i	0.669537	+	0.742779i	$0.266493\pi$
$360$	−3.51698	+	8.16684i	−0.185361	+	0.430430i
$361$	1.39074	+	0.802942i	0.0731966	+	0.0422601i
$362$	−13.0351	+	24.7587i	−0.685111	+	1.30129i
$363$	3.03290	−	3.03290i	0.159186	−	0.159186i
$364$		0			0
$365$	10.0686	+	10.0686i	0.527013	+	0.527013i
$366$	−4.87282	−	15.7088i	−0.254706	−	0.821110i
$367$	−14.7971	+	25.6293i	−0.772401	+	1.33784i	0.163843	+	0.986486i	$0.447611\pi$
$367$	−14.7971	+	25.6293i	−0.772401	+	1.33784i	−0.936244	+	0.351351i	$0.885722\pi$
$368$	3.29194	+	20.9381i	0.171604	+	1.09147i
$369$	−4.50303	−	7.79948i	−0.234419	−	0.406025i
$370$	6.05133	+	1.37108i	0.314594	+	0.0712791i
$371$		0			0
$372$	0.678649	+	1.91990i	0.0351863	+	0.0995424i
$373$	5.89618	+	1.57988i	0.305292	+	0.0818029i	0.408213	−	0.912887i	$-0.366152\pi$
$373$	5.89618	+	1.57988i	0.305292	+	0.0818029i	−0.102921	+	0.994690i	$0.532819\pi$
$374$	−23.1437	+	0.902750i	−1.19673	+	0.0466801i
$375$	8.20562	+	4.73752i	0.423736	+	0.244644i
$376$	−8.56957	−	1.24997i	−0.441942	−	0.0644623i
$377$		−	11.5500i		−	0.594857i
$378$		0			0
$379$	−15.1468	+	15.1468i	−0.778037	+	0.778037i	−0.979497	−	0.201460i	$-0.935432\pi$
$379$	−15.1468	+	15.1468i	−0.778037	+	0.778037i	0.201460	+	0.979497i	$0.435432\pi$
$380$	0.895861	+	11.4661i	0.0459567	+	0.588198i
$381$	11.5917	−	3.10599i	0.593862	−	0.159125i
$382$	−23.2998	−	21.5504i	−1.19212	−	1.10261i
$383$	−3.31074	−	5.73436i	−0.169171	−	0.293012i	0.768958	−	0.639300i	$-0.220776\pi$
$383$	−3.31074	−	5.73436i	−0.169171	−	0.293012i	−0.938129	+	0.346287i	$0.887442\pi$
$384$	6.86294	+	6.71217i	0.350223	+	0.342529i
$385$		0			0
$386$	−1.97318	+	8.70872i	−0.100432	+	0.443262i
$387$	5.86103	−	21.8736i	0.297933	−	1.11190i
$388$	−4.14734	+	2.84693i	−0.210549	+	0.144531i
$389$	−9.39256	−	35.0535i	−0.476222	−	1.77728i	−0.616698	−	0.787200i	$-0.711530\pi$
$389$	−9.39256	−	35.0535i	−0.476222	−	1.77728i	0.140476	−	0.990084i	$-0.455137\pi$
$390$	3.94606	+	2.07755i	0.199817	+	0.105201i
$391$		−	35.5921i		−	1.79997i
$392$		0			0
$393$			3.65981i			0.184613i
$394$	−3.55650	+	6.75515i	−0.179174	+	0.340320i
$395$	1.45202	+	5.41901i	0.0730590	+	0.272660i
$396$	10.9313	+	2.03240i	0.549317	+	0.102132i
$397$	−3.46662	+	12.9376i	−0.173985	+	0.649320i	0.822737	+	0.568422i	$0.192446\pi$
$397$	−3.46662	+	12.9376i	−0.173985	+	0.649320i	−0.996722	+	0.0808988i	$0.974221\pi$
$398$	35.3508	+	8.00960i	1.77198	+	0.401485i
$399$		0			0
$400$	−9.64193	+	7.78980i	−0.482097	+	0.389490i
$401$	−8.75691	−	15.1674i	−0.437299	−	0.757424i	0.560181	−	0.828370i	$-0.310732\pi$
$401$	−8.75691	−	15.1674i	−0.437299	−	0.757424i	−0.997480	+	0.0709458i	$0.977398\pi$
$402$	4.09744	−	4.43007i	0.204362	−	0.220952i
$403$	−3.12413	+	0.837109i	−0.155624	+	0.0416994i
$404$	−18.4076	−	15.7396i	−0.915812	−	0.783076i
$405$	−2.96274	+	2.96274i	−0.147220	+	0.147220i
$406$		0			0
$407$		−	7.75847i		−	0.384573i
$408$	−9.63409	−	12.9245i	−0.476959	−	0.639859i
$409$	8.98548	+	5.18777i	0.444303	+	0.256519i	0.705421	−	0.708788i	$-0.250758\pi$
$409$	8.98548	+	5.18777i	0.444303	+	0.256519i	−0.261118	+	0.965307i	$0.584091\pi$
$410$	0.300203	+	7.69629i	0.0148260	+	0.380093i
$411$	−9.49170	−	2.54329i	−0.468191	−	0.125451i
$412$	15.3751	−	32.1875i	0.757476	−	1.58577i
$413$		0			0
$414$	−3.77555	+	16.6636i	−0.185558	+	0.818971i
$415$	−8.94910	−	15.5003i	−0.439294	−	0.760880i
$416$	−11.4778	+	10.0370i	−0.562747	+	0.492106i
$417$	−1.35048	+	2.33910i	−0.0661332	+	0.114546i
$418$	13.7354	−	4.26069i	0.671821	−	0.208397i
$419$	12.6045	+	12.6045i	0.615771	+	0.615771i	0.944444	−	0.328673i	$-0.106601\pi$
$419$	12.6045	+	12.6045i	0.615771	+	0.615771i	−0.328673	+	0.944444i	$0.606601\pi$
$420$		0			0
$421$	−17.6588	+	17.6588i	−0.860635	+	0.860635i	−0.991412	−	0.130777i	$-0.958253\pi$
$421$	−17.6588	+	17.6588i	−0.860635	+	0.860635i	0.130777	+	0.991412i	$0.458253\pi$
$422$	−1.30453	−	0.686821i	−0.0635037	−	0.0334339i
$423$	−6.04590	−	3.49060i	−0.293962	−	0.169719i
$424$	11.0904	+	4.77600i	0.538599	+	0.231943i
$425$	18.0263	−	10.4075i	0.874405	−	0.504838i
$426$	7.40964	+	11.7509i	0.358998	+	0.569335i
$427$		0			0
$428$	−22.6481	+	8.00567i	−1.09474	+	0.386969i
$429$	1.44325	−	5.38629i	0.0696808	−	0.260052i
$430$	−13.1501	+	14.2176i	−0.634154	+	0.685634i
$431$	−4.79219	+	8.30031i	−0.230832	+	0.399812i	−0.958053	−	0.286591i	$-0.907478\pi$
$431$	−4.79219	+	8.30031i	−0.230832	+	0.399812i	0.727221	+	0.686403i	$0.240811\pi$
$432$	7.27033	+	16.3794i	0.349794	+	0.788054i
$433$	−0.958633			−0.0460690			−0.0230345	−	0.999735i	$-0.507333\pi$
$433$	−0.958633			−0.0460690			−0.0230345	+	0.999735i	$0.507333\pi$
$434$		0			0
$435$	3.54490	+	3.54490i	0.169965	+	0.169965i
$436$	−13.3577	+	15.6219i	−0.639719	+	0.748156i
$437$	5.71975	+	21.3464i	0.273613	+	1.02114i
$438$	12.3826	−	0.482999i	0.591664	−	0.0230786i
$439$	−8.63764	+	4.98695i	−0.412252	+	0.238014i	−0.691757	−	0.722130i	$-0.743163\pi$
$439$	−8.63764	+	4.98695i	−0.412252	+	0.238014i	0.279505	+	0.960144i	$0.409830\pi$
$440$	−7.46242	−	5.89319i	−0.355757	−	0.280947i
$441$		0			0
$442$	21.6579	−	13.6566i	1.03016	−	0.649576i
$443$	21.1524	+	5.66777i	1.00498	+	0.269284i	0.723531	−	0.690292i	$-0.242518\pi$
$443$	21.1524	+	5.66777i	1.00498	+	0.269284i	0.281450	+	0.959576i	$0.409185\pi$
$444$	4.45189	−	3.05598i	0.211277	−	0.145030i
$445$	22.5462	−	6.04125i	1.06879	−	0.286383i
$446$	7.78256	−	2.41413i	0.368515	−	0.114312i
$447$	2.75849			0.130472
$448$		0			0
$449$	−8.77877			−0.414296			−0.207148	−	0.978310i	$-0.566418\pi$
$449$	−8.77877			−0.414296			−0.207148	+	0.978310i	$0.566418\pi$
