LMFDB - Embedded newform 775.2.ck.c.524.5

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			524.5
Character	$\chi$	$=$	775.524
Dual form			775.2.ck.c.599.5

$q$-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	0.786449	−	0.617656i	$-0.211917\pi$
$2$	−0.0622295	−	0.0856516i	−0.0440029	−	0.0605648i	−0.830452	+	0.557091i	$0.811917\pi$
$3$	−0.541931	−	0.0569592i	−0.312884	−	0.0328854i	−0.0532148	−	0.998583i	$-0.516947\pi$
$3$	−0.541931	−	0.0569592i	−0.312884	−	0.0328854i	−0.259669	+	0.965698i	$0.583613\pi$
$4$	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	$0.0900397\pi$
$7$	0.520005	+	2.44643i	0.196543	+	0.924664i	−0.763715	+	0.645553i	$0.776627\pi$
$8$	−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	$0.0540106\pi$
$13$	1.62830	+	3.65723i	0.451610	+	1.01433i	−0.534029	+	0.845466i	$0.679323\pi$
$14$	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	0.973521	−	0.228599i	$-0.0734144\pi$
$17$	3.49613	+	3.14793i	0.847935	+	0.763484i	−0.125586	+	0.992083i	$0.540081\pi$
$18$	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	−0.473855	−	0.880603i	$-0.657138\pi$
$23$	−1.62870	+	0.529196i	−0.339607	+	0.110345i	0.134248	+	0.990948i	$0.457138\pi$
$24$	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	0.267427	−	0.963578i	$-0.413827\pi$
$37$	7.51600	−	4.33937i	1.23562	−	0.713387i	0.968197	+	0.250191i	$0.0804934\pi$
$38$	−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	−0.693281	−	0.720667i	$-0.743836\pi$
$43$	2.00772	−	4.50941i	0.306174	−	0.687679i	0.999456	+	0.0329881i	$0.0105023\pi$
$44$	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	−0.998359	−	0.0572628i	$-0.981763\pi$
$47$	−4.35601	+	5.99553i	−0.635389	+	0.874538i	0.362970	+	0.931801i	$0.381763\pi$
$48$	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	$0.203069\pi$
$53$	−1.25790	+	5.91794i	−0.172786	+	0.812892i	−0.976097	+	0.217333i	$0.930264\pi$
$54$	−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	0.0254744	−	0.999675i	$-0.491890\pi$
$67$	−6.77365	−	3.91077i	−0.827533	−	0.477776i	−0.853007	+	0.521899i	$0.825224\pi$
$68$	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	−0.999162	−	0.0409320i	$-0.986967\pi$
$73$	−9.08138	+	8.17691i	−1.06290	+	0.957035i	−0.0637331	+	0.997967i	$0.520301\pi$
$74$	−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	0.460600	−	0.887608i	$-0.347634\pi$
$83$	9.98211	−	1.04916i	1.09568	−	0.115160i	0.635079	+	0.772447i	$0.280968\pi$
$84$	−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	0.626561	−	0.779372i	$-0.284462\pi$
$97$	6.65149	+	2.16120i	0.675357	+	0.219437i	0.0487954	+	0.998809i	$0.484462\pi$
$98$	−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	−0.893585	−	0.448895i	$-0.851818\pi$
$103$	−16.9924	+	1.78597i	−1.67431	+	0.175977i	−0.780727	+	0.624872i	$0.785151\pi$
$104$	−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	0.955835	−	0.293905i	$-0.0949550\pi$
$107$	7.89720	+	7.11067i	0.763451	+	0.687415i	−0.192383	+	0.981320i	$0.561622\pi$
$108$	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	−0.937601	−	0.347714i	$-0.886958\pi$
$113$	−7.33264	+	6.60234i	−0.689797	+	0.621096i	0.247804	+	0.968810i	$0.420291\pi$
$114$	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	−0.503872	−	0.863778i	$-0.668092\pi$
$127$	−13.2565	−	1.39331i	−1.17632	−	0.123637i	−0.672451	+	0.740142i	$0.734758\pi$
