LMFDB - Embedded newform 775.2.ck.c.524.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [775,2,Mod(49,775)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("775.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(775, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([15, 26])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.ck (of order $30$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [80,0,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			524.6
Character	$\chi$	$=$	775.524
Dual form			775.2.ck.c.599.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0622295 + 0.0856516i) q^{2} +(0.541931 + 0.0569592i) q^{3} +(0.614570 - 1.89145i) q^{4} +(0.0288454 + 0.0499618i) q^{6} +(-0.520005 - 2.44643i) q^{7} +(0.401629 - 0.130497i) q^{8} +(-2.64400 - 0.561999i) q^{9} +(2.63294 + 2.92417i) q^{11} +(0.440790 - 0.990031i) q^{12} +(-1.62830 - 3.65723i) q^{13} +(0.177181 - 0.196780i) q^{14} +(-3.18176 - 2.31168i) q^{16} +(-3.49613 - 3.14793i) q^{17} +(-0.116399 - 0.261436i) q^{18} +(3.29674 + 1.46780i) q^{19} +(-0.142460 - 1.35542i) q^{21} +(-0.0866136 + 0.407485i) q^{22} +(1.62870 - 0.529196i) q^{23} +(0.225088 - 0.0478440i) q^{24} +(0.211919 - 0.367054i) q^{26} +(-2.95559 - 0.960329i) q^{27} +(-4.94689 - 0.519939i) q^{28} +(6.40326 - 4.65224i) q^{29} +(-5.37964 + 1.43510i) q^{31} -1.26097i q^{32} +(1.26031 + 1.73467i) q^{33} +(0.0520626 - 0.495343i) q^{34} +(-2.68792 + 4.65561i) q^{36} +(-7.51600 + 4.33937i) q^{37} +(0.0794349 + 0.373712i) q^{38} +(-0.674114 - 2.07471i) q^{39} +(-0.449386 - 4.27562i) q^{41} +(0.107228 - 0.0965488i) q^{42} +(-2.00772 + 4.50941i) q^{43} +(7.14906 - 3.18297i) q^{44} +(0.146680 + 0.106569i) q^{46} +(4.35601 - 5.99553i) q^{47} +(-1.59262 - 1.43400i) q^{48} +(0.680198 - 0.302844i) q^{49} +(-1.71535 - 1.90509i) q^{51} +(-7.91818 + 0.832234i) q^{52} +(1.25790 - 5.91794i) q^{53} +(-0.101671 - 0.312912i) q^{54} +(-0.528102 - 0.914699i) q^{56} +(1.70300 + 0.983227i) q^{57} +(0.796943 + 0.258943i) q^{58} +(-0.494881 + 4.70847i) q^{59} +0.682018 q^{61} +(-0.457691 - 0.371469i) q^{62} +6.76060i q^{63} +(-6.25552 + 4.54490i) q^{64} +(-0.0701486 + 0.215895i) q^{66} +(6.77365 + 3.91077i) q^{67} +(-8.10277 + 4.67814i) q^{68} +(0.912784 - 0.194018i) q^{69} +(13.9648 + 2.96832i) q^{71} +(-1.13525 + 0.119319i) q^{72} +(9.08138 - 8.17691i) q^{73} +(-0.839391 - 0.373721i) q^{74} +(4.80236 - 5.33356i) q^{76} +(5.78464 - 7.96188i) q^{77} +(0.135752 - 0.186847i) q^{78} +(6.00055 - 6.66429i) q^{79} +(5.86110 + 2.60953i) q^{81} +(0.338249 - 0.304561i) q^{82} +(-9.98211 + 1.04916i) q^{83} +(-2.65126 - 0.563542i) q^{84} +(-0.511178 + 0.108654i) q^{86} +(3.73511 - 2.15647i) q^{87} +(1.43906 + 0.830842i) q^{88} +(-2.24413 + 6.90671i) q^{89} +(-8.10043 + 5.88531i) q^{91} -3.40584i q^{92} +(-2.99713 + 0.471305i) q^{93} +0.784599 q^{94} +(0.0718241 - 0.683361i) q^{96} +(-6.65149 - 2.16120i) q^{97} +(0.0682674 + 0.0394142i) q^{98} +(-5.31810 - 9.21121i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 8 q^{6} - 4 q^{9} - 56 q^{11} + 12 q^{14} + 16 q^{16} + 26 q^{19} - 16 q^{21} + 164 q^{24} + 64 q^{26} - 84 q^{29} - 20 q^{31} - 64 q^{34} - 26 q^{36} - 74 q^{39} + 72 q^{41} + 112 q^{44}+ \cdots - 106 q^{99}+O(q^{100}) $ 80 * q + 20 * q^4 + 8 * q^6 - 4 * q^9 - 56 * q^11 + 12 * q^14 + 16 * q^16 + 26 * q^19 - 16 * q^21 + 164 * q^24 + 64 * q^26 - 84 * q^29 - 20 * q^31 - 64 * q^34 - 26 * q^36 - 74 * q^39 + 72 * q^41 + 112 * q^44 + 36 * q^46 + 62 * q^49 - 4 * q^51 - 44 * q^54 + 18 * q^56 + 2 * q^59 - 200 * q^61 - 34 * q^64 - 80 * q^66 - 16 * q^69 - 4 * q^71 + 4 * q^74 + 4 * q^76 + 134 * q^79 - 166 * q^81 - 52 * q^84 - 10 * q^86 - 40 * q^89 + 38 * q^91 - 260 * q^94 + 92 * q^96 - 106 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{8}{15}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.0622295	+	0.0856516i	0.0440029	+	0.0605648i	0.830452	−	0.557091i	$-0.188083\pi$
$2$	0.0622295	+	0.0856516i	0.0440029	+	0.0605648i	−0.786449	+	0.617656i	$0.788083\pi$
$3$	0.541931	+	0.0569592i	0.312884	+	0.0328854i	0.259669	−	0.965698i	$-0.416387\pi$
$3$	0.541931	+	0.0569592i	0.312884	+	0.0328854i	0.0532148	+	0.998583i	$0.483053\pi$
$4$	0.614570	−	1.89145i	0.307285	−	0.945726i
$5$		0			0
$5$		0			0
$6$	0.0288454	+	0.0499618i	0.0117761	+	0.0203968i
$7$	−0.520005	−	2.44643i	−0.196543	−	0.924664i	−0.960259	−	0.279111i	$-0.909960\pi$
$7$	−0.520005	−	2.44643i	−0.196543	−	0.924664i	0.763715	−	0.645553i	$-0.223373\pi$
$8$	0.401629	−	0.130497i	0.141997	−	0.0461378i
$9$	−2.64400	−	0.561999i	−0.881333	−	0.187333i
$10$		0			0
$11$	2.63294	+	2.92417i	0.793860	+	0.881671i	0.995201	−	0.0978503i	$-0.0311966\pi$
$11$	2.63294	+	2.92417i	0.793860	+	0.881671i	−0.201341	+	0.979521i	$0.564530\pi$
$12$	0.440790	−	0.990031i	0.127245	−	0.285797i
$13$	−1.62830	−	3.65723i	−0.451610	−	1.01433i	−0.985639	−	0.168866i	$-0.945989\pi$
$13$	−1.62830	−	3.65723i	−0.451610	−	1.01433i	0.534029	−	0.845466i	$-0.320677\pi$
$14$	0.177181	−	0.196780i	0.0473536	−	0.0525915i
$15$		0			0
$16$	−3.18176	−	2.31168i	−0.795440	−	0.577921i
$17$	−3.49613	−	3.14793i	−0.847935	−	0.763484i	0.125586	−	0.992083i	$-0.459919\pi$
$17$	−3.49613	−	3.14793i	−0.847935	−	0.763484i	−0.973521	+	0.228599i	$0.926586\pi$
$18$	−0.116399	−	0.261436i	−0.0274354	−	0.0616210i
$19$	3.29674	+	1.46780i	0.756324	+	0.336737i	0.748414	−	0.663232i	$-0.230816\pi$
$19$	3.29674	+	1.46780i	0.756324	+	0.336737i	0.00790965	+	0.999969i	$0.497482\pi$
$20$		0			0
$21$	−0.142460	−	1.35542i	−0.0310873	−	0.295776i
$22$	−0.0866136	+	0.407485i	−0.0184661	+	0.0868761i
$23$	1.62870	−	0.529196i	0.339607	−	0.110345i	−0.134248	−	0.990948i	$-0.542862\pi$
$23$	1.62870	−	0.529196i	0.339607	−	0.110345i	0.473855	+	0.880603i	$0.342862\pi$
$24$	0.225088	−	0.0478440i	0.0459460	−	0.00976611i
$25$		0			0
$26$	0.211919	−	0.367054i	0.0415607	−	0.0719852i
$27$	−2.95559	−	0.960329i	−0.568804	−	0.184815i
$28$	−4.94689	−	0.519939i	−0.934874	−	0.0982592i
$29$	6.40326	−	4.65224i	1.18906	−	0.863899i	0.195891	−	0.980626i	$-0.437240\pi$
$29$	6.40326	−	4.65224i	1.18906	−	0.863899i	0.993164	+	0.116726i	$0.0372401\pi$
$30$		0			0
$31$	−5.37964	+	1.43510i	−0.966211	+	0.257752i
$31$	−5.37964	+	1.43510i	−0.966211	+	0.257752i
$32$		−	1.26097i		−	0.222911i
$33$	1.26031	+	1.73467i	0.219392	+	0.301967i
$34$	0.0520626	−	0.495343i	0.00892866	−	0.0849506i
$35$		0			0
$36$	−2.68792	+	4.65561i	−0.447986	+	0.775935i
$37$	−7.51600	+	4.33937i	−1.23562	+	0.713387i	−0.968197	−	0.250191i	$-0.919507\pi$
$37$	−7.51600	+	4.33937i	−1.23562	+	0.713387i	−0.267427	+	0.963578i	$0.586173\pi$
$38$	0.0794349	+	0.373712i	0.0128860	+	0.0606240i
$39$	−0.674114	−	2.07471i	−0.107945	−	0.332220i
$40$		0			0
$41$	−0.449386	−	4.27562i	−0.0701823	−	0.667740i	−0.971897	−	0.235408i	$-0.924357\pi$
$41$	−0.449386	−	4.27562i	−0.0701823	−	0.667740i	0.901714	−	0.432332i	$-0.142309\pi$
$42$	0.107228	−	0.0965488i	0.0165457	−	0.0148978i
$43$	−2.00772	+	4.50941i	−0.306174	+	0.687679i	−0.999456	−	0.0329881i	$-0.989498\pi$
$43$	−2.00772	+	4.50941i	−0.306174	+	0.687679i	0.693281	+	0.720667i	$0.256164\pi$
$44$	7.14906	−	3.18297i	1.07776	−	0.479850i
$45$		0			0
$46$	0.146680	+	0.106569i	0.0216267	+	0.0157127i
$47$	4.35601	−	5.99553i	0.635389	−	0.874538i	−0.362970	−	0.931801i	$-0.618237\pi$
$47$	4.35601	−	5.99553i	0.635389	−	0.874538i	0.998359	+	0.0572628i	$0.0182373\pi$
$48$	−1.59262	−	1.43400i	−0.229875	−	0.206981i
$49$	0.680198	−	0.302844i	0.0971711	−	0.0432634i
$50$		0			0
$51$	−1.71535	−	1.90509i	−0.240198	−	0.266767i
$52$	−7.91818	+	0.832234i	−1.09805	+	0.115410i
$53$	1.25790	−	5.91794i	0.172786	−	0.812892i	−0.803312	−	0.595559i	$-0.796931\pi$
$53$	1.25790	−	5.91794i	0.172786	−	0.812892i	0.976097	−	0.217333i	$-0.0697359\pi$
$54$	−0.101671	−	0.312912i	−0.0138357	−	0.0425819i
$55$		0			0
$56$	−0.528102	−	0.914699i	−0.0705706	−	0.122232i
$57$	1.70300	+	0.983227i	0.225568	+	0.130232i
$58$	0.796943	+	0.258943i	0.104644	+	0.0340008i
$59$	−0.494881	+	4.70847i	−0.0644280	+	0.612991i	0.913901	+	0.405936i	$0.133055\pi$
$59$	−0.494881	+	4.70847i	−0.0644280	+	0.612991i	−0.978329	+	0.207055i	$0.933612\pi$
$60$		0			0
$61$	0.682018			0.0873235			0.0436617	−	0.999046i	$-0.486098\pi$
$61$	0.682018			0.0873235			0.0436617	+	0.999046i	$0.486098\pi$
$62$	−0.457691	−	0.371469i	−0.0581268	−	0.0471766i
$63$			6.76060i			0.851756i
$64$	−6.25552	+	4.54490i	−0.781940	+	0.568113i
$65$		0			0
$66$	−0.0701486	+	0.215895i	−0.00863469	+	0.0265749i
$67$	6.77365	+	3.91077i	0.827533	+	0.477776i	0.853007	−	0.521899i	$-0.174776\pi$
$67$	6.77365	+	3.91077i	0.827533	+	0.477776i	−0.0254744	+	0.999675i	$0.508110\pi$