$450$	−9.54363	+	2.96041i	−0.449891	+	0.139555i
$451$	9.30271	−	2.49265i	0.438047	−	0.117374i
$452$	−22.8126	+	15.6597i	−1.07302	+	0.736568i
$453$	14.8826	+	3.98779i	0.699246	+	0.187363i
$454$	−30.8202	+	19.4339i	−1.44646	+	0.912078i
$455$		0			0
$456$	7.85507	+	6.20328i	0.367847	+	0.290495i
$457$	1.62083	−	0.935788i	0.0758193	−	0.0437743i	−0.461611	−	0.887082i	$-0.652728\pi$
$457$	1.62083	−	0.935788i	0.0758193	−	0.0437743i	0.537430	+	0.843308i	$0.319395\pi$
$458$	1.02474	−	0.0399714i	0.0478832	−	0.00186774i
$459$	−7.78858	−	29.0674i	−0.363540	−	1.35675i
$460$	9.49616	−	11.1058i	0.442761	−	0.517812i
$461$	13.2713	+	13.2713i	0.618107	+	0.618107i	0.945046	−	0.326939i	$-0.106017\pi$
$461$	13.2713	+	13.2713i	0.618107	+	0.618107i	−0.326939	+	0.945046i	$0.606017\pi$
$462$		0			0
$463$	−1.89824			−0.0882189			−0.0441095	−	0.999027i	$-0.514045\pi$
$463$	−1.89824			−0.0882189			−0.0441095	+	0.999027i	$0.514045\pi$
$464$	−15.6665	+	6.95390i	−0.727299	+	0.322827i
$465$	0.701927	−	1.21577i	0.0325511	−	0.0563801i
$466$	−13.8686	+	14.9945i	−0.642451	+	0.694605i
$467$	0.396747	−	1.48068i	0.0183593	−	0.0685178i	−0.956138	−	0.292915i	$-0.905375\pi$
$467$	0.396747	−	1.48068i	0.0183593	−	0.0685178i	0.974498	+	0.224397i	$0.0720413\pi$
$468$	−11.5885	+	4.09633i	−0.535681	+	0.189353i
$469$		0			0
$470$	3.18448	+	5.05027i	0.146889	+	0.232952i
$471$	11.2348	−	6.48639i	0.517670	−	0.298877i
$472$	−18.2510	−	7.85964i	−0.840070	−	0.361769i
$473$	20.9719	+	12.1081i	0.964290	+	0.556733i
$474$	4.32024	+	2.27455i	0.198435	+	0.104474i
$475$	−9.13880	+	9.13880i	−0.419317	+	0.419317i
$476$		0			0
$477$	6.88296	+	6.88296i	0.315149	+	0.315149i
$478$	9.92397	−	3.07839i	0.453912	−	0.140802i
$479$	14.1486	−	24.5061i	0.646466	−	1.11971i	−0.337494	−	0.941328i	$-0.609579\pi$
$479$	14.1486	−	24.5061i	0.646466	−	1.11971i	0.983961	−	0.178385i	$-0.0570873\pi$
$480$	0.442202	−	6.60328i	0.0201837	−	0.301397i
$481$	4.28836	+	7.42766i	0.195532	+	0.338672i
$482$	1.01672	−	4.48737i	0.0463105	−	0.204394i
$483$		0			0
$484$	4.35766	−	9.12271i	0.198075	−	0.414668i
$485$	3.34986	+	0.897592i	0.152109	+	0.0407575i
$486$	0.882972	+	22.6367i	0.0400524	+	1.02682i
$487$	−5.36686	−	3.09856i	−0.243196	−	0.140409i	0.373449	−	0.927651i	$-0.378175\pi$
$487$	−5.36686	−	3.09856i	−0.243196	−	0.140409i	−0.616645	+	0.787242i	$0.711508\pi$
$488$	−23.1693	−	31.0825i	−1.04882	−	1.40704i
$489$			7.71698i			0.348974i
$490$		0			0
$491$	21.5658	−	21.5658i	0.973249	−	0.973249i	−0.0264026	−	0.999651i	$-0.508405\pi$
$491$	21.5658	−	21.5658i	0.973249	−	0.973249i	0.999651	+	0.0264026i	$0.00840519\pi$
$492$	5.09455	+	4.35615i	0.229680	+	0.196391i
$493$	27.8023	−	7.44959i	1.25215	−	0.335513i
$494$	−10.7947	+	11.6710i	−0.485678	+	0.525105i
$495$	−3.83262	−	6.63830i	−0.172264	−	0.298369i
$496$	3.01640	+	3.73359i	0.135440	+	0.167643i
$497$		0			0
$498$	−15.1914	−	3.44199i	−0.680743	−	0.154239i
$499$	0.898546	−	3.35342i	0.0402245	−	0.150120i	−0.942893	−	0.333096i	$-0.891907\pi$
$499$	0.898546	−	3.35342i	0.0402245	−	0.150120i	0.983117	+	0.182977i	$0.0585732\pi$
$500$	21.9574	+	4.08244i	0.981965	+	0.182572i
$501$	−0.145369	−	0.542525i	−0.00649461	−	0.0242382i
$502$	−1.93869	+	3.68232i	−0.0865281	+	0.164350i
$503$		−	13.1803i		−	0.587680i	−0.955855	−	0.293840i	$-0.905067\pi$
$503$		−	13.1803i		−	0.587680i	0.955855	−	0.293840i	$-0.0949332\pi$
$504$		0			0
$505$			16.6970i			0.743006i
$506$	−16.1675	−	8.51197i	−0.718732	−	0.378403i
$507$	−1.25943	−	4.70025i	−0.0559332	−	0.208746i
$508$	23.3210	−	16.0086i	1.03470	−	0.710267i
$509$	−0.561876	+	2.09695i	−0.0249047	+	0.0929457i	−0.977260	−	0.212046i	$-0.931987\pi$
$509$	−0.561876	+	2.09695i	−0.0249047	+	0.0929457i	0.952355	+	0.304992i	$0.0986539\pi$
$510$	−2.45576	+	10.8386i	−0.108743	+	0.479942i
$511$		0			0
$512$	20.5247	+	9.52558i	0.907072	+	0.420975i
$513$	9.34243	+	16.1816i	0.412478	+	0.714433i
$514$	11.3809	+	10.5264i	0.501990	+	0.464298i
$515$	−23.7540	+	6.36487i	−1.04673	+	0.280470i
$516$	1.31285	+	16.8032i	0.0577952	+	0.739718i
$517$	5.27893	−	5.27893i	0.232167	−	0.232167i
$518$		0			0
$519$		−	7.62680i		−	0.334779i
$520$	10.4016	+	1.51719i	0.456140	+	0.0665332i
$521$	−8.67501	−	5.00852i	−0.380059	−	0.219427i	0.297785	−	0.954633i	$-0.403752\pi$
$521$	−8.67501	−	5.00852i	−0.380059	−	0.219427i	−0.677844	+	0.735206i	$0.737086\pi$
$522$	−13.8068	+	0.538550i	−0.604306	+	0.0235717i
$523$	22.3050	+	5.97662i	0.975331	+	0.261339i	0.711077	−	0.703114i	$-0.248208\pi$
$523$	22.3050	+	5.97662i	0.975331	+	0.261339i	0.264254	+	0.964453i	$0.414874\pi$
$524$	2.87500	+	8.13339i	0.125595	+	0.355309i
$525$		0			0
$526$	−14.0589	−	3.18539i	−0.612997	−	0.138890i
$527$	−4.03004	−	6.98023i	−0.175551	−	0.304063i
$528$	−8.17491	+	1.28528i	−0.355767	+	0.0559346i
$529$	2.53877	−	4.39728i	0.110381	−	0.191186i
$530$	−2.46635	−	7.95091i	−0.107132	−	0.345366i
$531$	−11.3270	−	11.3270i	−0.491548	−	0.491548i
$532$		0			0
$533$	−7.52828	+	7.52828i	−0.326086	+	0.326086i
$534$	9.46346	−	17.9747i	0.409524	−	0.777842i
$535$	14.3418	+	8.28027i	0.620052	+	0.357987i
$536$	5.62589	−	13.0640i	0.243001	−	0.564277i
$537$	7.91452	−	4.56945i	0.341537	−	0.197186i
$538$	2.97380	−	1.87515i	0.128210	−	0.0808436i
$539$		0			0
$540$	5.32506	−	11.1480i	0.229154	−	0.479732i
$541$	−2.45206	+	9.15123i	−0.105422	+	0.393442i	−0.998393	−	0.0566736i	$-0.981951\pi$
$541$	−2.45206	+	9.15123i	−0.105422	+	0.393442i	0.892970	+	0.450116i	$0.148617\pi$
$542$	−5.87803	−	5.43669i	−0.252483	−	0.233526i
$543$	8.39383	−	14.5385i	0.360214	−	0.623908i
