LMFDB - Embedded newform 784.2.x.l.373.1

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			373.1
Character	$\chi$	$=$	784.373
Dual form			784.2.x.l.557.1

$q$-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 $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

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

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	0.487529	−	0.873107i	$-0.337898\pi$
$3$	0.819585	+	0.219607i	0.473188	+	0.126790i	−0.0143411	+	0.999897i	$0.504565\pi$
$4$	1.64889	+	1.13188i	0.824447	+	0.565939i
$5$	−1.33183	+	0.356864i	−0.595614	+	0.159594i	−0.544018	−	0.839074i	$-0.683098\pi$
$5$	−1.33183	+	0.356864i	−0.595614	+	0.159594i	−0.0515962	+	0.998668i	$0.516431\pi$
$6$	−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	0.803168	+	0.595752i	$0.203146\pi$
$11$	−0.631061	+	2.35515i	−0.190272	+	0.710105i	−0.993440	+	0.114353i	$0.963521\pi$
$12$	1.10284	+	1.28978i	0.318363	+	0.372327i
$13$	1.90592	−	1.90592i	0.528608	−	0.528608i	−0.391549	−	0.920157i	$-0.628061\pi$
$13$	1.90592	−	1.90592i	0.528608	−	0.528608i	0.920157	+	0.391549i	$0.128061\pi$
$14$		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	−0.909649	−	0.415378i	$-0.863649\pi$
$17$	−3.35849	−	5.81707i	−0.814552	−	1.41085i	0.0950964	−	0.995468i	$-0.469684\pi$
$18$	2.18945	+	2.36719i	0.516059	+	0.557952i
$19$	1.07944	+	4.02851i	0.247640	+	0.924205i	0.972038	+	0.234823i	$0.0754510\pi$
$19$	1.07944	+	4.02851i	0.247640	+	0.924205i	−0.724398	+	0.689382i	$0.757882\pi$
$20$	−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	−0.0616516	−	0.998098i	$-0.519637\pi$
$23$	−4.58892	−	2.64941i	−0.956855	−	0.552441i	−0.895204	+	0.445657i	$0.852970\pi$
$24$	−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	−0.930063	−	0.367400i	$-0.880248\pi$
$29$	−3.03004	+	3.03004i	−0.562663	+	0.562663i	0.367400	+	0.930063i	$0.380248\pi$
$30$	1.58024	+	0.490185i	0.288510	+	0.0894952i
$31$	−0.599978	−	1.03919i	−0.107759	−	0.186644i	0.807103	−	0.590411i	$-0.201034\pi$
$31$	−0.599978	−	1.03919i	−0.107759	−	0.186644i	−0.914862	+	0.403766i	$0.867701\pi$
$32$	−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	0.00283787	−	0.999996i	$-0.499097\pi$
$37$	3.07358	−	0.823563i	0.505294	−	0.135393i	0.502456	+	0.864603i	$0.332430\pi$
$38$	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	$-0.900194\pi$
$41$		−	3.94994i		−	0.616877i	0.951244	−	0.308438i	$-0.0998064\pi$
$42$		0			0
$43$	−7.02292	−	7.02292i	−1.07098	−	1.07098i	−0.997280	−	0.0737045i	$-0.976518\pi$
$43$	−7.02292	−	7.02292i	−1.07098	−	1.07098i	−0.0737045	−	0.997280i	$-0.523482\pi$
$44$	−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	−0.732502	−	0.680765i	$-0.761647\pi$
$47$	1.53093	−	2.65165i	0.223309	−	0.386783i	0.955811	+	0.293982i	$0.0949807\pi$
$48$	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	0.847584	+	0.530662i	$0.178057\pi$
$53$	−1.10495	+	4.12372i	−0.151776	+	0.566436i	−0.999360	+	0.0357747i	$0.988610\pi$
$54$	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	−0.740631	−	0.671912i	$-0.765473\pi$
$59$	1.81836	−	6.78621i	0.236730	−	0.883489i	0.977361	−	0.211577i	$-0.0678600\pi$
$60$	−1.92908	−	1.32421i	−0.249043	−	0.170954i
$61$	−3.54750	−	13.2394i	−0.454210	−	1.69514i	−0.690399	−	0.723429i	$-0.742565\pi$
$61$	−3.54750	−	13.2394i	−0.454210	−	1.69514i	0.236188	−	0.971707i	$-0.424102\pi$
$62$	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	−0.0504163	−	0.998728i	$-0.516055\pi$
$67$	−4.85753	−	1.30157i	−0.593442	−	0.159012i	−0.543026	+	0.839716i	$0.682721\pi$
$68$	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	$0.241061\pi$
$71$			11.5771i			1.37395i	−0.726682	+	0.686974i	$0.758939\pi$
$72$	0.930806	+	6.38144i	0.109696	+	0.752059i
$73$	−8.94350	+	5.16353i	−1.04676	+	0.604346i	−0.921740	−	0.387808i	$-0.873232\pi$
