LMFDB - Embedded newform 775.2.bl.c.276.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [775,2,Mod(51,775)] 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("775.51"); 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([0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.bl (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,2,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			276.3
Character	$\chi$	$=$	775.276
Dual form			775.2.bl.c.351.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0856516 - 0.0622295i) q^{2} +(-0.0569592 + 0.541931i) q^{3} +(-0.614570 + 1.89145i) q^{4} +(0.0288454 + 0.0499618i) q^{6} +(-2.44643 + 0.520005i) q^{7} +(0.130497 + 0.401629i) q^{8} +(2.64400 + 0.561999i) q^{9} +(2.63294 + 2.92417i) q^{11} +(-0.990031 - 0.440790i) q^{12} +(3.65723 - 1.62830i) q^{13} +(-0.177181 + 0.196780i) q^{14} +(-3.18176 - 2.31168i) q^{16} +(-3.14793 + 3.49613i) q^{17} +(0.261436 - 0.116399i) q^{18} +(-3.29674 - 1.46780i) q^{19} +(-0.142460 - 1.35542i) q^{21} +(0.407485 + 0.0866136i) q^{22} +(0.529196 + 1.62870i) q^{23} +(-0.225088 + 0.0478440i) q^{24} +(0.211919 - 0.367054i) q^{26} +(-0.960329 + 2.95559i) q^{27} +(0.519939 - 4.94689i) q^{28} +(-6.40326 + 4.65224i) q^{29} +(-5.37964 + 1.43510i) q^{31} -1.26097 q^{32} +(-1.73467 + 1.26031i) q^{33} +(-0.0520626 + 0.495343i) q^{34} +(-2.68792 + 4.65561i) q^{36} +(4.33937 + 7.51600i) q^{37} +(-0.373712 + 0.0794349i) q^{38} +(0.674114 + 2.07471i) q^{39} +(-0.449386 - 4.27562i) q^{41} +(-0.0965488 - 0.107228i) q^{42} +(-4.50941 - 2.00772i) q^{43} +(-7.14906 + 3.18297i) q^{44} +(0.146680 + 0.106569i) q^{46} +(-5.99553 - 4.35601i) q^{47} +(1.43400 - 1.59262i) q^{48} +(-0.680198 + 0.302844i) q^{49} +(-1.71535 - 1.90509i) q^{51} +(0.832234 + 7.91818i) q^{52} +(5.91794 + 1.25790i) q^{53} +(0.101671 + 0.312912i) q^{54} +(-0.528102 - 0.914699i) q^{56} +(0.983227 - 1.70300i) q^{57} +(-0.258943 + 0.796943i) q^{58} +(0.494881 - 4.70847i) q^{59} +0.682018 q^{61} +(-0.371469 + 0.457691i) q^{62} -6.76060 q^{63} +(6.25552 - 4.54490i) q^{64} +(-0.0701486 + 0.215895i) q^{66} +(3.91077 - 6.77365i) q^{67} +(-4.67814 - 8.10277i) q^{68} +(-0.912784 + 0.194018i) q^{69} +(13.9648 + 2.96832i) q^{71} +(0.119319 + 1.13525i) q^{72} +(8.17691 + 9.08138i) q^{73} +(0.839391 + 0.373721i) q^{74} +(4.80236 - 5.33356i) q^{76} +(-7.96188 - 5.78464i) q^{77} +(0.186847 + 0.135752i) q^{78} +(-6.00055 + 6.66429i) q^{79} +(5.86110 + 2.60953i) q^{81} +(-0.304561 - 0.338249i) q^{82} +(-1.04916 - 9.98211i) q^{83} +(2.65126 + 0.563542i) q^{84} +(-0.511178 + 0.108654i) q^{86} +(-2.15647 - 3.73511i) q^{87} +(-0.830842 + 1.43906i) q^{88} +(2.24413 - 6.90671i) q^{89} +(-8.10043 + 5.88531i) q^{91} -3.40584 q^{92} +(-0.471305 - 2.99713i) q^{93} -0.784599 q^{94} +(0.0718241 - 0.683361i) q^{96} +(-2.16120 + 6.65149i) q^{97} +(-0.0394142 + 0.0682674i) q^{98} +(5.31810 + 9.21121i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 2 q^{2} + q^{3} - 10 q^{4} + 4 q^{6} - 4 q^{7} - 13 q^{8} + 2 q^{9} - 28 q^{11} + 13 q^{12} + 6 q^{13} - 6 q^{14} + 8 q^{16} + 10 q^{17} + 27 q^{18} - 13 q^{19} - 8 q^{21} - 2 q^{22} + 12 q^{23}+ \cdots + 53 q^{99}+O(q^{100}) $ 40 * q + 2 * q^2 + q^3 - 10 * q^4 + 4 * q^6 - 4 * q^7 - 13 * q^8 + 2 * q^9 - 28 * q^11 + 13 * q^12 + 6 * q^13 - 6 * q^14 + 8 * q^16 + 10 * q^17 + 27 * q^18 - 13 * q^19 - 8 * q^21 - 2 * q^22 + 12 * q^23 - 82 * q^24 + 32 * q^26 + q^27 - 22 * q^28 + 42 * q^29 - 10 * q^31 - 4 * q^32 - 13 * q^33 + 32 * q^34 - 13 * q^36 - 12 * q^37 - 30 * q^38 + 37 * q^39 + 36 * q^41 + 64 * q^42 + 78 * q^43 - 56 * q^44 + 18 * q^46 + 4 * q^47 + 41 * q^48 - 31 * q^49 - 2 * q^51 - 49 * q^52 + 11 * q^53 + 22 * q^54 + 9 * q^56 - 38 * q^57 - 11 * q^58 - q^59 - 100 * q^61 + 35 * q^62 - 110 * q^63 + 17 * q^64 - 40 * q^66 - 30 * q^67 + 34 * q^68 + 8 * q^69 - 2 * q^71 - 151 * q^72 + 23 * q^73 - 2 * q^74 + 2 * q^76 - 36 * q^77 + 2 * q^78 - 67 * q^79 - 83 * q^81 - 2 * q^82 + 26 * q^84 - 5 * q^86 + 46 * q^87 - 70 * q^88 + 20 * q^89 + 19 * q^91 + 10 * q^92 + 67 * q^93 + 130 * q^94 + 46 * q^96 + 18 * q^97 + 65 * q^98 + 53 * 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 $

$2$	0.0856516	−	0.0622295i	0.0605648	−	0.0440029i	−0.557091	−	0.830452i	$-0.688083\pi$
$2$	0.0856516	−	0.0622295i	0.0605648	−	0.0440029i	0.617656	+	0.786449i	$0.288083\pi$
$3$	−0.0569592	+	0.541931i	−0.0328854	+	0.312884i	0.965698	+	0.259669i	$0.0836135\pi$
$3$	−0.0569592	+	0.541931i	−0.0328854	+	0.312884i	−0.998583	+	0.0532148i	$0.983053\pi$
$4$	−0.614570	+	1.89145i	−0.307285	+	0.945726i
$5$		0			0
$5$		0			0
$6$	0.0288454	+	0.0499618i	0.0117761	+	0.0203968i
$7$	−2.44643	+	0.520005i	−0.924664	+	0.196543i	−0.645553	−	0.763715i	$-0.723373\pi$
$7$	−2.44643	+	0.520005i	−0.924664	+	0.196543i	−0.279111	+	0.960259i	$0.590040\pi$
$8$	0.130497	+	0.401629i	0.0461378	+	0.141997i
$9$	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	$0.564530\pi$
$12$	−0.990031	−	0.440790i	−0.285797	−	0.127245i
$13$	3.65723	−	1.62830i	1.01433	−	0.451610i	0.168866	−	0.985639i	$-0.445989\pi$
$13$	3.65723	−	1.62830i	1.01433	−	0.451610i	0.845466	+	0.534029i	$0.179323\pi$
$14$	−0.177181	+	0.196780i	−0.0473536	+	0.0525915i
$15$		0			0
$16$	−3.18176	−	2.31168i	−0.795440	−	0.577921i
$17$	−3.14793	+	3.49613i	−0.763484	+	0.847935i	−0.992083	−	0.125586i	$-0.959919\pi$
$17$	−3.14793	+	3.49613i	−0.763484	+	0.847935i	0.228599	+	0.973521i	$0.426586\pi$
$18$	0.261436	−	0.116399i	0.0616210	−	0.0274354i
$19$	−3.29674	−	1.46780i	−0.756324	−	0.336737i	−0.00790965	−	0.999969i	$-0.502518\pi$
$19$	−3.29674	−	1.46780i	−0.756324	−	0.336737i	−0.748414	+	0.663232i	$0.769184\pi$
$20$		0			0
$21$	−0.142460	−	1.35542i	−0.0310873	−	0.295776i
$22$	0.407485	+	0.0866136i	0.0868761	+	0.0184661i
$23$	0.529196	+	1.62870i	0.110345	+	0.339607i	0.990948	−	0.134248i	$-0.0428619\pi$
$23$	0.529196	+	1.62870i	0.110345	+	0.339607i	−0.880603	+	0.473855i	$0.842862\pi$
$24$	−0.225088	+	0.0478440i	−0.0459460	+	0.00976611i
$25$		0			0
$26$	0.211919	−	0.367054i	0.0415607	−	0.0719852i
$27$	−0.960329	+	2.95559i	−0.184815	+	0.568804i
$28$	0.519939	−	4.94689i	0.0982592	−	0.934874i
$29$	−6.40326	+	4.65224i	−1.18906	+	0.863899i	−0.993164	−	0.116726i	$-0.962760\pi$
$29$	−6.40326	+	4.65224i	−1.18906	+	0.863899i	−0.195891	+	0.980626i	$0.562760\pi$
$30$		0			0
$31$	−5.37964	+	1.43510i	−0.966211	+	0.257752i
$31$	−5.37964	+	1.43510i	−0.966211	+	0.257752i
$32$	−1.26097			−0.222911
$33$	−1.73467	+	1.26031i	−0.301967	+	0.219392i
$34$	−0.0520626	+	0.495343i	−0.00892866	+	0.0849506i
$35$		0			0
$36$	−2.68792	+	4.65561i	−0.447986	+	0.775935i
$37$	4.33937	+	7.51600i	0.713387	+	1.23562i	0.963578	+	0.267427i	$0.0861733\pi$
$37$	4.33937	+	7.51600i	0.713387	+	1.23562i	−0.250191	+	0.968197i	$0.580493\pi$
$38$	−0.373712	+	0.0794349i	−0.0606240	+	0.0128860i
$39$	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	$-0.142309\pi$
$42$	−0.0965488	−	0.107228i	−0.0148978	−	0.0165457i
$43$	−4.50941	−	2.00772i	−0.687679	−	0.306174i	0.0329881	−	0.999456i	$-0.489498\pi$
$43$	−4.50941	−	2.00772i	−0.687679	−	0.306174i	−0.720667	+	0.693281i	$0.756164\pi$
$44$	−7.14906	+	3.18297i	−1.07776	+	0.479850i
$45$		0			0
$46$	0.146680	+	0.106569i	0.0216267	+	0.0157127i
$47$	−5.99553	−	4.35601i	−0.874538	−	0.635389i	0.0572628	−	0.998359i	$-0.481763\pi$
$47$	−5.99553	−	4.35601i	−0.874538	−	0.635389i	−0.931801	+	0.362970i	$0.881763\pi$
$48$	1.43400	−	1.59262i	0.206981	−	0.229875i
$49$	−0.680198	+	0.302844i	−0.0971711	+	0.0432634i
$50$		0			0
$51$	−1.71535	−	1.90509i	−0.240198	−	0.266767i
$52$	0.832234	+	7.91818i	0.115410	+	1.09805i
$53$	5.91794	+	1.25790i	0.812892	+	0.172786i	0.595559	−	0.803312i	$-0.296931\pi$
$53$	5.91794	+	1.25790i	0.812892	+	0.172786i	0.217333	+	0.976097i	$0.430264\pi$
$54$	0.101671	+	0.312912i	0.0138357	+	0.0425819i
$55$		0			0
$56$	−0.528102	−	0.914699i	−0.0705706	−	0.122232i
$57$	0.983227	−	1.70300i	0.130232	−	0.225568i
$58$	−0.258943	+	0.796943i	−0.0340008	+	0.104644i
$59$	0.494881	−	4.70847i	0.0644280	−	0.612991i	−0.913901	−	0.405936i	$-0.866945\pi$