$128$	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	$-0.779482\pi$
$137$	−8.53537	−	19.1707i	−0.729225	−	1.63787i	0.0402490	−	0.999190i	$-0.487185\pi$
$138$	−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	$-0.806467\pi$
$157$	−13.9136	−	19.1504i	−1.11042	−	1.52837i	−0.289633	−	0.957138i	$-0.593533\pi$
$158$	−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	0.177674	−	0.984089i	$-0.443143\pi$
$163$	11.4885	−	3.73284i	0.899848	−	0.292378i	0.722174	+	0.691711i	$0.243143\pi$
$164$	−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	−0.924734	−	0.380615i	$-0.875712\pi$
$167$	−0.298697	+	0.670884i	−0.0231139	+	0.0519146i	0.901620	+	0.432530i	$0.142379\pi$
$168$	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	0.780242	−	0.625477i	$-0.215096\pi$
$173$	−2.71821	−	6.10521i	−0.206662	−	0.464170i	−0.986904	+	0.161307i	$0.948429\pi$
$174$	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	$-0.726880\pi$
$193$	−5.06038	−	23.8072i	−0.364254	−	1.71368i	0.289674	−	0.957125i	$-0.406453\pi$
$194$	−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	−0.195606	−	0.980683i	$-0.562667\pi$
$197$	10.6567	−	9.59532i	0.759258	−	0.683639i	0.954864	+	0.297044i	$0.0960008\pi$
$198$	−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	−0.243363	−	0.969935i	$-0.578251\pi$
$223$	7.09242	−	4.09481i	0.474944	−	0.274209i	0.718307	+	0.695726i	$0.244917\pi$
$224$	−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	−0.598655	−	0.801007i	$-0.704298\pi$
$227$	−15.3330	+	1.61157i	−1.01769	+	0.106963i	−0.419034	+	0.907971i	$0.637631\pi$
$228$	−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	−0.504446	−	0.863443i	$-0.668303\pi$
$233$	7.21423	−	9.92954i	0.472620	−	0.650506i	0.977066	+	0.212938i	$0.0683031\pi$
$234$	−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	$0.349001\pi$
$257$	−5.16739	+	24.3107i	−0.322333	+	1.51646i	−0.779116	+	0.626879i	$0.784332\pi$
$258$	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	$0.520673\pi$
$263$	−16.1183	+	22.1849i	−0.993897	+	1.36798i	−0.928996	+	0.370089i	$0.879327\pi$
$264$	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	0.859661	−	0.510865i	$-0.170675\pi$
$277$	1.79997	+	2.47744i	0.108150	+	0.148855i	−0.751511	+	0.659720i	$0.770675\pi$
$278$			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	0.207948	−	0.978140i	$-0.433322\pi$
$283$	−3.34357	−	1.08639i	−0.198755	−	0.0645794i	−0.406703	+	0.913561i	$0.633322\pi$
$284$	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	0.710813	−	0.703381i	$-0.248327\pi$
$293$	1.46499	+	1.31908i	0.0855857	+	0.0770617i	−0.625227	+	0.780443i	$0.714994\pi$
$294$	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	0.449573	−	0.893243i	$-0.351576\pi$
$307$	12.3282	+	1.29574i	0.703607	+	0.0739521i	0.254033	+	0.967195i	$0.418243\pi$
$308$	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	0.495634	−	0.868531i	$-0.334936\pi$
$313$	14.1510	+	1.48733i	0.799860	+	0.0840687i	0.304226	+	0.952600i	$0.401602\pi$
$314$	−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	$-0.903761\pi$
$317$	−3.62576	−	17.0578i	−0.203643	−	0.958064i	0.750998	−	0.660304i	$-0.229573\pi$
$318$	−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	0.161403	−	0.986889i	$-0.448398\pi$
$337$	−5.28877	−	1.71843i	−0.288098	−	0.0936086i	−0.449501	+	0.893280i	$0.648398\pi$