$73$	−8.94350	+	5.16353i	−1.04676	+	0.604346i	−0.125018	+	0.992154i	$0.539899\pi$
$74$	−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	−0.957479	−	0.288502i	$-0.906843\pi$
$79$	−2.03442	+	3.52371i	−0.228890	+	0.396449i	0.728590	+	0.684951i	$0.240176\pi$
$80$	−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	0.00753873	−	0.999972i	$-0.497600\pi$
$83$	9.17886	−	9.17886i	1.00751	−	1.00751i	0.999972	−	0.00753873i	$-0.00239967\pi$
$84$		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	−0.997807	−	0.0661891i	$-0.978916\pi$
$89$	−14.6607	−	8.46436i	−1.55403	−	0.897221i	−0.556225	−	0.831032i	$-0.687751\pi$
$90$	−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	0.615007	+	0.788522i	$0.289153\pi$
$101$	−3.13421	+	11.6970i	−0.311866	+	1.16390i	−0.926872	+	0.375377i	$0.877513\pi$
$102$	−0.314154	+	8.05395i	−0.0311059	+	0.797460i
$103$	15.4461	+	8.91779i	1.52195	+	0.878696i	0.999664	+	0.0259230i	$0.00825246\pi$
$103$	15.4461	+	8.91779i	1.52195	+	0.878696i	0.522282	+	0.852773i	$0.325081\pi$
$104$	−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	−0.771512	−	0.636215i	$-0.780499\pi$
$107$	−11.6014	+	3.10860i	−1.12155	+	0.300519i	−0.350042	+	0.936734i	$0.613833\pi$
$108$	−1.63786	−	8.80925i	−0.157604	−	0.847671i
$109$	−9.92690	−	2.65991i	−0.950825	−	0.254773i	−0.250113	−	0.968217i	$-0.580468\pi$
$109$	−9.92690	−	2.65991i	−0.950825	−	0.254773i	−0.700712	+	0.713444i	$0.747134\pi$
$110$	−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	0.899855	−	0.436189i	$-0.143672\pi$
$131$	−1.11636	−	4.16631i	−0.0975368	−	0.364012i	−0.997392	+	0.0721767i	$0.977005\pi$
$132$	−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	−0.862966	−	0.505262i	$-0.831396\pi$
$137$	−10.0295	+	5.79055i	−0.856880	+	0.494720i	0.00608624	+	0.999981i	$0.498063\pi$
$138$	2.96214	+	5.62623i	0.252154	+	0.478936i
$139$	−2.25088	−	2.25088i	−0.190917	−	0.190917i	0.605175	−	0.796092i	$-0.293103\pi$
$139$	−2.25088	−	2.25088i	−0.190917	−	0.190917i	−0.796092	+	0.605175i	$0.793103\pi$
$140$		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	−0.127884	−	0.991789i	$-0.540819\pi$
$149$	3.14025	−	0.841428i	0.257260	−	0.0689325i	0.385144	+	0.922857i	$0.374152\pi$
$150$	3.71568	+	0.144935i	0.303384	+	0.0118339i
$151$	15.7259	−	9.07936i	1.27976	−	0.738868i	0.302953	−	0.953005i	$-0.402027\pi$
$151$	15.7259	−	9.07936i	1.27976	−	0.738868i	0.976804	+	0.214138i	$0.0686941\pi$
$152$	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	0.794382	−	0.607418i	$-0.207795\pi$
$157$	14.7682	+	3.95712i	1.17863	+	0.315812i	0.384246	+	0.923231i	$0.374461\pi$
$158$	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	−0.994764	−	0.102202i	$-0.967411\pi$
$163$	−2.35393	−	8.78498i	−0.184374	−	0.688093i	0.810390	−	0.585891i	$-0.199255\pi$
$164$	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	$0.00815332\pi$
$167$			0.661950i			0.0512232i	−0.999672	+	0.0256116i	$0.991847\pi$
$168$		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	0.996225	+	0.0868112i	$0.0276677\pi$
$173$	2.32642	+	8.68232i	0.176874	+	0.660104i	−0.819350	+	0.573293i	$0.805666\pi$
$174$	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	0.625730	−	0.780040i	$-0.284801\pi$
$179$	10.4037	+	2.78766i	0.777609	+	0.208360i	0.151878	+	0.988399i	$0.451468\pi$
$180$	4.08614	+	4.77877i	0.304563	+	0.356188i
$181$	13.9902	+	13.9902i	1.03989	+	1.03989i	0.999171	+	0.0407146i	$0.0129634\pi$
$181$	13.9902	+	13.9902i	1.03989	+	1.03989i	0.0407146	+	0.999171i	$0.487037\pi$
$182$		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	−0.0995834	−	0.995029i	$-0.531751\pi$
$191$	11.2211	−	19.4355i	0.811929	−	1.40630i	0.911512	−	0.411273i	$-0.134916\pi$
$192$	−3.22879	+	5.97089i	−0.233018	+	0.430912i
$193$	3.15704	+	5.46816i	0.227249	+	0.393607i	0.956992	−	0.290115i	$-0.0936936\pi$