$544$	−31.5633	−	21.1547i	−1.35327	−	0.907001i
$545$	14.1702			0.606985
$546$		0			0
$547$	−21.2058	−	21.2058i	−0.906695	−	0.906695i	0.0893091	−	0.996004i	$-0.471534\pi$
$547$	−21.2058	−	21.2058i	−0.906695	−	0.906695i	−0.996004	+	0.0893091i	$0.971534\pi$
$548$	−23.0918	+	1.80419i	−0.986434	+	0.0770713i
$549$	−8.08848	−	30.1866i	−0.345208	−	1.28833i
$550$	−0.416483	−	10.6773i	−0.0177589	−	0.455283i
$551$	−15.4773	+	8.93581i	−0.659354	+	0.380678i
$552$	−1.48395	−	12.6298i	−0.0631611	−	0.537561i
$553$		0			0
$554$	−22.7568	−	36.0900i	−0.966844	−	1.53332i
$555$	−3.59585	−	0.963504i	−0.152635	−	0.0408985i
$556$	−1.16374	+	6.25918i	−0.0493536	+	0.265448i
$557$	23.1654	−	6.20714i	0.981548	−	0.263005i	0.267852	−	0.963460i	$-0.413686\pi$
$557$	23.1654	−	6.20714i	0.981548	−	0.263005i	0.713696	+	0.700455i	$0.247020\pi$
$558$	1.14634	+	3.69552i	0.0485285	+	0.156444i
$559$	−26.7703			−1.13226
$560$		0			0
$561$	13.8963			0.586702
$562$	0.670421	+	2.16127i	0.0282800	+	0.0911678i
$563$	−10.2392	+	2.74358i	−0.431529	+	0.115628i	−0.468044	−	0.883705i	$-0.655041\pi$
$563$	−10.2392	+	2.74358i	−0.431529	+	0.115628i	0.0365146	+	0.999333i	$0.488374\pi$
$564$	5.10842	+	0.949785i	0.215103	+	0.0399932i
$565$	18.4261	+	4.93725i	0.775190	+	0.207712i
$566$	−15.3548	−	24.3512i	−0.645410	−	1.02356i
$567$		0			0
$568$	25.6979	+	20.2941i	1.07826	+	0.851520i
$569$	−38.1509	+	22.0264i	−1.59937	+	0.923396i	−0.607760	+	0.794121i	$0.707932\pi$
$569$	−38.1509	+	22.0264i	−1.59937	+	0.923396i	−0.991609	+	0.129276i	$0.958735\pi$
$570$	−0.268953	−	6.89513i	−0.0112652	−	0.288805i
$571$	3.45405	+	12.8907i	0.144548	+	0.539459i	0.999775	+	0.0212061i	$0.00675061\pi$
$571$	3.45405	+	12.8907i	0.144548	+	0.539459i	−0.855228	+	0.518253i	$0.826583\pi$
$572$	−1.02383	−	13.1040i	−0.0428086	−	0.547906i
$573$	13.4648	+	13.4648i	0.562500	+	0.562500i
$574$		0			0
$575$	16.4204			0.684777
$576$	12.5334	+	13.2525i	0.522223	+	0.552186i
$577$	−8.23157	+	14.2575i	−0.342685	+	0.593547i	−0.984930	−	0.172952i	$-0.944670\pi$
$577$	−8.23157	+	14.2575i	−0.342685	+	0.593547i	0.642246	+	0.766499i	$0.278003\pi$
$578$	29.1923	+	27.0004i	1.21424	+	1.12307i
$579$	1.38662	−	5.17493i	0.0576259	−	0.215063i
$580$	10.6628	+	5.09330i	0.442747	+	0.211488i
$581$		0			0
$582$	2.55300	−	1.60981i	0.105825	−	0.0667287i
$583$	−9.01470	+	5.20464i	−0.373351	+	0.215554i
$584$	27.1391	−	10.8007i	1.12303	−	0.446935i
$585$	7.33841	+	4.23683i	0.303406	+	0.175171i
$586$	−0.249576	+	0.474041i	−0.0103099	+	0.0195824i
$587$	−21.5452	+	21.5452i	−0.889267	+	0.889267i	−0.994453	−	0.105186i	$-0.966456\pi$
$587$	−21.5452	+	21.5452i	−0.889267	+	0.889267i	0.105186	+	0.994453i	$0.466456\pi$
$588$		0			0
$589$	3.53876	+	3.53876i	0.145812	+	0.145812i
$590$	4.05876	+	13.0844i	0.167097	+	0.538678i
$591$	2.29017	−	3.96669i	0.0942051	−	0.163168i
$592$	7.49301	−	10.2887i	0.307961	−	0.422863i
$593$	−13.1459	−	22.7693i	−0.539837	−	0.935024i	−0.998912	−	0.0466273i	$-0.985153\pi$
$593$	−13.1459	−	22.7693i	−0.539837	−	0.935024i	0.459076	−	0.888397i	$-0.348181\pi$
$594$	−15.0663	−	3.41366i	−0.618180	−	0.140064i
$595$		0			0
$596$	6.13034	−	2.16696i	0.251109	−	0.0887620i
$597$	−21.0063	−	5.62862i	−0.859730	−	0.230364i
$598$	20.1830	−	0.787261i	0.825342	−	0.0321935i
$599$	−24.0941	−	13.9107i	−0.984457	−	0.568376i	−0.0808440	−	0.996727i	$-0.525762\pi$
$599$	−24.0941	−	13.9107i	−0.984457	−	0.568376i	−0.903613	+	0.428350i	$0.859095\pi$
$600$	5.96272	−	4.44468i	0.243427	−	0.181453i
$601$			18.3631i			0.749047i	0.927217	+	0.374523i	$0.122194\pi$
$601$			18.3631i			0.749047i	−0.927217	+	0.374523i	$0.877806\pi$
$602$		0			0
$603$	8.10778	−	8.10778i	0.330174	−	0.330174i
$604$	36.2071	−	2.82891i	1.47325	−	0.115107i
$605$	−6.73244	+	1.80395i	−0.273713	+	0.0733411i
$606$	10.6677	+	9.86672i	0.433345	+	0.400808i
$607$	−4.95594	−	8.58394i	−0.201155	−	0.348411i	0.747746	−	0.663985i	$-0.231136\pi$
$607$	−4.95594	−	8.58394i	−0.201155	−	0.348411i	−0.948901	+	0.315574i	$0.897803\pi$
$608$	22.3298	+	7.61526i	0.905593	+	0.308839i
$609$		0			0
$610$	−5.90592	+	26.0661i	−0.239124	+	1.05539i
$611$	−2.13600	+	7.97168i	−0.0864135	+	0.322500i
$612$	−17.3348	−	25.2529i	−0.700716	−	1.02079i
$613$	11.1642	+	41.6652i	0.450916	+	1.68284i	0.699825	+	0.714315i	$0.253262\pi$
$613$	11.1642	+	41.6652i	0.450916	+	1.68284i	−0.248908	+	0.968527i	$0.580072\pi$
$614$	21.9100	+	11.5353i	0.884214	+	0.465528i
$615$		−	4.62112i		−	0.186341i
$616$		0			0
$617$		−	7.78309i		−	0.313336i	−0.987651	−	0.156668i	$-0.949925\pi$
$617$		−	7.78309i		−	0.313336i	0.987651	−	0.156668i	$-0.0500752\pi$
$618$	−9.97041	+	18.9376i	−0.401069	+	0.761782i
$619$	10.1211	+	37.7725i	0.406801	+	1.51820i	0.800709	+	0.599053i	$0.204456\pi$
$619$	10.1211	+	37.7725i	0.406801	+	1.51820i	−0.393908	+	0.919150i	$0.628877\pi$
$620$	0.604868	−	3.25328i	0.0242921	−	0.130655i
$621$	6.14419	−	22.9304i	0.246558	−	0.920166i
$622$	5.09591	+	1.15460i	0.204327	+	0.0462954i
$623$		0			0
$624$	7.11593	−	5.74902i	0.284865	−	0.230145i
$625$	0.0486668	+	0.0842933i	0.00194667	+	0.00337173i
$626$	−10.0540	+	10.8701i	−0.401837	+	0.434457i
$627$	−8.33433	+	2.23318i	−0.332841	+	0.0891845i
$628$	19.8722	−	23.2406i	0.792986	−	0.927402i
$629$	−15.1133	+	15.1133i	−0.602607	+	0.602607i
$630$		0			0
$631$		−	6.10120i		−	0.242885i	−0.992598	−	0.121442i	$-0.961248\pi$
$631$		−	6.10120i		−	0.242885i	0.992598	−	0.121442i	$-0.0387520\pi$
$632$	11.3879	+	1.66106i	0.452986	+	0.0660732i
$633$	0.766036	+	0.442271i	0.0304472	+	0.0175787i
$634$	−1.23120	−	31.5642i	−0.0488972	−	1.25357i