$59$	0.494881	−	4.70847i	0.0644280	−	0.612991i	0.978329	−	0.207055i	$-0.0663878\pi$
$60$		0			0
$61$	0.682018			0.0873235			0.0436617	−	0.999046i	$-0.486098\pi$
$61$	0.682018			0.0873235			0.0436617	+	0.999046i	$0.486098\pi$
$62$	−0.371469	+	0.457691i	−0.0471766	+	0.0581268i
$63$	−6.76060			−0.851756
$64$	6.25552	−	4.54490i	0.781940	−	0.568113i
$65$		0			0
$66$	−0.0701486	+	0.215895i	−0.00863469	+	0.0265749i
$67$	3.91077	−	6.77365i	0.477776	−	0.827533i	−0.521899	−	0.853007i	$-0.674776\pi$
$67$	3.91077	−	6.77365i	0.477776	−	0.827533i	0.999675	+	0.0254744i	$0.00810962\pi$
$68$	−4.67814	−	8.10277i	−0.567307	−	0.982605i
$69$	−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	$0.244969\pi$
$72$	0.119319	+	1.13525i	0.0140619	+	0.133790i
$73$	8.17691	+	9.08138i	0.957035	+	1.06290i	0.997967	+	0.0637331i	$0.0203006\pi$
$73$	8.17691	+	9.08138i	0.957035	+	1.06290i	−0.0409320	+	0.999162i	$0.513033\pi$
$74$	0.839391	+	0.373721i	0.0975772	+	0.0434442i
$75$		0			0
$76$	4.80236	−	5.33356i	0.550868	−	0.611801i
$77$	−7.96188	−	5.78464i	−0.907341	−	0.659221i
$78$	0.186847	+	0.135752i	0.0211563	+	0.0153709i
$79$	−6.00055	+	6.66429i	−0.675115	+	0.749791i	−0.979210	−	0.202851i	$-0.934979\pi$
$79$	−6.00055	+	6.66429i	−0.675115	+	0.749791i	0.304095	+	0.952642i	$0.401646\pi$
$80$		0			0
$81$	5.86110	+	2.60953i	0.651233	+	0.289948i
$82$	−0.304561	−	0.338249i	−0.0336331	−	0.0373533i
$83$	−1.04916	−	9.98211i	−0.115160	−	1.09568i	−0.887608	−	0.460600i	$-0.847634\pi$
$83$	−1.04916	−	9.98211i	−0.115160	−	1.09568i	0.772447	−	0.635079i	$-0.219032\pi$
$84$	2.65126	+	0.563542i	0.289276	+	0.0614874i
$85$		0			0
$86$	−0.511178	+	0.108654i	−0.0551217	+	0.0117165i
$87$	−2.15647	−	3.73511i	−0.231198	−	0.400446i
$88$	−0.830842	+	1.43906i	−0.0885681	+	0.153404i
$89$	2.24413	−	6.90671i	0.237877	−	0.732110i	−0.758850	−	0.651266i	$-0.774238\pi$
$89$	2.24413	−	6.90671i	0.237877	−	0.732110i	0.996727	−	0.0808442i	$-0.0257616\pi$
$90$		0			0
$91$	−8.10043	+	5.88531i	−0.849156	+	0.616948i
$92$	−3.40584			−0.355083
$93$	−0.471305	−	2.99713i	−0.0488721	−	0.310788i
$94$	−0.784599			−0.0809252
$95$		0			0
$96$	0.0718241	−	0.683361i	0.00733052	−	0.0697452i
$97$	−2.16120	+	6.65149i	−0.219437	+	0.675357i	0.779372	+	0.626561i	$0.215538\pi$
$97$	−2.16120	+	6.65149i	−0.219437	+	0.675357i	−0.998809	+	0.0487954i	$0.984462\pi$
$98$	−0.0394142	+	0.0682674i	−0.00398144	+	0.00689605i
$99$	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	$0.774879\pi$
$102$	−0.265476	−	0.0564286i	−0.0262860	−	0.00558727i
$103$	1.78597	+	16.9924i	0.175977	+	1.67431i	0.624872	+	0.780727i	$0.285151\pi$
$103$	1.78597	+	16.9924i	0.175977	+	1.67431i	−0.448895	+	0.893585i	$0.648182\pi$
$104$	1.13123	+	1.25636i	0.110926	+	0.123196i
$105$		0			0
$106$	0.585160	−	0.260530i	0.0568357	−	0.0253049i
$107$	−7.11067	+	7.89720i	−0.687415	+	0.763451i	−0.981320	−	0.192383i	$-0.938378\pi$
$107$	−7.11067	+	7.89720i	−0.687415	+	0.763451i	0.293905	+	0.955835i	$0.405045\pi$
$108$	−5.00017	−	3.63284i	−0.481141	−	0.349570i
$109$	5.69547	+	4.13800i	0.545527	+	0.396348i	0.826134	−	0.563474i	$-0.190536\pi$
$109$	5.69547	+	4.13800i	0.545527	+	0.396348i	−0.280607	+	0.959823i	$0.590536\pi$
$110$		0			0
$111$	−4.32032	+	1.92353i	−0.410066	+	0.182573i
$112$	8.98605	+	4.00085i	0.849102	+	0.378044i
$113$	6.60234	+	7.33264i	0.621096	+	0.689797i	0.968810	−	0.247804i	$-0.0797087\pi$
$113$	6.60234	+	7.33264i	0.621096	+	0.689797i	−0.347714	+	0.937601i	$0.613042\pi$
$114$	−0.0217619	−	0.207050i	−0.00203819	−	0.0193920i
$115$		0			0
$116$	−4.86424	−	14.9706i	−0.451633	−	1.38998i
$117$	10.5848	−	2.24987i	0.978566	−	0.208001i
$118$	−0.250619	−	0.434084i	−0.0230713	−	0.0399607i
$119$	5.88318	−	10.1900i	0.539310	−	0.934113i
$120$		0			0
$121$	−0.468615	+	4.45857i	−0.0426014	+	0.405325i
$122$	0.0584159	−	0.0424417i	0.00528873	−	0.00384249i
$123$	2.34269			0.211233
$124$	0.591740	−	11.0573i	0.0531398	−	0.992975i
$125$		0			0
$126$	−0.579056	+	0.420709i	−0.0515864	+	0.0374797i
$127$	1.39331	−	13.2565i	0.123637	−	1.17632i	−0.740142	−	0.672451i	$-0.765242\pi$
$127$	1.39331	−	13.2565i	0.123637	−	1.17632i	0.863778	−	0.503872i	$-0.168092\pi$
$128$	1.03229	−	3.17707i	0.0912427	−	0.280816i
$129$	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	$0.373980\pi$
$132$	−1.31774	−	4.05559i	−0.114695	−	0.352994i
$133$	8.82851	+	1.87656i	0.765529	+	0.162718i
$134$	−0.0865574	−	0.823539i	−0.00747742	−	0.0711429i
$135$		0			0
$136$	−1.81494	−	0.808064i	−0.155630	−	0.0692910i
$137$	19.1707	−	8.53537i	1.63787	−	0.729225i	0.638678	−	0.769474i	$-0.279482\pi$
$137$	19.1707	−	8.53537i	1.63787	−	0.729225i	0.999190	+	0.0402490i	$0.0128151\pi$
$138$	−0.0661078	+	0.0734201i	−0.00562747	+	0.00624994i
$139$	0.744157	+	0.540662i	0.0631186	+	0.0458583i	0.618897	−	0.785472i	$-0.287580\pi$
$139$	0.744157	+	0.540662i	0.0631186	+	0.0458583i	−0.555779	+	0.831330i	$0.687580\pi$
$140$		0			0
$141$	2.70215	−	3.00105i	0.227562	−	0.252734i
$142$	1.38083	−	0.614784i	0.115876	−	0.0515915i
$143$	14.3907	+	6.40714i	1.20341	+	0.535792i
$144$	−7.11341	−	7.90024i	−0.592784	−	0.658353i
$145$		0			0
$146$	1.26550	+	0.268989i	0.104733	+	0.0222617i
$147$	−0.125377	−	0.385870i	−0.0103409	−	0.0318260i
$148$	−16.8830	+	3.58859i	−1.38777	+	0.294981i
$149$	−0.117901	−	0.204210i	−0.00965879	−	0.0167295i	0.861156	−	0.508341i	$-0.169741\pi$
$149$	−0.117901	−	0.204210i	−0.00965879	−	0.0167295i	−0.870814	+	0.491612i	$0.836408\pi$
$150$		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	$0.879289\pi$
$152$	0.159297	−	1.51561i	0.0129207	−	0.122932i
$153$	−10.2879	+	7.47462i	−0.831730	+	0.604287i
$154$	−1.04192			−0.0839606
$155$		0			0
$156$	−4.33851			−0.347359
$157$	19.1504	−	13.9136i	1.52837	−	1.11042i	0.571229	−	0.820791i	$-0.306467\pi$
$157$	19.1504	−	13.9136i	1.52837	−	1.11042i	0.957138	−	0.289633i	$-0.0935332\pi$
$158$	−0.0992414	+	0.944218i	−0.00789522	+	0.0751180i
$159$	−1.01877	+	3.13547i	−0.0807941	+	0.248659i
$160$		0			0
$161$	−2.14157	−	3.70931i	−0.168780	−	0.292335i
$162$	0.664402	−	0.141223i	0.0522004	−	0.0110955i
$163$	−3.73284	−	11.4885i	−0.292378	−	0.899848i	−0.984089	−	0.177674i	$-0.943143\pi$
$163$	−3.73284	−	11.4885i	−0.292378	−	0.899848i	0.691711	−	0.722174i	$-0.256857\pi$
$164$	8.36332	+	1.77768i	0.653066	+	0.138813i
$165$		0			0
$166$	−0.711044	−	0.789694i	−0.0551877	−	0.0612922i
$167$	−0.670884	−	0.298697i	−0.0519146	−	0.0231139i	0.380615	−	0.924734i	$-0.375712\pi$
$167$	−0.670884	−	0.298697i	−0.0519146	−	0.0231139i	−0.432530	+	0.901620i	$0.642379\pi$
$168$	0.525784	−	0.234094i	0.0405651	−	0.0180607i
$169$	2.02524	−	2.24926i	0.155788	−	0.173020i
$170$		0			0
$171$	−7.89167	−	5.73363i	−0.603491	−	0.438462i
$172$	6.56886	−	7.29546i	0.500871	−	0.556273i
$173$	−6.10521	+	2.71821i	−0.464170	+	0.206662i	−0.625477	−	0.780242i	$-0.715096\pi$
$173$	−6.10521	+	2.71821i	−0.464170	+	0.206662i	0.161307	+	0.986904i	$0.448429\pi$
$174$	−0.417139	−	0.185722i	−0.0316232	−	0.0140796i
$175$		0			0
$176$	−1.61761	−	15.3905i	−0.121932	−	1.16011i
$177$	2.52348	+	0.536382i	0.189676	+	0.0403169i
$178$	−0.237588	−	0.731222i	−0.0178080	−	0.0548074i
$179$	3.28753	−	0.698786i	0.245722	−	0.0522297i	−0.0834043	−	0.996516i	$-0.526579\pi$
$179$	3.28753	−	0.698786i	0.245722	−	0.0522297i	0.329126	+	0.944286i	$0.393246\pi$
$180$		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	$0.00197066\pi$
$182$	−0.327575	+	1.00817i	−0.0242815	+	0.0747307i
$183$	−0.0388472	+	0.369606i	−0.00287167	+	0.0273221i
$184$	−0.585075	+	0.425082i	−0.0431323	+	0.0313374i
$185$		0			0
$186$	−0.226878	−	0.227380i	−0.0166355	−	0.0166723i
$187$	−18.5116			−1.35370
$188$	11.9239	−	8.66319i	0.869637	−	0.631828i
$189$	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	$0.0631377\pi$
$192$	2.10671	+	3.64893i	0.152039	+	0.263339i
$193$	−23.8072	+	5.06038i	−1.71368	+	0.364254i	−0.957125	−	0.289674i	$-0.906453\pi$
$193$	−23.8072	+	5.06038i	−1.71368	+	0.364254i	−0.756556	+	0.653929i	$0.773120\pi$