$193$	3.15704	+	5.46816i	0.227249	+	0.393607i	−0.729743	+	0.683722i	$0.760360\pi$
$194$	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	0.829887	−	0.557931i	$-0.188405\pi$
$197$	3.81709	+	3.81709i	0.271957	+	0.271957i	−0.557931	+	0.829887i	$0.688405\pi$
$198$	−6.95677	+	3.66265i	−0.494396	+	0.260293i
$199$	−22.1966	+	12.8152i	−1.57347	+	0.908445i	−0.577734	+	0.816225i	$0.696063\pi$
$199$	−22.1966	+	12.8152i	−1.57347	+	0.908445i	−0.995739	+	0.0922198i	$0.970604\pi$
$200$	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	−0.681278	−	0.732025i	$-0.738575\pi$
$211$	0.737145	−	0.737145i	0.0507472	−	0.0507472i	0.732025	+	0.681278i	$0.238575\pi$
$212$	−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	0.960101	−	0.279653i	$-0.0902195\pi$
$227$	24.8861	+	6.66820i	1.65175	+	0.442584i	0.691645	+	0.722237i	$0.256886\pi$
$228$	−4.00545	+	5.83505i	−0.265267	+	0.386435i
$229$	−0.700446	+	0.187684i	−0.0462868	+	0.0124025i	−0.281888	−	0.959447i	$-0.590961\pi$
$229$	−0.700446	+	0.187684i	−0.0462868	+	0.0124025i	0.235601	+	0.971850i	$0.424294\pi$
$230$	−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	0.850209	−	0.526445i	$-0.176475\pi$
$233$	12.5076	+	7.22125i	0.819399	+	0.473080i	−0.0308104	+	0.999525i	$0.509809\pi$
$234$	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	0.808864	−	0.587996i	$-0.200083\pi$
$241$	−1.62674	−	2.81759i	−0.104787	−	0.181497i	−0.913651	+	0.406499i	$0.866750\pi$
$242$	−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	0.769719	−	0.638383i	$-0.220396\pi$
$251$	2.08074	+	2.08074i	0.131335	+	0.131335i	−0.638383	+	0.769719i	$0.720396\pi$
$252$		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	−0.984784	−	0.173780i	$-0.944402\pi$
$257$	−5.48098	+	9.49334i	−0.341894	+	0.592178i	0.642890	+	0.765958i	$0.277735\pi$
$258$	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	−0.202504	−	0.979281i	$-0.564908\pi$
$263$	8.82750	−	5.09656i	0.544327	−	0.314267i	0.746831	+	0.665014i	$0.231575\pi$
$264$	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	0.184872	−	0.982763i	$-0.440813\pi$
$269$	−2.40123	−	0.643406i	−0.146405	−	0.0392292i	−0.331277	+	0.943533i	$0.607480\pi$
$270$	−5.93178	−	6.41332i	−0.360997	−	0.390302i
$271$	2.83083	−	4.90314i	0.171961	−	0.297845i	−0.767145	−	0.641474i	$-0.778323\pi$
$271$	2.83083	−	4.90314i	0.171961	−	0.297845i	0.939105	+	0.343630i	$0.111656\pi$
$272$	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	−0.173559	−	0.984824i	$-0.555527\pi$
$277$	7.80837	−	29.1412i	0.469159	−	1.75093i	0.642718	−	0.766103i	$-0.277807\pi$
$278$	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	$0.0151976\pi$
$281$			1.60009i			0.0954532i	−0.998860	+	0.0477266i	$0.984802\pi$
$282$	−3.25105	+	1.71164i	−0.193597	+	0.101926i
$283$	5.26857	−	19.6626i	0.313184	−	1.16882i	−0.612484	−	0.790483i	$-0.709830\pi$
$283$	5.26857	−	19.6626i	0.313184	−	1.16882i	0.925668	−	0.378336i	$-0.123504\pi$
$284$	−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	0.714888	−	0.699239i	$-0.246478\pi$
$293$	0.267863	+	0.267863i	0.0156487	+	0.0156487i	−0.699239	+	0.714888i	$0.746478\pi$
$294$		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	−0.965817	−	0.259223i	$-0.916534\pi$
$307$	−12.3805	+	12.3805i	−0.706594	+	0.706594i	0.259223	+	0.965817i	$0.416534\pi$
$308$		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	−0.587968	−	0.808884i	$-0.700072\pi$
$311$	−3.19969	+	1.84734i	−0.181438	+	0.104753i	0.406530	+	0.913637i	$0.366739\pi$
$312$	−6.01021	−	2.39191i	−0.340261	−	0.135415i
$313$	9.06728	+	5.23500i	0.512513	+	0.295900i	0.733866	−	0.679294i	$-0.237714\pi$
$313$	9.06728	+	5.23500i	0.512513	+	0.295900i	−0.221353	+	0.975194i	$0.571047\pi$
$314$	−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	−0.914618	−	0.404320i	$-0.867508\pi$