$635$	−18.8367	−	5.04727i	−0.747510	−	0.200295i
$636$	−6.53727	−	3.12267i	−0.259220	−	0.123822i
$637$		0			0
$638$	3.26508	−	14.4106i	0.129266	−	0.570521i
$639$	13.1982	+	22.8599i	0.522112	+	0.904325i
$640$	−4.20454	−	15.0222i	−0.166199	−	0.593805i
$641$	−4.40085	+	7.62249i	−0.173823	+	0.301070i	−0.939753	−	0.341853i	$-0.888945\pi$
$641$	−4.40085	+	7.62249i	−0.173823	+	0.301070i	0.765930	+	0.642924i	$0.222279\pi$
$642$	13.7653	−	4.26995i	0.543271	−	0.168521i
$643$	20.3898	+	20.3898i	0.804095	+	0.804095i	0.983733	−	0.179638i	$-0.0574926\pi$
$643$	20.3898	+	20.3898i	0.804095	+	0.804095i	−0.179638	+	0.983733i	$0.557493\pi$
$644$		0			0
$645$	8.21625	−	8.21625i	0.323515	−	0.323515i
$646$	−35.0560	−	18.4565i	−1.37926	−	0.726163i
$647$	−44.0344	−	25.4233i	−1.73117	−	0.999492i	−0.881517	−	0.472152i	$-0.843477\pi$
$647$	−44.0344	−	25.4233i	−1.73117	−	0.999492i	−0.849654	−	0.527340i	$-0.823189\pi$
$648$	3.17816	+	7.98584i	0.124850	+	0.313713i
$649$	14.8351	−	8.56502i	0.582327	−	0.336207i
$650$	6.30044	+	9.99187i	0.247124	+	0.391913i
$651$		0			0
$652$	6.06215	+	17.1499i	0.237412	+	0.671641i
$653$	−0.618835	+	2.30952i	−0.0242169	+	0.0903787i	−0.976977	−	0.213346i	$-0.931564\pi$
$653$	−0.618835	+	2.30952i	−0.0242169	+	0.0903787i	0.952760	+	0.303725i	$0.0982304\pi$
$654$	8.37357	−	9.05333i	0.327433	−	0.354013i
$655$	2.97361	−	5.15044i	0.116189	−	0.201244i
$656$	14.7439	+	5.67885i	0.575653	+	0.221722i
$657$	23.5463			0.918627
$658$		0			0
$659$	−3.01195	−	3.01195i	−0.117329	−	0.117329i	0.646005	−	0.763334i	$-0.276439\pi$
$659$	−3.01195	−	3.01195i	−0.117329	−	0.117329i	−0.763334	+	0.646005i	$0.776439\pi$
$660$	4.33607	+	3.70761i	0.168781	+	0.144319i
$661$	0.709069	+	2.64628i	0.0275796	+	0.102928i	0.978344	−	0.206987i	$-0.0663659\pi$
$661$	0.709069	+	2.64628i	0.0275796	+	0.102928i	−0.950764	+	0.309916i	$0.899699\pi$
$662$	13.5149	−	0.527166i	0.525272	−	0.0204889i
$663$	−13.3038	+	7.68094i	−0.516676	+	0.298303i
$664$	−36.4646	+	4.28443i	−1.41510	+	0.166268i
$665$		0			0
$666$	8.67899	−	5.47259i	0.336304	−	0.212059i
$667$	21.9324	+	5.87677i	0.849226	+	0.227549i
$668$	−0.749247	−	1.09149i	−0.0289892	−	0.0422309i
$669$	−4.72227	+	1.26533i	−0.182574	+	0.0489205i
$670$	−9.36578	+	2.90524i	−0.361831	+	0.112239i
$671$	33.4196			1.29015
$672$		0			0
$673$	17.6937			0.682041			0.341021	−	0.940056i	$-0.389227\pi$
$673$	17.6937			0.682041			0.341021	+	0.940056i	$0.389227\pi$
$674$	36.7327	−	11.3944i	1.41489	−	0.438896i
$675$	13.4102	−	3.59326i	0.516159	−	0.138304i
$676$	−6.49123	−	9.45627i	−0.249663	−	0.363703i
$677$	−15.3312	−	4.10797i	−0.589225	−	0.157882i	−0.0481259	−	0.998841i	$-0.515325\pi$
$677$	−15.3312	−	4.10797i	−0.589225	−	0.157882i	−0.541099	+	0.840959i	$0.681992\pi$
$678$	14.0429	−	8.85483i	0.539314	−	0.340068i
$679$		0			0
$680$	3.05681	+	26.0164i	0.117223	+	0.997684i
$681$	18.9319	−	10.9303i	0.725471	−	0.418851i
$682$	−4.13452	+	0.161272i	−0.158319	+	0.00617543i
$683$	2.48447	+	9.27215i	0.0950654	+	0.354789i	0.997029	−	0.0770223i	$-0.0245413\pi$
$683$	2.48447	+	9.27215i	0.0950654	+	0.354789i	−0.901964	+	0.431811i	$0.857875\pi$
$684$	14.4548	+	12.3597i	0.552692	+	0.472586i
$685$	11.2912	+	11.2912i	0.431415	+	0.431415i
$686$		0			0
$687$	−0.615292			−0.0234749
$688$	16.1175	+	36.3113i	0.614474	+	1.38435i
$689$	5.75355	−	9.96544i	0.219193	−	0.379653i
$690$	−5.95287	+	6.43612i	−0.226622	+	0.245019i
$691$	−12.5719	+	46.9191i	−0.478259	+	1.78489i	0.130407	+	0.991461i	$0.458372\pi$
$691$	−12.5719	+	46.9191i	−0.478259	+	1.78489i	−0.608666	+	0.793427i	$0.708295\pi$
$692$	−5.99130	−	16.9494i	−0.227755	−	0.644321i
$693$		0			0
$694$	4.46069	+	7.07421i	0.169326	+	0.268533i
$695$	3.80105	−	2.19454i	0.144182	−	0.0832436i
$696$	9.55503	−	3.80265i	0.362182	−	0.144139i
$697$	−22.9771	−	13.2658i	−0.870318	−	0.502479i
$698$	43.5043	+	22.9045i	1.64666	+	0.866946i
$699$	8.66519	−	8.66519i	0.327747	−	0.327747i
$700$		0			0
$701$	4.68514	+	4.68514i	0.176955	+	0.176955i	0.790027	−	0.613072i	$-0.210066\pi$
$701$	4.68514	+	4.68514i	0.176955	+	0.176955i	−0.613072	+	0.790027i	$0.710066\pi$
$702$	16.3108	−	5.05956i	0.615610	−	0.190961i
$703$	6.63547	−	11.4930i	0.250262	−	0.433466i
$704$	−17.1579	+	9.27822i	−0.646662	+	0.349686i
$705$	−1.79107	−	3.10222i	−0.0674555	−	0.116836i
$706$	10.4207	−	45.9923i	0.392189	−	1.73094i
$707$		0			0
$708$	10.7581	+	5.13883i	0.404313	+	0.193129i
$709$	−23.2407	−	6.22733i	−0.872823	−	0.233872i	−0.205515	−	0.978654i	$-0.565887\pi$
$709$	−23.2407	−	6.22733i	−0.872823	−	0.233872i	−0.667308	+	0.744782i	$0.732554\pi$
$710$	−0.879881	−	22.5575i	−0.0330213	−	0.846566i
$711$	8.03425	+	4.63858i	0.301308	+	0.173960i
$712$	6.91096	−	47.3803i	0.258999	−	1.77565i
$713$		−	6.35836i		−	0.238122i
$714$		0			0
$715$	−6.40747	+	6.40747i	−0.239626	+	0.239626i
$716$	13.9993	−	16.3723i	0.523178	−	0.611860i
$717$	−6.02163	+	1.61349i	−0.224882	+	0.0602569i
$718$	−7.58510	+	8.20085i	−0.283074	+	0.306053i
$719$	12.2521	+	21.2213i	0.456927	+	0.791420i	0.998797	−	0.0490421i	$-0.0156169\pi$
$719$	12.2521	+	21.2213i	0.456927	+	0.791420i	−0.541870	+	0.840462i	$0.682284\pi$
$720$	1.32863	−	12.5047i	0.0495152	−	0.466023i
$721$		0			0
$722$	−2.21492	−	0.501845i	−0.0824308	−	0.0186768i
$723$	−0.714486	+	2.66650i	−0.0265720	+	0.0991682i
$724$	7.23318	−	38.9036i	0.268819	−	1.44584i
$725$	3.43686	+	12.8265i	0.127642	+	0.476366i
$726$	−2.82585	+	5.36736i	−0.104877	+	0.199201i
$727$			41.6544i			1.54488i	0.635090	+	0.772438i	$0.280963\pi$
$727$			41.6544i			1.54488i	−0.635090	+	0.772438i	$0.719037\pi$
$728$		0			0