$338$	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	−0.380841	−	0.924641i	$-0.624365\pi$
$347$	4.27514	−	2.46825i	0.229501	−	0.132503i	0.610342	+	0.792138i	$0.291032\pi$
$348$	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	−0.849480	−	0.527621i	$-0.823084\pi$
$353$	2.08610	−	4.68547i	0.111032	−	0.249382i	0.960512	+	0.278239i	$0.0897507\pi$
$354$	−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	0.846816	−	0.531885i	$-0.178516\pi$
$367$	15.5097	+	8.95451i	0.809598	+	0.467422i	−0.0372182	+	0.999307i	$0.511850\pi$
$368$	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	$0.129131\pi$
$373$			15.2436i			0.789285i	−0.918835	+	0.394642i	$0.870869\pi$
$374$	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	−0.503233	−	0.864151i	$-0.667856\pi$
$383$	5.94122	−	5.34950i	0.303582	−	0.273347i	0.806815	+	0.590804i	$0.201189\pi$
$384$	−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	−0.483147	−	0.875539i	$-0.660506\pi$
$397$	0.667858	−	0.385588i	0.0335188	−	0.0193521i	0.516666	+	0.856187i	$0.327173\pi$
$398$	−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	$-0.956672\pi$
$433$		−	5.64744i		−	0.271399i	0.990750	−	0.135699i	$-0.0433281\pi$
$434$	−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	$0.146077\pi$
$443$	−2.16084	+	10.1659i	−0.102665	+	0.482999i	−0.999199	+	0.0400242i	$0.987257\pi$
$444$	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	−0.677738	−	0.735303i	$-0.737040\pi$
$457$	−16.9704	+	5.51400i	−0.793840	+	0.257934i	−0.116101	+	0.993237i	$0.537040\pi$
$458$	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	0.636298	−	0.771443i	$-0.280465\pi$
$463$	−6.32644	−	8.70760i	−0.294015	−	0.404677i	−0.930313	+	0.366767i	$0.880465\pi$
$464$	−31.1282			−1.44509
$465$		0			0
$466$	−1.29942			−0.0601944
$467$	14.6693	+	20.1906i	0.678816	+	0.934309i	0.999919	−	0.0127347i	$-0.00405371\pi$
$467$	14.6693	+	20.1906i	0.678816	+	0.934309i	−0.321103	+	0.947044i	$0.604054\pi$
$468$	−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	$-0.749669\pi$
$487$	5.00583	−	23.5506i	0.226836	−	1.06718i	0.933208	−	0.359337i	$-0.116997\pi$
$488$	−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	0.989018	−	0.147794i	$-0.0472173\pi$
$503$	0.569481	+	2.67920i	0.0253919	+	0.119459i	−0.963626	+	0.267253i	$0.913884\pi$
$504$	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	0.00776416	−	0.999970i	$-0.497529\pi$
$523$	−13.1206	−	4.26313i	−0.573722	−	0.186414i	−0.581486	+	0.813556i	$0.697529\pi$
$524$	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	−0.443341	−	0.896353i	$-0.646207\pi$
$547$	9.39639	−	8.46055i	0.401761	−	0.361747i	0.845101	+	0.534606i	$0.179540\pi$
$548$	−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	$-0.797733\pi$
$557$		−	28.0158i		−	1.18707i	0.804810	−	0.593533i	$-0.202267\pi$
$558$	−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	0.961319	−	0.275439i	$-0.0888231\pi$
$563$	28.5548	+	16.4861i	1.20344	+	0.694807i	0.242122	+	0.970246i	$0.422156\pi$
$564$	−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	$-0.464608\pi$
$577$	18.6226	−	41.8270i	0.775269	−	1.74128i	0.664310	−	0.747457i	$-0.268725\pi$
$578$	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	0.959509	−	0.281679i	$-0.0908914\pi$
$587$	9.57279	+	13.1758i	0.395111	+	0.543824i	−0.564397	+	0.825503i	$0.690891\pi$