$317$	−5.78104	−	21.5751i	−0.324695	−	1.21178i	0.589922	−	0.807460i	$-0.299158\pi$
$318$	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	−0.503599	−	0.863937i	$-0.667991\pi$
$331$	−9.23788	+	2.47528i	−0.507760	+	0.136054i	−0.00416093	+	0.999991i	$0.501324\pi$
$332$	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	−0.994762	−	0.102216i	$-0.967407\pi$
$347$	−1.53056	+	5.71214i	−0.0821649	+	0.306644i	0.912597	+	0.408859i	$0.134073\pi$
$348$	−7.24973	−	0.566430i	−0.388626	−	0.0303639i
$349$	−24.5827	+	24.5827i	−1.31588	+	1.31588i	−0.398877	+	0.917004i	$0.630600\pi$
$349$	−24.5827	+	24.5827i	−1.31588	+	1.31588i	−0.917004	+	0.398877i	$0.869400\pi$
$350$		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	−0.842927	−	0.538028i	$-0.819169\pi$
$353$	−16.6729	−	28.8783i	−0.887409	−	1.53704i	−0.0444826	−	0.999010i	$-0.514164\pi$
$354$	−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	0.669537	−	0.742779i	$-0.266493\pi$
$359$	6.84072	+	3.94949i	0.361039	+	0.208446i	−0.308497	+	0.951225i	$0.599826\pi$
$360$	−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	−0.936244	−	0.351351i	$-0.885722\pi$
$367$	−14.7971	−	25.6293i	−0.772401	−	1.33784i	0.163843	−	0.986486i	$-0.447611\pi$
$368$	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	−0.102921	−	0.994690i	$-0.532819\pi$
$373$	5.89618	−	1.57988i	0.305292	−	0.0818029i	0.408213	+	0.912887i	$0.366152\pi$
$374$	−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	0.201460	−	0.979497i	$-0.435432\pi$
$379$	−15.1468	−	15.1468i	−0.778037	−	0.778037i	−0.979497	+	0.201460i	$0.935432\pi$
$380$	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	−0.938129	−	0.346287i	$-0.887442\pi$
$383$	−3.31074	+	5.73436i	−0.169171	+	0.293012i	0.768958	+	0.639300i	$0.220776\pi$
$384$	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	0.140476	+	0.990084i	$0.455137\pi$
$389$	−9.39256	+	35.0535i	−0.476222	+	1.77728i	−0.616698	+	0.787200i	$0.711530\pi$
$390$	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	−0.996722	−	0.0808988i	$-0.974221\pi$
$397$	−3.46662	−	12.9376i	−0.173985	−	0.649320i	0.822737	−	0.568422i	$-0.192446\pi$
$398$	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	−0.997480	−	0.0709458i	$-0.977398\pi$
$401$	−8.75691	+	15.1674i	−0.437299	+	0.757424i	0.560181	+	0.828370i	$0.310732\pi$
$402$	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	−0.261118	−	0.965307i	$-0.584091\pi$
$409$	8.98548	−	5.18777i	0.444303	−	0.256519i	0.705421	+	0.708788i	$0.250758\pi$
$410$	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	−0.328673	−	0.944444i	$-0.606601\pi$
$419$	12.6045	−	12.6045i	0.615771	−	0.615771i	0.944444	+	0.328673i	$0.106601\pi$
$420$		0			0
$421$	−17.6588	−	17.6588i	−0.860635	−	0.860635i	0.130777	−	0.991412i	$-0.458253\pi$
$421$	−17.6588	−	17.6588i	−0.860635	−	0.860635i	−0.991412	+	0.130777i	$0.958253\pi$
$422$	−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	0.727221	−	0.686403i	$-0.240811\pi$
$431$	−4.79219	−	8.30031i	−0.230832	−	0.399812i	−0.958053	+	0.286591i	$0.907478\pi$
$432$	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	0.279505	−	0.960144i	$-0.409830\pi$
$439$	−8.63764	−	4.98695i	−0.412252	−	0.238014i	−0.691757	+	0.722130i	$0.743163\pi$
$440$	−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	0.281450	−	0.959576i	$-0.409185\pi$
$443$	21.1524	−	5.66777i	1.00498	−	0.269284i	0.723531	+	0.690292i	$0.242518\pi$
$444$	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	0.537430	−	0.843308i	$-0.319395\pi$
$457$	1.62083	+	0.935788i	0.0758193	+	0.0437743i	−0.461611	+	0.887082i	$0.652728\pi$
$458$	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	−0.326939	−	0.945046i	$-0.606017\pi$
$461$	13.2713	−	13.2713i	0.618107	−	0.618107i	0.945046	+	0.326939i	$0.106017\pi$