$729$		−	4.47546i		−	0.165758i
$730$	−17.8185	−	9.38120i	−0.659491	−	0.347214i
$731$	−17.2664	−	64.4391i	−0.638621	−	2.38337i
$732$	13.1636	+	19.1765i	0.486542	+	0.708783i
$733$	6.78421	−	25.3190i	0.250580	−	0.935179i	−0.719916	−	0.694062i	$-0.755820\pi$
$733$	6.78421	−	25.3190i	0.250580	−	0.935179i	0.970496	−	0.241117i	$-0.0775138\pi$
$734$	9.24829	−	40.8178i	0.341361	−	1.50661i
$735$		0			0
$736$	−13.2193	−	26.9022i	−0.487272	−	0.991630i
$737$	6.13080	+	10.6189i	0.225831	+	0.391151i
$738$	9.35025	+	8.64820i	0.344187	+	0.318345i
$739$	−6.74712	+	1.80789i	−0.248197	+	0.0665042i	−0.380773	−	0.924669i	$-0.624342\pi$
$739$	−6.74712	+	1.80789i	−0.248197	+	0.0665042i	0.132576	+	0.991173i	$0.457675\pi$
$740$	−8.74813	+	0.683503i	−0.321588	+	0.0251261i
$741$	6.74461	−	6.74461i	0.247769	−	0.247769i
$742$		0			0
$743$		−	17.8484i		−	0.654796i	−0.944887	−	0.327398i	$-0.893828\pi$
$743$		−	17.8484i		−	0.654796i	0.944887	−	0.327398i	$-0.106172\pi$
$744$	−1.72109	−	2.30891i	−0.0630981	−	0.0846486i
$745$	−3.88202	−	2.24128i	−0.142226	−	0.0821143i
$746$	−8.62604	+	0.336469i	−0.315822	+	0.0123190i
$747$	−28.5886	−	7.66028i	−1.04600	−	0.280275i
$748$	30.8825	−	10.9164i	1.12918	−	0.399142i
$749$		0			0
$750$	−13.0685	−	2.96099i	−0.477193	−	0.108120i
$751$	−9.17355	−	15.8891i	−0.334747	−	0.579800i	0.648689	−	0.761054i	$-0.275318\pi$
$751$	−9.17355	−	15.8891i	−0.334747	−	0.579800i	−0.983436	+	0.181254i	$0.941984\pi$
$752$	12.0988	−	1.90221i	0.441199	−	0.0693663i
$753$	1.24840	−	2.16229i	0.0454943	−	0.0787984i
$754$	4.83935	+	15.6009i	0.176239	+	0.568150i
$755$	−17.7042	−	17.7042i	−0.644322	−	0.644322i
$756$		0			0
$757$	4.90437	−	4.90437i	0.178252	−	0.178252i	−0.612341	−	0.790594i	$-0.709772\pi$
$757$	4.90437	−	4.90437i	0.178252	−	0.178252i	0.790594	+	0.612341i	$0.209772\pi$
$758$	14.1127	−	26.8054i	0.512597	−	0.973616i
$759$	9.49371	+	5.48119i	0.344600	+	0.198955i
$760$	−6.01424	−	15.1121i	−0.218159	−	0.548175i
$761$	−3.01761	+	1.74222i	−0.109388	+	0.0631553i	−0.553696	−	0.832719i	$-0.686783\pi$
$761$	−3.01761	+	1.74222i	−0.109388	+	0.0631553i	0.444308	+	0.895874i	$0.353450\pi$
$762$	−14.3558	+	9.05215i	−0.520056	+	0.327925i
$763$		0			0
$764$	40.5010	+	19.3462i	1.46527	+	0.699920i
$765$	−5.46538	+	20.3971i	−0.197601	+	0.737458i
$766$	6.87452	+	6.35836i	0.248387	+	0.229737i
$767$	−9.46834	+	16.3996i	−0.341882	+	0.592157i
$768$	−12.0823	−	6.19077i	−0.435981	−	0.223390i
$769$	−13.5559			−0.488837			−0.244418	−	0.969670i	$-0.578597\pi$
$769$	−13.5559			−0.488837			−0.244418	+	0.969670i	$0.578597\pi$
$770$		0			0
$771$	−6.57694	−	6.57694i	−0.236863	−	0.236863i
$772$	−0.983657	−	12.5898i	−0.0354026	−	0.453117i
$773$	7.45965	+	27.8398i	0.268305	+	1.00133i	0.960196	+	0.279326i	$0.0901109\pi$
$773$	7.45965	+	27.8398i	0.268305	+	1.00133i	−0.691892	+	0.722001i	$0.743222\pi$
$774$	1.24823	+	32.0009i	0.0448668	+	1.15025i
$775$	3.22032	−	1.85925i	0.115677	−	0.0667864i
$776$	4.40906	−	5.58310i	0.158276	−	0.200422i
$777$		0			0
$778$	27.3738	+	43.4121i	0.981399	+	1.55640i
$779$	15.9124	+	4.26371i	0.570120	+	0.152763i
$780$	−6.20051	−	1.15283i	−0.222014	−	0.0412780i
$781$	−27.2658	+	7.30585i	−0.975647	+	0.261424i
$782$	14.9127	+	48.0749i	0.533278	+	1.71916i
$783$	19.1978			0.686073
$784$		0			0
$785$	−21.0809			−0.752409
$786$	−1.53342	−	4.94338i	−0.0546954	−	0.176324i
$787$	−37.8633	+	10.1454i	−1.34968	+	0.361646i	−0.860017	−	0.510266i	$-0.829547\pi$
$787$	−37.8633	+	10.1454i	−1.34968	+	0.361646i	−0.489663	+	0.871912i	$0.662880\pi$
$788$	1.97350	−	10.6145i	0.0703030	−	0.378125i
$789$	8.35413	+	2.23848i	0.297415	+	0.0796921i
$790$	−4.23178	−	6.71118i	−0.150560	−	0.238773i
$791$		0			0
$792$	−15.6166	+	1.83489i	−0.554913	+	0.0651999i
$793$	−31.9946	+	18.4721i	−1.13616	+	0.655963i
$794$	−0.738294	−	18.9276i	−0.0262011	−	0.671715i
$795$	1.29270	+	4.82442i	0.0458474	+	0.171105i
$796$	−51.1050	+	3.99290i	−1.81137	+	0.141525i
$797$	−2.87837	−	2.87837i	−0.101957	−	0.101957i	0.654288	−	0.756245i	$-0.272968\pi$
$797$	−2.87837	−	2.87837i	−0.101957	−	0.101957i	−0.756245	+	0.654288i	$0.772968\pi$
$798$		0			0
$799$	−20.5664			−0.727588
$800$	9.75971	−	14.5617i	0.345058	−	0.514835i
$801$	19.2992	−	33.4272i	0.681904	−	1.18109i
$802$	18.1831	+	16.8179i	0.642069	+	0.593860i
$803$	−6.51701	+	24.3218i	−0.229980	+	0.858298i
$804$	−3.67835	+	7.70058i	−0.129725	+	0.271578i
$805$		0			0
$806$	3.86909	−	2.43968i	0.136283	−	0.0859341i
$807$	−1.82671	+	1.05465i	−0.0643033	+	0.0371255i
$808$	31.4583	+	13.5472i	1.10670	+	0.476590i
$809$	18.6610	+	10.7739i	0.656085	+	0.378791i	0.790784	−	0.612096i	$-0.209673\pi$
$809$	18.6610	+	10.7739i	0.656085	+	0.378791i	−0.134699	+	0.990887i	$0.543007\pi$
$810$	2.76047	−	5.24319i	0.0969931	−	0.184227i
$811$	20.4977	−	20.4977i	0.719772	−	0.719772i	−0.248787	−	0.968558i	$-0.580032\pi$
$811$	20.4977	−	20.4977i	0.719772	−	0.719772i	0.968558	+	0.248787i	$0.0800318\pi$
$812$		0			0
$813$	3.39687	+	3.39687i	0.119134	+	0.119134i
$814$	3.25072	+	10.4795i	0.113938	+	0.367307i
$815$	6.27008	−	10.8601i	0.219631	−	0.380413i
$816$	18.4282	+	13.4208i	0.645117	+	0.469823i
$817$	20.7111	+	35.8727i	0.724590	+	1.25503i
$818$	−14.3105	−	3.24240i	−0.500355	−	0.113368i
$819$		0			0
$820$	−3.63016	−	10.2698i	−0.126771	−	0.358635i
$821$	12.4414	+	3.33365i	0.434207	+	0.116345i	0.469300	−	0.883039i	$-0.344506\pi$
$821$	12.4414	+	3.33365i	0.434207	+	0.116345i	−0.0350936	+	0.999384i	$0.511173\pi$
$822$	13.8862	−	0.541650i	0.484338	−	0.0188922i
$823$	−35.9043	−	20.7294i	−1.25155	−	0.722580i	−0.280129	−	0.959962i	$-0.590377\pi$