$68$	−8.10277	+	4.67814i	−0.982605	+	0.567307i
$69$	0.912784	−	0.194018i	0.109886	−	0.0233571i
$70$		0			0
$71$	13.9648	+	2.96832i	1.65732	+	0.352274i	0.939127	−	0.343569i	$-0.111636\pi$
$71$	13.9648	+	2.96832i	1.65732	+	0.352274i	0.718193	+	0.695844i	$0.244969\pi$
$72$	−1.13525	+	0.119319i	−0.133790	+	0.0140619i
$73$	9.08138	−	8.17691i	1.06290	−	0.957035i	0.0637331	−	0.997967i	$-0.479699\pi$
$73$	9.08138	−	8.17691i	1.06290	−	0.957035i	0.999162	+	0.0409320i	$0.0130327\pi$
$74$	−0.839391	−	0.373721i	−0.0975772	−	0.0434442i
$75$		0			0
$76$	4.80236	−	5.33356i	0.550868	−	0.611801i
$77$	5.78464	−	7.96188i	0.659221	−	0.907341i
$78$	0.135752	−	0.186847i	0.0153709	−	0.0211563i
$79$	6.00055	−	6.66429i	0.675115	−	0.749791i	−0.304095	−	0.952642i	$-0.598354\pi$
$79$	6.00055	−	6.66429i	0.675115	−	0.749791i	0.979210	+	0.202851i	$0.0650206\pi$
$80$		0			0
$81$	5.86110	+	2.60953i	0.651233	+	0.289948i
$82$	0.338249	−	0.304561i	0.0373533	−	0.0336331i
$83$	−9.98211	+	1.04916i	−1.09568	+	0.115160i	−0.635079	−	0.772447i	$-0.719032\pi$
$83$	−9.98211	+	1.04916i	−1.09568	+	0.115160i	−0.460600	+	0.887608i	$0.652366\pi$
$84$	−2.65126	−	0.563542i	−0.289276	−	0.0614874i
$85$		0			0
$86$	−0.511178	+	0.108654i	−0.0551217	+	0.0117165i
$87$	3.73511	−	2.15647i	0.400446	−	0.231198i
$88$	1.43906	+	0.830842i	0.153404	+	0.0885681i
$89$	−2.24413	+	6.90671i	−0.237877	+	0.732110i	0.758850	+	0.651266i	$0.225762\pi$
$89$	−2.24413	+	6.90671i	−0.237877	+	0.732110i	−0.996727	+	0.0808442i	$0.974238\pi$
$90$		0			0
$91$	−8.10043	+	5.88531i	−0.849156	+	0.616948i
$92$		−	3.40584i		−	0.355083i
$93$	−2.99713	+	0.471305i	−0.310788	+	0.0488721i
$94$	0.784599			0.0809252
$95$		0			0
$96$	0.0718241	−	0.683361i	0.00733052	−	0.0697452i
$97$	−6.65149	−	2.16120i	−0.675357	−	0.219437i	−0.0487954	−	0.998809i	$-0.515538\pi$
$97$	−6.65149	−	2.16120i	−0.675357	−	0.219437i	−0.626561	+	0.779372i	$0.715538\pi$
$98$	0.0682674	+	0.0394142i	0.00689605	+	0.00398144i
$99$	−5.31810	−	9.21121i	−0.534489	−	0.925762i
$100$		0			0
$101$	2.37908	+	7.32207i	0.236728	+	0.728573i	0.996888	+	0.0788370i	$0.0251207\pi$
$101$	2.37908	+	7.32207i	0.236728	+	0.728573i	−0.760160	+	0.649736i	$0.774879\pi$
$102$	0.0564286	−	0.265476i	0.00558727	−	0.0262860i
$103$	16.9924	−	1.78597i	1.67431	−	0.175977i	0.780727	−	0.624872i	$-0.214849\pi$
$103$	16.9924	−	1.78597i	1.67431	−	0.175977i	0.893585	+	0.448895i	$0.148182\pi$
$104$	−1.13123	−	1.25636i	−0.110926	−	0.123196i
$105$		0			0
$106$	0.585160	−	0.260530i	0.0568357	−	0.0253049i
$107$	−7.89720	−	7.11067i	−0.763451	−	0.687415i	0.192383	−	0.981320i	$-0.438378\pi$
$107$	−7.89720	−	7.11067i	−0.763451	−	0.687415i	−0.955835	+	0.293905i	$0.905045\pi$
$108$	−3.63284	+	5.00017i	−0.349570	+	0.481141i
$109$	−5.69547	−	4.13800i	−0.545527	−	0.396348i	0.280607	−	0.959823i	$-0.409464\pi$
$109$	−5.69547	−	4.13800i	−0.545527	−	0.396348i	−0.826134	+	0.563474i	$0.809464\pi$
$110$		0			0
$111$	−4.32032	+	1.92353i	−0.410066	+	0.182573i
$112$	−4.00085	+	8.98605i	−0.378044	+	0.849102i
$113$	7.33264	−	6.60234i	0.689797	−	0.621096i	−0.247804	−	0.968810i	$-0.579709\pi$
$113$	7.33264	−	6.60234i	0.689797	−	0.621096i	0.937601	+	0.347714i	$0.113042\pi$
$114$	0.0217619	+	0.207050i	0.00203819	+	0.0193920i
$115$		0			0
$116$	−4.86424	−	14.9706i	−0.451633	−	1.38998i
$117$	2.24987	+	10.5848i	0.208001	+	0.978566i
$118$	−0.434084	+	0.250619i	−0.0399607	+	0.0230713i
$119$	−5.88318	+	10.1900i	−0.539310	+	0.934113i
$120$		0			0
$121$	−0.468615	+	4.45857i	−0.0426014	+	0.405325i
$122$	0.0424417	+	0.0584159i	0.00384249	+	0.00528873i
$123$		−	2.34269i		−	0.211233i
$124$	−0.591740	+	11.0573i	−0.0531398	+	0.992975i
$125$		0			0
$126$	−0.579056	+	0.420709i	−0.0515864	+	0.0374797i
$127$	13.2565	+	1.39331i	1.17632	+	0.123637i	0.672451	−	0.740142i	$-0.265242\pi$
$127$	13.2565	+	1.39331i	1.17632	+	0.123637i	0.503872	+	0.863778i	$0.331908\pi$
$128$	−3.17707	−	1.03229i	−0.280816	−	0.0912427i
$129$	−1.34490	+	2.32943i	−0.118412	+	0.205095i
$130$		0			0
$131$	4.15093	−	0.882308i	0.362669	−	0.0770876i	−0.0229734	−	0.999736i	$-0.507313\pi$
$131$	4.15093	−	0.882308i	0.362669	−	0.0770876i	0.385642	+	0.922648i	$0.373980\pi$
$132$	4.05559	−	1.31774i	0.352994	−	0.114695i
$133$	1.87656	−	8.82851i	0.162718	−	0.765529i
$134$	0.0865574	+	0.823539i	0.00747742	+	0.0711429i
$135$		0			0
$136$	−1.81494	−	0.808064i	−0.155630	−	0.0692910i
$137$	8.53537	+	19.1707i	0.729225	+	1.63787i	0.769474	+	0.638678i	$0.220518\pi$
$137$	8.53537	+	19.1707i	0.729225	+	1.63787i	−0.0402490	+	0.999190i	$0.512815\pi$
$138$	0.0734201	+	0.0661078i	0.00624994	+	0.00562747i
$139$	−0.744157	−	0.540662i	−0.0631186	−	0.0458583i	0.555779	−	0.831330i	$-0.312420\pi$
$139$	−0.744157	−	0.540662i	−0.0631186	−	0.0458583i	−0.618897	+	0.785472i	$0.712420\pi$
$140$		0			0
$141$	2.70215	−	3.00105i	0.227562	−	0.252734i
$142$	0.614784	+	1.38083i	0.0515915	+	0.115876i
$143$	6.40714	−	14.3907i	0.535792	−	1.20341i
$144$	7.11341	+	7.90024i	0.592784	+	0.658353i
$145$		0			0
$146$	1.26550	+	0.268989i	0.104733	+	0.0222617i
$147$	0.385870	−	0.125377i	0.0318260	−	0.0103409i
$148$	3.58859	+	16.8830i	0.294981	+	1.38777i
$149$	0.117901	+	0.204210i	0.00965879	+	0.0167295i	0.870814	−	0.491612i	$-0.163592\pi$
$149$	0.117901	+	0.204210i	0.00965879	+	0.0167295i	−0.861156	+	0.508341i	$0.830259\pi$
$150$		0			0
$151$	−4.85400	+	14.9391i	−0.395013	+	1.21572i	0.533939	+	0.845523i	$0.320711\pi$
$151$	−4.85400	+	14.9391i	−0.395013	+	1.21572i	−0.928952	+	0.370201i	$0.879289\pi$
$152$	1.51561	+	0.159297i	0.122932	+	0.0129207i
$153$	7.47462	+	10.2879i	0.604287	+	0.831730i
$154$	1.04192			0.0839606
$155$		0			0
$156$	−4.33851			−0.347359
$157$	13.9136	+	19.1504i	1.11042	+	1.52837i	0.820791	+	0.571229i	$0.193533\pi$
$157$	13.9136	+	19.1504i	1.11042	+	1.52837i	0.289633	+	0.957138i	$0.406467\pi$
$158$	0.944218	+	0.0992414i	0.0751180	+	0.00789522i
$159$	1.01877	−	3.13547i	0.0807941	−	0.248659i
$160$		0			0
$161$	−2.14157	−	3.70931i	−0.168780	−	0.292335i
$162$	0.141223	+	0.664402i	0.0110955	+	0.0522004i
$163$	−11.4885	+	3.73284i	−0.899848	+	0.292378i	−0.722174	−	0.691711i	$-0.756857\pi$
$163$	−11.4885	+	3.73284i	−0.899848	+	0.292378i	−0.177674	+	0.984089i	$0.556857\pi$
$164$	−8.36332	−	1.77768i	−0.653066	−	0.138813i
$165$		0			0
$166$	−0.711044	−	0.789694i	−0.0551877	−	0.0612922i
$167$	0.298697	−	0.670884i	0.0231139	−	0.0519146i	−0.901620	−	0.432530i	$-0.857621\pi$
$167$	0.298697	−	0.670884i	0.0231139	−	0.0519146i	0.924734	+	0.380615i	$0.124288\pi$
$168$	−0.234094	−	0.525784i	−0.0180607	−	0.0405651i
$169$	−2.02524	+	2.24926i	−0.155788	+	0.173020i
$170$		0			0
$171$	−7.89167	−	5.73363i	−0.603491	−	0.438462i
$172$	7.29546	+	6.56886i	0.556273	+	0.500871i
$173$	2.71821	+	6.10521i	0.206662	+	0.464170i	0.986904	−	0.161307i	$-0.0515710\pi$
$173$	2.71821	+	6.10521i	0.206662	+	0.464170i	−0.780242	+	0.625477i	$0.784904\pi$
$174$	0.417139	+	0.185722i	0.0316232	+	0.0140796i
$175$		0			0
$176$	−1.61761	−	15.3905i	−0.121932	−	1.16011i
$177$	−0.536382	+	2.52348i	−0.0403169	+	0.189676i
$178$	−0.731222	+	0.237588i	−0.0548074	+	0.0178080i
$179$	−3.28753	+	0.698786i	−0.245722	+	0.0522297i	−0.329126	−	0.944286i	$-0.606754\pi$
$179$	−3.28753	+	0.698786i	−0.245722	+	0.0522297i	0.0834043	+	0.996516i	$0.473421\pi$
$180$		0			0
$181$	6.65455	−	11.5260i	0.494629	−	0.856722i	−0.505352	−	0.862913i	$-0.668637\pi$
$181$	6.65455	−	11.5260i	0.494629	−	0.856722i	0.999981	+	0.00619098i	$0.00197066\pi$
$182$	−1.00817	−	0.327575i	−0.0747307	−	0.0242815i
$183$	0.369606	+	0.0388472i	0.0273221	+	0.00287167i
$184$	0.585075	−	0.425082i	0.0431323	−	0.0313374i
$185$		0			0
$186$	−0.226878	−	0.227380i	−0.0166355	−	0.0166723i
$187$		−	18.5116i		−	1.35370i
$188$	−8.66319	−	11.9239i	−0.631828	−	0.869637i
$189$	−0.812458	+	7.73002i	−0.0590976	+	0.562276i
$190$		0			0
$191$	4.41616	−	7.64901i	0.319542	−	0.553463i	−0.660851	−	0.750517i	$-0.729804\pi$
$191$	4.41616	−	7.64901i	0.319542	−	0.553463i	0.980392	+	0.197055i	$0.0631377\pi$
$192$	−3.64893	+	2.10671i	−0.263339	+	0.152039i
$193$	5.06038	+	23.8072i	0.364254	+	1.71368i	0.653929	+	0.756556i	$0.273120\pi$
$193$	5.06038	+	23.8072i	0.364254	+	1.71368i	−0.289674	+	0.957125i	$0.593547\pi$
$194$	−0.228809	−	0.704201i	−0.0164275	−	0.0505587i
$195$		0			0
$196$	−0.154785	−	1.47268i	−0.0110561	−	0.105192i
$197$	−10.6567	+	9.59532i	−0.759258	+	0.683639i	−0.954864	−	0.297044i	$-0.903999\pi$
$197$	−10.6567	+	9.59532i	−0.759258	+	0.683639i	0.195606	+	0.980683i	$0.437333\pi$
$198$	0.458012	−	1.02871i	0.0325495	−	0.0731074i
$199$	1.99545	−	0.888433i	0.141454	−	0.0629794i	−0.334789	−	0.942293i	$-0.608665\pi$