$462$		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	0.974498	−	0.224397i	$-0.0720413\pi$
$467$	0.396747	+	1.48068i	0.0183593	+	0.0685178i	−0.956138	+	0.292915i	$0.905375\pi$
$468$	−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	0.983961	+	0.178385i	$0.0570873\pi$
$479$	14.1486	+	24.5061i	0.646466	+	1.11971i	−0.337494	+	0.941328i	$0.609579\pi$
$480$	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	−0.616645	−	0.787242i	$-0.711508\pi$
$487$	−5.36686	+	3.09856i	−0.243196	+	0.140409i	0.373449	+	0.927651i	$0.378175\pi$
$488$	−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	0.999651	−	0.0264026i	$-0.00840519\pi$
$491$	21.5658	+	21.5658i	0.973249	+	0.973249i	−0.0264026	+	0.999651i	$0.508405\pi$
$492$	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	0.983117	−	0.182977i	$-0.0585732\pi$
$499$	0.898546	+	3.35342i	0.0402245	+	0.150120i	−0.942893	+	0.333096i	$0.891907\pi$
$500$	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	$0.0949332\pi$
$503$			13.1803i			0.587680i	−0.955855	+	0.293840i	$0.905067\pi$
$504$		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	0.952355	−	0.304992i	$-0.0986539\pi$
$509$	−0.561876	−	2.09695i	−0.0249047	−	0.0929457i	−0.977260	+	0.212046i	$0.931987\pi$
$510$	−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	−0.677844	−	0.735206i	$-0.737086\pi$
$521$	−8.67501	+	5.00852i	−0.380059	+	0.219427i	0.297785	+	0.954633i	$0.403752\pi$
$522$	−13.8068	−	0.538550i	−0.604306	−	0.0235717i
$523$	22.3050	−	5.97662i	0.975331	−	0.261339i	0.264254	−	0.964453i	$-0.414874\pi$
$523$	22.3050	−	5.97662i	0.975331	−	0.261339i	0.711077	+	0.703114i	$0.248208\pi$
$524$	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	0.892970	−	0.450116i	$-0.148617\pi$
$541$	−2.45206	−	9.15123i	−0.105422	−	0.393442i	−0.998393	+	0.0566736i	$0.981951\pi$
$542$	−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	−0.996004	−	0.0893091i	$-0.971534\pi$
$547$	−21.2058	+	21.2058i	−0.906695	+	0.906695i	0.0893091	+	0.996004i	$0.471534\pi$
$548$	−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	0.713696	−	0.700455i	$-0.247020\pi$
$557$	23.1654	+	6.20714i	0.981548	+	0.263005i	0.267852	+	0.963460i	$0.413686\pi$
$558$	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	0.0365146	−	0.999333i	$-0.488374\pi$
$563$	−10.2392	−	2.74358i	−0.431529	−	0.115628i	−0.468044	+	0.883705i	$0.655041\pi$
$564$	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	−0.991609	−	0.129276i	$-0.958735\pi$
$569$	−38.1509	−	22.0264i	−1.59937	−	0.923396i	−0.607760	−	0.794121i	$-0.707932\pi$
$570$	−0.268953	+	6.89513i	−0.0112652	+	0.288805i
$571$	3.45405	−	12.8907i	0.144548	−	0.539459i	−0.855228	−	0.518253i	$-0.826583\pi$
$571$	3.45405	−	12.8907i	0.144548	−	0.539459i	0.999775	−	0.0212061i	$-0.00675061\pi$
$572$	−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	0.642246	−	0.766499i	$-0.278003\pi$
$577$	−8.23157	−	14.2575i	−0.342685	−	0.593547i	−0.984930	+	0.172952i	$0.944670\pi$
$578$	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	0.105186	−	0.994453i	$-0.466456\pi$
$587$	−21.5452	−	21.5452i	−0.889267	−	0.889267i	−0.994453	+	0.105186i	$0.966456\pi$
$588$		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	0.459076	+	0.888397i	$0.348181\pi$
$593$	−13.1459	+	22.7693i	−0.539837	+	0.935024i	−0.998912	+	0.0466273i	$0.985153\pi$
$594$	−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	−0.903613	−	0.428350i	$-0.859095\pi$
$599$	−24.0941	+	13.9107i	−0.984457	+	0.568376i	−0.0808440	+	0.996727i	$0.525762\pi$
$600$	5.96272	+	4.44468i	0.243427	+	0.181453i
$601$		−	18.3631i		−	0.749047i	−0.927217	−	0.374523i	$-0.877806\pi$
$601$		−	18.3631i		−	0.749047i	0.927217	−	0.374523i	$-0.122194\pi$
$602$		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	−0.948901	−	0.315574i	$-0.897803\pi$