$194$	0.228809	+	0.704201i	0.0164275	+	0.0505587i
$195$		0			0
$196$	−0.154785	−	1.47268i	−0.0110561	−	0.105192i
$197$	9.59532	+	10.6567i	0.683639	+	0.759258i	0.980683	−	0.195606i	$-0.0626675\pi$
$197$	9.59532	+	10.6567i	0.683639	+	0.759258i	−0.297044	+	0.954864i	$0.596001\pi$
$198$	1.02871	+	0.458012i	0.0731074	+	0.0325495i
$199$	−1.99545	+	0.888433i	−0.141454	+	0.0629794i	−0.476243	−	0.879314i	$-0.658002\pi$
$199$	−1.99545	+	0.888433i	−0.141454	+	0.0629794i	0.334789	+	0.942293i	$0.391335\pi$
$200$		0			0
$201$	3.44809	+	2.50519i	0.243210	+	0.176702i
$202$	0.659421	+	0.479098i	0.0463967	+	0.0337092i
$203$	13.2459	−	14.7111i	0.929683	−	1.03252i
$204$	4.65760	−	2.07370i	0.326097	−	0.145188i
$205$		0			0
$206$	1.21040	+	1.34429i	0.0843327	+	0.0936609i
$207$	0.483867	+	4.60368i	0.0336311	+	0.319978i
$208$	−15.4005	−	3.27349i	−1.06784	−	0.226975i
$209$	−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	$0.691853\pi$
$212$	−6.01625	+	10.4204i	−0.413198	+	0.715679i
$213$	−2.40405	+	7.39890i	−0.164723	+	0.506964i
$214$	−0.117601	+	1.11890i	−0.00803906	+	0.0764866i
$215$		0			0
$216$	−1.31237			−0.0892956
$217$	12.4147	−	6.30831i	0.842761	−	0.428236i
$218$	0.745332			0.0504802
$219$	−5.38723	+	3.91405i	−0.364035	+	0.264487i
$220$		0			0
$221$	−5.81993	+	17.9119i	−0.391491	+	1.20488i
$222$	−0.250342	+	0.433605i	−0.0168018	+	0.0291016i
$223$	−4.09481	−	7.09242i	−0.274209	−	0.474944i	0.695726	−	0.718307i	$-0.255083\pi$
$223$	−4.09481	−	7.09242i	−0.274209	−	0.474944i	−0.969935	+	0.243363i	$0.921749\pi$
$224$	3.08489	−	0.655713i	0.206118	−	0.0438117i
$225$		0			0
$226$	1.02181	+	0.217192i	0.0679697	+	0.0144474i
$227$	−1.61157	−	15.3330i	−0.106963	−	1.01769i	−0.907971	−	0.419034i	$-0.862369\pi$
$227$	−1.61157	−	15.3330i	−0.106963	−	1.01769i	0.801007	−	0.598655i	$-0.204298\pi$
$228$	2.61688	+	2.90634i	0.173307	+	0.192477i
$229$	20.4072	+	9.08589i	1.34855	+	0.600412i	0.948702	−	0.316170i	$-0.102397\pi$
$229$	20.4072	+	9.08589i	1.34855	+	0.600412i	0.399846	+	0.916583i	$0.369064\pi$
$230$		0			0
$231$	3.58838	−	3.98530i	0.236098	−	0.262213i
$232$	−2.70408	−	1.96463i	−0.177532	−	0.128984i
$233$	−9.92954	−	7.21423i	−0.650506	−	0.472620i	0.212938	−	0.977066i	$-0.431697\pi$
$233$	−9.92954	−	7.21423i	−0.650506	−	0.472620i	−0.863443	+	0.504446i	$0.831697\pi$
$234$	0.766597	−	0.851392i	0.0501140	−	0.0556573i
$235$		0			0
$236$	8.60172	+	3.82973i	0.559924	+	0.249294i
$237$	−3.26980	−	3.63148i	−0.212396	−	0.235890i
$238$	−0.130213	−	1.23889i	−0.00844046	−	0.0803056i
$239$	21.3520	+	4.53851i	1.38115	+	0.293572i	0.837818	−	0.545949i	$-0.183831\pi$
$239$	21.3520	+	4.53851i	1.38115	+	0.293572i	0.543328	+	0.839521i	$0.317164\pi$
$240$		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	$0.533658\pi$
$242$	0.237317	+	0.411046i	0.0152553	+	0.0264230i
$243$	−6.40956	+	11.1017i	−0.411174	+	0.712174i
$244$	−0.419148	+	1.29000i	−0.0268332	+	0.0825841i
$245$		0			0
$246$	0.200655	−	0.145784i	0.0127933	−	0.00929487i
$247$	−14.4469			−0.919237
$248$	−1.27841	−	1.97334i	−0.0811789	−	0.125307i
$249$	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	$0.0523422\pi$
$252$	4.15487	−	12.7874i	0.261732	−	0.805528i
$253$	−3.36925	+	5.83572i	−0.211823	+	0.366889i
$254$	−0.705606	−	1.22215i	−0.0442736	−	0.0766842i
$255$		0			0
$256$	4.66950	+	14.3712i	0.291844	+	0.898203i
$257$	−24.3107	−	5.16739i	−1.51646	−	0.322333i	−0.626879	−	0.779116i	$-0.715668\pi$
$257$	−24.3107	−	5.16739i	−1.51646	−	0.322333i	−0.889578	+	0.456784i	$0.849001\pi$
$258$	−0.0297668	−	0.283212i	−0.00185320	−	0.0176320i
$259$	−14.5243	−	16.1309i	−0.902497	−	1.00232i
$260$		0			0
$261$	−19.5448	+	8.70189i	−1.20979	+	0.538633i
$262$	0.300628	−	0.333882i	0.0185729	−	0.0206273i
$263$	22.1849	+	16.1183i	1.36798	+	0.993897i	0.997892	+	0.0649004i	$0.0206730\pi$
$263$	22.1849	+	16.1183i	1.36798	+	0.993897i	0.370089	+	0.928996i	$0.379327\pi$
$264$	−0.732547	−	0.532227i	−0.0450852	−	0.0327563i
$265$		0			0
$266$	0.872953	−	0.388664i	0.0535242	−	0.0238305i
$267$	3.61513	+	1.60956i	0.221243	+	0.0985036i
$268$	10.4086	+	11.5599i	0.635806	+	0.706134i
$269$	−1.63895	−	15.5935i	−0.0999282	−	0.950754i	−0.923515	−	0.383563i	$-0.874697\pi$
$269$	−1.63895	−	15.5935i	−0.0999282	−	0.950754i	0.823586	−	0.567191i	$-0.191970\pi$
$270$		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	$0.926266\pi$
$272$	18.0979	−	3.84683i	1.09735	−	0.233248i
$273$	−2.72803	−	4.72509i	−0.165108	−	0.285976i
$274$	1.11085	−	1.92405i	0.0671091	−	0.116236i
$275$		0			0
$276$	0.193994	−	1.84573i	0.0116770	−	0.111100i
$277$	−2.47744	+	1.79997i	−0.148855	+	0.108150i	−0.659720	−	0.751511i	$-0.729325\pi$
$277$	−2.47744	+	1.79997i	−0.148855	+	0.108150i	0.510865	+	0.859661i	$0.329325\pi$
$278$	0.0973834			0.00584067
$279$	−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	$0.0636924\pi$
$282$	0.0446901	−	0.425198i	0.00266126	−	0.0253202i
$283$	−1.08639	+	3.34357i	−0.0645794	+	0.198755i	−0.978140	−	0.207948i	$-0.933322\pi$
$283$	−1.08639	+	3.34357i	−0.0645794	+	0.198755i	0.913561	+	0.406703i	$0.133322\pi$
$284$	−14.1968	+	24.5896i	−0.842425	+	1.45912i
$285$		0			0
$286$	1.63130	−	0.346743i	0.0964607	−	0.0205034i
$287$	3.32274	+	10.2263i	0.196135	+	0.603641i
$288$	−3.33401	−	0.708666i	−0.196459	−	0.0417586i
$289$	−0.536475	−	5.10421i	−0.0315573	−	0.300248i
$290$		0			0
$291$	−3.48155	−	1.55008i	−0.204092	−	0.0908676i
$292$	−22.2023	+	9.88510i	−1.29929	+	0.578481i
$293$	1.31908	−	1.46499i	0.0770617	−	0.0855857i	−0.703381	−	0.710813i	$-0.748327\pi$
$293$	1.31908	−	1.46499i	0.0770617	−	0.0855857i	0.780443	+	0.625227i	$0.214994\pi$
$294$	−0.0347512	−	0.0252482i	−0.00202673	−	0.00147251i
$295$		0			0
$296$	−2.45237	+	2.72363i	−0.142541	+	0.158308i
$297$	−11.1711	+	4.97371i	−0.648215	+	0.288604i
$298$	−0.0228062	−	0.0101540i	−0.00132113	−	0.000588205i
$299$	4.58740	+	5.09483i	0.265296	+	0.294642i
$300$		0			0
$301$	12.0760	+	2.56683i	0.696049	+	0.147950i
$302$	0.513899	+	1.58162i	0.0295715	+	0.0910118i
$303$	−4.10357	+	0.872240i	−0.235744	+	0.0501089i
$304$	7.09634	+	12.2912i	0.407003	+	0.704950i
$305$		0			0
$306$	−0.416036	+	1.28043i	−0.0237832	+	0.0731971i
$307$	−1.29574	+	12.3282i	−0.0739521	+	0.703607i	0.893243	+	0.449573i	$0.148424\pi$
$307$	−1.29574	+	12.3282i	−0.0739521	+	0.703607i	−0.967195	+	0.254033i	$0.918243\pi$
$308$	15.8345	−	11.5045i	0.902255	−	0.655527i
$309$	−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	$0.182245\pi$
$312$	−0.745294	+	0.541488i	−0.0421940	+	0.0306557i
$313$	1.48733	−	14.1510i	0.0840687	−	0.799860i	−0.868531	−	0.495634i	$-0.834936\pi$
$313$	1.48733	−	14.1510i	0.0840687	−	0.799860i	0.952600	−	0.304226i	$-0.0983977\pi$
$314$	0.774426	−	2.38344i	0.0437034	−	0.134505i
$315$		0			0
$316$	−8.91743	−	15.4454i	−0.501644	−	0.868874i
$317$	17.0578	−	3.62576i	0.958064	−	0.203643i	0.297760	−	0.954641i	$-0.403761\pi$
$317$	17.0578	−	3.62576i	0.958064	−	0.203643i	0.660304	+	0.750998i	$0.270427\pi$
$318$	0.107859	+	0.331956i	0.00604843	+	0.0186151i
$319$	−30.4633	−	6.47518i	−1.70562	−	0.362540i
$320$		0			0
$321$	−3.87472	−	4.30331i	−0.216266	−	0.240187i
$322$	−0.414258	−	0.184440i	−0.0230857	−	0.0102784i
$323$	15.5095	−	6.90528i	0.862972	−	0.384220i
$324$	−8.53786	+	9.48225i	−0.474325	+	0.526792i
$325$		0			0
$326$	−1.03465	−	0.751715i	−0.0573038	−	0.0416336i
$327$	−2.56692	+	2.85085i	−0.141951	+	0.157652i
$328$	1.65857	−	0.738444i	0.0915793	−	0.0407737i
$329$	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	$-0.0867665\pi$
$332$	19.5255	+	4.15027i	1.07160	+	0.227775i
$333$	7.24929	+	22.3110i	0.397259	+	1.22264i
$334$	−0.0760501	+	0.0161649i	−0.00416128	+	0.000884506i
$335$		0			0
$336$	−2.68002	+	4.64193i	−0.146207	+	0.253238i
$337$	1.71843	−	5.28877i	0.0936086	−	0.288098i	−0.893280	−	0.449501i	$-0.851602\pi$
$337$	1.71843	−	5.28877i	0.0936086	−	0.288098i	0.986889	+	0.161403i	$0.0516019\pi$
$338$	0.0334949	−	0.318683i	0.00182188	−	0.0173340i
$339$	−4.34985	+	3.16035i	−0.236251	+	0.171647i
$340$		0			0
$341$	−18.3607	−	11.9525i	−0.994289	−	0.647262i