$199$	1.99545	−	0.888433i	0.141454	−	0.0629794i	0.476243	+	0.879314i	$0.341998\pi$
$200$		0			0
$201$	3.44809	+	2.50519i	0.243210	+	0.176702i
$202$	−0.479098	+	0.659421i	−0.0337092	+	0.0463967i
$203$	−14.7111	−	13.2459i	−1.03252	−	0.929683i
$204$	−4.65760	+	2.07370i	−0.326097	+	0.145188i
$205$		0			0
$206$	1.21040	+	1.34429i	0.0843327	+	0.0936609i
$207$	−4.60368	+	0.483867i	−0.319978	+	0.0336311i
$208$	−3.27349	+	15.4005i	−0.226975	+	1.06784i
$209$	4.38800	+	13.5049i	0.303524	+	0.934151i
$210$		0			0
$211$	6.24586	+	10.8182i	0.429983	+	0.744752i	0.996871	−	0.0790424i	$-0.0251863\pi$
$211$	6.24586	+	10.8182i	0.429983	+	0.744752i	−0.566888	+	0.823795i	$0.691853\pi$
$212$	−10.4204	−	6.01625i	−0.715679	−	0.413198i
$213$	7.39890	+	2.40405i	0.506964	+	0.164723i
$214$	0.117601	−	1.11890i	0.00803906	−	0.0764866i
$215$		0			0
$216$	−1.31237			−0.0892956
$217$	6.30831	+	12.4147i	0.428236	+	0.842761i
$218$		−	0.745332i		−	0.0504802i
$219$	5.38723	−	3.91405i	0.364035	−	0.264487i
$220$		0			0
$221$	−5.81993	+	17.9119i	−0.391491	+	1.20488i
$222$	−0.433605	−	0.250342i	−0.0291016	−	0.0168018i
$223$	−7.09242	+	4.09481i	−0.474944	+	0.274209i	−0.718307	−	0.695726i	$-0.755083\pi$
$223$	−7.09242	+	4.09481i	−0.474944	+	0.274209i	0.243363	+	0.969935i	$0.421749\pi$
$224$	−3.08489	+	0.655713i	−0.206118	+	0.0438117i
$225$		0			0
$226$	1.02181	+	0.217192i	0.0679697	+	0.0144474i
$227$	15.3330	−	1.61157i	1.01769	−	0.106963i	0.419034	−	0.907971i	$-0.362369\pi$
$227$	15.3330	−	1.61157i	1.01769	−	0.106963i	0.598655	+	0.801007i	$0.295702\pi$
$228$	2.90634	−	2.61688i	0.192477	−	0.173307i
$229$	−20.4072	−	9.08589i	−1.34855	−	0.600412i	−0.399846	−	0.916583i	$-0.630936\pi$
$229$	−20.4072	−	9.08589i	−1.34855	−	0.600412i	−0.948702	+	0.316170i	$0.897603\pi$
$230$		0			0
$231$	3.58838	−	3.98530i	0.236098	−	0.262213i
$232$	1.96463	−	2.70408i	0.128984	−	0.177532i
$233$	−7.21423	+	9.92954i	−0.472620	+	0.650506i	−0.977066	−	0.212938i	$-0.931697\pi$
$233$	−7.21423	+	9.92954i	−0.472620	+	0.650506i	0.504446	+	0.863443i	$0.331697\pi$
$234$	−0.766597	+	0.851392i	−0.0501140	+	0.0556573i
$235$		0			0
$236$	8.60172	+	3.82973i	0.559924	+	0.249294i
$237$	3.63148	−	3.26980i	0.235890	−	0.212396i
$238$	−1.23889	+	0.130213i	−0.0803056	+	0.00844046i
$239$	−21.3520	−	4.53851i	−1.38115	−	0.293572i	−0.543328	−	0.839521i	$-0.682836\pi$
$239$	−21.3520	−	4.53851i	−1.38115	−	0.293572i	−0.837818	+	0.545949i	$0.816169\pi$
$240$		0			0
$241$	−9.41428	+	2.00107i	−0.606427	+	0.128900i	−0.500884	−	0.865515i	$-0.666992\pi$
$241$	−9.41428	+	2.00107i	−0.606427	+	0.128900i	−0.105544	+	0.994415i	$0.533658\pi$
$242$	−0.411046	+	0.237317i	−0.0264230	+	0.0152553i
$243$	11.1017	+	6.40956i	0.712174	+	0.411174i
$244$	0.419148	−	1.29000i	0.0268332	−	0.0825841i
$245$		0			0
$246$	0.200655	−	0.145784i	0.0127933	−	0.00929487i
$247$		−	14.4469i		−	0.919237i
$248$	−1.97334	+	1.27841i	−0.125307	+	0.0811789i
$249$	−5.46937			−0.346607
$250$		0			0
$251$	−0.197674	+	1.88074i	−0.0124771	+	0.118712i	−0.998988	−	0.0449864i	$-0.985676\pi$
$251$	−0.197674	+	1.88074i	−0.0124771	+	0.118712i	0.986511	+	0.163698i	$0.0523422\pi$
$252$	12.7874	+	4.15487i	0.805528	+	0.261732i
$253$	5.83572	+	3.36925i	0.366889	+	0.211823i
$254$	0.705606	+	1.22215i	0.0442736	+	0.0766842i
$255$		0			0
$256$	4.66950	+	14.3712i	0.291844	+	0.898203i
$257$	5.16739	−	24.3107i	0.322333	−	1.51646i	−0.456784	−	0.889578i	$-0.650999\pi$
$257$	5.16739	−	24.3107i	0.322333	−	1.51646i	0.779116	−	0.626879i	$-0.215668\pi$
$258$	−0.283212	+	0.0297668i	−0.0176320	+	0.00185320i
$259$	14.5243	+	16.1309i	0.902497	+	1.00232i
$260$		0			0
$261$	−19.5448	+	8.70189i	−1.20979	+	0.538633i
$262$	0.333882	+	0.300628i	0.0206273	+	0.0185729i
$263$	16.1183	−	22.1849i	0.993897	−	1.36798i	0.0649004	−	0.997892i	$-0.479327\pi$
$263$	16.1183	−	22.1849i	0.993897	−	1.36798i	0.928996	−	0.370089i	$-0.120673\pi$
$264$	0.732547	+	0.532227i	0.0450852	+	0.0327563i
$265$		0			0
$266$	0.872953	−	0.388664i	0.0535242	−	0.0238305i
$267$	−1.60956	+	3.61513i	−0.0985036	+	0.221243i
$268$	11.5599	−	10.4086i	0.706134	−	0.635806i
$269$	1.63895	+	15.5935i	0.0999282	+	0.950754i	0.923515	+	0.383563i	$0.125303\pi$
$269$	1.63895	+	15.5935i	0.0999282	+	0.950754i	−0.823586	+	0.567191i	$0.808030\pi$
$270$		0			0
$271$	−0.838582	−	2.58089i	−0.0509402	−	0.156778i	0.922350	−	0.386355i	$-0.126266\pi$
$271$	−0.838582	−	2.58089i	−0.0509402	−	0.156778i	−0.973291	+	0.229577i	$0.926266\pi$
$272$	3.84683	+	18.0979i	0.233248	+	1.09735i
$273$	−4.72509	+	2.72803i	−0.285976	+	0.165108i
$274$	−1.11085	+	1.92405i	−0.0671091	+	0.116236i
$275$		0			0
$276$	0.193994	−	1.84573i	0.0116770	−	0.111100i
$277$	−1.79997	−	2.47744i	−0.108150	−	0.148855i	0.751511	−	0.659720i	$-0.229325\pi$
$277$	−1.79997	−	2.47744i	−0.108150	−	0.148855i	−0.859661	+	0.510865i	$0.829325\pi$
$278$		−	0.0973834i		−	0.00584067i
$279$	15.0303	−	0.771051i	0.899839	−	0.0461616i
$280$		0			0
$281$	18.3365	−	13.3223i	1.09386	−	0.794739i	0.113817	−	0.993502i	$-0.463692\pi$
$281$	18.3365	−	13.3223i	1.09386	−	0.794739i	0.980048	+	0.198763i	$0.0636924\pi$
$282$	0.425198	+	0.0446901i	0.0253202	+	0.00266126i
$283$	3.34357	+	1.08639i	0.198755	+	0.0645794i	0.406703	−	0.913561i	$-0.366678\pi$
$283$	3.34357	+	1.08639i	0.198755	+	0.0645794i	−0.207948	+	0.978140i	$0.566678\pi$
$284$	14.1968	−	24.5896i	0.842425	−	1.45912i
$285$		0			0
$286$	1.63130	−	0.346743i	0.0964607	−	0.0205034i
$287$	−10.2263	+	3.32274i	−0.603641	+	0.196135i
$288$	−0.708666	+	3.33401i	−0.0417586	+	0.196459i
$289$	0.536475	+	5.10421i	0.0315573	+	0.300248i
$290$		0			0
$291$	−3.48155	−	1.55008i	−0.204092	−	0.0908676i
$292$	−9.88510	−	22.2023i	−0.578481	−	1.29929i
$293$	−1.46499	−	1.31908i	−0.0855857	−	0.0770617i	0.625227	−	0.780443i	$-0.285006\pi$
$293$	−1.46499	−	1.31908i	−0.0855857	−	0.0770617i	−0.710813	+	0.703381i	$0.751673\pi$
$294$	0.0347512	+	0.0252482i	0.00202673	+	0.00147251i
$295$		0			0
$296$	−2.45237	+	2.72363i	−0.142541	+	0.158308i
$297$	−4.97371	−	11.1711i	−0.288604	−	0.648215i
$298$	−0.0101540	+	0.0228062i	−0.000588205	+	0.00132113i
$299$	−4.58740	−	5.09483i	−0.265296	−	0.294642i
$300$		0			0
$301$	12.0760	+	2.56683i	0.696049	+	0.147950i
$302$	−1.58162	+	0.513899i	−0.0910118	+	0.0295715i
$303$	0.872240	+	4.10357i	0.0501089	+	0.235744i
$304$	−7.09634	−	12.2912i	−0.407003	−	0.704950i
$305$		0			0
$306$	−0.416036	+	1.28043i	−0.0237832	+	0.0731971i
$307$	−12.3282	−	1.29574i	−0.703607	−	0.0739521i	−0.254033	−	0.967195i	$-0.581757\pi$
$307$	−12.3282	−	1.29574i	−0.703607	−	0.0739521i	−0.449573	+	0.893243i	$0.648424\pi$
$308$	−11.5045	−	15.8345i	−0.655527	−	0.902255i
$309$	9.31044			0.529652
$310$		0			0
$311$	29.6457			1.68106			0.840528	−	0.541768i	$-0.182245\pi$
$311$	29.6457			1.68106			0.840528	+	0.541768i	$0.182245\pi$
$312$	−0.541488	−	0.745294i	−0.0306557	−	0.0421940i
$313$	−14.1510	−	1.48733i	−0.799860	−	0.0840687i	−0.304226	−	0.952600i	$-0.598398\pi$
$313$	−14.1510	−	1.48733i	−0.799860	−	0.0840687i	−0.495634	+	0.868531i	$0.665064\pi$
$314$	−0.774426	+	2.38344i	−0.0437034	+	0.134505i
$315$		0			0
$316$	−8.91743	−	15.4454i	−0.501644	−	0.868874i
$317$	3.62576	+	17.0578i	0.203643	+	0.958064i	0.954641	+	0.297760i	$0.0962394\pi$
$317$	3.62576	+	17.0578i	0.203643	+	0.958064i	−0.750998	+	0.660304i	$0.770427\pi$
$318$	0.331956	−	0.107859i	0.0186151	−	0.00604843i
$319$	30.4633	+	6.47518i	1.70562	+	0.362540i
$320$		0			0
$321$	−3.87472	−	4.30331i	−0.216266	−	0.240187i
$322$	0.184440	−	0.414258i	0.0102784	−	0.0230857i
$323$	−6.90528	−	15.5095i	−0.384220	−	0.862972i
$324$	8.53786	−	9.48225i	0.474325	−	0.526792i
$325$		0			0
$326$	−1.03465	−	0.751715i	−0.0573038	−	0.0416336i
$327$	−2.85085	−	2.56692i	−0.157652	−	0.141951i
$328$	−0.738444	−	1.65857i	−0.0407737	−	0.0915793i
$329$	−16.9328	−	7.53897i	−0.933535	−	0.415637i
$330$		0			0
$331$	−0.635474	−	6.04613i	−0.0349288	−	0.332325i	−0.998007	−	0.0631034i	$-0.979900\pi$
$331$	−0.635474	−	6.04613i	−0.0349288	−	0.332325i	0.963078	−	0.269222i	$-0.0867665\pi$
$332$	−4.15027	+	19.5255i	−0.227775	+	1.07160i
$333$	22.3110	−	7.24929i	1.22264	−	0.397259i
$334$	0.0760501	−	0.0161649i	0.00416128	−	0.000884506i
$335$		0			0
$336$	−2.68002	+	4.64193i	−0.146207	+	0.253238i
$337$	5.28877	+	1.71843i	0.288098	+	0.0936086i	0.449501	−	0.893280i	$-0.351602\pi$
$337$	5.28877	+	1.71843i	0.288098	+	0.0936086i	−0.161403	+	0.986889i	$0.551602\pi$
$338$	−0.318683	−	0.0334949i	−0.0173340	−	0.00182188i
$339$	4.34985	−	3.16035i	0.236251	−	0.171647i
$340$		0			0
$341$	−18.3607	−	11.9525i	−0.994289	−	0.647262i
$342$		−	1.03274i		−	0.0558439i