$607$	−4.95594	+	8.58394i	−0.201155	+	0.348411i	0.747746	+	0.663985i	$0.231136\pi$
$608$	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	−0.248908	−	0.968527i	$-0.580072\pi$
$613$	11.1642	−	41.6652i	0.450916	−	1.68284i	0.699825	−	0.714315i	$-0.253262\pi$
$614$	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	$0.0500752\pi$
$617$			7.78309i			0.313336i	−0.987651	+	0.156668i	$0.949925\pi$
$618$	−9.97041	−	18.9376i	−0.401069	−	0.761782i
$619$	10.1211	−	37.7725i	0.406801	−	1.51820i	−0.393908	−	0.919150i	$-0.628877\pi$
$619$	10.1211	−	37.7725i	0.406801	−	1.51820i	0.800709	−	0.599053i	$-0.204456\pi$
$620$	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	$0.0387520\pi$
$631$			6.10120i			0.242885i	−0.992598	+	0.121442i	$0.961248\pi$
$632$	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	0.765930	−	0.642924i	$-0.222279\pi$
$641$	−4.40085	−	7.62249i	−0.173823	−	0.301070i	−0.939753	+	0.341853i	$0.888945\pi$
$642$	13.7653	+	4.26995i	0.543271	+	0.168521i
$643$	20.3898	−	20.3898i	0.804095	−	0.804095i	−0.179638	−	0.983733i	$-0.557493\pi$
$643$	20.3898	−	20.3898i	0.804095	−	0.804095i	0.983733	+	0.179638i	$0.0574926\pi$
$644$		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	−0.849654	+	0.527340i	$0.823189\pi$
$647$	−44.0344	+	25.4233i	−1.73117	+	0.999492i	−0.881517	+	0.472152i	$0.843477\pi$
$648$	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	0.952760	−	0.303725i	$-0.0982304\pi$
$653$	−0.618835	−	2.30952i	−0.0242169	−	0.0903787i	−0.976977	+	0.213346i	$0.931564\pi$
$654$	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	−0.763334	−	0.646005i	$-0.776439\pi$
$659$	−3.01195	+	3.01195i	−0.117329	+	0.117329i	0.646005	+	0.763334i	$0.276439\pi$
$660$	4.33607	−	3.70761i	0.168781	−	0.144319i
$661$	0.709069	−	2.64628i	0.0275796	−	0.102928i	−0.950764	−	0.309916i	$-0.899699\pi$
$661$	0.709069	−	2.64628i	0.0275796	−	0.102928i	0.978344	+	0.206987i	$0.0663659\pi$
$662$	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	−0.541099	−	0.840959i	$-0.681992\pi$
$677$	−15.3312	+	4.10797i	−0.589225	+	0.157882i	−0.0481259	+	0.998841i	$0.515325\pi$
$678$	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	−0.901964	−	0.431811i	$-0.857875\pi$
$683$	2.48447	−	9.27215i	0.0950654	−	0.354789i	0.997029	+	0.0770223i	$0.0245413\pi$
$684$	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	−0.608666	−	0.793427i	$-0.708295\pi$
$691$	−12.5719	−	46.9191i	−0.478259	−	1.78489i	0.130407	−	0.991461i	$-0.458372\pi$
$692$	−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	−0.613072	−	0.790027i	$-0.710066\pi$
$701$	4.68514	−	4.68514i	0.176955	−	0.176955i	0.790027	+	0.613072i	$0.210066\pi$
$702$	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	−0.667308	−	0.744782i	$-0.732554\pi$
$709$	−23.2407	+	6.22733i	−0.872823	+	0.233872i	−0.205515	+	0.978654i	$0.565887\pi$
$710$	−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	−0.541870	−	0.840462i	$-0.682284\pi$
$719$	12.2521	−	21.2213i	0.456927	−	0.791420i	0.998797	+	0.0490421i	$0.0156169\pi$
$720$	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	$-0.719037\pi$
$727$		−	41.6544i		−	1.54488i	0.635090	−	0.772438i	$-0.280963\pi$
$728$		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	0.970496	+	0.241117i	$0.0775138\pi$
$733$	6.78421	+	25.3190i	0.250580	+	0.935179i	−0.719916	+	0.694062i	$0.755820\pi$
$734$	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	0.132576	−	0.991173i	$-0.457675\pi$
$739$	−6.74712	−	1.80789i	−0.248197	−	0.0665042i	−0.380773	+	0.924669i	$0.624342\pi$
$740$	−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	$0.106172\pi$
$743$			17.8484i			0.654796i	−0.944887	+	0.327398i	$0.893828\pi$
$744$	−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	−0.983436	−	0.181254i	$-0.941984\pi$