$342$	−1.03274			−0.0558439
$343$	15.6705	−	11.3853i	0.846129	−	0.614749i
$344$	0.217893	−	2.07311i	0.0117480	−	0.111775i
$345$		0			0
$346$	−0.353767	+	0.612743i	−0.0190187	+	0.0329413i
$347$	2.46825	+	4.27514i	0.132503	+	0.229501i	0.924641	−	0.380841i	$-0.124365\pi$
$347$	2.46825	+	4.27514i	0.132503	+	0.229501i	−0.792138	+	0.610342i	$0.791032\pi$
$348$	8.39009	−	1.78337i	0.449756	−	0.0955985i
$349$	10.5621	+	32.5068i	0.565376	+	1.74005i	0.666833	+	0.745208i	$0.267650\pi$
$349$	10.5621	+	32.5068i	0.565376	+	1.74005i	−0.101457	+	0.994840i	$0.532350\pi$
$350$		0			0
$351$	1.30045	+	12.3730i	0.0694130	+	0.660420i
$352$	−3.32006	−	3.68730i	−0.176960	−	0.196534i
$353$	−4.68547	−	2.08610i	−0.249382	−	0.111032i	0.278239	−	0.960512i	$-0.410249\pi$
$353$	−4.68547	−	2.08610i	−0.249382	−	0.111032i	−0.527621	+	0.849480i	$0.676916\pi$
$354$	0.249519	−	0.111093i	0.0132618	−	0.00590452i
$355$		0			0
$356$	11.6845	+	8.48932i	0.619280	+	0.449933i
$357$	5.18715	+	3.76869i	0.274533	+	0.199460i
$358$	0.238097	−	0.264434i	0.0125838	−	0.0139758i
$359$	−31.2359	+	13.9071i	−1.64857	+	0.733990i	−0.999639	−	0.0268580i	$-0.991450\pi$
$359$	−31.2359	+	13.9071i	−1.64857	+	0.733990i	−0.648930	+	0.760848i	$0.724783\pi$
$360$		0			0
$361$	−3.99944	−	4.44183i	−0.210497	−	0.233780i
$362$	−0.147286	−	1.40133i	−0.00774117	−	0.0736524i
$363$	−2.38955	−	0.507914i	−0.125419	−	0.0266586i
$364$	−6.15350	−	18.9385i	−0.322531	−	0.992648i
$365$		0			0
$366$	0.0196731	+	0.0340748i	0.00102833	+	0.00178112i
$367$	−8.95451	+	15.5097i	−0.467422	+	0.809598i	−0.999307	−	0.0372182i	$-0.988150\pi$
$367$	−8.95451	+	15.5097i	−0.467422	+	0.809598i	0.531885	+	0.846816i	$0.321484\pi$
$368$	2.08126	−	6.40547i	0.108493	−	0.333908i
$369$	1.21472	−	11.5573i	0.0632358	−	0.601649i
$370$		0			0
$371$	−15.1320			−0.785612
$372$	5.95858	+	0.950497i	0.308938	+	0.0492810i
$373$	15.2436			0.789285			0.394642	−	0.918835i	$-0.370869\pi$
$373$	15.2436			0.789285			0.394642	+	0.918835i	$0.370869\pi$
$374$	−1.58554	+	1.15197i	−0.0819866	+	0.0595667i
$375$		0			0
$376$	0.967100	−	2.97643i	0.0498744	−	0.153498i
$377$	−15.8429	+	27.4407i	−0.815952	+	1.41327i
$378$	−0.411447	−	0.712648i	−0.0211626	−	0.0366546i
$379$	23.0586	−	4.90127i	1.18444	−	0.251761i	0.426748	−	0.904370i	$-0.359659\pi$
$379$	23.0586	−	4.90127i	1.18444	−	0.251761i	0.757695	+	0.652609i	$0.226326\pi$
$380$		0			0
$381$	7.10474	+	1.51016i	0.363987	+	0.0773678i
$382$	−0.0977432	−	0.929965i	−0.00500098	−	0.0475811i
$383$	−5.34950	−	5.94122i	−0.273347	−	0.303582i	0.590804	−	0.806815i	$-0.298811\pi$
$383$	−5.34950	−	5.94122i	−0.273347	−	0.303582i	−0.864151	+	0.503233i	$0.832144\pi$
$384$	1.66295	+	0.740395i	0.0848623	+	0.0377831i
$385$		0			0
$386$	−1.72422	+	1.91494i	−0.0877606	+	0.0974680i
$387$	−10.7945	−	7.84269i	−0.548717	−	0.398667i
$388$	−11.2528	−	8.17562i	−0.571273	−	0.415054i
$389$	−0.220883	+	0.245315i	−0.0111992	+	0.0124380i	−0.748718	−	0.662888i	$-0.769330\pi$
$389$	−0.220883	+	0.245315i	−0.0111992	+	0.0124380i	0.737519	+	0.675326i	$0.235997\pi$
$390$		0			0
$391$	−7.36001	−	3.27689i	−0.372211	−	0.165719i
$392$	−0.210395	−	0.233667i	−0.0106265	−	0.0118020i
$393$	0.241716	+	2.29977i	0.0121930	+	0.116008i
$394$	1.48502	+	0.315650i	0.0748140	+	0.0159022i
$395$		0			0
$396$	−20.6909	+	4.39799i	−1.03976	+	0.221007i
$397$	0.385588	+	0.667858i	0.0193521	+	0.0335188i	0.875539	−	0.483147i	$-0.160506\pi$
$397$	0.385588	+	0.667858i	0.0193521	+	0.0335188i	−0.856187	+	0.516666i	$0.827173\pi$
$398$	−0.115627	+	0.200272i	−0.00579586	+	0.0100387i
$399$	−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	$0.243956\pi$
$402$	0.451231			0.0225054
$403$	−17.3378	+	14.0082i	−0.863656	+	0.697796i
$404$	−15.3115			−0.761774
$405$		0			0
$406$	0.219071	−	2.08432i	0.0108723	−	0.103443i
$407$	−10.5528	+	32.4782i	−0.523083	+	1.60988i
$408$	0.541293	−	0.937546i	0.0267980	−	0.0464155i
$409$	6.12119	+	10.6022i	0.302674	+	0.524246i	0.976741	−	0.214424i	$-0.0687875\pi$
$409$	6.12119	+	10.6022i	0.302674	+	0.524246i	−0.674067	+	0.738670i	$0.735454\pi$
$410$		0			0
$411$	3.53363	+	10.8754i	0.174301	+	0.536443i
$412$	−33.2380	−	7.06495i	−1.63752	−	0.348065i
$413$	1.23774	+	11.7763i	0.0609051	+	0.579474i
$414$	0.327929	+	0.364202i	0.0161168	+	0.0178996i
$415$		0			0
$416$	−4.61167	+	2.05325i	−0.226106	+	0.100669i
$417$	−0.335388	+	0.372486i	−0.0164240	+	0.0182407i
$418$	−1.21624	−	0.883650i	−0.0594882	−	0.0432207i
$419$	−10.6478	−	7.73611i	−0.520181	−	0.377933i	0.296491	−	0.955036i	$-0.404183\pi$
$419$	−10.6478	−	7.73611i	−0.520181	−	0.377933i	−0.816672	+	0.577102i	$0.804183\pi$
$420$		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	$0.651597\pi$
$422$	1.20818	+	0.537915i	0.0588131	+	0.0261853i
$423$	−13.4041	−	14.8868i	−0.651730	−	0.723819i
$424$	0.267067	+	2.54097i	0.0129699	+	0.123401i
$425$		0			0
$426$	0.254519	+	0.783330i	0.0123315	+	0.0379525i
$427$	−1.66851	+	0.354653i	−0.0807449	+	0.0171629i
$428$	−10.5672	−	18.3029i	−0.510784	−	0.884704i
$429$	−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	$-0.121666\pi$
$432$	9.88793	−	7.18400i	0.475733	−	0.345640i
$433$	−5.64744			−0.271399			−0.135699	−	0.990750i	$-0.543328\pi$
$433$	−5.64744			−0.271399			−0.135699	+	0.990750i	$0.543328\pi$
$434$	0.670771	−	1.31287i	0.0321981	−	0.0630200i
$435$		0			0
$436$	−11.3271	+	8.22962i	−0.542470	+	0.394127i
$437$	0.645986	−	6.14615i	0.0309017	−	0.294010i
$438$	−0.217855	+	0.670489i	−0.0104095	+	0.0320372i
$439$	−12.9575	+	22.4431i	−0.618430	+	1.07115i	0.371342	+	0.928496i	$0.378898\pi$
$439$	−12.9575	+	22.4431i	−0.618430	+	1.07115i	−0.989772	+	0.142656i	$0.954436\pi$
$440$		0			0
$441$	−1.96864	+	0.418447i	−0.0937448	+	0.0199261i
$442$	0.616163	+	1.89635i	0.0293079	+	0.0902004i
$443$	10.1659	+	2.16084i	0.482999	+	0.102665i	0.442975	−	0.896534i	$-0.353923\pi$
$443$	10.1659	+	2.16084i	0.482999	+	0.102665i	0.0400242	+	0.999199i	$0.487257\pi$
$444$	−0.983126	−	9.35382i	−0.0466571	−	0.443913i
$445$		0			0
$446$	−0.792085	−	0.352659i	−0.0375063	−	0.0166989i
$447$	0.117383	−	0.0522623i	0.00555203	−	0.00247192i
$448$	−12.9403	+	14.3717i	−0.611373	+	0.678998i
$449$	17.9060	+	13.0094i	0.845035	+	0.613954i	0.923773	−	0.382942i	$-0.125089\pi$
$449$	17.9060	+	13.0094i	0.845035	+	0.613954i	−0.0787378	+	0.996895i	$0.525089\pi$
$450$		0			0
$451$	11.3195	−	12.5715i	0.533012	−	0.591970i
$452$	−17.9270	+	7.98159i	−0.843213	+	0.375423i
$453$	−7.81946	−	3.48145i	−0.367390	−	0.163573i
$454$	−1.09220	−	1.21301i	−0.0512595	−	0.0569294i
$455$		0			0
$456$	0.812283	+	0.172656i	0.0380386	+	0.00808536i
$457$	−5.51400	−	16.9704i	−0.257934	−	0.793840i	−0.993237	−	0.116101i	$-0.962960\pi$
$457$	−5.51400	−	16.9704i	−0.257934	−	0.793840i	0.735303	−	0.677738i	$-0.237040\pi$
$458$	2.31332	−	0.491712i	0.108094	−	0.0229762i
$459$	−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	$-0.0163675\pi$
$462$	0.0593471	−	0.564650i	0.00276108	−	0.0262699i
$463$	−8.70760	+	6.32644i	−0.404677	+	0.294015i	−0.771443	−	0.636298i	$-0.780465\pi$
$463$	−8.70760	+	6.32644i	−0.404677	+	0.294015i	0.366767	+	0.930313i	$0.380465\pi$
$464$	31.1282			1.44509
$465$		0			0
$466$	−1.29942			−0.0601944
$467$	−20.1906	+	14.6693i	−0.934309	+	0.678816i	−0.947044	−	0.321103i	$-0.895946\pi$
$467$	−20.1906	+	14.6693i	−0.934309	+	0.678816i	0.0127347	+	0.999919i	$0.495946\pi$
$468$	−2.24958	+	21.4034i	−0.103987	+	0.989371i
$469$	−6.04509	+	18.6049i	−0.279136	+	0.859094i
$470$		0			0
$471$	6.44940	+	11.1707i	0.297173	+	0.514718i
$472$	1.95564	−	0.415684i	0.0900157	−	0.0191334i
$473$	−6.00208	−	18.4725i	−0.275976	−	0.849366i
$474$	−0.506048	−	0.107564i	−0.0232436	−	0.00494057i
$475$		0			0
$476$	15.6582	+	17.3902i	0.717693	+	0.797079i
$477$	14.9401	+	6.65176i	0.684060	+	0.304563i
$478$	2.11126	−	0.939995i	0.0965669	−	0.0429944i
$479$	−8.94267	+	9.93185i	−0.408601	+	0.453798i	−0.911960	−	0.410280i	$-0.865431\pi$
$479$	−8.94267	+	9.93185i	−0.408601	+	0.453798i	0.503358	+	0.864078i	$0.332098\pi$
$480$		0			0
$481$	28.1084	+	20.4219i	1.28163	+	0.931160i