$343$	−11.3853	−	15.6705i	−0.614749	−	0.846129i
$344$	−0.217893	+	2.07311i	−0.0117480	+	0.111775i
$345$		0			0
$346$	−0.353767	+	0.612743i	−0.0190187	+	0.0329413i
$347$	−4.27514	+	2.46825i	−0.229501	+	0.132503i	−0.610342	−	0.792138i	$-0.708968\pi$
$347$	−4.27514	+	2.46825i	−0.229501	+	0.132503i	0.380841	+	0.924641i	$0.375635\pi$
$348$	−1.78337	−	8.39009i	−0.0955985	−	0.449756i
$349$	−10.5621	−	32.5068i	−0.565376	−	1.74005i	−0.666833	−	0.745208i	$-0.732350\pi$
$349$	−10.5621	−	32.5068i	−0.565376	−	1.74005i	0.101457	−	0.994840i	$-0.467650\pi$
$350$		0			0
$351$	1.30045	+	12.3730i	0.0694130	+	0.660420i
$352$	3.68730	−	3.32006i	0.196534	−	0.176960i
$353$	−2.08610	+	4.68547i	−0.111032	+	0.249382i	−0.960512	−	0.278239i	$-0.910249\pi$
$353$	−2.08610	+	4.68547i	−0.111032	+	0.249382i	0.849480	+	0.527621i	$0.176916\pi$
$354$	−0.249519	+	0.111093i	−0.0132618	+	0.00590452i
$355$		0			0
$356$	11.6845	+	8.48932i	0.619280	+	0.449933i
$357$	−3.76869	+	5.18715i	−0.199460	+	0.274533i
$358$	−0.264434	−	0.238097i	−0.0139758	−	0.0125838i
$359$	31.2359	−	13.9071i	1.64857	−	0.733990i	0.648930	−	0.760848i	$-0.275217\pi$
$359$	31.2359	−	13.9071i	1.64857	−	0.733990i	0.999639	+	0.0268580i	$0.00855020\pi$
$360$		0			0
$361$	−3.99944	−	4.44183i	−0.210497	−	0.233780i
$362$	1.40133	−	0.147286i	0.0736524	−	0.00774117i
$363$	−0.507914	+	2.38955i	−0.0266586	+	0.125419i
$364$	6.15350	+	18.9385i	0.322531	+	0.992648i
$365$		0			0
$366$	0.0196731	+	0.0340748i	0.00102833	+	0.00178112i
$367$	−15.5097	−	8.95451i	−0.809598	−	0.467422i	0.0372182	−	0.999307i	$-0.488150\pi$
$367$	−15.5097	−	8.95451i	−0.809598	−	0.467422i	−0.846816	+	0.531885i	$0.821484\pi$
$368$	−6.40547	−	2.08126i	−0.333908	−	0.108493i
$369$	−1.21472	+	11.5573i	−0.0632358	+	0.601649i
$370$		0			0
$371$	−15.1320			−0.785612
$372$	−0.950497	+	5.95858i	−0.0492810	+	0.308938i
$373$		−	15.2436i		−	0.789285i	−0.918835	−	0.394642i	$-0.870869\pi$
$373$		−	15.2436i		−	0.789285i	0.918835	−	0.394642i	$-0.129131\pi$
$374$	1.58554	−	1.15197i	0.0819866	−	0.0595667i
$375$		0			0
$376$	0.967100	−	2.97643i	0.0498744	−	0.153498i
$377$	−27.4407	−	15.8429i	−1.41327	−	0.815952i
$378$	−0.712648	+	0.411447i	−0.0366546	+	0.0211626i
$379$	−23.0586	+	4.90127i	−1.18444	+	0.251761i	−0.757695	−	0.652609i	$-0.773674\pi$
$379$	−23.0586	+	4.90127i	−1.18444	+	0.251761i	−0.426748	+	0.904370i	$0.640341\pi$
$380$		0			0
$381$	7.10474	+	1.51016i	0.363987	+	0.0773678i
$382$	0.929965	−	0.0977432i	0.0475811	−	0.00500098i
$383$	−5.94122	+	5.34950i	−0.303582	+	0.273347i	−0.806815	−	0.590804i	$-0.798811\pi$
$383$	−5.94122	+	5.34950i	−0.303582	+	0.273347i	0.503233	+	0.864151i	$0.332144\pi$
$384$	−1.66295	−	0.740395i	−0.0848623	−	0.0377831i
$385$		0			0
$386$	−1.72422	+	1.91494i	−0.0877606	+	0.0974680i
$387$	7.84269	−	10.7945i	0.398667	−	0.548717i
$388$	−8.17562	+	11.2528i	−0.415054	+	0.571273i
$389$	0.220883	−	0.245315i	0.0111992	−	0.0124380i	−0.737519	−	0.675326i	$-0.764003\pi$
$389$	0.220883	−	0.245315i	0.0111992	−	0.0124380i	0.748718	+	0.662888i	$0.230670\pi$
$390$		0			0
$391$	−7.36001	−	3.27689i	−0.372211	−	0.165719i
$392$	0.233667	−	0.210395i	0.0118020	−	0.0106265i
$393$	2.29977	−	0.241716i	0.116008	−	0.0121930i
$394$	−1.48502	−	0.315650i	−0.0748140	−	0.0159022i
$395$		0			0
$396$	−20.6909	+	4.39799i	−1.03976	+	0.221007i
$397$	−0.667858	+	0.385588i	−0.0335188	+	0.0193521i	−0.516666	−	0.856187i	$-0.672827\pi$
$397$	−0.667858	+	0.385588i	−0.0335188	+	0.0193521i	0.483147	+	0.875539i	$0.339494\pi$
$398$	0.200272	+	0.115627i	0.0100387	+	0.00579586i
$399$	1.51983	−	4.67755i	0.0760866	−	0.234171i
$400$		0			0
$401$	5.67534	−	4.12337i	0.283413	−	0.205911i	−0.436992	−	0.899465i	$-0.643956\pi$
$401$	5.67534	−	4.12337i	0.283413	−	0.205911i	0.720405	+	0.693554i	$0.243956\pi$
$402$			0.451231i			0.0225054i
$403$	14.0082	+	17.3378i	0.697796	+	0.863656i
$404$	15.3115			0.761774
$405$		0			0
$406$	0.219071	−	2.08432i	0.0108723	−	0.103443i
$407$	−32.4782	−	10.5528i	−1.60988	−	0.523083i
$408$	−0.937546	−	0.541293i	−0.0464155	−	0.0267980i
$409$	−6.12119	−	10.6022i	−0.302674	−	0.524246i	0.674067	−	0.738670i	$-0.264546\pi$
$409$	−6.12119	−	10.6022i	−0.302674	−	0.524246i	−0.976741	+	0.214424i	$0.931213\pi$
$410$		0			0
$411$	3.53363	+	10.8754i	0.174301	+	0.536443i
$412$	7.06495	−	33.2380i	0.348065	−	1.63752i
$413$	11.7763	−	1.23774i	0.579474	−	0.0609051i
$414$	−0.327929	−	0.364202i	−0.0161168	−	0.0178996i
$415$		0			0
$416$	−4.61167	+	2.05325i	−0.226106	+	0.100669i
$417$	−0.372486	−	0.335388i	−0.0182407	−	0.0164240i
$418$	−0.883650	+	1.21624i	−0.0432207	+	0.0594882i
$419$	10.6478	+	7.73611i	0.520181	+	0.377933i	0.816672	−	0.577102i	$-0.195817\pi$
$419$	10.6478	+	7.73611i	0.520181	+	0.377933i	−0.296491	+	0.955036i	$0.595817\pi$
$420$		0			0
$421$	−29.2523	+	13.0240i	−1.42567	+	0.634749i	−0.967213	−	0.253968i	$-0.918264\pi$
$421$	−29.2523	+	13.0240i	−1.42567	+	0.634749i	−0.458456	+	0.888717i	$0.651597\pi$
$422$	−0.537915	+	1.20818i	−0.0261853	+	0.0588131i
$423$	−14.8868	+	13.4041i	−0.723819	+	0.651730i
$424$	−0.267067	−	2.54097i	−0.0129699	−	0.123401i
$425$		0			0
$426$	0.254519	+	0.783330i	0.0123315	+	0.0379525i
$427$	−0.354653	−	1.66851i	−0.0171629	−	0.0807449i
$428$	−18.3029	+	10.5672i	−0.884704	+	0.510784i
$429$	4.29191	−	7.43381i	0.207215	−	0.358907i
$430$		0			0
$431$	2.03087	−	19.3224i	0.0978234	−	0.930727i	−0.830014	−	0.557743i	$-0.811668\pi$
$431$	2.03087	−	19.3224i	0.0978234	−	0.930727i	0.927837	−	0.372985i	$-0.121666\pi$
$432$	7.18400	+	9.88793i	0.345640	+	0.475733i
$433$			5.64744i			0.271399i	0.990750	+	0.135699i	$0.0433281\pi$
$433$			5.64744i			0.271399i	−0.990750	+	0.135699i	$0.956672\pi$
$434$	−0.670771	+	1.31287i	−0.0321981	+	0.0630200i
$435$		0			0
$436$	−11.3271	+	8.22962i	−0.542470	+	0.394127i
$437$	6.14615	+	0.645986i	0.294010	+	0.0309017i
$438$	0.670489	+	0.217855i	0.0320372	+	0.0104095i
$439$	12.9575	−	22.4431i	0.618430	−	1.07115i	−0.371342	−	0.928496i	$-0.621102\pi$
$439$	12.9575	−	22.4431i	0.618430	−	1.07115i	0.989772	−	0.142656i	$-0.0455643\pi$
$440$		0			0
$441$	−1.96864	+	0.418447i	−0.0937448	+	0.0199261i
$442$	−1.89635	+	0.616163i	−0.0902004	+	0.0293079i
$443$	2.16084	−	10.1659i	0.102665	−	0.482999i	−0.896534	−	0.442975i	$-0.853923\pi$
$443$	2.16084	−	10.1659i	0.102665	−	0.482999i	0.999199	−	0.0400242i	$-0.0127435\pi$
$444$	0.983126	+	9.35382i	0.0466571	+	0.443913i
$445$		0			0
$446$	−0.792085	−	0.352659i	−0.0375063	−	0.0166989i
$447$	0.0522623	+	0.117383i	0.00247192	+	0.00555203i
$448$	14.3717	+	12.9403i	0.678998	+	0.611373i
$449$	−17.9060	−	13.0094i	−0.845035	−	0.613954i	0.0787378	−	0.996895i	$-0.474911\pi$
$449$	−17.9060	−	13.0094i	−0.845035	−	0.613954i	−0.923773	+	0.382942i	$0.874911\pi$
$450$		0			0
$451$	11.3195	−	12.5715i	0.533012	−	0.591970i
$452$	−7.98159	−	17.9270i	−0.375423	−	0.843213i
$453$	−3.48145	+	7.81946i	−0.163573	+	0.367390i
$454$	1.09220	+	1.21301i	0.0512595	+	0.0569294i
$455$		0			0
$456$	0.812283	+	0.172656i	0.0380386	+	0.00808536i
$457$	16.9704	−	5.51400i	0.793840	−	0.257934i	0.116101	−	0.993237i	$-0.462960\pi$
$457$	16.9704	−	5.51400i	0.793840	−	0.257934i	0.677738	+	0.735303i	$0.262960\pi$
$458$	−0.491712	−	2.31332i	−0.0229762	−	0.108094i
$459$	7.31007	+	12.6614i	0.341205	+	0.590984i
$460$		0			0
$461$	4.74381	−	14.5999i	0.220941	−	0.679987i	−0.777737	−	0.628590i	$-0.783632\pi$
$461$	4.74381	−	14.5999i	0.220941	−	0.679987i	0.998678	−	0.0513974i	$-0.0163675\pi$
$462$	0.564650	+	0.0593471i	0.0262699	+	0.00276108i
$463$	6.32644	+	8.70760i	0.294015	+	0.404677i	0.930313	−	0.366767i	$-0.119535\pi$
$463$	6.32644	+	8.70760i	0.294015	+	0.404677i	−0.636298	+	0.771443i	$0.719535\pi$
$464$	−31.1282			−1.44509
$465$		0			0
$466$	−1.29942			−0.0601944
$467$	−14.6693	−	20.1906i	−0.678816	−	0.934309i	0.321103	−	0.947044i	$-0.395946\pi$
$467$	−14.6693	−	20.1906i	−0.678816	−	0.934309i	−0.999919	+	0.0127347i	$0.995946\pi$
$468$	21.4034	+	2.24958i	0.989371	+	0.103987i
$469$	6.04509	−	18.6049i	0.279136	−	0.859094i
$470$		0			0
$471$	6.44940	+	11.1707i	0.297173	+	0.514718i
$472$	0.415684	+	1.95564i	0.0191334	+	0.0900157i
$473$	−18.4725	+	6.00208i	−0.849366	+	0.275976i
$474$	0.506048	+	0.107564i	0.0232436	+	0.00494057i
$475$		0			0
$476$	15.6582	+	17.3902i	0.717693	+	0.797079i
$477$	−6.65176	+	14.9401i	−0.304563	+	0.684060i
$478$	−0.939995	−	2.11126i	−0.0429944	−	0.0965669i
$479$	8.94267	−	9.93185i	0.408601	−	0.453798i	−0.503358	−	0.864078i	$-0.667902\pi$
$479$	8.94267	−	9.93185i	0.408601	−	0.453798i	0.911960	+	0.410280i	$0.134569\pi$
$480$		0			0
$481$	28.1084	+	20.4219i	1.28163	+	0.931160i
$482$	−0.757241	−	0.681823i	−0.0344914	−	0.0310562i