$751$	−9.17355	+	15.8891i	−0.334747	+	0.579800i	0.648689	+	0.761054i	$0.275318\pi$
$752$	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	0.790594	−	0.612341i	$-0.209772\pi$
$757$	4.90437	+	4.90437i	0.178252	+	0.178252i	−0.612341	+	0.790594i	$0.709772\pi$
$758$	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	0.444308	−	0.895874i	$-0.353450\pi$
$761$	−3.01761	−	1.74222i	−0.109388	−	0.0631553i	−0.553696	+	0.832719i	$0.686783\pi$
$762$	−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	−0.691892	−	0.722001i	$-0.743222\pi$
$773$	7.45965	−	27.8398i	0.268305	−	1.00133i	0.960196	−	0.279326i	$-0.0901109\pi$
$774$	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	−0.489663	−	0.871912i	$-0.662880\pi$
$787$	−37.8633	−	10.1454i	−1.34968	−	0.361646i	−0.860017	+	0.510266i	$0.829547\pi$
$788$	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	−0.756245	−	0.654288i	$-0.772968\pi$
$797$	−2.87837	+	2.87837i	−0.101957	+	0.101957i	0.654288	+	0.756245i	$0.272968\pi$
$798$		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	−0.134699	−	0.990887i	$-0.543007\pi$
$809$	18.6610	−	10.7739i	0.656085	−	0.378791i	0.790784	+	0.612096i	$0.209673\pi$
$810$	2.76047	+	5.24319i	0.0969931	+	0.184227i
$811$	20.4977	+	20.4977i	0.719772	+	0.719772i	0.968558	−	0.248787i	$-0.0800318\pi$
$811$	20.4977	+	20.4977i	0.719772	+	0.719772i	−0.248787	+	0.968558i	$0.580032\pi$
$812$		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	−0.0350936	−	0.999384i	$-0.511173\pi$
$821$	12.4414	−	3.33365i	0.434207	−	0.116345i	0.469300	+	0.883039i	$0.344506\pi$
$822$	13.8862	+	0.541650i	0.484338	+	0.0188922i
$823$	−35.9043	+	20.7294i	−1.25155	+	0.722580i	−0.971416	−	0.237382i	$-0.923711\pi$
$823$	−35.9043	+	20.7294i	−1.25155	+	0.722580i	−0.280129	+	0.959962i	$0.590377\pi$
$824$	−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	0.916088	−	0.400977i	$-0.131329\pi$
$827$	14.8134	+	14.8134i	0.515111	+	0.515111i	−0.400977	+	0.916088i	$0.631329\pi$
$828$	−1.88217	+	24.0898i	−0.0654098	+	0.837178i
$829$	−23.6252	−	6.33035i	−0.820537	−	0.219862i	−0.175956	−	0.984398i	$-0.556302\pi$
$829$	−23.6252	−	6.33035i	−0.820537	−	0.219862i	−0.644581	+	0.764536i	$0.722968\pi$
$830$	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	$-0.847749\pi$
$839$		−	26.6645i		−	0.920562i	0.887773	−	0.460281i	$-0.152251\pi$
$840$		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	0.462043	−	0.886858i	$-0.347117\pi$
$853$	−12.4072	−	12.4072i	−0.424815	−	0.424815i	−0.886858	+	0.462043i	$0.847117\pi$
$854$		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	−0.536113	−	0.844146i	$-0.680108\pi$
$857$	−2.14051	+	1.23582i	−0.0731184	+	0.0422149i	0.462995	+	0.886361i	$0.346775\pi$
$858$	0.307372	−	7.88008i	0.0104935	−	0.269022i
$859$	−25.9325	+	6.94860i	−0.884806	+	0.237083i	−0.672480	−	0.740116i	$-0.734771\pi$
$859$	−25.9325	+	6.94860i	−0.884806	+	0.237083i	−0.212327	+	0.977199i	$0.568104\pi$
$860$	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	−0.390223	−	0.920720i	$-0.627602\pi$
$863$	17.6924	−	30.6441i	0.602255	−	1.04314i	0.992479	−	0.122417i	$-0.0390645\pi$
$864$	−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	0.987484	−	0.157719i	$-0.0504140\pi$
$877$	1.58253	+	5.90609i	0.0534383	+	0.199434i	−0.934046	+	0.357153i	$0.883747\pi$
$878$	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	−0.999907	−	0.0136216i	$-0.995664\pi$
$883$	−29.3078	+	29.3078i	−0.986286	+	0.986286i	0.0136216	+	0.999907i	$0.495664\pi$
$884$	−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	0.211061	−	0.977473i	$-0.432308\pi$
$887$	−15.7825	−	9.11203i	−0.529924	−	0.305952i	−0.740986	+	0.671521i	$0.765641\pi$
$888$	−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	0.839900	+	0.542741i	$0.182614\pi$
$907$	−4.78386	+	17.8536i	−0.158845	+	0.592819i	−0.998745	+	0.0500777i	$0.984053\pi$