$482$	−0.681823	+	0.757241i	−0.0310562	+	0.0344914i
$483$	2.13217	−	0.949305i	0.0970173	−	0.0431949i
$484$	−8.14518	−	3.62647i	−0.370236	−	0.164840i
$485$		0			0
$486$	0.141864	+	1.34974i	0.00643506	+	0.0612255i
$487$	23.5506	+	5.00583i	1.06718	+	0.226836i	0.707841	−	0.706372i	$-0.249669\pi$
$487$	23.5506	+	5.00583i	1.06718	+	0.226836i	0.359337	+	0.933208i	$0.383003\pi$
$488$	0.0890015	+	0.273918i	0.00402891	+	0.0123997i
$489$	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	$0.143567\pi$
$492$	−1.43975	+	4.43108i	−0.0649088	+	0.199769i
$493$	3.89217	−	37.0315i	0.175294	−	1.66781i
$494$	−1.23740	+	0.899027i	−0.0556734	+	0.0404491i
$495$		0			0
$496$	20.4342	+	7.86988i	0.917524	+	0.353368i
$497$	−35.7075			−1.60170
$498$	0.468460	−	0.340356i	0.0209922	−	0.0152517i
$499$	1.67180	−	15.9061i	0.0748401	−	0.712056i	−0.891191	−	0.453629i	$-0.850129\pi$
$499$	1.67180	−	15.9061i	0.0748401	−	0.712056i	0.966031	−	0.258427i	$-0.0832042\pi$
$500$		0			0
$501$	0.200086	−	0.346559i	0.00893919	−	0.0154831i
$502$	0.100107	+	0.173390i	0.00446798	+	0.00773877i
$503$	2.67920	−	0.569481i	0.119459	−	0.0253919i	−0.147794	−	0.989018i	$-0.547217\pi$
$503$	2.67920	−	0.569481i	0.119459	−	0.0253919i	0.267253	+	0.963626i	$0.413884\pi$
$504$	−0.882240	−	2.71526i	−0.0392981	−	0.120947i
$505$		0			0
$506$	0.0745721	+	0.709506i	0.00331513	+	0.0315414i
$507$	1.10359	+	1.22566i	0.0490120	+	0.0544333i
$508$	24.2177	+	10.7824i	1.07449	+	0.478393i
$509$	−8.39209	+	3.73640i	−0.371973	+	0.165613i	−0.584205	−	0.811606i	$-0.698593\pi$
$509$	−8.39209	+	3.73640i	−0.371973	+	0.165613i	0.212232	+	0.977219i	$0.431927\pi$
$510$		0			0
$511$	−24.7266	−	17.9649i	−1.09384	−	0.794722i
$512$	6.69942	+	4.86742i	0.296075	+	0.215111i
$513$	7.50418	−	8.33423i	0.331318	−	0.367965i
$514$	−2.40381	+	1.07025i	−0.106028	+	0.0472065i
$515$		0			0
$516$	3.57947	+	3.97541i	0.157578	+	0.175008i
$517$	−3.04813	−	29.0010i	−0.134057	−	1.27546i
$518$	−2.24785	−	0.477795i	−0.0987648	−	0.0209931i
$519$	−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	$-0.482636\pi$
$522$	−1.13253	+	1.96159i	−0.0495693	+	0.0858565i
$523$	−4.26313	+	13.1206i	−0.186414	+	0.573722i	−0.999970	−	0.00776416i	$-0.997529\pi$
$523$	−4.26313	+	13.1206i	−0.186414	+	0.573722i	0.813556	+	0.581486i	$0.197529\pi$
$524$	−0.882196	+	8.39353i	−0.0385389	+	0.366673i
$525$		0			0
$526$	2.90321			0.126586
$527$	11.9174	−	23.3255i	0.519130	−	1.01607i
$528$	8.43274			0.366988
$529$	16.2348	−	11.7953i	0.705860	−	0.512837i
$530$		0			0
$531$	3.95462	−	12.1711i	0.171616	−	0.528180i
$532$	−8.97516	+	15.5454i	−0.389123	+	0.673980i
$533$	−8.60551	−	14.9052i	−0.372746	−	0.645615i
$534$	0.409804	−	0.0871066i	0.0177340	−	0.00376947i
$535$		0			0
$536$	3.23084	+	0.686736i	0.139551	+	0.0296625i
$537$	0.191439	+	1.82142i	0.00826118	+	0.0785999i
$538$	−1.11076	−	1.23362i	−0.0478881	−	0.0531851i
$539$	−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	$0.456417\pi$
$542$	−0.232433	−	0.168873i	−0.00998387	−	0.00725371i
$543$	5.86727	+	4.26282i	0.251788	+	0.182935i
$544$	3.96945	−	4.40852i	0.170189	−	0.189014i
$545$		0			0
$546$	−0.527701	−	0.234948i	−0.0225835	−	0.0100548i
$547$	8.46055	+	9.39639i	0.361747	+	0.401761i	0.896353	−	0.443341i	$-0.146207\pi$
$547$	8.46055	+	9.39639i	0.361747	+	0.401761i	−0.534606	+	0.845101i	$0.679540\pi$
$548$	4.36247	+	41.5061i	0.186356	+	1.77305i
$549$	1.80325	+	0.383294i	0.0769610	+	0.0163586i
$550$		0			0
$551$	27.9384	−	5.93850i	1.19022	−	0.252989i
$552$	−0.197039	−	0.341282i	−0.00838655	−	0.0145259i
$553$	11.2145	−	19.4240i	0.476888	−	0.825994i
$554$	−0.100186	+	0.308340i	−0.00425649	+	0.0131001i
$555$		0			0
$556$	−1.47997	+	1.07526i	−0.0627649	+	0.0456013i
$557$	28.0158			1.18707			0.593533	−	0.804810i	$-0.297733\pi$
$557$	28.0158			1.18707			0.593533	+	0.804810i	$0.297733\pi$
$558$	−1.23938	+	1.00137i	−0.0524673	+	0.0423913i
$559$	−19.7611			−0.835806
$560$		0			0
$561$	1.05440	−	10.0320i	0.0445170	−	0.423551i
$562$	0.741514	−	2.28214i	0.0312789	−	0.0962664i
$563$	16.4861	−	28.5548i	0.694807	−	1.20344i	−0.275439	−	0.961319i	$-0.588823\pi$
$563$	16.4861	−	28.5548i	0.694807	−	1.20344i	0.970246	−	0.242122i	$-0.0778435\pi$
$564$	4.01567	+	6.95535i	0.169090	+	0.292873i
$565$		0			0
$566$	0.115018	+	0.353988i	0.00483456	+	0.0148792i
$567$	−15.6957	−	3.33623i	−0.659159	−	0.140109i
$568$	0.630210	+	5.99604i	0.0264430	+	0.251588i
$569$	9.02683	+	10.0253i	0.378425	+	0.420283i	0.902027	−	0.431680i	$-0.142079\pi$
$569$	9.02683	+	10.0253i	0.378425	+	0.420283i	−0.523602	+	0.851963i	$0.675412\pi$
$570$		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	$0.422497\pi$
$572$	−20.9629	+	23.2817i	−0.876503	+	0.973455i
$573$	3.89369	+	2.82893i	0.162661	+	0.118180i
$574$	0.920978	+	0.669130i	0.0384409	+	0.0279289i
$575$		0			0
$576$	19.0938	−	8.50111i	0.795575	−	0.354213i
$577$	41.8270	+	18.6226i	1.74128	+	0.775269i	0.993825	+	0.110958i	$0.0353920\pi$
$577$	41.8270	+	18.6226i	1.74128	+	0.775269i	0.747457	+	0.664310i	$0.231275\pi$
$578$	−0.363583	−	0.403799i	−0.0151230	−	0.0167958i
$579$	−1.38634	−	13.1901i	−0.0576141	−	0.548162i
$580$		0			0
$581$	7.75745	+	23.8750i	0.321833	+	0.990500i
$582$	−0.394661	+	0.0838878i	−0.0163592	+	0.00347726i
$583$	11.9033	+	20.6170i	0.492983	+	0.853871i
$584$	−2.58028	+	4.46918i	−0.106773	+	0.184936i
$585$		0			0
$586$	0.0218159	−	0.207565i	0.000901208	−	0.00857442i
$587$	−13.1758	+	9.57279i	−0.543824	+	0.395111i	−0.825503	−	0.564397i	$-0.809109\pi$
$587$	−13.1758	+	9.57279i	−0.543824	+	0.395111i	0.281679	+	0.959509i	$0.409109\pi$
$588$	0.806908			0.0332763
$589$	19.8417	+	3.16509i	0.817563	+	0.130415i
$590$		0			0
$591$	−6.32173	+	4.59300i	−0.260041	+	0.188931i
$592$	3.56780	−	33.9454i	0.146636	−	1.39515i
$593$	4.25997	−	13.1109i	0.174936	−	0.538398i	−0.824694	−	0.565579i	$-0.808653\pi$
$593$	4.25997	−	13.1109i	0.174936	−	0.538398i	0.999631	+	0.0271805i	$0.00865287\pi$
$594$	−0.647314	+	1.12118i	−0.0265596	+	0.0460026i
$595$		0			0
$596$	0.458711	−	0.0975021i	0.0187895	−	0.00399384i
$597$	−0.367810	−	1.13200i	−0.0150535	−	0.0463298i
$598$	0.709967	+	0.150908i	0.0290327	+	0.00617110i
$599$	−3.08707	−	29.3715i	−0.126134	−	1.20009i	−0.856176	−	0.516685i	$-0.827166\pi$
$599$	−3.08707	−	29.3715i	−0.126134	−	1.20009i	0.730041	−	0.683403i	$-0.239501\pi$
$600$		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	$0.394443\pi$
$602$	1.19406	−	0.531630i	0.0486663	−	0.0216676i
$603$	14.1468	−	15.7117i	0.576104	−	0.639828i
$604$	−25.2734	−	18.3622i	−1.02836	−	0.747148i
$605$		0			0
$606$	−0.297198	+	0.330072i	−0.0120728	+	0.0134082i
$607$	20.9080	−	9.30883i	0.848629	−	0.377834i	0.0641130	−	0.997943i	$-0.479578\pi$
$607$	20.9080	−	9.30883i	0.848629	−	0.377834i	0.784516	+	0.620109i	$0.212912\pi$
$608$	4.15710	+	1.85086i	0.168593	+	0.0750623i
$609$	7.21792	+	8.01632i	0.292485	+	0.324838i
$610$		0			0
$611$	−29.0199	−	6.16837i	−1.17402	−	0.249546i
$612$	−7.81523	−	24.0528i	−0.315912	−	0.972277i
$613$	−43.9305	+	9.33773i	−1.77434	+	0.377147i	−0.974732	−	0.223378i	$-0.928292\pi$
$613$	−43.9305	+	9.33773i	−1.77434	+	0.377147i	−0.799606	+	0.600525i	$0.794958\pi$
$614$	0.656195	+	1.13656i	0.0264819	+	0.0458679i
$615$		0			0
$616$	1.28428	−	3.95261i	0.0517451	−	0.159255i
$617$	2.95205	−	28.0868i	0.118845	−	1.13073i	−0.758767	−	0.651362i	$-0.774198\pi$
$617$	2.95205	−	28.0868i	0.118845	−	1.13073i	0.877612	−	0.479372i	$-0.159135\pi$
$618$	−0.797454	+	0.579384i	−0.0320783	+	0.0233062i
$619$	−38.8055			−1.55973			−0.779863	−	0.625950i	$-0.784711\pi$
$619$	−38.8055			−1.55973			−0.779863	+	0.625950i	$0.784711\pi$
$620$		0			0
$621$	−5.32197			−0.213563
$622$	2.53921	−	1.84484i	0.101813	−	0.0739714i
$623$	−1.89858	+	18.0637i	−0.0760649	+	0.723709i
$624$	2.65121	−	8.15957i	0.106133	−	0.326644i
$625$		0			0
$626$	−0.753216	−	1.30461i	−0.0301046	−	0.0521427i
$627$	7.56864	−	1.60876i	0.302262	−	0.0642478i
$628$	14.5476	+	44.7729i	0.580512	+	1.78663i
$629$	−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	$0.876957\pi$