$483$	−0.949305	−	2.13217i	−0.0431949	−	0.0970173i
$484$	8.14518	+	3.62647i	0.370236	+	0.164840i
$485$		0			0
$486$	0.141864	+	1.34974i	0.00643506	+	0.0612255i
$487$	−5.00583	+	23.5506i	−0.226836	+	1.06718i	0.706372	+	0.707841i	$0.250331\pi$
$487$	−5.00583	+	23.5506i	−0.226836	+	1.06718i	−0.933208	+	0.359337i	$0.883003\pi$
$488$	0.273918	−	0.0890015i	0.0123997	−	0.00402891i
$489$	−6.43858	+	1.36856i	−0.291163	+	0.0618886i
$490$		0			0
$491$	1.60663	−	2.78276i	0.0725060	−	0.125584i	−0.827493	−	0.561476i	$-0.810234\pi$
$491$	1.60663	−	2.78276i	0.0725060	−	0.125584i	0.899999	+	0.435892i	$0.143567\pi$
$492$	−4.43108	−	1.43975i	−0.199769	−	0.0649088i
$493$	−37.0315	−	3.89217i	−1.66781	−	0.175294i
$494$	1.23740	−	0.899027i	0.0556734	−	0.0404491i
$495$		0			0
$496$	20.4342	+	7.86988i	0.917524	+	0.353368i
$497$		−	35.7075i		−	1.60170i
$498$	−0.340356	−	0.468460i	−0.0152517	−	0.0209922i
$499$	−1.67180	+	15.9061i	−0.0748401	+	0.712056i	0.891191	+	0.453629i	$0.149871\pi$
$499$	−1.67180	+	15.9061i	−0.0748401	+	0.712056i	−0.966031	+	0.258427i	$0.916796\pi$
$500$		0			0
$501$	0.200086	−	0.346559i	0.00893919	−	0.0154831i
$502$	−0.173390	+	0.100107i	−0.00773877	+	0.00446798i
$503$	−0.569481	−	2.67920i	−0.0253919	−	0.119459i	0.963626	−	0.267253i	$-0.0861161\pi$
$503$	−0.569481	−	2.67920i	−0.0253919	−	0.119459i	−0.989018	+	0.147794i	$0.952783\pi$
$504$	0.882240	+	2.71526i	0.0392981	+	0.120947i
$505$		0			0
$506$	0.0745721	+	0.709506i	0.00331513	+	0.0315414i
$507$	−1.22566	+	1.10359i	−0.0544333	+	0.0490120i
$508$	10.7824	−	24.2177i	0.478393	−	1.07449i
$509$	8.39209	−	3.73640i	0.371973	−	0.165613i	−0.212232	−	0.977219i	$-0.568073\pi$
$509$	8.39209	−	3.73640i	0.371973	−	0.165613i	0.584205	+	0.811606i	$0.301407\pi$
$510$		0			0
$511$	−24.7266	−	17.9649i	−1.09384	−	0.794722i
$512$	−4.86742	+	6.69942i	−0.215111	+	0.296075i
$513$	−8.33423	−	7.50418i	−0.367965	−	0.331318i
$514$	2.40381	−	1.07025i	0.106028	−	0.0472065i
$515$		0			0
$516$	3.57947	+	3.97541i	0.157578	+	0.175008i
$517$	29.0010	−	3.04813i	1.27546	−	0.134057i
$518$	−0.477795	+	2.24785i	−0.0209931	+	0.0987648i
$519$	1.12534	+	3.46343i	0.0493967	+	0.152027i
$520$		0			0
$521$	−19.1157	−	33.1094i	−0.837475	−	1.45055i	−0.891999	−	0.452037i	$-0.850698\pi$
$521$	−19.1157	−	33.1094i	−0.837475	−	1.45055i	0.0545246	−	0.998512i	$-0.482636\pi$
$522$	−1.96159	−	1.13253i	−0.0858565	−	0.0495693i
$523$	13.1206	+	4.26313i	0.573722	+	0.186414i	0.581486	−	0.813556i	$-0.302471\pi$
$523$	13.1206	+	4.26313i	0.573722	+	0.186414i	−0.00776416	+	0.999970i	$0.502471\pi$
$524$	0.882196	−	8.39353i	0.0385389	−	0.366673i
$525$		0			0
$526$	2.90321			0.126586
$527$	23.3255	+	11.9174i	1.01607	+	0.519130i
$528$		−	8.43274i		−	0.366988i
$529$	−16.2348	+	11.7953i	−0.705860	+	0.512837i
$530$		0			0
$531$	3.95462	−	12.1711i	0.171616	−	0.528180i
$532$	−15.5454	−	8.97516i	−0.673980	−	0.389123i
$533$	−14.9052	+	8.60551i	−0.645615	+	0.372746i
$534$	−0.409804	+	0.0871066i	−0.0177340	+	0.00376947i
$535$		0			0
$536$	3.23084	+	0.686736i	0.139551	+	0.0296625i
$537$	−1.82142	+	0.191439i	−0.0785999	+	0.00826118i
$538$	−1.23362	+	1.11076i	−0.0531851	+	0.0478881i
$539$	2.67648	+	1.19165i	0.115284	+	0.0513279i
$540$		0			0
$541$	−20.0726	+	22.2929i	−0.862990	+	0.958447i	−0.999482	−	0.0321938i	$-0.989751\pi$
$541$	−20.0726	+	22.2929i	−0.862990	+	0.958447i	0.136492	+	0.990641i	$0.456417\pi$
$542$	0.168873	−	0.232433i	0.00725371	−	0.00998387i
$543$	4.26282	−	5.86727i	0.182935	−	0.251788i
$544$	−3.96945	+	4.40852i	−0.170189	+	0.189014i
$545$		0			0
$546$	−0.527701	−	0.234948i	−0.0225835	−	0.0100548i
$547$	−9.39639	+	8.46055i	−0.401761	+	0.361747i	−0.845101	−	0.534606i	$-0.820460\pi$
$547$	−9.39639	+	8.46055i	−0.401761	+	0.361747i	0.443341	+	0.896353i	$0.353793\pi$
$548$	41.5061	−	4.36247i	1.77305	−	0.186356i
$549$	−1.80325	−	0.383294i	−0.0769610	−	0.0163586i
$550$		0			0
$551$	27.9384	−	5.93850i	1.19022	−	0.252989i
$552$	0.341282	−	0.197039i	0.0145259	−	0.00838655i
$553$	−19.4240	−	11.2145i	−0.825994	−	0.476888i
$554$	0.100186	−	0.308340i	0.00425649	−	0.0131001i
$555$		0			0
$556$	−1.47997	+	1.07526i	−0.0627649	+	0.0456013i
$557$			28.0158i			1.18707i	0.804810	+	0.593533i	$0.202267\pi$
$557$			28.0158i			1.18707i	−0.804810	+	0.593533i	$0.797733\pi$
$558$	1.00137	+	1.23938i	0.0423913	+	0.0524673i
$559$	19.7611			0.835806
$560$		0			0
$561$	1.05440	−	10.0320i	0.0445170	−	0.423551i
$562$	2.28214	+	0.741514i	0.0962664	+	0.0312789i
$563$	−28.5548	−	16.4861i	−1.20344	−	0.694807i	−0.242122	−	0.970246i	$-0.577844\pi$
$563$	−28.5548	−	16.4861i	−1.20344	−	0.694807i	−0.961319	+	0.275439i	$0.911177\pi$
$564$	−4.01567	−	6.95535i	−0.169090	−	0.292873i
$565$		0			0
$566$	0.115018	+	0.353988i	0.00483456	+	0.0148792i
$567$	3.33623	−	15.6957i	0.140109	−	0.659159i
$568$	5.99604	−	0.630210i	0.251588	−	0.0264430i
$569$	−9.02683	−	10.0253i	−0.378425	−	0.420283i	0.523602	−	0.851963i	$-0.324588\pi$
$569$	−9.02683	−	10.0253i	−0.378425	−	0.420283i	−0.902027	+	0.431680i	$0.857921\pi$
$570$		0			0
$571$	−7.61848	+	3.39197i	−0.318824	+	0.141949i	−0.559908	−	0.828555i	$-0.689164\pi$
$571$	−7.61848	+	3.39197i	−0.318824	+	0.141949i	0.241085	+	0.970504i	$0.422497\pi$
$572$	−23.2817	−	20.9629i	−0.973455	−	0.876503i
$573$	2.82893	−	3.89369i	0.118180	−	0.162661i
$574$	−0.920978	−	0.669130i	−0.0384409	−	0.0279289i
$575$		0			0
$576$	19.0938	−	8.50111i	0.795575	−	0.354213i
$577$	−18.6226	+	41.8270i	−0.775269	+	1.74128i	−0.110958	+	0.993825i	$0.535392\pi$
$577$	−18.6226	+	41.8270i	−0.775269	+	1.74128i	−0.664310	+	0.747457i	$0.731275\pi$
$578$	−0.403799	+	0.363583i	−0.0167958	+	0.0151230i
$579$	1.38634	+	13.1901i	0.0576141	+	0.548162i
$580$		0			0
$581$	7.75745	+	23.8750i	0.321833	+	0.990500i
$582$	−0.0838878	−	0.394661i	−0.00347726	−	0.0163592i
$583$	20.6170	−	11.9033i	0.853871	−	0.492983i
$584$	2.58028	−	4.46918i	0.106773	−	0.184936i
$585$		0			0
$586$	0.0218159	−	0.207565i	0.000901208	−	0.00857442i
$587$	−9.57279	−	13.1758i	−0.395111	−	0.543824i	0.564397	−	0.825503i	$-0.309109\pi$
$587$	−9.57279	−	13.1758i	−0.395111	−	0.543824i	−0.959509	+	0.281679i	$0.909109\pi$
$588$		−	0.806908i		−	0.0332763i
$589$	−19.8417	−	3.16509i	−0.817563	−	0.130415i
$590$		0			0
$591$	−6.32173	+	4.59300i	−0.260041	+	0.188931i
$592$	33.9454	+	3.56780i	1.39515	+	0.146636i
$593$	−13.1109	−	4.25997i	−0.538398	−	0.174936i	0.0271805	−	0.999631i	$-0.491347\pi$
$593$	−13.1109	−	4.25997i	−0.538398	−	0.174936i	−0.565579	+	0.824694i	$0.691347\pi$
$594$	0.647314	−	1.12118i	0.0265596	−	0.0460026i
$595$		0			0
$596$	0.458711	−	0.0975021i	0.0187895	−	0.00399384i
$597$	1.13200	−	0.367810i	0.0463298	−	0.0150535i
$598$	0.150908	−	0.709967i	0.00617110	−	0.0290327i
$599$	3.08707	+	29.3715i	0.126134	+	1.20009i	0.856176	+	0.516685i	$0.172834\pi$
$599$	3.08707	+	29.3715i	0.126134	+	1.20009i	−0.730041	+	0.683403i	$0.760499\pi$
$600$		0			0
$601$	30.5480	+	13.6008i	1.24608	+	0.554790i	0.920506	−	0.390728i	$-0.127777\pi$
$601$	30.5480	+	13.6008i	1.24608	+	0.554790i	0.325572	+	0.945517i	$0.394443\pi$
$602$	0.531630	+	1.19406i	0.0216676	+	0.0486663i
$603$	−15.7117	−	14.1468i	−0.639828	−	0.576104i
$604$	25.2734	+	18.3622i	1.02836	+	0.747148i
$605$		0			0
$606$	−0.297198	+	0.330072i	−0.0120728	+	0.0134082i
$607$	9.30883	+	20.9080i	0.377834	+	0.848629i	0.997943	+	0.0641130i	$0.0204218\pi$
$607$	9.30883	+	20.9080i	0.377834	+	0.848629i	−0.620109	+	0.784516i	$0.712912\pi$
$608$	1.85086	−	4.15710i	0.0750623	−	0.168593i
$609$	−7.21792	−	8.01632i	−0.292485	−	0.324838i
$610$		0			0
$611$	−29.0199	−	6.16837i	−1.17402	−	0.249546i
$612$	24.0528	−	7.81523i	0.972277	−	0.315912i
$613$	9.33773	+	43.9305i	0.377147	+	1.77434i	0.600525	+	0.799606i	$0.294958\pi$
$613$	9.33773	+	43.9305i	0.377147	+	1.77434i	−0.223378	+	0.974732i	$0.571708\pi$
$614$	−0.656195	−	1.13656i	−0.0264819	−	0.0458679i
$615$		0			0
$616$	1.28428	−	3.95261i	0.0517451	−	0.159255i
$617$	28.0868	+	2.95205i	1.13073	+	0.118845i	0.651362	−	0.758767i	$-0.274198\pi$
$617$	28.0868	+	2.95205i	1.13073	+	0.118845i	0.479372	+	0.877612i	$0.340865\pi$
$618$	0.579384	+	0.797454i	0.0233062	+	0.0320783i
$619$	38.8055			1.55973			0.779863	−	0.625950i	$-0.215289\pi$
$619$	38.8055			1.55973			0.779863	+	0.625950i	$0.215289\pi$
$620$		0			0
$621$	−5.32197			−0.213563
$622$	1.84484	+	2.53921i	0.0739714	+	0.101813i
$623$	18.0637	+	1.89858i	0.723709	+	0.0760649i
$624$	−2.65121	+	8.15957i	−0.106133	+	0.326644i
$625$		0			0
$626$	−0.753216	−	1.30461i	−0.0301046	−	0.0521427i
$627$	1.60876	+	7.56864i	0.0642478	+	0.302262i
$628$	44.7729	−	14.5476i	1.78663	−	0.580512i