$908$	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	0.341377	−	0.939927i	$-0.389107\pi$
$919$	−9.15317	−	5.28458i	−0.301935	−	0.174322i	−0.643312	+	0.765604i	$0.722440\pi$
$920$	−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	−0.685569	−	0.728008i	$-0.740446\pi$
$929$	8.76862	−	15.1877i	0.287689	−	0.498292i	0.973258	+	0.229716i	$0.0737797\pi$
$930$	−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	$-0.746678\pi$
$937$		−	43.7391i		−	1.42890i	0.699689	−	0.714448i	$-0.253322\pi$
$938$		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	0.0852335	−	0.996361i	$-0.472836\pi$
$941$	−10.4031	−	2.78751i	−0.339133	−	0.0908703i	−0.424366	+	0.905491i	$0.639503\pi$
$942$	−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	0.999310	−	0.0371493i	$-0.0118277\pi$
$947$	3.54840	+	13.2428i	0.115307	+	0.430333i	−0.884002	+	0.467483i	$0.845161\pi$
$948$	−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	$-0.983514\pi$
$953$		−	3.19629i		−	0.103538i	0.998659	−	0.0517690i	$-0.0164860\pi$
$954$	−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	$-0.863873\pi$
$967$		−	25.7940i		−	0.829479i	0.909940	−	0.414739i	$-0.136127\pi$
$968$	−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	0.0116402	−	0.999932i	$-0.496295\pi$
$971$	16.2562	−	4.35584i	0.521687	−	0.139786i	0.510047	+	0.860147i	$0.329628\pi$
$972$	−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	0.843266	−	0.537496i	$-0.180630\pi$
$977$	−1.37068	−	2.37409i	−0.0438519	−	0.0759537i	−0.887118	+	0.461542i	$0.847296\pi$
$978$	−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	0.265149	−	0.964207i	$-0.414579\pi$
$983$	38.6502	−	22.3147i	1.23275	−	0.711729i	0.967603	+	0.252478i	$0.0812456\pi$
$984$	−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	0.857284	−	0.514843i	$-0.172150\pi$
$991$	−0.542257	−	0.939218i	−0.0172254	−	0.0298352i	−0.874510	+	0.485008i	$0.838817\pi$
$992$	−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	−0.556845	−	0.830616i	$-0.687988\pi$
$997$	10.7579	−	40.1489i	0.340705	−	1.27153i	0.897550	−	0.440912i	$-0.145345\pi$
$998$	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.373.1		24
7.2	even	3		112.2.m.d.85.4	yes	12
7.3	odd	6		784.2.x.m.165.5		24
7.4	even	3	inner	784.2.x.l.165.5		24
7.5	odd	6		784.2.m.h.197.4		12
7.6	odd	2		784.2.x.m.373.1		24
16.13	even	4	inner	784.2.x.l.765.5		24
28.23	odd	6		448.2.m.d.113.5		12
56.37	even	6		896.2.m.g.225.5		12
56.51	odd	6		896.2.m.h.225.2		12
112.13	odd	4		784.2.x.m.765.5		24
112.37	even	12		896.2.m.g.673.5		12
112.45	odd	12		784.2.x.m.557.1		24
112.51	odd	12		448.2.m.d.337.5		12
112.61	odd	12		784.2.m.h.589.4		12
112.93	even	12		112.2.m.d.29.4	✓	12
112.107	odd	12		896.2.m.h.673.2		12
112.109	even	12	inner	784.2.x.l.557.1		24
224.51	odd	24		7168.2.a.bi.1.5		12
224.93	even	24		7168.2.a.bj.1.5		12
224.163	odd	24		7168.2.a.bi.1.8		12
224.205	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	112.93	even	12
112.2.m.d.85.4	yes	12	7.2	even	3
448.2.m.d.113.5		12	28.23	odd	6
448.2.m.d.337.5		12	112.51	odd	12
784.2.m.h.197.4		12	7.5	odd	6
784.2.m.h.589.4		12	112.61	odd	12
784.2.x.l.165.5		24	7.4	even	3	inner
784.2.x.l.373.1		24	1.1	even	1	trivial
784.2.x.l.557.1		24	112.109	even	12	inner
784.2.x.l.765.5		24	16.13	even	4	inner
784.2.x.m.165.5		24	7.3	odd	6
784.2.x.m.373.1		24	7.6	odd	2
784.2.x.m.557.1		24	112.45	odd	12
784.2.x.m.765.5		24	112.13	odd	4
896.2.m.g.225.5		12	56.37	even	6
896.2.m.g.673.5		12	112.37	even	12
896.2.m.h.225.2		12	56.51	odd	6
896.2.m.h.673.2		12	112.107	odd	12
7168.2.a.bi.1.5		12	224.51	odd	24
7168.2.a.bi.1.8		12	224.163	odd	24
7168.2.a.bj.1.5		12	224.93	even	24
7168.2.a.bj.1.8		12	224.205	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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