$588$			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	0.565579	−	0.824694i	$-0.308653\pi$
$593$	13.1109	+	4.25997i	0.538398	+	0.174936i	−0.0271805	+	0.999631i	$0.508653\pi$
$594$	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	$-0.979578\pi$
$607$	−9.30883	−	20.9080i	−0.377834	−	0.848629i	0.620109	−	0.784516i	$-0.287088\pi$
$608$	−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	$-0.705042\pi$
$613$	−9.33773	−	43.9305i	−0.377147	−	1.77434i	0.223378	−	0.974732i	$-0.428292\pi$
$614$	−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	−0.479372	−	0.877612i	$-0.659135\pi$
$617$	−28.0868	−	2.95205i	−1.13073	−	0.118845i	−0.651362	+	0.758767i	$0.725802\pi$
$618$	−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	−0.405691	−	0.914010i	$-0.632969\pi$
$643$	−4.98678	+	1.62030i	−0.196659	+	0.0638985i	0.209031	+	0.977909i	$0.432969\pi$
$644$	−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	−0.354580	−	0.935026i	$-0.615376\pi$
$647$	−30.2954	−	9.84357i	−1.19103	−	0.386991i	−0.836455	+	0.548035i	$0.815376\pi$
$648$	−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	$-0.972985\pi$
$653$	−19.6539	−	27.0512i	−0.769115	−	1.05860i	0.227285	−	0.973828i	$-0.427015\pi$
$654$	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	−0.973965	−	0.226700i	$-0.927206\pi$
$673$	0.207627	−	0.976808i	0.00800343	−	0.0376532i	0.981968	+	0.189047i	$0.0605397\pi$
$674$	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	−0.194104	−	0.980981i	$-0.562180\pi$
$677$	−29.6804	−	17.1360i	−1.14071	−	0.658589i	−0.946606	+	0.322392i	$0.895513\pi$
$678$	−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	$0.0277383\pi$
$683$			4.54905i			0.174064i	−0.996205	+	0.0870322i	$0.972262\pi$
$684$	−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	$0.00727386\pi$
$727$	30.3863	+	27.3599i	1.12696	+	1.01472i	0.127226	+	0.991874i	$0.459393\pi$
$728$	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	−0.743950	−	0.668235i	$-0.767050\pi$
$733$	−4.25440	+	3.83068i	−0.157140	+	0.141489i	0.586810	+	0.809724i	$0.300383\pi$
$734$	−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	$-0.896671\pi$
$743$		−	17.3877i		−	0.637893i	0.947773	−	0.318947i	$-0.103329\pi$
$744$	−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	$0.210516\pi$
$757$	19.7421	+	44.3415i	0.717539	+	1.61162i	−0.0716213	+	0.997432i	$0.522817\pi$
$758$	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	0.888273	−	0.459315i	$-0.151905\pi$
$773$	4.91963	+	6.77130i	0.176947	+	0.243547i	−0.711326	+	0.702862i	$0.751905\pi$
$774$	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	$-0.696798\pi$
$787$	11.6086	−	26.0734i	0.413803	−	0.929417i	0.993420	−	0.114528i	$-0.0365355\pi$
$788$	−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	$-0.670929\pi$
$797$	8.61795	−	40.5442i	0.305263	−	1.43615i	0.816816	−	0.576899i	$-0.195737\pi$
$798$	−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	0.263332	−	0.964705i	$-0.415178\pi$
$823$	−19.1797	−	17.2695i	−0.668562	−	0.601976i	−0.931895	+	0.362729i	$0.881845\pi$
$824$	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	−0.980606	−	0.195987i	$-0.937209\pi$
$827$	−54.6117	+	5.73992i	−1.89904	+	0.199597i	−0.918430	+	0.395584i	$0.870542\pi$
$828$	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	−0.991269	−	0.131855i	$-0.957907\pi$