$629$	39.9369	+	8.48885i	1.59239	+	0.338472i
$630$		0			0
$631$	−11.4161	−	12.6789i	−0.454469	−	0.504739i	0.471746	−	0.881735i	$-0.343624\pi$
$631$	−11.4161	−	12.6789i	−0.454469	−	0.504739i	−0.926215	+	0.376995i	$0.876957\pi$
$632$	1.54033	−	3.45963i	0.0612709	−	0.137617i
$633$	2.76863	+	6.21845i	0.110043	+	0.247161i
$634$	−1.23540	+	1.37205i	−0.0490641	+	0.0544912i
$635$		0			0
$636$	−5.30448	−	3.85393i	−0.210336	−	0.152818i
$637$	−2.21514	−	1.99452i	−0.0877669	−	0.0790257i
$638$	1.34111	+	3.01218i	0.0530950	+	0.119253i
$639$	−35.2548	−	15.6964i	−1.39466	−	0.620942i
$640$		0			0
$641$	1.47756	+	14.0581i	0.0583603	+	0.555261i	0.984164	+	0.177258i	$0.0567226\pi$
$641$	1.47756	+	14.0581i	0.0583603	+	0.555261i	−0.925804	+	0.378003i	$0.876611\pi$
$642$	0.127464	−	0.599669i	0.00503058	−	0.0236670i
$643$	4.98678	−	1.62030i	0.196659	−	0.0638985i	−0.209031	−	0.977909i	$-0.567031\pi$
$643$	4.98678	−	1.62030i	0.196659	−	0.0638985i	0.405691	+	0.914010i	$0.367031\pi$
$644$	−8.33214	+	1.77105i	−0.328332	+	0.0697892i
$645$		0			0
$646$	0.898702	−	1.55660i	0.0353590	−	0.0612435i
$647$	30.2954	+	9.84357i	1.19103	+	0.386991i	0.836455	−	0.548035i	$-0.184624\pi$
$647$	30.2954	+	9.84357i	1.19103	+	0.386991i	0.354580	+	0.935026i	$0.384624\pi$
$648$	2.69453	+	0.283206i	0.105851	+	0.0111254i
$649$	−15.0714	+	10.9500i	−0.591603	+	0.429825i
$650$		0			0
$651$	2.71154	+	7.08720i	0.106274	+	0.277769i
$652$			24.0240i			0.940853i
$653$	19.6539	+	27.0512i	0.769115	+	1.05860i	0.996401	+	0.0847682i	$0.0270150\pi$
$653$	19.6539	+	27.0512i	0.769115	+	1.05860i	−0.227285	+	0.973828i	$0.572985\pi$
$654$	0.0424535	−	0.403918i	0.00166006	−	0.0157944i
$655$		0			0
$656$	−8.45405	+	14.6429i	−0.330075	+	0.571707i
$657$	−28.6066	+	16.5160i	−1.11605	+	0.644351i
$658$	−0.407995	−	1.91947i	−0.0159053	−	0.0748286i
$659$	5.40178	+	16.6250i	0.210424	+	0.647617i	0.999447	+	0.0332540i	$0.0105870\pi$
$659$	5.40178	+	16.6250i	0.210424	+	0.647617i	−0.789023	+	0.614363i	$0.789413\pi$
$660$		0			0
$661$	−0.771035	−	7.33591i	−0.0299898	−	0.285334i	−0.999231	−	0.0392196i	$-0.987513\pi$
$661$	−0.771035	−	7.33591i	−0.0299898	−	0.285334i	0.969241	−	0.246114i	$-0.0791539\pi$
$662$	0.478315	−	0.430677i	0.0185903	−	0.0167387i
$663$	−4.17425	+	9.37551i	−0.162114	+	0.364115i
$664$	−3.87219	+	1.72401i	−0.150270	+	0.0669046i
$665$		0			0
$666$	2.00932	+	1.45985i	0.0778594	+	0.0565682i
$667$	7.96703	−	10.9657i	0.308485	−	0.424593i
$668$	−1.08538	−	0.977277i	−0.0419945	−	0.0378120i
$669$	−4.07684	+	1.81512i	−0.157620	+	0.0701768i
$670$		0			0
$671$	1.79571	+	1.99434i	0.0693226	+	0.0769906i
$672$	−1.70914	+	0.179638i	−0.0659316	+	0.00692969i
$673$	−0.207627	+	0.976808i	−0.00800343	+	0.0376532i	−0.981968	−	0.189047i	$-0.939460\pi$
$673$	−0.207627	+	0.976808i	−0.00800343	+	0.0376532i	0.973965	+	0.226700i	$0.0727936\pi$
$674$	0.181932	+	0.559928i	0.00700775	+	0.0215676i
$675$		0			0
$676$	3.00971	+	5.21298i	0.115758	+	0.200499i
$677$	29.6804	+	17.1360i	1.14071	+	0.658589i	0.946606	−	0.322392i	$-0.104487\pi$
$677$	29.6804	+	17.1360i	1.14071	+	0.658589i	0.194104	+	0.980981i	$0.437820\pi$
$678$	0.541378	+	0.175904i	0.0207915	+	0.00675557i
$679$	−1.82842	+	17.3963i	−0.0701683	+	0.667607i
$680$		0			0
$681$	8.40123			0.321936
$682$	−0.118832	−	2.31642i	−0.00455032	−	0.0887003i
$683$		−	4.54905i		−	0.174064i	−0.996205	−	0.0870322i	$-0.972262\pi$
$683$		−	4.54905i		−	0.174064i	0.996205	−	0.0870322i	$-0.0277383\pi$
$684$	−15.6949	+	11.4030i	−0.600109	+	0.436005i
$685$		0			0
$686$	0.633703	−	1.95034i	0.0241949	−	0.0744643i
$687$	−10.5418	−	6.08630i	−0.402194	−	0.232207i
$688$	16.8124	−	9.70666i	0.640968	−	0.370063i
$689$	−23.6915	+	5.03578i	−0.902574	+	0.191848i
$690$		0			0
$691$	−48.5104	−	10.3112i	−1.84542	−	0.392257i	−0.853713	−	0.520744i	$-0.825655\pi$
$691$	−48.5104	−	10.3112i	−1.84542	−	0.392257i	−0.991711	+	0.128487i	$0.958988\pi$
$692$	13.2182	−	1.38929i	0.502482	−	0.0528130i
$693$	−19.7692	+	17.8002i	−0.750968	+	0.676175i
$694$	−0.477450	−	0.212574i	−0.0181237	−	0.00806921i
$695$		0			0
$696$	1.21872	−	1.35352i	0.0461953	−	0.0513051i
$697$	−11.8882	+	16.3628i	−0.450299	+	0.619783i
$698$	2.12698	−	2.92754i	0.0805075	−	0.110809i
$699$	−4.47519	+	4.97021i	−0.169267	+	0.187990i
$700$		0			0
$701$	5.51158	+	2.45391i	0.208170	+	0.0926830i	0.508173	−	0.861255i	$-0.330321\pi$
$701$	5.51158	+	2.45391i	0.208170	+	0.0926830i	−0.300003	+	0.953938i	$0.596988\pi$
$702$	−0.978838	+	0.881350i	−0.0369439	+	0.0332644i
$703$	−31.1476	+	3.27375i	−1.17476	+	0.123472i
$704$	−29.7604	−	6.32578i	−1.12164	−	0.238412i
$705$		0			0
$706$	−0.531135	+	0.112896i	−0.0199895	+	0.00424891i
$707$	16.6758	−	9.62778i	0.627158	−	0.362090i
$708$	4.44340	+	2.56540i	0.166993	+	0.0964135i
$709$	−10.8054	+	33.2556i	−0.405805	+	1.24894i	0.514417	+	0.857540i	$0.328009\pi$
$709$	−10.8054	+	33.2556i	−0.405805	+	1.24894i	−0.920221	+	0.391398i	$0.871991\pi$
$710$		0			0
$711$	−19.6108	+	14.2481i	−0.735462	+	0.534344i
$712$			3.06679i			0.114933i
$713$	−8.00236	+	5.18423i	−0.299691	+	0.194151i
$714$	−0.678812			−0.0254039
$715$		0			0
$716$	−0.698697	+	6.64766i	−0.0261115	+	0.248435i
$717$	−11.3128	−	3.67575i	−0.422484	−	0.137273i
$718$	3.13496	+	1.80997i	0.116996	+	0.0675476i
$719$	−18.5666	−	32.1583i	−0.692418	−	1.19930i	−0.971043	−	0.238904i	$-0.923212\pi$
$719$	−18.5666	−	32.1583i	−0.692418	−	1.19930i	0.278625	−	0.960400i	$-0.410121\pi$
$720$		0			0
$721$	−13.2054	−	40.6421i	−0.491795	−	1.51359i
$722$	0.131566	−	0.618971i	0.00489639	−	0.0230357i
$723$	−5.21587	+	0.548210i	−0.193980	+	0.0203881i
$724$	−17.7112	−	19.6703i	−0.658233	−	0.731042i
$725$		0			0
$726$	−0.236276	+	0.105197i	−0.00876901	+	0.00390422i
$727$	−30.3863	−	27.3599i	−1.12696	−	1.01472i	−0.999739	−	0.0228495i	$-0.992726\pi$
$727$	−30.3863	−	27.3599i	−1.12696	−	1.01472i	−0.127226	−	0.991874i	$-0.540607\pi$
$728$	−2.48535	+	3.42080i	−0.0921133	+	0.126783i
$729$	−9.92014	−	7.20740i	−0.367413	−	0.266941i
$730$		0			0
$731$	21.2145	−	9.44532i	0.784648	−	0.349348i
$732$	0.300627	−	0.675219i	0.0111115	−	0.0249568i
$733$	4.25440	−	3.83068i	0.157140	−	0.141489i	−0.586810	−	0.809724i	$-0.699617\pi$
$733$	4.25440	−	3.83068i	0.157140	−	0.141489i	0.743950	+	0.668235i	$0.232950\pi$
$734$	−0.198191	−	1.88566i	−0.00731537	−	0.0696011i
$735$		0			0
$736$	−0.667303	−	2.05375i	−0.0245971	−	0.0757021i
$737$	6.39883	+	30.1041i	0.235704	+	1.10890i
$738$	−1.06549	+	0.615162i	−0.0392213	+	0.0226444i
$739$	16.1662	−	28.0007i	0.594684	−	1.03002i	−0.398907	−	0.916991i	$-0.630610\pi$
$739$	16.1662	−	28.0007i	0.594684	−	1.03002i	0.993591	−	0.113032i	$-0.0360562\pi$
$740$		0			0
$741$	0.822887	−	7.82925i	0.0302295	−	0.287615i
$742$	−0.941654	−	1.29608i	−0.0345692	−	0.0475804i
$743$			17.3877i			0.637893i	0.947773	+	0.318947i	$0.103329\pi$
$743$			17.3877i			0.637893i	−0.947773	+	0.318947i	$0.896671\pi$
$744$	−1.14223	+	0.580408i	−0.0418763	+	0.0212788i
$745$		0			0
$746$	1.30564	−	0.948603i	0.0478029	−	0.0347308i
$747$	26.9823	+	2.83595i	0.987231	+	0.103762i
$748$	−35.0137	−	11.3767i	−1.28023	−	0.415972i
$749$	−13.2892	+	23.0176i	−0.485576	+	0.841043i
$750$		0			0
$751$	8.46030	−	1.79829i	0.308721	−	0.0656206i	−0.0509462	−	0.998701i	$-0.516224\pi$
$751$	8.46030	−	1.79829i	0.308721	−	0.0656206i	0.359667	+	0.933081i	$0.382890\pi$
$752$	−27.7196	+	9.00663i	−1.01083	+	0.328438i
$753$	−0.214251	+	1.00797i	−0.00780776	+	0.0367326i
$754$	−0.350653	−	3.33624i	−0.0127700	−	0.121499i
$755$		0			0
$756$	14.1217	+	6.28737i	0.513600	+	0.228669i
$757$	−19.7421	−	44.3415i	−0.717539	−	1.61162i	−0.789160	−	0.614187i	$-0.789484\pi$
$757$	−19.7421	−	44.3415i	−0.717539	−	1.61162i	0.0716213	−	0.997432i	$-0.477183\pi$
$758$	−1.85473	−	1.67001i	−0.0673668	−	0.0606573i
$759$	2.97065	+	2.15830i	0.107828	+	0.0783413i
$760$		0			0
$761$	10.5810	−	11.7514i	0.383561	−	0.425987i	−0.520187	−	0.854052i	$-0.674138\pi$
$761$	10.5810	−	11.7514i	0.383561	−	0.425987i	0.903748	+	0.428065i	$0.140805\pi$
$762$	0.312777	+	0.702509i	0.0113307	+	0.0254492i
$763$	−7.16166	+	16.0854i	−0.259269	+	0.582329i
$764$	−11.7537	−	13.0538i	−0.425234	−	0.472270i
$765$		0			0
$766$	−0.827912	−	0.175978i	−0.0299137	−	0.00635835i
$767$	18.0258	−	5.85693i	0.650873	−	0.211481i
$768$	1.71197	+	8.05419i	0.0617754	+	0.290631i
$769$	10.6818	+	18.5015i	0.385197	+	0.667180i	0.991796	−	0.127827i	$-0.0408003\pi$
$769$	10.6818	+	18.5015i	0.385197	+	0.667180i	−0.606600	+	0.795007i	$0.707467\pi$
$770$		0			0
$771$	4.18508	−	12.8804i	0.150722	−	0.463875i
$772$	48.1402	+	5.05974i	1.73260	+	0.182104i
$773$	−4.91963	−	6.77130i	−0.176947	−	0.243547i	0.711326	−	0.702862i	$-0.248095\pi$