$823$	−35.9043	−	20.7294i	−1.25155	−	0.722580i	−0.971416	+	0.237382i	$0.923711\pi$
$824$	−7.28117	+	49.9184i	−0.253652	+	1.73899i
$825$			6.41104i			0.223204i
$826$		0			0
$827$	14.8134	−	14.8134i	0.515111	−	0.515111i	−0.400977	−	0.916088i	$-0.631329\pi$
$827$	14.8134	−	14.8134i	0.515111	−	0.515111i	0.916088	+	0.400977i	$0.131329\pi$
$828$	−1.88217	−	24.0898i	−0.0654098	−	0.837178i
$829$	−23.6252	+	6.33035i	−0.820537	+	0.219862i	−0.644581	−	0.764536i	$-0.722968\pi$
$829$	−23.6252	+	6.33035i	−0.820537	+	0.219862i	−0.175956	+	0.984398i	$0.556302\pi$
$830$	18.5822	+	17.1870i	0.644998	+	0.596569i
$831$	12.7992	+	22.1689i	0.444001	+	0.769032i
$832$	11.2979	−	18.3663i	0.391685	−	0.636738i
$833$		0			0
$834$	0.844060	−	3.72530i	0.0292274	−	0.128997i
$835$	−0.236226	+	0.881607i	−0.00817494	+	0.0305093i
$836$	−16.7675	+	11.5100i	−0.579917	+	0.398082i
$837$	−1.39139	−	5.19275i	−0.0480936	−	0.179488i
$838$	−22.3063	−	11.7440i	−0.770560	−	0.405690i
$839$			26.6645i			0.920562i	0.887773	+	0.460281i	$0.152251\pi$
$839$			26.6645i			0.920562i	−0.887773	+	0.460281i	$0.847749\pi$
$840$		0			0
$841$		−	10.6378i		−	0.366820i
$842$	16.4532	−	31.2509i	0.567015	−	1.07698i
$843$	−0.351391	−	1.31141i	−0.0121025	−	0.0451673i
$844$	2.04983	+	0.381116i	0.0705582	+	0.0131186i
$845$	−2.04658	+	7.63795i	−0.0704046	+	0.262754i
$846$	9.62886	+	2.18166i	0.331047	+	0.0750069i
$847$		0			0
$848$	−16.9812	−	1.80426i	−0.583136	−	0.0619586i
$849$	8.63609	+	14.9581i	0.296390	+	0.513362i
$850$	−19.9879	+	21.6105i	−0.685579	+	0.741234i
$851$	−16.2864	+	4.36392i	−0.558289	+	0.149593i
$852$	−14.9319	−	12.7677i	−0.511558	−	0.437414i
$853$	−12.4072	+	12.4072i	−0.424815	+	0.424815i	−0.886858	−	0.462043i	$-0.847117\pi$
$853$	−12.4072	+	12.4072i	−0.424815	+	0.424815i	0.462043	+	0.886858i	$0.347117\pi$
$854$		0			0
$855$		−	13.1115i		−	0.448404i
$856$	27.2370	−	20.3028i	0.930941	−	0.693934i
$857$	−2.14051	−	1.23582i	−0.0731184	−	0.0422149i	0.462995	−	0.886361i	$-0.346775\pi$
$857$	−2.14051	−	1.23582i	−0.0731184	−	0.0422149i	−0.536113	+	0.844146i	$0.680108\pi$
$858$	0.307372	+	7.88008i	0.0104935	+	0.269022i
$859$	−25.9325	−	6.94860i	−0.884806	−	0.237083i	−0.212327	−	0.977199i	$-0.568104\pi$
$859$	−25.9325	−	6.94860i	−0.884806	−	0.237083i	−0.672480	+	0.740116i	$0.734771\pi$
$860$	11.8051	−	24.7138i	0.402550	−	0.842733i
$861$		0			0
$862$	2.99516	−	13.2193i	0.102016	−	0.450251i
$863$	17.6924	+	30.6441i	0.602255	+	1.04314i	0.992479	+	0.122417i	$0.0390645\pi$
$863$	17.6924	+	30.6441i	0.602255	+	1.04314i	−0.390223	+	0.920720i	$0.627602\pi$
$864$	−16.6830	−	19.0778i	−0.567567	−	0.649039i
$865$	−6.19680	+	10.7332i	−0.210698	+	0.364939i
$866$	1.29485	−	0.401658i	0.0440006	−	0.0136489i
$867$	−16.8700	−	16.8700i	−0.572935	−	0.572935i
$868$		0			0
$869$	−7.01504	+	7.01504i	−0.237969	+	0.237969i
$870$	−6.27345	−	3.30289i	−0.212690	−	0.111979i
$871$	−11.7388	−	6.77739i	−0.397753	−	0.229643i
$872$	11.4971	−	26.6976i	0.389342	−	0.904096i
$873$	4.96652	−	2.86742i	0.168091	−	0.0970475i
$874$	−16.6697	−	26.4365i	−0.563862	−	0.894228i
$875$		0			0
$876$	−16.5231	+	5.84059i	−0.558263	+	0.197335i
$877$	1.58253	−	5.90609i	0.0534383	−	0.199434i	−0.934046	−	0.357153i	$-0.883747\pi$
$877$	1.58253	−	5.90609i	0.0534383	−	0.199434i	0.987484	+	0.157719i	$0.0504140\pi$
$878$	9.57756	−	10.3551i	0.323227	−	0.349466i
$879$	0.160712	−	0.278362i	0.00542068	−	0.00938890i
$880$	12.5488	+	4.83338i	0.423021	+	0.162933i
$881$	−26.3944			−0.889249			−0.444625	−	0.895717i	$-0.646663\pi$
$881$	−26.3944			−0.889249			−0.444625	+	0.895717i	$0.646663\pi$
$882$		0			0
$883$	−29.3078	−	29.3078i	−0.986286	−	0.986286i	0.0136216	−	0.999907i	$-0.495664\pi$
$883$	−29.3078	−	29.3078i	−0.986286	−	0.986286i	−0.999907	+	0.0136216i	$0.995664\pi$
$884$	−23.5319	+	27.5207i	−0.791462	+	0.925620i
$885$	−2.12734	−	7.93933i	−0.0715096	−	0.266878i
$886$	−30.9457	+	1.20707i	−1.03964	+	0.0405525i
$887$	−15.7825	+	9.11203i	−0.529924	+	0.305952i	−0.740986	−	0.671521i	$-0.765641\pi$
$887$	−15.7825	+	9.11203i	−0.529924	+	0.305952i	0.211061	+	0.977473i	$0.432308\pi$
$888$	−4.73283	+	5.99308i	−0.158823	+	0.201114i
$889$		0			0
$890$	−27.9225	+	17.6067i	−0.935963	+	0.590178i
$891$	−7.15683	−	1.91767i	−0.239763	−	0.0642443i
$892$	−9.50057	+	6.52164i	−0.318103	+	0.218361i
$893$	12.3348	−	3.30509i	0.412767	−	0.110601i
$894$	−3.72595	+	1.15578i	−0.124614	+	0.0386551i
$895$	−14.8508			−0.496407
$896$		0			0
$897$	−12.1185			−0.404626
$898$	11.8577	−	3.67822i	0.395695	−	0.122744i
$899$	4.96675	−	1.33084i	0.165650	−	0.0443858i
$900$	11.6504	−	7.99738i	0.388347	−	0.266579i
$901$	27.6989	+	7.42190i	0.922784	+	0.247259i
$902$	−11.5210	+	7.26462i	−0.383606	+	0.241885i
$903$		0			0
$904$	24.2523	−	30.7101i	0.806618	−	1.02140i
$905$	−23.6253	+	13.6400i	−0.785330	+	0.453410i
$906$	−21.7731	+	0.849287i	−0.723363	+	0.0282157i
$907$	−4.78386	−	17.8536i	−0.158845	−	0.592819i	−0.998745	−	0.0500777i	$-0.984053\pi$
$907$	−4.78386	−	17.8536i	−0.158845	−	0.592819i	0.839900	−	0.542741i	$-0.182614\pi$
$908$	33.4869	−	39.1632i	1.11130	−	1.29967i
$909$	19.5237	+	19.5237i	0.647560	+	0.647560i
$910$		0			0
$911$	21.3908			0.708708			0.354354	−	0.935111i	$-0.384701\pi$
$911$	21.3908			0.708708			0.354354	+	0.935111i	$0.384701\pi$
$912$	−13.2091	−	5.08770i	−0.437398	−	0.168471i
$913$	15.8252	−	27.4100i	0.523737	−	0.907139i
$914$	−1.79721	+	1.94310i	−0.0594463	+	0.0642721i
$915$	4.15029	−	15.4891i	0.137204	−	0.512054i
$916$	−1.36740	+	0.483348i	−0.0451801	+	0.0159703i
$917$		0			0