$853$	−16.3423	+	22.4932i	−0.559549	+	0.770153i	0.431720	+	0.902007i	$0.357907\pi$
$854$	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	$0.535115\pi$
$857$	−32.4970	+	29.2605i	−1.11008	+	0.999518i	−0.999984	+	0.00559710i	$0.998218\pi$
$858$	−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	0.734378	−	0.678741i	$-0.237474\pi$
$863$	15.0926	+	8.71374i	0.513760	+	0.296619i	−0.220618	+	0.975360i	$0.570807\pi$
$864$	−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	$-0.831404\pi$
$877$	3.87624	−	18.2363i	0.130891	−	0.615795i	0.993870	−	0.110555i	$-0.0352628\pi$
$878$	−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	−0.511664	−	0.859186i	$-0.670971\pi$
$883$	13.7755	−	18.9604i	0.463583	−	0.638067i	0.975247	+	0.221118i	$0.0709707\pi$
$884$	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	$0.310078\pi$
$887$	−12.7718	+	28.6858i	−0.428834	+	0.963176i	−0.990715	+	0.135958i	$0.956589\pi$
$888$	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	0.296054	−	0.955171i	$-0.404329\pi$
$907$	33.0378	−	10.7346i	1.09700	−	0.356437i	0.800948	+	0.598734i	$0.204329\pi$
$908$	−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	0.956611	−	0.291369i	$-0.0941106\pi$
$937$	−1.09607	−	5.15659i	−0.0358070	−	0.168458i	−0.992418	+	0.122910i	$0.960777\pi$
$938$	−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	0.998582	−	0.0532390i	$-0.0169545\pi$
$947$	32.3125	+	29.0943i	1.05001	+	0.945437i	0.0514329	+	0.998676i	$0.483621\pi$
$948$	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	0.270656	−	0.962676i	$-0.412759\pi$
$953$	32.5830	−	10.5869i	1.05547	−	0.342942i	0.784812	+	0.619734i	$0.212759\pi$
$954$	−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	0.370370	−	0.928884i	$-0.379231\pi$
$967$	42.2912	−	24.4168i	1.35999	−	0.785192i	0.989622	+	0.143692i	$0.0458976\pi$
$968$	−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	−0.896885	−	0.442264i	$-0.854175\pi$
$977$	−6.22372	+	8.56622i	−0.199114	+	0.274057i	0.697771	+	0.716321i	$0.254175\pi$
$978$	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	$-0.850195\pi$
$983$	3.36657	−	15.8385i	0.107377	−	0.505169i	0.998661	−	0.0517245i	$-0.0164718\pi$
$984$	−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	0.937381	−	0.348305i	$-0.113243\pi$
$997$	34.8727	+	20.1338i	1.10443	+	0.637643i	0.167050	+	0.985948i	$0.446576\pi$
$998$	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.524.5		80
5.2	odd	4		775.2.bl.c.276.3		40
5.3	odd	4		155.2.q.a.121.3	yes	40
5.4	even	2	inner	775.2.ck.c.524.6		80
31.10	even	15	inner	775.2.ck.c.599.6		80
155.48	even	60		4805.2.a.y.1.12		20
155.72	odd	60		775.2.bl.c.351.3		40
155.103	odd	60		155.2.q.a.41.3	✓	40
155.134	even	30	inner	775.2.ck.c.599.5		80
155.138	odd	60		4805.2.a.x.1.12		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.q.a.41.3	✓	40	155.103	odd	60
155.2.q.a.121.3	yes	40	5.3	odd	4
775.2.bl.c.276.3		40	5.2	odd	4
775.2.bl.c.351.3		40	155.72	odd	60
775.2.ck.c.524.5		80	1.1	even	1	trivial
775.2.ck.c.524.6		80	5.4	even	2	inner
775.2.ck.c.599.5		80	155.134	even	30	inner
775.2.ck.c.599.6		80	31.10	even	15	inner
4805.2.a.x.1.12		20	155.138	odd	60
4805.2.a.y.1.12		20	155.48	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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