$773$	−4.91963	−	6.77130i	−0.176947	−	0.243547i	−0.888273	+	0.459315i	$0.848095\pi$
$774$	1.41262			0.0507755
$775$		0			0
$776$	−2.95347			−0.106023
$777$	6.95237	+	9.56912i	0.249415	+	0.343290i
$778$	0.0347571	+	0.00365312i	0.00124610	+	0.000130971i
$779$	4.79426	−	14.7552i	0.171772	−	0.528661i
$780$		0			0
$781$	28.0886	+	48.6510i	1.00509	+	1.74087i
$782$	−0.177339	−	0.834315i	−0.00634164	−	0.0298351i
$783$	−23.3931	+	7.60088i	−0.836001	+	0.271633i
$784$	−2.86431	−	0.608827i	−0.102297	−	0.0217438i
$785$		0			0
$786$	0.163817	+	0.181937i	0.00584316	+	0.00648949i
$787$	−11.6086	+	26.0734i	−0.413803	+	0.929417i	0.579617	+	0.814889i	$0.303202\pi$
$787$	−11.6086	+	26.0734i	−0.413803	+	0.929417i	−0.993420	+	0.114528i	$0.963465\pi$
$788$	11.5998	+	26.0536i	0.413227	+	0.928122i
$789$	9.99863	−	11.1046i	0.355961	−	0.395334i
$790$		0			0
$791$	−19.9652	−	14.5056i	−0.709880	−	0.515758i
$792$	−3.33794	−	3.00550i	−0.118609	−	0.106796i
$793$	−1.11053	−	2.49429i	−0.0394361	−	0.0885750i
$794$	−0.0745867	−	0.0332082i	−0.00264698	−	0.00117851i
$795$		0			0
$796$	−0.454083	−	4.32031i	−0.0160945	−	0.153129i
$797$	−8.61795	+	40.5442i	−0.305263	+	1.43615i	0.511552	+	0.859252i	$0.329071\pi$
$797$	−8.61795	+	40.5442i	−0.305263	+	1.43615i	−0.816816	+	0.576899i	$0.804263\pi$
$798$	0.495218	−	0.160906i	0.0175305	−	0.00569601i
$799$	−34.1026	+	7.24874i	−1.20646	+	0.256442i
$800$		0			0
$801$	9.81503	−	17.0001i	0.346797	−	0.600670i
$802$	0.706347	+	0.229506i	0.0249420	+	0.00810414i
$803$	47.8214	+	5.02623i	1.68758	+	0.177372i
$804$	6.85754	−	4.98229i	0.241847	−	0.175712i
$805$		0			0
$806$	−0.613287	+	2.27874i	−0.0216021	+	0.0802653i
$807$			8.54396i			0.300762i
$808$	1.91102	+	2.63029i	0.0672295	+	0.0925334i
$809$	−5.64219	+	53.6818i	−0.198369	+	1.88735i	0.214741	+	0.976671i	$0.431109\pi$
$809$	−5.64219	+	53.6818i	−0.198369	+	1.88735i	−0.413109	+	0.910681i	$0.635557\pi$
$810$		0			0
$811$	−1.55637	+	2.69571i	−0.0546514	+	0.0946590i	−0.892057	−	0.451923i	$-0.850738\pi$
$811$	−1.55637	+	2.69571i	−0.0546514	+	0.0946590i	0.837405	+	0.546582i	$0.184071\pi$
$812$	−34.0951	+	19.6848i	−1.19650	+	0.690801i
$813$	−0.307448	−	1.44643i	−0.0107827	−	0.0507285i
$814$	−1.11724	−	3.43851i	−0.0391592	−	0.120520i
$815$		0			0
$816$	1.05387	+	10.0269i	0.0368929	+	0.351012i
$817$	−13.2379	+	11.9194i	−0.463134	+	0.417008i
$818$	0.527178	−	1.18406i	0.0184323	−	0.0413997i
$819$	24.7251	−	11.0083i	0.863963	−	0.384661i
$820$		0			0
$821$	9.48829	+	6.89364i	0.331144	+	0.240590i	0.740916	−	0.671598i	$-0.234392\pi$
$821$	9.48829	+	6.89364i	0.331144	+	0.240590i	−0.409772	+	0.912188i	$0.634392\pi$
$822$	−0.711598	+	0.979431i	−0.0248198	+	0.0341616i
$823$	19.1797	+	17.2695i	0.668562	+	0.601976i	0.931895	−	0.362729i	$-0.118155\pi$
$823$	19.1797	+	17.2695i	0.668562	+	0.601976i	−0.263332	+	0.964705i	$0.584822\pi$
$824$	6.59159	−	2.93476i	0.229629	−	0.102237i
$825$		0			0
$826$	0.838848	+	0.931635i	0.0291872	+	0.0324157i
$827$	54.6117	−	5.73992i	1.89904	−	0.199597i	0.918430	−	0.395584i	$-0.129458\pi$
$827$	54.6117	−	5.73992i	1.89904	−	0.199597i	0.980606	+	0.195987i	$0.0627912\pi$
$828$	−1.91408	+	9.00502i	−0.0665188	+	0.312946i
$829$	5.40196	+	16.6255i	0.187618	+	0.577428i	0.999984	−	0.00571978i	$-0.00182067\pi$
$829$	5.40196	+	16.6255i	0.187618	+	0.577428i	−0.812366	+	0.583148i	$0.801821\pi$
$830$		0			0
$831$	−0.834345	−	1.44513i	−0.0289431	−	0.0501309i
$832$	26.8076	+	15.4774i	0.929387	+	0.536582i
$833$	−3.33139	−	1.08243i	−0.115426	−	0.0375041i
$834$	0.00554688	−	0.0527750i	0.000192073	−	0.00182745i
$835$		0			0
$836$	28.2405			0.976720
$837$	17.2782	+	0.924655i	0.597221	+	0.0319607i
$838$			1.39342i			0.0481348i
$839$	−30.6934	+	22.3001i	−1.05966	+	0.769885i	−0.974025	−	0.226442i	$-0.927291\pi$
$839$	−30.6934	+	22.3001i	−1.05966	+	0.769885i	−0.0856307	+	0.996327i	$0.527291\pi$
$840$		0			0
$841$	10.3969	−	31.9983i	0.358514	−	1.10339i
$842$	−2.93588	−	1.69503i	−0.101177	−	0.0584146i
$843$	10.6959	−	6.17530i	0.368388	−	0.212689i
$844$	24.3005	−	5.16524i	0.836459	−	0.177795i
$845$		0			0
$846$	−2.07448	−	0.440944i	−0.0713220	−	0.0151600i
$847$	11.1513	−	1.17205i	0.383162	−	0.0402720i
$848$	−17.6828	+	15.9216i	−0.607228	+	0.546751i
$849$	1.75011	+	0.779197i	0.0600635	+	0.0267420i
$850$		0			0
$851$	−9.94493	+	11.0450i	−0.340908	+	0.378616i
$852$	9.09429	−	12.5172i	0.311565	−	0.428833i
$853$	16.3423	−	22.4932i	0.559549	−	0.770153i	−0.431720	−	0.902007i	$-0.642093\pi$
$853$	16.3423	−	22.4932i	0.559549	−	0.770153i	0.991269	+	0.131855i	$0.0420933\pi$
$854$	0.120841	−	0.134207i	0.00413508	−	0.00459247i
$855$		0			0
$856$	−4.09967	−	1.82529i	−0.140124	−	0.0623872i
$857$	32.4970	−	29.2605i	1.11008	−	0.999518i	0.110093	−	0.993921i	$-0.464885\pi$
$857$	32.4970	−	29.2605i	1.11008	−	0.999518i	0.999984	−	0.00559710i	$-0.00178162\pi$
$858$	0.903801	−	0.0949933i	0.0308552	−	0.00324302i
$859$	−33.3740	−	7.09386i	−1.13871	−	0.242039i	−0.400292	−	0.916387i	$-0.631091\pi$
$859$	−33.3740	−	7.09386i	−1.13871	−	0.242039i	−0.738414	+	0.674348i	$0.764425\pi$
$860$		0			0
$861$	−5.73123	+	1.21821i	−0.195320	+	0.0415165i
$862$	1.78137	−	1.02848i	0.0606739	−	0.0350301i
$863$	−15.0926	−	8.71374i	−0.513760	−	0.296619i	0.220618	−	0.975360i	$-0.429193\pi$
$863$	−15.0926	−	8.71374i	−0.513760	−	0.296619i	−0.734378	+	0.678741i	$0.762526\pi$
$864$	−1.21095	+	3.72692i	−0.0411974	+	0.126792i
$865$		0			0
$866$	−0.483712	+	0.351438i	−0.0164372	+	0.0119423i
$867$			2.79669i			0.0949805i
$868$	27.3586	−	4.30220i	0.928612	−	0.146026i
$869$	35.2866			1.19702
$870$		0			0
$871$	3.27302	−	31.1407i	0.110902	−	1.05516i
$872$	−2.82746	−	0.918699i	−0.0957500	−	0.0311111i
$873$	16.3719	+	9.45235i	0.554106	+	0.319913i
$874$	0.327142	+	0.566627i	0.0110658	+	0.0191664i
$875$		0			0
$876$	−4.09241	−	12.5951i	−0.138270	−	0.425551i
$877$	−3.87624	+	18.2363i	−0.130891	+	0.615795i	0.862979	+	0.505240i	$0.168596\pi$
$877$	−3.87624	+	18.2363i	−0.130891	+	0.615795i	−0.993870	+	0.110555i	$0.964737\pi$
$878$	2.72863	−	0.286791i	0.0920869	−	0.00967872i
$879$	−0.718790	−	0.798297i	−0.0242442	−	0.0269259i
$880$		0			0
$881$	23.3060	−	10.3765i	0.785199	−	0.349593i	0.0253385	−	0.999679i	$-0.491934\pi$
$881$	23.3060	−	10.3765i	0.785199	−	0.349593i	0.759861	+	0.650086i	$0.225267\pi$
$882$	−0.158348	−	0.142577i	−0.00533186	−	0.00480083i
$883$	−13.7755	+	18.9604i	−0.463583	+	0.638067i	−0.975247	−	0.221118i	$-0.929029\pi$
$883$	−13.7755	+	18.9604i	−0.463583	+	0.638067i	0.511664	+	0.859186i	$0.329029\pi$
$884$	30.3028	+	22.0162i	1.01919	+	0.740486i
$885$		0			0
$886$	1.00520	−	0.447543i	0.0337703	−	0.0150355i
$887$	12.7718	−	28.6858i	0.428834	−	0.963176i	−0.561881	−	0.827218i	$-0.689922\pi$
$887$	12.7718	−	28.6858i	0.428834	−	0.963176i	0.990715	−	0.135958i	$-0.0434112\pi$
$888$	−1.48415	+	1.33634i	−0.0498049	+	0.0448445i
$889$	−3.48480	−	33.1556i	−0.116876	−	1.11200i
$890$		0			0
$891$	7.80119	+	24.0096i	0.261350	+	0.804351i
$892$	3.38635	+	15.9315i	0.113383	+	0.533427i
$893$	23.1609	−	13.3719i	0.775049	−	0.447475i
$894$	−0.00680178	+	0.0117810i	−0.000227486	+	0.000394017i
$895$		0			0
$896$	−0.873341	+	8.30928i	−0.0291763	+	0.277594i
$897$	−2.19586	−	3.02234i	−0.0733176	−	0.100913i
$898$		−	2.34325i		−	0.0781951i
$899$	−27.7708	+	34.2167i	−0.926207	+	1.14119i
$900$		0			0
$901$	−23.0270	+	16.7301i	−0.767141	+	0.557361i
$902$	1.78118	+	0.187209i	0.0593066	+	0.00623338i
$903$	6.39815	+	2.07888i	0.212917	+	0.0691809i
$904$	2.08342	−	3.60858i	0.0692934	−	0.120020i
$905$		0			0
$906$	−0.886398	+	0.188410i	−0.0294486	+	0.00625949i
$907$	−33.0378	+	10.7346i	−1.09700	+	0.356437i	−0.800948	−	0.598734i	$-0.795671\pi$
$907$	−33.0378	+	10.7346i	−1.09700	+	0.356437i	−0.296054	+	0.955171i	$0.595671\pi$
$908$	6.37502	−	29.9921i	0.211562	−	0.995323i
$909$	−2.17530	−	20.6966i	−0.0721501	−	0.686462i
$910$		0			0
$911$	−20.7415	−	9.23472i	−0.687197	−	0.305960i	0.0332723	−	0.999446i	$-0.489407\pi$
$911$	−20.7415	−	9.23472i	−0.687197	−	0.305960i	−0.720470	+	0.693486i	$0.756074\pi$
$912$	−3.14563	−	7.06519i	−0.104162	−	0.233952i
$913$	−29.3502	−	26.4270i	−0.971349	−	0.874607i
$914$	1.52834	+	1.11040i	0.0505530	+	0.0367289i
$915$		0			0
$916$	−29.7272	+	33.0154i	−0.982215	+	1.09086i
$917$	−4.31701	−	9.69616i	−0.142560	−	0.320196i
$918$	−0.629568	+	1.41403i	−0.0207788	+	0.0466700i
$919$	28.2165	+	31.3376i	0.930777	+	1.03373i	0.999349	+	0.0360861i	$0.0114890\pi$
$919$	28.2165	+	31.3376i	0.930777	+	1.03373i	−0.0685720	+	0.997646i	$0.521844\pi$
$920$		0			0
$921$	−6.60722	−	1.40441i	−0.217715	−	0.0462768i
$922$	1.54571	−	0.502233i	0.0509054	−	0.0165402i