$918$	22.6991	+	35.9986i	0.749184	+	1.18813i
$919$	−9.15317	+	5.28458i	−0.301935	+	0.174322i	−0.643312	−	0.765604i	$-0.722440\pi$
$919$	−9.15317	+	5.28458i	−0.301935	+	0.174322i	0.341377	+	0.939927i	$0.389107\pi$
$920$	−8.17343	+	18.9797i	−0.269470	+	0.625741i
$921$	−12.8658	−	7.42805i	−0.423941	−	0.244763i
$922$	−23.4864	−	12.3653i	−0.773483	−	0.407229i
$923$	22.0650	−	22.0650i	0.726279	−	0.726279i
$924$		0			0
$925$	−6.97251	−	6.97251i	−0.229255	−	0.229255i
$926$	2.56400	−	0.795346i	0.0842582	−	0.0261367i
$927$	−20.3330	+	35.2178i	−0.667824	+	1.15671i
$928$	18.2474	−	15.9569i	0.599002	−	0.523810i
$929$	8.76862	+	15.1877i	0.287689	+	0.498292i	0.973258	−	0.229716i	$-0.0737797\pi$
$929$	8.76862	+	15.1877i	0.287689	+	0.498292i	−0.685569	+	0.728008i	$0.740446\pi$
$930$	−0.438710	+	1.93627i	−0.0143859	+	0.0634928i
$931$		0			0
$932$	12.4501	−	26.0641i	0.407817	−	0.853759i
$933$	−3.02811	−	0.811379i	−0.0991358	−	0.0265634i
$934$	0.0844961	+	2.16622i	0.00276480	+	0.0708809i
$935$	−19.5562	−	11.2908i	−0.639557	−	0.369249i
$936$	13.9366	−	10.3885i	0.455531	−	0.339558i
$937$			43.7391i			1.42890i	0.699689	+	0.714448i	$0.253322\pi$
$937$			43.7391i			1.42890i	−0.699689	+	0.714448i	$0.746678\pi$
$938$		0			0
$939$	6.28177	−	6.28177i	0.204998	−	0.204998i
$940$	−6.41737	−	5.48724i	−0.209311	−	0.178974i
$941$	−10.4031	+	2.78751i	−0.339133	+	0.0908703i	−0.424366	−	0.905491i	$-0.639503\pi$
$941$	−10.4031	+	2.78751i	−0.339133	+	0.0908703i	0.0852335	+	0.996361i	$0.472836\pi$
$942$	−12.4573	+	13.4686i	−0.405881	+	0.438829i
$943$	−10.4650	−	18.1259i	−0.340788	−	0.590262i
$944$	27.9451	+	2.96919i	0.909536	+	0.0966389i
$945$		0			0
$946$	−33.4004	−	7.56769i	−1.08594	−	0.246047i
$947$	3.54840	−	13.2428i	0.115307	−	0.430333i	−0.884002	−	0.467483i	$-0.845161\pi$
$947$	3.54840	−	13.2428i	0.115307	−	0.430333i	0.999310	+	0.0371493i	$0.0118277\pi$
$948$	−6.78845	−	1.26215i	−0.220479	−	0.0409926i
$949$	−7.20433	−	26.8869i	−0.233862	−	0.872787i
$950$	8.51491	−	16.1730i	0.276260	−	0.524723i
$951$			18.9522i			0.614568i
$952$		0			0
$953$			3.19629i			0.103538i	0.998659	+	0.0517690i	$0.0164860\pi$
$953$			3.19629i			0.103538i	−0.998659	+	0.0517690i	$0.983514\pi$
$954$	−12.1809	−	6.41307i	−0.394370	−	0.207631i
$955$	−8.00879	−	29.8892i	−0.259158	−	0.967192i
$956$	−12.1147	+	8.31609i	−0.391817	+	0.268962i
$957$	−2.29448	+	8.56312i	−0.0741700	+	0.276806i
$958$	−8.84300	+	39.0290i	−0.285704	+	1.26097i
$959$		0			0
$960$	2.16942	+	9.10447i	0.0700177	+	0.293845i
$961$	14.7801	+	25.5998i	0.476776	+	0.825800i
$962$	−8.90449	−	8.23591i	−0.287092	−	0.265536i
$963$	26.4519	−	7.08777i	0.852401	−	0.228400i
$964$	0.506852	+	6.48718i	0.0163246	+	0.208938i
$965$	−6.15604	+	6.15604i	−0.198170	+	0.198170i
$966$		0			0
$967$			25.7940i			0.829479i	0.909940	+	0.414739i	$0.136127\pi$
$967$			25.7940i			0.829479i	−0.909940	+	0.414739i	$0.863873\pi$
$968$	−2.06365	+	14.1480i	−0.0663284	+	0.454735i
$969$	20.5852	+	11.8849i	0.661293	+	0.381798i
$970$	−4.90081	+	0.191162i	−0.157355	+	0.00613784i
$971$	16.2562	+	4.35584i	0.521687	+	0.139786i	0.510047	−	0.860147i	$-0.329628\pi$
$971$	16.2562	+	4.35584i	0.521687	+	0.139786i	0.0116402	+	0.999932i	$0.496295\pi$
$972$	−10.6772	−	30.2059i	−0.342472	−	0.968855i
$973$		0			0
$974$	8.54740	+	1.93663i	0.273876	+	0.0620535i
$975$	−3.54359	−	6.13768i	−0.113486	−	0.196563i
$976$	44.3185	+	32.2761i	1.41860	+	1.03313i
$977$	−1.37068	+	2.37409i	−0.0438519	+	0.0759537i	−0.887118	−	0.461542i	$-0.847296\pi$
$977$	−1.37068	+	2.37409i	−0.0438519	+	0.0759537i	0.843266	+	0.537496i	$0.180630\pi$
$978$	−3.23334	−	10.4235i	−0.103391	−	0.333306i
$979$	29.1867	+	29.1867i	0.932810	+	0.932810i
$980$		0			0
$981$	16.5691	−	16.5691i	0.529012	−	0.529012i
$982$	−20.0935	+	38.1652i	−0.641209	+	1.21790i
$983$	38.6502	+	22.3147i	1.23275	+	0.711729i	0.967603	−	0.252478i	$-0.0812456\pi$
$983$	38.6502	+	22.3147i	1.23275	+	0.711729i	0.265149	+	0.964207i	$0.414579\pi$
$984$	−8.70650	−	3.74938i	−0.277553	−	0.119526i
$985$	−6.44591	+	3.72155i	−0.205384	+	0.118578i
$986$	−34.4318	+	21.7112i	−1.09653	+	0.691425i
$987$		0			0
$988$	9.69062	−	20.2872i	0.308300	−	0.645422i
$989$	13.6210	−	50.8342i	0.433122	−	1.61643i
$990$	7.95819	+	7.36066i	0.252928	+	0.233937i
$991$	−0.542257	+	0.939218i	−0.0172254	+	0.0298352i	−0.874510	−	0.485008i	$-0.838817\pi$
$991$	−0.542257	+	0.939218i	−0.0172254	+	0.0298352i	0.857284	+	0.514843i	$0.172150\pi$
$992$	−5.63865	−	3.77919i	−0.179027	−	0.119990i
$993$	−8.11482			−0.257516
$994$		0			0
$995$	24.9888	+	24.9888i	0.792200	+	0.792200i
$996$	21.9615	−	1.71588i	0.695877	−	0.0543698i
$997$	10.7579	+	40.1489i	0.340705	+	1.27153i	0.897550	+	0.440912i	$0.145345\pi$
$997$	10.7579	+	40.1489i	0.340705	+	1.27153i	−0.556845	+	0.830616i	$0.687988\pi$
$998$	0.191365	+	4.90602i	0.00605756	+	0.155297i
$999$	−12.3458	+	7.12786i	−0.390605	+	0.225516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.l.557.1		24
7.2	even	3	inner	784.2.x.l.765.5		24
7.3	odd	6		784.2.m.h.589.4		12
7.4	even	3		112.2.m.d.29.4	✓	12
7.5	odd	6		784.2.x.m.765.5		24
7.6	odd	2		784.2.x.m.557.1		24
16.5	even	4	inner	784.2.x.l.165.5		24
28.11	odd	6		448.2.m.d.337.5		12
56.11	odd	6		896.2.m.h.673.2		12
56.53	even	6		896.2.m.g.673.5		12
112.5	odd	12		784.2.x.m.373.1		24
112.11	odd	12		448.2.m.d.113.5		12
112.37	even	12	inner	784.2.x.l.373.1		24
112.53	even	12		112.2.m.d.85.4	yes	12
112.67	odd	12		896.2.m.h.225.2		12
112.69	odd	4		784.2.x.m.165.5		24
112.101	odd	12		784.2.m.h.197.4		12
112.109	even	12		896.2.m.g.225.5		12