$632$	−3.45963	−	1.54033i	−0.137617	−	0.0612709i
$633$	−6.21845	+	2.76863i	−0.247161	+	0.110043i
$634$	1.23540	−	1.37205i	0.0490641	−	0.0544912i
$635$		0			0
$636$	−5.30448	−	3.85393i	−0.210336	−	0.152818i
$637$	−1.99452	+	2.21514i	−0.0790257	+	0.0877669i
$638$	−3.01218	+	1.34111i	−0.119253	+	0.0530950i
$639$	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	$0.876611\pi$
$642$	−0.599669	−	0.127464i	−0.0236670	−	0.00503058i
$643$	1.62030	+	4.98678i	0.0638985	+	0.196659i	0.977909	−	0.209031i	$-0.0670310\pi$
$643$	1.62030	+	4.98678i	0.0638985	+	0.196659i	−0.914010	+	0.405691i	$0.867031\pi$
$644$	8.33214	−	1.77105i	0.328332	−	0.0697892i
$645$		0			0
$646$	0.898702	−	1.55660i	0.0353590	−	0.0612435i
$647$	9.84357	−	30.2954i	0.386991	−	1.19103i	−0.548035	−	0.836455i	$-0.684624\pi$
$647$	9.84357	−	30.2954i	0.386991	−	1.19103i	0.935026	−	0.354580i	$-0.115376\pi$
$648$	−0.283206	+	2.69453i	−0.0111254	+	0.105851i
$649$	15.0714	−	10.9500i	0.591603	−	0.429825i
$650$		0			0
$651$	2.71154	+	7.08720i	0.106274	+	0.277769i
$652$	24.0240			0.940853
$653$	−27.0512	+	19.6539i	−1.05860	+	0.769115i	−0.973828	−	0.227285i	$-0.927015\pi$
$653$	−27.0512	+	19.6539i	−1.05860	+	0.769115i	−0.0847682	+	0.996401i	$0.527015\pi$
$654$	−0.0424535	+	0.403918i	−0.00166006	+	0.0157944i
$655$		0			0
$656$	−8.45405	+	14.6429i	−0.330075	+	0.571707i
$657$	16.5160	+	28.6066i	0.644351	+	1.11605i
$658$	1.91947	−	0.407995i	0.0748286	−	0.0159053i
$659$	−5.40178	−	16.6250i	−0.210424	−	0.647617i	−0.999447	−	0.0332540i	$-0.989413\pi$
$659$	−5.40178	−	16.6250i	−0.210424	−	0.647617i	0.789023	−	0.614363i	$-0.210587\pi$
$660$		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	$-0.0791539\pi$
$662$	−0.430677	−	0.478315i	−0.0167387	−	0.0185903i
$663$	−9.37551	−	4.17425i	−0.364115	−	0.162114i
$664$	3.87219	−	1.72401i	0.150270	−	0.0669046i
$665$		0			0
$666$	2.00932	+	1.45985i	0.0778594	+	0.0565682i
$667$	−10.9657	−	7.96703i	−0.424593	−	0.308485i
$668$	0.977277	−	1.08538i	0.0378120	−	0.0419945i
$669$	4.07684	−	1.81512i	0.157620	−	0.0701768i
$670$		0			0
$671$	1.79571	+	1.99434i	0.0693226	+	0.0769906i
$672$	0.179638	+	1.70914i	0.00692969	+	0.0659316i
$673$	−0.976808	−	0.207627i	−0.0376532	−	0.00800343i	0.189047	−	0.981968i	$-0.439460\pi$
$673$	−0.976808	−	0.207627i	−0.0376532	−	0.00800343i	−0.226700	+	0.973965i	$0.572794\pi$
$674$	−0.181932	−	0.559928i	−0.00700775	−	0.0215676i
$675$		0			0
$676$	3.00971	+	5.21298i	0.115758	+	0.200499i
$677$	17.1360	−	29.6804i	0.658589	−	1.14071i	−0.322392	−	0.946606i	$-0.604487\pi$
$677$	17.1360	−	29.6804i	0.658589	−	1.14071i	0.980981	−	0.194104i	$-0.0621798\pi$
$678$	−0.175904	+	0.541378i	−0.00675557	+	0.0207915i
$679$	1.82842	−	17.3963i	0.0701683	−	0.667607i
$680$		0			0
$681$	8.40123			0.321936
$682$	−2.31642	+	0.118832i	−0.0887003	+	0.00455032i
$683$	4.54905			0.174064			0.0870322	−	0.996205i	$-0.472262\pi$
$683$	4.54905			0.174064			0.0870322	+	0.996205i	$0.472262\pi$
$684$	15.6949	−	11.4030i	0.600109	−	0.436005i
$685$		0			0
$686$	0.633703	−	1.95034i	0.0241949	−	0.0744643i
$687$	−6.08630	+	10.5418i	−0.232207	+	0.402194i
$688$	9.70666	+	16.8124i	0.370063	+	0.640968i
$689$	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	$0.958988\pi$
$692$	−1.38929	−	13.2182i	−0.0528130	−	0.502482i
$693$	−17.8002	−	19.7692i	−0.676175	−	0.750968i
$694$	0.477450	+	0.212574i	0.0181237	+	0.00806921i
$695$		0			0
$696$	1.21872	−	1.35352i	0.0461953	−	0.0513051i
$697$	16.3628	+	11.8882i	0.619783	+	0.450299i
$698$	2.92754	+	2.12698i	0.110809	+	0.0805075i
$699$	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	$0.596988\pi$
$702$	0.881350	+	0.978838i	0.0332644	+	0.0369439i
$703$	−3.27375	−	31.1476i	−0.123472	−	1.17476i
$704$	29.7604	+	6.32578i	1.12164	+	0.238412i
$705$		0			0
$706$	−0.531135	+	0.112896i	−0.0199895	+	0.00424891i
$707$	−9.62778	−	16.6758i	−0.362090	−	0.627158i
$708$	−2.56540	+	4.44340i	−0.0964135	+	0.166993i
$709$	10.8054	−	33.2556i	0.405805	−	1.24894i	−0.514417	−	0.857540i	$-0.671991\pi$
$709$	10.8054	−	33.2556i	0.405805	−	1.24894i	0.920221	−	0.391398i	$-0.128009\pi$
$710$		0			0
$711$	−19.6108	+	14.2481i	−0.735462	+	0.534344i
$712$	3.06679			0.114933
$713$	−5.18423	−	8.00236i	−0.194151	−	0.299691i
$714$	0.678812			0.0254039
$715$		0			0
$716$	−0.698697	+	6.64766i	−0.0261115	+	0.248435i
$717$	−3.67575	+	11.3128i	−0.137273	+	0.422484i
$718$	−1.80997	+	3.13496i	−0.0675476	+	0.116996i
$719$	18.5666	+	32.1583i	0.692418	+	1.19930i	0.971043	+	0.238904i	$0.0767880\pi$
$719$	18.5666	+	32.1583i	0.692418	+	1.19930i	−0.278625	+	0.960400i	$0.589879\pi$
$720$		0			0
$721$	−13.2054	−	40.6421i	−0.491795	−	1.51359i
$722$	−0.618971	−	0.131566i	−0.0230357	−	0.00489639i
$723$	−0.548210	−	5.21587i	−0.0203881	−	0.193980i
$724$	17.7112	+	19.6703i	0.658233	+	0.731042i
$725$		0			0
$726$	−0.236276	+	0.105197i	−0.00876901	+	0.00390422i
$727$	−27.3599	+	30.3863i	−1.01472	+	1.12696i	−0.0228495	+	0.999739i	$0.507274\pi$
$727$	−27.3599	+	30.3863i	−1.01472	+	1.12696i	−0.991874	+	0.127226i	$0.959393\pi$
$728$	−3.42080	−	2.48535i	−0.126783	−	0.0921133i
$729$	9.92014	+	7.20740i	0.367413	+	0.266941i
$730$		0			0
$731$	21.2145	−	9.44532i	0.784648	−	0.349348i
$732$	−0.675219	−	0.300627i	−0.0249568	−	0.0111115i
$733$	3.83068	+	4.25440i	0.141489	+	0.157140i	0.809724	−	0.586810i	$-0.199617\pi$
$733$	3.83068	+	4.25440i	0.141489	+	0.157140i	−0.668235	+	0.743950i	$0.732950\pi$
$734$	0.198191	+	1.88566i	0.00731537	+	0.0696011i
$735$		0			0
$736$	−0.667303	−	2.05375i	−0.0245971	−	0.0757021i
$737$	30.1041	−	6.39883i	1.10890	−	0.235704i
$738$	−0.615162	−	1.06549i	−0.0226444	−	0.0392213i
$739$	−16.1662	+	28.0007i	−0.594684	+	1.03002i	0.398907	+	0.916991i	$0.369390\pi$
$739$	−16.1662	+	28.0007i	−0.594684	+	1.03002i	−0.993591	+	0.113032i	$0.963944\pi$
$740$		0			0
$741$	0.822887	−	7.82925i	0.0302295	−	0.287615i
$742$	−1.29608	+	0.941654i	−0.0475804	+	0.0345692i
$743$	−17.3877			−0.637893			−0.318947	−	0.947773i	$-0.603329\pi$
$743$	−17.3877			−0.637893			−0.318947	+	0.947773i	$0.603329\pi$
$744$	1.14223	−	0.580408i	0.0418763	−	0.0212788i
$745$		0			0
$746$	1.30564	−	0.948603i	0.0478029	−	0.0347308i
$747$	2.83595	−	26.9823i	0.103762	−	0.987231i
$748$	11.3767	−	35.0137i	0.415972	−	1.28023i
$749$	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	$0.382890\pi$
$752$	9.00663	+	27.7196i	0.328438	+	1.01083i
$753$	−1.00797	−	0.214251i	−0.0367326	−	0.00780776i
$754$	0.350653	+	3.33624i	0.0127700	+	0.121499i
$755$		0			0
$756$	14.1217	+	6.28737i	0.513600	+	0.228669i
$757$	−44.3415	+	19.7421i	−1.61162	+	0.717539i	−0.997432	−	0.0716213i	$-0.977183\pi$
$757$	−44.3415	+	19.7421i	−1.61162	+	0.717539i	−0.614187	+	0.789160i	$0.710516\pi$
$758$	1.67001	−	1.85473i	0.0606573	−	0.0673668i
$759$	−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	$0.140805\pi$
$762$	0.702509	−	0.312777i	0.0254492	−	0.0113307i
$763$	−16.0854	−	7.16166i	−0.582329	−	0.259269i
$764$	11.7537	+	13.0538i	0.425234	+	0.472270i
$765$		0			0
$766$	−0.827912	−	0.175978i	−0.0299137	−	0.00635835i
$767$	−5.85693	−	18.0258i	−0.211481	−	0.650873i
$768$	−8.05419	+	1.71197i	−0.290631	+	0.0617754i
$769$	−10.6818	−	18.5015i	−0.385197	−	0.667180i	0.606600	−	0.795007i	$-0.292533\pi$
$769$	−10.6818	−	18.5015i	−0.385197	−	0.667180i	−0.991796	+	0.127827i	$0.959200\pi$
$770$		0			0
$771$	4.18508	−	12.8804i	0.150722	−	0.463875i
$772$	5.05974	−	48.1402i	0.182104	−	1.73260i
$773$	6.77130	−	4.91963i	0.243547	−	0.176947i	−0.459315	−	0.888273i	$-0.651905\pi$
$773$	6.77130	−	4.91963i	0.243547	−	0.176947i	0.702862	+	0.711326i	$0.251905\pi$
$774$	−1.41262			−0.0507755
$775$		0			0
$776$	−2.95347			−0.106023
$777$	9.56912	−	6.95237i	0.343290	−	0.249415i
$778$	−0.00365312	+	0.0347571i	−0.000130971	+	0.00124610i
$779$	−4.79426	+	14.7552i	−0.171772	+	0.528661i
$780$		0			0
$781$	28.0886	+	48.6510i	1.00509	+	1.74087i
$782$	−0.834315	+	0.177339i	−0.0298351	+	0.00634164i
$783$	−7.60088	−	23.3931i	−0.271633	−	0.836001i
$784$	2.86431	+	0.608827i	0.102297	+	0.0217438i