$923$	−11.8832	−	55.9059i	−0.391139	−	1.84016i
$924$	−5.33269	−	9.23650i	−0.175433	−	0.303858i
$925$		0			0
$926$	−0.352128	+	1.08374i	−0.0115717	+	0.0356139i
$927$	−45.9316	−	4.82761i	−1.50859	−	0.158559i
$928$	−5.86635	−	8.07434i	−0.192573	−	0.265053i
$929$	10.5493			0.346112			0.173056	−	0.984912i	$-0.444636\pi$
$929$	10.5493			0.346112			0.173056	+	0.984912i	$0.444636\pi$
$930$		0			0
$931$	2.68695			0.0880612
$932$	14.3476	+	19.7478i	0.469971	+	0.646860i
$933$	16.0659	+	1.68860i	0.525975	+	0.0552822i
$934$	0.816492	−	2.51290i	0.0267164	−	0.0822247i
$935$		0			0
$936$	2.28490	+	3.95757i	0.0746844	+	0.129357i
$937$	1.09607	+	5.15659i	0.0358070	+	0.168458i	0.992418	−	0.122910i	$-0.0392227\pi$
$937$	1.09607	+	5.15659i	0.0358070	+	0.168458i	−0.956611	+	0.291369i	$0.905889\pi$
$938$	1.96972	−	0.640001i	0.0643137	−	0.0208968i
$939$	−7.58413	−	1.61206i	−0.247499	−	0.0526075i
$940$		0			0
$941$	−7.45637	−	8.28114i	−0.243071	−	0.269957i	0.609248	−	0.792979i	$-0.291471\pi$
$941$	−7.45637	−	8.28114i	−0.243071	−	0.269957i	−0.852319	+	0.523022i	$0.824805\pi$
$942$	−0.555444	+	1.24755i	−0.0180973	+	0.0406473i
$943$	−2.99456	−	6.72589i	−0.0975162	−	0.219025i
$944$	12.4591	−	13.8372i	0.405509	−	0.450364i
$945$		0			0
$946$	−1.66362	−	1.20869i	−0.0540890	−	0.0392980i
$947$	−32.3125	−	29.0943i	−1.05001	−	0.945437i	−0.0514329	−	0.998676i	$-0.516379\pi$
$947$	−32.3125	−	29.0943i	−1.05001	−	0.945437i	−0.998582	+	0.0532390i	$0.983045\pi$
$948$	−3.95287	−	8.87829i	−0.128383	−	0.288353i
$949$	−44.6920	−	19.8982i	−1.45077	−	0.645922i
$950$		0			0
$951$	0.993308	+	9.45069i	0.0322102	+	0.306460i
$952$	−1.03309	+	4.86033i	−0.0334828	+	0.157524i
$953$	−32.5830	+	10.5869i	−1.05547	+	0.342942i	−0.784812	−	0.619734i	$-0.787241\pi$
$953$	−32.5830	+	10.5869i	−1.05547	+	0.342942i	−0.270656	+	0.962676i	$0.587241\pi$
$954$	−1.69358	+	0.359981i	−0.0548316	+	0.0116548i
$955$		0			0
$956$	−21.7067	+	37.5971i	−0.702044	+	1.21598i
$957$	16.1402	+	5.24426i	0.521738	+	0.169523i
$958$	1.40718	+	0.147900i	0.0454638	+	0.00477844i
$959$	42.4615	−	30.8501i	1.37115	−	0.996201i
$960$		0			0
$961$	26.8810	−	15.4406i	0.867128	−	0.498085i
$962$			3.67837i			0.118596i
$963$	16.8840	+	23.2388i	0.544079	+	0.748861i
$964$	−2.00081	+	19.0365i	−0.0644419	+	0.613123i
$965$		0			0
$966$	0.123549	−	0.213994i	0.00397513	−	0.00688513i
$967$	−42.2912	+	24.4168i	−1.35999	+	0.785192i	−0.989622	−	0.143692i	$-0.954102\pi$
$967$	−42.2912	+	24.4168i	−1.35999	+	0.785192i	−0.370370	+	0.928884i	$0.620769\pi$
$968$	0.393622	+	1.85185i	0.0126515	+	0.0595206i
$969$	−2.85877	−	8.79840i	−0.0918370	−	0.282645i
$970$		0			0
$971$	2.36686	+	22.5192i	0.0759562	+	0.722675i	0.964536	+	0.263952i	$0.0850261\pi$
$971$	2.36686	+	22.5192i	0.0759562	+	0.722675i	−0.888580	+	0.458722i	$0.848307\pi$
$972$	18.9462	−	17.0592i	0.607698	−	0.547174i
$973$	−0.935727	+	2.10168i	−0.0299980	+	0.0673766i
$974$	−2.32865	+	1.03678i	−0.0746149	+	0.0332207i
$975$		0			0
$976$	−2.17002	−	1.57661i	−0.0694606	−	0.0504661i
$977$	6.22372	−	8.56622i	0.199114	−	0.274057i	−0.697771	−	0.716321i	$-0.745825\pi$
$977$	6.22372	−	8.56622i	0.199114	−	0.274057i	0.896885	+	0.442264i	$0.145825\pi$
$978$	−0.517890	−	0.466310i	−0.0165603	−	0.0149109i
$979$	−26.1050	+	11.6227i	−0.834321	+	0.371464i
$980$		0			0
$981$	12.7333	+	14.1417i	0.406542	+	0.451510i
$982$	0.338327	−	0.0355596i	0.0107965	−	0.00113475i
$983$	−3.36657	+	15.8385i	−0.107377	+	0.505169i	0.891284	+	0.453445i	$0.149805\pi$
$983$	−3.36657	+	15.8385i	−0.107377	+	0.505169i	−0.998661	+	0.0517245i	$0.983528\pi$
$984$	−0.305714	−	0.940892i	−0.00974582	−	0.0299946i
$985$		0			0
$986$	−1.97108	−	3.41401i	−0.0627720	−	0.108724i
$987$	−8.74699	−	5.05008i	−0.278420	−	0.160746i
$988$	−27.3257	−	8.87867i	−0.869347	−	0.282468i
$989$	−0.883606	+	8.40695i	−0.0280970	+	0.267326i
$990$		0			0
$991$	−11.7448			−0.373085			−0.186542	−	0.982447i	$-0.559728\pi$
$991$	−11.7448			−0.373085			−0.186542	+	0.982447i	$0.559728\pi$
$992$	1.80962	+	6.78358i	0.0574556	+	0.215379i
$993$		−	3.31278i		−	0.105128i
$994$	3.05841	−	2.22206i	0.0970068	−	0.0704796i
$995$		0			0
$996$	−3.36131	+	10.3451i	−0.106507	+	0.327796i
$997$	−34.8727	−	20.1338i	−1.10443	−	0.637643i	−0.167050	−	0.985948i	$-0.553424\pi$
$997$	−34.8727	−	20.1338i	−1.10443	−	0.637643i	−0.937381	+	0.348305i	$0.886757\pi$
$998$	−1.46642	+	0.846639i	−0.0464188	+	0.0267999i
$999$	26.3814	−	5.60755i	0.834672	−	0.177415i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.ck.c.524.6		80
5.2	odd	4		155.2.q.a.121.3	yes	40
5.3	odd	4		775.2.bl.c.276.3		40
5.4	even	2	inner	775.2.ck.c.524.5		80
31.10	even	15	inner	775.2.ck.c.599.5		80
155.17	even	60		4805.2.a.y.1.12		20
155.72	odd	60		155.2.q.a.41.3	✓	40
155.103	odd	60		775.2.bl.c.351.3		40
155.107	odd	60		4805.2.a.x.1.12		20
155.134	even	30	inner	775.2.ck.c.599.6		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.q.a.41.3	✓	40	155.72	odd	60
155.2.q.a.121.3	yes	40	5.2	odd	4
775.2.bl.c.276.3		40	5.3	odd	4
775.2.bl.c.351.3		40	155.103	odd	60
775.2.ck.c.524.5		80	5.4	even	2	inner
775.2.ck.c.524.6		80	1.1	even	1	trivial
775.2.ck.c.599.5		80	31.10	even	15	inner
775.2.ck.c.599.6		80	155.134	even	30	inner
4805.2.a.x.1.12		20	155.107	odd	60
4805.2.a.y.1.12		20	155.17	even	60

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.ck (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0622295 + 0.0856516i) q^{2} +(0.541931 + 0.0569592i) q^{3} +(0.614570 - 1.89145i) q^{4} +(0.0288454 + 0.0499618i) q^{6} +(-0.520005 - 2.44643i) q^{7} +(0.401629 - 0.130497i) q^{8} +(-2.64400 - 0.561999i) q^{9} +(2.63294 + 2.92417i) q^{11} +(0.440790 - 0.990031i) q^{12} +(-1.62830 - 3.65723i) q^{13} +(0.177181 - 0.196780i) q^{14} +(-3.18176 - 2.31168i) q^{16} +(-3.49613 - 3.14793i) q^{17} +(-0.116399 - 0.261436i) q^{18} +(3.29674 + 1.46780i) q^{19} +(-0.142460 - 1.35542i) q^{21} +(-0.0866136 + 0.407485i) q^{22} +(1.62870 - 0.529196i) q^{23} +(0.225088 - 0.0478440i) q^{24} +(0.211919 - 0.367054i) q^{26} +(-2.95559 - 0.960329i) q^{27} +(-4.94689 - 0.519939i) q^{28} +(6.40326 - 4.65224i) q^{29} +(-5.37964 + 1.43510i) q^{31} -1.26097i q^{32} +(1.26031 + 1.73467i) q^{33} +(0.0520626 - 0.495343i) q^{34} +(-2.68792 + 4.65561i) q^{36} +(-7.51600 + 4.33937i) q^{37} +(0.0794349 + 0.373712i) q^{38} +(-0.674114 - 2.07471i) q^{39} +(-0.449386 - 4.27562i) q^{41} +(0.107228 - 0.0965488i) q^{42} +(-2.00772 + 4.50941i) q^{43} +(7.14906 - 3.18297i) q^{44} +(0.146680 + 0.106569i) q^{46} +(4.35601 - 5.99553i) q^{47} +(-1.59262 - 1.43400i) q^{48} +(0.680198 - 0.302844i) q^{49} +(-1.71535 - 1.90509i) q^{51} +(-7.91818 + 0.832234i) q^{52} +(1.25790 - 5.91794i) q^{53} +(-0.101671 - 0.312912i) q^{54} +(-0.528102 - 0.914699i) q^{56} +(1.70300 + 0.983227i) q^{57} +(0.796943 + 0.258943i) q^{58} +(-0.494881 + 4.70847i) q^{59} +0.682018 q^{61} +(-0.457691 - 0.371469i) q^{62} +6.76060i q^{63} +(-6.25552 + 4.54490i) q^{64} +(-0.0701486 + 0.215895i) q^{66} +(6.77365 + 3.91077i) q^{67} +(-8.10277 + 4.67814i) q^{68} +(0.912784 - 0.194018i) q^{69} +(13.9648 + 2.96832i) q^{71} +(-1.13525 + 0.119319i) q^{72} +(9.08138 - 8.17691i) q^{73} +(-0.839391 - 0.373721i) q^{74} +(4.80236 - 5.33356i) q^{76} +(5.78464 - 7.96188i) q^{77} +(0.135752 - 0.186847i) q^{78} +(6.00055 - 6.66429i) q^{79} +(5.86110 + 2.60953i) q^{81} +(0.338249 - 0.304561i) q^{82} +(-9.98211 + 1.04916i) q^{83} +(-2.65126 - 0.563542i) q^{84} +(-0.511178 + 0.108654i) q^{86} +(3.73511 - 2.15647i) q^{87} +(1.43906 + 0.830842i) q^{88} +(-2.24413 + 6.90671i) q^{89} +(-8.10043 + 5.88531i) q^{91} -3.40584i q^{92} +(-2.99713 + 0.471305i) q^{93} +0.784599 q^{94} +(0.0718241 - 0.683361i) q^{96} +(-6.65149 - 2.16120i) q^{97} +(0.0682674 + 0.0394142i) q^{98} +(-5.31810 - 9.21121i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 8 q^{6} - 4 q^{9} - 56 q^{11} + 12 q^{14} + 16 q^{16} + 26 q^{19} - 16 q^{21} + 164 q^{24} + 64 q^{26} - 84 q^{29} - 20 q^{31} - 64 q^{34} - 26 q^{36} - 74 q^{39} + 72 q^{41} + 112 q^{44}+ \cdots - 106 q^{99}+O(q^{100}) \) 80 * q + 20 * q^4 + 8 * q^6 - 4 * q^9 - 56 * q^11 + 12 * q^14 + 16 * q^16 + 26 * q^19 - 16 * q^21 + 164 * q^24 + 64 * q^26 - 84 * q^29 - 20 * q^31 - 64 * q^34 - 26 * q^36 - 74 * q^39 + 72 * q^41 + 112 * q^44 + 36 * q^46 + 62 * q^49 - 4 * q^51 - 44 * q^54 + 18 * q^56 + 2 * q^59 - 200 * q^61 - 34 * q^64 - 80 * q^66 - 16 * q^69 - 4 * q^71 + 4 * q^74 + 4 * q^76 + 134 * q^79 - 166 * q^81 - 52 * q^84 - 10 * q^86 - 40 * q^89 + 38 * q^91 - 260 * q^94 + 92 * q^96 - 106 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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