224.11	odd	24		7168.2.a.bi.1.8		12
224.53	even	24		7168.2.a.bj.1.5		12
224.123	odd	24		7168.2.a.bi.1.5		12
224.165	even	24		7168.2.a.bj.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.d.29.4	✓	12	7.4	even	3
112.2.m.d.85.4	yes	12	112.53	even	12
448.2.m.d.113.5		12	112.11	odd	12
448.2.m.d.337.5		12	28.11	odd	6
784.2.m.h.197.4		12	112.101	odd	12
784.2.m.h.589.4		12	7.3	odd	6
784.2.x.l.165.5		24	16.5	even	4	inner
784.2.x.l.373.1		24	112.37	even	12	inner
784.2.x.l.557.1		24	1.1	even	1	trivial
784.2.x.l.765.5		24	7.2	even	3	inner
784.2.x.m.165.5		24	112.69	odd	4
784.2.x.m.373.1		24	112.5	odd	12
784.2.x.m.557.1		24	7.6	odd	2
784.2.x.m.765.5		24	7.5	odd	6
896.2.m.g.225.5		12	112.109	even	12
896.2.m.g.673.5		12	56.53	even	6
896.2.m.h.225.2		12	112.67	odd	12
896.2.m.h.673.2		12	56.11	odd	6
7168.2.a.bi.1.5		12	224.123	odd	24
7168.2.a.bi.1.8		12	224.11	odd	24
7168.2.a.bj.1.5		12	224.53	even	24
7168.2.a.bj.1.8		12	224.165	even	24

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.35072 + 0.418990i) q^{2} +(0.819585 - 0.219607i) q^{3} +(1.64889 - 1.13188i) q^{4} +(-1.33183 - 0.356864i) q^{5} +(-1.01502 + 0.640026i) q^{6} +(-1.75295 + 2.21972i) q^{8} +(-1.97458 + 1.14003i) q^{9} +O(q^{10})\)	\(q+(-1.35072 + 0.418990i) q^{2} +(0.819585 - 0.219607i) q^{3} +(1.64889 - 1.13188i) q^{4} +(-1.33183 - 0.356864i) q^{5} +(-1.01502 + 0.640026i) q^{6} +(-1.75295 + 2.21972i) q^{8} +(-1.97458 + 1.14003i) q^{9} +(1.94846 - 0.0760019i) q^{10} +(-0.631061 - 2.35515i) q^{11} +(1.10284 - 1.28978i) q^{12} +(1.90592 + 1.90592i) q^{13} -1.16992 q^{15} +(1.43771 - 3.73269i) q^{16} +(-3.35849 + 5.81707i) q^{17} +(2.18945 - 2.36719i) q^{18} +(1.07944 - 4.02851i) q^{19} +(-2.59998 + 0.919042i) q^{20} +(1.83917 + 2.91674i) q^{22} +(-4.58892 + 2.64941i) q^{23} +(-0.949225 + 2.20421i) q^{24} +(-2.68370 - 1.54943i) q^{25} +(-3.37293 - 1.77581i) q^{26} +(-3.16792 + 3.16792i) q^{27} +(-3.03004 - 3.03004i) q^{29} +(1.58024 - 0.490185i) q^{30} +(-0.599978 + 1.03919i) q^{31} +(-0.377976 + 5.64421i) q^{32} +(-1.03442 - 1.79166i) q^{33} +(2.09908 - 9.26441i) q^{34} +(-1.96551 + 4.11477i) q^{36} +(3.07358 + 0.823563i) q^{37} +(0.229890 + 5.89367i) q^{38} +(1.98062 + 1.14351i) q^{39} +(3.12678 - 2.33073i) q^{40} +3.94994i q^{41} +(-7.02292 + 7.02292i) q^{43} +(-3.70630 - 3.16911i) q^{44} +(3.03665 - 0.813668i) q^{45} +(5.08827 - 5.50133i) q^{46} +(1.53093 + 2.65165i) q^{47} +(0.358595 - 3.37499i) q^{48} +(4.27413 + 0.968410i) q^{50} +(-1.47510 + 5.50513i) q^{51} +(5.29994 + 0.985393i) q^{52} +(-1.10495 - 4.12372i) q^{53} +(2.95164 - 5.60630i) q^{54} +3.36187i q^{55} -3.53876i q^{57} +(5.36229 + 2.82318i) q^{58} +(1.81836 + 6.78621i) q^{59} +(-1.92908 + 1.32421i) q^{60} +(-3.54750 + 13.2394i) q^{61} +(0.374991 - 1.65504i) q^{62} +(-1.85433 - 7.78212i) q^{64} +(-1.85822 - 3.21853i) q^{65} +(2.14790 + 1.98663i) q^{66} +(-4.85753 + 1.30157i) q^{67} +(1.04642 + 13.3931i) q^{68} +(-3.17918 + 3.17918i) q^{69} -11.5771i q^{71} +(0.930806 - 6.38144i) q^{72} +(-8.94350 - 5.16353i) q^{73} +(-4.49661 + 0.175396i) q^{74} +(-2.53979 - 0.680534i) q^{75} +(-2.77991 - 7.86439i) q^{76} +(-3.15439 - 0.714705i) q^{78} +(-2.03442 - 3.52371i) q^{79} +(-3.24685 + 4.45826i) q^{80} +(1.51940 - 2.63168i) q^{81} +(-1.65499 - 5.33527i) q^{82} +(9.17886 + 9.17886i) q^{83} +(6.54884 - 6.54884i) q^{85} +(6.54347 - 12.4285i) q^{86} +(-3.14879 - 1.81795i) q^{87} +(6.33400 + 2.72768i) q^{88} +(-14.6607 + 8.46436i) q^{89} +(-3.76075 + 2.37136i) q^{90} +(-4.56783 + 9.56270i) q^{92} +(-0.263519 + 0.983466i) q^{93} +(-3.17888 - 2.94019i) q^{94} +(-2.87526 + 4.98010i) q^{95} +(0.929726 + 4.70892i) q^{96} -2.51522 q^{97} +(3.93102 + 3.93102i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} - 4 q^{3} + 6 q^{4} - 4 q^{5} + 8 q^{6} - 8 q^{8}+O(q^{10}) \) 24 * q - 2 * q^2 - 4 * q^3 + 6 * q^4 - 4 * q^5 + 8 * q^6 - 8 * q^8	\( 24 q - 2 q^{2} - 4 q^{3} + 6 q^{4} - 4 q^{5} + 8 q^{6} - 8 q^{8} + 4 q^{10} - 8 q^{12} - 48 q^{15} - 10 q^{16} + 8 q^{17} - 40 q^{20} + 28 q^{22} + 8 q^{24} + 20 q^{26} + 8 q^{27} - 8 q^{29} + 28 q^{30} + 8 q^{31} - 12 q^{32} + 16 q^{34} - 32 q^{36} + 20 q^{37} - 16 q^{38} + 8 q^{40} + 32 q^{43} - 14 q^{44} - 40 q^{45} + 28 q^{46} - 16 q^{47} + 32 q^{48} + 88 q^{50} + 16 q^{51} + 16 q^{52} - 4 q^{53} - 64 q^{54} - 14 q^{58} + 16 q^{59} - 60 q^{60} + 20 q^{61} + 16 q^{62} - 36 q^{64} - 32 q^{65} - 12 q^{66} - 24 q^{67} + 28 q^{68} - 8 q^{69} - 6 q^{72} + 38 q^{74} + 40 q^{75} + 96 q^{76} - 152 q^{78} - 24 q^{79} - 24 q^{80} + 44 q^{81} + 16 q^{82} - 40 q^{83} - 16 q^{85} - 38 q^{86} + 14 q^{88} - 80 q^{90} + 64 q^{92} + 48 q^{93} + 24 q^{94} + 16 q^{96} + 96 q^{97} + 64 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 - 4 * q^3 + 6 * q^4 - 4 * q^5 + 8 * q^6 - 8 * q^8 + 4 * q^10 - 8 * q^12 - 48 * q^15 - 10 * q^16 + 8 * q^17 - 40 * q^20 + 28 * q^22 + 8 * q^24 + 20 * q^26 + 8 * q^27 - 8 * q^29 + 28 * q^30 + 8 * q^31 - 12 * q^32 + 16 * q^34 - 32 * q^36 + 20 * q^37 - 16 * q^38 + 8 * q^40 + 32 * q^43 - 14 * q^44 - 40 * q^45 + 28 * q^46 - 16 * q^47 + 32 * q^48 + 88 * q^50 + 16 * q^51 + 16 * q^52 - 4 * q^53 - 64 * q^54 - 14 * q^58 + 16 * q^59 - 60 * q^60 + 20 * q^61 + 16 * q^62 - 36 * q^64 - 32 * q^65 - 12 * q^66 - 24 * q^67 + 28 * q^68 - 8 * q^69 - 6 * q^72 + 38 * q^74 + 40 * q^75 + 96 * q^76 - 152 * q^78 - 24 * q^79 - 24 * q^80 + 44 * q^81 + 16 * q^82 - 40 * q^83 - 16 * q^85 - 38 * q^86 + 14 * q^88 - 80 * q^90 + 64 * q^92 + 48 * q^93 + 24 * q^94 + 16 * q^96 + 96 * q^97 + 64 * q^99

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