$785$		0			0
$786$	0.163817	+	0.181937i	0.00584316	+	0.00648949i
$787$	26.0734	+	11.6086i	0.929417	+	0.413803i	0.814889	−	0.579617i	$-0.196798\pi$
$787$	26.0734	+	11.6086i	0.929417	+	0.413803i	0.114528	+	0.993420i	$0.463465\pi$
$788$	−26.0536	+	11.5998i	−0.928122	+	0.413227i
$789$	−9.99863	+	11.1046i	−0.355961	+	0.395334i
$790$		0			0
$791$	−19.9652	−	14.5056i	−0.709880	−	0.515758i
$792$	−3.00550	+	3.33794i	−0.106796	+	0.118609i
$793$	2.49429	−	1.11053i	0.0885750	−	0.0394361i
$794$	0.0745867	+	0.0332082i	0.00264698	+	0.00117851i
$795$		0			0
$796$	−0.454083	−	4.32031i	−0.0160945	−	0.153129i
$797$	40.5442	+	8.61795i	1.43615	+	0.305263i	0.859252	−	0.511552i	$-0.170929\pi$
$797$	40.5442	+	8.61795i	1.43615	+	0.305263i	0.576899	+	0.816816i	$0.304263\pi$
$798$	0.160906	+	0.495218i	0.00569601	+	0.0175305i
$799$	34.1026	−	7.24874i	1.20646	−	0.256442i
$800$		0			0
$801$	9.81503	−	17.0001i	0.346797	−	0.600670i
$802$	0.229506	−	0.706347i	0.00810414	−	0.0249420i
$803$	−5.02623	+	47.8214i	−0.177372	+	1.68758i
$804$	−6.85754	+	4.98229i	−0.241847	+	0.175712i
$805$		0			0
$806$	−0.613287	+	2.27874i	−0.0216021	+	0.0802653i
$807$	8.54396			0.300762
$808$	−2.63029	+	1.91102i	−0.0925334	+	0.0672295i
$809$	5.64219	−	53.6818i	0.198369	−	1.88735i	−0.214741	−	0.976671i	$-0.568891\pi$
$809$	5.64219	−	53.6818i	0.198369	−	1.88735i	0.413109	−	0.910681i	$-0.364443\pi$
$810$		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	$0.184071\pi$
$812$	19.6848	+	34.0951i	0.690801	+	1.19650i
$813$	1.44643	−	0.307448i	0.0507285	−	0.0107827i
$814$	1.11724	+	3.43851i	0.0391592	+	0.120520i
$815$		0			0
$816$	1.05387	+	10.0269i	0.0368929	+	0.351012i
$817$	11.9194	+	13.2379i	0.417008	+	0.463134i
$818$	1.18406	+	0.527178i	0.0413997	+	0.0184323i
$819$	−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	$0.634392\pi$
$822$	0.979431	+	0.711598i	0.0341616	+	0.0248198i
$823$	−17.2695	+	19.1797i	−0.601976	+	0.668562i	−0.964705	−	0.263332i	$-0.915178\pi$
$823$	−17.2695	+	19.1797i	−0.601976	+	0.668562i	0.362729	+	0.931895i	$0.381845\pi$
$824$	−6.59159	+	2.93476i	−0.229629	+	0.102237i
$825$		0			0
$826$	0.838848	+	0.931635i	0.0291872	+	0.0324157i
$827$	−5.73992	−	54.6117i	−0.199597	−	1.89904i	−0.395584	−	0.918430i	$-0.629458\pi$
$827$	−5.73992	−	54.6117i	−0.199597	−	1.89904i	0.195987	−	0.980606i	$-0.437209\pi$
$828$	−9.00502	−	1.91408i	−0.312946	−	0.0665188i
$829$	−5.40196	−	16.6255i	−0.187618	−	0.577428i	0.812366	−	0.583148i	$-0.198179\pi$
$829$	−5.40196	−	16.6255i	−0.187618	−	0.577428i	−0.999984	+	0.00571978i	$0.998179\pi$
$830$		0			0
$831$	−0.834345	−	1.44513i	−0.0289431	−	0.0501309i
$832$	15.4774	−	26.8076i	0.536582	−	0.929387i
$833$	1.08243	−	3.33139i	0.0375041	−	0.115426i
$834$	−0.00554688	+	0.0527750i	−0.000192073	+	0.00182745i
$835$		0			0
$836$	28.2405			0.976720
$837$	0.924655	−	17.2782i	0.0319607	−	0.597221i
$838$	−1.39342			−0.0481348
$839$	30.6934	−	22.3001i	1.05966	−	0.769885i	0.0856307	−	0.996327i	$-0.472709\pi$
$839$	30.6934	−	22.3001i	1.05966	−	0.769885i	0.974025	+	0.226442i	$0.0727095\pi$
$840$		0			0
$841$	10.3969	−	31.9983i	0.358514	−	1.10339i
$842$	−1.69503	+	2.93588i	−0.0584146	+	0.101177i
$843$	6.17530	+	10.6959i	0.212689	+	0.368388i
$844$	−24.3005	+	5.16524i	−0.836459	+	0.177795i
$845$		0			0
$846$	−2.07448	−	0.440944i	−0.0713220	−	0.0151600i
$847$	−1.17205	−	11.1513i	−0.0402720	−	0.383162i
$848$	−15.9216	−	17.6828i	−0.546751	−	0.607228i
$849$	−1.75011	−	0.779197i	−0.0600635	−	0.0267420i
$850$		0			0
$851$	−9.94493	+	11.0450i	−0.340908	+	0.378616i
$852$	−12.5172	−	9.09429i	−0.428833	−	0.311565i
$853$	22.4932	+	16.3423i	0.770153	+	0.559549i	0.902007	−	0.431720i	$-0.142093\pi$
$853$	22.4932	+	16.3423i	0.770153	+	0.559549i	−0.131855	+	0.991269i	$0.542093\pi$
$854$	−0.120841	+	0.134207i	−0.00413508	+	0.00459247i
$855$		0			0
$856$	−4.09967	−	1.82529i	−0.140124	−	0.0623872i
$857$	−29.2605	−	32.4970i	−0.999518	−	1.11008i	−0.993921	−	0.110093i	$-0.964885\pi$
$857$	−29.2605	−	32.4970i	−0.999518	−	1.11008i	−0.00559710	−	0.999984i	$-0.501782\pi$
$858$	0.0949933	+	0.903801i	0.00324302	+	0.0308552i
$859$	33.3740	+	7.09386i	1.13871	+	0.242039i	0.738414	−	0.674348i	$-0.235575\pi$
$859$	33.3740	+	7.09386i	1.13871	+	0.242039i	0.400292	+	0.916387i	$0.368909\pi$
$860$		0			0
$861$	−5.73123	+	1.21821i	−0.195320	+	0.0415165i
$862$	−1.02848	−	1.78137i	−0.0350301	−	0.0606739i
$863$	8.71374	−	15.0926i	0.296619	−	0.513760i	−0.678741	−	0.734378i	$-0.737474\pi$
$863$	8.71374	−	15.0926i	0.296619	−	0.513760i	0.975360	+	0.220618i	$0.0708075\pi$
$864$	1.21095	−	3.72692i	0.0411974	−	0.126792i
$865$		0			0
$866$	−0.483712	+	0.351438i	−0.0164372	+	0.0119423i
$867$	2.79669			0.0949805
$868$	4.30220	+	27.3586i	0.146026	+	0.928612i
$869$	−35.2866			−1.19702
$870$		0			0
$871$	3.27302	−	31.1407i	0.110902	−	1.05516i
$872$	−0.918699	+	2.82746i	−0.0311111	+	0.0957500i
$873$	−9.45235	+	16.3719i	−0.319913	+	0.554106i
$874$	−0.327142	−	0.566627i	−0.0110658	−	0.0191664i
$875$		0			0
$876$	−4.09241	−	12.5951i	−0.138270	−	0.425551i
$877$	18.2363	+	3.87624i	0.615795	+	0.130891i	0.505240	−	0.862979i	$-0.331404\pi$
$877$	18.2363	+	3.87624i	0.615795	+	0.130891i	0.110555	+	0.993870i	$0.464737\pi$
$878$	0.286791	+	2.72863i	0.00967872	+	0.0920869i
$879$	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	$0.225267\pi$
$882$	−0.142577	+	0.158348i	−0.00480083	+	0.00533186i
$883$	−18.9604	−	13.7755i	−0.638067	−	0.463583i	0.221118	−	0.975247i	$-0.429029\pi$
$883$	−18.9604	−	13.7755i	−0.638067	−	0.463583i	−0.859186	+	0.511664i	$0.829029\pi$
$884$	−30.3028	−	22.0162i	−1.01919	−	0.740486i
$885$		0			0
$886$	1.00520	−	0.447543i	0.0337703	−	0.0150355i
$887$	−28.6858	−	12.7718i	−0.963176	−	0.428834i	−0.135958	−	0.990715i	$-0.543411\pi$
$887$	−28.6858	−	12.7718i	−0.963176	−	0.428834i	−0.827218	+	0.561881i	$0.810078\pi$
$888$	−1.33634	−	1.48415i	−0.0448445	−	0.0498049i
$889$	3.48480	+	33.1556i	0.116876	+	1.11200i
$890$		0			0
$891$	7.80119	+	24.0096i	0.261350	+	0.804351i
$892$	15.9315	−	3.38635i	0.533427	−	0.113383i
$893$	13.3719	+	23.1609i	0.447475	+	0.775049i
$894$	0.00680178	−	0.0117810i	0.000227486	−	0.000394017i
$895$		0			0
$896$	−0.873341	+	8.30928i	−0.0291763	+	0.277594i
$897$	−3.02234	+	2.19586i	−0.100913	+	0.0733176i
$898$	2.34325			0.0781951
$899$	27.7708	−	34.2167i	0.926207	−	1.14119i
$900$		0			0
$901$	−23.0270	+	16.7301i	−0.767141	+	0.557361i
$902$	0.187209	−	1.78118i	0.00623338	−	0.0593066i
$903$	−2.07888	+	6.39815i	−0.0691809	+	0.212917i
$904$	−2.08342	+	3.60858i	−0.0692934	+	0.120020i
$905$		0			0
$906$	−0.886398	+	0.188410i	−0.0294486	+	0.00625949i
$907$	10.7346	+	33.0378i	0.356437	+	1.09700i	0.955171	+	0.296054i	$0.0956707\pi$
$907$	10.7346	+	33.0378i	0.356437	+	1.09700i	−0.598734	+	0.800948i	$0.704329\pi$
$908$	29.9921	+	6.37502i	0.995323	+	0.211562i
$909$	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	$0.756074\pi$
$912$	−7.06519	+	3.14563i	−0.233952	+	0.104162i
$913$	26.4270	−	29.3502i	0.874607	−	0.971349i
$914$	−1.52834	−	1.11040i	−0.0505530	−	0.0367289i
$915$		0			0
$916$	−29.7272	+	33.0154i	−0.982215	+	1.09086i
$917$	−9.69616	+	4.31701i	−0.320196	+	0.142560i
$918$	−1.41403	−	0.629568i	−0.0466700	−	0.0207788i
$919$	−28.2165	−	31.3376i	−0.930777	−	1.03373i	−0.999349	−	0.0360861i	$-0.988511\pi$
$919$	−28.2165	−	31.3376i	−0.930777	−	1.03373i	0.0685720	−	0.997646i	$-0.478156\pi$
$920$		0			0
$921$	−6.60722	−	1.40441i	−0.217715	−	0.0462768i
$922$	−0.502233	−	1.54571i	−0.0165402	−	0.0509054i
$923$	55.9059	−	11.8832i	1.84016	−	0.391139i
$924$	5.33269	+	9.23650i	0.175433	+	0.303858i
$925$		0			0
$926$	−0.352128	+	1.08374i	−0.0115717	+	0.0356139i
$927$	−4.82761	+	45.9316i	−0.158559	+	1.50859i
$928$	8.07434	−	5.86635i	0.265053	−	0.192573i
$929$	−10.5493			−0.346112			−0.173056	−	0.984912i	$-0.555364\pi$
$929$	−10.5493			−0.346112			−0.173056	+	0.984912i	$0.555364\pi$
$930$		0			0
$931$	2.68695			0.0880612
$932$	19.7478	−	14.3476i	0.646860	−	0.469971i
$933$	−1.68860	+	16.0659i	−0.0552822	+	0.525975i
$934$	−0.816492	+	2.51290i	−0.0267164	+	0.0822247i
$935$		0			0
$936$	2.28490	+	3.95757i	0.0746844	+	0.129357i
$937$	5.15659	−	1.09607i	0.168458	−	0.0358070i	−0.122910	−	0.992418i	$-0.539223\pi$
$937$	5.15659	−	1.09607i	0.168458	−	0.0358070i	0.291369	+	0.956611i	$0.405889\pi$
$938$	0.640001	+	1.96972i	0.0208968	+	0.0643137i
$939$	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	$0.824805\pi$
$942$	1.24755	+	0.555444i	0.0406473	+	0.0180973i
$943$	6.72589	−	2.99456i	0.219025	−	0.0975162i
$944$	−12.4591	+	13.8372i	−0.405509	+	0.450364i
$945$		0			0
$946$	−1.66362	−	1.20869i	−0.0540890	−	0.0392980i
$947$	−29.0943	+	32.3125i	−0.945437	+	1.05001i	0.0532390	+	0.998582i	$0.483045\pi$
$947$	−29.0943	+	32.3125i	−0.945437	+	1.05001i	−0.998676	+	0.0514329i	$0.983621\pi$
$948$	8.87829	−	3.95287i	0.288353	−	0.128383i
$949$	44.6920	+	19.8982i	1.45077	+	0.645922i
$950$		0			0
$951$	0.993308	+	9.45069i	0.0322102	+	0.306460i
$952$	4.86033	+	1.03309i	0.157524	+	0.0334828i
$953$	−10.5869	−	32.5830i	−0.342942	−	1.05547i	−0.962676	−	0.270656i	$-0.912759\pi$
$953$	−10.5869	−	32.5830i	−0.342942	−	1.05547i	0.619734	−	0.784812i	$-0.287241\pi$
$954$	1.69358	−	0.359981i	0.0548316	−	0.0116548i
$955$		0			0
$956$	−21.7067	+	37.5971i	−0.702044	+	1.21598i
$957$	5.24426	−	16.1402i	0.169523	−	0.521738i
$958$	−0.147900	+	1.40718i	−0.00477844	+	0.0454638i
$959$	−42.4615	+	30.8501i	−1.37115	+	0.996201i
$960$		0			0
$961$	26.8810	−	15.4406i	0.867128	−	0.498085i
$962$	3.67837			0.118596
$963$	−23.2388	+	16.8840i	−0.748861	+	0.544079i
$964$	2.00081	−	19.0365i	0.0644419	−	0.613123i
$965$		0			0
$966$	0.123549	−	0.213994i	0.00397513	−	0.00688513i
$967$	24.4168	+	42.2912i	0.785192	+	1.35999i	0.928884	+	0.370370i	$0.120769\pi$
$967$	24.4168	+	42.2912i	0.785192	+	1.35999i	−0.143692	+	0.989622i	$0.545898\pi$
$968$	−1.85185	+	0.393622i	−0.0595206	+	0.0126515i
$969$	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	$0.848307\pi$
$972$	−17.0592	−	18.9462i	−0.547174	−	0.607698i
$973$	−2.10168	−	0.935727i	−0.0673766	−	0.0299980i
$974$	2.32865	−	1.03678i	0.0746149	−	0.0332207i
$975$		0			0
$976$	−2.17002	−	1.57661i	−0.0694606	−	0.0504661i
$977$	−8.56622	−	6.22372i	−0.274057	−	0.199114i	0.442264	−	0.896885i	$-0.354175\pi$
$977$	−8.56622	−	6.22372i	−0.274057	−	0.199114i	−0.716321	+	0.697771i	$0.754175\pi$
$978$	0.466310	−	0.517890i	0.0149109	−	0.0165603i
$979$	26.1050	−	11.6227i	0.834321	−	0.371464i
$980$		0			0
$981$	12.7333	+	14.1417i	0.406542	+	0.451510i
$982$	−0.0355596	−	0.338327i	−0.00113475	−	0.0107965i
$983$	−15.8385	−	3.36657i	−0.505169	−	0.107377i	−0.0517245	−	0.998661i	$-0.516472\pi$
$983$	−15.8385	−	3.36657i	−0.505169	−	0.107377i	−0.453445	+	0.891284i	$0.649805\pi$
$984$	0.305714	+	0.940892i	0.00974582	+	0.0299946i
$985$		0			0
$986$	−1.97108	−	3.41401i	−0.0627720	−	0.108724i
$987$	−5.05008	+	8.74699i	−0.160746	+	0.278420i
$988$	8.87867	−	27.3257i	0.282468	−	0.869347i
$989$	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	$0.559728\pi$
$992$	6.78358	−	1.80962i	0.215379	−	0.0574556i
$993$	3.31278			0.105128
$994$	−3.05841	+	2.22206i	−0.0970068	+	0.0704796i
$995$		0			0
$996$	−3.36131	+	10.3451i	−0.106507	+	0.327796i
$997$	−20.1338	+	34.8727i	−0.637643	+	1.10443i	0.348305	+	0.937381i	$0.386757\pi$
$997$	−20.1338	+	34.8727i	−0.637643	+	1.10443i	−0.985948	+	0.167050i	$0.946576\pi$
$998$	−0.846639	−	1.46642i	−0.0267999	−	0.0464188i
$999$	−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.bl.c.276.3		40
5.2	odd	4		775.2.ck.c.524.6		80
5.3	odd	4		775.2.ck.c.524.5		80
5.4	even	2		155.2.q.a.121.3	yes	40
31.10	even	15	inner	775.2.bl.c.351.3		40
155.14	even	30		4805.2.a.x.1.12		20
155.72	odd	60		775.2.ck.c.599.5		80
155.79	odd	30		4805.2.a.y.1.12		20
155.103	odd	60		775.2.ck.c.599.6		80
155.134	even	30		155.2.q.a.41.3	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.q.a.41.3	✓	40	155.134	even	30
155.2.q.a.121.3	yes	40	5.4	even	2
775.2.bl.c.276.3		40	1.1	even	1	trivial
775.2.bl.c.351.3		40	31.10	even	15	inner
775.2.ck.c.524.5		80	5.3	odd	4
775.2.ck.c.524.6		80	5.2	odd	4
775.2.ck.c.599.5		80	155.72	odd	60
775.2.ck.c.599.6		80	155.103	odd	60
4805.2.a.x.1.12		20	155.14	even	30
4805.2.a.y.1.12		20	155.79	odd	30

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.bl (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0856516 - 0.0622295i) q^{2} +(-0.0569592 + 0.541931i) q^{3} +(-0.614570 + 1.89145i) q^{4} +(0.0288454 + 0.0499618i) q^{6} +(-2.44643 + 0.520005i) q^{7} +(0.130497 + 0.401629i) q^{8} +(2.64400 + 0.561999i) q^{9} +(2.63294 + 2.92417i) q^{11} +(-0.990031 - 0.440790i) q^{12} +(3.65723 - 1.62830i) q^{13} +(-0.177181 + 0.196780i) q^{14} +(-3.18176 - 2.31168i) q^{16} +(-3.14793 + 3.49613i) q^{17} +(0.261436 - 0.116399i) q^{18} +(-3.29674 - 1.46780i) q^{19} +(-0.142460 - 1.35542i) q^{21} +(0.407485 + 0.0866136i) q^{22} +(0.529196 + 1.62870i) q^{23} +(-0.225088 + 0.0478440i) q^{24} +(0.211919 - 0.367054i) q^{26} +(-0.960329 + 2.95559i) q^{27} +(0.519939 - 4.94689i) q^{28} +(-6.40326 + 4.65224i) q^{29} +(-5.37964 + 1.43510i) q^{31} -1.26097 q^{32} +(-1.73467 + 1.26031i) q^{33} +(-0.0520626 + 0.495343i) q^{34} +(-2.68792 + 4.65561i) q^{36} +(4.33937 + 7.51600i) q^{37} +(-0.373712 + 0.0794349i) q^{38} +(0.674114 + 2.07471i) q^{39} +(-0.449386 - 4.27562i) q^{41} +(-0.0965488 - 0.107228i) q^{42} +(-4.50941 - 2.00772i) q^{43} +(-7.14906 + 3.18297i) q^{44} +(0.146680 + 0.106569i) q^{46} +(-5.99553 - 4.35601i) q^{47} +(1.43400 - 1.59262i) q^{48} +(-0.680198 + 0.302844i) q^{49} +(-1.71535 - 1.90509i) q^{51} +(0.832234 + 7.91818i) q^{52} +(5.91794 + 1.25790i) q^{53} +(0.101671 + 0.312912i) q^{54} +(-0.528102 - 0.914699i) q^{56} +(0.983227 - 1.70300i) q^{57} +(-0.258943 + 0.796943i) q^{58} +(0.494881 - 4.70847i) q^{59} +0.682018 q^{61} +(-0.371469 + 0.457691i) q^{62} -6.76060 q^{63} +(6.25552 - 4.54490i) q^{64} +(-0.0701486 + 0.215895i) q^{66} +(3.91077 - 6.77365i) q^{67} +(-4.67814 - 8.10277i) q^{68} +(-0.912784 + 0.194018i) q^{69} +(13.9648 + 2.96832i) q^{71} +(0.119319 + 1.13525i) q^{72} +(8.17691 + 9.08138i) q^{73} +(0.839391 + 0.373721i) q^{74} +(4.80236 - 5.33356i) q^{76} +(-7.96188 - 5.78464i) q^{77} +(0.186847 + 0.135752i) q^{78} +(-6.00055 + 6.66429i) q^{79} +(5.86110 + 2.60953i) q^{81} +(-0.304561 - 0.338249i) q^{82} +(-1.04916 - 9.98211i) q^{83} +(2.65126 + 0.563542i) q^{84} +(-0.511178 + 0.108654i) q^{86} +(-2.15647 - 3.73511i) q^{87} +(-0.830842 + 1.43906i) q^{88} +(2.24413 - 6.90671i) q^{89} +(-8.10043 + 5.88531i) q^{91} -3.40584 q^{92} +(-0.471305 - 2.99713i) q^{93} -0.784599 q^{94} +(0.0718241 - 0.683361i) q^{96} +(-2.16120 + 6.65149i) q^{97} +(-0.0394142 + 0.0682674i) q^{98} +(5.31810 + 9.21121i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + q^{3} - 10 q^{4} + 4 q^{6} - 4 q^{7} - 13 q^{8} + 2 q^{9} - 28 q^{11} + 13 q^{12} + 6 q^{13} - 6 q^{14} + 8 q^{16} + 10 q^{17} + 27 q^{18} - 13 q^{19} - 8 q^{21} - 2 q^{22} + 12 q^{23}+ \cdots + 53 q^{99}+O(q^{100}) \) 40 * q + 2 * q^2 + q^3 - 10 * q^4 + 4 * q^6 - 4 * q^7 - 13 * q^8 + 2 * q^9 - 28 * q^11 + 13 * q^12 + 6 * q^13 - 6 * q^14 + 8 * q^16 + 10 * q^17 + 27 * q^18 - 13 * q^19 - 8 * q^21 - 2 * q^22 + 12 * q^23 - 82 * q^24 + 32 * q^26 + q^27 - 22 * q^28 + 42 * q^29 - 10 * q^31 - 4 * q^32 - 13 * q^33 + 32 * q^34 - 13 * q^36 - 12 * q^37 - 30 * q^38 + 37 * q^39 + 36 * q^41 + 64 * q^42 + 78 * q^43 - 56 * q^44 + 18 * q^46 + 4 * q^47 + 41 * q^48 - 31 * q^49 - 2 * q^51 - 49 * q^52 + 11 * q^53 + 22 * q^54 + 9 * q^56 - 38 * q^57 - 11 * q^58 - q^59 - 100 * q^61 + 35 * q^62 - 110 * q^63 + 17 * q^64 - 40 * q^66 - 30 * q^67 + 34 * q^68 + 8 * q^69 - 2 * q^71 - 151 * q^72 + 23 * q^73 - 2 * q^74 + 2 * q^76 - 36 * q^77 + 2 * q^78 - 67 * q^79 - 83 * q^81 - 2 * q^82 + 26 * q^84 - 5 * q^86 + 46 * q^87 - 70 * q^88 + 20 * q^89 + 19 * q^91 + 10 * q^92 + 67 * q^93 + 130 * q^94 + 46 * q^96 + 18 * q^97 + 65 * q^98 + 53 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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